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MODERN ASPECTS OF ELECTROCHEMISTRY No. 33

LIST OF CONTRIBUTORS RYOICHI AOGAKI

TORlBIO FERNANDEZ OTERO

National Research Laboratory for Magnetic Science Japan Science and Technology Corporation 1-1-56 Shibashimo Kawaguchi, Saitama 333-0848 JAPAN

Facultad de Quirnica Depto. de Quemica-Fisica Laboratorio de Electroquimica Pa Manual de Lardizabal s/n Apdo. De Correos 1072 20080 San Sebastian, Spain

GERALD L. BAUER 3M Chemicals 3M Center Blg. 236-3C-89 St. Paul, MN 55144-1000 W. VES CHILDS 3M Chemicals 3M Center Blg. 236-3C-89 St. Paul, MN 55144-1000 ENN LUST Department of Physical Chemistry and Electrochemistry University of Milan Laboratory of Electrochemistry Via Venezian, 21-20133 Milan, Italy

PETER G. PICKUP Department of Chemistry Memorial University of Newfoundland St. John's, Newfoundland Canada AlB 3x7 SERGIO TRASAITI Department of Physical Chemistry and Electrochemistry University of Milan Laboratory of Electrochemistry Via Venezian, 21-20133 Milan, Italy

Hahn-Meitner-Institut Bereich Physikal. Chemie Glienicker Str. 100 D-14109 Berlin, Germany

MODERN ASPECTS OF ELECTROCHEMISTRY No. 33 Edited by

RALPH E. WHITE University of South Carolina Columbia, South Carolina

J. O'M. BOCKRIS Texas A&M University College Station, Texas

and

B. E. CONWAY University of Ottawa Ottawa, Ontario. Canada

KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

eBook ISBN: Print ISBN:

0-306-46917-0 0-306-45968-X

02002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print 0 1999 Kluwer Academic / Plenum Publishers New York All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at:

http://kluweronline.com http://ebooks.kluweronline.com

This volume contains six chapters and a cumulative index for numbers 1-33. The topics covered include the potential of zero charge; nonequilibrium fluctuation in the corrosion process; conducting polymers, electrochemistry, and biomimicking processes; microwave (photo)electrochemistry;improvements in fluorine generation; and electronically conducting polymer films. Chapter 1 is a review of literature on the potential of zero charge. Trasatti and Lust discuss the concept of potential of zero charge, electrode potentials, and energy scales, and the relation of the potential of zero charge to other quantities. The experimental aspects of zero charge unfold as they discuss methods for the measurement of the potential of zero charge, estimation of the surface area of solid electrodes, and experimental data. They analyze experimental data by discussing comparisons of compilations, crystal-face specificity, the potential of zero charge and work function, ultrahigh vacuum versus solution data, the concept of "hydrophilicity," other solvents, and indirect evidence of the "interfacial parameter" scale. The second chapter is by Aogaki and includes a review of nonequilibrium fluctuations in corrosion processes. Aogaki begins by stating that "metal corrosion is not a single electrode reaction, but a complex reaction composed of the oxidation of metal atoms and the reduction of oxidants." He provides an example in the dissolution of iron in an acidic solution. He follows this with a discussion of electrochemical theories on corrosion and the different techniques involved in these theories. He proceeds to dscuss nonequilibrium fluctuations and concludes that "we can again point out that the reactivity in corrosion is determined, not by its distance from the reaction equilibrium but by the growth processes of the nonequilibrium fluctuations."

Preface

In Chapter 3, Otero describes conducting polymers, electrochemistry, and biomimicking processes. He discusses the electropolymerization of conducting polymers: electrochemical versus chemical polymerization of conducting polymers; self-doped polymers, polymeric composites, and hybrid materials; the physical properties of dry conducting polymers; electrochemical properties; electrochemistry and electrode structure; experimental chronoamperograms and chronocoulograms under conformational relaxation control; polymer-solvent interactions from the electrochemically stimulated conformational relaxation (ESCR) model; voltammetry under conformational relaxation control; experimental and theoretical voltammograms; experimental and theoretical coulovoltagrams; conducting polymers as soft and nonstoichiometric materials; conducting polymers as three-dimensional electrodes at the molecular level; soft, wet, and complex materials mimicking biological processes; and technological applications of the ESCR model. Microwave (photo)electrochemistry is the topic of Chapter 4. Tributsch begins by discussing some of the history of microwave electrochemical measurements and explaining why they need to be combined with electrochemistry. He summarizes and evaluates some of the new information available from the field of microwave (photo)electrochemistry. He concludes that research opportunities remain unexplored in the field of transient photoinduced microwave conductivity (PMC) measurements at semiconductorelectrodes in the exploration of surface states and representative electrical circuits of semiconductor liquid junctions. He gives credit to the significant knowledge that has been gained about semiconductor electrochemistry in this relatively new field and hopes that more research groups will become involved. Bauer and Childs describe the development of a new fluorine cell design in Chapter 5. They discuss the initial challenge and conceptual model development. They proceed through preliminary engineering modeling, laboratory tests, and more engineering modeling. They conclude with pilot plant tests using commercial-scale anodes in cells similar to those that would be used commercially and state that a pilot plant with four of these anodes with no evidence of anode degradation has been in operation for over a year. The final chapter, by Peter Pickup of Memorial University of Newfoundland, gives a comprehensive account of the major and rapidly developing field of the electrochemistry of electronically conducting polymers and their applications. Following the discovery of these materi-

Preface

vii

als some 20 or more years ago, new fields of electrochemistry, materials science, and synthetic metals have developed in remarkably original ways. The author examines these ways in his thorough and critical chapter, with the support of extensive references to the literature. University of South Carolina Columbia South Carolina

Ralph E. White

Molecular Green Technology College Station, Texas

J. O'M. B o c k s

University of Ottawa Ottawa, Canada

B. E. Conway

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Contents Chapter 1 THE POTENTIAL OF ZERO CHARGE Sergio Trasatti and Enn Lust I. Introductory Concepts ................................ 1 1. Potential of Zero Charge. . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Electrode Potentials and Energy Scales.................. 7 3. Relation of the Potential of Zero Charge to Other Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 I1. Experimental Aspects................................ 30 1. Methods for Measurement of the Potential of Zero Charge.. 30 2. Estimation of the Surface Area of Solid Electrodes...... 42 3. Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 111. Analysis of the Experimental Data ...................... 149 1. Comparison of Compilations........................ 149 2. Crystal-Face Specificity. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 3. Potential of Zero Charge and Work Function ......... 156 4. UHV versus Solution Data.......................... 169 5. "Hydrophilicity" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 6. Other Solvents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 7. Indirect Evidence of the "Interfacial Parameter" Scale... 176 IV . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 References ......................................... 193

Contents

x Chapter 2

NONEQUILIBRIUM FLUCTUATIONS IN THE CORROSION PROCESS Ryoichi Aogaki I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 I1. Active, Passive. and Transpassive States of Metals ........ 222 1. Passive Film Formation ........................... 224 2. Passive Film Breakdown ........................... 232 3. Fluctuation with Film Breakdown and Its Repair ........ 233 4. Film Breakdown Models ........................... 236 5. Stability of Pitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 I11. Nonequilibrium Fluctuations in Corrosion ............... 247 1. Instability of Asymmetrical Fluctuations in Pitting Dissolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 2. Determination of the Pitting Potential ................ 258 3. Determination of Electric Charge Coefficients........... 261 4. Instability of Symmetrical Fluctuations in the Diffusion Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .266 5 . Instability in Ion Transfer through a Protective Film..... 272 6. Determination of Local Corrosion States by Measuring Dissolution Current............................... 277 7 . Morphological Pattern Formation in Pitting Dissolution of the Polishing State ............................. 295 IV. Conclusion ........................................ 302 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Chapter 3

CONDUCTING POLYMERS. ELECTROCHEMISTRY. AND BIOMIMICKING PROCESSES Toribio Fernindez Otero I. Introduction

....................................... 307

Contents

xi

n. Electropolymerization of Conducting Polymers ........... 314 1. Empirical Kinetics of Initiation and Polymerization from

Tafel Slopes.................................... 314 2. Gravimetric ex Situ Empirical Kinetics ............... 318 3. Characterization of the Polymerization Process: Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 4. Electrochemical Characterization of Electrogenerated Films: Storage Capacity ........................... 321 5. Efficiency of the Polymerization Charge in Producing Electroactive Polymers ...........................324 6. Simultaneous Electropolymerization and Degradation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 7. Simultaneous Chemical Polymerization.............. 329 8. Cross-Linking ..................................330 9. Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 10. Conclusions about Electrochemically Initiated Polymerization Processes . . . . . . . . . . . . . . . . . . . . . . . . . 333 HI. Electrochemical versus Chemical Production of Conducting Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 IV. Self-Doped Polymers, Polymeric Composites, and Hybrid Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 . V . Physical Properties of the Dry Conducting Polymers ....... 336 VI . Electrochemical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 1. Composition and Conductivity . . . . . . . . . . . . . . . . . . . . . . 341 2. Electrochemomechanical Properties. Molecular Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 3. Macroscopic Motors. Artificial Muscles ...............343 4 . Color Mimicking . Electrochromic Properties . . . . . . . . . . . 361 5. Storage of Energy . Polymeric Batteries ................ 367 6. Electron-Ion Transduction .......................... 369 7. Electroporosity and Smart Membranes ................ 372 VII . Electrochemistry and Electrode Structure . . . . . . . . . . . . . . . . 372 1. Electrochemically Stimulated Conformational Relaxation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 2. Anomalous Electrochemical Results.................. 375 3. Conformational Relaxation Time..................... 377 4. Nucleation and Expansion of the Oxidized Amorphous Regions .........................................382

xii

Contents

5. Anodic Chronoamperograms under Conformational Relaxation Control ............................... 384 6. Coalescence between Oxidized Regions . . . . . . . . . . . . . . 385 7. Relaxation-Controlled Oxidation . . . . . . . . . . . . . . . . . . . . 385 8. Diffusion-Controlled Completion of 0 xi d a t i o n ......... 389 9. Theoretical Chronoamperograrns and Chronocoulograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 VIII . Chronoamperograms: Experimental and Theoretical ....... 392 1. Influence of the Cathodic Potential of Prepolarization and Closing of the Structure........................ 394 2. Influence of Anodic Potential on the Opening and Oxidation of the Polymer . . . . . . . . . . . . . . . . . . . . . . . . . . 395 3. Influence of Temperature on Polymer Oxidation ........ 396 4. Influence of Electrolyte Concentration................ 397 5. Separation of the Relaxation and Diffusion Components... 397 IX. Polymer-Solvent Interactions from the Electrochemically Stimulated Conformational Relaxation Model ................ 398 X . Chronocoulograms .................................. 404 XI . Voltammetry under Conformational Relaxation Control...... 408 1. Growth of the Conducting Zones . . . . . . . . . . . . . . . . . . . . 410 2. Diffusion-Controlled Completion of Oxidation . . . . . . . . . 415 3. Anodic Voltammograms . . . . . . . . . . . . . . . . . . . . . . . . . . .418 4. Anodic Coulovoltagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 419 XI1. Experimental and Theoretical Voltammograms............ 420 1. Relaxation and Diffusion Components................ 421 XI11. Experimental and Theoretical Coulovoltagrams........... 422 XIV. Conducting Polymers as Soft and Nonstoichiometric Materials . Electrochemical Evidence ................... 423 XV. Conducting Polymers as Three-Dimensional Electrodes at the Molecular Level ................................. 424 XVI . Soft, Wet, and Complex Materials Mimicking Biological Processes ................................ 425 XVII. Soft Materials and Electrochemical Applications . . . . . . . . . . 426 XVIII. Technological Applications of the ESCR M o d e 1........... 427 Acknowledgments .................................. 428 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

Contents

Chapter 4 MICROWAVE (PHOT0)ELECTROCHEMISTRY

H . Tributsch I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 1. Electrochemistry Combined with Microwave Measurements ................................... 435 2. Electric Transport in Materials at Microwave Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 3. Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .440 I1. Experimental. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 1. Required Properties of Electrode M a t e r i a 1s .............441 2. Electrodes ....................................... 443 3. Microwave Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 4 . Stationary Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . 447 5. Time-Resolved Measurements ....................... 447 6. Space-Resolved Measurements ...................... 450 7. Microwave Phase Detection Experiments .............. 451 8. Potential Sweep or Potential Modulation Techniques ... 455 111. Theoretical Challenge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 1. A Fully Determined System......................... 457 2 . Measurement Opportunities and Prospects of Microwave Electrochemistry........................ 460 3. Analytical Expression for Potential-Dependent Microwave Conductivity ........................... 461 4. Accuracy of Derived Analytical Formulas . . . . . . . . . . . . . 464 IV. Potential-Dependent Stationary Microwave Conductivity Measurements........................... 469 1. n-Type Semiconductor/ElectrolyteJunctions . . . . . . . . . . . 469 2. Metal Oxide/Semiconductor Junctions . . . . . . . . . . . . . . . .472 3. p-Type Semiconductor Electrodes .................... 475 4 . Meaning of the Dammed-Up Charge Carriers........... 475 5. PMC Decay in the Depletion Region ................. 479 6. Determination of Flatband Potential.................. 483 7. Determination of Interfacial Rate Constants ............ 485 8. Accumulation Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487

xiv

Contents 9. Influence of Surface Recombination on the PMC

Signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .490 10. Quantitative Data from PMC Measurements: The Sensitivity Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 V. Potential-Dependent Time-Resolved Me as u r e m e n t s ........ 493 1. Experience with Time-Dependent Measurements . . . . . . . 493 2. Control of Interfacial Lifetime in Silicon with Polymer/Electrolyte Junction . . . . . . . . . . . . . . . . . . . . . . . 497 3. Potential-Dependent Measurements with Organic Electrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .501 4. Access to Kinetic Constants via PMC Transients ...... 503 VI . Potential-Dependent Periodic Measurements ............. 506 1. Potential Modulation-Induced Microwave Reflectivity.... 506 2. Combination of Intensity-Modulated Photocurrent and Microwave Spectroscopy .......................... 508 VII . Oxides and Sensitization Cells ........................ 510 1. Potential Dependence of Interfacial Rate Constants...... 510 2. Nanocrystalline Dye SensitizationCell Studied by Microwave Transients ............................. 514 VIII . Microwave Phase Measurements ....................... 514 IX . Summary and Discussion ............................. 516 Acknowledgments .................................. 520 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

Chapter 5 IMPROVEMENTS IN FLUORINE GENERATION Gerald L. Bauer and W. Ves Childs I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 I1. The Challenge .....................................524 1. Preliminary Considerations ......................... 524 2. Application of Some Fundamentals of Wetting to the Problems ....................................... 530 3. An Engineering Model for the Flow of Fluorine in the Grooves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532

xv

Contents

4. Estimating Production Rates for Hydrogen and Fluorine ........................................ 535 5. Anode Life in the Laboratory . . . . . . . . . . . . . . . . . . . . . . . 536 6. Additional Preliminary Considerations for the Piiot Plant.... 538 7. More Engineering Models .......................... 539 8. Practical Large Anodes ............................ 542 Acknowledgments .................................. 545 Appendix: Notes on Laboratory Operations .............. 545 References ................................................. 547

Chapter 6 ELECTROCHEMISTRY OF ELECTRONICALLY CONDUCTING POLYMER FILMS Peter G. Pickup I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 11. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 111. Electrochemical Polymerization and Film Deposition ..... 554 IV. Cyclic Voltammetry ................................. 558 1. p-Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 2 . n-Doping ....................................... 562 V . Overoxidation ...................................... 563 VI . Charge Transport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567 1. In Situ Electron Transport Measurements . . . . . . . . . . . . . . 568 2. Ion Transport ................................... -573 VII. Solvent Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. 582 VIII. Charge-Transfer Kinetics ............................. 582 M. Nucleation Models for Oxidation of Conducting Polymers ... 584 X . Mediation of Redox Reactions in Solution ............... 585 XI . Electrocatalysis ..................................... 588 XI1. Ion Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588 XI11. Conclusions ........................................ 590 Acknowledgment ................................... 591 References ......................................... 591

The Potential of Zero Charge Sergio Trasatti Department of Physical Chemistry and Electrochemistry, University of Milan, 20133 Milan, Italy

Enn Lust Institute ofphysical Chemistry, University of Tartu, 2400 Tartu, Estonia

I. INTRODUCTORY CONCEPTS 1. Potential of Zero Charge An electrode is customarily thought of as an ensemble of an electronic conductor (most frequently a metal) in contact with an ionic conductor (electrolyte solution, solid electrolyte, or molten salt). It is the change of charge carriers from ions to electrons across the interface that makes it possible to convert chemical into electrical energy (and vice versa) because ofthe vanishingly small solubility of metals in most solvents (apart from the instability of electrons in liquids). In some organic solvents the solubility of specific metals is such that they behave as sparingly soluble salts. In these cases a metal in solution is no longer an electrode; it is a system in chemical equilibrium and as such is unable to perform work. As a metal is brought in contact with an electrolyte, various phenomena occur that result in the onset of an electric potential difference where M and S stand for metal and solution (the most usual electrolyte), respectively. The kind of phenomenon depends on the nature of the

(eM

Modern Aspects of Electrochemistry, Number 33, edited by Ralph E. White et al. Kluwer Academic/PlenumPublishers, New York, 1999.

SergioTrasatti and Enn Lust

2

interface. In this respect, two limiting categories are considered1: polarizable and nonpolarizable interfaces, respectively, depending on whether the phase boundary is permeable to charged species (of any knd, electrons or ions). These limiting cases describe ideal situations. Real interfaces behave intermediately, approaching one of the two best. Thermodynamically, all metal/solution interfaces are nonpolarizable, i.e., they can exchange electrical charges freely across the phase boundary. It is the extreme slowness of these exchanges that turns a nonpolarizable into a polarizable interface. Therefore polarizable interfaces are a limiting case of nonpolarizable interface^.^

(i) Nonpolarizable Interfaces Nonpolarizable interfaces correspond to interfaces on which a reversible reaction takes place. An Ag wire in a solution containing Ag'ions is a classic example of a nonpolarizable interface. As the metal is immersed in solution, the following phenomena occur3:(1) solvent molecules at the metal surface are reoriented and polarized; (2) the electron cloud of the metal surface is redistributed (retreats or spills over); (3) Ag' ions cross the phase boundary (the net direction depends on the solution composition). At equilibrium, an electric potential drop occurs so that the following electrochemical equilibrium is established:

from which

Equation (2) is nothing but the well-known Nernst equation. It shows that (p eS)is governed by the composition of the solution and cannot be changed without changing the latter. The redistribution of charges leading to Eq. (1) involves both free charges and dipolar layers. Therefore (p- eS)can be split into two terms4:

-

(P- $9= g ( W * g(dip) where ion stands for free charges. Therefore, from Eq. (2):

(3)

The Potential of Zero Charge

3

In Eq. (4) the left-hand side (1.h.s.) expresses the thermodynamic driving force, while the right-hand side (r.h.s.) gives a structural, physical description of the interfacial region.' Since pyg+is a constant while pi,+ can be varied, there exists a composition of the solution at which the charge located at the interface vanishes. Under these circumstances g(ion) = 0 and Equation (5) shows that the electric potential drop consists only of dipolar contributions. The corresponding electrode potential is what is termed the potential of zero charge (pzc). If the concentration of the metal ion is not negligible at the potential of zero charge, the electrode potential varies linearly with log c according to Eq. (2) and there is no distinctive sign of the situation where the charge at the interface vanishes. The Nernst approach is obviously unsuitable for defining the nature and the amount of the charge at an interface. If the concentration ofthe metal ion at the pzc is small or very small, the behavior of the interface becomes that of a polarizable electrode.

(ii) Polarizable Interfaces Since a metal is immersed in a solution of an inactive electrolyte and no charge transfer across the interface is possible, the only phenomena occurring are the reorientation of solvent molecules at the metal surface and the redistribution of surface metal electron^.^' The potential drop thus consists only of dipolar contributions, so that Eq. (5) applies. Therefore the potential of zero charge is directly established at such an interfa~e.~>'-'~ Experimentally, difficulties may arise because of impurities and local microreactions~but this is irrelevant from the ideal point of view.

(iii) Total and Surface Charge Equation (5) tells us that the potential of zero charge is the same for the same metal under both nonpolarizable and polarizable conditions (provided no other effects are present). This is true from a structural point of view in that the presence of metal ions in solution only provides surface charging conditions. However, the charge referred to earlier as the one governing the magnitude of g(ion) is the charge physically residing on either side of the metal/solution interface. T h s is not the charge therrno-

4


dynamically defined by the Gibbs equation and therefore the one experimentally determinable. This aspect has been emphasized by ~ r u r n k i nand ~ 1,8,11 discussed several times in the literature. At constantp and T, the Gibbs adsorption equation for an electrode interface leads to the well-known Lippmann equation12:

where y is the surface tension of the metal, E is the electrode potential, p includes all independent components of the solution, and q is the electric charge per unit area of the interface. For an ideal polarizable electrode, q has a unique value for a given set of conditions.' It measures the elechic charge residing on either side of the interface; in this case it is replaced by the symbol a (surface charge density). On the metal it is determined by the surface excess or deficiency of electrons. For an ideally polarizable electrode, q has a unique value for a given set of conditions.' For a nonpolarizable electrode, q does not have a unique value. It depends on the choice of the set of chemical potentials as independent variables1 and does not coincide with the physical charge residing at the interface. This can be easily understood if one considers that q measures the electric charge that must be supplied to the electrode as its surface area is increased by a unit at a constant potential." Clearly, with a nonpolarizable interface, only part of the charge exchanged between the phases remains localized at the interface to form the electrical double layer. As an alternative vie^,^>'^ in the case of a metal in a solution containing ions of the same metal, the charge is defined by

where rM+ is the amount of metal ions that must be supplied to the solution to keep its composition constant. Thermodynamically this is the only charge that can be determined experimentally. q includes the free charge at the interface:

where Ahl+(the symbol has been introduced by rumk kin)" is the fraction of charge that has crossed the interface moving from one phase to the other. This charge is not found at the interface.


5

A nonpolarizable interface behaves as a capacitor C and a resistor R in parallel; a polarizable interface responds as a pure capacitor. The higher the resistance R, the closer the behavior of the former to the latter. For R 4 =, a nonpolarizable interface becomes polarizable. The condition R + = corresponds to AM++ 0. This condition is met when the amount of M+ in the null solution is negligibly small. As a consequence of the thermodynamic analysis sketched above, it has been proposed14to call the potential at which q = 0, the potential of zero total charge (pztc), and the potential at which q = a = 0, the potentia of zerofree charge (pzfc). The latter definition is rigorous only ifphenomena of partial charge transfer in chernisorbed species are absent. A potential of zero total charge has been observed and measured only for the Pt group metals due to chernisorption of H atoms. In all other cases, the pzfc is usually observed and measured. The latter will be termed for simplicity potential of zero charge (pzc), and denoted by Eed.

(iv) Importance of the Potential of Zero Charge The most important quality of the pzc is that it contains information about the structural details of the metal/solution interface. In the absence of surface-active electrol tes, the pzc depends only on the nature of the metal and the solvent.3~4~~Conversely, the pztc is not exclusively relevant to the structure of the interface; this is truer the larger the value of AM+ in Eq. (8) (or ofAi where i is the species to which the electrode is reversible; e.g., W+ for the Pt group metals in the H adsorption region). For a metdsolution interface, the pcz is as informative as the electron work function is for a metal/vacuum interfa~e.~."It is a property of the nature of the metal and of its surface structure (see later discussion); it is sensitive to the presence of impurities. Its value can be used to check the cleanliness and perfection of a metal surface. Its position determines the potential ranges of ionic and nonionic adsorption, and the region where double-layer effects are possible in electrode kinetics.8,10,16 Although the pzc contains all the essential structural information about the metal/solution interface, this information is not immediately apparent but must be appropriately decoded. Ths necessitates a description of (qM - $'lo in microscopic terms that require a minimum of model a s ~ u r n ~ t i o nAnother s . ~ problem is that (#M - #s)o is not directly accessible to experimental determination. What is actually measured, usually de-

6

Sergio Trasatti and Enn Lust

noted by End is (#M - b '# plus additional terms.l7 A discussion of this point is necessary before examining the experimental data. Since the measured Ed is a quantity relative to a reference electrode, an analysis of the relationship between relative and "absolute" potential scales is also ne~essary.~

(v) Previous Reviews The relevance of the pzc to the structure of the metal/solution interface and its relation to the metal/vacuum situation was first emphasized by Frumkin and Gorodetrkaya in 1928.18The first compilation of pzc values was prepared by Frumkin in 1933." The notion of pzc is absent in early textbooks. A table with pzc values for about 10 metals (but for only 5 are reliable values claimed) was given by Parsons in 1954 in the first volume of this ~eries.~ After a more complete attempt by Frurnlun in 1965~' to compare EM and work function, extensive work on pzc was reported by Perkins and Andersen9in this series and by Frumkin et alB8in another series. Compilations of pzc values were also made by ~ a m ~ a n e l l a~, 2r ~ a s a t t i , 6Frumkin .~~ et al.," and Frumkin and petrii14 up to 1979. A book by rumk kin" devoted entirely to the potential of zero charge was published posthumously in 1979. It appears that no comprehensive review was published after Perkins and Andersen' s work. Nevertheless, articles devoted to particular aspects have been written. Thus collections of data were compiled by Hamelin et a1.24for single-c stal face electrodes (Cu, Ag, Au, Sn, Pb, Zn, and Bi) in 1983, by Trasatt?126 in 1986 and 1992, by Khrushcheva and ~ a z a r i n o v ~ ~ in 1986, and by Lust et al." in 1996 for Bi, Sb, and Cd. Owing to the rapid development of the field from an experimental point of view, and the persistence of discussions on some of the aspects outlined above, a chapter on the pzc that includes a discussion of the relation between the electrochemical and the ultrahigh vacuum (UHV) situation in reference to the conditions at the pzc seems timely. This review of the literature will not be exhaustive but selective, taking into account the compilations already existing. In any case, the objective is to evaluate the existing data in order to recommend the most reliable. Finally, the data on pzc will be discussed in comparison with electron work function values. The role and significance of work functions in electrochemistry were discussed by ~ m s a t tin i ~1976.


2. Electrode Potentials and Energy Scales

-

(i) Measurability of (p f)o Drops in electric potential between dissimilar phases are not experimentally mea~urable.~~ This aspect was discussed at length in the literature between the early 1970s and 1990. The discussion was about what is actually measured as electrode potentials are measured. Now a general consensus seems to have been acheved. While readers are referred to the original literature,3,5,15,17,29-31 the main conclusions are summarized here. The measurement of ( Q -~4)requires that the two terminals of the measuring instruments be connected to M and to S, respectively. While the former is a metal-metal contact, the latter implies immersion of the metal of the terminal (e.g., Cu) in solution. Thus a new interface (a new electrode) is created. Instead of (#M - #'), the sum of three A# is thus

where @' differs from for the electrical state of the metal. Since Cu and M are in electronic equilibrium @FU=jir):

From Eqs. (9) and (10):

(eM

Equation (I I) shows that instead of (#M - f), or a relative value of #'), a difference in electronic energy (expressed in volts) is actually measured. This is perfectly reasonable since electrons move in an external circuit because their total energy (and not only the electrical part) is different in the two electrodes. A more general approach has been recently provided by ~ r a s a t t i . ~ ~ . ~ ~ Let us consider the cell illustrated in Fig. l(a), whose potential difference is AE:

If M and R are in the same solvent S containing only an inert, surface-inactive supporting electrolyte, AE equals the difference in the potentials of zero charge between the two metals:

m

M ._ ...*...-..I.

*.

R W

'.

9*

I

A€

s..+

f

\ W

@I Figure 1. Sketch of an elechhemical cell whose equilibrium (open circuit) potential diffmnce is U.(a) Conventional configuration a d (b) short-circuited configuration with an air gap. M and R are he -, S is the solvent (ektmlyte solution). Cu indicates the cab& connedng the two e h d e s to a measuring instnunent (or to each other). P is the work to msfer an electron from M (or R) to the exterior of the phm h g h S.

Cu is the metal constituting the cables connecting the terminals of the cell to the measuring instrument. The work to bring an electron from M to R is equal to %A& along the external cirmit and includes the contributions of the two electrodes [Eq. (13)] which, however, cannot be measured separately if only cell (a) is used. Actually, since the terminals are of the same metal, we have

i.e., the measured potential differenceequals the Volta potentid difference between the two terminals. Therefore

Let us consider now the same cell but in a different configuration, shown in Fig. I@):


9

If the two Cu cables are short circuited while the cell is broken into two parts by splitting the liquid phase, it can easily be proved that the same AE as for cell (12a) is measured as a contact potential difference (cpd) between the two solutions. In fact

Since Aly depends only on the nature of the phases in contact and not on their actual electrical state, AE in Eq. (16) must equal AE in Eq. (15). However, in the cell of Fig. l(b) it is readily seen that the work to bring an electron from M to R is zero, so that

where @' is the work to extract an electron from the metal across the solvent. Therefore @* measures the energy of the electrons in the metal constituting the electrode." Equation (17) is similar to Eq. (13); in both cases the outcome is that AE measures a difference in electronic energy. However, Eq. (17) is more complete since it consists of measurable quantities while Eq. (13) is incomplete for a constant term, which turns out to be dropped. This is a consequence of the approach used to separate All into the various components.

(ii) Components of the Electrode Potential Equation (17) expresses the cell potential difference in a general way, irrespective of the nature of the electrodes. Therefore, it is in particular valid also for nonpolarizable electrodes. However, since #*can be better envisaged in terms of interfacial structure, only polarizable electrodes at their potential of zero charge will be discussed here. It was shown earlier that the structural details are not different for nonpolarizable electrodes, provided no specifically adsorbed species are present. As a metal comes in contact with a liquid polar phase (a solvent), the situation can be depicted as in Fig. 2. The electron work function will be modified by A@ so that

where @ is the electron work function in UHV (metal/vacuum)conditions. A@ is a contact potential difference between M and S:

Figure 2. Sketch of an uncharged metal surfam (simulated by the jellium d l ) c o d t a~ 'c solvent layer, showingthe a q m n t s ofthedechk potential

w.x

+ ~ ~ ~ ~ o f t h e m a , ~ b y t f i e m l v e n t lxSa +y e r ; is the surface potential of the solvent m a e d by the contact with the metal; xSis the unmodified srrrface p e a l ofthe solw layer at ltextend surface.

thus A@ is a measurable quantity. According to Fig. 2, as M comes in contact with s , the ~ electron distribution at the metal surface (giving the surface potential xM)will be perturbed (&M). The same is the me for the surfaceorientationof solvent molecules (yS+ 6 x 3 In addition, a potential drop has to be taken into account at the free surface of the liquid layer toward the air kq. On the whole, the variation of the electron work function (if no charge separation takes place as assumed at the pzc of a polarizable electrode) will measure

the extent of perturbation at the surfaces of the two phases, i.e., where dXMand 6~~depend on the nature of S and M,respectively. In addition, they are in principle, especially bxS, sensitive to the presence of free charges. Thus, for a metal at a different potential from Em4, A@ includes one more term:


11

where the subscript a is used to denote a charged interface. g(ion) = Oas a = 0. Clearly, contact potential differences for charged electrodes do not possess any straightforward structural character in view of the nonseparability of the two terms on the r.h.s. of Eq. (21).

(iii) Potentials in the UHV Scale From Eqs. (13) and (17) it is readily evident that

seavs. UHV = Equation (22) shows that since electrode potentials measure electronic energies, their zero level is the same as that for electronic energy. Equation (22) expresses the possibility of a comparison between electrochemical and UHV quantities. Since the definition of @ is6"the minimum work to extract an electron from the Fermi level of a metal in a vacuum," the definition of electrode potential in the UHV scale is "the minimum work to extract an electron from the Ferrni level of a metal covered by a (macroscopic) layer of solvent." While there are no problems in the definition of the configuration leading to @*, difficulties are encountered in the procedure to reproduce the electrochemical situation. In fact, Eq. (17) has meaning only if the MIS interface has exactly the same structure during the measurement of E (relative to a reference electrode+lectrochemical configuration) as well as during the measurement of @*. For correlating relative End values with values in the UHV scale (@* values), two quantities must be known: @ and A@. Contact potential measurements at metal/solution interfaces can be mea~ured.~ In that case the interfacial structure is exactly that in the electrochemical situation (bulk liquid phase, room temperature). However, @to convert E into @' must be independently known. It may happen that the metal surface state is not exactly the same during the measurements of @and A@. On the other hand, surface physicists often measure @* which represents the work function of metals as modified by adsorption of polar (water) molecules.35-39 What they are measuring (although they may not realize it) is precisely the potential of zero charge of the given metal in the UHV scale. The value of @ is exactly known in that case, but the relevance of the value of A@ is in d ~ u b t . ' ~ ~In" fact, only a few layers of a solvent

on a metal surface may not reprduce the actual electrochemical situation in which the liquid phase p s m s e s the pqerties of a bulk phase. Moreover, # measurements are customarily carried out at very low temperatures (15&200 K) at which the interfacial structure may differ from the actud one at an elecbode. Finally, UHV conditions ofmeasurement ensure neutrality of the interface, not of the metal surface, as required by the electmhemical situation. In a uw of partial charge transfer, the UHV configuration may include an addrtional term, or one differing in some way from that at the actual electrcde interface. A third experimental configuration was pro@ by Kolb and Hansen? emmed electrda. Ifan elscb.ode is emend from a solution while the control of the potential is maintained, the solvent layer dragged off with the metal (FI~.3) would reproduce UHV conditions, but with potential control and at room temperature, as in the actual electrode situation. This appears to be the most convenient configuration for measuring #'. Howeva, there are doubts that the solvent la a retains the properties of a bulk phase. It has in fact been demonstratedX that a contact potential difference exists between an elwtmk in the emersed state and the same electrode regularly immersed in solution.

Figm 3. Sketch of an emersedelam&. M is the metal, S is hhe solvent ( e h l y t e solution). (a) W is the work to exmt an electron from M through S.(b)The wnessed ekdmk drags a liquid layer with it, thmugh which the mw,urement of W is apKarenty the same as in (a). The question mark is meant to cast doubts on that.

The Potential of Zero Cholrge

(iv) EO(P/lZIa)versus UHV Electrode potentials are customarily tabulated on the standard hydrogen electrode (SHE) scale (although the SHE is never actually used experimentally because it is inconvenient in many respects). Therefore, conversion of potentials into the UHV scale requires the determination of EO(H+iH2) vs. UHV. According to the cunqts developed above, such a potential would measure the energy of electrons in the Pt wire of the hydrogen electrode, modified by the contact with the solution. Table 1 shows that two ranges of experimental values are available for the SHE in the UHV scale: one, determined with higher accuracy: is 4.44 V (4.44 eV is the energy of eIectrons in the metal of the electrode), and the other is close to 4.8 V. It is intriguing that the fmt value has been obtained with an Hgj et electrode in two different labmt~ries~~" about 30 years apart with a reproducibility of better than 3 mV. In practice, A@ has been measured between Hg and a suitable solution. All of the uncertainty comes5 from the value of the work function of Hg taken from the literature as 4.50 f 0.02 eV. The uncertainty concernsM in particular whether the Hg surface in the stream is really bare, or if it is contaminated by the atmosphere (water vapor and oxygen). Experiments carried out by Hansen et ol."" have demonstrated that there should be no effect ofthe atmosphere on the state of the Hg surface, which is thus to be regarded as clean. However, it is remarked that no

14


recent @ value has been reported for Hg, which is presumably related to problems of metal evaporation under UHV conditions. A value close to 4.8 V has been obtained in four different laboratories using quite different approaches (solid metaVsolution emersed electrodes?47 work function changes4'), and is apparently supported by indirect estimates of electronic energy levels. The consistency of results around 4.8 V suggests that the value of 4.44 V is probably due to the value of @ not reflecting the actual state of an Hg jet or pool. According to some authors,44the actual value of @ for Hg in the stream should be 4.8 V in that the metal surface would be oxidized. It seems hard to support the above hypothesis on the basis of work function measurements for Hg in the presence of residual gases. Adsorption of water indeed reduces the work function and this is also the case with inert gases. There remains the possibility of surface oxidation by residual oxygen, but the values of Aly measured with the Hg stream have been to be stable even in the presence of O2 impurities provided the gas flows rapidly, as was the case during the experiments. The same conclusion has been reached recently by measuring the work function of Hg in ambient gas.& On the other hand, potential measurements at the free surface of purified water have shownsothat the value for a flowing surface differs by about 0.3 V from that for a quiescent surface, as a result of adsorption of surface-active residual impurities in the solution (probably also coming from the gas phase). Since emersed electrodes drag off the surface layer of the solution as they come out of the liquid phase, the liquid layer attached to emersed solid surfaces might also be contaminated. It is intriguing that upon emersion the value of A@ changes up to about 0.3 V compared with the immersed state.41This has been a t t r i b ~ t e d ~to~ . ~ ' the different structure of the liquid interfacial layer in the two conditions. In particular, the airlsolvent interface is missing at an emersed electrode because of the thinness of the solvent layer, across which the molecular orientation is probably dominated by the interaction with the metal surface. The situation believed to exist at an emersed electrode is sketched in Fig. 4. It is seen that while A@ in the immersed state is given by Eq. (20) rewritten as

The Potential of Zero Charrge

Water

F

-4. Sketch to illustrate the W o n believed to exist at a mml surfowe upon ~ C q t i o n ~ f ~ f r o m t h e phase(w&tbeslaC&wof gas an e& ek&&). In pdcular, tfte layer t h k h is~ 80~ dthat tmie orieamion of solvent molecules at the exkmd surface is songgly affemd by the mkmticm d the i n m d surface. where gs(dip) is the surface potential contribution due to oriented solvent dipoles at the metal surface, A@ in the ernersed state can be tentativety written as

where X S is the dipole contribution at the unperturbed solvent surface toward air, its value is estimated7 to be positive around 0.1 V. gA(dip) is the dipole contribution beyond the normal surface layer. In view of the thickness of the solvent layer, the orientation in these layers is probably the same as that in the surface layer adjacent to the metal, which is believed to make a negative conbibutionm2* T h e ~ e f assuming ~~, dX and gs(dip) do not change in the two cases, the difference in work function between immersed and em& states arnounts to [x' g'S(diP)].~heexperirnents carried out by Samec et al?' provide unquestionable proof that emersed electrodes are not the most appropriate tool for determining potentials in a UHV scale. There remains the estimated value of eD(WM2)vs. UHV based on binding energies for image potential-induced surface statesPg which is,

-

16


however, difficult to assess both quantitatively and qualitatively. For the above reasons, for the time being the value of 4.44 V is preferred here and will be used in what follows. This value, however, does not convince most surface physicists, as mentioned earlier. The debate will not be completely terminated as long as a new determination of work function for Hg is carried out under conditions believed to be the most appropriate for such a system. A further contribution to the discussion will be provided in the following section on the basis of indirect evidence.

(v) Mercury: A Reference Surface Although liquid Hg would never be used as a reference (model) surface in surface physics because its liquid state and high vapor pressure do not allow appropriate UHV conditions, this metal turns out to be a reference surface in electrochemistry for precisely the same reasons: reproducibility of the surface state, easy cleaning of its surface, and the possibility of measuring the surface tension (surface thermodynamic conditions). In particular, the establishment of a UHV scale for potentials is at present based on data obtained for Hg. The contact potential difference between Hg and water (actually a dilute aqueous solution of a surface-inactive electrolyte) has been measured'?." to be -0.25 V. The negative sign means that the work function of Hg decreases upon contact with water. Since 4.5qf0.02)eV is the currently acceptedSvalue for @ of Hg, the value of 0' for the uncharged metal (at the potential of zero charge) is 4.25 eV. There are no direct, reliable measurements of @'based upon adsorption of water from the gas phase. Therefore, 4.25 eV applies to a macroscopic water layer as in the electrochemical configuration. The decrease in upon water adsorption is a general occurrence with metals. The value of A# observed with Hg is the lowest among those available in the l i t e r a t ~ r e With . ~ ~ >reference ~~ to Eq. (20), this means that the perturbations of the surfaces of the two phases are small for the Hglwater contact. In other words, the interaction between Hg and water is weak (hydrophobic). The decrease in @ implies a negative value of axMor 6xS,or both. No attempt will be made here to separate the two contributions: this has been done elsewhere.6,7,25,52 We keep here to the measured value. What we can say is that the modifications occurring in the surface regions of the two phases are such as to decrease @ and that even larger modifications are observed with other metals, always in the negative direction. Since X S


17

for water is estimated to be around 0.1 V, a negative implies a reorientation leading to a less positive value. A negative value of GXM(the electronic theory ofmetals tells us3 that the spillover ofelectrons produces positive XM, even for solid surfaces) implies that the electron tail contracts as the metal comes in contact with the solvent. The potential-of-zero charge of Hg in water is known with high precision, i.e.,53-0.192(M.O01)V vs. saturated calomel electrode (SHE). It can be converted to the UHV scale if a' for the SHE is known. Actually, the value of 4.44 V vs. UHV for SHE has been derived5 from

E"(H*/H3 vs. UHV = E,*(Hg) vs. UHV - E,+(Hg) vs. SHE (25) Conversely, let us examine the situation from a different point of view. Let us suppose that the UHV value for SHE is about 4.8 V. In this case the UHV value for EgSO of Hg would work out to be 4.61 V. This would measure @*, the work function of Hg in contact with water. If@ for clean Hg is indeed 4.50 V as measured, the outcome is that the work function of Hg would increase by 0.11 eV upon contact with water. This result is highly improbable on the basis of common observations. On the other hand, the objection of some surface physicists is that the @ of Hg under the conditions of experiments carried out with a stream would be different from 4.50 eV because of surface contamination. If this is the case, the actual work function would be higher. However, contamination normally leads to a decrease in work function, especially if the contaminating species is water35'36or an inert gas." An increase in work function would be possible if oxygen were chemisorbed, which has been ruled out experimentally. If an oxide layer is formed, a decrease in 8 is also expected. On the other hand, if the @ of Hg in the stream is modified by contamination in the cpd measurement, this should not be the case during the measurement of the potential-of-zero charge. If the value of 4.8 eV is accepted for the SHE in the UHV scale, the value of4.61 eV for @*ofHg at the pzc would imply that for @to decrease upon water adsorption, the @ of clean Hg should be substantially higher than 4.61 eV. No experimental evidence exists for this for the time being. In conclusion, acceptance of 4.8 V as the potential of the SHE in the UHV scale leads to apparently contrasting arguments: on one hand, the experiments with the streaming electrode leading to 4.44 V are vitiated by surface contamination of Hg, whose actual @wouldbe about 4.8 V during the experiments. On the other hand, a decrease in @ upon contact with

18


water in the measurement of Ea=o for Hg vs. SHE would require that @ be substantially higher than 4.61 V. Thus the two arguments would converge to claim almost the same value of 4 for the clean as well as the contaminated surface of Hg. The discrepancy would be resolved if about 4.8 eV were the actual work function of clean Hg. In this case, however, it would be difficult to understand why 4.50 eV has been consistently measured: it is hard to imagine what kind of contamination is responsible for such a highly reproducible situation. On the other hand, if 4.80 eV were the value of @ for clean Hg, then most of the other metals would show a decrease in work function upon water adsorption less negative than Hg, which is at variance with the expected chemistry of metal surfaces (see later discussion).

3. Relation of the Potential of Zero Charge to Other Quantities

(i) Electrode Potential versus Work Function Equation (17) shows the relationship between electrode potentials and electronic energy. The electrode potential is measured by the electron work function of the metal, modified by the contact with the solution (solvent). This establishes a straightforward link, not only conceptually but also experimentally, between electrochemical and UHV situations.6332 In many cases, electrochemical interfaces are "synthesized in UHV conditions55-58 by adding the various components separately, with the aim possibly of disentangling the different contributions. While the situation can be qualitatively reproduced, it has been shown above that there may be quantitative differences that are due to the actual structural details. In principle, a measurement of 4 upon water adsorption gives the value of the electrode potential in the UHV scale. In practice, the interfacial structure in the UHV configuration may differ from that at an electrode interface. Thus, instead of deriving the components of the electrode potential from UHV experiments to discuss the electrochemical situation, it is possible to proceed the other way round, i.e., to examine the actual UHV situation starting from electrochemical data. The problem is that only relative quantities are measured in electrochemistry, so that a comparison with UHV data requires that independent data for at least one metal be available. Hg is usually chosen as the reference (model) metal for the reasons described earlier.


19

For an electrochemical cell consisting of a metal at the potential of zero charge in a solution of surface-inactive electrolyte and a reference electrode (let us assume that any liquid junction potential can be neglected), the electrode potential is given by (cf. Eq. (20)]

&=-, vs. Ref. = @ +&M

+ bS+ const

(26)

The two perturbation terms are specific to the given interface and are experimentally inseparable. They measure the contact potential difference at the MIS contact. However, since no cpd is measured in this case dXM+ dXSare grouped into a single quantity denoted by X, called the interjacial term34:

End vs. Ref. = d + X + const

(27)

The constant term includes the contributions from the reference electrode. In purely electrochemical experiments the constant term is unknown. Therefore, from a measure of Emd, no information can be derived about the interfacial structure. However, if two metals are compared,

Equation (28) shows that the constant term is eliminated. Nevertheless, A@ must be known independently in order to derive information about AX. There is no way to avoid this; it is a consequence of the nature of the electrode potential [see Section 1.2(ii)]. Em& is measured in electrochemistry and is usually known with an accuracy to f0.01 V or better.' On the other hand # is measured with surface physics techniques that have an accurac of 0.05 eV, rarely better and often worse (because of imperfect surfaces).5% Thus, Eq. (28) does not ensure an appropriate accuracy for AX, so that the uncertainty may outweigh the value itself. The best way to proceed is to plot End vs. @ for a number of metals and to derive information about AX from eventually recognizable graphical correlations using statistical analysis. Figure 5 shows a sketch of the plot of End vs. CP according to Eq. (28). If a metal is taken as a reference surface, a straight line of unit slope through its point would gather all metals with AX = 0, i.e., those whose sum of perturbation terms is exactly the same. For these metals the difference in pzc is governed only by the difference in @. In Fig. 5 two more points are shown for exemplification. Metal Ml is on the left of M (i.e., has a more negative En4), while M2is on the right

SergioTmatti and Enn Lust

Figure 5. Sketch of a work function-potential of zero charge plot. The line through the point of Hg has unit slop. The horizontal distance of MI and M Ifrom the line measuces AX in Eq. (28).

(i.e., has a more positive Ed than expected from the straight line). For these metals, the horizontal distance of the point from the straight line precisely measures AX = p,i.e., the interfacial term measured relative to that of metal M. Thus, for metal MIf l is more negative than p,while the case is oppositefor MZ.In UHV terms,X measures A# upon

-

water adsorption; therefore, AX = A* - LIP. Knowing A@ for metal M, A 9 can be known for any other metal and compared with values measured drrectly in UHV. This will be done in the last part of this chapter after experimental data on Ed are collected. The main problem in the analysis of Eq4vs. @plots is that the two quantities are usually measured independently on different samples. It may happen that the surface structure differs somewhat so that # for the sample on which Edis measured is different from that of the sample used in UHV experiments. This is especially the case with polycrystalline surfaces, whose structural reproducibility is occasional, but it is also the case with well-defined crystal faces if reconstruction phenomena are p o s ~ i b l eThe . ~ problem persists also in the absence ofreconstruction since the concentration andlor distribution of surface defects may be different.33*6]


21

The preparation of metal surfaces as a rule differs in UHV and in electrochemistry. In the former case, "dry" procedures are used6' (sputtering, annealing, etc.), while "wet" treatments prevail with electrode^^^ (electropolishing, chemical polishing, voltammetry, etc.). In some cases a particular kind of flame annealing is used for electrodes, which are then immediately dipped into the solution. However, the surface structure may change upon contact with the liquid or upon polarization, so that it is necessary to check the surface structure before and after the experiment^.^^ The most appropriate experimental procedure is to treat the metal in UHV, controlling the state of the surface with spectroscopic techniques (low-energy electron diffraction, LEED; atomic emission spectroscopy, AES), followed by rapid and protected transfer into the electrochemical cell. This assemblage is definitely appropriate for comparing UHV and electrochemical experiments. However, the effect of the contact with the solution must always be checked, possibly with a backward transfer. These aspects are discussed in further detail for specific metals later on.

(ii)

Crystal-Face Spec$city

It is well known that the @ of a metal depends on the surface crystallographic orientation.6,65,66 In particular, it is well established that CD increases with the surface atomic density as a consequence of an increase in the surface potential XM. More specifically, for metals crystallizing in the face-centered cubic (fcc) system, @ increases in the sequence (1 10) < (100) < (1 11); for those crystallizing in the body-centered cubic (bcc) system, in the sequence (1 1 1) < (100) < (1 10);and for the hexagonal close-packed (hcp) system, (1 120) < (1010) < (0001). It is clear from Eq. (27) that owing to the crystal face specificity of a, End is expected to vary with the crystallographic orientation as well. Moreover, since the interfacial term X results from interfacial molecular interactions, it must be face-specific also. For a well-defined metal surface, Eq. (27) becomes

where (hkl) are general Miller indices of crystal faces. Polycrystalline surfaces are sometimes used with solid electrodes, although their use is progressively becoming obsolete. The metal surface can be regarded as consisting ofpatches of single-crystal faces. Equation (29) applies to each of the patches, but as a consequence of the surface heterogeneity and the

22


equipotentiality of the metal surface, the condition of zero charge cannot be fulfilled everywhere. At most, it is fulfilled as an average condition over the entire metal The applicability of Eq. (27) to polycrystalline surfaces depends on whether the various quantities are averaged in the same way over the whole surface. This turns out to depend on the particular property and the experimental method used to measure it. Thermodynamical1 an average work function can be defined for a polycrystalline surfaceli:

where ai is the work function of patch (face) i and Bi is the fraction of surface occupied by face i on the actual sample. The "average" value of @ can be obtained only by the method of contact potential difference, which is a thermodynamic experimental approach. Other techniques possess more local character and may probe some specific spots.69 The potential of zero charge is very often obtained by observing the condition of maximum diffusiveness of the ionic atmosphere around the electrode surface, for instance from the minimum of the experimental capacitan~e.';~~~ While it has long been recognized7' that the heterogeneity of a surface reduces the sharpness of the results, it has been shown quantitatively67,68 that because of the asymmetric behavior ofdouble-layer properties around the potential of zero charge, ionic atmosphere diffusiveness effects for the different patches on an electrode surface turn out not to be averaged as simply as in the case ofthe electrode work function. This makes End for polycrystalline surfaces aquestionable quantity that should be handled with caution. The degree of heterogeneity of a metal surface is determined by the looseness of its surface atoms. This is qualitatively measured by the melting point and more specifically by the lattice cohesion and the atomic More quantimass, which govern the tendency of atoms to autodiff~se.~' tatively, the variation of @ from face to face may give a straightforward idea of the degree of heterogeneity of a polycrystalline surface of a given metal. The heterogeneity of a metal surface is responsible for the curvature of the Parsons-Zobel (PZ) plot (l/Cvs. I/Cdwhere Cis the experimental capacitance and Cdthe diffuse layer capacitance calculated on the basis of


23

the Gouy-Chapman theory).72 Such a plot emerges from the GouyChapman-Stern-Grahame (GCSG) model of the electrical double layer and has often been used to determine the "true" surface area of solid electrodes.63,73,74 A recent model calculation by Foresti et n ~has. exam~ ~ ined the problem of the linearity of these plots. The potential-of-zero charge is an intensive quantity and does not depend on the extent of the surface area. However, it depends on the heterogeneity of the metal surface if the method to determine it is affected by such a feature. It was mentioned earlier that the measurement of @ by the cpd method is expected to respond to the average surface structure. Similarly, the immersion method,879which consists of measuring the charge flow as a clean metal is dipped in solution, should provide an average value ofE,* that is different from that obtained with the minimum capacitance method. In principle, the immersion method should provide End directly with truly clean, inert metal surfaces in the absence of impurities in solution, as well as in the absence of strong chemical interactions with the solvent. (iii)

Effect of Temperature

With reference to Eq. (26), an effect of temperature is expected since both aMand the perturbation terms depend on temperature. In particular, the effect can be written as a temperature coefficient:

= awar + a(sx * y a ~ + a(sx S ) ~+aconst' ~ (3 1) where the const' includes the temperature coefficient of the reference electrode. Alternatively, the reference electrode can be kept at constant temperature, but this implies neglecting any thermodiffusion potential at liquid junctions. All contributions on the r.h.s. of Eq. (31) are in principle different from zero. In terms of the interfacial termX, Eq. (31) becomes

&,&a?-

The temperature coefficient of the potential of zero charge has often been suggested to indicate the orientation of solvent molecules at the metal/solution interface. However, this view is based only on the response of a simple two-state model for the interfacial solvent, and on neglecting any contribution from the electronic This is in fact not the case. The temperature coefficient of @in many instances is negative and of the

24


same order of magnitude as the temperature coefficient of E,*.~~I~ is thus in principle difficult to assign the sign of a aE,JaTto the first or the second term on the r.h.s. of Eq. (32)." Equation (32) suffers from the same shortcomings as Eq. (27). In particular, a@/aTmust be known independently for the same metal sample as the one used as an electrode. Moreover, in view of the crystal-face specificity of End, its temperature coefficient is also expected to depend on the crystallographic orientation. Being a differential quantity, aE,JaT is an even more delicate experimental quantity than Enlo itself. For Hg, the temperature coefficient of was determined by Randies and whiteley7' and found to k equal to 0.57 mV K-'.o~ the basis of a simple up-and-down molecular model for water," this positive value has been taken to indicate a preferential orientation, with the negative end of the molecular dipole (oxygen) toward the metal surface. While this may well be the case, the above discussion shows that the analysis of the experimental value is far more complex. While no other value exists for Hg (which testifies to the delicacy of the experimental approach), Farrell and ~ c ~ i ~ have u e measured ~ ' the temperature coefficient of the cpd between Hg and water. This quantity is aX/aT, from which a value of -0.4 meV K-'has been estimated for a@/aT for Hg. It is thus evident that relating aE,&Tto the interfacial structure is much more difficult than for End, which suggests that one should always proceed cautiously in trying to decode experimental quantities in molecular terms. In principle, the situation can be simplified to some extent by comparing temperature coefficients for the same metal in different solvent^,^' and for different faces of the same metal in the same solvents. 32,34 In these cases, correlations are possible which allow some rationalization of the experimental picture. Specific discussions will be provided later on.

(iv) Effect of Ionic and Nonionic Adsorbates The potential of zero charge depends on the composition of the solution if adsorption takes place. If partial or total charge transfer occurs, the situation becomes more complex than in a perfect condenseqs2 as discussed in Section I. 1(iii). As ionic adsorption takes place, normally the potential of zero char e varies linearly with the amount adsorbed.83Such a variation is used8 ,85 as a means of extrapolating to zero concentration of the adsorbing sub-

H


25

stance to find out the actual potential of zerofree charge. Under similar circumstances, the specifically adsorbed charge is balanced at a = Oby a diffuse layer of oppositely charged ions.32At the same time, the ionic adsorbate can modify the solvent orientation around itself (thus modifying 6 ~ ~as1well , as the electron distribution at the surface of the metal, at least at the metal site where it is adsorbed (thus modifying kM). It is evident that the variation of End includes all effects, among which the one related to the ionic layer as a rule prevails. In the case of ionic adsorbates, the variation in E n d snormally unable to provide a clue to the molecular structure ofthe solvent since free charge contributions outweigh dipolar effects. In this case UHV experiments are able to give a much better resolved molecular picture of the situation. The interface is synthesized by adsorbing ions first and solvent molecules afterward. The variation of work function thus provides evidence for the effect of the two components separately and it is possible to see the different orientation of water molecules around an adsorbed ion.58,86,87 Examples are provided in Fig. 6. While from a structural point of view metal/solution and metallvacuum interfaces are qualitatively comparable even ifquantitatively dissimilar, in the presence of ionic adsorbates the comparability is more difficult and is possible only if specific conditions are met.33This is sketched in Fig. 7. A UHV metal surface with ions adsorbed on it is electrically neutral because of a counter-charge on the metal phase. These conditions cannot be compared with the condition of 0 = 0 in an electrochemical cell, but with the conditions in which the adsorbed charge is balanced by an equal and opposite charge on the metal surface, i.e., the condition of zero diffuse-layer charge. This is a further complication in comparing electrochemical and UHV conditions and has been pointed out in the case of Bra adsorption on Ag single-crystal faces.88 In the case of adsorption of neutral polar molecules, the effect on End is more tractable in molecular term^.^.^^ Adsorption is believed to occur79 by displacement of solvent molecules close to the metal surface which are replaced by adsorbate r n o l e c ~ l e s . ~0 ~=~0 t(no adsorbate),Emo is more conveniently written from Eq. (26) as

where

Sergio Tfasatti and E m Last

@I

figure 6. Effect of madsorption of water with other s p i e s on Cu(ll0). (a) Cmhrption with various dms ofbromine (to sirnulate anion adsorption). (.....) Water only; (1) bromine only; (2) ta (5)water on increasing amounts ofbromine. (b) Coadsorptlon with various doses of Cs (to simulatecation adsorption). (--I Water only (Bc, = 0);(1) to (3)water on different coverages of Cs. Ba: (1) 0.03, (2) 0.05, and (3) 0.07. Adapted born Refs. 58 arad 87. F"g lu r e qa) from D H Grider, K Bange, and J.K. Sass, J. E l e c m k m . Soc.30, U7,Fig.2, 1983. R e p h d by permission of the EMmhenical W&y, Tnc. Figure 6(b)reprinted from J.K Sass, J. Schott, and D.Lacky, J. Ekctromal. C h 283 441, Fig. 2, 1Wl, @ 1890 with permission from E b i e r Science.]

is the solvent dipole contribution at the interface and the term xS has been included in the constant term. When the surface is saturated with adsorbate (8 = I), the pzc can be written as

where 2(dip) is the surface contribution from the adsorbate molecules replacing the solvent. Comparison of Eq. (35)with Eq. (34) gives

Equation (36) shows that information on gs(dip) can be obtained only if = b~ and f(dip) = 0 or is precisely known. Both cases are difficult to meet.

df

n e Potential of Zero Charge

Figure 7. Adswon of tm ekcmnegarive w e s from tbe gas phase onto a su&e genea dipolar layer due to e l m m&~~metalto~~Adsorptionofsnions~~ elear& simalates the s i t d o n when the p d v e charge on the metal cmpma for the dmkd negative charge (madiffuselayer charge), and not when the charge rm the metal is m.

While Eq. (36) is valid for B = 1, a qualitatively similar equation is obtained at any value of B. Since the condition B = 1is difficult to reach experimentally, the value of dE,+ (adsorphon potential shift) is often estimated by means of extrapolation to 8 = 1. This procedure is very delicate and the result is often misleading. The variation of Emd with 0 may be linear or nonlinear, depending on lateral interactions between

28

Sergio Trasatti and EnnLust

molecules (assuming for simplicity that no chemical interaction with the metal surface takes place). If the replacement of a solvent molecule at the electrode surface does not involve any disturbance of the neighboring particles (this might be defined as a "regular" behavior), the potential shift is a linear function of 8. If lateral interactions are involved (including those with the metal surface), other terms that are not explicit in Eq. (36) become operative.919 An aspect that is difficult to treat is the nature ofthe boundary between the adsorbate layer and the bulk of the solution. Solvent molecules are now in contact with an organic layer and the kind ofinteraction is expected to differ substantially from that with a bare metal surface. The layers of solvent molecules in the immediate proximity of the adsorbate might exhibit some preferential orientation, which is not explicitly accounted for in Eq. (36), and this adds some additional ambiguity to the physical interpretation of the results. A comparison of the adsorption of a given molecule at the airlsolution and at the metal/solution interface is a convenient way of obtaining some information on the role of the metal surface.93,94 At the air/solution interface the potential shift is simply

From Eqs. (36) and (37),

Equation (38) still includes the electronic term. On the other hand, gB(dip)i, may differ from gB(dip) at the metal surface as a consequence ofdifferent interactions with the environment. Therefore the interpretation of adsorption potential shifts is always subject to a number of assumptions that cannot be easily checked. Figure 8 shows an example of the most common behavior of Mud as a function of adsorbate coverage. Linear behavior, if ever observed, is seen at the airlsolution interface." At metal/solution interfaces, if chemical interactions with the metal can be ruled out, electrostatic interactions cannot be avoided, and these are responsible for the downward curvat ~ r e . Upward ~' curvatures are often observed at airlsolution interfaces as a consequence of lateral interaction^.^' Models have been proposed to reproduce the curves in Fig. 8. Behavior at metal electrodes was discussed by Frurnkin and Damaskin in this

The Potential of Zen, Charge

figure 8. Typical adsolpaonpteniial shifts as a function of a d s o m surface comemuion (I) At the free surface d a solutim (d Wvior), (2) deal behavior, and (3) at a m t a l (Hg)/mlution interface. Expimental pints for dsqtirn of 1,4-butaaediolfrom Ref. 328.

seriess in terms of two capacitors in parallel. The curves are reproduced by means of macroscopic experimental quantities such as capacitance at B = O and 8 = I. The m e authors have dso discusssd linear behavior in terms of two capacitors in series. In both cases molecular details are not very evident. A 'hmacroscopic'' model for "regular" aidsolution interfaces has been p@ by Koczorowski et aLW The model is based on the Helmholtz formula for dipole layers using macroscopic quantities such as dielectric constants and dipole moments. The model quantitatively qmiuces A f values (37)], but it needs improvement to account for lateral interac-

m.

tion effects. More recently, the curvature at aidsolution interfaces has been accounted for by Nikitas and ~ a ~ ~ a - ~ oinuterms i s i of~ a~specific molecular model that predicts a linear dependence of (IlAf) on (lit?) The same model also reproduces the behavior at meWsolution intedaces, specifi-

cally Hg electrodes, for which most of the experimental data exist. Nikitas' treatment provides a method for an unambiguous extrapolation of the adsorptionpotential shift to 8 = 1. However, the interpretation of the results is subject to the difficulties outlined above. Nikitas' approach does provide

30


some physical interpretation of the experimental parameters, e.g., the slope and the intercept of the straight lines.

11. EXPERIMENTAL ASPECTS

The electrical double-layer structure at various metals has been discussed in many papers. 1-34,99-129 A large number of techniques have been developed for the experimental determination of the potential of zero charge. 1,9,10,12,128-219 These methods can be roughly classified as follows: (1) interfacial and surface tension methods (contact angle, capillary rise, tension vibration measurement); (2) impedance (capacitance) measurement methods; (3) immersion, open-circuit (streaming electrode), and potentiostatic scrape methods; (4) methods based on ionic, organic, and gas adsorption; (5) repulsion of diffuse double layers; (6) friction methods (oscillating Herbert pendulum, static friction); (7) ultrasonic methods (ultrasonic potential, dispersion of the electrode); and (8) optical and spectroscopic methods (photoemission, light intensity minimum, striascopic, Koester laser interferometry, Fourier transform infrared (FTIR) and subtractively normalized interfacial Fourier transform infrared spectroscopy (SNIFTIRS), and other methods). The following are among the more suitable methods: electrocapillary, streaming electrode, capacitance, immersion, scrape, static friction and tension vibration. For liquid metals (Hg, Ga) and liquid alloys [In(Ga), Tl(Ga)], good agreement (IhEgd I 5 0.01 V) has been achieved 1,3,4,7,10,25,26,120,125 between the End values obtained by the streaming electrode, electrocapillary maximum, and impedance methods. For solid polycrystalline electrodes, the agreement between the values determined for a given metal by various methods is rather poor.7~8~10~15~24725~32 The greatest success has been achieved only with capacitance measurements at ideally polarizable single-crystal facelelectrolyte solution interfaces. 15,24-34,61,63,64,67,74,107,149-156 A description of the methods for determining E,,, was given by Perkins and Andersen in a previous chapter in this series,9and by Frumkin et ~ 2 . ~ ~ ~

~


31

(i) Integacial and Su$me TensionMethods In the case of liquid metals and alloys [Hg, Ga, In(Ga), Tl(Ga)], EOd can be derived directly from the maximum of the corresponding electrocapillary curve ( y , E-curve).7,8,10,15,16,18,25,99-109,120,125 As shownby several authors, 1-8,10,131-137 the thermodynamic laws that give the relation between the interfacial tension y, the electrode potential E, and the Gibbs adsorption (fi) andactivity of ions and molecules in the solution are applicable to the electrode/electrolyte solution interface. At constant pressure (p) and temperature (T), the fundamental electrocapillary equation for a liquid electrodelelectrolyte interface can be written in the form

(ai)

where y is the interfacial tension, q is the charge density, R is the gas constant, pi is the chemical potential, and ai is the activity of component i. In the general case, the quantity q in Eq. (39) is the Gibbs adsorption of potential-determining ions, expressed in electric units. In the case of ideally polarizable electrodes (i.e., electrodes having a large energy barrier for charge transfer), q coincides with the surface charge density 6.Thus, according to Eq. (6), the charge of an electrode/solution interface is zero at the maximum of the electrocapillary curve. It should be noted that there are no difficulties in the conception of the pzc for an ideally polarizable interface. Difficulties appear as one has to deal with a nonpolarizable (or as in the usual case, with a partly polarizable) electrode, because as charge flows into an electrode and its potential undergoes a change, some of the charge is retained on the electrode surface while some is transferred to the other side of the interface, namely, some electrode reaction occurs. This aspect was discussed by ~ o r e n z "and ~ later by Vetter and ~chultze"' in the development of the concept of partial charge transfer in adsorption at interfaces. The analysis by Frurnkin et al. in 1970 led to the conclusion that it is possible to thermodynamically treat not only polarizable but also nonpolarizable electrodes. A detailed thermodynamic analysis ofpolarizable and nonpolarizable interfaces has been given by as sons' (see Section I). While the method based on the surface tension measurement has been established since the pioneering work of Gouy, 128,130 conceptual and experimental problems arise with solid electrodes, whose surfaces cannot


32

be considered in structural and energetic equilibrium. Substantial work has been done in this area during the past 20 years. The electrocapillary equation for a solid electrode under elastic strain at constant Tandp can be written as1,136-138

where y (specific surface work) is the reversible work spent in forming a unit new area of the surface by cleavage; Y (elastic surface stress) is the reversible work required to form a new unit area of surface by stretching; E , is the elastic surface strain [for liquid electrodes y = Y; the strain terms disappear and the above equation reduces to Eq. (39)l. For solid electrodes the usual derivatives give

- -ar

(a"

bppi

= ~ + ( y - Y ) ( z j _ , ~

If the surface strain changes under an electric field (electrostriction) or by adsorption of surface-active species, the left-hand side of Eqs. (41) and (42) is not equal to u and 4, respectively. Some a ~ t h o r s ~have ~~,'~~ reported unrealistically high values of OJ - Y), while Murphy and Wainright'^^ have provided evidence that the surface stress term is negligible. However, to a first approximation, the electrostriction term can be regarded as a second-order effect; thus, the second term in Eq. (41) can be neglected. Also, as shown by parsons,' to a first approximation, the dependence of E , on the chemical potential of component i can be neglected, and in this case the second term in Eq. (42) disappears. Therefore, y can be taken as the appropriate quantity, and the specific surface work-electrode potential (y, E) curve can be used to obtain information about the electrical double-layer structure (EOd) of solid electrodelelectrolyte interfaces.

'


(a) Surface tension methods

for Hg, as well as for other liquid metals has been obtained The using the Lippman e~ectrometer'~ (y, E curve method) modified by G ~ U ~ m, m' k~ i n~, ' ~~' o e n i n ~ and , " ~others. The principles of the technique and its problems have been extensively described in previous reviews 1,10,16 and will not be dealt with further here. Another method for measuring y that is based on the study of the geometrical form of a sessile drop of a liquid metal has been discussed by ~ u t 1 e 1 -and l ~ ~Smoulders and ~ u ~ v i sVos . ' et~ a1.165 ~ have used a spectroscopic laser imaging procedure to obtain the absolute surface tension of an Hg sessile drop electrode. T h s approach has been further developed by Melik-Gaikazyan et al.,159~uEiera,l~' and Barradas et al.161A detailed ' discussion of these methods has been given by rumk kin," ~ e v i c h , ' ~and 163,164 Conway et al. A novel method for the determination of the pzc of Hg or liquid l ~ ~ method amalgams has been described by Conway and ~ 0 1 l e d a n .The is based on the effect ofpotential on the surface tension of the liquid metal, which gives rise to changes in the curvature of an Hg (liquid electrode) drop. These are transduced to a varying light-intensity signal through reflection of a collimated thin laser beam that is incident on the top of the drop. The values of Eed for aqueous solutions of various electrolytes have been found to be in good agreement with those obtained from impedance and surface tension data. 10,112 The measurement of Ea4 in nonaqueous solvents encounters the problem of the unknown contribution of the liquid junction potential of the reference electrode/solution contact. Comparison of Ea4 in different solvents on a common potential scale is a problem for which an unambiguous solution has not yet been found. However, in practice, Eg4 values are often recalculated in the bis-bipiheny lchromium (BBCr) (VO) scale, which is assumed to be solvent independent. 108>109Half-wave potentials of BBCr, measured in a given solvent vs. an aqueous calomel electrode in 0.1 M NaCl, are given in Table 2. 108,109 A comparison of various data10,107,127,163shows that the accord between Em,-, values obtained by different methods is good. On this basis, Conway and colledan16' have noted that their new method is applicable in various nonaqueous solvents with various concentrations of electrolyte. There have been many attempts to apply the surface tension (y, E curve) method to solid electrodes, and various experimental approaches


have been proposed.10,100,138,168-171 However, the interfacid tension method has turned out to be applicable without reservation only to liquid electrodes. As shown by ~ o k h s t e i n , who ' ~ ~ has been able to relate the vibrations induced by an oscillating potential. of an L-shaped electrode to charge, the solidification of an elhas a considerable influence on the dependence of y on E. The estmce (a term introduced by Gokhstein) *& can have several nullpohts, whereas for a liquid electrode such a derivative passes through zero only once, i.e., at E,+ The shift of the estance zero from E& has been related to the dependence of the work: function on the elastic deformation.16' Values of Edonly slightly different from those obtained by impedance have been obtained.'" Fredlein and B o ~ k r i sused ~ ~a 'laser ~ ~optical ~ ~ system ~ ~ to measure the bending caused by potential changes in a thin glass strip metallized on one side; they found that their Ay, E dependence (by = yo y) gave End values with an accuracy of M.1. V compared with other (impedance)

-


35

methods. Murphy and wainwright13' have measured y for solid metals by determining the change of weight upon immersion, which according to the authors is related to the force of the metal/solution interface tension. These measurements have provided evidence that the surface stress term is negligible. 138,171 A new technique based on electrocapillary phenomena at partially immersed solid metal electrodes has been developed by Jin-Hua et a ~ . The ~ ~method ~ ,involves ~ ~ the~ detection of the rise of a solution meniscus by a bulk acoustic wave sensor.146~147~172 The method was used to measure the End of p ~ - A gand l ~ ~~ c - A u .Good ' ~ ~ agreement with other methods was found. This method has been shown to be applicable to concentrated and dilute as well as nonaqueous solutions, and the effect of the pseudo-capacities existing in the capacitance method do not need to be considered. This method appears to make it possible to determine the EUd values of any metallic or nonmetallic conductor and semiconductor that is not corroded in the tested solutions.146,147 The problem of surface tension of solid electrodes has recently been carefully studied by Heusler and Lang. 173-176 These authors have shown that the anisotropic specific surface energies of solids change in different ways after a change in state, depending on the possibility of mass transport between the equilibrium surfaces. If mass transport is impossible, the solid is deformed by a nonhydrostatic stress field and the chemical potentials of the components become anis~tropic.'~~ In order to establish full equilibrium with constant chemical potentials throughout the whole system, mass transport is necessary. Since it is slow for solids, there will be irreversible contributions to the specific surface energy. Changes in specific surface energy were measured175as a function of E and electrolyte composition by the Koesters laser interferometry method and compared with changes in mass and charge. In all cases investigated, the electre capillary curves for pc-Au in aqueous solution of various electrolytes [Na2S04,NaCI, Pb(C104)2,ZnS04] changed slowly with time, thus confirming that surface relaxation and modification occurred. The method has also been applied to adsorption of neutral s ~ b s t a n c e s . ' ~ ~ -

(ii) Impedance (Capitance) Measurement Methods For (ideally) polarizable metals with a sufficiently broad double-layer region, such as Hg, Ag, Au, Bi, Sn, Pb, Cd, Tl, and others, End can be obtained from measurements of the double-layer capacitance in dilute

36

SergioTrasatti and EM Lust

solutions, where it is detected by a pronounced minimum in the capacitance-potential (C, E) curve. 1,4-8,lO In contrast to the electrocapillary curves, which can be obtained only by a limited number of methods, the capacitance of the electrical double layer can be measured by a great variety of techniques. lo)' 1~16~100~105~1 14-1 16~177In the case of ideally polarized or "blocked interfaces, direct measurement of a,as for example in chronocoulometric experiments, is possible. The related differential capacitance, C, defined as

can be measured directly with an impedance bridge or a phase-sensitive detector as in a frequency response analyzer. At a high electrolyte concentration, linear sweep voltammetry can provide similar information since the current density is given by

where dE/dt is the sweep rate v. If C is constant with v, j = Cv

and C =j / v

(45)

There are several other possibilities for obtaininf a measure of C, as discussed in detail in many papers. 10,16,100,101,105,11-116 The model more generally accepted for metal/electrolyte interfaces envisages the electrical double layer as split into two parts: the inner layer and the diffuse layer, which can be represented by two capacitances in series.1,3-7,10,15,32 Thus, the total differential capacitance C is equal to

where Ci is the inner (Helmholtz) layer capacitance,99,112 independent of the surface-inactive electrolyte concentration and Cdis the diffuse (Gouy) layer capacitance,128~129expressed according to the Gouy-Chapman theory8~10~99-101~128~129 for a z,z-type electrolyte by

#d

is the potential drop in the diffuse layer equal to


37

w,

where A = ~d is the dielectric constant of the diffuse layer, usually taken to be equal to the macroscopic dielectric permittivity of the solvent. Thus, according to Eq. (46), Cd,E curves have a minimum at EOd (a = 0) since at this potential the value of Cddecreases linearly with 6. According to the Gouy-Chapman-Stern-Grahame model, 1,lO-16,99,128,129 in a surface-inactive electrolyte solution the value of the inner layer capacitance Ci does not depend on c, and to a first approximation the potential of the differential capacitance minimum in the C,E curve would correspond to the condition 0 = 0, i.e., to an Eaavalue. E,* in the presence of adsorption can be obtained by linear extrapolation of E ~ as, a function of the electrolyte c~ncentration.'~~" As shown in some WOrk,125,178 a small dependence of Eh, on c,l 2 0.01 M must exist irrespective of the occurrence of specific adsorption, and its value depends on the value of Ci,aci/aa, as well as on a at which the maximum in Ci, a curves occurs. Depending on the above parameters, there exists a critical electrolyte concentration (c,,) above which the diffuse-layer minimum in the experimental C,E curve disappears. It is thus possible to estimate M,, = Emin 125*178at c = c,, (Ed is the "true" zero charge potential). The value of&, was found to be equal to 96, 100, 110, 35, and 45 mV for Hg, Bi(l1 I), Sb(l1 I), In, and Ag(ll1) electrodes, respectively. However, AE,, decreases rapidly with the dilution of the electrolyte solution 125,178,179 and for a 0.05 M NaF aqueous solution, AE was found to be 30, 33, 36, and 27 mV for Hg, Bi(l1 1), Sb(ll1) and Ag(l 11), respectively. For 0.01 M NaF, the calculated value of A& is only a few mdlivolts. Thus, only an appreciable dependence of Ei, on c at c , ~S 0.01 M can be taken as an indication of weak specific adsorption of the anion around End at an ideally polarizable electrode. The value of la,/ for Hg, Bi(l1I), Sb(l1I), In, and Ag(11l) electrodes is on the order of 2 to 2.5 PC cmS, and the value of c, was found to be equal to 0.075, 0.08, 0.09, 0.03, and 0.12 for these electrodes. It should be noted that the values of A&, and c, are influenced by the nature of the metal through the so-called "hydrophilicity" of the electrode material (Ci, a curves), i.e., by the metal-water interaction strength. The concentration dependence of the diffuse-layer minimum potential in dilute solution was determined by Levich et al. 177,180,181 using an ~

~

~

~

>

~

~

~

1

~

38


amplitude demodulation method. The values of End thus obtained were in good agreement with surface tension and impedance

(iii) Immersion, Open-Circuit, and Potentiostatic Scrape Methods The differential capacitance method cannot be used for reactive metals, such as transition metals in aqueous solutions, on which the formation of a surface oxide occurs over a wide potential re ion. An immersion method was thus developed by Jakuszewski et al. 18 ,183 with this technique the current transient during the first contact of a freshly prepared electrode surface with the electrolyte is measured for various immersion potentials. The electrode surface must be absolutely clean and discharged prior to immersion. 182-184 A modification of this method has been described by Sokolowski et al. The values of Eg4 obtained by this method have been found to be in reasonable agreement with those obtained by other methods, although for reactive metals this may not be a sufficient condition for reliability. The immersion method at a modern experimental level has been applied by Hamm et al.'" to determine End for Pt(l1 l)/H@ and Au(l1 l)/H20 interfaces. Clean and well-ordered Au(ll1) and Pt(ll1) electrodes were prepared in a UHV chamber by several cycles of sputtering and annealing until no impurities could be detected by AES and the surface yielded sharp LEED spots. After such a preparation, the (22 x 6) reconstsuction of Au(l11) was found. The Au(l11) and Pt(l11) electrodes were then transferred to the electrochemical cell by a closed system and immersed in 0.1 M HC104 aqueous solution at various Es. The current transients during the potential-controlled immersion experiments were recorded by a digital storage oscilloscope. The value of Endwas derived from a,E plots where a is the charge flowing during the contact with the electrolyte under E = const. The Au(ll1) electrode was used as a test system and the value of E,& was found to be in good agreement with that obtained by the impedance method.140,187,188 The well-known streaming electrode method, used with liquid electrodes (including Ga and its liquid alloys), belongs to the group ofmethods where a new electrode surface is formed underneath the solution surface at open circuit. In the case of liquid electrodes, the surface renewal is accomplished by injecting into the solution a fine stream of microscopic metal droplets. The streaming electrode method was first used by P a ~ h e nand l ~ ~developed by Grahame et a1.,53Randles and Whiteley,7' as

8

,,,


39 167

well as by Jenkins and Newcombe. The method is very useful in the case of nonaqueous electrolyte solutions, where electrode contamination with organic impurities is possible. In the case of liquid metals, the agreement between End values obtained from the electrocapillary maximum, the streaming electrode, and the impedance methods is very good (Mod 5 0.01 v). The o en-circuit scrape method was developed by Andersen et a1.9,141,189,1'to obtain values of some solid metals. The principle of this method is the same as that for the streaming liquid electrode method: a transitory fresh metal surface is produced over the entire electrode and the open-circuit potential is measured before subsequent reactions can appreciably change the electrode surface. It is possible to obtain End because the high activation energy for a transfer of charge across the double layer enables one to measure the preexisting potential. Simple inorganic ions are under equilibrium conditions during the entire process. Variants of this method have been implemented by Noninski and ~azaroval~ and l Zelinskii and ~ e k ' Various ~' specific aspects have been ~ > ' ~ ~ treatments have been provided discussed by ~ a z a r o v a . l ~Theoretical by Safonov et n2.l9' When the electrode/solution system contains substances that are oxidized or reduced faster than the surface can be renewed, the potentials observed during the surface renewal are shifted.

(iv) Adsorption Methods According to the theory of organic compound adsorption at electrodes, the maximum adsorption of neutral aliphatic compounds at Hg-like metals (physical adsorption) takes place in the region of thus methods based on back integration and the salting-out effect have been using CO adsorption worked out.8,10,154 More recently Clavilier et at fixed potentials on Pt single crystals to measure the related charge transient, have provided definite EM values for Pt(ll0) and Pt(ll1) in 0.1 M HCIO., (with the assumption that the CO dipole contributes negligibly to the double-layer potential). However, the measurement of a charge transient point by point along the potential axis is difficult, and since a transient charge from the whole surface is measured, it is not yet clear whether this method can be used to distinguish between the local potential of zero total charge of terraces and steps. Attard and Ahmadi '97 have used a method based on the adsorption and electroreduction of N20to estimate


40

the Ew values of single-crystal Pt-metal electrodes. A direct correlation has been found between Ew and the maximum rate of N20reduction. Long ago Balashova and ~azarinov"' suggested an approach based on the determination of the adsorption of anions and cations as a function ofpotential using a radiotracer technique. Equal surface concentrations of cationic and anionic charges indicate a zero free surface charge ( 2 J - F = z+T+F).An advantage of this method is that it can be applied to any materials (metals, nonmetals, semiconductors, ets.); a disadvantage is that it is restricted to ions with radioactive isotopes emitting a or /? radiation. Actually, y emitters are difficult to use because the range of y rays is such that the background overwhelms the emission from the electrode. This method gives the concentration of nuclei in the double layer, but it does not distinguish between free and total charge; only dilute surface-inactive electrolyte solutions can be studied.

(v) Friction Methods The interaction between two double layers was first considered by These concepts were used to measure the friction Voropaeva et between two solids in solution. Friction is proportional to the downward thrust of the upper body upon the lower. However, if their contact is mediated by the electrical double layer associated with each interface, an electric repulsion term diminishes the downward thrust and therefore the net friction. The latter will thus depend on the charge in the diffuse layer. Since this effect is minimum at EOd, friction will be maximum, and the potential at which this occurs marks the minimum charge on the electrode. B o c h s and ~ a r r ~ - ~ o nwere e s l ~the~ first to carry out experiments with a pendulum to measure the friction between a wetted substrate and the pivot upon which the pendulum swung. It should be noted that Rebinder and W e n ~ t r o mused ' ~ ~ such a device for an objective similar to that of Bockris and Parry-Jones, but they claimed that the characteristics of the pendulum oscillations reflected the hardness of the solid surface. The plastic breakdown determinin this would be a function of v and this is a potential-dependent value. 100, 01 More extensive determinations were made later by Bockris and Argade200;the theoretical treatment was given by Bockris and In the absence of adjustable parameters in the theory, a good agreement between theory and experimental data was assumed.201The studies by Bockris and Parry-Jones indicated that the

B

41


maximum in the friction potential relation corresponds to The method should be applicable to any conducting material.lOO>lO1

(vi) Optical and Spectroscopic Methods Barker et have developed a photoemission method to obtain End at metal/electrolyte interfaces. Later, the method was applied by Brodsky et al.203-205 to Pb, Bi, Hg, Cd, and In; good agreement (AEgd = 0.02 V) with impedance data1' was found. In situ Fourier transform infrared and in situ infrared reflection spectroscopies have been used to study the electrical double layer structure and adsorption of various species at low-index single-crystal faces of Au, Pt, and other electrodes.206-210 It has been shown that if the ions in the solution have vibrational bands, it is possible to relate their excess density to the experimentally observed surface. the SNIFTIR technique can be According to experimental data, used to probe the electrical properties of the electrical double layer even in more concentrated solutions where cyclic voltammetry (cv), impedance, chronocoulometry, and other techniques are not applicable. Iwasita and xia210have used FTIR reflection-adsorption spectra to identify the potential at which the orientation of water molecules changes from hydrogen down to oxygen down. Another spectroscopic technique, high-resolution electron energy loss spectroscopy (HREELS), has been used by Wagner and ~ o y l a n ~inl ' combination with cyclic voltammetry to estimate ED&of a Pt(ll1) electrode from the reaction of H30+formation. Recently, Koesters laser interferometry has been used to detect the minute deformations of the electrode that are due to changes in specific surface energy. 173,174,212 The experimental details are given in the original papers. It has been found that the specific surface energy of the pcAu/K2S04+ H20interface shows a maximum at E = 0.00 V (SCE) and this potential is independent ofelectrolyte concentration and solution pH. In the presence of KC1, End shifts to more negative values as the electrolyte concentration increases, which indicates specific adsorption of CI-on gold.24 or both electrolytes, the specific surface energy was observed to continue to change with time after the mass became constant as a consequence of surface stress relaxation. It has been shown that faradaic currents do not affect surface energy or mass. 173,174,212 '081209


The piezoelectric method should be noted as another technique for measuring the pzc. Introduced by Clavilier and ~ u o n and ~ used , ~ by ~ ~ Bard et a2.,214>215 the piezoelectric method has been used more recently by Seo et aL216and Dickinson et aL217

2. Estimation of the Surface Area of Solid Electrodes The estimation of the working surface area of solid electrodes is a difficult matter owing to irregularities at a submicroscopic level.10,15,20,24,32,6S64,67,68,73,74,218-224 Depending on the irregularity-toprobe size ratio, either the entire surface or only a fraction of it is accessible to a particular measurement. Only when the size of the molecule or ion used as a probe particle is smaller than the smallest surface irregularity can the entire surface be evaluated. 10,15,32,73,74,218 Various in situ and ex situ methods have been used to determine the real surface area of solid electrodes. Each met hod 10,15,32,67,73,74,218 is applicable to a limited number of electrochemical systems so that a universal method of surface area measurement is not available at present. On the other hand, a number of methods used in electrochemistry are not well founded from a physical point of view, and some of them are definitely questionable. In situ and ex situ methods used in electrochemistry have been recently reviewed by Trasatti and petri7' A number of methods are listed in Table 3.

The in situ methods more commonly used to obtain the surface roughness R = SRaI/Sg,, (where Sd and Sgemare the working surface and the geometric area, respectively) of electrodes are10>24>6"73174>218 (1) differential ca acitance measurements in the re ion of ideal polarizability,10,l5,20,24,32~3,64,67~68~73~219-224 including the arsons-Zobel plot,72 Valette-Hamelin approach," and other similar methods 24,63,74,218,225.(2) mass transfer under diffusion control with an assumption of homogeneous current distribution73,226,, (3) adsorption ofradioactive organic compounds (4) v ~ l t a m r n e t r y ~and ~~i~~~; or of H, 0, or metal monolayers73.142>227-231; (5) microscopy [optical, electron, scanning tunneling microscopy (STM), as well as a number of ex situ and atomic force microscopy (AFM)]234-236; 237-246 methods. Microscopy is one of the most direct physical methods for determin-

d

ing surface roughness. The resolution can go from macroscopic to atomic

size, depending on the technique. Thus the order of magnitude of the range of observation is the millimeter for optical microscopy, the micrometer for


Table 3 Methods for the Determination of the Real Surface Area of Rough and Porous Electrodes --

-

References In siru

Measurements of double-layer capacitance Drop weight (or volume) Capacitance ratio Measurements based on the Gouy-Chapman-Stem theory to determine the diffuse double-layer capacitance Parsons-Zokl plot Measurements of the extent of monolayer adsorption of an indicator species Hydrogen adsorption from solution Oxygen adsorption from solution Underpotential deposition of metals Adsorption of probe molecules from solution Vol tammetry Open-circuit potential relaxation Negative adsorption Ion-exchange capacity Mass transfer Scanning tunneling microscopy (STM) Atomic force microscopy (AFM) Ex situ Gravimetric methods Volumetric methods Adsorption of probe molecules from the gas phase Weighing of a saturated vapor adsorbed on a solid Hysteresis of adsorption isotherms Themodesorption Porosimetry Liquid permeability and displacement Gas permeability and displacement Wetting heat (Harkins-Jura method) Surface potential of pure melal thin films Metal dissolution rate SEM,STM,A M , profilomeler, and stereoscan method Diffuse light scattering X-ray diffractornew Nuclear magnetic resonance spin-lattice relaxation Radioisotopes Source: Trasatti and Petrii.?'

10,24,63.70,74,218-225

10,24,72,74

226-231

232,233 237 238

239

73,226 234-236

241.242 24 1,242 240

241,242 243-245 243.244 242 242 242 243,244

245 245 246 241 24 1 24 1 242.243

44


scanning electron microscopy (SEM), and the nanometer for atomic force microscopy and for scanning tunneling microscopy. Advances in A M and STM are making their use in situ possible.218,234-236 A lateral resolution of 1 nm and vertical resolutions better than 0.1 nm can be achieved.23v236 However, it is useful to stress again that the value of R depends on the method used. 10,15,24,32,63,64,73,74,218-234 Further scrutiny of the various methods is thus welcome.

(i) Applicability of the Gouy-Chapman-Stern-Grahame Model to Solid Electrodes The dependence of the C,E curves for a solid metal on the method of electrode surface preparation was reported long ago. 10,20,67,70,219-225 In addition to the influence of impurities and faradaic processes, variation in the surface roughness was pointed out as a possible reason for the effect. 10,67,70,74,219 For the determination of R it was first proposed to compare the values of C of the solid metal (M) with that of Hg, i.e., R = c ~ / c ~ . ' The ~ data ~ ~at Ea=o ~ . for ~ the ~ most ~ - dilute ~ ~solution ' (usually 0.001 M) were typically used for such a comparison to eliminate the influence of possible differences in the inner-layer capacities. However, Ci of different solid metals, as well as of liquid Ga, In(Ga), and Tl(Ga) alloys have shown such a large variation that this approach can hardly be considered as appropriate. It should be noted that the error in C, which for solid electrodes is much higher than for liquid electrodes, increases with the decrease of eel; further, as shown later (Section 11.2 (iv)), the effects of surface crystallographic inhomogeneity also prove especially appreciable,24,67,74 Frumkin was the first to give a qualitative consideration of the electrochemical properties ofpc electrode^.^^'^^^^ He noted that the charge ajat individual faces j may be different at a fixed value of the potential E and this may change the form of the capacitance curve near the diffuselayer capacitance minimum. Important results were obtained in a pioneering paper by Valette and ame el in.^^ They compared experimental capacitance curves for a pc-Ag electrode and its three basic faces. They found that the capacitance of a pc-Ag electrode can be obtained by the superposition of the corresponding C' E curves for individual faces exposed at the pc surface, i.e.

The potential of Zero charge

45

A weighted sum of C,E curves for the faces was found to be similar to the C,E curve for a pc electrode. According to Valette and ~ a m e l i n , 6all~ main

Ag faces [(I 1I), (loo), and (1lo)] are exposed on the surface, their fractions Bj on the surface being 0.31, 0.23, and 0.46, respectively. These authors demonstrated that the diffuse-layer capacitance minimum potential E S , of a pc-Ag electrode was only slightly less negative (30 mV) than the pzc of the Ag(ll0) face, i.e., for the face with the more negative value of End. The diffuse-layer capacitance minimum for pc-Ag was wider and less deep than for the Ag faces. The influence of the crystallographic inhomogeneity of polycrystalline and monocrystalline electrodes (with various surface defects) has been discussed for various metals in many papers.24,67,74,75,149-156,247-267 Bagotskaya et ~ 1showed . that ~ integration ~ ~ ofthe partial C,E curves from End of each face to G, on the polycrystalline electrode with account ' m at where taken of the fraction of plane gives arg = -0.04 C * offg = ~OJV,. At E ~ the . Ag(l10) plane has a positive charge (a = 0.01 to 0.02 C m-2) and other planes a negative charge (aAg{m,l = -0.02 to -0.04 C mm2; a,,(, = -0.03 to -0.06 C rn-q; at the surface of pc-Ag there are no surface regions with o = 0. The same conclusions hold for pc-Au (off. = -0.03 C m-*), pc-Bi (OK = -0.005 C rn-3 and for other pc electrodes.262-267 Mathematical simulation of Cp, E curves shows that the shape of the diffuse-layer capacitance minimum depends on the difference of E,* in individual faces and their fractions, as well as on the shape of partial C,,E curves (Fig. 9). The results of experimental capacitance studies at two lane model pc-Bi electrodes were in agreement with these conclusions.2El-266 Thus it has been shown that the potential of the diffuse-layer capacitance minimum for a pc electrode does not correspond to the zero charge potential of the whole surface, i.e., 48,q # 0at Efin.

an

(ii) Parsons-ZobeE Plot Substantial contributions to the interpretation of the experimental data for solid electrodes have been made by Leilas et nJ.223:224 and by Valette and am el in.^^ Both approaches are based on the same model: the

S e r g i o h d i ornd E m Lust

C,E ems (1, 2 3) for singl8-crystal b s aad (4) for a nrsdel polycrystalline strrface calculatedby the ~uperpositionof lb C,Ecurves at E = mt (4911 with 4 = Bt r 4 = 1n:l.(a) Faces with qtmng hydrophilicity and (b, c) h s with weak bydropMlicity. ( ~ tb) , &g(maxj a 0.4 V d Ccl M,4lfilolr)i= 0.09 V.

F i 9. Themetid

m.

value of and of the inner-layer capacitance per unit of "true" surface area Ci are assumed to be constant over the whole s ~ r f a c e . Thus, ~~~~"~~ the GCSG model is considered as applicable to the capacitance characteristics related to the unit of "true" surface area, which differ by a factor R' from those per unit "apparent" surface area

where CAQ)is the diffuse-la er capacitance obtained according to the Gouy-Chapman theory. l,lO,l ,129 was to identify the potential of the The idea in these capacitance minimum in dilute eIectrolyte solutions with the actual value of EN& (i.e.. apean(EndJ = Ofor the whole surface) and to obtain the value of R as the inverse slope of the Parsons-Zobel plot at E ~ , , Extrapolation ?~ of C-' vs. cj1to C- = 0 provides the inner-layer capacitance in the RCi,-, and not c;kaI as assumed in several papers.6768,223,224 1, the absence of ion-specific adsorption and for ideally smmth surfaces, these plots are expected to be l i n k with unit slope. However, data for Hg and single-crystal face electrodes have shown that the test is somewhat more complicated.63,74219,247-249 More specifically,247,248 PZ plots for Hgl

1

-rm

47


surface-inactive electrolyte solution interfaces at a = 0 as well at a < 0, albeit usually linear, exhibit reciprocal slopes that are somewhat greater than unity. The main reason for this has been s h o ~ n ~to ~be~ , ~ ~ ~ - ~ ~ ~ experimental errors in measuring C, as well as the hyperbolic form of C in the GCSG model. The GCSG model predicts that Cd=f(ceI)while Ci, which is not directly measurable, can be derived from Eq. (46) provided ions are not specifically adsorbed. The error in Ci is the total differential of Eq. (52):

where dC, for a given value of a,includes the experimental error in the determination of C and the error from the integration of the differential capacitance-potentialcurves. When x (x = C-' - C ~ I ) is small, dCi is lar e and tends to infinity; when x is large, dCi is small and tends to dC.247, 48 For a given positive x (at End for instance), the smaller Cd,the more an error in C affects Ci.As s h o ~ n , the~ same ~ error ~ ~ for~ Bi,~ Cd,~ and - ~ ~ ~ ~ ~ ~ ~ Ag atfixed c,, causes the errorin Ci to increase in the same order of metals since the value of Ciincreases. The same experimental error entails alarger uncertainty in Cifor the lowest eel and a. At la1>> 0, the uncertainty in C does not bear on Ci since x is large. Error analyses show that at AC = f0.2 pF cm-2 ACi = f5 pF ~ r n if- C~ N =~ 0.001 ~ M,Ci = 26 pF cm-*and a = 0. At la12 3 pC cm-2 and AC = M . 2 pF ACi = W.15pF ~ r n - which ~, is a high accuracy for In the case of liquid Hg, the uncertainty in the measurement may be induced by possible errors connected with (1) experimental measurement of C, (2) preparation of solutions of the exact c,,, (3) incomplete dissociation of electrolytes, (4) slight specific adso tion of anions, and (5) deviations from the Gouy-Chapman theory.%7,248 In the case of solid electrodes, in addition to the above-mentioned reasons, sources of inaccuracy are the possible erratic preparation of the electrodes with the same geometric surface area and the same crystallographc orientation.10,247-260 Studies with wedge-shaped, two-faced Bi electrodes show that with increasing of different faces exposed at a model pc electrode surface, the deviation of the Parsons-Zobel lot from linearity increases and the value of fpz also increases. 152,153,264-2 6 A comparison of the data for F-, BG ,and C10i solutions showsthat frnincreases in the order F < BE; c ClOi with increasing weak specific adsorption.254

5

1

48


The use of Parsons-Zobel plots to determine the roughness factor R = has been questioned recently.75,250 It has been remarked that the experimental value of fpZ depends on the surface charge density and sometimes on the electrolyte concentration eel.The real R cannot depend on a and on c,,. However, experimental PZ plots for single-crystal face ~ ) show slopes electrodes in the region of E,,, (-3 < a < 3 pC ~ r n - often increasingwith lal, i.e., the apparent R decreases as lot rises.24,63,67,74,251-254 These findings indicate that fpZ is not a real measure of the actual R. The only possibility of testing the validity of the GC theory consists75,250 in finding experimental conditions for which the potential drop in the diffuse layer ItjA < 70 mV.Thus, the practically unit slope of the C-'. plots for Hg, Bi, Cd, Sb, Ag, and Au,24,63,73,74,247-262 and for other systems with correlation coefficients better than 0.996 provides convincing evidence both for the validity of the GC theory and for the lack of experimentally detectable deviations of the roughness factor from unity. Slopes of c', S' plots much lower than unity very near En, (-0.5 S o < 1 pC ~ m - ~ ) can be interpreted75,250 as deviations from the simple GC theory caused by the roughness of the electrode surface.

fPZ

(4 Surface Roughness and Shape of Inner-Layer Capacitance Curves In 1973 Valette and ame el in^^ proposed another method to determine the roughness factor R of solid polycrystalline surfaces and to test the GCSG theory on the basis of Eqs. (50) and (51). For each c,~, a set of Ci, cr curves was calculated* for various R values and the optimum value of R was selected on the basis ofthe assumption that near Ed,the Ci*0 curve must be smooth. The experimental values of R were found to increase as c,, decreased (1.40 to 1.80). This was explained by the fact that R is a complex quantity, being R =fR'fCR,wherefais a factor of crystallographic inhomogeneity of the polycrystalline electrode surface. fcR is higher the larger the difference between End of individual planes (homogeneous regions exposed at a pc surface) and the more dilute the solution, and fCR decreases as la1 increases, fR was assumed to be the actual surface roughness factor independent of c,, and a. Using the experimental C,E *In Ref. 67 the shape of C-odurves was analyzed using the following equation: [ci- (%dl*' = [C-(u,)I-' - R'G'(ud)


49

curves for Ag single-crystal faces, the C,E curve for a pc-Ag electrode was calculated by the superposition of C,E curves at E = const, (49b) dP'(E)= R Bjq(E)

2 i

where %(E) refers to the unit area of the true surface and q : ' refers to the unit area of the apparent surface of the electrode. For pc-Aulelectrolyte interfaces, Clavilier and Nguyen Van ~ u o n also concluded that the crystallographic inhomogeneity factor depends on c,l. Later, the influence of the crystallographic inhomogeneity of pc and monocrystalline electrodes (with various surface defects) was discussed in many papers.75,152,154,156,247-259 It has been shown that the potential of the diffuse-layer capacitance minimum for a polycrystalline electrode does not correspond to Ea=oofthe whole surface, i.e., Z; B p i # 0 at E ~ , .

(iv) Electrical Double-Layer Models for Polycrystalline Electrodes Current theories describe pc solid electrode surfaces as a combination of different monocrystalline faces.10,67,68,223,224,26&267 [cf. Eq. (49b)l. As discussed above, the coefficient R expresses the geometric roughness of the surface area to which the measured differential capacitance is referred. For solid electrodes, R also reflects the energetic inhomogeneity of the surface caused by crystallographically different grains (single-crystal faces), grain boundaries, and other crystallographic defects exposed at the surface of solid polycrystalline electrodes, as well as at the surface of real (as opposed to ideal) single-crystal f a ~ e s . ~ ~ , ~ ~ , ~ ~ ~ - ~ ~ ~ Electrical double-layer models for c electrodes can be roughly classified into two groups.67,68,74,153,154,261- 67 Models in the first group consider a pc electrode surface as consisting of relatively large monocrystalline regions with a linear parametery* >> 10 nm (v* is the characteristic length), corresponding to macropolycrystallinity ( M P C ) . ~ Within ~>~~~ these areas both the inner and the diffuse layers are envisaged as independent. Accordingly,

!

xjCvC,.q/(Cu+ C4)

C$'= R

(53)

I

where Ciiand C4 are the inner-layer and diffuse-layer capacitances of face j, respectively. This is the model of independent diffuse layers (IDL) [Fig. 10(a>l.

~

~

~

~

Rguw 10. TfiPareliul modF1 for the e k c t r w duabla layer at mn elmmb with a @ymystdline surface. IP) Madel of mdcpeadant diffuse lapm (53)], and fi) madal of common diffu= layer [Eq.(54%

In the second group of models, the pc surface consists only of very small crystallites with a linear parameter y', whose sizes are comparable with the electrical double-layer parameters, i.e., with the effective Debye screening length in the bulk of the diffuse layer near the facej. 262,263 the case of such electrodes, inner layers at different monocrystalline areas are considered to be independent, but the diffuse layer is common for the entire surface of a pc eIectrode and depends on the average charge density o, = R V,Q~ Fig. lWb)]. The capacitance CF is obtained by the equation

-

This model is known as the model of the common diffuse layer (cDL)?~ Both models can describe only some limiting casesm and the expression for the total capacitance of a pc electrode (equivalent circuit) depends on the relationship among three lengths: (I) the characteristic size of the individual faces at the pc electrode surface, i ;(2) the effective screening length in the bulk of the diffuse layer near face j [LD$gj)]where Lo is the Debye screening length, and (3) eLq, where E is the bulk dielectric constant of the solvent and the Iength Li.I is determined by the capacitance of the inner layer of face j.


51

According to a theoretical analysis,262,267 the CDL model is valid for pc electrodes with very small grains (y* < 5 to 10 nm)with a moderate = 0.1 to 0.15 V) and for difference of E,& for the different faces (Mud dilute electrolyte solutions (c I0.01 M) near the point of total zero charge. For the other cases, the IDL model should be valid. According to electron diffraction s t ~ d i e s , 'a~solid ~ , ~ drop ~ ~ Bi electrode with a remelted surface ( B ~ D E consists ~) of comparatively large homogeneous surface regionswith y* > 10 nm and Miller indexes of (OOl), (1 1I), and (101). Between large homogeneous areas there are aggregates that consist of very small crystallites whose y* c b ( o ) .The electrical ~ ~ S by the CDL model and double-layer at such patches of B ~ D Edescribed the total capacitance of B ~ D at E ~E = const can be expressed by the relation265

om+,+ q=, 8, = 1,

0, = 1, m > n. The results of computer of many experimental CzP,Ecurves for various B ~ D E ~ simulations show that the standard deviation ~ ( A c )is smaller if Eq. (55) is used instead of (53) or (54), and thus 10-30% ofthe whole surface of B ~ D is E covered ~ with small crystallites (Y' < 10 nm).Studies of the wedge-shaped, twofaced model pc electrode show that the fraction of small crystallites at the surface is not more than 5-10%. It should be noted that the value of IT at for a pc electrode is never zero and depends on the shape of the C,E curves of individual planes, as well as on ej,but E , i n mainly corresponds to EaZo for the face with the most negative pzc.

with

264-266

63168>741152-154,260-267

(v) Electrical Double-Layer and Fractal Structure of Surfaces Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or nonfaradaic) at a given applied potential.268,269 EIS has been used to study polycrystalline Au, Cd, Ag, B i, Sb, and other electrodes. 152>249.27@273


The main difficulty in the analysis of impedance spectra of solid electrodes is the "frequency dispersion" of the impedance values, referred and modeled in the to the constant phase or fractal behavio?68,2691274 equivalent circuit by the constant phase element (CPE). The frequency dependence is usually attributed to the geometric nonuniformity and the roughness of pc surfaces having a fractal nature with self-similarity or self-affinity of the structure, resulting in an unusual fractal dimension of the interface according to the definition of ~andelbrot."~Such a structural nonuniformity may result in a nonuniform distribution of a at the electrode surface owing to the different EaZoof the different grains existing at the electrode surface. The fractal carpet is representative of this approach. The impedance of a fractal electrode is

where Zo is a preexponential factor (analogous to the inverse of the capacitance of the electrical double-layer (l/C)), w = 2 7 is~the angular frequency, j = G,and a is a dimensionless parameter with a value usually between 0.5 and 1. The CPE angle yl is related to a by

The value a = I corresponds to ideal capacitive behavior. The fractal ~ quantity that attains dimension D introduced by ~ a n d e l b r oist ~a ~formal a value between 2 and 3 for a fractal structure and reduces to 2 when the surface is flat. D is related to a by

The CPE model has been used 152,154,27&274 and it has been found that for electrochemically polished surfaces, the surface roughness is very small compared with mechanically polished surfaces.

(vi) Surface Roughness and Debye Length-Dependent Roughness Factor A new approach to the double-layer capacitance of rough electrodes The concept of a Debye lengthhas been given by Daikhin et a1.276-278 dependent roughness factor [i.e., a roughness function R(L~) that deter-


53

mines the deviation of capacitance from Gouy-Chapman model for a flat interface] has been introduced. It has been shown276278 that in the low charge limit, a limiting value of capacitance at short Debye lengths LD should follow the equation

i.e., but with Sgm, replaced by S,,] = RSgeom* In the limit of large Debye lengths (low electrolyte concentrations) the roughness would not bear on capacitance, which would thus obey Eq. (59). In other words, two limiting cases may beconsidered: (I)LD is shorter than the smallest characteristic correlation length of roughness Ih, [a(-)]= R > 1 and (2) LD> l,,,,, (i.e., LD is greater than the maximal correlation length Im,, R = 1). It should be noted that the two limiting conditions can be realized experimentally by changing, for instance, celor a. The concept of characteristic correlation length is not valid for fractal surfaces.276-278 The slope of Parsons-Zobel plots is predicted to be lower than 1 at higher c,, (small &values) monotonically approaching unity in the region of small simple extrapolation to the high concentration limit (l/Cd + 0) will considerably reduce the apparent value of c;'.Thus the treatment of capacitance data for rough surfaces should be reconsidered: (1)The value of the roughness factor cannot be derived from the reciprocal slope of the Parsons-Zobel plot in the range ofsmall c,~.(2) The intercept obtained by extrapolation of the plot from the range of small cClinto the high c,, limit does not give 1/RC~". In order to get this value, one should treat the whole lIC(l/Cd)curve by nonlinear r e g r e s ~ i o n . ~ ~ ~ . ~ ~ ~ Considerable curvature of Parsons-Zobel plots has been found in the region of small eel;thus this plot is not convenient for the characterization of surface roughness. More convenient would be the plot of R(LD)= [(I / C - 1/c~)]-'( 1 /CGC)VS. Ld, where the value of Ci is evaluated from the measurements at high concentration (c = 0.1 M) according to the Valette-Hamelin method." R(L~) is a roughness function ranging from 1 for 1/LD= 0 to >1 for 1/LD = At c > 0.1 M there is another source of deviation from the GC theory that is due to the structure of the solvent [discussed in Section II.2(vii)] which could partially compensate for the deviations caused by surface roughness.276278As noted,27gif the accuracy is high, limiting cases can be studied, enabling one to obtain

-.

54


important roughness parameters. A nonlinear regression fit of the whole curve would give the lateral correlation lengths ofroughness. It should be noted that the predicted effects could be screened by the crystallographic inhomogeneity of a rough surface, which is not taken into account.27&278 Contrary to the theoretical deviations of experimental Parsons-Zobel plots toward lower values of C' have been systematically obsen/-ed if decreases.24,28,63,67,75, 152-254,25&267,27 1-273 el This effect is mainly caused by the crystallographic nonuniforrnity of the real solid electrode surface (single-crystal faces with various surface defects).

(vii) Electrical Double-Layer Structure in Concentrated Electrolyte Solutions The division of the interface into an inner layer and a diffuse layer has been a matter of discussion in view of the molecular dimensions of the inner layer.122-126,279-285 However, the contribution of a constant capacitance is an experimental fact. Furthermore, molecular theories for electrolytes near a charged hard wall282as well as phenomenological nonlocal electrostatic theories"' predict such a component without artificial introduction of any "inner layers." This turns out to be an effect ofthe short-range structure of the solvent.279-285 Carnie and ~ h a and n Blum ~ ~ and ~ ~ e n d e r s o n ~have ~ ' calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). The full MSA expression for the capacitance is complex. However, at low eelit is com osed of concentration-independent and concentrationdependent terms.28 The concentration-independent term is not associated with any specific region of the interface, but quantitative agreement between experimental and theoretical values of capacitance at low c,l is achieved only if the contribution of the metal phase is included. Schmickler and ~ e n d e r s o n have ~ ' ~ studied several solvents and metals, using the jellium model for the metal and the MSA for the solution. Deviations of the Parsons-Zobel plot from linearity in the experimental resUlts72,286-288 at the highest concentration have been attributed to the onset of ion-specific adsorption. However, data at other electrode charges


55

show a similar behavior, whereas specific adsorption of anions should increase with increasing electrode charge. The effect of specific adsorption, as illustrated for HgMCl + ~ ~ is 0 clearly : different. ~ The extent of the agreement of the theoretical calculations with the experiments is somewhat unexpected since MSA is an approximate theory and the underlying model is rough. In particular, water is not a system of dipolar hard spheres.281However, the good agreement is an indication of the utility of recent advances in the application of statistical mechanics to the study of the electric dipole layer at metal electrodes. The nonlocal diffuse-layer theory near End has been developed28" with a somewhat complicated function ot&nd of solvent structural parameters. At low concentrations,f (Lo)approaches unity, reaching the Gouy-Chapman Cdatc +0. At moderate concentrations, deviations from this law are described by the "effective" spatial correlation range A of the orientational polarization fluctuations of the solvent. Thus, deviations from linearity of Parsons-Zobel plots are comparable with expectations from nonlocal electrostatic the0 although the analysis is restricted to only a single point on these plots.3 3 3 The physical meaning of this interpretation is similar to a recently reported interpretation in terms of the MSA of a dipole-ion mixture near a weakly charged hard ~ a l l . This ~ approximation ~ ~ ~ ~ ~provides 1 ~ a~ microscopic calculation of the spheres to which both the constant capacitance term and the deviation from the Parsons-Zobel plots were scaled. The correlation length A for such a model is proportional to the radius of the spheres. It may be simulated by a modification ofthe Gouy theory for a Debye plasma in a semi-infinite continuum with a dielectric constant that varies with the distance from the boundary. Furthermore, it is independent of specific solvent models, relying only on the assumption of an exponential decay of the polarization correlations with a characteristic spatial length A ? ~ ~ , ~ ~ ~ The local solvent structural information inherent in deviations from Parsons-Zobel plots suggests that this effect deserves further experimental i n v e ~ t i g a t i o n . " ~ . 'The ~ ~ >reported ~ ~ ~ accuracy of recent capacitance data (5%) for dilute solutions,285however, must be improved before unambiguous conclusions about deviations can be drawn.

(viii) Parsons-Zobel Plot in the Case of Nonideal Solutions Data from many experiments6j>71.72>74>287-25" indicate that the differential capacitance of an ideally polarizable electrode at Em&in nonideal

56


solutions can be described by a straight line dependence in the c', coordinates, whose slope is very close to unity. This experimental fact has been explained on the basis of a theoretical analysis of the diffuse-layer theory carried out by Grafov and ama ask in:^^ in which the theory of the diffuse layer near EC4 is built up in a general form without using the concept of ideal solution. The differential capacitance for ideal solutions differs from the capacitance Cdof the diffuse layer in nonideal electrolyte solutions. However, according to the authors, Cd at Ead in nonideal electrolyte solutions is closely related to the capacitance calculated on the basis of the Gouy-Chapman theory if the correction term indicating activity coefficients is small. For example, the concentration derivative of the mean activity coefficient ranges up to 0.10 only in concentrated NaOH solutions; thus, to a first approximation, in a wide concentration region (c 10.1 M) one can expect that c ~ / =c1.~ The above considerations can serve as a plausible explanation for the experimental behavior of the differential capacitance of ideally polarizable electrodes at in nonideal electrolyte solutions.290 In concentrated NaOH solutions, however, the deviations of the experimental data from the Parsons-Zobel plot are quite n~ticeable.~~ These deviations can be used290to find the derivative of the chemical potential of a single ion with respect to both the concentration of the given ion and the concentration of the ion of opposite sign. However, in concentrated electrolyte solutions, the deviations of the Parsons-Zobel plot can be caused by other effects,126,279-284 e.g., interferences between the solvent structure and the Debye length. Thus various effects may compensate each other for distances of molecular dimensions, and the Parsons-Zobel plot can appear more straight than it could be for an ideally flat interface.

3. Experimental Data

(i) Mercury (a) Hg in aqueous solutions Mercury in aqueous solutions is undoubtedly the most investi ated electrode interface and has been discussed in many reviews. I-1&4,99120>12' There is little to add to what is already known. A variety of methods have been used to measure Ea=o in the absence of specific adsorption (essentially, NaF and Na2S04 solutions at c + 0).


A typical set of experimental datamm is shown in Fig. 1 1. All measurements converge to the value measured by Graharnem2% At present, the EM of Hg in water can be confidently indicated5 as -0.433 f 0.001 V (SCE),i,e., -0.192 f 0.001 V (SHE). The residual uncertainty is related to the unknown liquid junction potential at the boundary with the SCE, which is customarily used as a reference electrode. The temperature coefficient of Ed of the H interface has been measured and its significance discussed.7,161

#HP

(b) Hg in nonaqueous solutions

has been discussed in the literaExperimentaldata are summarized in Table 4, where the potential in the BBCr scale is also indicated.10,109 The temperature coefficient of E#d is also available for a number of solvents.'" It is mostly positive as for aqueous solutions, but for alcohols such as methanol and ethanol, it is negative. The entropy of formation of th;: H solution interface has been determined for a number of ~ 0 1 v e n t s . " ~ ' ' ~ ~ It ~ ~is positive for all The effect of the solvent on

~~~e.l,l0,3lll08,l~,~ 12-127,zsC28g7291-324

4 1 9 2 f -1 4.1P3f&OM 4 1 9 2 f Q001

ato a05

dm *a am

am a@ dm

am 4.m

a06 40s

-*am -QO&4*Qcm

-tam OJW 41Sf Q a 4 1 5 1t a005

4-3

4129faOM

solvents investigated and smaller than in the bulk of the solution. This implies that Hg possesses a "structure-making"ability for these solvents. The preferential orientation of solvent molecules at the h e li uid surface as well as at the Hg/solvent interface has been discussed.I.I?ISJZ~IDS The structure of Hglalcohol interfaces has been investigated in several 14127m2953osJl4317-319 H&IMeQH hinterfacehas been studPapem*


59

ied by Borkowska and ~ a w c e t t ' ~ ~in. "the ~ presence of KF and LiC104. These authors have measured End (-0.326 V vs. SCE in H20)and the effect of temperature. The observed T dependence of capacitance is considerably lower than for the Hg/H20 interface. The experimental data have been interpreted in terms of a three-state model3" for the solvent at the interface. The three states correspond to solvent dipoles oriented up, down, and flat. The model has been found to reproduce the experiments at negative charges and around End, but not at strongly positive charges. This is because more orientations should be considered and in addition solvent molecules do not behave as hard spheres. Fawcett et al.317-3 19 have studied the HgIEtOH interface in the presence of various anions (BK, C104, C1-, Br-, I-). The surface activity of the anions has been found to increase in the above order. The double-layer data for HgIEtOH have been found to be similar to those for MeOH,127,293 with some difference attributable to the bigger size of EtOH molecules. The double-layer thickness has been found to differ from that expected from the real cross section of the solvent molecules.325 The higher capacitance at a = 0 for EtOH than for MeOH has been explained b a higher association of EtOH compared with MeOH.127,29331 This concept has been criticized by ~ u i d e l l i on l ~ ~the basis of Ndutas' analysis327on the role of images. The effect of temperature was also studied at the Hglethanol interface.311-319 The results are very similar to those for the HgMeOH interface.37,293 The electrical double layer in 1-PrOH + NaC104has been studied by Protskaya et and the value of En, from the potential of the electrocapillary maximum was equal to -0.31 V (SCE in H20). Japaridze et al.321-323 have studied the interface between Hg and a number of vicinal and nonvicinal diols such as 1,2-, 1,3-, 2,3- and 1,4-butanediol (BD), ethanediol (ED), and 1,3-propanediol. KF and LiC104 were used as surface-inactive electrolytes. The potential of zero charge was measured by the capacitance method against an SCE in water without correction for the liquid junction potential at the solvent/H20 contact (such a potential drop is estimated to be in the range of 20 to 30 my). The potential of the capacitance minimum was found to be independent of the electrolyte concentration while capacitance decreased with dilution. Therefore, Ed, was taken to measure Egd. These values are reported in Table 4.

T

Sergio TmWi and EM Lust

The experimental data with the diols are such that the solvents can be split into two groups: (1) those for which E,&is constant (-0.33 V vs. SCE in H20) (ED, 1,2-BD, and 2,3-BD) and the simple GCSG model is not followed because of the occurrence of specific adsorption, and (2) those forwhich End is somewhat more negative by 40 to 60 mV and whose interfacial behavior confirms the simple GCSG model of an electrode interface. Similar splitting has also been observed in the adsorption of these diols at the free surface of water.328 It has been pointed that the two groups of solvents differ by some definite structural features. In particular, ED, 1,2-BD,and 1,3-BD possess vicinal OH groups that can form intramolecular hydrogen bonds. For these solvents, the ability of the organic molecule to interact with neighboring molecules is reduced. This results in the possibility of a different orientation at the interface because of different interactions of the OH groups with the Hg surface.323The different molecular structure leads to different dipolar cooperative effects. As a result, the dependence of C on the bulk permittivity follows two different linear dependencies. The H~IN-methylforma&de(NMF) interface has been &died by the capacitance method as a function of temperature.108>294.303 The potential of Hg was measured with respect to the reference electrode Ag10.05 M AgC104 + 0.05 M NaC104 in water. The specific adsorption of C10i was found to be negligible at o < 6 pC cm-'. The experimental capacitance data have been discussed in terms of the four-state model,121,291,294 which assumes the presence of both monomers and clusters in the surface layer of the solvent. The model has been found to describe the experimental picture qualitatively but not quantitative1 . This is related to the fact that NMF is a strongly associated solvent.10f,109,294,303 The HgINMF interface has been studied more recently also by Amokrane and ~ a d i a l i l on ~ ?the basis of their new theoretical approach to capacitances. The Hgldimethyl formamide (DMF) interface has been studied by capacitance measurements in the presence of various tetraalkylammonium and alkali metal perchlorates in the range of temperatures -15 to 40°C. The specific adsorption of (C2H5)4NC104was found to be negligible.108.109 The properties of the inner layer were analyzed on the basis of a three-state model. The temperature coefficient of the inner-layer potential drop has been found to be negative at Eed, with a minimum at -5.5 pC ~ r n - Thus ~ . the entropy of formation of the interface has a maximum at this charge. These data cannot be described 10,1201294,301,310


61

by a three-state model which proves inappropriate for that specific case despite the fact that DMF is an unassociated aprotic solvent. Impedance and electrocapillary measurements of the Hglpropylene carbonate (PC) interface have been carried out in a range of temperatures by payne312and Cuong Nguyen et aL302In 0.1 M KPF6 solution, the interfacial tension of Hg was found to exhibit a maximum at E = -0.216 V vs. a calomel electrode in 0.5 M (C2H5)4NC104. The difference in End between the two techniques was less than 1 mV. End was observed to move toward more negative values as the temperature was increased. The behavior of the Hglpc interface is very similar to the HgIDMF interface.294,301,310 It can be qualitatively described by a multistate model."' However, although the model can reproduce the electric field and temperature dependencies of the inner-layer roperties, the shortcomP ings of the approach should not be o~erlooked.~ The Hgldimethyl sulfoxide (DMSO) interface has been studied by electrocapillary and capacitance measurements in a range of temperat u r e ~ .E~ ~ was ~ ' measured ~ ~ using the streamingelectrode method. All potentials were recorded in a nonisothermal cell against a 0.1 M NaCl calomel electrode (CE) in water at 25OC. The potential difference of the cell CElO.1 M NaC104 (aq.)/O.l M NaC104 (DMS0)lCE was -0.096 V. This value was used to recalculate the data.312 The entropy of formation of the interface was calculated from the temperature coefficient of the interfacial tension.3MThe entropy of formation has been found to increase with the nature of the electrol te in the same sequence as the single cation entropy in DMSO.108, 09,329 m e entropy of formation showed a maximum at negative charges. The difference in AS between the maximum and the value at Endcan be taken as a measure of the specific ordering of the solvent at the electrode/solution interface. Data lR1093314have shown that A(Wdecreases in the sequence NMF > DMSO > DMF > HzO > PC > MeOH. A negative temperature coefficient of the inner-layer potential drop was observed, -0.8 mV K-'.Estimates of dipole potential drops due to 22,23,29,30 solvent molecules gave much larger values for DMSO than for HzO,which can be ex lained by a strong preferential orientation of DMSO at the Hg surface.26,s ,304 Capacitance and interfacial tension measurements were used to study the interface between Hg and mixtures of acetone + nitr~methane.~~OThe potential was measured against an SCE in H20and corrected for the liquid junction potential by measuring the half-wave potential of the ferrocene-

'

'

P

62


ferrocinium redox couple. In 0.01 M KPF6,the pzc in pure acetone (AC) is 140 mV vs. SCE, while in pure nitromethane it is -385 mV. With the correction of the potential scale, the pzc in pure acetone becomes -220 mV. Studies of pzc in mixed solvents were also carried out by Blaszczyk eta^.^" using the dipping method. They worked in mixtures of formamide and NMF and estimated the shift of the standard potential of the hydrogen electrode, of the surface dipole potential at Hg, and of the liquid junction potential. The vibrating interface method was used by Meynczyk and coworkers'" to measure the pzc of Hg in various nonaqueous solvents, such as methanol, acetone, glycerol, formamide, N,N-dimethylformamide, propylene carbonate, and 1,4-dioxane-water mixtures. KPF6 and NaC104 were mostly used as supporting electrolytes. (ii) Gallium, Indium(Ga), and Tallium(Ga)

The double-layer structure of Ga and its liquid alloys was discussed by Trasatti in a chapter in this series in 1980~and by Bagotskaya in 1986.120Other discussions can be found in books of the NATO series.25326 (a) Ga, In(Ga), and TZ(Ga) in Aqueous Solutions

The electrical double-layer structure at the liquid Ga/H20 interface Pezhas been studied by Frumkin and Bagotskaya et al 10~103~120>335335 zatini et a1.336-338 Butler and Meehan,339Horanyi and Takas,340and Doubova et a1.341Studies of the double-layer structure at the liquid gallium electrode in aqueous surface-inactive electrolyte solutions have formed the basis for the concept of specific interaction of the electrode metal atoms with the negative (oxygen) end of water molecules. 10,103,120 Later it was found that the specific interaction of the solvent with the electrode depends on the lyophilic properties of the solvent. 10.120.334 he electrical double-layer structures of Ga/H20, In (Ga)M20,and TI(Ga)/H20 interfaces have been reported by Bagotskaya120,342,343 and rum kin" and in this work we give only a very short review of these data. Indium and thallium are surface-active compounds in these liquid alloys, so their electrochemical properties are close to those of the pure metals indiUm344,345 and thallium220,224,346,347if their atomic percentages in the alloys are 16.4 and 0.02%, respectively.


63

The values of Eud for Ga, In(Ga), and Tl(Ga) electrodes have been obtained using the unpolarized streaming electrode method as well as the impedance method, and are summarized in Table 5. In the case of the G-0 interface, the potential of the diffuse layer minimum in C,Ecurves depends on the concentration of ClOS, Cl-,and SO:- anions, and for these systems the values of End have been obtained by extrapolation of the Ed,, dependence to c:,'~ + The values of Emo obtained from the dependence of the maximum of the electrocapillary curve on cclo,- are in good agreement with the Eva values obtained from C,E measurements. It is interesting that the Ed, value for the Ga/H20 + LiC104 interface becomes more positive if +lo; increases (Allgd = 0.09 V if cNaCIO, rises from 0.01 to 1.0 M), which is in contradiction to the behavior expected for the specific adsorption of Cl- and other surface-active anions at the Ga/H20 interface.10,120,343 This effect was explained by the specific structure of the Ga/H20interface or by the negative adsorption of C104 anions at the G a 6 0 interface. For the other systems [In(Ga) and Tl(Ga)], Ed, was practically independent of c c ! ~.; Guidelli and c o - ~ o r k e r measured s ~ ~ ~ ~the ~ potential ~ of zero charge by chronocoulometry. They found that the pzc was independent of the electrolyte concentration in both NaC104 and Na2S04.However, Ea=o in the presence of sulfates was ca. 40 mV more negative. These authors have explained this apparent discrepancy in terms of the perturbation of the solvent structure at the interface by the ions at the electrode surface, which are, however, nonspecifically adsorbed. n ~ measured ~ ~ for the Ga1O.l M HCIO, Butler and ~ e e h a have interface. Horanyi and ~ a k ameasured s ~ the pzc of liquid Ga in a variety ofelectrolyte solutions using a modified version of the streaming electrode that takes into account the possibility of faradaic current contributions with nonideally polarizable electrodes such as Ga near the pzc. These have found pzc values in close agreement with those measured by Guidelli and co-workers. The differential capacity, as well as the inner-layer capacity at a In(Ga) > Hg, i.e., as the hydrophilicity of the electrode decreases.

CA

(b) Ga, In(Ga), and Tl(Ga) in nonaqeous solutions

The electrical double layer at the Tl(Ga), In(Ga), and Ga/AN + LiCf04 interface has been investigated by the impedance method.10,103,120,343,344,354,355 It was found that C at o < -0.04 C m-2 depends very slightly on E and on the metal studied, and increases in the order Ga < Tl(Ga) S In(Ga) < Hg. The values of E,& have been obtained using the unpolarized streaming electrode, as well as the C,Ecurve method (Table 5). The value of End was independent of c~iao,.At a > -0.04 C rn-', the capacity starts to increase as a rises; and at a = 0, the value of C as well as Ci increases in the order Hg < Tl(Ga) < In(Ga) < Ga. Compared with HzO, the dependence of C on E (Ci on a) is remarkably less pronounced,andthe a,Ecuwes are linear in a very wide region of a (-0.10 C m-Z< 0 < -0.02 C m-2). At a > -0.02 C m-', the a,E curves are only slightly nonlinear and this nonlinearity increases in the order Hg < Tl(Ga) < In(Ga) < Ga. Accordingly, the specific interaction of AN molecules with the surface is thought to increase in the above sequence of electrodes. The electrical double layer at Ga, In(Ga), and Tl(Ga)/DMSO + LiCIO, interfaces has been investigated by the impedance and streaming electrode he value of Ed,, was independent of cclo; The applicability of the GCSG model has been verified.357In contrast to acetonitrile (AN) + LiC104 and H20+ LiC104 solutions, a,E plots for DMSO + LiC104 solution are linear only at very negative (a < -0.12 C

66


m-2). As the negative charge density decreases, C starts to increase owing to the specific adsorption of the solvent, and the value of Ciat a = 0 increases in the order Hg < Tl(Ga) < In(Ga) < Ga. 120,355,356The maximum of the Ci,ocurves for GaIDMSO and In(Ga)/DMSO interfaces is located at small negative charge densities [for In(Ga) at a -0.03 C md2,and for Ga at a -0.05 C m-'1. The specific interaction energy of solvent molecules with the metal surface increases in the order of solvents AN < H20< DMSO, and for all solvents in the sequence of electrodes Hg I Tl(Ga) < In(Ga) < Ga. The electrical double-layer structure at GaIDMF, In(Ga)/DMF, and Tl(Ga)/DMF interfaces upon the addition of various amounts of NaC104 as a surface-inactive electrolyte has been investigated by differential capacitance, as well as by the streaming electrode method.358The capacitance of all the systems was found to be independent of the ac frequency, v. The potential of the diffuse layer minimum was independent of CN~CIO,and For Ga, In(Ga), and Tl(Ga) electrodes, the potential measured by the streaming electrode was -30 mVless negative than the value of Enso from C,E curves. For Hg there was no such difference. 301,358 The reason for the dependence of E;, on the method used was not discussed. At high negative charge densities, C is apparently independent of the electrode studied, being mainly determined by the size of the solvent (0.068 F m-2). As the negative value of o decreases, C begins to increase and becomes dependent on the nature of the electrode. At E,*,the value of C increases in the order Hg 5 Tl(Ga) < In(Ga) < Ga. According to the data in Table 5, the specific adsorption energy of solvent (DMF) molecules increases in the sequence Hg < Tl(Ga) < In(Ga) < Ga. Parsons-Zobel plots have been constructed for all the systems at a = 0 in the range 0.02 < c < 0.2 M. These plots were linear, with the value of the slope very close to unity. The values of Ciobtained by extrapolation of the C-',c;' plots to ~ 2 ='0 were in good agreement with those calculated from the C,E curves for the 0.1 M NaC104 + DMF system according to the GCSG The value of Ciincreases in the sequence of electrodes Hg < Tl(Ga) < In(Ga) < Ga as the hydrophilicity of the electrode surface rises. Ga, In(Ga), Tl(Ga), and Hg in N-methylformamide t NaC104 solutions have been studied by the impedance method.359The capacitance of the electrical double-layer for all electrodes in the frequency range 200 Hz < v < 5000 Hz was independent of v. The values of EaZowereusually

-

-


67

determined by the streaming electrode, as well as from the dependence of Con E for dilute surface-inactive electrolyte solutions. In the case of Ga, the value of Eh, is constant, but for In(Ga), Tl(Ga), and Hg electrodes, Eh, depends on eel, shifting to less negative values as the solution is diluted. Thus slight specific adsorption of C10i at In(Ga) and Tl(Ga)

seems possible. The applicability ofthe GCSG model has been tested by the ParsonsZobel approach; the Parsons-Zobel plots were linear for all systems, with the value of fpZ very close to unity. The values of C : ~obtained by extrapolation ofthe l/C(l/Cd)curves to 1/Cd = 0 were in good agreement with the values of cP* calculated by Grahame' s method. The Ci,a curves for Ga, In(Ga), Tl(Ga), and Hg apparently merge at u, ~ ~ specific adsorption of F at Ag electrodes is mainly due to themetal- Finteraction and this interaction seems to be ener etically more favorable at stepped surfaces, i.e., at an Ag(110) s ~ r f a c e8.74 . ~Using polished (with C a ) A g single-crystal electrodes, it was found that the weak specific adsorption of Er increases in the order (110) S (3 11)387>388 and G=Oincreases in the sequence of planes Ag(111) < Ag(100) < Ag(11O) as the reticular density of the planes decreases. This order of planes is in good agreement with the conclusions of Leiva and Schrnickler,428,429 who represented the metal as ajellium (with and without pseudo-potentials) and the electrolyte solution as an ensemble of hard sphere ions and According to this ~ o r k , ' " ~the , ~ most ~~ compact plane should have the smallest, and the most open face the largest interfacial capacitance. This rule was found to be the electrochemical analog of the rule that the most compact plane has the highest electronic


76

work function.3,5-7,15,32,406-410 The capacitance of the metal phase CMof the Ag(ll1) face, and the capacitance of the solvent monolayer Cs have been studied by Amokrane et al.122,414,415 Good agreement between Ci and the dipole moment of the solvent (H20)molecules (i.e., by the hydrophilicity of metals) established by Trasatti 25"1 was found and the reasons for this phenomenon were ex~ l a i n e dThe . ~ ~Valette ~ and Hamelin data150>251987-391 are in agreement with the data from quantum-chemical calculations of water adsorption at metal clusters,43w39 where for fcc metals it was found that the electrodeHz0 interaction increases as the interfacial density of atoms decreases. The adsorption of aliphatic alcohols, which adsorb on metals with the hydrocarbon tail facing the electrode surface, shows different patterns on real Ag crystal faces 440,441 with respect to quasi-perfect single-crystal face electrodes.442444 This specific point will be discussed in detail in Section 111.

According to Vitanov et al.,61,151 Ci varies in the order Ag(100) < Ag(lll), i.e., in the reverse order with respect to that of Valette and ame el in.^^^^^^^^^^^^^^-^^^ The order of electrolytically grown planes clashes with the results of quantum-chemical calculations,436,439 as well as with the results of thejeliumihard sphere model for the metal/electrolyte interface.428,429,435 A comparison of Ci values for quasi-perfect Ag planes with the data of real Ag planes shows that for quasi-perfect Ag planes, the values of q=" are remarkably higher than those for real Ag planes. A definite difference between real and quasi-perfect Ag electrodes may be the higher number of defects expected for a real Ag crystal. 15,32, 125,401,407410,416-422 Since the defects seem to be the sites of stronger adsorption, one would expect that quasi-perfect surfaces would have a smaller surface activity toward H20molecules and so lower values. The influence of the surface defects on H20adsorption at Ag from a gas phase has been demonstrated by Klaua and ~ a d e ~ . ~ ~ The temperature dependence of the electrical double-layer parameters has been determined for real393,398 as well as quasi-perfect Ag planes.3822394 For quasi-perfect Ag electrodes, the value of aEOa/aT has been found to be higher for Ag(100) than for Ag(lll), and so it was concluded that Ag(ll1) is more hydrophilic than Ag(100). For real surface~,""~"~'" 86Ead//T increases in the order (110) < (100) < (1 1I). The same order of planes has been observed for A u . ~ ~ ~ ~ linearly ~ ~ ~ E , ~ / ~ T (interfacialparameter) decreases, i.e., as the hydrophilicity increases as of Ag and Au electrodes decreases. 1 5 1 2 3 3 > 3 9 7 3 8 1 4 4 ~ 8

cd

~


77

Ag single-crystal facelelectrolyte interfaces have been studiedMgby electroreflectance spectroscopy. The shift in transition energy Ed,with E is a direct measure of the potential gradlent in the electrical double layer. It reflects the potential difference between the metal surface and the location of the maximum density of the surface state. In the region of End, there is a marked change in the slope of the Edi,(E)curve. For a < 0, the slope is typically between 0.2 and 0.3 eV V- , while for a > 0, the slope is between 0.9 and 1.2 eV V-I for Ag and Au if there are specifically adsorbed anions in solution.449,450 These results are in agreement with those obtained from surface plasmon excitation451,452 and second harmonic generation (SHG)"~ experiments, in which the optical response varies with E much more at u > 0 than at a < 0.These effects show that at a > 0 the perturbation of the metal's electronic properties is due to a closely packed layer of anions. The electronic structure of Ag single-crystal face/H20 + NaF interfaces has been studied by Chao et al.454456 by ellipsometry and differential capacitance. They found that the optical spectra at End vary strongly with the crystallographic orientation of the electrode surface, i.e., the bulk properties are different because of the anisotropy of ndm*(the ratio of the free electron density to its effective mass). The adsorption tail height increases as the atomic roughness of the Ag surface increases in the order (1 11) < (loo), which is the order of decrease in the corresponding ECd 15,3263 The large variation of A with a at a > 0,which strongly depends on the crystal orientation, has been explained in terms of a strong anddifferent Ag/H20 interaction. According to experimental data,434-456 the A,a dependence rises in the order Ag(100) < Ag(1 1l), which can be explained by a more pronounced hydrophilicity of Ag(111) than Ag(100), or by a higher adsorption activity of F a t Ag(l11) than at Ag(100). A very small interaction of Ag with H20is possible.454

'

(iv) Gold (a) PC-Au in aqueous solutions The electrical double layer at a pc-Au/H20 interface has been studied mainly by Clavilier and Nguyen Van ~ u o n g , 2 ~ame~ el, in,^^^^^ ~ ~ ~ , ~ ~ ~ ~ Beck et al.,468-470 and others.471,472 Detailed reviews have been given by ~rurnkin,"~amelin,6~ and ~ o r o t ~ n t s eOnly v . ~ ~a few comments will be added here.


A diffuse-layer minimum was found at E = -0.04 V (SCE) for 213,462 Its potential was indepc-Au/H20 (Nd, KC104, HC104) (Table 8). pendent of solution pH and but showed a slight negative shift with inmasing cl(no, and c ~The ~Parsons-Zobel ~ . plots at E* gave an average slope fpZ 2.0 for NaF, but for LiC104the linear region of these plots was very narrow. At u O the reconstructiondisappears andthe (1 x 1) structureis observed. On the reconstructad Au(l1 I) surface there are 4.4%more atoms than on the (1 x 1) smcture and on the reconstcucted Au(100) there are 24% more atoms than on the (1 x I) s l r ~ c t u r e . ~ This ' ~ ~phase transition shifts in the negative direction with the adsorbability of the anion. The adsorptioninduced surface reconstruction of Au(l11) el& has been studied in situ by second harmonic generation by Pettinger er al."' According to LEED, X-ray diffraction, electron microscopy, and STM studies, Aull 10) is reconstructed in UHV and (1 x 2) and (1 x 3) symmetries are o b s e r v ~ d . 5 ~In~contact ~ - ~ ~with ' 0.1 M KC104 at o


85

0, stacked sets ofparallel ribbon segments have been observed using STM along the [lTO] direction.467,504 Shifting the potential in the positive direction results in the disappearance of the reconstructed surface within a few seconds and formation of the (1 x 1) structure. These potential-induced structural changes are reversible and rapid; the reconstructed surface forms 2 s after the potential is movedfrom a > 0 to E = -0.3 V (SCE). According to Kolb et al.538,540 the reconstruction of an Au(ll1) surface involves a 4% compression along one of the three [I 101 directions, which yields a (1 x 23) superstructure pattern in L E ~ and ~ imposes ' a twofold symmetry on top of the threefold one?40The STM images of a reconstructed Au(ll1) surface show pairwise arranged corrugation liness4' with a periodicity of approximately 6.4 nm and a corrugation height of about 0.02 nm. A reconstructed Au(ll1) electrode has an that is about 90 mV more positive than that ofthe unreconstructed Au( 111) (Table 9).&' A freshly prepared flame-annealed Au(100) surface has been found to be reconstructed188,487,534,538 and the surface atoms exhibit a hexagonal close-packed structure to yield the (hex)-structure. One-directional longrange corrugation of 1.45 nm periodicity and 0.05 nm height has been ~ ~ , ~the ~ reconstruction ~ is lifted due found on the Au(100) s ~ r f a c e . 'When to specific adsorption of SO:- anions at more positive E, the surface changes to a (1 x 1) structure.s38 The influence of the cooling procedure after flame annealing has been studied?" The crystal was allowed to cool in air for several minutes. Thereafter the electrode was immersed in the electrochemical cell (0.1 M H2S04) under potential control at about -0.2 V (SCE). The Au(100) surface was clean, well-ordered, and completelyreconstructed.538,541 In a second experiment, after flame annealing, the Au(100) electrode was allowed to cool in air for about 4 s before being quenched in ultrapure HzO.The electrode was transferredinto theelectrolyte (0.1 M H2SO4) at E = -0.2 V (SCE) in a droplet of H20. The reconstruction rows covered about 70430% of the total surface, but on some parts of the surface the reconstruction had been lifted upon contact with the electrolyte, and on some places monoatomic Au islands were found.538After a potential cycle up to 0.25 V (SCE), the reconstmction was lifted by specific adsorption ofso!-. The unreconstructed surface is covered with small monoatomic gold islands, which are formed out of the more densely packed (hex) structure. These islands are roughly 1-2 nm in diameter, but they grow

86


with time owing to surface diffusion (two-dimensional Ostwald ripening).538,541,542 Finally, after flame annealing, the gold crystal was immediately quenched in ultrapure water in order to eventually reduce the danger of surface contamination in air, and immersed into the 0.1M &So4solution ' ' " ~treatment ~ at E = -0.2 V (SCE). According to STM s t ~ d i e s , 5 ' ~ ~ ~this yields a highly disordered surface that seems to be in a rather unreconstructed state. The subsequent application of a positive scan to eventually lift existing areas with a (hex) structure did not produce extra gold islands, supporting the view that a rapid quenching does not yield reconstructed surface areas of any significant extent. The phenomenon of surface diffusion has been studieds3! the rate of electrochemical annealing increases with E and is higher for strongly adsorbing anions. A few oxidation-reduction cycles change the surface topography by creating monoatomic deep holes that are more or less uniformly distributed over the terraces. These holes increase considerably in size at each successive oxidation-reduction cycle; they merge and form channels, while the number of newly created monoatomic deep holes remains small. The growth of the holes did not reflect any preferential crystallographic orientation. However, the merging and formation of channels suggest a preferential removal of the substrate material between neighboring holes during the oxidation-reduction cycle.5is Kolb and Franke have demonstrated how surface reconstruction phenomena can be studied in situ with the help of potential-induced surface states using electroreflectance (ER) spectroscopy.449,488,543,544 The optical properties of reconstructed and unreconstructed Au(100) have been found to be remarkably different. In recent model calculations it was shown that the accumulation of negative charges at a metal surface favors surface reconstruction because the increased sp-electron density at the surface gives rise to an increased compressive stress between surface atoms, forcing them into a densely packed structure?32 A modiied immersion method has been used by Hamm et n ~ . to' ~ obtain Ed of an Au(ll1) electrode. Clean and well-ordered Au(ll1) electrodes were prepared in a UHV chamber, transferred to an electrochemical cell by a closed-transfer system, and immersed in 0.1 M HC104 solution at various &. EOd was derived from the charge flowing during the contact with the electrolyte under potential control. For the reconstructed AM111>(22 x 610.1 M HCIOl interface, EUd =O. 3 1 f 0.04V (SCE) (Table 9). Using the impedance method, EM = 0.34 V (SCE) for recon-


87

structed Au(1 11)lO.Ol M HCIOI has been obtained.538The 30-mV shift of Ef14 has been explained by weak specific adsorption of anion.'" The behavior of Au faces in pH > 7 solutions has been stud24,63,391545-546 ied. Surface oxide formation is a two-step process: a peak at a less positive E has been explained by OH' specific adsorption24~63~'8899'~@5547; that at a more positive E in terms ofirreversible oxide formation by examining the negative moving i, E profile at various ~~~501,548

The specific adsorption of OH- ions depends on the electrode surface structure increasing in the order Au(ll1) < Au(100) < Au(311)."l The similarity of the results obtained in alkaline solutions and those observed in acid and neutral media have led the authors of many papers to conclude that surface reconstruction occurs at a < 0 and is removed at a > 0. The temperature behavior of low446,491,503558 as well as high Miller index crystal faces of Au447,448 has been examined in 0.01 M perchloric acid solutions. For all gold surfaces studied, Cd, was found to decrease and E~~ moved to less negative values with increasing T.446448,491,503,558 En*, Tplots were found to be linear: values ofdE,*/dT are presented in Table 10. The values of were in good agreement with those obtained for the same faces. For the faces of the same zone, the by Lecoeur et values of End are less positive the higher the step density on the surfaCe.24,63,446-448,503,558

The faces situated in the [OlT]zone-(51 I), (31I), (533), (755)exhibit the lowest values ofdE,,/dT, while the faces situated in the other two zones ([Ol] and [lTO]) have approximate1 similar values of dGa/dT, though slightly higher forthe 11101 zone.Ls" The values ofthe temperature coefficient obtained for the three singular faces are the highest, which confirms earlier observations that the introduction of steps lowers the values of both and d&+/dT. dE,*/dT increases for the following step-terrace combinations: (111)-(100) < (100)-(110) < (111)(1 11); i.e., the decrease in dE,*/dT is higher because the step orientation is different from the terrace orientation. This effect has been explained by Lecoeur et al.559with a model in which the adsorption of the solvent dipoles on steps occurs with the oxygen atom away from the metal, thus leading to a positive contribution of the solvent dipole to the potential and to a simultaneous reduction in the metallic &pole moment. This effect has been considered to be larger for quaternary sites of Au(100) than for ternary sites of Au(l11).


Table 10 Ead at 298 K aad d E d T for Au Single-Crystal Faces la 0.01 M HClOd Aqueous Solutions Miller in&x of the face

Lang notation

E a a f O.OiN ve. SHE

dEbddTIrnV K-'

Soum: Silva, Sonomaya, UKL MMina, I. Chem SOC.Fatwhy k. 92.3695, lhbk 1. Reproduced with pedsdoo of Thc Royal Society of Chemirq.

Owing to the smoothng effect suggested by ~ r n o l u c h o w s ka~ ~ ~ separate account of the effects of steps and terraces is not possible for the faces studied, since the terrace width is not larger than six Au atoms.561 However, the randomizing effect of an increased dT is certainly smaller for more strongly adsorbed dipoles on steps than for dipoles adsorbed on terraces. According to the results,64,561,562 the (1lo), (31I), and (1 11) faces are reconstructed in a vacuum while the (1 x 1) structure is present in solution near E.+ The (6x 22) surface reconstruction of the Au(ll1) face under UHV has been described previously using L E E D ' ~and STM.188,471,538,545 It has been shown5" that the Au vicinal planes of the n(ll1) x (100) type, situated on the [OlT)zone between the (111) and (755) e 6(111) x (100) faces, have an identical atomic structure in solution and in UHV [faceted or (1 x 1) structure]. Crystal faces, such as (11,9,9) lO(111) x (100) or (433) # 7(111) x (100) for example, show an electrochemical behavior similar to that of a surface consisting of (755)


89

and (111) faces. The (111) and (755) orientations have their own E,*+ and so each vicinal face has a pseudo-pzc E;:Y. Unlike a true EUd. the value of Eva cannot be determined directly using the C,E-curve method since the Cd, observed in dilute solution does not correspond to the pseudo-pzc of the vicinal face studied. A method for the determination of ~ $has9 been developed. A plausible explanation for the apparent contradiction of v i e ~ has been s offered ~ by Komyshev ~ ~and Vil-~ fan.563On the basis of model calculations for noble metal (1lo), (11I), and (100) faces, an interplay has been demonstrated between a dlrect effect of the electric field and field-induced ionic adsorption. A phase diagram which in the charge-temperatureplane has been obtained the~reticall?~~ shows that deconstructionfrom the (1 x 2) phase to the (1 x 1) phase as a changes to more positive values proceeds via three transitions. Starting at negative potentials and going toward positive E, the surface first constructs to a disordered phase by an order-disorder Ising transition and thereafter undergoes a roughening transition of the Kosterlitz-Thouless universality class. Finally, at more positive charge, deroughening of the electrode surface takes place by another transition to the 1 x 1 phase. The range of a within which the intermediate surface state exists is 1 pC ~ r n - ~The . interaction of the surface with fluctuating H 2 0 molecules may affect the phase transitions. The double-humped structure of the C,E curve for Au(ll0) has been related to the difference in the pattern of molecular reorientations on the two different surface configurations: the hump at more positive E is composed of two peaks, one of which is due to the deroughening of the Au(ll0) surface to the (1 x 1) phase structure. The missing spike at the ordering transition to the (1 x 1) structure has been explained by the existence of water feedback but it might be only an extra smeared maximum with a width one-fourth of the separation between the humps.563

(a) PC-Cu in aqueous solutions

PC-Cu samples as well as single-crystal planes have been studied564-587 in contact with various aqueous electrolyte solutions. The data are somewhat controversial, since the main experimental difficulty with Cu is its great tendency to surface oxidation. The potential of the minimum in C,E

~

~

~

90


curves depends on the electrolyte as well as on the method of surface preparation564466,568 and lies at small negative E (Table 1l), i.e., outside the region of ideal polarizability of Cu electrodes. This minimum probably corresponds to Cu covered with surface oxides. Using the open-circuit potentiostatic scrape method, remarkably negative values of End have been obtained for fresh pc-Cu electrodes. 141370.580 According to these data, the value of Enafor pc-Cu is independent of the nature of nonadsorbed electrolytes (NaF, Na2S04), while it becomes more negative in the sequence NaC104 < NaF < Na$04 < NaCl< NaOH < KI. Adso tion of SO:- has been confirmed by radiotracer and SERS studies.58115'sq Ed is independent of the nature of the c a t i ~ n . ' ~Using ' . ~ ~ ~an immersion method, Turowska and Soko l o ~ s k have i ~ ~ found ~ = -0.06 V (vs. AdAgCl in 0.01 M LiCl) in 0.01 M sulfate solution. Although the pzc has been found to be independent of pH between 2 and 8.5, and the authors rule out surface oxidation, the value falls suspiciously close to the high range of pzc values. Electroreflectance data for ~ c - C Uconfirm ' ~ ~ that the capacity minimum at E = -0.2 to -0.3 V (SCE) is due to the oxidation of the electrode surface. According to impedance data, as for pc-Ag and pc~ ~ , 6 3 , 6 7 , 7the 4 roughness factor for a pc-Cu electrode is approximately 2, which has been explained by the high surface inhomogeneity of the electrode surface. Using impedance data of TBN' adsorption and back-integration,z9>588a more reliable value of Ed was found for a pc-Cu electrode574,576 (Table 11). Therefore, differences between the various Em values are caused by the different chemical states and surface structures of pc-Cu electrodes prepared by different methods (electrochemical or chemical polishing, mechanical cutting). Naumov et n~.'~' have observed these differences in the pzc of electroplated Cu films prepared in different ways. (b) Cu single-crystal faces in aqueous solutions

Cu crystallizes in the fcc and its melting point is 1356 K. The experimental data for single-crystal Cu/H20interfaces are also controversial. 567-570s72-57s The first studies with Cu(111), Cu(100), and Cu(ll0) in surface-inactive electrolyte solutions (NaF, Na2S04) show a capacitance minimum at E less negative than the positive limit of ideal polarizability of Cu electrodes (Table 11). Ed, depends on the method of surface


92


preparation (electrochemical polishing, selective chemical polishing).5",V1-578 E ~decreases , as the reticular density of the plane increases. Thus the difference between E ~ for , various planes is approximately 200 mV and the value of Ei, for pc-Cu is somewhat less negative than Ed,, for the plane with the less negative value of En+ 571 The applicability of the GCSG theory to Cu single-crystal face electrodes has been tested572by the Parsons-Zobel method. At E ~ "fpz, is equal to 2 and this large value has been explained by the joint effect of a large surface roughness and the energetic inhomogeneity of the faces. However, it is thought that the large value of fpzcan be explained by the surface oxidation of Cu electrodes. The same tendency has been found for electropolished single-crystal faces of Bi, slightly oxidized at moderate anodic potentials in neutral surface-inactive electrolyte solutions, for which the value of the reci rocal slope of the PZ plot increases as the oxidation of Bi takes place.L More reliable values of for Cu single-crystal faces have been obtained by Lecoeur and ~ e l l i e with r ~ ~ electropolished ~ Cu(ll1) and Cu(100) in NaC104+ H20solutions (Table 1I). Ed,has been found to be independent of c ~ d and ~ v, , i.e., ClO; anions are surface inactive at Cu single-crystal faces. The Parsons-Zobel lots are linear, with values offm very close to unity. Foresti et ~ l . ~ ~ ' h a v ebeen able to study the Cu(1 lO)/aqueous solution interface by impedance as well as chronocoulometry. These authors have found Eaa = -0.93 f 0.01 V (SCE). Also, the validity of the GCSG model has been verified. As for Zn single-crystal electrodes, reliable values of End have been obtained indirectly from the dependence of the adsorption-desorption peak potential EmU of TBN' on the crystallographic orientation.574,576 It has been found that F shifts toward more negative potentials in the sequence Cu(1ll) < Cu(100) < Cu(1lo), and this order is related to the increase of E , for the correspondng face. Thus the value of En4 decreases as the atomic density of the face decreases, which is in good agreement with the general behavior observed with fcc metals (Au, 4 3 ) 5'24'63 (see Section III for more details). ~ o r n a n o w s k has i ~ ~at~ tempted theoretical calculations of the capacitance and work function of Cu faces. Reconstruction of the Cu(l11) close-packed surface at room temperature upon oxygen adsorption has been reported by ~ i e h u s . This ' ~ result is in good agreement with data on cyclic voltammetry and second-harmonic generatiod9'; it has been concluded that oxygen-containing spe-


93

cies are present on the Cu(l1l) surface, which implies that the Cu(111)/ H20+ NaC104 (pH-7) interface is not ideally polarizable in the electrical double-layer region. In situ atomic force microscopy has been used to study the interfacial properties of the low-index faces of Cu single crystals in aqueous HzS04 and HC104 solutions.5921593 Cu(ll1) has been found to exhibit the correct hexagonal structure in H20+ HCD4 solution (pH = 1 to 3), while an 0x0-overlayer has not been found. Cu(100) at E = -0.63 V (SCE) in 0.1 M HC104 solution shows a square configuration with an atomic spacing of 0.26 f 0.02 nm, which is the correct structure and spacing for the Cu(100) orientation. Upon sweeping to more positive E [(-0.08 V (SCE)], a square lattice was also evident, but it was rotated 45" with respect to the underlying substrate with an interatomic separation of 0.36 f 0.02 nm; i.e., this structure was consistent with a c2 x 2 ~ v e r l a ~ e r . ~ ~ ~ In situ resolution of the crystalline order has been achieved by Villegas et on Cu(100) electrodes purposely disordered by oxidation or ion bombardment. Ordering was achieved by chemical and electrochemical etching and confirmed by LEED, SEM, and STM. The Cu(11O) surface in dilute (0.003 M, pH=2.5) HC104 at E= -0.13 V (SCE) (160 mV more ne ative than the rest potential) exhibits a correct unreconstructed structure.593 Sweeping the potential back to the rest potential created additional features whose most probable source is an oxide (or hydroxide) adlayer. The behavior of these adlayers qualitatively obeys the Pourbaix diagram.592-594 ~ e s u l t s obtained '~~ in the pH-potential region of the Pourbaix diagram,595where the bulk Cu@ oxide formation is thermodynamically unfavorable, indicate that these adlayers are related to the initial stage of oxide formation on Cu(100) and Cu(11O). The strength of the Cu-0 bond will be lower on the Cu(ll1) face than on the Cu(100) and ~ u ( l l ~ ) .Indeed, "~ the Cu-0 stretching frequency in UHV is lowest on the (1 11) face and only a disordered oxygen structure is observed.'" These results suggest that a specific Pourbaix pH-E phase diagram is needed to describe the behavior of each low-index face of Cu. The electrical double layer at Cu(l1 I ) electrodes in aqueous electrolytes (NaF and Na2S04) at various pH values has been studied by CV and ac impedance methods by Hartinger and ~ o b l h o f e r . ~ The " electrode pretreatment consisted of electrochemical polishing (3 min in &PO4 + H2S04 solution) followed by annealing in a nitrogen atmosphere (3 hr at 600 "C). These authors found that in the whole region of E, the prerequisite

94


of "ideal polarizability" of the Cu(ll1) electrode in aqueous electrolytes is not satisfied owing to the occurrence of HzO electrosorption, and no information on End of the Cu(l11)/H20+ NaF interface can be deduced from these features. From radiotracer studies it has been known that the adsorption of ClO;S, HSOi, and Cl-at Cu starts at very negative E.143,598 It has also been shown that the surface coverage with ions depends on the solution's pH and on E. This suggests that both specifically adsorbed anions as well as OH*- are present on the surface of a Cu(ll1) electrode and the rnixedphase oxides are plausible at pH < 7, whereas CuzO is predicted to be unstable in the potential and pH region studied by Hartinger and Doblhofer. It is concluded that the electrosorption reaction is likely to involve coadsorbed anions along with hydroxyl groups.597

(vi) Lead (a) PC-Pb in aqueous andnonaqueous solutions The impedance characteristics of pc-Pb have been obtained in aqueous 220,221,599 -607 and nonaqueous (glacial acetic acid, MeOH, EtOH, dimethyl formamide)10,74,60&612 surface-inactive electrolyte solutions. The first attempt to obtain the potential of zero charge of pc-Pb with a mechanically polished and remelted surface was made by Borissova et 220,221 in 1948 and 1950. PC-Pb anodcally polished in H20+ NaF (0.001 < c ~ -0.03 C m'2, the curves were nonlinear, which was related to an increase in Ciin the order (0001) < (lorn)< (1 120). The same order was obtained by computer interpolation of the calculated Ci,a cusves at a = o.~' Studies in surface-inactiveelectrolyte solutions with various organic compounds (cyclohexanol, 1-pentanol, 2-butanol, camphor, tetra-buthyl arnmoniumion, TBN+)show that the adsorption-desorption peak shifts to more negative potentials in the order (0001) < (lorn)< (1 1m);this was explained by the increasing negative value of E,,* in the same direclion.259,62%35

C, E curves have been obtained for Zn(0001) andZn(lOT0) at various cwa with different additions of T U ! ~ ~The~ data ~ ~for - Zn(0001) ~ ~ ~ at cm = const have been used to obtain c'.~ l p l o t sNonlinear . plots have resulted, with the value of the reciprocal slope remarkably dependent on cW.At CTU = 0.1 M, the reciprocal slope of the PZplot is 1.1, increasing with decreasing cn]. Such an effect has been related to the weak specific adsorption of OH' on Zn. This explanation has been critically discussed by ~ o r o t ~ n t s who e v ~has ~ assumed that the effect635,636 is connected with the variation in the compact layer composition of the ZR(H20+ TU interface as CTU varies.


103

The R of electropolished Zn single-crystal face electrodes has been obtained from the shape of the adsorption-desorption peak of cyclohexan01 at various Zn and Hg surfaces.'" The roughness factor of Zn electrodes has been found to increase in the order Zn(0001)< Zn(IOTO) < Zn(l120)with values in the range 1.1 to 1.25.

(ix) Cadmium (a) PC-Cd in aqueous solutions The electrical double layer of pc-Cd electrodes has been studied in many works,10,220,221,271,637,662 but the picture is still somewhat unclear. The first attempt to determine the electrical double layer parameters at solid Cd, Pb, and Tl electrodes by the impedance method was made by Borisova et al.220,221 A diffuse-layer minimum was found in the C, E curves, but the capacitance dispersion was appreciable and the value of C at Ed, for Cd was higher than that calculated using the C, E curve for Hg.10~220~221 It was notedlo that one of the reasons for this was the roughness of the pc-Cd surface. Therefore, Cd, Pb, and ll electrodes were remelted in an inert atmosphere to give solidified drop electrodes. The capacitance dispersion was somewhat lower, but the difference between calculated and experimental capacitance was still substantial.221 According to experimental results, 10,22&224,637443 only P appears to be surface inactive at p c - C W O interfaces,with Ednindependent of C N ~ and v. Specific adsorption of anions increases in the order F 5 SOS < CIOi < O K c NO; S N Q < Cr < Br' < 1'. The Parsons-Zobel plot was linear and at Ed gave the value fpz = 1 . 3 0 . ~ ~In' some pap e r ~ the ~f ? ~ ~ for ~ pc-Cd/NaF+H20ranged from l. 10 to liJ? ,~ obtained The same value was obtained for 0.005 to 0.1 M KF + H,O solutions. Ci,5 curves have been reported in some papers,10~74~1u)~271~357~w but the spread of C; values at a = 0 was remarkable (ACi = f15 /rFcm-').~ realistic value of probably ranges from 30 to 40 pF cm-2 and at o 221,643 and can be explained by the inhomogeneous surface structure of chemically treated electrodes. Experimental investigations in aqueous solutions of "structurebreaking"ions (ClOi,BF ) show some new features with respect to NaF: (1) a moderate shift of Efi, to more negative potentials with increasing c,,, (2) higher values of capacitance at Efi,, (3) higher values of fpz for LiC104than for NaF solutions, and (4) higher values of c:=' On the basis of these features it can be concluded that the surface activity of C10i is higher than that of F . ~ ~ ~ D and fractional exponent a (Table 15) show that the surface of electrochemically polished Cd electrodes is flat and free from components of pseudo-capacitance. The somewhat higher values of D for electrochemically polished high-index planes and for chemically treated electrodes indicate that the surface of these electrodes is to some extent geometrically and energetically inhomogeneous. However, the surface of chemically treated Cd electrodes, in comparison with the surface of mechanically polished or mechanically cut electrodes, is relatively flat. 153,249

.

The inner-layer capacitance of Cd faces increases as the atomic density decreases. It has been suggested that hydrophilicity increases in the order Cd(0001) < Cd(lOT0) < Cd(lTZ0).The same order has been proposed on the basis of data on organic compound adsorption.15" (x) Bismuth

The electrochemical ro erties of bismuth solid drop electrodes have been studied extensively lY2 466M97 and several reviews74,153,219,254,670-672 have been published.

PP

(a) PC-Biin aqueous solutions The pc-Bilaqueous solution interface has been studied mainly by Palm et a1.666-669Ed and other fundamental characteristics were obtained. The electrical double-layer structure at a bismuth solid drop O )investigated by Salve electrode with remelted surface ( B ~ D E ~ M ~was

111


and palmb7' (Table 16). F and SO$ as well as Li'and Na+were found to be surface inactive, while C104 ,, ' K Pb', and Cs'showed weak specific adsorption. The dispersion of C with v in the region 60 < v < 20,000 Hz was 5 to 6%.666-61 2 The Parsons-Zobel plots were linear for -0.03 < a < 0.02 C m-2with fpZ = 1.01 to 1.03. These data have been interpreted in terms of a high geometric uniformity of BiDER .670 Ci,a curves for the B ~ D E ~ Minterface ~ O have been simulated by the ~ a r s o n and s ~ ~~ ~a m a s k i n - ~ r u m k imodels.672 n ~ ~ ~ > ~Unlike ~ ~ the data for Hg and Cd, in the case of B ~ D Ethe ~ , agreement of the experimental results with theoretical calculations is not g o d for a 2-0.03 C rn-2. Better agreement has been observed after correction of the inner-layer model for the component of the potential drop in the metallic layer (i.e., for the capacitance of the metallic phase). In spite of the high geometrical uniformity, the surface of B ~ D Eis ~energetically (crystallographically) inhomogeneous, as indicated by the splitting into three or four independent maxima of the adsorption-desorption peaks for various organic compounds.153,219,254,671 Electronographic studies show that at the B ~ D E ~ surface, monocrystalline regions with a linear parameter I > 10 nm exist. A more detailed discussion is given in Section II.2 (iv).

Table 16 Potentials of Zero Charge of pc-Bi in Various Solvents E n d f 0.01N VS. uq.

Solvent Hz0 MeOH EtOH I -PIOH 2-PrOH 1-BuOH 2-Me-1-PIOH 2-BuOH EGa AN

DMF DMSO 'EG. ethylene glycol.

SHE

Ead f 0.01/V vs. BBCr

References

112


Thermally evaporated thin bismuth films (thckness 20 to 150 nm) have been studied in aqueous solution of various electrolytes (NaF, Na2S04, LiCIO,) by the resistometric meth0d.6~~ An important feature of the resistometric response of Bi is the intersection of the AG, E curves (AG = surface conductance change) at E = -0.6 V (SCE), which is somewhat ~~~ more positive than E,, for pc-Bi [-0.625 f 0.01 V ( s c E ) ] . ~ ~This has been explained by the fact that AG is mainly determined by the electrode free charge a and the surface scattering effect of the carriers is small. The values of C for thicker films674are in the range 15 to 20 pF crnq2, which are in agreement with C values measured by impedance.6 6 6 7 2 Mishuk et a1.675,676 have applied the modified amplitude demodulation method to electrochemically polished pc-Bi in aqueous NaF solution. The curves of the real component of the nonlinear impedance 2" as a function of the electrode potential, unlike pc-Cd and pc-Pb, intersect for various CN.F at E = -0.62 V (scE):~~ i.e., at En* for PC-Bi, as obtained by impedance.666672The different behavior of pc-Bi from pc-Cd and pc-Pb at a > 0 has been explained by the semimetallic nature of pc-Bi electrodes. A comparison of inner-layer nonlinear parameter values for Hg, Cd, and Bi electrodes at 0 c 0 shows that the electrical double-layer structure at negative charges is independent of the metal.675,676 Small amounts of molecular oxygen can influence the value of E ~With ~the rise. of the ~ 0,concentration ~ ~ in the electrolyte solution, the form of the Z':E curve changes and the value of Ea+ shifts toward less negative values. However, the effect is weak; after saturation of the solution with molecular hydrogen and holding the pc-Bi electrode for 30 min at E = -1.35 V (SCE), the original shape ofthe Z', Ecurves and the original value of End is restored. This indicates that oxidation and reduction of a pc-Bi electrode surface are reversible processes.

(b) PC-Bi in nonaqueous solutions The electrical double laver at B ~ D E has~ been studied in various 677,678 ~ ~ ~ , 6 7 9 , 6 m nona ueous solutions: MeOH, ~ ~ , 4DMSO:~~ 8 ~ ~ 2 - p f i ~ , @isomers 2 of BuOH,693496 and ethylene EtOH,%93m 1-PrO~P91 glycol ( E G ) ~ ~ The B ~ D E ~ / M ~ O interface H has been studied in the presence of various electrolytes (Na', K+,Rb', C s', N H f , and ,'F C10;). The Parsons-Zobel plots show a remarkable curvature at eel < 0.05 M KF (Table 16). At c < 0.01 M, a more remarkable deviation from linearity has

~ ~


113

been observed.677,678 These deviations for more dilute KF solutions have been explained by weak specific adsorption of K*ions at a < < 0 and F anions at a 2 -0.03 C m-*,as well as by ionic association in the bulk of the solution and an abnormal dielectric constant value within the GouyChapman layer. Critical discussions of the data for the B ~ D E ~ I M ~ ) H system have been given.74,153,254 A more detailed analysis of this system shows that a more probable reason for this effect is the crystallographic inhomogeneity of the B~DE' electrode. C,o curves have been derived a curve from that and for CKF 5 0.01 M, a noticeable deviation of the Ci, for concentrated KF has been observed. l h s deviation can be explained by experimental errors in obtaining the values of C, c,l, and S,, as well as by the crystallographic and energetic inhomogeneity of the B ~ D E ~ electrode sWfaCe.152715376777678 The B~DE~/DMF + NaCIOI interface has been investigated for 679,680 The capacitance dispersion 0.002 5 cnno, S 0.5 M by impedance. with v is not greater than 2-3%. A very deep diffuse-layer minimum was , well as of v. Thus C10i observed, and Ed, is independent of C N ~ O as and Na+ are surface inactive at this interface. Parsons-Zobel plots in the range -0.03 S a S 0.03 C m-' are linear, withfavery close to unity. Higher values of fpZ at ~7= 0.02 C m-2 have been explained by weak specific adsorption of C10i Ci obtained according to the GCSG method is independent of cclo;Thus the deviation of the B~DE~DMF + NaCIO, interface from the GCSG model is substantially smaller than in AN or -

.

~~0~~480,677482.

The influence of the content of Hz0 in DMF (from o to 90%) has been studied in a 0.01 M KF solution.679>680If the addition of H@ is g 20%, the value of Ehn const. A pronounced dependence of Ed, on the amount of H20(>25%) is observed; and for 90% H20+ 10% DMF, Emin = Edfor H20+ KF solution. The B~DE"IANinterface has been studied by impedance in LiCIOI as well as in solutions containing Cl', Br-, I-,and SCN-.480,681 In LiC104 solution, the capacitance dispersion in the region 905 v < 1100 Hz is no greater than 2-5%. The diffuse-layer minimum potential Edn is independent of cclo; for cclo; < 0.005 M. For more concentrated solutions, a moderate shift of EA, to the negative side has been observed, which is explained by the weak specific adsorption of C104' .C*,a curves have been calculated for various c,l according to the GCSG theory. At c,, > 0.02 M, a small dependence of C; on c,i has been observed. A high value off,= 1.30 has been obtained. According to data for Bi single-crystal face

-

114


electrodes in ~ ~ , a probable ~ ~ reason ~ for 7 the~ deviation ~ ~of 7 B ~ D B ~ / A+ N LiC10, from the GCSG model is the crystallographic inhomogeneity of a polycrystalline Bi surface. The B~DE~DMso+ LiCIOl interface has been studied by impedance and a very well-developed diffuse layer minimum has been observed, with Ehn independent of c ~ ~ The ~ ~capacitance , ! ~ ~ dispersion was no greater than 2 to 3% in the region -1.5 I;E < -0.3 V (SCE in HzO). Linear Parsons-Zobel plots with fpz very close to unity were obtained, Ci was independent of cuao,. The B~DE'/E~OHinterface has been studied in various electrolyte solutions [LiC104, LiF, KF. (CJH9)4NCI04,LiC1, LiI, LiSCN] using i r n p e d a n ~ e . The ~ ~ ' capacitance ~~~~ dispersion in the range 60 < v < 5000 Hz was negligible (3 to 4%). E ~ was , independent of CL~CIQ, and v. The same value of E d , has been obtained using very dilute KF + EtOH solutions. The Parsons-Zobel plots for -0.03 c o ^^^ models. The experimental Ki, T dependence has a minimum at T = 20°C. The influence of the potential drop in the metal phase has been taken into account. The electrical double layer at B~DE~/ROH and B ~ D E ~ / ~ - R Oin-H terfaces with the addition of various electrolytes (LiC104, Lil, LiSCN, KSCN) has been studied using impedance.691693 The Em was independent of c,, and v. A weak dependence of C on v has been found at cuao4< 0.01 M and at e > 4.03 C m-2, and the equilibrium differential capacitance Cd has been obtained by linear extrapolation of C vs. to wl'* = 0. Parsons-Zobel plots at o = 0 arelinear,with fez = 1.01 f 0.01. The values of 01 have been obtained according to Grahame and Soder-

~

~

~


115

berg,bB76W and at all rand bl. i.e., the specific adsorption of anions is weak. The electrical double layer at B ~ D Ein ~1-butanol, 2-methyl-lpropanol, and 2-butanol + LiC1O4 solution has been studied by irnpedance.69H96 The values of chave been recalculated taking into account the incomplete dissociation of LiC104 and the effect of ionic association in butanolic solutions. The values of C have been extrapolated to w = 0 using the C, dl2dependence. The capacitance dispersion was small at 0 < < 0, but at u 2 4 0 3 C m'2, it increased somewhat (AC = 5 % at u = 0). EA, was independent of Q ~ O , for all butanol isomers. The Parsons-Zobel plots were linear, with fpz close to unity. The Ci, a curves increases in at a < < 0 were independent of the butanol isomer, but the sequence 2-methyl-l-propanol < 1-BuOH < 2-BuOH. The inner layer integral capacity Ki(a)plots have been calculated, Ki at ad, increases in the sequence 2-BuOH < 2-PrOH < 1-BuOH < 1-PrOH< EtOH < MeOH. But at o = 0,Ki for 2-PrOH and 2-BuOH is remarkably higher than for MeOH, EtOH, and 1 - M H . For solvents with a linear hydrocarbon chain, adnis independent of the length of the hydrocarbon chain, while for solvents with a nonlinear hydrocarbon chain, oh, is appreciably more negative. T h s has been explained in terms of decreasing specific interaction between solvent molecules and metal atoms in the order 1-PrOH < 2-PrOH < 2-BuOH, as well as by a more pronounced association of 2-PrOH and 2-BuOH in the inner layer compared with EtOH, 1-PrOH, and 1-BuOH. Thus the increase of the negative value of Eud in the sequence of solvents 2-PrOH < I-PrOH < EtOH < MeOH < H20can be explained by an increasing specific interaction of solvent molecules with surface Bi atoms.696 LiC104. The ~ i ~ ~ ~ l e t hglycol ~ l einterface ne has been studied in LiNQ3, LiC1, NaBr, NaI, and CsCl solutions using impedance. The dispersion of C with vin LiCIQ, LiNO,, and KF solutions is no greater than 2-3% if 110< v < 1100 Hz. The adsorption of ions increases in the sequence of cations Li', Na' < K+< Cs+,and in the sequence of anions F, ClOi < N Q < C1-, Br- < I-. 697 Ed. was independent of cm and v. The linear character ofthe a,Ecurves is taken to indicate that the potential drop in the adsorbed solvent layer and thus the orientation of EG molecules is independent of a for Bi as well as Hg electrodes.323,697,703 The distance between the a,E curves for Hg and Bi at a < < 0 is equal to the difference in the zero-charge potential for the same metals in EG: A # & ~ = 0.18 V. Only at a 20 is the curvature of the a. E curve

116


somewhat higher for Hg/EG than for Bi/EG. This has been explained by stronger specific adsorption of ClOi at the Hg/EG interface7" than at the B~DE~/EG interface.697

(c) Bi single-crystal faces in aqueous solutions The Bi external electronic configuration is (sZp3);it crystallizes in a rombohedral system, with two Bi atoms linked to each lattice point of the unit cell. The melting point is 544 K. Electrochemically polished Bi single-crystal faces were first used for electrical double-layer studies by Frumkin, Palm, and co-workedw in 1974 using impedance. The Ed, (Table 17) was observed to be shifted 30 mV toward more negative potentials compared with B ~ D E and~ electrochemically polished polycrystalline Bi (p~-~i).6M70 The En=,-, for Bi(ll1) in Na2S04 solution was 30 mV more negative than in NaF (KF) solutions owing to the nonsyrnmetrical type of electrolyte.7MParsonsZobel plots in KF solution were linear, with fpZ very close to unit for BiDE and pc-Bi, whereas a higher value fPZ = 1.25was obtained7J for Bi(ll1). Later, Bi(OlT), Bi(2TT), Bi(001), and Bi(lO1) faces were studied.28,152,253,254,705 The accuracy of the experimental results has been established by statistical analysis. A very slight variation in capacitance (3-6%)with v (from 60 to 21,000 Hz) was observed for electrochemically polished single-crystal Bi. Therefore, to a first approximation, the measured admittance was identified with the differential capacitance C. In the case of the (OOl), (OlT), (101), and (2TT) Bi faces, the dependence of End on the atomic density of the face is small ( AE =20 mV) (the sZp3electron configuration is the same), but a definite trend of End to become more negative with increasing atomic density can be detected.28,253,254 However, the difference between En=* for the above faces and the Bi(ll1) face is noticeably higher (55-75 mV) and this can be explained by the different surface states of the Bi faces. According to pearson," the surface atoms of the (OOl), (101), (OlT), and (27T) Bi faces have unsaturated covalent bonds (sZp3-valencestate) whereas the surface atoms of the Bi(ll1) face are chemically saturated, being able to form bonds with the aid of hybridized sp3d20rbitals.Moreover, the electronic properties of Bi strongly depend on the crystallographic orientation, and it may be assumed707J08 that in the case of Bi(lll), the value of the dielectric permittivity of the Bi phase EM = e33 = ell = 78, while for

Table 17 EJectrSd DonMe-Layer Parametem of Bi Single-Crystal Faces in Vari ~ a a vs. 4. Solvcnt

Elccmdc

SHE

&.dV vs. BBCr

( a w a1mV

CY

fk

D

d

118


Bi(O1T) and Bi(2TT), e~ = ell = e 2 =~el = 100. Talung the Thomas-Fermi reciprocal length roughly independent of the crystallographic orientation, (kW)-' = 0.38 n m the thickness lM and the potential drop in the metal phase can be According to these calculations, iM and the potential drop in the surface layer of Bi(ll1) are somewhat higher than for Bi(2TT) and Bi(0lT). Thus the work function is lower for Bi(111) than that for Bi(O1T) and Bi(2TT), and therefore End must have a more negative value for Bi(ll1) than for other Bi planes.28,253,254 Parsons-Zobel plots are linear [except for Bi(2TT;;for 0.003 c CN* c 0.1 Mwithf, = 1.01 to 1.10 at a = 0.28,152,153,254 The Parsons-Zobel plot for Bi(2T T) is linear only for 0.007 5 c,l 5 0.1 M. The nonlinear character of the Parsons-Zobel plot for Bi(2TTl at eel < 0.007 M has been explained by the nonsingular surface structure of this plane (Section 11.2).~5~J53

Fractal dimension D and fractional exponent a,presented in Table 17, show that the surface of electrochemically polished Bi electrodes is flat and free from components of pseudo-capacitance. A comparison of the data for LiF, NaF, and KF solutions with those for LiC104 and NaBF4 solutions shows that a very weak specific adsorption of BE and ClOa anions occurs at the Bi/&O interface as 0 2 0. At the potential of the shallow capacity minimum (cr c < 0), only a very slight rise in the capacity has been observed in the sequence LiF S LiC104 5 NaF < NaBF4 < KE The Eh, for NaBF4 and LiC104 aqueous solutions is shifted approximately 15 to 30 mV and 30 to 50 mV, respectively, to more negative values compared with NaF aqueous solution. The Parsons-Zobel factor fpz and the height of the capacitance "hump" in the Ci* u curve at 0.03 < a < 0.05 C rn" increase in the sequence NaF i KF < NaBF4 < LICI04, which can be explained by stronger adsorption of ClOa than of F.152,153 Ci, a curves have been derived according to the GCSG theory and the Valette-Hamelin approach.67 Ci rises as the atomic density of the face decreases, except for ~ i ( l l l ) . " Thls is in good agreement with the theoretical calculations by Leiva and ~chrmckler:~~ which predicted the lowest interfacial capacitance for the most densely packed planes. The capacitance of the metal phase CMhas been calculated according to the Amokrane-B adiali model, and the thickness lM= 1/4xcM as a function of decreases in the order Bi(ll1) > Bi(lO1) > Bi(2TT) > Bi(O1T) > Bi(OOl), which is in agreement with other data.28,152,153,707,708 The influence of the surface pretreatment of Bi single-crystal faces has been studied, and a noticeable dependence of End on the surface structure has been established.152,133


119

The effect of the addition of various surface-active organic compounds (cyclohexanol, camphor) to an aqueous solution of Na2S04 in contact with Bi single-crystal faces has been studied by Raud et al.709-7 11 using ellipsometry. sG- was not specifically adsorbed, but at E> -0.5 V (SCE), slight oxidation of the Bi faces was possible. (d) Bi single-crystalfaces in nonaqueous solutions

The admittance of Bi single-crystal faces in alcohol + LiC104 (methanol, ethanol, and 2-propanol) hai been measured between 80 and 410 Only a slight variation of C with v (3-5%) has been found. Equilibrium C values have been obtained by extrapolation of the , independent of linear C, oln dependence to oln -+ 0.The E ~ was cclo; in 1 x lw3724 Splitting of the adsorption-desorption peak into two independent maxima has been f o ~ n dfor~ cyclohexanol ~ ~ > ~ ~adsorption ~ at an electrochemically polished pc-Sb electrode; accordingly, the difference between the of individual faces has been estimated to be on the order of 80 to 100 mV. Pullerits et a1.723studied specific adsorption of 1-from an aqueous solution at constant ionic strength.

Table 18 Electrical Double-Layer Parameters of Sb in Various Solven Et74Nvs.q.

Solution

H f l + m03 HS+KF;NI~F H20+ NaF McOH +

H20+ KF

Elcdmk

S ~ D E ~ -0.18 f 0.01 S ~ D E ~ -0.17 f 0.01 pcsb

S~DE~ Sb(l11) sb('J01)

worn

E m + LiC104

SHE

sa(2rr> Sb(l11) Sb(OQ1)

&d,Nvs.

BBCr 0.47 f 0.01 0.48 f 0.01

(&&,/a

log cYmV

-

-

Jk 0.90-0.95 1.10-1.14

122


In MeOH + HC104, Eh was independent of C ~ C I O ,as well as of v; thus it has been taken as of Sb in MeOH (Table 18). The values of Gaderived from the experimental data7" are somewhat lower than for the Bilmethanol interface. (b) Sb single-crystalfaces in aqueous and nonaqueous solutions

Sb possesses the same external electronic configuration (s2p3)and crystalhzes in the same rombohedral system as Bi. Its melting point is 904 K. Single-crystal Sb electrodes were prepared with the same method as that developed for Bi electrodes.281152.153>725>726 The (111) face is the most perfect, and the (001) plane is the additional plane of cleavage of Sb; therefore the (1 11) and (001) orientations can also be defined by cleaving the massive crystal at the temperature of liquid nitrogen. The final surface was prepared by electrochemical polishing in saturated aqueous solution of KI with 0.5% HCl. Impedance measurements have shown that the Ead of the (111) and (001) faces is roughly equal to -0.46 V and -0.37 V (SCE), respectively, i.e., En* is about 30 to 50 mV more positive than the potential at which the oxidation of the Sb single-crystal faces starts. Therefore, cyclic voltammograms and impedance measurements were made in weakly acidified (with HC1, pH = 4 to 5) NaF solutions. As for Bi single-crystal faces in H20, Sb(ll1) exhibits an appreciably more negative value of Ed compared with the other planes (Table 18). The difference in Madfor Sb(001), Sb(OlT), and Sb(2K) is no more than 0.05 V, and decreases as the atomic density of the surface increases. The E,=o for the S ~ D electrode E ~ has an intermediate value.28,152,153 According to the independent diffuse-layer electrode model,67,26&263 result indicates that the faces, which have more positive values of E ~ than Sb( 111), predominate at the S ~ D surface. The Parsons-Zobel plots are linear in the range of concentrations 0.002 c c,, 5 0,l M,with fpz somewhat higher than unity. Just as for Bi single-crystal faces, fadecreases slightly with increasing v and bl.Ths indicates that an,fpz somewhat higher than unity at a = Ois mainly caused by the crystallographic inhomogeneity of the electrode surface. The fractal dimension D for Sb single-crystal faces is somewhat higher than for Bi, which can be explained by-the higher energetic and-crystallographic anisotropy of the S b electrode sulface or by a more pronounced anion adsorption at cr = 0.28,725,726


123

The Ci values for Sb faces28,725,726 are noticeably lower than those for Bi. Just as for Bi, the closest-packed faces show the lowest values of Ci [except Bi(ll1) and Sb(l1l)].28,152,153 This result is in good agreement with the theory428,429 based on the jellium model for the metal and the simple hard sphere model for the electrolyte solution. The adsorption of organic compounds at Sb and Bi single-crystal face electrodes28,152,726 shows that the surface activity of Bi(ll1) and Sb(ll1) is lower than for the other planes. Thus the anomalous position of Sb(ll1) as well as Bi(ll1) is probably caused by a more pronounced influence of the capacitance of the metal phase compared with other Sb and Bi faces.28 The electrical double-layer structure in the region of ideal polarizability of Sb(l11)EtOH and Sb(001)EtOH interfaces has been investigated by impedance and cyclic voltammetry.28,714 The value of Eh, is independent of cclo;, with an accuracy of f 10 mV in the range 5 x lod4< cnq < 5 x 10-3 M. AS for H ~ o , AE,,=,-,in ~ ~ EtOH ~ for ~ Sb(001) ~ ~ and ~ . Sb(ll1) is higher than for Bi(ll1) and Bi(001). The Parsons-Zobel plots in EtOH are linear with fpz somewhat lower than for aqueous solutions, which can be attributed to the weaker dependence ofthe values of E,*on the crystallographic orientations in EtOH than in HzO. The Cil o curves calculated according to the Valette-Hamelin approach67 are monotonic since the fitting coefficient is equal to 1.03 for Sb(ll1) and 1.06 for Sb(001) at clja4 = 0.1 M. for Sb single-crystal faces in EtOH are lower than for Bi, which has been explained by the lower lyophilicity of Sb, as well as the higher thickness of the thin metal layer.28,152,153

cd

(xii) Iron

(a) PC-Fe in aqueous and nonaqueous solutions Fe electrodes with electrochemically polished (cathodically pretreated for 1 hr) and renewed surfaces have been investigated in H20+ KF and HzO+ Na2S04by Rybalka et ~ 1 . ~by~impedance. ~ ; ~ ' A ~ diffuse-layer minimum was observed at E = -0.94 V (SCE) in a dilute solution of Na2S04 (Table 19). In dilute KC1 solutions Ei, was shifted 40 to 60 mV toward more negative potentials. The adsorbability of organic compounds (I-pentanol, 1-hexanol, cyclohexanol, diphenylamine) at the Fe electrode was very small, which has been explained in terms of the higher hydrophilicity of Fe compared with Hg and Hg-like metals.

~

~

~



125

(l/oC), E curves of pc-Fe electrodes with a renewed surface have been recorded 1 min after the electrode was cut by a ruby knife.728In KF solution End was in good agreement with En=,,for electrochemically polished Fe electrodes.727As in the case of Hg and other "Hg-Iike" electrodes,1° Ed for Fein Na2S04+ H@ solution is 30 mV more negative than in KF (NaF, LiF) solution, owing to the asymmetry of the electrolyte. A diffuse-layer minimum in C,E curves has not been found with electrodes kept 3 min at E = -0.74 V, i.e., at a potential close to the rest potential of ~ e . *Complete ~ cathodic reduction at Ecc-0.74 V (SCE) is not achieved since a diffuse-layer minimum is not found for cathodically reduced electrodes. This effect has been explained by the oxidation of Fe. According to impedance data, strong specific adsorption of C1' anions at renewed Fe electrodes occurs since a very large shift of E,*takes place going from KF to KC1 solutions. According to Safonov etal. ,729the &d for pc-Fe obtained in aqueous solutions727,728 corresponds to an active iron surface, free from any oxides. A dependence of the pzc on pH has been observed and discussed by ~ a z a r o v a . ~A~collection ' of experimental data up to 1994 is given in a paper by Turowska and ~ o k o l o w s k i . ~ ~ ~ The electrical double layer at the renewed Fe(LiCI04interface has been studied in nonaqueous aprotic solvents by Safonov et al. using impedance.729>732-736 Renewed Fe electrodes are ideally polarizable in a limited region of potentials in the following aprotic LiC104 solutions: 1,1,3,3-tetramethylurea (TMU); N,N-dimethylformamide; N,N-dimethylacetamide (DMAA); N-methyl-N-2-pyridylformamide(MPF), and hexamethylphosphoramide (HMPA). The rest potential of a renewed Fe electrode in an LiC104 + TMU system is equal to -0.35 V (SCE in H20), independent of q~clo,.-ANand DMSO were unstable in contact with a renewed Fe surface.733 The Eh, in C,E curves depends on time; for F e m U + LiC104,E ~= ,-0.8 V (SCE in H20) just after surface renewal and -0.35 V (SCE in HzO)after 15 min. One minute after the Fe electrode is cut, the decrease in the components of impedance (1 /C, and R) at E = const is no greater than 5 to 7% in the regon -1.4 V < E < 0 V, and the dispersion of C with v (70 to 1OOO Hz) is no greater than 10%.729>732-73" The values obtained729for Ed are summarized in Table 19. The ParsonsZobel plot at Ed, is linear, with fpZ equal to 5.0 in TMU and 4.8 in HMPA.~ The ~ ~surface structure of renewed electrodes consists mainly of patches of close-packed faces with a linear parameter of 5 4 nm. The relaxation of the surface back to the equilibrium state is very slow ( 7 -


126

10-15 min.). X-ray diffraction data show that in some places the surface of renewed Fe, Pt, and Ag electrodes is amorphous and the thickness of such a "Beilby" layer is on the order of 5 to 10 nm. Thus, reconstruction of the surface is probable during the experiments with a decrease in surface roughness with In the region of Emin+ a very good correspondence has been found between experimental and calculated C,Ecurves and this has been taken to indicate that the electrical double-layer structure conforms to the GCSG theory. Comparison of the Ci,E curves for HgITMU and Fe/TMLJ shows that the dependence of Cion E is less pronounced for an Fe electrode than for H RMU, and the values of Ci for Fe are remarkably lower than for ~ g . ~The ' same is the case for Fe/D)ME DMAA, MPF, and HMPA interfaces.732-736 On the basis of a,E curves obtained by integration of C,E curves, it has been estimated that the contribution of the solvent to the interfacial potential drop is substantially higher for Fe than for Hg in TMU. Accordingly, strong chemisorption of solvent molecules, weakly depending on E, is probable at an Fe/TMU interface.729,732-736 C1-has been found to be ~ , values of C (in specifically adsorbed. However, at a 2 + 2.OpC ~ r n -the 0.02 KC1) are lower than those in 0.02 M LiC104.The same effect has ~ , and ~Pt, and ~ has~been 1explained ~ by ~ a ~ been reported for Ni, ~ partial charge transfer from C1- to the If eel- > 0.02 M, at 0 > 0. anodic dissolution of Fe occurs. The activity of anions at the Fe/TMU interface increases in the sequence ClOa c CI-c Br- < I-. The values of C at E = const are independent of the chemical nature of the cations.729

C

(b) Fe single-crystal faces in aqueous solutions

Fe crystallizes in the bcc system and its melting point is 1808 K. The atomic density of the faces increases in the order Fe(ll1) < Fe(100) < Fe(ll0) (Table 19). Fe(100) and (111) single-crystal faces in sulfate or perchlorate solutions (pH = 2.5) have been studied by impedance.739The electrodes were grown at 750 to 780°C from FeBrzinpure H2atmosphere and reduced for 1 hr at E = -0.95 V (SCE) in the working solution. A diffuse-layer capacitance minimum was observed, with Ed, independent of c,l (Na2S04,KCl, NaC104).Thus, SO:' and ClOi are surface inactive on Fe single-crystal faces. The Parsons-Zobel plots for Fe(100) and Fe(ll1) were linear, with fpZ somewhat higher than unity. This has been explained

1

~

~

~

127


by problems related to obtaining the exact working area of the Fe single crystal. The inner-layer capacitance decreases from Fe(ll1) to Fe(100) as the atomic density of the face increases.

(xiii) Nickel (a) PC-Ni in aqueous solutions

The E,& of pc-Ni is located in the ne ative potential range and depends strongly on the solution's pH. According to impedance data,7m~d,in aqueous H2S04depends on pH: Ed,, (V, SCE) = -0.461, -0.493, -0.528, and -0.572 for pH = 0.94; 1.4, 2.14, and 2.97, respectively. Using the method of galvanostatic pulses, minima have been found at E = -0.38 V and 4.68 V for pH 3.5 and 5.8, respectively.741Using the closed-circuit scrape method, E ~ =,-0.48 V at pH = 3 and -0.61 V at pH = 5.6.7" Using the hardness method, Tyurin et a1.742have reported two pzc values and &) for pc-Ni as a function of potential. pH effects have also been observed [at pH €4, EAd = -0.44 V;E : =~-0.64 V(SCE)]. Thus, widely scattered Ed, values have been reported by different aUthors730,7w742at similar solution pHs (Table 20). (b) Ni single-crystal faces in aqueous solutions

Ni crystallizes in the fee system: the atomic density of the faces increases in the order (110) < (100) < (111). Its melting point is 1726 K. Ni single-crystal faces in H20+ H C l Q or H2S04solutions have been investigated by Arold and Tamrn using impedance.743Ni (100), (1lo), and (1 11) single-crystal faces were prepared by the method described by Table 20

EIectrical Double-Layer Parameters of Ni in Aqueous Solutions E Electrode pc-Ni

Ni(100) Ni(ll0)

Solution H2S04 (pH = 2.97) H2S04(pH=3.5) H2SO4(pH = 3.0) HC104 (0.003M) HC104(0.003 M)

d vs. SHE

Atomic dcnsitylcm-2 References

-0.33

-

-0.11

2.2

-0.24

-

-0.39 f 0.02 -033 f 0.02

I .O 1.0

-

-

-

1.614~10'~ 1.141~10'~

740

74 1 730 743 743

128


Batrakov and ~ a u r n o v a . A ~ ~diffuse-layer ' minimum has been observed, , of v and c,, (Table 20). In the case of Ni(l11) and with E ~ independent pc-Ni, the capacity also decreases with dilution, but no deep minimum was observed in the C,E curves.743 The Parsons-Zobel plot at Eminwas linear, giving an fpZ = 1.Very low Ci values have been obtained. This result is surprising in light of Ni and Fe hydrophilicit y : by analogy with sp-metals (Ga, Zn), one would expect relatively high Ci values. The difference between sp- and sd-metals has been explained by a different strength of the interaction between the metal surface and solvent molecules.743The Efin for Ni( 100) is slightly dependandunlike HC104solutions, a maximum at Ci, a curves has ent on CWWI, been found at a > 0. These observations probably indicate that weak specific adsorption of SO:- or HSO; occurs. This has been suggested743 as a plausible reason for the marked dependence solution' s pH730,74@742

Water adsorption and dissociation on Ni( 111) and Ni8(6 + 2) clusters have been studied by ab initio quantum-chemical calculations.744-746

(xiv) Aluminum First attempts to study the electrical double layer at A1 electrodes in aqueous and nonaqueous solutions were made in 1962-1965, 182,747,748 but The electrical double-layer structure at the results were not successf~l.~" a renewed Al/nonaqueous solution of surface-inactiveelectrolytes such as (CH3)4NBF4,(CH3)4NC104,(CH3).$JPF6, and (C4&)flBF4, has been investigated by impedance.749-75 1 y-butyrolactone (y-BL), DMSO, and DMF have been used as solvents. In a wide region of E [-2.5 < E < -1.0 V (SCE in HzO)], C is independent of time, and renewed A1 electrodes can be considered ideally polarizable. C increases in the sequence y-BLI DMSO < DMF. In dilute solutions, a minimum in the C,Ecurves has been observed, with Efi, independent of eel.The Parsons-Zobel plots for various solvents are linear, with the values of fPZ in the range 1.12 (DMSO) to 2.0 ( y - ~ ~ ) 7 4 9(Table , 7 5 1 2 1). C,E curves were integrated to obtain a,E curves. As in the case of Fe/DMSO, Fe/DMF. PtIDMF, Pt/AN, Pd/DMSO, and PdAN, 108,109,729the da/dEforAl/DMFandAY~BLsystem is halfthat for Hg or ~ i .The ~ value of daldE for an Al/DMSO system is comparable with HgIDMSO. A comparison of the C,E curves for A1 electrodes with the corresponding

~

>

~

~


curves for Hg,Bi, Ga, and In{Ga) shows that C incram in the order Hg < Bi < Ga < A1 and for A1 e l e c w in the order y-Bt < DMSO < DMFMF74%75 1

(a) PC-Pt-gmupmetals in paueous solutions

Pt and Pt-group metals (ply- and single crystals) have long been among the most intensively studied systems in electrochemisnevertheless reliable Ed values have been determined only recently. The first attempt to obtain the pzc of R-group metals in H@ by impedance was made in 195tSaam The E& was found to depend on solution pH. These results and other experimental problems have been critically discussed by Frumkin et a2.8J0*11*759 A dependence of Ed on solution pH for a pc-Pt ekclde (heated a few minutes in a hydrogen atmosphexe at 673 K and thereafter for 4 5 hr in pure Ar at 723 K)was reported by Bocks et a1.,3701760 who provided a quantitative relation Em = 0.5623 (RT/E) pH (SHE). As noted by Frumkin,loa pHdependent Emd70,760probably m p n d s to a p P t surface o o v d by chemisorbed OH radicals. The capacitance at anodically polarized pc-Pt elecides was measured by Schuldinw et al.761,762 using very short current pulses, In H2m4solution, a minimum in the C,E curve was observed at &= 0.23 V versus the reversible hydrogen el(RHE). The effect of heat treatment on the E& of p l A d R has been investigated by Pehii and U ~ h m a e v & . ~ has been found to shift to the negative side with increasing temperature of the heat treatment. @y6K1QllJap1441@18W15752--

130


Frumkin et al.'s analysis8~11~14 in 1970 led to the conclusion that in the case of nonpolarizable electrodes, since the Pt-group metals are in the regions of H or 0 adsorption, two values of zero-charge potential can be defined: End and Ew (see Section I). The pzc of H-adsorbing metals depends on a solution's pH, and the values are given in Table 22. A "classical" adsorption method has been used to determine pzc, and the = 0. surface excess of protons has been obtained by titration: at Ew, fH+ The values of End obtained by the scrape method [Ed = -0.22 V at pH = 7.0; E,,& = -0.54 V (SCE) at pH = 11.01~"are in reasonable agreement with the data of Frumkin et al.8,10,11 On the basis of the ronounced influence of anions on hydrogen adsorption on pc-Pt,8,10,11,1 it has been inferred that Ed must lie in that potential region. However, such a small positive En* value is in contradiction to the high work function of pc-Pt (@ 2 5.7 eV).782,783 Recently it has beenestablished that specific adsorption of various anions (SO:-) also occurs on negatively charged surfaces.140,186,188 It is thus an inadequate approximation to relate the value of En=,-,to the potential where anion adsorption commences. The influence of foreign metal adatoms on E,= of Pt and Rh has been investigated by Podlovchenko and co-workers.7&-765 It should be stressed that in the case of pc-Pt electrodes the crystallographic structure of the surface probably exerts a very pronounced influence, so that the experimental pzc and pztc values do not correspond = 0. to the condition Results for other metals of the Pt-group are due to Frumkin and co-workers8,10,11,14 (Table 22). However, an electrode with the surface renewed in closed circuit has been used by ~ a z a r o v ato~study ~ ~ Ed of Rh as afunction ofpH. In 0.005 M Na2S04,End = -0.09 0.02 V (SCE), while in 0.5 M NazS04, pH2.5, E o a = -0.22 V is reported. E d has been found to depend linearly on pH with a slope of ca. 55 mV. Ths has been explained by the adsorption properties of Rh toward H and 0 , which shift En4 to more negative values. Anions have been observed to specifically adsorb on Rh mojg strongly than on Pt in the sequence SO:- < Cl- < Br- < I-.

P

zK

(6) Pt-group metal single-crystalfaces in aqueous solutions The surface electrochemistry of Pt single-crystal electrodes has been exhaustively studied using cyclic voltammetry.100~186-188~197J09~4'2~753756,771,-n3n79-788,7W-796 This technique has been proved to be highly


'Ilrble 22 Continued Metal

ElaAmlyk

0.3 M HF + 0.12 M KF QH = 2.4) 0 5 M Na$Or + 0.005 M Hz% @H = 2A) 0.1 M KU + 0.01 M HCI @H = 20) N&04 @H = 1.0) N a 0 4 @H = 7.0;

w v s .

SHE W v s . SHE

4.01

-

4-06

0.10

-0.13 0.21 052

0.06

-

-


133

sensitive both to the crystallographic structure and to the surface chemical composition of Pt. Its use for in situ surface characterization has been widely developed in the past few years and a detailed description has been achleved for stepped surfaces at an atomic leve1.754-756 Phenomena such as step reconst~uction~~~ and step coalescence756have been investigated by voltammetry. Most adsorption studies have been carried out at Pt(l1 I), which is a relatively simple surface without reconstsuction over a wide range of interfacial conditions (E, chemical composition); nevertheless, its electrochemical behavior is not yet fully understood.186,754-756,785,794-7% A detailed study of the voltammograms of Pt(1 11) prepared by the flame annealing method shows anomalous peaks associated with the specific adsorption of anions rather than with hydrogen adsorption.754-756 In the case of HC104 and HF solutions, such features have been attributed to the adsorption of OH', but in H2SO4solution they are explained by SO:- or bisulfate adsorption.757Double-layer charging has been observed only in a very narrow potential region [0.1 < E < 0.35 V (SCE) in 0.05 M H2SO4] which depends on the chemical nature of the anion. Recent LEED and electrochemical STM studies have brought some insight into the relationship between the microscopic surface structure and the electrochemical properties of Pt electrodes.768,769 In several recent in situ infrared (IR) studies, potential-dependent ion adsorption has been discussed in terms of spectral parameters, such as band splitting, band intensity, and band center shifts.2M.207.210J7@772 Some data for anion adsorption suggest an influence of H20on their adsorption. Vibrational spectra of H@ adsorbed at the gaslsolid interface have been obtained for different metals. EELS data at Pt(1 11) indicate the predominance ofintermolecular H-bonding, giving rise to icelike structures matching the pattern of the metal substrate.774 ore recently, isolated water molecules adsorbed on Pt(l11) have been observed at low coverages (8 < 0.13)y5Wagner and ~ o ~ l a have n ~ estimated ' for Pt( 111) in HF aqueous solutions the value of 0.22 V (RHE) for Ea4 by comparing voltammetric curves and high-resolution electron energy loss spectroscopic data for water +H+ coadsorption from the gas phase. However, the number of other methods useful for liquidlsolid interfaces is limited and among these, X-ray scattering should be mentioned,776,777 Some Ed measurements with Pt single-crystal faces have been published recently.140,210,773 Iwasita and Xia210prepared platinum single crystals according to the method of Clavilier et a1.186>773 After flame annealing and cooling in an Hz+ Ar mixture, the electrode was protected

'


134

with a droplet of H20and transferred into the cell .Cyclic voltammograms were recorded to locate the double-layer region 0.35 < E < 0.6 V(RHE). FTIR reflection adsorption spectra for Pt(ll1) in H-0+ HC104 (0.1 M)"' have shown bands corresponding to 0-H stretching and H-0-H in-face deformation of adsorbed H20 molecules. At 0.35 V (RHE), water orientation changes from hydrogen down to oxygen down and this has been taken to indicate that the zero-charge potential of Pt(ll1) is close to this value. In the potential region corresponding to the anomalous peaks of Pt(lll), the bending frequency decreases consistently with a strengthening of the H20-Pt interaction. Surface water clusters (trimers, tetramers) prevail on the surface at 0.35 V (RHE), adsorbed molecules being tilted with respect to the surface. At higher potentials, the molecular plane becomes oriented perpendicularly and lateral H-bonds are broken. Above 0.50 V (RHE), the H20-metal interaction has been observed to increase, with eventual dissociation of H20at the ~urface.~" Hamm et a1.14' treated a Pt(ll1) surface in a UHV chamber by sputtering and annealing until the surface was clean and well ordered.779>780 Transfer of the electrode to the electrochemical cell was carried out in an Ar atmosphere in a closed system. The voltammogram in 0.1 M HC104 was identical to that for flame-annealed Pt electrodes in a conventional electrochemical ce11.140,'86J53J*7781 The current peaks in the potential range -0.16 to 0.13 V (SCE) were attributed to hydrogen adsorption with a total charge density 140 f 20pC ~ r n - ~and , in the range 0.28 < E < 0.58 V (SCE) to OH' adsorption (HzO decomposition) (total charge density 106 12 pC cm-'). A very narrow potential region, 0.13 <E It' ~was ~ "found that the pztc depends on pH in different ways for Pt(1 11) and Pt(1 lo), which demonstrates that not only is the pztc structure sensitive, but also that it varies with pH.795The value of pztc for Pt(1 11) is more positive than that for Pt(1 lo), and dEw/apHis higher for Pt( 111) than for Pt( 110). A detailed study of N20reduction on a variety of single-cr stal Pt-group metal electrodes has been reported by Attard et al. 1!27,$6.787 Single crystals were polished to a mirror finish, flame annealed several hours, and quenched in dilute HF. Cyclic voltammograms were recorded in 0.1 M HCI04.By comparison with previous experimental data196'783 it has been noted that N20reduction current maxima occurred exactly at Clavilier' s Ew. Thus, it has been suggested that there is a direct correspondence between Ew and the potential of N20reduction at amaximum rate. 197,786,787 The importance of a local value of EQ4 has been emphasized, especially with respect to reconstructing metal surfaces such as Pt(100) and Pt(l lo), which can beprepared in a variety ofcrystallographic states. The sensitivity of NzO reduction to local pztc, &Fs1, has been suggested to derive from blocking N20 adsorption by ionic species, whose surface concentration is a function of the local surface charge. values estimated by Attard et a1.46are reported in Table 23.

ED'


-a8----8-

-4 -

0 0 0 0 0 0 0 0 0

@ d

m

@ e U

W

X

X

X

X

X

X

XAAXXXXZX

~

-

d

e

-

e

d

-

~

d

-

d

d

d

w w Y w V V w w V

t 2

$ 7 6 aw ags

x E

?$!! 2

6 Z c ;

d

~

d



According to Table 23, the values of Ew for single-crystal face electrodes are in reasonable agreement with those for pc-Pt metal electrodes, although on (111) surfaces possessing good long-range order, the As a function of value of tends to lie at more negative Ethan E Z# > @a'm1 W > ow ever, the metal, the sequence is @ in contradiction to the trend expected on the basis of the atomic density of Pt surfaces and experimental results for other FCC metals&8,24,74 (i.e., observed experimental order for Pt is It should be noted (see Section I) that Em, by its nature, cannot be related to the work function as definitely as E.+ Therefore expectations based on the behavior of End are inadequate for Ew shifts toward negative values as anions are adsorbed. Thus the anomalous position of can be explained by higher anion adsorption (probably ClO;) at Pt(ll1) in accordance with the general behavior of fcc metals. For the same reason, the value of Ew for terraces has been found to be more positive than that for steps. As mentioned, the value of Em reported by Clavilier et a ~ . for ' ~ an~ electrochemically faceted Pt(ll1) surface lies between and G)sk~. It should be stressed that for pc electrodes a single value of Ew is ambiguous, and it is better to refer to such a potential as "pseudo-potential of total zero charge" since both positively and negatively charged regions may coexist on the surface (a= 0 ) (see Section II.2).

. @locpP;"~*'.

EE'

w)RD)

(c) Pt-group metals in nonaqueous solutions

Pt and Pd with a renewed surface obtained by cutting with a ruby knife under the working solution have been studied by Petrii and Khomchenko7" in AN. The roughness factor of platinum, obtained from the hydrogen desorption peak in an aqueous solution,?98was about 3.94.0, and for Pd 3.3-3.4 (Table 24). The frequency dependence of capacitance did not exceed 10-12% inO.O1 M LiC104 and 15% in 0.001 M LiC104. A minimum appears in the C,Ecurves in dilute solutions of LiC10, in AN, and its potential 1-0.48 f 0.02 V (A@. l M AgN03in AN)] does not shift with the electrolyte concentration. The Parsons-Zobel approach has been used to study the nature of the minimum.797The PZ plot has been found to be linear, which has been attributed to the diffuseness of the electrical double layer. The slope of the plot is close to 1, whch has been taken as supporting the correctness of the choice of the roughness factor and of the

Table 24 Potentials of Zero Charge of Pt-Group Metals in Nonaqueous Sol Metal

Solvent

PC-R PC-R Pt(l00)

AN DMSO AN

R(111)

AN

PC-Pd

AN DMSO

PC-w

"Fcrriciniumlfammm sak.

Electrolyte

&.o+O.O3V vs. aq. SHE

vs. F e r r i h "

0.14

-

0.09

NaC104 NaC104

-

-

0.32 0.24

&=r~+o.OlV

-0.51 f 0.01 -0.51 f 0.01 -

-

&4+0.02V vs. BBCr 0.73 0.69

-

-

0.91 0.84

140


dielectric constant of AN in the diffuse layer (bulk value). The constancy of the potential of the minimum with the concentration of LiC104 indicates an absence of specific adsorption. No indication of diffuseness has been found in solutions of NaC104,which may be due to certain specific adsorption of the less solvated Na' cation. According to data for aqueous solutions, specific adsorption of cations is higher on Pt-group metals than on other metals. The potential of zero charge of Pt in AN solutions is more positive than for Hg, Bi, Ga, and InIGa alloy.3543531m The shift of E,,, in the transition from the latter metals to Pt does not correspond to the change in @, which indicates strong chemisorption of AN on the Pt surface. The minimum in the C,E curves for Pt and Pd is retained as a small quantity of H20 is added to AN, while En=,-, shifts to the positive direction as the amount of H20increases. In the presence of C&. the potential of the diffuse-layer capacitance as well as the minimum value of the capacity remain unchanged, which has been explained in terms of very weak adsorption of C6& on Pt The potential dependence of Con Pd in AN is somewhat more marked than for Pt, and the values of Care somewhat higher. This has been related to different chemisorption of AN on Pt and Pd. As for Pt, the potential E,* of Pd shifts to positive values as the amount of HzOin AN increases. The addition of C&& does not change the values of Cand Em, for ~d.'" The adsorption behavior of AN on Pt has been investigated by Conway and c o - w o r k e r for ~ ~ both ~ ~ ~polycrystalline ~ and single-crystal surfaces. The orientation of AN molecules at Pt sin le-crystal face electrodes has been studied by Fawcett and co-worker& using SNIFTIRS. It was found that En=,, for PtIAN is independent of the crystallographic structure, which has been explained by the very strong adsorption of AN at Pt single-crystal face electrodes. At renewed Pt and Pd electrodes in AN with different additions of (C2H5)4NBF4,Petrii et a ~ . ~have " observed a broad capacitance minimum in a wide potential range (-1 V for Pt and 0.8 V for Pd). The values of En* have been observed at -0.43 f 0.03 V for Pt and -0.30 f 0.03V (AdO.1 M AgCl in AN) for Pd. Ed is independent of the nature of the The PZ plots are linear, with fPZ = 1.0. It has been anion (ClO;, BE). foUnd802,803that very small additions of Na+ (1 x lod M)in the dilute

LiC104 + AN solutions cause the disappearance of the diffuseness of the electrical double layer at both Pt/AN and PdIAN interfaces. Thus the activity a', which has been of cations increases in the order Li' < (C2H5)JN*< N explained in terms of lower solvation energy for Na+than ~ i + . ~ ~ ~ - ~ ~ ~


141

The electrical double-layer structure of a PtIDMSO interface has been investigated using the potentiostatic pulse method.80sThe value of C at E = const, as well as the potential of the diffuse layer minimum, have been found to depend on time, and this has been explained by the chemisorption of DMSO dipoles on the Pt surface, whose strength depends on time. Eg4 has been found1' at E = -0.64 V (SCE in HzO). Renewed polycrystalline Pt and Pd electrodes in DMSO have been studied by impedance.'% Pt and Pd electrodes appear to be ideally polarizable in the region of potential -0.6 < E < +0.2 V (SCE in HzO) where C is independent of time. Minima in the C,E curves, caused by the diffuseness of the electrical double layer, have been found at Ed, = -0.15 V for Pt and at E = 0.00 V for Pd (SCE in H20)in DMSO solutions of LiC104, NaC104,and KClO4.Efi, was independent of eeland time, as well as the nature of the cations. The Parsons-Zobel plots at a = 0 were linear, with fn(Pt) = 19and & (W) = 2 . 0 . The ~ agreement between calculated and experimental C,Ecurves over the whole potential range has been taken to indicate the applicability of the GCSG theory to Pt/DMSO and Pd/DMSO interfaces. The dramatic difference between Ega obtained by the potentiostatic pulse method805and by impedance (Mad =0.49 V) has been explained in terms of slow but very strong chernisorption of DMSO molecules on oriented with the positive end of the dipole toward Pt. This has been explained by strong preferential adsorption of DMSO molecules, even at negatively charged Pt and Pd surfaces. Specdic adsorption of cations in DMSO is very weak compared with AN, and the adsorption activity only slightly increases in the sequence Li+ < Na' < K+ as the solvation energy of cations decreases. Unlike cations, the adsorption activity of CI-,Br-, and I- at Pt electrodes is appreciable806and increases in the given sequence of anions. At cr 399 In another case it has been claimed-'343,859 that the decrease of EVd with @ is not true, as manifested by correlating metals within the same group, for instance Ga, In, and TI. It has even been shown by the same authors that inDMSO Ed increasesas @decreases (see later discussion). In water, as Fig. 14 shows, EC4 is almost constant within the above group of metals while # varies up to 0.2 eV. However, the approach based on groups rather than on periods is chemically inadequate. It is of course possible to obtain any kind of correlation, depending on the points correlated. However, the choice must be based on sound arguments. In his theory on the variations of the bond strength and magnetic properties, Paulingg6'correlated the properties of metals along a period and not down a group. This is because a meaningful correlation involving electronic properties can be best followed as a given electronic shell is progressively filled and not as filled shells of core electrons are added down a group. According to the structure of the periodic table, metals in the same group possess similar chemical properties. Therefore they should not be correlated with the aim of obtaining evidence of a variation in the chemical properties. ' recently measured the pzc of a number of In Koene et a ~ . ' ~have amalgams of different compositions and have plotted Ee4vs. the electron work function determined in another laboratory 20 years earlier. They obtained a linear correlation of unit slope for 0.02 < xh < 0.6.However, from pure Hg to xh = 0.02, a drop in Egd of 85 mV corresponds to a change in 9 of only 10 meV. For this reason it is doubtful that such a plot can be used as a typical Ea4 vs. @ dependence. The shift in End for 0 5 x 5 0.02 corresponds to almost the whole shift from pure Hg to pure In. Thus the unit slope of the plot can be interpreted as a constancy in the X term, reflecting that of an In surface. m s implies that a variation of Ed reflects a variation in 9 (which includes a bulk term, the chemical potential of electrons, which depends on amalgam composition) rather than a surface property. Precisely for this reason, the family of In amalgams cannot be taken as representative of a continuous series of metal phases for studying the metal dependence of interfacial. properties?8 In other words, the result with amalgams cannot be used to question the correlation found for sp-metals, but rather the latter is useful to explain the former. If sp-metals are gathered in a single group as in Fig. 14, the straight line that best fits the data has the equation

The Potential of Zoro Charge

This equation does not differ appreciably from that poposed by ~ r a s a t t i ~ in 1971, whose slope was 1.33. However, in that plot there were metals inadequately placed, such as Ag and A u, because of the unreliability (as it was discovered later) of some data available at that time. Equation (62) shows that the deviations from the unit slope dependence are in turn linearly rehted to # (and &I. The horizontal distance (along the Ed axis) ofeach metal point from the line of unit dope through Hg measure AX with respect to Hg, i.e.

dX measures the relative values of the cpd at the meidwater interface. The values of AX have been s m in Table 27. Taking for XHI the value of-0.25 VzA3 [see Section ILZ(v)], the cpd for the other metals can be calculated. Thex values are also reported in ThIe 27. XM measures the changes occurring at the surfaces of a metal and water as the two phases are brought in contact to create an interface. In surface science concepts, XM corresponds to the d a m e in work function

162


upon adsorption of water.313 However, as pointed out earlier, sp-metals are of little relevance for surface science studies so that no directly measured values of A@ 1XM are available for comparison. AX results from a small difference between two large figures. Tahng into account the uncertainty in the experimental quantities involved, the uncertainty in AX may be quite high, probably of the same order of magnitude as the quantity itself for metals with low values of AX.This does not detract from the validity of the approach based on the derivation of AX the trend is more important than the precise value, and the trend, as shown later, is corroborated by a number of other correlations. The separate position of Ga is not random. It cannot be related to the uncertainty in @ or Boa values. The latter is known with high accuracy, while it can be ruled out that @ can be lower by 0.3 eV. On the other hand, it has been shown in previous correlations that Zn is probably close to Ga. The point of Zn is shown408in Fig. 14 with a question mark because of the lack of a reliable value for 4,but values of pzc for single-crystal faces suggest that Zn cannot fall in the main group of sp-metals. Thus, Ga and Zn have in common a much higher value of AX than the other sp-metals with comparable work functions. Since X a dXH + b,the major contribution is probably in 62, but this aspect will be discussed later. In Fig. 14 the points for Cu, Ag, and Au are also shown. In view of the large heterogeneity effect on the value of Ea4 for these metals, the points are those for the (110) face which, however, shows behavior close to that of a polycrystalline s ~ r f a c eWhile . ~ these metals will be discussed in a separate plot, they are also shown here to highlight the relationship with the sp-metals. Cu, Ag, and Au are sd-metals (the d-band is complete but its top is not far from the Ferrni level, with a possible influence on surface bond formation) and belong to the same group (I B) of the periodic table. Their scattered positions definitely rule out the possibility of making correlations within a group rather than within a period. Their AX values vary in the sequence Au < Ag < Cu and are quantitatively closer to that for Ga than for the sp-metals. T h s is especially the case of Cu. The values of AX have not been included in Table 27 since they will be discussed in connection with single-crystal faces. Although ECd for d-metals is not very reliable and no substantial advances have been aclueved recently, the points of Fe and Ni are included in Fig. 14 as broadly representative of d-metals. A separate discussion will


163

be given later for Ft because of its exceedingly high values for both @ and

Eu& Ni and Fe are the only d-metals for which capacitance curves displaying a nice diffuse-layer minimum have been obtained.727,743 These minima are in reasonable agreement with values obtained with renewable surface~.~" However, strongly heterogeneous surfaces are expected for these metals and therefore the behavior of a pc sample can be taken as close to the most open main single-crystal face. It has been suggested in previous correlations6,7,22,25 that d-metals probably gather around a straight line of unit slope. If this is the case, the dashed straight line in Fig. 14 has the equation: Eu4 vs. S

W = @/eV

- 5.09

(64)

This equation has been derived only as a reference for a comparative discussion of data for sd- and d-metals later on. However, the meaning of such a line is that there exists a limit to AX values in the sense that after a given top effect, a further increase in metal-water interaction will not produce higher AX value^.^'^ An indirect confirmation of this is given by the observation of a top value in the decrease of @ upon water adsorption on d-metals from the gas p h a ~ e . ~ ~ " ~ The values of AX for pc Ni and Fe are reported in Table 27 in brackets. Polycrystalline surfaces of these metals are still used both in surface science and in electrochemical studies. The relevance of Eud to the potential of initial passivation of metals has been pointed

(ii) Single-Crystal Faces Figure 15 shows a plot of Eed vs. 0 for single-crystal faces of Cu, Ag, and Au. A similar plot was reported by Trasatti for the first time in 198S407and several other times later.25,26,32,408 For a discussion of the selection of @ data, see the previous papers. It should be noted that the ECd and @ data used for Fig. 15 do not refer to the same samples. It is remarkable that each metal forms a separate group in which the faces are aligned along apparently parallel straight lines. It is intriguing that the slope of the straight lines is to a first approximation the same as that for the group of sp-metals in Fig. 14. On average, the points for the same face (the metals crystallize in the same fee system) are placed with respect to the line of mercurylike metals so that Mvaries in the sequence

SergioTrasatti and E m Lust

Fgm 15, P t o t o f ~ ~ a l o f z e m ~ ~ v s . t l ~ ~ w o o d r function, #, forthe nuin I o w - h h fact%ofQ A& ad Au. (-, Straigbt -me)

linesofunitslope.(-)~~~~~~sameslopeasthedfm spmalsinF~.M(+)W,581.FmRef.3q&d

Au < Ag < Cu and for the same metal with the crystal face (1 11) < (100) < {110), The above sequence of faces has been questioned and the opposite order has been proposedmmm However, ~ r a ~ a t t ihas ~ " shown that a proper seIedon of 9 values for still better, o f 4 sequences) leads without doubt to the order of face specificity evident in Fig. 15, On the other hand, Lemur et al.M362unambiguously proved that AX hcmm as Ed b a r n s more negative, They m u r e d 9 and EM using the same samples of several different plane and stepped surfaces of Au. These data are reported in Fig. 16 and show that the points definitely deviate horn a straight line of unit slope toward more negative AX values, as in Fig. 15. The points for the (110) and the (31 1) faces are scattered because different surface structures (reconstruction) were present in UHV and in solution.@ The dotted line has a slope of 1.27, the same as in Fig. 15. While the situahon of &* is s d e d for Au and Ag, this is not yet the case for Cu. Recently, Foresti et al.587have been able to determine & for Cu(l10). This value is shown in Fig. 15. using ofcoursethe same value

The P0tenti.dof Zen, charge

of b as before. The value is dose to the previous set of data, although a bit more negative, probably because it was obtained in acid solution with a really oxide-fm surface. On the whole, the position of Cu in the plot is confirmed by the latest results. Assuming that the dashed lines in Fig. 15 gather the different faces of a given metal, values of AX have been derived and summarized in Table 28, where the "absolute" cpd for each face is also reported based on the value of -0.25 V for Hg.As discussed in previous h o r n , Xm m e a s m the drop in work function as the given crystal face is brought in contact with water. These values ofdx are the same as those derived in previous pqmsW since there have been no recent developments. The new point for Cu(l10) has not been taken into account for the derivation of AX since homologous values for the other faces would be necessary. Note that the onIy values of AX of high reliability are in principle those for Au, specifically Au(l1 l), for which "congruent" pairs of data exist for Q and Eh Although the approach suggests that all faces should lie on the same line, no AX has been estimated for faces other than the

166


Table 28 Relative and Absolute Interfacial Parameter for Metal Single-Crystal Faces in Contact with Water Metal crystal face -Wa -X (11 dXM + G X S ) N

'From Fig. 15.

three main ones since no (even indicative) work function values are available for Cu and Ag. For the same reasons, data on single-crystal faces for metals such as Zn, Sb, Bi, Sn, and Cd have not been plotted in Fig. 15. In order to indicate the probable position of d-metal surfaces, the line described by Eq. (64) has also been drawn in Fig. 15. It is interesting that all the points for sd-metals fall between the sp- and the d-metal groups. The crystal face specificities of E,& for Sb and Bi are complicated by their semimetallic nature. In any case, no dataon 9 exist for a series of faces of these elements (only "electrochemical" work functions are available).28,864

(iii) The Case of Pt(ll1) Thus far, Ft has never found a definite position in ECd vs. @ correlations, more for the uncertainty in the reliability of its pzc than for its work function. On the other hand, Pt is a highly heterogeneous metal and the fact that only polycrystalline surfaces have been used in double-layer studies has not helped remove suspicions. According to Frurnkin's data,l0>l4 the pzc of pc-Pt is around 0.2 V(SHE) (in acidic solution). If this value is introduced into Fig. 14 (the @ of pc-Pt is around 5.5 e ~ ) , ~ ~ the, point ~ of~Pt would , ~ fall ~ far~distant , ~from~the ~line ,of ~ mercurylike metals and near the line of d-metals.

~

~

~

~

~


Recently, with the improvement achieved in the preparation and control of surfaces, a number of approaches have been devoted to the estimation of the pzc of pt(l1 l).14197210a211 These are summarized in Table 29 for convenience of the reader. The value recommendedfor pc-Pt is also rqmtedfor comparison. In three cases the pzc has been athaid indirectly and the value is strikingly close to the pzc of polycrystalline Pt. In view of the heterogeneity of Pt surfaces, h s closeness is puzzling and suggests that the phenomenon used to estimate the pzc does not conform to the concept of zero charge. The value obtained by Harnm et ~ 1 . directly ' ~ by the immersion method is strikingly different and much more positive than others reporGed It is in the right direction with respect to a polycrystalhe surface, even though it is an extrapolated value that does not cornspond to an existing surface state. In other w d ,the pzc corresponds to the state of a bare surfacein the double-layer region, whereas in m l i t y a?that potential the actual surface is oxidizsd. Thus, such a pzc realizes to some extent the concept of ideal reference state, as in the case of ions in infinitery dilute solution. It is intriguing to try to discuss such a pzc within a framework of all other metals,The first problem is the selwtion of a work function. A search of the recent liter at^^?^^^ shows that there is a range of values between 5.6 and 6.4 eV, with a strong indication that 6.1 eV may be the most appropriate value." Figure 17 shows a fust picture of the situation where Hg (as a spmetal) and Au(ll1) (as the closest sd-metal) are included. It is evident that the uncertainty in the 9 value is high enough to leave some ambiguity. However, on the whole, the point of Pt is further

Sergio Trasatti and E m Lust

away from the Hg line than Au(l1 I), i.e., the variation of AX is Pt( 1 I 1) > Au( 11I), This contrasts with the conclusions of the authors of the original paper,140who have opted for a O value of Pt( 111) in the lower range of values without any spec& motivation, If the vdue of # = 6.1 eV is taken as the work function of Pt( 11l), some speculation is possible about the value of AX.This is illusbated in Fig. 18, where it is assumed that the different faces of Pt,including the pc surface, are grouped on a straight line parallel to that fox the singleaystal faces of sd-metals (and spmetals). If so, the value of E,* given by ~rumkin''would imply that #= 5.4 eV for the pc surface of Pt, which is within the usual range of expenmental data. However, there remains the puzzling aspect that while Ed refers to a surface with hydrogen adsoxbed on it, I values do not include contributions from H adsorbed from the gas

PW* If, on the other hand, the pzc estimated at around 0.35 V(SIIE)im2'0 is taken for Pe(l11) (see Table 29), the point of Pt would be located further from the line for d-metals, with a high value of AX that is notjustified by

The Potential of Zen,Charge

the known behavior of the Pt surface. The~forethe value of EM found by the immersion method appears to fit in we11 with the general picture of all other metals. The value derived for AX from Fig. 18 is 0.33 V, while that (extrapolated)for a polycrystalline surface is speculated to be 0,57V. 4

rJHV vs. Solution Data

As discussed in M o n 1.3(i), AX indicates the variation in the work hnction of a metal as an interface is created by bringing a solid and a liquid in contact. In principle, it should be possible to compare AX vdues with A# values measured directly in gas phase experiments. This is the aim dUHV synthesis ofthe electrochemicaldouble layers68 in which the elinterface is created molecule by molecule, starting with the bare metal surface. It is thus possible to obtain evidence of ion-water interactions that can be envisaged from electsochemical measurements but that are not directly demonstrable. ~ a g n e ? has given a recent comprehensive review of "electrochemical"UHV experiments. UHV A 9 and eleclrwhernicd AX are compared in Table 30. A quantitative comparison with reliable recent data is possible only for

Sergia Trasatti and E m Lust

Ag(l lo), Cu(1 lo), and Pt(11 I), Qualitatively, the gas phase data confirm the sequence o w e d electtwhemically. In particular, A@ varies in the order Au < Ag < Cu [A@ for Au is compared with AX for the (1 10) face]; also,A 9 forCu(1lO)>Pt( 11 I). Quantitatively, however, it is evident that directly measured A@ values are on average 0.2 to 0.3 eV higher than MI values. This shift in the "potential" scale has been discussed by ~msatti,~~" who has attributed such a systematic difference to the different conditions of measurement (different temperatures, nonequivalence between thin water layers and bulk water, uncompensated prtd charge transfer in UHV). For a more &Me.. discussion, the reader is referred to the original papers.

AX as well as A# measure changes in the structure of the surface layers of a m d and of a solvent as the two phases are brought in contact. These changes are ass0che.d with the reorientation of solvent moIeculs and the redistribution of the electron tail at the surface of the metal. In principle, these are not energetic parameters, but in fact reorientation of a molecule is possible if there are orienting forces acting on it which in the absence

of an electric field (u = Q) can only be short-range chemical interac,.ions,15,25,26,408,869 Thus, AX can also be irkqmted in terns of metalwater interaction. A high value of AX entails an appreciable modification of the surface structure as a consequence of strong interactions between the phases and vice versa. The concept of "hydrophilicity" has been


i n t r o d ~ o e dto~ ~deal ~ with metal-water interactions in the double laYerFm1 (i) Compm'son with TDS D a b

While A@ values are directly comparable with AX values, metalwater interactions are better pmbed by thermal desorption spedmscopy (TDS) in which heat is used to detach molecules from a surface. TDS data are in parallel with A@ (and AX) data This is itlustrated in Fig. 19? The spectrum of Ag(ll0) shows onIy one peak at 150 K, corresponding to ice sublimation. This means that Ag-H@ interactions are weaker than Hz& H@ in&ractions (althoughthey are still able to change the structureofthe

TIK F-19,

~ a 11) A8It lo), (2) P0(111),0) Ru@D1).

*

~

and (4) Ni(1lQ). T.E

m, Sir$ Sci,R

from RA. W d

m 7 258,PPg.B, 1987,

0I 9 8 7 ~ ~ o f ~ S e i s l w r s . )

~


172

surface region). There are TDS data for Cu(ll0) showing an additional peak at 175 K, which is not present on the (111) and the (100) faces; this corresponds to a weakly chemisorbed sti~te.'~~;"~ These data support the conclusion based on AX that M-H20 interactions are stronger on Cu than on A ~874. Figure 19 also shows that there is a peak at 170-175 K on the surface of Pt(lll), which confirms that such a surface is more reactive than that of sd-metals. In particular, in agreement with Mdata, the high-temperature TDS peak of Pt(ll1) is very close to that of Cu(l10). More complex spectra are exhibited by Ni(llO), which is known to be easily oxidized and thus tends to react strongly with water molecules.875In conclusion, TDS and M (A@) data are qualitatively in agreement in ranking different metals and different crystal faces on a scale of metal-H20 interaction strength. A comparison of the two sets of data also supports the view that there is a limiting value of AX (limiting restructuring effects) while the actual M-H20 bond strength (chemical affinity) continues to increase. (ii) Quantum Chemical Calculations

Quantum chemical calculations, molecular dynamics (MD) simulations, and other model approaches have been used to describe the state of water on the surface of metals. It is not within the scope of this chapter to review the existing literature; only the general, quahtative conclusions will be analyzed. The decrease in @ at the surface of Ag(ll0) has been successfully reproduced by a jellium-point di ole model by 'assuming a disordered water structure at the i n t e r f a ~ e .It~ is intriguing - that for hydrophobic surfaces, models generally predict a stronger penetration into bulkwater of the disturbance of the local s t r u c t ~ r e . ' ~Thus, ~ ~ ' ~in~ the case of hydrophilic surfaces, the first layer (or two) of water is strongly oriented by the forces emanating from the surface, but the bulk structure is soon recovered in a few layers after some very disorganized layers in between. This picture confirms the model proposed by ~rost- ans sen," although on a larger scale (each region was composed of several layers). MD simulations have been used for water at Pt(100) and (11I),8 W 8 2 as well as at Ag(1 11 ).883 The structure of water is predicted to conform to a hexagonal pattern and the metal-water interaction is probably stronger for the (111) than the (LOO) surfaces8" On the basis ofthe extended Hiickel theory, Estiu et a1.8841885 have reached different conclusions in favor of the

2


173

(100) face. The predicted surface potential drops are in general much higher than expected,170 although the Monte Carlo method has given a value of 70 mV for the surface potential of water on a neutral planar surface (simulating a hydrophobic ~ u r f a c e ) . ~ ~ Water reorientation is usually predicted by theoretical models. However, in the case of Ag(lll), MD simulations883do not confirm the dramatic increase in water population near a charged surface claimed by Toney et al.776,777 on the basis of surface X-ray scattering experiments. The same results have been claimed as indicating that water molecules are oriented with the hydrogen down on a negatively charged surface. This picture is not confirmed by far-IR spectroscopy resultsp5?according to which, although they change orientation with charge, water molecules always point the oxygen atom toward the solid surface. Such a picture was proposed by ~ r a s a t t ion ~ .the ~ basis of double-layer evidence. A reason suggested for this behavior is that water molecules do not behave as isolated monomers (as assumed in the early molecular models), but are located in a network of hydrogen-bonded molecules.888 Rotating a bound molecule entails breaking hydrogen bonds and requires a much higher energy than rotating an isolated molecule. The importance of the presence of other molecules for the interaction of a water molecule with a metal surface is seen clearly in calculafor water on a metal surface, i.e., with the lone pair directed toward the solid and the dipole tilted toward the solution. The adsorption energy calculated for H20 on Hg is -32.2 id molpl, which is less than that for hydrogen bonding; therefore Hg behaves as a hydrophobic surface.890 Quantum chemical calculations have recently been extended to ~ n Adsorption has been found to be nondissociative and the metal-water interaction has been proposed to be in the sequence Hg < Ag(100) < In < Cu(100). Compared with the data in Tables 27 and 28, it appears that the positions of In and Ag(100) are exchanged. A consistently anomalous (with respect to electrochemical evidence) position of Au has been found by two different groups. According to ~ ~complete neglect of differential overlap (CNDO) Kuznetsov et a ~ . , "the method predicts for any given metal a weaker interaction on the more dense surface. Thus the predicted sequence is (1 11) < (100) < (110) for fcc metals such as Cu, Ag, and Au; and (0001) < (1100) for hcp metals such as Zn and Cd. However, for the most compact surfaces, the calculated sequence is Hg < Ag(l11) < Cu(ll1) Zn(0001) < Au(l11) < Cd(0001).

-

.

~

~

~

174

Sergio Trasatti and EM Lust

It is difficult to accept that Zn can be less hydrophilic than Au, and also that Au can be more reactive than Cu. More recent calculations by a relatively new technique have in part modfied the above sequence.438The proposed order for the (100) face is Ag < Au < Cu. This confirms the position of Cu in Table 28, but Au still appears to be more reactive than Ag. There are also other interesting aspects. The most adsorbing position has been found to be the "top" or "bridge" rather than the "hollow" site. On the other hand, the adsorption energy has been calculated to be -31.8 kJ mol-' for Cu, which is the same value as that found for water on Hg by other authors.893 On the whole, theoretical calculations provide only a general insight into the problem of water-metal interactions, probably because not all factors are appropriately taken into account. Thus the agreement of AX data with A@ and TDS results is much closer than with theoretical calculations. Nevertheless, each author claims good agreement with some experimental facts, with the outcome that plenty of "hydrophilicity" scales have been suggested23,153,352,389,39,83434870,8909o892,893 based on different parameters; the& have increased the entropy of the situation with a loss- of clarity.

(iii) Controversies over AX While contrasting results obtained by different experimental techniques as well as different theoretical methods are not surprising, internal controversies over AX values in electrochemistry are more serious. The controversy refersed to here32is that about the sequence of metal-water interactions for the different faces of fcc metals. More recently, a controversy has also arisen about single-crystal faces of Cd. The AX sequence (111) < (100) < (110) in Table 28 has been questioned by who proposed (110) < (100) < (111). He also suggested2" the sequence Ag < Au < Cu rather than Au < Ag < Cu. It happens that these two different pictures have been obtained using the same experimental values of En& In particular, data for exactly the same electrodes of Ag are used to arrive at different conclusions. It is clear that the controversy issues from a different concept of selection of @ values. ~rasatti~" has discussed this point at length and has proven that Valette's "hydrophlicity" series for Cu, Ag, and Au is based on an inadequate "choice" of work function values.


175

Another, more serious controversy, issues from the data of Popov et al.382,443 They also claim the sequence of hydrophilicity Ag(ll1) > (loo), but their claim is based on their own results obtained with electrodes prepared in a quite different way: grown in a Teflon capillary rather than crystallized, oriented, cut, and polished. These authors define their electrodes as "quasi-perfect" while they call the others "real." The meaning is clear: the former electrodes are considered structurally more adequate than the latter. The puzzling point is that both sets of electrodes give the same values of End. Thus, on the basis of End vs. 0 correlations, the same conclusions should be reached. However, Popov et al. do not discuss M( values; they arrive at their hydrophilicity scale on the basis of other parameters, which will be considered later on. If the situation is true, the two sets of electrodes can give different AX sequences only if different 9 values are involved. However, h s would mean that surfaces of a given metal can have the same End but adifferent a.This ambiguous situation has been pointed out by ~rasatti~* in a recent paper and calls for further study.

6. Other Solvents Results in other solvents are scanty for metals other than Hg.81,108,109 Liquid Ga and its Tl and In liquid alloys have been studied in DMSO, DMF, NMF, AN,"^^^^^ M~OH~@' and E ~ O H . Among ~ ~ ' solid metals, only 25,26,109 A17750,751 ~i,28,'~' AU, and ~e~~~have been investigated in a number of nonaqueous solvents. Pt and Pd have been studied in DMSO and ~~,25,802,806,895

The general picture emerging from the pzc in aqueous solutions is that the major variation of Ealo between two metals is due to @, with a minor contribution from AX that is governed by metal-solvent interactions. If this is also the case in nonaqueous solvents, a similar picture should be obtained. T h s is confirmed by Fig. 20 in which the data in DMSO are reported. As in aqueous solution, all points lie to the left of the point of Hg. Bi, In(Ga), and Tl(Ga) lie with Hg on a common line deviating from the unit slope. As in aqueous solution, Ga is further apart. Au is in the same position, relatively close to the Hg line. Finally, the point of Pt is (tentatively) much farther than all the other metals. The same situation is also found with the other solvents, the difference being the magnitude of AX. Since AX includes a contribution from the

Sergio Trasatti and Em Lmt

3.d

I

-3.2

-0.8

E,,,

-0.4 VS

0

0.1 NCE I V

Figm 20. PIot of the porential of zero charge, End. vs. the electron work function, R for metals in DMSO solutions, exhibiting the same general features as for aqueous solutions (Fig. 14).

solvent, it is expected to be a function of some pm@es of the solvent. This point has been dealt with exhaustively by Bagotskaya et al.334,343,350,894 For instance, AX values are higher for DMSO than for water, and these are higher than for AN. The sequence can be understood in terms of polarizability, chemical interaction, and orientation of solvent molecules. Given the scope of this chapter, no more quantitative discussion is possible since there are no data that can be used to check the AX values. Specific discussions of this point have been given by Trasatti elsewhere.252631

7. Indirect Evidence of the 'CLnterfacial PamneteIJ' Scale AX is proportional to the modifications occurring at the interface with respect to the separate phases. Therefore any events occurring at the interface should in some way be influenced by AX or should to some extent reflect AX,

ThPotential ofZen, Charge

(i)

171

Metal-Water Afiraiiy

Using AX or X makes no difference from a conceptual point of view. However, since the value of X for Wg is questioned by some authors, AX values will be used in the following discussion. Since X measures the impact of metal-water interactions on the value of Ed, X should be proportiona1 to the thermodynamic affinity of metals for water. There are no tabulated data for a hypothetical M--OH2compound, but since interactions are expected to take place through the oxygen atom of water molecules, Tmatti55869,871 suggested that the needed parameter can be +H", the enthalpy of formation of the generic oxide MO. This parameter has also been used to make thermodynamic predictions regarding the type of water adsorption on metals from the gas phase, and it has been shown3' to work in that case as well. figure 21 shows a plot of AX against +W.As expected, the broad trend is that AX increases with the negative value of +H", It is even more interesting that metals can be gathered into different groups, with sp-metals in two distinct groups and sd-metals in a separate group. It is also

Figme 21. Correlation between the enthalpy of formation of the oxide MO and the relative value of the interfacial parameter, AX, derived from Fig. 14.

178

Sergio k t t i and Enn Lust

intriguing that in terms of AfHO,the sd-metals are arranged in the same sequence as AX, i.e., Au < Ag < Cu. A possible objection to the use of AIHOisthat it refers to the formation of bulk compounds and not to adsorbate monolayers only. The AfHOfor bulk compounds would include metal-metal bond breaking, which is not expected to occur upon adsorption unless there is an exchange of places between the metal and the adsorbate. However, this is only partly true: as chemisorption takes place, surface electrons will be concentrated (or diluted) at the surface site where the adsorbate is placed, with delocalized effects on neighboring sites. The effect of chemisorption on surface conductivity is a practical example, the other being the difference between M-H bond strength in solution and in the gas phase.406,896 Therefore the A/HO values are very likely to be consistent with the original concepts. However, an attempt to correct the AfHOvalues for a metal-metal surface bond by subtracting the metal sublimation heat produces26an intriguing arrangement of the metals, as shown in Fig. 22. The metals can still be gathered in three main groups but, quite interestingly, according to the periods of the Mendeleev table. It is intriguing that the slopes of the straight lines tentatively drawn in Fig. 22 are now of opposite sign with respect to Fig. 21. Within a given group, the value of AX increases as the affinity for water decreases. Au and Ag are known to be among the very few metals that adsorb water associatively from the gas phase.35Nevertheless, they show a large value of AX, A possible explanationgP7is that in the case of Au and Ag, the polariaability of the surface electrons, as measured by GxM.is more important than water reorientation as measured by GxS.~hequite isolated position of Hg in Fig. 22 is noteworthy. This may be primarily related to the fact that the liquid metal is used as a reference state for thermodynamic parameters at 25°C. In other words, the point of Hg simply cannot fit the plot of Fig. 22.

(ii) Contact (Volta) Potential Difference The meaning attached to X is precisely that of the cpd at the metausolution interface, i.e., X measures the change in CPof a given metal as it is covered with a macroscopic film of solution at CT = O.The cpd, A@ -- X, includes a contribution from metal electrons and from solvent dipoles. While it may be difficult to compare the behavior of different metals, as Figs. 21 and 22 show, because of the lack of a parameter unambiguously

Elgm22. Correlations between the interfacial term, AX, derived from fig. 14, and the enthalpy of formation of the oxide MO,corrected for the work to break metal-metal bonds. I, & IJI mean first, second, and third periods of the periodic table of elements. From Ref. 26, u@ated. (From R Guidelli, ed, Elecrr$zed Interfaces im Physics, Cherttishy, md Biology, p. 25Z Fig. 3, Copyrigbt O 1 9 2 Kluwer Academic Publishers. Reprducsd with permission.)

related to X, for a given metal in contact with different solvents dXM may be less important than axSThus X could probably be compared as a function of the nature of the various solvents.

Assuming the tendency of a solvent to form a bond to be measured, to a first approximation, by its donor number (DN), ~ r a s a t t i ~has ~,~' obtained a broad correlation between AyM and DN: the higher the DN, the higher the cpd as a result of stronger metal-solvent interactions. Such a plot has been improved by ~ a w o r s k iwho , ~ ~ has pointed out that as for the ellectronegativityof a metal, the donor-acceptor properties of solvents are more adequate than just the donicity. Jaworski has thus been able to produce a much less scattered plot (Fig. 23). Figure 23 proves that Awd, i.e., Xis related to the strength of the interaction between the metal surface and the solvent molecules.

DMSO ; '

*

A",

@'' ,a' DMF ,*

*ACE

Figure 23. Plot of the expen'rnental contact (Volts) potential difference at metaVsolventinterfaces (n=0)vs. the values calculated by ~aworski'~ as a function of solvent donor (DN)and acceptor (AN) numbers using hequation: Ay14 = 0.007 AN - 0.011 DN - 0.445. (Repduced from J.S. Jaworski; Electrochim Acta 34 486, Fig.2, 1989, Coppght O 1989 with permission of Hsevier Science.)

(iii) Interfachl Permittivity

It is an experimental fact that the capacitance of an electde in a given solvent is a function of the nature of the metal. This was pointed out by Fmmkin et a ~ and. has~ been ~ discussed ~ several times in the literam.7.349,8~,899,m ~ ~ ~ ~ ~ ~ ~showed i 3 4 , that 9 0 the 1 reciprocal of the differen-

tial capacitance at 0 = 0 is linearly comlated with the strength of the metal-water interaction. The reader is referred to the original papers for a detailed discussion. The idea is that X must govern in some way a11 properties of the

interface, including the permittivity. The latter includes an electronic and a molecular term, which have been tentatively separated7on the basis of

model approaches. In this chapter, only the correlation of the capacitance with X is relevant. The correlation bemeen ZIC and AX has been demonstrated for eight metals in aqueous solution. It has been that the

correlation derived from sp-metals is fit also by single-crystal faces of sd-metals. In particular, the capacitance of Ag increases in the sequence

(112) < (100) < (110). The point for Au(100) is also located near the general The increase of C as X increases appears to be a general occurrence.26 Since the Ed VS. @ plots in nonaqueous solvent reproduce the main features ofthe plot in aqueous solution, Fig. 24 shows that in the same plot linear correlations of 1SC vs. AX are obtained for water and DMSO. Any attempt to extend the analysis to other solvents is frustrated by the scatter of the point for Tl(Ga). A general trend can be identified, but any systematic dependence of the slope on the nature of the solvent cannot be established. Figure 24 shows that the values of M: derived from Figs. 14 and 15 are consistent with the values of C measured by ~alette." On the other hand, the same values of Ccannot fit Fig. 24 if the values of &Yestimated by valettem9are used. The same is the case for the values of C as reported by Popov et ~ 1 . ~for~ single-crystal ' faces grown in a Teflon capillary. These authors observed the opposite sequence, i.e., C(1 I 1) > C( 1OO), thus concluding that the (111) face is more hydrophilic than the (100) face. However, as pointed out earIier, they measured the same E,d as the other

-

interfacial parameter, A X f V

Figure 24. Linear dependence of the mipal of the inner-layer capacitance at a =0 on the interfacial parameter, AX.- C ) Line for aqueous sol~tions.~' (-----)Line for DMSO solutions.

182


authors and thereforethe Mvalues should also be the same. This indicates that differently prepared surfaces of Ag single crystals behave not only quantitatively but also qualitatively differently.32 Capacitance data for various crystal faces are available for Bi and Sb.28AS a broad trend, the faces with more negative values of Enla show higher values of C. Although this is qualitatively in line with the behavior of "real" Ag surfaces, the response of Bi and Sb is complicated by their semimetal nature, which gives rise to space-charge effects. For this reason it is not straightforward to compare the absolute values of C and their crystal face sequences with those of metals. Single-crystal faces of Cd prepared in different laboratories show the same anomalies as Ag single crystals. In particular, Lust et a1.,249using polished surfaces, obtained higher capacitances for the faces with the more negative pzc. On the contrary, Naneva etal.,156,660,661 using surfaces grown in a Teflon capillary, have reported a reverse order of capacitances, on the basis of which these authors have assigned the higher hydrophilicity to the basal plane (0001). Thus the same situation experienced with Ag is reproduced with Cd electrodes. These results pose the problem of which of these two sets of data is more realistic.

(iv) Temperature Coefficient of the Potential of Zero Charge The extent ofperturbation brought by a change in temperature in the interfacial layer is expected to depend on the structure of the layer itself. In other words, aEgd /aT must depend in some way on AX. This point has been discussed at length by Trasatti". in previous papers and only some recent aspects will be illustrated here. This has long been taken to be a Values of aEd &Tare usually 9. confirmation of the orientation of water at a metal (Hg) surface, with the negative end of the dipole (oxygen) pointing to the metal.' However, this interpretation suffers from two limitations: (I) it rests on a simplistic model for a molecular layer of water consisting of up and down &poles only, and (2) it totally neglects the entropic contribution of metal electronsn (i.e., a@&?). These limitations are well illustrated by the negative temperature coefficient of Ed for Hg in ethanol and methanollo8even though the orientation of the solvent dipoles does not differ qualitatively ' significance of aEn&lT for Hg has been from that of ~ a t e r . ~The discussed elsewhere by ~ r a s a t t i and ? ~ the reader is referred to the original papers.

The Potential of Zero

183

In this chapter it is of interest to discuss the dependence of aE,d/aTon AX. Data for a number of faces of Ag and Au are available and constitute the basis for some correlations. In particular, Trasatti and ~ o u b o v ahave ' ~ shown that a common correlation exists pig. 25) between aE&T and AX for single-qstal faces of Ag and Au in the sense that aE&T becomes less positive as AX increases. As a limiting case, a negative temperature coefficient has been found3mfor Ag(1 lo), which exhibits the highest AX. A contmveny exists over the interpretation of such a correlation. According to the sirnpIe two-state mode1 for water at interfaces, the higher the preferential orientation of one of the states, the higher the value of aE,&'F. Kthe preferentially orient4 state is that with the negative end of the dipole down to the surface, the temperature coefficient of E,, is positive (and vice versa). Thus, in a simple picture, the more positive aE&T+ the higher the orientation of water, i.e., the higher the hydrophilicity of the surface. On this basis, Silva et ~ 1 . " have ~ 'proposed the

-

interfacial pararnetw, AX I V Figure 25. Plot ofthe temperature coefficient of the potential of zero charge for

different crystal faces of Ag and Au, vs. the interfacial parameter, a. From 'Ref. 32. (Repduced from S. Trasatti and L.M. Donbova, J. Chew. Soc. Fasadq Trans. 91,3318, Fig. 7, 1995 with perrrrision of Tk Royal Society of L'hhstry.)

184

Sergio 'hasatti and Enn Lust

following sequence of "hydrophilicity" for Au single-crystal faces: (111) > (100) > (110). The interpretation based on the thermal disorganization of a dipolar layer neglects the role played by the dipole-metal interactions. If a molecule is strongly oriented, it is more weakly affected by a temperature change since the thermal energy (kT) has to overcome a chemical bond strength. Therefore a higher value of aE,&T is instead an indication of a more loosely bound dipolar layer. More recently, Silva et al.447,448 have found that the temperature for a number of stepped Au surfaces do not fit coefficients of aE,&T into the above correlation, being much smaller than expected. These authors have used this observation to support their view of the hydrophilicity sequence: thelow aE,&T on stepped surfaces occurs because steps randomize the orientation of water dipoles. Besides being against common concepts of reactivity in surface science and catalysis, this interpretation implies that stepped surfaces are less hydrophilic than flat surfaces. According to the plot in Fig. 25, an opposite explanation can be offered: the small dEg4/aT of stepped surfaces is due to the strong chernisorption energy of water molecules on these surfaces. The difference between smooth and stepped surfaces for Au has been discussed by ~rasatti?starting from the observation reported by ~ o n d ~ ~ ~ - ~ ~ that this metal in catalysis is surprisingly active in some morphological states. Au is certainly an sp-metal when it is negatively charged since the Ferrni level is inside the sole sp band. However, inorganic chemistry suggests that Au should be regarded as a transition metal and this is certainly true since Au possesses empty d-levels in its ionic forms. Consistently, on very rough surfaces (and at stepped surfaces) it may be that at some sites Au atoms exhibit transition metal characteristics. This is particularly the case of atoms in a kink position, where the electronic smoothing effect can deprive them of the screening of the external valence electrons. Thus it is difficult to envisage a stepped surface as less reactive than a compact, smooth one. The results of Popov et a1.382are again in contrast with those above. is higher for (100) than for the (111). In thls In the case of Ag, aE&T case, on the basis of Silva's interpretation, the more hydrophilic surface would be the (loo),in contrast to the conclusion of the same authors based on the value of the capacitance. In the case of Cd, Popov et a1.662have found that aE,,daTis higher for the (0001) face than for the polycrystal-


185

line surface and have concluded that the former is more hydrophilic than the latter. Thus, two interpretations based on two different concepts of the effect of temperature on dipole orientation have been put forward. The two views clash with each other on physical as well as chemical grounds. However, the view based on the correlation of Fig. 25 introduces chemical concepts that are absent in the other, which ignores some definite facts. For instance, although a value for aEO4/aT is not available for Ga, the temperature coefficient of C is apparently small.905Ga is universally recognized as a strongly hydrophilic metal. Therefore, according to the simple model of up-and-down dipoles, the effect of temperature should be major, which is in fact not the case.

(v) Adsorption of Neutral Compounds Adsorption at electrodes is universally considered to be a solvent replacement reaction90,906,907.

where B is an adsorbing substance replacing n water molecules on the electrode surface. Adsorption will affect the pzc since water dipoles are replaced by adsorbate dipoles.21However, deriving molecular parameters from adsorption potential shifts is not a simple task since the various contributions can only be separated on the basis of model assumptions.97g8 This aspect has not yet been developed within a theory of water-metal interactions and will not be dealt with further here. On the other hand, the adsorption Gibbs energy of a given adsorbate B can be divided into several contributions: where S stands for solvent, G is the bond strength, and Eq. (66) simply means that in order for B to be adsorbed (this may be physical adsorption only), B must travel from the solution, breaking B-S bonds, to the metal surface, thus replacing M-S bonds. Lateral interactions are neglected in this simplified view (or better, their effects are included in the other terms). If the same adsorbate is studied on different metals in the same solvent, then G(B-S) = ccost. Furthermore, if only physical adsorption occurs, G(M-B) = const. Under similar circumstances, &GO(B) is only a function of G(M-S), hence it is expected to be correlated with AX, the

186

SmgioThatti and E m J&t

interfacial parameter. In particular, &c"(S) is p-edcted to decrease (lower adsorption) as AX increases. This approach has been discussed by ~ r a s a t t i ~ ' ~in*several ~~~*~ papers and the reader is referred to the original work for more quantitative discussion. In this chapter, only recent developments will be emphasized. According to the concepts developed above, &Gm(B) is the only experimental parameter that probes energy terms rather than orientation effects. Therefore it is the most appropriate for describing metaI-water interactions at electrodes. Figure 26 show? the variation of &Gn(B) with AX for pentanol and hexanol. A nice linear correlation is observed, with A d P demeasing as AX increases, In physical terms, as the adsorbate B enters the interface, it feels the difference between the bulk and the local structure. The higher this difference, the more difficult it is to penetrate the interface, i.e., to be adsorbed. Thus the more hydrophilic metals (or faces) adsorb less. Two aspects are especially intriguing: (I) The slope of the correlation depends marginally on the nature of the adsorbate, i.e., it is a property of the interface. Adsorption of AN on Hg and pc-~g'@ also confonns to the picture. (2) The correlation is valid for both polycrystalline and single-

Figure 26. Plot ofthe Gibbs energy of adsorption of organic substances at a = 0 vs. the interfacial parameter, AX. (1) 1-Hemol, (2) 1-penWl,

and (3) acetonitrile. From Ref. 32, updated. Additional pints: (1) Au(l11)?" Bi(l1 1),l5%d (2) ~ a . ~ ' ~

188


kilojoules mol-'. Estimates on the same order of magnitude were made on the basis of the effect of water on the surface tension of Hg?07 Thus, Figs. 26 and 27 are a direct confirmation of the view that AX and water-metal interaction strength are parallel. Therefore the hydrophilicity scales of Popov et al., Silva et al., and Valette cannot be sustained on the basis of sound experimental and theoretical arguments. Other data support the above picture. Hexanol adsorbs very weakly on Ag(1 lo), more weakly than expected, and in any case less than on the (100) faceeU0Such a poor adsorption on (110) faces has been explained in terms of steric hindrance caused by the superficial rails o f atoms. Consistently, w o n on the (110) face of Cu is vanishing Predictions based on a linear regression analysis of the data for pentanol (nine metals) give a value of -12 kJ mol-' for Cu(ll0) and about -16 kJ mol-' for Au(ll0). No data are available for polycrystalline Au, but Au(111) is placed in the correct position in the adsorption of hexan01.~'~ Thus, these data confirm the hydrophilicity sequence Hg < Au < Ag and the crystal face sequence for fcc metals (1 11) < (100) < (110). The data of Popov et al.443for Ag contradict the above sequence. They found that pentanol adsorbed more strongly on Ag(100) than on Ag(1ll). Similarly, Cd(0001) adsorbs less strongly than pc-~d.66'The data for Sb and Bi are to some extent contradictory since the trend is broadly correct but with scatter, which is attributed to the crystal face specificity of space-charge effects.ls3 For instance, adsorption of cyclohexanol on Bi conforms to the sequence (011) > (101) > (21 1) > (001) > (11l), while the capacitance at a = 0 varies in the sequence (001) > (011) > (21 1) > (101) > (111). Thus only the faces (OOl), (21l), and (1 11) are in the expected order."" Surprisingly, the Cd data of Lust et al.li3 show similarities with those of Naneva et a ~ . ; ' ~although capacitances disagree. Thus the order of cyclohexanol adsorbability is (1010) > (0001) while the capacitance varies in the order (1010) > (1120) > (OOOl), i.e., the other way round. In these cases one might wonder whether the G(M-B) term is really independent of face. Another case study supporting the AX hydrophilicity scale is the adsorption of terminal diols. Figure 28 shows that adsorption on A U ~ "is weaker than on Hg912as expected, while adsorption increases with the number of carbon atoms almost in parallel for the two metals. It is intriguing that the adsorption of 1,4-butanediol at the air/solution interface and is of the same order of magnitude as on Au. is weaker than on H~~~~

Figure 28. Dependence of the Gibbs energy of a d w o n of diols on the number ofcarbon atoms in h e molecule. Data for Hg from Ref. 912; data for Au from Ref. 911.

If the tam G(M-B) is not constant, the adsorbability scale turns out to be different. In particular, for pyrazine,P13Au(ll1) > Ag(ll1) (which is opposite to the effect of hydrophilicity); for u r a c i l ~ Au(100) ~'~ >

Au(ll1) > Ag(100) > Ag(ll1) > Hg; and for pyridineYt5Au(311) > Ag(3 11) > Hg as well as Au(210) > Au(l1 1). In all these cases the adsorbate interacts with the metal via its ~r-electrons.The partial d-character ofAu gives to this metal the ability to form stronger bonds. The situation thus resembles that described by Silva et al.?",e., G(M-B) increases more rapidly than G(M-S). However, just the opposite sequence of that hypothesized by the authors is obtained.

IV, CONCLUSIONS The analysis in this chapter has shown that during the past l&15 years there have been only marginal modifications in our understanding of the structure of rnetallsolu tion interfaces based on the potential of zero charge. The general picture for the relative behavior of the various metals seems well established. In particular, new, more reliable data,where available, have confirmed trends already identifiabfe in a more ambiguous situation.

W)


A few aspects need to be stressed, either because they are still ambiguous, or because they have been definitely clarified. 1. The potentials of zero charge considered in this chapter are those in the absence of specific adsorption of ionic as well as nonionic species. There has been no attempt to review the enormous amount of data on the effect of specific adsorption on Eadr except for the few cases where extrapolation back to zero specific adsorption has been used as a more accurate way to determine En4. However, specific adsorption is difficult to relate quantitatively to the structure of interfacial water as well as to the effect of the metal. 2. The potential of zero charge measures, on a relative scale, the electron work function of a metal in an electrochemical configuration, i.e., immersed in a solution rather than in a vacuum. Converted to an "absolute value" (UHV scale) and compared with the classic electron work function of the given metal, the difference between the two quantities tells us what occurs from the local structural point of view as the metal comes in contact with the solution. 3. While the measurement of the work function is losing importance in UHV studies (because other more specific techniques have been developed), such a quantity retains its role in electrochemistry because it is intimately related to the electrode potential. A major problem is thus the dichotomy between samples for which End is known but not 9, and vice versa. Thls is one ofthe major obstacles to the unambiguous interpretation of Ead-@ plots. However, this point has been recently addressed in a few cases and the outcome has allowed us to clarify some debated aspects. It is now well established that within a major group of sp- and sd-metals AX (the decrease in sb as the metal comes in contact with the solution) increases as @ decreases. 4. Conversion of End into an "absolute" (UHV) scale rests on the values of End and 6,for Hg used as areference surface. While the accuracy of Ead is indisputable, the experimental value of @, and especially its relevance to the conditions for the determination of the contact potential difference between Hg and H20, are a subject of continued dispute. Efforts have been made in this chapter to try to highlight the elements of the problem. However, a specialized experimental approach to the measurement of @ (and A@ upon water adsorption) of Hg would definitely remove any further ambiguity as well as any reasons not to accept certain conclusions.


191

5. While the picture for sp- and sd-metals is satisfactory, the situation is still ambiguous for d-metals. This is due to the difficulty of determining a reliable Eg4 free from the effects of adsorption (hydrogen andlor oxygen from water). There is some evidence that the AX for d-metals is probably independent of the nature of the metal (unlike sp- and sd-metals). This points to a top effect in the orientation of water molecules in contact with these metal surfaces. This view has long been sustained by Trasatti; it stems from the consideration that water molecules are hydrogen bonded to each other in a continuous network, and reorientation is possible only to the extent allowed by these bonds. It is thus inadequate to consider an "up" and "down" free (and almost symmetric) rotation of water molecules at electrode surfaces under the action of a changing electric field. Orientation with the 0 atom down to the surface is favored by the possibility of M-0 bond formation, while orientation with the H atoms down is chemically unfavorable, thus requiring a much higher activation energy to break the structural network of water molecules in the liquid phase. 6. Pt-group metals are usually considered model electrodes for kinetic and voltammetric studies because of the possibility of controlling their surface state. Unfortunately, for precisely the same reasons, these metals are not polarizable model systems. Thus, the structure of their interfaces is still a mysterious object in terms of the electrical double layer because the determination of End is inhibited by interferences related to strong interactions with the solvent (water). There are now pioneering results for Pt(ll1) suggesting that End refers to a surface situation that does not exist in reality, i.e., a "virtual" surface state attained by extrapolation. Results for other Pt faces as well as other metals of the Pt-group would be welcome to assess the situation more comprehensively. The picture obtained with the data for Pt(ll1) is promising. 7. A term that is widely used (and sometimes abused) in discussions about metal-water interactions is "hydrophilicity." By this term is meant the strength of interaction between a metal surface and water molecules in contact with it, and the term usually implies chemical bond strength. However, there is a problem with the way "hydrophilicity" scales are built up. Various quantities (capacitance, adsorption energy, etc.) are used to rank the metals, and the "hydrophilicity" scale may differ for different parameters. In this chapter it has been shown that what happens as an interface is formed is directly measured by AX as derived from End vs. @ plots. AX

1M.


explains in electrical units all the modifications occurring at the interface with respect to the separate phases. Thus one can say that interactions are weak if AX is small and that they are strong if AXis large. Rather than "hydrophilicity," one can speak of "hardness" and "softness" with a structural meaning. Thus alarge AX is indicative of a "hard" interface, i.e., of an interface with a structure that it is difficult to further modify by thermal, electrical, or chemical perturbations. It is therefore straightforward to understand why adsorption is weak at an interface with a large AX (adsorbing species penetrate the interface with difficulty), and dE,&T is small (the disorienting effect of temperature is dampened). 8. Almost all that is known about the crystal face specificity of double-layer parameters has been obtained from studies with metal single-crystal faces in aqueous solutions. Studies in nonaqueous solvents would be welcome to obtain a better understanding of the influence of the crystallographic structure of metal surfaces on the orientation of solvent molecules at the interface in relation to their molecular properties. 9. Experiments at present are concentrated on sd-metals and Ptgroup metals. The sp-metals, on which theories of the double layer have been based, are somewhat disregarded. In some cases the most recent results date back more than 10 years. It would be welcome if double-layer studies could be repeated for some sp-metals, with samples prepared using actual surface procedures. For instance, in the case of Pb, the existing data manifest a discrepancy between the crystalline system and the crystal face sequence of End. In other cases (e.g., Sn and Zn) the determination of End is stdl doubtful. For most of sp-metals, there are no recent data on the electron work function. 10. As a final point, there is the dichotomy created by the different results obtained with the same single-crystal face prepared with different procedures. This is the case for Ag but also for Cd. This is a serious point since it leads to two opposite "truths." Although the End values are the same, single-crystal faces of Ag or Cd suggest different "hydrophilicity" scales since different sequences of double-layer parameters are obtained. It is intriguing that in terms of AX, different hydrophilicities imply different AX values. If E,& is the same, then @ must be different. This is easy to prove. But if Eo, is the same, how can vary? This is an interesting question since it involves the degree to which a change in @ affects single-crystal faces and the nature of this influence.


193

ACKNOWLEDGMENTS S. T. is grateful to the National Research Council (C.N.R., Rome) and the Ministry for University and Scientific and Technological Research (M.U.R.S.T., Rome) for financial support. The authors are indebted to J. M. Feliu and A. F. Silva for providing some unpublished data.

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197. 3 9 9 Valette, ~. J. Electroanal. Chem. 230 (1987) 189. 4 0 0 ~ Lopez, . J. R. Vilche, and A. L Arvia, J. Electwanal. Chem. 162 (1984) 207. 40'G.Valette, A. Hamelin, and R. Parsons, 2. Phys. Chem. 113 (1978) 71. 40 k.Waser and K. G. Weil, J. Electroanal. Chem. 150 (1983) 89. 403 B. Wichman, J. P. van der Eerden, H. Meekes, and J. Gerritsq Electrochim. Acta 32 (1992) 2331. 4 0 4 ~ .Chen, - ~ . T. M. Devine, D. F. Ogletree, and M. Salmeron, Surf Sci. 258 (1991) 346. Trasatti, J. Chem. Soc. Faratlay Trans. 170 (1974) 1752. 4 0 6 ~ Trasatti, . Electrochim. Acta 28 (1983) 1083. 4 0 7 Trasatti, ~. Mater. Chem. Phys. 12 (1985) 507. 408~. Trasatti, Croat. Chern. Acta 60 (1987) 357. 4 0 9 Trasatti, ~. J. Electroanal. Chem. 172 (1984) 27. 4 1 0 ~Trasatti, . J. Electroanal. Chem. 329 (1992) 237. 41 1 S. Trasatti, Elektrokhimiya 31 (1995) 777. 41 k.Adzic, in Modern Aspects ofElectrochemistry, No. 21, R. E. White, J. OM. Bockris, and B. E. Conway, eds., Plenum Press, New York, 1990, p. 163. 41%.N. ROSS,in Structure of Electrified Intelfaces, J. Lipkowski, and P. N. Ross, eds., VCH, New York, 1992 p. 35. 414 S. Amokrane and J. P. Badiali, J. Electroanal. Chem. 266 (1989) 21. 415 S. Amokrane, V. Russier, and J. P. Badiali, Surf Sci. 210 (1989) 251. 41 'R. Christoph, H. Siegenthaler, H. Rohrer, and H. Wiese, Electrochim. Acta 34 (1989) 259. 417 M. Hottenhues, M. Mickers, J. Gessitzen, and J. P. van der Eerden, Su$ Sci. 24% (1989) 259. 418 J. P, van der Eerden, M. Mickers, J. Genitzen, and M. Hottenhues, Electrochim. Acta 34 (1989) 1141. 419 V. Bostanov and W. Obretenov, Electrochim. Acta 34 (1989) 1193. 420 M. Hiiptner, W. Obretenov, K. Jiittner, W. J. Lorenz, G. Staikov, V. Bostanov, and E. Budevski, Surf Sci. 248 (1991) 225. 421 W. Obretenov, M. HGptner, W. J. Lorenz, E. Budevski, G. Staikov, and I-L Siegenthaler, Suvf: Sci. 271 (1992) 191. 422 R. R. Adzic, M. E. Hanson, andE. B. Yeager, J. Electrochem. Soc. 131 (1984) 1730. 42%.B. Budevski, in Comprehensive Treatise ofElectrochemistry, Vol. 7, B. E. Conway, J. O'M. Bocks, E. Yeager, S. U. M. Khan, and R. E. White, eds.,Plenum Press, New York, 1983,p. 339. 424 V. Bostanov, A. Kotzeva, and E. Budevski, Bull. Inst. Chem. Phys., Bulg. Acad. Sci. 6 (1967) 33, 4 2 5 ~Budevski, . V. Bostanov, T. Vitanov, Z. Stoynov, A. Kotzeva, and R. Kaischev, Electrochim. Acta 11 (1966) 1697. 426 R. De Levie, J. Electroanal. Chem. 280 (1990) 179. 4 2 7 ~Budevski, . V. Bostanov, and G. Staikov,Ann. Rev. Mater. Sci. 10 (1980) 85. 4 2 8 ~Leiva . and W. Schmickler, J. Electroanal. Chem. 205 (1986) 323. 4%. Leiva and W. Schmickler, J. Electroanal. Chem. 229 (1987) 39. 430 J. P. Badiali, M. L. Rosinberg, and J. Goodisman, J. Electroanal. Chem. 130 (1981) 31. 4 3 1 P. ~ . Badiali, M. L. Rosinberg, and J. Goodisman, J. Electroanal. Chem. 143 (1983) 73. 432 W. Schmickler, J. Electroanal. Chem. 150 (1983) 19. 4 3 3 ~ A. . Komyshev, M. B. Partensk, and W. Schmickler, Z Natui$orsch 39a (1984) 1122. 4 3 4 ~Schmickler . and D. Henderson, J. Chem. Phys. 80 (1984) 3381. 4 3 5 ~Henderson . and W. Schmickler, J. Chem. Phys. 82 (1985) 2825. 4 3 6 ~ nKuznetsov . and J. Reinhold, Z. Phys. Chem. 267 (1986) 824.

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3.

4 shows an S-shaped bend. Such adsorption behavior

232

Ryoichi Aogaki

corresponds to a lund of two-dimensional phase transition from the condensed phase to a &lute phase or vice versa. Therefore the vertical line passing through 8 = 1/2 is the boundary potential for this first-order phase transition; a dotted line indicates the quasi-stable region. Consequently, when the electrode potential passes over the boundary potential, the electrode surface in an active dissolution state is suddenly covered with a passive film, i.e., it transfers to the passive state with rapid decrease in the current. From these discussions, it is concluded that this boundary potential is equal to the passivation potential Ep. When the interaction between the adsorbed intermediates is not so strong, anodic passivation cannot be expected. For example, intermediate MOH' in the oxide film formation for passivation creates a hydroxy bridge or an 0x0 bridge whose binding energy is large, whereas intermediate MCl' in chloride film formation is combined with Coulomb's interaction, whose binding energy is small. We can thus explain why for nickel or iron electrodes, dissolved oxygen induces passivation and chloride ions do not.8

2. Passive Film Breakdown Once a passive film is formed on a metal surface, as long as the electrode potential remains in the passive potential region, the surface is stable, i.e., scarcely dissolved. However, if there are film-destructive anions like chloride ions in solution, the passive film is locally broken, so that local dissolution of the metal substrate proceeds at the same place. Figure 11 shows the schematic diagram of an anodic polarization curve for passive-film breakdown in the presence of film-destructive anions? If film-destructive anions are absent, the passive film is stable over the whole passive-potential area. When such anions exist in solution, in the potential range between the breakdown potential Eb and the critical pitting potential Epir,oscillation of the anodic dissolution current corresponding to the localized rupture and repair of the film appears. Then at the potential region more noble than the critical pitting potential Epit,we can observe the rapid increase of anodic current due to pitting dissolution at the film-broken sites. The film-destructive anions are C1-, I-, CIOS, SO;, etc. for iron electrodes and in addition to these ions, NOS, SCN-, etc. for aluminum electrodes.19In many cases, the film-destructive anions are the anions of strong acids; the most well-known and studied anion is the chloride anion.

Noneqdibrium Fluctnations in the Cormion Procw

Fipm 11, Schematic diagram of anodic poldardoR cumof wive-middeckdm whsa sweqhgekctrade~inbaobls~on.Tbsdoradline ladicamsWphdzrcianminthmr~ofCI-

irwtr,~hsrsrad#~linsistkpolrri&Cu~ in t b pmonso of CT ions? Er puivntion p m Pal; E, h a h b w n potential:Ebrt mt uiticalpipotential; QPtmmparsivt potendal. (From M. Sate. I. E i e c t d e m . Sm. 129,255, 1982, Rg. I. R e p d u d by peamission of Ths Bhcmchcmkd Saeiety, Inc.)

At the area between the breakdownpotential Eb and the critical pitting potential E@@, local film breakdown occurs, which leads to the creation of pit nuclei. However, these nuclei are immsdiately repassivatad. Consequently, in this potential region it is concluded that breakdown and repair are continuouslyreparepeatedwithout creating pit growth.

3. Fluctuation with Film Breakdown and Its Re* The breakdown and repair of a passive film prior to pitting dissolution creates a kind of nonequilibrium fluctuation all over the elsurface, which results from the localized inequality of film dissolution and formation. Since this type of film is too thin for direct observation of the

Ryoichi Aogaki

Imbed fracture, we can indiredy determine the behavior of the fluctuation by the current or potentid change with time. Figure 12 schematically shows the current-time curves after chloride ions are added to the solution; the curves cornpond to the cases where the elechode potential is kept at that of the passive area (from Ep to Eb), the breakdown area (from Eb to Ep3, and the pit-growth area (beyond At the passive area, only a quite small current flows

w, sustain the passive fdm. At the breakdown area, an osdhtory current to

appears with the fluctuation and is acmrpnied by the occurrence of pit nuclei and repsivation. Then at the pit-growth area, after an induction period with the addition of chloride ions, the osciUating current rapidly s t a b to grow, i.e., pitting dissolution progmses. From this evidence it is concluded that the nonequilibrium fluctuation is created at the potential that is more noble than the breakdownpotential Eb, and beyond the critical pitting potential pits grow, being big@ by this fluctuation. As mentioned earlier, although we cannot directly observe the local breakdown process of passive film, according to Shibata and ~ a k e ~ a r n a the , ~ ~stochastic "~ breakdown of passive film follows Poisson's distribution.

+

Nonequilibrium F l u ~ t i o n in s the Corrosion Process

Figure W shows the relationship between the time interval At of passive film breakdown of stainless steel with chloride ions and the logarithms of cumulativeprobability P(dc) for breakdown at time intervals longer than At. From these results, it is clear that the logarithm of the probability is almost proporiional to the time interval, and therefore the

cumulative probability for film breakdown follows Poisson's distribution, i.e., the following equation is obtained,

where A is the frequency of film breakdown. Figure 14 shows the relationship between the logarithm of thefrequency R and the electrode potential. The frequency A largely &cmm with dmeasing el& potential, converging to zero at a certain potential. This result suggests that there is a minimum value of the potential where we can obsewe film breakdown, which can be the breakdown potential Eb.

Ryoichi A@

4 Film B-om

Models

It is not yet complekly clear why passivity breakdown occurs with anions like chloride ions. However, some models for the mechanism have been pl.oposed. Therefore, after briefly describing such models,we will examine the electrocapillary model from the viewpoint of nonequilibrium

fluctuation.

(i) Chertmiid and Mechnicad B r e d o w n Models L m l breakdown of passive film results from a localized increase in the film dissolution rate at the anion adsorption sites that are attacked by chloride ions, as wilI be discussed later, in the same manner as substrate metal dissolution. Such acceleration of the dissolution rate was ascribed to the formation of metal chloride? or the local degeneration of film surface by the formation of surface electron 1eveh7 Macdonald et maintained that the adsorption of chloride ions enhances the formation ofcation vacancies ofmetal ions and their transfer

Nonequilibriurn Fluctuations in the Corrosion Process

237

in the film; consequently, the vacancies are condensed at the metaufilm boundary, inducing film breakdown.25According to this condensation model of cation vacancies, the breakdown potential Eb is given as 4.606 RT

Eb

= wF

Jm

2.303 RT

1 0 8 ~ - aF

log aa-

(18)

where z, is the charge number of the cation (metal ion), F is the Faraday constant, R is the gas constant, a is the effective ratio of the potential difference at the film/solution interface to the whole electrode potential difference, J, is the extinction rate of cation vacancies at the metallfilm interface (in other words, the transfer speed of metal ions from the metal phase to the film phase), f'is the transfer speed of cation vacancies in the film when the oxygen ion concentration at the film surface is equal to unit concentration, and u is a parameter regarding the concentration of oxygen ion vacancies occupied by chloride ions. This equation (la), as will be discussed later, qualitatively agrees with that of the critical pitting potential Ed,. On the other hand, it was also considered that passive film is mechanically broken; local stress resulting from passive film formation induces the breakdown. The mechanical stresses induced in the film fall into several groups: stress induced by the volume change that accompanies film growth, stress caused by the intense electric field under anodic polarization, stress caused by the hydration of oxides, and stress from the impurities contained in the film. Furthermore, when oxygen ions are accumulated at a metallfilm interface, the specific volume of the film becomes larger than that of the metal, so that compressive stress is generated in the film. On the other hand, if metal ions transfer to the solution side, stretchng stress occurs in the film. The stress from electrostriction in a thick film is determined only by the electric field strength in the film and the dielectricity of the film, being independent of film thickness. However, in the case of a thin film like passive film, the effect of interfacial tension cannot be disregarded, so that we must consider effects of both electrostriction and interfacial tension. The film-compressive stress P in the direction of film thickness induced by electrostriction and ~ ~ interfacial tension is given by ~ a t aso follows,

238

Ryoichi Aogaki

where K is specific dielectricity, Y is the interfacial tension, F is the electric field strength, and d is the film thickness.The first term on the right side of Eq. (19) expresses the electrostriction and the second term the interfacial tension. According to this model, the breakdown potential Eb is written as the following,

is the chloride ion concentration, and rcris the adsorption where Ccldensity of chloride ions on the film surface. All the models discussed above are based on a deterministic point of view. However, there is another type of model (i.e., a nondeterministic model) that includes the concept of nonequilibrium fluctuation. In the following section, we discuss such a model, i.e., the electrocapillarity breakdown model.

(ii) Electrocapillarity Breakdown Model A passive film is stable in the region between the passivation and breakdown potentials; if any part of the film is broken, it is rapidly repaired. Therefore it is necessary to derive a model that depicts the processes by which such local destruction and restoration are continuously repeated. This process can be regarded as a kind of nonequilibrium fluctuation concerning passivity. Using energetics, sato7 analyzed such fluctuation processes as follows. The local breakdown of passive film is initiated by the formation of a breakdown nucleus, which requires some amount of electrocapillary energy. The energy required for a cylinhcal breakdown nucleus with radius r to be formed in a passive film is expressed as a linear combination of capillary energy and electrical energy in the following,

where h is the film thickness, 0, is the interfacial tension of the metallelectrolyte interface, a is the interfacial tension of the film/electrolyte interface, ACd is the capacity difference per unit area between the passivated electrode and the film-free, electrode and AE is the electrical potential difference between the metal and electrolyte. Assuming E is the potential of the passivated electrode, and E p is the potential at the point of zero

Nonequilibrium Fluctuations in the Corrosion Proms

-

charge, the potential difference AE is defined as AE =E b. The relationship between the formation energy for the breakdown nucleus Ab and the pore radius r can be expressed as shown in Fig. 15 by acurve with a maximum value A; at certain radius r*.A; cornponds to the activation energy for the breakdown nucleus to be d. Differentiating Ab with regard to r, and equating it to be zero,we have the following equations for the activation barrier 4and the critical pore radius re,

and

Ryoichi Aogaki

From the conceptual diagram in Fig. 15, it is obvious that if the radius of the nucleus exceeds the critical radius r*, the nucleus will grow into a macroscopically ruptured small pore. The passive film is more or less defective and the size of the defect will fluctuate from moment to moment. It is therefore reasonable to assume a certain probability that pore nuclei larger than the critical radius are formed in the film. According to Eq. (23), the critical pore radius r* greatly decreases with increasing electrode potential. It is seen that above a certain critical the active barrier as well as the critical pore radius decreases potential Ub steeply with anodic potential. l k s critical potential Ai!$ is the lowest potential of pore formation and below this potential the passive film is stable against electrocapillary breakdown because of an extremely high activation barrier and the large size of pore nucleus required. Figure 16 shows the effect of the potential of passivated electrode and the interfacial tension of film-free metallelectrolyte interface on the activation barrier for film breakdown. From Eq. (22), the minimum potential corresponding to A; = is given by for film breakdown

mb

-

This potential depends on the interfacial tension 6, of a passivated metal/electrolyte interface shifting to the lower potential side with decreasing 0,. The lowest film breakdown potential LIE'b depends on the surface tension of the breakdown site at which the film-free metal surface comes into contact with the electrolyte. A decrease in the surface tension from om= 0.41 J m-2 to cr,,, = 0.21 J m-*, which may result from chloride ion adsorption or nonmetallic inclusions on the metal surface, will cause a shift of the lowest breakdown potential by about 0.3 V in the less noble direction. After examining the film breakdown process, we have another question: Once broken, how is the film reformed? To answer this question, it is necessary to calculate the formation energy for a passive-film nucleus on the film-free surface. The contribution of chemical energy is newly added to the electrocapillary energy. The total energy is thus given by

Nonequil'ibrium Fluctuations in the Corrosion P m e s

where r is the radius of the film nucleus, k is the film thicknas, is the capacity difference per unit surface area between the film-free metal and the passivad metal, p, is the molecular density of the film (the number of oxide moiecules in unit volume), z is the electron number involved in the formation of one oxide molecule, e is the elemental charge of an electron, and q is the overpotential of film formation, In Eq. (25), the third term on the right side represents the chemical energy associated with the film formation. The depdme of the energy Aj on the radius of a nucleus of film is, as shown in Fig. 17, &.scribedby a curve with a maximum cmesporading to the activation h e r A; and the critical radius tf for the film nucleation,

Figure 18 shows the dependence of the activation barrier for film nucleation on the electrode potential. The activation barrier, which at the equilibrium film-formation potential Ej, depends only on the surface tension and electric field, is seen to decrease with increasing a n d c potential, and an overpotential of a few tenths of a volt is required for the activationenergy to decmse to the order of bT.However, for some metals such as iron:a31 in the passivation pmess metal dissolution takes place simultaneously with film formation, and kinetic factors such as the rate of metal dissolution and the accumulation of ions in the diffusion layer of the electmlyte on the metal surface have to be taken into account, requiring a more refined treatment. From these treatments, it can be said that there is a potential region from the passivation potential to the lowest flm-breakdown potential within which the passive film is stable against electrocapillq breakdown. At the potential beyond the critical pitting potential, not only passive film

Nonequilibrium Fluctuations in the Corrosion Process

Rgm IS. a p a d c ~ a o f u p l v ~ b n i s r ~ ; foatk~daddnortidsAlmanthsmst.t rwf~r~~ddomod.para*l$ir me~~eot#lti.lobrnodicd&fama. lion?^ d i d lins ~h. nllpof~; a g a i n t + d b ~ ~ ~ CIIU -forth 81mf&m8hAE=Of V, c,.,=-I P ~ - ~ , U ~ = 1rn-',aa&01 O.~I ~rn-,

m

~

p,=4x1~,1?h=1x104~~=2(~m~. $a& J. i l k & SOC. lt9.255.1982 Pig.6.

~~pemri~ofTbsElaetroehemi* cd #why,Inc.)

breakdown but also the dissolution of substrate metal takes place (i.e., the occurrence of pitting). In the following section, the stability of this pitting is explained from the viewpoint of energetics. 5. Stability ofpitting

As mentioned in Section 11.3,in the presence of filmdestructive anions such as chloride ions, beyond the critical pitting potential Qb pitting dissolution proceeds, creating semispherical pits (polishing-state pits), which are different in shape from the irregular pits that develop at the active region that is less noble than the activation potential E,, where the corrosive reaction moves from the passive state to the active state (usually the activation potentid E, is different and less noble than the passivation p~tentialEp).

Ryoichi Aogaki

Figure 19 schematically shows the potential region of the polishingstate pits, which shifts to the less noble side with an increasing concentration of am-destructive anions, and the area of active-state pits which on the contrary moves to the more noble potential side with increasingp t o n concentration. At a passive metal electrode immersed in aqueous solution, as pitting progresses, the rest potential (corrosion potential) moves to the less noble side. As long as the passive potend region remains between the current curves of the polishing state and active state dissolution, passivation takes place with decreasingpotential, so that pit growth ceases. As the concentration of film-destructive anions increases, the passive region decreases and finally disappears. In this case, in spite of decreasing potential, polishing-state pits are not repasshatedand move to active-state dissolution. G e n d y , as the pits develop with time, film-destructive

anions are accumulated, especially at the bottom of the pit, so that the dissolution at the bottom turns from a polishing state to an active state. Ifwe define the passivestate and active-state modes to be stable and unstable, respectively (as long as pits grow;as mentioned in the following sections, nonequilibrium fluctuations are always unstable), in the case of repassivation, pits grow stably in the polishing-state mode, finally being

Rp19.E&&dc&i&bnurdp&mon dismludmwmtdpauiw metalma@i -lo&Cl-1. pH r ps. pbC uld r r . plt Indiuk plidhg-shtepit ddw-suepis msp* tiwly. a&

-.

Nonequilibrium fluctuations in the Corrosion Procm

passivated. If repassivation does not take place, the pits develop unstably with time in an active-state mode. sato7 studied the polishing-state dissolution of stahless steel in a sulfuric acid solution containing chloride ions, According to his beatmet, the critical state for the transition from the stable to the unstable state is as follows: If the electrode potential shifts to the less noble side, the polishing-state pit becomes repassivated at a certain potential (pitrepassivation potential, ER). ER is therefore the critical potential for the pit stability, and is less noble than the critical pitting potential &.Figure 20 shows the relationship between the pit-repasivation potential ER, the radius rir of the semispherical polishing-state pit, and the pit-dissolution current density j& at the critical state for pit stability. As shown in this

246

Ryoichi Aogaki

figure, the pit-repassivation potential ERdecreases with increasing radius r;,. At the same time, thepit-dissolution currentdensity j;, also decreases. From these results, the following experimental equations are obtained:

where since the coefficient b is experimentally equal to b ', j;, and have a proportional relationship between them. Using this proportionality, as discussed later, it is shown that the total concentration of hydrates inside apit at the pit-repassivation potential ER (the critical state of the polishing-state dissolution) does not depend on the pit-repassivation potential itself (i.e., it remains constant). Inside a pit in electrolytic solution, anodic dissolution (the critical dissolution current density, jii3 and diffusion of dissolved metal hydrates to the bulk solution outside the pit take place simultaneously, so that the mass transfer is kept in a steady state. According to the theory of mass transport at an electrode surface for anodic dissolution of a metal electrode," the total increase of the hydrates inside a pit, AC(0) = A Z , < O ) , is given by the following equation33,34..

where Ci(0)is the concentration of hydrate ion i inside the pit, C,{OO) is the is the dissolution concentration of hydrate ion i in the bulk solution, jpit current density in the pit, rpilis the pit radius, z is the charge number of dissolved metal ions, F is the Faraday constant, and D is the diffusion coefficient of the hydrate metal ion. The critical value AC'(O), which is derived from r;, and j;, in Fig. 19 by using Eq. (30), is indifferent to the pit-repassivation potential ER,and equal to the constant value, AC*(O) = 1.8 krnol mp3.Consequently, it is concluded that the critical condition for the stability ofpolishng-state dissolution is determined by the increase in the total concentration of hydrates (which are almost hydrated metal chlorides in the case of pitting by chlorides). That is, if the increase in the concentration of total hydrates, AC(O), becomes higher than the critical


247

value AC(O)*, the polishing-state pit grows stably; the stability condition is given by

On the other hand, when the increase in the concentration inside a pit AC(O) is lower than Ac(O), the pit becomes unstable, moving from the polishing state to an active state. Namely, the unstable condition is

where for a metal in natural corrosion, the total anodic dissolution current flowing at pits agrees with the total cathodic current on the passive metal surface except for the pitting parts. With the progress of pitting, the area of pits increases, so that the total dissolution current also increases. This means that since both total anodic and total cathodic current increase, the rest potential (corrosion potential) shifts to the lower side of the anodic potential. In this case, if the electrode potential inside the pit remains in the passive potential region, repassivation occurs immediately.

111. NONEQUILIBRIUM FLUCTUATIONS IN CORROSION In the preceding sections, various types of fluctuations and instabilities essential to corrosion were examined. As a result, it was shown that a corrosion system involves various kinds of problems of stability and instability. Unlike thermodynamic equilibrium systems, in nonequilibrium systems like corrosion systems, adrastic change in the reaction state should be defined as a bifurcation phenomenon. Usually bifurcation phenomena can be classified into two types: one is the change in the structure with time and the other is the change in the structure with space. The former case is well known as the Hopf bifurcation, which creates the change from a static state to a time-periodic state (i.e., nonlinear oscillations of given physical quantities). Therefore a bifurcation of this type is utilized for analyses of the periodic current and potential that are accompanied by the rupturing and repairing of passive film15135 near the Flade potential.36Various reaction models have been proposed for this process.37>38 The same k n d of analysis was performed for anodic dissolution of copper through ion-transfer film where a current or potential oscillation

248

Ryoichi Aogaki

is observed in the presence of chloride ions.394 The behavior of such a system near the bifurcation point is examined as follows49-52. , first a series of nonlinear equations describing the corrosion phenomenon are derived. Then the linear equations that obtain when a small perturbation is imposed on the steady-state solution are deduced. Finally, the oscillatory behavior is examined by solving the linearized equations. There is another type of bifurcation called Turing bifurcation, which results in a spatial pattern rather than oscillation. A typical example where a new spatial structure emerges from a spatially unique situation is Binard's convection cells. These have been well examined and are formed with increasing heat c o n d ~ c t i o nPrigogine .~~ called this type of structure a dissipative structure. 54-56 As shown in Fig. 21, in this case, the entire system is composed of an open vessel with a flat bottom, containing a thin layer of liquid. Steady heat conduction from the flat bottom to the upper 1iquidJair interface is maintained by heating the bottom constantly. Then as the temperature of the heat plate is increased, after the critical temperature is passed, the liquid suddenly starts to move to form steady convection cells. Therefore in this case, the critical temperature is assumed to be a bifurcation point. The important point is the existence of the standard state defined by the nonzero heat flux without any fluctuations. Below the critical temperature, even though some disturbances cause the liquid to fluctuate, the fluctuations receive only small energy from the heat flux, so that they cannot develop, and continuously decay to zero. Above the critical temperature, on the other hand, the energy received by the fluctuations increases steeply, so that they grow with time; this is the origin of the convection cell. From this example, it can be said that the pattern formation requires both a certain nonzero flux and complementary fluctuations of physical quantities. Similarly, we can pick another example in crystal growth in melt. In this case, the growth occurs at the interface between the melt and a substrate that is kept at a constant temperature that is lower than the critical temperature for crystallization. The morphology characteristic of the instability is formed by the coupling of the heat flux and the surface-form fluctuation. This problem was first theoretically analyzed by Mullins and Sekerka.5742 Aogaki et al.63-77 first examined from both theoretical and experimental viewpoints the morphological instability in which the mass flux of metal ions produced by shifting of the electrode potential to the less noble

Nonequflibrianr Fluctuations in the Corrosion Process

(a) Benard ells under an air surface

I

heater

I

@)Cross-stxiionof &nard cells Figure 2 1. B6nat-d cells.

side is coupled with the surface-form fluctuation. They examined various problems of electrochemical nucleation. In all these treatments, c'nonquilibrium fluctuation" plays the most important role. This is defined as the fluctuation of a physical quantity that deviates from the standard state determined by the nonzero flux in a nonequilibrium state. Such fluctuation has a kind of symmerry in that the area average is equal to zero although the flux changes locally. Therefore, macroscopically, such fluctuation does not affect the flux itself. This means that the flux must be determined a ptiori and is indifferent to the

fluctuations.

250

Ryoichi Aogaki

As has been discussed in the previous section, in the presence of chloride ions in a solution, near the pitting potential, passive-film breakdown and repair take place continuously on apassive metal surface; in this sense, the electrode surface is fluctuating. However, as long as the electrode potential is not applied beyond the critical pitting potential, pitting does not proceed, and the fluctuations decay with time. That is, the electrode system is stable, so that the surface is kept pristine and without any pits. On the other hand, if the electrode potential is applied beyond the pitting potential, the fluctuations develop rapidly, yielding many pits. Namely, the electrode system becomes unstable. Therefore, in this case, the critical pitting potential is expected to be a bifurcation point. Indeed, the corrosion current (corresponding to the reaction rate or mass flux) also takes quite different values below and above the critical pitting potential. That is, the current in the stable passive state below the critical pitting potential is, as mentioned, about ten thousand times smaller than that in the unstable pitting state above the pitting p~tential.~ This implies that the mass flux controlling reaction and diffusion changes completely, together with the nonequilibrium fluctuations. Thus it can be assumed that the mass flux is created by the complementary nonequilibrium fluctuation itself. From this point of view, in the passive state, the fluctuations are repeatedly appearing and disappearing all over the surface, so that the dissolution current remains approximately zero. In the pitting state, the current increases, with rapid growth of the fluctuations. Accordingly, it can be said that the fluctuations are defined as onesided deviations from the standard state without any flux. Fluctuations of this type have therefore a kind of asymmetry in that the area averages are not equal to zero, having a constant sign (negative or positive). The most important point is that the reaction and the fluctuation have complete equality; they can become both the cause and the result. In other words, the pitting reaction controls the asymmetrical fluctuation, whereas the fluctuations in turn control the reaction. Aogaki et a1.7879 have recently established these conceptsPE1and in the following section the instability of the nonequilibrium fluctuations in pitting dissolution will be discussed.

1. Instability of Asymmetrical Fluctuations in Pitting Dksolution In an electrode system, two different kinds of thermodynamic equilibrium play substantially important roles: (I) Nernstian equilibrium with regard

NonequilibrIum Fluctuations in the Corrosion Process

251

to e I e c t d e reactions and (2) electrostatic equilibrium arising from the formation of the electrical double layer. When an electmle potential that is initially settled at the rest potential is shifted to the anodic direction, the electrode system begins to move to a new equilibrium state. The resultant reconstruction of the doubIe layer induces dielectric relaxation, which yields a new potential difference, maintaining electrostatic equilibrium. The newly formed equilibrium, however, is broken easily and incessantly by the thermal motion of solution particles. Since the electrode system is not in Nemstian equilibrium at the potential, such a breakdown (nonequilibrium fluctuation) produces pitting dissolution. The physical quantities related to the dissolution fluctuate on one side of the electrostatic equilibrium, that is, the fluctuations take place toward the direction in which the reaction p e e d s . As shown in Fig. 22, since the dissolved metal ions are locally enriched near the surface, the fluctuation in concentration takes a positive value. In this fluctuation process, the passive film does not provide the absolute condition for protecting the substrate dissolution because, as shown in the preceding section, a breakdown in local passivity prior ]to

mr

" F i f i s c

r Diffusion Caver

rl

b

Figure 2. Schematicdepiction of asymmetrical mcenhnationfluctuation. In the case of dissolution, it takes a positive value from the electrostatic equilibrium state.7x

252

Ryoichi Aogaki

pitting occurs randomly and continuously, so that the existence of apassive film does not always mean that there is the protection against pitting. The nonequilibrium asymmetrical fluctuations are defined as deviations from the electrostatic equilibrium. As mentioned earlier, the nonequilibrium fluctuation of the concentration C,(x, y, z, t ) of a dissolved metal ion is written as

where C',(z, t) is the concentration at the electrostatic equilibrium, which is assumed to be unique in the directions parallel to the surface. In the present case, the electrode surface is taken as the x-y plane in Cartesian coordinates. The superscript a indicates the asymmetrical feature of the fluctuations. Similarly, for the electrostatic potential @(x, y, z, t ) and the surface form Z(x,y,z,t) at the outer Helmholtz plane, we can define the following asymmetrical fluctuations, i.e.,

and

where b*(z,t ) and f ( x . y) are the electrostatic equilibrium components of @(x, y, z,t ) and Z(x, y, t),respectively. The most important quantity that determines the instability in pitting dissolution is the fluctuation of the electrochemical potential of dissolved metal ions in the electric double layer. In the presence of a large amount of supporting electrolyte, the fluctuation can be formulated with the fluctuations of the potential y, t)' of the Helmholtz layer and the concentration c,,,(x, y, Ca, t)' as follows,

where (;" implies the outer Helmholtz plane (OHP) deformed by dissolution, ( ( x , y, t)", and c, is the average critical concentration fluctuation and has a positive value. Then, #'f is related to the diffuse-layer potential fluctuation & as follows,


253

where ( ) indicates the average value over the surface and and are the potential differences of the Helmholtz layer and the diffuse layer, respectively. The subscript p suggests that the chemical potentials (activities) of all the components are kept constant. The effect of surface deformation in the Helmholtz layer should also be involved in Eq. (35). In consideration of specific adsorption of anions, such effects can be expressed by the potential gradient L, = {%@(x, y, Z, r ) ? / a ~ )as~ follows,

Hence, in Eq. (36), which sign, positive or negative, should be chosen depends on the adsorption state of ionic species in the Helmholtz layer; if any kind of specific adsorption is neglected or such adsorption is not so intense, the positive sign can be adopted because there is no inversion of the signs of the electric potentials, as depicted in Fig. 23. This means that the sign of the potential difference in the Helmholtz layer is the same as that of the potential difference in the diffuse layer, i.e., /&@2)),4

> 0.

However, for intense specific adsorption, as shown in Fig. 23, such inversion can be expected. Accordingly, in Eq. (36), the negative sign is selected, so that the unstable condition (a(q)/a(@),, c Ois obtained. Substituting Eqs. (35) and (36) into Eq. (34), the electrochemical potential fluctuation of dissolved metal ions at OHP is deduced. Then, disregarding the fluctuation of the chemical potential due to surface deformation, the local equilibrium of reaction is expressed as 6pz = 0. With the approximation c,,,(x, y, 0, t)" = c,(x, y, Ca, t)', we can thus derive the following equation,

In the presence of a large amount of supporting electrolyte, the diffusion equation in a static solution without any convection is expressed as

Ryoichi Aogaki

Figure 23. Elecfric potential distribution in e l h c double layer. HL, Helmholtz layer; DL, diffuse

layer.

%/w

where a 8/# + + 8/az< and 4 is the diffusion coefficient ofthe metal ion. Then, disregarding the surface diffusion, the surface form changes according to the mass flux at the surface, that is,

where Q is the molar volume of the dissolvd metal. Nonequilibrium fluctuation can be described as spatial waves with

various wave numbers, which are two-dimensional plane waves composed of x and y components. The concentration fluctuation and surface-form

255


fluctuation corresponding to a wave number vector (k,, by

5)are represented

r,

where &, tla and P(tlaare the amplitudes of 4 and respectively. With the boundary condition that the concentration fluctuation disappears at the bulk solution, i.e., c,(x, y, 2, t)a -,0

for z +

-

(41)

Equation (38) is solved and gives the amplitude c:(z, 2)" in Eq. (40a). Disregarding the time dependence of the other parts of the amplitude in comparison with that of the exponential function, the actual form is given as follows, &(2.

C1 1

= c:(o,o)' exp(-k) cxp f(l)dl

142a)

From Eq. (39), the amplitude of the surface form fluctuation is

P(tla= CO(O)~

cxp

(42b)

where $f(t)dt is the amplitude factor, and f(t) is given as

(e

where k + $)'''. For an unstable electrode system, the asymmetrical fluctuations first become unstable, then cascadehke transitions to the unstable state of the symmetrical fluctuations occur, if possible. As shown in Eqs. (42a) and (42b), when the amplitude factor becomes positive for certain wave numbers, the fluctuations become unstable, and the pits start to grow. When the amplification factor is negative for all wave numbers without exception, the growth of pits is depressed. From Eq. (43), the amplitude

256

Ryoichi Aogaki

factor can be expressed simply by neglecting the other part z,FaD,,,k/RT,

where the unstable condition is equivalent to the positive F((Q2)) value, and + and - signs are ascribed to the cases of nonspecific adsorption and specific adsorption, respectively. Using the ex ression of 4(4= - (@#A, derived from the usual double-layer theorygo), Eq. (44) can be rewritten as

where the symbol f in Eq. (44) is changed to T, and L is Debye's length. Since c, is defined positive as shown in Fig. 22, and (al)remains positive for anodic reaction, F((G2))should be examined for two different cases: nonspecific or weak specific adsorption and intense specific adsorption. In nonspecific or weak specific adsorption, as mentioned earlier,

> 0 holds, so that as shown in Fig. 23, (G2) > 0 is derived. The and {a,) important point is, in this case, to select the negative sign in Eq. (45). Thus, F((@)) becomes negative and the instability does not occur. For intense specific adsorption

and ( 9 1 ) > 0 holds. Therefore, as shown in Fig. 23, (@2) < 0 is derived. In consideration of intense specific adsorption, the positive sign should be becomes positive and the system turns adopted in Eq. (45); F((az)) unstable. In conclusion, the present discussion reveals the important theoretical prediction that anodic dissolution can occur if and only if there is strong specific adsorption to keep (~@l)/a(#&,negative.


257

Generally, for s ecific and nonspecific adsorption, the following equation is derived: ! F

where s is the dielectric constant, CHis the differential capacity per unit area of the OHP, and and Q; are electm charge densities in the Helmholtz layer and diffuse layer, respectively. Therefore the instability condition for asymmetrical fluctuations is

a

Even in the presence of specific adsorption, if this condition is not fulfilled, such instability is not expected. From the above discussion, the critical conditions are expressed as

That is, the critical condition, using Eq. (46), is given by

As shown in Fig. 24, the mechanism of the instability is elucidated as follows: At the portion where dissolution is accidentally accelerated and is accompaniedby an increase in the concentration of dissolved metal ions, pit formation proceeds. If the specific adsorption is strong, the electric potential at the OHP of the recessed part decreases. Because of the local equilibrium of reaction, the fluctuation of the electrochemical potential must be kept at zero. As a result, the concentration component of the fluctuation must increase to compensate for the decrease in the potential component. This means that local dissolution is promoted more at the recessed portion. Thus these processes form a kind of positive feedback cycle. After several cycles, pits develop on the surface macroscopically through initial fluctuations.

figure 24. Instabif ity process of asymmetrical fluctuations in pitting dissolution.

2. Determination ofthe Pitting Potential In the potential region where nonequilibrjum fluctuations are kept stable, subsequent pitting dissolution ofthe metal is kept to a minimum. In this case, the passive metal apparently can be treated as an ideally polarized electrode. Then, the passive film is thought to repeat more or less stochastically, rupturing and repairing all over the surface. So it can be assumed that the passive film itself (at least at the initial stage of dissolution) behaves just like an adsorption film dynamically formed by adsorbants. This assumption alIows us to employ the usual double-layer theory including a diffuse layer and a Helmholtz layer. An ideally polarized electrode is rigorously defined as the electrode at which no charge transfer across the metaYsolution interface can occur, regardless of the potential externally imposed on the electrode. At any fixed potential, such an electrde system attains a true state ofequilibrium.


259

However, this equilibrium is not the familiar Nernstian type, but is a state of electrostatic equilibrium in the electrical double layer. Strictly speaking, no real electrode system can meet t h s stringent requirement; such an equilibrium is easily broken by the thermal motion of solution species. Physical quantities in a system not at the Nernstian equilibrium, as mentioned in Section 111.1, fluctuate on one side of the electrostatic equilibrium in a direction to promote reactions. Therefore if the systemis stable for any fluctuations, it can approach ideal polarizability very closely although the range of the imposed electrode potential is restricted. However, in the case where the system is unstable, the fluctuations grow with time, and the electrode reactions are accelerated with increasing faradaic current. Such a transition from stable to unstable state occurs at a certain potential, i.e., a bifurcation point for pitting dissolution, which is expected to be the critical pitting potential. To determine the critical pitting potential in experiments, it is shown here that an extrapolation from the potential range corresponding to the stable state can be used. We can thus apply the usual theory to ideal polarized electrodes to determine the critical potential. Generally, for ideally polarized electrodes, the plots of the electsode potential against either the chemical potential of the component in question or its activity are referred to as the Esin and Markov plots; the slope Aogaki et al." first of the plot is called the Esin and Markov coeffi~ient.~ established the expression of the critical pitting potential with respect to the composition of the solution (i.e., the Esin and Markov relations corresponding to the critical condition of the instability obtained in the preceding sections) and also verified them experimentally in the case of Ni dissolution in NaCl solution. For simplicity, they treated a solution containing only one supporting electrolyte in addition to dissolved metal ions. Then, using a reference electrode (indicator electrode) reversible to one of the three kinds of ions (a dissolved metal ion, and an anion and cation of the supporting electrolyte), they examined the difference in potential between the worlung and indicator electrodes. Furthermore, the expressions derived were rewritten to correspond to the actual case when the potential of the working electrode was measured with respect to a conventional reference electrode as follows: As mentioned earlier, they treated a solution containing only three kinds of ions (i.e., a dissolved metal ion that was classified as the minority ion, and an anion and cation of the supporting electrolyte which formed

260

Ryoichi Aogaki

the majority ions); the metal ion, anion, and cation were denoted by the symbols m, -, and +, respectively. The dependence of the critical pitting potential on the mean ionic activity of the supporting electrolyte as the salt of the majority ions is derived as follows,

where the subscript p' indicates that the &,-is kept constant. The dependence of E', on the single-ion activity of the metal ion is

where the subscript p'indicates that p:, is kept constant. The critical coefficients derived above correspond to the case when the metal ion m is the minority ion, and the cation + and anion - of the supporting electrolyte form the majority ions. The critical potential coefficients can be also obtained when the cation + of the supporting electrolyte is taken as the minority ion and the metal ion rn and the anion - form the majority ions. Such equations are easily obtained if the subscripts m and + are converted to + and m, respectively, in Eqs. (50) and (51); for constant QL and p:,

Moreover, for the constants and &-, the critical potential coefficient with respect to the single-ion activity a: of the cation, the minority ion, is written using Eq. (51)

where the subscript p'indicates that pl-is kept constant.

Nonquilibrium Fluctoations in the Corrosion Process

261

3. Determination of EMric Charge Coefficients As shown in Fig. 25, an exarnpk of the extrapolation of the current transient obtaind from the potential sweep yields the critical potential after ascertaining that the data obtained are independent of the sweep rate.

Figure 26 exhibits the results of the critical pitting potential measurement for the majority salt of NaCl and the minority ion of M2+ when the concentration of NaCl is varied under the condition of constant ~ i ~ + i o n i c concentration. From the plot in Fig. 26, it follows that

Figure 27 shows the experimental results forchanging ionic concentrations at constant NaCl concentration under the same situation as Fig.

26.

Ll

k

0.2 0.4 Potential

0.6

Figure 25. Diagram forcritical potential meas~ r e r n e n t The ~ ~ : sweep rate it 4 x ID-' V s-'. miC12] = 100mol m", MI]= 0.1 mol mm3. T= 300 K. (Fmm R. Aogaki, E.Yarnamoto, and M.Asanurna, J. Elecsrochem Soc 142,2964, 1995, Fig. 2. Reproduced by permission of The Elecbmhemical Society, 1nc.j

[NaCI] (mol mJ) Figure 26. Dependence of the critical potential on NaCl mncenmion when the Ma+ion is the minority ion and NaCF is the majority salt? WiC12] = 1 mol m", T = 300 K. From R. Aogaki, E. Yamamoto, and M. Asanuma, J. Blectrochem. Sac. 142,2964, 1 9 5 , Fig. 7. R e p d u d by permission of

The Electmhemical Society, Inc.)

When NiClz i s a rnajority salt and the Na+ ion is a minority ion, Fig. 28 indicates the critical potentials measured with changing NiClz concentration at constant Na+ionic concentration

In the same case as Fig. 28, as shown in Fig. 29, critical potentials have k e n measured as the Na'ionic concentration is altered with constant NiClz concentration. Then the experimental result is

NonequilibriumFluctuationsinthe CorrosionProcess

Figure 27. Dependence of the critical potential on ~ i ' * ionic concentration when the ~ i ion~ is the + minori ion and NaCl is h e majority salt? [NiCl] = 100 md m-"5 T = 300 K,.(From R. Aogaki, E Yamamoto, and M. Asanuma,

.

J. Eleclrochem. Soc. 1% 2964, 1995, Fig. 4. Reprodud by permission of The Electrochemical Swiety, Tnc.)

Using these results, we can calculate the electric charge coefficients; from Eqs. (50) to (53),

0 1o2

103

[NiCP2](mol mm5)

Figure 3, Dependence of the critical potential on NiQ2 conmintion when the Na4 ion is the minority ion and WCll is the majority salt : Wac11= 0.5 mol m-3, T s 300 K.(From R, Aogaki, E, Yamamoto, and M. Asanuma, J. Elec~rochem.Suc. 142, WI 1995, Fig. 5. Reprodwed by permission of Tlte E l m chemical Society, Inc.)

Therefore it follows that

NonequiIibrium Fluctuations in the Corrosion Process

265

Figure 29. Dependence of the critical potential on Na*ionic concentration where Na' ion is the minority ion and NiCll is the majority saltm:(Md~=1Oomol md9.T =300 K. (From R. Aqaki, E. Yarnamoto, and M. Asanuma, J. 1:'lectrochetn.Soc. 142,2964, 1995,

Fig. 6. R e p d u d by permission of The Electre chemical S ~ i e t yInc,) ,

H~E, Eqs. (59a) to (59c) express the variations in the electric charges of adsorbed species in the Helmholtz layer when the unit charge on the electrode side is altered. From this viewpoint, as shown in fig. 30, Eq. (5%) suggests the intense specific adsorption of C1' ions: -3.4 units of charge ot'C1' ions are adsorbed for an increase of+l unit ofcharge in the electrode phase. Na*ions of +1 -78units are desorbed, is., the ratio of the number of adsorbed CI' ions to desorbed NIB'ions is about 2:1. Generally, aIkali metal ions like Na* ions are thought to be weakly adsorbed in the Helmholtz layer, so that such desorption behavior of Na' ions is attributed to the intense specific adsorption of Cl- ions. From Eq. (59b), Ni2* ions are slightly adsmbed in spite of their e l h c repulsions, 4.134 units corresponding to an increment of-I-1 unit of electricity. This may be caused by the weak specific adsorption of Ni" ions. Finally, with the data of Eq. (5% to (593,the following electric charge coefficient was obtained

Figure 30. Adsorptiondesorption p m m of ions on the nickel surface in NaCl solution at the citical state,which was concluded from the experimental results shown in Fi.26 to 29.

From this result, as discussed in the preceding section, the instability in this case belongs to the case where the coefficient is smaller than -1. Hence it is concfudd that the instability takes place when (Bz)becomes negative

-

because of (aQ;/a&), < 1. This also explains why pitting dissolution in this case occurs from the intense adsorption of C1' ions. 4, Instability of Symmetrical Huchations in the Diffusion Layer

At the potential beyond the critical pitting potential, the passive metal electrode system turns unstable. As mentioned before, the asymmetrical fluctuations arise from the electrostatic interaction between the electrode surface and solution particles in the double layer, so that the pitting current develops rapidly, and pits grow simultaneously. Moreover, as the reaction progresses, the mass flux of the asymmetrical concentration fluctuation foms a diffusion layer outside the double layer, and nonequilibrium flactuations d another type occur in the diffusion layer; these come from the mass transfer of dissolvsd metal ions perturbed by the thermal motion ofsolution particles. A fluctuation ofthis type was analyzed by Aogaki ef ~ 1 . ~As' shown in Fig. 31, the mass flux fluctuates around its average value, i-e., the fluctuations are both positive and negative, and in this sense have symmetry. This type offluctuation is

Noneqnilibrinm Fluctuations in the Corrosion Process

-

distance

0

Figure 31. Schematic depiction of symmetrical concentration fluctuation. The fluctation takes p itive and negative values around the averagevalue.78

defined as the difference from the average value of the concentration. The symmetrical concentration fluctuation is thus written in the form crnk YItl f3" = CmCx, y, z, t)

- (CJx,

y, z, t))

(6181

where the superscript s indicates the symmetrical feature ofthe fluctuation varying on both sides of the average value, and ( ) indicates the average over the elecbde surface. For the electrostatic potential and the surface form, similar to the asymmetrical fluctuations, the following symmetrical fluctuations can be

defined: &x, y* z, tY

and

-

q x , Y,tt ~ 1 C91xl Y,t,tl}

(61bS

The average values of all these fluctuations are thus equd to zero. Therefore it should be noted that this type of fluctuation dms not affect the total reaction rate.

268

Ryoichi Aogaki

The symmetrical fluctuation of the electrochemical potential of metal ions is given in the form

where #(x,y,(:t)' is the potential fluctuation arising from the ohrmc drop in the solution, which, therefore, in the presence of a large amount of supporting electrolyte, can be disregarded. The implies the surface deformation by the symmetrical fluctuations, S(x,y,t)'. With the assumption that

and Eq. (61a), the concentration term in Eq. (62) can be rewritten as

Here, as the surface morphology changes with dissolution, the concentration distribution in the diffusion layer also changes. This influence is exhibited by the first-order expansion outside the double layer

where L implies the average concentration gradient in the diffusion layer, which is caused by the asymmetrical fluctuations accompanied by pitting dissolution. The actual expression is

where c,(x, y, z,1)sindicates the asymmetrical concentration fluctuation arising from the diffusion of the dissolved metal ions, as explained in Section 111.5. Substituting Eqs. (64) and (65) into Eq. (62), and neglecting the electrostatic potential term owing to the large amount of supporting electrolyte, the following expression of the electrochemical potential fluctuation at the surface is obtained:

+

RTL C(x, Y * tIS (C,,,(x* y*0, 0)


269

The basic equation and boundary conditions for the symmetrical fluctuations are the same as those for the asymmetrical fluctuations except for the superscript s. The diffusion equation is written in the form

The mass balance at the interface can be expressed as

The concentration fluctuation is solved under the following boundary condition c,(x, y, Z, t)'

-+ 0

for z + 0 0

(70)

The above equations are solved for the following two-dimensional spatial waves

where the notation is the same as that of the asymmetrical fluctuations except for the superscript s. With the assumption that the time dependence of the parameters other than those in the exponential part is negligibly small, the solutions are the amplitudes at the electrode surface

and

where the amplitude factor is given as

So, from Ecy. (731, we can derive the unstable condition as

For pitting dissolution after applying a constant potential step, however, as shown in Fig. 32, the sign of L remains negative, so that the above condition is not fulfilled. Therefore the iniltial fluctuations do not p w , but decrease as the dissolution proceeds. As shown in Fig. 33, the desming mechanism of this fluctuation is s m e d as follows: At a place on the electrode surface where metal dissolution happens to occur, the surface concentration of the metal ions simultaneously increases. Then the dissolved part continues to grow. Consequenltly, as the concentration gradient of the diffusion layer takes a negative value, the electrochemfcal potential component contributed by the concentration gradient increases. Here it should be noted that the electrochemical potential is composed of two components: one comes from the concentration gradient and the other from the surface concenltration. Then from the reaction equilibrium at the electrode surface, the electrochemical potential must be kept constant, so that the surface concentration component acts to compensate for the increment of the concen-

Figure 32. Concentration distribution of diffusion layer in anodic dissolution.

Nonequilibrinm Fluctnations in the Corrosion Process

of metal ions due to dis~alution

Dtvelbpmcnt of recessed portion

of rnctal ions

Kept electrochemical porzntiak

ptent~nloontnbutcd by concentration ~sadientmmponcnt

fl uctuarion

e Concentration gradient cornpncnt

Figure 33. Stabilizing process of symmetrical fluctuation in diffusion layer for anodic dissolution.

tration gradient component, that is, it d-s. This means that the metal dissolution is depressed, and the symmetrical fluctuations decay to zero. Therefore, from the analyses of the asymmetrical and symmetrical fluctuations in Sections m.1 and llT.4, it is concluded that the polishing state pits discussed here, which appear beyond the critical pitting potential, have only one representative length (i.e., the autoconelation distance of the asymmetrical fluctuations),which suggests that the morphologqr of the

Ryoichi Aogaki

pit consists of an aggregation of hemispherical hollows of one representative length, i.e., the autocorrelation distance. 5. Instability in Ion Transfer through a Prote&ve Film 0kadaR3first analyzed another type of instability that occurs during metal dissolution coupled with a metal ion transfer in protective film and complex formation between a metal ion and aggessf ve anions. He examined some perturbations (i.e., syrrnmetrical nonequilibriurn fluctuations) of the concentrations of both aggressive ions and dissolved metal ions and also of the electrostatic potentials. Okada showed that such perturbations can initiate l d activation of pitting nucleation on the metal surface. However, in the original paper, too many phenomena were considered at once, so that his treatment became too complicated to obtain a physical image of thfs phenomenon, and it even contained some contradictions. It is a1so impossible to derive the explicit chmcteristic equation with regard to the perturbations. Therefore, in the following discussion, let us try to reconstruct a simple theory in the same way as in the preceding sections. The first assumption of this treatment is metal ion dissolution through the protective film, as shown in Fig. 34, where the potential difference between both sides of the film is defined as A G , & , y t t).The potential

Figure 34. Dissolution of metal through a metal oxide layer with oornplex formation.

NonequilibriumFluctuations in the CorrosionProcess

273

at the outer Helmholtz plane on the film surface is expressed as @(x, y, 0, t), and is determined by the concentration overpotential and the ohmic drop in the bulk of the solution. According to the discussion at the end of Section 111.5, at the steady state, the total overpotential of anodic dissolution is determined by the ohrmc drop, so that the A@Mo/s(~,y, t) is assumed to be approximately zero at steady state:

Therefore, from Eq. (754, we can write the following equations concerning the fluctuations and average values:

where, as mentioned in the foregoing section, a superscript s indicates a symmetrical fluctuation, and() implies the area average over the surface. After arriving at the film surface, the metal ion Mzm+ forms an adsorbed complex (Wm)*d with the aggressive anion X-. Then the complex quickly dissociates into the metal ion and aggressive ions in the solution. This is the second and the most important assumption. The reaction mechanism is described as

where lattice and sol are the crystal lattice and solution phases, respectively, and the subscript ad implies adsorption, z, is the charge number of the metal ion, and m is the coordination number of the complex. The first reaction in Eq. (76a) is rate determining, so that the dissolution rate is controlled by the concentration of aggressive anions. From the second reaction in Eq. (76b), it can be said that the concentration fluctuation of the metal ions is coupled with that of the aggressive anions. Thus,

holds, where c$, and cS_ are the concentration fluctuations of the dissolved metal ions and aggressive anions, respectively.

274

Ryoichi Aogaki

From the first reaction, assuming that the anion adsorption process is rate determining, and neglecting the potential difference as shown in Eq. (754, the average dissolution current density is written as a function of the surface concentration of the aggressive ions, (C-(x, y, 0, t)), i.e.,

where m' is the apparent reaction order, and the surface coverage of (WmId is neglected by assuming that it is sufficiently small, implies the rate constant, and a,is the transfer coefficient. In consideration of Eq. (75b) [i.e., the fluctuation of Ad$,,o/s(x, y, t ) is equal to zero], the fluctuation component of the current density is written as

Then the diffusion equation for the fluctuation of the metal ion concentration is given by Eq. (68), and the mass balance at the film/solution interface is expressed by Eq. (69). These fluctuation equations are also solved with the same boundary condition as shown in Eq. (70). Assuming that the average state attains a steady state, the following expressions of the fluctuations are used,

c-(x, y, z, 2)s

J&, Y.

2.

0 s = c-(z) exp[i(k,x €I

s

t)S =JJZ) exp[i(k,x

+ k9) +pt]

(79b)

+ Q)+pt]

(79~)

0 s where ci(z)', c-(z) ,and ~0~ (z 2are) the amplitudes of &, d and ji, respectively, k, and k,, are the x and y components of the wave number vector (k,, k,), respectively, and p is the amplitude coefficient. The characteristic equation can be obtained in the same manner as in the preceding section: Namely,

where k is, as has been mentioned (i.e., the absolute value of the wave number vector) [s(# + $)1'2]. Figure 35 shows some examples of p-k curves, which indicate that the fluctuations have a kind of white noiselike


Figure 35. Amplitude factor of the symmetrical fluctuation for anodic dissolution through a metal oxide layer with corn !ex formation. DmE 1.0x lo4 rn' s-, k! = 3.0 m a-' d-', m' = 2 m r 2; 1.Curves 1,2, and 3 x

B

cmmpond to the sldace concentrations of the anion, {CJx. y, 0))= 14 50, and I W mo?m->,respectively.

spatial spectra in the lower wave number area h a u s e of their constant

distrjbutions, that is, fluctuations of this type tend to yield a random surface morphology that is quite different from that of polishing-state pits.Mqlm From Eqs. (7%) to (79~1,it is easily understood ]thatonly the fluctuation components having a positive amplitude coefficient p can grow unstably with time. According to Eq. (801, the critical wave number is obtained under the condition p = 0 as follows,

Here the critical wavelength 1 , = 2x/R, is thought to represent the minimum value ofpit diameter. Some values of il,m shown in Table 1. From Eq. (801, the maximum amplitade factor is written by

Then the reciprocal of the maximum amplitude factor, T m lip- is thought to express the induction time for pit generation. Somecalculated values are shown in Table 2. The mechanism of this type ofinstability can be elucidated as follows:

Fit, at the portion where the anion concentration happens to be higher than other portions of the surface, according to the first reaction equation m.(76a)], the dissolutioncurrent density alsobecomes higher. From Eq. (78b), the m n t density fluctuation is expressed by the following simpUed equation,

Nonequilibrium Fluctuations in the Corrosion P m s s

figure 36. Instability p m of symmetrical fluctuation in andic diss01utionthrough metal oxide layer with complex formation.

Simultaneously, according to the second reaction equation [Eq. (76b)], the metal ion concentration also increases with increasing metal dissolution, which can be described by

The metal ion forms a complex with the anions, so that the increase in the metal ion concentration enhances the anion adsorption onto the surface, according to the following equation,

Consequently, returning to the initial stage of Eq. (83a), the portion in contact with the increasing anion concentration receives additional dissolution. These processes are shown in Fig. 3.At the same time, from Eqs. (83a) to (83c), we can derive the same equation as Q. (80). 6. Detedmtion of lLoml C o m s h States by M m d n g Dissolution C m t

Tne measurement of corrosion current has provided, as is well known, a quite useful electrochemical technique for determining corrosion rates. However, contrary to homogeneous corrosion, pitting corrosion is a typical heterogeneous reaction on a metal surface, so that it is difficult to estimate the actual corrosion state from the usual corrosion current data.

That is, to determine the m

t corrosion rates in pitting c o d o n , as

shown in Fig. 37, it is necessary to h o w the local carrosion currents on the e~~ surface. The d o n current observed is7 however, ob tained as the total m n t , which is mllected by the lead wire of the electrode. From the usual electrwhmical measurement, we can thus determine only an average corrosion current (is.,the corrosion rate). Hence if we can find some way to relate such an a v q e rate to each local cornion rate, the local cornsion state can be determined even with the usual electrochemical method. One of the great advantages of introducing asymmetrical nonequilibrium fluctuation is, as drscussed in the p m g d o n s , that the local reactionrates can be describedby means of spatd fluctuations. Therefore, once we can determine the spatial distribution of the 1 4 reaction rates tie., the spatial spedrm of the fluctuations), we can easily obtain the local information on pitting corrosion, such as conmion rates inside pits and the morphological change associated with pit formation, In other words, this means that the determination of the spectrum is equivalent to that of the local corrosion state. Using the same concept as mentioned above, Tadano and Aogaki examined eIectrochemid nucleation.85-88

Asanuma and Aogaki, on the other hand, have treated pitting dissolution.- In this section, let us try to clarify the relationship between the local corrosion rate and the ave e corrosion rate amding to the analysis by Asanurna and Ao*. 3%

Figure 37, Transform of e m information. J, to#tlcurrent;(j&mean c m t density; Jrhdcut.rentdensity;A,~Warea


279

(i) Theoretical As discussed in the preceding sections, nonequilibrium fluctuations are provided with two kinds of irreversible processes (i.e., pitting dissolution and diffusion of dissolved metal ions). Immediately after a potential step beyond the critical pitting potential is applied to a passive metal electrode, dissolution with passive film breakdown following doublelayer charging produces nonequilibrium concentration fluctuations with asymmetry, creating a diffusion layer outside the double layer. The asymmetrical fluctuations are, as shown in Section 111.1, defined as the differences of the physical quantities from the electrostatic equilibrium state. Therefore, taking the electrode surface as the x-y plane, the asymmetrical fluctuation of the metal ion concentration is expressed by c , ( x , y ~ , r ) ~ C,,,(x,y~,r) C+,(z = =) ,where the fluctuation takes a positive value owing to the enrichment of metal ions, and the superscript a indicates the asymmetrical fluctuation. The asterisk denotes the electrostatic equilibrium. Since the diffusion layer extends into the bulk of the solution, the main role for mitigating the fluctuation is transferred from the reaction at the electrode surface to the diffusion of dissolved metal ions in the bulk of the solution. Then, other fluctuations (i.e., symmetrical fluctuations) emerge, as proved before, and decay to zero. The average value of the symmetrical fluctuation becomes zero because of its symmetry. So, for average values, we can neglect all the symmetrical fluctuations.

-

(a) Amplitude equations

Nonequilibrium fluctuations are eventually formed by reaction at the interface and diffusion in the solution. That is, they can be expressed by the following conservation law,

where the subscripts D and R indicate the components generated by diffusion and reaction, respectively. As will be shown later, the subscript i indicates stable (s) or unstable (u) components of the asymmetrical fluctuations. All the fluctuations are grouped, as shown in Fig. 38, into four components.

Ryoichi Aogaki


281

The concentration fluctuations arising from the diffusion process in a static solution with a large amount of supporting electrolyte are followed by

On the other hand, the fluctuations due to reactions are controlled by the rate equation at the interface,

where k, is the anodic reaction coefficient for pitting dissolution, using H = crz,F/RT

where a is the transfer coefficient for the reaction, is the anodic reaction coefficient at the critical pitting potential, and (el) is the average Helmholtzlayer overpotential. These equations are solved under the initial and boundary conditions as follows: Since all the fluctuations at t = 0 are produced by electrode reactions, the initial components induced by diffusion are equal to zero. Therefore, cm(x.Y*Z, O ) ~ D =0

(88)

holds as the initial condition. From Fick's first law, as the boundary condition,

In the same way as elucidated in the preceding sections, substituting the two-dimensional wave

of the concentration fluctuation into Eq. (85), and considering the conditions Eqs. (88) and (89) together with Eq. (86), we can formally solve Eq. (85) by the use of Green's function." Thereafter, the solution is substituted into Eq. (84), so that the following equation is derived at the interface

Ryoichi Aogaki

The amplitude &(0,t)': will develop with time according to the process discussed in Section 111.1. The stable component c$(0,t): tends to remain constant according to the intrinsic power spectrum, as will be mentioned later.

(b) Average values of jZuctuations The average value of the asymmetrical fluctuation is defined as the root mean square (rms) value. Using the Rayleigh theorem? the average value of the surface concentration fluctuation, for example, can be written

as

where X and Y imply the x-and y-side lengths of the electrode, respectively. As shown in Eq. (92), it can be said that the average values of the fluctuations are calculated in terms of their amplitudes. In the case of dissolution, the plus sign is assigned to the rms value owing to the enrichment of the metal ions. According to Eq. (86), the averaging procedure mentioned above leads to the following total reaction current J,

where S is the effective surface area. (c) Intrinsic spectrum

After the electrode potential is changed beyond the critical pitting potential, the fluctuations turn unstable through the critical state. At the same time, the reactions occurring at the surface yield new asymmetrical fluctuations in accordance with the potential difference. In general, with the normalization of the critical fluctuation, the initial spatial spectrum of the concentration fluctuation corresponding to the wave number components, Sand 5,is given as


283

where the subscript int implies the intrinsic spectrum component c:(o. I&, which determines the initial condition of the amplitude of the asymmetrical fluctuation at the interface. This intrinsic component is initially produced by the electrode reaction, then is slowly modulated by the overall reaction process, c,is the rms value, i.e., the average value of the critical concentration fluctuation. Assuming an isotropic Gaussian distribution with normalization, we have the actual form of the power spectrum,

where a is the autocorrelation distance, which depends on the electrode conditions, and k is equal to (k: + g)'''. The autocorrelation distance is determined by the total overpotential (eo)of the double layer, which is measured from the critical pitting potential and the coverage 8 of the passive film. From the experimental results which will be discussed later, the actual function form is determined as where P is positive constant ( = 1/2). The symbol - indicates the value corresponding to the completely active surface without any passive films. B is positive and takes the following form,

where Bl and cg are constant. Since the amplitude is also considered to increase with the coverage of the active area, for the intrinsic amplitude, the following equation,

can be assumed. Corresponding to Eq. (98), the critical average value of the concentration fluctuation can also be expressed as

Ryoichi Aogaki

284

Here it can be said that not all the initial fluctuations increase with time; some parts of them actually turn unstable, but others still remain stable. Therefore, according to the classification of Fig. 38, the amplitudes of the intrinsic asymmetrical fluctuation are divided into stable and unstable components, that is,

where the subscripts s and u indicate stable and unstable components, respectively. Then, introducing the stability ratio :y and instability ratio y t , the stable component is written as

and the unstable component is

If the phases of both components are assumed to be random, the following relationslvp between yj and :y can be derived.

(d) Fluctuation-diffusion current

When a constant anodic potential step beyond the critical pitting potential is applied to an electrode system, a charging current flows first, owing to the reorganization of the electncal double layer. Immediately after the double-layer charging is completed, as shown in Fig. 39, a slowly decaying curve appears. At this stage, the diffusion layer is still barely developed i.e., the thickness of the diffusion layer is much less than the autocorrelation distance of the asymmetrical fluctuation. Since the diffusion layer thickness and autocorrelation distance can be estimated as =and l/k, respectively, the following condition holds,

Then, after solving Eq. (91), according to the averaging procedure of

Eq. (92), the fluctuation is averaged. At the initial stage, the following fluctuation-diffusion current equation is obtained,


Figure 39. Current-time variation in nickel pitting d k e lution in NaCl solution.w9' 1, double-layer charging current; 2, fluctuation-diffusion cunent;3, minimum d i s solution c m t ; 4, pit-growth current (Reprinted from M.Asanuma and R. Aogaki, "NonequiIibriurnfluctuation theory on pitting dksolution. II. Determimion of surface mvaage of nickel passive film," J. Chem. Phys. 10Q 9938,1997, Eg. 2. Copyright 197, American Institute of

Physics.)

(e)

Minimum dissolutiun current

As the reaction the diffusion layer extends into the bulk of the solution outside the double layer. When the diffusion-layer thichess increases much more than the autoconelationdistance of the asymmetrical nonequilibrium fluctuation, a steady state emerges. In contrast to Eq. (103), in this case the following condition holds,

286

Ryoichi Aogaki

In addition, assuming that the rate-determining step is the bulk diffusion (i.e.,k,/(D,,,k) >> 1holds), we can derive the minimum dissolution current observed after the fluctuation-diffusion current, that is,

where the critical pitting current J, at the critical pitting potential V = 0 is given by

and a, is the critical concentration gradient,

(f) Pit-growth current

As the unstable growth of the fluctuations proceeds, the minimum current starts to increase. According to Section 111.1, the unstable component of the asymmetrical concentration fluctuation is provided by the amplitude equation

where the initial value, c ~ 0 . 0 )in~ Eq. (42a) in Section 111.1 is replaced by c20, t)P,, in consideration of the modulation by the reactions, and f(t) is a positive function given by Eq. (43). Equation (91) is solved by using Eq. (log), and then the solution is averaged according to Eq. (92). Finally, the pit-growth current is approximately expressed in the form

where Jo is the current component, which becomes unstable at the minimum state, that is,

1; is the growth factor of pits, expressed as


287

where the supporting electrolyte is assumed to be a simple 1:l salt like NaCl so that A. is represented in the following,

According to Eq. (1lo), the dissolution current initially increases with time; however, it is gradually suppressed by a subsequent decrease in the double-layer overpotential as follows: The overpotential Vapplied to the electrode has the following relationship with other overpotentials,

where (W) is the average concentration overpotential. At constant V, the total double-layer overpotential (@o} decreases with increasing ohmic drop, RSJ/S, and the overpotential (a2)approaches zero, i.e., the critical condition of the instability. Therefore, J finally becomes equal to (V- (H))S/Rs. In the present case, with the assumption that (H) is kept small, it is predicted that J will gradually approach VS/Rs. As mentioned in Section III.5, according to the above discussion, another kind of overpotential, such as the overpotential between the protective film, also decays to zero.

(ii) Experimental (a) Surface coverage of nickel passivefilm

Using the theoretical equations obtained in the preceding section, we can determine the various aspects of pitting dissolution. Some experiments were carried out in order to examine the breakdown phenomenon of nickel passive film in the presence of aggressive C1' ions as follows: Since the passive film ruptures with an increasing amount of aggressive ions, the coverage should be a function of its concentration. If we use a proper equation for extrapolation to the infinity of aggressive anion concentration, an anodic dissolution current on the completely active surface without any films can be obtained. As discussed in Section 111.1, the local breakdown of electrostatic equilibrium arising from rupturing and repairing of passive film produces the nonequilibrium fluctuations. In this

extrapolated extremecase,we can thus determine the physical parametem of the fluctuations on the completely active surface. After a constant potential step beyond the pitting potential is applied solution, the current transient shown in Fig. 39 is observd. The J vs. I/* plot according to Eq. (104) is shown in Fig. 40. From the linear @on corresponding to Eq. (104), the slop of the plot can be described as a function of the surface coverage B of the passive film in the following to a nickel electde in NaCl

where 1AO) is the slope for the completely active surface,

P i 40. Plot of the f l t l m a i i o n ~ o ncurrent J vs. I/$?' Id is tfie dqx oftfie o on diffusion cmm givenby Eq. (115). S o l i d a n d M b ~ t o h e t b & d and e x p r h m l results, respectively. [[Nad 0.lmo1m-3. DsCI]=7mol m-3. V=0.1 V,T=300K. (Rqmkd from M. Asamuna and R. Aogakj, " N o q d i -

-

brium~ontfieoryonpitting~hltioaII.Detemzination of surface merage of nickel pmive film," J. Chem. Phys. 10Q,938, 1997, FQ. 8. Copyright 1W, Americau Instime of Physics.)

Nonequilibrium Huctuations in the Corrosion Process

was examined in Figs. 41 and 42. As shown in these figures, UQis not affectedby ~ % o n s but , by Cl-ions. To see the effect of C1' ions more clearly, a Langmuir-type plot [i.e., 1/16(8) vs. 1/c(z=-) J was made; a g d linear relation can be sen in the range of high NaCl concentration. From the extrapolation of th~sLinear w o n to infinite NaCl concentration D.e, 1/Cf(z = -1 +01, the slope IAO) cmespondmg to B +0 can be obtained, Then the effect of coexisting ions on

Using the data of 1AO), Eq. (116) allows us to reckon the value & of the average critical concentrationfluctuation on the completely active surface,

Figure 41. slop dthe fluctuationdiffusimcrnnt @ &(, @nstsnNi i ~ o i c m d o n I. N ~ ~~c ~E ~ = I S O ~ ~ ~ - ) , T=300K~~M.AsanumaandRAo~ '%nequUrim fluctuation tkmy on p W g diwllltim IL Demnimionbsllrface~of~pamive~J. C h Phys, 16 938,1897,Fg 10. W@ 1B7, t Amdcan Institute ofphysics,)

Figure 42 The slope of the fluctuationdi&sion m n t against NaCI tioam3' I = j01) K (Rephkdfrom M. Asamma and R. Aogaki, 'Nunequiliium f l u c t a ~d m y on pi#ing dimM~1IL ~ o f ~ ~ ~ o a n i c ~ v e i Y m , " J&m . Phys,w9938 15197, l3g 11.CopyTight 1997, ~ c a n I n s t i t u t e o f

k

e

l

R Y ~ )

Since the nonequilibrium concentration fluctuation arises from the dism lution of substrate metal, as shown in Fig. 43, the value of FWis independent of the metallic ion cuncenbation in the bulk solution. Figure 44 shows the coverage 8 against an NaCl concentration that converges to a value less than 1,O as the concentration of Cl'ion decreases; even in the absence of C1- ions, passive film has already been broken at least about 15%. This is the reason why the slope 1A6)in Fig. 42 seems to be constant at the region of low NaCl concentration. The pH of the test solution remains constant, that is, 5.7 f 0.1, so this phenomenon may be attributed to a change in the role of the passivity-destroying ions from Ctions to H+ ions.9s196

(b) Pit growth on nickel surJace After the fluctuation-diffusion current flows, a minimum state emerges, which can be expressed by Eq. (106)


Figure 43. Average critical concentration fluctuation C on a completely active surface against ~i''7onic wncenhation?' T = 300 K. (Refid from M, Asanuma and R. Aogalu, "Nonequilibriumfluctuationtheory on pitting dissolution. II. Determination of surface coverage of nickel p;bssive film," J . Chem, Phys. 106,933,1997,'Fig. 13. Copyright 1997, American Institute of Physics.)

where P = 1/2 is experimentally decided. With Eqs. (107) and (108), J, is written as

According to Eq. (lM), the extrapolation of this plot to V = 0 gives the J , value. Then, using Eq. (1 20) with the value of ?,' in Eq. (1 18), the critical autocorrelation distance on the completely active surface can be calculated. An extraordinarily large value in comparison with the scale of the fluctuations is found. That is,

The reason such a Iarge value is obtained can be elucidated as follows: Since in the stable region, all the fluctuations are decayed to zero to maintain the electmle surface as flat and stable, the autoconelation distance tends to approach infinity. On the other hand, in the unstable region, many new fluctuations grow,so that the autocorrelation distance will take a small value. At the critical state (i.e.,the boundary between the two regions), therefore, a fluctuation with an extraordinarily large autocorrelation distance appears; this value is considered to have a generality

independent of the characteristics of reaction because it is usually determined by the coupling of the nonequilibrium fluctuation and the thermal motion of solution @cIes. In fact, it is approximately in good agreement with the value of 0.782 nun obtained for silver nucleation onto a platinum eIectrode at the same After passing the minimum state,the dissolutioncurrent starts to grow owing to the unstable growth of the asyrrrmetrical fluctuations, which is expressed by Q. (110). Taking logarithms of both sides of Eq. (1lo), it follows that

As shown in Fig. 45, in plotting logvl vs. ?, .fa and lo are obtained from the intercept to the ordinate and the sllope of the plot, rqxtively, Jo is expressed by Eqs. (106) and (111) in the following,

Noneqdibrium Fluctuations in the Corrosion Procress

Figure 45. Semilog plot of the pit-growth current, J vs. 3." v = 50 rnq I N I C = ~ ~5 mol mqJ, = 1 0 0 0 m o l ~ ~ . ~ = 3 0 0 ~h.el currentcompnent ~iS shown in Q. (Ill), which W e s mtable at the minimum state and b is the growth factor of the pits ex@ by Eq, (1 12). (RephhI from M.Asmuma

and R. Ao& 'Wonequilibrium fluctuation theory on pitting dis~lutimIU.m n t a l examhtions on critical fluctuation andits growthin nickel dissd~tim,''~ Chem. Phys. 206, W, 15197, Fig. 14. Copyright 1W, American Institute of Physics.)

where experimentally, y: = 0.81 and P = 1/2 are determined. The B is, as shown in Eq. (93,a function of 8. The coefficients Bl and in Eq. (97) can be experimentally determined as

B1= 3.6 The growth current is characterized by the coefficient &. Figure 46 is a loglog plot of 1, vs, NaCl concentration,whichyields a linear relation with the slope of 202; lG is proportional to the m n d or& of NaCl concentration. However, in Eq. (112), k; is apparently in proportion to the fmt order of NaCl concentration. This apparent dimpancy can be solved by assuming that the coefficient B is a function of the coverage &which depends on NaCl concentration as shown in Fig. 44. So, including the

1Q

lo'

mrmohr'

Fgm46. l k p d a e ofthegrowth factorIG ofthe pitEing 7 expimental rlsta: a, d m - 3 . T - 3 0 0 ~ .(Rephted from M.Asanuma and R. Ao&, "Nonequilibriumfluctuation &myonpittingM l l t i o n I EE x p r h m d exmidons an criticalfluctuation and its gmwthptocess in nickeldissolution," K. Ckem Phys. 106 944, 19m, Fg. 13. Cop* 197, Am&m Institute offiysb.)

current oo NaCI themticaldata NQJ=O.I

contribution of NaCl concentration, lo is again plotted in open circles in Fig. 46. The replotted data give an almost straightline with a slope of 2.18, Assuming that the function form d k; with regard to the applied overpotential V is detemhed by the exponential part, under the condition of constant NaCl concentration, is also ex@ as a function of the applied overpotential V as follows,

where B becomes a constant because of constant 8 at constant NaCl concentration. As shown in fig. 47, the semilog plot of lo vs. 1 ~ yields ' ~ a straight line, which is indifferent to M2*ionic concentration. From the slope afthe line,the folIowing value of B is experimentally decided,


Figure 47. Semi$#ot

of the growth factor& of the-pittinj

v"'. . ~ , [ N ~ c I1Jmcllrn4;~INiCla]=5 = +, mich]= 10 m o ~m-'; 4 ~ N ~JC=I U)m o m"; ~

current vs. Mm-';

8,(NQj = 100mol rn-3;9 (N~C~J =2 ~mol 1 m4, fNaCI]= 100[) mol m-I, T X 300 K.(Reprinted from M.Asanuma and

R. Aogah, "Nonequilibrium fluctuation theory on pitting dissolution, Ill Experimental examinations on critical fluctuation and its growth pwts in nickel dissolution,"J. Chem. Phys. 106, 9944, 1W, Fig. 14. Copyright 1997, American Institute of Physics.) This can be compared with the data shown in Eqs. (1241)and (1 24b). Substituting 8 = 0 into Eq. (93 and assuming a high NaCl concentration, 28 = 22.0 v1l2 is obtained, which agrees well with the above experimental data.

7. Morphological Pattern Formation in Pitting Dimlution of the Polishing State It is dso well known that a local breakdown passivity that leads to pitting can k treated as a random phenomenon occurring stochastically with

respect to time and location on the surface of the meta1.2'"3,97 Reigata et al?' have recently formulated the stochastic formation mechanism of a pit

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Ryoichi Aogaki

tunnel by using a two-dimensional Monte Carlo method. Figure 48 shows their two-dimensional forms of the polishing-state and active-state pits. On the other hand, as mentioned in Sections III.1 and III.4, it can be said that the pit-formation process in the polishing state is controlled by only one representative length (i.e., the autocorrelation distance), so that the morphology is thought to be formed by aggregations of some hemispherical hollows with the same size (i.e., polishing-state pits are created). Such a morphological change is thought to be one of the attern formation phenomena, which according to Asanuma and Aogaki,9?! can be obtained in the following way: First, the amplitude ci(0, t)tRis calculated by Eq. (91). Then, taking the Fourier inversion of the amplitude, the space-variable component of the surface concentration fluctuation is obtained,

where em(%,y, 0, t&' has positive and negative values owing to the symmetrical nature of the Fourier transform. In order to derive the essential asymmetrical fluctuation having positive value with the average (c,(x, y, 0, t):;), the following conversion from c,(x, y, 0, t)r3' to c,(x, y, 0, t x Ris carried out,

where the average is defined as the root mean square value with a positive sign. The total reaction current density is expressed as the linear combination of the stable and unstable components,

where each component is calculated by Eq. (90). Therefore, the change in the surface pattern is reckoned from

As shown by the flow chart in Fig. 49, at first a wave number plane is divided into a mesh with 128 x 128 rectangular mesh points. Then the amplitude of the concentration fluctuation at t = 0 corresponding to each

Nonequilibrium Fluctuations in the Corrosion Proms

Figure 48. Pit morphology calculated by a -0na1 Monte Carlo simdah,' (a) pokhg-state pit and (b) scrive-state pit. (Reprinted from R.Reigata, F,Sagues, andJ. M.Costa, 'MonteCado simulatiw ofl& colmion," J. Ckem Pkys. la m, 199$, figs. 6 and 7. Copyright 194, American Institute ofPhysics.)

Ryoichi Aogaki

Figure 49. Flow chart to compute the pit pattern-fmtion (Reprinted from M. Asanma and R. Aogaki, " Morpholqcal pattern formation in pitting camion," J . Electruamal. Chern. 396 241,1995, Fig. 6 Copyright 15% reproduced with permission from El-

sevier Science.)


-

figure 50. Conversion from h e point [k, $1 on dae k, 4 plane m the poi# (x,y) on the x-y plane mmpanied by Fourier inversion. ( R e mfm M.Asanuma and R Aogaki, "Morphological pattern formationinpittingommion,'' J. Ekcdroanal. Ckm. 241, 1995, F@ 7. Copyrrght 1995, r e p d u d with prmissim from Elsevier h c e , )

mesh pint (kD5)is determined by using Eqs. (94) and (95).The randomness of the fluctuations is introducsd by regular random numbers. Using the amplitude equation [Eq. (91)] with the initial amplitudes obtained, the amplitudes at t = tan reckoned for all the mesh points, and the surface concentration fluctuations are determined at t =t with the Fourier inversion of ail the amplitudes. It should be noted that each point, as shown in Fig. SO,is convetted fromthe point (km 4) on the kx S, plane to the point (x, y) on the x -y plane. After the stable and unstable components of the reaction current are summed up with Eq. (129), the local amount of dissolved metal at each mesh point can be computed by the integration in Eq. (130), which deduces the pattern-formation process of the pitting surface. The actual computation is prformed for the case of nickel dissolution in the soIution with C1' ions. The unstable growth of the asymmetrical fluctuation controlling the progress of pitting is determined by Eqs. (42a), (42b), and (43). However, since the intrinsic amplitude 40. has the spectrum shown in IQ. (93, of which the autocm~lationdistance is Q is given by

-

Ryoichi Aogaki

in the presence of a large amount of passivity-breakdown ions (i.e.,C1' ions), 8 4 is assumed. From Eq. (97) with Eqs. (124a) and (124b), B = 11.0 rJt2 is thus derived. Finally,V = 0.05 V is assumed, so that a =85 x lws m is reckoned from Fq. (131). This result agrees with the pit diameters in Fig. 51, which are drawn by a computer calculation under the above conditions. The effect of Cl' ions on pit diameters is not so obvious because both l? and B are functions of CI' ionic concentration. Figures 52 and 53 c m m p n d to the Cl' ionic concentrations of 300 mol mW3 and 60 mol m-', resptively. These figures show that the pit diameters are approximately equal although the depths are different; the former gives a = l(r m and the latter a = 8.5 x 10-'rn, which are also nearly equal. Finally, the effect of the symmetrical fluctuation discussed in Section m.4 is represented in fig. 54, which shows the inner surface of a pit in Fig. 51. It is m a m e d about 10 diameters by the use of computer calculation. Many minute irregularities can be seen, which are concluded

Nonequilibriurn ]Fluctuationsin the Corrosion Process

Figure 52 Nickel s& computed at t = aJ s a h impsing tbe ~stepbe).wdthecritical~tiatWa4llerdatafor~

atthesmuinEg.51. ( R q h t d h M , AsarurmaadR, Acgab, b ~ h ~ I o g i pa#em c a l fordonia pitting d m , ' ' J. E k t r o m I . a m . 36,241, 1 B , Eig. 9. Copytight 1995, rqmluced with permission from EIsevier S6iem.)

mditiotbs a in F m 53. Nickel surfax computed under the Rg.51 exaeptthatthe~'ionicaoncent.ratiOnis~fifthlowerthm from M.Asmuma in Rg.5l, ie., [ N d ] = 60ma1

andR Aogald, ' ~ h o b g k a l p a t m ~ t i o n h ~ ~ 1.Electwad. C h 3%, 24l, 1% Fg,13. CoWrigbt 1995, q o ducedHith~fxamM-)

Ryoichi Aogaki

to be indents caused by the symmetrical fluctuations at the initial stage of

pitting dissolution. This is attributed to the fact that the symmetrical fluctuations decay to zero. Fnrm these results it is concluded that the morphology of the polishing-statepit, which mm at the potential region beyond the critical pitting potential, tends to take a hemispherical shape that is detained by the mtmorrelation distance.

IV. CONCLUSION Cornion, especially pitting corrosion, is a typical heterogeneousreaction composed of several processes, Usually, it is reduced to each elemental phenomenon, such as breakdown of passive film and subslrate dissolution, which are treated separately to establish the theoretical and experimental basa of corrosion. However, such a cornion process forms a typical complex system, in which the reaction pmeds in a complicated fashion, remaining linked to each phenomenon in the pmm. Therefore, the nonequilibrium fluctuations discussed here have grat significance since by using these


303

fluctuations, the whole system can be described as it exists, without any reduction into elements. Moreover, fluctuations of this kind are important, not only because they provide a useful method for describing such a complex system, but also because they actually exist in the reaction process. Thus it can be said that the corrosion reaction progresses according to the formation of nonequilibrium fluctuations. The most important point is that there is complete reciprocity between reactions and fluctuations; a reaction is controlled by the fluctuations, while the fluctuations are controlled by the reaction itself, Therefore, we can again point out that the reactivity in corrosion is determined, not by its distance from the reaction equilibrium, but by the growth process of the nonequilibrium fluctuations. The author thanks Dr. Norio Sato, Professor Emeritus of Hokkaido University for stimulating, fruitful discussion, and also thanks Professor Asanuma at Gunma Polytechnic College and Dr. Shinohara at NRLM-JST for providing many data for this paper.

REFERENCES 1

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N. Sato, in Proc. of the First Soviet-Japanese Seminar on Corrosion and Protection of Metals, Ya. M. Kolotyrkin, ed., p. 258, Nauka, Moscow, 1979.

2 1 ~Shibata . and T. Takeyama, Nature 260 (1976) 315. 2?. Shibata and T. Takeyama, Corrosion 33 (1977) 243. 2 3 ~ Sato, . J. Electrochem. Soc. 123 (1976) 1197. 24 K. J. Vetter and H. H. Strehblow,Ber. Bunsenges. Phys. Chem. 74 (1970) 1024. 2 k .F. Lin, C. Y. Chao, andD. D. Macdonald, J. Electrochem. Soc. 128 (1981) 1187. '62. F. Lin, C. Y. Chao, and D. D. Macdonald, J. Electrochem. Soc. 128 (1981) 1194. 2 7 ~ U-Macdonald . and D. D. Macdonald J. Electrochem. Soc. 134 (1987) 41. "D. D. Macdonald, J. Electrochem. Soc. I39 (1992) 3434. 2 9 ~Sato, . Electrochim. Acta 16 (1971) 1683. 3 0 ~ F. . Frank, 2.Natu$orsch. TeilA 4 (1949) 378. 3 1 ~Noda, . K. Kudo, and N. Sato, Boshoku Gijutsu 20 (1971) 525. 3 2 ~Kaeshe, . Z. Phys. Chem. N. F. 34 (1962) 87. 33 Y. Hisamatsu, Passivity and Its Breakdown on Iron and Iron Base Alloys, R. W. Steahle and H. Okada, eds., p. 99, National Association of Corrosion Engineers, Houston, TX, 1976. 3 4 ~Tsujikawa . Boshoku Gijutsu 31 (1982) 488. 35 U. F. Frank and K. Wed, Z. Elektrochem. 56 (1952) 814. 36F. Flade, Z Phys. Chem. 76 (1911) 513. 37 J. Wojtowicz, in Moderndspects of Electrochemistry, J . O'M Bockris and B. E. Conway, eds., No. 8, p. 51, Plenum Press, New York, 1972. 3 8 ~ F. . Cooper, R. H. Muller, andC. W. Tobias, J. Electrochem. Soc. 127 (1980) 1733. 3 9 ~ .Meunier, C. R. I1 Re'union du CITCE 1951, 242. '% Meunier, C. R. IIIRe'union du CITCE 1952, 247. 4 1 ~Meunier . and G. Germain, C. R. 111Rkunion clu CITCE 1952, 263. 42 R. S. Cooper and J. M. Bartlett, J. Electrochem. Soc. 105 (1958) 109. 43 A. J. Pearlstein, H. P. Lee, and K. Nobe, J. Electrochem. Soc. l32 (1985) 2159. 4 4 ~ R. . Bassett and J. L. Hudson, J. Phys. Chem. 92 (1988) 6963. 45 M. R. Bassett and J. L. Hudson, J. Electrochem. Soc. 137 (1990) 1815. %.Li, X. Wang, and K. Nobe, J. Electrochem. Soc. 137(1990) 1184. 448 7 ~Li,. K Nobe, and A. J. Pearlstein, J. Electrochem. Soc. 140 (1993) 721. W. Li and K. Nobe, J.Electrochem. Soc. 140(1993)1642. 4 9 ~F..Bonhoeffcr and H. Gerischer, 2.Electrochem. 52 (1948) 149. [email protected]. Frank and R. FitzHugh, Z. Elektrochem. 65 (1961) 156. 5 1 ~ B. . Talbot and R. A. Oriani, Electrochim. Acta 30 (1985) 1277. 5 2 ~ B. . Talbot, R. A. Oriani and M. J. DiCarlo, J. Electrochem. Soc. 132 (1985) 1545 53 S. Chandrasekhx, Hydrodynamic and Hydmmagnetic Stability, Oxford University hess, London, 1%1. 5 4 ~ .Glansdorff and I. Prigogme, Thermodynamic Theory of Structure, Stability and Fluctuations,Wiley-Interscience, New York, 1971. 55 I. F'rigogine, FromBeing to Becoming, W. H. Freeman, San Francisco, 1980. 56i. Prigogine and I. Stcngers, Order Out of Chaos,Bantam Books, New York, 1984. 5 7 ~ W. . Mullins and R.F. Sekerka, J. Appl. Phys. 34 (1963) 323. 5 X ~ F. . Sekerka, J. Crystal Growth 3,4 (1968) 71. 5 9 T. ~ Delves, J. Crystal Growth 3,4 (1968) 562. 6 0 T. ~ .J. Hurle, J. Crystal Growth 5 (1%9) 162. 6 1 ~ S. . Chen and K. A. Jackson, J. Crystal Growth 8 (1971) 184. 6 2 ~F.. Sekerka, 7. Crystal Growth 10 (1971) 239. 6 3 ~ Aogaki, . K. Kitazawa, Y. Rose and K. Fueki, Electrochim. Acta 25 (1980) %5. 6 4 ~ Aogaki . and T. Makino, Electrochim. Acta 26 (1981) 1509. 6 5 ~ Aogaki, . J. Electrochem. Soc. 129 (1982) 2442.


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@R.Aogaki, J. Electrochem. Soc. 129 (1982) 2447. 6 7 ~ . ~ a n d aEPRI u , Report EM-2393, Electric Power Research Institute, Research Reports Center, Palo Alto, CA, 1982. 6 8 ~Aogaki . and T. Makino, J. Electrochem. Soc. 131 (1984) 40. 6 9 ~ Aogaki . and T. Makino, J. Electrochem. Soc. 131 (1884) 46. 7 0 ~ Aogaki . and T. Makino, J. Chem. Phys. 81 (1984) 2154. 7 1 ~Aogaki . and T. Makino, J. Chem. Phys. 81 (1984) 2164. 9. Makino and R. Aogalu, J. Chem. Phys. 81 (1984) 5137. 7?. Makino and R. Aogaki, J. Chem. Phys. 81 (1984) 5145. 7 4 ~P.. Barkey, R. H. Muller, and C. W. Tobias, 1Electrochem. Soc. 136 (1989) 2199. 7 5 ~P..Barkey, R. H. Muller, and C. W. Tobias, 1Electrochem. Soc. 136 (1989) 2207. 7 6 ~ . Chen - ~ . and J. Jorne, 1Electrochem. Soc. 138 (1991) 3305. n~.-G.Sundstriim and F. H. Bark, Electrochim. Acta 40 (1995) 599. 7 8 ~Aogaki, . 1Electrochem. Soc. 142 (1995) 2954. 7 9 ~Aogaki, . E. Yamamoto, andM. Asanuma, 7. Electrochem. Soc. 142 (1995) 2964. '8O1R. Aogaki, J. Chem. Phys. 103 (1995) 8602. R. Aogaki, A. Yamada, and A. Tadano, J. Chem. Phys. 103 (1995) 8616. 82 D. M. Mohilner, in Electroanalytical Chemistry, A. J. Bard, ed.,Vol. 1, p. 292, Marcel Dekker, New York, 1966. 8 3 ~Okada, . J. Electrochem. Soc. 132(1985) 537. 8 4 ~ Sato, . Corrosion Science 37 (1995) 1947. 8 5 ~Tadano, . M. Asanuma, and R. Aogaki, J. Crystal Growth 166 (1996) 1111. 86 A. Tadano and R. Aogaki, J. Chem. Phys. 106 (1997) 6126. 888 7 ~Tadano . and R. Aogaki, J. Chem. Phys. 106 (1997) 6138. A. Tadano and R. Aogaki, J. Chem. Phys. 106 (1997) 6146. %. Aogaki and M. Asanuma, in Material Science Forum, Vols. 192-194, p. 101, Trans Tech Publications, Switzerland, 1995. '%A. Asanuma and R. Aogaki, J. Chem. Phys. 106 (1997) 9930. 9 1 ~Asanuma . and R. Aogaki, J. Chem. Phys. 106 (1997) 9938. 9 2 Asanma ~ and R. Aogaki, J. Chem. Phys. 106 (1997) 9944. 9 3 ~Imamura, . Physics and Green Function, p. 52, Iwanami Syoten, Inc., Tokyo, 1978. 9 4 ~ .N. Bracewell, The Fourier Transform and Its Applications, p. 112, McGraw-Hill, Singapore, 1986. 9 5 ~ MacDugall . and M. J. Graham, J. Electrochem. Soc. 127 (1980) 789. 9 6 ~MacDugall . and M. J. Graham, Electrochim. Acta 27 (1982) 1093. 9 7 ~BertOcci . and F. Huet, Corrosion 51 (1995) 131. 9 8 ~ Reigata, . F. Saguk, and J. M. Costa, J. Chem. Phys. 101 (1994) 2329. 99 M. Asanuma and R. Aogaki, J. Electroanal. Chem. 3% (1995) 241. '%. Aogaki and M. Asanuma, Material Science Forum Vols. 289-292, p. 835, Trans Tech Publications, Zurich, Switzerland 1998.

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Conducting Polymers, Electrochemistry, and Biomimicking Processes Toribio Fernindez Otero Laboratory of Electrochemistry, Faculty of Chemistry, University of the Basque Country P.O. Box 1072 20080, Sun Sebastian, Spain

I. INTRODUCTION

Most electrochemical reactions occur at an interface between an electronic conductor system and an ionic conductor system. An interface has three components: the two systems and the surface of separation. The electronic conductor stores one of the required chemicals: electrons or wide electronic levels. The ionic conductor stores the other chemical needed for an electrochemical reaction: the electroactive substance. A reaction occurs only if both components meet physically at the interface separating the two systems. Models and theories have been developed by scientists that allow a good description of the double layers at each side of the surface either at equilibrium, under steady-state conditions, or under transition conditions. Only the surface has remained out of reach of the science developed, which cannot provide a quantitative model that describes the surface and surface variations during electrochemical reactions. For this reason electrochemistry, in the form of heterogeneous catalysis or heterogeneous catalysis has remained an empirical part of physical chemistry. However, advances in experimental methods during the past decade, which allow the observation Modem Aspects of Electrochemistry, Number33, edited by Ralph E. White et al. Kluwer Academic/ Plenum Publishers, New York, 1999.

308

Toribio Fernhndez Otero

of the surface at an atomic level under reaction conditions, have provided the empirical basis for a theoretical description and quantification of the surface. The aim of traditional electrochemistry for the next decade should be the inclusion of surface structural and energetic changes during the reaction in their theoretical models. There are fascinating electrically driven biological systems, such as neurons, natural membranes, electric organs of living beings, or muscular contractions that work as electrical (ionic) systems even at the molecular level. A theoretical description of these processes will require the integration of molecular structures (macromolecular) and electrochemical theories. By tradition, electrochemistry has been considered a branch ofphysical chemistry devoted to macroscopic models and theories. We measure macroscopic currents, electrodic potentials, consumed charges, conductivities, admittance, etc. All of these take place on a macroscopic scale and are the result of multiple molecular, atomic, or ionic events taking place at the electrode/electrolyte interface. Great efforts are being made by electrochemists to show that in a century where the most brilliant star of physical chemistry has been quantum chemistry, electrodes can be studied at an atomic level and elemental electron transfers measured.' The problem is that elemental electrochemical steps and their kinetics and structural consequences cannot be extrapolated to macroscopic and industrial events without including the structure of the surface electrode. Two hundred years were required before the molecular structure of the double layer could be included in electrochemical models. The time spent to include the surface structure or the structure of three-dimensional electrodes at a molecular level should be shortened in order to transform electrochemistry into a more predctive science that is able to solve the important technological or biological problems we have, such as the storage and transformation of energy and the operation of the nervous system, that in a large part can be addressed by our work as electrochemists. Here we introduce a personal point of view about the interactions between conducting polymers and electrochemistry: their synthesis, electrochemical properties, and electrochemical applications. Conducting polymers are new materials that were developed in the late 1970s as intrinsically electronic conductors at the molecular level. Ideal monodimensional chains of polyacetylene, polypyrrole, polythiophene, etc. can be seen in Fig. 1. One of the most fascinating aspects of these polymeric

Conducting Polymers, Electrochemistry, and Biomimicking Processes

309

Fqgm 1. Some of the more usual chains of conducting po1ymers (monodimensionat, nonmss-linked, a dnondegraded,i.e., themticall).

Toribio Fernhdez Otero

materials is that they mimic inorganic metals being oxidid and reduced under elecbrx:hemical control. Under oxidation, deal cations (polarons in the dominant physical terminology) accumulate along the polymeric chains before they m m b i i e , by the extmction of new electrums, to give dications (bipolarom). Both states on an ideal linear polymeric chain are qmsnted in Fig.2. Anions coming from the solution guarantee the electroneutrality. The injection of e l m from the mtal promotes the electrochemical reduction of the charged species moving to the neutral,

urx:harged state of the polymeric molecule. A few polymers can be reduced from the neutral state, givingradical anions or dianions (alsopolarom and bipolarom, from a physical point of view). Most of the usud conducting p o l p n have a cross-linked structure (Fig. 31, but again they can be elecirachemically oxidized and reduced. The electrochemical responses must follow eledmhefniica models and

Conducting Polymem, Electrochemistry, and Biomimicking Processes

312

Toribio Fernandez Otero

theories, but considering the polymeric nature of these materials, they have to be simultaneously described by polymer science. Conducting polymers are adequate systems for an attempt to integrate these two parts ofphysical chemistry. This will require electrochemical models that include the structure of the polymer and the structural changes taking place during electrochemical processes inside the electrode at the molecular level. The presence of polymer, solvent, and ionic components in conducting polymers reminds one of the composition of the materials chosen by nature to produce muscles, neurons, and skin in living creatures. We will describe here some devices ready for commercial applications, such as artificial muscles, smart windows, or smart membranes; other industrial products such as polymeric batteries or smart mirrors; and processes and devices under development, such as biocompatible nervous system interfaces, smart membranes, and electron-ion transducers, all of them based on the electrochemical behavior of electrodes that are three dimensional at the molecular level. During the discussion we will emphasize the analogies between these electrochemical systems and analogous biologcal systems. Our aim is to introduce an electrochemistry for conducting polymers, and by extension, for any electrodicprocess where the structure of the electrode is taken into account. There is another field where electrochemistry is applicable to conducting polymers: electrosynthesis. We will briefly attempt to show that electropolymerization is a complex mechanism that gives a variety of materials. Only the availability of models of interfacial reactions, including all the parallel reactions initiated when the current starts to flow, will allow us to design experimental conditions of synthesis that produce materials with improved properties for new applications. Nevertheless, little attention has been paid to the empirical kinetics of the different processes coexisting during most of the electrogeneration of films thick enough for industrial applications: electropolymerization, electrochemically induced degradation, parallel chemical polymerization, or polyelectrolyte adsorption. Each of those parallel reactions follows a multistep mechanism. The electrogeneration of conducting polymers has to be understood as an open question requiring hard and coordinated kinetic studies in order to develop models of interfacial reactions that allow us to design conditions of synthesis that can improve a defined property or a specific application. The decision to characterize polymerization processes, polymeric properties, and current efficiencies in any kinetic study as a function of


313

the different conditions of synthesis was based on a combination of electrochemical and ex situ ultramicrogravimetric techniques. The electropolymerization reaction generating a film is quantified by the productivity of the consumed current as the weight of polymer generated per unit of consumed charge. The film quality is quantified by the charge stored per mass unit. The efficiency of the charge consumed during polymerization to produce an electroactive polymer in the final film is quantified by the amount of polymerization charge consumed to generate a film where a unit of charge is stored. So the combination of those two techniques gives us powerful tools for characterizing both polymerization processes and polymeric properties as a function of the polymerization conditions. Any parallel reaction occurring during polymerization and influencing the film's properties will be detected by changes in any of the characterizations, or in several of them. However, such studies, although very easy from an experimental point of view, have been performed in only a few systems. Only a few models of interfacial reactions are available in the literature, limiting the possibility of obtaining specific materials. An important point related to conducting polymers is the interest that physicists have shown in their properties and applications. Although the same materials are used by electrochernists, there is a great difference that is related to the field of interest. Physicists always use conducting polymers as dry materials while most of the electrochemical interest is centered on soft and wet materials. This is an important difference because those two states of the same material follow quite different physical laws. The considerable effort that has been spent on developing a purely electrochemical model of the electrochemical behavior of conducting polymers seems to be linked to the great influence of the physicists and the fascinating physical applications of dry and hard polymer materials. If possible, they prefer ordered systems with a high crystallinity. Some practical results of their work, such as all-organic light-emitting diodes (LED), all-organic transistors and microelectronic devices, or ionic and electromagnetic shielding have forced electrochemists to take similar directions in their work. All solid-state batteries, smart windows, smart mirrors, etc., have been constructed. In order to avoid the experimental fact that conducting polymers swell and shrink during electrochemical reactions or that they have a monodimensional molecular nature, increasingly complicated porous structures were included in theoretical models to keep a two-dimensional interface between the polymer and the solution.

Toribio F d d e a Otem

We hope to show here that the electrcchemical properties and applications of conducting polymers considered as dry materials represent poor and limiting electmhemical p m e s for those materials considered as tkree-dmensional structures.

The electrochemical oxidation of monomen such as pyrrole," thiopheneFga~dine,"'~ etc., or their derivatives, initiates a polymerization process at the electrodelectrolyte interface that promotes the formation of a polymeric f h that adheres to the electrode. A similar homogeneous polymerization s can ke initiatedby chemical oxidation or chemicaI polymerization. Some monomers can be polymerized as well by electrochemical or chemical reduction.

5"" "'

1. Empirical Kinetics of Initiation and Pdymerhation from Tafel Slopes

The Tafel s l o p obtained under concentrations of the chemical m p nen&that we suspect act on the initiation reaction (monomer, electrolyte, water contaminant, tempmture, etc.) and that m p n d to the direct discharge of the monomer on the clean electrode, allow us to obtain knowledge of the empirical kinetics of initiation and nucleation.22-36 These empmcal hetics of initiation were usually interpreted as polymerization kinetics. Monomeric oxidation generates radical cations, which by a polycondensation mechaxllsm give the ideal. hear chains:

ConductingPolymem, EIectrtwhemistry ,and BiomimickhgPro-

If we want to use the Tafel slopes to obtain the empirical kinetics of polymerization, we have to use a metallic ekkode coatad with a previously electrogenerated thin and uniform film of the polymer in a fresh solution of the monomer. In some cases expenmental Tafel plots present the two components (Fig. 4) befm and after coatmg. Both initiation and polymerization kinetics obtained from Tafel s l o p @g. 5 ) are related to the formation of very thin films, which are not useM for most applications of conducting polymers. A similar mtriction can be at?ributedto the combination ofele.dmhemical and gravimet-


F i 4 . Logintensicyvs.potentid~(Tafelplmts)ob~fnamtire v o ~ t w ofapIatiwm ~ s -submitted to a 2 RIV~ - ~ ~ o t e n t i a ~ sweep p h i z e d in a a1 M xdmitdk shtioa having different ~

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ric measmments obtained from a quartz crystal microbalance. A xmd important restriction in this case is that most of the published papers do not take into account the fact that a change in the polymeric viscoelasticity can have a much more important effect on the overall variation in frequency than the mass term. As we will see k, these films behave hke swelling and shinking gels during oxidation-reduction processes. Electrochernial models and mechaakms obtained by such methods are not able to include experimental @ which are important from a technological point of view, because there is a demase in the ability to store charge per milligram ofpolymer when the thickness of the polymer increases. This fact (see Table 1) makes it difficult to generate very thick

films of conducting polymers without an important loss of any desired property. Only if we have a complete modd describ'mg the parallel prmses involved after the formation of a few nanometers of thin film and continuing during the film growth can we be successful in producing

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Conducting Polymers, Electrochemistry, and BiomimckEng Processes

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conducting polymers for technological applications in competition with other methods of synthesis.

2 Gravimetric ex S h Empirical Kinetics Empirical kinetics are useful if they allow us to develop chemical models of interfacial reactions from which we can design experimental conditions

of synthesis to obtain thick films of conducting polymers having properties tailored for specific applications. Even when those properties are electrochemid, the coated electrode has to be extracted from the solution of synthesis, rinsed, and then immersed in a new solution in which the electrochemical properties are studied. So only the polymer attached to the electrode after it is rinsed is useful for applications. Only this polymer has to be considered as the final product of the electrochemical reaction of synthesis from the point of view of polymeric applications. This means that we can follow the empirical kinetics of the electropolymerization process, at a constant overpotential (Fig. 61, by tracking the weight of the rinsed and dried polymer film,'"' as we do in homogeneous polymerization processes of conducting or nonconducting poly-

Conducting Polymers, Electrmhemistry, and Biomimicking Processes

Figure 6. (a) Evolutim of an ekdqmemted pofypym,1e weight, &md and dried om, during the polymerization time from different pymle concentrations employed in synthesis at 800mV.WQOJ = 0,1 M,T = 25%. fi) IMemhtion from gravhmk results ofthe e r n order relative to the pp& &on (R, values were obtained from the d o p of tbe weight-time lines for every p p l e cormcentmtionstudied).

men, or as we do in the heterogeneous electroinitiated processes of homogeneous polymerizations. The weight of f i h s generated under different concentrations of electrolytes, different concentrations of monomer, or at different temperatures, follows straight lines along the polymerization time pig. 6(a)]. SIopes from these lines are the polymerization rate (R, = mg sd). A double logarithmic representation of the polymerization rates vs. the monomer concentration allows us to obtain (when the result is a straight line) the reaction order related to the monomer pig. 6(b)].In a similar way, by changing other chemical components, we can obtain the reaction order dependence on the electrolyteconcentration, the residual water content, or the average activation energy. The empirical kinetics obtained are quite close in most of the cam studied to those obtained from Tafel slopes using polymer-coated electrodes (Table 2).


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3. Characterhtion of the Polymerization Fhms Productivity By integration of the experimental chronoamperogram we obtain the charge consumed during the polymerization (QPl). From both experimental magrutudes, the electrogenerated polymer weight (W) and the consumed charge (Q), we obtain the productivity of the current424 for evely eleckogenemted film (W/QPI = mg mC1). Any variation observed in productivity (Table 3) will indicate a mdfication of the polymerization mechanism during the polymerization time, or after modification of one of the variables of synthesis. In this way we can characterize the p u l p erization process for every electrogenerated film. 4. E l ~ h e m i c a Characterization l of Electmgenerated Films:

Storage Capacity Characterization of the polymerization p e s s through either its productivity or the order of reactions can m s k the presence of any simultaneous slow degradation reactions that are occurring and not affecting the polymer production, but that have an important influence on the polymeric propat~esand their subsequent technological applications. This problem is avoided by determination of a physical property that is d~ectlyrelated to any other physical property of the film or to any of its possible applications: the electroactivity of every electmgenerated film as the charge stored per mass unit (storage capacity) when the neutral fiIm is oxibed up to a defined overpotential in a chosen electrolyte at a constant temperature. The storage capacity will also indicate other parallel processes giving nonelectroactive material in the film, such as some parallel chemical polymerizations, or adsorption on the growing film of larger

Toribio Fernslndex Otero

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(a) Voltammop of a plypple film after elecbgamtim in a different cell and usually with different elmlyte o M m (&l and redwtiw &I charges. (Re printed from Handbook of Orgmic Condatiw MoZecuks and Polymers, H. S. Nalwa, d, Vol. 4, 1997, Fw.10.13, 10.15% 10.18,10.36.R w with permission of John Why & Sam hi, Cbichesm,UK.) (b)Q r m m m of ~ control, (c) @g. 323) Chronop tentiogmms of control.

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momts of polyelectmlytes than those required to keep the electruneut d t y in the composite. Every dried and weighed film is controlled by voltammetry Fig. 7(a)], chronomperornetry pig. 7(b)], or chronocoulommetry [M.7(c)] in an electrolyte (the same one used during electropolymerization or a different one). From the elsctrochernical reswe obtain the charge consumed during oxidation (&), or the charge m v e r e d during reduction (QA. Once reduced, the film is dried and we@@ thus giving the weight of the reduced polymer [W A .

324


These experimental parameters allow us to obtain the electrical charge stored per mass unit of the electroactive film as Q,,/Wd, or QEd/Wd (Table 4). Any parallel reaction present during the electrogeneration of the electroactive polymer giving nonelectroactive polymer or promoting a partial degradation of the electrogenerated material will be detected by the variation in the storage capacity during the polymerization time, or when a variable of synthesis is changed.

5. Efficiency of the Polymerization Charge in Producing Electroactive Polymers The electrogeneration of composites of conducting polymers and polyelectrolytes can contaminate both productivity and storage capacity through the presence of extra polyelectrolyte in the composite over that required to keep the electroneutrality. T h ~polyelectrolyte s originates in a strong parallel adsorption on the clean electrode before the current flow, or during the polymer growth, or in both cases. The final composition of every composite is influenced not only by the chemical variables of synthesis but also by the polymerization time; different analytical techniques are required to obtain the average composition of each film. Even under such conditions, electrochemical techniques combined with ex situ microgravimetry provide a very fast method for estimating the efficiency of the polymerization charge in producing electroactive polymer in a composite film. Under ideal conditions, (Schemes 1 to 3), the polycondensation of radical cations requires a consumption of two electrons to incorporate a monomeric unit into a linear polymeric chain. Those chains are electroactive, the oxidation potential being lower than the polymerization potential in accordance with the Hiickel theory. If we assume that a positive charge is stored every four monomeric units (as accepted empirically in the literature), 2.25 electrons are required to polymerize and oxidize a monomeric unit during the polymerization process. During electrochemical control, 0.25 electrons are required to oxidize it. So Charge efficiency ($6) =

00, x-x0.25 ,'Q 2.25

100

is the percentage of charge consumed during polymerization to produce an electroactive polymer in the final mixed material (Table 4). The


325

remaining charge was consumed in parallel reactions, some of them promoting a partial degradation of the just-generated electroactive polymer. The charge efficiency only takes into account the detection by the subsequent electrochemicalcontrol (Qred)of the electrogenerated polymer remaining as an electroactive polymer at the end of the polymerization. Only this electroactive fraction of the material mass controls physical and electrochemical properties, or applications, of the obtained films. The quantification of the charge efficiency gives information about the charge consumed by parallel electrochemical reactions, such as degradation processes, during polymerization. Empirical kinetics, together with the productivity of the current consumed for a polymerization process, the storage capacity of the electrogenerated film, and the efficiency of the polymerization charge in producing electroactive polymers leads to the conclusion that the electrochemical initiation of polymerization processes triggers a fast and complex mechanism by which the electrochemical synthesis of the electroactive conducting polymer coexists with degradation processes that generate a fraction of nonelectroactive material, and with a chemically initiated polymerization that produces adsorbed and nonelectroactive material. The final product is a mixed material with properties that are a function ofits composition. We will come back later to this complexity in order to take advantages of it to produce tailored materials.

6. SimultaneousElectropolymerization and Degradation Pmceses The presence of simultaneous reactions during electrochemical polymerization that promote a partial degradation of the electroactive film is deduced from the decreasing storage capacity of films obtained at increasing polymerization times (Table 1).Low degradation rates, compared with high polymerization rates, do not influence the polymer production rates until very h g h polymerization times. If the polymeric degradation rate increases faster than the polymerization rate when the potential of electrogeneration increases, then the films obtained have decreasing storage capacity (Fig. 8). Degradation processes can be caused b the discharge of residual water in acetonitrile solutions of thi~~hene!~' The presence of increasing amounts ofresidual water in this media promotes a faster degradationpassivation of the growing film when it is generated at constant potential. A subsequent faster drop of the flowing current is obsesved (Fig. 9).

Toribio FernSndez Otero

~ i a ~ h a r g e s a o r a g e t m p .yp om~ i d o n ~ ~ * t i r i r a e d ~ h ~ p ~ l y ~ ~ m , k B ~ ~ ~ a t ~ a n o d i c ~ U s w e r e ~ b y c y & v o ~ i n t h e ~ u n d ~ @ e .

~~tieSware~from&eratioktweentbechargeandduringPplymerdmdk~wei&~hm MRS S y m p h Vol. 328,Elect&& Q@uI muiMqnetic Proptics o j Orgattic Materikh,A. F.CoollriOo, A*-K-Ykv, C,Y. h, aacI L. R. Dalton, eda, p 805,F J2,1994, with pnbiun ofthe ~

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These facts are different demonstrations of the same event: de@tion reactions occur simultaneously with elecbopolymerization.4 M 9 'llhesereactions had also been called "overoxidation" in the Iiterature. The concept is well established in polymer science and consists of those d o n s between the pristine polymer and the ambient that promote a deterioration of the original polymeric pperhes. The electrochemid consequence of a strong degradation is a passivation ofthe film through a decrease in the electrical conductivity that allows a lower current flow at the saw potential than the pristine and nondegraded polymer film did. Passivation is also a well-established concept in the electmhmhy of

oxide films or electropamting. Since one of the main chemical and technological problems of conducting poIpers is their Iow stability for long-term applications, and since storage capacity is a quantification of the basic property of these

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Time (s) Figure 9. Chronoamperomebic curves for the growth of a polythiophene film on a statiomy platinum disk electrcde, from 0.1 M thiophene and 0.1 M tiCI04acetonirrile solutions, at different water contents: -( O.M%,( - - - -) 0.148, (.-.-. ) 0.44% ( - . - .. ) 1.04%. (Reprinted from T.F.%ID and J. Rodrfguez, Polyhophene electrogeneration on a rotating disc electrode. The water content influence on polymerization and on the polymeric propdes. J. Elecdroanal Chem., 310, 219, 1991, Fig. 9. Copyright 1991. Reprinted with permission of Elsevier Science.)

materials as they relate to other physical and eIectrochemica1 properties, we can design a method to follow the kinetics of the degradation p s s as a function of different electrochemical or chemical variables. The polymer degrades in every electrolyte as a function of the potential and the polarization time (b,), In order to quantify the influence of both variables in any electrolyte, we can polarize an electrogenerated film at a defined potential for different polarization times. At the end of every polarization time, the electrochemicd control of the film, by voltammefry or chronoamperometry,gives the remaining stored charge (Qred). After every control, the reduced polymer is dried and weighed to obtain the reduced weight. A representation of QEdvs. tpi, or o f ( a a/Q0) x 100 vs. tPl. gives the degradation kinetics (Fig. 10). Similar studies for different potentials of polarization, different concentrations of electrolyte, or of any residual substance, different temperatures, etc., allow one to determine the

-

empirical kinetics of degradation. Parallel analysis of the mmaining polymer gives the complementary information on the development of degradation mechanisms. Not much effort has been made to study and understand these mechanisms. Nevertheless, this is the key factor in

Figure 1Q (a) Evolution of the charge storage degradation rate as a function of the polarization times for different potentials of degradation. (b) Degradation rate: I(& Q,)/ad,as a function of polaaizatim potentials. (Reprinted from T.F. Oteco and V.OlazM, Porfug.Ekdrmhim.Acaa, El,48, 1995, Pigs.2,3. Copyright 19%.Rephted with permission of Elsevia Sciem.)

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Conducting Polymers, Electrochemistry, and Biomimicking Pmeses

329

attaining stability (high stability is equivalent to low degradation rates) and long-term electrochemical devices. The final conclusion from the different kinetic studies that simultaneously followed productivity, consumed current, storage capacity of the obtained films, and the current efficiency in generating electroactive polymer in the final film is that any electropolymerization of conducting polymers occurs together a partial degradation of the electroactive polymer. The final film is a mixed material. From the kinetic studies we know the variables that increase or deplete the degradation reaction in relation to the polymerization reaction. 7. Simultaneous Chemical Polymerization When polypyrrole was electrogenerated from dry acetonitrile electrolytes, a black polymer grew and adhered to the electrode. After a few seconds of electropolymerization, a black cloud was observed around the electrode. The film obtained had poor electrochemical and physical properties. Increasing the water content to 2% (wlw) gives, at 800 mV, films with improved properties. The black cloud around the electrode disappears. The basic mechanism ofpolycondensation of radical cations assumes that two protons are liberated at the electrode surface per monomeric unit incorporated in a polymer chain. This causes a significant increase in the proton concentration around the electrode after polymerization starts. Some of the pyrrole molecules arriving by diffusion from the solution bulk protonate before oxidation on the electrode, initiating a chemical polymerization to give protonated (nonconducting) polymeric molecules. This possibility was studied kinetically2' by adding HC104 in acetonitrile solutions containing LiC104 and pyrrole (Py) and increasing the water content. The chemical polymerization kinetics were followed by in situ UV visible spectroscopy, arriving at the empirical kinetics:

which explains and quantifies the participation of the pyrrole, the salt, the water, and the protons in the reaction rate. The negative reaction dependence of the water content is related to the competitive protophylic nature of water and pyrrole. The higher basic constant of the water eliminates protons from the reaction layer around the electrode when this substance is present.

330

Toribio Femhndez Otem

In pure acetonitnle, the electropolymerization of an electroactive polymer on the electrode takes place at the same time as chemical generation of protonated and nonconducting polymer around the electrode. A fraction of this polymer interacts and adsorbs on the growing film, giving a mixed material with low storage capacity in the absence of water. Using a small amount of water avoids chemical polymerization and improves physical properties. However, a concentration higher than 2% promotes increasing nucleophylic attack and degradation of the oxidized and electroactive polymer.

8. C r o s s - L i i g Ideal electrochemical polymerization was considered to give ideal linear and conjugated polymeric chains. The real situation is that films electrogenerated from the basic monomers are insoluble and infusible. Only polyaniline films are partially soluble in some solvents. There are more than two reactive carbons per monomeric molecule that are the origin of branches from the central chain and cross-linking between chains. These events result in the presence of sp3carbons (Fig. 11) along the chain, which have been detected by different analytical techniques, and which result in decreasing conjugation lengths and properties. A cross-linlung polymer interacts with a good solvent by swelling, giving a gel; the polymeric chains between cross-linking points become part of the network. The network does not solubilize. The cross-linking of the polymer is one of the initial processes induced by soft electrochemical degradationMfi1during electropolymerization. To avoid cross-linlung in one of the j9 carbons, the hydrogen linked to this atom was substituted by a chemical group having several carbon atoms. From these substituted monomers, soluble oligomers were obtained that had interesting physical and electrochemical properties, but that were different than those of the insoluble polymers. Oxidized and reduced states of some of those oligomers can have different solubilities in electrolytes owing to a change in the polymer-solvent interactions through the formation or annihilation of charges along the chain. A faradaic electrodissolution of the oligomeric films is possible in these cases, mimicking electrodissolution of inorganic metals (see references on heteroaromatics in Section IV).

Figure 1 I . Cross-linking point in the presence of bee d v e carbons in a polypyrrole unit.

9. Morphology

Technological applicationsrequire, in some cases, god control of the film morphology in order to get g d physical contact between two polymeric films (flat surface) or a polymeric film and a gas or an electrolyte (rough surface). The electrochemically initiated polymerization starts by nucleation and growth of the conducting polymer on a metal, followed by diffusion control of the polymerization, through a diffusion layer crossed by the monomer from the solution side to the electrcde side and by protons in the opposite direction. Both nucleation and diffusion p e s s e s can be controlled by the shape of the potential, or current, waves sent to the electrode. In h s way very rough, annealed, or smooth polymeric films can be obtained- using consecutive square waves of potential, consecutive potential cycles, orconsecutivetrapezoidal potential waves of increasing frequency. Current waves can be used in a similar way. The results studied and patented by our group for polypyrrole and polythiophene films


F w 12 Mod% ofinterfacial reactions ppdfor the e k h g e n d w ofpolypple from aqueous and wexonitrik solutions. @p&ed from T,F,Otem and J, -R .??leccrochim. Acta 39,245, 194, Fw.2,7. Copyright 1997. lbpmhd with W from Elsevier Science.)

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Conducting Polymers, Electrochemistry, and Biomimicking P r o c e ~ ~

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were later confirmed during the synthesis of different conducting polymers.

10. Conclusions abut Electrochemically Initiated Polymerization Processes The final conclusion of this short discussion is that electropolymerization is a fast method (a film of about 5 prncan be obtained by polarization in 1 rnin) that uses a complex mechanism (Fig. 12) in which electropolymerization, cross linking, degradation, and chemical polymerization can coexist to produce a mixed material with a cross-linked and electroactive part and a passive However, ifwe control the variables acting on the kinetics of the different simultaneous reactions, the complexity also provides flexibility, allowing us to obtain materials tailored for specific applications. III. ELECTROCHEMICAL VERSUS CHEMICAL PRODUCTION OF CONDUCTING POLYMERS

The complexity of the partially understood electrochemical mechanism for the synthesis of conducting polymers is analogous to the chemical mechanism when the polymer is generated in a homogeneous medium by chemical oxidation using a redox couple, i.e., k3+. Two protons are liberated, as in electrochemically initiated polymerization, to incorporate a monomeric unit in a chain. So any parallel protonation initiating a chemical polymerization in organic solvents will follow the same empirical kinetics stated above (Eq. 2 was obtained from a homogeneous media). The redox couple also attacks the oxidized polymer, promoting its partial degradation during polymerization.72-75 The polymer obtained is contaminated with the redox couple, which increases the degradation lunetics and decreases the long-term stability. Chemical synthesis does not have the powerful and elastic mechanistic tools of the electrochemical variables and requires several production and purification steps to attain the final product. Only for a fabric's coating can the chemical route improve, for physical reasons, the electrochemical possibilities for producing tailored polymers for specific applications. If chemical methods of generating conducting polymers are commercialized before electrochemical methods of synthesis, it can only be attributed to the laziness of electrochemists.

Not much effort has been made, except for the Tafel studies, to establish the empirical kinetics and models of interfacial reactions to obtain thick polymeric films (>I00 nm) of industrial interest from different monomers. However, this is much more than the few kinetic studies performed until now to understand the mechanism of chemically initiated polymerization. Electrochemical models still have an advantage in obtaining priority in the industrial production of tailored materials.

IV. SELF-DOPED POLYMERS, POLYMERIC COMPOSITES, AND HYBRID MATERIALS This chapter is mainly devoted to polymeric films obtained from pyrrole, thiophene, aniline, etc. monomers by electrogeneration, and studied electrochemically in solutions containing small inorganic or organic ions. Nevertheless when we say, e.g., polypyrrole, we are talking about a large family of different materials, different redox rates, different solubilities, different stabilities, different biocompatibilities, materials interchanging mainly anions, or materials interchanging cations during reverse electre chemical oxidation or reduction. At the moment we can envisage six different groups of materials in this family:

1. Polypyrrole relatives obtained by electrosynthesis in the presence of different small inorganic or organic counter-ions that are interchanged with the electrolyte during electrochemical control of the material. 2. Polypyrrole derivatives [Fig. 13(a)] with nonionic substituents, producing films formed by oligomers; these films are soluble in most organic solvents. 3. When the substituent is an ionic chain [Fig. 13(b)] with the anion on the organic side, some of the lateral anions act as counter-ions during electrochemical oxidation. The cation of the salt is expelled from, or included in, the material during oxidation or reduction, respectively. These are self-compensating or self-do in chemical or physical terminology, respectively) materials. g c 4. Heteroasomatic copolymers, formed from heteroaromatic CD monomers pig. 13(c)], giving films of oligomers that can solubilize in organic solvents following faradaic clectroQssolution in some electrolytes.7 7 4 1

42

F i g u ~13. (a) Substituted plypyrrole, (b) selfdo@ polypple, (c) heteroaromatic polymer showing the monomer unit, (d) composite polypymolepolyelm1yte, and (e) hybrid material. (Polyaniline macroion photo supplied by G6mez-Romero ad M.Lira.)

336


5. Polypyrrole composites [Fig. 13(d)], electrogenerated from

monomeric solutions of polyelectrolytes.82-89 6. Polypyrrole hybrids [Fig. 13(e)], electrogenerated from solutions containing the monomer and a salt of an inorganic macroion or a polyoxide.90-92

Stable molecular magnetic composites or hybrids having a specific energy two or three times the specific energy of the pristine conducting polymer, biocompatible materials, materials for high rates of redox processes, etc. are being obtained. A new field ofelectrochernically controlled molecular engineering of materials is being developed in which molecular or ionic properties are transferred to the macroscopic polymer. A fuller discussion of this electrochemical molecular engineering is outside the scope of this chapter. We can point out here that this engineering is based on the same parallel processes as those described for the electropolymerization of thick films of basic polymers (polypyrrole, polythiophene, polyaniline) in the presence of small ions, with the introduction now of electrodic new processes, such as polyelectrolyte adsorption. Changes of the relative rates of the parallel processes during the polymerization time allows different composition gradientss7to be obtained across the film and thus different properties.

V. PHYSICAL PROPERTIES OF THE DRY CONDUCTING POLYMERS The interest of physicists in the conducting polymers, their properties and applications, has been focused on dry Most of the discussions center on the conductivity of the polymers and the nature of the carriers. The current knowledge is not clear because the conducting polymers exhibit a number of metallic properties, i.e., temperature-independent behavior of X , a linear relation between thermopower and temperature, and a free carrier absorption typical of a metal. Nevertheless, the conductivity of these specimens is quite low (about 1 S cm-I), and increases when the temperature rises, as in semiconductors. However, polymers are not semiconductors because in inorganic semiconductors, the dopant substitutes for the host atomic sites. In conducting polymers, the "dopants" are not substitutional, they are part of a nonstoichiometric compound, the composition of which changes from zero up to 40-50% in

Conducting Polymem, Electrochemistry,and Biomimicking Processes

337

weight, requiring conformational changes along the chains in order to create the free volume required to host counter-ions (or dopant ions). The large variation in conductivity with the composition of the oxidized polymer leads to such applications as organic wires. The semiconducting properties of the neutral polymers and in particular those of the neutral and crystalline oligomers, which are more easily manipulated and understood than the oxidized and amorphous polymer, are used to produce plastic diodes and plastic transistors (field-effect transistors FETs). Electrolurninescence, the generation of light by electrical excitation, is another characteristic of the organic semiconductors being used to produce light-emitting diodes. All the optical properties and more precisely those based on the second and third harmonic, the nonlinear optics (NLO), are one of the main areas of interest for the physicists, but once again they require materials that are solid, dry, and as crystalline as possible (which requires the use of oligomers). The great capacity of conducting polymers to interact with electromagnetic or ionic radiation produces important applications, such as electromagnetic or ionic shielding. In summary, the exciting electrical and optical properties of these materials that have attracted the most interest from scientists and engineers are in marked contrast to the lack of theoretical models that can explain the astonishing simultaneous metallic and semiconducting characteristics of those materials when the experimental results are interpreted using models developed for inorganic and crystalline materials. In this context a clear preference for using solid, dry, and crystalline oligomers is observed, mimicking the physical conditions of the traditional metals and inorganic compounds and using a low degree of "doping." Cross-linked polymers are avoided and polymeric gels with large changes in the degree of oxidation (like most of those used for electrochemical studies) are ignored.

VI. ELECTROCHEMICAL PROPERTIES As electrochemists, our interest is attracted by the electrochemical properties of materials based on conducting polymers. The study of these properties requires putting a dry material inside an electrolyte. Since most of the electrolytes employed are based on a salt that is first dissolved in a solvent, we will refer to liquid electrolytes. At the end of this chapter we

338


will come back to the possibility of using a solid electrolyte and consider the great difference between properties and applications of the two kind of systems. The flow of a current through an electrochemical system demonstrates the main difference between material based on conducting polymers and all the other industrial nonconducting polymers: conducting polymers oxidize and reduce electrochemically in a reverse way, as do metals or redox couples:

Later we will describe both oxidation and reduction processes that are in agreement with the electrochemically stimulated conformational relaxation (ESCR) model presented at the end of the chapter. In a neutral state, most of the conducting polymers are an amorphous cross-lmked network (Fig. 3). The linear chains between cross-linking points have strong van der Waals intrachain and interchain interactions, giving a compact solid pig. 14(a)]. By oxidation of the neutral chains, electrons are extracted from the chains. At the polymer/solution interface, positive radical cations (polarons) accumulate along the polymeric chains. The same density of counter-ions accumulates on the solution side. Neighboring chains bearing positive charges are subjected to electrostatic repulsions. The chains relax by conformational movements [Fig. 14(b)], generating a free volume inside the solid which is immediately occupied by the counter-ion and solvent molecules. The process goes on inside the solid. The polymer swells (Fig. 15). A conducting polymer having a high percentage of clectroactive material behaves as a uniform gel. Both the composition and volume of the gel are a function of the oxidation depth: they behave as nonstoichiometric compounds (cationic polymeric chains + anions + solvent). The anion moving into the polymer during oxidation can be inorganic (cI-?'%F,~ r ? -and I-,% BF~?' PF~;,"etc.) or organic [(Bu)N]." The weight percentage of the counterion in the composite changes in a continuous way during the oxidation from zero until a range between 25 and 50 % isreached , which depends on the nature and charge of the counter-ion.

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Rgure 14. (a) Compactedchainand (b) relaxed chaia

FQm 15. I3kmhmicaUy stirrmlated swelling (a to f) or shrhkhg (f to a) d the polymeric structure. (Taken from t k Web page of the IAmtq of Ehtmhem, Univ* of dx B q % GmmQ with pewrission ofthe authm)


The process is ~ v by changing d the direction of the current flow. A cathodic current injects electrons into the polymeric chains. Positive

charges are annihilated and counter-ions and solvent are expelled from the solution. The abmce of positive charges along the chains gives strong polymer-polymer van der Waals interactions, promohg conformational changes that allow the plymeric chains to occupy the free volume after the counkr-ions depart. The gel shrinks. This reverse electmhemical control of the gel composition and volume is the basis for the singular electrochemical and the concomitant applications of conducting polymers. Reactions and properties based on polypyrrole films can be summarized as shown in Table 5 and below:

The elechochemical reaction drives a transition from a solid to a ge~lmThe oxidation depth can be limited at any point. The composition of the nonstoichiometric compound is assumed to be uniform whatever

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the percentage of the oxidized state. This assumption is not valid at the initial stages of the oxidation, when the polymer oxidizes under conformational relaxation control, as will be seen later. Once a defined oxidation percentage is attained, the compound can be dried in order to study the physical properties of the material. The composition of the dried material is assumed to keep the uniformity attained under oxidation. The nonstoichiometry of the conducting polymers originates in the fact that in real cross-linked polymers the ideal linear chains only exist between two consecutive cross-linked points, or between a cross-linked point and a carbonyl group produced by polymeric degradation. The length of those linear conjugated chains must follow a broad gaussian distribution, as does the molecular weight distribution in soluble nonconducting films. The first ionization potential, as stated by the Hiickel model for conjugated molecules, decreases as the chain length increases. The large distribution of the conjugation length and the high degree of crosslinking which hinders fast diffusion of counter-ions inside the material cause an overlap between consecutive ionization potentials that generates polaronic levels and an overlap between polaronic and bipolaronic levels. The final result is that the electrochemical extraction of electrons from the chains during a potential sweep occurs over a large potential range. The resulting voltammogram is a broad "potato" (as electrochemists working with redox couples say). The fact is that the polymer film behaves as a nonstoichiometric compound with a composition that changes as a function of the electrochemical potential (more precisely, of the consumed charge) over a large potential range. Under this hypothesis, reversing the reasoning, the electrochemical response must include structural information. Later we will show other electrochemical and spectroelectrochernical evidence for the nonstoichiometry.

1. Compmition and Conductivity A neutral polymer contains alternate single and double bonds along its chain. The UV visible spectra give a broad band in the UV region, indicating the presence of a large band gap between n and n* levels. A very low population of electrons can jump, under ambient temperature, from the occupied ~rband to the unoccupied n' band. The conductivity of a neutral polymer is low. Polymeric oxidation generates empty (electrons are lost) polaronic and bipolaronic bands in the midgap. The width ofevery

new band is proprtional to the population of polarom or bipolarom, these populations being controlled by the oxidahon depth (Fig. 16). Since the new bands can house elwtm11s because the gap to the valence band is lower than the n-x* gap, increasing mounts of electrons canjump,at ambient temperature, between the valence band and the new polaronic and bipolaronic bands, In this way, the width of the polaronic levels, at is, the probability of the eIcztmnic jumps increasing the number of cartiers ( e l m n s and holes)], and the conductivity inas oxidation advances. Taking into account that the composition of the new compound changes from zero up to close to a 50% (wlw) of counterions in areverse and continuous way, the conductivity has a large, continuous, and reversible variation101-102 from 10'9-iw7to re-ld s ml.Both initid and f d values change from one polymer to another and are different far two f i h s of "the same polyme?' synthesized under different conditions. Since most of the polaronic levels are g a d during the initial 10 to 2 M o of variation in composition, the largest change in the conductivity is abed during this change in composition,

P.8. PB.

F i g w 16 Evolution of the population of the polaronic and biilaronic bands during polymeroxidation.CB,conducting band,P.B., polmnic band, V.B.,valenceband, B.PB., bipohnic baud.

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2. ElectrochernomechanicalProperties. Molecular Motors The extraction of electrons from a polymeric chain during oxidation promotes a rearrangement of the double bonds along the chain. Length and angles between consecutive monomeric units change. If we imagine a very long linear polymeric chain, one end adhering to a microelectrode, in an electrolyte in which the polymer-solvent interaction is not as strong as the polymer-polymer van der Waals interaction, the spontaneous conformational changes occurring at ambient temperature allow an interaction between two polymeric segments separated by a long distance in the chain. This interaction forces the two segments to remain close. In a similar way, other separated segments interact, and so on. Under these conditions, strong polymer-polymer (intramolecular) interactions in a neutral chain lead to a random coil configuration pig. 17(a)]. During oxidation, repulsions between the positive charges stored along the chain, rearrangements of the double bonds, concomitant conformational changes, strong coulombic polymer-counter-ion interactions, and new polymer-solvent interactionspromote the continuous expansion of the chain to a rodlike configuration [Fig. 17(b)]. Since the conformational changes are stimulated by an electrochemicalreaction, they can be stopped at any point or reversed at any point. Such control of the molecular configuration means that the mechanical molecular energy can be controlled: we have a molecular motor transforming electrical energy into mechanical energy through an electrochemical reaction. This stimulates conformational changes along the chains, working at constant temperature that is, without following Carnot's rule. The resulting property has been named electrochemomechanical. Molecular motors stimulated by thermal, mechanical, electrical, or optical energies have attracted great interest, as will be seen later.

3. Macroscopic Motors. Artificial Muscles In a film, the cooperative effort of the different molecular motors, between consecutive cross-linked points, promotes film swelling and shrinking during oxidation or reduction, respectively, producing a macroscopic change in volume (Fig. 18). In order to translate these electrochemically controlled molecular movements into macroscopic and controlled movements able to produce mechanical work, our laboratory designed, constructed, and in 1992 patented bilayer and m ~ l t i l a y e r ' ~ ~polymeric -~'~

Figure 17. MoFecular motor: reverse conformational changes (mechanical energy) stimulated by oxidation or reduction of the polymeric chain, a) d u d chain b) oxidized chain.

devices. Thick polypyrrole films (from 2 to 100 pm) were electrogenerated on 3-cm2stainless steel electrodes using a method developed by our group that allows control of both morphology and Once rinsed with acetonitrile and dried, a flexible, adherent, and nonconducting polymeric tape was fastened to the coated steel electrode (Fig. 19). The bilayer pol ypyrrole-adherent fi lrn was vied from the e l e c w e and used as a new electrode (2 X 1 cm) in L i C Q aqueous solution. As counterelectrode we used a platinum foil. The reference electrode was a satzlrated calomel electrode. The flow of an anodic current oxidizes the conducting polymer and the film swells. At the p l y p p l d t a p e interface, elec~hemicallystimulated confornational changes in the polymer promote an expansion that

Figure 1& (a) Twd~nedonalrepweatation:O Tangled structure afterreduction at high cathodic potentials. IXX) I T@ an& potentials ace needed to inject positive charges, open the structure, a d allow counter-ions to (Reprinted from Handbook oforganic Condctive Mokcules &Polymers, H.S. Nalwa, ed.. V d 4, 1997, Egs. 10.13. 10.1% 10.18,10.36. ~ w i t h ~ o n o f J o h n W i I &e Sons,M,-,UK.)(b) y Threedimmid r q r w ~ i o f lA: compact eIement of volume (having a length I ) inrreases its length to 1 + blduring oxidation: e m at lost from the polymer, h e l s rn ad hydraxed counter-ions petrate from the solution to retain electmeutdity. (Reprhd from T.F. Oterq H.Ga& and J. Rodriguez, "A conformational relaxation approach to polypymie voItamm&y'' Synth. Mea. 86,1077,1997, FG.2. Copyright 1W. Reprinted with permission from Elsevier Science.)

Figure 19. (1) Oxidized polypyrroTe (PPy) film elmgmented on a steel eJecde. (2) A tape was fastened to the dry polrpyrrole film (A). B is doublesided tape and C is a protective sheet of p a p . (3) The bilayer device with a protective film is removed from the electrode. (4) The pmtective sheet is peeled off and the bifayer is ready to work (Reprinted from Handbook of Organic ConrJwIive Molecules a d l'olymers, H.S. Nal wa, ed.,Vol.4, 1997,Fjgs. 10.13, 10.15%10.18, lQ36,Reproducd with p i s s i o n of John Wiley & Sons, Ltd., Chichestet. UK.)

AgureZU. ~ c i a l r n w k ~ w & I n ~ ~ ( A ) ~ m ~ i n j ~ i n t o t h e polymercbaias. M v e chagcs are anddated bnter-ians and w a t e r m k d a ate exfled. the polymer^ amlcmpdm s t w g m l h f s appearateachpointofthe interfaceof the two pdpmers. 'hfree end ofthe bilaymbi'bes an angularmcwement toward the left side. (B) Oppite pwem rmnd mwmts acwr under &on. (R@nted from T.F. Okra ad J. R&gmq in Idrimica& Conducting PoIymers: An 12Copyright m.Reputed Emerging Technology,M. Aldissi ed,pp. 1WW with kind p&im of Kluwer A d a & h b l i s k . )

Toribio F m h d e z OEero

figure 21. Angular mmmt of the k end of a bilayer during the flow of a cathodic current using the conducting polymer as A platinum she& (left side of the pidm) is wid as anode.%referenceelectrodeis W e d a t t h e b m abe:Mwemmtduring the reducrion process; e to E Movement under flow ofan anodic current. The movement is stopped at any intermediate point (a, b, c, d, or e) by stoKping the current flow, and this position is maintained for a long time without polahtion.

Figure 21. (continued)

generates free volume to accommodate the counter-ions. These conformational changes curl the tape chains, promoting an expansion stress at the interface (Fig. 20). The macroscopic result is a bend from the vertical in the free end of the device, the tape side being in the concave part of the

bend.

During reduction, the polypynole fiIm shrinks, causing reverse potesses: an increasing compression stress is induced at every point of the interface. The bilayer bends, finishing with the tape now on the convex part. Under a current flow of 30 mA,a bilayer containing 3 mg ofpolyrner requires 3.6 s to describe an angle of 180" (-90" to +No related to the initial verticaI position) with a continuous movement (Fig. 21). The bilayer is able to move a mass up to 1OOO times the weight of the polypyrrole film adhered to the bottom of the bilayer, once the Archimedes effect is discounted. The device acts at the same time as a sensor and as an actuator, sensing any variable, such as the potential of work (Fig. 221, the current density, the electrolyte concentration, the bilayer dimensions, or the moved weight, when all the other parameters are kept constant. The improved conditions of synthesis of the conducting polymers, obtained from the kinetic studies, made it possible to construct devices able to

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Figure 22. Cfironoamperometricmpses OM when a bilayer was submitted to step potentials from 200 mV to different anodic potentials in the 600 to m m V range in 0.1 M hQU, aqueous solution. (Reprintedfrom T.F.OtemandJ. Rodn'guez,in Intrinsically Conducting Polymers: An Emerging Technology, M.AlW, ed, pp. lW!XI, Figs. l , Z Copyright 193. Reprinted with kind permission ofKluwer Ademic Publishers.)

d d b e more than 3W in both directions from a vertical position in a few ssconds. An electric current can be made to flow in the device twice by using (Fig. 23) a triple-layer design consisting of a conducting polymer, a two-sided tape, and a conducting polymer. When one of the polymer acts as anode, the second acts as a cathode. The substitution of the twesided tape with a film of an ionic conductor gives (Fig. 24) a triple-layered muscle working in air.Il4The tape now acts as a solid electmlyte. Nevertheless, the system only works if the relative humidity in air surpasses 60%. Under these conditions, move ments and rates similar to those shown by a triple layer working in aqueous solution were obtained. This device was developed in cooperation with Dr. M. A. De Paoli from the Campinnas University (Campinnas, Brazil). At the moment s e v d p u p s are developing actuators, muscles, and electrochemomechmicaI devices based on bilayer or multilayer structures,

115-12?

-

Cm ' ~ s a a p Y 3"prI'sag % ~ P mlow M n o ~ ~ W ~ m ~ 'BE'OT n r '8d1'0a1 %SI'OI ~ 'E 1.01 'a!d '~661'P 'IOA "P*MPNS'H ' ~ ~ W o dfrn3azow p u ~ a w ~ ow 3 a o @ (byooqpm~ ww QWW.xoq q m P%J =~VJ~I-I& av1'3 tr a m -7 3 ~ 3 ) paorrpaJ s! 11 al-ld ' ~av4P PW =3 w -Y 3 w )P w F o s! I a ~ o d d x ~ ou da y :=!hap ~ s g y m y om s y m dmp ~ paumsu03 arl~..alddXtod -d@ ~ ~ P U O ~ U O U ~ l3 i~q pararoJ ~ I 9~p!39DV 'ad~

am

Figure 24. An "all solid" muscle working in air. An ionic conductor elastomer was substituted for the nonccaducling tap from Fig. 23. (From Ref. 1U3,

(i) Eleciruchempos~oning Devkes The electrochernomechanicalproperty is directly related to the degree of oxidation. Taking into account that the degree of oxidation changes with the charge consumed, or as a function of the potential applied, a direct relationship exists between the applied potential, or the consumed anodic or cathodic charge, and the @tion (angle) of the free end of the bilayer (Table 6). So we can define a position by application of a potential, or we can describe a defied angle by sending a specific charge. This is the principle of an e~ectrochemopositioningdevice,

Figme25. M u v e m e n t r a t e o f ~ ~ ~ C d m g a n ~ a f wiwith different dhmim (d&mt poiypymle weights) vesus applied e l m i d current pa.mass unit (m* ly-'). @& ph&dfromT. h a dJ. M ' B i I a p ~ m and movement d muscla."Bi~iectrmkemBiaemrgemtics 4l, 117, 1997, Frg. 4, CoWtigbt 1997. Reprinted with p m h i i f r o m ~ ~ }

(ii) Control of Movement

Since the rate of mavement is controlled by the rate of the eIectm chemical reaction, when we oxidize mreduce the conductins plymer of the device at constant m n t , we will have a uniform movemnt with @ectcontroldthe movementmtc themovement is stq@ by stopping the current flow; the movement is RY& by reversing the dimtion of the current flow. By doubling the current density, we obtain a movement rate that is twice the previous one. Rates and mechanical energy are proportional to the current consumed per mass unit Fig. 25). (iii) Sirnihdy between Natural Muscles a d Polymeric Achaators In general, movement is an intrinsic property of living creatures. It occurs at different structural levels, including ion transfer through membranes, separation ofreplicated chromrnm, beating of cilia and flagella or, the most cornon, con~actionof muscles. These contractions enable

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355

F i 26. An electric (ionic) pulse anives from the brain though a nerve to the muscle, where it *em confof~ationalchanges in proteins and chemical d o n s . All the are three-dimensional. lhgenersrtor(brain)is atthe same time an i m i c d c t o r . (Reprinted from T.F. Otero in Polymer Sensors andAcfziutors, Y.Usah and D.De Rossi, eds., Fig.1, p., 19. Copyright 19XX.Reprinted with permission of SEarmger-Vdag.)

organisms to carry out sophisticated movements, such as walking, flying, breathing, and digesting food, that generate mechanical energy. Muscles are elegant devices, developed through millions of years of evolution to transform chemical energy into mechanical energy and heat at constant temperature, that is, outside the limitations imposed on internal

Figure 27, (a) The sliding filament model of skeletal muscle contraction, The decl.lease in sarcomere length is due to dmwses in the width of the I band and H zone, with no change in the width of the A band. Thlese o ~ o m mean that h e lengths of both the thick and thin filmen ts do not change during conkaction. Instead, the thick and thin filaments slide along one mother, (b) @g. 357) Proposed mechanism for the generation of fwce by interaction of an S1 unit of a myosin filament with an actin filament. In the power stcoke, the thin filament mom relative to the thick filament when S1 undergm conformational changes accompanying the =lease of ADP. (Reprinted from Biockmisiry 4LE by L.Shyer, F!I. 15-21. Copyright 1B5 by Lubert Sqer. Used with permission of W.H.Freeman and Company.)

Figure 27. (continued}

358


combustion engines or thermal engines by Carnot's rules. This transformation in muscles is triggered by an electric pulse that arrives from the brain, through nerves (Fig. 26), and promotes an increase of ~ a % inside the sarcomere from lo-' M to M. This increase of the ionic concentration is the origin of the troponin-tropomyosin conformational changes [Fig. 27(a)]. The energy required for these conformational changes is generated by adenosine 5 '-triphosphate (ATP) hydrolysis, ATP being the bonding ion between myosin heads and actin filaments. The ATP is obtained from adenosine 5Ldiphosphate (ADP) through the glucose cycle, the final products being COz, water, mechanical energy, and the heat required to adjust the entropic changes. At the conclusion of the cycle, the sarcomere contracts (Fig. 27a). So, natural muscles and our polymer-based devices have the following similarities: both of them are constituted of complex systems formed by polymers, water, and inorganic ions giving soft and wet materials; an electric pulse (ionic in muscles, electronic in our device) promotes ionic interchanges between polymeric molecules and the surrounding media; these ionic interchanges induce conformational changes in polymeric molecules, producing molecular motors; mechanical energy is translated from the molecules into macroscopic mechanical energy by stress gradients (through sliding polymer-polymer filaments in muscles, through a polymer-polymer stressed interface in our device); both devices work at constant temperature; in both cases a chemical reaction (electrochemical) provides the required energy; the potential of the nervous impulse triggering the movement is 160 mV; the artificial device works between an overpotential of 50 mV up to 1.2 V; both systems are three-dimensional devices based on linear polymeric motors. Given all these similarities, the artificial devices were named artificial muscles.

(iv) Differences between Natural and Artificial Muscles There are some differences between both devices: the driving power in muscles is the chemical energy produced by combustion of glucose at constant temperature, the nervous impulse acting as a trigger. The driving power in artificial muscles is the electric charge consumed, the polymer oxidation or reduction acting as a mediator for the transformation of the electrical energy into mechanical energy. Muscles only work under contraction owing to the irreversibility of the driving chemical reaction; the relaxation of the nervous pulse and the

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work of a complementary muscle are required to recover the initial position. Artificial muscles constructed from conducting polymers are

based on reverse electrochemical motors so they can be made to work under contraction as well as under expansion by changing the direction of the driving current flow.

(v) Other Artificial Molecular Motors in the Literature The isothermal conversion of chemical energy into mechanical work underlies the motility of all living systems. These are efficient systems because no intermediate steps producing heat are present, as was shown early in this century by van' t Hoff. In 1948, Kuhn et al. lZ6 demonstrated that three-dimensional collagen fibers undergo reversible dimensional

changes on transitions from cyclic helices to random coils when they are immersed cyclically in salt solutions and water. Katchalsky referred to this as a "mechanochemical" system (today the term "chemomechanical" is preferred, because it is more precise and avoids confusion with terminology about chemical reactions induced by mechanical stresses). In general, contraction and expansion of gel fibers provide a means of converting chemical energy into mechanical energy, which can be used to develop artificial muscles and actuators. A great advance in the understanding of chemomechanical systems was achieved a few years later, when Floryl" proposed an equation of state for equilibrium swelling of gels. It consists of four terms: a rubberlike elasticity term, a mixing entropy term, a polymer-solvent interaction term, and an osmotic pressure term due to free counter-ions.128The gel volume is also influenced by temperature, the kind of solvent, the free ion concentration, the degree of cross linking, and the degree of dissociation of groups on polymer chains. Since Katchalsky and Flory's work, various polymer gels have been studied as actuators and materials for chemomechanical energy conversion.129-131 Nevertheless, there have been few advances in practical devices. Many recent studies on polymer

gels show that mechanochemical properties are related to volume phase

transitions, 132-136 the volume change at the transition being as large as

1000 times the initial volume of the sa1n~1e.l" These transitions are normally driven by changes of temperature, the response rates being on theorderof lo2-lo3 s!37-138 Polyelectrolyte gels that showed bending motion by shrinking in an electric field 139-145 were called e2ectrochemomechanicaldevices, electro-

360


driven chemomechanical systems, or musclelike actuators. Mechanical deformation in polyelectrolyte gels can be induced by electric fields via electrodiffusion-induced changes in the intramolecular ionic environment and/or electrokinetically induced pressure gradients. These are very slow processes, so long times (about 10-lo4 s) are needed to complete overall volume variations (if phase transitions are not considered) up to 250%, that is, fractional length changes of about 50%. ASthe response time depends on both a characteristic length and the diffusion coefficient, the only way to improve response times is to modify the actuator geometry. 148-149 Another disadvantage of these systems is that they require high electric potentials to work (up to 100 V), which are applied by means of two metal electrodes immersed in aqueous solutions, and no information is available on the consumption of electrical energy or the reversibilit of the movement. Some reviews of those systems are available.131,146,l 0-152 Another kind of actuator is derived from the use of piezoelectric polymers like poly(viny1idene fluoride), as reported by ~au~hman.") These devices are based on fast and reversible charge polarization processes (no chemical reaction occurs, so they can be called electromechanical actuators) induced by high potentials (around 30 V), so very low response times are obtained (on the order of 1o5 s). The main disadvantage of piezoelectric polymers is that the dimensional variations attained are lower than 0.3% in volume, or 0.1% in length, so their commercial applications are limited to microactuators with high current efficiency. Photochemomechanical systems based on photostimulation of conformational levels givin reversible macroscopic changes of volume have also been studied.154-16 The volume changes reported so far, however, are limited to less than It is also feasible to generalize about the possibility of constructing molecular machines that can work as transducers of intensive variables into mechanical work. Proteins having hydro hilic-hydrophobic temperature transitions have been used with this aim. 18 These machines can be conceived of as changing any kind of energy (chemical, electrical, thermal, radiative, etc.) into mechanical energy, producing chemomechanical, thermomechanical, photomechanical, baromechanical, etc. actuators. Researchers are facing difficulties in improving the properties and response rates of chemomechanical and electrochemomechanical systems based on polymer gels or proteins that are intended to be used as actuators in robotics. Lack of mechanical toughness and long-term durability are other problems to be solved. A basic improvement in the low efficiency

7

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of energy conversion should also be made. This is the first generation of nonelectronic, conducting polymer-based artificial muscles. Devices based on conducting polymers (electronic and ionic conductors) that can link reverse chemical reactions occurring at the molecular level to macroscopic changes of volume are the second generation of fast, energetic, and low potential artificial muscles. From a conceptual point of view, a thorough discussion is required in order to clarify and differentiate among chemomechanical, electromechanical, electro-osmotic, and electrophoretic-driven actuators or electrochemomechanical devices. The main problem is to differentiate when chemical reactions are present in the first generation of nonconducting polymer gels.

4. Color Mimicking. Electrochromic Properties The energy required to promote an electronicjump from the valence band to the conducting band in a neutral chain of most conducting polymers is the energy contained in a UV photon. This means that uniform and thin films of conducting polymers are transparent to visible light, showing very clear yellow or green interference colors. The new polaronic or bipolaronic bands appearing and thickening in the midgap during the oxidation process allow electronic transitions requiring lower energy; photons from the visible light are absorbed (Fig. 28). The number of available empty polaronic or bipolaronic levels defines the probability of the photon absorption; since this number is controlled by the number of electrons extracted from the polymer during oxidation, the intensity of the light absorption is under control of the oxidation depth. The degree of oxidation, as stated earlier, can be stopped at any value, or reversed from any value, or changed in any direction by an infinitesimal amount. The same can be done with light absorption or transmission [Fig. 29(a)-(b)]. Shifts on the absorption-reflection spectrum produce macro~ ~ films ~ ~move ~ from ~ yellow scopic changes in C O ~ andO the~polymeric or clear green to dark blue or black (polypyrrole and polyaniline) or to red (polythiophenes). Since the reverse changes of color are related to the electrochemical reaction, they are called electrochromic changes, although it is more adequate to use electrochemichrornic, to differentiate them from the color changes caused by electric fields in liquid crystals, where chemical reactions are not involved, only phase transitions, and that means that infinitesimal variations are not possible.

Figure 28, Energetic tio om in neutral and ~ p o l a m n i sradbipohmic c lev&. Easergy bansitions fit W and visible

m,v t i v d y .

(i) Spectroelectmchemistry

and Nonstoichionae~

Polamns and b i p h n s are usually misinterpreted as redox couples stored in the chains. The main characteristic of redox couples is a perfect definition of both: the redox potential of the couple and the wavelength of the absorption maximum or maxima, independent of the concentration of the rdox couple. Cross-linked conducting polymers show a large oxidation-reduction potential range without any definition of wellseparated maxima related to polaronic or bipolaronic levels. Nevertheless those levels are there, as can be seen from the large band observed in Fig. 29. However, there we observe, as well, the presence of important energetic shifts of the maxima in the population of the two species toward more energetic content. Shifts as high as 1.2 eV are observed, which is in contradiction with any redox couple behavior being a characteristic of a nonstoichiornetric compound. The observed shift in either absorption or transmission spectra is reIated to the degree of

Conducting Polymers, Electrochemistty, and Biomimicking Processes

Figm 29. (a) Evohdon ofthe h r p t i m afai e k t m ~pa~basa~woftheoxldati~~potent d m i n g v o l ~ b e a ~ a n d 4 0 0 m£mma2JMUC104 V ~ ~ 1 u t i a T b e v o ~ w u ~ a t a s m m t 20 mV a"1, promRef. 161). (b) BvotuC~ofthe abwpb sgectra o f m ~ p o l ~ ~ a ~ o n d ~ m i ~ n t i a I o ~ d u r i n g v o I ~ b e t w m 4 0 0 ~ ~ b m a 2,sM Lia04aqyem solution. llre voI-etq m perf w n e d a t a m n r a t r : o f a ~ m ~ i(Fnm~ef. '. 161)

ial~ e d

u & n m V

364


oxidation and can be moved infinitesimally in any direction under electrochemicalcontrol.

(ii) Spectroelectrochemistry and Energy ofthe Molecular Motor Experimental results corroborate that shifts of 1.2 eV are always present if any of the variables acting on the electrochemical process are changed: the solvent, the salt, or the temperature of work. We cannot attribute the observed shift to solvatochromic, counter-ion-chromic, or thermochromic effects taking place inside the film during oxidationreduction processes. So, as predicted, these shifts are a consequence of the way the chains store or relax energy through conformational changes stimulated by electrochemical oxidation or reduction, respectively.

(iii) Smart Windows Electrochromism is an intrinsic property of conducting polymers,163 metal oxidesla and polyoxides, inorganic macroions, and some inorganic and organic redox couples, etc. Among these materials we have complementary substances, such as polypyrrole and tungsten oxides. Thin and uniform films of neutral polypyrrole show a pale yellow and transparent color. After oxidation they show a blue-black, almost black, color. Tungsten oxide films show a dark blue color in a reduced state and are transparent and colorless when oxidized. Two complementary electrode cells with a thin film of a transparent electrolyte form a smart window [glasslITO (Indium Tin Oxides)/ polypyrrole/electrolyte/W03/ITO/glass (Fig. 30)] that can be used for uniform, intelligent, and constant illumination in buildings, cars, planes, etc. (Fig. 31). In such a window, the photocell generates an electric signal proportional to the intensity of the light arriving at it. The regulatoractuator specifies a range of illumination that indicates the range of the current densities arriving from the photocell from il to iS. If the intensity of the light arriving from the photocell is higher, the window is submitted to an anodic current on the polypyrrole electrode and a cathodic current on the tungsten oxide electrode. Through darkening of the two electrodes, the absorbed light increases and the luminosity in the room decreases. The current generated by the photocell falls as it comes inside the stated range. Then the current flow is stopped.


---

m a w

figure 31. Automatic assembly to keep a constantluminosity.

Conducting Polymers, Ekctmhemistry, and Biomhickjng Pruceses

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At dusk the window becomes lighter. When the polypyrrole film is completely reduced and the oxide is fully oxidized and darkening continues, the current of the photocell decreases at il and the electric light in the room is switched on. The intensity of the electric current sent to the lamp is increased in such a way that the luminosity in the room remains constant at all times. In cars or for other applications, the device can work automatically or by hand, darkening all the windows when the car is parked on a sunny day. Optical filters for UV, visible, or IR domains and specific wavelengths can be constructed in a similar way.

(iv) Smart Mirrors, Flnt Screens, or CamoufZnge Cloth In a mirror-polished metal electrode substitute for the tungsten electrode we have a smart mirror. A similar photodetector-actuator automatically darkens a smart mirror in a car when arearcar uses high-beam lights. The use of small electrochrornic points allows the construction of monochromic or multichromic flat screens. Using different conducting polymers with complementary colors on ITO-coated flexible plastics (now available commercially), camouflage cloths can be envisaged which, once connected to a video camera and a system of image treatment, would be able to mimic any surrounding, as chameleons or cuttlefish do.

5. Storage of Energy. Polymeric Batteries Reaction (3) represents the storage of positive charges along the polymeric chain. The reversibility of the reaction involves the possibility of recovering this energy acting as a positive electrode in a battery. The development of all-organic batteries in aqueous media will be a closer step to the electric organs of electric eels. At the moment, most of the interest of the international battery industry is focused on developing lithium ion batteries. The simplest of these devices use lithium metal as anode,16s169 a polymer as cathode, and a liquid electrolyte. This distribution causes a problem: the best-described conducting polymers interchange anions with the electrolyte, and the Li electrode liberates Li'during discharge. The salt accumulates in the electrolyte pig. 32(a)], requiring a great volume and mass in order to avoid the precipitation of the salt. This fact reduces the specific energy of the battery to impractical values.

Several fields of research and development are now working to produce polymeric anodes that interchange cations during charge and discharge: selfdoped polymers, polymeric composites, hybrid materials, The polymeric composites would accept Li+from the electmIyte during discharge and expel those cations during charge. Under these conditions, the electr01yte acts as a path for the transfer of the cations from the lithium electrode to the poIymeric electmde during discharge and in the opposite

direction during charge.There is no accumulation in the electrolyte, which can be reduced to the thinnest possible film mg. 32(b)]. The main problem now is the formation of dendrites in the Li, which can perforate the membrane. The scenergy ofthe system was ~~~dby dmming the electrolyte volume and mass. 'Ibis h a m e is partially cornpensatad for by a decrease in the specific energy of the poIymer caused by the incorporation of the polyanion mass. A more profitable solution is the use of selfdoped polymers. A new field is appearing with the use of hybrid materids that have the sarrme effect as plyelectrolytes but that include electmactive materids (the polyanions) that can inthe specific energy of the conducting polymer up to three times. The cost, however, is a higher instability. A lot af work has to lx done to attain moE practical and competitive devices in these new fields. The main advantage of all these devices is the high potential of the individual cell, ranging between 2 and 4 V,depending on the polymeric electrode. One of the grob3ems of these batteries, dways o b e d but never explained, is that the electrodic potential dearam continuously

370


other side is connected to a conducting polymer. At the end of the conducting polymer is solution. Current flow induces redox processes in the polymer with an interchange of ions. The solution promotes a decrease or increase in the ionic concentration close to the electrode, which is related to the bulk solution and induced by the electric pulses in the metal wire.16g-170 This device is a transductor of electronic to ionic signals. The Nerst equation allows transduction of the ionic changes to electronic signals.

(i) Modulntion of Ionic Concentration Electron-ion transduction allows local modulation of the ionic concentration in a solution at a distance from the electrode that is less than the thickness of the diffusion layer.171-173 The solution volume can be modified through the hydrodynamic conditions or the viscosity of the polymeric surrounding in order to reduce or enlarge the thickness of the diffusion layer. Polymers like those in the polyaniline family interchangeprotons and anions with the solution, allowing a local modulation of pH. Composites that interchange cations allow the modulation of any cation concentration. Efforts are being devoted to the synthesis of polymer or polymeric derivatives having great cationic specificity.

(ii) Interface with the Nervous System The nervous system can be envisaged as a complex multielectrochemical system in which some neurons act at the same time as pulse generators, signal processors, information stores, and signal transmitters. This complexity gives the nervous organs their great capacity and flexibility. A tremendous effort has been made by scientists to understand and to mimic the most fascinating and inaccessible of the organs developed by evolution. In spite of the efforts devoted to observing and understanding the morphology of the different components of the nervous system, the conformational structure of the amorphous channels responsible for signal transduction remains unsolved. Nevertheless, the main problem related to the nervous system is centered on the nervous impulse: how it is formed, how many components it has, what kind of information drives every component, and how we can interact with these components in order to


371

initiate a dialog between the nervous system and electronic equipment (video cameras used as artificial eyes, microphones used as artificial ears, artificial arms, etc.). The nervous impulse can be observed at the interface between the axon of a neuron and the dendrite of the next neuron. The ionic (Na*,K*, ca2+) and chemical (neurotransmitters)nature of the nervous impulse has been stated and clarified during the past decades. Most of the neurotransmitters have an ionic nature. So the nervous impulse contains both ionic (electrical) and chemical information, and most of the carriers have been modulated in a different way. Knowledge of the "technology" of the human system has been advanced in two ways: by identification of most of the chemical components, and through remote listening to the voltage induced on metallic electrodes by the electric (ionic and membrane polarization) components of the nervous impulse. The different nature of the carriers present in metal electrodes (electrons) and in nerves (ions and chemicals) makes any dialog between both systems impossible. A transducer is required that can receive, separate, and translate every one of the electrical and chemical components into electronic information. The transducer has to remain in contact with the axon, so it has to be biocompatible. It has to be able to differentiate among the different chemical components, so it has to contain some specificity. The only available materials that come close to meeting these conditions are conducting polymers. We are able to construct mechanical arms that reproduce movements quite close to those performed by the human arm. The problem in implanting these arms is that movements have to be coordinated with all the other body movements under the brain's direction. There is one possibility for connecting the electronic systems of the artificial arm to the nervous signals (Fig. 33) coming from the brain in order to obtain coordinated movements: separate those signals into different components and amplify every component to drive an artificial muscle or electric motor.

(iii) Medical Dosage Oxidized conducting polymers, or conducting polymer composites can be envisaged as stores of anions or cations, respectively. As stated earlier, these ions can be liberated, under a well-defined control, in a solution. This idea is being developed in order to store ions of pharma-

Toribio Femhdez Otero

Figm 33. Rqmd interface between an elecmk m m p m t (Wcanma) and a

neme(oQticalme) t h a t ~ ~ u c e e ~ ~ h m t b e e q a i p r n e n t t o ~ %i&tbatmbmby-.

cological interest which, once implanted and connected to a sensor, can release directly into the blood the amount required to maintain a defined concentration.

7. El-dty

and hat Membranes

Desalination of sea water, or purif~cationto eliminate dangerous ionic contaminants from industrial waste water involves important technological, scientific and financial risks. Most of them are related to the development of cheaper smart membranes that can rnimic bidogicd membranes. Oxidized conducting polymer act as anion-conducting membranes. The degree of oxidation controls the radius of the membrane pores,176175 allowing control of the transport index for anions having different soIvated radii, or different charges. Polymers like polythiophene can be oxidized and reduced, moving from an anionic conductor membrane to a cationic conductor membrane where the degree of reduction controls the transport index of cations having different solvated radii.

VII. ELECTROCHEMISTRYAND ELECTRODE STRUCTURE Most of the models developed to describe the electrochemical behavior of the conducting polymers attempt an approach through porous structure, percolation thresholds between oxidized and r e d u d regions, and changes of phases, including nucleation pesses, etc. (see Refs. 93,94, 176, 177, and references therein). Most of them have been successful in describing some specific behavior of the system, but they fail when the

ConductingPolymers, Electrochemistry, and Biomimicking Processes

conditions of work are changed, or if there is "anomalous"behavior of the polyme~. Our laboratory has planned the theoretical approach to those systems and their technological applications from the point of view that as elec-

trochemical systems they have to follow electrochemical theories, but as polymeric materials they have to m p d to the mdels of polymer science. The solution has been to integrate electrochemistry and polymer science.'78This task required the inclusion of the electrode structureinside electrochemical models. Apparently the task would be easier if regular and crystallographic stnrctures were involved, but most of the electrogenerated conducting polymers have an amorphous and cross-linked structure. Even when they have a partial crystallinity, conducting polymers swell and shrink, changing their volume in a reverse way during redox processes; a relaxation of the polymeric structure has to occur, decreasing the crystallinity to zero percent after a new cycle. In the literature, different relaxation theories (Table 7) have been developed that include structural aspects at the molecular level; magnetic or mechanical properties of the constituent materials at the macroscopic level; or the depolarbtion currents of the materials.

Experimental results and developed devices allow us to divide the oxidation of the neutral conducting polymers into four steps:

374


1. Loss of electrons from the polymer chain with the formation of radical cations (polarons) and dications (bipolarons). 2. Stimulation of the conformational relaxation movements of the polymeric chains (by repulsion between the nascent positive charges), with the generation of free volume. Local nuclei or general and simultaneous relaxation occur, depending on the initial compaction of the polymer film. 3. Exchange of counter-ions (and solvent) between the polymer and the solution in order to keep the electroneutrality in the film. In a compacted or stressed film, these kinetics are under conformational relaxation control while the structure relaxes. After the initial relaxation, the polymer swells, and conformationalchanges continue under counter-ion diffusion control in the gel film from the solution. 4. Additional exchange of ion pairs and solvent molecules as in any other membrane formed by polyelectrolytes. Theoretical models available in the literature consider the electron loss, the counter-ion diffusion, or the nucleation process as the rate-limiting steps; they follow traditional electrochemical models and avoid any structural treatment of the electrode. Our approach relies on the electrochemically stimulated conformational relaxation control of the process. Although these conformational movements179are present at any moment of the oxidation process (as proved by the experimental determination of the volume change or the continuous movements of artificial muscles), in order to be able to quantify them, we need to isolate them from either the electrons transfers, the counter-ion diffusion, or the solvent interchange: we need electrochemical experiments in which the lunetics are under conformational relaxation control. Once the electrochemistry of these structural effects is quantified, we can again include the other components of the electrochemical reaction to obtain a complete description of electrochemical oxidation. If such a model is to be self-consistent, it has to include, and to be able to simulate, all the electrochemicalresponses treated by the previous models as well as all the so-called "anomalous effects.??18&183 Any variable acting on those anomalous effects has to be described by the model without need of further development.

Conducting Polymers, Electrochemistry,and Biamimicidng Prowssa

375

2 Anomalous Electrochemical R d t s The study of the electrochemistry of the conducting polymers in organic solvents having a high cathdc potential of reduction (> -2V) showed that any polarization at high cathdc potentials induces a strong mdification of the subsequent polymeric oxidation. These include anodic shifts of the oxidation potential [Fig. 34(a)J, changes in the voltammogram shape, the appearance of nucleationlike processes on the chronoampemgrams pig. 34(b)], and increasing hysteresis effects between oxidation and reduction p s s e s . Any of these anomalous effects is influenced by the polarization time at a constant cathodic potential, by the cathodic potential of polarization at a constant polarization time, by the anodic

Hgure 24. (a) Voltammetric behavior of a polypyrrole in 0.1 M LiCIOl propylene carbonate solution. The potential sweep was carried out at 30 mV s-' between different cathodic potentials and 300

mV vs. SCE.The cathodic potentials were from left to right: 4 K l , -1m, -1400, -1600, -1800, -2W, -2M10, -m,-2600 and -2800 vs. SCE (b) (pg.379 Potential steps carridout on a plypyrrole el=& in a 0.1 M UC104pmpylene h n a k solution from different cathodic potentials, indicated on the figure, to 300 mV vs. SCE. (Reprinted from T.F. Otero and E. Angulo, 'Qxidation-reduction of polypyrrole films. Kinetics, structurd model, and applicatim." Solid State Ionics &M4, 803, 193, Eigs. 1-3. Copyrrght 1 9 3 . Reprinted with kind permission of Hsevier Science-NL, Sara

Burgerhartstmat 25, 1055, KV Amsterdam, The Nethalands,)

Figm 34. (continued)

potential for potential steps from the same cathodic gotential retained during the same polarization time, by the temperature of cathodic polarization, by the temperature of the potential step (or sweep) when the temperature of the cathodic polarization is the same, by the counter-ion concentration, by the solvent, etc, According to our initial hypothesis, these anomalous effects are the experimental results occurring under kinetic control of conformational relaxation. Here confornational relaxation is ex@ over its entire length to the influence of the electrochemical variables, the temperature, the polymer-pol ymer interactions, the polymer-solvent iatedons, etc. These are the monitors that can be used to validate each new step of theoretical development during our attempt to integrate electrochemistry and polymer science. Steps 1 and 2 of polymer oxidation described in the previous section can be considered as a relaxation step. Then the oxidation is completed by swelling18"' 86 under diffusional control. The elecbrochemically stimulated conformational relaxation, swelling, and oxidation of a conducting polymer is shown in Fig. 35.

J,

Conducting Polymers, EIectmhemistry, and Biomimicking Processes

.

.

377

Slllv,iltrI c.bt itui*

d iff uskm

..

+

em

Partial

rduction

Partial cruidatiu~~

n~ndrrconbrmatioml mlaxation contml

Eull reduct~on + compaction

. .., I

, 0

i

, :, ,

.,

.

a

.

.

..

S l v a t e d anions

.. .. .; Prlsitive charge f i x c d

:. on pdymetic chains . : I'olymcric chains

Figure 35. Schematic representation of the reversible variation of volume aswiated with the electrochemica1switching of plypyrrole. Changes in free volume are mainly due to two effects: e l w t a t i c repulsions between fixed positive charges and exchange of cations, anions,and solvent molecules between the polymer and he solution. (Reprinted from T.F. Otero, A.-J. Grande, and J. Rodriguez, Phys. Chem. 101 3688, 1947, Figs. 1, 3,6, 7, 13. Copyright 1997. Reprinted with the permission of the American Chemical Wety.)

3. Conformational Relaxation lime Any relaxation theory is based'87on the definition of a relaxation time (r)

This mathematical definition is the same regardless of the relaxation theory. Physically, in our case, z is the time required to change the conformation of a polymeric segment, previously submitted to a cathodic potential E, (Fig. 36), when it is oxidizsd to an anodic potentid E. A polymeric segment is the minimum chain length whose conformational movements allow ionic interchanges between the polymer and the sohtion. The conformational relaxation of a mole of segments requires a molar conformational energy (M).

Figure36. Voltarmnograms made on areduoedand m m m p k dp o l p l e film (-- --3 and a compemcted film (), Ep clo& potential; 8 , closing overpotential; E,, oxidationptmW ~ , o x i & t i m o v e r p oEMnucfeationpotentialforthe~ted ~, film; qe nucleation ovqmmial;

The conformational changes are stimulated by cathodic compaction of the structure, by anodic oxidation and swelling, or, in absence of any external electric field, by thermal In any case, they are a combination of the poIymer-soIvent interactions. S o w can be ex@ as a sum of three terms

where A# is the conformational energy consumed per mole of polymeric segments in the absence of any external electricfield, MH, represents the increment in conformational energy per mole of segments arising from the closwe of the polymeric matrix induced by electrochemical reduction under cathodic polarization, and Meincludes the increase in conforma-

Conducting Polymers, Electrochemistry,and Biomimicking Processes 379

tional energy per mole of segments caused by the opening of the polymeric matrix that is induced by its electrochemical oxidation under anodic polarization. An increase or decrease in the conformational energy has to be understood here as a relative term required for quantification reasons because both energies can be used to produce macroscopic mechanical (positive) energy, as was shown in muscles, but in a different direction (+ or -) of movement. From an energetic point of view, in situ absorptionreflection spectroelectrochemical experiments showed polaronic and bipolaronic shifts toward more energetic content (Figs. 29, a and b) when the stress is increased at higher degrees of oxidation. In the absence of any electrochemical processes, the behavior of conducting polymers (either in the neutral state or positively or negatively charged) in an electrolyte is described by polymer science. The relative energies involved in polymer-polymer, polymer-solvent, polymer-ion and ion-solvent interactions play an important role in the swelling or compacting behavior (depending on the relative values of those energies) of the polymeric states. This means that A& includes the polymer science in our model, which has to be more fully developed in the next few years. Nucleationlike processes appear on the experimental anodic chronoamperograms only after polymeric compaction by cathodic polarization, during a constant time t, if the cathodic potential surpasses a potential threshold EJ that is experimentally determined.The closure and compaction of the polymeric matrix can be assumed to be proportional to the cathodic overpotential (q,)

After polarization to more anodic potentials than E,, the subsequent polymeric oxidation is not yet controlled by the conformational relaxation-nucleation, and a uniform and flat oxidation front, under diffusion control, advances from the polymer/solution interface to the polymerlmetal interface by polarization at potentials more anodic than Eo. A polarization to any more cathodic potential than Espromotes a closing and compaction of the polymeric structure in such a magnitude that extra energy is now required to open the structure (LW,is the energy needed to relax 1 mol of segments), before the oxidation can be completed by penetration of counter-ions from the solution: the electrochemical reaction starts under conformational relaxation control. So AH, is the energy required to compact 1 mol of the polymeric structure by cathodic polarization. Taking


into account the uniform shifting of the oxidation overpotential when the film is compacted at increasing cathodic overpotential pig. 34(a)J, we can assume a linear dependence between AH,and the cathodic overpotential (tg J or compaction overpotential

Since AHc is a molar energy, the product ZJ, has to be an energy as well, so t,the cathodic coefficient of electrochemical compaction, is the charge required to compact 1 mol of polymeric segments. In orderto relax 1 mol of m p x t e d polymeic segments, the material has to be subjected to an anodic potential (E) higher than the oxidation potential (Eo)of the conducting polymer (the starting oxidation potential of the nonstoichiometriccompound in the absence of any conformational control), Since the relaxation-nucleation processes (Fig, 37) are faster the bigher the anodic limit of a potential step ffom the same cathodic potential limit, we assume that the energy involved in this relaxation is proportional to the anodic overpotential (ql where 2, is the anodic coefficient of the electrochemically stimulated oxidation, i.e,, the charge required to relax 1 mol of polymeric segments. Thus the relaxation time at the anodic potential E after compaction of the structure at the cathodic potential Ec becomes:

F@E 37. htd se&m a f a t p 1 ~ film c during the nucleation and p w h ofthe c d m h g m m after a potential step (Reh m T.F.Okm, &-I. &a&, d J. RddgUq "A new d d fQr6lawhw o w m ofpolypynu,le underoonf-t i o d wlaxation oonh1." J. ELectrmwL Ickem, 39d, 21I, 15145, Eg. 2 5 . Copfight

1995. Reprinted with p l h i o n b n w e bW K e . )


381

This equation includes magnitudes related to the polymeric structure, as ro and &,together with pure electrochemical variables (?,and q ) and variables acting on or related to the electrochemistry of the system through the polymeric structure (T, z, and G). This is the relaxation time of the polymer oxidation under electrochemically stimulated conformational relaxation control. So features concerning both electrochemistry and polymer science are integrated in a single equation defining a temporal magnitude for electrochemical oxidation as a function of the energetic terms acting on this oxidation. A theoretical development similar to the one performed for the ButlerVolmer equation yields i = io exp

[polymer]" [clO;la

(10)

where [polymer] indicates the concentration of electroactive centers in the film and [ClOa] indicates the concentration of free perchlorates inside the film. This concentration can be obtained as a function of the salt dissociation equilibrium in the solvent, equilibriums and dissociation constants between the solvent and the gel, and the Donnand potential of the polymer film or the osmotic pressure term of Flory's model. If this equation includes electrochemical and macromolecular magnitudes related to the oxidation of conducting polymers, it means that any electrochemical response (such as chronoamperograms, voltammograms, chronocoulograms, coulovoltagrams, and impedance), and the influence of any electrochemical, chemical, or macromolecular variable acting on those responses, must be explained by this equation. Moreover if the physical chemistry of the conducting polymers is implicit, any magnitude or any constant (such as polymer-polymer, polymer-solvent, or polymerion interaction parameters; degree of cross-linking; swelling; porosity; and free volume) is also included there and it should be possible to design adequate electrochemical experiments to obtain them. This is a difficult task for the coming years, requiring cooperation among electrochemists, polymer scientists, membrane engineers, biologists, medical doctors, etc. As part of the effort to explain the proposed consequences of equation (10)

we are attempting to determine the electrochemical implications of oxidation occurring under stimulated conformational relaxation control.

4 Nucleation and Expad011of the Ozddized Amorphous Regions Once formed, the columns of an oxidized polymer begin to expand (Fig. 38), this process being controlled by conformational relaxation in the borders between the oxidized and reduced regions. In order to advance the development of our model by the inclusion of this process, the following simplifications and hypotheses were considered: 1. N, nuclei per cm-' appear at the beginning of the oxidation process

under constant temperature md electroIyte concentration in a specific solvent. 2. Relaxation nuclei expand concentrically as cylinders until they coalescence.

F p 38. Evolution of the proposed s

u b of a polypyrrole film during anoxidation mtim initiated from bigb catbdc potentials (R < -800 mV vs. SCE). The chronorrmperomdc response is shown at the bottom. Expimtrll confmatim caa b seen in the pictures in Ref. 177. (Reprinted from T,F. Otero a d E. Angulo, "Oxidation-reductionof polypyde films. Kinetics, smctural model, and appWons.* Solid State lmics M,803, 1993, Figs. 1-3. Copyright 1993.Reprinted with kind pnhsion of EIsevh ScienceNL, Sara Burgerhammat 25, 1M5, KV Amsterdam, The Nether-

w.1


383

3. During this time, oxidized and neutral phases coexist, having clear 4.

5.

6. 7.

separation surfaces (i.e., the lateral area of the cylinders). Oxidized regions are uniform in composition and consequently in charge density at every polarization time. Regions of neutral polymer have, as well, a uniform composition. Both oxidized and neutral regions have an amorphous structure. The relaxation of a mole of segments on the oxidizedlneutral polymer borders involves the loss of q, electrons and the subsequent storage of q, positive charges.At the same time, qr solvated monovalent anions penetrate into the polymer from the solution. The relaxation of an elemental segment is completed after a time o f t seconds. This assumption likens the relaxation process to a step function. The overall charge (Qr)consumed to oxidize the film by apotential step from Ec to E has two components: the charge consumed to relax the compact structure, which will be called the relaxation charge (Q,), and the charge consumed under diffusion control to complete the oxidation, called the later diffusion charge (Qd). The following equation is obeyed:

Capacitive charges are neglected in this approach. Under these conditions, it can be stated that the radius, r, of the cylinders increases by a length 1 in a time r, R and T being the length and relaxation time of a single polymeric segment, respectively: dr - - 3, exp (-AH/RT) ----dt

T

q,

And by integration r=

R exp (-M/RT)t To

This indicates a constant expansion rate for each cylinder during the polarization time. The expansion rate decreases with increasing cathodic potential of prepolarization, decreasing anodlc potentials, or decreasing step temperatures, which is in good agreement with experimental results, as will be shown later.

384

Toribio F e h d e z Otem

In order to obtain the current consumed during the nucleated relaxation process under a constant potential, we assume that a stationary density of charge (83 will be stored in the polymer at the polarization potential E. The storage of these charges is controlled by both conformational relaxation (6,) and diffusion (dd) processes, so

All these densities are related to the volume (V) of the film, given by

h being the thickness of the polymer film and A the area of the polymer/solution interface. The surface concentration of polymeric segments relaxed by conformational movements on the borders of the oxidized regions (a) can be expressed as follows:

The amount of polymeric segments relaxing on the borders of the expanding cylinders by unit of time and unit of area (k) can be obtained by dividing Eq. (16) by the relaxation time (7):

5. Anodic Chronoamperograms under Conformational Relaxation Control If h is the height of every cylinder (i.e., the thickness of the polymer film), the expansion of which follows Eq. (12), the current associated with the relaxation-controlled oxidation, I,'(t), in the borders of the cylinder can be stated as 3,

I,' ( t )= 2nrh9,k = 2nrh8, T

Equation (18) can be modified by application of Eqs. (4), (13), and (15), and by assuming that A!, nuclei are growing simultaneously:


385

6. Coalescence between Oxidized Regions Equation (12) works until coalescence starts between adjacent nuclei (Fig. 38). Assuming the symmetry of the growing process, our three-dimensional system is reduced to a problem of two dimensions, so Avrami's treatment can be applied:

Here I, (t)is the electrical current flowing after coalescence, I,, is the extended value of intensity given by Eq. (19), and Sex,is the extended oxidation area without considering the existence of coalescence, referenced to the total film area (A).The value of s,,, can be easily deduced from Eq. (13): S,,

nlY',A2

= --,exp ( - ~ A H / R T ) P 7oA

7. Relaxation-ControlledOxidation

The relaxation charge consumed is obtained by integration along the polarization time:

These two equations quantify the evolution of the relaxation current and the relaxation charge as a function of the polarization time when the conducting polymer is submitted to a potential step from E, to E. They are the relaxation chronoamperogram and the relaxation chronocoulogram,

386

Toribio Fernindez Otero

respectively. The conformational relaxation controls the shape of the chronoamperograms. Therefore these equations, even though the relaxation charge represents only a small fraction of the overall charge consumed during the complete oxidation, fulfill all the requirements for simulating the point in time at which the chronoamperograms attain the maximum current as a function of the different variables:

For chronoamperograms obtained by potential steps from the same cathodic potential to different anodic potentials:

The experimental results (Fig. 39) fit the semilogarithrmc theoretical prediction, allowing z, to be obtained from the slopes. The relaxation coefficient z, changes, as can be seen here, when different initial potentials are chosen to compact the structure. This is due to the physical meaning of this relaxation coefficient as the charge required to open 1 mol of compacted polymeric segments. More negative initial potentials promote a more compact entanglement, and therefore more charge will be consumed during the structural relaxation process. The relaxation coefficients range from 4372 C mol-' for an Ec of -1400 mV, to 7726 C mol-' for an initial potential of -3200 mV (Fig. 40). When the potential step starts from different cathodic potentials to the same anodic potential, Eq. (24) becomes

As predicted, the experimental results follow a semilogarithmic dependence of t,, on Ec (Fig. 41). When the experiments were repeated by potential steps to different anodic potentials, from different anodic potentials every time, parallel lines were obtained. The slopes are related to the charge consumption required during cathodic polarization to close and compact 1 mol of polymeric segments. A value of 4626 C mol-l, independent of the anodic potential, was obtained for G. Meanwhile 2, remains constant for a defined film and the relaxation coefficient 2, increases linearly with increasing cathodic potentials of departure or with an increase in the temperature at which the polymer is oxidized. That means that z, and& only occasionally are the same. This

Conducting Polymers, Electrothemistry,and Biomimicking M e s

Figure 39. Semilogarithmic representation oft,, vs. anodic potential from a mies of potential steps. Eachwies was performed between a cathodic potential and different anodic potentials in a 0.1 M LiaOsolution. (Reprinted from T.F. Otero, H.-J. Grande, and J. Rodriguez, "A new model for electrochemical oxidation of polypyrrole under conformational relaxation control." J. Eleciroanal. Chem W, 21 1, 1W, Figs. 2-5. Copyright 19%. Reprinted with permission from Elsevier Science.)

asymmetry between the charges involved in the relaxation or compaction of 1 mol of polymeric segments points to the presence of a second deep and intrinsic structural relaxation that is independent of the electrochemically stimulated conformational relaxation, but is also related to the cathodic potential of prepolarization and the oxidation temperature. This intrinsic asymmetry could be the origin of the unexplained asymmetry between oxidation and reduction branches of the voltammograms, whatever the experimental conditions. We will come back later to this concept in order to discuss the universal hysteresis observed on coulovoltagrams. In a similar way we have obtained the evolution of the oxidized area as a function of the polarization h e :

Toribio Fernhdez Wro

Rgm 40, EvoIution of tbe d c i e n t of e&mbemicrrl reJaxation at differe n t ~ p o t e n t i a l s o f dV~ a. l u a o f ~ w ~ o h a h i f i o r n t b ~ i n Fi 39, @printed h m T . F.Omo,H-J. Grande, andJ.Rodrfgaez, "A new model for deumkwW o x i d a h uf polyppIe under oonfmnaiid d a x a t h control" J. Ekc~mml.C h 398, 211, I%, Figs. 2 5 . @yri@ W t e d with panhian from Ekder !kha.)

The expressions obtained can be betterexamined when a new parameter, a, is defined:

So Eqs. (22), (231, and (27) become I,(#) = 2u t Q, exp(-d2)

These are the simplest expressions for the evolution of the relaxation current, the relaxation charge, and the oxidized area during the polarization time.

Conducting Polymers, Electrochemistry, and Biomimicking Processes I

.

.

.

I

I

,

I

l

1

I

1

-

-mmv 4

-1OOmV OmV

e

h

lOOrnV

h

2UJ mV

mrnv

-

;\

t

r

. -

E vr SCE

I

e

1

1

r

1

1

1

1

1

1

1

1

3

r

-1B75

1

1

- 1300

Ec l mV vs SCE Figure 41. Semilogarithmicqresentation of 1, vs. cathodic potential for potential steps to different anodic potentials. The cwficient of cathodic polarization was calculated from the slopes. (Reprinted from T. F. WID,H.-J. Grande, and J. M g u q "A new model for eIectrochemical oxidation of polypyrrole under conformational relaxation mml." J. Elecrroanak C h 394 2 1 1, 1% Figs. 2-5. Copyright 1995. Reprinted with permission from Elsevier Science.)

8 Difffision-Controlled Completion of Oxidation When a polymer relaxes at a constant anodic potential, the relaxation and partial opening of the polymeric structure involve a partial oxidation of the polymer. Once relaxed, the oxidation and swelling of the relaxed polymer p s on until total oxidation is reached; this is controlled by the diffusion of the counter-ions through the film from the solution. This hypothesis seem to be confirmed by the current decay after the chronoamprometric maximum is reached. We will focus now on the diffusion control. The concentration of the remaining oxidation centered on the relaxed film at any oxidation time is defined by the difference between the density of charge stored in the point at which the film attains an oxidation steady state at the working potential and large polarization times (~5~).and the charge density stored after a given polarization time [Sdt)],So the diffusion flow of ions is given by


where D is the diffusion coefficient of counter-ions in the swelling polymer film (it is a function of either the temperature or the anodic potential and both the nature and concentration of the electrolyte in the solution) and 1 is the diffusion transport length across the polymer, the average value of which can approach hl2, h being the film thickness. An infinitesimal fraction of the polymer will be considered, consisting of all the segments that are relaxed at the same time (t').As result of the flow given by Eq. (32), the increment of charge stored under diffusion control [dQd(t)]in this infinitesimal portion of the polymer at a given time t > J, will be given by

which can be simplified by the introduction of a new constant, b, expressed as

In Eq. (33), dQd is the overall diffusion charge for the segments relaxed at a time t'. Its value can be related to the infinitesimal increment in the area of the conducting regions between J and t' + dt', according to Eq.(31):

With these modifications, Eq. (33) becomes dad(t) = hQd 't exp(-")

(1

- ~xN-bft - /)] )dt'

(36)

The integration of Eq. (36) yields the diffusion charge consumed until a given time in those regions where the structure was opened:

The current flowing through the electrode due to diffusion-controlled oxidation can be easily deduced from Eq. (37):

Conducting Polymers, Electrochemistry, and Biomirnicking Processes

391

If the polymeric structure is open at the beginning of the oxidation, t' becomes equal to zero for every segment. So the equations for charge and intensity become

Equation (29) can be represented in a linear form, which allows the constant, b, and its evolution to be obtained as a function of the different electrochemical variables. From experimental data

9. Theoretical Chronoamperograms and Chronocoulograms Equations (37) and (38), along with Eqs. (29) and (30), define the electrochemical oxidation process of a conducting polymer film controlled by conformational relaxation and diffusion processes in the polymeric structure. It must be remarked that if the initial potential is more anodic than E,, then the term depending on the cathodic overpotential vanishes and the oxidation process becomes only diffusion controlled. So the most usual oxidation processes studied in conducting polymers, which are controlled by diffusion of counter-ions in the polymer, can be considered as a particular case of a more general model of oxidation under conforrnational relaxation control. The addition of relaxation and diffusion components provides a complete description of the shapes of chronocoulograms and chronoamperograms in any experimental condition:

392

Toribio Femaindez Otero

These equations describe the full oxidation of a conducting polymer Submitted to a potential step under electrochemically stimulated confermational relaxation control as a function of electrochemical and structural variables. The initial term of I(t) includes the evolution of the current consumed to relax the structure. The second term indicates an interdependence between counter-ion diffusion and conformational changes, which are responsible for the overall oxidation and swelling of the polymer under diffusion control. VIII. CHRONOAMPEROGRAMS: EXPERIMENTAL AND THEORETICAL

If our model is self-consistent, it has to include the influence of any electrochemical or chemical variable. In order to check it, we use an electrochromic polypyrrole film of 0.22pm average thickness (obtained by ex situ ultramicrogravimetric determination of the dry polymer mass and by flotation determination of the density of a peeled film), synthesized on a mirror-polished platinum electrode. The film was polarized in 0.1 M LiC104 propylene carbonate solutions for 2 min to a different cathodic potential every time. Then the potential was stepped to 300 mV. The current maximum related to the nucleation-relaxation processes can be observed only when the potential is stepped from more cathodic potentials than -900 mV. The starting oxidation potential, obtained from voltammetric experiments initiated at potentials more anodic than -900 mV in order to avoid conformational control, and performed at a low sweep rate, was E, = -550 mV vs. SCE. An electrochrornic film allows the following to occur in the oxidation process: blue circles appear, spread over the film. The number of blue oxidized cylinders formed per square centimeter of our redox yellow film was 7; z, = 4600 C mol-'was obtained by relaxation measurements, being dependent on the z, of the cathodic potential of prepolarization: Z, = 3650 + 1827(E,- E,) C mol-I, and A d = 27.500 J mol-' . The integration of the chronoamperograms performed at different anodic potentials allows the overall electrical charge stored in the film to be obtained as a function of that variable: Q(E) = 9362 + 0.0156 E (where the charge is expressed in millicoulombs, and the anodic potential in

Conducting Polymers, Electrochemistry, and Biomimickhg Proc?esses

millivolts). From the decaying part of the c h r o n o a m p the ~ constant b was obtained as a function of the andc potential: b = 0.367 + 0 . W E (8-I). iving values of the diffusion coefficient ranging between 1 x 1 ~ ' cm2 ' 's at 300 mV and 6.6 x 1r9 cm2's 1 at -100 mV vs. SCE. The charge consumed to relax the structure is estimated to be equal to the experimental charge consumed to close the structure from the potential E" to the potential E" and is obtained by cyclicvoltammetry: QJQ ratios rangmg between zero at -900mV and 0.36 at -3200 mV vs. SCE were obtained. Finally, the value of the quotientAhowas estimated as 1x loJ crn sml, which m p d s to an expansion rate of the conducting ~gions of 3 x 10-* cm B'', as observed on an electrode submitted to a potential step from -2000 to 300 mV. The inclusion of all these experimental

8

magnitudes in Eq. (43) allowed us to obtain the theoretical chronoamperograms.

1. InUuence ofthe Cathodic Potdal ofhpohhtim and Closing ofthe Structure The cathdic overpotential q, controls the compactness d the polymeric structure included in the constant a of the equation through AH. Any variation in q, promotes a change in the current required to oxidize the system at any time because a is contained by the two terms of Eq. (43). Figure 42 shows both theo~ticaland experimental chronomperograms.

Figwt 43, m e r i t d (-3 k ~ ~ ~ o a

l---)*- ( m a @ y p ~ ~ i n a 0 , 1 M L i ~ ~ s o l u ~ ~ - ~ m V ~ W e r e n t ~ z i m a s , w h i c h m M ~ ~ a ~ fim @ @ ~ E e d f h ~T. ~ P. WO* E-J. C h k , id J.m J. P ~ s C. b 109, 3688, 1W9F&g.1,3,&7, 13.Gqy~ightW.RepdntedwithpermissiOn~lhe hE&anQemical~.)

~

~

a

Conducting Polymers, Electrmhemistry, md Biomimickbg Processes

2 M u e e of Anadic Potdial on the Openimgand Oxidation of the Polymer The anodic overpotential rg controls both the rate and d e w of oxidation, which means that the opening of the compacted structure is faster the greater the anodic potential, and oxidation is not completed until a steady state is attained at every anodic potential. This overpotential is also included in the constant a, with a subsequent influence on the two terms

of the chronoampexometric equation. Both experimental and theoretical results in Fig. 43 show good agreement.

Toribio Fedndez Otero

3. Influence of T~~

on Polymer Oxidatim

Temperature is an energetic termaffecting AH' as well as the relaxation and relaxation-diffusionterms.So the same theoretical equation indicates to us that in order to avoid any overlapping or synergetic effects on compaction, two kinds of experimental measurementsmust be performed: (1) compaction by cathodic polarization at a different temperature every time,keeping q, and the eIectrolyte concentration constant, followed by oxidation-relaxation always at the same temperature and the same potential step; and (2) compaction keeping either q, T,or the electrolyte concentration constant, followed by oxidation-relaxation at a different temperature every time, using the same potentid step and a constant concentration of the electrolyte. Experimental and theoretical results related to this second methodology are shown in Fig. 44. A good fit is observed if we take into account that the compacted film was kept wet

Conducting Polymers, Electrochemistry, and Biomimicking Processes 397

over the solution in an N2atmosphere during the time required to change the temperature of the bath. 4. Influence of Electrolyte Concentration Dissociation equilibriums in both electrolyte and polymer gels and the ionic concentration partition (Donnand potential) between solutions and polymer gels allowlg9the relaxation-oxidation current to be obtained as a function of the perchlorate concentration:

4 (t)=

2ziVd2 1/k$4

xexp

Qr [ c ~ ~ , exp ~ JI-2M/RTJr

[--"'"" 1I@

[ C s M ~ exp [ - ~ w / R T ] $

Experimental and theoretical chronoamperograms are shown in Fig. 45.

5. Separation of the Relaxation and Diffusion Components The representation of the overall theoretical chronoamperogram and those of the two mathematical components from Eq. (43), the relaxation-nucleation and the diffusion-relaxation ones, can be observed in Fig. 46. The oxidation under conformational relaxation control describes the initial slope of the curve that is responsible for the time at which the chronoamperometric maximum is formed. Nevertheless, in the absence of any external mechanical stress, although it is the controlling kinetic step, it consumes only a small fraction of the oxidation charge. Meanwhile the diffusion controlling the completion of oxidation of the system, which only acts once the system is relaxed, consumes most of the oxidation charge and closely approaches both the shape and the magnitude of the chronoamperograrn. So the time of the chronoamperometric maximum is better described by the relaxation component, Eqs. (24), (25) and (26) being considered a test for the presence of conformational relaxation-controlling processes; Eq. (43) is the simplest expression for obtaining diffusion coefficients as a function of the different variables.

Toribio Fernsndez Otero 4

-48

-0110f theOVdl~xidationCU#h btW~-e!Ebt i m ~ e , ~ ~ l e f o r t h ~ ~ a n d t f r e p s s i tl i o hn o fe ~ o ~ c ~um,anda~oncmfhat~ontrohtheaveralI&apoffhe~ (Rtphkd~III T.F,O ~ DHrJ, , Grande, and J. -R J. Phy. C h 101, 1,3,6,?, 1 3 . C u p 1 5 1 9 7 . Repin@ with pmbi011 h m tbe 3688 1W7, AmericanChernicalm.)

M. rnLYMER*OLVENT INTERACTIONS FROM THE JILECTIROCHEMTCALLY STIMULATED CONFORMATIONAL RELAXATION MODEL Most of the previous electmhemical devices and theoretical developments related to the polymer oxidation and reduction have been studied in the same solvent: water or propylene carbonate. The solvent plays an

important role in the swelling and shrinking processes occurring during electrochemical reactions.lwAn important part of the overall change of volume (and hence of the conformational rearrangements) has to be attributed to the interchange of solvent between the film and the elecbdyte during the redox processes. Solvent interchanges have two main components: the interchange of solvated counter-ions, and reverse variations in

Conducting Polymers, Elechrhemistry, and Biomimicking m s e s

the polymer-solvent coulombic interactions during the oxidation and reduction of every chain. The contribution of the last componentto a faster or slower opening of the structure allows faster or slower oxidation processes. The influence of the solvent on the oxidation of film under conformational relaxation control is illustrated in Fig. 47, which shows chronoamperograms obtained by steps from -XMH to 300 mV vs. SCE at room temperature (25°C) over 50 s in 0.1 M tiCIO4 solutions of different solvents: acetonitrile, acetone, propylene carbonate, (PC), dimethyl sulfoxide @MSO), and sulfolane. Films were reduced over 1% s in the cmsponding background solution, Despite the large differences observed in the relative h p e of the cwves obtained in different solvents, shifts in the times for the current maxima (t-) are not important. 'Ihis fact points to a low influence of the solvent on the rate at which confor-

Figure47. Chmnoampmetric mpnm topatentid steps carriedout using a polypymIe electrode from -MWWl to 300mV vs. 9CE for 50 s, in 0.1 M Ua04solutions of different ~Ivents.

(Reprintedfrom H-J. Graade, T.F. M,and I. Cantem, 'anMend relaxation in conducting polymm: Effect of the polymer-wlventintembns." J. Non-Cryst. Sol BB7,619, 198, Fw.1-3, Copyright 1998 RqdUOBd with kind pesnission of Elsevier Science-NL, Sara Burgeshmtraat 25, I055 KV

hsterdam, The N&*.)

rnational changes in the r e d u d matsix occur. However, a clear dependence of the diffusional current decay on the solvent used is observed at long polarization times. This influence is clearly shown by Fig. 48, where apparent diffusion coefficients ( D d exmcted from the experimental curves in Fig. 47 are shown against the background solution of ionic conductivities (K). A slraight line was obtained. Theseresults indicatethat once the polymeric structure has been o p e d as a result of the insertion ofcounter-ionsand solvent molecules, the chemical ambient inside resembles that of the surrounding solution, thus determining electrochemical

responses. The eletrmhemical responses were quantified through both compaction and relaxation coefficients that represent the energy required to compact or relax I mol of polymeric segments. A series of experiments were performed in each solvent by potential steps from different cathodic potentials (-1600, -1800, -2000, -2m,and -2A00 mV vs. SCE) with the same anodic potential, changing this potential for every serie (-250,

F i p 48. Evolution of the qpmt diffusion c-ent @&as a fmaion of oflation hnh a d d v i t y (~).IReprinted from E-J. Grande, T.F. h , d L Csmm, ''CCooforms#lwatrelaxadwin

wdwting pnlynws:E t of tbep o l ~ 4 0 e n t 6.~ ~ " NmWst. SOL BSB7, 619, 19941 F@- 1-3b Repmledwithkind*ofm-mm Eluqpbmm 25, lB5 KV Amstdam, The Ne&aW.)


Acetoni trile m \

401

I

4 (C mat')

Figure 49. Evolution of the coefficient of decmhemical relaxation as a function of the coefficient of cathodic polarization (q). (Reprinted from H.-J. Grande,T. F. Otero, and I. Cantero,"Confomational relaxation in conducting polymers: Effect of the polymer-solvent

(z,)

intrxactions."J. Rron-Cryst. Sol. 235277,619, 1% Figs. f -3, Copyright 1998. Reproduced with kind permission of Elsevia Scienoeb%, Sara Bu~+gerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)

-100,50, 200, and 350 mV vs. SCE). Semilogarithmicplots, such as those shown in the figures, allowd us to obtain the t, and z, in every solvent. Values of &ranging between 3094 C mol-' in sulfolane and5616 C mol-' in acetonitile solutions, and &coefficientsranging between 2684 ~rnol-' in acetonitrile and 8974 C mol" in sulfolane were obtained. The and z, energetic coefficients from different solvents shifted in opposite directions, as can be observed by plotting z, vs. z, (see Fig. 49). In other words, in those solvents where the cathodic closure of the polymeric entanglement was more difficult, further opening and swelling by anodic oxidation was easier. These resuIts can k explained in the context of polymer-solvent interactions. Greater polymer-solvent interactions must require more cathodic overpotentials to attain the same degree of polymeric compaction. Using the same potential range of closure and compaction for each solvent, the d e w of compaction is less in those media having a greater polyrner-solvent interaction. Thus lower compaction means less energy

402 Toribio Fernhndez Otero

consumed per mole of polymeric segments and lower t. But at the same time, the increase in volume associated with further doping will be larger. In this way the opening of the polymeric structure is favored, thus requiring lower anodic overpotentials to attain stronger relaxation and swelling and consuming larger charges (higher 2,) than in a solvent having a low polymer-solvent interaction. Following this reasoning, the lower polymer-solvent interaction corresponds to acetonitrile, whereas the higher interactions occur in the presence of sulfolane. Moreover, z, should reach its maximum value in that solvent where no interactions with the polymer are present, that is, when z, = 0. In these conditions, conformational rearrangements are hindered, so oxidation cannot proceed. According to Fig. 49, the maximum value of I, obtained by extrapolation (henceforth it will be symbolized by e)is 6458 C mol-'. The ESCR model allows us to derive from both Eq. (5 1) and the above experimental results an expression for the interchain free volume (ud) left inside the polymeric structure after polarization at a given cathodic overpotential qc:

where 07 represents the interchain free volume when z,reaches its highest value and all the other terms have their usual meaning. Equation (45) can be compared to that obtained from theories of swelling in amorphous cross-linked polymers110: u d = 0 7 exp (-XI

Here x is the polymer-solvent interaction parameter defined by Flory for polymeric swelling; its value becomes more negative as the interaction between the solvent and the polymer increases. By comparing Eqs. (45) and (46), we arrive at

This equation offers a simple relationship between magnitudes related to electrochemistry ( q and through t~, and the relaxation time, all the other electrochemical and chemical magnitudes) and those specifically from polymer science. According to this result, coefficient zc will be lower and coefficient z, higher, as stronger interactions are present, which is confirmed by experimental results. On the other hand, high values of z, are

Conducting Polymers, Electrwbemistry,and Biomimicking Processes

403

Figure 50. Semilogarithmic plot of cathodic (E,) and anodic (E) potentials against values of l/Q [&r~d?] extracted from Figs. 52 and 53. Following Eq. (a), values of the coefficient d e1ectrochemical relaxation (2,) and the cmficient of cathodic polarization (4) can be deduced from the slopes, (Reprinted from T. F. Otero and H.-J. Grade, '%eversible 2D to 3D elabode transition in polypymle films,"ColloidSu$ A. 134 85, 1898, Figs. 4-9. Copyright 1998. Reproduced with kind permission of Elsevier ScienceNL, Sara Burgerhartstraat 25, 165 Amsterdam, The Netherlands.)

connected to great variations in volume during doping and undoping. This fact supports the experimental observation that artificial muscles only work in solvents having strong interactions with the polymer, as water does. The polymer-solvent interaction parameter, which is a key constant defining the physical chemistry of every polymer in a solvent, can be obtaind from electrochemical experiments. Definition and inclusion of this interaction was a milestone in the development of polymer science at the beginning of the 1950s. We hope that Eq.47 will have similarinfluence in the development of all the cross-interactions of electrochemistry and polymer science by the use ofthe ESCR model. A second point is that Eq. 47 provides us with an efficient tool to obtain this constant in electroactive

Toribio FernsindezOhm

gels, that is, in a system having a high polymeric concentration and a relatively low solvent content. In polymer science only recent methods such as inverse chromatography have all0wed this constant to be obtained outside of traditional dilute solutions containing a 1% w/w of polymer.

After the potential step, polymeric oxidation is followed by an oxidation charge to open, swell, and oxidize the compact film. At the start, the charge consumed to relax the compacted polymeric structure is the only COW nent of the oxidation charge. Thus any quantitative information about the

figure 5 1. Arrhenius plot of In [ 1/Q[ d t Q ( t ~ d f ifrom ) data companding to Fig. 54. The conformational energy ~ u m e per d mole of polymeric segments in the absence of any e x t a d electric &Id (M1can be obtained h m the slope. (Rqmted from T. F. O t m and H.-J. Grande, "Reversible 2D to 3D el& mition in polypyrroIe films."Colloid SurJT A. 134, 85, 1998, Figs. 4-9. Copyright 1998. Reproduced with kind permission of Elsevier Sciermce-NL,Sara Burgerhartstmat 25, 1055 Amsterdam, The Netherlands.)

Conducting Polymers, El-&try,

and Biomimicking Pr-s

Figure 52 Normalized expimental () and hemetical(--) c h r o n ~ ~ ~ d o g r a t m related to potentid steps d e d out on a polypple electrode in a 0.1 M LiCQ-p pylene &mate solution from different cathodic patentiah to 300 mV vs. SCE. (Reprinted from T.F. Oteso and H.-J. Grande, 'RewRevemible 2D to 31) electrodetransition in polypyrrole films." Colbid Swf A 13q 85, 1% Figs. 49. Copy@ 1998. Reproduced with kind permission of Elsevier ScienceNL, Sara Burgmhartstraat 25, 1055 Amsterdam, 'Izle Netherlands.)

kinetics of confomtiond relaxation must be obtained from Eqs. (91, (30), and (28). I3y combining these equations, we arrived at

This equation can be checked by experimental results performed by the following potential steps: at the same anodic potential and constant temperature but different cathodic potentials; with the same cathodic potential, at constant temperature, to different anodic potentials; and

P i p 53. Comparison of normalized experimental 1-( and theoretical ( - - - - ) cImnwouIodc to potential steps canied out on a plypyrrole e k m k , in a 0.1 M UCIO,- pmpylenecacbonate solution, from -2000 mV to different anodic limits. (Reprinted from T.F.O t m and H.-J. Grande, ''Xeversible 2D to 3D eIecorode transition in polypyrrole fh," CoHoidSurf: A. EM, 85, 1998, F I . 44. Copyright 1998. Reproduced with kind permission of Ekevier S c i m N L , Sam Burgdartstmat 25, 1055 Amsterdam,

The Netherlands.)

keeping the same potential step, at different tern~eratures.'~' As predictsd from this equation, two linear relationships wexe obtained fxom experiments performed with different cathdic potentials [Fig. 50(a) J or to different anodic potentials pig. 50(b)]. Both compaction and relaxation coefficients are deduced from the slopes obtaining 2530 c mol" and 6040 C mol-', respectively. From experimental results obtain4 at different temperatures, an Arrhenius repsentation of the above equation gives (Fig. 5 I) a & of 21.3 w mol-'. All these results are quite close to those obtained from other experiments.


407

Figure 54. Normalizedexpwimentd )-( and theoretical (- - - - ) chron~~~ulornetFic mpws to the application of potential steps from -2000 mV to 300 mV at different ternperm in a 0.1M UCl0,-propylene carbonate solution. (Reprinted from T.F.Otero and H.-J. Grande, "Reversible 2D to 3D electrde transition in pol ypyrrole films." Colloid SurJ A. W, 85, 1998, FQS.4-9. Copyright 1998. Remuced with kind permission of Elsevier Science-NL, Sara Burgerhartstraat25, 1055 Amsterdam, The Netherlands.)

The completion of the swelling-oxidation p c e s s by diffusion control plus the initial relaxation-oxidation descriks through Eq. (43) the overall oxidation. This equation allows the theoretical chronocoulograms to be obtained as a function of the experimental variables. Predicted theoretical results are presented together with experimental results in Figs. 52, 53, and 54 for different initial (compaction) potentials, different oxidation potentials, and different temperatures. The relative influence of the relaxation-oxidation and swelling-diffusion charges on the overall charge, in the absence of any external mechanical stress, at every oxidation time is shown in Fig. 55.

Figure 55. Separation of the o v d l oxidation curve into its two compments: a relaxation part [aooording to Eq. responsible for the initial shape of the curve, and a diffusion part [3953, which con~rolsthe final shape of the chronoOuIo&ram.(Reprinted from T.F. O t m and H.4. W e , "Reversible ZD to 3D electrode bansition in polypymle W."Colloid Sutf: A. 134, 85, 1998, Figs. 4-9. Copyright 1998. RepPodwed with kind pemkion of Elsevier ScienceNL, Sara Burgerhartstmat 25, 1m5 Amsterdam, The

m.

Netherlands.)

XI. VOLTAMMETRY UNDER CONFORMATIONAL RIELAXATION C O L The same model allows us to describe anodic voltammograms obtained under conformational relaxation control. Voltammograms obtained with different cathodic potentials retain& for 2 min before the potential sweep was started are shown in Fig. 34(a). Higher potentials of cathodic prepolaization assume an increasing compaction ofthe polymeric s t m ture. Most of the energy is needed to initiate the oxidation nucleation during the anodic potential sweep. At constant temperature, the only energetic source is the ~ v e r ~ o t e n t i a l ' ~ ~increasing - ~ ~ ' : nucleation overpc-

ConductingPolymers,Electrochemistry,and BiomimickingProcesses

409

tentials were observed when the polymer was prepolarized at higher cathodic potentials. We define a nucleation overpotential q,,, = EN Eo (Fig. 36) required to make the Nooxidation nuclei appear. The nucleation overpotential is related to the degree of closure (compaction) of the polymeric entanglement (8), expressed as the fraction of interchain free volume destroyed after polarization at a given potential Ec, compared with the amount of free volume present at E,. When t9 = 0, the structure is no longer under conformational relaxation control (EN= E,) and q~ =0.The oxidation starts at the "equilibrium" oxidation potential because no extra energy is needed to oxidize the open (relaxed) polymer. The oxidation takes place under counter-ion diffusion control. On the other hand, when 6 = 1, all the free volume existing at E, is destroyed: the film is fully compacted and a maximum of energy is required to initiate the nucleation. According to the above reasoning, a maximum nucleation overpotential will appear on the correlated voltammogram (&). Any other cathodic polarization will give a lower overpotential:

-

This equation makes it possible to obtain the dependence between the degree of closure and the cathodic potential at which the polymer is reduced. The probability (P) of a conformational change that will allow the reduction and compaction of a segment can be expressed as the inverse of the relaxation time. If all the other terms of Eq. (9) are included in P, then

When q , = 0, the polymeric structure is considered to be open enough (6 = 0) that any subsequent oxidation will not occur under conformational relaxation control, hence P = 1. Every polymeric chain at the polymerlsolution interface acts as a nucleus; a planar oxidation front is formed that advances from the solution interface toward the metal/polymer interface at the diffusion rate. By contrast, at large values of 7, the compactness of the structure is so great (fl = I) that the probability of spontaneous conformational

410


changes and polymeric oxidation becomes zero (P = 0). This fact has important technological applications, as will be seen later. Thus P is a structural parameter ranging between 0 and 1 that acts at the initial moments of the oxidation process of every segment: the higher the degree of closure (v), the lower the probability (P)of any spontaneous conformational changes and the greater the anodic overpotential required to create arelaxation nucleus. Under these conditions both magnitudes are related by

and coming back to the nucleation potential

This nucleation potential will approach its maximum value asymptotically as the potential of prepolarization is shifted to more cathodic values. In order to check the experimental validity of this prediction, this equation can be rearranged:

This describes a semilogarithmic dependence between the overpotential for the opening of the polymeric structure (qN) and the cathodic overpotential (qJ at which it was closed. The experimental results (Fig. 56) fit Eq. (53). This equation also contains an asymptotic approach to the opening potential (qN)when the cathodic potential of prepolarization increases.

1. Growth of the Conducting Zones After a critically sized nucleus is formed, it starts to grow. Under the same hypothesis stated above for chronoamperometric growth, and taking into account that the radial growth of each cylinder occurs at the same time that the overpotential ( q )rises owing to the potential sweep (u):

ConductingPolymers, Electrochemistry, and Biomimicking Pmsses

-

Figure 56. Hot of (a) 1 I N / l $ vr. we and (b) e~ m. rf. for polypyt~olefilms submitted to pkntial sweeps, from which the nucleation pameters (band tf;;) can be obtained. meprintedfrom T.F. Otero,H.-J. Grande, and J. Rodriguez, Phys. Chem 101,8525, 1997, Figs 3-1 1, 13. Copyright 197. Reproduced with permission from the American Chemical Sdety.)

By integration of this equation we obtain the evolution of the radius of a cylinder as a function of the overpotential

where AHNrepresents the value of AH at the beginning of the oxidation process (when 4 = gN). Assuming the formation of Nonuclei at the first stages of oxidation, the effective relaxed area (taking into account the overlap between neighboring expanding conductive regions) at every overpotential tl can be estimated by means of the Avrarni equation.'77We arrive at

Toribio F e d d e z Otero

[ - ( :=

2zlV,A2

RT Q, -exp(-W/RT) [exp (-AH/RT) - e x p (-AHN/RT)]

U A ~ zr

Equations (57) and (58) describe the electrochemical oxidation of conducting polymers during the anodic potential sweep: voltammograms (I, vs. q ) or coulovoltagrams (Q, vs. q ) under conformational relaxation control of the polymeric entanglement initiated by nucleation in the reduced film. They include electrochemical variables and structural and geometric magnitudes related to the polymer. These equations contain useful information about how the relaxation control affects the voltammetric peaks when different electrochemical, chemical, structural, and geometric variables are changed. If we assume that the peak overpotential (q,) is much greater than the nucleation overpotential, the maximum of Eq. (58) can be written as

Conducting Polymers, Electrochemistry, and B i o d c k h g Proceses

Thus, at constant temperature and at a constant sweep rate, the influence of the cathodic overpotential (q,) on the peak overpotential ()I& of the voltammogram obtained under conformational relaxation

control of the polymeric structwe is described by

So a linear dependence between the potential of the voltammetric peak and the increasing cathodic initial potential for the volt ammo^ (Fig. 57) points to an oxidation pm.ess occurring under conformational relaxation control of the electrode structure. If we work at different temperatures, keeping u and q, constant, the model predicts

Figure 57. Evolution of the peak potential (Ed as a function of the cathodic potential of p p W o n (E,). @qrinted 6.om T.F. O m ,H.-J. Grande, and J. R d g w z , J. Pkys. Ckm. 101,8525, 1997, Figs. 3-1 1,13. Copyright 1W. R q d u c e d with permission from Me American Chemical Society.)

Toribio F e d n d a Otero

which is a semilogarithmic variation of q$T vs. T is expected when the oxidation, occuning under confornational relaxation control of the e I e ~ t d e structure, was carried out at increasing temperatures. This variation was confumed by experimental results (Fig. 58). Voltammetry performed at different sweep rates, keeping both the cathodic overpotential and the temperatureconstant, is predicted to have

a semilogarithmic dependence between the potential of the peak and the sweep rate, as was observed by the experimental pioneering work of Odin and ~echtscheinl~~ and confirmed by our experimental results (Fig. 59). Reversing the previous reasoning, the presence of a conformational relaxation control in voltammetric responses can be detected in a single

Figm 58.~ hof tqp&. h T.~Iinearde@axe WB o b h d , epwially f o ~ h i g h t e m@ . pimhim T . F.O m ,E-J. GranQ, ami J. RoMgwq J. Pbys. chea 101, 1997, 3-11, 13. Copy@ 1B7. Rqmbd with pmb8ion from & American amicd May.)

*.

Conducting Polymers, Hectrachdtry,and Biomimicking Processes

FQm 59. S d l o @ t h k plot ofthe @I ptenlxd (E& vs. the scan rate ID). (Rfrum T.F.Oterq HA.Grande, and J. Rodriguez, J. Phys. Ckem IM, 8525, 1997, Figs. 3-11, 13. Copyright 197. R e p b c e d with permission from the American Chemical

Society.)

step by checking if the evolution of the anodic peak potentials as afunction of the different variables fits Eqs. (60),(61), or (62).

2. Diffusion-Controlled Completion of Oxidation The charge consumed by oxidation swelling under diffusion control, once the structure is relaxed, depends on the anodic potentials applisd at each moment. The process can be quantified by Fick's law:

where F[q)is the molar flow of counter-ion into the oxidized polymer; D and I were previouslydefined; B&) is the real charge density within the oxidized regions when the f h attains a steady state of the oxidation

Toribio F e M e z Otem

related to the applied potential (q);and 6Aq) is the charge density stored in the conducting regions at a given potential, Taking into account the variation in the oxidized area as a function of the overpotential, and the counter-ion flows, the charge consumed during the potential sweep in those regions where the structure was previously opened under confomtional relaxation cunlrol, is given by

E ~ ~ ~ ~ ~ c a r r i e d o u t o a a p d y f @ m b

~inw~.lMuf4~fene~9olutrOnh-~~30QmV,~3a

-

~vr1snd~~ttemperahnes~behveen-l~andmc~,~~ ~ w w h y 8 ~ ~ a t ~ f m i l ~ f o r 2 m i e , a ~ ~ a n y ~ i n o f d m m b f t h e & I l & ~ ~ a t m ~ ~ ~ a l ~ *

~~

w h T . E m , K - J , Grande,&J, m J , Pb,C k I@, 85% IW,figs. '3- 11,13. C@& 1W. Rqmdmd with pmWn firom the A m h n

W-)

Conducting Polymers, Etectrochemisby,and Biomimickhg Processes

417

where c is a potential-dependent diffusion ccefficient: c = D/q2o and q' is the effective potential, equal to or greater than q , [taking into account whether the segment is the origin of the nucleus or is placed at a distance (r) from this center]. The current flowing at every potential is

So we arrive at

3. Anodic v 0 1 - w The current consumed to oxidize the polymer will be

I(vl=

! A d + ldivl

Figure 62. M c a l simulation of a series of Voltammogram i n i t i d h m different cathodic potentials (ranging between -1000 and -3000 mV vs. XE]. (Reprinted from T.F. Otero, H.-J. Grande, and 1. R d i g w z , J. Phys. Chem 101,8525, 1987, Pw 3-1 I, 13. Copyright 1%'. R e p d u d with permissin from ?heAmerican Chemical Soieq.)

Conducting Polymers, Electrochemistry, md Biomimicking I P r o c : ~

419

Equations (58) and (66) give us the expression required to simulate the voltammograms and what they change as a function of the different chemical or el&mchemical variables.

From Eqs. (57) and (64) the variation in the overall charge as a function of the overpotential is obtained:

which allows a theoretical simulation.


XU EXPERIMENTAL AND THEORETICAL

VOLTAMMOGRAMS Working under conditions similar to those described for chronoamperometric measurements, using the same films, experimental voltammograms were obtained Figures Wa),60,and 61 were obtained for different cathodic initial potentials, different temperatures, and different sweep rates. These voltammograms were simulated using the above final quation with the same values of the constants used for chronoampmetric simulation. Figures 62,63, and 64 were obtained, as well as the correlation between theoretical and experimentaI values of the current at the voltammetric maxima in Fig. 65.Once again, despite important simplifications,

Figure 64. Voltammetric behavior simulated for increasing scan rates (10 to MmV #-I), when the cathodic potentialof departurewas -2500 mV,the anodic limit 300 mV,a dthe temperature 25°C. (Reprinted from T.F.Otero, H.-J. Grande, and 1. Roddguez, J. Phys. Ckem. 101,8525,1997, Rgs. 3-1 1, 13. Copyright 1997, Reprodud with permission from the American Chemical Wety.)

Conducting Polymem, Electrochemistry, and Biomimicking Pmmses

Figm 6.Cmehtim bet h e o d d and ex-ntal dues far t b currentmaxima ofthe vohmkehic m a .(Rqtmbdh m T.F. Qtero, R-J, Gradde, and J. RaWgwa, J. P h y ~Chem 101,8525,1997,Figs. 3-11 13. w& 1997. t kpmked withpimhion fPom the Anaerican C h i c f w.1

the model predicts the influence of the different variables in good a ment with experimental results.

p

1. FMaxation and DifMon Compents As in chronoamperograms, the fraction of the overall oxidation charge involved in relaxation prwesm is quite small in the absence of any

external stress. The share of the overall current at every potential between electrochemical processes occurring under relaxation control and those driven by swelling-diffusion control can be observed in Fig. 66 I(r) has

its main effect on the definition of the potential of the maximum and]& on its current.

XIIL EXP-NTAL AND TmOMTICAL, COULOVOLTAGRAMS From Eq. (68), following a procedure similar to that demibed for chronmmpemgrams and voltammograms, theoretical coulovoltagmms were obtained as a function of the variables studied he resultdmcan be observed in Fig. 67.S o w new effects can be deduced from these experimental curves, which will allow us to provide a complete description of the electmhemistry of conducting polymers.

Figure 66, Sepuabrn of the overall oxidation curve into its relaxation (I& anddiffusion (I,) components. (Reprinted from T.F.Otero, H.-J, Grande, and J. Rodn'guez,J. Phys. Chem. 101, 8525, 1199, @p3-1 1, 13. Copyright 19m, R e p d u d with permission from the American Chemical

e..)

Conducting Polymers, Electrochemistry, and Biomimickhg Processa

Figure 67. Experimental (land theoretical (----)normalized chargepotential responses to pokntial sweep mid out on a plypyrrole electrodein a 0.1 M LiClO, propylenecarbonate solution from different cathodic ptentials, indicated on the figure, to 300 mV vs. SCEat 30 mV I" and room temperature. (From H.-J. Grande and T.F.Otero, unpublished results.)

XIV. CONDUCTING POLYMERS AS SOFT AND NONSTOICHIOMETRIC MATERZALS. ELECTROCHEMICAL EVIDENCE Electrochemically synthesized and then oxidized and reduced conducting polymers, such as polypyrrole, polythiophene, and polyaniline. which are amorphous, are nonstoichiometric compounds:

They present a large and reverse redox potential range, in contrast to the well-defined narrow peaks of the inorganic or organic redox couples During oxidation they undergo a large and reverse change in

composition During the redox change -they undergo a large, continuous, and reverse change in electrical conductivity

Toribio F e h d e z Otem -

they undergo a large, continuous, and reverse change in light

absorption

the maxima of the absorptionbands present alarge, continuous, and reverse hipsochromic-bathochromic shift of the UV visible bands (1.2 eV). When the oxidation of an electrochrornic film is produced under conformational relaxation control, and the current is stopped before the coalescence between blue nuclei is produced, the electrodic potential remains constant but the expansion of the nucleus goes on, at the expense of a decrease in the degree of oxidation inside the nucleus until a uniform composition is achieved, with uniform darkening of the film. Cross-linking films always give large and reverse voltammetric maxima without any differentiation of the radical cation [polarons or dications (bipolarons)] energetic levels, owing to the large distribution of the conjugation lengths; this latter promotes the -

simultaneous population of the polaronic and bipolaronic levels in chains with different lengths, at the same potential. XV. CONDUCTING POLYMERS AS THREE-DIMENSIONAL ELECTRODES AT THE MOLECULAR LEVEL At several points in this chapter, brief comments were made about the fascinating new properties of the conducting polymers when considered

as dry and hard materials. Later we focused on their electrochemical properties, their applications, and the new perspectives they are opening up. We also showed that any approach to the theoretical treatment ofthese materials must consider both the electrode structure and polymer-solvent interactions. Given this view, most of the improvements attempted in the technological development of new electrochemical devices by electro-

chemists are contaminated by theoretical considerations developed by physicists for LED, FET, electromagnetic shielding, etc., applications, which require solid, rigid, and, in the case ofLEDs, crystalline oligomers. These requirements are just the opposite of those included in the ESCR model, which takes into account counter-ions and solvent moving into and

out the polymer, with strong variations in the molecular interactions during oxidation and reduction of the polymer. Either the kinetics of the electrochemical reactions and the electrochemical properties, or


425

their subsequent applications, are linked to the structural changes, and these are associated with the interactions between the polymer and the solvent. Such materials are amorphous. Only short oligomers retain a high degree of crystallinity. As a consequence, they are much more friendly for either theoretical treatments from different physical points of view or structural studies using experimental techniques. Since they are oligomers, they can be considered in the oxidized state as stoichiometric compounds. They have an electrochemical behavior showing two well-defined redox maxima related to polaronic and bipolaronic states and well-defined UV visible maxima, retaining a constant wavelength for the different maxima during in situ spectroelectrochernical oxidation. A theoretical treatment of the electrochemical responses obtained using amorphous conducting polymers as electrodes requires the inclusion of the electrode structure. Taking into account the polymeric nature of the electrode, this is equivalent to an integration of electrochemistry and polymer science. Macroscopic swelling and shrinlung processes were considered to be caused by conforrnationalchanges stimulated by electrochemical oxidation or reduction of the individual chains. In order to simplify the treatment, experimental conditions in which the electrochemical rate was under conforrnational relaxation control were chosen. This treatment was completed by the addition of the counter-ion diffusion equations describing the completion of oxidation-diffusion and swelling, which includes most of the overall oxidation charge. The structure is already open and every molecular chain is a one-dimensional electrode surrounded by solvent and counter-ions. Oxidation of the film, the concomitant swelling of the film by conformational changes, electron loss, and interchange of counter-ions and solvent constitute a three-dimensional electrode at the molecular level. If the conducting polymer has islands where degradation and a high degree of cross linking occur during polymerization, the three-dimensional molecular structure of the electrode is interrupted by those islands. XVI. SOFT, WET, AND COMPLEX MATERIALS MIMICKING BIOLOGICAL PROCESSES At this point we have to consider that we are working with a complex material containing a mixed polymer (as was proved by the influence of the conditions of synthesis on electrochemical properties), a solvent, and

426

Toribio Fernaindez Otero

ions (mainly counter-ions, but since the film behaves like a membrane, we have ion pairs as well). This is the simplest expression of the different materials included in the family of any conducting polymer-based materials. It is also the basic expression of many of the materials that make up functioning organs in biological systems. We are working with anew class of wet and soft materials. The most promising, interesting, and fascinating applications of polymers occur, not in the dry state that has until now been the focus of physicists and most electrochemists, but in their wet and soft state. The three-dimensional molecular structure of the oxidized conducting polymers used as electrodes constitutes a soft material with a high content of polymer, solvent, and ions. This composition is closer to the materials forming the organs of animals than any other material developed by human technology. Soft and wet conducting polymers interact with electric pulses as biological materials do, producing electrochemical reactions involving changes in the mechanical energy stored by the polymeric conformations, changes in the electrical energy stored at the molecular level, interchange of ions with the surrounding medium, changes in the porous structure of the material, changes in both ionic and electronic conductivity, and changes in the absorption of light. These properties and their changes under electrochemical control mimic muscle, electric organs, nervous impulses, biological membranes, shn, and light filters. Most of these properties have evolved through different generations of basic devices at laboratory scale, with some industrial applications of batteries or smart mirrors. However, little effort has been made to develop the most fascinating of these possibilities: nervous system interfaces and artificial nerves. The main problem seems to be the synthesis of conducting polymers having specific discrimination for K*,Na', ca2+, and the different neurotransmitters. In a reverse sense, a thorough inclusion of polymer science in the electrochemical models could give us a better understanding (and quantification possibilities) of the way the nervous system, electric organs, or enzymatic processes work. XVII. SOFT MATERIALS AND ELECTROCHEMICAL APPLICATIONS

Our poor understanding of how the conditions of electropolymerization affect the properties and stability of the final product (a thick film suitable for technological applications) hinders any possibility for determining the


427

electrochemical conditions of synthesis needed to produce tailored materials for specific applications. This requires well-checked interfacial reaction models that describe initiation, polymerization, and nucleation processes together with parallel-degradation, cross-linking, and chemical polymerization processes that affect the properties of the final thick film. When electrogenerated films, most of them obtained without any optimization of the conditions of synthesis, were used to produce electrochemical devices, they were treated as dry materials. The results are long response times or low electric power. These results are expected when analyzed from the point of view of the ESCR model. Decreasing solvent content, or decreasing polymer-solvent interactions require longer times for conformational changes in a solid polymer and produce lower electrochemical rates. A redefinition of the limits of the electrochemical technologies of conducting polymers used as both dry or wet materials is required. In general, those properties of industrial interest that are related to the electrochemical rates change several orders of magnitude when the conditions of synthesis are improved and when a solvent suitable for the specific application is used to produce the polymeric gel. We found this to be the case in our laboratory between the first and second generation of artificial muscles, with electrochromic films, or with specific energies. Other electrochemical applications of conducting polymers, such as electrocatalytic applications, have not been included in this chapter because of the greater complexity of the conforrnational changes introduced by new compounds. In some cases of electrocatalysis or enzymatic processes, researchers prefer to use "overoxidized and partially degraded polymers to avoid cross-linking conformational changes inside the film. Other electrochemical applications require one or more and different conformational movements: examples are photostimulated changes in photoelectrochemical transformations or conformational enzymatic changes when enzymes are trapped in electroactive films of conducting polymers. XVIII. TECHNOLOGICAL APPLICATIONS OF THE ESCR MODEL The action of a muscle is a consequence of electrochemically stimulated conforrnational relaxation processes that occur along every electroactive chain inside a polymeric film. A free-volume model dependent on the

428


degree of oxidation is being developed by our group in order to quantify the influence of any physical or chemical variable on the work of a muscle. This is an open model. The present state of development of the model also allows practical applications to electronic devices based on dry conducting polymers by increasing their stability or by production of new and stable devices. The high reactivity of conducting polymers in air is well known. This makes long-term storage difficult for any device constructed on the basis of electrochemical applications. The degradation rate being under diffusion control, the deterioration of the material is eliminated by avoiding oxygen diffusion inside the sample. This aim can be attained by compaction under electrochemically stimulated conformational relaxation control. Using this method, polypyrrole compacted and dried films have retained a bulk conductivity of 10" S cm-' for years after atmospheric storage.198-199 When they were electrochemically oxidized, the storage capacity was the same as that obtained before compaction.19S200 When these reduced and compacted films were used for ionic implantation under low-energy ionic bombardment, the polymeric structures recovered at the polymer surface the compacted state they had before doping.19' Implanted ions penetrate inside the polymer. The polymeric structure has a memory property and compacts again after penetration of the ions, avoiding attack by oxygen when the system is extracted from storage and exposed to air. In this way p-njunctions and Schottky barriers stable in the atmosphere were obtained using these compacted films. Any device (battery, supercapacitor, smart mirror, or muscle) stored in a compacted state requires an initial activation-relaxation before use. ACKNOWLEDGMENTS

The author wishes to thank Diputaci6n Foral de Guipuzcoa, Gobierno Vasco, and Ministeriio de Educaci6n y Cultura for their financial support. I am grateful to Dr. J. Rodriguez of CIDETEC for his close collaboration for many years. I would also like to thank all my past and present colleagues for their help in various levels of work over the past 15 years, in particular Dr. H. Grande, who performed the mathematical treatment of the ESCR model. I also recognize the fruitful collaboration with Prof. E. Brillas and Dr. J. Carrasco from the University of Barcelona in developing faradaic electrodissolution of conducting polymers. Some aspects


429

of the spectroelectrochemistry were developed in collaboration with Dr. T. Lopez-Navarrete from the University of Malaga. We have had fruitful

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A

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Microwave (Photo)electrochernistry H. Tributsch Department of Solare Energetik, Hahn-Meitner Institute, Berlin, Gennany

I. INTRODUCTION 1. Electrochemistry Combined with Microwave Measurements Electrochemical techniques have been developed into very powerful tools for research and technology. However, decades ago, researchers started to understand that even more insight could be obtained if electrochemical techniques were combined with additional spectroscopic tools. Among these it is sufficient to mention infrared spectroscopy, Raman spectroscopy, luminescence techniques, electroreflection or ellipsometry. Frequently, electrochemical information can be interpreted better in the presence of additional nonelectrochemical information. Typically, however, there is one significant restriction: electrochemical and spectre scopic techniques often do not detect exactly the same mechanisms. With spectroscopic measurements (e.g., infrared spectroscopy), products that are formed by electrochemical processes may be detected. In other cases (luminescence techniques) mechanisms may be found by which charge carriers are trapped and recombine. Other techniques (electroreflection studies) allow the nature of electronic transitions to be determined and provide information on the presence or absence of an electric field in the surface of an electrode. With no traditional technique, however, is it Modern Aspects of Electrochemistry,Number 33, edited by Ralph E. White et al. Kluwer Academic / Plenum Publishers, New York, 1999.

possible to obtain the information on the behavior of photogenerated electronic chargecarriers and electrochemicallygenerated ions or dipoles that would allow eIectrochemistry to be deveIoped to a stage that could, for example, provide convenient xcess to absolute rate constants for interfacial reactions. Such rate constants are typically poorly accessible because of capacitive res@aintsand because the photoelectrochemical system is underdcfined (thereare more variables than equations). Electm chemical kinetics only gives information on charge carrien leaving the electrode; information on the charge carriers lost in recomb'mtion pmma is not accessible. This situation appears to be different when microwave conductivity measurements are usedin padel with electmhemical measurements. As Fig. 1 shows, there is a marked p d e l i s m between electrochemical processes and microwaveconductivity mechanisms. In both cases electrical fields interact with electronic or ionic charge carriers as well as dipoles. In eledmhemicalpmwes, it is a static or low-frequencyelectrical field that is moving electrical charge carriers or orienting dipoles, In a micm wave measurement, the electric field of h e microwave interacts with

X'igufe 1. DmwQ s M g how static Meal &his and microwave &Ids interact with the same electrorric ar ionic charge caniecs and electtical dipla.

Microwave (Photo)electrochemistry

437

electronic charge carriers, thereby losing energy or carrying out a reorientation interaction with a dipole. This means that both electrochemical and microwave conductivity processes display interactions with the same species in semiconductorlelectrolyte interfaces. (The strength of interaction may, however, be different. In the case of interaction with dipoles, it will be frequency dependent.) By combining electrochemical and microwave conductivity techniques, it is hoped that more complete information on electrochemical processes can be gained. Microwave measurements are typically performed at frequencies between 8 and 40 Gcls. The sensitivity with which photogenerated charge carriers can be detected in materials by microwave conductivity measurements depends on the conductivity ofthe materials, but it can be very high. It has been estimated that 10~-10'~ electronic charge carriers per cubic centimeter can be detected. Infrared radiation can, of course, also be used to detect and measure free electronic charge carriers. The sensitivity for such measurements, however, is several orders ofmagnitude less and has been estimated to be around 10" electronic charge carriers per cubic centimeter.' Microwave techniques, therefore, promise much more sensitive access to electrochemical mechanisms. The analogy between standard photoelectrochemical and microwave conductivity measurements can be formulated in more precise terms: Microwave (photo)electrochemistry is a contact-free experimental technique that is based on the measurement of the relative change of rnicrowave power reflected from semiconductor liquid interfaces as a consequence of changes in electrode potential, electrolyte composition, illumination, or time. It is a technique which, like (photo)electrochemistry, probes the behavior of charge carriers and dipoles in solid/liquid interfaces, but via an independent circuit that does not involve the RC time constants of the electrochemical circuit (R = resistance, C = capacitance) and certain polarization effects that accompany direct-current measurements. A time resolution of at least 25 ps (which is required for the passage of a microwave in the detector during measurement) and a sensitivity that permits detection of lo9to 10'' charge carriers are characteristic advantages as well as the possibility of monitoring photoactivated charge carriers that do not reach the external circuit. In (photo)electrochemistry,the expected photocurrent change, Ai, is typically dependent in a nonlinear way on the changes in the potential applied. The reciprocal complex impedance, llA2, is the variable. The real part (BAG') is proportional to the conductivity change across the elec-

(w*)

trode/electrolyte interface. The imaginary part is dependent on the dielectric constant (8,) and determines the phase shift. It can be used to measure the interfacial capacitance:

Ai(V, hv, t )

AV

- z(V,Ihu, t ) = BAa'

+ iA/3'(V, hv, 1)

(1)

where Vis the potential, hv is the photon energy, and t is the time. This relation for photoelectrochemistry is now compared with the correlations for microwave conductivity measurements.

2. Electric Transport in Materials at Microwave Frequencies Photoinduced microwave conductivity measurements in solid and liquid Because of the much lower (ion) mobility materials have a long history.293 involved, it is much more difficult to measure photoinduced processes in liquids. However, reliable measurements have been made using thin liquid layers and significant insight into molecular processes has been obtained.? This suggests that microwave electrochemistry, which looks at processes generated by photoreactions in solid/liquid interfaces, has a good chance of becoming a valuable technique for studying (photo)electrochemically induced electrolyte processes (which, owing to a lack of experimental data, are not discussed here). At microwave frequencies (w), electric transport in materials (including interfaces) is determined by the dielectric function ~ ( w ) : The dielectric displacement is

where E(x) is the electric field with4

with

and

439

Microwave (Photo)eledrochernishy

where ef is the dielectric constant, d'is induction (free charge carriers cannot follow), E" is the dielectric loss (absorption of energy), and d is the energy loss through free charge carriers. The relative reflected microwave power is (S is a proportionality factor):

The relative microwave power (MIP)reflected from an electrodelelectrolyte interface can thus be considered to be proportional to the change in the imaginary propagation constant for microwaves (4") caused by a change in potential, illumination, electrolyte, or time. It is proportional to the induced change of conductivity (ACT)in both charge carriers and dipoles (ni is the concentration of charge carriers of type i; bi is their mobility) :

(u),

The real part describes the change in the phase factor which depends on the change in the dielectric constant (e,) responsible for the phase shift. The change in the reflected microwave power as a consequence of an imposed potential change can therefore be written [by rewriting relation (6) with A' as the proportionality constant]: w(v,hv,t) p = [i@(V, he t ) + A'Aa(V, hv, t)]

AV

AV

(8)

Although the conductivitychange Aa [relation (8)] of microwave conductivity measurements and the AO' of electrochemical measurements [relation (I)] are typically not identical (owing to the theoretically accessible frequency dependence of the quantities involved), the analogy between relations (1) and (8) shows that similar parameters are addressed by (photo)electrochemicaland photoinduced microwave conductivity measurements. This includes the dynamics of charge carriers and dipoles, photoeffects, flat band and capacitive behavior, and the effect of surface states. When two different experimental techniques are measuring the same variables (electronic charge carriers, dipoles) it is hoped that the combined

information provide a fuller description of the system. That this is actually the case will be shown in the course of this chapter by matching the mathematical formalism for potential-dependent photocurrents of semiconductor electrodes with that for potential-dependent microwave conductivity.

3. Historical Notes The first microwave electrochemical measurements were performed in 1971 at the University of California in Berkeley in the Laboratory of Chemical Biodynamics. The author was working as a postdoctoral fellow on dye sensitization of solar cells based on zinc oxide electrodes. The doctoral student R. A. Bogomolni was working nearby on the detection of photogenerated charges in photosynthesis using microwave conductivity techniques. They decided to put an electrochemical cell into a microwave resonator to find out whether the photogenerated charge carriers could be detected in semiconductorelectrodes during potential-dependent electrochemical activity. The experiments succeeded and the results were submitted to the Journal of Physical Chemistry. The paper was accepted but in the mean-time the participants had drifted apart and the corrections for the revised manuscript were made only 10 years later.5 After starting his own laboratory in 1982, the author built microwave measurement facilities with his collaborators and resumed research on microwave electrochemicalphenomena. While the potential of combining photoelectrochemistry with microwave conductivity techniques became evident very soon,637it was some time before microwave experiments could be performed at semiconductor electrodes under better-defined microwave technical condition^.^ Many experimental results on microwave measurements were collected with layer-type materials (e.g., tungsten diselenide), but the microwave conductivity-potential curves, which were very different from photocurrent potential dependencies, could not be understood. A peak of microwave absorption near the onset of the photocurrent in the depletion region was especially puzzling. Classical photoelectrochemicaltheory clld not account for an accumulation and damming-up of minority carriers prior to interfacial charge transfer. In fact, no existing theory predicted this phenomenon. The reason for the difficulty in calculating this effect was the complication encountered in solving the transport equations for charge carriers in semiconductor interfaces in such a way as to be able to calculate


441

the potential-dependentintegral microwave absorption in a semiconductor electrode. An important step toward the understanding and theoretical description of microwave conductivity was made between 1989 and 1993, during the doctoral work of G. Schlichthorl, who used silicon wafers in contact with solutions containing different concentrations of ammonium fluoride.g The analytical formula obtained for potential-dependent, photoinduced microwave conductivity (PMC) could explain the experimental results. The still puzzling and controversial observation of dammed-up charge carriers in semiconductor surfaces motivated the collaboration with a researcher (L. Elstner) on silicon devices. A sophisticated computation program was used to calculate microwave conductivity from basic transport equations for a Schottky barrier. The experimental curves could be matched and it was confirmed for silicon interfaces that the analytically derived formulas for potential-dependent microwave conductivity were identical with the numerically derived nonsimplified functions within 10%.1° After tlvs step, the understanding of microwave electrochemical mechanisms deepened rapidly. G. Schlichthorl went to the laboratory of L. Peter to combine potential-modulated microwave measurements with impedance measurements, while our efforts focused on laser pulse-induced microwave transients under electrochemical conditions. It is hoped that the still relatively modest knowledge provided will stimulate other groups to participate in the development of microwave photoelectrochemistry.

11. EXPERIMENTAL

1. Required Properties of Electrode Materials A significant precondition for the measurement of excess photogenerated charge carriers in electrode materials is that the electrical components of the microwave field reach the site where conductivity variations are generated. A second condition is that the change in conductivity generated be large enough that the signal can be detected in the reflected microwave power. The penetration depth, 6,of high-frequency electromagnetic radiation in media with an electrical conductivity a is well known:

This shows that the penetration depth decreasesdramatically with inmeasing conductivity of the medium to be penetrated. This has been plotted fig. 2) for different specific resistivities of the medium and the frequency of 1040 GC/S"at which microwave conductivity measurements are typically performed. It can be seen that with a specific resistivity of 10 ln cm,a penetration depth of only 2 rnm can be expected. Figure 2 furthermore shows the doping densities at which the m@ve penetration depths can be expected for silicon. Whereas the lower frequency X-band of microwaves (8-12.5 Gcls) offers some advantages for materials with very low resistance, the high-frequency microwave Ka-band (26.54

Microwave (Photo)electmchemistry

Gcls) offers the advantage that permanent dipoles will less easily follow the electrical field of the microwaves. Before constructing an electrodefor microwave electrochemical studies, the question of microwave petration in relation to the geometry of the sample has to I x evaluated carefully. Typically only moderately doped semiconductors can be well investigated by microwave electrochemical techniques.On the other hand, if the microwaves are interacting with thin layers of materials or liquids also highly doped or even metallic films can be used, provided an appropriate geomeby is alected to allow interaction of the microwaves with a thin oxide-, Helmholtz-, or space-charge layer of the materials.

The materials to be investigated have to IE incorporated into electrochemical cells in such a way as to permit the influx and the reflection of

microwaves, The e I d e s have to be adjusted to the microwave techniques that will be used for the investigation. Basically three different measurement approaches can be distinguished (Fig. 3). The simplest technique for microwave conductivity studies mg. 3(a)] is to place the sample directly at the exit of an ordinary waveguide. This setup has the advantage of being very simple and relatively transparent with respect to the phenomena occurring. Microwave power is reflected from the sample

Figure 3. Merent H e s for mimwave &vity m e a s m t s , (a) SSample (black q u m ] at end d microwaveguide, @) sample in ~ C C O W B V and ~ (c) ~ sample , above dielectric microwave spiral. The &mid field E of the micmave is &om schdcally.

in a nearly ideal way. Thus it has to be considered that some microwave power may also penetrate the sample to be reflected somewhere in the environment and it is advisable to shield the surrounding. Thls simple technique has been preferred in our laboratory. It has the advantage that errors can be avoided relatively easily, in contrast to the second geometry [Fig. 3(b)], which uses a microwave cavity. Microwave cavities, ofcourse, allow a much more sensitive measurement. Typically the sensitivity is increased by one order of magnitude compared with the geometry of Fig. 3(a). However, the sample (and the entire electrochemical cell) has to be accommodated within the resonator, which may cause a significant perturbation of the electrical field distribution. Also, the electrical wires of the electrochemical cell may function as antenna in extracting microwave energy from the resonator. Therefore an optimized geometry has to be searched for, typically by trial and error. Figure 3(c) shows an alternative geometry in which microwave energy is fed through an integrated circuit forming a spiral-shaped dielectric conduit above which a strong exponentially decaying electrical microwave field will build up. This integrated microwave device has not yet been explored for microwave electrochemistry, but owing to its simplicity, it may turn out to be the most convenient way to provide microwave energy for electrochemical studies. Figure 4 shows a simplified schematic of an electrochemical cell for microwave conductivity studies that is used directly above the exit of a microwave conduit pig. 4(a)]. Since water dipoles strongly absorb microwave energy, the energy is conducted through a semiconducting slab that forms the base and working electrode of an electrochemical cell. The electrolyte is placed so that it reflects microwave energy back into the microwave guide, but also absorbs and transmits part of it. The reference and counter-electrodesdip into this electrolyte. The connection of the back contact to the working electrode is important. It cannot cover the entire semiconductor surface since this would suppress penetration of microwave energy to the semiconductor/electrolyte interface. The electric contact must either be a ring contact that leaves the inside of the semiconductor back contact open or it must be a small single or multiple contact with thin wires that leaves enough space for the penetration of microwaves. Entirely different factors have to be considered when the electrochemical cell is placed in a microwave cavity [Fig. 4(b)]. Only a very small volume of water can be introduced into the cavity without drastically

Microwave (Phat0)el~hemiptry

figure 4a. Ehhmbemical cells for microwave conductivity m w memen&. CeIl above microwave conduit: (1) ektmhemical cell (plastictub, p W on workrng e m l M) (2), counterelee W Q)r e f m a (4) el-lyb (5) sp~toecharge layer, (9diffusion hyer, ('7) contactto working electrode, (8) wave@.

ducing its quality. The electrodes of the electrochemical cell have to be kept out of the resonator as much as possible, In the example shown, part of the electrochemical cell is accomm&ed within a cylindrical access hole to the cavity. The e l d c a l contact wire to the working electrode is bent in such a way as to follow a path of minimum microwave energy to the outside in order to keep it h m working as an antenna, extsacting microwave energy from the cavity. The position of the electrochemical cell has to be optimized to provide a cavity quality factorthat is msonably favorable for the measurement. Even though microwave electrochemical measurements in cavities are more subject to possible errors, the results obtained with this geometry are qualitatively similar to those obtained with the simple geometry of Fig. 4(a) using zinc oxide electrodes?~'

cell e hcewiv: (1) momtor, (2) waveguide, (3) cylibdrical mitt (4) e l a m chemical cell, (3warkingeledmk, (6)ekadyte,

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(7) c o u n t e r - e m (3) comet wite to wofking e m (9) o p i d W guide.

3. Microwave Ciuits A classical setup for microwave conductivity measurements is based on the utdmtion of the waveguides, A simple installalion consists of a

microwave generator (typically a gun di&) which, when the &-band is used, can be operated in the frequency region of 2 & 4Gds; this is protected by an isolator against back-reflections from the rest of the microwave circuit. The microwave power is conducted by an anenuator across a circulator into the microwave conductor branch at the end of which the electrochemical cell is mounted. The microwave power reflected from the electrochemical sample is conducted via the circulator into the microwave detector. It typically consists of a diode that acts as an antenna, receiving the electrical alternating field, rectifying it, and con-

Microwave (Photo)el&ochemisgY

447

verting it into a voltage signal. It increases proportionally with the absorbed microwave power. Since the reflected microwave power is photomodulated, a lock-in amplifier is needed for its measurement. The photomodulated current is measured simultaneously with a second lock-in amplifier and both the photocurrent and the reflected microwave power are measured as a function ofthe potential applied to the working electrode in the electrochemical cell (Fig. 5). For the excitation of semiconductor electrodes, conventional light sources, UV-lasers (for large gap oxides), or laser diodes can be used which can conveniently be modulated between 1Oand 1o4cPs.

4. Stationary Measurements Stationary microwave electrochemical measurements can be performed like stationary photoelectrochemical measurements simultaneously with the dynamic plot of photocurrents as a function of the voltage. The reflected photoinduced microwave power is recorded. A simultaneous plot of both photocurrents and microwave conductivity makes sense because the technique allows, as we will see, the determination of interfacial rate constants, flatband potential measurements, and the determination of a variety of interfacial and solid-state parameters. The accuracy increases when the photocurrent and the microwave conductivity are simultaneously determined for the same system. As in ordinary photoelectrochemistry, many parameters (light intensity, concentration of redox systems, temperature, the rotation speed of an electrode, or the pretreatment of an electrode) may be changed to obtain additional information. Stationary potential-dependent measurements are not the only measurements that can be performed with microwaves. Figure 6 shows a scheme indicating the different techniques that can be used for microwave characterization of semiconductor electrodes.

5. Time-Resolved Measurements Time-resolved microwave conductivity measurements with electrodes in electrochemical cells can conveniently be made with pulsed lasers (e.g., an Nd-YAG laser) using either normal or frequency-doubled radiation. Instead of a lock-in amplifier, a transient recorder is used to detect the pulse-induced microwave reflection. While transient microwave experiments with semiconducting crystals or powders have been performed

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frequently, the history of laser pulse-induced microwave transients in electrodes of photoelectrochemical cells is relatively short. Since time resolutions of up to 25 ps can be expected with this technique, which does not directly depend on the RC constant of an electrochemical circuit, the future potential for analysis of fast reactions at electrode/electrolyte interfaces may be significant. The use of a resonance cavity results, as mentioned, in a sensitivity that is approximately one order of magnitude greater than that for a normal reflection cell. The consequence is, however, a sacrifice in time resolution, which is typically also of one order of magnitude.

6. Space-Resolved Measurements By simply moving the sample on an XY table and allowing a laser spot to scan the entire surface, a basis for space-resolved measurements is provided. This technique, developed in our laboratory 13-15 is commercially available, but it has been used very little for the potential-dependent investigation of electrodes. The technique of producing photoinduced microwave conductivity images may now appear simple, but the spatial resolution of 1-3 pm obtained with a microwave of a wavelength of approximately 1 cm was originally not evident. The high resolution is possible only because the measurement occurs in the near field of microwave generation and not after the microwaves have reached the far field (radar applications). Space-resolved microwave conductivity images of space-resolved microwave transients provide significant insight into material properties and when potential-dependent measurements are included, permit the characterization of still more properties and a distinction between the quality of materials in different locations of the investigated sample. The really usable spatial resolution is typically limited by the diffusion length of the materials (e.g., 40pm in technical silicon wafers), which means that photogenerated minority carriers diffuse that distance or are trapped within that distance, making higher resolution impossible. However, most semiconductormaterials have a much smaller diffusion length so that very high resolution can be obtained. Figure 7 shows an example of a space-resolved microwave conductivity measurement of the semiconducting surface of a natural pyrite (FeS2)sample (from Murgul, Turkey). The overflow of the PMC signal (white color) was adjusted to a level that shows the patterns of distribution of low photoeffects (dark areas). Figure 8 shows a similar image in which,

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.

however, the lifetimes of microwave conductivity transients are shown It gives insight into the patterns of surface recombination. The sample was a 20-~m-thicksilicon wafer onto which 11 droplets of a zeolith suspension were depositd and dried. Although the dry zeolith layers are not sensitive to visible light, they reduce the lifetime of electronic charge carriers in silicon by influencing surface recombination. 7. Microwave Phase Detection E x p e h n t s

As with alternating electrical currents, phase-sensitive measurements are also possible with microwave radiation. The easiest method consists of measuring phase-shifted microwave signals via a lock-in technique by modulating the electrode potential. Such a technique, which measures the phase shift between the potential and the microwave signd, will give specific (e.g., kinetic) information on the system (see later discussion). However, it should not be taken as the equivalent of impedance measurements with microwaves. As in electrochemical impedance measurements,

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where the thermodynamic force (the electrical potential) is mdulatsd to measure the phase shift with respect to the flux (the current), the micre wave impedance measurement requires a modulation of the rnicrowave power (the thermodynamic force P) for a phase shift with respect to the reflmtcd microwave powcr (the rdative "flu x " b P / P ) . Since such tmh-

niques will become relevant in a more advanced stage of development of microwave electrochemistry, Fig. 9(b) shows acircuit that can be used for phase-sensitive measurements of microwave conductivity. The microwave measurement system is basically split into two branches between which .

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Microwave (Photo)el~hemislry

Figure 9. (a) Elmale and rqmxataiivecircuit forpbsensitive electtachwnicalmeasurements( i i m e a s ~ ~ e m e n t s ) c o m p a r e d with (b) sew for phassmsitive mimwave ( i m p b e ) measuremen&.

Microwave

Hall experiments have been performed in our Iabora-

toxy.16 They have shown that the mobility of charge carriers in

semiconductors can be measured quite reliably even if the semiconductors are only available in the form of a powder. The measurement technique itself is relativelycomplicatedand involves, forexample, rectangular waveguides, which can be rotated against each other on opposite sides of the sample to monitor the phase rotation. In the "two-mde resonator,"two modes of

the microwaves, E, and Eh rotated against each other by d4, interact in such a way h a t at the entrance they couple to a field of E, + &while at the exit the field is E, Eb.Coupling elements are used around this resonator to adjust this situation, while a switched-on magnetic field will change the phase and unbalance theconstellation to allow a phase rotation rrWiSuRmenF. The theory of such a measurement still needs further improvement. Figure 10 shows the drawing of a "two-mode resonator" with its calibration elements for microwave Hall effect measurement,

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Figure 10. (a) Twemode cavity and (bS microwave circuit for Faraday rotation (microwave Hall effect) experiments.


455

together with the corresponding microwave circuit.16This technique has been applied to the measurement of charge carriers in photosynthetic membranes. Its application to electrodes under variable potential has still to be demonstrated. It will, for example, be interesting to find out how the mobility of electronic charge carriers in sensitized nanocrystalline oxides (e.g., 'Ii02,ZnO) depends on illumination intensity (number of mobile electrons in nanocrystals) and applied (photo)potential, or how minority carriers react in the accumulation region of a semiconductor.

8. Potential Sweep or Potential Modulation Techniques Instead ofchanging the light intensity to detect photoinduced microwave conductivity changes, it is equally possible to change or modulate the electrode potential to detect potential-dependent or potential-modulated (derived microwave conductivity) (MC) changes. If this leads to a change in the MC, it may provide information on electrode processes. However, the information obtained may be complicated to evaluate and may need systematic research in individual cases. As an example we may mention ZnO in contact with an aqueous electrolyte (1 M KC1 at pH 2). The MC-potential curves at different sweep velocities (Fig. 11) show pronounced features, which are not seen in an ordinary current voltage diagram. The interpretation of this electrochemical MC diagram for ZnO must consider the cathodic reduction and formation of metallic zinc, which, as a thin surface layer may shield part of the electric microwave field, thus decreasing the MC effect [by changing the sensitivity factor S defined in relation (6)]. Charge carriers may also be trapped and the effective doping of the surface ZnO layer may be changed. During the positive sweep, the metallic zinc atoms on the ZnO are dissolved and released into the electrolyte, which leads to a gradual corrosion of the semiconducting oxide. With all these complications, the example shows how potential-dependent MC measurements can lead to new information on electrochemical processes. Another technique consists of MC measurements during potential modulation. In this case the MC change is measured synchronously with the potential change at an electrode/electrolyte interface and recorded. To a first approximation this information is equivalent to a first derivative of thejust-explained MC-potential curve. However, the signals obtained will depend on the frequency of modulation, since it will influence the charge carrier profiles in the space charge layer of the semiconductor.

figure 11. Dynamic &wave conductivity-potentialcurves taken with a a0 sit@ crystal and shown for two potential sweep velocities (a) and (b) and a m m p h g dynamic @hoto)current-potential curve (bottom). 'IZle daxk effects and photoeffects ace indicated for the two cases. Cwes 1 and 2 m dto Ca) and @)-4~.


457

It is interesting that potential-modulated MC signals can also be obtained from metal electrodes (e.g., Pt in contact with an aqueous electrolyte). Since the MC signal includes contributions from dipole orientation [water, compare Eqs. (6) and (7)], it may be that potentialdependent changes of the water structure near the electrode surface will be seen. This would mean that the oriented water structure makes different contributions to microwave absorption or reflection at different electrode potentials. The potential-dependent formation of ultrathin oxide layers with their possibly mobile charge carriers or an adsorption layer of electrochemical reaction products may also be seen. The fact that photoinduced molecular charge separation has been clearly detected by microwave conductivity in liquid systems3 suggests that electrochemically or photoelectrochemically generated products will also be seen with sufficiently sensitive PMC systems. When, during an electrochemicalreaction, ions (N,)with the mobility p, are generated as well as species (N,) with a rotational charge mobility M,, then a change in microwave conductivity of

can be expected.3 The rotational charge mobility can be calculated to be proportional to the square of the dipole moment and inversely proportional to the rotational relaxation lifetime. It is frequency dependent and approaches a limiting rotational charge mobility at high frequencies. Up to now only qualitative data have been available on potentialdependent MC measurement s of electrochemical interfaces. When metals or other highly conducting materials are used, or when liquids are in play, special care has to be taken to allow access of microwave power to the active electrode/electrolyte interface. 111. THEORETICAL CHALLENGE

1. A Fully Determined System At the beginning of this chapter we presented evidence that a combination of (photo)electrochemistry with photoinduced microwave conductivity measurements promises more direct access to kinetic parameters involv-

ing elmnic charge carriers. This is now dixussed in more detail (compare Ref 9), While photoelectrochemical measurements allow the measurement of the photocurrent (Id,that is, the current of photogenemted charge carriers, whch can leave the s e m i c o n ~ r l e l ~ l y interface, te the photoindud microwave conductivity signal provides integral information m the total amount of photogenerated charge carrien which, in equilibrium with recombinationpmwm, are present in the semiconductor electrode (among them are also those charge carriers that are finally lost through recombination). Figure 12 demonsfrates via an energy &agram the situation in the semiconductorlelectrolyteinterface, Shown are the minority carriers dp(x1, which are drifting toward the electrode interface, where a surface concentration of &, develops. This determines surface recombination and the interfacial charge transfer, which are controlled by therateconstants sr and k, respectively. An n-typ semiconductor is given as an example [the followhg equations can be formulated in an analogous way for p-type semiconductors with electrons (An) as minority carriers).

The photcmmnt l* can be described by the following relation:

Figure 12 Energy diagram of a wniconductorlelectmlyteinterface showing photogamtion and loss mechanisms (via surface m m h a t i o n and interfacial charge transfer for minority charge carriers). 7he staface ooncentxdm of minority &m, & is also indicated


459

where q is the electric charge and A W = U-Up. The photoinduced microwave conductivity signal, on the other hand, can be described by the following integral over the excess minority carriers, to be taken over both the diffusion and the space charge region:

where S is the sensitivity factor to be calculated or calibrated, which depends on the geometry of the measurement cell; d is the thickness of the electrode; and W is the width of the space charge layer. This means that the PMC signal will, apart from the generation rate of minority carriers and a proportionality constant, be determined by the interfacial charge transfer rate constant k, and the interfacial charge recombination rate s, There is an additional simple relation between the surface concentration Apsof photogenerated minority carriers and the charge recombination and charge transfer rates s, and k, to be considered:

where I, is the calculable minority carrier flux toward the semiconductor interface, AU = U - Ufi. These three equations (ll), (12), and (13) contain three unknown variables, Ap,, k, and s,. The rest are known quantities, provided the potential-dependent photocurrent (Iph) and the potential-dependent photoinduced microwave conductivity are measured simultaneously. The problem, which these equations describe, is therefore fully determined. This means that the interfacial rate constants kr and s, are accessible to combined photocurrent-photoinduced microwave conductivity measurements. The precondition, however is that an analytical function for the potential-dependent microwave conductivity (12) can be found. This is a challenge since the mathematical solution of the differential equations dominating charge carrier behavior in semiconductor interfaces is quite complex, but it could be as will be outlined below. In this way an important expectation with respect to microwave (photo)electrochemistry, obtaining more insight into photoelectrochemical processes

than that provided by classical photoelectrochemistry, can apparently be fulfilled.

2 Mmamment Opportdtics and Prospects of Microwave

el^^

Since photoelectrochemistry is not limited to photocurrentmeasuremenis, it may at this point be useful to think about some general new research possibilities to be expected from the combination of el&rochemical and microwave measmments. Table 1 shows obvious combination possibilities between electmhemicaI and microwave measurements.

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen M s . (1 11, (1 2), and (13)], the interfacial rate constants for minority carrier reactions (k, sr) as well as the surface concentration of photoindued minority a e r s (bp,) (and a series of solid-state parameters of the electrode

material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of eletrde pmases, a combhation of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms,especially very fast ones,which would not be accessible with conventional electmhemid techniques owing to RC restraints. Also, more specific kinetic information may become accessible; for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemica1 impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-


46 1

sion). However, a general theory for the combination of electrochemical and microwave potential modulation will have to be developed. Electrochemical impedance spectroscopy leads to information on surface states and representative circuits of electrode/electrolyte interfaces. Here, the measurement technique involves potential modulation and the detection of phase shifts with respect to the generated current. The driving force in a microwave measurement is the microwave power, which is proportional to E~ (E = electrical microwave field). Therefore, for a microwave impedance measurement, the microwave power P has to be modulated to observe aphase shift with respect to the flux, the transmitted or reflected microwave power M/P. Phase-sensitive microwave conductivity (impedance) measurements, again provided that a reliable theory is available for combining them with an electrochemical impedance measurement, should lead to information on the kinetics of surface states and defects and the polarizability of surface states, and may lead to more reliable information on real representative circuits of electrodes. We suspect that representative electrical circuits for electrode/electrolyte interfaces may become directly determinable by combining phase-sensitive electrical and microwave conductivity measurements. However, up to now, in this early stage of development of microwave electrochemistry, only comparatively simple measurements can be evaluated. In the following section the mathematical derivation ofthe stationary, potential-dependent,photoinduced microwave conductivity signal, which integrates over all photogenerated charge carriers in the semiconductor interface, is explained. This is a necessary requirement for the interpretation of the PMC-potential curves.

3. Analytical Expression for Potential-Dependent Microwave Conductivity In order to calculate the integral (12) describing the microwave conductivity signal, we have to obtain an analytical expression for the behavior of charge carriers in the semiconductor interface. The G&ner model,18 which assumes minority carrier collection by a potential-dependent space charge layer, is too simple for this purpose, since it does not consider interfacial charge-transfer and surface recombination rate constants. The formalisms of ~ e i s s "or ~ i l s o n "do consider them, but provide expressions too complicated to be practical for calculating an analytical expression for microwave conductivity. Starting from the basic equations

[continuity equation (14)], the transport equation for electrons (15) and holes (16), and the Poisson equation (17)]

and considering the influx of additional charge carriers from the field-free interior of the semiconductor, a new effort had to be made to calculate the distribution of the minority carrier concentration in a semiconductor/electrolyte j u n ~ t i o n .Among ~ the simplifications introduced were a linear electric field dro in the space charge layer, Ld < 1/a(Ld = Debye length = (e/qND)(kT/q),a = absorption coefficient),Ld 100 mV,where a reasonably low surface recombination velocity is found, the PMC signal can consequently be approached by

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where Aps is the surface concentration of minority carriers and since the photocurrent iph is proportional to the surface concentration of minority carriers,

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4. Accuracy of Derived Analytical Formulas

(i) Numerical Solution of Basic Equations It is possible to solve the fundamental transport equations for photogenerated charge carriers in a semiconductorjunc tion (14)-(17) without any simplification. This has been done for a silicon Schottky barrier,'' which may serve as a reasonable model system for a semiconductor/electrolyte junction. The numerically computed potential-dependent PMC signal showed a minimum in the flatband region of the semiconductor and significant peak structures in both the positive and negative potential region of a semiconductor electrode. These peaks are strongly influenced by surface recombination and charge-transfer rate constants, but also by the bulk recombination lifetime. The influence of different values of rate constants on the shape of these features is shown in Fig. 13. The PMC peak in the depletion region is shown in Fig. 13(a) and in the accumulation

Microwave (Photo)electmhemistrg

Figure 13. Numerically calculated PMC potentid CU~YH from transport: equations (14)-(17) without simplifications for different interfacial rem tion rate castant8 for minority carriers (hoh in n - t p semiconductor): (a) PMC p k in d e p l h n regim Bulk lifetime 10 s, combined interfacial rate oonstolnts Is, = s, + 4) inserted in drawing. Dark points, calculation from analytical formula (18). (b) PMC peak in accumuIation regioa Bulk lifetime: W 5 s . The combined in-ial charge-mmferand recombination rate m p from I0 (11, 100 (Z), ld (33 x ld (4), lo4 (5),3 x f d (6)to 186(7) aa i' he. flatband potential is indicated

region in Fig. 13(b). The influence of interfacial rate constants is shown for both PMC peaks. These same features of the PMC signal can be reproduced by plotting the calculated analytical formula for the depletion region [relation (18)l. This is shown for the positive PMC peak in Fig. 14. By inserting the same parameters into both the numerical and analytical computation pmdures, it is found that the analytical solution coincides with the numerical one

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467

within 1Wo [the filled-in points in Fig. 13(a)]. This means that the simplifications introduced for calculating the analytical relation (18) were reasonable. The stepwise increase in the PMC signal toward increased accumulation [Fig. 13(b)] cannot yet be simulated with areliable analytical formula because of complications with solving the intricate integrals for the space charge layer under these conditions. However, as indicated before, the ratio between PMC,, and PMCd, (at the flatband potential) amounts to 1 + a ( r , ~ ) ' "and is therefore dependent on the bulk lifetime of minority carriers q,.Since we have succeeded in calculating the PMC curve quantitatively, the derived PMC formula (18) can help us to understand and evaluate details of microwave electrochemical behavior of semiconductor electrodes.

(ii) Photocurrent Expression from Theory Another interesting test which may give an idea of the use of the simplifications introduced in deriving the analytical formula for photoinduced microwave conductivity can be obtained from a comparison between the simple Giirtner model for the potential-dependent photocurrent18 and the theoretical photocurrent derived from the just-described approach. The Giirtner model simulates charge collection by a potential-dependent space charge layer and considers diffusion into the space charge layer of charge carriers generated deep inside the semiconductor. The well-known Girtner formula for the photocurrent Iphis

In our approximation we start with relation (20) for the surface concentration of minority charge carriers and derive via formula (11). It follows that Iph is (only photons loleading to minority carrier generation are considered)

Assuming that &ere is no surface recombhatiion (sr = 0) and an infinite interfacial charge-transferrate (k,=-h as assumed in the G i e r approach, the denominator of relation (27) becomes equal to one. The expression for the photmmnt then has the same structure as the Giirmer formula. Formula (27) has the quality of showing the influence of the surface recombination rate and the charge-transferrate. When the (potentialdependent) surface recombination is large, the photwumnt becomes low. A high surface recombination rate near the flatband potentid will displace the photocurrent curve toward higher potentials (see Fig. 15). A low

Figm 15. Effect of intdacial mte constmts on PMC behavior and on th p h o t o c m t (lo = 1 cm?. (a) Fast interfad chqptnnsfer rate, and (b) low inmhial c h g 8 - d e r rate.


469

charge-transfer rate will obviously decrease the photocurrent. The "diffusion" term ( D / L ) ~ - ~ ' in ~ ' relation ~ (27) is interesting. It increases with increasing surface concentration of minority carriers in the presence of a high rate of interfacial charge transfer. It obviously considers an effective

diffusion loss into the field-free region (decreased diffusion into the space charge layer) when charge carriers are accumulatingthere. This shows that the compact photocurrent-voltage relation (27) is highly reasonable. It may serve to replace the Giirtner formula, which is not realistic for photoelectrochemistry. We consider it support for the reliability of the derived formula (18). In Fig. 15 the photocurrent voltage curves and the microwave conductivity potential curves are compared for two different cases. In Fig. 15(a), a high interfacial charge-transferrate (k, = 100crn S-') was assumed and in Fig. 15(b) low charge-transfer rates (kr = 0.05-0.1 cm s-I). The surface recombination was assumed to depend on the electrode potential and was considered for different exponential parameters Cf,). It can clearly be seen that an inhibited charge transfer displaces the photocurrent voltage curve towards higher positive electrode potentials. Simultaneously, a smoothly decreasing PMC signal [a high interfacial rate constant, Fig. 15(a)] is giving way to a PMC peak the height of which depends on the interfacial rate constant [Fig. 15(b)]. It is obvious that by measuring the integral over the excess carriers in a semiconductor electrode, which is the basis of the PMC measurement, minority charge carriers can be seen, which are dammed up toward the semiconductor interface owing to low interfacial charge-transfer rates and modest surface recombination rates.

IV. POTENTIAL-DEPENDENT STATIONARY MICROWAVE CONDUCTIVITY MEASUREMENTS

1. n-Type Semiconductor/E1ectrolyte Junctions As mentioned in the introduction, before an adequate theory was developed, it was difficult to understand the experimentally determined photoinduced PMC signals, especially the minority carrier accumulation near the onset of photocurrents.The reason was that neither conventional solid-state semiconductor theory nor photoelectrochemical theory had taken such a phenomenon into account. But we have shown that it is real and microwave (photo)electrochemical experiments clearly confirm it.

Figure 16 shows such PMC pealcs in the depletion region for electrodes of S i 9 W S ~ 'and ZnO.lZThey all appear near the onset of a n d c photocmnts. They have different shapes, which, however, can easily be explained with the assumption of potential-dependent interfacial charge transfer and charge recombination rates. Figure 17(a) shows the PMC peak, in the accumulation region (at negative potentials) of silicon in contact with a propylene carbonate

Microwave (Photo)electrochernistry

Figure 17. PMCbehavhin h e a c c u m ~ o @on, n (a) PMC ptmtial curve and p h ~ - ~curve a (dasbed l line) for silicon (dotted with Pt particles) in cuntact with propylene cadmate electrolytecontaining fawene?' @) PMC potential curve and photocurrent-potential c u m (dashed line) for a s p u m d 2hO layer [tesistivity 1.5 x I d a cm, on oonducting gtass (lTO)] in contractwith m alkaline e l ~ I y t (NaOH, e pH a 12) ,measured against a satumd calomel electrod$

H. Tributsch

472

electrolyte2' as predicted by theory. Here photogenerated minority carriers are pulled into the interior of the negative space charge layer by the increasing negative potential. In this way they increase their lifetime (through suppression of surface recombination). In the depletion region of this electrode/electrolyte junction, two PMC shoulders are seen-a weak one near the onset of the photocurrent and a second high one where This oxide formation starts on Si owing to water traces in the electr~l~te.~' oxide formation reduces the charge-transfer rate for photoinduced minority carriers and leads to a significant accumulation of charge carriers in the space charge layer. Figure 17(b) shows that PMC peaks in the accumulation region can also be detected with a sputtered oxide layer in contact with an alkaline ele~trolyte.~~ Figure 18 shows the clearly pronounced accumulation-PMC peak for a silicon electrode in contact with a 50 mM F ~ ( c N ) ~ ~ - "aqueous electrolyte and the depletion PMC peak at positive electrode potentials. The PMC-potential curves were measured for different light intensities.

2. Metal Oxide/Semicondudor Junctions With respect to charge carrier dynamics, serniconductor/electrolytej unctions behave very similar to Schottky barriers, or, when a thin oxide layer is present in the interface, similar to metal oxide/semiconductor (MOS) junctions. Figure 19 shows a PMC model experiment with such an MOS device in which a 2 nm oxide layer separates the Si semiconductor from the metal contact. The comparison of photocurrent-voltage dependencies with PMC-voltage curves clearly confirms the theory: where the photocurrent appears in the depletion region, a PMC maxima appears. Such a peak also appears in the accumulation region. It can be seen that the PMC peaks do not increase proportionally with light intensity. It can also be seen that the PMC signal in the accumulation region decreases again toward more negative potentials. This phenomenon is also recognized in the theoretical curves [Fig.l3(b)]. It turns out that at increased forward potentials the dark current also increases, creating an ohmic voltage drop. A field is created, along which the holes drift into the bulk. The concentration profile toward the electrode interface is thereby flattened'' and charge carriers are more easily lost at the back contact, which decreases the PMC signal. It is interesting to note that PMC peaks depend on the frequency of periodic excess carrier generation. At higher frequencies, the PMC peak

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cleenode potential PH[hCMI

7r-/V

Figure 18. (a) PMC potential curves and 0)photocurrent curves for n-silicon in contact with a 50 mM P ~ ( c N ] ~ - ' ~ ' aqueous electmlyte for different light intensities. Scan rate: 20 mV.The light intenqity is varied from I 0 0 mW em" (top curves), to 50,20, and 10 mW cmq2(bottom curves)."

becomes smaller as if interfacial rate constants would increase. This is shown for an n-Si/Si-oxiddAu (100 A)MOSjunction (Fig. 20). At higher excitation frequencies, passage of minority carriers through the oxide layer in the MOS junction is apparently faster while the same number of carriers manage to cross the interface.

Egure 19. PMC p o U and photccment-ptedal curva for an Si-MOS device (2 nm S i Q at different photon flux densities (indicated for phommmts).

figure 20. Idhence ofllght ppulsing q u e n c y on PMC plb O f n s i in antact with a 10 nm Au at 20 m W cm light intensity, mrpd with influence on photmmmt. Pulsing fresuencies were 110, 1520, and B N cps


475

3. p-Type Semiconductor Electrodes Up to now, relatively few experiments have been carried out using p-type semiconductor electrodes. The theory predicts that the curves should be changed in mirror image form from positive to negative potential at the flatband position. However, the PMC minimum between positive and negative peak shifts in the positive direction by approximately 700 to 800 mV, which is equivalent to the shift of the Fermi level when switching from an n-type to a p-type material. Experiments with p-type silicon have confirmed this expectation (Fig. 21).~An excess minority carrier peak (electrons) is found that coincides with the onset of cathodic photocurrents toward negative potentials (entirely symmetrical to the corresponding PMC peak of n-type electrodes at positive potentials). The (potentialdependent) interfacial charge-transfer rate and the surface recombination rate of photogenerated electrons will, for p-type electrodes, determine the amplitude and the shape of the PMC peak at negative electrode potentials.

4. Meaning of the Dammed-Up Charge Carriers Why do minority carriers accumulatein the depletion region near the onset of photocurrents? Theoretically, three factors are decisive for this phenomenon: an increasing lifetime of charge carriers owing to the increasing electrical field in the space charge layer, which causes a separation of charge carriers a surface recombination rate, s, which decreases away from the flatband potential with increasing electrode potential an interfacial charge transfer rate that may increase with the electrode potential but should not become very fast Any change in theconstants kr,s, and Ap should of course be reflected in a change in the PMC peak. The increased lifetime of photogenerated minority carriers can be measured experimentally. Ths is shown for a single-crystal ZnO-electrode (Fig. 22). Both the stationary PMC peak and the potential-dependent lifetime in the depletion region, measured with transient microwave conductivity techniques are plotted.25It is seen that the stationary PMC peak coincides with a peak in the lifetime of minority carriers. This

electrode potendalN Figure 21. (a) PMC potential and (b) cathodic photocurrent-potentialcurve,$for a p-Si (1 1l) e l e c w (mistivity, 10 cm). Electrolyte, 1 M W F ;Tight intensity; 1 m W cm-'. Sweep toward negalive potentials.

lifetime peak could, however, be clearly seen only with mderate lam pulse energies. Too high photon densities of laser pulses apparently interfere with the electric field distribution and concentration profiles in the semiconductor interface. Since the magnitude and shape of this PMC peak depend on the rate constants of minority charge carriers, the PMC peak provides a m s to kinetic measurements. It is interest that the height as well as the shape of the PMC peak change withthe frequency of light pulsing. This is shown

electrode potential& V Figure 22. (a) Comparison of stationary PMC peak at psitive potentials and (b) peak in PMC mnsient lifetime, measured for n-ZnO single crystals.2s

in Fig. 23 for n-WSer in contact with a 50-mM ~e~~ solution (5 m M H2S04). While the photocurrent-potential curve does not change significantly when the pulsing frequency is varied between 1 1 and 1 10 cps, both the height and the shape ofthe PMC peak do.26This indicates that kinetic constants change, apparent1y because of pulsing frequency-dependent

profiles of the charge carrier distribation in the space charge layer.

figure 23. Influence of light pulsing frequency on peak height and peak position of n-WSez in contact with 50 mM ~e~'''' (5 m M H2SOd. PuIsing frequencies between I1 and 1.10cp aem@for the PMC and photocumnt curves (light intensity, 50 m W cm-I).

In microwave eIectrochemiea1 measurements with unstable elec~ d e ~ e c t m l yinterfaces, te the PMC signals may change drastically in time. During a first sweep of a silicon electrode toward more positive electrode potentials, a pronounced PMC peak may be seen, which disappears during the return sweep toward negative potentialsz3(Fig. 24). The reason is that during the psitive sweep the Si interface corcOds$ to form sites for interfacial charge recombination (an increase in s,), which also leads to a decrease in anodic photocurrents. Figure (25) compares two

.O 5

00

05

1 .O

15

20

electrode potential SCeN Figure 24. Degradation .of n-Silelectrolyte (0.1 M NaSO,, pH 3) interface as seen from the hysteresis of the PMC signd and the photocurrent (dotted line).

experiments, one with n-Si (treated with Pt particles) in contact with a 5 M HBr10.05 M Br2aqueous solution, and one with n-WSQ in contact with an aqueous O M M ~ e ~ l " solution. + Silicon was allowed to degrade and WSQ was cathodically polaizd. In both cases, while the anodic photocurrent decreases, the PMC peak shifts toward more positive potentials. The reason is an increased surface recombination near the flatband potential. In studies on Pt dotted silicon electrodes, PMC measurements reveald that tiny Pt dots hcreasd the interfacial chuge transfer compared with bare silicon surfaces in contact with aqueous electrolytes. 'However, during an aging effect, the thickness of the oxide layer between the silicon and the pIatinum dots gradually increased so that the kinetic advantage again decreased with time."

5. PMC Decay in the Depletion Region

Experimental evidence with very different semiconductors has shown that at semiconductor interfaces where limited surface recombination and a modest interfacial c harge-transfer rate for charge carriers generate a peak

P i 25. Effect o f d m and prepol&on on (a) PMC voltage and (b) photoclnrent voltage d q d m e . Left: n-Si (wM with Pt particles) in contact with a 5 M HBfl.05 M Br2 aqueous dution. A c m p r h is rnade of the PMC p k d h g the first ad the third m t i d swqx. Right: n-WSq haantactwith an a q u w 0.05 M -'%I sorution. l b effect of cathodic onan @tion omd height of the PMC p k is shown.

of microwave conductivity, this conductivity signal dscreases in the depletion region with increasing elpotential 16 and 19). The explanation of this phenomenon is not straightfornard, since it occurs in a potentid region where practically all charge canrim reach the semiconductor interface to react with the electrolyte. This is clearly indicatsd by the presence of a limiting current in this potential region. The numerical calculation of the potential-dependent microwave conductivity clearly describes this decay of the microwave signal toward higher potentials @g. 13). The simplified andytrcal calculation describes the phenomenon within 1030 accuracy, at least for the case of silicon Schottky barriers, which serve as a good approximation for semiconductodelectrolyte interfaces. The fact that the analyhcal expression derived for the potential-dependent microwave conductivity describes this phenomenon means that analysis of the mathematical formalism should

Microwave (Photo)electnwhemistry

provide a reasonable explanation. In fact, it is found that the decay of microwave conductivity in the depletion region is dominated by a mathematical function (@) [relation (1911. The dependence of this function on band bending in the semiconductor interface is shown in Fig. 26. It describes the minority charge carrier concentration profile in the space charge layer and thus affects the PMC signal, even in the limiting photocurrent region and in the presence of a constant interfacial charge transfer k, by d m h g it toward larger band bending. Charge carrier profiles have been calculated for p o i d silicon interfaces1' and show that with increasing elmhie potentials photogenerated charge carriers concentrate near the semiconductorlelsctrolyte interface (Fig. 27). Since in the absence of electrostatic interaction the space charge region can be crossed with thermal velocity, it will be the increasing closeness of minority catriers to the interface that will control the escape through an interfacial reaction. While at lower positive electde potentids reacting charge carriers will be further away from the interfaces, they will be available closer to the interface at higher electrode potentiaIs. With increasing elpotential, their average stay in the space charge layer will therefore decrease, thus decreasing mimwave conductivity, which is

Figure 26. Depetadeuce of fanction e A U ) [relation (19x and of IiNAU) on the e.W& pokdd (~~erlsllred against lhe flatband ptential) AU a U Up

-


483

proportional to the concentration of mobile carriers. Since with increasing depletion of the space charge region the photogenerated charge carriers are found to concentrate more toward the interface, they are therefore reacting more rapidly and spending less time in the space charge layer. [Since Iph= k, . Lip,, k, and Aps increase and decrease complementarity within the limiting photocurrent range (compare Fig. 301. The consequence is that the PMC signal decreases with increasing electrode potential within the region of limiting photocurrent. There is a simple example that can make this remarkable phenomenon intuitively more accessible (Fig. 28). Allowing the passage of photoinduced minority carriers through the space charge layer at different electrode potentials in the limiting current region is equivalent to pressing water at a constant rate through tubes with decreasing cross sections (the increasing electrical field corresponds to the increasing pressure in the model experiment with the water tubes). Measuring microwave conductivity is equivalent to measuring the average number of water molecules in tubes ofdifferent sizes. Even though the same amount of water per time is pressed through the tubes, much less water is found in the thinner tubes, through which water is passing at a higher velocity. The decrease ofthe PMC signal toward increasing depletion therefore reflects the increasing dynamics of minority carriers passing the space charge layer. No classical electrochemical technique has up to now permitted observation of this phenomenon with such clarity.

6. Determination of Flatband Potential The theory locates the flatband potential between the PMC peak in the accumulation and the PMC peak or the photocurrent shoulder in the depletion region. If peaks or shoulder are sufficiently close to each other, the determination of the flatband potential is sufficiently accurate. A high surface recombination rate, however, can move the peaks apart. In the case of a high interfacial charge-transfer rate, the PMC peak in the depletion region may completely disappear and give way to a gradually decreasing signal. Under this condition of high charge-transfer rate, the formula for the potential-dependent PMC signal (18) loses the term that contains the surfaceconcentration (&) of minority carriers (20), (which becomes very small). Formula (21) can be rewritten to give (W, the width of the space charge layer, is inserted and the thickness of the electrode is assumed to be large):

Figm 28. Semimdwtor interfaces with b m s h g eIectric lkl&in the s p charge layer (fromtop to b m )compared with tubes of different diameten through wbich an equivalent amount of water is pwedper unit time (equivalent to limiting current).

with B=%-

and ~ = l % D [:Jn

When relation (28) is properly fitted,B,C, and the flatband potential Ufi can be determined. For a silicon electrode in contact with 0.6 M NH#

P i p B,PMC p m d d E m d p The flafband potential Ufi is indieatd,

~~ u r vte sforn-Si ~ in contad with 06 M

solution, which dissolves the interfacial oxide layer the potential coincided with a flatband value detmnhed using a conventional The Debye length of the electrde material can be determined from the constant B, and the sensitivity factor S h m C,provlded the diffusion length and the diffusion constant for minority carriers are known. In the experiment discussed (n-Si/Od M m, the flatbandpotential (0.8 V vs. a saturated Hg-sulfate electrode) would have been immediately recognizable as the pronounced minimum between PMC and the photocurrent curve (Fig. 29). Another technique for flatband determination is based on the measurement of potential-modulated microwave conductivity signals and is described further in the next section.

As outlined at the beginning of this chapter, combined photocurrent and microwave conductivity measurements supply the information needed to determine three relevant potential-dependent quantities: the surface concentration of excess minority carriers (&), the interfacial recombination rate (q),and the interfacial chargetransfer rate (kr),By inserting the

measuredphotocurrent and PMC values into the proper relations, these quantities can be readily obtained, provided the remaining parameters of the system, including the sensitivity factor S are h o w n or can be determined, Such evaluations have been done with n-Si wafers in contact with ammonium fluoride solutions of different concentrations? With a thin

Pigure 30. (51)Me.m.d PMC-ptaM and zpr-potenialcurves for n-6 in contact with a 0.2MNH@soluti~1aixl(b)s,kpand&bp,vahac b l a t d as afunctiw of&Um& potential.

Microwave (Photo)eledmchemistry

487

interfacial oxide layer present on Si in contact with a 0.2 M W F solution, a pronounced PMC peak is identified near the onset of the photocurrent curve in the depletion region [Fig. 30(a)]. In Fig. 30(b) the potentialdependent surface recombination rate s, and the interfacial charge transfer rate k, as well as the potential-dependent surface concentration of minority carriers Ap, are shown. It should be pointed out that the indicated values are quantitative values, which could be measured because of the experimental determination of the sensitivity factor S. As expected, s, strongly decays with increasing potential, while the surface concentration of holes, bg,, stays nearly constant in the region oflimiting photocurrent. However, it is not exactly constant. It decreases slightly while the charge-transfer rate increases, so that their product yields a constant limiting photocurrent according to relation (11). Following the same procedure, the kinetic constants have been determined for very different electrochemical conditions. When n-WSe2 electrodes are compared in contact with different redox systems it is, for example, found9 that no PMC peak is measured in the presence of 0.1 M KI, but a clear peak occurs in presence of 0.1 M &[Fe(CN)6], which is known to be a less efficient electron donor for this electrode in liquid junction solar cells. When K4[Fe(CN)6] is replaced by K3[Fc(CN)6],its oxidized form, a large shoulder is found, indicating that minority carriers cannot react efficiently at the semiconductor/electrolyte junction (Fig. 31). Interesting results have also been obtained with light-induced oscillations of silicon in contact with ammonium fluoride solutions. The quantum efficiency was found to oscillate complementarity with the PMC signal. The calculated surface recombination rate also oscillated complementarily with the charge transfer rate.27J8The explanation was a periodically oscillating silicon oxide surface layer. Because of a periodically changing space charge layer, the situation turned out to be nevertheless relatively complicated. These results clearly show that microwave electrochemical techniques are providing valuable new insights into the lunetics of relevant interfacial mechanisms.

8. Accumulation Region It is well known that photoelectrochemical measurements do not indicate photocurrents in the accumulation region of an illuminated semiconductor. The reason is that majority carriers control interfacial reactions, which

Fpe31. PMCpotmtial~~r~esindepMon~jegion~for mn-W~eh&incmtact with0.1 MQO.1 M w a

and 0.1 M Km-. are so abundant that their concentration cannot be changed significantly through illumination. The exms minority carriers that are generated, on the otherhand, are: pulled into the interior of the semiconductor electrode, where they are lost through recombhation with majority carriers.

Photoinducd microwave conductivity measurements obviously allow the measurement of minority carriers in the accumulationregion (Fig. 17). In fact, both charge carriers are measured simultaneously since the PMC signal can k assumed to be proportional to the photoinduced conductivity change (This condition is fulfilled when the microwave field is not significantly attenuated within the illuminated layer.)

I&.

This means that the minority carriers are measured, however 'Tormally," with an effectively changed motnhty, which also includes the mobility of photogenerated majority carriers. The potentid-dependent behavior of minority carriers in the accumulation region has up ta now not been accessible to electrochemistry.


489

Therefore, no experimentalknowledge is available on interfacial reaction mechanisms under such conditions. These now become accessible via PMC measurements. As theory shows [Fig. 13(b)],the PMC signals in the accumulation region are controlled by potential-dependent surface recombination and charge-transfer rates, as well as by the bulk lifetime of charge carriers. It is not yet clear how useful information on minority carriers in the accumulation region will become in practice. Two interesting applications may be suggested here, where information on minority carriers in the accumulation region may be of special interest. One is the mechanism of photoinduced insertion into and passage of protons through a pynte layer (via cathodic insertion and diffusion as hydrogen). Photogenerated minorThe ity carriers are found to support insertion of adsorbed hydrogen.29.30 other example is the separation of surface recombination from bulk recombination through electropassivation of silicon (by applying a negative potential to an n-type electrode). The field applied in the accumulation region forces minority carriers to diffuse into the interior of the semiconductor, suppressing surface recombination. An important aspect ofthe increase in the PMC signal toward negative potentials of n-type semiconductor electrodes is that the surface recombination process of charge carriers is gradually neutralized. The minority carriers increasingly drift into the interior of the electrode, where they are subject to recombination with majority carriers. An increasingly effective bulk lifetime of charge carriers therefore also increases the PMC signal, which has been confirmed by computer simulation (Fig. 13) and by solving the transport equation by introducing simplifications. Toward increasingly negative potentials, however, an additional potential drop may also occur as a consequence of the passage of a high dark current. The result is that minority carriers will diffuse faster into the interior, thus flattening their concentration profile and transporting them (in the case of thin layers or wafers) faster to the back contact, where they may be lost through recombination. Such aprocess is significant in the case of silicon, where large diffusion lengths prevail. The PMC peak in the accumulation region is significantly lower for thin wavers than for thicker ones or ones in which the back surface has been passivated. When large dark currents are not passing through the electrode in the accumulation region, other phenomena may account for the decrease of the PMC signal toward higher negative potentials. For example, new tunneling possibilities may arise owing to strong energy band bending and lead to recombination processes.

490

H. Tributsch

It has been observed that the amplitude or presence of a PMC peak in the accumulation region is also dependent on the nature of the electrolyte.12 ZnO in the presence of an aqueous electrolyte shows a photoinduced PMC peak in the depletion region only at positive potentials. No accumulation peak is seen up to -2V (vs. a saturated sulfate electrode). When an organic electrolyte (propylene carbonate with ferrocene) is used, the PMC signal also appears in the accumulation region. Adding small amounts of water to the propylene carbonate again causes the PMC signal to disappear. The reason for this behavior may be a drastically changing interfacial charge-transferrate constant. As shown in the numerical simulation in Fig. 13, the PMC peak in the accumulation region indeed decreases with increasing interfacial recombination and charge-transfer rate constants, which leads to a disappearance of minority carriers. Since minority carriers themselves do not react electrochemically at such negative potentials, it must be the majority carriers that react. These react well with protons but not with (reduced) ferrocene. Since the measurement of positive and negative carriers is linked in the PMC measurement [compare relation (30)],and the imposed electrode neutrality has to be maintained, the disappearance of an electron at the interface will lead to the extraction of a positive charge at the back contact. The total PMC signal will therefore decrease. On the other hand, when the electron transfer is suppressed, both excess electrons and holes will stay in the electrode. The accumulation of excess electrons in the interface will, however, push excess holes into the interior, thus keeping the PMC signal large. This may happen at a ZnO/interface in contact with propylene carbonate and ferrocene. We conclude that the interfacial kinetics of excess majority carriers control the PMC signal in the accumulation region, while it is the minority carriers, as we have seen, that control the PMC signal in the depletion region.

9. Influence of Surface Recombination on the PMC Signal Surface recombination processes of charge carriers are mechanisms that cannot easily be separated from real semiconductor interfaces. Only a few semiconductor surfaces can be passivated to such an extent as to permit suppression of surface recombination (e.g., Si with optimized oxide or nitride layers). A pronounced dip is typically seen between the potentialdependent PMC curve in the accumulation region and the photocurrent potential curve (e.g., Fig. 29). This dip may be partially caused by a surface

-1.0

-0.8

-4.8

4.4

42

Figure 32. Shapea of PMCcmes and pholmmnt curves in a p*n junction f d from an n-type material by allowing in-diffusion ofan ampfor (bomn). The abmu of interface states (s, = O) genea s t m g overlappihg of the two curves.

recombmation that is high at the flatband potential and that strongly decays with increasing band bending. In order to visualize the effect of surface recombination, PMC and photocurrent curves are compared for a p+n junction30(Fig. 32). This was adetectorjunction in which a 240pm thick n-type Si layer was superficially (1 pm)highly doped (1020 cmU3) with boron. It does not have a phase boundary coinciding with a real interface and therefore has no interface recombination Is,= 0). As a result a very large effective charge-transfer rate (kr2 cm a-'1. It can be seen that the PMC and photmurrent curves strongly ovaIap. The intersection should correspond to the potential where the energy bands of the n-type silicon layer are flat.

10. QuantitativeDats from PMC Meanrrements: The sensitivity Factor The theoretically derived formula (21) relating PMC measurements to the surface concentration of minority &ers and interfacial rate constants contains a proportionality constant, S,the sensitivity factor. This factor depends on both the conductivity distribution in the semiconductor elec-

492

H. Tributsch

trode and the geometry of the cell, as well as the experimental environment. It is illusory to try to calculate it exactly. Therefore it must be determined experimentally. This can be done by making well-defined changes in the PMC signal of the sample, measuring the corresponding PMC signals, and calculating the sensitivity factor by quantitatively considering the imposed differences. For an electrode with high interfacial rate constants, for example, relation (28) can be plotted, which yields the flatband potential. It allows determination of the constant C, from which the sensitivity factor S can be calculated when the diffusion constant D, the absorption coefficient a, the diffusion length L, and the incident photon density lo (corrected for reflection) are known:

Another way to determine the sensitivity factor consists in determining the difference between the PMC minimum (flatband potential) and the PMC maximum in the accumulation region (the infinite and negligible surface recombination rate). This difference can be calculated to be17

The diffusion length can thus be calculated since a is typically known, or since L = ( r f l ) l R , the bulk lifetime rb, provided the diffusion coefficient D for minority carriers in the material is known. The sensitivity factor can be determined from the maximum or minimum PMC signal. Using the minimum PMC signal at the flatband potential (&# = 0, W = O),we derive from Equation (21).

it follows that


493

This is a relation in which PMC@, the photoinduced microwave conductivity signal at the flatband potential, is measured and the rest of the constants are known. Other situations may also occur that allow a simple determination of the sensitivity factor. When, for example, a sufficiently negative electrode potential forces all minority carriers to drift into the interior of the semiconductor electrode, where they recombine subject to the bulk lifetime rb, we will see a limiting PMC signal (given a sufficiently thick electrode). Knowing the photon flux I. (corrected for reflection), we may expect the following formula to hold:

from which the sensitivity factor S can readily be determined when measuring the limiting PMC signal and inserting the other solid-state parameters. Other ways to determine the sensitivity factor S are possible, for example, by comparing microwave reflectance and admittance responses in a potential region with ideal junction behavior."'

V. POTENTIAL-DEPENDENT TIME-RESOLVED MEASUREMENTS 1. Experience with TimeDependent Measurements Time-resolved microwave conductivity measurements have a long history and have, as a contact-free technique, successfully been applied to dry semiconducting crystals, layers, and powders. 2,32-35 It is well established that both bulk properties (bulk lifetime, defects, deviations from stoichometry, carrier mobilities) and surface properties (surface states, adsorbed molecules, surface roughness) affect the hnetics of PMC transients. More detailed information can be obtained by performing transient measurements under systematically varying conditions. Possibilities are excitation at different wavelength, at different excitation density, at different temperatures, and under bias illumination (which may change the band bending).36 Taking titanium dioxide as an example, we may mention that PMC transients decay rapidly in therutile phase (lo4 s) and much slower in the (catalytically more active) anatase phase (1r2-1 s).)' When a Ti02

494

H. Tributsch

powder (Degussa P25) that contains both phases is illuminated with a 20-ns laser flash (266 nm), a complicated PMC decay is seen on a logarithmic time scale, with 10% of the charge carriers living up to 10-I s.35When the powder is moistened with 2-propanol, 30% of the charge carriers live for 1 s. However, after treatment with tetranitromethane (which is able to act as an electron donor), the transients become significantly faster, with most charge carriers disappearing within lW7s and few surviving to 10'~s. Even though interesting qualitative information can be drawn from such contact-free measurements, microwave photoelectrochemical studies suggest that the interpretation of such transients is not straightforward. PMC signals depend on the bending of energy bands (that is, the effective field present in the space charge region of the interphase). Chemical

species, when adsorbing to the interphase, may affect the band bending and this may also change during the recombination of charge carriers after flash excitation of the samples (which, when strong, may temporarily flatten the energy bands). Bias illumination of the semiconductor sample to flatten energy bands may be of only qualitative help, since the band bending of uncontacted samples is typically unknown as is the effect of light intensity on the rebending of energy bands (which will depend on interfacial recombination rates). It makes scientific sense to test these considerations and to try well-defined potential-dependent PMC measurements with semiconductor electrodes. The fact that a potential-dependent lifetime peak for PMC transients has been found which coincides with the stationary PMC peak in the depletion region near the onset of photocurrents Fig. 22) is very relevant since the stationary PMC peak is determined by the interfacial rate constants of charge carriers (Figs. 13 and 14); this should also be the case for the transient PMC peak. To demonstratethis correlation, the following formalism can be developedlO: When a turnover of minority carriers is assumed to take place only at the electrode/electrolyteinterface (which is reasonable), the time-dependent change in the integral of minority carriers rAp(x, f)dr can be expressed

as


495

which means that the integral over all minority carriers decreases proportionally to the surface concentration of minority carriers with the sum of surface recombination rate and interfacial charge transfer rate as a proportionality factor. Substituting for the integral over the charge carriers (21) the expression derived for slow interfacial charge turnover (22) and ~ but dimensionapproximately setting @(All) = 0.08 I / ( A u ) ' ~ ( A u ~volts, less, since @(Am is a dimensionless function) (10) W

Jmx)dr =A ~ ~ ~ ~ W ( A = OL I. )O

B ~ ~ ~ ~ ~ ~ ~ (37) A L I ) - ~ ~

0

and solving the resulting equation yields

which describes an exponentially decaying PMC signal with a decay time of (AUagain introduced in volts but assumed dimensionless)

This lifetime for PMC transients results, as indicated, with moderately fast or slow interfacial charge turnover. It is determined not only by the interfacial rate constants k, and s, which consume the minority carriers, but also by the electrical field in the space charge layer as determined by the bending of the energy bands AU = U - Ufi, and by solid-state parameters as contained in the Debye length Ld(such as eand ND).This conclusion should equally be true for transient PMC measurements of semiconducting powders (the surface of which, in contact with air, is typically covered by a very thin water layer). Additional information (on the band-bending AU,on Ld and on the relative contribution of k, and s,) is necessary to interpret the transient PMC signal in terms of a specific rate constant. T h s may be obtained by changing the exciting or bias light intensity (change of AU) or changing the concentration of a redox species (affecting k,). With electrochemically studied semiconductor samples, the evaluation of t [relation (3911 would be more straightforward. AU could be increased in a well-defined way, so that the suppression of surface recombination could be expected. Provided the Debye length of the material is known, the interfacial charge-transfer rate and the surface recombination

H. Tributsch

496

rate could be determined, based on only two transient measurements at different electrode potentials. It is important to note that there may be at least two reasons for obtaining deviations from a purely exponential behavior for a PMC transient. These are a too high excess carrier generation, which may cause interfacial rate constants that are dependent on carrier concentration, and an interfacial band bending AU,which changes during and after the flash. For fast charge transfer, a more complicated differential equation has to be solved. It is interesting to note that independent, dlrect calculations of the PMC transients by Ramakrishna and Rangarajan (the time-dependent generation term considered in the transport equation and solved by Laplace transformation) have yielded an analogous inverse root dependence of the PMC transient lifetime on the electrode potential.37This shows that our simple derivation from stationary equations is sufficiently reliable. It is interesting that these authors do not discuss a lifetime maximum for their formula, such as that observed near the onset of photocurrents (Fig. 22). Their complicated formula may still contain this information for certain parameter constellations, but it is applicable only for moderate flash intensities. How can we demonstrate that microwave transients qualitatively follow the potential-dependent stationary PMC signals? We have seen that the PMC signal is dependent on the interfacial rate constants (k,+ s,). Assuming a slow interfacial charge turnover [Eq. (18) with only the first term, multiplied by Aps,being relevant] and a potential sufficiently positive from the flatband potential so that exp (AUdk7) can be neglected, we can substitute (k, + s,) into the formula describing the transient lifetime (39) and obtain (for the depletion region) -t=

PMC

This relation shows that the lifetime of PMC transients indeed follows the potential dependence of the stationary PMC signal as found in the experiment shown in Fig. 22. However, the lifetime decreases with increasingly positive electrode potential. This decrease with increasing positive potentials may be understood intuitively: the higher the minority carrier extraction (via the photocurrent), the shorter the effective lifetime


497

measured. With increasing light intensity I. in the denominator of (40), the lifetime should also decrease. However, the measured PMC signal simultaneously increases in the numerator according to (18), that is, it is proportional to Id(k,+ s, + ...).If the charge-transfer or surface recombination rate remain constant, r should not change with light intensity. If the surface recombination rate increases with light intensity, the PMC signal should increase slower than proportionally with the light intensity (which is typically observed). This may explain why the lifetime peak in the depletion region of ZnO (Fig. 22) decreases with light intensity and is seen only with the low light intensities of exciting laser pulses. The real situation, however may be more complicated. A comparison of the frequency dependence of photocurrents and PMC signals, measured with WSe2electrodes in contact with an aqueous FC-electrolyte, shows that the size and position ofPMC peaks change with the pulsing frequency of excess carrier generation (Fig. 23). Obviously, at higher light chopping frequencies, the kinetics at the interface are effectively improved, since fewer minority carriers are dammed up at the interface. This indicates that the kinetic constants entering into relation (18) may be frequency dependent. In other words, the minority carrier profiles in the space charge layer should be dependent on the frequency of periodic excitation of excess charge carriers. Such behavior is not unusual for electrode/electrolyte interfaces. Periodically excited currents often show a decreased interfacial resistance (which is not seen for the photocurrent in Fig. 23 because of the limiting current behavior, which allows all minority charge carriers to reach and cross the interface).

2. Control of Interfacial Lifetime in Silicon with Polymer/Electrolyte Junction Equation (40) relates the lifetime of potential-dependent PMC transients to stationary PMC signals and thus interfacial rate constants [compare (18)l. In order to verify such a correlation and see whether the interfacial recombination rates can be controlled in the accumulation region via the applied electrode potentials, experiments with silicon/polymerjunc tions were performed.38 The selected polymer, poly(epich1orhydrine-coethylenoxide-co-allyl-glycylether, or technically (Hydrine-T), to which lithium perchlorate or potassium iodide were added as salt, should not chemically interact with silicon, but can provide a solid electrolyte contact able to polarize the silicon/electrode interface.

Figure 33. PMC lifehe map of n-type silicon wafer contactedwith a polymer elmtmlyte @ o l y ( e p i c b l o r h ~ y l e n ~ d y l - g l y c y 1 e t h e witb r } lithium perchtorate) at 0 V at -5 V (cathodic polari&on) m m m d against a counterelect& (also in contact with the polymer electrolyte). The diagrams show (a) ari average lifetime for charge carriers of l 0 c s b e k (statistical distriiutim), and Co) a (wbite) overfIowwith an average lifetime of aNS after applying a negstive potential of -5 V,It can be seen that the polymer contact is not homogeneous (the polymer shrinks during drying). For color versions please see color plates opposite p. 453.


499

When an n-type silicon wafer is placed in contact with such a Hydrine-T polymer layer containing lithium perchlorate in a cell forming a sandwich with a thin IT0 layer on glass, a space-resolved microwave transient measurement can be made with the technique described in Fig. 6 and demonstrated with the example ofFig. 7. The spatial distribution of lifetime over an area of 5 x 5 mm is shown in Fig. 33(a) for the case when zero voltage is applied between silicon and the IT0 contact layer, separated by a polymer electrolyte. In the plot of the statistical lifetime distribution shown to the right, apeak lifetime of lops can be seen. Figure 33(b) shows the situation when a potential of -5 V (accumulation) is applied to the silicon electrode with respect to the IT0 electrode. The distribution of lifetimes shows that the peak has broadened and reached a maximum of 22 ps, while a significant fraction of points (5%) have reached a lifetime near 60 ps (white areas, lifetime measured independently). The fact that high PMC lifetimes of 60ps are reached only within restricted areas [the white patches in Fig. 33(b)] may be due to a trivial problem, an inhomogeneous contact between the polymer and the silicon wafer caused by the shrinking of the polymer during the drying process. The polymer layer of several tenths of a millimeter produces a significant resistance loss for the passing current, so that only a small fraction of the applied potential effectively drops at the silicon/polymer junction. At a total potential of -10 V, Lit ions start reacting with the silicon. The consequence is a significant drop in the PMC lifetime for photogenerated charge carriers. As Fig. 34 shows, nearly 50% of the sficon surface loses its photoconductivity, indicating that a solid-state chemical reaction has occurred in the semiconductor surface. This does not happen when Li perchlorate is replaced by the redox system KV12.In this case, only electrons can be transferred across the Si/electrolyte interface. When potential-dependent measurements are performed for a selected spot on the sample, a PMC lifetime-potential dependence is obtained, which is reproducible but during cycling shows aclear hysteresis (Fig. 35). A marked shoulder is seen in the negative potential region (the accumulation region of n-Si), a minimum at the flatband potential of Si, and a pronounced peak in the depletion region. This peak is absent during a sweep toward negative potentials, indicating that iodide oxidation affects the interface, increasing interfacial rate constants. With the exception of the larger potential range (owing to the significant potential drop in the polymer layer), this PMC lifetime-potential curve has a shape similar to

Figure 34 PMC lifetime map of n-type siliwdplymer ( p l y ( e p i c h l 0 r h y ~ ethyl&Myl-glycyle&erplus Wide)j d o n at -10 V potential ( m d y dropping acmsstheplymerlayes),after~i+~has ~ t h e s i l i o o n i n t e $ a c e'I.he W c a l evaluation shows the W c drop in hPMC lifethe. Fos cdar vmiw please see mlor m m p 453,

35. Dynamic change oflifethe in an n - t y p e s i l i ~ l y -

=( P O ~ Y ~ W ~ W ~ W ~ Y ~ - ~ ~ F Y *

p l u s i 0 d i d e ) j r m C t i o n ~ r t ~ t i aTlh~e. m s h o w the Wonofsweep @25 V #-'x A shddahthe accmda

tionregimmdaplcinthe~~region0f~~cZearfy seen.


501

that of stationary theoretical and experimental PMC-potential curves (Figs. 13, 16, 17, 22, 30). This shows that potential-dependent PMC structures are at least in part due to potential-dependent changes in the lifetimes of minority charge carriers. These results also demonstrate that the relation found between potential-dependent PMC transient lifetimes and the stationary potential-dependent PMC signal [relation (40)] is basically correct. Two transients, measured at 0 V and -5 V with a s~conlpolymer junction, are shown in Fig. 36. They clearly show the effect of a negative electrical field on recombination processes. Minority carriers are apparently pulled by the negative electrical field into the interior of the Si electrode, where they recombine with an effectively longer lifetime. Since silicon has a very large diffusion length for charge carriers, they can diffuse through the 200-pm-thick Si wafer; most of them recombine at the back side, which thus limits their lifetime. Both silicon surfaces, the front and the back side, must be electropassivated (polarized to accumulation) to force charge carriers to survive to the bulk lifetime. 3. Potential-Dependent Measurements with Organic Electrolytes

Time-resolved, potential-dependent PMC measurements have also been performed with silicon in contact with propylene carbonate containing 0.1 M TBAP and 1 rnM ferr~cene.".~~ Both signal amplitudes and the lifetimes of transients excited by laser pulses (532 nm) are shown in Fig. 37 in dependence on the electrode potential. Both curves show a clear minimum at the flatband potential. This indicates that surface recombination plays a significant role under such conditions and that the applied electricalpotential definitely controls the lifetime of charge carriers. These results again confirm that the derived relation (40) between transient lifetime and the PMC signal (controlled by interfacial rate constants) indeed exists. The laser excitation (532 nm) occurred with a 10-ns flash, while the transients were measured in the 20-100-11s time region. The PMC transients measured are much faster than the RC time constant of the electrodelelectrolyte system and, since they are controlled by kinetic constants, will provide access to fast charge-transfer mechanisms at semiconductorlelectrolyte interfaces. It is interesting that the flatband minimum of the amplitudes of PMC transients [Fig. 37(a)] is much less pronounced when a longer excitation

Figure 36. Microwave conductivity transients of an n-type siliconlpolymer @oly(epichlorhydtine-co-ethyleaoxi~ally1-g1ycy1& plus i d ) j d o n at 0 and -5v.

wavelength (A= 1064 nm)is used,which allows the light to penetrate much deeper into me semiconductor materials." Under such conditions, more charge carriers are generated inside the semiconductor and surface recorn bination kcoms less important,


I

amplitude

532 nm

electrode potential/ V Apre 37. Potential dependence of (a) amplitudes and (b) lifetimes of laser-indud PMC transients (532 run) of silicon in contact with propylene carbonate conraining 0.1 M TBAP and lrriM f m n e (flatband at -05 V),

4, A m s to Kinetic Constants via PMC Transients

The PMC transient-potential diagrams and the equations derived for PMC transients clearly show that bending af an energy band significantly influences the charge carrier lifetime in semiconductor/el8~trolyte junctions and that an accurate interpretation of the kinetic meaning of such transients is only possible when the band bending is known and contsolled.

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Otherwise, the effect of electrode potential and lunetic parameters as contained in the relevant expression for the PMC signal (21), which controls the lifetime of PMC transients (40), may lead to an erroneous interpretation of kinetic mechanisms. The fact that lifetime measurements of PMC transients largely match the pattern of PMC-potential curves, showing peaks in accumulation and depletion of the semiconductor electrode and a minimum at the flatband potential [Figs. 13, 16-18, 34, and 36(b)], demonstrates that kinetic constants are accessible via PMC transient measurements, as indicated by the simplified relation (40) derived for the depletion layer of an n-type electrode. The fastest reliable PMC transients recorded at electrodes (ZnO single crystals24)were limited by the lifetime of a l@ns laser flash. It was apparent from the nondeconvoluted signal at shorter time scales that much faster decay processes took place and would be accessible with faster laser pulses. It is a significant challenge to study kinetic mechanisms of charge carriers at electrodes with much faster time constants (ns- to ps-range), since such mechanisms are typically buried in RC-limited electrochemical decay processes. Only special experimental procedures (e.g., discharging the electrode via a very high resistance, measuring the developing photopotential, and modeling the transient^^^) gives partial access to fast electrode processes (mostly recombination processes within the electrode material). Typically, individual interfacial rate constants are not obtained since they cannot be separated (being, for example, ratios of individual rate constants). As mentioned at the beginning of this chapter, the time resolution for the measurement of PMC transients (2840 Gclps) should be expected to be in the range of 25 ps. If we assume a picosecond flash of photons to generate charge carrier pairs in an electrochemically polarized n-type semiconductor/electrolyte junction, these charge carriers will start reacting, but only the contribution of minority carriers will significantly influence the kinetic equilibrium at the semiconductor/electrolyte interface. The majority carriers will, via the external circuit, immediately start to recharge the interface. However, this process will be much slower than the time needed for the (independent and contact-free) PMC transient measurement. The photogenerated minority carriers will reach the electrode interface with a thermal velocity of approximately 10' cm s-', which is a picosecond process. Afterward, surface recombination and charge transfer kinetics will determine their

Microwave (Photo)el~hemistrg

consumption. Such pmmm should therefore be measurable on a fast time scale and in a potential-dependent manner. Som precautions will be Ileeded for successful measmments, The shorter the time scale the higher the photon densities that will k required. This leads to very high generation of excess charge &en ancl to nonlinear phenomena of a complicated nature. How can such problems be counterbalanced? Since a large capacitance of a se1niconductorlelect101ytejunction will not negatively affect the PMC transient measurement, a Iarge area electrode (nanos~ructuredmaterials) should be selected to decrease the effective excess charge carrier concentmtion (excess carriers per surface area) in the interface. PMC transient measurements have been performal at a sensitized nanostructurd liquidjunction solar cellPoWith a l@mlaser pulse excitation, only the slow daay processes can be studied. The very fast rise time cannot be resolved, but this should be the aim of p i m n d studies. Such experiments are being prepared in our laboratory,but using nanostructured

Fqpre 38 Decay d ~ ~ i emaswed a t wi ~tha 1P0,bwed n m ~ m h h d tionsolar cell (mtheniumsomplexas msitizain thepwwecfQ1MTBAPinpropylene dmate).~hs~ransientsares@~~a & c t e d b y ~ ~ c b ~ 4 0 ( e ) m ~ . ( b ) 2 m~ re(c)w m~ r,(4am s.

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ZnO instead of TiOz because ZnO provides a 220 times higher mobility for photoinjected electrons, which would allow reduction of the exciting laser intensity. The slow PMC decay of Tiorbased nanostructured sensitization solar cells (the Ru complex as sensitizer), which cannot be matched by a single exponential curve and is influenced by a bias illumination, is strongly affected by the concentration of iodide in the electrolyte (Fig. 38). On the basis of PMC transients and their dependence on the iodide concentration, a kinetic mechanism for the reaction of photoinjected electrons could be elab~rated.~' On the basis of our theoretical considerations and preliminary experimental work, it is hoped that fast processes of charge carriers will become directly measurable in functioning photoelectrochemical cells, Typical semiconductor electrodes are not the only systems accessible to potentialdependent microwave transient measurements. This technique may also be applied to the interfacial processes of semimetals (metals with energy gaps) or thin oxide or sulfide layers on ordinary metal electrodes. VI. POTENTIAL-DEPENDENT PERIODIC MEASUREMENTS 1. Potential Modulation-Induced Microwave Reflectivity It was indicated earlier that microwave conductivity-potential curves can be obtained not only during a dynamic potential scan (Fig. 11) but also in phase with periodic potential modulations. These potential modulations give rise to MC changes that reflect changes in electronic charges in the space charge region of the semiconductor. Such potential-modulated signals can be obtained both in the dark and under illumination, as shown in Fig. 39, where such measurements are presented for WS* in contact with a redox electrolyte.25A full theoretical analysis of this technique and its possibilities has still to be given. An interesting special application has been proposed by Schlichthorl and It aims at deconvolution of electrochemical impedance data to separate space charge and surface capacitance contributions. The method relies on detection of the conductivity change in the semiconductor associated with the depletion of majority carriers in the space charge region via potential-modulated microwave reflectivity measurements. The electrode samples were n-Si(ll1) in contact with fluoride solution.

Microwave ~oto)ele&&emii;try

Figme 39. P O W - m d u l a t e d(daived) microm'econductivity andwtiaI-

and(b)ill~n-~~incrmtactwitha50mM e l d y t e solution.

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Since under normal depletion conditions, conductivity changes are dominated by majority carriers, and interfacial electron transfer can be neglected in the dark, the carrier profile can be found by solving Poisson's equation:

where d is the thickness of the electrode sample. A linear expansion of this equation for a small-amplitude potential modulation, SU,leads to the microwave reflectivity change

which, when the space charge capacitance is inserted, leads to

This formula shows a linear relation between the microwave conductivity change AMC and the space charge capacitance C,. If energy band unpinning can be neglected, the potential-modulated MC signals follow the capacitance of the space charge layer. Good Mott-Schottky behavior is therefore found for potential-modulatedMC signals, even in presence of surface states.31A1The flatband potential can thus be conveniently determined and the energetic distribution of surface states deconvoluted using both MC and electrical capacitance measurements. 2. Combination of Intensity-Modulated Photocurrent and Microwave Spectroscopy Relaxations in photoprocesses, which may be due to surface recombination, minority carrier diffusion, or capacitive discharges, are typically measured as transients of photocurrents or photoprocesses. An analysis of such processes in the time domain encounters some inherent problems. Therefore intensity-modulated photocurrent Spectroscopy has been developed by Peter and co-workers as a tool for the analysis of photocurrent responses in the frequency d ~ m a i n . l 'An > ~ ~optoacoustic coupler is


509

used to generate a sinusoidally modulated light intensity. This technique is based upon transformation of both the perturbing function and the transient response into the frequency domain. Such transformations can be performed by both Fourier and Laplace transformations. A photocurrent transient f(t) may, for example, be transformed into the Laplace space

where s is the Laplace frequency (s = a +jo).The real axis transform is obtained by substituting s = a and the imaginary axis by substituting s = jw. Complex plane plots of the transformed data can be made and interpreted. Surface recombination has been studied in such systems as Gap and GaAs under conditions of fixed-band bending. The frequency domain studied was 1 Hz to 50 H z . At higher frequencies, the relaxation of the space charge-layer capacitance with the frequency at the imaginary minimum corresponding to (R,c,)-' is found (R, is the series resistance and C, is the space charge-layer capacitance).44 Intensity-modulated photocurrent spectroscopy has been used in combination with microwave reflectivity measurements to investigate hydrogen evolution at a p-type silicon45 and an n-type silicon.46The measurement of amplitude and phase under harmonic generation ofexcess carriers, performed by ~ t a r e d i a non ~ ~silicon wafers in an attempt to separate bulk and surface recombination, should also be mentioned here. In contrast to photocurrent measurements, photoinduced microwave conductivity measurements are not limited by RC time constants. Using sufficiently high-frequency excitation sources (laser diodes or optoacoustic modulators), it should be possible to explore much faster time or higher frequency domains. This is an interesting challenge since fast electrode processes are typically obscured by the trivial RC time constant for capacitive discharge (see, however, Ref. 39 for a strategy to overcome the RCproblem). When intensity-modulatedphotocurrents and PMC signals are evaluated in the time domain, and characteristic values (e.g., the maximum frequency) measured, the corresponding mathematical formula (containing kinetic parameters) can be solved, yielding more information than one technique alone.

H. Tributsch

VII. OXIDES AND SENSITIZATION CELLS 1. Potential Dependence of Interfacial Rate Constants ZnO was the first photoactive electrode in contact with an electrolyte to be studied by PMC techniques.5 The PMC peak in the depletion region near the onset of the anodic photocurrent [originally measured in a cavity (Fig. 40)] has been perfectly reproduced with a geometrically much simpler setup for microwave measurements (Fig. 16). In these measurements the PMC peak turned out to be quite narrow, in contrast to theoretical PMC peaks or PMC peaks obtained with other serniconductor/electrolytejunctions (Figs. 13,14,16,18).The most evident difference between a theoretical PMC peak and the PMC peak of a ZnO electrode/electrolyte junction is the much faster decay of the signal toward higher positive electrode potentials. This decay is, as we learned, determined by the @(All) function, which describes the potential-dependent profile of the charge carrier distribution in the space charge layer. This profile somehow changes with the electrode potential in a different way than that calculated for constant interfacial charge-transfer rates. The reason has recently been examined.12Equation (24) relates (for an already sufficiently low surface recombination s,) the PMC signal to the photocurrent Iphr the charge-transferrate constant, k, and @(All). It can be rewritten to yield

Since the potential-dependent photocurrent and the potential-dependent PMC signal were measured and @(All) is a known function, the potential-dependent interfacial rate constant k, can be determined. It turns out that it increases exponentially with the electrode potential applied

which accounts for the fast decay of the PMC signal toward an increasingly positive potential. The explanation of this surprising result is not straightforward, but can be narrowed down on the basis ofthe experiments performed. ZnO is a large-gap semiconductor (AE,=3.2 eV) that during UV excitation can photo-oxidize water to molecular oxygen but also photocorrodes during this process. Part of the oxygen released during the

Microwave (Phot0)electrochemistry

photoreaction therefore comes from the ZnO-cry stal lattice. When ZnO is anodically polarized in the presence of aqueous solutions containing H2S0&KCl, or NaCOOH, as was dune in the experiments that led to the sharp PMC peak, a strong electrochemical interaction has to be assumed at the ZnOIelectrolyte interface during anodic elecfmn transfer. This may be the reason why the classic Marcuffierischer theory on isoenergetic interfacial electron transfer, which pred~ctsa largely potential-independent charge-transfer rate (no significant shift in the energy band position is expected), is not applicable. When an organic redox electrolyte is selected (propylene carbonate with femme), which is known to interact only weakly with an e l d e , the potential-dependent decay of the PMC signal of ZnO toward a higher e l d e potential is clearly slower12(even though it is not as slow as expected from the theory on the basis of &, =

const). It is interesting that in presence of an organic electrolyte, the PMC signal also increases toward negative potentials (Fig. 4 I).'~A shoulderis seen immediately negative from the flatband potential, which indicates that charge carriers in the accumulation region can be measured more

W p 40. PMC pe& dwith a ZnO siqbaystal e h m k in a mimwaw reswator near the onst of the a n dp h ~ m m n t . ~

F p 41. PMC potential curves for rr ZnO single crystalm m m d in contactwith prapylene d o n ate (0.1 M TBAP) mmhhg 10 mPIll ( m e I), d withhmdng concentmtions (5,10, ad 20%)of water (cum 24). IIIuminoltion with He.€dUVk,5mW.

accurately than in the presence of an aqueous electrolyte. Apparently, in the presence of an organic electrolyte and ofonly a reduced redox species (femne), excess charge &en have an increased lifetime in the e l e c W . The fact that electrons cannot easily escape from the elatmk may help to build up a larger negative charge in the interface, which may direct positive minority carriers toward the interior of the ekdde, generating larger lifetimes. This experiment seem to show how the PMC signal is influenced by the nature of the redox electroTyte. The reason for the exponential increase in the electron transfer rate with increasing electmk potentid at the ZnOlelectrolyte interface must be further explored, A possible explanation is provided in a recent study on water photoelectrolysis which describes the mechanism of water oxidation to molecular oxygen as one of strong molecular interaction with nonisoenergetic electron transfer subject to irreversible thermodynami c ~ . ~Under ' such conditions, the rate of electron transfer will depend on the thermodynamic force in the serniconductor/electrolyte interface to


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which the applied electrode ptentid may contribute. However, more trivial explanations should be consid& first. The involvement of a hypothetical potential-dependent concentration of surface states in water oxidation could also explain the phenomenon, as visualizsd in Fig. 42. This discussion has shown how useful PMC measurements are fur addressing new questions in semiconductor electrochemistry,

Marcus-Gerischer model

Figure 42. Scheme comparing expected potential-independent charge-transfer mtcs from Marcu&erischer theory of interfacia) electron transfer (left) with possible mechanisms for explaining the experimental observation of potential-dependent elemon-transfer rates (right): a potentialdependent concentration of surface states, or a charge-transfer rate &at depends on the thermodynamic force (electric potential difference) in the interface.

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2. Nanocrystalline Dye Sensitization Cell Studied by Microwave Transients

Up to now only preliminary PMC measurements have been performed with nanocrystalline sensitization solar cells based on Ti02,which has a very low electron mobility. In Fig. 38 we showed transient measurements performed with a 10-ns laser flash. A very fast rise time is observed which, as discussed earlier, may be resolved further only by picosecond excitation. The decay of the PMC signal is, on the other hand, sufficiently slow to be studied. It reflects the reverse reaction of injected conduction band electrons with the redox electrolyte. This can be clearly demonstrated by adding iodide to the electrolyte. This reducing species slows the reverse reaction significantly,which has been explained by a kinetic model.40This experiment shows that transient PMC measurements are suitable for the study of dye sensitizationcells and electrodes of nanocrystalline materials. However, high flash photon densities are needed to see these signals because of the low mobility of electrons in Ti02.Even though experiments made under such conditions can be interpreted, they limit information on potential-dependent behavior. One solution would be to use a much more sensitive resonator cavity for measurements on TiOTbased nanostructured sensitization solar cells. Another would be to concentrate research on nanostructured sensitization cells of ZnO-based substrates, which show an approximately 220 times higher electron mobility. Both strategies are being investigated in our laboratory. Preliminary measurements with space-resolved PMC techniques have shown that PMC images can be obtained from nanostructured dye sensitization cells. They showed a chaotic distribution of PMC intensities that indicate that local inhomogeneities in the preparation of the nanostructured layer affect photoinduced electron injection. A comparison of photocurrent maps taken at different electrode potentials with corresponding PMC maps promises new insight into the function of this unconventional solar cell type.

VIII. MICROWAVE PHASE MEASUREMENTS As mentioned at the beginning of t h s chapter real phase-sensitive measurements of electrochemical systems have not yet been performed. Not only is the experimental technique difficult, but a reliable theory of

Mimwave (PhotoMectbchemistry

microwave phase shift as a function of electmhemical parameters (electrical fields, surface states, photoeffects, electrolytes) is missmg. In analogy to electrochemical impedance measurements, where the thermodynamic force, the applied potential, is modulated to measure phase shifts, in mimswslve conductivity measurements the microwave power, P,which provides the microwave electrical field, has to be m d u lated to obtain phase shifts. The dependence of these phase shifts on the electrude potential and additional pamneters (e.g., light intensity) can then be determined. The field of phase-sensitive microwave photoelectrochemical measurements will have to be explored very gradually. In our Iaboratory up to now only a special case, phase rotation in a magnetic field (Faraday

rotation), has been investigated. It allows us to perform contact-free mobility measurements of electronic charge carriers. This may serve to determine the sign and mobility of photogenerated charge carriers ar the dependence of the mobility of charge carriers in nanostructured materials on particle size or electrical polarization. Measurements of a pyrite sample with atwo mode resonators6yielded the magnetic field dependence of microwave transmission (fig. 43) from

Fw43. Mimowave~mibatwu-m&resonatorasa function of the magdc h l d sue@ for mmmement of the microwave Hdl e m in pcSr (two mwmts with an offset diffmn~e).'~

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which electron mobilities of 272 cm2/V s and 277 cm2/V s (two measurements, one with offset) could be derived. An electrically contacted sample from the same batch using conventional Hall measurement gave a mobility of 280 cm2w s. More experience has to be gained before phase-sensitive measurements can be performed on the potential-dependence of electrochemical systems, especially because of the presence of an electrolyte. Such measurements may, as already mentioned, provide new information on a variety of questions relevant for electrochemical interfaces. The separation of photogenerated minority carriers and majority carriers, for example, which both contribute to the PMC signal, promises interesting new insights into the electrochemical lunetics of semiconducting interfaces. In particular, the understanding of the photoelectrochemical behavior in the accumulation region, which is accessible to PMC techniques and still unexplored, will require a separation of majority and minority carrier mechanisms. This will be possible through phase-sensitive PMC and MC measurements. IX. SUMMARY AND DISCUSSION In this chapter we have attempted to summarize and evaluate scientific information available in the relatively young field of microwave photoelectrochemistry. This discipline combines photoelectrochemical techniques with potential-dependent microwave conductivity measurements and succeeds in better characterizing the behavior of photoinduced charge carrier reactions in photoelectrochemical mechanisms. By combining photoelectrochemical measurements with microwave conductivity measurements, it is possible to obtain dlrect access to the measurement of interfacial rate constants. This is new for photoelectrochemistry and promises better insight into the mechanisms of photogenerated charge carriers in semiconductor electrodes. The schemes in Figs. 44 and 45 may serve to summarize the main results on photoinduced microwave conductivity in a semiconductor electrode (an n-type material is used as an example). Before a limiting photocusrent at positive potentials is reached, minority carriers tend to accumulate in the space charge layer pig .44(a)], producing a PMC peak pig. 45(a)], the shape and height of which are controlled by interfacial rate constants. Near the flatband potential, where surface recombination

is intensive, minority carriers are depleted, causing a pronounced minimum of the PMC signal (Fig. 45). In the accumulation region of the semiconductor at negative potentials, minority carriers tend to drift into the interior of the electrde and are controlled by the bulk recombination

Figwe 44. Energy scheme showing esmtial phenomena for phmixwaveconductivitymchmimx (a) h u m Won ofminoity &ers near the msa of@ommwio the depletionregion, (b)Driftofminority~ershtotb~wof a n ~ 0 1 1 P e g i o a , t h U s ~ s ~ ~ ~ m .

electrode pottntialN

Figure 45. (a) Schematic of PMC signal behavior in accumulation region (i), flatband region ($, and depletion region (iii) with (b) visualization d energy band situation of an n-type miconductor.

lifetime pig. 44(b)]. This produces a PMC shoulder, the height of which is controlled by the bulk lifetime of minority carriers and the shape of which is influenced by interfacial rate constants of the electronic charge carriers and the electric field distribution as affected by current flow. This complementary infomation on charge carriers, as provided by PMC measurement, added to photoe!ectrochernical information, based on a suitable theoretical formalism, is the key advantage ofmicrowave electrochemistry.


519

At present, the microwave electrochemical technique is still in its infancy and only exploits a portion of the experimental research possibilities that are provided by microwave technology. Much experience still has to be gained with the improvement of experimental cells for microwave studies and in the adjustment of the parameters that determine the sensitivity and reliability of microwave measurements. Many research possibilities are still unexplored, especially in the field of transient PMC measurements at semiconductor electrodes and in the application of phase-sensitive microwave conductivity measurements, which may be successfully combined with electrochemical impedance measurements for a more detailed exploration of surface states and representative electrical circuits of semiconductor liquid junctions. In the more distant future, integrated microwave circuits generating intensive microwave fields above a dielectric spiral may simply be attached as a thin slab to the back side of a semiconductor electrode for PMC measurements. By selecting the appropriate geometry and by choosing optimized geometrical forms for electrodes (ultrathin layers, nanostructured materials) many compounds that are not considered to be typical semiconductors may also become accessible for microwave conductivity studies; these include oxide layers on metal surfaces as well as photogenerated charge carriers in semimetals. Even the Helmholtz layer of liquid junctions may become accessible to potential-dependent microwave conductivity studies (contributions of ions and dipoles). Instead of modulating the light, the electrode potential can also be modulated and in this way photoinactive electrode materials can be investigated with microwave techniques. Since the time resolution for microwave experiments is on the order of 25 ps with the microwave frequencies used, very fast electrochemical processes will become accessible for investigation. The fact that microwave conductivity measurements can be performed in a contact-free manner allows us to use them for quality control during the production of photoactive powders or thin layers, or for electrochemical process technology. After the buildup of sufficient knowledge, microwave conductivity measurements themselves, independent of classic electrochemical information, may be used to obtain electrochemical information in cases where conventional techniques are not convenient or accessible. Such interesting prospects should not distract us from the fact that we still have to continue to build on the foundation of this research discipline. There is sufficient room for further improvement of electrochemical PMC

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theory, and some applications (e.g., phase-sensitive measurements as applied to electrochemical problems) still need a theoretical basis. Although it is still in a rudimentary stage of development, microwave electrochemistry has contributed some significant knowledge to semiconductor electrochemistry. Among the most interesting results is the detection of charge carrier accumulation in the depletion region near the onset of photocurrents, access to a quantitative determination of interfacial charge-transfer and recombination rates, the measurement of surface concentrations of minority carriers, access to the measurement of minority carriers in the accumulationregion of semiconductors (where typically no photocurrents are observed), and access to ultrafast photoelectrochemical mechanisms. Interesting information has also been obtained on the behavior of charge carriers within the space charge region as measured by the potential dependent decay of the PMC signal in the limiting photocurrent range. Microwave photoelectrochemistry has also provided a series of techniques for the measurement of electrode parameters (e.g., flatband potentials, diffusion lengths, energetic distribution of surface states) and may lead to reliable techniques for the separation of bulk and surface recombination lifetimes of minority carriers. When more experience is gained on microwave electrochemical phenomena, they could, for example, be used to characterize electrochemical systems in a contact-free way. The PMC signal alone could describe the system sufficiently for understanding its behavior. An interesting application would then be fast electrochemical sensors that, while implanted or separated by a glass diaphragm, could be scanned and evaluated without electrical contacts. It is hoped that additional research groups willj oin in the development of microwave electrochemistry. ACKNOWLEDGMENTS The author would like to acknowledge the valuable experimental and theoretical contributions of various collaborators during the development of the research technique described here. Among them are M. Kunst, D. Messer, G. Schlichthorl, D. Jokisch, F. Wiinsch, A. M. Chaparro, and H. Schulenburg. Additional thanks are due to Mr. D. Jokisch for his help in preparing the drawings and to Dr. F. Wiinsch for proofreading anddiscussing the manuscript.


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REFERENCES 1

J. L. Boone, M. D. Shaw, G. Cantwell, and W. C. Harsch, Rev. Sci. Instrum. 59 (1987) 591. 2 ~Jacobs, . F. R. Brand, J. D. Meindl, S. Weitz, R. Beniarnin, and D. A. Holmes, Proc. IEEE 51 (1963) 581. 3 M. P. DeHaas and J. M. Warman. Chem. Phvs. 73 (19821 35. 4 C. J. F. Biittcher and P. ~ordekijk, of~olarkation,Vol. 11. Dielectrics in Time-Dependent Fields, Vol. 18, Elsevier, Amsterdam, 1978. 5 R. Bogomolni, H. Tributsch, G. Petermann, and M. P. Klein, L Chem. Phys. 78(5) (1982) 157%2584. 6 ~Kunst . and H. Tributsch, Chem. Phys. Lett. 105(2) (1984) 1B126. 7 ~ Kunst, . G. Beck, and H. Tributsch, J. Electrochem. Soc. 131(1984) 954-956. 8 B. Messer and H. Tributsch, J. Electrochem. Soc. l33 (1986) 2212-2213. G. Schlichthorl and H. Tributsch, Electrochimica Acta 37(5) (1991) 919. 'OH. Tributsch, G. Schlichthiirl, and L. Elstner, Electrochim. Acta 38(1) (1993) 141-152. 11 F. Wiinsch, PhD Thesis, Dept. of Physics Technical University, Berlin, 1997. 12A.F. Chaparro and H. Tributsch, J. Phys. Chem. 101 (1997) 7428. l3 G. Beck and M. Kunst, Rev. Sci. Instrum. 57 (1986) 197. l4 H. Tributsch, G. Beck, and M. Kunst, European Patent, EP 01 55 225 B 1 (1991). l5 G. Schlichthiirl, G. Beck, J. Lilie, and H. Tributsch, Rev. Sci. Instrum. 60(9) (1989) 2992. 1 6 ~ Schrape, . M. P. Klein, M. Kunst, and H. Tributsch, Rev. Sci.Instrum. (submitted). l7 G. Schlichthiirl, PhD Thesis, Dept, of Chemistry, Freie University of Berlin, 1992. la W. W. G i e r , Phys. Rev. 116 (1959) 84. 1 9 ~J..Reiss, J Electrochem. Soc. 125 (1978) 937. 2 0 ~ H. . Wilson, J. Appl. Phys. 48 (1977) 4292. 2 1 ~Wunsch, . Y. Nakato, M. Kunst, andH. Tributsch, J. Chem. Soc., Faraday Trans. 92(20) (1996) 40534059. 2 2 ~M.. Chaparro, K. Ellmer, and H. Tributsch, Electrochim Acta 44 (1999) 1655. 2 3 ~Messer . and H. Tributsch, Chem. Phys. Lett. 142(6) (1987) 546-550. 24 F. Wiinsch and H. Tributsch (to be published). 2 5 ~ F. . Chaparro, Ch. Colbeau-Justin, M. Kunst, and H. Tributsch, Semicond. Sci. Technol. 13 (1998) 1472. 2 6 ~Messer . and H. Tributsch, unpublished measurement. "H. J. Lewerenz and G. Schlichthorl, J. Electroanal. Chem. 337 (1992) 85. 2 8 ~J. .Lewerenz and G. Schlichthiirl, J. Appl. Phys. 75 (1994) 3544. 2 9 ~Bungs . and H. Tributsch, Ber. Bunsenges. Phys. Chem. 101 (1997) 1844. 3 0 ~Wunsch, . G. Schlichthiirl, and H. Tributsch, J. Physics, D: Appl. Phys. 26 (1993) 2041. 31 G. Schlichthijrl and L. M. Peter, J. Electrochem. Soc. 141 (1994) L171. 32 J. M. Warman, M. P. de Haas, M. Griitzel, and P. P. Infelta, Nature 310 (1984) 306. 3 3 ~Kunst . and G. Beck, J. Appl. Phys. 60 (1986) 3558. 34 R. W. Fessenden andP. V. Kamat, Chem. Phys. Lett. 123 (1986) 233. 3 5 ~M.. Schindler and M. Kunst, J. Phys. Chem. 94 (1990) 8222. 3 6 ~ v Kunst, l. Mat. Res. Soc. Syrnp. Proc. 189 (1991) 75. 3 7 ~ Ramakrishna . and S. K. Rangarajan, J. Phys. Chem. 99 (1995) 12613. 38 H. Schulenburg and H. Tributsch (to be published). 3 9 ~Schwarzburg . and E Willig, J. Phys. Chem. B 101 (1997) 2451. 4 0 ~Griinwald . and H. Tributsch, Chem. Phys. Lett. (submitted). 41 G. Schlichthiirl and L. M. Peter, 1 Electroanal. Chem. 381 (1995) 55. 42 J. Li and L. M. Peter, J. Electroanal. Chem. 193 (1985) 27; 199 (1986) 1. 43 R. Peat and L. M. Peter, L Electroanal. Chem. U)9 (1986) 307.

he&

522

H. Tributsch

4 4 ~C.. Searson,D. D. Macdonald, andL. M. Peter, J. Electrochem. Soc. 139 (1992) 2538. 4 5 ~ Schlichthiirl, . E. A. Ponomarev, and L. M. Peter, J. Electrochem. Soc. 143(9) (1995) 3062-3067. 46 G. Schlichthorl and L. M. Peter, J. Electrochem. Soc. 142(8)(1995) 2665-2669. 47 T. Otaredian, Solid-State Electronics 36 (1993) 153. 48 P. Salvador, M. Mir, N. Alonso-Vante, and H.Tributsch, J. Phys. Chem. (submitted).

Improvementsin Fluorine Generation Gerald L. B auer and W. Ves Childs 3M Fluoromaten'als Research Group, 3M Center, St. Paul, Minnesota, 55144-1000

I. INTRODUCTION It has been known1-l2 for many years that the formation of lenticular bubbles of fluorine on carbon-based anodes limits the operating current density. We have conceived of, developed, and operated a new anode that dramatically mitigates the effect of these bubbles. In this chapter we describe the conception, the development, and the testing of that design using commercial-scale anodes in cells much like those that would be used commercially. Laboratory anodes of this design have been operated at over 300 mA cm-2 for more than 1OOO hours, and at 600 mA cm-2 for tens of minutes. The ohmic resistance of amorphous carbon used in fluorine cells leads tojoulian heating and poor current distribution; this has limited the anode size and the individual anode operating current. We describe here design and fabrication techniques for constructing anodes 20 cm in diameter and 120 cm in length that operate at 2000 A (over 300 mA ~ r n - ~ A ) , pilot plant with four of these anodes has operated for over a year69 with no evidence of degradation. We refer the reader to the statement on the hazards of HF by Peters ' ~ following cautions should be noted: and ~ i e t h c h e n .The Modern Aspects of Electrochemistry, Number 33, edited by Ralph E. White et al. Kluwer Academic / Plenum Publishers, New York, 1999.

524

Gerald L. Bauer and W. Ves Childs

A Caution: Hydrogen fluoride and fluorine are dangerous materials. Exposure to them will cause severe, painful, and perhaps fatal injury. Exposure may not be evident for several hours. The procedures described here pose the risk of exposure to hydrogen fluoride and to elemental fluorine and should only be carried out by, or under the direct supervision of, qualified professionals. Qualified first aid treatment and professional medical resources must be established prior to working in the area. Prompt treatment is necessary to reduce the severity of damage from expasure and should be sought immediately following expasure or suspected exposure. Material safety data sheets are available from HF and fluorine suppliers. Their recommendations should be followed scrupulously. 11. THE CHALLENGE The challenge was to provide 3M with a copious supply of reliable and cheap fluorine.

1. Preliminary Considerations

(i) Electrochemistry The net electrochemistry is straightforward. At the anode, 2HF-2e'=Fz+2H+ At the cathode, The reversible voltage is 2.8-3.0 V and the operating voltage is >7 V. Details about electron transfer from the bulk electrolyte into the carbon base of the anode are not clear.

(ii) Electrolyte The electrolyte is nominally potassium diacid fluoride, KF-2HF.We use it slightly rich in HF, 20.75 to 20.95 meq of HFper gram ofelectrolyte, as determined by titration with standard sodium hydroxide solution to the phenolphthalein end point; running slightly rich eliminates the formation of a layer of the salt on the bottom of the cell lid and in effluent ports.

Improvements in Flourine Generation

525

KF.2HF melts at about 60°C and in the usual operating range of 90 to 100 "C it has a tolerable HF vapor pressure. It has a low viscosity, and is water clear, but in operation gas bubbles make it difficult to see through. (iii) Artode Materials The anodes were based on YBDTMamorphous carbon (obtained from UCAR Carbon Co.). Amorphous carbon, or simply carbon, is reasonably stable in KF.2HF, but is usually operated at a low current density because of "polarization" (see later discussion). Unless suitable provision is made for current collection, the relatively high resistance of the carbon leads to joulian (resistive or ohmic) heating of the carbon, and the high temperatures will cause degradation of the carbon through reaction with elemental fluorine. This reaction first gives "mushy" carbon and ultimately leads to burning and failure. We describe techniques that allow the operation of carbon anodes at current densities of 600 mA cm-*and that mitigate the effects of joulian heating. Nickel can be used as an anode for fluorine generation, but losses due to electrolytic corrosion make it impractical for commercial production.

(iv) Fluorine Cost Related to Current Density Figure 1 shows an estimate of the cost of fluorine (in arbitrary units) as a function of current density. This estimate is based on a four-anode callandria cell2-8,14 with anodes that are 20 cm in diameter and 120 cm long (a standard YBD size). It shows that above about 300 to 400mA there is little gain with increasing current density. Cooling could also become a serious constraint at higher current densities, and circulation to external cooling might be required instead of the simple gas lift circulation used in this design. With this in mind, we attempted to develop a simple and reliable process that would operate in the range of 300 to 400 mA ~xn-~.

(v) Current Passage and Terminal Voltage Amorphous carbon is wet by KF.2HF, but the passage of anodic current converts the surface to CFx,which is not wet by KF.2HF. Figure 2 shows the results from an experiment." in which a fresh piece of carbon was made anodic in KF-2HF.The initial voltage at a constant 15 mA cm12

Gerald L,Barnand W.Ves Chi&

Figm L ReMve opstoffluorine as a f u n c t i o n o f c w e a t ~ o na four-modecallandriacell using20 x 20 cm araodes;RUlAcmmpnds to 3W mA anw2.(Repmted from G, L Bauer and W,V, Wds, J, Electrockem. Soc. 142,22862290,lW.Repducd with -on of Tfae ElMemiccat Society, hc.)

Agum 2 The effect ofcumentpwgg on terminalvohge~withmcarboa ~teiifrQmG.L.BauerdW.V. Chitds, J. E l e c t m h . Sac. 1 4 Zl& BXl, 194. R e g d u d with permission of T b E l e c b d a h l Society, Inc.)

Improvements in Fluorine Generation

Figure 3. New carbon at 100°C is wet by K F - m , (Rqxbtedh m Q L B m r mdlW. V. Childs, J. Electrochem Soc. 1 4 ESSZHl, IW. Ramdud with remissionc f h Flee-

current density was about 3 V, a bit more than is required to generate fluorine; it rises rapidly and plateaus at about 5 V. This voltage rise is caused by resistance to current passage through a layer of CFxfonned on the carbon surface; additional energy is required to move electrons from the bulk electrolyte, through the CP,layer, and into the an& bulk. Figure 2 shows that the terminal voltage is a little more than 6 V at about 40 mA cmMn2; at higher current densities, the terminal voltage will be bigher. Figure 3 is a sketch made at the start of an experiment"14with a fresh piece of carbon. Clearly, the fresh carbon piece is wet by the molten KFZHF. Figure 4 is a sketch ofthe same system a few minutes after the &on is made anodic by applying 5 V between the carbon block and a piece of nickel wire in the KF.2HF electrolyte. The CF, layer forms (xe Fig, 2) and is not wet by the KFoWF. In fact, the KF2HF forms a ball and behaves Iike water on clean polytetrafluoroethyleneor mercury on clean glass. (The contact angle has been to be 1W.) Figure 5 is a section looking down through a fluorine cell perhaps 20 cm below the electrolyte level before any charge has passed. A MonelTM alloy screen (electrically floating) separates the fluorine from hydrogen. Just after electrolysis starts, the situation will be like that sketched in Fig. 6. (This corresponds to the first few seconds of Fig. 2.) Hydrogen

C

Adkw 4 . Passagedcurrent~carbon nonwcUing. @q&ed horn G.L Bauer and W . V . C uJ, E k c t r o c k Soc.1 4 228622% 1994. R e p d u d with peamissiw of The l z k k d d d Society,Inc.)

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GerolliL h

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Figm 5. M o n looking down through a flu& d p e r h a p s 2 0 c m ~ o wh e b l y t e s l r r f a c e showing cathode, electrolyte,meen, and new carbon piecebefore any current pawge

bubbles will form at the cathode and break away and rise. Fluorine bubbles will form at the anode and break away and rise, but some of the fluorine will react with the surface of the carbon piece to form CF,. This CP,leads to problems. After the surface is covered with CFItit is no longer wet by the electrolyte and the low-energy configuration shows the formation of lenticular (lens-shaped) bubbles as shown in Fig. 7.These bubbles cover perhaps 95% of the surfacelo and greatly reduce anode contact with the electrolyte.

Pigure 6 Sectioa through a fluorine d l phap 20 cm beIow the e b d y t e surface showing mkk, electrolyte, meen, a d new carbon just after a

3-Vcurrent starts.


529

Figure 7. Section through cell after electroIysis s t m q (7 V) with operating &n-bawd anode showing lenticular bubbles of fluorine on anode surface.

Polarization is the most serious problem arising from these lenticular bubbles. In this context, polarization has a special meaning; it is a rather sudden increase in the cell voltage and (if the power supply 1s Iirnited, to say 15 V) a decrease in the current to a small fraction of the expected

current. Barring drastic treatment, this is an irreversible process; treatment of a polarized anode with voltages on the order of 30 to 75 V for a few minutes have been reported to be reasonably su~cessful.'"~'~ Typically this drastic treatment must be repeated in a few hours or days.

Where contact is made, the Iwl current density is high. The Iocal temperature is also high; the carbon will be more highly fluorinated and the resistance to current passage will increase even more (in a positive feedback fashion). This problem of polarization caused by lenticular bubbles has been reco,gized for many years. To mitigate their effect, workers in the field have used a variety of methods (discussed cogently with references in Bai and conway'). The methods include

Adding material to the electrolyte to encourage the bubbles to break free * Using p m u s carbon so that the fluorine would enter the pores and move up through an internal reticulated network of pores * Introducing nucIeating sites in the carbon to induce the fluorine to 8

break away Vibrating the anode to shake off the bubbles

Polishing the surface of the anodes Rotating the mode to spii off the bubbles Devising ways to port the fluorine away from the surface into conduits within the anode We did not feel any of these methods would work reliably on a commercial scale at current densities in the range of 300 mA cm-' or for commercial periods (at least 4000 hr). Rudge's w ~ r k ~with . ' ~ porous carbon anodes was a very elegant solution to the problem (and forrried the basis for the Phillips Electmhe~nicdFluorination pmess), but the high electrical resistance of the porous carbon limited it to small anodes at high current densities or lower current densities on large anodes.

2. Application of Some Fundamentals of Wetting to the Problems While we know that eIectron density distribution is important in wetting, the significant breakthrough was the realization that geometry is also important in wetting systems. (If one is careful and has steady hands, it is possible to float a needle on water (W.V. Childs, persona1 observation); insects walk on water (W.V. Childs, personal observation); and leaf hairs help keep rainwater from plugging the stomata through which leaves transpire.15) Figures 8, 9, and 10 show how this realization was implemented in a cell. Figure 8 is a view looking down through a section of a laboratory fluorine cell that has had grooves inserted in the face of the carbon. This is fresh carbon so the grooves are wet by and filled with electrolyte, KF.2I-F. Our Innovation

Figure 8. Section through an incipient fluorine cell incorporating a fresh carbon "ande" with gmves.

Improvements in Fhrorine Generation

After electrolysis is under way @g, 9), the system becomes nonwetting, the fluorine ejects the electrolyte from the grooves, the F e s turn into channels tperhaps they are really conduits, with carbon on three sides and electroIyte on the fourth side), and the fluorine flows through the channels and escapes into the vapor space. The argument has been made that all we have done is increase the surface area of the anode in contact with the elwlyte. In the laboratory ell, we nearly doubled the potential contact area,but we increased the c m n t carrying capacity of the apparent surface (zx dx h) by abut an order ofmagnitude. we have run laboratory anodes (35 cm long and 3.5 m diameter) at MX) mA an-?, which was the

532

GeraldL. Bauer and W. Ves Childs

power supply limit, for tens of minutes; the cooling system was not adequate for extended runs .I Figure 10 shows the face of the anode. As indicated, there are doubtless some droplets of electrolyte moving in the channels. The fluorine moves these droplets along just like a gas lift pump lifts water in a goldfish bowl cleaner or a swimming pool vacuum. The electrolyte still does not wet the anode very well, but the low-energy situation makes it easier to move electrons from the electrolyte into the carbon base.

3. An Engineering Model for the Flow of Fluorine in the Grooves Some simple calculations were carried out to establish that the crosssection and spacing relationship of the grooves could carry the fluorine from the generation site to the vapor space. A major constraint is that the thinnest saw blade that will hold together when this carbon is cut is about 0.2 mm. We used 0.2 mm as the width of the grooves for the laboratory anodes, but switched to 0.3 mm to reduce the saw blade loss on the large anodes. The groove depth of 2 mm was based on engineering intuition. Assuming laminar flow, a gas density of 0.00128 g ~ r n - a~ ,gas viscosity of 2.87 x loq4poise, an electrolyte density of 1.90 g ~ r n - ~and . a groove immersed length of 107 cm, each groove will cany 3.08 cm3 s-I of fluorine. T h s is equivalent to a current of 20 A and to support 2000 A we would need about 100 ooves. (This calculation is based on a homework I B problem in Bird et al. ) Figure 11 is a sketch of the face of one of our laboratory cells? The cell body is made of a MonelTMalloy and is about 60 cm tall. The cell is fed HF and electricity and fluorine and hydrogen are taken out. The Kel-FTMpoly~hlor~triflu~roethylene view ports let us see what is happening on the hydrogen side of the screen (see later discussion). If it were really necessary to view the fluorine side, sapphire or diamond windows could probably be used. It is difficult to see below the electrolyte level of an operating cell because of gas bubbles. ~ some details of the cell interior. The skirt is a solid Figure 1 2 shows Monel alloy sleeve extending about 2 cm below the electrolyte. (TeflonTM and Kel-F fluoropolymers could not be used as slurts for extended periods because they react with fluorine at the temperatures used; they could probably be used as screens, however.) The screen (not shown) is an extension of the skirt. It consists of a Monel alloy sleeve with numerous 1-mm holes. The skirt and screen float electrically. They are bipolar and


It Sk-etd~showingt h e ~ d a fluorine cell. (Rqmted from G. L. Bauer and W.V. CMds, J. Electrochem. Soc. 142, 1W. Reprodwedwith~ofm~ Society, k) F i g u r e

~

Figure 12. Section view of a laboratory f l u d d. (Reprinted from G.L.Bauer and W.V. Wb, J. E l e c t m h Soc. 1 4 1 H . R e p d u d with permission of -cal biety, Znc.)

rn

~~

534


depend on a passive fluoride layer for protection from corrosion; this protection is not perfect and there is some corrosion, which may be a significant operating constraint. Tempered water at >60"C is circulated through thejacket for temperature control. Makeup HF mixed with nitrogen is added as the vapor on demand. Probes at four levels are used for HF control and safety: Control probe at the reference level Low-level shutdown probe at -1 cm High-level shutdown probe at +I cm High-high shutdown probe at t 2 cm The control, low-level, and high-level probes provide computer inputs and trigger the appropriate shutdown functions. The level is controlled over a range of about 2 mrn. The high-high probe is completely independent ofthe other probes and is hardwired to shut down the system completely, independent of the computer. (In the preliminary safety review, the hazards associated with HF overfeed were identified as important; thus the independent high-high shutdown probe system was installed.) All systems are designed to fail into safe conditions. The HF control valves are air operated and of a design that makes it impossible for HF to contaminate the air supply. The probes are 1-mm nickel rods with square ends. They are powered by 100-V dc power supplies. The positive side of the power supply is connected to the cell body. (This makes the probes cathodic to the case.) The control modules have 12 kf2 resistance so that when contact is made, less than 10 mA flows through the circuit; this is not a dangerous current. (The use of a 12-V power supply and lower resistance modules d d not reliably deliver a control signal when contact was made; this may have been caused by the buildup of a passive film on the probe that was not cleared by the lower voltage.) The electrolyte circulation is driven by gas lift from the electrode products. Figure 1 3 is ~ a sketch of some of the details around the anode. The carbon piece is 35 cm long and 3.5 cm in diameter. The metal hanger to the carbon connection shown was made with a nickel split sleeve with commercial galvanized steel banding clamps. (Nickel and Monel alloy banding clamps did not work well; they stretched.) This mode of connec-


Figure13 S k e t c h o f s o m e o f t h e d e t d s ~ ~

a n o d e ~ l y(RqintedfiomG. . L.B m e r d W . Sot. 14& 22&=

V, Childs, J, Etectmchern

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tim w d e d d

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-

y well, but it was qW with an improved mwk

(see below).

If the anode is irmnersed to 30 cm, the wetted area is 330 an?.To make things simple, we view the slrirt as blocking off enough a m to reduce the weaed area to 300 c m l . design ~ worked s a t i s f d y at 200 mA and fairly well at 300mA A laboratory-& version of the design worked w d at 600 mA w2, but cell cooling capacity limited operation to tens ofminutes. 4 Estirmating M u d i o n Rates for Hydrogen a d Fluorhe As shown in Fig. 14," reference flows (known flow rates of nitrogen, or on occasion, helium) are introduced into the cathode and anode chambers, where they mix with the hydrogen and fluorine. The gas chromatograph (GC)is a Hewlett-Packard 5890 GC with a thermal conductivity detector. A 5A mole sieve column is used with argon carrier gas;this gives peaks going in the same direction for both hydrogen

and nitrogen. A side stream from the cathale product mixture is passed over a mom temperature alumina bed to remove HE The nitrogenhydrogen ratio is estimated, and h m this ratio and the known flow rate of the nitrogen reference stream, the current efficiency for hydrogen production is calculated. A side stream from the mode product mixture is passed over a hot (lW1lS°C) a l u m i ~bed where the fluorine reacts quantitatively to produce aluminum fluoride and oxygen. The nitrogenloxygen ratio is

Gerald L, Bauer and W.Ves Childs

Figm 14. M @ a l layout and flows. Refer to text for h t i o n a I descriptions. (Reprinted from C. L. Bauer and W.V. Childs, J. EIectrochem Soc.182,28&2290,1994. Reproduoed with permission of 'Ihe EBczhwbmM Smety, hc.)

estimated, and from this ratio and the known flow rate of the nitrogen reference stream, the current efficiency for fluorine production is c a b lated. Over the range of 100 to 6M)mA ~ r n - ~the, current efficiency for the production of hydrogen was 100%, with a standard deviation of 2%.Over the range of 103 to 600 mA cm-', the current efficiency for the production of'fluorine was lOOLTu with a standard deviation of 2%. Essentially the same results were obtained with helium reference flows.

5. Anode Life in the Laboratory At a current density of 300 mA cm-', the final anode designs from which the practical large an& were derived had lifetimes in excess of 1OOO hr.

When these anodes were removed after operating over a thousand hours (when there is no indication of failure, it is dificult to justify running a test for more than 2 months), they still showed machine marks and there was no evidence of the mushiness reported elsewhere17(and observed in our laboratory with the simple band design at high current densities) with other designs operated at much lower current densities. This mushiness was most noticeablew h e there ~ was no cooling above theelectrolyte level and below the hanger.


The laboratory layout is sketched in Fig. 1 5 .The ~ power supply is a 3-phase silicon controlled rectifier, SCR, controlIed supply capable of delivering 200 A at 50 V. HF is supplied from a 1WJb cylinder on an electronic sale which has a l@g resolution. The cylinder is heated to 3 7 O C with a band heater with two integral temperature sensors, one for control and an independent one for shutdown in case of overheating. From the cylinder, the HF passes through a throttling valve, a backup shutdown valve, and a control valve. A continuous nitrogen flow (actually the cathode reference flow) was added downstream of the control valve. The burner is operated on natural gas and air in a fuel-rich mode. Fluorine reacts with excess fuel to form HF and CF+ A11 of the air that g m through the containment cell (hood) is scrubbed with caustic before being r e l d . (We considered destroying the fluorine by reaction with caustic, but our calculations suggested that this reaction was too slow.) The temperature control fluid is a 2Wo solution of commercial antifreeze in water. The fluid memoir is a 20-liter insulated reservoir; the fluid is kept above WC. Fluid from the reservoir is pumped through an electric heater to thejacket; the fluid is heated to maintain the electrolyte temperature at WC.

Fgue 15. Sketchofthe laboratory layout (Fkpnted h m G.L Bauer and W,V. Chi& J. Electrochem Soc. 1Q ZW2290, 1%. Rqmduced with pmission of The E4dmhnid !b&y, Inc.)


The analytical equipment was explained earlier (Fig. 14). System control and data acquisition are done with a personal computer using ParagonTM software. About 150 input and output modules were used for the two laboratory cells. This is expensive and may seem excessive, but a lot of the inputs and outputs are used for safety purposes so that the celI can operate unattended 24 hr a day, 7 days a week to get good long-tern data.

6. Additional Preliminary ~ e r a i i o nfor s the Pilot Plant It was clear from the start that pilot plant and uItimately the plant designs require: 1. A safe operating procedure 2. A simple cell design 3. High current density

4. Large anodes 5. A low resistance and stable carbon-metd connection The requirement for a safe operating procedure is restated here because HF and fluorine are indeed very hazardous.13 A simple cell design is required to reduce capital costs. The cost of the raw materials,HF and electricity, are not negligible, but they are minor. The pilot plant cell design shown in Fig. 16 is derived from the callandria cell developed for the Phillips ECF process.'4The cell body and internals

are of mild steel pipe selected to be resistant to hydrogen embrittlement. Figure 17 is a horizontal section through the working part of the cell.

Figure 16 A cutaway view of a pilot plant cell with four plant-scale (2000 A) anodes. ( R e p d u d with permission from papr 933 presented at the May 197 meeting of l hEla3mchemical Swiety in Montreal)

Improvements in Fluonhe Generation

Figure 17. A horizontal d o n through the anodes in a callandria cell. ( R e p r o d d with permission from paper 933 prmnted at the May 1W meeting of The Electo chemical M e t y in Montreal.)

The high current density requirement means that the bubbles must be moved out of the way so that current can pass from the electrolyte into the an& base. The vertical channelslgrooves in the anode face provide a low-energy path for the bubbles to move from the surface to the vapor space and exit the cell. 7. More Erghmring Models We did finite-element modeling for some large anode designs at high current densities. Figure 18 shows the results from a finite-element model of the temperature distribution in an anode of the design shown in Fig. 13 scaled to 20 crn diameter and 120 crn long and operating at 2000 A. (Zienkiewicz and Taylor have a general reference to the finite-element method in The Finite-ElementMethod, McGraw-Hill, 1989.)Theseresults show how inadequate a scaleup of the anode of Fig. 13 would have been. Note the temperatures well above ZWC. At this temperature, carbon reacts with fluorine. Just above the electrolyte, the carbon may get mushy or it may burn. We saw both in the laboratory. Figure 19 shows the results from a finite-elementmodel of the voltage as measured from the cathode to various points in the anode of Fig. 18.

figwe 18. Calculatedtanpamedist&don in alargecyWwlcarbon anodeinwhichalloftkecumntentusthehpieoethrwghthehanger.

From the star- we knew we needed large anodes to meet the challenge of inexpensive fluorine; these cdculations clearly show the need for a better design for large anodes. The obvious solution is to put a metal conductor down the middle of the an&. Figure 20 shows the results from a finite-element model ofthe temperature distribution in such an improved large anode with a central metal conductor,

Improvements in Fluorhe Generation

Figure 21 shows the results from a finite-element calculation of the voltage from the cathode to various points in the anode for an anode design with an internal metal conductor as in Fig. 20. Further details on the pilot plant are beyond the scope of this chapter.

Figm 19. Wulafed voltage as measllred fmm the admk to various pointsin theanodefor an surdedesigninwbichalloftbecurrententers through the hanger as in F% 18.

Gerald L. huer and W.ves mlds

542

It is not possible to fabricate a practical anode such as that shown in Figs. 20 and 2I. One approach is to drill and tap a hole in the carbon piece and s m w a piece of threaded copper into the hole. This works fairIy well for a hole 10cmdeep, perhaps 15 cmdeep ifone iscareful, but not very much beyond that. There are two major problems: (1) It is difficult to get a good

I I

Not to scale

Figure 20. Calculated temperatul-e distribution in a large cylindrical design with an internal metal conductor.

carbon an&

Not to scale

Figure 21. Calculated voltage as measured from the cathde to various points in the anode for an anode design with an internal metail condt~ctor as in Fig 20. (Reproduced with permission from paper 933 presented at the May 1W meeting of The Electrochemical k i e t y in Montreal .)

match of the male and female threads. (2) The carbon crumbles as it is machined and as the threaded piece is m w e d into it. A second approach is to carefully machine the rod and hole to obtain a g o d press fit. The copper is soft and difficult to machine, but it can be done, The carbon is hard and difficult to machine, but it also can be done. It is a lot of work and it is difficuIt to push a piece of copper into acloseIy fitting hole 110 crn deep in a piece of carbon.

Gerdd L. Bauer and W.Ves Childs

However, even when this is successful there remains a serious problem 'Bms'' carbon is very porous. Even if the surface is not wetted by the electrolyte, below about a loan depth there is enough hydrostatic

pressure to push electrolyte into the poxes and into the cupperIcaxbon interface. When the electrolyte reaches it, the copper carrodes. Since the corrosion products occupy more volume than the copper,the carbon is put under tensile s h w and fails by cracking. Figure 22 shows a practical large anode. The an& started as a rough cylinder of YBD carbon about 2) cm in diameter and 120 cm long, A central cavity 10 crn in m e t e r and 110 cm deep was machined in as shown. The pores in the carbon were filled with a cummercial epoxy material using standard techniques. (The material was a mixture of


545

AralditeTM PY306 resin, HY917 hardener, and DY070 catalyst, all from Ciba-Geigy.) The epoxy was mixed and cured according to the manufacturer's directions. The surface of the impregnated piece was machined down to 20 cm diameter, and vertical channels 0.3 mm wide, 2 mm deep, and spaced about 6 mm apart were provided to ease the passage of the fluorine out of the lenticular bubbles into the vapor space. The central cavity was lightly machined to remove some epoxy and expose carbon for a base for the electrolytic plating of a layer of nickel. A layer of nickel was plated onto the carbon surface of the central cavity using a standard nickel plating method; then a layer of copper was electrolytically plated onto the nickel using a standard copper plating method. The central metal (copper) conductor was carefully put in place, with copper wool packed around it to hold it in place and to conduct current from the central conductor to the copper plate and then to the carbon piece and out to the electrolyte. The 6-mm spacing (108 channels or grooves) appears to be adequate, but anodes with 160 channels or grooves run at slightly lower voltages.

ACKNOWLEDGMENTS Support for this work by 3M Company and permission to publish is gratefully acknowledged. We thank Dave Lindemann for the finite-element modeling and 3M's Division Engineering, especially Don Peacock, for all their work. Bob Maline of 3M's Specialty Materials Division was supervisor of pilot plant operations. Some of this material was taken from paper 1042presented at the San Francisco meeting of The Electrochemical Society, May 22-27, 1994; some from paper 933 presented at the Montreal meeting of The Electrochemical Society, May 4-9, 1997 (and published in the proceedings of the symposium on Electrochemistry in the Preparation of Fluorine and Its Compounds); and some from a paper published in the Journal of the Electrochemical Society, volume 142, pages 2286-2290. APPENDIX: NOTES ON LABORATORY OPERATIONS Analysis of Process hazards. The proposed operation must be thoroughly analyzed for hazards before the project is undertaken. After the

546


apparatus is assembled and before it is wetted-out, another thorough analysis of the "as-built" project must be performed. Cleaningforfluorine service. It is important that materials that may contact elemental fluorine be thoroughly cleaned to remove any traces of grease or other substance that may ignite on contact with fluorine. Furthermore, it is important to passivate all surfaces that may contact fluorine. Refer to the manufacture's fluorine material safety data sheet for more information. The assembled anodes used in the laboratory were degreased by refluxing overnight with trichlorotrifluoroethane in an oversiied Soxhlet extractor. Materials compatibility. We use scrupulously clean and scratch-free FEP PEP is the acronym for the copolymer of tetrafluoroethylene and hexafluoropropylene) tubing for handling our mixtures of fluorine and nitrogen at ambient temperature. Corrugated FEP tubing is convenient for making strain-free assemblies. We have found that Monel is excellent for use with dry molten KF.2HF. Mild steel corrodes slowly and stainless steels corrode rapidly. Kel-F polychlorotrifluoroethylene is satisfactory for use with HF and with KF.2HF; polypropylene and polymethylpentene are not satisfactory. Preparation of KF.2HF. This is prepared by carefully adding hydrogen fluoride vapor mixed with nitrogen to solid potassium bifluoride. l3 Potassium bifluoride is available in convenient quantities from some supply houses (Aldrich 23,928-3, for example). The addition of hydrogen fluoride vapor to potassium fluoride is extremely exothermic and is best not attempted. The addition of liquid hydrogen fluoride to potassium bifluoride is also extremely exothermic and is best not attempted. Potassium bifluoride is weighed into the cell with the lid off and the lid is then attached and the cell is heated to 85 O C . Hydrogen fluoride is weighed in from a warm 45-kg cylinder on a scale with a resolution of 10 g. The HF is mixed with nitrogen and carefully added through an FEP tube that is started at the top of the cell and slowly worked down to near the bottom. We have found that it takes most of a day to make this addition. (If HF addition is interrupted, the FEP tube should be raised above the electrolyte level to prevent its being frozen in.) The nitrogen is left on until the tube is above the electrolytelevel. The carefully and thoroughly stirred electrolyte is analyzed by titrating several 1.5- to 2.0-g samples to the phenolphthalein end point with standard 1 M NaOH.


REFERENCES I

L. Bai andB. E. Conway, J. Appl. Electrochem. 18(1988) 839.

k.Bai and B. E. Conway, J. Appl. Electrochem. 2Q(1990)916.

%. Bai and B. E. Conway, J. Appl. Electrochem. 20 (1990) 925. 4

~ V.. Childs and G. L. Bauer,

J. Electrochem. Soc. 142(7) (1995) 2286.

5 ~ L.. Bauer, W. V. Childs, C. F. Kolpin, and D. T. Rutten, U.S. Pat. 5,290,413 (1995).

6G. L. Bauer and W. V. Childs, WO Pat. 95M763 (1995).

7

G. L. Bauer and W. V. Childs, paper 933 presented at the 1997 Montreal meeting of The Electrochemical Society. 'G. L. Bauer and W.V. Childs in Proc. Electrochemistry in the Preparation of Fluorine and Its Compounds, W. V . Childs and T. Fuchigami, eds., Electrochemical Society, Pennington, NJ, 1997. 9 ~J. Rudge, . in Industrial ElectrochemicalProcesses, A. T. Kuhn, ed., Chapter 1, Elsevier, New York, 1971. 'A. J. Rudge, The Manufacture and Use of Fluorine and Its Compounds,Oxford University Press, London, 1%2. 11 R. J. k n g and D. Roysten, A Review of Fluorine Cells and Fluorine Production Facilities AAEClE281, Australian Atomic Energy Commission Research Establishment, Lucas Heights, Australia, 1973. 125.F.Ellis and G. E May, J. Fluorine Chem. 33 (1986) 133-147. 1 %. Peters and R. Miethchen, J. Fluorine Chem. 79 (19%) 161. 14w.V. ChildS in Techniques of Electroorganic Synthesis, N. L. Weinberg and B. B. Tilak, eds., Chapter VII, Wiley, New York, 1982. 1 5 ~S.. Hartley, in Wetting, a discussion organized by the Society of Chemical Industry, Bristol Section, London. Mongraph No. 25 (1967)4 3 W 8 . 1 6 ~B.. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, p. 62, Wiley, New Y& 1960. 17paulHough, paper 932 presented at the 1997 Montreal meeting of The Electrochemical Society.

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Electrochemistry of Electronically Conducting Polymer Films Peter G. Pickup Department of Chemistry, Memorial University of Newfoundland, St. John's, Newfoundland, Canada AlB 3x7

I. INTRODUCTION It is now 20 years since the first report on the electrochemistry of an electrode coated with a conducting polymer film.' The thousands of subsequent papers have revealed a complex mosaic of behaviors arising from the multiple redox potentials and the large changes in conductivity and ion-exchange properties that accompany their electrochemistry. Much of the theory for the electrochemistry of conducting polymers has been adopted directly from work on redox polymers. Although the similarities are strong, and conducting polymers can be viewed as a form of redox polymer, their high electronic conductivities mean that ion transport rather than electron transport is generally the rate-limiting process in their electrochemistry. Redox polymer models based solely on electron diffusion are inappropriate, but have nevertheless been used extensively. Furthermore, unlike redox polymers, the electrochemistry of conducting polymers deviates greatly from that predicted by the Nernst equation. Because of these important differences between conducting and redox polymers, this chapter is restricted to conducting polymers, which Modem Aspects of Electrochemistry, Number 33, edited by Ralph E. White et al. Kluwer Academic / Plenum Publishers, New York, 1W.

Peter G. Pickup

will be defined here as polymers with long-range conjugation,

This

delinition excludes redox polymers based on electroactive metal centers or localized organic redox centers. Conjugated polymers containing these types of redox centers can behave as either type or in some cases both types simultaneously,depnding on the applied potential. The electrochemistry of conducting polymers has k e n the subject of several reviews24 and has been included in artides on chemically modified ele~hodes."~The primary purpose of this chapter is to review fundamental aspects of the electrochemistry ofconducting polymer films. Applications, the diversity of materials available, and synthetic methods are not covered in any detail, No attempt has kenmade at a comprehensive coverage of the relevant literature and the materials that have been studied. Specific examples have been selected to illustrate general principles, and so it can often be assumed that other materials will behave similarly. 11. BACKGROUND

A conducting polymer, as defined here, is a polymer containing a chain of alternating single and double bonds (Structure 1 and its geometric isomers). Generally, the chain is carbon based, but there are a growing number of examples with nitrogen atoms in the conjugatsd pathway (e.g., polyazines and poIypyridines) . Any polymer with extended conjugation will exhibit electronic conductivity when suitably "doped" (i,e.,oxidized or reduced), although in many cases the conductivity can=main quite low. The diversity of conducting polymers is k t illustrated by Krivoshei and Skmbogatov's book1'although many more examples have since been repkd. The most widely studied classes, from an electrochemical point of view, are the polypymles,1618 polyth~ophenes,'~~ and polyanilines211"(Structures 2-4), and these are the focus of this chapter. A wide

Electrochemistry of Electronically Conducting Polymer Films

551

variety of substituents (Ri) have been used, including alkyl, alkoxy, and aryl groups; fused rings; and most of the other functional groups available in organic chemistry. In fact, by using an appropriately substituted alkyl chain, almost any functionality (organic or inorganic) can be attached to the polymer chain. Conjugated polymers are generally poor conductors unless they have been doped (oxidized or reduced) to generate mobile charge carriers. This can be explained by the schematic band diagrams shown in Fig. I." Polymerization causes the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the monomer to split into n and n* bands. In solid-state terminology these are the valence and conduction bands, respectively. In the neutral forms shown in Structures 1 4 , the valence band is filled, the conduction band is empty, and the band gap (E,) is typically 2-3 e ~ . "There is therefore little intrinsic conductivity. Simplistically, p-doping (oxidation) can be viewed as the creation of mobile holes in the valence band, and n-doping as the addition of mobile electrons to the conduction band. However, these modifications actually change the band structure, creating various rnidgap states (Fig. 1). For p-doping, removal of one electron from a segment of the chain creates a mobile polaron (radical cation). Removal of a second electron, or the combination of two polarons, creates a mobile bipolaron (dication). These charge carriers cause local (extending over ca. 4 monomer units) distortions in the geometry of the chain, and create states above the top of the valence band, as shown in Fig. 1. Similar states are createdjust below the conduction band when the polymer is n-dope~l.~~ Since the doping of a conjugated polymer involves redox processes, it can be achieved and studied by using electrochemical methods, and this has created a very rich and intriguing area of electrochemistry. For electrochemical studies, conducting polymers are generally prepared by electrochemical (almost exclusively anodic) polymerization (see Section III),"" although a wide range of chemical methods is also available.l5 Electrochemical polymerization produces a polymer film on the electrode surface, which, although difficult to characterize chemically, is generally ideal for electrochemical studies. The thickness of an electrochemically deposited film can be accurately controlled from a few nanometers to more than 1 mm. It will be formed in a partially oxidized state, and so will contain the ions and solvent necessary for facile electrochemistry.

Peter G. Pickup

For electrochemical studies on chemically prepared conducting polymers, the polymer is generally cast as a thin film onto an electrode surface. Often a solution of the polymer is simply allowed to dry on the e k e tde,xn although spin coatingB is a better method for producing uniform films of controlled thickness, and dip coating has also been used.29 The electrochemistry of conducting polymers has also been investigated in solution," using pressed pellets:' and in c&on paste electrodes." Conducting polymers g e n d y exhibit both oxidative and reductive eledrmhedstry relative to the neutral states shown in structures 1 4 . Oxidation is often referred to as gdoping, while reduction is termed ndoping.These terms are useful to avoidconfusion between, for example, reduction of the o x i W form (undoping ofthe p-form) and reduction of the neutral form (n-doping). The redox can usually be reversed, although the o x i W andlor redwed states of many polymers have limited stabity (Section v ) . ~ ~ Voltammograms of a polythrophene film showing reasonably revasible electrochemistry of both types are shown in Fig. 2." The formal potentials (average of the anodic and &odic peak potentials) for p and n-doping can provide useful estimates of the energies of Ehe polymer's valence and conduction bands and its band gap.% The electrochemistry of conducting polymer films involves ion expulsion or insertion to maintain electroneutrality. As illustrated in Eqs. (I)


Figure 2. Cyclic voItammograms of a poly(Z2'-bithiophene 14 coated electrode in acetonittilecontaining 0.1 M BuflCIO,. (Reprinted from G.Zotti, C. Schiavon, and S. Zecchin, "he versible processes in the elecbmhemical reduction of polythiophenes. Chemical modifications of the polymer and chargetrapping phenomena,'' Synih. Mei. 72 (3) 275-281, 1!M, with kind permission from Elsevier Sciences S.A.)

and (21, the predominant p e s s for p-doping is normally anion insertion, while for n-doping it is cation insertion.

However, when films are cycled between the doped and undoped states, both types of ions will be involved to some extent, and the film wilI contain some salt;% The stoichiometry of the redox reactions of conducting polylners (n and m in reactions 1 and 2) is quite variable. Under the most widely used conditions, polypy~~oles and poly thiophenes can be reversibly oxidized to a level of one hole per ca. 3 monomer units (i.e., a degree of oxidation, n, of ca. 0.3)~However, this "Limit" is dictatedby the stability of the oxidized film under the conditions employed (Section V). With particularly dry and unreactive solvents, degrees of oxidation of 0.5 can be reversibly atti~ined:~and for poly-(4,4-dimethoxybithiophene),a value of n = 1has been reprtsd.)8 Although much fewer data are available for n-doping, it appears to involve similar stoichiometries [i.e., m in Eq. (2) is typically ca. 0.31.343e41 Polyanilines can in principle be reversibly p-doped to one

Peter G. Pickup

554

electron per ring (iz, n = 1)P2although the few reported experimental values are all significantly lower than t h ~ s . ~ " ~ Conducting polymers have found applications in a wide variety of areas?4s and many more have been proposed. From an electrochemical perspective, the most important applications46appear to be in batteries and superca acitor~,"~"~ electroanalysis and sensors,49-5 1 electrocatalysis,12.1 .s2 display and electrochrornic devices: and electromechanical

P

actuator^.'^

111. ELECTROCHEMICAL POLYMERIZATION AND FILM DEPOSITION

Most 2,5-unsubstituted pyrroles and thiophenes, and most anilines can be polymerized by electrochemical oxidation. For pyrroles, a~etonitrile,~~ or aqueous55electrolyte solutions are normally used, while the polymerization of thiophenes is performed almost exclusively in nona ueous solvents such as acetonitrile, propylene carbonate, and benzonitrile.l o Polyanilines are generally prepared from a solution of aniline in aqueous acid.*' Platinum or carbon electrodes have been used in most work, although indium-tin oxide is routinely used for spectroelectrochemical experiments, and many other electrode materials have also been employed.2021 Cyclic voltammetry is most commonly used to investigatethe polymerization of a new monomer. Polymerization and film deposition are characterized by increasing peak currents for oxidation of the monomer on successive cycles, and the development of redox waves for the polymer at potentials below the onset of monomer oxidation. A "nucleation loop," in which the current on the reverse scan is higher than on the corres onding R These forward scan, is commonly observed during the fist cycle.s6> features are all illustrated in Fig. 3 for the polymerization of a substituted pyrrole.58 Polymerization at constant current is most convenient for controlling the thckness of the deposited film Charges of ca. 0.3, 0.2, and 0.08 C cm-2 are required to produce 1 Frn of polypyrrole~poly(3-methylthiophene)a (no data are available for polythiophene), and polyaniline," respectively. Although these values can reasonably be used to estimate the thicknesses of most electrochemically formed conducting polymer films, it should be noted that they have considerable (ca. f30%) uncertainties. For each polymer, the relationship between charge and film thickness can

Electrathemistry of Electronically Conducting Polymer Films

T--

2mkanP

d ill

Figure 3. Cyclic voltammograms o f 3 - m e t h y ~ M a r b m y i Cacid in atembile + o . l ~ E @ N C lM o ~ ~- P . G. PEclolp, " P o l y < 3 - ~ 1 d 1 y ~ ylic acid) an^^ wnduct5ngiwech@p o m p J. LCktmad. a m . 225, 1987, with kind pecmissiodf b m Elsevier Wm S.A.)

vary significantly among laboratories?gMSome of the reasons for this are discussed at the end of this d o n . The most widely accepted mechanism for the anodic polymerization of pyrroles and thiophenes involves the coupling of radical cations produced at the elecbode (Scheme I).~The oligomers so produced, which are more easily oxidized than the monomer, are rapidly oxidized and couple with each other and with monomer radical cations. Coupling occurs predominantly at the a-positions (i.e.,2- and 5-position),5 and so pyrroles and thiophenes with substituents in either of these positions do not undergo anodic polymerization. The reaction is stoichiometric in that two

Peter G. Pickup

electrons are required for each monomer unit to be i n v W into a chain (one for end units). In most case$ oligomers are initially generated in solution,61d4but most rapidly precipitate onto the elect& surface andlor couple with adsorbed chains, and becnne oxidized."z63@As a result, an oxidized Ipdoped) polymer film is deposited on the electde surface with, in most cases, high faradaicefficiency. Since ca 0.3 electrons are required to dope the film to the polymerization potend, the overall polyrn&tion + deposition pmess consumes ca. 2.3 electsons per monomer unit. Strong evidence for the radical cation-mdical cation coupling mechanism shown in Scheme 1 has been obtained from double-step chronoarnperometry studies.667 However, an alternative polymerization mechanism, involving the coupling of radical cations with unoxidizsd molecules, has been claimed by a number ~ f a u t h o r s . ~ Some ~ " of the


557

strongest evidence arose from the observation that oligomers (bi- and ter-thiophene) promote the polymerization + deposition of thiophenes." It was argued that it was only necessary to oxidize the oligomeric additives, and that these coupled with unoxidized thiophene monomers. However, it has since been demonstrated that oxidation of the monomer is necessary, and that the "catalytic" effect of the oligomers results from the nucleation of film deposition70 that they cause. The anodic polymerization of aniline can occur by a radical cation coupling mechanism analogous to that shown in Scheme 1, with coupling occurring between the N of one molecule and the para-position of another (Structure 4).21"2However, a variety of other mechanisms have also been and it is likely that their relative rates depend upon the conditions (solvent, potential, pH, etc.) employed. The links between monomers are therefore not exclusively between the N and para-position (head-to-tail coupling). Head-head (-N=N-)and tail-tail (para-para) coupling occur more often as the pH is i n ~ r e a s e d . ~ ~ Although the mechanisms discussed above are still topics of debate, it is now firmly established that the electrodeposition of conducting polymers proceeds via some kind of nucleation and phase-growth mechanism, akin to the electrodeposition of metals.56>72-74 Both cyclic voltammetry and potential step techniques have been widely used to investigate these processes, and the electrochemical observations have been supported by various types of s p e ~ t r o s c o p and ~ ~ microscopy. ~ ~ ~ ~ - ~ 7860 ~ In cyclic voltammetry studies, the "nucleation loop" commonly observed on the first scan (Pig. 3) is characteristic of conducting phase formation by a nucleation and growth me~hanism?~"The electrodeposition of polymers by potential step techniques presents a well-defined chronoarnperometric response with a characteristic rising current-time transient in the initial stages, followed in most cases by a decay to an approximately constant current?6172 The rising part of the current transient has generally been found to be proportional to t2, indicating either an instantaneous nucleation with three-dimensional growth or successive nucleation with two-dimensional growth.56,72,73 Both types of mechanism appear to be possible, depending on the monomer used. The issue of nucleation and growth is complicated by the formation of oligomeric and polymeric species in solution and their precipitation onto the electrode surface, which may be the primary mechanism for nuclei formation." The expansion of nuclei and film growth arise both from the precipitation of oligomeric intermediates formed in solution and

558

Peter G. Pickup

from the addition of monomers and oligomers to chain ends in the growing polymer film.62,65,81 The reproducibility of the electrodeposition of conducting polymer films has been a very difficult issue. It has long been realized that each laboratory produces a different material and that results from different laboratories are not directly comparable." We have experienced reproducibility problems with almost all of the electrochemically polymerized materials used in our work. Part of the problem is the variety of solvents, electrolytes, concentrations, and electrochemical techniques (potentiostatic, galvanostatic, potential sweep, etc.) that have been employed.20 However, even when stringent efforts are made to keep all parameters and condtions constant, there are still problems with reproducibility.83 One of the major problems with electrochemically formed films is that their morphology varies across the film.81.8486 During the early stages of film deposition, a compact film is deposited. However, as the concentration of oligomers in solution builds up, their precipitation rate increases and the film deposits in a more porous morphology as it thickens." The rate at which this happens will depend on many factors, including the solvent, electrolyte, concentrations, the polymerization method and rate, the electrode size, cell geometry, etc. It is undoubtedly a significantfactor in the poor reproducible of conducting polymer film deposition, and can make analysis of transport data dubiou~.~' A number of approaches are available to improve the morphology and homogeneity of electrochemically deposited conducting polymer films. Priming of the electrode surface with a monolayer of adsorbed or covalently bonded monomer leads to more compact deposits of polyanilpolythiophene,80and polypyrrole.89~90 Electrode rotation has been shown to inhibit the deposition of powdery overlayers during poly(3methylthiophene) deposition.81

IV. CYCLIC VOLTAMMETRY

Figure 4 compares cyclic voltammograms for a redox polymer (polyhn+)91 and p-doping and undoping [Fe(S-amino-I , 10-phenanthr~line)~] of a conducting polymer (polypyrrole)." The voltammogram for the redox

Elmtrochedm of Electronically Conducting Polymer Films

polymer is symmetrical, with close to a m p k separation. Its shape is chactmktic of a mersible couple in a thin layer, and can be m&ld reasonably well by using the Nemst eq~ation.~ In contrast, the voltammogram for the conducting polymer is very asymmetric. There is a large peak separation, which is virtually independent of the scan spead, and the anodic andcathodic waves have very different shapes. The current remains high on ?hepositive side of the wave, rather than decaying to close to zero, as observed for the redox polymer. Although a wide variety of wave shapes have been o w e d for conducting polymers, most differ from a redox polymer response in the same way as highlighted above for polypyrrole. Since ~einze'has discus& the origins of these differences in some &tail, the discussion here will be brief. The increased peak separation is not n o d y kinetic in origin, although it can have a kinetic component. Its origins have been discussed

560

Peter G. Pickup

in general terms by Feldberg and ~ubinstein," who invoked N-shaped Gibbs energy curves as an explanation. For conjugated polymers, the peak-potential behavior appears to be due in part to the transition from a twisted to a planar conformation following doping.95The doped form becomes stabilized and more difficult to undope. Conformation changes following doping can also explain the differences in wave shapes between the anodic and cathodic scans. The large currents observed positive of the voltammetric wave for p-doping of a conducting polymer (or negative of an n-doping wave) resemble those for a pure capacitance, and it has been argued that they are due to the charging of a double layer at the interface between conducting polymer fibers and the solution.96Although this model has been popular, there is little firm evidence to support it, and its validity is now doubtful. Heinze and c o - w ~ r k e r shave ~ ~ ~shown that these currents can be explained by the existence of multiple redox sites in the polymer. Since conjugated segments of polymers with different lengths (or different length oligomers) have different redox potentials, a single redox wave would not be expected. The distribution of potentials needed to simulate voltamrnograms like those shown in Fig. 4(B) appears to be reasonable, based on experimental data for oligomers in solution.97However, it has become clear that it is too simplistic to model conducting polymers as an ensemble of noninteracting redox sites. Interactions between oxidized chains have been clearly identified (e.g., the formation of n d i m e r ~ ' ~ ~ ~ ' ~ ~ ) and implicated in the hysteresis observed in cyclic v ~ l t a r n r n e t r y .It~ ~ ~ ' ~ ~ has also been shown that films of oligomers of uniform length (e.g., hexaor octa-thiophene), which should exhibit two discrete redox processes, also exhibit capacitancelike behavior.'" It may be better to use a calculated solid-state band structure to model the cyclic voltammetry of conducting polymer^,^^^^^^ although this approach is problematic because of the effects of solvation of the film, and the structural changes that accompany oxidation or reduction. It can be concluded that there is currently no accurate method for modeling the cyclic voltammetry of conducting polymers. From the foregoing discussion it will be clear that the stoichiometry of the oxidation [n in Eq. (I)] has no thermodynamic significance. It should not be used in the Nemst equation to describe the potential dependence of the equilibrium shown in Eq. (1). It is therefore better to describe n as the degree of oxidation of the polymer (i.e., the average number of holes per monomer unit). n is a potential-dependent parameter,


561

and can be calculated [Eq. (3)] from the charge under the anodic branch of a voltammogram (Qox), integrated to the desired potential, E:

where,,,,,n is the moles of monomer units in the film. Thus, by control of the potential, n can be varied from zero to values as high as 1 (Section II). Cyclic voltammetry can be used to measure n as a function of E, or d n is known at a certain potential, it can be used to estimate the number of moles of polymer in the film. The film thickness (4can then be estimated by using Eq. (4):

where M is the molar mass of the monomer unit, p is the density of the undoped film, and A is the electrode area. Other important issues in the cyclic voltammetry of conducting polymers are the nature of the charge carriers produced and the multiple peaks associated with the different charge carriers. Work on thiophene oligorner~'~~ has clearly shown that paramagnetic polarons (singly charged electron holes)23 and diamagnetic bipolarons (doubly charged electron hole pairs) are formed in two discrete steps. The similarity between the voltammograms of polybithiophene and methyl-capped hexathiophene (Fig. 5),lo5electron spin resonance (ESR) measurement^,?^ and spectr~electrochernistry~~ provide strong evidence that the two cathodic waves seen for reduction of p-doped polythiophene are due to separatereductions of bipolarons and polarons. Forpolypyrrole, polarons and bipolarons have similarredox potentials and so multiple peaks are not o b ~ e r v e d . ' ~The ~ ~cyclic ' ~ ~ voltammetry of polyaniline (e.g., Fig. 6)'@ involves two distinct, one-electron redox processes, each of which involves polaron and then bipolaron f~rmation.~' Cyclic voltarnmograms of conducting polymers are very sensitive to the preparation conditions used1l0and the medium in which the voltammetry is performed.54,85,111-119 This sensitivity arises in part from chemical defects, such as substitution by water,33irregular linkage^,^ and cross linking.12' More important though is the influence of preparation and cycling conditions on the structure and morphology of the film. Of particular importance is the mobility of counter-ions, which is strongly influenced by the porosity and degree of solvation of the film, and the nature of the counter-ion [see Section VI.2 (vi)].

~uapudapLl3uo~1sw pm p ' ow u y - v ~ Eqvqyxa ualjo sauaqdoyfi[od JO 8u1dop-u1oj~ o-sauaydoyL1d ~ uo p n m jaAvq ~saws Te3&3as3ala ~somos pue 'saugrueAlod JO sapudi(lod jo Bu!dop-u jo slrod3J OU U33q 3AEy 3 1 3 u ar-rzr~oP*etE'(~ ''83) %!dop-d JOJ 3SOql SE samlEaj ams a q Lwuassa IrqFqxa Zydopun pm Svdop-u ~ osun& j -OUIW[OA I E ~ Ja ~ ~ q a1qqpl! u! arrt i ~ yrr~lep l aycL ' w o j pedopu 1py1 u! &!l!qqs p a q q amq w p 01 papnls s~aw6~od ]sour a s n q 8u!dop-d u q uoguau~ssq mj p a ~ p ms q mwIC~od8uynpuo3 jo %ydoa-u

o


Figure 6. Cyclic voltammogram of polyaniline in 1.0 ~cyaq).'~

563

M

on the cation in s o l u t i ~ n~. h~ e s effects e occur because of limited mobility of cations in the fhs;' and are particularly pronounced with Lit because of its large solvation sphere.l13

The term "overoxidation" refers to degradation of the conductivity and electroactivity of an o x i d i d conducting polymer by reaction with a nucleophile. This topic has recently been thoroughly reviewed,33and so the treatment here will be brief. In aqueous solutions, and nonaqueous solutions that have not been rigorously dried, water attacks electrophilic sites on the polymer backbone, leading to substitution with carbonyl groups. Figure 7'" shows an example of the overoxidation of poly(3-methylthiophene) in highperformance 1iquid chromatography (HPLC)-grade acetonitrile (Fisher), which typically contains ca, 0 3 % water. The films were stable to potential cycling between -0.2 and +I .O V, and could be repetitively pdoped and unduped without simcant degradation, However, cycling the potential to +2.0 V produced a large irreversible oxidation wave at ca.

Peter G . Pickup

Electmhemistrg of Electronidly Conducting Polymer Films

+1.8V (note the change of scale in Fig. 7) and virtually eliminated the electroactivity of the fdm on subsequent cycles. For polypyrroles and polyho henes, the basic mechanism for overoxidation shown in Scheme 2'$lza is widely accepted, although an alternative mechanism has recent1y been proposed for polythiophenes.lZ7 Details of the reaction, including the extent of substitution and the formation of other functional groups, depend on the polymer and experimental conditions." Monosubstitution of approximateIy one third of the monomer units has beencommonly proposed, althoughthe largecharges passed during overoxidation indicate that there is often more extensive substitution and possibly multiple substitution of some ringd3 Reactions with other nucleophiles follow a similar mechanism. For the reaction of C1- with poly(3-meth lthio hene in acetonitde, the reaction stops at structure 5 (Scheme 2). A fully conjugated, C1-substituted product 6 can subsequently be obtained by electrochemical or chemical dehydrogenati~n.'~~ With Br and alcohols, the overoxidation

L P '

Peter G, F'ickup

reaction praxds directly to structure 6. In methanol, multimethoxylation of polypymole rings can occur.lE The e l ~ h e m i c a cl m t i c s of overoxidation vary widely among polymers, solvents, and nu~leo~hiles.'~~ Its rate depends on the d e p of oxidation of the polymer (and therefore on the potential applied), and the concentrati~n'~~ and reactivity of the nucleophile. Polypyrroles usually become overoxidized at lower potentials than plythiophenes because of their lower formal potentials for pdoping. In acetonitrile, the reactivity of the halides follows their nucleophilicity in aprotic solvents,

cr > Br- > I-, 129

The overoxidation of polyanhnes has been studied most extensively in aqueous solutions.33It occurs much more slowly than the overoxidation of polypples and polythiophenes, requiring extensive cycling through the second oxidation wave (at ca. 4.7 V in Figs. 6 and 81,or many minutes at a potential beyond this wave." ~ u r i ncyclic g voltammetry in acid (Fii, 8), the redox waves at ca. 0.1 V and 0.7 V are slowly replaced by a single reversible wave at ca. 05 V, which slowly decays with continued cy-

F@m8. Cyclic v o W m g m m s of plyaniline following (a) lQ 0 45, a n d ( c ) 8 5 & d ~ w w s ~ g i n MH#W,~'~ l


567

cling.'" Although the nature of the structures responsible for this new wave is uncertain? it is known that one of the degradation products is benzoquinone, which is slowly lost into the s01ution.l~~ Because of the high potentials required to polymerize many monomers, overoxidation often occurs to some extent during the electrochernical synthesis and deposition of conducting polymers. It is well known that electrochemically prepared polypyrroles contain significant oxygen impurities from this source.131The observation that polythiophene is not stable at the potentials used for its synthesis has been termed the "polythiophene paradox," since highly conductive films can be produced.132Part of the resolution of this paradox is that the iR drop in the solution during the polymerization means that the potential is not as high as expected.133 However, another important factor is the high concentration of monomer relative to water adventitiously present. The water in the diffusion layer will be quickly consumed, and its mass transport from the bulk solution will be slow relative to the polymerization rate. Although the overoxidation of conducting polymers is in most cases a severe disadvantage because of degradation of the polymer's conductivity and electroactivity, it has been used to advantage. Overoxidized polypyrrole films are finding increasing use as electrode coatings in electroanalysis and ~ e n s o r s . l ~They ~ J ~exhibit ~ permselectivity against anions, and their permeability and selectivity toward cations can be controlled by varying the overoxidation c ~ n d i t i o n s . l ~Overoxidation ~J~~ in the presence of suitable nucleophilcs may also be a useful way to generate novel substituted conducting polymer~.l~9J~~ VI. CHARGE TRANSPORT

The electrochemistry of a polymer-modified electrode is determined by a combination of thermodynamics and the kinetics of charge-transfer and transport processes. Thermodynamic aspects are highlighted by cyclic voltammetry, while kinetic aspects are best studied by other methods. These methods will be introduced here, with the emphasis on how they are used to measure the rates of electron and ion transport in conducting polymer films. Charge transport in electroactive films in general has recently been reviewed el~ewhere.~."

Peter G. Pickup

1. In Situ Electron Transport Measurements The huge literature on the electronic conductivity of dry conducting polymer samples will not be considered here because it has limited relevance to their electrochemistry. On the other hand, in situ methods, in which the polymer is immersed in an electrolyte solution under potential control, provide valuable insights into electron transport during electrochemical processes. It should be noted that in situ and dry conductivities of conducting polymers are not directly comparable, since concentration polarization can reduce the conductivity of electrolyte-wetted films considerably.139 Thus in situ conductivities reported for polypyrrole,140,141 polythiophene,37and polyaniline37are orders ofmagnitude lower than dry conductivities.l5 In situ electron transport measurements on conducting polymers are commonly made by using a pair of parallel-band electrodes bridged by the polymer [Fig. 9(A)] .141>142 Other dual-electrode techniques in which the polymer film is sandwiched between two electrodes pig. 9(B)],139,140 rotating-disk voltammetry [Fig. 9(~)],@'>'~~ impedance spectroscopy,'u>145 chron~amperometr~,'~~ and chronop~tentiometr~'~~ have also been used. In the dual-electrode techniques, the potential of each electrode is controlled with a bipotentiostat so that a small constant potential difference is maintained across the polymer film as its potential is slowly scanned, relative to a reference electrode. Figure 10 shows the results of this type of experiment for poly(3-methylthiophene) in SOz(l)." The parallel-band electrode method [Fig. 9(A)] is technically straightforward if polymer films can be grown so as to bridge the gap between the electrodes, or can be spin or drop coated. This method is well suited to the measurement of high conductivities (>lo4 S cm-I). For less conductive materials, for measurements at low doping levels, or for materials that do not form thick films, the sandwich technique is better, although technically more difficult. The relative merits of the various types of dual electrode have been discussed.148An additional important point is that the thin films used in sandwich electrodes (and rotating-disk voltammetry and impedance spectroscopy) may have properties significantly different from the much thicker films required for the parallel-band method (see Section 111). Rotating-disk voltammetry has a practical range of about lo-' to lo4 S cm-' and is particularly useful for investigating the conductivity of very

Electrochemistry of Electronidly Conducting Polymer Films

E m 9. Schematic dhgmm of {A) padel-band ehde,'411142 (B) s d wiched decmk'3R1M 8nB (C)mtahgdisk w~tammcry~'" meti& for making ~ s ~ e l e c t r o n ~ ~ t s o n p o I p ~ f i l m s ,

lightly doped films.a143A redox probe in solution (e.g., ferrocene), which does not penetrate significantlyinto the polymerfilm, wes as an elsctron source or sink at the polymerlsolution interface. Conductivity vs. potential data are obtained from a simple transfornation of the current vs. potential cume horn a slow dc scan.143,149 Impedance spectroscopy is best suited for the measurement of eltronic conductivities in the range 1v7to 10-1S cm-'.l" In principle, it is perhaps ~e best method for this range, but it is o h n difficult to interpret impdance data for conducting polymer films. The chargetmsfer resistance can make measurements of bulk film resistances inaccurate,'45 and it is often difficult to distinguish between the film's ionic and electronic resistances. This is even more of a problem with chron~am~metry and chr~no~otentiometly,'" so that these methods are best avoided.

'"

"

Peter G, Pickup

Em

10. Cyclic voltarmnetry (top) aad in situ e b W c mimnce m m ) of poIyj3-methylthiopbene) from paaWband e h d e 9(A)] exin 0.1 M B F & 3 7 (Reprinted with q l pmWm from J. Am C h Sot. ll& %6%7879, 1 m Copfigla MI, American chemical kckq.)

Electrachemistry of Elec4ronicslIy Conducting Polymer Films

The electronic conductivity of a conducting polymer can vary by more than 10 orders of magnitude with changing potentid. For lightly pdoped materials, the conductivity generally increases exponentially with increasing potential (seeFig. 1 1). S l o p of 6 1 3 0r n decade-' ~ are

Figure 11. Cyclic votammetry (top) and in si&elmnic conductivity hrn rotating-disk voltammetry [4, Fg.%C)] and sandwich el& voltam~netrytQ Fg.901 for poiy(3-methylthiqhme) in acetonitrile coataining 0.1 M Bn&lOe 60 (Rqrhkd from J. Odmmsh and P.G. Rckq, "In situ conductivity of poly-(3-methy lthiophene) and (3-methylthi~phene)~~u(22'-bip@k)z ( 3 - ( p y r r o l - l - y ~ 1 } pyridine)ala c o p d ~ J." Elecbr&. C h 297, 211-224, 1991, with kind p e d o n from Elsevier %acesSA.)

572

Peter G, Pickup

typical. There is no well-defined on/off transition; measurable conductivities can be observed at potentials as much as 700 mV prior to the voltammetric peak potential.MAt high potentials, the conductivity levels off and then declines, as illustrated in Fig. 10. It should be noted that in most cases the reversible decline in conductivity at high potentials is very difficult to observe. SOzwas used as the solvent for the experiment in Fig. to minimize the irreversible overoxidationthat occurs in acetonitrile, water, and other solvents (Section V). Overoxidationcauses an irreversible decline in conductivity.33 The electronic conductivity of lightly doped polymers is proportional to the concentration of charge carriers (polarons) and can therefore be treated as redox conduction (i.e., driven by a concentration gradient of oxidized sites with a constant diffusion c~efficient).'~~>'~~>'~~ At higher doping levels, bipolarons become the dominant charge carriers.103,106,151 The fully oxidized polymer is nonconductive, suggesting that bipolarons move by electron hopping from polaron or unoxidized sites.37This type of "mixed valence" conductivity will disappear when there are no unoxidized or polaron sites.37However, another way of looking at this is to say that the valence band is empty. Electron transport in n-doped polymers has been studied much less than in p-doped materials. One of the main reasons for this is the poor stability of most n-doped materials, which makes it very difficult to measure reproducible conductivities that are characteristic of the material, rather than its extent of degradation. However, by using low temperatures and very dry CHjCN or NH3 as the solvent, Wrighton and co-workers were able to make in situ conductivity vs. potential measurements on n-doped poly(3-methylthiophene) (Fig. 12).152The ndoped form showed a much narrower region of conductivity than the p-doped form, and the maximum conductivity was several orders of magnitude lower. These results suggest that the conduction band of the polymer (filled during n-doping) is narrower than its valance band (emptied during p-doping). Similar results were obtained for poly(dithienylvinylene), which is more easily n-doped than poly(3methylthiophene), although in this case the lower conductivity of the n-doped form was attributed to the effect of the larger counter-ion inserted into the film.39

Electrochemistry of Electronically Condnchg Polymer Films

F i 12 Cyclic vultammogmm and dedmk mdmtion m t at a fixed potential difference for poly(3-mthylthiophene) in acetonitrile containing 0.1 M B ~ N P P ~ '(Repntd " wilh pmi&m from Chm Marfer.1,2-4, NB.Cowright lass,McanChmical~.)

Because of their high electronic conductivities, the rates of electrochemical pmesses in conducting polymers are generally controlled by ion transThe ionic content of a film also has a strong influence on its

Peter G*Pickup

thermodynamic properties. Knowlsdge of the ion transport properties of conducting polyme~is therefore crucial to a full understanding of their electrochemistry. The next subsections M b e how ion transport in conducting polymers has been investigated, The final subsection illustrates how ion trans@ effects are manifested in cycIic voltammetry. (i) Resistance Measurements on F r e e - S h d n g Filnas

The most direct method for measuring the ionic conductivity of a conducting polymer film is to bathe each side with an electroIyte solution and measm the dc or ac resistance between the two pools of electrolyte. By usin a film grown on a gold minigrid @g. 13), Burgmayer and were able to measure the ionic conductivity of polypymle as a function of its oxidation state. They found that the neutral (undo@) polymer was almost impermeable to ions, while the o x i d i d Woped) form exhibited a high anion conductivity but low cation conductivity. The cationic pdoped polymer was therefore concluded to be permselective. Direct current resistance measurements on free-standing fiIms of polypyrrolel" and a pyridinium-substituted polyWrmle'56have provided important reference data for understanding the ~hronoam~rornetry~~~ and impedancelMof conducting polymer films on electrodes. More recently, ac measurements on ke-standing films have been used to measure the


575

ionic conductivity of polyaniline as a function of pH and potential,lS7to distinguish between bulk and interfacial impedances,1s8and to demonstrate cation permselectivity for a polypyrrole-polyanion composite.159

(ii) Chronoamperometry, Chronocoulometry, and Chronopotentiometry It was realized early on that because of their hgh electron transport rates, the charging rates of conducting polymer films would be controlled predominantly by the rate at which charge-compensating ions [Eq.(l)] could be extracted from, or ejected into, the bathing electrolyte solution.160,161 However, these and some other studies em loying chronoamperometry and Chronocoulometry are flawed8,85, 55,162 because the transport of ions was treated as diffusion, with the much greater migration component being neglected. This can result in errors in estimated ionic conductivities and ion diffusion coefficients of two orders of magnitude or more.ls5 Because the diffusion component is so much smaller than the migration component, it can, in fact, be safely neglected in most cases. Another important issue in the use of potential step methods is the magnitude of the step.8.163For work in solution and on redox polymermodified electrodes, it is conventional to step right across the redox wave using a large-amplitude step. Ths avoids problems due to the uncompensated solution (and film) resistance, and allows the bulk concentration to be used in the Cottrell equation. However, for conducting polymermodified electrodes, this presents problems because the properties of the films change so much with potential. For example, a potential step on a fully reduced polypyrrole film [e.g., -1.0 V in Fig. 4(B)], to a potential at which the film is highly oxidlzed (e.g., +0.5 V), causes the electronic conductivity of the film to increase by more than six orders of magnitude,140while its ionic conductivity increases by at least a factor often.164 The resulting current-time response often shows a peak (see Fig. 1 4 ) ' ~ ~ and clearly cannot be analyzed using a simple model based on single electronic and ionic conductivity parameters. Although a number of attempts have been made to model large-amplitude potential step data for conducting polymers (see Section IX),data from small-am litude steps A series have been more useful for measuring ionic conductivities.l5' ' of small-amplitude experiments could even provide information on the potential dependence of the film's ionic conductivity.

P

Peter G.Pickup

As an alternativeto potential step experiments, current steps have also been used.16311Q167 Again, small-amplitudeexperiments are preferable,163 and a migration model should be used for data analysis.'67 i

Impedance Spectroscopy

As a small-amplitude technique, impdance spectroscopy is particulady attractive for investigating ion transport in conducting polymers. The impedance characteristics of conducting polymer films can be very complex, and many different models and equivalent circuits have been employed in data analysis.'68However, in many oses the ionic resistance of the film can be quite easily estimated from a complex impktnce plot, without assuming any particular physical model.'" As with potential and current step methods, ion transport should be treated as a migration process (the diffusion component can generally be neglected).144 Use of a diffusion made1 yields diffusion coefficients (or mobilities) that can be several orders of magnitude too high.l"

Electrochemistry of EIectronicaUy Conducihg Polymer Films

Figure 15 shows a set ofcomplex plane impedance pIots for polypyrrole in NaClo4(sq).170These data sets are all relatively simple because the electronic resistance of the film and the charge-transferresistance are both negligible relative to the uncompensated solution resistance (R,) and the film's ionic resistance (R,).They can be approximated quite well by the transmission line circuit shown in Fig. 16, which can represent a variety of physicavchernical/morphological cases from redox polymers'7 to porous electrodes.ln Whichever physical interpretation is chosen, the difference between the high-frequency real axis intempt Ern)]and the low-frequency limiting real impedance [Z'(low)] is one-third of the film's ionic resistance (i.e., RI = 3[Z'(low) - Z'(high)]). Ideally, the real component of the

RplrslS- C o a p h r d . l l s i m p d m o . ~ f w t r o l ~ ~ ( A ~ O * I I ~ -Om& (C) 4 . 2 (, 1))4 3 , d (E) 4.4 V us. br NaOdrp). Ths4ddpoinQIst6iwahmPt~~ofsobetwlpU m s ~ t n b a r a , ~ f m a r X , R c n a a d E ! O . ~ ~ ~ ~ o f ~ d u e t M t y a e m p r o b s c b r ~ i u r ~ h s m i w h d Nypyrmls 5h%lbI.E k # m n d a m &3% 359-364, IW, with kind p d & tn#n Ba#viw m e $,A,)

Peter G . Pickup

impedance should become constant at low frequency, However, inhomogeneities and slow pimesses within the film usually cause 2' to continue increasing slightly even at the lowest accessible frequencies. R ' (low) is thereforektestimatedby extrapolating the low-frequency data as shown in Fig, 15. The emns from this approximation appear to be minor.59,169

(iv) Electrochemical Quam Crysak Microbalance (EQCM)Studies The above methds measure ion transport rates as ionic conductivities. By varying the parameters of the elcperirnent, it is often possible to indirectly identify the mobile ion(s),ln and in some cases to estimate individual ion mobilities or diffusion coeff~cients.'~~ Because of the uncertainty in identifyingandquantifyingmobile ions in this way, EQCM studies that provide the (net)mass change accompanying an electrochemical pmmxhave played an important complementary role. The results from EQCM studies on conducting polymer films can be ambiguous because the measured mass change results from acornbination of independent ion transport, coupIed ion transport (i.e., salt transport), and solvent transport, In addition, changes in the viscoelasticity of the films can cause apparent mass changes. The latter problem can be minimized by checking the frequency w n s e of the EQCM,'" while the various mass transport components can be separated by careful data analysis.175,176

Electrachemistry of Electronically Conducting Polymer Films

The value of the EQCM is exemplified by the data shown in Fig. 17."" The fmt reduction of the polypyrrole film was initially a m m p e d by a mass demme, as e x p k d for anion expulsion according to Eq. (I). However, after the reduction was ca. 75% complete, the mass began to in-, indicating a switch of the charge neu-on mechanism to d o n insertion (5)1.

m.

Peter G. Pickup

580

(-pyn+-)nA'

+ nC+ (solution) + ne +(-py-)nCA

(5)

Subsequent cycles show similar mass changes, with cation transport being dominant at low potentials and anion transport dominant at high potentials. This and other EQCM studies have shown that the balance between anion and cation transport in polypyrroles is very sensitive to a variet of experimental conditions, including the rate of film growth, 1% the counter-anion, 178-180 the cation in solution,179,181 and substituents on the p y r r ~ l e . ' ~ ~On > ' ~the~ >other ' ~ ~hand, ion transport in polythiophenes is dominated by anion t r a n ~ p o r t . ~ ~For ~ . ' poly~~.'~~ aniline, which is normally studied in aqueous acid, a combination of anion and proton transport has been observed.lp6In situ measurements of mass changes using a regular analytical balance have revealed that proton transport is dominant at low pH values, but anion transport becomes more important as the H is increased.lp7Anion transport is dominant in nonaqueous media.f87

(v) Other Techniques A variety of other techniques have been used to investigate ion transport in conducting polymers. The concentrations of ions in the polymer or the solution phase have been monitored by a variety of in situ and ex situ techniques! such as radiotracer studies,188X-ray photoelectron spectroscopy (xPs),'~~potentiometry,'" and Rutherford backscattering. he probe-beam deflection method, in which changes in the density of the solution close to the polymer surface are monitored, provides valuable data on transient ion transport.191Rotating-disk voltammetry, using an electroactive probe ion, provides very direct and reliable data, but its utility is very limited.156,192,193 Scanning electrochemical microscopy has also been used.194

(vi) Cyclic Voltammetry Revisited Although cyclic voltammetry in a variety of electrolyte systems, and with a variety of doped polymers, has shown strong effects due to ion transport, it has provided little understanding. In fact, one of the important uses of ion transport data from the techniques discussed in the preceding subsections is that they help to provide an understanding of the cyclic voltammetry behavior of conducting polymer films. Their importance will

Electmhemistrg of Electronidly Conducting Polymer Films

be illustrated with polypymle, which is probably the most temperamental of the commonly studied materials, Figure 18 shows cyclic voltammograms of polypyrrole in propylene carbonate." The fust scans in the 0.5 to -0.2 V (vs. Ag/AgCl) region and the first cathodic scan to -1.1 V are very different from subsequent scans over the wider potential range. SimiIar behavior has been m e d in acet~nitrile~~~~" and in water for polypylrole c m ~ a large g anion.lu It is caused by the low mobility of the counter-anion, which results in uptake of cations during the fmt reduction M, (my rather than the expected expulsion of anions 1Eq.(1)1. The mobility of anions in polypyrrole, and hence the film's cyclic voltammetry, is dependentupon the anion, the solvent, and the structureof the film. Sirmce cations can alsobe involved in the electrochemistry of the film, they too can influence its v o l ~ t r i c characteristics.'%

Peter G. Pickup

VII. SOLVENT TRANSPORT As illustrated in the previous sections, the electrochemical properties of conducting polymer films are strongly influenced by polymer-ion interactions. These interactions are in turn influenced by the nature of the solvent and the solvent content of the film. Consequently, the electrochemical behavior of conducting polymer films can be highly solvent dependent.59,114,115,197 Films can even become electrochemically inactive because of lack of solvation.114,197 The solvation of conducting polymer films, and solvent transport during the following doping and undoping, have been investigated primarily by gravimetry . The electrochemical quartz crystal microbalance can provide useful information on solvent transport if the contributions of solvent, salt, and ions to the change in mass can be unravelled.175,176 Studies on polybithiophene in acetonitrile revealed transport of ca. 0.5 solvent molecules per electron into the film during oxidation, and subsequent expulsion during reduction.lS4 In situ gravimetry on polyaniline has revealed a complicated dependence of solvent content and transport of the solvent (aqueous or nonaqueous) on p ~ . 1 8Two 7 to three water molecules per electron can be inserted during oxidation in strongly acid solutions, while in propylene carbonate, less than one solvent molecule is involved. Propylene carbonate is first ejected from the film during oxidation, then inserted, and finally ejected again in the final stages. The rate of water transport through polyaniline has been measured by mass spectrometsy.19sConsistent with the gravimetric results cited above, the permeability of the oxidized state was found to be much higher than that of the reduced state. Information about solvent transport during electrochemical cycling can also be obtained by monitoring changes in film thickness. Ellip~ o m e t and ~ ' ~in ~situ scanning tunneling and atomic force microscopies198> O0 have been used. VIII. CHARGE-TRANSFER KINETICS

The kinetics of charge transfer between metallic electrodes and conducting polymer films have proved to be difficult to investigate, and little reliable data exist. Charge-transfer limitations have been claimed in cyclic voltammetry, and Butler-Volmer kinetics have been used in a number of


583

models for v ~ l t a m r n e t r y . ~However, ~ ' ~ ~ ~ ~the unusual voltammetry of conducting polymers, and especially the nonkinetic peak separations, make estimation of charge-transferkinetic parameters from cyclic voltammetry highly suspect. The only way to obtain reliable charge-transfer kinetic data appears to be through use of impedance spectroscopy, and even with this technique there are many potential pitfalls. Albery and ~ o u n t have ~ ' ~ provided a theoretical treatment of the effects of the charge-transfer resistance on the impedance response of an electroactive polymer film. The impedance response depends to some extent on whether the charge-transfer resistance is at the polymerlelectrode interface (electron-transfer resistance) or the polymer/solution interface (ion-transfer resistance) and the relative magnitudes of the film's electronic and ionic resistances. In all cases, a high-frequency semicircle is observed in the complex plane impedance plot, and so its assignment is nontrivial,'" despite the criteria provided by the theoretical treatment. Assignment is further complicated by the fact that high-frequency semicircles can also result from bulk rocesses2 M W and can involve several processes with similar resistances.E 8 From an analysis of data for polypyrrole, Albery and Mount concluded that the high-frequency semicircle was indeed due to the electrontransfer resistance.203We have confirmed this using a polystyrene sulfonate-doped polypyrrole with known ion and electron-transport resist a n c e ~ .The ' ~ ~charge-transfer resistance was found to decrease exponentially with increasing potential, in parallel with the decreasing electronic resistance. The slope of 60 mvfdecade indicates a Nernstian response at low doping levels. By comparing impedance results for polypyrrole in electrolytepolymer-electrolyte and electrode-polymer-electrolyte systems, Deslouis et al. 15' have shown that the charge-transfer resistance in the latter case can contain contributions from both interfaces. Charge-transfer resistances at the polymer/electrode interface were about five times higher than those at the polymerlsolution interface. Thus the assignments made by Albery and ~ o u n t , and ~ ' ~by Ren and ~ i c k u p ' ~are ' supported, with the caveat that only theprimary source of the high-frequency semicircle was identified. Contributions from the polymerlsolution interface, and possibly from the bulk, are robably responsible for the deviations from the theoretical expressions.8 5 Amemiya et aL2O6have combined spectroelectrochemical and impedance experiments to probe the origin of high-frequency semicircles in

584

Peter G. Pickup

impedance behavior. For polypyrrole polystyrene sulfonate in Bu4NCI(aq), they found that changes in the absorbance of the film matched the impedanceresponse in t h s high-frequency region, indicating that the semicircle results from faradaic charging of the film. They therefore assigned the semicircle to charging of the outer surface of the film, with adsorption rather than insertion of the bulky cation.

IX. NUCLEATION MODELS FOR OXIDATION OF CONDUCTING POLYMERS The unusual cyclic voltammograms and responses to large-amplitude potential steps of a variety of conducting polymer films have prompted a number of groups to develop nucleation models for their oxidation. The key features that they have sought to explain are the peaks observed in anodic chronoamperometry (see Fig. 14), and the dependence of the anodic eak position on scan ratem7and the time spent in the undoped state.208w Aoki and co-workers have developed, and used extensively, a model for oxidation based on the propagation of a conductive front.'07 The polymer is assumed to be fully oxidized and highly conductive on the electrode side of the front, and fully reduced and nonconductive on the solution side. Oxidation occurs at the front according to Butler-Volmer kinetics. Although this model doesn't appear to be physically reasonable, its predictions do agree reasonably well with experimental observations ~ ~ ~chronoamper~metry~'~ on polypyrrole from cyclic ~ o l t a r n m e t r yand films. Furthermore, the conductive front has been observed visually in an experiment where a 6-mm-long strip of polypyrrole with an electrical contact at one end was extended into an electrolyte solution.211 ow ever, inspection of concentration vs. distance profiles obtained using absorbance~from a photodiode array (Fig. 19) reveals that there is no sharp boundary between the oxidized and reduced zones. The profiles in Fig. 19 are clearly not purely diffusional, but they invalidate Aolu' s model, which requires a sharp, atomic-scale boundary. It is also important to note that the geometry of Aoki's photometric experiment2" differs from that of the conventional coated-electrode geometry, and that the rate-limiting process may be different. In Aolu's experiment, ion transport will occur across the film, while electron transport occurs along the length of the film. Since these dimensions differ by a factor of 600,electron transport becomes rate

Electrochemistry of EiectmnicaUy ConductingPolymer Films

limiting. With a conventional coated electrode, both ion and electron transport occur across the film thickness, and so it is more likely that ion transport will be rate limiting. Otero and co- worker^^,^'^ have visually observed nuclei of oxidized polymer in thin polypyrrole films on electrodes, They attribute these to sites of counter-ion and solvent ingress. A nucleation model based on the growth of ionically conductive zones provides good agreement with experimental chronomperometric responses. Nucleation models have also been invoked for the oxidation of

polyaniline films.209,213 In both cases, the nucleation of electronically conductive zones was assumed, following Aoki's well-documented model. The possibility that the nucleation of ionically conductive regions couId be rate Iimiting does not appear to have been considered.

X. MEDIATION OF REDOX REACTIONS IN SOLUTION One of the major potential applications of conducting polymers is as mediators or catalysts for electrochemical sensors and electrosynthesis.

Peter G. Pickup

There has therefore been much interest in the mediation of redox reactions in wlution by conducting polymer-modifed elatmh. Theoretical aspects of mediation and electrwatalysis by polymercoated e l m s have most recently been reviewed by L y o n ~ . In ' ~ order for elatrochemisby of the solution s p i e s (substrate) to occur, it must either diffuse through the polymer fdm to the underlying elmor there must be some mechanism for electron tramport across the film (Fig. 20). Depending on the relative rates of these pmmses, the mediated reaction can occur at the polymerlelectrode interface (a), at the polymedso~utioninterface (b), or in a zone within the polymer film (c). The equations governing the readion depend on its lmtion,12which is there fore an important issue. Studies of mediation also provide information on the rate and mechanism of electron transport in the film, and on its

permeability.

Rotating-disk voltammetry is the most appropriate and most commonly employed methd for studying mediation. In most systems that have been studied, there has been little penetration of the subsbate in solution into the polymer film. Tbis can be demonstrated most easily if the polymer film is nonconductive at the f o n d potential of the substrate. Then the absence of a redox wave close to this potential for an eI-e dwith a very thin film provides excellent evidence that the substrate daes not penetrate the film ~ i g n i f i r n t l ~For . ' ~ cases ~ where the film is conductive at the formal potential of the substrate, more subtle argu-

Electrochemistry of Electronically Conducting Polymer F i

587

ments214are required, or resort can be made to various analytical methods to prove that the substrate is not present in the films.215 Once it has been established that the substrate is oxidized or reduced at the polymer/solution interface, it is important to identify next the rate-limiting step and the mechanism. There appear to be a number of conflicting conclusions in the literature in this respect, but closer inspection reveals that these are due largely to differences in the systems studied. The crux of the debate has focused on how the potential drop across the metallpol mer/solution interface is distributed. Kazarinov and co-workers214, 16,217 claim that the doped polymer behaves like a metal or a semiconductor and that the potential drop is primarily at the polymerlsolution interface. The mechanism of electron transfer to and from the substrate is then analogous to electron transfer at a metal/solution interface and follows Butler-Volmer-type k ~ n e t i c sThis . ~ ~approach ~ was successful for interpreting data for a number of systems in which the substrate was oxidized at potentials at which the conductivity of the polymer was high (e.g., ferrocene oxidation at polythlophene216). On the other hand, ~oblhofe?" has pointed out that since conducting polymer films are solvated and contain mobile ions, the potential drop occurs primarily at the metallpolymer interface. As with aredox polymer, electrons move across the film because of concentration gradients of oxidized and reduced sites, and redox processes involving solution species occur as bimolecular reactions with polymerredox sites at the polymerlsolution interface. This model was found to be consistent with data for the reduction and oxidation of a variety of species at poly(N-methylpyrrole). This polymer has a relatively low maximum conductivity - S cm") and was only partially oxidized in the mediation experiments, which may explain why it behaved more like a redox polymer than a typical conducting polymer. Mao and ~ i c k ufound ~ ' ~ that ~ for cobaltocene oxidation at polypyrrole and ferrocene oxidation at films of a pyridinium-substituted polypyrrole, the rate-limiting step at currents below the diffusion-limited current was electron transport through the polymer films. In other words, the potential drop was primarily across the film. This was proven by the fact that electronic conductivities obtained from rotating-disk voltammograms were in good agreement with values from independent methods.149It was shown that the electronic and redox conduction models provided equivalent descriptions of electron transport (hopping) through the film. Exarn-

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ples of penetration of the substrate into the polymer film during mediation are rare,156and there has been no analysis of the kinetics in these cases.

XI. ELECTROCATALYSIS Although the parent conducting polymers shown in Structures 2-4 have shown electrocatalytic activity for a variety of substrates, the main use of conducting polymers in electrocatalysis has been as supports for other catalytic species. These have been incorporated as covalently attached substituents, by ion exchange, by electrochemical or chemical deposition and intercalation, and by encapsulation during the polymerization. Electrocatalysis by modified polypyrrole filmsl7>l8 and b conducting polymer films containing metal particles52or enzymes219>2JO has been reviewed elsewhere. Polypyrrole shows catalytic activity for the oxidation of ascorbic a ~ i d c, a~t e ~c h ~o l ~>,and ~~~ '~the~quinone-hydroquinone couple.223Polyaniline is active for the quinone-hydroquinone and ~ e ~ + / l ? ecou~* ples;2z>225oxidation of hydrazine226and formic acid:27 and reduction of nitric Poly@-phenylene) is active for the oxidation of reduced nicotinamide adenine dinucleotide (NADH), catechol, ascorbic acid, acetaminophen, and p-aminophenol.229Poly(3-methylthiophene) catalyzes the electrochemistry of a large number of neurotransmitter^.^^^ XII. ION EXCHANGE Oxidized (p-doped) conducting polymers are generally cationic and therefore contain charge-balancing counter-anions [Eq. (I)]. Sincethese anions are exchangeable,"' most p-doped conducting polymers are also anionexchange polymers. Similarly, n-doped polymers are generally cationexchange polymers. The ion-exchange properties and capacity of a conducting polymer clearly will depend on its oxidation state and therefore can be controlled electrochemically. This has led to applications in ion-releasing devices," ion-gate devices,'" and electrochemical deioni-

ati ion.^^^

There has been much interest in modifying the ion-exchangeproperties of conducting polymers with substituents or polymeric counter-ions. Cationic substituents, such as ammonium234and pyridinium235groups, increase the polymer's anion-exchange capacity and increase anion trans-


589

port rates.ls6Anionic substituents such as carboxylates8and s ~ l f o n a t e ' ~ ~ groups impart cation-exchange properties and can compensate for the positive charge on the backbone of ap-doped polymer, leading to so-called "self-doped materials.236Polyanions such as polystyrene sulfonate, incorporated as charge-compensating anions during polymerization, also impart cation-exchange properties when the positive charge on the conducting polymer backbone is decreased by reduction or partial reducLike other ion-exchange polymers, conducting polymers have been used to immobilize electroactive ions at electrode surfaces. Often the goal is electrocatalysis, and conducting polymers have the potential advantage of providing a fast mechanism for electron transport to and from the electrocatalytic ions. The intrinsic ion-exchangeproperties of p-doped polymers have been used to bind electrocatalytic anions such as p o r p h y r i n ~and ~ ~phthalocy~ a n i n e ~ .cation-substituted ?~~ polymers have been used to bind anions such as [ F ~ ( c N ) ~ ~ - ' ~o- ~? o~ m e t a l l a t e s and , ~ ~ ~porphyrins241; and anionsubstituted polymers have been used to bind a variety of cationic species such as lCo(2.2'-bipyridineh]3+n+,58 [RU(NH~)~]~'~'~~' and porphyrins.242 The electrochemical characteristics of an electroactive ion immobilized in a conducting polymer film de end on whether the film is conductive at the formal potential of the ion.%3 If the film is nonconductive, the ion must diffuse to the electrode surface before it can be oxidized or reduced, or electrons must diffuse (hop) through the film by self-exchange, as in regular ionomer-modified electrode^.^ Cyclic voltarnrnograms have the characteristic shape for diffusion control, and peak currents are proportional to the square root of the scan speed, as seen for species in solution. This is illustrated in Fig. 21 (A) for F(CN)~]'-'& in polypyrrole with a pyridinium substituent at This N-substituted polypyrrole does not become conthe ~-~osition.~" ductive until potentials significantly above the formal potential of the [F~(CN)~]'-'~ couple. In contrast, a similar polymer with a pyridinium substituent at the 3-position is conductive at this potential. The polymer can therefore mediate electron transport to and from the immobilized ions, and their voltammetry becomes characteristic of thin-layer electrochemistry [Fig. 21(B)], with sharp symmetrical peaks that increase linearly with increasing scan speed.

-21. ~yckvdmmgmm(at20tp 1 ~ m ~ s - l ) oIR(Wf eWmhtiCany trq@ in pdypymk h s with an alkyl pyridinium arb&umtatthe(A) 1 - 0 r @ ) 3 ~ o n . ~ ~ w i t . h p e r m i s s i o n fmm J. P h y . C h 96, 33&5610,1992 C@& l!B&American

i h m i d kiq.)

XIII. CONCLUSIONS Although the electrochemistry of conducting polymers is now a quite mature subject, there is still considerable debate over most of the basic pmmse.s. In part, the issues have been clouded by the diversity of different polymers that have been studied. It is often assumed that concllusions drawn from data on a certain polypymle, for example, can be extended


591

to other polypyrroles, polythiophenes, and perhaps other conducting polymers. Although this is often reasonable, it is difficult to maintain awareness of the potential pitfalls. These are compounded by the fact that the same polymer prepared at different times, by different people, or under different conditions, can exhibit significantly different properties. One of the most problematic issues, still to be fully resolved, is the dependence of the degree of oxidation on potential, as measured most commonly by cyclic voltammetry at low scan rates. There is currently no accepted model to describe the shape of the curve and the hysteresis between anodic and cathodic scans. The debate over whether the charge has a significantcomponent due to a polymer/solution double layer is still not fully resolved. However, despite this lack of a basic understanding of the electrochemistry of these materials, much progress has been made in characterizing polymerization mechanisms, degradation processes, transport properties, and the mediation of the electrochemistry of species in solution. These advances have facilitated the development of numerous applications of conducting polymers, and so it can be anticipated that interest in their electrochemistry will remain high.

ACKNOWLEDGMENT The author thanks Zhigang Qi, Colin Cameron, Nengyou Jia, and Brian MacLean for their helpful comments during the preparation of this chapter.

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Cumulative Author Index for Numbers 1-33 Author

Agarwal, H. P. Albella, J. M. Allongue, P. Amokrane, S. Andersen, J. E. T Andersen, H. C. Andersen, T. N. Andersen, T. N. Aogaki, R. Appleby, A. 1 Aramata, A. Arvia, A. J. Arvia, A. J. Augustynski, J. Badawy,W. A.

Title

X Rays as Probes of Electrochemical Interfaces Reaction Kinetics and Mechanisms on Metal Single Crystal Electrode Surfaces Recent Developments in Faradaic Rectification Studies Electric Breakdown in Anodic Oxide Films Physics and Applications of Semiconductor Electrodes Covered with Metal Clusters Analysis of the Capacitance of the Metal-Solution Interface. Role of the Metal and the Metal-Solvent Coupling Automated Methods of Corrosion Measurement Improvements upon the Debye-Huckel Theory of Ionic Solutions The Manganese Dioxide Electrode in Aqueous Solution Potentials of Zero Charge of Electrodes Nonequilibrium Fluctuations in the Corrosion Process Electrocatalysis Underpotential Deposition on Single-Crystal Metals Transport Phenomena in Electrochemical Knetics A Modern Approach to Surface Roughness Applied t o ~lechochemicalsystems Application of Auger and Photoelectron Spectroscopy of Electrochemical Problems Photovoltaic and Photoelectrochemical Cells Based on Schottky Barrier Heterojunctions

Number

600

Cumulative Author Index Author

Badiali, J. P. Baker, B. G. Balsene, L. Barthel, J. Batchelor, R. A. Bauer, G. L. Bauer, H. H. Bebelis, S. I. Bech-Nielsen, G. Becker, R. 0.

Benderskii, V. A. Benjamin, I. Berg, H. Berwick, A. Bisgkrd, A.D. Blank, M. Bloom, H. Bloom, H. Blyholder, G. Bockris, J. O'M. Bockris, J. O'M. Bochs, J. O'M.

Title

Analysis of the Capacitance of the Metal-Solution Interface. Role of the Metal and the Metal-Solvent Coupling Surface Analysis by Electron Spectroscopy Application of Auger and Photoelectron Spectroscopy to Electrochemical Problems Temperature Dependence of Conductance of Electrolytes in Nonaqueous Solutions Surface States on Semiconductors Improvements in Fluorine Generation Critical Observations on the Measurement of Adsorption at Electrodes The Electrochemical Activation of Catalytic Reactions Automated Methods of Corrosion Measurement Electrochemical Mechanisms and the Control of Biological Growth Processes Electrocatalytic Oxidation of Oxygenated Aliphatic Organic Compounds at Noble Metal Electrodes Phase Transitions in the Double Layer at Electrodes Molecular Dynamic Simulations in Interfacial Electrochemistry Bioelectrochemical Field Effects: Electrostimulation of Biological Cells by Low Frequencies The Study of Simple Consecutive Processes in Electrochemical Reactions Automated Methods of Corrosion Measurement Electrochemistry in Nerve Excitation Models for Molten Salts Molten Electrolytes Quantum Chemical Treatment of Adsorbed Species Electrode Kinetics Ionic Solvation The Mechanism of Charge Transfer from Metal Electrodes to Ions in Solution

Number

601


Bockris, J. O'M. Bockris, J. O'M. Bockris, J. O'M. Boguslavsky, L. I. Breiter, M. W. Breiter, M. W. Brodskii, A. N. Burke, L. D. Burney, H. S. Charle, K. P. Cheh,H .Y . Childs,W. V. Chstov, S. G. Conway, B. E. Conway, B. E. Conway, B. E. Conway, B. E. Conway, B. E. Conway, B. E. Conway, B. E. Covington, A. K.

Title

The Mechanism of the Electrode Position of Metals Molten Electrolytes Photoelectrochemical Kinetics and Related Devices Electron Transfer Effects and the Mechanism of the Membrane Potential Adsorption of Organic Species on Platinum Metal Electrodes Low-Temperature Electrochemistry at High- T2 Superconductor/Ionic Conductor Interfaces Phase Transitions in the Double Layer at Electrodes Electrochemistry of Hydrous Oxide Films Membrane Chlor-Alkali Process Spin-Dependent Kinetics in Dye-Sensitized Charge-Carrier Injection into Organic Crystal Electrodes Theory and Applications of Periodic Electrolysis ~m~rovements in Fluorine Generation Quantum Theory of Charge-Transfer Processes in Condensed Media The Behavior of Intermediates in Electrochemical Catalysis Aspects of Anodic Fundamental and Chlorine Production Ionic Solvation Proton Solvation and Proton Transfer Processes in Solution Solvated Electrons in Field- and Photo-assisted Processes at Electrodes The Temperature and Potential Dependence of Electrochemical Reaction Rates, and the Real Form of the Tafel Equation Electroanalytical Methods for Determination of Alto3 In Molten Cryolite NMR Studies of the Structure of Electrolyte Solutions

li lied

Number

Cumulative Author Index

602 Author

Dakhm, L. I. Damaskin, B. B. Damjanovic, A. Dwnjanovic, A. Desnoyers, J. B. Despit, A.

Drazic, D. M. Efrima, S. Eisenberg, H. Elving, P. J.

Erdey-Ghz, T. Fahidy, T. Z. Fahidy, T.Z. Falkenhagen, H.

Title

Phase Transitions in the Double Layer at Electrodes Adsorption of Organic Compounds at Electrodes The Mechanism of the Electrodeposition of Metals Mechanistic Analysis of Oxygen Electrode Reactions Hydration Effects and Thermodynamic Properties of Ions Electrochemistry of Aluminum in Aqueous Solutions and Physics of Its Anodic Oxide Transport-Controlled Deposition and Dissolution of Metals Electrochemical Deposition and Dissolution of Alloys and Metal Components-Fundamental Aspects Electrodeposition of Nickel-Iron Alloys Electroanalytical Methods for Determination of A1203 in Molten Cryolite Iron and Its Electrochemistry in an Active State Surface-Enhanced Raman Scattering (SERS) Physical Chemistry of Synthetic Polyelectrolytes Critical Observations on the Measurement of Adsorption at Electrodes Mechanism of the Hydrogen Electrode Reaction as Studied by Means of Deuterium as a Tracer Sorption of Hydrogen on and in HydrogenAbsorbing Metals in Electrochemical Environments Proton Transfer in Solution Recent Advance in the Study of the Dynamics of Electrode Processes The Effect of Magnetic Fields on Electrochemical Processes The Present State of the Theory of Electrolytic Solutions

Number


Farges. J.-P. Farges, J.-P. Findl, E. Floyd, W. F. Foley, J. K. Friedman, H. L.

Fuller, T. F. Fuoss, R. M. Galvele, I. R. German, E. D. Gileadi, E. Gileadi, E. Girault, H. H. Goddard, E. D. Goodisman, J. Gores, H.-J. Goruk, W. S.

Grvzel, M.

Green, M.

603 Title

Charge-Transfer Complexes in Electrochemistry An Introduction to the Electrochemistry of Charge Transfer Complexes I1 Bioelectrochemistry-ElectrophysiologyElectrobiology Electrochemical Properties of Nerve and Muscle Interfacial Infrared Vibrational Spectroscopy Computed Thermodynamic Properties and Distribution Functions for Simple Models of Ionic Solutions Adsorption of Organic Compounds at Electrodes Metal Hydride Electrodes Physical Chemistry of Synthetic Polyelectrolytes Electrochemical Aspects of Stress Corrosion Cracking The Role of the Electronic Factor in the lnetics of Charge-Transfer Reactions The Behavior of Intermediates in Electrochemical Catalysis The Mechanism of Oxidation of Organic Fuels Charge Transfer across Liquid-Liquid Interfaces Electsochemical Aspects of Adsorption on Mineral Solids Theories for the Metal in the Metal-Electrolyte Interface Temperature Dependence of Conductance of Electrolytes in Nonaqueous Solutions Anodic and Electronic Currents at High Fields in Oxide Films Interfacial Charge Transfer Reactions in Colloidal Dispersions and Their Application to Water Cleavage by Visible Light Electrochemistry of the Semiconductor-Electrolyte Interface

Number

CumulativeAuthor Index

604 Author

Gregory, D. P. Gu, Z. H. Gurevich, Y. Y.

Gutmann, F. Gutmann, F. Gutmann, F. Habib, M. A. Haering, R. R. Hamann, S. D. Hamelin, A. Hamnett, A. Hansma, P. K. Harrington, D. A. Heiland, W. Herman, P. J. Hickling, A.

Hoar, T.R. Hopfinger, A. J. Humffray, A. A. Hunter, R. J. Jaegermann,W

Title

Electrochemistry and the Hydrogen Economy Recent Advance in the Study of the Dynamics of Electrode Processes Electrochemistry of Semiconductors: New Problems and Prospects Potential-Modulated Reflectance Spectroscopy Studies of the Electronic Transitions of Chernisorbed Carbon Monoxide Charge-TransferComplexes in Electrochemistry The Electrochemical Splitting of Water An Introduction to the Electrochemistry of Charge Transfer Complexes I1 Solvent Dipoles at the Electrode-Solution Interface Physical Mechanisms of Intercalation Electrolyte Solutions at High Pressure Double-Layer Properties at sp and sd Metal Single-Crystal Electrodes Surface States on Semiconductors Scanning Tunneling Microscopy: A Natural for Electrochemistry Ultralugh-Vacuum Surface Analytical Methods in Electrochemical Studies of Single-Crystal Surfaces The Structure of the Metal-Vacuum Interface Critical Observations on the Measurement of Adsorption at Electrodes Electrochemical Processes in Glow Discharge at the Gas-Solution Interface Chemistry and Chemical Engineering in the Chlor-Alkali Industry The Anodic Behavior of Metals Structural Properties of Membrane Ionomers Methods and Mechanisms in Electroorganic Chemistry Electrochemical Aspects of Colloid Chemistry The Semiconductor/ElectrolyteInterface: A Surface Science Approach

Number

605


Johnson, C. A. Jolieoeur, C.

JurkiewiczHerbich, M. Kebarle, P. Kelbg, G. Kelly, E. I. Kahn, S. U. M. Kahn, S. U. M.

Kahn. S. U. M. Krischer, K.

Lefebvre, M. C. Lust, E. Lyklema, J. Lynn, K. G. Lyons, M. E. G. MacDonald, D. D. MacDonald, D. D.

Title

The Electrochemical Activation of Catalyhc Reactions The Metal-Gas Interface Hydration Effects and Thermodynamic Properties of Ions Electrochemical Deposition and Dissolution of Alloys and Metal Components-Fundamental Aspects MetalISolution Interface: An Experimental Approach Gas-Phase Ion Equilibria and Ion Solvation The Present State of the Theory of Electrolytic Solutions Electrochemical Behavior of Titanium Photoelectrochemical Kinetics and Related Devices Quantum Mechanical Treatments in Electrode Kinetics Some Fundamental Aspects of Electrode Processes Principles of Temporal and Spatial Pattern Formation in Electrochemical Systems The Mechanism of Coarse and Disperse Electrodeposits Electrochemical Impedance Spectroscopy and Its Applications Establishing the Link Between Multistep Electrochemical Reaction Mechanisms and Experimental Tafel Slopes The Potential of Zero Charge Interfacial Electrostatics and Electrodynamics in Disperse Systems The Nickel Oxide Electrode Electrochemistry of Hydrous Oxide Films The Electrochemistry of Metals in Aqueous Systems at Elevated Temperatures Impedance Measurements in Electrochemical Systems

Number

606


Title

Maksimovit, M.D.

Theory of the Effect of Electrodeposition at a Periodically Changing Rate on the Morphology of Metal Deposits Electrochemical Processes at Biological Mandel, L. J. Interfaces Marchiano, S. L. Transport Phenomena in Electrochemical Ionetics Lithium Batteries with Liquid Depolarizers Marincic, N. Markin, V S. Thermodynamics of Membrane Energy Transduction in an Oscillating Field Martinez-Duart,J. M. Electric Breakdown in Anodic Oxide Films The Mechanism of Charge Transfer from Matthews, D. B. Metal Electrodes to Ions in Solution Mauritz, K. A. Structural Properties of Membrane Ionomers McBreen, J. The Nickel Oxide Electrode McKinnon, W. R. Physical Mechanisms of Intercalation McKubre, M. C. H. Impedance Measurements in Electrochemical Systems Mizuno, T. Sorption of Hydrogen on and in Hydrogen-Absorbing Metals in Electrochemical Environments Analysis of Mass Transfer and Fluid Flow for Modi, V. Electrochemical Processes The Electrochemical Splitting of Water Murphy, 0. J. Nagarkan, P. V. Nigy, Z. Nigy, Z. Neophytides, S. G. Newman, J Newman, J. Newman, J. Newman, K. E. Nielsen, L. V.

Electrochemistry of Metallic Glasses DC Electrochemical Techniques for the Measurement of Corrosion Rates DC Relaxation Techques for the Investigation of Fast Electrode Reactions The Electrochemical Activation of Catalytic Reactions Photoelectrochemical Devices for Solar Energy Conversion Determination of Current Distributions Governed by Laplace's Equation Metal Hydride Electrodes NMR Studies of the Structure of Electrolyte Solutions Automated Methods of Corrosion Measurement

Number


Author Niganci@lu, K.

Novak, D. M. O'Keefe, T.J. Orazem, M. E. Oriani, R. A. Otero, T. F. Padova, J. I.

Parkhutik, V. P. Parsons, R. Pavlovic, M. G. Perkins, R. S. Pesco, A. M. Pickup, P. G. Piersma, B. Pilla, A. A. Pintauro, P. N. Pleskov,Y.V. Plonski, I.-H.

Pons, S.

6(n

Title Design Techniques in Cathodic Protection Engineering ~undamentalind Applied Aspects of Anodic Chlorine Production Electrogalvanizing Photoelectrochemical Devices for Solar Energy Conversion The Metal-Gas Interface Conducting Polymers, Electrochemistry, and Biomimicking Processes Ionic Solvation in Nonaqueous and Mixed Solvents Ellipsometry in Electrochemistry Electrochemistry of Aluminum in Aqueous Solutions and Physics of Its Anodic Oxide Electric Breakdown in Anodic Oxide Films Equilibrium Properties of Electrified Interphases Electrodeposition of Metal Powders with Controlled Particle Grain Size and Morphology Potentials of Zero Charge of Electrodes Theory and Applications of Periodic Electrolysis Electrochemistry of Electronically Conducting Polymer Films The Mechanism of Oxidation of Organic Fuels Electrochemical Mechanisms and the Control of Biological Growth Processes Transport Models for Ion-Exchange Membranes Electrochemistry of Semiconductors: New Problems and Prospects Effects of Surface Structure and Adsorption Phenomena on the Active Dissolution of Iron in Acid Media Advanced Electrochemical Hydrogen Technologies: Water Electrolyzers and Fuel Cells Interfacial Infrared Vibrational Spectroscopy

Number


608 Author

Popov, K. I. Popov, K. I. Popov, K. I. Popov, K. I. Pound, B. G. Power, G. P.

Title

Electrodeposition of Metal Powders with Controlled Particle Grain Size and Morphology The Mechanism of Formation of Coarse and Disperse Electrodeposits Theory of the Effect of Electrodeposition at a Periodically Changing Rate on the Morphology of Metal Deposits Transport-Controlled Deposition and Dissolution of Metals Electrochemical Techniques to Study Hydrogen Ingress in Metals Metal Displacement Reactions

Number

24

30 19 7

25 1I

Reeve, J. C.

Automated Methods of Corrosion Measurement Reeves, R. M. The Electrical Double Layer: The Current States of Data and Models, with Particular Emphasis on the Solvent Environmental Cracking of Metals: Electrochemical Aspects Ritchie, I. M. Metal Displacement Reactions Advanced Electrochemical Hydrogen Rohland, B. Technologies: Water Electrolyzers and Fuel Cells Electrochemical Investigations of the Roscoe, S. G. Interfacial Behavior of Proteins Electrochemistry and Electrochemical Rusling, J. F. Catalysis in Microemulsions Interfacial Infrared Vibrational Spectroscopy Russell, J. Rysselberghe,P. Van Some Aspects of the Thermodynamic Structure of Electrochemistry Sacher, E.

Theories of Elementary Homogeneous Electron-Transfer Reactions Saemann-Ischenko,G. Low-Temperature Electrochemistry at High-T2 Superconductor/Ionic Conductor Interfaces A Modern Approach to Surface Roughness Salvarezza, R. C. Applied to Electrochemical Systems Sandstede, G. S. Water Electrolysis and Solar Hydrogen Demonstration Projects

3 28

28 27

CumulativeAuthor Index Author

Savenko,V. I. Scharifker, B. R. Schmickler,W. Schneir, J. Schultze, J. W. Scott, K. Searson, P. C. Sepa, D. B. Seversen, M. Shchukin, E. D. Sides, P. J. Snook, I. K. Sobkowski, J. Somasundaran. P. Sonnenfeld, R. Soriaga, M. P. Stickney, J. L. Stonehart, P Szklarczyk,M.

Tarasevich, M. R.

609 Title

Electric Surface Effects in Solid Plasticity and Strength Microelectrode Techniques in Electrochemistry Electron Transfer Reactions on Oxide-Covered Metal Electrodes Scanning Tunneling Microscopy: A Natural for Electrochemistry Electron Transfer Reactions on Oxide-Covered Metal Electrodes Reaction Engineering and Digital Simulation in ElectrochemicalProcesses Electrochemistry of Metallic Glasses Energies of ~ctkationof Electrode Reactions: A Revisited Problem Interfacial Infrared Vibrational Spectroscopy Electric Surface Effects in Solid Plasticity and Strength Phenomena and Effects of Electrolytic Gas Evolution Models for Molten Salts MetaVSolution Interface: An Experimental Approach Electrochemical Aspects of Adsorption on Mineral Solids Scanning Tunneling Microscopy: A Natural for Electrochemistry Ultrahigh-Vacuum ~ & c e Analytical Methods in Electrochemical Studies of Single-Crystal Surfaces Ultrahigh-Vacuum Surface Analytical Methods in Electrochemical Studies of Single-Crystal Surfaces Preparation and Characterization of Highly Dispersed Electrocatalytic Materials Electrical Breakdown of Liquids Electrochemical and Photoelectrochemical Reduction of Carbon Dioxide Electrocatalytic Properties of Carbon Materials

Number

610


Thirsk, H. R. Tilak, B. V. Tilak, B. V. Trasatti, S. Trasatti, S. Tributsch, H. Tributsch, H.

Title

The Study of Simple Consecutive Processes in Electrcchemical Reactions Chemistry and Chemical Engineering in the Chlor-Alkali Industry Fundamental and Applied Aspects of Anodic Chlorine Production The Potential of Zero Charge Solvent Adsorption and Double-Layer Potential Drop at Electrodes Microwave (Photo)electrochernistry Photoelectrolysis and Photoelectrochemical Catalvsis Thermodynamics of Membrane Energy Transduction in an Oscillating Field J

Uosaki, K.

Theoretical Aspects of Semiconductor Electrochemistry

Van Leeuwen, H. P.

Interfacial Electrostatics and Electrodynamics in Bsperse Systems The Electrochemical Activation of Catalpc Reactions Phase Transitions in the Double Layer at Electrodes Transport Models for Ion-Exchange Membranes Electro-Osmotic Dewatering of Clays, Soils, and Suspensions Perspectives in Electrochemical Physics Chemistry and Chemical Engineering in the Chlor-Alkali Industry NMR Studies of Electrolyte Solutions Modern State of Double Layer Study of Solid Metals

Vayenas, C. G. Velichko, G. I. Verbrugge, M. W. Vijh, A. K. Vijh, A. K.

Viswanathan, K. Von Goldammer, E. Vorotyntsev, M. A. Wachter, R. Wendt, H. Wenglowski, G.

Temperature Dependence of Conductance of Electrolytes in Nonaqueous Solutions Advanced Electrochemical Hydrogen Technologies: Water Electrolyzers and Fuel Cells An Economic Study of Electrochemical Industry in the United States

Number


West, A. C. West, A. C. Wieckowski, A. Wiekowski, A. Willig, F. Wojtowicz, J. Woods, R. Wroblowa, H. S. Wurster, R.

Yang, J. D. Yeager, E. B. Yeager, H. L. Yeo, R. S. Young, L. Zana, R. Zobel, F. G. R.

611 Title

Analysis of Mass Transfer and Fluid Flow for Electrochemical Processes Determination of Current Distributions Governed by Laplace's Equation Ultrahigh-Vacuum Surface Analytical Methods in Electrochemical Studies of Single-Crystal Surfaces In Situ Surface Electrochemistry: Radioactive Labeling Spin-Dependent Kinetics in Dye-Sensitized Charge-Carrier Injection into Organic Crystal Electrodes Oscillatory Behavior in Electrochemical Systems Chemisorption of Thiols on Metals and Metal Sulfides Batteries for Vehicular Propulsion Water Electrolysis and Solar Hydrogen Demonstration Projects Analysis of Mass Transfer and Fluid Flow for Electrochemical Processes Ultrasonic Vibration Potentials Structural and Transport Properties of Perfluorinated Ion-Exchange Membranes Structural and Transport Properties of Perfluorinated Ion-Exchange Membranes Anodic and Electronic Currents at l3gh Fields in Oxide Films Ultrasonic Vibration Potentials Anodic and Electronic Currents at High Fields in Oxide Films

Number


Cumulative Title Index for Numbers 1-33 Title Adsorption of Organic Compounds at Electrodes Adsorption of Organic Species on Platinum Metal Electrodes Advanced Electrochemical Hydrogen Technologies: Water Electrolyzers and Fuel Cells Analysis of the Capacitance of the Metal-Solution Interface. Role of the Metal and the Metal-Solvent Coupling Analysis of Mass Transfer and Fluid Flow for Electrochemical Processes The Anodic Behavior of Metals Anodic and Electronic Currents at High Fields in Oxide Films Application of Auger and Photoelectron Spectroscopy to Electrochemical Problems Automated Methods of Corrosion Measurement

Batteries for Vehicular Propulsion The Behavior of Intermediates in Electrochemical Catalysis Bioelectrochemical Field Effects: Electrostimulation of Biological Cells by Low Frequencies Bioelectrochemistry-ElectrophysiologyElectrobiology

Author Frumkin, A. A. N. Damaskin, B. B. Breiter, M. W. Plzak, v. Rohland, B. Wendt, H. Amokrane, S. Badiali, J. P. Yang, J. D. Modi, V. West, A. C. Hoar, T. P. Young, L. Goruk, W. S. Zobel. F. G. R. Augustynslu, J. Balsenc, L. Bech-Nielsen, G. Andersen, J. E. T. Reeve, J. C. BisgM, A. D. Nielsen, L. V. Wroblowa, H. S. Gileadi, E. Conway, B. E Berg, H. Findl, E.

Number

Cumulative Title Index

614

Title Charge Transfer across Liquid-Liquid Interfaces Charge-Transfer Complexes in Electrochemistry Chemisorption of Thiols on Metals and Metal Sulfides Chemistry and Chemical Engineering in the Chlor-Alkali Industry

Author Girault, H. H. Farges,J.-P. Gutmann, F. Woods, R. Mine, F.

Tilak, B. V. Viswanathan, K. Computed Thermodynamic Properties and Friedman, H. L. Distribution Functions for Simple Models of Ionic Solutions Otero, T. F. Conducting Polymers, Electrochemistry, and Biornimiclung Processes Critical Observations on the Measurement Bauer, H. H. Herman, P. J. of Adsorption at Electrodes Elving, P. J.

DC Relaxation Techniques for the Investigation of Fast Electrode Reactions DC ElectrochemicalTechmques for the Measurement of Corrosion Rates Design Techniques in Cathodic Protection Engineering Determination of Current Distributions Governed by Laplace' s Equation Double-Layer Properties at sp and sd Metal Single-Crystal Electrodes

Nagy, Z. Nagy, Z. NiganciGlu, K.

West, A. C. Newman, J. Hamelin, A.

Wenglowski, G. An Economic Study of Electrochemical Industry in the United States Fahidy, T. Z. The Effect of Magnetic Fields on Electrochemical Processes Effect of Surface Structure and Adsorption Plonski, 1.-H. Phenomena on the Active Dissolution of Iron in Acid Media Szklarczyk, M. Electrical Breakdown of Liquids The Electrical Double Layer: The Current Reeves, R. M. Stahls of Data and Models, with Particular Emphasis on the Solvent

Number

Cumulative Title Index Title

615

Author

Electric Breakdown in Anodic Oxide Films Parkhultik,V. P. Albella, J. M. Martinez-Duart, J. M. Electric Surface Effects in Solid Plasticity Shchukin, E. D. and Strength Kochanova, L.A. Savenko, V. I. Electroandytical Methods for Diokic. S. S. Determination of A1203in MoIten Conway, B, E. Cryolite ElectrocataIysis Appleby, A. I. Electrocatdytic Oxidation of Uxygenatd Beden, B. Aliphatic Organic Cornpounds at Noble Uger, J.-M.

Metal Electrdes Electrocatalpic Properties of Carbon Materials The E l m k ~ c a Activation l of Catalytic Reactions Electrochemical Aspects of Adsorption on Mineral Solids Electrochemical Aspects of Colloid

Number 23 24 26

9 22

hmy,C.

Tarasevich, M.R, Khrushcheva, E. I. Vayenas, C. G. Jaksic, M. M. Bebelis, S. I. Neophytides, S. G. Somasundamn,P.

19

29

13

Goddart, E. D. I-Tunter,R. J.

11

Kelly, E. 5. Roscoe, S. G.

29

chehstry

Electcochemical Behavior of Titanium Electrochemical Investigations of the Interfacial Behavior of Proteins Electrocfiemica1 Mechanisms and the Conk01 of Biological Growth Processes Electrochemical and Photoelectrochemical Reduction of Carbon Dioxide Electrochemical Processes at Biological Interfaces Hectrochemical Processes in Glow Discharge at the Gas-Sdution Interface Electrochemical Properties of Nerve and Muscle The Electrochemical Splitting of Water E1~31~~hemjcal Techniques to Study

Hydrogen Ingress in Metals

14

Becker, R. 0. Pilla, A. A. Taniguchi, I.

20

Mandel, L. J.

8

Hickling, A.

6

Floyd, W. F.

1

Gutmann, E Murphy, 0.J, Pound, B. G.

10

15

25


616 Title

Author

Electrochemistry and Electrochemical

Catalysis in Microemulsions Electrochenistry and the Hydrogen 'Economy Electrochemistry of Aluminum in Aqueous Solutions and Physics of its Anodic

Oxide Electmhemistry of Electronically Conducting Polymer Films Electrochemistry of Hydrous Oxide Films

Ikspi6,A.

Parkhutik,V. Pickup, P.G.

Burke, L. D. Lyons, M. E. G. Electrochemistry of Metallic Glasses Searson, P. C. Nagarkan, P.V. Latanision,R. M. The Electrochemistry of Metals in Aqueous Macdonald, D.D. Systems at Elevated Temperatures Blank, M. Electrochemistry of Nerve Excitation Electrochemistry of Semiconductors: New Pleskov, Y. V. Gurevich, Y. Y. Problems and Prospects Electrochemistry of the Green, M. Semiconductor-Electrolyte Interface Electrochemistry of Sulfide Minerals Kwh, D.F. A. Elecmchernical Aspects of Stress Galvele, J. R. Corrosion Cracking Electrochemical Deposition and Dissolution Bspic. A. R. Jovie, V. D. of Alloys and Metal Components-Fundamental Aspects E l m h e m i c a l Impadance Spectroscopy and Its Applications Bockris, J. O'M. Electmle Kinetics Popov, K. I. Electrodeposition of Metal Powders with Pavlovic, M. G. Controlled Particle Grain Size and Morphology Djohc, S. S. Electrodeposition of Nickel-Iron Alloys Maksimovic, M. D. Lindsay, J. H. O'Keefe, T.J. Hamam, S, D. Electrolyte Solutions at High Pressure Boguslavsky, L. I. Elmon Transfer Effects and the Mechanism of the Membrane Potential

Number


Title Electron Transfer Reactions on Oxide-Covered Metal Electrodes Electro-Osmotic Dewatering of Clays, Soils, and Suspensions Ellipsometry in Electrochemistry Energies of Activation of Electrode Reactions: A Revisited Problem Environmental Cracking of Metals: Electmhemical Aspects Equilibrium Properties of Electrified Interphases Establishing the Link Between Multistep Electrochemical Reaction Mechanisms and Experimental Tafel Slopes Fundamental and Applied Aspects of Anodic Chlorine Production

617

Author Schmickler, W. Schultze, J.W. Vijh, A. K.

Parsons, R. Lefebvre, M. C.

Novak, D. M. Tilak, B. V. Conway, B. E.

Gas-Phase Ion Equilibria and Ion Solvation Kebarle, P.

Hydration Effects and Thermodynamic Properties of Ions

Desnoyers, J. B. Jolieoeur, C.

Impedance Measurements in Electrochemical Systems Improvements in Fluorine Generation

Macdonald, D. D. McKubre, M. C. H. Bauer, G. L. Childs,W. V. Andersen, H. C.

Improvements upon the Debye-Hiickel Theory of Ionic Solutions In Situ Surface Electrochemistry: Wiekowski, A. Radioactive Labeling Interfacial Charge Transfer Reactions in Colloidal Dispersions and Their Application to Water Cleavage by Visible Light Interfacial Electrostatics and Van Leeuwen, H. P. Electrodynamics in Disperse Systems Lyklema, J.

Number 17


618

Title

Interfacia! Infrared Vibrational SP~~~OPY

An Intscduction to the EIsctsochemistry of Charge Transfer Complexes I1 Ion and Electron Transfer across Mondayers of Organic Surfactants Ionic Solvation

Author Pons, S. Foley, J. K. Russell, J. Seversen, M. Gutmann, E Farges, J.-P. Lipkowski, J.

Number

17

13 23

Conway, B, E Bocbs, J.O'M. Padova, J. I.

7

Drazic, I).M.

19

Lithium Batteries with Liquid Dqmlarizers Low-Temperature Electcochemistry at High-T2 Superconductorfionic Conductor Interfaces

Marincic, N. hrenz. W. J. Saemann-Iscfienko, G.

28

The Manganese Dioxide Electrode in Aqueous Solution The Mechanism of Charge Transfer from Metal Electrodes to Ions in Solution The Mechanism of the Electrdepsition of Metals The Mechanism of Formation of Coarse and Disperse Electrodeposits Mechanism of the Hydrogen Electrode Reaction as Studied by Means of kuteriunr as a Tracer

Andersen, T. N.

The Mechanism of Oxidation of Organic

Gileadi, E Piersma, B. Losev,V. V.

Ionic Solvation in Nonaqueous and Mixed Solvents Iron and Its Electrochemistry in an Active State

Fuels Mechanisms of Stepwise Electrode Processes on Amalgams Mechanistic Analysis of Oxygen Electrode Reactions Membrane Chler-Alkali Pmess Metal Displacement Reactions

Breiter, M. W.

Matthews, D.B. Bockris, J. O'M. Bockris, J. O M . Darnjanovic, A. Popov, K. 0. Krsltajic. N. V, Enyo, M.

Burney, H.S. Power, G.P. Ritchie, I. M.

1

15


Title

619

Author

The Metal-Gas Interface

Oriani, R. A. Johnson, C. A. Metal Hydride Electrodes Fuller, T. H. Newman, J. MetaVSolution Interface: An Experimental Sobkowski, J. Approach Jurkiewicz-Herbich, M. Methods and Mechanisms in Electroorganic Humffray, A. A. Chemistry Microelectrode Techniques in Scharifker, B. R. Electrochemistry Microwave (Photo)electrochemistry Tributsch, H. Models for Molten Salts Bloom, H. Snook, I. K. A Modern Approach to Surface Roughness Salvarezza, R. C. Arvia, A. J. Applied to Electrochemical Systems Vorotyntsev, M. A. Modern State of Double Layer Study of Solid Metals Molecular Dynamic Simulations in Benjamin, I. Interfacial Electrochemistry Molten Electrolytes Bloom, H. Bockris,J. O'M.

McBreen, J. Lynn, K. G. NMR Studies of Electrolyte Solutions von Goldarnrner, E. NMR Studies of the Structure of Electrolyte Covington, A. K. Solutions Newrnan, K. E. Nonequilibrium Fluctuations in the Aogaki, R. Corrosion Process The Nickel Oxide Electrode

Osciliatory Behavior in Electrochemical Systems

Wojtowicz, J.

Perspectives in Electrochemical Physics Phase Transitions in the Double Layer at Electrodes

Vijh, A. K. Benderskii, V. A. Brodskii, A. N. Daikhin, L. I. Velichko G. I. Sides. R. J.

Phenomena and Effects of Electrolytic Gas Evolution

Number

5 27

31 8 22

33 9 28 17 31

2 21 10 12 33

8 17 26

620


Title PhotoelectrochemicalDevices for Solar Energy Conversion Photoelectrochemical Kinetics and Related Devices Photoelectrolysis and Photoelectrochemical Catalysis Photovoltaic and Photoelectrochemical Cells Based on Schottky Barrier Heterojunctions Physical Chemistry of Ion-Exchange Resins Physical Chemistry of Synthetic Polyelectrolytes Physical Mechanisms of Intercalation

Author Orazem, M. E. Newman, J. Khan, S. U. M. Bockris, J. O'M. Tributsch, H. Badawy, W. A.

Kitchener, J. A. Eisenberg, H. Fuoss, R. M. McKinnon, W. R. Haering, R. R. Physics and Applications of Semiconductor Allongue, P. Electrodes Covered with Metal Clusters Potential-Modulated Reflectance Spectroscopy Studies of the Electronic Transitions of Chemisorbed Carbon Monoxide Trasatti, S. The Potential of Zero Charge Lust, E. Perkins, R. S. Potentials of Zero Charge Electrodes Andersen, T. N. Power Sources for Electric Vehicles Kordesch, K. V. Principles of Temporal and Spatial Pattern Krischer, K. Formation in Electrochemical Systems Preparation and Characterization of Highly Kinoshita, K. Stonehart, R. Dispersed Electrocatalytic Materials Falkenhagen, H. The Present State of the Theory of Kelbg, G. Electrolytic Solutions Proton Solvation and Proton Transfer Conway, B. E. Processes in Solution Erdey-Gniz, T. Proton Transfer in Solution Lengyel, S. Quantum Chemical Treatment of Adsorbed Blyholder, G. Species Quantum Mechanical Treatments in Khan, S. U. M. Electrode Kinetics

Number


Title

621

Author

Quantum Theory of Charge-Transfer Processes in Condensed Media

Christov, S. G.

Reaction Engineering and Digital Simulation in Electrochemical Processes Reaction Kinetics and Mechanism on Metal Single Crystal Electrode Surfaces Recent Advances in the Study of the Dynamics of Electrode Processes Recent Advances in the Theory of Chasge Transfer Recent Developments in Fasadaic Rectification Studies The Role of Electrochemistry in Environmental Control The Role of the Electronic Factor in the Kinetics of ChasgeTransfer Reactions Scanning Tunneling Microscopy: A Natural for Electrochemistry

Scott, K.

The Semiconductor/Electrolyte Interface: A Surface Science Approach Small-Particle Effects and Structural Considerations for Electrocatalysis Solvated Electrons in Field- and Photo-Assisted Processes at Electrodes Solvent Adsorption and Double-Layer Potential Drop at Electrodes Solvent Dipoles at the Electrode-Solution Interface Some Aspects of the Thermodynamic Structure of Electrochemistry Some Fundamental Aspects of Electrode Processes Sorption of Hydrogen on and in Hydrogen-Absorbing Metals in Electrochemical Environments

AdZit, R.

Fahidy, T. Z. Gu, Z. H. Kuznetsov, A. M. Agarwal, H. P Kuhn, A. T. German, E. D. Kuznetsov, A. M. Sonnenfeld, R. Schneir, J. Hansma, P. K. Kinoshita, K. Conway, B. E. Trasatti, S.

Rysselberghe, P. van Khan. S. U. M. Mizuno, T. Enyo, M.

Number

Cumulative Title Inde x

622

Title Spin-Dependent Kinetics in Dye-Sensitized Charge-Canier Injection into Organic Crystal Electrodes Structural and Transport Properties of Perfluorinated Ion-Exchange Membranes Structural Properties of Membrane lonomers The Structure of the Metal-Vacuum Interface The Study of Simple Consecutive Processes in Electrochemical Reactions Surface Analysis by Electron Spectroscopy Surface-Enhanced Raman Scattering (SERS) Surface Potential at Liquid Interfaces Surface States on Semiconductors

Author Charle, K.-P. Willig, F. Yeo, R. S. Yeager, H. L. Mauritz, K. A. Hopfinger, A. J. Heiland, W.

Bewick, A. Thirsk, H. R. Baker, B. G. Efrima, S.

Llopis, J. Batchelor, R. A. Harnnett, A. Temperature Dependence of Conductance Barthel, J. of Electrolytes in Nonaqueous Solutions Wachter, R. Gores, H.-J. The Temperature and Potential Dependence Conway, B. E. of Electrochemical Reaction Rates, and the Real Form of the Tafel Equation Uosalu, K. Theoretical Aspects of Semiconductor Electrochemistry Kita, H. Goodisman, J. Theories for the Metal in the Metal-Electrolyte Interface Theories of Elementary Homogeneous Sacher, E. Electron-Transfer Reactions Laidler, K. J. Pesco, A. M. Theory and Applications of Periodic Electrolysis Cheh, H. Y. Popov, K. I. Theory of the Effect of Electrodeposition at Maksimovic, M. D. a Periodically Changing Rate on the Morphology of Metal Deposits Markin, V. S. Thermodynamics of Membrane Energy Transduction in an Oscillating Field Tsong, T. Y. Despic, A. R. Transport-ControlledDeposition and Dissolution of Metals Popov, K. I. Transport Models for Ion-Exchange Verbrugge, M. W. Membranes Pintauro, P. N.

Number


Title

623

Author

Number

Transport Phenomena in Electrochemical Kinetics

Arvia, A. J. Marchiano, S. L.

6

Ultrahigh-Vacuum Surface Analytical Methods in Electrochemical Studies of Single-Crystal Surfaces

Soriaga, M. P. Harrington, D. A. Stichey, J. L. Wieckowski, A. Zana, R. Yeager, E. B. Aramata, A

28

Ultrasonic Vibration Potentials Underportential Deposition on Single-Crystal Metals

14

31

Water Electrolysis and Solar Hydrogen Demonstration Projects

Sandstede, G. Wurster, R.

27

X-Rays as Probes of Electrochemical Interfaces

Abriina. H.D.

20


Index Absolute potential difference, Frumkin's contribution to, 17 Accumulation region, at photo electrodes, 487 Activation barriers, as a function of pore breakdown, 241 Actuators, via piezo electric action, 360 Adsorbates, effect of the potential of zero charge, 25 Adsorption of anions on electrode surface and the potential of zero charge, 27 Clavilier on CO adsorption on electrochemically facetted platinum, 135 of chloride, specifically as adsorbed on iron, and changes in potential of zero charge, 125 of chloride ion on passive films and the dissolution potential, 244 MacDonald on the adsorption of chloride ions in passivation, 237 of CO on electrochemically facetted platinum, 135 of diols on mercury, 188 of neutral compounds on electrodes, 185 of perchlorate ions, copper and, 94 specific adsorption, anodic dissolution and, 256 of tetrabutyl ammonium ions on tin surfaces, 99 of water calculations of by quantum chemical method, 172 Gibbs energy for and the interfacial parameter, 187

Adsorption energy for organic substances as a function of the interfacial parameter, 186 of the solvent as a function of the metal, 66 Adsorption method for potential of zero charge, 39 Adsorption processes diagrammed, 266 Adsorption spectra of electrochromic polypyrrole, 363 Affinity for metal-water, 177 Air-solution interface, Nikitas on the potential of zero charge at, 30 Albury and Mount, interpretation of the semi-circle, 584 Alloys, potential of zero charge gold and silver, 142 tin and lead, 142 Kukk and Puttsepp on, 145 metals alloys, 141 Alloy concentration, critical potential as a function of, and passivity, 262 Aluminum and the double layer parameters, tabulated, 129 and the properties of its interfaces with aqueous solutions, 128 Amalgams, Koene, and the potential of zero charge on, 160 Amplitude demodulation and determination of the potential of zero charge for cadmium-aqueous solution interfaces, 105

Index Amplitude (cont.) of dissolution currents in pit formation, 2% Amplitude equations and fluctuations during passivation, 279 Analytical formulae for microwave frequency effects, accuracy of, 464 Andersen on the open circuit scrape method for potential of zero charge, 39 Anisotropic surface potential and the potential of zero charge, (Heusler and Lang), 34 Anode life, in laboratories, 536 Anodes, large, in fluorine generation, 542 Anodic dissolution and specific adsorption, 256 Anodic photo currents for zinc oxide, 470 Anodic potential, oxidation of the polymer and, 395 Antimony double layer on, 121 non-aqueous solvents, 122 properties in aqueous solutions, 120 single crystal phases, 122 Aogaki and Tadano, examination of electrochemical nucleation, 278 Aoki, model for the formation of electronically conducting polymers, 585 Area of the electrode and the potential of zero charge, 23 Artificial muscles difference between natural muscles and, 358 diagrammed, 352 Katchalsky and Flory, 359 Kuhn et al., 359 and macroscopic motors, 343 role of three dimension collagen fibers in,(Kuhn et al.), 359 under work, 347 working, 353 Asymmetrical fluctuations controlling progress in pitting, 299 in pitting dissolution, 251 and unstable systems, 255

Auto correlation distance and total overpotential, 283 Avrami equation and polymer formation, 412 Bagotskaya and the integration of capacitance-potential curves for the determination of surface charges, 45 Bai and Conway, discussion of bubbles, 529 Band bipolaronic, 342 polaronic, 342 potential measurements, 51 1 structure in conducting polymers, 552 Barker on photo emission method for the potential of zero charge, 41 Batteries and electrode structures, 368 Baughman on piezo electric polymers, 360 Bi-layer angular movement during current flow, 348, 349, 350 Biological processes, mimicked, 425 Bipolaronic bands as a function of oxidation depth, 342 Bipolar iron-selective film, 226 Bismuth alloys of cadmium and, potential of zero charge, 145 double layer on, in contact with various electrolytes, 114 double layer parameters in various solvents, tabulated, 117 in non-aqueous solutions, the potential of zero charge, 112, 115 potential of zero charge, tabulated, 111 single crystals aqueous solution phases in, 116 potential of zero charge, 110 non-aqueous solution, 119 Boclais and Argade, friction method for the potential of zero charge, 40 Bockris and Habib, entropy of the double layer as a function of potential, 60

Index Bockris and Pany-Jones, friction method for the potential of zero charge, 40 Bockris and Sen, theory of the friction method for determining the potential of zero charge, 40 Bubbles Bai and Conway discussion, 529 effect of polarization and fluorine generation on, 528 Butler-Volmer kinetics and mechanism of electron transfer, 587 Cadmium effect of polishing on potential of zero charge of, 109 electrical double layer, parameters of cadmium in aqueous solution, 105, 106 potential of zero charge alloys of cadmium and bismuth, 145 cadmium and lead, 146 in aqueous solutions properties of cadmium, 103 single crystals, 107 in non-aqueous solutions, 107 at interfaces which have been cut, 104 properties of in aqueous solutions, 103 Cadmium-solution interface (Vitanov and Popov), 108 Campinnas University and its electrochemical group, 351 Capacitance method for the potential of zero charge, 35 Capacitance Daikhin, double layer capacitance of solid at rough electrodes, 52 of the double layer, of non-aqueous solutions, 61 as a function of Helmholtz and Gouy layers, 36 reciprocal, as a function of capacitances of layers of the interface, 37 Capacitance-potential curves, integration of for the determination of surface charges, (Bagotskaya), 45

Carbon electrodes temperature distribution thereat in fluorine generation, 540 impregnation with epoxy for fluorine generation, 544 Carbon, made non-wetting by passage of current, 527 Carrier lifetime change with potential in n-type silicon, 500 with polymer-electrolytejunctions, 496 in semiconductors, 495 Cathode potential electrochemical relaxation as a function of, 388 peak potential as a function of, and polymer formation, 413 Cells for estimating absolute potential differences, 8 for microwave conductivity measurements, 445 Charge carriers dammed-up, 475 nature of, Cyclic voltammetric studies, 561 Charge transfer kinetics for electronically conducting polymer formation, 583 Charge transport in polymers, 567 Chemical breakdown model for passivity, 236 Chloride ion adsorbed on iron, and changes in potential of zero charge, 125 adsorption on passive films and the dissolution potential, 244 adsorption of in passivation, (MacDonald)237 transformation and pit diameters, 300 Chronoamperograms experimental and theoretical, 3%, 393 theory of, 391 Chronocoulograms, 404 Chronocoulometry, 575 Clavilier and Nguyen Van Huong, study of the gold-solution interface, 77

Index Clavilier, CO adsorption on electrochemically facetted platinum, 135 Collagen fibers, three dimensional, their part in artificial muscles, (Kuhn et al.), 359 Color mimicking by means of electrochemistry, 361 Completion of oxidation for polymers and diffusion control, 414 Concentration effects of microwave energy, 442 Concentration fluctuation, in the double layer, 267 of metal ions in the double layer, 274 Concentration variation of diffusion layer, 270 Conducting polymer films, 7 Diiblehofer, 587 Pickup, 549 conducting zones in polymer formation, 409 Conducting polymers, 307 charge transfer kinetics for formation of, 583 chemical and electrochemical production, 333 shown diagrammatically, 309 Diiblehofer on, 587 dry, their physical properties, 336 electrochemical and chemical production of, 333 and electrochemistry, 308, 3 13 as material for electrochemistry, 423 and electrode polymerization, 314 films, 587 Krivoshei and Skorobagatov on, 550 n-doping, 562 nucleation modes for oxidation of, 584 stability, 327 as three dimensional electrodes, 424 Conducting zones in polymer formation, 409 Conductivity electronic, of lightly doped polymers, 572

Conductivity (cont.) measurements made during photo induced microwave effects, 488 Conformational changes in polymer formation, 378 Conway and Colledan, determination of the potential of zero charge, 34 Copper and adsorption of perchlorate ions, 94 double layer parameters for in aqueous solutions, 91 potential of zero charge in aqueous solutions, 89 single crystal phases, in aqueous solution, 90 Corrosion determination of local corrosion states by measuring dissolution currents, 277 fluctuation and corrosion processes, 217 and non-equilibrium fluctuations, 246 at photo electrodes, 480 Cost for fluorine generation, 525 for fluorine generation as a function of current density, 525 of fluorine, for four-anode callandra cells, 526 Coulovoltammograms, 419, 422 Critical potential as a function of alloy concentration, and passivity, 262 as a function of ion concentration for nickel, 263 Cross-linked structure of polypyrrole, 3 11 Cross-linking, 330 Crystal face specificity of the potential of zero charge, 21 Crystal phase and the potential of zero charge, 44 Crystal surface specificity of the potential of zero charge, 152 Current-potential curves for bipolar membranes, 228 of iron dissolution in phosphoric acid, 224

Index Cyclic voltammetric studies involving polymers, 558 and the nature of charge carriers, 561 and the nucleation loop, 557 of poly (3-methylthiophene), 564 and parallel-band electrodes, 570 Cyclic voltammograms as a function of scan rate, 559 involving polymerization, 559 with polyanaline, 566 of polypyrrole film, 581 AX, controversies over, 174 AX value, formation of the corresponding oxide and, 179 Daikhin, double layer capacitance of solid at rough electrodes, 52 Debye screening and diffuse layer near the surface, 50 Decay transients,photoelectrodesand,505 Degradation rate as a function of polarization time, 328 Degradation reactions simultaneous with electrode polymerization, 326 DeLevie on the density of broken bonds and the effect on the potential of zero charge, 75 Depletion region in microwave measurements at photo electrodes, 479 Diffusion-fluctuation currents, 284 Diffusion, 86 annealed, 86 control and completion of oxidation, for polymers, 414 electrochemical, 86 surface, 86 Diffusion components and polymer formation, 421 Diffusion layer, concentration variation thereof, 270 Diffuse layer near the surface, Debye screening and, 50 Diffusion length in typical semi conductor electrodes, 492 Diffusion-fluctuation currents, 284 Diols, adsorption on mercury, 188

Dipole potential dependence at electrode surface, 15 Dissolution, fluctuations during, 252 Dissolution current, in passivation, 292 fluctuations, 292 minimal, 285 determination of local corrosion states by measuring, 277 Dissolution potential and chloride ion adsorption, 244 Doblhofer, on conducting polymer films, 587 Dosage, medical, 371 Double layer on antimony, 121 on bismuth, in contact with various electrolytes, 114 concentration fluctuation in, 267 concentration fluctuations of metal ions in, 274 for copper in aqueous solutions, 91 Daikhin, double layer capacitance of solid at rough electrodes, 52 electrical in iron, tabulated parameters, 124 properties in lead, tabulated, 96 parameters of cadmium, in aqueous solution, 105, 106 in silver, in aqueous solutions, tabulated, 69 at silver, 67 and fractal structure of surfaces, 51 and gallium at interfaces involving it, 62 at indium, 62 models for at solids electrodes, 50 at polycrystalline electrodes, 49 at thalium, 62 Double layer capacitance of solid at rough electrodes, 52 Double layer parameters, for aluminum, tabulated, 129 and concentration fluctuations, 268, 269 for copper in aqueous solutions, 91 on iron, tabulated, 124

630 Double layer parameters (cont.) for nickel, in aqueous solutions, 127 Double layer properties in various solvents, 121 Double layer structure in concentrated solutions, 54 for platinum-DMSO interfaces, 141 Electric charge coefficients, determination thereof, 261, 265 Electric fields, and microwave fields, their interaction, 436 Electric transport, and materials, at microwave frequencies, 438 parameters of cadmium, an aqueous solution, 105,106 Electrical double layer in silver, in aqueous solutions, tabulated, 69 at silver, 67 parameters of nickel in aqueous solutions, 127 Electrocapillary breakdown model energy for the formation of breakdown, 239 for passivity, 238 Electrocatalysis, involving polypyrrole, 588 Electrochemical cells for microwave conductivity measurements, 445 Electrochemical measurements with microwave frequencies, diagrammated, 448, 449 with microwaves, 478 Electrochemical polymerization Feldberg and Rubinstein theory of, 560 kinetics of, 318 Electrochemical reaction orders in electrode polymerization, 3 17 Electrochemical relaxation, as a function of cathode potential, 388 Electrochemical responses during polymer formation, 400 Electrochemical results, anomalous, 374 Electrochemistry and conducting polymers, 308

Index and microwave measurements, 435 Electrochemistry (cont.) and polymer science, 402 Electrochromic devices, 365 Electrodes carbon impregnation with epoxy for fluorine generation, 544 temperature distribution thereat in fluorine generation, 540 dipole potential difference at surface of, 15 emersed, 12 fluctuations at, theory of, 281 fluorine-producing, 534 Frumkin analysis of non-polarizable electrodes, 130 early work on the electrochemical properties of solid electrodes, 44 non-polarizable, analysis of (Frumkin), 130 photo decay transients for 505 depletion region in microwave measurements at, 479 polycrystine, models of the double layer for, 49 polymer film of, evolution thereon, 382 on microwave effects, 443 rough Daikhin's analysis, 52, 53 double layer capacitance of solid at, 52 semi conductor, diffusion length, 492 solid early work on the electrochemical properties of (Frumkin), 44 models, for double layer at, 50 thin strip, bending due to change in surface charge, 34 Electrode materials and microwave frequency effects, 441, 444

with proper properties for microwave effects, 441

Index Electrode potentials components of, 9 energy scales and, 7 photo currents as a function of, 473 Electrode polymerization of conducting polymers, 3 14 and degradation, 325 degradation reactions simultaneous with, 326 electrochemicalreaction orders in, 3 17 schematic, 315 Electrode structure batteries and, 368 and effect on electrochemical polymer formation, 372 Electrode surface, and dipole potential difference or potential dependence, 15 Electrode systems, unstable, with asymmetrical fluctuations, 255 Electrode-electrite interface, microwave power and its effect on, 439 Electrogenerated films, storage capacity, 321 Electron transfer mechanism Butler-Volmer kinetics and, 587 in electronically conducting polymers, 568 Electron transfer rate and its exponential increase at zinc oxide-electrolyte interfaces, 512 Electronic conductivity as a function of potential, 571 in electronically conducting polymers, 571 of lightly doped polymers, 572 Electronically conducting polymers, 550, 590,591 book on, 550 and impedance spectroscopy, 576 ion exchange involving, 589 Krivoshei and Skorobagatov on, 550 and quartz crystal micro-balance, 578 Electronically conducting polymer films (Pickup), 549 Electron-ion transduction, 369 Electrosynthesis, 3 12

Emersed electrode, 12 Energy scales and electrode potentials, 7 Energy hansitions via polaronic and bipolaronic levels, 362 Engineering models, for fluorine generation cells, 539 Esin and Markov plots, 25S260 Experimental data comparison thereof, 149 on potential of zero charge, 56 Faraday rotation, microwave circuit for, 454 Fawcett, and the structure of the mercury-ethanol interface, 59 Feldberg and Rubinstein, theory of electrochemical polymerization, 560 Film bipolar iron-selective, 226 instability, for ion transfer through protective films, 272 reformation of, 240 Film breakdown fluctuations of during repair, 233 nucleation and, 243 Film breakdown processes, 240 Film formation, in passivity, diagrammed, 224 Flade potential, 247 Flame-annealed gold surfaces and the work of Kolb, 81 Hat band potential, 483 Fluctuations asymmetrical and unstable systems, 255 controlling progress in pitting, 299 in pitting dissolution, 251 and corrosion processes, 2 17 during dissolution, 252 at electrodes, theory, 281 during film breakdown, 233 and mathematical expressions thereof, 276 non-equilibrium, and corrosion 246,249 in passivation currents, 293 in solution concentration, 291

Index Fluctuations (cont.) in the steady state, 274 symmetrical, a theory thereof, 253 theory of, 270 Fluctuation-diffusion current, 284 in corrosion processes, 302 as a function of nickel ion concentration, 289 as a function of time, 288 Fluorine estimated production rates, 535 cost of generation, 525 as a function of current density, 525 related to current density, 525 cost of, for four-anode callandra cells, 526 flow, in grooves, 532 pilot plant for production, 538 Fluorine anode, happenings in its channels, 531 Fluorine cell diagrammated, 533 and laboratory operation, 545, 546 Fluorine generation, 523 cells for, and engineering models, 539 and impregnation with epoxy, 544 at large anodes, and temperature distribution, 542 and temperature distribution at the electrodes, 541 Fluorine-producing electrodes, and probe measurements, 534 Fractal dimensions, and effect on surface charge, 118 Fractal structure of surfaces and the double layer, 51 Fractal surfaces, Mandelbrot's work, 52 Fredlein and Bockris, use of a laser-optical process to measure the potential of zero charge, 34 Free-standing films of polymers, resistance, 574

Friction methods for the potential of zero charge, 40 Bockris and Argade, 40 Bockris and Parry-Jones, 40 Bockris and Sen, 40 Frumkin on the absolute potential difference, 17 analysis of non-polarizable electrodes, 130 and Demaskin, on the temperature variation of the potential of zero charge, 28 on the electrochemical properties of solid electrodes, 44 on the gallium-solution interface, 62 on the potential of zero charge of platinum group metals, 129 review of the potential of zero charge, 6 on the temperature variation of the potential of zero charge (Frumkin and Demaskin), 28 on the work function related to potential of zero charge, 169 Gallium and the double layer at interfaces involving it, 62 potential of zero charge measurements (Horanyi and Takas), 63 potential of zero charges in non-aqueous solutions, 65 Gallium-solution interface (Frumkin), 62 Galvani potential difference, measurability of, 7 Gibbs energy for the adsorption of water and the interfacial parameter, 187 Gokstein and the piezo electric method for the determination of the potential of zero charge, 42 Gold potential of zero charge, 77 111 phase and, 168 non-aqueous solutions, 79 and surface reconstruction, 83

Index Gold surfaces flame annealed, and the work of Kolb, 81

Kolb, reconstruction of, 85 Gold-solution interface (Clavilier and Nguyen Van Huong), 77 Guidelli, and the methods for the determination of the potential of zero charge, 63 Hall experiments and the microwave region, 453 Hamm et al., work on platinum surfaces, 134 Heusler and Lang, the anisotropic surface potential and the potential of zero charge, 34 Helmholtz and Gouy layers, capacitance as a function of, 36 HF generation hazards (Peters and Miethschen), 524 Horanyi and Takas, and the potential of zero charge of liquid gallium, 63 Hydrophobicity, 170 and various solvents, 176 Impedance, for measurement of the potential of zero charge, 35 Impedance blocks, for polypyrrole, 577 Impedance spectroscopy of electronically conducting polymers, 576 Indium and the double layer at interfaces involving it, 62 potential of zero charge in non-aqueous solutions, 65 Instability for ion transfer through protective films, 272 mechanism thereof, 257 and passivation, 257 Instability theory of the behavior of metals, 221 Interface double layer at interfaces involving gallium, 62

Interface (cont.) entropy of formation, 60 with the nervous system, 369 nonpolarizable, 2 polarizable, 3 Interfacial electron transfer, Marcus model inapplicability, 513 Interfacial parameter and Gibbs energy for the adsorption of water, 187 and the potential of zero charge, 184 Interfacial parameter scale, 177 Interfacial permitivity, 180 Interfacial rate constants determination at photo electrodes, 485 for photo currents, 468 Ion exchange involving electronically conducting polymers, 589 Ion transport in electronically conducting polymers, 573 Ion transfer instability through protective films, 272 Iron and non-aqueous solutions, 123 the potential of zero charge, 123 single crystals in aqueous solutions, 126 tabulated electrical double layer parameters, 124 Iron dissolution in phosphoric acid, the current-potential curve, 224 Iwasita and Xia, preparation of platinum single crystals, 133 Jellium model of a non-charged metal interface, 10 Katchalsky and Flory, work on artificial muscles, 359 Kinetics Butler-Volmer kinetics (and mechanism of electron transfer), 587 charge transfer kinetics (for electronically conducting polymer formation), 583 of electrochemical polymerization, 3 18

Index Kinetic equations, and polymer formation, 381 Kinetic view of passivation, 230 Koene, and the potential of zero charge on amalgams, 160 Kolb and Franke, 86 gold surfaces flame annealed, 81 reconstruction of, 85 and single crystal phases of various metals, 82 surface reconstruction (Kolb and Franke), 86 Kripsonsov and quantum mechanical calculations for the metal-solution interface, 174 Krivoshei and Skorobagatov on electronically conducting polymers, 550 Kuhn et al. on the role of three dimensional collagen fibers in artificial muscles, 359 Kukk and Puttsepp, study of the potential of zero charge on alloys, 145 Laser-optical process used to measure the potential of zero charge predlein and Bockris), 34 Lead, electrical double layer properties, tabulated, % Leikis, method for obtaining true surface area, 46 Lifetime for carriers and semi conductors, 495 for carriers in n-type silicon, 500 of carriers with polymer-electrolyte junctions, 4% change with potential, 500 mapped for n-type silicon in contact with the polymer electrolyte, 497 Light pulsing frequency, effect on photo currents, 474 Lippmann equation, 4 MacDonald on the adsorption of chloride ions in passivation, 237

Macroscopic motors, and artificial muscles, 343 Mandelbrot, on fractal surfaces, 52 Mao and Pickup, their work on the oxidation of polypyrrole, 587 Marcus model, inapplicability for interfacial electron transfer, 513 Mechanical breakdown model for passivity, 236 Mediation, and redox reactions in solution, 585 Medical dosage, 371 Mercury adsorption of diols on, 188 and non-aqueous solutions, 57 and the potential of zero charge, 57 a reference system, 16 Mercury-ethanol interface, structure of (Fawcett), 59 Metals, alloys, 141 and potentials of zero charge of molten salts, 146 Metal-solution interface, quantum mechanical calculations for (Kripsonsov), 174 Metal-water affinity, 177 Micro-balance, quartz crystal, 578 Microwave circuit, 446 for Faraday rotation, 454 Microwave conductivity an analytical expression for its potential dependence, 461 measurements and the needed electrochemical cell, 445 their potential dependence, 469 photo-induced, at high frequencies, 509 potential modulated, 507 theory thereof, 462, 463 Microwave conductivity transients, 452, 502 Microwave conductivity-potentialcurves, 456 Microwave effects and the needed electrode materials, 441

Index Microwave electrochemistry, prospects of, 460 Microwave energy, concentration effects of, 442 Microwave fields, interaction with electric fields, 436 Microwave frequencies and electric transport, 438 electrochemical measurements with, 447-479

Microwave frequency effects corresponding electrode materials, 444 history of, 440 potential sweep, 455 theoretical challenge, 457 Microwave frequency measurements and time-resolved measurements, 447 Microwave measurements depletion region in at photo electrodes, 479 and electrochemistry, 435 information on minority carriers from, 489 theory, 459 Microwave phase detection experiments, 451 measurements, 5 15 Microwave photoelectrochemistry, 435, 516-520

Microwave power and its effect on the electrode/electrolyte interface, 439 Microwave region, Hall experiments, 453 Microwave spectroscopy, intensity modulated photo currents, 508 Microwave transients for nano crystalline desensitized cells, 514 Microwave transmission, as a function of magnetic field, 515 Minority carriers as a function of distance from the interface, 482 information from microwave measurements, 489 Molecular motors artificial, 359 electrochemical properties, 343

Molecular simulations, for water and co-electrodes, 173 Morphology, 331 as a function of polishing, 275 Murphy and Waynewright, and change of upthrust on emersed metal as a method of measuring the potential of zero charge, 34 and negligible surface stress terms, 32 Muscle-like activators, electrochemical, 359 Muscles, (see also artificial muscles) actions of and electrochemical terms, diagrammated, 355 difference between natural and artificial, 358 skeletal, in contraction, 356, 357 N-type silicon, 500

change of lifetime with potential for carriers in, 500 mapping of lifetime in contact with the polymer electrolyte, 497 Nervous system, 369 Nickel critical potential as a function of ion concentration, 263 electrical double layer parameters in aqueous solutions, 127 ion concentration, fluctuation-diffusion current as a function of, 289 passive layer, surface coverage of, 287 surface, computed, 301 Nikitas, and the potential of zero charge at the air-solution interface, 30 Non-aqueous solutions, potentials of zero charge of gold in, 79 gallium, indium, and thalium in, 65 iron in, 123 mercury in, 57 platinum group metals in, 137 Non-charged metal interface, Jellium model, 10 Non-equilibrium fluctuations, 254 classification, diagrammed, 280 and corrosion, 246,249

Index Nonpolarizable interfaces, 2 Non-ideal solutions, Parsons-Zobel plot for, 55 Nucleation electrochemical (Tadano and Aogaki), 278 and film breakdown, 243 as a first stage in the oxidation process for polymers, 41 1 loop and cyclic voltammetsic studies, 557 modes for oxidation of conducting polymers, 584 and polymer formation, 379 Okada, and the mechanism for pitting, 272 Oligomers, 556 Overoxidation, 563 Oxidation diffusion control of in polymer formation, 389 of polyanaline, 563 of the polymer and anodic potential, 395 of polymers, a schematic, 565 relaxation control, 385 Oxide semiconductorjunctions, 472 Oxides, photo measurements at, 510 Oxidized area as a function of polarization time in polymer formation, 387 Photo currents at p-Si, 476 Packham on his rapid emergent method for potential of zero charge, 38 Parsons-Zobel plot, 22,45 and interpretation of curvature, 54 for non-ideal solutions, 55 roughness factor, 47, 74 Passivation adsorption of chloride ions in, 237 and the amplitude equations for fluctuations, 279 dissolution current in, 292 a kinetic view, 230 MacDonald, 237 and mechanism of instability, 257 Passivation process, 227 fluctuations in, 302

Passivation currents, fluctuations in, 293 Passivation potential, and thermodynamic phase formation, 218 Passive film adsorption of chloride ion on, 244 breakdown of, 232 and dissolution potential, 244 formation, diagrammed, 224 as a variation of thickness with potential formation, 225 Passive layer of nickel and surface coverage of, 287 Passivity chemical breakdown model 236 and critical potential as a function of alloy concentration, 262 destruction, 234 electrocapillary breakdown model, 238 film formation, diagrammed, 224 mechanical breakdown model, 236 types of time variation, 234 Peak potential as a function of cathode potential and polymer formation, 413 Perkins and Andersen compilation of potential of zero charge data for 1%9, 149 methods for the potential of zero charge, 31 review on the potential of zero charge, 6 Perchlorate ions, copper and the adsorption of, 94 Peters and Miethschen, and the hazards of HF generation, 524 Phase detection experiments, with microwaves, 45 1 Phase formation and the passivation potential, 218 Phase transitions, at thermodynamic equilibrium, 219 Photo current expressions, from theory, 467 Photo current-potential curves, as a function of pulsing frequency, 477 Photo currents anodic, for zinc oxide, 470 as a function of electrode potential, 473

Index Photo currents (cont.) as a function of interfacial rate constants, 468 intensity modulated, 508 and light pulsing frequency, effects of, 474 and microwave spectroscopy, 508 at p-Si, 476 Photo effects, as a function of flat band potential, 481 Photoelectrochemical conductivity, and microwave conductivity, 437 Photo electrodes and decay transients, 505 depletion region in microwave measurements at, 479 determination of interfacial rate constants, 485 rate constants for reactions at, 503 in pico second measurements, 504 and time resolved measurements, 493 Photo emission method for the potential of zero charge (Barker), 4 1 Photo measurements at oxides, 510 Piezo electric action, actuators via, 360 Piezo electric method for the determination of the potential of zero charge (Gokstein), 42 Piezo electric polymers (Baughman), 360 Pit dissolution, current densities as a function of potential, 245 formation, digramated, 220 growth, 290 growth current, 286 morphology, in two dimensional Monte Carlo stimulation, 297 structure, 246 Pit diameters, and chloride ion transformations, 300 Pitting assymetrical fluctuations controlling progress in pitting, 299 in pitting dissolution, 251 mechanisms, (Okada), 272 polishing and, 271

Pitting (cont.) stability, 243 Pitting currents, as a function of chloride concentration, 294 Pitting potential, determination of, 258 Pit-patent formation, flow chart to compute, 298 Platinum Clavilier, 135 CO adsorption on electrochemically facetted (Clavilier), 135 Hamm et al., 134 surfaces (Hamm et al.), 134 Platinum group metals in aqueous solutions, 132 and Frumkin's work on the potential of zero charge thereon, 129 Iwasita and Xia, 133 and non-aqueous solutions, 137 potentials of zero charge, 132, 137 preparation of platinum single crystals (Iwasita and Xia), 133 Platinum-DMSO interfaces, double layer structure, 141 Polarization time, 328 Polarons, 310 Polaronic bands as a function of oxidation depth, 342 Polarizable interfaces, 3 Polishing and pitting, 271 effect on the potential of zero charge, 95 of cadmium, 109 Polyanaline, a cyclic voltammogram of its oxidation, 563 Polymer film conducting Diiblehofer, 587 Pickup, 549 of electrodes, 382 formation, a detailed mechanism, 380 Polymer formation conducting, charge transfer kinetics for, 583 conducting zones in, 409 conformational changes in, 378

Index Polymer formation (cont.) diffusion components and, 421 diffusion control ofoxidation in, 389 electrochemical responses, 400 influence of concentration, 397 and kinetic equations, 381 nucleation and 379 oxidized area, 387 peak potential as a function of cathode potential and, 413 and the potential step method, 386 rate of, 383 voltammograms and, 417 Polymer layers, on semi conductor electrodes, 499 Polymer lifetime, mapped for n-type silicon in contact with the polymer electrolyte, 497 Polymer science and electrochemistry, 402 Polymers charge transport in, 567 conducting, 500, 589 conductivity of lightly doped polymers, 572 electrochemical and chemical production of, 333 electrochemistry and, 308 electron transfer mechanism in, 568 ion exchange, involving, 589 Krivoshei and Skorobagatov on, 550 cyclic voltammetric studies involving, 558 and diffusion control, 415 electricity stored in, 323 electrochemical properties, 337 free-standing films, resistance, 574 neighboring chains in, with positive charge and electrostatic repulsion, 338 oxidation, diffusion control and completion of oxidation, 414 nucleation, as a first stage in, 41 1 schematic, 565 and temperature, influence of, 3% self-doped, 334

Polymers (cont.) soft material polymers, electrochemical applications of, 426 Polymer-electrolytejunctions, lifetimes of carriers with, 496 Polymer-solvent interactions, 398, 401, 403 Polymeric actuators and natural muscles, 354 Polymeric chains, and oxidation and reduction processes, a schematic, 344 Polymerization anodic, 555-556 chemical, 329 and conductivity changes, 551 cyclic voltammograms as a function of scan rate involving, 559 degradation reactions simultaneous with, 326 efficiency introducing polymers, 324 electrochemical, and film deposition, 554 electrochemical reaction orders in, 3 17 Polymerization process, its productivity, 320 Polyanaline, oxidation of, 563 Polycrystine electrodes, models of the double layer for, 49 Polypyrrole composition, and conductivity, 341 cmss linked structure, 311 and electrocatalysis, 588 impedance blocks for, 577 Mao and Pickup, their work on the oxidation of, 587 model of its formation, 332 oxidation of, 587 oxidized, the picture at electrodes, 346 polypysrole film formation, currents and change of mass for, 579 properties, tabulated, 340 and rate of its formation as a function of concentration, 319 substituted, 335 Popov and hydrophobicity, 175

Index Popov (cont.) temperature coefficient of the potential of zero charge, 184 Potential of actual free charge, 26 and energy scale, 7 on the UHV scale, 11 Potential dependence of microwave conductivity, analytical expression for, 461 of microwave conductivity measurements, 469 periodic measurements, at photo electrodes, 506 Potential difference, 8 cells used for estimating absolute, 8 of dipole at electrode surface, 15 rumk kin, on the absolute potential difference, 17 Galvani, measurability of, 7 Potential distribution in passivation, 229 Potential formation as a variation of thickness with passive film, 225 Potential of zero charge, 1, 5-6, 18S192 accuracy of determination, 19 and the adsorption method, 39 at the air-solution interface mikitas), 30 and alloys, 142 Kukk and Puttsepp study of on alloys, 145 of tin and cadmium, 144 on amalgams (Koene), 160 effect of anion adsorption, 27 and anisotropic surface charges (Heusler and Lang), 34 and the area of the electrode, 23 and the atomic structure of the interface, 153 Barker, photo emission method, 41 on bismuth, 111 in non-aqueous solutions, 112 on cadmium and bismuth alloys, 145 of cadmium in non-aqueous solutions, 107 changes in for chloride, specifically adsorbed in iron, 125

Potential of zero charge (cont.) contribution of the solvent, 158 Conway and Colledan, and the determination of, 34 on copper, and aqueous solution, 89 crystal phase and, 44 crystal face specificity of, 21 and the crystal surface specificity, 152 DeLevie, on the effect of the density of broken bonds on, 75 dependence upon crystal phase, 154 dependence upon time of measurement, 150,151 effect of the density of broken bonds on (DeLevie), 75 experimental data, 56 as a function of electrolyte concentration, 56 Fredlein and Bockris, use of a laser-optical process to measure, 34 Frumkin, and Demaskin, and the temperature variation of, 28 pioneering review of the potential of zero charge, 6 and the potential of zero charge of platinum group metals, 129 and the work function related to potential of zero charge, 169 of gallium, indium, and thalium in non-aqueous solutions, 65 tabulated, 64 of gallium, measurements by Horanyi and Takas, 63 of gold 111 phase and, 168 of gold single crystals, tabulated, 84 and non-aqueous solutions, 79 tabulated, 78 Guidelli, and methods for the determination of, 63 Heusler and Lang, anisotropic surface potential and, 34 and the impedance method, 35 importance, 5 interfacial parameter and, 184

Index Potential of zero charge (cont.) of iron effect of adsorbed ions on, 125 and non-aqueous solutions, 123 Koene, measurements of on amalgams, 160 Kukk and Puttsepp, study of on alloys, 145 on mercury and various solvents, 58 and non-aqueous solutions, 57 methods for measurement of, 30 Barker, photo emission method, 41 capacitance method, 35 change of upthrust on emersed metal method (Murphy and Waynewright), 34 Conway and Colledan, 34 Fredlein and Bockris, use of a laser-optical process, 34 friction method, 40 Gokstein, and the piezo electric method, 42 Guidelli, 63 impedance method, 35 Koene, 160 use of a laser-optical process, 34 Murphy and Waynewright, 34 Packham, the rapid emergent method, 38 Perkins and Andersen, 31 photo emission method (Barker), 41 potentiostatic scrape method, 38 piezo electric method (Gokstein), 42 rapid emergent method (Packham), 38 spectroscopic methods, 41 in molten salts for various metals, 146, 148 Murphy and Waynewright, and change of upthrust on emersed metal, as a method of measuring, 34 Nikitas, at the air-solution interface, 30 in non-aqueous solutions, 71 for a nonpolarizable electrode, 4

Packham, the rapid emergent method of measurement, 38 Perkins and Andersen, a compilation of potential of zero charge data for 1969, 149 methods for measurement of potential of zero charge, 30 review, 6 at platinum-111 in aqueous solutions, 167 for platinum-group metals, 136, 137 in non-aqueous solutions, tabulated, 138,139 for poly-crystalline platinum-group metals in aqueous solutions, 131 polishing, effect of, 95 preparation of metal surfaces in measurements of, 21 related to other quantities, 18 results on silver as a function of crystal phase, 72 on soft and hard metals, 155 solvent dependence, 58 and the temperature coefficient, 182,184 and temperature effects, 23 temperature variation of (Frumkin and Demaskin), 28 and the work function, 18, 20, 156, 159,164,169 for low index and stepped surfaces, 165 Frumkin, 169 for zinc, 92, 100 tabulated, 101 zinc-solutions, and, 92 Potential step method, in polymer formation, 386 Potential sweep and microwave frequency effects, 455 Potential sweep kinetics, with polymer formation, 416 Potential sweep measurements, with microwave frequency effects, 455 Pourbaix diagrams, applied to adlayers on copper, 93 Prepolarization and cathode potential, 394

Index Probability for pit generation as function of time, 235 Probe measurements at fluorine producing electrodes, 534 Processes, biomimicking, 306 Production rates, for hydrogen and fluorine, 535 Protective films, instability for ion transfer through, 272 Pulsing frequency, photo current-potential curves as a function of. 477 Quantum chemical calculations, 172 Quantum chemical method, calculations of the adsorption of water by, 172 Quantum mechanical calculations for the metal-solution interface (Kripsonsov), 174 and water adsorption, 76 Quartz crystal micro-balance, used for electronically conducting polymer formation, 578 Quasi-perfect surface pitanov and Popov), 73 Radio tracer studies, and adsorption of perchlorate ions on copper, 94 Raman's scattering, and differential capacitance, 80 Randalls and Whiteley, and the temperature coefficient of the potential of zero charge, 24 Rate constants for minority carriers, 466 for reactions at photo-electrodes, 503 Real surface areas, various methods for determining them, 43 Reciprocal capacitance as a function of capacitances of layers of the interface, 37 Redox reactions in solution and mediation, 585 Reference device, use of mercury for, 16 Relaxation and diffusion components in polymer formation, 397

Relaxation control conformational, during anodic chronoamperogram, 384 and oxidation 385 and polymer formation, 413 Relaxation model, electrochemically stimulated, 373 Relaxation times, in polymer formation, 377

Ren and Pickup, interpretation of the semi-circles in polymer formation, 584 Resistance of polymers in free-standing films, 574 Responses, electrochemical, during polymer formation, 400 Rotating disk voltammetry diagrammated, 569 in electrochemical polymer formation, 580 with polymers, 586 Rough electrodes double layer capacitance of solid at (Daikhin), 52 Parsons-Zobel plot, 22, 45 Roughness factor from the Parsons-Zobel plot, 47,74 Valette and Hamlin method, 48 Roughness, surface, and the Debye-Iength, 52 Sat0 and dissolution arising from degeneration of surface-electron levels, 224 and his analysis of fluctuations in passivation, 238 Scan rate involving polymerization, cyclic voltammograms as a function of, 559 Schlichthrol, contributions to microwave conductivity, 441 Schmickler and Hendersen, theory of the double layer, 54 Schuldiner, determination of the capacitance of platinum-solution interfaces, 129

Index Scrape method and potential of zero charge, 39 Self-diffusion, for lead atoms, on surfaces, 143 Self-doped polymers, 334 Semicircles, Albery and Mount interpretation of, 584 Semiconductor electrodes with polymer layers, 499

diffusion length in, 492 Semiconductors, lifetime for carriers and,

495 Semiconductor-electrolyte interface, photo generation and loss mechanism, 458 Semiconductor-oxidejunctions, 472 Semiconductor-solution interface, and the space charge region, 484 Sensitivity, of electrodes, under photo irradiation, 491 Silicon, n-type change of lifetime with potential for carriers in, 500 lifetime mapped for in contact with the polymer electrolyte, 497 Silva, and the temperature coefficient of the potential of zero charge, 184 Silver and the electrical double layer, 67 in aqueous solutions, tabulated, 69 in non-aqueous solutions, 68 . potential of zero charge in aqueous solutions, tabulated, 69, 70 and single crystal phases, potential of zero charge results, 72 Single crystal phases in aqueous solution, 97 of bismuth in aqueous solution, 115 and non-aqueous solution, 119 for iron in non-aqueous solution, 127 Kolb, 82 potential of zero charge, discussed, 163 of various metals (Kolb), 82 Single crystals of gold potential of zero charge and aqueous solutions, 81

Single crystals (cont.) of gold (cont.) potential of zero charge as a function of crystal phase, 88 on gold and non-aqueous solutions, 81 Iwasita and Xia, their preparation of platinum single crystals, 133 Iron, single crystals, in aqueous solutions, 126 Single crystal surfaces metal-single crystal surfaces in contact with water, the surface potential, 166 zinc, in aqueous solutions, 100 Smart windows, 364, 366 Soft and hard metals, their potential of zero charge, 155 Soft material polymers, Electrochemical applications of, 426 Solid electrodes, models for double layer at, 50 Solid-solution interface, 50 Solutions, concentrated and double layer structure, 54 and the Parsons-Zobel plot, 54 Solvent adsorption energy, 66 effect upon polymer formation, 399 Solvent-polymer interaction, 403 Space-resolve measurements with microwave frequencies, 450 Spectra, thermal desorption, 171 Spectroelectrochemistryand non-stoichiometry, 361 Spectrum, intrinsic, of fluctuations at electrodes, 282 Stability morphological during film breakdown, 248 in pitting, 243 Standard potential, on the UHV scale, 13 Steady state, fluctuations in, 274 Stem model applied to copper in aqueous solutions, 92 applied to solid electrodes, 44 tested by Parsons-Zobel plot, 67

Index Storage of electricity and batteries, (MacDiarmid), 368 Structures, tangled, diagrammed after reduction at cathodic potentials, 345 Surface charge effect of fractal dimensions on, 118 thin strip electrode bending due to changes in, 34 total, 3 Surface area of solid electrodes, determination, 42 true, 46 Surface diffusion and electrochemically annealed surfaces, 86 Surface potential anisotropic and the potential of zero charge (Heusler and Lang), 34 metal-single crystal surfaces in contact with water, 166 Surface potential results, discussion, 162 Surface reconstruction (Kolb and Franke), 86 Surface recombination, at semi conductors, 490 Surface reconstruction of gold, 83 and work of Kolb, 86 Surface tension and determination of the potential of zero charge, 32 Surface tension methods, and the potential of zero charge, 32 Surfaces, fractal, for solid electrodes, 51 of solid electrodes, by electron defraction, 51 quasi-perfect, defined by Vitanov and Popov, 74 Swelling, 339 of polymers, during electrode polymerization, 407 Symmetrical fluctuations instability in the diffusion layer, 267 a theory thereof, 253 Tadano and Aogaki, electrochemical nucleation, 278

Tafel plots, during electrode polymerization, 316 Technology of electrochemical polymer formation, 427 Temperature coefficient and the interfacial parameter, 183 and the potential of zero charge, 182 of potential of zero charge as a function of crystal phase, 87 Temperature dependence, for potential of zero charge on silver in contact with solution, 76 Temperature effects on the potential of zero charge, 23 upon polymerization, 406 Temperature variation of the potential of zero charge (Frumkin and Demaskin), 28 Thalium and the double layer at interfaces involving it, 62 potential of zero charge in non-aqueous solutions, 65 Theory, of fluctuations, in corrosion processes, 253 Thermal desorption spectra, 171 Thermodynamic equilibrium, phase transitions at, 219 Thermodynamic phase formation, passivation potential and, 218 Time resolved measurements in the microwave frequency range, 447 photo electrodes and 493 Tin and cadmium, their alloys and potential of zero charge, 144 and electrical double layers thereon, 98 Tin surfaces, and the adsorption of tetrabutyl ammonium ions, 99 Total overpotential, and auto correlation distance, 283 Passivation potential, and thermodynamic phase formation, 218 Transition, passive to pit formation, 219 Transpassive state, of metals, 223

Index Transport equation, for microwave frequency effects of the electrode, 465 Trasatti and discussion of the potential of zero charge, 149 parameter for metal-water affinity, suggestion of, 178 review of the potential of zero charge, 7 and work function data, 165 Trasatti and Doubova, effect of density of broken bonds on the potential of zero charge, 75 True surface area, origination of method for obtaining (Leikis), 46 Turnover numbers, for minority carriers, 494 Two dimensional and three dimensional polypyrrole forms, 405 UHV and solution data, 169 UHV scale and potentials, 11 and the standard potential, 13 Ukshe and Bukun, difference of potential of zero charge's for two metals in molten salts, 147 Valette, and the adsorption of fluoride ions, 73 Valette and Hamlin, data for solvent adsorption, agrees with quantum mechanical calculation, 76 method for determining roughness factors, 48 the potential of zero charge and the crystal phase, 44 Vitanov and Popov and the cadmium-solution interface, 108 and the quasi-perfect surface, 73 Volta, potential differences, 178 Voltage at various points on the electrodes in fluorine generation, 543

Voltammetry, with electrochemical polymers, 408 Voltammograms anodic, 418 involving conducting polymers, 553 and polymer formation, 417 theory and experiment for polymer formation, 420 Water co-adsorption and the effect on the interfacial potential, 26 influence on the bismuth-solution interface on the presence of DMF, 113 and quantum mechanical calculations, 173

Wetting, theoty, 530 Windows, smart, 364 Work function data, some difficulties, 157 and polycrystalline surfaces, 22 and the potential of zero charge, 156, 164 plotted, 159 and preparation of metal surface for measurement of it, 21 Work function-potential of zero charge plot, 20 Zinc

and its potential of zero charge, 100 tabulated, 102 single crystal surfaces, in aqueous solutions, 100 Zinc oxide, anodic photo currents for, 470 Zinc oxide layers, spotted, 47 1 Zinc oxide-electrolyte interfaces, electron transfer rate and its exponential increase at, 512 Zinc-solutions, and the potential of zero charge, 92

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