ISBN: 0-8247-0457-6 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New Y...
50 downloads
954 Views
7MB Size
Report
This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form
ISBN: 0-8247-0457-6 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright # 2001 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced on transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA
Preface
Boundary membranes play a key role in the cells of all contemporary organisms, and simple models of membrane function are therefore of considerable interest. The interface of two immiscible liquids has been widely used for this purpose. For example, the fundamental processes of photosynthesis, biocatalysis, membrane fusion and interactions of cells, ion pumping, and electron transport have all been investigated in such interfacial systems. Processes occurring at the interface between two immiscible liquids present a challenge of great interest because heterogeneous structures of this kind are frequently encountered in Nature. In particular, the electrical double layer at the oil–water interface occurs in a heterogeneous interfacial region that separates different bulk regions of conductive polarized media with a spatial separation of charges. The electrical double layer at the interface between two immiscible liquids determines the kinetics of charge transfer across the phase boundaries, stability and electrokinetic properties of lyophobic colloids, mechanisms of phase transfer or interfacial catalysis, charge separation in biological energy transduction, and heterogeneous enzymatic catalysis. The elucidation of the structure of the interface between two immiscible liquids and the mechanism of charge separation is a fundamental problem of modern chemistry and chemical technology. The interface between two immiscible electrolyte solutions can be either polarizable or nonpolarizable, depending on its permeability to charged particles in the system. If the interface is impermeable to charged particles or the transfer between the phases is difficult, it is called polarizable. A completely nonpolarizable interface containing at least one common ion can pass a high current in either direction without giving rise to a deviation of the interfacial potential difference from the equilibrium value. Although in practice we encounter neither ideally polarizable nor completely nonpolarizable interfaces, under certain conditions the properties of some interfaces are close to ideal. Since any interface is permeable to ions to some extent, only an approximation of the limiting version of a polarizable interface can be realized experimentally. Michael Faraday first studied electron transfer reactions at oil–water interfaces to prepare colloidal metals by reducing metal salts at the ether–water or carbon disulfide– water interfaces. As the field progressed after Faraday’s pioneering observations, it iii
iv
Preface
became clear that vectorial charge transfer at the interface between two dielectric media is an important stage in many bioelectrochemical processes such as those mediated by energy-transducing membranes. Studies have been made on redox and hydrolysis reactions catalyzed by enzymes, photosynthetic pigments, metal complexes of porphyrins, bacteria, and submitochondrial particles, as well as in systems with an extended surface—in microemulsions, vesicles, and reversed micelles. Naturally immobilized enzymes and pigments embedded in a hydrophilic-hydrophobic interface have properties similar to their functional state in a membrane. For instance, certain enzymes can be highly active at the interface but virtually inactive in a homogeneous medium. The interface between two immiscible liquids with immobilized photosynthetic pigments can serve as a convenient model for investigating photoprocesses that are accompanied by spatial separation of charges. The efficiency of charge separation defines the quantum yield of any photochemical reaction. Heterogeneous sytems will be most effective in this regard, where the oxidants and the reductants are either in different phases or sterically separated. Different solubilities of the substrates and reaction products in the two phases of heterogeneous systems can alter the redox potential of reactants, making it possible to carry out reactions that cannot be performed in a homogeneous phase. Elucidation of photosynthetic mechanisms is also significant in designing artificial systems for solar energy utilization. The quantum yield of the photocatalytic reaction depends first of all on the efficiency of the photochemical charge separation. The most effective system should be a heterogeneous system in which the oxidant and the reductant are either in different phases or sterically separated. The difference in solubilities of the substrates and reaction products in both phases of such a heterogeneous structure as the octane–water interface can shift the reaction equilibrium. The redox potential scale is thereby altered, making it possible to carry out reactions that cannot be performed in a homogeneous phase. Extraction of the reaction products and adsorption of the reaction components determine high catalytic properties of the interface between two immiscible liquids, recognized recently as interfacial catalysis. Chemical models of photosynthesis have been used to investigate two types of reactions: photosynthesis and photocatalysis. In photosynthetic processes the standard Gibbs free energy of the reaction is positive, and solar energy is utilized to perform work. In photocatalytic processes the free energy is negative and solar energy is used to overcome the activation barrier. The processes of life have been found to generate electric fields in every organism that has been examined with suitable and sufficiently sensitive measuring techniques. The electrochemical conduction of electrochemical excitation over specialized structures must be regarded as one of the most universal properties of living organisms. It arose at the early stages of evolution in connection with the need for transmission of a signal about an external influence from one part of a biological system to another. Clearly, then, the chemical and physical properties of liquid interfaces represent a significant interdisciplinary research area for a broad range of investigators, such as those who have contributed to this book. The chapters are organized into three parts. The first deals with the chemical and physical structure of oil–water interfaces and membrane surfaces. Eighteen chapters present discussion of interfacial potentials, ion solvation, electrostatic instabilities in double layers, theory of adsorption, nonlinear optics, interfacial kinetics, microstructure effects, ultramicroelectrode techniques, catalysis, and extraction. The second part, on biological applications of interfacial phenomena, has ten chapters that deal successively with protein encapsulation, membranes, effects of phospholi-
Preface
v
pids, biocatalysis, oscillation of membrane potentials, and fundamentals of interfacial electrochemical phenomena in green plants. The final part, on pharmaceutical applications, consists of five chapters and includes topics such as drugs at liquid interfaces, NMR studies, and drugs and gene delivery. We thank the authors for the time they spent on this project and for teaching us about their work. Alexander G. Volkov
Contents
Preface iii Contributors Part I.
xi
Chemistry at Liquid Interfaces
1.
Interfacial Potentials and Cells Zbigniew Koczorowski
1
2.
Ion Solvation and Resolvation 23 Toshiyuki Osakai and Kuniyoshi Ebina
3.
Electroelastic Instabilities in Double Layers and Membranes Michael B. Partenskii and Peter C. Jordan
4.
The GvdW Theory: A Density Functional Theory of Adsorption, Surface Tension, and Screening 83 Sture Nordholm and Robert Penfold
5.
Adsorption at Polarized Liquid–Liquid Interfaces Takashi Kakiuchi
6.
Nonlinear Optics at Liquid–Liquid Interfaces Pierre-Francois Brevet
7.
The Lattice-Gas and Other Simple Models for Liquid–Liquid Interfaces Wolfgang Schmickler
8.
Dynamic Aspects of Heterogeneous Electron-Transfer Reactions at Liquid–Liquid Interfaces 179 David J. Fermı´n and Riikka Lahtinen
9.
Dynamic Behaviors of Molecules at Liquid–Liquid Interfaces Using the TimeResolved Quasi-Elastic Laser Scattering Method 229 Isao Tsuyumoto and Tsuguo Sawada
51
105
123 153
vii
viii
Contents
10.
Microstructure Effects on Transport in Reverse Microemulsions 241 John Texter
11.
Investigation of Oil–Water Interfaces by Spectroscopic Methods. Relations with Rheological Properties of Multiphasic Systems 257 Eric Dufour, C. Lopez, and S. Herbert
12.
Scanning Electrochemical Microscopy as a Local Probe of Chemical Processes at Liquid Interfaces 283 Anna L. Barker, Christopher J. Slevin, Patrick R. Unwin, and Jie Zhang
13.
Hydrodynamic Techniques for Investigating Reaction Kinetics at Liquid–Liquid Interfaces: Historical Overview and Recent Developments 325 Christopher J. Slevin, Patrick R. Unwin, and Jie Zhang
14.
Catalytic Effect of the Liquid–Liquid Interface in Solvent Extraction Kinetics Hitoshi Watarai
15.
Voltammetry at Micro-ITIES 373 Biao Liu and Michael V. Mirkin
16.
Dynamics of Polar Solvent Motion at Liquid Interfaces Nancy E. Levinger and Ruth E. Riter
17.
Capacitance and Surface Tension Measurements of Liquid–Liquid Interfaces Zdeneˇk Samec
18.
Liquid Membrane Ion-Selective Electrodes: Response Mechanisms Studied by Optical Second Harmonic Generation and Photoswitchable Ionophores as a Molecular Probe 439 Yoshio Umezawa
Part II.
399
Liquid Interfaces in Biological Applications
19.
Water-in-Oil Microemulsions: Protein Encapsulation and Release Douglas G. Hayes
20.
Biomimetic Charge Transfers Through Artificial Membranes 487 Sorin Kihara, Hiroyuki Ohde, Kohji Maeda, Yumi Yoshida, and Osamu Shirai
21.
DNA-Modified Electrodes. Molecular Recognition of DNA and Biosensor Applications 515 Koji Nakano
22.
Phospholipids at Liquid–Liquid Interfaces and Their Effect on Charge Transfer 533 Lasse Murtoma¨ki, Jose´ A. Manzanares, Salvador Mafe´, and Kyo¨sti Kontturi
23.
Biocatalysis in Liquid–Liquid Biphasic Media: Coupled Mass Transfer and Chemical Reactions 553 Mohamed Gargouri
24.
Design of Biocompatible Ion Sensors Keiichi Kimura
585
355
469
415
Contents
ix
25.
The Oscillation of Membrane Potential or Membrane Current Kohji Maeda and Sorin Kihara
26.
Selective Ion Transfer of Alkali and Alkaline Earth Metal Ions Facilitated by Naphtho-15-Crown-5 Across Liquid–Liquid Interfaces and a Bilayer Lipid Membrane 629 Hidekazu Doe
27.
Langmuir and Langmuir–Blodgett Films of Chlorophyll a and Photosystem II Complex 641 Roger M. Leblanc and Veeranjaneyulu Konka
28.
Interfacial Electrical Phenomena in Green Plants: Action Potentials Alexander G. Volkov and John Mwesigwa
Part III.
609
649
Pharmaceutical Applications: Drugs at Liquid Interfaces
29.
Voltammetric Study of Drugs at Liquid–Liquid Interfaces Mitsugi Senda, Yuko Kubota, and Hajime Katano
30.
Electrical Potential Oscillation Across a Water–Oil–Water Liquid Membrane in the Presence of Drugs 699 Kensuke Arai and Fumiyo Kusu
31.
Transfer Mechanisms and Lipophilicity of Ionizable Drugs Fre´de´ric Reymond
32.
NMR Studies on Lipid Bilayer Interfaces Coupled with Anesthetics and Endocrine Disruptors 775 Emiko Okamura and Masaru Nakahara
33.
Lipid Bilayers in Cells: Implications in Drug and Gene Delivery T. Marjukka Suhonen, Pekka Suhonen, and Arto Urtti
Index
845
683
729
807
Contributors
Kensuke Arai Department of Analytical Chemistry, Tokyo University of Pharmacy and Life Science, Tokyo, Japan Anna L. Barker
Department of Chemistry, University of Warwick, Coventry, England
Pierre-Francois Brevet Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland Hidekazu Doe
Department of Chemistry, Osaka City University, Osaka, Japan
Eric Dufour De´partement Qualite´ et Economie Alimentaires, ENITA ClermontFerrand, Lempdes, France Kuniyoshi Ebina Kobe, Japan
Division of Sciences for Natural Environment, Kobe University,
David J. Fermı´n Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland Mohamed Gargouri Department of Biological and Chemical Engineering, National Institute for Applied Science and Technology, Tunis, Tunisia Douglas G. Hayes Department of Chemical and Materials Engineering, University of Alabama in Huntsville, Huntsville, Alabama S. Herbert
INRA-LEIMA, Nantes, France
Peter C. Jordan Massachusetts
Department
of
Chemistry,
Brandeis
University,
Waltham,
Takashi Kakiuchi Department of Energy and Hydrocarbon Chemistry, Kyoto University, Kyoto, Japan Hajime Katano Sorin Kihara
Department of Bioscience, Fukui Prefectural University, Fukui, Japan Department of Chemistry, Kyoto Institute of Technology, Kyoto, Japan xi
xii
Contributors
Keiichi Kimura Department of Applied Chemistry, Faculty of Systems Engineering, Wakayama University, Wakayama, Japan Zbigniew Koczorowski Poland
Department of Chemistry, University of Warsaw, Warsaw,
Veeranjaneyulu Konka Florida
Department of Chemistry, University of Miami, Coral Gables,
Kyo¨sti Kontturi Department of Chemical Technology, Helsinki University of Technology, Espoo, Finland Yuko Kubota
Department of Bioscience, Fukui Prefectural University, Fukui, Japan
Fumiyo Kusu Department of Analytical Chemistry, Tokyo University of Pharmacy and Life Science, Tokyo, Japan Riikka Lahtinen Laboratory of Physical Chemistry and Electrochemistry, Department of Chemical Technology, Helsinki University of Technology, Espoo, Finland Roger M. Leblanc Florida
Department of Chemistry, University of Miami, Coral Gables,
Nancy E. Levinger Colorado
Department of Chemistry, Colorado State University, Fort Collins,
Biao Liu Department of Chemistry and Biochemistry, City University of New York, Queens College, Flushing, New York C. Lopez
INRA-LEIMA, Nantes, France
Kohji Maeda
Department of Chemistry, Kyoto Institute of Technology, Kyoto, Japan
Salvador Mafe´ Valencia, Spain
Department of Thermodynamics, University of Valencia, Burjasot,
Jose´ A. Manzanares Department of Thermodynamics, University of Valencia, Burjasot, Valencia, Spain Michael V. Mirkin Department of Chemistry and Biochemistry, City University of New York, Queens College, Flushing, New York Lasse Murtoma¨ki Department of Chemical Technology, Helsinki University of Technology, Espoo, Finland John Mwesigwa
Department of Chemistry, Oakwood College, Huntsville, Alabama
Masaru Nakahara
Institute for Chemical Research, Kyoto University, Kyoto, Japan
Koji Nakano Department of Chemical Systems and Engineering, Kyushu University, Fukuoka, Japan Sture Nordholm
Department of Chemistry, Go¨teborg University, Go¨teborg, Sweden
Hiroyuki Ohde Japan
Department of Chemistry, Kyoto Institute of Technology, Kyoto,
Emiko Okamura Toshiyuki Osakai
Institute for Chemical Research, Kyoto University, Kyoto, Japan Department of Chemistry, Kobe University, Kobe, Japan
Contributors
xiii
Michael B. Partenskii Massachusetts
Department of Chemistry, Brandeis University, Waltham,
Robert Penfold Food Materials Science Division, Institute of Food Research, Norwich, England Fre´de´ric Reymond Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland Ruth E. Riter
Department of Chemistry, Agnes Scott College, Decatur, Georgia
Zdeneˇk Samec J. Heyrovsky´ Institute of Physical Chemistry, Academy of Sciences of The Czech Republic, Prague, Czech Republic Tsuguo Sawada Tokyo, Japan
Department of Advanced Materials Science, University of Tokyo,
Wolfgang Schmickler Germany Mitsugi Senda
Department of Electrochemistry, University of Ulm, Ulm,
Department of Bioscience, Fukui Prefectural University, Fukui, Japan
Osamu Shirai Department of Nuclear Energy System, Japan Atomic Energy Research Institute, Ibaraki, Japan Christopher J. Slevin Department of Chemistry, University of Warwick, Coventry, England Pekka Suhonen Finland
Department of Pharmaceutics, University of Kuopio, Kuopio,
T. Marjukka Suhonen Finland John Texter
Department of Pharmaceutics, University of Kuopio, Kuopio,
Strider Research Corporation, Rochester, New York
Isao Tsuyumoto Department of Environmental Systems Engineering, Kanazawa Institute of Technology, Ishikawa, Japan Yoshio Umezawa
Department of Chemistry, University of Tokyo, Tokyo, Japan
Patrick R. Unwin England Arto Urtti
Department of Chemistry, University of Warwick, Coventry,
Department of Pharmaceutics, University of Kuopio, Kuopio, Finland
Alexander G. Volkov Alabama Hitoshi Watarai Yumi Yoshida Jie Zhang
Department of Chemistry, Oakwood College, Huntsville,
Department of Chemistry, Osaka University, Osaka, Japan Department of Chemistry, Kyoto Institute of Technology, Kyoto, Japan
Department of Chemistry, University of Warwick, Coventry, England
Current affiliation: DiagnoSwiss, Monthey, Switzerland.
1 Interfacial Potentials and Cells ZBIGNIEW KOCZOROWSKI Warsaw, Poland
I.
Department of Chemistry, University of Warsaw,
INTRODUCTION
Liquid surfaces and liquid–liquid interfaces are very common and have tremendous significance in the real world. Especially important are the interfaces between two immiscible liquid electrolyte solutions (acronym ITIES), which occur in tissues and cells of all living organisms. The usual presence of aqueous electrolyte solution as one phase of ITIES is the main reason for the electrochemical nature of such interfaces. Every liquid interface is usually electrified by ion separation, dipole orientation, or both (Section II). It is convenient to distinguish two groups of immiscible liquid– liquid interfaces: water–polar solvent, such as nitrobenzene and 1,2-dichloroethane, and water–nonpolar solvent, e.g., octane or decane interfaces. For the second group it is impossible to investigate the interphase electrochemical equilibria and the Galvani potentials, whereas it is normal practice for the first group (Section III). On the other hand, these systems are very important as parts of the voltaic cells. They make it possible to measure the surface potential differences and the adsorption potentials (Section IV). Electrochemical studies of liquid–liquid interfaces brought very significant advances during the last quarter of the 20th century. Traditional electrochemical experiments and theoretical approaches of interfacial chemistry have contributed much to our present understanding of the phenomena occurring at the ITIES. The fast development of this discipline has been documented in many review articles. Among them should be mentioned some reviews published during the last several years [1–16]. The brief history of achievements, and references to them, can be found in a number of papers [1,3,4,8,11,17,18]. Liquid–liquid interfaces occur as macro- and also as micro- and nanoheterogenous systems (termed small systems), described in colloidal chemistry as, e.g., miscelles, vesicles, and microemulsions [14,19] (see also Section V). Up to now, fast progress concerns mainly the macrosystems (> 100 m), including all types of natural and artificial membranes.
1
2
II.
Koczorowski
ELECTRIFIED LIQUID–LIQUID INTERFACES AND THEIR ELECTRICAL POTENTIALS
At a phase boundary (or interface) the molecular species experience anisotropic forces, which vary with the distance from the interface. This causes a net orientation of solvent and other molecular dipoles and a net excess of ions near the phase boundary, on both sides of the solution. The term ‘‘electrified’’ interface means that there occur differences in potential, charge densities, dipole moments, and electric currents. The system and terminology of the thermodynamic and electrical interfacial potentials, recommended for description of all electrified phases and interfaces [18,20,21], is also very useful for the liquid–liquid boundaries [3,8,14,15–17,22–35], e.g., at the interfaces of two immiscible electrolyte solutions: water (w), and an organic solvent (s). The presence of an electrical potential drop, i.e., interfacial potential, across the boundary between two dissimilar phases, as well as at their surfaces exposed to a neutral gas phase, is the most characteristic feature of every interface and surface electrified due to the ion separation and dipole orientation. This charge separation is usually described as the formation of the ionic and dipolar double layers. The main interfacial potential is the Galvani potential (termed also by Trasatti the operative potential), ws ’, which is the difference of inner potentials ’2 and ’s of both phases. It is a function only of the chemical nature of the contacting phases in the equilibrium, but it is not a measurable quantity. In the equilibrium state, the electrochemical potentials of each i ion, present simultaneously in both phases are identical: wi ¼ si
ð1Þ
Using the definition of the electrochemical potential this can be rewritten in the following forms: ws ’ ¼ ’w ’s ¼ ð1=zi FÞws i
ð2Þ
s s 0;w þ RT ln awi þ zi F’w ¼ 0;s i i þ RT ln ai þ zi F’
ð3Þ
w s where i0;w , 0;s i stand for standard chemical potentials of ions, ai and ai represent their activities in both phases, and R, F, and T have their usual meanings, namely the gas constant, Faraday constant, and temperature (K). From Eq. (3) one can derive the dependence of the Nernst dependence of the Galvani potential at the single interface.
ws ’ ¼ ’w ’s ¼ ws ’0i þ
RT asi ln zi F awi
ð4Þ
It follows from Eq. (4) that the Galvani potential can be calculated from the values of the standard potential and the activity of any ion participating in the equilibrium distribution. The standard Galvani potential is defined as follows: ws ’0i ¼ sw G0i =zi F
ð5Þ
This dependence is fundamental for electrochemistry, but its key role for liquid–liquid interfaces was first recognized by Koryta [1–5,35]. The standard transfer energy of an ion 0;ws , denoted in abbreviated form from the aqueous phase to the nonaqueous phase, Gtr;i w 0 by the symbol s Gi is the difference of standard chemical potential of standard chemical potentials of the ions, i.e., of the standard Gibbs energies of solvation in both phases,
Interfacial Potentials and Cells
ws G0i ¼ 0;w i0;s i
3
ð6Þ
Equation (4) can be rewritten in the form: ws ’ ¼ ws ’0i þ
RT is csi ln zi F iw cwi
ð7Þ
where sw and iw represent the activity coefficients. Besides the Galvani potential, another important interfacial potential is the Volta potential, ws , sometimes called the contact potential. ws is the difference of the outer potentials of the phases, which are in electrochemical equilibrium with regard to the charged species, i.e., ions or electrons. As for any two-phase electrochemical system, including the w/s system, it may be characterized by the commonly known relation: ws ¼ zi Fðwi wi Þ
ð8Þ
s where M i and i are the real potentials of the charged species i, defined as the sum of its chemical potential and the electrical term containing the surface potential of the phase, e.g., for the solution:
si ¼ si þ zi Fs
ð9Þ
The electrical potentials assumed to exist at liquid–liquid interfaces, including inert gas or liquid dielectric environments are presented in Fig. 1. Equations (1) and (2) together with ws ¼ 2s ’ 2s
ð10Þ
make it possible to find some important electrochemical information. The Volta potential, in contradiction to the Galvani potential, has the advantage of being measurable but also the disadvantage that it is not determined only by the chemical nature of the phases which create the interface, but also by the state at their surfaces, represented by the surface potentials, Eqs. (8) and (9). In principle, the distribution of ions and dipoles at the w/s interface is different from that at the free w and s surfaces. Therefore, the Galvani potential may be also written, in the absence of specific adsorption, as the sum of the charge and dipole components [15,20– 22]: ws ’ ¼ gws ðionÞ þ gws ðdipÞ
FIG. 1 The electric potentials assumed to exist at liquid–liquid interfaces.
ð11Þ
4
Koczorowski
Usually gws ðionÞ 6¼ 2s and gws ðdipÞ 6¼ ws . This is caused by mutual influence of the contacting phases on the orientation of dipolar molecules in the interfacial zone. The situation that no charge transfer across the interface occurs is named the ideal polarized or blocked interface. Such interfaces do not permit, due to thermodynamic or kinetic reasons, either electron or ion transfer. They possess Galvani potentials fixed by the electrolyte and charge. Of course, the ideal polarizable interface is practically a limiting case of the interfaces with charge transfer, because any interface is always permeable to ions to some extent. Therefore, only an approximation of the ideal polarizable interface can be realized experimentally (Section III.D). If the interface is in the zero charge state, named also the point of zero charge (pzc), the Galvani potential should be equal to the dipolar term [19–21]: ws ’ðpzcÞ ¼ ws gðdipÞ
ð12Þ
The specific adsorption, which in the case of ITIES is usually the adsorption of ionic pairs [8], contributes to the Galvani potential, as well as changes the zero charge of this interface. The surface potential of a liquid solvent s, s , is defined as the difference of electrical potentials across the interface between this solvent and the gas phase, with the assumption that the outer potential of the solvent is zero [21,22]. The potential s of pure molecular liquid arises from a preferred orientation of the solvent dipoles in the free surface zone. At the surface of solution the electric field responsible for the surface potential may arise from a preferred orientation of the solvent and solute dipoles, and from the ionic double layer (Section IV). The potential s , as the difference of electrical potential across the interface between the phase and gas, is not measurable. But its relative changes caused by the change of solution composition can be determined using the proper voltaic cells (see Section IV). The name ‘‘surface potential’’ is unfortunately also often used for the description the ionic double layer potential (i.e., the ionic part of the Galvani potential) at the interfaces of membranes, microemulsion droplets and micelles, measured usually by the acid–base indicator technique (Section V).
III.
LIQUID GALVANIC CELLS AND THE GALVANI POTENTIALS
The interface separating two immiscible electrolyte solutions, e.g., one aqueous and the other based on a polar organic solvent, may be reversible with respect to one or many ions simultaneously, and also to electrons. Works by Nernst constitute a fundamental contribution to the electrochemical analysis of the phase equilibrium between two immiscible electrolyte solutions [1–3]. According to these works, in the above system electrical potentials originate from the difference of distribution coefficients of ions of the electrolyte present in the both phases. Nernst’s approach was supported by Verwey and Niessen’s interpretation [23], and by the experiments of Randles and Karpfen [24], and others, cited in Ref. 3. These authors, and in particular Davies and Rideal [17] consolidated the description of Galvani potential in the case of the 1 : 1 electrolyte distribution. As mentioned in the Introduction, in the discussion of liquid electrochemical cells it is necessary to distinguish two groups of immiscible liquid–liquid interfaces: water–polar organic solvent, e.g., nitrobenzene, and water–nonpolar organic solvent (water–oil or water–hydrocarbon), e.g., octane type systems. It is schematically presented as
Interfacial Potentials and Cells
5
j j
polar solvent (s) þ ions
water (w) þ ions
ws ’ SCHEME 1 and j j
nonpolar solvent (ns) + ions
water (w) + ions
w=ns SCHEME 2 The main difference is the presence of a dissociated electrolyte in the organic phase of the first group in contradiction to the second. As clearly shown by Davies and Rideal [17], this decides about the character of the interfacial potential to be measured. If the organic phase constitutes the solution of the dissociated electrolyte, the ionic double layer is created there, and the Galvani potential changes may be measured. In the opposite case, the voltaic cell allows one to measure the surface potential changes (see Section IV). Of course, in liquid galvanic cells only the water–polar solvent interfaces can be investigated. A.
Galvani Potential and Ionic Distribution Equilibria
Le Hung presented a general theoretical approach for calculating the Galvani potential ws ’ at the interface of two immiscible electrolyte solutions, e.g., aqueous (w) and organic solvent (s) [25]. Le Hung’s approach allows the calculation of ws ’ when the initial concentration (ci ), activity coefficients (i ) and standard energies of transfer of ions (ws G0i ) are known in both solutions. According to Le Hung, one deals, in general, with a system composed of two liquid immiscible phases containing Iizi ions; this can be described as follows: w
j
s
Iizi
j
Iizi
Vw
$ SCHEME 3
Vs
where zi represents the charge of the Iizi ion, and Vw and Vs are the volumes of phases w and s, respectively. In the equilibrium state the electrochemical potentials of each ion are the same in both phases, and the equations (1) to (7) are fulfilled. It is apparent from the mass conservation law that: Vw cwi þ Vs csi ¼ mi
ð13Þ
where mi represents the number of moles of condition of electroneutrality is still valid: j X 1
zi cwi ¼ 0
j X 1
zi csi ¼ 0
j X
Iizi
ions in both phases. For these phases the
zi mi ¼ 0
ð14Þ
1
Using Eqs. (7), (13), and (14), Le Hung derived the general dependence describing the difference of Galvani potentials between the phases w and s:
6
Koczorowski j X 1
iw zi F w w 0 ’ s ’i Vw þ Vs s exp ¼0 zm m i RT s i
ð15Þ
or in the form: h X
zi ci0;w
i
V w zF 1 þ s is exp i ws ’ ws ’0i þ RT V w i þ
j X
zi ci0;s
h
Vw iw zi F w w 0 ’ s ’i 1þ ¼0 exp RT s Vs is
ð16Þ
Ions having initial concentrations, i.e., not equilibrium conditions, c0;w and ci0;s , marked i with indices from 1 to h and from h to j, occur in the phases w and s, respectively. When 0;s w 0 w the values of zi , Vw , Vs , iw , is , c0;w i , ci , s ’i , and T are known, one can find s ’. The convenient form of Hung’s equation is the dependence [14] h X i¼1
h X zi ciw;0 rzi cis;0 ¼0 w s þ 1 þ rði =i Þ i¼1 1 þ rðiw =is Þei
ð17Þ
where r ¼ V s =V w
ð18Þ
ei ¼ exp ðzi F=RTÞðws ’eq ws ’0i Þ
ð19Þ
and
The above equation allows the calculation of Galvani potentials at the interfaces of immiscible electrolyte solutions in the presence of any number of ions with any valence, also including the cases of association or complexing in one of the phases. Makrlik [26] described the cases of association and formation of complexes with participation of one of the ions but in both phases. In a later work [27] Le Hung extended his approach and also considered any mutual interaction of ions and molecules present in both phases. Buck and Vanysek performed the detailed analysis of various practical cases, including membrane equilibria, of multi-ion distribution potential equations [28,29]. The few cases of Le Hung’s equation, for practically important and simple systems, are discussed below.
B.
Distribution Potentials for Binary Electrolytes
In the case of an electrolyte of the type Mm Xx , in the state distribution equilibrium, i.e., for the system: w
j
s
Mm Xx Vw
$ j
Mm X x Vs
SCHEME 4 Eq. (16) can be written as follows:
Interfacial Potentials and Cells
w M zM þ F w þ w 0 s ’ s ’ðM þ Þ Vw þ Vs s exp Zm ; mM þ RT M þ Xw ZX F w w 0 s ’ s ’ðX Þ Vw þ Vs s exp ¼0 þ ZX mX RT X
7
ð20Þ
From Eqs. (14) and (20) one can obtain: ws ’0 ¼
zM þ ws ’0M þ zX ws ’0X RT s þ Xw ln M þ w s ðzX þ zM þ ÞF M zX þ zM þ þ X
ð21Þ
When the distribution equilibrium refers to the 1 : 1 valent electrolyte, e.g., MX, where zX ¼ 1, i.e., for the system j $
w MþX
s MþX
SCHEME 5 Vw ¼ Vs Eq. (21) appears in the form: ws ’ðMXÞ ¼
s w ws ’0ðM þ Þ þ ws ’0ðX Þ RT M þ ln w Xs þ 2F M þ X 2
ð22Þ
The above dependence, which has been known for a long time, can be directly derived from Eq. (3) and the electroneutrality conditions of Eq. (14) which for that case are in the form: RT s ln aM þ =awM þ F RT lnðasX =awX Þ ws ’ ¼ ws ’0 ðX Þ F ws ’ ¼ ws ’0 ðM þ Þ þ
ð23Þ ð24Þ
and csM þ cwX ¼1 cwM þ csX
ð25Þ
The formal Galvani potential, described by Eq. (22), practically does not depend on the concentration of ions of the electrolyte MX. Since the term containing the activity coefficients of ions in both solutions is, as experimentally shown, equal to zero it may be neglected. This results predominantly from the cross-symmetry of this term and is even more evident when the ion activity coefficients are replaced by their mean values. A decrease of the difference in the activity coefficients in both phase is, in addition, favored by partial hydration of the ions in the organic phase [31–33]. Thus, a liquid interface is practically characterized by the standard Galvani potential, usually known as the distribution potential. For symmetrical electrolytes, of, e.g., type 1 : 1, such a liquid–liquid interface, in equilibrium, is described by the standard Galvani potential, usually called the distribution potential. This very important quantity can be expressed in the three equivalent forms, i.e., using the ionic standard potentials, or standard Gibbs energies of transfer, and employing the limiting ionic partition coefficients [3]:
8
Koczorowski
ws ’ðMXÞ ¼ 12 ws ’0 M þ þ ws ’0 ðX Þ
ð26Þ
ws ’0 ðMXÞ ¼
1 w 0 G þ ws G0X 2F s M
ð27Þ
ws ’0 ðMXÞ ¼
RT Bws;0 ðM þ Þ ln s;0 2F Bw ðX Þ
ð28Þ
It is obvious from Eq. (21) that Eqs. (22), (26), (27), and (28) apply to all symmetrical electrolytes, i.e., to electrolytes dissociating into the same number of cations and anions. According to Eq. (26), which directly ensues from Eq. (22), the distribution potential is the arithmetic mean of the Galvani potentials of cations and anions. These potentials are the ionic constituents of the distribution potential, and in fact, according to Eq. (5) they can be considered as electrical representations of the ionic transfer energies Gi , or limiting distribution coefficients of the ions, Bi [3]. Here, the reader is referred to the following equations: þ Fws ’0 ðM þ Þ ¼ ws G0M þ ¼ RT ln Bs;0 w ðM Þ
ð29Þ
Fws ’0 ðX Þ ¼ ws G0X ¼ RT ln Bws;0 ðX Þ
ð30Þ
It is noteworthy [3,31] that for the case where þ w;0 1 Bw;0 M ¼ Bs ðX Þ s
ð31Þ
it appears that ws ’0 ðMXÞ ¼ ws ’0 ðM þ Þ ¼ ws ’0 ðX Þ
ð32Þ
Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, Bws;0 ðM þ Þ and Bws;0 ðX Þ, are related to the extraction constant KMX and to the distribution coefficient of the B0MX electrolyte in the manner described below [24]. The standard distribution constant describing the equilibrium in the system M þ ðwÞ þ X ðwÞ
$ SCHEME 6
M þ ðsÞ þ X ðsÞ
can be expressed, in the equilibrium state, as follows: as þ asX 0 ¼ exp G0MX =RT ¼ M KMX awM þ awX
ð33Þ
Expressing the distribution constant in terms of the mean electrolyte activities one obtains: s a KMX ¼ ð34Þ aw From the above dependence, and from the definition of the limiting or activity distribution coefficient of electrolyte, i.e., from the equation: Bs;0 wðMXÞ ¼
as aw
ð35Þ
Interfacial Potentials and Cells
9
a relationship between the above-mentioned functions is as follows: h i1=2 1=2 s;0 s;0 Bs;0 wðMXÞ ¼ KMX ¼ BwðM þ Þ BwðX Þ
ð36Þ
The transfer energies and distribution coefficients refer to two mutually saturated, i.e., in a sense, mixed solvents. It should be noted that this is a case where, under conditions of distribution equilibrium, the quantities in question can be experimentally measured; this would not be possible with mutually miscible solvents [34]. C.
Interfaces Reversible with Respect to Single Ions
The interface between w and s containing electrolytes of the MX1 and MX2 type, respectively, and represented in the form: w
j
s
M þ X1
j
M þ X2
SCHEME 7 constitutes an interface reversible with regard to the common cation M þ under the following conditions [1–3]: sw G0X1 0 sw G0X2 0
ð37Þ
sw G0X2 < sw G0M þ < sw G0X1 It is obvious from the above conditions that the transfer of strongly hydrophylic X1 anions from phase w to s and of strongly hydrophobic X2 anions from phase s to w is much more difficult compared to the transfer of the common hydrophylic–hydrophobic M þ cations. In the equilibrium state, the Galvani potential is defined in terms of the Nernst equation (4): ws ’ ¼ ws ’ðM þ Þ ¼ ws ’0ðM þ Þ þ
RT awM þ ln s F aM þ
ð38Þ
When the concentration of M þ ions is the same in both phases of the system of Scheme 7, the interface is characterized by the formal Galvani potential of the M þ ions, i.e. by the equation: ws ’fðM þ Þ ¼ ws ’0ðM þ Þ þ
w RT M þ ln s F M þ
ð39Þ
Equations (38) and (39) have been known and used for a long time as special relations describing Haber’s ion-selective systems. D.
Liquid Galvanic Cells
Measurement of electrical potential differences requires a complete electrical circuit, i.e., the electrochemical cell. An electrochemical galvanic cell consisting of all conducting phases, and among them at least one interface separating two immiscible electrolyte solutions is called for short a liquid galvanic cell. In contrast, the system composed of con-
10
Koczorowski
ducting, condensed phases in series, with a gas gap or dielectric liquid phase is called a liquid voltaic cell (see Section IV). It is known [3] that galvanic liquid cells, being in the state of complete equilibrium, i.e. containing reversible electrodes in both phases, cannot constitute any subject of research interest, because according to the second law of thermodynamics such systems would have a zero or constant value of EMF. Therefore, the application of salt bridges, providing practically constant or negligible diffusion potentials, constitutes a nonthermodynamic procedure usually necessary in many electrochemical experiments. Also in the case of investigation of interfaces between immiscible electrolyte solutions only a liquid galvanic cell with transport allows the characterization of the interface. Practically all liquid cells with reversible interfacial equilibria examined can be considered as liquid galvanic cells of the Nernst, Haber, or intermediate type [3]. Usually, a dashed vertical bar (j) is used to represent the junction between liquids. A double dashed vertical bar (k) represents a liquid junction in which the diffusion potential has been assumed to be eliminated. Galvanic cells of the Nerst type are also termed cells with ‘‘dissolution membranes’’ or ‘‘solvent type membranes’’ [3]. Such systems are defined by the distribution equilibria in which all ions, present in aqueous and in organic solvents, participate (Section III.A). The general examples of the liquid concentration and chemical galvanic cells of this type are presented in the form of Schemes 8 and 9. The concentration cells of the Nernst type can be represented in the form of the scheme
SCE
k
aqueous
j organic
j aqueous
k
k k
solution M þ A ; c1
j solution j M þ A
j solution j M þ A ; c2
k k
j j
j j
k k
k k
Bc1 Bc2 ðc1 6¼ c2 Þ
SCE
SCHEME 8 where the completely dissociated MA electrolyte, with the distribution coefficient B (concentrations c1 6¼ c2 ), generates an EMF practically equal to the diffusion potential in the organic phase. As predicted by Nernst, independently of concentration, the distribution potentials of both liquid interfaces should be identical (Section III.B). In the above scheme SCE represents a saturated calomel electrode. Chemical cells of the Nernst type can be represented by the following scheme:
SCE
k
aqueous
j organic
j aqueous
k
k k
solution M þ A ; c1
j solution j M þ A M þ L
j solution j M þ L ; c2
k k
j
j
k
k
Bc1 Bc2
SCE
SCHEME 9 In such cells, aqueous solutions contain electrolytes with a common cation M þ . The EMF of this cell is equal to the difference of distribution potentials of both electrolytes and to the diffusion potential in the organic phase. Under appropriate conditions the EMF depends only on the difference of distribution potentials. It should be noted that cells of this type can also contain many and various ions in both phases.
Interfacial Potentials and Cells
11
Liquid cells containing an ion exchanger in the organic phase, e.g., a salt with a highly hydrophobic anion or cation Rþ , could be considered [3] as concentration cells:
SCE
k k
aqueous solution
j organic j solution
k k
MþX ; c1
j j
j aqueous k j solution k
Rþ X c1 c2
j j
MþX ; c2
k k
SCE
SCHEME 10 or as chemical cells:
SCE
k
aqueous
j organic
j aqueous k
k k
solution MþX ;
j solution j Rþ X
j solution j M þ L
k k
k
c1
j
j
k
c2
SCE
SCHEME 11 There are large cations in these cells, e.g., tetra-alkylammonium cations in the organic phase; and the interfacial ion exchange involves only so-called critical ions, here X and L . M þ ions are practically not transferred through the organic phase. Both liquid interfaces are reversible with respect to the appropriate anion, X or L . EMF is, in practice, also influenced by the diffusion potential in the organic phase, and in the case of cells of the type in Scheme 11 – by the difference of standard transfer energies of both ions (Section III.A) Cells of the type in Scheme 10 represent the simplest case of an ion-selective liquid cell; its EMF is often called a membrane, or monoionic, potential [3]. The first term is too narrow due to the fact that the membrane potential corresponds to the behavior of a number of cells, including those of Schemes 8 to 11, and to the cells with solid membranes and with Donnan equilibrium. Cells of the type in Scheme 11 represent the simplest case of cells with a bi-ionic potential [3]. Hence, in the case of a larger number of ions transferred through the organic phase a multi- or polyionic potential should be considered. Liquid ion-selective electrodes operate on the basis of cells of the type in Scheme 10; their selectivity can be examined with the use of Scheme 11 and polyionic cells. In modern investigations of the electrochemical properties of immiscible electrolyte solutions mixed cells are used, i.e., cells containing one interface, e.g., that under investigation – Nernstian or polarizable, and a second reference interface of the Haber types (Scheme 7 or 10). The system usually in the form shown below: w TBAþ Cl
j j
n TBA TPhB
0:01 M
j SCHEME 12
0:01 M
þ
is a typical reference interface commonly used in the above investigations. It follows from Le Hung’s analysis [25] that in the presence of tetrabutylammonium chloride in water and tetraphenylborate (TBATPhB) in nitrobenzene (or 1,2-dichloroethane), the interface appears to be reversible with respect to TBAþ ions.
12
Koczorowski
Interfaces of the type in Scheme 8 are used as liquid ion-selective electrodes. It is apparent that they constitute a special case of distribution systems reversible in regard to two or more ions. Here, Le Hung’s equation, (16) and (17), allows quantitative evaluation of the influence of the presence of other ions on the selectivity of these systems. E.
Polarizable Interfaces
The interface between an aqueous solution containing a strongly hydrophilic electrolyte, e.g., LiCl, and a nitrobenzene solution containing a strongly hydrophobic salt, e.g., tetrabutylammonium tetraphenylborate (TBATPhB), schematically shown below: j j
w LiCl
n TBATPhB
SCHEME 13 constitutes a very important system in studies of immiscible electrolyte solutions. Since the distribution coefficients of the above electrolytes can be defined by the inequalities [1,2] Bn;0 w ðLiClÞ 1
and
Bwn;0 ðTBATPhBÞ 1
ð40Þ
the interface of Scheme 13, in certain potential limits, behaves nearly as ideally polarizable (see Section II). The degree of polarizability of system can be found from the data calculated by Le Hung [25] with the use of Eqs. (16) and (17). In the equilibrium state of the interphase between the solutions of 0.05 M LiCl in water and 0.05 M TBATPhB in nitrobenzene, the concentrations of Liþ and Cl in the organic phase lower than 107 M, and the concentrations of TBAþ and TPhB in the aqueous phase are about 3 107 M each [3]. These concentrations are too low to establish permanent reversible equilibria. They are, however, significantly higher compared to those of the components present in the mercury–aqueous KF solution system [20]. A detailed analysis of this behavior, as well as its analogy to the mercury–KF solution system, can be found in several papers [1–3,8,14]. The ions of both electrolytes, existing in the system of Scheme 13, are practically present only in one of the phases, respectively. This allows them to function as supporting electrolytes in both solvents. Hence, the above system is necessary to study electrical double layer structure, zero-charge potentials and the kinetics of ion and electron reactions at interface between immiscible electrolyte solutions. F. Redox Systems Heterogeneous electron reactions at liquid–liquid interfaces occur in many chemical and biological systems. The interfaces between two immiscible solutions in water–nitrobenzene and water–1,2-dichloroethane are broadly used for modeling studies of kinetics of electron transfer between redox couples present in both media. The basic scheme of such a reaction is Oxw1 þ Red2s
$ SCHEME 14
Red1w þ Oxs2
Red and Ox represent the components at the redox couples. Usually, the reactant in aqueous phase was the ½FeðCNÞ6 3=4 couple, and various couples in the organic phase
Interfacial Potentials and Cells
13
[30–35]. The Nernst equation for the electrochemical equilibrium of the type in Scheme 14 [30] is ws ¼ E2s;0 E1w;0 þ ws ’0Hþ þ ðRT=nFÞ ln
asox2 awRed1 asRed2 awox1
ð41Þ
where E1s;0 and E2w;0 are standard redox potentials of both couples related to the standard Hþ =H2 reference electrode in the respective phases, ws ’0H þ is the standard proton transfer potential, and n is the number of electrons transferred in th reaction of Scheme 14. Equation (41) is valid if none of the ionic components are transferable across the interface, and the only common charged components are electrons. However, some the redox species are necessarily charged components, and counterions of redox couples also exist in the two phases. All of these ionic components can essentially distribute over the two phases, depending on its w0 ’0i value. In this case, the equilibrium point is affected by the partition of ionic components and the value of the mixed Galvani potential occurs (see Section III.G). It is determined by two physically different system properties. The presence of supporting electrolytes also influences the point of equilibrium through the redistribution of constituent ions. This special type of mixed potential is important not only for defining the initial state of the electrochemical studies of electron transfer reactions but also for understanding other phenomena which involve free-energy coupling of electron and ion transfer reactions, e.g., energy transfer in biological systems and redox-reaction-driven uphill transport of ions across a liquid membrane [14,33,36,37]. A method of calculating equilibrium conditions for electron and ion transfer coupling has been proposed [14,31].
G.
Common Properties of ITIES
The investigations of interfacial phenomena of immiscible electrolyte solutions are very important from the theoretical point of view. They provide convenient approaches to the determination of various physciochemical parameters, such as transfer and solvation energy of ions, partition and diffusion coefficients, as well as interfacial potentials [1– 7,12–17]. Of course, it should be remembered that at equilibrium, either in the presence or absence of an electrolyte, the solvents forming the discussed system are saturated in each other. Therefore, these two phases, in a sense, constitute two mixed solvents. The electrochemisty of ITIES is developing mainly on the basis of the studies of the water–nitrobenzene and water-1,2-dichloroethane interfaces. The polarizability ranges of these interfaces in the presence of typical electrolytes (Scheme 13) are about 0.30 V. Extension of these ranges has been achieved using other organic ions or/and solvents [2,8]. For example, TBAþ ions may be substituted by tetraphenylarsonium crystal violet cations and TPhB ions by dicarbollyl cobaltate (III) anions [1,2]. Standard ionic potentials ws ’0 can be calculated from the ionic distribution coefficients or transfer energies; see Eq. (30). In order to perform such calculations, an appropriate nonthermodynamic assumption that allows division of the B0ðMXÞ or G electrolyte function into ionic constituents has to be made. At the present time, the assumption about the equality of the transfer energies of tetraphenylarsonium cations (TPhAsþ ) and tetraphenylborate anions (TPhB ) is considered as most appropriate [2,36]. It can be presented in the following form: 0 1 2 G ðTphAsTPhBÞ
¼ G0 ðTPhAsþ Þ ¼ G0 ðTPhB Þ
ð42Þ
14
Koczorowski
Another proposed procedure of finding the ionic data is the application of a special salt bridge, which provides practically constant or negligible liquid junction potentials. The water–nitrobenzene system, containing tetraethylammonium picrate (TEAPi) in the partition equilibrium state, has been proposed as a convenient liquid junction bridge for the liquid voltaic and galvanic cells. The distribution potential of this system, and the diffusion potential at the contact of nitrobenezene with many organic solvents, are close to zero [3,38–40]. The cell containing TEAPi–bridge can be represented by the following scheme: k SCE
w
k k
j
k
s
j MX
j
n
k MX
j
w
j
k SCHEME 15
TEAPi j
k k
TEAPi
SCE
k
Alternatively, it has been found that the Galvani potential of zero charge, in the absence of specific adsorption, equals zero. This means that there is no specific orientation of the molecules of both solvents, and the dipolar part of the Galvani potential, Eq. (12), is zero [8,22,41]. The observed discrepancies between the results of various measurements in different ITIES systems have been mainly caused by the specific adsorption [8]. Recently, the analysis of thermodynamic and free charge potentials at ITIES was performed by Volkov [42]. The ionic potentials ws ’0i can be experimentally determined either with the use of galvanic cells containing interfaces of the type in Scheme 7 or electroanalytically, using for instance, polarography, voltammetry, or chronopotentiometry. The values of ws G0i and ws ’0i , obtained with the use of electrochemical methods for the water–1,2-dichloroethane, water–dichloromethane, water–acetophenone, water–methyl-isobutyl ketone, o-nitrotoluene, and chloroform systems, and recently for 2-heptanone and 2-octanone [43] systems, have been published. These data are listed in many papers [1–10,14,37]. The most probable values for a few ions in water–nitrobenzene and water–1,2-dichloroethane systems are presented in Table 1. It is worthwhile mentioning that the interfacial potential created at the liquid–liquid interface is governed by single ionic or redox equilibrium only in the simple cases. The presence of various, often two, interfacial processes is a source of the steady-state potential, named also the mixed or the rest potential. Its value is situated between the two equilibrium potentials, near that one which corresponds to the higher exchange current
TABLE 1 The Recommended Standard Potentials of Ions in Water– Nitrobenzene (w/n) and Water–1,2-Dichloroethane (w/d) Systems [44] ws ’0 (mV) Ion Pi ClO 4 Me4 Nþ Et4 Nþ Bu4 Nþ Ph4 Asþ
w/n
w/d
38 95 30 66 275 375
57 170 160 19 225 365
Interfacial Potentials and Cells
15
density. The modern theory of liquid membrane ion-selective electrodes and their selectivity coefficients has been developed on the basis of the concept of mixed potentials [45–47]. The closeness of the values of the equilibrium and mixed state potentials, as well as the shape of the time-dependence of interfacial potential [48] during the ion partition process, are the reasons that sometimes it is difficult to find whether the examined system is in equilibrium or in the stationary state. As was observed and described by the theoretical model, after the fist several seconds, changes of potential occurring during the ion partition process become very slow [48]. It was shown that during the process, the ion first is transferred by a very fast interfacial step (the time of the ‘‘local interfacial equilibrium’’ formation [29]), followed by a mixed transfer–diffusion stage, and finally moved by slow diffusion.
IV.
LIQUID VOLTAIC CELLS
Liquid voltaic cells are systems composed of conducting, condensed phases in series, with a thin gap containing gas or liquid dielectric (e.g., decane) situated between two condensed phases. The liquid voltaic cells contain at least one liquid surface [2,15]. Due to the presence of a dielectric, special techniques for the investigation of voltaic cells are necessary. Usually, it is the dynamic condenser method, named also the vibrating plate method, the vibrating condenser method, or Kelvin–Zisman probe. In this method, the capacity of the condenser created by the investigated surface and the plate (vibrating plate), is continuously modulated by periodical vibration of the plate. The a.c. output is then amplified, and fed back to the condenser to obtain null-balance operation [49,50]. Recently, scanning Kelvin probes and microprobes, as high-resolution surface analysis devices, have been developed. They allow one to investigate the lateral distribution of the work functions of the surfaces of various phases, including the determination of the potential profiles of metals and semiconductors under very thin films of electrolytic solution, and also of the surface potential map of various polymer- and biomembranes [50–56]. The lateral resolution and the sensitivity are in the 100 nm and 1 mV ranges, respectively [54]. A.
Volta Potentials of ITIES
The liquid voltaic cell type ref
k k
w
el:
k
MþX
j j j gas j j
j
s MþX
j j
w
j MþX
k ref: j k j Ek ¼ ws k el:
j
SCHEME 16 contains the interface created at the contact of an aqueous and organic solutions of electrolyte MX being in the partition equilibrium. The compensating voltage, Ek , from a potentiometer is adjusted until the electric field strength in the gas space between the two condensed phases is zero. This state means that the Volta potential is zero, and simultaneously that the compensating voltage equals the sum of all Galvani potentials existing in the system plus the difference of surface potentials (instead of Galvani potential) between the liquid phases, which contact the gas space. The application of two identical reference electrodes and the elimination of the liquid junction potentials by proper salt bridges (k),
16
Koczorowski
removes their contributions to the compensation potential. Using Eq. (3), after simple rearrangement we have [15]: E ¼ sw ðMXÞ
ð43Þ
Thus, the Volta potential may be operationally defined as the compensating voltage of the cell of Scheme 16. However, it should be stressed that the compensating voltage of a voltaic cell is not always the direct measure of the Volta potential. The appropriate mutual arrangement of phases, as well as application of reversible electrodes or salt bridges in the systems, allows measurement of not only the Volta potential but also the surface and the Galvani potentials. These possibilities are schematically illustrated by [15] k
w
j gas
j
s
j
w
k
Ek ¼ ws
j
s
k
Ek ¼ ws
k
Ek ¼ ws ’
SCHEME 17 k
w
j gas
j
s SCHEME 18
k
w
j gas
j
w SCHEME 19
Practically, the Volta potential at the water–nonaqueous solvent interface, sw , is measured as the difference in the compensating voltages of the cells of Schemes 20 and 21 [57–59]. The vibrating plate is the mediatory electrode for both cells: s M
Vib:pl
gas Mþ þ X
j
w
j j Mþ þ X
SCE M; E20
SCHEME 20 M
Vib:pl
w
j j
Mþ þ X SCHEME 21
j
gas
2w ðMXÞ ¼ E20 E21
SCE
M; E21
ð44Þ
The reliability of the experimental ws ðMXÞ values was checked for systems containing nitrobenzene [57,58], nitromethane and 1,2-dichloroethane [59] as organic solvent, by comparing the differences in these values for various pairs of salts with the differences in the Galvani potentials, ws ’ðMXÞ for the same pairs [3]. The differences should be the same. The ws ’ or ws data can be used for the estimation of ion solvation energies in the water saturated solvent. The results are reliable if the influence of the electrolyte MX on the surface potential of solvent in the investigated concentration range, is negligibly small. The liquid–liquid partition systems discussed above are in fact very similar to various membrane-type interfaces and may serve as a model for them. A good example is, for instance, the distribution of a dissociated salt between aqueous solution and a permeable organic polymer [60].
Interfacial Potentials and Cells
B.
17
Adsorption Potentials of Dipolar Compounds
The adsorption of the dipolar organic compound B on the water surface can take place as the result of either spreading B from the appropriate solution over water, i.e. formation of a Langmuir monolayer, or expelling the molecules of the considered compound from the bulk aqueous solution, i.e. formation a Gibbs layer or monolayer [6,11,15,17,18]. The first way is used for relatively large, amphipathic molecules, i.e., molecules composed of hydrophobic parts, most commonly a flexible hydrocarbon chain, with the number of carbon atoms in the chain greater than ten. There is also a large number of such compounds, including molecules of biological interest, with aromatic hydrophobic groups. The total number of the adsorbed B molecules per, e.g., 1 m2 of the surface, NB , may be easily evaluated from the amount of the spread compound B. The second way is common for molecules easily soluble in water, and is called the adsorption from solution. Surface tension measurements make it possible to calculate, from the Gibbs isotherm, the surface excess of substance B, which is a relative quantity. Replacement of gas by the nonpolar, e.g., hydrocarbon phase (or oil phase) is used to modify the interactions between molecules in a spread film of investigated longchain substances [6,15,17,18]. The nonpolar solvent–water interface possesses the advantage over that between gas and water, that the cohesion (i.e., interactions between adsorbed molecules due to dipole and van der Waals forces) is negligible. Thus, at the oil–water interfaces behavior of adsorbates is much closer to ideal, but quantitative interpretation may be uncertain, in particular for the higher chains which are predominantly dissolved in the oil phase to an unknown activity. Adsorption of dipolar substances at the w/a and w/o interfaces changes surface tension and modifies the surface potential of water [15]: ref: k el:
k k
w
w
k
MX þ B
k k
gas MþX
ref: Ek ¼ w el:
SCHEME 22 As seen in this sketch, the change of compensation voltage E, due to adsorption is the surface potential difference, usually called shortly surface potential, or better the adsorption potential E ¼ w ¼ w W þB
ð45Þ
The experimental investigation of w may be performed directly as presented in the cell of Scheme 22, or by using two measuring cells (Schemes 23 and 24). In the first case, the voltaic cell with differential ionizing probe or jet method can be used. In the second case, the ionizing probe or vibrating plate method are applied (see Section IV). These probes are two versions of so-called air electrodes, which mediate in the measurement of voltaic cells. The air electrode, e.g., vibrating plate, creates in fact the two following cells:
18
Koczorowski
w M
Vib:pl
gas
Ref:el
M; E23
Ref:el
M; E24
MX SCHEME 23 w M
Vib:pl
gas MX þ B SCHEME 24
and E ¼ E23 E24 ¼ w
ð46Þ
The presence of supporting electrolyte MX in the aqueous phases secures the stability of the measurements. However, MX must not adsorb at the surface to avoid an influence on w potential. It is common in the literature to link w with the properties of the neutral adsorbate by means of the Helmholtz equation [6,11,15,17,18] w ¼ NB P? B =0
ð47Þ
where 0 and are the electrical permittivity of vacuum, and the relative permittivity of the interfacial region, respectively, and p? B is the normal component of the molecular dipole moment of the substance B. Either from the known value NB , or from the slope of the experimental relationship of w vs. NB , the quantity p ¼ p? B =0
ð48Þ
can be derived. It may be treated as the apparent surface dipole moment of the adsorbate. The effect of an electric field on the surface tension and surface excess of adsorbed solutes can be calculated from the experimental data of adsorption potential, using Maxwell relations found from a thermodynamic analysis of the Volta potential [61]. It is known that the p values derived from experimental w data, e.g., for insoluble monolayers, with the assumption e ¼ 1 are substantially different from the dipole moment for the same molecule in the bulk of the solution [17]. The reasons offered to explain this difference are manifold e.g. (1) inappropriate value of e, (2) reorientation of water molecules around the adsorbate, and (3) lateral interaction between adsorbed molecules in the monolayer. The various models of p have been described in a number of papers [61–67]. The very popular applications of the adsorption potential measurements are those dealing with the surface potential changes at the water–air and water–hydrocarbon interfaces when a monolayer film is formed by an adsorbed substance. Phospholipid monolayers, for instance, formed at such interfaces have been extensively used to study the surface properties of the monolayers, which are expected to represent, to some extent, the surface properties of bilayers, and biological, as well as various artificial membranes. An interest in a number of applications of the ordered thin organic films, e.g., Langmuir– Blodgett layers, dominated the insoluble monolayer research activity during the last decade. Equations (47) and (48) concern the case of neutral adsorbates, where there is no ionic double layer to contribute to the surface potential. In the case of charged, i.e., ionic adsorbates the measured potential w consists of two terms. The first term is due to dipoles oriented at the interface, which may be described by the above formulas, and the
Interfacial Potentials and Cells
19
second term presents the potential of the ionic double layer at the interface from aqueous side w ¼ p=AB þ gw ðionÞ
ð49Þ
w
where g (ion) is the electrical potential drop between the film of adsorbed long-chain ions and the bulk of aqueous solution. AB is the reciprocal value of NB and expresses the surface area per ion. The physical meaning of the gw (ion) potential depends on the accepted model of ionic double layer. The proposed models correspond to the Gouy–Chapman diffuse layer, with or without allowance for the Stern modification and/or the penetration of small counterions above the plane of the ionic heads of the adsorbed large ions [17,18]. The presence of adsorbed Langmuir monolayers may induce very high changes of the surface potential of water. For example, w shifts attaining ca. 0:9 (hexadecylamine hydrochloride), and ca. þ1:0 V (perfluorodecanoic acid) have been observed [68]. Studies of the adsorption of surface active electrolytes at the oil–water interface provide a convenient method for testing electrical double layer theory and for determining the state of water and ions in the neighborhood of an interface. The change in the surface amount of the large ions modifies the surface charge density. For instance, the surface ionic area of 100 A2 per ion corresponds to 16 ; C=cm2 . The measurement of the concentration dependence of the changes of surface potential were also applied to find the critical concentration of formation of the micellar solution [18]. The possibility of determination of the difference of surface potentials of solvents, see Scheme 18, among others, has been used for the investigation of ws between mutually saturated water and organic solvent: namely nitrobenzene [57,58], nitroethane and 1,2-dichloroethane (DCE) [59], and isobutyl methyl ketone (IB) [69]. The results show a very strong influence of the added organic solvent on the surface potential of water, while the presence of water in the nonaqueous phase has practically no effect on its s potential. The information resulting from the surface potential measurements may also be used in the analysis of the interfacial structure of liquid–liquid interfaces and their dipole and zero-charge potentials [3,15,22].
V.
SMALL LIQUID–LIQUID INTERFACES
The microheterogenous and nanoheterogenous (mesoscopic) liquid–liquid systems may be concisely called the small systems. They comprise the micro- and nanodomains, described in colloidal chemistry as a variety of structures, e.g., micelles, rods, disks, vesicles, microemulsions, monolayers, and Langmuir–Blodgett layers [6,17–19,70]. The properties of these systems depend strongly on the interfacial potentials created at the interface. They arise from oriented molecular dipoles, from ionization of the surfactant hydrophylic groups, and from the partition and adsorption of ions presented in the environment. Unfortunately, we do not have microinterface voltmeters, and we can use only indirect methods like various chemical probes and electrokinetic methods. These methods make it possible to estimate only part of the Galvani potential, denoted here ws ’ . The common method of estimation of the interfacial potential in microheterogeneous systems is to use pH indicators adsorbed at for instance charged micelles. The ‘‘local interfacial’’ proton activity is related to the bulk activity and to an interfacial potential by Boltzmann’s law according to the equation [17,70–72]
20
Koczorowski
pHa ¼ pH0a ðws ’ F=2:3RT Þ
ð50Þ
Changes of pH are about 3 pH units to the alkaline side for adsorbed acids and to the acidic side for adsorbed amines have been reported [17]. However, the equilibrium of the indicator adsorbed at an interface may also be affected by a lower dielectric constant as compared to bulk water. Therefore, it is better to use instead pH, the ‘‘interfacial’’ and ‘‘bulk’’ pK values in Eq. (50). The concept of the use at pH indicators for the evaluation of ws ’ is also basis of other methods, like spinlabeled EPR, optical and electrochemical probes [19,70]. The results of the determination of the ws ’ by means of these methods may be loaded with an error of up to 50 mV [19]. For some the potentials determined by these methods, ws ’ values are in a good agreement with the electrokinetic (zeta) potentials found using microelectrophoresis [73]. It is proof that, for small systems, there is lack of methods for finding the complete value of ws ’. Fortunately the microinterfaces between two immiscible electrolytes seem to be a very useful experimental model of small liquid–liquid systems. The formation and investigation of the micro-ITIES is continuously perfected [74–76]. The smallest diameter so far achieved was 5 m. The main utilization of micro-ITIES is developed, in parallel with application of ultramicroelectrodes. Kakiuchi performed a very important analysis of the distribution potential in the small systems [14,31]. Using the general Le Hung approach, he discussed the behavior of ws ’eq at its extreme, when r ! 0 or 1. When all ions are initially dissolved only in the w phase, Eq. (17) takes a simple form: X
zi ciw;0
Y
1 þ rðjw =js Þej ¼ 0
ð51Þ
j6¼i
i
where j 6¼ k under the product means that the product is taken over all ionic species except i. It can be further simplified when r ! 0: X i
" zi ciw;0
X
jw =js
# ej ¼ 0
ð52Þ
j6¼i
Using the equation, very strong concentration effects in small systems have been calculated. For instance, if the macroaqueous phase contains 1 M NaCl and 1 M NaTPB, the concentration of this electrolyte in the micro-organic phase at partition equilibrium is 1390 M [14]! This approach is valid if the phases in small systems are thick enough (> 1 m), in comparison to the Debye screening length, to fulfill the electroneutrality conditions.
ACKNOWLEDGMENT The author is pleased to acknowledge the financial support from the Polish Committee on Scientific Research (BST-623/19/99).
Interfacial Potentials and Cells
21
REFERENCES 1. 2. 3.
4.
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.
P. Vanysek, Lecture Notes in Electrochemistry, vol. 39, Springer-Verlag, New York, 1985, pp. 1–106. J. Koryta. Electrochim. Acta 32:419 (1987). Z. Koczorowski, in The Interface Structure and Electrochemical Processes at the Boundary Between Two Immiscible Liquids (V. E. Kazarinov, ed.), Springer-Verlag, Berlin–Heidelberg, 1987, pp. 143–178. L. I. Boguslavsky and A. G. Volkov, in The Interface Structure and Electrochemical Processes at the Boundary Between Two Immiscible Liquids (V. E. Kazarinov, ed.), Springer-Verlag, Berlin–Heidelberg, 1987, pp. 77–106. Z. Samec. Chem Rev. 88:617 (1988) K. S. Birdi, Lipid and Biopolymer Monolayer at Liquid Interface, Plenum Press, New York– London, 1988, chaps. 4 and 5. V. S. Martin and A. Volkov. J. Colloid Interface Sci. 131:382 (1989). H. H. Girault and D. Schiffrin, in Electroanalytical Chemistry (A. J. Bard, ed.), vol. 15, Marcel Dekker, New York, 1989, pp. 1–144. V. S. Markin and A. G. Volkov. Adv. Colloid Interface Sci. 31:111 (1990). M. Senda, T. Kakiuchi, and T. Osakai. Electrochim. Acta 36:253 (1991). A. Ulman, An Introduction to Ultrathin Organic Films: from Langmuir–Blodgett to SelfAssembly, Academic Press, Boston, 1991. P. Vanysek, in Electrochemistry and Dispersions (R. M. Mackay and T. Texter, eds.), VCH Publishers, New York, 1992, pp. 71–84. H. H. Girault, in Modern Aspects of Electrochemistry (J. O’M. Bockris, B. E. Conway, and R. E. White, eds.), No. 25, 1993, pp. 1–62. T. Kakiuchi, in Liquid–Liquid Interfaces: Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 1–18. Z. Koczorowski, in Liquid–Liquid Interfaces. Theory and Methods (A. G. Volkov and D. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 19–37. A. G. Volkov, D. W. Deamer, D. L. Tanelian, and V. S. Markin, Liquid Interfaces in Chemistry and Biology, Wiley-Interscience, New York, 1998, pp. 130–319. T. Davies and E. K. Rideal, Interfacial Phenomena, Academic Press, New York, 1963, chaps. 2–6. J. Llopis, in Modern Aspects of Electrochemistry (J. O’M. Bockris and B. E. Conway, eds.), No. 6, Plenum Press, New York, 1971, pp. 91–159. N. A. Kotov and M. G. Kuzmin, in Liquid–Liquid Interfaces. Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 213–224. R Parsons, in Modern Aspects of Electrochemistry (J. O’M. Bockris and B. M. Conway, eds.), Butterworths, London, 1954, vol. 1, chap. 3. S. Trasatii and R. Parson. Pure Appl. Chem. 58:1251 (1986). Z. Koczorowski. J. Electroanal. Chem. 190:257 (1985). E. J. V. Verwey and K. F. Niessen. Phil. Mag. 28:435(1939). F. M. Karpfen and J. E. B. Randles. Trans. Faraday Soc. 49:823 (1953). L. Q. Hung. J. Electroanal. Chem. 149:1 (1985). E. Makrlik. Electrochim. Acta 28:573 (1995). L. Q. Hung. J. Electroanal. Chem. 149:1 (1985). R. P. Buck and P. Vanysek. J. Electroanal. Chem. 292:73 (1990). P. Vanysek and R. P. Buck. J. Electroanal. Chem. 297:19 (1991). Z. Samec. J. Electroanal. Chem. 99:197 (1979). T. Kakiuchi. Electrochim. Acta. 40:2999 (1995). A. G. Volkov, M. I. Gugeshashvili, and A. W. Deamer. Electrochim. Acta 40:2849 (1995). V. J. Cunnane, G. Geblewicz, and D. Schiffrin. Electrochim Acta 40:3005 (1995). V. J. Cunnane and L. Murtomaki, in Liquid–Liquid Interfaces. Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 401–416.
22
Koczorowski
35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73 74. 75. 76.
A. G. Volkov and A. W. Deamer. Progr. Colloid Polym. Sci. 103:21 (1997). O. Popovych and R. G. Bates. Crit. Revs. Anal. Chem. 1:73 (1970). J. Koryta, P. Vanysek, and M Brezina. J. Electroanal. Chem. 75:211 (1977). Z. Koczorowski. J. Electroanal. Chem. 127:11 (1981). Z. Koczorowski and G. Geblewicz. J. Electroanal. Chem. 152:55 (1983). G. Geblewicz and Z. Koczorowski. J. Electroanal. Chem. 158:37 (1983). H. H. Girault and D. Schiffrin. Electrochim. Acta 31:1341 (1986). A. G. Volkov. Langmuir 12:3315 (1996). Y. Cheng and D. J. Schiffrin. J. Electroanal. Chem. 429:37 (1997). T. Wandlowski, V. Marecek, and Z. Samec. Electrochim. Acta 15:1173 (1990). T. Kakiuchi and M. Senda. Bull. Chem. Soc. Jpn. 57:1801 (1984). S. Kihara and Z. Yoshida. Talanta 31:789 (1984). T. Kakiuchi, I. Obi, and M. Senda. Bull. Chem. Soc. Jpn. 57:1636 (1985). C. A. Chang, E. Wang, Z. Pang. J. Electroanal. Chem. 266:143 (1989). W. A. Zisman. Rev. Sci. Instrum. 3:367 (1932). J. M. Palau and J. Bonnet. J. Phys. E: Sci. Instrum. 21:674 (1988). M. Fujihira and K. Hirosuke. Thin Solid Films 242:163 (1994). M. T. Nguyen, K. K. Kanazawa, P. Brock, and A. F. Diaz. Langmuir 10:597 (1994). I. D. Baikie, P. J. S. Smith, D. M. Portfield, and P. J. Estrup. Rev. Sci. Instrum. 70:1842 (1999). W. Nabhan, B. Equer, A. Broniatowski, and G. De Rosny. Rev. Sci. Instrum. 68:3108 (1997). E. Moons, A. Goossens, and T. Savenije. J. Phys. Chem. B 101:8492 (1997). I. Frateur, E. Bayet, M. Keddam, and B. Tribollet. Electrochem. Commun. 1:336 (1999). Z. Koczorowski and I Zago´rska. J. Electroanal. Chem. 159:183 (1983). I. Zago´rska and Z. Koczorowski. J. Electroanal. Chem. 204:273 (1986). I. Zago´rska, Z. Koczorowski, and I. Paleska. J. Electroanal. Chem. 282:51 (1990). K Doblhofer and M. Cappadonia. Colloids Surfaces 41:211 (1989). A. N. Frumkin, B. B. Damaskin, and A. A. Survila. J. Electroanal. Chem. 16:493 (1968). B. B. Damaskin, A. N. Frumkin, and A. Chizhov. J. Electroanal. Chem. 28:93 (1970). R. J. Demchak and T. Fort Jr. J. Colloid Interface Sci. 46:191 (1974). V. Vogel and D. Mo¨bius. J. Colloid Interface Sci. 126:408 (1988). O. N. Oliveira Jr, A. Riul, and L. G. F. Fereira. Thin Solid Films 242:239 (1994). Z. Koczorowski, S. Kurowski, and S. Trasatti. J. Electroanal. Chem. 329:25 (1992). P. Nikitas and A. Pappa-Louisi. J. Electroanal. Chem. 385:257 (1995). A. N. Frumkin, X. A. Jofa, and M. A. Gerovich. Zh. Fiz. Khim. 30:1456 (1956). Z. Koczorowski, I. Zago´rska, and A. Kalin´ska. Electrochim. Acta 34:1857 (1989). R. B. Gennis, Biomembranes, Springer-Verlag, New York, 1989, pp. 235–269. M. S. Fernandez and P. Fromherz. J. Chem. Phys. 81:1755 (1977). C. J. Drummond, F. Grieser, and T. W. Healy. J. Am. Chem. Soc. 92:2604 (1988). A. M. Carmona-Ribeiro and B. R. Midmore. J. Phys. Chem. 96:3542 (1992). G. Taylor and H. H. Girault. J. Electroanal. Chem. 208:179 (1986). P. Vanysek. Electrochim. Acta 40:2841 (1995). V. J. Cunnane, D. J. Schiffrin, and D. E. Williams. Electrochim. Acta 40:2943 (1995).
2 Ion Solvation and Resolvation TOSHIYUKI OSAKAI
Department of Chemistry, Kobe University, Kobe, Japan
KUNIYOSHI EBINA Division of Sciences for Natural Environment, Kobe University, Kobe, Japan
I.
INTRODUCTION
Much attention has been directed since olden times towards ion solvation, which is a key concept for understanding various chemical processes with electrolyte solutions. In 1920, a theoretical equation of ion solvation energy (G0s ) was first proposed by Born [1], who considered the ion as a hard sphere of a given radius (r) immersed in a continuous medium of constant permittivity (), and then defined G0s as the electrostatic energy for charging the ion up to ze (z, the charge number of the ion; e, the elementary charge): N z2 e2 1 1 G0s ðBornÞ ¼ A ð1Þ 80 r where NA is the Avogadro constant, and 0 the permittivity of vacuum. Since the term ‘‘1’’ in the parentheses of the RHS of Eq. (1) is 1/[the relative permittivity of vacuum (¼ 1, by definition)], G0s (Born) can also be regarded as the electrostatic energy required for the transfer of the ion from vacuum to the medium having the permittivity of . Accordingly, the Gibbs free energy of ion transfer (G0;O!W ), i.e., the resolvation energy for the tr transfer of an ion from one medium (e.g., organic solvent, O) to another (e.g., water, W) can be expressed as N A z2 e2 1 1 0;O!W ðBornÞ ¼ Gtr ð2Þ 80 r O W where O and W are the relative permittivities of O and W, respectively. The Born equation thus derived is based on very simple assumptions that the ion is a sphere and that the solvents are homogeneous dielectrics. In practice, however, ions have certain chemical characters, and solvents consist of molecules of given sizes, which show various chemical properties. In the simple Born model, such chemical properties of ions as well as solvents are not taken into account. Such defects of the simple Born model have been well known for at least 60 years and some attempts have been made to modify this model. On the other hand, there has been another approach that focuses on short-range interactions of an ion with solvent molecules. The purpose of this chapter is to discuss mainly recent development in the theory of ion solvation energy. Because we allowed much space for introducing our new, non23
24
Osakai and Ebina
Bornian theory of the Gibbs free energy of ion resolvation, a vast amount of work dealing with ion solvation and resolvation could not fully be reviewed. The reader is referred to some books [2–5] and review articles [6–10] for a general survey.
II.
MODIFICATIONS OF THE BORN MODEL
The defects of the Born equation [1] may be put into two categories; one is for large ions and the other for small ions. The defect for large ions is concerned with the fact that the Born equation does not take account of the energy of the formation of a cavity for introducing an ion into the solvent. This energy, which corresponds to the so-called ‘‘solvophobic’’ interaction, is more noticeable for large ions. Consequently, a modification has generally been made by adding a nonelectrostatic term, G0s ðneÞ, to the Born equation: G0s ¼ G0s ðelÞ þ G0s ðneÞ
ð3Þ
where G0s ðel) is the electrostatic term which is given by the Born equation (or its modifications). As described by the previous authors [9], the division shown in Eq. (3) is somewhat arbitrary, because different effects may overlap. However, such a division is useful for evaluating the individual effects in a heuristic way. The evaluation of the nonelectrostatic term is usually empirical and multifarious. Based on a skillful argument, however, Volkov and coworkers [9,11,12] proposed that the nonelectrostatic term of the ion transfer energy, G0;O!W (ne), should be expressed by a tr semiempirical equation called the Uhlig equation [13], which is given by 0;O!W Gtr ðneÞ ¼ 4NA r2 O;W
ð4Þ
when the surface tension at the boundary of organic solvent (O) with air is smaller than that of water (W) with air. In this formula, the difference in the energies for forming a surface around an ion in O and in W is to be evaluated simply by using the interfacial tension (O;W ) between the two phases. The Uhlig formula is shown to be valid for O;W > 10 mN m1 and r > 0:2 nm [9]. The other defect of the Born equation is for relatively small ions and is concerned with the change in the solvent structure around an ion when it is inserted in the solvent; this change is caused by the high electric field formed by the ion. Many attempts have been made since long ago to mitigate this defect by modifying the Born equation in various ways: (1) by correcting the ionic radii (for example, see Ref. 14), (2) by taking account of the effect of dielectric saturation (i.e., the lowering of the permittivity of solvents adjacent to an ion due to the high electric field) [9,11,12,15–17], or (3) by doing both (1) and (2) [18]. In modification (1), a constant value (r) is added to the crystal ionic radius (r), and the value of r þ r is used in place of r in Eq. (1). By using the values of r þ r (dependent on the ionic valence) determined empirically, fairly good agreement was obtained between experimental and theoretical values for the ion hydration energy. An example [14] is shown in Fig. 1. The solid lines in the figure represent the plots obtained by using the crystal ionic radii for r in the Born equation. It should be noted that the plots for the cations showed a curved line inconsistent with the Born equation [See Eq. (1) again]. However, adding a constant rð¼ 0:85 A˚) to the crystal ionic radius for all the cations could make the curved line straight, as shown by a dashed line. But, the physical meaning
Ion Solvation and Resolvation
25
FIG. 1 Modification of the Born equation by correcting ionic radii. Solid curves for crystal radii, dotted for corrected radii (for cations, r ¼ 0:85 A˚; for anions, r ¼ 0:1 A˚). (From Ref. 14. Copyright 1939 the American Institute of Physics.)
of r still remains obscure. Such a modification seems unable to come to the essential solution to this problem. The modification by method 2 is more acceptable. Although several types of modifications have been reported, Abraham and Liszi [15] proposed one of the simplest and well-known modifications. Figure 2(b) shows the proposed ‘‘one-layer’’ model. In this model, an ion of radius r and charge ze is surrounded by a local solvent layer of thickness (b r) and dielectric constant 1 , immersed in the bulk solvent of dielectric constant b . The thickness (b r) of the solvent layer is taken as the solvent radius, and its dielectric constant 1 is supposed to become considerably lower than that of the bulk solvent owing to dielectric saturation. The electrostatic term of the ion solvation energy is then given by G0s ðelÞ
N z2 e2 ¼ A 80 r
1 1 1 1 1 1 þ 1 1 r b b b
ð5Þ
On the assumption that 2 ¼ 2, the theoretical values of the ion solvation energy were shown to agree well with the experimental values for univalent cations and anions in various solvents (e.g., 1,1- and 1,2-dichloroethane, tetrahydrofuran, 1,2-dimethoxyethane, ammonia, acetone, acetonitrile, nitromethane, 1-propanol, ethanol, methanol, and water). Abraham et al. [16,17] proposed an extended model in which the local solvent layer was further divided into two layers of different dielectric constants. The nonlocal electrostatic theory [9,11,12] was also presented, in which the permittivity of a medium was assumed to change continuously with the electric field around an ion. Combined with the abovementioned Uhlig formula, it was successfully employed to elucidate the ion transfer energy at the nitrobenzene–water and 1,2-dichloroethane–water interfaces. It should be noted that in the modified Born equation of Eq. (5), the value of 1 ð¼ 2Þ is extremely small compared with that of b ð¼ 78:54 for water). In the Born equation as well as its modifications, the reciprocal of the permittivity (1=) crucially determines the magnitude of the ion solvation energy. As b > 10 (i.e., 1=b < 0:1) for most polar sol-
26
Osakai and Ebina
FIG. 2 (a) The Born model [1]. (b) The one-layer model proposed by Abraham and Liszi [15]. (From Ref. 10. Copyright the Japan Society for Analytical Chemistry.)
vents, we see how great the modification is when we set 1 ¼ 2 (i.e., 1=1 ¼ 0:5). It seems far beyond the ‘‘modification.’’ What does the assumption ‘‘1 ¼ 2’’ really mean? Since the permittivity reflects the extent of the rotational fluctuation of molecular dipoles of the solvent, the low permittivity means that the solvent molecules are strongly restricted in their movements in the vicinity of the ion which has the high electric field at the surface. This suggests that the short-range ion–solvent interactions, including such chemical interactions as hydrogen bonds, should play the most significant role in the ion solvation energy. As mentioned above, the Born equation is essentially based on the long-range ion–solvent interaction. Ironically enough, however, its modifications insist on the importance of the short-range interactions rather than the long-range ones.
III.
EMPIRICAL APPROACHES TO SHORT-RANGE INTERACTIONS
In the Born equation, the ion–solvent interaction energy is determined only by one physical parameter of the solvent, i.e., the dielectric constant. However, since actual ion– solvent interactions include ‘‘specific’’ interactions such as the charge-transfer interaction or hydrogen bonds, it is natural to think that the Born equation should be insufficient. It is well known that the difference in the behavior of an ion in different solvents is not often elucidated in terms of the dielectric constant. Since around 1950, in studies of solvent effects for organic reactions, empirical solvent parameters have been used; these parameters represent the capabilities of solvents for the solute–solvent interactions (especially Lewis acid–base interactions). Though the solute–solvent interactions should depend on the solute as well as on the solvent, the empirical solvent parameters are considered to be irrelevant to solutes; in other words, the use of only these parameters enables us to evaluate the solvation energies. Strictly
Ion Solvation and Resolvation
27
speaking, this is not correct. In practice, however, good correlations of the empirical parameters with the solvent effects have been seen in a number of systems (for reviews, see Refs. 19 and 20). The best-known solvent parameters are the donor number [21] and acceptor number [22] proposed by Gutmann and coworkers. The donor number (DN) for a donor solvent D is defined as the positive value of the enthalpy difference H (kcal mol1 ) for the reaction of D with an acceptor-halide SbCl5 (D þ SbCl5 ! D SbCl5 ) in an inert medium such as 1,2-dichloroethane. DN is a fair measure for the donor properties of a solvent. The correlations of DN with the solvation energies are known to be good particularly for solvation of cations. A typical example [19] is shown in Fig. 3. The acceptor number (AN) for a solvent A is determined by comparing the electronpair accepting ability of the solvent with that of SbCl5 , from the oxygen atom of triethylphosphine oxide Et3 PO in 1,2-dichloroethane [22]. To put it concretely, the 31 P-NMR chemical shift of Et3 PO in solvent A, ðEt3 PO AÞ, which would reflect the electron density around the 31 P nucleus, was measured, and then its relative value against the chemical shift of Et3 PO SbCl5 in 1,2-dichloroethane was defined as AN: AN ¼
ðEt3 PO AÞ 100 ðEt3 PO SbCl5 Þ
ð6Þ
AN is known to show good correlations with the solvation energies of anions. Also, AN has good correlations with other solvent parameters defined in different reaction systems, e.g., Grunwald and Winstein’s Y-value [24], Kosower’s Z-value [25], Dimroth and Reichardt’s ET -value [26,27], etc. Taft et al. [28] proposed the solvatochromic parameters, , , and , which describe three solvent’s abilities, respectively, to stabilize a charge or a dipole by virtue of its dielectric effect, to donate a proton (or accept an electron pair), and to accept a proton (or donate an electron pair). It was shown that the AN for nonprotonic solvents correlates
FIG. 3 Correlation between the Gibbs free energy of transfer of Kþ from CH3 CN to a solvent and DN. The free energies of transfer were determined by EMF measurements [23] based on the assumption of negligible liquid junction in a cell: KðHgÞj0:01 M KClO4 (solvent) k0:1 M Et4 NPic ðCH3 CNÞk0:01 M KClO4 ðCH3 CNÞjKðHgÞ. NM: nitromethane; TMS: tetramethylene sulfonate; PDC: propanediol-1,2-carbonate; DMF: dimethylformamide; NMP; N-methyl-2-pyrrolidone, DMA: dimethylacetamide; DMSO: dimethyl sulfoxide; HMPA: hexamethylphosphoramide. (From Ref. 19. Copyright 1978 Plenum Press, New York.)
28
Osakai and Ebina
well with and for protonic solvents with a linear combination of and . It was therefore concluded that AN was, in fact, a combined measure of solvent polarity/polarizability and hydrogen bond donor ability. It was also shown that DN was linear to for oxygen bases and RCN nitrogen bases, though the correlation broke down for pyridine. In Taft et al.’s studies, the macroscopically defined solvent parameters were analyzed at a molecular level; therefore their conclusions are full of interesting suggestions for the understanding of solute–solvent interactions.
IV.
A VOLTAMMETRIC STUDY WITH POLYANIONS
The above-mentioned solvent parameters are the solvent-side measures for describing the solute–solvent interactions. Accordingly, they are useful for predicting the effects observed when the solvent is changed, but inadequate when the solute is changed. On the other hand, the Born equation includes the parameters for both the solvent and solute (ion), i.e., the dielectric constant () as a solvent parameter and the ionic charge and radius (z and r) as ion parameters. This is an advantage of the Born equation and therefore the reason why the Born equation has been widely used for many years notwithstanding a lot of criticisms. However, in theoretical studies with the Born equation or its modifications, the r-dependence of the solvation energy was generally examined for the ions with the common zvalue; the dependence on the z-value has not been elucidated successfully. Previously, Osakai and coworkers [29–31] employed ion-transfer voltammetry to 0 determine the standard ion-transfer potentials (W O ) of heteropoly- and isopolyoxometalate anions (in short, polyanions) at the nitrobenzene (NB)/W and 1,2-dichloroethane 0 (1,2-DCE)/W interfaces; W O is directly related to the transfer energy by G0;O!W tr ð7Þ zF 0 0;O!W The values of W , obtained for the NB/W interface, are summarO as well as Gtr 0 ized in Table 1. As seen, the value of W O for the polyanions, so their transfer energies as well, depend only on the ionic size and charge. Thus there was no indication that the iontransfer potential (or the energy) was significantly influenced by such ‘‘specific’’ solvation as due to electron localization in a polyanion. This seems to support the hypothesis that the surface charge of such a polyanion is nonlocalized. If we assume the polyanion to be a hard sphere with a uniform surface electric field strength (E), then E is a function only of z and r: ze E¼ ð8Þ 40 r2 0 W O ¼
0 In order to clarify the role of the surface field strength, we have plotted the values of W O
against E [see Fig. 4(A) [29]]. Surprisingly, all the data lie on a straight line despite the large differences in sizes, charges, and even structures, as seen in the figure. A similar linear plot was also obtained for the polyanion transfer at the 1,2-DCE/W interface [30]. Because polyanions are generally quite large, a contribution from the solvophobic interaction (i.e., the cavity formation energy) to its solvation energy should not be 0 neglected. Accordingly, from the observed W O -values, the contribution was subtracted with the help of the Uhlig equation [Eq. (4)]. Even after this subtraction, the linear 0 relationship still manifested itself in the resultant ‘‘electrostatic’’ term, W O ðelÞ 0;O!W ¼ ½Gtr ðelÞ=zF, as shown in Fig. 4(B) [33]. This excellent correlation strongly
Ion Solvation and Resolvation
29
0 0;O!W TABLE 1 Values of W of Polyanions for the NB/W System [29] and Their O and Gtr Values of r and E
No. 1 2 3 4 5 6 7 8 9
Polyanion ; -[XM12 O40 4 (X ¼ Si; Ge; M ¼ Mo; WÞ ; -½XM12 O40 3 (X ¼ P; As; M ¼ Mo; WÞ -½X2 Mo18 O62 6 ðX ¼ P; AsÞ -½S2 Mo18 O62 4 ½S2 VMo17 O62 5 ½P2 Mo18 O61 4 (containing P2 O4 7 Þ ½Mo6 O19 2 ½VMo5 O19 3 -½Mo8 O26 4
r (nm)
Ea (10 V m1 )
0 W O
(V)
0.56b
1:84
0:067 0:003
25.9
0.56b
1:38
0:248 0:004
71.8
0.648c
2:06
0:005 0:000
2.9
0.648c 0:648c 0.644c
1:37 1:72 1:39
0.269 0.085 0.239
103.8 41.0 92.2
0.437c 0.437c 0.485c
1:51 2:26 2:45
0.164 0:119 0:137
31.6 34:4 52:9
10
G0;O!W tr (kJ mol1 )
a
Calculated from Eq. (8). Literature value [32]. c Evaluated using the simple relation r ðnmÞ ¼ 0:164n1=3 (with n the number of oxygen atoms in the polyanion) [30]. Source: From Ref. 33. b
0 W FIG. 4 Plots of (A) W O and (B) O (el) of polyanions at the NB/W interface against E. (From Ref. 33. Copyright 1996 Elsevier Science B.V., Amsterdam.)
30
Osakai and Ebina
suggests that the surface field strength E should play an important role in the resolvation energies of polyanions. 0 Then, what would the linear E-dependence of W O mean? If we suppose that the 0;O!W 0 Gtr for the polyanions is given by the Born equation, W O ðelÞ should be proportional to z=r [cf. Eqs. (2) and (7)]; this dependence would come from the overall inte0 gration of a function of the electric field. In actuality, however, W O ðel) depends on the 2 value of E at the surface, which is proportional to z=r . This suggests that the shortrange ion–solvent interactions, rather than the Born-type long-range electrostatic interaction, play a major role in the z-dependence of the resolvation energy of polyanions. 0 Thus it is unsuitable to refer to W O ðelÞ as the ‘‘electrostatic’’ term. Instead, the term 0 will be referred to as the charge (z)-dependent term, being written as W O ðz-dep) [cf. Eq. (26)].
V.
A MODEL HAMILTONIAN APPROACH TO ION–SOLVENT INTERACTIONS
0 The authors [33] have elucidated the linear dependence of W O ðz-depÞ on E for the polyanions by a quantum chemical consideration. A model Hamiltonian approach to the charge transfer (CT) interaction between a polyanion and solvents has been made on the basis of the Mulliken’s CT complex theory [34]. Let us consider a case in which an ion (donor, Dz ) and a solvent (acceptor, A) form a CT complex. The ground state energy WN (see Fig. 5) can be obtained as a solution of the secular equation: W0 X W01 S01 X ð9Þ ¼0 W01 S01 X W1 X
where W0 is the energy in a no-bond state, j 0 i ¼ j ðDz AÞi, in which Dz and A come into contact without changing their electronic configurations; W1 is the energy in a dative state, j 1 i ¼ j ðDzþ1 A Þi, corresponding to the transfer of an electron from Dz to A; and W01 and S01 are defined by W01 ¼ h 0 jHj 1 i (H being the Hamiltonian operator) and S01 ¼ h 0 j 1 i, respectively. The CT interaction energy W, i.e., the resonance energy in the ground state is given by W ¼ W0 WN
FIG. 5 The charge transfer between an ion (donor, Dz ) and a solvent (acceptor, A).
ð10Þ
Ion Solvation and Resolvation
31
In the previous paper [33], the effect of the ionic charge z on W was investigated for the CT interaction between a polyanion and water. The effect will come out through W1 and W01 . By using a simple model in which an electron in the surface atom of a polyanion is transferred to a solvent molecule, the effect of z on W through W1 is considered as follows: if the ionic radius r is much larger than the CT distance d and the radius of the surface atom rO , the z-dependence of W1 can be expressed in terms of the surface field strength E of the polyanion as ed W1 W~ 1 þ E ð11Þ r where the E-independent term will be approximated as W~ 1 ¼ W0 þ Ip0 Ea ðAÞ
e2 40 r d
ð12Þ
with Ip0 being the ionization potential of the surface atom, Ea ðAÞ the electron affinity of the solvent, and r the relative permittivity of the solvent in the first solvation shell (being assumed to be equal to the optical permittivity, op ¼ 1:8 for water). The last term has been introduced as a correction factor for electrostatic effects of the liquid medium. Next, the effect of z on W through the transition matrix element W01 is considered as follows: for rigorous determination of W01 , all electrons in the system should be treated. However, for the sake of simplicity, we devote our attention only to the transferring electron; the other electrons would be regarded as forming the ‘‘effective’’ potential Veff ðxÞ for the transferring electron (x the coordinate of the electron given from the ion center). This enables us to reduce the many-body problem to a one-body problem: D E H one-body LUMO ð13Þ W01 HOMO D A where HOMO is the highest occupied molecular orbital (HOMO) of Dz , LUMO the lowest D A unoccupied molecular orbital (LUMO) of A, and H one-body the one-body Hamiltonian being given by H one-body ¼
h2 r2 þ Veff ðxÞ 82 m
ð14Þ
In order to give a concrete expression for Veff ðxÞ, a simple model has been assumed (see Fig. 6). In this model, it is postulated that an electron in the HOMO (essentially the 2p orbital) of the surface oxygen atom (Osurg ) of the polyanion partially transfers to the LUMO of water (the 4a1 molecular orbital). Then Veff ðxÞ can be expressed as Veff ðxÞ ¼ Vcharge-electron ðxÞ þ Vcharge-hole þ Vps ðxÞ
ð15Þ
where Vcharge-electron ðxÞ and Vcharge-hole represent potential energies ascribed to the Coulomb interactions between the ionic charge and the transferring electron and between the ionic charge and a positive hole formed on the Osurf atom, respectively, and where Vps ðxÞ is the pseudopotential, i.e., the effective potential formed by the nucleus of the Osurf atom and its electrons other than the transferring electron. Although it is difficult to obtain an exact expression for Vps ðxÞ, its appropriate expression only in the overlapping region (shown in D in Fig. 6) will be necessary for evaluating the matrix element with Eq. (13). As seen in Fig. 6, the overlapping region located around the place where the electron density of the 2p (Osurf ) orbital is the highest. The pertinent potential around this place
32
Osakai and Ebina
FIG. 6 Quantum chemical model of the CT complex of a polyanion and water. (From Ref. 33. Copyright 1996 Elsevier Science B.V., Amsterdam.)
should be used; the Coulomb potential has been employed here, on assuming that a positive charge of 2 is located at the center of the Osurf atom. Thus, the corresponding jVps ðxÞj LUMO i can be calculated approximately. energy h HOMO D A Finally, under the condition that r rO , the z-dependence of W01 can be expressed as a function of E, as in the case of W1 [Eq. (11)]: W01 ¼ W~ 01 þ eE with
D E ¼ rO D ¼ rO HOMO j LUMO D A * + 2 D h HOMO 2 LUMO þ W~ 01 ¼ 2 r A D 8 m
ð16Þ
ð17Þ
HOMO Vps ðxÞ LUMO D A
E
ð18Þ
From the above analysis, it is found that both W1 and W01 are linear functions of the surface electric field strength E, so that W obtained from Eq. (9) is also a function of E. The important point is that the z-dependence of the matrix element can be expressed only through E. By actually solving the secular equation (9), it has been found that the Edependence of W is well represented by a quadratic equation: W ¼ 0 þ 1 E þ 2 E 2
ð19Þ
It should be noted, however, that this equation represents the energy for a one-to-one ion– solvent interaction. When the ion is much larger than the solvent, it can be assumed that the number (N) of solvent molecules adjacent to the ion is proportional to the surface area of the ion: N ¼ 4r2 (where is the number of solvent molecules per unit surface area of the ion). Accordingly, the contribution of the CT interaction to the ion solvation energy G0s is given by
Ion Solvation and Resolvation
33
G0s ðCTÞ ¼ N W ¼ 0 þ 1 E þ 2 E 2
ð20Þ
with n ¼ 4r n ðn ¼ 1; 2; 3Þ; note that n is proportional to r . The contribution of is then given by the CT interaction to the ion-transfer energy G0;O!W tr 2
2
2 G0;O!W ðCTÞ Gs0;W ðCTÞ G0;O s ðCTÞ ¼ 0 þ 1 E þ 2 E tr
ð21Þ
O with n ¼ W n n . Here, the superscripts ‘‘W’’ and ‘‘O’’ refer to water and organic phases. Accordingly, the contribution of the CT interaction to the ion-transfer potential [being given by Eq. (7)] can be expressed as 0 1 þ 1 þ 2 E W O ðCTÞ ¼ 0 E
ð22Þ
O O with n ¼ ðW W n n Þ=0 which depends neither on z nor r. In view of the necessity of knowing an approximate value of the coefficient 2 of the linear term in Eq. (22), we have (CT) consists of only the contribution from made a daring assumption that G0;O!W tr water, namely, G0;O!W ðCTÞ G0;W ðCTÞ. This leads to the following approximation: s tr 0 W 1 þ 1W þ 2W E W O ðCTÞ ¼ 0 E
ð23Þ
where nW ¼ W W n =0
ðn ¼ 1; 2; 3Þ 2W
ð24Þ
Thus the coefficient can be evaluated from and The approximate value of W 18 2 ð¼ 9:4 10 molecules m ) is obtained from the density of bulk water by assuming that the thickness of the first solvation shell equals the diameter (0.28 nm) of a water molecule, 22 ðeVÞ V2 m2 from the whereas the value of W 2 has been obtained to be 2:025 10 W estimation of the E-dependence of W. Finally, the coefficient 2 has been evaluated to be 3:5 1011 m. This value is close to the experimental value of 2:85 1011 m, which 0 comes from the slope of the W O ðelÞ vs. E plot in Fig. 4(B). From this result, the authors [33] have concluded that the CT interaction plays a major role in the observed linear 0 W 0 dependence of W O ðelÞ or O ðz-depÞ on E, though this conclusion seems to be overstated to some extent.
VI.
W
W 2 .
SELECTIVE HYDRATION OF IONS IN ORGANIC SOLVENTS
0;O!W In almost all theoretical studies of Gtr , it is postulated or tacitly understood that when an ion is transferred across the O/W interface, it strips off solvated molecules completely, and hence the crystal ionic radius is usually employed for the calculation of . Although Abraham and Liszi [17], in considering the transfer between mutually G0;O!W tr saturated solvents, were aware of the effects of hydration of ions in organic solvents in which water is quite soluble (e.g., 1-octanol, 1-pentanol, and methylisobutyl ketone), they concluded that in solvents such as NB and1,2-DCE, the solubility of water is rather small and most ions in the water-saturated solvent exist as unhydrated entities. However, even a water-immiscible organic solvent such as NB dissolves a considerable amount of water (e.g., ca. 170 mM H2 O in NB). In such a medium, hydrophilic ions such as Liþ , Naþ , Ca2þ , Ba2þ , Cl , and Br are selectively solvated by water. This phenomenon has become apparent since at least 1968 by solvent extraction studies with the Karl–Fischer method [35–45]. Rais et al. [35] and Iwachido and coworkers [36–39] determined hydration numbers, i.e., the number of coextracted water molecules, for alkali and alkaline earth metal
34
Osakai and Ebina
ions in NB. Some inorganic anions (Cl , Br ,, I , SCN , ClO 4 , and NO3 ) have also been found to coextract water into NB [40–42]. Similar phenomena have further been observed in solvents other than NB (e.g., 1,1- and 1,2-dichloroethane, 4-methyl-2-pentanone, chloroform, NB–benzene mixtures) [42–45]. If these observations are valid, we should reconsider the previous theories of G0;O!W in which the hydration of ions in O is not tr properly taken into account. From this point of view, Osakai et al. [46] reaffirmed the coextraction of water into NB for a variety of common ions and determined their accurate hydration numbers in NB. In the previous study [46], various kinds of cations and anions (listed in Table 2) were extracted from water to NB using several extractants: tetraphenylborate (TPB ) and dipicrylaminate (DPA ) for the cations; n-Bu4 Nþ , n-Pen4 Nþ , n-Hep4 Nþ , and tris(1,10phenanthroline)iron(II) ([Fe(phen)3 2þ Þ for the anions. The increase in the water concentration in the NB phase, ½H2 O, with extraction of an ion was evaluated as a function of equilibrium concentration of the ion in NB. A typical example, obtained in the DPA
TABLE 2 at 25 C
Numbers (n) of Coextracted Water Molecules in NB and Radii (rh ) of Hydrated Ions n
Cation Liþ Naþ Kþ Rbþ Csþ Ca2þ Ba2þ Me4 Nþ Et4 Nþ n-Bu4 Nþ Ph4 Asþ
TPB system 6.3 4.0
15 10 0 0 ( 0[42])
DPA system 5.7 (4.2[35]; 5.5[36]) 3.6 (3.6[35]; 3.5[36]) 1.0 (1.0[35]; 1.3[36]) 0.7 (0[35]; 0.7[36]) 0.4 (0[35]; 0.7[36]) 12 (13[36]) 11 (9.4[36]) 0 0 0
av
rh (nm)
ra (nm)
6:0 0:4 3:8 0:3 1.0 0.7 0.4 14 2 11 1 0 00 0 0
0.351 0.307 0.220 0.212 0.206 0.467 0.435
0.073 0.116 0.152 0.166 0.181 0.114 0.149 0.279 0.337 0.413 0.426
n
Anion Cl Br I SCN ClO 4 NO 3 TPB a
n-Bu4 Nþ system
2.1 (1.8[43]) 0.9 1.1 0.3 ( 1:4½42Þ 0ð 0[42])
n-Pen4 Nþ system 4.0 (3.3[43]) 2.1 0.8 1.1 0.2 0
n-Hep4 Nþ system
2.0 1.0 1.0 0.2 0
½FeðphenÞ3 2þ system —b (5.5[41]) 1.0c (2.1[41]) 1.1c (1.9[41]) 0.1c (0.64[41]) 1.7c 0c
av 4.0 2:1 0:1 0:9 0:1 1:1 0:1 0:2 0:1 1.7 0
rh (nm)
ra (nm)
0.322 0.276 0.248 0.260 0.244 0.267
0.167 0.182 0.206 0.213 0.236 0.189 0.421
Crystal (or bare) ionic radii (see Table 3). No reliable value could be obtained due to extremely low extractability (the distribution ratio D < 0:03). c Corrected for the contribution (n ¼ 0:3) from ½FeðphenÞ3 2þ . Source: From Ref. 46. b
Ion Solvation and Resolvation
35
system, is shown in Fig. 7. The hydrophobic organic cations (Me4 Nþ , Et4 Nþ , and TPAsþ ) showed no increase in water concentration, indicating that these cations as well as DPA had no ability to transport water to NB. In contrast, hydrophilic metal ions showed a distinguishing increase. The slope of each linear plot should correspond to the number (n) of water molecules coextracted to NB with a metal ion, which are listed in Table 2 together with those determined in other systems. As seen in the table, for both cations and anions, the n values determined were only slightly dependent on the nature of extractant (i.e., coion). This implies that ion-pair formation in NB is of less significance or that the ions are almost dissociated. Thus accurate numbers of water molecules, being certainly associated with individual ions, could be determined. Based on these measurements, a new model of the transfer of hydrophilic ions across the O/W interface was proposed (see Fig. 8). In this model, the hydrophilic ion transfers from W to O with some water molecules associated with the ion. A typical example in Fig. 8 shows that a sodium ion transfers across the NB/W interface with four water molecules. of such a hydrophilic ion, therefore, the transferring In theoretical treatment of G0;O!W tr species should be regarded as the ‘‘hydrated’’ ion. In accordance, the radii (rh Þ of hydrated ions in NB were estimated from the hydration numbers (n) and crystal ionic radii (r) by rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3 n þ r3 ð25Þ rh ¼ 4 d where d is the density of water in the hydration shell (here, the value of d is assumed to be the same as that of bulk water, i.e., 3:33 1028 molecule m3 ). The estimated values of rh are also shown in Table 2. As seen in Table 2, the order of the magnitude of rh for alkali metal ions is the reverse of that of the magnitude of r. This means that a more hydrophilic ion has a larger rh . However, this fact does contradict the expectation from Bornian electrostatic theories. As can be seen in the Born equation [Eq. (2)], it is expected that the larger the radius an ion 0;O!W has, the more positive the Gtr value the ion has, that is, the more hydrophobic it
FIG. 7 Plots of the increase of water concentration in NB (½H2 OÞ with extraction of cations with DPA against the equilibrium cation concentration in NB. Each value in the parentheses shows the number (n) of coextracted water molecules per ion. (From Ref. 46. Copyright 1997 American Chemical Society.)
36
Osakai and Ebina
FIG. 8 Proposed model of the transfer of a hydrophilic ion across the O/W interface. The illustration shows the transfer of Naþ from W to NB as a typical example. (From Ref. 46. Copyright 1997 American Chemical Society.)
becomes. This would show that Liþ , as an example, is more hydrophobic than Csþ , but this is of course not the case. Thus, if hydrated radii of ions are used, Bornian electrostatic solvation models are invalid. Then we made a new approach that recognizes short-range interactions of a 0;O!W for hydrophilic ions could be hydrated ion with solvents. By this approach, Gtr elucidated on the basis of the proposed model in Fig. 8 (see Section VII). A similar model for some hydrophilic ions, was also employed by Sa´nchez et al. [47] to elucidate G0;O!W tr but using a Bornian electrostatic theory. Recently, the abilities of primary to tertiary alkylammonium ions with Me, Et, and n-Bu groups to transport water to NB have been studied [48]. As the result of careful consideration of the ion-pair formation, it has been shown that the hydration numbers (nh ) of the ammonium ions in NB, being little affected by the alkyl chain length, are simply dependent on the class of the ammonium ion: nh ¼ 1:64, 1.04, 0.66, respectively, for the primary, secondary, and tertiary ammonium ions.
VII. A.
NON-BORNIAN THEORY OF THE RESOLVATION ENERGY OF IONS Theoretical Model
Based on the above-mentioned experimental and theoretical findings, we have proposed a new, non-Bornian theory of G0;O!W of ions [49]. In this theory, it is assumed that a tr hydrophilic ion which is selectively hydrated in organic solvent transfers across the O/W interface as the hydrated ion, and a hydrophobic ion which is not hydrated in the O phase transfers as a bare ion, as depicted in Fig. 9. In a conventional manner we divide G0;O!W into two terms: tr 0;O!W 0;O!W Gtr ¼ Gtr ðz-indepÞ þ G0;O!W ðz-depÞ tr
ðz-indepÞ G0;O!W tr
ð26Þ
is the charge-independent term corresponding to the solvophowhere bic interaction or the energy of the formation of a cavity in solvents, and G0;O!W ðz-depÞ tr is the charge-dependent term, which has so far been considered mainly as describing
Ion Solvation and Resolvation
37
FIG. 9 Proposed model of the transfer of (a) a hydrophilic ion and (b) a hydrophobic ion across the O/W interface. (From Ref. 49. Copyright 1998 American Chemical Society.)
electrostatic (i.e., long-range) ion–solvent interaction, but is here treated as describing specific (short-range) interactions. ðz-indepÞ, we employed the Uhlig formula [Eq. (4)]. For the evaluation of G0;O!W tr This formula may be applicable to the NB/W interface (O;W ¼ 25:2 mN m1 [50]) and to all ions studied (see Table 3), which include the ‘‘hydrated’’ ions with a hydrated radius rh ð¼ rÞ larger than 0.20 nm as well as the ‘‘unhydrated’’ ions of r > 0:23 nm. 0;O!W ðz-dep) in Eq. (26) is here assumed to be govThe charge-dependent term Gtr erned by short-range ion–solvent interactions. The long-range interactions of an ion with the solvents in the second and further solvation shells are ignored in the present theory. Because the short-range (i.e., chemical) interactions recognize some overlap of the electron orbitals of the ion and the solvent molecule in its immediate vicinity, they should be explained on quantum chemical considerations. In ab initio molecular orbital studies [58], the self-consistent-field (SCF) energy of the ion–molecule interaction, USCF , is partitioned into several terms including Coulomb (COU), polarization (POL), charge-transfer (CT), and exchange (EX) terms: USCF ¼ UCOU þ UPOL þ UCT þ UEX
ð27Þ
The first two terms UCOU and UPOL correspond to the empirical energy of ion–dipole and ion–induced dipole interactions, being given by UCOU ¼ Ehcos i
ð28Þ
1 UPOL ¼ E 2 2
ð29Þ
and
where and are the dipole moment and electronic polarizability of the solvent molecule, respectively, is the angle between the dipole axis and the line connecting the point dipole and point charge, h i indicates the ensemble average, and E is the ‘‘effective’’ electrical field strength, which can be approximated by the surface field strength of the ion given by Eq. (8), when r is much larger than the radius of the dipole (i.e., solvent molecule).
38
Osakai and Ebina
TABLE 3 Charge Numbers and Radii of Ions and Their Hydration Numbers and Hydrated Radii in NB at 25 C Ion Hydrated cations Liþ Naþ Kþ Rbþ Csþ Ca2þ Ba2þ Nonhydrated cations Me4 Nþ Et4 Nþ n-Pr4 Nþ n-Bu4 Nþ Ph4 Asþ ðTPAsþ Þ ½NiðbpyÞ3 2þ ½NiðphenÞ3 2þ ½FeðphenÞ3 2þ Hydrated anions Cl Br I SCN NO 3 Nonhydrated anions ClO 4 IO 4 2,4-dinitrophenol 2,4,6-trinitrophenol Ph4 B ðTPB Þ Polyanions ; -½XM12 O40 4 ; -½XM12 O40 3 -½X2 Mo18 O62 6 -½S2 Mo18 O62 4 ½S2 VMo17 O62 5 ½P2 Mo18 O61 4 ½Mo6 O19 2 ½VMo5 O19 3 -½Mo8 O26 4
z
ra (nm)
nb
rh c (nm)
1 1 1 1 1 2 2
0.073 0.116 0.152 0.166 0.181 0.114 0.149
6.0 3.8 1.0 0.7 0.4 14 11
0.351 0.307 0.220 0.212 0.206 0.467 0.435
1 1 1 1 1 2 2 2
0.279d 0.337d 0.379d 0.413d 0.416f 0.527g 0.544g 0.541g
0 0 0e 0 0 0e 0e e 0 (0.3)
1 1 1 1 1
0.167 0.182 0.206 0.213h 0.189i
4.0 2.1 0.9 1.1 1.7
1 1 1 1 1
0.236i 0.249i 0.315j 0.332j 0.421f
0e (0.2) 0e 0e 0e 0
4 3 6 4 5 4 2 3 4
0.56k 0.56k 0.648k 0.648k 0.648k 0.644k 0.437k 0.437k 0.485k
0e 0e 0e 0e 0e 0e 0e 0e 0e
0.322 0.276 0.248 0.260 0.267
Ion Solvation and Resolvation
39
The third term, UCT , in Eq. (27) is due to the partial electron transfer between an ion and solvents in its immediate vicinity. The model Hamiltonian approach [33], described in Section V, has shown that UCT ð¼ W in Ref. 33) per primary solvent molecule, for an ion such as the polyanion, can also be expressed as a function of E, approximately a quadratic equation: UCT ¼ 0 1 E 2 E 2
ð30Þ
The coefficients 0 , 1 , and 2 (denoted as 0 , 1 , and 2 in Ref. 33) are influenced by various molecular properties of the solvent and an ion, including their electron-donating or accepting abilities. Hence, these coefficients are specific to the ion. Nevertheless, they may be considered as common to a family of ions such as the polyanions whose surface atoms, directly interacting with solvents, are oxygens. This is the case for ‘‘hydrated’’ cations or anions whose surfaces are composed of some water molecules that interact with outer water molecules in the W phase or with organic solvents in the O phase. The remaining term, UEX , in Eq. (27) represents the nonclassical repulsion term, being inherently independent of E. By summarizing the above argument, we conclude that the short-range interaction energy, USR ð¼ USCF Þ, can be given by a quadratic function of E: USR ¼ A BE CE 2
ð31Þ
A ¼ 0 þ UEX
ð32Þ
B ¼ Ehcos i þ 1 C ¼ þ 2 2
ð33Þ
with
ð34Þ
The validity of Eq. (31) has been confirmed by an approach from redox potentials of heteropoly oxometalate anions as well [59]. In Eq. (31) we should note that USR represents the interaction energy per primary solvent molecule. Then the number of solvent molecules that can be interact directly with an ion in phase S ð¼ O or W) is denoted as N S . Accordingly, the contribution of the shortof the ion phase S (i.e., transfer range interactions to the solvation energy G0;vac!S tr energy from vacuum) is given from Eq. (31) as
Footnotes to Table 3 a Shannon’s crystal ionic radii [51], except where otherwise noted. b Ref. 46. c Estimated by Eq. (25). d van der Waals radii calculated from the partial molar ionic volumes [52]. e Assumed. f Ref. 6. g van der Waals radii calculated from the partial molar ionic volumes [53,54]. h Ref. 55. i Thermochemical radii [56]. j From van der Waals volumes calculated from atomic increments [57]. k See Table 1. Source: From Ref. 49.
40
Osakai and Ebina
G0;vac!S ðSRÞ ¼ N S USR ¼ AS N S BS N S E C S N S E 2 tr
ð35Þ
where the superscript S of A, B, and C represents the S phase. Because the transfer energy G0;O!W is the difference between G0;S s ’s in O and W, the contribution of short-range tr can be expressed as interactions to G0;O!W tr 0;O!W ðSRÞ ¼ 1 2 E 3 E 2 Gtr
ð36Þ
1 ¼ A W N W A O N O
ð37Þ
2 ¼ BW N W BO N O
ð38Þ
3 ¼ C W N W C O N O
ð39Þ
with
0;O!W (SR) Gtr
is given approximately by a quadratic equation of E. The In this manner coefficients 1 , 2 , and 3 are related to various molecular properties of the ion and solvents [see Eqs. (32)–(34) and Eqs. (37)–(39)]. To estimate theoretically these coefficients using an appropriate model may not be impossible, but rather difficult at the present stage, because there is insufficient information on the above-mentioned molecular properties (in particular, the charge-transfer properties). Consequently, coefficients 1 , 2 , and 3 in Eq. (36) have been determined empirically, as shown below. B.
Experimental Data
In the present analyses [49], 34 ions are classified into five groups: (1) hydrated cations, (2) nonhydrated cations, (3) hydrated anions, (4) nonhydrated anions, and (5) polyanions. Here, the term ‘‘hydrated’’ or ‘‘nonhydrated’’ means that the ion is associated with some water molecules in the O phase or not, respectively. 1. Ionic Radii All ions studied are assumed to be spherical, and radii (r) of the bare ions are listed in Table 3. Unless otherwise noted, authorized values of crystal ionic radii or van der Waals radii are adopted [51–57]. 2. Hydration Numbers of Ions in NB The numbers (n) of coextracted water molecules shown in Table 3 are from Table 2 [46]. In the case of n-Pr4 Nþ , metal complex cations, larger anions of r > 0:23 nm, and polyanions, it is assumed that n ¼ 0. Although the n value of ½FeðphenÞ3 2þ or ClO 4 was reported to be as small as 0.3 or 0.2 [46], these ions have been classified as ‘‘nonhydrated’’ (i.e., n ¼ 0) so that comparatively better results may be obtained. In Table 3 are also shown the hydrated radii (rh ) which are evaluated with n and r by Eq. (25). A good correlation of rh with the Stokes radius [60] (rs ) has been observed for hydrated cations (alkali and alkaline earth metal ions) [46]: rh ðnmÞ ¼ 1:310 rs ðnmÞ þ 0:055
ðR ¼ 0:997Þ
ð40Þ
In this equation and the following remarks, R shows the correlation coefficient. For the prediction of G0;O!W of a hydrophilic ion whose n value is unknown, it is tr desirable that the n value can be obtained with r and z only. Since the interactions of a small ion with water molecules in the hydration shell may be mostly electrostatic, the
Ion Solvation and Resolvation
41
dependence of n on (z=r) has been investigated for hydrophilic cations and anions. As a result, it has been found that the plots of n against (z=r) lie on a quadratic curve: For cations: ðR ¼ 0:966Þ n ¼ 0:566 þ 0:0091ðz=rÞ þ 0:04745ðz=rÞ2 For anions: n ¼ 5:844 þ 3:775ðz=rÞ þ 0:5661ðz=rÞ2 ðR ¼ 0:930Þ
ð41Þ ð42Þ
where r is in nanometers. Equations (41) and (42) are applicable in the range of ðz=rÞ > 5 and ðz=rÞ < 4, respectively. Using these equations, we can predict, though somewhat roughly, the n value of a hydrophilic ion. Regarding the cations, however, their n values could be obtained more accurately from the Stokes radii by using the relations of Eqs. (25) and (40). 3.
Gibbs Energies of Transfer of Ions
0;O!W In 1977 Koryta et al. [61] reported the Gtr values of several common ions at the NB/W interface, which were calculated from the extraction data using an extra thermodynamic assumption. Afterward, a newly developed electrochemical technique (so-called ion-transfer voltammetry) with a polarizable O/W interface was employed to determine G0trO!W for a variety of ions [33,62–71]. In Table 4 the reliable values of G0;O!W tr are compiled. Regarding the ions whose G0;O!W values are available for both electrotr chemical and extraction measurements, the electrochemical data, which seem to be more accurate, have been chosen preferentially. For several ions, somewhat different G0;O!W tr values from electrochemical measurements have been reported, as also seen in the database provided by Girault on a website [72]. In this study, however, we have carefully chosen reliable values for the respective ions, which were determined under well-defined conditions (reference electrodes, solution compositions, etc.).
C.
Data Analyses
1.
Calculation of Cavity Formation Energies
Using the Uhlig formula [Eq. (4)] the values of G0;O!W (z-indep) have been obtained tr from ionic radii, as shown in Table 4. For the hydrated cations and anions, their hydrated 0;O!W (zradii (rh Þ have been employed for r in Eq. (4). Table 4 also shows the values of Gtr 0;O!W (z-indep) from the total G0;O!W dep) which have been obtained by subtracting Gtr tr [see Eq. (26)]. 2. Regression Analyses for Hydrated Ions Unless noted otherwise, it has been assumed that the number of the solvent molecules N S (S ¼ O or W) that can interact directly with a hydrated ion in phase S is equal to the hydration number: NO ¼ NW ¼ n
ð43Þ
For Ca2þ and Ba2þ , whose n values are larger than 10, however, it is thought that some hydrated water molecules not only in the first hydration shell but also in the second hydration shell are cotransferred into NB. Accordingly, it can be supposed that some water molecules in the first hydration shell (i.e., in the vicinity of the ion) are covered with the second hydration shell, so that they cannot be associated with outer solvent
42
Osakai and Ebina
TABLE 4 Standard Gibbs Energies of Transfer of Ions from NB to W and Their ChargeIndependent and Charge-Dependent Components at 25 C
Ion Hydrated cations Liþ Naþ Kþ Rbþ Csþ Ca2þ Ba2þ Nonhydrated cations Me4 Nþ Et4 Nþ n-Pr4 Nþ n-Bu4 Nþ Ph4 Asþ ðTPAsþ Þ ½NiðbpyÞ3 2þ ½NiðphenÞ3 2þ ½FeðphenÞ3 2þ Hydrated anions Cl Br I SCN NO 3 Nonhydrated anions ClO 4 IO 4 2,4-dinitrophenol 2,4,6-trinitrophenol Ph4 B ðTPB Þ Polyanions ; -½XM12 O40 4 ; -½XM12 O40 3 -½X2 Mo18 O62 6 -½S2 Mo18 O62 4 ½S2 VMo17 O62 5 ½P2 Mo18 O61 4 ½Mo6 O19 2 ½VMo5 O19 3 -½Mo8 O26 4
G0;O!W tr (kJ mol1 )
G0;O!W (z-indep)a tr (kJ mol1 )
G0;O!W (z-dep)b tr (kJ mol1 )
38:2c;d 34:2c;d 23:5c;d 19:4c;d 15:4c;d 67:3d;e 61:8d;e
23.6 17.9 9.2 8.6 8.1 41.6 36.0
61:8 52:1 32:7 28:0 23:5 108:9 97:8
3:4c;d 5.3f 16:4g 26:5h 35:9c;d 30:5i 41:3i 44:0j
14.8 21.7 27.4 32.5 34.6 53.0 56.4 55.8
18:2 16:4 11:0 6:0 1.3 22:5 15:1 11:8
38:2k 27:8l 18:4l 15:8l 25:2l
19.8 14.6 11.7 12.9 13.5
58:0 42:4 30:1 28:7 38:7
7:9l 6m 5:7n 6:7n 35:9d
10.6 11.8 18.9 21.0 33.8
18:5 17:8 24:6 14:3 2.1
25:9o 71.8o 2:9o 103:8o 41:0o 92:2o 31:6o 34:4o 52:9o
59.8 59.8 80.1 80.1 80.1 79.1 36.4 36:4 44.9
33:9 12.0 77:2 23.7 39:1 13.1 4:8 70:8 97:8
Ion Solvation and Resolvation
43
molecules (W or NB). Such an effect is here called ‘‘shielding.’’ In these cases, N S cannot be equated simply to n and should be reduced to some extent. It has been found that for the above two cations, the subtraction of 4 from the net n values may lead to the best result in the following regression analysis. If we suppose that G0trO!W (z-dep) for the hydrated ions is ruled out by short-range interactions, a combination of Eqs. (36)–(39) and Eq. (43) yields G0trO!W ðz-depÞ=n ¼ A BE CE 2
ð44Þ
with A ¼ A A , B ¼ B B , and C ¼ C C . In Fig. 10 the values of G0;O!W (z-dep)=n for the hydrated cations (*) and anions (*) are plotted against E, tr being calculated by Eq. (8) with r ¼ rh . Note that the plots of Ca2þ and Ba2þ have been compensated for the ‘‘shielding’’ effect: the symbols () in Fig. 10 represent the plots with the net values of n ð¼ 14 or 11 for Ca2þ or Ba2þ , respectively). 0;O!W (z-dep) per hydrated water As seen in Fig. 10, in accordance with Eq. (44), Gtr becomes progressively greater as E is enhanced. Since the contribution from the interaction in W to G0;O!W (z-dep) is probably more significant than that from the interaction tr in NB, the dependences shown in Fig. 10 seem to suggest that the hydrogen bonds, which are formed around a hydrated ion in W and which must be broken in its transfer to NB, are strengthened by the surface field of the hydrated ion. The solid lines in Fig. 10 represent the quadratic curves obtained in regression analyses. W
O
W
O
W
O
For hydrated cations: G0;O!W ðz-depÞ=n ¼ 8:90 þ 4:506E 4:853E 2 tr For hydrated anions: G0;O!W ðz-depÞ=n ¼ 50:17 52:51E 19:33E 2 tr where
0;O!W (z-dep) Gtr
is in kJ mol
1
10
ðR ¼ 0:931Þ ðR ¼ 0:999Þ
ð45Þ ð46Þ
1
and E is in 10 V m .
3. Regression Analyses for Nonhydrated Ions As for the nonhydrated ions including the polyanions, it has been assumed that N S is proportional to the surface area of the ion:
Footnotes to Table 4 a Evaluated using Eq. (4) (note that r ¼ rh for the hydrated ions). b 0;O!W 0;O!W G0;O!W (z-depÞ ¼ Gtr Gtr (z-indep). tr c Ref. 61. d Determined using extraction data; the other values were determined by electrochemical measurements. e Ref. 62. f Ref. 63. The value is revised by employing Me4 Nþ as an internal reference in the place of n-Bu4 Nþ . g Unpublished data obtained by means of the former electrochemical technique [64]. h Ref. 65. i Ref. 66. j Ref. 67. k Ref. 68. l Ref. 69. m Ref. 70. n Ref. 71. o Calculated from the standard ion-transfer potentials compiled previously [33]. Source: From Ref. 49.
44
Osakai and Ebina
FIG. 10 Plots of G0;O!W (z-depÞ=n against E (with r ¼ rh ) for hydrated cations (*) and anions tr (*). Note that the n values for the plots of Ca2þ and Ba2þ have been corrected for the ‘‘shielding’’ effect (see text) by subtracting 4 from their net values of n; () represents the plots with the net values. Solid lines show the regression curves [Eqs. (45) and (46)]. (From Ref. 49. Copyright 1998 American Chemical Society.)
N S ¼ 4r2 S
ð47Þ
where is the number of solvent molecules per unit surface area of the ion in phase S (z-dep) is ruled only by short-range ð¼ O or W). We have also assumed that G0;O!W tr interactions in the same manner as the hydrated ions and then have obtained from Eqs. (36)–(39) and Eq. (47): S
0;O!W ðz-depÞ=ð4r2 Þ ¼ A 0 B 0 E C 0 E 2 Gtr 0
0
ð48Þ 0
with A ¼ A A , B ¼ B B , and C ¼ C C . (z-dep)/(4r2 ) have been plotted In accordance with Eq. (48), the values of G0;O!W tr against E in Fig. 11. The respective plots for the three ion groups have been found to lie on a single quadratic curve. W W
O O
W W
O O
W W
For nonhydrated cations: G0;O!W ðz-depÞ=ð4r2 Þ ¼ 28:19 43:08E þ 9:582E 2 tr For nonhydrated anions: G0;O!W ðz-depÞ=ð4r2 Þ ¼ 33:04 þ 47:53E þ 9:518E 2 tr For polyanions: G0;O!W ðz-depÞ=ð4r2 Þ ¼ 13:40 7:685E 11:08E 2 tr 0;O!W (z-dep) Gtr
1
10
O O
ðR ¼ 0:987Þ
ð49Þ
ðR ¼ 0:967Þ
ð50Þ
ðR ¼ 0:989Þ
ð51Þ
1
is in kJ mol , r in nm, and E in 10 V m . It is noteworthy that where the plots of the polyanions with a wide variety of charges (z ¼ 2 to 6) lie on a single curve. 4. Total Gibbs Energies of Transfer of Ions 0;O!W The values of Gtr have been calculated using the Uhlig formula [Eq. (4)] for the charge-independent part and the empirical equations [Eqs. (45), (46), (49), (50), and (51)] 0;O!W for the charge-dependent part. Table 5 gives the calculated values of Gtr for 34 ions, and the values are compared in Fig. 12 with the observed values shown in Table 4. As seen
Ion Solvation and Resolvation
45
FIG. 11 Plots of G0trO!W (z-depÞ=ð4r2 Þ against E for nonhydrated cations (~) and anions (~) and polyanions (&). Solid lines show the regression curves [Eqs. (49), (50), and (51)]. (From Ref. 49. Copyright 1998 American Chemical Society.)
FIG. 12 Comparison of the calculated and observed values of G0trO!W for 34 ions: (*) hydrated cations, (*) hydrated anions, (~) nonhydrated cations, (~) nonhydrated anions, and (&) polyanions. (From Ref. 49. Copyright 1998 American Chemical Society.)
46 TABLE 5
Osakai and Ebina Calculations of Standard Gibbs Energies of Transfer of Ions from NB to W (25 C)
Ion Hydrated cations Liþ Naþ Kþ Rbþ Csþ Ca2þ Ba2þ Nonhydrated cations Me4 Nþ Et4 Nþ n-Pr4 Nþ n-Bu4 Nþ Ph4 Asþ ðTPAsþ Þ ½NiðbpyÞ3 2þ ½NiðphenÞ3 2þ ½FeðphenÞ3 2þ Hydrated anions Cl Br I SCN NO 3 Nonhydrated anions ClO 4 IO 4 2,4-dinitrophenol 2,4,6-trinitrophenol Ph4 B ðTPB Þ Polyanions ; -½XM12 O40 4 ; -½XM12 O40 3 -½X2 Mo18 O62 6 -½S2 Mo18 O62 4 ½S2 VMo17 O62 5 ½P2 Mo18 O61 4 ½Mo6 O19 2 ½VMo5 O19 3 -½Mo8 O26 4 a
Ea (10 V m1 ) 10
(z-dep)b G0;O!W tr (kJ mol1 )
(calc)c G0;O!W tr (kJ mol1 )
61:5 50:9 38:3 30:7 19:6 114:1 93:1
37:9 33:0 29:0 22:1 11:5 72:5 57:1
ðþ0:3Þe ðþ1:2Þ ð5:5Þ ð2:7Þ ðþ3:9Þ ð5:2) ðþ4:7Þ
18:3 15:7 9:7 2:9 0.1 21:6 17:3 18:1
3:5 5.9 17.7 29.6 34.7 31.4 39.1 37.7
ð0:1Þ ðþ0:6Þ ðþ1:3Þ ðþ3:1Þ ð1:2Þ (þ0:9Þ (2:2) (6:3)
64:1 45:9 31:8 30:9 42:7
44:3 31:3 20:1 18:0 29:2
ð0:3Þ ðþ1:5Þ ðþ0:2Þ ð0:1Þ ð1:3Þ
2:59 2:32 1:45 1:31 0:81
18:4 20:3 19:8 17:7 1.6
7:7 8:9 0:9 3.3 35.4
ðþ1:4Þ ð2:4Þ ðþ4:8Þ ð3:4Þ ð0:5Þ
1:84 1:38 2:06 1:37 1:71 1:39 1:51 2:26 2:45
38:8 11.7 93:3 16.3 31:6 14.1 0:5 62:2 101:1
21.0 71.5 13:3 96.4 48.5 93.2 35.9 25:7 56:3
(4:9) ð0:3Þ ð16:2Þ ð7:4Þ ðþ7:5Þ ðþ1:0Þ ðþ4:3Þ ðþ8:7Þ (3:4)
1.17 1.53 2.97 3.19 3.38 1.32 1.52
(27.0)d (10.7) (6.23) (5.23) (4.39) (22.2) (13.0)
1.85 1.27 1.00 0.84 0.79 1.04 0.97 0.98 1:39 1:89 2:35 2:13 2:03
ð5:16Þd ð4:35Þ ð3:39Þ ð3:17Þ ð4:03)
Evaluated from Eq. (8). For the hydrated ions, their hydrated radii were employed for the value of r. Calculated using Eqs. (45), (49), (46), (50), and (51) for hydrated cations, nonhydrated cations, hydrated anions, nonhydrated anions, and polyanions, respectively. c 0;O!W Obtained by adding the calculated values of G0;O!W (z-dep) to the values of Gtr (z-indep) in Table 4. tr d The values in parentheses are surface field strengths of the bare ions. e The values in parentheses show the deviations from the observed values. Source: From Ref. 49. b
Ion Solvation and Resolvation
47
from the figure, satisfactory agreement has been observed (R ¼ 0:994; standard deviation, 0 0;O!W by Eq. (7), the correSD ¼ 4:63 kJ mol1 ). Also, for the W O being related to Gtr lation of the calculated and observed values has been found to be very good (R ¼ 0:995; SD ¼ 0:023 V). D.
Predictions
0 (and W Based on the proposed theory, the values of G0;O!W O ) have been predicted for tr þ 2þ 2þ 2þ 2þ 3þ hydrophilic ions (NH4 , Mg , Sr , Ni , Fe ; Fe , ClO3 , BrO 3 , CN , IO3 , HCO3 , 0;O!W values have been reported, but their hydration numbers are NO2 , OH ), whose Gtr unknown. In the predictions, the first decision on whether the ion is hydrated in NB is made by means of ðz=rÞ; as described above, if ðz=rÞ > 5 (r in nm) for a cation or ðz=rÞ < 4 for an anion (except polyanions), the ion should be hydrated in NB to a certain extent. For these hydrated ions, the hydration number and the hydrated radius are evaluated. 0;O!W Then the charge-independent and -dependent terms of Gtr are calculated using the Uhlig formula and the empirical equation, respectively. Finally, the summation of the two . terms yields the total value of G0;O!W tr (z-dep) for highly hydrated cations (Mg2þ , Sr2þ , Ni2þ , In the calculation of G0;O!W tr 2þ 3þ Fe , Fe ) with n > 10, the values of n for use in Eq. (45) have been corrected for the ‘‘shielding’’ effect, on the assumption that the corrected value of n is proportional to the surface area of the hydrated ion:
ncorr ¼ f ð4r2 Þ
ð52Þ
The factor f has been determined to be 42.05 by a regression analysis, so that the ncorr values of Ca2þ and Ba2þ may be approximated to n 4 (see above). Although the results of the predictions (see Table 5 in Ref. 49) are not shown here, it has been found that the proposed theory is promising not only for an understanding of but also for its prediction. G0;O!W tr E.
Discussion
In the proposed theory, short-range ion–solvent interaction energies are formulated as Eq. (31). the coefficients A, B, and C in the quadratic equation are related to coefficients 1 , [Eq. (36)]. The above-mentioned regression 2 , and 3 in the formula for G0;O!W tr analyses have clearly shown that these coefficients are common to a family of ions. This suggests that the surface chemical constitution of an ion should play a major role in its short-range interactions with solvents. For hydrated ions, their surfaces are composed of water molecules, which may prevent the inner ion from interacting directly with outer solvent molecules. Accordingly, the quantum chemical properties of the inner ion hardly influence direct interactions of the hydrated ion with solvents. The inner ion may function only as the origin of the surface electrical field of the hydrated ion, which should affect the short-range interaction energy, as shown in Eq. (31). As for the nonhydrated cations studied, their surfaces are mainly composed of C–H atomic groups, while the five nonhydrated anions, being forced to be classified into one group, have miscellaneous surfaces. As also described above, the surfaces of the polyanions are composed of oxygens without exception. Thus Eq. (31) turns out to be quite promising for an understanding of G0;O!W for ions with the common surface. tr The coefficients in Eq. (44) or (48) coming from those in Eq. (31) have been determined empirically in the present study. As shown above, these coefficients are related to
48
Osakai and Ebina
some molecular properties of the ion and the solvent. However, it seems premature to discuss these relations quantitatively, because the coefficients would be heavily affected by 0;O!W . It is desired to collect accurate and reliable values of the experimental errors in Gtr 0;O!W Gtr for many other kinds of ions. In the present non-Bornian theory it should be noted again that the long-range electrostatic interactions of an ion with solvents in the second and further solvation shells are ignored. However, the electrostatic energies should contribute to a considerable extent to the solvation energies of ions in each phase. Nevertheless, the proposed equations for G0;O!W , in which short-range interactions are only considered, have been found to be tr fitted very well to the experimental data. This may be understood by recognizing that is the difference in the solvation energy between the two phases. It is most G0;O!W tr probable that the long-range electrostatic solvation energies in the respective phases are 0;O!W for the most part canceled in Gtr . This will result in the predominant contribution of 0;O!W . Thus, our daring ignoring of the long-range electroshort-range interactions to Gtr than Bornian electrostatic models. static energies have given a better account of G0;O!W tr
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
M. Born. Z. Phys. 1: 45 (1920). Y. Marcus, Ion Solvation, Wiley, Chichester, 1985. Y. Marcus, Ion Properties, Marcel Dekker, New York, 1997. R. R. Dogonadze, E. Ka´lma´n, A. A. Kornyshev, and J. Ulstrup (eds.), The Chemical Physics of Solvation: Part A, Theory of Solvation, Elsevier, Amsterdam, 1985. P. Politzer and J. S. Murray (eds.), Quantitative Treatments of Solute/Solvent Interactions, Elsevier, Amsterdam, 1994. Y. Marcus. Rev. Anal. Chem. 5:53 (1980). Y. Marcus. Pure Appl. Chem. 62:899 (1990). Y. Marcus, in Liquid–Liquid Interfaces: Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 39–61. V. S. Markin and A. G. Volkov. Electrochim. Acta 34:93 (1989). T. Osakai and K. Ebina. Bunseki 1998:589 (1998) (in Japanese). A. A. Kornyshev and A. G. Volkov. J. Electroanal. Chem. 180:363 (1984). A. A. Kornyshev, in Ref. 4, pp. 77–118. H. H. Uhlig. J. Phys. Chem. 41:1215 (1937). W. M. Latimer, K. S. Pitzer, and C. M. Slansky. J. Chem. Phys. 7:108 (1939). M. H. Abraham and J. Liszi. J. Chem. Soc. Faraday Trans. 1 74:1604; 2858 (1978). M. H. Abraham, J. Liszi, and L. Me´sza´ros. J. Chem. Phys. 70:2491 (1979). M. H. Abraham and J. Liszi. J. Inorg. Nucl. Chem. 43:143 (1981). Y. Marcus. J. Chem. Soc. Faraday Trans. 87:2995 (1991). V. Gutmann, The Donor–Acceptor Approach to Molecular Interactions, Plenum Press, New York, 1978. K. Burger, Solvation, Ionic and Complex Formation Reactions in Non-Aqueous Solvents: Experimental Methods for Their Investigation, Akade´miai Kiado´, Budapest, 1983. V. Gutmann and E. Wychera. Inorg. Nucl. Chem. Lett. 2:257 (1966). U. Mayer, V. Gutmann, and W. Gerger. Monatsch. Chem. 106:1235 (1975). D. A. Owensby, A. J. Parker, and J. W. Diggle. J. Am. Chem. Soc. 96:2682 (1974). E. Grunwald and S. Winstein. J. Am. Chem. Soc. 70:846 (1948). E. M. Kosower. An Introduction to Physical Organic Chemistry, Wiley, New York, 1968, p. 259. K. Dimroth, C. Reichardt, T. Siepmann, and F. Bohlmann. Liebigs Ann. Chem. 661:1 (1963). C. Reichardt. Angew. Chem. Int. Ed. Engl. 4:29 (1965).
Ion Solvation and Resolvation
49
28. R. W. Taft, N. J. Pienta, M. J. Kamlet, and E. M. Arnett. J. Org. Chem. 46:661 (1981). 29. T. Osakai, H. Katano, K. Maeda, S. Himeno, and A. Saito. Bull. Chem. Soc. Jpn. 66:1111 (1993) and references therein. 30. T. Osakai, S. Himeno, A. Saito, K. Maeda, and H. Katano. J. Electroanal. Chem. 360:299 (1993). 31. T. Osakai, S. Himeno, and A. Saito. Bunseki Kagaku 43:1 (1994) (in Japanese with English abstract). 32. T. Kurucsev, A. M. Sargeson, and B. O. West. J. Phys. Chem. 61:1567 (1957). 33. T. Osakai and K. Ebina. J. Electroanal. Chem. 412:1 (1996). 34. R. S. Mulliken. J. Am. Chem. Soc. 74:811 (1952). 35. J. Rais, M. Kyrs˘ , and M. Pivon˘kova´. J. Inorg. Nucl. Chem. 30:611 (1968). 36. S. Motomizu, K. Toˆei, and T. Iwachido. Bull. Chem. Soc. Jpn. 42:1006 (1969). 37. M. Kawasaki, K. Toˆei, and T. Iwachido. Chem. Lett. 417 (1972). 38. T. Iwachido, M. Minami, A. Sadakane, and K. Toˆei. Chem. Lett. 1511 (1977). 39. T. Iwachido, M. Minami, M. Kimura, A. Sadakane, M. Kawasaki, and K. Toˆei. Bull. Chem. Soc. Jpn. 53:703 (1980). 40. Y. Yamamoto, T. Tarumoto, and T. Tarui. Chem. Lett. 459 (1972). 41. Y. Yamamoto, T. Tarumoto, and T. Tarui. Bull. Chem. Soc. Jpn. 46:1466 (1973). 42. T. Kenjo and R. M. Diamond. J. Phys. Chem. 76:2454 (1972). 43. T. Kenjo and R. M. Diamond. J. Inorg. Nucl. Chem. 36:183 (1974). 44. S. Kusakabe, M. Shinoda, and K. Kusafuka. Bull. Chem. Soc. Jpn. 62:333 (1989). 45. S. Kusakabe and M. Arai. Bull. Chem. Soc. Jpn. 69:581 (1996). 46. T. Osakai, A. Ogata, and K. Ebina. J. Phys. Chem. B. 101:8341 (1997). 47. C. Sa´nchez, E. Leiva, S. A. Dassie, and A. M. Baruzzi. Bull. Chem. Soc. Jpn. 71:549 (1998). 48. A. Ogata, Y. Tsujino, and T. Osakai. Phys. Chem. Chem. Phys. 2:247 (2000). 49. T. Osakai and K. Ebina. J. Phys. Chem. B 102:5691 (1998). 50. T. Kakiuchi, M. Nakanishi, and M. Senda. Bull. Chem. Soc. Jpn. 61:1845 (1988). 51. R. D. Shannon. Acta Cryst. A32:751 (1976). 52. E. J. King. J. Phys. Chem. 74:4590 (1970). 53. H. Yokoyama, K. Shinozaki, S. Hattori, F. Miyazaki. and M. Goto. J. Mol. Lig. 65/66:357 (1995). 54. H. Yokoyama, K. Shinozaki, S. Hattori, and F. Miyazaki. Bull. Chem. Soc. Jpn. 70:2357 (1997). 55. H. D. B. Jenkins and K. P. Thakur. J. Chem. Educ. 56:576 (1979). 56. Y. Marcus, in Ref. 2, pp. 46–47; for IO 4 , see A. F. Kapustinskii. Quat. Rev. 10:283 (1956). 57. J. T. Edward. J. Chem. Educ. 47:261 (1970). 58. A. Karpfen and P. Schuster, in Ref. 4, pp. 265–312. 59. T. Osakai, K. Maeda, K. Ebina, H. Hayamizu, M. Hoshino, K. Muto, and S. Himeno. Bull. Chem. Soc. Jpn. 70:2473 (1997). 60. E. R. Nightingale, Jr. J Phys. Chem. 63:1381 (1959). 61. J. Koryta, P. Vanysek, and M. Br˘ ezina. J. Electroanal. Chem. 75:211 (1977). 62. V. Marec˘ek and Z. Samec. Anal. Chim. Acta 151:265 (1983). 63. T. Osakai, T. Kakutani, Y. Nishiwaki, and M. Senda. Bunseki Kagaku 32:E81 (1983). 64. T. Kakutani, T. Osakai, and M. Senda. Bull. Chem. Soc. Jpn. 56:991 (1983). 65. Z. Samec, V. Marec˘ek, and D. Homolka. Faraday Discuss. Chem. Soc. 77:197 (1984). 66. D. Homolka and H. Wendt. Ber. Bunsen-Ges. Phys. Chem. 89:1075 (1985). 67. T. Kakutani, Y. Nishiwaki, and M. Senda. Bunseki Kagaku 33:E175 (1984). 68. B. Hundhammer and S. Wilke. J. Electroanal. Chem. 266:133 (1989). 69. T. Osakai and K. Muto. Anal. Sci. 14:157 (1998). 70. S. Kihara, M. Suzuki, K. Maeda, K. Ogura, and M. Matsui. J. Electroanal. Chem. 210:147 (1986). 71. T. Ohkouchi, T. Kakutani, and M. Senda. Bioelectrochem. Bioenerg. 25:81 (1991). 72. http://dcwww.epfl.ch/cgi-bin/LE/DB/InterrDB.pl.
3 Electroelastic Instabilities in Double Layers and Membranes MICHAEL B. PARTENSKII and PETER C. JORDAN Department of Chemistry, Brandeis University, Waltham, Massachusetts
I.
INTRODUCTION
Electrical double layers and membranes have certain common features. Both are quasitwo-dimensional structures. In both, variation of applied voltage influences the distribution of charge as well as the structural parameters (effective thickness). And in both cases coupling between the electric field and these parameters can lead to instabilities and phase transitions. These instabilities may be described and understood using an electroelastic metaphor first introduced in 1973 by Crowley [1] in relation to membrane breakdown (‘‘electroporation’’). Although this model failed to quantitatively describe the onset of instability at small voltage with little deformation, it generated significant interest in studies of the electroelasticity of membranes. In some aspects, the electrical response of membranes is similar to the action of an external pressure (such as osmotic stress). But it also has features with no direct analogy to mechanical effects, such as specific interaction of an applied voltage with surface undulations which can cause instabilities in membranes. Similar phenomena appear equally important in the behavior of electrochemical interfaces where electrical stress affects structural parameters of electrical double layers. These are most closely related to the question of whether, for electrical double layers, it is possible for the differential capacitance, C, to be negative. It has been shown that the prediction of C < 0 in some models of double layers has a direct analogy in the behavior of the elastic capacitors. And, as in membranes, it is also related to possible instabilities and interfacial phase transitions at the interfaces. This chapter is devoted to the behavior of double layers and inclusion-free membranes. Section II treats two simple models, the ‘‘elastic dimer’’ and the ‘‘elastic capacitor.’’ They help to demonstrate the origin of electroelastic instabilities. Section III considers electrochemical interfaces. We discuss theoretical predictions of negative capacitance and how they may be related to reality. For this purpose we introduce three sorts of electrical control and show that this anomaly is most likely to arise in models which assume that the charge density on the electrode is uniform and can be controlled. This ‘‘control’’ is a convenient theoretical construct, but in real applications only the total charge or the applied voltage can be fixed. We then show that predictions of C < 0 under control may indicate that in reality the symmetry breaks. Such interfaces undergo a transition to a nonuniform state; the initial uniformity assumption is erroneous. Most 51
52
Partenskii and Jordan
of this discussion is couched in terms of the electroelastic analogy. Section IV describes electroelastic phenomena in inclusion free membranes with possible relation to instabilities. We first treat the Crowley model (a rigid interface). We then consider the ‘‘hydrodynamic,’’ ‘‘electroporative,’’ and ‘‘smectic bilayer’’ perspectives on the initiation of an electroelastic instability. Finally, we describe some attempts to modify the smectic model to account for the basic experimental observation: membrane rupture occurs at low voltages with little electrostriction. These are based on the idea that nonlocality of the elastic moduli softens the symmetrical modes thus enhancing thickness fluctuations at short wavelengths. Possible consequences of this hypothesis for different membrane properties are discussed.
II.
ELECTROELASTIC INSTABILITIES. SIMPLE EXAMPLES
A.
Charges on a Spring (Elastic Dimer)
The nature of the instabilities related to coupling of electrical and elastic degrees of freedom can be illustrated by a very simple example. Consider two charges, q and q, separated by a spring. The corresponding Hamiltonian is H¼
q2 þ E0 ðlÞ 40 l
ð1Þ
where E0 is the bond energy. In an harmonic approximation we write E0 ¼
K ðl l0 Þ2 2
ð2Þ
where K is a ‘‘spring constant,’’ l is the distance between charges, and l0 is the length of the isolated spring. For the sake of convenience we use dimensionless units W¼
H Kl02
q Q ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 40 Kl03
z¼
l l0
ð3Þ
so that W ¼
Q2 1 þ ð1 zÞ2 2 z
ð4Þ
Global behavior of the system is determined by a single parameter, the reduced charge Q; relative distance z is the internal variable, defined by the equilibrium condition @W ¼0 @z
which follows from
@H ¼0 @l
ð5Þ
Before proceeding further we analyze the behavior of the system by viewing its energy surface WðQ; zÞ (Fig. 1). At short distances, z ! 0, the elastic force cannot compete with the electrostatic attraction and W ! 1 for any Q 6¼ 0. For sufficiently smallp jQj a local ffiffiffiffiffiffiffiffiffiffi minimum 0 < z 1 exists. It disappears when Q reaches its critical value Qc ¼ 4=27 and z has contracted to zc ¼ 2=3. Both Qc and zc can be defined by solving Eq. (5) together with the marginal equilibrium condition. As we see, ‘‘molecular equilibrium’’ at finite z, if its exists, is always local, while globally, charges are stable only in direct contact (the collapsed state). In reality, however, additional short-range repulsion would prevent the system from collapsing. Figure 2 incorporates this additional interaction. We see that the
Electroelastic Instabilities
FIG. 1 Energy of elastically coupled charges.
FIG. 2 Energy of elastically coupled charges with an additional short-range repulsion term.
53
54
Partenskii and Jordan
‘‘molecule’’ becomes bistable, and Qc now corresponds to charge at which the barrier between the two minima disappears. B.
Elastic Capacitors
Our elastic molecule illustrates the onset of instability. However, conditions when charges can be smoothly controlled by the observer are hard to achieve. In applications and studies of interfacial phenomena the controlled electrical variable is usually a voltage V across the interfaces rather than charges involved in their polarization. The distributions of charges composing electrical double layers of different origin can be approximated by ‘‘interfacial capacitors.’’ As we will see in Section III, the distributions of charges are flexible and strongly affected by the applied voltage. As a result, not only the charge q on the ‘‘plates’’ of interfacial capacitors, but also the effective ‘‘gap’’ between the plates depends on V. This naturally leads to ‘‘relaxing gap’’ capacitors, which in many cases can be described as ‘‘elastic capacitors’’ (ECs). The energy of an EC under fixed voltage is [2] H ¼ H0 ðq; lÞ qV
ð6Þ
where H0 ðq; lÞ ¼
q2 l þ AE0 ðlÞ 20 A
ð7Þ
is the energy of isolated capacitor with charge q, A is the surface area of its ‘‘plates,’’ and l are the effective dielectric constant and the gap width respectively, and E0 is the elastic energy per unit area. The contribution qV in Eq. (6) is responsible for charge exchange between the potentiostat (battery) and the capacitor. The equilibrium conditions @H ¼0 @l
@H ¼0 @q
@2 H >0 @2 l
ð8Þ ð9Þ
define the equilibrium gap lðVÞ and equilibrium charge qðVÞ. Notice that Eq. (7) assumes that charge distributions are uniform. The validity of this assumption will be discussed in Section III. In the uniform case all properties can be equally well described by the surface charge density q ð10Þ ¼ A In equilibrium, as follows from Eqs. (7) and (8) 2 @E þ 0¼0 20 @l
ð11Þ
l ¼V 0
ð12Þ
Equation (12) leads directly to an expression of H through V and l: ! 0 V 2 þ E0 ðlÞ A H¼ 2l
ð13Þ
Electroelastic Instabilities
55
Equation (13) becomes equivalent to Eq. (1) if q2 is replaced by V 2 =2. In the units of Eq. (3), introducing the dimensionless voltage, V ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Kl03 =0
ð14Þ
and using Eq. (2), we have H¼
2 1 þ ð1 zÞ2 2z 2
ð15Þ
From the previous analysis it follows that the harmonic elastic capacitor collapses when approaches its critical value rffiffiffi 2 2 and zc ¼ 2=3 ð16Þ c ¼ 3 3 C.
General Observations
Several questions must be addressed with respect to the simple examples just outlined. Despite their formal similarity, it is important to keep in mind that the first instability describes an isolated system, where charge is a controlled variable. In contrast, the EC as introduced becomes unstable only in contact with a potentiostat (battery), when V is fixed and charge can change. Thus, the collapse of an EC leads to infinite growth of q 1=l, accompanied by electric current from a battery to the EC. If isolated, the EC remains stable for all values of q corresponding to l > 0, as can be seen from Eq. (7). The major difference from the elastic dimer is that electrical energy of an isolated EC is positive and finite for all q and l while for the dimer it goes to 1 when l ! 0. In the next section we reexamine this result and show that the uniformity assumption for the charge distribution across the plates of a capacitor can fail, and this can influence the stability condition for an isolated EC. Another observation should be made with respect to the term ‘‘elastic’’ in describing interfacial capacitors. It was originally introduced by Crowley [1] for membranes and reflects the compressibility of lipid layers which behave in some respects like an elastic film. Its relation to electrochemical interfaces is less obvious. Consider an interface between a metal electrode and an electrolyte. As we will see in Section III, the effective gap of the interfacial capacitor is the distance between the centers of mass of the electronic, ‘‘e,’’ and ionic, ‘‘i,’’ charge density distributions ne;i : l ¼ x i xe Ð þ1 xe;i ¼
1
ð17Þ ni;e ðxÞx dx e;i
ð18Þ
where e ¼ i ¼ , the surface density of electron charge. Both distributions depend on (and V) and l usually changes with charging. Consequently, the interface may be represented as a ‘‘relaxing gap’’ capacitor. Consider a hypothetical attempt to alter the equilibrium electron and ion density profiles, causing the displacement of xe and xi from their equilibrium positions. The corresponding increase in free energy can be expressed through the effective restoring force opposing the variation of l from its equilibrium value. In turn, the restoring force can usually be expressed in terms of an effective elastic constant. This is where the analogy with the EC comes into play.
56
Partenskii and Jordan
The ‘‘elasticity’’ can be related to very different contributions to the energy of the interface. It includes classical and nonclassical (exchange, correlation) electrostatic interactions in ion–electron systems, entropic effects, Lennard–Jones and van der Waals-type interactions between solvent molecules and electrode, etc. Therefore, use of the macroscopic term should not hide its relation to ‘‘microscopic’’ reality. On the other hand, microscopic behavior could be much richer than the predictions of such simplified electroelastic models. Some of these differences will be discussed below.
III.
NEGATIVE DIFFERENTIAL CAPACITANCE AND ELECTRICAL DOUBLE LAYER STABILITY
A.
Historical Review
The traditional treatment of a double layer at electrode–electrolyte interfaces is based on its separation into two series contributions: the compact (‘‘Helmholtz’’) layer and the diffusive (‘‘dif’’) layer, so that the inverse capacitance is 1 1 1 Cdl ¼ CH þ Cdif
ð19Þ
Both terms affect whether the double layer capacitance can become negative. 1. ‘‘Molecular Capacitor’’ (MC) and the Cooper–Harrison Catastrophe The problem of negative capacitance first arose in theoretical studies of CH based on socalled ‘‘molecular models.’’ Molecular or ‘‘dipolar capacitor’’ models treat the layer of water molecules adjacent to a metal electrode as a lattice of point or finite-size dipoles [3,4]. Many studies have focused on the response of such a layer to electrode charging and comparison with the measurements of the compact layer capacitance, CH ðÞ using the technique suggested by Grahame [5,6]. Much of this work has been inspired by the ‘‘Cooper–Harrison (CH) catastrophe,’’ the prediction of negative CH ðÞ in molecular models of the compact layer. Here we only briefly discuss the origin of this anomaly (see Ref. 7 for more details and references). (a) General Characteristics of an MC. Consider the isolated MC with a charge density on its plates. Focusing on the capacitance C (the index ‘‘H’’ is omitted), we first introduce the potential drop across the MC as
¼ F0 d þ d
ð20Þ
where* F0 ¼ 4
ð21Þ
is the external field created by the plates of MC, and
d ¼ 4Px
Px ¼ Ns hpx i
ð22Þ
in which hpx i is the average normal-to-plane projection of the dipolar moment, and Ns is the number of dipoles per unit area. Using the definition of differential capacitance (per unit area),
* Unlike the rest of the chapter, here we adopt Gaussian electrostatic units which are typically used in the literature devoted to molecular capacitors and double layer theory.
Electroelastic Instabilities
C¼
d
d
57
ð23Þ
we find 1 ¼ 4ðd 4 Þ 4C
ð24Þ
where ¼ Ns
dhpx i dF0
ð25Þ
is the susceptibility of the dipolar lattice. It follows from Eq. (24) that if it were possible that d=4
ð26Þ
then it would be possible for C to become negative. (b) The MC in a Mean Field Approximation (MFA). In the majority of papers including the original CH paper [8], the MC was treated in Ising-type n-state models with dipoles perpendicular to the plates: px ¼ psx where the vector sx is limited to equally spaced values between 1 and 1. We consider the simplest ‘‘spin 1/2’’ model n ¼ 2 (Fig. 3), a choice justified by the fact that the appearance of the CH catastrophe is independent of n. The local field acting on a specific dipole in a lattice is F ¼ F0 þ Fd þ F 0
ð27Þ
0
where the field F describes interaction between a dipole and its own images. Interaction with this field does not depend on the dipolar orientation and can be omitted [7]. The field Fd created by the rest of the dipolar lattice has been a subject of considerable controversy. Following most authors, we restrict analysis to the MFA assuming that all dipoles except one have moments equal to their mean value hpx i. Then, Fd ¼
nL Jhsx i p
ð28Þ
where J ¼ p2 =a3 is the interaction energy between antiparallel nearest neighbors, a is the lattice constant, and nL is the effective number of nearest neighbors. For a bare lattice where dipolar fields are not shielded by the plates of capacitor, nL equals X 3 n0L ¼ a3 r1i ð29Þ i
is 9 and 11 for square and hexagonal lattices respectively. Focusing on the CH catastrophe we notice from Eq. (26) that the most ‘‘dangerous’’ point is where is largest. In the MC models considered this obviously corresponds to ¼ 0; increasing orients dipoles and makes them less susceptible to variation of the n0L
FIG. 3 Molecular capacitor in ‘‘spin 1/2’’ model.
58
Partenskii and Jordan
external field (in the limit ! 1 the lattice is totally frozen and ! 0). In this ‘‘zero charge’’ point for ‘‘spin 1/2’’ [8] we have ¼
Ja3 Ns kT þ JnL
ð30Þ
from which is clear that two factors oppose the orientation of dipoles in the MC: temperature and dipolar interactions. The latter occurs because in the Ising model considered, the interaction energy between two lattice dipoles is minimal when dipoles are opposed. Equation (30) emphasizes the importance of the effective number of nearest neighbors; with p, Ns , and T fixed, the susceptibility becomes larger for smaller nL . (c) Effective Number of Nearest Neighbors and the CH Catastrophe. It follows from Eqs. (30) and (26) that C becomes negative if nL
0 and the CH catastrophe disappears. The p-approach corresponds to Ad =A ! 1 with both A and Ad ! 1. In this case the CH catastrophe disappears because of the uniform contribution which increases the effective number of nearest neighbors. In other words, both summation procedures are valid.* They describe different physical situations. In the c-summation the size of the dipolar array is much smaller than the size of the capacitor, while in the p-approach both are equal. One can imagine an infinite number of different summation orders corresponding to different relations between A and Ad , leading to results between the p- and c-limits. To solve the problem unambiguously, one must consider a finite dipolar lattice between finite plates, which requires accounting for edge effects and makes the whole problem much more complicated. (e) Conclusion, and a Further Question. We have seen that the CH catastrophe arises as a result of inconsistencies in the treatment of the electric field and the potential in the molecular capacitor. Were they analyzed consistently, then, at least in the framework of Ising models and the MFA, a catastrophe would not appear and the capacitance of an MC would always be positive. But another question arises. Does this imply that the capacitance of a double layer can never become negative? Before addressing this question we will analyze some other occurrences of the C < 0 problem in the theory of electrified interfaces. 2.
Diffuse Electron and Ionic Distributions in a Double Layer and the Problem of C < 0 Statistical mechanical and microscopic theories of the double layer have often been intensively reviewed. Our focus is only on features related to the problem of negative C.
* The following example helps in visualization of the difference between the two ways of summation. Consider the potential difference ðL; RÞ ¼ ðLÞ ðLÞ between points L and L on the axis of a uniform dipolar disk (where Px is the surface dipole moment density) in the limit of infinite R and L. Since ðL; RÞ ¼ 4Px ½1 L2 =ðL2 þ R2 Þ, limR!1 limL!1 ðL; RÞ ¼ 0, while limL!1 limR!1 ðL; RÞ ¼ 4Px . The first result obviously corresponds to the c-approach, while the second one corresponds to the p-approach.
60
Partenskii and Jordan
(a) Diffuse Models of Ionic Distributions in Electrolytes. The first model of the diffuse ionic distribution in electrolytes was developed by Gouy and Chapman (GC) many years ago. In this and similar ‘‘local models’’ the charge density is considered to be a local function of the potential ðxÞ, nlocal ðxÞ ¼ f ½ ðxÞ
ð34Þ
In such models capacitance can never become negative [12]. The GC model for a 1 : 1 electrolyte is illustrative: Cdif ¼ aðb þ 2 Þ
ð35Þ
where a and b are positive and depend on temperature, ionic concentration, and bulk dielectric constant. However, the question of C < 0 inevitably emerges in theoretical studies of the diffuse layer that go beyond the local approach (see, e.g., Refs. 13–18). This anomaly is related to some specific properties of ionic distributions. (b) Properties of the Ionic Distribution Which Can Cause a Capacitance Anomaly. Let us examine the features of an ionic distribution that can lead to Cdif < 0. Quite generally, the potential drop across the double layer, ð1Þ ð1Þ (where x ¼ 1 and x ¼ 1 correspond to the bulk electrode and electrolyte respectively) can be represented as ¼ 4 ½xi ðÞ xe ðÞ 4Px
ð36Þ
Then, using Eq. (23) we find 1 dl dPx ¼ lðÞ þ 4C d d
ð37Þ
where the effective gap of the interfacial capacitor, l, is defined by Eq. (17). Focusing on the effect of the ionic distribution, we consider the so-called primitive model where ions occupy a region of uniform dielectric constant . In addition we temporarily ignore the diffuseness of the electronic distribution (the perfect conductor model) assuming xe ¼ const: ¼ 0. Then for the diffuse layer capacitance ð1 ð 1 @ 1 ð0Þ ð38Þ ¼ n ðxÞx dx n ðxÞx dx=
4Cdif ðÞ @ 0 0 Here we assume ð1Þ ¼ 0 and choose > 0. It is now clear that differential capacitance becomes negative at some value of if the centroid of the ionic distribution induced by a small variation becomes negative. Given that ions do not penetrate the region x < 0, this can only happen if nðxÞ is a nonmonotonic function of variable polarity. However, the total electrolyte charge density, nðxÞ, is not necessarily oscillating, and it can even be monotonic. Figures 4–6 illustrate the various possibilities. nðxÞ represents a nonmonotonous charge density corresponding to some variation of . It is a function constructed to reflect two features of the ionic shielding of the electrode charge. Ð1 1. Neutrality condition (required): 0 nðxÞ dx ¼ . 2. ‘‘Charge condensation’’ near the electrode (quite a typical feature, which is necessary but not sufficient for attaining C < 0): charging is accompanied by increased charge density near the electrode at the expense of some depletion in the tail regions of the ionic distribution. Figure 4 depicts a generalized Raleigh [19] model originally designed to explain extremely high values of interfacial capacitance in contacts of metals and solid electrolytes, silver-ion conductors (such as AgCl). This is a two-layer model satisfying conditions 1 and
Electroelastic Instabilities
61
FIG. 4 Induced potential drop ðxÞ in the Raleigh model of the ionic distribution. k ¼ 0:2 (curve 1), 0.33 (curve 2), and 0.4 (curve 3). Gray area shows the Raleigh distribution of the induced charge with a ¼ 0:3 nm and k ¼ 0:33 (see text) which corresponds to curve 2. The total induced charge is normalized
2. Charge densities in the layers are n1 at x < a and kn1 at a < x < 2a; the layer thickness a and the dimensionless constant k < 1 are the parameters of the model. Using this to mimic the distribution induced by , we find that n1 ¼ =að1 kÞ. The center of mass of this distribution is ¼ xRaleigh i
n1 a2 að1 3kÞ ð1 3kÞ ¼ 2 1k
ð39Þ
xi becomes negative for k > 1=3. Figure 4 demonstrates that C becomes negative when xi is negative. This transition is obvious from the behavior of ðxÞ [see Eq. (38)]. For curve 1 (k ¼ 0:2) the additional barrier ð0Þ ð 0:75Þ has a ‘‘normal’’ positive sign; for curve 2 (k ¼ 1=3) this barrier disappears, and for curve 3 ðk ¼ 0:4) it becomes negative ( 0:5). Figure 5 presents a more realistic picture where nðxÞ is continuous. QðxÞ is the total ionic charge accumulated between x ¼ 0 and the point x:
FIG. 5 Model-induced charge density profile nðxÞ (curve 1), QðxÞ (curve 2), and ðxÞ (curve 3) in the diffuse layer ( ¼ 0:2, dimensionless units).
62
Partenskii and Jordan
QðxÞ ¼
ðx
nðx 0 Þ dx 0
0
and ðxÞ ¼ 4½ þ QðxÞx þ
ðx
x 0 nðx 0 Þ dx 0
ð40Þ
0
It demonstrates an important feature promoting negative C: ‘‘overshielding’’ of the electrode charge in the adjacent region of electrolyte. This is the cause of depletion in the more distant parts of the double layer causing effective displacement of the charge centroid towards the electrode.* Figure 6 demonstrates the possibility that if the initial potential profile 0 ðxÞ corresponding to some 0 is monotonic (GC-type), then a small additional nonmonotonic variation in ðxÞ arising from the additional charge density of Fig. 5 and leading to C < 0 may still leave the total potential profile ðxÞ monotonic. The same is true for the total charge density nðxÞ. This speculation mimics the results of numerical experiments described in Refs. 17 and 18. The same can be true for charge density profiles. It demonstrates that charge density oscillations are neither necessary nor sufficient to give rise to negative C. 3. Negative Capacitance in Primitive Models of Electrolyte A possible reason that the problem of C < 0 did not receive much attention was the assertion [15] (BLH) that such an anomaly was forbidden. The proof was based on the statistical mechanical analysis of the primitive model of electrolytes between two oppositely charged planes, and . It was noticed in Ref. 10 that the BLH analysis missed a very simple contribution to the Hamiltonian, direct interaction between the charged walls, 2L 2 (L is the distance between the walls). With proper choice of the Hamiltonian the condition on the capacitance would be C > 2=L. It simply means that due to ionic shielding of the electric field, the capacitance exceeded its ‘‘geometrical’’ value corresponding to the electrolyte-free dielectric gap.
FIG. 6 Potential profile for 0 (curve 1) and 0 þ (curve 2).
* Such a behavior can represent, for instance, condensation near an electrode of a monotonous charge density n ðxÞ following a variation of [18].
Electroelastic Instabilities
63
This analysis has been developed further [20–22]. At the same time attention focused on the analogous anomaly in the theory and simulations of the double layer [17,18]. Progress was, however, slightly misdirected by the assertion [21] that there are no restrictions on the sign of C, regardless of the model considered or the choice of experimental conditions. In what follows we will show that there are severe restrictions strongly limiting the possibility of capacitance anomalies. But here we only stress that it has never been proven that negative capacitance is forbidden for any model of an electrolyte at a uniformly charged interface. 4. Contribution of Metal Electrons and the Negative Capacitance Problem In the early 1980s it became clear that metal electrons play an important role in the electrical response at metal–electrolyte interfaces. Different aspects have been extensively reviewed [23–27]. Here we only briefly discuss the problem of negative capacitance, and how it arose in these studies. Although it was clear that separation of an interface into ‘‘surface’’ and ‘‘bulk’’ components as in Eq. (19) is artificial and must disappear in a consistent microscopic analysis, electronic effects were initially discussed in terms of a ‘‘compact layer’’ and its capacitance CH . It was apparent early on that the electrons strongly influence double layer properties [28–33]. In traditional models of an electrified interface, metal electrons are artificially localized within the electrode. This leads to misinterpretation of the electronic influences on the compact layer. CH in those models would always be smaller than its ‘‘ideal conductor’’ limit (with electrode charge spread over an infinitesimally thin region at the electrode surface x ¼ 0) IC ¼ H ð41Þ 4CH xH where xH is the effective width of the compact layer, and H is the effective permittivity. Self-consistent analysis of electronic effects altered this simple view substantially. By analogy to Eqs. (36) and (37), compact layer capacitance in the simplest model, accounting only for electronic effects, is now defined by 1 dx ¼ xH xe e 4CH d
ð42Þ
It was first noticed in Ref. 31 that at moderate negative the condition xe
dxe xH d
ð43Þ
may be fulfilled for contacts of metals with solid electrolytes (silver-ion conductors), so that CH ðÞ can become negative. Similar anomalies have been found in contacts of metals with solvents [34,35], results which have not been easily accepted. Moreover, in some calculations they have been carefully avoided, partially in the belief that they are prohibited by the BLH theorem (for a discussion see Refs. 7 and 36). 5.
Electroelastic Models. Proof that Negative Capacitance is Admissible for Uniformly Charged Interface Models Elastic capacitors (Section II) are very useful as ‘‘electromechanical’’ analogs of microscopic interfacial capacitors [22,31,34]. But most importantly, they demonstrate that nega-
64
Partenskii and Jordan
tive capacitance can coexist with interfacial equilibrium and stability as long as the total charge is fixed and the charge density is kept uniform. Under these conditions, corresponding to so-called -control [37], the elastic capacitor is described by the Hamiltonian, Eq. (7). In dimensionless units this becomes 1 W ¼ s2 z þ ð1 zÞ2 2
ð44Þ
where s ¼ ð4=kl0 Þ2 , the dimensionless charge density. Other units are the same as in Eq. (3). From the equilibrium conditions for fixed s it follows that [37]: zðsÞ ¼ 1
s2 2
vðsÞ ¼ s
s2 3
3 C 1 ¼ 1 s2 2
ð45Þ
and C1 0 for jsj > s0 ¼ ð2=3Þ1=2 . At the same time, @2 W=@l 2 ¼ 1 > 0, and in this region the system is stable. Thus capacitance under -control can be negative. And as this is possible for one simple model, it should also be possible for some other models obeying the same conditions of -control.
B.
The Sign of C and Different Types of Electrical Control
In the analysis of molecular capacitors, the diffuse layer and elastic capacitors, we have always assumed that the electrode charge density could be controlled. Under such conditions it is generally possible for C to become negative while the system remains stable. For example, contraction of the gap z in an elastic capacitor proceeds smoothly with growing until the plates come in contact, while C becomes negative for z < 2=3. At the same time, as shown in Section II for an EC connected to a battery, the EC collapses after z 0:6 is reached. How can these seemingly contradictory results be reconciled? And how can -control be related to reality? Is C < 0 observable? These questions are addressed in this section. 1. Three Types of Control (a) -Control. In the vast majority of studies in double layer theory, the charge density is considered an independent control variable. This forms the framework where the question of negative C originated. But this assumption must be treated very carefully. In practice there is no way to control . Therefore, -control is a purely theoretical construct. It works perfectly well only if an interface ‘‘chooses’’ to remain uniform.* (b) Isolated Capacitor, q-Control. In real experiments with ‘‘ideally polarizable’’{ interfaces there are basically two options: either the cell is isolated, or it is connected to a potentiostat (battery). For an isolated capacitor the total charge on the electrode is fixed (‘‘q-control’’). If the system remains uniform, then - and q-controls are equivalent, being defined by Eq. (10). However, when for any reason a uniform distribution becomes unstable, then only q-control is a valid description of the isolated interface.
* We are not describing microscopic structural nonuniformity, which is discussed in another chapter of this book, and assume that the electrode surface is uniform. { We exclude situations where there is electric current across the interface which would cause some additional complications.
Electroelastic Instabilities
65
(c) Global System, -Control. Now consider a cell connected to a battery. Usually, the subsystem is immersed between two metal electrodes. Here electrical control of the cell is maintained via the electronic subsystems of the electrodes [38]. The real controlled variable is the difference between the electrochemical potentials of electrons of both electrodes, 1 and 2 . To avoid the complexities due to contact phenomena (‘‘Volta potential’’) we assume both electrodes are made of the same metal and therefore have the same chemical potentials (Fermi energies). The difference between chemical potentials equals the voltage:
¼
1 2 e
ð46Þ
In this case the voltage across the interface is the actual controlled variable and we deal with -control. 2.
Stability Conditions
(a) C is Nonnegative Under -Control. The transition from an isolated to a global system is accompanied by transformation of the Hamiltonian [see Eq. (6)]: H ¼ H0 q
ð47Þ
It is generally true (for a discussion see Ref. 39) that for Hamiltonians of the form H ¼ H0 XF the susceptibility is 2 1 ðX hXiÞ 0 @X=@F ¼ kT
ð48Þ
ð49Þ
where h i denotes a statistical average with the Hamiltonian, Eq. (48). The transition from isolated ðH0 Þ to global ðHÞ belongs to this class [see Eq. (6)], which is why capacitance under -control is defined as 2 @hi A ¼ ð hiÞ C¼ ð50Þ @
kT [40–43] and is strictly nonnegative. (b) Isolated Capacitor. Suppose now that the charge q is fixed. As mentioned, if could be kept uniform, then C can unconditionally become negative. The elastic capacitors we have studied are examples of systems for which - and q-controls are equivalent. Indeed, with plates rigid, any nonuniform redistribution of charge density can only increase the EC’s energy, and therefore cannot become stable. It would be different if the plates of an EC were somewhat deformable. Transition to a nonuniform state could then occur due to coupling between the electrical and ‘‘elastic’’ degrees of freedom. In reality, the electronic and ionic ‘‘plates’’ of an interfacial capacitor are never absolutely rigid. Therefore, a uniform distribution should always be tested with respect to its stability under some nonuniform perturbations. Recently [7] we constructed an example showing that interfacial flexibility can cause instability of the uniform state. Two elastic capacitors, C1 and C2 , were connected in parallel. The total charge was fixed, but it was allowed to redistribute between C1 and C2 . It was shown that if the interface was absolutely ‘‘soft’’, i.e., contraction of the two gaps was not coupled, the uniform distribution became unstable at precisely the point where the dimensionless charge density s reached the critical value, s0 ¼ ð2=3Þ1=2 . In other words, the uniform distribution became unstable at the point where, under control, C 1
66
Partenskii and Jordan
would have changed sign, so that the region with C < 0 is unacceptable for such interfaces. If, however, the Ci are coupled by a spring, then the stability region expands towards larger . We can also use another argument similar to one suggested by Nikitas [44]. Consider a small area of the interface. Given that this area is much smaller than the total area of contact, we may consider the rest of the interface a potentiostat which keeps the potential in the chosen area fixed. Then, the selected area can be considered under -control and its local capacitance cannot be negative. Therefore, the selected area is likely to undergo a transition simultaneously accepting some charge from the rest of the interface. As this reasoning can be applied to any area of the interface, it strongly suggests that in the isolated system, the uniform state becomes unstable in a region where -control predicts C < 0. C.
Summary
The question of the allowed sign of C was and remains a topic of discussion with significant contradictions. We suggest here that a major reason for these contradictions is that theoretical calculations for electrified interfaces are more easily carried out assuming a uniform electrode charge. Most studies have used this condition and, on some occasions, the restriction of -control took its toll. And those were exactly the situations where negative capacitance was predicted. The conviction that C should be strictly positive was so compelling that it has been typically believed to also apply under -control conditions (see Refs. 7 and 36 for a review). In some other cases, confusion was caused by an opposite extreme, dropping the restrictions on C < 0 even for -control. The discussion in Refs. 17 and 18 is illustrative. Torrie [17] presented very important results for grand canonical Monte Carlo simulations of an electrical double layer in 2 : 1 electrolytes. Those results provide very convincing evidence that C < 0 can occur under control. However, instead of analyzing the consequences of this fact for real systems, the author simply quotes the statement [21] that sign of C is not restricted, even for -control. Reliance on this result (see a critique in Ref. 22) simply ignored the problem and discouraged closer study of this system. Similarly, Wei et al. [18] made analogous predictions of C < 0 using hypernettedchain theory and incorporating molecular polarizability. However, the discussion was again restricted to the plausibility of negative C under -control. We suggest that results yielding C < 0 under -control have considerable importance, even though this type of control is unrealistic. They provide an important indication that in a system studied under q-control there is a range of where the plane uniform state is unstable, and the system undergoes a transition to a nonuniform state with charge density varying along the plane of electrode. Therefore, a computational paradigm could be formulated as follows: ‘‘If C becomes negative under -control, study the stability of this state towards ‘charge density’ perturbations. It is very possible that a phase transition to a nonuniform state appears.’’ The same system treated under -control becomes unstable in the vicinity of c (which corresponds to C ! 1) and can also undergo a phase transition (see Refs. 7 and 24 for discussion). But, unlike the isolated system under q-control, it can acquire some additional charge from the battery, so that the initial and final states would correspond to different values of q. The relation of transitions under q- and -control is another prospective area of research.
Electroelastic Instabilities
IV.
67
ELECTROELASTIC INTERACTIONS, STABILITY, AND BREAKDOWN IN MEMBRANES
Study of the mechanisms of membranes’ interaction with electric fields and the consequences for membrane stability and electroporation are very important both for better understanding of membranes’ properties and for different applications involving electrical manipulation of their behavior [45–48]. By controlling the electrical setup it is possible to influence transmembrane permeability and thus gain some control over processes such as targeted drug delivery, DNA transport into cells, etc. This is also important for development of ‘‘bioelectrochemical’’ sensors, where membranes are in contact with electrodes and applied voltage is used for monitoring changes caused by the interaction with the environment [49–52]. A.
Some Perspectives on Membrane Instability
1.
Crowley’s Model
The first model of membrane electroporation was suggested by Crowley [1]. In Crowley’s model the membrane is viewed as the isotropic elastic material. The necessary background for understanding its voltage-induced instability was discussed in Section II. Crowley’s approximation for the elasticity energy term in Eq. (7) is E0 ðhÞ ¼ Bh0 z½lnðzÞ 1 ¼ Ez½lnðzÞ 1
ð51Þ
where h ¼ hðÞ is the local thickness of the membrane ( is a two-dimensional radius vector in the membrane plane), h0 is its unperturbed value, B and E are the Young’s and ‘‘stretching’’ moduli, respectively. Using Eq. (51) with Eqs. (7) and (8), we find a relation between the membrane ‘‘contraction’’ factor, z ¼ h=h0 (h is the equilibrium thickness) and the voltage V [53]: E lnðzÞ ¼ pE h0
ð52Þ
where pE ðV; hÞ ¼
m 0 V 2 2h2
ð53Þ
is the electrical pressure as a function of the applied voltage and membrane thickness, and m is the membrane dielectric constant. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2Eh0 1 ð54Þ ln V ¼ z z m 0 The critical membrane contraction can be derived in the manner outlined in Section II: zc ¼ expð0:5Þ 0:61
ð55Þ
which corresponds to critical membrane thinning 39%. The corresponding critical voltage, derived from Eq. (54), is sffiffiffiffiffiffiffiffi Eh0 ð56Þ Vc 0:61 0 Equation (55) illustrates the major shortcoming of the original electroelastic model; it predicts membrane thinning of almost 40%, a result vastly different from the experimental
68
Partenskii and Jordan
finding that critical thinning never exceeds 2–3%. The computed critical voltage Vc equals 3:4 V and 5:9 V for representative ‘‘soft’’ [stearoyloleoylphosphatidyl-choline (SOPC)] and rigid [SOPC-cholesterol]) (SOPC:CHOL, 1 : 1)] membranes respectively (see Table 1 for the membrane parameters). Experimentally, the characteristic critical voltage Vexper depends on the duration of the applied electrical pulse. For brief pulses, 0:01 0:1 S, Vexper 1 V, and for longer ones ( 1 S) Vexper < 0:5 V. As a result, both the extent of the membrane contraction and the breakdown voltage predicted by Crowley’s model greatly exceed the experimental values.*
2. Hydrodynamic Models An alternative description of membrane stability has been based on hydrodynamic models, originally developed for liquid films in various environments [54–56]. Rupture of the film was rationalized by the instability of symmetrical ‘‘squeezing modes’’ (SQM) related to the thickness fluctuations. In the simplest form it can be described by a condition [54] ðd 2 Vdis =dh2 Þ0 < 22 =a2 where Vdis is the interaction contribution related to the ‘‘disjoining pressure,’’y is the surface tension and a is the characteristic size of the film. At the critical film thickness h0 , defined by this condition, the free energy cost of fluctuation due to the disjoining pressure is negative and overwhelms the positive contribution due to the surface tension at the wavelength ¼ a. When this happens, there is flow in the film from the thinner to the thicker regions leading to spontaneous growth of interfacial perturbations [57]. Similar instability is caused by the electrostatic attraction due to the applied voltage [56]. Subsequently the hydrodynamic approach was extended to viscoelastic films apparently designed to imitate membranes (see Refs. 58–60, and references therein). A number of studies [58, 61–64] concluded that the SQM could be unstable in such models at small voltages with low associated thinning, consistent with the experimental results. However, as has been shown [60, 65–67], the viscoelastic models leading to instability of the SQM did not account for the elastic force normal to the membrane plane which opposes thickness
TABLE 1 Elastic Parameters for Representative Soft (SOPC) and Rigid (SOPC : CHOL, 1 : 1) Membranes (Parameters E, Kc , and H0 are Taken from Refs. 117–119, , k1 and r1 from Ref. 53) Membrane ‘‘Soft’’ ‘‘Rigid’’
E (N/m)
Kc (J)
h0 (nm)
k1
r1
0.002 0.006
0:9 1017 2:4 1017
2.8 3.4
0.014 0.0087
0.1 0.1
0.06 0.04
* The values of stretching constant E that Crowley quoted in his original paper were substantially underestimated. As a result, his estimates of Vc were in better agreement with experiment. However, zc did not depend on E and reached the same subnormal value. It must be noted that critical thinning 1 zc almost universally reaches 30–40% for various models of the elastic energy [7]. y Disjoining pressure was attributed in Ref. 54 to the combined effect of van der Waals attraction and long-range electrostatic repulsion between similarly charged membrane surfaces.
Electroelastic Instabilities
69
fluctuations. The most obvious manifestation of this neglect is the prediction of zero breakdown voltage for vanishing surface tension [61]. Thus, this approach is more appropriate for liquid systems where thickness fluctuations arise from redistribution of molecules between surface and inner regions of the film. In addition, this model is also descriptive of ‘‘colored’’ lipid films. But it is hardly appropriate for lipid bilayers where steric interaction between the hydrocarbon tails of lipid molecules provides the quasielastic force opposing the thickness fluctuations, a force which stabilizes the bilayer. After the viscoelastic model is modified to account for this force [66], the original Crowley model problem recurs; breakdown requires extensive thinning (see reference 32 in Partenskii et al. [53]). 3. The Pore Formation Model The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear fluctuations, rather than loss of stability for small (linear) fluctuations. This theory of electroporation has been intensively reviewed [68–70], and we will discuss it only briefly. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in first-order phase transitions. The idea of applying this approach to pore formation in bimolecular free films can be traced back to the work of Deryagin and Gutop [71]. It was extended to describe spontaneous rupture of lipid bilayers [72,73] and electroporation [74] (see also Ref. 70 and references therein). The energy of the membrane with a virtual water-filled pore of a radius r subject to an applied voltage V is [70,74] Wp ¼ 2r r2 0:5 CV 2 r2
ð57Þ
where is the energy per unit length along the circumference needed to form the pore, is the energy per unit area of the flat, pore-free membrane, and p 1 C0 ð58Þ C ¼ m is the approximate change of the capacitance due to the presence of the pore; C0 is the capacitance per unit area of a pore-free membrane, p and m are the permittivity of water inside the pore and of the membrane respectively. The critical pore radius, rc , and critical barrier, Wp , are both defined by minimizing Eq. (57) with respect to r: rc ¼
þ 0:5C V 2
Wp;c ¼
2 þ 0:5C V 2
ð59Þ
As has been described in Ref. 70, this approach can reasonably account for membrane electroporation, reversible and irreversible. On the other hand, a theory of the processes leading to formation of the initial (hydrophobic) pores has not yet been developed. Existing approaches to the description of the probability of pore formation, in addition to the barrier parameters , , and some others (accounting, e.g., for the possible dependence of on r), also involve parameters such as the ‘‘diffusion constant in r-space,’’ Dp , or the ‘‘attempt rate density,’’ 0 . These parameters are hard to establish from first principles. For instance, the rate of critical pore appearance, c , is described in Ref. 75 through an Arrhenius equation: c ¼ 0 Vm expðWp;c =kTÞ where Vm is the total volume of the membrane. Nucleation of a hydrophobic pore requires cooperative motion of 8 lipid molecules and 8–10 water molecules. Given that lipid
70
Partenskii and Jordan
molecules are not rigid, the corresponding entropy contribution (or the ‘‘attempt rate’’ density 0 ) is hard to quantify with precision. Estimates [75] of 0 are very approximate and vary over 9–10 orders of magnitude. Estimates of Wp;c vary from 30 to 50 kT. It is basically assumed [75] that the uncertainty in 0 is balanced by the uncertainty in the barrier, so that taken together they result in a reasonable concentration of pores. These assumptions are difficult to verify. Another concern is related to the fact that this approach ignores the role of membrane undulations. These are known to be important in membranes’ macroscopic behavior (stretching diagram, adhesion, capacitance) and as they noticeably interact with the electric field, they are likely to also contribute in the processes related to electroporation. At least one such relation is well known: at small surface tension the bending modes of membrane undulations become unstable at low voltages. In the next section we describe the membrane undulations and present a hypothesis as to their role in membrane instability. B.
The Smectic Bilayer Model (SBM) in an Electric Field
The most successful continuum description of membrane elasticity, dynamics, and thermodynamics is based on the smectic bilayer model (for examples of different versions and applications of this approach see Ref. 76–82 and references therein). We introduce this model in conjunction with the question of membrane undulations. 1. Membrane Undulations in the SBM Let U þ ðÞ and U ðÞ be z-components of the displacement of the upper (þ) and lower () membrane surfaces; is a two-dimensional radius vector in the XY plane. We express these as U ¼ u0 þ u
ð60Þ
where u0 is the displacement caused by external forces (such as electrical or mechanical stress) while u describes a nonuniform fluctuation of the membrane surface. For further analysis we decompose membrane fluctuations into a Fourier series, X u ðÞ ¼ u ðqÞ expðiqÞ ð61Þ q
(a) Elastic energy. We now treat separately the peristaltic (symmetrical, s-) and bending (antisymmetrical, a-) modes of membrane undulations, uþ s ¼ us ¼ u
uþ a ¼ ua ¼ u
ð62Þ
The elastic energy (per unit area) consists of three contributions [78–80]: 1.
Compression (stretching) energy, W1 , for which we choose Crowley’s form, Eq. (51). For small undulations this becomes W1 ¼
E ðz zÞ2 2h20 z
ð63Þ
with z z ¼ uþ u : 2. Splay (‘‘bending’’ or ‘‘curvature’’) defined by a splay constant K1 , or by a curvature elastic modulus Kc ¼ K1 h [76],
Electroelastic Instabilities
W2 ¼
3.
71
Kc 2 2 ðr uÞ 2 ?
ð64Þ
where r? ¼ @=@ is the gradient operator in the plane of the membrane. Surface tension contribution defined by a stress applied to a membrane, typically expressed as [77] W3 ¼ ðr? uÞ2 =2 þ 2 =2E
ð65Þ
where the first contribution is related to undulations and the second to elastic stretching.* (b) Interaction with the Electric Field. In most studies of the effect of an applied voltage on membranes, the model of ideal conductor ( ¼ 1) is used for the surrounding solvent. Then the membrane surface can be considered an equipotential. The solution of the Laplace equation leads to following results for the electrostatic energies of membrane undulations [56,78,88]: ( Welectr ¼ 2qjuq j pE 2
tanhðqh=2Þ
ða-modeÞ
cothðqh=2Þ
ðs-modeÞ
ð66Þ
The ‘‘ideal conductor’’ model does not account for diffuseness of the ionic distribution in the electrolyte and the corresponding ‘‘spreading’’ of the electric field with a potential drop outside the membrane. To account approximately for these effects we apply Poisson–Boltzmann theory. The results for the modes’ energies can be summarized as follows [89]: W
s;a
¼ m þ s
B2 F 2 a0 a1 h þ a0 Bs;a þ s;a s;a 2q
!
2 2 2 þ q2 2 c0 þ 2c0 c1 þ c0 Ds;a þ Ds;a 2 4
!
ð67Þ
where
* The origin of the ‘‘surface tension’’ in membranes recently became a subject of intensive discussion (see, e.g., Refs. 83–87, and references therein). To outline the problem, we note that thermodynamic ‘‘surface tension’’ in liquids is a result of molecular exchange between surface and inner volumes when a new surface is created. The corresponding free energy contribution is a result of the different surroundings of a molecule in the bulk and on the surface. In isolated bilayers, however, such exchange is impossible. Area (projected) can only change due to unfolding the bilayer’s undulations and elastically stretching the bilayer. The tension at equilibrium is zero. However, the situation can be different if area can grow due to molecular exchange with an environment. Such a situation can occur, for instance, in experiments with black lipid films, where exchange between the bilayer and the rim is possible.
72
Partenskii and Jordan
Bs;a ¼ a0 r a1 ¼ s;a
ðr 1Þ þ s;a
Ds;a ¼
Fs;a =q þ 1 1=r s;a
a0 ¼
r 1þ
r c 2 B þ Ds;a ð þ Þ ð ÞDs;a þ Bs;a c1 ¼ 0 s;a 2ð1 þ Þ 2ð1 þ Þ 4 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ m =s ¼ 1 þ rFs;a =q ¼ 2 þ q 2 ¼ rh=2
and Fs ¼ tanhðqh=2Þ
Fa ¼ cothðqh=2Þ
lD1 is the reciprocal Debye length and s is the dielectric constant of the solvent. Through most of what follows we use the ideal conductor approximation, Eq. (66). Ionic effects will be considered in Section IV.D. 2. Dispersion Equations Using Eqs. (61) and (54), and combining Eqs. (63), (64), and (65), we find ws;a ¼
Ejuq j2 fs;a ðx; zÞ h20
ð68Þ
1 xz fs ðx; zÞ ¼ þ b1 x2 þ b2 x4 þ x lnðzÞ coth z 2 xz fa ðx; zÞ ¼ x2 þ x4 þ x lnðzÞ tanh 2
ð69Þ ð70Þ
where ¼
Kc 4Eh20
¼
4E
x ¼ qh0
ð71Þ
The dimensionless constants b1 and b2 were introduced by Leikin [78]; they account for the fact that contributions from each monolayer to the bending modulus and the surface tension can differ for the two modes considered. Such effects are probably small so that b1 b2 1 [78]. We note that the electrical potential enters Eqs. (69) and (70) only through the parameter z. 3. Instability of Membrane Undulations Under an Applied Voltage (a) Bending Modes. In some sense, the bending modes of membrane undulations at long wavelengths (small x) are similar to those in simple fluids. The curvature contribution is x4 and can be neglected in this limit, while the stretching moduli (another important peculiarity of the double layers) does not manifest itself in bending. As a result, the stability condition for a-modes is similar to results for free liquid films (see, e.g., Refs. 56,65). It can be derived from Eq. (70). In the limit of small x where the membrane is especially ‘‘soft’’ and the instability is most likely to occur, fa ðx; zÞ x2 ð þ z lnðzÞ=2Þ The bending mode is stable if
ð72Þ
Electroelastic Instabilities
1 þ z lnðzÞ > 0 2
73
ð73Þ
For the physical interesting region, z 1, we find z > 1 2. Combining the last condition with Eq. (52) and using Eq. (71) we find that the a-mode becomes unstable at sffiffiffiffiffiffiffiffiffi h0 a V Vc
ð74Þ m 0 It follows from Eqs. (73) and (74) that the only stabilizing force for a-modes at long is the membrane tension, and critical voltage vanishes as ! 0. In experiments with black lipid membranes the surface tension arises from the contact of the bilayer with the bulk phase contained in the surrounding rim and is typically 0:002 N=m. Then choosing h0 3 109 m, we find Vca 0:6 V. Experimentally, the characteristic critical voltage Vexper depends on the duration of the applied electrical pulse. For brief pulses, 0:01 0:1 s, Vexper 1 V, and for longer ones ( 1 sÞ Vexper 0:5 V [90]. Further increase of leads to even smaller Vexper [see Refs. 70 and 91 for liquid membranes and Ref. 92 for bilayers with inclusions (fluid mosaic cell membranes) and references therein]. Thus the onset of BM instability is likely related to the long pulse instability. The increase of the electroporation threshold [91] is also in qualitative agreement with Eq. (74). The long- instability of bending modes does not lead directly to formation of pores because it does not affect the internal structure of the membrane. But it can possibly lead to ripping the membrane off the rim and resulting‘‘permeabilization.’’ From our viewpoint, neglect of such an instability is one of the shortcomings of the pore formation models (see the previous discussion). (b) Squeezing Modes. We now analyze Eq. (69). In the limit x ! 0, fs ! 1 þ 2 lnðzÞ. As a result, the condition of instability, fs ¼ 0, leads to Crowley’s results, Eqs. (55) and (56), derived for a plane membrane. Some softening of this condition can be expected at x 6¼ 0 because the stabilization due to electric field grows with x [the function x cothðxz=2Þ in Eq. (69) is essentially a linearly increasing function of x for x 1]. Indeed, instability is first lost at finite (for SOPC it corresponds to x 1:25 [53]). However, the corresponding reduction of Vc and zc is insignificant (for instance, Vc drops by only 5 mV [53]). C.
Nonlocal Model of Membrane Instability
It follows from previous discussion that the destabilizing electrostatic contribution grows in absolute value with x (with increasing ). But the influence of the nonuniform electrical force is overwhelmed by the stabilizing bending and stretching contributions. As a result, the traditional smectic model cannot explain how a small transmembrane voltage can lead to membrane breakdown. The obvious solution is to abandon this approach and to develop an alternative, such as the ‘‘pore formation model.’’ However, as we noticed before, this approach postulates rather than proves the appearance of hydrophobic pores. Another option is to try to modify the smectic model in order to account for the lowvoltage, low-thinning instability. It was suggested in Ref. 53 that the instability could be explained as due to s-modes if (1) the membrane moduli depended on the wavelength of fluctuations, and (2) this dependence resulted in substantial softening of s-modes at short . Condition (1) is quite common and normally is described as ‘‘nonlocality.’’ In general, nonlocality of constitutive equations means that forces acting at a point r and conjugate to a fluctuating variable s, depend not only on the value sðrÞ at r, but also on its behavior in
74
Partenskii and Jordan
more distant regions. This leads directly to a two-point integral for the energy W so that (in an harmonic approximation) ð ð75Þ W ¼ Kðr; r 0 ÞsðrÞsðr 0 Þ dr dr 0 where, depending on the property considered, the kernel Kðr; r 0 Þ depends on a nonlocal susceptibility or a nonlocal modulus. For instance, in nonlocal electrostatics, the role of K is played by ðr; r 0 Þ, the nonlocal dielectric constant, while electric field strength, EðrÞ, corresponds to sðrÞ [93–95]. In nonlocal elastic theory K is the elastic modulus Dðr; r 0 Þ and s describes displacements uðrÞ [93,96]. The local limit in a uniform systemÐcorresponds to Kðr; r 0 Þ ¼ K ðr r 0 Þ where ðrÞ is a delta-function in which case W ¼ K s2 ðrÞ dr. As long as K is a function of r r 0 (the uniformity condition), the Fourier transform of Eq. (75) is X KðqÞjsq j2 ð76Þ W¼ q
Ð where KðqÞ ¼ expðiqrÞKðrÞ dr. Thus, nonlocality can be either described through the spatial dependence of the generalized susceptibility, Kðr; r 0 Þ, or through the dependence of its Fourier transform on wave vector q. Condition (2) is also quite common. For instance, in crystals it results in a reduced sound velocity, vs ðqÞ when q approaches a boundary of the Brillouin zone [93,96], a direct result of the periodicity of a crystal lattice. In addition, interaction between modes can lead to creation of ‘‘soft mode’’ with q 6¼ 0 and corresponding structural transitions [97,98]. The importance of nonlocality at fluid interfaces and the corresponding softening of surface modes has been demonstrated recently, both theoretically [99] and experimentally [100]. In a phenomenological treatment [53] the parameters describing the nonlocal softening of the s-mode were chosen to fit the conditions that the membrane becomes unstable at voltages corresponding to low thinning, z < 3% It was also assumed that at long (small x) the mode energy approaches Eq. (69). Two approximations for the mode energies in the short- limit were suggested in Ref. 53; their effects on membrane undulations are almost identical. Here we use only one of them (see also Refs. 89,101): fsNL ðx; zÞ ¼ ½1 tðxÞ4 ðk1 þ r1 x4 Þ þ tðxÞ4 fs ðx; zÞ
ð77Þ
where tðxÞ ¼
expðsaÞ þ 1 exp½sða xÞ þ 1
ð78Þ
The parameters a and s were chosen to satisfy the conditions that the transition to the short- behavior occurs at 1:5h0 and that it is steep enough so that by ð2 3Þh0 the long- limit is quite reliable. Given that membrane thinning does not exceed 2–3%, the model parameters r1 and k1 have been selected so that the s-mode energy approaches 0 as z ! zcr ¼ 0:97. In addition, it was required that the corresponding critical wavelength, cr is of the order of h0 . This procedure is illustrated in Fig. 7. The thick curve corresponds to V ¼ 0. The thinner curve illustrates the case where the applied voltage leads to instability at cr ðx 2Þ. The membrane parameters for the local and nonlocal approximations are presented in Table 1.
Electroelastic Instabilities
75
FIG. 7 Nonlocal (dimensionless) energy fsNL ðx; zÞ of the s-mode for the transitional and short- regions at V ¼ 0 ðz ¼ 1, upper curve) and V ¼ 1:3 V (z ¼ 0:97, lower curve). (Reprinted from Ref. 53, by permission, Journal of Chemical Physics.)
D.
Elastic Nonlocality and Equilibrium Membrane Properties
It the previous section we suggested a possibility of effective softening of the s-mode as a mechanism leading to membrane breakdown. However, this phenomenological assumption requires microscopic justification. But before proceeding further, it is important to check if this assumption is consistent with the description of such equilibrium membrane properties as the membrane stretching diagram, thickness fluctuations, and the low-voltage membrane capacitance. These properties are well described in the local approximation and introduction of nonlocality should lead to similar predictions. 1. Membrane Stretching Diagram and Thickness Fluctuations It is well known that surface undulations strongly influence the stretching diagram of membranes. They are responsible for the ‘‘entropic’’ behavior, the extremely steep increase of projected area A? at small tensions. In the analysis of these phenomena based on the local model the contribution of the s-modes to A? can be neglected as it is strongly reduced due to the high values of membrane stretching constant, E. As a result, the major contribution comes from the soft long- bending modes [76]. However, the assumption of softening of the symmetrical modes made in the nonlocal model may enhance their contribution to the projected area at short and thus alter the stretching diagram. Such a possibility has been analyzed in Ref. 53. Analysis very similar to that of Ref. 77 leads to the following expression for the fractional variation ¼ A? =A of the projected area: ¼
kT 16Eh20
ð xmax xmin
x3
1 1 þ dx f2 ðx; zÞ fa ðx; zÞ
ð79Þ
Stretching diagrams calculated in local (L) [Eqs (69) and (70)] and nonlocal (NL) [with Eq. (77) instead of Eq. (69)] approximations are contrasted in Fig. 8. It can be seen from Fig. 8 that nonlocal results are in good agreement with the local approximation and, consequently, with experiment. At small tensions ( 2 104 N=m) the slope of the stretching diagram is very steep. This domain corresponds to the ‘‘nonelastic’’ or ‘‘entropic’’ region of membrane stretching. For 0ð3 4Þ103 N=m the slope is practically constant. In the intermediate region there is a sharp transition between these two regimes. Unlike local calculations, nonlocal results depend on the choice of min (or
76
Partenskii and Jordan
FIG. 8 Stretching diagram for soft (S) and rigid (R) membranes for (a) min ¼ 1:5 nm and (b) min ¼ 1:2 nm. ‘‘L’’ corresponds to the local model, while ‘‘NL’’ describes the nonlocal calculations (see text). The parameters of Table 1 are used (1 dyne=cm ¼ 103 N=m). (Reprinted from Ref. 53, by permission, Journal of Chemical Physics.)
xmax ). As a result, for the cut-off min 1 nm, close to the size of the lipid headgroups, the differences may reach 10–15%, being more significant for soft membranes. However, as noted in Ref. 53, this discrepancy might be an artifact due to the same expression, 1 A? ðqÞ ¼ A½quðqÞ2 2
ð80Þ
being used for the mode contributions in the variation of the projected area. In fact, this expression is based on the assumption that there is tilting of the lipids such that headgroups are always aligned parallel to the membrane–water interface, which is only valid at long . At short wavelengths, 1:0–2.0 nm, this condition is harder to achieve and up and down displacements of the lipids, which may consume less projected area than the parallel alignment, are the natural ones. In other words, Eq. (80) should be modified to account for the short dispersion of the projected area. Effectively, it is equivalent to an increase of min . The value 1:5–2.0 nm is a reasonable limit for the validity of the macroscopic expression, Eq. (80). Membrane thickness fluctuations were initially discussed in the local approach by Hladky and Gruen (HG) [102] in conjunction with their possible effect on membrane capacitance. They are directly related to the spectrum of s-modes: ð 2 kT xmax x dx ð81Þ ðh h0 Þ ¼ 2E xmin fs ðx; zÞ In Ref. 53 these calculations were reproduced using the nonlocal approach. Following HG, the results were contrasted for two cutoffs, min ¼ 1 nm and min ¼ 10 nm. The nonlocal results for RMS thickness fluctuations h~ ¼ hðh h0 Þ2 i1=2 are comparable in magnitude, but slightly smaller than those found by HG. However, the nonlocal model predicts that the fluctuation spectrum should peak at wavelengths 2–5 nm. Thus a
Electroelastic Instabilities
77
valuable test of the nonlocal hypothesis can come from investigating this range of fluctuations, either by means of molecular dynamics simulation or directly, by soft x-ray scattering from real membranes. 2.
Effect of Undulations on Membrane Capacitance
Initially the effect of applied voltage on membrane capacitance was attributed to the uniform electrostriction, in the manner of the elastic capacitor model [1,103]. The effect of undulations was first considered by Leikin [78]. In Ref. 89 the combined effect of undulations and uniform compression is studied, including the possible influence of nonlocality. The differential capacitance Cd is presented as C d ¼ C0d þ Cud where C0d
@h ¼ m2 0 h V @V h
ð82Þ ! ð83Þ
is the capacitance of the uniform membrane compressed by the electric field and " # ð kT X xmax 1 @2 fl ðx; zÞ @fl ðx; zÞ2 d Cu ¼ fl ðx; zÞ dx @V Ah20 l¼s;a xmin fl ðx; zÞ2 @V 2
ð84Þ
is the contribution from undulations. At comparatively small voltages (91 V) it is sufficient to use the approximation h h0 ð1 bV 2 Þ b¼ m 0 ð85Þ 2Eh0 which follows from Eq. (52). The differential capacitance can be expressed as C d ðVÞ C d ð0Þð1 þ V 2 Þ where C d ð0Þ corresponds to V ¼ 0 and parameter characterizes the effect of voltage. To compare with experiment, the integral membrane capacitance C must be defined. It is [89] 2 CðVÞ ¼ Cð0Þ 1 þ V 3 The results are presented in Table 2. TABLE 2 Voltage Variation Factor as a Function of Tension () for the Uniform Membrane, and with Undulation Included in both Local (L) and Nonlocal (NL) Approximations, for Soft/ Rigid Membranes in the Metallic Approximation, Eq. (66) ð103 N=mÞ 2 3 4 5 10
Uniform
Undulations (L)
Undulations (NL)
0.016/0.005 0.016/0.005 0.016/0.005
0.024/0.007 0.021/0.006 0.020/0.005 0.020/0.005 0.017/0.005
0.028/0.008 0.023/0.007 0.021/0.006 0.020/0.006 0.018/0.005
78
Partenskii and Jordan
In addition, the effect of ionic screening was analyzed [89] using Eqs. (67). The ionic concentrations considered (1.0 M, 0.1 M, 0.01 M) correspond to Debye lengths lD ¼ 0:3; 1 and 3 nm. The results for lD ¼ 3 nm, the most dilute electrolyte, where ionic screening is least effective, are presented in Table 3. The results can be summarized as follows: 1.
2.
3. 4.
The nonlocal results for CðVÞ are consistent with local calculations. Introducing softening of the s-modes at short only changes the undulative contribution to C by 10–15%. Electrostriction dominates the voltage dependence of membrane capacitance. However, at low tensions (94 103 N=m) the contribution of undulations is also important. The latter is in good agreement with the results of [78] if the same membrane parameters are chosen. At higher tension undulations are damped and their role becomes less significant. In rigid membranes is small; however, the relative undulatory contribution is still significant. Ionic screening has only a minor effect on the voltage dependence of the capacitance for the ionic strengths considered, 0:01 M.
Results at 0:002–0.004 N/m are found to be in good qualitative agreement with the ‘‘short pulse’’ experiments [104] with exper ranging from 0.018 to 0.036. E.
Summary
We have shown that postulating short- softening of the s-modes of membrane undulations, which can explain the low-voltage low-thinning instability, is consistent with observed equilibrium properties of membranes. This finding supports the hypothesis but obviously does not prove it. Although partially hidden in averaged thermodynamic properties such as the stretching diagram or the voltage dependence of capacitance, nonlocality can play a more important role when the influence of short-scale perturbations is significant. It can have a direct relation to the anomalous roughness of a membrane surface suggested to account for the discrepancy between calculations of the adhesion energy based on the Young equation and on the conventional (local) theory of entropic forces between the membranes [105]. Mode softening could be a reason for this roughness and for the corresponding hidden projected area [105]. This suggestion complements the hypothesis of special types of structural defects (hats and saddles) [106]. It may also be related to the finding of ‘‘remarkable out-of-plane vibrational motion’’ of lipid molecules [107] which can contribute strongly to short-range repulsive forces between membranes [108]. Another group of phenomena where short- behavior could be important is related to peptide insertion into membranes. TABLE 3 Effect of Ionic screening on the Capacitance at V ¼ 0, Cð0Þ, and on the Factor , Describing the Voltage Dependence of C, for Two Tensions, 1 ¼ 0:002 and 2 ¼ 0:01 N/m, for the Representative Soft Membranes (SOPC)
‘‘Metallic,’’ Eq. (66) lD ¼ 3 nm, Eq. (67)
C(0) (F/m)
ð1 Þ
ð2 Þ
6:4 103 5:9 103
0.028 0.028
0.018 0.017
Electroelastic Instabilities
79
Typically, the insertion induces sharp variation of the membrane profile at the distances 0.5–1.0 nm from the membrane–peptide interface [79–82]. The steepness of this perturbation indicates that the short- behavior of membrane moduli must be important in the estimates of the elastic energy. In addition, a peptide inserted in a membrane almost certainly perturbs the membrane’s elastic moduli in the immediate vicinity of the inclusion. Both these effects, membrane nonlocality and nonuniform modification of elastic properties by insertions, might play an important role in resolving the contradiction between the local calculations [80] and the experimental data for the mean lifetime of a gramicidin channel [81,109,110].* In our approach to membrane breakdown we have only taken preliminary steps. Among the phenomena still to be understood is the combined effect of electrical and mechanical stress. From the ‘‘undulational’’ point of view it is not clear how mechanical tension, which suppresses the undulations, can enhance the approach to membrane instability. Notice that pore formation models, where the release of mechanical and electrical energy is considered a driving force for the transition, provide a natural explanation for these effects [70]. The linear approach requires some modification to describe such phenomena. One suggestion is that membrane moduli should depend on both electrical and mechanical stress, which would cause an additional mode softening [111]. We hope that combining this effect with nonlocality will be illuminating. Further progress in understanding membrane instability and nonlocality requires development of microscopic theory and modeling. Analysis of membrane thickness fluctuations derived from molecular dynamics simulations can serve such a purpose. A possible difficulty with such analysis must be mentioned. In a natural environment isolated membranes assume a stressless state. However, MD modeling requires imposition of special boundary conditions corresponding to a stressed state of the membrane (see Refs. 84,87,112). This stress can interfere with the fluctuations of membrane shape and thickness, an effect that must be accounted for in analyzing data extracted from computer experiments. Other possible direct probes are optical experiments similar to studies [113] of vesicles but expanded towards shorter (20–30 A˚). Alternatively neutron spin-echo studies of stacked bilayer arrays, which can probe the 10–30 A˚ range [114], might possibly be applicable here. Finally, the x-ray grazing-incidence technique has been shown to be a powerful tool for studying short wavelength fluctuations at fluid interfaces [100]. The application of this technique to the investigation of membrane surface fluctuations can reasonably be expected in the near future [115,116].
ACKNOWLEDGMENT This work was supported by a grant from the National Institutes of Health, GM-28643.
* An assumption that continuum parameters are inappropriate at the short length scale was introduced in Ref. 109.
80
Partenskii and Jordan
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44.
J. Crowley. Biophys. J. 13:711 (1973) L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1960. W. R. Fawcett. Israel J. Chem. 18:3 (1979). R. J. Watts-Tobin. Philos. Mag. 6:133 (1961). D. C. Grahame. Chem. Rev. 41:441 (1947). D. C. Grahame. J. Am. Chem. Soc. 76:4819 (1954). M. B. Partenskii, V. Dorman, and P. C. Jordan. Int. Rev. Phys. Chem. 11:153 (1996). I. L. Cooper and J. A. Harrison. J. Electroanal. Chem. 66: 85 (1975). S. L. Marshall and B. E. Conway. J. Electroanal. Chem. 337:67 (1992). M. B. Partenskii and V. J. Feldman. J. Electroanal. Chem. 273:57 (1989). W. Schmickler. J. Electroanal. Chem. 149:15 (1983). M. B. Partenskii, Z. B. Kim, and V. J. Feldman. Sov. Phys. J. 30:907 (1987). L. Blum. J. Phys. Chem. 81:136 (1977). D. Henderson, L. Blum, and W. R. Smith. Chem. Phys. Lett. 63:381 (1979). L. Blum, J. L. Lebovitz, and D. Henderson. J. Chem. Phys. 72:4249 (1980). S. L. Carnie, D. Y. G. Chan, D. J. Mitchell, and B. W. Ninham. J. Chem. Phys. 74:1472 (1981). G. M. Torrie. J. Chem. Phys. 96:3772 (1992). D. Wei, G. M. Torrie, and G. N. Patey. J. Chem. Phys. 99:3990 (1993). D. O. Raleigh, in Electrode Processes in Solid State Iionics, Reidel Publ. Co., Dordrecht, Holland, 1976, pp. 119–146. M. B. Partenskii and L. Blum. Unpublished results, 1990. P. Attard, D. Wei, and G. N. Patey. J. Chem. Phys. 96:3767 (1992). M. B. Partenskii and P. C. Jordan. J. Chem. Phys. 99:2992 (1993). W. Schmickler and D. Henderson. Progr. Surf. Sci 22:323 (1986). V. J. Feldman, M. B. Partenskii, and M. M. Vorobjev. Prog. Surf. Sci. 23:3 (1986). A. A. Kornyshev. Electrochim. Acta 34:1829 (1989). S. Amokrane and J. P. Badiali, in Modern Aspects of Electrochemistry (B. E. Conway, J. O’M. Bockris, and R. E. White, eds.), vol. 22, Plenum Press, New York, London, 1993, pp. 1–96. S. Walbran, A. Mazzolo, J. W. Halley, and D. L. Price. J. Chem. Phys. 109: 8076 (1998). J. P. Badiali, M. Rosinberg, and J. Goodisman. J. Electroanal Chem. 143:73 (1983). J. P. Badiali, M. Rosinberg, and J. Goodisman. J. Electroanal. Chem. 150:25 (1983). J. P. Badiali, M. Rosinberg, F. Vericat, and L. Blum. J. Electroanal. Chem. 158:253 (1983). M. B. Partenskii and M. M. Vorobjev. Sov. Phys. Dokl. 29:746 (1984). V. J. Feldman, A. A. Kornyshev, and M. B. Partenskii. Solid State Commun. 53:157 (1985). J. W. Halley, B. Johnson, D. Price, and M. Schwalm. Phys. Rev. B 31:7695 (1985). V. J. Feldman, M. B., Partenskii, and A. A. Kornyshev. J. Electroanal. Chem. 237:1 (1987). J. W. Halley and D. Price. Phys. Rev. B 35:9095 (1987). Z. B. Kim, A. A. Kornyshev, and M. B. Partenskii. J. Electroanal. Chem. 265:1 (1989). V. J. Feldman, M. B. Partenskii, and M. M. Vorobjev. Electrochim. Acta 31:291 (1986). R. Parsons, in Modern Aspects of Electrochemistry (J. O’M. Bockris and B. Conway, eds.), vol. 1, Academic Press, New York, 1954, pp. 103–179. R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, London, New York, 1982, Ch. 1. C. W. McCombie, Problems in Thermodynamics and Statistical Physics (P. T. Landsberg, ed.), Pion, London, 1971, p. 459 (from [43]). P. Nikitas. J. Electroanal. Chem. 300:607 (1991). P. Nikitas. Electrochim. Acta 37:81 (1992). J. Stafiej. J. Electroanal. Chem. 351:1–27 (1993). P. Nikitas. J. Electroanal. Chem. 306:13 (1991).
Electroelastic Instabilities 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83.
84. 85. 86. 87.
81
T. Y. Tsong. Biophys. J. 41:135 (1991). S. A. Freeman, M. A. Wang, and J. C. Weaver. Biophys. J. 67:42 (1994). U. Zimmerman and G. Neil (eds.), Electromanipulation of Cells, CRC Press, 1996. A. G. Volkov, D. W. Deamer, D. L. Tanelian, and V. S. Markin, Liquid Interfaces in Chemistry and Biology, J. Wiley & Sons, New York, 1998. H. T. Tien. Adv. Mater. 2:316 (1990). M. Stelze, G. Weissmuller, and E. Sackmann. J. Phys. Chem. 97:2974 (1993). E. Sackmann. Science 271:43 (1996). B. A. Cornell, V. L. Braach-Maksvytis, L. G. King, P. D. J. Osman, B. Raguse, L. Wieczorek, and R. J. Pace. Nature 387:580 (1997). M. B. Partenskii, V. L. Dorman, and P. C. Jordan. J. Chem. Phys. 109:10361 (1998). A. Vrij. Discuss. Faraday Soc. 42:23 (1966). A. Sheludko. Adv. Colloid Interface Sci 1:391 (1967). D. H. Michael and M. E. O’Neill. J. Fluid. Mech. 41:571 (1970). C. S. Kishore, S. Salaniwal, and A. Sharma. Phys. Fluids 7:1832 (1995). D. S. Dimitrov and K. R. Jain. Biochim. Biophys. Acta 779:438 (1984). P. M. Bisch and H. Wendel. J. Chem. Phys. 83:5953 (1985). P. M. Bisch and H. Wendel. J. Chem. Phys. 83:5962 (1985). D. S. Dimitrov. J. Membr. Biol. 78:53 (1984). C. Maldarelli, R. K. Jain, I. B. Ivanov, and E. Ruckenstein. J. Colloid Interface Sci. 78:118 (1980). C. Maldarelli and R. K. Jain. J. Colloid Interface Sci. 90:233 (1982). C. Maldarelli and R. K. Jain. J. Colloid Interface Sci. 90:263 (1982). A. Steinchen, D. Gallez, and A. Sanfeld. J. Colloid Interface Sci. 85:5 (1982). D. Gallez. Biophys. Chem. 18:165 (1983). D. Gallez and A. Steinchen. J. Colloid Interface Sci. 94:296 (1983). J. C. Weaver and A. Barnett, in Guide to Electroporation and Electrofusion (D. C. Chang, B. M. Chassy, J. A. Sanders, and A. E. Sowrs, eds.), Academic Press, 1992, pp. 91–117. Y. Chizmadzhev, in Electrified Interfaces in Physics, Chemistry and Biology (R. Guidelli, ed.), Kluwer Academic Publishers, Netherlands, 1992, pp. 491–507. J. C. Weaver and Yu. A. Chizmadzhev. Biolectrochem. Bioenerg. 41:135 (1996). B. V. Deryagin and Yu. V. Gutop. Colloid J. 370 (1962). J. D. Lister. Phys. Lett. 193 (1975). C. Tsupin, M. Dvolaitzky, and C. Sauterey. Biochemistry 14:4771 (1975). I. Abidor, V. Arakelyan, L. Chernomordik, Y. A. Chizmadzhev, V. Pastushenko, and M. Tarasevich. Bioelectrochem. Bioenerg. 6:37 (1979). J. C. Weaver and R. A. Mintzer. Phys. Lett. 86A:57 (1981). W. Helfrich. Z. Naturforsch. 28c:693 (1973). W. Helfrich. Z. Naturforsch. 30c:841 (1975). S. Leikin. Biologicheskie Membrani (in Russian) 2(8):820 (1985). H. W. Huang. Biophys. J. 50:1061 (1986). P. Helfrich and E. Jakobsson. Biophys. J. 57:1075 (1990). T. A. Harroun, W. T. Heller, T. M. Weiss, L. Yang, and H. W. Huang. Biophys. J. 76:3176 (1999). S. May and A. Ben-Shaul. Biophys. J. 76:751 (1999). D. Sornette and N. Ostrowsky, in Micelles, Membranes, Microemulsions, and Monolayers (W. Gelbart, A. Ben-Shaul, and D. Roux, eds.) Springer-Verlag, New York, 1994, pp. 251–302. S.-W. Chiu, M. Clark, V. Balaji, S. Subramaniam, H. L. Scott, and E. Jakobsson. Biophys. J. 69:1230 (1995). F. Jahning. Biophys. J. 71:1348 (1996). B. Roux. Biophys. J. 71:1346 (1996). S. E. Feller and R. Pastor. Biophys. J. 71:1350 (1996).
82
Partenskii and Jordan
88. D. Andelman, in Handbook of Biological Physics (R. Lipowsky and E. Sackmann, eds.), vol. 1, Elsevier Science, Washington, D.C., 1995, pp. 603–642. 89. M. Partensky and P. Jordan. Mol. Phys. 98:193 (2000). 90. R. Benz and U. Zimmermann. Biochim. Biophys. Acta 597:637 (1980). 91. G. Troiano, L. Tung, V. Sharma, and K. Stebe. Biophys. J. 75:880 (1998). 92. J. Akinlaja and F. Sachs. Biophys. J. 75:247 (1998). 93. W. Harrison, Solid State Theory, Sinauer Associates, Sunderland, MA, 1984. 94. A. Kornyshev, in Chemical Physics of Solvation (R. Dogonadze, E. Kalman, A. Kornyshev, and J. Ulstrup, eds.), vol. C, Elsevier, Amsterdam, 1985, ch. 6. 95. P. Bopp, A. Kornyshev, and G. Sutmann. J. Chem. Phys. 109:1939 (1998). 96. N. Ashcroft and N. Mermin, Solid State Physics, Holt, Rinehart and Winston, New York, 1977. 97. M. Kaplan and B. Vekhter, Cooperative Phenomena in Jahn–Teller Crystals, Plenum Press, New York, 1995. 98. B. Strukov and A. Levaniuk, Ferroelectric Phenomena in Crystals: Physical Foundations, Springer, Berlin, New York, 1998. 99. K. Mecke and S. Dietrich. Phys. Rev. E59:6766 (1999). 100. C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant. Nature 403:871 (2000) 101. M. Partenskii and P. Jordan. Biophys. J. A54 (1999). 102. S. Hladky and D. Gruen. Biophys. J. 38:251 (1982). 103. S. White and T. Thompson. Biochim. Biophys. Acta 323:7 (1973). 104. O. Alvarez and R. Latorre. Biophys. J. 21:1 (1978) 105. W. Helfrich, in Handbook of Biological Physics. (R. Lipowsky and E. Sackmann, eds.), vol. 1, Elsevier Science, New York, 1995, pp. 691–721. 106. W. Helfrich. Liq. Crys. 5:1647 (1989). 107. E. Sackmann, in Handbook of Biological Physics (R. Lipowsky and E. Sackmann, eds.), vol. 1, Elsevier Science, Washington, DC, 1995, pp. 213–304. 108. J. N. Israelachvili and H. Wennerstroem. Langmuir 6:873 (1990). 109. C. Nielsen, M. Goulian, and O. Andersen. Biophys. J. 74:1966 (1998). 110. J. A. Lundbæk and O. Andersen. Biophys. 76:889 (1999). 111. V. Dorman, M. Partenskii, and P. Jordan. Biophys J. 72:A69 (1997). 112. R. Goetz and R. Lipowsky. J. Chem. Phys. 108:7397 (1998). 113. H. Engelhart, H. Duwe, and E. Sackmann. J. Phys. Lett. 46:395 (1985). 114. W. Pfeifer, S. Konig, L. J. F., T. Bayerl, D. Richter, and E. Sackmann. Europhys. Lett. 23:457 (1993). 115. C. Fradin, D. Luzet, A. Braslau, M. Alba, F. Muller, J. Daillant, J. Petit, and F. Rieutord. Langmuir 14:7327 (1998). 116. L. Perino-Gallice, B. Amalric, E. A. Braslau, T. Charitat, J. Daillant, G. Fragneto, and F. Graner, Colloids and Polymers (2000) (submitted). 117. D. Needham and R. M. Hochmuth. Biophys. J. 55:1001 (1989). 118. D. Needham and R. Nunn. Biophys. J. 58:997 (1990). 119. E. A. Evans and W. Rawicz. Phys. Rev. Lett. 64:2094 (1990).
4 The GvdW Theory: A Density Functional Theory of Adsorption, Surface Tension, and Screening STURE NORDHOLM Department of Chemistry, Go¨teborg University, Go¨teborg, Sweden ROBERT PENFOLD Food Materials Science Division, Institute of Food Research, Norwich, England
I.
INTRODUCTION
The debt owed to J. van der Waals for revealing the essence of fluid behavior in his famous analysis of the binding energy and excluded volume mechanisms [1,2] is widely recognized as enormous. Less known is the fact that van der Waals also extended his theory to nonuniform fluids [3]. This work was a beginning of the development of so-called density functional theories which have only recently gained prominence in both quantum chemistry [4,5] and statistical mechanics [6,7]. Here we shall review the origin of the generalized van der Waals (GvdW) theory with the aim to show that the remarkable accuracy of simple mechanistic analysis applies also to a wide range of nonuniform fluid phenomena such as adsorption, surface tension, and electrolyte screening. Thus the traditional equation of state of van der Waals as well as the Debye–Hu¨ckel and Poisson–Boltzmann theories of electrolyte screening are simple special cases of the GvdW theory which unify and considerably extend these well-known traditional approximations to account, in particular, for nonlocal entropy and short-range packing structure. The key idea of the GvdW theory is a greatly simplified treatment of correlations in the fluid. Note that if there were no interactions then the ideal gas partition function would be a sum over all possible configurations of the fluid. In a realistic interacting fluid these configurations would occur with a weighting factor for each. This weighting factor would reflect the potential energy VðRÞ associated with the configuration R through the Boltzmann factor exp½VðRÞ. This innocent-looking weighting factor introduces enormous complexity which will continue to be the subject of analysis and approximation in liquid state theory for all the foreseeable future. van der Waals introduced the idea that for bulk fluids the weighting factor be allowed only two possible values, 0 or 1. In this way the ensemble of configurations and weights was dramatically simplified. The configurations which showed overlap between hard repulsive parts of the pair potentials acting between the particles were simply eliminated by the so-called ‘‘excluded volume effect.’’ The average potential energy was then calculated by the mean field approximation, i.e., over the truncated but otherwise unweighted ensemble of configurations. In this way entropy, internal energy, and free energy could be obtained by greatly simplified calculations. 83
84
Nordholm and Penfold
This approach certainly does not always yield thermodynamic properties of high accuracy. It is, however, uniquely well suited to the treatment of simple fluids. We shall see that it works very well for Lennard–Jones models of simple fluids which have quite shortrange interactions. It also works very well, in principle better, for primitive models of electrolyte solutions. We are able by this GvdW theory to resolve both short-range packing structure at hard walls and long-range screening mechanisms in electrolyte solutions. We feel therefore that this theory should be of great utility in the field of electrochemistry where both short-range fluid properties and long-range electrolyte screening mechanisms meet and mingle. Perhaps the greatest advantage of the theory is that it retains great simplicity, while offering generality and numerical efficiency through the variational nature of the density functional formulation. Thus, it need not remain in the hands of a few specialists but will, hopefully, be useful for nearly any practitioner of chemistry.
II.
THE VAN DER WAALS LEGACY: GENERALIZED
Every chemist knows the van der Waals equation of state, P¼
kB T a 2 v v0 v
ð1Þ
In it the pressure P is found in terms of temperature T and volume per particle v. The interactions enter through two parameters: v0 , the excluded volume per particle, and a, the binding energy per particle at unity density in a bulk fluid. The equation of state arose as an extension of the ideal gas law, P¼
kB T v
ð2Þ
It was assumed that the volume V was reduced by the presence of ‘‘other particles’’ to the free volume V Nv0 where N is the number of particles. In arriving at the binding energy effect the mean field approximation was used, which says that the soft (negative) part of the pair potential was sampled in an uncorrelated manner as if the system was an ideal gas. The corresponding free energy per particle in the bulk fluid is n ð3Þ f ¼ 3kB T ln þ kB T ln kB T an 1 nv0 where is the thermal wavelength which does not depend on volume and n is the particle density N=V. The third term on the RHS, kB T, is the so-called communal entropy term which reflects the large density fluctuations in the bulk ideal gas. If we instead restrict the ideal gas particles to singly occupied cells, each of volume v ¼ V=N, then the communal entropy term disappears and we get n fc ¼ kB T ln an ð4Þ 1 nv0 Here we have limited ourselves to the configurational free energy per particle fc , i.e., we have omitted the kinetic part which in classical statistical mechanics just yields the first term 3kB T ln . The first minor generalization of van der Waals’ original derivation is the omission of the communal entropy. We will be dealing with interacting, often dense, fluids which do not display the same density fluctuations as do the corresponding ideal gases.
The GvdW Theory
85
Thus we prefer to make the cell model our reference for density fluctuations. Density fluctuations are thereby truncated but in a well-defined way open to correction. The second generalization is the reinterpretation of the excluded volume per particle v0 . Realizing that only binary collisions are likely in a low-density gas, van der Waals suggested the value 2 3 =2 for hard spheres of diameter and for particles which were modeled as hard spheres with attractive tails. Thus, for the Lennard–Jones fluid where the pair potential actually is " # 12 6 ð5Þ
ðrÞ ¼ 4 12 6 r r the interaction is typically approximated as a hard sphere potential for r < . The estimate of van der Waals is chosen to give the correct second virial coefficient B2 ðTÞ at low densities. At higher densities the excluded volume per particle decreases due to the overlap of excluded volume spheres centered on each particle. Thus the effective excluded volume v0 is density dependent and it decreases monotonically with density. If we are to treat a wide range of fluid densities it is then better to determine a constant excluded volume v0 in the high-density limit. In fact, in the simplest form of GvdW theory denoted GvdW(S) [8], v0 is taken to be 3 to give the pressure divergence at the close packing limit in the simple cubic crystal structure. We shall use the Lennard–Jones fluid as the illustrative example as we review the GvdW theory. In the GvdW(S) theory the equation of state is just like the vdW equation of state above with the parameters given by v0 ¼ 3 and a ¼ 16 3 =9. This equation of state works moderately well. However, we do not wish to deal only with bulk thermodynamic properties. We wish to treat surface tension and adsorption, screening phenomena in electrolyte solutions, etc. To do this we need a free energy density functional, i.e., an expression for the configurational free energy as a function of the particle density which is now considered to be a function of position. If all particle–particle interactions were local in the fluid then the functional would have been of the form ð ð ð6Þ Fc ¼ drnðrÞfc ðnðrÞÞ þ drnðrÞVext ðrÞ where fc ðnÞ is the free energy per particle in the corresponding bulk fluid. Here Vext ðrÞ is an external potential. This type of fully local potential has some limited use, e.g., to consider adsorption in a slowly varying external potential. It fails, however, to describe the most important phenomena such as surface tension and adsorption at most types of interfaces. These phenomena reflect in a fundamental way the nonlocal interactions in the fluid. The most obvious nonlocality of the free energy arises due to the range of the attractive or soft interactions represented by the second term in the equation of state, a=v2 . The corresponding potential energy can be obtained by the functional ð ð 1 drnðrÞ dr 0 nðr 0 Þ s ðr; r 0 Þ EV ¼ ð7Þ 2 Here s is the soft and normally attractive part of the pair potential. This simple bilinear form of functional lacks correlation effects except that which is introduced by the truncation of the integral at the onset of the inner hard part of the potential. We are then using an extended form of the mean field approximation as did van der Waals in his original
86
Nordholm and Penfold
work. We can now write down the first truly useful free energy density functional in the form ð ð ð ð nðrÞ 1 drnðrÞ dr 0 nðr 0 Þ s ðr; r 0 Þ þ drVext ðrÞ þ ð8Þ Fc ¼ kB T drnðrÞ ln 1 nðrÞv0 2 This type of functional, which we refer to as ‘‘coarse-grained,’’ can be used to calculate both surface tension and adsorption isotherms to quite good accuracy for many fluids and interfaces. It can also be used for screening problems in the theory of electrolytes. We shall illustrate the applicability of the GvdW(S) functional above by considering the case of gas–liquid surface tension for the Lennard–Jones fluid. This will also introduce the variational principle by which equilibrium properties are most efficiently found in a density functional theory. Suppose we assume the profile to be of step function shape, i.e., changing abruptly from liquid to gas density at a plane. In this case the binding energy integrals in EV can be done analytically and we get for the surface tension [9] ¼
3 4 27 ðnl ng Þ2 ¼ aðnl ng Þ2 4 64
ð9Þ
This expression is not particularly accurate, as shown in Fig. 1, but it tells a large part of the story of surface tension. It arises predominantly due to the loss of binding energy of the liquid-phase particles at the interface. It is roughly proportional to the product of the binding energy constant a and the range of the attractions . It is also in this approximation proportional to the square of the density difference nl ng . We shall see, however, that this proportionality is more nearly to the fourth power of the density difference. A more accurate result can be obtained by allowing the density profile at the interface to relax. The optimal profile is the one which minimizes the free energy. The surface tension is computed by first calculating the free energy for the interface (over a sufficiently wide slice of the liquid and gas phases) and then subtracting the corresponding free energy obtained from the fully local functional. The fully optimized profile can be obtained by iteratively refining it point by point to yield the best possible shape, i.e., that corresponding to the lowest free energy. More conveniently, and very nearly as accurately, we can
FIG. 1 The calculated surface tension of an argon fluid represented as a Lennard–Jones fluid is shown as a function of temperature. The GvdW(HS-B2 )-functional is used in all cases. The filled squares correspond to step function profile and local entropy, the filled circles to tanh profile with local entropy, and the open circles to tanh profile with nonlocal entropy. The latter data are in good agreement with experiment.
The GvdW Theory
87
choose a plausible profile shape with a width parameter and then find the optimal value. A favored profile shape is the tanh profile, n l ng nðxÞ ¼ ng þ ð10Þ 1 þ expðxÞ The corresponding result for the surface tension [9] provides quite reasonable accuracy for a Lennard–Jones fluid or an inert gas fluid, except helium which displays large quantum effects. Thus we can conclude that the leading mechanisms of surface tension in a simple fluid is the loss of binding energy of the liquid phase at the gas–liquid interface and the second most important mechanism is likely to be the adsorption–depletion at the interface which creates a molecularly smooth density profile instead of an abrupt step in the density. The next most important mechanism affecting the surface tension at a single component simple fluid gas–liquid interface is, we believe, associated with the nonlocality of the repulsive interactions. To account for this mechanism, observe that it enters by way of the excluded volume effect. In the coarse-grained GvdW(S) theory above, the free volume factor ðrÞ is given by ðrÞ ¼ 1 nðrÞ 3
ð11Þ
for a Lennard–Jones fluid. The role of the density in this expression is to describe the number of other particles within repulsive range. If the particle density is varying significantly on the length scale then the local particle density nðrÞ should clearly be replaced by some nonlocal average. The natural domain for such an average is the sphere of radius , the range of the hard repulsion, centered on the location of our test particle at r. Thus, we get in the so-called ‘‘fine-grained’’ GvdW(S) theory [10] ðrÞ ¼ 1 n ðrÞ 3 where n ðrÞ is the coarse-grained particle density defined by ð 3 dsn ðsÞ n ðrÞ ¼ 4 3 jrsj 0. Even in the absence of externally applied potential, are not surface active when W O
0:4 V, depending on the ionic the distribution potential can vary between 0:4 W O
FIG. 5 Electrocapillary curves for the interface between aqueous solution of 0.05 mol dm3 LiCl and nitrobenzene solution of 0:1 x mol dm3 tetrapentylammonium tetraphenylborate þ x mol dm3 hexadecyltrimethylammonium tetraphenylborate at 25 C: x ¼ 0 (*), 0.005 (~), 0.02 (&), 0.05 (*), and 0.1 (~). (From Ref. 39, reproduced by permission. The Chemical Society of Japan.)
116
Kakiuchi
species involved [42]. The observed marked dependence of the surface activity on W O
may therefore be of considerable importance in understanding the surface activity of ionic components in actual systems, e.g., microemulsion and vesicles. The interaction between the adsorbed molecules and a chemical species present in the opposite side of the interface is clearly seen in the effect of the counterion species on the HTMAþ adsorption. Electrocapillary curves in Fig. 6 show that the interfacial tension at a given potential in the presence of the HTMAþ ion adsorption depends on the anionic species in the aqueous side of the interface and decreases in the order, F , Cl , and Br [40]. By changing the counterions from F to Cl or Br , the adsorption free energy of HTMAþ increase by 1.2 or 4.6 kJ mol1 . This greater effect of Br ions is in harmony with the results obtained at the air–water interface [43]. We note that this effect of the counterion species from the opposite side of the interface does not necessarily mean the interfacial ion-pair formation, which seems to suppose the presence of salt formation at the boundary layer [44–46]. A thermodynamic criterion of the interfacial ion-pair formation has been discussed in detail [40]. Another interesting example of the interaction of adsorbates with ions belonging to the opposite side of the interface is the adsorption of nonionic surfactants having an oligo(ethylene glycol) unit as a hydrophilic group. Figure 7 shows the electrocapillary curves for the adsorption of tetra(ethylene glycol) mono-n-dodecyl ether (C12E4) at the nitrobenzene–water interface [47]. Unlike ionic surfactants, the interfacial tension is lowered over the entire range of the potential window. However, the adsorbed amount of this
FIG. 6 Comparison of electrocapillary curves for the interface between nitrobenzene solution of 0.1 mol dm3 hexadecyltrimethylammonium tetraphenylborate and aqueous solution of 0.05 mol dm3 LiF (*), LiCl (~), and LiBr (&). (From Ref. 40, reproduced by permission. The Chemical Society of Japan.)
Adsorption at Polarized Liquid–Liquid Interfaces
117
FIG. 7 Electrocapillary curves at 25 C for the interface between nitrobenzene solution of 0.1 mol dm3 tetrapentylammonium tetraphenylborate and aqueous solution of 0.5 mol dm3 LiCl in the presence of x mmol dm3 C12E4: x ¼ 0 (curve 1), 1 (curve 2), 2 (curve 3), 5 (curve 4), 7 (curve 5), 10 (curve 6), 15 (curve 7), 20 (curve 8), 30 (curve 9), 40 (curve 10), 50 (curve 11), 70 (curve 12), 80 (curve 13), and 100 (curve 14). (From Ref. 47, reproduced by permission. The Chemical Society of Japan.)
surfactant shows a pronounced dependence on the phase-boundary potential as shown in Fig. 8. This dependence is caused by the interaction of the tetraethylene glycol unit of adsorbed C12E4 from the nitrobenzene side with Liþ ions at the interface. As W O is made more positive, the surface concentration of Liþ ions in the aqueous solution side of the interface increases, which favors the interaction of the tetraethylene glycol unit and Liþ ions. By using the Gouy–Chapman theory for the dependence of the surface concentration of Liþ ions, the observed dependence of the adsorption of C12E4 is satisfactorily explained [48]. Recent studies of complex formation reactions between calix[4]arene in 1,2-dichroloethane and divalent cations in water using a pendant drop method [49] and a Langmuir–Blodgett monolayers [50] have shown the importance of the surface process in the heterogeneous environment. Since poly(oxyethylene)-type nonionic surfactants have a capability of facilitating the transfer of cations [51,52], the above interphase complexation may be seen as an example of precomplex formation before the bulk transfer of ions, which is seen when W O
is sufficiently positive. The presence of such precomplex formation at the interface, which is detectable voltammetrically [53], may have significance in the rate of complex formation and the selectivity in the bulk facilitated transfer. B.
Electrochemical Techniques
Among a few electrochemical techniques available for studying the adsorption, the AC impedance technique has been most widely employed. Its high sensitivity to the physico-
118
Kakiuchi
FIG. 8 Dependence of the adsorbed amount of C12E4 on the applied potential. Concentration of C12E4 in nitrobenzene is 50 (curve 1), 20 (curve 2), 10 (curve 3), and 5 (curve 4) mmol dm3 . (From Ref. 47, reproduced by permission. The Chemical Society of Japan.)
chemical state of the liquid–liquid interface in addition to its ease of measurements, makes the double layer capacitance a particularly attractive probe for studying the adsorption at polarized liquid–liquid interfaces. The capacitance measurements have been employed for studying the adsorption of phospholipids [54–54] and other surfactants [57] at the polarized oil–water interface. The capacitance is sensitive enough to detect the phase transition of adsorbed phospholipid monolayers [58,59]. Cyclic voltammetry can also be employed to assess the magnitude of double layer capacitance [60]. Potential-step measurements using a micropipet have been used for evaluating the capacitance of and the transfer across a phospholipid monolayer [61]. Phospholipids are adsorbed at the nitrobenzene–water interface from the nitrobenzene solution side. The interaction of adsorbed dipalmitoylphosphatidylserine and Ca2þ or Mg2þ causes a dramatic effect in the state of the monolayer; the critical concentration was found to be 2 mmol dm3 for both Ca2þ and Mr2þ ions to cause the phase transition of the monolayer from a liquid-expanded to a condensed state, demonstrating the importance of the interphase electrostatic interactions [56]. This phase transition caused by the interphase interaction was utilized for detecting the interfacial enzymatic hydrolysis of phosphatidylcholine monolayer by phospholipase D at the nitrobenzene–water interface, using the fact that adsorbed phosphatidates, a product of hydrolysis, form a solid monolayer in the presence of divalent cations in W [62,63]. Interfacial hydrolysis itself is a good example of the interphase reaction, or a liquid–liquid two-phase biocatalysis, where the heterogeneous environment created by the interface plays a significant role in characterizing the chemical processes. For example, the effect of the surface charge density on the rate of hydrolysis has been quantitatively estimated [63,64].
Adsorption at Polarized Liquid–Liquid Interfaces
IV.
119
CONCLUSIONS
The interphase interactions inferred from macroscopic approaches introduced above have raised many intriguing questions, which wait microscopic interpretation and evidence at a molecular level. Among several possible techniques, e.g., FT-IR, x-ray and neutron scattering, surface second-harmonic generation and sum-frequency generation are promising [65–68] and have already provided valuable information about molecular orientation at liquid–liquid interfaces [69–72]. Such microscopic studies and theoretical modeling in parallel with thermodynamic approaches will allow us to have an integrated view and understanding of interfacial properties and processes at liquid–liquid interfaces.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
R. B. Gennis, Biomembranes – Molecular Structure and Function, Springer-Verlag, New York, 1994. B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell, 3rd edn, Garland, New York, 1994. C. Tanford, Ben Franklin Stilled the Waves, Duke University Press, Durham, 1989. K. J. Laidler, The World of Physical Chemistry, Oxford University Press, Oxford, 1993. R. G. Linford. Chem. Rev. 78:81 (1978). J. Lipkowski, W. Schmickler, D. M. Kolb, and R. Parsons. J. Electroanal. Chem. 452:193 (1998). J. Lipkowski and P. N. Ross (eds.), Imaging of Surfaces and Interfaces, Wiley-VCH, New York, 1999. J. Koryta. Electrochim. Acta 24:293 (1979). J Koryta. Ion-Selective Electrode Rev. 5:131 (1983). J. Koryta. Electrochim. Acta 29:445 (1984). P. Vanysck, Electrochemistry at Liquid–Liquid Interfaces, Springer-Verlag, Berlin, 1985. J. Koryta. Electrochim. Acta 32:419 (1987). V. E. Kazarinov (ed.), The Interface Structure and Electrochemical Processes at the Boundary Between Two Immiscible Liquids, Springer-Verlag, Berlin, 1987. J. Koryta. Electrochim. Acta 33:189 (1988). Z. Samec. Chem. Rev. 88:617 (1988). H. H. Girault and D. J. Schiffrin, in Electroanalytical Chemistry (A. J. Bard, ed.), Marcel Dekker, New York, 1989, vol. 15, ch. 1. M. Senda, T. Kakiuchi, and T. Osakai. Electrochim. Acta 36:253 (1991). H. H. Girault, in Modern Aspects of Electrochemistry (R. E. White, B. E. Conway, and J. O. Bockris, eds.), Plenum, New York, 1993, vol. 25, p. 1. Z. Samec and T. Kakiuchi, in Advances in Electrochemistry and Electrochemical Science (H. Gerischer and C. W. Tobias, eds.), VCH, Weinheim, 1995, vol. 4, pp. 297–361. A. G. Volkov and D. W. Deamer, Liquid–Liquid Interfaces: Theory and Methods, CRC Press, Boca Raton, 1996. A. G. Volkov, D. W. Deamer, D. L. Tanelian, and V. S. Markin, Liquid Interfaces in Chemistry and Biology, Wiley-Interscience, New York, 1998. F. C. Goodrich and A. I. Rusanov (eds.), The Modern Theory of Capillarity, Akademie-Verlag, Berlin, 1981. V. S. Markin and A. G. Volkov, in Liquid–Liquid Interfaces: Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, p. 63. A. G. Volkov, D. W. Deamer, D. L. Tanelian, and V. S. Markin, in Liquid Interfaces in Chemistry and Biology, Wiley-Interscience, New York, 1998, ch. 3.
120
Kakiuchi
25. J. T. Davies and E. K. Rideal, in Interfacial Phenomena, 2nd edn, Academic Press, New York, 1963, ch. 2. 26. R. Parsons, in Modern Aspects of Electrochemistry (J. O’M Bockris and B. Conway, eds.), Butterworths, London, 1954, vol. 1, p. 103. 27. D. M. Mohilner, in Electroanalytical Chemistry (A. J. Bard, ed.), Marcel Dekker, New York, 1966, vol. 1, p. 331. 28. T. Kakiuchi and M. Senda. Bull. Chem. Soc. Jpn. 56:1753 (1983). 29. A. G. Volkov, D. W. Deamer, D. L. Tanelian, and V. S. Markin, in Progress in Surface Science (S. G. Davison, ed.), Pergamon, Oxford, 1996, vol. 53, pp. 1–134. 30. T. Kakiuchi, M. Nakanishi, and M. Senda. Bull. Chem. Soc. Jpn. 62:403 (1989). 31. T. Kakiuchi and M. Senda. Bull. Chem. Soc. Jpn. 56:1322 (1983). 32. J. E. B. Randles, in Advances in Electrochemistry and Electrochemical Engineering (P. Delahay and C. W. Tobias, eds.), Interscience, New York, 1963, vol. 3, p. 1. 33. Markin, V. S. and A. G. Volkov, in Liquid–Liquid Interface: Theory and Methods, (A. G. Volkov and D. Deamer, Eds.), CRC Press, Boca Raton, 1996, ch. 4. 34. A. G. Volkov, D. W. Deamer, D. L. Tanelian, and V. S. Markin, in Liquid Interfaces in Chemistry and Biology, Wiley-Interscience, New York, 1998, ch. 7. 35. T. Kakiuchi, in Liquid–Liquid Interfaces: Theory and Methods (A. G. Volkov and D. Deamer, eds.), CRC Press, Boca Raton, 1996. 36. J. T. Davies and E. K. Rideal, in Interfacial Phenomena, 2nd edn, Academic Press, New York, 1963, ch. 8. 37. D. C. Grahame. J. Am. Chem. Soc. 80:4201 (1958). 38. B. B. Damaskin, O. A. Petrii, and V. V. Batrakov, Adsorption of Organic Compounds on Electrodes. Plenum Press, New York, 1971. 39. T. Kakiuchi, T. Kobayashi, and M. Senda. Bull. Chem. Soc. Jpn. 60:3109 (1987). 40. T. Kakiuchi, T. Kobayashi, and M. Senda. Bull. Chem. Soc. Jpn. 61:1545 (1988). 41. C. Gavach, P. Seta, and B. d’Epenoux. J. Electroanal. Chem. 83:225 (1977). 42. L. Q. Hung. J. Electroanal. Chem. Interfacial Electrochem. 115:159 (1980). 43. E. D. Goddard, O. Kao, and H. C. Kung. J. Colloid Interface Sci. 27:616 (1968). 44. H. H. Girault and D. J. Schiffrin. J. Electroanal. Chem. 170:127 (1984). 45. C. M. Pereira, A. Martins, M. Rocha, C. J. Silva, and F. Silva. J. Chem. Soc. Faraday Trans. 90:143 (1994). 46. A. K. Kontturi, K. Kontturi, J. A. Manzanares, S. Mafe´, and L. Murtoma¨ki. Ber. Bunsenges. Phys. Chem. 99:1131 (1995). 47. T. Kakiuchi, T. Usui, and M. Senda. Bull. Chem. Soc. Jpn. 63:2044 (1990). 48. T. Kakiuchi, T. Usui, and M. Senda. Bull. Chem. Soc. Jpn. 63:3264 (1990). 49. V. Marec˘ek, A. Lhotsky´, and. Electrochim. Acta 44:155 (1998). 50. H. Ja¨nchenova, A. Lhotsky´, K. Holub, and I. Stibor. Electrochim. Acta 44:155 (1998). 51. Z. Yoshida, and S. Kihara. J. Electroanal. Chem. 227:171 (1987). 52. T. Kakiuchi. J. Electroanal. Chem. 345:191 (1993). 53. T. Kakiuchi. J. Colloid Interface Sci. 156:406 (1993). 54. T. Kakiuchi, M. Yamane, T. Osakai, and M. Senda. Bull. Chem. Soc. Jpn. 60:4223 (1987). 55. T. Wandlowski, S. Rac˘insky´,, V. Marec˘ek, and Z. Samec. J. Electroanal. Chem. 227:281 (1987). 56. T. Kakiuchi, T. Kondo, and M. Senda. Bull. Chem. Soc. Jpn. 63:3270 (1990). 57. T. Kakiuchi, Y. Teranishi, and K. Niki. Electrochim. Acta 40:2869 (1995). 58. T. Kakiuchi, M. Kotani, J. Noguchi, M. Nakanishi, and M. Senda. J. Colloid Interface Sci. 149:279 (1992). 59. T. Kakiuchi, T. Kondo, M. Kotani, and M. Senda. Langmuir 8:169 (1992). 60. V. Cunnane, D. J. Schiffrin, M. Fleischmann, G. Geblewicz, and D. Williams. J. Electroanal. Chem. 243:455 (1988). 61. A. K. Kontturi, K. Kontturi, L. Murtoma¨ki, B. Quinn, and V. Cunnane. J. Electroanal. Chem. 424:69 (1997). 62. T. Kondo, T. Kakiuchi, and M. Senda. Biochim. Biophys. Acta 1124:1 (1992).
Adsorption at Polarized Liquid–Liquid Interfaces 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73.
121
T. Kondo and T. Kakiuchi. Bioelectrochem. Bioenerg. 34:93 (1994). T. Kondo and T. Kakiuchi. Bioelectrochem. Bioenerg. 36:53 (1995). K. B. Eisenthal. Acc. Chem. Res. 26:636 (1993). R. M. Corn and D. A. Higgins. Chem. Rev. 94:107 (1994). P. F. Brevet and H. H. Girault, in Liquid–Liquid Interfaces: Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, p. 103. P. F. Brevet. Surface Second Harmonic Generation, Press Polytech. Univ. Romandes, Lausanne, 1997. D. A. Higgins and R. M. Corn. J. Phys. Chem. 97:489 (1993). J. C. Conboy and G. L. Richmond. J. Phys. Chem. B. 101:983 (1997). R. A. Walker, J. A. Gruetzmacher, and G. L. Richmond. J. Am. Chem. Soc. 120:6991 (1998). P. B. Miranda and Y. R. Shen. J. Phys. Chem. B. 103:3293 (1999). T. Kakiuchi, in preparation.
6 Nonlinear Optics at Liquid^Liquid Interfaces PIERRE-FRANCOIS BREVET Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland
I.
INTRODUCTION
Processes at interfaces are ubiquitous in nature. They occur in respiration or photosynthesis reactions, for example, and one of the elementary steps in these mechanisms often involves the transfer of charged species across the interface. As a result, any experimental studies attached to the investigation of these transfer reactions entail the development of a surface sensitive technique. For charged species transfer reactions, the methodology of choice has long been derived from standard electrochemistry, since the transfer of a charged particle across an interface gives rise to a current which is amenable to detection by conventional electrochemical techniques [1]. The field of liquid–liquid electrochemistry has greatly benefited from these general ideas [2–4]. A major drawback of this approach, though, is that the distinction between the different transferring species is not an easy matter. This is an important problem in many aspects relevant to biological processes, as the transfer of an electron across the interface is often coupled to the simultaneous transfer of an ion. More selective techniques have been devised, and the most successful rely on spectroscopy principles. Indeed, the signature of a transferring species may be obtained from its absorption or emission spectrum and therefore UV-visible absorption and fluorescence spectroscopy have been employed extensively [5–10]. The use of other techniques like resonance Raman spectroscopy has also been reported [11,12]. Nevertheless, linear optical techniques have no intrinsic surface specificity and therefore require an optimized optical configuration to gain surface specificity. The geometry of choice in this case is the total internal reflection (TIR) geometry whereby the light impinges onto the interface from the medium of highest refractive index n1 , usually the organic phase, with an angle of incidence larger than the critical angle given by arcsinðn2 =n1 Þ. The electromagnetic wave present in the low-index phase (index n2 ) is thus an evanescent wave for which the penetration depth is only of the order of 100 nm. This depth is only a fraction of the diffusion layer in mass transport limited processes but is still far greater than the Debye screening length and therefore precludes any studies addressing the problem of adsorption or double layer effects at interfaces. This is clearly a major limitation, circumvented only on rare occasions [13,14]. This problem has led to the development of nonlinear optical techniques that do have a much more reduced probing depth at the interface owing to symmetry rules. The simplest nonlinear techniques are the three wave mixing techniques, namely sum 123
124
Brevet
frequency and difference frequency generation (respectively SFG and DFG) whereby two fundamental photons of frequency !1 and !2 are converted into one photon at the frequency !1 þ !2 in SFG or !1 !2 in DFG [15]. In the simple case where a single fundamental frequency is used, two photons at the frequency ! are converted into one photon at the frequency 2!. The technique is called second harmonic generation (SHG) and is probably the one that is the most widely used because of the simplicity of the experimental arrangement. Although originally applied in surface science to study molecular adsorption on clean surfaces under high-vacuum conditions, the field has rapidly expanded to other domains [16,17]. The first study of liquid–liquid interfaces has been reported by S. G. Grubb et al. in 1988 for the orientation of compounds at the water–carbon tetrachloride interface [18]. Subsequently, the structure and the dynamics of liquid interfaces have been the focus of interest and the problem of charge transfer reactions across the polarized liquid–liquid interfaces has only been addressed recently [19,20]. The present review intends to cover the work reported on nonlinear optics at liquid– liquid interface since the first report of S. G. Grubb et al. [18]. The theoretical aspects of nonlinear optics are first introduced in Section II. The experimental results covering the molecular structure of liquid interfaces are presented in Section III, followed by a section devoted to the dynamics and the reactivity at these interfaces. Section V focuses on new aspects where spherical interfaces with radii of curvature of the order of the wavelength of light are investigated. Section VI presents the field of SFG.
II.
THEORETICAL APPROACHES
A.
General Theoretical Framework
The problem is restricted in this section to SHG only and hence to a single monochromatic electromagnetic wave impinging at the interface between two dielectric media. This is the general framework describing SHG at both air–liquid and liquid–liquid interfaces. The light source is taken as a well-defined monochromatic harmonic plane wave and is characterized by its wave vector kð!Þ and its electric field vector Eð!Þ. On impinging at the interface between the two media from medium 1, the wave is refracted into medium 2 and reflected back into medium 1 according to the usual laws of linear optics (see Fig. 1) [21]. In particular, the Snell–Descartes law holds for the angles of incidence, reflection, and refraction at the fundamental frequency. The fundamental electromagnetic wave induces a polarization wave in the medium while traveling, as a result of the action of the electric field Eð!Þ on all the particles constituting the dielectric medium. At optical frequencies ranging between 1013 and 1015 Hz, only the electronic motion is of interest and the polarization is reduced to its electronic part. In most cases, one can assume that the polarization oscillates at the exciting frequency. However, for large field amplitudes, one has to include the nonlinear components oscillating at harmonic frequencies owing to the nonlinear response of the electrons of the material to the excitation field. The first-order nonlinear contribution varies quadratically with the excitation field and therefore contains a contribution oscillating at the second harmonic frequency of the exciting field. Introducing the electronic susceptibility tensor ð2Þ ð2!; !; !Þ characterizing the materials, this component is given by [15,22]: P NL ð2!Þ ¼ 0 K ð2Þ ð2!; !; !Þð2Þ ð2!; !; !Þ : Eð!ÞEð!Þ
ð1Þ
Nonlinear Optics at Liquid–Liquid Interfaces
125
FIG. 1 Geometry for the SHG process at the interface between two centrosymmetrical materials. The nonlinear polarization is a sheet of polarization in the plane of the interface located at the origin of the Z axis.
where 0 is the vacuum permittivity. The quantity K ð2Þ ð2!; !; !Þ arises from the definition of the polarization and accounts in particular for the degeneration of the fundamental electric field. For SHG, K ð2Þ ð2!; !; !Þ ¼ 1=4, but for SFG, K ð2Þ ð2!; !; !Þ ¼ 1=2 [22,23]. Solving the wave equation in the medium, it appears that the component of the nonlinear polarization as given in Eq. (1) acts as a source for an electromagnetic wave propagating at twice the fundamental frequency within the medium. The properties of the nonlinear polarization source induced in the medium are found in the susceptibility tensor ð2Þ ð2!; !; !Þ that possesses the symmetry properties of the material it describes. In particular, for liquids, the susceptibility tensor possesses the property of inversion symmetry. This symmetry operation transforms the co-ordinates (x; y; z) of any point in the medium into the co-ordinates (x; y; z). As a result, dropping the frequency dependencies for clarity, the nonlinear polarization is transformed as: P NL ¼ 0 K ð2Þ ð2Þ EE ¼ 0 K ð2Þ ð2Þ ðEÞðEÞ ¼ P NL
ð2Þ
using the inversion symmetry operation on the vectors, a relationship only fulfilled if the susceptibility tensor ð2Þ ð2!; !; !Þ vanishes altogether. This property for the susceptibility tensor describing liquids is the origin of the surface specificity of the SHG process at the interface between two centrosymmetrical media [24–26]. For liquids, the susceptibility tensor vanishes except at interfaces where the inversion symmetry operation transforms any point in Liquid 1 into a point in Liquid 2. The nonvanishing surface tensor, written as ð2Þ S ð2!; !; !Þ with a subscript, still possesses the remaining symmetry properties of the interface and in particular the isotropy within the surface plane. As a result, from the ð2Þ initial 27 S;IJK components, only four survive, three only being independent: ð2Þ ð2Þ ð2Þ ð2Þ , and S;ZZZ , the normal to the interface being taken along the S;XZX ¼ S;XXZ , S;ZXX ^ ^ Z axis with the X axis in the interface plane. The surface nonlinear polarization P NL S ð2!Þ is localized at the interface and is usually described as a nonlinear polarization sheet. This approximation holds because the thickness corresponding to the physical region of the
126
Brevet
interface where the bulk properties of one liquid change to the bulk properties of the other liquid is much smaller than the wavelength of light. Within this formalism, the problem can be treated with the help of the laws of linear optics yielding for the SH intensity I SHG [15,22,27,28]: qffiffiffiffiffiffiffi Re 2! 1 !2 SHG 2 ! 2 ¼ ð3Þ I 2 jj ðI Þ 80 c3 2 pffiffiffiffi!ffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2! 2! Re 1 m cos m where !1 and 2! 1 are the relative optical dielectric constants of Liquid 1 at the fundamental and the harmonic frequency, and I ! is the fundamental wave intensity. 2! m is the optical dielectric constant of the interfacial region, which may be taken as the average of the constant of both adjacent liquid phases [29,30]. The factor is given by:
ð2Þ ð2Þ ð2Þ 2 sin 2 sin þ a2 S;XZX þ a3 ð2Þ þ a ¼ a1 S;XZX 4 S;ZZZ cos cos S;ZXX ð4Þ 2 þ a5 ð2Þ sin cos S;ZXX where the coefficients ai , i ¼ 1; . . . ; 5 contain all the geometrical parameters and the optical linear dielectric constants [22]. and are respectively the fundamental and the harmonic light polarization angle. For example, with ¼ 0 the fundamental wave is ppolarized, whereas with ¼ 90 the fundamental wave is s-polarized. Equations (3) and (4) fully express the output SH intensity in terms of the linear and the nonlinear properties of the interface and the geometrical angles. They are the basic equations for the analysis of the data obtained from SHG experiments. Equations (3) and (4) give the SH intensity obtained in reflection mode. Although this is usually the most convenient experimental arrangement, the interfacial nonlinear polarization radiates both in the upward and the downward direction and therefore a transmitted wave does also emerge from Liquid 2, allowing a detection in transmission mode (see Fig. 1) [2]. A feature of interest is the possibility of obtaining the condition of total internal reflection (TIR). Under this condition, the fundamental beam impinges on the interface from the liquid with the highest index of refraction yielding a SH intensity enhancement of more than a hundred times. Two TIR angles exist, given by the following relationships: n!1 sin 1! ¼ n!2
and
n!1 sin 1! ¼ n2! 2
ð5Þ
nji
is the optical index of medium i at frequency j, derived from the generalized where Snell–Descartes law [31]. B.
The Case of Pure Solvents
The theoretical framework developed above is valid in the electric dipole approximation. In this context, it is assumed that the nonlinear polarization P NL S ð2!Þ is reduced to the electric dipole contribution as given in Eq. (1). This assumption is only valid if the surface susceptibility tensor ð2Þ ð2!; !; !Þ is large enough to dwarf the contribution from higher orders of the multipole expansion like the electric quadrupole contribution and is therefore the simplest approximation for the nonlinear polarization. At pure solvent interfaces, this may not be the case, since the nonlinear optical activity of solvent molecules like water, 1,2-dichloroethane (DCE), alcohols, or alkanes is rather low. The magnitude of the molecular hyperpolarizability of water, measured by DC electric field induced second harmonic
Nonlinear Optics at Liquid–Liquid Interfaces
127
generation (EFISH), has been found to be about 0:56 1031 esu [32,33], that of 1,2dichloroethane to be about 0:42 1030 esu, and of nitrobenzene 2:3 1030 esu [34]. Conversely, the magnitude of the molecular hyperpolarizability of very efficient nonlinear optical compounds may reach values in excess of 1000 1030 esu, as for donor–acceptor polyenes [35]. Hence Eq. (1) fails to fully describe the nonlinear polarization of neat liquid interfaces and higher orders of the multipole expansion have to be introduced [22,27,36,37]. This problem severely hinders the surface specificity of the SHG process, since the next contribution to take into account is the electric quadrupole contribution, neglecting any effects of magnetic origin. The nonlinear polarization is then given by: NL P NL ð2!Þ ¼ P NL DE ð2!Þ þ P QE ð2!Þ
ð6Þ
where the electric quadrupole term is given by [22,27,38]: P NL QE ð2!Þ ¼ r Qð2!Þ
ð7Þ
The electric quadrupole Qð2!Þ involves both the gradient of the electromagnetic incident electric field Eð!Þ and the gradient of the electric quadrupole susceptibility tensor ð2Þ Q ð2!; !; !Þ. This problem is nonetheless solved by the mere addition of supplementary terms in the surface susceptibility tensor. As a result, the surface susceptibility tensor becomes an effective tensor instead of a purely surface specific one [27,38]: ð2Þ ð2Þ ð2Þ eff ;XZX ¼ S;XZX þ rQ;XZXZ ð2Þ ð2Þ ð2Þ eff ;ZXX ¼ S;ZXX þ rQ;ZZXX þ fg;ZXX
ð8Þ
ð2Þ ð2Þ ð2Þ eff ;ZZZ ¼ S;ZZZ þ rQ;ZZZZ þ fg;ZZZ
Interestingly, the contributions from the gradient of the electromagnetic field across the interface, fg;ZXX and fg;ZZZ , which scale with the mismatch in the optical dielectric constants of the media forming the interface [37], only appear in the susceptibility tensor ð2Þ components ð2Þ eff ;ZXX and eff ;ZZZ . Therefore, these contributions may be rejected with a proper selection of the light polarization of the SH wave. Indeed, with ¼ 90 , the SH wave is s-polarized and only depends on the susceptibility tensor element ð2Þ eff ;XZX . Nevertheless, the contribution from the gradient of the electric quadrupole susceptibility tensor is still measured with the surface contribution. As mentioned above, the major drawback of this situation is the loss of the surface specificity of the technique because the gradient of the electromagnetic field extends over the scale of a wavelength on both sides of the interface. This problem can turn out to be a severe impediment at air–liquid interfaces where the electromagnetic field gradients are large, owing to the optical dielectric constant mismatch between air and liquids. This has been clearly emphasized at the air–water interface, whereas at liquid–liquid interfaces, the field gradients are much smaller owing to the better matching of the optical dielectric constants. The loss of surface specificity at the latter interfaces is not as dramatic [39]. Absolute magnitudes for the effective susceptibility tensor have been reported for several interfaces and show a rather large spread (see Table 1) [40]. The air–water interface ð2Þ has a susceptibility value of 6:04 1018 esu for the eff ;XZX susceptibility component [26,40,41]. This large magnitude arises from the overwhelming contribution of the electric quadrupole contribution, the gradient of the electromagnetic field in particular. The same observation can be made for the air–alcohol interfaces although some surface specificity may be obtained when the s-polarized output SHG signal is collected. Conversely, liquid– liquid interfaces present much more reduced values, in particular the water–DCE inter-
128
Brevet
TABLE 1 Absolute Magnitude of the Nonvanishing Susceptibility Tensor Component at Several Air–Liquid and Liquid–Liquid Interfaces [40]. All units are in esu but Transformation into SI Units is Obtained Using the Relationship 1 esu ¼ 3:72 1021 C3 m3 J2 1018 ð2Þ eff ;XZX
Interface Air–water Air–octanol Water–octanol Water–hexane Water–DCE
6.04 4.11 2.46 0.095 0.55
1018 ð2Þ eff ; ZXX 3.38 3.01 2.43 0.104 0.60
1018 ð2Þ eff ; ZZZ 12.58 11.89 7.39 0.39 1.88
ð2Þ face, with a magnitude of 0:5 1018 esu only for the eff ;XZX component, or the water– alkane interface [39]. This is in line with the picture of water molecules lying rather flat at the interface with the dipole moment oriented parallel to the interface [42,43]. Surprisingly, water–alcohol interfaces yield absolute magnitude similar to the air–alcohol ones; see the case of octanol in Table 1, for example. This feature may stem from a strong surface contribution originating from the molecular alignment at the interface subsequent to the interaction of the polar hydroxyl headgroup of the alcohol with water molecules [40].
C.
The Molecular Description
If the electric dipole contribution dominates in the total SH response, the macroscopic response can be related to the presence of optically nonlinear active compounds at the interface. In this case, the susceptibility tensor is the sum of the contribution of each single molecule, all of them coherently radiating. For a collection of compounds, it yields: ð2Þ S ¼
X
NS;i hT i i i
ð9Þ
i
where NS;i is the number of molecules of type i per unit surface and i the hyperpolarizability tensor of a single molecule. The transformation tensor T i links the macroscopic surface susceptibility tensor to the molecular hyperpolarizability tensor. The brackets therefore emphasize that an ensemble average must be performed over all the possible molecular configurations of a molecule sitting at the interface (see Fig. 2). As expected, the quantity hT i i vanishes if the averaging is performed over all the possible orientations, irrespective of the amphiphilic character of the moiety. This indicates that a nonoriented distribution of molecules at the interface does not lead to any SH signal as required by the rule of centrosymmetry. However, if a preferential orientation does exist owing to the amphiphilic character of the surface species, the quantity hT i i does not vanish. Complete expressions for the quantity hT i i have been given in the literature for many different systems [22,44]. In most experiments, the SH wavelength is tuned near an electronic resonance of the surface compounds, thereby reducing the number of nonvanishing elements of the hyperpolarizability tensor i . A resonance at the second harmonic frequency is usually preferred, since this configuration avoids the spurious effects coming from one photon absorption process with the intense fundamental beam. A two-state model involving the ground and the first excited electronic states S0 and S1 is then adequate to
Nonlinear Optics at Liquid–Liquid Interfaces
129
FIG. 2 Molecular orientation angles at liquid interfaces for rodlike molecules. The out-of-plane motion is a rotation away from the OZ axis, whereas the in-plane motion is performed with the (OX, OY) plane.
describe the nonlinear optical activity of the molecule, the tensor elements ð2Þ ijk taking the following form [45]: ð2Þ ijk ¼ "
e3 ð0Þ g ð0Þ e 2 2h
# ri rj rk !2eg þ 2!2 þ ri rj rk þ rk rj !2eg !2 ½!2eg !2 ½!2eg 4!2
ð10Þ
ð0Þ where ð0Þ g and e are the ground and the excited state population respectively, !eg is the transition frequency between the ground and the excited state, ri is the transition moment along the molecular axis i and ri is the change in the dipole moment along the axis i ð2Þ is obtained when both the transiundergone during the transition. The maximum of ijk tion moment and the change in dipole during the transition are maximized. This explains why compounds undergoing large charge transfer during the transition from the ground to the excited state are good candidates as nonlinear optical probes. If the transition moment and the change in dipole occur along the same axis of the molecule, only one tensor element dominates, the expression of which is: ð2Þ;NR þ ð2Þ zzz ¼ zzz
!2eg
A 4!2 4i!
ð11Þ
where A is a constant and the width of the resonance. The hyperpolarizability element is the sum of a resonant and a nonresonant contribution. As a consequence, the set of equations (9) can be vastly reduced for a single component monolayer at the interface, namely: ð2Þ 2 ð2Þ 20 ð2Þ S;XZX ¼ 20 S;ZXX ¼ Ns hcos sin i zzz 3 ð2Þ 0 ð2Þ S;ZZZ ¼ Ns hcos i zzz
if random distributions are assumed for the two other and equations set, the orientational parameter D given by:
ð12Þ Euler angles. From this
130
Brevet
D¼
hcos3 i hcos i
ð13Þ
is usually extracted but the knowledge of a distribution function has to be assumed beforehand to get the angle of orientation. Although a Gaussian distribution function would be more adequate, albeit with the disadvantage of introducing as an extra parameter the width of the distribution, a Dirac distribution function is often used. This implies the assumption of an infinitely sharp distribution for the molecular angle . In absence of a distribution of angles determined by an independent method, the angle of orientation must only be used as a convenient parameter to describe the interface angular distribution [46,47]. Before closing this section, it is worth mentioning that the hyperpolarizability tensors are complex quantities usually given in the old cgs system of units of esu (electrostatic units). The transformation into the International System is readily obtained with the relationship: ð2Þ ðSIÞ ¼ 3:71 1021 ð2Þ ðesuÞ
ð14Þ
where the SI units are C3 m3 J3 . D.
Polarized Interfaces
The case of polarized interfaces is usually described within the context of the metal– electrolyte interface where the metal charge dependence of the SH intensity is dramatic because of the strong interfacial electric field present at the interface [16]. It has long been a real challenge at the polarized liquid–liquid interface but has, however, been observed at charged air–water interfaces [48]. At polarized interfaces, the static DC electric field established across the interface couples to the electromagnetic field impinging onto the surface. This process is described with the following nonlinear polarization: 1 P ð2Þ ð2!Þ ¼ 0 K ð3Þ ð3Þ ð2!; !; !; 0ÞEð!ÞEð!ÞEð0Þ 6
ð15Þ
with K ð3Þ ¼ 1=4. Although it is a third-order nonlinear optical process mixing four waves, the nonlinear polarization only oscillates at the harmonic frequency owing to the coupling to a static electric field. Because the magnitude of the third-order susceptibility tensor ð3Þ ð2!; !; !; 0Þ is much smaller than the magnitude of the second-order susceptibility tensor ð2Þ ð2!; !; !Þ, coupling to strong electric fields only gives rise to a nonnegligible contribution. This is the reason why the observation of this DC-field-induced SHG contribution has been mainly restricted to the metal–electrolyte interface. As opposed to second-order nonlinear processes, this contribution does not possess the symmetry cancellation in media with inversion symmetry and therefore the surface specificity of this contribution finds its origin in the confinement to the region where the static electric field is nonvanishing. This means that, in principle, this contribution extends over the whole double layer region. E.
Circular Dichroism
In order to describe the problems of the nonlinear optical response from biological systems, the question of chirality must be addressed. Linear circular dichroism (CD) has been investigated extensively for biological compounds and a wealth of data are available on
Nonlinear Optics at Liquid–Liquid Interfaces
131
this topic [49]. Inversely, in nonlinear optics, this problem has been barely touched on and only few reports have appeared so far [50,51]. The surface susceptibility tensor of a chiral surface possesses different symmetry properties as compared to the surface susceptibility tensor of an isotropic surface. The main difference for a chiral surface arises from the axes OX and the OY, the two axes in the plane of the surface, which are no longer indistinguishable. The nonvanishing elements of the susceptibility tensor are then [52]: ð2Þ ð2Þ ð2Þ ð2Þ S;XZX ¼ S;XXZ ¼ S;YYZ ¼ S;YYZ ð2Þ ð2Þ S;ZXX ¼ S;ZYY
ð2Þ S;ZZZ
ð16Þ
ð2Þ ð2Þ ð2Þ ð2Þ S;XYZ ¼ S;XZY ¼ S;YXZ ¼ S;YZX
Only for achiral surfaces does the last tensor element vanish altogether. Equation (4) retains a similar form but now accommodates a new tensor element. To date, very few experimental works have been reported on chiral surfaces, although the nonlinear effects are expected to be rather large [51].
III.
MOLECULAR STRUCTURE
A.
Surface Coverage
The SH signal directly scales as the square of the surface concentration of the optically active compounds, as deduced from Eqs. (3), (4), and (9). Hence, the SHG technique can be used as a determination of the surface coverage. Unfortunately, it is very difficult to obtain an absolute calibration of the SH intensity and therefore to determine the absolute number for the surface density of molecules at the interface. This determination also entails the separate measurement of the hyperpolarizability tensor i , another difficult task because of local fields effects as the coverage increases [53]. However, with a proper normalization of the SH intensity with the one obtained at full monolayer coverage, the adsorption isotherm can still be extracted through the square root of the SH intensity. Such a procedure has been followed at the polarized water–DCE interface, for example, see Fig. 3 in the case of 2-(n-octadecylamino)-naphthalene-6-sulfonate (ONS) [54]. The surface coverage takes the form:
a G0Ads zbF w c o ð17Þ þ ln ¼ ln i 1 RT RT asol RT where ai and asol are respectively the solute and the solvent bulk activities and G0Ads is the Gibbs energy of adsorption. The electrostatic contribution to the adsorption energy has been made explicit and a plot of ln½ =ð1 Þ with the applied potential wo across the interface yields the value of b, the extent of the potential drop actually felt by the adsorbing species. This introduces a discussion on the molecular arrangement of the monolayer at the interface and in particular on the exact location of the plane of adsorption [54]. In the case of ONS, the adsorption was taking place from the organic phase and the polar head of ONS species was found to significantly protrude into the aqueous phase. The last term in Eq. (17) accounts for the intermolecular interactions within the monolayer through the Frumkin parameter c.
132
Brevet
FIG. 3 Adsorption isotherm of ONS at the polarized water–DCE interface: (square) experimental, (dotted) Langmuir isotherm, and (solid) Frumkin isotherm. (From Ref. 55, copyright American Chemical Society.)
The relationship between the square root of the SH intensity and the surface coverage of the surface active species only holds provided the bare interface does not give rise to any significant background SH signal. If this assumption is not true, interference between the signal from the background and the monolayer occurs, yielding a perturbed isotherm at low coverage. This has been clearly demonstrated at the quartz–air interface for the adsorption of rhodamine 110 in the case of a destructive interference [55]. Nevertheless, with compounds of very high hyperpolarizability like the donor–acceptor polyenes for example, fractions of monolayers as low as 0.001% should readily be detected. Another source for erroneous conclusions is the possibility of intralayer rearrangements or reorientation processes leading to a change in the susceptibility tensor element while the surface density of the active compounds remains unchanged. This has been observed at the air–water interface for a monolayer of the protein glucose oxidase (GOx) [56]. A change of the polarization configuration is usually enough to disentangle adsorption from intralayer rearrangement processes. Besides these effects, interfacial measurements have demonstrated the ability of the nonlinear technique to investigate biological membranes. Polypeptides have also received attention. Clear evidence for coadsorption as the result of multipoint electrostatic interaction has been observed for the synthetic poly-L-glutamic acid polypeptide [57].
B.
Molecular Orientation
One question addressed in the literature is the relationship between the angle of orientation of the adsorbed species within the monolayer and their amphiphilic character. The case of surfactants like fatty acids or phospholipids is deferred until Section VI, since the technique of choice is SFG in order to perform a surface vibrational study. Phenol deri-
Nonlinear Optics at Liquid–Liquid Interfaces
133
vatives have been extensively studied at the air–water interface and a light polarization analysis shows a preferential orientation [47,58–61]. The angle of orientation has been related to the surface activity of the moiety for a series of simple phenol derivatives, namely p-nitrophenol, phenol, and p-propylphenol. At full monolayer coverage, for a hydrophilic substituent as in the case of p-nitrophenol, the molecule is shown to lie with a rather flat position at the air–water interface and to take a position more perpendicular to the interface as the substituent’s hydrophobicity is increased. Hence phenol was shown to take a position more tilted towards the surface normal and p-propylphenol to take an even straighter position. Furthermore, the effect of the change of the polarity of the nonpolar solvent, hexane replacing air, was shown to screen these hydrophilic–hydrophobic interactions with the aqueous surface yielding an identical orientation for all compounds [47]. These results are in line with molecular dynamics calculations [62,63]. One major assumption at the basis of these works is the absolute orientation of the moiety at the interface, whether pointing up with the hydroxyl group in the aqueous phase or down. For the phenol derivatives, the hydroxyl group was always assumed to point into the aqueous phase. However, only absolute phase measurements can yield such a determination, an experiment realized through interference between the SH signal from the monolayer and a quartz reference [64]. In a recent experimental work, the reference was obtained from another compound coadsorbed at the interface with the molecule of interest [65]. Other classes of compounds investigated include the rhodamine and the eosin dye families involving a xanthene ring. With rhodamine 6G for example, two different resonant configurations were used: either resonant with the fundamental wave or with the harmonic wave [66,67]. The orientation of the long axis of the xanthene ring was found to be oriented with an angle of about 55 with the surface plane. The role of the carboxylic group in the process of adsorption at the hydrophilic air-fused silica surface was also emphasized. SHG has been used extensively for the determination of the structure of surfactant monolayers to address the question of the role of long-tail chains in intermolecular repulsion interactions. The orientation of the surfactants was thus monitored for soluble and insoluble naphthalene sulfonate derivatives, with an alkyl chain containing respectively 6 and 18 carbon atoms. They were shown to exhibit a similar angle of orientation irrespective of the surface coverage and to present an identical surface density at full monolayer coverage. This results supports the view that a soluble surfactant forms a saturated monolayer by adsorption very much identical in its structure to an insoluble monolayer formed by the spreading of the compound on the surface [68]. Reorientation as a function of surface coverage is usually very weak but was nevertheless observed for dodecylnaphthalene sulfonate or 1-(3 0 ; 5 0 -di-t-butyl)phenyl-3-glycero-rac-glycerin at the air–water interface [69,70]. The kinetics of adsorption, phase transition from the liquid expanded to the liquid condensed state, and surface diffusion were also observed [43,71–76]. Finally, it is worth adding that very small molecules are amenable to detection at interfaces. This has been proven for compounds like SO2 at the air–water interface or for the more environmentally relevant stratospheric ozone reaction products like HOCl at the surface of ice [77,78]. C.
Interfacial Solvation
The heterogeneity of the solvent at the interface introduces another degree of complexity in the problem. Molecular dynamics calculations have been able to give a molecular picture of the interfacial solvation of adsorbates but experiments have long been a chal-
134
Brevet
lenge [79]. The problem has though recently been addressed by SHG with the recording of surface SHG spectra and the comparison with the corresponding UV-visible bulk phase spectra. The maximum of the nonlinear and the linear optical spectra usually differ but the exact location of the resonance must be carefully extracted from the nonlinear optical measurements because of the contribution of the nonresonant term in the hyperpolarizability tensor, see Eq. (11) [80]. The general scheme underlying the experimental approach is to extend the polarity scale of homogeneous media to interfacial regions with the use of an appropriate molecular probe. The compound usually taken as the reference compound is 4-(2,4,6-triphenylpyridinium)-2,6-diphenylphenoxide, ET ð30Þ, which belongs to the family of the betaine dyes. It possesses a large solvatochromic shift and this shift, when renormalized on a general solvent scale, defines the polarity of the medium. The solvatochromic shift of ET ð30Þ arises from the charge transfer band and is defined as 0 for tetramethylsilane (TMS) and 1 for water [81]. The scale is defined with the normalized parameter ETN ð30Þ as: ETN ð30Þ ¼
ET ðsolventÞ ET ðTMSÞ ET ðwaterÞ ET ðTMSÞ
ð18Þ
where ET (solvent) is the location of the charge transfer absorption band maximum. The air–water polarity thus has a polarity of 0.01 in this scale and the n-heptane–water interface 0.52, bulk phase n-heptane having itself a value of 0.01 on this polarity scale [30]. The ETN (30) scale was confirmed with another compound, N,N-diethyl-p-nitroaniline (DEPNA), yielding a scale consistent with the ETN (30) one. In a rather general manner, the polarity of the interface is deduced from the average of the polarity Pi of the two adjacent bulk media: Pw=o ¼
Pw þ Po 2
ð19Þ
This indicates that the polarity of a medium is a long-range property that goes much further than the first solvation shell and therefore involves the two adjacent bulk media properties. This result is, however, valid for compounds the solvation of which is not determined by specific interactions with the first solvent shell, but rather by long-range forces like dipole interactions. The solvation of DEPNA was determined by molecular dynamics too and similar conclusions were drawn [82]. D.
Surface Equilibrium
As a consequence of the change of the polarity of the interface as compared to the bulk solution, chemical equilibrium may be shifted towards the reactants or the products if changes in the charges or the dipoles are involved. A thermodynamic cycle between the surface and the bulk phase can thus be defined with the Gibbs energies of adsorption and the different equilibrium constants. The energy of adsorption contains two contributions, a chemical part G0Ads assumed unaffected by changes in the charge, and an electrostatic part WBorn the magnitude of which, evaluated with the Born model [83,84], emphasizes the dependence of WBorn with the charge z. Hence, neutral species are much more favored at interfaces than charged species owing to the reduced polarity of water next to a hydrophobic wall. This observation is of great relevance in surface chemistry for the acid–base equilibrium for example. The protonation–deprotonation reaction will involve a change in the charge of the species and therefore a change in the surface equilibrium constant, assuming that the chemical term is constant. The pKaS observed at the interface is thus:
Nonlinear Optics at Liquid–Liquid Interfaces
pKaS ¼ pKa
1 ½WBorn ðAHÞ WBorn ðAÞ 2:3RT
135
ð20Þ
provided the proton equilibrium between the surface and the bulk phase follows a Boltzmann equilibrium: pHS ¼ pH
Fsb
2:3RT
ð21Þ
where sb is the potential drop between the bulk phase and the surface. In Eq. (20), WBorn ðAHÞ vanishes if the form AH is neutral. A surface equilibrium has been reported for several compounds at the air–water interface: anilinium, phenolates, hemicyanine, or eosin B and the observed shift of the surface pKaS is usually of several units [75,85–87]. For the equilibrium between p-nitrophenol and its anion, the surface pKaS is 7.9 as compared to a value of 7.15 in the bulk aqueous phase. Similarly, for the dye eosin B, which has two protonation sites and therefore presents a neutral acid, a singly charged and a doubly charged anionic form at the interface presents two surface pKaS of 4.0 and 4.2 at the air– water interface as compared to 2.2 and 3.7 in bulk aqueous solution. The location of the adsorption plane for the different forms at the interface was inferred from the different shift observed for the two equilibrium constants. The doubly charged form of eosin B was thus found to lie further into the aqueous phase as compared to the singly charged form. The case of 4-(4 0 -dodecyloxyazobenzene)-benzoic acid (DBA) has been studied at the water–DCE interface [88]. At liquid–liquid interfaces though, the problem is complicated by the possible transfer of species across the interface. The SH signal may be used as a surface titration tool (see Fig. 4). Yet, the midpoint of the titration curve is not the point where the surface concentrations of the acid and the base are equal. Indeed, a proper account of the ratio of the hyperpolarizability tensor of the two forms has to be taken and consequently the point of equal surface concentration may lie far away from the midpoint.
FIG. 4 SHG intensity from the dye eosin B adsorbed at the air–water interface as a function of the pH of the bulk aqueous solution. The aqueous dye concentration is 30 M and the fundamental wavelength is 532 nm.
136
Brevet
Different orientations for the protonated and deprotonated species as well as a change of the surface coverage with the bulk aqueous pH can further complicate the problem. Another determination of the surface equilibrium entails the use of the coupling of the DC electric field present at charged interfaces with the electromagnetic field, as described in the theoretical section. Integration of the nonlinear polarization over the whole double layer leads to the following expression of the effective susceptibility tensor: ð2Þ eff ¼ A þ B ð0Þ
ð22Þ
where the surface potential ð0Þ can be separately calculated from a Gouy–Chapman model. This method has been used for the determination of the surface pKaS of p-hexadecylaniline at the air–water interface, the surface pKaS of which was found to be 3.6 at the interface and 5.3 in the bulk aqueous phase. These results confirm that neutral forms are favored at the interface [89]. E.
Polarized Interfaces
Interfaces between two immiscible electrolyte solutions (ITIES) have scarcely been investigated by nonlinear optics. Some literature is available on adsorption and orientation at ITIES and was covered in the sections above [54,88,90]. No reorientation of the adsorbates as a function of the applied potential was observed in the course of these experiments, a feature probably due to the weak interaction energy between the molecular dipole and the DC electric field. The influence of the ion transfer reaction across the interface in the thermodynamic equilibrium between the bulk phases and the interface was, however, underlined [88]. At ITIES, the origin of the second harmonic signal may stem from the change in surface concentration of the active species with the externally applied potential or from the coupling of the DC electric field with the electromagnetic fields. This matter is still a question of debate but in an attempt to address it, the SH intensity was measured at the water–DCE interface as a function of the applied potential in presence of the supporting electrolytes only [91]. The aqueous electrolyte was LiCl and different organic supporting electrolytes were used. In particular, the organic cation was either tetrabutylammonium (TBAþ ), which possesses only four alkyl chains and therefore has a weak hyperpolarizability tensor, or tetraphenylarsonium (TPhAsþ ) which has four phenyl rings and thus a much larger hyperpolarizability. The organic anion was tetraphenylborate (TPhB ). The SH response exhibited a parabolic shape similar to the one observed at the metal–electrolyte interface for TPhAsþ . However, for the cation TBAþ , the SH intensity vanished at the negative end of the potential window where the organic cation is accumulated at the interface. The authors were thus led to the conclusion that the SH signal finds its origin in the potential-dependent concentration of the organic supporting electrolytes. In all cases, the influence of the aqueous supporting electrolyte was negligible.
IV.
INTERFACIAL DYNAMICS AND REACTIVITY
A.
Interfacial Dynamics
Molecules adsorbed at interfaces are in constant motion, both from the point of view of their orientation and of the dynamic exchange with the bulk solution. The distribution of orientation angle is characterized by the parameter D, see Eq. (13), or the angle of orientation . Complete randomness for the angle , the angle of rotation around the principal
Nonlinear Optics at Liquid–Liquid Interfaces
137
molecular axis, is assumed hereafter. The two angles and define the in-plane and the out-of-plane motion of the molecule at the surface and are readily accessed by experiment. The anisotropy of the rotation motion of compounds at interfaces has been clearly evidenced in the case of the dye coumarin C314 [92]. The strategy operating to separate the two in-plane and out-of-plane motions relies on the selective preparation of the excitedstate distribution of molecules with a pump pulse of well-defined state. Indeed, the perturbation of the initial distribution is produced by a pump pulse photoexciting the molecules form their ground state to their excited state. The probe pulse, which is actually performing the SHG process at the interface, subsequently samples the relaxing molecular distribution at fixed time intervals. With the use of a selective excitation according to the polarization state of the pump pulse with respect to the polarization state of the probe pulse, the two motions have different weights and can be deconvoluted. One of the major caveats of these experiments is the clear separation of the orientation processes from other processes like radiative and nonradiative decays of the excited population. Population effects are usually observed a time scales of a few nanoseconds and correspond to processes like fluorescence emission, for example. Orientation processes occur on the picosecond time scale. For coumarin C314, the out-of-plane motion was found to have a relaxation time of about 350 ps, whereas the in-plane motion had a relaxation time of about 600 ps. Such a difference was attributed to the restoring force acting on the molecules for the out-of-plane motion, whereas no such force is acting in the case of the inplane motion. The time scale of the two different motions reported for C314 at the air–water interface can also be compared to the rotation motion in the bulk phase. As has also been reported for rhodamine 6G at the same interface, the relaxation time is longer than the rotational diffusion time in bulk water at the interface for the out-of-plane motion [92,93]. These longer time scales are explained by rotational motions at the interface chiefly controlled by the friction on the aqueous side of the air–water interface. These results are at odds with the experimental findings observed for the dye eosin B at the same interface (see Fig. 5) [94]. The relaxation time of the out-of-plane motion of the doubly charged anionic form of this dye was observed after a complete randomization of the orientation distribution corresponding to the angle . The time scale at the interface was found to be 90 ps, a relaxation time much shorter than the one observed in the bulk aqueous phase at about 350 ps. This was explained by the reduced hydrogen bonding at the interface between the dye and the water molecules, owing to an increased competition with other water molecules. Population and orientation decays are not the fastest events in the dynamics of solutes at interfaces. Solvation processes indeed occur on the femtosecond time scale. In the ground state of a molecule, the electronic distribution, and therefore the charge distribution in the molecular volume, is such that a polar solvent is specifically oriented around the molecule in the bulk phase to minimize the energy of the state. In the excited state, the electronic distribution is often rearranged and this process may be quite extensive in a charge transfer excited state where the change in dipole moment from the ground to the excited state is rather large. As a result, the solvation properties of the excited state are the ones pertaining in the ground state, since the electronic excitation is a much faster event than the solvent reorganization. This configuration is highly unfavorable. The solvent thus undergoes a reorganization in order to minimize the energy of the excited state. This feature, known as the Stoke shift, is usually observed through the time evolution of emission spectra [95]. At the interface, this effect is observed as a shift of the SH spectrum at early times subsequently to the photoexcitation. Conversely, and because this phenom-
138
Brevet
FIG. 5 Time-resolved SHG intensity from the doubly charged eosin B at the air–water interface after randomization of the orientation distribution. (a) Square root of the SH signal recorded for the s-polarized SHG output intensity and the fundamental beam 45 -polarized. (b) Square root of the SH signal recorded for the p-polarized SHG output intensity and the fundamental beam s-polarized. (From Ref. 96, copyright Elsevier Science BV.)
enon occurs on a fast time scale, the solvent reorganization process can be observed as the early time evolution of the SHG signal at a single frequency. This technique has been used at the air–water interface for coumarin C314, which possesses a large change in dipole during the excitation from the ground to the excited state. The time scale of the solvent reorganization was measured to be 790 fs, a value close to the longitudinal dielectric relaxation of bulk water, the value of which is only 590 fs [96]. This is attributed to the long-range effects of solvation and in particular of the solute–solvent interactions, in accordance with the polarity scale, which describes the similar long-range effects.
B.
Photoisomerization
The photoisomerization reaction gives a valuable tool to investigate the molecular friction at the interface. Depending on the exact location of the reaction path, whether predominantly in one or the other phase, the time scale of the rate of the reaction is severely modified. The photoisomerization reaction of the dyes malachite green and 3,3 0 -diethyloxadicarbocyanine iodide (DODCI) has been reported at several interfaces, the air–
Nonlinear Optics at Liquid–Liquid Interfaces
139
water and different alkane–water interfaces, to illustrate this phenomenon [97,98]. Malachite green is present at the interface with its phenyl ring protruding out of the aqueous phase, whereas the two dimethylaniline groups are anchored into the aqueous phase. The isomerization reaction rate is found insensitive to the phase adjacent to the aqueous phase, the relaxation rate being 3.5 ps at the air–water interface and 3.6 ps at the pentadecane–water interface. Both rates are slower than the rate in the bulk aqueous phase, i.e., 0.7 ps. They are also faster than the rate observed at the silica–water interface, which is 6.2 ps. Inversely, the isomerization rate of DODCI is measured to be 220 ps at the air–water interface, whereas it is 520 ps in the bulk phase water. These differences were attributed to the exact location of the path of the isomerization reaction. In the case of malachite green, the isomerization is thought to occur through rotation around the two carbophenyl bonds protruding into the aqueous phase without involving the phenyl group sticking into the other phase. As a result, the motion is slowed down because the molecular friction on the aqueous side of the interface is increased. For DODCI, the isomerization reaction is thought to occur through the one of the methylene bonds protruding out of the aqueous phase into the air. Thus, the two different behaviors of malachite green and DODCI may be reconciled by assuming that the isomerization path involves the part of the molecule in the aqueous phase for malachite green and the part in the air for DODCI at the air–water interface. This assumption implies that the influence of molecular friction on reaction rates at interfaces is path-dependent. On the aqueous side of the air–water interface, the molecular friction appears stronger than the bulk phase one. Photoisomerization was also reported at the water–DCE interface for the organic dye 4-(4 0 -dodecyloxyazobenzene)-benzoic acid (DBA) [99]. This dye is under the trans form in its ground state but can be converted into its cis isomer when illuminated with UV light. In the bulk DCE phase, the thermally driven back-conversion from the cis isomer to the trans isomer is rather slow as a result of the high energy barrier of nearly 100 kJ mol1 . At the water–DCE interface, the conversion from the trans to the cis isomer with UV light is also efficient, however, no significant thermally driven relaxation to the trans isomer is observed. This surprising result is attributed to intermolecular interactions within the dye monolayer at the interface, like hydrogen bonding through the azo nitrogens of the azobenzene DBA either with other DBA molecules or with the aqueous solvent. C.
Electron Transfer Reactions
Electron transfer reactions constitute an ubiquitous class of chemical reactions. This is particularly true in biological systems where these reactions often occur at interfaces, in photosynthesis for instance. It is therefore challenging to use the surface specificity and the time resolution of the SHG technique to investigate these processes. At liquid–liquid interfaces, these processes are mimicked through the following scheme: Dorg þ Aaq
hv D þ Aaq !Dþ org þ Aaq ! org SCHEME 1
where the two redox couples are located in the organic and the aqueous phase during the whole duration of the experiment. Hence, Scheme 1 describes a true heterogeneous electron transfer (ET) reaction across the interface. One of the major problems usually arising during this reaction scheme is the simultaneous transfer of one of the reactants or products across the interface as this process is difficult to uncouple from the ET reaction. Several systems have been devised and one of the most efficient ones so far is formed by zinc
140
Brevet
porphyrins located in the aqueous phase and ferrocene derivatives in the organic phase [100]. The SHG technique is an adequate technique to follow these ET reactions and the experiment has been performed on a system constituted by tris-(2,2 0 -bipyridinyl) ruthenium (II) RuðbpyÞ2þ 3 dissolved in the aqueous phase as the sensitizer and trans-1-ferrocenyl-2-(4-(trimethylammonio)phenyl)ethylene (1þ ) located in the organic phase as the donor species [101]. The RuðbpyÞ2þ 3 species were first photoexcited by light at 488 nm and the time evolution of the donor 1þ at the water–DCE interface was followed by SHG (see Fig. 6). The heterogeneous ET reaction was clearly observed and its rate limited by the diffusion rate of the excited RuðbpyÞ2þ 3 species to the interface. This experiment clearly demonstrated the advantages of nonlinear optics over linear optical techniques like fluorescence in total internal reflection (TIR) or transient absorption owing to its surface specificity [102,103].
D.
Ion Transfer Reactions
Charge transfer reactions at ITIES include both ET reactions and ion transfer (IT) reactions. One question that may be addressed by nonlinear optics is the problem of the surface excess concentration during the IT reaction. Preliminary experiments have been reported for the IT reaction of sodium assisted by the crown ether ligand 4-nitro-benzo-15crown-5 [104]. In the absence of sodium, the adsorption from the organic phase and the reorientation of the neutral crown ether at the interface has been observed. In the presence of the sodium ion, the problem is complicated by the complex formation between the crown ether and sodium. The SH response observed as a function of the applied potential clearly exhibited features related to the different steps in the mechanisms of the assisted ion transfer reaction although a clear relationship is difficult to establish as the ion transfer itself may be convoluted with monolayer rearrangements like reorientation.
FIG. 6 SHG intensity as a function of time (ON) with and (OFF) without illumination of the interface by a probe UV pulse. The increased SHG intensity during illumination arises from the production of the species 1þ at the interface by photoinduced electron transfer, see text for more details. (From Ref. 103, copyright American Chemical Society.)
Nonlinear Optics at Liquid–Liquid Interfaces
141
Other studies involved the measurements of the SHG response from ion selective electrodes (ISE) [105,106] but one of the difficulties lies in the reabsorption of the SH signal generated at the interface in the bulk of one phase as the active species transfer.
V.
SHG FROM CENTROSYMMETRICAL PARTICLES
In the sections above, only infinite planar interfaces between air and an aqueous phase or two immiscible liquids like water and DCE were considered. Reducing the question to this class of surfaces only would be a severe limitation in the scope of the review as more reports appear in the literature debating on the SH response from small centrosymmetrical particles [107–110]. It is the purpose of this section to discuss the SHG response from interfaces having a radius of curvature of the order of the wavelength of light. In the theoretical section above, the nonlinear polarization induced by the fundamental wave incident on a planar interface for a system made of two centrosymmetrical materials in contact was described. However, if one considers small spheres of a centrosymmetrical material embedded in another centrosymmetrical material, like bubbles of a liquid in another liquid, the nonlinear polarization at the interface of a single sphere is a spherical sheet instead of the planar one obtained at planar surfaces. When the radius of curvature is much smaller than the wavelength of light, the electric field amplitude of the fundamental electromagnetic wave can be taken as constant over the whole sphere (see Fig. 7). Hence, one can always find for any infinitely small surface element of the surface
FIG. 7 Schematics of the SHG process at the surface of a sphere of a centrosymmetrical medium with a radius much smaller and of the order of the wavelength of light. The cancellation or the addition of the nonlinear polarization contribution is given explicitly and underlines the effect of the electromagnetic field and the surface orientation.
142
Brevet
another infinitely small surface element on the other side of the sphere with a corresponding nonlinear polarization of equal amplitude pointing in the opposite direction. The net result of this finding is that the overall surface nonlinear polarization of the particle vanishes altogether and no SHG signal may be observed from such a particle. This case would be observed for small nanoparticles the diameter of which is in the range of 1 to 20 nm. In fact, in the case of metallic nanoparticles, this case is nearly reached, although an SHG signal can still be collected from the contribution arising from the electromagnetic field gradients [111–113]. Since all particles in the solution radiate at the harmonic frequency without any phase relationship, the SH signal collected from a monodispersed solution of particles is incoherent [114]. This process is known as hyper-Rayleigh scattering (HRS). For particles with a radius of curvature of the order of, or larger than, the wavelength of light, the incoming fundamental electric field cannot be assumed constant over the particle diameter any longer. Hence, the compensation of the nonlinear polarization from two opposite surface elements is incomplete and an SHG signal from the particle is collected. This phase matching condition is given as [115]: ¼ 1 expðikLÞ
ð23Þ
where L is the coherence length and k ¼ k2! 2k! is the wave vector mismatch. The maximum SH intensity is therefore obtained when ¼ 2 or similarly for kL ¼ . This condition defines a coherence length of about a few microns. The problem of particles having a diameter of the order of the wavelength of light has been recently discussed for the dye malachite green adsorbed on polystyrene particles of about 1 m diameter [115]. The SH intensity was shown to depend on the square of the number of adsorbed malachite green molecules per particle, indicating that the adsorbed dye molecules of a single polystyrene particle were coherently radiating at the harmonic frequency. The SH intensity was, however, shown to depend linearly with the number density of the polystyrene particles, underlining a noncoherent SH generation from the assembly of particles. The most striking advantage of this configuration is the possibility of investigating liposome bilayers and transport processes across these layers. Protein monolayers have already been investigated at planar surfaces [56] but liposome spherical bilayers are also accessible by nonlinear optics in bulk solution. The transport of the dye malachite green across a phospholipid bilayer membrane has thus been reported [116], the experiment relying on the adsorption of malachite green at the aqueous media–bilayer membrane on both the internal and the external side (see Fig. 8). Because the two sides of the membrane have an opposite orientation, the two opposite contributions of the nonlinear polarization are expected to cancel each other. As a result, the initial point of the experiment was obtained with the malachite green only adsorbed on the external membrane side of the dioleoylphosphatidylglycerol (DOPG) liposome bilayer by adding the dye after the liposome preparation. The transport of the dye across the membrane to the internal side was then followed through the loss of the SH signal as the internal side contribution to the signal increased, therefore compensating the external side contribution. The loss of the SHG intensity was occurring on time scales of about 100 s but the transport could be blocked for a bilayer of dipalmitoylphosphatidylglycerol (DPPG). The difference between DOPG and DPPG were interpreted in terms of the structure of the bilayer, DPPG being in a gel state where the restricted arrangement prevents the transport of the dye. These results undoubtedly will raise a strong interest in the biological sciences.
Nonlinear Optics at Liquid–Liquid Interfaces
143
FIG. 8 SHG intensity as a function of time for a solution of DOPG and DPPG liposomes in presence of the dye malachite green in the solution and adsorbed at the liposome surface. The effect of transport across the bilayer is observed through the decay of the SHG intensity at short times. (From Ref. 117, copyright Elsevier Science BV.)
VI.
SUM FREQUENCY GENERATION
A.
Theoretical Background
Equation (1) has been set above in the case of the SHG process. This process entails the mixing of two identical frequency electromagnetic waves and therefore constitutes a particular case of the general problem of the mixing of two different frequency waves. The general form of Eq. (1) is therefore [15,22]: P NL ð!3 Þ ¼ 0 K ð2Þ ð!3 ; !1 ; !2 Þð2Þ ð!3 ; !1 ; !2 Þ : Eð!1 ÞEð!2 Þ
ð24Þ
where we have either the condition !3 ¼ !1 þ !2 , the process known as sum frequency generation (SFG), or !3 ¼ !1 !2 , this process being known as difference frequency mixing (DFG). Although experiments may be readily performed with two visible frequencies, one interesting configuration lies in the possibility of using one visible frequency and one infrared frequency, which can be tuned over vibrational resonances of the molecular adsorbates. In this case, a surface vibrational spectrum is recorded, the surface specificity arising from the three-wave mixing process. This possibility has been widely used in recent years to investigate surfactants and phospholipids at liquid interfaces [117]. These species are present at liquid surfaces in a wide range of phenomena but it was very difficult to get a clear molecular picture of the interface. SFG IR Vis Generalization of the Snell–Descartes law yields nSFG ¼ nIR 1 w3 sin1 1 w1 sin 1 þ n1 Vis SFG w2 sin 1 defining an outgoing SFG wave angle 1 close to the outgoing fundamental
144
Brevet
visible wave angle 1Vis . Similarly, the outgoing angle 1DFG is determined through the Vis IR IR w3 sin 1DFG ¼ nVis relation nDFG 1 1 w2 sin 1 n1 w1 sin 1 . With a collinear configuration of the two incoming beams, the SFG wave has usually a smaller angle than the visible outgoing fundamental wave and the DFG one a larger angle, although the experimental apparatus requires a careful rejection of the fundamental waves. For this reason, the counterpropagating configuration is sometimes preferred. The SFG intensity takes a form similar to the one given in Eq. (3), although the SFG intensity depends linearly on both fundamental wave intensities [22]. The hyperpolarizability tensor is obtained in a way similar to the case of SHG. However, the selection rules for an SFG resonance at the IR frequency implies that the vibrational mode is both IR and Raman active, as the SF hyperpolarizability tensor elements involve both an IR absorption and a Raman–anti-Stokes cross-section. Conversely, the DFG hyperpolarizability tensor elements involve an IR absorption and a Raman–Stokes cross-section. The hyperpolarizability tensor elements can be written in a rather compact form involving several vibrational excitations as [117]: X Aq ð2Þ ð2Þ ð25Þ S ¼ S;NR þ !IR !q þ iq q where the summation is made over the vibrational modes. The appearance of the nonresonant contribution ð2Þ S;NR in the hyperpolarizability tensor is the source for interference in the SFG spectra. Interestingly, Eq. (25) must be slightly modified for the case of DFG: X Aq ð2Þ ð2Þ ð26Þ S ¼ S;NR þ ! !q iq IR q this simple change in phase allowing one to disentangle the nonresonant from the resonant contribution if the SFG and the DFG spectra are collected [118]. B.
Vibrational Surface Spectrum of Solvents
The first vibrational surface spectrum recorded was that of the CH stretch region of methanol at the air–methanol interface [119]. It yielded a molecular picture of the interface where the end CH3 group is pointing into the air in agreement with the theoretical predictions [120]. This work initiated the studies on the surface vibrational spectrum of water, since water surfaces represent by far the most widely used system. The spectral region of interest is the OH stretching region extending from 3000 cm1 to 3800 cm1 (see Fig. 9) [121]. Three vibrational modes dominate: the OH stretching mode at 3680 cm1 , the OH stretch at 3400 cm1 , and the OH stretch at 3200 cm1 . The first mode characterizes the free OH bonds pointing out of the water phase. The second one corresponds to bonded O and H atoms within a disordered network, and therefore characterizes the waterlike structure, whereas the third one corresponds to the bonded O and H atoms in a more regular network hence characterizing the icelike structure. The relative magnitude of these modes is indicative of the hydrogen bonding network prevailing at the surface. It was deduced from different sets of experiments involving water–alcohol mixtures and temperature dependence measurements, that the water hydrogen bonding network resembles that of ice next to the interface [122]. The molecular network is formed at the interface by water molecules tetrahedrally coordinated through hydrogen bonds. In this structure, about 25% of the water molecules have a dangling OH bond protruding in the hydrophobic phase. This icelike network is, however, severely distorted, since the peak at 3400 cm1
Nonlinear Optics at Liquid–Liquid Interfaces
145
FIG. 9 Vibrational sum frequency spectrum in the OH mode region of the neat air–water interface at different temperature for the fundamental visible and infrared beams respectively s- and p-polarized and the SFG beam s-polarized. (From Ref. 120, copyright American Physical Society.)
characterizing liquid water is still rather large. A molecular dynamics study has led to similar surface vibrational spectra [123]. These results suggest that liquid surfaces are more ordered than their bulk phase, owing to the strong hydrogen bonding network. This has also been observed at air–alcohol surfaces [124] and also at the water–hexane [122] and the water–CCl4 interfaces [125]. In the CH2 stretching spectral region between 2800 cm1 and 3000 cm1 , information on the alkyl chain conformation can be inferred. For symmetry reasons, the CH2 stretching mode should not be nonlinear optically active in all-trans chains because of the cancellation of the contribution from CH2 groups on both sides of the alkyl chain. Hence, this mode is a nice tool to measure the extent of gauche defects in these chains. Experimentally, at the air–alcohol interface, the weak magnitude of the CH2 stretching mode indicated that the alkyl chains remain almost all-trans with very few gauche defects. The number of defects is rather insensitive to the length of alkyl chain. These results suggest that chain–chain interactions are highly effective in ordering the chains at the interface. At water–alkane interfaces a similar observation can be made, although an increase in the temperature introduces defects in the chain [126,127]. In fact, according to the weak magnitude of the CH3 antisymmetrical stretching mode, the alkyl chains are oriented perpendicular to the surface [126]. The molecular order at the interface can be severely disrupted as it has been demonstrated when methanol is added to an aqueous solution [122]. Inversely, adsorption can lead to an enhancement of the order as is the case
146
Brevet
with small additions of sulfuric acid at the air–water interface [128]. At high acid concentrations, the aqueous surface resembles that of sulfuric acid. Other mixtures have been studied, in particular glycerol–water [129], acetonitrile–water [130], and aqueous salt solutions [131]. C.
Surfactants and Phospholipids
Liquid interfaces have been also investigated in the presence of cationic and anionic surfactants. In the CH2 and the CH3 regions between 2800 and 3000 cm1 , information on the chain–chain interactions can be obtained, whereas in the OH region, information on the water hydrogen bonding network is obtained. The vibrational spectrum of pentadecanoic acid (PDA) at the air–water interface at full coverage for example is dominated by the CH3 symmetrical stretch and the CH3 Fermi resonance modes [127]. The absence of the CH2 modes clearly indicates the high degree of order of the alkyl chains, which take a predominantly all-trans configuration. It also appears that as the surface coverage is reduced, the constraints are released and the number of gauche defects increases, as seen from the increase of the ratio of the intensity of the CH2 mode intensity to the CH3 mode intensity. Interestingly, the headgroup of the surfactant seems to play a nonnegligible role in the ordering process. For a polar cationic head, in the case of dodecylammonium chloride or dodecyltrimethylammonium chloride, the number of gauche defects was lower as compared to the case of sodium dodecylsulfate or sodium dodecylsulfonate for the same alkyl chain length [132]. This was explained in terms of the penetration depth of the polar cationic heads into the aqueous phase, the number of gauche defects being reduced as a result of the shorter length of the alkyl chain protruding outside the aqueous phase. The general picture emerging from these studies can be even more refined if complementary information from other techniques like neutron reflection experiments are included [133]. In the spectral region of the OH modes, the structure of water itself is obtained in the presence of the surfactant monolayer. In the case of pentadecanoic acid at the air–water interface, the OH peak at 3200 cm1 was found to dominate over the one at 3450 cm1 , underlining the tetrahedral arrangement of the hydrogen bonding network of the water molecules in an icelike structure [127]. More strikingly, it has been possible to observe the orientation flip of the water molecules with the sign of the surface charge introduced by the surfactants polar heads. A constructive interference in the region of 2970 cm1 between the CH3 Fermi resonance mode and the OH stretching mode lying at 3200 cm1 has been observed for the cationic surfactant dodecylammonium chloride. Conversely, a destructive interference between these two modes was reported for the anonic surfactant sodium dodecylsulfonate [134,135]. The interference arises from the reversal of the alignment direction of the water dipoles in the vicinity of the interface upon the change of the sign of the surface charge. With a cationic surfactant, the water molecules are preponderantly oriented with the oxygen pointing towards the surface, whereas in the presence of the anionic surfactant, the hydrogen atoms point towards the surface. At neutral surfaces, where a mixed monolayer of cationic and anionic surfactants was spread, the alignment of the water molecules was lost and the corresponding signal of the OH stretching mode at 3200 cm1 was negligible. One major interest in vibrational surface spectroscopy is the ability to directly probe lipid layers. Similarly to the previous case, the structure of the alkyl chains of phospholipids is readily determined from the ratio of the magnitude of the CH2 and CH3 symmetrical stretching modes [136,137]. At the D2 O–CCl4 interface, a layer of
Nonlinear Optics at Liquid–Liquid Interfaces
147
dilauroylphosphatidylcholine (DLPC) at a coverage of 50 A2 /molecule was found to possess a high degree of order (see Fig. 10) [138]. Indeed, the ratio of the two CH2 and CH3 symmetrical stretching modes indicated the dominance of the CH3 symmetrical stretching mode as a result of the cancellation of the contribution of the different CH2 groups along the chains. This is the result of nearly gauche defect free chains, indicative of high chain order. The alkyl chain of DLPC is 12 carbons long and these results were compared to longer alkyl chain length phosphatidylcholines, like dimyristoyl (DMPC), dipalmitoyl(DPPC), and distearoyl- (DSPC) phosphatidylcholines with alkyl chains 14, 16, and 18 carbons long, respectively. Surprisingly, it is observed that, at odds with the results obtained at the air–water interface, at the D2 O–CCl4 interface the longer the alkyl chain length is, the larger is the disorder [138]. A similar behavior has been observed at the solid–liquid interface [139]. The reason is that the organic solvent screens the chain– chain interactions leading to the reduction of the constraints within the chains. As opposed to the air–water interface, long alkyl chains at oil–water interfaces are more readily permeable to the organic solvent.
VII.
CONCLUSIONS
Liquid interfaces are widely found in nature as a substrate for chemical reactions. This is rather obvious in biology, but even in the diluted stratospheric conditions, many reactions occur at interfaces like the surface of ice crystallites. The number of techniques available to carry out these studies is, however, limited and this is particularly true in optics, since linear optical methods do not possess the ultimate molecular resolution. This resolution is inherent to nonlinear optical processes of even order. For liquid–liquid systems, optics turns out to be rather powerful owing to the possibility of nondestructively investigating buried interfaces. Furthermore, it appears that planar interfaces are not the only config-
FIG. 10 Vibrational sum frequency spectrum of saturated monolayers of dilauroyl- (DLPC), dimyristoyl- (DMPC), dipalmitoyl- (DPPC), and distearoyl-phosphatidylcholine (DSPC) at the D2 O–CCl4 interface at ambient temperature in the region of the methylene and methyl symmetrical stretches. (From Ref. 139, copyright American Chemical Society.)
148
Brevet
uration accessible to the experiment as recently demonstrated for spherical microscopic particles. The molecular resolution obtained by spectroscopy, combined with the surface specificity of nonlinear optics, has brought to light a detailed picture of interfaces in good agreement with the data obtained by other techniques like neutron reflection, for example, or calculations, molecular dynamics, or continuum models. One parameter of great interest has been the possibility of determining an angle of orientation for the compounds sitting at the interface. Unfortunately, information on the distribution function for this angle is difficult to obtain by independent measurements. Nevertheless, this is of real interest for interfacial reactions involving light absorption like photosynthesis or interfacial ET reactions. This is probably the reason for the large predominance of reports appearing in the literature on this topic as compared to dynamics or reactivity at interfaces. The latter two fields will certainly emerge as two new directions as new laser sources with better time resolution appear on the market. SFG will certainly benefit too from these technological advances as long wavelengths become easier to produce.
ACKNOWLEDGMENTS The author acknowledges the generous support of the Fond national Suisse and fruitful discussions at the Laboratoire d’Electrochimie of the Ecole Polytechnique Fe´de´rale de Lausanne with J. Rinuy, A. Piron, P. Galletto, D. J. Fermin, and H. H. Girault. The Laboratoire d’Electrochimie is part of the European Network on Training and Mobility of Researchers ‘‘Organization, Dynamics and Reactivity of Electrified Liquid–Liquid Interfaces (ODRELLI).’’
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
A. J. Bard and L. R. Faulkner, in Electrochemical Methods, Fundamentals and Applications, Wiley, New York, 1980. A. G. Volkov and D. W. Deamer (eds.), Liquid–Liquid Interfaces, Theory and Methods, CRC Press, Boca Raton, 1996. H. H. Girault, in Modern Aspects of Electrochemistry (J. O’Bockris et al., eds.), vol. 25, Plenum Press, New York, 1993. H. H. Girault and D. J. Schiffrin, in Electroanalytical Chemistry (A. J. Bard, ed.), vol. 15, Marcel Dekker, New York, 1989. Z. Ding, R. G. Wellington, P. F. Brevet, and H. H. Girault. J. Electroanal. Chem. 420:35 (1997). T. Kakiuchi, Y. Takasu, and M. Senda. Anal. Chem. 64:3096 (1992). T. Kakiuchi and Y. Takasu. Anal. Chem. 66:1853 (1994). T. Kakiuchi and Y. Takasu. J. Phys. Chem. B. 101:5963 (1997). H. Duong, P. F. Brevet, and H. H. Girault. J. Photochem. Photobiol. A: Chemistry 117:27 (1998). D. J. Fermin, Z. Ding, P. F. Brevet, and H. H. Girault. J. Electroanal. Chem. 447:125 (1998). T. Takenaka and T. Nakanaga. J. Phys. Chem. 80:475 (1976). T. Takenaka. Chem. Phys. Lett. 55:515 (1978). J. M. Perera, J. K. McCulloch, B. S. Murray, F. Grieser, and G. W. Stevens. Langmuir 8:366 (1992). M. J. Wirth and J. D. Burbage. J. Phys. Chem. 96:9022 (1992).
Nonlinear Optics at Liquid–Liquid Interfaces 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.
149
Y. R. Shen, The Principles of Nonlinear Optics, Wiley, New York, 1986. G. L. Richmond, in Electroanalytical Chemistry (A. J. Bard, ed.), vol. 17, Marcel Dekker, New York, 1991, p. 87. Y. R. Shen. Ann. Rev. Mater. Sci. 16:69 (1986). S. G. Grubb, M. W. Kim, T. Rasing, and Y. R. Shen. Langmuir 4:452 (1988). K. B. Eisenthal. Chem. Rev. 96:1343 (1996). R. M. Corn and D. A. Higgins. Chem. Rev. 94:107 (1994). M. Born and E. Wolf, The Principles of Optics, Pergamon Press, Oxford, 1980. P. F. Brevet, Surface Second Harmonic Generation, Presses Polytechniques Universitaires Romandes, Lausanne, 1997. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, Cambridge University Press, Cambridge 1992. N. Bloembergen and P. S. Pershan. Phys. Rev. 128:606 (1962). N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee. Phys. Rev. 174:813 (1968). C. C. Wang. Phys. Rev. 178:1457 (1969). T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena (V. M. Agranovich and A. A. Maradudin, eds.), vol. 29, North-Holland, New York, 1991. V. Mizrahi and J. E. Sipe. J. Opt. Soc. Am. B 5:660 (1988). I. Benjamin. J. Phys. Chem. A 102:9500 (1998). H. Wang, E. Borguet, and K. B. Eisenthal. J. Phys. Chem. B. 102:4927 (1998). J. C. Conboy, J. L. Daschbach, and G. L. Richmond. J. Phys. Chem. 98:9688 (1994). J. F. Ward and C. K. Miller. Phys. Rev. A 19:826 (1979). B. F. Levine and C. G. Bethea. J. Chem. Phys. 65:2429 (1976). J. L. Oudar, D. S. Chemla, and E. Batifol. J. Chem. Phys. 67:1626 (1977). M. Blanchard-Desce, V. Alain. P. V. Bedworth, S. R. Marder, A. Fort, C. Runser, M. Barzoukas, S. Lebus, and R. Wortmann. Chem. Eur. J. 3:1091 (1997). P. Guyot-Sionnest and Y. R. Shen. Phys. Rev. B 38:7985 (1988). P. Guyot-Sionnest and Y. R. Shen. Phys. Rev. B 35:4420 (1985). P. F. Brevet. J. Chem. Soc. Faraday Trans. 92:4547 (1996). A. A. Tamburello-Luca, P. He´bert, P. F. Brevet, and H. H. Girault. J. Chem. Soc. Faraday Trans. 91:1763 (1995). R. Antoine, F. Bianchi, P. F. Brevet, and H. H. Girault. J. Chem. Soc. Faraday Trans. 93:3833 (1997). T. Raising, G. Berkovic, Y. R. Shen, S. G. Grubb, and M. W. Kim. Chem. Phys. Lett. 130:1 (1986). M. C. Goh, J. M. Hicks, K. Kemnitz, G. R. Pinto, K. Bhattacharyya, K. B. Eisenthal, and T. F. Heinz. J. Phys. Chem. 92:5074 (1988). M. C. Goh and K. B. Eisenthal. Chem. Phys. Lett. 157:101 (1989). R. M. Corn and D. A. Higgins, in Molecular Orientation in Thin Films as Probed by Optical Second Harmonic Generation, vol. 6, Manning Publishers, Greenwich, 1994. J. L. Oudar and J. Zyss. Phys. Rev. A. 26:2016 (1982). G. J. Simpson and K. L. Rowlen. J. Am. Chem. Soc. 121:2635 (1999). A. A. Tamburello-Luca, P. He´bert, P. F. Brevet, and H. H. Girault. J. Chem. Soc. Faraday Trans. 92:3079 (1996). A. Castro, K. Bhattacharyya, and K. B. Eisenthal. J. Chem. Phys. 95:1310 (1991). L. D. Barron, Molecular Light Scattering and Optical Activity, Cambridge University Press, Cambridge, 1982. T. Petralli-Mallow, T. M. Wong, J. D. Byers, H. I. Yee, and J. M. Hicks. J. Phys. Chem. 97:1383 (1993). T. Verbiest, S. V. Elshocht, M. Kauranen, L. Hellemans, J. Snauwaert, C. Nuckolls, T. J. Katz, and A. Persoons. Science 282:913 (1998). L. Hecht and L. D. Barron. Mol. Phys. 89:61 (1996). P. Ye and Y. R. Shen. Phys. Rev. B 28:4288 (1983).
150
Brevet
54. 55. 56. 57. 58.
D. A. Higgins and R. M. Corn. J. Phys. Chem. 97:489 (1993). G. Berkovic, Y. R. Shen, G. Marowsky, and R. Steinhoff. J. Opt. Soc. Am. B 6:205 (1989). J. Rinuy, P. F. Brevet, and H. H. Girault. Biophys. J. 77:3350 (1999). H. Paul and R. Corn. J. Phys. Chem. B 101:4494 (1997). K. Das, N. Sarkar, S. Das, A. Datta, D. Nath, and K. Bhattacharyya. J. Chem. Soc. Faraday Trans. 92:4993 (1996). N. Sarkar, K. Das, S. Das, D. Nath, and K. Bhattacharyya. J. Chem. Soc. Faraday Trans. 91:1769 (1995). J. M. Hicks, K. Kemnitz, K. B. Eisenthal, and T. F. Heinz. J. Phys. Chem. 90:560 (1986). A. J. Bell, J. G. Frey, and T. J. VanderNoot. J. Chem. Soc. Faraday Trans. 88:2027 (1992). A. Pohorille and I. Benjamin. J. Chem. Phys. 94:5599 (1991). A. Pohorille and I. Benjamin. J. Phys. Chem. 97:2664 (1993). K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz. Chem. Phys. Lett. 131:285 (1986). J. Rinuy, A. Piron, P. F. Brevet, H. H. Girault, and M. Blanchard-Desce, Chem. Eur. J, in press. T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen. Phys. Rev. Lett. 48:478 (1982). P. D. Lazzaro, P. Mataloni, and F. D. Martini. Chem. Phys. Lett. 114:103 (1985) V. Vogel, C. S. Mullin, and Y. R. Shen. Langmuir 7:1222 (1991). T. Rasing, Y. R. Shen, M. W. Kim, P. Valint, and J. Bock. Phys. Rev. A 31:537 (1985). U. Elstner, G. Marowsky, G. Busse, and M. Kahlweit. Anal. Sci. 14:31 (1998). T. Rasing, T. Stehlin, Y. R. Shen, M W. Kim, and P. Valint. J. Chem. Phys. 89:3386 (1988). T. Rasing, Y. R. Shen. M. W. Kim, and S. G. Grubb. Phys. Rev. Lett. 55:2903 (1985). X. Zhao, M. C. Goh, S. Subrahmanyan, and K. B. Eisenthal. J. Phys. Chem. 94:3370 (1990). O. N. Slyadneva, M. N. Slyadnev, V. M. Tsukanova, T. Inoue, A. Harata, and T. Ogawa. Langmuir 15:8651 (1999). X. Zhao, M. C. Goh, and K. B. Eisenthal. J. Phys. Chem. 94:2222 (1990). T. Nakano, Y. Yamada, T. Matsuo, and S. Yamada. J. Phys. Chem. B. 102:8569 (1998). D. J. Donaldson, J. A. Guest, and M. C. Goh. J. Phys. Chem. 99:9313 (1995). F. M. Geiger, A. C. Tridico, and J. M. Hicks. J. Phys. Chem. B 103:8205 (1999). I. Benjamin. J. Chem. Phys. 95:3698 (1991). H. Wang, E. Borguet, and K. B. Eisenthal. J. Phys. Chem. A 101:713 (1997). C. Reichardt, Solvent and Solvent Effects in Organic Chemistry, VCH Publishers, Weinheim, 1988. D. Michael and I. Benjamin. J. Phys. Chem. B. 102:5145 (1998). Y. Kharkats and J. Ulstrup. J. Electroanal. Chem. 308:17 (1991). A. A. Tamburello-Luca, P. He´bert, P. F. Brevet, and H. H. Girault. Langmuir 13:4428 (1997). K. Bhattacharyya, E. V. Sitzman, and K. B. Eisenthal. J. Chem. Phys. 87:1442 (1987). X. D. Xiao, V. Vogel, and Y. R. Shen. Chem. Phys. Lett. 163:555 (1989). X. Xiao, V. Vogel, Y. R. Shen, and G. Marowsky. J. Chem. Phys. 94:2315 (1991). R. R. Naujok, D. A. Higgins, D. G. Hanken, and R. M. Corn. J. Chem. Soc. Faraday Trans. 91:1411 (1995). X. Zhao, S. Subrahmanyan, and K. B. Eisenthal. Chem. Phys. Lett. 171:558 (1990). D. A. Higgins, R. R. Naujok, and R. M. Corn. Chem. Phys. Lett 213:485 (1993). J. Conboy and G. Richmond. J. Phys. Chem. B 101:983 (1997). D. Zimdars, J. I. Dadap, K. B. Eisenthal, and T. F. Heinz. J. Phys. Chem. B. 103:3425 (1999). A. Castro, E. V. Sitzmann, D. Zhang, and K. B. Eisenthal. J. Phys. Chem. 95:6752 (1991). R. Antoine, A. A. Tamburello-Luca, P. He´bert, P. F. Brevet, and H. H. Girault. Chem. Phys. Lett. 288:138 (1998). G. R. Fleming, Chemical Applications of Ultrafast Spectroscopy, International Series of Monographs on Chemistry, vol. 13, Oxford University Press, Oxford, 1986. I. Benjamin. Chem. Rev. 96:1449 (1996). E. Borguet, X. Shi, and K. B. Eisenthal. Springer Series in Chemical Physics 60:304 (1994).
59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97.
Nonlinear Optics at Liquid–Liquid Interfaces 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139.
151
E. V. Sitzmann and K. B. Eisenthal. J. Phys. Chem. 92:4579 (1988). R. R. Naujok, H. J. Paul, and R. M. Corn. J. Phys. Chem. 100:10497 (1996). D. J. Fermin, H. D. Duong, Z. Ding, P. F. Brevet, and H. H. Girault. J. Am. Chem. Soc. 121:10203 (1999). K. L. Kott, D. A. Higgins, R. J. McMahon, and R. M. Corn. J. Am. Chem. Soc. 115:5342 (1993). R. A. W. Dryfe, Z. Ding, R. G. Wellington, P. F. Brevet, A. M. Kuznetzov, and H. H. Girault. J. Phys. Chem. 101:2519 (1997). H. D. Duong, P. F. Brevet, and H. H. Girault. J. Photochem. Photobiol. A: Chemistry 107:27 (1998). M. J. Crawford, J. G. Frey, T. J. vanderNoot, and Y. Zhao. J. Chem. Soc. Faraday Trans. 92:1369 (1996). K. Tohda, Y. Umezawa, S. Yoshiyagawa, S. Hashimoto, and M. Kawasaki. Anal. Chem. 67:570 (1995). S. Yajima, K. Tohda, P. Buhlmann, and Y. Umezawa. Anal. Chem. 69:1919 (1997). R. Antoine, M. Pellarin, B. Prevel, B. Palpant, M. Broyer, P. Galletto, P. F. Brevet, and H. H. Girault. J. Appl. Phys. 84:4532 (1998). P. Galletto, P. F. Brevet, H. H. Girault, R. Antoine, and M. Broyer. J. Phys. Chem. B 103:8706 (1999). E. C. Y. Yan, Y. Liu, and K. B. Eisenthal. J. Phys. Chem. B 102:6331 (1998). E. C. Y. Yan and K. B. Eisenthal. J. Phys. Chem. B 103:6056 (1999). G. S. Agarwal and S. S. Jha. Solid State Commun. 41:499 (1982). P. Galletto, P. F. Brevet, H. H. Girault, R. Antoine, and M. Broyer. Chem. Commun. 581 (1999). J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz. Phys. Rev. Lett. 83:4045 (1999). K. Clays, E. Hendrikx, M. Triest, and A. Persoons. J. Mol. Liq. 67:133 (1995). H. Wang, E. C. Y. Yan, E. Borguet, and K. B. Eisenthal. Chem. Phys. Lett. 259:15 (1996). A. Srivastava and K. B. Eisenthal. Chem. Phys. Lett. 292:345 (1998). P. B. Miranda and Y. R. Shen. J. Phys. Chem. B 103:3292 (1999). P. He´bert, A. le Rille, W. Q. Zheng, and A. Tadjeddine. J. Electroanal. Chem. 447:5 (1998). R. Superfine, J. Y. Huang, and Y. R. Shen. Phys. Rev. Lett. 66:1066 (1991). M. Matsumoto and Y. Kataoka. J. Phys. Chem. 90:2398 (1988). Q. Du, R. Superfine, E. Freysz, and Y. R. Shen. Phys. Rev. Lett. 70:2313 (1993). Q. Du. E. Freysz, and Y. R. Shen. Science 264:826 (1994). I. Benjamin. Phys. Rev. Lett. 73:2083 (1994). C. D. Stanners, Q. Du, R. P. Chin, P. Cremer, G. A. Samorjai, and Y. R. Shen. Chem. Phys. Lett. 232:407 (1995). D. E. Gragson and G. L. Richmond. Langmuir 13:4804 (1997). G. A. Sefler, Q. Du, P. B. Miranda, and Y. R. Shen. Chem. Phys. Lett. 235:347 (1995). P. Guyot-Sionnest, J. H. Hunt, and Y. R. Shen. Phys. Rev. Lett. 59:1597 (1987). C. Raduge, V. Pflumio, and Y. R. Shen. Chem. Phys. Lett. 274:140 (1997). S. Baldelli, C. Schnitzer, M. Shultz, and D. Campbell. J. Phys. Chem. B 101:4607 (1997). D. Zhang, J. H. Gutow, K. B. Eisenthal, and T. F. Heinz. J. Chem. Phys. 98:5099 (1993). S. Baldelli, C. Schnitzer, M. J. Schultz, and D. J. Campbell. Chem. Phys. Lett. 287:143 (1998). J. C. Conboy, M. C. Messmer, and G. L. Richmond. J. Phys. Chem. B 101:6724 (1997). G. R. Bell, C. D. Bain, Z. X. Li, R. K. Thomas, D. C. Duffy, and J. Penfold. J. Am. Chem. Soc. 119:10227 (1997). D. E. Gragson, B. M. McCarthy, and G. L. Richmond. J. Am. Chem. Soc. 119:6144 (1997). D. E. Gragson and G. L. Richmond. J. Am. Chem. Soc. 120:366 (1998). R. A. Walker, J. A. Gruetzmacher, and G. L. Richmond. J. Am. Chem. Soc. 120:6991 (1998). B. L. Smiley and G. L. Richmond. J. Phys. Chem. B 103:653 (1999). R. A. Walker, J. C. Conboy, and G. L. Richmond. Langmuir 13:3070 (1997). P. B. Miranda, V. Pflumio, H. Saijo, and Y. R. Shen. Chem. Phys. Lett. 267:387 (1997).
7 The Lattice-Gas and Other Simple Models for Liquid^Liquid Interfaces WOLFGANG SCHMICKLER Ulm, Ulm, Germany
I.
Department of Electrochemistry, University of
INTRODUCTION
The lattice gas has been used as a model for a variety of physical and chemical systems. Its application to simple mixtures is routinely treated in textbooks on statistical mechanics, so it is natural to use it as a starting point for the modeling of liquid–liquid interfaces. In the simplest case the system contains two kinds of solvent particles that occupy positions on a lattice, and with an appropriate choice of the interaction parameters it separates into two phases. This simple version is mainly of didactical value [1], since molecular dynamics allows the study of much more realistic models of the interface between two pure liquids [2,3]. However, even with the fastest computers available today, molecular dynamics is limited to comparatively small ensembles, too small to contain more than a few ions, so that the space-charge regions cannot be included. In contrast, Monte Carlo simulations for the lattice gas can be performed with 105 to 106 particles, so that modeling of the space charge poses no problem. In addition, analytical methods such as the quasichemical approximation allow the treatment of infinite ensembles. Therefore the lattice-gas model has proved most useful for the study of those processes in which the ionic double layer plays a major role, and there are quite a few. So it has been used to investigate the interfacial capacity, electron and ion-transfer reactions, and even such complex processes as ion pairing and assisted ion transfer. Because of its simplicity we cannot expect this model to give quantitative results for particular systems, but it is ideally suited to qualitative investigations such as the prediction of trends and orders of magnitude for various effects. In the following we will review recent applications of the lattice-gas model to liquid– liquid interfaces. We will start by presenting the basics of the model and various ways of treating its statistical mechanics. Then we will present model calculations for interfacial properties and for electron- and ion-transfer reactions. It is one of the virtues of the latticegas model that it is sufficiently flexible to serve as a framework for practically all processes at these interfaces. Of course, the lattice gas is not the only simple model that has been proposed for liquid–liquid interfaces. So we will conclude this review by a survey of several other models, which have usually been devised for certain aspects such as the interfacial capacity or ion transfer. Some of these models give a similar view of the interface, while others are radically different. 153
154
II.
Schmickler
THE BASICS OF THE LATTICE-GAS MODEL
All applications of the lattice-gas model to liquid–liquid interfaces have been based upon a three-dimensional, typically simple cubic lattice. Each lattice site is occupied by one of a variety of particles. In the simplest case the system contains two kinds of solvent molecules, and the interactions are restricted to nearest neighbors. If we label the two types of solvents molecules S1 and S2 , the interaction is specified by a symmetrical 2 2 matrix wij , where each element specifies the interaction between two neighboring molecules of type Si and Sj . Whether the system separates into two phases or forms a homogeneous mixture, depends on the relative strength of the cross-interaction w12 with respect to the self-interaction terms w11 and w22 , which can be expressed through the combination: w ¼ w12 ðw11 þ w22 Þ=2
ð1Þ
If w=kT is large, the system separates into two phases: phase 1 contains mainly solvent molecules S1 and has only a low concentration of S2 , and phase 2 is mainly composed of S2 . If w is small, entropy wins and the systems forms one phase. Details will be discussed below. If the system separates, it can be extended to a model for the interface between two solutions by introducing ions. In the basic case the system contains a salt composed of cations K1þ and anions A 1 which is preferentially solvated by the solvent S1 , but badly solvable in solution 2, and a salt K2þ A 2 that is preferentially dissolved in solvent 2. This can be achieved by choosing suitable interaction parameters between the ions and the two solvents. In addition to the nearest-neighbor interaction, each ion experiences the electrostatic potential generated by the other ions. In the literature this has generally been equated with the macroscopic potential calculated from the Poisson–Boltzmann equation. This corresponds to a mean-field approximation (vide infra), in which correlations between the ions are neglected. This approximation should be the better the low the concentrations of the ions.
III.
METHODS FOR TREATING THE LATTICE GAS
A.
The Mean-Field Approximation
The simplest treatment of the lattice-gas model is through the mean-field or randommixing approximation, which is treated in a number of textbooks (see, e.g., Refs. 1 and 4). We give a short summary of its application to liquid–liquid interfaces, since it nicely illustrates under what conditions the phases separate. We consider a system composed of N1 solvent molecules S1 and N2 molecules S2 ; by Nij , i; j ¼ 1; 2 we denote the numbers of nearest-neighbor pairs fi; jg. The energy E of the mixture is then: E ¼ N11 w11 þ N22 w22 þ N12 w12
ð2Þ
The numbers of pairs are related to the numbers of molecules and the number m of nearest neighbours: mN1 ¼ 2N11 þ N12
ð3Þ
mN2 ¼ 2N22 þ N12
ð4Þ
The Lattice-Gas and Other Models
155
These relations can be used to introduce the quantities: E11 ¼ mN1 w11 =2
ð5Þ
E22 ¼ mN2 w22 =2
ð6Þ
and to rewrite the energy in the form: E ¼ E11 þ E22 þ N12 w
ð7Þ
where w has been defined in the previous section. So far the treatment has been exact. The mean-field approximation consists in assuming that the particles are randomly mixed, so that: N12 ¼ mNx1 x2
with
x1 ¼ N1 =N; x2 ¼ N2 =N
ð8Þ
where N is the total number of molecules, and the two mole fractions are related by x1 þ x2 ¼ 1. The Helmholtz free energy is obtained by adding the entropy term; this equals the Gibbs free energy, since the lattice is fixed and does not change with pressure. Hence we obtain: G ¼ E11 þ E22 þ mNx1 x2 w þ NkT ðx1 ln x1 þ x2 ln x2 Þ
ð9Þ
The last two terms give the free energy of mixing, which we rewrite in the compact form: Gmix ¼ x1 ð1 x1 Þ þ x1 ln x1 þ ð1 x1 Þ lnð1 x1 Þ NkT
ð10Þ
where ¼ mw=kT. Figure 1 shows the Gibbs energy of mixing as a function of the composition x1 for various values of . All curves are symmetrical with respect to the line x1 ¼ 1=2. For > 2 the curve has a maximum at x1 ¼ 1=2 and two symmetrically placed minima. In this case the mixture will separate into two phases, each corresponding
FIG. 1 Gibbs energy of mixing as a function of the composition in the mean-field approximation; the values of are from top to bottom: 3.0, 2.5, 2.0 (critical value), 1.0, 0.0, 0:5. (After Ref. 1 with permission from the author.)
156
Schmickler
to a minimum. For < 2 there is only one minimum at x1 ¼ 1=2, and the mixture will not separate. While these results are qualitatively correct, in an exact treatment of the model the critical interaction is generally not at ¼ 2, but lies at a different value, which will depend on the geometry of the lattice and not only on the number of nearest neighbors. Also, this treatment says nothing about the structure of the interface. It can be extended by introducing gradient terms, which allow the calculation of density profiles for the two solvents [1,5]. Since there are more accurate methods available for this purpose we refer to the cited literature. B.
The Quasichemical Approximation
The mean-field approximation neglects correlations between the particles and is therefore not very accurate. The quasichemical approximation improves upon this by accounting for the correlations between pairs of neighboring particles. We briefly give the essence of this method, since it will be used in a few studies reported below. Detailed accounts can be found in the literature [6]. We consider the basic case in which the system is composed of two solvents. The formation of pairs (1,2) is supposed to be in equilibrium with pairs (1; 1) and (2; 2), and considered to be a reaction of the type: 2ð1; 2Þ Ð ð1; 1Þ þ ð2; 2Þ
ð11Þ
The equilibrium condition is expressed through the partition functions qij per pair of particles: q11 / expðw11 =kT Þ
q22 / expðw22 =kT Þ
q12 / 2 expðw12 =kT Þ
ð12Þ
all with the same proportionality constant; the extra factor of 2 in the last term is due to the twofold degeneracy. This gives: 1 N12 ¼ ðN11 N22 Þ1=2 expðw=kTÞ 2
ð13Þ
From this equation and Eqs. (2) and (4) the energy of the system can be obtained. The entropy is more difficult to derive, and we refer to the literature [4,6]. Generally, the quasichemical gives better results than the mean-field approximation, since it allows for local order. We note that for the three-dimensional lattice gas no exact analytical solution exists. C.
Monte Carlo Simulations
Monte Carlo simulations offer a convenient way of obtaining numerically exact results. If the short-range interactions are restricted to nearest neighbors, and the Coulomb interaction effected through the average macroscopic potential, quite large ensembles can be handled, and the incorporation of the space-charge regions poses no problems. The simulations are typically performed on a three-dimensional lattice, each site being numbered by a triple ðl; m; nÞ of integers. Let the region l < 0 be occupied by solution 1, l > 0 by solution 2. The simulations usually start with the particles pertaining to solution 1, i.e., the solvent S1 and, if present, the ions K1þ and A 1 , distributed randomly in l < 0; similarly, the particles of solution 2 are in the region l > 0. Equilibrium is attained through a Metropolis [7] algorithm, which can be implemented in the following way:
The Lattice-Gas and Other Models
157
During one Monte Carlo step each particle is sampled in turn; a nearest neighbor is chosen at random, and the energy E for an exchange of the two particles is calculated. If E < 0, the two particles are always exchanged. If E > 0, a random number r 2 ð0; 1Þ is chosen, and the exchange is effected if expðE=kTÞ > r. The first N steps, with N being of the order of 104 –105 , are discarded, and in the subsequent steps the distributions of the particles and of the electrostatic potential, and other properties of the system are sampled. The interface can be charged by adding an excess number of cations to one phase, and an equal number of anions to the other phase. For certain purposes extra particles may be added to the basic setup. The Monte Carlo method is quite flexible, and for reasonable ensemble sizes such as 100 20 20 particles, it is also quite fast, a typical run taking no more than a few hours on a decent computer.
IV.
RESULTS OF MODEL CALCULATIONS FOR THE LATTICE GAS
A.
Structure of the Interface
We first consider the simplest system consisting of two pure, immiscible solvents. Within the lattice-gas model the energetics of the system on a particular lattice are governed by the single parameter w [see Eq. (1)], which determines the structure of the interface and the particle profiles. The results presented in this section are for a simple cubic lattice. Monte Carlo simulation shows [8] that at a given instance the interface is rough on a molecular scale (see Fig. 2); this agrees well with results from molecular-dynamics studies performed with more realistic models [2,3]. When the particle densities are averaged parallel to the interface, i.e., over n and m, and over time, one obtains one-dimensional particle profiles f1 ðlÞ and f2 ðlÞ ¼ 1 f1 ðlÞ for the two solvents S1 and S2 , which are conveniently normalized to unity for a lattice that is completely filled with one species. Figure 3 shows two examples for such profiles. Note that the two solvents are to some extent soluble in each other, so that there is always a finite concentration of solvent 1 in the phase
FIG. 2 Snapshot of the interface of a gas on a simple cubic lattice with dimensions 100 16 16 for w=kT ¼ 0:6; the average position of the interface is between l ¼ 50 and l ¼ 51.
158
Schmickler
FIG. 3 Fig. 2.
Density profile f2 ðlÞ of the solvent S2 for two different values q=kT; other parameters as in
that consists mainly of solvent 2, and vice versa. The smaller w, the larger this solubility – remember that for sufficiently small values of w the two solvents mix completely. The width of the interface can be defined by fitting these profiles to a suitable function; a possible choice is: f ðxÞ ¼ fb þ
1 2fb ð1 þ tanhðx xs Þ=Þ 2
ð14Þ
where fb is the bulk concentration of solvent S1 in phase 1, xs is the position of the interface, and measures the width of the interface. There is a simple correlation between the width of the interface, the surface energy, and the miscibility of the solvents (see Table 1): the lower the surface energy, the wider is the interface, and the greater the miscibility of the solvents. This relation, which is intuitively expected, has also been observed in a density-functional study of an ensemble of dipoles [5], on which we will report below (see Section V.B). In the simple systems discussed so far the particle profiles are necessarily symmetrical with respect to the interface. This need no longer be the case for more complicated systems with several particles. As an example we show in Fig. 4 the particle profiles at the interface between an aqueous solution and a PVC-based membrane. B.
The Interfacial Capacity
The simplest model for the ionic distribution at liquid–liquid interfaces is the Verwey– Niessen model [10], which consists of two Gouy–Chapman space-charge layers back to TABLE 1 Interaction Parameter w, Decay Length (in Lattice Constants), and Bulk Composition fb for a Lattice Gas. Other System Parameters as in Fig. 2 w 0.5 0.6 0.7
fb
2.1 1.2 0.8
0.885 0.956 0.979
The Lattice-Gas and Other Models
159
FIG. 4 Particle profile at the interface between an aqueous solution (open triangles) and a PVCbased membrane (full squares). Data taken from [9].
back. One would expect this model to work well at low ionic concentrations, however, there one often finds that the interfacial capacity is higher than that predicted by Verwey and Niessen. This is illustrated in Fig. 5, which shows the interfacial capacity at the potential of zero charge for several 10 mM solutions in contact with an aqueous solution. In contrast, at metal–solution interfaces the capacity is typically lower than predicted by the Gouy–Chapman theory.
FIG. 5 Comparison of the experimental capacity Cexp and the Verwey–Niessen capacity CVN at the potential of zero charge for 10 mM ionic solutions in various solvents. Details of these systems can be found in Ref. 11.
160
Schmickler
An explanation of this fact was offered by Pereira et al. [11] and by Huber et al. [12]: the overlap of the two solvents at the interface entails an overlap of the two space-charge regions. Thus the average separation between the opposing charges is reduced, and the capacity enhanced. Both groups performed explicit calculations; the former employed the quasichemical approximation, while the latter performed Monte Carlo simulations. To some extent these two techniques complement each other: the quasichemical approximation should be good at low electrolyte concentrations, while the Monte Carlo simulations, because of the finite ensemble size, are performed for more concentrated solutions. We first summarize the work of Pereira et al. [11]. The authors assume that the distribution of the two solvents is fixed, and given by: ( 1 12 expðx=Þ for x < 0 f1 ðxÞ ¼ ð15Þ 1 for x > 0 2 expðx=Þ where measures the width of the interface. The nearest-neighbor interactions of the ions with the solvents have to be chosen þ such that the ions K1þ and A 1 are preferentially solvated in solvent 1, K2 and A2 in solvent þ 2. The simplest choice is to set the interaction of K1 and A1 with S1 equal u, and with solvent S2 equal to u, where u < 0. Similarly, the interactions of K2þ and A 2 with S1 and S2 are u and u, respectively. Of course, nonsymmetrical choices are also possible, and are discussed in the original paper. The interaction parameter u determines the energy of transfer of the ion between the two pure solvents, which is 2mu. The energy of the cations K1þ can be written as: þ þ E1þ ¼ uN11 uN12
ð16Þ
where N1jþ ði ¼ 1; 2Þ denotes the number of pairs of ions K1þ and solvent molecules i. Within the quasichemical approximation the number of pairs can be expressed through the numbers N1þ of cations K1þ and solvent molecules N1 and N2 : þ N11 / N1þ N1 exp u
ð17Þ
þ N12 / N1þ N2 exp u
ð18Þ
with the same constant of proportionality. For low ionic concentrations: þ þ N11 þ N12 ¼ mN1þ
ð19Þ
From Eqs. (18) and (19) the numbers of pairs are easily calculated: þ N11 ¼ mN1þ þ ¼ mN1þ N12
f1
f1 e u u e þf
f1 e
f2 e u
2e
u
u
þ f2 e u
ð20Þ ð21Þ
where ¼ 1=kT. The electrochemical potential of the ion is obtained by taking the energy per particle, and by adding an entropy term and the electrostatic interaction per particle; for the entropy Pereira et al. take the expression for an ideal solution. This gives: ~ þ 1 ¼ mu
f1 e u f2 e u þ kT ln cþ 1 þ e0
f1 e u þ f2 e u
ð22Þ
where cþ 1 denotes the concentration, and the electrostatic potential. All ions are assumed to be monovalent. The distribution of the cation K1þ near the interface is obtained from
The Lattice-Gas and Other Models
161
the condition that its electrochemical potential must be the same as in the bulk of solvent S1 , where it has the value: ~ þ 1 ð1Þ ¼ mu þ kT ln c0 þ e0 ð1Þ
ð23Þ
A short calculation gives: þ cþ 1 ðxÞ ¼ c0 exp e0 ½ ðxÞ ð1Þ g1 ðxÞ
ð24Þ
where ðxÞ ¼ exp 2 mu gþ 1
f2 e u f1 e u þ f 2 e u
ð25Þ
Similar equations can be derived for the other ions. The charge density ðxÞ is then obtained by adding the charge densities pertaining to all four kinds of ions. Both ðxÞ and the electrostatic potential ðxÞ are calculated by solving the Poisson equation selfconsistently, and the particle distributions then follow by substituting ðxÞ into Eq. (25) and the respective equations for the other ions. As an example Fig. 6 shows the distribution of the ions for a potential difference of ¼ ð1Þ ð1Þ ¼ kT=e0 between the two bulk phases. In these calculations the dielectric constant was taken as ¼ 80 for both phases, and the bulk concentrations of all ions were assumed to be equal. This simplifies the calculations, and the Debye length LD , which is the same for both solutions, can be used to scale the x axis. The most important feature of these distributions is the overlap of the space-charge regions at the interface, which is clearly visible in the figure.
FIG. 6 Normalized distribution cðxÞ=c0 of the ions for a potential drop of 0 =kT ¼ 1. The full lines give the distribution of the majority ions; in the region x < 0 these are the anions, in x > 0 these are the cations. The dashed lines give the distributions of the counterions. System parameters: m ¼ 4, u ¼ 3kT.
162
Schmickler
The charge density that is stored at the interface is obtained from the particle profiles: ð1 ð1 e0 cþ ðxÞ c ðxÞ ¼ e0 cþ ð26Þ ¼ 1 1 2 ðxÞ c2 ðxÞ 1
1
The interfacial capacity is then obtained by calculating the profiles for various potential drops and subsequent differentiation. Figure 7 shows several examples of capacity– potential characteristics for several widths of the interface. Obviously, the wider the interface, the higher the capacity. In all cases investigated it was higher than that calculated from the Verwey–Niessen model, in which: 1 e
CVN ¼ C0 cosh 0 2 4kT
(Verwey--Niessen)
ð27Þ
with C0 ¼ 0 =LD . In the figure, all capacities have been normalized by dividing through C0 . Huber et al. [12] investigated the same model by Monte Carlo simulations; however, they focused on a different aspect: the dependence of the interfacial capacity on the nature of the ions, which in this model is characterized by the interaction constant u. Samec et al. [13] have observed the following experimental trend: the wider the potential window in which no reactions take place, the lower the interfacial capacity. Since the width of the window is determined by the free energy of transfer of the ions, which is 2mu in this model, the capacity should be lower, the higher juj. In order to check this prediction, Huber et al. performed simulations on a lattice of dimensions 200 20 20; the lattice constant was taken as 4 A˚, and a dielectric constant of ¼ 80 was assumed throughout the system. Since a fair number of ions is needed to obtain good statistics, the ionic concentrations in this study are of the order of 0.1 M. Figure 8 shows the distribution of the ions K1þ and A 1 for two different values of the interactions constant u. The smaller juj, the lower is the repulsion of these ions from phase
FIG. 7 Normalized interfacial capacity versus the potential drop for various widths of the interface. (1) =LD ¼ 0:2; (2) =LD ¼ 0:1; (3) =LD ¼ 0:05; (4) Verwey–Niessen capacity.
The Lattice-Gas and Other Models
163
FIG. 8 Distribution of the cations Kþ 1 and anions A1 at the interface for an excess-charge density of 0.0225 C m2 ; the full symbols are for u ¼ 3kT, the open symbols for u ¼ 1kT. The Debye length was LD ¼ 13:9 A˚, the solvent interaction w ¼ 0:55kT. The lines are meant as guides for the eye.
2, and the larger is the overlap of the space-charge regions; this entails a higher capacity, as can be seen from Fig. 9. These capacity curves illustrate also another effect that becomes important at higher ionic concentrations: when the lattice spacing is of the same order of magnitude as the Debye length, the size of the ions can no longer be neglected, as is usually done in the quasichemical and similar approximations. This finite-size effect reduces the interfacial capacity; therefore, depending on the other system parameters, the capacity can be either higher or lower than predicted by the Verwey–Niessen model. Thermodynamics show that the surface tension becomes lower when the interface is charged; this should lead to a widening of the interface. This has indeed been observed by
FIG. 9 Interfacial capacity for various ion–solvent interactions. System parameters: (1) u ¼ 3kT, (2) u ¼ 2kT; (3) u ¼ 1kT. The crosses denote the Gouy–Chapman capacity. Other parameters as in Fig. 8.
164
Schmickler
TABLE 2 Interfacial Width for Various Energies of Transfer of the Ions; the Other Parameters Are the Same as in Fig. 8 u ðkTÞ 1 1 2 2 3 3
ðVÞ
(A˚)
0 0.091 0 0.1 0 0.1
7.03 8.85 7.03 7.42 7.03 7.16
Huber et al. [12] (see Table 2). Another way of explaining this effect is the following: when the interface is charged the ions experience a stronger field that pulls them toward the other side. Thus they penetrate further into the other solution, and pull a few of their surrounding molecules with them. As expected, this effect is more marked when the free energy of transfer of the ions is small, because then the energy barrier at the interface is lower. C.
Interfacial Ion Pairing
As noted above, the capacity of liquid–liquid interfaces depends on the nature of the ions dissolved in the two adjoining phases. In some cases the capacity is related o the free energy of transfer of the ions involved, but in other cases quite strong dependencies are observed which can be explained by a tendency to form ion pairs at the interface. Evidence for this effect, which was first discussed by Hajkova et al. [14], was obtained in a paper by Cheng et al. [15], who observed marked changes in the capacity when they varied the composition of the aqueous phase. Further examples were provided by Pereira et al. [16], who also performed explicit calculations for ion pairing based on the lattice-gas model. Indeed, ion pairing can be introduced quite easily into the lattice gas by letting one pair of ions pertaining to different phases, e.g., K1þ and A 2 , interact through an attractive potential v < 0. The resulting model can be treated within the quasichemical approximation [16] by calculating the number of pairs of K1þ and A 2 along the line of Eqs. (16) to (21), or by Monte Carlo simulations [17]. Both approaches give qualitatively quite similar results. We review the results of the simulations, which are more recent. Technically, these simulations are very similar to those of Huber et al. [12]; the major difference is the introduction of the attractive potential between the pairing ions. In addition, these authors introduce different dielectric constants 1 and 2 for the two solutions. Near the interface the dielectric constant varies locally according to the simple prescription: x ¼ 1 f1 ðxÞ þ 2 f2 ðxÞ
ð28Þ
In the simulation the values 1 ¼ 80 and 2 ¼ 10 were taken. When phase 1 is negatively charged, the ions K1þ and A 2 are repelled from the interface, and the particle distribution is the same as in the absence of ion pairing. However, when phase 1 is positively charged, these ions are driven towards the surface, where they may form pairs. Hence their concentration at the interface is enhanced (see Fig. 10). This effect is the larger, the higher the excess-charge density, since the probability of
The Lattice-Gas and Other Models
165
FIG. 10 Distribution of the ions Kþ 1 and A2 in the presence (full lines) and in the absence (dashed lines) of ion pairing. In the former case, the ionic interaction parameter was taken as v ¼ 9kT. The surface-charge density was taken as ¼ 2:34 C cm2 in phase 1.
ion pairing depends on the product of the concentrations of K1þ and A 2 , and hence roughly on the square of the excess charge. Ion pairing increases the charge that is stored at a given potential, and hence the interfacial capacity. The capacity characteristics in Fig. 11 show the asymmetry that is quite typical for ion pairing [15].
D.
Ion-Transfer Reactions
In Section IV.B the energy of an ion was calculated by a simple version of the quasichemical approximation. The same procedure can be used to calculate the potential of mean force pmf ðxÞ of an ion [18], which is the average potential that the ion experiences as a function of its position x in the direction perpendicular to the surface. This consists of two
FIG. 11 Interfacial capacity as a function of the total potential drop in the presence and in the absence (solid line) of ion pairing. Dotted line: v ¼ 9kT; dashed line: v ¼ 10kT.
166
Schmickler
components: the chemical part, which in the lattice-gas model is due to the interaction with the nearest neighbors, and the electrostatic part. From Eqs. (20) and (21) we obtain:
pmf ðxÞ ¼ mu
f1 e u f2 e u þ ze0 ðxÞ f1 e u þ f2 e u
ð29Þ
where the first term is the chemical part; z is the charge number of the ion. The potential of mean force is similar to the electrochemical potential, but it does not depend on the concentration; it is the potential that a single ion experiences as it moves toward, and possibly across, the interface. In the two bulk phases the potential of mean force is constant, but it may vary near the interface. The difference in the bulk values of the chemical part is the free energy of transfer of the ion, which in our model is 2mu (we assume u < 0). Let us consider the situation in which the ion-transfer reaction is in equilibrium, and the concentration of the transferring ion is the same in both phases; the system is then at the standard equilibrium potential 00 . In this case the potential of mean force is the same in the bulk of both phases; the chemical and the electrostatic parts must balance: 0 ¼ 2mu
at equilibrium
ð30Þ
Both terms vary near the interface: the chemical term rises by an amount 2mu over a region of width 2, while the electrostatic term drops by the same amount over a region, whose width is given by the two Debye lengths. Figure 12 shows the case where the Debye lengths are the same in both phases. Unless the concentration of the background electrolyte is very high, LD > . Therefore the potential of mean force first decreases as the ion moves from the bulk of phase 1 towards the interface, reaches a minimum, and rises rapidly in the region where the two solvents mix. It attains its maximum when the ion is mostly surrounded by solvent 2, and then decreases towards the bulk value. On application of an overpotential the free energy of the reaction is changed, and so is the potential of mean force. A positive overpotential lowers the maximum and deepens the minimum; the reverse is true for negative overpotentials (see Fig. 13). For very high overpotentials the two extrema disappear. Thus a very high positive overpoten-
FIG. 12 The potential of mean force for an ion-transfer reaction at equilibrium: (1) chemical term; (2) electrostatic term; (3) total potential. System parameters: u ¼ 0:5kT, n ¼ 4, =LD ¼ 0:1.
The Lattice-Gas and Other Models
167
FIG. 13 The potential of mean force for various overpotentials. (1) 0 ¼ 2kT; (2) 0 ¼ kT; (3) 0 ¼ 0; (4) 0 ¼ 2kT; (5) 0 ¼ 2kT. The system parameters are the same as in Fig. 12.
tial leads to a barrierless transition; in this case ion transport is likely to be rate determining. Conversely, at high negative overpotentials the transition occurs without activation. From the potential of mean force the rate constant can be calculated. We first assume that transition-state theory is valid, and approximate the potential near the minimum and near the maximum by parabolas. The rate of escape of a particle from the well over the barrier is then [19]: ¼
! v vmin exp max 2 kT
ð31Þ
where ! is the frequency at the bottom of the well, and vmin and vmax are the values of the potential at the minimum and at the maximum, respectively. The reaction rate is given by the product of with the concentration cs of the ions in the bulk. The latter are in equilibrium with the well – otherwise the rate is determined by mass transport. Setting the chemical potential in the well equal to that in the bulk gives: rffiffiffiffiffiffiffiffiffiffiffiffi 2kT v cs ¼ c0 ð32Þ exp min 2 kT m! where c0 is the concentration in the bulk, and m the effective mass. The rate constant is then: rffiffiffiffiffiffiffiffiffi kT v v ð33Þ k¼ exp max k0 exp max 2m kT kT Both the frequency of the well and its depth cancel, so that the free energy of activation is determined by the height of the maximum in the potential of mean force. The height of this maximum varies with the applied overpotential (see Fig. 13). To a first approximation this dependence is linear, and a Butler–Volmer type relation should hold over a limited range of potentials. Explicit model calculation gives transfer coefficients between zero and unity; there is no reason why they should be close to 1=2. For large overpotentials the barrier disappears, and the rate will then be determined by ion transport.
168
Schmickler
If friction plays a role in the crossing of the energy barrier, the reaction is slower than predicted by transition-state theory. According to Kramers’ theory [20] the preexponential factor must then be replaced by: k00 ¼
k ; !b 0
with
¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2b þ 2 =2
ð34Þ
where k0 is the preexponential factor in the transition-state theory [see Eq. (33)], !b is the barrier frequency, and the coefficient of friction on the barrier. In the overdamped case, when !b , the preexponential factor simplifies to: k00 ¼
!b k 0
ð35Þ
The rate constant is then inversely proportional to the coefficient of friction. Unfortunately, at the present time the experimental results for ion-transfer reactions are contradictory, so that it is not possible to verify the predictions of this model. Also, this model is only valid if the rate is determined by the ion-transfer step, and not by transport, and if the concentration of the supporting electrolyte is sufficiently low so that the extension of the space-charge regions is less than the width of the region where the two solvents mix. These conditions are not always fulfilled in experiments. The above model can be extended to assisted ion transfer, in which the ion forms a complex with a suitable ionophore. The various mechanisms for such reactions have been classified by Shao et al. [21] and reviewed by Girault [22]. Schmickler [23] has examined the case of transfer by interfacial complexation, which is marked by the following reaction sequence (see Fig. 14): The transferring ion moves from the bulk of solution 1 towards the interface with solution 2, in which it is poorly soluble. At the interface it reacts with an ionophore from solution 2, and then the complexed ion is transferred towards the bulk of solution 2. The reaction is again governed by the potentials of mean force for the participating particles. A typical situation is shown in Fig. 15: the reacting ion has a large energy of transfer from solution 1 to solution 2, so that the transfer of the uncomplexed ion is highly unfavorable. In contrast, the ionophore and the complexed ion are highly soluble in solution 2, but poorly soluble in solution 1. The most favorable reaction path is therefore along the potential of mean force of the ion towards the interface; there the ion reacts with
FIG. 14
Ion transfer assisted by interfacial complexation (schematic).
The Lattice-Gas and Other Models
169
FIG. 15 Potential of mean force for the ion, the ionphore, and the complexed ion [23]. The Debye lengths for the two solutions have been taken as LD ¼ 30 A˚, and width of the interface as 3 A˚. The absolute value of the free energy of transfer was taken as 6kT for all particles, and the potential drop across the interface as 0 ¼ 3kT.
the ionophore, and the complexed particle can then move with little or no energy of activation to the bulk of phase 2. The rate of the ion transfer is governed by the complexation reaction, whose rate constant should not depend on potential since it is a purely chemical reaction. However, the concentrations of the reactant change with potential. Typically, the ionophore is uncharged, so that a change in the potential drop affects only the concentration of the ions at the interface. If the thickness of the interface is neglected, the concentration of the ion at the interface is given by: 0 z s cs ¼ c0 exp ð36Þ kT where the potential s at the interface can, to a first approximation, be calculated from the Verwey–Niessen theory. Explicit calculations within the lattice-gas model [23] show some quantitative corrections to these simple relations, but they also support the assertion that the change of the rate with potential is governed by changes in the ionic concentration at the interface.
E.
Electron-Transfer Reactions
Electron-transfer reactions at liquid–liquid interfaces have the form: ð2Þ ð1Þ ð2Þ Oxð1Þ 1 þ Red2 Ð Red1 þ Ox2
ð37Þ
where the subscript labels the chemical species, and the superscript indicates the solution in which it is situated. They are just a special case of electron transfer in solutions, and should therefore, to a first approximation, obey the theories of Marcus [24] and Hush [25]. So the rate of electron transfer from a reduced species labeled , situated at r , and an oxidized species at r can be written in the form:
170
Schmickler
ðE FÞ2 r ¼ A r r exp s 4kT
ð38Þ
where the preexponential factor A depends on the electronic overlap, Es is the energy of reorganization, and F the reaction free energy. The latter contains a chemical and an electrostatic term: F ¼ F 0 0 ðz Þ ðz Þ ð39Þ and thus depends on the position of the reactants. In principle, the energy of reorganization could also vary with position, but this dependence is expected to be small [26]. The preexponential factor usually decays exponentially with the separation of the reactants: A ¼ B exp r r ð40Þ where the inverse decay length is of the order of 1 A˚1 . In order to obtain an expression for the rate constant, we introduce the normalized red ox red particle densities ox ðzÞ and ðzÞ, which obey the conditions ð1Þ ¼ ð1Þ ¼ 1. They are related to the potential of mean force through: ðzÞ ¼ exp
pmf ðzÞ kT
ð41Þ
and can therefore be calculated from the lattice-gas model. With the aid of these quantities the rate constant for electron transfer from solution 2 to solution 1 can be written in the form: ð ð red 0 0 ket ¼ B dz dr 0 ox ðzÞ ðz Þ exp ðjr r jÞ ð42Þ fEs F 0 þ e0 ½ ðzÞ ðz 0 Þg2 exp 4kT The integrals have to be performed over the region in which the two reactants do not overlap. Equation (42) can serve as a basis for the calculation of the reaction rate and of current–potential curves. However, some basic features can be obtained by simple considerations. The two reactants meet at the interface in the region where the two solvents mix. Typically, the width of this region will be much smaller than the Debye lengths of the two solutions. Therefore the potential drop between the two reactants is small, and does not change much with the total potential . So a change of affects mainly the concentration of the reactants at the interface, and not the driving force for the reaction [22,26]. In this respect electron-transfer reactions at liquid–liquid interfaces resemble those at the interface between a semiconductor and an electrolyte solution. If the variation of the reactants’ concentration at the interface is calculated from the Verwey–Niessen theory, the following expression for the transfer coefficient results:
red ¼ zox 1 þ z2
þ coshð =2Þ zred 2 1 þ 2 þ 2 coshð =2Þ
with
¼
2 L1D 1 L2d
ð43Þ
red In the symmetrical case, where ¼ 1, this simplifies to ¼ ðzox 1 z2 Þ=2, and the transfer coefficient is independent of the potential. In the general case the transfer coefficient varies, and Tafel plots are expected to exhibit some curvature. These considerations are borne out by explicit model calculations (see Fig. 16), which give results close to those predicted by simple application of the Verwey–Niessen
The Lattice-Gas and Other Models
171
FIG. 16 Current–potential curves for various charge numbers of the reactants. System parameters: red ox red for curves (1)–(3) Debye lengths L1 ¼ L2 ¼ 40 A˚, 1 ¼ 2 ; (1) zox 1 ¼ 1, z2 ¼ 1; (2) z1 ¼ 1, z2 ¼ 0; ox red ox red ˚ (3) z1 ¼ z2 ¼ 0; (4) L1 ¼ L2 ¼ 10 A, 1 ¼ 2 , z1 ¼ z2 ¼ 0.
model. The deviations are larger, the greater the width of the interface, the smaller the Debye lengths, and the larger the reactants. Experimental results for electron-transfer reactions are contradictory at the present time: investigations by Ding et al. [27] indicate that a change in the potential drop affects mainly the reactants’ concentration and only to a minor extent the driving force. This is in contrast to results by Tsionsky et al. [28] which suggest that only the driving force and not the concentration is changed. Very recently Liu and Mirkin [29] studied electron transfer from neutral zinc porphyrin molecules to an aqueous phase and found a potential-independent rate constant; this indicates that in this system neither the driving force nor the concentration for the neutral reactant is changed, which is in line with the model presented above. Perhaps this important issue will have been clarified by the time this book appears.
V.
OTHER MODELS FOR LIQUID–LIQUID INTERFACES
So far, the lattice gas has been the only model that makes predictions both about structure and reactions at liquid–liquid interfaces. There are however, various other models for particular features of these interfaces. Some of them give similar, others give contradictory results. In the following, we briefly review a few of these models. A.
The Modified Verwey–Niessen Model
The Gouy–Chapman theory for metal–solution interfaces predicts interfacial capacities which are too high for more concentrated electrolyte solutions. It has therefore been amended by introducing an ion-free layer, the so-called Helmholtz layer, in contract with the metal surface. Although the resulting model has been somewhat discredited [30], it has been transferred to liquid–liquid interfaces [31] by postulating a double layer of solvent molecules into which the ions cannot penetrate (see Fig. 17); this is known as the modified Verwey–Niessen model. Since the interfacial capacity of liquid–liquid interfaces is
172
Schmickler
FIG. 17
The modified Verwey–Niessen model.
often higher than predicted by the simple Verwey–Niessen model, there is little reason to introduce such an ion-free layer; nevertheless, this model is still quite popular. In itself, the modified Verwey–Niessen model has little predictive value, since the properties of the dividing layer are not known, and its thickness and dielectric constant can be fitted to any experimental data. It has been combined with the modified Poisson–Boltzmann theory [32], in particular with the version known as MPB4 [33,34]. However, even the combined model still has an adjustable parameter, so that its validity is difficult to assess. B.
Density-Functional Theory
Density-functional theory is best known as the basis for electronic structure calculations. A variant of this theory can be used to calculate the structure of inhomogeneous fluids [35]: the free energy of the fluid is expressed as a functional of the density of the various components; a theorem asserts that this functional attains its minimum for the true density profiles. Henderson and Schmickler [5] applied this formalism to the interface between two liquids. They considered an ensemble containing two kinds of spherical molecules which interact through their dipole moments and through a Yukawa potential. The free energy for the homogeneous system was calculated from perturbation theory, and the phase diagram was determined. Whether a separation into two phases occurs or not depends on the system parameters. Roughly speaking, phase separation is favored when the two dipole moments differ greatly, and when the cross-interaction between different molecules is much smaller than the self-interaction between identical molecules. When the two phases separate the distribution of the solvent molecules is inhomogeneous at the interface; this gives rise to an additional contribution to the free energy, which Henderson and Schmickler treated in the square gradient approximation [36]. Using simple trial functions, they calculated the density profiles at the interface for a number of system parameters. The results show the same qualitative behavior as those obtained by Monte Carlo simulations for the lattice gas: the lower the interfacial tension, the wider is the interfacial region in which the two solvents mix (see Table 3). It would be desirable to extend this model to electrolyte solutions, but it is extremely difficult to calculate a free-energy functional that accounts for the presence of ions. C.
Capillary Waves
Both the lattice-gas model and computer simulations predict that the interface is rough on a molecular scale. If this roughness is not too large, the interface can be represented by a
The Lattice-Gas and Other Models
173
TABLE 3 Interfacial Widths, Bulk Composition, and Interfacial Tension Es in erg cm2 at the Interface Between Two Dipolar Liquids [5]. x01 Denotes the Mole Fraction of Solvent Si in Phase i (A)
x01
x02
Es
3.24 5.23 7.40 13.80
1.00 0.96 0.91 0.85
1.00 0.96 0.92 0.84
153.0 44.0 20.0 6.5
function Sðx; yÞ at a particular moment of time. The two-dimensional Fourier components AðqÞ of this surface function are known as capillary waves; q is a two-dimensional wave vector. Thus, a rough surface can be considered as a superposition of capillary waves, which are present at all wavelengths. Of course, they cannot be observed as traveling waves, but only as a fluctuating surface roughness. The energy stored in a capillary wave is proportional to the surface area it creates. This entails a prediction for the distribution of the amplitudes:
AðqÞA ðqÞ ¼
kT Es jqj2
ð44Þ
where the angular brackets denote thermal expectation values. This relation has indeed been observed in computer simulations of liquid–liquid interfaces [2,3]. The concepts of capillary waves and surface roughness can also be used to explain how the surface roughness increases the interfacial capacity beyond the Verwey–Niessen value. For this purpose Pecina and Badiali [37] have solved the linear Poisson–Boltzmann equation across the interface between two solutions with different dielectric constants and Debye lengths separated by a corrugated surface. A major difficulty is the boundary condition at the rough interface, which these authors handle by a perturbation expansion treating the roughness as a small parameter. Following Daikhin et al. [38], who had considered a similar problem for rough metal electrodes, Pecina and Badiali express the deviation from the Verwey–Niessen theory through a roughness function R~ ði ; i Þ, which depends on the dielectric constants of the two solutions and on their Debye inverse lengths i ¼ 1=Li . So the interfacial capacity per area is written as: C ¼ CVN R~ ði ; i Þ
ð45Þ
Obviously, if the two Debye lengths are much larger than the average height of the surface corrugation, the roughness plays no role, so that the roughness function tends to unity in that limit. On the other hand, when the two Debye lengths are much smaller than the corrugation – a case which should be difficult to obtain in practice – the roughness function is the ratio of the geometrical area to the area of the flat surface. As an illustration Pecina and Badiali consider a simple one-dimensional corrugation of the form: SðxÞ ¼ h cos kx
ð46Þ
Figure 18 shows the dependence of the roughness function on the two dimensionless parameters 1 h and 2 h. In accord with the limits considered above, the roughness function increases monotonically with both variables.
174
Schmickler
FIG. 18 Roughness function in dependence of the dimensionless parameters 1 h and 2 h. The dielectric constants have been taken as 1 ¼ 80, 2 ¼ 10. The ratio of the geometrical area to that of the flat surface was taken as 1.62 [37].
Recently, these authors have treated specific adsorption at corrugated liquid–liquid interfaces [39]; however, because of the complicated mathematics involved this work does not fall under the heading ‘‘simple models.’’ Also, Urbakh et al. [40] have extended the results for the interfacial capacity to the nonlinear region. D.
Kakiuchi’s Model for Ion Transfer
In the lattice-gas model, as treated in Section IV.D above, ion transfer is viewed as an activated process. In an alternative view it is considered as a transport governed by the Nernst–Planck or the Langevin equation. These two models are not necessarily contradictive: for high ionic concentrations the space-charge regions and the interface have similar widths, and then the barrier for ion transfer may vanish. So the activated mechanism may operate at low and the transport mechanism at high ionic concentrations. Kakiuchi [41] has examined the transport mechanism in some detail. He considers the interface as a region of thickness in which friction is considerably larger than in the bulk. The transferring ion has different electrochemical potentials ~ i ði ¼ 1; 2Þ in the two bulk phases; as usual, they can be decomposed into their chemical and their electrostatic parts: ~ i ¼ i þ ze0 i , where z is the charge number of the ion. When the system is in equilibrium, and the concentration of the ion is the same in the two solutions, then the difference in the inner potential is given by: ¼ ð47Þ 1 2 =z0 where the superscript denotes the standard state. serves as the reference potential drop. When the actual potential drop differs from this value, the electrostatic driving force is given by: f ¼
ð48Þ
The drop in the electrochemical potential across the boundary layer is assumed to be linear, and the diffusion coefficient D taken as constant. Following the work of
The Lattice-Gas and Other Models
175
FIG. 19 Normalized current density jn ¼ j=Dc1 as a function of the normalized driving force y according to Kakiuchi [41]. Full line: c2 ¼ c1 ; dashed line: c2 ¼ c1 =2; dotted line: c2 ¼ c1 =10:
Goldman [42], Kakiuchi derives the following approximate solution to the Nernst–Planck equation for the ion transport across the interface and the concomitant current density: D yey yey c c j ¼ zF ð49Þ sinh y 1 sinh y 2 where ci is the concentration of the ion in the indicated phase, and zF f ð50Þ 2RT is the normalized electrostatic driving force. The two terms in the square brackets in Eq. (49) denote the difference between a forward and a backward current. The current–potential relationship predicted by Eqs. (49) and (50) differs strongly from the Butler–Volmer law. For y 1 the current density is proportional to the electrostatic driving force. Further, the shape of the current–potential curves depends on the ratio c1 =c2 ; the curve is symmetrical only when the two bulk concentrations are equal (see Fig. 19), otherwise it can be quite unsymmetrical, so that the interface can have rectifying properties. Obviously, these current–potential curves are quite different from those obtained from the lattice-gas model. As we have noted in Section IV.D, there are no reliable experimental data for iontransfer reactions, so that a comparison with experiment is not possible at this time. y¼
VI.
CONCLUSIONS
The simple models that we have reviewed here help in visualizing the structure of liquid– liquid interfaces and the reactions that occur at them. In addition, they predict trends and orders of magnitudes. So far, the lattice gas has been unique in that it can serve as a unifying model for practically all processes at the interface. The other models that we have discussed aim to explain particular features. Several models are just different ways of representing the same physical phenomenon. For example, the lattice-gas model, capillary waves, and the density functional calculations presented above basically have the same view of the interface. However,
176
Schmickler
other models are not compatible with each other; for example, the modified Verwey– Niessen theory cannot be reconciled with the lattice-gas model for the interfacial capacity. Unfortunately the development of models is hindered by a lack of reliable experimental data. For example, the rates of ion-transfer reactions measured at different times and by different groups vary widely. Also, it has been suggested that the high interfacial capacities that are measured in certain systems are an experimental artifact [13]. While this is frustrating for the researcher who wants to decide between competing models, it can also be viewed as a sign that the electrochemistry of liquid–liquid interfaces is an active field, where fundamental issues are just being explored.
ACKNOWLEDGMENT Financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
W. Schmickler, Interfacial Electrochemistry, Oxford University Press, Oxford, New York, 1996. I. Benjamin. Chem. Rev. 96:1449 (1996). I. Benjamin. Ann. Rev. Phys. Chem. 48:407 (1997). T. L. Hill, Introduction to Statistical Thermodynamics, Addison-Wesley, Reading, Mass., 1960. D. Henderson, and W. Schmickler. JCS Faraday 92:3839 (1996). R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge, 1939. N. Metropolis, A. W. Rosenbluth, A. H. Teller, and E. Teller. J. Chem. Phys. 21:1087 (1953). W. Schmickler, unpublished results. A. Vinze, G. Horvai, F. A. M. Leermaker, and J. M. H. M. Sheutjens. Sensors Actuators 18– 19:42 (1994). E. J. W. Verwey and K. F. Niessen. Philos. Mag. 28:435 (1939). C. M. Pereira, W. Schmickler, A. F. Silva, and M. J. Sousa. Chem. Phys. Lett. 268:13 (1997). T. Huber, O. Pecina, and W. Schmickler. J. Electroanal. Chem. 467:203 (1999). Z. Samec, A. Troja´nek, and J. Langmeier. J. Electroanal. Chem. 444:1 (1998). P. Hajkova, D. Homolka, V. Marecek, and Z. Samec. J. Electroanal. Chem. 151:277 (1983). Y. Cheng, V. J. Cunnane, D. J. Schiffrin, and L. Mutoma¨ki. J. Chem. Soc. Faraday Trans. 81:107 (1991). C. M. Pereira, W. Schmickler, F. Silva, and M. J. Sousa. J. Electroanal. Chem. 436:9 (1997). S. Frank and W. Schmickler, submitted to J. Electroanal. Chem. W. Schmickler. J. Electroanal. Chem. 426:5 (1997). R. Landauer and J. A. Swanson. Chem. Rev. 121:1668 (1961). H. A. Kramers. Physica 7:284 (1940). Y. Shao, M. Osborne, and H. Girault. J. Electroanal. Chem. 318:101 (1991). H. Girault, in Modern Aspects of Electrochemistry (J. O’M. Bockris, B. E. Conway, and R. E. White, eds.), vol. 25, Plenum Press, New York, 1993. W. Schmickler. J. Electroanal. Chem. 460:144 (1999). R. A. Marcus. J. Chem. Phys. 24:966 (1956). N. S. Hush. J. Chem. Phys. 28:962 (1958). W. Schmickler. J. Electroanal. Chem. 428:123 (1997). Z. Ding, D. J. Fermı´ n, P.-F. Brevet, and H. H. Girault. J. Electroanal. Chem. 458:139 (1998). M. Tsionsky, A. J. Bard, and M. V. Mirkin. J. Phys. Chem. 100:17881 (1996). B. Liu and M. V. Mirkin. J. Am. Chem. Soc. 121:8352 (1999).
The Lattice-Gas and Other Models
177
30. W. Schmickler. Chem. Rev. 96:3177 (1996). 31. P. Vanysek, Electrochemistry on Liquid–Liquid Interfaces, Lecture Notes in Chemistry, vol. 39, Springer, New York, 1985. 32. C. W. Outhwaite, L. B. Bhuyiyan, and S. Levine. J. Chem. Soc. Faraday Trans. II 76:1388 (1980). 33. Q. Cui, G. Zhu, and E. Wang. J. Electroanal. Chem. 372:15 (1994); 383:7 (1995). 34. T. Wandlowski, K. Holub, V. Marecek, and Z. Samec. Electrochim. Acta 40:2887 (1996). 35. D. Henderson (ed.), Fundamentals of Inhomogenous Fluids, Dekker, New York, 1992. 36. F. F. Abraham. J. Chem. Phys. 63:157 (1975). 37. O. Pecina and J. P. Badiali. Phys. Rev. E 58:6041 (1998). 38. L. I. Daikin, A. A. Kornyshev, and M. Urbakh. Phys. Rev. E 53:6192 (1996). 39. O. Pecina and J. P. Badiali. J. Electroanal. Chem. 475:46 (1999). 40. M. Urbakh, A. A. Kornyshev, and L. I. Daikin, submitted to J. Electroanal. Chem. 41. T. Kakiuchi. J. Electroanal. Chem. 322:55 (1992). 42. D. E. Goldman. J. Gen Physiol. 27:37 (1943)
8 Dynamic Aspects of Heterogeneous Electron-Transfer Reactions at Liquid^ Liquid Interfaces DAVID J. FERMI´N Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland RIIKKA LAHTINEN Laboratory of Physical Chemistry and Electrochemistry, Department of Chemical Technology, Helsinki University of Technology, Espoo, Finland
I.
INTRODUCTION
The molecular nature of interfaces between two immiscible electrolyte solutions (ITIES) provides a well-defined framework for fundamental studies of heterogeneous electrontransfer processes (ET). The potential impact of this topic has been recognized even before carrying out comprehensive work. Outstanding contributions by Samec [1], Kharkats and Volkov [2], and Marcus [3–6] delivered basic descriptions of the ET dynamics involving two redox couples separated by a polarized liquid–liquid junction. Further developments including lattice-gas [7] and molecular dynamics modeling [8,9] have complemented these initial steps. By contrast, experimental studies have been able to address electron-transfer kinetics across ITIES only in the last few years. Among these recent advances, photoinduced heterogeneous ET has provided some exciting insights into the elementary processes at dye-sensitized liquid–liquid interfaces. The present chapter reviews these contributions, not only highlighting the experimental aspects and establishing comparisons with existing ET models, but also analyzing new perspectives for areas of practical interest such as twophase catalysis and solar energy conversion.
II.
FUNDAMENTAL CHALLENGES SURROUNDING ELECTRON-TRANSFER REACTIONS
The interpretation of phenomenological electron-transfer kinetics in terms of fundamental models based on transition state theory [1,3–6,10] has been hindered by our primitive understanding of the interfacial structure and potential distribution across ITIES. The structure of ITIES was initially studied by electrochemical and thermodynamic analyses, and more recently by computer simulations and interfacial spectroscopy. Classical electrochemical analysis based on differential capacitance and surface tension measurements has been extensively discussed in the literature [11–18]. The picture that emerged from 179
180
Fermı´n and Lahtinen
these studies described the interface as two diffuse layers separated by an ‘‘inner layer.’’ This approach, commonly referred to as the modified Verwey–Niessen model (MVN), has raised a great number of controversies, especially in connection to the nature of the ‘‘inner layer.’’ Molecular dynamics and Monte Carlo computer simulations have provided detailed microscopic pictures of liquid–liquid junctions [19–21]. One of the most interesting features underlined by these studies is that the interface is molecularly sharp, featuring ‘‘fingering’’ phenomena between both solvents. At the picosecond time scale, this phenomenon introduces a degree of roughness to the junction within a region of 10 A˚. Time averaging of these events defines a region in which dielectric, solvation, and transport properties depend on the position along the axis perpendicular to the interface. However, it is not clear yet how these phenomena would affect the kinetics of charge transfer process. These theoretical calculations are based on a collection of a few hundred solvent molecules where no electrolyte species are taken into account. Considering that homogeneous and heterogeneous ion–ion interactions play important roles on interfacial processes, only limited comparison with experimental data can be performed. The lattice-gas model has proved to be a rather useful theoretical approach to the study of ionic interactions at liquid–liquid interfaces [7,22]. By contrast to quantitative molecular dynamics, where Newton’s equations of motion are solved for all particles in the system over a certain period of time, the lattice-gas model considers only interactions between nearest neighbors in a cubic lattice arrangement. Basic aspects regarding this type of calculation have been described in recent publications [22,23]. Ionic distributions in the absence [7,22] and presence of ion-pairing interaction [24–27] have been considered as a function of the Galvani potential difference. The potential dependence of the heterogeneous ET rate constant is one of the most important outputs of this work. Simulations suggested that if the Debye lengths in each electrolyte solution are larger than the width of the interface, the potential drop across the reactants is very small, therefore any potential perturbation will manifest itself by changes in the interfacial concentration of reactants [7]. From the experimental point of view, structural aspects have been addressed by interfacial spectroscopic methods such as neutron reflectivity [28–32] and quasielastic laser scattering [33–36]. The latter technique has provided valuable information on the frequency of capillary waves generated by thermal fluctuations at the liquid–liquid junction. Although this technique has been employed for adsorption studies at nonpolarized interfaces, it is also expected to provide useful information on the interfacial structure during charge-transfer processes. Important advances have also emerged from nonlinear optics, in particular second harmonic generation (SHG). The noncentrosymmetrical nature of the liquid–liquid junctions allows SHG responses as well as sum frequency generation (SFG) signals from species at the interface, providing information on the excess concentration, molecular orientation, and structure. Basic aspects of these powerful techniques have been comprehensively described [37,38] and more recent contributions are reviewed in this book (Chapter 6). These spectroscopic and theoretical developments have stimulated the recent advances on electron-transfer dynamics at ITIES. In addition to the correlation between structure and dynamics of charge transfer, fundamental problems in connection with the energetics of ET reactions remain to be fully addressed. We shall consider these problems primarily before discussing kinetic aspects in full detail.
Dynamic Aspects of Electron-Transfer Reactions
A.
181
Energetics of ET and Photoinduced ET Reactions
From the thermodynamic point of view, the occurrence of a heterogeneous ET event at a liquid–liquid interface is determined not only by the relation of redox potentials between reactants in each phase, but also by the Galvani potential difference. Let us consider the general reaction, o w o Ow 1 þ R2 Ð R1 þ O2
ð1Þ
where the superscripts ‘‘w’’ and ‘‘o’’ correspond to the aqueous and organic phases. The Nernst equation associated with the equilibrium conditions is given by w o RT aO1 aR2 w 0 ln ð2Þ
¼
w o o et o nF aw R1 aO2 0 where the standard potential w o et is determined by 0 0;o 0;w w o et ¼ EO2=R2 EO1=R1
ð3Þ
In order to express the standard redox potentials of the two couples located in different 0;o can be expressed in terms of solvents on a same potential scale, e.g., SHE in water, EO2=R2 0;w the corresponding redox potential in water ðEO2=R2 Þ and the Gibbs energies of transfer of the species R2 and O2 , 0;o 0;w EO2=R2 ¼ EO2=R2 þ
G0;w!o G0;w!o R2 O2 nF
ð4Þ
So far, the experimentally obtained formal electron-transfer potentials have not been rationalized in terms of Eqs. (3) and(4). In view of the lack of a suitable redox reference for organic electrolytes, we have recently studied the oxidation of ferrocene (Fc) by the hexacyanoferrate redox couple at the water–1,2-dichloroethane (DCE) interface. Figure 1(a) displays a typical cyclic voltammogram recorded on a four-electrode potentiostat for the cell configuration represented in Fig. 1(b). The Galvani potential scale was estimated considering the so-called TATB assumption [39,40]. Under this approximation the transfer potentials of several standard ions such as tetrapropylammonium (TPAþ ) and tetramethylammonium (TMAþ ) are documented (see database at www.epf.ch/le). Unless otherwise indicated, the convention adopted throughout this review defines positive currents to the transfer of positive charges from water to DCE. The voltammogram in Fig. 1(a) shows the electron-transfer signal in comparison with the transfer wave of TPAþ . From the difference in the half wave transfer potentials, it can be estimated that the formal electron0 transfer potential is w o et ¼ 0:160 0:010 V. Taking into account that the concentration of the hexacyanoferrate couple is in large excess with respect to ferrocene, the observed formal ET potential can be effectively expressed as ! RT FeðCNÞ3 w 00 0;DCE 0;w 6 ln o et ¼ EðFcþ =FcÞ EðFeðCNÞ3 =FeðCNÞ4 Þ ð5Þ 6 6 F FeðCNÞ4 6 Under similar conditions, the formal redox potential of the aqueous couple has been estimated as 0:358 0:005 ; V vs SHE. From Eq. (5), it is obtained that the formal 0 0 ;DCE redox potential of Fc in DCE is EFc þ =Fc ¼ 0:635 0:015 V vs SHE. The redox potential of Fc obtained from the cyclic voltammetry experiments at the water–DCE interface can be verified by evaluating the thermodynamic cycle given by Eq. (4). It follows that
Fermı´n and Lahtinen
182
FIG. 1 (a) Cyclic voltammogram of the heterogeneous oxidation of ferrocene by the hexacyanoferrate redox couple at the water–DCE interface at 10 mV s1 . The convention adopted throughout the review defines positive currents as the transfer of a positive charge from water to DCE. (b) The composition of the cell schematically represented. BTPPA and TPBCl stand for bis(triphenylphosphoranylidene)-ammonium and tetrakis(4-chlorophenyl) borate respectively. The current was measured through two platinum counterelectrodes located in each phase. The surface area of the liquid– liquid junction was 1:53 cm2 . The cation tetrapropylammonium (TPAþ Þ was also present in the aqueous phase as a reference for the Galvani potential scale.
0
0 ;DCE o;w w 0 0;w!o EFc =F þ =Fc ¼ EðFcþ =FcÞ þ o Fcþ GFc
ð6Þ
corresponds to the Fc Gibbs energy of transfer from water where the parameter G0;w!o Fc 0 0 ;w to the DCE phase. An average value for the Fc redox potential of EFc þ =Fc ¼ 0:381 0:006 V was derived from voltammetry at ultramicroelectrodes [41], while the parameter ¼ 24:3 0:2 kJ mol1 has been estimated from extraction methods. The third G0;w!o Fc parameter required in Eq. (6) was obtained by monitoring the transfer of Fcþ accumulated during the oxidation of Fc by CuSO4 at the water–DCE interface. Figure 2 shows cyclic voltammograms featuring the 0transfers of Fcþ and the standard TMAþ , from which the 0 formal transfer potential w o Fcþ ¼ 0:005 0:010 V can0 be estimated. Introducing all these 0 ;DCE data into Eq. (6) gives a value of 0:638 0:020 V for EFc þ =Fc . It should be noticed that this analysis implicitly considered that the hydration energies of Fcþ , TMAþ , and TPAþ are not substantially affected by the difference in ionic strengths in the experiments of Figs. 1 and 2. Despite this simplifying assumption, the redox potentials for Fc calculated from both approaches are consistent within the error margins. A similar analysis can also be carried out by referring the potential scale to the potential of minimum differential capacitance curve. This potential is close to the potential of zero charge for interfaces where interfacial ion-pairing or specific adsorption phenomena are negligible. Hanzlı´ k et al. have obtained similar values for the same thermodynamic cycle [Eq. (4)] at the water– nitrobenzene interface [42].
Dynamic Aspects of Electron-Transfer Reactions
183
FIG. 2 Cyclic voltammogram of the ferricenium transfer across the water–DCE interface at 10 mV s1 . The electrochemical cell featured a similar arrangement to Fig. 1(b), but the organic phase contained 2 mM of ferrocene. Heterogeneous oxidation of Fc occurred in the presence of 0.2 mM CuSO4 in the aqueous phase. Supporting electrolytes were 10 mM Li2 SO4 and 10 mM BTPPATPBCl. The transfer of the standard tetramethylammonium (TMAþ ) under the same condition is also superimposed.
Semiquantitative relations between the redox scales in both electrolyte phases allow a clearer description of the energetics involved in ET reactions at ITIES. A graphic representation of the relations between redox potentials for various aqueous and organic phase couples is shown in Fig. 3. For instance, the interfacial oxidation of dimethylferrocene (DMFc) and the reduction of tetracyanoquinodimethane (TCNQ) by ferro/ferricyanide can take place within the ideally polarizable potential range, while the oxidation of TPBCl is outside the potential range. These considerations are consistent with the experimental studies reported by Ding et al. [43]. This kind of analysis is particularly relevant in studies of electron transfer rates as a function the Gibbs energy of electron transfer [44– 46]. Furthermore, it also allows comparisons between the Gibbs energy of electron transfer and the transfer of ionic species present at the liquid–liquid junctions. For a given relation of redox potentials and concentration ratio of electroactive species, the onset of the ET reaction is determined by the Galvani potential difference [see Eqs. (2) and (3)]. However, a special case can be envisaged when redox species are photoexcitable dyes adsorbed at the interface. Assuming that the excited-state lifetime is comparable to the characteristic time of ET, the faradaic reaction can be initiated by illumination of the interface. The redox potentials associated with the ground and triplet states of the water-soluble zinc tetra-N-methyl-4-pyridium porphyrin (ZnTMPyP4þ ) are schematically shown in Fig. 4(a) [47]. At externally polarized interfaces, the ET from Fc to the porphyrin species can proceed only via the excited state of the dye. This is the fundamental phenomenon behind the recent developments on dye-sensitized liquid–liquid interfaces [48–50]. As discussed in Section V of this review, ‘‘uphill’’ electron-transfer processes can take place between two redox species at the liquid–liquid interface mediated by the excited state of adsorbed dye species. The energetics involved in these types of photosynthetic processes are schematically illustrated in Fig. 4(b) [51]. In this mechanism, part of the incident photon energy is employed to compensate the negative Get . B.
General Overview on the Controlling Factors of ET Kinetics
Similarly to charge-transfer processes at solid–electrolyte interfaces, the ET rate for heterogeneous reactions at ITIES is determined by the flux of reactants to the interface as well
184
Fermı´n and Lahtinen
FIG. 3 Comparison of potential scales for redox species in aqueous and DCE phases versus SHE. Redox potentials in DCE were experimentally measured against the couple Fcþ =Fc. The formal redox potential of this couple in DCE was obtained by evaluating the parameters in the thermodynamic cycle given by Eq. (7).
as the dynamics of the ET step. Mass transport processes have been rigorously described for planar diffusion regimes [52–55], spherical diffusion at microinterfaces [56], and more recently for ‘‘approach curves’’ familiar from scanning electrochemical microscopy (SECM) [45,57] and microelectrochemical measurements at expanding droplets (MEMED) [58,59]. On the other hand, the kinetics of the ET step and its dependence on the Galvani potential difference remain largely controversial. We shall concentrate on the latter aspects throughout this review. As mentioned earlier, a good deal of these controversies are due to the primitive understanding of the double layer structure. Extending the formalism for ET in homogeneous phase, reactions at liquid–liquid interfaces can be described in terms of a series of elementary steps initiated by the approach of reactants to the interfacial region and the formation of the ET precursor complex [1,5,60],
Dynamic Aspects of Electron-Transfer Reactions
185
FIG. 4 (a) Latimer diagram of the water soluble zinc tetra-N-methyl-4-pyridium porphyrin (ZnTMPyP4þ ). (Reprinted with permission from Ref. 47.) (b) Schematic representation of a photosynthetic process based on porphyrin sensitized water–organic interface. Dotted line corresponds to the back electron-transfer process. (Reprinted from Ref. 51 with permission from Elsevier Science.)
o w o Ow 1 þ R2 Ð O1 jR2 w o o Ow 1 R2 Ð O1 R2 w o o O1 R2 Ð Rw 1 O2 O w o R1 O2 Ð Rw 1 O2 w o o Rw 1 O2 Ð R1 þ O2
Precursor complex formation
ð7Þ
Precursor reorganizations
ð8Þ
Electron transfer
ð9Þ
Successor reorganization
ð10Þ
Successor dissociation
ð11Þ
The first controversial point in this mechanism is the nature of the reaction planes where the precursor formation and the ET reaction take place. Samec assumed that the ET step occurs across an ion-free layer composed of oriented solvent molecules [1]. By contrast, Girault and Schiffrin considered a mixed solvent region where electrochemical potentials are dependent on the position of the reactants at the interface [60]. From a general perspective, the phenomenological ET rate constant can be expressed in terms of ket ¼ Z expðGact =RTÞ
ð12Þ
where Z is a preexponential factor related to the position of the reactants at the interface, and the activation energy Gact is determined by the reorganization energy , the formal
Fermı´n and Lahtinen
186 0
Gibbs energy of electron transfer (Get0 Þ and the work terms for precursor formation (wp Þ and successor dissociation ðws Þ, !2 0 þ Get0 þ ws wp Gact ¼ wp þ ð13Þ 4 From classical transition state theory, the phenomenological rate constant of ET can be expressed as h
i a b exp z F
z F
=RT exp ðeFab Þ=RT ð14Þ ket ¼ kpzc O1 R2 w o et where e is the charge transferred in Eq. (9), and ‘‘a’’ and ‘‘b’’ correspond to the position of the reaction planes in the aqueous and organic phases along the axis perpendicular to the liquid–liquid boundary. The differences in the so-called ‘‘ion-free layer’’ and ‘‘mixed solvent layer’’ formalisms are translated in the physical meaning of the preexponential pzc parameter kpzc et . Samec defined ket as the ‘‘true’’ forward heterogeneous ET rate constant at zero Galvani potential difference [1], kpzc et ¼ BVm d exp½=4RT
ð15Þ
where the parameter B is associated with the electronic overlap, Vm is the mean molar volume of reactants, d is the thickness of the inner layer and is the total reorganization energy. For the ‘‘mixed solvent layer formalism,’’ the preexponential parameter kpzc et was estimated by extension of the Newton and Sutin approach [61], 0 0 0 0 kpzc et ¼ R exp½=4RT exp wp =RT exp pzc wp ws þ eF O1 =R2 =RT ð16Þ w0p and w0s are the potential independent terms of wp and ws . is the effective electron hopping frequency, while R is the region where the electronic coupling between the reactants is substantial. It is evident that the validation of either approach is difficult to address from the experimental point of view, especially considering that the potential dependencies are formally identical [Eq. (14)]. However, the most important conclusion up to this point is that the Galvani potential difference can affect the interfacial concentration of ionic reactants, bringing about changes in the observed ET rate. Alternatively, changes of the junction polarization can modify the potential drop between redox species, giving rise to variations on the free energy of ET. The mechanisms, in which the interfacial potential can operate on the observed ET rate, correspond to the so-called concentration polarization and Butler–Volmer behavior respectively. In subsequent works, Marcus developed his theory further in a series of papers providing expressions for the work terms, the reorganization energy and the macroscopic ET rate constants [3–6]. Assuming a sharp liquid–liquid boundary, the solution of the mean molar volume of reactants yields an expression for ket of the form ket ¼ 2ðaO1 þ aR2 ÞðRÞ3 expðGact =RT Þ
ð17Þ
where aO1 , aR2 , and correspond to the molecular radii of the reactant species and the transmission coefficient respectively. As discussed in the next section, recent measurements of ket for reactions involving large driving forces provided a maximum value of the order of 102 M1 cm s1 [45]. This value is of the same order as the preexponential factor in Eq. (17), assuming R 0:1 nm and aO1 þ aR2 1 nm.
Dynamic Aspects of Electron-Transfer Reactions
187
In order to fully evaluate Eq. (17), expressions involving the outer-sphere reorganization term 0 , as well as the work terms, were also established [5], op ðeÞ2 1 1 ðeÞ2 1 1 ðeÞ2 Dop o Dw þ op op Dsw Dso 2aO1 Dop 2aR2 Dop 4d1 Dop w w ðDo þ Dw Þ o op Ds Ds ðeÞ2 Dop Dsw Dso w Do s o s ws op op Dw ðDo þ Dw Þ 4d2 Dop Dso ðDsw þ Dso Þ o ðDw þ Do Þ 2ðeÞ2 1 1 op Dsw þ Dso R Dop w þ Do ! ðzO1 Þ2 ðzR2 Þ2 Dso Dsw 2 zO1 zR2 þ wp ¼ s s s s R Dsw þ Dso 4d1 Dw 4d2 Do Do þ Dw 0 ¼
ð18Þ ð19Þ
where Ds and Dop are the static and optical dielectric constants for both media, d is the perpendicular distance from the ion center to the interfacial boundary, and R is the centerto-center distance between the reactant species. The expression for ws can be easily obtained by replacing the charges of the reactants by the corresponding values of the products. Initial comparisons of rate constants obtained from Eqs. (13) and (17–19), and from experimental studies based on cyclic voltammograms and impedance measurements give support to this approach [62,63]. However, one limitation is that the Galvani potential difference is not explicitly defined in the expressions of the work terms. In that respect the analysis leading to Eqs. (14)–(16) provides a clearer description. The ‘‘flat’’ interface model employed by Marcus does not seem to be in agreement with the ‘‘rough’’ picture obtained from molecular dynamics simulations [19,21,64–66]. Benjamin examined the main assumptions of work terms [Eq. (19)] and the reorganization energy [Eq. (18)] by MD simulations of the water–DCE junction [8,19]. It was found that the electric field induced by both liquids underestimates the effect of water molecules and overestimates the effect of DCE molecules in the case of the continuum approach. However, the total field as a function of the charge of the reactants is consistent in both analyses. In conclusion, the continuum model remains as a good approximation despite the crude description of the liquid-liquid boundary. The lattice-gas modeling by Schmickler also extended the Marcus approach to the work terms [7]. In this case, detailed analysis of particle distributions allowed estimations of ket without defining a mean reaction volume. Furthermore, the study of particle distribution as a function of the interfacial potential provided an explicit description of the effect of the Galvani potential difference on the observed rate constant. As mentioned earlier, these calculations indicated that changes in the Galvani potential difference have a negligible effect on Gact as long as the separation between the redox centers is substantially shorter than the Debye lengths in each electrolyte phase. In this case, the potential dependence of ket will be only given by the first exponential term in Eq. (14). However, as discussed throughout this chapter, experimental results provide clear evidence that concentration polarization effect is not the only factor involved in the behavior of ket as a function of the applied potential. The theoretical aspects highlighted in this section show that describing heterogeneous ET dynamics by the continuum model can be regarded as reasonable. In the next section, we shall discuss in detail the experimental advances and how some results cast doubts in the picture outlined so far.
Fermı´n and Lahtinen
188
III.
ELECTRON-TRANSFER REACTION AT ITIES
Heterogeneous ET reactions have been consistently studied as a function of the bias potential applied through reference electrodes located at each electrolyte phase. This approach limits the potential range for ET studies to the region where the interface behaves as an ideally polarizable junction. On the other hand, recent developments have incorporated techniques based on the SECM concept, in which the Galvani potential difference is determined by the ratio of a common ion between the two liquid phases. Both approaches require appropriate experimental conditions in order to minimize competing processes, which can complicate the analysis of the heterogeneous ET responses. We shall review some experimental aspects concerning both types of approaches before considering the dynamics of ET reactions in detail. A.
Electron-Transfer Reactions at Externally Polarized Interfaces
Heterogeneous ET reactions at polarizable liquid–liquid interfaces have been mainly approached from current–potential relationships. In this respect, a rather important issue is to minimize the contribution of ion-transfer reactions to the current responses associated with the ET step. This requirement has been recognized by several authors [43,62,67–72]. Firstly, reactants and products should remain in their respective phases within the potential range where the ET process takes place. In addition to redox stability, the supporting electrolytes should also provide an appropriate potential window for the redox reaction. According to Eqs. (2) and (3), the redox potentials of the species involved in the ET should ‘‘match’’ in a way that the formal electron-transfer potential occurs within the potential window established by the transfer of the ionic species present at the liquid–liquid junction. The results shown in Figs. 1 and 2 provide an example of voltammetric ET responses when the above conditions are fulfilled. A difference of 0 w 0 approximately 150 mV is observed between w o et and o Fcþ . The organic solvent should feature a low solubility in water and a high dielectric constant. Numerous studies have been reported for liquid–liquid junctions involving DCE [43,62,70,71,73], nitrobenzene [67,68,74,75], and nitrophenyloctylether (NPOE) [56]. Various hydrophobic electrolytes have been employed in these solvents. Tetraphenylarsonium (TPAsþ Þ [[71,75,76], bis-triphenylphosphoranylidene (BTPPAþ ) [43,50], and hydrophobic tetra-arylammonium [77,78] are among the cations used in the organic phase. The choice for anions has been mostly restricted to borate derivatives, tetraphenylborate (TPB ) [70,79,80], tetrakis(4-chlorophenyl)borate (TPBCI ) [43,81,82], and tetrakis(penta-fluoro)phenylborate (TPFB ) [49,83], as well as dicarbollylcobaltate [75]. The redox stability organic of phase cations is commonly very high in comparison to the anionic phenylborate derivatives. It has been proposed that Fcþ is reduced to Fc in DCE in the presence of TPB ðPh4 B Þ [71], 2Fcþ þ Ph4 B ! Ph2 þ Ph2 Bþ þ 2Fc
ð20Þ
This reaction has been associated with anomalous voltammetric responses during ET reactions in the presence of aqueous redox couples [71,84]. However, as indicated in Fig. 3, the redox potential of TPB is considerably more positive than Fc in DCE, therefore the reaction in Eq. (20) must involve a complex interfacial catalytic mechanism to indeed take place. On the other hand, Ding et al. have studied the oxidation of 1,1 dimethylferrocene (DMFc) and the reduction of TCNQ by FeðCNÞ36 =4 at the water–
Dynamic Aspects of Electron-Transfer Reactions
189
DCE interface in the presence of TPBCl [43,82]. The accumulation of products of the redox reactions were followed by spectrophotometry in situ, and quantitative relationships were obtained between the accumulation of products and the charge transfer across the interface. These results confirmed the higher stability of this anion in comparison to TPB . It was also reported that the redox potential of TPBCl is 0.51 V more positive than 0;DCE EFc þ =Fc (see Fig. 3). However, the redox stability of the chlorinated derivative of tetraphenylborate is not sufficient in the presence of highly reactive species such as photoexcited water-soluble porphyrins. Fermı´ n et al. have shown that TPBCl can be oxidized by adsorbed zinc tetrakis-(carboxyphenyl)porphyrin at the water–DCE interface under illumination [50]. Under these conditions, the fully fluorinated derivative TPFB has proved to be extremely stable and consequently ideal for photoinduced ET studies [49,83]. Another anion which exhibits high redox stability is PF6 ; however, its solubility in the water phase restricts the positive end of the ideally polarizable window to w o < 0:2 V [85]. Requirements for redox potential matching and high transfer energy have limited the 3 =4 choice for the aqueous redox species to ½FeðCNÞ [43,56,62,63,70,71,74,76,81,82,86], 6 þ þ þ þ Fe2 =3 in the presence of citrate [71] or at low pH [87], Ce3 =4 and permanganate [80]. These redox couples have been employed for simple one-electron-transfer reactions involving ferrocene derivatives [43,56,67,68,71,74,80,82,84], TCNQ [43,63,76,80,82], lutetium diphthalocyanine LuðPCÞ2 [62,63], ruthenium bis(pyridine)(meso-tetraphenylporphyrinato) (RuðTPPÞðPyÞ2 Þ [70,76], and tetrathiafulvalene TTF [80,88]. Other interesting redox active species employed in the organic phase is the tetraoctylammonium tetrachloroaurate (TOAAuCl4 ). The interfacial reduction of the Au complex by ferrocyanide at the water–DCE junction leads to the formation of gold particles [89]. More recently, the nucleation of Pd particles has been reported from reduction of ammonium tetrachloropalladate in the aqueous phase by ferrocene derivatives in DCE [90,91]. In general, successful studies of heterogeneous ET have featured highly charged ionic species in the aqueous phase and rather hydrophobic couples in the organic electrolyte. Furthermore, high ionic strength and excess concentration of the redox couple in the aqueous phase are commonly part of the experimental practice followed in these studies. These two additional conditions minimize the partition of the organic redox couple by ‘‘salting out effect’’ and allow one to treat the electrochemical responses in terms of a pseudo-first-order process (a constant composition approximation). Spectroscopic detection of ET products has also been employed for monitoring the progress of the reaction. Obviously, the essential requirement for this analysis is the stability of the spectroscopic probe. Compton and coworkers have developed a cell arrangement for in-situ EPR detection of the radical ions generated during the reduction of TCNQ, 2,3,5,6-tetrachloro-p-benzoquinone (TCBQ), 2,3,5,6-tetrafluoro-p-benzoquinone (TFBQ), and the oxidation of tetrathiafulvalene (TTF) in DCE [88,92]. It was confirmed for all the organic redox species studied that the radical ion was stable in the organic phase in the presence of the electrolytes BTPPATPBCl, TPAsTPBCl, and TBAPF6 . These results were consistent with the spectrophotometric analysis of the TCNQ reduction reported by Ding et al. [43]. In this work, the accumulation of the radical TCNQ following the ET from ferrocyanide was followed by UV-visible reflectance in total internal reflection (TIR) according to the scheme in Fig. 5(a). The evolution of the absorption peaks associated with the radical anions in Fig. 5(b) is clearly observed at the onset of the ET potential range depicted in the cyclic voltammograms of Fig. 5(c). Furthermore, it is also shown that the differential cyclic voltabsorptograms at 650 nm shown in Fig. 5(d) are directly proportional to the voltammetric responses. The propor-
190
Fermı´n and Lahtinen
FIG. 5 (a) Schematic diagram of the heterogeneous reduction of TCNQ by the hexacyanoferrate couple at water–DCE interface monitored by UV-visible spectroscopy in TIR. (b) Evolution of the absorption bands associated with the radical TCNQ as the Galvani potential difference is swept from 0.190 to 0.260 V, with a difference of 40 mV between each spectrum. (From Ref. 82, reproduced by permission of The Royal Society of Chemistry.) (c) Cyclic voltammograms corresponding to the same process at various scan rates. (d) Differential cyclic voltabsorptogram obtained in situ at 670 nm. The composition of the electrochemical cell is identical to that in Fig. 1(b), but with a 4 ratio 0.01 M/0.4 M FeðCNÞ3 in the aqueous phase and 6 104 M TCNQ in DCE. 6 =FeðCNÞ6 (Figures (c) and (d) were reprinted from Ref. 43 with permission from Elsevier Science.)
Dynamic Aspects of Electron-Transfer Reactions
191
tionality between the absorbance in TIR (ATIR Þ and the faradaic current (I f ) is given by [43] dATIR 2TCNQ f ¼ I dt FS cos
ð21Þ
where TCNQ and correspond to the molar absorption coefficient of the product in the organic phase and the light incident angle, respectively. The satisfactory correlation between spectroscopic and electrochemical responses provides a suitable framework for the kinetic analysis of these systems. B.
‘‘Open-Circuit’’ Liquid–Liquid Junctions
Techniques based on the concept of scanning electrochemical microscopy (SECM) have provided valuable kinetic information for charge-transfer processes at ITIES [44,45,57,93,94]. These techniques allow the monitoring of concentration profiles of the ET products via an ultramicroelectrode (UME) approaching the liquid–liquid junction (Chapter 13). In this case, the Galvani potential difference can be controlled by the partition of a common ion between the electrolyte solutions. A variety of organic solvents has been studied, e.g., benzene, nitrobenzene, and DCE. The Galvani potential difference is generally controlled by the ratio of ClO 4 ions present in both phases. Similarly to experiments under potentiostatic conditions, success in the analysis of ET kinetics relies on the fact that neither products nor reactants can transfer across the interface. Various redox couples in the aqueous phase have been studied, including 3=4 3=4 2=3 3=2þ =2 , RuðCNÞ , MoðCNÞ , Fe , FeEDTA , IrCl , and CoðIIIÞ=ðIIÞ FeðCNÞ3=4 6 6 8 6 sepalchrate [44,45,95]. In the organic phase, zinc meso(tetraphenyl)porphyrin (ZnPor), TCNQ, Fc, and DMFc have been most frequently employed. The condition for redox potential matching is rather different for this approach in comparison to externally biased interfaces. In the case of SECM, one of the reactants is generated at the UME tip at some distance from the interface, therefore the ET driving force with respect to the redox species in the opposite phase could be extremely high. This condition allows a unique possibility of accessing rate constants in the inverted Marcus region [44,45] or studying electrogenerated chemiluminescence phenomena [96]. Another interesting approach to ET reactions at liquid–liquid interfaces has been recently introduced by Shi and Anson [77,78,97]. Thin organic electrolyte layers were suspended in dry and polished pyrolytic graphite electrodes, which were subsequently introduced in the aqueous electrolyte. The thin organic layer contains supporting electrolytes such as tetra-N-hexylammonium perchlorate (THAClO4 ) and various organic redox . The species, while the aqueous phase contained NaClO4 and the couple FeðCNÞ3=4 6 sequence of experiments displayed in Figs. 6(a) and 6(b) demonstrates that direct ET from the aqueous redox couple to the solid electrolyte does not take place in the presence of the thin organic layer. In the presence of only decamethylferrocene (DCMFc) in the organic layer, Fig. 6(c), a reversible voltammetric response is observed associated with the generation of DCMFcþ . Figure 6(d) illustrates an enhancement of the cathodic current when both redox couples are introduced in respective phases, indicating that DCMFc is heterogeneously oxidized by FeðCNÞ3 6 across the water–nitrobenzene interface and that the product accumulation is monitored at the solid electrode. Although this analysis was extended to large variety of redox couples, a major complication arises from the effective control of the Galvani potential difference across the liquid–liquid junction. For instance, the authors rationalized the dependence of the redox potentials for various couples in the
Fermı´n and Lahtinen
192
FIG. 6 Cyclic voltammograms of 0.5 mM RuðNH3 Þ3þ 6 at a pyrolytic graphite electrode before (A) and after (B) depositing a thin layer of nitrobenzene containing 0.08 M tetraethylammonium perchlorate. Scan rate 5 mV s1 and S ¼ 5 mA. Cyclic voltammogram of 0.2 mM DCMFc in the nitrobenzene thin layer, S ¼ 2 A (C). Steady-state current as function of the applied potential of the graphite-modified electrode in the presence of 0.2 mM DCMFc and 2 mM RuðNH3 Þ3þ 6 , S ¼ 2 A (D). (Reprinted with permission from Ref. 97. Copyright 1999 American Chemical Society.)
organic layer with the concentration ratio of ClO 4 [97] via the relations established by Kakiuchi on partition equilibriums for large volume ratios [98]. However, a surprising 0 independence of the ET rate with the G0et , which is incompatible with Eqs. (13) and (14), casts some doubts on the potential distribution across these types of interfaces. C.
Dark Electron-Transfer Kinetics
Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67–70,79]. The formal pseudo-first-order electron-transfer rate constants [ket ðcm s1 Þ were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M1 cm s1 . Values of ket of the order of 1–2 103 cm s1 (0.05 to 0.1 M1 cm s1 ) were reported for FeðCNÞ36 =4 in the aqueous phase and the redox species LuðPCÞ2 , SnðPCÞ2 , TCNQ, and RuTPPðPyÞ2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. Nonfaradaic components associated with the uncompensated resistance between reference electrodes (Ru ) and the double layer capacitance (Cdl Þ can be accurately determined by AC impedance measurements. In this technique, a small AC potential perturbation is superimposed to the DC bias, and the resulting AC current is measured as a function of the frequency of modulation. The simplest circuit considered for a polarizable
Dynamic Aspects of Electron-Transfer Reactions
193
liquid–liquid interface is illustrated in Fig. 7 [101–103]. The impedance component associated with the transfer of the supporting electrolyte is represented by Zb , while the ET impedance element corresponds to Zf . From the equivalent circuit in Fig. 7, it follows that f the real ðYref Þ and imaginary ðYim Þ components of the faradaic admittance are given by Yref ¼ Yret Yreb
ð22Þ
f t b ¼ Yim Yim Yim
ð23Þ
where the superscripts ‘‘t’’ and ‘‘b’’ correspond to the admittance measured in the presence and absence of the redox couples respectively. Equations (22)–(23) allow a simple evaluation of the resistive and capacitive components of the faradaic impedance,
2 2 f f f f Yre þ Yim ð24Þ Zre ¼ Yre f Zim
¼
f Yim
2 2 f f Yre þ Yim
ð25Þ
f f and Zim as a function of the frequency of potential modulation (Randles’ Analysis of Zre plots) provides the phenomenological ET rate constant [63,74]. It should be noted that the f extrapolation of Zre at high frequency gives effectively the sum Rct þ Ru , where Rct is the charge transfer resistance,
Rct ¼
RT z2 F 2 Aket c
ð26Þ
determined by the pseudo-first-order ket ðcm s1 ), the surface area A and the concentration of the limiting reactant c. The accurate determination of the uncompensated resistance is an essential condition for reliable determination of the ET rate constant. One of the first analyses of ET kinetics based on AC impedance was reported by Chen et al. [74] from the oxidation of Fc by FeðCNÞ36 =4 at the water–nitrobenzene interface. Figure 8 contrasts the impedance responses in the complex plane in the presence and absence of Fc. These
FIG. 7 Simplified equivalent circuit for charge-transfer processes at externally biased ITIES. The parallel arrangement of double layer capacitance (Cdl ), impedance of base electrolyte transfer (Zb ) and electron-transfer impedance (Zf ) is coupled in series with the uncompensated resistance (Ru ) between the reference electrodes. (Reprinted from Ref. 74 with permission from Elsevier Science.)
194
Fermı´n and Lahtinen
FIG. 8 Complex impedance plot associated with the heterogeneous oxidation of Fc by ferri/ferrocyanide at the water–nitrobenzene interface. The responses only in the presence of 0.1 M ferrocene (&) are contrasted with (&) those obtained upon addition of 1 mM K3 FeðCNÞ6 and 0.1 mM K4 FeðCNÞ6 . (Reprinted from Ref. 74 with permission from Elsevier Science.)
authors did not extent their analysis into the magnitude of ket ; however, it was indicated that the exchange current density obtained from Rct was exponentially dependent on the 0 Galvani potential difference as well as on Get0 [74]. Cheng and Schiffrin [63] employed this approach for the analysis of the systems involving FeðCNÞ36 =4 in the aqueous phase and LuðPCÞ2 , RuðTPPÞðPyÞ2 , and TCNQ in DCE. A major disadvantage of this technique is that the spectra are rather featureless and the frequency range is limited to less than 1 kHz. Calculation of the faradaic impedance via the analysis of the admittance [Eqs. (22)–(26)] in the range of 1 to 30 Hz provided rate constants within a 50 mV range of the formal ET potential. The potential dependence of ket will be discussed in the next section. The formal ET rate constants were roughly of the same order as in the previous reports [62,70], i.e., 1 to 5 103 cm s1 (0.05 to 0:1 M1 cm s1 ). Although these values were successfully interpreted in terms of the Marcus model for flat interfaces [Eqs. (17)–(19)], it was realized that the continuum model for a ‘‘mixed solvent layer’’ also approaches these experimental values [3–6]. The accuracy of the AC-impedance analysis far exceeds the previous studies based on cyclic voltammetry. However, the limited frequency range available for liquid–liquid interfaces imposes severe restrictions for the deconvolution of the various responses associated with the elements in Fig. 7. An alternative approach was introduced by Ding et al.
Dynamic Aspects of Electron-Transfer Reactions
195
FIG. 9 Real component of the AC current (a) and imaginary part of the normalized potentialmodulated reflectance (b) for the TCNQ reduction by ferrocyanide at the water–DCE interface. Experimental conditions as in Fig. 5. The potential modulation was 30 mV rms at 3.2 Hz. (c) Optical Randles plot obtained from the frequency-dependent analysis of the PMR responses. (Reprinted from Ref. 43 with permission from Elsevier Science.)
[43] based on the frequency dependence of spectroscopic responses, commonly referred to as potential modulated reflectance spectroscopy (PMR) [104–109]. In this case, the interface is perturbed in an identical fashion to AC impedance, but the frequency-dependent reflectance in TIR is measured as opposite to the AC current (I~f ). In the configuration described in Fig. 4, and for small potential amplitudes, the normalized AC reflectance [ðR=RÞAC ] is proportional to the frequency-dependent concentration of TCNQ at the interface. Following Eq. (21), it can be easily demonstrated that the optical responses are 90 out of phase with respect to the faradaic current [108,109]. FA cos I~f ¼ ðR=RÞAC i! 2TCNQ
ð27Þ
where ! corresponds to the angular frequency of potential modulation. The phase shift between the frequency-dependent optical and electrical responses is exemplified in Fig. 9. The real component of the AC current during the reduction of TCNQ by ferrocyanide [Fig. 9(a)] exhibits the same potential dependence as the quadrature component of R=R [Fig. 9(b)]. The most relevant aspect of this approach is that the faradaic impedance is directly accessed from the optical responses. It follows from Eqs. (24), (25) and (27),
Fermı´n and Lahtinen
196
Zre ¼
2TCNQ w !1 ðR=RÞim o 1 2 2 FS cos ’ ðR=RÞ þ ðR=RÞ re
Zim ¼
ð28aÞ
im
2TCNQ w !1 ðR=RÞre o 1 2 2 FS cos ’ ðR=RÞ þ ðR=RÞ re
ð28bÞ
im
where w o 1 corresponds to the amplitude of potential modulation. The second terms in Eqs. (28a) and (28b) were defined as the optical impedance parameters Fre and Fim respectively. Similarly to the Randles method, the charge-transfer resistance Rct can be effectively estimated from extrapolation of Fre to high frequencies. Figure 9(c) illustrates a typical example obtained for the ferrocyanide–TCNQ system [43]. A further advantage of this technique is that the extrapolated value of the parameter Fre is proportional to Rct , i.e., independent of the uncompensated resistance. The formal pseudo-first-order ET rate constant obtained from the optical analysis was largely consistent with the electrical impedance studies [63]. A further spectroscopic approach was employed in the work by Ding et al. [43], in which the absorption transient is recorded after a potential step. For the case of TCNQ, the absorption transient is given by ! 2TCNQ ½TCNQkf 2 t1=2 1 ð29Þ ATIR ¼ 2 cos ’ 1=2 where ¼
kf 1=2 DTCNQ
þ
kb 1=2 DTCNQ
ð30Þ
and the rate constants kf and kb stand for the forward and backward electron transfer. The rate constants obtained for the ferrocyanide–TCNQ system by chronoabsorptometry were consistent with the data derived from PMR. The combination of the two optical analyses allowed accessing ET rate constant values over a wider potential range than in the case of the electrical impedance analysis. This is a particularly relevant aspect for studies of the potential dependence of the interfacial ket . Initial analysis of ET kinetics under open circuit was performed at different experimental conditions than those described for externally biased interfaces [44,93,94]. Recent developments on SECM and MEMED (Chapters 12 and 13) have proved to monitor ET kinetics over a wide range of time scales. Barker et al. have extended the analysis of concentration profiles beyond the constant composition approximation [45] previously employed for SECM studies. For redox species exhibiting similar diffusion coefficients, the constant composition approximation requires in excess of 15 to 20 times of the species which regenerates the probe at the liquid–liquid junction. However, extension of the analysis to a variety of concentration ratios allows measurements of very fast processes, which would otherwise appear as diffusion controlled. For instance, it was estimated that the bimolecular heterogeneous rate constant between the radical ZnTPPþ and FeðCNÞ4 6 approaches 55 M1 cm s1 at the water–benzene interface. This result remarkably contrasts with the 1:8 M1 cm s1 reported by Shi and Anson obtained for suspended thin organic electrolyte layers on graphite electrodes [97]. The recently developed MEMED technique provides accurate measurements for rather slow processes, beyond the range available for SECM [59]. In this approach, the liquid–liquid interface is an expanding droplet, and the concentration profiles of the redox
Dynamic Aspects of Electron-Transfer Reactions
197
species located in the static phase are monitored by a microelectrode as the drop expands. Contrary to the results obtained by Liu and Mirkin employing SECM [46], Unwin et al. successfully analyzed the ET kinetics between ferrocyanide and TCNQ at the water–DCE interface by MEMED [110]. The discrepancies between these two approaches may be connected to the reliability of SECM to measure rather slow charge-transfer kinetics. The dynamics of ET can also be severely affected by the addition of surfactants to the liquid–liquid junctions. The approach of redox species to the interfacial region can be effectively hindered by adsorbed surfactant molecules featuring phosphocholine heads [44,76,111], inducing a substantial decrease of ket . The extent of the ET blocking depends on the arrangement of the lipid layer, the structure of the surfactant, and the size of the redox species. Tsionsky et al. attempted to analyze the value of ket of the þ RuðCNÞ4 6 =ZnTPP system as a function of the length of the phospholipid hydrocarbon chain [44]. Although a decrease of the rate constant was evident with increasing number of methylene groups, the trend was complicated by variations on the properties of the lipid layer. For instance, the rate constant obtained for the C-10 chain was rather similar to that for C-20. This behavior was interpreted in terms of partial penetration of ZnTPPþ through the lipid layer, providing faster transfer kinetics than expected. Cheng and Schiffrin observed that ET involving ferri/ferrocyanide and RuðTPPÞðpyÞ2 and LuðPCÞ2 was inhibited by lecithin–cholesterol adsorbed at the water–DCE interface, although electron transfer to TCNQ was still measurable. This difference was rationalized in terms of the size of the redox species. While the Ru and Lu complexes are rather bulky, TCNQ is considerably smaller and therefore able to penetrate the lipid layer. Delville et al. demonstrated that the electronic structure of the phospholipid can also play a role on the ET dynamics [111]. In this work, it was shown that electrons are transferred faster through polyconjugated chains in comparison with saturated ones. D.
Butler–Volmer vs. Concentration Polarization
The potential dependence of the ET rate constant is one of the most controversial issues in this field. By accessing the fraction of the Galvani potential difference operating on the ET step, also known as the transfer coefficient , essential information on the potential distribution and structure of the interface can be obtained. As discussed in Section II.B, two mechanisms can contribute to the dependence of ket on w o : concentration polarization and changes in the free energy of ET (Butler–Volmer). While the latter is traditionally associated with metal–electrolyte interfaces, the former is commonly observed at semiconductor–electrolyte junctions where the density of charge carriers in the solid is finite. Lattice-gas modeling of the interface established that if the distance separating the redox couples is smaller than the Debye lengths at the interface, changes in w o will mostly affect the interfacial concentrations of the ionic species [7]. However, a great deal of the experimental studies have been carried out at rather high ionic strengths, where the Debye lengths could be rather short and different from the classical Gouy–Chapman expression. The theoretical approach by Samec based on the ion-free compact layer model established that the ‘‘true’’ apparent transfer coefficient is obtained after correction for concentration polarization effect [1] [see Eq. (14)]. Subsequent studies by Samec and coworkers on the ferricyanide–Fc system provided values of smaller than the expected 0.5. Preliminary attempts to rationalize this behavior were based on defining effective interfacial charges and separation distance between reactants [79]. The inconclusive trends reported in these studies were ascribed to complications arising from ion pairing of the ferro/ferricyanide ions. Later analysis of the same system appeared to show that ket is
Fermı´n and Lahtinen
198
rather independent of the Galvani potential difference, and the observed dependence is mainly connected to concentration polarization [67]. The kinetic analysis by Cheng and Schiffrin of the TCNQ reduction by ferrocyanide arrived at a different conclusion [63]. In this case, the aqueous phase features a rather high ionic strength and an excess of the redox couple with respect to the organic phase. The cyclic voltammogram exhibited a peak-to-peak difference close to 59 mV as exemplified in Fig. 5(c). The authors rationalized this behavior by considering the aqueous phase acting as a ‘‘metallic’’ electrode, under the assumption that the excess concentration of the aqueous redox couple remains unaffected by the Galvani potential difference. Impedance analysis following Eqs. (22)–(26) provided a potential dependence of the observed ket , which did not follow a pure Butler–Volmer behavior. The observed deviations were interpreted in terms of a perturbation of the local potential due to interfacial ion pairing of the ionic redox couple in the aqueous phase and the organic supporting electrolyte. This conclusion is not entirely consistent with the admittance analysis itself, as the ion-pairing excess charge would introduce an extra contribution to the total imaginary t admittance Yim which cannot be separated from the faradaic admittance by simple subb [Eq. (23)]. For instance, this excess charge traction of the base electrolyte response Yim would manifest itself as an increase of the differential capacitance with respect to theoretical values obtained in the absence of ion pairing [24,25,112]. The non-steady-state optical analysis introduced by Ding et al. also featured deviations from the Butler–Volmer behavior under identical conditions [43]. In this case, the large potential range accessible with these techniques allows measurements of the rate constant in the vicinity of the potential of zero charge (kpzc obs ). The potential dependence as obtained from the optical analysis of the of the ET rate constant normalized by kpzc obs TCNQ reduction by ferrocyanide is displayed in Fig. 10(a) [43]. This dependence was analyzed in terms of the preencounter equilibrium model associated with a ‘‘mixed-solvent layer’’ type of interfacial structure [see Eqs. (14) and (16)]. The experimental results were compared to the theoretical curve obtained from Eq. (14) assuming that the potential drop between the reaction planes (ab ) is zero. The potential drop in the aqueous side was estimated by the Gouy–Chapman model. The theoretical curve underestimates the experimental trend, and the difference can be associated with the third term in Eq. (14). Figure 10(b) shows the inner potential as a function of the Galvani potential difference assuming a value of 0.5 for the transfer coefficient . From this analysis it is estimated that about 30% of the Galvani potential difference is developed between the redox reaction planes. It should be mentioned that these calculations are approximate, especially considering the primitive model employed for calculating ion distributions under high ionic strength. However, we believe that a more sophisticated model would not change substantially the physical aspects highlighted in this approach. The previous analysis indicates that although the voltammetric behavior suggests that the aqueous phase behaves as a ‘‘metal electrode’’ dipped into the organic phase, the interfacial concentration of the aqueous redox couple does exhibit a dependence on the Galvani potential difference. In this sense, it is not necessary to invoke potential perturbations due to interfacial ion pairing in order to account for deviations from the Butler– Volmer behavior [63]. This phenomenon has also been discarded in recent studies of the same system based on SECM [46]. In this work, the authors observed a potential independent ket for the reaction sequence, 3 RuðCNÞ4 6 !RuðCNÞ6 þ e
(at the microelectrode tip in water phase)
ð31Þ
Dynamic Aspects of Electron-Transfer Reactions
199
FIG. 10 Potential dependence of the electron-transfer rate constant (ket ) normalized to the value at the potential of zero charge (kpzc obs ) for the TCNQ reduction by hexacyanoferrate at the water–DCE interface. Full line was estimated from Eq. (14), assuming that the potential drop across the inner layer is negligible. Dependence of the potential drop across the ET reaction plane with the Galvani potential difference, as obtained from recalculation of the two trends in (a), assuming a transfer coefficient of 0.5 (b). These results suggest that approximately 30% of the Galvani potential difference is developed between the reacting species under the experimental conditions defined in Figs. 5 and 9. (Reprinted from Ref. 43 with permission from Elsevier Science.)
ket 4 þ RuðCNÞ3 6 ðwÞ þ ZnTPPðoÞ ! RuðCNÞ6 ðwÞ þ ZnTPP ðoÞ
(at ITIES)
ð32Þ
This result was taken as an experimental confirmation of the model developed by Schmickler [7]. However, it appeared somehow contradictory with other results obtained with SECM. It was also suggested that concentration polarization phenomena occurring at the aqueous side are negligible as the whole potential drop is presumably developed in the benzene phase. This assumption can be qualitatively verified by evaluating a simplified expression for the potential distribution based on a back-to-back diffuse double layer [40,113], w w RT c 1 0 w ln 0 0
w ¼ 1=2o ð33Þ 2F c where and c correspond to the dielectric constant and concentration of the ionic species in the corresponding electrolyte solution. Taking an arbitrary value of 0.2 V for the Galvani potential difference w o , the potential developed in the aqueous side could range from 5 mV to 50 mV depending on the composition of the electrolyte in the organic phase. For the sake of comparison, this potential drop is similar to that observed for the
Fermı´n and Lahtinen
200
water–DCE junction under the conditions described in Fig. 1 and Ref. [43]. Although a more thorough analysis would require an estimation of the Galvani potential difference, it is clear that the potential drop in the aqueous phase is not necessarily negligible and therefore concentration polarization effects for highly charged species such as RuðCNÞ3 6 should be considered. In other words, the weak increase of observed ket as
becomes more positive can be attributed to a combined depletion of RuðCNÞ3 the w o 6 and increase of the real heterogeneous ET rate constant. Similar SECM studies by Tsionsky et al. [44,93] revealed a strong potential dependence of ket , featuring an apparent transfer coefficient of 0.5, for the system described in Eqs. (31) and (32). In this report, the feedback current was measured for the ZnTPP species instead of the aqueous redox couple. The value of was confirmed over a potential range of 120 mV and various concentration of RuðCNÞ4 6 in the aqueous phase under the constant composition approximation. This behavior was rationalized in terms of conventional ET theories transposed to liquid–liquid junctions as initially postulated by Samec in 1979 [1]. The apparent value of was also taken as a criterion for neglecting concentration polarization phenomena. Furthermore, as the difference in the ET driving force was increased by changing the redox couple in the aqueous phase, the transfer coefficient decreased until the ET kinetics was diffusion controlled [44]. These crucial experimental results provide a first confirmation of the ket dependence on the free energy of electron transfer [5]. A more spectacular demonstration was later reported by Barker et al., who extended the SECM analysis beyond the constant composition approximation obtaining kinetic responses on the inverted Marcus region [45]. Although the correlation between ket and the driving force determined by Eq. (14) has been confirmed by various experimental approaches, the effect of the Galvani potential difference remains to be fully understood. The elegant theoretical description by Schmickler seems to be in conflict with a great deal of experimental results. Even clearer evidence of the ket dependence on w o has been presented by Fermı´ n et al. for photoinduced electron-transfer processes involving water-soluble porphyrins [50,83]. As discussed in the next section, the rationalization of the potential dependence of ket in these systems is complicated by perturbations of the interfacial potential associated with the specific adsorption of the ionic dye.
IV.
PHOTOINDUCED ET REACTIONS
Photoinduced ET at liquid–liquid interfaces has been widely recognized as a model system for natural photosynthesis and heterogeneous photocatalysis [114–119]. One of the key aspects of photochemical reactions in these systems is that the efficiency of product separation can be enhanced by differences in solvation energy, diminishing the probability of a back electron-transfer process (see Fig. 11). For instance, Brugger and Gra¨tzel reported that the efficiency of the photoreduction of the amphiphilic methyl viologen C14 V2þ by RuðbpyÞ2þ 3 is effectively enhanced in the presence of cationic micelles formed by cetyltrimethylammonium chloride [120]. Flash photolysis studies indicated that while the kinetics of the photoinduced reaction,
2þ þ RuðbpyÞ2þ ! RuðbpyÞ3þ 3 þ C14 V 3 þ C14 V
ð34Þ
Dynamic Aspects of Electron-Transfer Reactions
201
FIG. 11 General mechanism for the heterogeneous photoreduction of a species ‘‘Q’’ located in the organic phase by the water-soluble sensitizer ‘‘S.’’ The electron-transfer step is in competition with the decay of the excited state, while a second competition involved the separation of the geminate ion-pair and back electron transfer. The latter process can be further affected by the presence of a redox couple able to regenerate the initial ground of the dye. This process is commonly referred to as supersensitization. (Reprinted with permission from Ref. 166. Copyright 1999 American Chemical Society.)
remains unaffected by the presence of the cationic micelles, the rate of the back electron transfer þ 2þ ! RuðbpyÞ2þ RuðbpyÞ3þ 3 þ C14 V 3 þ C14 V
ð35Þ
was substantially decreased. These results suggest that the lower hydrophilicity of the radical C14 Vþ allows it to be trapped inside the micellar cage, avoiding back electron transfer by keeping away the oxidized dye by electrostatic repulsion. In a series of papers by Kotov and Kuzmin, the effect of polarizable liquid–liquid junctions on the separation of photoproducts was studied by photocurrent measurements [121–123]. The systems studied featured homogeneous quenching of protoporphyrin by quinone, and quinone by tetraphenylborate, as well as self-quenching of tetraphenylporphyrin in the organic phase. For all cases, charged photoproducts were generated and the transfer of these species across the liquid–liquid junction was followed by photocurrent measurements. The time scales of the photoresponses were in the range of fractions of a minute to minutes. Rather complex analysis was proposed in order to account for the various possible photoprocesses, including photo-oxidation of the organic supporting electrolyte. A comprehensive review of these works has been presented elsewhere [117]. As mentioned in previous sections, we shall concentrate on systems where photoactive species and redox quenchers are separated by the liquid–liquid junction. Although the distance separating the redox species effectively slows down the back electron transfer, it also brings about a decrease of the photoinduced ET reaction in comparison to homogeneous processes. As represented in Fig. 11, the overall efficiency of the photoreaction is initially determined by the ratio between ket and the rate of excited state decay (kd ). In this respect, vectorial ET can be enhanced by specific interaction of the reactants with the liquid–liquid junction, e.g., specific adsorption, self-assembling, and interfacial ion pairing. Considering the role of these interfacial interactions, ITIES can be regarded as a photochemical molecular device (PMD), i.e., an assembly of molecules capable of performing light-induced functions [124,125].
Fermı´n and Lahtinen
202
A.
Recent Spectroscopic Studies on Photoinduced ET at Liquid–Liquid Interfaces
The elementary steps involved in photoinduced ET processes are schematically represented in Fig. 11. At the interfacial region, the electron-transfer step is in competition with the relaxation of the excited state. The intermediate species generated after the ET step can be associated with the geminate ion pair familiar from classical photochemistry. In the case of a heterogeneous photoreaction, the ET products are located in different electrolyte phases with their solvation shells. Subsequently, a new competition is developed between the separation of photoproducts and back electron transfer. Two ways can be envisaged for monitoring the dynamics of photoinduced reactions, (1) spectroscopic detection of reactants and/or products by time-resolved spectroscopy or (2) monitoring the flux of charge transfer under potentiostatic conditions upon illumination (photocurrent measurements). The former approach is treated in this section. Corn and coworkers provided one of the first spectroscopic evidences of photoinduced ET reactions at liquid–liquid interfaces employing optical second harmonic generation (SHG) [126]. The interfacial photochemical reaction involving RuðbpyÞ2þ 3 and the SHG probe trans-1-ferrocenyl-2-[4-(trimethylammonium)phenyl] ethylene was studied at the water–DCE interface. Experimental details and results have been reviewed in the chapter on nonlinear optics (Chapter 6). The photo-oxidation of the ferrocene unit in the surface active species introduces a strong change in the nonlinear optic parameters of the interface under illumination. The rise time and decay for the SHG signal upon a square-wave light perturbation were of the order of 10 to 20 s1 . The rather slow dynamic responses are not essentially related to the kinetics of charge transfer but to other processes such as diffusion of the excited state to the interface, lateral diffusion of the oxidized probe, and product desorption. A more direct approach to the photoinduced ET dynamics involves monitoring the lifetime of the excited state at the interface. By illuminating the interface in TIR from the electrolyte phase containing the quencher species, the generation of excited state is limited to the characteristic penetration depth given by the evanescent wave () [127], ¼
2
1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 n1 sin ðn22 =n21 Þ
ð36Þ
where is the wavelength of illumination, is the incident angle, n1 and n2 correspond to the refractive indexes of the phase containing the dye and the light propagating phase respectively. For the water–DCE interface under illumination from the organic side in the visible range at higher than the critical angle (67:56 ), the penetration depth into the aqueous phase is of the order of 100 nm. In the presence of a dye species, the penetration depth is further reduced according to the Beer–Lambert expression, resulting in a distribution of the excited state c ðxÞ of the form c ðxÞt¼0 ¼ A expðxÞ
ð37Þ
where is the penetration depth of light into the aqueous phase corrected for dye absorption. Considering the diffusion controlled interfacial quenching of the excited state, it follows that the time dependent fluorescence signal is proportional to
pffiffiffiffiffiffi
pffiffiffiffiffiffi A exp 2 Dt erfc Dt exp 2 Dt erfc Dt NðtÞ ¼ expðkd tÞ ð38Þ
Dynamic Aspects of Electron-Transfer Reactions
203
where the parameter includes the bimolecular rate constant of heterogeneous quenching kq . ¼
kq cq D
ð39Þ
kd and D correspond to the rate of decay and diffusion coefficient of the excited state respectively, while cq is the bulk concentration of the quencher species. On the basis of Eqs. (36)–(39), the fluorescence transients for two dyes with different excited-state lifetime are simulated in Fig. 12. A noticeable difference in the luminescent decay between the limits of infinitely fast quenching and kq ¼ 0 is observed for Eu(III). The rate constant of excited-state decay for this cation is 104 s1 , which is approximately two orders of magnitude slower than for RuðbpyÞ2þ 3 . In the latter case, the decay of the luminescence is very similar for the infinitely fast and infinitely slow limits. Indeed, these simulations indicate that the dynamics of heterogeneous quenching at the liquid–liquid junction can be accessed by time-resolved spectroscopy only if the diffusion of the excited state can effectively compete with the relaxation process. The above analysis was entirely consistent with the experimental behavior observed for the systems Eu(III) and anthracene as well as RuðbpyÞ2þ 3 and TCNQ at the water–DCE interface [127]. The dependence of the rate of fluorescent decay for Eu(III) on the anthra-
FIG. 12 Simulation of fluorescent decays for dye species located in the aqueous phase following laser pulses in TIR from the water–DCE interface according to Eq. (38). A fast rate constant of excited state decay (106 s1 ) was assumed in (a). The results showed no difference between infinitely fast or slow kinetics of quenching. On the other hand, a much slower rate of decay can be observed for other sensitizers like Eu3þ and porphyrin species. Under these conditions, heterogeneous quenching associated with the species Q can be readily observed as depicted in (b). (Reprinted with permission from Ref. 127. Copyright 1997 American Chemical Society.)
204
Fermı´n and Lahtinen
cene concentration allowed estimations of the interfacial quenching rate constant of the order of 20 M1 cm s1 . The value of kq is of the same order as the maximum electron– transfer rate constant observed experimentally for the reduction of ZnTPPþ by FeðCNÞ4 6 at the water–benzene interface [45]. It is also close to the limit determined by Eq. (17) for separation between redox species over few nanometers. Although the latter reaction takes place in the dark, the large driving force involved (see redox potential diagram) may lie close to that expected for a photoinduced process. A rather important aspect that should be considered is that interfacial quenching of dyes does not necessarily imply an electron-transfer step. Indeed, many photochemical reactions involving anthracene occur via energy transfer rather than ET [128]. A way to discern between both kinds of mechanisms is via monitoring the accumulation of photoproducts at the interface. For instance, heterogeneous quenching of water-soluble porphyrins by TCNQ at the water–toluene interface showed a clear accumulation of the radical TCNQ under illumination [129]. This system was also analyzed within the framework of the excited-state diffusion model where time-resolved absorption of the porphyrin triplet state provided a quenching rate constant of the order of 92 M1 cm s1 .
B.
Photocurrent Responses Originating from Heterogeneous Quenching of Dyes
Under potentiostatic conditions, the perturbation of the charge across the interface associated with the photoinduced ET step is relaxed through the counterelectrodes located in each phase. In the absence of coupled ion-transfer reactions, the photocurrent responses are proportional to the flux of charge associated with the heterogeneous quenching of the dye species. From the mechanism in Fig. 11, it is also observed that not only heterogeneous ET occurs via the dye-excited state, but also via back electron transfer involving the interfacial geminate ion pair. By contrast to time-resolved spectroscopy, photocurrent responses at well-defined systems are a definitive evidence of heterogeneous photoinduced electron transfer. However, these measurements are carried out at time scales longer than fractions of milliseconds. This restriction is imposed by the time constant of charging the interfacial double layer (Ru Cdl Þ under potentiostatic conditions. The first report on photocurrent measurements at liquid–liquid interfaces was published by Marecek et al. for the photoreduction of methylviologen in the aqueous phase by RuðbpyÞ2þ 3 located in the organic phase (DCE or benzonitrile) [48], 2þ þ RuðbpyÞ2þ ! RuðbpyÞ3þ ð40Þ 3 DCE þ MV 3 DCE þ MV water water The cationic dye was associated with the anion (7,8,9,10,11,12 Br6 -1-CB11 H6 Þ in order to dissolve it in the organic phase. The polarizable window available for photoinduced electron transfer in this system extended over 100 mV for the conditions specified in Fig. 13. The photocurrent responses were measured under chopped light and lock-in detection at 8.4 Hz. Figure 13(b) shows that some photoresponses occur only in the presence of the dye species, which the authors attributed to the transfer of RuðbpyÞ2þ 3 to the aqueous phase as a result of interfacial polarization induced by the chopped light [130]. Upon addition of MV2þ in the aqueous phase, an increase in the amplitude of the photocurrent is observed in conjunction to a slight change of phase shift. The authors proposed that these effects can be taken as an evidence for heterogeneous photoinduced ET. However, the analysis of curves 2 and 3 in Fig. 13(c) appears rather inconsistent with this idea. The ‘‘photoinduced’’ transfer of the cationic dye would involve a current
Dynamic Aspects of Electron-Transfer Reactions
205
FIG. 13 Cyclic voltammogram (a) and potential dependence of the photoresponses (b)–(c) to chopped illumination and lock-in detection associated with the photoreaction in Eq. (40). The CV shows that the polarizable window extended to less than 100 mV. The photocurrent measurements carried out were done in the presence (trace 3) and absence (trace 2) of the redox quencher in the organic phase. (Reprinted with permission from Ref. 48. Copyright 1989 American Chemical Society.)
response of opposite sign to the ET phenomenon; therefore it is difficult to reconcile both faradaic processes with an increase of the photocurrent amplitude. Furthermore, if it is assumed that the ET is the predominant step, the phase shift should be approximately 180 with respect to the signal observed in the absence of MV2þ . Another point subject to criticism from this work is the apparent absence of DC photocurrents upon constant illumination. Although the responses in Fig. 13(c) appear effectively in phase at the chopping frequency, it is possible that slow photoinduced perturbation of accumulated charge at the interface can be connected with these photoresponses, e.g., photoionization of the dye [72]. In this respect, clearer evidence of photoinduced ET was introduced by Brown et al. for the reaction [49] 2þ 3þ RuðbpyÞ3 water þTCNQDCE ! RuðbpyÞ3 water þTCNQ ð41Þ DCE Within the potential range where RuðbpyÞ2þ 3 remains in the aqueous phase, photocurrent responses are clearly observed with a slow rising time of the order of 10 s as shown in Fig. 14(a). According to the convention employed by these authors, positive currents correspond to the transfer of a negative charge from water to DCE. No photoresponses were observed in the absence of either the dye in the aqueous phase or TCNQ in DCE. Further analysis of the interfacial behavior of the product TCNQ revealed that the ion transfer occurred outside of the polarizable window [cf. Fig. 14(d)], confirming that these photoresponses are not affected by coupled ion-transfer processes. An earlier report also showed photoeffects for the photoreduction of the viologen C7 V2þ under similar conditions [131]. Although the reports by Brown et al. provided strong evidence of photoinduced heterogeneous ET responses [49], the rather slow rising times observed in the transients of Fig. 14(a) are difficult to rationalize on the basis of the mechanism in Fig. 11. Another puzzling point is the potential dependence of the photocurrent obtained under chopped
206
Fermı´n and Lahtinen
FIG. 14 On–off photocurrent responses (a) associated with the reaction in Eq. (41) at w o ¼ 0:225 V. In this figure, positive currents correspond to the transfer of a negative charge from water to DCE. The potential dependence of the photocurrent (b) was obtained under chopped illumination and lock-in detection. The maximum in the photocurrent–potential curve contrasts with the small changes in the dark current shown in (c). These responses are developed within the polarizable window described in (d). (From Ref. 49. Reproduced by permission of The Royal Society of Chemistry.)
illumination and lock-in detection exemplified in Fig. 14(b). As the Galvani potential difference was swept negative, an increase of the photocurrent was detected in the region between 0:10 to 0:20 V. This behavior is consistent with kinetically controlled ET reaction from the aqueous to the organic phase. As the potential becomes more negative a decrease of the photocurrents is observed which is difficult to analyze solely in terms of total amplitude. In principle, the attenuation of the photocurrent can be associated with a decrease of the interfacial concentration of the cationic dye. Another possibility is that as the interfacial capacitance increases steeply in this region, therefore increasing the attenuation of the photocurrent due to the slow dynamics of double layer charging–discharging [132]. In order to explore these phenomena, a full analysis of the photocurrent amplitude and phase shift at various chopping frequencies is required. This type of analysis will be discussed in the next section. More recently, a series of papers based on photocurrent responses involving water soluble porphyrin species has allowed to address the various aspects involved in the mechanism of Fig. 11 [50,73,83]. Photocurrent transients at the water–DCE interface in the presence of zinc tetrakis(carboxyphenyl) porphyrin (ZnTPPC4 ) and Fc under monochromatic light are shown in Fig. 15 at various Galvani potential differences [50]. The
Dynamic Aspects of Electron-Transfer Reactions
207
FIG. 15 Photocurrent responses associated with the heterogeneous quenching of ZnTPPC4 by diferrocenylethane at the water–DCE interface at various Galvani potential differences. The increase of the photocurrent upon illumination is remarkably faster than for the transients shown in Fig. 14(a). (Reprinted with permission from Ref. 50. Copyright 1998 American Chemical Society.)
porphyrin species does not transfer to the organic phase within the available potential region. A wealth of interesting features can be considered from these results: 1.
2.
Despite the large driving force involved in ET from Fc to the excited state of the porphyrin [compare potentials in Figs. 3(a) and 4], photocurrents are only observed at positive Galvani potential differences. Furthermore, photocurrent studies with various electron donors feature very similar potential dependencies [83]. As the Galvani potential increases, it is expected that the interfacial concentration of the ionic dye decreases; however, the photocurrent readily increases.
Fermı´n and Lahtinen
208
3.
4.
The maximum photocurrent occurs simultaneously with the light perturbation within the millisecond time scale, except at rather positive Galvani potential difference where phase shift associated with photo-oxidation of the supporting electrolyte ðTPBCl ) and Ru Cdl attenuation is observed. Between 0.20 and 0.30 V, a decay of the initial photocurrent and a negative overshoot after interrupting the illumination are developed. This behavior resembles the responses observed at semiconductor–electrolyte interfaces in the presence of surface recombination of photoinduced charges [133–135] but at a longer time scale. These features are in fact related to the back-electron-transfer processes within the interfacial ion pair schematically depicted in Fig. 11.
Before each of these points is addressed, some other points should be discussed in connection with the nature of these photoresponses. The photocurrent dependence on the wavelength of illumination depicted in Fig. 16 clearly indicates that these responses are connected with the excited state of the dye species [73]. Furthermore, upon replacing an electron donor by an acceptor in the organic phase such as TCNQ, the sign of the photocurrent is reversed as contrasted for a photoactive porphyrin ion pair in Figs. 17(a) and (b). It is also observed that the back ET responses are rather strong, i.e., the steady-state photocurrent is effectively zero. Figure 11 shows that aqueous phase redox couples, which are able to react swiftly with the intermediate species, can eventually decrease the probability of back ET. This is exemplified in Fig. 17(b), where the backelectron-transfer responses are effectively diminished upon addition of the hexacyanoferrate couple to the aqueous phase. This effect is analogous to supersensitization processes familiar from the dye-sensitized semiconductor–electrolyte interface [136].
C.
Basic Aspects Concerning Dynamic Photocurrent Measurements
The advantage of employing periodic perturbation of light intensity, e.g., using a chopper, and phase-sensitive detection are beyond a simple enhancement of the signal-to-noise ratio. For photoinduced electron-transfer mechanisms, as schematized in Fig. 11, the
FIG. 16 Photocurrent spectra corresponding to the photo-oxidation of DCMFc by ZnTPPC4 at the water–DCE interface under chopped illumination and lock-in detection. The main features of the spectra coincide with the onset of the Soret band and the Q-bands of the porphyrin ring. (From Ref. 73. Reproduced by permission of the Royal Society of Chemistry.)
Dynamic Aspects of Electron-Transfer Reactions
209
FIG. 17 Reversal of the photocurrent sign upon replacing the electron donor DCMFc (a) by the electron acceptor TCNQ (b) in the presence of the porphyrin heterodimer ZnTMPyP–ZnTPPS at the water–DCE interface. The strong back electron-transfer features in the photoreduction of TCNQ were diminished upon addition of an equimolar ratio of ferri/ferrocyanide acting as supersensitizer in the aqueous phase (b). The mechanism of supersensitization is described in Fig. 11. From the potential relationship between these redox couples (Fig. 4), these phenomena can be regarded as interfacial photosynthetic processes as defined in Fig. 3(b). (Reprinted with permission from Ref. 87. Copyright 1999 American Chemical Society; and from Ref. 166 with permission from Elsevier Science.)
amplitude and phase shift of the frequency-dependent photocurrent contain information on the dynamics of each of the steps involved. Intuitively, photoresponses at low frequencies comprise contributions from the various processes in the overall mechanism, i.e., steady-state conditions, while as the frequency is increased only the faster processes are observed. Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simplified equivalent circuit for the liquid–liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clarified later, the photoinduced ET
Fermı´n and Lahtinen
210
FIG. 18 Simplified equivalent circuit for externally biased ITIES under illumination. The perturbations introduced by the photoreactions in Fig. 11 are contained within the generator term g. Cdl and Ru are associated with the interfacial capacitance and the uncompensated resistance. (From Ref. 83. Reproduced by permission of the Royal Society of Chemistry.)
step is effectively in phase with light perturbations at low illumination levels, consequently the faradaic component can be treated as a generator factor. In essence, the representation in Fig. 18 describes the generation of an excess charge at the interface, which relaxes through the Cdl and Ru [83]. From the schematic representation in Fig. 18, it follows that for a perturbation featuring a DC bias light (I0 ) and a sinusoidal component of amplitude I1 , I ¼ I0 þ I1 expði!tÞ
ð42Þ
the frequency-dependent photocurrent (j1 ) is given by j1 ¼ g1 ½1=ð1 þ Ru Cdl i!Þ
ð43Þ
where g1 corresponds to the AC flux of electron transfer across the interface. Equation (43) describes the behavior of an ideal diode, from which the maximum frequency accessible under potentiostatic conditions can be determined. As we discuss later in this section, Eq. (43) can be further developed in order to include the various kinetic parameters associated with the photoinduced electron-transfer mechanism. The most common types of light intensity perturbations include light pulses as well as periodic square and sinusoidal functions. Short light pulses from femto- to nanosecond time scales have been extensively employed for time-resolved photovoltage measurements at semiconductor–electrolyte interfaces [137–142]. To our knowledge, no reports on timeresolved photovoltage measurements at ITIES have been published so far. However, considering the large Ru Cdl characterizing these junctions, it could be anticipated that photovoltage measurements can provide direct access to photoinduced ET rate constants. Mauzerall and coworkers have also employed this technique for studying photoprocesses involving porphyrin species at lipid bilayers [143–147]. The basic experimental arrangements for photocurrent measurements under periodic square and sinusoidal light perturbation are schematically depicted in Fig. 19. In the previous section, we have already discussed experimental results based on chopped light and lock-in detection. This approach is particularly useful for measurement at a single frequency, generally above 5 Hz. At lower frequencies the performance of lock-in amplifier and mechanical choppers diminishes considerably. For rather slow dynamics, DC photocurrent transients employing optical shutters are more advisable. On the other hand, for kinetic studies of the various reaction steps under illumination, intensity modulated photocurrent spectroscopy (IMPS) has proved to be a very powerful approach [132,133,148– 156]. For IMPS, the applied potential is kept constant and the light intensity is sinusoid-
Dynamic Aspects of Electron-Transfer Reactions
211
FIG. 19 Block diagrams for photocurrent measurements with chopped light and lock-in detection (a) as well as for intensity-modulated photocurrent spectroscopy (b). (Adapted from Ref. 85.)
ally modulated employing an acousto-optic modulator [Fig. 19(b)]. The frequency range available for these measurements spanned from mHz to just below 100 kHz. Of course, the high-frequency limit is often determined by the Ru Cdl constant of the cell or the bandwidth of the potentiostat. Photocurrent analysis under chopped illumination and lock-in detection is largely complementary to IMPS. While the former provides a simple approach for studying the dependence of the photocurrent on applied potential or illumination wavelength (see examples in Figs. 13, 14, and 16), the latter allows reliable kinetic analysis as a function
212
Fermı´n and Lahtinen
of the frequency of perturbation. In both approaches, the periodic optical response should be synchronized with the phase-sensitive detector or the DTF analyzer. This can be simply done by collecting either the reflected or transmitted light from the liquid–liquid junction into a fast light detector (fast photodiode or a photomultiplier tube). D.
Dynamics of the Various Processes Involved in Photoinduced ET
The first estimations of ket for photoinduced processes were reported by Dvorak et al. for the photoreaction in Eq. (40) [157,158]. In this work, the authors proposed that the ‘‘impedance under illumination’’ could be estimated from the ratio between the AC photopotential under chopped illumination and the AC photocurrent responses. Subsequently, the ‘‘faradaic impedance’’ was calculated following a treatment similar to that described in Eqs. (22) to (26), i.e., subtracting the impedance under illumination and in the dark. From this analysis, a pseudo-first-order photoinduced ET rate constant of the order of 102 to 103 m s1 was estimated, corresponding to a rather unrealistic ket > 106 M1 cm s1 . Considering the nonactivated limit for adiabatic outer sphere heterogeneous ET at liquid–liquid interfaces given by Eq. (17) [5], the maximum bimolecular rate constant is approximately 1000 smaller than the values reported by these authors. In our opinion, the interesting photoresponses described by Dvorak et al. were incorrectly interpreted by the spurious definition of the photoinduced charge transfer impedance [157]. Formally, the impedance under illumination is determined by the AC admittance under constant illumination associated with a sinusoidal potential perturbation, i.e., under short-circuit conditions. From a simple phenomenological model, the dynamics of photoinduced charge transfer affect the charge distribution across the interface, thus according to the frequency of potential perturbation, the time constants associated with the various rate constants can be obtained [156,159–163]. It can be concluded from the magnitude of the photoeffects observed in the systems studied by Dvorak et al., that the impedance of the system is mostly determined by the Ru Cdl time constant. Analysis of the ZnTPPC4 –Fc system within the framework of the model schematically described in Fig. 11 has delivered self-consistent information on the dynamics of photoinduced ET [50]. The dependence of the photocurrent on the porphyrin concentration at various Galvani potential differences is displayed in Fig. 20. These results were obtained in the linear region of the photocurrent with the light intensity. Under these conditions, diffusion effects can be neglected, and the excited-state generation can be taken as constant at a given potential and light intensity. The behavior in Fig. 20 suggests that the photoresponses are associated with adsorbed porphyrin species, and that the coverage effectively decreases as the Galvani potential difference increases. Neglecting back electron transfer and Ru Cdl attenuation effects at the measuring frequency, the photocurrent responses can be expressed in terms of the flux of photoinduced electron injection (g) from the quencher to the excited state, ket cb g ¼ eI0 N ð44Þ ket þ kd 1 þ cb s where e is the electronic charge, I0 is the photon flux, is the optical capture cross-section of the adsorbed porphyrin, is the Langmuir isotherm parameter, cb is the porphyrin bulk concentration, and Ns is the maximum surface density. This expression is based upon a competition between photoinduced ET and relaxation of the excited state. Fitting of Eq. (44) to the data in Fig. 20 confirmed the effective desorption of the porphyrin with increasing potential, indicating that ket must increase in order to account for the increase
Dynamic Aspects of Electron-Transfer Reactions
213
FIG. 20 Photocurrent dependence on the concentration of the porphyrin ZnTPPC4 at the water– DCE interface in the presence of Fc at various Galvani potential differences. (Reprinted with permission from Ref. 50. Copyright 1998 American Chemical Society.)
in the overall photocurrent response. Furthermore, the photoinduced ket should be also of the same order as kd , i.e. 105 ; s1 as obtained from flash photolysis experiments in TIR. In order to compare this magnitude with previous studies on heterogeneous ET, the value of pseudo-first-order ket estimated from the photocurrent analysis has to be integrated over the distance separating the reactants. Assuming a reaction distance of 1 nm, a value of 102 cm s1 can be estimated for the pseudo-first-order and 10 M1 cm s1 for the bimolecular heterogeneous rate constants. Despite the fact that this value is rather close to the Marcus limit for ET [see Eq. (17) and Ref. 45], the observed potential dependence of ket indicates that the photoinduced ET still involves activation energy. It should also be recalled that the photocurrent measurements do not provide a direct estimation of ket . Only the ratio ket =ðket þ kd Þ is available after considering porphyrin coverage and back ET responses. E.
Intensity-Modulated Photocurrent Spectroscopy (IMPS) Studies on Heterogeneous Quenching of Porphyrin
A more quantitative description of the photocurrent responses, taking into account the contributions from back electron transfer and Ru Cdl attenuation, was achieved by IMPS measurements [83]. Considering the mechanism in Fig. 11, excluding the supersensitization step, and the equivalent circuit in Fig. 18, the frequency-dependent photocurrent for a perturbation as in Eq. (42) is given by kps þ i! 1 ð45Þ j 1 ¼ g1 krec þ kps þ i! 1 þ RCint i! where the parameter g1 corresponds to the AC flux of electron injection, ket cb g1 ¼ eI1 N ket þ kd þ i! 1 þ cb s
ð46Þ
Equation (45) resembles the generalized expression of IMPS for semiconductor– electrolyte interfaces [149,164]. This similarity between the dynamic photoresponses for both types of interfaces is only valid in phenomenological terms, as the natures of the
214
Fermı´n and Lahtinen
photoinduced charge generation processes are essentially different. For instance, charge separation in the semiconductor space charge region occurs in the 1012 s time scale, which is out of the frequency range available under potentiostatic conditions. Charge separation in the context of liquid–liquid interfaces corresponds to the photoinduced electron-transfer step, which may occur in the range of 106 s. This time scale is also out of the experimental frequency range due to the large Ru Cdl time constant that characterizes these junctions, i.e., ket þ kd i!. Therefore, despite the fact that the generation term is developed at completely different rate, it can be considered effectively in phase with the light intensity perturbation below the MHz range. A complex representation of IMPS data obtained for the heterogeneous quenching of ZnTPPC4 –diferrocenylethane is displayed in Fig. 21(a). The semicircular response in the first quadrant corresponds to the competition between product separation and back electron transfer, while the lower quadrant is determined by the Ru Cdl time constant. The Ru Cdl attenuation limited the frequency range to less than 1 kHz. Equation (45) describes the experimental spectra at various Galvani potential differences [solid lines in Fig. 21(a)],
FIG. 21 Complex IMPS spectra obtained for the photo-oxidation of DFcET by ZnTPPC4 at the water–DCE interface (a). The opposite potential dependencies of the phenomenological ET rate constant and the porphyrin coverage (b) are responsible for the maximum on the flux of electron injection obtained from IMPS responses for DFcET and Fc (c). The potential dependence of the back electron-transfer rate constant is also shown in (d). (From Ref. 83. Reproduced by permission of The Royal Society of Chemistry.)
Dynamic Aspects of Electron-Transfer Reactions
215
allowing the evaluation of the AC flux of electron injection as well as the phenomenological rate constants of product separation (kps ) and back electron transfer (krec ). Very similar behavior was observed for ferrocene and diferrocenylethane concerning the competing processes at low frequencies. For instance, a potential independent kps of the order of 5 s1 was obtained from this analysis. This rather slow value is difficult to rationalize within classical photoelectrochemical models in the homogeneous phase [128]. The dependence of the flux of electron injection and the back electron-transfer rate constant on the applied potential did reveal very interesting trends as depicted in Figs. 21(b)–(d). The behavior of g1 for both quenchers confirmed the porphyrin desorption and the increase of ket with increasing Galvani potential differences. Both trends are schematically shown in Fig. 21(b). The combined effect of these two phenomena is responsible for the maximum observed in the flux of electron injection as obtained from IMPS spectra [Fig. 21(c)]. The adsorption of ZnTPPC4 showed a weak dependence on the applied potential taking into account the charge of the anion. More recent studies have shown that rather complex processes such as partial protonation and interfacial ion pairing are related to the specific adsorption of the porphyrins [165]. The behavior of ket in Fig. 21(b) can be described as a first approximation by a Tafel type of expression, ket ¼ ket0 expðFw o =RT Þ
ð47Þ
where ket0 is the phenomenological rate constant for Galvani potential difference equal to 0 V. The difference in g1 between ferrocene and diferrocenylethane only lies in the value of ket0 . By contrast, the rate constant krec features an inverse exponential dependence on the applied potential [Fig. 21(d)] but with a similar transfer coefficient, 0 krec ¼ krec expðFw o =RT Þ
ð48Þ
where the observed value was around 0.4. The similar potential dependence of the phenomenological rate constant for the two ET processes was rationalized in terms of effective changes in the Gibbs activation energy [83]. From a qualitative point of view, a decrease in the activation energy for the photoinduced ET step should bring about an increase of this parameter for the back electron transfer within the framework of the mechanism considered in Fig. 11. However, the exact physical meaning of in this approach remains unknown. In the case of ZnTPPC4 , not only interfacial ion pairing but also specific adsorption introduces strong perturbations of the interfacial potential as indicated from capacitance–potential curves [50]. Inversion of the local electric field at positive potential can be envisaged as a result of the excess charge associated with the anionic porphyrin. It is believed that these effects are responsible for the apparently serendipitous onset potential of the photocurrent and porphyrin desorption. It is clear that one of the major limitations of this analysis is the assumption of constant excited-state coverage. Deviations from the behavior described by Eq. (45) in the low frequency range have been observed at photocurrent densities higher than 106 A cm2 [50]. These deviations are expected to be connected to excited-state diffusion profiles similar to those considered by Dryfe et al. [see Eq. (38)] [127]. A more general expression for IMPS responses is undoubtedly required for a better understanding of the dynamics involved in back electron transfer as well as separation of the photoproducts.
Fermı´n and Lahtinen
216
V.
TECHNOLOGICAL RELEVANCE OF HETEROGENEOUS ET PROCESSES AT ITIES
The recent experimental developments on ‘‘dark’’ and photoinduced ET reactions give support to the previous speculations on the relevance of these interfaces in such fields as catalysis and solar energy conversion. These disciplines have been, and still are centered on processes at solid–solution interfaces. However, particular applications require molecularly defined interfaces, where reactants exhibit different solubility properties. In this section, we shall consider some of these systems and the advances reported so far. A.
Solar Energy Conversion at ITIES
As mentioned earlier, a great deal of literature has dealt with the properties of heterogeneous liquid systems such as microemulsions, micelles, vesicles, and lipid bilayers in photosynthetic processes [114,115,119]. At externally polarizable ITIES, the control on the Galvani potential difference offers an extra variable, which allows tuning reaction paths and rates. For instance, the rather high interfacial reactivity of photoexcited porphyrin species has proved to be able to promote processes such as the one shown in Fig. 3(b). The inhibition of back ET upon addition of hexacyanoferrate in the photoreaction of Fig. 17 is an example of a photosynthetic reaction at polarizable ITIES [87,166]. At Galvani potential differences close to 0 V, a direct redox reaction involving an equimolar ratio of the hexacyanoferrate couple and TCNQ features an ‘‘uphill’’ ET of approximately 0.10 eV (see Fig. 4). However, the excited state of the porphyrin heterodimer can readily inject an electron into TCNQ and subsequently receive an electron from ferrocyanide. For illumination at 543 nm (2.3 eV), the overall photoprocess corresponds to a 4% conversion efficiency. An alternative photosynthetic (supersensitization) mechanism has been recently described by Lahtinen et al. in a very similar system [51]. Upon replacing TCNQ by benzoquinone, the redox potential of the organic couple is shifted by approximately 500 mV toward more negative values. The decrease in the driving force for the photoinduced ET brings about a decrease in the photocurrent response and an increase in the back electron-transfer rate. The effect of the hexacyanoferrate redox couple under these con4 M. The increase of the ditions is observed at higher concentrations, ½FeðCNÞ4 6 > 5 10 hexacyanoferrate (II) concentration introduced an increase of the overall photocurrent and a decrease of the back ET rate constant. Analysis of IMPS data suggested that the excited state is rapidly quenched by FeðCNÞ4 6 , generating an intermediate species which subsequently reduces benzoquinone across the liquid–liquid junction. Unfortunately, complications, probably due to coupled ion-transfer processes, hindered quantitative analysis of the dynamic photoresponses. Despite the potential impact of novel photosynthetic routes based on these developments, the most ambitious application remains in the conversion of solar energy into electricity. Dvorak et al. showed that photocurrent as well as photopotential response can be developed across liquid–liquid junctions during photoinduced ET reactions [157,158]. The first analysis of the output power of a porphyrin-sensitized water–DCE interface has been recently reported [87]. Characteristic photocurrent–photovoltage curves for this junction connected in series to an external load are displayed in Fig. 22. It should be mentioned that negligible photoresponses are observed when only the platinum counterelectrodes are illuminated. Considering irradiation AM 1, solar energy conversions from 0.01 to 0.1% have been estimated, with fill factors around 0.4. The low conversion
Dynamic Aspects of Electron-Transfer Reactions
217
FIG. 22 Characteristic output power for water–DCE junctions in the presence of ZnTPPS– ZnTMPyP and TAA (a), SnTPPS and TAA (b), and SNTPPS and TCNQ (c). The supporting electrolytes were Li2 SO4 and BTPPATPFB. The supersensitizer for all cases was the couple Fe3þ =Fe2þ at pH 1 with equimolar ratio for (a) and (b), and 1/10 for (c). Light input was 103 W cm2 at 543 (a and c) and at 442 nm (b).
efficiencies are mostly related to the very poor light harvest at the liquid-liquid junction. On the other hand, the low fill factors could be associated with the strong potential dependence of the photoresponses for the porphyrin-sensitized interfaces. Despite these limitations, the preliminary conversion efficiencies estimated so far should be regarded as very promising. One of the most important goals in solar cell design is to separate the generation and transport of photogenerated carriers. In solid-state devices, this feature is rather difficult to achieve efficiently and at low cost due to the occurrence of interfacial defects at the semiconducting heterojunctions. Solar cells based on dye-sensitized colloidal semiconducting films feature rather efficient generation–collection properties; this has created a huge interest in the photoelectrochemical community [167,168]. The photogeneration of charge carriers occurs at the semiconductor–dye interface, while the transport takes place through the highly defective film until the back contact. Although very high efficiencies exceeding 7% have been reported, the complex generation–collection dynamics remains rather controversial [169]. In the case of liquid–
Fermı´n and Lahtinen
218
liquid interfaces, the electron transport is replaced by the relatively simple ionic transport in a homogeneous medium. In order to further develop liquid–liquid interfaces towards photovoltaic applications, thin electrolyte layer systems must be considered. In this respect, the interesting studies on surfaces modified by thin organic electrolyte layers [78,97] as well as by hydrophilic polypeptide multilayer films [170] are important steps forward.
B.
Electrochemical Phase Formation at ITIES
Despite the fact that the electrodeposition of copper and silver at the water–DCE and the water–dichloromethane interfaces has been generally regarded as the first experimental evidence for heterogeneous ET at externally biased ITIES [171], a very limited amount of work has dealt with this type of process. This reaction has also theoretical interest because the molecular liquid–liquid interface can be seen as an ideal substrate for electrochemical nucleation studies due to the weak interactions between the interface and the newly formed phase and the lack of preferential nucleation sites always present at metallic electrodes. As discussed in Section III.A, heterogeneous electrodeposition of metals at liquid– liquid junctions requires that the metallic complex and the reducing agent remain in the respective phases in the potential range where the electron transfer occurs. This condition is exemplified in Fig. 23 for the generation of Au particles via the reduction of TOAAuCl4 by ferrocyanide at the water–DCE interface [89]. The charge-transfer reaction observed at potentials around 0.10 V corresponds to the transfer of the gold complex from DCE to water. In the presence of ferrocyanide, two additional peaks are observed at more negative potentials, which the authors assumed to correspond to the heterogeneous reduction of gold complex. In-situ and ex-situ spectroscopy of the interfacial deposit clearly confirmed the generation of Au particles. In particular, in-situ spectrophotometric analysis showed a red shift in the plasmon resonance of maximum absorbance, indicating the growth of the metal particles at the interface. However, the choice of the experimental system was rather adverse, resulting in complex voltammetric behavior and hindering any systematic analysis on the nucleation reaction at ITIES.
FIG. 23 Cyclic voltammograms for ET between 0.2 mM TOAAuCl4 and 0.1 mM K4 FeðCNÞ6 at the water–DCE interface at 0.05 V s1 (a). The control experiments in the absence of the aqueous couple (b) and the metal complex (c) are also displayed. (From Ref. 89. Reproduced by permission of The Royal Society of Chemistry.)
Dynamic Aspects of Electron-Transfer Reactions
219
Recent studies have shown that the reduction of tetrachloropalladate in aqueous solution by ferrocene derivatives in the organic solvent leads to the generation of Pd particles at the water–DCE interface [90,91,172]. A typical voltammogram for the Pd nucleation by Fc is shown in Fig. 24. By contrast to the case AuCl 4 , the transfer of does not take place within the polarizable window. Upon cycling from negative to PdCl2 4 positive potentials, a large increase of the current is observed at potentials close to 0.2 V. A loop is observed at more positive potentials, and a transfer response occurs in the reverse cycle. The quasireversible response corresponds to the transfer of Fcþ generated during the irreversible reduction of palladate. The onset of the PdCl2 4 reduction is shifted toward more negative values in the second cycle, indicating the presence of electroactive Pd particles at the interface. Johans et al. derived a model for diffusion-controlled electrodeposition at liquid– liquid interface taking into account the development of diffusion fields in both phases [91]. The current transients exhibited rising portions followed by planar diffusion-controlled decay. These features are very similar to those commonly observed in three-dimensional nucleation of metals onto solid electrodes [173–175]. The authors reduced aqueous ammonium tetrachloropalladate by butylferrocene in DCE. The experimental transients were in good agreement with the theoretical ones. The nucleation rate was considered to depend exponentially on the applied potential and a one-electron step was found to be rate determining. The results were taken to confirm the absence of preferential nucleation sites at the liquid–liquid interface. Other nucleation work at the liquid–liquid interface has described the formation of two-dimensional metallic films with rather interesting fractal shapes [176]. Recent advances on electrochemical phase formation at ITIES include electropolymerization reactions. Cunnane and Evans reported the accumulation of oligomers of methyl- and phenylpyrrole at externally biased water–DCE interface [177]. The oligomerization reaction was initiated by heterogeneous oxidation of the monomer by Fe3þ located in the aqueous phase. The radical cation undergoes various chemical reactions in the homogeneous phase leading to the formation of oligomers in solution. More recent studies by the same group include the oligomerization of 2,2 0 :5 0 ,2 00 -terthiophene in DCE [178]. In this case, the oligomerization reaction seems to occur in a more controlled fashion at externally biased as well as open-circuit junctions.
FIG. 24 Cyclic voltammograms for the heterogeneous reduction of 0.01 M PdCl2 4 by 1 mM Fc at the water–DCE interface at 0.03 V s1 . The loop observed in the first cycle and the changes observed in the second cycle correspond to the formation of interfacial Pd nuclei.
Fermı´n and Lahtinen
220
C.
Two-Phase Catalysis and Photocatalysis
Catalysis at interfaces between two immiscible liquid media is a rather wide topic extensively studied in various fields such as organic synthesis, bioenergetics, and environmental chemistry. One of the most common catalytic processes discussed in the literature involves the transfer of a reactant from one phase to another assisted by ionic species referred to as phase-transfer catalyst (PTC). It is generally assumed that the reaction process proceeds via formation of an ion-pair complex between the reactant and the catalyst, allowing the former to transfer to the adjacent phase in order to carry out a reaction homogeneously [179]. However, detailed comparisons between interfacial processes taking place at externally biased and open-circuit junctions have produced new insights into the role of PTC [86,180]. Cunnane et al. compared the oxidation of SnðPCÞ2 by ferri/ferrocyanide at externally biased and open-circuit water–DCE junctions [86]. Under open-circuit conditions, the potential was controlled by the partition of tetra-aryl ammonium cations, which are commonly employed as phase transfer catalysts. Good correlation was obtained for the formal redox potential measured under potentiostatic conditions and from the partition ratio of TEAþ or TPAþ . These important results suggest that the role of the PTC is to fix a Galvani potential difference between the two liquid phases, allowing heterogeneous ET processes to take place. This approach was adopted by Tan et al. [180] in the study of the Williamson ether synthesis and later Forssten et al. [181] for the oxidation of cis-cyclooctene in DCE or dichloromethane by aqueous permanganate. Also in these cases the role of the PTC was seen in fixing the Galvani potential difference which then acted as the driving force for transferring the aqueous ionic reactants to the organic phase. Catalytic cycles can also be achieved via interfacial redox mediators acting as charge shuttles between redox species separated by long distance. In Section III.C, we discussed the experiments by Cheng and Schiffrin where TCNQ acted as a redox mediator for the oxidation of a Ru complex by ferricyanide at water–DCE interfaces modified by phospholipid monolayers [76]. Recently, Willner and Joselevich introduced a new concept based on ‘‘shuttle photosensitizers’’ at water-in-oil microemulsions [182]. In their approach, ethyl eosin is employed as sensitizer initially located in the water phase also in the presence of the electron acceptor ferricyanide, while tributylamine is the electron donor. The basic mechanism is illustrated in Fig. 25(a), in which the homogeneous quenching of the sensitizer by ferricyanide leads to the formation of a hydrophobic eosin radical. This radical readily transfers to the organic media where it is reduced by tributylamine. The transfer of the eosin radical to the organic phase decreases the probability of back electron transfer from ferrocyanide similarly to the principle developed by Brugger and Gra¨tzel on charged micelles [120]. Recently, Shao et al. [183] demonstrated how ITIES could be used in studying complex catalytic microemulsion reactions. The problem in investigating electrochemical kinetics in microemulsions is the undefined interfacial area. Using the well-defined liquid– liquid interface as a model system, together with the established electrochemical methods described in the previous sections of this review, offers a clear advantage for kinetic and mechanistic considerations. In their approach, Shao et al. used SECM to study the reaction between CoðIÞ form of vitamin B12 electrochemically generated in the aqueous phase with trans-1,2-dibromocyclohexane in benzonitrile. They were able to extract some information on apparent heterogeneous rate constants, and the effects of reactant concentration, Galvani potential difference and surfactant adsorption on the kinetics.
Dynamic Aspects of Electron-Transfer Reactions
221
FIG. 25 (a) Schematic representation for a photocatalytic mechanism based on ‘‘shuttle photosensitizers’’ at liquid–liquid interfaces. (Reprinted with permission from Ref. 182. Copyright 1999 American Chemical Society.) (b) This mechanism is compared to the photo-oxidation of 1-octanol by the heterodimer ZnTPPS–ZnTMPyP in the presence of the redox mediator ZnTPP. (From Ref. 185.)
A more complex catalytic mechanism has been presented by Tabushi and Noboru involving a synergetic combination of redox mediators and ‘‘phase transfer catalyst’’ at liquid–liquid interfaces [184]. For instance, the oxidation of benzyl alcohol and other organic substrates by NaOCl has been reported to be catalyzed by trioctylmethylammonium and MnTPPCl acting as PTC and redox mediator respectively at the water–CH2 Cl2 interface. This process is rather difficult to control electrochemically due to the rather high reactivity of NaOCl in the aqueous phase. Lahtinen et al. proposed a different approach in which the NaOCl is substituted by the photoactive heterodimer ZnTPPS–ZnTMPyP in the water phase and the hydrophobic ZnTPP is used instead of MnTPPCl in the DCE phase [185]. As illustrated in Fig. 25(b), the main goal is the photo-oxidation of 1-octanol in DCE by the porphyrin heterodimer, employing ZnTPP as a mediator and replacing the PTC by potentiostatic control. Preliminary results indicate that the heterodimer can effectively oxidize ZnTPP to ZnTPPþ upon illumination, although relatively fast back electron transfer is observed. The back electron transfer effectively competes with the homogeneous oxidation of 1-octanol in the DCE phase [see Fig. 25(b)]. In the presence of the aqueous couple Fe2þ =Fe3þ acting as supersensitizer, the back electron-transfer features were partially diminished. Under these conditions, a substantial increase of the photocurrent was readily observed upon increasing concentration of 1-octanol, suggesting the regeneration of ZnTPP by 1-octanol at the interface.
Fermı´n and Lahtinen
222
The catalytic properties of electrodeposited metallic particles at liquid–liquid interfaces are yet to be systematically explored. The only data available were presented by Cheng and Schiffrin at the Kyoto meeting on ‘‘Charge Transfer at Liquid–Liquid and Liquid–Membrane Interfaces’’ in 1996. The authors reported the catalytic dehalogenation of 2-bromoacetophenone to acetophenone in the presence of electrogenerated Pd particles at the water–DCE interface. In this respect, electroactive metallic particles at liquid–liquid junctions can be regarded as ‘‘surface states,’’ employing a terminology familiar from surface science. This kind of surface state might be able to enhance electron transfer by enhancing adsorption or coadsorption of redox species. Another kind of interaction, which can be envisaged, is the photoinduced charging of particles via interfacial dye species. The stored charge can subsequently induce reduction processes in the organic phase. A recent report by Lahtinen et al. provided the first demonstration of photocatalytic reduction of species in DCE catalyzed by in-situ generated Pd particles at the ZnTPPC4 sensitized water–DCE junction [172]. VI.
CONCLUDING REMARKS
A consistent picture for dynamics of heterogeneous ET has been emerging in the last 5 years with the development of new experimental approaches. Techniques such as AC impedance, modulated and time-resolved spectroscopy, SECM, and photoelectrochemical methods have extended our knowledge of charge-transfer kinetics to a wide range of time scales. This can be exemplified by comparing impedance analysis, which is limited to ket of the order of 101 M1 cm s1 , against SECM studies that have provided values close to 102 M1 cm s1 . The dependence of ket on the ET driving force given by Eqs. (13) and (14) has provided an experimental validation to the continuum model. Although molecular dynamics and lattice-gas modeling provide pictures rather different from the mathematically flat liquid–liquid junctions employed by Marcus, the main derivations of his model appear consistent with experimental results assuming an average distance of 107 cm between redox centers at the interface. This distance can be modified by adsorption of amphiphilic species at the molecular junction. Among the most important aspects that remain to be solved, is the dependence of the observed ket on the Galvani potential difference. This issue holds essential information on the potential distribution and structure of the interface. Photoinduced heterogeneous ET at ITIES is opening new perspectives in the area of photoelectrochemistry. Vectorial control of the electron injection can be achieved not only by selecting appropriate redox species and photoactive redox dyes, but also by the applied Galvani potential difference. Photocatalytic and photosynthetic mechanisms initiated by the heterogeneous quenching of dyes have already been described at these interfaces. Finally, we do believe that these developments have provided a realistic alternative to solar energy conversion and photovoltaics. In conclusion, the increasing understanding on charge-transfer processes at liquid–liquid interfaces is not only establishing firm ground to potential technological applications, but also providing new alternatives in areas traditionally associated with solid-state junctions. ACKNOWLEDGMENTS We would like to express our gratitude to Professor Hubert Girault and Dr Pierre Franc¸ois Brevet for their encouragement and fruitful discussions. Our special thanks go
Dynamic Aspects of Electron-Transfer Reactions
223
also to Zhifeng Ding, Hong Duong, Henrik Jensen, Rodrigo Iglesias, Hirohisa Nagatani, Christoffer Johans, Bernadette Quinn, Laure Tomaszewski, Nicolas Eugster, and Stephane Gorgerat for their contributions and discussions. R. L. acknowledges the financial support by the Neste Foundation, Finland. D. J. F. is also grateful for the support by the Fonds National Suisse de la Recherche Scientifique (project 20-055692.98/1). The Laboratory of Physical Chemistry and Electrochemistry and the Laboratoire d’Electrochimie are part of the European Training and Mobility Network ODRELLI (Organization, Dynamics and Reactivity at Electrified Liquid–Liquid Interfaces).
REFERENCES 1. Z. Samec. J. Electroanal. Chem. 99:197 (1979). 2. Y. I. Kharkats and A. G. Volkov. J. Electroanal. Chem. 184:435 (1985). 3. R. A. Marcus. J. Phys. Chem. 94:4152 (1990). 4. R. A. Marcus. J. Phys. Chem. 94:7742 (1990). 5. R. A. Marcus. J. Phys. Chem. 94:1050 (1990). 6. R. A. Marcus. J. Phys. Chem. 95:2010 (1991). 7. W. Schmickler. J. Electroanal. Chem. 428:123 (1997). 8. I. Benjamin. J. Phys. Chem. 95:6675 (1991). 9. I. Benjamin. J. Phys. Chem. 568:409 (1994). 10. H. H. Girault. J. Electroanal. Chem. 388:93 (1995). 11. H. H. J. Girault and D. J. Schiffrin. J. Electroanal. Chem. 170:127 (1984). 12. H. H. J. Girault, D. J. Schiffrin, and B. D. V. Smith. J. Colloid Interface Sci. 101:257 (1984). 13. H. H. J. Girault and D. J. Schiffrin. J. Electroanal. Chem. 161:415 (1984). 14. T. Kakiuchi and M. Senda. Bull Chem. Soc. Jpn. 56:2912 (1983). 15. T. Kakiuchi and M. Senda. Bull. Chem. Soc. Jpn. 56:1753 (1983). 16. Z. Samec, V. Marecek, and D. Homolka. J. Electroanal. Chem. 126:121 (1981). 17. Z. Samec, V. Marecek, and D. Homolka. Faraday Discuss. Chem. Soc. 197 (1984). 18. Z. Samec, V. Marecek, and D. Homolka. J. Electroanal. Chem. 170:383 (1984). 19. I. Benjamin. Annu. Rev. Phys. Chem. 48:407 (1997). 20. K. J. Schweighofer and I. Benjamin. J. Electroanal. Chem. 391:1 (1995). 21. P. A. Fernandes, M. N. D. S. Cordeiro, and J. A. N. F. Gomes. J. Phys. Chem. B 103:6290 (1999). 22. W. Schmickler. J. Electroanal. Chem. 426:5 (1997). 23. W. Schmickler, Interfacial Electrochemistry, Oxford University Press, New York, 1996. 24. C. M. Pereira, W. Schmickler, A. F. Silva, and M. J. Sousa. Chem. Phys. Lett. 268:13 (1997). 25. C. M. Pereira, W. Schmickler, F. Silva, and M. J. Sousa. J. Electroanal Chem. 436:9 (1997). 26. T. Huber and W. Schmickler, in Euroconference on Modern Trends in Electrochemistry of Molecular Interfaces, Kirkkonummi, 1999, p. L-26. 27. S. Frank, W. Schmickler, J. Electroanal. Chem. 483:18 (2000). 28. J. S. Phipps, R. M. Richardson, T. Cosgrove, and A. Eaglesham. Langmuir 9:3530 (1993). 29. L. T. Lee, D. Langevin, and B. Farnoux. Phys. Rev. Lett. 67:2678 (1991). 30. J. Penfold, R. M. Richardson, A. Zarbakhsh, J. R. P. Webster, D. G. Bucknall, A. R. Rennie, R. A. L. Jones, T. Cosgrove, R. K. Thomas, J. S. Higgins, P. D. I. Fletcher, E. Dickinson, S. J. Roser, I. A. Mclure, A. R. Hillman, R. W. Richards, E. J. Staples, A. N. Burgess, E. A. Simister, and J. W. White. J. Chem. Soc. Faraday Trans. 93:3899 (1997). 31. M. Sferrazza, C. Xiao, R. A. L. Jones, D. G. Bucknall, J. Webster, and J. Penfold. Phys. Rev. Lett. 78:3693 (1997). 32. J. Strutwolf, A. L. Barker, M. Gonsalves, D. J. Carvana, P. R. Unwin, D. E. Williams, and J. R. P. Webster. J. Electroanal Chem. 483:163 (2000).
224
Fermı´n and Lahtinen
33. Z. H. Zhang, I. Tsuyumoto, S. Takahashi, T. Kitamori, and T. Sawada. J. Phys. Chem. A 101:4163 (1997). 34. Z. H. H. Zhang, I. Tsuyumoto, T. Kitamori, and T. Sawada. J. Phys. Chem. B 102:10284 (1998). 35. S. Takahashi, I. Tsuyumoto, T. Kitamori, and T. Sawada. Electrochim. Acta 44:165 (1998). 36. I. Tsuyumoto, N. Noguchi, T. Kitamori, and T. Sawada. J. Phys. Chem. B 102:2684 (1998). 37. P.-F. Brevet and H. H. Girault, in Liquid/Liquid Interfaces: Theory and Methods (A. G. Volkov, ed.), CRC Press, Boca Raton, 1996. 38. P.-F. Brevet, Surface Second Harmonic Generation, Presses Polytechniques Universitaires Romandes, Lausanne, 1997. 39. J. Koryta. Electrochim. Acta 24:293 (1979). 40. J. Koryta. Electrochim. Acta 29:445 (1984). 41. S. Daniele, M. A. Baldo, and C. Bragato. Electrochem. Commun. 1:37 (1999). 42. J. Hanzlı´ k, Z. Samec, and J. Hovorka. J. Electroanal. Chem. 216:303 (1987). 43. Z. Ding, D. J. Fermı´ n, P.-F. Brevet, and H. H. Girault. J. Electroanal. Chem. 458:139 (1998). 44. M. Tsionsky, A. J. Bard, and M. V. Mirkin. J. Am. Chem. Soc. 119:10785 (1997). 45. A. L. Barker, P. R. Unwin, S. Amemiya, J. F. Zhou, and A. J. Bard. J. Phys. Chem. B 103:7260 (1999). 46. B. Liu and M. V. Mirkin. J. Am. Chem. Soc. 121:8352 (1999). 47. K. Kalyanasundaram, Photochemistry of Polypyridine and Porphyrin Complexes, Academic Press, London, 1992. 48. V. Marecek, A. H. De Armond, and M. K. De Armond. J. Am. Chem. Soc. 111:2561 (1989). 49. A. R. Brown, L. J. Yellowlees, and H. H. Girault. J. Chem. Soc. Faraday Trans. 89:207 (1993). 50. D. J. Fermı´ n, Z. Ding, H. Duong, P.-F. Brevet, and H. H. Girault. J. Phys. Chem. B 102:10334 (1998). 51. R. Lahtinen, D. J. Fermı´ n, K. Kontturi, and H. H. Girault. J. Electroanal. Chem., 483:81 (2000). 52. Z. Samec. J. Electroanal. Chem. Interfacial Electrochem. 103:1 (1979). 53. A. A. Stewart, J. A. Campbell, H. H. Girault, and M. Eddowes. Ber. Bunsen-Ges. Phys. Chem. 94:83 (1990). 54. E. Makrlik. J. Electroanal. Chem. 158:295 (1983). 55. E. Makrlik. Electrochim. Acta 29:7 (1984). 56. B. Quinn, R. Lahtinen, L. Murtomaki, and K. Kontturi. Electrochim. Acta 44:47 (1998). 57. A. J. Bard, D. E. Cliffel, C. Demaille, F. R. F. Fan, and M. Tsionsky. Ann. Chim. 87:15 (1997). 58. C. J. Slevin and P. R. Unwin. Langmuir 13:4799 (1997). 59. C. J. Slevin and P. R. Unwin. Langmuir 15:7361 (1999). 60. H. H. J. Girault and D. J. Schiffrin. J. Electroanal. Chem. 244:15 (1988). 61. M. D. Newton and N. Sutin. Annu. Rev. Phys. Chem. 35:437 (1984). 62. G. Geblewicz and D. J. Schiffrin. J. Electroanal. Chem. 244:27 (1988). 63. Y. Cheng and D. J. Schiffrin. J. Chem. Soc. Faraday Trans. 89:199 (1993). 64. I. Benjamin. Chem. Rev. 96:1449 (1996). 65. K. J. Schweighofer, U. Essmann, and M. Berkowitz. J. Phys. Chem. B 101:10775 (1997). 66. K. J. Schweighofer, U. Essmann, and M. Berkowitz. J. Phys. Chem. B 101:3793 (1997). 67. J. Hanzlik, J. Hovorka, Z. Samec, and S. Toma. Collect. Czech. Chem. Commun. 53:903 (1988). 68. Z. Samec, V. Marecek, and J. Weber. J. Electroanal. Chem. Interfacial Electrochem. 96:245 (1978). 69. Z. Samec, V. Marecek, and J. Weber. J. Electroanal. Chem. 103:11 (1979). 70. Y. Cheng and D. J. Schiffrin. J. Electroanal. Chem. 314:153 (1991). 71. V. J. Cunnane, G. Geblewicz, and D. J. Schiffrin. Electrochim. Acta 40:3005 (1995).
Dynamic Aspects of Electron-Transfer Reactions 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111.
225
A. R. Brown. Photoelectrochemical Processes at the Interface Between Two Immiscible Electrolyte Solutions. PhD Thesis, University of Edinburgh, Edinburgh, 1992. D. J. Fermı´ n, Z. Ding, H. D. Duong, P. F. Brevet, and H. H. Girault. J. Chem. Soc. Chem. Commun. 1125 (1998). Q. Z. Chen, K. Iwamoto, and M. Seno. Electrochim. Acta 36:291 (1991). E. Makrlik. Z. Phys. Chem. 268:212 (1987). Y. Cheng and D. J. Schiffrin. J. Chem. Soc. Faraday Trans. 90:2517 (1994). C. N. Shi and F. C. Anson. J. Phys. Chem. B. 102:9850 (1998). C. N. Shi and F. C. Anson. Anal. Chem. 70:3114 (1998). Z. Samec, V. Marecek, J. Weber, and D. Homolka. J. Electroanal. Chem. 126:105 (1981). S. Kihara, M. Suzuki, K. Maeda, K. Ogura, M. Matsui, and Z. Yoshida. J. Electroanal Chem. 271:107 (1989) M. Lher, R. Rousseau, E. Lhostis, L. Roue, and A. Laouenan. C. R. Acad. Sci. Paris Se´r. IIb 322:55 (1996). Z. Ding, P.-F. Brevet, and H. H. Girault. Chem. Commun. 2059 (1997). D. J. Fermı´ n, H. Duong, Z. Ding, P-F. Brevet, and H. H. Girault. Phys. Chem. Chem. Phys. 1:1461 (1999). B. Quinn and K. Kontturi. J. Electroanal. Chem. 483:124 (2000). Z. Ding. Spectroelectrochemistry and Photoelectrochemistry of Charge Transfer at Liquid/ Liquid Interfaces. PhD Thesis, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, 1999. V. J. Cunnane, D. J. Schiffrin, C. Beltran, G. Geblewicz, and T. Solomon. J. Electroanal. Chem. 247:203 (1988). D. J. Fermı´ n, H. Duong, Z. Ding, P.-F. Brevet, and H. H. Girault. Electrochem. Commun. 1:29 (1999). R. D. Webster, R. A. W. Dryfe, B. A. Coles, and R. G. Compton. Anal. Chem. 70:792 (1998). Y. F. Cheng and D. J. Schiffrin. J. Chem. Soc. Faraday Trans. 92:3865 (1996). D. J. Schiffrin and Y. Cheng, in Charge Transfer at Liquid/Liquid and Liquid/Membrane Interface, Kyoto, 1996, pp. 61–63. C. R. C. Johans, R. Lahtinen, and K. Kontturi, in Euroconference on Modern Trends in Electrochemistry of Molecular Interfaces, Kirkkonummi, 1999, p. P-21. R. A. W. Dryfe, R. D. Webster, B. A. Coles, and R. G. Compton. Chem. Commun. 779 (1997). M. Tsionsky, A. J. Bard, and M. V. Mirkin. J. Phys. Chem. 100:17881 (1996). C. Wei, A. J. Bard, and M. V. Mirkin. J. Phys. Chem. 99:16033 (1995). J. Zhang, C. J. Slevin, and P. R. Unwin. Chem. Commun. 1501 (1999). Y. B. Zu, F. R. F. Fan, and A. J. Bard. J. Phys. Chem. B 103:6272 (1999). C. N. Shi and F. C. Anson. J. Phys. Chem. B 103:6283 (1999) T. Kakiuchi. Anal. Chem. 68:3658 (1996). R. S. Nicholson. Anal. Chem. 37:1351 (1965). J. C. Imbeaux and J. M. Save´ant. J. Electroanal. Chem. 44:169 (1973). T. Wandlowski, V. Marecek, and Z. Samec. J. Electroanal. Chem. 242:291 (1988). T. Osakai, T. Kakutani, and M. Senda. Bull. Chem. Soc. Jpn. 57:370 (1984). T. Osakai, T. Kakutani, and M. Senda. Bull. Chem. Soc. Jpn. 58:2626 (1985). M. Kalaji and L. M. Peter. J. Chem. Soc. Faraday Trans. 87:853 (1991). Z. Q. Feng, T. Sagara, and K. Niki. Anal. Chem. 67:3564 (1995). Z. Q. Feng, S. Imabayashi, T. Kakiuchi, and K. Niki. J. Electroanal. Chem. 394:149 (1995). A. K. Gaigalas, V. Reipa, and V. L. Vilker. J. Colloid Int. Sci. 186:339 (1997). D. J. Fermı´ n, Z. Ding, P. F. Brevet, and H. H. Girault. J. Electroanal. Chem. 447:125 (1998). Z. F. Ding, F. Reymond, P. Baumgartner, D. J. Fermı´ n, P. F. Brevet, P. A. Carrupt, and H. H. Girault. Electrochim. Acta 44:3 (1998). J. Zhang and P. R. Unwin. J. Phys. Chem. B. 104:2341 (2000). M. H. Delville, M. Tsionsky, and A. J. Bard. Langmuir 14:2774 (1998).
226
Fermı´n and Lahtinen
112. Y. Cheng, V. J. Cunnane, D. J. Schiffrin, L. Murtomaki, and K. Kontturi. J. Chem. Soc. Faraday Trans. 87:107 (1991). 113. H. H. J. Girault and D. J. Schiffrin. J. Electroanal. Chem. 195:213 (1985). 114. K. Kalyanasundaram. Photochemistry of Microheterogeneous Systems, Academic Press, London, 1987. 115. A. G. Volkov, M. I. Gugeshashvili, and D. W. Deamer. Electrochim. Acta 40:2849 (1995). 116. A. G. Volkov. Langmuir 12:3315 (1996). 117. A. G. Volkov and D. W. Deamer, Liquid–Liquid Interfaces: Theory and Methods, CRC Press, Boca Raton, 1996. 118. A. G. Volkov, D. W. Deamer, D. I. Tanelian, and V. S. Markin, Liquid Interfaces in Chemistry and Biology, John Wiley, New York, 1998. 119. J. N. Robinson and D. J. Cole-Hamilton. Chem. Soc. Rev. 20:49 (1991). 120. P.-A. Brugger and M. Gra¨tzel. J. Am. Chem. Soc. 102:2461 (1980). 121. N. A. Kotov and M. G. Kuzmin. J. Electroanal. Chem. 285:223 (1990). 122. N. A. Kotov and M. G. Kuzmin. J. Electroanal. Chem. 341:47 (1992). 123. N. A. Kotov and M. G. Kuzmin. J. Electroanal. Chem. 338:99 (1992). 124. V. Balzani and F. Scandola. Supramolecular Photochemistry, Horwood, Chichester, 1991. 125. P. J. Clapp, B. Armitage, P. Roosa, and D. F. Obrien. J. Am. Chem. Soc. 116:9166 (1994). 126. K. L. Kott, D. A. Higgins, R. J. McMahon, and R. M. Corn. J. Am. Chem. Soc. 115:5342 (1993). 127. R. A. W. Dryfe, Z. F. Ding, R. G. Wellington, P. F. Brevet, A. M. Kuznetzov, and H. H. Girault. J. Phys. Chem. A 101:2519 (1997). 128. G. J. Kavarnos, Fundamentals of Photoinduced Electron Transfer, VCH Publishers, New York, 1993. 129. H. D. Duong, P. F. Brevet, and H. H. Girault. J. Photochem. Photobiol. A 117:27 (1998). 130. V. Marecek, A. H. De Armond, and M. K. De Armond. J. Electroanal. Chem. 261:287 (1989). 131. F. L. Thomson, L. J. Yellowlees, and H. H. Girault. J. Chem. Soc. Chem. Commun. 1547 (1988). 132. L. M. Peter. Chem. Rev. 90:753 (1990). 133. L. M. Peter, in Photocatalysis and Environment (M. Schiavello, ed.), Kluwer Academic Publishers, London, 1988. 134. R. H. Wilson, in Photo-Effects at Semiconductor–Electrolyte Interfaces (A. E. Nozik, ed.), ACS Publishers, Washington DC, 1981. 135. R. H. Wilson. J. Appl. Phys. 48:4292 (1977). 136. H. Gerischer and F. Willig, in Physical and Chemical Applications of Dyestuffs 61 (A. Davison, M. J. S. Dewar, K. Hafner, E. Heilbronner, U. Hofmann, J. M. Lehn, K. Niedenzu, K. I. Schafer, and G. Wittig, eds.), Springer-Verlag, Berlin, 1976. 137. J. H. Richardson, S. B. Deutscher, A. S. Maddux, J. E. Harrar, D. C. Johnson, W. L. Schmelzinger, and S. P. Perone. J. Electroanal. Chem. 109:95 (1980). 138. K. Bitterling, F. Willig, and F. Decker. J. Electroanal. Chem. 228:29 (1987). 139. D. E. Malcolm and N. S. Lewis. J. Am. Chem. Soc 112:3682 (1990). 140. E. A. Ponomarev, G. Nogami, and S. D. Babenko. J. Electrochem. Soc. 140:2851 (1993). 141. P. V. Kamat and M. A. Fox. J. Phys. Chem. 87:59 (1983). 142. S. A. Haque, Y. Tachibana, D. R. Klug, and J. R. Durrant. J. Phys. Chem. B 102:1745 (1998). 143. F. T. Hong and D. Mauzerall. J. Electrochem. Soc. 123:1317 (1976). 144. K. C. Hwang and D. Mauzerall. Nature 361:138 (1993). 145. A. Ilani, T. M. Liu, and D. Mauzerall. Biophys. J. 47:679 (1985). 146. M. C. Woodle and D. Mauzerall. Biophys. J. 50:431 (1986). 147. M. C. Woodle, J. W. Zhang, and D. Mauzerall. Biophys. J. 52:577 (1987). 148. R. Peat and L. M. Peter. J. Electroanal. Chem. 228:351 (1987). 149. E. A. Ponomarev and L. M. Peter. J. Electroanal. Chem. 396:219 (1995). 150. A. R. de Wit, D. Vanmaekelbergh, and J. J. Kelly. J. Electrochem. Soc. 139:2508 (1992). 151. B. H. Erne, D. Vanmaekelbergh, and I. E. Vermeir. Electrochim. Acta 38:2559 (1993).
Dynamic Aspects of Electron-Transfer Reactions 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185.
227
D. Vanmaekelbergh, A. R. Dewit, and F. Cardon. J. Appl. Phys. 73:5049 (1993). G. H. Schoenmakers, D. Vanmaekelbergh, and J. J. Kelly. J. Chem. Soc. Faraday Trans. 93: 1127 (1997). G. Schlichtho¨rl, N. G. Park, and A. J. Frank. J. Phys. Chem. 103:782 (1999). D. J. Fermı´ n, E. A. Ponomarev, and L. M. Peter, in Photoelectrochemistry, Paris, 1997, p. 62. D. J. Fermı´ n, E. A. Ponomarev, and L. M. Peter. J. Electroanal. Chem. 473:192 (1999) O. Dvorak, A. H. De Armond, and M. K. De Armond. Langmuir 8:508 (1992). O. Dvorak, A. H. De Armond, and M. K. De Armond. Langmuir 8:955 (1992). D. Vanmaekelbergh, A. R. de Witt, and F. Cardon. J. Appl. Phys. 73:5049 (1992). D. Vanmaekelbergh and F. Cardon. Electrochim. Acta 37:837 (1992). J. Schefold. J. Electroanal. Chem. 394:35 (1995). J. Schefold. J. Electroanal. Chem. 341:111 (1992). E. A. Ponomarev and L. M. Peter. J. Electroanal. Chem. 397:45 (1995). L. M. Peter, E. A. Ponomarev, and D. J. Fermı´ n. J. Electroanal. Chem. 427:79 (1997). H. Jensen, J. Kakkassery, H. Nagatani, D. J. Fermı´ n, and H. H. Girault, J. Am. Chem. Soc. submitted. D. J. Fermı´ n, H. Duong, Z. Ding, P.-F. Brevet, and H. H. Girault. J. Am. Chem. Soc. 121:10203 (1999). B. O’Reagan and M. Gra¨tzel. Nature 353:737 (1991). M. Gra¨tzel. Platinum Metal Rev. 38:151 (1994). L. M. Peter and D. Vanmaekelbergh, in Advances in Electrochemical Science and Engineering (R. C. Alkire and D. M. Kolb, eds.), Wiley-VCH, Weinheim, 1999. Y. Cheng and R. M. Corn. J. Phys. Chem. B 103:8726 (1999). M. Guainazzi, G. Silvestri, and G. Serravalle. Chem. Commun. 200 (1975). R. Lahtinen, D. J. Fermı´ n, H. Jensen, K. Kontturi, and H. H. Girault. Electrochem. Commun. 2:230 (2000). G. Gunawardena, G. J. Hills, I. Montenegro, and B. Scharifker. J. Electroanal. Chem. 138:225 (1982). J. Mostany and B. R. Scharifker. J. Electroanal. Chem. 177:13 (1984). M. Sluyters-Rehbach, J. H. O. J. Wijenberg, E. Bosco, and J. H. Sluyters. J. Electroanal Chem. 236:1 (1987). S. Nakabayashi, A. Ryoichi, A. Karantonis, U. Iguchi, K. Ushida, and M. Nawa. J. Electroanal. Chem. 473:54 (1999). V. J. Cunnane and U. Evans. Chem. Commun. 2163 (1998). V. J. Cunnane and U. Evans, in Euroconference on Modern Trends in Electrochemistry of Molecular Interfaces, Kirkkonummi, 1999, p. L-13. E. V. Dehmlow and S. S. Dehmlow, Phase Transfer Catalysis, Wiley-VCH, Weinheim, 1993. S. N. Tan, R. A. Dryfe, and H. H. Girault. Helv. Chim. Acta 77:231 (1994). C. Forssten, D. E. Williams, and J. Strutwolf, in Euroconference on Modern Trends in Electrochemistry of Molecular Interfaces, Kirkkonummi, 1999, p. P-13. I. Willner and E. Joselevich. J. Phys. Chem. B 103:9262 (1999). Y. Shao, M. Mirkin, and J. F. Rusling. J. Phys. Chem. B 101:3202 (1997). I. Tabushi and K Noboru. Tetrahed. Lett. 3681 (1979). R. Lahtinen, D. J. Fermı´ n, K. Kontturi, and H. H. Girault, in Euroconference on Modern Trends in Electrochemistry of Molecular Interfaces, Kirkkonummi, 1999, p. P-23.
9 Dynamic Behaviors of Molecules at Liquid^Liquid Interfaces Using the TimeResolved Quasi^Elastic Laser Scattering Method ISAO TSUYUMOTO Department of Environmental Systems Engineering, Kanazawa Institute of Technology, Ishikawa, Japan TSUGUO SAWADA Department of Advanced Materials Science, University of Tokyo, Tokyo, Japan
I.
INTRODUCTION
Experimental probes of liquid–liquid interfaces have been done mainly by spectroscopic and electrochemical techniques, which are suited to monitoring the interface between two bulk phases because their measurements result in no mechanical perturbation [1,2]. The quasi-elastic laser scattering (QELS) method has advantages as a tool for in situ, noncontact time-resolved measurements of dynamic behavior of molecules at liquid–liquid interfaces and liquid–air interfaces [3–9]. The method monitors the frequencies of capillary waves, which are spontaneously generated by a thermal fluctuation at liquid–liquid interfaces. Since the capillary wave frequency is a function of interfacial tension, and the change in the interfacial tension reflects the change in the number density of surfactant molecules at the interface, the QELS method allows observation of dynamic changes of liquid–liquid interfaces such as the change in number density of surfactant molecules and the formation of a lipid monolayer. Owing to its improved time resolution, each power spectrum can be obtained in 1 ms to 1 s, so the method can be used to monitor dynamic changes at liquid–liquid interfaces in a real environment. Furthermore, this method has good interface selectivity for overcoming the problem of interference by bulk phases, because the capillary wave is a characteristic phenomenon at the interfaces and its frequency can be detected by an optical heterodyne technique. In the past five years, it has been demonstrated that the QELS method is a versatile technique which can provide much information on interfacial molecular dynamics [3–9]. In this review, we intend to show interfacial behavior of molecules elucidated by the QELS method. In Section II, we present the principle and the experimental apparatus of the QELS along with the historical background. The dynamic collective behavior of molecules at liquid–liquid interfaces was first obtained by improving the time resolution of the QELS method. In Section III, we show the molecular collective behavior of surfactant molecules derived from the analysis of the time courses of capillary wave frequencies. Since the 229
230
Tsuyumoto and Sawada
method is useful for monitoring the interfacial behavior of surfactants, it is applicable to practical systems which utilize the specificity of liquid–liquid interfaces, such as phase transfer catalysis and chemical oscillation systems. In Section IV we present an application of the QELS method to a phase-transfer catalyst system and describe new results on the reaction place of the catalyst. This is the first application of the QELS method to a practical liquid–liquid interface system.
II.
QUASI–ELASTIC LASER SCATTERING METHOD
A.
Capillary Waves
Capillary waves occur spontaneously at liquid surfaces or liquid–liquid interfaces due to thermal fluctuations of the bulk phases. These waves have been known as surface tension waves, ripples, or ripplons for the last century, and Lamb described their properties in his book Hydrodynamics in 1932 [10]. Before that, William Thomson (Lord Kelvin) mentioned these waves in some of his many writings. Here we briefly present the relevant theory of capillary waves. The thermally excited displacement ðr; tÞ of the free surface of a liquid from the equilibrium position normal to the surface can be Fourier-decomposed into a complete set of surface modes as X ðr; tÞ ¼ 0 exp½ik r þ t ð1Þ k
The complex wave frequency ð¼ i!0 Þ is related to k via a dispersion relation. For an inviscid liquid, Lamb’s equation is well-known as a classical approximation for the dispersion relation [10] 12 3 1 k2 f ¼ 2 U þ L
ð2Þ
where f is the capillary wave frequency; , the interfacial tension; U , the density of the upper phase; L , the density of the lower phase; and k, the wavenumber of the capillary wave. This equation is valid for both liquid surfaces and liquid–liquid interfaces. For capillary wave at a liquid surface, U is regarded as zero in Eq. (2). In this equation, only the normal component of the interfacial tension is considered to act as a restoring force on the thermally excited displacement ðr; tÞ. Although this equation neglects the effect of surface viscosity, it gives a good fit in the relation between frequency and wavenumber of capillary waves at a liquid surface such as ethanol, anisole, or water [10,11]. For the surface of a low-viscosity liquid, Levich [12] has derived the following dispersion relation: DðSÞ ¼ ðS þ 1Þ2 þ y ð2S þ 1Þ1=2 ¼ 0
ð3Þ
where S ¼ =2k2 , y ¼ =42 k. Here is the kinematic viscosity ð=, where is the viscosity of the liquid). In this equation, both the normal components of the surface tension and the stress by the viscosity are considered to act as a restoring force on the displacement ðr; tÞ. Based on this equation, a heterodyne power spectrum in the frequency domain becomes a Lorentzian profile centered at !0 ¼ 2f ¼ jImðÞj
ð4Þ
Dynamic Behaviors of Molecules
231
having the full width at half-maximum (FWHM) f ¼ jReðÞj Equation (3) is simplified to 1 1 2 32 k f ¼ 2
ð5Þ
ð6Þ
and f ¼ 2k2 =
ð7Þ
Equation (6) is the same as Lamb’s classical approximation, Eq. (2).
B.
Historical Overview
Capillary waves at liquid surfaces were observed some years before the invention of lasers. Goodrich [13] reported on using a cathetometer to observe the damping of water waves by monomolecular films. Strictly speaking, this wave was a forced one and not a spontaneously generated capillary wave. The observation of spontaneously generated capillary waves was first reported by Katyl and Ingard [14,15]. They measured spectra from a methanol surface and an isopropanol surface using a He–Ne laser. Lucassen [16,17] theoretically derived the transverse mode of capillary waves and experimentally verified its existence. Bouchiat and Meunier [18] measured the liquid–gas interface of carbon dioxide near the critical point and reported agreement with theoretical predictions on the surface tension and viscosity. Mann et al. [19] investigated the dispersion relation at air–water interfaces using the QELS method and reported conformity with Lamb’s equation. They also mentioned the possibility of application to interfacial tension measurements. Ha¨rd et al. [20] measured surface tensions using the QELS method and reported that the experimental values agreed with the theoretical ones within deviations of 2–10%. Sano et al. [11] measured the surface tensions of water and anisole and reported they were within deviations 5% of the theoretical values. They also reported that the first-order approximation, i.e., Lamb’s equation, was sufficient to calculate the surface tensions from capillary wave frequencies. Earnshaw and coworkers [21–23] have investigated liquid surfaces of surfactant solutions and reported on such fundamental properties as surface viscosity. As reviewed above, there have been many QELS studies on liquid surfaces. However, until a few years ago, reports were scarce on molecular dynamics at liquid– liquid interfaces which used time courses of capillary wave frequency. Molecular collective behavior at liquid–liquid interfaces from a QELS study was first reported by Zhang et al. in 1997 [5].
C.
Principle
The incident beam normal to the interface is quasi-elastically scattered by the capillary wave with a Doppler shift at an angle determined by the following equation (Fig. 1): K tan ¼ k
ð8Þ
where K and k are the wavenumbers of the incident beam and the capillary wave, respectively. Thus, the wavenumber k of the capillary wave is obtained by giving . A transmis-
232
Tsuyumoto and Sawada
FIG. 1 Principle of the quasielastic laser scattering method.
sion diffraction grating is arranged in front of the cell to adjust the angle [20]. The angle is determined by the following equation using the spacing d and the order n of the diffraction grating, d sin ¼ n
ð9Þ
where is the wavelength of the laser beam. From Eqs. (8) and (9), we obtain the wavenumber k and the wavelength of the observed capillary wave: k ¼ 2n=d
ð10Þ
¼ d=n
ð11Þ
The capillary wave frequency is detected by an optical heterodyne technique. The laser beam, quasi-elastically scattered by the capillary wave at the liquid–liquid interface, is accompanied by a Doppler shift. The scattered beam is optically mixed with the diffracted beam from the diffraction grating to generate an optical beat in the mixed light. The beat frequency obtained here is the same as the Doppler shift, i.e., the capillary wave frequency. By selecting the order of the mixed diffracted beam, we can change the wavelength of the observed capillary wave according to Eq. (11).
D.
Experimental Apparatus
A schematic diagram of the experimental setup is shown in Fig. 2. The beam from a diode-pumped YAG laser is incident on the transmitting diffraction grating and passes through the bottom of the sample cell. The cell is made of quartz glass and has an optically flat bottom, which is indispensable to maintaining good reproducibility of the experimental results. After passing through the sample, the diffracted beams are mixed with scattered light from the capillary wave, and one of them is selected by an aperture positioned in front of a photodiode. The optical beat of the mixed light is measured by the photodiode. The signals are Fourier transformed and saved by a digital spectrum analyzer.
Dynamic Behaviors of Molecules
233
FIG. 2 Schematic diagram of the experimental setup. T, glass tube; W, water phase; NB, nitrobenzene; PD, photodiode; AMP, preamplifier; FFT, FFT analyzer.
III.
DYNAMIC MOLECULAR BEHAVIOR OF SURFACTANT MOLECULES AT LIQUID–LIQUID INTERFACE
The molecular collective behavior of surfactant molecules has been analyzed using the time courses of capillary wave frequency after injection of surfactant aqueous solution onto the liquid–liquid interface [5,8]. Typical power spectra for capillary waves excited at the water–nitrobenzene interface are shown in Fig. 3: (a) without CTAB (cetyltrimethylammonium bromide) molecules, and (b) 10 s after the injection of CTAB solution to the water phase [5]. The peak appearing around 10–13 kHz represents the beat frequency, i.e., the capillary wave frequency. The peak of the capillary wave frequency shifts from 12.5 to 10.0 kHz on the injection of CTAB solution. This is due to the decrease in interfacial tension caused by the increased number density of surfactant molecules at the interface. Time courses of capillary wave frequency after the injection of different CTAB concentrations into the aqueous phase are reproduced in Fig. 4. An anomalous temporary decrease in capillary wave frequency is observed when the CTAB solution beyond the CMC (critical micelle concentration) was injected. The capillary wave frequency decreases rapidly on injection, and after attaining its minimum value, it increases
FIG. 3 Power spectra for capillary waves excited at the water–nitrobenzene interface (a) without CTAB molecules and (b) 10 s after injection of a CTAB solution (0.5 mL, 10 mM) into the water phase.
234
Tsuyumoto and Sawada
FIG. 4 Capillary wave frequency vs. time after injection of the CTAB aqueous solutions (0.5 mL, 2–30 mM). The concentrations of the injected solution (C) are shown, along with the average concentrations (Ceq ) in the aqueous phase.
gradually. The initial sudden change means an abrupt increase in the molecular number density at the interface. The relationship between the interfacial coverage and the concentration of CTAB was estimated using the minimum value of the capillary wave frequency, as shown in Fig. 5. The experimental data are in good agreement with the calculated Langmuir adsorption isotherm. The experimental adsorption energy of CTAB onto the interface is calculated as 29:4 kJ/mol from the isotherm. The theoretical adsorption energy of the CTAB micelles is estimated as 25:0 kJ/mol from the difference between the theoretical adsorption energy of CTAB molecules (51:4 kJ/mol) and the micelle formation energy (26:4 kJ/mol). The experimental adsorption energy ð29:4 kJ/mol) calculated from the Langmuir isotherm is in agreement with the theoretical adsorption energy of CTAB micelles (25:0 kJ/mol), and not with that of CTAB molecules (51:4 kJ/mol). This indicates that the CTAB micelles are in equilibrium with the adsorbed CTAB molecules, and consequently, the CTAB micelles collapse to molecules immediately before the adsorption onto the interface.
FIG. 5 Interface coverage with CTAB molecules vs. CTAB average concentration in the water phase. Experimental data are shown as squares, and the calculated Langmuir adsorption isotherm is the solid line.
Dynamic Behaviors of Molecules
235
FIG. 6 Time courses of the capillary wave frequencies after injection of (a) SDS and (b) Triton X100 aqueous solutions into the interface.
Similar experiments and discussions have also been made for different surfactant molecules, such as SDS (sodium dodecyl sulfate) and Triton X-100 [8]. SDS, Triton X-100, and CTAB are anionic, nonionic, and cationic surfactants, respectively. The relationship between the relative number density of SDS molecules and the bulk aqueous concentration is shown in Fig. 6(a). When the concentration is below the CMC (9.8 mM at 25 C), the number density increases with an increase in concentration. The experimental data are in agreement with the Langmuir adsorption isotherm, suggesting that the SDS molecules are adsorbed onto the interface as a monolayer. The adsorption energy of the SDS molecules at the interface is estimated as ca. 21:9 kJ/mol from the experimental data. The theoretical free energy change when the molecules move from the water phase to the interface is estimated as higher than 37:6 kJ/mol. This discrepancy suggests that about 60% of the methylene groups in the SDS molecules are transported to the nitrobenzene phase and may be a reflection of molecular orientation, because SDS does not form a well-ordered monolayer at the water–nitrobenzene interface. When the concentration is above the CMC, the number density of SDS molecules at the interface decreases with an increase in the concentration. This may be due to a local change in the aggregation state at the interface from the monolayer to molecular aggregates. The molecular aggregates observed here are assumed to be micelles or reversed micelles, but further investigation is necessary to verify this. Using resonant TIR-SFG, Richmond’s group observed a reduction in ordering of the chain of the SDS at the D2 O/CCl4 interface at higher concentrations [24,25]. They also reported that the alkyl chains of the cationic surfactants DTAC and DAC possess the fewest gauche defects, whereas the anionic surfactants SDS and DDS display more disorder in the hydrocarbon chains at similar surface concentrations [25]. Similar results have been reported by others for SDS adsorption onto hydrophobic substrates from water [26,27].
236
Tsuyumoto and Sawada
The relationship between the relative number density of Triton X-100 molecules and the bulk aqueous concentration is shown in Fig. 6(b). When the concentration is below the CMC (0.2 mM at 25 C), the experimental data in Fig. 6(b) are in good agreement with the calculated Langmuir adsorption isotherm. This indicates that the adsorbed Triton X-100 molecules are confined to a monolayer. When the concentration is above the CMC, a slight decrease in the number density appears. It is reasonable to consider that the slight decrease is due to a change in aggregation state at the interface, such as by formation of micelles, whereas the latter slow increase is due to the increase of molecular aggregates at the interface. This result suggests that the phase transition from a monolayer to molecular aggregates occurs at a certain concentration, unlike the case with SDS. The molecular behavior at the interface may be affected by the ionic nature, ion pair formation, solvent polarity, or the chain conformation of surfactants.
IV.
MOLECULAR BEHAVIOR OF PHASE-TRANSFER CATALYST AT LIQUID–LIQUID INTERFACE IN ITS CYCLIC REACTION
The interfacial behavior of a phase-transfer catalyst, tetrabutylammonium bromide (TBAB), has been investigated using the QELS method [9]. The scheme of the phasetransfer catalytic reaction in a water–nitrobenzene system is shown in Fig. 7 [28]. At the beginning of the reaction, TBAB reacts with C6 H5 ONa to form TBAþ C6 H5 O . This ion pair is transported into the organic phase where it reacts with DPPC to produce triphenyl phosphate [ðC6 H5 OÞ3 PO]. During this reaction, TBAþ Cl is also formed and transported into the water phase to react again with C6 H5 ONa. TBAB activates the production of triphenyl phosphate by circulating between the two phases. Capillary wave frequency dependence on concentrations of TBAB and C6 H5 ONa is shown in Fig. 8. The adsorption behavior of the ion pair, TBAþ C6 H5 O , in one transfer process in which the formed ion pair is transferred from the water phase to the nitrobenzene phase is described by the data. When C6 H5 ONa alone is in the water phase, the frequency is independent of the C6 H5 ONa concentration. On the other hand, when both TBAB and C6 H5 ONa are present, the frequency decreases gradually and only slightly with increasing C6 H5 ONa concentration and then becomes constant at a certain C6 H5 ONa concentration. Thus, the decrease of frequency corresponds to the formation of ion pairs such as TBAþ C6 H5 O , and these ion pairs are adsorbed at the interface. The constant frequency above a certain concentration indicates that the
FIG. 7 Reaction scheme between C6 H5 ONa and DPPC in the water–nitrobenzene system. The part surrounded by the dashed line is the investigated process.
Dynamic Behaviors of Molecules
237
FIG. 8 Capillary wave frequency dependence on the concentrations of TBAB and C6 H5 ONa.
number of interfacial adsorptions of ion pairs that occurs has become constant. This suggests that the reaction between C6 H5 ONa and TBAB is in equilibrium, and the number of ion pairs that occurs has become constant. This stable formation brings about the saturated interface. The equilibrium concentration of C6 H5 ONa above which the adsorption was saturated depends on the TBAB concentration. The relationship between the TBAB concentration and the C6 H5 ONa concentration is shown in Fig. 9. These equilibrium concentrations were used to analyze the reaction between the two reactants, assuming that at these concentrations the reaction proceeds without residue and deficiency. The ratio of the TBAB concentration to the C6 H5 ONa concentration deviates from the line for 1:1 below 50 mM. When the TBAB concentration is above 50 mM, the ratio of the TBAB concentration to the C6 H5 ONa concentration at the water–nitrobenzene interface is unity. On the other hand, when the TBAB concentration is below 50 mM, the ratio of the C6 H5 ONa concentration to the TBAB concentration is more than unity. In general, the formation of an ion pair TBAþ C6 H5 O occurs by the reaction between one TBAB molecule and one C6 H5 ONa molecule in the water phase. Thus, the ratio of the C6 H5 ONa concentration to the TBAB concentration should be unity if the reaction has occurred in the water phase. The behavior above 50 mM can be simply explained by the reaction in the water phase between one TBAB molecule and one C6 H5 ONa molecule. However, the behavior below 50 mM cannot be explained by this
FIG. 9 Relationship between the TBAB and C6 H5 ONa concentrations in equilibrium.
238
Tsuyumoto and Sawada
simple water phase reaction. It is generally said that the concentration or activity at the interface differs from that in the water phase. From these results, the following model is suggested. Below 50 mM, the ratio of the two concentrations at the interface is unity, and the reaction between the TBAB molecules and the C6 H5 ONa molecules occurs at the interface. Below 50 mM the formation reaction for ion pairs occurs at the interface, while above 50 mM the reaction occurs in the water phase.
V.
FINAL REMARKS
In this chapter, the quasi-elastic laser scattering (QELS) method was introduced and recent reports on molecular dynamics at liquid–liquid interfaces using this method are reviewed. The QELS method has been applied to monitor the dynamics of surfactant molecules at the liquid–liquid interfaces. Time-resolved measurements of interfacial molecular number density can provide new information on molecular collective behavior of surfactants at the liquid–liquid interface. The transfer of CTAB micelles across the interface was found to occur according to the following scheme: the collapse of micelles at the interface region; the oriented adsorption onto the interface with formation of a monolayer; and the desorption from the interface. Findings suggested that below the critical micelle concentration (CMC), sodium dodecyl sulfate (SDS) molecules were adsorbed onto the interface, forming a monolayer; above the CMC the monolayer was disrupted and some molecular aggregates such as micelles or reversed micelles were formed. In the case of Triton X-100 molecules below the CMC the molecules were adsorbed onto the interface, forming a monolayer; above the CMC, the monolayer was disrupted and some molecular aggregates such as micelles were formed, and with further increases in concentration, the number of micelles increased. The QELS method was also applied to monitor the interfacial molecular behavior of phase-transfer catalyst. Findings suggested that the reaction place between tetrabutylammonium bromide (TBAB) and C6 H5 ONa changed with TBAB concentration; the reaction place was in the water phase above 50 mM, whereas it was at the interface below 50 mM. The results above reflect interfacial specificity for mass transfer and chemical reaction. In future studies the advantages of the QELS method can be used to provide details on interfacial specificity for chemical processes by nonperturbative measurements.
REFERENCES 1. 2.
R. M. Corn and D. A. Higgins. Chem. Rev 94:107 (1994). J. C. Wright, M. J. LaBuda, D. E. Thompson, R. Lascola, and M. W. Russell. Anal. Chem.68:600A (1996). 3. S. Takahashi, A. Harata, T. Kitamori, and T. Sawada. Anal. Sci. 7:645 (1991). 4. S. Takahashi, A. Harata, T. Kitamori, and T. Sawada. Anal. Sci. 10:305 (1994). 5. Z. Zhang, I. Tsuyumoto, S. Takahashi, T. Kitamori, and T. Sawada. J. Phys. Chem. A 101:4163 (1997). 6. I. Tsuyumoto, N. Noguchi, T. Kitamori, and T. Sawada. J. Phys. Chem. B 102:2684 (1998). 7. S. Takahashi, I. Tsuyumoto, T. Kitamori, and T. Sawada. Electrochim. Acta 44:165 (1998). 8. Z. Zhang, I. Tsuyumoto, S. Takahashi, T. Kitamori, and T. Sawada. J. Phys. Chem. B 102::10284 (1998). 9. Y. Uchiyama, I. Tsuyumoto, T. Kitamori, and T. Sawada. J. Phys. Chem. B 103:4663 (1999). 10. H. Lamb,, Hydrodynamics, 6th edn, Dover, New York, 1945.
Dynamic Behaviors of Molecules
239
11. M. Sano, M. Kawaguchi, Y. L. Chen, R. J. Skarlupka, T. Chang, G. Zografi, and H. Yu. Rev. Sci. Instrum. 57:1158 (1986). 12. V. G. Levich, Physiochemical Hydrodynamics, Prentice-Hall, New York, 1962, Ch. 11. 13. F. C. Goodrich. J. Phys. Chem. 66:1858 (1962). 14. R. H. Katyl and U. Ingard. Phys. Rev. Lett. 19:64 (1967). 15. R. H. Katyl and U. Ingard. Phys. Rev. Lett. 20:248 (1968). 16. J. Lucassen. J. Chem. Soc. Farad. Trans. 64:2221 (1968). 17. J. Lucassen. J. Chem. Soc. Farad. Trans. 64:2230 (1968). 18. M. A. Bouchiat and J. Meunier. Phys. Rev. Lett. 23:752 (1969). 19. J. A. Mann, J. F. Baret, F. J. Dechow, and R. S. Hansen. J. Colloid Inter. Sci. 37:14 (1971). 20. S. Ha¨rd, Y. Hamnerius, and O. Nilsson. J. Appl. Phys. 47:2433 (1976). 21. J. C. Earnshaw, R. C. McGivern, A. C. McLaughlin, and P. J. Winch. Langmuir 6:649 (1990). 22. J. C. Earnshaw, and P. J. Winch. J. Phys. Condens. Matter 2:8499 (1990). 23. J. C. Earnshaw and E. McCoo. Langmuir 11:1087 (1995). 24. M. C. Messmer, J. C. Conboy, and G. L. Richmond. J. Am. Chem. Soc. 117:8039 (1995). 25. J. C. Conboy, M. C. Messmer, and G. L. Richmond. J. Phys. Chem. B 101:6724 (1997). 26. R. N. Ward, D. C. Duffy, and P. B. Davies. J. Phys. Chem. 98:8536 (1994). 27. C. D. Bain, P. B. Davies, and R. N. Ward. Langmuir 10:2060 (1994). 28. S. Asai, H. Nakamura, M. Tanabe, and K. Sakamoto. Ind. Eng. Chem. Res. 33:1687 (1994).
10 Microstructure E¡ects on Transport in Reverse Microemulsions JOHN TEXTER
I.
Strider Research Corporation, Rochester, New York
INTRODUCTION
Isotropic single-phase microemulsions of oil and water can adopt a variety of microstructures, including water-in-oil droplets (reverse microemulsions), swollen oil-in-water micelles, and irregular bicontinuous microstructures of low to zero mean curvature with interpenetrating oil and water domains separated by a monolayer of surfactant. Various field variables can drive transitions from one of these microstructures to another. The transport of charge, ions, and molecular species as monitored by electrical conductivity or faradaic electron transfer and by NMR self-diffusion measurements, respectively, can be used to experimentally define an order parameter for quantitatively tracking the onset of microstructure formation and the amount of a particular microstructure present at equilibrium under a given set of field variables. Transitions from isolated reverse micelles in reverse microemulsions through the formation of percolating clusters to the formation of irregular bicontinuous microstructure are reviewed. Electrochemistry [1], synthesis [2], and catalysis [3,4] in reverse microemulsions [5] are significantly affected by microstructure and the effects of microstructure on ionic and molecular transport. Such transport can occur by several distinct mechanisms. The first involves diffusion of ions and molecules through the oil (pseudocontinuous) phase of the reverse microemulsion. This kind of transport is encountered in simple solutions, except that additional factors affecting viscosity and tortuosity come into play. A second mechanism involves the diffusion of reverse micelles with the concomitant transport of solutes contained therein. Such diffusive transport is generally more than an order of magnitude slower than the first mechanism. A third mechanism of transport involves ion and molecular transport through reverse micelles (droplets) and exchange between such droplets [6,7]. This third mechanism has most often been probed by percolation in electrical conductivity [8], in faradaic electron transfer [9], in dielectric susceptibility [10], and in selfdiffusion measured by NMR pulsed gradient spin-echo (PGSE) techniques [11,12].
A.
Percolation
Percolation in microemulsions and concomitant microstructural changes are the focal points of this review. A complete understanding of percolation phenomena in reverse microemulsions will require an understanding of droplet interactions and the associated thermodynamics of droplet fusion, fission, aggregation to form clusters of varying fractal 241
242
Texter
dimension, and the transformation of droplets and clusters of droplets to irregular bicontinuous [13] microstructures of low to zero mean curvature. This last transformation has generated some controversy in the literature. The observation of percolation has at times been equated with bicontinuous microstructure formation [14]. Alternatively, percolation is equated with droplet aggregation and clustering [15,16]. A prime objective of this review is to illustrate how to experimentally distinguish between these alternative microstructures, each of which appears attendant to percolation-related transitions. B.
Disperse Phase Volume Fraction
Electrical conductivity is an easily measured transport property, and percolation in electrical conductivity appears a sensitive probe for characterizing microstructural transformations. A variety of field (intensive) variables have been found to drive percolation in reverse microemulsions. Disperse phase volume fraction has been often reported as a driver of percolation in electrical conductivity in such microemulsions [17–20]. Lagu¨es et al. [17] found that the percolation theory for hard spheres could be used to describe dramatic increases in electrical conductivity in reverse microemulsions as the volume fraction of water was increased. They also showed how certain scaling theoretical tools were applicable to the analysis of such percolation phenomena. Cazabat et al. [18] also examined percolation in reverse microemulsions with increasing disperse phase volume fraction. They reasoned the percolation came about as a result of formation of clusters of reverse microemulsion droplets. They envisioned increased transport as arising from a transformation of linear droplet clusters to tubular microstructures, to form wormlike reverse microemulsion tubules. C.
Temperature
Temperature is also an often-studied field variable in driving percolation and associated microstructural transitions [21–25]. Jada et al. [21] found that the percolation induced by temperature increases in a water, decane, AOT reverse microemulsion could be nicely correlated with the bimolecular rate constant for solute exchange between colliding droplets. Kim and Huang [22] found that temperature-driven percolation in reverse microemulsions occurred when the effective droplet volume as defined by a hopping range exceeded the hard-sphere close-packing limit of 0.65. Peyrelasse and Boned [23] showed that temperature-driven percolation yielded similar critical exponents to those obtained in scaling analyses of disperse phase volume-fraction-driven percolation. An extensive study by Alexandridis et al. [24] suggests that temperature-driven percolation involves enthalpically disfavored clustering of droplets. The net driving force emanates from positive entropic changes that increase with temperature and that are attributed to free volume dissimilarity between the surfactant tails and the respective organic solvents. D.
Chemical Potential
The last, and less extensively studied field variable driving percolation effects is chemical potential. Salinity was examined in the seminal NMR self-diffusion paper of Clarkson et al. [12] as a component in brine, toluene, and SDS (sodium dodecylsulfate) microemulsions. Decreasing levels of salinity were found to be sufficient to drive the microemulsion microstructure from water-in-oil to irregular bicontinuous to oil-in-water. This paper was
Microstructure Effects on Transport
243
one of the first to demonstrate the power of PGSE NMR determinations of self-diffusion coefficients in resolving microstructure in surfactant systems. The influence of alcohols as cosurfactants also falls in this chemical potential category. Lang et al. [26] found that a variety of alkanols and benzyl alcohol tended to suppress percolation in reverse microemulsions otherwise induced by disperse phase volume fraction increases. They studied water, chlorobenzene, TBDAC (tetradecylbenzyldimethylammonium chloride) reverse microemulsions and found that longer-chained alcohols retarded the onset of percolation to a greater extent. Somewhat similar retarding effects of alcohols have more recently been reported by Naza´rio et al. [27]. At fixed disperse phase volume fraction, increasing straight-chain alcohol (cosurfactant) concentration suppressed percolation until higher temperatures were reached, relative to the temperature at which percolation was driven in the absence of cosurfactant. It was surmised that the physical effect of added alcohol was to decrease interfacial fluidity and hypothesized that the alcohols intercalate between AOT tail groups, thereby increasing the alkyl chain packing density. This decrease in fluidity then necessitates a higher temperature for overcoming the enthalpic barrier to cluster formation and ensuing percolation. Electrochemical redox studies of electroactive species solubilized in the water core of reverse microemulsions of water, toluene, cosurfactant, and AOT [28,29] have illustrated a percolation phenomenon in faradaic electron transfer. This phenomenon was observed when the cosurfactant used was acrylamide or other primary amide [28,30]. The oxidation or reduction chemistry appeared to switch on when cosurfactant chemical potential was raised above a certain threshold value. This switching phenomenon was later confirmed to coincide with percolation in electrical conductivity [31], as suggested by earlier work from the group of Francoise Candau [32]. The explanations for this amide-cosurfactant-induced percolation center around increases in interfacial flexibility [32] and increased disorder in surfactant chain packing [33]. These increases in flexibility and disorder appear to lead to increased interdroplet attraction, coalescence, and cluster formation. Another example of chemical-potential-driven percolation is in the recent report on the use of simple poly(oxyethylene)alkyl ethers, Ci Ej , as cosurfactants in reverse water, alkane, and AOT microemulsions [27]. While studying temperature-driven percolation, Naza´rio et al. also examined the effects of added Ci Ej as cosurfactants, and found that these cosurfactants decreased the temperature threshold for percolation. Based on these collective observations one can conclude that linear alcohols as cosurfactants tend to stiffen the surfactant interface, and that amides and poly(oxyethylene) alkyl ethers as cosurfactants tend to make this interface more flexible and enhance clustering, leading to more facile percolation. E.
Microstructural Transitions
Self-diffusion NMR measurements have been shown to be very useful in characterizing microstructural transitions in microemulsions [9,34]. Much uncertainty remains, however, in describing transitions from oil-in-water to irregular bicontinuous to water-in-oil microemulsions. Irregular bicontinuous microstructure of low to zero mean curvature has often been inferred on the basis of intermediate to large magnitudes of self-diffusion coefficients [35]. However, it has recently been shown that diffusion coefficients of such magnitude arise naturally in reverse microemulsions as a result of a dynamic partitioning of various solutes (e.g., water and cosurfactant) between continuous and disperse pseudophases [36]. It will be illustrated here that quantitative consideration of such partitioning provides means to quantify effects on transport attendant to percolation processes.
244
Texter
The remainder of this chapter develops this quantitative treatment of percolation as it relates to self-diffusion data from NMR PGSE experiments and to an overarching qualitative treatment also derived from self-diffusion data and from conductivity data. This qualitative treatment focuses upon the coincidence of the upturn in water proton selfdiffusion with the onset of percolation in electrical conductivity. This treatment also focuses upon observations that the upturn in surfactant self-diffusion usually occurs at a higher field variable than do the water proton self-diffusion increase and the onset of electrical conductivity percolation. The fact that these processes occur at different field variables is used to qualitatively distinguish reverse microemulsion droplet aggregation and clustering of percolating droplets from the onset of irregular bicontinuous structure formation A more quantitative approach is based upon a two-state analysis of the NMR water proton self-diffusion data. This two-state analysis is used to derive an order parameter for percolating cluster formation, and this order parameter is applied to the analysis of percolation driven by disperse phase volume fraction, temperature, and cosurfactant chemical potential.
II.
VOLUME-FRACTION-INDUCED PERCOLATION
The influence of disperse phase volume fraction and of temperature on driving microstructure transitions in a brine (0.6% aqueous NaCl), decane, and AOT (12% w/w) microemulsion system was studied extensively by Chen et al. [20]. They used smallangle neutron scattering to measure the mean curvature over an extensive range of disperse phase volume fraction and over a range in temperature. The Shinoda diagram for this system is illustrated in Fig. 1, where denotes the weight ratio of decane to decane plus brine. The quantity 1 denotes the weight ratio of brine to brine plus decane, and
FIG. 1 Partial phase diagram of brine, decane, and AOT system as a function of temperature (T) and decane-to–brine weight fraction (). The brine is aqueous 0.6% (w/w) NaCl; the AOT composition is constant at 12% (w/w). The double-ended arrow depicts the isothermal composition range examined in this study at 45 C. The lamellar (L ), and two-phase regions (2; 2 ) are described in the text. (Adapted from Fig. 5 of Ref. 20.)
Microstructure Effects on Transport
245
the disperse phase (brine) volume fraction is proportional to 1 . This diagram illustrates a large single-phase isotropic microemulsion domain bounded by a lamellar region (L ), an upper two-phase region (2) comprising a decane-rich phase and a decane-in-brine microemulsion, and a lower two-phase region (2 ) comprising a brine-rich phase and a brine-in-decane microemulsion. Chen et al. [20] found that the mean curvature changed sign and went through zero as composition in the single-phase region changed with from brine-in-water droplets at high , to irregular bicontinuous microstructure at intermediate , to oil-in-brine droplets at low and higher temperatures (60–80 C). The measurements described shortly were all obtained [37] at 45 C along the double arrow-ended isotherm pictured in Fig. 1 in the isotropic single-phase microemulsion domain. Results for lowfrequency conductivity and self-diffusion over the composition range 1:0 ! 0:3 in are described along this isotherm. Low-frequency conductivity data [37] obtained along this 45 C isotherm are illustrated in Fig 2. The initial oscillatory variation in the conductivity for > 0:9 can be assigned to variations in AOT partitioning among dimers and other low aggregates and reverse micelles, as reverse micelles are nucleated by added water (brine). These variations will be discussed in greater detail in another publication. The key behavior for the purposes of this exposition is the onset of the electrical conductivity percolation at ¼ 0:85. The conductivity increases two orders as decreases from 0.85 to 0.70, and as shown in the inset, the conductivity increases another two orders as a decreases from 0.7 to 0.3. Self-diffusion data [37] derived from NMR PGSE measurements for decane, water, and AOT are illustrated in Fig. 3. The self-diffusion of decane decreases gradually as decreases from 1.0 to 0.3. The magnitude of decane self-diffusion suggests that the microstructure remains substantially continuous in decane over this composition range. Both water and AOT diffusion initially decrease as decreases. One can readily see that in this
FIG. 2 Low-frequency conductivity at 45 C as a function of composition, (weight fraction decane relative to decane and brine) for brine, decane, and AOT microemulsions exhibiting the phase behavior illustrated in Fig. 1. The breakpoint at ¼ 0:85 corresponds to the onset of percolation. This conductivity increases by two orders as decreases from 0.85 to 0.7. (Reproduced by permission of the American Institute of Physics from Ref. 37.)
246
Texter
FIG. 3 Self-diffusion coefficients of decane (~), water (&), and AOT (*) in brine, decane, and AOT microemulsions at 45 C as a function of decane weight fraction, (relative to decane and brine). Breakpoints in the self-diffusion data for both water and AOT are observed at ¼ 0:85 and at 0.7. (Reproduced by permission of the American Institute of Physics from Ref. 37.)
system, at least, water is necessary for the existence of reverse micelles. In the absence of added water (brine), the AOT diffusion approaches that of monomeric water, suggesting that very, very small aggregates (e.g., dimers) of AOT form at very low water contents. These reverse micelles grow as added brine (water) increases ( decreases), and the selfdiffusion of water and of AOT concomitantly slow. Water proton self-diffusion exhibits a break point and begins to increase at ¼ 0:85. In the case of AOT self-diffusion, a breakpoint also occurs, but AOT self-diffusion continues to slow as decreases further. These breakpoints in both water and AOT selfdiffusion behavior at ¼ 0:85 coincide with the breakpoint in electrical conductivity illustrated in Fig. 1, where the onset of electrical conductivity percolation occurs. At ¼ 0:7 two more breakpoints in the water proton and AOT self-diffusion are seen. Water proton self-diffusion increases more markedly and AOT self-diffusion beings to increase markedly. A.
Two-State Model
A simple two-state model for the observed water proton self-diffusion may be put forward in the form Dobs ¼ xDc þ ð1 xÞDmic
ð1Þ
where Dobs is the observed water proton self-diffusion coefficient, Dc is the self-diffusion coefficient of molecular water in decane, Dmic is the self-diffusion coefficient of the reverse micelles, and x is the mole fraction of water dispersed molecularly in the decane. The coefficient Dc was taken as 0:93 105 cm2 s1 from independent measurements [37] of molecular water diffusion in decane. The coefficient Dmic was approximated by the observed self-diffusion coefficient for AOT for 0:7 and by the dotted curve illustrated in Fig. 3 for < 0:7. With these assumptions and measurements, the mole fraction x of
Microstructure Effects on Transport
247
FIG. 4 Apparent mole fraction (x) water in continuous phase of brine, decane, and AOT microemulsion system derived from the water self-diffusion data of Fig. 3 using the two-state model of Eq. (1).
water in the continuous phase may be derived from these self-diffusion data. This derivation is illustrated in Fig. 4, where it appears that the amount of water in the continuous decane pseudophase increases steadily as decreases below 0.85. B.
Order Parameter
The apparent increase in water solubilized in the continuous decane pseudophase that is illustrated in Fig. 4 goes counter to chemical intuition. The amount of water in the decane pseudophase should partition between micelles and the decane relatively quickly as brine is added to the microemulsion. This in fact appears to occur by the time has decreased to 0.95, and this partitioning may be expected to remain constant over some interval of further brine increase. The mole fraction of water in decane should hold constant and then decrease as total water (brine) in the system increases. The horizontal asymptote illustrated in Fig. 4 and extrapolated to the right in the direction of decreasing represents this partitioning approximation. The mole fraction of water in decane should not go above this level, no matter how much total brine is added to the system. We define x^ as the anomalous mole fraction of water in the continuous phase and as the quantity represented by the vertical arrow in Fig. 4. We further assign this quantity as the amount of water in percolating clusters and irregular bicontinuous microstructure. With this definition, we can define the following order parameter S for the amount of water in such clusters and microstructures, S¼
x^ 1 x þ x^
ð2Þ
where 1 x is simply the amount of water in nonpercolating clusters and isolated reverse microemulsion droplet and where 0 S 1. This order parameter describes quantita-
248
Texter
FIG. 5 Order parameter for disperse pseudophase water (percolating clusters versus isolated swollen micelles and nonpercolating clusters) derived from self-diffusion data for brine, decane, and AOT microemulsion system of single-phase region illustrated in Fig. 1. The a and arrow denote the onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. The other arrow (b) indicates where AOT self-diffusion begins to increase.
tively how water is distributed among disperse phase microstructures: (1) isolated reverse micelles and nonpercolating micellar clusters; (2) percolating micellar clusters and irregular bicontinuous microstructures. The order parameter values calculated from the data of Fig. 4 are illustrated in Fig. 5. The data there suggest the existence of two continuous transitions, one at ¼ 0:85 and another at ¼ 0:7. The first transition at ¼ 0:85, denoted by the arrow labeled ‘‘a’’ in Fig. 5, is assigned to the formation of percolating clusters and aggregates of reverse micelles. The onset of electrical percolation and the onset of water proton self-diffusion increase at this same value of (0.85) as illustrated in Figs. 2 and 3, respectively, are qualitative markers for this transition. This order parameter allows one to quantify how much water is in these percolating clusters. As decreases from 0.85 to 0.7, this quantity increases to about 2–3% of the water. Another more abrupt transition in this order parameter occurs at ¼ 0:7 under the arrow labeled ‘‘b.’’ This transition is assigned to the onset of irregular bicontinuous microstructure formation, and is indicated qualitatively by the marker illustrated in Fig. 3, where the onset in AOT self-diffusion increase occurs.
III.
TEMPERATURE-INDUCED PERCOLATION
A somewhat different water, decane, and AOT microemulsion system has been studied by Feldman and coworkers [25] where temperature was used as the field variable in driving microstructural transitions. This system had a composition (volume percent) of 21.30% water, 61.15% decane, and 17.55% AOT. Counterions (sodium ions) were assigned as the dominant charge transport carriers below and above the percolation threshold in electrical
Microstructure Effects on Transport
249
conductivity. A charge-hopping mechanism above the percolation threshold was also invoked. This mechanism was outlined as emanating from the hopping of AOT molecules between droplets in percolating clusters. Low-frequency conductivity data and NMR PGSE self-diffusion results for water protons and for AOT were obtained [25] over 6–40 C. These data are illustrated in Fig. 6. The water self-diffusion data exhibit a breakpoint at about 18–19 C in close proximity to the onset of percolation in electrical conductivity. This ‘‘onset’’ is highlighted in Fig. 6 by the arrow labeled p at about 18 C. A separate breakpoint in the AOT self-diffusion data appears at about 28 C. This coincidence in the onset of percolation in electrical conductivity with a breakpoint in water self-diffusion increase appears similar to the qualitative markers seen for the onset of formation of percolating clusters in the discussion of the previous section, where disperse phase volume fraction was the field variable driving percolation. Additionally, the separate breakpoint for increasing AOT self-diffusion at higher field variable (temperature 28 C) is similar to the breakpoint seen in Fig. 3 at ¼ 0:7. Again, this surfactant self-diffusion increase marker can be assigned to the onset of irregular bicontinuous microstructure formation. These qualitative similarities to the system analyzed in the previous section suggest a similar order parameter analysis may be warranted. Independent self-diffusion measurements [38] of molecularly dispersed water in decane over the 8–50 C interval were used, in conjunction with the self-diffusion data of Fig. 6, to calculate the apparent mole fraction of water in the pseudocontinuous phase from the two-state model of Eq. (1). In these calculations, the micellar diffusion coefficient, Dmic , was approximated by the measured self-diffusion coefficient for AOT below 28 C, and by the linear extrapolation of these AOT data above 28 C. This apparent mole fraction x was then used to graphically derive the anomalous mole fraction x^ of water in the pseudocontinuous phase. These mole fractions were then used to calculate values for
FIG. 6 Self-diffusion and conductivity data reported by Feldman et al. [25] for reverse water, decane, and AOT microemulsion as a function of temperature. The p and arrow between 18 and 19 C shows the approximate onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. Another breakpoint, at about 28 C, occurs in the AOT self-diffusion data where AOT self-diffusion begins to markedly increase.
250
Texter
FIG. 7 Order parameter for disperse pseudophase water derived from self-diffusion data for water, decane, and AOT reverse microemulsion illustrated in Fig. 6. The p and arrow denote the approximate onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. The arrow labeled AOT shows a second continuous transition corresponding to the onset of AOT self-diffusion increase.
the order parameter of Eq. (2). This order parameter is illustrated in Fig. 7, where breakpoints suggest the occurrence of two continuous transitions. The first of these at about 18 C and marked with an arrow labeled p occurs at the temperature at which the onset in electrical conductivity percolation begins and at the temperature at which the water selfdiffusion data exhibit a breakpoint. This first continuous transition corresponds to the onset of percolating cluster formation. The second breakpoint in the order parameter occurs at about 28–29 C where the AOT self-diffusion coefficients begin to increase. This second transition is assigned to the onset of irregular bicontinuous microstructure formation. These qualitative microstructure transition assignments may be extended to other reverse microemulsion systems reported in the literature. Geiger and Eicke [39] applied both electrical conductivity and NMR self-diffusion measurements to the study of a water, isooctane, and AOT microemulsion driven into percolation by increasing temperature. Inspection of the data published in their figures indicates a coincidence in the temperature at which electrical conductivity percolation commences and at which water proton selfdiffusion markedly begins to increase. In addition, the self-diffusion of AOT begins to increase markedly at a higher temperature, indicating the existence of two distinguishable microstructural transitions, such as those discussed here. Similar qualitative markers may be seen by inspection of the data published by Jonstro¨mer et al. [40], where reverse microemulsions of water (HDO), N-methylformamide (NMF), isooctane, and AOT were examined. Their NMR self-diffusion data showed that the HDO and NMF selfdiffusion exhibited a breakpoint in the neighborhood of 19–20 C where they markedly began to increase. These breakpoints correspond to the onset of electrical conductivity percolation. At higher temperature, at about 26 C, the self-diffusion of AOT begins to increase significantly. Again, these qualitative markers strongly suggest that the processes of percolating cluster formation and irregular bicontinuous microstructure formation are experimentally distinguishable, at least for the microemulsion system reviewed herein.
Microstructure Effects on Transport
IV.
251
CHEMICAL-POTENTIAL-DRIVEN PERCOLATION
As described in the introduction, certain cosurfactants appear able to drive percolation transitions. Variations in the cosurfactant chemical potential, RT ln (where is cosurfactant concentration or activity), holding other compositional features constant, provide the driving force for these percolation transitions. A water, toluene, and AOT microemulsion system using acrylamide as cosurfactant exhibited percolation type behavior for a variety of redox electron-transfer processes. The corresponding low-frequency electrical conductivity data for such a system is illustrated in Fig. 8, where the water, toluene, and AOT mole ratio (11.2 : 19.2 : 1.00) is held approximately constant, and the acrylamide concentration, , is varied from 0 to 6% (w/w). At about ¼ 1:2%, the arrow labeled p in Fig. 8 indicates the onset of percolation in electrical conductivity. NMR PGSE self-diffusion coefficients obtained [36] for toluene, water, acrylamide, and AOT in this microemulsion system are illustrated in Fig. 9 as a function of , the acrylamide concentration. The self-diffusion coefficients for water, acrylamide, and AOT exhibit breakpoints at about ¼ 1:2%, as marked by the arrow labeled p . Again, the onset of percolation in electrical conductivity coincides with the onset of water proton selfdiffusion increase, and these markers indicate that percolating cluster formation (alternatively, cluster percolation) commences at about ¼ 1:2%. While water and acrylamide self-diffusion coefficients coincide for 1:2%, they diverge for 1:2%. The AOT and acrylamide self-diffusion coefficients run parallel to one another, but the AOT values are much lower. The higher values observed for acrylamide may be assigned to the partitioning of acrylamide into the continuous toluene pseudophase, resulting from the nontrivial solubility of acrylamide in toluene. A major qualitative difference observed in this system, compared to the two systems described, respectively, in the previous two sections, is that the self-diffusion of AOT does not exhibit a significant increase at any observed field variable. There is no qualitative marker, therefore, for the formation of irregular bicontinuous microstructure in this system. A quantitative analysis of these self-diffusion data according to the two-state model of Eq. (1) to generate the order parameter of Eq. (2) is straightforward. Dc was found to be
FIG. 8 Low-frequency conductivity () of water, toluene, and AOT reverse microemulsions at 25 C as a function of acrylamide (cosurfactant) concentration, (wt%). The p and arrow at ¼ 1:2% shows the approximate onset of percolation in low-frequency conductivity.
252
Texter
FIG. 9 Measured self-diffusion coefficients at 25 C for toluene (~), water (*), acrylamide (&), and AOT (^) in water, toluene, and AOT reverse microemulsions as a function of cosurfactant (acrylamide) concentration, (wt%). The breakpoint at about 1.2% acrylamide approximately denotes, the onset of percolation in electrical conductivity.
5:41 105 cm2 s1 by measuring molecularly dispersed water in toluene and by correcting for local viscosity differences between toluene and these microemulsions [36]. Values for Dmic were taken as the observed self-diffusion coefficient for AOT. The apparent mole fraction of water in the continuous toluene pseudophases was then calculated from Eq. (1) and the observed water proton self-diffusion data of Fig. 9. These apparent mole fractions are illustrated in Fig. 10 (top) as a function of . The apparent mole fraction in Fig. 10 is approximately constant at x ¼ 0:013 for 1:2%. This constancy corresponds to equilibrium partitioning of water between toluene and the reverse micelles. An extrapolation of this partitioning to higher is illustrated in Fig. 10 (top) by the dashed line. In analogy to the process illustrated in Fig. 4, the anomalous mole fraction of water in the pseudocontinuous phase, x^ , is defined as the difference between this dashed line and x. The corresponding order parameter is then calculated according to Eq. (2) and is illustrated in Fig. 10 (bottom). A single breakpoint is depicted by the arrow labeled p at about ¼ 1:2%. This breakpoint corresponding to the single continuous transition is assigned to the onset of percolating cluster formation. Since no additional continuous transition is revealed in this order parameter with increasing , it can be concluded that there is no indication of irregular bicontinuous microstructure formation in this system, at least over the composition range investigated.
V.
EQUILIBRIUM MODEL
Several unifying conclusions may be based upon the order parameter results illustrated here for microstructural transitions driven by three different field variables, (1) disperse phase volume fraction, (2) temperature, and (3) chemical potential. It appears that the onset of percolating cluster formation may be experimentally and quantitatively distinguished from the onset of irregular bicontinuous structure formation. It also appears that
Microstructure Effects on Transport
253
FIG. 10 (Top) Mole fraction (x) of water in the continuous (toluene) phase as a function of acrylamide content, (wt%), for water, toluene, and AOT reverse microemulsions. (Bottom) Order parameter for disperse pseudophase water derived from mole faction data above. The p and arrow at about 1.2% (w/w) acrylamide indicate the approximate onset of percolation in lowfrequency conductivity
the formation of percolating clusters does not necessarily lead to formation of irregular bicontinuous microstructure, as exemplified in the system driven by acrylamide (cosurfactant) chemical potential. The order parameter approach reviewed here provides explicit support for the cluster-bicontinuous cartoon presented in 1990 by Chen et al. [20] in their neutron scattering study of curvature evolution. Furthermore, this order parameter approach provides a quantitative measure of the amount of water present in each disperse pseudophase. Such a quantitative measure should provide a basis for testing phenomenological and statistical mechanical theories that advance to the point of being able to discern such microstructural transitions. The quantitative estimates for the distribution of water among the different microstructures provide a basis for new thinking about these isotropic microemulsion domains. It appears that irregular bicontinuous microstructure evolves gradually from reverse microemulsion droplets and/or from percolating clusters of such droplets. The formation of such irregular bicontinuous microstructure has heretofore only been considered in the context of first-order transitions between multiple phase domains [41]. While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains.
254
Texter
ACKNOWLEDGMENTS The collaboration of Edwin Garcı´ a of Eastman Kodak Company in the early stages of this work is gratefully acknowledged. The skillful collaboration of Brian Antalek of Eastman Kodak and of Tony Williams while at Kodak has been essential and invaluable in generating the extensive NMR PGSE data upon which the order parameter approach reviewed here was based. Many fruitful ideas and results were also generated in collaboration with Nissim Garti and Yuri Feldman, and their students, at the Hebrew University of Jerusalem.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
24. 25. 26. 27. 28. 29.
R. A. Mackay and J. Texter (eds.), Electrochemistry in Colloids and Dispersions, VCH Publishers, New York, 1992. M.-P. Pileni (ed.), Structure and Reactivity in Reverse Micelles, Elsevier, Amsterdam, 1989. P. Douzou, E. Keh, and C. Balny. Proc. Natl. Acad. Sci. U.S.A. 76:681 (1979). N. Miyoshi and G. Z. Tomita. Z. Naturforsch. 35b:107 (1980). S.-H. Chen and R. Rajagopalan (eds.), Micellar Solutions and Microemulsions, Springer-Verlag, New York, 1990. R. Zana and J. Lang, in Microemulsions: Structure and Dynamics (S. E. Friberg and P. Bothorel, eds.), CRC Press, Boca Raton, pp. 153–172. H.-F. Eicke, J. C. W. Shepherd, and A. Steinemann. J. Colloid Interface Sci. 56:168 (1976). J. Peyrelasse and C. Boned. Phys. Rev. A 41:938 (1990). J. Texter, B. Antalek, E. Garcı´ a, and A. J. Williams, in Amphiphiles at Interfaces (J. Texter, ed.), Steinkopff Verlag, Darmstadt, 1997, pp. 160–169; Prog. Colloid Polym. Sci. 106:160 (1997). Y. Feldman, N. Kozlovich, I. Nir, and N. Garti. Phys. Rev. E 51:478 (1995). B. Lindman and U. Olsson. Ber. Bunsenges. Phys. Chem. 100:344 (1996). M. T. Clarkson, D. Beaglehole, and P. T. Callaghan. Phys. Rev. Lett. 54:1722 (1985). L. E. Scriven. Nature 263:123 (1976). B. Lagourette, J. Peyrelasse, C. Boned, and M. Clausse. Nature 281:60 (1979). M. Lagu¨es. J. Phys. (Paris) Lett. 40:L331 (1979). R. Jo´hannsson, and M. Almgren. Langmuir 9:2879 (1993). M. Lagu¨es, R. Ober, and C. Taupin. J. Phys. 39:L487 (1978). A.-M. Cazabat, D. Chatenay, D. Langevin, and J. Meunnier. Faraday Discuss. Chem. Soc. 76:291 (1982). D. Chatenay, W. Urbach, A.-M. Cazabat, and D. Langevin. Phys. Rev. Lett. 54:2253 (1985). S.-H. Chen, S.-L. Chang, and R. Strey. J. Chem. Phys. 93:1907 (1990). A. Jada, J. Lang, and R. Zana. J. Phys. Chem. 93:10 (1989). M. W. Kim and J. S. Huang. Phys. Rev. A 34:719 (1986). J. Peyrelasse and C. Boned, in Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution (S.-H. Chen, J. S. Huang, and P. Tartaglia, eds.), Kluwer Academic Publishers, Dordrecht, 1992, pp. 801–806. P. Alexandridis, J. F. Holzwarth, and T. A. Hatton. J. Phys. Chem. 99:8222 (1995). Y. Feldman, N. Kozlovich, 1. Nir, N. Garti, V. Archipov, Z. Idiyatullin, Y. Zuev, and V. Fedotov. J. Phys. Chem. 100:3745 (1996). J. Lang, N. Lalem, and R. Zana. J. Phys. Chem. 95:9533 (1991). L. M. M. Naza´rio, T. A. Hatton, and J. P. S. G. Crespo. Langmuir 12:6326 (1996). E. Garcı´ a and J. Texter. Proc. Electrochem. Soc. 93(1):2166 (1993). E. Garcı´ a, S. Song, L. E. Oppenheimer, B. Antalek, A. J. Williams, and J. Texter. Langmuir 9:2782 (1993).
Microstructure Effects on Transport
255
30. E. Garcı´ a and J. Texter. J. Colloid Interface Sci. 162:262 (1994). 31. B. Antalek, A. Williams, E. Garcı´ a, D. H. Wall, S. Song, and J. Texter, in Dynamic Properties of Interfaces and Association Structures (V. Pillai and D. O. Shah, eds.), Champaign, IL: AOCS Press, 1996, pp. 183–196. 32. M. T. Carver, E. Hirsch, J. C. Whittmann, R. M. Fitch, and F. Candau. J. Phys. Chem. 93:4867 (1989). 33. B. Antalek, A. J. Williams, E. Garcı´ a, and J. Texter. Langmuir 10:4459 (1994). 34. P. Stilbs, B. Lindman. Progr. Colloid Polymer Sci. 69:39 (1984). 35. P. Gue´ring and B. Lindman. Langmuir 1:464 (1985). 36. B. Antalek, A. J. Williams, and J. Texter. Phys. Rev. E 52:R5913 (1996). 37. J. Texter, B. Antalek, and A. J. Williams. J. Chem. Phys. 106:7869 (1997). 38. B. Antalek, A. J. Williams, J. Texter, Y. Feldman, and N. Garti. Colloids Surf. A. Physiochem. Eng. Aspects 128:1 (1997). 39. S. Geiger and H.-F. Eicke. J. Colloid Interface Sci. 110:181 (1986). 40. M. Jonstro¨mer, U. Olsson, and W. O. Parker, Jr. J. Phys. Chem. 11:61 (1995). 41. Y. Talmon and S. Prager. J. Chem. Phys. 69:2984 (1978).
11 Investigation of Oil^Water Interfaces by Spectroscopic Methods. Relations with Rheological Properties of Multiphasic Systems ERIC DUFOUR De´partement Qualite´ et Economie Alimentaires, ENITA Clermont-Ferrand, Lempdes, France C. LOPEZ and S. HERBERT
I.
INRA-LEIMA, Nantes, France
INTRODUCTION
Emulsions and gels are important in the formulation of products in the food and pharmaceutical industries, and they must be stable throughout the lifetime of the product. Proteins are often used to stabilize food emulsions. Due to their amphipathic nature, proteins adsorb efficiently at the oil–water interface and both lower the surface tension and stabilize the systems. The emulsifying activity of a protein depends on its molecular properties and environmental factors. In general, proteins with a flexible structure display a better emulsifying activity than those with a rigid structure [1]. The flexible casein molecules can spread widely over the interface, whereas the spreading is not as great in the case of more rigid proteins, such as whey proteins [2]. In all cases, the adsorption of a protein onto an interface induces conformational changes of the protein. It may be assumed that hydrophobic amino acids will be close to the oil surface and that hydrophilic residues will point toward the aqueous phase, but this will be constrained by the amino acid sequence of the protein. Texture is an important criterion used to evaluate the quality of gels. It is a reflection of their structure at the microscopic and molecular levels. For example, milk gel is a complex matrix of milk proteins, fat globules, minerals, and water. It is well established that milk composition and treatment affect the microstructure of the coagulum. Milk treatments performed in dairy plants, i.e., ultrafiltration, homogenization, and heating, modify the fat particle size and change the milk fat globule membrane [3–6]. As a consequence, cheeses made from skim milk standardized with homogenized cream have different properties in comparison with those made from fresh whole milk [7,8] It is important to characterize the material adsorbed at the interface, as well as the conformation of the adsorbed proteins, because it determines the properties of the emulsions and gels. However, little is known about the conformational changes of proteins upon adsorption at oil–water interfaces. The main reason for this is the lack of experi257
258
Dufour et al.
mental techniques allowing structural informatiaon to be obtained directly from complex systems.
II.
SPECTROSCOPIC STUDY OF TURBID AND CONCENTRATED SAMPLES
Adsorption of proteins onto surfaces has long been a subject of interest in the emulsion and biomaterial worlds. It is possible to assess the dimensions of the adsorbed protein layers of emulsions droplets using the techniques of dynamic light scattering, small-angle x-ray scattering, and neutron reflectance. This makes it possible to distinguish between the caseins, which provide rather extended layers, up to about 12 nm thick [9], and whey proteins such as -lactoglobulin (BLG), giving layers which are only about 2 nm thick [10]. It indicates that the thickness of the layer is made up by one layer of BLG molecules, given that the diameter of the monomeric protein in solution is about 3 nm. Access to the fine three-dimensional structure of adsorbed proteins should be a key to the evaluation of the energy variation associated with the conformational changes [11]. The most efficient techniques used for protein structure determination are, however, not adapted to adsorbed proteins. X-ray diffraction implies the use of crystalline samples, which cannot be used in adsorption studies. In NMR the size of the protein, as well as the size of the adsorption surface, is a limited factor. Circular dichroism is a technique routinely used to quantify the secondary structure of proteins and peptides in solution. This technique also gives quantitative information on the secondary structures of adsorbed proteins, but it is severely limited by light scattering of particles with diameters above 20 nm. For this reason, studies of secondary structure changes in protein upon adsorption are scarce. Nevertheless, circular dichroic data on the effect of surface adsorption of synthetic peptides [12], melittin [13], bovine serum albumin [14], and BLG [15,16] have been published. The data were obtained using a cell containing several quartz surfaces [12,13,15,16] and also ultrafine silica particles [14]. For example, the interactions of BLG with phospholipid monolayers were studied by circular dichroism [15,16]. Phospholipid monolayers were formed at a fixed film pressure and then the protein was added in the subphase. The protein–lipid complexes were transferred to quartz plates and the spectra were recorded. It was shown that the interactions were mainly electrostatic at acidic pH and that the binding of BLG induced no conformational changes. Secondary structure alterations were only observed when BLG in chloroform–methanol solution was injected in the film subphase. In this case, BLG conformation was primarily -helical [15]. Conformational changes of bovine serum albumin on its adsorption to gas–liquid or solid–liquid interfaces have been investigated by intrinsic fluorescence and circular dichroism of resolubilized foamed protein [17], by total internal reflection fluorescence measurements [18,19], and by direct circular dichroism measurements [14]. However, methods allowing one to study directly the conformational changes of adsorbed proteins on nonplane liquid–liquid interfaces are still in development. It is generally assumed the fluorescence and Fourier transform mid-infrared (FT-IR) spectroscopies do not suffer from the above-mentioned inconveniences and may be applied to turbid samples. Front-face (fluorescence) and attenuated total reflection (FTIR) techniques may provide information on the structure of adsorbed proteins. Fluorescence spectroscopy offers several inherent advantages for the characterization of molecular interactions and reactions. First, it is 100–1000 times more sensitive than spectrophotometric techniques. Second, fluorescent compounds are extremely sensitive to their environment. Tryptophan residues that are buried in the hydrophobic interior of a
Investigation of Oil–Water Interfaces
259
protein, for example, have different fluorescent properties than residues that are on a hydrophilic surface. This environmental sensitivity enables to characterize conformational changes such as those attributable to the thermal, solvent, or surface denaturation of proteins, as well as the interactions of proteins with other food components. Third, most fluorescence methods are relatively rapid. Fluorescent probes are divided in two categories, i.e., intrinsic and extrinsic probes. Tryptophan is the most widely used intrinsic probe. The absorption spectrum, centered at 280 nm, displays two overlapping absorbance transitions. In contrast, the fluorescence emission spectrum is broad and is characterized by a large Stokes shift, which varies with the polarity of the environment. The fluorescence emission peak is at about 350 nm in water but the peak shifts to about 315 nm in nonpolar media, such as within the hydrophobic core of folded proteins. Vitamin A, located in milk fat globules, may be used as an intrinsic probe to follow, for example, the changes of triglyceride physical state as a function of temperature [20]. Extrinsic probes are used to characterize molecular events when intrinsic fluorophores are absent or are so numerous that the interpretation of the data becomes ambiguous. Extrinsic probes may also be used to obtain additional or complementary information from a specific macromolecular domain or from an oil–water interface. Most fluorescence experiments are done on dilute solutions with absorbance of the sample below 0.1: it is a classical right-angle fluorescence spectroscopy. When the absorbance of the sample is higher than 0.1, the screening effect (or inner filter effect) induces a decrease of fluorescence intensity and a distortion of excitation spectra [21]. To avoid these problems, an alternative method – frontal illumination fluorescence spectroscopy, has been developed [22]. Front-face fluorescence allows investigation of the fluorescence of powdered, turbid, and concentrated samples (Fig. 1). The method has been used to quantitatively determine hemoglobin in undiluted blood [23], and to study hemoglobin R ! T transition kinetics [24] or proteins in wheat gluten [25]. But searching in the literature, very few papers are encountered dealing with the application of front-face fluorescence in the characterization of food products. This could be explained by the fact that food products are complex products containing numerous fluorescent compounds. In such a case the signals of the different chromophores may overlap and, for example, it becomes difficult to predict the concentration of one particular compound. However, fluorescence spectroscopy in combination with multivariate statistical methods has been used for predicting the concentrations of two component synthetic mixtures [26].
III.
FRONT-FACE FLUORESCENCE SPECTROSCOPY APPLIED TO THE STUDY OF PROTEIN CONFORMATION AT THE OIL–WATER INTERFACE OF EMULSIONS
To our knowledge, there are few publications dealing with direct study of conformational changes of proteins adsorbed on nonplane liquid–liquid interfaces, such as those found in emulsions [27,28]. Detailed information on the conformation of caseins at the oil–water interface have been obtained using proteases [27,29,30]. By comparing the peptides produced during the proteolysis of the protein in solution or adsorbed at the interface, it has been possible to identify the proteinase-sensitive bonds which are masked by being adsorbed to the oil phase. Antibodies to s1 -casein have also been used to probe its topography at an oil–water interface [31].
260
Dufour et al.
FIG. 1 Schematic representations for (a) right-angle and (b) front-face fluorescence spectroscopies.
Among spectroscopic methods, essentially front-face fluorescence has been used to investigate modifications of the conformation of a protein upon its adsorption at the oil– water interface. Castelain and Genot [28] have shown for the first time that front-face fluorescence measurements performed directly on oil-in-water emulsion provide information on the structural changes of proteins upon their adsorption at interface. They conclude from the protein fluorescence spectra recorded directly on the emulsion that the adsorption of bovine serum albumin (BSA) onto the interface to stabilize dodecane-inwater emulsions involve drastic conformational changes in the protein molecule. A 15 nm blue shift of the emission maximum of BSA tryptophans and a significant increase of its quantum yield were observed following the adsorption of the protein onto the interface. As the tryptophan residues of the protein move to an apolar environment, it suggests that they are in contact with dodecane or that aromatic amino acids are buried in hydrophobic pockets located inside the protein structure. These authors also indicate that the method may be used to evaluate the partition of adsorbed and nonadsorbed protein in a complex system. However, conformational changes of proteins rarely induce such a large shift as the one observed following bovine serum albumin adsorption of the oil–water interface. For -lactoglobulin (BLG) adsorption at the oil–water interface, the emission maximum of tryptophan residues is blue shifted by only 3 nm [32]. Experiments were carried out on emulsion samples with ratios of soluble BLG/adsorbed BLG ranging between 0 and 2.88, which were prepared by adding known amounts of BLG in solution to the cream and were used in order to investigate the changes in tryptophan emission fluorescence upon BLG adsorption at the oil–water interface. When the BLG in solution was in excess over the adsorbed BLG, the emission spectrum was typical of the native BLG spectrum with a maximum at 329 nm (Fig. 2). The decrease in the soluble BLG/adsorbed BLG ratio induced a shift of the maximum emission toward lower wavelengths. For the sample containing only adsorbed BLG, the maximum emission was located at 326 nm. These results suggested that the tertiary structure of BLG was modified upon adsorption at the oil–water interface and that at least one tryptophan in adsorbed BLG was in a more hydrophobic environment. In addition, circular dichroism and mid-infrared experiments indicate that the secondary structure of adsorbed BLG is slightly modified [32,33]. The observed fluorescence blue shift following BLG adsorption was, however, small compared with the one observed for bovine serum albumin [28]. Univariate analysis
Investigation of Oil–Water Interfaces
261
FIG. 2 Emission fluorescence spectra of -lactoglobulin tryptophans for three different samples: R ¼ 0 (---), R ¼ 0:96 ( ), and R ¼ 2:24 (—). R ¼ ðsoluble BLG/adsorbed BLG).
FIG. 3 PCA similarity map defined by principal components 1 and 2. Each label corresponds to a spectrum. Soluble BLG/adsorbed BLG ratios of 0 (0), 0.32 (1), 0.64 (2), 0.96 (3), 1.33 (4), 1.92 (5), and 2.56 (6). The spectrum of each sample was recorded in triplicate using different aliquots.
262
Dufour et al.
techniques are not always appropriate for the study of systems exhibiting slight differences. Principal component analysis (PCA), a multivariate analysis technique, has been used by Dufour et al. [32] to extract information related to protein conformation changes following emulsification. This method is well suited to optimize the description of the data collection with a minimum loss of information. Moreover, the eigenvectors corresponding to the principal components are homologous to spectra. They provide information about the regions of the fluorescence spectrum which explain the differences between the samples observed on the map. In this study, the collection contained tryptophan emission spectra of samples with different ratios of soluble BLG/adsorbed BLG. In practical terms, a discrimination of the samples in relation to the ratio of soluble BLG/adsorbed BLG was observed according to principal component 1 (Fig. 3). The corresponding eigenvector indicates a shift toward lower wavelengths for the emulsions containing mainly adsorbed BLG. PCA results tally with the fluorescence spectra recorded at different soluble BLG/ adsorbed BLG ratio [32]. It appears that multivariate analysis techniques are well suited to analyze sets of fluorescence spectra exhibiting slight differences. Indeed, PCA has been successfully applied to front-face fluorescence spectra in order to discriminate between bulk, heated, and/or homogenized samples of milk [5] (Fig. 4). The treatments applied to milk are well known to modify protein structure, fat globule shape, and protein–lipid interactions. Indeed, heating may denature proteins. Denaturation is characterized by the changes of protein structure modifying tryptophan quantum yield, and by the exposure to the surface of hydrophobic regions. Homogenization breaks up fat globules into smaller ones, increasing drastically the area of the lipid–water interface. The stabilization of the interface created by homogenization
FIG. 4 PCA similarity map defined by the principal components 1 and 2 for the tryptophan emission spectra. Samples were coded NHO, NHP, HOM, and HOP for raw, heated, homogenized, and homogenized þ heated milks, respectively. Each label corresponds to a spectrum.
Investigation of Oil–Water Interfaces
263
results from the adsorption of proteins at the interface [34]. The adsorption of proteins at the interface changes their structure, as well as their binding and fluorescence properties [28,32]. The differences observed in the spectra recorded on raw, heated, or homogenized milks clearly indicate that the physical treatments applied to the milk modify the characteristics of the fluorescent probe investigated. The changes of tryptophan quantum yields upon heating suggest that the thermal treatment of the samples partly denatured the milk proteins. Based on the fluorescence data only, it appears more difficult, however, to explain, at a molecular level, the effects of homogenization on milk components. In this case, the modification of fat globule size may also perturb light scattering and induce changes in the fluorescence spectra which would not be related to the quantum yield of the probes. In order to get more explanations of the observed fluorescence modifications of milk samples following physical treatments, tryptophan fluorescence of washed creams, fat globule size, and the kind of proteins adsorbed at the surface of the fat globule were studied. The tryptophan fluorescence intensity of washed cream from raw milk is relatively weak, since the proteins associated with the native membrane of the fat globule are found in small amounts [34]. After heating of raw milk, the fluorescence intensity of the washed cream doubled, suggesting that heat treatment induces binding of proteins to the fat globules. The highest fluorescence was observed for the homogenized sample. This dramatic increase of the fluorescence intensity at about 330 nm indicates that the interface created by the homogenization of milk is stabilized by proteins [5]. These assumptions were confirmed by the electrophoresis study of the washed creams. Electrophoresis of purified fat globules is a convenient method to characterize and quantify proteins adsorbed at the oil–water interface [35]. Electrophoretic data indicate that no casein, nor whey proteins, were adsorbed at the surface of raw-milk fat globule. Upon homogenization, caseins adsorbed preferentially at the lipid–water interface. In this case, bound -lactalbumin accounted for 16% of the total interfacial proteins. Heat treatment also induced the interaction of proteins with the fat globules. The amount of bound proteins (per mg of lipids) for heated raw milk was half that for homogenized milk.
IV.
FLUORESCENCE SPECTROSCOPY INVESTIGATION OF THE EFFECTS OF THE COMPOSITION OF THE FAT GLOBULE SURFACE ON THE COAGULATION OF MILK
Texture is an important criterion used to evaluate the quality of dairy products. It is a reflection of their structure at the microscopic and molecular levels. Structurally, milk gel is a complex matrix of milk proteins, fat globules, minerals, and water. It is well established that milk composition and treatment affect the microstructure of the coagulum. Milk treatments performed in daily plants, i.e., ultrafiltration, homogenization, and heating, modify the fat particle size and change the milk fat globule membrane [3–6]. Milk proteins are surface-active compounds that constitute a group of strongly interacting proteins and caseins adsorb efficiently at the fat–water interface stabilizing emulsions. The molecular state of caseins, whether in the micellar or soluble form, is important in determining their functionality as an emulsifier. The emulsifying activity of a protein depends on its molecular properties and on environmental factors. In general, proteins with a flexible structure display a better emulsifying activity than those with a rigid structure. The flexible casein molecules can spread widely over the interface [27], whereas
264
Dufour et al.
the spreading is not as important in the case of globular proteins, such as -lactoglobulin [32]. As a consequence, cheeses made from skim milk standardized with homogenized cream have different properties in comparison with those made from fresh whole milk [7,8]. There is evidence in the literature that fat globules participate in the protein network formation, and that the fat globule membrane plays a structural role in milk gels [36–38]. Acid–milk–fat composite gels formed by heating reconstituted milk made with skim milk and emulsified fat prepared using different proteins were investigated by Xiong and Kinsella [38]. The kinetic and structural aspects of protein–protein and protein–fat globule interactions determine the rheological properties of coagula and their syneresis behavior. It has been reported recently that the changes in tryptophan fluorescence emission spectra corresponding to an evolution in the environment of the intrinsic probe allow one to follow the different stages of the acidification and coagulation phases and to characterize the gelation times [39,40]. Tryptophan fluorescence spectra also allow to discriminate the coagulation processes of reconstituted milks stabilized by different fat–water interfaces. The time course evolutions of tryptophan fluorescence emission spectra during the coagulation kinetics studied differ as a function of fat–water interface, resulting in different paths and different gel textures [39]. Fluorescence methods may be useful to investigate at a molecular level the fat–water interface evolution during the coagulation kinetics of milks varying by the composition of fat globule surface. An amphiphilic and extrinsic fluorescent probe, Laurdan, known to bind essentially at the oil–water interface, was used in this study. The structural evolutions of reconstituted milks characterized by different fat–water interfaces were studied during the 2 h of an acidification phase by glucono--lactone and during the 3 h of a rennetinduced coagulation phase using front-face fluorescence spectroscopy.
A.
Material and Methods
Anhydrous milk fat (melting point ¼ 28 C) was provided by Socie´te´ France Beurre (Quimper, France). Skim milk powder and -lactoglobulin were provided by INRA Rennes (France) and Lactalis (Retiers, France), respectively. -Casein (90% pure) was purified in the laboratory as described previously [41]. Cream, obtained after skimming of fresh whole milk purchased from a local dairy plant, is constituted by natural milk fat globules. Glucono()lactone (GDL, 99% pure), commercial calf rennet (520 mg/L) and Laurdan were purchased from Roquette (France), SKW (Baupte, France) and Sigma (St Quentin, France), respectively. 1. Milk Reconstitution Skim milk (35 g/L) and -lactoglobulin (5 g/L) solutions were prepared by dissolving skim milk powder and -lactoglobulin powder in distilled water and stirring at room temperature for 4 h. -Casein (5 g/L) had been hydrated in a phosphate buffer (100 mM, pH 8) and stirred at 4 C for one night [27]. Sodium azide (0.1%, wt/v) was added to prevent bacterial growth. After heating at 40 C, liquid anhydrous milk fat (1 v) and the different protein solutions (10 v) were premixed using a polytron (PT 3000, Kinematica) and emulsified with a homogenizer (ALMO, Legrand, France) at about 40 C in order to obtain oil-inwater emulsions. After separation from the aqueous phase by centrifugation for 5 min at 1000g, milk fat droplets stabilized by different proteins were washed twice with a phos-
Investigation of Oil–Water Interfaces
265
phate buffer (100 mM) in the case of the -casein-stabilized emulsions and with a mineral solution (30 mM CaCl2 ; 25 mM NaCl) for the others in order to remove proteins not bound at the fat–water interface. Four reconstituted milks were prepared by blending hydrated skim milk powder (35 g/L) with four different emulsions (35 g/L) differing by composition of the fat–water interface. Whole reconstituted milks were coded MP (milk proteins), BCAS ( -casein), and BLG5 ( -lactoglobulin 5 g/L): Skimming fresh whole milk allowed us to obtain milk fat globules with natural membranes that were blended at a concentration of 35 g/L with hydrated skim milk powder (35 g/L). This reconstituted milk was coded CREAM. 2.
Coagulation
The pH of the reconstituted milks was adjusted to 6.4 with 1 N HCL. First, the acidification phase was carried out with glucono()lactone (2 g/L) at 30 C in order to exponentially decrease the pH and obtain a stabilized value corresponding to pH ¼ 6:0 after 2 h incubation. Then, rennet was added to the acidified reconstituted milks at a final concentration of 19.5 mg/L and the coagulation phase was performed at 30 C for 3 h. 3. Characterization of the Milks and Gels A Malvern Mastersizer (Malvern Instruments Ltd, Malvern, UK) with optical parameters defined by the manufacturer’s presentation code 0505 was used to determine the droplet size distribution. The measurement was made in triplicate at room temperature. Water was used to disperse the emulsion droplets. Gel formation was monitored using a controlled-stress rheometer (Carri-Med CS50, TA Instruments, France) with a cone-plate geometry (4 cm diameter, 3 58 0 angle). The bottom plate was equipped with a Peltier temperature controller that allowed regulation of the temperature at 30 C. The surface of the sample set to the plate was covered with silicone oil to prevent evaporation. The evolutions of the storage (G 0 ) and loss (G 00 ) moduli of the acidified reconstituted milks were recorded just after rennet addition in the following conditions: frequency 1 Hz, deformation 1%, and strain 6 mN=m2 , considered to be low enough to make a measurement without disturbing the gelation process. Data were collected and rheological parameters calculated using Carri-Med 50 software. The experiments were done in triplicate for all the reconstituted milks. 4.
Front-Face Fluorescence Spectroscopy and Mathematical Processing
Fluorescence spectra were recorded using an SLM 4800C spectrofluorimeter (Bioritech, Chamarande, France) mounted with a variable-angle front-surface accessory. The incidence angle of the excitation radiation was set at 56 to ensure that reflected light, scattered radiation, and depolarization phenomena were minimized. Emission spectra (resolution: 0.5 nm, averaging: 10) were recorded at 30 C with emission and excitation slits set at 4 nm. All spectra were corrected for instrumental distortions in excitation using a rhodamine cell in the reference channel. The fluorescence excitation spectra of Laurdan (250–420 nm) were recorded with emission wavelength set at 439 nm. For each reconstituted milk studied, the measurement was made in triplicate during the 2 h of the acidification phase and the 3 h of the coagulation phase. To reduce scattering effects and to allow a comparison between the different reconstituted milks, the data were normalized by reducing the area under each spectrum to a
266
Dufour et al.
value of 1 [42]. Principal component analysis (PCA) was applied to the normalized data. This method is well suited to optimize the description of the fluorescence data sets by extracting the most useful data and rejecting the redundant data [43]. From a data set, PCA assesses principal components and their corresponding spectral pattern. The principal components are used to draw maps that describe the physical and chemical variations observed between the samples. While the similarity maps allow the comparison of the spectral in such a way that two similar spectra are represented by two neighbouring points, the spectral patterns exhibit the absorption bands that explain the similarities observed on the maps. PCA software has been written by D. Bertrand (INRA Nantes) and is described elsewhere [44]. B.
Results and Discussion
1. Size Characterization of Fat Droplets The average sizes of the emulsion droplets dispersed in reconstituted milks and stabilized by different fat–water interfaces are presented in Table 1. Fat globules in CREAM have an average diameter of 4:5 m, which is similar to fat globule size in whole milk without any treatments [5]. Similar average diameters were obtained for fat droplets in BCAS and BLG5, whereas MP showed larger values. Considering MP emulsion, the large average diameter (7:2 0:5 m) was quite surprising. However, this result was obtained with a good reproducibility. 2. Spectral Changes During the Coagulation Kinetics of BLG5 Milk The excitation spectrum of Laurdan presented a maximum at 363 nm and two shoulders at 320 and 386 nm (Fig. 5). During the kinetics, the changes in the normalized spectra were mainly observed at 320 and 386 nm. As the fluorescence intensity at 320 nm increased between 30 and 300 min, the intensity of the shoulder at 386 nm decreased with time. Figure 6 shows the changes of the fluorescence intensity at 363 nm during the time course of the BLG5 coagulation. During the acidification step (0–120 min), the fluorescence intensity remained roughly constant. The addition of rennet induced an increase in fluor-
TABLE 1 Average Diameter of the Natural Milk Fat Globules and Emulsified Milk Fat Droplets Stabilized by Different Fat– Water Interfaces in Reconstituted Milks Fat–water proteins interface Milk fat globule (CREAM)a -casein (BCAS)a -lactoglobulin 5 g/L (BLG5)a Milk (MP)a a
Code of the different reconstituted milks.
Average diameter ðmÞ 4:5 0:7 4:2 0:3 3:8 0:8 7:2 0:5
Investigation of Oil–Water Interfaces
267
FIG. 5 Laurdan fluorescence excitation spectra recorded between 250 and 420 nm (emission wavelength, 439 nm) at different times during the acidification and the rennet-induced coagulation kinetics of BLG5 reconstituted milk: 35, 70, 125, 175, and 300 min. A:U: ¼ arbitrary units.
escence intensity, remaining constant between 120 min and 140 min, followed by a sharp increase from 145 to 165 min. Then the fluorescence intensity continued to increase, but with a smaller slope. The change in the slope of the fluorescence intensity evolution observed between 140 and 300 min corresponded to the gelation point determined visually. PCA was applied to the set of spectra recorded during BLG5 milk coagulation in order to obtain additional structural information. This method is well suited to optimize the description of data collection by extracting the most useful data and rejecting redundant data. Figure 7 shows a PCA similarity map defined by the principal components 1 and 2 for Laurdan excitation fluorescence spectral data of the BLG5 system. The first two principal components accounted for 99.4% of the total variability with a predominance of component 1 (98.7%). A separation of spectra was observed as a function of time according to component 1. Moreover, it appeared that the spectrum T160, corresponding to the gelation time determined by the rheology method, exhibited co-ordinates close to ð0; 0Þ. The spectra recorded before gelation (T5–T155) had negative scores according to component 1, whereas spectra recorded after milk gelation (T160–T300) had positive scores. These results showed that acidification and gelation of milk induced different modifications in the fluorescence properties of protein tryptophans. However, considering the data variablities explained by principal components 1 and 2, it appears that gelation modifies milk protein fluorescence properties more dramatically than acidification. The spectral pattern associated with principal component 1 is presented in Fig. 8. It provided the characteristic wavelengths which were the most discriminant to separate the
268
Dufour et al.
FIG. 6 Evolution of the maximal fluorescence intensity of Laurdan at 363 nm (expressed in arbitrary units) recorded vs. time during BLG5 reconstituted milk acidification and coagulation phases (excitation: 250–420 nm; emission: 439 nm).
FIG. 7 Principal component analysis similarity map defined by the principal components 1 and 2 (A1, A2) for Laurdan fluorescence excitation spectral data recorded during the BLG5 milk coagulation. The digits correspond to the elapsed time. Each label corresponds to a spectrum.
Investigation of Oil–Water Interfaces
269
FIG. 8 Spectral pattern corresponding to the principal component 1 (—).
spectra on the map. The most discriminant wavelengths were 315 and 385 nm. In addition, the contrast between a positive peak at 315 nm and a negative one at 385 nm was observed, indicating opposite changes of the fluorescence intensities of the shoulders at 320 and 385 nm during the kinetics. 3.
Comparison of the Fluorescence Data Set of the Four Milks
The tryptophan emission spectra of the four milks were pooled in one matrix and this table was analyzed by PCA to obtain a maximum of information concerning the differences observed with the recording of fluorescence spectra and relative to the structural changes in the environment of the extrinsic probe studied. Figure 9 presents a PCA similarity map defined by the principal components 1 and 2 for Laurdan fluorescence excitation spectral data of BCAS, MP, BLG5, and CREAM reconstituted milks. The first two principal components accounted for 98.9% of the total variability, with a predominance of component 1 (96.6%). The similarity map clearly discriminated between the different systems investigated along the second principal component. The scores were negative for MP and mainly positive for BLG5, CREAM, and BCAS. The principal component 1 (PC1) separated the acidification phases of BLG5, CREAM, BCAS, and MP clustered with negative values, from their rennet-induced coagulation phases that spread in a specific order associated with time from the left to the right of the map. These results showed that acidification and gelation of reconstituted milks induced different modifications in the fluorescence properties of Laurdan. Few techniques allow one to investigate, at a molecular level, structural evolutions during milk coagulation. Fluorescence spectroscopy allows one to characterize weak changes in protein environment or structure. For example, the titration of -lactoglobulin in the micromolar concentration range by fatty acids can be monitored by this technique [45]. But classical right-angle fluorescence spectroscopy only allows one to investigate
270
Dufour et al.
FIG. 9 Principal component analysis similarity map defined by the principal components 1 and 2 (A1, A2) for Laurdan fluorescence excitation spectral data. The letter corresponds to the type of milk and the digits correspond to the elapsed time. Each label corresponds to a spectrum. The letters B, C, L, and P correspond to BLG5, BCAS, CREAM, and MP, respectively.
dilute solutions. Considering emulsions or colloidal systems such as food products, frontface fluorescence can be used, since it makes it possible to record the excitation and emission spectra of powdered, turbid, and concentrated samples. The results reported in this study demonstrate that changes in Laurdan fluorescence excitation spectra corresponding to an evolution in the environment of the extrinsic probe allow one to follow the coagulation phase and to characterize the gelation times. Front-face fluorescence spectroscopy also allows one to discriminate between the coagulation processes of reconstituted milks stabilized by different fat–water interfaces. The time course evolutions of Laurdan fluorescence excitation spectra during the coagulation kinetics studied differ as a function of fat–water interface, resulting in different paths, as shown on the PCA similarity map (Fig. 9).
4. Dynamic Rheological Properties of the Reconstituted Milks During the Coagulation Kinetics Rheological measurements were carried out to investigate the rheological properties of emulsions stabilized by different fat–water interfaces and the influence of fat droplets on the formation of the protein networks during a process of gelation. The starting time for rheological measurements correspond to t ¼ 120 min. Indeed, the rheological parameters were only recorded during the rennet-induced coagulation phase to avoid structural modifications during the acidification phase which may consequently influence the gelation process. Elastic and viscous properties of reconstituted milks
Investigation of Oil–Water Interfaces
271
were characterized during coagulation kinetics by the recording of the storage modulus (G 0 ) and the loss modules (G 00 ), respectively. The evolutions of the elastic modulus (G 0 ) recorded vs. time during the rennet-induced coagulation phase of the different reconstituted milks are shown in Fig. 10. All the samples showed a pregel stage characterized by a G 0 modulus close to the 0 N=m2 value. Considering the gelation time, the samples can be divided in two distinct groups with characteristic rheological behaviors. The gel point times for BCAS, BLG5, and MP were observed between 40 and 46 min after rennet addition, whereas CREAM presented a shorter gel point time corresponding to 32 and 33 min after rennet addition, respectively (Table 2). The elastic modulus (G 0 ) of MP, BCAS, and BLG5 rapidly rose to plateaus that corresponded to different G 0 saturations (G0sat ) (Table 2). MP and BCAS coagula showed 0 value (142 N=m2 ), meaning that the emulsions stabilized by skim the more important Gsat milk proteins (mainly casein micelles) and -casein formed the coagula with the strongest protein network. Considering CREAM, a sudden decrease in G 0 modulus was observed 15 min and 32 min after the gel point time, respectively. The rapid increase in the G 0 modulus followed by a sudden decrease was always observed for this sample. This experiment has been carried out three times giving reproducible results. As this phenomenon could result from a sliding of the cone caused by syneresis, experiments were performed using a ridge cone and reduced stress conditions. The shape of the G 0 curve obtained in these conditions was similar to the results reported in Fig. 10. It was concluded that this
FIG. 10 Evolution of the elastic modulus (G 0 ) recorded during the 3 h of the rennet-induced coagulation phase of the reconstituted milks.
272
Dufour et al.
TABLE 2 Rheological Parameters Measured for the Reconstituted Milks and Skim Milk During Coagulation Kinetics
CREAMb;c BCASb BLG5b MPb
Gelation time (min)a
0 Gsat (N/m2 )
00 Gsat (N/m2 )
32:0 0:4 40:3 4:2 42:3 4:0 42:3 2:0
— 142 2 108 4 142 3
— 36 1 28 2 37 1
a
Elapsed time after rennet addition. Reconstituted milks with natural milk fat globules (CREAM) or emulsified milk fat droplets stabilized by -casein (BCAS), -lactoglobulin 5 g/L (BLG5), skim milk proteins (MP). c Atypical curve (see the text and Fig. 10). b
reproducible phenomenon did not result from the syneresis of the mixed system. But, at the moment, we are not able to explain this phenomenon. 0 The rheological properties, such as Gsat allow one to know the strength of the coagulum resulting from protein–protein and/or protein–fat globule interactions formed during milk coagulation. There is evidence in the literature that fat globules participate in the protein network formation, and that the fat globule membrane plays a structural role in milk gels (36–38). Acid–milk–fat composite gels formed by heating reconstituted milk made with skim milk and emulsified fat prepared using different proteins were investigated by Xiong and Kinsella [38]. They showed that, under equal gelling conditions, milk fat emulsions stabilized by whey protein isolate form the strongest gels, followed by the emulsions stabilized by sodium caseinate and whole skim milk proteins, as indicated by the G 0 modulus. The Tween 80 emulsified milk fat and the blank without fat presented similar gel properties. As it is generally assumed that the number of crosslinks in protein gels at equilibrium is proportional to the magnitude of G 0 , the authors concluded that the presence of fat droplets covered with caseins or whey proteins increases the rate of crosslinking. Considering our experiments, the pHs of the milks were 6.0 at the time of renneting. It has been reported [46,47] that the firmness of a renneted-milk curd attains a maximum at about pH 6. Increased activity of the chymosin at this pH increases the enzymatic phase of coagulation, whereas diminution of micelle stability, linked to both charge neutralization and the liberation of the calcium, increases the aggregation reaction [48–50]. Nevertheless, there are marked differences in the rheological properties of the reconstituted milk coagula containing fat droplets stabilized by different emulsifiers (Fig. 10). While the G 0 modulus values for MP, BLG5, and BCAS gels range between 108 and 142 N=m2 , CREAM gel exhibits a particular behavior with G 0 modulus values lower than 20 N=m2 after 300 min. Although the same results have been reported for raw milk [51], this phenomenon is still discussed. It is generally assumed that the interactions between the proteins adsorbed at the fat–water interface and the proteins in the continuous phase likely influence the viscoelastic behavior of the coagula. Concerning CREAM, the natural milk fat globule membrane plays a particular role during the gelation process. Fat globules in CREAM obtained after skimming of fresh whole milk are stabilized by a membrane constituted by phospholipids, proteins, and lipo- and glycoproteins [34]. As the
Investigation of Oil–Water Interfaces
273
natural milk fat globule membrane is devoid of caseins and whey proteins [5], the fat globules are weakly or noninteractive with the protein network and may behave like plasticizers during shearing. Due to the charge and the composition of the milk fat globule membrane, hydrophobic interactions cannot take place between the membrane and the proteins of the aqueous phase forming the matrix. In addition, casein micelles and milk fat globule membranes exhibit negative charges at pH 6.0, prohibiting ionic interactions. In the case of CREAM, it is possible that native fat globules are loosely entrapped in the gel matrix. This result supports the observations of van Vliet and Dentener-Kikkert [37] and Xiong and Kinsella [38] who showed that Tween 80- and polyvinyl alcohol-stabilized emulsions have little effect on the rheological properties of milk gel. While the rheological measurements differentiate MP, BLG5, and BCAS gels from CREAM gel, a different trend is observed with fluorescence data (Fig. 9). According to principal component 2, the scores were negative for MP, while BCAS, BLG5, and CREAM formed a cluster with positive scores. It is concluded that the interactions and the organizations of protein networks are different. The results suggest that fat globules can either act as copolymers and be integrated into the matrix of the casein–fat globule network, or act as fillers [38]. Considering our data, it appears that the small fat globules (3–4 m) do not perturb the formation of the protein network and can serve as fillers. Indeed, the fluorescence results (Fig. 9) suggest similar organizations of the protein networks for the coagula obtained with BLG5, BCAS, and CREAM. However, in the case of MP, the larger fat globules (6–7 m) perturb the formation of the protein network during coagulation and can serve as copolymers forming a casein–fat globule network [38]. Fats emulsified with MP present casein micelles at the surface of the droplets that can strongly interact with the casein network during the coagulation process.
V.
FLUORESCENCE SPECTROSCOPY INVESTIGATION OF ACID- OR RENNET-INDUCED COAGULATION OF MILK
Milk coagulation is the primary step in the production of most dairy products. Coagulation can be induced by acid, rennet, or both. Rennet coagulation is characterized by three phases. The first of these is an enzymatic phase which involves the cleavage of the surface -casein in the casein micelles to para--casein and soluble caseinomacropeptides. The resulting para-casein micelles spontaneously aggregate in a second phase of the process before a rearrangement step takes place [3,52]. In the case of the acid-induced gelation, the process is different. Upon lowering the pH of milk, colloidal calcium phosphate is solubilized from casein micelles, micellar disintegration takes place and the caseins associate to form a gel [21,32]. The major driving force for protein–protein interactions during the enzymatic and acid coagulation of casein micelle are hydrophobic interactions [53,54]. However, electrostatic and hydrogen bonds contribute to the specificity and stability of the interactions and, as a consequence, to specific structures. Generally, the caseins associate during coagulation to form a protein network entrapping fat globules [55,56]. The kinetics of coagulation and the structural aspects of protein–protein and protein–fat globule interactions determine the rheological properties of gels and thus their syneresis behavior. The six major proteins of milk, s1-, s2-, - and -casein, -lactoglobulin, and lactalbumin, contain at least one tryptophan residue [57], the fluorescence of which allows the monitoring of the structural modifications of proteins and their physicochemical environment during the coagulation processes. Emission fluorescence spectra of the protein tryptophanyl residues were recorded for the milk coagulation kinetics induced by
274
Dufour et al.
acidification, rennet, or both [51]. Principal component analysis was applied to the collections of normalized fluorescence spectral data of the three systems to optimize their description. The results showed that front-face fluorescence allowed the detection of the structural changes in casein micelles during coagulation and the discrimination of the different dynamics of the three coagulation systems. Using front-face fluorescence spectroscopy, it has been possible to demonstrate that gels exhibiting different rheological properties have different structures at the molecular level [51]. In addition, it was possible to follow the different steps of the gelation process using intrinsic fluorescence properties of protein tryptophans. Milk retains also fat-soluble vitamins such as vitamins A, D, E, and K. Vitamin A occurs in more than one form, but it is generally found as retinol. Because of its alcohol group, retinol readily forms esters. In milk, almost all the vitamin occurs in the palmitate or acetate ester forms. Vitamin A (about 1 mol/L in bovine milk) is located in the core and in the membrane of the fat globule [58]. Due to its conjugated double bonds, retinol is a good fluorescent probe with excitation and emission wavelengths at about 330 and 450 nm, respectively. A very weak fluorescence is observed for aqueous solution of retinol, but its quantum yield is drastically enhanced in apolar environments [59]. As the fluorescence properties of vitamin A change as a function of its environment, it may be an interesting intrinsic fluorescent probe of milk. It could be very useful to monitor fat–water interface evolution during milk coagulation and to investigate the changes of protein–lipid interactions during the milk coagulation process. In order to reach this goal, the fluorescence properties of vitamin A located in the fat globules was considered. Indeed, fluorescence transfer may occur between protein and vitamin A in the membrane of the fat globule when the two fluorescence probes are close enough (less than 40 A˚) [60]. This approach requires the ability to discriminate between different dynamic and structural changes. For this reason, the study was conducted using three different milk coagulation processes known to yield different structures and textures [53]. A.
Materials and Methods
1. Coagulation Systems Raw bovine milk was purchased from a local dairy plant. For all experiments, the pH of the milk was adjusted to 6.7 using 1 N HCl. Sodium azide (0.02%) was added to the milk to prevent bacterial growth. Three types of coagulation were considered. The gluconoðÞlactone (GDL)-induced coagulation system (GDL system) was prepared by acidification with 1.75 g/L GDL (Roquette, Lestrem, France). The rennet-induced coagulation system (rennet system) was prepared by the addition of calf rennet (SKW, Baupte, France) at 25:6 g/L of milk. The GDL þ rennet-induced coagulation system (mixed system) was prepared by acidification with 0.45 g/L GDL for 2 h followed by the addition of rennet at 15:4 g=L of milk. The experimental conditions for each system were selected in order to achieve gelation without syneresis. Coagulation kinetics were performed at 30 C. 2. Rheology Gel formation was monitored using a controlled-stress rheometer (Carri-Med CS 50, TA Instruments, Guyancourt, France) with cone-and-plate geometry (cone diameter 4 cm, angle 3 58 0 ). The bottom plate was fitted with a Peltier temperature controller that
Investigation of Oil–Water Interfaces
275
allowed regulation of the temperature at 30 C. The surface of the sample was covered with silicone oil to prevent evaporation. The storage modulus (G 0 ) was recorded at a frequency of 1 Hz under 0.015 strain amplitude until stabilization of the protein network. In order to reduce stress in the sample, G 0 recording started just before the gelation time which corresponds to the time at which G 0 deviated from the baseline. Data were collected and rheological parameters were calculated using Carri-Med 50 software. For each system, the experiments were performed in triplicate. 3.
Front-Face Fluorescence Spectroscopy and Mathematical Processing of the Spectra Fluorescence spectra were recorded using an SLM 4800 spectrofluorimeter (Bioritech, Chamarande, France) fitted with a thermostat-controlled (30 C) front-surface accessory. The incidence angle of the excitation radiation was 60 . Coagulation kinetics were performed in a quartz cuvette 1 cm 1 cm. All spectra were corrected for instrumental distortions in excitation using a rhodamine cell in the reference channel. Vitamin A was selected as intrinsic probe of fat globules. The excitation spectrum of vitamin A (250 to 350 nm) was recorded with emission wavelength set at 410 nm. The spectra of vitamin A were recorded throughout the whole coagulation time (i.e., 5 h). For the GDL and rennet systems, the excitation spectrum of vitamin A was recorded every 5 min during the first 3 h and every 10 min for the last 2 h. Considering the mixed system, a spectrum was collected every 5 min during the first, third, and fourth hours and every 10 min for the second and fifth hours. Three coagulation kinetics were performed for each coagulation system. To reduce intensity effects, the data were normalized by reducing the area under each spectrum to a value of 1 [42]. Principal component analysis (PCA) was applied to the normalized data. This method is well suited to optimize the description of the fluorescence data sets by extracting the most useful data and rejecting the redundant ones [43]. From a data set, PCA assesses principal components and their corresponding spectral pattern. The principal components are used to draw maps that describe the physical and chemical variations observed between the samples. Software for PCA has been written by D. Bertrand (INRA Nantes) and is described elsewhere [44]. B.
Results and Discussion
1.
Investigation of Protein–Lipid Interaction Development During Acid-Induced Milk Coagulation Kinetics
Fluorescent properties of fluorophores are very sensitive to changes of environment [61]. Applications of front-face fluorescence to food systems have been scarce due to the complexity of these systems and to the lack of familiarity with the technique principles among the food scientists. However, the potential for research and quality control applications of this technique to food systems is enormous. Recently, it has been reported that the shape of the vitamin A excitation spectrum is correlated with the physical state of the triglycerides in the fat globules of an emulsion [20]. If structural changes occur in fat globules during cheese ripening, front-face fluorescence should allow one to characterize them. As a consequence, vitamin A fluorescence properties may allow one to characterize the development of protein–fat globule interaction during milk coagulation. It has been reported that the shape of the excitation spectrum of vitamin A is modified following milk homo-
276
Dufour et al.
FIG. 11 Vitamin A excitation spectra between 250 and 350 nm (emission wavelength: 410 nm) recorded during the coagulation kinetics for GDL system at 0 (—), 120 ( ), and 300 (---) min.
genization or pasteurization. These changes are induced by the binding at the fat–water interface of milk proteins, i.e., caseins and whey proteins [5]. The excitation fluorescence spectra of vitamin A located in the fat globules of milk showed a maximum of 322 nm and two shoulders at 309 and 296 nm. As shown in Fig. 11, the shape of the spectra changes during the kinetics of acid-induced milk coagulation. Between 0 and 300 min, the shapes of the spectra are characterized by a decrease of the intensities at 322 nm and 310 nm and an increase of the intensity at 296 nm. These changes indicate that the environment of the fluorescent probe is modified during acid-induced coagulation of milk. In order to visualize all the data collection (50 spectra), PCA was applied to the set of normalized fluorescence spectra. The first principal component took into account 96% of the total variation and discriminated between the samples as a function of time [62]. The spectra recorded at the beginning of the kinetics have negative scores, whereas positive scores were observed or spectra recorded at the end of the kinetics. The examination of the spectral pattern associated wit the principal component 1 showed an opposition between a positive peak at 296 nm and a negative peak at 322 nm. This pattern is in agreement with a fluorescence transfer between vitamin A and proteins during the time course of the acidinduced gelation. Moreover, the plot of the changes of fluorescence intensity at 322 nm versus the pH evolution during the kinetics shows that any change in the fluorescence intensity is observed between pH 6.7 and 5.1. For pH below 5.1, the fluorescence intensity at 322 nm decreases drastically. This second phase begins with gelation of the milk [62]. A similar trend was observed when the emission fluorescence intensity of tryptophan at 320 nm was plotted versus pH [51].
Investigation of Oil–Water Interfaces
277
These modifications in the fluorescence properties of milk proteins can be paralleled with the well-known effects of pH on micelle structure and milk gelation [48–50,55,63,64]. Indeed, the alteration of micelle structure during milk acidification involves two main steps. The first step from pH 6.7 to pH 5.3–5.1 is characterized by the solubilization of micellar calcium phosphate [48–50]. Between pH 5.8 and pH 5.3–5.1, solubilization of micellar calcium becomes faster and at pH 5.3–5.1, practically all the micellar inorganic phosphate is transferred to the serum phase. In this study, the end of the first phase corresponds to pH 5.1. It has also been reported that the release of calcium phosphate on lowering the pH involves the dissociation either of -caseins only from micelles into the serum phase [50,64] or of all caseins (s1-, s2-, -, and -caseins) from the micelles [49,63]. However, casein dissociation is temperature dependent and, at 30 C, less than 10% of total caseins dissociate [63]. Moreover, this first phase is characterized by a diminution in micelle voluminosity [49,50,64] from pH 6.7 to pH 6.0–5.8 and by an increase in the voluminosity of casein micelles with a maximum at pH 5.4–5.2, which is attributed to the swelling of the micelles and the dissociation of casein micelles [50,64]. During this first step, a partial micellar disintegration takes place, which causes a looseness in the micelle. The second stage from pH 5.2 to pH 4.45 is marked mainly by the reabsorption of caseins and the aggregation of micelles involving the formation of new particles completely different in structure and composition from the original micelles [49,55]. These changes induce a large decrease in the voluminosity of casein micelles, with a minimum at pH 4.6 [50,64], and from 4.6 the voluminosity increases again [64], leading to the formation of the final network of the acid milk gel [49,55]. The change in fluorescence intensity at 320 nm parallels the changes of casein micelle structure induced by lowering of the pH. It appears that the change in the fluorescence intensity at 320 nm reflects pH-induced physicochemical changes of casein micelles and in particular, structural changes in the micelles. The alteration of casein micelle structure results in casein–fat globule interaction inducing specific modifications in the shape of the fluorescence spectra of vitamin A. The PCA map defined by the principal components 1 and 2 describes the modifications of protein–fat globule interactions during milk coagulation. 2.
Structural Evolution During the Three Different Coagulation Processes The vitamin A excitation spectra of the three systems were pooled in one matrix and this table was analyzed by PCA. Figure 12 presents a PCA similarity map defined by the principal components 1 and 2 for vitamin A fluorescence spectral data of GDL, rennet, and mixed systems. The first two principal components account for 99.5% of the total variability, with a predominance of component 1 (93%). Discrimination among the three systems is observed on the map. The results clearly show that the first principal component discriminates among the spectra as a function of time, whereas the principal component 2 allows one to discriminate among the three coagulation systems. Figure 13 shows the spectral pattern associated with principal component 1. Its shape is similar to that described above (Section V.B.1) and is characterized by an opposition between a negative peak at 296 nm and a positive peak at 322 nm. Again, these data indicate that protein–fat interactions develop during the cogulation kinetics of the three systems. It appears that vitamin A is a valuable probe to monitor the changes in fat–protein interactions during milk coagulation. From the map defined by principal components 1 and 2, we also conclude that the interactions developed during the gelation are different for the three coagulation systems.
278
Dufour et al.
FIG. 12 Principal component analysis similarity map defined by the principal components 1 and 2 for vitamin A excitation fluorescence spectral data. Sample coding: L, R, and X stand for the GDL, rennet, and mixed systems, respectively; the digits are for the time elapsed since the beginning of the kinetics.
FIG. 13
Spectral pattern corresponding to the principal component 1.
Investigation of Oil–Water Interfaces
3.
279
Kinetics of Gelation Studied by Dynamic Rheological Measurements
In order to check that different gel structures – as deduced from fluorescence experiments, induce different rheological properties, rheological measurements were performed during the milk coagulation process by the recording of the G 0 modulus [51]. The changes in the G 0 modulus over the 600 min experiment are very different for the three coagulation procedures. For the rennet system, initiation of gel formation begins at 180 min and the G 0 modulus increases slowly and reaches a plateau after 470 min. The GDL system has a gelation time of 110 min and the G 0 modulus increases more rapidly to reach a plateau after 270 min. For the mixed system, the gelation time is at 190 min and the change in the G 0 modulus is more rapid, exhibiting a gel strength greater than that of the other systems. Moreover, a sudden decrease in G 0 is observed at 240 min. After the addition of rennet (at 120 min of acidification), the mixed system shows a shorter gelation time and a greater strength of gel than the rennet system. The differences observed result from the differences in pH between the two systems. Whereas the pH is 6.7 for the rennet system, the mixed system is pH 6.1 at the time of renneting. It has been reported [46,47] that the firmness of a renneted-milk curd reaches a maximum at about pH 6. Increased activity of the chymosin increases the enzymatic phase, whereas diminution of micelle stability, linked to both charge neutralization and the liberation of the calcium, increases the aggregation reaction. On the other hand, the gel obtained with the GDL system was weaker, since lowering of the pH involves disintegration of the micelles: the resulting gel consists of dispersed clusters of demineralized caseins, devoid of suitable binding to develop a contraction strength [65]. The mixed system is characterized by a rapid increase in the G 0 modulus followed by a sudden decrease. This study has shown that the process used to coagulate milk has a broad effect on fat globule–protein interactions and on the molecular structure of the gel. In addition we have shown that the different molecular structures of the three coagula correspond to different rheological properties.
VI.
CONCLUSION
The aim of this review was to summarize those aspects of fluorescence spectroscopy that may have value for solving problems in food science and technology. The techniques described, which are mainly based on front-face fluorescence spectroscopy coupled with multidimensional statistical methods, have been illustrated by examples taken from the literature and the work done in our laboratory. Although fluorescence spectroscopy is a technique whose theory and methodology have been extensively exploited for studies of both chemistry and biochemistry, the utility of fluorescence spectroscopy for molecular studies has not yet been fully recognized in food science. Fluorescence spectroscopy has the same potential to address molecular problems in food science as in the biochemical science field, because the scientific questions that need to be answered are closely related. We hope that this coverage will introduce a novel class of techniques in the emulsion and gel fields.
280
Dufour et al.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.
40.
M. C. Phillips. Food Technol. 35:50 (1981). J. A. Hunt and D. G. Dalgleish. Food Hydrocolloids 8:175 (1994). D. F. Darling and D. W. Butcher. J. Dairy Res. 45:197 (1977). J. G. Davis, in Cheese (J. A. Churchill, ed.), vol. 1, London, 1965. E. Dufour and A. Riaublanc. Lait 77:657 (1997). M. A. Rudan, D. M. Barbano, and P. S. Kinstedt. J. Dairy Sci. 81:2077 (1998). A. H. Jana and K. G. Upadhyay. Aust. J. Dairy Technol. 47:72 (1992). L. E. Metzger and V. V. Mistry. J. Dairy Sci. 77:3506 (1994). D. G. Dalgleish. Coll. Surf. 46:141 (1990). A. R. Mackie, J. Mingins, and R. Dann, in Food Polymers, Gels and Colloids, (E. Dickinson, ed.), Royal Society of Chemistry, Cambridge, 1991, pp. 96–111. T. A. Horbett and J. L. Brash, in Proteins at interfaces: Physico-chemical and biochemical studies, (J. L. Brash and T. A. Horbett, eds.) ACS Symposium series 343, Washington DC, 1987, pp. 1–33. L. J. Harvey, G. Bloomberg, and D. C. Clark. J. Coll. Interface Sci. 170:161 (1995). L. J. Smith and D. C. Clark. Biochim. Biophys. Acta 1121:111 (1992). A. Kondo, S. Oku, and K. Higashitani. J. Coll. Interface Sci. 143:214 (1991). D. G. Cornell. J. Coll. Interface Sci. 88:536 (1982). D. G. Cornell and D. L. Patterson. J. Agric. Food Chem. 37:1455 (1989). D. C. Clark, L. J. Smith, and D. R. Wilson. J. Colloid Interface Sci. 121:136 (1988). V. Hlady, D. R. Reinecke, and J. D. Andrade. J. Colloid Interface Sci. 111:555 (1986). V. Hlady and J. D. Andrade. Colloids Surf. 32:359 (1988). E. Dufour, C. Lopez, A. Riaublanc, and N. Mouhous Riou. Agoral 10:209 (1998). C. Genot, F. Tonetti, T. Montenay-Garestier, and R. Drapon. Sci. Alim. 12:199 (1992). C. A. Parker, in Photoluminescence of Solutions with Applications to Photochemistry and Analytical Chemistry (C. A. Parker, ed.), Elsevier, Amsterdam, 1968, pp. 128–302. W. E. Blumberg, F. H. Doleiden, and A. A. Lamola. Clin. Chem. 26:409 (1980). R. E. Hirsch and R. L. Nagel. Anal. Biochem. 176:19 (1989). C. Genot, F. Tonetti, T. Montenay-Garestier, D. Marion, and R. Drapon. Sci. Alim. 12:687 (1992). W. Lindberg, J. A. Persson, and S. Wold. Anal. Chem. 55:643 (1983). J. Leaver and D. G. Dalgleish. Biochim. Biophys. Acta 1041:217 (1990). C. Castelain and C. Genot. Biochim. Biophys. Acta 1199:59 (1994). M. Shimizu, A. Ametani, S. Kaminogawa, and K. Yamauchi. Biochim. Biophys. Acta 869:259 (1986). S. Kaminogawa, M. Shimizu, A. Ametani, S. W. Lee, and K. Yamauchi. J. Amer. Oil. Chem. Soc. 64:1688 (1987). A. Ametani, M. Shimizu, S. Kaminogawa, and K. Yamauchi. Agric. Biol. Chem. 53:1297 (1989). E. Dufour, M. Dalgalarrondo, and L. Adam. J. Coll. Interface Sci. 207:264 (1998). F. Yang and D. G. Dalgleish. J. Coll. Interface Sci. 196:292 (1997). P. Walstra, in Advanced Dairy Chemistry – 2. Lipids (P. F. Fox, ed.), Elsevier, New York, 1995, pp. 131–178. S. K. Sharma and D. G. Dalgleish. J. Agric. Food Chem. 41:1407 (1993). J. M. Aguilera and H. G. Kessler. Milchwissenschaft 43:411 (1988). T. van Vliet and A. Dentenet-Kikkert. Neth. Milk Dairy J. 36:261 (1982). Y. L. Xiong and J. E. Kinsella. Milchwissenschaft 46:207 (1991). C. Lopez. Influence de la nature de l’interface matie`re grasse/eau de laits reconstitue´s sur la cine´tique de coagulation et les caracte´ristiques du coagulum. Stage de DEA et d’inge´nieur I.S.T.A.B., Universite´ de Bordeaux, 1997. C. Lopez and E. Dufour, in preparation.
Investigation of Oil–Water Interfaces
281
41. J. C. Mercier, J. L. Maubois, S. Poznanski, and B. Ribadeau Dumas. Bull. Soc. Chim. Biol. 50:521 (1968). 42. D. Bertrand and C. N. G. Scotter. Appl. Spectrosc. 46:1420 (1992). 43. I. T. Jollife, Principal Component Analysis, Springer, New York, 1986. 44. D. Bertrand, M. Lila, V. Furstoss, P. Robert, and G. Downey. J. Sci. Food Agric. 41:299 (1987). 45. D. Frapin, E. Dufour, and T. Haertle´. J. Prot. Chem. 12:433 (1993). 46. P. F. Fox and D. M. Mulvihill, in Food Gels: Casein (P. Harris, ed.), Elsevier Applied Science, London, 1990, pp. 121–173. 47. A. C. M. van Hooydonk, H. G. Hagedoorn, and I. J. Boerrigter. Neth. Milk Dairy J. 40:281 (1986). 48. D. G. Dalgleish and A. J. R. Law. J. Dairy Res. 56:727 (1989). 49. E. Gastaldi, A. Lagaude, and B. Tarodo de la Fuente. J. Food Sci. 61:59 (1996). 50. A. C. M. van Hooydonk, I. J. Boerrigter, and H. G. Hagedoorn. Neth. Milk Dairy J. 40:297 (1986). 51. S. Herbert, A. Riaublanc, B. Bouchet, D. J. Gallant, and E. Dufour. J. Dairy Sci. 82:2056 (1999). 52. L. G. B. Bremer, T. van Vliet, and P. Walstra. J. Chem. Soc. Faraday Trans. 85:3359 (1989). 53. N. A. Bringe and J. E. Kinsella, in Developments in Food Proteins (B. J. F. Hudson, ed.), Elsevier Applied Science, London, 1987, pp. 159–194. 54. D. G. Dalgleish, in Advanced Dairy Chemistry. Vol 1. Proteins (P. F. Fox, ed.), Elsevier Applied Science, London, 1986, pp. 579–619. 55. I. Heertje, J. Visser, and P. Smits. Food Microstruct. 4:267 (1985). 56. S. P. F. M. Roefs, P. Walstra, D. G. Dalgleish, and D. S. Horne. Neth. Milk Dairy J. 39:119 (1985). 57. S. G. Dalgleish and D. S. Horne. Milchwissenschaft 36:417 (1991). 58. A. M. Hartman and L. P. Dryden, in Fundamentals of Dairy Chemistry (B. H. Webb, A. H. Johnson, and J. A. Alford, eds.), The Avi Publishing Company, Westport, CT, 1978, pp. 325– 401. 59. E. Dufour, C. Genot, and T. Haertle´. Biochim. Biophys. Acta 1205:105 (1994). 60. E. Dufour, M. C. Marden, and T. Haertle´. FEBS Lett. 277:223 (1990). 61. A. G. Marangoni. Food Res. Int. 25:67 (1992). 62. S. Herbert. Caracte´risation de la structure mole´culaire et microscopique de fromages a` paˆte molle. Analyse multivarie´e des donne´es structurales en relation avec la texture. The`se de Doctorat, Universite´ de Nantes, Nantes, 1999. 63. D. G. Dalgleish and A. J. R. Law. J. Dairy Res. 55:529 (1988). 64. T. H. M. Snoeren, H. J. Klok, A. C. M. Van Hooydonk, and A. J. Damman. Milchwissenschaft 39:461 (1984) 65. J. P. Ramet, in Le Fromage (A. Eck and J. C. Gillis, eds.), 3rd edn, Lavoisier, Paris, France, 1997, pp. 44–47.
12 Scanning Electrochemical Microscopy as a Local Probe of Chemical Processes at Liquid Interfaces ANNA L. BARKER, CHRISTOPHER J. SLEVIN, PATRICK R. UNWIN, and JIE ZHANG Department of Chemistry, University of Warwick, Coventry, England
I.
INTRODUCTION
In just a few years, scanning electrochemical microscopy (SECM) has emerged as a powerful technique for investigating chemical kinetics at liquid interfaces, as described in several recent reviews [1–3]. The considerable interest in SECM is that it overcomes many of the problems inherent in conventional methodologies for studying reactions at liquid–liquid interfaces, particularly charge transfer at the interface between two immiscible electrolyte solutions (ITIES). SECM employs an ultramicroelectrode (UME) [4–7], typically a diskshaped electrode with a diameter on the micrometer scale, positioned in close proximity to a target interface, to initiative and/or monitor an interfacial process of interest. The response of the UME probe provides local kinetic and chemical information. In this chapter we highlight the SECM techniques that can be used to study electron transfer (ET), ion transfer (IT), and various molecular transfer processes at liquid–liquid interfaces. We also discuss developments in the methodology that facilitate the investigation of liquid–gas interfaces and molecular monolayers at liquid surfaces. We begin by reviewing the principles of SECM methods, and present an overview of the instrumentation needed for experimental studies. A major factor in the success of SECM, in quantitative applications, has been the parallel development of theoretical models for mass transport. A detailed treatment of the theory for the most common SECM modes that have been used to study liquid interfaces is therefore given, along with key results from these models. A comprehensive assessment of the applications of SECM is provided and the prospects for the future developments of the methodology are highlighted.
II.
PRINCIPLES AND MODES OF OPERATION
One of the attractive features of SECM is that the UME tip response is based on wellestablished electrochemical principles, making the technique quantitative. This aspect of SECM can be illustrated by considering the case of simple diffusion-limited electrolysis at an amperometric disk-shaped tip. When the tip is positioned a long way from the target 283
284
Barker et al.
FIG. 1 (a) Schematic of the hemispherical diffusion-field established for the steady-state diffusionlimited oxidation of a solution species, Red, at a disk-shaped UME, giving rise to a current ið1Þ. (b) When the UME is positioned close to an inert target interface, diffusion of Red is hindered and the current, i, is less than that measured in (a).
interface, d > 10a, where d is the tip–interface distance and a is the electrode radius, it behaves as a conventional UME. In this situation, a steady-state current, ið1Þ, is rapidly established due to hemispherical diffusion of the target species [Red in Fig. 1(a)]. As the tip is brought close to an interface which is inert with respect to the species involved in the electrode process, diffusion to the UME becomes hindered [Fig. 1(b)] and the steady-state current, i, decreases compared to ið1Þ. In general, measurements of i=ið1Þ as a function of d are termed ‘‘approach curves,’’ This type of experiment has been used most to study liquid interfaces. Since the dependence of the i=ið1Þ ratio on d and the tip geometry can be calculated theoretically [8], simple current measurements with mediators which do not interact at the interface can be used to determine d. When either the solution species of interest, or electrolysis product(s), interact with the target interface, the hindered mass transport picture of Fig. 1(b) is modified. The effect is manifested in a change in the tip current, which is the basis of using SECM to investigate interfacial reactivity. Hitherto, there are primarily three ways in which an amperometric electrode can be used to simultaneously induce and monitor interfacial processes. These are illustrated schematically in Fig. 2 for the most general case where diffusion may occur in both of the liquid phases, which comprise the interface of interest. The feedback mode [Fig. 2(a)] is one of the most widely used SECM techniques, applicable to the study of interfacial ET processes. The basic idea is to generate a species at the tip in its oxidized or reduced state [generation of Ox1 in Fig. 2(a)], typically at a diffusion-controlled rate, by electrolysis of the other half of a redox couple (Red1 ). The tip-generated species diffuses from the UME to the target interface. If it undergoes a redox
SECM as a Local Probe of Chemical Processes
285
FIG. 2 Principal methods for inducing and monitoring interfacial processes with SECM: (a) feedback mode, (b) induced transfer, and (c) double potential step chronoamperometry.
reaction, which converts it to the original form, it diffuses back to the tip, thereby establishing a feedback cycle and enhancing the current at the UME. The theory of this mode is developed in Section IV and applications are discussed in Section V. SECM-induced transfer [SECMIT; Fig. 2(b)] can be used to characterize reversible phase transfer processes at a wide variety of interfaces. The basic idea is to perturb the process, initially at equilibrium, through local amperometry at the UME. Hitherto, diffusion-limited electrolysis has mainly been used in conjunction with metal tips, but ion transfer voltammetric probes (discussed briefly in Section III, and in detail in Chapter 15) can also be used. The application of a potential to the tip, sufficient to deplete the
286
Barker et al.
species of interest in phase 1 [oxidation of Red1 to Ox1 in Fig. 2(b)], drives the transfer of species Red from phase 2 to phase 1. Collection of this species at the tip enhances the current flow compared to the situation where there is no net transfer across the target interface and species Red reaches the tip by hindered diffusion through phase 1 only. For a given tip–interface separation, the overall current response is governed by diffusion in the two phases and the interfacial kinetics [9]. The technique was originally employed in a time-dependent potential step chronoamperometric mode to probe desorption processes at solid–liquid interfaces [10], and was subsequently shown to be a powerful probe of dissolution kinetics under both steady-state and time-dependent operation [11–17]. As will be discussed in Sections V and VI, the technique has very recently proven a powerful approach for probing the kinetics of solute transfer across interfaces formed between immiscible liquids [9,18] and between liquids and gases [19]. When there are no kinetic limitations to the interfacial transfer process, SECMIT is also an effective analytical technique for determining the permeability, concentration, and diffusive properties of a solute in a phase, without the UME having to enter or contact that phase, as discussed in Section IV. This is obviously advantageous for situations where direct voltammetric measurements would otherwise be impractical, for example, due to high resistivity or a limited solvent window. This aspect of SECMIT has also been used to great effect where the intimate presence of the UME would damage the structural integrity of the sample under investigation, as in the case of biological tissues [20,21]. To expand the range of interfacial processes that can be studied with SECM, our group has recently introduced double potential step chronoamperometry (DPSC) for initiating and monitoring reactions on a local scale. When employed at UMEs, DPSC has proven a powerful technique for characterizing the lifetime of transient species involved in solution processes down to the microsecond time scale [22] and the diffusion coefficients of electrogenerated species, independent of knowledge of the concentration and number of electrons transferred [23]. In the SECM configuration, the follow-up chemical reaction involving the tip-generated species is effectively confined to the interface under study. The basic concept [Fig. 2(c)] is to employ the UME to generate a reactive species in an initial (forward) step for a fixed period. The potential is stepped from a value where there are no redox reactions to one where Red1 is oxidized to Ox1 at a diffusioncontrolled rate. During this step, the tip-generated species (Ox) diffuses away from the UME and intercepts the interface. If Ox interacts with the interface (e.g., by adsorption, absorption, or a chemical reaction), its concentration profile is modified compared to the situation where there is no interaction and Ox simply leaks out of the tip–interface gap by hindered diffusion. Consequently, when the potential is reversed, in a final step to collect Ox by electrolysis, the flux at the UME, and the corresponding current–time characteristics, depend strongly on the nature of the interaction of species Ox with the target interface. The application of this technique to probe transfer processes at liquid–liquid and liquid–air interfaces will be discussed further in Sections V and VI.
III.
INSTRUMENTATION
A.
Probes
SECM employs a mobile UME tip (Fig. 3) to probe the properties of a target interface. Although both amperometric and potentiometric electrodes have found application in SECM, amperometry – in which a target species is consumed or generated at the probe UME – has found the most widespread use in kinetic studies at liquid interfaces, as
SECM as a Local Probe of Chemical Processes
287
FIG. 3 (a) Block schematic of the typical instrumentation for SECM with an amperometric UME tip. The tip position may be controlled with various micropositioners, as outlined in the text. The tip potential is applied, with respect to a reference electrode, using a potential programmer, and the current is measured with a simple amplifier device. The tip position may be viewed using a video microscope. (b) Schematic of the ‘‘submarine’’ UME configuration, which facilitates interfacial electrochemical measurements when the phase containing the UME is more dense than the second phase. In this case, the glass capillary is attached to suitable micropositioners and electrical contact is made via the insulated copper wire shown.
288
Barker et al.
discussed in Section II. Typically, amperometry involves electrolysis at a solid UME, usually a disk-shaped electrode, with a diameter of 0.6–25 m. This type of electrode is readily fabricated by sealing a wire of the material of interest in a glass capillary, making an electrical connection, and polishing the end flat [24–28]. Pt, Au, and C electrodes have been successfully fabricated in this way. For most SECM studies, the ratio of the diameter of the entire tip end (electrode plus surrounding insulator, 2rs ) to that of the electrode itself, 2a, RG ¼ rs =a is typically around 10. A polarized ITIES can also be used to drive ET processes [29], and microelectrode probes for use in SECM may be fabricated using capillary tips to support the liquid–liquid interface. This type of probe also enables the amperometric detection of ions which cannot be determined by conventional electrolysis at solid electrodes, e.g., Kþ [30,31]. Such probes have been used in SECM [29,32,33], but will not be considered further here, as they are discussed in detail in Chapter 15. When a liquid–liquid interface is to be investigated using an electrode in the more dense phase, or for studies at the water–air interface, a ‘‘submarine’’ electrode can be deployed [18,19,34], depicted schematically in Fig. 3(b). In this case, the electrode is inverted in the cell, such that the tip points upwards, and an insulated connection is made through the solution. Metal electrodes down to the nanometer scale can also be fabricated by sealing an etched Pt or Pt–Ir wire in a suitable insulating material, leaving just the etched end exposed [35–37].
B.
Positioning
The tip is attached to positioners, which allow it to be moved and positioned relative to the interface under investigation. A variety of positioners have been employed in SECM instruments, with the choice depending on the type of measurement and spatial resolution required. For the highest (nanometer) resolution, piezoelectric positioners similar to those used in STM are mandatory [38]. In contrast to SECM at solid–liquid interfaces, where high-resolution x, y, z positioning and scanning is usually required, most SECM measurements at liquid–liquid interfaces simply involve the translation of a tip towards and/or away from a specific spot on an interface, in the perpendicular (z) direction. In this situation, it is only necessary to have high-resolution z-control of the tip, typically using a piezoelectric positioner, while manual stages suffice for the other two axes [2,9,18]. The use of a video microscope, aligned such that the electrode may be observed from the side, has proved useful in facilitating the positioning of the UME relative to the interface [9,18]. As mentioned above, when the electrode is positioned in the more dense liquid phase, a ‘‘submarine’’ electrode may be employed. An alternative configuration is to form the interface at the tip of a capillary positioned in the base of the cell, through which the lower density phase may be delivered. This approach allows the use of conventional UMEs [39].
C.
Electrochemical Instrumentation
The electrochemical circuitry required for SECM is relatively straightforward. Since the interface is not generally externally polarized in SECM measurements of liquid–liquid interfaces, a simple two-electrode system suffices (Fig. 3). A potential is applied to the tip, with respect to a suitable reference electrode, to drive the process of interest at the tip and the corresponding current that flows is typically amplified by a current-to-voltage converter.
SECM as a Local Probe of Chemical Processes
IV.
289
THEORY
The success of SECM methodologies in providing quantitative information on the kinetics of interfacial processes relies on the availability of accurate theoretical models for mass transport and coupled kinetics, to allow the analysis of experimental data. The geometry of SECM is not conducive to exact analytical solution and hence a number of semianalytical [40,41], and numerical [8,10,42–46], methods have been introduced for a variety of problems. The treatment of the two-phase SECM problem applicable to immiscible liquid– liquid systems, requires a consideration of mass transfer in both liquid phases, unless conditions are selected so that the phase that does not contain the tip (denoted as phase 2 throughout this chapter) can be assumed to be maintained at a constant composition. Many SECM experiments on liquid–liquid interfaces have therefore employed much higher concentrations of the reactant of interest in phase 2 compared to the phase containing the tip (phase 1), so that depletion and diffusional effects in phase 2 can be eliminated [18,47,48]. This has the advantage that simpler theoretical treatments can be used, but places obvious limitations on the range of conditions under which reactions can be studied. In this section we review SECM theory appropriate to liquid–liquid interfaces at the full level where there are no restrictions on either the concentrations or diffusion coefficients of the reactants in the two phases. Specific attention is given to SECM feedback [49] and SECMIT [9], which represent the most widely used modes of operation. The extension of the models described to other techniques, such as DPSC, is relatively straightforward. For the two modes of interest in this section we first describe the relevant diffusion equations and boundary conditions and then present results from numerical simulations obtained using the alternating direction implicit finite-difference method (ADIFDM) [50]. This is an efficient digital technique for solving two-dimensional time-dependent problems. It was first used to model diffusion at UMEs by Heinze [51–53] and for SECM by Unwin and Bard [43], and has since proved to be a versatile method for treating a wide variety of steady-state and transient problems in the SECM geometry, particularly by our group. The advantages of the ADIFDM are typical of most successful digital methods; involving relatively simple algorithms with a high efficiency of computation and flexibility that allows easy adaptation to different kinetic situations and SECM operating modes. Most SECM experiments at liquid–liquid interfaces have principally involved the determination of the steady-state tip current response as a function of the separation between the tip and the interface (approach curve measurements). However, in some situations complementary information can be gleaned from the transient behavior (as illustrated below for SECMIT). We therefore describe models for the time-dependent problem from which the steady-state characteristics can be developed from the longtime limit. All the simulations reported in this chapter relate to a disk-shaped UME, characterized by RG ¼ 10, which is typical of the probes used in SECM experiments and for most previous theoretical treatments. A.
Feedback Mode
In SECM feedback studies of ET reactions at ITIES, four main processes contribute to the magnitude of the tip current (Fig. 4); (1) mediator diffusion in phase 1 between the tip and the ITIES, (2) mediator diffusion in phase 2, (3) the rate of the ET reaction at the ITIES, and (4) charge compensation by ion transport across the ITIES.
290
Barker et al.
FIG. 4 Schematic of SECM feedback at an ITIES with the co-ordinate system used for the theoretical model. The co-ordinates r and z are measured from the center of the UME in the radial and normal directions, respectively. The UME is characterized by an electrode radius, a, while rs is the distance from the center of the electrode to the edge of the surrounding insulating sheath. The ITIES is located at a distance, d, from the UME in the z direction. Species Red1 and Ox1 are confined to phase 1, while species Red2 and Ox2 are present in phase 2.
Under conditions where mediator diffusion in phase 2 and ion transport across the ITIES are nonlimiting [conditions (2) and (4)], the steady-state tip current response has been found to be accurately described by the following equations [44,47,48]: ! ITins k k IT ¼ IS 1 c þ ITins ð1Þ IT ISk ¼
0:78377 ½0:68 þ 0:3315 expð1:0672=LÞ þ Lð1 þ 1=Þ ½1 þ FðL; Þ
ð2Þ
where ITc , ITk , and ITins denote the normalized tip currents for diffusion-controlled regeneration of a redox mediator, finite substrate kinetics and insulating subtrate (i.e., no mediator regeneration), respectively, and ISk is the kinetically controlled normalized substrate current. These various currents are normalized with respect to the steady-state tip current, ið1Þ. The remaining terms in these two equations are defined as follows: L ¼ d=a is the normalized tip–substrate separation; ¼ kf d=D1 , where kf is the apparent heterogeneous rate constant (cm s1 ) for the ET reaction at the ITIES and D1 is the diffusion coefficient of the redox mediator in phase 1; FðL; Þ is given by FðL; Þ ¼ ð11 þ 7:3Þ=½ð110 40LÞ
ð3Þ
Approximations for the quantities ITc and ITins have been given previously [54]: 0:78377 þ 0:3315 expð1:0672=LÞ þ 0:68 ð4Þ L ¼ 1= 0:15 þ 1:5358=L þ 0:58 expð1:14=LÞ þ 0:0908 exp½ðL 6:3Þ=ð1:017LÞ ð5Þ
ITc ¼ ITins
SECM as a Local Probe of Chemical Processes
291
Although the use of this model considerably simplifies the quantitative analysis of data, it implicitly assumes that phase 2 is maintained at a constant composition during a measurement. Henceforth, we refer to the model described by Eqs. (1)–(5) as the constantcomposition model. 1.
Beyond the Constant-Composition Model
To extend the applicability of the SECM feedback mode for studying ET processes at ITIES, we have formulated a numerical model that fully treats diffusional mass transfer in the two phases [49]. The model relates to the specific case of an irreversible ET process at the ITIES, i.e., the situation where the potentials of the redox couples in the two phases are widely separated. A further model for the case of quasireversible ET kinetics at the ITIES is currently under development. For the case where the oxidized form of a redox species, Ox1 , is electrolytically generated at the tip in phase 1 from the reduced species, Red1 , the reactions at the tip and the ITIES are: Tip: ITIES:
Red1 ne ! Ox1 k12 Ox1 þ Red2 ! Ox2 þ Red1
ð6Þ ð7Þ
where Red2 and Ox2 denote, respectively, the reduced and oxidized form of the redox couple confined to phase 2 and k12 is the heterogeneous bimolecular rate constant (cm s1 M1 ). Under constant-composition conditions, k12 ¼ kf =cRed2 where cRed2 denotes the initial bulk concentration of Red2 in phase 2. In the development of the model, the diffusion coefficients of Red1 and Ox1 are considered to be equal, i.e., DRed1 ¼ DOx1 with only the reactant, Red1 , initially present in phase 1, at concentration cRed1 . This assumption allows the principle of mass conservation to be invoked in phase 1: 0 r rs ; 0 < z < d:
cOx1 ðr; zÞ ¼ cRed1 cRed1 ðr; zÞ
ð8Þ
where cOx1 ðr; zÞ and cRed1 ðr; zÞ are the spatial-dependent concentrations of Ox1 and Red1 , respectively, within the region of interest (see Fig. 4), defined in terms of r and z, which are the co-ordinates in the directions radial and normal to the electrode surface measured from the center of the electrode. The use of Eq. (8) simplifies the problem to the consideration of species Red1 and Red2 alone. Although the diffusion coefficients of Red1 and Ox1 may differ slightly in real systems [55–59], it has been shown that under steady-state conditions (the primary interest in this application) the ratio DOx1 =DRed1 has no effect on the diffusion-limited positive feedback current characteristics [55]. Time-dependent diffusion equations, appropriate to the axisymmetrical cylindrical geometry of the SECM can be written for the species of interest in each phase, " # @cRed1 @2 cRed1 1 @cRed1 @2 cRed1 ¼ DRed1 þ Phase 1: þ ð9Þ r @r @t @r2 @z2 " # @cRed2 @2 cRed2 1 @cRed2 @2 cRed2 ¼ DRed2 þ Phase 2: þ ð10Þ r @r @t @r2 @z2 where cRed2 and DRed2 are, respectively, the concentration and diffusion coefficient of species Red2 in phase 2 and t is time. In order to calculate the tip current response, the diffusion equations must be solved subject to the boundary and initial conditions of the system. Prior to the potential step,
292
Barker et al.
phase 1 and 2 contain only species Red1 and Red2 , respectively. The initial condition is thus t ¼ 0;
0 r rs ; 0 z d:
cRed1 ¼ cRed1
ð11Þ
0 r rs ; z d:
cRed2 ¼ cRed2
ð12Þ
At time t > 0, the potential of the UME tip is stepped from a value where no electrode reaction occurs, to one sufficient to drive the oxidation of Red1 at a diffusioncontrolled rate. Species Red1 is assumed to be inert with respect to the insulating glass sheath surrounding the electrode and to remain at bulk concentration values beyond the radial edge of the tip (throughout phase 1). In phase 2, species Red2 attains its bulk concentration for r > rs and at a semi-infinite distance from the electrode. Consequently, the exterior boundary conditions may be summarized as follows: 0 r a; z ¼ 0:
cRed1 ¼ 0
a < r rs ; z ¼ 0:
DRed1
@cRed1 ¼0 @z
ð13Þ ð14Þ
0 r rs ; z ! 1:
cRed2 ¼ cRed2
ð15Þ
r > rs ; 0 < z < d:
cRed1 ¼ cRed1
ð16Þ
r > rs ; z > d:
cRed2
ð17Þ
cRed2 ¼
Equations (16) and (17) are reasonable assumptions provided that RG 10 [8]. The axisymmetrical geometry of the SECM implies that there is no radial flux of the species at the cylindrical axis of symmetry: r ¼ 0; 0 < z < d: r ¼ 0; z > d:
@cRed1 ¼0 @r @cRed2 DRed2 ¼0 @r
DRed1
ð18Þ ð19Þ
The final internal boundary condition applies to the interface between phase 1 and phase 2, and relates the flux of species Red1 and Red2 , at the ITIES, to the rate of the second-order redox reaction occurring at the interface. z ¼ d; 0 r rs :
DRed1
@cRed1 @cRed2 ¼ DRed2 ¼ k12 cRed1 cRed1 cRed2 @z @z
ð20Þ
To obtain general solutions, the problem is reformulated in terms of the following dimensionless quantities: tDRed1 a2 r R¼ a z Z¼ a ¼
ð21Þ ð22Þ ð23Þ
SECM as a Local Probe of Chemical Processes
DRed2 DRed1 cRed ¼ i cRedi
¼ CRedi
293
ð24Þ ðinteger i ¼ 1 or 2Þ
ð25Þ
K¼
k12 acRed2 DRed1
ð26Þ
Kr ¼
cRed2 cRed1
ð27Þ
The UME current is related to the flux of Red1 at the electrode surface and hence the dimensionless current ratio for the tip UME is given by [12,14–16]: ð i 1 @CRed1 ¼ R dR ð28Þ ið1Þ 2 0 @Z Z¼0 where the steady-state diffusion-limited current at an inlaid disk electrode positioned at an effectively infinite distance from the interface is given by [60]: ið1Þ ¼ 4nFaDRed1 cRed1
ð29Þ
where n is the number of electrons transferred per redox event and F is Faraday’s constant. The numerical model developed to treat this problem [49], involves the parameters K, , Kr and the normalized tip–interface distance, L ¼ d=a. To develop an understanding of the factors governing the SECM feedback response, which is of importance in the interpretation of experimental data, we briefly describe the effect of these parameters on the tip current. A key aim is to define precisely the conditions under which the simpler constant-composition model Eqs. (1)–(5) can be used. 2. When Does the Constant–Composition Model Apply? The effect on the normalized approach curves of allowing Kr to take finite values is illustrated in Fig. 5, which shows simulated data for three rate constants, for redox couples characterized by ¼ 1. The rate parameters considered: K ¼ 100 (A), 10 (B), and 1 (C), are typical of the upper, medium, and lower constants that might be encountered in feedback measurements at liquid–liquid interfaces. In each case, values of Kr ¼ 1000 or 100 yield approach curves which are identical to the constant-composition model [44,47,48]. This behavior is expected, since the relatively high concentration of Red2 compared to Red1 ensures that the concentration of Red2 adjacent to the liquid–liquid interface is maintained close to the bulk solution value, even when the interfacial redox process is driven at a fast rate. For Kr 10, the normalized currents are lower than predicted by the constantcomposition model, particularly at close tip–interface separations, where the diffusion rate of the Red1 =Ox1 couple in phase 1 is highest and competes effectively with the diffusion of Red2 in phase 2. The deviation of the current from that predicted assuming constant-composition conditions becomes increasingly significant as Kr is reduced, resulting in increasing diffusional limitations from Red2 in phase 2. The constant-composition assumption breaks down for Kr 10, irrespective of the size of the rate constant characterizing the interfacial process (within the range considered).
294
Barker et al.
FIG. 5 Simulated normalized steady-state current as a function of tip-interface distance for (A) K ¼ 100, (B) K ¼ 10, and (C) K ¼ 1. In each case ¼ 1 and Kr takes the values (a) 1000, (b) 100, (c) 10, (d) 5, (e) 2, and (f) 1. (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)
The reasons for the deviation of the constant-composition model from the full model are apparent when the concentrations of Red1 and Red2 are examined. Due to the axisymmetrical SECM geometry, the concentration profiles of Red1 and Red2 are best shown as cross-sections over the domain R 0, Z 0, as illustrated schematically in Fig. 6. Note that in this figure the tip position has been inverted compared to that in Fig. 4. Figure 7
SECM as a Local Probe of Chemical Processes
295
FIG. 6 Schematic of the region (cross-hatched) represented by the concentration profiles. The ITIES is located at Z ¼ d=a.
FIG. 7 Steady-state concentration profiles for species Red1 and Red2 in phases 1 and 2, respectively, for K ¼ 100 and ¼ 1, with Kr taking the values (A) 1000, (B) 10, and (C) 5. The normalized concentrations of Red in phases 1 and 2 are, respectively, denoted by CRed1 and CRed2 . (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)
296
Barker et al.
shows profiles for K ¼ 100, at a normalized tip–interface separation, d=a ¼ 0:1 (which is typical of the smallest d=a attainable in SECM measurements). The normalized concentration distributions are shown in terms of CRedi (where the integer i ¼ 1 or 2) for Kr ¼ 1000, 10, and 5. With the former value of Kr , phase 2 is maintained at constant composition and the profile for this case [Fig. 7(A)] is thus provided for phase 1 only. This profile shows the characteristic concentration distribution for positive feedback, where concentration changes in phase 1 are maintained primarily within the zone directly under the tip. For lower Kr , the turnover of Red1 at the portion of the interface directly under the tip is sufficiently fast that Red2 is depleted in this interfacial region, even when Kr ¼ 10, and consequently a quasihemispherical diffusion field of Red2 is established in phase 2 [Fig. 7(B)]. The effect is to diminish the extent of positive feedback, as reflected by the change in the phase 1 profile between Fig. 7(A) and (B), resulting in the lower current observed at close tip–interface separations, compared to the constant–composition case. For Kr ¼ 5, the depletion of Red2 in phase 2 becomes very significant, such that the Red1 profile in phase 1 develops a considerable hindered diffusion component [Fig. 7 (C)]. Although the tendency for depletion in phase 2 becomes less significant as the interfacial rate constant is decreased, there are still considerable diffusional limitations from Red2 in phase 2 even for K ¼ 1, with Kr ¼ 5. An assessment of the applicability of the constant-composition assumption, compared to the full model, is shown in Fig. 8. This is a plot of the percentage error in the interfacial rate constant that would result from analyzing experimental data at logðd=aÞ ¼ 1:0, obtained with arbitrary Kr , using the earlier constant-composition theory [44,47,48]. The use of the constant-composition model to analyze data obtained under conditions of finite Kr results in an underestimation of the rate constant. Figure 8 shows that for Kr > 40, the constant-composition model is a good one, resulting in errors of less than 10–15%, over the full range of rate constants. For Kr < 20, however, sizeable errors result, particularly in the fast kinetic regime. This diagram can be used as a guide as to the likely errors involved in analyzing data for particular conditions with the constant-composition model. 3. Accessing Rapid ET Kinetics In addition to extending the range of conditions under which SECM feedback measurements can be made at ITIES, lifting the restriction on the composition of phase 2 is particularly beneficial for enhancing both the range and precision with which fast kinetics can be investigated. This is not only due to the fact that decreasing the bulk concentration of Red2 in phase 2 lowers the dimensionless rate constant for the system [Eq. (26)], but also because the approach curves in the fast kinetic limit are more readily distinguished from one another when Kr < 10. This point is well-illustrated by the data presented in Fig. 9, which shows simulated tip approach curves for a range of normalized rate constants: (A) under the constant-composition approximation, and (B) with Kr ¼ 3 and ¼ 1. Although there are differences in the approach curves with the constant-composition model, it would be extremely difficult to distinguish between any of the K cases practically, unless K was below 10. Even for K ¼ 10, an uncertainty in the tip position from the interface of 0:1d=a would not allow the experimental behavior for this rate constant to be distinguished from the diffusion-controlled case. For a typical value of DRed1 ¼ 105 cm2 s1 and electrode radius, a ¼ 12:5 m, this corresponds to an effective first-order heterogeneous rate constant of just 0:08 cm s1 . Assuming Kr 20 is necessary
SECM as a Local Probe of Chemical Processes
297
FIG. 8 Contour plot of percentage error in the rate constant k12 that results from analyzing data in terms of the constant-composition model, rather than the full diffusion model. The data are for a tip–ITIES separation, d=a ¼ 0:1, with a range of K and Kr values. (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)
to ensure constant composition conditions, and that phase 1 contains 0.5 mM of mediator for reasonable measurements (as in many previous experimental investigations of ITIES by SECM), this corresponds to an upper limit on k12 of 8 cm s1 M1 . In contrast, for Kr ¼ 3, the approach curves are such that ready kinetic discrimination should be possible for K 100 [Fig. 9(B)]. For the same values of DRed1 and a, with a bulk concentration of Red2 in phase 2, cRed2 ¼ 1:5 mM, this corresponds to a bimolecular rate constant, k12 of ca. 500 cm s1 M1 . It is also interesting to note that since the approach curves in Fig. 9(B) have peaks (at least for the fast kinetic cases that are most of interest), it is not necessary to know the tip to ITIES separation absolutely. Rather, the rate constant for the process of interest could be deduced by simply measuring the peak current value of a tip approach curve. These attributes have been exploited in the practical measurement of rapid ET kinetics at ITIES as discussed in Section V.
298
Barker et al.
FIG. 9 Simulated approach curves of i=ið1Þ versus normalized tip–interface separation, d=a, for (A) constant-composition conditions with K ¼ ðaÞ 100, (b) 50, (c) 20, (d) 10, (e) 5, (f) 2, and (g) 1; (B) full model conditions with Kr ¼ 3 and K ¼ ðaÞ 1000, (b) 100, (c) 50, (d) 20, (e) 10, (f) 5, (g) 2, and (h) 1. (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)
SECM as a Local Probe of Chemical Processes
B.
299
SECMIT Mode
In SECMIT, the UME tip is positioned in phase 1, close to the interface between two phases, such as two immiscible liquids, each containing a common electroactive species, Red. The partitioning of this species between the two phases can be represented as follows: k1 Red1
Ð Red2
ð30Þ
k2 where k1 and k2 are first-order interfacial rate constants for the transfer of Red from phases 1 and 2, respectively. Assuming that the target interface can be modeled as a quiescent, sharp boundary, with Eq. (30) initially at equilibrium there is zero net flux of species Red across the interface and each phase has a uniform composition of Red, cRedi (where the integer i ¼ 1 or 2). The initial condition is identical to Eqs. (11) and (12). A potential step is subsequently applied to the UME in phase 1, sufficient to electrolyze Red1 at the tip, at a diffusion-controlled rate. This perturbs the interfacial equilibrium, inducing the transfer of the target species across the interface, from phase 2 to phase 1, as shown in Fig. 10. The time-dependent diffusion equations for Red appropriate to the axisymmetrical geometry, shown in Fig. 10, are identical to Eqs. (9) and (10), given earlier. Although phase 2 is assumed to be semi-infinite in the z-direction, the model can readily be modified for the situation where phase 2 has a finite thickness [61]. The boundary conditions relevant to the problem under consideration are given by Eqs. (13)–(19), together with the following: 0 r rs ;
z ¼ d:
DRed1
@cRed1 @cRed2 ¼ DRed2 ¼ k2 cRed2 Ke cRed1 @z @z
ð31Þ
where Ke ¼
cRed2 k1 ¼ cRed1 k2
FIG. 10 The co-ordinate system used to define the two-phase model for SECMIT.
ð32Þ
300
Barker et al.
Thus, the problem is similar to the feedback mode case except for the internal boundary condition described by Eqs. (31) and (32), which relate to the first-order process at the target interface. The internal boundary condition describes the net diffusive flux of Red across the interface from phase 2 to phase 1, as the system attempts to reattain equilibrium following the electrolytic depletion of Red1 in phase 1. For the formulation of a general solution, the dimensionless quantities defined by Eqs. (21)–(25) are used, but the dimensionless rate constant is defined by Eq. (33) rather than Eq. (26). K¼
k2 a DRed2
ð33Þ
The normalized tip current response is again calculated from Eq. (28). Further details of the solution of the problem using the ADIFDM have been given elsewhere [9]. For the SECMIT mode the tip current response is governed primarily by K, Ke , , and the dimensionless tip–substrate distance, L. Here, we briefly examine the effects of these parameters on the chronoamperometric and steady-state SECMIT characteristics. All chronoamperometric data are presented as normalized current ratio versus 1=2 in order to emphasize the short-time characteristics, for the reasons outlined previously [12,14–16]. Steady-state characteristics, derived from the chronoamperometric data in the long-time limit, are considered over the full range of tip–substrate separations generally encountered in SECM. For completeness it should be mentioned that some of the theoretical conclusions for SECMIT are analogous to earlier treatments for the transient and steady-state response for a membrane-covered inlaid disk UME, which was investigated for the development of microscale Clark oxygen sensors [62–65]. An analytical solution for the steady-state diffusion-limited problem has also been proposed [66,67]. 1. Effect of Partition Coefficient, Ke The effect on the current–time behavior of varying Ke while keeping the kinetics of the interfacial process high and nonlimiting is shown in Fig. 11, for a typical tip–interface distance logðLÞ ¼ 0:5. The general trends in Fig. 11 can be explained as follows. At short times, the diffusion field at the UME tip is not of sufficient size to intercept the interface, and there is thus no perturbation of the interfacial equilibrium. In this time regime, 1=2 > 8, the tip current is similar for all of the cases considered. This is a common feature of SECM potential step chronoamperometry [10,12,14–16,42,43]. At longer times, the diffusion field of the UME intercepts the interface and the flux of Red1 to the UME (and hence current) is then governed by the value of Ke . Given that, under the defined conditions, there is no interfacial kinetic barrier to transfer from phase 2 to phase 1, the concentrations immediately adjacent to each side of the interface may be considered to be in dynamic equilibrium throughout the course of a chronoamperometric measurement. For high values of Ke the target species in phase 2 is in considerable excess, so that the concentration in phase 1 at the target interface is maintained at a value close to the initial bulk value, with minimal depletion of Red in phase 2. Under these conditions, the response of the tip (Fig. 11, case (a)] is in agreement with that predicted for other SECM diffusion-controlled processes with no interfacial kinetic barrier, such as induced dissolution [12,14–16] and positive feedback [42,43]. A feature of this response is that the current rapidly attains a steady state, the value of which increases
SECM as a Local Probe of Chemical Processes
301
FIG. 11 SECMIT chronoamperometric characteristics for logðd=aÞ ¼ 0:5, K ¼ 105 and ¼ 1. The curves correspond to the equilibrium partition coefficient, Ke , taking the values (a) 1000, (b) 50, (c) 10, (d) 5, (e) 2, (f) 1, (g) 0.5, and (h) 0.1. The lower dashed curve represents the behavior for an inert interface (i.e. no transfer from phase 2 to phase 1). (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)
dramatically as the separation between the tip and interface decreases, as illustrated by case (a) in Fig. 12. At the other extreme, for low Ke , the relatively small concentration of Red2 compared to Red1 , is insufficient to maintain the concentrations of Red on both sides of the interface at their initial bulk values, during SECMIT measurements. Consequently, there is extensive depletion of Red in both phases. The smaller the value of Ke the more extensive is the depletion of Red, as illustrated by Fig. 13, which depicts the steadystate concentration profiles of Red for Ke ¼ 0:1 (a), 1 (b), and 10 (c). Notice, however, that although Red is depleted in both phases, equilibrium conditions prevail at the interface, i.e., there is no abrupt discontinuity in the normalized concentrations of Red on crossing the interface (for any value of R). The main result of the preceding observations for SECMIT measurements is that as Ke decreases, the current tends to increasingly smaller values (Figs. 11 and 12). In the limit Ke ! 0, the chronoamperometric (Fig. 11) and steady-state (Fig. 12) current responses approach the characteristics predicted previously for an inert interface [8,42,43]. The plot of normalized steady-state current vs. tip–interface distance, shown in Fig. 12, demonstrates that as the tip–interface distance decreases the steady-state current becomes more sensitive to the value of Ke . Under the defined conditions the shape of the approach curve is highly dependent on the concentration in the second phase, for Ke values over a very wide range, with a lower limit less than 0.1 and upper limit greater than 50. This suggests that SECMIT can be used to determine the concentration of a target solute in a phase, without the UME entering that phase, provided that the diffusion coefficients of the solute in the two phases are known.
302
Barker et al.
FIG. 12 Simulated normalized steady-state current as a function of normalized tip–interface distance for K ¼ 105 , ¼ 1, and Ke taking the values (a) 1000, (b) 50, (c) 10, (d) 5, (e) 2, (f) 1, (g) 0.5, and (h) 0.1. The lower dashed line represents the approach curve for an inert interface (i.e., no transfer from phase 2 to phase 1). (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)
2. Effect of Diffusion Coefficient Ratio, As might be expected, similar trends to those identified above are observed as is varied, while maintaining Ke constant and K high and nonlimiting. The transient and steady-state current responses, shown respectively in Figs. 14 and 15 for Ke ¼ 1 and K ¼ 105 , vary between a lower limit which is close to the response for an inert interface when < 0:01, and an upper limit (when 1000) which is characteristic of SECM diffusion-control in phase 1 with no resistance from interfacial kinetics or transport in phase 2. The effect of increasing is to increase the diffusion coefficient of the solute in phase 2 compared to that in phase 1. For a given value of Ke this means that when a SECMIT measurement is made, the higher the value of the less significant are depletion effects in phase 2 and the concentrations at the target interface are maintained closer to the initial bulk values. Consequently, as increases, the chronoamperometric and steady-state currents increase from a lower limit, characteristic of an inert interface, to an upper limit corresponding to rapid interfacial solute transfer, with no depletion of phase 2. Under conditions of nonlimiting interfacial kinetics the normalized steady-state current is governed primarily by the value of Ke , which is the relative permeability of the solute in phase 2 compared to phase 1, rather than the actual value of Ke or . In contrast, the current–time characteristics are found to be highly dependent on the individual Ke and values. Figure 16 illustrates the chronoamperometric behavior for K ¼ 105 , logðLÞ ¼ 0:8 and for a fixed value of Ke ¼ 2. It can be seen clearly from this plot that whereas the current-time behavior is sensitive to the value of Ke and , in all cases the curves tend to be the same steady-state current in the long-time limit. This difference between the steadystate and chronoamperometric characteristics could, in principle, be exploited in determining the concentration and diffusion coefficient of a solute in a phase that is not in direct contact with the UME probe.
SECM as a Local Probe of Chemical Processes
303
FIG. 13 Steady-state profiles of the distribution of Red in the two phases during SECMIT, for K ¼ 105 , ¼ 1 and Ke taking the values (a) 0.1, (b) 1.0, and (c) 10. The normalized concentrations for phases 1 and 2 are, respectively, denoted by CRed1 and CRed2 . (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)
3.
Effect of Interfacial Kinetics
The influence of an interfacial kinetic barrier on the transfer process is readily illustrated by fixing the concentrations and the diffusion coefficients of Red for the two phases and examining the current response of the UME as K is varied. For illustrative purposes, we arbitrarily set Ke and ¼ 1, i.e., initially the equilibrium conditions are such that there are equal concentrations of the target solute in the two phases, and the solute diffusion coefficient is phase-independent. Figure 17 shows the chronoamperometric characteristics for several K values from zero up to 1000. Under the defined conditions, these values of K reflect the ease with which the transfer process can respond to a perturbation of the local concentration of Red in phase 1, due to electrolytic depletion.
304
Barker et al.
FIG. 14 SECMIT chronoamperometric characteristics for log(d=aÞ ¼ 0:5, K ¼ 105 , and Ke ¼ 1. The curves correspond to the ratio of the diffusion coefficients, , taking the values (a) 1000, (b) 100, (c) 10, (d) 2, (e) 1, (f) 0.5, (g) 0.1, and (h) 0.01. The lower dashed curve represents transient behavior for an inert interface. (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)
For small K, i.e., K ¼ 0:5 in Fig. 17, the response of the equilibrium to the depletion of species Red1 in phase 1 is slow compared to diffusional mass transport, and consequently the current-time response and mass transport characteristics are close to those predicted for hindered diffusion with an inert interface. As K is increased, the interfacial process responds more rapidly to the electrochemical perturbation in phase 1. The transfer of the target species across the interface generates an enhanced flux to the UME, causing
FIG. 15 Simulated normalized steady-state current as a function of normalized tip–interface distance for K ¼ 105 , Ke ¼ 1 and taking the values (a) 1000, (b) 100, (c) 10, (d) 2, (e) 1, (f) 0.5, (g) 0.1, and (h) 0.01. (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)
SECM as a Local Probe of Chemical Processes
305
FIG. 16 SECMIT chronoamperometric characteristics for logðd=aÞ ¼ 0:8, K ¼ 105 for constant Ke ¼ 2:0. The curves correspond to (a) Ke ¼ 40:0, ¼ 0:05, (b) Ke ¼ 20:0, ¼ 0:1, (c) Ke ¼ 4:0, ¼ 0:5, (d) Ke ¼ 2:0, ¼ 1:0, (e) Ke ¼ 1:0, ¼ 2:0, (f) Ke ¼ 0:5, ¼ 4:0, (g) Ke ¼ 0:1, ¼ 20:0, and (h) Ke ¼ 0:05, ¼ 40:0.
the long-time current to be larger than predicted for an inert interface. The higher the value of K, the greater the extent of interfacial transfer and the larger the current flow. For large K (K ¼ 1000 in Fig. 17) an upper limit is reached, where the interfacial kinetics are sufficiently fast – on the time scale of the SECM measurement – such that the concentrations of Red in the two phases, adjacent to the interface, are always in equilibrium even though Red is generally depleted. The tip current response is then dependent
FIG. 17 SECMIT chronoamperometric characteristics for log ðd=aÞ ¼ 0:5, ¼ 1, and Ke ¼ 1. The curves correspond to K taking the values (a) 1000, (b) 20, (c) 5, (d) 2, (e) 1, (f) 0.5, and (g) 0.0. (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)
306
Barker et al.
on the rate of mass transfer within both phases, and for Ke ¼ 1 and ¼ 1 resembles that predicted for a conventional UME in bulk solution [68]. The normalized steady-state current vs. tip–interface distance characteristics (Fig. 18) can be explained by a similar rationale. For large K, the steady-state current is controlled by diffusion of the solute in the two phases, and for the specific Ke and values considered is thus independent of the separation between the tip and the interface. For K ¼ 0, the current–time relationship is identical to that predicted for the approach to an inert substrate. Within these two limits, the steady-state current increases as K increases, and is therefore diagnostic of the interfacial kinetics.
4. Experimental Implications The theoretical results described have implications for the design of experimental approaches for the study of transfer processes across the interface between two immiscible phases. The current response in SECMIT is clearly sensitive to the relative diffusion coefficients and concentrations of a solute in the two phases and the kinetics of interfacial transfer over a wide range of values of these parameters. For comparable diffusion coefficients of the target solute in the two phases and nonlimiting transfer kinetics, systems characterized by different Ke should be resolvable on the basis of transient and steady-state current responses to a value of Ke up to 50 at practical tip–interface separations. If the diffusion coefficient in phase 2 becomes lower than that in phase 1, diffusion in phase 2 will be partly limiting at even higher values of Ke . On the other hand, as the value of increases or interfacial kinetics become increasingly limiting, lower values of Ke suffice for the constant-composition assumption for phase 2 to be valid. A further practical consequence relates to the different dependencies of the steadystate and transient currents on Ke and . It should be possible to determine independently
FIG. 18 Simulated normalized steady-state current as a function of normalized tip–interface distance for ¼ 1 and Ke ¼ 1 with K taking the values (a) 1000, (b) 20, (c) 5, (d) 2, (e) 1, (f) 0.5, and (g) 0.0. (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)
SECM as a Local Probe of Chemical Processes
307
both Ke and by correlating measurements of the steady-state current, as a function of distance of the tip from the interface, with chronoamperometric measurements (if there is no interfacial kinetic barrier). Alternatively, steady-state measurements alone provide a powerful approach to determining the product Ke . These observations are of considerable practical importance, opening up a new route for measuring concentrations and diffusion coefficients in phases that have, hitherto, been difficult to study with dynamic electrochemistry [9,20,21]. As with previous kinetic applications of SECM, it should be noted that experimental measurements can be tuned to the kinetic region of interest by varying the radius of the electrode [Eq. (33)] and the separation between the tip and interface. In essence, the smaller the UME, and/or tip–interface separation, the higher the diffusion rates that may be generated and, consequently, the greater the tendency for interfacial kinetic limitations.
V.
EXPERIMENTAL APPLICATIONS TO LIQUID–LIQUID INTERFACES
A.
Electron-Transfer (ET) Kinetics
Since the first use of SECM to study ET kinetics at a liquid–liquid interface in 1995 [47], the methodology has been proven a powerful approach for investigating the dependence of ET rate constants on the Galvani potential drop across an ITIES. The basic concept of using the SECM feedback mode to probe ET reactions at an ITIES was highlighted in Section II and theoretical characteristics for this mode were considered in Section IV. A key feature of the SECM approach is that a well-defined interfacial area is targeted for investigation and conditions are generally such that the overall contributions to the tip current, from mass transport and interfacial processes, can readily be resolved. The high local mass transport rates generated as a result of the small sizes of the UME probes employed in SECM, and the close tip–interface separations that can be attained, enable accurate quantification of rapid interfacial processes under welldefined and calculable conditions. In particular: (1) the SECM current allows discrimination between electron- and ion-transfer processes at the interface, (2) distortions associated with iR drop and charging current are eliminated, and (3) it is not necessary to externally polarize the interface, thereby avoiding complications due to the polarization window of the ITIES and the possible variation of the interfacial properties with applied potential. In pioneering studies [47], the SECM feedback mode was used to study the ET reaction between ferrocene (Fc), in nitrobenzene (NB), and the aqueous mediator, FcCOO , electrochemically generated at the UME by oxidation of the ferrocenemonocarboxylate ion, FcCOO . Tetraethylammonium perchlorate (TEAP) was applied in both phases as the partitioning electrolyte. The results of this study indicated that the reaction at the ITIES was limited by the ET process, provided that there was a sufficiently high concentration of TEAP in both phases. In initial ET rate measurements, both the NB and aqueous phases contained 0.1 M TEAP, enabling measurements to be made with a constant Galvani potential difference across the liquid junction. In these early studies, the concentration of Fc used in the organic phase (phase 2) was at least 50 times the concentration of the electroactive mediator in the aqueous phase which contained the probe UME (phase 1). This ensured that the interfacial process was not limited by mass transport in the organic phase, and that the simple constant-composition model, described briefly in Section IV, could be used.
308
Barker et al.
Tip approach curve measurements indicated a first-order dependence of the interfacial rate on the concentration of Fc in the organic phase, from which a value of 0.6 cm M1 s1 was extracted for the bimolecular ET rate constant. Good agreement between the measured rate constant and that predicted from Marcus theory [69–71], was considered, by assuming the ITIES to have a thickness of 2 nm. These studies, however, may have been compromised by the partitioning of Fc and Fcþ into the aqueous phase. 1. Potential Dependence of ET Rates According to Marcus theory [69–71], in the absence of work terms, the Gibbs free energy of activation for an ET reaction is given by: G 2 6¼ 1þ G ¼ ð34Þ 4 where is the reorganization energy. For a system where the ET reaction occurs between an electrogenerated oxidant in the organic phase and an electron donor in the aqueous phase, G is given by: G ¼ F ðE þ ow Þ
ð35Þ
where E is the difference of the standard potentials between the redox couples in the organic and aqueous phases and ow ¼ o w is the potential drop across the oil–water interface. When the driving force (E þ ow ) is close to zero, a Butler–Volmer type approximation can be considered to apply as a simplification of Eq. (34): G6¼ ¼ F ðE þ ow Þ
ð36Þ
where is the ET coefficient. With a fixed concentration of redox species in phase 2, the dependence of the ET rate constant, kf , on the driving force can be written as [48,70]: kf ¼ const exp ðG6¼ =RTÞ
ð37Þ
According to Eqs. (34)–(37), an increase in the rate constant with the driving force, with an value of 0.5 should be observed in the limit where the driving force is close to zero. At much higher driving forces, the rate constant should pass through a maximum and then decrease with increasing driving force. Although Marcus theory has been examined and verified in a number of chemical and biological systems [72], there is no general consensus on whether this model should apply to ET kinetics at ITIES [73]. Building on initial work [47], the main focus of SECM in the study of ET at ITIES has been to identify and understand the potential-dependence of ET rates. In these studies, the potential drop across an ITIES has been controlled by varying the concentration of potential-determining ions in the two phases. The potential drop across an ITIES follows the Nernst–Donnan equation [74,75], RT a w w
¼
8 þ ð38Þ ln o o o zF aw w o is the standard ion-transfer potential (these values for some ions can be found in Ref. 74), z is the number of the charge of the potential-determining ion, ao and aw are the activities of the potential-determining ion in the oil and water phases, respectively.
SECM as a Local Probe of Chemical Processes
309
For studies with ClO 4 as the potential-determining ion, under conditions where the activity coefficients of the ion in each phase remain constant, Eq. (38) can be written as: 0
w 0:059 log w o ¼ o ClO 4
½ClO 4 w ½ClO 4 o
ð39Þ
0
where w is the formal transfer potential of ClO o ClO 4 . For a reaction between a parti4 cular redox couple in each phase the E value is fixed. Moreover, if the ½ClO 4 o is a , then the combination of Eqs. constant and the potential is varied by changing ½ClO 4 w (36), (37), and (39) yields
log kf ¼ const 2:303 log½ClO 4 w
ð40Þ
log½ClO 4 w
dependence should be linear with a slope proportional to Thus, the log kf vs. in the limit of low driving force. A method advocated by Bard and coworkers [48] for measuring the relative interfacial potential drop is to record steady-state linear sweep voltammograms for a reversible redox couple in the organic phase, with respect to a reference electrode in the aqueous phase. According to Eq. (39), the formal potential of the organic couple, measured with respect to the aqueous reference electrode, should shift by 59 mV with a decade change in ½ClO 4 w (with ½ClO4 o fixed) assuming that the activity coefficients of the potential-determining ion remain constant. Typical experimental results obtained from such measurements are shown in Fig. 19. In early work on the effect of potential on ET reactions [76], Solomon and Bard showed that an ET reaction between FeðCNÞ4 6 in an aqueous phase and 7,7,8,8-tetracyanoquinodimethane (TCNQ) in 1,2-dichloroethane (DCE) could be promoted by judiciously adjusting the potential drop across the ITIES, using tetraphenylarsonium cation as a potential determining ion. In a similar period, Selzer and Mandler [77] reported a study of the ET reaction between aqueous IrCl2 6 and Fc in a NB phase, without any potential determining ion in either phase. A first-order rate constant of 0:013 cm s1 was obtained
FIG. 19 Dependence of the half-wave potentials for Fc (curve 1) and ZnPor (curve 2) oxidation in benzene on C1O 4 concentration in the aqueous phase. In these measurements, half-wave potentials were extracted from reversible steady-state voltammograms obtained at a 25 mm diameter Pt UME. The benzene phase contained 0.25 M tetra-n-hexylammonium perchlorate (THAP) and either 5 mM Fc or 1 mM ZnPor. All potentials were measured with respect to an Ag/AgCl reference electrode in the aqueous phase. (Reprinted from Ref. 48. Copyright 1996 American Chemical Society.)
310
Barker et al.
for this process, for which the rate-determining step could have involved Fcþ transfer from NB to the aqueous phase. Tsionsky et al. [48] investigated the potential-dependence of the ET rate for the reaction between 5,10,15,20-tetraphenyl-21H,23H-porphine zinc cation (ZnPorþ ) which served as an oxidant in benzene and aqueous electron donors, using ClO 4 in each phase as a potential-determining ion. In this study, ZnPorþ was generated in the organic phase by oxidation of the neutral species, ZnPor, at the SECM tip electrode. ZnPorþ diffused to the 4 ITIES where it was reduced to ZnPor by reaction with RuðCNÞ4 6 or FeðCNÞ6 . The measured ET coefficient was about 0.5, suggesting that conventional Butler–Volmer theory was applicable to heterogeneous ET at an ITIES. The results were consistent with a sharp boundary model for the interface [69–71], rather than a relatively thick mixed solvent layer with significant penetration by the redox species [78,79]. Liu and Mirkin [80] subsequently studied the oxidation of neutral ZnPor in benzene by aqueous oxidants (e.g., RuðCNÞ3 6 ), with the potential drop across the ITIES estabas the potential determining ion. A fixed concentration of 0.05 M tetralished using ClO 4 n-hexyl ammonium perchlorate (THAP) was used as the supporting electrolyte in the organic phase, with various concentrations of ClO 4 in the aqueous phase. The measured ET rate constants were found to be independent of interfacial potential drop, but dependent on the driving force contributed by the aqueous redox species. They concluded that this result agreed with Schmickler’s model for ET at an ITIES [79]. Based on these results, it was suggested that the -value obtained in previous investigations [48], could have been complicated by diffuse layers effects, similar to the Frumkin effect [81] at metal electrodes. These effects were considered to be negated by employing neutral ZnPor as the reactant in the organic phase. The rate constant for the forward ET reaction between ZnPorþ and RuðCNÞ4 6 was compared to that of the reverse reaction at zero driving force. The reverse ET rate constant was about 20 times the forward ET rate constant, which was attributed to diffuse layer effects. As discussed in Section IV, many studies of ET kinetics with SECM have been under conditions where constant composition in phase 2 can be assumed, but this severely restricts the range of kinetics that can be studied. With the availability of a full model for diffusion, outlined in Section IV, that lifts this restriction, Barker et al. [49] studied the reaction between ZnPorþ in benzene or benzonitrile and aqueous reductants, using ClO 4 or tetrafluoroborate as potential-determining ions. Figure 20 shows approach curves for the reaction between electrogenerated ZnPorþ 4 and FeðCNÞ4 6 at the benzene–water interface, for a range of concentrations of Fe(CN)6 in the aqueous phase. This case highlights the advantages of using low relative concentrations of a reactant in phase 2 in the study of rapid kinetics. For the highest concentration ratio in these experiments (Kr ¼ 14 and 7), the interfacial redox reaction appears to be diffusion-controlled and the rate constant cannot be determined, as found in previous studies on the same system [55]. However, as Kr decreases it becomes possible to distinguish the measured approach curves from those predicted for a diffusion-controlled process. In particular, at low Kr , the approach curves for fast ET have characteristic peaks with magnitudes that are diagnostic of the rate constant. This allows the peak to be fitted to a theoretical approach curve with a precise knowledge of the distance between the tips and ITIES. From an analysis of the approach curves, for the lowest three concentration ratios in Fig. 20, a rate constant of 91 cm s1 M1 was determined [49]. Similar experiments were performed to measure the ET rate constants for the reac4 tion between ZnPorþ in benzonitrile and aqueous reductants, RuðCNÞ4 6 , MoðCNÞ8 and 2 FeEDTA (where EDTA denotes ethylenediaminetetra-acetic acid). Although the
SECM as a Local Probe of Chemical Processes
311
FIG. 20 Experimental approach curves (&) for the oxidation of ZnPor at a tip UME in benzene approaching a benzene–aqueous interface, with the aqueous phase containing Fe(CN)4 6 . The bulk concentration conditions in the organic and aqueous phases, respectively, were as follows: (a) 4 [ZnPor] ¼ 0:500 mM, [Fe(CN)4 6 ¼ 7:00 mM; (b) [ZnPor] ¼ 0:500 mM, [Fe(CN)6 ¼ 3:50 mM; 4 (c) [ZnPor] ¼ 0:380 mM, ½FeðCNÞ6 ¼ 0:700 mM; (d) [ZnPor] ¼ 0:380 mM, [Fe(CN)4 6 ¼ 0:350 mM; (e) [ZnPor] ¼ 0:380 mM, [Fe(CN)4 6 ¼ 0:255 mM. The solid lines show the behavior predicted for ¼ 1:7 and a bimolecular rate constant, k12 ¼ 91 cm s1 M1 , while the dashed lines show the behavior for a diffusion-controlled process for each of the five cases considered. The diffusioncontrolled characteristics for the two cases with the highest Kr are indistinguishable. (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)
organic solvent used in the FeðCNÞ4 6 study was different from that used for the other three reductants, the rate constants obtained for the four systems investigated in Ref. 49 showed an interesting dependence on the driving force for the reaction (Fig. 21). The overall trend was consistent with the predictions of Marcus theory, showing first an increase in ET rate with increasing driving force, followed by a decrease in the inverted region. The proposed existence of interfacial inverted region behavior suggested by these studies is in agreement with an earlier study of ET at an ITIES modified with a monolayer of surfactant [82] and with later observations of electrogenerated chemiluminescence at an unmodified ITIES [83] The ET reaction between aqueous FeðCNÞ4 6 and the neutral species, TCNQ, has been investigated extensively with SECM, in parallel with microelectrochemical measurements at expanding droplets (MEMED) [84], which are discussed in Chapter 13. In the SECM studies, a Pt UME in the aqueous phase generated FeðCNÞ4 6 by reduction of FeðCNÞ3 6 . TCNQ was selected as the organic electron acceptor, because the half-wave potential for TCNQ ion transfer from DCE to water is 0.2 V more positive than that for ET from FeðCNÞ4 6 to TCNQ [85]. This meant that the measured kinetics were not compromised by TCNQ transfer from DCE to the aqueous phase within the potential window of these experiments. In these studies, ClO 4 was used as the potential-determining ion, with 0.1 M THAP employed as the supporting electrolyte in the DCE phase, together with various concentrations of NaClO4 in the aqueous phase. In contrast to studies of ZnPor oxidation [80],
312
Barker et al.
FIG. 21 Plot of log k12 vs. E1=2 showing the dependence of ET rate on the driving force for the reaction between ZnPorþ and four aqueous reductants. The difference between the half-wave potentials for an aqueous redox species and ZnPor, E1=2 ¼ E80 þ ow , where E80 is the difference in the formal potentials of the aqueous redox species and ZnPor and ow is the potential drop across the ITIES. The solid line is the expected behavior based on Marcus theory for ¼ 0:55 eV and a maximum rate constant of 50 cm s1 M1 . (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)
the ET rates were found to depend strongly on the interfacial potential drop with an ET coefficient () in the range of 0.3–0.4. Typical tip approach curves from this investigation are shown in Fig. 22. As the concentration of ClO 4 in the aqueous phase increases, the driving force for TCNQ reduction at the ITIES decreases, resulting in a diminution in the feedback effect and thus a lower tip current. An value of 0:41 0:04 was obtained for this ET process. The ET reaction between aqueous oxidants and decamethylferrocene (DMFc), in both DCE and NB, has been studied over a wide range of conditions and shown to be a complex process [86]. The apparent potential-dependence of the ET rate constant was contrary to Butler–Volmer theory, when the interfacial potential drop at the ITIES was adjusted via the ClO 4 concentration in the aqueous phase. The highest reaction rate was observed with the smallest concentration of ClO 4 in the aqueous phase, which corresponded to the lowest driving force for the oxidation process. In contrast, the ET rate increased with driving force when this was adjusted via the redox potential of the aqueous oxidant. Moreover, a Butler–Volmer trend was found when TBAþ was used as the potential-determining ion, with an value of 0.38 [86]. A feature of these studies was the further demonstration that higher ET rate constants can be measured more readily by using a lower relative concentration of the redox reactant in the second phase. For example, Fig. 23 shows approach curves for the oxidawhich is characterized by a rate constant of tion of DMFc by tip-generated IrCl2 6 180 cm s1 M1 , with 0.1 M ClO 4 in each phase, and readily distinguished from a diffusion-limited ET process.
SECM as a Local Probe of Chemical Processes
313
FIG. 22 Dependence of ET rates on ClO 4 concentration in the aqueous phase for the reduction of . The aqueous phase contained 0.1 M Li2 SO4 with various TCNQ in DCE by aqueous Fe(CN)4 6 concentrations of NaClO4 , while the DCE phase contained 0.1 M THAP. The SECM approach 3 curves for the generation of Fe(CN)4 6 by the reduction of Fe(CN)6 present in the bulk aqueous phase, were obtained with a 25 mm diameter Pt UME. From top to bottom, the first four solid experimental curves are shown for: [ClO 4 ]w ¼ 0:01, 0.025, 0.1, and 0.25 M. For the bottom solid line, there was no TCNQ in the DCE phase. The dashed lines are the corresponding theoretical curves for: k12 ¼ 0:3, 0.2, 0.04, 0.015, and 0 cm s1 M1 . (Reprinted from Ref. 84. Copyright 2000 American Chemical Society.)
FIG. 23 SECM approach curves for the reaction between tip-generated aqueous IrCl2 6 (via the oxidation of IrCl3 6 ) and DMFc in DCE obtained with a 25 mm diameter Pt UME. The potential across the ITIES was established with 0.1 M NaClO4 in the aqueous phase and 0.1 M THAP in the DCE phase. The aqueous phase also contained 0.1 M NaCl and 1 mM IrCl3 6 . The solid curves are the experimental data for Kr ¼ 2 (upper curve) and 1 (lower curve), and the dashed theoretical curves are for k12 ¼ 180 cm s1 M1 for these two cases. The dotted theoretical curves are shown for k12 ¼ 1000 cm s1 M1 with Kr ¼ 2 (top curve) and 1 (bottom curve) which is close to the diffusion-limited behavior. (Reprinted from Ref. 86. Copyright Elsevier Science.)
314
Barker et al.
2. Distance Dependence of ET Rates The effect on the ET rate of changing the distance between the aqueous and organic redox centers has been investigated by adsorbing phospholipid monolayers with a range of chain lengths on the ITIES [82]. The ET rate constants measured in the presence of the phospholipid monolayer were lower than for the lipid-free interface and generally decreased as the number of methylene groups in the hydrocarbon chain of the phospholipid increased. Some deviations from this trend were observed that were attributed to possible partial penetration of the ZnPorþ species into the lipid monolayer. A further important outcome from these studies was that at high overpotentials the ET rate appeared to decrease with increasing driving force, consistent with the predictions from Marcus theory of an inverted reaction free energy profile. In a separate study [87], the rate of the interfacial ET reaction when conjugated phospholipids were adsorbed at the ITIES was found to be at least twice as rapid as that measured when saturated phospholipids were used. This effect was ascribed to the delocalized conjugated chain acting as a ‘‘conductive wire embedded in an insulating matrix’’ and thereby increasing the rate of the reaction. The difference between the ET rates was sufficiently high to enable the SECM feedback mode to be used to image the reactivity of the adsorbed monolayer [87]. When a 25 m diameter UME was scanned laterally across a mixed monolayer comprising a saturated and a conjugated phospholipid, regions of relatively high and low ET rate were detected. These had dimensions of tens of microns and were identified as being associated with domains that were rich in one of the types of lipid. The effect of temperature on the interfacial ET rates for saturated phospholipids was also investigated. A sharp decrease in the rate constant at a critical temperature was attributed to a phase transition changing the tunneling distance between the redox species contained in the two contacting solutions, and hence changing the ET rate. The ITIES with an adsorbed monolayer of surfactant has been studied as a model system of the interface between microphases in a bicontinuous microemulsion [39]. This latter system has important applications in electrochemical synthesis and catalysis [88–92]. Quantitative measurements of the kinetics of electrochemical processes in microemulsions are difficult to perform directly, due to uncertainties in the area over which the organic and aqueous reactants contact. The SECM feedback mode allowed the rate of catalytic reduction of trans-1,2-dibromocyclohexane in benzonitrile by the Co(I) form of vitamin B12 , generated electrochemically in an aqueous phase to be measured as a function of interfacial potential drop and adsorbed surfactants [39]. It was found that the reaction at the ITIES could not be interpreted as a simple second-order process. In the absence of surfactant at the ITIES the overall rate of the interfacial reaction was virtually independent of the potential drop across the interface and a similar rate constant was obtained when a cationic surfactant (didodecyldimethylammonium bromide) was adsorbed at the ITIES. In contrast a threefold decrease in the rate constant was observed when an anionic surfactant (dihexadecyl phosphate) was used.
B.
Ion and Molecular Transfer Process
The transfer of neutral molecules and ions across immiscible liquid–liquid interfaces can be studied by both SECMIT and SECM DPSC.
SECM as a Local Probe of Chemical Processes
1.
315
SECM-Induced Transfer
SECMIT is particularly suitable for investigating the reversible transfer of neutral molecules and ions across liquid–liquid interfaces. As discussed in Sections II and IV, this mode of SECM can be used to measure interfacial kinetics and also as a noninvasive analytical probe for determining the permeability of a solute in a two-phase system. In the first category, SECMIT has been used to investigate the kinetics of Cu2þ extraction and stripping between an aqueous phase and an organic medium (DCE or heptane) containing the oxime ligand Acorga P50 (LH) [9,18]. The extraction–stripping process, defined by Eq. (41), was first allowed to come to equilibrium. ð41Þ
The interfacial transfer kinetics were then investigated by perturbing the equilibrium, through the depletion of Cu2þ in the aqueous phase, by reduction to Cu at an UME located in close proximity to the aqueous–organic interface. This process promoted the transfer of Cu2þ into the aqueous phase, via the transport and decomplexation of the cupric ion–oxime complex, resulting in an enhanced steady-state current at the UME. Approach curve measurements of i=ið1Þ vs. d allowed the kinetics of the transfer process to be determined unambiguously [9,18]. In the second category, SECMIT has been used to probe the relative permeability of oxygen between water and DCE or NB, with no supporting electrolyte present in any phase. Under the conditions employed, direct voltammetric measurements in the organic phase would be impractical due to the high solution resistivity (DCE or NB) or limitations of the solvent window available (NB). Figure 24 shows the steady-state current for the
FIG. 24 Steady-state diffusion-limited current for the reduction of oxygen in water at an UME approaching a water–DCE (*) and a water–NB () interface. The solid lines are the characteristics predicted theoretically for no interfacial kinetic barrier to transfer and for ¼ 1:2, Ke ¼ 5:5 (top solid curve) or ¼ 0:58, Ke ¼ 3:8 (bottom solid curve). The lower and upper dashed lines denote the current–distance characteristics for the situation where there is no interfacial transfer and where transfer occurs without limitations from diffusion in the organic phase. (Adapted from Ref. 9. Copyright 1998 American Chemical Society.)
316
Barker et al.
diffusion-limited reduction of oxygen at an UME tip approaching an aqueous–DCE and aqueous–NB interface [9]. The measured currents in both cases were lower than predicted for Ke ! 1, indicating that there were diffusional limitations in the organic phase. By fitting the approach curves to the model outlined in Section IV, the relative permeabilities of oxygen between the aqueous and organic phases were assigned. The advantages of using the SECMIT mode in applications where the physical presence of the UME could damage the structural integrity of the target phase being studied have been well illustrated by investigations of solute transfer in cartilage [20,21]. 2. SECM DPSC To expand the range of processes that can be studied with SECM, we have recently suggested the use of DPSC for the investigation of irreversible phase transfer processes [34]. This approach was used to measure the rate of transfer of Br2 from aqueous 0.5 M sulfuric acid solution to DCE. In the forward potential step, Br2 was generated at the tip UME through the diffusion-limited oxidation of Br (present at mM levels). The current– time characteristics for this forward-step process provided a very accurate measure of the tip–interface separation, since the form of the transient is governed by the hindered diffusion of Br through the aqueous phase to the UME which, in turn, depends only on the normalized tip–interface separation, L, and the diffusion coefficient of Br , both parameters are known with high precision. The driving force for the transfer process was the enhanced solubility of Br2 in DCE, ca 40 times greater than that in aqueous solution. To probe the transfer processes, Br2 was recollected in the reverse step at the tip UME, by diffusion-limited reduction to Br . The transfer process was found to be controlled exclusively by diffusion in the aqueous phase, but by employing short switching times, tswitch , down to 10 ms, it was possible to put a lower limit on the effective interfacial transfer rate constant of 0:5 cm s1 . Figure 25 shows typical forward and reverse transients from this set of experiments, presented as current (normalized with respect to the steady-state diffusion-limited current, ið1Þ, for the oxidation of Br ) versus the inverse square-root of time. DPSC was recently used to examine whether DMFcþ transfers across the water– DCE interface at typical interfacial potential drops encountered in SECM studied [86]. For this measurement, the DCE phase contained 10 mM DMFc and 0.1 M THAP, while the aqueous phase contained 0.01 M NaClO4 and 0.1 M NaCl. In general, DPSC data obtained for tip–interface separations of 4:4 m to 14:6 m were found to be in close agreement with the theoretical predictions for no transfer of electrogenerated DMFþ c across the interface on the SECM time scale. Typical forward and reverse step data for a tip–interface distance of 4:4 m and tswitch ¼ 0:371 s, are shown in Fig. 26.
VI.
PROBING MOLECULAR TRANSFER AT LIQUID–GAS INTERFACES AND LIQUID INTERFACES MODIFIED WITH LANGMUIR MONOLAYERS
SECM has been extended successfully to investigate chemical processes at aqueous–air interfaces and Langmuir monolayers supported on them [19,34,93]. Initial work concentrated on molecular transfer processes across the aqueous–air interface, with and without a monolayer of surfactant. A ‘‘submarine’’ UME (described in section III) was utilized which could approach the air–water interface from below. The first study employed the DPSC mode to investigate the transfer kinetics of electrogenerated Br2 , from aqueous
SECM as a Local Probe of Chemical Processes
317
FIG. 25 Typical DPSC data for the oxidation of 10 mM bromide to bromine (forward step; upper solid curve) and the collection of electrogenerated Br2 (reverse step; lower solid curve) at a 25 mm diameter disk UME in aqueous 0.5 M sulfuric acid, at a distance of 2.8 mm from the interface with DCE. The period of the initial (generation) potential step was 10 ms. The upper dashed line is the theoretical response for the forward step at the defined tip–interface separation, with a diffusion coefficient for Br of 1:8 105 cm2 s1 . The remaining dashed lines are the reverse transients for irreversible transfer of Br2 (diffusion coefficient 9:4 106 cm2 s1 ) with various interfacial firstorder rate constants, k, marked on the plot. (Reprinted from Ref. 34. Copyright 1997 American Chemical Society.)
FIG. 26 Typical DPSC data for the oxidation of DMFc to DMFcþ (forward step of 0.371 s duration, upper solid line) and the collection of DMFcþ by reduction to DMFc (reverse step, lower solid line) at a tip in a DCE phase, positioned at a distance of 4.4 mm from the DCE–aqueous interface. The upper dashed line shows the theoretical characteristics for hindered diffusion of DMFc to the tip. The lower dashed line is the theoretical response when there is no DMFcþ transfer across the ITIES. (Reprinted from Ref. 86. Copyright Elsevier Science.)
318
Barker et al.
0.5 M sulfuric acid to air [34]. As discussed above, for the aqueous–DCE interface, the rate of this irreversible transfer process (with the air phase acting as a sink) was limited only by diffusion of Br2 in the aqueous phase. A lower limit for the interfacial transfer rate constant of 0:5 cm s1 was found [34]. The transfer of oxygen across an air–aqueous interface in the absence and presence of a monolayer of 1-octadecanol was subsequently investigated [19]. The interface was formed in a Langmuir trough, enabling the effect of monolayer compression on the oxygen transfer rate to be assessed. The study provided information on reaeration rates, which are of value in natural environments [94,95]. The configuration could also be considered as a simple model for studies of oxygen transfer across biomembranes. For these investigations, the UME was positioned in the aqueous subphase containing 0.1 M KNO3 and held at a potential to reduce oxygen at a diffusion-controlled rate, in order to promote the transfer of O2 from air (phase 2) to the aqueous solution (phase 1), with subsequent collection at the tip (Fig. 27). Under SECMIT conditions, the flux of oxygen from air to water is given by: jo2 ¼ kaw ca kwa cw;i
ð42Þ
where kwa and kaw are the first-order interfacial rate constants for transfer from water to air and from air to water, respectively, and cw;i is the interfacial concentration of oxygen in the water phase. Due to the high diffusion coefficient and effective concentration, ca , of oxygen in the air phase, depletion effects were unimportant, so that jo2 ¼ k 0 kwa cw;i
ð43Þ
where k 0 represents the zero-order rate constant for oxygen transfer from air to water. At equilibrium the following holds: k 0 ¼ kaw ca ¼ kwa cw
ð44Þ
FIG. 27 Schematic (not to scale) of the SECM-induced transfer of oxygen across a 1-octadecanol monolayer, at the air–water interface, in a Langmuir trough.
SECM as a Local Probe of Chemical Processes
319
FIG. 28 Normalized steady-state diffusion-limited current vs. UME–interface separation for the reduction of oxygen at an UME approaching an air–water interface with 1-octadecanol monolayer coverage (*). From top to bottom, the curves correspond to an uncompressed monolayer and surface pressures of 5, 10, 20, 30, 40, and 50 mN m1 . The solid lines represent the theoretical behavior for reversible transfer in an aerated atmosphere, with zero-order rate constants for oxygen transfer from air to water, k0 =108 mol cm2 s1 of 6.7, 3.7, 3.3, 2.5, 1.8, 1.7, and 1.3. (Reprinted from Ref. 19. Copyright 1998 American Chemical Society.)
The results of this study demonstrated that the rate of oxygen transfer across a clean air–water interface was diffusion-controlled on the time scale of SECM measurements. The rate of this transfer process was, however, significantly reduced with increasing compression of a 1-octadecanol monolayer. Figure 28 illustrates this point, showing approach curves for O2 reduction recorded with the monolayer at different surface pressures. The transfer rate was found to depend on the accessible free area of the interface, as described by the following equation: A 0 0
¼ k ¼1 1 ¼0 k 0 ¼ k ¼1 ð45Þ A where represents the fraction of the interface that is free from surfactant, A is the surface area, usually written as the area per molecule of surfactant, and A ¼0 is the area per molecule for which the transfer rate is zero. Figure 29 is the analysis of the data in Fig. 28 in terms of Eq. (45), which can be seen to provide a good description of the effect of monolayer density on the transfer process. A similar approach has been used to investigate lateral diffusion processes in monolayers [93], specifically, the transport of protons along a stearic acid assembly. Lateral diffusion processes of this type are crucial in defining the activity of membrane-bound reactive centers in cellular bilayers. For initial studies, a submarine UME was positioned in a Langmuir trough, filled with an aqueous solution containing protons (2.0– 5:0 105 M), close to the air–water interface on which a monolayer of stearic acid was spread. Operating in a configuration analogous to the SECMIT mode described in Section II, the UME was biased to reduce protons to hydrogen at a diffusion-controlled rate. The resulting local depletion drove the acid dissociation reaction, which in turn created a proton diffusion gradient, both in solution and at the surface (Fig. 30). The transport-
320
Barker et al.
FIG. 29 Oxygen-transfer rate constants derived from Fig. 28 as a function of the reciprocal of the interfacial area per molecule. (Reprinted from Ref. 19. Copyright 1998 American Chemical Society.)
limited current flowing at the electrode provided a measure of the rates of the two processes, which were investigated as a function of the surface coverage of stearic acid by controlling the monolayer compression. These measurements showed that in-plane lateral proton diffusion was facilitated at air–water interfaces on which stearic acid monolayers were formed, with a surface diffusion coefficient that depended critically on the physical state of the monolayer, and which was at most ca. 15% of the magnitude in bulk solution. These promising initial studies
FIG. 30 Schematic (not to scale) of the arrangement for SECM measurements of proton transport at a stearic acid monolayer deposited at the air–water interface. The UME typically had a diameter, 2a, in the range 10–25 mm and the tip–interface distance, d 2a.
SECM as a Local Probe of Chemical Processes
321
suggest that SECM is a potentially powerful probe of a variety of chemical processes in ultrathin two-dimensional assemblies. We are currently extending these studies to investigate the lateral diffusion of amphiphiles at liquid–air interfaces.
VII.
CONCLUSIONS
This chapter has highlighted the significant impact SECM has had on the electrochemical investigation of chemical processes at liquid–liquid interfaces, particularly fundamental studies of ET, IT, and molecular transfer. The key general attributes of SECM include the possibility of carrying out measurements on a targeted portion of an interface, under conditions of variable and high mass transport. The ability to model mass transport in the SECM geometry allows interfacial kinetic effects to be resolved over a wide dynamic range from tip current measurements. In the field of charge transfer at ITIES – where SECM has found most application – the methodology overcomes problems in conventional techniques used to investigate ET and IT. In particular, distortions associated with iR drop are eliminated, the tip current discriminates between ET and IT, and it is not necessary to externally polarize the interface to change the potential across the ITIES. SECM has already provided interesting insights into the nature of ET processes at ITIES, although many further studies are needed to examine existing theories for the dependence of ET rates on potential. Although the study of IT using both SECMIT and SECM DPSC has received some attention, there is clearly scope for much further work in this area and in the study of interfacial molecular transfer processes. The demonstration that SECM can be used to study chemical processes at liquid–gas interfaces and monolayers on water surfaces, in particular, opens up a number of exciting possibilities for further studies. In addition to investigations of solute transfer across organized molecular assemblies, the diverse range of SECM modes available should facilitate local, noninvasive studies of various physiochemical processes in ultrathin films. Our group has begun studies of lateral proton diffusion at molecular monolayers, and we are currently extending this approach to amphiphile diffusion, lateral charge transfer, and adsorption–desorption kinetics.
ACKNOWLEDGMENTS The support of our SECM studies of liquid–liquid interfaces and related areas, by the EPSRC, BBSRC, Avecia, and the Wellcome Trust, is gratefully acknowledged. We have benefited from helpful discussions with several colleagues, including Prof. A. J. Bard and his group (University of Texas at Austin), Prof. D. E. Williams, Dr J. Strutwolf and Dr D. Caruana (University College London, UK), and Dr J. H. Atherton (Avecia, Huddersfield). At Warwick, Dr M. Gonsalves, and Dr J. V. Macpherson have provided valuable contributions to some of the work described in this chapter.
REFERENCES 1. 2.
M. V. Mirkin. Anal. Chem. 68:177A (1996). A. L. Barker, M. Gonsalves, J. V. Macpherson, C. J. Slevin, and P. R. Unwin. Analytica Chim. Acta 385:223 (1999).
322 3. 4. 5. 6. 7.
8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44.
Barker et al. M. V. Mirkin. Mikrochim. Acta 130:127 (1999). R. M. Wightman. Science 240:415 (1988). J. Heinze. Angew Chem. Int. Ed. Engl. 32:1268 (1993). R. J. Forster. Chem. Soc. Rev. 23:289 (1994). C. Amatore, in Physical Electrochemistry: Principles, Methods and Applications, in Electroanalytical Chemistry, (I. Rubinstein, ed.), Marcel Dekker, New York, 1995, pp. 131– 208. J. Kwak and A. J. Bard. Anal. Chem. 61:1221 (1989). A. L. Barker, J. V. Macpherson, C. J. Slevin and P. R. Unwin. J. Phys. Chem. B 102:1586 (1998). P. R. Unwin and A. J. Bard. J. Phys. Chem. 96:5035 (1992). J. V. Macpherson and P. R. Unwin. J. Chem. Soc. Faraday Trans. 89:1883 (1993). J. V. Macpherson and P. R. Unwin. J. Phys. Chem. 98:1704 (1994). J. V. Macpherson and P. R. Unwin. J. Phys. Chem. 98:11764 (1994). J. V. Macpherson and P. R. Unwin. J. Phys. Chem. 99:3338 (1995). J. V. Macpherson and P. R. Unwin. J. Phys. Chem. 99:14824 (1995). J. V. Macpherson and P. R. Unwin. J. Phys. Chem. 100:19475 (1996). J. V. Macpherson, P. R. Unwin, A. C. Hillier, and A. J. Bard. J. Am. Chem. Soc. 118:6445 (1996). C. J. Slevin, J. A. Umbers, J. H. Atherton, and P. R. Unwin. J. Chem. Soc. Faraday Trans. 92:5177 (1996). C. J. Slevin, S. Ryley, D. J. Walton, and P. R. Unwin. Langmuir 14:5331 (1998). J. V. Macpherson, D. O’Hare, P. R. Unwin, and C. P. Winlove. Biophys. J. 73:2771 (1997). M. Gonsalves, A. L. Barker, J. V. Macpherson, P. R. Unwin, D. O’Hare, and C. P. Winlove. Biophys. J. 78:1578 (2000). C. P. Andrieux, P. Hapiot, and J. M. Save´ant. J. Phys. Chem. 92:5992 (1988). J. V. Macpherson and P. R. Unwin. Anal. Chem. 69:2063 (1997). A. J. Bard, F.-R. F. Fan, J. Kwak, and O. Lev. Anal. Chem. 61:132 (1989). J. Kwak and A. J. Bard. Anal. Chem. 61:1794 (1989). A. J. Bard, F.-R. F. Fan, and M. V. Mirkin, in Electroanalytical Chemistry (A. J. Bard, ed.), vol. 18, Marcel Dekker, New York, 1993, pp. 243–373. R. M. Wightman and D. O. Wipf, in Electroanalytical Chemistry (A. J. Bard, ed.), vol. 15, Marcel Dekker, New York, 1989, pp. 267–353. C. Lee, C. J. Miller, and A. J. Bard. Anal. Chem. 63:78 (1991). T. Solomon and A. J. Bard. Anal. Chem. 67:2787 (1995). Y. Shao, M. D. Osborne, and H. H. Girault. J. Electroanal. Chem. 318:101 (1991). P. D. Beattie, A. Delay, and H. H. Girault. J. Electroanal. Chem. 380:167 (1995). Y. Shao and M. V. Mirkin. J. Electroanal. Chem. 439:137 (1997). N. J. Evans, M. Gonsalves, N. J. Gray, A. L. Barker, J. V. Macpherson, and P. R. Unwin. Electrochem. Commun. 2:201 (2000). C. J. Slevin, J. V. Macpherson, and P. R. Unwin. J. Phys. Chem. B 101:10851 (1997). A. A. Gewirth, D. H. Craston, and A. J. Bard. J. Electroanal. Chem. 261:477 (1989). R. M. Penner, M. J. Heben, T. L. Longin, and N. S. Lewis. Science 250:1118 (1990). C. J. Slevin, N. J. Gray, J. V. Macpherson, M. A. Webb and P. R. Unwin. Electrochem Commun. 1:282 (1999). H. Y. Liu, F.-R. F. Fan, C. W. Lin, and A. J. Bard. J. Am. Chem. Soc. 108:3838 (1986). Y. Shao, M. V. Mirkin, and J. F. Rusling. J. Phys. Chem. B 101:3202 (1997). M. V. Mirkin and A. J. Bard. J. Electroanal. Chem. 323:1 (1992). M. V. Mirkin and A. J. Bard. J. Electroanal. Chem. 323:29 (1992). A. J. Bard, G. Denuault, R. A. Friesner, B. C. Dornblaser, and L. S. Tuckerman. Anal. Chem. 63:1282 (1991). P. R. Unwin and A. J. Bard. J. Phys. Chem. 95:7814 (1991). A. J. Bard, M. V. Mirkin, P. R. Unwin, and D. O. Wipf. J. Phys. Chem. 96:1861 (1992).
SECM as a Local Probe of Chemical Processes 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90.
323
Q. Fulian, A. C. Fisher, and G. Denuault. J. Phys. Chem. B 103:4387 (1999). Q. Fulian, A. C. Fisher, and G. Denuault. J. Phys. Chem. B 103:4393 (1999). C. Wei, A. J. Bard, and M. V. Mirkin. J. Phys. Chem. 99:16033 (1995). M. Tsionsky, A. J. Bard, and M. V. Mirkin. J. Phys. Chem. 100:17881 (1996). A. L. Barker, P. R. Unwin, S. Amemiya, J. Zhou, and A. J. Bard. J. Phys. Chem. B 103:7260 (1999). D. W. Peaceman and H. H. Rachford. J. Soc. Ind. Appl. Math. 3:28 (1955). J. Heinze. J. Electroanal. Chem. Int. Electrochem. 124:73 (1981). J. Heinze. Ber. Bunsen-Ges. Phys. Chem. 85:1096 (1981). J. Heinze and M. Storzbach. Bunsen-Ges. Phys. Chem. 90:1043 (1986). M. V. Mirkin, F.-R. F. Fan, and A. J. Bard. J. Electroanal. Chem. 328:47 (1992). R. D. Martin and P. R. Unwin. J. Electroanal. Chem. 439:123 (1997). R. D. Martin and P. R. Unwin. Anal. Chem. 70:276 (1998). R. G. Compton, B. A. Coles, and R. A. Spackman. J. Phys. Chem. 95:4741 (1991). R. G. Compton, B. A. Coles, and A. C. Fisher. J. Phys. Chem. 98:2441 (1994). R. G. Compton, B. A. Coles, J. J. Gooding, A. C. Fisher, and T. I. Cox. J. Phys. Chem. 98:2446 (1994). Y. Saito. Rev. Polarogr. Jpn. 15:177 (1968). J. Strutwolf, A. L. Barker, M. Gonsalves, D. Caruanna, P. R. Unwin, D. E. Williams, and J. Webster. J. Electroanal. Chem. 483:163 (2000). D. J. Gavaghan, J. S. Rollett, and C. E. W. Hahn. J. Electroanal. Chem. 325:23 (1992). D. J. Gavaghan, J. S. Rollett, and C. E. W. Hahn. J. Electroanal. Chem. 348:1 (1993). D. J. Gavaghan, J. S. Rollett, and C. E. W. Hahn. J. Electroanal. Chem. 348:15 (1993). L. Sutton, D. J. Gavaghan, and C. E. W. Hahn. J. Electroanal. Chem. 408:21 (1996). J. Galceran, J. Salvador, J. Puy, J. Cecilia, and D. J. Gavaghan. Analyst 12:1863 (1996). J. Galceran, J. Salvador, J. Puy, J. Cecilia, and D. J. Gavaghan. J. Electroanal. Chem. 440: (1997). D. Shoup and A. Szabo. J. Electroanal. Chem. 140:237 (1982). R. A. Marcus. J. Phys. Chem. 94:1050 (1990). R. A. Marcus. J. Phys. Chem. 94:4152 (1990); addendum, J. Phys. Chem. 94:7742 (1990). R. A. Marcus. J. Phys. Chem. 95:2010 (1991); addendum, J. Phys. Chem. 99:5742 (1995). R. D. Cannon, Electron Transfer Reactions, Butterworths, London, 1980. B. B. Smith, J. W. Hallery, and A. J. Nozik. Chem. Phys. 205:245 (1996). A. G. Volkov, D. W. Deamer, D. L. Tanelian, and V. S. Markin, Liquid Interfaces in Chemistry and Biology. Wiley, New York, 1998. H. H. Girault and D. J. Schiffrin. in Electroanalytical Chemistry vol. 15, (A. J Bard, ed.), Marcel Dekker, New York, 1989, pp. 1–141. T. Solomon and A. J. Bard. J. Phys. Chem. 99:17487 (1995). Y. Selzer and D. Mandler. J. Electroanal Chem. 409: 15 (1996). H. H. Girault and D. J. Schiffrin. J. Electroanal. Chem. 244:15 (1988). W. Schmickler. J. Electroanal. Chem. 428:123 (1997). B. Liu and M. V. Mirkin. J. Am. Chem. Soc. 121:8352 (1999). A. J. Bard and L. R. Faulkner, Electrochemical Method, Wiley and Sons, New York, 1980, p. 541. M. Tsionsky, A. J. Bard, and M. V. Mirkin. J. Am. Chem. Soc. 119:10785 (1997). Y. B. Zu, F.-R. F. Fan, and A. J. Bard. J. Phys. Chem. B 103:6272 (1999). J. Zhang and P. R. Unwin. J. Phys. Chem. B 104:2341 (2000). Y. F. Cheng and D. J. Schiffrin. J. Chem. Soc. Faraday Trans. 90:2517 (1994). J. Zhang, A. L. Barker, and P. R. Unwin. J. Electroanal. Chem. 483:95 (2000). M. H. Delville, M. Tsionsky, and A. J. Bard. Langmuir 14:2774 (1998) G. N. Kamau, N. Hu, and J. F. Rusling. Langmuir 8:1042 (1992). D. L. Zhou, J. Gao, and J. F. Rusling. J. Am. Chem. Soc. 117:1127 (1995). D.-L. Zhou, H. Carrero, and J. F. Rusling. Langmuir 12:3067 (1996).
324 91. 92. 93. 94.
Barker et al.
G. N. Kamau and J. F. Rusling. Langmuir 12:2645 (1996). J. Gao, J. F. Rusling, and D. L. Zhou. J. Org. Chem. 61:5972 (1996). C. J. Slevin and P. R. Unwin. J. Am. Chem. Soc. 122:2597 (2000). L. T. Thibodeaux, Environmental Chemodynamics: Movement of Chemicals in Air, Water and Soil, 2nd edn, Wiley, New York, 1996. 95. R. P. Schwarzenbach, P. M. Gschwend, and D. M. Imboden, Environmental Organic Chemistry, Wiley, New York, 1993.
13 Hydrodynamic Techniques for Investigating Reaction Kinetics at Liquid^Liquid Interfaces: Historical Overview and Recent Developments CHRISTOPHER J. SLEVIN, PATRICK R. UNWIN, and JIE ZHANG Departme nt of Chemistry, University of Warwick, Coventry, England
I.
INTRODUCTION
As discussed throughout this book, reactions that occur at the interface between two immiscible liquids are common in a wide range of areas. For example, industrially important processes, such as solvent extraction [1,2] and phase transfer catalysis [3], rely on optimizing reactions at liquid–liquid interfaces. In addition, immiscible liquid–liquid interfaces can be considered as useful analogs of biomembranes [4–6] for the experimental investigation of cell membrane transfer processes, including drug delivery systems [7]. On a more general level, interest in the fundamental aspects of charge transfer processes at the interface between two immiscible electrolyte solutions (ITIES) has been increasing recently [8,9]. This research has led to developments in areas such as analysis with amperometric ion-selective electrodes [10], as well as in understanding the fundamentals of charge transfer mechanisms at liquid–liquid interfaces [8,11]. Many of the areas highlighted require an understanding of the kinetics and mechanisms of interfacial processes. An important aspect of progress in this field has been the introduction of new techniques which are able to provide increasingly improved kinetic and mechanistic insight. The investigation of the kinetics of reactions that occur at liquid– liquid interfaces requires a number of factors to be considered. As depicted in the schematic in Fig. 1, the overall rate may be limited by the transport of reactants, intermediates, or products to and from the interface, interfacial processes, reactions in solution (not shown), or by a combination of factors. In order to accurately measure interfacial reaction rates, it is necessary to either operate under conditions where the overall rate is limited only by the interfacial (or solution) chemical reaction, i.e., ensure that the transport step is relatively fast and nonlimiting, or to make the transport step well-defined and calculable, so that its effect can be accounted for when interpreting rate data [3,12,13]. For the study of reactions at immiscible liquid–liquid interfaces, achieving welldefined contact between the two phases, with known interfacial area, under conditions where variable and high rates of mass transport are attainable, is nontrivial. 325
326
Slevin et al.
FIG. 1 Simplified schematic illustrating the types of steps involved in an interfacial reaction at a liquid–liquid interface.
Complications introduced when a liquid–liquid interface, rather than a solid–liquid interface, is studied include the possibility that transport on both sides of the interface, in each of the phases, may need to be considered, and achieving a stable interface of known area is much more difficult. The general criteria for an experimental investigation of the kinetics of reactions at liquid–liquid interfaces may be summarized as follows: known interfacial area and welldefined interfacial contact are essential; controlled, variable, and calculable mass transport rates are required to allow the transport and interfacial kinetic contributions to the overall rate to be quantified; direct interfacial contact is preferred, since the use of a membrane to support the interface adds further resistances to the overall rate of the reaction [14,15]; a renewable interface is useful, as the accumulation of products at the interface is possible. Finally, direct measurements of reactive fluxes at the interface of interest are desirable. Many of the electrochemical techniques described in this book fulfill all of these criteria. By using an external potential to drive a charge transfer process (electron or ion transfer), mass transport (typically by diffusion) is well-defined and calculable, and the current provides a direct measurement of the interfacial reaction rate [8]. However, there is a whole class of spontaneous reactions, which do not involve net interfacial charge transfer, where these criteria are more difficult to implement. For this type of process, hydrodynamic techniques become important, where mass transport is controlled by convection as well as diffusion. In this chapter, we describe some of the more widely used and successful kinetic techniques involving controlled hydrodynamics. We briefly discuss the nature of mass transport associated with each method, and assess the attributes and drawbacks. While the application of hydrodynamic methods to liquid–liquid interfaces has largely involved the study of spontaneous processes, several of these methods can be used to investigate electrochemical processes at polarized ITIES; we consider these applications when appropriate. We aim to provide an historical overview of the field, but since some of the older techniques have been reviewed extensively [2,3,13], we emphasize the most recent developments and applications.
Hydrodynamic Techniques
II.
THE LEWIS CELL
A.
Methodology
327
Some of the earliest attempts to address the difficulties associated with making kinetic measurements at immiscible liquid–liquid interfaces were made by Lewis [16,17] using the stirred cell design illustrated in Fig. 2. The Lewis cell employs direct contact between the two immiscible liquids, and reaction rates are evaluated by measuring concentration changes in the bulk of one of the two phases, usually by a batch extraction technique. The rate of change of concentration, dc=dt, is related to the interfacial reaction flux, j, by dc jAint ¼ dt V
ð1Þ
where Aint is the interfacial area and V is the volume of the phase in which the concentration change is monitored. Stirrers are employed in each phase to generate convective transport on both sides of the interface. This reduces the contribution of diffusion to the overall kinetics, and it is generally assumed that the reaction rate can be evaluated by neglecting diffusion. This, of course, places limitations on the range of kinetics that can be investigated, as discussed shortly. The basic cell employs stirrers rotating at the same speed to minimize surface breakup, resulting in a relatively flat interface of determinable area. Although the rate of mass transport to the interface can be enhanced by increasing the rate of stirring, the hydrodynamics are relatively ill-defined and transport rates cannot be calculated absolutely. This technique therefore relies on the determination of interfacial reaction kinetics from the plateau region of a plot of reaction rate vs. stirring rate, with the assumption that the interfacial kinetics can be outrun by generating sufficiently high mass transport rates. At the maximum attainable stirring rate, the size of the concentration boundary layer (or diffusion layer) is in fact still relatively large, since high stirring rates cannot be used, as convective effects close to the interface would cause excessive break-up of the interface. In practice, the minimum diffusion layer thickness, D , is ca. 100 m, introducing a mass transport resistance, kT ðcm s1 ), which may be evaluated using kT ¼
D D
FIG. 2 Schematic of the basic Lewis cell design.
ð2Þ
328
Slevin et al.
where D is the diffusion coefficient of the reactant of interest. For typical values of D ¼ 105 cm2 s1 and D ¼ 100 m, the mass transport resistance is of the order of 103 cm s1 . This limits the technique to rather slow kinetics, with first-order interfacial rate constants, ki kT . Another complication, caused by stirring the two phases at the same speed, occurs when the two solutions have different viscosities, which is common for immiscible liquids. The key fluid flow parameter is the Reynolds number, Re, which is the ratio of inertial to viscous forces in the solution, as indicated by Re ¼
vl
ð3Þ
where v is the fluid velocity, l is a characteristic length, and is the kinematic viscosity of the fluid. When the two phases have different viscosities, the Reynolds numbers are different for each side of the interface. Developments in the Lewis cell were made to overcome some of the problems associated with the initial design. With the introduction of screens close to the interface, on either side [18], stirring could be carried out at different speeds in each phase, allowing the same Reynolds number to be attained on both sides of the interface. This modification to the cell also allowed more vigorous stirring and efficient mixing in the bulk region without disturbances to the interface, thereby reducing the size of the stagnant diffusion layer and increasing the kinetic range of the technique. A further useful development in the design was the introduction of a flow loop [19], eliminating the need for large volumes of solution, and enhancing the batch sampling procedures. Additional advances included the use of a porous gauze [20] to support the interface with stirring close to the gauze employed to enhance mass transport. However, even with these improvements, the main problems associated with using this type of cell remain, primarily that mass transport is poorly characterized and rather slow. The technique is essentially limited to the measurement of first-order interfacial rate constants, ki < 105 cm s1 [3]. B.
Applications
Although the Lewis cell was introduced over 50 years ago, and has several drawbacks, it is still used widely to study liquid–liquid interfacial kinetics, due to its simplicity and the adaptable nature of the experimental setup. For example, it was used recently to study the hydrolysis kinetics of n-butyl acetate in the presence of a phase transfer catalyst [21]. Modeling of the system involved solving mass balance equations for coupled mass transfer and reactions for all of the species involved. Further recent applications of modified Lewis cells have focused on stripping–extraction kinetics [22–24], uncatalyzed hydrolysis [25,26], and partitioning kinetics [27].
III.
CONSTANT INTERFACIAL CELL WITH LAMINAR FLOW
Controlled contact between two immiscible liquids has also been achieved by flowing one liquid along a solid support submerged in the second phase [28,29]. Several different arrangements have been used, although all are based on similar principles. For example, a wetted wall column which offered liquid–liquid contact times of 0.5–10 s was used to measure solute transfer rates [29].
Hydrodynamic Techniques
329
A significant advance in this area was recently made by Li and coworkers [30,31], who developed a laminar flow technique, that allowed the direct contact of two liquids with better-defined mass transport compared to the Lewis cell. Laminar flow of the two phases parallel to the interface was produced through the use of flow deflectors. By forcing flow parallel to, rather than towards, the interface, it was proposed that the interface was less likely to be disrupted. Reactions were followed by sampling changes in bulk solution concentrations. A schematic of the apparatus developed is shown in Fig. 3. Stirrers mix and push the lighter and heavier phases in each compartment, with the maximum rotation speed governed by the need to maintain the interface steady. Flow deflectors ensure that the phases are circulated in each chamber and that flow near the interface is laminar. The interfacial plate (thickness 2 mm) is rectangular with a hole at its center. The distance from the interface to the flow deflectors is less than 6 mm. The two phases are analyzed by withdrawing small volumes via sampling holes. The hydrodynamic and diffusion theory of this technique were obtained based on the following assumptions: isothermal operation; constant densities; constant viscosities; constant diffusivities; negligible diffusion along the interfacial plate direction; steady-state operation; negligible flow in the y and z directions (see Fig. 4); and negligible stagnation regions near the edges of the interfacial plates. The thickness of the concentration boundary layer, D , was found to be governed by: 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 1 96LDH 2 A ð4Þ 2D ¼ @9H 2 81H 4 U 2 where H is the distance between the interface and flow deflectors, L is the length of contacting interface in the flow direction, and U is the mean solution velocity. The mass transfer equation applicable to the transport-limited extraction of a solute from an aqueous solution to an organic phase (sink conditions), was derived: V w cw 3 Aint Dt b;0 1 exp Tr ¼ ð5Þ 2 V w D Aint ð1 þ Þ where Tr is the mass transferred per unit area, is the partition coefficient of the solute between the organic and aqueous phase, V w is the volume of aqueous phase, cw b;0 is the initial concentration of the solute in the aqueous phase and t is time. Equation (5) can be also written as " # w 1 cb 1 A k w þ1 w ð6Þ f ðcb Þ ¼ ln ¼ intw T ð þ 1Þt cb;0 V
FIG. 3 Schematic of the constant interfacial cell with laminar flow.
330
Slevin et al.
FIG. 4 The co-ordinate system for the constant interfacial cell.
where cw b denotes the bulk aqueous solute concentration at time, t. The mass transfer coefficient is kT ¼
3 D o 2 w D þ D
ð7Þ
The superscripts o and w denote the organic and aqueous phases, respectively. Equation (6) suggests a linear dependence of f ðcw b Þ on t for a diffusion-controlled process. This technique has been used to study the extraction kinetics of rare-earth elements from an aqueous phase into heptane by 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (HEH/EHP) [31]. The linear dependence of f ðcw b Þ on t in Fig. 5 was considered to indicate that the extraction of ErCl3 by HEH/EHP is a diffusion-controlled process. The technique offers a known interfacial area under convective flow conditions that are quite well-defined, with mass transport rates that are enhanced compared to the Lewis cell and its analogs. However, in common with many other approaches, interfacial fluxes must be determined indirectly from bulk solution measurements.
FIG. 5 Extraction of ErCl3 by HEH/EHP–heptane at pH 2.49 and 30 C. The experimental system was characterized by the following parameters: L ¼ 6:0 cm, Aint ¼ 21:0 cm2 , H ¼ 0:6 cm, 3 u ¼ 3:4 cm s1 , V w ¼ 96 cm3 , and cw M. The organic phase initially contained 3:0 b;0 ¼ 3 10 2 10 M HEH/EHP. (Reprinted from Ref. 31. Copyright 1998, Elsevier Science Ltd.)
Hydrodynamic Techniques
IV.
THE ROTATING DIFFUSION CELL
A.
Principles
331
The rotating diffusion cell (RDC) [14] enables the study of liquid–liquid reaction kinetics under conditions where interfacial hydrodynamics are well-defined and calculable. The design of the RDC is based on the rotating disk electrode (RDE) [32], which has been widely used for kinetic measurements at solid electrodes. The RDE consists of a diskshaped electrode sealed in an insulating cylinder rotated in solution, giving rise to welldefined hydrodynamics, which have been calculated to give a complete description of the flow field in the contacting solution [33]. The mass transfer coefficient for this device, under transport-limited conditions, is given by [33]: kT ¼ 1:554D2=3 1=6 W 1=2
ð8Þ
where W is the rotation frequency of the disk (Hz). The assumptions behind the derivation of Eq. (8) are that flow is laminar and the Schmidt number, Sc ¼ =D, is in excess of 103 . These assumptions generally hold for most practical conditions [34]. In practice, the rate of mass transport to the disk can be controlled readily through the rotation speed. For rotation speeds up to 100 Hz, which is experimentally accessible for a solid electrode, the corresponding mass transport parameter, for typical D and values of 1 105 cm2 s1 and 1 102 cm2 s1 , respectively, is variable up to 1:5 102 cm s1 . This corresponds to a diffusion layer (concentration boundary layer) thickness of ca.7 m. The RDC, depicted schematically in Fig. 6, operates with the interface supported at a thin porous membrane between the inner and outer compartments of the cell. A number of different arrangements are possible, with a common configuration involving aqueous solutions in both the inner and outer compartments, with the organic phase impregnated within the membrane. Abbreviated to w/o/w, this results in two aqueous–organic phase interfaces. Alternatively, w/o/o, w/w/o, and o/o/o arrangements, etc., have also been used [15]. The membrane is rotated in the solution and the hydrodynamic profiles of the rotating disk are established on both sides of the membrane. Liquid–liquid contact is achieved with a known area by treating the membrane with a solution which blocks the pores, except in a small circular section in the center, which is untreated. Interfacial reactions are usually studied by measuring changes in the bulk concentrations of reacting
FIG. 6 Schematic of the rotating diffusion cell. The reaction is usually followed by sampling the bulk solution of the outer phase using a suitable analytical technique.
332
Slevin et al.
species, as described above for the Lewis cell, although interfacial fluxes can be measured directly by modifying the technique with the addition of a ring electrode, as described later. The kinetics of the reaction must be calculated from the measured flux, taking into account transport to and from the disk-shaped contacting area and through the membrane. The flux of a target species may be quantified according to the following equations; here we consider a simple solute transfer reaction from an organic donor phase to an aqueous receptor phase in the o/o/w configuration. Firstly, the flux across the diffusion layer towards the membrane on the donor side is given by j ¼ Do ðcob coi Þ=oD
ð9Þ coi
cob
and are the where Do is the diffusion coefficient of the solute in the oil phase, concentrations of the solute in the organic donor phase at the membrane surface, and in the bulk of the organic solution, respectively. The diffusion layer thickness for the hydrodynamic rotating disk arrangement, D , is given by gD ¼ 0:643D1=3 1=6 W 1=2
ð10Þ
where g denotes phase o or w. This applies to both donor and receptor compartments. The flux through the membrane is given by j ¼ Do ðcom cw m Þ=lm
ð11Þ
and are the where is the membrane porosity, lm is the membrane thickness, and concentrations of the solute within the membrane, specifically, where the membrane meets the organic donor and water receptor, respectively. For this particular arrangement, coi and com are equal, since there is no transfer resistance on the donor compartment side. The interfacial transfer reaction is controlled by com
w j ¼ ðkow cw m kwo ci Þ
cw m
ð12Þ
cw i
is the corresponding concentration at the other side of this interface. The rate where constants kwo and kow are for transfer across the organic–water interface from the water to the organic and the organic to the water phases respectively. Finally, the diffusion away from the interface into the receptor phase may be evaluated from w w j ¼ Dw ðcw i cb Þ=D
ð13Þ
cw b
is the bulk concentration of the solute in the water receptor phase. where Given that Pow ¼ kwo =kow is the solute partition coefficient, then the expression for the total flux for this particular case can be written as P cob Pow cw o l 1 b ¼ ow D;w þ D þ m þ j Dw Do Do kow
ð14Þ
Combining Eq. (10) and (14) yields
! 1=6 cob Pow cw Pow 1=6 l 1 w b 1=2 o ¼ 0:643W þ þ m þ 2=3 2=3 j
Do kow Do Dw
ð15Þ
Analysis of data obtained from the RDC usually involves plotting the reciprocal of the measured flux, j 1 , against W 1=2 , and extrapolating to infinite rotation speed (W 1=2 ! 0), such that the diffusion layer thicknesses tend to zero and diffusion in the solution on either side of the membrane is discounted. The intercept on the j 1 axis then gives a measure of the flux, governed by the interfacial kinetics and the transport resistance
Hydrodynamic Techniques
333
[for example, the last two terms on the right-hand side of Eq. (15)]. The membrane transfer resistance must be subtracted in order to obtain the true interfacial resistance. B.
Drawbacks and Improvements
In contrast to the RDE, the range of rotation speeds used in the RDC is rather limited. The upper limit is around 6–8 Hz, while Eq. (8) breaks down below approximately 1–2 Hz, where the hydrodynamic boundary layer, H ¼ 1:4ð=WÞ1=2
ð16Þ
becomes comparable with the rotating disk radius [35]. Consequently, rate data are obtained over a very narrow range of mass transport coefficients, the maximum kT available being ca. 4 103 cm s1 . Significant extrapolation of reciprocal flux data to W 1=2 ! 0 has been suggested to be an unreliable way to determine interfacial kinetics [15]. A modification of the RDC design, based on the ring–disk arrangement of the RDE [36], incorporated an arc electrode [37,38] deposited on the surface of the membrane around the untreated area. This facilitated the electrochemical detection of species reacting at the interface at short times following the reaction. This method was used to study the solvent extraction of cupric ions, which were detected by reduction to copper metal at the arc electrode. The resulting current flow was related to the interfacial flux at the membrane. There are several drawbacks to the RDC that need to be emphasized. First, the fact that the interface must be supported adds a considerable resistance to the transport of species, which is in addition to that from the concentration boundary layers on both sides of the membrane. This limits the range of kinetics that can be studied. Second, in practical applications, blocking of the membrane can be problematic for some reactions. Third, measurements are generally made in the bulk of the solution and not at the interface although, as mentioned above, for certain processes it is possible to measure fluxes via a ring or an arc electrode. C.
Applications
The majority of RDC studies have concentrated on the measurement of solute transfer resistances, in particular, focusing on their relevance as model systems for drug transfer across skin [14,39–41]. In these studies, isopropyl myristate is commonly used as a solvent, since it is considered to serve as a model compound for skin lipids. However, it has since been reported that the true interfacial kinetics cannot be resolved with the RDC due to the severe mass transport limitations inherent in the technique [15]. The RDC has also been used to study more complicated interfacial processes such as kinetics in a microemulsion system [42], where one of the compartments contains an emulsion. A comprehensive study of the complex interfacial processes involved in the solvent extraction of cupric ion by oxime ligands represents one of the most detailed and successful studies carried out with the RDC [37,38]. Recently, the technique was also used to study the transfer of tetrabutylammonium cations [43] and the kinetics of partitioning of compounds between octanol and water [44]. In the latter study, Fisk and coworkers investigated the rates of partitioning of 23 compounds from octanol to an aqueous phase. The RDC arrangement used most frequently in this work is of the o/o/w type. So according to Eq. (15), Pow and kow can be calculated from the gradient and intercept of
334
Slevin et al.
FIG. 7 Analysis of RDC data for the partition kinetics of cyanazine between octanol and water.
a plot of c 0 =j vs. W 1=2 , where c 0 ¼ cob Pow cw b . Figure 7 illustrates some typical results for cyanazine transfer from octanol to the aqueous phase.
V.
THE LIQUID JET RECYCLE REACTOR (LJRR)
Developed by Freeman and Tavlarides [45,46], and based on the liquid jet technique [47,48], the LJRR provides a method of measuring liquid–liquid reaction kinetics with direct contact, known interfacial area, renewable interface, and reasonably defined hydrodynamics. This method operates by employing an aqueous liquid jet in a concurrent, coaxially flowing organic solution, shown schematically in Fig. 8. The aqueous solution flows from the jet nozzle to a receiving capillary with no overflow into the outer stream, resulting in short contact times of around 0.05 s. Analysis is implemented by flowing the outer organic phase continually through a closed loop and monitoring concentration changes spectrophotometrically. The apparatus used by Freeman and Tavlarides employed capillaries with internal diameters of 2 mm, and the
FIG. 8 Schematic diagram of the liquid jet recycle reactor (LJRR).
Hydrodynamic Techniques
335
jet length was 3.54 cm. The aqueous jet was arranged vertically, and a gravity fed flow system was used. This approach enabled measurements to be made on a clean interface with a known area (measurable by photography). The following equations of mass transfer from the jet are based on certain assumptions, namely, isothermal operation; constant densities, viscosities, and diffusivities; no ionization or homogeneous reactions; small penetration depth; negligible curvature; negligible axial diffusion; and steady-state operation: @co @c @2 c þ v o ¼ Do 2o @x @y @y
y>0
ð17Þ
@cw @c @2 c þ v w ¼ Dw 2w @x @y @y
y1
log k1 (M1 s1 )
log k10 (M1 s1 Þ
5.65 5.70 5.52 — 5.32
n.d. 6.36 5.00 4.30 5.19
Catalytic Effect of the Liquid–Liquid Interface
369
FIG. 10 Extraction rate profiles of Ni(II) with dithizone and phen in which an interfacially adsorbed intermediate complex is formed.
FIG. 11 Concentration change of Hpan and PADA in the catalytic extraction of NiðpanÞ2 into the toluene phase. Initial concentrations are ½Ni2þ ¼ 1:0 105 M, ½Hpan ¼ 4:0 105 M and ½PADA ¼ 1:7 105 M at pH ¼ 5:6.
SCHEME 4
Catalytic role of PADA in the extraction of Ni(pan)2 .
370
Watarai
MD calculations could simulate the high adsorptivity of the complex ion, affording the adsorption energy from aqueous phase to the interface as 7:4 kcal mol1 . 2. Acid Catalysis in Metal Extraction In general, an acidic condition is not favored for the extraction rate of metal ions, because the dissociation of an extractant is suppressed or a co-ordinating atom in the extractant is protonated. However, we found an interesting phenomenon in the extraction of Pd(II) with 5-Br–PADAP; a lowering of pH accelerated the extraction rate [26]. This phenomenon was ascribed to the interfacial adsorption of the protonated 5-Br–PADAP which accelerated the interfacial complexation. The protonation of 5-Br–PADAP was made at the nitrogen atom of diethylamine, which is a nonco-ordinating atom. Therefore, the interfacial protonation in this system worked so as to increase the interfacial concentration of a reactable ligand. Interfacial reactions in this system are represented by þ PdCl2 þ H2 Lþ i ! PdLClo þ Cl þ 2H
ki1 1:0 103 M1 s1
þ þ PdCl 3 þ H2 Li ! PdLClo þ 2Cl þ 2H
ki2 3:3 102 M1 s1
PdCl 4
ki3 3:2 10 M
þ
H2 L þ i
! PdLClo þ 3Cl þ 2H
þ
2
ð17Þ
1 1
s
This finding a new type of catalysis will provide a useful hint for the design of molecular structures of interfacially adsorbable and strongly reactive ligands for a specific metal ion. E.
Analysis of Interfacial Complex by a Time-Resolved Fluorescence Spectroscopy
In the mechanism of an interfacial catalysis, the structure and reactivity of the interfacial complex is very important, as well as those of the ligand itself. Recently, a powerful technique to measure the dynamic property of the interfacial complex was developed; time resolved total reflection fluorometry. This technique was applied for the detection of the interfacial complex of Eu(III), which was formed at the evanescent region of the interface when bathophenanthroline sulfate (bps) was added to the Eu(III) with 2-thenoyltrifuluoroacetone (Htta) extraction system [11]. The experimental observation of the double component luminescence decay profile showed the presence of dinuclear complex at the interface as illustrated in Scheme 5. The lifetime (31 s) of the dinuclear complex was much shorter than the lifetime (98 s) for an aqua-Eu(III) ion which has nine co-ordinating water molecules, because of a charge transfer deactivation. Rotational dynamics of a fluorescent dye adsorbed at the interface provides useful information concerning the rigidity of the microenvironment of liquid–liquid interface in terms of the interfacial viscosity. The rotational relaxation time of the rhodamine B dye was studied by time-resolved total internal reflection fluorescent anisotropy. In-plane
SCHEME 5 Interfacial formation of dinuclear europium(III) complex.
Catalytic Effect of the Liquid–Liquid Interface TABLE 4 Interface
371
Rotational Relaxation of Octadecylrhodamine B at Toluene–Water
Surfactant
Conc. (M)
No Triton X-100 SDS
— 1:0 106 1:0 107 1:0 106 1:0 107 1:0 106
HDHP
In-plane rotational Interfacial viscosity relaxation time (ns) (Pa s) 10 M probing rapid complexation reactions. C.
Electron Transfer
Studies of electron transfer (ET) at micro-ITIES are scarce. Solomon and Bard first observed the ET between TCNQ (in DCE) and ferrocyanide (in water) at a microITIES supported by micropipettes [5]. The pipette was used as a SECM probe for electrochemical imaging. The current was controlled by the rate of the bimolecular ET reaction at the micro-ITIES 3 TCNQ ðDCEÞ þ FcðCNÞ4 6 ðaqÞ Ð TCNQ ðDCEÞ þ FcðCNÞ6 ðaqÞ
ð15Þ
The concentrations of aqueous oxidized and reduced species inside the pipette were much larger than that of the redox species in the organic phase. As was shown previously at large ITIES [33], the voltammograms obtained under these conditions (Fig. 12) were similar to voltammograms of the same redox species at a Pt electrode. The aqueous phase, therefore, behaved as a metal electrode. Quinn et al. studied ET at micro-ITIES supported by micropipettes or microholes [16]. The studied systems involved ferri/ferrocyanide redox couple in aqueous phase and ferrocene, dimethylferrocene, or TCNQ in either DCE or o-nitrophenyl octyl ether. Sigmoidal, steady-state voltammograms were obtained for ET at the water–DCE interface supported at a micropipette. The semilogarithmic plot of E versus log½ðId IÞ=I was
FIG. 12 Voltammogram for the two-phase electron transfer at a micro-ITIES. The pipette contained 1.0 M Li2 SO4 , 0.4 M K4 FeðCNÞ6 , and 0.01 M K3 FeðCNÞ6 . The organic phase (DCE) contained 1 mM TCNQ and 1 mM TPAsTPB supporting electrolyte. (The potential sweep rate was 50 mV/s. Reprinted with permission from Ref. 5. Copyright 1995 American Chemical Society.)
Voltammetry at Micro-ITIES
391
linear with the slope of 61 mV/decade, i.e., similar to the Nernstein value, 59 mV/decade, and the pipette resistance was too high for accurate kinetic measurements. The voltammograms at the microhole-supported ITIES were analyzed using the Tomes˘ criterion [34], which predicts jE3=4 E1=4 j ¼ 56:4=n mV (where n is the number of electrons transferred and E3=4 and E1=4 refer to the three-quarter and one-quarter potentials, respectively) for a reversible ET reaction. An attempt was made to use the deviations from the reversible behavior to estimate kinetic parameters using the method previously developed for UMEs [21,27]. However, the shape of measured voltammograms was imperfect, and the slope of the semilogarithmic plot observed was much lower than expected from the theory. It was concluded that voltammetry at micro-ITIES is not suitable for ET kinetic measurements because of insufficient accuracy and repeatability [16]. Those experiments may have been affected by reactions involving the supporting electrolytes, ion transfers, and interfacial precipitation. It is also possible that the data was at variance with the Butler–Volmer model because the overall reaction rate was only weakly potential-dependent [35] and/or limited by the precursor complex formation at the interface [33b]. D.
Micropipettes as SECM Tips
In scanning electrochemical microscopy (SECM) a microelectrode probe (tip) is used to examine solid–liquid and liquid–liquid interfaces. SECM can provide information about the chemical nature, reactivity, and topography of phase boundaries. The earlier SECM experiments employed microdisk metal electrodes as amperometric probes [29]. This limited the applicability of the SECM to studies of processes involving electroactive (i.e., either oxidizable or reducible) species. One can apply SECM to studies of processes involving electroinactive species by using potentiometric tips [36]. However, potentiometric tips are suitable only for collection mode measurements, whereas the amperometric feedback mode has been used for most quantitative SECM applications. In a conventional feedback experiment the UME tip is placed in a solution containing some redox species. A redox mediator is reduced (or oxidized) at the tip electrode: O1 þ e ¼ R1
ð16Þ
The product of this reaction diffuses to the substrate where it may be reoxidized (or rereduced). This process produces an enhancement in the faradaic current at the tip electrode depending on the tip–substrate separation (positive feedback) [29]. This experiment can be modified by replacing metal tip with a micropipette filled with a solvent immiscible with the outer solution. Such a pipette can work as an amperometric UME. Solomon and Bard [5] used micropipettes for feedback mode SECM imaging. The tip process in Ref. 5 was electron transfer between aqueous ferrocyanide inside a micropipette and TCNQ in the outer DCE solution. Accordingly, the pipette behaved in the same manner as a metal tip. The micropipette tips have several advantages over metal tips. First, they are much easier to fabricate, especially for tips with submicrometer diameters. Moreover, although very small (nanometer) metal tips can be used in SECM to image insulator surfaces, high-resolution imaging of conductive surfaces by SECM is not possible because of the onset of tunneling when the tip approaches to within 5–10 nm of surface. Such tunneling may not occur with glass micropipettes. Recently [8b,30], a new IT feedback mode of SECM was introduced, in which the tip process is a simple or assisted ion transfer. In this mode, a micropipette filled with solvent (e.g., aqueous) immiscible with the outer solution (e.g., organic) serves as an SECM tip.
392
Liu and Mirkin
The tip current in Ref. 8b was produced by transfer of Kþ from the aqueous solution inside the pipette into DCE assisted by DB18C6 [reaction (10a)]. With the tip biased at a sufficiently positive potential and the cKCl cDB18C6 , the tip current was limited by diffusion of DB18C6 to the pipette orifice. When the tip approached the bottom (aqueous) layer potassium ions were released from the complex and transferred to the aqueous solution. DB18C6, which served as a mediator, was regenerated via interfacial dissociation mechanism [reaction (10b) occurring at the ITIES]. Similarly to conventional SECM feedback experiments, the interfacial dissociation produced an enhancement in the tip current (positive feedback). Unlike the assisted IT processes, no mediator species are involved in a simple IT reaction, e.g., transfer of a cation (Mþ ) from organic phase into the aqueous filling solution inside the pipette: Mþ ðoÞ ! Mþ ðwÞ
(at the pipette tip)
ð17aÞ
In this case, both the top and the bottom liquid phases contain the same ion at equilibrium. A micropipette tip is used to deplete concentration of this ion in the top solvent near the ITIES. This depletion results in the ion transfer across the ITIES (Fig. 13), which can produce positive feedback if the bottom phase contains a sufficiently high concentration of Mþ : Mþ ðwÞ ! Mþ ðoÞ
(at the ITIESÞ
ð17bÞ
The tip current depends on the rate of the interfacial IT reaction, which can be extracted from the tip current vs. distance curves. One should notice that the interface between the top and the bottom layers is nonpolarizable, and the potential drop is determined by the ratio of concentrations of the common ion (i.e., Mþ ) in two phases. Probing kinetics of IT at a nonpolarized ITIES under steady-state conditions should minimize resistive potential drop and double-layer charging effects, which greatly complicate voltammetric studies of IT kinetics. In Ref. 30, the transfer of tetraethylammonium (TEAþ ) across nonpolarizable DCE–water interface was used as a model experimental system. No attempt to measure kinetics of the rapid TEAþ transfer was made because of the lack of suitable quantitative theory for IT feedback mode. Such theory must take into account both finite quasireversible IT kinetics at the ITIES and a small RG value for the pipette tip. The mass transfer rate for IT experiments by SECM is similar to that for heterogeneous ET measurements, and the standard rate constants of the order of 1 cm/s should be accessible. This technique should be most useful for probing IT rates in biological systems and polymer films. By scanning the pipette tip over the phase boundary the topographic images and maps of IT reactivity of the interface can be obtained. Figure 14 shows a gray-scale image of a 5 m pore in the 10 m-thick polycarbonate membrane obtained with an 3 mdiameter pipette. The feedback is negative when the pipette tip is over a solid surface, while a significantly higher current corresponds to the tip facing the pore. The feedback mode images were obtained without any current flowing across the interface. A high lateral resolution can be achieved because of the absence of diffusion broadening. Such an image represents distribution of IT reactivity on the interfacial boundary. Filling a pipette with an organic solvent was essential for experiments with polycarbonate membranes which are soluble in organic media. The same setup can be employed to map ion transfers occurring at a polymer–solution interface and in living cells which also have to be studied in water. A water-filled micropipette should be used as an SECM tip for imaging in organic media. A potential advantage of the pipette tips is that they can easily be made
Voltammetry at Micro-ITIES
393
FIG. 13 Schematic illustration of the SECM feedback mode based on a simple ion-transfer reaction. Cations are transferred from the top (organic) phase into the aqueous solution inside the pipette tip. Positive feedback is due to IT from the bottom (aqueous) layer into the organic phase. Electroneutrality in the bottom layer is maintained by reverse transfer of the common ion across the ITIES beyond the close proximity of the pipette where its concentration is depleted. (Reprinted with permission from Ref. 30. Copyright 1998 American Chemical Society.)
very small (see Section III.C). Some technical problems, such as better tip–substrate alignment, have yet to be solved to make nanometer-scale IT imaging feasible.
E.
Micro-ITIES as Sensors
According to Eq. (1) the steady-state current across a micro-ITIES is proportional to the bulk concentration of the transferred species. Thus, the micro-ITIES can function as an amperometric ion-selective sensor. Similarly, the peak current in a linear sweep voltammogram of ion egress from the micropipette obeys the Randles–Sevc˘ik equation. Both types of measurements can be useful for analysis of small samples [18a].
394
Liu and Mirkin
FIG. 14 Constant height mode gray–scale image of a 5 m-diameter pore in a polycarbonate membrane obtained with a 3 m pipette tip. The filling DCE solution contained 10 mM TBATPBCl. The aqueous phase contained 0.4 mM TEACl þ 10 mM LiCl. The scale bar corresponds to 10 m. The tip scan speed was 10 m/s. (Reprinted with permission from Ref. 30. Copyright 1998 American Chemical Society.)
Senda et al. [4b] studied the voltammetry of acetylcholine (Achþ ) at a polarizable NB–water interface formed at the tip of a micropipette. Both the height of a sigmoidal wave of the Achþ transfer into the pipette and the peak current of the reverse IT reaction were found to be proportional to bulk concentrations of Achþ in two liquid phases. An experimental scheme similar to conventional stripping voltammetry was used to improve sensitivity of amperometric ion detection. During the first step (accumulation or preelectrolysis, 1 min long), a sufficiently negative potential was applied to the NB-filled pipette to induce the transfer Achþ from the outer aqueous solution. This was followed by a potential sweep in the positive direction, which resulted in a peak-shaped voltammogram of Achþ efflux from the pipette. The peak height was a linear function of the ion concentration in the aqueous phase and increased proportionally to the square root of the accumulation time. This preconcentration effect appears promising for determination of ions at very low concentration levels. (One should notice that pipette surface in Ref. 4b was not silanized, and water most likely has penetrated inside the pipette.) Using a similar technique, Huang et al. determined vitamin B1 down to 4:6 106 M in aqueous solution with a linear range of 5 105 to 1 103 M [37]. A microhole-based ITIES has been used by Osborne et al. for amperometric determination of ionic species in aqueous solutions [12]. They studied the assisted ammonium transfer with DB1816 at the water–DCE interface. Because the concentration of ionophore in the organic phase was high, the measured steady-state current was proportional to the concentration of ammonium in the aqueous phase. The time required to reach a steady state was relatively short (e.g., 5 s for an 11 m hole). A linear relationship was found between the steady-state plateau current and the ammonium concentration over the range 1 to 500 M.
Voltammetry at Micro-ITIES
395
Although amperometric detection of ionic species based on ITIES is feasible, the mechanical instability of a liquid–liquid interface is a major problem which has to be circumvented to develop a commercial ion sensing system. A lot of work has been done to gelify the organic phase in order to achieve a better handling of liquid–liquid systems [38]. Most publications related to IT reactions at a liquid–gel interface have shown that although the diffusion coefficients of ions in the gel are significantly reduced, the IT processes could still be used for amperometric detection. The gelation of the organic phase increases its resistivity, and the higher uncompensated resistance impedes the amperometric determination. Osborne et al. found that this difficulty could be alleviated by using the arrays of microliquid–liquid interfaces [39]. They used this approach to develop the urea and creatinine sensors based on amperometric detection of ammonium. More recently, Girault’s group prepared microfabricated composite polymer membranes, which combine the advantages of the gelified organic phase and micro-ITIES [40]. The composite membrane comprised two polymer layers, i.e., a supporting film of polyethylene terephthalate on which an electrolyte film containing polyvinylchloride was cast. The polyester layer had a laser-etched pattern of microholes (22 m diameter). The polyvinylchloride layer contained 2-nitrophenyl octyl ether plasticizing solution of TBATPBCl electrolyte. The ion transfer behavior of the microhole array interface between an analyte solution and a PVC gel electrolyte was similar to that of conventional micro-ITIES. The steady-state IT current through each hole could be estimated from Eq. (1) when the hole orifices were well-separated. When a composite polymer membrane was used for amperometric sensing of choline [40], the plot of the plateau current against concentration was linear over the range from 0.1 to 0.9 mM of choline. By adding appropriate ionophores (e.g., DB18C6, valinomycin) to the PVC layer, Lee et al. made microinterface polymer membranes work as transducers for the amperometric sensing of alkali metal ions [41]. A composite polymer membrane has also been used as an effective amperometric detector for ion exchange chromatography [42] and showed detection limits similar to those obtained with a conductivity detector. An advantage of the amperometric detector based on micro-ITIES over the conductometric detector is that selectively can be tailored by proper choice of the ionophore. For instance, the selectivity of the membrane toward ammonium in the presence of an excess of sodium could be substantially increased by introducing an ammonium-selective ionophore (such as valinomycin) in the gel membrane [42]. A dual-pipette device can also be used as a sensor for water-soluble (or organic) gaseous species that can change the composition and ionic conductivity of the thin liquid layer linking its barrels [11]. When the outer glass surface is not silanized the pipette orifices are linked by a thin aqueous film formed on the outer pipette wall. Such a film can be sufficiently thick and conductive to yield a reasonable quality voltammetric response suitable for qualitative and quantitative analytical determinations. The response of a -pipette ‘‘in air’’ is largely determined by the properties of the aqueous surface layer, and it is very sensitive to changes in film composition. Such changes occur when the pipette is exposed to a soluble gas. A small ratio of the film thickness to its surface area should result in a high sensitivity and fast response time of such a sensor. Voltammetric experiments without external solution were carried out using a -pipette with one barrel filled with an aqueous solution and the second barrel filled with organic phase. In a two-electrode setup, voltage was applied between Ag=AgCl and Ag=AgTPBCl reference electrodes inserted in two barrels.
396
Liu and Mirkin
In Ref. 11, IT voltammograms of NHþ 4 and NO3 were obtained when a -pipette was exposed to vapors of ammonia and nitric acid, and linear dependence of the voltammetric response on concentration of vapor-generating solution has been demonstrated. The surface liquid layer in all pipettes used in that work was aqueous, and only the detection of water-soluble gases was discussed. However, the detection of organic compounds in the gas phase may also be possible using a -pipette with a nonaqueous sensing film.
REFERENCES 1.
2. 3.
4.
5. 6. 7.
8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
21.
(a) H. H. Girault and D. J. Schiffrin, in Electroanalytical Chemistry vol. 15, (A. J. Bard, ed.), Marcel Dekker, New York, pp. 1–141. (b) A. G. Volkov and D. W. Deamer, Liquid–Liquid Interfaces. Theory and Methods, CRC Press, Boca Raton, 1996. G. Taylor and H. H. Girault. J. Electroanal. Chem. 208: 179 (1986). (a) J. A. Campbell and H. H. Girault. J. Electroanal. Chem. 266:465 (1989). (b) J. A. Campbell, A. A. Stewart, and H. H. Girault. J. Chem. Soc. Faraday Trans. 85:843 (1989). (c) A. A. Stewart, Y. Shao, C. M. Pereira, and H. H. Girault. J. Electroanal. Chem. 305:135 (1991). (d) Y. Shao, M. D. Osborne, and H. H. Girault. J. Electroanal. Chem. 318:101 (1991). (e). Y. Shao and H. H. Girault. J. Electroanal. Chem. 334:203 (1992). (a) M. Senda, T. Kakutani, T. Osakai, and T. Ohkouchi, in Bioelectroanalysis 1. Proceedings of the 1st Bioelectroanalytical Symposium (E. Pungor, ed.), Akademiai Kiado, Budapest, 1987, pp. 353–364. (b) T. Ohkouchi, T. Kakutani, T. Osakai, and M. Senda. Anal. Sci. 7:371 (1991). (c) P. Vanysek and I. C. Hernandez. J. Electrochem. Soc. 137:2763 (1990). (d) P. Vanysek, I. C. Hernandez, and J. Xu. Microchem. J. 41:327 (1990). T. Solomon and A. J. Bard. Anal. Chem. 67:2787 (1995). V. J. Cunnane, D. J. Schiffrin, and D. E. Williams. Electrochim. Acta 40:2943 (1995). (a) K. Tokuda, F. Kitamura, Y. Liao, M. Okuwaki, and T. Ohsaka, in Charge Transfer at Liquid/Liquid and Liquid/Membrane Interface, Kyoto, 1996, pp. 7–8. (b) Y. Liao, M. Okuwaki, F. Kitamura, T. Ohsaka, and K. Tokuda. Electrochim. Acta 44:117 (1998). (a) Y. Shao and M. V. Mirkin. J. Am. Chem. Soc. 119:8103 (1997). (b) Y. Shao and M. V. Mirkin. J. Electroanal. Chem. 439:137 (1997). C. Wei, A. J. Bard, and S. W. Feldberg. Anal. Chem. 69:4627 (1997). Y. Shao, B. Liu, and M. V. Mirkin. J. Am. Chem. Soc. 120:12700 (1998). B. Liu, Y. Shao, and M. V. Mirkin. Anal. Chem. 72:510 (2000). M. D. Osborne, Y. Shao, C. M. Pereira, and H. H. Girault. J. Electroanal. Chem. 364:155 (1994). J. Josserand, J. Morandini, H. J. Lee, R. Ferrigno, and H. H. Girault. J. Electroanal. Chem. 468:42 (1999). L. Murtoma¨ki and K. Kontturi. J. Electroanal. Chem. 449:225 (1998). S. Wilke and T. Zerihun. Electrochim. Acta 44:15 (1998). B. Quinn, R. Lahtinen, L. Murtoma¨ki, and K. Kontturi. Electrochim. Acta 44:47 (1998). H. H. Girault. In Modern Aspects of Electrochemistry, vol. 25 (J. O.’M. Bockris, B. E. Conway, and R. E. White, eds.), Plenum Press, New York, 1993, pp. 1–62. (a) A. A. Stewart, G. Taylor, H. H. Girault, and J. McAleer. J. Electroanal. Chem. 296:491 (1990). (b) P. D. Beattie, A. Delay, and H. H. Girault. J. Electroanal. Chem. 380:167 (1995). Y. Shao and M. V. Mirkin. Anal. Chem. 70:3155 (1998). (a) D. Shoup and A. Szabo. J. Electroanal. Chem. 160:27 (1984). (b) Y. Fang and J. Leddy. Anal. Chem. 67:1259 (1995). (c) J. L. Amphlett and G. Denualult. J. Phys. Chem. B102:9946 (1998). K. B. Oldham, J. C. Myland, C. G. Zoski, and A. M. Bond. J. Electroanal. Chem. 270:79 (1989).
Voltammetry at Micro-ITIES
397
22. C. Amatore, in Physical Electrochemistry: Principles, Methods, and Applications (I. Rubinstein, ed.), Marcel Dekker, New York, 1995, pp. 131–163. 23. C. G. Phillips and H. A. Stone. J. Electroanal. Chem. 437:157 (1997). 24. P. D. Beattie, A. Delay, and H. H. Girault. Electrochim. Acta 40:2961 (1995). 25. (a) R. Ferrigno, P.-F. Brevet, and H. H. Girault. Electrochim. Acta 42:1895 (1997), (b) L. C. R. Alfred and K. B. Oldham. J. Phys. Chem. 100:2170 (1996). 26. User’s Manual for Micropipette Puller Model P-2000. Sutter Instruments, Novato, CA, 1998. 27. M. V. Mirkin and A. J. Bard. Anal. Chem. 64:2293 (1992). 28. T. Kakiuchi. J. Electroanal. Chem. 322:55 (1992). 29. A. J. Bard, F.-R. F. Fan, and M. V. Mirkin. in Electroanalytical Chemistry, vol. 18, (A. J. Bard, ed.), Marcel Dekker, New York, 1994, pp. 243–373. 30. Y. Shao and M. V. Mirkin. J. Phys. Chem. B 102:9915 (1998). 31. B. R. Horrocks and M. V. Mirkin. Anal. Chem. 70:4653 (1998). 32. (a) T. W. Welch and H. H. Thorp. J. Phys. Chem. 100:13829 (1996). (b). M. T. Carter, M. Rodriguez, and A. J. Bard. J. Am. Chem. Soc. 111:8901 (1989). (c) M. T. Carter and A. J. Bard. J. Am. Chem. Soc. 109:7528 (1987). (d) J. Swiatek. J. Coord. Chem. 33:191 (1994). 33. (a) G. Geblewicz and D. J. Schiffrin. J. Electroanal. Chem. 244:27 (1988). (b) H. H. Girault and D. J. Schiffrin. J. Electroanal. Chem. 244:15 (1988). 34. A. J. Bard and L. R. Faulkner. Electrochemical Methods, John Wiley, New York, 1980. 35. B. Liu and M. V. Mirkin. J. Am. Chem. Soc. 121:8352 (1999). 36. (a) G. Denuault, M. H. T. Frank, and L. M. Peter. Faraday Discuss. Chem. Soc. 94:23 (1992). (b) C. Wei, A. J. Bard, G. Nagy, and K. Toth. Anal. Chem. 67:1346 (1995). 37. B. Huang, B. Yu, P. Li, M. Jiang, Y. Bi, and S. Wu. Anal. Chim. Acta 312:329 (1995). 38. (a) F. Silva, M. J. Sousa, and C. M. Pereira. Electrochim. Acta 42:3095 (1997). (b) P. Vanysek. Adv. Chem. Ser. 235:55 (1994). (c) V. Marecek, H. Janchenova, M. Brezina, and M. Betti. Anal. Chim. Acta 244:15 (1991). (d) E. Wang and H. M. Ji. Electroanalysis 1:75 (1989). (e) T. Osakai, T. Kakutani, and M. Senda. Anal. Sci. 4:529 (1988). (f) O. Dvorak, V. Marecek, and Z. Samec. J. Electroanal. Chem. 284:205 (1990). 39. (a) M. D. Osborne and H. H. Girault. Electroanalysis 7:714 (1995). (b) M. D. Osborne and H. H. Girault. Mikrochim. Acta 117:175 (1995). 40. H. J. Lee, P. D. Beattie, B. J. Seddon, M. D. Osborne, and H. H. Girault. J. Electroanal. Chem. 440:73 (1997). 41. H. J. Lee, C. Beriet, and H. H. Girault. J. Electroanal. Chem. 453:211 (1998). 42. H. J. Lee and H. H. Girault. Anal. Chem. 70:4280 (1998).
16 Dynamics of Polar Solvent Motion at Liquid Interfaces NANCY E. LEVINGER Fort Collins, Colorado RUTH E. RITER Georgia
I.
Department of Chemistry, Colorado State University,
Department of Chemistry, Agnes Scott College, Decatur,
INTRODUCTION
As this volume attests, a wide range of chemistry occurs at interfacial boundaries. Examples range from biological and medicinal interfacial problems, such as the chemistry of anesthesia, to solar energy conversion and electrode processes in batteries, to industrialscale separations of metal ores across interfaces, to investigations into self-assembled monolayers and Langmuir–Blodgett films for nanoelectronics and nonlinear optical materials. These problems are based not only on structure and composition of the interface but also on kinetic processes that occur at interfaces. As such, there is considerable motivation to explore chemical dynamics at interfaces. Kinetics of chemical reactions at liquid interfaces has often proven difficult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface specifically has been developed. In bulk solution dynamics of fast chemical reactions, such as electron transfer, have been shown to depend on the dynamical properties of the solvent [2,3]. Specifically, the rate at which the solvent can relax is directly correlated with the fast electron transfer dynamics. As such, there has been considerable attention paid to the dynamics of polar solvation in a wide range of systems [2,4–6]. The focus of this chapter is the dynamics of polar solvation at liquid interfaces. 399
400
Levinger and Riter
Solvation dynamics refers to the rate of solvent reorganization in response to an abrupt change in solute properties [2,4–7]. In most experiments measuring this phenomenon, the solute is a chromophore that undergoes an electronic transition resulting almost exclusively in a change in its charge distribution. The dynamic response of the system to this change in solute properties is usually monitored by measuring the time-resolved fluorescence Stokes shift (TRFSS) in the chromophore’s emission spectrum [5] or through various photon echo spectroscopies [4,8–14]. In many chemical reactions, especially those involving electron transfer, the dynamic solvent response to a solute-induced electrostatic perturbation plays an important role, making solvation dynamics not only interesting in its own right, but an essential component of understanding the effects of solvents on chemical reactions [3,15–17]. This connection to chemical reactions, as well as experimental advances that have made it possible to observe solvation dynamics on the subpicosecond time scale, have generated a great deal of recent interest in this phenomenon and a considerable amount of new information about it. Several recent reviews summarize the advances in this field, primarily focussing on solvation dynamics in bulk liquids [4,8–14]. In contrast to the well-studied bulk liquids, much less is known about the topic of this chapter, the dynamics of polar solvation occurring in heterogeneous media or at liquid interfaces. To investigate the solvation dynamics at liquid interfaces, researchers have primarily employed TRFSS methods or analogs thereof. TRFSS experiments measure solvation dynamics by monitoring the time evolution of the Stokes shift of the fluorescence spectrum of chromophores, such as coumarin dyes, which undergo very little structural change on electronic excitation. Figure 1(a) displays a representative picture of the time-evolving shifting fluorescence spectrum of coumarin 343 (C343 structure is shown in Fig. 2). The TRFSS arises primarily from the change in the solute–solvent interaction potential brought about by the solute S0 ! S1 electronic transition [4]. The frequency shift monitored in the experiment can therefore be expressed as ðtÞ ¼ g þ EðtÞ=h
ð1Þ
where g is the transition frequency for the isolated molecule, h is Planck’s constant, the overbar represents an average over different chromophores, and E ¼ U1 U0
ð2Þ
where U1 and U0 are the solute–solvent potentials for the solute in the S1 and S0 electronic states. For these chromophores that undergo a substantial change in dipole on electronic excitation, E is primarily electrostatic in nature, that is, due primarily to the change in the solute charge distribution, usually represented as a change in partial charges. In terms of E, the TRFSS response function CðtÞ is given by EðtÞ Eð1Þ CðtÞ SðtÞ ¼ ð3Þ Eð0Þ Eð1Þ where t, 0, and 1 refer to the time of the measurement, instantaneously after transition, and at equilibrium, respectively. Thus, experimentally E is estimated by the peak or average frequency of the fluorescence spectrum. Figure 1(b) shows the CðtÞ function generated from the data in Fig. 1(a). To extrapolate back to t ¼ 0, the technique given by Fee and Maroncelli has been used [18]. Solvation dynamics have been measured for a wide range of polar (and some not so polar) solvents. In all solvents, two distinct types of motion comprise the response [7]. The
Dynamics of Polar Solvent Motion
401
FIG. 1 (a) Time evolution of the fluorescence spectrum of coumarin 343 in water demonstrating the time-resolved fluorescence Stokes shift; (b) experimentally derived CðtÞ function from data in part (a).
inertial response is always ultrafast occurring on the sub-75 fs timescale and is due to underdamped molecular motion. The diffusive response can range from subpicosecond to nanoseconds or longer and arises from collective motion of the solvent. Water, a component of most liquid–liquid interfaces, is a very fast relaxing solvent; both inertial and diffusive relaxation are complete for bulk water in less than a picosecond [19]. While completely nonpolar solvents do not contribute to polar solvation dynamics, solvents such as benzene can contribute to the polar solvation dynamics through induced dipole effects [5]. Thus, one could imagine liquid–liquid interfaces in which either only one or both phases contribute to the dynamics. For the remainder of this chapter, we discuss results for various studies of interfacial solvation dynamics. We first discuss studies at liquid–liquid interfaces at planar interfaces and in microheterogeneous media in Section II. In Section III, we discuss solvation dynamics at liquid–solid interfaces. In Section IV, we review theoretical models and simulations of solvation dynamics at liquid interfaces. Finally, we conclude with a discussion of future studies.
402
Levinger and Riter
FIG. 2 Structures of the probe molecules used in the studies reviewed.
II.
DYNAMICS AT LIQUID–LIQUID INTERFACES
Dynamics of polar solvation have been studied at a range of differing liquid–liquid interfaces. These include planar liquid–liquid, and liquid–air interfaces as well as those found in microheterogeneous media. We discuss each case separately. A.
Planar Interfaces
The first investigation of dynamical processes at well-defined liquid–liquid boundaries was reported in the 1980s. Srinivasan and de Levie [20] examined the rates of nucleation and growth of organic films at the interface between mercury and various aqueous solutions using mercury as an electrode. Since then, various studies allude to dynamical properties of the solvent at a liquid–liquid interface. To date, there has been only one report of solvation dynamics at a planar liquid–liquid interface. Bessho et al. [21] investigated the microenvironments of 8-anilino-1-naphthalensulfonate (ANS, structure shown in Fig. 2). at the heptane–water interface using time-resolved total internal reflection fluorescence spectroscopy. They found a biexponential response to the fluorescence dynamics. They interpreted this result as indicative of two distinct probe environments. Specifically, they report the longer response time, ¼ 1:8 ns, to indicate molecules residing within a few
Dynamics of Polar Solvent Motion
403
nanometers of the interface, and a shorter response time, ¼ 330–420 ps, corresponding to molecules in a range of positions further from the interface. While it is hard to imagine the surface perturbation extending nanometers away from the surface, the results reported demonstrate perturbation of the solvent dynamics by the interface. Unfortunately, the apparatus used for these experiments had limited time resolution (> 50 ps instrument response) precluding direct comparison with solvation dynamics in bulk water. Recently, Eisenthal and coworkers have developed time-resolved surface second harmonic techniques to probe dynamics of polar solvation and isomerization reactions occurring at liquid–liquid, liquid–air, and liquid–solid interfaces [22]. As these experiments afford subpicosecond time resolution, they are analogous to ultrafast pump–probe measurements. Specifically, they excite a dye molecule residing at the interface and follow its dynamics via the resonance enhance second harmonic signal. To date, the interfacial solvation dynamics studies by the Eisenthal group have probed water–air interfaces [23,24]. These experiments are analogous to TRFSS measurements. Zimdars et al. [23] have recently reported on the solvation dynamics of water at the air–water interface using the probe molecule coumarin 314 (C314, structure shown in Fig. 2). They found that interfacial solvation dynamics has a time constant of 790 30 fs, which is slightly slower but very similar to what is observed for diffusive water motion in bulk [19]. More recently, they have been able to investigate how the solute orientation at the interface affects the measured solvation dynamics response by taking advantage of the polarization sensitivity of the second harmonic generation [24]. As shown in Fig. 3, they find that solvation dynamics measured for solute molecules lying in the plane of the interface are faster, ¼ 820 fs, than the solvation dynamics measured for solute molecules oriented perpendicular to the interface, ¼ 1215 fs. They interpret these results as indicative of shifting spectral envelopes for the differently oriented solute molecules. Eisenthal and coworkers have explored interfacial photoisomerization reactions and rotational dynamics for probe molecules at several interfaces including the water–air, water–alkane, and water–silica interface using femtosecond time-resolved second harmonic generation. While these studies do not probe solvation dynamics, they are related to solvation dynamics because they provide information about frictional forces that constitute a part of the polar solvent response. Eisenthal and coworkers have explored the photoisomerization of two different systems, DODCI at the water–air interface and malachite green at water–air and water–alkane interfaces [25,26]. These dye structures are shown in Fig. 2. In the case for DODCI at a water–air interface, the isomerization was faster at the interface than it was in bulk aqueous solution, 220 ps vs. 520 ps, respectively [25]. For malachite green, a molecule whose isomerization dynamics are quite insensitive to polarity but highly sensitive to viscosity in bulk solution, the interfacial isomerization occurred more slowly than in bulk, 2 ps vs. 700 fs at the water–air interface and in bulk water, respectively [26]. Surprisingly, the malachite green isomerization dynamics at water–alkane interfaces were insensitive to the viscosity of the alkane phase. At first glance, these results appear to be contradictory as they indicate both decreased and increased friction at the same (water–air) interface. However, they can be reconciled by considering the exact portion of the interface that the probe molecule samples. Since DODCI and malachite green are significantly different molecules, there is no reason to believe that they would occupy the same location or depth in the interface. Eisenthal and coworkers have also measured interfacial friction via the rotational dynamics of probe molecules at the interface. In their first study, Eisenthal and coworkers probed the rotational dynamics of rhodamine 6G (R6G, structure shown in Fig. 2) at the
404
Levinger and Riter
FIG. 3 Solvation dynamics dependence of coumarin 314 probe molecule orientation at the air– water interface. Signals are generated with a 420 nm pump photon and probed by surface second harmonic signal with 840 nm (SH at 420), ð2Þ xzx element. The normalized change in SH field is plotted vs. pump delay. is derived from a single exponential fit to the data. (a) Pump polarization S (inplane), (b) Pump polarization P (out-of-plane). (Reprinted from Ref. 24 with permission from the American Chemical Society.)
Dynamics of Polar Solvent Motion
405
water–air interface [27]. They found that the rotational dynamics slowed down at the interface compared to bulk solution [27]. More recently, they measured rotational dynamics for the solvation dynamics probe molecule, C314, at the water–air interface [28]. Here they measured faster molecular rotation for motion out of the plane of the interface, r ¼ 350 ps, than for in-plane rotation, r ¼ 600 ps. They note that the reorientation times for both in-plane and out-of-plane motion are slower than rotation in bulk solution, where r ¼ 100 ps. The out-of-plane rotational time agrees well with their previous results on R6G. They attribute the increased rotation time to increased friction at the interface. These results are somewhat nonintuitive because theoretical predictions suggest that there should be decreased friction at the interface. However, as the authors note, it is possible that the probe molecule resides in a preferred orientation with respect to hydrogen bonding and that molecular rotation reflects the time necessary to break those hydrogen bonds. Overall, while the experiments probing photoisomerization and rotational motion are intriguing, there remains a lot to be done before we can develop intuition about the impact of the interface on such molecular motion. B.
Interfaces in Microheterogeneous Media
While solvation dynamics have only been studied at a few planar interfaces, the interface present in self-assembled systems has recently show significant activity. While Sarkar et al. have measured solvation dynamics at the liquid interfaces of normal micelles, these systems have not been extensively examined [29]. Using picosecond time-resolved fluorescence spectroscopy of coumarin 480 (C480, structure shown in Fig. 2) they have investigated solvation dynamics of three normal micelle solutions prepared with the neutral surfactant Triton X-100 (TX), cationic cetyltrimethylammonium bromide (CTAB), and anionic sodium dodecyl sulfate (SDS). Above the critical micellar concentration, these surfactants are well known to form spherical micellar aggregates of 100–150 surfactant molecules with radii of 50 A˚ for TX and CTAB and 30 A˚ for SDS. Small-angle x-ray, neutron scattering, NMR, and fluorescence studies show that the micellar core consists of hydrocarbon chains and the Stern layer is a shell, 6–9 A˚ thick, comprising polar headgroups, counterions, and water. As with the results from Bessho et al. [21], these experiments were limited by time resolution of approximately 50 ps, thus any bulklike water motion would not be observed. The solvation dynamics of the three different micelle solutions, TX, CTAB, and SDS, exhibit time constants of 550, 285, 180 ps, respectively. The time constants show that solvent motion in these solutions is significantly slower than bulk water. The authors attribute the observed time constants to water motion in the Stern layer of the micelles. This conclusion is supported by the steady-state fluorescence spectra of the C480 probe in these solutions. The spectra exhibit a significant blue shift with respect the spectrum of the dye in bulk water. This spectral blue shift is attributed to the probe being solvated in the Stern layer and experiencing an environment with a polarity much lower than that of bulk water. This work also shows that the time constants for the ionic surfactant micelle solutions are twice as fast as the TX solution time constant. Differences between the Stern layers of the micelles appear to be the charge of the surfactant polar headgroups and the presence of counterions. However, these differences do not account for the observed dynamics. Since the polar headgroups and counterions should interfact more strongly with the water molecules, the water motion at the interface should be slower. This view is supported by recent investigations where systematic variation of surfactant counter-
406
Levinger and Riter
cations revealed significant effects on the solvation dynamics measured in reverse micelles [30,31]. In addition, the observed time-dependent Stokes shift of the probe in the TX solution is 1035 cm1 , while the magnitude of the Stokes shift is half that for the ionic surfactant solutions. Hence, these results suggest that the environment sensed by probe molecules differs significantly for the three micellar solutions. In the past few years, a range of solvation dynamics experiments have been demonstrated for reverse micellar systems. Reverse micelles form when a polar solvent is sequestered by surfactant molecules in a continuous nonpolar solvent. The interaction of the surfactant polar headgroups with the polar solvent can result in the formation of a welldefined solvent pool. Many different kinds of surfactants have been used to form reverse micelles. However, the structure and dynamics of reverse micelles created with Aerosol-OT (AOT) have been most frequently studied. AOT reverse micelles are monodisperse, spherical water droplets [32]. The micellar size is directly related to the water volume-tosurfactant surface area ratio defined as the molar ratio of water to AOT, w¼
½H2 O ½surfactant
ð4Þ
AOT is an anionic surfactant complexed to the counterion, usually sodium. The water molecules in the intramicellar water pool are either free or bound to the interface. The bound water can interact with various parts of the surfactant. These interactions include hydrogen-bonding interactions with oxygen molecules on the sulfonate and succinate groups, ion–dipole interactions with the anionic surfactant headgroup and counterion, dipole–dipole interactions with the succinate group, and dispersive forces with the hydrocarbon tails. Several research groups have investigated the dynamical response of AOT reverse micellar systems. The first work showing clear evidence for water motion in reverse micelles was done by Zhang and Bright [33]. They investigated the reorganization of water in the interior of AOT reverse micelles on the nanosecond time scale as a function of w and temperature using time-resolved fluorescence spectroscopy of ANS. At low water levels, w < 2:5, they observed two relaxation processes with time constants of 0.5–1.7 and 3.5–11.8 ns, that they attributed to ‘‘free’’ and ‘‘bound’’ water motion, respectively. For w > 2:5, a single reorganization process with a time constant of 0.8–1.2 ns was reported. In general, they found that the observed rate constants decrease with increasing w. They also determined that at low water content, the activation barriers for ‘‘free’’ and ‘‘bound’’ water motion are essentially equivalent and that frequency factors influence the rates. While at higher water content, the height of the activation barrier for water motion is relatively small. Cho et al. [34] also probed the interior of AOT reverse micelles using timeresolved fluorescence of ANS with time resolution of 50 ps. Their results were similar to Zhang and Bright observing the two characteristic relaxation times. They attributed the slowest water motion to water molecules near the surfactant interface behaving icelike owing to the strong interactions with the polar-headgroup surface of high curvature. Faster dynamics were attributed to bulklike water 6–18 A˚ from the interface. Using incoherent quasielastic neutron scattering (IQENS), Crupi et al. examined the low-frequency diffusive motions of water molecules in AOT reverse micellar solutions of deuterated cyclohexane [35]. IQENS follows the motion of water by measuring the incoherent cross-sections of H protons. They observed a narrowing of the quasielastic spectrum of water within the reverse micelles as compared to bulk. This narrowing suggests water motion inside the micelles is confined to an approximately 3 A˚ region.
Dynamics of Polar Solvent Motion
407
The observation of slow, confined water motion in AOT reverse micelles is also supported by measured dielectric relaxation of the water pool. Using terahertz timedomain spectroscopy, the dielectric properties of water in the reverse micelles have been investigated by Mittleman et al. [36]. They found that both the time scale and amplitude of the relaxation was smaller than those of bulk water. They attributed these results to the reduction of long-range collective motion due to the confinement of the water in the nanometer-sized micelles. These results suggested that ‘‘free’’ water motion in the reverse micelles are not equivalent to bulk solvation dynamics. Investigation of water motion in AOT reverse micelles determining the solvent correlation function, CðtÞ, was first reported by Sarkar et al. [29]. They obtained time-resolved fluorescence measurements of C480 in an AOT reverse micellar solution with time resolution of > 50 ps and observed solvent relaxation rates with time constants ranging from 1.7 to 12 ns. They also attributed these dynamical changes to relaxation processes of water molecules in various environments of the water pool. In a similar study investigating the deuterium isotope effect on solvent motion in AOT reverse micelles, Das et al. [37] reported that the solvation dynamics of D2 O is 1.5 times slower than H2 O motion. Using time-resolved fluorescence-upconversion spectroscopy with femtosecond resolution, the solvation dynamics of water in the AOT reverse micelles has been reported by Levinger and coworkers [30,31,38]. In general, as w increases, the mobility of water increases, as shown in Fig. 4. This suggests that micellar size plays a role in restricting solvent motion in the reverse micelles. However, the specific details of the micellar interior and morphology appear also to play significant roles in the observed dynamics. In addition, the interior of the AOT reverse micelles is highly ionic, partially due to the presence of the surfactant’s countercation, and this highly concentrated, ionic environment may also play a role. In order to examine the effect of the countercation on water motion in the reverse micelles, Levinger and coworkers [30,31] exchanged the sodium ion commonly complexed to the AOT surfactant for various cations and measured the solvation dynamics in these þ micelles. The countercations examined were ammonium NHþ 4 , potassium K , and calcium 2þ Ca . This work showed that water motion inside the reverse micelles is slower than bulk water motion regardless of the counterion and that the countercation does play a role in reducing water motion in the reverse micelles. As the effective charge of the countercation increases, relatively stronger interactions between water and the cation occurs, resulting in slower solvation dynamics. However, this work also revealed that the immobilization or confined water motion in the reverse micelles is largely due to the restrictive size of the micelles rather than specific water–ion interactions. Water motion in reverse micelles formed with other surfactants has also been examined. Willard et al. [39,40] have investigated the dynamics of water in lecithin reverse micelles as a function of morphology. For lecithin reverse micelles in cyclohexane with w ¼ 4:8, the reverse micelle solutions are nonviscous with isolated, spherical micelles, and a single, very slow relaxation time is observed for water motion inside the micelles. As small amounts of water are added to the sample, the micelles form into an entangled tube network and the micelle solutions become more and more viscous, while the water motion inside the micelle becomes more and more mobile. Three relaxation times are observed with time constants of 0.5, 15, and 200 ps, the fastest of which correlates to free water motion. These results were further confirmed by investigating the water motion in lecithin reverse micelles in benzene [40]. In contrast to lecithin reverse micelles in alkanes, the micelles remain isolated and largely spherical with increasing w. This work suggests that the lecithin perturbs the water pool to a much greater extent than similar AOT reverse
408
Levinger and Riter
FIG. 4 Time-resolved fluorescence Stokes shift of coumarin 343 in Aerosol OT reverse micelles; (a) normalized time-correlation functions, CðtÞ ¼ ðtÞ ð1Þ=ð0Þ ð1Þ, and (b) unnormalized time-correlation functions, SðtÞ ¼ ðtÞ ð1Þ, showing the magnitude of the overall Stokes shift in addition to the dynamic response. w0 ¼ 1:1 (*), 5 (!), 7.5 (&), 15 (^), and 40 (*) and for bulk aqueous Naþ solution (~). Points are data and lines that are multiexponential fits to the data. (Reprinted from Ref. 38 with permission from the American Chemical Society.)
micelles and that the surfactant interface between the water pool and continuous nonpolar solvent phase sequesters water to a much greater degree than has been previously predicted. In addition, water motion has been investigated in reverse micelles formed with the nonionic surfactants Triton X-100 and Brij-30 by Pant and Levinger [41]. As in the AOT reverse micelles, the water motion is substantially reduced in the nonionic reverse micelles as compared to bulk water dynamics with three solvation components observed. These three relaxation times are attributed to bulklike water, bound water, and strongly bound water motion. Interestingly, the overall solvation dynamics of water inside Triton X-100 reverse micelles is slower than the dynamics inside the Brij-30 or AOT reverse micelles, while the water motion inside the Brij-30 reverse micelles is relatively faster than AOT reverse micelles. This work also investigated the solvation dynamics of liquid tri(ethylene glycol) monoethyl ether (TGE) with different concentrations of water. Three relaxation time scales were also observed with subpicosecond, picosecond, and subnanosecond time constants. These time components were attributed to the damped solvent motion, seg-
Dynamics of Polar Solvent Motion
409
mental motion, and the co-operative motion of the polymer solution, respectively. The results of this work show that while the restrictive micellar environment does play a role in the solvation dynamics of water inside nonionic reverse micelles, it is only a minor role. In fact, the interaction of water with the polymer-like headgroups of the surfactants plays the key role in immobilizing water in the micelles. Finally, polar solvation dynamics using solvents other than water has been reported in AOT reverse micelles. Riter et al. have measured the motion of formamide in AOT reverse micelles with w ¼ 1:1. The vibrational spectra of formamide in the reverse micelles indicate that the intramicellar formamide retains a large degree of hydrogen bonding character, and its structure appears significantly less perturbed by the restricted environment than water. However, this work showed that the diffusive solvent motion in the reverse micelles is essentially frozen and the solvation dynamics is very similar to what is observed for water. In addition, Shirota and Horie [42] have reported on the solvation dynamics of methanol and acetonitrile in the AOT reverse micelles. They also found that the solvation dynamics in the reverse micelles are significantly slower than observed in bulk solutions. As for water, methanol motion increases with increasing w. However, the solvation dynamics of acetonitrile in the micelle interior is independent of w. The authors attribute these results to the role of intermolecular hydrogen bonding of the polar solvent in the reverse micelles. The results of TRFSS experiments have shown us that the reverse micellar interior has the effect of limiting solvent mobility [30,31,38–40,42,43] The origin of this immobilization is still unclear. While specific interactions with the surfactant headgroups seem to play a role, the reverse micellar milieu seems more important than a high concentration of ions.
III.
DYNAMICS AT LIQUID–SOLID INTERFACES
Due to the interactions of solvent molecules with the solid surface, one would expect the dynamics at interfaces to differ from bulk solution. Yanagimachi et al. [44] studied solvation dynamics of 1-butanol at silica surfaces. While the shorter solvent relaxation time components could not be resolved due to the > 60 ps time resolution of their instrument, the longer time components increased for the interfacial butanol, and the solvent appeared to be influenced a substantial distance from the interface. Richert and coworkers have probed solvation dynamics in geometrically confined silica sol–gel glass pores using TRFSS [45]. They find that solvent at the silica–solvent interface can exhibit motion orders of magnitude slower than bulk solvent. Using time-resolved optical Kerr effect measurements, Fourkas and coworkers [46,47] have probed liquid dynamics in porous silicate sol– gel glasses. They demonstrate that for weakly wetting solvents, such as CS2 and CH3 I, the dynamics of the molecules at the surface are slowed down due to geometrical confinement. In contrast, for more interacting solvents, such as acetonitrile, the dynamics are influenced by molecular interactions with the surface. Pant and Levinger have measured the solvation dynamics of water at the surface of semiconductor nanoparticles [48,49]. In this work, nanoparticulate ZrO2 was used as a model for the TiO2 used in dye-sensitized solar photochemical cells. Here, the solvation dynamics for H2 O and D2 O at the nanoparticle surface are as fast or faster than bulk water motion. This is interpreted as evidence for reduced hydrogen bonding at the particle interface.
410
Levinger and Riter
As discussed in Section II.A, Eisenthal and coworkers have studied the related problem of isomerization at liquid–solid interfaces. They used time-resolved second harmonic generation to investigate the barrierless photoisomerization of malachite green at the silica–aqueous interface using femtosecond time-resolved second harmonic generation [26]. They found that the photoisomerization reaction proceeded but was an order of magnitude slower at the water–silica interface than in bulk solution.
IV.
THEORETICAL DESCRIPTIONS OF SOLVATION DYNAMICS AT LIQUID INTERFACES
While there exist many models of liquids at interfaces, there are very few that consider solvation dynamics. Compared to experimental studies, there are even fewer models for solvent dynamics at any kind of liquid interface [50–52]. Molecular dynamics calculations have been used to simulate polar–nonpolar interfaces, e.g., water–benzene [53], water– hexanol [54], and water-1,2 dichloroethane [55]. The most striking results from these studies is that the interface is molecularly sharp in all three cases, and there is increased hydrogen bonding on the aqueous side of the interfaces. Molecular dynamics simulations investigating the dynamics of polar solvation occurring in interfacial environments, specifically dynamics of water at liquid–liquid interfaces, have recently been reported by Benjamin and coworkers [51,56–60]. Benjamin’s calculations following solvent relaxation in response to interfacial charge transfer show that the interfacial solvent molecules relax more slowly than bulk solvent [51]. However, as close as one monolayer away from the interface, the water dynamics appear completely bulklike [51]. Michael and Benjamin investigated the solvation dynamics at the water–octanol interface modeled by the 50/50 mixture that was phase separated. In this case, the solvent response occurred on a subpicosecond as well as picosecond time scale. In comparison, the relaxation rate observed one monolayer into the octanol layer, 5 A˚ thick, would be more than two orders of magnitude slower. These results suggest a probe molecule would not only be sensitive to solvation dynamics at interfaces, it would also probe the nature of the interface. In his work, Benjamin has also simulated solvent dynamics at the interface between water and 1,2 dichloroethane [55]. The solvation dynamics are predicted to be modestly affected by the nonisotropic interfacial environment with the largest difference in the calculated time correlation functions arising from increased hydrogen bonding. Chandra and his coworkers have developed analytical theories to predict and explain the interfacial solvation dynamics. For example, Chandra et al. [61] have developed a time-dependent density functional theory to predict polarization relaxation at the solid– liquid interface. They find that the interfacial molecules relax more slowly than does the bulk and that the rate of relaxation changes nonmonotonically with distance from the interface They attribute the changing relaxation rate to the presence of distinct solvent layers at the interface. Senapati and Chandra have applied theories of solvents at interfaces to a range of model systems [62–64]. While they are not direct theories or simulations of solvation dynamics, per se, several groups have modeled liquid dynamics at interfaces. Ursenbach et al. [50] have developed a model for water at the surface of a silicon single crystal. Their results show that the vibrational modes of water molecules at the surface are virtually unchanged from their bulk values. However, they suggest that ultrafast motions of the interfacial solvent, occurring on the time scale of molecular vibrations, may impact interfacial electron transfer. Using molecular dynamics calculations, Hartnig et al. [65] have simulated water
Dynamics of Polar Solvent Motion
411
motion within model polar and nonpolar cylindrical pores. In nonpolar pores, reduced hydrogen bonding at the surface results in a translational motion and dipolar motion that is faster than bulk water. However, in polar pores, generated by adding surface charges to the model system, the translation motion and dipolar relaxation times are longer than bulk. Using molecular dynamics calculations, Shinto et al. [66] have modeled the response of water at NaCl surfaces. While their simulations show that the water diffusivity is reduced at the surface, they also observe a strong perturbation to the hydrogen-bonding network for solvent molecules at the solid surfaces. A few groups have modeled dynamics at interfaces and in the aqueous core of selfassembled structures. Brown and Clarke [67] modeled an aqueous reverse micelle in a nonpolar solvent using a cationic surfactant. They reported that the anions associated with the surfactant are tightly bound to the cation headgroup surface although water molecules can significantly penetrate into the hydrophobic region. Additionally, water molecules at the interface interact strongly with the anions and therefore do not have bulklike characteristics. Linse [53] investigated the structure and dynamics of water in reverse micelles formed with an anionic surfactant similar to AOT. He reported that interactions of water molecules with the ionic headgroups of the surfactant interface essentially break the hydrogen-bonding network of the water and that although the hydrophobic portion of the interface plays a role in breaking this network, it is only a minor one. He also attributed the interaction of the water with sodium ions and anionic headgroup to reduced translational and rotational motion of water in the micellar environment. Very recently, Faeder and Ladanyi have modeled the interior of AOT reverse micelles including solvation dynamics [68]. They observe water motion that is strongly impacted by the interfacial chemistry and that water does not relax like bulk solvent at all. The slower relaxation in this case is attributed to strong interactions of the water molecules at the reverse micellar inner interface.
V.
CONCLUSIONS AND FUTURE WORK
The overall picture arising from a comprehensive view of the solvation dynamics studies at interfaces that have been done can be summarized; interfacial dynamics differ from bulk solution and cannot simply be considered the same as the bulk. In most cases, the structure of the interface appears to impact the dynamics by slowing them down. However, in a few cases, the dynamics appear to speed up. While apparent from the amount of work that can be reported, it is obvious that we really do not have a comprehensive view of the dynamics of polar solvation at liquid interfaces. Especially lacking are studies probing the inertial response to the dynamics of polar solvation occurring at interfaces. There is enormous room for growth in the entire field as there exist such an extensive range of interfaces that are important in chemistry, biology, and physics. We can look forward to more detailed studies on the vast array of available systems.
REFERENCES 1. 2.
G. J. Hanna and R. D. Noble. Chem. Rev. 85:583 (1985). P. F. Barbara and W. Jarzeba, in Advances in Photochemistry, vol. 15 (eds. D. H. Volman, G. S. Hammond, and K. Gollnick) John Wiley, 1990, pp. 1–68.
412 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.
Levinger and Riter P. F. Barbara, T. J. Meyer, and M. A. Ratner. J. Phys. Chem. 100:13148 (1996). M. Maroncelli. J. Mol. Liq. 57:1 (1993). M. L. Horng, J. A. Gardecki, A. Papazyan, and M. Maroncelli. J. Phys. Chem. 99:17311 (1995). G. R. Fleming and M. H. Cho. Annu. Rev. Phys. Chem. 47:109 (1996). R. M. Stratt and M. Maroncelli. J. Phys. Chem. 100:12981 (1996). J. D. Simon. Acc. Chem. Res. 21:128 (1988). J. D. Simon. Pure Appl. Chem. 62:2243 (1990). B. Bagchi. Annu. Rev. Phys. Chem. 40:115 (1989). B. Bagchi and A. Chandra. Adv. Chem. Phys. 80:1 (1991). P. F. Barbara and W. Jarzeba. Adv. Photochem. 15:1 (1990). W. Jarzeba, G. C. Walker, A. E. Johnson, and P. F. Barbara. Chem. Phys. 152:57 (1991). R. M. Stratt and M. Maroncelli. J. Phys. Chem. 100:12981 (1996). H. Heitele. Angew. Chem. 105:378 (1993). (See also Angew. Chem. Int. Ed. Engl. 1993, 1932(1993), 1359–1997.) J. T. Hynes. Understand. Chem. React. 7:345 (1994). P. J. Rossky and J. D. Simon. Nature (London) 370:263 (1994). R. S. Fee and M. Maroncelli. Chem. Phys. 183:235 (1994). R. Jimenez, G. R. Fleming, P. V. Kumar, and M. Maroncelli. Nature 369:471 (1994). R. Srinivasan and R. de Levie. J. Phys. Chem. 91:2904 (1987). K. Bessho, T. Uchida, A. Yamauchi, T. Shioya, and N. Teramae. Chem. Phys. Lett. 264:381 (1997). E. Eisenthal. Chem. Rev. 96:1348 (1996) D. Zimdars, J. I. Dalap, K. B. Eisenthal, and T. F. Heinz. Chem. Phys. Lett 301:112 (1999). D. Zimdars and K. B. Eisenthal. J. Phys. Chem. B 103:10567 (1999). E. V. Sitzmann and K. B. Eisenthal. J. Phys. Chem. 92:4579 (1988). X. Shi, E. Borguet, A. N. Tarnovsky, and K. B. Eisenthal. Chem. Phys. 205:167 (1996). A. Castro, E. V. Sitzmann, D. Zhang, and K. B. Eisenthal. J. Phys. Chem. 95:6752 (1991). D. Zimdars, J. I. Dalap, K. B. Eisenthal, and T. F. Heinz. J. Phys. Chem. B 103:3425 (1999). N. Sarkar, K. Das, A. Datta, S. Das, and K. Bhattacharyya. J. Phys. Chem. 100:10523 (1996). D. Pant, R. E. Riter, and N. E. Levinger. J. Chem. Phys. 109:9995 (1998). R. E. Riter, E. P. Undiks, and N. E. Levinger. J. Am. Chem. Soc. 120:6062 (1998). T. De and A. Maitra. Adv. Colloid Interface Sci. 59:95 (1995). J. Zhang and F. V. Bright. J. Phys. Chem. 95:7900 (1991). C. H. Cho, M. Chung, J. Lee, T. Nguyen, S. Singh, M. Vedamuthu, S. H. Yao, J. B. Zhu, and G. W. Robinson. J. Phys. Chem. 99:7806 (1995). V. Crupi, S. Magazu´, G. Maisano, D. Majolino, and P. Migliardo. Physica Scripta 50:200 (1994). D. M. Mittleman, M. C. Nuss, and V. L. Colvin. Chem. Phys. Lett. 275:332 (1997). S. Das, A. Datta, and K. Bhattacharyya. J. Phys. Chem. A 101:3299 (1997). R. E. Riter, D. M. Willard, and N. E. Levinger. J. Phys. Chem. B 102:2705 (1998). D. M. Willard, R. E. Riter, and N. E. Levinger. J. Am. Che. Soc. 120:4151 (1998). D. M. Willard and N. E. Levinger, J. Phys. Chem., submitted (2000). D. Pant and N. E. Levinger. Langmuir, submitted (2000). H. Shirota and K. Horie. J. Phys. Chem. B 103:1437 (1999). R. E. Riter, E. P. Undiks, J. R. Kimmel, and N. E. Levinger. J. Phys. Chem. B 102:7931 (1998). M. Yanagimachi, N. Tamai, and H. Masuhara. Chem. Phys. Lett. 200:469 (1992). C. Streck, Y. B. Melnichenko, and R. Richert. Phys. Rev. B Condensed Matter 53:5341 (1996). B. J. Loughnane, R. A. Farrer, and J. T. Fourkas. J. Phys. Chem. B 102:5409 (1998). B. J. Loughnane and J. T. Fourkas. J. Phys. Chem. B 102:10288 (1998). D. Pant and N. E. Levinger. Chem. Phys. Lett 292:200 (1998). D. Pant and N. E. Levinger. J. Phys. Chem. B 103:7846 (1999). C. P. Ursenbach, A. Calhoun, and G. A. Voth. J. Chem. Phys. 106:2811 (1997).
Dynamics of Polar Solvent Motion
413
51. I. Benjamin, in Reaction Dynamics in Clusters and Condensed Phases (J. Jortner, ed.), Kluwer Academic Publishers, Netherlands, 1994, pp. 179–194. 52. D. Michael and I. Benjamin. J. Phys. Chem. B 102:5145 (1998). 53. P. Linse. J. Chem. Phys. 86:4177 (1987). 54. J. Gao and W. L. Jorgensen. J. Phys. Chem. 92:5813 (1988). 55. I. Benjamin. J. Chem. Phys. 97:1432 (1992). 56. I. Benjamin. Chem. Phys. 180:287 (1994). 57. I. Benjamin, in Liquid–Liquid Interfaces (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, FL, 1996, pp. 179–211. 58. I. Benjamin. Annu. Rev. Phys. Chem. 48:407 (1997). 59. D. Michael and I. Benjamin. J. Phys. Chem. 99:1530 (1995). 60. D. A. Rose and I. Benjamin. J. Phys. Chem. 96:9561 (1992). 61. A. Chandra, S. Senapati, and D. Sudha. J. Chem. Phys. 109:10439 (1998). 62. A. Chandra and S. Senapati. J. Mol. Liq. 77:77 (1998). 63. S. Senapati and A. Chandra. Theochem. J. Mol. Struct. 455:1 (1998). 64. S. Senapati and A. Chandra. Chem. Phys. 231:65 (1998). 65. C. Hartnig, W. Witschel, and E. Spohr. J. Phys. Chem. B 102:1241 (1998). 66. H. Shinto, T. Sakakibara, and K. Higashitani. J. Phys. Chem. B 102:1974 (1998). 67. D. Brown and J. H. R. Clarke. J. Phys. Chem. 92:2881 (1988). 68. J. Faeder and B. M. Ladanyi. J. Phys. Chem. B 104:1033 (2000).
17 Capacitance and Surface Tension Measurements of Liquid^Liquid Interfaces ZDENE˘K SAMEC J. Heyrovsky´ Institute of Physical Chemistry, Academy of Sciences of The Czech Republic, Prague, Czech Republic
I.
INTRODUCTION
The structure of the interface between two immiscible electrolyte solutions (ITIES) has been the matter of considerable interest since the beginning of the last century [1]. Typically, such a system consists of water (w) and an organic solvent (o) immiscible with it, each containing an electrolyte. Much information about the ITIES has been gained by application of techniques that involve measurements of the macroscopic properties, such as surface tension or differential capacity. The analysis of these properties in terms of various microscopic models has allowed us to draw some conclusions about the distribution and orientation of ions and neutral molecules at the ITIES. The purpose of the present chapter is to summarize the key results in this field.
II.
THERMODYNAMIC ANALYSIS
A.
Gibbs Adsorption Equation
Thermodynamics of the ITIES was developed by several authors [2–6] on the basis of the interfacial phase model of Gibbs or Guggenheim. General treatments were outlined by Kakiuchi and Senda [5] and by Girault and Schiffrin [6]. At a constant temperature T and pressure p the change in the surface tension can be related to the relative surface excess concentrations iw;o of the species i with respect to both solvents [6], d ðT; p ¼ constÞ ¼
k X
~i w;o i d
ð1Þ
i¼1
where ~ i ¼ i þ zi F’ is the electrochemical potential, i is the chemical potential, zi is the number of the elementary charges (charge number) carried by the species i, F is the Faraday constant, and ’ is the inner (Galvani) potential of the phase and the summation is carried out over all species (i.e., ions and ion pairs) present in both phases. The relative surface excess concentrations iw;o are defined by 415
416
Samec
w;o ¼ i nwi i
w noi o
ð2Þ
where i ¼ ni =A is the surface concentration (ni is the total number of moles of the species i in the interfacial region and A is the interfacial area), no and nw are the number of moles of a component (ion, ion pair, or solvent) in the organic and water phase respectively, and , w , or o are the following determinants: w o w no nww nw w no o ð3Þ ¼ ¼ ¼ o w o no nw no now o w o w Equation (2) is considerably simplified if the mutual solubility of the two solvents is low, i.e., now nww and nwo noo , w;o ¼ i i
nwi noi w w o o nw no
ð4Þ
Further simplifications are possible if the species i is not present in one or the other liquid phase ðni ¼ 0Þ, i.e., the second or the third term in Eq. (4) vanishes. The equilibrium partition of ions present in the system gives rise to the equilibrium Galvani potential difference wo ’ ¼ ’ðwÞ ’ðoÞ between the phases w and o (Nernst potential) [7,8] wo ’ ¼ wo ’0i þ ðRT=zi F Þ lnðaoi =awi Þ
ð5Þ
where ao and aw are the activities of ions in the organic and water phase respectively, and wo ’0i is the standard potential difference, which is related to the standard Gibbs energy of ion transfer from w to o, ow G0i , wo ’0i ¼ ow G0i =zi F
B.
ð6Þ
Nonpolarized ITIES
The simplest system is represented by the nonpolarized interface, which is formed in the presence of a single binary electrolyte RX completely dissociating into ions Rþ and X in each phase, Rþ X ðoÞ
j
Rþ X ðwÞ
ð7Þ
where the stroke represents the interface. At equilibrium the potential difference (distribution potential) will establish [7] wo ’ ¼ wo ’0R þ wo ’0X =2 þ f ði Þ ð8Þ where f ði Þ ¼ ðRT=2FÞ lnðþw o =þo w Þ is the activity coefficients term. Note that Eq. (8) implies that the distribution potential of a single binary electrolyte is explicitly independent of electrolyte concentration. For this system the Gibbs adsorption equation, Eq. (1), takes the form [2] w;o w;o dRX ¼ 2RTRX d ln a d ðT; p ¼ constÞ ¼ RX
ð9Þ
where RX is the chemical potential of the electrolyte RX, a is its mean activity, and w;o RX is its relative surface excess concentration. In view of the electroneutrality condition, w;o RX equals the excess surface concentration of the cation and the anion,
Capacitance and Surface Tension
417
w;o w;o w;o RX ¼ Rþ ¼ X
ð10Þ
Girault and Schiffrin [4] used a similar approach to derive the expression for the relative surface excess of water with respect to the electrolyte RX and the organic solvent, dðT; p ¼ constÞ ¼ RX;o dw w
ð11Þ
where w;o w ¼ w
nww now w RX o o nRX no
ð12Þ
Examples of more complicated systems constituting the nonpolarized ITIES can be described by the schemes Cþ Y
j Rþ X ; Cþ X
ðoÞ
ð13Þ
ðwÞ
or Sþ Y ; Cþ Y ðoÞ
j Rþ X ; Cþ X ðwÞ
ð14Þ
where Cþ represents the common cation, which determines the equilibrium potential difference across the ITIES if the inequalities wo ’0Sþ , wo ’0X wo ’0Cþ wo ’0Y , wo ’0Rþ are fulfilled. When in the system (13) the reference electrodes reversible to anion X and cation Cþ are connected to the phase w and o respectively, the Gibbs adsorption equation reads w w;o w;o dðT; p ¼ constÞ ¼ QdEoþ þ Rþ dRX þ Y dCY
ð15Þ
with w;o w;o w;o Q=F ¼ Rþ X ¼ w;o Y Cþ
ð16Þ 0
w Eoþ
and is the potential difference between the metal contacts M and M to the aqueous w ¼ ’ðMÞ ’ðM 0 Þ. Analogously, and organic solvent reference electrodes respectively, Eoþ when in the system (14) the reference electrodes that are reversible to anion X and cation Sþ are connected to the phase w and o respectively, the Gibbs adsorption equation reads w w;o w;o dðT; p ¼ constÞ ¼ QdEoþ þ Rþ dRX þ Y dSY þ w;o Cþ dCX
ð17Þ
w;o w;o w;o w;o Q=F ¼ Rþ þ Cþ w;o X ¼ Y Sþ
ð18Þ
with
C.
Ideally Polarized ITIES
Koryta et al. [9] have shown that the system with two different electrolytes RX and SY in the phase w and o respectively, S þ Y ðoÞ
j Rþ X ðwÞ
ð19Þ
can have the properties of an ideally polarizable electrode, provided that the inequality wo ’0Sþ , wo ’0X wo ’0Y , wo ’0Rþ is fulfilled. Upon taking into account the ion pairing in the bulk phase or at the interface, e.g.
418
Samec
Rþ ðwÞ þ Y ðoÞ ¼ Rþ Y ðÞ
ð20Þ
Eq. (1) can be written in the form [6] w;o w w;o w;o þ Rþ þ RX þ RY dðT; p ¼ constÞ ¼ QdEoþ dRX w;o w;o w;o þ Y þ SY þ RY dSY
ð21Þ
w;o w;o w;o w;o w;o w;o w;o Q=F ¼ Rþ X þ RY w;o SX ¼ Y Sþ þ RY SX
ð22Þ
with
D.
Surface Excess Charge and Concentrations
w The extensive variable Q associated with the electrical potential Eoþ in Eqs. (15), (17), and (21) is the thermodynamic surface excess charge density, which is defined by
@ Q¼ w @Eoþ
ð23Þ T;p;
Note that for systems (13) and (14) there is one salt component, i.e., CX and CY respectively, the chemical potential of which can be varied independently allowing for a change w w in Eoþ . On the other hand, for an ideally polarized ITIES a change in Eoþ at constant chemical potentials of all components can be accomplished by supplying the charge Q from the external electric source. As it has been pointed out [6], Q is not a surface charge density in the sense discussed for the metal–solution interface, but the amount of the electricity flowing to the interphase when its area is increased by a unit amount, i.e., socalled total charge in Planck’s terminology [10]. The closely related quantity is the differential capacity C, which is defined by:
@Q C¼ w @Eoþ
ð24Þ T;p;
Eqs. (15), (17), and (21) can be used to define other observable quantities, such as relative surface excess concentrations of ions, which also comprise the contributions from the free ionic and ion-pair surface excesses, e.g., for the ideally polarized ITIES,
@ w;o w;o ¼ Rþ þ RX þ w;o RY @RX T;p;E w ;SY oþ @ w;o w;o ¼ ¼ Y þ w;o SY þ RY @SY T;p;E w ;RX
w;o þ ¼ w;o
ð25Þ ð26Þ
oþ
w;o w;o Apparently, the relative surface excess concentrations þ and represent the total þ amount of the components R and Y (either as free ions or as ion pairs) that should be w added to the system to maintain SY and RX respectively as well as Eoþ constant when the area of the interface is increased by a unit amount.
Capacitance and Surface Tension
III.
MICROSCOPIC MODELS
A.
Modified Verwey–Niessen Model (MVN)
419
According to the earliest model by Verwey and Niessen [11] the ITIES can be represented by the diffuse double layer with one phase containing an excess of the positive space charge and the other phase an equal excess of the negative space charge [Fig. 1(a)]. The model was analyzed [11] with the help of the theory of Gouy [12] and Chapman [13] (GC). Following the analogy with Stern’s modification [14] of the GC theory, Gavach et al. [2] introduced the concept of the ion-free layer of the oriented solvent molecules, which separates the two space charge regions at the ITIES. In this model, the potential difference wo ’ splits into three potential differences wo ’ ¼ wo ’i þ ’o2 ’w2
ð27Þ
o w where w o ’i is the potential difference across the inner layer and ’2 and ’2 are the potential differences across the space charge regions in the phases o and w, respectively. In the absence of the specific ion adsorption, the differential capacity C can be represented as a series combination of the capacity of the inner layer Ci and of the capacities of the space charge regions (diffuse double layer) C2w and C2o on the aqueous and the organic solvent side of the interface respectively [15],
1 dwo ’ 1 1 1 1 1 ¼ ¼ þ ¼ þ þ C dQ Ci Cd Ci C2w C2o
ð28Þ
where Ci ¼ dQ=dwo ’i and C2s ¼ dQ=d’s2 : Relatively high values of the experimental capacity Ci have led Samec et al. [16] to propose that ions can penetrate into the inner layer over some distance. The effect of the ion penetration was taken into account by solving the linearized Poisson–Boltzmann (PB) equation in all three regions of the MVN model with the result [17], 1 1 1 ¼ þ þ C Ci Cd
ð29Þ
where the correction term < 0 depends on the Debye screening length in the inner layer and is responsible for the increased value of the inner-layer capacity.
FIG. 1 Structure of the ITIES: (a) Verwey–Niessen model [11], (b) mixed solvent layer model [4], and (c) molecular dynamics simulation [24].
420
B.
Samec
Primitive Model
Torrie and Valleau [18] used the Monte Carlo technique to examine several features of the ITIES that are not properly accounted for by the GC theory. They considered in particular (a) ion–ion correlations in the space charge region, (b) ion–ion correlations between the two space charge regions, (c) interpenetration of the two space charge regions, and (d) image forces for the primitive model, which was represented by the hard-sphere ions placed in a uniform dielectric medium. An important consequence of allowing for the finite size of ions is the thinner diffuse layer and the smaller potential diffuse-layer potential difference, as compared with the estimates based on the GC theory. This feature was also examined [17] with other statistical–mechanical theories of the diffuse double layer [19]. The modified Poisson–Boltzmann (MPB) theory of Outhwaite et al. [20] was used to predict the theoretical dependence of the capacity C on the interfacial potential difference by Cui et al. [21]. These authors have taken into account the ion penetration into the inner layer by adding a linear term to the electrostatic potential. A lack of consistency in this approach was criticized by Wandlowski et al. [22]. The latter authors used the MPB theory for an estimate of the diffuse-layer potential difference from the experimental charge density, which was obtained by an integration of the capacity curves. On this basis, the inner-layer potential difference and the inner-layer capacity were evaluated [22]. C.
Mixed Solvent Layer
Girault and Schiffrin [4] proposed an alternative model, which questioned the concept of the ion-free inner layer at the ITIES. They suggested that the interfacial region is not molecularly sharp, but consist of a mixed solvent region with a continuous change in the solvent properties [Fig. 1(b)]. Interfacial solvent mixing should lead to the mixed solvation of ions at the ITIES, which influences the surface excess of water [4]. Existence of the mixed solvent layer has been supported by theoretical calculations for the lattice-gas model of the liquid–liquid interface [23], which suggest that the thickness of this layer depends on the miscibility of the two solvents [23]. However, for solvents of experimental interest, the interfacial thickness approaches the sum of solvent radii, which is comparable with the inner-layer thickness in the MVN model. Benjamin [24], Schweighofer and Benjamin [25], and Michael and Benjamin [26] investigated the structure and dynamics of the water–1,2-dichloroethane [24,25] or nitrobenzene [26] interfaces by using molecular dynamics computer simulations. The relevant molecular dynamics studies have been reviewed [27,28]. These simulation indicated that the liquid–liquid interfaces are molecularly sharp but very rough. The interfacial roughness can be described as the protrusion of water molecules, hydrogen-bonded to each other, into the organic solvent [24,26], or as thermally populated capillary waves on the sharp interface [28]. Hence, the interfacial structure is best represented by Fig. 1(c). It has been shown that the electric field tends to broaden the interface by increasing the amplitude of fingerlike distortions [25].
IV.
SURFACE TENSION MEASUREMENTS
A.
Nonpolarized ITIES
Surface tension of the nonpolarized ITIES was investigated by using the drop-weight [2,3,29], maximum bubble pressure [30] and pendant drop [4] methods. The latter method
Capacitance and Surface Tension
421
has been improved considerably by introducing computer analysis of the video image of the pendant drop [32,33]. Gavach et al. [2] measured the surface tension of the nonpolarized water–nitrobenzene interface in the presence of various tetra-alkylammonium halides. The relative surface excess w;o RX of the salt RX, Eq. (9), was found to be proportional to the square root of the equilibrium electrolyte concentration in the aqueous phase, in an agreement with the GC theory [2]. By solving the PB equation of the GC theory the following relationship was derived [2], w o w o w w w;o RX RX ¼ Rþ þ Rþ ¼ X þ X ¼ ðA =F Þ ½expðF’2 =2RT Þ 1 ð30Þ þp1=2 ½expðF’o2 =2RT Þ 1 where wi and oi are the surface concentrations of the ion i on the aqueous and the organic solvent side of the interface respectively, Aw ¼ ð2RTw 0 c0;w Þ1=2 , p ¼ ðo c0;o =w c0;w Þ, and 0 are the relative dielectric permittivity of the solvent and the permittivity of vacuum respectively, c0;w and c0;o are the equilibrium electrolyte concentrations in the aqueous and the organic solvent phase respectively. In addition [2], RT 1 þ p exp½F ðwo ’ wo ’i Þ=2RT w ln ’2 ¼ ð31Þ F 1 þ p exp½F ðwo ’ wo ’i Þ=2RT Provided that jwo ’ wo ’i j ¼ const, then also ’o2 and ’w2 are constant, and RX is proportional to ðc0;w Þ1=2 . The observed nonlinearity at higher electrolyte concentrations [2] is probably due to a change in the inner-layer potential difference w ’i with the surface excess charge density. The inner-layer potential difference (< 50 mV) was evaluated from the linear part of the RX vs. ðc0;w Þ1=2 plot, and was found to depend on the nature of the salt, i.e., on the distribution potential, Eq. (8). The same system has been studied previously by Boguslavsky et al. [29], who also used the drop weight method. While qualitatively the same behavior was observed over the broad concentration range up to the solubility limit, the data were fitted to a Frumkin isotherm, i.e., the ions were supposed to be specifically adsorbed as the interfacial ion pair [29]. The equation of the Frumkin-type isotherm was derived by Krylov et al. [31], on assuming that the electrolyte concentration in each phase is high, so that the potential difference across the diffuse double layer can be neglected. Girault and Schiffrin [4] measured the surface tension of the nonpolarizable ITIES in the presence of various inorganic electrolytes (LiCl, NaCl, KCl, MgSO4 ). By using Eq. (11) they evaluated the relative surface excess of water at the water–nitrobenzene, water– 1,2-dichloroethane and water–n-heptane interfaces and estimated the thickness of the ionfree layer. Implicit assumption was that the second and the third term on the right-hand side of Eq. (12) can be neglected. Indeed, because the standard Gibbs energies of transfer of inorganic cations and anions involved are nearly equal, the distribution potential is close to zero and hence RX 0. Since the thickness of the ion-free layer was dependent on the polarity of the organic solvent, and for polar solvents was less than unity, the authors concluded that the interfacial region consists of a mixed solvent region with a continuous change in the solvent properties, cf. the Section II.C. Gross et al. [3] and Reid et al. [30] measured surface tension of the water–nitrobenzene interface in the presence of bromides of sodium and tetra-alkylammonium ions in water and tetra-alkylammonium tetraphenylborates in nitrobenzene, i.e., tetra-alkylammonium served as the potential-determining ion, cf. the scheme (13). The surface tension vs. the potential difference wo ’ plot (electrocapillary curve), cf. Eq. (15), was constructed by varying the concentration of tetra-alkylammonium bromide in water, while holding
422
Samec
constant the concentration of the electrolyte in nitrobenzene. A comparison of the measured surface tension with that calculated by an integration of the surface charge density suggested that the potential difference is concentrated in the diffuse double layer, and that the zero-charge potential difference wo; ’pzc ¼ wo ’i ¼ 1 mV [3] or 0 mV [30]. Note, however, that this conclusion is at variance with the analysis of the surface tension of the nonpolarized ITIES by the same authors [2], as well as with the results of the study of the ideally polarized ITIES reviewed in the next section. Recently, the newly developed time-resolved quasielastic laser scattering (QELS) has been applied to follow the changes in the surface tension of the nonpolarized water– nitrobenzene interface upon the injection of cetyltrimethylammonium bromide [34] and sodium dodecyl sulfate [35] around or beyond their critical micelle concentrations. As a matter of fact, the method is based on the determination of the frequency of the thermally excited capillary waves at liquid–liquid interfaces. Since the capillary wave frequency is a function of the surface tension, and the change in the surface tension reflects the ion surface concentration, the QELS method allows us to observe the dynamic changes of the ITIES, such as the formation of monolayers of various surfactants [34]. B.
Ideally Polarized ITIES
1. Structure of the ITIES in the Absence of the Specific Adsorption Kakiuchi and Senda [36] measured the electrocapillary curves of the ideally polarized water–nitrobenzene interface by the drop time method using the electrolyte dropping electrode [37] at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes. An example of the electrocapillary curve for this system is shown in Fig. 2. The surface excess charge density Q, and the w;o þ relative surface excess concentrations Liþ and w;o TPB of the Li cation and the tetraphenylborate anion respectively, were evaluated from the surface tension data by using Eq. w;o (21). The relative surface excess concentrations w;o Cl and TBAþ of the Cl anion and the tetrabutylammonium cation respectively were then evaluated by using Eq. (22), in which the contributions from the interfacial ion pairs are neglected. The dependencies of the relative surface excess concentrations of all four ions on the charge density Q were found to be consistent with the MVN model and with the prediction of the GC theory. In particular, these relative surface excesses can be calculated by using Eq. (2), with the surface ion concentration given by the expression that follows from the GC theory for the case of absence of the specific ion adsorption, e.g., for cations and anions of the aqueous phase [36] h 1=2 i ¼ w ¼ ðAw =F Þ y þ y2 þ 1 1 ð32Þ where y ¼ Q=2Aw . The absence of the specific ion adsorption is also corroborated by the w w =@RX Þq;SY and ð@Eoþ =@SY ÞQ;RX [36]. values of the Jesin–Markov coefficients ð@Eoþ Recently, Samec et al. [38] have investigated the same system by the video-image pendant drop method. Surface tension data from the two studies are compared in Fig. 2, where the potential scale from the study [36] was shifted so that the positions of the electrocapillary maxima coincide. The systematic difference in the surface tension data of ca. 3%, cf. the dotted line in Fig. 2, was ascribed to the inaccurate determination of the drop volume, which was calculated from the shape of the drop image and used further in the evaluation of the surface tension [38]. A point of interest is the inner-layer potential difference wo ’i , which can be evaluated relative to the zero-charge potential difference wo ’pzc by using Eq.
Capacitance and Surface Tension
423
FIG. 2 Potential dependence of the surface tension of the interface between 0.1 M LiCl in water and 0.05 M tetrabutylammonium tetraphenylborate in nitrobenzene, taken from Ref. 38 (*) and Ref. 36 (&). The dotted line represents the data from Ref. 38 multiplied by a factor of 0.97. The potential scale from Ref. 36 was shifted so that the positions of the electrocapillary maxima coincide.
(27) and the GC relationship between the excess surface charge density Q and the potential differences ’w2 and ’o2 [36], Q ¼ 2Aw sinhðF’w2 =2RT Þ ¼ 2Ao sinhðF’o2 =2RT Þ
ð33Þ
where Ao ¼ ð2RTo 0 c0;o Þ1=2 . This potential difference was found to contribute significantly to the interfacial potential difference wo ’ depending on the value of Q (cf. Fig. 3), which probably reflects the effect of the electric field on the orientation of the surface dipole [38]. By using the standard potential difference for the tetrabutylammonium ion (wo ’0TBAþ ¼ 0:248 V) as a reference, the zero-charge potential difference wo ’pzc was evaluated as being equal to approximately 20 mV [36]. On the other hand, the value wo ’pzc ¼ 33 mV was found to be more consistent with the potential scale based on the equilibrium potential measurements for a series of tetra-alkylammonium ions [38]. The latter value suggests that in the absence of the electric field the surface dipole points to the organic phase, in an agreement with the results of molecular dynamics simulations [26]. Girault and Schiffrin [6] and Samec et al. [39] used the pendant drop video-image method to measure the surface tension of the ideally polarized water–1,2-dichloroethane interface in the presence of KCl [6] or LiCl [39] in water and tetrabutylammonium tetraphenylborate in 1,2-dichloroethane. Electrocapillary curves of a shape resembling that for the water–nitrobenzene interface were obtained, but a detailed analysis of the surface tension data was not undertaken. An independent measurement of the zero-charge potential difference by the streaming-jet electrode technique [40] in the same system provided the value identical with the potential of the electrocapillary maximum. On the basis of the standard potential difference of 0:225 V for the tetrabutylammonium ion transfer, the zero-charge potential difference was estimated as equal to 8 10 mV [41].
424
Samec
FIG. 3 Inner-layer potential difference wo ’i relative to the zero-charge potential difference wo ’pzc vs. the excess surface charge Q for the interface between LiCl in water and tetrabutylammonium tetraphenylborate in nitrobenzene: Ref. 38 (full line) and Ref. 36 (dotted line).
2. Structure of the ITIES in the Presence of Ionic and Nonionic Surfactants Kakiuchi et al. [42–45] studied the adsorption of ionic and nonionic surfactants on the ideally polarized water–nitrobenzene interface by the drop-time method. The adsorption of hexadecyltrimethylammonium (HTMAþ ) cation was found to be markedly dependent on the interfacial potential difference [42] (cf. Fig. 4). No specific adsorption was observed when the aqueous phase was positive, while a strong adsorption occurred when the potential of the aqueous phase was negative with respect to the potential of the nitrobenzene phase. The specific adsorption of HTMAþ led to a change in the structure of the electrical double layer. The polar headgroup of this ion probably protrudes into the aqueous phase, which is accompanied by the inversion of the outer Helmholtz potential ’o2 in nitrobenzene from a negative to positive value. The magnitude of the surface tension depression due to the specific adsorption of HTMAþ ion was influenced by the counteranion [43]. The effect became larger in the order F < Cl < Br indicating a specific counterion binding at the ITIES in this order, i.e., the formation of the interfacial ion pair [43]. On the other hand, a strong adsorption of nonionic surfactants such as tetraethylene glycol monododecyl ether [44], hexa- and octaethylene glycol monododecyl ethers [45] was observed over the whole potential range of the ideally polarized ITIES. The adsorption was stabilized by the complex formation with the Liþ cation in the aqueous phase. The standard Gibbs energy of adsorption was found to depend on the number n of oxyethylene units, indicating an increasing preference for the complex formation with the increasing n. An effect of the interfacial potential difference on the adsorption has led the authors [45] to a conclusion that, owing to the complex formation at the interface, the adsorbed neutral ethers behave as cationic surfactants. In a closely related study, Marec˘ek et al. [46] used the pendant drop video-image method to investigate the adsorption and surface reactions of calix[4]arene ligands at the ideally polarized water–1,2-dichloroethane interface. The difference between the surface tensions in acidic and alkaline media was ascribed to a difference in the charge on the adsorbed ligand. A formation of the surface complex with Ba2þ and Ca2þ cations was found to reduce the change in the surface tension, as compared with the case of adsorbed
Capacitance and Surface Tension
425
FIG. 4 Electrocapillary curve for the interface between 0.05 M LiCl in water and (0:1 x) M tetrapentylammonium tetraphenylborate+x M hexadecyltrimethyammonium tetraphenylborate in nitrobenzene at 25 C: x ¼ 0 (*), 0.005 (~), 0.02 (&), 0.05 (*), and 0.1 (~). (From Ref. 42.)
dissociated ligands possessing a higher charge. The effect of the charge of adsorbed ions on their surface concentration was then studied for a series of negatively charged ions [47]. The limiting surface concentration s was found to be related to the charge number z of the adsorbed ions, in an agreement with the derived formula s ¼ 1:42 106 =z4=3 mol m2 . A conclusion was made that small charged molecules can hardly form a compact monolayer and that the formation of such a monolayer requires that the size of adsorbed molecules must be comparable with the distance between the adsorbed molecules which, however, depends on their charge number. Owing to repulsive interactions in the adsorbed layer, the drop in the surface tension can be large even if the limiting surface concentration is low. 3.
Adsorption of Compounds of Biological Significance
Koryta et al. [48] first stressed the relevance of adsorbed phospholipid monolayers at the ITIES for clarification of biological membrane phenomena. Girault and Schiffrin [49] first attempted to characterize quantitatively the monolayers of phosphatidylcholine and phosphatidylethanolamine at the ideally polarized water–1,2-dichloroethane interface with electrocapillary measurements. The results obtained indicate the importance of the surface pH in the ionization of the amino group of phosphatidylethanolamine. Kakiuchi et al. [50] used the video-image method to study the conditions for obtaining electrocapillary curves of the dilauroylphosphatidylcholine monolayer formed on the ideally polarized water– nitrobenzene interface. This phospholipid was found to lower markedly the surface tension by forming a stable monolayer when the interface was polarized so that the aqueous phase had a negative potential with respect to the nitrobenzene phase [50,51] (cf. Fig. 5).
426
Samec
FIG. 5 Electrocapillary curve for the interface between 0.05 M LiCl in water and 0.1 tetrapentylammonium tetraphenylborate in nitrobenzene at 25 C in the presence of x M dilauroylphosphatidylcholine in nitrobenzene: x ¼ 0 (*), 0.5 (~), 1 (&), 2(^), 5 (*), 10 (~), 20 (&), and 50 (!). (From Ref. 51.)
On the other hand, when the aqueous phase became positively charged, the adsorbed molecules started to desorb from the interface, giving rise to the disruption of monolayer. Only in the former potential range, the electrocapillary curve was found to be thermodynamically meaningful. The area of the interface occupied by dialauroylphosphatidylcholine molecule in the saturated monolayer was estimated at 0.93 nm2 , indicating that the monolayer was in the liquid-expanded state [51]. The potential of zero charge shifted to a negative potential, probably due to the specific adsorption of Liþ ions to the headgroup of phospholipid exposed to the aqueous phase [51]. Monolayers of distearoylphosphatidylcholine spread on the water–1,2-dichloroethane interface were studied by Grandell et al. [52] in a novel type of Langmuir trough [53]. Isotherms of the lipid were measured at controlled potential difference across the interface. Electrocapillary curves derived from the isotherms agreed with those measured under the true thermodynamic equilibrium. Weak adsorption or a stable monolayer was found to be formed, when the potential of the aqueous phase was positive or negative respectively, with respect to the potential of the 1,2-dichloroethane phase [52]. This result
Capacitance and Surface Tension
427
is consistent with those obtained from measurements of phospholipid adsorption at the polarized water–nitrobenzene interface [50,51].
V.
CAPACITANCE MEASUREMENTS
A.
Analysis of Impedance Data
While the surface tension is accessible by direct measurement, the differential capacity C of the ITIES, Eq. (27), has to be evaluated by a careful analysis of experimental impedance data. Impedance measurements at the ITIES are usually carried out in a four-electrode electrochemical cell, where the interfacial potential difference is controlled or measured with the help of a couple of two reference electrodes and the current is supplied by means of two counterelectrodes [54]. Typically, a small sinusoidal voltage of a defined frequency (0.1–1000 Hz) and amplitude (< 10 mV peak to peak) is applied across the ITIES and the corresponding sinusoidal current is measured by means of the alternating-current bridge or phase-selective detection yielding the complex impedance of the cell. The sinusoidal voltage is either superposed on the triangular voltage sweep (AC polarographic or AC voltammetric method), or it is applied at a constant cell potential (impedance method). The impedance data have been usually interpreted in terms of the Randles-type equivalent circuit, which consists of the parallel combination of the capacitance ZC of the ITIES and the faradaic impedances ZfN of the charge transfer reactions, with the solution resistance Rs in series [15], cf. Fig. 6. While this is a convenient model in many cases, its limitations have to be always considered. First, it is necessary to justify the validity of the basic model assumption that the charging and faradaic currents are additive. Second, the conditions have to be analyzed, under which the measured impedance of the electrochemical cell can represent the impedance of the ITIES. In particular, the coupling between the ion transfer and ion adsorption process has serious consequences for the evaluation of the differential capacity or the kinetic parameters from the impedance data [55]. This is the case, e.g., of the interface between two immiscible electrolyte solutions each containing a transferable ion, which adsorbs specifically on both sides of the interface. In general, the separation of the real and the imaginary terms in the complex impedance of such an ITIES is not straightforward, and the interpretation of the impedance in terms of the Randles-type equivalent circuit is not appropriate [54]. More transparent expressions are obtained when the effect of either the potential difference or the ion concentration on the specific ion adsorption is negli-
FIG. 6 Randles equivalent circuit for the ITIES: ZC is the interfacial capacitance, ZfN are the faradaic impedances of the charge transfer reactions, and Rs is the solution resistance.
428
Samec
gible. In the latter case, the system can exhibit the behavior of the Randles equivalent circuit, provided that certain kinetic conditions are fulfilled. Evaluation and interpretation of impedance data is often complicated by the nonideal behavior of the measuring device (e.g., potentiostat) and/or of the electrochemical cell itself. The role of experimental artifacts has been addressed first by Reid et al. [56] and by Silva and Moura [57], who ascribed the high-frequency impedance semicircle to the geometrical bulk-phase capacitance [56] or to the capacitive coupling between the reference electrodes [57]. Cells of various designs were then tested and a conclusion was made that the main origin of the observed high-frequency dispersion is the high value of the resistance of the reference electrode connected to the organic solvent phase [58]. Samec et al. [59] analyzed the role of the parasitic couplings in the four-electrode cells employed in measurements at the ITIES or membranes. The cell was represented by an eight-element electrical equivalent circuit, which accounted for the finite impedances of the reference and counterelectrodes, as well as for various parasitic couplings. The model allowed prediction of the conditions under which the impedance plots exhibit the high-frequency capacitive and/or inductive features. An analytical expression was derived, which enables the valuation of the parasitic elements from experimental impedance data and the simulation of the impedance behavior. As a limiting case, the model also describes the behavior of a threeelectrode cell. Recent impedance measurements of the ideally polarized water–nitrobenzene interface [38] indicated that the potentiostatic circuit was not symmetrical in a sense that different impedance spectra were obtained when the input of the current follower was connected to the counterelectrode of the organic or the aqueous phase. The conclusion was made that the former configuration should be avoided owing to the strong effect of the capacitive coupling between the counterelectrodes and reference electrodes connected to the organic solvent phase on the measured impedance [38]. Since the ion transfer is a rather fast process, the faradaic impedance Zf can be replaced by the Warburg impedance ZW corresponding to the diffusion-controlled process. Provided that the Randles equivalent circuit represents the plausible model, the real Z 0 and the imaginary Z 00 components of the complex impedance Z ¼ Z 0 jZ 00 [j ¼ ð1Þ1=2 ] are given by [60] 1 ð34Þ Z 0 ¼ Rs þ ZC X ðX þ 1Þ2 þ 1 1 ð35Þ Z 00 ¼ ZC XðX þ 1Þ ðX þ 1Þ2 þ 1 where ZC ¼ ð!CÞ1 , ! is the angular frequency and X ¼ ðZW =ZC Þð21=2 Þ. In the analysis of impedance data, the solution resistance Rs is evaluated first as the high-frequency limit of the impedance Z and then X and C are obtained from Eq. (34) and Eq. (35). A more sophisticated approach makes use of the nonlinear least-square fitting of impedance data obtained for a series of frequencies ! [61], which is nowadays provided by commercially available software packages (e.g., EQUIVCRT, ZVIEW). Alternatively, the capacity C can be evaluated by using the galvanostatic pulse technique [62,63]. When a current step I ¼ I0 ¼ const is imposed on the interface, the charging current IC decreases with time t, while the faradaic current If increases. At very short times, I ¼ I0 ¼ IC þ If ¼ CðdE=dtÞ þ If CðdE=dtÞ
ð36Þ
where dE=dt is the rate of the change of the interfacial potential difference measured. Under these conditions, the ohmic potential drop E0 ¼ I0 Rs appears as a step on the galvanostatic transient at the beginning of the pulse and the initial slope of the transient is controlled mainly by the capacity C.
Capacitance and Surface Tension
B.
429
Effect of the Interfacial Potential Difference
Samec et al. [15] used the AC polarographic method to study the potential dependence of the differential capacity of the ideally polarized water–nitrobenzene interface at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes. The capacity showed a single minimum at an interfacial potential difference, which is close to that for the electrocapillary maximum. The experimental capacity was found to agree well with the capacity calculated from Eq. (28) for 1=Ci ¼ 0 and for the capacities of the space charge regions calculated using the GC theory, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C2s ¼ ðFAs =RT Þ 1 þ ðQ=2As Þ2
ð37Þ
which indicated that the inner-layer potential difference remains constant and close to zero. A similar conclusion was made by Reid et al. [64]. However, it should be noted that the authors [15] assumed that the faradaic impedance Zf is much greater than the capacitance ZC and evaluated the capacity C from the imaginary component Z 00 ¼ ZC ¼ 1=!C. Therefore, the value of the capacity was overestimated, in particular at higher electrolyte concentrations. Analogously, an increasing overestimation of the capacity with the increasing electrolyte concentration was likely to be involved in the analysis of the galvanostatic transients [16,17] that was based on Eq. (36). Wandlowski et al. [22] remeasured the impedance data for the water–nitrobenzene [15] and water–1,2dichloroethane [65] interfaces at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes, and evaluated the capacity C with the help of Eq. (34) and Eq. (35) (cf. the capacity curves in Fig. 7). These results confirmed an interesting feature noted earlier [17,65], namely that the plot of the inverse capacity 1=C against the inverse GC capacity of the diffuse double layer 1=Cd is not linear, contrary to expectation based on Eq. (28) (cf. Fig. 8). An appreciable drop from the expected straight line at low electrolyte concentrations, which is pronounced more for the water–1,2-dichloroethane interface, was ascribed to a relatively higher interpenetration
FIG. 7 Differential capacity C vs. interfacial potential difference wo ’ of the water–nitrobenzene interface. Concentrations (in mol dm3 ) of LiCl in water and tetrabutylammonium tetraphenylborate in nitrobenzene: 0.01 (*), 0.02 (*), 0.05 (!), and 0.1 (!). (From Ref. 22.)
430
Samec
FIG. 8 Inverse differential capacity C01 at the zero surface charge vs. inverse capacity Cd1 of the diffuse double layer for the water–nitrobenzene (*) and water–1,2-dichloroethane (*,), interface. The diffuse layer capacity was evaluated by the GC (*) or the MPB (*,), theory. (From Ref. 22.)
of ions at low electrolyte concentrations [17], or to the relatively higher effect of the finite ion size [22]. The latter effect was estimated [22] by using the MPB theory [20]. Recently, it has been shown that an increase of the capacity can also be caused by the corrugation of the interface by capillary waves [66]. The results of the capacitance measurements have been found consistent with those of the surface tension measurements for both the water–nitrobenzene and the water–1,2chloroethane interfaces [17,22,37–39,67]. Thus, the excess surface charge density Q obtained by an integration of the capacity curves agrees well with that obtained by a differentiation of the electrocapillary curve [37,67], at least in a limited potential range [38,39]. Analogously, the values of Q from the two measurements yield comparable values of the inner-layer potential differences [17,22,38,39] (cf. Fig. 3). On the other hand, at the potential differences that are about 100 mV more positive or negative than the zero-charge potential difference, the agreement is less satisfactory [38,39]. Unlike the surface excess charge density inferred from the surface tension measurements, that obtained by the integration of the capacity curve increases with the potential difference much more steeply, which corresponds to a higher capacity compared with the second derivative of the electrocapillary curve [38,39]. This capacity enhancement is not probably associated with the specific ion adsorption and can be explained by the model, which links the measured impedance to the electromechanical oscillations in the interfacial region during the impedance measurements [68,69]. The model is based on the theoretical considerations [28] that the thermally excited capillary waves give rise to an apparent width of a liquid–liquid
Capacitance and Surface Tension
431
interface, which was supposed [69] to represent the mean charge separation between the two electrolyte solutions, i.e., the thickness of the inner layer. Changes in the inner-layer thickness induced by the applied sinusoidal voltage result in a change in the ratio of the charging and the faradaic currents, which requires a modification of the Randles equivalent circuit. The complex impedance Z~ a of the modified circuit is given by [68,69]. Z~ a ¼
Z~ I þ Rs 1 ðxZ~ I =Z~ C Þ
ð38Þ
where Z~ I ¼ ðZ~ f1 þ Z~ C1 Þ1 , Z~ C ¼ ðj!CÞ1 , Z~ f ¼ Rct þ Z~ W , Rct and Z~ W are the charge transfer resistance and the complex Warburg impedance respectively, and the parameter x ¼ jQðwo ’i wo ’pzc Þ=2j. The value of the latter parameter is negligible at the potential differences close to the zero-charge potential difference, where also Eq. (38) describes the behavior of the Randles equivalent circuit. However, with the increasing potential difference, x increases due to the increasing surface excess charge density Q and the increasing inner-layer potential difference wo ’i , and due to the decreasing surface tension . An analysis of the impedance data simulated with the help of Eq. (38) indicated that the effect of capillary waves can become significant at approximately the same potentials, where the sharp increase in the capacity is observed experimentally [38].
C.
Effect of Electrolyte
The effect of electrolyte type on the capacity of an ideally polarized ITIES was studied first by Homolka et al. [70]. These authors concluded that the formation of the inner layer at the water–nitrobenzene interface accompanied by a drop in the capacitance is associated with the presence of certain ions in the double layer, e.g., very hydrophilic Mg2þ cations in water or very hydrophobic tetraphenylarsonium cation in nitrobenzene. More recently, this effect was investigated systematically by Yufei et al. [71] and Pereira et al. [72] for the water–nitrobenzene [71] and water–1,2-dichloroethane [71,72] interfaces. A capacity increase was observed in the range of the potential differences wo ’ > 0, which followed the order of ions in water (Liþ < Naþ < Rbþ < Csþ Þ [71], and in the range of the potential differences wo ’ < 0, which followed the order of ions in 1,2-dichloroethane (tetraoctylammoniumþ < tetrabutylammoniumþ < tetrapropylammoniumþ ) [72]. This order corresponds to the order of the Gibbs energies of transfer [72]. Figure 9 shows the capacity curves for the water–o-nitrophenyl octyl ether interface in the presence of two different electrolytes in the organic solvent obtained by impedance measurements [68,73]. A comparison with the potential dependence of the faradaic admittance coefficient Y0 [Fig. 10] points to a correlation between the capacity and admittance enhancements or the Gibbs energies of transfer. At a constant faradaic admittance, the ITIES appears to exhibit the same capacity irrespective of the nature of the ion that controls the faradaic process [39,68]. These results have been initially considered as evidence for specific ion adsorption at ITIES [71,72]. Its origin was ascribed to extensive ion pair formation between ions in the aqueous phase and ions in the organic phase [71] [cf. Eq. (20)], or to a penetration into the interfacial region [72]. The former model, which has been considered in this context earlier [60], allows one to interpret the enhanced capacity in terms of Eq. (22). Pereira et al. (74) presented more experimental data demonstrating the effect of electrolytes and proposed a simple model, which is based on the lattice-gas model of the liquid–liquid interface [23]. Theoretical calculations showed that ion pairing can lead to an increase in the stored
432
Samec
FIG. 9 Differential capacity C of the interface between 0.1 M LiCl in water and 0.02 M tetrabutylammonium tetraphenylborate (&) or tetrapentylammonium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (&) in o-nitrophenyl octyl ether as a function of the interfacial potential difference wo ’. (From Ref. 73.)
charge at the interface, while the space charge, and hence the potential difference across the interface, does not change much because the charges on the paired ions compensate each other [74]. The amount of ion pairing should depend on both the association constant and on the width of the interface and, therefore, it is generally not possible to obtain the interfacial association constant from the capacity data [74]. However, the surface tension data that would confirm the specific adsorption of hydrophilic and semihydrophobic ions are lacking. Absence of the specific ion adsorption in these cases is corroborated by the analysis of the surface tension data for the nonpolar-
FIG. 10 Faradaic admittance coefficient Y0 for the interface between 0.1 M LiCl in water and 0.02 M tetrabutylammonium tetraphenylborate (&) or tetrapentylammonium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (&) in o-nitrophenyl octyl ether as a function of the interfacial potential difference wo ’. (From Ref. 73.)
Capacitance and Surface Tension
433
ized [3] and ideally polarized [36] water–nitrobenzene interfaces. Besides, the electrocapillary curves in the latter case appear to have a parabolic shape, which would correspond to the linear dependence of the surface charge on the potential difference and to a constant differential capacity [37–39]. Simulations based on Eq. (38) show that both the capacity enhancement at far positive and far negative potential differences and its dependence on the electrolyte present can be explained by the model [68,69] that links the measured impedance to the thermally excited capillary waves.
D.
Effects of Adsorbed Layers
There is a group of substances, in the presence of which significant changes in the surface tension of the ITIES were observed, which are also likely to influence the differential capacity of the ITIES correspondingly. These substances include various ionic and nonionic surfactants (Section IV.B.2) and amphiphilic phospholipids (Section IV.B.3) or affinity dyes. Attention has focused on phospholipids. Kakiuchi et al. [75] used the capacitance measurements to study the adsorption of dilauroylphosphatidylcholine at the ideally polarized water–nitrobenzene interface, as an alternative approach to the surface tension measurements for the same system [51]. In the potential range, where the aqueous phase had a negative potential with respect to the nitrobenzene phase, the interfacial capacity was found to decrease with the increasing phospholipid concentration in the organic solvent phase (Fig. 11). The saturated monolayer in the liquid-expanded state was formed at the phospholipid concentration exceeding 20 mol dm3 , with an area of 0:73 nm2 occupied by a single molecule. The adsorption was described by the Frumkin isotherm,
FIG. 11 Equilibrium double layer capacity of the interface between 0.05 M LiCl in water and 0.1 tetrapentylammonium tetraphenylborate in nitrobenzene at 25 C in the presence of x M dilauroylphosphatidylcholine in nitrobenzene: x ¼ 0 (*), 1 (*), 2 (~), 10 (~), and 50 (&). (From Ref. 75.)
434
Samec
c ¼
expð2a Þ 1
ð39Þ
where ¼ expðG0ads =RTÞ is the adsorption coefficient, G0ads is the standard Gibbs energy of adsorption, a is the interaction parameter, is the surface coverage, and c is the phospholipid concentration, with G0ads ¼ 31 kJ mol1 and a ¼ 0:25. The latter value points to weak attractive interactions between the adsorbed molecules corresponding to the penetration of nitrobenzene molecules and, possibly, ions between the hydrocarbon chains of phospholipid [75]. This penetration explains the rather high capacity of 11 C cm2 for the adsorbed monolayer. In the potential range, where the aqueous phase had a positive potential, the capacity increased with the increasing phospholipid concentration. Since in this potential range the surface tension shows a tendency to recover [51], the observed increase of the capacity was ascribed to a change in the orientation of adsorbed molecules, possibly accompanied by a partial desorption [75]. Wandlowski et al. [76,77] used the impedance technique to study the adsorption of dilauroyl-, dimyristoyl, and dipalmitoylphosphatidylcholine at the same interface. The surface coverage evaluated from the impedance measurements also fits the Frumkin isotherm. The value of G0ads was found to decrease with the increasing number of methylene groups in the hydrocarbon chain from 35:7 kJ mol1 to 37:9 kJ mol1 and the value of the parameter a ¼ 0:4, which corresponds to weak attractive interactions between the absorbed molecules. Thus, the picture emerging from these studies is qualitatively the same as above, but the estimated parameters of the Frumkin isotherm are slightly different. Kakiuchi et al. [78] investigated the effects of temperature and the chainlength on the monolayer characteristics of six phosphatidylcholines on the polarized water–nitrobenzene interface at phospholipid concentrations higher than 10 mol dm3 . The dilauroyl- and dimyristoylphosphatidylcholine monolayers were found to be in the liquid-expanded state between 5 and 30 C (Cmin 10 C cm2 Þ, whereas distearoyl-, diarachidoyl-, and dibehenoylphosphatidylcholine monolayers were found to be in the liquid-condensed state over the same temperature range ðCmin 4 C cm2 ). The dipalmitoylphosphatidylcholine monolayer exhibited a temperature-induced phase transition at 13 C. Two interesting features were revealed by capacitance measurements of phospholipids containing the ethanolamine or serine moiety instead of choline. In contrast to dilauroylphosphatidylcholine forming liquid-expanded monolayers, dilauroylphosphatidylethanolamine has an adsorption isotherm with a characteristic kink, which is associated with the phase transition from the liquid-expanded to the liquid-condensed state as the concentration of the latter lipid in nitrobenzene is increased. The transition is accompanied by the change in the occupied area of this phospolipid from 0.83 nm2 to 0.5 nm2 [79]. The phospholipid monolayer is stable over the potential range of about 300 mV when the aqueous phase is neutral, while the potential dependence of the adsorption resembles an anionic or cationic surfactant when the pH is made alkaline or acidic respectively. The monolayer characteristics of dipalmitoylphospatidylserine at the water–nitrobenzene interface are similar to those of dipalmitoylphosphatidylcholine. However, in the presence of Ca2þ or Mg2þ at a concentration greater than 2 mol dm3 in the aqueous phase a striking drop in the capacity was observed, which was ascribed to the phase transition of the monolayer from the liquid-expanded state to the liquid-condensed or solid state [80]. Capacitance measurements of phospholipid monolayers at the ITIES have been proposed as a suitable tool for studying the enzyme activity under the precise control of the electrical state of the monolayer [81]. Kinetics of hydrolysis of phosphatidylcholine
Capacitance and Surface Tension
435
monolayers in the presence of phospholipase was followed by making use of the large difference in the capacity before and after hydrolysis [81–83]. Kakiuchi et al. [84] studied the adsorption properties of two types of nonionic surfactants, sorbitan fatty acid esters and sucrose alkanoate, at the water–nitrobenzene interface. These surfactants lower the interfacial capacity in the range of the applied potential with no sign of desorption. On the other hand, the remarkable adsorption– desorption capacity peak analogous to the adsorption peak seen for organic molecules at the mercury–electrolyte interface can be observed in the presence of ionic surfactants, such as triazine dye ligands for proteins [85].
VI.
CONCLUSIONS
Capacitance and surface tension measurements have provided a wealth of data about the adsorption of ions and molecules at electrified liquid–liquid interfaces. In order to reach an understanding on the molecular level, suitable microscopic models have had to be considered. Interpretation of the capacitance measurements has been often complicated by various instrumental artifacts. Nevertheless, the results of both experimental approaches represent the reference basis for the application of other techniques of surface analysis.
ACKNOWLEDGMENTS Financial support from the Ministry of Education of the Czech Republic (Grant. No. ME 161) is gratefully acknowledged.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
E. H. Riesenfeld. Ann. Phys. 8:616 (1902). C. Gavach, P. Seta, and B. d’Epenoux. J. Electroanal. Chem. Interfacial Electrochem. 83:225 (1977). M. Gross, S. Gromb, and C. Gavach. J. Electroanal. Chem. Interfacial Electrochem. 89:29 (1978). H. H. Girault and D. J. Schiffrin. J. Electroanal. Chem. Interfacial Electrochem. 150:43 (1983). T. Kakiuchi and M. Senda. Bull. Chem. Soc. Jpn. 56:2912 (1983). H. H. J. Girault and D. J. Schiffrin. J. Electroanal. Chem. Interfacial Electrochem. 170:127 (1984). F. M. Karpfen and J. E. B. Randles. Trans. Faraday Soc. 498:823 (1953). LeQ. Hung. J. Electroanal. Chem. Interfacial Electrochem. 115:159 (1980). J. Koryta, P. Vany´sek, and M. Br˘ ezina. J. Electroanal. Chem. Interfacial Electrochem. 75:211 (1977) B. B. Damaskin, O. A. Petrii, and V. V. Batrakov, Adsorption of Organic Compounds on Electrodes, Plenum Press, New York, 1971, pp. 387–435. E. J. Verwey and K. F. Niessen. Philos. Mag. 28:435 (1939). G. Gouy. C. R. Acad. Sci. 149:654 (1910). D. L. Chapman. Philos. Mag. 25:475 (1913). O. Stern. Z. Elektrochem. 30:508 (1924).
436
Samec
15. Z. Samec, V. Marec˘ek, and D. Homolka. J. Electroanal. Chem. Interfacial Electrochem. 126:121 (1981). 16. Z. Samec, V. Marec˘ek, and D. Homolka. Faraday Discuss. Chem. Soc. 77:197 (1984). 17. Z. Samec, V. Marec˘ek, and D. Homolka. J. Electroanal. Chem. Interfacial Electrochem. 187:31 (1985) 18. G. M. Torrie and J. P. Valleau. J. Electroanal. Chem. Interfacial Electrochem. 206:69 (1986). 19. G. M. Torrie and S. L. Carnie. Adv. Chem. Phys. 56:141 (1984). 20. C. W. Outwaite, L. B. Bhuiyan, and S. Levine. J. Chem. Soc. Faraday Trans. II 76:1388 (1980). 21. Q. Z. Cui, G. Y. Zhu, and E. Wang. J. Electroanal. Chem. Interfacial Electrochem. 372:15 (1984). 22. T. Wandlowski, K. Holub, V. Marec˘ek, and Z. Samec. Electrochim. Acta 40:2887 (1995). 23. D. J. Henderson and W. Schmickler. J. Chem. Soc. Faraday Trans. 92:3839 (1996). 24. I. Benjamin. J. Chem. Phys. 97:1432 (1992). 25. K. J. Schweighofer and I. Benjamin. J. Electroanal. Chem. Interfacial Electrochem. 391:1 (1995). 26. D. Michael and I. Benjamin. J. Electroanal. Chem. Interfacial Electrochem. 450:335 (1998). 27. I. Benjamin. Chem. Rev. 96:1449 (1996). 28. I. Benjamin. Annu. Rev. Phys. Chem. 48:407 (1997). 29. L. I. Boguslavsky, A. N. Frumkin, and M. I. Gugeshashvili. Elektrokhimiya 12:856 (1976); Sov. Electrochem. 12:799 (1976). 30. J. D. Reid, O. R. Melroy, and R. P. Buck. J. Electroanal. Chem. Interfacial Electrochem. 147:71 (1983). 31. V. S. Krylov, V. A. Myamlin, L. I. Boguslavsky, and M. A. Manvelyan. Elektrokhimiya 13:834 (1977); Sov. Electrochem. 13:707 (1977). 32. H. H. J. Girault, D. J. Schiffrin, and B. D. V. Smith. J. Electroanal. Chem. Interfacial Electrochem. 137:207 (1982). 33. H. H. J. Girault, D. J. Schiffrin, and B. D. V. Smith. J. Colloid. Interface Sci. 101:257 (1984). 34. Z. Zhang, I. Tsuyumoto, S. Takahashi, T. Kitamori, and T. Sawada. J. Phys. Chem. A 101:4163 (1997). 35. Z. Zhang, I. Tsuyumoto, T. Kitamori, and T. Sawada. J. Phys. Chem. B 102:10284 (1998). 36. T. Kakiuchi and M. Senda. Bull. Chem. Soc. Jpn. 56:1753 (1983). 37. T. Kakiuchi and M. Senda. Bull. Chem. Soc. Jpn. 56:1322 (1983). 38. Z. Samec, A. Lhotsky´, H. Ja¨nchenova´, and V. Marec˘ek. J. Electroanal. Chem. Interfacial Electrochem., 483:47 (2000). 39. Z. Samec, A. Lhotsky´, and V. Marec˘ek. Electrochim. Acta 45:583 (1999). 40. H. H. J. Girault and D. J. Schiffrin. J. Electroanal. Chem. Interfacial Electrochem. 161:415 (1984). 41. H. H. J. Girault and D. J. Schiffrin. J. Electroanal. Chem. Interfacial Electrochem. 195:213 (1985). 42. T. Kakiuchi, M. Kobayashi, and M. Senda. Bull. Chem. Soc. Jpn. 60:3109 (1987). 43. T. Kakiuchi, M. Kobayashi, and M. Senda. Bull. Chem. Soc. Jpn. 61:1545 (1988). 44. T. Kakiuchi, T. Usui, and M. Senda. Bull. Chem. Soc. Jpn. 63:2044 (1990). 45. T. Kakiuchi, T. Usui, and M. Senda. Bull. Chem. Soc. Jpn. 63:3264 (1990). 46. V. Marec˘ek, A. Lhotsky´, K. Holub, and I. Stibor. Electrochim. Acta 44:155 (1998). 47. V. Marec˘ek, A. Lhotsky´ and H. Ja¨nchenova´. J. Electroanal. Chem. Interfacial Electrochem., in press 1999. 48. J. Koryta, L. W. Hung, and A. Hofmanova´. Studia Biophys. 90:25 (1982). 49. H. H. J. Girault and D. J. Schiffrin. J. Electroanal. Chem. Interfacial Electrochem. 179:277 (1984). 50. T. Kakiuchi, M. Nakanishi, and M. Senda. Bull. Chem. Soc. Jpn. 61:1845 (1988). 51. T. Kakiuchi, M. Nakanishi, and M. Senda. Bull. Chem. Soc. Jpn. 62:403 (1989). 52. D. Grandell, L. Murtoma¨ki, K. Kontturi, and G. Sundholm. J. Electroanal. Chem. Interfacial Electrochem. 463:242 (1999).
Capacitance and Surface Tension
437
53. D. Grandell and L. Murtoma¨ki. Langmuir 14:556 (1998). 54. Z Samec, V. Marec˘ek, and J. Weber. J. Electroanal. Chem. Interfacial Electrochem. 100:841 (1979). 55. Z. Samec. J. Electroanal. Chem. Interfacial Electrochem. 426:31 (1997). 56. J. D. Reid, P. Vanysek, and R. P. Buck. J. Electroanal. Chem. Interfacial Electrochem. 170:109 (1984). 57. F. Silva and C. Moura. J. Electroanal. Chem. Interfacial Electrochem. 177:317 (1984). 58. M. C. Wiles, D. J. Schiffrin, and T. J. VanderNoot. J. Electroanal. Chem. Interfacial Electrochem. 278:151 (1990). 59. Z. Samec, J. Langmaier, and A. Troja´nek. J. Chem. Soc. Faraday Trans. 92:3843 (1996). 60. P. Ha´jkova´, D. Homolka, V. Marec˘ek, and Z. Samec. J. Electroanal. Chem. Interfacial Electrochem. 151:277 (1983). 61. T. J. VanderNoot and D. J. Schiffrin. Electrochim. Acta 35:1359 (1990). 62. V. Marec˘ek and Z. Samec. J. Electroanal. Chem. Interfacial Electrochem. 149:185 (1983). 63. V. Marec˘ek and Z. Samec. J. Electroanal. Chem. Interfacial Electrochem. 185:263 (1985). 64. J. D. Reid, P. Vany´sek, and R. P. Buck. J. Electroanal. Chem. Interfacial Electrochem. 161:1 (1984). 65. Z. Samec, V. Marec˘ek, K. Holub, S. Rac˘insky´, and P. Ha´jkova´. J. Electroanal. Chem. Interfacial Electrochem. 225:65 (1987). 66. L. I. Daikhin, A. A. Kornyshev, and M. Urbakh. Electrochim. Acta 45:685 (1999). 67. M. Senda, T. Kakiuchi, T. Osakai, and T. Kakutani, in The Interfacial Structure and Electrochemical Processes at the Boundary Between Two Immiscible Liquids (V. E. Kazarinov, ed.), Springer-Verlag, Berlin, Heidelberg, 1987, pp. 107–121. 68. Z. Samec, J. Langmaier, and A. Troja´nek. J. Electroanal. Chem. Interfacial Electrochem. 444:1 (1998). 69. Z. Samec, J. Langmaier, and A. Troja´nek. J. Electroanal. Chem. Interfacial Electrochem. 463:232 (1999). 70. D. Homolka, P. Ha´jkova´, V. Marec˘ek, and Z. Samec. J. Electroanal. Chem. Interfacial Electrochem. 159:233 (1983). 71. C. Yufei, V. J. Cunnane, D. J. Schiffrin, L. Murtoma¨ki, and K. Konturri. J. Chem. Soc. Faraday Trans. 87:107 (1991). 72. C. M. Pereira, A. Martins, M. Rocha, C. J. Silva, and F. Silva. J. Chem. Soc. Faraday Trans. 90:143 (1994). 73. Z. Samec, J. Langmaier, and A. Troja´nek, unpublished. 74. C. M. Pereira, W. Schmickler, F. Silva, and M. J. Sousa. J. Electroanal. Chem. Interfacial Electrochem. 436:9 (1997). 75. T. Kakiuchi, M. Yamane, T. Osakai, and M. Senda. Bull. Chem. Soc. Jpn. 60:4223 (1987). 76. T. Wandlowski, S. Rac˘insky´, V. Marec˘ek, and Z. Samec. J. Electroanal. Chem. Interfacial Electrochem. 227:281 (1987). 77. T. Wandlowski, V. Marec˘ek, and Z. Samec. J. Electroanal. Chem. Interfacial Electrochem. 242:277 (1988). 78. T. Kakiuchi, M. Kotani, J. Noguchi, M. Nakanishi, and M. Senda. J. Colloid Interface Sci. 149:279 (1992). 79. T. Kakiuchi, T. Kondo, M. Kotani, and M. Senda. Langmuir 8:169 (1992). 80. T. Kakiuchi, T. Kondo, and M. Senda. Bull. Chem. Soc. Jpn. 63:3270 (1990). 81. T. Kondo, T. Kakiuchi, and M. Senda. Biochem. Biophys. Acta 1124:1 (1992). 82. T. Kondo, T. Kakiuchi, and M. Senda. Bioelectrochem. Bioenerg. 34:93 (1994). 83. T. Kondo and T. Kakiuchi. Bioelectrochem. Bioenerg. 36:53 (1995). 84. T. Kakiuchi, Y. Teranishi, and K. Niki. Electrochim. Acta 40:2869 (1995). 85. M. C. Wiles, T. J. VanderNoot, and D. J. Schiffrin. J. Electroanal. Chem. Interfacial Electrochem. 281:231 (1990).
18 Liquid Membrane Ion-Selective Electrodes: Response Mechanisms Studied by Optical Second Harmonic Generation and Photoswitchable Ionophores as a Molecular Probe YOSHIO UMEZAWA Japan
I.
Department of Chemistry, University of Tokyo, Tokyo,
INTRODUCTION
Liquid membrane type ion-selective electrodes (ISEs) provide one of the most versatile sensing methods because it is possible to customize the sensory elements to suit the structure of the analyte. A wealth of different synthetic and natural ionophores has been developed, in the past 30 years, for use in liquid membrane type ISEs for various inorganic and organic ions [1]. In extensive studies [2–4], the response mechanism of these ISEs has been interpreted in terms of thermodynamics and kinetics. However, there have been few achievements in the characterization of the processes occurring at the surface of ISEs at molecular level. According to generally accepted theoretical models of poly(vinyl-chloride) (PVC)based liquid membrane type ion-selective electrodes (ISEs), the membrane potential is described as the sum of the diffusion potential across the membrane bulk and the phase boundary potentials at the interfaces of the membrane and the inner filling and sample solutions [5–8]. Of these factors, a change in the phase boundary potential at the membrane–aqueous sample solution interface contributes mainly to the quick response of ISEs, because a change in the diffusion potential in the membrane bulk takes place only very slowly [9–12]. The generation of the phase boundary potential is explained on the basis of the permselective uptake of primary ions, leaving the counterions on the aqueous side of the interface. It is therefore necessary to correlate the phase boundary potential with the amount as well as the distribution of electric charge at the interface to understand the molecular mechanism of the membrane potential. Recently, we [13,14] evidenced by ATR-IR spectroscopy that the membrane potential of ionophore-incorporated, PVC-based liquid membranes is governed by permselective transport of primary cations into the ATR-active layer of the membrane surface. More recently, we [14–16] observed optical second harmonic generation (SHG) for ionophore-incorporated PVC-based liquid membranes, and confirmed that the membrane potential is primarily governed by the SHG active, oriented complexed cations at the 439
440
Umezawa
membrane surface, facing across the interface the hydrophilic counteranions in the adjacent aqueous phase. Also, an experimental method for evaluating the relationship between the surface charge density and the phase boundary potential was proposed by using photoswitchable ionophores as a molecular probe [17]. The purpose of this chapter is to describe these experimental approaches for understanding the molecular mechanism of the membrane potentials for ionophore-incorporated liquid membrane ion-selective electrodes.
II.
FTIR-ATR STUDY ON CATION PERMSELECTIVITY [13]
Pungor and coworkers first observed the complex formation between a crown ether derivative and Kþ in ISE membranes by FTIR-ATR spectrometry. They found that there is only a low concentration of the Kþ -crown complex at the phase boundary between the membranes and aqueous KCl; these were easily removed by rinsing with water. In contrast, membranes treated with aqueous KSCN contain a large amount of the complexes accompanied by SCN ions; those complexes are not easily removed by rinsing and the transport rate of the complex into the bulk of the membrane was found to be much slower than the potentiometric response time. Pungor et al. concluded that the observed potential response of this type of ISE is determined essentially at the surface of the membrane and not in the bulk [9–15]. We further extended the above work and first evidenced by FTIRATR spectrometry permselective cation transport into ISE liquid membranes in terms of the quantitative stoichiometric ratio of counteranions and complex cations. When primary ion solutions with an IR-active hydrophilic counteranion, SO2 4 , were used, the IR spectra of the membranes only indicated the presence of complexed cations, and no IR peak due to the counteranion was found. The intensity of the former peaks was found to be dependent on the membrane concentration of added anionic sites, introduced either by the use of carboxylated poly(vinyl chloride) or a derivative of tetraphenylborate, and also on the penetration depth of the IR beam used. In contrast, the use of a hydrophobic counteranion, SCN , led to IR signals from both the complexed cation and the corresponding counteranion. Their stoichiometric ratios depended on the concentrations of the primary ion and of the tetraphenylborate derivative in the membrane. It was also found that the depth of completely permselective transport of cations, that is, exclusion of the hydrophilic counteranions was as great as 1:0 m and that the type of ionophore and the presence of added anionic sites in the membrane were significant factors governing the magnitude of this penetration depth [14]. FTIR-ATR has thus been demonstrated to be a very useful technique for the characterization of processes at the surface of liquid membrane ISEs. The depth accessible to FTIR-ATR is of the order of 0:1 1:0 m and is thus too large for the observation of phenomena at the very surface.
III.
SHG OBSERVATION OF LIQUID–LIQUID INTERFACE OF ISES [16]
Optical second harmonic generation (SHG), which is the conversion of two photons of frequency ! to a single photon of frequency 2!, is known to be an inherently surfacesensitive technique, because it requires a noncentrosymmetrical medium. At the interface between two centrosymmetrical media, such as the interface between two liquids, only the molecules which participate in the asymmetry of the interface will contribute to the SHG [18]. SHG has been used as an in-situ probe of chemisorption, molecular orientation, and
Liquid Membrane Ion-Selective Electrodes
441
adsorbate organization at a wide variety of surfaces, namely the air–solid [20–23,29], liquid–solid [19–21,29], liquid–air [20,24–29], and liquid–liquid [18,28,29] interfaces, because of its ability to discriminate between surface species and species in the adjacent bulk media. Corn et al. reported the application of surface SHG to monitor the adsorption of an anionic surfactant molecule at a liquid–liquid (water/1,2-dichloroethane) interface, to which an electrical potential was applied, and determined the surface concentration of the surfactant molecule as a function of the potential [18]. Shen et al. reported on the molecular orientation of surfactants at liquid–liquid (water–decane and water–carbon tetrachloride) interfaces [28]. The SHG technique is therefore a valuable probe for insight into the surface chemistry of liquid membrane ISEs. A.
SHG Induced by Surface Ionophore–Metal Ion Complexation
The SHG signal intensity, Ið2!Þ , arising at the liquid–liquid interface is known to be proportional to the square of the second-order nonlinear electric susceptibility, cð2Þ , at the surface [18,28,29], 2 2 ð1Þ Ið2!Þ / eð2!Þ ð2Þ eð!Þ eð!Þ Ið!Þ ð2Þ ¼ NhTið2Þ
ð2Þ
where Ið!Þ is the input light power, eð!Þ and eð2!Þ are the electric polarization vectors describing the input and output light fields, respectively, N is the surface concentration of SHG active species, ð2Þ the molecular and second-order nonlinear electric polarizability, T the co-ordinate transformation connecting the laboratory and molecular axes, and the angular brackets denote an average over all molecular orientations. From Eqs. (1) and pffiffiffiffiffiffiffiffi ffi (2) follows that the square root of the SHG intensity, Ið2!Þ , is directly proportional to N, hTi and ð2Þ ; namely pffiffiffiffiffiffiffiffiffi Ið2!Þ / NhTið2Þ ð3Þ The measurement of SHG intensities thus provides information on the concentration N, the molecular orientation hTi, and the polarization ð2Þ of SHG active species at the interface. The SHG measuring system is shown in Fig. 1. The dependence of the SHG intensity, Ið2!Þ , of a membrane incorporated with ionophore 2 (membrane 2, see Fig. 2) in contact with 0.18 M aqueous KCl on the power of the irradiation light beam, Ið!Þ , is shown in Fig. 3. A linear relationship is seen between the input power, Ið!Þ , and the square pffiffiffiffiffiffiffiffiffi root of the SHG intensity, Ið2!Þ . This relation satisfies the principle of SHG [see Eq. (1)] and thus confirms that the light detected in this system is indeed arising from SHG. pffiffiffiffiffiffiffiffiffi Figure 4 shows the dependence of the square root of the SHG intensity, Ið2!Þ , on the concentration of Liþ ion (LiCl) in the aqueous solution, using membrane 1 with an ionophore concentration of 10 mM. The SHG intensity increased steeply at low Liþ ion concentrations but leveled off at higher concentrations. In the absence of Liþ ions, the SHG signal was found to be negligible. The SHG response for a membrane without ionophore, i.e., a PVC–DOS membrane, was also negligible at otherwise identical conditions. The generation of the SHG signal can be ascribed to the formation of oriented Liþ ionophore 1 complexes at the membrane surface, facing across the interface the hydrophilic counteranions, Cl , in the adjacent aqueous phase. In fact, when a relatively hydro-
442
Umezawa
FIG. 1 Schematic diagram of the present SHG measuring system and detailed structure of the optical cell: (a) 45 right angle prism; (b) glass plate reflector; (c) infrared transparent filter (> 690 nm); (d) aqueous CuSO4 filter; (e) spherical quartz lens; (f) interference filter (530 nm, 10 nm of FWHM); (g) beam damper; (h) stainless cover; (i) silicone rubber packing; (j) solvent polymeric membrane; (k) slide glass; (l) sample cuvette. The s-polarized 1064 nm output of a Qswitched ND:YAG laser was used with an 8–9 ns pulse width and 10 Hz repetition rate. (From Ref. 15.)
phobic anion, SCN , was used instead of a Cl ion as the counteranion, the observed SHG signal decreased at high salt concentrations, probably due to a decrease in the number of oriented cation complexes at the surface upon extraction of SCN ions into the membrane bulk (vide infra). The fact that the SHG signal virtually leveled off at high Liþ ion concentrations means that the number of SHG active species located at the membrane interface became constant beyond a certain Liþ ion concentration, assuming negligible changes in the molecular orientation (see Eq. (3)]. The SHG response of membranes 2, 3, and 4, respectively, was similar to that of membrane 1; the SHG signal increased with increasing primary cation concentrations in the aqueous solution, and again leveled off at high cation concentrations (vide infra). The saturation of the SHG response at high cation concentrations suggests that the process of complex formation at the membrane surface may be treated by a Langmuirisotherm type analysis [24,27]. At constant temperature, the Langmuir equation is given by 1 1 1 1 ¼ ð4Þ þ N Nmax K Cb Nmax where N is the number of the cationic complexes located at the surface, Nmax the maximum of the cationic complexes at the interface, Cb the aqueous bulk cation concentration
Liquid Membrane Ion-Selective Electrodes
443
FIG. 2 Structures of the ionophores 1–4. 1=dibenzyl-14-crown-4; 2=bis(benzo-15-crown-5); 3=dibenzo-18-crown-6; 4=dibenzo-24-crown-8; these ionophores are selective for Liþ , Kþ , Kþ and Naþ , respectively. (From Ref. 15.)
and K the binding constant (M1 ) (the complexation stability constant between the cation and the ionophore at the membrane surface), respectively. It should be noted that 1=N is inversely proportional to the bulk cation concentration, Cb . A nearly linear relation was in fact found between the reciprocal of the square root of the SHG intensity and the reciprocal of the bulk cation concentration for membrane 1,
pffiffiffiffiffiffiffiffiffi FIG. 3 Dependence of the square root of the SHG intensity Ið2!Þ on the power of the irradiated fundamental light, as obtained with membrane 2 with an ionophore concentration of 3:0 102 M. The adjacent aqueous solution was 1:8 101 M KCl. Inset: dependence of the SHG intensity on the input optical power. (From Ref. 15.)
444
Umezawa
pffiffiffiffiffiffiffiffiffi FIG. 4 Dependence of the square root of the SHG intensity Ið2!Þ on Liþ ion concentrations with 2 membrane 1 (&), (ionophore concentration 1:0 10 M) or with a membrane without ionophore 1 (*). (From Ref. 15.)
as shown in Fig. 5. Also for membranes 2, 3, and 4, Langmuir type binding isotherms were found (figures not shown). It seems that a Langmuir type ‘‘saturation’’ is indeed reached at the membrane surface. Figure 5 also shows the effect of the ionophore concentration of the Langmuir type binding isotherm. The slope of the isotherm fora membrane with 10 mM of ionophore 1 was roughly three times larger than that with 30 mM of the same ionophore. The binding constant, K, which is inversely proportional to the slope [Eq. (3)], was estimated to be 4:2 M1 and 11:5 M1 for the membranes with 10 mM and 30 mM ionophore 1, respectively. This result supports the validity of the present Langmuir analysis because the binding constant, K, should reflect the availability of the surface sites, the number of which should be proportional to the ionophore concentration, if the ionophore is not surface active itself. In addition, the intercept of the isotherm for a membrane with 10 mM of ionophore 1 was nearly equal to that of a membrane with 30 mM ionophore 1 (see Fig. 5). This suggests the formation of a closest-packed surface molecular layer of the SHG active Liþ -ionophore 1 cation complex, whose surface concentration is nearly equal at both ionophore concentrations. On the other hand, a totally different intercept and very small slope of the isotherm was obtained for a membrane containing only 3 mM of ionophore 1. This indicates an incomplete formation of the closest-packed surface layer of the cation complexes due to a lack of free ionophores at the membrane surface, leading to a kinetic limitation. In this case, the potentiometric response of the membrane toward Liþ was also found to be very weak (vide infra). The results of the above-mentioned Langmuir analysis of the SHG responses may be interpreted in terms of a tightly packed monolayer of the SHG active cation complexes at the membrane surface. The tight layer may, however, also be a layer thicker than a monolayer in which the potential aligns the complexes to the electric field. As a consequence of the increase of the potential near the surface, the oriented complexes would on the average be nearer to the surface than the average of all complexes.
Liquid Membrane Ion-Selective Electrodes
445
pffiffiffiffiffiffiffiffiffi FIG. 5 Plots of the reciprocal of the square root of the SHG intensities 1= Ið2!Þ versus the reciþ procal of Li ion concentrations in the adjacent aqueous solutions (the Langmuir isotherm) as obtained with membrane 1. The ionophore concentrations were 3:0 103 M (~), 1:0 102 M (*), and 3:0 102 M (&), respectively. The data points present averages for three sets of measurements. Error bars show standard deviations. (From Ref. 15.)
B.
Correlation Between the SHG Signals and ISE Potentials
As shown in Fig. 6(a), the SHG response of membrane 2 to aqueous KSCN was found to be different from that to KCl. Upon increasing the KSCN concentration, the SHG signal initially increased but reached a maximum at 0.2 M, and then decreased. The potentiometric response of the same membrane also exhibited a maximum at a Kþ ion activity of ca. 0.1 M [see inset in Fig. 6(a)]. Thus, the decrease in the SHG and potentiometric responses were found to start roughly at the same KSCN concentration. This may be attributed to a decrease in the number of oriented Kþ -ionophore 2 complexes at the interface with the appearance of SCN ions in the membrane. To prevent such anionic effects, so-called added anionic sites are conventionally used as additives for ISE membranes [35]. In fact, upon addition of KTpClPB, a marked improvement of the SHG response for KSCN was observed at higher analyte concentrations [Fig. 6(b)]. Because a membrane containing only KTpClPB, i.e., a PVC–DOS– KTpClPB membrane, did not show any SHG response toward Kþ ions, this result suggests that TpCIPB may assist the surface orientation of the Kþ -ionophore 2 complexes by inhibiting the uptake of SCN ions from the adjacent aqueous solution. The parallel changes in membrane potentials and SHG signals allow us to conclude that the observed membrane potential changes in the above case are primarily governed by the SHG active oriented species at the membrane surface. Anionic effects were observed by FT-IR-ATR spectrometry with a membrane containing not ionophore 2 but a different kind of ionophore, ETH 129 [13]. When the lipophilic counteranion, SCN , was used for the primary ion solutions, the spectra from both the complexed cation and corresponding counteranion were seen, of which the stoichiometric ratio was nearly equal to that of ETH 129 complex-SCN salt at relatively high concentrations of the primary ion solutions. With KTpCIPB in the membrane,
pffiffiffiffiffiffiffiffiffi FIG. 6 Dependence of the square root of the SHG intensity ( Ið2!Þ Þ for membrane 2 without KTpCIPB (a) with þ KTpCIPB (b) on K ion concentrations in the adjacent aqueous solution containing KCl (*) and KSCN (*), respectively. Inset: The corresponding observed EMF to KCl and KSCN. The concentrations of ionophore 2 and KTpCIPB were 3:0 102 M and 1:0 102 M, respectively for both SHG and EMF measurements. The data points present averages for three sets of measurements. Error bars show standard deviations. (From Ref. 15.)
446 Umezawa
Liquid Membrane Ion-Selective Electrodes
447
the decrease in the uptake of SCN ions into the ETH 129-based membrane relative to the complexed cation was observed. The ATR results for the ETH 129-based membranes with and without KTpCIPB indicate that KTpCIPB resisted and inhibited by as much as 70% the uptake of SCN ions into the membrane phase, a trend which is inconsistent with the findings relevant to the anionic effects of the potentiometric and SHG responses of membrane 2. More explicit and in-depth discussion on the effect of charged (anionic) sites will be given in Section IV. Another important property of the SHG response of membranes 1–4 is that saturation occurs at higher cation concentrations, where Nernstian potentiometric responses are still observed [Figs. 7(a)–(d) and their insets]. This shows that the generation of the membrane potential at very high primary cation concentrations is governed not only by the SHG active cation complexes at the membrane surface but also by complexes located behind the SHG active layer, which are SHG inactive due to a lack of molecular orientation. One should remember, however, that electroneutrality requires that almost all cation complexes have to be within a few Debye lengths from the membrane surface as long as their charge is not balanced by an anionic site. To evaluate the contribution of the SHG active oriented cation complexes to the ISE potential, the SHG responses were analyzed on the basis of a space-charge model [30,31]. This model, which was proposed to explain the permselectivity behavior of electrically neutral ionophore-based liquid membranes, assumes that a space charge region exists at the membrane boundary: the primary function of lipophilic ionophores is to solubilize cations in the boundary region of the membrane, whereas hydrophilic counteranions are excluded from the membrane phase. Theoretical treatments of this model reported so far were essentially based on the assumption of a double-diffuse layer at the organic–aqueous solution interface and used a description of the diffuse double layer based on the classical Gouy–Chapman theory [31,34]. Following this model, the charge density of the complex cations, o , on the membrane side and that of the hydrophilic counteranions, a , on the aqueous side can be expressed as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fð 0 b Þ o ¼ 8RT C b v sinh ð5Þ 2RT pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fð 0 b Þ a ¼ 8RTCb v sinh ð6Þ 2RT where Cb and Cb are the concentrations of the ions in the bulk of the membrane and of the aqueous solution, respectively, v the permittivity of free space, and the dielectric constants of the membrane and of water, 0 and 0 the electric potentials at the outer Helmholtz planes at the interface of the membrane and of the aqueous side, respectively,
b and b the electrical potential in the bulk of the membrane and of the aqueous solution, respectively, and R and T have their usual meanings. It is possible to describe the electrical potential difference between the aqueous and membrane bulk, b b , as a function of the charge densities, o and a , in the simplified case where 0 ¼ 0 , as 2RT o arcsinh pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
b b ¼ ð 0 b Þ 0 b ¼ F 8RTv Cb ð7Þ a arcsinh pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8RTv Cb
FIG. 7 Dependence of the SHG signals and of the calculated charge densities for membranes 1, 2, 3, and 4, respectively, on the primary cation concentrations in the adjacent aqueous solutions, and the corresponding observed EMFs (inset). The ionophore concentrations for the membrane 1 (a), 2 (b), 3 (c), and 4 (d) are 1:0 102 M, 3:0 102 M, 2:5 102 M, and 3:0 102 M, and their primary ions are Liþ , Kþ , Kþ , and Naþ , respectively. The data points present averages for three sets of measurements. Error bars show standard deviations. (From Ref. 15.)
448 Umezawa
Liquid Membrane Ion-Selective Electrodes
449
When the extraction of the hydrophilic counteranion from the aqueous solution into the membrane bulk is negligible (cation permselectivity preserved), the concentration of the complex cation in the membrane bulk Cb , is equal to that of the fixed anionic sites, X , in the membrane matrix, due to the electroneutrality condition within the membrane bulk: Cb ¼ X ¼ const:
ð8Þ
Because the net charge at the interface should be zero, ¼ 0, the electrical potential difference, b b , in Eq. (7) can be rewritten as 2RT o o arcsinh pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi arcsinh pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð9Þ
b b ¼ F 8RT v X 8RTv Cb o
a
The determination of the number of the SHG active complex cations from the corresponding SHG intensity and thus the surface charge density, o , is not possible because the values of the molecular second-order nonlinear electrical polarizability, að2Þ , and molecular orientation, hTi, of the SHG active complex cation and its distribution at the membrane surface are not known [see Eq. (3)]. Although the formation of an SHG active monolayer seems not to be the only possible explanation, we used the following method to estimate thep surface ffiffiffiffiffiffiffiffiffi charge density from the SHG results: since the square root of the SHG intensity, Ið2!Þ , is proportional to the number of SHG active cation complexes [see Eq. (3)], the observed SHG intensity is a measure of the charge density (C=cm2 ), o , at the membrane surface. Using the molecular area of the charged complex, as estimated from a CPK molecular model, and assuming a full coverage of the cation complexes, Nmax of the Langmuir equation was estimated [see Eq. (4) and Fig. 5]. Surface charge densities can then be obtained from Eq. (4). The surface charge density and the SHG intensity dependence on the cation concentration is shown in Figs. 7(a)–(d) for four different membrane types. The electrical potential differences, o b , calculated from the surface charge densities, o , according to Eq. (9) are shown in Fig. 8 together with the observed potentials. The concentration of anionic sites in the membrane, X , which is necessary for determining b b according to Eq. (9), was varied from 0.05 to 0.6 mM. This covers the reported concentration range of anionic sites in PVC–plasticizer membranes without added sites [36]. The change of the X value within this range however hardly affected the slope of the calculated potentials, whereas the absolute potentials shifted. For membrane 1 with 10 mM ionophore, the slope of the calculated membrane potential was 58 mV/decade in the Liþ ion concentration range from 2:0 103 M to 3:0 101 M, which is close to a Nerstian response (59.2 mV/decade, 25 C). This is consistent with the observed EMF response. This result indicates that the potential increase in this case is essentially determined by the SHG active cation complexes. However, for a membrane with a concentration of ionophore 1 of 30 mM, as a result of the SHG intensity saturation, the slope of the calculated potential became small at higher primary ion (Liþ ) concentrations. This is in clear contrast to the observed result showing a nearly Nernstian response in the same concentration range. For the membrane with 3 mM ionophore 1, the slope of the calculated potentials was calculated to be only 25 mV/decade, which is close to that of the observed value. This ionophore concentration dependence reflects the extent of surface coverage by the SHG active cation complexes; at high ionophore concentrations, the surface saturation of the SHG active complex cation occurs even at lower primary ion concentrations. The calculated membrane potentials consequently leveled off, deviating from the observed EMF function. Similar results were observed with other membranes: the slopes of the calculated potentials for membranes 2, 3, and 4 were consistent with those
450
Umezawa
FIG. 8 Calculated potential differences, b b , across the membrane boundary as a function of the primary cation activity, as calculated from Eq. (9). The upper data set shows the corresponding observed EMF. (a) Membrane 1; primary ion: Liþ , ionophore concentration: 3:0 103 M(&), 1:0 102 M (*) and 3:0 102 M (*), respectively, (b) membrane 2; primary ion: Kþ , ionophore concentration: 3:0 102 M, (c) membrane 3; primary ion: Kþ , ionophore concentrations: 2:5 102 M, (d) membrane 4; primary ion: Naþ , ionophore concentration: 3:0 102 M. The following parameters were used: ¼ 4:0, ¼ 78:3, T ¼ 298 K, and X ¼ 1:0 107 mol=cm3 . (From Ref. 15.)
Liquid Membrane Ion-Selective Electrodes
451
of the observed EMFs at relatively low cation concentrations (Figs. 8(b)–(d)] and deviations between the calculated and observed potentials were found at relatively high cation concentrations. The increase in the extent of charge separation due to the increasing ionophore concentration without substantial change in the observed EMF, as can be seen in Fig. 8, may be surprising. One must, however, bear in mind that the increased ionophore concentration leads to an increase in the phase boundary potentials at both the outer and inner interface of the ISE membrane and that these two effects should cancel out. The deviation of the calculated EMF responses from Nernstian slopes at high cation and ionophore concentrations, in contrast to the observed EMFs, may be explained as follows: in the space charge model, the surface charge is treated as the sum of point charges that are Boltzmann distributed within the diffuse double layer. Due to neglect of field-dipole forces and specific molecular interactions occurring at the phase boundary, saturation of the SHG active layer cannot be taken into account. Although the space charge model seems to be valid for the explanation of the electrical potential drop across the interface, the SHG observation is expected to provide refinements of this model in terms of the charge distribution as well as the orientation of the cation complexes.
IV.
MOLECULAR PROBE FOR ISE MEMBRANE POTENTIALS BASED ON PHOTOSWITCHABLE AZOBIS(BENZO-15-CROWN-5) IONOPHORES [17]
Shinkai and coworkers [36–38] synthesized a series of azobis(benzo-15-crown-5), which can adopt the trans and cis forms by reversible photoisomerization. The cis-ionophore forms a stable sandwich-type 1 : 1 cation–ionophore complex with Kþ ions, whereas the corresponding complexation affinity of the trans-ionophore is very weak [36]. Photocontrol of the cation-extracting [36,37] and cation-transport [38] properties of these compounds was intensively studied. More recently, Osa and coworkers [39–41] reported photoinduced potential changes with PVC-based liquid membranes containing photoswitchable ionophores such as azobenzene-linked crown ethers. When the membrane in contact with the primary cation solution was exposed to UV light, a change in the membrane potential due to photoisomerization of the ionophore in the membrane was observed. Although the direction of the photoinduced potential change was discussed in terms of the structural change of the ionophore, quantitative treatment of the potential change was not carried out. If the photoequilibrium concentrations of the cis and trans isomers of the photoswitchable ionophore in the membrane bulk and their complexation stability constants for primary cations are known, the photoinduced change in the concentration of the complex cation in the membrane bulk can be estimated. If the same amount of change is assumed to occur for the concentration of the complex cation at the very surface of the membrane, the photoinduced change in the phase boundary potential may be correlated quantitatively to the amount of the primary cation permeated to or released from the membrane side of the interface under otherwise identical conditions. In such a manner, this type of photoswitchable ionophore may serve as a molecular probe to quantitatively correlate between the photoinduced changes in the phase boundary potential and the number of the primary cations permselectively extracted into the membrane side of the interface. Highly lipophilic derivatives of azobis(benzo-15-crown-5), 1 and 2, as well as reference compound 3 were used for this purpose (see Fig. 9 for the structures) [43]. Compared to azobenzene-modified crown ethers reported earlier [39–42], more distinct structural difference between the cis
452
Umezawa
FIG. 9 Chemical structures of photoswitchable ionophores 1–3. (From Ref. 17.)
and trans isomers can be expected for ionophores 1 and 2 because in the latter compounds the 15-crown-5 rings are directly attached to the benzene rings of the azobenzene group. A.
Photoinduced Changes in Phase Boundary Potentials
Similarly to Section II [6,30–33], Gouy–Chapman type double-diffuse layers were again assumed as a space charge region that enables charge separation across the membrane– aqueous solution interface (Fig. 10). But more explicit formulation will be given below because more ionic species are involved in this case. On the basis of this assumption, the phase boundary potential was quantitatively correlated with the amount of space charge in that region. However, since the factors controlling the amount of the space charge were not specified, the relationship between the phase boundary potential and the concentration of the primary cation in the aqueous sample solution could not be discussed. In the present photoswitchable molecular probe approach, the amount of space charge is quantitatively correlated with the number of cationic complexes at the membrane surface by considering the complexation equilibrium between the membrane and aqueous sides of the interface (vide supra). Consequently, the relationship between the photoinduced change in the phase
Liquid Membrane Ion-Selective Electrodes
453
FIG. 10 Schematic representation of the proposed surface model: (a) the concentration and (b) the electrical potential profiles at the interface of the membrane and aqueous sample solution. x ¼ 0 and 0 are the positions of ions in the planes of closest approach (outer Helmholtz planes) from the aqueous and membrane sides, respectively. (From Ref. 17.)
boundary potential and in the number of the cationic complex at the membrane surface can be evaluated in a quantitative manner. The sample solution contains a fixed concentration of supporting electrolyte Eþ L and a varying concentration of primary salt Mþ X . The ionophore I is confined in the membrane. Only the primary cation Mþ can be complexed with the ionophore I (given stoichiometry 1 : 1; stability constant bIM ). The complex MIþ and the anionic site A are the lipophilic species that are present only in the membrane phase. In this system, the electroneutrality condition at the membrane bulk leads to mem mem mem mem þ CM þ CEmem ¼ CA þ CX þ CLmem CIM mem ¼ CA þ
aq 2 kM kX ðCM Þ kE kL ðCEaq Þ2 þ mem CM CEmem
ð1Þ
with kspecies ¼ exp
o;aq o;mem species species RT
aq mem where Cspecies and Cspecies are the concentrations of each species in the membrane and sample aqueous solution bulk, respectively, kspecies is the distribution constant of each o;aq o;mem and species are the chemical standard potentials of each species at the species, species aqueous and membrane phases, respectively, and R and T have their usual significance. In the proposed model, the phase boundary potential Eb can be expressed as aq aq aq mem Eb ¼ mem mem ð2Þ bulk bulk ¼ 0 bulk ð 0 bulk Þ
454
Umezawa
mem where aq bulk and bulk are the electrical potentials in the bulk of the aqueous solution and mem are the potentials at the outer Helmholtz planes membrane, respectively, and aq 0 and 0 (OHPs) on the aqueous and membrane sides of the interface, respectively. From the equilibrium requirement that the chemical potential involving all ionic species be uniform throughout the phase boundary, the distribution of ions within the electrical double layer can be expressed by the Boltzmann equation:
X
aq Cþð0Þ
X X X
aq Cð0Þ mem Cþð0Þ
mem Cð0Þ
aq F 0 aq bulk ¼ exp RT aq X aq F 0 aq bulk ¼ C exp RT X F ð mem mem 0 bulk Þ mem ¼ C exp RT X F ð mem mem 0 bulk Þ mem ¼ C exp RT X
aq C
ð3Þ
with X X X X
aq aq aq Cþð0Þ ¼ CMð0Þ þ CEð0Þ ;
X
aq aq aq Cð0Þ ¼ CXð0Þ þ CLð0Þ ;
aq aq aq C ¼ CM þ CEaq ¼ CX þ CLaq ; mem mem mem mem Cþð0Þ ¼ CIMð0Þ þ CMð0Þ þ CEð0Þ ;
X
mem mem mem mem Cð0Þ ¼ CAð0Þ þ CXð0Þ þ CLð0Þ ;
mem mem mem mem mem ¼ CIM þ CM þ CEmem ¼ CA þ CX þ CLmem C
aq mem where Cspeciesð0Þ and Cspeciesð0Þ are, respectively, the concentrations of the corresponding species at the OHPs on the aqueous and membrane sides of the interface. According to the Gouy–Chapman theory, the surface charge densities on the aqueous and membrane sides, aq and mem , respectively, can be expressed as
aq
mem
aq qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X aq F 0 aq bulk C sinh ¼ 8RT0 aq 2RT qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X F ð mem mem 0 bulk Þ mem ¼ 8RT0 mem C sinh 2RT
ð4Þ
where 0 is the permittivity of a vacuum, aq and mem are the relative permittivities of water and the membrane, respectively. Using Eqs. (3) and (4), the relationship between the surface charge density and the ionic concentrations at the OHPs on the membrane side of the interface can be expressed as X
mem Cþð0Þ þ
X
mem Cð0Þ ¼2
X
2
mem C þ
ð mem Þ 2RT0 mem
ð5Þ
Liquid Membrane Ion-Selective Electrodes
455
Equation (5) can be rewritten as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mem mem mem mem mem mem 2RT0 mem CIMð0Þ þ CMð0Þ þ CEð0Þ þ CXð0Þ þ CLð0Þ CAð0Þ 0 1 mem mem mem pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiBqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CIM þ CM þ CE C mem mem mem qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2RT0 mem @ CIMð0Þ þ CMð0Þ þ CEð0Þ A mem mem mem CIMð0Þ þ CMð0Þ þ CEð0Þ
mem ¼
ð6Þ
This relationship implies that the membrane side of the interface becomes positively or negatively charged depending on whether the sum of the surface concentrations of each cationic species is larger or smaller than the total concentration of the corresponding mem mem mem mem þ CM þ CEmem ¼ CA þ CX þ CLmem Þ in the membrane bulk. cations ðCIM Next, the complexation equilibrium at the interface must be taken into account. Under the distribution equilibrium of the primary ion Mþ between the aqueous and membrane sides of the interface, the complexation reaction between the primary ion and the ionophore occurs at the membrane side of the interface, i.e., Mmemð0Þ Ð Maqð0Þ Mmemð0Þ þ Imemð0Þ Ð IMmemð0Þ
ð7Þ
where Maqð0Þ and Mmemð0Þ represent the ion Mþ at the OHPs on the aqueous and membrane sides of the interface, respectively, Imemð0Þ and IMmemð0Þ are, respectively, the uncomplexed and complexed ionophore at the OHP on the membrane side of the interface. Under the assumption that the concentration of the uncomplexed ionophore is constant mem throughout the membrane phase, the quantity CIMð0Þ can be expressed as mem mem mem CIMð0Þ ¼ IM CMð0Þ Cl ¼
mem mem mem IM CMð0Þ Cl;tot mem mem mem IM CMð0Þ Cl;tot CA 1 þ IM CM
ð8Þ
mem where Cl;tot is the total concentration of the complexed and uncomplexed ionophore in the mem membrane bulk. The quantity CMð0Þ can be expressed as a function of the concentration of aq , as the primary cation in the aqueous bulk, CM
2qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 aq P mem C þ CEaq mem CM aq ffiffiffiffiffiffi p aq 5 pffiffiffi þ aq CM þ CE x qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aq ffi pffiffiffiffiffiffi aq þ CEaq þ aq CM þ CEaq xmem CM
aq 4 CM aq mem ¼ KI CMð0Þ ¼ CMð0Þ
ð9Þ
with x ¼ kM 1 þ
mem IM Cl;tot aq aq mem CM þ kE CE 1 þ IM CM
By inserting Eq. (8) into Eq. (6) the charge density at the membrane surface, mem , can be described in relation to the concentration of the primary cation at the aqueous aq solution side of the interface, CMð0Þ :
456
Umezawa
mem
8vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
3 2 u > mem mem u aq 1 þ IM CM þ Cl;tot pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ IM CM CM : P mem C ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mem mem aq 1 þ IM CM þ Cl;tot aq aq CE kM CMð0Þ þ kE CMð0Þ aq mem 1 þ IM CM CM
g
ð10Þ
Because the net charge at the interface should be zero, i.e., mem þ aq ¼ 0, the phase boundary potential (Eb Þ can be expressed by Eq. (11), which can be derived on the basis of ¼ aq Eq. (3) in the simplified case where mem 0 0 . 39 > = 7 6 archsinh pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eb ¼ 5 P memffi þ arcsinh4qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aq > F > 8RT0 mem C : þ CEaq ; 8RT0 aq CM 8 > 2RT
100 mM), NMR enables us to determine static and dynamic properties of both drugs and membranes. Here we review the molecular level DD research carried out by NMR. The drugs discussed are summarized in Table 1. The structures of the drugs, which are classified into anesthetics and endocrine disruptors, are shown in Fig. 1. Anesthetics, which induce general and local anesthesia, are examples of the most popular drugs clinically used. The anesthetic mechanisms have been extensively discussed over the past century in view of the Meyer–Overton correlation [3] proposed just at the end of the 19th century. However, the mechanism has not yet been fully understood. The molecular mechanism still remains unsolved. On the other hand, endocrine disruptors are concerned with the most recent and sensational problems of the endocrine damage of wildlife. They are hydrophobic organic compounds exhibiting a high affinity with lipid membranes [4]. They are environmental pollutants and exogeneous chemicals that interfere with the endocrine system of intact organisms. They include bisphenol A, alkylphenols, and alkylbenzenes. Molecular study of lipid bilayer interfaces is necessary for a better understanding of the membrane–drug interaction and DD into biomembranes. The points to be clarified are: (1) How can we determine DD sites at the bilayer interface? (2) What kind of method is advantageous? (3) Is it possible to unambiguously specify the bilayer interfacial portion coupled with drugs? (4) What are most important characteristics of DD at the bilayer interface? In order to answer these important questions, this chapter has been planned. We will emphasize the significance of the molecular level information obtainable from NMR studies. In the 1970s the structure and dynamics of lipid bilayer membranes were extensively investigated by NMR. The principles of the NMR spectroscopy applied to the study of biomembranes are reviewed in Ref. 5, together with the fruitful achievements in the early stage. In the 1980s the NMR biomembrane research was carried out mainly by applying the solid-state NMR techniques [6–11]. Generally, the solid-state spectra are of low reso-
TABLE 1
List of Drugs Discussed
Anesthetics
Endocrine disruptors
General anesthetics
Alkanols Halothane Enflurane Isoflurane Halogenated cyclobutanes Xenon
Local anesthetics
Dibucaine Procaine Tetracaine Lidocaine Benzyl alcohol
Bisphenol A Alkylbenzenes
Benzene Toluene Ethylbenzene Propylbenzene
NMR Studies on Lipid Bilayer Interfaces
777
FIG. 1 Molecular structures of the drugs examined in the delivery study: the general anesthetics, alkanols (I), halothane (II), enflurane (III), isoflurane (IV), halogenated cyclobutane (V); the local anesthetics, dibucaine hydrochloride (VI), procaine hydrochloride (VII), tetracaine hydrochloride (VIII), lidocaine hydrochloride (IX), benzyl alcohol (X); the endocrine disruptor, bisphenol A (XI), and alkylbenzenes, benzene (XII), toluene (XIII), ethylbenzene (XIV), and propylbenzene (XV).
778
Okamura and Nakahara
lution due to the dipole–dipole interactions. Now the spectral resolution has been improved to a large extent by the combined application of cross polarization (CP) and magic angle spinning (MAS). In the case of solid-state NMR, high signal-to-noise ratios are obtained usually with the aid of labeled 2 H, 13 C, and 15 N nuclei; enriched samples are, however, expensive. High-resolution solution NMR is more informative and can be used for the study of biomimetic membranes for the following reasons: membrane lipids are rapidly fluctuating under physiological conditions. Vital functions of biomembranes are actually associated with large fluctuations of the membrane components. The larger the surface curvature, the larger the fluctuations. Surface curvatures are often related to biomembrane function and integrity. For example, the synaptic vesicles in axons involve the highest membrane curvatures in eucaryotic cells [12]. It is well-known that plasma lipoproteins regulate apolipoprotein binding by controlling their surface curvatures; the average diameters of the aggregates range from 200 to 10 nm in the lipid metabolism processes [13]. For the case of these biological membrane systems with large fluctuations, therefore, it is of great interest to apply the solution NMR with high-sensitivity and high-resolution, using low-cost and naturally abundant samples. The scope of this review is to summarize the recent development of the solution NMR to DD from aqueous phase to lipid bilayer membranes on the basis of our recent NMR work. Relevant physicochemical and computational aspects of the membrane DD are also referred to here.
II.
CHARACTERIZATION OF LIPID BILAYER INTERFACES
Before going to the discussion of DD, we first summarize the general features of lipid bilayer structures and dynamics.
A.
Methods
Physicochemical techniques so far applied to the study of structural and dynamical properties of phospholipid bilayers are the following: x-ray diffraction [14–17], neutron scattering [18], infrared (IR) and Raman scattering [19–25], nuclear magnetic resonance (NMR) [5,15,26–30], electron spin resonance (ESR) [31–33], fluorescence [34], calorimetry [35–37], dilatometry [38–40], and molecular dynamics (MD) simulations [2,41–44]. These methods are listed for comparison in Table 2. Each method provides structural information averaged on a characteristic length scale and dynamical information on a characteristic time scale. NMR is a versatile noninvasive technique. It can provide information not only on microscopic structure at an atomic scale but also dynamics in a range from picoseconds to seconds. Low-sensitivity problems have nowadays been overcome by the introduction of the Fourier transform (FT) technique, the dramatic improvement of the computerized instrumentation, and the stable and homogeneous generation of the high magnetic field. Recent progress in 13 C NMR enables us to obtain reliable site-selective information on membrane structure and dynamics without labeling nuclei. Unlike neutron scattering and IR absorption, no solvent peaks of water can interfere with the membrane and drug signals in the 13 C NMR spectra.
b
a
Atom ð126Þ Static Dynamic
Atom–Atom (14–12) Static
IR/Raman
Electron microscopy. Molecular dynamics simulation.
Scale Log(time/s) Probe Information
NMR
Molecule 1 Static
EMa
Molecule (11–9) þ Dynamic
ESR
Molecule (10–6) þ Static Dynamic
Fluorescence
Molecule (14–12) Static
Neutron scattering
TABLE 2 Physicochemical Techniques for the Characterization of Lipid Bilayers
Atom–Atom >2 Static
X-ray
Calorimetry 1 >2 Static
Light scattering 1 2 Static Dynamic
Atom (12–9) Static Dynamic
MDb
NMR Studies on Lipid Bilayer Interfaces 779
780
B.
Okamura and Nakahara
Static and Dynamic NMR
One of the most important advantages of the NMR method is the selectivity of the atomic site of interest. NMR spectroscopy enables us to investigate the structure and dynamics of lipid bilayers at each atomic site. The static and dynamic parameters of lipid bilayers obtainable from NMR are the chemical shift, , the spin coupling constant, J, the linewidth, 1=2 , the longitudinal relaxation time, T1 , the transverse relaxation time, T2 , and the self-diffusion coefficient, D. These are summarized in Table 3 to show the characteristic information. The chemical shift is the most popular parameter that reflects the molecular environment of an atom; it gives sensitive and detailed information about the molecular structure [45]. The spin coupling constant also gives the structural or geometrical information via nuclear spin interactions through one or more bonds. Since the position and the orientation of molecules fluctuate with time, the chemical shift and the coupling constant are observed as averaged values. Linewidth can be broadened dynamically and statically; the dynamic and static broadenings are due to a decrease in the motional narrowing effect and an increase in inhomogeneity, respectively. Linewidth and two relaxation times reflect the molecular and molecular-assembly motions. The self-diffusion coefficient also reflects the translational mobility of molecules. Two-dimensional (2D) NMR tells us about the average atom–atom distances. Atomic nuclei often used for the NMR study of lipid bilayers are 1 H, 2 H, 13 C, 14 N, 15 N, and 31 P; natural and model lipid membranes are usually composed of these atomic nuclei. Magnetic properties of these nuclei are summarized in Table 4. 1 H is the most sensitive, the chemical shift being reliable within 0:001 ppm. 2 H is useful to specify the hydrogen atom position by the isotope labeling on enrichment. Hydrophilic and hydrophobic moieties of bilayers are usually composed of carbon atoms, so 13 C can give us sharp information about structure and dynamics of bilayers. It is a unique nucleus for probing ester carbonyls, which are important as a DD site in lipid bilayer interfaces. The sensitivity has been improved by the proton-decoupling technique and the nuclear Overhauser effect (NOE). 2 H and 14 N are quadrupolar nuclei, which can provide local and short-range information on functional motions and microenvironments around the probed nuclei; these are to be compared with such dipolar (half-spin) nuclei as 1 H, 13 C, 15 N, and 31 P. 17 O, 19 F, 23 Na, and 35 Cl are sometimes used to investigate DD from aqueous phase to lipid bilayers.
TABLE 3 High-Resolution NMR Parameters Providing Static and Dynamic Information on Lipid Bilayers Parameter
J 1=2 T1 ; T2 D
Information Molecular structure Environment (electron density, hydrogen bonding, solvent effect, hydration etc.) Conformations Segmental motions, order parameters, exchange rates Segmental motions, relaxation rates Atomic, molecular, and aggregate motions
NMR Studies on Lipid Bilayer Interfaces
781
TABLE 4 Magnetic Properties of Atomic Nuclei Used for the NMR Study of Lipid Bilayers and Drug Delivery Nucleus 1
H H 13 C 14 N 15 N 17 O 19 F 23 Na 31 P 35 Cl 2
Ia
Abundanceb
Sensitivityc
Frequencyd
Site selectivity
1/2 1 1/2 1 1/2 5/2 1/2 3/2 1/2 3/2
99.98 0.015 1.108 99.63 0.37 0.0037 100.00 100.00 100.00 75.53
1.00 0.0097 0.016 0.0010 0.0010 0.029 0.83 0.093 0.066 0.0047
100.00 15.35 25.14 7.22 10.13 13.56 94.08 26.45 40.48 9.80
Zone I, II, III Zone I, IIe , III Zone I
Zone I
a
Nuclear spin. Natural abundance in percent. c Sensitivity relative to 1 H NMR. d Frequency in MHz in the case of the external magnetic field, 2.35 T. e13 — O in zone II. C NMR is the only method to probe ester C — b
C.
Classification of Zones of Lipid Bilayers
Biomembranes mainly consists of phospholipid matrices, and the major component is phosphorylcholines (PC). PC is an amphiphile consisting of hydrophilic headgroup and hydrophobic long chains. In view of the amphiphilic feature of PC, we can divide hydrated lipid bilayers into the three zones, I, II, and III. The zone model, which has been used in a recent NMR study of DD [46–48], is illustrated in Fig. 2. Zone I is the hydrophilic part of the bilayer. It includes the polar headgroup consisting of positively charged choline ammonium group and negatively charged phosphate
FIG. 2 A zone model of bilayer vesicles consisting of amphiphilic lipid molecules.
782
Okamura and Nakahara
group. Electrostatic interactions between PNþ dipoles and the PNþ and water dipoles are important in this zone. Water can easily come into this part; strong hydration is always the case. Zone II is the interfacial region between the hydrophilic and the hydrophobic parts of the lipid. Glycerol and ester carbonyl groups belong to this region. This region is most sensitive to the bilayer curvature or the aggregate size. In this region the water penetration also depends on the curvature. Zone III is the hydrocarbon chain region and composes the bilayer core. This region is nonpolar, and it is dominated by the hydrophobic interactions of the chains. Thus water rarely penetrates into this core region. It is to be noted that the zone boundary in Fig. 2 is an averaged one; it usually fluctuates due to the molecular, segmental, and overall aggregate motions. Lipid bilayer membranes can cover a wide range of polarity in a limited colloidal or mesoscopic space as shown in Fig. 3. Corresponding to the zone model in Fig. 2, it is schematically illustrated how the dielectric constant " and the water density ðH2 OÞ distribute in the layer. In the hydrophilic zone I, " and ðH2 OÞ are very close to the bulk in the aqueous phase due to the substantial hydration. A marked decrease in " and ðH2 OÞ with a large gradient is characteristic of the interfacial zone II. No substantial hydration is recognized in the hydrophobic zone III. Thus, zone II is expected to play a key role in connecting the hydrophilic and hydrophobic microenvironments in a short range. Zone II can be a gate interface for various biological functions and DD (cf. the ion channel). D.
Phase Behavior of Lipid Bilayers
Polymorphic phase behavior of hydrated lipid bialyers can be one of the controlling factors of DD, because DD depends on the dynamical features of the bilayer which abruptly change upon phase transition. The most typical transitions of biological significance are the thermotropic transition [the gel (G) to liquid–crystalline (LC) phase transition] and the barotropic transition [49]. The overview of the phase transition phenomena is beyond the scope of this review; see Refs. 37, 49, and 50. Most extensively investigated is the phase transition behavior of 1,2-dipalmitoyl-sn-glycero-3-phosphorylcholine (DPPC), the lipid component occurring frequently in natural membranes. A phase diagram of fully hydrated DPPC bilayers is shown in Fig. 4 [50]. At ambient pressure, gel ðL 0 Þ, rippled gel ðP 0 Þ, and liquid-crystalline ðL Þ phases usually appear with increasing temperature. At
FIG. 3 A schematic representation of the variation of the dielectric constant " and water density ðH2 OÞ in the water medium (bulk) and three zones of lipid bilayers.
NMR Studies on Lipid Bilayer Interfaces
783
FIG. 4 Phase diagram of fully hydrated DPPC bilayers. Different phases found are also schematically shown: L 0 , gel; P 0 , rippled gel; L I, interdigitated gel; and L , liquid crystalline phases. (From Ref. 50. Copyright # 1999 The Japan Society of High Pressure Science and Technology.)
high pressures, the interdigitated gel phase ðL IÞ is formed as a result of high molecular packing. 1 H, 2 H, 13 C, and 31 P NMR are valuable for the elucidation of structural and dynamical aspects of the phase behavior on the molecular level, as reviewed in Refs. 5 and 26. 13 C NMR spectroscopy is advantageous because of its ability to distinguish the individual carbon atom site in the bilayer. It enables us to probe all carbon atoms of cholines in zone I, glycerol and carbonyls in zone II, and alkyl chains in zone III simultaneously. 31 P NMR tells us only headgroup information in zone I; see Table 4. There has been, however, relatively few number of reliable 13 C NMR studies due to the low sensitivity in the case of natural-abundance samples. Using a large-size NMR tube (10 mm o.d.) we have succeeded in observing high-resolution 13 C NMR spectra of DPPC membranes over a wide temperature range encompassing the G/LC phase transition [51]. Using the chemical shifts, we have examined the continuity and discontinuity of their temperature dependence, as summarized in Table 5. The nature of the first-order transition is most pronounced with respect to ðCH2 Þn in the hydrophobic core. It has been proved that the ester carbonyl group in zone II is most susceptible to the change in hydration induced by the transition. This finding is relevant to the DD mechanism because DD into bilayer membranes from aqueous phase often affects the hydration of the bilayer interface and drugs. 14 N is a unique quadrupole nucleus for probing the choline ammonium of the hydrophilic headgroup of DPPC in zone I. It is interesting to examine the phase transition behavior of DPPC bilayers also by 14 N NMR [52]. Contrasting features have been disclosed by the comparison between the 14 N and the 13 C NMR spectra of the choline group in DPPC bilayers and analogous lysoPC micelles as a function of temperature. As shown in Fig. 5, 14 N NMR spectra are strikingly sensitive to the temperature and the surface curvature of the membrane, whereas the 13 C signals of the choline methyl ðÞ are almost independent of these parameters. Difference in the sensitivity between the quadrupolar 14 N and the dipolar 13 C is interesting because choline nitrogen and methyl carbons are close to each other. In other words, 14 N NMR specra provide more local and short-ranged information on the segmental motion and microenvironments of nitrogen atoms, as com-
784
Okamura and Nakahara
TABLE 5 NMR Characterization of Thermal Phase Transition in Zones I–III of Phospholipid Bilayers Zone I
II
III
Site
Type of transition
Choline N(CH3 Þ3 CH2 N POCH2 Phosphatea
Continuousc Continuous Constantd Almost continuous
Glycerol CH2 OP CHORb CH2 OR Carbonyl
Constant Constant Constant Almost continuous
Alkyl chain (CH2 Þn CH3
Discontinuouse Almost continuous
a
From Ref. 26. R ¼ acyl. c Monotonous change against temperature. d Independent of temperature. e Abrupt change against temperature. b
pared with such dipolar nuclei like 1 H, 13 C, and 15 N. Quite similar trends have been found in small and large unilamellar vesicles of egg yolk phosphatidylcholine (EPC). 14 N NMR study is useful to the DD study, because the hydrophilic phosphoyrlcholine in zone I is the first contact site of DD from aqueous phase and directly affected by the first step of the DD process.
III.
BASIC CONCEPTS OF DRUG DELIVERY
As a primary step of the biological action, both anesthetics and endocrine disruptors are delivered into lipid bilayer membranes from the aqueous phase. The delivery site of drugs in membranes is closely related to the subsequent action mechanism. It is thus important and valuable to directly determine the DD sites and orientation of drugs in membranes. Most recently, we have succeeded in specifying the DD site in small unilamellar vesicles (SUV) of EPC with a diameter of 50 nm, by taking advantage of the atomic site selectivity of NMR [46]. As model membranes, EPC SUV are useful to investigate DD by high-resolution solution NMR because of the large fluctuation of the EPC molecules.
A.
Drug Delivery Sites and Membrane–Drug Interactions
Here the basic concepts and the method for strictly determining DD sites in lipid bilayer membranes are viewed, together with some examples of their applications.
NMR Studies on Lipid Bilayer Interfaces
785
FIG. 5 14 N NMR (left) and 13 C NMR spectra (right) of the small and large unilamellar vesicles, SUV and LUV, of DPPC at various temperatures. For comparison, the spectra of palmitoyl lysophosphatidylcholine micelles at 308C are given by trace a. Traces b and c denote the spectra of the DPPC SUV with a diameter of 55 nm at 30 and 508C, respectively; trace d represents the spectra of the DPPC LUV with 100 nm diameter at 508C. Saturated KNO3 in D2 O was used as an external reference for the 14 N NMR spectra. In the 13 C NMR spectra, the signal assignment is also shown; , , and denote the choline methylene and methyl carbons POCH2 , CH2 N, and N(CH3 Þ3 , respectively. Asterisks (*) indicate the CH and two CH2 signals of the glycerol group.
1.
Categories of Drug Delivery Sites
DD sites have been classified into the three categories, as illustrated in Fig. 6 [46]. Category I is where drugs are adsorbed on the hydrophilic surfaces of bilayer membranes, zone I in Fig. 2, by Coulombic interactions or hydrogen bonding. In this case, drugs are generally polar and water-soluble; for example, procaine hydrochloride (VII) in Fig. 1. No significant effect of drugs is induced in the membrane interior, zone III. Category II is the case where drugs slightly penetrate into and are trapped at the interfacial site of the membranes, zone II. These drugs are less hydrophilic than those of category I, such as alkanols (I), dibucaine hydrochloride (VI), lidocaine hydrochloride (IX), benzyl alcohol (X), bisphenol A (XI), and benzene (XII) in Fig. 1. These drugs do not significantly perturb the inner hydrophobic chains in zone III. Membrane structure is perturbed mainly at the interfacial glycerol and carbonyl sites of phospholipids in zone II. Category III is where drugs deeply penetrate into the hydrophobic chain region of the membranes. These drugs are ethylbenzene (XIV) and propylbenzene (XV) in Fig. 1; almost insoluble in water, nonpolar, and highly lipophilic. In this case, the membrane interior, zone III, can be most remarkably perturbed.
786
Okamura and Nakahara
FIG. 6 Classification of drug delivery sites in lipid bilayers.
In order to distinguish the two membrane-trapped states of categories II and III, we have paid attention to the membrane curvature difference between inner and outer layers [46]. When drugs are trapped at the interfacial site (category II), the NMR signal splitting can be recognized due to the curvature difference. There is, however, no effect when drugs are incorporated deeply into the hydrophobic membrane interior (category III). Since drugs penetrate into the outer layer of the membrane and are finally transported to the inner layer, the distinction of these two layers plays an important role in monitoring the DD processes.
2. Noninvasive Determination of Drug Delivery Sites by NMR In this section, we focus on how to determine DD sites by NMR. The specification of the DD sites in bilayers can be done by utilizing the NMR signals of both drugs and membrane lipids. An example of the delivery site determination is given for the case of two benzene derivatives, propylbenezene (PrBe) and benzyl alcohol (BzOH) in egg phosphatidylcholine (EPC) bilayers [46]. Alkylbenzenes are suspected to be endocrine disruptors, and BzOH is one of the local anesthetics. (a) Changes of Molecular Environments of Drugs. In order to determine the trapped site of drugs at the atomic-site level from their direct NMR signals, we have followed the empirical rule that the NMR signals largely shift to a higher field when molecules are dehydrated in the nonpolar environment [46]. Here we call it the hydration chemical shift (HCS) rule. According to this simple and powerful rule, the NMR signals of the trapped drugs should shift to a higher field in the order, category Iethylbenzene>toluene>benzene, which is consistent with the sequence of the insolubility in water.
802
VI.
Okamura and Nakahara
CORRELATION BETWEEN DRUG DELIVERY SITES AND SOLVENT POLARITY
It should be noted that the delivery sites of drugs determined by NMR are closely related to their affinity for solvents with different polarities. Drugs of category I are substantially hydrophilic. High affinity for the polar solvents like water opposes transportation to the hydrophobic lipid bilayer; zone I is the most preferential delivery site. The interesting phenomenon is that some of the drugs classified into category II do not have such high affinity either for water or the hydrophobic solvents; these drugs favor the solvents with intermediate polarities, as shown schematically in Fig. 16. Typical examples are DBCHþ and BPA. The solubility profile of DBCHþ is represented by curve (a) in Fig. 16. As described before, DBCHþ is soluble in water (" ¼ 79) but it forms micelles at high concentrations. It is highly soluble in acetone (" ¼ 21) and chloroform ð" ¼ 5Þ. Surprisingly, however, DBCHþ has low solubility in alkanes (" ¼ 2). The neutral species DBC, extremely less soluble in water, is not so much soluble in alkanes; it is more soluble in acetone and chloroform [83], as shown in curve (b). The solubility profile of BPA is similar; BPA has a high affinity for alcohol with a medium polarity, despite less solubility in water and alkanes [curve (b)]. From this it is reasonable that these drugs most favor zone II in the bilayer. PrBe is highly soluble in nonpolar solvents, although it is sparingly soluble in water. The preferential location in zone III of the bilayer is reasonable in view of this solubility feature. The systematic information on the solubility of drugs thus enables us to predict the most suitable DD sites in membranes.
VII.
CONCLUDING REMARKS AND FUTURE PERSPECTIVES
Basic concepts and the methods for determining DD sites in lipid bilayer membranes have been developed by NMR on the atomic site level. Lipid bilayer interfaces as delivery sites can be specified by taking advantage of the site selectivity of NMR. DD sites can be generally classified into the three categories in Fig. 6. The distinction is based on the difference in the micropolarity in membranes around the drug. It has been briefly mentioned how to evaluate dynamic properties of drugs in membranes.
FIG. 16 Solubility profiles of drugs in solvents with varying dielectric constant ". For curves (a) and (b), see the text.
NMR Studies on Lipid Bilayer Interfaces
803
The method introduced here can be widely applied to a variety of drugs, such as anesthetics and EDs. For example, most of the EDs have ring protons and are highly lipophilic. The NMR method developed here should make a significant contribution to elucidating the molecular mechanism of the ED delivery into the lipid bilayer as a primary step of the membrane disrupting action. The present method can be also powerful in monitoring the decomposition and the release of EDs accumulated in the membrane interior. For the purposes of detoxication and prevention of the ED accumulation, molecular-level research is now in progress in our group. The method utilizing 1D NMR is simple and convenient. Hence the NMR method discussed here can be applied to the systematic investigation of the membrane–drug interactions, closely related to the vital function in biomembranes. It is expected that the application can be extended to the lipid–peptide interaction and protein uptake. We are now applying the method to apolipoprotein binding with lipid bilayers and emulsions. Preferential protein binding sites in membranes can be specified by NMR on the molecular level. One of the most interesting subjects to be investigated is the effect of the phase transition behavior of membrane lipids on the partitioning of drugs in membranes. Lipid matrices of biomembranes are usually in the LC state. As described in our NMR phase transition study of DPPC bilayers [51,52] in Section II.D, the hydrocarbon chains of the lipid components are flexible. Hydrophobic interaction is still dominant in the chain region. Hydrophilic headgroups containing dipoles are essential to retain the bilayer structure. Headgroups, however, fluctuate considerably in the LC state. The information on the bilayer phase transition effect on DD is valuable because various portions of biomembranes are microscopically inhomogeneous; the gel-like structure locally appears for an instant, although the bilayers are macroscopically in the LC state. We are now studying the temperature dependence and phase transition effect on the delivery of DBCHþ and BPA from water to bilayers. Although the drug delivery to the lipid bilayer membrane is just the first step for bioactivities and phopholipid vesicles are rather simple in view of the composite structure of biomembranes, the unambiguous specification of the preferential location of the drug is essential; the successive processes of the action are expected to be induced via the delivery site in membranes. We expect more advances in the dynamic NMR study, so that we can get insight into the mechanism of DD in membranes.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
S. J. Singer and G. L. Nicolson. Science 175:720 (1972). D. P. Tieleman, S. J. Marrink, and H. J. C. Berendsen. Biochim. Biophys. Acta 1331:235 (1997). H. H. Meyer. Arch. Exp. Pathol. Pharmakol. 42:109 (1899). P. Preziosi. Pure Appl. Chem. 70:1617 (1998) and references cited therein. R. E. Jacobs and E. Oldfield. Prog. NMR Spectrosc. 14:113 (1981). J. Wittebort, C. F. Schmidt, and R. G. Griffin. Biochemistry 20:4223 (1981). J. Forbes, J. Bowers, X. Shan, L. Moran, E. Oldfield, and M. A. Moscarello. J. Chem. Soc. Faraday Trans. 1 84:3821 (1988). W. Wu and L.-M. Chi. Biochim. Biophys. Acta 1026:225 (1990). C. R. Sanders II, B. J. Hare, K. P. Howard, and J. H. Prestegard. Prog. NMR Spectrosc. 26:421 (1994).
804
Okamura and Nakahara
10. A. Watts. Biochim. Biophys. Acta 1376:297 (1998). 11. J. A. Urbina, B. Moreno, W. Arold, C. H. Taron, P. Orlean, and E. Oldfield. Biophys. J. 75:1372 (1998). 12. T. Brumm, K. Jorgensen, O. G. Mourtisen, and T. M. Bayerl. Biophys. J. 70:1373 (1996). 13. D. M. Small, in Plasma Lipoproteins and Coronary Artery Disease (R. A. Kreisberg and J. P. Segrest, eds.), Blackwell Scientific Publications, London, 1992, pp. 57–91. 14. M. J. Janiak, D. M. Small, and G. G. Shipley. Biochemistry 15:4575 (1976). 15. H. Hauser, I. Pascher, R. H. Pearson, and S. Sundell. Biochim. Biophys. Acta 650:21 (1981). 16. M. C. Wiener, R. M. Suter, and J. F. Nagle. Biophys. J. 55:315 (1989). 17. J. F. Nagle, R. Zhang, S. Tristrarn-Nagle, W. J. Sun, H. I. Petrache, and R. M. Suter. Biophys. J. 70:1419 (1996). 18. G. Bu¨ldt, H. U. Gally, A. Seelig, J. Seelig, and G. Zaccai. Nature 271:182 (1978). 19. B. P. Gaber and W. L. Peticolas. Biochim. Biophys. Acta 465:260 (1977). 20. H. L. Casal and H. H. Mantsch. Biochim. Biophys. Acta 779:381 (1984). 21. P. T. Wong, D. J. Siminovitch, and H. H. Mantsch. Biochim. Biophys. Acta 947:139 (1988). 22. M. T. Devlin and I. W. Levin. J. Raman Spectrosc. 21:441 (1990). 23. E. Okamura, J. Umemura, and T. Takenaka. Biochim. Biophys. Acta 1025:94 (1990). 24. E. Okamura, J. Umemura, and T. Takenaka. Vibrational Spectrosc. 2:95 (1991). 25. P. T. Wong. Biophys. J. 66:1505 (1994). 26. J. Seelig. Biochim. Biophys. Acta 515:105 (1978). 27. P. R. Allegrini, G. van Scharrenburg, G. H. de Haas, J. Seelig. Biochim. Biophys. Acta 731:448 (1983). 28. G. Lindblom, in Advances in Lipid Methodology (W. W. Christie, ed.), Oily Press, Dundee, UK, 1996, pp. 133–209. 29. D. Huster, K. Arnold, and K. Gawrisch. J. Phys. Chem. B 103:243 (1999). 30. Z. Zhou, B. G. Sayer, D. W. Hughes, R. E. Stark, and R. M. Epand. Biophys. J. 76:387 (1999). 31. M. Ge, D. E. Budil, and J. H. Freed. Biophys. J. 66:1515 (1994). 32. R. H. Crepeau, S. Saxena, S. Lee, B. Patyal, and J. H. Freed. Biophys. J. 66:1489 (1994). 33. D. Marsh and L. I. Horvath. Biochim. Biophys. Acta 1376:267 (1998). 34. M. Ameloot, H. Hendrickx, W. Herreman, H. Portel, F. van Cauwelaert, and W. van der Meer. Biophys. J. 46:525 (1984). 35. J. M. Sturtevant. Ann. Rev. Phys. Chem. 38:463 (1987). 36. M. Kodama, T. Miyata, and Y. Takaichi. Biochim. Biophys. Acta 1169:90 (1993). 37. C.-h. Huang and S. Li. Biochim. Biophys. Acta 1422:273 (1999). 38. D. A. Wilkinson and J. F. Nagle. Biochemistry 18:4244 (1979). 39. Y. Kita, L. J. Bennet, and K. W. Miller. Biochim. Biophys. Acta 647:130 (1981). 40. Y. Kita and K. W. Miller. Biochemistry 21:2840 (1982). 41. T. R. Stouch. Mol. Simul. 10:335 (1993). 42. K. Tu, J. Tobias, and M. L. Klein. Biophys. J. 69:2558 (1995). 43. K. Tu, J. Tobias, J. K. Blaise, and M. L. Klein. Biophys. J. 70:595 (1996). 44. W. Shinoda, N. Namiki, and S. Okazaki. J. Chem. Phys. 106:573 (1997). 45. C. J. Jameson. Ann. Rev. Phys. Chem. 47:135 (1996). 46. E. Okamura and M. Nakahara. J. Phys. Chem. B 103:3505 (1999). 47. E. Okamura, R. Kakitsubo, and M. Nakahara. Langmuir 15:8332 (1999). 48. E. Okamura, R. Kakitsubo, and M. Nakahara, to be published. 49. R. Koynova and M. Caffrey. Biochim. Biophys. Acta 1376:91 (1998). 50. S. Kaneshina, H. Matsuki, and H. Ichimori. Rev. High Pressure Sci. Technol. 9:213 (1999). 51. E. Okamura, Y. Tsujii, T. Miyamoto, and M. Nakahara, to be published. 52. E. Okamura, C. Wakai, N. Matubayasi, and M. Nakahara. Chem. Lett. 1997:1061 (1997). 53. H. Konishi, N. Matubayasi, and M. Nakahara, to be published. 54. J. A. Hamilton and D. M. Small. Proc. Natl. Acad. Sci. 78:6878 (1981). 55. P. J. Spooner and D. M. Small. Biochemistry 26:5820 (1987). 56. G. Lipari and A. Szabo. J. Am. Chem. Soc. 104:4546 (1982).
NMR Studies on Lipid Bilayer Interfaces 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83.
805
D. P. Bossev, M. Matsumoto, and M. Nakahara. J. Phys. Chem. B 103:8251 (1999). G. Lindblom and G. Ora¨dd. Prog. NMR Spectrosc. 26:483 (1994). M. Nakahara, C. Wakai, Y. Yoshimoto, and N. Matubayasi. J. Phys. Chem. 100:1345 (1996). D. Driscoll, S. Samarasinghe, S. Adamy, J. Jonas, and A. Jonas. Biochemistry 30:3322 (1991). X. Peng and J. Jonas. Biochemistry 31:6383 (1992). X. Peng, A. Jonas, and J. Jonas. Biophys. J. 68:1137 (1995). X. Peng, A. Jonas, and J. Jonas. Chem. Phys. Lipids 75:59 (1995). H. Hauser, S. A. Penkett, and D. Chapman. Biochim. Biophys. Acta 183:466 (1969). J. Cerbo´n. Biochim, Biophys. Acta 290:51 (1972). M. S. Ferna´ndez and J. Cerbo´n. Biochim. Biophys. Acta 298:8 (1973). Y. Boulanger, S. Schreier, L. C. Leitch, and I. C. P. Smith. Can. J. Biochem. 58:986 (1980). M. Auger, H. C. Jarrell, and I. C. P. Smith. Biochemistry 27:4660 (1988). M. Wakita, Y. Kuroda, Y. Fujiwara, and T. Nakagawa. Chem. Phys. Lipids 62:45 (1992). Y. Kuroda, M. Wakita, and T. Nakagawa. Chem. Pharm. Bull. 42:2418 (1994). Y. Kuroda, M. Ogawa, H. Nasu, M. Terashima, M. Kashara, Y. Kiyama, M. Wakita, Y. Fukiwara, N. Fujii, and T. Nakagawa. Biophys. J. 71:1191 (1996). P. L. Yeagle, W. C. Hutton, and R. Bruce Martin. Biochim. Biophys. Acta 465:173 (1977). J. Baber, J. F. Ellena, and D. S. Cafiso. Biochemistry 34:6533 (1995). C. North and D. S. Cafiso. Biophys. J. 72:1754 (1997). P. Tang, B. Yan, and Y. Xu. Biophys. J. 72:1676 (1997). Y. Xu and P. Tang. Biochim. Biophys. Acta 1323:154 (1997). Y. Xu, P. Tang, and S. Liachenko. Toxicol. Lett. 100–101:347 (1998). E. Okamura and M. Nakahara, unpublished results. C. Chipot, M. A. Wilson, and A. Pohorille. J. Phys. Chem. B. 101:782 (1997). K. Tu, M. Tarek, M. L. Klein, and D. Scharf. Biophys. J. 75:2123 (1998). P. Westh and C. Trandum. Prog. Anesth. Mech. 6:556 (2000). R. J. Abraham, J. Fisher, and P. Loftus, Introduction to NMR Spectroscopy, 2nd edn, John Wiley, Chichester, 1988, ch. 2. E. Okamura, R. Kakitsubo, and M. Nakahara, to be published.
33 Lipid Bilayers in Cells: Implications in Drug and Gene Delivery T. MARJUKKA SUHONEN, PEKKA SUHONEN, and ARTO URTTI Department of Pharmaceutics, University of Kuopio, Kuopio, Finland
I.
INTRODUCTION
Lipid bilayers have important structural and functional roles in the human physiology. The lipids for the bilayers are synthesized in the cells by the biosynthetic pathways and their synthesis is biochemically regulated. Basically the lipid bilayers and the membrane proteins constitute the membranes bordering the cells and the intracellular organelles. In general, the lipid bilayer is able to maintain the important gradients of ions and many other biochemicals across the membranes by preventing their free diffusion. Therefore, the lipid bilayers are a crucial part of the cell physiology. This role is based on the barrier properties of the lipids and on their ability to embed membrane proteins that have an active role in transport and signaling of the cells. These basic functions affect also the pharmcokinetic role of the lipid bilayers: they are the barriers limiting drug permeation and, conversely, the proteins in the membranes regulate the processes of active transport and efflux. Biomembranes act as selective barriers of drug permation and, therefore, they have a profound impact on pharmacokinetics and pharmcodynamics at several levels.
II.
ROLE OF CELLULAR MEMBRANES IN PHARMACOKINETICS
Targets of drug action are usually proteins, such as enzymes, transporters, and receptors [1]. For activity, drugs must be able to reach these targets. Most targets are cellular proteins that are located either in the membranes in the cell membrane or in the intracellular organelles. Even those drugs that are targeted to the cell surface receptors must be able to permeate through several lipid bilayers in the body, because they should get across the cellular barriers between different compartments of the body (e.g., the cellular barriers between blood circulation and tissues). Obviously, in the case of intracellular targets, such as nuclear receptors or intracellular viruses, the drug must diffuse through many lipid bilayer barriers. The simplest case of pharmacokinetics is intravenous injection [1]. In this case the drug is injected directly into the bloodstream. The drug may permeate to different tissues depending on its ability to get across the blood vessel walls and the cellular barriers in the particular tissue targets (Fig. 1). If the drug has small molecular weight and adequate 807
808
Suhonen et al.
FIG. 1 Schematic presentation of pharmacokinetics in the human body. The arrows indicate possible routes of drug adminsitration and the direction of the blood flow in the circulation.
lipophilicity it diffuses through the cellular barriers to tissues like the brain. Such drugs may be distributed to a large apparent volume in the body and they may be stored for a long time in the tissues. This leads to a long half-life of drug elimination. Intravenously injected drug is eliminated from the body usually by metabolism (predominantly in the liver) or excretion (mostly via kidney) [1,2] (Fig. 1). The ability of the drug to permeate through the cell membranes affects the metabolism and excretion processes. Metabolic enzymes in the liver are located in the cells (hepatocytes) and the drug must be able to pass through the cell membrane in order to reach the enzymes for the metabolic reaction. Renal excretion of drugs depends on two main processes: glomerular filtration and tubular reabsorption. Glomerular filteration is simple filtration with an approximate molecular size cutoff of 40,000 daltons: only smaller molecules are able to filtrate from blood to the urine [2]. After the filtration the drug may be reabsorbed into the blood through the lipid bilayers of the tubular cells in the kidney. Therefore, those drugs that are able to permeate across the membranes can be reabsorbed and their excretion is slower than that of the hydrophilic drugs. The reader should note that after injection there are many processes going on simultaneously: protein binding in plasma, distribution to various tissues, metabolism, and excretion. In such situations it is not easy to predict the impact of a single physicochemical parameter on the pharmacokinetics on the scale of the whole body. Most drug treatment is exercised by using extravascular routes of drug administration. In these cases, the drug is given to other sites than blood circulation (Fig. 1) [2]. Common examples are per oral, nasal, pulmonary, and transdermal routes of drug delivery. After extravascular administration, the drug must be absorbed into the blood circulation before it can distribute to the tissues. Different routes of drug administration have their own particular features that are out of the scope of this review (see Ref. 3). There are some generic determinants that affect drug absorption. For example, long retention of the drug at the site of absorption and a large membrane surface for drug absorption tend to
Lipid Bilayers in Cells
809
increase drug absorption. Those properties of the drug that favor the diffusion across the lipid bilayer naturally increase drug absorption. Those features of lipid bilayers and drugs are discussed in more detail later in this review. Lipid bilayers affect all phases of pharmacokinetics: absorption, distribution, metabolism, and excretion (Fig. 1). Cells may form monolayers or multilayered structures between the body compartments [4]. These structures, endothelia and epithelia, limit drug transport between macroscopic body compartments during drug absorption, distribution, and elimination. For example, the blood–brain barrier of the brain capillary vessel walls limits access of exogenous compounds to the brain [5]. Similarly, the blood retinal barrier (BRB) prevents the entry of harmful agents to the retina of the eye [6]. The physiological role of these barriers is to prevent the acess of harmful agents and to facilitate transport of nutrients and other vital compounds to the tissues. This protective role makes drug delivery more difficult. Important nutrients and other constituents are shuttled through the body by active transport mechanisms (Fig. 2). Active transport is based on membrane proteins, transporters, that have an extracellular domain (that is recognized by the ligand), a membrane spanning part, and an intracellular cytoplasmic domain [4]. For transport the drug should bind in specific manner to the transporter and, therefore, the drug must have a structural resemblance to the endogenous ligand of the transporter. There are carriers in the body for several amino acids, nucleosides, sugars, monocarboxylic acids, oligopeptides, and phosphates [7,8]. Efflux proteins are membrane proteins that affect the pharmocokinetics by effluxing drugs from the cytoplasm of the cell to the extracellular space (Fig. 2). These proteins include multiple drug resistance (MDR) gene products like P-glycoprotein [9]. They limit absorption and distribution of drugs for those compounds that are ligands to these fairly nonspecific proteins. New transporters and efflux proteins are found continuously in the Human Genome Project and it seems that they are much more important in the pharmacokinetics than was previously thought.
FIG. 2 Mechanisms of drug transfer in the cellular layers that line different compartments in the body. These mechanisms regulate drug absorption, distribution, and elimination. The figure illustrates these mechanisms in the intestinal wall. (1) Passive transcellular diffusion across the lipid bilayers, (2) paracellular passive diffusion, (3) efflux by P-glycoprotein, (4) metabolism during drug absorption, (5) active transport, and (6) transcytosis [251].
810
Suhonen et al.
Drugs may pass cellular membranes by passive diffusion along the thermodynamic electrochemical gradient. Drugs may diffuse either through or between the cells (Fig. 2). Paracellular diffusion (between the cells) is limited by the molecular size and the limited porosity (i.e., small surface area) of the intercellular space [4,10]. For drug discovery scientists the ideal drug should pass through the cells by transcellular passive diffusion. Drugs that are able to diffuse effectively through the lipid bilayers of the cells have usually adequate bioavailability and distribution in the body to reach their targets. Understanding drug permeation across the lipid bilayers is important because it may help to choose the best candidate molecules for further development. During recent years the rapid progress in combinatorial chemistry, automated synthesis, and high throughput screening of the drug candidates have shifted the bottleneck of the drug discovery process to the early pharmacokinetic screening. Since about 40% of the drug discovery projects fail for biopharmaceutical and pharmacokinetic reasons, the drug discovery field badly needs ways to predict permeation of new drug candidates across the lipid bilayers and, subsequently, to predict drug absorption. Understanding of the drug diffusion in lipid bilayers should augment the development of high throughput methods for early prediction of drug absorption. Another great challenge in modern drug discovery is related to the difficult delivery of biotechnological drugs, like peptides, proteins, and gene-based drugs (oligonucleotides, genes). Special delivery systems are needed in order to deliver these large and often hydrophilic compounds across the lipid bilayers. This review gives an overview of the structure of the lipid bilayers and their role in limiting drug delivery.
III.
PERMEATION OF SMALL MOLECULES ACROSS LIPID BILAYERS: ROLE OF BILAYER STRUCTURE
A.
Bilayer Lipids
Lipids may be defined as a large group of molecules with a substantial portion of aliphatic or aromatic hydrocarbon. Included are molecules with diverse chemical characteristics, such as the hydrocarbons, soaps, detergents, acylglycerols, steroids, phospholipids, sphingolipids, and fat-soluble vitamins, and, subsequently, with diverse physical behavior. One of the most important characteristics of lipids from a biological aspect is their behavior in aqueous environments, as all cells exist in an aqueous milieu. In this respect, the lipids range from almost total insolubility to nearly complete solubility. The hydrocarbon portion of the lipid molecule may be saturated [Fig. 3(A)] or unsaturated [Fig. 3(B),(C)]. The moelcules may be unsubstituted or substitution of an atom or chemical group, e.g., carboxylic acid or alcohol, for a hydrogen can occur anywhere along the hydrocarbon chain [Fig. 3(D)]. Several fatty acids are the building blocks of all complex lipids present in membrane lipids. In these compounds, they are esterified with alcohols (e.g., with glycerol), sphingosine, or cholesterol. Phospholipids, the main constituents of cellular membranes, have a glycerol backbone. A fatty acid is esterified to two of the hydroxyl groups and the third is esterified by a phosphate group and a nitrogenous compound (choline, ethanolamine, or serine) [Fig. 3(E)]. One family of phospholipids contains inositol, a six-carbon sugar-alcohol. Phospholipids isolated from natural sources vary in their fatty acids.
Lipid Bilayers in Cells
811
FIG. 3 Representative structures of lipid molecules.
In sphingolipids, an amino alcohol with a long side chain, sphingosine, is amide bonded to a fatty acid forming a ceramide, the precursor of the sphingolipids [Fig. 3 (F)]. Sphingophospholipids are found in large quantities in the brain and in nervous tissue. Sphingomyelin, the most important sphingolipid has a phosphocholine grouping attached to the terminal hydroxyl of the ceramide [Fig. 3(G)], whereas the glycolipids, cerebrosides, and gangliosides contain no phosphorus but have a sugar or a chain of sugars attached to this hydroxyl terminus [Fig. 3(H)]. Glycolipids are present in all tissues on the outer surface of the plasma membrane.
812
Suhonen et al.
Cholesterol, a polycyclic alcohol [Fig. 3(I)] is present in all animal tissues. It is a major constituent of cellular membranes, where it contributes to the fluidity of the membrane. The storage and transport forms of cholesterol are its esters with fatty acids.
B.
Phase Behavior of Membrane Lipids
All major lipids in membranes are amphipathic, i.e., they contain both hydrophilic (headgroups) and hydrophobic (acyl chains) regions. These molecules assume a variety of structures in aqueous dispersions depending on the shape of the molecule, i.e., the relative effective sizes of the polar headgroup and the acyl chain region (Fig. 4). The shape of a lipid molecule is an outcome of a variety of molecular forces [11] and, thus, the lipids organize themselves into a form that thermodynamically satisfies both ends of the molecule. Specific conditions are needed for bilayer formation as the nature of the phase depends on lipid species, lipid concentration, temperature, pH, and ionic strength [12]. In particular, the region of the hydrated headgroups needs to create an area large enough to accommodate the acyl chains. 1. Lipid Phases (a) Crystalline and Gel Phases. Lipids can exist in solid crystalline structures in a hydrated state at relatively low temperatures. These structures are densely packed stacked bilayers with their acyl chains either tail to tail or partially interdigitating at the bilayer center [13,14]. Due to differences in molecular shape there is a considerable variation in molecular packing patterns in the bilayer structures (Fig. 5). Crystalline phases pack into two distinct classes of subcells depending on chemical structure and environmental factors. The first class is characterized by specific chain–chain
FIG. 4 shape.
Schematic representation of various lipid phase structures influenced by lipid molecular
Lipid Bilayers in Cells
813
FIG. 5 Schematic representation of packing arrangements of natural amphipathic double-chain lipids with different headgroup size in crystalline bilayers. The small filled circles indicate the accommodation of spacer molecules, such as water or ions. (Reprinted by permission from Ref. 14, copyright 1992, Elsevier Science.)
interactions [15]. On a plane through the hydrocarbon chains perpendicular to their axes, two types of two-dimensional lattices may be found: rectangular or oblique (Fig. 6). With increasing temperature the hydrated lipid crystals revert into a more expanded gel phase [13]. In gel phases, the hydrocarbon chains remain in ordered bilayers, and essentially in the all-trans configuration. This second class of crystalline chain packing includes the hexagonal lattice and hexagonal or quasihexagonal subcells [13,15] (Fig. 6). The individual carbon atoms, however, are allowed to rotate a few degrees within the lattice as the chains lose some of their specific interactions. Both the volume per — CH2 — group and the area per hydrocarbon chain are greater than in tightly packed crystals [15]. At a pretransition temperature, the lipid headgroup mobility as well as interfacial area per molecule increase substantially and the membrane adopts a rippled appearance, in which it is transformed from a planar to an undulating surface with fairly long, regular periodicity [13,16]. (b) The Liquid Crystalline Phase. At the main ‘‘gel-to-liquid crystalline’’ transition temperature, Tm , there is a drastic increase in acyl chain mobility, and, subsequently, an abrupt increase in the area per hydrocarbon chain and the volume per — CH2 — group [15]. The transition temperature is influenced by the amount of water present, by the length of the acyl chains, and by the number of double bonds and other substituents [15]. Membrane lipids can exhibit many different liquid-crystalline phases (Fig. 7) consisting of aggregates with different shapes such as spheres, rods, or lamellae [11]. These units are geometrically arranged to form lamellar, hexagonal (of the normal or reversed type), or cubic phases. (c) Nonlamellar Phases. Some lipids prefer to pack in nonbilayer structures such as the inverted hexagonal HII (Fig. 4) or cubic phases. In addition to the rapid axial rotations of
FIG. 6 The three types of two-dimensional lattices of hydrocarbon chains.
814
Suhonen et al.
FIG. 7 Structures of various liquid-crystalline phases of membrane lipids. (A) Normal hexagonal phase (HI ); (B) lamellar phase; (C) inverted hexagonal phase ðHII ). Cubic phases consisting of (D) spherical, (E) rod-shaped, and (F) lamellar units. The hydrocarbon regions are shaded and the hydrophilic regions are white. (Reprinted by permission from Ref. 11, copyright 1984, Kluwer Academic Publishers.)
a phospholipid about its long axis exhibited by the bilayer structures, additional motional averaging occurs owing to the ability of the lipids to diffuse laterally around the cylinders with the polar headgroups pointing inwards, characteristic of the HII phase [17]. Whereas bilayers arrange in planar structures, inverted nonlamellar phases exhibit a curved morphology due to the larger cross-sectional area available for the acyl chains relative to the small headgroups [18]. In the HII phase and in the inverted micellar cubic phase, the water associated with the polar headgroups is trapped inside a ring structure and is not in rapid exchange with bulk water [18]. In a bicontinuous cubic phase, however, there is a continuous network of aqueous channels. An increase in temperature above the gel-to-liquid crystalline phase transition can cause a transition from lamellar liquid crystalline phase to an inverted cubic or an HII phase [19]. A higher population of gauche isomers (Fig. 8) is introduced into the hydrocarbon chains leading to more wedge-shaped molecules and reduced packing ability. Isothermally, a variety of factors may induce the transition to inverted nonlamellar phases. For a more thorough review the reader is referred to, e.g., Refs. 11, 20, and 21. Briefly, among glycerolipids, increased acyl chain unsaturation, especially cis-double
Lipid Bilayers in Cells
815
FIG. 8 Schematic representation of the ordering/disordering of acyl chains within a bilayer. Note the strong disordering effect of a gauche conformer.
bonds, increased acyl chain length, and reduction of the size of the headgroup are conditions which favor the HII phase and transition from a lamellar to an HII phase occurs at a lower temperature. The phase structure formed by ionic lipids can be affected by a change in pH of the surrounding water phase. A transition from a lamellar to an HII phase may take place due to reduction of the electrostatic repulsive forces between the headgroups, which in turn decreases the surface area occupied by the hydrocarbon–water interface. Cations such as Ca2þ , Mg2þ , and Mn2þ have been found to trigger a transition from a lamellar to an HII phase for the anionic lipids at a neutral pH. At neutral pH, the polar headgroups of these lipids are negatively charged. Introduction of the divalent cations neutralizes the negative charge leading to a reduction of surface area. Dehydration of the polar headgroups has a similar effect on the phase behavior of lipid molecules [22]. 2.
Polymorphism of Membrane Lipids
Although biomembranes contain a substantial amount of nonbilayer-forming lipids [23], the membrane is maintained as a bilayer. It has turned out that the amount and structure of these nonbilayer-forming lipids are precisely regulated [24,25], implying that the effects of the nonbilayer-forming lipids on the membrane are of biological importance [26]. Nonbilayer phase formation has been found to play an important role in membrane transport, fusion, and exo- and endocytosis [23,27,28]. In addition, the presence of peptides and proteins promotes the formation of nonbilayer phases [29,30], which may be needed to keep them in a functional state [18,31].
C.
Bilayer Lateral Structure and Lipid Domains
According to the Singer–Nicolson fluid-mosaic model of the structure of biological membranes [32] the lipids form a fluid bilayer in which the incorporated proteins as well as the lipids themselves are randomly distributed and free to diffuse laterally. To date, it is established that membranes are not laterally homogeneous but formation of domains with distinct lipid and protein composition is a major driving force in membrane organization [33,34]. There are recent data indicating that the membrane components tend to adopt regular distributions, superlattices, in fluid, mixed bilayers (for a recent review, see Ref. 35). The superlattices represent the energetically most favorable packing of the membrane components and they are in dynamic equilibrium with randomly arranged domains or with superlattices of different composition.
816
Suhonen et al.
Lipid mixtures may separate into distinct domains due to differences in their structures and phase behavior [12]. The domains sustained may be liquid–liquid, liquid–solid, or solid–solid in character. Lateral phase separation may be induced among charged lipid mixtures by the introduction of ions such as Ca2þ [12,36]. Charged lipids repel each other electrostatically, and thus they will be homogeneously distributed throughout the model membrane. The ions introduced would crosslink the headgroups and thereby induce clustering. Phase separation may also be encouraged by dehydration [37], by the addition of cholesterol (e.g., Ref. 38), or a solute such as alcohol [39] or by the insertion of proteins and peptides [40,41] (Fig. 9).
D.
Transverse Structure and Fluidity of Lipid Bilayers
As illustrated in Fig. 10 the lipid bilayer consists of several layers of chemically different microenvironments [42,43]. The perturbed water region protruded by lipid dipolar headgroups plays a crucial role in the interaction of the membrane with other membranes or with proteins. The total water density decreases sharply and the lipid density reaches its maximum in the hydrated headgroup interface region including the ester–ether linkages between the headgroups and upper parts of the acyl chains. Therefore, the diffusion coefficients of water and other small molecules are lowest in this region of the bilayer. The ordered acyl chain region is characterized by low free volume and is recognized as the main barrier to the permeation of small molecules. A region of relatively disordered acyl chain segments near the bilayer center occupies about one-half of the fluid bilayer thickness [44]. It is characterized by a low density and a high fraction of free volume, which allows for incorporation of larger molecules [42]. Due to its hydrophobicity this region favors the solution of hydrophobic molecules. The polarity of the lipid bilayer displays appreciable variation with position along the hydrocarbon chain and probably reflects the degree of water penetration into the bilayer [45,46]. The acyl chains form a hydrophobic core of the bilayer with a low polarity. Macroscopic approaches have yielded dielectric constant values of around 2–4 for this region, comparable to those found in alkanes [47]. The polar headgroup region, therefore, represents a region with a high gradient of polarity with measured dielectric constant values in the range 10–45, finally reaching a value of 80 at the bulk water region. The degree of molecular order obtained by NMR as a function of bilayer depth is relatively constant between carbons 1 and 9 and then falls significantly for positions deeper
FIG. 9 A scheme representing lateral phase separation for anionic lipids from zwitterionic lipids in a mixed lipid bilayer induced by the peptide antibiotic, polymyxin-B. (Reprinted by permission from Ref. 41, copyright 1998, Elsevier Science.)
Lipid Bilayers in Cells
817
FIG. 10 Top: The polarity profile of a microsomal lipid bilayer from calf liver as derived from spinlabel ESR experiments [45]. Center: A scheme representing the different regions in lipid bilayers. (Center: reprinted by permission from Ref. 88, copyright 1998, Springer-Verlag GmbH & Co. KG.) Bottom: Fourier synthesis of electron density distribution across a lecithin bilayer. The solid curve is the spectrum for the wet state; the dashed curve is that for the dry state. (Reprinted by permission from Ref. 252, copyright 1968, Macmillan Magazines Ltd.)
in the bilayer, reaching a minimum at the center [48,49]. Similar results have been obtained by moelcular dynamics calculations [50]. The value at the minimum is about threefold smaller than the value at the surface of the bilayer. The trend parallels increased mobility of the acyl chains towards the interior of the bilayer (Fig. 11) [12]. A decrease in the motional order, i.e., an increase in fluidity of the acyl chains, may be taken to correspond to an increase in the conformational freedom, i.e., the rate and extent of acyl chain
818
Suhonen et al.
FIG. 11 Order parameter variation along acyl chains in red cell ghosts (&), small unilamellar vesicles of egg phosphatidylcholine (r), and paraffin oil (þ), as determined by the fluorescence anisotropy decay of the n-anthroyloxy fatty acid probes. (Reprinted by permission from Ref. 12.)
excursion away from some initial chain orientation [51]. This is often associated with an increase in trans–gauche isomerization by individual lipid molecules and an increase in ‘‘kink’’ concentration representing mobile, small free volumes in the hydrocarbon phase of the membrane [52]. Major determinants of membrane fluidity may be grouped within two categories [53]: (1) intrinsic determinants, i.e., those quantifying the membrane composition and phase behavior, and (2) extrinsic determinants, i.e., environmental factors (Table 1). In general, any manipulation that induces an increase in the molal volume of the lipids, e.g., increase in temperature or increase in the fraction of unsaturated acyl chains, will lead to an increase in membrane fluidity. In addition, several intrinsic and extrinsic factors presented in Table 1 determine the temperature at which the lipid molecules undergo a transition from the gel state to liquid crystalline state, a transition associated with a large increase in bilayer fluidity. Biological membranes often exhibit asymmetry in the fluidity of apical and basolateral membranes (for a review, see Ref. 53). There are also differences in the fluidity of cell types of different origin [54,55]. Both of these phenomena may be associated with variations in the cholesterol content of the membranes, as cholesterol has been recognized to fluidize gel phase liquids and to cause an ordering effect on the liquid-crystalline phase lipids [56]. Moreover, the fluidity state of the plasma membranes is dependent on physiological [53,57–59] and pathological [53,60–62] conditions. The addition of exogenous compounds such as drugs or solvents also alters the fluidity of biological [63–72] and artificial [67,68,72–76] membranes. Alterations in cell membrane fluidity in turn are associated with marked changes in various transport systems, such as Naþ , Kþ -ATPase, Nadependent glucose transport, and Na-dependent phosphate transport, due to the sensitivity of proteins to their lipidic environment [53].
Lipid Bilayers in Cells TABLE 1
819
Major Determinants of Membrane Fluidity [53] Extrinsic
Parameter Temperature Pressure Cell volume Cations (divalent) [Hþ ] a b
Intrinsic
Effect on fluiditya " # " #b #b
Parameter Cholesterol Sphingomyelin Protein/lipid Satur./unsatur. Chain length
Effect on fluiditya # # # # #
The arrows indicate the effect of increase in the corresponding parameter on fluidity. Depends on membrane phospholipid composition (headgroups negatively charged).
E.
Molecular Dynamics of Bilayer Lipids
Lipid membranes may be depicted as structured fluids forming highly dynamic systems [77]. The various molecular motions of phospholipids organized in a bilayer structure depend strongly on temperature and are likely to be restricted by the amphiphilic nature of the molecules with the polar headgroups being anchored at the aqueous interface. Above the gel-to-liquid crystalline phase transition temperature the lipid hydrocarbon chains undergo rapid rotational motion about their long axis [16]. The rotational diffusion coefficient at the terminal end of the acyl chains is similar to that in n-alkanes, but at the center of the chain, the movement is significantly more restricted [78]. In addition to internal rotations, lipid molecules undergo two kinds of translational movements: (1) lateral diffusion, or the exchange of molecules that lie next to each other in a single leaflet of a bilayer; and (2) flip-flop, or movement of molecules from one bilayer leaflet to another involving the polar moiety passing through the hydrophobic region of the bilayer (Fig. 12). Lateral diffusion rates of phospholipids in bilayers are dependent on the physical state of the bilayer and are much more rapid in the liquid crystalline phase than for those in the gel state. The transbilayer movement rates of different phospholipids in bilayers vary over a considerable range. Generally, the rates show a maximum in the temperature range at which the gel-to-liquid crystalline phase transition occurs. Transversely, mammalian biomembranes exhibit a general pattern for preferential localization of choline-containing phospholipids [such as phosphatidylcholine (PC) and
FIG. 12 Different types of motions of lipid molecules in bilayers. (Reprinted by permission from Ref. 78, copyright 1986, Kluwer Academic Publishers.)
820
Suhonen et al.
sphingomyelin (SM)] and aminophospholipids [such as phosphatidylserine (PS) and phosphatidylethanolamine (PE)] in an outer and inner membrane bilayer leaflet, respectively (see Ref. 79 for a review). In addition, cholesterol content displays asymmetry between the two leaflets of the bilayer in biomembranes [53,80]. In model membranes, generally, lipids with larger headgroup area are expected to distribute preferentially into the outer monolayer in mixed lipid vesicles with small radius curvature [11]. Hydrogen bonding may play a role in transbilayer lipid distribution as it has been found that interactive lipids such as PS and PE are preferentially localized in the inner leaflet of the bilayer in model membranes of small unilamellar vesicles (SUV) in mixtures with PC [81]. The preference of PS and PE for the inner monolayer decreases as the pH is raised indicating the requirement for an interactive charged state rather than a repulsively charged state. In large unilamellar vesicles (LUVs), transbilayer asymmetry of certain ionizable lipids, such as phosphatidylglycerol (PG) and phosphatidic acid (PA), can be induced due to transmembrane pH gradients [82].
F. Transport Across Lipid Bilayers Substances pass through membranes primarily by passive diffusion. In addition, in biological membranes, substances may penetrate through specific transport mechanisms. The basic flux across the membranes may be related to that across a thin film [83]. Fick’s First Law of Diffusion indicates that the total flux of diffusant across a homogeneous membrane, J, is proportional to the concentration gradient of the diffusant: J ¼ Aj ¼ AD
dC dx
ð1Þ
where A is the area across which diffusion occurs, j is the flux per unit area, D is the diffusion coefficient of the diffusant, C is the diffusant concentration, and x is the distance perpendicular to the surface of the membrane. Fick’s Second Law relates the change in diffusant concentration with time, dC=dt, to the change in concentration gradient at a given point in the membrane: dC d 2C ¼D 2 dt dx
ð2Þ
At a steady state, the change in concentration gradient with time at a given point in the membrane equals zero. In a typical experimental situation a membrane is used between two compartments, one containing a drug solution (‘‘donor’’ compartment) and the other sink conditions (i.e., zero concentration; ‘‘receiver’’ compartment). For a homogeneous barrier membrane of thickness h, Fick’s First Law may be written as j¼
dQ DðC1 C2 Þ ¼ dt h
ð3Þ
where Q is the diffusant amount, and C1 and C2 are the diffusant concentrations on the donor and receiver sides of the membrane, respectively. Because exact measurements of C1 and C2 may be difficult, the partition coefficient, Km , relates C1 and C2 to Cd and Cr , the measurable concentrations in the donor and receiver compartments adjacent to the barrier membrane, respectively. Thus, the flux of diffusant per unit area is related to the partition coefficient, the concentration difference, and the membrane thickness:
Lipid Bilayers in Cells
j¼
DKm ðCd Cr Þ h
821
ð4Þ
In most experimental situations, it is practical to determine the permeability coefficient, P, according to P¼
DKm h
ð5Þ
which may be substituted into Eq. (4) to give j ¼ PC
ð6Þ
Thus, the rate of change for the cumulative mass of diffusant passing through a membrane per unit area, or the flux of diffusant, j, may be evaluated from the steady-state portion of the permeation profile of a drug, as shown in Eq. (3). If the donor concentration and the steady-state flux of diffusant are known, the permeability coefficient may be determined. Several models have been proposed for the molecular mechanism of transport of substances across phospholipid membranes, as reviewed by Jin and Hopfinger [84]. The most commonly employed model for describing the passive transport of permeants across lipid membranes is the solubility–diffusion model, which relates a given solute’s permeability coefficient to its ability to partition into and diffuse across the lipoidal membrane interior [85]. The permeation process is described in three steps: (1) the molecule dissolving into the membrane; (2) the molecule diffusing through the membrane interior; and (3) the molecule dissolving into the surrounding environment again. The solubility–diffusion theory assumes that solute partitioning from water into and diffusion through the membrane lipid region resembles that which would occur within a homogeneous bulk solvent. Thus, the permeability coefficient, P, can be expressed as P¼
Dhc Khc=w hhc
ð7Þ
where Khc=w is the partition coefficient of the permeant between water and a bulk organic solvent (e.g., a liquid hydrocarbon), hhc is the thickness of the hydrocarbon interior, and Dhc is the diffusion coefficient of the permeant within the membrane, which is approximated by the diffusion coefficient of the permeant in a bulk hydrocarbon solvent [85]. The solubility–diffusion theory, however, is highly oversimplified, as it fails to take into account the complex properties of real bilayers and biomembranes. Solute permeation in lipid bilayers shows a much steeper dependence on permeant size than on diffusion in bulk solvents [86], and diffusion coefficients calculated from permeability coefficients are orders of magnitude smaller than those obtained in bulk solvents. Recently, chain ordering has been shown to be a major determinant of molecular transport across liquid-crystalline bilayers [87]. Further, changes in bilayer phase structure has been found to alter the location and hydrophobicity of the transport barrier domain and, e.g., the transition from the gel phase to liquid-crystalline phase shifts the barrier domain deeper within the ordered chain region [88,89]. A scaling factor, the permeability decrement f , has been introduced to account for the decrease in permeability coefficient from that predicted by solubility–diffusion theory owing to chain ordering in lipid bilayers [90]: Pm ¼
Dbarrier Kbarrier=water ¼ fP hbarrier
ð8Þ
where Kbarrier=water is the partition coefficient of the permeant between water and the barrier domain; dbarrier is the barrier thickness, and Dbarrier is the diffusion coefficient of
822
Suhonen et al.
the permeant within the barrier domain. It was found that the lipid bilayer permeability can be predicted from the chain-packing properties in the bilayer through a dependence of f on bilayer free-surface area [90]. As discussed above, lipid membranes are dynamic structures with heterogeneous structure involving different lipid domains. The coexistence of different kinds of domains implies that boundaries must exist. The appearance of leaky interfacial regions, or defects, has been suggested to play a role in abrupt changes in solute permeabilities in the twophase coexistence regions [91,92]. Studies of the effect of permeant’s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. ‘‘Kinks’’ may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational ‘‘kink’’ ðg tg Þ isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks.
IV.
PERMEATION OF SMALL MOLECULES ACROSS LIPID BILAYERS: ROLE OF PERMEANT STRUCTURE
A.
Partitioning in Membranes
The lipophilicity of a solute affects its permeability in lipid bilayers. Lipophilicity is usually expressed in terms of its partitioning between water and an organic solvent, such as olive oil [95], oleyl alcohol [96], ether [97], or octanol [98]. Partition coefficient (PC) of a compound is expressed as its concentration ratio between organic medium and water at equilibrium: PC ¼ Coctanol =Cwater
ð9Þ
The partition coefficient is a measure of the relative secondary interactions between the solute and each liquid. Partitioning into bilayers is more complicated than homogeneous systems due to the heterogeneity of the lipid bilayers. For this reason the distribution of solutes in the bilayer is not homogeneous [99]. According to the theory of Marqusee and Dill the solutes of differing hydrophilicities will preferentially partition into different bilayer regions [100]. Thus, different solutes may reside in different areas of the bilayer, depending on the nature of the solute. For example, partitioning into bilayers is more selective to branched solutes than partitioning into bulk hydrocarbons. Presumably, this is due to the parallel arrangement of the acyl chains [99]. B.
Methods to Evaluate Solute Partitioning
The log octanol–water partition coefficient ðlog Po=w Þ probably is the most frequently used physicochemical parameter in medicinal chemistry [101–104]. Octanol, with a polar head and a flexible, nonpolar tail, has hydrogen-bonding capabilities and amphilicity similar to
Lipid Bilayers in Cells
823
those of the phospholipids in biological membranes. Therefore, it is used as a predictor for drug partitioning to the lipid bilayers [101]. Despite some good correlations with in vivo pharmacokinetics [105], log Po=w seems to have only a limited performance in predicting brain–blood concentrations (log BB) [106– 109] or oral drug absorption [110]. The octanol–water system still has no serious rival, but alternative partition systems that might give a better description have been suggested and investigated. Notable attempts include the use of cyclohexane–water [111–113] or the use of log P between octanol–water and cyclohexane–water [109,114,115]. In cellular membranes, the principal diffusion barrier consists of the lipid bilayer, a highly anisotropic system, which can be divided into distinct regions such as the polar headgroup–water interface region, and the nonpolar hydrocarbon region (Fig. 10). Deuterium nuclear magnetic resonance (2 H-NMR) [48,116] and neutron diffraction measurements [117] have shown that the order of the hydrocarbon chains is relatively high in the region near the lipid–water interface and decreases strongly towards the bilayer center (Fig. 10). These results show that a bilayer cannot be properly mimicked by an isotropic hydrocarbon phase. Indeed, molecular dynamics simulations show that the rate of diffusion differs considerably even in the membrane hydrocarbon region, being slow in the region of high order and fast in the more disordered central part [118]. Despite the well-established anisotropy of lipid bilayers, the vast majority of investigators still rely on the measurement of partition coefficients between an organic solvent (e.g., octanol, hexane, or cyclohexane) and water to assess the ability of a drug to diffuse through the BBB. Interesting modifications of this approach are HPLC methods where alkyl chains (e.g., C-18) [119], or carboxyacyl phosphocholine chains [120,121] are covalently attached to silica. These systems show a limited anisotropy. However, the packing density is still dictated by the chemistry of the covalent linkage to silica and is distinctly lower than the lipid packing density of natural membrane [122] or a bilayer model membrane [123]. It is therefore not surprising that octanol–water partition coefficients or lipophilicity parameters obtained from reversed-phase HPLC measurements do not correlate satisfactorily with the ability of a drug to diffuse through a lipid membrane. C.
Membrane Barrier to Solutes
One of the major issues in developing structure–activity relationships for various biological processes and in designing effective drugs and drug delivery systems is the determination of the locations and physicochemical nature of barrier domains in biological membranes for the transport of various molecular agents. Even in the absence of membrane proteins, uncertainty as to the location of the barrier domain arises due to the heterogeneity of transbilayer atomic distributions, reflecting a hydrated headgroup interface, the ester–ether linkages between the headgroups and acyl chains, an ordered acyl chain region, and a region of relatively disordered acyl chains near the bilayer center (Fig. 10). This heterogeneity is known to underlie the bell-shaped polarity profile within a bilayer interior as demonstrated in Fig. 10 [45,46]. In the absence of chain ordering effects, the least polar region would impose the highest energetic barrier to the transport of polar permeants. However, chain ordering in bilayers imposes an additional diffusional resistance and an entropic barrier to partitioning, respectively [100,118,124] such that the actual location of the transport barrier domain is determined by the balance of these factors. The degree of success achieved using Hansch parameters, obtained from octanol–water partition coefficients [125], in correlating transport processes in biological membranes support Overton’s suggestion that solute permeability across biological membranes
824
Suhonen et al.
correlates with corresponding bulk oil–water partition coefficient [126]. However, membranes with different lipid compositions display different chemical selectivity to solute transport. Functional group contributions have shown that the barrier domain for transport across human stratum corneum of the skin (the barrier properties of which are generally attributed to the multiple lamellae of lipid bilayer membranes localized within its intercellular spaces) closely resembles octanol in its selectivity to permeant structure [127,128]. In addition, correlations between octanol–water partition coefficients and transport of solutes across the blood–brain barrier have been established [129,130]. On the other hand, the studies on egg lecithin bilayers have demonstrated a chemical selectivity for this membrane more closely resembling that expected if the barrier domain were hydrocarbon like, with negligible hydrogen-bonding capacity [131,132]. Many natural membranes exist in a highly ordered state either through changes in phase structure or through intercalation of various ordering agents such as cholesterol and sphingomyelin [133]. For example, some natural plasma membranes contain up to 50% mole fraction of cholesterol. Increases in bilayer chain ordering are known to systematically decrease solute permeabilities [87,90]. Some evidence also suggests that the carbonyl dipoles present in most phospholipids have an important effect on polarity within the bilayer interior [134]. However, the effect of the mode(s) of linkage of the hydrocarbon chains to the glycerol moiety in phospholipid on barrier properties has not yet been indicated. Although the linkage is through an ester bond in most phospholipids of biological interest, ether bonded lipids exist in mammalian membranes and other biological membranes and the functional potency of certain lipids is attributed to this ether linkage [135]. Thus, a comparative study of the effects of ester and ether linkages on the chemical selectivity of the barrier domain in phospholipid bilayers would shed light on changes of local polarity as a result of these linkage alterations.
D.
Physicochemical Factors Affecting Structure-Permeability Relationships
The primary physicochemical properties of a drug influencing its passive absorption across biological membranes are its partition coefficient (PC), extent of ionization, molecular weight, and hydrogen bonding by the drug molecule. The passive transport rates of small molecules across biological membranes are often explained, at least qualitatively, by means of a bulk-phase solubility diffusion model [85,136–138]. This model may be traced to the formulation of Overton’s rules [126]. In general, membrane permeability for a solute increases with increasing partition coefficient, but two exceptions have been found. Highly branched compounds penetrate the membrane more slowly and small polar molecules penetrate the membrane more readily than expected [139,140]. The latter observation resulted in the development of the lipid-sieve membrane concept whereby one envisions aqueous ‘‘pores’’ in the membrane surface. Wright and Diamond postulate that these small, polar, relatively lipid-insoluble compounds penetrate the membrane by following a route lined by the polar groupings of membrane constituents [139,140]. The evaluation of this route would be limited primarily by the molecular size of the compound as a result of steric hindrance. Branched compounds must disrupt the local lipid structure of the membrane and they encounter greater steric hindrance than straight-chain molecules. 1. The Size of the Solute and the Degree of Lipid Chain Packing in Membranes It is well known that the permeabilities across biological membranes and model lipid bilayers strongly depend on both the degree of lipid chain packing in the membranes
Lipid Bilayers in Cells
825
[87,90,141,142] and on the size of the permeating solute [131,143]. The influence of lipid chain packing on permeability is most clearly demonstrated by the dramatic increase in transmembrane transport rates that appears because of a gel-to-liquid crystalline phase transition [90,144,145]. Membranes that are more ‘‘ordered’’ as a result of polar headgroup composition, or because of increased cholesterol concentrations or lower temperatures, or monolayers under high lateral pressures have greater resistances to permeation than predicted from a bulk solubility diffusion model, often by orders of magnitude [85,146–152]. A steep size selectivity is exhibited by both biological membranes and lipid bilayers by several groups [86,93,128,143,153]. These phenomena cannot be explained by bulk solubility diffusion theory. It has been common to interpret both the effects of chain ordering on permeability [142] and the steep dependence of permeation rates on permeant size [154,155] only in terms of changes in solute diffusivity within membranes. However, large size effects on solute partitioning into interphases are evident from the high resolution attainable on chromatographic separations on the basis of subtle differences in size and shape [156]. Kirjavainen et al. studied the effects of phospholipids on drug partitioning and on fluidity of skin lipid bilayers using steady-state fluorescence anisotropy [157]. They concluded that the increased distribution of drugs into the stratum corneum lipid liposomes (SCLL) was at least partially due to the increased fluidity of SCLL bilayers by phospholipids. Also permeation enhancers may interrupt the rate-limiting lipid domains of the bilayers causing increased permeant diffusivity in this region. Yoneto et al. investigated the influence of the 1-alkyl-2-pyrrolidones (APs) on permeant partitioning into hairless mouse stratum corneum (SC) under isoenhancement concentration conditions using -estradiol (E2 ) as the model permeant [158]. They suggested that inducing a higher partitioning tendency for E2 into the lipoidal pathway of hairless mouse SC is a principal mechanism of action of the APs in enhancing transdermal transport. It has been investigated both theoretically [100] and experimentally [87,159] that increasing chain ordering within lipid bilayers substantially decreases solute partitioning into bilayers. These effects are particularly evident in the more ordered regions of the bilayer, which were confirmed by neutron diffraction experiments [160] and molecular dynamics simulations [42,161]. Further studies in these laboratories suggest that the size selectivity in partitioning is amplified with increases in bilayer chain ordering. The structure–transport relationships developed solely on the basis of lipophilicity or hydrogenbonding potential without consideration of molecular size effects and the influence of bilayer composition (i.e., chain ordering) on these size effects may be misleading. Walter and Gutknecht report that literature data for the incremental free energy changes accompanying the addition of a methylene group to various homologous series of permeants derived from transport studies across a variety of model bilayer and biological membranes were highly variable, ranging from nearly zero up to 900 cal/mol [162]. In addition to the inappropriate treatment of unstirred layer effects in some of these studies pointed out by Walter and Gutknecht, the differences in membrane composition and complexity in terms of lipid chain packing (e.g., gel and liquid-crystalline phases) may also have contributed to the variability in the effects of permeant chain length on permeability. The difficulties in investigating the influence of permeant size on permeability arise from the fact that changes in permeant size are usually accompanied by changes in lipophilicity, with the latter effects often overshadowing the effects of permeant size alone. Xiang and Anderson studied the effects of lipid chain packing and permeant size and shape on permeability across lipid bilayers [163]. They carried out the experiments in gel
826
Suhonen et al.
and liquid-crystalline dipalmitoylphosphatidylcholine (DPPC) bilayers by a combined NMR line-broadening–dynamic light scattering method using short-chain monocarboxylic acids as permeants. They investigated simultaneously the effects of permeant size on permeability in bilayers varying the packing density, which enabled them to establish a model, which combines the effects of bilayer chain packing and permeant size on permeability across lipid bilayer membranes. Previous studies have shown that because of the ordering of lipid molecules in bilayer membranes, solute molecules residing in the bilayer interior are oriented with their long axes preferentially along the bilayer normal (Fig. 13) [164–166]. Theoretically, this alignment minimizes the work required to create a cavity to accommodate the solute molecule in the lipid bilayer. Thus, the resistance to the transbilayer movement of a solute in the bilayer interior due to the partitioning term may depend primarily on the cross-sectional area along the long axis of the solute [163]. A statistical mechanical theory developed by Xiang and Anderson also suggests that solute partitioning into the barrier region of lipid bilayers is disfavored by chain ordering and that the selectivity of the barrier domain for permeant size is amplified with an increase in surface density (i.e., a decrease in free surface area) (Fig. 13) [164]. These results have been confirmed by molecular dynamics simulations, which have demonstrated a strong size dependence for solute partition coefficients in the order chain region in lipid bilayers and that the size dependence is amplified at high surface densities [167,168]. 2. Influence of pH Gradients on the Transbilayer Transport of Drugs Most drug molecules are either weak acids or bases which are ionized to an extent determined by the pKa of the compound and the pH of the biological fluid in which it is dissolved. Because biological membranes are predominantly lipophilic, drugs penetrate these membranes mainly in their undissociated form. Brodie and Hogben were the first researchers who applied this principle, the pH-partition hypothesis [169]. The pH-partition principle has been tested in a large number of in vitro and in vivo experiments, but it is only partly applicable in real biological membranes [170]. In many cases, the nonionized form as well as the ionized form partitions into the membranes, and the drug is substan-
FIG. 13 A schematic illustration of the effects of the free surface area of lipid bilayer membranes on the permeation of two permeants with the same molecular volume, but different cross-sectional areas. (a) A lower free surface area. (b) A higher free surface area.
Lipid Bilayers in Cells
827
tially transported across lipophilic membranes. For example, the in vitro permeability coefficient for the ionized form of sulfathiazole may actually exceed that for the nonionized form of the drug. Permeation of the neutral form leads to large transmembrane concentration gradients of certain weak bases or weak acids when transmembrane pH gradients are present, which led to their use to assay pH gradients in cells or organelles [171,172]. These observations for cells and organelles were extended to model membrane liposomal systems [173]. Utilizing the quenching of a fluorescence probe, Deamer et al. demonstrated that gradients of 2–4 pH units (interior acidic) could be established and measured in small unilamellar vesicle (SUV) systems. They extended these results to demonstrate uptake of weak catecholamine bases into liposomes in response to pH gradient [174]. Let us consider uptake of a weak base containing a single amine into an LUV with an acidic interior. [A]o ([AHþ ]o ) and [A]i ([AHþ ]i ) refer to the concentrations of the neutral (protonated) form(s) of the amine on the outside and inside of the vesicle, respectively. Then the total external and internal concentrations of the amine can be written as þ ½Atot i ¼ ½Ai þ ½AH i
ð10Þ
þ ½Atot o ¼ ½Ao þ ½AH o
ð11Þ
We consider the case where the weak base is initially introduced in the external aqueous medium containing the LUVs with an acidic interior (Fig. 14). Assuming that the neutral base is the only membrane permeable form, the rate of uptake of the weak base into the LUVs is given by d½Atot d½Ao o ¼ dt dt
ð12Þ
FIG. 14 A model for the uptake of weakly basic compounds into lipid bilayer membrane (inside acidic) in response to the pH difference. For compounds with appropriate pKa values, a neutral outside pH results in a mixture of both the protonated form AHþ (membrane impermeable) and unprotonated form A (membrane permeable) of the compound. The unprotonated form diffuse across the membrane until the inside and outside concentrations are equal. Inside the membrane an acidic interior results in protonation of the neutral unprotonated form, thereby driving continued uptake of the compound. Depending on the quantity of the outside weak base and the buffering capacity of the inside compartment, essentially complete uptake can usually be accomplished. The ratio between inside and outside concentrations of the weakly basic compound at equilibrum should equal the residual pH gradient.
828
Suhonen et al.
N(A) is the number of molecules of the neutral form of the external weak base, PC is the permeability coefficient of the neutral form, Am is the surface of the membrane, and Vo is the external aqueous volume. Then, dNðAÞ ¼ ðPCÞAm ð½Ao ½Ai Þ dt
ð13Þ
The same approach derived for weak bases can also be applied to the uptake of simple weak acids, and to the transbilayer transport of acidic lipids, such as fatty acids and some phospholipids. We consider uptake of a simple weak acid into an LUV with basic interior. Let [AH]o ([A ]o ) and [AH]i ([A ]i ) refer to the concentrations of the neutral (ionized) form(s) of the weak acid on the outside and inside of the vesicle, respectively. Then, the total external and internal concentrations of the weak acid can be written as ½Atot o ¼ ½A o þ ½AHo
ð14Þ
½Atot i ¼ ½A i þ ½AHi
ð15Þ
We consider the case where the weak acid is initially introduced in the external aqueous medium containing the LUVs with a basic interior. Assuming that the neutral (protonated) acid is the only membrane permeable form, the rate of uptake of the weak acid into LUVs is given by d½Atot PAm ½Hþ o tot o ¼ ½Atot o ¼ k½Ao dt Vo Ka
ð16Þ
where Ka ð¼ A o ½Hþ o =½AHo Þ is the dissociation constant of the weak acid, and k ¼ ðPAm ½Hþ o =Vo Ka Þ is the rate constant associated with uptake. We consider only the case where the aqueous interior of the LUV is sufficiently well-buffered that the accumulated weak acid does not significantly change the interior pH. Then, the uptake will continue until the internal and external concentrations of the neutral form of the weak acid are equal, i.e., until ½AHi ¼ ½AHo . As Ka (inside) ¼ Ka (outside) it follows that ½Hþ o =½Hþ i ¼ ½A i =½A o
ð17Þ
Thus, at equilibrium, the transbilayer concentration gradient of the weak acid reflects the inverse of the transbilayer concentration gradient of protons (Fig. 14). For example, a pH difference of 2 units (e.g., internal pH ¼ 9 and external pH ¼ 7) shoud lead to 100-fold higher concentration of weak acid within the vesicle as compared to the external concentration. Many biological membranes exhibit transmembrane pH gradients of 2–3 units. Biological compounds, which are weak bases, such as biogenic amines, are strong candidates for transmembrane accumulation in response to a pH gradient. Although the uptake of biogenic amines such as dopamine into secretory vesicles is usually thought to involve specific transport proteins [175], pH gradients (acidic interior) exist between these membranes [176,177]. It has been shown that dopamine and catecholamines can be accumulated within LUVs exhibiting such a pH gradient [174]. Thus, at least portion of the uptake into the secretory vesicles would be expected to be protein-independent. One interesting example of the potential importance of intracellular pH gradients is found in the phenomenon of multidrug resistance (MDR). The MDR protein acts as a molecular pump, actively pumping chemotherapeutic agents out of the cell. Tumor cells, which are susceptible to chemotherapeutics have often a lower intracellular pH [178], which would lead to enhanced accumulation of these drugs in response to the pH differ-
Lipid Bilayers in Cells
829
ence. In contrast, the intracellular pH of resistant cells is significantly higher than that of nonresistant cells [179,180], giving rise to a reduced pH difference, which would lead to reduced intracellular accumulation of drugs. Thus, it is possible that the proteins responsible for MDR exert at least some of their effect by altering intracellular pH, which then reduces the drug uptake by pH difference. Roepe observed a near-linear relationship between the intracellular pH and the efflux of doxorubicin in human myeloma cells [179]. In addition, studies involving systematic alteration in tumor cell intracellular pH reveal that acidification of the intracellular pH results in fast accumulation of drug, whereas shifts to alkaline pH result in drug efflux [178]. Another important role of transbilayer pH gradients is in the area of membrane lipid asymmetry. Simple lipids such as fatty acids can sequestered to the inner layer of LUVs in response to the pH difference (inside basic) [181], which suggests that fatty acids will be preferentially located in the cytoplasmic monolayer of organelles such as the endoplasmic reticulum, which has an acidic interior [182,183]. The pH-dependent fatty acid transbilayer asymmetry has been observed in adipocytes, where increasing the internal pH leads to accumulation of fatty acids in a manner consistent with passive diffusion of the neutral form [184], which is in good agreement with results using model systems [181]. Similar considerations also apply to other acidic lipids, such as phosphatidic acid (PA) and phosphatidylglycerol (PG), which will also preferentially locate in the monolayer experiencing the highest pH. Alternatively, lipids with amino groups such as sphingosine would be expected to locate in monolayers facing acidic environments. This pH-difference-dependent regulation of transbilayer distributions of lipids could regulate bioavailability and hence modulate metabolic processes. Transmembrane pH gradients cannot account for lipid asymmetry such as observed in erythrocyte membrane, where phosphatidylserine (PS) and phosphatidylethanolamine (PE) are concentrated in the inner leaflet, while phosphatidylcholine (PC) and sphingomyeline (SPM) are localized on the external leaflet [185], as the neutral form of these lipids is associated with a zwitterionic headgroup resulting in low membrane permeability. There is strong evidence that asymmetrical transbilayer distributions of PE and PS are maintained by an ATP- and Mg2þ -dependent aminophospholipid translocase [79,186]. In summary, pH gradients can play a significant role in the transbilayer transport of a wide variety of weak bases and weak acids of biological interest. This has led to a variety of applications, ranging from drug loading of liposomes for drug delivery to the use of LUVs containing electron dense ions as potential contrast-agents in imaging protocols. Studies on lipid asymmetry induced by pH gradients have led to new insights on regulation of such fundamental processes as membrane fusion and factors, which regulate membrane morphology. In addition, pH gradients across organelle membranes may be expected to strongly influence the intracellular distribution and bioavailability of drugs and certain biological compounds. E.
Alternative Methods to Evaluate Drug Absorption
Using molecular mechanics calculations to assess the three-dimensional shape of a molecule, various surface properties such as polarity and size can be calculated. The dynamic molecular surface properties can be determined from the (low energy) conformation(s) of the drug molecule obtained by molecular mechanics calculations of conformational preferences. The potential advantage of this method is that the calculated surface charactersitics determine numerous physicochemical properties of the molecules including lipophilicity, the energy of hydration and the hydrogen bond formation capacity [187–
830
Suhonen et al.
190]. For instance, the surface properties of a molecule that forms an intramolecular hydrogen bond may be less polar, resulting in an enhanced membrane permeability in comparison to a homologous molecule [191]. It can, therefore, be hypothesized that the relative importance of each physicochemical factor will be reflected by a single measure such as the polar molecule surface area calculated from low-energy conformations of the drug molecule. However, the influence of the surface characteristics on each of the physicochemical properties may also vary from one conformation of a drug molecule to another. Thus, it is inappropriate and also misleading to select a single conformer for the calculation of static surface area properties [192]. A dynamic method, which takes into account all preferred (low-energy) conformations, should give a better description of the surface properties than methods that consider only single conformations. Such methods have been available for a long time and are routinely used for the prediction of drug molecule–receptor interactions, i.e., in prediction of structure–activity relationships [193]. Palm et al. compared dynamic surface properties of a series of beta-adrenoreceptor antagonists and drug permeabilities in Caco-2 monolayers and rat intestinal segments in order to predict passive drug absorption [110,194]. Excellent correlations were obtained between the dynamic polar van der Waals surface areas and the permeabilities in Caco-2 cells and rat intestine. The correlations were stronger than those obtained with calculated log Doct values. Moreover, the permeability coefficients were ranked in the correct order in both models using the dynamic polar molecular surface areas, but not using the calculated log Doct values or the number of potential hydrogen bonds. Van der Waterbeemd and Kansy established a relationship between the calculated polar molecular surface areas of drug molecules and blood–brain barrier uptake [195]. The polar molecular surface area of a drug molecule is defined as the sum of the parts of the surface area associated with polar atoms, e.g., oxygen, nitrogen, and hydrogen attached to the polar atoms. Although the criteria for the selection of the molecule conformations used in the calculation of the surface areas were unclear, and no consideration was given to the flexibility of the molecules, a relatively strong correlation was found. Furthermore, Barlow and Satoh have reported a similar relationship between percentage polar surface area of peptide-like molecules and log Doct [187]. Together, these results suggest that molecular surface properties are of potential interest as predictors of drug absorption for conventional drugs (small organic molecules) as well as for slightly larger peptide-like molecules. The decreased permeability of very lipophilic ðlog Poct 4Þ compounds is generally related to their high solubility in the lipophilic cell membranes. Although these drugs distribute rapidly into a cell membrane, their cellular transport is decreased by a slow distribution from the cell membrane into the extracellular (aqueous) fluids [196]. However, Wils et al. [197], who observed a parabolic relationship between permeability in HT29-18-C1 monolayers and log Doct , could not correlate the decreased permeability of the most hydrophobic drugs to an increased cellular uptake. Thus, other factors, such as polarity, could have contributed to the low permeability of the hydrophobic drugs. Palm et al. found that some of the very hydrophobic drugs had larger polar van der Waals surface area than expected [198]. This finding provides an alternative explanation for the low permeability of the drugs in HT29 cell monolayers [197]. Thus, while the low permeability of some lipophilic drug molecules undoubtedly results from retention in the lipophilic cell membranes [196,199], the low permeability of other lipophilic drugs may be related to their polarity [198]. These results suggest that the dynamic polar surface area can be used as an alternative model for the theoretical prediction of drug absorption.
Lipid Bilayers in Cells
F.
831
Membrane Perturbation by Drugs and Excipients
Membrane fluidity determines the rate at which lipids and proteins can diffuse in the membrane. The lipid composition of the membrane, the proteins in the membrane, and the surrounding electrolyte composition of the surrounding solutions influence the fluidity. Membranes can exist in two phases. The liquid phase is the presumed phase of most membranes under physiological conditions. In the liquid phase, the lipid headgroups are tightly packed, but the hydrocarbon chains have considerable flexibility. As the temperature is lowered, there is a sudden shift in the behavior of the membrane as it undergoes a phase transition to a more solid, or crystalline, phase. In the crystalline phase, the hydrocarbon chains become tightly packed and less flexible. The effect of different membrane components on the phase transition temperature is indicative of their role in modulating membrane fluidity. Biological membranes are complex mixtures of many lipids and proteins, and the role of each of these in the behavior of the membrane is not completely understood. The importance of membrane fluidity is demonstrated by the relationship between the activity of membrane transport protein and the temperature. The result is not a line as would be expected from cytoplasmic enzymes, but a curve with sudden breaks occurring where the phase transition of the membrane occur. Thus, as the membrane undergoes a transition to the crystalline phase there is a sudden drop in the activity of the protein. The molecular mechanisms involved in the pharmacological effects by a variety of drugs upon binding to proteins and lipid membranes is a question of fundamental importance in molecular pharmacology [200]. It is well known that a large number of drugs with different chemical structures and pharmacological effects are able to bind to lipid membranes and alter the physical properties of membranes [201,202]. Examples include general and local anesthetics, nonsteroidal anti-inflammatory agents and calcium channel-blocking drugs. In particular, the influence of local and general anesthetics on lipid membrane structure and dynamics has been extensively studied [105,202,203]. One hypotyhesis relates the molecular action of anesthetics to a change in the lateral pressure profile of the lipid membrane and a subsequent effect on the conformational flexibility and function of membrane-spanning proteins [204]. NMR studies have suggested that the interaction and binding to the interfacial lipid membrane–water interface, which is followed by a disruption of the hydration shell, is involved in the target and action sites for amphilipic agents [205]. In addition, data obtained from infrared, thermal, and fluorescence spectroscopic studies of the outermost layer of skin, stratum corneum (SC), and its components imply enhancer-improved permeation of solutes through the SC is associated with alterations involving the hydrocarbon chains of the SC lipid components. Data obtained from electron microscopy and x-ray diffraction reveals that the disordering of the lamellar packing is also an important mechanism for increased permeation of drugs induced by penetration enhancers (for a recent review, see Ref. 206).
G.
Fusogenic Lipids
Liposomes are vesicles with an aqueous core surrounded by lipid bilayer walls. Drugs may be encapsulated into the liposomes, either in the bilayers or into the aqueous core of the liposomes. Liposomes have been widely investigated by systemic and local drug delivery in different cavities of the body. Interaction of the liposomal lipids with cellular lipid bilayers or other lipid bilayers in the body (e.g. skin lipids) depends on the nature of the lipids in the liposome. In order to
832
Suhonen et al.
cause structural changes and subsequently permeability enhancement in the cellular bilayers, the lipids should be able to fuse with the target lipid bilayer. Simple binding and aggregation are not expected to enhance membrane permeability, although liposomal encapsulation affects the drug distribution in the body in macroscopic sense [207]. Upon lipid fusion the contacting lipid bilayers undergo lipid mixing with each other. This takes place, for example, in the viral entry into cells, i.e., viruses utilize lipid fusion in order to enter the cell interior [208]. For lipid fusion to take place, certain structural features of lipids are required. The long-range lipid organization has been discussed in this review earlier. In the case of lipid fusion the most crucial conformation for the lipids is the inverted hexagonal (HII ) conformation (Figs. 4 and 7). Lipids that can adopt hexagonal conformation may facilitate lipid fusion between bilayers [17,209]. In the hexagonal phase (HII ) the lipid headgroups are organized in a highly curved conformation (Figs. 4 and 7), and, therefore, the lipids with small headgroups and cone shape, like phosphatidyl ethanolamine, can form an inverted hexagonal phase easier than the lipids with larger headgroups [209]. The effective size of the polar headgroup is further affected by electrostatic repulsion and hydrogen bonding. The increased length of the alkyl chains as well as their unsaturation favor hexagonal phase formation. Dioleoyl (18:1) phosphatidyl ethanolamine (DOPE) is a commonly used fusogenic lipid. DOPE has structural features required for fusogenicity: small headgroup and unsaturated C-18 acyl chains [209]. Usually fusogenic lipids, like DOPE, do not form stable liposomes as such, but they can be used as a component, i.e., helper lipid, in the liposomes. Fusogenic liposomes are applied for two main purposes: enhancement of membrane permeability and improvement of intracellular drug delivery. Importance of lipid fusion in transdermal liposomal delivery of drugs was demonstrated by Kirjavainen et al. [210]. Nonfusogenic liposomes cannot improve drug delivery through the skin, but rather decrease it. Fushion of liposomal lipids with the skin lipids could be improved by DOPE or ethanol solution [211]. In these cases the lipid fusion was facilitated and, as a consequence of fusion, the lipid order in the skin lipid barrier is decreased as evidenced by fluorescence anisotropy [157]. Such an increase in the fluidity of the lipid bilayers increases both the diffusivity of the drug in the lipid barrier [88] and the partitioning of the drugs in the bilayers [157]. Increased partitioning causes a higher concentration gradient in the membrane at steady state and, therefore, it increases the permeability in the membrane. In contrast, the nonfusogenic saturated lipids do not increase the lipid bilayer fluidity or drug partitioning into the lipid bilayers [157]. In living cells, liposomes are taken up by endocytosis (an active process of internalization in which the cell membrane surrounds the liposome and forms an endocytic vesicle inside the cell) [207]. In many cases drug should escape from the endosome to the cytoplasm and possibly to the nucleus of the cell for activity [212,213]. The endosomal wall is a lipid bilayer with embedded membrane proteins and this wall may prevent the entry of drug into the cytoplasm. For permeabilization of the wall the liposomal lipids should fuse with the endosomal wall. This takes place in the case of the pH-sensitive liposomes that are formed when the stabilizing component has an acidic (e.g., oleic acid or cholesteroyl hemisuccinate, CHEMS) or basic [e.g., cholesterol-(3-imidazol-1-yl propyl) carbamate, DPIm] headgroup with pKa in the neutral range [214–216]. They undergo L ! HII transition and fusion with the endosomal wall when pH is decreasing in the endosomes and the acidic headgroup is neutralized. Lipid fusion may be important also in the intracellular delivery of genes and other gene-based drugs [217,218]. This is discussed later in this chapter.
Lipid Bilayers in Cells
H.
833
Amphipathic Peptides
Amphipathic peptides contain amino acid sequences that allow them to adopt membrane active conformations [219]. Usually amphipathic peptides contain a sequence with both hydrophobic amino acids (e.g., isoleucine, valine) and hydrophilic amino acids (e.g., glutamic acid, aspartic acid). These sequences allow the peptide to interact with lipid bilayer. Depending on the peptide sequence these peptides may form -helix or -sheet conformation [219]. They may also interact with different parts of the bilayer. Importantly, these interactions result in a leaky lipid bilayer and, therefore, these features are quite interesting for drug delivery application. Obviously, many of these peptides are toxic due to their strong membrane interactions. Amphipathic peptides are important for the viruses when they enter the interior. Many viruses have amphipathic peptides on their surface. A classic example is Haemophilus influenzae [208]. Amphipathic peptide on the viral surface undergoes a conformational change when the endosomal pH is acidified and, subsequently, this peptide is able to fuse with the endosomal bilayer. Consequently, the virus is able to escape from the endosome to the cytoplasm. Many amphipathic peptides are pH-dependent so that they are activated in the endosomal compartment [219]. Virosomes are virus-mimicking systems that contain liposomal bilayer and pHdependent protein impregnated in the liposomal wall. Virosomes are produced by a detergent dialysis procedure. Many researchers have demonstrated that the virosomes facilitate the leakage of the encapsulated drugs from the endosomes into the cytoplasm. This is, however, complicated technology and, so far, no virosome products are used in the clinical practice.
V.
TRANSPORT OF GENE-BASED DRUGS ACROSS CELLULAR LIPID BILAYERS
A.
Challenge of Gene-Based Drug Delivery
The Human Genome Project will provide in the near future all DNA sequences of approximately 140,000 human genes. Rapid progress of the Human Genome Project, bioinformatics, and biotechnology generates a rapidly increasing number of potential targets for drug and gene therapy. Simultaneously, new diagnostic methods, such as DNA arrays and proteomics technology enable the rapid identification of the genes and gene products that are linked to the disease [220–222]. Thus, information about the nucleotide sequences with therapeutic potential increases rapidly, and it is commonly predicted that the number of targets of drug action will increase rapidly from a few hundred to several thousands, even up to 10,000. In disease, the gene product may be expressed at too low or too high level. In both cases the gene-based drugs provide potential treatments. Gene-based drugs are based on the nucleotide chemistry and nucleotide sequences of the target genes [223,224]. Genebased drugs are divided into gene therapy, gene inhibitors, gene correction, and DNA vaccination. In principle, after completion of the Human Genome Project, the function of any human gene could be attenuated or augmented using gene-based drugs. In gene therapy, production of missing or poorly expressed protein is induced by transferring the coding sequence to the cells in plasmid DNA [223]. In principle, the sequence of any protein can be transferred to the cells for protein production. Regulatory elements of DNA, such as cell specific and inducible promotors, can be
834
Suhonen et al.
used to improve the control of gene expression. In DNA vaccination, a gene that is coding for an antigen is transferred to antigen presenting cells to provide immunity. In both cases, DNA-based therapy has significant advantages compared to protein therapy. For example, DNA is much more stable, cheaper to produce, and DNA technology allows better control of the gene product localization in the body. Gene inhibition is practiced by using oligonucleotides: single-stranded chains of DNA, RNA, or chemically modified DNA or RNA [225,226]. They bind selectively to the complementary mRNA or DNA and inhibit either transcription (antigene effect) or translation (antisense, ribozymes), thus inhibiting selectively the function of the target gene. Gene correction is based on chimeric oligonucleotides that correct mutations permanently. Gene-based drugs show great potential in medical treatment. After identification of the target gene or gene product, the nucleotide sequence for gene therapy or DNA vaccination is known. Current technology enables rapid identification of the targets and the selection of gene-based drug (i.e., sequence) [222]. These advances can be realized in the prevention and treatment of diseases only if the gene-based drugs can be delivered safely and efficiently to their target sites in the cells [225]. It is important to note that the sites of action for the gene-based drugs reside inside the cells in the cytoplasm or nucleus. Despite the promising features of gene-based drugs, their delivery to the target sites is not straightfoward due to their high moleculear weights (5000–millions) and negative charges [213]. Each phosphodiester linkage between the nucleotides contains one negative charge. Therefore, a typical oligonucleotide contains about 20 negative charges and their molecular weights are about 5–10 kDa. Oligonucleotides do not diffuse passively across the cell membranes to their sites of action in the cytoplasm (antisense, ribozymes) or in the nucleus (antigene, gene correction) [227]. Oligonucleotides bind to the cell surface, presumably to scavenger receptor for polyanions, and they are internalized [227]. This may not result in good drug activity due to the poor escape of oligonucleotides from the endosomes to the cytoplasm [225]. In gene therapy, plasmid DNA is introduced into the human cells for the production of protein. The aim is to provide a new gene to substitute a mutated gene sequence (e.g., in cystic fibrosis), to increase the production of a therapeutic protein (e.g., in cancer, transplantation), or to render cell susceptible to the defense mechanisms of the body or drug treatment (e.g., suicide genes, DNA vaccination) [223]. In all these cases the required DNA sequences must be transferred efficiently and safely to the nucleus of the cells. From the previous discussion on transcellular drug diffusion it is obvious that plasmid DNA with its molecular weight of millions is too big to diffuse through the plasma membrane. Delivery systems for gene-based drugs are needed to fulfill their promise in the medical treatment. Interactions of the potential delivery systems with the lipid bilayers are of crucial importance, since the lipid bilayer barrier must be overcome either at the level of plasma membrane or in the endosomes.
B.
Interactions of Some Delivery Systems with Lipid Bilayers
1. Liposomes Liposomes have been investigated in the delivery of the gene-based drugs for more than a decade. The cellular transfer of genes and oligonucleotides is obtained with cationic lipo-
Lipid Bilayers in Cells
835
somes [228]. Some gene transfer is obtained with pH-sensitive liposomes, but their gene transfer efficacy is an order of magnitude less than that of cationic liposomes [215]. The cationic liposomes do not encapsulate DNA in the classical sense of liposomal encapsulation. Instead, the cationic liposomes form a complex with DNA and oligonucleotides electrostatically [229]. Depending on the number of the anionic charges of the oligonucleotide/DNA and the cationic charges of the lipids, different complexes with varying charge ratios and surface charges are formed [230]. Ja¨a¨skela¨inen et al. found out that upon complexation of the oligonucleotides the cationic liposomes first aggregate and then fuse together [231]. This was shown by resonance energy transfer experiments in which dilution of the fluorescent lipid probes in the bilayers suggests fusion of the liposomes. Eventually, the liposomal structure may be lost, particularly, if the liposomes contain fusogenic lipid, e.g., DOPE [232]. DOPE is used in cationic liposomes to facilitate the fusion of the liposomes with the endosomal wall, but DOPE affects the complex formation between oligonucleotide/DNA and the liposomes. Freeze-fracture EM pictures show that the cationic liposomes with DOPE are able to adopt tubular hexagonal lipid phases [232]. Furthermore, hexagonal phase formation is more prominent if the complexes are exposed to high ionic strengths (e.g., cell culture medium). Cationic liposomes form complexes with plasmid DNA. Also, in this case DOPE affects the architecture of the complexes. DOTAP liposomes without DOPE are able to condense DNA, while DOTAP/DOPE liposomes do not condense DNA, presumably due to HII -phase formation [230,233]. Interestingly, multivalent cationic liposomes, such as DOGS, can condense DNA more efficiently than monovalent cationic liposomes [233]. If the complexation is carried out at high ionic strength the DNA condensation is less prominent than in plain water. Cationic liposomes are most efficient in delivering DNA [217] and oligonucleotides [234] into the cells at positive +/ charge ratios. This coincides with their ability to react with anionic lipid bilayers that mimic the endosomal wall [231]. Positively charged oligonucleotide–liposome complexes could disrupt the anionic liposomal walls during incubation causing release of the encapsulated calcein from the liposomes. Good delivery properties of the positively charged complexes may also be due to the better adherence of the complexes with anionic cell surface and, subsequently, a higher rate of internalization of the complexes. Oligonucleotides and plasmid DNA must be released from the liposomal complexes in the cells. Otherwise, they cannot be activated. Zelphati and Szoka showed by confocal microscopy and resonance energy transfer techniques that oligonucleotide is released from the cationic liposomes at the endosomal wall [235]. They suggested that the cationic surface of the liposome–oligonucleotide complex induces flipping of negatively charged lipids from the outer leaflet of the bilayer as illustrated in Fig. 15. Fusogenic liposomes are able to fuse with the endosomal wall and, consequently, the cationic lipids are stripped from the olignucleotide complex, leading to the release of oligonucleotide from the endosome to the cytoplasm. Later Ja¨a¨skela¨inen et al. showed that DOTAP/DOPE liposomes, but not DOTAP, release oligonucleotide in the presence of endosome mimicking liposomes [232]. Accordingly, only those oligonucleotide–lipid complexes that are able to fuse (either due to DOPE or amphipathic peptide) with the endosomal wall could elicit antisense effects in the cells [236]. It is known that free oligonucleotide is able to diffuse freely from the cytoplasm into the nucleus [237]. Therefore, oligonucleotide release at endosomal level should be advantageous for the antisense activity. In the case of plasmid DNA the intracellular target (i.e., transcription machinery) is located in the nucleus. Plasmid DNA is a much larger molecule than oligonucleotides, and
836
Suhonen et al.
FIG. 15 Cellular entry and intracellular kinetics of the cationic lipid-DNA complexes. Cationic lipid–DOPE liposomes form electrostatic complexes with DNA, and, in this case, also transferrin (Tf) is incorporated. Cellular uptake by endocytosis and endosomal acidification can be blocked with cytochalasin B and bafilomycin A1 , respectively. DNA is proposed to be released at the level of endosomal wall after fusion of the carrier lipids with endosomal bilayer. This process is facilitated by the formation of inverted hexagonal DOPE phase as illustrated in the lower corner on the right. After its release to the cytoplasm DNA may enter the nucleus. (From Ref. 253. By permission of Nature Publishing Group.)
therefore, the nuclear entry of plasmid DNA from the cytoplasm to the nucleus is poor [238,239]. Release of plasmid DNA from the cationic lipids in the cells has not been investigated, but Xu and Szoka demonstrated that coincubation with anionic liposomes releases plasmid DNA from the complexes with cationic lipids [240]. In contrast to the oligonucleotides, it appears that the cationic liposomes without DOPE are able to deliver DNA as well or even better than cationic liposomes with DOPE [233]. Several factors may
Lipid Bilayers in Cells
837
be responsible for the difference between the results with oligonucleotides and DNA. One of the reasons may be different lipid interactions with the endosomal lipid bilayer, another possibility being different kinetics in the cytoplasm and nucleus.
2.
Polycations
Plasmid DNA can be complexed electrostatically with cationic polymers. These complexes can be used for gene transfer [241]. Like the complexes of DNA with cationic lipids these complexes adhere to the cell surface with their cationic surface charges. Thereafter, they are internalized, presumably by adsorptive endocytosis. Interactions of the cationic polymer–DNA complexes with endosomal lipid bilayer have not been investigated in detail. There are substantial differences between polycations in terms of their gene transfer efficacy [233], but the reasons for the differences are poorly understood. Anyway, complexation with DNA is not adequate for gene transfer. For example, polyamidoamine dendrimers and polyethylene imine (PEI) show much higher gene delivery than polylysines [233]. The reasons for this are not well understood. Tang et al. [242] and Boussif et al. [243] have suggested that dendrimers and PEI act as proton sponges and swell in the endosomes. These properties may lead to the rupture of the endosomal wall by electrostatic binding and, subsequent stretching of the endosomal membrane. Intensity of DNA binding is also different: PEI releases DNA easier than polylysine [233]. 3. Peptides Peptides have been used for the delivery of gene-based drugs. Several rationales have been utilized. Cationic peptides are used to neutralize the charges of DNA or oligonucleotide. These peptides include polylysines and polyarginines [241,244,245]. They form complexes with DNA or oligonucleotide, thereby resulting in enhanced cellular uptake. The rationale in using amphipathic peptides is to mimic the mechanisms of viral gene transfer. Amphipathic peptides undergo conformational change due to the pH change in the endosomes [246,247]. Subsequently, they form -helical pores in the endosomal bilayer and, eventually, lyse the endosomes and release DNA to the cytoplasm. Among the amphipathic peptides are viral peptides, like INF-7 and JTS-1, and synthetic peptides, like KALA and GALA [248]. Most of these peptides are not cationic, but they can be complexed together with a cationic polymer or cationic liposome. Interestingly, KALA peptide is cationic and amphipathic. Therefore, this peptide is able to complex DNA as such and to mediate transfer of oligonucleotides and DNA into the cells [248]. Several studies have shown that amphipathic peptides are able to augment gene transfer into the cells, but their efficacy in vivo is not as clear. Peptide sequences are important both for viruses and cells in different transfer functions. Some peptide sequences facilitate protein localization in the cells across lipid barriers, while others help viruses to infect cells. These membranes translocating peptides are often hydrophobic. Although a peptide sequence may transfer its protein cargo across the cell membranes efficiently [249] it may not function similarly when it is linked to oligonucleotide. Antopolsky et al. conjugated the membrane translocating peptide sequences from Kaposi’s sarcoma fibroblast growth factor to oligonucleotides [250]. The conjugates were taken up preferentially by the cells via endocytic mechanism, but still the conjugate could not exert antisense activity. This was due to the entrapment of the conjugates to the endosomes: they could not escape from the endosomes to the cytoplasm
838
Suhonen et al.
as such. After liposomal complexation endosomal escape and antisense effect were observed. Membrane translocating peptides are promising vehicles for the transfer of macromolecules into the tissues. Recent report of Schwarze et al. [249] demonstrated that a signal peptide from HI-virus could transfer betagalactosidase protein to virtually all tissues in rat after intravenous and intraperitoneal injections. In the case of proteins, folding phenomena affect their membrane translocation and these features may be different for gene-based drugs.
VI.
CONCLUDING REMARKS
Lipid bilayers affect drug delivery at several levels of pharmocokinetics, both at macroscopic and microscopic levels. Understanding the structure and function of the bilayers aids in the development of better drug delivery systems. Delivery is particularly important for the success of the gene-based drugs.
ACKNOWLEDGMENTS The authors wish to thank Ms. Anne-Mari Oksman for technical assistance and Dr. Michelle Marra for useful suggestions and discussion. The Academy of Finland is acknowledged for funding.
REFERENCES 1.
2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12. 13.
J. Hardman, L. Limbird, P. Molinoff, R. Ruddon, and A. Goodman Gilman, eds., Goodman & Gilman’s The Pharmacological Basis of Therapeutics, 9th edn., McGraw-Hill, New York, 1996. M. Rowland and T. Tozer, Clinical Pharmacokinetics, 3rd edn., Williams & Wilkins, Media PA, 1995. C. Wilson and N. Washington, Physiological Pharmaceutics: Biological Barriers to Drug Absorption, Ellis Horwood, Chichester, 1989. N. Wills, L. Reuss, and S. Lewis, eds., Epithelial Transport: A Guide to Methods and Experimental Analysis, Chapman & Hall, Bury St Edmunds, 1996. W. M. Pardridge. Physiol. Rev. 63:1481 (1983). D. Maurice and S. Mishima, in Handbook of Experimental Pharmacology, vol. 69, Pharmacology of the Eye, Springer-Verlag, Berlin–Heidelberg, 1984, pp. 16–119. I. Tamai and A. Tsuji. Adv. Drug Deliv. Rev. 20:5 (1996). P. Swaan, F. Szoka Jr., and S. Øie. Adv. Drug Deliv. Rev. 20:59 (1996). V. Wacher, L. Salphati, and L. Benet. Adv. Drug Deliv. Rev. 20:99 (1996). K. Ha¨ma¨la¨inen, K. Kontturi, L. Murtoma¨ki, S. Auriola, and A. Urtti. J. Control Rel. 49:97 (1997). L. Rilfors, G. Lindblom, A . Wieslander, and A. Christiansson, in Biomembranes, vol. 12, Membrane Fluidity (M. Kates and L. Manson, eds.), Plenum Press, New York, 1984, pp. 205– 245. A. Kleinfeld, in Membrane Fusion (J. Wilschut and D. Hoekstra, eds.), Marcel Dekker, New York, 1991, pp. 3–33. G. Cevc. Biochim. Biophys. Acta 1062:59 (1991).
Lipid Bilayers in Cells 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56.
839
I. Pascher, M. Lundmark, P.-G. Nyholm, and S. Sundell. Biochim. Biophys. Acta 1113:339 (1992). D. Small, The Physical Chemistry of Lipids—from Alkanes to Phopholipids, Plenum Press, New York, 1986. M. Janiak, D. Small, and G. Shipley. Biochemistry 15:4575 (1976). P. Cullis, C. Tilcock, and M. Hope, in Membrane Fusion (J. Wilschut and D. Hoekstra, eds.), Marcel Dekker, New York, 1991, pp. 35–64. R. Epand. Biochim. Biophys. Acta 1376:353 (1998). D. Marsh. Chem. Phys. Lipids 57:109 (1991). J. M. Boggs. Can. J. Biochem. 58:755 (1980). J. Seddon. Biochim. Biophys. Acta 1031:1 (1990). C.-H. Hsieh, S.-C. Sue, P.-C. Lyu, and W.-g. Wu. Biophys. J. 73:870 (1997). P. Cullis and B. de Kruijff. Biochim. Biophys. Acta 559:399 (1979). A . Wieslander, A. Christiansson, L. Rilfors, and G. Lindblom. Biochemistry 19:3650 (1980). H. Goldfine, N. Johnston, J. Mattai, and G. Shipley. Biochemistry 26:2814 (1987). V. Luzzati. Curr. Opin. Struct. Biol. 7:661 (1997). M. J. Lamson, L. G. Herbette, K. R. Peters, J. H. Carson, F. Morgan, D. C. Chester, and P. A. Kramer. Int. J. Pharm. 105:259 (1994). G. Cevc and H. Richardsen, Adv. Drug. Deliv. Rev. 38:207 (1999). J. Killian, A. de Jong, J. Bijvelt, A. Verkleij, and B. de Kruijff. EMBO J. 9:815 (1990). M. Auger. Biophys. J. 68:233 (1997). B. Kruijff. Nature 386:129 (1997). S. Singer and G. Nicolson. Science 175:720 (1972). R. Welti and M. Glaser. Chem. Phys. Lipids 73:121 (1994). K. Simons and E. Ikonen. Nature 387:569 (1997). P. Somerharju, J. Virtanen, and K. Cheng. Biochim. Biophys. Acta 1440:32 (1999). G. Cevc, in Liposome Technology, vol. 1, 2nd edn. (G. Gregoridiadis, ed.), CRC Press, Boca Raton, 1993, pp. 1–36. J. Lehtonen and P. Kinnunen. Biophys. J. 68:525 (1995). D. Huster, K. Arnold, and K. Gawrisch. Biochemistry 37:17299 (1998). E. Rowe. Biochemistry 26:46 (1987). I. Polozov, A. Polozova, J. Molotkovsky, and R. Epand. Biochim. Biophys. Acta 1328:125 (1997). A. Watts. Biochim. Biophys. Acta 1376:297 (1998). D. Tieleman, S. Marrink, and H. Berendsen. Biochim. Biophys. Acta 1331:235 (1997). O. Mouritsen and K. Jørgensen. Pharm. Res. 15:1507 (1998). T. Gil, J. Ipsen, O. Mouritsen, M. Sabra, M. Sperotto, and M. Zuckermann. Biochim. Biophys. Acta 1376:245 (1998). O. Griffith, P. Dehlinger, S. Van. J. Membr. Biol. 15:159 (1974). W. Subczynski, A. Wisniewska, J.-J. Yin, J. Hyde, and A. Kusumi. Biochemistry 33:7670 (1994). J.-F. Tocanne and J. Teissie´. Biochim. Biophys. Acta 1031:111 (1990). J. Seelig and A. Seelig. Q. Rev. Biophys. 13:19 (1980). P. Macdonald, B. Sykes, and R. McElhaney. Can. J. Biochem. Cell Biol. 62:1134 (1984). M. Wilson and A. Pohorille. J. Am. Chem. Soc. 116:1490 (1994). B. R. Lentz. Chem. Phys. Lipids 64:99 (1993). H. Tra¨uble. J. Membr. Biol. 4:193 (1971). C. Le Grimellec, G. Friedlander, E. Yandouzi, P. Zlatkine, and M.-C. Giocondi. Kidney Int. 42:825 (1992). W. J. van Blitterswijk, R. P. van Hoeven, and B. W. Van der Meer. Biochim. Biophys. Acta 644:323 (1981). H. Pottel, B. W. Van de Meer, and W. Herreman. Biochim. Biophys. Acta 730:181 (1983). P. Yeagle, Biochim. Biophys. Acta 822:267 (1985).
840
Suhonen et al.
57. Z. Sojcic, H. Toplak, R. Zuehlke, U. E. Honegger, R. Bu¨hlmann, and U. N. Wiesmann. Biochim. Biophys. Acta 1104:31 (1992). 58. P. Herman, K. Konopa´sek, J. Pla´sek, and J. Svobodova´. Biochim. Biophys. Acta 1190:1 (1994). 59. H. Toplak, V. Batchiulis, A. Hermetter, T. Hunziker, U. E. Honegger, and U. N. Wiesmann. Biochim. Biophys. Acta 1028:67 (1990). 60. M. G. Tozzi-Ciancarelli, A. Di Giulio, E. Troiani-Sevi, A. D’Alfonso, G. Amicosante, and A. Oratore. Cell Biophys. 15:225 (1989). 61. A. Villacara, G. Zanchin, M. Spatz. Microcir. Endoth. Lymphat. 6:46 (1990). 62. A. Hermetter, B. Rainer, E. Ivessa, E. Kalb, J. Loidl, A. Roscher, and F. Paltauf. Biochim. Biophys. Acta 978:151 (1989). 63. R. J. Hitzemann, H. E. Schueler, C. Graham-Brittain, and G. P. Kreishman. Biochim. Biophys. Acta 859:189 (1986). 64. W. G. Wood and F. Schoeder. Life Sci. 43:467 (1988). 65. S. Kitagawa and H. Hirata. Biochim. Biophys. Acta 1112:14 (1992). 66. A. Alvarado, D. A. Butterfield, and B. Henning. Int. J. Biochem. 26:575 (1994). 67. J. Custodio, L. Almeida, and V. Madeira. Biochim. Biophys. Acta 1153:308 (1993). 68. J. M. Vanderkooi, R. Landesberg, H. Selick, II, and G. G. McDonald. Biochim. Biophys. Acta 464:1 (1977). 69. K. L. Audus, R. Tavakoli-Saberi, H. Zheng, and E. N. Boyce. J. Dent. Res. 71:1298 (1992). 70. K. L. Audus and M. A. Gordon. J. Immunopharmacol. 6:105 (1984). 71. E. LeCluyse, L. Appel, and S. C. Sutton. Pharm. Res. 8:84 (1991). 72. M. Antunes-Madeira, R. Videira, and V. Madeira. Biochim. Biophys. Acta 1190:149 (1994). 73. G. Zavoico, L. Chandler, and H. Kutchai. Biochim. Biophys. Acta 812:299 (1985). 74. R. A. Videira, M. Antunes-Madeira, M. L. W. Klu¨ppel, and V. M. C. Madeira. Med. Sci. Res. 22:391 (1994). 75. B. Shi and H. Tien. Biochim. Biophys. Acta 859:125 (1986). 76. S. Balasubramanian and R. Straubinger. Biochemistry 33:8941 (1994). 77. O. Mouritsen and K. Jørgensen. Chem. Phys. Lipids 73:3 (1994). 78. Y. Lange, in The Physical Chemistry of Lipids – from Alkanes to Phosopholipids (D. Small, ed.), 2nd ed., Plenum Press, New York, 1986, pp. 523–554. 79. A. Schroit and R. Zwaal. Biochim. Biophys. Acta 1071:313 (1991). 80. U. Igbavboa, N. Avdulov, F. Schroeder, and W. Wood. J. Neurochem. 66:1717 (1996). 81. J. Boggs, in Biomembranes, vol. 12, Membrane Fluidity (M. Kates and L. Manson, eds.), Plenum Press, New York, 1984, pp. 3–53. 82. P. Cullis, M. Hope, M. Bally, T. Madden, L. Mayer, and D. Fenske. Biochim. Biophys. Acta 1331:187 (1997). 83. E. Cussler, Diffusion – Mass Transfer in Fluid Systems, 2nd edn., Cambridge University Press, Cambridge, UK, 1997. 84. B. Jin and A. Hopfinger. Pharm. Res. 13:1786 (1996). 85. A. Finkelstein. J. Gen. Physiol. 68:127 (1976). 86. T.-X. Xiang and B. Anderson. J. Membr. Biol. 140:111 (1994). 87. T.-X. Xiang and B. Anderson. J. Membr. Biol. 148:157 (1995). 88. T.-X. Xiang and B. Anderson. J. Membr. Biol. 165:77 (1998). 89. M. Marra Feil, Lipid Phase Contributions to Bilayer Barrier Function, Ph.D. dissertation, University of Utah, Salt Lake City, UT, 1995. 90. T.-X. Xiang and B. Anderson. Biophys. J. 72:223 (1997). 91. D. W. Deamer and J. Bramhall. Chem. Phys. Lipids 40:167 (1986). 92. T.-X. Xiang and B. Anderson. Biochim. Biophys. Acta 1370:64 (1998). 93. W. Lieb and W. Stein. Nature 224:240 (1969). 94. T.-X. Xiang. Biophys. J. 65:1108 (1993). 95. E. Overton, Studien u¨ber die Narkose, Fischer, Jena, 1901. 96. K. Meyer and M. Hemmi. Biochem. Zeit. 277:39 (1935).
Lipid Bilayers in Cells 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143.
841
R. Collander and H. Ba¨rlund. Acta Botan. Fenn. 11:1 (1933). C. Hansch, P. Maloney, T. Fujita, and R. Muir. Nature 194:178 (1962). J. M. Diamond and Y. Katz. J. Membr. Biol. 17:121 (1974). J. Marqusee and K. Dill. J. Chem. Phys. 85:434 (1986). C. Hansch and W. J. D. Dunn. J. Pharm. Sci. 61:1 (1972). C. Hansch and J. M. Clayton. J. Pharm. Sci. 62:1 (1973). H. Kubinyi. Prog. Drug. Res. 23:97 (1979). J. K. Seydel and K. J. Schaper. Pharmacol. Ther. 15:131 (1981). N. P. Franks and W. R. Lieb. Nature 274:339 (1978). M. H. Abraham, H. S. Chadha, and R. C. Mitchell. J. Pharm. Sci. 83:1257 (1994). E. Chikhale, K. Ng, P. Burton, and R. Borchardt. Pharm. Res. 11:412 (1994). T. Salminen, A. Pulli, and J. Taskinen. J. Pharm. Biomed. Anal. 15:469 (1997). R. C. Young, R. C. Mitchell, T. H. Brown, C. R. Ganellin, R. Griffiths, M. Jones, K. K. Rana, D. Saunders, I. R. Smith, and N. E. Sore. J. Med. Chem. 31:656 (1988). K. Palm, K. Luthman, A. L. Ungell, G. Strandlund, and P. Artursson. J. Pharm. Sci. 85:32 (1996). L. Perbellini, F. Brugnone, D. Caretta, and G. Maranelli. Br. J. Ind. Med. 42:162 (1985). M. H. Abraham, K. Taka´cs-Nova´k, and R. C. Mitchell. J. Pharm. Sci. 86:310 (1997). J. A. Calder and C. R. Ganellin. Drug Des. Discov. 11:259 (1994). M. H. Abraham, H. S. Chadha, G. S. Whiting, and R. C. Mitchell. J. Pharm. Sci. 83:1085 (1994). P. Seiler. Eur. J. Med. Chem. 9:473 (1974). J. Seelig and A. Seelig. Biochem. Biophys. Res. Commun. 57:406 (1974). G. Bu¨ldt, H. U. Gally, A. Seelig, J. Seelig, and G. Zaccai. Nature 271:182 (1978). D. Bassolino-Klimas, H. E. Alper, and T. R. Stouch. Biochemistry 32:12624 (1993). R. Kaliszan. Quant. Struct.-Act. Relat. 9:83 (1990). S. Ong, H. Liu, X. Qui, G. Bhat, and C. Pidgeon. Anal. Chem. 67:755 (1995). C. Yang, S. Cai, H. Liu, and C. Pidgeon. Adv. Drug Deliv. Rev. 23:229 (1997). R. A. Demel, W. S. Geurts van Kessel, R. F. Zwaal, B. Roelofsen, and L. L. van Deenen. Biochim. Biophys. Acta 406:97 (1975). A. Seelig. Biochim. Biophys. Acta 899:196 (1987). T.-X. Xiang and B. Anderson. J. Chem. Phys. 103:8666 (1995). A. Leo, C. Hansch, and D. Elkins. Chem. Rev. 71:525 (1971). E. Overton. Vierteljahrsschr. Naturforsch. Ges. Zurich 44: 88 (1899). B. D. Anderson, W. I. Higuchi, and P. V. Raykar. Pharm. Res. 5:566 (1988). B. D. Anderson and P. V. Raykar. J. Invest. Dermatol. 93:280 (1989). S. I. Rapoport, K. Ohno, and K. D. Pettigrew. Brain Res. 172:354 (1979). V. A. Levin. J. Med. Chem. 23:682 (1980). T.-X. Xiang and B. D. Anderson. J. Pharm. Sci. 83:1511 (1994). T.-X. Xiang, X. Chen, and B. D. Anderson. Biophys. J. 63:78 (1992). W. J. van Blitterswijk, B. W. Van der Meer, and H. Hilkmann. Biochemistry 26:1746 (1987). R. F. Flewelling and W. L. Hubbell. Biophys. J. 49:541 (1986). M. L. Blank, E. A. Cress, Z. L. Smith, and F. Snyder. Lipids 26:166 (1991). S. Paula, A. G. Volkov, A. N. Van Hoek, T. H. Haines, and D. W. Deamer. Biophys. J. 70:339 (1996). R. Fettiplace and D. A. Haydon. Physiol. Rev. 60:510 (1980). T. Hanai and D. A. Haydon. J. Theor. Biol. 11:370 (1966). E. M. Wright and J. M. Diamond. Proc. R. Soc. Lond. B Biol. Sci. 171:227 (1969). E. M. Wright and J. M. Diamond. Proc. R. Soc. Lond. B Biol. Sci. 171:203 (1969). H. J. Worman, T. A. Brasitus, P. K. Dudeja, H. A. Fozzard, and M. Field. Biochemistry 25:1549 (1986). M. B. Lande, J. M. Donovan, and M. L. Zeidel. J. Gen. Physiol. 106:67 (1995). A. Walter and J. Gutknecht. J. Membr. Biol. 90:207 (1986).
842
Suhonen et al.
144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157.
D. Papahadjopoulos, K. Jacobson, S. Nir, and T. Isac. Biochim. Biophys. Act 311:330 (1973). M. Jansen and A. Blume. Biophys. J. 68:997 (1995). Z. Bar-On and H. Degani. Biochim. Biophys. Acta 813:207 (1985). J. Brahm. J. Gen. Physiol. 81:283 (1983). R. L. Magin and M. R. Niesman. Chem. Phys. Lipids 34:245 (1984). R. Peters and K. Beck. Proc. Natl. Acad. Sci. USA 80:7183 (1983). E. Sada, S. Katoh, M. Terashima, H. Kawahara, and M. Katoh. J. Pharm. Sci. 79:232 (1990). A. P. Todd, R. J. Mehlhorn, and R. I. Macey. J. Membr. Biol. 109:53 (1989). A. P. Todd, R. J. Mehlhorn, and R. I. Macey. J. Membr. Biol. 109:41 (1989). W. R. Lieb and W. D. Stein. J. Membr. Biol. 92:111 (1986). W. Stein and I. Nir. J. Membr. Biol. 5:246 (1971). W. Stein, Transport and Diffusion across Cell Membranes, Academic Press, Orlando, FL, 1986. S. Wise, W. Bonnet, and F. Guenther. J. Chromatogr. Sci. 19:457 (1981). M. Kirjavainen, J. Mo¨nkko¨nen, M. Saukkosaari, R. Valjakka-Koskela, J. Kiesvaara, and A. Urtti. J. Control Rel. 58:207 (1999). K. Yoneto, S. K. Li, W. I. Higuchi, and S. Shimabayashi. J. Pharm. Sci. 87:209 (1998). L. R. De Young and K. A. Dill. Biochemistry 27:5281 (1988). S. White, G. King, and J. Cain. Nature 290:161 (1981). E. Egberts, S. J. Marrink, and H. J. Berendsen. Eur. Biophys. J. 22:423 (1994). A. Walter and J. Gutknecht. J. Membr. Biol. 77:255 (1984). T.-X. Xiang and B. D. Anderson. Biophys. J. 75:2658 (1998). T.-X. Xiang and B. D. Anderson. Biophys. J. 66:561 (1994). J. Pope, L. Walker, and D. Dubro. Chem. Phys. Lipids 35:259 (1984). F. Mulders, H. van Langen, G. van Ginkel, and Y. Levine. Biochim. Biophys. Acta 859:209 (1986). T.-X. Xiang and B. Anderson. J. Chem. Phys. 110:1807 (1999). S. Marrink and H. Berendsen. J. Phys. Chem. 100:16729 (1996). B. Brodie and C. Hogben. J. Pharm. Pharmacol. 9:345 (1957). R. H. Turner, C. S. Mehta, and L. Z. Benet. J. Pharm. Sci. 59:590 (1970). H. Rottenberg. J. Bioenerg. 7:61 (1975). H. Rottenberg. Methods Enzymol. 55:547 (1979). D. W. Deamer, R. C. Prince, and A. R. Crofts. Biochim. Biophys. Acta 274:323 (1972). J. W. Nichols and D. W. Deamer. Biochim. Biophys. Acta 455:269 (1976). G. Rudnick and J. Clark. Biochim. Biophys. Acta 1144:249 (1993). D. Njus, P. A. Sehr, G. K. Radda, G. A. Ritchie, and P. J. Seeley. Biochemistry 17:4337 (1978). R. P. Casey, D. Njus, G. K. Radda, J. Seeley, and P. A. Sehr. Horiz. Biochem. Biophys. 3:224 (1977). S. Simon, D. Roy, and M. Schindler. Proc. Natl. Acad. Sci. USA 91:1128 (1994). P. D. Roepe. Biochemistry 31:12555 (1992). P. D. Roepe, L. Y. Wei, J. Cruz, and D. Carlson. Biochemistry 32:11042 (1993). M. J. Hope and P. R. Cullis. J. Biol. Chem. 262:4360 (1987). R. Rees-Jones and Q. Al-Awqati. Biochemistry 23:2236 (1984). F. The´venod, T. P. Kemmer, A. L. Christian, and I. Schulz. J. Membr. Biol. 107:263 (1989). B. L. Trigatti and G. E. Gerber. Biochem. J. 313:487 (1996). J. A. Op den Kamp. Annu. Rev. Biochem. 48:47 (1979). P. F. Devaux. Biochemistry 30:1163 (1991). D. Barlow and T. Satoh. J. Control. Rel. 29:283 (1994). W. J. D. Dunn, M. G. Koehler, and S. Grigoras. J. Med. Chem. 30:1121 (1987). T. Ooi, M. Oobatake, G. Ne´methy, and H. A. Scheraga. Proc. Natl. Acad. Sci. 84:3086 (1987). A. ter Laak, R. Tsai, G. Donne´-Op den Kelder, P.-A. Carrupt, B. Testa, and H. Timmermann. Eur. J. Pharm. Sci. 2:373 (1994). L. L. Wright and G. R. Painter. Mol. Pharmacol. 41:957 (1992).
158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191.
Lipid Bilayers in Cells 192. 193. 194. 195. 196. 197. 198. 199. 200. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211. 212. 213. 214. 215. 216. 217. 218. 219. 220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231.
843
K. Lipkowitz, B. Baker, and R. Larter. J. Am. Chem. Soc. 111:7750 (1989). D. Boyd and K. Lipkowitz. J. Chem. Educ. 59:269 (1982). K. Palm, K. Luthman, A. L. Ungell, G. Strandlund, F. Beigi, L. Lundahl, and P. Artursson. J. Med. Chem. 41:5382 (1998). H. van der Waterbeemd and M. Kansy. Chimia 46:299 (1992). T. J. Raub, C. L. Barsuhn, L. R. Williams, D. E. Decker, G. A. Sawada, and N. F. Ho. J. Drug Target 1:269 (1993). P. Wils, A. Warnery, V. Phung-Ba, S. Legrain, and D. Scherman. J. Pharmacol. Exp. Ther. 269:654 (1994). K. Palm, K. Luthman, and P. Artursson. Pharm. Res. 12:S-297 (1995). G. A. Sawada, N. F. Ho, L. R. Williams, C. L. Barsuhn, and T. J. Raub. Pharm. Res. 11:665 (1994). H. J. Little. Pharmacol. Ther. 69:37 (1996). D. Goren, A. Gabizon, and Y. Barenholz. Biochim. Biophys. Acta 1029:285 (1990). J. G. Bovill. Minerva Anestesiol, 65:210–214, 1999. L. I. Horva´th, H. R. Arias, H. O. Hankovszky, K. Hideg, F. J. Barrantes, and D. Marsh. Biochemistry 29:8707 (1990). R. S. Cantor. Biochemistry 36:2339 (1997). J. A. Barry and K. Gawrisch. Biochemistry 33:8082 (1994). T. M. Suhonen, J. Bouwstra, and A. Urtti. J. Control Rel. 59:149 (1999). D. Lasic. J. Control Rel. 48:203 (1997). T. Stegman, D. Hoekstra, G. Scherprof, and J. Wilschut. J. Biol. Chem. 261:10966 (1986). D. C. Litzinger and L. Huang. Biochim. Biophys. Acta 1113:201 (1992). M. Kirjavainen, A. Urtti, I. Ja¨a¨skela¨inen, T. M. Suhonen, P. Paronen, R. Valjakka-Koskela, J. Kiesvaara, and J. Mo¨nkko¨nen. Biochim. Biophys. Acta 1304:179 (1996). M. Kirjavinen, A. Urtti, R. Valjakka-Koskela, J. Kiesvaara, and J. Mo¨nkko¨en. Eur. J. Pharm. Sci. 7:279 (1999). D. Lasic and N. Templeton. Adv. Drug. Deliv. Rev. 20:221 (1996). O. Zelphati and F. Szoka. J. Control Rel. 41:99 (1996). R. M. Straubinger, N. Du¨zgu¨nes, and D. Papahadjopoulos. FEBS Lett. 179:148 (1985). J. Y. Legendre and F. C. J. Szoka. Pharm. Res. 9:1235 (1992). V. Budker, V. Gurevich, J. E. Hagstrom, F. Bortzov, and J. A. Wolff. Nat. Biotechnol. 14:760 (1996). J. H. Felgner, R. Kumar, C. N. Sridhar, C. J. Wheeler, Y. J. Tsai, R. Border, P. Ramsey, M. Martin, and P. L. Felgner. J. Biol. Chem. 269:2550 (1994). J. Mo¨nkko¨nen and A. Urtti. Adv. Drug. Deliv. Rev. 34:37 (1998). R. Brasseur, T. Pillot, L. Lins, J. Vandekerckhove, and M. Rosseneu. Trends Biochem. Sci. 22:167 (1997). P. O Brown and D. Botstein. Nat. Genet. 21:33 (1999). A. Dove. Nat. Biotechnol. 17:233 (1999). D. J. Duggan, M. Bittner, Y. Chen, P. Meltzer, and J. M. Trent. Nat. Genet. 21:10 (1999). R. G. Crystal. Science 270:404 (1995). C. A. Stein and Y. C. Cheng. Science 261:1004 (1993). R. A. Stull and F. C. J. Szoka. Pharm. Res. 12:465 (1995). R. W. Wagner. Nature 372:333 (1994). C. Beltinger, H. U. Saragovi, R. M. Smith, L. LeSauteur, N. Shah, L. DeDionisio, L. Christensen, R. Raible, L. Jarett, and A. M. Gewirtz. J. Clin. Invest. 95:1814 (1995). P. L. Felgner, T. R. Gadek, M. Holm, R. Roman, H. W. Chan, M. Wenz, J. P. Northrop, G. M. Ringold, and M. Danielsen. Proc. Natl. Acad. Sci. USA 84:7413 (1987). H. Gershon, R. Ghirlando, S. B. Guttman, and A. Minsky. Biochemistry 32:7143 (1993). B. Sternberg, F. L. Sorgi, and L. Huang. FEBS Lett. 356:361 (1994). I. Ja¨a¨skela¨inen, J. Mo¨nkko¨nen, and A. Urtti. Biochim. Biophys. Acta 1195:115 (1994).
844
Suhonen et al.
232. I. Ja¨a¨skela¨inen, B. Sternberg, J. Mo¨nkko¨nen, and A. Urtti. Int. J. Pharm. 167:191 (1998). 233. M. Ruponen, S. Yla¨-Herttuala, and A. Urtti. Biochim. Biophys. Acta 1415:331 (1999). 234. C. Bennet, M.-Y. Chiang, H. Chan, J. Shoemaker, and C. Mirabelli. Mol. Pharmacol. 41:1023 (1992). 235. O. Zelphati and F. C. J. Szoka. Proc. Natl. Acad. Sci. USA 93:11493 (1996). 236. I. Ja¨a¨skela¨inen, S. Peltola, P. Honkakoski, J. Mo¨nkko¨nen, and A. Urtti. Eur. J. Pharm. Sci. 10:187 (2000). 237. D. J. Chin, G. A. Green, G. Zon, F. C. J. Szoka, and R. M. Straubinger. New Biol. 2:1091 (1990). 238. J. Zabner, A. J. Fasbender, T. Moninger, K. A. Poellinger, and M. J. Welsh. J. Biol. Chem. 270:18997 (1995). 239. M. E. Dowty, P. Williams, G. Zhang, J. E. Hagstrom, and J. A. Wolff. Proc. Natl. Acad. Sci. USA A 92:4572 (1995). 240. Y. Xu and F. C. J. Szoka. Biochemistry 35:5616 (1996). 241. E. Wagner, M. Zenke, M. Cotten, H. Beug, and M. L. Birnstiel. Proc. Natl. Acad. Sci. USA 87:3410 (1990). 242. M. X. Tang, C. T. Redemann, and F. C. J. Szoka. Bioconjug. Chem. 7:703 (1996). 243. O. Boussif, F. Lezoualc’h, M. A. Zanta, M. D. Mergny, D. Scherman, B. Demeneix, and J. P. Behr. Proc. Natl. Acad. Sci. USA 92:7297 (1995). 244. C. Plank, M. X. Tang, A. R. Wolfe, and F. C. J. Szoka. Hum. Gene Ther. 10:319 (1999). 245. P. Dash, V. Toncheva, E. Schacht, and L. Seymour. J. Control Rel. 48:269 (1997). 246. C. Plank, B. Oberhauser, K. Mechtler, C. Koch, and E. Wagner. J. Biol. Chem. 269:12918 (1994). 247. J. Y. Legendre and F. C. J. Szoka. Proc. Natl. Acad. Sci. USA 90:893 (1993). 248. T. B. Wyman, F. Nicol, O. Zelphati, P. V. Scaria, C. Plank, and F. C. J. Szoka. Biochemistry 36:3008 (1997). 249. S. R. Schwarze, A. Ho, A. Vocero-Akbani, and S. F. Dowdy. Science 285:1569 (1999). 250. M. Antopolsky, E. Azhayeva, U. Tengvall, S. Auriola, I. Ja¨a¨skela¨inen, S. Ro¨nkko¨, P. Honkakoski, A. Urtti, H. Lo¨nnberg, and A. Azhayev. Bioconjug. Chem. 10:598 (1999). 251. H. Kanerva, Pharmacokinetic Studies on Deramciclane, Ph.D. dissertation, University of Kuopio, Kuopio, 1999. 252. Y. Levine, A. Bailey, and M. Wilkins. Nature 220:577 (1968). 253. S. Simo˜es, V. Slepushkin, P. Pires, R. Gaspar, M. Pedroso de Lima, and N. Du¨zgu¨nes. Gene Therapy 6:1798 (1999).
Index
Acceptor number, 27 Acid rain, 659–661 Activity coefficient, 3, Adsorption, 83–101 at polarized liquid-liquid interfaces, 118 energy, 235, 359 free energy, 110, 111 Gibbs equation, 415, 416 interfacial, 609 isotherm, 109, 110 Langmuir isotherm, 109, 234–236 nonlocalized model, 539 phenomena, 106 protein, 261, 594 specific, 3, 4,201 Alternating direction implicit finite-difference method (ADIFDM), 289 Amphiphilic isotherm, 109 Anesthetics, 690, 775–803 activity, 715 delivery sites, 797 discharging, 796–797 general, 797 local, 715, 792, 796 volumetric properties, 797 Aphid, 654 Assisted proton transfer, 694–695 Atmospheric, electricity, 658 electrochemistry, 658–661 Axon, 651–653 hillock, 653 squid giant, 676
Back-extraction method, 480–481 Berthelot rule, 91 Bienzymatic systems, 575 Biocatalysis, 553–580 Biocatalyst, 558–563, 568 Biocompatibility, 586, 594–596 Bioconversion, 558, 574 Bioreactor, 554, 563, 578 biphasic, 572 Biosensor, 515–530, 592 Biotransformation, 553 Blood-brain barrier (BBB), 809, 824 Boltzmann equation, 454 Born equation, 23, 24, 25, 26, 28, 30 Born model, 25, 134 Butler–Volmer, approximation, 308, 349 equation, 378, 385, 534 law, 175 relationship, 112, 167 Capacitance, 56, 60, 64, 77, 78, 179, 415–435 differential, 179 double layer, 192 interfacial, 206 negative, 62–64 Capillary waves, 172–174, 230, 231, 236 interfacial, 537 frequency, 232, 233, 236, 237 power spectra, 233 Carbonylcyanide-4trifluoromethoxyphenylhydrazone (FCCP), 665–669 Carcinogen, 664 845
846 Catalytic reduction, 497 Cell, 656 aggregation, 563 cell signaling, 515 chemical, 10, 11 companion, 650 ,652 concentration, 10, 11 conducting, 650 electrochemical, 689 excitable, 660 galvanic, 9, 10, 14 interfacial, 328 Lewis, 327–328, 349568, 571–573 living, 649 motor, 650 nerve, 675 organelles, 660 phloem, 675 physiology, 807 promoters, 833 rotating diffusion, 331 Schwann, 653 sensory, 650 signaling, 807 structure, 630 voltaic, 10, 14, 15, 16, 17 Centrifugal liquid membrane method (CLM), 337–339, 356 Centrosymmetric particles, 141 Charge transfer, 488, 522, 533–549 mechanism, 325 reaction, 490 Chlorophyll a, 641–647 Chloroplast, 641 Chronoamperometry, 695 Circular Dichroism (CD), 258 Compensating voltage, 16 Communication, intercellular, 651 intracellular, 651 Conductive bundles, 650 Constant-composition model, 291–296 Cooper-Harrison catastrophe, 56–59 Coulomb, fluids, 102 integral, 94, 99 Crowley’s model, 67, 68 Cyclic, voltabsorptogram, 189, 190 voltammetry, 118, 192, 194 voltamogram, 181, 182, 189, 192, 218, 219 Cytoplasm, 652
Index Debye length, 123, 173, 180 Debye-Huckel, approach, 99 charge densities, 103 equation, 94 hole-corrected, 94 limit, 94 theory, 93–95, 99, 102 Dendrite, 653 Density-functional theory, 172 Dielectric relaxation, 138 Dielectric saturation, 25 Difference frequency generation (DFG), 124, 143 Diffusion controlled-electrodeposition, 219 2,4-Dinitrophenol (DNP), 661–664, 694 Distribution coefficient, 4, 8,10, 12, 13 Distribution constant, 8 standard, 8 DNA, 655 based therapy, 834 chemically modified, 834 delivering, 835 plasmid, 833–837 regulatory elements, 833 replication, 515 single-stranded chain, 834 technology, 834 vaccination, 834 Donor number, 27 Doppler shift, 232 Double layer, 2, 18, 19, 51–79, 115, 118, 123, 153, 192, 454, 543, 658–661, 710 diffuse, 419, 447, 452, 544 dipolar, 2 electrical, 710 ionic, 2, 4,5, 153 relaxation, 209 Drug, 699–726 absorption, 809, 810, 829–831 action, 729 administration, 808 bioavailability, 829 biotechnological, 810 delivery (DD), 729, 775–786, 807–838 gene based, 833–834 diffusion, 810 discovery, 810 disposition, 729 efficiency, 729 intracellular distribution, 829 ionizable, 729–761 membrane perturbation, 831
Index [Drug] narcotic, 758 pharmacological effect, 831 structurally nonspecific, 715 transport, 809, 826 Dynamic condenser method, 15 Elastic capacitor, 51, 54, 63, 64 Elastic dimmer, 51 Elastic stretching, 71 Electric field induced second harmonic generation (EFISH), 126, 127 Electrocardiogram, 656 Electrode, antimony, 656 aqueous gel, 631 calomel, 656 classification, 655 counter, 631 DNA-modified, 515–530 dual-pipette, 379–381 electrolyte dropping, 339, 630, 631 ion-selective, 12, 15, 439–466, 586, 595 mercury-mercuric oxide, 656 mercury-mercurous sulfate, 656 nonpolarizable, 651, 655, 658 reference, 658–659, 688 response to DNA-binding protein, 526–527 response to DNA-binding small molecules, 523–525 reversible, 656 rotating disk, 331 second type, 655–656 silver-silver chloride, 656–658 working, 658–670 Electroelastic, instabilities, 51–80 model, 67 phenomena, 52 Electroencephalogram, 656 Electrogenerated chemiluminescence phenomena, 191 Electrolysis, 509 controlled potential, 488, 500, 502, 507 Electromyogram, 656 Electron-transfer (ET), 179–222, 399, 487, 488, 496–499, 503, 504, 542 heterogeneous, 213 kinetics, 179, 196, 307–316 photoinduced, 181–183, 200, 202–208, 212 processes, 200 reaction, 179 Electroporation, 69
847 Electrospay (ES), 630 Energy, activation, 185, 215 cavity formation, 41 chemical solvation, 8 configurational, 85 density functional, 89 elastic, 70 electrostatic, 23, 95 Fermi, 65 functional, 88 Gibbs, 23, 155, 181–186, 655, 736, 737 hydration, 182 interaction, 30, 57 interfacial, 538 ion hydration, 24 ion solvation, 25, 26 of elastically coupled charges, 53 of transfer of ions, 5, 8,9, 13, 33, 42, 44, 46, 160, 614 of transfer of lipid, 539 potential, 83 reorganization, 170, 185 repulsive interaction, 537 resolvation, 23, 24, 30, 36 resonance, 30 short-range interaction, 39, 47 solar, 179 solvation, 13, 24–28, 32, 200 standard transfer, 11 surface, 52, 158 Endocrine disruptors, 775–803 Enhanced cation transfer, 542 Entropic effect, 90 Entropy, 84, 85 nonlocal, 87, 91 Equilibrium, distribution, 110 electrochemical, 3, 13 interfacial, 10 local interfacial, 15 molecular, 52 Nernst distribution, 8 partition, 15, 20 redox, 14 Excitability, 649, 660, 663 state, 654 threshold, 654 Excitable structure, 650 Excitation, 649–679 function, 651 reaction, 650 wave, 649
848 Excluded volume effect, 83 FCCP, 694 Fermi resonance, 146 Fick’s, First Law, 820 Second Law, 820 Field, electrostatic, 658 gravitational, 650 magnetic, 650 FitzHugh-Nagumo (FHN) model, 677 Fixed-bed reactor, 580 Fluorescence, 259–264, 269, 276, 279 spectroscopy, 259, 260, 265, 269, 279 front-face, 270, 275 Fluorescent probes, 258 Fourier transform infrared (FT-IR), 258 Free-volume model, 822 Frumkin isotherm, 132 Fundamental beam, 126 Fundamental wave, 126, 133 Gene, delivery, 807–838 expression, 655 Generalized van der Waals theory (GvdW), 83–103 Genetic information, 526 Gibbs adsorption equation, 106 Gibbs energy, 2 of adsorption, 131 of transfer, 7, 41, 491 Gibbs isotherm, 17 Goldman-Hodgkin-Katz equation, 490 Gouy-Chapmen (GC), model, 198 space charge layer, 158 theory, 115, 117, 159, 171, 429, 447, 454, 549 Haber’s ion-selective systems, 9 Hamiltonian approach to ion-solvent interactions, 30 Hansch equation, 758 Hartree-Fock wave function, 90 Helmholtz equation, 18 Henderson equation, 490 Henry law, 110 Heparin, 595 Herbicide, antibacterial, 664 antifungal, 664
Index [Herbicide] general, 664 High-speed stirring method (HSS), 356 Hodgkin-Huxley (HH) equation, 676, 677 space-clamped, 676 Human Genome Project, 809 Hydrodynamic approach, 68 Hydrodynamic model, 68 Hydrophilic-hydrophobic balance (HLB), 111, 469, 775 Hyperpolarizability tensor, 144 Hyper-Rayleigh scattering (HRS), 142 Ideal gas law, 84 Immobilization, 516, 517 Impedance, 193–194, 427, 521–522, 524 Insect-induced signal, 673–675 Intensity-modulated photocurrent spectroscopy (IMPS), 211, 213–215 Interactions, acid-base, 26 antigen-antibody, 105 Born-type long-range, 30 casein-fat, 277 chain-chain, 146 Coulomb, 92, 102, 156 dipole-dipole,534 electrostatic, 48, 118, 160, 525, 537 headgroup, 538 hydrophobic, 273 intermolecular, 105, 110 ion-induced dipole, 37 ion-ion, 180 ion-molecule, 37 ion-solvent, 30, 32, 37 Lennard-Jones, 56 long-range, 37 molecular, 258, 533 nonlocal, 88 protein-fat, 275, 277, 279 protein-lipid, 274 repulsive, 88 self-consistent-field, 37 short-range, 26, 37, 39, 40, 43 solute-solvent, 26, 358 specific, 51, 201 water-ion, 407 Interface, 1, 2,9, 12, 86, 105, 123, 180 air-alcohol, 127, 128, 145 air-liquid, 105, 124, 127, 229 air-water, 106, 127, 130, 132, 135, 137–139, 144, 146, 147, 288, 318–321, 536, 540, 642–647
Index [Interface] alkane-water, 139, 145 angular distribution, 130 aqueous-membrane, 487, 499, 511 aqueous-organic, 487, 488, 554, 555 biomembrane-water, 696 blocked, 4 charged, 136 complexation, 359–371 coverage, 234 D2O-CCl4, 147 electrified, 2, 59, 66 electrochemical, 1 fat-water, 265, 266, 270, 274, 276 flat, 194 gas-liquid, 258, 316, 355 heptane-water, 134, 363, 534 hexane-water, 145 ideal polarized, 4 lipid bilayer, 778–784 lipid-water, 261, 263 liquid-liquid, 1, 2,4, 19, 105, 106, 119, 123–148, 153–176, 179–222, 229–238, 259, 283, 288, 289, 293, 307– 316, 325–351, 355–372, 415–435, 461, 462, 540, 549, 554, 555, 683–696 dye-sensitized, 179, 183 membrane-peptide, 79 membrane-water, 76 metal-electrolyte, 130, 136, 197 metal-solution, 159, 487 molecularly defined, 216 nonpolarizable, 107 nonpolar-water, 106 oil-water, 115, 257, 260 polar-nonpolar, 410 polarizable, 12, 106, 107, 188 polarized, 136 polymer-solution, 392 porphyrin-sensitized, 217 rigid, 52 semiconductor-dye, 217 semiconductor-electrolyte, 208, 210, 213 solid-liquid, 105, 147, 258, 288, 325, 355, 409–410 solid-solid, 105 solid-solution, 216 water-benzene, 542 water-DCE, 127, 131, 135, 136, 139, 181, 197, 216, 218–220, 542, 546, 547 water-dichloromethane, 218 water-hydrocarbon, 4
849 [Interface] water-n-dodecane, 536 water-nitrobenzene, 182, 191, 233, 236, 237 water-oil, 4, 259, 263, 346, 534, 536–538, 540, 575, 699–714 water-phenol, 629 water-toluene, 204, 363 irregular dynamic fluctuation, 699 polarized, 710 Interfacial, accumulation, 371 adsorption, 371–372, 609–614 area, 359 boundary, 187 capacitor, 54, 55, 63 capacity, 162, 163, 176 charge transfer, 410, 488 complexation, 168 concentration, 180 dynamics, 136 electrical phenomena in green plants, 649–679 electron transfer, 410 equilibrium, 300 formation, 371 ion pairing, 164 ion transfer, 543, 609, 610 kinetics, 302–306, 327, 333 photoisomerization reaction, 403 reaction, 314, 371, 403 reactivity, 136 region, 371, 547 rotation, 371 solvation, 133 spectroscopy, 179 tension, 106 transfer kinetics, 315 Internal reflection fluorescence spectroscopy, 402 Ion-channel concept, 522 Ion-free layer, 186, 197 Ionic partition diagram, 750 Ion-sensitive field-effect transistor (ISFET), 585–593, 602–605 Ion transfer, 487, 488, 498, 504, 510, 534, 540–549 coupled, 205, 488, 498, 503 energy, 24 facilitated, 636 reaction, 204, 510–511 selective, 629–639 spontaneous, 495–496 Irritant, 650
850 Irritation, 649, 650 Isomerization, rate, 139 reaction, 139 Isotherm, amphiphilic, 109 Frumkin, 434 Langmuir, 360, 363, 444, 474 pressure-area, 538, 644, 646 water-oil, 534 ITIES (Interface between two immiscible liquids) 1, 13, 15, 20, 136, 179, 183, 193, 210, 218, 219, 222, 286, 289–292, 295–297, 307, 308, 310, 314, 321, 326, 340, 346, 349, 373, 378, 415– 435, 533, 534, 543–548, 629, 639, 735– 759 microhole-supported, 375, 377 Kelvin probe, 15 Kelvin-Zisman probe, 15 Kinematic viscosity, 328 Kink shift diffusion mechanism, 822 Langevin equation, 174 Langmuir, film, 641–647 isotherm, 132 method, 643 technique, 641, 642 Langmuir-Blodgett, approach, 541 film, 641–647 monolayer, 117 Laplace equation, 71 Latimer diagram, 185 Lattice-gas model, 153–176, 180, 537 Le Hung’s, approach, 5–6 equation, 6, 12 Lennard-Jones fluid, 85, 86, 87, 89, 92 mixtures, 91 model, 84, 88 potential, 89 Linear Circular Dichroism (CD), 130 Liquid jet technique, 334 Liquid-liquid, extraction (LLE), 475–480 bioaffinity-based, 479 nonionic surfactant-based, 479 junction, 180, 183, 191–192, 303, 209, 212, 216, 222
Index Local probe, 283 Lorentz-Berhelot rule, 89 Magic angle spinning (MAS), 778 Mass transfer, 326, 553–580 MC simulations, 57 MFA Mean Field Approximation, 57, 83, 154–156, 537 Membrane, 641, 642 apical, 818 artificial, 1, 609 barrier, 823 basolateral, 818 bilayer lipid, 488, 641 biological, 730, 818, 828 biomimetic, 778 chemically modified, 603 current oscillation, 609–627 induction, 617–622 inhibition, 617–622 enzyme, 596 excitable, 675–678 heparin-immobilized, 595 ion-exchange resin, 488 ion-sensing, 585, 593–595, 598, 600, 604 liquid, 439–466, 488–491, 610, 627, 799–726 ISE, 440 mammalian, 819 mitochondrial inner, 498 model, 676 natural, 1 ion-sensing, 586 permeability, 824 perturbation, 789 plasma, 651, 652, 818 plasticized-PVC, 585, 587, 596, 604 polyvinyl chloride, 488 potential, 611, 663 potentiometric ion, 603 protein, 807 PS II, 642 quaternary-ammonium-encapsulating, 603 reactor, 578–580 resistance, 491 resting, 660 silicone-rubber, 587–590, 596–599, 603–605 Singer-Nicolson fluid-mosaic model, 815 sol-gel-derived, 591–594, 600–605 solvent-polymeric, 585 surface, 824 thylakoid, 641 transport, 487–511
Index Metropolis algorithm, 156 Meyer-Overton, correlation, 776 theory, 797 Michaelis-Menten mechanism, 569 Micro-ITIES, 373–396 Microelectrochemical measurements at expanding droplets (MEMED), 340–349 Microscopy, atomic force, 642, 646, 647 scanning tunneling (STM), 646, 647 surface, 642 Microstructure effects, 241–254 Milk reconstitution, 264, 265 Mitochondria, 652 Mixed solvent layer, 186 Modified Verwey-Niessen model (MVN), 419 Molecular capacitor, 56 Molecular dynamics, 180, 229, 358–359, 819, 820 Molecular probe, 439–466 Molecular recognition of DNA, 515–530 Monte Carlo simulations, 95, 153, 156, 157, 160, 162, 172, 180 Motor end plate, 653 Moving-drop method, 335 Multidrug resistance (MDR), 828, 829 protein, 828 Multiple drug resistance (MDR), 809 Myelin, 653 Nernst equation, 9, 110, 181, 736–737, 752 Nernst-Donnan equation, 308, 346 Nernst-Planck equation, 174, 175, 490 Neuron, 609, 652–653 Neurotransmitter, 683 Neutron reflectance, 258, Newton’s equation, 180 Nicholson method, 192 NMR, 775–803, 816 combined line-broadening-dynamic light scattering, 826 Nonlinear optics, 123–148 Nonlinear polarization, 125, 126, 127, 141 Non-local electrostatic theory, 25 Nucleus, 652 One-component plasma model, 99 Oligodendrocyte, 653
851 Oligomerization reaction, 219 Orbit, connecting, 675 heteroclinic, 675 homoclinic, 675 Overton’s rule, 824 P680, 646, 647 Pentachlorophenol (PCP), 664–665, 694 Pesticide, 661–669, 683 Pharmacokinetics, 808–809 Phase transition, 534, 537, 538 first order, 539 second order, 538 Phloem, 650–679 translocation, 654 unloading, 651 Phospholipid, 533–549 adsorption, 539 zwitterionic, 548 Photocatalysis, 220–222 Photoisomerization, 138–139 Photosynthesis, 641 Photosystem II, 641–647 Photoswitchable ionophore, 439–466 Ping-pong mechanism, 569 Plasmodesmata, 651 Poisson-Boltzmann, equation, 93, 94, 161, 173 theory, 102, 172 Polarized liquid-liquid junction, 179 Polarogram, 631 current-scan, 632 Polarography, 488, 630 Pollutant, 661–669 Polyanions, 28–31 Potential, action, 649–679 adsorption, 1, 17 applied, 688 boundary, 439, 452, 453 chemical, 3, 108, 167, 242–243, 416 Coulomb, 32 dependence, 308 diffusion, 10, 14, 439 distribution, 6, 8,10, 14, 545–546 effective, 31 electrical, 2, 543, 651, 660 electrochemical, 2, 160, 166, 185 electron-transfer, 181, 188 electrostatic, 154, 157, 161 formal, 9, 685, 690
852 [Potential] Galvani, 2, 3,4, 5,7, 8,9, 15, 16, 180, 181, 183, 184, 186, 188, 198–200, 206–212, 214, 220, 415, 416, 536, 543, 547, 548, 685, 711, 732, 752 half-wave, 376, 377, 637, 683 inner, 2, 415 interfacial, 1–20, 200, 707–708 intracellular, 654 ISE, 447 ionic, 14 ionization, 31 ion-transfer, 28, 308 liquid junction, 14 mean force, 165 membrane, 439, 488, 490 oscillation, 609–627 midpoint, 683, 688 mixed, 13, 15 molecular lipophilicity (MLP), 754 observed, 688 operative, 2 oscillation, 699–726 outer, 3, 4 phase boundary, 106, 110, 111, 113 photoinduced, 451 profile, 543 real, 3 redox, 13, 39, 182–184, 188, 189 response, 588, 598 resting, 651 scales, 184 simulated, 547 standard, 181 chemical, 2 equilibrium, 166 ion transfer, ionic, 13 redox, 12 surface, 3, 15, 16, 17, 18, 546, 642–647 transmembrane, 660 window, 116, 631, 693 Volta, 3, 15, 16, 18 Yukawa, 172 zero charge (PZC), 12, 18, 108, 159, 624 zeta, 20 Pourbaix’s diagram, 750 Principal component analysis, 261 Protein, encapsulation, 469–482 extraction, 479
Index [Protein] P, 652 release, 469–482 Proton decoupling, 778 Protonophore, 661–669 Quantitative structure-activity relationship (QSAR), 683, 715, 733, 758–759 Quasielastic light scattering (QELS), 537 Random-mixing approximation, 154 Real-space renormalization group method, 537 Reflex arch, 650 Refractory period, 654 Resolvation, 23–48 Reversed micelles, 556, 575 RNA, 655 Rotational dynamics, 403, 405 Rotation motion, 137 Scanning Electrochemical Microscopy (SECM), 283–321, 386, 391–393, 542 feedback, 289, 293, 307 geometry, 289, 292 induced transfer (SECMIT), 285, 286, 289, 301, 304–306 mode, 299–307 operating modes, 289 theory, 289 Scattering, dynamic light, 258 small-angle x-ray, 258 Second harmonic generation (SHG), 124, 125, 138, 140–142, 180, 403, 439–466 Sensor, 609 amperometric, 592, 596 anion, 602–603 bioaffinity, 522–525 blood electrolyte, 586 electrochemical, 516 gene, 516, 528–530 chemical, 520 ion biocompatible, 585–606 ion-channel, 520 potentiometric, 585, 606 SF6847, 694 Shannon sampling theorem, 658 Sieve plate, 652 Sieve-tube, 654 element, 650, 654 system, 654
Index Shell-Descartes law, 124, 126, 143 Smectic bilayer model (SBM), 70 Solvation, 2, 23–48 dynamics, 400–411 Solvatochromic parameters, 27 Solvent extraction kinetics, 355–372 Solvent reorganization, 138 Solvophobic interaction, 24 Solubility-diffusion, model, 821 theory, 821 Solute transfer, 540 Spectrometry, electrospray ionization mass (ESMS), 630, 631, 635 Spectroscopy, transient absorption difference, 647 Stirred-tank reactor, 578 Stoke shift, 137 Sum Frequency Generation (SFG), 124, 143–147, 180 Surface, activity, 112 adlayer, 529 coverage, 434 excess, 18, 106–108, 338, 415–418 isotropic, 131 pressure, 534, 642, 644 tension, 18, 24, 83–101 dynamic, 537 tension reducing mechanism, 91 vibrational spectra, 145 viscosity, 231 Synapse, 653 Tension, 78 interfacial, 24, 108, 114–115, 536 surface, 24, 69, 71, 109 Time-domain spectroscopy, 407 Time-resolved, fluorescence spectroscopy, 370–371 fluorescence Stokes shift (TRESS),400 quasielastic laser scattering, 229–238 Transition state theory, 167, 168, 186 Total internal reflection (TIR), 123, 357 Transfer energy, 2 standard, 2
853 Tunnel diode, 677 Two-phase, catalysis, 179, 220–222 stopped method, 356–357 Ultramicroelectrode (UME), 340, 373 Uncoupler, 661–669, 683, 693–696 UV-laser photoablation technique, 373 Vacuole, 652 Van der Waals, equation of state, 84 theory, 102 Verwey-Niessen model, 115, 158, 163, 169, 170, 180 modified, 171, 172 theory, 176 Vibrating plate, 15 Vibrational resonance, 143 Vibrational surface spectroscopy, 146 Vibrational surface spectrum, 144–146 VITIES, 610 Voltammetry, 373–396, 487, 488, 683–696 cyclic, 520–521, 683–696 ion-transfer, 41, 612–613, 683–696 of acids, 687–688 of bases, 684–686 of 2, 4-dichlorophenol, 692–694 of doxylamine, 690–692 of procaine, 688–690 normal pulse, 683 potential step, 683 potential-sweep, 683, 688 Voltammetric elucidation, 488 probe, 285 study of drugs, 683–696 theory, 684–688 Voltammogram, 490, 492–494, 542, 618, 632, 688–696 Volta’s law, 655 Volume-fraction-induced percolation, 244 Walden’s rule, 744 X-ray diffraction, 536