Thermal Behavior of Dispersed Systems (Surfactant Science)

SURFACTANT SCIENCE SERIES FOUNDING EDITOR MARTIN J. SCHICK 1918–1998 SERIES EDITOR ARTHUR T. HUBBARD Santa Barbara Scie...

Author: Nissim Garti

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SURFACTANT SCIENCE SERIES FOUNDING EDITOR MARTIN J. SCHICK 1918–1998 SERIES EDITOR ARTHUR T. HUBBARD Santa Barbara Science Project Santa Barbara, California ADVISORY BOARD

DANIEL BLANKSCHTEIN

ERIC W. KALER

Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts

Department of Chemical Engineering University of Delaware Newark, Delaware

S. KARABORNI

CLARENCE MILLER

Shell International Petroleum Company Limited London, England

Department of Chemical Engineering Rice University Houston, Texas

LISA B. QUENCER

DON RUBINGH

The Dow Chemical Company Midland, Michigan

The Proctor & Gamble Company Cincinnati, Ohio

JOHN F. SCAMEHORN

BEREND SMIT

Institute for Applied Surfactant Research University of Oklahoma Norman, Oklahoma

Shell International Oil Products B.V. Amsterdam, The Netherlands

P. SOMASUNDARAN Henry Krumb School of Mines Columbia University New York, New York

JOHN TEXTER Strider Research Corporation Rochester, New York

1. 2. 3. 4. 5.

Nonionic Surfactants, edited by Martin J. Schick (see also Volumes 19, 23, and 60) Solvent Properties of Surfactant Solutions, edited by Kozo Shinoda (see Volume 55) Surfactant Biodegradation, R. D. Swisher (see Volume 18) Cationic Surfactants, edited by Eric Jungermann (see also Volumes 34, 37, and 53) Detergency: Theory and Test Methods (in three parts), edited by W. G. Cutler and R. C. Davis (see also Volume 20) 6. Emulsions and Emulsion Technology (in three parts), edited by Kenneth J. Lissant 7. Anionic Surfactants (in two parts), edited by Warner M. Linfield (see Volume 56) 8. Anionic Surfactants: Chemical Analysis, edited by John Cross 9. Stabilization of Colloidal Dispersions by Polymer Adsorption, Tatsuo Sato and Richard Ruch 10. Anionic Surfactants: Biochemistry, Toxicology, Dermatology, edited by Christian Gloxhuber (see Volume 43) 11. Anionic Surfactants: Physical Chemistry of Surfactant Action, edited by E. H. Lucassen-Reynders 12. Amphoteric Surfactants, edited by B. R. Bluestein and Clifford L. Hilton (see Volume 59) 13. Demulsification: Industrial Applications, Kenneth J. Lissant 14. Surfactants in Textile Processing, Arved Datyner 15. Electrical Phenomena at Interfaces: Fundamentals, Measurements, and Applications, edited by Ayao Kitahara and Akira Watanabe 16. Surfactants in Cosmetics, edited by Martin M. Rieger (see Volume 68) 17. Interfacial Phenomena: Equilibrium and Dynamic Effects, Clarence A. Miller and P. Neogi 18. Surfactant Biodegradation: Second Edition, Revised and Expanded, R. D. Swisher 19. Nonionic Surfactants: Chemical Analysis, edited by John Cross 20. Detergency: Theory and Technology, edited by W. Gale Cutler and Erik Kissa 21. Interfacial Phenomena in Apolar Media, edited by Hans-Friedrich Eicke and Geoffrey D. Parfitt 22. Surfactant Solutions: New Methods of Investigation, edited by Raoul Zana 23. Nonionic Surfactants: Physical Chemistry, edited by Martin J. Schick 24. Microemulsion Systems, edited by Henri L. Rosano and Marc Clausse 25. Biosurfactants and Biotechnology, edited by Naim Kosaric, W. L. Cairns, and Neil C. C. Gray 26. Surfactants in Emerging Technologies, edited by Milton J. Rosen 27. Reagents in Mineral Technology, edited by P. Somasundaran and Brij M. Moudgil 28. Surfactants in Chemical/Process Engineering, edited by Darsh T. Wasan, Martin E. Ginn, and Dinesh O. Shah 29. Thin Liquid Films, edited by I. B. Ivanov 30. Microemulsions and Related Systems: Formulation, Solvency, and Physical Properties, edited by Maurice Bourrel and Robert S. Schechter 31. Crystallization and Polymorphism of Fats and Fatty Acids, edited by Nissim Garti and Kiyotaka Sato

32. Interfacial Phenomena in Coal Technology, edited by Gregory D. Botsaris and Yuli M. Glazman 33. Surfactant-Based Separation Processes, edited by John F. Scamehorn and Jeffrey H. Harwell 34. Cationic Surfactants: Organic Chemistry, edited by James M. Richmond 35. Alkylene Oxides and Their Polymers, F. E. Bailey, Jr., and Joseph V. Koleske 36. Interfacial Phenomena in Petroleum Recovery, edited by Norman R. Morrow 37. Cationic Surfactants: Physical Chemistry, edited by Donn N. Rubingh and Paul M. Holland 38. Kinetics and Catalysis in Microheterogeneous Systems, edited by M. Grätzel and K. Kalyanasundaram 39. Interfacial Phenomena in Biological Systems, edited by Max Bender 40. Analysis of Surfactants, Thomas M. Schmitt 41. Light Scattering by Liquid Surfaces and Complementary Techniques, edited by Dominique Langevin 42. Polymeric Surfactants, Irja Piirma 43. Anionic Surfactants: Biochemistry, Toxicology, Dermatology. Second Edition, Revised and Expanded, edited by Christian Gloxhuber and Klaus Künstler 44. Organized Solutions: Surfactants in Science and Technology, edited by Stig E. Friberg and Björn Lindman 45. Defoaming: Theory and Industrial Applications, edited by P. R. Garrett 46. Mixed Surfactant Systems, edited by Keizo Ogino and Masahiko Abe 47. Coagulation and Flocculation: Theory and Applications, edited by Bohuslav Dobiáš 48. Biosurfactants: Production • Properties • Applications, edited by Naim Kosaric 49. Wettability, edited by John C. Berg 50. Fluorinated Surfactants: Synthesis • Properties • Applications, Erik Kissa 51. Surface and Colloid Chemistry in Advanced Ceramics Processing, edited by Robert J. Pugh and Lennart Bergström 52. Technological Applications of Dispersions, edited by Robert B. McKay 53. Cationic Surfactants: Analytical and Biological Evaluation, edited by John Cross and Edward J. Singer 54. Surfactants in Agrochemicals, Tharwat F. Tadros 55. Solubilization in Surfactant Aggregates, edited by Sherril D. Christian and John F. Scamehorn 56. Anionic Surfactants: Organic Chemistry, edited by Helmut W. Stache 57. Foams: Theory, Measurements, and Applications, edited by Robert K. Prud’homme and Saad A. Khan 58. The Preparation of Dispersions in Liquids, H. N. Stein 59. Amphoteric Surfactants: Second Edition, edited by Eric G. Lomax 60. Nonionic Surfactants: Polyoxyalkylene Block Copolymers, edited by Vaughn M. Nace 61. Emulsions and Emulsion Stability, edited by Johan Sjöblom 62. Vesicles, edited by Morton Rosoff 63. Applied Surface Thermodynamics, edited by A. W. Neumann and Jan K. Spelt 64. Surfactants in Solution, edited by Arun K. Chattopadhyay and K. L. Mittal 65. Detergents in the Environment, edited by Milan Johann Schwuger

66. Industrial Applications of Microemulsions, edited by Conxita Solans and Hironobu Kunieda 67. Liquid Detergents, edited by Kuo-Yann Lai 68. Surfactants in Cosmetics: Second Edition, Revised and Expanded, edited by Martin M. Rieger and Linda D. Rhein 69. Enzymes in Detergency, edited by Jan H. van Ee, Onno Misset, and Erik J. Baas 70. Structure–Performance Relationships in Surfactants, edited by Kunio Esumi and Minoru Ueno 71. Powdered Detergents, edited by Michael S. Showell 72. Nonionic Surfactants: Organic Chemistry, edited by Nico M. van Os 73. Anionic Surfactants: Analytical Chemistry, Second Edition, Revised and Expanded, edited by John Cross 74. Novel Surfactants: Preparation, Applications, and Biodegradability, edited by Krister Holmberg 75. Biopolymers at Interfaces, edited by Martin Malmsten 76. Electrical Phenomena at Interfaces: Fundamentals, Measurements, and Applications, Second Edition, Revised and Expanded, edited by Hiroyuki Ohshima and Kunio Furusawa 77. Polymer-Surfactant Systems, edited by Jan C. T. Kwak 78. Surfaces of Nanoparticles and Porous Materials, edited by James A. Schwarz and Cristian I. Contescu 79. Surface Chemistry and Electrochemistry of Membranes, edited by Torben Smith Sørensen 80. Interfacial Phenomena in Chromatography, edited by Emile Pefferkorn 81. Solid–Liquid Dispersions, Bohuslav Dobiáš, Xueping Qiu, and Wolfgang von Rybinski 82. Handbook of Detergents, editor in chief: Uri Zoller Part A: Properties, edited by Guy Broze 83. Modern Characterization Methods of Surfactant Systems, edited by Bernard P. Binks 84. Dispersions: Characterization, Testing, and Measurement, Erik Kissa 85. Interfacial Forces and Fields: Theory and Applications, edited by Jyh-Ping Hsu 86. Silicone Surfactants, edited by Randal M. Hill 87. Surface Characterization Methods: Principles, Techniques, and Applications, edited by Andrew J. Milling 88. Interfacial Dynamics, edited by Nikola Kallay 89. Computational Methods in Surface and Colloid Science, edited by Malgorzata Borówko 90. Adsorption on Silica Surfaces, edited by Eugène Papirer 91. Nonionic Surfactants: Alkyl Polyglucosides, edited by Dieter Balzer and Harald Lüders 92. Fine Particles: Synthesis, Characterization, and Mechanisms of Growth, edited by Tadao Sugimoto 93. Thermal Behavior of Dispersed Systems, edited by Nissim Garti

ADDITIONAL VOLUMES IN PREPARATION Surface Characteristics of Fibers and Textiles, edited by Christopher M. Pastore and Paul Kiekens Analysis of Surfactants: Second Edition, Revised and Expanded, Thomas M. Schmitt Fluorinated Surfactants and Repellents: Second Edition, Revised and Expanded, Erik Kissa Physical Chemistry of Polyelectrolytes, edited by Tsetska Radeva Detergency of Specialty Surfactants, edited by Floyd E. Friedli Reactions and Synthesis in Surfactant Systems, edited by John Texter Liquid Interfaces in Chemical, Biological, and Pharmaceutical Applications, edited by Alexander G. Volkov

THERMAL BEHAVIOR OF DISPERSED SYSTEMS

edited by Nissim Garti The Hebrew University of Jerusalem Jerusalem, Israel

ISBN: 0-8247-0432-0 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distributio Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright © 2001 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA

Preface

Many important everyday materials are known to be colloidal heterogeneous systems. Milk, margarine, ice cream, mayonnaise, cosmetic creams, hand lotions, blood, ink, paint, and other substances are heterogeneous systems that can flow or become solid, and contain structural entities with at least one linear dimension in the size range of several nanometers to tens of microns. Colloidal systems consist of a dispersed phase of particles, droplets, and bubbles in a second continuous phase called the dispersion medium. Dispersed systems are said to be stable if, over a certain period of time, there is little detectable aggregation or settling of particles. In many colloidal systems, a stable thermodynamic state is reached only when all particles or droplets have become united in a single homogeneous lump of dispersed phase and, therefore, any apparent stability must be regarded as purely kinetic phenomenon. Dispersed systems are stabilized by a third component known to have amphiphilic properties and surface activity. The amphiphiles migrate to the interface and modify it to reduce the interfacial free energy and to minimize interactions between particles and droplets. It is obvious that any temperature change will affect the mobility of the amphiphiles from the continuous phase to the interface, and vice versa, and will affect the thermodynamic and geometric parameters of the interface. Therefore, the thermal behavior of dispersed systems is an essential parameter in studying structural and thermodynamic aspects. For generations, attempts have been made to heat and cool foams, emulsions, dispersions, and heterogeneous colloidal systems, and to learn about the stability of the systems through their thermal behavior. Differential scanning calorimetry (DSC) and differential thermo gravimetry (DTG) are classical instruments that

iii

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Preface

through complex heating-cooling protocols provide important information on the behavior of the components of the dispersions. Dispersions (mostly emulsions and microemulsions) are used as microreactors or nanoreactors for important organic and enzymatic processes, and serve as reservoirs for the solubilization of materials. The behavior of the solubilized matter is also dramatically affected by thermal fluctuations. Hydration or solvation, as well as other interactions of cosolvents, are also studied through thermal treatment. It is therefore important to bring to the reader’s attention the options and the scope, as well as the limitations, of the thermal behavior of dispersed systems. This book calls attention to some of the recent studies that have been carried out on heterogeneous colloidal (dispersed) systems. Chapter 1, by Turco Liveri (Italy), reviews calorimetric investigations on reversed micelles, in which the apolar molecules interact by dispersion forces that are always attracted independently of their relative orientation. The author describes the tendency of the apolar medium in reverse micelles to form a longrange, ordered molecular arrangement in condensed phases. The amphiphilic molecules, characterized by the coexistence of spatially separated polar and apolar moieties, work together to drive the intermolecular aggregation, giving rise to dimensionally limited supramolecular aggregates. From a thermodynamic point of view, self-aggregation of amphiphilic molecules in apolar solvents involves a favorable enthalpic term due to intermolecular bonding counteracted by an unfavorable entropic term as a result of partial loss of molecular translational and rotational degrees of freedom. V. Turco Liveri discusses structural aspects, the state of water and other solutes in reversed micelles, intermicellar interactions and percolation phenomena, solubilization of nonionic solutes, and the reversed micelles as nanoreactors. The second chapter, by D. Vollmer (Germany), brings a quantitative comparison of experimental data and theoretical predictions on thermodynamic and kinetic properties of microemulsions based on nonionic surfactants. Phase transitions between a lamellar and a droplet-phase microemulsion are discussed. The work is based on evaluation of the latent heat and the specific heat accompanying the transitions. The author focuses on the kinetics of phase separation when inducing emulsification failure by constant heating. The chapter is a comprehensive, detailed study of all the aspects related to the phase separation phenomenon in microemulsions. In Chapter 3, Ezrahi et al. (Israel) discuss the use of subzero temperature behavior of water in microemulsions as an analytical tool to enable better understanding of the interfacial behavior of the surfactant. Microemulsions are cooled to subzero temperatures and the water in the internal reservoir freezes. In the heating cycle the thawing of the water is measured. The authors critically discuss the problems related to the use of this technique and the advantages derived from it.

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v

Chapter 4, by Schulz et al. (Argentina and Mexico), describes the use of DSC techniques for studying binary and multicomponent systems containing surfactants. The authors explain how DSC helps to elucidate such properties as type of transition, phase boundaries, enthalpies of phase transition, and heat capacity of systems in heterogeneous states. Fouconnier et al. (France) introduce us in Chapter 5 to dispersed systems that are not stable thermodynamically, such as emulsions and double emulsions, and teach us how to carry out DSC measurements properly in order to obtain valuable information on the stability of the emulsions. Various physical and chemical phenomena that occur during cooling and heating have been pointed out. They may be associated with either the dispersed, the continuous, or the interfacial phase. A tentative description of some of these events is presented, and a correlation was made with the resulting properties of the emulsions themselves. Simple water-in-oil (W/O) or oil-in-water (O/W) emulsions, mixed emulsions, and multiple emulsions can be found during the fabrication process. Their storage and their use are considered. Senatra (Italy), who was a pioneer in the use of DSC as a technique to study interfacial phenomena, offers in Chapter 6 some interesting physical parameters and the essence of these observations. Chapter 7 is an interesting review by Kodama and Aoki (Japan) on the behavior of water in phospholipid bilayer systems. The authors distinguish between nonfreezable interlamellar water and freezable intralamellar and bulk water, and estimate the number of molecules of water in each category. They also examine the relationship between lipid phase transitions and ice-melting behavior in lipidwater systems. The behavior of water is also discussed in the gel phase of systems such as DPPC, DMPE, and DPPG. Part II concentrates on solid–liquid interfaces. Chapter 9, by Király (Hungary), attempts to clarify the adsorption of surfactants at solid/solution interfaces by calorimetric methods. The author addresses questions related to the composition and structure of the adsorption layer, the mechanism of the adsorption, the kinetics, the thermodynamics driving forces, the nature of the solid surface and of the surfactant (ionic, nonionic, HLB, CMC), experimental conditions, etc. He describes the calorimetric methods used, to elucidate the description of thermodynamic properties of surfactants at the boundary of solid–liquid interfaces. Isotherm power-compensation calorimetry is an essential method for such measurements. Isoperibolic heat-flux calorimetry is described for the evaluation of adsorption kinetics, DSC is used for the evaluation of enthalpy measurements, and immersion microcalorimetry is recommended for the detection of enthalpic interaction between a bare surface and a solution. Batch sorption, titration sorption, and flow sorption microcalorimetry are also discussed. Chapter 10, by Dékány (Hungary), describes the microcalorimetric control of liquid sorption on hydrophilic/hydrophobic surfaces in nonaqueous dispersions.

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The dispersed systems are mostly silicates. The author discusses interparticle interactions as a tool for evaluating the stability of dispersions. Parameters such as heat of immersion at solid–liquid interfaces and adsorption capacity are determined, and the mathematical treatment for determining the enthalpy isotherms is described. The heat of wetting in amorphous silica dispersion and on zeolites is discussed. Füredi-Milhofer (Israel), in Chapter 11, provides a broad overview of the role of thermal analysis techniques in basic and applied studies of the formation and transformation of crystalline dispersions. Crystalline disperisons are formed by a succession of some of the following precipitation processes: nucleation, crystal growth, flocculation, Ostwald ripening, and/or phase transformation. After a brief elaboration of the theories underlying these processes, a review is given of experimental studies on the formation and transformation of ionic precipitates from bulk electrolyte solutions. At relatively high supersaturations, compounds that include hydrophilic cations (such as Ca, Al, Fe, etc.) are likely to form highly hydrated amorphous precipitates via homogeneous nucleation and subsequent flocculation. A number of important crystalline compounds, such as hydroxyapatite or zeolites, are formed by phase transformation via amorphous and/or gel-like precursor phases. Thermal analysis techniques yield information on the amount of incorporated water, and mechanism and strength of bonding, and pore sizes of such amorphous and poorly crystalline materials. In some cases they have been successfully used to detect the initiation of phase transformation, such as the formation of ordered subunits of a quasicrystalline zeolite phase within amorphous alumosilicate precursors. At low and medium supersaturations, hydrophilic cations form different crystal hydrates by heterogeneous nucleation and subsequent crystal growth and phase transformation. Dehydration curves give information on the modes of water incorporation resulting from different modes of crystallization. A useful application of thermal analysis is the analytical approach: by determining the mass loss due to dehydration, it was possible to quantitatively determine the proportion of different calcium oxalate hydrates in mixtures, which have been qualitatively analyzed by other techniques (X-ray powder diffraction, IR spectroscopy, etc.). The method yielded excellent results in studies of the kinetics of phase transformation and has been successfully used to demonstrate the potential of surfactant micelles to control the nature of the crystallizing phase. Chapter 11 also deals with crystallization in O/W emulsions and W/O microemulsions. Filipoviƒ-Vincekoviƒ and Tomašiƒ (Croatia) have contributed Chapter 12, “SolidState Transitions of Surfactant Crystals,” which discusses the effect of surfactants on the crystallization of materials in aqueous and nonaqueous solutions. The chapter describes the crystalline structure of surfactant and its thermal

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behavior, and the effects related to its crystallization. Single- and double-chain surfactants are reviewed, and the differences in their thermal behavior are elucidated. Chapter 13 is the only chapter that discusses thermal behavior of real complex systems. Raemy et al. (Switzerland and Israel) in “Thermal Behavior of Foods and Food Constituents,” reveal the complexity of studying such systems using different thermal calorimetric techniques. In conclusion, this book presents only a very small fraction of the options, scope, and limitations of using thermal behavior of dispersed systems as an analytical and physical tool for the evalution of phenomena occurring at the interface between the dispersed phase and the dispersion phase. It must be noted that much more work is required to enable better understanding of complex systems and real dispersions. These systems will be discussed in a separate book that will be devoted to complex dispersion systems that have been converted into commercial products. Nissim Garti

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Contents

Preface iii Contributors xi Part I 1.

Calorimetric Investigations of Solutions of Reversed Micelles Vincenzo Turco Liveri

1

2.

Thermodynamics and Phase-Separation Kinetics of Microemulsions Doris Vollmer

23

3.

Subzero Temperature Behavior of Water in Microemulsions Shmaryahu Ezrahi, Abraham Aserin, Monzer Fanun, and Nissim Garti

59

4.

DSC Analysis of Surfactant-Based Microstructures Pablo C. Schulz, J. F. A. Soltero, and Jorge E. Puig

121

5.

Effects of Cooling–Heating Cycles on Emulsions B. Fouconnier, J. Avendano Gomez, K. Ballerat-Busserolles, and Daniele Clausse

183

6.

Thermal Analysis of Self-Assembling Complex Liquids Donatella Senatra

203

7.

Water Behavior in Phospholipid Bilayer Systems Michiko Kodama and Hiroyuki Aoki

247

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Contents

x 8.

Heat Evolution of the Self-Assembly of Amphiphiles in Aqueous Solutions Dov Lichtenberg, Ella Opatowski, and Michael M. Kozlov

295

Part II 9.

10.

11.

Calorimetric Methods for the Study of Adsorption of Surfactants at Solid/Solution Interfaces Zoltán Király

335

Microcalorimetric Control of Liquid Sorption on Hydrophilic/ Hydrophobic Surfaces in Nonaqueous Dispersions Imre Dékány

357

The Formation and Transformation of Crystalline Dispersions as Studied by Thermal Analysis Helga Füredi-Milhofer

413

12.

Solid-State Transitions of Surfactant Crystals Nada Filipoviƒ-Vincekoviƒ and Vlasta Tomašiƒ

451

13.

Thermal Behavior of Foods and Food Constituents Alois Raemy, Pierre Lambelet, and Nissim Garti

477

Index 507

Contributors

Hiroyuki Aoki Department of Biochemistry, Okayama University of Science, Okayama, Japan Abraham Aserin Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel K. Ballerat-Busserolles UTC–Départment Génie Chimique, Laboratoire Génie des Procédés, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Procédés Industriels, Compie n e, France Daniele Clausse UTC–Départment Génie Chimique, Laboratoire Génie des Procédés, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Procédés Industriels, Comp ie n e, France Imre Dékány Department of Colloid Chemistry, University of Szeged, Szeged, Hungary Shmaryahu Ezrahi Materials and Chemistry Department, The Ordnance Corps, Israel Defense Forces, Ramat Gan, Israel Monzer Fanun Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel Nada Filipoviƒƒ-Vincekoviƒƒ Department of Physical Chemistry, Ruper Boškoviƒ Institute, Zagreb, Croatia

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Contributors

B. Fouconnier UTC–Départment Génie Chimique, Laboratoire Génie des Procédés, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Procédés Industriels, Compie n e, France Helga Füredi-Milhofer Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel Nissim Garti Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel J. Avendano Gomez UTC–Départment Génie Chimique, Laboratoire Génie des Procédés, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Procédés Industriels, Compie ne, France Zoltán Király Department of Colloid Chemistry, University of Szeged, Szeged, Hungary Michiko Kodama Department of Biochemistry, Okayama University of Science, Okayama, Japan Michael M. Kozlov Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel Pierre Lambelet Nestlé Research Center, Nestec Ltd., Lausanne, Switzerland Dov Lichtenberg Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel Ella Opatowski Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel Jorge E. Puig Departamento de Ingeniería Química, Universidad de Guadalajara, Guadalajara, Mexico Alois Raemy Nestlé Research Center, Nestec Ltd., Lausanne, Switzerland Pablo C. Schulz Departamento de Química e Ingenieria Química, Universidad Nacional del Sur, Bahía Blanca, Argentina Donatella Senatra Department of Physics—INFM Group, University of Florence, Florence, Italy

Contributors

xiii

J. F. A. Soltero Departamento de Ingeniería Química, Universidad de Guadalajara, Guadalajara, Mexico Vlasta Tomašiƒƒ Department of Physical Chemistry, Ruper Boškoviƒ Institute, Zagreb, Croatia Vincenzo Turco Liveri Department of Physical Chemistry, University of Palermo, Palermo, Italy Doris Vollmer Institute for Physical Chemistry, University of Mainz, Mainz, Germany

xiv


1 Calorimetric Investigations of Solutions of Reversed Micelles VINCENZO TURCO LIVERI Department of Physical Chemistry, University of Palermo, Palermo, Italy

I. Introduction

1

II. Reversed Micelles as Nanocontainers: The State of Water and Other Solutes Within Reversed Micelles

8

III. Intermicellar Interactions and Percolation

12

IV. Water-Containing Reversed Micelles as Nanosolvents: The Solubilization of Nonionic Solutes

13

V. Reversed Micelles as Nanoreactors

17

VI. Conclusion

19

References

20

I. INTRODUCTION Apolar molecules interact by means of dispersion forces, which are always attractive independently of their relative orientation, and for this reason they display little tendency to give a long-range ordered molecular arrangement in condensed phases. On the other hand, polar molecules interact also by means of dipole–dipole interactions, which are attractive or repulsive depending on the relative orientation of the molecules. It follows that these molecules display a more marked tendency to give a three-dimensionally unlimited ordered molecular arrangement. In the case of amphiphilic molecules, characterized by the coexistence of spatially separated apolar (alkyl chains) and polar moieties, both these parts

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Turco Liveri

concur to drive the intermolecular aggregation giving rise to dimensionally limited supramolecular aggregates. In particular, when dissolved in apolar solvents, as a consequence of both dispersion and dipole–dipole interactions triggered by steric hindrance and thermal agitation, amphiphilic molecules self-assemble, forming a more or less wide spectrum of dynamical structures that differ in aggregation number, shape (linear, cyclic, three-dimensional), and lifetime [1]. Some examples of twodimensional aggregates of “amphiphilic molecules” (obtained by combining rubber pipette bulbs and magnetic stir bars) oriented according to dipole–dipole interactions are shown in Fig. 1. From a thermodynamic point of view, self-aggregation of amphiphilic molecules in apolar solvents involves a favorable enthalpic term due to intermolecular bonding counteracted by an unfavorable entropic term due to a partial loss of molecular translational and rotational degrees of freedom. Using vapor pressure osmometry, for example, it has been found that the enthalpies of formation of molecular aggregates of dodecylammonium propionate in benzene and cyclohexane are –83.4 KJ/mol and –57.4 KJ/mol, whereas the entropy changes for the same processes are –0.23 KJ/mol and –0.14 KJ/mol, respectively [2]. It is generally agreed that the equilibrium concentrations of monomers and aggregates are well described by a multiple equilibrium model [3,4]. The relative populations of these aggregates are maintained in thermodynamic equilibrium by fast breaking and re-forming processes of labile intermolecular interactions and are controlled by some internal (nature and shape of the polar group and of the apolar molecular moiety of the amphiphile) and external (concentration of the amphiphile, temperature, etc.) parameters. Within a more or less restricted range of these parameters some amphiphilic molecules self-assemble in apolar solvents,

FIG. 1 Examples of linear and cyclic two-dimensional aggregates of “amphiphilic molecules” (obtained by combining rubber pipette bulbs and magnetic stir bars).

Solutions of Reversed Micelles

3

forming globular aggregates called reversed micelles, which are structurally characterized by an internal polar core constituted by opportunely arranged hydrophilic headgroups surrounded by the alkyl chains of the amphiphile (see Fig. 2) [5]. This kind of aggregation involves the formation of “supermolecules,” which appear from the outside as apolar objects dispersed in the apolar solvent. Many amphiphilic substances are able to form reversed micelles. Certainly, the most studied is sodium bis (2-ethylhexyl) sulfosuccinate (AOT) [6]. From this salt, other interesting surfactants able to form reversed micelles have been derived by simply changing the counterion [7]. Other frequently used surfactants are didodecyldimethylammonium bromide [8], benzyldimethylhexadecylammonium chloride, lecithin [9], tetraethylene glycol monododecyl ether (C 12 E 4 ) [10], decaglycerol dioleate [11], and dodecylpyridinium iodide [12]. With extensive aggregation, a number of translational and rotational degrees of freedom of surfactant molecules are converted into translational, rotational, and internal degrees of freedom of the entire aggregate. In the case of a reversed micelle, its dynamics are characterized by a wide variety of processes such as diffusion of a surfactant molecule within the aggregate, conformational dynamics of the polar and apolar molecular moieties, micellar shape fluctuation, exchange of surfactant molecules between bulk solvent and micelle, structural collapse of the aggregate leading to its dissolution and vice versa, diffusion and rotation of the entire aggregate, and intermicellar collisions [13–16]. Dry reversed micelles of AOT have a mean aggregation number of 23 and a radius of 15 Å, exchange monomers with the bulk in a time scale of 10-6 s, and dissolve completely in a time scale of 10-3 s [17,18].

FIG. 2 Micellar aggregate of “amphiphilic molecules.”

4

Turco Liveri

Water, aqueous solutions and many other strongly hydrophilic substances can be solubilized within the micellar core [19,20]. Water solubilization involves hydration of the surfactant headgroup accompanied by an increase in the headgroup area, a micellar swelling, a marked increase in the surfactant aggregation number, and, at constant surfactant concentration, a decrease in the number density of reversed micelles [21]. A representation of a spherical reverse micelle entrapping a polar solubilizate in the core is shown in Fig. 3. Moreover, in the case of ionic surfactants, the addition of water weakens the electrostatic interactions between the counterion and the surfactant ionic head, forming solvent-separated ion pairs. For electrostatic reasons, counterions and ionic heads together with molecules of water of hydration are confined in a restricted interfacial shell. Nearly unperturbed water molecules (“bulk” water) exist in the micellar core [22,23]. The size and shape evolution of reversed micelles as a function of the water and surfactant concentrations are system-specific. The micellar size is mainly controlled by the strong tendency of the surfactant to be located at the interface between water and apolar solvent, which involves an enormous value of the interfacial surface and micelles of nanometric size. Spherical micelles result from a minimization of the micellar surface-to-volume ratio, i.e., a minimization of water–surfactant interactions less favorable than water–water and/or surfactant–surfactant interactions, while rodlike micelles, characterized by a greater surface-tovolume ratio, result from water–surfactant interactions more favorable than

FIG. 3 Micellar aggregate of “amphiphilic molecules” entrapping a “polar solubilizate.”


5

water–water and/or surfactant–surfactant interactions. In the case of AOT, the radius (r) of nearly spherical and monodisperse reversed micelles increases linearly with the molar ratio R (R = [water]/[surfactant]; r (nm) = 1.5 + 0.175R) and is quite independent of the surfactant concentration [14,24]. With increasing R, the fraction of water molecules located in the core of spherical micelles (or the time fraction spent by each water molecule in the core) increases progressively as a consequence of the parallel increase in the micellar radius. In contrast, lecithin, being able to establish strong hydrogen bonds with water, forms very long rodlike watercontaining reversed micelles [25,26]. Solubilization of water within the micellar core transforms reversed micelles from small and labile aggregates to more stable aggregates with a greater persistence in the size and shape of the entire aggregate (even if each molecular component is continuously exchanged with the surroundings), influences the intermicellar interactions, and widens the spectrum of their dynamics [27]. In addition to the dynamics of dry micelles, fast exchange of water molecules between the surface and the center of the hydrophilic core, micellar shape and charge (in the case of ionic surfactant) fluctuations, breaking and re-forming of adhesive bonds between contacting micelles, and intermicellar exchange of material are generally considered. In the case of AOT, less than 1 in 1000 intermicellar collisions leads to micelle coalescence followed by separation and a material exchange process occurring in the microsecond to millisecond time scale [13,28]. The intermicellar exchange of material can also be assisted by the exocytotic–endocytotic mechanism, i.e., through the formation of minimicelles that encapsulate hydrophilic molecules in their interior and their subsequent coalescence with other micelles [15,21]. In spite of the closed structure of reversed micelles, some mechanisms have been suggested to account for their attractive interactions. In the case of water-containing AOT reversed micelles, it has been suggested that a pivotal role in the intermicellar interactions is played by the surfactant dissociation, which leaves hydrated charged heads at the micellar surface and hydrated counterions in the aqueous core [29]. Then, the continuous jumping of AOT- anions (hopping mechanism) [30] among neighboring micelles forming oppositely charged micelles is responsible for the attractive intermicellar interactions leading to the formation of extended clusters of reversed micelles and for the conductometric behavior of water–AOT–hydrocarbon microemulsions [29,31]. Another mechanism, postulated to explain the conductometric behavior of these microemulsions, attributes it to the transfer of sodium counterions from one reversed micelle to another through water channels opened by intermicellar coalescence [32,33]. In the case of water-containing lecithin reversed micelles, an enhancement of hydrogen bonding induced by an increase in water and/or micellar concentration has been suggested to account for the huge increase in intermicellar interactions [21,34].

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Interesting properties are observed when the concentration of reversed micelles is increased, the temperature is changed, or suitable solutes are added. In some cases, in fact, a dramatic increase has been observed in some physicochemical properties such as viscosity, conductance, static permittivity, and sound absorption. Two main interpretive pictures have been proposed to rationalize this percolative behavior. One attributes percolation to the formation of a bicontinuous structure [35,36], and the other to the formation of very large transient aggregates of reversed micelles [30]. In this respect, most interesting is the observation that the percolation threshold is dependent on the physicochemical property. As an example, in Fig. 4 the trends of the viscosity and conductance of AOT–n-heptane solutions as a function of the volume fraction of AOT are reported. As can be seen in a range where a divergence of the viscosity is observed, the conductance does not display significant variations. This implies that a deeper understanding of percolation requires a detailed description of the molecular processes involved and, in particular, that different molecular processes are responsible for charge and momentum transfer in these systems [37].

FIG. 4 Viscosity ( ) and conductivity ( ) of AOT–n-heptane solutions as a function of the surfactant volume fraction. (Data from Ref. 37.)


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Temperature or water and surfactant concentrations can influence the intermicellar interactions and/or the micellar number density. Both effects could induce an extensive intermicellar connectivity due to intermicellar interactions or for topological reasons, creating a network able to enhance momentum and/ or charge transfer in the system. By considering the viscosimetric behavior of water–AOT–n-heptane microemulsions at various values of R, it can be observed that at very low R values or at R > 10 these systems behave as suspensions of quite monodisperse hard sphere particles whereas at intermediate R values they interact strongly. This interesting conclusion can be drawn from Fig. 5, where the dependence of the relative viscosity (η/η 0 ) on the volume fraction (Φ) at various R values is compared with that of a suspension of hard silica spheres in cyclohexane [37,38]. This is consistent with the finding that, in the semidilute region, AOT reversed micelles form micellar clusters in the range 0 < R < 10 whereas they do not at R > 10 [39] and also that the globular structure of reversed micelles persists even at the higher volume fractions of the dispersed phase and bicontinuous structures never set in [40].

FIG. 5 Comparison of the relative viscosity of dispersions of silica hard spheres and water–AOT–n-heptane microemulsions. ( ) Hard spheres; (Ο) R = 0; ( ) R = 5; ( ) R = 10; ( ) R = 20; (∆) R = 30; ( ) R = 40. (Data from Refs. 37 and 38.)

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A number of investigations have been performed on solubilization of solutes within water-containing reversed micelles to probe micellar structure and dynamics, to define their preferential solubilization site, and to emphasize mutual modifications due to solute–micelle interactions. Electrolytes and strongly polar molecules are obviously solubilized in the micellar core. Adding electrolytes to water containing AOT reversed micelles has an effect that is opposite to that observed for direct micelles, i.e., decreases are observed in the micellar radius and intermicellar attractive interactions [41] owing to the stabilization of AOT ions at the water/surfactant interface. Polar solutes, increasing the micellar core matter, induce an increase in the micellar radius, while amphiphilic molecules, being preferentially solubilized at the water/surfactant interface and consequently increasing the interfacial surface, lead to a decrease in the micellar radius [42,43]. As a consequence of their size and specific interactions, hydrophilic macromolecules or solid nanoparticles cause strong changes in micellar size and dynamics, and their properties are strongly affected [4,44]. II. REVERSED MICELLES AS NANOCONTAINERS: THE STATE OF WATER AND OTHER SOLUTES WITHIN REVERSED MICELLES The study of the state of water within reversed micelles has received a lot of attention as it simulates the water confined in biological membranes or tightly bonded to biopolymers, enzymes, and proteins. There has been some controversy over the number of types of water encapsulated within reversed micelles and the appropriate model to describe the distribution among them. In the case of AOT reversed micelles, three main states can be hypothesized: water hydrating the sodium counterion, water hydrating the surfactant anionic headgroup, and water in the core. Some contributions to the measured physicochemical property could arise from the small fraction of water dispersed monomerically in the bulk solvent. Taking into account the spatial distribution of water molecules within the reversed micelles and assuming a nearly constant ratio between the numbers of water molecules hydrating the headgroup and the counterion, only two types of water can be hypothesized, “interfacial” water interacting with surfactant headgroups and counterions and “bulk-like” water in the micellar core. These types of water exchange on the nanosecond time scale (a time scale greater than the infrared window) and can be considered in a continuous equilibrium or existing above a critical molar ratio R below which only interfacial water exists. Several authors have investigated the energetic state of water in reversed micelles by calorimetry [45–50]. To emphasize the information gained on this subject by use of calorimetry, the enthalpies of solution of water in AOT or in lecithin reversed micelles as a


9

function of the molar ratio R are reported in Fig. 6 [51,52]. These values, strongly different from the enthalpy of solution of water in apolar organic solvents (+33.1 kJ/mol) [53,54], immediately indicate that water is practically totally encapsulated in the micellar core. Incidentally, it must be pointed out that the heat effect arising from the very small fraction of water that dissolves monomerically in the organic solvent must be taken into account in order to avoid misinterpretations of the calorimetric data, especially at the lower R values [54]. The continuous variation of the enthalpy of solution of water for both systems is consistent with a continuous model of water partitioned between the micellar core and the interface of a reversed micelle, which swells with R. The small and positive values of enthalpies of solution of water in AOT reversed micelles indicate that the energetic state of the water is only slightly changed and that water solubilization (unfavorable from an enthalpic point of view) is mainly driven by a favorable change in entropy (the water state at the interface and its dispersion as nanodroplets could be prominent contributions) [48,51]. In contrast, the solubilization of water in lecithin is a relatively strong exothermic process. This has been taken as an indication that water interacts favorably

FIG. 6 Enthalpy of solution of water in AOT ( , left-hand scale) or lecithin ( , righthand scale) reversed micelles as a function of R. (Data from Refs. 51 and 52.)

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with the zwitterionic headgroup of lecithin, promoting the formation of strong intermolecular hydrogen bonds, which can account for the rodlike structure of lecithin reversed micelles (i.e., micelles with a surface-to-volume ratio greater than that of spherical micelles) [52,55]. Both thermodynamic and spectroscopic properties of “core” water in AOT reversed micelles are similar to those of pure water. This indicates that the penetration of counterions in the micellar core is negligible. From differential scanning calorimetric measurements a marked cooling–heating cycle hysteresis has been observed, showing that water encapsulated in AOT reversed micelles is only partially freezable and that the freezable fraction displays marked supercooling behavior as a consequence of the very small size of the micellar core. The nonfreezable fraction has been identified as the water hydrating the AOT ionic heads [56,57]. The state of water within AOT reversed micelles has also been probed indirectly through measurements of the specific heat of water–AOT–n-heptane microemulsions [54,58]. An analysis of these data made it possible to calculate the apparent specific heat (CAOT) of AOT (see Fig. 7). The observed decrease of CAOT

FIG. 7 Apparent specific heat capacity of AOT (CAOT) in the micellar phase as a function of R. (Data from Ref. 54.)


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with R (i.e., by decreasing the AOT concentration in the micellar phase) was explained in terms of the breakdown of the water structure by the hydration of AOT ionic heads. Other strongly hydrophilic substances such as methanol, formamide, nmethylformamide, and ethylenediamine solubilized in dry AOT reversed micelles are able, like water, to create their own micellar core [20,59,60], whereas amphiphilic solubilizates such as 1-pentanol and cholesterol are partitioned between the micellar palisade layer and the bulk organic solvent. As an example of the evolution of the partitioning process of an amphiphilic solubilizate as its concentration increases, the molar enthalpy of solution of 1-pentanol in the AOT–n-heptane system is shown in Fig. 8 as a function of the alcohol molality at various AOT concentrations [61]. An analysis of these data showed that at infinite dilution of the alcohol, following a Poisson distribution, 1-pentanol molecules distribute between AOT reversed micelles and the continuous organic phase, whereas at finite alcohol concentration, given the ability of alcohol to self-assemble in the apolar organic solvent, a coexistence between reversed micelles (solubilizing

FIG. 8 Enthalpy of solution of 1-pentanol in AOT–n-heptane solutions as a function of the alcohol molal concentration (mPentOH) at various AOT concentrations. ( ) [AOT] = 0 mol/kg; ( ) [AOT] = 0.049 mol/kg; ( ) [AOT] = 0.0986 mol/kg; ( ) [AOT] = 0.196 mol/kg; ( ) [AOT] = 0.292 mol/kg. (Data from Ref. 61.)

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1-pentanol) and alcoholic aggregates (incorporating AOT molecules) is realized. The observed humps have been qualitatively explained in terms of two opposite effects. The first (predominant at low alcohol concentrations and responsible for the initial increase in ∆H) was ascribed to the decrease in the binding constant with 1-pentanol concentration and attributed to rapid saturation of the binding sites of AOT reversed micelles or to alcohol-induced changes in the AOT reversed micelle structure. The second effect (predominant at high alcohol concentrations and responsible for the decrease in ∆H) was attributed to the self-association of the alcohol molecules by intermolecular hydrogen bonds.

III. INTERMICELLAR INTERACTIONS AND PERCOLATION With a high degree of approximation, solutions of reversed micelles can be described as solutions of supramolecular objects that display more or less strong intermicellar interactions. By changing the concentration of these aggregates one can attain different physical conditions corresponding to various physical phenomena. In particular, above threshold values of the concentration of reversed micelles, a dramatic increase in static viscosity can be observed, leading to the formation of systems, called organogels, that are particularly interesting for industrial applications (biocatalysis, biomembrane mimetic systems, extraction processes, and preparation of nanoparticles) [62]. Using calorimetry, it has been observed that the enthalpy of dilution of water– AOT–n-heptane microemulsions and the apparent specific heat capacity of the micellar phase vary monotonically with the micellar concentration without any change in rate during the crossover of the percolation threshold [54]. The observed trends suggested that even at the highest values of the volume fraction of the dispersed matter (Φ), the microemulsions are made up of water-containing reversed micelles dispersed in the hydrocarbon and that the intermicellar interactions decrease as R increases, vanishing when R > 10. This hypothesis is in agreement with the observation that the percolation threshold of these microemulsions at R > 10 occurs at a Φ value of approximately 0.5, a value that corresponds to the packing fraction of a cubic array of contacting spheres. Moreover, it is consistent with the viscosimetric behavior of these microemulsions reported above. Whereas the dilution of solutions of AOT reversed micelles at R > 10 is an athermal process (clustering results from topological effects), the dilution of water– lecithin reversed micelles is a strongly endothermic process [52,54]. This has been attributed to a strong dependence of the micellar size upon the lecithin


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reversed micelle concentration involving the breakage of many hydrogen bonds with dilution. IV. WATER-CONTAINING REVERSED MICELLES AS NANOSOLVENTS: THE SOLUBILIZATION OF NONIONIC SOLUTES Solutions of water-containing reversed micelles are systems characterized by a multiplicity of domains: apolar bulk solvent, oriented alkyl chains of the surfactant, hydrated surfactant headgroup region at the water/surfactant interface, and “bulk” water in the micellar core. Many polar, apolar, and amphiphilic substances, which are preferentially solubilized in the micellar core, in the bulk organic solvent, and in the domain comprising the alkyl chains and the hydrated surfactant polar heads, henceforth referred to as the palisade layer, respectively, may be solubilized in these systems at the same time. Moreover, it is possible that (1) local concentrations of solubilizate are very different from the overall concentration, (2) molecules solubilized in the palisade layer are forced to assume a certain orientation, (3) solubilizates are forced to reside for long times in a very small compartment (compartmentalization, quantum size effects), (4) the structure and dynamics of the reversed micelle hosting the solubilizate as well as those of the solubilizate itself are modified (personalization). All these peculiarities have been exploited by using these systems as useful solvent and reaction media for technological applications. Also, some resemblance between these systems and biological environments has been the driving force to employ solutions of reversed micelles to model or to mimic biological processes or to realize pharmaceutical preparations [63]. Knowledge of the solubilization site in microemulsions and the interaction forces driving the partitioning of a solute between the different microregions is fundamental to the rationalization of many complex phenomena. Among the various techniques, calorimetry has been used to determine the complete set of thermodynamic parameters of the partitioning process and also to gain information on the solubilization site and on the mutual changes following the solubilization process [59,60]. The quantity experimentally determined is the thermal effect accompanying the mixing in the calorimetric cell of a solubilizate–organic solvent solution with a water–surfactant–organic solvent microemulsion at a given surfactant concentration ([S]). This thermal effect, corrected for the enthalpy of dilution of both solutions and referred to 1 mole of the solubilizate, corresponds to the enthalpy of transfer (∆Ht) of the solubilizate from the organic to the micellar phase. In order to analyze the calorimetric data (∆H t , [S]), it is also necessary to develop

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a suitable model. Here I report briefly on a simple one that has been proven to explain consistently the experimental data of nonionic solubilizates. Using a Nernstian approach to the partitioning of solubilizates among three different microdomains (organic continuum, micellar palisade layer, and micellar aqueous core), the following distribution constants may be defined: (1) (2) where mp, mw, and mo are the equilibrium molal concentrations of the solubilizate in the palisade layer, aqueous core, and organic continuum, respectively. Kp is the distribution constant of the solubilizate between the organic continuum and the micellar palisade layer, and Kw is the distribution constant of the solubilizate between the organic continuum and the micellar aqueous core. Using Eqs. (1) and (2), it can be easily shown that the fraction of molecules bonded to the micelles, Xb (Xw to the micellar core and Xp to the palisade layer), is given by (3) where (4) and Ps and Pw are the molecular weights of surfactant and water (expressed in kilograms), respectively. The last equation is important because from the dependence of K and R the solubilization site of the solubilizate can be defined. Taking into account that ∆Ht is related to the fractions of solubilizate molecules transferred to the aqueous core (Xw) and to the micellar palisade layer (Xp) by the equation (5) and are the enthalpies of transfer from the organic solvent to the where palisade layer and to the aqueous core, respectively, and combining Eqs. (3)–(5), it can also be found that (6)

Solutions of Reversed Micelles where

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is given by the equation

Then an analysis of the calorimetric data (∆Ht, [S]) by Eq. (6) and using Eqs. (4) and (7) allow us to obtain the complete set of thermodynamic parameters for the transfer process. In order to show the information gained through calorimetric investigations on the partitioning of nonionic solubilizates, Table 1 lists the thermodynamic parameters for the transfer process of some amphiphilic solubilizates from the organic continuum to the micellar palisade layer or the micellar aqueous core. The standard free energies of transfer were obtained from the equations

and

where and are the Kp and Kw values converted to the molarity scale as suggested by Ben-Naim [64]. A perusal of the data reported in Table 1 shows that the distribution constants Kw decrease with increases in the hydrophobic character of the solubilizate while the opposite is true for K p and that for the more hydrophilic solubilizates the preferential solubilization site changes as the water content of reversed micelles increases. It can also be observed that in terms of standard free energies the additivity rule holds for the transfer between microdomains. The enthalpies of transfer from the apolar solvent to the micelles are exothermic, and, in principle, changes in the micellar structure and/or preferential orientation of the solubilizate in the palisade layer also contribute to their values [59]. It can also be observed that the standard enthalpies of transfer from the organic continuum to the palisade layer are between –26 and –20 kJ/mol whereas the corresponding quantities for the transfer from the organic continuum to the aqueous core are in the range of –45 to –21 kJ/mol. This indicates that in the palisade layer the solubilizates are forced to be oriented such that only one polar group of a diamine interacts with a hydrophilic head of AOT, whereas this does not happen in the aqueous core, where both polar groups of the diamines can be hydrated [60]. In the case of Kryptofix 221D, a cryptand able to complex the alkali metal cations [65], it has been observed that it is solubilized mainly in the palisade layer of the AOT reversed micelles, and from an analysis of the enthalpy of transfer of this solubilizate from the organic to the micellar phase it has been established that the driving force of the solubilization is the complexation of the sodium counterion. Moreover, the enthalpy values made it possible to show the

16 TABLE 1 Thermodynamic Parameters for the Transfer of Some Nonionic Solubilizates from the Organic Continuum to the Micellar Palisade Layer or the Micellar Aqueous Core

Solubilizate

Kp

Kw

Methanol n-Propanol n-Pentanol Ethylenediamine N,N-Dimethylaminoethylamine N,N,N’,N’-Tetramethylenediamine Cholesterol

41 22 20 48 17 1.4 25

187 20 — 1990 319 17 —

(kJ/mol)

(kJ/mol)

(kJ/mol)

(kJ/mol)

21 24 24 25 22 20 26

22 21 — 45 41 35 —

10 9.0 8.7 11 8.3 2.1 9.2

14 8.4 — 20 15 8.0 —

Source: Refs. 59 and 60.

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peculiar solvation state of sodium counterions and demonstrate that they are essentially located near the water/AOT interface [66]. V. REVERSED MICELLES AS NANOREACTORS The small size of water-containing reversed micelles together with their stability in form but not in constituent molecules (persistence of shape accompanied by fast material exchange dynamics) suggests the use of these systems as peculiar nanoreactors. It can be expected that reaction rates, reaction mechanisms, and equilibrium constants can be affected significantly compared to the same processes occurring in bulk [67]. Preferential solubilization involves local concentrations different from the analytical values and catalytic effects. In addition, since reversed micelles share some fundamental features of biomembranes (dominance of interfacial effects, ordered arrangement of amphiphilic molecules), water-in-oil microemulsions have also been proposed as advantageous reaction media for the investigation of biochemical reactions. A calorimetric investigation of the substitution reaction [Pd(bipy)(en)] 2+ + en → [Pd(en)2 ] + bipy (where bipy = 2,2'-bipyridine and en = ethylenediamine) performed in water–AOT–n-heptane microemulsions demonstrated that with increases in R the reaction becomes less exothermic and its rate constant decreases, approaching the value observed in water. These features were rationalized in terms of the peculiar solvation state of reactants inside the AOT reversed micelles and/or the peculiar physicochemical properties of the micellar core [68]. Another field recently opened is the use of water-in-oil (W/O) microemulsions as reaction media for the synthesis of solid nanoparticles. The interest in synthesizing nanoparticles in solutions of reversed micelles is due to their important technological applications as catalysts for redox reactions [69] or their use to model or mimic processes occurring in geological or biological environments [70]. Some calorimetric investigations have shown that the enthalpy of formation of metallic nanoparticles and the molar enthalpy of precipitation of inorganic salts become more negative with increasing R (i.e., increasing micellar radius) and level off at higher R values. This experimental evidence has been rationalized in terms of the formation of nanoparticles dimensionally controlled by the micellar radius [70–73]. Typical behavior is shown in Fig. 9, where the enthalpy of formation of AgCl nanoparticles in AOT reversed micelles is reported as a function of the molar ratio R at various salt concentrations. As can be seen, the enthalpies become more exothermic as R increases. The small ∆H values at lower R, corresponding to

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FIG. 9 Enthalpy of formation of AgCl nanoparticles in water–AOT–n-heptane microemulsions as a function of R at various concentrations (C) of the reagent salts in the aqueous microphase. ( ) C = 0.005 mol/kg; ( ) C = 0.03 mol/kg; ( ) C = 0.05 mol/kg. (Data from Ref. 66.)

lower values of the micellar radii, indicate the formation of smaller microcrystals with higher surface-to-volume ratios and consequently in a higher energetic state. In the synthesis of ZnS nanoparticles in various W/O microemulsions, further effects have been revealed [74]. In Fig. 10 the molar enthalpy of precipitation of ZnS nanoparticles in some W/O microemulsions is reported as a function of R. The continuous line indicates the molar enthalpy for the same process performed in water. As can be seen, with increases in R the molar enthalpy value becomes more negative, and in the case of AOT it tends to level off at higher R values. Moreover, these molar enthalpies are always less negative than the corresponding value in water. This is consistent with an increase in the nanoparticle size with R. By comparing the enthalpies at the same R value it can be noted that these quantities are in the order DDAB > C 12 E 4 > lecithin > AOT. Moreover, since the enthalpies of precipitation of ZnS at the same nanoparticle radius were different for the various microemulsions, it was also concluded that some


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FIG. 10 Enthalpy of formation of ZnS nanoparticles in W/O microemulsions [( ) DDAB; ( ) C12E4; ( ) AOT; ( ) lecithin] as a function of R. The continuous line indicates the enthalpy of formation of bulk ZnS in water. (Data from Ref. 74.)

enthalpic contributions arise from interactions between nanoparticles and the water/ surfactant interface.

VI. CONCLUSION In this chapter I have attempted to present a panoramic view of the contributions of calorimetry to the study of solutions of reversed micelles. In particular, it has been shown that it is possible with calorimetry to obtain information on the energetic state of water and that of other solubilizates within reversed micelles, the complete set of thermodynamic parameters for the solubilization process, and the preferential solubilization site as well as information on the intermicellar interactions and the energetic state of solid nanoparticles entrapped in the micellar core. All these data together with those obtained by other techniques help to better and better define the structural and dynamical picture of solutions of reversed micelles and to exploit their potential technological applications.

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Finally, it must be remarked that in spite of the importance of the information that can be gained by calorimetry, the numbers of calorimetric investigations on solutions of reversed micelles and relative to other experimental techniques are still very small.

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53. R De Lisi, M Goffredi, V Turco Liveri. J Chem Soc Faraday Trans I 76:1660– 1662 (1980). 54. F Goffredi, V Turco Liveri, G Vassallo. J Colloid Interface Sci 151:396–401 (1992). 55. YA Shchipunov, EV Shumilina. Mater Sci Eng C3:43–50 (1995). 56. C Boned, J Peyrelasse, M Moha-Ouchane. J Phys Chem 90:634–637 (1986). 57. H Hauser, G Haering, A Pande, PL Luisi. J Phys Chem 93:7869–7887 (1989). 58. JP Morel, N Morel-Desrosiers, C Lhermet. J Chim Phys 81:109–112 (1984). 59. A D’Aprano, ID Donato, F Pinio, V Turco Liveri. J Solution Chem 18:949–955 (1989). 60. G Pitarresi, C Sbriziolo, ML Turco Liveri, V Turco Liveri, J Solution Chem 22:279–287 (1993). 61. A D’Aprano, A Lizzio, V Turco Liveri. J Phys Chem 92:1985–1987 (1988). 62. P Terech, RG Weiss. Chem Rev 97:3133–3159 (1997). 63. JH Fendler. Chem Rev 87:877–899 (1987). 64. A Ben-Naim. J Phys Chem 82:792–803 (1978). 65. JM Lehn, JP Sauvage. J Am Chem Soc 75:6700–6707 (1975). 66. A D’Aprano, ID Donato, F Pinio, V Turco Liveri. J Solution Chem 19:589–595 (1990). 67. JH Fendler. Membrane Mimetic Chemistry, Wiley, New York, 1982. 68. ML Turco Liveri, V Turco Liveri. J Colloid Interface Sci 176:101–104 (1995). 69. A Sobczynski, AJ Bard, A Campion, MA Fox, T Mallouk, SE Webber, JM White. J Phys Chem 91:3316–3320 (1987). 70. V Arcoleo, M Goffredi, V Turco Liveri. Thermochim Acta 233:187–197 (1994). 71. A D’Aprano, F Pinio, V Turco Liveri. J Solution Chem 20:301–306 (1991). 72. V Arcoleo, G Cavallaro, G La Manna, V Turco Liveri. Thermochim Acta 254:111–119 (1995). 73. F Aliotta, V Arcoleo, S Buccoleri, G La Manna, V Turco Liveri. Thermochim Acta 265:15–23 (1995). 74. V Arcoleo, M Goffredi, V Turco Liveri. J Thermal Anal 51:125–133 (1998).

2 Thermodynamics and PhaseSeparation Kinetics of Microemulsions DORIS VOLLMER Institute for Physical Chemistry, University of Mainz, Mainz, Germany

I.

Introduction

24

II.

Phase Behavior of Microemulsions

27

A. B. C. D. E. F. G.

27 27 29 31 34 39 41

Microemulsions Phase diagrams Characteristic size of droplets Specific heat Free energy Latent heat Step in the specific heat

III. Phase Separation Kinetics A. B. C. D. IV.

Energy barrier Experimental observation of oscillations Mechanism of phase separation Temperature dependence of the droplet–droplet distance

43 43 45 47 48

Conclusion

54

References

56

23

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I. INTRODUCTION Mixtures containing surfactants and hydrophilic (for instance, water) and hydrophobic (for instance, alkanes) components show a fascinating thermodynamic and kinetic behavior. Gaining an understanding of this behavior poses a large variety of interesting physical and chemical challenges, which have been a focus of fundamental research in colloid science throughout recent decades. In addition to this interest from a statistical physics point of view, this research is also strongly stimulated by applications. Surfactants are ingredients of various products such as pharmaceuticals, lubricants, and cosmetics [1]. They are of importance for tertiary oil recovery and for emulsion polymerization. To improve production capacities, a better understanding of the varying forces of interaction between the surfactant molecules and the other ingredients in the course of production is desirable. In this review, we highlight recent insights into the driving forces of phase transitions and their kinetics in these mixtures that have been made possible by microcalorimetric studies. Binary and ternary mixtures of water, alkanes, and surfactants show a rich variety of phases [2–4]. At room temperature, they are typically organized on the scale of a few tens of nanometers, so that mesoscopic water and oil domains are separated by a surfactant monolayer. The domains can have various structures. Nearly monodisperse droplets or disordered cylindrical structures, lamellar arrangements of alternating water and oil layers, and spongelike structures have been observed. For several model systems, the approximate extent of these structures in the phase diagram is known [5–12]. There can be as many as five transitions between structures with vastly different mechanical properties in temperature intervals of only 10 K, and there are extended two-phase (2Φ) and threephase (3Φ) regions, where these structures coexist with each other or with water- or oil-rich excess phases. Analysis of the underlying microstructures and understanding of the origin of the phase transitions between the structures have received a lot of attention (see Ref. 13 for a review). The improved experimental characterization of the phase behavior formed a basis for theoretical and computational modeling of phase diagrams [13–24]. In recent years the relevant parameters entering into the equilibrium free energies have been identified. However, their precise values, as well as their dependence on components, temperature, and composition, are still under debate [23,25–31]. Fascinating kinetics is observed when the systems are driven out of equilibrium. Typically, this is accomplished by mechanical treatment, by a sudden change of composition, or by a temperature jump. The most intensively studied mechanically induced transition is the formation of multilamellar vesicles (“onions”), which occur on shearing of a lamellar phase [32–36]. A sudden change of composition may lead to the formation of myelins [36–39]. Mechanical pinch-

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ing of a cylindrical vesicle might lead to a pearling instability, where the cylinder disintegrates into a row of equidistant droplets [40,41]. Temperature jump experiments have been performed to investigate the phase separation of bicontinuous, sponge, lamellar, or droplet phases into one or several coexisting phases of different morphologies [42–44]. Unlike the thermodynamics of surfactant mixtures, their kinetics is poorly understood. A main problem in modeling the kinetics is that, typically, temporal changes of the thermodynamic properties have to be combined with a complex hydrodynamics. In this chapter we argue that differential scanning microcalorimetry (DSC) is an outstanding method for investigating the thermodynamic and kinetic properties of surfactant mixtures [29,30,45–47], since it is highly sensitive to small changes in the surfactant monolayer. This is demonstrated for a three-component mixture of water, octane, and the nonionic surfactant C12E5, i.e., CH 3(CH2)11(OCH2CH2)5OH, where we focus on two structural transitions. This restraint allows us to compare quantitative predictions on the behavior of the mixtures with detailed experimental data. We investigate the thermodynamics of the temperature-induced phase transitions between a lamellar phase and a droplet phase and of the failure of water droplets to emulsify all water in a sample when the temperature is increasing (emulsification failure) [48]. A schematic drawing of the varying microstructure for the phase sequence lamellar–droplet–2Φ is given in Fig. 1. The values for the latent heat of the transition between a lamellar and a droplet phase and for the height of a step in the specific heat at emulsification failure are determined. Both are compared with predictions for the equilibrium free energies describing the mixtures. This permits identification of the important contributions to the free energy. An application of DSC to study the kinetics of phase separation is demonstrated for the case of the phase separation of a droplet phase microemulsion. When heated across the emulsification boundary the droplets tend to decrease in size (Fig. 1c). However, due to the small mutual solubility of the components this is hindered by the conservation of the area of the internal interface between water and oil and of the partial volumes of water, oil, and surfactant. As a consequence, the droplet size changes only when, with considerable over-heating (or after exceedingly long times), large droplets are formed. They can be viewed as nuclei of the coexisting water-rich phase [43,49] that grow quickly by taking up excess water of small droplets and merging with larger ones (Fig. 1d). This leads to a fast decay of their number and average distance. Eventually, the distance between large droplets becomes so large that the diffusive transport of water from small to large droplets becomes inefficient. Under constant heating, the small microemulsion droplets (Figs. 1d, 1e, or 1b) are overheated again until another wave of nucleation sets in (Fig. 1d). To emphasize this step-

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FIG. 1 Schematic drawing of the temperature-dependent microstructure of a mixture of water, oil, and a nonionic surfactant. The temperature-induced phase sequence from lamellar to droplet phase microemulsion to two-phase microemulsion is shown. In the 2Φ region constant heating leads to a decrease in the average size of droplets in a stepwise manner. This is due to the process of repeated nucleation and growth, as indicated by the arrow below the schematically drawn test tubes. The mechanism is discussed in detail in Section III.

wise change in the droplet size, we term this phase separation “cascade nucleation” [50]. This chapter is organized as follows. In Section II we concentrate on a discussion of the thermodynamics of microemulsions. After a definition (Section II.A), special emphasis is put on a description of the temperature-dependent phase behavior (Section II.B) and typical length scales (Section II.C). In Section II.D we discuss the temperature-dependent specific heat of phase transitions. After a discussion of various contributions to the free energy (Section II.E), a quantitative comparison between experimentally determined values and theoretical estimates for the latent heat (Section II.F) and for the step in the specific heat accompanying emulsification failure (Section II.G) is carried out. In Section III we discuss the kinetics of emulsification failure. The parameter dependence of the energy barrier preventing phase separation is discussed in Section III.A. This is followed up by a discussion of oscillations in the specific heat that are induced by cascade nucleation (Section III.B). In Section III.C the mechanism of cascade nucleation is described, and in Section III.D we point out that a slight nonmonotonous dependence of the period of oscillation is due to the dependence of the diffusion length between small droplets on composition. Finally, in Section IV the main results are summarized.

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II. PHASE BEHAVIOR OF MICROEMULSIONS A. Microemulsions Water and oil are immiscible. A sample containing water and oil will phase separate into macroscopic water and oil domains, since the surface tension of the interface between water and oil tends to minimize the interfacial area. However, when surfactant molecules are added, the interfacial tension between the water and oil domains may decrease by several orders of magnitude [27,31,51–53]. These molecules have a water-soluble polar headgroup and an oil-soluble apolar tail, separating the water and oil domains by a liquid-like monolayer of fixed average area per surfactant molecule [54]. In the case of very low interfacial tension, morphologies requiring a large interfacial area may be thermodynamically stable. Schulmann et al. [55] defined microemulsions as mixtures of water, oil, and surfactant that are thermodynamically stable, isotropic, and of low viscosity. In the present review, we follow this convention and denote the system as an “amphiphilic mixture” when we wish to also include lamellar and other locally ordered structures of higher viscosity. B. Phase Diagrams At present, amphiphilic mixtures containing surfactants of the type C i E j (alkylpolyglycol ether) are most completely characterized. Their phase behavior has been extensively studied by Kahlweit, Olsson, Strey, and coworkers, and detailed knowledge of the temperature- and composition-dependent morphology of such amphiphilic mixtures is available [2,11,22,23,31,53,54,56–58]. In view of this, the majority of theoretical work aiming at a comparison with experiments focuses on these mixtures. 1. Gibbs Phase Triangle Figure 2 schematically shows an isothermal cut through the Gibbs phase prism. Depending on composition, the mixture may be single-phase (1Φ), two-phase (2Φ), or three-phase (3Φ). 1Φ: In the single-phase region, the microemulsion solubilizes all water and oil. The mixture is macroscopically homogeneous. Its microstructure depends, however, on temperature and composition. Oil droplets in water, oil cylinders in water, bicontinuous and lamellar morphologies, water cylinders in oil, and water droplets in oil* have been observed.

* Oil and water droplets are also called swollen and reversed swollen micelles, respectively.

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FIG. 2 Schematic drawing of the Gibbs phase triangle for a mixture of water, alkane, and nonionic surfactant (C i E j ). 1Φ 2Φ, and 3Φ stand for a single-phase microemulsion, a microemulsion coexisting with a water- or oil-rich phase, and a microemulsion coexisting with a water-rich phase and an oil-rich phase.

2Φ: In the two-phase region, there is a microemulsion phase containing almost all amphiphile, which coexists with an oil-rich (2Φ, Winsor I [59]) or with a water-rich (2Φ, Winsor II [59]) phase [56]. 3Φ: If the mixture separates into three phases (Winsor III [59]), the amphiphile is mainly dissolved in the middle phase, which coexists with phases containing predominantly water and oil, respectively [56]. The extent of the 1Φ, 2Φ, and 3Φ regions in the Gibbs phase triangle depends on composition, on temperature, and on the choice of the components [2,13,53]. 2. Fish Cut Nonionic surfactants of the type of CiEj show a strongly temperature-dependent phase behavior. In the present chapter we restrict ourselves to mixtures of water, octane (Merck, Darmstadt, Germany), and C12E5 (Nikko Chemicals, Tokyo, Japan). These intensively studied mixtures show extended droplet phases [10,11,31,54,58,60]. Sample compositions are given by the volume fractions of water φw, octane φo, and surfactant φs. Figure 3a shows a section through the phase prism as a function of temperature and surfactant concentration. The ratio φw/φo of the volume fractions of water and oil is fixed. Because of its characteristic fishlike shape, this section is called a “fish cut” [57]. The phase diagram is to a good approximation mirror symmetrical with respect to the phase inversion temperature , where the value for depends only on the choice of components and takes the value = 305.6 K for

Microemulsions

29

the investigated mixtures. For T ≤ the surfactant monolayer is curved on the average toward oil, whereas for T ≥ it is curved toward water. For φ 3 ≤ 0.05 a three-phase region (3Φ) is formed close to T = , , , whereas for higher surfactant concentrations the mixture becomes single-phase. For still higher surfactant concentrations a lamellar phase (lam), i.e., an alternation of water–surfactant–oil– surfactant layers is found (see Fig. 3a). The lamellar phase is birefringent and may be of high viscosity. It is bounded in the phase diagram by two clear microemulsion phases, enclosing oil (L 1) or water (L 2). The L 1 and L2 phases are separated from the lamellar phase by a two-phase region whose width is not shown in Fig. 3. For φw < φ o the microstructure in the L2 region conforms to water droplets embedded in an oil matrix. Analogously, in the microemulsion channel L1 oil droplets are formed for φo < φw. Even further from , the single-phase microemulsion phase separates. The corresponding phase boundaries are called the water (for L2 to 2Φ) and oil (for L 1 to 2Φ) emulsification boundaries. For temperatures sufficiently above the water emulsification boundary (i.e., well inside the 2Φ region), a water droplet microemulsion is in equilibrium with a water-rich phase. With increasing temperature the average size of the droplets decreases, leading to an increase in the volume fraction of the coexisting water-rich phase. A schematic drawing of a water droplet covered by a surfactant monolayer is given in Fig. 3b. The average radius of the hydrophilic part of the water droplet is given by R1φ, and ls denotes the average thickness of the monolayer. For simplicity, the hydrophilic headgroup [OCH2CH2], OH is drawn as a circle. The microstructure of the chain is similar to its hydrophobic counterpart H[CH2],. C. Characteristic Size of Droplets For microemulsions containing various types of nonionic or ionic surfactants, the composition- and temperature-dependent size of microemulsion droplets was determined by highly sensitive scattering experiments [10,31,58]. These studies permit a determination of the average droplet size and of the effective thickness of the surfactant monolayer with relative errors of roughly 10%. 1. The One-Phase Region In the 1Φ region the droplet size is determined by composition. To a good approximation it does not depend on temperature. The average radius R 1Φ of the droplets is determined by the conservation of their enclosed volume, , and of their surface area, , from which one finds (1)

30

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Microemulsions

31

To distinguish water from oil droplets, we take water droplets to have a positive radius and oil droplets to have a negative radius. The enclosed volume φd is the sum of the interior phase volume, i.e., water or oil, and the volume of the respective water- or oil-soluble part of the surfactant molecules. N denotes the number of droplets in a volume element V [11,31,58]. The effective thickness of the surfactant monolayer has been determined to be ls ≈ 1.3 nm [54]. Depending on composition, the droplet radius is on the order of 2–20 nm, the total oil/water interfacial area is on the order of 100 m2, and 1016–1018 droplets are formed per cubic centimeter.

2. The Two-Phase Region In the 2Φ region only the surface area of the droplets is preserved; their volume can be adjusted so that the droplets take their optimum size Ropt, i.e., a radius that locally minimizes the interfacial free energy. Ropt depends only on temperature; it is independent of composition [23]. At the emulsification boundary Ropt = R1Φ, whereas in the 2Φ region . For temperatures sufficiently below those corresponding to the micellar size and several degrees away from , the optimum radius has been determined by small-angle neutron scattering (SANS) experiments to vary as [31] (2)

where a = 1.2 × 10-3 K -1 Å-1. D. Specific Heat The specific heat is measured by using a differential scanning microcalorimeter (VP-DSC, Microcal Inc.). This microcalorimeter measures the difference in the FIG. 3 (a) Section through the phase prism for mixtures of water, octane, and C12E 5 for varying volume fractions of surfactant and nearly equal volume fractions of octane and water (φ o = 0.95φ w). The filled squares show experimentally determined values for the phase boundaries. L 1 and L2 denote single-phase microemulsions, lam denotes a lamellar phase, 2Φ denotes a microemulsion phase in equilibrium with a water-rich (2Φ) or an oil-rich (2Φ) phase, and 3Φ denotes a microemulsion phase in equilibrium with a water-rich phase and an oil-rich phase. At sufficiently high temperatures, the microstructure close to and above the water emulsification boundary corresponds to water droplets in oil, as indicated by the circles. The variation in the size of the circles shows the composition and temperature dependence of the droplet size in the 2Φ region. The increase in the volume fraction of the water-rich phase with increasing temperature is indicated by the size of the shaded area in the “test tubes.” (Data points taken from Ref. 31.) (b) Schematic drawing of a surfactantcovered water droplet.

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specific heat between the sample and a suitably chosen reference system. By this means it provides a very accurate description of the variation of the specific heat (T) relative to a baseline set by the reference sample. A more detailed description of the application of this technique to microemulsions is given in Ref. 45.* Figure 4a shows the thermogram of a heating and cooling scan performed on a sample of equal volume fractions of water and oil (φ w = φ o = 0.40; φs = 0.20). A heating rate of υs ≈ 5 K/h and a cooling rate of υ s ≈ –5 K/h were chosen. The solid line indicates the variation of the signal for the specific heat due to heating, while the dashed line shows the variation of (T) due to cooling. For convenience, the optically determined phase transition temperatures between singleand two-phase microemulsions are marked by arrows below the thermograms. Immediately after the start of the heating scan (solid line) at 294 K, i.e., slightly above the 2Φ → L1 phase boundary, the signal for the specific heat shows a peak at T = 296.5 K. For T < 296.5 K the mixture is clear and gel-like, whereas in the L1 region for T > 296.5 K the mixture remains clear and is of a lower viscosity. After going through a minimum, (T) increases sharply. It passes a very narrow peak, which is immediately followed by a large and relatively broad one. From a comparison with the phase diagram it can be concluded that the mixture is lamellar. The test probe appears slightly turbid and birefringent. According to the (T) signal, the mixture shows a single-phase lamellar region with a width of only 3 K, which is followed by another large peak (307–311 K). Comparison with the optically determined phase boundaries suggests that the latter is due to the phase transition of the lamellar phase into the L 2 channel. Before the signal has dropped toward the value it had in the lamellar phase, (T) increases again and starts to oscillate. The origin and parameter dependence of these oscillations is discussed in detail in Section III. The cooling scan (dashed line) starts in the L 2 channel. Both, the L2 ? lam and the lam ? L 1 phase boundaries give rise to a peak in the specific heat. Due to hysteresis, the peaks are shifted toward slightly lower temperatures compared to the boundaries observed during the heating scan. A broad peak in the L 1 channel is visible. We attributed this peak to a structural transition accompanying an appearance of local ordering in the L 1 region. Passing the L 1 → 2Φ phase boundary leads to a small peak in (T). Within the range 288 K < T < 293 K the signal for the specific heat is nearly constant; it increases only at T 285 K, where another large peak is visible. From optical investigations it is expected that the peak at T = 293.5 K is due to the entrance into the 2Φ region. However, the mixture is metastable. Close to T = 293.5 K the mixture remains clear, and * The difference between the MC2-MicroCal described in Ref. 45 and the VP-DSC is that the latter has a cell volume of 0.519 cm 3 and better baseline reproducibility.

FIG. 4 A heating scan (solid line) and a cooling scan (dashed line) for the specific heat relative to a reference mixture containing appropriate amounts of water and oil. The vertical bars indicate the optically determined phase boundaries for the compositions. The numbers above the bars denote the optically determined phase transition temperatures. (a) φ s = 0.2, φ w = φo = 0.4; (b) φ s = 0.2, φ w = 0.15, and φ o = 0.65. The inset in (b) shows the low temperature region on an enlarged scale.

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it is several hours before a macroscopic phase separation is observed. Below T 285 K the mixture immediately becomes turbid.* Finally, we point out that the width of a peak gives a measure for the width of the two-phase region separating the two single-phase regions. It has been checked that the width does not depend on scan speed. The area under a peak corresponds to the heat absorbed during a phase transition; i.e., in first-order phase transitions it is a measure of the latent heat of the transition. As required by thermodynamics, all transitions are endothermic for up scans and exothermic for down scans. A more detailed discussion of the structure of the thermograms and the peak shape is given in Ref. 30. For equal-volume fractions of oil and water, the peaks related to the transition from a lamellar into an L 1 or L 2 phase, respectively, are broad and look similar. Note, however, that the transition lam → L1 gives rise to two peaks that are very close to each other. The differences between the high and low temperature regions become even more apparent upon entry into the 2Φ or 2Φ region. This is interesting to note, since the phase diagram (see, e.g., Fig. 3a) gives the impression that the microstructure and the thermodynamic properties do not change when T is replaced by 2 – – T and water and oil are simultaneously interchanged. Therefore, the C12E5–water–octane system is called a symmetrical microemulsion [31]. The influence on the thermograms of changing the water-to-oil ratio is demonstrated in Fig. 4b, where (( (T) is shown for a sample with φw= 0.15, φo = 0.65, and φs = 0.2. For both the heating (solid line) and cooling (dashed line) scans, a heating rate of |υs | ≈ 6 K/h is used. In comparison to Fig. 4a, the spectrum looks strongly asymmetrical. In contrast, the transition lam → L2 gives rise to a narrow large peak, whereas the transition lam → L1 is accompanied by a small peak at T ≈ 292 K. A second small peak is visible when the region is entered. Also, in the L 1 channel, (T) does not remain constant, but the signal shape suggests that in the L1 channel the microstructure changes with temperature (inset in Fig. 4b). On the other hand, (T) is nearly constant in the L2 channel, and, again, passing the water emulsification boundary leads to a step in the specific heat. E. Free Energy To describe the phase behavior, contributions to the free energy arising from the bending of the interfacial monolayer, Fb; from undulations of the lamellae, Fu; and from the entropy of mixing of water and oil domains, Fmix, are discussed in * Similar behavior was observed by Olsson and coworkers [42], who investigated the turbidity after quenching the mixture into the 2Φ region.

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the literature for mixtures of water, alkane, and surfactant [14–17,19,21–24]. Since in the present review we deal solely with nonionic surfactants, electrostatic contributions to the free energy need not be considered. The surfactant film is treated as an incompressible, tensionless two-dimensional fluid. In addition, it is assumed that all surfactant molecules are located at the interface and that water and octane are immiscible. Both assumptions hold to within a few percent for this model system, and the corrections can be incorporated into the theory when the deviations become more significant. The free energy per unit area arising from the bending of the interfacial monolayer was introduced by Helfrich [61] and applied to amphiphilic mixtures by various authors [15,19,23,30]; (3) Here, R1 and R2 denote the local radii of curvature [30]. The bending modulus k, the Gaussian modulus , and the spontaneous curvature * c 0 (T) are empirical material constants; k and describe the elastic energy needed to curve the interface away from its preferred curvature. According to Refs. 22 and 29, they take the values k = 0.8kB and = –0.4 kB . For monodisperse spheres of radius R, the local radii of curvature identically fulfill = . In that case, the bending free energy per unit volume becomes

(4)

w h e r e R = R 1Φ in the single-phase region and R = R opt in the 2 Φ region and [63]. The factor φs/lsR2 corresponds to the interfacial area per unit volume. For a flat lamellar phase one has , yielding

It will be assumed that the linear dependence of c 0 (T) on temperature, , still holds. Equations (4) and (5) do not account for fluctuations

* The relationship between the spontaneous curvature and the optimum radius is still under debate. The relationship used here is a good approximation for the investigated mixture if (1) the microstructure conforms to droplets and (2) the droplets are sufficiently larger than micelles.

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of the interface. Undulations of the lamellae are expected to give important contributions to the free energy of lamellar structures [17,20]. To account for this, Helfrich’s result [62] for the free energy of undulating lamellar liquid crystals has been generalized heuristically [17]:

(6)

Following Ref. 17 we choose χ = 0.05. The free energy is positive and represents the entropic repulsions between fluctuating sheets that cannot cross. Additional contributions to the free energy result from equivalent possibilities to realize surfaces with a given structure in space. In particular, there are many different possibilities to distribute a given set of droplets in space, giving rise to a free energy of mixing [17], (7)

(8)

In the 1Φ region, Fu and Fmix depend only on temperature owing to the factor k B T. After crossing the emulsification boundary, the volume fraction of droplets φd becomes temperature-dependent, (9) leading to a second temperature-dependent term in F mix . In that case F mix ≠ – TS. Figure 5a shows a survey of the temperature dependence of the bending free energies per unit volume according to Eqs. (4) and (5) for the case φs = 0.2 and φw = φo = 0.4. The indices o and w on the symbol for the free energies distinguish between morphologies, where the average curvature of the monolayer is toward oil and water, respectively. and denote the free energy for an oil and water droplet phase microemulsion, respectively, where the droplets take their optimum radius. The dashed lines visualize the evolution of the free energies for a lamellar structure Flam and those of oil and water droplets . The solid line

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37

shows the temperature evolution of the thermodynamic free energy. By definition, it follows the lowermost of these curves, provided the constraints of conservation of the respective partial volumes can be fulfilled. It has different branches crossing over between morphologies. The free energy follows Fopt except for a temperature window around , where there is too little water or oil to let the droplets assume their optimum size. Consequently, the temperature of the intersection between every two such energies can serve as an estimate for the phase transition temperature. The resulting calculated phase diagrams agree within a few degrees with experiment [22].* In Fig. 5b, the influence of Fu and Fmix on the previously discussed energies is shown. The composition of the sample is kept the same. Fu leads to a significant increase in the free energy of the lamellar phase. The entropy of mixing Fmix leads to a comparatively smaller decrease in free energy. Close to T = , (T) is not defined. After all, the optimum size of the droplets diverges in such a manner that the constraints due to the conservation laws can no longer be fulfilled. [This is underlined by the divergence of φd(T) = φ s/[3lsa(T – )], although, clearly, φd(T) may never exceed 1.] Note that the entropy of mixing does not affect the position of the emulsification boundary, since R1Φ = Ropt at that boundary. In contrast, both Fmix and Fu decrease the range of stability of a lamellar morphology, so the phase boundary between the droplets and the lamellar phase moves closer toward . The influence of the water-to-oil ratio on the temperature dependence of the free energies is demonstrated in Fig. 5c, where the bending free energies Fs, Flam, and Fopt are shown for φs = 0.2, φw = 0.15, and φo = 0.65. Note that Fopt and Flam remain the same since their values are affected only by φs; they do not depend on φw and φo. In contrast, this change in composition strongly changes the free energies for the droplet structures;

depends on φo, and

depends on φw.

In comparison with Fig. 5a, the slope of (T) has increased around , and its minimum is shifted toward lower energies. This implies that the intersection of (T) and Flam(T) and that of (T) and (T) are shifted toward higher temperatures. In contrast, the slope of (T) decreases close to , and its minimum increases. Note that for this composition and temperature interval, (T) does not correctly describe the morphology, since it has been shown to be cylindrical or bicontinuous for T < [54]. Surprisingly, although an incorrect morphology is considered, the temperatures of the intersections of the free energies deviate from the experimentally determined ones (see Fig. 4b) by only a few degrees [22]. * Taking the intersection of the free energies as the position of the phase transition does not account, however, for the width of the 2Φ region, which can be calculated by evaluating the components’ chemical potentials in the respective coexisting phases (cf. Refs. 17,21,20).

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FIG. 5 Survey of different contributions to the free energy. (a) The bending free energy for nonfluctuating interfaces of oil droplets , water droplets , and a lamellar morphology (Flam). (b) Free energies when undulations of lamellae Fu and the entropy of mixing F mix are included. For these parts the composition is φ w = φ o = 0.4 and φ s = 0.2. (c) Influence of composition on the temperature-dependent bending free energy; φw = 0.15, φ o = 0.65, and φs = 0.2.

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(c)

F. Latent Heat The experimentally determined values for the heat absorbed during a transition, ∆Qexp, can be compared directly to theoretical estimates ∆Qth. The value for the latent heat of a first-order phase transition can be calculated from the free energy, yielding

(10)

where the last equation was obtained by partial integration and we defined F’(T) ≡ T ∂F(T)/∂T. Note that this expression for ∆Qth contains only the values for the free energy and its first derivative with respect to temperature, evaluated at the borders T - and T + of the coexistence region. Figure 6 gives a survey of the contributions to the latent heat due to the temperature derivatives F’ = –TS(T) of the free energies Fopt, Fs, Flam, and Fmix. The

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FIG. 6 Dependence of the heat –TS = T∂F/∂T = F’ on temperature for φs = 0.2 and φw = φo = 0.4.

composition is again (cf. Figs. 5a and 5b) φs = 0.2 and φw = φo = 0.4. The heat quantities , and show a linear temperature dependence. , and have slopes of a comparable magnitude. However, they are shifted of is of comparable magnitude but has the relative to each other. The slope almost vanishes in the single-phase region and in the 2Φ opposite sign. region. is not shown, since it almost vanishes in the relevant parameter range, too. All heat curves depend explicitly on surfactant concentration. In addition, the slopes of and depend on the water-to-oil ratio. The contribution of the difference F(T+) – F(T-) of the free energies to the latent heat [see Eq. (10)] can in general be neglected, since it is much smaller than the difference F’(T+) – F’(T-) (note the vastly different scales of the y axes of Figs. 5 and 6). Using Eq. (10) and the experimentally determined values of T+ and T-, the values for the latent heat of a phase transition can be read off from Fig. 6 by taking the difference of the respective values belonging to T+ and T-. 1. Lamellar to L2 Transition We now evaluate the values for the latent heat for the transition of a lamellar phase into a microemulsion phase of water droplets. According to Eq. (10), the latent heat is given by

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(11)

where we have already dropped the contribution (T +) + F mix(T +) – F lam(T - ) – F u(T -) to ∆Q th . Moreover, for narrow and large peaks, the value for the latent heat is dominated by the temperature derivative of the bending free energy evaluated at T + ≈ T - ≈ T peak, where T peak corresponds to the temperature of the (T) (see Fig. 6). Inserting Eqs. (4) and maximum of the corresponding peak in (5) into Eq. (11) yields [29,30] (12) Figure 7 shows experimental data (squares) and the corresponding theoretical predictions (solid line) for the values of the latent heat for the lam → L 2 transition for varying surfactant concentrations and a fixed ratio of water and octane, φ o/φ w = 5.67. We find close agreement between the theoretical curve and the experimental results, both in absolute magnitude and in the dependence on the surfactant volume fraction. The errors for the calculated values for the latent heat depend strongly on the width-to-height ratio of the peak [30]. For the samples studied the peaks are comparatively narrow, leading to errors for ∆Qth on the order of 10% when Eq. (12) is applied rather than Eq. (11). G. Step in the Specific Heat when the emulsification According to Fig. 4, there is a step in the specific heat of the step in the specific heat is plotted boundary is passed. In Fig. 8, the height for different sample compositions. The different data points for a single surfactant concentration denote repeated measurements at different heating rates between 8 and 50 K/h. In evaluating the height of the step, it should be kept in mind that the values for may depend on υs. Within experimental accuracy no scan speed dependence is observed for when the measurement is started in the L2 channel and the L2 channel is entered during the cooling and stirring of a mixture that was previously in a region or when it is started in the L1 channel and the L1 channel is entered during the heating and stirring of a mixture that was previously in the region. The , can be calculated from the thermodynamic value for the height of the step, i.e., free energies via Eq. (4):* * In principle, the entropy of mixing [cf. Eq. (8)] will also contribute to the step. It has been checked that in general this contribution is much smaller than the one resulting from the bending free energy [47]. Therefore, we neglect it in the following.

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FIG. 7 The latent heat ∆Q per cubic centimeter of sample volume for the transition lam → L2 is plotted as a function of φs at a fixed ratio φo/φw = 5.67. The squares are obtained from the calorimetric spectra, and the solid line is the prediction of Eq. (12) for the heat changes obtained from the interfacial model [29]. The inset shows the location of the sample compositions in the Gibbs phase triangle.

(13)

The predicted value increases linearly with surfactant concentration. It is in remarkably good agreement with the experimental data shown in Fig. 8. We stress that the good agreement between calculated and calorimetrically determined data is found without fitting parameters. This underlines the dominant role that the bending free energy, Eq. (3), plays in the description of the equilibrium behavior of the mixtures. Entropic contributions determine the width of the coexistence regions between different morphologies [13,20]. However, for a first prediction of the topology of the phase diagram, the positions of phase boundaries, and connected anomalies in the specific heat, they are of minor importance.

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FIG. 8 Dependence of the height of the step in the specific heat on surfactant concentration φs. The squares correspond to φ o/φ w = 5.67, and the crosses to φ o/φw = 0.35 [47]. To a good approximation the height of the step depends linearly on φ s, as predicted by the theory (solid line).

III. PHASE SEPARATION KINETICS To explore the origin of the oscillations in the signal for the specific heat (see e.g., Fig. 4a) we first discuss the parameter dependence of the energy barrier preventing the formation of smaller droplets coexisting with a water-rich phase. This oscillating phase separation involves a complex collective nucleation process, which will be identified as the origin of the stepwise phase separation. A. Energy Barrier The formation and growth of a nucleus, i.e., of a droplet having a radius larger than the optimum radius, is energetically hindered by the unfavorable bending energy of that droplet. On the other hand, because of volume and surface conservation, large droplets must be formed to allow the majority of small droplets to attain their optimum size. The height of the energy barrier the microemulsion droplets have to pass in order to be able to form a single large droplet is the maximum value of the difference ∆F s between the bending free energy F s(N, R)

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of the supersaturated state of N monodisperse droplets of radius R (cf. Fig. 1c) and that of the state Fs(N’, R’) + Fs(1, ρ) (see Fig. 1d), where N’ droplets of radius R’ (R > R’ Ropt) coexist with a single large droplet of radius ρ [49]: (14) As soon as ∆Fs < 0, it is energetically favorable to form N’ droplets of radius R’ and a single big droplet of radius ρ. For a system with initially 1000 monodisperse droplets, Fig. 9 shows the dependence of ∆Fs on the reduced size of the large droplet, (ρ — R1φ)/ρ, at different degrees of overheating, τ ≡ R1φ/Ropt α (T — ). The monodisperse state corresponds to (ρ – R1φ)/ρ = 0, whereas (ρ — R1φ)/ρ → 1 for ρ >> R1φ. Thermodynamically stable monodisperse systems are characterized by values for τ less than 1, while τ > 1 corresponds to the twophase system. For a system with a finite number of particles N, the phase transition can occur only at τ > 1, and it only requires the production of a finite size excess

FIG. 9 Dependence of the energy difference ∆F s separating a system of monodisperse droplets (radius R 1φ) from a phase-separated state of smaller droplets coexisting with a single large droplet of radius ρ. The initial number of droplets is fixed at N = 1000. The different curves correspond to different degrees of overheating, τ. (Dashed line: τ = 1.1; solid line: τ = 1.15; dotted line: τ = 1.22.)

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droplet. For small values of τ (τ = 1.1, dashed line), the energy difference ∆Fs always increases as the reduced size of the large droplet increases. The monodisperse system is still stable, showing that more than 1000 droplets are needed to form a phase-separated state. As the overheating increases, a second minimum shows up. For τ ≈ 1.15, the energy difference can become negative for the first time (solid line). In this case, the mixture has to pass an energy barrier the order of 10 kBT to reach phase separation, and the excess droplet takes on a reduced size larger than (ρ — R 1φ )/ρ ≈ 0.75, i.e., ρ ≈ 4R 1φ . Its volume exceeds that of the microemulsion droplets by more than a factor of 50. For even greater overheating, rapidly decreases, becoming only a few k BT for τ =1.22, where it becomes negative for (ρ — R 1φ)/ρ ≈ 0.55, i.e., for ρ ≈ 2R 1φ (dotted line). The height of the energy barrier depends only slightly on the number of droplets. However, due to the conservation of volume and total interfacial area, a minimal number of droplets are required to build a sufficiently large droplet for ∆Fs to become negative (Fig. 9). Energy barriers of a few kBT require values for R1φ/Ropt ≈ 1.2 in accordance with experimental observations [46]. In this case, a few hundred droplets participate in nucleating a large droplet. Consequently, the nucleation of large water droplets is a strongly collective process. B. Experimental Observation of Oscillations In the last paragraph we observed that the conservation of volume and interfacial area is essential for the occurrence of the energy barrier. In contrast to classical nucleation processes [65,66], it is energetically unfavorable for a single large droplet to be formed and to grow. Large droplets form only in order to decrease the free energy of the whole system. This novel feature can modify the phase separation kinetics significantly. This comes to light when the system is driven into the 2Φ region by constant heating. Constant heating may lead to periodic clouding and clearing of the mixture [46,49,64]. The repeated appearance of clouding is due to strong threshold behavior in the formation of aggregates (i.e., water-rich domains) larger than the wavelength of light, which is reflected in an oscillating variation of the turbidity [46,64]. Two to four periods of clouding can be discerned optically for most compositions and heating rates. More detailed information about the kinetics of this phase separation can be achieved from microcalorimetric measurements [46]. In contrast to optical measurements, which are sensitive to large particles in the system, the DSC signal is affected by all droplets. After all, it measures changes in the average curvature of the interface (see Section II.E and Ref. 29). In particular, it is therefore governed by the vast majority of small droplets. As a consequence, the values for the specific heat contain less noise. They even show an oscillating signal when

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nothing can be discerned any longer in the optical data. Up to 20 oscillations can clearly be dissolved. Due to their favorable signal-to-noise ratio, the microcalorimetric data allow us to quantitatively investigate the oscillations. Figure 10 shows the temperature-dependent variation of the microcalorimetric signal for the specific heat (T) for different heating rates υs. All thermograms show about 15 oscillations. From the scan speed dependence it is clear that the thermograms do not resemble the equilibrium values for the specific heat. Rather, they reflect aspects of the phase separation kinetics. To stress this nonequilibrium nature of the data we denote them as “apparent specific heat.” In agreement with expectations from thermodynamics, the onset of the oscillations shifts to higher values for increasing surfactant concentration. The time lag ∆T between two succeeding maxima (cf. inset of Fig. 10) increases with increasing υs. In Refs. 46 and 50 it is shown that .

FIG. 10 Temperature-dependent variation of the apparent specific heat (T) while entering the 2Φ region by constant heating for φ s = 0.1 and φ w = 0.33 and different heating rates. Top to bottom: υs = 4 K/h, solid line; υs = 14 K/h, dotted line; υ s = 27 K/h, crosses. The respective baselines are chosen in such a way that thermograms do not cross. The inset shows the definition of the height of a peak ∆C v and of the period of oscillation ∆T.

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The time lag ∆T between the peaks of changes nonmonotonously with the number of oscillations, i.e., with the temperature. This dependence is most evident when the signal for the apparent specific heat also shows a pronounced superimposed structure. An explanation of the dependence of ∆T on the number of oscillations will give a hint about a relevant process to understand the kinetics of this phase separation. C. Mechanism of Phase Separation We now further discuss Fig. 1, in order to clarify the origin of cascade nucleation in more detail (also see Refs. 49 and 50). To this end, we observe that for a small degree of supersaturation (Fig. 1c, τ 1.15), nucleation is strongly suppressed for energetic and kinetic reasons, while it becomes fast for larger values of τ, leading locally to a structure such as the one shown in Fig. 1d. Typically, a large droplet is nucleated from a few thousand small ones. Nevertheless, in a very short time, a macroscopic number of nuclei ( 1012) appear in the sample (note that there are 1016–1018 droplets per cubic centimeter). They are homogeneously distributed with typical distances of less than a few hundred nanometers between them, so they induce rapid relaxation of the size distribution of droplets to a state close to equilibrium. At the same time, the nuclei grow in size and merge into water-rich domains, whose mutual distance soon exceeds 10–100 µm. By that time, a typical neighborhood of a water-rich domain contains a few thousand small droplets. It looks very much like those sketched in Fig. 1b. Due to the large distance between the water-rich domains and typical neighborhoods of small droplets, water transport—no matter whether by molecular diffusion of water through the oil or by diffusion and collisions of droplets—from small droplets to the of a single water-rich domains is negligible on the time scales ∆T/υs oscillation. Consequently, the droplets cannot change in size upon heating, leading again to supersaturation (Fig. 1c) and eventually to nucleation (Fig. 1d), but now for droplets with a slightly different radius and density. This possibility for repeated bursts of nucleation is hinted at in Fig. 1 by the arrow pointing back from parts (d) and (e) to part (b). The stepwise decrease in the droplet size is hence due to an alternation between long periods of slow heating and a comparatively rapid relaxation after nucleation arises in the system. As a consequence, cascade nucleation involves at least two, typically quite different, time scales t1 and t2: The time scale t1 ~ (a Ropt υs)-1 characterizes the change in the optimum radius of droplets due to heating. The time scale t2 ~ γ-1 is set by the inverse of the decay rate γ of the number of big droplets in the system due to coalescence. When the Stokes–Einstein law is applied, t2 depends on the distance between large droplets Dbig and on like their diffusion velocity

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For a theoretical discussion of this picture from a more general point of view, we refer to Ref. 50. Here, we remark only that the bottom line of the arguments presented in that paper is that the time ∆T/υs between subsequent bursts of nucleation scales as the geometric mean of the time scales t1 and t2. This leads to (15) Moreover, the distance Dbig between large droplets can be related to the composition of the microemulsion by equating with the volume occupied by N small droplets in the region of the sample containing only a single large droplet, (16) Combining Eqs. (15) and (16) leads to the prediction (17) when one assumes that D diff and N can be considered constant. For the first oscillations after crossing the emulsification boundary the radius of droplets is still very close to its value in the single-phase region, R opt ≈ R1Φ. In this situation, the prediction of Eq. (17) agrees remarkably well with experimental data, as demonstrated in Fig. 11. When ∆T is plotted against on a log-log scale, the data for a variety of compositions and scan speeds converge to a single line with a slope of 0.5, as predicted by Eq. (17). D. Temperature Dependence of the Droplet–Droplet Distance In Fig. 11, the dependence of ∆T on (υ s R 1Φ ) 1/2 is shown only for the respective first oscillations. This is the most accurate test of the theoretical prediction, because there are only small errors in the composition, which is still very close to the one in the 1Φ region. On the other hand, it leaves the question open as to how to explain the evolution of ∆T with the number of oscillations. As shown in Fig. 10, the specific heat may show a pronounced superimposed structure. To shed light on this behavior, one has to keep track of the temperature dependence of the volume fraction and radius of the microemulsion droplets. According to Eq. (2), the radius of the droplets decreases with increasing temperature. Accompanying the decrease of R opt (T), the volume fraction of droplets decreases also. To a good approximation, the small droplets account for all the interface in the sample, and they occupy the volume .

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FIG. 11 Dependence of the period of the first oscillation log(∆T) on log . The symbols show the results of microcalorimetric measurements on nine different compositions and typically three different heating rates per sample. The straight line is a fit through the data points with a slope of 0.5. Sample compositions: ( ) φ d = 0.096, R = 5.8 nm; (+) φd = 0.094, R = 16 nm; (∆) φd = 0.19, R = 5.8 nm; ( ) φd = 0.19, R = 6.8 nm; ( ) φd = 0.19, R = 15 nm; (∆) φ d = 0.38, R = 6.0 nm; ( ) φd = 0.37, R = 8.2 nm; ( ) φ d = 0.38, R = 11 nm; (×) φ d = 0.38, R = 15 nm.

In the 2Φ region depends on the temperature and on surfactant concentration, = φs/[3lsa(T – )] according to Eq. (9). Figure 12 shows the variation in the period of ∆T for different heating rates and two surfactant concentrations. However, now ∆T is plotted as a function of the scaling variable υs . The open triangles correspond to φs = 0.1 and the filled squares to φs = 0.05. The heating rate increases from the left (vs 1 K/h) to the right (v s 31 K/h.) The data points still follow the scaling of ∆T with (υ s ) 1/2. However, in all cases one clearly discerns a superimposed nonmonotonous behavior of ∆T; it first increases and then decreases under increasing υ s . In view of this observation, we conclude that the nonmonotonous dependence of the oscillation amplitude may be caused by a variation of the period of the oscillations due to an adiabatic change of composition. For larger ∆T also the amplitude of the oscillations increases, since the system is driven further into the metastable region and hence more heat is released when nucleation sets in.

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FIG. 12 Log-log representation of the dependence of ∆T on υ s . ( ) φs = 0.1; ( ) φ s = 0.05. The scan speed increases from left to right; ( ) υ s = 1.2, 4, 13, and 27 K/h; ( ) υs = 1.4, 4, 15, and 31 K/h.

To understand this additional temperature dependence of ∆T, the implications of volume and surface conservation for the number of droplets and the average droplet–droplet distance D d-d have to be considered. In contract to the volume fraction of droplets, their number density n increases with increasing temperature, (18) The average droplet–droplet distance in the 2Φ region can be estimated by assuming a locally close-packed arrangement of droplets [67]: (19) where Eqs. (9) and (2) have been used to express in terms of the conserved quantity φs and in terms of the droplet radius Ropt. Dd-d decreases with increasing

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temperature and surfactant concentration. For the collision frequency, however, not the average droplet–droplet distance but the diffusion length D2 between the interfaces of neighboring droplets is relevant. Its square root is given by (20)

i.e., it comprises the difference of two different power laws in T – . As a consequence, D 2 always shows a maximum. The changes in Ropt, n, and Dd-d with increasing temperature are schematically shown in Fig. 13. (The relationship of the droplet sizes is chosen to reflect the situations at the beginning and end of a typical experiment.) In Fig. 13a, a droplet configuration is given as it might exist close to the emulsification boundary. The droplets take their optimum radius denotes the average distance between the respective surfaces of neighboring droplets. In Fig. 13b, at T = T 2, the mixture is deep in the region. The size of the droplets has decreased toward Ropt (T 2), and the average droplet–droplet distance has decreased toward Dd-d (T2). Due to conservation of the total interfacial area and of the volume fraction of all components, the number of droplets has increased but their total surface area is preserved. The excess water, which is no longer dissolved in the smaller droplets, has been expelled into a water-rich phase formed at the bottom of the test tube. In Fig. 14, the temperature dependence of ∆T (left axis, squares) is compared to the temperature dependence of D (T)2 (right axis, solid line). Similar to ∆T, for small values of (T – = T – 305.6 K), the distance D(T) increases with

FIG. 13 Sketch of the radius of the droplets R, the average droplet-droplet distance Dd-

and the average distance between droplet boundaries D for (a) a mixture at a temperature close to the emulsification boundary T = T1, and (b) deep in the -region at T = T2. d

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FIG. 14 The variation of ∆T and diffusion length D2 with temperature for φ s = 0.1 and υs = 4 K/h.

increasing temperature, then it passes a maximum at T = T max, and eventually it decreases with increasing temperature. The nonmonotonous temperature dependence of D(T)2 arises from a crossover: Close to , D2 increases due to the fast decrease of R opt with increasing temperature, until at sufficiently high temperatures the diffusion length D2 is dominated by the decrease in Dd-d, which is caused by an increase in the number of droplets with increasing temperature. Similar to the volume fraction of droplets in the microemulsion phase [cf. Eq. (18)], D 2 depends solely on temperature and on surfactant concentration. On the other hand, the emulsification temperature [solving R1φ = Ropt(T) for T] depends on the overall volume fraction of water φw in the sample. For sufficiently small φw and fixed φs, the emulsification temperature is to the right of the maximum, leading to a monotonously decreasing behavior of ∆T with increasing temperature (as noted in Ref. 46), while for sufficiently high φw, ∆T can go through a maximum as shown in Figs. 12 and 14. To verify that the temperature-dependent change in the average distance droplet has to diffuse before it can collide with another droplet is the dominant process determining the nonmonotoneous behavior of ∆T, the data for ∆T shown in Fig.

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on the number of oscillations N for φ s = 0.1 and FIG. 15 Dependence of ∆T D -2 φw = 0.33. The data points correspond to four different scan speeds. ( ) υ s = 1.2 K/h; (∆)υs = 4 K/h; (*) υ s = 13 K/h; ( ) υs = 27 K/h.

12 were replotted. Since the presented argument does not depend on υs, the observed square root dependence of ∆T on

should remain valid [46].

Figure 15 shows the evolution of ∆TD with the number of oscillations N, i.e., with temperature. The different symbols denote different heating rates, while the composition of the mixture is kept constant (φs = 0.1 and φw = 0.33). Within the margin of error, the data for ∆TD-2 no longer depend on N, in contrast to the pronounced maxima for ∆T shown in Fig. 12. The slight as the heating rate increases may be due to different concentrations decrease in ∆TD-2 of oil and surfactant in the water-rich phase. This additional change in composition (besides the expulsion of water) is more pronounced for high heating rates, because in that case the water-rich phase has less time to relax to a state close to equilibrium. This leads to more significant changes in the composition of the microemulsion on N phase. In any case, however, the very weak dependence of ∆TD-2 strongly suggests that the observed nonmonotonous variation of ∆T with temperature is due to the change in the average distance between droplet boundaries. This dependence of ∆T on the diffusion length supports our earlier assumption that the water transport from small to big droplets is via diffu-2

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sion and mass exchange during collisions of the nanometer-sized microemulsion droplets. IV. CONCLUSION We have surveyed recent experimental and theoretical developments of a thermal characterization of phase transitions and the kinetics of the emulsification failure in water–oil–surfactant mixtures. As a model surfactant, we chose the nonionic surfactant C 12E5 . Microcalorimetric measurements are demonstrated to be an efficient method to determine phase transitions, the width of the accompanying coexistence regions, and the kinetics of the phase separation. This method traces changes in the average curvature of the surfactant monolayer with a very high sensitivity [29]. Its value as a method that is complementary to more traditional approaches such as optical inspection and scattering techniques is highlighted by three findings. 1. Mixtures of water, octane, and C12E5 are commonly considered as typical symmetrical surfactant mixtures, since under optical inspection the phase behavior is almost unchanged when the volume fractions of water and oil are exchanged and the temperature is varied from T to 2 – T. Surprisingly, however, for equal volume fractions of water and oil, the thermograms (cf. Fig. 4) are not at all mirror symmetrical under this change of temperature, suggesting that the symmetry does not necessarily hold on the microscopic level. Furthermore, under these conditions, the peaks are especially broad. Although the mixtures appear to be single-phase close to the microemulsion channels L 1 and L2, the higher level of the baseline close to the water emulsification boundary (cf. Fig. 4a) strongly suggests that almost always, microstructures of different morphologies coexist on a microscopic scale. This should be kept in mind when setting up other experiments and calculating polydispersities. 2. Microcalorimetry yields a direct measure of the latent heat ∆Q of first-order phase transitions in the mixtures. Comparing the experimental data with the predictions of various models allows us to identify relevant contributions to the free energy describing the mixture. Quantitative predictions can most easily be performed for a large ratio of peak height to-width. In that case, the theoretical estimate for the latent heat is dominated by the bending free energy. Up to the factor T, it is to a very good approximation the difference between the slopes of the free energy functionals (in mean-field approximation) for the respective structures at their point of intersection. In addition, the latter gives a good estimate of the phase transition temperature. No fluctuations of the interface need to be considered for this. For a small peak height-to-width ratio, the extent of the two-phase region has to be taken into account in calculating the latent heat (also cf. Ref. 30). We stress that the good agreement between experiments and predictions

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was obtained without fitting any parameters. It requires only a knowledge of the bending rigidities of the surfactant monolayer at the interface between the water and oil microdomains and of its spontaneous curvature. These material constants have been tabulated for many amphiphilic mixtures (e.g., in Ref. 27). Alternatively [29,47], they can be determined by fitting the results of a few independent temperature scans. 3. Crossing the emulsification boundary by means of constant heating leads to an oscillating signal for the specific heat. An alternation between a slow increase in supersaturation due to heating and a fast relaxation at strong supersaturation appears to be the origin of this dynamic instability of the phase separation. The delay of relaxation is caused by an efficient energy barrier, which the droplets have to pass in order to collectively decrease their average radius at the expense of a large droplet taking up the excess water. The height of the energy barrier can be estimated from the bending free energy of the interface. It decreases strongly with increasing degree of overheating. The time lag ∆T between bursts of nucleation depends, like , on the heating rate υs. This dependence not only holds for a vast range of compositions but also remains valid throughout the entire phase separation process. An additional variation of ∆T with the number of oscillations is found to be properly described by the temperature-dependent change in the average distance between the surfaces of neighboring droplets, which strongly influences the transport of water from small to large droplets. This distance varies nonmonotonously with temperature due to the interplay of a temperature-induced decrease in the droplet size and increase in the number of droplets. The success of this modeling shows that the bending free energy may also serve as a starting point to describe the local equilibrium of surfactant mixtures driven far outside equilibrium. In conclusion, we point out that the presented measurements strongly suggest that (1) the temperature dependence of the preferred curvature of the surfactant monolayer, (2) the conservation of the total interfacial area, and (3) the conservation of the partial volumes of water and oil are the dominant parameters needed to understand temperature-dependent phase transitions in the considered mixtures. We expect that these are also the crucial parameters needed to describe the equilibrium properties and kinetics in other amphiphilic mixtures. ACKNOWLEDGMENTS It is a pleasure to thank M. Schmidt for support in performing this work and R. Strey and J. Vollmer for fruitful and pleasant collaborations. Stimulating discussions with B. Dünweg, U. Olsson, M. Kahlweit, and M. E. Cates are gratefully acknowledged. This work has been supported by the Deutsche Forschungsgemeinschaft.

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RE Goldstein, P Nelson, T Powers, U Seifert. J Phys II France 6:767 (1996). J Morris, U Olsson, H Wennerström. Langmuir 13:606 (1997). H Wennerström, J Morris, U Olsson. Langmuir 13:6972 (1997). A Kabalnov, J Weers. Langmuir 12:1931 (1996). D Vollmer, P Ganz. J Chem Phys 103:4697 (1995). D Vollmer, R Strey, J Vollmer. J Chem Phys 107:3619 (1997). D Vollmer, J Vollmer. Physica A 249:307 (1998). SA Safran, LA Turkevich. Phys Rev Lett 50:1930 (1983). J Vollmer, D Vollmer, R Strey. J Chem Phys 107:3627 (1997). J Vollmer, D Vollmer. Faraday Disc 112:51 (1999). D Langevin, J Meunier. In: Micelles, Membranes, Microemulsions, and Monolayers (WM Gelbart, A Ben-Shaul, D Roux, eds.) Springer-Verlag, Berlin, 1994, pp. 485–519. K Bonkhoff, A Hirtz, GH Findenegg. Physica A 172:174 (1991). M Kahlweit, R Strey, G Busse. J Phys Chem 94:3881 (1990). R Strey, O Glatter, K-V Schubert, EW Kaler. J Chem Phys 105:1175 (1996). JH Schulmann, W Stoeckenius, LM Prince. J Phys Chem 53:1677 (1959). M Kahlweit, R Strey. Angew Chem Int Ed 24:654 (1985). M Kahlweit, R Strey, P Firman. J Phys Chem 90:671 (1986). H Bagger-Jörgensen, U Olsson, K Mortensen. Langmuir 13:1413 (1997). PA Winsor. Trans Faraday Soc 44:376 (1948). M Gradzielski, D Langevin, T Sottmann, R Strey. J Chem Phys 106:8232 (1997). W Helfrich. Z Naturforsch C 28:693 (1973). W Helfrich. Z Naturforsch C 33a:305 (1978). SA Safran. Phys Rev A 43:2903 (1991). D Vollmer, J Vollmer, R Strey. Europhys Lett 39:245 (1997). K Binder. Rep Prog Phys 50:783 (1987). JL Gunton, M San Miguel, PS Sahni. In: Phase Transitions and Critical Phenomena, Vol. 8. (C Domb, JL Lebowitz, eds.), Academic Press, New York, pp. 1–175. NW Ashcroft, ND Mermin. Solid State Physics, Holt-Saunders, Philadelphia, 1976.


3 Subzero Temperature Behavior of Water in Microemulsions SHMARYAHU EZRAHI Materials and Chemistry Department, The Ordnance Corps, Israel Defense Forces, Ramat Gan, Israel ABRAHAM ASERIN, MONZER FANUN, and NISSIM GARTI Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

I.

Introduction

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II.

The Behavior of Water Near Surfaces

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III.

State of Water

61

IV.

Methodology

63

V.

Information Obtained via the Exothermic Scanning Mode A. Structural transitions B. Percolation transitions

67 67 69

VI.

Information Obtained via the Endothermic Scanning Mode A. Ethoxylated alcohols B. Ethoxylated siloxanes C. Sucrose esters D. Phosphatidylcholine

76 76 77 77 80

VII. Results and Discussion A. Variation of water peak temperatures with water content B. Full hydration of the surfactant C. Free water D. Nonfreezable water E. Evaluation of the thickness of the bound water layer F. Alcohol interaction with other constituents

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60 G. Exothermic peaks H. The problem of phase separation

98 107

VIII. Conclusion

113

References

114

I. INTRODUCTION The purpose of this review is to examine several methodological aspects concerning the use of subzero temperature differential scanning calorimetry (hereafter designated as SZT-DSC), for the study of surfactant–water interactions and to highlight some recent results related to (mostly) nonionic microemulsions. In contrast to the common view that there need not be any a priori relation between properties of hydration measured at low temperatures and those measured at room temperature [1], we shall try to show that if the water–surfactant interaction is defined in terms of a perturbation to the freezing (or melting) of water at about 0°C, then the thermal behavior of microemulsions at ambient temperature is directly related to that at subzero temperatures. It should be stressed that SZT-DSC allows us only a dim glance into the microstructure of microemulsions and an even dimmer glance into its details. Yet the combination of SZT-DSC data and the results of spectroscopic measurements may deepen our understanding of these problems, as will be shown in this review. The review is organized as follows. First we define several states of water in terms of their thermal behavior. Then we compare the exothermic and endothermic modes of SZT-DSC and discuss how to evaluate the relative amounts of free and bound water in a microemulsion sample. After some information obtained via the exothermic scanning mode is demonstrated, we concentrate on the endothermic scanning mode. We analyze the distribution of free and bound water as a function of (total) water content in microemulsion systems. This is followed by a discussion of nonfreezable water and evaluation of the thickness of the bound water layer. The interaction of alcohol with other components of microemulsion systems and the significance of exothermic peaks are also highlighted. Special emphasis is put on the often ignored problem of phase separation during the cooling and freezing of microemulsion samples. Finally, the role of SZT-DSC in the investigation of microemulsions is summarized. II. THE BEHAVIOR OF WATER NEAR SURFACES It is widely known that liquid water departs considerably from its average bulk behavior due to the presence of adjacent interfaces, be they organic, such as biomembranes and proteins, or inorganic, such as clays and ion exchangers [2,3].

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The investigation of the interaction between water and such interfaces is relevant to the study of such problems as the behavior of water in living organisms [4,5] and sludge dewatering [6]. Moreover, water enclosed in very small volumes plays a dominant role as the medium that controls structure and behavior near biological membranes, for example, and microemulsions may well serve as model systems for the study of water in confined spaces [2,7,8]. III. STATE OF WATER When describing the state of water in relation to any surface, several distinguishably different types of water, ranging from the most tightly bound (nonfreezable) to free, bulk-like water, may be considered. Besides the general distinction between “free” and “bound” water, more detailed classifications have been suggested. Senatra et al. [9], for example, have used a differentiation based on the difference in melting (freezing) points: 1. 2. 3.

“Free” water melts at 0°C. “Interphasal” (or “interfacial” [8]) water melts at about –10°C. “Bound” water melts at temperatures lower than –10°C.

The distinction between “interphasal” and “bound” water is based on empirical observations pertinent to specific surfactant-based systems (including some of our model systems, as is shown later on). The melting temperatures of these types of water vary as a function of composition. Two examples will suffice to show our point. Thus, altering the (total) water content may shift the melting point of interphasal water between –15°C and –5°C in some cases. In other cases the shift is only 2–3 degrees. Also, the transition from quaternary systems (containing water, alcohol, oil, and surfactant) to binary systems (containing water and surfactant) shifts the melting point of interphasal water to higher (less negative) temperatures, as is demonstrated later in relation to our model system A (see Section VI.A). The melting temperature, –10°C, is just an arbitrary (and not always sharp) limit between various grades of water–surfactant interactions. Moreover, it should also be emphasized that the attribute “bound” does not refer to covalent binding but rather to dipole–dipole interactions (in nonionic systems) and dipole–ion interactions (in ionic systems). Thus, the degree of order and mobility and the strength of the binding in water–surfactant interactions are lower than might be inferred from the somewhat misleading term “bound” water [10]. Thermograms depicting these three types of water are shown in Fig. 1 for the system dodecane–potassium oleate–water–hexanol [11]. Schulz [8] classified water in microstructured systems in a more descriptive way:

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FIG. 1 Typical DSC thermograms of K-oleate–hexanol–dodecane–water microemulsion samples. Surfactant/oil = 0.2 g/mL; alcohol/oil = 0.4 ml/mL; water/(water + oil) = 0.222–0.4 g/g. Curve a, W/O microemulsion sample; curve b, D 2O/oil microemulsion sample. Endothermic peaks due to the fusion of D 2O (277 K), “free” water (273 K), dodecane and “interphasal” water (263 K), “bound” water (233 K), and hexanol (220 K) were identified. (From Ref. 11.) 1. 2. 3. 4.

Free water Interstitial water, which remains unfrozen at temperatures well below the normal freezing point Surface water—physically and/or chemically adsorbed water Internal water—chemically bound water

The nature of water–substrate interactions and the extent to which water is bound have been investigated using spectroscopic methods such as nuclear magnetic resonance (NMR) [2,12–14], infrared (IR) spectroscopy [15–21], electron spin resonance (ESR) [12], and calorimetric methods, which may be divided into ambient [21–25] and low-temperature [11,12,26,27] measurements. In aqueous solutions of several globular proteins, the degrees of hydration calculated from calorimetric and NMR measurements of frozen samples agree well [28]. In the case of tropocollagen, for instance, hydration numbers of 2.4 and 2.7 mol water per residue were evaluated by using calorimetric and NMR techniques, respectively [29].


63

Analysis of low-temperature thermal events such as freezing and supercooling is important for understanding the behavior of water in microporous materials, gels, biological tissues, foods, and other microstructured fluids at subzero temperatures [8]. IV. METHODOLOGY Low-temperature behavior of surfactant-based systems may conveniently be investigated by utilizing SZT-DSC. Such measurements are usually performed in either the exothermic (i.e., controlled cooling of samples) or endothermic (i.e., controlled heating of previously frozen samples) scanning mode. A characteristic feature of the exothermic mode is the supercooling (or undercooling) phenomenon. Under equilibrium conditions, water freezes at 0°C and ice is the stable phase at subzero temperatures. Usually, in the absence of ice crystallites, water will remain liquid below 0°C. The degree of this supercooling depends on factors such as the volume of water, its purity, and the cooling rate. Once frozen, this unstable, supercooled liquid state cannot be regained directly by heating; the ice must first be melted at 0°C [30]. Actually, the melting of ice in a polycrystalline sample begins at subzero temperatures. The freezing point depression of water between ice crystals is due to the occurrence of hydration forces in films of water. These forces cause the chemical potential and freezing point of water to decrease with decreasing film thickness. Thus, the onset of ice melting (as determined by the beginning of the deviation of the endotherm from the baseline) occurs at about –50°C [30]. In a similar way, the separation of ice from the aqueous solution is based on the generation of crystal nuclei, which are capable of growing into macroscopic crystals. Nucleation is a stochastic process caused by random density fluctuations owing to Brownian diffusion of molecules and leading to the formation of a transient embryonic crystallite that has a sufficiently long lifetime for further condensation of molecules to occur. The nucleation probability at any subzero temperature is inversely proportional to the volume of the water droplets [31]. The almost inevitable presence of particulate matter leads to ice formation via a heterogeneous nucleation mechanism at a temperature that depends on the catalytic efficiency of the catalyst particle, its radius of curvature, and its degree of wetting by ice and water. For example, in suspensions of dipalmitoylphosphatidylcholine (hereafter designated as DPPC) vesicles, the formation of ice by such a mechanism occurs first in the extraliposomal space at about –20 to –25°C. The remaining supercooled water will diffuse through the phospholipid bilayers to the ice-containing regions or will form ice between the bilayers via a homogeneous nucleation mechanism at about –45 to –50°C. The slower the cooling rate, the smaller the amount of water that will freeze after homogenous nucleation [30].

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In both modes, the calorimeter measures and records the heat flow rate (dH/dt) of the samples as a function of temperature T, while the samples undergo the aforementioned thermal events (in accordance with the respective scanning mode). The instrument also determines the total heat transferred in the observed thermal processes. The enthalpy changes associated with thermal transitions are evaluated by integrating the area of each pertinent peak [10]. DSC peaks obtained in the exothermic mode are sharper than those of the endothermic mode. This was ascribed to the effect that the substrate had on the melting process, while ice nucleation has preserved its autonomy [32]. Moreover, the overlapping of close peaks, which may occur in the endothermic mode, is not usually observed in the exothermic mode [8] (albeit peak overlap is still problematic in aqueous solutions of polyethylene glycols of sufficiently high molecular weights [33]). Cooling curves were utilized by de Vringer et al. [34]. However, the experimental determination of the enthalpy of fusion is difficult, even if the effect of supercooling is allowed for [33]. On the other hand, it has been argued [35] that the exothermic scanning mode may be used to obtain microstructural information about microemulsions. In our opinion, such information should be treated with caution and be fully corroborated by independent techniques. Even then, we must often settle for something less than a detailed microstructural picture of microemulsions. The endothermic scanning mode is more frequently used to circumvent possible complications from supercooling. In the following, we show some of the results obtained in the endothermic mode for several types of (mostly) nonionic microemulsions. We followed the method used by Senatra et al. [2,9,11,36–39] in which the endothermic scanning mode was applied and the peaks representing various states of water were identified and analyzed. The simple but elegant way by which Senatra and coworkers solved the problem of identifying interphasal water in dodecane-containing systems should be noted. Both interphasal water and dodecane melt at about –10°C, thus leading to overlapping of their fusion peaks. However, the existence of interphasal water may be clearly shown by taking the following into consideration [10]: 1. The heat of fusion, measured at –10°C, is higher than that required for the known amount of dodecane in the system. By subtracting the enthalpy change due to the dodecane, the contribution of the interphasal water is readily calculated by the equation [10] (1) where WI is the interphasal water concentration (in weight percent); ∆H I (exp) is the measured enthalpy change for the –10°C peak, which includes contributions of interphasal water and dodecane; ∆HD is the heat of fusion


65

of pure dodecane (191.6 J/g); fD is the dodecane weight fraction; and ∆HI is the heat of fusion of interphasal water. This enthalpy depends on the polymorphic form of ice that is assumed by the interphasal water at its freezing points. Some authors neglect the polymorphism of ice and use the crystallization enthalpy of water without introducing an appreciable error [40]. We followed Senatra et al. [26] and used the corrected enthalpy: ∆HI = 312.28 J/g. In some systems, part of the oil may be trapped between the alkyl chains of the surfactant. For example, in the system water–AOT (dioctyl sulfosuccinate)–isooctane, only about 50% of the oil contributed to the melting peak [41]. In such a case, an appropriate correction should obviously be applied. 2. The endothermic peak at –10°C remained in the absence of dodecane or when hexadecane was substituted for dodecane [10,26,35,37,38,42] (see Fig. 2). 3. Analysis of samples in which D 2O was used instead of water, with all other components and compositions being the same, showed a typical shift of the D 2 O-relevant endothermic peaks toward higher temperatures [2,10,11,35,36,39,41–47] (see Fig. 1). In a similar way, the concentration of free water is calculated, using the equation [8,10] (2) where WF is the free water concentration (in weight percent), ∆HF (exp) is the is the heat of fusion of pure measured enthalpy change for the 0°C peak, and water, measured at the same experimental conditions. The heat of fusion of freezable water is slightly lower than that of pure water (about 334 J/g). We measured = 323.72 J/g [10,45]. A similar value (321 J/g) was extrapolated from data derived for the water–polyoxyethylene 1550 system during the heating stage of the DSC cycle [34]. Antonsen and Hoffmann [33] measured = 307 J/g. For our model system A (a quaternary microemulsion; see below) we obtained [45] = 308 J/g by a similar extrapolation procedure, in good agreement with our ~ 324 J/g for pure water [10,45]. Even lower values of were obtained measured in binary water–polymer systems by extrapolating ∆HI(exp) vs. polymer weight fraction (w1) plots to w1 = 0. Thus, for aqueous solutions of methoxypoly(ethylene glycol) 750 and polyoxyethylene 440, the extrapolated enthalpy of melting for pure water was 280 and 246 J/g, respectively [33]. For a polyoxyethylene 1550–water system investigated in the exothermic mode, the extrapolated was 289 J/g [34]. These rather low values were ascribed to overlapping between peaks of free and interfacial water. The same phenomenon occurs in biopolymers, and it was attributed to the presence of small amounts of solutes in the water [48].

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FIG. 2 Differential scanning calorimetric endotherms of the system K-oleate + hexanol 3:5 (w/w)–hexadecane (samples a, b, c) or dodecane (sample d)–water. In all samples, the surfactant/oil weight ratio is 0.68 and the water concentration C was expressed as the weight ratio of added water to total sample. Ca = 0.071, C b = 0.108, Cc = 0.290, C d = 0.275; dT/dt = 4 K/min. ∆Hx, ∆Hb, (∆Hw)263, ∆Hd, ∆Hw, and ∆Hh are the enthalpies of fusion for hexanol, bound water, interphasal water, dodecane, free water, and hexadecane, respectively. Note that the dodecane peak at 263 K superimposes on the peak of interphasal water shown for sample b. (From Ref. 38.)

Neglecting [34] the heat of mixing may also contribute to the decrease in : The area under the endothermic peak about 0°C represents the heat consumed in the melting of ice not to pure water but rather to water in a mixed phase. This contribution is, however, rather small [49]. For example, in 10% polyoxyethylene– 90% water solutions, the correction is only 5 J/g [34]; for 50 wt% water–50 wt% polyoxyethylene, this correction is about 6 J/g [34]. When the decrease in the melting point of pure water is significant, the following correction should be applied [50]:

Subzero Behavior of Water in Microemulsions ∆HF =

67

+ (CP,W – CP,I) (Tf – 273.16) (3)

where Tf is the fusion temperature and CP,W – CP,I is the difference between the respective specific heats of liquid water and ice, which is usually taken as 2.3 J/(g · K) [34]. The original designation of the enthalpic terms was changed in order to adjust it to that of Eqs. (1) and (2). The correction for supercooling (including melting point depression) leads to = 325 J/g, using the exothermic mode for polyoxyethylene 1550–water systems [34]. Another prediction of the enthalpy of the ice–water transition in bulk is based on its lowering by about 1% per 1°C depression. With the addition of surface effects the apparent enthalpy may be lowered to about 200 J/g. Thus, the enthalpy of “ice” melting inside the aqueous spacing between bilayers of DPPC was evaluated as about 173 J/g [32]. An additional method for the determination of the bound water fraction is to use the equation [51] (4) where φ is the fraction of nonfreezing (bound) water, f is the weight fraction of water present in the sample, ∆H m is the measured enthalpy change, and ∆Hw is the heat of fusion of pure water at 0°C ( in our notation). According to de Vringer et al. [34], the method based on Eq. (4) is very sensitive to small errors in the measured enthalpy changes or in the estimated water fractions for samples with a high water content. V. INFORMATION OBTAINED VIA THE EXOTHERMIC SCANNING MODE In spite of the aforementioned complications, several studies have used the exothermic scanning mode to obtain more insight into the structure of microemulsions and to identify percolation processes in model systems. A. Structural Transitions Senatra et al. [35] studied the system H2O–hexadecane or dodecane–K-oleate– hexanol [with mass ratios K-oleate:hexanol = 0.6 and (K-oleate + hexanol): oil = 0.4]. They argued that the exothermic scanning mode may provide some information about the structural modifications occurring in the system as a function of water content. Typical thermograms recorded in the exothermic mode are shown in Fig. 3. The compositions of all the microemulsions tested lie along the dilution line PP´ (see Fig. 4).

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FIG. 3 DSC-exo recordings of the water in hexadecane microemulsion samples with increasing water content C (expressed as the weight ratio of added water to total sample). Concentrations: C a = 0.069, Cb = 0.087, C c = 0.105, Cd = 0.138, Ce = 0.169, C f = 0.25; dT/dt = 2 K/min. The designation iso.T refers to a 10 min isothermal period that followed the dynamic part of the thermogram. ∆H h, ∆H w , ∆H b , and ∆H x are enthalpy changes relating to hexadecane, water, bound water, and hexanol, respectively. (From Ref. 35.)

The variation of water freezing temperature with (total) water content C is considered to provide structural information (see Fig. 5). The plateaus in Fig. 5 are thought to indicate microstructural transitions as summarized in Table 1. A basic question that might be raised here concerns whether objective criteria for establishing this quite detailed picture can be ascertained. We can seldom reach this level of description with regard to microstructure of surfactant-based systems when we rely on only calorimetric data. The salient features of such


69

FIG. 4 Pseudoternary phase diagram of the water in hexadecane system. All measurements were performed in microemulsion samples whose compositions lie on the experimental path PP′. According to Clausse [52], line Γ 1 defines compositions at which all the available surfactant molecules are engaged in shells of W/O micelles possessing a core of “free” water. Line Γ 2 defines compositions at which the system forms nonspherical micelles or, more likely, micellar clusters resulting from the aggregation of spherical micelles that tend to “flocculate” so as to offer the optimum surface-to-volume ratio. Dots on the PP′ line correspond to the composition of the samples at the intersection points between the PP′ line and the W/O microemulsion monophasic domain (dots 1 and 5) as well as between the PP′ line and the curves designated by Γ 1 and Γ 2. LC designates a liquid crystalline phase region. (From Ref. 35.) structural transitions as those described in Table 1 should obviously be substantiated by more direct evidence. However, since the initial concentration of the surfactant on the dilution line PP′ is relatively high (weight fraction of 0.6 × 0.4 = 0.24), spectroscopic methods would fail to give accurate details. As an alternative (albeit similar) interpretation we would suggest that a plateau in a vs. C plot means that the strength of the water–surfactant interaction is approximately the same within the respective concentration subinterval. The difference between the plateaus just reflects the difference between various grades of such interactions, which may not be directly related to definite microstructures. B. Percolation Transitions It is known [53–63] that percolation processes are revealed at certain volume fractions of droplets or at specific temperatures (designated here as Tp). Senatra

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FIG. 5 Water freezing temperature versus increasing water concentration C for the water in hexadecane system. Values taken from DSC recordings performed at 2 K/min. The first experimental point reported corresponds to the very first exotherm observed at C b = 0.087. (From Ref. 35.)

et al. [41] showed that the thermal behavior of “percolative microemulsions” could be readily characterized. The first-order exotherms associated with the freezing of the dispersed phase did not show a sharp, well-shaped peak but rather a distribution of thermal events that were not always well separated (Figs. 6–8). They interpreted these typical thermograms by assuming that the nonuniform water clusters (or pools) formed at temperatures close to T p freeze at different temperatures when the system undergoes the exothermic scanning procedure. The smaller the water cluster, the lower its freezing temperature. T p was identified using three methods [41]: 1. Electrical conductivity measurements as a function of temperature. It is known that at a certain temperature (or volume fraction of droplets) the electrical conductivity increases sharply by several orders of magnitude [56–58]. 2. Heat capacity measurements as a function of temperature [59]. 3. DSC recording (dH/dt vs. dT). Tp is revealed as a peak in the plot.

Thermal Characteristics of W/O Microemulsions in the System Water–Hexadecane–K-Oleate–Hexanol DSC-ENDO study

a

∆C

Free water

0.03–0.105 0.105–0.122

— —

0.122–0.198 0.198–0.273 0.273–0.355

≠0 ≠0 ≠0

Interphasal waterb

(∆Hw)263

DSC-EXO studyd Hexadecanec

Enthalpy contribution — Small ∆Hw contribution 1st plateau 2nd plateau 3rd plateau

(∆Hw)fz

1st ∆Hw exotherm ∆Hw ≠ 0 ∆Hw ≠ 0 ∆Hw ≠ 0

Type of structure — 234

From hydrated soap aggregates to the onset of W/O microemulsions

242 249 252

From monodisperse W/O droplets to the appearance of larger droplets: prolate elipsoids (onset of bicontinuous structure?)


TABLE 1

(Total) water concentration ( )intervals within which typical thermal events occur. (∆Hw)263 = enthalpy change of interphasal water. (This type of water melts at 263 K). c = enthalpy change of pure hexadecane. d (∆Hw)fz = enthalpy change of water at freezing. Source: Ref. 35. a

b

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FIG. 6 Top: DSC-exo thermogram of the system D 2 O–sodium dioctylsulfosuccinate, hereafter designated as Na(AOT)–decane [volume fraction (water + surfactant)/total = 0.35; molar ratio of water to surfactant = 40.7]. The 4 K difference in the D 2 O melting temperature with respect to that of H 2 O helps to distinguish between the freezing contributions of water and decane (which, due to supercooling, freeze at about the same temperature) and shows the spreading of the exothermic peaks due to the freezing of the dispersed phase. Bottom: The corresponding endo spectrum compared with DSC recording of the system water–Na(AOT)–decane [volume fraction (water + surfactant)/total = 0.35; water/surfactant molar ratio = 40.8]. The 10 min isothermal period that followed or preceded the dynamic part of the thermogram is also shown. (From Ref. 41.) The use of SZT-DSC in relation to percolation transitions (which obviously occur at ambient temperatures) requires close scrutiny. The detection of T p is very sensitive to experimental conditions such as the type of surfactant, heating rate, and thermal history [41]. Thus, Senatra et al. could not detect the percolation transition a second time immediately after it had occurred (Fig. 9), implying that


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FIG. 7 DSC-exo (top) and endo (bottom) of two samples of the system water– Na(AOT)–isooctane [volume fraction (water + surfactant)/total = 0.31; water/ surfactant molar ratio = 37]. The isooctane freezes at 145 K and thus does not influence the thermal behavior of the water phase. Curve 1, T 0 (the temperature at which the samples were kept isothermally at the very beginning of the DSC analysis) = 313 K; curve 2, T 0 = 300 K. The small exotherm in the melting curve is due to recrystallization. (From Ref. 41.) liquid samples first frozen and then thawed maintain the memory of their thermal history. Relying on these data to answer the question of how the microemulsion structure is altered due to freezing is not a simple matter. “Percolation” is a term frequently used to describe microemulsions as having a bicontinuous structure. However, “bicontinuity” describes a situation with dynamic equilibrium structure that results from a particular spontaneous curvature of the surfactant films, with a minor contribution of the volume fraction of the specific solvent. Thus, at the same composition, different systems may have either water droplets, oil droplets, or a bicontinuous structure. “Percolation”, on the other hand, describes

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FIG. 8 DSC-exo thermograms of the system water–Ca(AOT)2 –decane. Microemulsions of this system do not percolate. Curve 1, T 0 = 308 K; curve 2, T 0 = 298 K; curve 3, T0 = 283 K. (From Ref. 41.)

a process conceived as a temporary opening of extended pathways between droplets [64]. The difference between these two concepts was highlighted by using DSC measurements. Vollmer et al. [59] demonstrated that T p does not coincide with the temperature of formation of a single-phase bicontinuous structure, T b . In fact, T p may be several degrees below T b . All this may prima facie be considered not to be connected with SZT-DSC. Yet the very fact that a percolative transition was observed after the microemulsion sample had been frozen (and thawed) in the first thermal cycle and the characteristic thermograms (Figs. 6 and 7) clearly show that the freezing process did not cause the microemulsion to separate into just oil and water bulk phases. This conclusion is further supported by the observation that microemulsion samples that had been quenched in liquid


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FIG. 9 (a) DSC recordings of the percolative transition in water–Na(AOT)–decane microemulsions. (1) T 0 (temperature of the isothermal stage at the very beginning of the DSC analysis) = 303 K, sample mass 18.250 mg; (2) T0 = 278 K, mass 13.413 mg; (3) T 0 = 302 K, mass 10.259 mg. (b) Top: Onset analysis of the transition of curve 3 of part (a). Bottom: Curve 1, an oscillating trend obtained by measuring a second time the higher order phase transition with or without again following the temperature scanning procedure used for the detection of Tp. Curve 2, an example of failure recorded on a sample of water–Na (AOT)–decane microemulsion [volume fraction of (water + surfactant)/total = 0.35; water/surfactant molar ratio = 40.8]. If a scan speed of 4 K/ min is applied during the scanning procedure used for the determination of T p, the percolative transition escapes detection. (From Ref. 41.)

nitrogen did not phase separate. After several cycles of freezing and thawing, once melted, the samples that were marble white in their frozen state appeared newly isotropic and transparent. Only microemulsions with compositions close to the transition line between the one-phase and two-phase domains were unstable and phase separated [35]. The inability to detect Tp in the consecutive thermal cycles may be connected with the presumed mechanism underlying the percolation transition. For example, Vollmer et al. [59] suggested that at room temperature surfactant molecules in the contact area of two droplets may be excited to flip. This entropy-driven mechanism might fail if the heating rate in the thermal cycles were too fast for the water and surfactant molecules to reorganize themselves. More work is certainly needed to clarify this point. An additional underlying cause for this behavior may be the distillation of some free water from the aqueous system onto the lid of the sample pan and its subsequent freezing in the cooling stage of the DSC cycle. This amount of evaporated water (or part of it)

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might not participate in the dynamic processes that lead to percolation if the preceding isothermal step, 20 K below T p [41] is too short (only 10 min) [41]. Condensation and subsequent freezing of water on the DSC pan lid were also suggested as an explanation for the appearance of an ice-melting peak at about 0°C during the warming of frozen solutions of polyvinylpyrrolidone and hydroxyethyl starch [65] and in DPPC–water dispersions [30]. In our opinion, this evaporating water is free in the sense that it has virtually no interaction with the surfactant (or polymer) molecules. Such water molecules would melt at about 0°C even if they are not involved in the evaporation and condensation processes. Therefore, the relative distributions of free and bound water do not change. Our argument may prima facie seem to be hardly tenable, since it was found that the endothermic peak at about 0°C did not appear when the samples were covered by oil [30,66]. Yet a three-component [surfactant (or polymer)–water–oil] system does not necessarily have the same structure as the binary [surfactant (or polymer)–water] one. The addition of oil may restrict the mobility of both evaporating and nonevaporating “free” water molecules. The melting peak of “less free” water (for example, in a core of a W/O microemulsion before the inversion to an O/W microemulsion) shifts to lower (more negative) temperatures [10,45]. In such a case, it may merge into the broad endothermic peak of “bound” water. The general problem of phase separation, due to freeze–thaw cycles, is further discussed in the following section VII.H. VI. INFORMATION OBTAINED VIA THE ENDOTHERMIC SCANNING MODE The endothermic scanning mode is more frequently used than the exothermic mode in SZT-DSC measurements. We exemplify the information that can be obtained from such a technique by reviewing some recent results related to several model systems based on various types of nonionic (and zwitterionic) surfactants that we studied with SZT-DSC. A. Ethoxylated Alcohols System A. Water–pentanol + dodecane 1:1 (by weight)–octaethylene glycol mono n-dodecyl ether) [hereafter designated as C 12(EO) 8]. This system was investigated along the water dilution line for which the surfactant/alcohol/oil weight ratio is 2:1:1. Henceforth, this dilution line is marked as W5 (see Fig. 10). System B. Water–butanol + dodecane 1:1 (by weight)–polyoxyethlene [10] oleyl alcohol [hereafter designated as C 18:1(EO) 10 or Brij 97]. This system was investigated along the water dilution line for which the surfactant/alcohol/


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FIG. 10 Phase diagram for the system dodecane + pentanol 1:1 (by weight)–C12(EO) 8– water at 27°C. The dashed line represents the water dilution line W5 along which the dodecane/pentanol/C 12(EO) 8 weight ratio is 1:1:2. LC designates the liquid crystalline phase region. (From Ref. 67.)

oil weight ratio is 4:3:3. Henceforth, this dilution line will be marked as XB4 (see Fig. 11). B. Ethoxylated Siloxanes Another group of model systems was based on polymethylhydrogen siloxanes (PHMS) grafted with polyoxyethylene (POE). As a representative of this group we used the surfactant known by its commercial name Silwet L-7607 (molecular weight 1000; EO content 75 wt%). System C. Water–Silwet L-7607–dodecanol. This system was investigated along two water dilution lines for which the oil (dodecanol)/surfactant weight ratios are 1:1 and 7:3, respectively [46] (see Fig. 12). C. Sucrose Esters Sucrose esters have two attractive properties: biocompatibility and temperature insensitivity [68–77]. We are investigating microemulsions based on sucrose esters in order to use them as microreactors for enzymatic and chemical reactions [42,78,79]. SZT-DSC has been applied to model microemulsion systems based on sucrose monostearate (HLB 15, also designated as S-1570). System D. Water–butanol + dodecane 1:1 (by weight)–S-1570. The thermal behavior of this system was studied along two dilution lines for which the surfactant/alcohol/oil weight ratios were 0.94:1:1 and 1.5:1:1, respectively.

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FIG. 11 Phase diagram for the system dodecane + butanol 1:1 (w/w)–Brij 97–water at 27°C. Along the XB4 water dilution line, the Brij 97/butanol/dodecane weight ratio is 4:3:3. LC designates the liquid crystalline phase region. (From Ref. 67.)

The respective initial concentrations of S-1570 on these dilution lines are about 32 wt% and 43 wt% (see Fig. 13). System E. Water–butanol + hexadecane 1:1 (by weight)–S-1570. This system was studied along the water dilution line 43 for which the surfactant/alcohol/oil weight ratio is again 0.94:1:1 (see Fig. 14).

FIG. 12 Phase diagram for the system dodecanol–water–Silwet L-7607. Along the water dilution lines 1 and 2 the dodecanol/Silwet L-7607 weight ratios are 1:1 and 3:7, respectively. (From Refs. 46 and 47.)


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FIG. 13 Phase diagram for the system dodecane–butanol–S-1570–water. No attempt was made to further identify the liquid crystals (not shown) or any other phase within the two-phase area. The dashed lines represent the water dilution lines along which the dodecane/butanol/S-1570 weight ratios are kept constant at 1:1:0.94 (dilution line 32) and 1:1:1.5 (dilution line 43), respectively. (From Ref. 42.)

FIG. 14 Partial phase diagram for the system hexadecane–butanol–S-1570–water. The dashed line represents the water dilution line 43 along which the hexadecane/ butanol/S-1570 weight ratio is 1:1:0.94. (From Ref. 42.)

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D. Phosphatidylcholine The zwitterionic surfactant phosphatidylcholine (PC) was used for the study of enzymatic hydrolysis reactions in microemulsions [80–82]. The oil used in all the investigated systems was tricaprylin (TC). System F. Tricaprylin + butanol (60 wt% in varying weight ratios)–PC (25 wt%)–water (15 wt%). System G. Tricaprylin + alcohol (60 wt%, molar ratio of 1:5, respectively)–PC (25 wt%)–water (15 wt%). VII. RESULTS AND DISCUSSION In this section we describe some parameters relevant to water behavior at subambient temperatures that were evaluated by using SZT-DSC. A. Variation of Water Peak Temperatures with Water Content The variation of the temperatures of the midpoints of the peaks related to water (bound, interphasal, and free) as a function of water content followed the same pattern: a gradual increase of the temperature to a less negative value and then a more or less constant temperature. Such behavior was observed for systems A [10], B [45], D [42], and E [42]; for the binary system water–C12(EO)8 [45]; and for aqueous solutions of polymers (here as a function of the sorbed water content) such as poly(4-hydroxystyrene) [40] and mucopolysaccharides [83]. For example, system A has an endothermic peak at about –10°C, which is ascribed to the melting of interphasal water (and dodecane). In fact, it begins at about –12°C, increases in height with increasing water content, and levels off at about –10°C, when (total) water content approaches 30 wt%. For the binary system water + C 12(EO) 8, interphasal water melts between –3 and –4°C [45,84]. The case of system E is rather unusual. Increasing its (total) water content from 8 to 16 wt% gradually leads to the merging (or more precisely, superposition) of the melting peaks of the interfacial and free water at –3 ± 1°C (see Figs. 15a and 15b). A similar superposition of water melting peaks was observed for the xanthan– water system [85]. In contrast to system E, in the corresponding system D (where the hexadecane was replaced by dodecane) these melting peaks remain separate even at much higher concentrations [42] (see Figs. 15c and 15d). Two other related differences between systems D and E should be mentioned:


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FIG. 15a Thermograms for system E microemulsion samples with varying amounts of water along dilution line 43. Heating rate 5°C/min. (From Ref. 42.) 1. The maximum water solubilization is 80 wt% in system E and only 40 wt% in system D. 2. The first observation of free water is at 14 wt% of (total) water in system D and at 16 wt% (i.e., the concentration at which the water melting peaks merge) in system E [42]. A similar difference in the appearance of free water was shown for the system AOT–isooctane or dodecane–water [27]. Thus, in the case of dodecane, all the water except for the last 6.5 water molecules freezes when the AOT reversed micelles are cooled down to –50°C. The same applies to the isooctane microemulsion, where all the water except for the last 4.5 water molecules freezes when the AOT reversed micelles are cooled down to –50°C. It was suggested that this effect is due to diminished penetration of the longer dodecane within the hydrophobic chains of AOT molecules [27]. On a molecular level, this phenomenon may be interpreted in terms of the Hou and Shah mechanism [86–88].

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FIG. 15b Melting temperatures of the interfacial water as a function of water content for system E along dilution line 43. (From Ref. 42.)

The reduced penetration of the oil into the alkyl chains of the surfactant (and the consurfactant) in the palisade layers of ternary (or quaternary) microemulsions tends to cause the interface to become less curved, thereby favoring the growth of the natural (or spontaneous) radius of curvature, Ro, and the formation of larger W/ O microemulsion droplets [89] as well as increasing the accessibility of the binding sites on the surfactant molecules. The merging of the water melting peaks in system E is yet to be investigated, but it may be associated with the presence of more butanol molecules at the interface relative to system D [42]. The amount of alcohol present at the interface of microemulsion systems increases with the chain length of the oil. Thus, we evaluated [45] the molar ratio of alcohol to surfactant, NA/NS, for the system water–C12(EO)8 + hexanol (1:1)–oil, using an equation derived by Kunieda et al. [90] for the determination of the surfactant/alcohol weight ratio at the interface (for systems present on the border between Winsor III and Winsor IV). For heptane, NA/NS = 1.8; for decane, N A/NS = 2.4; and for hexadecane, NA/NS = 3.3. The role of alcohol in surfactant-based systems is discussed later in this review. Here it is sufficient to say that alcohol molecules present at the interface of such a system may weaken the association between the surfactant and the outer interfacial water layers, although for the complete detachment of these


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FIG. 15c Thermograms for system D microemulsion samples with varying amounts of water along dilution line 43. Heating rate 5°C/min. (From Ref. 42.)

layers—thus transforming them to free water—a critical alcohol concentration is needed [45]. Another possible explanation that may help in understanding this phenomenon of merging melting peaks is that significant microstructural changes must have occurred in view of the intensive water solubilization in system E. B. Full Hydration of the Surfactant In system A the surfactant becomes saturated with water at NW/EO = 3, where NW/EO is the number of (interphasal) water molecules per ethylene oxide (EO) group of the surfactant. For this water/surfactant molar ratio, (total) water content is again about 30 wt%. A similar value was determined for the system water/dodecanol + polydimethylsiloxane 1:4 (by weight) [46,47]. The hydration of EO groups in surfac-

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FIG. 15d Melting temperatures of the free water as a function of water content for system D along dilution line 43. (From Ref. 42.)

tants and polymers has been amply investigated. Yet when values of NW/EO obtained in different systems by different techniques are compared, two points should be considered: 1. NW/EO depends significantly on the method of measurement [91]. 2. The value of NW/EO may be altered owing to factors such as temperature or qualitative and quantitative composition of the system. Thus, for C12(EO)8, NW/EO values lower than 5 but closer to 2–3 were measured by O relaxation NMR [92], values between 2.6 and 3.3 by sedimentation [93], about 6 by micellar self-diffusion, between 3 and 4 by self-diffusion of water [91], and between 8 and 9 by self-diffusion of water, according to a cell model [94]. SZTDSC was used for the determination of NW/EO in binary systems. For 70–90 wt% water–30–10 wt% C12(EO)8, NW/EO = 4.3–3.7 [84]. For water–C16(EO) 20 and water– C12(EO)23, NW/EO = 3.07 [16,44]. Much more attention has been paid to aqueous solutions of polyoxyethylene. For example, values of NW/EO = 2.3–3.8 (depending on molecular weight) were measured by SZT-DSC [33]; NW/EO = 2.8 [51]; NW/EO = 3 in crossed gels (even at 100°C) [95]; and N W/EO = 2–3 (depending on molecular weight) [96]. Similar values have generally been obtained also by other techniques: NW/EO = 3 by ESR 17


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and NMR; between 2 and 6 by the relaxation rate of 17O and 2H; between 5 and 6 by dielectric measurements; NW/EO = 2 by NMR and IR; and NW/EO = 2.9 by molecular simulation [97–100]. To summarize, for polyoxyethylene, NW/EO values ranging between 0.9 and 6 have been determined by using various techniques [97]. The close agreement between system A and the binary systems water–C16(EO)20 and water–C12(EO)23 may, prima facie, lead to the conclusion that the water–surfactant interaction is independent of the length of the hydrophilic headgroup of the ethoxylated surfactant and that the presence of pentanol (and dodecane) does not affect the interaction between water and the EO groups of nonionic surfactants. The picture, however, is not so simple, because long headgroups form coils in which water molecules may become trapped. These molecules do not interact directly with polar atoms of the headgroup, but nonetheless they form part of kinetic unit in the water–surfactant system, thereby increasing NW/EO [44]. Even for the relatively short surfactant C12(EO)8 we find that NW/EO for the binary system water–C12(EO)8 is nearly twice that for the quaternary system (model system A). This observation was interpreted as being the result of the hexagonal liquid crystalline structure of the binary system: A considerable part of the interphasal water is trapped within the voids of the mesophase cylinders without being bound to a specific site on the surfactant headgroup. It should be emphasized that all interfacial (including the trapped) water manifests itself as a distinct endothermic peak at about –3°C. Therefore, from the viewpoint of the intensity of the water–surfactant interaction, these two types of water states (trapped and directly bound to surfactant headgroups) should be treated as though there were no sharp distinction between them in the binary water–C12(EO)8 system. The amount of water thus assigned to each EO group is on average larger than in the case of the quaternary system, leading to NW/EO ~ 5.7 [45]. Similar considerations apply to other water binding sites. For example, protein hydration is based on various types of sites: ionic, polar (—OH, —NH, >CO), and apolar (hydrophobic hydration). The perturbation of water by the protein decays as a function of distance, and the decay function depends on the particular hydration site on the polypeptide chain [28]. Franks [28] even thinks that the expression of hydration numbers as the water/organic residue molar (or weight) ratio is “likely to be meaningless,” because some water is trapped randomly within the freeze-concentrated amorphous solid rather than being associated with specific polar sites. In our opinion, the crucial question is whether this trapped water manifests itself as a distinct melting peak during the heating stage of the DSC cycle (see below). The case of zwitterionic surfactants (such as in binary water–PC systems) is instructive. The “hydration shells” around the PC headgroups are reported to include between 1 [101,102] and 25 [103] moles of water per mole of lipid, utilizing various methods such as the isolation of mono- [102] and dihydrate of DPPC [104,105]; adsorption isotherms [106–109] and water distribution data

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for two-phase systems [110]; a radiotracer technique using gel filtration [111]; hydrodynamic methods using viscosity [112,113] and ultracentrifugation [114] measurements; X-ray diffraction [102,115–118]; calorimetry [30,32,119–121] with different cooling protocols giving different results; and NMR spectroscopy [101,109,122–132]. This wide range of results extends from tightly bound [“inner shell” or “nonfreezable” water (see below)] to weakly bound water intercalated between phospholipid bilayers. The motional characteristics of this “trapped” water approach those of free water. There is also a rapid exchange (>104 S-1) between trapped and bound water molecules [133]. The different results may reflect different phospholipids (synthetic and natural phosphatidylcholines) or different binding sites (phosphate [101,127,132,133] or trimethylammonium [132,133]; for example, using 2H NMR relaxation and intensity measurements, it was argued that five to six water molecules reside near the (CH3)3N group and only one or two water molecules are associated with the PO4 group [132]; and different structures (which may have different cross sections for the headgroups and alkyl chains of the lipids and different degrees of tilt [117] such as anhydrous crystals, small spherical micelles in organic solvents, lamellar liquid crystals, and vesicles [133]. For instance, Nagle and Wiener [118] inferred from various diffraction data that 8.6, 13.6, and 23 water molecules are bound per DPPC molecule in the C (crystal, Lc), G (gel, Lβ’), and F (fluid, L α) phases, respectively. Another problem is the experimentally difficult detection of the onset of phase separation between water and phospholipid units [119]. Yet remarkable agreement was achieved between the various hydration numbers. Based on the different rotational correlation times, it was found that the innermost hydration shell of PC consists of one tightly bound molecule. The main hydration shell consists of 11–12 water molecules per lipid [133]. This is the minimal number of water molecules needed to construct a hydrogen-bonded hydration shell around the phosphorylcholine headgroup according to space-filling molecular models [123]. This hydration number was derived from the results of X-ray diffraction [115], proton NMR [123,124], and 2H NMR [122,125,130] data and measurements of the diffusion coefficients of 3H-labeled water [132]. From DSC measurements [102,120,122] a range of 11–15 mol water per mole of lipid is obtained. Hydrodynamic techniques give about 25 mol water/mol lipid as the total hydration, but this hydration number reduces to 12–16 when allowance is made for the water in the core of the lipid aggregate. The water in excess of 24 mol water/mol lipid is free, being outside the phospholipid bilayers and exchanging only slowly (> RCS (3–4 s), (12)

(13) CS depends on the composition of the emulsion and on the specific heat of all the different phases constituting the system. Equation (13) represents the baseline, a line parallel to the zero signal of the calorimeter. CS is considered to be almost constant when no thermal phenomenon occurs. If CS varies during the melting or solidification transition, the baselines before and after the transformation are shifted apart. This baseline drift induces a difficulty in the interpretation and is analyzed later in the chapter. In the general equation, Eq. (9), dh/dt is the sum of three terms. The first term, –dq/dt, represents the power recorded by the calorimeter. The second is the difference between the baseline and the zero level of the signal due to the difference between the specific heats of the sample and the reference. The third term is the slope of the recorded curve multiplied by the time constant RCS. Temperatures are not obtained directly by DSC. The problem is to determine the sample emulsion temperature T S knowing the temperature T P of the oven. The combination of the energy conservation equations (10) and (11) with the expression of heat flow, Eq. (8), gives the equation (14)

dq/dt represents the signal deviation from the baseline during the transition. RC S(dT P/dt) is a term of inertia for the sample cell, which is almost constant during the cooling or heating.

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R(dQ/dt) depends on the thermal phenomenon amplitude and remains equal to zero when dh/dt = 0 and t > 3–4 s. It is therefore possible to calibrate the calorimeter to determine temperature T S by studying pure compounds with well-known melting temperatures. Knowing those physical considerations, we can now analyze the thermograms obtained for a pure compound during the melting and solidification processes. Those results can then be extended to emulsion systems. For a pure compound the shape of the melting signal can theoretically be determined from the expression dh/dt by considering two points: 1. When the sample reaches the melting temperature T m, the temperature of the sample, T S, remains equal to Tm throughout the melting process. Therefore, dTS/ dt = 0 and (15) 2. After the melting, dh/dt = 0, and (16) The observed peak (Fig. 5) is composed of an initial linear part where the slope is

FIG. 5 Shape of thermogram of a pure compound melting.

Effects of Cooling–Heating Cycles

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given by (1/R)(dTp/dt) followed by an exponential return to the baseline through Ae t/RC + B. The melting temperature is determined by the intersection of the baseline s with the tangent to the (1/R)(dTp/dt) slope. The signal recorded can be analyzed if one knows the relationship existing between dh/dt and dq/dt [Eq. (9)]. The area A of the signal is defined by the integral

(17) where t1 is the time at which the transition begins and t2 the time it ends. From Eq. (9) Eq. (17) can be expressed as

(18)

(19)

(20) If melting or solidification transitions are supposed to occur with no specific heat variation, the term I is equal to zero because

Thus, the area of signal delimited by the extension of the baseline gives the energy released or absorbed during the transition. When there is a significant difference between the solid and liquid values for CS [for example, with water, = 2.09 J/(g · K) and = 4.18 J/(g · K)], the signal has to be delimited as shown in Fig. 5. It has not been yet mentioned that the dispersed solid droplets melt at the same temperature. The determinations of thermal signal shape and area are similar to those for bulk systems if the continuous medium does not show high thermal resistance. To reach those conditions, the heating rate has to be less than 2 K/min and the mass sample sufficiently small. To study emulsions quantitatively, it is necessary to know precisely the total mass of dispersed liquid, m L . The

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integration of the melting peak allows us to determine the amount of liquid if its latent heat of fusion L m is known and is expressed as Eq. (21). This method is often used to estimate the amount of dispersed water contained in W/O emulsions [18]. (21) Let us now study solidification. Generally, crystallization of a pure compound is an instantaneous phenomenon that occurs at a temperature lower than Tm depending on the volume according to relation (4). The thermogram shape has been calculated [14] by writing the equation (22) where ∆H c represents the total quantity of heat released during transition and δ(t – tc) is the Dirac function. At t ≤ tc, (23) At t ≥ tc, (24) The crystallization occurs at t = tc or Tc, and the signal is composed of a line perpendicular to the baseline followed by an exponential return to the baseline (Fig. 6). The energy released is directly determined from the area delimited by a straight line between the baselines before and after the transition. The transition temperature is given by the intersection of the vertical segment and the baseline. In the case of a rather big sample and a rather high cooling rate (&Tdot; > 5 K/min) crystallization is not instantaneous. The important release of heat during the transformation induces the solidification of some parts of the sample at higher temperature. Thus, the enthalpies of solidification measured are overestimated. Bulk water represents the most unfavorable case: Its latent heat of crystallization varies strongly with temperature. In the case of monodispersed systems, dh/dt can be stated, supposing that the heat of solidification varies only a little with temperature during the transformation [19], as (25)


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FIG. 6 Shape of thermogram of a pure compound solidifying.

with L C = ∆HC/mL · ρ is the mass per unit volume of the droplets, r the radius of a droplet, and dN/dt the number of droplets crystallizing per unit time. Thus, knowing dh/dt, we can deduce dN/dt or dN/dT. The relationship between dh/dt and the recorded value dq/dt is not straightforward, and therefore it is not so easy to get dh/dt from the thermogram. Nevertheless, according to the analysis done in Section II, it can be expected that the shape of the thermogram will show a peak. The apex of the peak is very close to the point of maximum freezing events. It has been checked that the slower the cooling rate, the closer the apex temperature is to the maximum deduced from Eq. (7). This temperature has been referred to as the most probable temperature of freezing of the dispersed droplets. A safe way to determine the freezing rate of the droplets versus time or temperature is to proceed as follows. First the sample is cooled until time tt or temperature T i and then immediately heated to the melting point. The melting area Ai is proportional to the quantity of liquid crystallized. From Eq. (14), the sample temperature is known at time ti. Thus, the plot of curve Ai/A as function of the temperature provides at any time or temperature the proportion of liquid solidified at . A is the total dispersed liquid melting. (26) From integral curve (26), it is possible to plot the differential curve and obtain dN/dt as a function of or ti. Therefore, the signal for the crystallization is

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represented by a Gaussian distribution, and the probable melting temperature is given by the apex of the peak, which means that 50% of the sample is crystallized [20,21]. This method is applicable owing to the low thermal inertia of the calorimeter and the stability of the emulsion. Nevertheless, when the cooling programmed temperature is reached at time ti the sample continues to crystallize. To avoid this and then melted more perturbation, the sample is rapidly heated to temperature slowly. Techniques such as microscopy or the use of a Coulter counter are common techniques to study O/W emulsion stability, but they are applicable only to dilute systems. DSC represents a suitable technique to characterize a W/O emulsion without disturbing the system. Characterization of a water-in-crude oil emulsion has been studied in the laboratory. The degree of undercooling and the probable temperature obtained from a cooling thermogram allows the determination of the distribution size of dispersed droplets. By knowing the latent heat of solidification, it is also possible to determine the number of droplets crystallized at temperature T*.

IV. EXPERIMENTAL RESULTS The thermodynamic and physical concepts explained above can help in solving phase transition problems as well as mass transfer or composition ripening in different kinds of emulsions. Figures 7–14 are illustrations of the results obtained with different kinds of emulsions submitted to regular cooling and heating in a Perkin-Elmer DSC 2. Figure 7 presents thermograms of the solidification of water and the melting of ice in a simple W/O emulsion (emulsion 1) made of vaselin oil and lanolin (lipophilic emulsifier) as the continuous phase and deionized water as the dispersed phase. Figure 8 shows the cooling and the heating thermograms of another W/O emulsion (emulsion 2) constituted of Exxol D80 and Berol 26 (nonionic surfactant) as the oilcontinuous phase and a dispersed aqueous solution of 5% (w/w) sodium chloride. For both cooling thermograms, the signals observed are related to the crystallization of the dispersed droplets at temperature T* that is given by the apex of the Gaussian peak as discussed in Section II. At this apex temperature, 50% of the droplets have been crystallized by breakdown of undercooling. In Figs. 7 and 8 the baselines before and after the crystallization are shifted apart due to the difference between the specific heats of the supercooled liquid and the crystallized droplets. Generally in W/O emulsions the size distribution of pure water droplets varies between 1 and 5 µm, and they crystallize at about –40°C as


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FIG. 7 Solidification and melting of dispersed water in a simple W/O emulsion of vaselin oil and lanolin as the continuous phase.

FIG. 8 Solidification and melting of dispersed saline aqueous solution in a simple W/O emulsion made of Exxol D80 and Berol as the continuous oil phase.

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shown in Fig. 7. The presence of solute in the water delays the solidification of dispersed droplets. This delay in solidification varies with the concentration of salt as shown in Ref. 3. In Fig. 8, the solidification of the dispersed droplets is delayed and occurs at – 48°C. The presence of solute is indicated by the thermogram because the solid–liquid equilibrium temperature, T SL, is changed. For pure ice, the fusion occurs at about 0°C as shown in Fig. 7 and the shape of thermogram is similar to the theoretical shape for a pure compound during melting. Nevertheless, the melting temperature is slightly displaced, probably due to the presence of the surfactant added to stabilize the emulsion. The temperature is determined by the intersection of the baseline and the tangent to the point of greatest slope. In Fig. 8 the melting of aqueous salted frozen droplets begins at the eutectic temperature T e (first peak at – 21°C) and continues until ice–solution equilibrium is reached (following the second peak at T SL = – 7°C). In this case, the shape of the thermogram is divided into four parts [22]: For T s < T e at t < t0, the heat flow shape follows Eq. (13). For T s = T e at t0 < t < t1, the shape is a straight line. This is the case of a pure compound melting at constant temperature T e. For Te ≤ T s < T SL at t1 < t < t2, there is equilibrium between the solid and liquid phases. T SL is the temperature at which the progressive melting ends and is expressed using Eq. (14) as (27) The equilibrium temperature is given by the intersection of the baseline and the tangent to the point of greatest slope during the progressive melting. This tangent is a straight line parallel to the tangent plotted to determine the eutectic temperature. For T s > T SL at t > t2, the sample is entirely liquid, and the shape of the thermogram is represented by an exponential return to the baseline, following Eq. (16). Calorimetry is able to distinguish dispersed water from bulk water. Water crystallization is volume-dependent; the probable temperature of bulk water solidification is around – 14°C for cm 3 or mm 3 volume [22]. W/O system destabilization can be detected during cooling by using the solidification temperature. If W/O emulsions break, water behaves as bulk water. Figure 9 presents a cooling thermogram of an emulsion made of the same chemicals as emulsion 2, whose dispersed droplets do not contain sodium chloride. The cooling is performed just after the emulsion preparation and shows that the system is unstable because the water solidification appears at – 17°C. The solidification is instantaneous, and


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FIG. 9 Solidification and melting of dispersed deionized water in a simple W/O emulsion made of Exxol D80 and Berol as the continuous oil phase.

the curve shape is given by Eqs. (23) and (24). It can be concluded that salt acts as a stabilizer for this system. Figure 10 presents the cooling and heating thermograms of a W/O/W multiple emulsion. The internal phase is constituted of water dispersed in vaselin oil stabilized by lanolin as lipophilic emulsifier. This primary emulsion is then dispersed in water stabilized by sodium lauryl sulfate as hydrophilic surfactant. The droplets dispersed in the oil drops crystallize at – 42°C, and the external water phase solidifies at – 17°C. There is no measurable delay in the melting of the solidified droplets. Hence, all droplets of both aqueous phases melt at the same temperature, around 0°C. The shape of the thermogram is similar to that of the melting of a pure compound mentioned in Section II. Another interesting phenomenon that can be studied by calorimetry is socalled composition ripening. In that case, an O/W emulsion can be formed in which the dispersed medium is characterized by droplets of two different oils in a common aqueous solvent. The mixed solution is prepared by blending two different O/W simple emulsions of well-known compositions. An instability is then created in the emulsion, due to the difference in the nature of the drops. The oils will tend to diffuse through the water medium from one drop to another, finally forming mixed droplets of the same composition. The kinetics of the ripening depends on various parameters. The major ones are the nature and solubility of the oils, the nature and concentration of the surfac-

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FIG. 10 Solidification and melting of internal and external water phases in a W/O/W multiple emulsion in which the oil membrane is composed of vaselin oil and lanolin surfactant.

tants, the size of the droplets, and the oil/water ratio. Let us take the example of nhexadecane–n-tetradecane (50:50 w/w) in water emulsions. As the freezing temperatures of the two oils are different enough, at time t0 when we put the two O/ W emulsions containing the same mass of oil phase together, the thermogram will exhibit three characteristic peaks, as shown in Fig. 11. The first peak, around – 2°C, is associated with the crystallization of n-hexadecane, whereas the peak around – 17°C is related to n-tetradecane crystallization. The peak around – 23°C corresponds to the freezing point of the water (the continuous medium). At time t > t0, new thermograms are registered. Figure 12 shows thermograms obtained at different times t from 0 to 24 h. The shifts of the oil peaks as well as the areas of those peaks give precise and quantitative information on the concentration ripening. At t large enough (24 h in Fig. 12) the concentration equilibrium is reached and the thermogram exhibits a single peak for the two oils with a more probable temperature at about – 9°C. This temperature corresponds to the freezing point of mixed droplets. To evaluate the composition of the droplets it is possible to realize a calibration curve for the system. For that, thermograms were obtained for equilibrated emulsions containing the same ratio of oil phase to water phase as in the emulsion previously described but with a variable composition of the oil phase (variation of the hexadecane/vs tetradecane ratio). From those curves we extracted the temperature of crystallization of the oil droplets


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FIG. 11 Crystallization thermogram for the mixed emulsion containing 15 wt% nhexadecane droplets and 15 wt% tetradecane droplets.

FIG. 12

Crystallization thermograms for the mixed emulsion for different times t.

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FIG. 13 Calibration curve for crystallization temperature of mixed droplets versus percent n-tetradecane.

versus percentage of tetradecane in the oil phase. Those results are reported in Fig. 13. That representation shows a linear evolution. If we now report the temperature obtained in Fig. 12 at 24 h, it is possible to determine that at equilibrium there is 57% tetradecane in the droplet. If all the oil were in the droplets or if the solubilities of the two oils were the same, the temperature should correspond to 50% tetradecane in the droplet. Let us now study the thermograms obtained during the mass transfer. It is obvious from the thermograms that only the peak corresponding to hexadecane shifts to a lower temperature. The position of the tetradecane peak remains constant with t. At the same time, the area of the tetradecane peak decreases significantly, clearly indicating that most of the tetradecane diffuses into hexadecane drops, whereas hexadecane diffusion into hexadecane droplets is quite negligible. As the number of moles of oil in a droplet is proportional to the enthalpy of crystallization [23], we calculated the area of the hexadecane peak A with respect to time to quantify the kinetics of diffusion of tetradecane into hexadecane drops. Considering that at t0 = 0 the area A0 is the reference one, we report in Fig. 14 the ratio A/A0 versus time. This ratio is assumed to vary between 1 (t = t0) and 0 (t = te, end of transfer). The ratio decreases almost exponentially, and te is reached after approximately 15 h of diffusion. The same kinds of results were reported by Clausse et al. [23] for water-in-oil emulsions, but in that case the equilibrium time was much smaller than in our case (about 1 h).


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FIG. 14 Kinetics of diffusion of n-hexadecane in mixed emulsion.

V. CONCLUSION The purpose of this chapter was to illustrate with examples what goes on when different kinds of emulsions are submitted to regular cooling and heating. We focused on liquid–solid transitions, the most obvious of the expected phenomena. Numerous techniques allow qualitative information to be obtained about phenomena such as droplet composition or composition ripening. However, most of them have to be used in very dilute conditions, far from real application conditions. We have shown that calorimetry is a powerful tool for the study of those systems because it does not require dilution and the results obtained give quantitative information. Therefore, it appears to be one of the most efficient techniques for studying phenomena within emulsions, such as composition ripening and phase transitions. REFERENCES 1. BP Binks, JH Clint, PDI Fletcher, S Rippon, SD Lubetkin, PJ Mulqueen. Langmuir 15:4495–4501 (1999). 2. L Taisne, P Walstra, B Cabane. J Colloid Interface Sci B 184:378–390 (1996). 3. D Clausse. J Dispersion Sci Technol 20(1/2):315–316 (1999). 4. J Avendano Gomez, JL Grossiord, D Clausse. Entropie 224/225:98–104 (2000). 5. S Raynal, JL Grossiord, M Seiller, D Clausse. J Controlled Release 26:129–140 (1993).

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6. S Raynal, I Pezron, L Potier, D Clausse, JL Grossiord, M Seiller. Colloids Surf A: Physicochem Eng Aspects 91:191–205 (1994). 7. NN Li. AIChE J 17(2):459–463 (1971). 8. Kuswandi, JL Grossiord, D Clausse. Rec Progr Gén Proc 13:277–284 (1999). 9. D Clausse, I Pezron, S Raynal. Cryo-Letters 16:219–230 (1995). 1 0 . S Matsumoto. ASC Symp Ser 272:415–436 (1987). 1 1 . N Garti, S Magdassi. J Colloid Interface Sci 104:587 (1985). 1 2 . JL Grossiord, M Seiller, F Puisieux. Rheol Acta 32:168–180 (1993). 1 3 . RP Cahn, NN Li. Separ Sci 9(6):505–519 (1974). 1 4 . JP Dumas. PhD Thesis, Pau, 1976. 1 5 . L Dufour, R Defay. Thermodynamics of Clouds, Academic Press, New York, 1963. 1 6 . H Pruppacher, D Klett. Microphysics of Clouds and Precipitation, Reidel, Dordrecht, 1980, pp. 162–180. 1 7 . AP Gray. In: Analytical Calorimetry, Vol. 1, (RJ Porter, JF Johnson, eds.) Plenum Press, New York, 1968, p. 209. 1 8 . D Clausse, JP Dumas, F Broto. CR Acad Sci 279:415–418 (1974). 1 9 . JP Dumas, D Clausse, F Broto. Therm Acta 13:261–275 (1975). 2 0 . D Clausse. In: Encyclopedia of Emulsion Technology, Vol. 2, Applications (P Becher, ed.), Marcel Dekker, New York, 1985, pp. 77–157. 2 1 . F Broto, D Clausse. J Phys C: Solid State Phys 9:4251–4257 (1976). 2 2 . O Sassi, I Sifrini, JP Dumas, D Clausse. Phase Transitions 13:101–111 (1988). 2 3 . D Clausse, I Pezron, A Gauthier. Fluid Phase Equil 110:137–150 (1995).

6 Thermal Analysis of Self-Assembling Complex Liquids DONATELLA SENATRA Department of Physics—INFM Group, University of Florence, Florence, Italy

I.

Introduction

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II.

The A. B. C.

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III.

Phase Diagrams

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IV.

DSC A. B. C.

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V.

Phase Transitions A. First-order phase transitions: melting endotherms study B. Interphasal water C. Structural transitions associated with the interphase region

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VI.

DSC-ENDO Spectra: Deuterated Components

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DSC Approach DTA and DSC From ∆T to ∆Q The DSC signal (dH/dt)

Analysis of Microemulsions Standard reference liquids Thermal cycles Sample weight and thermal rate

VII. First-Order Phase Transitions: Freezing Exotherms Study

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VIII. Higher Order Phase Transitions

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IX.

The Percolation Transition

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References

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I. INTRODUCTION This chapter deals with the use of differential scanning calorimetry (DSC) in the study of some of the properties of self-assembling thermodynamically stable, multicomponent systems that appear to the naked eye as homogeneous and monophasic. Typical examples are micellar and microemulsion systems [1]. Both of these liquids are characterized by the presence of a dispersed phase, whether in the form of aggregates or droplets (diameter ≈10 nm), a dispersing medium, and a large interphasal area that becomes increasingly important as the “particle” size decreases. From a microscopic point of view, these systems are heterogeneous. To understand their thermodynamic stability, the equilibrium condition valid for heterogeneous systems in the condensed state must be considered. In other words, the system as a whole is assumed to be closed, which means that it may exchange only energy with the surrounding world. In this closed system there is a dispersed phase that behaves as an open system and may therefore exchange both energy and matter with the surrounding bulk medium. The equilibrium condition implies thermal, mechanical, and chemical equilibrium. In an equilibrium system, only reversible processes can take place. The question of the influence of temperature on the heat effect due to chemical reactions is outside the scope of this chapter. By introducing the enthalpy state function (H) defined by H = E + pV, where E is the system’s total energy, p the pressure, and V the volume, and by using the condensed state condition (∆V ≅ 0), it follows from the first and second laws of thermodynamics that at constant pressure, ∆H = ∆Q and a change in the enthalpy equals the change in the heat (Q) released or absorbed by the system during any thermal process. Since the heat change or the heat content at a given transition, in the frame of the reversible processes taking place in an equilibrium system, is the fundamental parameter to deal with in this study, we have found the “probe” for testing some of the main properties of our liquid multicomponent systems. It is the bulk behavior of the massive phases, phase transitions, and the role of the interphasal region. The main problem is how to measure the heat associated with a given thermal event. The extent to which we can rely on the measured heat exchange depends on the particular instrument used, on the calibration procedure followed, and on some experimental “considerations” that must be taken into account. II. THE DSC APPROACH “Thermal analysis” refers to the group of methods in which some physical property of a sample is continuously measured as a function of temperature while the sample is subjected to heating or cooling at a controlled rate (dT/dt). The temper-

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ature change is the driving force that determines the ability of a material to transfer heat to or accept heat from other materials or sources. The effect of heat can be wide-ranging, and it causes changes in many properties of a sample. In thermal analysis, changes in weight form the basis of thermogravimetry (TG), while measurements of energy changes form the basis of differential thermal analysis (DTA) and differential scanning calorimetry (DSC). Thermomechanical analysis (TMA) follows dimensional changes as a function of temperature. DTA and DSC are the most widely used techniques for investigating phase changes and phase equilibria, structural changes, thermal stability, qualitative analysis, quantitative analysis of mixtures, quality control as an assessment of purity, hydration, solvation and coordination effects, thermodynamic studies, and the determination of thermal constants. The range of materials that can be studied by thermal methods includes biological materials, building materials such as concretes and cements, ceramics and glasses, fats, oils, soaps and waxes, fuels and lubricants, liquid crystals, polymers and plastics, pharmaceuticals, textiles and fibers, and so on. Before entering the specific argument about the application of DTA-DSC techniques to multicomponent liquids consisting of water or oil droplets coated with a surfactant shell and dispersed into an oil or water continuous phase, we consider some technical details of these two thermal methods of analysis [2]. A. DTA and DSC The techniques of DTA and DSC are not identical. Let us consider the essential difference between them. In DTA, the heat changes within the material are monitored by measuring the difference in temperature (∆T) between a sample and an inert reference. In a classical DTA equipment both the sample (S) and the reference (R) are heated by the same furnace (Fig. 1a). The temperature sensors are inserted directly into the sample and reference, while in a modification of classical DTA, called Boersma DTA (Fig. 1b) they are in contact with the container but not with the materials under test. The temperature difference between the sample and the inert reference is recorded as a function of temperature (T) or time (t). In DSC, the sample and the reference materials are provided with their own separate furnaces as well as with their own separate temperature (T) sensors. In DSC, the sample and reference are maintained at identical temperatures by controlling the rate at which heat is transferred to them (Fig. 1c). Differential scanning calorimetry differs from differential thermal analysis in that instead of allowing a temperature difference to develop between the reference and the sample, the former measures directly the energy that has to be applied to keep the temperature the same, that energy being the amount of heat that must be supplied during an endothermic process (∆H < 0), for example, the melting of a substance, or subtracted during an exothermic process (∆H > 0), when the

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FIG. 1 Instrumental setup for thermal analysis. (a) Classical DTA; (b) modified DTA; (c) DSC, two furnaces. The parameters R, S, T R, TS, and ∆T are defined in the text.

thermal energy is, for instance, released as the material crystallizes from the melt. If δH > 0, the sample heater is energized and a corresponding signal is obtained; if ∆H < 0, the reference heater is energized in order to compensate for the temperature difference between the furnace of the sample and that of the reference until the temperatures of the two heat sources become equal again. The second process gives a signal opposite that of the first. Since the energy inputs are proportional to the magnitude of the thermal energies involved in the transition, the records give the calorimetric measurements directly. The latter aspect of DSC measurements is one of the greatest advantages of this technique. For this reason, this type of calorimeter is called power-compensated DSC. Typical DTA and DSC recordings are depicted in Figs. 2a and 2b, respectively. There is a third type of process, heat flux DSC, in which the electronic response of the instrument is coupled with the heat flow across an interface while


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FIG. 2 (a) Typical DTA recording. The temperature difference (∆T) between sample and reference is plotted on the ordinate axis. (b) Typical DSC recording. The differential heat input (mW) is plotted on the ordinate axis. In both cases, the abscissa can be either time or temperature.

both the sample and the reference are in close contact with the latter. The interface is usually a sapphire disk in which both the sample and reference are inserted in their own housings surrounded by thermocouples embedded in the same disk. In this case, both the sample and reference are contained in a single furnace as in DTA, and the temperature difference (T s – Tr) is related to the instantaneous rate of heat generation (dH/dt) by the sample through an equation that links together the temperature differences between the sample, the reference, and the instrument heat source at a temperature T 0, the thermal rate applied (dT/dt), the sample heat capacity at constant pressure (C s), the reference heat capacity (Cr ), and the instrument constant (R) that accounts for both the thermal resistivity and the geometry of the calorimetric device. Most of the results reported in the forthcoming sections were obtained with a heat flux DSC thermal analyzer. B. From ∆T to ∆Q It is well known that heat can flow within a system only if energy is transferred because of a temperature gradient from some point at a temperature T 1 to another point at a temperature T2 with T 1 > T 2.

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FIG. 3 Newton’s law for the flux of heat through a homogeneous material of cylindrical geometry. The parameters Q, L, A, ∆x, T1 , and T 2 are defined in the text.

With reference to Fig. 3, the amount of heat flux within a time interval ∆t is governed by the relation (1) where k is the thermal conductivity coefficient of the material constituting the cylinder through which the heat flows, L is the length of the cylinder, and A is its cross-sectional area. In SI units the heat flux is measured in watts and k is therefore expressed in watts per meter per kelvin. By introducing the thermal resistivity R, defined as (2) where R is expressed in kelvins per watt (K/W) or in kelvin-seconds per joule (K · s/J) and ∆x is the thickness of an infinitesimal slab, the rate of heat flux (dq/ dt) across ∆x, with ∆T > 0 can be written as (3) Equation (3) is known in the literature as Newton’s law. We assume that (1) the heat energy per unit time (dq/dt) is supplied by the instrument source at a temperature T = T 0; (2) Ts is the temperature of the sample and sample pan; (3) (dH/dt)1 is the instantaneous heat generated (dH/dt > 0) or


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absorbed (dH/dt < 0) by the sample because of an exothermic or endothermic process, and (4) (dH/dt)2 is a term that accounts for the heat transfer to or from the sample, expressed as a function of both the (sample + sample pan) heat capacity at constant pressure (Cs) and the rate of change of the sample temperature (dTs/dt). Taking into account that the total heat balance must be constant, it follows that (4) where dq/dt is the heat supplied per unit time by the furnace. From Newton’s law, the latter is (5) The term (dH/dt)1 is the instantaneous heat due to the sample enthalpic change, and (dH/dt)2 is the term that accounts for the fact that, depending on whether (dH/dT)1 is positive or negative, the sample temperature may be increased or decreased. This must be counterbalanced by a cooling device in addition to the thermal resistor of the instrument source. Expressing the sample heat capacity at constant pressure, (6) and omitting from now on the p subscript, we have (7) Substituting Eqs. (5) and (7) into Eq. (4), we obtain an expression for the difference between the source temperature T 0 and that of the sample T s, (8) Now we can solve the same problem from the reference side. For the reference we have (dH/dt)1 = 0: No change in the heat content occurs in the empty reference pan, and all the heat is used to change the reference temperature T r. However, the reference pan heat capacity C r can differ from that of the sample. Thus, we may write, always according to Newton’s law [Eq. (3)], the analogous expres-

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sion for the reference because the quantity dq/dt is supplied by the same source. We have (9) and Eq. (4) for the reference becomes, by substituting (dH/dt) 2 = Cr(dT r/dt), (10) The latter, with Eq. (9), gives (11) Therefore, the difference between the source and the reference temperature has the form (12) Subtracting Eq. (12) from (8), we obtain (13) By adding to both sides of Eq. (13) the quantity RCs dTr/dt and rearranging, it follows that

where the subscript 1 has been omitted. Equation (14) expresses the instantaneous rate of heat generation by the sample as a function of the “measured” temperature difference between sample and reference, taking into account other parameters such as the heat capacities for both the sample and reference, the thermal rate (dT r/dt = dT/dt), and the instrument constant R. As a further step we must understand the meaning of the three terms on the right-hand side of Eq. (14) and also try to recognize which of them can be experimentally handled to optimize the heat flux DSC measurements. In Eq. (14), apart from the first term on the right, whose meaning is obvious, the second term represents the baseline displacement from the electric zero level, while the third, multiplied by the constant R and the sample heat capacity, is the term responsible for the thermal peak in the DSC recordings. In a pure DTA


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setup, this term represents the slope at any point of the peak [2]. Since the products RCr,s have the dimension of time (τ), i.e., RCr,s = τ, where the dimensions of τ are (K . s/J)(J/K) = s, we can rewrite Eq. (14) as follows: (15) From Eq. (15) it emerges that the R(dH/dt) term depends on the temperature difference between the sample and the reference, on the thermal rate dT/dt, on ∆τr,s = τr – τs and on τs = RCs. In order to understand how ∆τr,s and τs can be optimized to improve the quality of the measurements, we must enter the argument from a practical point of view by introducing a given heat flux DCS instrument. From now on we report on the results obatined with a Mettler-Toledo TA 3000 unit equipped with a TC 10A processor and two low-temperature cells, namely a DSC 30 and a DSC 30 Silver. As stated earlier, we cannot have any heat flux without ∆T ≠ 0. The latter condition is fulfilled in this DSC instrument in such a way that, assuming T 0 – Tr > 0 (see Fig. 4), the reference temperature lags behind the source temperature by the quantity (16) In Eq. (16), the time constant is called the “tau lag”; it depends on the particular instrument used. Moreover, Eq. (16) follows directly from Eqs. (9)–(12) with dTr/ dt = dT/dt, the latter being the applied thermal rate. The value of the tau lag constant is usually provided with the DSC equipment. However, this time constant can be optimized experimentally by repeating the same measurement

FIG. 4 Heat flux DSC. Relation between the furnace temperature (T 0) and reference temperature (T r). [See Eq. (16) in the text for further explanation.]

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without changing anything but the thermal rate. The calculated value τ* is given by the relation (17) where T 1 and T 2 are the melting temperatures of a standard, whether a solid or a liquid, measured at two different thermal rates, dT 1/dt and dT2/dt, with dT 1/dt > dT 2/dt; the number 60 transforms the time unit to seconds. Usually, dT1/dt = 8–11 K/min and dT2/dt = 1–2 K/min. Several measurements must be performed and the average value used. For the low-temperature range, this procedure must be repeated with a component such as n-pentane, which has a melting temperature of ~ 143 K. Therefore, to assess the instrument behavior within the working temperature interval, the average of the two τ* values can be evaluated and used in the configuration list. The latter value represents the time constant, in seconds, required to equilibrate the temperature difference between the furnace and the DSC sensor. Going back to Eq. (15), we will try to understand how it is possible to optimize the second term on its right-hand side, ∆τr,s (dT/dt). The latter can be optimized in two steps: 1. By compensating for the weight difference between the crucibles that will be used for the measurement 2. By compensating for the difference arising from the sample’s thermal conductivity In the first case, a measurement must be performed with two “empty” crucibles, both for the reference and the sample, within the temperature interval that will be used in the final DSC measurement. The measurement can be stored and the result thereafter subtracted from the final DSC analysis obtained by using the same crucibles for the reference and sample and, obviously, the same scan speed. Such a procedure is known as blank correction. In the second case, a measurement must be performed by filling both the reference and sample pans with a “reference” sample. By “reference sample” we mean exactly the system under test, provided it has previously been ascertained that within the temperature interval required to perform the correction of the time constant no transitions of any order are occurring in the sample. A relation similar to Eq. (17) is used. However, in this second case a time constant (τ**) is evaluated with both pans filled with the “reference” system. We have (18)


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The tau lag constant (τ*) must therefore be replaced with the τ** value. Greater details about this topic are given later. The main problem relates to the availability of a standard for the system as a whole. Practically, the inability of a sample to follow a given thermal program can be tested experimentally from the steplike pattern occurring at the end of the dynamic part of the DSC recording, between the latter and the isothermal part (ISO): The larger the step, the worse the situation. This means that the sample temperature lags too much behind the furnace temperature. In other words, in a melting analysis, for example, the sample ends with T s > T r. These problems can be overcome by reducing the sample mass or by lowering the thermal rate and by careful control of the τ* constant. An example of the steplike pattern at the end of the dynamic part of a DSC recording is reported in Section IV.C. The third term on the right-hand side of Eq. (14) or (15) contains another time constant called the “tau signal,” τ s = RC s . The latter can also be experimentally evaluated and therefore optimized. Before entering into this argument we must discuss how the heat flux DSC instrument handles the dH/dt signal. C. The DSC Signal (dH/dt) If we assume that the second term on the right-hand side of Eq. (14) or (15) is a known constant evaluated as discussed in the previous section, we get (19) By introducing the sensitivity of the thermocouples (S), defined as ∆V = S ∆T, where ∆V is a voltage difference, we may write (20a)

(20b) We recall that S is the thermometric sensitivity of the DSC sensor that converts the thermocouple voltage (∆V) to the temperature difference ∆T. Since the second term on the right-hand side of Eq. (20b) can be disregarded, we obtain, by substituting (20a) and (20b) into (19), (21)

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In Eq. (21), RCs is the already defined “tau signal” (τs); its value, given in the instrument handbook, can be inserted in the configuration list. The tau signal accounts for the type of crucible used (whether aluminum, gold, or glass). The product RS is called the calorimetric sensitivity and is replaced with E. Both R and S depend on temperature. The calorimetric sensitivity E can be divided into two terms, one of which, E IN, does not depend on temperature, while the other, EREL, does depend on temperature, and its temperature dependence is contained in the TA processor as a polynomial, EREL = A + BT + BT2 Therefore the T dependence of the relative calorimetric sensitivity is directly governed by the instrument’s software. The heat flow to the sample (dH/dt) is given by (22) The EIN part of the E constant can be experimentally determined through a careful calibration procedure, by measuring the latent heat of pure indium pellets in a melting DSC run. This procedure defines the heat flux calibration. It requires that several measurements be made of the constant EIN, each time using a new, previously unmelted indium pellet. Thereafter the average value can be inserted into the configuration list. We recall that with the standard sensor in the “medium” sensitivity, the measuring range is 60 m W, with a calorimetric sensitivity of 11 µ V/mW and 2400 points/K; in the “high” sensitivity position, the measuring range is 17 mW and the number of points per kelvin rises to 8500. Unless specified, the medium sensitivity setup is used in the DSC measurements reported in this chapter. The tau signal τs can be assessed by using a crucible filled with a sample of the system under test. By performing an isothermal measurement it must be verified how quickly the baseline is reached by the DSC signal. Such a procedure is essential in the study of chemical reactions, but it can be used to improve the DSC measurements in the study of other processes as well. III. PHASE DIAGRAMS As already mentioned in the Introduction, micelles and microemulsions are complex multicomponent fluids consisting of two liquids, namely water and oil, and a surfaceactive agent (for a three-component system). For a four-component system, in addition to the surfactant a cosurfactant is also added (usually an alcohol). In systems containing more than four components, some salt is added, solubilized in either water or oil.


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The composition of a multicomponent system is depicted by points on the plane of an equilateral triangle for three components and of a regular tetrahedron for four components. In the first case, the apices of the equilateral triangle correspond to pure components, the points on its sides to two-component systems, and the points inside the triangle to ternary mixtures. Since the composition is generally expressed as a fraction or percent (molar volume, weight), the sides of the triangle are divided into 10 (or 100) parts, and straight lines parallel to the respective sides are drawn through the points of division. The ratios of the components are determined either on the basis of the fact that the sum of perpendiculars dropped from any point onto the sides of an equilateral triangle equals its altitude, taken equal to 1 (or 100), or that the sum of lines drawn from any point inside an equilateral triangle, parallel to its sides, up to their intersection with another side of the triangle equals a side of the triangle, which is taken equal to 1 (or 100). Both methods give the same result, since the sides and the altitudes of an equilateral triangle are proportional to one another. Moreover, 1. A straight line parallel to the side opposite a given apex is a line representing a constant concentration of the component to which this apex corresponds. 2. A straight line passing through the apex of the triangle corresponding to a given component is a line with a constant ratio between the other two components. Points 1 and 2 follow directly from the proportionality of perpendiculars dropped from any point of a line to the corresponding sides of the triangle. In the case of the regular tetrahedron describing the composition of fourcomponent systems, the length of its edges is taken as 100%, while its apices correspond to the pure substances. The tetrahedron edges depict the binary systems, its faces the ternary ones. Planes parallel to the faces correspond to systems containing a constant percent of the component opposite this face. The latter feature is quite often used to construct “pseudoternary” phase diagrams in which one apex of an equilateral triangle represents, for instance, the amount of surfactant + consurfactant in a given and fixed molar, weight, or mass ratio or percent, while the other components, namely the water and the oil, are represented on the other two remaining apices. In the latter case, the rules given for ternary systems apply. The confined domains depicted in Fig. 5 represent the regions where macroscopically homogeneous and single-phase systems are found. However, these domains do not necessarily represent micellar or microemulsion systems. The characterization of such systems requires a great deal of experimental work, usually interdisciplinary. Structural properties can be investigated by small-angle neutron scattering (SANS) [3–5] or by quasi-elastic light scattering (QELS) [6–8]. Interphasal properties can be studied by dielectric spectroscopy and electrical conductivity mea-

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FIG. 5 Phase diagrams. (a,b) Pseudoternary phase diagrams of two four-component systems. The continuous line encloses the domain within which monophasic, homogeneous samples are confined. PP’ lines are experimental paths followed in the DSC study by adding water to samples characterized by the constant ratio (S + COS/O) of 0.70 and 0.68 for systems (a) and (b), respectively. The compositions are given in Table 2. (c) Phase diagram of a three-component system with perfluoropolyether (PFPE) oil (O), PFPE surfactant (S), and water (W). The composition of the system along the dilution line W/S = 11 is given in Table 4.

surements, fluid properties by viscosity measurements [9–12], and basic thermodynamic behavior by differential scanning calorimetry (DSC) [13–14]. In laboratory practice, samples may be prepared by weighing the components. Sometimes, mostly when dealing with volatile components or strongly hygroscopic surfactants, it is difficult to dose exact amounts of any given component in preparing a sample. If one starts with a basic stock solution and thereafter proceeds to add fixed


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amounts of a component to it, it is easier to follow the evolution of the system behavior and thus to understand its properties as a function of the change of only one component. The latter procedure becomes increasingly important as we approach the border of the monophasic domain of the given system. IV. DSC ANALYSIS OF MICROEMULSIONS Three main topics are fundamental to DSC study of microemulsions: 1. Standard reference liquids 2. Thermal cycles 3. Sample weight and thermal rate A Standard Reference Liquids The melting temperatures (Tm) and the enthalpy of melting (∆Hm) values of the pure liquid components are necessary to identify the different contributions of each of the system’s components to the DSC spectrum. The literature data for both T m and ∆Hm must be used as reference values for testing whether the instrumental setup is working properly in order to identify the different peaks in the thermal spectrum. However, for quantifying the contribution of each component, it is better to use as standard values for both T m and ∆Hm the experimentally measured values of the pure bulk compounds used to formulate a given system. Another procedure that may help in identifying the thermal events is the substitution of a given component by the corresponding deuterated one, provided that the melting temperature of the latter differs by about 3–4 K from that of the normal liquid. One precaution must be followed in applying this procedure: The substitution of one of the microemulsion components by its deuterated counterpart may modify the monophasic domain of the system phase diagram, so one must ascertain that even if the proportions between the components are the same, one is working far from the boundary of the monophasic region across which a phase transition to lyotropic mesophases or macroscopic phase separation may occur. The melting spectra of systems with deuterated components are given later. Some melting temperatures and enthalpy values of liquids commonly used in the formulation of microemulsions are listed in Table 1. The compositions of the systems analyzed in this work are given in Tables 2, 3, and 4. B. Thermal Cycles As shown in Fig. 6, during a melting or freezing thermal process, a temperature difference develops between the sample and the reference. Therefore, it is important, in a dynamic DSC measurement (as a function of temperature), both to precede and to follow the thermal analysis with an isothermal period (ISO) of

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218 TABLE 1 Melting Temperatures and Enthalpy Values Compound

Formula

n-Pentane Benzene n-Hexane Toluene Isooctane n-Decane n-Dodecane n-Hexadecane Water Heavy water Interphasal water (n-Hexadecane) d34

MW

C5H12 C6H6 C6H14 C7H8 C8H18 C10H22 C12H26 C16H34 H 2O D 2O H 2O C16D34

MP (K)

72.5 78.11 86.18 92.14 114.23 142.28 170.34 226.41 18.016 20.029 18.016 329.248

143.3 278.53 177.7 178.01 165.7 243.3 263.4 292.9 273.0 276.82 263.0 286.0

∆H (J/g) 116.69 127.40 151.75 74.35 89.73 202.25 216.27 235.44 333.42 313.54 312.38 —

TABLE 2 Composition of Four-Component W/O Microemulsions a

System 1

Oil (%) Dodecane 57.22 Hexadecane 57.73

2

Surfactant (%) K-oleate 15.30 K-oleate 14.94

Cosurfactant (%) n-Hexanol 25.03 n-Hexanol 24.35

Dispersed phase (%) Water 2.45 Water 2.98

Component proportions: surfactant/oil = 0.2 g/mL; cosurfactant/oil = 0.4 mL/mL. Percentages are by weight. a

TABLE 3 Composition of Three-Component W/O Microemulsions System Water–Na(AOT) c –decane D 2 O–Na(AOT)–decane Water–Na(AOT)–isooctane a b c d

Φ a (mL/mL) 0.35 0.35 0.31

Volume fraction (water + surfactant)/total. Molar fraction water/surfactant. Sodium di-2-ethylhexyl sulfosuccinate. Percolation temperature.

(mol/mol)

(K)

40.8 40.7 37.0

300 312 306


219

TABLE 4 Composition of Perfluoropolyether W/O Micromulsions Along the Dilution Line W/S = 11 a Φ b,c 0.205 0.327 0.395 0.462 0.501 a b c d

%W

%S

%O

3.95 6.37 7.80 9.20 10.05

14.05 22.86 27.90 33.00 36.03

82.00 70.77 64.30 57.80 53.92

T p (K) d 305.5 292.3 289.5 285.5 282.3

± ± ± ± ±

0.2 0.3 0.3 0.3 0.3

W/S molar fraction. Percentages are by weight, W = water; S = PFPE surfactant; O = PFPE oil (see Ref. 28). Φ-volume fraction (W + S)/total. Percolation temperatures from Ref. 34.

at least 10 min at the starting temperature as well as at the final temperature reached in the experiment in order to allow the sample temperature (Ts) to approach that of the reference and to ensure that the dynamic part of the DSC recording is performed between two equilibrium temperatures. Utilizing a given thermal cycle may help in confronting the data, testing the reproducibility of the measurements, gaining evidence as to whether repeated thermal cycles do affect the thermal results, and controlling the sample’s thermal history. Examples of typical thermal cycles for DSC analysis of microemulsion systems are plotted in Figs. 7 and 8. Obviously, the highest temperature reached

FIG. 6 Temperature difference between the sample and the reference pans when a melting or freezing thermal event occurs in the sample. (From Ref. 13.)

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FIG. 7 Example of a thermal cycle that can be applied for DSC analysis of microemulsion systems. Each thermal run is preceded as well as followed by an isothermal period. (L = liquid; S = frozen solid). (From Ref. 13.)

FIG. 8 Typical thermal cycle for the study of W/O microemulsions exhibiting percolative behavior. The cycle starts with an isothermal period of 20 min at a temperature equal to the percolative temperature T p evaluated by dielectric and conductivity measurements. After the DSC-EXO measurement, a second isotherm of 40 min follows on the frozen sample. The heating measurement, DSC-ENDO, ends with a third isotherm at a temperature TL < Tp at which the sample is again in the liquid state. The last measurement (C p Run) completes the thermal analysis. The thermal rate dT/dt of the latter run is higher than the 2 K/min rate used in both the exothermic and endothermic stages. Thermal rates varying from 4 to 10 K/min are applied depending on the surfactant used to formulate the system. (From Ref. 14.)


221

in the heating part of the measurement must not exceed the maximum temperature at which the microemulsion is still stable. C. Sample Weight and Thermal Rate In a multicomponent system such as a microemulsion, several plateaus of the type shown in Fig. 6 may occur. The larger the amount of a given component involved in a thermal event, the larger will be the difference between the reference and sample temperatures. Therefore a careful choice of the sample weight for reasonably good temperature accuracy is necessary. If small samples (2–6 mg) are used and low thermal rates ( N w(a) (i.e., in the presence of nonfreezable and freezable interlamellar and bulk water), respectively.

of bulk water, NI(f) at each Nw is calculated by subtracting Nw(b) from Nw. For Nw > Nw(a) (III), i.e., in the presence of bulk water, NI(f) is obtained by subtracting Nw(b) from the NI value calculated from (∆HT – ∆HIV)/1.436 at each Nw. The estimations of NI(nf), NI(f), and NB for varying water contents are summarized as follows: 1. For N w ≤ N w(b) (I), N I(nf) = N w, N I(f) = 0, N B = 0. 2. For Nw(b) < N w ≤ Nw(a) (II), N I(nf) = Nw(b), N I(f) = N w – Nw(b), NB = 0. 3. For N w > N w(a) (III), N I(nf) = Nw(b), NI(f) = N I (=Nw – N B) – Nw(b), NB = ∆HIV /1.436.

Water in Phospholipid Bilayer Systems

255

FIG. 5 Water distribution diagram for limited hydration of a lipid–water system. The cumulative number of water molecules (per molecule of lipid) in different bonding modes is plotted against the water/lipid molar ratio (N w).

D. Water Distribution Diagrams Values of NI(nf), NI(f), and NB obtained according to the above calculations were used to construct a water distribution diagram for limited hydration of a lipid–water system (Fig. 5), where the cumulative number of molecules of water (=NI(nf) + NI(f) + N B) per molecule of lipid is plotted against N w. The diagram provides much information such as (1) the number of water molecules in different binding modes at each Nw; (2) the mode, whether limited or infinite, for the uptake of the water molecules; and (3) the N w value at which the system is fully hydrated. III. RELATIONSHIP BETWEEN LIPID PHASE TRANSITIONS AND ICE-MELTING BEHAVIOR IN LIPID–WATER SYSTEMS Lipid–water systems usually exist in either a gel or a liquid crystal phase depending on temperature. In this case, the gel-to-liquid crystal phase transition of

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the lipid is observed by DSC. However, the systems are occasionally present in a semicrystalline or crystalline phase, generally called the subgel phase (for diacylphosphatidylcholine, see Refs. 1, 14–16, 24–26; for diacylphosphatidylethanolamine, Refs. 18–20, 27–32; for diacylphosphatidylglycerol, Refs. 33–39), which transforms to either the gel or the liquid crystal phase on heating. If the ice-melting DSC peak (whether broad or sharp) is successively followed by the gel-to-liquid crystal phase transition, the melting behavior is known to be derived from the water molecules of the gel phase. If no phase transition is observed at a temperature higher than that of the ice melting, then the ice is assigned to one of the liquid crystal phases. Furthermore, if the phase transition of either the subgel to gel or subgel to liquid crystal follows the ice-melting peak or thermal event, the ice is assigned to one of the subgel phases. On this basis, we measured the ice-melting behavior of both the gel and subgel phases and constructed the water distribution diagrams of both phases according to the method discussed above. In this chapter, our recent results are referred to with a view to answering the following questions: 1. Is there any difference between neutral and acidic phospholipids in the mode of incorporation of water molecules between their lamellae? 2. What is the role of water molecules in the lipid phase transitions such as gel to liquid crystal, subgel to gel, and subgel to liquid crystal? 3. What is the role of water molecules in the conversion of the gel to the subgel phase? IV. EXPERIMENTAL TECHNIQUES Phospholipids are major components of biomembranes and constitute a fundamental part of their bilayer structure. The phospholipids used in the present study are dipalmitoylphosphatidylcholine (DPPC) and dimyristoylphosphatidylethanolamine (DMPE) as neutral lipids and dipalmitoylphosphatidylglycerol (DPPG) as an acidic lipid. The polar headgroups of these lipids are compared in Fig. 6 [40–43]. It is worthy of note that these headgroups provide many binding sites for a water molecule on the surface of a bilayer. On the other hand, phosphatidylcholine (PC) and phosphatidylethanolamine (PE) constitute the majority of the total phospholipids in biomembranes and are present as dipolar zwitterions at neutral pH. Phosphatidylglycerol (PG) is a ubiquitous phospholipid in mitochondrial and chloroplast membranes and is negatively charged at neutral pH. Since these lipids have charged groups, electrostatic forces operate not only between adjacent headgroups in an intrabilayer (intermolecular force) but also between adjacent bilayers (intersurface force), although the forces are opposite in sign or direction for the neutral and acidic lipids. Furthermore, results of X-ray crystallographic studies previously reported by other workers should be mentioned here.


257

FIG. 6 Difference in the polar headgroups of diacylphosphatidylcholine (PC), diacylphosphatidylethanolamine (PE), and diacylphosphatidylglycerol (PG).

Thus, two adjacent PC molecules in an intrabilayer are linked to each other via a water-based hydrogen bond [41,44]. However, PE molecules in an intrabilayer interact directly via a hydrogen bond formed between the amino group of one molecule and the phosphate group of an adjacent molecule [41,42,44]. For PG used in Na+-PG, the counterions are present in a layer sandwiched by the headgroups of adjacent bilayers [45]. On the other hand, the present lipids have different chain lengths. This is because when the dimyristoylphosphatidylcholine (DMPC) system is used in place of the DPPC system, its subgel phase exists at temperatures below at least 0°C (i.e., it is impossible to measure the ice-melting curve for the subgel phase). Similarly, when the dipalmitoylphosphatidylethanolamine (DPPE) system is used in place of the DMPE system, the system requires much longer periods (at least 40 days) for completion of the conversion of the gel to the subgel phase by annealing. The water distribution diagram shown in Fig. 5 was composed of the results of at least 30 samples of a lipid–water mixture containing from 0 to at least 40 wt% water. The value of NT in Eq. (2), determined by weighing both the lipid and water, is also a dominant factor in the accuracy of the present method, similarly to the value of ∆H B discussed above. From this viewpoint, samples of varying water content were prepared in the present study by successive additions of the desired amounts of water to the same dehydrated lipid. Thus, only the weight of water was changed throughout the preparation of a series of samples. The dehydrated lipid was prepared as follows. A lipid (approximately 30 mg) in a high pressure crucible cell was dehydrated under high vacuum (10-4 Pa) at room temperature for at least 3 days until no mass loss was detected by electroanalysis. The crucible cell containing the dehydrated lipid was sealed off in a dry box filled with dry

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N2 gas and then weighed with a microbalance. All the samples were weighed after adding the desired amounts of water and annealed by repeating thermal cycling at temperatures above and below the lipid phase transition until the same transition behavior was attained. After the annealing, the loss of water in the samples was checked with the microbalance [13,21].

V. ICE-MELTING BEHAVIOR FOR A MINUTE AMOUNT OF FREEZABLE INTERLAMELLAR WATER Figure 7 shows a series of typical DSC curves for samples of the DPPC–water mixture with increasing water content expressed as [(g water)/(g lipid + g water)] × 100 and designated as W H O. The ice-melting peaks are followed by two lipid 2 transition peaks of the gel (L β’)-to-gel (Pβ’) and subsequent gel (Pβ’)-to-liquid crystal phase transitions, generally called the T p and T m transitions, respectively.

FIG. 7 A series of DSC curves of the DPPC–water system ranging in water content from 11.5 wt% (N w = 5.3) to 40.9 wt% (N w = 28.2).


259

FIG. 8 Variation of the broad component of ice-melting DSC curves at low water contents up to 20.1 wt% for the gel phase of the DPPC–water system. Water contents (wt%) are a, 11.5 (5.3); b, 12.6 (5.8 7); c, 12.8 (5.9 8 ); d, 13.1 (6.2); e, 14.1 (6.7); f, 14.8 (7.0); g, 16.1 (7.8); h, 17.4 (8.6); i, 20.1 (10.2), where the numbers in parentheses are the corresponding N w values.

In Fig. 8, enlarged scale ice-melting peaks are compared for W H O < 20 wt%, where 2 the water content is successively changed at short intervals of about 1 wt%. A characteristic feature of this figure is that the broad components of ice-melting peaks d–i cannot be superimposed on one another. Only at water contents less than 13 wt% (i.e., Nw < 6) is such a superposition observed. This phenomenon indicates that the interbilayer freezable water molecules interact with one another in different hydrogen bonding modes and their bonding modes become closer to that of free water with increasing water content. Furthermore, it is suggested that the hydrogen bonding mode of the freezable water molecules existing in interbilayer regions is little affected by the addition of more interlamellar water. On the other hand, as discussed later, the freezable interlamellar water of the DPPC–water system begins to appear at Nw ~ 5 (W H O ~ 11 wt%); therefore, 2 Nw(b) ~ 5. However, as shown in Fig. 8, the ice-melting behavior (curves a–c)

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for 5 < Nw < 6 is different from that (curves d–i) for N w > 6. Thus, a broad, low, flat peak extending over a fairly wide temperature range is observed for a very small amount of freezable interlamellar water (Nw = 5.3, W H O = 11.5 wt%) (curve a). Yet, 2 even though the amount of freezable interlamellar water is slightly less than one molecule of H2O per molecule of lipid (Nw = 5.9 8, WH2O = 12.8 wt%) (curve c), the melting peak is broader and is not fitted to similar peaks observed for Nw > 6. Furthermore, the thermal behavior is observed to depend on the procedure used for the cooling of the sample, as shown in Fig. 9. Thus, when the sample is cooled to –60°C at a rate higher than 1°C/min, its heating curve shows an exothermic phenomenon at temperatures just below the ice-melting peak (Fig. 9, curve a). The exothermic peak completely disappears after annealing at temperatures around –40°C (exothermic temperatures), but the resulting icemelting peak is still broad (Fig. 9, curve b). In contrast, no exothermic peak is observed when the sample is cooled at a rate as slow as 0.2°C/min (Fig. 9, curve c). Such phenomena are characteristic of freezable interlamellar water in amounts of less than one molecule per molecule of lipid, namely, for

FIG. 9 Characteristic behavior of ice-melting DSC curves at a water content of 12.8 wt% (N w = 5.98 ) for the gel phase of the DPPC–water system. Curves a, b, and c are explained in the text.


261

5 < Nw < 6. By assuming multiple sites on the bilayer surface to which the water molecules can bind, it is suggested that one molecule of H2O per molecule of lipid of freezable interlamellar water is not enough to cover all the binding sites. As a result, a localized increase in the transformation of the water molecules into ice on cooling would occur on the bilayer surface, resulting in a broadening of the icemelting peak. Presumably, the hydrogen bonds in such localized ice are unstable or metastable, and so the exothermic peak due to the stabilization is observed upon heating. On this basis, it is suggested that one molecule of H2O per molecule of lipid is a critical amount required for the freezable interlamellar water to form icelike hydrogen bonds between lamellae. VI.

ANALYSIS OF WATER MOLECULES IN THE GEL PHASE OF LIPID–WATER SYSTEMS

A.

DPPC–Water System

According to the method discussed above, the ice-melting DSC peaks for N w > 6 (W H2O > 13 wt%), characterized by similar shapes, are deconvoluted. In Fig. 10, typical results of the deconvolution analysis are compared at water contents of 16.1, 20.1, and 22.1 wt%. On the whole, the number of deconvoluted curves increases and the area of each curve becomes larger with increasing water content. The broad peak for the freezable interlamellar water is shown to be finally deconvoluted into four curves—I, II, III, and IV—which successively appear with increasing water content. A deconvoluted curve V for the bulk water is observed at water contents of 20.1 and 22.1 wt%. In Fig. 11 the ice-melting enthalpies ∆HI, ∆HII, ∆HIII, and ∆HIV of the respective deconvoluted curves I, II, III, and IV are plotted against Nw, together with the sum of these enthalpies, ∆H I(f). Similarly, in Fig. 12 the icemelting enthalpy ∆HV of the deconvoluted curve V, comparable to ∆HB in Eq. (3), is plotted against N w. To make clear the relationship between the icemelting enthalpies for the freezable interlamellar and bulk water, the ∆HB (=∆H V) and ∆H I(f) curves are compared in Fig. 13. Furthermore, Table 1 summarizes values of ∆H I(f) and ∆HB per mole of lipid at varying water contents (W H2O) shown together with the corresponding water/lipid molar ratios (Nw). First, focusing on Fig. 11, it is seen that with increasing water content, the ∆HI, ∆HII, ∆HIII, and ∆HIV curves appear in this order and reach maxima in the same order. Every curve gently increases before arriving at a plateau, so that the ∆HI(f) curve also shows the same behavior. Consequently, Nw (~ 15) at the beginning of the plateau of the ∆HI(f) curve is higher than that (~ 10) predicted from the extrapolated (dashed) lines. On the other hand, the ∆HI(f) curve intersects the abscissa at N w ~5. Therefore, the limiting, maximum number of nonfreezable interlamellar water molecules for the gel phase of the DPPC–water system is 5 H2O per molecule of lipid.

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FIG. 10 Deconvolution analysis of ice-melting DSC curves for the gel phase of the DPPC–water system. Water contents (wt%); a, 16.1 (7.8); b, 20.1 (10.2); c, 22.1 (11.6). The numbers in parentheses show the corresponding Nw values. The deconvoluted curves I–V and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.


263

FIG. 11 Plots of ice-melting enthalpies for freezable interlamellar water versus N w in the gel phase of the DPPC–water system. ∆HI(f) is the sum of the individual enthalpies of the deconvoluted curves I, II, III, and IV for the freezable interlamellar water shown in Fig. 10.

Next, the ∆HB curve is also shown (Fig. 12) to increase gently up to Nw ~ 15, after which it increases linearly and parallel to the theoretical ∆H T line. Accordingly, the amount of total interlamellar water is the same for water contents above the boundary Nw (~ 15), indicating the appearance of a fully hydrated gel phase. In this case, the maximum amount of total interlamellar water can be determined graphically by extrapolating the linear ∆HB curve to Nw below 15. Thus, Nw of the intersection point just corresponds to the maximum number of interlamellar water molecules, i.e., 10 H2O per molecule of lipid for the DPPC– water system. Focusing on the nonlinear increase observed for both the ∆HI(f) and ∆HB curves, it is seen from Fig. 13 that the phenomenon for both curves takes place in the same water content region, 8 < Nw < 15. Therefore, it is understandable that the deviations of the ∆HI(f) curve from the extrapolated ideal (dashed) line is caused by the bulk water that appears although the limiting, maximum amount of interlamellar water is not yet reached (in other words, the gel phase is not

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FIG. 12 A plot of the ice-melting enthalpy ∆H B for the bulk water versus N w in the gel phase of the DPPC–water system. The theoretical ∆HT curve is shown for comparison.

FIG. 13 ∆H T , ∆H B, and ∆H I(f) curves for the gel phase of the DPPC–water system. Hatch lines within the range 8 < N w < 15 represent the pre-region (see text).

265


Table 1 Ice-Melting Enthalpies of Freezable Interlamellar and Bulk Water, ∆HI(f) and ∆H B, Respectively, per Mole of Lipid and the Numbers of Nonfreezable and Freezable Interlamellar and Bulk Water Molecules, NI(nf), NI(f), and NB, respectively, per Lipid Molecule at Varying Water Contents (WH2O) in the Gel Phase of the DPPC–Water System Ice-melting enthalpy (per mole of lipid) (kcal)

Number of water molecules (per molecule of lipid)

WH O 2

System

(wt%)

Nw

∆HI(f)

∆HB

NI(nf)

a b c d e f g h i j k l m n o p

12.6 12.8 13.1 14.1 14.8 16.1 17.4 20.1 22.1 24.1 26.0 28.9 31.9 35.0 37.9 40.9

5.9 6.0 6.2 6.7 7.0 7.8 8.6 10.2 11.6 12.9 14.3 16.6 19.1 21.9 24.8 28.2

0.45 0.98 1.34 1.80 2.44 3.31 4.18 5.03 5.35 5.75 5.85 5.85 5.85 5.85 5.85 5.85

0 0 0 0 0 0 0.50 1.29 3.05 4.96 6.48 9.85 12.85 17.10 21.58 26.01

5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0

NI(f) 0.9 1.0 1.2 1.7 2.1 2.8 3.4 4.1 4.5 4.9 5.0 5.0 5.0 5.0 5.0 5.0

NB 0 0 0 0 0 0 0.2 1.1 2.1 3.1 4.3 6.6 9.1 11.9 14.8 18.2

fully hydrated). This indicates the existence of a specific region (8 < Nw < 15), taken as a pre–region [6,8,9,21,22] and designated by hatch lines in Fig. 13. In this region, the bulk water content likewise increases, little by little, until the maximum amount of freezable interlamellar water is reached. Above this amount, all the added water is present as bulk water, so that the ∆HB curve becomes parallel to the straight ∆HT line. Furthermore, a point to notice in Fig. 13, except for the pre-region, is the difference in slope between the linear curves of ∆HI(f) (Nw < 8) and ∆HB (Nw > 15). Thus, although the ∆HI(f) curve is also linear at Nw values below the preregion, it is not parallel to the ∆H T line and therefore not parallel to the linear ∆H B curve at Nw values above the pre-region. The slopes of the linear curves of ∆HB and ∆HI(f) are characterized only by the bulk and freezable interlamellar water, respectively, and so give individual molar ice-melting enthalpies for both types of water. On this basis, the individual average molar melting enthalpies for the bulk and freezable interlamellar water were estimated from the slopes of the respective straight ∆HB and ∆H I(f) lines obtained by a least squares method.

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The average melting enthalpy for the bulk water is 1.420 kcal/mol H2O and is very close to the known value estimated from the ∆H T line. For the freezable interlamellar water, the estimated average melting enthalpy is 1.201 kcal/mol H2O and is smaller than that for the bulk water. The above estimates evidence a difference in the molar ice-melting enthalpy between the freezable interlamellar and bulk water, and this difference is related to different hydrogen bond modes for the two types of water. Again, we remark on the linear relationship between ∆HI(f) and Nw observed at water contents below the pre-region. This indicates that the molar melting enthalpy for the freezable interlamellar water is nearly the same for 5 < N w < 8. However, this result does not agree with our analysis because the multiplecomponent deconvolutions of the ice-melting peak for the freezable interlamellar water suggest the existence of water molecules in different hydrogen bond modes. The values of NI(nf), NI(f), and NB for varying water contents were estimated according to the method discussed above, and the results are summarized in Table 1. Furthermore, in Fig. 14, the cumulative values of NI(nf), NI(f), and NB are

FIG. 14 Water distribution diagram for the gel phase of the DPPC–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted against N w.


267

plotted against Nw. On the basis of the water distribution diagram, the following results are obtained for the gel phase of the DPPC–water system: 1. The limiting, maximum numbers of water molecules are approximately 5 H2O and 5 (= 10 – 5) H2O per molecule of lipid for the nonfreezable and freezable interlamellar water, respectively. 2. These maximum values are reached at water/lipid molar ratios of approximately 5 and 15, respectively. 3. The pre-region exists in the range of ~8 < Nw < ~15 before the attainment of full hydration of the gel phase. B. DMPE–Water System [21] A series of ice-melting DSC peaks for the DMPE–water system is shown in Fig. 15. In this figure, the ice-melting curve c at Nw ~ 3 is shown to deviate from

FIG. 15 A series of ice-melting DSC curves at varying water contents for the gel phase of the DMPE–water system. Water contents (wt%): a, 2.3 (0.8); b, 6.0 (2.25); c, 8.0 (3.1); d, 10.2 (4.0); e, 12.2 (4.9); f, 14.1 (5.8); g, 16.1 (6.8); h, 18.1 (7.8); i, 20.0 (8.8); j, 22.0 (10.0); k, 25.0 (11.8); l, 28.0 (13.7); m, 32.0 (16.6). The numbers in parentheses show the corresponding N w values.

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similar shapes observed for N w > 3. This is the same phenomenon as that observed in the DPPC–water system (see Fig. 8), for which the amount of freezable interlamellar water is less than 1 H2O per molecule of lipid. Deconvolution results of the ice-melting curves are compared at different water contents in Fig. 16. The broad peak for the freezable interlamellar water is shown to be finally deconvoluted into three curves designated I, II, and III. In Fig. 17, the estimated sum of the icemelting enthalpy ∆HI(f) for the freezable interlamellar water is plotted against Nw and is compared with the ∆HB curve obtained from the deconvoluted curve IV for the bulk water, together with the ∆H T line. A gentle increase with water content is observed for both the ∆HI(f) and ∆H B curves over the Nw range from approximately 4 to 10, indicating the existence of a pre-region similar to that observed for the DPPC–water system. Except for the pre-region, both the ∆H I(f) and ∆H B curves are linear for N w < 4 and N w > 10, respectively. The

FIG. 16 Deconvolution analysis of ice-melting DSC curves for the gel phase of the DMPE–water system. Water contents (wt%): a, 10.2 (4.0); b, 12.2 (4.9); c, 14.1 (5.8); d, 22.0 (10.0). The numbers in parentheses show the corresponding N w values. The deconvoluted curves (I–IV) and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.


269

FIG. 17 Comparison of ∆HT, ∆HB, and ∆HI(f) curves for the gel phase of the DMPE– water system.

linear ∆HI(f) line intersects the abscissa at Nw = 2.3, whereas the linear ∆H B line extrapolated to Nw < 10 intersects the abscissa at Nw ~ 6. Thus, the maximum numbers of interlamellar water molecules are estimated to be 2.3 H2O and 3.7 (= 6 –2.3) H 2 O per molecule of lipid for the nonfreezable and freezable interlamellar water, respectively. On the other hand, similarly to the case of the DPPC–water system, the linear ∆HB line is almost parallel to the straight ∆HT line, in contrast to the linear ∆HI(f) line, which is characterized by a slope of 1.283 kcal/mol H2O. The N I(nf), NI(f), and NB values at varying water contents were calculated from Eq. (3). Table 2 summarizes data concerning ∆HI(f) and ∆HB and also values of NI(nf), NI(f), and NB at increasing water contents (WH2O) shown together with

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Table 2 Ice-Melting Enthalpies of Freezable Interlamellar and Bulk Water, ∆H I(f) and ∆H B , Respectively, per Mole of Lipid and the Numbers of Nonfreezable and Freezable Interlamellar and Bulk Water Molecules, NI(nf) , NI(f), and NB, Respectively, per Lipid Molecule at Varying Water Contents (W H2O ) in the Gel Phase of the DMPE– Water System Ice-melting enthalpy (per mole of lipid) (kcal)

Number of water molecules (per molecule of lipid)

WH2O System

(wt%)

Nw

∆HI(f)

∆HB

a b c d e f g h i j k l m

2.3 6.0 8.0 10.2 12.2 14.1 16.1 18.1 20.0 22.0 25.0 28.0 32.0

0.8 2.2 5 3.1 4.0 4.9 5.8 6.8 7.8 8.8 10.0 11.8 13.7 16.6

0 0 1.09 2.45 3.41 3.90 4.34 4.56 4.85 4.98 5.06 5.02 5.11

0 0 0 0 0.25 1.05 1.97 3.04 4.28 5.76 8.21 11.13 15.07

NI(nf) 0.8 2.2 5 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3

N I(f)

NB

0 0 0.8 1.7 2.4 2.8 3.1 3.4 3.5 3.7 3.7 3.7 3.7

0 0 0 0 0.2 0.7 1.4 2.1 3.0 4.0 5.8 7.7 10.6

the corresponding Nw values for the gel phase of the DMPE–water system. The water distribution diagram is shown in Fig. 18 for the gel phase of the DMPE– water system. C. DPPG–Water System [22] A series of typical ice-melting DSC peaks for the DPPG–water system are compared in Fig. 19A. However, the onset temperature of the sharp peak of ice-melting endotherms is about 3–4°C lower than that of the corresponding peak for the neutral lipid systems discussed above. In other words, the temperature axis of the sharp peak is shifted by 3–4°C to the lower temperature side. This suggests that the bonding mode of the freezable interlamellar water is very close to that of the bulk water. Accordingly, the deconvolution of the sharp peaks of the DPPG system was performed by setting up a new Gaussian curve other than that for the bulk water, as shown in Fig. 19B. Furthermore, the water content of this system was continuously changed up to 90 wt% (Nw = 374) to investigate whether the hydration is limited or infinite. In Fig. 20, curves of ∆HT, ∆HI(f), and ∆HI(nf) are compared up to Nw = 250.


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FIG. 18 Water distribution diagram for the gel phase of the DMPE–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus Nw.

The water distribution diagram of this system is shown over the wide Nw range up to 400 in Fig. 21A. In addition, for comparison with the DPPC and DMPE systems, an enlarged scale diagram of the DPPG system up to Nw = 50 is shown in Fig. 21B. A characteristic feature of this diagram is the infinite uptake of freezable interlamellar water, i.e., infinite hydration of DPPG bilayers, in contrast with the limited hydration of the neutral lipid bilayers discussed above. Thus, as shown in Fig. 20, the linear ∆HB line observed for Nw > 150 is not parallel to the straight ∆HT line, showing an increase in the enthalpy difference between the ∆HT and ∆HB given in Eq. (3) with increasing water content. This is reflected in the ∆H I(f) curve, which continues to increase up to N w = 400. Furthermore, it is shown by this figure that the bulk water of this system begins to appear at Nw ~ 35, which is quite a bit higher than the corresponding Nw values of approximately 8 and 4 for the DPPC and DMPE systems, respectively. These facts indicate that both the freezable interlamellar and bulk water continuously increase over the wide Nw range (35–400) investigated, as shown in Fig. 21. In this case,

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FIG. 19 (A) A series of ice-melting DSC curves at varying water content for the gel phase of the DPPG–water system. Water contents (wt%): a, 8.1 (3.6); b, 11.9 (5.6); c, 14.1 (6.8); d, 16.0 (7.9); e, 18.0 (9.1); f, 21.1 (11.1); g, 23.9 (13.0); h, 27.0 (15.3); i, 29.9 (17.7); j, 34.9 (22.1); k, 39.9 (27.4); l, 44.9 (33.7); m, 49.9 (41.2). The numbers in parentheses show the corresponding Nw values. (B) Deconvolution analysis of ice-melting DSC curve j shown in (A). The deconvoluted curves (I–V) and their sum (the theoretical curve) are shown by dotted lines, and the DSC curve is represented by a solid line.

FIG. 20 Comparison of ∆H T , ∆H B , and ∆H I(f) curves for the gel phase of the DPPG–water system.


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FIG. 21 Water distribution diagram up to (A) N w = 400 and (B) Nw = 50 for the gel phase of the DPPG–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus Nw.

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the overall regions for Nw > ~ 35 would be taken as the pre-region, since there is no saturation point for the hydration of the gel phase. VII. SUBGEL PHASES IN LIPID–WATER SYSTEMS In Fig. 22, three typical types of DSC curves are shown for the DMPE–water system at the same water content. A distinct difference in the thermal behavior is observed not only for the phase transition of the lipid but also for the melting of the ice. Figure 23 shows a schematic diagram of relative enthalpy (∆H) versus temperature (t) curves that was constructed on the basis of the transition enthalpies and temperatures associated with the lipid phase transitions shown in Fig. 22. By reference to the diagram, it becomes apparent that the DMPE–water system can be present in two phases, designated the L- and H-subgel phases, other than the gel phase at temperatures where the hydrocarbon chains of the lipids are in a solid-like state and the thermodynamic stability of these phases increases

FIG. 22 Three typical types of DSC curves of the DMPE–water system at the same water content (W H2O = 25.0 wt%, N w = 11.8). The phase transition peaks of the lipid are characterized as (a) gel to liquid crystal, (b) L-subgel to gel followed by gel to liquid crystal, and (c) H-subgel to liquid crystal.


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FIG. 23 Schematic diagram of the relative enthalpy (∆H) versus temperature (t) for the DMPE–water system, constructed from the transition enthalpies and temperatures associated with the lipid phase transitions shown in Figs. 22a–22c. The system is also present in the H- and L-subgel phases, which are different from the gel phase.

in the order gel < L-subgel < H-subgel. The designations L and H for the subgel phases are due to their transitions, which appear, respectively, at temperatures lower and higher than that of the gel-to-liquid crystal phase transition. As shown in Fig. 24, similar behavior is observed for the DPPC–water system, although the H-subgel phase is missing in this system. To date, many studies on the stability of the gel phase have been performed for various phospholipids (PC, Refs. 1, 14–16, 24–26; PE, Refs. 18–20, 27–32; PG, Refs. 33–39), and it is generally accepted that the gel phase is a metastable state. Thus, the gel phase, which is first realized by cooling the liquid crystal phase to temperatures below that of the phase transition, converts into more stable phases, generally called subgel phases. In this conversion, lateral packings of the lipid molecules in the intrabilayer are changed with a view to enhancing the van der Waals interaction force operating between the hydrocarbon chains [46,47]. In fact, the difference in the van der Waals interaction energy between the gel and subgel phases calculated from the chain–chain separation is consistent with the calorimetric enthalpy difference between the two phases [30,33,39]. However, such a conversion is achieved only when the thermal annealing adopted for the gel phase is adequate. Therefore, it is necessary to search for adequate annealing conditions relating to a temperature range and a time period. In the case of the DMPE–water system,

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FIG. 24 Two typical types of DSC curves of the DPPC–water system at the same water content (W H2O = 28.0 wt%, N w = 15.9), characterized by the lipid phase transitions of (a) gel to liquid crystal and (b) L-subgel to gel followed by gel to liquid crystal.

the annealing condition is different for the respective conversions to the L- and Hsubgel phases [18–20]. Thus, the conversion to the L-subgel phase is achieved by annealing at temperatures of –5 to +5°C for periods of 2–4 weeks (depending on the water content of the sample). For the conversion to the H-subgel phase, two steps of annealing at different temperatures are necessary; the gel sample is kept at around –60°C for at least 5 h (nucleation) and is then kept at a temperature just below the gel-to-liquid crystal phase transition for about 24 h (nuclear growth). For the DPPC–water system, a two-step annealing for the processes of nucleation at –60°C and nuclear growth at 4°C is required to complete the conversion to the Lsubgel phase [16]. For a DPPC sample that is not fully hydrated, a long period of annealing, up to 3 weeks, is required for the process of nuclear growth. Accordingly, the lipid phase transitions for the DMPE system shown in Figs.


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22a, 22b, and 22c are from the gel, L-subgel, and H-subgel to the respective liquid crystal phases, and the transitions for the DPPC system shown in Figs. 24a and 24b are from the gel and L-subgel to the respective liquid crystal phases. The difference in the ice-melting behavior observed in Figs. 22 and 24, respectively, indicates the difference in the state of the water molecules between the gel and subgel phases of solidlike hydrocarbon chains. The ice-melting endotherm for the L-subgel phase of the DMPE system in Fig. 22b is characterized by a shoulder peak at around –5°C, and the endotherm for the H-subgel phase (Fig. 22c) is characterized by an enlarged sharp peak at around 0°C. Similarly, the ice-melting endotherm for the L-subgel phase of the DPPC system in Fig. 24b presents a shoulder peak at around –5°C. Such differences are reflected in the ∆HB and ∆HI(f) curves and the water distribution diagram for the subgel phases of the DPPC and DMPE systems. VIII. ANALYSIS OF WATER MOLECULES IN THE SUBGEL PHASES OF LIPID–WATER SYSTEMS A. DPPC–Water System Gel samples with varying water contents of the DPPC system were annealed according to the procedure described above. DSC curves for the resultant L-subgel phase are compared at varying water contents in Fig. 25. Furthermore, to make clear the difference in the ice-melting behavior between the gel and subgel phases, the results of the deconvoluted ice-melting curves are compared for the two phases at the same water content in Fig. 26. Compared with the individual deconvoluted curves for the gel phase, the areas of the deconvoluted curves I, II, and III for the Lsubgel phase decrease, respectively, but that of the deconvoluted curve IV increases. Consequently, as shown in Fig. 27, the ∆H I(f) curve for the subgel phase is lower than that for the gel phase (dashed lines) over all water contents tested, and the intersection point of the extrapolated linear ∆H I(f) line with the abscissa gives approximately 6 H2O per molecule of lipid as the maximum number of nonfreezable interlamellar water molecules for the L-subgel phase of the DPPC system. This limiting value is larger by 1 H2O per molecule of lipid than the corresponding value for the gel phase. Furthermore, as shown in Fig. 27, ∆HB for the subgel phase increases along a curve nearly the same as that of ∆HB for the gel phase (dashed lines), although there are some inconsistencies in the preregion. This indicates that the amount of total (nonfreezable plus freezable) interlamellar water is nearly the same for the gel and subgel phases at each N w. The water distribution diagram for the L-subgel phase was prepared from the estimated values of N I(nf), N I(f), and N B, and the resultant diagram is shown in Fig. 28. The amount of nonfreezable water for the L-subgel phase is

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FIG. 25 (A) A series of DSC curves of the DPPC–water system for samples thermally annealed according to the procedure described in the text. Water contents are from 10.8 wt% (N w = 4.9) to 35.0 wt% (N w = 21.9). (B) Ice-melting curves and lipid transition peaks of L-subgel to gel phase are compared, in an enlarged scale. Water contents (wt%): a, 10.8 (4.9); b, 12.8 (6.0); c, 16.1 (7.8); d, 17.4 (8.6); e, 20.1 (10.2); f, 22.1 (11.6); g, 23.8 (12.8); h, 24.8 (13.7); i, 28.0 (15.9); j, 31.1 (18.4); k, 35.0 (21.9). The numbers in parentheses show the corresponding N w values.


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FIG. 26 Comparison of deconvoluted ice-melting curves between (a) L-subgel phase and (b) gel phase of the DPPC–water system at the same water content (W H O = 28.0 2 wt%, N w = 15.9). The deconvoluted curves (I–V) and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.

greater by approximately one H2O per molecule of lipid than that for the gel phase over all water contents at Nw > 6. The extra nonfreezable interlamellar water, characteristic of the L-subgel phase, is shown to arise from the freezable interlamellar water present in the gel phase. Furthermore, it is seen from Fig. 26 that the bonding mode of a great part of the freezable interlamellar water of the L-subgel phase is very close to that of the bulk water.

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FIG. 27 ∆HB and ∆H I(f) curves for the L-subgel phase of the DPPC–water system. For comparison, corresponding curves for the gel phase are shown by dashed lines.

FIG. 28 Water distribution diagram for the L-subgel phase of the DPPC–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus Nw.


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FIG. 29 A series of DSC curves of the DMPE–water system for samples (N w > 10) annealed according to the procedure described in the text. Water contents (wt%): a, 21.1 (9.4); b, 25.5 (12.1); c, 28.2 (13.9); d, 30.7 (15.6). The numbers in parentheses show the corresponding N w values. The ice-melting curves are followed by the lipid phase transitions of L-subgel to gel and gel to liquid crystal.

B. DMPE–Water System * In Fig. 29, DSC curves of the DMPE system for the L-subgel phase obtained by annealing are compared at different water contents for Nw > 10, because conversion of the gel to both L- and H-subgel phases (which are different in stability) is observed only when the gel phase is not fully hydrated (Nw < 10). In Fig. 30, deconvoluted ice-melting curves are compared for the L-subgel and gel phases at the same water content, as an example. A marked enlargement of the deconvoluted curve III for the freezable interlamellar water is observed in the L-subgel phase, similarly to that observed for the L-subgel phase of the DPPC system

* See also Refs. 18–20.

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FIG. 30 Comparison of deconvoluted ice-melting curves between (a) L-subgel and (b) gel phases of the DMPE–water system at the same water content (WH O = 22.0 wt%, N w 2 = 10.0). The deconvoluted curves (I–IV) and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.

shown in Fig. 26. Simultaneously, a decrease of the deconvoluted curve IV for the bulk water is observed in the L-subgel phase. In Fig. 31, a ∆H B vs. N w curve for the L-subgel phase of the DMPE system is shown, along with the corresponding curve for the gel phase (dashed lines). The amount of bulk water for the L-subgel phase is shown to be smaller by approximately one molecule of H2O per molecule of lipid than that for the gel phase over all water contents at Nw > 10.


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FIG. 31 Comparison of ∆H B and ∆H I(f) curves for the L-subgel phase of the DMPE– water system at N w > 10. Corresponding curves for the gel phase are shown by dashed lines.

The maximum total amount (nonfreezable plus freezable) of interlamellar water estimated from the extrapolated line is approximately 7 H2O/lipid for the L-subgel phase, which is larger by 1 H2O/lipid than that (6 H2O/lipid) for the fully hydrated gel phase. Furthermore, the ∆HI(f) vs. Nw curve for a fully hydrated L-subgel phase shown in Fig. 31 is almost identical with the corresponding curve for the gel phase (dashed lines). On this basis, although there are no data for N w < 10 (i.e., it is impossible to estimate from the value of N w where the ∆H I(f) curve intersects the abscissa), the maximum amount of freezable interlamellar water for the Lsubgel phase is evaluated to be comparable to that for the gel phase, i.e., approximately 3.7 (= 6 – 2.3) molecules of H 2 O per molecule of lipid. Consequently, the maximum amount of nonfreezable interlamellar water for the L-subgel phase is estimated to be approximately 3.3 (= 7 – 3.7) molecules of H 2 O per molecule of lipid and is found to increase by about 1 H 2 O/lipid compared with the gel phase (2.3 H 2 O/lipid). The increment of nonfreezable interlamellar water is comparable to that observed for the L-subgel phase of the

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FIG. 32 Water distribution diagram for the L-subgel phase (N w > 10) of the DMPE– water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus N w.

DPPC system. Accordingly, it is suggested that in the conversion of the gel to the L-subgel phase, one molecule of H 2O per molecule of lipid of the freezable interlamellar water present in the gel phase changes to nonfreezable interlamellar water in regions between the lipid headgroups in the resultant subgel phase. However, such a migration of water molecules would induce an empty space in the interbilayer regions, and this space would be filled by an infusion of the bulk water existing outside the bilayer. As a result, compared with the gel phase, the amount of bulk water of the L-subgel phase is less by one molecule of H2O per molecule of lipid and the amount of freezable interlamellar water is the same, as shown by a comparison of the water distributions in Figs. 18 and 32 for the two phases. However, no participation of bulk water in the conversion of the gel to the L-subgel phase by annealing is observed for the DPPC system, differently from the DMPE system. On the other hand, complete conversion of the gel to the H-subgel phase by


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annealing was observed even at a low water content at which only nonfreezable interlamellar water is present in the gel phase (i.e., in the absence of freezable interlamellar and bulk water). This is contrasted with the conversion to the Lsubgel phase discussed above. An example of deconvolution analysis of the icemelting peak for the H-subgel phase is shown in Fig. 33, and curves of ∆HB vs. Nw and ∆HI(f) vs. Nw for this phase are shown in Fig. 34, along with the corresponding curves for the gel phase. In Fig. 33, the deconvoluted curves I and II are not observed for the H-phase. Accordingly, the extrapolated ∆H I(f) line for

FIG. 33 Deconvoluted ice-melting curves of (a) H-subgel phase and (b) gel phase of the DMPE–water system at the same water content (W H O = 22.0 wt%, N w = 10.0). The 2 deconvoluted curves (I–IV) and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.

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FIG. 34 ∆H B and ∆H I(f) curves for the H-subgel phase of the DMPE–water system. Corresponding curves for the gel phase are shown by dashed lines.

the H-subgel phase is shown to intersect the abscissa at an extremely low Nw value of around 0.3, indicating that there is almost no nonfreezable interlamellar water for this phase. In contrast, the deconvoluted curve IV for bulk water shown in Fig. 33 is markedly enlarged for the H-subgel phase, so that the ∆HB curve for this phase is noticeably higher than that for the gel phase (dashed lines) over all water contents studied. The extrapolated linear ∆H B line for the H-subgel phase, which is parallel to the ∆HT line, gives the maximum amount of total interlamellar water as approximately 1.3 H2O/lipid. Consequently, the amount of freezable interlamellar water is estimated to be approximately 1 (= 1.3 – 0.3) H2O/ lipid for the fully hydrated H-subgel phase. The water distribution diagram for the H-subgel phase is shown in Fig. 35. In the conversion of the fully hydrated gel to the H-subgel phase, as many as 4.7 (= 6 – 1.3) interlamellar water molecules per molecule of lipid are excluded outside the bilayers and present as bulk water in the resultant H-subgel phase. The 4.7 H 2 O/lipid comes from 2.0 (= 2.3 – 0.3) nonfreezable interlamellar water molecules plus 2.7 (= 3.7 – 1) freezable interlamellar water molecules present in the gel phase.


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FIG. 35 Water distribution diagram for the H-subgel phase of the DMPE–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus Nw.

IX. ROLE OF WATER MOLECULES IN PHASE TRANSITIONS OF LIPIDS Finally, we discuss the role of interlamellar water in lipid phase transitions. As shown in Fig. 36, the phase behavior of the lipid in the DMPE–water system is complex in the absence of freezable interlamellar water [21]. Presumably, in a region of such low water content, the lipid bilayers exist as hydrated crystals containing only nonfreezable interlamellar water. However, with the appearance of freezable interlamellar water (curves d–m), the lipid phase transition comes to be characterized by a certain peak that is gradually shifted to lower temperatures with increasing water content and finally converges to a fixed temperature, generally ascribed to the gel-to-liquid crystal phase transition. Such phase behavior suggests that freezable interlamellar water is absolutely necessary for the formation of the gel phase of lipid–water systems. In this respect, another noticeable point is that the fixed peak of the gel-to-liquid crystal transition is obtained above a certain water content where a maximum uptake of the freezable interlamellar

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FIG. 36 Variation of the transition peak of gel to liquid crystal phase with increasing water content for the DMPE–water system. Water contents (wt%); a, 2.3 (0.8); b, 6.0 (2.25); c, 8.0 (3.1); d, 10.2 (4.0); e, 12.2 (4.9); f, 14.1 (5.8); g, 16.1 (6.8); h, 18.1 (7.8); i, 20.0 (8.8); j, 22.0 (10.0); k, 25.0 (11.8); l, 28.0 (13.7); m, 32.0 (16.6). The numbers in parentheses show the corresponding N w values.

water is attained (curves j–m). Thus, as shown for the DMPE system in Fig. 37, both the lipid transition temperature and the half-height width of the transition peak are constant for Nw > 10, at which the limiting, maximum amount of freezable interlamellar water is reached. A similar role for the freezable interlamellar water is observed for the DPPC–water system. Thus, as shown in Fig. 38, fixed transition peaks are obtained not only for the main transition (Pβ’ gel to liquid crystal) but also for the pretransition (L β’ gel to Pβ’ gel) at water contents above


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FIG. 37 Variation with increasing N w of the temperature (t m ) of the gel-to-liquid crystal phase transition and of the half-height width (∆T 1/2) of its transition peak in the DMPE–water system.

the limiting point (N w ~ 15–16) of the freezable interlamellar water shown in Fig. 14. Furthermore, focusing on the pretransition in Fig. 38, it is noticeable that a growth of the transition peak from a trace up to a fixed large peak takes place in the pre-region of 8 < Nw < 15 shown in Fig. 14. Considering that the pretransition is a phenomenon characteristic of tilted hydrocarbon chains adopted by a lipid that has bulky headgroups [48], the growth of the pretransition peak in the pre-region suggests that the hydrocarbon chains of DPPC become more tilted up to Nw ~ 15 at the saturation point of the lipid with freezable interlamellar water. Furthermore, from the standpoint of water, it is suggested that the appearance of bulk water in the pre-region—namely, prior to the limiting uptake of the freezable interlamellar water—is caused by a change in the bilayer lamellae from planar to curved surfaces and finally to a vesicular form [6,8,9,21,22]. Presumably, the water trapped within regions between adjacent vesicular assemblies behaves like bulk water. However, such structural changes in the pre-region would induce higher surface curvatures of the bilayer, resulting in looser packing of the hydrocarbon chains and consequently in weaker

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FIG. 38 A series of DSC curves focusing on the lipid transitions of the L β’ gel to P β’ gel and P β’ gel to liquid crystal phases of the DPPC–water system. Water contents (wt%): a, 12.6 (5.9); b, 12.8 (6.0); c, 13.1 (6.2); d, 14.1 (6.7); e, 16.1 (7.8); f, 17.4 (8.6); g, 20.1 (10.2); h, 22.1 (11.6); i, 24.1 (12.9); j, 26.0 (14.3); k, 31.9 (19.1); l, 35.0 (22.0); m, 38.9 (25.9). The numbers in parentheses show the corresponding N w values.

van der Waals interaction energies for them. Therefore, to compensate for the energy loss, the hydrocarbon chains would adopt more tilted positions in order to shorten the chain–chain separation related to the van der Waals energy [30,33,39]. This seems to be the reason for the appearance of the pretransition peak and its saturation observed in the pre-region. On the other hand, as discussed above, the L-subgel phase of the DPPC–water system involves the extra nonfreezable interlamellar water up to one molecule of H 2 O per molecule of lipid, compared with the gel phase. This nonfreezable interlamellar water comes from the freezable interlamellar water present in the gel phase, indicating the critical role of this freezable water in the conversion of the gel to the L-subgel phase. In fact, as shown in Fig. 25B, the conversion to the L-subgel phase by annealing is not realized for a gel sample at N w < 5 (see curve a), i.e., when there is no freezable interlamellar water (see Fig. 14). Furthermore, as shown in Fig. 25B, the fixed peak of the L-subgel-to-gel phase transition is observed above Nw ~ 12–13 where the subgel phase is fully hydrated (see


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Fig. 28), although the Nw value is lower than the corresponding Nw ~ 15–16 for the gel phase (see Fig. 14). This fact indicates that both the fully hydrated subgel and gel phases are characterized by limiting, fixed peaks of their transitions to the respective high temperature phases. This is because, after the attainment of the fully hydrated gel and subgel phases, lateral packings of lipid molecules in a bilayer are unchangeable, even though the water content is further increased [49]. Finally, the most stable H-subgel phase of the DMPE system, which directly transforms to the liquid crystal phase, is discussed from the standpoint of the interlamellar water. As shown in Fig. 35, the H-subgel phase is characterized by a much smaller amount of interlamellar water compared with the L-subgel and

FIG. 39 Variation of a lipid transition peak with increasing water content for the DPPG– water system. Water contents (wt%): a, 23.9 (12.0); b, 29.9 (17.7); c, 39.9 (27.5); d, 49.6 (40.7); e, 60.0 (62.1); f, 69.9 (96.1); g, 74.9 (123.0); h, 80.0 (166.0); i, 85.0 (235.0); j, 90.0 (373.0). The numbers in parentheses show the corresponding N w values.

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gel phases (see Figs. 18 and 32), and so conversion of the gel to the H-subgel phase by annealing accompanies the exclusion of the interlamellar water. Accordingly, the conversion does not require the presence of freezable interlamellar or bulk water in the gel phase, in contrast with the conversion of the gel to the L-subgel phase. In fact, the conversion is accomplished, even for a gel sample containing as little as 5 wt% water (Nw = 1.8) where only nonfreezable interlamellar water is present (see Fig. 18). In addition, a fixed transition peak to the liquid crystal phase is observed for the fully hydrated H-subgel phase, like the transitions for the fully hydrated gel and L-subgel phases in the DPPC and DMPE systems. However, as shown in Fig. 39, a fixed transition peak is not observed for the infinitely hydrated DPPG gel phase (see Fig. 21), and the hydration results in disruption of the multilamellar vesicles into unilamellar vesicles in a dilute aqueous region [22,43,50–53].

REFERENCES 1. 2. 3. 4. 5. 6.

MJ Ruocco, G Shipley. Biochim Biophys Acta 691:309 (1982). TJ McIntosh, SA Simon. Biochemistry 25:4058 (1986). TJ McIntosh, SA Simon. Biochemistry 25:4948 (1986). JM Seddon, G Cevc, RD Kayer, D Marsh. Biochemistry 23:2634 (1984). RP Rand, VA Parsegian. Biochim Biophys Acta 988:351 (1989). G Klose, B König, HW Meyer, G Schulze, G Degovics. Chem Phys Lipids 47:225 (1988). 7. MC Wiener, RM Suter, JF Nagle. Biophys J 55:315 (1989). 8. JF Nagle, R Zhang, T Stephanie-Nagle, W Sun, HI Petrache, RM Suter. Biophys J 70:1419 (1996). 9. K Gawrisch, W Richter, A Möps, P Balgavy, K Arnold, G Klose. Studia Biophys 108:5 (1985). 1 0 . J Ulmius, H Wennerström, G Lindblom, G Arvidson. Biochemistry 16:5742 (1977). 1 1 . EG Finer, A Darke. Chem Phys Lipids 12:1 (1974). 1 2 . D Chapman, RM Williams, BD Ladbrooke. Chem Phys Lipids 1:445 (1967). 1 3 . M Kodama, M Kuwabara, S Seki. Thermochim Acta 50:81 (1981). 1 4 . M Kodama, H Hashigami, S Seki. Thermochim Acta 88:217 (1985). 1 5 . M Kodama. Thermochim, Acta 109:81 (1986). 1 6 . M Kodama, H Hashigami, S Seki. J Colloid Interface Sci 117:497 (1987). 1 7 . M Kodama, S Seki. Adv Colloid Interface Sci 35:1 (1991). 1 8 . M Kodama, H Inoue, Y Tsuchida. Thermochim Acta 266:373 (1995). 1 9 . H Aoki, M Kodama. J Thermal Anal 49:839 (1997). 2 0 . H Takahashi, H Aoki, H Inoue, M Kodama, I Hatta. Thermochim Acta 303:93 (1997). 2 1 . M Kodama, H Aoki, H Takahashi, I Hatta. Biochim Biophys Acta 1329:61 (1997). 2 2 . M Kodama, J Nakamura, T Miyata, H Aoki. J Thermal Anal 51:91 (1998). 2 3 . JF Nagle, MC Wiener. Biochim Biophys Acta 942:1 (1988). 2 4 . SC Chen, JM Sturtevent, BJ Gaffeny. Proc Natl Acad Sci USA 77:5060 (1980).

293 2 5 . HH Fuldner. Biochemistry 20:5705 (1981). 2 6 . DG Cameron, HH Mantsh. Biophys J 38:175 (1982). 2 7 . H Chang, RM Epand. Biochim Biophys Acta 728:319 (1983). 2 8 . HH Mantsch, SC Hsi, KW Butler, DG Cameron. Biochim Biophys Acta 728:325 (1983). 2 9 . S Mulukutla, GG Shipley. Biochemistry 23:2514 (1984). 3 0 . DA Wilkinson, JF Nagle. Biochemistry 23:1538 (1984). 3 1 . J Silvius, PM Brown, TJ O’Leary. Biochemistry 25:4249 (1986). 3 2 . PM Brown, J Steers, SW Hui, PL Yeagle, JR Silvius. Biochemistry 25:4259 (1986). 3 3 . DA Wilkinson, TJ McIntosh. Biochemistry 25:295 (1986). 3 4 . AE Blaurock, TJ McIntosh. Biochemistry 25:299 (1986). 3 5 . KK Eklund, IS Salonen, PKJ Kinnunen. Chem Phys Lipids 50:71 (1989). 3 6 . IS Salonen, KK Eklund, JA Virtanen, PKJ Kinnunen. Biochim Biophys Acta 982:205 (1989). 3 7 . RM Epand, B Gabel, RF Epand, A Sen, SW Hui, A Muga, WK Surewicz. Biophys J 63:327 (1992). 3 8 . M Kodama, T Miyata, T Yokoyama. Biochim Biophys Acta 1168:243 (1993). 3 9 . M Kodama, H Aoki, T Miyata. Biophys Chem 79:205 (1999). 4 0 . R Harrison, GG Lunt. Biological Membranes, 2nd ed., Blackie, London, 1980, p. 68. 4 1 . GG Shipley. In Handbook of Lipid Research, Vol. 4 DM Small, ed., Plenum Press, New York, 1986, p. 97. 4 2 . JM Boggs. Biochim Biophys Acta 906:353 (1987). 4 3 . M Kodama, T Miyata. Colloid Sur A 109:283 (1996). 4 4 . H Hauser, I Pascher, RH Pearson, S Sundell. Biochim Biophys Acta 650:21 (1981). 4 5 . I Pascher, S Sundell, K Harlos, H Eibl. Biochim Biophys Acta 896:77 (1987). 4 6 . JF Nagle, DA Wilkinson. Biophys J 23:159 (1978). 4 7 . DA Wilkinson, JF Nagle. Biochemistry 20:187 (1981). 4 8 . TJ McIntosh. Biophys J 29:237 (1980). 4 9 . G Cevc, D Marsh. Biophys J 47:21 (1985). 5 0 . D Atkinson, H Hauser, GG Shipley, JM Stubbs. Biochim Biophys Acta 339:10 (1974). 5 1 . H Hauser, F Paltauf, GG Shipley. Biochemistry 21:1061 (1982). 5 2 . H Hauser. Biochim Biophys Acta 772:37 (1984). 5 3 . M Kodama, T Miyata. Thermochim Acta 267:365 (1995).


8 Heat Evolution of the Self-Assembly of Amphiphiles in Aqueous Solutions DOV LICHTENBERG, ELLA OPATOWSKI, and MICHAEL M. KOZLOV Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel I.

Introduction

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II.

General Theoretical Considerations A. The origin of self-assembly B. Factors determining the cmc C. ITC measurements, major findings, and interpretation D. Enthalpy associated with dissolving hydrocarbons E. The enthalpy of micelle formation

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III.

Experimental Titration Protocols, Procedures, and Interpretation of Data A. Determination of the heat evolution of the self-assembly of surfactants B. Partitioning of solutes between membranes and aqueous solutions C. The heat evolution of bilayer–micelle phase transformation in mixtures of phospholipids and detergents

IV.

V.

Heat Evolution of the Transfer of Amphiphilic Molecules Between Aggregates and Water A. Heat of micellization and its dependence on temperature and composition B. Heat of partitioning of amphiphiles between lipid bilayers and aqueous media C. Heat of phase transformations in mixtures of bilayer-forming and micelle-forming amphiphiles

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Concluding Remarks

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References

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I. INTRODUCTION A common feature of all amphiphiles is their tendency to self-assemble in aqueous solutions above a critical concentration, denoted as the critical aggregation concentration or, for micelle-forming amphiphiles (surfactants), the critical micellar concentration, abbreviated cmc [1–3]. The structure of the resultant aggregates depends on the molecular geometry of the amphiphiles and varies from micelles of various geometries (e.g., spheres, ellipsoids, or rods) to bilayers, cubic, or hexagonal phases [4,5]. The driving force for the self-assembly is the hydrophobic effect resulting from interplay between entropic and enthalpic contributions to the free energy of the process. Although the entropic effects are believed to be the leading ones in most cases, the enthalpy associated with the self-assembly is of fundamental interest because it reflects the energetics of the many molecular interactions involved in the process. This enthalpy is a complex and not fully understood function of the molecular structure of the amphiphile, the composition of the aqueous medium, and the temperature. In reviewing the existing data, we try to contribute to the understanding of these relationships. The enthalpy of micellization of many surfactants in aqueous solution has been determined in the past, using mostly cell type and flow microcalorimeters [6–8]. These determinations were based on measurements of the excess heat associated with dilution of a surfactant from a concentration above the cmc to a concentration below the cmc, which results in demicellization of the preexisting micelles. One difficulty with these determinations relates to the dependence of the heat evolution (∆Q) on the initial and final concentrations, probably due to secondary self-aggregations of the surfactants at high concentrations and/or premicellar dimer formation at low surfactant concentrations [6,9]. These difficulties are at least partially responsible for the lack of consistent data on the thermodynamics of micelle formation [6]. Recent advancements in the sensitivity of microcalorimeters made it possible to study low surfactant concentrations, thus improving the quality of data obtained through dilution experiments (see below). In this review we address the scope, the limitations, and the difficulties associated with interpretation of high sensitivity isothermal titration calorimetry (ITC) in studying aqueous solutions of amphiphiles. In reviewing the existing knowledge, we first present the theoretical background required for interpretation of the results of ITC experiments. Then we describe the experimental approaches and protocols that can be used to 1. Obtain reliable heats of formation of micelles and other self-assemblies in aqueous media. We also show how these approaches can be used to estimate the cmc of the surfactants. 2. D e t e r m i n e t h e p a r t i t i o n i n g o f a m p h i p h i l e s b e t w e e n a m p h i p h i l i c self-assemblies and aqueous media.

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3. Determine the heat associated with the composition-induced transformations between various phases. Finally, we summarize and discuss some of the results obtained thus far regarding these issues. This presentation is neither comprehensive nor objective. Its general theme is to describe the scope of ITC and draw awareness of its limitations in studying the self-assembly of amphiphiles in aqueous solutions. II. GENERAL THEORETICAL CONSIDERATIONS A. The Origin of Self-Assembly The chemical potential of a surfactant monomer in a dilute aqueous solution µw is given by (1) where is the standard chemical potential of a surfactant monomer in the aqueous medium and is the mole fraction of the surfactant in the solution. Similarly, the chemical potential of a surfactant molecule in a micelle is given by (2) is the standard chemical potential of surfactant molecules in the micelle, where m is the aggregation number, and is the mole fraction of aggregated surfactant. At equilibrium, when micelles and monomers coexist, µ w = µ m the aqueous concentrations of the aggregated ( ) and unaggregated ( ) surfactant are related by (3) where denotes the difference of the standard chemical potentials. For most surfactants, m is sufficiently large to make the contribution of lnm 1/m negligible so that (4) This means that at any given temperature, for any given total detergent concentration ( ), the relationship between the concentrations of monomeric surfactant ( ) and micellar surfactant ( ) is determined by the difference in standard chemical potentials, , according to (5)

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B. Factors Determining the cmc The cmc of a surfactant is commonly defined as being that total detergent concentration at which micelle formation is already considerable (experimentally detectable) but most of the surfactant is still monomeric ( ), so that the concentration of monomers is still close to the total detergent concentration ( ). It is therefore convenient to define cmc’ [1] by the equation (6) This definition along with Eq. (3) determines the micellization in terms of the value of cmc’, (7) Notably, the law of mass action, (8) defines micellization in terms of an equilibrium constant K: (9) Rewriting Eq. (7) as (10) and comparing it with Eq. (9) yields an expression that connects K with cmc’: (11) This means that exact determination of the cmc is theoretically sufficient for [Eq. (6)] and K [Eq. (11)]. determination of both The distribution of surfactant molecules between micelles and monomers depends also on the aggregation number m [Eq. (7)]. This dependence is schematically depicted in Fig. 1 in terms of the dependence of Dw and Dm on the total surfactant concentration Dt, as computed on the basis of Eq. (7) for a surfactant with cmc = 1 mM, assuming two aggregation numbers: m = 10 (solid lines) and m = 100 (dashed lines). As evident from this figure, at that total concentration defined by Eq. (7) as the cmc (1 mM in Fig. 1), both Dw and Dm depend on the aggregation number. Thus, if the cmc is defined according to Eq. (7), the apparent cmc, at which micelles begin to form, depends on the aggregation number. Furthermore, the actual partitioning of surfactant molecules between micelles


299

FIG. 1 Dependence of the concentrations of monomeric (D w ) and micellar (D m ) surfactant on the total concentration of a surfactant of cmc = 1 mM as computed from Eq. (7) assuming m = 100 (broken line) and m = 10 (solid line).

and soluble monomers at other concentrations depends on m such that at m = 100 the “breaks” in the curves are much more pronounced than at m = 10 and the monomer-to-micelle transition resembles a first-order phase transition. This means that exact determination of the partitioning of surfactant between micelles and monomers (especially around the cmc) can be used to estimate not only the value of but also the aggregation number (m) and the association constant (K). In addition, accurate determination of the cmc as a function of temperature can be used to evaluate the excess molecular enthalpy of micellization, according to van’t Hoff’s equation [1,10], (12 Hence, determination of the cmc and its dependence on temperature are theoretically sufficient for complete characterization of the thermodynamics of micelle formation: For any given temperature, can be calculated directly from the (temperature-dependent) cmc, (which is also temperature-dependent) can

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be computed from the first derivative of the cmc with respect to temperature, the molecular heat capacity, can be computed from the first derivative of with respect to temperature, (13) and the molecular entropy of micellization, , can then be computed from the Gibbs– Helmholtz equation,

C. ITC Measurements, Major Findings, and Interpretation and the cmc as Calorimetric titration yields reliable determination of both well as a reasonable approximation for the micelle-to-monomer ratio in the range of the cmc (see below). The data obtained by this method can thus be used to fully characterize the system according to Eqs. (12)–(14). Two major finding of ITC measurements are that 1.

, which is regarded as being the major contributor to the “hydrophobic effect” [1], is positive throughout the range of temperature up to 100°C [10]. This result is likely to be due to the elimination of ordered hydration shells around the hydrophobic parts of monomeric amphiphiles when the monomers self-assemble into micelles. 2. The sign of depends on temperature. For many surfactants, micellization is exothermic only at relatively high temperatures and endothermic at low temperatures [11,12]. In relating to the heat evolution of micellization, it is important to note that the above discussion addresses the changes in the free energy only in terms of the sum of changes in the entropy and enthalpy of the system due to removal of surfactant molecules from the aqueous medium into a micelle. From Eqs. (14) and (4) it follows that (15) On the other hand, partitioning of amphiphile is also dependent on the concentrationdependent entropy of translation (∆S trans), which always favors dissociation of micelles, reducing the “ordering” introduced into the system by aggregation of monomers into micelles. The heat associated with micellization is therefore the sum of two entropic terms of opposite sign,


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(16) where ∆S trans (the entropy associated with translation) is defined as (17) D. Enthalpy Associated with Dissolving Hydrocarbons In terms of molecular interactions, demicellization is analogous to dissolving hydrocarbons in water, which has been viewed [13] as being a two-step process: 1. Breaking van der Waals attraction interactions between hydrocarbon molecules, which is endothermic. 2. Hydrating the individual hydrocarbon molecules in the dilute aqueous solutions, which has been shown to be exothermic [13]. Hence, (18) ∆H vdW can be regarded as being analogous to the endotherm associated with evaporation of the hydrocarbon, (19) A major contributor to the heat of hydration (∆H hydration) relates to the hydrogen bonds that link individual water molecules to each other in the absence of solutes (∆H ww). This arrangement is disrupted by any solute dissolved in water. For nonpolar solutes, such as a hydrocarbon, the expected net result of breaking the water structure is an increase in the enthalpy of the solution. Nonetheless, the heat of hydration can be regarded as being the sum of two enthalpy terms, one of which, ∆H ww, relates to the water–water hydrogen bonds that were present in the aqueous solution in the absence of the hydrocarbon and were broken by the hydrocarbon, whereas another term, ∆Hcw, relates to the molecular interactions that exist in the system only in the presence of the hydrocarbon [1,14]. (20) Combining Eqs. (18)–(20) yields (21) Both ∆Hevap and ∆H ww are positive (endothermic), whereas ∆Hcw may be either positive or negative. This means that while the solubility of a hydrophobic mole-

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cule in water is associated with a heat loss due to reduction of both water–water hydrogen bonds and lipid–lipid van der Waals interactions, the solubility is also associated simultaneously with some heat gain due to water–hydrocarbon interactions and/or the strengthening of water–water hydrogen bonds in comparison with the system that exists in the absence of hydrocarbon (see below). In fact, the absolute value of the enthalpy associated with the overall process of dissolving hydrocarbons in water at 25°C, ∆Hsolution, is an order of magnitude smaller than that of the heat of their evaporation, which is always endothermic (Table 1). This must mean that solvatation (hydration) of the hydrocarbons is exothermic and of the same order of magnitude as the heat of evaporation. It can therefore be concluded that the new bonds created in the presence of hydrocarbons (∆Hcw) are enthalpically more beneficial than the hydrogen bonds between the water molecules that break down as a consequence of the introduction of a hydrocarbon chain into water (∆Hww). This finding has been previously explained in terms of the strength of the water– water hydrogen bonds at the surface of the cavity created by a nonpolar solute [13,14]. Rearrangement of these water molecules may be sufficient to regenerate the broken hydrogen bonds, and the newly formed hydrogen bonds may be stronger than before. The data given in Table 1 show that the absolute values of both the experimentally determined heat of evaporation and the computed heat of hydration are larger for hexane than for pentane. Similar results were observed for alkylbenzenes (Table 1). In the temperature range of 15–35°C, ∆Hsolution increases (becomes more endothermic) with increasing temperature. In both series, when the chain length increases, the absolute value of ∆H evap increases more than the absolute value of ∆H hydration, so the overall process of dissolving the hydrocarbon in water becomes more endothermic (or less exothermic) upon increasing the chain length. The same trend was obtained for a larger series of short-chain alkanes as well as for alkyl alcohols (Table 2) [1]. Notably, dissolving alcohols of chain length greater than 2 was always more exothermic than dissolving the corresponding TABLE 1

∆H Values That Relate to Dissolving Hydrocarbons in Water

Compound Pentane Hexane Toluene Ethylbenzene Propylbenzene Source: Ref. 13.

∆Hsolution (kJ/mol) –2.0 ± 0.2 0.0 ± 0.2 1.7 ± 0.1 2.0 ± 0.1 2.3 ± 0.1

∆H evaporation (kJ/mol) 26.7 31.6 38.0 42.3 46.2

± ± ± ± ±

0.2 0.1 0.1 0.1 0.1

∆H hydration (kJ/mol) –28.7 –31.6 –36.3 –40.2 –43.9

± ± ± ± ±

0.3 0.2 0.2 0.1 0.1


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TABLE 2 Dependence of ∆H solution on the Chain Length of Hydrocarbons and Alcohols as Measured at 25°C Alkane

∆Hsolution (kJ/mol)

Alkanol

∆Hsolution (kJ/mol)

C2H6 C3H8 C4H10 C5H12

–10.42 –7.09 –3.33 –2.09

C2H5OH n-C 3H 7OH n-C 4H 9OH n-C5H 11OH

–10.13 –10.09 –9.378 –7.79 (7.95)

Source: Refs. 1 and (in parentheses) 15.

paraffins, probably due to the contribution of hydrogen bonds of the hydroxyl group with water. E. The Enthalpy of Micelle Formation Assuming that the differences between the interactions of the headgroups of amphiphiles with water in the monomeric and micellar forms are smaller than those between the respective interactions of the hydrophobic chains, it follows that the overall heat associated with micelle formation can be treated similarly to the solubility of hydrocarbons, i.e., in terms of the interplay between three major contributing stabilizing interactions, 1. Van der Waals interactions between hydrophobic moieties in the aggregates (∆Hvdw), which favor micellization 2. Hydrogen bonds between water molecules (∆Hww), which also contribute to micelle formation 3. Hydration of hydrophobic moieties and consequent formation of strong hydrogen bonds (∆Hcw), which, according to Gill et al. [13], should strongly favor transition of surfactant molecules into the water (i.e., favors demicellization) Accordingly, (22) The observed exothermic nature of demicellization of many surfactants at low temperatures (around 25°C) (see above) must mean that the heat gain associated with hydration of the hydrophobic moieties (possibly due to stronger hydrogen bonds in the water [14]) is greater than the sum of heat losses associated with reduction of the original hydrogen bonds in the water and disruption of the van der Waals interactions between hydrophobic moieties in the aggregates. Elevation of the temperature is likely to result in reduction of all the stabilizing energies. The observed endothermic nature of demicellization at high temperature

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(see below) must therefore mean that ∆H cw becomes reduced more than the sum of the other two contributing factors. One possible explanation of this behavior is that the excessive attractive energy is indeed due to “stronger hydrogen bonding” and that this binding is affected by increasing the temperature more than the other interactions are. As a consequence, the heat of demicellization at high temperature is governed by the latter forces, which favor micellization, so that demicellization becomes endothermic. This is schematically depicted in Fig. 2.

FIG. 2 Schematic explanation for the dependence of the heat of demicellization on chain length and temperature. The bold arrows represent the overall enthalpy of demicellization, the dotted arrows represent the excess enthalpy of hydration of the hydrophobic moieties of the amphiphiles, and the dashed arrows represent the sum of enthalpies resulting from van der Waals interactions between hydrophobic moieties in the aggregates and from hydrogen bonds between water molecules.


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A similar rationale may explain the effect of chain length on the heat of demicellization of surfactant micelles. Specifically, chain elongation is likely to enhance all the stabilizing energies represented in Eq. (22), but not necessarily to the same extent. The finding that chain elongation makes demicellization less exothermic (or more endothermic) indicates that upon increasing the chain length ∆Hcw increases less than the other two attractive interactions, as illustrated in Fig. 2. III. EXPERIMENTAL TITRATION PROTOCOLS, PROCEDURES, AND INTERPRETATION OF DATA The general protocol of an ITC experiment involves titration of a small volume, vt, of a solution of a certain composition into a cell containing a much larger volume, vc, of another solution. Simultaneously, a volume v t is removed from the cell so as to maintain a constant volume of solution in the cell, while the temperature is kept constant either by cooling the cell when the reaction is exothermic or heating it when the reaction is endothermic. A.

Determination of the Heat Evolution of the SelfAssembly of Surfactants

Surfactant solutions may contain monomers and micelles. In addition, under certain conditions the solution may contain premicellar aggregates and/or aggregates of very high aggregation numbers due to “secondary aggregation” at high surfactant concentrations [16]. A surfactant solution with a concentration Dt higher than the cmc contains at least two species, i.e., monomers of a concentration only slightly higher than the cmc (Dw ≅ cmc mM) and micelles of a concentration of Dm = (Dt – cmc) mM. Upon dilution, both the micelles and monomers are diluted. If the surfactant concentration in the cell is lower than the cmc, the dilution results in dissociation of micelles into monomers (complete dissociation being obtained when the final concentration D t is lower than the cmc). The heat involved can thus be described as being due to three processes: dilution of monomers, dilution of micelles, and dissociation of micelles into monomers. (23) When demicellization occurs, the heats of dilution of both monomers and micelles usually make only a minor contribution to the overall evolution of heat. In the following discussion we neglect these contributions. However, a more accurate evaluation of the heat of demicellization must be based on independent determination of the contribution of the heat of monomer dilution, which can be experimentally measured by dilution of a solution of a concentration below the cmc. This, of course, is possible only when the heat of dilution of monomers is

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sufficiently large to be experimentally detected. Determination of the heat associated with micelle formation is possible only if the calorimetric titrations cause the surfactant to be repartitioned between its aggregated and monomeric forms. This requires that in one of the two solutions to be mixed in the calorimetric cell the surfactant concentration must be above the cmc, whereas in the other solution the concentration must be below the cmc. (Mixing two dilute monomeric solutions of concentrations below the cmc will not result in micellization, whereas mixing two concentrated solutions each of which already contains micelles will not result in demicellization.) Accordingly, mixing two appropriately selected solutions in the calorimeter results in the dissociation of micelles into monomers, and the measured heat evolution can be used to compute the heat of demicellization, as described below. In general, after a surfactant solution of volume v t and concentration D t is injected into a cell of volume v c containing a surfactant of concentration D0, the amount of surfactant in the cell, a 1, is given by (24) and the concentration D1 is (25) After evacuation of a volume vt, the remaining fraction of surfactant in the cell will be given by (26) and the remaining amount will be (27) The concentration and amount of surfactant in the calorimetric cell following subsequent steps of titration can be computed similarly (see below). In practical terms, two protocols are commonly used for the determination of ∆H, “infinite dilution” and infinitesimal dilution. 1. “Infinite Dilution” The “infinite dilution” protocol involves titration of a concentrated amphiphile solution with Dt > cmc into a cell containing no amphiphile, namely D0 = 0. After titration, the concentration in the cell is D1 = Dtv t/(vc + vt), where D 1 < cmc. Since v c >> v t, this protocol is denoted as “infinite dilution” and the heat evolution of the process reflects demicellization of all the micelles that were present in the titrated volume. The major contribution to the heat of dilution (∆Q) is the heat of demicellization of (D t – cmc)v t moles of surfactant. Hence,


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(28) If a series of one-step titration experiments are conducted using a constant volume of titrant but different concentrations D t, the experimentally observed dependence of ∆Q on Dt can be used to evaluate ∆Hdemic and the cmc from the slope and intercept of the linear dependence (29) When such a linear dependence is observed experimentally, it can be used to determine both ∆Hdemic and the cmc (see Fig. 3). By contrast, when the titrated (micellar) solution contains micelles that undergo secondary aggregation and/or when the “infinitely diluted” (supposedly monomeric) solution contains premicelles (dimers, etc.), the line describing ∆Q = f(Dt) will deviate from linearity.

FIG. 3 Schematic description of the expected dependence of the heat of demicellization on the total surfactant concentration in infinite dilution experiments.

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For the range of D t where ∆Q is a linear function of D t, as long as the concentration in the cell is lower than the cmc, all the injected micelles will dissociate into monomers and the observed heat will remain constant [as given by Eq. (28)]. Upon subsequent steps of titration of surfactant into the cell, the total concentration in the cell will increase, but since some of the detergent is removed after each titration step, the amount of surfactant in the cell after n steps of titration will be smaller than nvtD t. After the first step of titration and removal of a volume vt, the amount of surfactant left in the cell, as given by Eq. (27), will be (30) The amount of surfactant added in the second step of titration is again Dtv t, so that after the second addition (prior to the removal of the excess volume v t) the amount of surfactant in the cell is given by (31) After removing the excess volume, the amount of surfactant in the cell is (32) Hence, (33) Similarly, after a series of n subsequent steps of titration and evacuation, (34) This concentration can be expressed as the sum of a geometric series, (35) As long as D n is much smaller than the cmc, computation of D n is of minor importance, because essentially all the micellar surfactant in the titrated solution will become dissociated. Only when Dn approaches the cmc must determination of ∆Hdemic take into account the change in the concentration of micelles in the cell. Under these conditions, the heat evolution is given by (36) and interpretation of ITC experiments conducted in this concentration range can be used to determine the cmc.


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2. Infinitesimal Dilution In another series of experiments, small volumes of aqueous solutions containing no surfactant are injected into the cell. When the initial concentration in the cell (D 0 ) is lower than the cmc, the (relatively low) heat of dilution of monomers can be determined. When D o >> cmc and v c >> v t, the titration results in partial demicellization, the titrated volume becomes saturated with monomeric surfactant, and the total amount of surfactant that becomes dissociated equals v t cmc so that (37) Hence, as long as the concentration in the cell remains much higher than the cmc, ∆Q can be expected to be independent of the surfactant concentration in the cell unless at that concentration the cell contains “secondary aggregates.” B. Partitioning of Solutes Between Membranes and Aqueous Solutions Similar to the partitioning of solutes between water and oil, partitioning of amphiphiles (including surfactants at concentrations below the cmc) between water and aggregates, such as bilayer membranes, can in principle be measured by ITC using three different protocols. Experimentally, the least suitable protocol is the injection of a small volume of the solute into a cell of large volume containing the aggregates. The use of this protocol for detection of the heat of partitioning of detergents with low cmc’s between membranes and water is problematic, because the concentration of the titrated detergent solution in these cases may have to be higher than the cmc to enable detection of the heat associated with partitioning. As a consequence, dilution of the titrated solution will cause demicellization accompanied by partitioning, which complicates the measurement of the heat of the latter process. Nonetheless, for certain surfactants the detection of the heat evolution of the partitioning is possible by titration of a detergent solution below the cmc. In those cases this protocol yielded reliable information [17,18]. Similarly, its use for studying the partitioning of other solutes (e.g., alcohols) is limited by the heat associated with dilution of the solute in the cell prior to partitioning. Accordingly, most of the investigators who studied the heat of partitioning used the “incorporation” protocol based on the injection of a small volume containing aggregates into a large volume of dilute solute (e.g., alcohol or detergent). Using this protocol, the heats of dilution (and/or demicellization) are minimal, and the measured heat can be interpreted in terms of the insertion of solute into the added aggregates.

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As long as the partitioning of solute between aggregates and water obeys a constant partition coefficient (i.e., as long as the solute in the aggregates does not change the partition coefficient), the following relationship is valid: (38) where S a and S w are the concentrations of solute that reside in the aggregates and water, respectively, and [A] is the concentration of the aggregates. For [A] >> S a, (39) where S T is the total concentration of the solute in the cell. Rewriting Eq. (39) results in (40) The amount of solute that becomes transferred from water into the added aggregates is given by vcSa, and the heat associated with this process can be expressed by (41) Inserting Eq. (40) into Eq. (41) and rewriting it results in the equation (42) Hence, in principal, the description of 1/∆Q as a function of 1/[A] for a constant ST yields interpretable values of the slope and intercept. K can then be computed from the ratio intercept/slope = K, and ∆Hw?a can then be computed from the intercept and the known values of S T and vc (Fig. 4). Alternatively, Heerklotz et al. [19] introduced a new protocol denoted as a “release” protocol. In this protocol a dispersion of mixed vesicles containing surfactant in the bilayer (and monomeric surfactant) is injected into a cell containing buffer. This titration results only in a partial release of the surfactant into the buffer. The latter two protocols should, of course, give the same ∆H values (∆H w→a = –∆H a→w) unless the solute cannot cross the membrane within the time scale of the ITC experiment. Comparison of the data obtained by the “incorporation” and “release” protocols therefore yields information on whether the partitioning of solute represents a state of equilibrium or is kinetically controlled.


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FIG. 4 Schematic presentation of the effect of the concentration of the aggregates on the heat associated with partition of an amphiphile into aggregates. The experimental protocol involves stepwise addition of the aggregates into the surfactant solution (S T ≈ constant). U denotes the ratio U = 1/(v cS T ∆H w→a) [see Eq. (42)].

In all the experimental protocols, the heat evolution (∆Q) is a product of the standard molar enthalpy of association (∆H w→a) and the change in the number of aggregate-associated molecules of solute (∆nw→a). When the latter factor is a welldefined function of the partition coefficient K, ∆Q is a well-defined function of ∆H w→a and K. The most straightforward way to interpret the results of an ITC experiment is to determine K in an independent experiment. This can be done by determining the concentration of solute in the aqueous solution (Sw), using equilibrium dialysis or independent ITC experiments designed specifically to determine the solute concentration in a system containing aggregates and solutes. Such experiments were based on the solvent-null method of Zhang and Rowe [20], which is conducted by titration of a solute of a concentration S tit into a mixture of aggregates with the same solute. In the latter mixture, the total concen-

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tration of solute in the cell, St, is a sum of the solute concentrations in the solution, S w, and in the aggregate, S a. When Stit < Sw, Sa will decrease due to repartitioning of the solute into the medium, whereas when Stit > S w, some of the added solute will repartition into aggregates. Only when Stit = S w no repartitioning will occur, and the titration will be isocaloric. Hence, Sw can be determined from a series of titration experiments with different Stit values. When the heat of dilution of the added solute does not contribute significantly to the overall heat of titration, such experiments can be used to determine the partition coefficient, K. Furthermore, even when the heat of dilution does contribute to the overall heat, Sw (and K) can still be evaluated from the solvent-null method by conducting a series of control experiments in which solutions of different Stit values are titrated into a solution containing no aggregates. From the latter series of experiments, the heat associated with the dilution can be determined, so that the heat associated with aggregate–solute interactions can be evaluated. When the latter, corrected value of ∆Q becomes zero, Stit = Sw, and K can be computed from the values of Sw and Sa (Sa = ST – Sw). Alternatively, the heat evolution obtained upon sequential titration steps can be used to estimate both ∆Hw→b and K if it is assumed that both of these factors are concentration-independent. Under this assumption, ∆Q for each titration step can be related to ∆Hw→b and K: ∆Q = f(∆H2→b, K) [17,18]. Under conditions of sequential titration of vesicles into a solution of the amphiphile, the difference in ∆Q between consecutive titration steps is particularly sensitive to the value of K (e.g., large K values produce a fast decrease in the titration peaks), whereas the plateau level of the cumulative heat of reaction is essentially determined by ∆Hw→b. Consequently, K and ∆H w→b are not strongly coupled, so their determination is quite unambiguous [21]. C. The Heat Evolution of Bilayer–Micelle Phase Transformation in Mixtures of Phospholipids and Detergents Due to their cylindrical molecular shape [4,22], most phospholipids tend to aggregate along flat surfaces. Consequently, in aqueous solutions they spontaneously form bilayer structures. By contrast, amphiphiles of “conical shape” form micelles. Figure 5 depicts, in the form of a schematic phase diagram, the type of aggregates in a mixture of a micelle-forming amphiphile (detergent) and a bilayerforming amphiphile, such as a phospholipids [23]. As seen in this scheme, when the ratio of nonmonomeric detergent to phospholipid is lower than , the mixture contains bilayer vesicles and monomers, and when the ratio is higher than another critical value, , the mixture contains micelles and monomers, whereas in the range of Re between the latter two critical ratios, vesicles, micelles, and monomers coexist.


313

FIG. 5 A schematic phase diagram for detergent–lipid mixtures. The bold lines describe the dependence of D sat and D sol on lipid concentration. The slopes of these lines ) and the minimal value of R e in represent the maximal values of R e in vesicles ( mixed micelles ( ), respectively. The intercepts of the lines ( and ) represent the respective (extrapolated) values of monomer concentrations. The broken lines denoted by I, II, and III illustrate the three protocols of ITC experiments as described in the text.

Isothermal titration calorimetric studies of the transfer of molecules between these phases have been conducted using various experimental protocols. Three such protocols are indicated in Fig. 5. Protocol I. Injection of buffer into a mixed micellar solution, which results in the transfer of micellar detergent from mixed micelles into water and, subsequently, in the transformation of mixed micelles into mixed vesicles followed by extraction of detergent molecules from these vesicles into aqueous solution. Protocol II. Injection of pure PC vesicles into a cell containing detergent at a concentration c 0 either below or above the cmc. When c0 < cmc, detergent will partition between the added vesicles and the aqueous media, whereas when c0 > cmc the added vesicles may be solubilized by the detergent. Protocol III. Injection of detergent (of varying concentrations) into a cell containing pure PC vesicles, which results in partitioning of the added detergent between vesicles and water and subsequently causes partial solubilization of the vesicles when Re approaches the value . The three phases present in the phase diagram are characterized by their compositions. The aqueous solution of surfactant monomers is characterized by the deter-

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gent concentration in the water, Dw, whereas the mixed micelles and vesicles are characterized by the ratios and respectively. The equilibrium of each mixture is determined by an equation of state that relates to the intensive thermodynamic parameters. The variables changing along the phase diagram are the compositions. Therefore, the equations of state that determine the behavior of the mixture are given by the functions ( Dw) in the micellar range of the phase diagram, (Dw) in the vesicular range, and the relationships between the compositions of all three phases in the range of coexistence of micelles and vesicles [24]. The energetics of the process of self-assembly are determined by the energetics of transition of the different components between the different phases. Considering the changes in enthalpy as characteristics of the transition, the relevant values for our analysis are 1. The molar enthalpy of transition of detergent from mixed micelles to water, , 2. The molar enthalpy of transition of detergent from mixed micelles to mixed vesicles, 3. The molar enthalpy of transition of lipid from mixed micelles into vesicles

Notably, all these enthalpies depend on the composition of the corresponding phases and consequently can have different values for different points of the phase diagram. Titration of the mixture within the range of coexistence results in considerable exchange of the two amphiphiles between mixed micelles and mixed vesicles. In addition, surfactant molecules may be transferred from the aqueous solution into the aggregates, or vice versa. Although the enthalpic consequence of this repartitioning is significant, its effect on the concentration of monomeric surfactant (Dw) is relatively small. For the sake of simplification, we assume that within the range of coexistence the aqueous concentration of monomeric detergent remains constant and equal to /2. Under this assumption, supported by theoretical considerations (see below), the heat of one titration step can be presented as follows: First we consider a solution of a titrant that contains both lipid at a concentration cL and detergent at a concentration cD. The total number of lipid molecules in the system is the sum of lipid molecules in bilayers and micelles, (43) Detergent molecules also reside in the water at a concentration

. Hence, (44)


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The changes in the total volume and in the total numbers of lipid and detergent molecules are given by (45) Combining these equations with Eqs. (43) and (44), we obtain expressions for the changes in the numbers of molecules of lipid and detergent inside the micelles and the vesicles: (46) (47) (48) (49) where The resulting heat accompanying one injection is therefore given by

(50) In the first of the five terms on the right-hand side of Eq. (50), we take into account that the concentration of the detergent in the titrant, c D , can be higher than the cmc, so that after injection the pure micelles undergo monomerization, which is related to the molar heat of transition, . The first two terms in the total heat, Eq. (50), are independent of the concentrations in the titrant (c D and c L ); the third contribution is proportional to the concentration of lipid c L ; and the last two contributions are proportional to the concentration of detergent, c D, in the titrant. This feature makes it possible to design experimental investigations of the molar heats of transition of the two components inside the range of coexistence. This may be done by determination of ∆Q for several values

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of cL and cD according to protocols II and III, respectively. Consideration of the slopes and intercepts of the dependence of ∆Q on c L and c D allow determination of the values of the molar heats [25]. Thus, in the range of coexistence we can determine not only the heat of transfer of detergent between aqueous solution and aggregates but also the heat of transition of lipid and detergent between the mixed vesicles and the mixed micelles, IV. HEAT EVOLUTION OF THE TRANSFER OF AMPHIPHILIC MOLECULES BETWEEN AGGREGATES AND WATER A. Heat of Micellization and Its Dependence on Temperature and Composition Although the change in entropy is the main driving force for micellization, the enthalpy of micellization may also contribute significantly to the Gibbs energy of this process, particularly in the case of amphiphiles with long alkyl chains. As described earlier, micellization is often endothermic at low temperatures but exothermic at higher temperatures. Comprehensive evaluation of the influence of the molecular structure of amphiphiles on the heat of their micellization therefore requires comparison of the heat associated with micellization of the various amphiphiles as a function of temperature. Since the experimental protocols yield information on the heats of demicellization, the data cited below refer to ∆H demic. Most of the data published thus far on the effects of molecular structure on the heat evolution relate to a constant temperature (usually 30 ± 5°C). At this temperature, demicellization may be either endothermic or exothermic, depending on both the chain length and the headgroup of the surfactant. Examples are given in Tables 3–5 for three series of surfactants (alkyltrimethylammonium bromides in Table 3, alkyl-N-acetylamino saccharides in Table 4, and alkyl oligoethylene oxides in Table 5). The data given in these tables can be used to evaluate the effects of elongation of the hydrocarbon chain on ∆Hdemic, ∆G demic TABLE 3 Thermodynamic Parameters and cmc for Three Alkyltrimethylammonium Bromides at 30°C Surfactant

Cn

cmc (mM)

DTAB T TA B CTAB

C12 C14 C16

15.98 (17.85) 3.98 (3.31) 1.03 (0.95)

Source: Refs. 26 and (in parentheses) 27.

∆Hdemic (kJ/mol) 5.1 (1.8) 8.5 (7.4) 13.9 (8.6)

∆Gdemic (kJ/mol) 20.5 24.0 27.4

T ∆Sdemic (kJ/mol) –15.4 –15.5 –13.5


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(computed from the cmc value of the surfactant), and T ∆S demic (computed from the values of ∆Hdemic and ∆Gdemic at the given temperature). The general finding of these studies is that the major driving force for micellization is entropic, whereas the enthalpy associated with micellization can either add to this driving force (as for the trimethylammonium bromides listed in Table 3 and for most of the carbohydrate-derived surfactants of Table 4) or have the opposite effect (as for the CnEm surfactants of Table 5). Another generalization that can be drawn from Tables 3–5 is that increasing the chain length lowers the cmc and makes demicellization either less exothermic or more endothermic [28]. For the three cationic surfactants of Table 3, the effect of chain elongation on ∆H demic is sufficient to explain the effect of the chain length on the cmc, whereas the entropic term associated with demicellization of these surfactants remains almost constant. Table 4 presents the thermodynamic parameters that relate to demicellization of four groups of nonionic surfactants in which alkyl chains are linked through Nacetyl amine bonds to different sugar headgroups at 40°C. It is obvious from these data that demicellization of the surfactants of these series is either endothermic or exothermic, depending on the chain length and headgroup. Similar to the previous example, for each series of surfactants with a given headgroup, elongation of the chain results is higher (more positive) molar enthalpy of demicellization; that is, micellization becomes more exothermic. As to the effect of the headTABLE 4 Thermodynamic Parameters for Four Series of Nonionic CarbohydrateDerived Surfactants in Which the Alkyl Chains are Linked Through an N-Acetyl Amine Bond to Different Sugar Headgroups at 40°C

Compound Headgroup

Cn

Glucitol

C8 C 10 C 12 C8 C 10 C 12 C8 C 10 C 12 C8 C 10 C 12

Glucose Lactitol Lactose

Endothermic. Source: Ref. 28. a

cmc (mM) 21 2.0 0.18 21 2.9 0.26 24 3.3 0.31 35 4.6 0.45

∆Hdemic (kJ/mol)

∆Gdemic (kJ/mol)

T ∆Sdemic (kJ/mol)

>–0.9 2.6 7.2 —a 3.0 7.7 >–1.1 1.9 6.6 –2 1.4 5.3

20.4 26.6 32.8

–21.5 –24 –25.6

25.6 31.9 20.1 25.3 31.4 19.1 24.4 30.4

–22.6 –24.2 –21.2 –23.4 –24.8 –21.1 –23.0 –25.1

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group (for any given chain length), it appears that increased hydrophilicity of the surfactant, as expressed by higher cmc values, results in less exothermic micellization. The same trend was observed when the sugar moiety was linked to the hydrocarbon chain through an N-propionyl amine bond [28]. Similar to the surfactants of Table 3, when Cn ≥ 10, micellization of surfactants of these series is enthalpically favorable. Again, the enthalpy of micellization becomes more exothermic upon elongation of the chain length whereas the entropic term remains almost constant. Different results were obtained for the nonionic surfactants composed of hydrocarbon chains of varying length Cn linked by an ether bond to polyethylene oxides of two different lengths, E5 and E6 (Table 5). For each of these surfactants, the published values of the cmc vary over a large range. Hence, the values given in this table for ∆Gdemic and T ∆Sdemic can only be regarded as rough estimates of the actual values. Yet it is clear from these data that the entropically driven micellization of the surfactants of Table 5 occurs in spite of them being endothermic (i.e., enthalpically unfavorable). Interestingly, in these series of surfactants ∆Hdemic is affected much less than T ∆S demic by the chain length of either the hydrocarbon chain or the polyethoxy headgroup. As for other groups of surfactants, elongation of the hydrocarbon chain makes demicellization less exothermic, whereas elongation of the headgroup makes it more exothermic. However, in contrast to the surfactants in Tables 3 and 4, the entropic term of the surfactants of Table 5 exhibits strong dependence on the hydrocarbon chain length. Chain elongation results in large values of T ∆Sdemic (i.e., micellization becomes more favorable entropically). In addition, chain elongation reduces the enthalpic driving force against micellization, but this effect is much smaller than that observed for the surfactants of Tables 3 and 4. TABLE 5 Thermodynamic Parameters for a Series of Nonionic Surfactants C n E m as Measured at 25°C on a Thermal Analysis Monitor Surfactant C n Em C6E5 C8E5 C10E5 C12E5 C8E6 C10E6 C12E6

cmc (mM) 107–130 9–11 0.6–1.1 0.058

0.064

∆Hdemic (kJ/mol)

∆Gdemic (kJ/mol)

T ∆Sdemic (kJ/mol)

–15.2 –14.46 (15.9) a –13.3 –13.46 b –19.68 c –14.67 c –14.79 b

15.0–15.4 21.1–21.6 26.8–28.3 34.0

–30.2 (–30.6) a –35.56 (–36.06) a –40.1 (–41.6) a –47.5

33.8

–48.6

Values in parentheses from Ref. 30. From Ref 31. c From Ref 32. Source: Ref. 29 except as noted. a

b


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For many series of surfactants, demicellization is associated with an exothermic contribution of the headgroup and an endothermic contribution of the tail [28]. Hence, at a certain temperature these two contributions may cancel each other, leading to zero transition enthalpy (∆Hdemic = 0). A systematic study devoted to the effect of temperature on the thermodynamics of demicellization revealed, for the four studied surfactants (SDS, sodium cholate, sodium deoxycholate, and octylglucoside), that demicellization becomes less exothermic (or more endothermic) as the temperature increases [11]. By contrast, the cmc goes through a minimum at the temperature where ∆H demic = 0 (Fig. 6). The latter finding was explained by Paula et al. [11] in terms of van’t Hoff’s

FIG. 6 The enthalpy of demicellization and the cmc of selected surfactants as a function of temperature. (Data taken from Ref. 11.)

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law [Eq. (12)], (51) Specifically, at the temperature where ∆Hdemic = 0, the first derivative of the cmc with respect to temperature equals zero, indicating a minimal value of the cmc. It should be noted that both the cmc and ∆Hdemic values given in Fig. 6 are less accurate for the bile salts than for SDS and octylglucoside because micellization of bile salts exhibits significantly broader transitions between monomers and micelles due to the much smaller aggregation numbers of these surfactants (see above). In an attempt to gain an understanding of the effect of the structure of surfactants on the temperature dependence of ∆H demic, we studied a series of three alkyl glucosides of different chain lengths (Opatowski et al, Heat capacity of micelle formation of alkyl glucosides, in preparation). The temperature dependence of ∆H demic obtained for the three studied alkylglucosides with different chain lengths (C7, C8, and C9) are depicted in Fig. 7. Each

FIG. 7 The enthalpy of demicellization of three alkylglucosides of different chain lengths (C 7 , C 8, and C 9 ) as a function of temperature. The lines plotted through the point where T = 25°C and ∆Hdemic = 0 are parallel to the respective experimental lines.


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of these dependences can be characterized by its slope and by the temperature T0 at which micelle formation is isocaloric (∆Hdemic = 0). It is obvious from Fig. 7 (and the table given as an inset to this figure) that the increase in chain length n CH2 results in lower values of T 0 and larger slopes of the apparently linear dependence of ∆Hdemic on temperature (i.e., in increased ∆Cp). Notably, the value of ∆Cp appears to depend linearly on the chain length [∆Cp/nCH2 = 0.048 ± 0.008 kJ/(mol · K)], as in other hydrophobic systems with varying chain length [12]. To explain the differences among the values of T 0 of the three studied alkyglucosides, we note that for the studied alkanes (e.g., Table 2), T 0 is almost constant and equal to 25°C [13]. Hence, the difference in T 0 relates to the headgroups. Figure 7 shows that at a temperature T = = 25°C, the values of ∆Hdemic of the three studied alkylglucosides are close (–7.1 to –9.0 kJ/mol). Because the alkyl chains are assumed not to contribute to ∆Hdemic at this temperature, we propose that the major contributor to ∆Hdemic at 25°C relates to headgroup– headgroup interactions. Assuming that the enthalpy associated with the latter interactions is temperature-independent, we can present the temperature dependence of ∆H demic in terms of the dependence term that relates to the alkyl chains. This term is given for each of the surfactants of Fig. 7 by the computed lines that intersect ∆H demic = 0 at 25°C. These lines supposedly represent the temperature dependence of the enthalpy that relates solely to the sum of all the enthalpic terms that relate to the interactions of the alkyl groups. However, many more data are required to assess this hypothesis and its generality. B. Heat of Partitioning of Amphiphiles Between Lipid Bilayers and Aqueous Media In the presence of amphiphilic bilayers, such as phospholipid vesicles or biological membranes, water-soluble amphiphiles partition between the bilayer and the aqueous media. Many studies have been devoted to the partitioning of alcohols between bilayers and water as well as to the enthalpy associated with the introduction of alcohols into bilayers, the effects of the alcohols on the physical properties of the bilayers, and the dependence of all these factors on the structure and properties of both the bilayers and the alcohols. The heat associated with the incorporation of three different short-chain alcohols into DMPC bilayers at 26°C and 40°C are given in Table 6. As is obvious from these data, the incorporation of the alcohols into the bilayers, as measured at both temperatures, is endothermic and only slightly dependent on the chain length. The molar enthalpies associated with the incorporation of the alcohols into the bilayers at any given temperature are of the same magnitude as but of opposite sign to the enthalpies associated with transferring the alcohols from their pure liquid state into buffer (Table 2). Notably, the transfer of alcohol molecules

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TABLE 6 of Alcohols of Different Chain Lengths into DMPC Vesicles at 26°C and 40°Ca (kJ/mol) Alcohol

26°C

40°C

Ethanol Propanol Butanol

16 16.1 18

8 9.8 10

Note that Source: Ref. 33.

a

is also denoted as ∆Hw

b

.

from water into bilayers (Table 6) is somewhat less endothermic than their transfer into pure liquid alcohol (Table 2). According to Trandum et al. [33], this difference may relate to dehydration of the alcohols upon association with the lipid bilayers. (“Dehydration of alcohol is the predominant contributor to ") Different results were obtained for the partitioning of long-chain alcohols between DPPC vesicles and aqueous solutions (Table 7). In this system, at 45°C the DPPC bilayers are in their liquid crystalline phase, similar to DMPC at 25°C. The heat evolution in this system exhibited much greater dependence on the chain length, (the enthalpy associated with transferring a solute molecule from water into lipid bilayers) being more exothermic for the longer alcohols. This difference may result from different changes in lipid–lipid interactions within the lipid bilayer due to the introduction of alcohols of different chain lengths. Partitioning of the alcohols can be described in terms of a chain-length-dependent partition coefficient, which increases with the chain length of the alcohol (Table 7). This increase in partitioning is accompanied by more negative enthalpy. The strong chain length dependence of the enthalpy of partitioning of alcohols into lipid bilayers is not consistent with purely hydrophobic interactions, which relate only to dehydration of nonpolar moieties by removal from water. This has been interpreted by Rowe et al. [34] in terms of some specific interactions between the alcohols and the lipid moieties and/or changes in specific interactions among lipid molecules due to the introduction of alcohol molecules into the bilayers. This interpretation is supported by the finding that the sign of enthalpy at 45°C changes from positive to negative with increasing chain length, for which the most straightforward interpretation is that short-chain alcohols disrupt the lipid–lipid interactions in the bilayer whereas the longer chain alcohols enhance and participate in such interactions.

DPPC DPPC/cholesterol = 4/1 (kJ/mol) Alcohol Cn C6 C7 C8 C9

45°C

48°C

50°C

6.7 –5.0 –8.8 –16.7

–7.5 –12.6 –15.9

–7.9 –14.7 –18.0

53°C

55°C

60°C

–0.8

–0.8 –10.5 –16.7 –20.1

–11.3 –20.1 –20.9

–14.7 –19.3

K, 45°C

K, 45°C

839 2150 1.81 × 10 4 5.55 × 10 4

296 1615 7657 2.7 × 10 4

(kJ/mol), 45°C


TABLE 7 Thermodynamic Parameters for the Partitioning of Alcohols into DPPC Bilayers a at Different Temperatures

67 42 28 8

The lipid bilayers were made of DPPC or DPPC/cholesterol = 4/1. Source: Ref. 34.

a

323

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is such that upon an increase in The temperature dependence of temperature, the introduction of alcohols into the DPPC bilayer becomes more exothermic (Table 7). Counterintuitively, the partition constant was found to be only slightly dependent on temperature [34]. Further work will be needed to confirm and explain these findings. The data given in Table 7 also show that inclusion of cholesterol in DPPC bilayers reduces the bilayer/water partitioning of the alcohols (at 45°C) and makes the introduction of alcohols into the bilayers more endothermic. Both these effects are particularly pronounced for short-chain alcohols. These results are consistent with the interpretation that short-chain alcohols disrupt the packing within bilayers, reducing the energy of the interactions between lipid chains [33,34]. In the absence of cholesterol this reduction of stabilizing interaction overcomes the effect of the alcohol–bilayer interaction only for alcohols with chain lengths of six carbon atoms or less, whereas in cholesterol-containing membranes, in which the packing is tighter, even the introduction of nonanol is endothermic. As a consequence, the dependence of the enthalpy on the chain length is greater than in the absence of cholesterol. Recent studies demonstrate that both the partition coefficient and the enthalpy associated with the introduction of octanol into bilayers depend on the composition (and physical properties) of the bilayers. From the data depicted in Table 8, it appears that the variation of the enthalpy is relatively small and that no obvious correlation can be defined between the partition coefficient and . More data are needed to gain an understanding of this process and its dependence on factors such as lipid acyl chain unsaturation. Several systematic studies addressed the enthalpy associated with the introduction of surfactants into phospholipid bilayers and phospholipid–detergent mixed micelles. These include several investigations of the enthalpy of partitioning of the nonionic surfactant octylglucoside (OG) into PC bilayers. The results of these studies (Table 9) reveal that, similar to the partitioning of alcohols, increasing the temperature results in more exothermic introduction of OG into lipid bilayers. TABLE 8 Partitioning of Octanol into Different Lipid Bilayers at 45°C Lipid Dilinoleylphosphatidylethanolamine (DLPE) Dioleylphosphatidylglycerol (POPG) Dipalmitoylphosphatidylcholine (DPPC) Dioleylphosphatidylcholine (DOPC) Stearoylarachidonylphosphatidylcholine (SAPC) Source: Ref. 34.

K × 10 -4 1.19 1.29 1.81 1.98 2.12

(kJ/mol) –5.0 –6.7 –8.8 –8.0 –5.4

± ± ± ± ±

0.4 0.8 2.5 0.4 0.4


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TABLE 9 Enthalpies Associated with the Transfer of OG from Water into Aggregates, (Micelles, Mixed Micelles, and Other Bilayers), at 27°C and 70°C (kJ/mol) a Aggregate

K (M-1) a at 27°C

OG micelles

39 [18]

OG–PC mixed micelles Dimiristoyl PC (DMPC bilayer) 75 [18] Soybean PC bilayer 77 [18] Palmitoyloleyl PC (POPC bilayer ) 88 [35] POPC bilayer (30 nm) diluted 120 ± 10 [17] POPC bilayer (200 nm) diluted 130 ± 5 [17] 120 ± 10 [17] POPC bilayer (400 nm) diluted POPC/POPG bilayer (75:25) 100 [17] 110 [17] POPC/cholesterol bilayer (95:5) POPC/cholesterol bilayer (50:50) bilayer 90 [17] Egg–PC bilayer (30 nm) diluted 78 [17] 40 [25] Egg–PC bilayer a

At 27°C

At 70°C

6.3, 7.0 [11], 7.1 [24] 7.3 [25] 12.7 [18] 5.6 [18] 7.11 [35] 5.4 [17] 7.3 [17] 7.9 [17] 6.7 [17] 7.3 [17] 9.4 [17] 6.2 [17] 10.0 [25]

–8.6, –8.2 [11], –8.8 [24] –9.03 [18] –8.9 [18]

Sources as noted.

The value of the partition coefficient increases with decreasing surfactant concentration. Furthermore, similar to the heat of micelle formation, transfer of OG molecules into the bilayers is endothermic at room temperature but exothermic at high temperature (Table 9). The enthalpy at any given temperature depends on the composition and size of the vesicle bilayers (Table 9). Thus, at room temperature, the introduction of OG into POPC bilayers appears to become more endothermic as the size of the vesicles increases as well as when either POPG or cholesterol is included in the POPC vesicles. However, even when the bilayers contain relatively high cholesterol concentrations, is only a factor of up to 2 larger than the heat of micellization of pure OG (Table 9). Notably, the enthalpy associated with transfer of OG from water into DMPC or POPC bilayers at 27°C is somewhat more positive than the heat of transfer into micelles. As a result, the transfer of OG from micelles into bilayers at 27°C is endothermic (see below). The systematic studies of Keller et al. [18] revealed that the partition coefficient that describes the partitioning of OG into PC bilayers remains almost constant throughout the temperature range of 28–50°C (K = 120 ± 10 M -1), whereas decreases linearly with increasing temperature (from 5.2 kJ/mol at 28°C to – 1.05 kJ/mol at 45°C). Such linear regression indicates that the molar heat capacity (∆Cp) for transfer of OG from water into bilayers is large and nega-

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tive [∆Cp = –0.314 kJ/(mol · K)]. Such large ∆Cp values are usually considered to be fingerprints of the hydrophobic effect, similar to the results obtained for the incorporation of other amphiphilic compounds into model membranes [36,37]. Reaction enthalpies close to zero at 25°C and large negative heat capacities are also typical for the transfer of hydrophobic molecules from aqueous phase into organic environment (see above). In recent studies we investigated the heat evolution obtained upon stepwise dilution of OG–PC mixed micelles. This process first results in extraction of OG from mixed micelles to the aqueous solution, which subsequently results in transformation of the mixed micelles into vesicles, and thereafter in extraction of OG from the bilayers to the water. Our major findings were that 1. The heat associated with the dilution varied from one step to the next. 2. Dilution was isocaloric at about 40°C, exothermic at temperatures below 40°C, and endothermic above 40°C, similar to the dilution of pure detergent micelles. 3. The absolute value of the heat evolution, measured at any temperature, was larger in the range of coexistence than in either the vesicular or micellar range. To interpret these results, we first note that in the “pure phase,” where only one lipidic aggregate is present, the heat is due to the extraction of OG from either micelles or vesicles into the aqueous solution. Given the similar temperature dependence of the range of coexistence, it follows that this heat also relates to the extraction of OG from mixed aggregates into water. This means that the heat associated with this process is much greater than the heat associated with the transformation of micelles into vesicles. This interpretation also means that dilution of lipid–detergent mixtures in the range of coexistence results in the extraction of more OG into the diluting aqueous medium than similar dilution of a pure (micellar or vesicular) phase. Assuming that the molar enthalpy of extraction at any temperature ( ) is constant implies that the heat associated with each titration step is determined only by the number of OG molecules that become extracted from the mixed aggregates into the water, . For any assumed value of , the observed ∆Q can be used to compute as a function of added aqueous solution. This in turn can be used to compute the dependence of the OG/ PC ratio in mixed aggregates (Re) on the concentration of monomeric OG. This dependence is, of course, a function of the value assumed for . Since the phase boundaries, and , are particularly sensitive to the value of , these independently determined boundaries can be used to estimate from the best fit between their computed and experimental values [24]. The best fit between our ITC data and the phase boundaries yields the “equation of state” depicted in Fig. 8. This fit was obtained for ∆Hextraction = 7.1 kJ/mol [24]. This value is similar to that of ∆Hdemic obtained for pure OG at 28°C


327

FIG. 8 Dependence of the monomer concentration of OG on the OG/PC effective ratio (R e).

(Table 9). The more detailed experimental approach used to estimate the enthalpy of transferring individual OG and PC molecules from micelles to vesicles at 28°C (see experimental protocols in Section III.C and Ref. 25) yielded estimates for the ∆H values associated with transferring OG from both bilayers and micelles into water (

and

, respectively) as well as for the much smaller heat

associated with transferring OG from micelles to bilayers ( ). Similar experiments are presently under way in our laboratory with other surfactants to test whether the heat associated with extracting surfactant molecules from lipidic aggregates into water is always much greater than the heat associated with the transfer of surfactant molecules between different types of aggregates. An interesting feature of the equation of state (Fig. 8) is that within the range of coexistence the concentration of monomeric OG is not constant. The observed increase of D w within this range is apparently inconsistent with the simplest thermodynamic expectations. This contradiction can, however, be explained by more sophisticated considerations [38]. The heat evolution of transfer of a surfactant molecule from water into bilayers depends on the hydrophobicity of the surfactant. As an example, octyl thioglucoside (OTG) is a more hydrophobic surfactant than OG. Its cmc (9 mM) is lower than that of OG, and its partition coefficient between bilayers and water (240

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M -1) is higher than that of OG (120 M-1) [17]. Thermodynamic analysis of the OTG–POPC system is more complex than analysis of the OG–lipid system because the partition enthalpy for the transfer of OTG from the aqueous phase to the membrane apparently depends on the mole fraction of detergent in the membrane [17]. Titration of SUV into OTG solutions below results in partitioning of the detergent into the SUV bilayers without affecting the integrity of the bilayers. Under these conditions, the apparent reaction enthalpy increased almost linearly with OTG concentration [17]. Specifically, varied linearly with the mole fraction of OTG in the membrane, being exothermic at low OTG/POPC ratios but endothermic when the bilayer contained more OTG, approaching values that are similar to the heat of micellization (∆Hmic = 4.6 kJ/mol) at OTG concentrations close to . Interestingly, according to Wenk and Seelig [17], the partition coefficient K is constant and independent of the presence of cholesterol in the bilayer throughout the temperature range 28–45°C. The nonionic detergent octaethylene oxide dodecyl ether (C12EO8) is even more hydrophobic than OTG (cmc = 0.11 mM). Thermodynamic parameters that relate to this surfactant are compared with those of OTG and OG in Table 10. The only conclusions that can be drawn from this comparison are that increasing the hydrophobicity of the surfactant results in lower cmc values, more endothermic micellization, and higher values of the surfactant’s partitioning into bilayers. By contrast, no simple relationship between the nature of the surfactants and the heat involved in transferring them into bilayers can be derived. An understanding of the factors that govern the enthalpy associated with transfer of amphiphiles into membranes requires more information on the enthalpy of this process for these and other surfactants under different conditions. C. Heat of Phase Transformations in Mixtures of Bilayer-Forming and Micelle-Forming Amphiphiles The heat associated with the transformation of bilayers into micelles is a sum of the heats associated with the transfer of lipid molecules from micelles into bilayers and the respective heat of transfer of detergent ( ). In addiTABLE 10 Critical Micelle Concentration and Enthalpies Associated with Micellization and with the Transfer of Detergent Molecules into POPC Bilayer and Partition Coefficient Values Surfactant OG OTG C 12EO8

cmc (mM)

∆H mic (kJ/mol)

K (M -1)

≅23 [11] 9 [17] 0.11 [41]

6.2 [11] 4.6 [39] 15.9 [31]

120 [21] 240 [17] 3900 [41]

(kJ/mol) 5.44 [21] –0.08–(+0.6) [17] 31.4 [41]


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tion, the concentration of monomeric detergent (Dw) varies slightly within the range of coexistence, where the phase transformation occurs [25]. The compositioninduced transformation between vesicles and mixed micelles is therefore accompanied by redistribution of surfactant between aggregates and water. As discussed above, the heat associated with transferring surfactant molecules between different types of aggregates is much less than the heat associated with their transfer from lipid aggregates into water (i.e., ). As a consequence, although the variation of D w in the range of coexistence is small, cannot be neglected. The overall ∆Q therefore depends on at least three individual unknown molar enthalpies ( and ). Determination of these unknown factors therefore requires a combination of a series of experimental protocols. The general expression for ∆Q [Eq. (50)], which relates to the heat evolution of one titration step within the range of coexistence, is valid for all the experimental protocols. When lipid vesicles are titrated into a mixture of lipids and detergent within this range (protocol II), the heat is given by

(52)

where Vt and c L are the volume and concentration, respectively, of the titrated lipid [25,40]. Similarly, the heat evolution of one step of titration of detergent into the mixed system (protocol III) is given by

(53)

When the cmc of the surfactant is very low, both Dw and the cmc are approximately equal to zero. The variation of D w that accompanies the phase transformation is small, and its contribution to the heat evolution is negligible, so that and can be straightforwardly estimated from two experiments that each yield a value of ∆Q for a given concentration of the surfactant. Namely, Eq. (52) yields the simplified equation (54)

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and Eq. (53) yields (55) This is the case for the nonionic detergent C12(EO)8. Given the very low cmc of this detergent (0.11 mM), when it is added to phospholipid vesicles it partitions almost completely into the vesicle bilayers (D b >> Dw). Hence, combining Eqs. (54) and (55) enables the computation of the heats of phase transformations ( and ). Using this strategy, Heerklotz et al. [41] concluded that for C12(EO)8 at 25°C, transferring detergent from micelles to bilayers is endothermic ( = 10 kJ/mol), whereas transferring lipids from micelles to bilayers is exothermic ( = –2.5 kJ/mol). For the more general case, when cmc 0, determination of the relevant molar enthalpies requires more experimentation. In this case, two series of experiments can be conducted according to protocols II and III, using varying concentrations of lipid and detergent (cL and cD, respectively). The results of these experiments can then be interpreted in terms of Eqs. (52) and (53) to yield the relevant molar enthalpies as described above. Using this approach we found [25], in good agreement with our expectation, that transferring detergent molecules from micelles to bilayers is endothermic ( = 2.7 kJ/mol) whereas transferring “curvophobic” lipid molecules from curved micelles into relatively flat bilayers is exothermic ( = –2.5 kJ/mol). The observed enthalpies can be used to describe the packing tendency of various amphiphiles in general and particularly that of various phospholipids. No other straightforward method is available for experimental evaluation of this characteristic attribute of membrane phospholipids. Another potentially useful approach based on ITC experiments is to determine the enthalpy difference between two different states by comparing the heat evolution of transferring both these states into a common state. As an example, phospholipid vesicles of different sizes differ in their enthalpy level. Solubilization of a given amount of phospholipid by a given micelle-forming surfactant results in mixed micelles whose properties are independent of the size of the solubilized vesicles [42]. This can be used to estimate the enthalpy difference between vesicles of various sizes by determining the difference between the heats of solubilization of these vesicles, as illustrated in Fig. 9. Using this approach we found that at 27°C the enthalpy difference between small and large POPC (liquid crystalline) vesicles is merely 0.724 kJ/mol, compared to an enthalpy difference of 10.5 kJ/mol found for DPPC (gel phase) vesicles [43]. A similar approach can be used to study other characteristics of lipid bilayers and membranes. For example, in a membrane composed of two phospholipids, these two components may be either mixed or phase-separated in the plane of the membrane. Differentiating between these two possibilities can be based on


331

FIG. 9 A schematic diagram for the enthalpy of large unilamellar vesicles (LUV s) and small unilamellar vesicles (SUVs) with respect to mixed micelles.

a comparison between the heat of solubilization of the studied membrane and the heat associated with solubilizing a mixture of two populations of vesicles each composed of one of the components. Since solubilization of vesicles and subsequent equilibration of the resultant mixed micellar systems are believed to be rapid, a comparison of ∆Q of solubilizing the mixed lipid system with that of solubilizing the mixture of vesicles can be used to estimate the heat associated with mixing the two lipids in the mixed bilayer. The feasibility of this approach has yet to be investigated. V. CONCLUDING REMARKS Isothermal titration calorimetry is a very potent tool in the field of self-assembly of amphiphiles. Given the recent improvements of the sensitivity of this technique, it can be used to investigate many processes of interest in this field. The possibility of using a variety of experimental protocols increases confidence in the experimental evidence. In conjunction with other, independent techniques,

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ITC can yield answers to specific questions that cannot be addressed by any other technique. Thus, ITC studies of the dilution of detergents can be used not only to determine the enthalpy of micelle formation but also the detergent’s cmc and hence the free energy difference. Thus, ITC experiments are sufficient for complete characterization of the thermodynamics of micellization. Other processes that have been studied by ITC include the partitioning of amphiphilic molecules between water and lipid bilayers and the compositionally induced vesicle–micelle phase transition. The examples presented above are of several studies that demonstrate the potential of ITC measurements. Thus far, this potential has been only partially exploited and only for a limited number of amphiphilic systems. Present and future research in this field will undoubtedly make much more use of this potent method. This will hopefully clarify many of the fundamental questions to which we presently have only partial answers. ACKNOWLEDGMENTS We thank the Israel Science Foundation, founded by the Israel Academy of Science and Humanities—Centers of Excellence Program, for financial support, and the members of the center devoted to self-assembly of mixtures of amphiphiles, D. Andelman, A. Ben Shaul, S. Safran, and Y. Talmon, for helpful discussions. REFERENCES 1. C Tanford. The Hydrophobic Effect, Plenum Press, New York, 1981. 2. K Shinoda, T Nakajawa, B Tamamushi, T Isemura. Colloid Surfactants, Academic Press, New York, 1963. 3. P Mukerjee. The nature of the association equilibria and hydrophobic bonding in aqueous solutions of association colloids. Adv Colloid Interface Sci 1:241–275 (1967). 4. JN Israelachvili, Intermolecular and Surface Forces, Academic Press, London, 1985. 5. SM Gruner, MW Tate, GL Kirk, PTC So, DC Turner, DT Kaene, CPS Tilcock, PR Cullis. X-ray diffraction study of the polymorphic behavior of N-methylated dioleoylphosphatidylethanolamine. Biochemistry 27:2853–2866 (1988). 6. H Hoffmann, W Ulbricht. In: Thermodynamic Data for Biochemistry and Biotechnology (H Hinz, ed.), Springer-Verlag, Berlin, 1986. 7. L Benjamin. Calorimetric studies of the micellization of dimethyl-n-alkylamine oxides. J Phys Chem 68:3575–3581 (1964). 8. P Stenius, S Backlund, O Ekwall. In: Thermodynamic and Transport Properties of Organic Salts (P Franzosini, M Sanesi, eds.), IUPAC Chem Data Ser 28, Pergamon, Oxford, 1980, p. 295. 9. R De Lisi, G Perron, J Paquette, JE Desnoyers. Thermodynamics of micellar systems: Activity and entropy of sodium decanoate and n-alkylamine hydrobromides in water. Can J Chem 59:1865–1871 (1981). 1 0 . A Moroi. Micelles: Theoretical and Applied Aspects, Plenum Press, New York, 1992.


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1 1 . S Paula, W Sus, J Tuchtenhagen, A Blume. Thermodynamics of micelle formation as a function of temperature: A high sensitivity titration calorimetry study. J Phys Chem 99:11742–11751 (1995). 1 2 . M Okawauchi, M Hagio, Y Ikawa, G Sugihara, Y Murata, M Tanaka. A lightscattering study of the temperature effect on micelle formation of N-alkanoylN-methylglucamines in aqueous solutions. Bull Chem Soc Jpn 60:2718–2725 (1987). 1 3 . SJ Gill, NF Nichols, I Wadsoe. Calorimetric determination of enthalpies of solution of slightly soluble liquids. II. Enthalpy of solution of some hydrocarbons in water and their use in establishing temperature dependence of their solubility. J Chem Thermodyn 8:445–452 (1976). 1 4 . HS Frank, MW Evans. Free volume and entropy in condensed systems. III. Entropy in binary liquid mixtures; partial molar entropy in dilute solutions: structure and thermodynamics in aqueous electrolytes. J Chem Phys 13:507–532 (1945). 1 5 . I Johnson, G Olofsson. Solubilization of pentanol in sodium dodecylsulphate micelles. J Chem Soc Faraday Trans 1 85:4211–4225 (1989). 1 6 . DM Small. In: Bile Acids: Chemistry, Physiology and Metabolism, Vol. 1. (P Nair, D Kritchevsky, eds.), Plenum Press, New York, Chapter 8 (1971). 17. M Wenk, J Seelig. Interaction of octyl-β-thioglucopyranoside with lipid membranes. Biophys J 73:2565–2574 (1997). 1 8 . M Keller, A Kerth, A Blume. Thermodynamics of interaction of octyl glucoside with phosphatidylcholine vesicles: Partition and solubilization as studied by high sensitivity titration calorimetry. Biochim Biophys Acta 1326:178–192 (1997). 1 9 . HH Heerklotz, H Binder, RM Epand. A release protocol for isothermal titration calorimetry. Biophys J 76:2606–2613 (1999). 2 0 . F Zhang, ES Rowe. Titration calorimetric and differential scanning calorimetric studies of the interactions of n-butanol with several phases of dipalmitoylphosphatidylcholine. Biochemistry 31:2005–2011 (1992). 2 1 . M Wenk, T Alt, A Seelig, J Seelig. Octyl-beta-D-glucopyranoside partitioning into lipid bilayers: Thermodynamics of binding and structural changes of the bilayer. Biophys J 72:1719–1731 (1997). 2 2 . JN Israelachvili, S Marcelja, RG Horn. Physical principles of membrane organization. Quart Rev Biophys 13:121–200 (1980). 2 3 . D Lichtenberg. Liposomes as a model for solubilization and reconstitution of membranes. In: Handbook of Nonmedical Applications of Liposomes, Vol. 2, Models for Biological Phenomena (Y Barenholz, DD Lasic, eds.), CRC Press, Boca Raton, FL, 1996, p. 199. 2 4 . E Opatowski, MM Kozlov, D Lichtenberg. Partitioning of octyl glucoside between octyl glucoside/phosphatidylcholine mixed aggregates and aqueous media as studied by isothermal titration calorimetry. Biophys J 73:1448–1457 (1997). 2 5 . E Opatowski, D Lichtenberg, MM Kozlov. The heat of transfer of lipid and surfactant from vesicles into micelles in mixtures of phospholipid and surfactant. Biophys J 73:1458–1567 (1997). 2 6 . PR Majhi, SP Moulik. Energetics of micellization: Reassessment by a highsensitivity titration microcalorimeter. Langmuir 14:3986–3990 (1998). 2 7 . SP Moulik. Micelles: Self-organized surfactant assemblies. Curr Sci India 71:368– 376 (1996).

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2 8 . JM Pestman, J Kevelam, MJ Blandamer, HA van Doren, RM Kellogg, JBFN Engberts. Thermodynamics of micellization of nonionic saccharide-based Nacyl-N-alkylaldosylamine and N-acyl-N-alkylamino-1-deoxyalditol surfactants. Langmuir 15:2009–2014 (1999). 2 9 . O Ortona, V Vitagliano, L Paduano, L Costantino. Microcalorimetric study of some short-chain nonionic surfactants. J Colloid Interface Sci 203:477–484 (1998). 3 0 . K Weckstrom, K Hann, JB Rosenholm. Enthalpies of mixing a non-ionic surfactant with water at 303.15°K studied by calorimetry. J Chem Soc Faraday Trans I 90:733–738 (1994). 3 1 . G Olofsson. Microtitration calorimetric study of the micellization of three poly(oxyethylene) glycerol dodecyl ethers. J Phys Chem 89:1473–1477 (1985). 3 2 . JM Corkill, JF Goodman, JR Tate. Calorimetric determination of the heats of micelle formation of some non-ionic detergents. Trans Faraday Soc 60:996– 1002 (1964). 3 3 . C Trandum, P Westh, K Jorgensen, OG Mouritsen. A calorimetric investigation of the interaction of short chain alcohols with unilamellar DMPC liposomes. J Phys Chem B 103:4751–4756 (1999). 3 4 . ES Rowe, F Zhang, TW Leung, JS Parr, PT Guy. Thermodynamics of membrane partitioning for a series of n-alcohols determined by titration calorimetry: Role of hydrophobic effects. Biochemistry 37:2430–2440 (1998). 3 5 . M Wenk, J Seelig. Vesicle–micelle transformation of phosphatidylcholine/octylbeta-D-glucopyranoside mixtures as detected with titration calorimetry. J Phys Chem B 101:5224–5231 (1997). 3 6 . PL Privalov, SJ Gill. The hydrophobic effect: A reappraisal. Pure Appl Chem 61:1097–1104 (1989). 3 7 . RL Baldwin. Temperature dependence of the hydrophobic interaction in protein folding. Proc Natl Acad Sci USA 83:8069–8072 (1986). 3 8 . Y Roth, E Opatowski, D Lichtenberg, MM Kozlov. Phase behavior of dilute aqueous solutions of lipid–surfactant mixtures: Effects of finite size of micelles. Langmuir In press. (1999). 3 9 . JC Brackman, NM van Os, JBFN Engberts. Polymer–nonionic micelle complexation. Formation of poly(propylene oxide)-complexed n-octyl thioglucoside micelles. Langmuir 4:1266–1269 (1988). 4 0 . MM Kozlov, E Opatowski, D Lichtenberg. Calorimetric studies of the interactions between micelle forming and bilayer forming amphiphiles. J Thermal Anal 51:173–189 (1998). 4 1 . HH Heerklotz, H Binder, G Lantzsch, G Klose, A Blume. Thermodynamic characterization of dilute aqueous lipid/detergent mixtures of POPC and C 12 EO 8 by means of isothermal titration calorimetry. J Phys Chem 100:6764–6774 (1996). 4 2 . GC Kresheck, HB Long. Determination of the relative molal heat content of dipalmitoylphosphatidylcholine vesicles in the various physical states. Colloids Surf 30:133–143 (1988). 4 3 . D Lichtenberg. Size-dependent properties of phosphatidylcholine unilamellar vesicles. In: Supramolecular Structure and Function, 5th ed. (G Pifat-Mrzljak, ed.), Ruder Boskovic Institute, Croatia, 1997.

9 Calorimetric Methods for the Study of Adsorption of Surfactants at Solid/Solution Interfaces ZOLTÁN KIRÁLY Department of Colloid Chemistry, University of Szeged, Szeged, Hungary I.

Introduction

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II.

Classification of Calorimeters A. Isotherm power compensation calorimetry B. Isoperibolic heat flux calorimetry

336 337 338

III.

Enthalpies of Displacement Obtained with Different Microcalorimetric Methods A. Definition of the enthalpy of displacement B. Immersion microcalorimetry C. Batch sorption microcalorimetry D. Titration sorption microcalorimetry E. Flow sorption microcalorimetry F. Noncalorimetric enthalpies of displacement

339 340 341 343 344 346 349

Literature Survey on Calorimetric Studies of Surfactant Adsorption on Solid Substrates

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References

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IV.

I. INTRODUCTION The adsorption of surfactants at solid/solution interfaces has long been the subject of extensive experimental and theoretical research. Various aspects have been addressed, among them the composition and structure of the adsorption layer, the mechanism of the adsorption (different stages), the kinetics, the thermodynamics 335

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(driving force), the nature of the solid surface (charged, uncharged, hydrophilic, hydrophobic, modifications, roughness, porosity), the nature of the surfactant (ionic, nonionic, HLB number, chain length, headgroup effect, stereochemistry), and experimental conditions (pH, temperature, salinity). The first step in the quantification of adsorption phenomena is the determination of the adsorption isotherms (material balance or mass exchange). Today, measurements of adsorption isotherms are supplemented by a variety of experimental techniques. Among the various methods available, calorimetry is the most powerful tool for elucidating the thermodynamic properties of surfactants at solid/solution interfaces (enthalpy balance or heat exchange). By means of calorimetry, the sign and magnitude of the enthalpies associated with the adsorption process are measured directly. Differential molar enthalpy data provide information on how strongly the adsorbate is bound to the surface, on intermolecular interactions in the adsorption layer, on surface heterogeneity, and on phase transitions or other structural changes within the adsorption layer. Heat capacities, obtained from the temperature dependence of the enthalpy data, are particularly sensitive to such changes. A combination of the enthalpy isotherm with the Gibbs free energy (conveniently obtained from the adsorption isotherm) allows calculation of the entropy function, thereby resulting in a full description of the adsorption process by means of thermodynamic potential functions. However, characterization of the structure of the adsorption layer at a molecular level requires complementary measurements with the use of more structure-sensitive methods such as ellipsometry, neutron reflection, the force balance technique, atomic force microscopy, and spectroscopy. The aim of this chapter is to describe the fundamentals of calorimetric methods currently available for determining the enthalpies of displacement of water by surfactants at solid surfaces. Typical applications of these techniques are reported and commented on. Finally, an extensive list of references is provided, with specifications of the particular systems studied. II. CLASSIFICATION OF CALORIMETERS The adsorption of surfactants on solid surfaces is usually associated with the release of heat to, or the absorption of heat from, the surroundings. This heat can be measured by allowing the adsorption process to occur inside a sample cell (sorption vessel) located in the “measuring block” of a calorimeter. Although a large variety of instruments are available commercially, home-made calorimeters may possess particular advantages for special applications. The new production techniques, and especially the rapid progress in electronics, mean that modern calorimeters permit accurate and reliable measurements, usually controlled by an external computer, which also furnishes the possibility of fast data processing. In general, calorimeters can be classified on the basis of the measuring princi-

Surfactants at Solid/Solution Interfaces

337

ple, the mode of operation, and the construction principle [1,2]. Since the material balance of the adsorption process is measured at constant temperature (adsorption isotherm), the enthalpy balance of the adsorption is also to be determined at constant temperature (enthalpy isotherm), allowing the calculation of differential molar enthalpies as a function of, say, surface coverage. The mode of operation of a sorption calorimeter is therefore either isothermal or isoperibolic. As far as the measuring principles are concerned, thermoelectric compensation and heat conduction calorimeters currently predominate, though a number of combinations exist among the various measuring principles, modes of operation, and construction principles [1,2]. As for the construction principle, calorimeters may be either single or twin. In differential calorimetry, two equal, independent measuring units (sample and reference) are situated symmetrically in the same thermostat, with their thermoelectric detector piles are connected in opposition. A twin calorimetric system is free from fluctuations in zero reading and is unaffected by variations in the thermostat temperature. The twin arrangement improves the sensitivity over that of the single configuration. A. Isotherm Power Compensation Calorimetry In isotherm power compensation calorimetry [3–5], the inactive reference cell is maintained throughout at the temperature of the thermostat, while in the active sample cell the heat of the thermal event (adsorption) is compensated internally by Peltier cooling (if exothermic) or by Joule heating (if endothermic). To this end, the temperature of the sample is continuously monitored relative to that of the reference, and every small deviation is corrected by means of a closed-loop control system (Fig. 1). The values of the current temperature of the sample and the set temperature of the reference are fed through a comparator into an electrical control unit, which activates the Peltier cooler or the Joule heater in the sample cell if its temperature deviates from the desired temperature. Thermoelectric compensation can be applied in various configurations. The best performance is achieved when the Peltier cooler cools the sample cell at a constant rate while a feedback circuit activates the electric heater to maintain the sample cell at the same temperature as that of the reference cell. In the absence of thermal events, the feedback power is constant and a resting calorimeter baseline is obtained. Exothermal or endothermal effects produced by the sample are compensated for by temporarily reducing or increasing, respectively, the feedback power, which causes deflections from the resting baseline until the temperature balance is restored. The power compensation appears as a calorimetric peak. If the product of the voltage U(t) and the current I(t) is recorded continuously during time t (calorimeter power signal), then the electrically generated compensatory heat, Q = U(t)I(t)dt (i.e., the area under the calorimetric peak), is equal to, but opposite in sign to, the heat evolved during the thermal event in the sample cell.

338

FIG. 1

Király

The closed-loop control system of a power compensation calorimeter.

B. Isoperibolic Heat Flux Calorimetry In isoperibolic heat flux calorimetry [6–8], the temperature differences along the heat-conductive connections between the sample cell and its surroundings (a constant-temperature bath) are continuously monitored during time t with respect to the reference cell, which is also connected to the thermostat (Fig. 2). The occurrence of thermal events (adsorption or desorption) in the sample cell either increases (exothermic process) or decreases (endothermic process) the temperature of the sample, which generates an equalizing heat flux dQ/dt either toward the infinite heat sink or in the reverse direction. The heat flow takes place through extremely sensitive thermopile blankets until equilibrium is reached. Upon establishment of the new equilibrium state, the temperature difference ∆T(t) vanishes and the entire system reverts to the initial temperature. The heat exchanged, Q = K ∆T(t)dt, is equal to the heat produced or absorbed by the sample. The constant K is proportional to the (finite) thermal resistance of the heat-conductive connections between the sample cell and the thermostat. The results (calorimetric peaks) are quantified by electrical calibration, where known power values are passed through built-in resistors. Other measuring principles, for instance the monitoring of thermoelectric compensation applied to the reference element, may also be used in isoperibolic operation. Formally, the major difference between isothermal and isoperibolic operations is that the thermal resistance between the measuring system and the constant-


339

FIG. 2 Heat flow calorimeter in a twin arrangement.

temperature surroundings is infinitesimally small for the former, whereas it is of finite magnitude for the latter. Therefore, although the surroundings and the measuring system in isothermal calorimeters have practically the same temperature during the thermal event produced by the sample, independently of time, in isoperibolic calorimeters the temperature of the measuring system changes in time until the heat exchange with the surroundings is accomplished. It should be noted that only quasi-isothermal operations may take place, because heat transport is not possible in the absence of (at least small) temperature differences. Commercially available power compensation and heat flux calorimeters are competitive in stability, accuracy, and sensitivity, fractions of a millijoule being detectable with good reproducibility. Although thermoelectric compensation is more efficient in time (larger power values are detected in shorter time intervals), the kinetics of adsorption may impose limitations on this advantage. III. ENTHALPIES OF DISPLACEMENT OBTAINED WITH DIFFERENT MICROCALORIMETRIC METHODS Calorimeters can be classified further in terms of the choice of methodology (technical characteristics). Modern calorimeters are supplied with standard mea-

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suring units and optional accessories so that the experimentalist can select the preferred configuration for a particular application. There are four major techniques for study of the adsorption of surfactants from solutions on solid surfaces: immersion, batch, titration, and liquid flow methods [9]. Although the designation “microcalorimeter” should be avoided, as it does not reveal whether the term “micro” refers to the size of the device, the sample container, or the quantity of heat measured, the term “microcalorimetry” is often used in studies of adsorption phenomena when the overall heat evolved is not more than a few hundred millijoules. Of course, the magnitude of the measured heat is dependent not only on the strength of the adsorption but also on the total surface area of the solid present in the calorimeter vessel. As far as the duration of an adsorption calorimetric experiment is concerned, the recorded phenomenon may require a few minutes to several hours, depending on the kinetics of adsorption. A.

Definition of the Enthalpy of Displacement

Adsorption from solution may be represented by a stoichiometric displacement reaction between molecules of the adsorbed solvent (water, component 2) and the solute (surfactant, component 1) [10–12]: (1) where superscripts s and l refer to the adsorption layer and the bulk liquid phase, respectively, and r is the amount of solvent displaced by 1 mol of solute at concentration c1. We define the differential molar enthalpy of displacement (∆ 21h 1 ) as the difference between the partial molar enthalpies (h 1) of the two components in the adsorption layer and the equilibrium bulk solution [10–12]: (2) where ∆21H is the integral enthalpy of displacement and is the amount of solute actually present in the adsorption layer. In the case of dilute solutions and preferential adsorption of the solute, the real amount adsorbed, , is practically equal to the surface excess concentration, , the latter being an experimental 1 quantity [13]. The integral enthalpy of displacement, ∆21H, is defined [11] as the enthalpy change of the adsorbed phase when the pure solvent (component 2) initially filling the adsorption space is displaced (partly or totally, depending on the experiment) by the solute (component 1), itself provided by a solution in which its final concentration is c 1. This enthalpy change is equal to the difference between the enthalpies of formation of the phases adsorbed from the solution and from the pure solvent, respectively. In general, calorimetric enthalpies of displacement are measured with reference to the equilibrium bulk solution, which


341

can then be transferred to other reference states, e.g., the solute at infinite dilution or the pure components [11]. For further details concerning thermodynamic quantities of displacement, the reader is referred to earlier works [10–12,14]. B.

Immersion Microcalorimetry

A typical immersion experiment may be described [15–18]. The solid sample is outgassed in a glass bulb that has a capillary break-seal. The sealed ampoule is attached to a push-rod, which may also be used to drive a stirrer, and placed in the immersion liquid inside the calorimeter vessel (Fig. 3). Depression of the plunger breaks the seal, the solid is wetted by the surrounding liquid, and the heat evolved is detected. The experimental heat Q exp comprises three components, only one of which is relevant to the immersion effect. The correction term Q corr originates from the breaking of the ampoule and the subsequent heat of evapora-

FIG. 3 Immersion microcalorimetry setup. (Adapted from Ref. 18.)

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tion [15–18]; it can be determined in a separate blank experiment by using an empty bulb. The dilution term ∆ dil H is related to the change in the bulk composition upon adsorption. It can be determined by breaking ampoules containing appropriate volumes of concentrated surfactant solutions into the solvent to give final concentrations in the same range as in the case of the adsorption experiments. The dilution term may be given by

where n1 is the number of moles of surfactant remaining in solution after adsorption and the enthalpy terms in the brackets are the molar heats of dilution of a concentrated solution of surfactant to the final (c 1) and initial ( ) surfactant concentrations in the adsorption experiments [19,20]. Depending on the solid-toliquid ratio, the equilibrium concentration c1 may differ significantly from the initial concentration . In general, c1 < due to the partition of the surfactant molecules between the adsorption layer and the bulk phase (adsorption). The equilibrium composition can be determined by a suitable analytical method (spectrophotometry, differential interferometry, differential refractometry), or it can be calculated by an iteration procedure (described in Section III.D) from the separately measured adsorption isotherm. The enthalpy of immersional wetting is then calculated as ∆wH = Qexp – Qcorr – ∆dilH, which may be expressed per unit mass or unit surface area of the solid. If the immersion experiment is repeated at different solution concentrations, the enthalpy isotherm of immersion, ∆wH vs. c 1, is obtained. For immersion calorimetry, the presentation of the results is often more appropriate in terms of the relative enthalpy of immersion, ∆21Hw, which, for dilute solutions, is equal to the integral enthalpy of displacement ∆21Hd, more generally obtained from batch or flow sorption microcalorimetric measurements. The relative enthalpy of immersion is defined as the enthalpy of immersion in the solution minus the enthalpy of immersion in pure solvent 2: where The size of the immersion cell may lie in the range 1–100 mL, depending on the calorimeter design. The immersion method is usually less satisfactory for study of the adsorption of surfactants than other calorimetric methods, for several reasons. Among others, the initial and final state s o f t h e a d s o r b e n t m a y l a c k reproducibility, due to improper sample preparation, poor wetting, slow equilibration, etc. The heat correction terms are likewise often ill-defined. Further, the relative enthalpy of immersion is obtained by taking the difference of two large quantities, and this difference may be comparable in magnitude with the dis-


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turbing heat effects. Even though considerable efforts have been made to improve the accuracy of immersion calorimetry, including the design of vacuum-tight immersion vessels, the use of improved bulb-breaking devices, and the introduction of various kinds of agitation techniques [16,17,21], immersion calorimetry still cannot compete in accuracy with the titration and flow sorption calorimetric methods. Further limitations include the facts that only one heat effect can be measured in each experiment and that this technique cannot be applied for the study of desorption processes. Nevertheless, immersion calorimetry is unique in that it is the only method that is able to detect the enthalpic interaction between a bare surface and a solution. Further, the method can be applied advantageously to study adsorption phenomena on fine powders, including the swelling of clays. C. Batch Sorption Microcalorimetry Formally, the technical procedure of the immersion method described in Section III.B can be applied to measure the relative enthalpy of immersion in a single step instead of in two steps. In this case, a suspension of the adsorbent in the solvent is sealed in the bulb and thermally equilibrated with the surrounding solution in the calorimeter vessel [22]. When the ampoule is broken, the solution mixes with the solvent and the adsorption proceeds until a new equilibrium state is attained. The experiment is then repeated in the absence of the solid in order to determine Qcorr + ∆dilH, the heat attributable to the breaking of the ampoule plus the enthalpy of dilution of the solution in the solvent. The relative enthalpy of immersion is calculated as

Similar calorimetric enthalpies can be obtained, but now in simultaneous adsorption and blank experiments, by using a rotating block calorimeter in a twin arrangement [23]. The block consists of a sample cell and a reference cell; each cell has two compartments, the contents of which mix when the block is rotated. During the experiment, the surfactant solution mixes with the adsorbent slurry in the sample cell, and the same amount of surfactant solution mixes with the diluent in the reference cell. Hence, the heat evolved, Qexp, is measured with respect to the heat of mixing, ∆dilH, so that ∆21Hw is obtained directly. An application of the above-mentioned blank correction and the measurement in a differential arrangement takes into account the enthalpy of dilution of a (concentrated) mother surfactant solution to the initial concentration but not to the equilibrium concentration of the adsorption. Correction for the dilution due to adsorption requires considerations similar to those described under immersion calorimetry in Section III.B.

344 D.

Király Titration Sorption Microcalorimetry

In the titration operation mode (also referred to as a batch method), a feed solution of surfactant is introduced in a number of successive steps into the microcalorimetric cell, where the solid material is maintained in suspension by effective agitation [9,16,18,24–28]. The size of the titration vessel varies from 2 to 100 mL, depending on the calorimeter design. One possible setup is outlined in Fig. 4. In the initial state, the solid is suspended in pure solvent under stirring. A portion of the mother solution from an external reservoir is then delivered through an efficient heat exchanger by means of a pump or a motor-operated syringe. The aliquot of the titrant and the rate of injection can be adjusted as required. Upon injection of the titrant, the overall enthalpy change ∆ injH is measured. After ther-

FIG. 4 Batch (titration) microcalorimetry setup. (Adapted from Ref. 18.)


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mal equilibration, the next portion is added, and the procedure is repeated several times (typically 10–20 steps). A full experiment is so designed that at the end of the experiment the equilibrium concentration in the suspension slightly exceeds the critical micelle concentration, cmc. The mother solution is therefore at a concentration above the cmc, whereas the concentration in the sorption vessel during the experiment is mainly below the cmc. It follows that a dilution enthalpy ∆dilH is involved in the experiment. This quantity consists of the enthalpy of demicellization, the enthalpies of dilution of the micelles and the monomers (depending on the stage of the titration), and the enthalpy of dilution due to adsorption [18,25–28]. ∆dilH can be measured in a series of blank experiments, i.e.,in the absence of the solid, but otherwise under the same experimental conditions. However, during the blank titration experiment, the equilibrium concentration c 1 in the calorimeter vessel is equal to the total surfactant concentration . In contrast, c1 is unknown during the sorption titration experiment. Fortunately, the separately determined adsorption isotherm Γ1 vs. c1 allows the calculation of c1 in the titration vessel via a mathematical iteration routine. For dilute solutions, the amount adsorbed in a static system may be given by [13,29] (3) where V0 is the volume of the solution, m is the mass of solid of specific surface area as, is the initial (or total) surfactant concentration in the sorption vessel, and c1 is the equilibrium concentration of the surfactant in the supernatant. Under the calorimetric conditions, V0 and gradually increase as the titration proceeds, but their values are readily calculated, at any stage of the experiment, from the total amount of titrant added. According to Mehrian et al. [27], Eq. (3) can be solved by iteration to obtain c1. Values of c1 are generated periodically, starting from zero, say, and using sufficiently small concentration increments. After each cycle, the resulting Γ1 vs. c 1 values are compared with the adsorption isotherm. If the values do not satisfy the isotherm simultaneously, the Γ 1 vs. c 1 pair is rejected and the iteration proceeds until the isotherm is satisfied within a certain error. A graphical method is described by Partyka et al. [25]. The bulk dilution term was very thoroughly analyzed by Zajac et al. [30]. For each titration step, the pseudo-differential molar enthalpy of displacement may be obtained from [27,30] (4) where ∆Γ1 is the change in the amount adsorbed during the given titration step. If the succeeding enthalpy differences ∆injH – ∆dilH are summed in the concen-

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Király

tration range of interest, the cumulative (or integral) enthalpy isotherm of displacement, ∆21H vs. c 1, is obtained. Titration calorimetry allows a number of successive heat determinations in a single experiment using the same solid sample. The method is particularly well suited to follow adsorption phenomena on fine particles (typical colloids). In the case of suspensions, stirring is of crucial importance. The problem of finding a compromise between sufficient mixing and minimum mechanical heat evolution was recently solved by employing a magnet-driven propeller with a rapid–slow reciprocating motion [9,16,24–26] or a circular horizontal disk moving up and down at low frequency [27]. The accuracy of titration calorimetry may be seriously affected by the change in the rheological properties of the suspension upon adsorption. Aggregation–disaggregation and change in viscosity may cause changes in the thermal power dissipated by constant-rate stirring. There are other disadvantages of the titration method. The heat of dilution (correction term) may be comparable in magnitude with the corresponding heat relating to the adsorption process. Further, the evaluation of raw data requires the adsorption isotherm, which must be determined in a separate experiment. Titration microcalorimetry is unsuitable (or less suitable) for following desorption phenomena because only a limited concentration range can be covered by back-titration with the solvent. The adsorption of ionic surfactants on charged surfaces in a static system may give rise to a drift of the solution pH or salinity [31]. This effect may be influenced by the liquid-to-solid ratio, which increases continuously as the titration proceeds. In contrast, the equilibrium pH and salinity can readily be held constant by using the method of flow frontal analysis [31]. In any case, to obtain reliable differential enthalpy data, adsorption and calorimetric measurements should be performed under identical, or at least very similar, experimental conditions. E. Flow Sorption Microcalorimetry The experimental protocol of flow sorption microcalorimetry is closely related to that of flow frontal analysis solid/liquid chromatography applied at low pressure [10,12,32–36]. The sorption vessel (a small chromatographic column) is loaded with the solid material (typically 0.05–0.4 g) and placed inside the measuring block of the calorimeter. Initially, pure solvent (water) is percolated through the column (by using a micropump) until thermal equilibrium is reached. The liquid flow is then switched to that of a dilute surfactant solution in continuous operation. As the new solution enters the column, surface-bound water molecules are displaced by adsorbing surfactant molecules until the new equilibrium state is established. The replacement experiment is successively repeated up to the desired concentration (say, slightly beyond the cmc) by using small concentration increments, and the associated heat effects ∆disH are recorded for each step. Typi-


347

cally, the cmc is reached in 10–20 concentration steps. One of the major advantages of flow sorption microcalorimetry over the other methods is that the exit port of the calorimeter can be connected to a suitable analytical device (spectrophotometer or differential refractometer) for the continuous monitoring of surfactant concentration. A fully automated measuring system designed for simultaneous measurements of the material balance and the enthalpy balance of adsorption is shown in Fig. 5 [35]. Typical instrumental response curves (calorimeter signals and refractive index detector signals) are illustrated in Fig. 6. From the concentration waves (breakthrough curves), the retention volumes and hence ∆Γ1, the amounts successively adsorbed on the same solid sample, can be calculated [37–39]: (5) where Q is the (constant) flow rate, mas is the surface area of the solid in the column, ∆c 1 is the concentration difference for the step , t CR is the corrected retention time (tR – tD, the retention time minus the dead time), and vCR is the corrected retention volume (v R – vD, the retention volume minus the dead volume). It should be noted that the Γ1 terms in Eq. (3) (static system) and Eq. (5) (dynamic system) are completely equivalent [37]. Strictly speaking, Γ1 is the

FIG. 5 Apparatus for flow sorption microcalorimetry simultaneously with flow frontal analysis solid/liquid chromatography. L1–L6, solutions; D1, D2, degassers; 7PV, electric seven-port valve; PC1, PC2, personal computers; MP, HPLC micropump; PR, pressure regulator; 6WV, six-way valve; L, loop; T1, T2, thermostats; TAM, microcalorimeter; COL, column; RID, refractive index detector; SC, RID sample cell; RC, RID reference cell; A, amplifier; FM, flowmeter; W, waste. (Adapted from Ref. 35.)

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FIG. 6 Instrumental response curves (calorimeter signals and refractive index detector signals) of the step-by-step displacement of water (2) by n-octyltrimethylammonium bromide (1) on Vulcan 3G graphitized carbon black at 298.15 K. The adsorption path is followed by the desorption path. The concentration increments are indicated in the figure in mmol/dm 3.

volume-reduced surface excess concentration , which in dilute solutions and for preferential adsorption of the solute over the solvent becomes equal to the real amount adsorbed, [13]. Although the breakthrough curves closely mimic the concentration profile, an exact correction for the dilution effect in the liquid flow experiment is less straightforward than in a batch experiment [11,14]. However, in dilute solutions and for closely spaced concentrations, the heat of mixing at the interface between replacing and replaced solutions can be neglected to a fairly good approximation


349

[11,14]. The blank experiments required for this correction can be performed by using glass pearls [34] or Teflon powder [40], which are inert solids with small specific surface areas, as the column packing materials. If the step-by-step displacement enthalpies and the amounts adsorbed are collected after k = 1, ..., K steps and the cumulative data are gathered, the integral enthalpy isotherm of displacement, k ∆disHk = ∆ 21H vs. c1 and the adsorption isotherm k ∆Γ 1,k = Γ1 vs. c1 are obtained. Alternatively, the measured heat can be divided by the amount adsorbed for each step: (6) where ∆(∆ 21 H) = ∆ dis H. The pseudo-differential molar enthalpies of displacement ∆21h1 obtained in this way are essentially free of systematic errors. Systematic errors in the calculation of ∆21h 1 may arise from a combination of separately measured enthalpy and adsorption isotherms. A further advantage of flow sorption microcalorimetry is that the reversibility of the adsorption process can be readily checked by using successive concentration steps in the opposite direction (desorption path). Repeated one-step adsorption/one-step desorption jumps, i.e., starting from and returning to the solvent for each step, offer an alternative to the step-by-step method [41]. In general, the flow sorption calorimetric assembly requires a stable, constant flow rate (about 10 cm3/h) and essentially zero pressure drop along the column. Flow resistance variation through the sample bed limits the performance of the method. Therefore, coarse particles (≥40 µm) are mainly used as the column packing material. Fine particles may pass through or block the filter of the column. A sorption vessel has been designed that is claimed to yield good baseline stability even at high pressure (up to 100 bar) and elevated flow rates [42]. Application of this HPLC calorimeter vessel may offer new perspectives in sorption calorimetric studies. Since the chromatographic effect (retention) plays a dominant role in flow sorption microcalorimetry, Eq. (5) can be advantageously used to estimate what systems can be studied and under what experimental conditions (mass of the solid, flow rate, and concentration increments). This aspect is particularly important in the case of surfactants with low cmc values, because the retention time for a small concentration step can be unreasonably high (1 day or even more) for an ill-designed experiment. F. Noncalorimetric Enthalples of Displacement The differential molar enthalpy of displacement can be approximated by the isosteric heat of adsorption, ∆ sth 1. This indirect (noncalorimetric) method is based on measurement of the adsorption isotherms at neighboring temperatures. For

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adsorption from dilute solutions, where the solvent may be regarded as in the pure state in the liquid phase, the Clausius–Clapeyron equation reads [11,43,44] (7) This approximation should be applied with reservation for several reasons. Among others, the activity coefficient of the solute may change with temperature, even at infinite dilution; the only quantity (Γ1) that can be experimentally determined may be insufficient to specify the surface composition (little is known about Γ2), so Γ1/Γ2 may not be independent of temperature; and the nature and number of the active sites of the adsorbent, hydration of the solid surface and hydration of the surfactant molecules may also be sensitive to temperature variations. In any case, a direct calorimetric experiment is always safer. IV. LITERATURE SURVEY ON CALORIMETRIC STUDIES OF SURFACTANT ADSORPTION ON SOLID SUBSTRATES The adsorption of surfactants on solid surfaces takes place in essentially two distinct stages. In the first stage, at low concentrations, surfactant molecules adsorb in direct contact with the solid surface via either Coulombic attraction, hydrogen bonding, or van der Waals forces. In the second stage, at higher concentrations, these adsorbate molecules induce surface aggregation at the “critical surface aggragate concentration” (csac < cmc), and the cooperative adsorption levels off near the cmc. A variety of surface aggregate structures may exist, such as globular micelles, full bilayers, patchy bilayers, half-cylindrical aggregates, or even full cylinders [45–48]. For illustration, our recent results on the adsorption of a nonionic surfactant (N, N-dimethyldecylamine-N-oxide) on hydrophilic (CPG silica glass) and hydrophobic (Vulcan 3G graphitized carbon black) surfaces are displayed in Fig. 7. The corresponding integral enthalpy isotherms of displacement are given in Fig. 8 [36]. On the hydrophilic surface of CPG silica, weakly adsorbed surfactant molecules at low concentrations induce surface aggregation at higher concentrations as the cmc in the bulk solution is approached (S-type isotherm). In contrast with the hydrophilic substrate, the hydrophobic surface of V3G strongly adsorbs surfactants at high dilutions in water. The adsorption proceeds further with increasing concentration until it turns to a plateau value (LS-type isotherm). The differential enthalpies of displacement ∆21h1 = ∆(∆21H)/∆Γ1 are plotted in Fig. 9 as a function of surface coverage Γ1 (upper graph) and of solution concentration c1 (lower graph) [36]. It is seen from the figure that the differential molar enthalpy functions undergo dramatic changes at the csac; the functions turn from an exo-


351

FIG. 7 Adsorption isotherms of N,N-dimethyldecylamine-N-oxide from aqueous solutions on CPG silica glass (Ο) and Vulcan 3G graphitized carbon black ( ) at 298.15 K.

FIG. 8 Cumulative enthalpy isotherms of displacement of water by N,Ndimethyldecylamine-N-oxide onto CPG silica glass (Ο) and Vulcan 3G graphitized carbon black ( ) at 298.15 k.

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FIG. 9 Differential molar enthalpies of displacement of water by N,Ndimethyldecylamine-N-oxide on CPG silica glass (Ο) and Vulcan 3G graphitized carbon black ( ) at 298.15 K.

thermic to an endothermic direction. It is interesting to note that the points indicated in the figure are raw experimental data, obtained directly from simultaneous adsorption and calorimetric measurements, and were not calculated from smoothed curves. The enthalpies of surface aggregate formation are 9.2 kJ/mol on CPG and 9.0 to 3.5 kJ/mol on V3G, which are close to the corresponding enthalpy of micelle formation in the bulk solution, ∆mich = 9.6 kJ/mol [36]. The close agreement is calorimetric evidence that the driving force of surface


353

TABLE 1 Literature Relating to Calorimetric Studies of Surfactant Adsorption on Solid Substrates Surfactant Adsorbent Reference Alkyl polyoxyethylenes Silica (gel) 41, 50–52, 64 Graphitized carbon black 19, 20, 51, 53, 54 Alkylbenzene polyoxye Silica (gel) 18, 25, 28, 31–33, 55–60, 62 thylenes Quartz 18, 31 Alumina 59 Titanium dioxide 59 Tin dioxide 59 Sandstone 24 Kaolin 24, 61 Bentonite 58 Activated carbon 25, 62 Reverse phase silica gel 33, 58, 60 Alkylsulfinylalkanols Graphitized carbon black 63 n-Octyl β-D-monogluSilica glass 36, 41, 64 coside Graphitized carbon black 36 N,NDimethyldecylamine- Silica glass 36, 64, this work N-oxide Graphitized carbon black 36, this work n-Decylmethylsulfoxide Carbon black 65,a 66a Alkyltrimethylammonium halides Silica (gel) 26, 28, 33, 58, 60, 67, 68 Graphitized carbon black 35 Reverse-phase silica gel 33, 58, 60 Kaolinite 43,a 69, 70a Na-, Fe-, Al-montmoril 71, 72 lonite Bentonite, illite 70a Bentonite, hectorite 73 Alkylpyridinium chloSilica (gel) 44,a 52, 59, 74, 75 rides Alumina 59, 74 Titanium dioxide 59, 74 Tin dioxide 59, 74 Kaolinite 27, 43,a 69, 70a Sepiolite 75 Bentonite, illite 70a Alkylbenzyldimethylam- Silica 76 monium bromides Quartz 77 Bentonite, hectorite 73 Tetrabutylammonium ni- Silver iodide 43a trate Aerosol OT Silica (gel), alumina, 33, 58 Reverse-phase silica gel 58

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TABLE 1 Continued Surfactant

Adsorbent

Aerosol OT (from toluene) Silica (gel), alumina, Reverse-phase silica gel Sodium alkylsulfates Silica (gel) Reverse-phase silica gel Scheelite, calcite Alumina Zirconium dioxide Graphitized carbon black Sodium hexanoate Graphitized carbon black Sodium oleate Scheelite, calcite Sodium alkylbenzene Sandstone sulfonates Kaolin Alumina Activated carbon Zirconium dioxide Sodium alkylxylenesul Alumina fonates Zwitterionics (betaines) Silica (gel) a

Reference 33, 58 58 33, 58 33, 58 22 26 77 20 78 22 24, 34, 61 24 61, 62 62 77 23 28, 30, 79

Isosteric heats.

aggregation is similar in nature to the driving force of aggregate formation in the bulk solution, predominantly attributed to entropically driven hydrophobic interactions. Obviously, the structure of the surface aggregates in a particular interfacial environment must be in some respect distorted in comparison with that in the bulk solution; this is reflected by the difference between the corresponding enthalpies of aggregate formation. A review providing insight into the contribution of calorimetry to the revelation of surfactant adsorption phenonomena will be published shortly [49]. Table 1 provides a list of references to the particular systems studied so far. ACKNOWLEDGMENT I thank the Alexander von Humboldt Foundation for a research fellowship at the Technical University of Berlin and the Hungarian Scientific Foundation (grant OTKA T025002) for financial support. REFERENCES 1. W Hemminger, G Höhne. Calorimetry: Fundamentals and Practice, Verlag Chemie, Weinheim, 1984.


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2. E Calvet, H Prat, HA Skinner. Recent Progress in Microcalorimetry, Pergamon Press, Oxford, UK, 1963. 3. JJ Christensen, JW Gardner, D Eatough, RM Izatt, PJ Watts, RM Hart. Rev Sci Instrum 44:481–484 (1973). 4. RM Izatt, EH Redd, JJ Christensen. Thermochim Acta 64:355–372 (1983). 5. T Wiseman, S Williston, JF Brandts, LN Lin. Anal Biochem 179:131–137 (1989). 6. J Suurkuusk, I Wadsö. Chem Scripta 20:155–163 (1982). 7. MG Nordmark, J Laynez, A Schön, J Suurkuusk, I Wadsö. J Biochem Biophys Methods 10:187–201 (1984). 8. I Wadsö. Thermochim Acta 85:245–250 (1985). 9. J Rouquerol. Pure Appl Chem 57:69–77 (1985). 1 0 . GH Findenegg. Calorim Anal Therm 16:1–11 (1985). 1 1 . R Denoyel, F Rouquerol, J Rouquerol. J Colloid Interface Sci 136:375–384 (1990). 1 2 . Z Király, I Dékány, E Klumpp, H Lewandowski, HD Narres, MJ Schwuger. Langmuir 12:423–430 (1996). 1 3 . Z Király, I Dékány. Colloid Polym Sci 266:663–671 (1988). 1 4 . GW Woodbury Jr, LA Noll. Colloid Surf 28:233–245 (1987). 1 5 . S Partyka, F Rouquerol, J Rouquerol. J Colloid Interface Sci 68:21–31 (1979). 1 6 . J Rouquerol, Thermochim Acta 96:377–390 (1985). 1 7 . DH Everett, AG Langdon, P Maher. J Chem Thermodyn 16:981–992 (1984). 1 8 . R Denoyel, F Rouquerol, J Rouquerol. In: Proceedings of the 2nd Engineering Foundation Conference on Fundamentals of Adsorption, (AI Liapis, ed.), Am Inst Chem Eng, New York; 1987, pp. 199–210. 1 9 . MJ Hey, JW MacTaggart, CH Rochester. J Chem Soc Faraday Trans 1 80:699–707 (1984). 2 0 . A Gellan, CH Rochester. J Chem Soc Faraday Trans 1 81:1503–1512 (1985). 2 1 . G Della-Gatta. Thermochim Acta 96:349–363 (1985). 2 2 . W von Rybinsky, MJ Schwuger. Ber Bunsenges Phys Chem 88:1148–1152 (1984). 2 3 . A Sivakumar, P Somasundaran, S Thach. J Colloid Interface Sci 159:481–485 (1993). 2 4 . J Rouquerol, S Partyka. J Chem Biotechnol 31:584–592 (1981). 2 5 . S Partyka, M Lindheimer, S Zaini, E Keh, B Brun. Langmuir 2:101–105 (1986). 2 6 . S Partyka, E Keh, M Lindheimer, A Groszek. Colloid Surf 37:309–318 (1989). 2 7 . T Mehrian, A de Keizer, AJ Korteweg, J Lyklema. Colloid Surf 73:133–143 (1993). 2 8 . S Partyka, M Lindheimer, B Faucompre. Colloid Surf 76:267–281 (1993). 2 9 . DH Everett. Pure Appl Chem 58:967–984 (1986). 3 0 . J Zajac, C Chorro, M Lindheimer, S Partyka. Langmuir 13:1486–1495 (1997). 3 1 . R Denoyel, J Rouquerol. J Colloid Interface Sci 143:555–571 (1991). 3 2 . R Denoyel, F Rouquerol, J Rouquerol. In: Adsorption from Solution (RH Ottewill, CH Rochester, AL Smith, eds.), Academic Press, London, 1983, pp. 225–234. 3 3 . LA Noll. Calorim Anal Therm 16:12–19 (1985). 3 4 . NM van Os, G Haandrikman. Langmuir 3:1051–1056 (1987). 3 5 . Z Király, GH Findenegg. J Phys Chem 102:1203–1211 (1998). 3 6 . Z Király, GH Findenegg. Langmuir (2000, in press). 3 7 . HL Wang, JL Duda, CJ Radke. J Colloid Interface Sci 66:153–165 (1978). 3 8 . CS Koch, F Köster, GH Findenegg. J Chromatogr 406:257–269 (1987).

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10 Microcalorimetric Control of Liquid Sorption on Hydrophilic/Hydrophobic Surfaces in Nonaqueous Dispersions IMRE DÉKÁNY Department of Colloid Chemistry, University of Szeged, Szeged, Hungary I.

Introduction

II.

Adsorption and Heat of Immersion on Solids in Pure Liquids and Binary Liquid Mixtures A. Heat of immersion at solid/liquid interfaces B. Adsorption of binary liquid mixtures on dispersed solid particles C. Combination of adsorption excess isotherms and enthalpy isotherms: new way to determine adsorption capacity D. Adsorption excess and enthalpy isotherms on solids in binary liquids E. Classification of enthalpy isotherms

III.

IV.

Heat of Immersion on Hydrophilic and Hydrophobic Colloidal Particles in Different Liquid Mixtures A. Heat of Wetting in amorphous silica dispersion and on zeolites B. Immersional wetting on nonswelling clay minerals C. Heat of wetting on swelling clay minerals D. Adsorption of n-butanol from water on modified silicate surfaces Properties of the Adsorption Layer and Stability of Aerosil Dispersions in Binary Liquids A. B.

Influence of the adsorption layer on the aggregation of aerosil dispersions in binary liquids Characterization of the stability of nonaqueous dispersions by calorimetric and adsorption measurements

358 359 359 362 365 367 375 377 377 380 386 392 397 398 401

357

358 V.

Dékány Small-Angle X-Ray Scattering of SiO2 Particles in Binary Liquids

408

References

409

I. INTRODUCTION The stabilization of colloidal disperse systems in various liquids is primarily influenced by the difference between the polarities of the solid particles and the liquid. Thus, metal oxides may be dispersed in aqueous media to form stable hydrosols or in alcohols to produce stable alcosols [1]. Stable dispersions are also obtained in the same way in organic media if the polarity of the surface is altered, i.e., hydrophobized by long alkyl chains, resulting in the establishment of stable organosols or suspensions [2–6]. The determinative factor is the magnitude of the interparticle interaction potential, which can be calculated on the basis of Hamaker constants [7]. The equations describing interaction potential, thus allowing the calculation of interparticle interactions, were formulated by Vold [3] and Vincent [5]. Interparticle interactions and consequently the stability of disperse systems may also be adequately characterized by the properties of the sorption layer formed on the surface of solid particles. When a solid particle is immersed in a liquid and is readily wetted, an exothermic heat of immersion is liberated due to the strong solid–liquid interaction. The reason for this is presumably the formation of an adsorption layer several molecules thick on the surface of the particles. If the particles are well wetted by the given liquid, there is a good chance of obtaining a stable disperse system. If the adsorption interaction between particle and liquid is weak, the heat of wetting is small and the dispersion is unstable because interparticle adhesion forces are larger. Thus, on the basis of the observations mentioned, the stability of a disperse system in a nonelectrolyte (e.g., in an aromatic or aliphatic liquid) is determined by the relationship between wetting and adhesion. According to these observations, the solid–liquid interaction can be quantitatively characterized by the magnitude of the heat of immersion in pure liquids or in mixtures and solutions [8–11]. Further information is obtained if the amount of liquid adsorbed on the surface of the particle is also determined, permitting the combination of the data on heat of immersion with those on the amount of adsorbed liquid. Thus, molar adsorption enthalpies can be given for the characterization of the stabilizing adsorption layer [12– 16]. A further benefit of adsorption excess isotherms is that it is possible to calculate from them the free enthalpy of adsorption as a function of composition. When these data are combined with the results of calorimetric measurements, the entropy change associated with adsorption can also be calculated on the basis of the second law of thermodynamics. Thus, the combination of these two techniques makes possible the calculation of the thermodynamic potential functions describing adsorption [14,17–19].

Liquid on Surfaces in Nonaqueous Dispersions

359

The monitoring of interparticle interactions in disperse systems is very important. One of the simplest methods to achieve this is through the determination of the rheological characteristics of the system, because this property is highly dependent on interparticle adhesion [20–27]. Modern physical methods such as light scattering, small-angle X-ray scattering (SAXS), or small-angle neutron scattering (SANS) obviously yield new information on the structure of disperse systems and the interparticle interactions operative therein [28–30]. On the other hand, direct interparticle interactions in a given liquid or solution may also be determined by surface force microscopy [31–34]. In this chapter, solid–liquid interactions and interparticle interactions are described not only for pure liquids but also for binary mixtures. The reason for this is that in the individual pure liquids, conditions of sorption and wetting are determined by the chemical nature of the components, and it is not easy to systematically vary them (e.g., to change the polarity of the medium). If, however, these pure liquids are combined to yield binary mixtures, the polarity of the medium can be adjusted at will and can be arbitrarily chosen within the limits set by the polarities of the two liquid components. Heat of wetting and consequently the stability of the dispersion can be regulated in a similar way in nonelectrolytes by varying the composition of the mixture so that conditions of sorption and wetting within the limits of miscibility can be adjusted [35–38]. Thus, parallel analysis of adsorption and wetting makes possible a many-sided approach to the stability of disperse systems. Given the knowledge of Hamaker constants, interaction potential functions can be calculated, yielding quantitative data on interparticle interactions. However, calculations of interaction potentials are affected by the composition and thickness of the adsorption layer on the surface of the particles. Quantitative information on the adsorption layer makes possible an even more precise calculation of these interactions [29–39]. II. ADSORPTION AND HEAT OF IMMERSION ON SOLIDS IN PURE LIQUIDS AND BINARY LIQUID MIXTURES A. Heat of Immersion at Solid/Liquid Interfaces A simple and straightforward way for quantifying the solid–liquid interfacial interaction is immersion microcalorimetry. In the course of this measurement, the surface previously heat-treated in vacuo is brought into contact with the pure wetting liquid [8,9,40]. It is advisable to choose a liquid of different polarity, so that the extent of the hydrophobicity or hydrophilicity of the surface can be estimated from the magnitude of the heat of wetting. Thus, the wetting a hydrophilic surface with a polar liquid liberates a large exothermic enthalpy of wetting, and

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FIG. 1 Schematic picture of immersional wetting (solid/gas into solid/liquid) in pure liquids.

wetting a hydrophobic surface with a polar liquid produces a smaller heat effect (Fig. 1). When a solid adsorbent is immersed in a binary mixture, the heat of wetting is greatly affected by the composition of the bulk phase, and values intermediate between the heat effects of wetting measured in the pure components 2 and 1, respectively, are obtained. This is the so-called immersion technique, which supplies direct information on the strength of the solid–liquid interaction with the mixture (Fig. 2) [41–44]. When ∆n1 moles of component 1 of the binary mixture is added to the suspension made up in the liquid mixture with molar amount n = n1 + n 2 (i.e., to the solid/liquid interface), the original composition x 1 is changed to and consequently the composition of the interfacial layer is shifted by the value = . The amount of adsorbed material present in the interfacial layer is therefore where and are the material contents of the adsorption layer of components 1 and 2, respectively. The changes in composition in the bulk phase (∆x1) and in the interfacial phase ( ) bring about a change in the so-called enthalpy of displacement, ∆21H, which is the difference between the heats of wetting characteristic of the two states with different compositions (Fig. 3). When the change in composition is started from component 2 ( ), increasing x 1 in the direction x1 1, the isotherm of enthalpy of displacement ∆21H = f(x 1) is obtained (Fig. 4) [12–14].


361

FIG. 2 Schematic picture of immersional wetting (S/G into S/L) in binary liquid mixtures. n o and are the liquid material amount and mixture molar fraction, respectively, in the initial state. In equilibrium state: liquid material amount n, mixture molar fraction x 1, surface layer amount n s.

FIG. 3 Schematic picture of the heat evolution (enthalpy of displacement ∆ 21H) in the solid/liquid adsorption layer. After adding component 1 (∆n 1 ) to the liquid mixture, the composition of the bulk and the adsorption layer will be exchanged (notation with *).

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FIG. 4 Schematic representation of the enthalpy of displacement isotherm in binary mixtures in the case of U-shaped adsorption excess isotherms.

B.

Adsorption of Binary Liquid Mixtures on Dispersed Solid Particles

When solid particles are dispersed in liquid medium, solid–liquid interfacial interactions will cause the formation of an adsorption layer, the so-called lyosphere, on their surface. The material content of the adsorption layer is the adsorption capacity of the solid particle, which may be determined in binary mixtures if the adsorption excess isotherm is known [45–50]. Due to adsorption, the initial composition of the liquid mixture, , changes to the equilibrium concentration x1. This change, – x1 = ∆x 1, can be determined by simple analytical methods. The relationship between the reduced adsorption excess amount calculated from the change in concentration, = n0( – x1), and the material content of the interfacial layer is given by the Ostwald–de Izaguirre equation [46–49]: (1) where n 0 is the total amount of liquid mixture in the disperse system,

+

363


= n s is the material content of the adsorption layer, and is the composition of the interfacial layer. Given the knowledge of the adsorption excess isotherm [46–48].

= f(x1), the so-called individual isotherms are given by the equations

(2) and (3) is the adsorption capacity relative to pure component 1 and r* = Vm,2/ where Vm,1 is the ratio of the molar volumes of the components. In the case of U-shaped excess isotherms, adsorption capacity ( ) can be determined from the linearized Everett–Schay function [49,50]. As soon as the adsorption capacity is known, the volume of the layer is obtained from the equation Vs = Vm,1. The volume fraction of the adsorption layer, can be calculated from the data of excess isotherms by using the equation (4) 1. Free Enthalpy of Wetting of the Solid/Liquid Interface and the Thickness of the Adsorption Layer The free enthalpy of adsorption of solid/liquid interfaces can be calculated with the Gibbs equation [48–50] and knowledge of the isotherm

= f(x 1): (5)

where a1 = f1x1 is the activity of component 1, which can be calculated with the help of the Redlich–Kister equations [51], given the knowledge of the solid–vapor equilibrium data. Different types of adsorption excess isotherms (U- and S-shaped functions) naturally yield different free enthalpy functions ∆21G = f(x 1), the course of which is characteristic of the minimum energy of wetting at the solid/liquid interface, a parameter diagnostic of the stability of the disperse system. In calculations of stability for disperse systems, knowledge of the thickness of the stabilizing adsorption layer is highly important [36,39]. If the specific sur-

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face area (a s) of the particles is known, then the thickness of the layer, ts = Vs/as, can be calculated from Eq. (4): (6) where and 1 are the volume fractions of the adsorption layer and bulk phase, respectively, in adsorption equilibrium. The layer thickness ts calculated according to Eq. (6) is nearly constant; in nonideal liquid mixtures, however, its value may be strongly dependent on the composition of the bulk phase [52,53]. 2. Enthalpy of Immersional Wetting in Binary Mixtures According to Everett’s adsorption layer model [8,10,11,40], the heat of immersional wetting (∆w Ht), a thermodynamic parameter characteristic of the solid–liquid interaction, can be easily calculated when the molar enthalpies, h1 and h2, of the components of the system are known. When a solid adsorbent is immersed in a liquid mixture, the amount of which is the interfacial forces of adsorption cause the formation of an adsorption layer on the surface of the adsorbent, the material content of which is ns = . According to Everett [40,50], the change in enthalpy of wetting between the equilibrium and initial states (H e – H 1) is given by the equation (7)

It is assumed in Eq. (7) that the enthalpy of the solid adsorbent is not altered by wetting. The introduction of molar fractions and the material balance n 0( – x1) = n s( – x1) brings Eq. (8) to the form (8a) where ∆He = He(x1) – He( ) is the change in the enthalpy of mixing of the bulk phase. When ∆x 1 = – x 1 is known for a given liquid mixture, the function ∆He(x 1) can be calculated from the functions of enthalpy of mixing described in the literature. If only the change in enthalpy relative to the adsorption layer is to be calculated, then the function ∆wH t = f(x1) has to be corrected by the function ∆He = f(x1). Introducing the volume fractions of the adsorbed layer and the heat of immersion of pure components, Eq. (8a) can be given as follows: (8b)


365

C. Combination of Adsorption Excess Isotherms and Enthalpy Isotherms: New Way to Determine Adsorption Capacity The adsorption of binary systems is described by the Ostwald–de Izaguirre equation, which establishes a relationship between the specific reduced adsorption excess amount ( ) and the material amount in the interfacial layer (n s = ) [40–46]: (9) The adsorption volume filled by the components of the mixture being adsorbed on a solid surface is (10) In general, (11) where Vm,i is the partial molar volume of the components in the adsorption layer. Equation (11) is formally identical with the description of the so-called porefilling model, but it is also applicable for planar nonporous adsorbents, because the thickness of the adsorption layer is determined solely by the range of the forces of adsorption. Thus, the adsorption volume Vs designates the volume falling within the range of adsorption forces; in certain regions of the isotherm, its value may be nearly constant, but it may also be a function of equilibrium composition. If molecular sizes within the adsorption space are not identical, i.e., if r* = Vm,2/ Vm,1 1, and Vs = V m,1, then Eq. (11) may also be formulated for : (12) Equation (12) already incorporates the assumption that there exists a concentration range where the volume of the adsorption layer—on a constant surface area—is independent of the composition of the bulk phase. However, no statement can yet be made as to whether this layer is monomolecular or multilayered. If the behavior of the bulk liquid and interfacial layer is ideal, the = f(x1) function can be calculated from calorimetric data by Eqs. (8b, or 18 and 19). In this case Eq. (4) may be rewritten as [14–16] (13)

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Dékány

(14) The right-hand side of Eq. (14) is made up exclusively of terms consisting of adsorption capacities. The intersection of the straight line is and the slope is then the second term of Eq. (14) is zero. Knowing the values of the integral exchange enthalpy, the adsorption capacity ( ), and the molar adsorption enthalpy of the layer , a combination of Eqs. (1) and (8a) and the substitution (for an ideal adsorption layer and for the case ∆21Hse = 0) yield [14–16,37,38] (15) and are independent The ideal behavior of the adsorption layer also means that of the concentration of the mixture, a condition that is rarely met. It is apparent from arguments we present later, however, that molar differential exchange enthalpy is constant in a certain range of composition; our assumption therefore has to be accepted. Equation (15) is also a linear function, with intersection b = and slope S = ns( ); i.e., the adsorption capacity is n s = S/b. Equation (15) was first applied for the interpretation of flow microcalorimetric measurements (on dilute solutions only) by Woodbury and Noll [12,13]. If the size of the molecules is uniform, then the slope of Eq. (15) is given by the formula (16) the slope of the equation yields the total exchange enthalpy of the adsorption displacement process. This value can also be directly determined by calorimetry. In the case of S-shaped excess isotherms, the value of the adsorption azeotropic composition is known. At the azeotropic point = 0; therefore, x 1 = , according to Eq. (1). Since , the adsorption capacity n s can be divided into two terms with the help of the equations [14–16] (17a) and (17b)

Liquid on Surfaces in Nonaqueous Dispersions D.

367

Adsorption Excess and Enthalpy Isotherms on Solids in Binary Liquids

1. U-Shaped Excess Isotherms and Enthalpy Isotherms Calculations regarding the composition of the adsorption layer and the determination of adsorption capacity and the heterogeneity of the surface have been discussed in several publications by Everett [40,50], Schay [47–49] Berger and Dékány [52,53], and members of the Polish adsorption school [45,55–57]. The energetics of the exchange (displacement) process taking place in the adsorption layer have been the subject of considerably fewer publications, and these deal mostly with the adsorption of dilute solutions. The change in enthalpy accompanying the adsorption exchange process in organic media on apolar surfaces has been studied in detail by Denoyel et al. [17,18,42], Groszek [41], and Findenegg and coworkers [43,44]. Studies published by Allen and Patel [58] and by Woodbury and coworkers [12,13] include the simultaneous analysis of adsorption excesses and calorimetric data. Billett et al. [8] determined heats of immersion wetting in a system of benzene– cyclohexane/activated carbon in the entire range of mixing, parallel with the determination of adsorption excess isotherms. In this chapter we give a parallel analysis of the liquid sorption excess isotherms and adsorption exchange enthalpy isotherms of benzene–n-heptane and methanol– benzene mixtures on adsorbents with polar and apolar surfaces. Systems with Uor S-shaped excess isotherms were selected. Our aim is to examine the presence and character of a connection between adsorption excess and enthalpy isotherms for the various isotherm types [36]. The determination of enthalpy changes occurring in the course of flow microcalorimetric measurements necessitates a simultaneous analysis of the material balance and enthalpy balance of adsorption. According to Dékány et al. [14–16] and Király and Dékány [59–61], these relationships, expounded according to either the adsorption layer model or the Gibbs model of adsorption excess amounts, are suitable for the exact determination of changes in exchange enthalpy observable in flowing systems and for the correct interpretation of the sorption exchange process. Adsorption excess isotherms of benzene (1)–n-heptane (2) and methanol (1)– benzene (2) mixtures are shown in Figs. 5 and 6. Both isotherms are U-shaped, with the difference that in the methanol (1)–benzene (2) system methanol is preferentially adsorbed on silica gel. Pretreatment of silica gel by methanol was necessary to eliminate the effect associated with the chemisorption of methanol, so that data reflecting only physical adsorption would be measured [14,15]. In the case of benzene–n-heptane mixtures, the excess isotherm on silica gel has no linear region: Parallel with increasing the concentration of component 1 in the bulk phase, the composition of the interfacial layer changes continuously

368

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FIG. 5 (a) Adsorption excess and (b) enthalpy of displacement isotherms in benzene (1)–n-heptane (2) mixture on silica gel (a s = 358 m/g).


369

FIG. 6 (a) Adsorption excess and (b) enthalpy of displacement isotherms in methanol (1)–benzene (2) mixture on silica gel (a s = 358 m 2 /g).

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TABLE 1 Results of Analysis of Adsorption Excess and Enthalpy Isotherms on Selected Porous Adsorbents (mmol/g) Adsorbent

Liquid mixture

S,Na

Eq. (15)

Silica gel Silica gel Silica gel C18 Chemviron F400 Printex 300

Methanol–benzene Benzene–n-heptane Methanol–benzene Methanol–benzene Methanol–benzene

5.31 — 4.80 9.10 1.01

5.14 2.02 4.10 10.41 1.00

a

–∆21Ht –( ) (J/g) (kJ/mol) 36.71 11.30 9.50 –10.52 –1.23

7.10 5.60 4.00 5.31 –0.50

SN: Schay–Nagy extrapolation method [46–49].

(Fig. 5a). This is well reflected by the enthalpy isotherm shown in Fig. 5b, which also indicates a gradual, step-by-step heat exchange and, correspondingly, a gradual process of displacement. Enthalpy changes accompanying the full exchange of the components (∆21Ht) are listed in Table 1. These data reveal that the full exchange of n-heptane for benzene on the surface of silica gel is an exothermic process and results in the liberation of –11.3 J/g of heat. In the case of an exchange of molecules in the reverse direction, on the other hand (see the open circles in Fig. 5b), identical but endothermic heat effects are obtained. In the case of the methanol–benzene/silica gel system, adsorption occurs and about 89–90% of the total exchangeable heat (∆ 21Ht) is liberated at the initial section of the isotherms. In that range of composition where the excess isotherm of the methanol (1)–benzene (2) liquid pair is linear (Fig. 6a) (and here the composition of the interfacial layer is nearly constant), some heat effect of exchange is still observable (Fig. 6b). This means that the composition of the interfacial layer is still changing; these changes are too small to be adequately monitored by our analytical methods but are readily detected by calorimetry. This observation is a direct experimental proof for a theoretical statement by Rusanov that, strictly speaking, the composition of the interfacial layer may not be constant within the linear section of the isotherm [39]. The excess isotherm determined on the surface of graphitized carbon has an inverse U-shape, i.e., the adsorption excess for polar methanol is negative within the entire concentration range (Fig. 7a). Accordingly, when the amount of methanol in the mixture is increased from x 1 = 0 to x1 = 1, the effects measured are always endothermic, because the displacement of benzene from the surface is an energyconsuming process (Fig. 7b).


371

FIG. 7 (a) Adsorption excess and (b) enthalpy of displacement isotherms in methanol (1)–benzene (2) mixture on graphite (Printex 300) surface.

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2. S-Shaped Excess Isotherms and Enthalpy Isotherms An excess isotherm determined in a methanol–benzene mixture on silica gel is Ushaped. If, however, the silica surface is modified by octadecyldimethylchlorosilane (silica gel C18) in methanol–benzene mixtures, an S-shaped excess isotherm is obtained, the azeotropic point of which is = 0.615 (Fig. 8a). When the displacement process is started from benzene, it can be seen that up to a molar fraction of x1 = 0.6 the incorporation of methanol into the adsorption layer results in a change in enthalpy of about 7.35 J/g. However, the displacement of benzene is not yet complete; up to the azeotropic point the adsorption layer will also contain benzene. A common characteristic of the two isotherms presented in Fig. 8 is that the isotherm = f(x 1 ) is linear in a very wide range of composi-

FIG. 8 (a) Adsorption excess and (b) enthalpy of displacement isotherms in methanol (1)–benzene (2) mixture on hydrophobized silica gel (a s = 312 m 2/g).


373

tion (x1 = 0.1–0.7), while the enthalpy isotherm ∆21H = f(x1) is approximately constant. In other words, within this range of composition, a very small exchange heat effect is produced; consequently the composition of the layer is not constant. The maximum value of the enthalpy isotherm is at the azeotropic composition; further heat effects are endothermic, and the integral enthalpy isotherm therefore exhibits a tendency to decrease. Endothermic effects occurring from x 1 = 0.6 to x1 = 1 are associated with the displacement of benzene from the adsorption layer. The azeotropic composition of the excess isotherm determined on Chemviron (Union Carbide USA) activated carbon, an adsorbent with a large specific surface area, is = 0.095, indicating that the adsorption layer still contains a little methanol (Fig. 9). This methanol is bound to the polar regions of the surface of the adsorbent, as shown by the exothermic heat effect detectable from x1 = 0 to x 1 = 0.1.

FIG. 9 (a) Adsorption excess and (b) enthalpy of displacement isotherms in methanol (1)–benzene (2) mixture on Chemviron F-400 active carbon.

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If x 1 > , the excess isotherm is practically linear between x 1 = 0.1 and 0.7, and the enthalpies of exchange measured are moderately endothermic. If the molar fraction of the bulk phase is larger than x1 = 0.8, the displacement of benzene by methanol will preferentially occur, resulting in a considerable endothermic effect on the porous apolar surface. When adsorption displacement proceeds from x1 = 1 toward x 1 = 0, the heat effects detected are of a reverse sign in the case of each isotherm. This means that the processes of displacement are reversible to a close approximation. A very little irreversibility was detected only in the case of activated carbon Chemviron, which is probably caused by incomplete displacement of methanol from the micropores by benzene. 3.

The Linearized Functions

The applicability of Eq. (15) for U-shaped excess isotherms is next discussed. Functions for the case of U-shaped excess isotherms are

FIG. 10 Combination of the adsorption excess amounts and calorimetric data in (Ο) benzene (1)–n-heptane (2) mixture on silica gel (a s = 358 m 2 /g), and in methanol (1)–benzene (2) mixture on (∆) silica gel (as = 458 m2/g and ( ) silica gel (as = 358 m2/g).


375

shown in Fig. 10. Adsorption capacities (n s) obtained in this representation as the ratio of the slope ns( /r*) and the intersection ( /r*) are identical with the values mentioned above. The advantage of Eq. (15) is that the intersection yields the value of ( /r*), and this value is then multiplied by , yielding the calculated value of the total integral exchange enthalpy ∆21H t, which can be compared with the experimentally determined value of ∆21H t (Table 1). The interaction of adsorbents with various surface energies with the liquid components studied are adequately characterized by the differences in molar adsorption enthalpies between components 1 and 2, – (1/r*) , listed in Table 1. In the case of the adsorption of the methanol–benzene liquid pair, these enthalpy differences in the adsorption layer are decreased by the effect of hydrophobization. E. Classification of Enthalpy Isotherms* In the case of adsorption of ideal or quasi-ideal mixtures on adsorbents with polar or apolar surfaces, usually U-shaped excess isotherms are obtained (type I according to the Schay–Nagy classification [46–49]. On adsorbents with polar surfaces, in the case of liquid pairs made up of components with a large difference in polarity (e.g., alcohol–benzene), the polar component is preferentially adsorbed on the surface (type II) and again U-shaped excess isotherms are obtained. Thus, in these systems the composition of the interfacial layer ( or ) increases monotonously as a function of equilibrium composition; consequently, according to Eq. (8b), the enthalpy isotherm ∆wH will also be a monotonously increasing function (Fig. 11a). When alcohol–benzene mixtures are adsorbed on adsorbents with low surface energies, S-shaped excess isotherms are measured [15,16,35–38]. When changes in enthalpy accompanying the adsorption displacement process are examined in these systems, the integral exchange enthalpy isotherms usually do not increase monotonously but possess a backward section. After having reached adsorption azeotropic composition, changes in concentration (∆x1) are accompanied by endothermic heat effects of exchange, and these changes do not follow changes in the composition of the surface layer (Fig. 11b.). For S-shaped excess isotherms (Schay–Nagy types IV and V [46–49]), is nearly constant in a relatively wide concentration range, and at i.e., adsorption azeotropic composition, appears. In this case the value of ∆wH changes very little in the middle section of the enthalpy isotherm, where is constant; then at the azeotropic composition a maximum * See also Refs. 14–16 and 35. ** Notation of the interfacial layer volume fraction is data (see Eqs. 18, 19). This is identical with

, calculated from calorimetric

, calculated from the excess isotherm.

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FIG. 11 Classification of immersional wetting enthalpy isotherms: (a) U-shaped excess isotherm, with corresponding enthalpy of immersion isotherm. (b) S-shaped excess isotherm, with corresponding enthalpy of immersion isotherm.

is observed (∆wHa). Thus, in the case of S-shaped excess isotherms, integral enthalpy isotherms ∆ 21H = f(x 1) have to be divided into two sections at the azeotropic composition ; 1. From x1 = This section is essentially a version of the total measurable section of U-shaped isotherms, shortened in proportion with . 2. From x1 = to x1 = 1, the displacement factor can be calculated by the formula


377

(19) Division of the enthalpy isotherms into two sections can be considered justified only if the adsorption layer is ideal in the vicinity of azeotropic composition, i.e., ∆21Hse = 0. Displacement enthalpy isotherms calculated according to Eqs. (18) and (19) change parallel with the isotherms = f(x1) calculated from adsorption measurements [14–16, and 35]. III. HEAT OF IMMERSION ON HYDROPHILIC AND HYDROPHOBIC COLLOIDAL PARTICLES IN DIFFERENT LIQUID MIXTURES Adsorption excess isotherms were determined on hydrophilic and partially hydrophobic layered silicates in methanol–benzene mixtures [62–65]. From these isotherms the free energy of adsorption ∆21G = f(x1) that is characteristic of surface polarity is derived [60–62]. Displacement enthalpy isotherms were also determined by immersion microcalorimetry so that the entropy changes could be calculated. The preferential adsorption on adsorbents with different surface hydrophobicities can be properly described by the thermodynamic data of the adsorbed layer [66–69]. When the components in a binary mixture are very different in polarity, as they are in methanol–benzene mixtures, the polarity of the surface can be characterized from the shape of the excess isotherms and the azeotropic composition. The free energy function ∆21G = f(x1) calculated from the excess isotherms gives quantitative information about the decrease in free energy due to the displacement [see Eq. (5)], the integral enthalpy isotherms can be determined with microcalorimetry, and the thermodynamic description of the adsorption layer is complete [67–69]. According to Regdon et al. [70,71] and Marosi et al. [72], the displacement enthalpy data give information about the solid–liquid interaction, and the second main law of thermodynamics allows the calculation of the displacement entropy functions. The combination of displacement free energy and enthalpy functions with the excess isotherms gives a new way to determine the adsorption capacities [Eq. (15)]. This combination also gives data (∆21g, ∆21h) that describe the polarity of a surface in a certain liquid mixture [73,74]. A.

Heat of Wetting in Amorphous Silica Dispersion and on Zeolites

Hydrophilic (A 200) and hydrophobic (R 972) varieties of amorphous SiO2 (Aerosil derivatives, Degussa AG, Germany) were studied by immersion microcalorimetry in various liquids (methanol, benzene, n-heptane), and the results are listed in Table 2. Clearly, the heat of immersion on the hydrophilic surface (A 200) is

378

TABLE 2 Heat of Wetting on Hydrophilic (A 200) and Hydrophobic (R 972) Aerosils in Selected Liquids –∆ wH (J/g)

a (BET) (m 2 /g)

Methanol

Benzene

231

40.05

19.4

s

Absorbent A 200

∆ wh (mJ/m2) n-Heptane

Methanol

8.5

175

Benzene

n-Heptane

84

37 125

R 972

120

25.7

33.8

15.1

214

281

A 200/CH 3 OH a

228

19.7

38.2

16.5

86

167

72

R 972/CH 3 OH a

123

25.5

33.0

17.8

207

268

144

a

Aerosil powders were pretreated with methanol before the immersion experiment.

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the largest in methanol, moderate in toluene, and the smallest in n-heptane. The heat effect measured in the aromatic solvent benzene is intermediate between the values for toluene and n-heptane. Heats of immersion per unit surface in millijoules per square meter are also given in Table 2 for the various liquids [63,64]. The effect of surface treatment is also easily detected by the determination of heats of immersion. When the surface of the hydrophilic Aerosil is treated with methanol, heats of immersion are changed considerably because Si—OH groups on the surface are replaced by Si—O—CH3 groups. It is revealed by the data in Table 2 that the BET surface is unchanged by methanol treatment; however, the change in enthalpy of wetting per unit surface area of A 200 is significantly increased by surface treatment with methanol (surface methylation) in both benzene and nheptane. The largest value for heat of wetting on the original hydrophilic SiO2 surface (175 mJ/m2) is measured in methanol; the heat effect is considerably smaller in benzene, and an effect due solely to dispersion interactions (37 mJ/m2) can be detected in n-heptane (Table 2). Further information on heat alteration of surface energy due to dealumination and on the depolarization of zeolite surfaces can be obtained by the determination of the heat of wetting [65]. The values determined in alcohols of various chain lengths, benzene, and n-heptane are listed in Table 3. The values of specific heats of immersion (∆wH) on Na-Y zeolite are very large in the alcohols; in benzene and n-heptane the wetting effect measured is less significant. In each liquid, the values measured on the dealuminated sample are significantly lower than those determined on Na-Y zeolite. It is clear from the data of Table 3 that on dealuminated samples the values of heat of wetting in benzene and in n-heptane are nearly identical and do not differ significantly from the values measured in methanol and ethanol. In contrast, it can be seen that the effects measured on Na-Y samples in alcohols and benzene are significantly higher than those determined in apolar n-heptane. TABLE 3 Heat of Wetting on Hydrophilic (Na-Y) a and Hydrophobic (Dealuminated) Zeolites in Different Liquids Liquid Methanol Ethanol n-Propanol n-Butanol Benzene n-Heptane

Na-Y zeolite, –∆ wH (J/g) 214.0 ± 2.4 196.5 ± 2.0 190.6 ± 2.0 175.0 ± 2.8 129.5 ± 8.9 73.4 ± 7.6

Dealuminated zeolite, –∆ wH (J/g) 41.4 30.1 20.5 16.4 29.1 32.9

± ± ± ± ± ±

8.5 8.7 6.7 9.7 6.5 7.6

Na-Y zeolite is a microporous hydrophilic aluminosilicate with high cationic exchange capacity. a

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B. Immersional Wetting on Nonswelling Clay Minerals Clay minerals and their modified (organophilic) derivatives are usually readily dispersed in solvents or solvent mixtures of various polarities. The stability and structure building of these suspensions vary over a wide range, depending on the surface properties of disperse particles and the polarity of solvents. Illite, as a nonswelling mineral of layered structure, plays a very important role in our studies. This special role is due to the fact that both sides of the surface of the silicate lamellae are made up of SiO4 tetrahedron planar lattices, and this structure—even when hydrophobized—is identical with the surface structures of montmorillonite and vermiculite, both of which are of the swelling type. The swelling clay minerals (e.g., montmorillonites) are of colloidal dimensions (d < 2 µm) and are therefore able to adsorb significant amounts of various molecules, owing to their large specific surface area. It follows from the above-mentioned structural properties that sorption processes and adsorption capacity will be basically determined by whether the mineral studied is of the swelling or nonswelling type. Several papers on the liquid sorption properties of the hydrophobic clay minerals were published at our institute in Hungary [35–37,67–79]. The adsorption capacities for S-shaped excess isotherms determined on nonswelling illite derivatives were analyzed by using the Schay–Nagy extrapolation and the adsorption space-filling model. Figure 12 shows the excess isotherms for hydrophilic illite and three gradually organophilized hexadecylpyridinium (HDP) illites in methanol–benzene mixtures. The amount of methanol in the adsorption layer decreases with increasing coverage by HDP cations bonded on the illite surface [75–78]. The sorption exchange process taking place at the solid/liquid interface can be described in thermodynamically exact terms when the activities of the interfacial layer and those of the bulk phase are known. In accordance with the exchange equilibrium at the solid/liquid interface, (20) the liquid sorption equilibrium constant is given by the formula (21a) Assuming that 1, i.e., the activity coefficients of the interfacial phase compensate for each other [71,73], (21b0


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FIG. 12 Adsorption excess isotherms on Na-illite and on HDP-illite derivatives in methanol (1)–benzene (2) mixtures. Na, sodium illite; 1, 2, 3, hexadecylpyridinium illites.

If the activity data of the bulk phase are known, the value of K’ can be calculated at a given value of r* = Vm,2/Vm,1 by means of computer iteration [71,73]. The Redlich–Kister equation has proven perfectly reliable for calculating the activities; its application allows the calculation of the activity coefficients of components 1 and 2, and, on this basis, functions a 1 = f(x1) and a2 = f(x2) can be given [51]. The applicability of Eq. (21) is demonstrated in Fig. 13. It is revealed by the adsorption equilibrium diagrams that for the adsorption of a liquid pair made up of components significantly different in polarity covered by alkyl chains, the value of the equilibrium constant K’ decreases with increasing hydrophobicity of the surface. The excess free energy functions given by integration of the excess isotherms, Eq. (5), reflect the extent of the hydrophobization (Fig. 14). Methanol displaces benzene with a maximum change in free energy on sodium illite. The displacement process results in smaller free energy changes on HDP-treated surfaces—the functions shown for the sample with maxima at the azeotropic compositions.

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FIG. 13 Adsorption equilibrium diagrams on solid/liquid interface in methanol– benzene mixtures at different equilibrium constants. K 1 = 103, K2 = 10 2, K 3 = 10, K 4 = 1, K 5 = 10-1. Calculated with Eq. (21).

FIG. 14 Free enthalpy of adsorption on Na-illite and on HDP-illite and on HDP-illite derivatives in methanol (1)–benzene (2) mixtures. Na, sodium illite; 1,2,3 hexadecylpyridinium illites.


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FIG. 15 Immersional wetting enthalpy isotherms on Na-illite and on HDP-illite derivatives in methanol (1)–benzene (2) mixtures. Na; sodium illite; 1,2,3, hexadecylpyridinium illites.

The free energy function for the sample with maximum hydrophobicity changes sign, which means that the displacement of benzene by methanol is not favored. Illites and their organophilic derivatives can be well dispersed in methanol–benzene mixtures; therefore their wetting properties can be studied with batch microcalorimetry [78]. The solid–liquid interaction can be given as ; its integral isotherm is plotted in Fig. 15. The immersion wetting enthalpy is appreciable on Na-illite. The majority of heat evolution is due to preferential adsorption of methanol (see Fig. 12). The enthalpy change decreases upon hydrophobization, and it becomes endothermic even in x1 > 0.5 compositions. The application of Eq. (15) is more favorable, because it clarifies the difference between the molar adsorption enthalpies of components (Fig. 16). The parameters of Eq. (15) give the adsorption capacity and the molar wetting enthalpy change. These data show that the change in molar wetting data decreases with increasing hydrophobicity (Table 4).

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FIG. 16 Determination of the adsorption capacities from Eq. (15). 1, Na-illite; 2,3,4, HDP-illites; 5; Na-montmorillonite, all in methanol (1)–benzene (2) mixtures.

TABLE 4 Results of Analysis of Adsorption Excess and Enthalpy Isotherms on Selected Nonswelling Clays Adsorbent Na-kaolinite HDP-kaolinite a Na-illite HDP-illite 1 b HDP-illite 2 b HDP-illite 3 b a b

(mmol/g)

Eq. (15) (mmol/g)

–∆21Ht (J/g)

–( ) (kJ/mol)

1.05 2.07 0.84 1.25 1.30 1.42

1.00 1.98 0.85 0.95 1.18 1.38

5.65 0.42 11.10 1.70 1.35 0.85

6.25 1.38 13.65 4.32 3.21 2.27

HDP-kaolinite: 0.048 mmol HDP + cations/g clay. HDP cation content: HDP-illite 1, 0,097; 2, 0,139; 3, 0,233 mmol/g clay.


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The specific immersion wetting enthalpies of kaolinite, illite, and their organophilic derivatives were investigated in methanol and benzene in our earlier publications [35,37,38]. These data reveal that the heat of immersion in methanol is the highest in the case of the dialyzed hydrophilic mineral, and with increasing surface modification its value decreases. The comparison of immersion wetting enthalpies relative to unit mass of the adsorbent is justified only when the specific surface area of the adsorbent is constant. It is also known, on the other hand, that the value of liquid sorption capacity, is a function of surface modification: θ2 = , where is the hydrophobic surface area and as is the total surface area of the adsorbent [35,37,38]. If a uniform treatment of immersion wetting data is desirable, it is advisable to relate the wetting enthalpy to the material amount in the interfacial phase, i.e., to use molar immersion wetting enthalpies, ∆wH m (in kilojoules per mole), in the calculations. In this way the changes in specific surface caused by disaggregation need not be separately monitored, because our data always refer to enthalpy changes accompanying the sorption of molar amounts of the adsorbed material [62,78,79]. The changes in molar immersion enthalpies, ∆wH m, that accompany surface modification in toluene are presented in Fig. 17 for increasing organophilicity of

FIG. 17 Immersional wetting enthalpies as a function of alkylammonium chain lengths in (Ο) methanol and ( ) toluene.

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the surface. The ∆wHm values increase nearly exponentially on the nonswelling HDP illite surface, whereas on HDP-montmorillonite they decrease significantly. The difference between these curves is the molar enthalpy of swelling (∆swH). These data reveal that the heat of immersion in methanol is the highest in the case of the dialyzed hydrophilic mineral, and on increasing surface modification its HDP+ cation value decreases [75–79]. C. Heat of Wetting on Swelling Clay Minerals When the originally hydrophilic surface is modified by long alkyl chains [80–92], heats of immersion display significantly greater differences. This is well demonstrated by adsorption and X-ray diffraction measurements in toluene (Table 5). If montmorillonite, a layered silicate, is hydrophobized, then, depending on the length of the alkyl chain (n c = 12–18), the value of ∆wH will decrease in polar methanol with increasing alkyl chain length [87–92]. As shown by the data in Fig. 18, the extent of wetting by the polar solvent methanol is nearly exponentially decreased as the increasing number of carbon atoms in the alkyl chain increases. The decrease in heat of wetting by toluene is surprising, as the increased organophilicity of the surface must be associated with an increase in the enthalpy of immersion wetting in the aromatic solvent as was measured in the case of nonswelling HDP-illites. The immersional wetting of hydrophobized montmorillonites in methanol, toluene, and their mixtures gives rise to three types of detector signals, as shown in Figs. 19–21. The isotherm batch microcalorimetry of these hydrophobic clays in methanol yields an exothermic effect, because in these organoclays interlamellar swelling is not very significant (dL = 3.2 nm). Significant swelling is observed in toluene; therefore, either endothermal–exothermal signals separated in time are registered within the same measurement or the wetting results in only an TABLE 5 Interlamellar Sorption and Swelling on Hydrophobic Montmorillonites in Methanol (1)–Benzene (2) Mixtures Organoclay a Montmorillonite TDP-montmorillonite HDP-montmorillonite ODP-montmorillonite DMDH-montmorillonite

Organic cation (mmol/g)

(mmol/g)

(nm)

(nm)

0.00 0.82 0.85 0.82 0.83

3.44 8.51 8.25 8.33 8.90

1.23 1.84 1.82 1.82 2.91

1.25 3.33 3.86 4.20 4.51

TDP, tetradecylpyridinium; HDP, hexadecylpyridinium; ODP, octadecylpyridinium; DMDH, dimethyldihexadecylammonium. a


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FIG. 18 Immersional wetting enthalpies on hydrophobized montmorillonite in toluene as function of surface coverage (θ 2 ) with hexadecylpyridinium cation.

FIG. 19 Exothermic heat of wetting on hydrophobic (hexadecylammonium) montmorillonite in methanol (d L = 3.2 nm).

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FIG. 20 Endothermic–exothermic heat of wetting on hydrophobic (hexadecylammonium) montmorillonite in toluene (d L = 3.8 nm). (a) Opening the elastic silicate layer by adsorbed molecules is endothermic. (b) Adsorption in the interlamellar space is exothermic heat effect.

FIG. 21 Endothermic heat of wetting on hydrophobic (octadecylammonium) montmorillonite in 5:95 methanol–toluene mixture (d L = 4.6 nm). The swelling effect overcompensate the exothermic adsorption heat in the interlamellar space.


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endothermal heat effect [37,38,62,78,79]. In the swelling of clay mineral organocomplexes in organic solvents, however, the amount of energy required for interlamellar expansion (in toluene, dL = 4.1 nm) may be so high that the exothermic heat effect accompanying the sorption of the liquid penetrating into the interlamellar space cannot compensate for it; therefore, the total heat effect is endothermic, as verified by Fig. 19. The total endothermic change in enthalpy appears only when the length of the alkyl chain is 2.6–2.8 nm. Thus, the entropy of solvated alkyl chains situated in the expanded interlamellar space may be considerably increased compared to their original state (see Figs. 23–25). It is this increase in entropy that ensures that the change in free enthalpy associated with the process of wetting will have a negative value, i.e., that wetting and swelling will proceed spontaneously. If we investigate the liquid sorption properties of swelling HDPmontmorillonites, we find that the enthalpies of wetting in toluene also decrease; what is more, in the case of n c = 18 or 20 the process of wetting is endothermic, indicating that under the conditions of substantial interlamellar expansion, wetting is an entropy-controlled process. Figure 22 shows the heat effects determined by batch microcalorimetry as a function of the mass of the organocomplex. The points representing different surface hydrophobicities on a swelling organoclay fall on

FIG. 22 Enthalpy of wetting for different masses of hydrophobic montmorillonites— (1) Tetradecylpyridinium and (2) hexadecylpyridinium montmorillonites in methanol and (3) octadecylpyridinium and (4) dimethyldioctadecylammonium montmorillonites in toluene.

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a straight line with a positive slope in methanol, while in the case of dimethyl dioctadecylammonium clay, which swells to a greater extent, the heat evolution decreases with increasing mass of the adsorbent in toluene. The lines do not intersect at the origin because the liquid influx at mass m = 0 produces 75–78 mJ of heat in the measuring cell. The endothermal effect associated with the swelling of bentonites was first pointed out by Zettlemoyer et al. [9], van Olphen [80], and Slabaugh and Hanson [82]. They established that good swelling and gel formation result in small exothermal or exclusively endothermal effects. According to these authors, when the immersion wetting of swelling systems is considered, both the interaction of polar molecules with a silicate surface and the solvation of apolar molecules by alkyl chains as well as the interlamellar expansion have to be taken into account. The first two of these interactions are always exothermal, whereas the interlamellar expansion may often be endothermal [35,37,78]. Figure 23 shows the degree of swelling for the liquid sorption equilibrium systems ethanol (1)–toluene (2)/hexadecylammonium vermiculite as a function

FIG. 23 The mole fraction of toluene in the interfacial layer and the basal spacing (d L ) in ethanol (1)–toluene (2) mixtures on hexadecylammonium vermiculite.


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FIG. 24 Orientation of the cationic alkyl chains between silicate layers at high layer charge density (degree of hydrophobization) for different degrees of swelling. (a) Monolayer, (b) expanded monolayer, (c) bilayer structure (numbers show the distances in Ångström).

of the liquid mixture composition of the bulk phase. It can be established that within the entire series of mixtures the value of d L increases, i.e., the alkyl chains and the silicate layers expand (Fig. 24). The composition of the interfacial layer is therefore also indicated in Fig. 23, and it is apparent that this increase is gradual. This means that the displacement of the polar component (ethanol) from the interlamellar space leads to an increase in basal distance. The same conclusion is demonstrated by Fig. 24, assuming that the orientation of the alkyl chains is perpendicular to the silicate layers. The expansion or contraction of hydrophobized silicate lamellae is well reflected by the enthalpy values presented in Fig. 25 as a function of the volume fraction of adsorbed toluene in the interfacial layer . It is evident that significant swelling occurs only if the interlamellar space of the organoclay is enriched with toluene. For parallel investigation of adsorption and swelling, flow microcalorimetry was used to control the enthalpy of displacement (∆21H) as a function of the surface layer composition. It is clear

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FIG. 25 Basal distance (d L) and enthalpy of displacement at different volume fractions of toluene in the interfacial layer in ethanol (1)–toluene (2) mixtures on hexadecylammonium vermiculite.

from Fig. 25 that the “opening” of the interlamellar space is an endothermic process, because the expansion and solvation of alkyl chains are entropy-driven effects. D. Adsorption of n-Butanol from Water on Modified Silicate Surfaces The structure and the sorption properties of partially hydrophobized silicates (dodecylammonium and dodecyldiammonium vermiculites) were investigated in aqueous solutions of n-butanol. The alcohol is preferentially adsorbed on the surface. The interlayer composition is calculated from adsorption and X-ray diffraction data. In the air-dried state the organic cations lie flat on the interlamellar surface. In aqueous n-butanol solutions, the basal spacing of dodecylammonium vermiculite gradually increases with the extent of n-butanol adsorption because the chains increasingly point away from the surface. The basal spacing of dodecyldiammonium vermiculite is virtually independent of the interlayer composition, because the expansion of the interlayer space is sterically restricted and a


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FIG. 26 Adsorption excess isotherms for n-butanol–water solutions on (Ο) dodecylammonium vermiculite and ( ) dodecyldiammonium vermiculite.

relatively rigid structure is formed. The enthalpy of the displacement of water by 1-butanol was determined by flow sorption microcalorimetry [72,93,–96]. Adsorption of n-butanol from water on the surface of vermiculite hydrophobized by alkyl chains of two different structures is illustrated by Fig. 26. It can be established that there is a very large difference between dodecylammonium derivatives with carbon chains of identical lengths but different interlamellar structures. The reason for this is directly shown in Fig. 27, which demonstrates that differences in interlamellar swelling are also quite large. Similarly to adsorption, dodecylammonium (C 12 – NH 3 + ) vermiculite swells considerably more than dodecyldiammonium [C12 – (NH3+)2] vermiculite. As shown by a detailed discussion in our previous publications [72,93,94], the swelling of the diammonium derivative is limited due to the “bridges” formed by the alkyl chains, and the distance between lamellae is nearly constant (d L = 2.35–2.45 nm). Thus, this s a m p l e h a s a s m a l l e r f r e e i n t e r l a m e l l a r v o l u m e (V i n t – V alc ) t h a n t h e dodecylammonium derivative (see Fig. 28b). Figure 29 shows free energy functions on the two different hydrophobic vermiculites, and Fig. 30 shows the ∆Gs = f(x1,r) isotherms, calculated (corrected) according to a dilution term, between the bulk and surface layer [69–74], from known values of the isotherms = f(x1,r). It is obvious that the change in free energy that accompanies the adsorption ex-

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FIG. 27 Basal spacings of ( ) dodecylammonium vermiculite and ( ) dodecyldiammonium vermiculite in n-butanol–water solutions.

FIG. 28 Schematic representation of the hydrophobic vermiculite at different basal distances: (a) monolayer; (b) “bridging”; (c) bilayer orientation.


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FIG. 29 Free enthalpy of adsorption in n-butanol–water solutions on ( ) dodecylammonium vermiculite and on ( ) dodecyldiammonium vermiculite.

FIG. 30 Thermodynamic potential functions of the adsorption layer on dodecylammonium vermiculite in n-butanol–water solutions.

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change process changes parallel with adsorption. On the other hand, it has to be stressed that the value of ∆G s is significantly lower in the restrictedly swollen system with lamellae bound together by alkyl chains (∆Gs = 4.1 J/g) than in swollen systems with lamellae that move independently relative to each other (∆Gs = 8.5–10.3 J/g). Enthalpy of displacement isotherms were determined by the flow technique. The heat effects recorded on dodecylammonium and dodecyldiammonium vermiculites are found to be endothermic in both cases, i.e., the measured heat exchange process results in heat extraction. Since the adsorption isotherms unambiguously indicate positive adsorption of n-butanol, the question arises as to why an exothermic exchange enthalpy is not recorded. In our opinion, the reason for this is the endothermic enthalpy of dilution [59–61,69], which overcompensates for the interlamellar adsorption of butanol. When, knowing the adsorption excesses, the enthalpy isotherm ∆21Hs = f(x1,r) characteristic of the solid/liquid interfacial adsorption layer can be calculated, it is indeed the exothermic adsorption enthalpy isotherm specific for the surfacial interaction that is obtained (Fig. 30). This measurement suggests that the interlamellar adsorption of n-butanol is thermodynamically preferred and is accompanied by the liberation of a very large amount of heat (∆21H s = 16.0–16.5 J/g). The ∆G s and T ∆S s functions are also included in Figs. 30 and 31, in order

FIG. 31 Thermodynamic potential functions of the adsorption layer on dodecyldiammonium vermiculite in n-butanol–water solutions.


397

to describe the incorporation of the adsorbate in terms of change in enthalpy also. In Fig. 30, the entropy term of dodecylammonium vermiculite is decreased owing to an increase in the adsorption of butanol (T ∆ 21Ss < 0). Conversely, in the case of the restrictedly swollen dodecyldiammonium sample, an increase in entropy (T ∆21Ss > 0) is observed up to x1,r≤= 0.7, and it is only in the range of adsorption saturation that a decrease in entropy occurs (Fig. 31). This means that in the case of the restrictedly swollen system, water molecules are arranged in the interlamellar space in a more orderly manner (presumably in clusters) than n-butanol molecules. The reason for this is that if ∆S 2(water) > ∆S 1(n-butanol), then ∆21S = ∆S2 – ∆S 1 = 0. IV. PROPERTIES OF THE ADSORPTION LAYER AND STABILITY OF AEROSIL DISPERSIONS IN BINARY LIQUIDS The stability of colloidal disperse systems is basically determined by the adhesive interactions between the particles and by particle–liquid interactions (wetting). The structural building properties of sols and suspensions therefore depend on the magnitude of the energies of these interactions. The state of aggregation of a disperse system can be regulated by altering the adhesive and wetting properties at a constant particle concentration—by selecting a dispersion medium or mixture medium of appropriate polarity or by surface modification [27,36,63,64]. The analysis of the sedimentation and rheological properties of a disperse system (sol or suspension) usually yields only qualitative information about the interparticle interactions. However, the solid–liquid interaction, i.e., the heat of wetting, can be accurately determined by microcalorimetry. When the viscosity of a suspension is measured by rotational viscosimetry, the Bingham yield value characteristic of the interparticle interaction can be determined from the so-called flow curves (in a system of a given concentration). The Bingham yield value is measured in non-Newtonian rheological systems and can be used for the calculation of the energy of separation [20–26,97–101] characteristic of adhesive interactions (aggregation). Disperse systems of a great variety of structures aggregated in different ways can be practicably analyzed by small-angle X-ray scattering (SAXS), because the intensity of scattered light is basically determined by the size of the particles and the structural factor characteristic of the system. Thus, SAXS measurements also make possible the determination of structural parameters describing the degree of aggregation of the disperse system studied, which can then be compared with the rheological properties of the suspension and with the wetting characteristics of the particles. A combination of the methods mentioned can greatly increase our knowledge of the stability of structured disperse systems and promote a wider range of practical applications [102].

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A. Influence of the Adsorption Layer on the Aggregation of Aerosil Dispersions in Binary Liquids From a knowledge of the adsorption, immersion, and wetting properties of solid particles, we have examined the influence of particle–particle and particle–liquid interactions on the stability and structure formation of suspensions of hydrophobic and hydrophilic Aerosil particles in benzene–n-heptane and methanol–benzene mixtures. For the binary mixtures, the Hamaker constants have been determined by optical dispersion measurements over the entire composition range by calculation of the characteristic frequency (νk) from refractive index measurements [7,29,36,64]. The Hamaker constant of an adsorption layer whose composition is different from that of the bulk has been calculated for several mixture compositions on the basis of the above results. Having the excess isotherms available enabled us to determine the adsorption layer thickness as a function of the mixture composition. For interparticle attractive potentials, calculations were done on the basis of the Vincent model [3–5,39]. In the case of hydrophobic particles dispersed in benzene–nheptane and methanol–benzene mixtures, it was established that the change in the attractive potential was in accordance with the interactions obtained from rheological measurements. The Hamaker constant (A) is calculated according to Gregory [103] and Tabor and Winterton [104] by using the equation (22) where h is the Planck constant, Vk is the characteristic frequency, and ε is the relative permittivity of the liquids. The interparticle interaction potential can be described with the help of the Hamaker constant on the basis of the comprehensive work by Hamaker [7] and Visser [105], who developed the calculation of London interactions between macroscopic spherical particles. It was taken into account by Vold [3] that each particle is surrounded by a lyosphere with a thickness ts. The calculation of van der Waals attraction forces between colloidal particles with adsorption layers was developed by Vincent and coworkers [4,5,39], who formulated the following equation for the description of the attraction potential VA: (23) where Am, A ls, and Ap are the Hamaker constants relative to the bulk medium, the lyosphere (adsorption layer), and the particle, respectively, and Hls, Hpls are


399

the distance functions [5,29,39]. Hpls is the distance function relative to the particle/ liquid interface. According to our investigations, Eq. (23) is corrected in the sense that the Hamaker constant Als is given for the adsorption layer of composition and—instead of calculating them using a constant, and estimated, layer thickness—ts values derived from adsorption excess isotherms calculated by Eq. (6) and varying as a function of equilibrium composition are used in the Hls functions. Equation (23) allows the calculation of the attraction potential VA at a given interparticle distance h in the entire range of mixture composition; at a given composition, or in a pure liquid, the value of the attraction potential function V = f(h) can be obtained [29,30,39]. Let us first examine the results of the rheological analysis of the hydrophobic Aerosil dispersion R 972 in the entire range of mixture composition of benzene (1)–n-heptane (2) mixtures. The flow curves of a 2 g/100 cm3 dispersion measured in the pure liquid component are presented in Fig. 32a. The “ascending” and “descending” flow curves obviously do not coincide but form a hysteretic loop; a slight thixotropy is observed. The Aerosil suspensions yield a series of flow curves over the entire mixture composition range, the most characteristic of which are shown in Fig. 32b. Non-Newtonian behavior is observed in the entire mixture composition range; shear stress (τ) increases with the shear gradient (D) in a nonlinear fashion. At very low shearing rates the stress is elastic, and at higher values the behavior is pseudoplastic [99–101]. Based on the Bingham equation τ = τB + ηplD, the plastic viscosity ηpl and the Bingham yield value τB can be calculated from the flow curves [20–27,29,36,39,64]. The dependence of the yield value τB on the molar fraction of benzene is presented in Fig. 33. Since the yield value is a parameter characteristic of the interparticle interaction [27,29,64], it can be established that the aggregation of silica particles is significantly affected by the composition of the mixture medium and that an increase in the fraction of benzene in the mixture results in a decrease in aggregate size—in other words, interparticle adhesion is reduced, which means increased stability. Hydrophobic Aerosil (Degussa AG, Germany) dispersions of various concentrations were studied in methanol (1)–benzene (2) mixtures, in the entire mixture composition range. The 2 g/100 cm3 dispersion was chosen for detailed analysis. The flow curves of the Aerosil dispersions (Fig. 34) reveal that plastic viscosity and Bingham yield value are the highest in pure benzene, and increases in the molar fraction of methanol in the mixture lead to a decrease in these parameters (Fig. 35). The rheological flow curves reveal that in n-heptane there are strong adhesive interactions between hydrophobic particles. The Bingham yield value (τ B) characteristic of interparticle interactions changes in parallel with the optical density of the suspension (Fig. 36). Aggregation is also demonstrated by the observation that the turbidity of the suspension changes with the composition of the mixture.

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FIG. 32 Rheological flow curves of hydrophobic Aerosil (2% m/v) suspensions (a) in benzene (x 1 = 1) and n-heptane (x 1 = 0) and (b) in benzene (1)–n-heptane (2) mixtures at different compositions.


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FIG. 33 The Bingham yield values of hydrophobic Aerosil (2% m/v) suspensions in benzene (1)–n-heptane (2) mixtures in the entire composition range.

When attraction potentials are calculated using the Hamaker constants Als and Am and the layer thickness ts prevailing in the given liquid mixtures, the value of the attraction potential is reduced by the wetting effect of benzene in the benzene–nheptane mixture series at a constant interparticle distance of 0.1 nm, in complete agreement with our thermodynamic considerations. In the range of x 1 = 0.4–0.6 for the methanol–benzene liquid pair, the minimal interparticle attraction can also be calculated from the attraction potential function and is found to coincide exactly with the appearance of the Newtonian flow characteristics of the suspension and the minima of the thermodynamic potential functions [36,39,64]. B. Characterization of the Stability of Nonaqueous Dispersions by Calorimetric and Adsorption Measurements The parallel representation of the adsorption isotherms and heats of immersion measured in binary mixtures, presented above, gave information on solid–liquid interfacial interactions. If the stability of disperse systems is approached from the

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Dékány

FIG. 34 Rheological flow curves of hydrophobic Aerosil (2% m/v) suspensions in methanol (1)–benzene (2) mixtures at different compositions.

side of interparticle interactions, the rheological properties of the given colloidal dispersion should be examined. The most straightforward way of doing this is to measure the flow curves of the disperse system in a rotational viscosimeter in mixture media of various compositions. This means that the shearing stress (τ) arising during shearing (D) is plotted against the shear gradient, i.e., the functions τ = f(D) (flow curves) are determined. If these flow curves are linear and pass through the origin, the liquid studied is Newtonian, whereas in the opposite case, rheological behavior of the non-Newtonian or pseudoplastic type is observed (Fig. 32a). If interparticle adhesion forces increase significantly, the dispersion possesses a yield value (Bingham yield value, τB), meaning that an amount of energy characterized by the value of τB has to be invested in order to start the flow. Thus, rheological data can be used for the characterization of interparticle interactions on the basis of macroscopic measurements. Let us now examine the relationship between rheological data characterizing interparticle interactions and those obtained by adsorption measurements and calorimetry. Figure 37 displays characteristic data measured in hydrophobic Aerosil in benzene–n-heptane mixtures yielding U-shaped excess isotherms and the cal-


403

FIG. 35 The Bingham yield values of hydrophobic Aerosil (2% m/v) suspensions in methanol (1)–benzene (2) mixtures in the entire composition range.

culated functions (Fig. 37a). The aromatic component is positively adsorbed on the surface of the hydrophobic SiO2 particles, i.e., benzene is accumulated in the interfacial layer. Given the knowledge of the excess isotherm and the activities of the bulk phase, the change in free enthalpy associated with adsorption, i.e., ∆21G = f(x1), can be calculated by using the integrated form of the Gibbs equation (Fig. 37b). It can be established that the accumulation of toluene in the interfacial layer produces a significant decrease in free enthalpy. In parallel measurements of heats of immersion in the various mixtures, large heat effects are recorded. ∆wH is obviously much larger in the preferentially adsorbed benzene and in mixtures rich in benzene than in pure n-heptane. The reason for this is that n-heptane is bound to the hydrophobic surface of SiO2 only by dispersion interactions, whereas the aromatic structure of toluene can be polarized on the hydrophobized SiO 2 surface (Fig. 37c). This concept is also supported by the adsorption layer thickness function ts = f(x1) calculated from the adsorption excess isotherm. These calculations were presented in the publications and Dékány [52,53], Marinin et al. [106], and Aranovich [107]. The function ∆21G = f(x1) was used for the calculations [52,53]. The results reveal that in n-heptane a monomolecular

404

Dékány

FIG. 36 ( ) Optical density and ( ) Bingham yield stress vs. mole fraction of hydrophobic Aerosil (2% m/v) suspensions in benzene (1)–n-heptane (2) mixture.

adsorption layer is formed (Fig. 37e), the heat of immersion is minimal, and consequently interparticle adhesion is maximal (Fig. 37d). An increasing heat of immersion also means an increasing adsorption layer thickness; however, τ B decreases, resulting in lower interparticle adhesion. Thus, in pure toluene, where there is a considerable heat of wetting and the adsorption layer is about 6–7 nm thick, interparticle attraction is quite weak and the suspension is far more stable than in n-heptane. Dispersion of hydrophobic Aerosil in the methanol (1)–benzene (2) liquid pair yields a much more stable system. In this case the excess isotherm is S-shaped. This means that in the molar fraction range of x 1 = 0–0.35, methanol is positively adsorbed on the surface, whereas in the range of x 1 = 0.35–1.0, the positive adsorption of benzene is observed. (This section in Fig. 38a indicates negative adsorption with respect to ethanol, as adsorption excesses of component 1 are displayed.) After integration according to the Gibbs equation, the function ∆ 21G has a minimum in the range of x1 = 0.2–0.4, also including the so-called adsorption azeotropic composition (Fig. 38b). Measurements of the heat of immer-


405

FIG. 37 The solid/liquid interfacial extensive functions and Bingham yield stress for interparticle interactions in hydrophobic Aerosil (2% m/v) suspensions in benzene (1)–n-heptane (2) mixtures in the entire composition range.

406

Dékány

FIG. 38 The solid/liquid interfacial extensive functions and Bingham yield stress for interparticle interactions in hydrophobic Aerosil (2% m/v) suspensions in methanol (1)–benzene (2) mixtures in the entire composition range.


407

sion ∆wH also reveal maximal heat effects in this composition range (Fig. 38c), and this is where the adsorption layer reaches maximal thickness (Fig. 38e). In the azeotropic composition range, the yield value τB calculated from rheological measurements is zero, i.e., the suspension exhibits Newtonian rheological characteristics (Fig. 38d). Thus, maximal adsorption layer thickness and heat of wetting both indicate that a strong interaction is established between particles and adsorbed solvent molecules, making possible the minimization of interparticle attraction forces. The three parallel series of experiments described above demonstrate that in suspensions of systems with S-shaped excess isotherms, the disperse system may be stabilized in the vicinity of the azeotropic composition, indicated by (1) the minimum of the free enthalpy function, (2) maximal exothermic heat of immersion, (3) maximal thickness of the adsorption layer, and (4) Newtonian rheological properties, i.e., the minimum of interparticle interactions [36,38,39,64].

FIG. 39 Small-angle X-ray scattering curves of hydrophobic silica in benzene (1)–nheptane (2) mixture in (2% w/v) suspension (a) in n-heptane, (b) in benzene, (c) in x 1 = 0.7 mixture.

408

Dékány

V. SMALL-ANGLE X-RAY SCATTERING OF SiO2 PARTICLES IN BINARY LIQUIDS Hydrophilic and hydrophobic colloidal SiO2 particles dispersed in benzene–nheptane mixtures in capillary tubes were studied by small-angle X-ray scattering in a helium atmosphere [107,108]. According to the scattering intensty (I) vs. wave vector (h) curves in Fig. 39, the difference between hydrophilic and hydrophobic particles is well characterized by the scattering intensities. Correlation length and the course of the distance distribution function P(r) calculated from it yield information on aggregation and on the stability of the disperse system. The rheological flow curves reveal that in n-heptane there are strong adhesive interactions between hydrophobic particles. Aggregation is also demonstrated by the observation that the relative internal surface of the suspension changes with the composition of the mixture. Measurements of wetting and adsorption cor-

FIG. 40 Distance distribution function of hydrophobic silica (R 972) particles in benzene (1)–n-heptane (2) mixture in (2% w/v) suspension. (a) in n-heptane; (b) in x 1 = 0.7 mixture; (c) in benzene.


409

roborate this assumption, since positive adsorption of benzene in the surface layer increases the enthalpy of wetting and decreases the tendency of particles to aggregate. Thus, SAXS measurements also make possible the determination of structural parameters describing the degree of aggregation of the disperse system studied, which can then be compared with the rheological properties of the suspension and with the wetting characteristics of the particles. A combination of the methods mentioned can greatly increase our knowledge of the stability of structured disperse systems and promote a wider range of practical applications [108]. In Fig. 40, the P(r) vs. r distance distribution functions are presented that were calculated from the scattering curves by inverse Fourier transformation [102,108,109]. It can be clearly seen that the numerical values of the functions indicate the differences in the density of aggregates in the liquid mixtures of different polarities. The interparticle interactions are thus regulated via the selective liquid sorption process on the disperse particles, and it can be established that the interfacial layer composition, the layer thickness, and the heat of wetting are crucial factors for the stability of colloidal dispersions in nonaqueous liquids.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

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11 The Formation and Transformation of Crystalline Dispersions as Studied by Thermal Analysis HELGA FÜREDI-MILHOFER Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

I.

Introduction

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II.

Theoretical Background A. Nucleation B. Crystal growth C. Flocculation D. Aging: Ostwald ripening and solution-mediated phase transformation

415 416 417 417

III.

IV.

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Formation and Transformation of Ionic Precipitates from Electrolyte Solutions A. Formation and transformation of amorphous precursor phases B. Nucleation, crystal growth, and solution-mediated phase transformation of crystal hydrates C. Control of crystallization by additives

422 426

Crystallization in Confined Spaces: Emulsions and Microemulsions A. Emulsions: induced crystallization at the oil/water interface B. Crystallization in microemulsions

434 434 437

References

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419 420

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Füredi-Milhoer

I. INTRODUCTION Methods of thermal analysis date back to the beginning of the 20th century, but only recently, as advanced equipment has made the task of measurement simpler and more rapid, have they become an essential part of the characterization of inorganic and organic compounds. One of the earliest applications was as a tool in phase analysis. In his classical work, Duval [1] gives a compilation of methods suggested for automatic thermogravimetric analysis and describes and evaluates thermolytic curves of some 1200 inorganic compounds. Several excellent monographs describing modern methods of thermal analysis and their application have been published [2,3], along with comprehensive reviews on the thermochemistry of organic, organometallic, and inorganic compounds, including relevant thermodynamic parameters extracted from calorimetric measurements [4,5]. “Thermal analysis” denotes a group of methods and techniques in which a property of a substance is measured as a function of temperature while the substance is subjected to a controlled temperature program. Thus, it is possible to monitor the temperature of the sample [e.g., by differential thermal analysis (DTA) or differential scanning calorimetry (DSC)], its weight loss upon heating [thermogravimetric (TG) and differential thermogravimetric (DTG) analysis] as well as a host of other properties that change with temperature (mechanical strength, morphology, crystal structure, dimensions, etc.). For comprehensive lists and descriptions of available methods see Refs. 2 and 3. Using these methods, information on the thermal behavior of a substance is readily obtained. By employing several methods simultaneously or sequentially to characterize a sample it is possible to obtain complete information about the sequence and thermodynamic parameters (enthalpy, entropy) of decomposition reactions and polymorphic transitions occurring as a consequence of increasing temperature [3]. In addition, complementary methods for physicochemical characterization such as thermal microscopy, X-ray diffraction, and Fourier transform infrared (FTIR) spectroscopy are used. A requirement for obtaining meaningful data is the strict definition of the experimental conditions employed, particularly those that may influence the rate of gas diffusion from inside the sample and the rate of heat transport (i.e., the shape and size of the crucible, sample size, heating rate, etc.). Thermoanalytical methods have been frequently employed in the characterization of complex samples such as minerals and clays [6] and carbonate stones used in the construction of monuments [7]. They have become a routine analytical tool for the characterization of new compounds in the pharmaceutical industry, where molecules are frequently prepared as hydrates or pseudosolvates to ensure good water solubility and good stability in moist environments [8]. Biochemical and biological applications of thermal analysis are also the subject of a recent review [9].

Crystalline Dispersions

415

In this chapter we concentrate on applications of thermal analysis in basic and applied research, leading to better understanding of the processes involved in the formation and transformation of crystalline dispersions both from electrolyte solutions and in confined spaces such as emulsions and microemulsions. II. THEORETICAL BACKGROUND Crystalline dispersions are formed by a succession of precipitation processes, nucleation, crystal growth, flocculation, and various aging processes (Fig. 1). In this section we present a short review of the thermodynamic principles that define these processes. For a comprehensive treatise on the subject the reader is directed to Ref. 10.

FIG. 1 Processes involved in the formation and transformation of slightly soluble precipitates.

416 A.

Füredi-Milhoer Nucleation

Nucleation is the initial process leading to the formation of a new phase. Classical nucleation theory [11–13] describes homogeneous nucleation as the breakdown of a metastable state that occurs at a critical activation energy, which is achieved at a critical subcooling (in melts) or supersaturation (in solution). The homogeneous nucleus is conceived of as an aggregate of critical size in unstable equilibrium with the parent phase. At concentrations below the critical level the cluster grows or dissociates reversibly, (1a) at the critical size irreversible growth commences upon the addition of one more ion or molecule: (1b) For a spherical nucleus, the energy barrier to nucleation, ∆G 0, is simply related to the volume free energy of cluster formation and to the energy required for the formation of a new surface: (2) where ∆G v is the change in the molecular volume free energy associated with cluster formation, σS/L is the cluster/solution (solid/liquid) interfacial energy, and r is the radius of the new nucleus. Maximization of Eq. (2) with respect to r gives, for the critical radius, (3) and for the activation energy, (4) In Eqs. (3) and (4), v is the molecular volume, k is the Boltzmann constant, T is the absolute temperature, and S is the supersaturation. For constant temperature and pressure, the supersaturation can be defined as the ratio of ionic activity products. Thus, for a binary electrolyte, S = AP/Ksp, where AP is the ionic activity product in the supersaturated solution and K sp is the solubility product of the respective solute. Equation (3) is known as the Gibbs–Thompson relation, and Eq. (4) was first derived by Gibbs [14] to describe the condensation of droplets from vapor. The rate of nucleation, J, is an exponential function of ∆G0*:


417

(5) where Ω is a preexponential factor (1033) and all other quantities are defined as above. Equation (5) shows an exponential dependence of the nucleation rate on the supersaturation. A consequence of this dependence is that, ideally, if no catalyzing impurities are present, the rate of nucleation should remain negligibly small until a critical supersaturation, S*, is reached. At this point a sharp increase in the number of particles marks the onset of homogeneous nucleation. If the reaction is conducted in a closed system (with no inflow or outflow of reagent solutions), at S > S* the supersaturation is likely to be used up in the creation of new nuclei. The result is a colloidal dispersion that, depending on the electrolytic environment, will either aggregate or form a stable sol. In practice, both in industrial systems and in biological and pathological mineralization, nucleation is usually induced at much lower supersaturations by heterogeneous nuclei that lower the activation energy, i.e., ∆G het < ∆G0*. These can be nonspecific impurities, which are always present in solution, or templates, which are specifically added with the purpose of producing a certain kind of precipitate. The number of particles formed by heterogeneous nucleation cannot exceed the number of seeds or impurity particles, which, in aqueous solutions, is estimated to be N ~ 106–107 particles per cubic centimeter. B. Crystal Growth Crystal growth is visualized as the result of a succession of events, i.e., transport of ions through the solution, adsorption at the solid/solution interface, surface diffusion, reactions at the interface (dehydration, two-dimensional nucleation), and incorporation into the crystal lattice. The rate of crystal growth is controlled by the slowest of these processes, which determines the size and shape of the resulting crystals. The ratecontrolling crystal growth mechanism depends on the supersaturation (Fig. 1). At low supersaturation, the rate of growth is likely to be controlled by one or more surface processes, and as a result compact crystals are obtained. At medium supersaturation, the diffusion of ions through the bulk may be rate-controlling, resulting in the development of large dendritic crystals. If the initial supersaturation exceeds S*, crystal growth is almost insignificant, because the supersaturation is used up in the creation of new nuclei by homogeneous nucleation (Fig. 1). C. Flocculation* Once formed, particles in solution interact with each other because of Brownian motion. The theory of rapid flocculation was first proposed by Smoluchowski, * For a detailed treatise, see Ref. 15.

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who treated the problem as one of the diffusion of spherical particles in an initially monodisperse system, leading, with every collision and in the absence of repulsive forces, to permanent contact [15]. The total number N of particles that are present at time t is given by (6) where No is the initial number of particles and t1/2 is the time necessary to reduce No by half. For aqueous dispersions at 25°C, t1/2 ≈ 2 × 1011/Nos. Thus, in the case of heterogeneous nucleation, t1/2 ~ 2 × 104–2 × 105 s, or 5.5–55 h. Apparently, in such systems flocculation is not significant in the early stages of precipitate formation but will be preceded by crystal growth [10]. However, if precipitation is initiated by homogeneous nucleation, the number of particles will be larger by several orders of magnitude, in fact ~ 1012 particles per cubic centimeter have been detected experimentally [16]. For that number the half-time of flocculation would be t1/2 ~ 0.1 s. With the number of particles only 10 times larger, t1/2 would be approximately 0.01 s, which is within the time scale predicted for induction periods for homogeneous nucleation [10]. Clearly, in the supersaturation region exceeding S*, flocculation of nuclei or primary particles becomes a significant factor, occurring in parallel or immediately after nucleation. Homogeneous nucleation thus leads to heavy flocculation unless the particles are charged and therefore stabilized by Coulombic forces or are subjected to repulsive forces arising from solvation, adsorbed layers, etc. For further information, the reader is referred to Ref. 17, a comprehensive treatise covering adsorption at interfaces and the electrical double layer. D. Aging: Ostwald Ripening and Solution-Mediated Phase Transformation Any two-phase system consisting of a polydisperse precipitate in contact with its mother liquid will be thermodynamically unstable because of its large interfacial area, which is a source of free energy. There are two possible ways for the system to minimize its free energy: (1) Small particles dissolve and large ones grow until, after infinite time, only one large crystal remains, or (2) parts of the crystallites with high energy (edges, corners, dendrite arms) dissolve preferentially and the excess solute is redeposited at surface positions of lower energy. This phenomenon has been termed Ostwald ripening [18,19] and was theoretically treated by several authors [20,21], who showed that it is significant even in the early stages of nucleation and crystal growth. This, then, is an important factor (apart from flocculation) that influences the properties of particles in a nascent crystalline dispersion. Many commonly occurring crystals may exist in a wide variety of forms such as different polymorphs, crystal hydrates, or solvates. For a given set of experi-


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mental conditions such as temperature, pressure, and composition (transition points excluded), only one solid phase will be consistent with the minimum free energy of the system. This phase will be the thermodynamically stable one with the lowest solubility but will not necessarily precipitate first from a supersaturated solution. When crystallization of several solid phases is possible, the relative rates of nucleation and crystal growth will determine which form separates first [20]. The thermodynamic drive toward minimizing the free energy of the system will then cause the metastable phase to transform into a more stable one. Such a transformation can occur in the solid state by internal rearrangement of molecules. Frequently this occurs as a consequence of heating and can be conveniently studied by DTA, augmented by methods for phase analysis such as X-ray diffraction and infrared spectroscopy. Another route available for phase transformation is aging in contact with a solvent, usually the mother liquid. Such a transformation involves concomitant dissolution of the metastable form and precipitation of the next, more stable form. This phenomenon was observed in the early 1800s and was later formulated as Ostwald’s rule of stages [19]. More recently, Cardew and Davey presented a kinetic analysis [22] that takes into account the rate of dissolution of the metastable phase and the growth rate of the stable phase and shows that the supersaturation profile depends strongly on the relative kinetics of growth and dissolution. It appears that such profiles are dominated by a plateau supersaturation, which is the region where the growth and dissolution processes are balanced. This region is determined by the relative surface areas of the phases and their kinetic constants of dissolution (kD) and growth (kG), respectively. Any change in experimental conditions that influences either one or both rate constants will then exert an influence on the rate and possibly on the outcome of the phase transformation.

III. FORMATION AND TRANSFORMATION OF IONIC PRECIPITATES FROM ELECTROLYTE SOLUTIONS The properties of precipitates formed from electrolyte solutions depend on the relative rates of the precipitation processes described in Section II. These in turn depend on a number of experimental factors such as the degree of supersaturation, reactant concentration ratio, temperature, ionic strength, and the presence of impurities or additives in the crystallizing solution. It is therefore essential to design reproducible experimental procedures by which to control these factors. A simple way to control the initial supersaturation and reactant concentration ratio is to rapidly mix equal volumes of known concentrations of the cationic and anionic components of an ionic precipitate (for instance, a solution of calcium chloride and sodium oxalate to obtain calcium oxalate). Knowing the initial concentra-

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tions, precipitation kinetics can then be followed by monitoring the depletion of solution concentration and/or one or more precipitate properties as a function of time. The role of thermal analysis in this context is in the characterization of the solid phase(s) at given time intervals and after termination of the reaction. Several interesting examples follow. A.

Formation and Transformation of Amorphous Precursor Phases

The rate and mechanism of nucleation are of prime importance in determining the nature of the first solid phase formed from a supersaturated solution. We have seen [Eq. (3)] that the size of the critical nucleus is inversely proportional to the degree * of supersaturation. At high supersaturations ( ), where homogeneous nucleation prevails, the critical radius may be rather small, and for crystals with large unit cells (such as hydroxyapatite) it may become smaller than one unit cell [23]. On the other hand, the rate of nucleation increases exponentially with the supersaturation [Eq. (5)]. Under such conditions, poorly crystalline or amorphous particles are formed that enlarge by flocculation rather than by crystal growth (Fig. 1). If the amorphous precipitate contains hydrophilic cations, which in aqueous solution coordinate a number of water molecules (such as calcium or aluminum ions), it will most likely be energetically favorable to incorporate such bound water into the nascent precipitate. Thus, such poorly crystalline precipitates are likely to be highly hydrated; examples are amorphous calcium phosphate [24] and gellike structures such as Al2O3 · 3H2O · H2O, Fe2O 3 · 3H2O · H 2O, or H2SiO3 · H2O [25]. Thermal analysis gives information on the amount of water incorporated and on the mechanism and strength of bonding. (For a comprehensive discussion of the modes and mechanisms of water incorporation with special regard to inorganic compounds, see Refs. 25 and 26.) Amorphous precipitates tend to be metastable and change in contact with the mother liquid into more stable structures, but nevertheless the history of the sample can in many cases be deduced even after prolonged aging. An interesting example is the formation of hydroxyapatite (HA). A convenient way to prepare stoichiometric hydroxyapatite is to induce precipitation in a nitrogen atmosphere by dropwise addition of a phosphate solution into a calcium hydroxide solution, the molar ratio of the reagents being 1.67 [27]. In the course of such preparations, highly hydrated amorphous calcium phosphate precursors are formed that later transform into HA. Near stoichiometric HA prepared by this method was examined by mass spectrometric temperature-programmed dehydration (MSTPD) analysis [28]. The sample was outgassed at 25°C until the instrument pressure fell to a steady value (~10 -7 torr) and then heated at a rate linear with time while the effluent water vapor was monitored by means of a mass spectrometer (for details of the technique see Ref. 29). Figure 2 shows the


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FIG. 2 Mass spectrometer temperature-programmed dehydration (MSTPD) spectra showing the evolution of water as a function of temperature from (1) hydroxyapatite precipitated from an aqueous solution via an amorphous precursor phase, (2) hydroxyapatite prepared in a hydrothermal bomb, and (3) apatite from a mineral source. (After Ref. 28.)

results (curve 1) compared with those obtained from a sample of HA prepared by the hydrothermal bomb technique [30] (curve 2) and with another one obtained from a mineral source (Holly Springs apatite, curve 3). The interesting part of Fig. 2 lies in the temperature region between 150°C and 300°C, where a very pronounced peak was found for the sample formed via the amorphous precursor phase but none for the hydrothermally prepared or mineral HA. This unique behavior was attributed to the evolution of water from narrow internal micropores that were present only in samples formed by precipitation from aqueous solution via an amorphous precursor phase [28]. These findings have added significance if one considers that in biomineralization (mineralization of bone and teeth) hydroxyapatite is most probably formed in a similar way from body fluids [31]. Temperature-programmed desorption techniques are also successfully used to estimate pore sizes of adsorbents consisting of amorphous materials or arrays of

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poorly oriented crystallites (silica gels, aluminum oxides, active carbons, etc.) [32]. An important class of crystalline compounds that are formed via amorphous precursor phases are zeolites. Zeolites are aluminum silicates with a network of uniform pores of molecular dimensions incorporating exchangeable cations and water. They have numerous applications as adsorbents, catalysts, and membranes. Thermal analysis can give useful quantitative and/or semiquantitative information on the process of water adsorption and desorption and the thermal behavior of different types of zeolites, including information on the pore structure, degree of hydration of cations, interaction of hydrated cations with the aluminosilicate matrix, etc. [25,33–35]. Of particular interest for the present volume is the information that thermal analysis yields on the process of the transformation of amorphous aluminosilicate gel precursors into crystalline zeolite structures [35–37]. Differential thermogravimetric curves of amorphous aluminosilicate gels show endothermic peaks at low temperatures (50–60°C) corresponding to the desorption of loosely held moisture from the inner and outer surfaces of the gels and/or from the dehydration of Na+ ions from residual NaOH (curves 1–3 in Fig. 3). The formation of ordered structural subunits or particles of a quasicrystalline zeolite phase is evidenced by a second endothermic peak in the DTG spectrum that appears between 120°C and 150°C (curves 2 and 3 in Fig. 3). The appearance of this peak was explained by the assumption that the energy needed for the desorption of water molecules from Na+ ions positioned in structural subunits similar to those of zeolites is higher than the energy needed for the release of water molecules from the amorphous gel matrix [37]. The relative intensities of the two peaks change as a consequence of the increase in concentration of the quasicrystalline phase in the aluminosilicate matrix (Fig. 3) [35–37]. It was thus possible to use this sensitive method to investigate a number of experimental parameters that influence the formation of structural subunits that play a decisive role in the nucleation of zeolites from gel systems [35–37]. B.

Nucleation, Crystal Growth, and SolutionMediated Phase Transformation of Crystal Hydrates

At low and medium supersaturations the number of particles formed depends on the number of heterogeneous nuclei and usually does not exceed 107 cm-3 (Fig. 1). Once formed, crystals enlarge by deposition of solute ions at the surface, surface diffusion to a suitable site, and incorporation into the crystal lattice (see also Sections II.A and II.B). Under these conditions strongly hydrated cations are likely to form different crystal hydrates with different solubilities. Crystals thus formed are coarser and contain less—primarily crystalline—water than


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FIG. 3 DTG curves (rate of mass change as a function of temperature; schematic), representing the transformation of amorphous aluminosilicate gels into crystalline zeolite phases. Curve 1 shows a peak characteristic of the amorphous phase (50– 60°C); curves 2 and 3 show the progressive appearance of a second endothermic peak (120–130°C), indicating the formation of ordered structural subunits. (Adapted from Ref. 35.)

when crystallization is initiated by homogeneous nucleation. The difference between the amount and mode of binding of water molecules in crystals formed by heterogeneous nucleation and in crystals formed by homogeneous nucleation is illustrated by calcium oxalate precipitates. Calcium oxalate crystallizes in the form of three different hydrates. The thermodynamically stable monohydrate, CaC2O4 · H2O (COM), crystallizes in the form of monoclinic (– 101) plates [38]. Two other, metastable, crystal forms are known, the tetragonal calcium oxalate dihydrate [CaC2O 4 · (2 + x) H2O, x = 0.5 (COD)] and the triclinic trihydrate [CaC2O4 · (3 – x) H2O, x ≤ 0.5 (COT)]. COM and COD are important as the main constituents of kidney stones [39] and occur in many plants [40], and COT has been extensively investigated in the laboratory [41–44].

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The monohydrate (COM) was one of the first compounds studied by thermogravimetric analysis, and it was suggested that it should be used as a calibration standard [1]. Upon heating, it loses water between 100°C and 150°C in one distinct step [1,44]. The anhydrous CaC2O 4 decomposes between 300°C and 525°C according to the relation CaC2O4 ? CaCO3 + CO [1,45]. Finally, CaCO3 above 800°C decomposes into CaO + CO 2 [1]. The exact decomposition temperatures depend on the experimental conditions, i.e., the amount of sample, heating rate, size and shape of the crucible, and other factors. Thermograms of COD and COT differ from those of COM and from one another both qualitatively and quantitatively in the part corresponding to dehydration. COT loses water in two distinct steps, i.e., between 75°C and 100°C (about two water molecules) and between 100°C and 200°C (approximately one water molecule), whereas the dehydration of COD starts at 25–30°C and proceeds more gradually [44]. A comparison of the qualitative differences of various dehydration curves gives information on differences in the modes of water incorporation resulting from different modes of crystallization. An example is given in Fig. 4, which shows partial thermogravimetric curves (dehydration only) obtained from calcium oxalate precipitates prepared at different initial reactant concentrations. Curve 1 represents dehydration curves typically obtained from samples of COM of different morphologies formed by heterogeneous nucleation (including compact crystals and dendrites); curve 2 is

FIG. 4 Partial TG curves (dehydration only) showing the loss of water from (1) compact and dendritic crystals of COM and (2) microcrystalline aggregates with the structure of COD, dm 1 and dm 2 are the total mass loss (i.e., loss of hydration water) corresponding to 1 mol of H 2 O (dm 1 for COM) and 2.5 mol of H 2 O (dm 2 from microcrystalline aggregates) per mole of calcium oxalate. (Adapted from Ref. 44.)


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representative of microcrystalline aggregates initiated by homogeneous nucleation. These aggregates exhibit X-ray diffraction powder patterns characteristic of COD and contain between two and three molecules of water per molecule of calcium oxalate. The gradual loss of water between 25°C and 200°C, shown by their dehydration curve, suggests the presence of different kinds of water bound with a wide spectrum of energies. This can be explained by considering the crystal structure of COD and the size and shape of the microcrystalline aggregates. In the crystal structure of COD [46,47] the calcium atoms are coordinated to six oxalate oxygen atoms and two water oxygens. Additional water molecules (x = 0.5, see formula given earlier in this section) are included into channels that run throughout the crystal and are formed by the oxalate anions because of their unique positions in the crystal structure. These additional water molecules are structurally disordered, i.e., they do not occupy one stable position within the crystal lattice but occupy different positions and are bound with different energies within the water channels. Additional water molecules may be adsorbed at external and/or internal surfaces of the microcrystalline aggregates and are expected to evolve between 20°C and 100°C depending on the type of bonding [25]. By determining the mass loss due to dehydration (dm1 and dm2 in Fig. 4), it is possible to quantitatively determine the phase composition of mixtures of crystal hydrates provided it was qualitatively ascertained by some other method (for instance, by X-ray powder diffraction). This method has been used to determine the influence of various experimental parameters on the phase composition of calcium oxalate precipitates. Several examples are given in Figs. 5–9. Figure 5 shows the influence of the initial reactant concentration, ci, on the water content of calcium oxalate precipitates aged from 3 min to 3 h. Here c* is the concentration that corresponds to S*, the critical supersaturation for homogeneous nucleation. It is seen that at c 1 < c * the amount of water corresponded to 1 mol H2O per mole of calcium oxalate, i.e., COM was the prevailing precipitate. This was confirmed by X-ray diffraction powder patterns [44]. However, at c i = c *, the water content in the precipitates gradually increased to about 2–3 mol H2O per mole of calcium oxalate, and X-ray diffraction powder patterns showed that COD was the prevailing precipitate. This change in composition was matched by significant changes in the number, size, and morphology of the particles [44,48]. Thus, the profound influence of the initial reactant concentrations (i.e., the initial supersaturation) on the properties of the precipitates was confirmed. It is interesting to note that in a number of cases the main characteristics of particle sizes and morphology (i.e., compact crystals, dendrites, microcrystalline aggregates) persist even after aging for 24 h. Thus, it was possible to recognize the heterogeneous/homogeneous nucleation boundary and determine S * from 24 h precipitation diagrams and thus to calculate the interfacial energy of the homogeneous nucleus for several slightly soluble precipitates [49].

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FIG. 5 Schematic presentation of changes of the average water content in crystalline calcium oxalate precipitates as a function of the initial reactant concentrations, [Ca] = [Ox]. Time of aging in contact with the mother liquid was from 10 min to 3 h. c * denotes reactant concentrations corresponding to S *, as defined in Section II.A (i.e., at c c * , homogeneous nucleation prevails). (Adapted from Ref. 44.)

An interesting kinetic study deals with the solution-mediated phase transformation of COT and COD into the thermodynamically stable COM [50]. The experimental conditions were adjusted so that either COT or mixtures of COD and COM crystallized initially as confirmed by X-ray diffraction powder patterns. The systems were then aged in contact with the mother liquid, and the transformation of COT or COD into COM was followed by monitoring the total crystal volume as a function of time (by Coulter counter) and determining (by thermogravimetric analysis) the relative proportion of the crystal hydrates at fixed time intervals. In addition, supersaturation profiles (i.e., activity products) were determined by solution calcium analysis. In all cases the transformation was completed within approximately 80–100 h. A schematic presentation of the transformation of COT into COM is shown in Fig. 6. In accordance with the analysis of Cardew and Davey [22] (Section II.D), the activity product (Fig. 6a) exhibits a plateau in the region where the dissolution of COT and growth of COM are balanced (Fig. 6b). Interpretation of the kinetics data showed that dissolution of COT is a first-order process (i.e., diffusioncontrolled) whereas growth of COM is a second-order process, as was also found in seeded crystal growth experiments [51]. C. Control of Crystallization by Additives Any impurity present in the crystallizing solution (“impurity” denoting any ions, small molecules, or macromolecules that are not constituents of the nascent crys-


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FIG. 6 Kinetic analysis of solution-mediated phase transformation of in situ precipitated calcium oxalate trihydrate (COT) into calcium oxalate monohydrate (COM). (a) Solution analysis: Variation of ion activity product vs. time. (b) Solid phase analysis: Total crystal volume (curve 1) and volume fractions of COT (curve 2) and COM (curve 3) vs. time. (Schematic presentation adapted from Ref. 50.)

tal phase) may adsorb at the crystal/solution interface and modify the rate of nucleation and/or crystal growth. If adsorption is nonspecific, the growth process is likely to be retarded, resulting in a reduction in crystal sizes. If the impurity is preferentially adsorbed at selected crystal faces, growth in the direction perpendicular to those faces is slowed down. The result is habit modification, with the affected crystal faces appearing larger than usual. Such a case is schematically represented in Fig. 7a, which shows how a platelet-like crystal transforms into a needle when an impurity is adsorbed on its lateral faces. Finally, when the solution is supersaturated to two (or more) crystal polymorphs or different crystal hydrates, an impurity can influence their relative rates of nucleation and growth by preferentially adsorbing at one of them. In that case, growth of the affected crystal phase will be inhibited, while the other phase(s) can grow faster from the same supersaturation. We may thus experience a change in the crystallizing polymorph. This is schematically shown in Fig. 7b, where phase B grows on account of phase A, which is selectively inhibited by an impurity. By understanding these phenomena, one can hope to design additives to crystallizing systems capable of producing crystals of desired particle sizes and morphology or even to induce growth of a desired crystal polymorph. Control of the crystallizing phase by additives is of considerable importance in the production of specialty chemicals such as pharmaceuticals, dyes, and pesticides [8,22]. The formation of metastable polymorphs and/or higher hydrates is often desired be-

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FIG. 7 Schematic presentation showing (a) control of crystal morphology and (b) control of the crystallizing phase by an additive. (a) Preferential adsorption of an additive at the lateral faces of a growing crystal. This type of interaction results in a change of crystal morphology from platelet to needle-like. (b) In a solution supersaturated to two solid phases (polymorphs), an additive (small circles) preferentially adsorbs at the nuclei of phase A and inhibits their growth. As the supersaturation is essentially unaffected, phase B will grow instead.

cause of their advantageous properties, whereas in other cases metastable phases are undesirable because subsequent phase transformation during storage must be avoided. One of the keys to the understanding of specific additive–crystal interactions is the structural approach. As early as the 1950s attempts were made to explain crystal habit modification by the formation of an adsorbed impurity layer structurally similar to a growing crystal face. Thus, Whetstone [52] showed that habit modification of soluble inorganic salts can be achieved by organic dyes if the interatomic distances of the polar groups of the dye match the ionic arrangement of the substrate. This structural approach culminated in the 1980s with the design of “tailor-made” additives for control of the growth and dissolution of organic


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crystals. In their classical work Addadi et al. [53] showed that one can design inhibitors for the engineering of organic crystals with the desired morphologies and moreover for the resolution of conglomerates and enantiomers. It is required that a stereochemical relationship exist between the crystal structure, its modified morphology, and the molecular structure of the inhibitor. Also, in inorganic crystallization systems, organic macromolecules can exert control over the morphology and nature of the crystallizing phase [54–56]. This ability has been routinely used by living organisms to control the properties of biominerals (calcium carbonate in marine organisms, hydroxyapatite in bones and teeth, etc.) [56,57]. As above, the underlying cause of these effects is specific molecular recognition based on strict stereochemical correlation between the structures of the affected crystal faces and the molecular structure of the additive, which acts as inhibitor. The macromolecules commonly involved in biomineralization seem to be acidic proteins with arrays of negatively charged (carboxylate and/or phosphate) groups. These macromolecules specifically recognize crystal faces with characteristic structural motifs emerging at their surfaces [57]. Another factor of importance in selective crystal–additive interactions is the difference in electric charge between different crystal faces, which is caused by differences in their ionic structures. This is particularly evident in some crystal hydrates. Thus, for instance, during growth of some plate-like calcium phosphate crystals (octacalcium phosphate, calcium hydrogen phosphate dihydrate) from electrolyte solution, the largest face may, for most of the time be covered by a hydration layer that shields it from electrostatic interactions [55,58]. As a consequence, small molecules with high charge density exhibit face-selective interactions that result in habit modification although there is no long-range structural and stereochemical compatibility with the affected crystal faces [59,60]. The selectivity is due to preferential adsorption of the molecules at the charged side faces of the crystal as a consequence of their inability to penetrate the hydration layer. Other examples of selective interactions of surfactants with calcium oxalate hydrates, are given below. Surfactants are particularly suitable as additives for the control of crystallization because of their specific molecular structure. A surfactant molecule consists of an ionic or nonionic hydrophillic headgroup coupled with a hydrophobic tail. In a crystallization system the headgroup binds to the crystal surface while the tail provides steric hindrance for the incorporation of growth units into the crystal lattice. As surfactants are relatively inexpensive and readily available in many different designs, they should be regarded as ideal crystallization modifiers for industrial applications. The ability of anionic surfactants to control nucleation from solutions supersaturated with different calcium oxalate hydrates will be discussed in some detail. Of all three calcium oxalate hydrates, COD has the lowest crystallization rate. It does not readily crystallize from electrolytic solutions but frequently appears

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in the form of large aggregated crystals in pathological mineral deposits such as occur in crystalluria [61] (the formation of crystals in urine) and kidney stones [39]. It was therefore of interest to understand the reasons for COD crystallization under pathological conditions. One of the apparent reasons is the presence in urine of a large number of soluble organic molecules and macromolecules that can promote crystallization of COD by inhibiting the growth of COM and/or COT nuclei (see Fig. 7b). Because many of the urinary organic molecules and macromolecules have surfactant properties, synthetic surfactants were considered ideal model additives for the study of such interactions [62]. In the ensuing studies, crystallization of COM and COD from solutions containing different concentrations of ionic and/or nonionic surfactants (Table 1) was systematically investigated [62–67]. Qualitative and quantitative information on the precipitate composition was obtained by X-ray powder diffraction and thermogravimetric analysis, respectively. From the thermogravimetric data (see Fig. 4), the amount of water in the precipitate was calculated and translated into weight percent of COD, assuming the formula CaC 2O 4 · 2H 2O. X-ray powder patterns showed that in the controls (systems without added surfactant) and at low surfactant concentrations [below the critical micellar concentration (cmc)], COM was the prevailing crystallizing phase. This was also true when crystallizaTABLE 1 Model Surfactants Used in Crystallization Studies


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FIG. 8 Crystallization of calcium oxalates in the presence of anionic surfactants (0.3 M sodium chloride solutions supersaturated to COM and COD, pH 6.5, temperature 37°C). Changes in the mass fraction of COD in the precipitate are shown as a function of the surfactant concentration expressed in multiples of the respective critical micelle concentrations (cmc’s). The mass percent of COD (vertical axis) was calculated from thermogravimetric data assuming a formula C2O4 ˙ 2H2O for COD. (After Ref. 62.)

tion experiments were carried out in the presence of any concentration of cationic [67] or nonionic [65] surfactant. However, when crystallization was carried out in the presence of an anionic surfactant, an upsurge in COD content was observed at surfactant concentrations close to and/or above the cmc, with the effect decreasing in the order SDS > sodium cholate > AOT (Fig. 8) [62–66]. In another set of experiments [68] the kinetics of solution-mediated phase transformation of preprepared, well-defined model COD crystals was investigated in the presence of micellar concentrations of an anionic (SDS) and a cationic (DDACI) surfactant. Figure 9 shows that both surfactants almost completely inhibited phase transformation (SDS was slightly more effective than DDACl [68], which is not shown in Fig. 9). We have thus demonstrated that (1) anionic surfactants can control the composition of crystallizing calcium oxalates (Fig. 8), whereas (2) both anionic and cationic surfactants inhibit the solution-mediated phase transformation of COD into the thermodynamically stable COM (Fig. 9). Both results can be readily explained if one considers the respective adsorption isotherms and adsorption densities of surfactants at COM and COD crystal/solution interfaces (see Fig. 10 and Table 2) [68,69]. Adsorption of surfactants at polar surfaces has been extensively investigated because of the importance of modifying particle surfaces for many industrial applications [70,71]. A number of models have been proposed, most of which are based on experimental and theoretical studies of the adsorption of ionic surfactants at the oxide/water interface [72–75]. All authors agree that at low surfactant concentrations, adsorption at charged surfaces (oxides, salts) is driven by

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FIG. 9 Schematic presentation of the kinetics of solution-mediated phase transformation of preprepared, well-defined COD crystals into COM. t A (horizontal axis) is the aging time. Curves: (1) suspension of COD crystals without surfactant (for control) and (2) in the presence of micellar concentrations of SDS or DDACl. Samples were filtered at different time intervals, and the composition of the solid phase was analyzed by thermogravimetric analysis. (Adapted from Ref. 68.)

electrostatic interactions, resulting in molecular adsorption with the headgroups of individual molecules oriented toward the surface. A subsequent upsurge in the slope of the isotherm is due to the formation of surfactant aggregates in the adsorbed layer caused by hydrophobic tail–tail interactions (see inserts in Fig. 10). Finally, a leveling off of the adsorption, coinciding with the cmc of the surfactant, is ascribed to a constant chemical potential sink caused by the formation of micelles in the bulk solution. The isotherms characterizing adsorption of surfactants at the COM/ solution and/or COD/solution interface are in agreement with that general picture [68,69]. As an example, adsorption isotherms of AOT onto COM and COD are shown in Fig. 10. In agreement with the above considerations, the AOT/COM isotherm shows a region of low adsorption and a region of high adsorption with a steep inflection between them. In the AOT/COD system the region of low adsorption is not apparent, but the rest of the isotherm is similar. It is important for our argument that the course of the thermogravimetric curves represented in Fig. 8 is in general agreement with the course of the adsorption isotherms (Fig. 10), i.e., the phase change is concomitant with the upsurge in adsorption density. A comparison of the plateau adsorption densities of the investigated surfactants at COM/solution and COD/solution interfaces shows (Table 2) that both anionic surfactants (SDS and AOT) adsorb much more strongly on COM than on COD surfaces, whereas for the cationic surfactant the


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FIG. 10 Schematic presentation of adsorption isotherms (adsorbed amount, Γ, as a function of the equilibrium surfactant concentration, C eq) characterizing the adsorption of AOT at the surfaces of (a) COM and (b) COD crystals. Inserts indicate monolayer adsorption at low surfactant concentrations and the formation of a double layer at surfactant concentrations exceeding the cmc of the surfactant. (Adapted from Ref. 69.)

TABLE 2 Plateau Adsorption Densities of Ionic Surfactants at Calcium Oxalate/Electrolyte Solution Interfaces Sorbent a

Sorbate a

Molecules per square nanometer

Ref

COM COD COM COD COM COD

SDS SDS AOT AOT DDACl DDACl

31.9 20.5 14.22 7.45 16.3 13.3

68 68 69 69 68 68

a

For definitions see text.

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adsorption densities at the surfaces of the two substrates are comparable. It is therefore conceivable that anionic surfactants, when present at micellar concentrations in a solution of calcium oxalate supersaturated with both COD and COM, preferentially adsorb on the faster growing COM nuclei and block their growth, thus enabling the growth of COD crystals (see Fig. 7b). For the cationic surfactant we would not expect such selectivity, because the adsorption densities on the two substrates are comparable. In contrast to nucleation control, inhibition of phase transformation does not require selectivity, as interactions with both substrates (inhibition of dissolution of the metastable phase and growth of the stable phase) may be rate-controlling [22,50] (see also Sections II.D and III.B and Fig. 6). It is therefore not surprising that both the anionic SDS and the cationic DDACl effectively inhibit the transformation of COD into the thermoynamically stable COM (Fig. 9) [68]. The difference between the adsorption densities of anionic surfactants at the surfaces of COM and COD crystals, respectively (Table 2), has been explained [68,69] on the basis of the difference in the crystal structures of the two compounds: COM has negatively charged faces with high charge density [38], whereas COD forms highly hydrated crystals with relatively low surface charge [46,47]. (see Section III.B for a more detailed explanation of the COD crystal structure). In all cases, surfactant adsorption is mediated by calcium ions in the electrolyte solution. IV. CRYSTALLIZATION IN CONFINED SPACES: EMULSIONS AND MICROEMULSIONS In the preceding sections, we discussed the formation and transformation of ionic precipitates from bulk electrolyte solutions. We saw that the rates and mechanisms of the processes governing crystallization (nucleation, crystal growth, flocculation, and aging) depend on the experimental conditions such as supersaturation, temperature, and additives. It has been shown that surfactant micelles have a profound influence on crystallization, even to the extent of controlling the nature of the crystallizing phase (Fig. 8). In this section, we concern ourselves with crystallization of molecular crystals and/or inorganic clusters within confined spaces and/or at the oil/water interface such as occurs in emulsions and microemulsions. A.

Emulsions: Induced Crystallization at the Oil/ Water Interface

The critical supersaturation for nucleation of molecular crystals from a melt or solution is conveniently achieved by cooling the sample until a crystallization temperature, Tc is reached. Another critical point is the melting temperature, T m,


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which is obtained by controlled heating of the crystals. The critical supercooling for , is, like the critical supersaturation S*, a homogeneous nucleation, thermodynamic quantity characteristic of the crystallization system. However, it is almost impossible to achieve this degree of supercooling in a bulk melt because of the presence of numerous impurities, which act as heterogeneous nuclei (for a discussion of homogeneous and heterogeneous nucleation, see Section II.A). The effect of these catalytic impurities can be minimized if the sample is broken up into a large number of isolated droplets, which may be achieved by emulsifying. Emulsions thus obtained are micrometer-sized droplets of an organic (oil) phase in water or, vice versa, water droplets in a liquid organic phase (oil) dispersed by an amphiphilic emulsifier. Crystallization from such systems was first studied in the context of homogeneous nucleation [76]. Since then, many studies of the crystallization of an oil phase in oil-inwater emulsions [77–81] and of the freezing of water or aqueous solutions dispersed within an oil phase [82–84] have been carried out. In this section we discuss the crystallization of molecular crystals in oil-in-water emulsions; for a review on waterin-oil emulsions, see chapter 5. Most experimental studies on crystallization in emulsions are concerned with nucleation and crystal growth kinetics. In these studies thermal analysis is an indispensable tool. Thus, as a measure of the efficacy of an initiator of heterogeneous nucleation, the supercooling, ∆T = T m – T c is determined. In many cases T c is significantly higher than . To evaluate ∆T, the system is subjected to cooling and heating cycles and some property is measured as a function of temperature. Alternatively, the variation of the chosen property of the system is followed isothermally as a function of time to evaluate the kinetics of crystallization at constant temperature. For these measurements a number of experimental techniques are available: dilatometry [77], NMR spectroscopy [85], ultrasonic velocity measurements [78,85], and DSC [86], among others. In addition, DTA and DSC are used to yield information on the enthalpies of freezing, ∆H f, or melting, ∆Hm, and the heat capacity, cp. Nucleation of oil in individual emulsion droplets can be either homogeneous or heterogeneous, with the catalytic impurity distributed throughout the bulk (bulk heterogeneous nucleation) or at the oil/water interface [77–79] (surface heterogeneous nucleation). A fourth mechanism, interdroplet heterogeneous nucleation, has also been proposed [80,81]. It is the third mechanism, interfaceinduced nucleation, that concerns us most in this volume. In 1963 Skoda and Van den Tempel observed [77] that the temperature at which crystallization of triglycerides started in emulsified systems was invariably lower than in nonemulsified solutions and depended on the emulsifying agent used. With some emulsifiers T c was so low that the authors assumed the existence of homogeneous nucleation. Other molecules effected a rise in T c , apparently catalyzing nucleation. It was observed that the catalytic activity was the greater

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the more the molecular structure of the emulsifier resembled that of the crystallizing phase. A mechanism was assumed whereby emulsifier molecules adsorbed at the surface of the oil droplets orient triglyceride molecules close to the surface and thus catalyze nucleation. This structural approach was corroborated by Davey et al. [79], who studied the nature of nucleation catalysis at the oil/water interface using as an example meta-chloronitrobenzene (m-CNB)-in-water emulsions prepared with a wide range of emulsifiers. The crystallization temperature, morphology, and crystal orientation at the oil/water interface were determined and correlated to the molecular packing and structure in the amphiphile monolayer at the interface. It was found that nucleation catalysis occurred when the surface area per molecule of the amphiphile approached that of the crystallizing substrate. In addition, in the presence of emulsifiers whose molecular structure resembled that of the (020) crystal face, crystals were oriented with that face in the plane of the interface in contact with the aqueous phase. This was proven by X-ray powder patterns, which unequivocally showed preferential crystal orientation. In a recent study by Kaneko et al [78], the dual role of an impurity in emulsion crystallization of n-hexadecane was convincingly demonstrated, thus corroborating earlier bulk crystallization studies showing the dual role of impurities in inorganic crystallization [87]. These authors emulsified n-hexadecane in water using polyoxyethylene (20) sorbitan mono-dodecanoate (Tween-20) as an emulsifier. Before emulsification, a highly hydrophobic food emulsifier, a sucrose polyester with a palmitic acid moiety (P 170), was added to the n-hexadecane. Crystallization was then studied by monitoring changes in ultrasound velocity during temperature changes and in isothermal kinetic experiments. The experiments were based on the fact that ultrasound velocity changes abruptly as a consequence of solid–liquid transformation, showing a sharp increase at the onset of crystallization (for a detailed description of the technique, see Ref. 85). Figure 11 shows that two parameters, Tc and the change in ultrasound velocity, ∆V, could be independently measured in the same experiment. It is seen that while T c increased, ∆V decreased with increasing concentration of the impurity (for more data see Ref. 78). This result has been interpreted as showing that the impurity induces nucleation when adsorbed at the oil/water interface while at the same time it retards crystal growth. In parallel experiments in a bulk system, there was no detectable effect of the impurity on nucleation, but crystal growth was retarded. Apparently, it is the arrangement of the impurity molecules at the oil/water interface that produces the catalytic effect. The foregoing studies point to conclusions similar to those of the extensive research on induced crystallization of inorganic and organic crystals under closepacked amphiphilic Langmuir monolayers [88–92]. All these studies show that it is possible to design interfaces that will not only catalyze nucleation but will also orient the nascent crystals in a well-defined and reproducible manner. The


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FIG. 11 Schematic presentation of changes in the ultrasound velocity V (arbitrary units) with temperature during the controlled cooling of n-hexadecane in water emulsions, emulsified with Tween-20. Parameters determined are the crystallization temperature Tc and the magnitude of the change in V due to crystallization (∆V). Curve 1, control; curve 2, in the presence of an impurity (P-170). (Adapted from Ref. 78.)

underlying mechanisms are geometrical, electrostatic, and stereochemical complementarity between the incipient nuclei and the functionalized substrates [90,92]. B.

Crystallization in Microemulsions

In contrast to emulsions, which are unstable macrodisperse systems (1–10 µm in droplet diameter), microemulsions are homogeneous, optically transparent, thermodynamically stable systems that can be formed only in specific ranges of temperature, pressure, and composition. They consist of droplets of water tens of nanometers in size dispersed within an immiscible organic (oil) phase [inverse micelles, or water-in-oil (W/O) microemulsions] or vice versa, oil pools dispersed within an aqueous phase [direct micelles, or oil-in water (O/W) microemulsions]. The droplets are encased in a surfactant shell as in emulsions or, more frequently, in a shell consisting of a suitable surfactant and a cosurfactant (usually an alcohol) and are thus stabilized. Water-in-oil microemulsions are characterized by a micellar core formed by the polar heads of the surfactant protruding into the water droplet, surrounded by a layer of alkyl chains protruding into the surrounding apolar liquid (Fig. 12). The micellar size and shape depend on the nature of the surfactant molecule, the water/ surfactant molar ratio, and the presence and location of solutes within the micellar core [93].

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FIG. 12 Schematic representation of the location of solubilizates within water/isooctane microemulsions stabilized with AOT. (a) Without solubilizate; (b) ions and/or ionic clusters located within the water pools; (c) aspartame molecules located at the water/ isooctane interface, with the aspartyl end pointing toward the water pool and the phenylalanine end oriented toward the oil phase.

In recent years, W/O microemulsions have found numerous applications as “microreactors” for specific reactions (for comprehensive reviews, see Refs. 94 and 95). Thus, it has been shown that hydrophilic enzymes can be solubilized without loss of enzymatic activity and used to catalyze various chemical and photochemical reactions [96,97]. Other interesting applications involve the polymerization of solubilizates in microemulsions [98] and the preparation of microporous polymeric materials by polymerization of single-phase microemulsions [99]. Furthermore, microemulsions have been used as microreactors for the synthesis of nanosized particles for various applications [93,95] such as metal clusters (Pt, Pd, Rh, Au) for catalysis [100,101], semiconductor clusters [102–104] (ZnS, CdS, etc.), silver halides [105], calcium carbonates, and calcium fluoride [106]. Recently it was shown [107,108] that it is possible to use W/O microemulsions for the control of polymorphism of water-soluble organic compounds. In most of these applications, one or more reactants are solubilized within a microemulsion and then a reaction is initiated. Depending on its molecular structure,


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a solute may be located at different sites within a microemulsion [93]. The two locations that concern us most in this presentation are within the water pools (Fig. 12b) and at the water/oil interface (Fig. 12c). Experimental studies concerning crystallization from W/O microemulsions use thermal analysis methods to characterize the microemulsions themselves, to determine thermodynamic parameters of crystallization, and to characterize the final products. A large number of studies are concerned with the state of water in ionic [109] and nonionic [110] W/O microemulsions. It has been shown that because of the close proximity of the interface, the properties of the water molecules are quite different from those of water in the bulk, and this difference in itself may have a profound effect on the solubilization and crystallization of solutes. The problem is discussed in detail in two other chapters (by Schulz et al. and by Garti et al.) in this book and will not be reiterated here. In this presentation we describe (1) calorimetric studies of the formation of nanosized inorganic crystallites and (2) the use of TG and DSC in the characterization of a water-soluble organic compound crystallized in a W/O microemulsion. The ability to synthesize inorganic crystallites in the size region of tens of angstroms (i.e., hundreds to thousands of atoms) within microemulsions has attracted widespread interest [94,95]. Such crystallites are properly termed clusters, because they have properties intermediate between those of molecules and those of bulk solids [102,104]. They are conveniently prepared by solubilizing a water-soluble metal salt and a reducing agent (for metal clusters) or a water-soluble cationic salt and a water-soluble anionic salt (for metal salts including semiconductors, silver halides, etc.) in two separate microemulsions of the same composition and then mixing the microemulsions. For example, nanosized gold particles were prepared by in situ reduction of tetrachloroauric(III) acid by hydrazine sulfate, both reagents being solubilized in microemulsions of the same composition [101], and silver chloride was prepared by mixing two microemulsions, one containing solubilized AgCl and the other, NaNO3 [105]. As reaction media, water–AOT–hydrocarbon microemulsions are preferred by many investigators [95,104] because (1) AOT self-assembles without cosurfactant, (2) the phase diagrams have relatively large L 2 (water-in-oil) regions, and (3) the microemulsions consist of well-defined droplets (water pools). In order to understand why cluster size particles are formed and stabilized within microemulsions, we briefly consider the precipitation reaction: The water-soluble reagents are situated within the water pools of the microemulsions (Fig. 12b) and are randomly distributed among the droplets according to a Poisson distribution [111]. Thus, the reaction that occurs upon mixing is due to exchange between droplets containing different reactants [104]. As in emulsion crystallization (Section IV.A), the effect of heterogeneous nuclei (impurities) is minimized by compartmentalization. Thus, if the nascent salt has a low solubility product and S* is exceeded, particles form by way of homogeneous nucleation. The clusters thus formed would have a tendency to grow by

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flocculation rather than by the addition of ions to the crystal lattice (see Section II.A and Fig. 1). However, because the particles have a large surface-to-volume ratio, they will be protected from flocculation by the adsorption of one of the reactant ions and/or by the surrounding surfactant shell. In a W/O microemulsion stabilized by AOT, the size of the nascent particles is a function of the water pool size, which is given by the equation [104] (7) where r (in nm) is the hydrodynamic radius and (8) is the water/AOT molar concentration ratio. So the size of the compartmentalized water droplets can be varied by simply changing w and can then be used to control the size of the precipitating clusters [104]. The enthalpies of precipitation of a variety of nanoparticles in W/O microemulsions have been studied by calorimetry. These include metal particles such as palladium [112] and gold [101], silver halides [105], calcium salts [106], and semiconductors such as ZnS [103]. It was shown that particle formation is an exothermic process, the values of the molar enthalpies, –∆H, increasing with increasing w. In all cases, the values of –∆H for cluster formation in microemulsions were less negative than when the corresponding process was conducted in a bulk aqueous solution. Clearly, submicrometer-sized clusters had higher energies than the corresponding micrometersized crystals formed from bulk solutions. In a recent study of the formation of ZnS nanoparticles [103], Arcoleo et al. separated the contribution of the particle size from other contributions to the molar enthalpy by independently measuring particle sizes by UV spectroscopy. (Note that the UV spectroscopic method is based on changes in UV-Vis spectra corresponding to size changes of semiconductor clusters. That is, a shift of λmax toward lower wavelengths is observed with decreasing particle size [103,104].) Thus, it was shown that the –∆H values are indeed a function of particle size, because they increased linearly with increasing λmax. However, at constant λmax (i.e., at the same nanoparticle radius), the –∆H values increased with increasing [S-]/[Zn2+] molar ratio and depended on the nature of the surfactant stabilizing the microemulsion. This result was interpreted as indicating contributions to the enthalpy from the adsorption of HS- ions at particle surfaces and from particle–surfactant interactions at the oil/water interface [103]. Recently, the possibility of using microemulsions as microreactors for the control of polymorphism of organic compounds, specifically amino acids and peptides, was demonstrated by Füredi-Milhofer et al. [107,108]. In these experiments, the organic molecules were solubilized in hot microemulsions and crystallized by slow cooling. In some cases, in contrast to the precipitation of ionic clusters (see above), the procedure was most effective when the solute mole-


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cules were situated at the water/oil interface rather than within the water pools of the reversed micelles (Fig. 12c). Thus, the surfactant was brought into intimate contact with the nascent solid phase and could influence crystal nucleation and growth as in micellar systems (Section III.C and Fig. 7). We used the method to selectively crystallize one of the polymorphs of phenylalanine, whereas a mixture of two different polymorphs crystallizes from bulk aqueous solutions (J Yano, H Füredi-Milhofer, N Garti, unpublished results). We also succeeded in preparing a previously unknown crystal hydrate of the artificial sweetener aspartame (APM III) by recrystallization from water/isooctane microemulsions stabilized with AOT [107,108]. The latter example is described in more detail below. Aspartame (N-L-α-aspartyl-L-phenylalanine methyl ester; APM) is widely used as an artificial sweetener because of its high sweetening power (150–200 times sweeter than sucrose), no aftertaste, and relatively good compatibility for human consumption [113]. However, when obtained by conventional recrystallization procedures its crystals tend to have unfavorable morphological characteristics and poor dissolution kinetics. It was therefore of great interest to obtain new crystal forms of aspartame with improved dissolution behavior. The aspartame molecule, HOOC—CH2 —CH(NH2 )—CO —NH—CH(COOCH 3)—CH 2 C 6H 5 is a dipeptide composed of a highly hydrophilic aspartyl residue and a hydrophobic phenylalanine methyl ester entity. In the basic crystal structure [114], the aspartame molecules are arranged in columns formed by an extensive hydrogen bond network, interconnecting zwitterionic N-terminal ends of the aspartyl residue and hydration water molecules. The outer surfaces of the columns are highly hydrophobic, because they are covered with phenyl and methyl groups stemming from the esterified phenylalanine end. As this columnar structure is probably responsible for the poor dissolution behavior and aspartame’s tendency to form fibers, it was assumed that one way to improve the dissolution behavior would be to disrupt the hydrogen bonding networks by introducing an additive or additional water molecules into its interior. It seemed that a good method to achieve this objective might be the recrystallization of aspartame from a suitable microemulsion. Among a number of microemulsions studied, water/isooctane/AOT microemulsions most effectively solubilized aspartame. At constant temperature and atmospheric pressure, the maximum amount of aspartame that could be solubilized, n(APMs), where n is the number of moles, exceeded by several times the amount that could be dissolved in the same volume of water. Furthermore, n(APMs) depended linearly both on the concentration of AOT and on the amount of free water in the microemulsion; i.e., a linear dependence on w was obtained when w exceeded 10. Thus, we can write (9)

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where (10) is the slope of the straight line described by Eq. (9). The respective intercept obtained by extrapolation to w = 0 gives the n(APMs)/n(AOT) ratio at the water/ oil interface for a given temperature. The relationship is schematically represented in Fig. 13. At 25°C, under the experimental conditions employed in Ref. 108, the n(APMs)/n(AOT) molar ratio at the water/oil interface was 0.16, corresponding to six molecules of AOT per molecule of aspartame. The location of the aspartame molecules at the water/oil interface is probably similar to that depicted in Fig. 12c, i.e., the hydrophobic phenylalanine end points toward the nonpolar medium while the aspartyl end points toward the water pool. Having established that aspartame molecules are located at the water/oil interface, commercial aspartame was then solubilized in a hot microemulsion and recrystallized by cooling [107,108]. Because of the intimate contact with the surfactant during crystallization, the resulting crystal form was expected to be less organized and higher in energy than crystals formed from bulk aqueous solutions. Indeed, after washing the crystals to remove the remaining oil and surfactant a new crystal form, APM III, that shows much improved dissolution kinetics was obtained. The crystals exhibit a distinct X-ray diffraction powder pattern, which is significantly different from the patterns of previously known polymorphs of aspartame. However, NMR spectra of the product dissolved in D2O are identical

FIG. 13 Schematic representation of the maximum molar ratio n(APMs)/n(AOT) in water/isooctane/AOT microemulsions as a function of w = n H 2O/n(AOT), where n is the number of moles. At w > 10 the dependence is linear; the slope, K = tanα , is given by Eq. (10); and the intercept, y 0 , is the APM/AOT molar ratio at the water/isooctane interface. (Adapted from Ref. 108.)


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to those of commercial aspartame, indicating that the molecular structure is unchanged. In the following, we give details of the characterization of APM III by DTG and DSC; for further characteristics of the product, see Refs. 107 and 108. Thermal decomposition of aspartame was first studied by Chauvet at al. [115], who used thermal microscopy and NMR spectroscopy to identify the decomposition products. According to these authors, TG/DTG and DSC peaks appearing at temperatures lower than 120°C are due to the loss of hydration water, whereas those appearing at higher temperatures are due to decomposition. Two decomposition peaks are apparent in the TG/DTG spectra, the first, at 170–200°C, being associated with the evolution of—OCH3 in the course of the formation of diketopiperazine (3-benzyl-2,5-piperazine dione-6-acetic acid), and the second, at 250–450°C, being due to the decomposition of that compound. In the corresponding temperature range, two endothermic DSC peaks, corresponding to (i) the formation of diketopiperazine (189–191°C) and (ii) fusion of this compound (at 252–254°C) have been reported in Ref. [115] and a third one (at 322–326°C) corresponding to the decomposition of diketopiperazine, was identified in Ref. 107. An additional exothermic DSC peak (at 203°C) was obtained when experiments were conducted with an open sample holder and was ascribed to recrystallization of diketopiperazine [115]. Spectra obtained from commercial aspartame (Nutrasweet) and from APM III by TG/DTG and DSC [107] are in general agreement with the above-described analysis, but differences in the curves obtained from different samples are apparent in the region corresponding to dehydration (Fig. 14). The TG/DTG curves show that APM III contains significantly more hydration water (7 wt% as opposed to 3.7 wt% in Nutrasweet aspartame and 1.77 wt% reported in Ref. 115), which evolves at lower temperatures (peak temperatures 91°C and 109°C for APM III and Nutrasweet aspartame, respectively). The corresponding endothermic DSC peak for APM III (curve 2 in Fig. 14a) is broader than the one obtained from the commercial sample (curve 1 in Fig. 14a); in fact, it appears to be composed of two peaks, one with a maximum at about 50°C and the other a sharp peak appearing near the boiling point. We therefore concluded [107] that some of the hydration water in APM III is loosely bound while at least part of it is tightly bound crystal water. It should be noted that even when DSC spectra were recorded from – 100°C at a rate of 5°C/min, no peak corresponding to free freezing water was detected. Studies of crystallization in emulsions and microemulsions are part of a new area of materials research, the aim of which is to produce advanced inorganic, organic, and inorganic–organic composite materials with well-defined properties. The research has been inspired by biomineralization, i.e., the strategies that living organisms use to form their skeletons or store minerals for various purposes.

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FIG. 14 Partial (a) DSC (rate of heat flow as a function of temperature) and (b) DTG curves (dehydration peaks only) showing the difference between commercial (Nutrasweet) aspartame (curves 1) and aspartame recrystallized from water/ isooctane/AOT microemulsions (APM III, curves 2). In diagram (a) the enthalpy changes, ∆H, associated with dehydration were calculated by integration of the respective peak area. Scanning rate 10°C/min. (Adapted from Ref. 107.)

Remarkably, organisms routinely form tough yet flexible organic–inorganic composite systems (their skeletons) in aqueous environments at relatively low temperatures, i.e., under nondestructive conditions. It is therefore well worth learning more about the strategies employed. The main principles of biomineralization can be discerned from several excellent reviews that are available on the subject [56,57,116,117]. The first step in many forms seems to be space delineation by cells. Materials frequently used for this purpose are lipid bilayers either in the cell wall or as a part of matrix vesicles located outside the cell. A less frequently used material is composed of polymerized, water—insoluble proteins and/or polysaccharides [116]. Several mechanisms of crystallization within biological cells or vesicles have been described: 1. In some cases mineral may form in the center of a vesicle and rapidly spread to form spherulites. This form of mineralization has been observed inside small intracellular vesicles where the crystals function as temporary storage sites for ions important in metabolism [117]. In such cases, the presumed function of the vesicle wall is merely to inhibit further crystal growth.


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2. In other cases (such as in the storage of iron in organisms by the protein ferritin), the membrane walls are probably involved, but the level of nucleation control is limited to spatial constraints and charge and polar interactions [92]. 3. Many biological mineralization processes involve oriented nucleation strictly controlled by organized organic interfaces that interact with the nascent crystals by virtue of structural and stereochemical recognition processes [57,91,92,117]. Clearly, the adaptation of the principles of biomineralization in the laboratory opens exciting new avenues in materials research, specifically in the development of advanced materials [91,92,94,95]. The main ideas “borrowed” so far from biological organisms are compartmentalization and molecular recognition at organized interfaces, which may be involved in crystal nucleation. There is a vast potential in the use of self-assembling organic materials for the construction of compartments for nucleation and crystal growth. Furthermore, by designing the materials for compartmentalization, it is possible to tailor interfaces to exert control over the crystallization processes. Thus, it should be possible to develop low temperature, nondestructive synthetic routes to advanced materials with special properties such as uniform particle sizes, nanoscale dimensions, tailored morphologies, and/or crystal orientation. In this review we have discussed several examples, many more being available in the cited literature. The potential of this novel approach has yet to be fully realized to satisfy the high demand for advanced materials that exists in many industries (electronics, telecommunication, aerospace, automotive, chemical, food, pharmaceutical, biomaterials and others). In this endeavor, important contributions to the characterization of materials and products as well as to the determination of the energetics and kinetics of reactions are being made by various methods of thermal analysis. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

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7 3 . P Somasundaran, DW Fuerstenau. J Phys Chem 70:90–96 (1966). 7 4 . JF Scamehorn, RS Schechter, WH Wade. J Colloid Interface Sci 85:463–493 (1982). 7 5 . NP Hankins, JH O’Haver, JH Harwell. Ind Eng Chem Res 35:2844–2855 (1996). 7 6 . D Turnbull, JC Fisher. J Chem Phys 17:71–73 (1949). 7 7 . W Skoda, M Van den Tempel. J Colloid Sci 18:568–584 (1963). 7 8 . N Kaneko, T Horie, S Ueno, J Yano, T Katsuragi, K Sato. J Crystal Growth 197:263–270 (1999). 7 9 . RJ Davey, AM Hilton, J Garside, M de la Fuente, M Edmondson, P Rainsford. J Chem Soc Faraday Trans 92:1927–1933 (1996). 8 0 . E Dickinson, J Ma, MJW Povey. J Chem Soc Faraday Trans 92:1213–1215 (1996). 8 1 . DJ McClements, SR Duncan. J Colloid Interface Sci 186:17–28 (1997). 8 2 . F Broto, D Clausse. J Phys C: Solid State Phys 9:4251–4257 (1976). 8 3 . D Clausse, L Babin, F Broto, M Aguerd, M Clausse. J Phys Chem 87:4030–4034 (1983). 8 4 . RK Kadiyala, CA Angell. Colloids Surf 11:341–351 (1984). 8 5 . E Dickinson, DJ McClements. Advances in Food Colloids, Blackie, London, 1996. 8 6 . DJ McClements, E Dickinson, SR Dungan JE Kinsella JG Ma, MJW Povey. J Colloid Interface Sci 160:293–297 (1993). 8 7 . H Füredi-Milhofer, S Sarig. Prog Crystal Growth Charact Mater 32:45–74 (1996). 8 8 . EM Landau, M Levanon, M Leiserowitz, M Lahav, J Sagiv. Nature 318:353–356 (1985). 8 9 . S Wolf-Grayer, L Leiserowitz, M Lahav, M Deutsch, K Kjaer, J Als-Nielsen. Nature 328:63–66, (1987). 9 0 . D Jacqemain, S Grayer-Wolf, F Leveiller, M Deutsch, K Kjaer, J Als-Nielsen, M Lahav, L Leiserowitz. Angew Chem Int Ed Engl 31:130–152 (1992). 9 1 . BR Heywood, S Mann. Adv Mater 6:9–20 (1994). 9 2 . S Mann, DD Archibald, JM Dydimus, T Douglas, BR Heywood, FC Meldrum, NJ Reeves. Science 261:1286–1292 (1993). 9 3 . MP Pileni. J Phys Chem 97:6971–6973 (1993). 9 4 . MP Pileni, ed. Structure and Reactivity in Reverse Micelles, Elsevier, New York, 1989. 9 5 . JH Fendler. Membrane-Mimetic Approach to Advanced Materials (Adv Polym Sci 113), Springer, Berlin, 1994. 9 6 . YuL Khmelnitsky, AV Kabanov, NL Klyachko, AV Levashov, K Martinek. In: Structure and Reactivity in Reverse Micelles (MP Pileni, ed.), Elsevier, New York, 1989, pp. 230–261. 9 7 . N Garti, D Lichtenberg, T Silberstein. Colloids Surf A: Physicochem Eng Aspects 128:17–25 (1997). 9 8 . YS Leong, F Candau. J Phys Chem 86:2269–2271 (1982); YS Leong, SJ Candau, F Candau. In: Surfactants in Solution, Vol. 3 (KL Mittal, B Lindman, eds.), Plenum Press, New York, 1983, pp. 1897–1910. 9 9 . M Sasthav, WR Palani Raj, M Cheung. J Colloid Interface Sci 152:376–385 (1992). 1 0 0 . Y Berkovich, N Garti. Colloids Surf A: Physicochem Eng Aspects 128:91–100 (1997).


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1 0 1 . F Aliotta, V Arcoleo, S Buccoleri, G La Manna, V Turco Liveri. Thermochim Acta 265:15–23 (1995). 1 0 2 . ML Steigerwald, LE Brus. In: Structure and Reactivity in Reverse Micelles (MP Pileni, ed.), Elsevier, New York, 1989, pp. 189–197. 1 0 3 . V Arcoleo, M Geoffredi, V Turco Liveri. J Thermal Anal 51:125–133 (1998). 1 0 4 . TF Towey, A Khan-Lodhi, BH Robinson. J Chem Soc Faraday Trans 86:3757– 3762 (1990). 1 0 5 . AD Aprano, F Pinio, V Turco Liveri. J Solut Chem 20:301–306 (1991). 1 0 6 . V Arcoleo, M Goffredi, V Turco Liveri. Thermochim Acta 233:187–197 (1994). 1 0 7 . H Füredi-Milhofer, N Garti, A Kamyshny. Aspartame and process of preparation thereof. Israeli Patent Appl, Oct. 29, 1997; Int Patent Appl, October 1998. 1 0 8 . H Füredi-Milhofer, N Garti, A Kamyshny. J Crystal Growth 198/199:1365–1370 (1999). 1 0 9 . PC Schulz. J Thermal Anal 51:135–149 (1998). 110. N Garti, A Aserin, I Tiunova, S Ezrahi. J Thermal Anal 51:63–78 (1998). 1 1 1 . SS Atik, JK Thomas. J Am Chem Soc 103:3543–3550 (1981). 1 1 2 . V Arcoleo, G Cavallaro, G La Manna, V Turco Liveri. Thermochim Acta 254:111– 119 (1995). 1 1 3 . MS Peterson, AH Johnson, eds. Encyclopedia of Food Science, Vol. 3, Avi, New York, 1978, p. 720. 1 1 4 . M Hatada, J Jancarik, B Graves, SH Kim. J Am Chem Soc 107:4279–4282 (1985). 1 1 5 . A Chauvet, H De Saint-Julien, GD Maury, J Masse. Thermochim Acta 71:79–91 (1981). 1 1 6 . HA Lowenstam, S Weiner. On Biomineralization, Oxford Univ Press, New York, 1989. 1 1 7 . L Addadi, S Weiner. Angew Chem Int Ed Engl 31:153–169 (1992).


12 Solid-State Transitions of Surfactant Crystals NADA FILIPOVI -VINCEKOVI and VLASTA TOMAŠ Department of Physical Chemistry, Ruper Boškoviƒ Institute, Zagreb, Croatia

I.

Introduction A. Surfactant crystals B. Thermal behavior of surfactant crystals C. Methods of phase transition analysis

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II.

Single-Chain Surfactants

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III.

Catanionic Surfactants A. Symmetrical catanionic surfactants B. Asymmetrical catanionic surfactants

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IV.

Double-Chain Surfactants

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References

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I. INTRODUCTION The typical surface-active or surfactant molecule consists of at least one polar hydrophilic part and one apolar hydrophobic part, such as a hydrocarbon or fluorocarbon chain. Although there is normally only one headgroup per surfactant molecule, there are frequently several nonpolar tails. These can be linear or branched, the most common being single and linear. Because of the coexistence of two opposite types of behavior inside the same molecule, surfactants can build different submicroscopic aggregates in water that can organize themselves into various supramolecular structures of macroscopic dimensions and different properties. The variety of supramolecules ranges from micelles to liquid crystalline 451

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phases. In most cases, those structures can transform from one to the other as a result of sometimes subtle changes in the solution conditions (e.g., concentration, electrolyte addition, temperature changes). Literature relating to the phase spectra of surfactants in aqueous and nonaqueous solutions is plentiful. Changes in the structures are manifested by abrupt changes in physical characteristics of the solution (viscosity, conductivity, and other transport phenomena; birefringence; or the existence of characteristic X-ray diffraction patterns) [1]. With decreasing solvent content, interactions between adjacent structures increase, leading to the formation of the liquid crystalline phase. On further decreasing the solvent content, dry surfactant crystals are formed, often via solventcontaining surfactant crystals. The terms liquid crystal, mesophase, or mesomorphic state are used synonymously to describe a number of different states of matter in which the molecular order lies between the almost perfect long-range positional or orientational order of solid crystals and the long-range disorder found in ordinary isotropic liquids. Two main classes of liquid crystals are usually distinguished: lyotropic and thermotropic. In lyotropic mesophases, the combination of order and mobility can be achieved by using a solvent; thermotropic mesophases are based on the temperature-induced mobility of form-anisotropic molecules in the melt. Surfactants can often form both thermotropic and lyotropic liquid crystals; i.e., they possess amphitropic properties [2]. We are interested here only in phase transitions arising solely from the action of thermal energy on single- and double-chain surfactant crystals (synthetic bilayerforming amphiphiles) and in a novel class of surfactants—catanionic surfactants, which are composed of oppositely charged ionic single-chain surfactants. We do not discuss the vast field of molecules of primarily amphiphilic character such as lipids, proteins, and copolymers. A. Surfactant Crystals Many surfactants in the dry state exist as well-formed crystals. Like most compounds that contain a long hydrocarbon chain, the resulting structures usually appear to be lamellar with alternating head-to-head or tail-to-tail arrangement [3]; i.e., the polar heads and hydrocarbon chains are both arranged in bilayers but segregated from each other. The bilayer structural element of a crystal has macroscopic dimensions in the x and y directions but molecular dimensions in the z direction. Stacking together many bilayers in the z direction forms the bulk crystalline phase. Ordinarily, the atoms in the outer planes do not penetrate significantly into the opposing plane of the adjacent bilayer during stacking; i.e., in most surfactant crystals, the functional groups of one layer do not penetrate into the space occupied by the functional groups of another [4]. Most surfactant molecules exist in an extended all-trans conformational structure within perfect single crystals. Structural anisotropy of the cross section of straight-chain lipophilic

Solid-State Transitions of Surfactant Crystals

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groups is principally responsible for the existence of polymorphism and structural complexity in the crystal states of long-chain molecules [5]. Numerous quantitative variants of the bilayer structure exist in surfactant crystals. One important variable is the tilt angle of molecular pairs with respect to the xy plane of the bilayer, and another is the rotational orientation about the z axis of adjacent molecules. Possible of bilayer arrangements of molecules consisting of one polar group and one or two hydrocarbon chains include bilayer structures with vertical chains or tilted chains, chain penetration structures, and others [6]. Some of the surfactants do not have a bilayer as a basic structural element. Alternative possibilities are interdigitated and monolayer structures. In an interdigitated structure, the head of one molecule is adjacent to the tail of the next one within the structural layer of the crystal, and the surfaces of these structural layers include both the heads and tails of the surfactant molecules [7]. The characteristic of a monolayer structure is that molecules within a monolayer are similarly oriented, but the polar surface of each monolayer lies against the nonpolar surface of the next monolayer [8]. The hydrocarbon chain-packing modes are usually described by means of a subcell, which gives the symmetry relations between equivalent positions in one chain and its neighbors [9,10]. Four types of subcells have been identified: (1) The planes contain parallel hydrocarbon chains, (2) the chains are perpendicular to each other, (3) the chain axes are crossed, and (4) the chains are packed in a hexagonal lattice. By lateral repetition of the subcell, the entire structure of the chain region is obtained. Structural analysis of normal paraffins with more than nine carbon atoms in the chain revealed mainly four possible distinct crystal structures: hexagonal, triclinic, monoclinic, and orthorhombic [11]. Crystal hydrates are formed from strongly polar surfactants whose shape does not allow them to pack densely without water being present. The role of water molecules is to (1) energeticly interact with the polar functional groups and (2) perform a space-filling function to improve crystal packing. When a molecule can pack nicely in a dense crystal, then crystal hydrates are unlikely [4]. B. Thermal Behavior of Surfactant Crystals Solids and fluids change their structure with temperature as a reaction to specific thermal molecular motions. Continuous thermal expansion may be followed by abrupt changes in the form of the solid crystalline–solid crystalline transition and melting. Phase transitions are generally accompanied by the cooperative onset of one or several specific types of molecular movements. In the case of a solid crystalline–solid crystalline phase transition, restricted motions of mainly rotational character occur, while in a melting transition the large scale of intramolecular conformational changes connected with long distance translational diffusion leads to a breakdown of the crystalline lattice.

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Many surfactants undergo polymorphic and melting phase transitions in much the same manner as do most other crystals with hydrocarbon chains, except that they often do not transform directly to an isotropic phase; i.e., they pass through a liquid crystalline phase before reaching the isotropic liquid phase [12]. The general picture of a surfactant crystal phase transition includes the trans to gauche configurational change for each C—C bond; i.e., the disorder of a low temperature phase, in which the hydrocarbon chains are parallel and, in the all-trans configuration, is attained by a gauche rotation of some C—C bonds. Hydrocarbon chains take up a variety of conformations as a function of temperature. The conformational disordering of the alkyl chains at lower temperature causes the polymorphic transitions in the solid state, while melting mainly implies the bidimensional disordering of the ionic layers from the crystalline to the liquid crystalline organization [13]. As the alkyl chains assume an ordered arrangement with weak intermolecular forces, the thermal liberation of rotational freedom around the chains takes place at a relatively low temperature. Molecular motion within the chain increases gradually as the temperature increases until, at characteristic temperatures, there is a considerable increase in the molecular motion, causing the formation of various polymorphs. Polymorphic crystals may be defined as crystals that are formed from the same molecule and have the same composition but are different in crystal structure. During a phase transition the crystal that exists at low temperatures may be transformed on heating into a different structure. Two different kinds of polymorphs exist; equilibrium and metastable [14,15]. A form that has a range of temperature over which it is stable with respect to other polymorphs is said to be an equilibrium polymorph. An equilibrium polymorph exhibits thermodynamically reversible isothermal phase transitions. Metastable polymorphs are kinetically stable states whose existence depends on the presence of a kinetic barrier to the attainment of equilibrium polymorphs. The transformation of a metastable polymorph to the corresponding equilibrium polymorph is an irreversible process. The packing of hydrocarbon chains into a crystalline alignment is difficult because of the many possible configurations of the chain units. That difficulty is reflected in the relatively low melting points and low crystallinity of most hydrocarbons. The melting points of surfactant crystals range from far below 273 K to greater than 623 K. The upper limit of these melting points indicates that the polar groups contribute to crystal stability, because the estimated melting point of linear hydrocarbons of infinitely long chain length is about 417 K [16]. In comparison to most inorganic crystals, surfactant crystals are low melting, and sometimes they do not melt reversibly; i.e., they are not stable at their melting point. Because of molecular structural breakdown, definitive physical studies cannot be performed. In the case of a surfactant with a liquid crystalline phase, several melting transitions take place, but finally an isotropic phase will form.


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Generally, in the transformation of a lamellar crystal to a lamellar liquid crystal of the same composition, the average chain length in the bilayers actually decreases because of a change from all-trans to gauche conformations. However, depending on the tilt angle of the chains in the crystal, a net increase or decrease in interlayer spacing is to be expected. In the case of strongly tilted chains, interlayer spacing may increase. Liquid crystals are a state of matter in which liquid-like disorder exists in one or two dimensions. Three types of thermotropic liquid crystalline states are commonly recognized: nematic, smectic, and cholesteric [17]. In the nematic state, the centers of gravity of the elongated molecules are arranged in a nonordered manner, but the long axes are oriented in a definite direction. The nematic mesophases are the least ordered liquid crystalline phases and are also usually the most stable at high temperatures in thermotropic systems. They are typically the last phase to melt, and when found they usually coexist with an isotropic liquid phase. In the smectic state, the centers of gravity and the ends of the molecules are located in planes equidistant from one another. A number of different types of smectic phases are known, divided into a number of subclasses. The common feature of smectic mesophases is that, apart from the orientational ordering along the directrix, there is a further arrangement of the molecules in layers. According to the molecular order within the layers and the angle of the directrix with respect to the layer, it is possible to differentiate various smectic phases (usually denoted as A, B, C, D, etc.). The cholesteric state can be regarded as twisted nematic. The local directrix in each nematic plane describes a helical pattern. Generally, the thermal behavior of solid crystalline surfactants depends on the molecular packing properties, which include length, branching, and unsaturation of a hydrocarbon chain, polar headgroup, and counterion size. Therefore, it is very difficult to discuss quantitatively the relationship between the geometrical packing property of surfactant molecules and the microscopic and macroscopic rearrangement of molecules caused by heating or cooling. An accurate treatment of a thermal phase transition would require evaluation of a partition function, which involves all the possible contributions to the total energy of a given configuration of the system. These contributions include, in the case of a bilayer, the repulsive excluded-volume interactions, the attractive van der Waals, rotamer, and headgroup interactions. A rigorous statistical-mechanical solution to this problem is extremely complicated, and this is the reason that phase transitions described in the literature are mainly discussed only from a purely phenomenological point of view. C. Methods of Phase Transition Analysis Methods for the examination of solid-state phase transitions are thoroughly discussed in a review by Threlfall [18]. All solid-state properties of the different

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polymorphic modifications of a compound will be different, but often only marginally so, to the point of instrumental indistinguishability. For this reason it is important to use a variety of techniques to avoid erroneous conclusions. Techniques that have been available for many years include hot-stage microscopy, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), differential thermal analysis (DTA), X-ray powder and single-crystal diffraction (XRD), and solubility and density measurements. Techniques that have become readily or more widely available within the past decade are solid-state NMR, diffuse reflectance infrared spectroscopy, near-infrared spectroscopy (NIR), Raman spectroscopy, the use of area detectors on a diffractometer, and combined techniques including hot-stage infrared spectroscopy, infrared microscopy, and video recording on the microscope. The same methods can also be used to study the liquid crystalline behavior of a wide class of surfactants, but the outstanding method for a preliminary examination is polarizing microscopy. A polarizing microscope equipped with a heating stage permits qualitative visual observation of the phase transformations that occur when a compound passes through the liquid crystalline state. Very often, a simple observation of morphology and orientation patterns displayed by a thinfilm preparation of a liquid crystalline phase is sufficient to establish its main structural type. Differential thermal analysis and differential scanning calorimetry are the most common techniques for studying the thermal phase behavior of surfactants. They yield quantitative data (heat and entropy changes of phase transitions, transition temperatures, specific heats, and kinetic parameters [19], but do not necessarily identify the nature of the relevant processes. In most cases when the forms are stable to grinding and the transitions are rapid, the resulting curves are reproducible. In other cases, the thermograms obtained may depend on the heating rate; i.e., the apparent location of a thermal event is much influenced by the heating and cooling rates. Sometimes, the number and intensity of detected thermal events depend on the actual thermal history applied to a sample; i.e., a late run may differ from an earlier one because of tempering on standing with a loss or gain of seed nuclei of other forms. This is sometimes the reason that one has to use exclusively the first scan for temperature-induced transitions. II. SINGLE-CHAIN SURFACTANTS A lamellar structure is usually found in crystals of single-chain surfactants [20]. The unit cells of single-chain surfactant crystals typically contain either a pair of molecules or a small number of pairs. In the case of an ionic surfactant, one or more types of ion pairs are found [21]. X-ray diffraction patterns are typical, with long spacing in the ratio 1:1/2:1/3:1/4 characteristic of a lamellar structure.


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A structural variation of synthetic single-chain amphiphiles indicates that a certain length of the flexible tail, usually a linear alkyl chain of seven or more C atoms, is required for the formation of a bilayer. The development of the bilayer structure is improved with increasing chain length. A systematic investigation by Skoulios and Luzzati [22] resulted in the well-known model of ionic amphiphilic molecules in which the two polar layers are separated by the hydrocarbon layer. In the liquid crystalline phase, molecules exist in one of an enormous number of conformational states, and they are constantly and rapidly undergoing restructuring among these different conformations. Busico et al. [13] proposed an electrostatic model for both the mesomorphic phase and the isotropic liquid of ionic singlechain surfactants. They concluded that the electrostatic energy alone would mainly account for the stability of the mesomorphic state, because the conformational entropy of the alkyl chains is substantially the same in both states and the residual translational and orientational entropy of a mesomorphic liquid is low. Single-chain surfactants can be classified in different ways depending on the nature of the hydrophilic or hydrophobic group. According to the number of carbon atoms in the straight aliphatic chains, they range from very short (~20) compounds. The common single-chain surfactants are salts of short- and long-chain fatty acids [6,22–28], long-chain primary n-alkyl-ammonium salts [29– 31], quaternary ammonium salts [32–34], and synthetic bilayer-forming amphiphiles [35,36]. A design principle of synthetic bilayer-forming amphiphiles includes the use of molecular modules: a tail, a connector, a spacer, and a headgroup [35]. In synthetic single-chain surfactants, a flexible alkyl tail (usually a normal alkyl chain, rarely branched, with a vinyl linkage and an ester linkage) with a carbon number of at least 8 is used. A connector is a rigid segment (diphenylazomethine, biphenyl, azobenzene, azoxybenzene, or units composed of two or three benzene rings connected by various atoms or groups) between a tail and a spacer. A spacer is the structural unit between the headgroup and the rigid segment; usually it is a linear methylene chain or an alanyl unit. A hydrophilic head can be cationic (a trimethylammonium group or modified ammonium group), anionic, nonionic, or zwitterionic. Stable bilayers are obtained when the sum of the tail and spacer carbon numbers is not less than 14 and the tail carbon number is at least 8 [35]. The first results of single-chain surfactant thermal phase transitions were reported on anionic single-chain surfactants, metal carboxylates [26–28]. These salts exhibit polymorphism and mesomorphism with two different smectic phases [13]. Salts, which decompose with melting, exhibit only polymorphism. An example is calcium stearate, which decomposes with melting at 423 K and exhibits two reversible polymorphic transformations [26]. Two smectic phases in metal carboxylates are denoted as smectic I (viscous and birefringent with regular layer stacking) and smectic II (fluid and optically isotropic owing to the small dimensions of the liquid crystalline domains; often described in the literature as an

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isotropic liquid). The introduction of a double bond in the proximity of the carboxylate group modifies the thermal stability of the mesomorphic phase [37]. An unusual ability to form a liquid crystalline mesophase with negative anisotropy is shown by short-chain carboxylates [24]. A smectic structure with negative anisotropy is confirmed for all short sodium chain carboxylates. It may be explained by two competing effects, which determine the overall polarizability anisotropy of a material. One is a contribution to a positive anisotropy of the hydrocarbon chains perpendicular to the layers, and the other is a contribution of the layer arrangement to a negative anisotropy. For long chain lengths, the positive polarizability anisotropy contribution is dominant and the birefringence is positive. The n-alkylammonium halides exhibit several successive high entropy phase transitions in the solid state that are reproducible for preheated samples [30]. The room temperature structure is formed by the stacking of double layers of parallel chains in the all-trans conformation facing each other with their methyl ends. The low temperature phases of these salts show a monoclinic or orthorhombic structure, whereas high temperature polymorphs show a tetragonal structure. As shown by wide-line NMR, the molecular mobility increases stepwise in connection with the phase changes in the solid state [34]. X-ray diffractometric investigation shows an intermediate phase, a plastic phase with conformational disordering of the hydrocarbon moieties occurring first in a three-step melting. Molten chains in a plastic phase are held together by their ionic end groups packed in crystalline planar arrays [29]. The transitions from the plastic phase to the smectic liquid crystalline phase mainly occur by a bidimensional fusion of the ionic layers. Two smectic phases are found as in alkali metal carboxylates. A comparison of thermodynamic parameters as well as melting and clearing points and transition temperatures between n-alkylammonium salts and various metal carboxylates reveals similarities in their mesomorphic behavior. The crystalline structure of long-chain n-alkyltrimethylammonium halides [32] belongs to the monoclinic form. Ammonium cations and halide anions are bidimensionally extended to form an ionic layer that is sandwiched between the hydrocarbon chain layers. These compounds exhibit one endothermic solid–solid phase transition in the range of temperature 350–400 K. This transition is caused by melting of the hydrocarbon chain layer while the rigid ionic layer retains its regular arrangement. The salts in this phase are not typical mesomorphic salts. Observation with an optical microscope and a thermobalance reveals that this transition is neither a full melting nor a decomposing process. A supercooled state is observed in the cooling process, and complete recovery to the original state is difficult. Single-chain pyridinium surfactants can be prepared by quaternization or protonation of pyridine derivatives [38]. Phase transitions of pyridinium salts are affected by the nature of the headgroup and counterions. Compounds with an N-


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protonated pyridinium show a simple phase transition from the solid state to an isotropic liquid. In the case of N-methylated pyridinium, sometimes a rich polymorphism and mesomorphism are observed. This observation is explained by the relatively high melting points of the protonated derivatives compared with those of the methylated derivatives. The chloride ion as a counterion could be unfavorable for the liquid crystalline formation because of its small radius, which could lead to lesser shielding of the positive charges of the pyridinium ring. The formation of different smectic phases (A, B, C, and H) depends on the nature of the polar headgroup and packing conditions in the lamellar structure. In conclusion, the number and kinds of thermal phase transitions of singlechain surfactant molecules vary from a simple phase transition, the solid crystalline to isotropic liquid, to a complex polymorphism and mesomorphism. More than one thermotropic state may exist in the same system, each being the stable phase within a particular range of temperature (and pressure). Phase transitions are usually reversible through all the intermediate forms to a structure that is thermodynamically stable at room temperature, or they are partially reversible through one or more, but not all, of these transitions, and the room temperature product is an undercooled form of a phase that is stable at some intermediate temperature [26]. The values of phase transition temperatures, the enthalpy and entropy changes of single-chain amphiphiles, increase almost linearly with the number of carbon atoms of the aliphatic chains [32,33], but not always in a straightforward manner [24,28]. It is evident that the longer the alkyl chain, the greater are the area per chain in the layers, the electrostatic energy per mole of ion pairs, and the total conformational entropic gain increases [13,24]. The aging experiments of some crystalline samples after heating demonstrate the slow reversion of metastable forms to stable forms, with both patterns present, superposed on each other [26]. For salts of longer chain fatty acids, the higher the temperature, the more symmetrical (closer to the hexagonal cell) is the shape of the unit cell, and in phases in which the spacing is strongly dependent on temperature the coefficient of linear thermal expansion is negative [22]. III. CATANIONIC SURFACTANTS Phase equilibria of systems containing oppositely charged ionic surfactants have been the subject of extensive experimental and theoretical investigations [39–61]. Competition between various molecular interactions (van der Waals, hydrophobic, electrostatic, hydration forces, etc.) may result in a variety of microstructures, mixed micelles, vesicles, and catanionic surfactant salts. Mixing aqueous solutions of anionic surfactant with an equivalent amount of cationic surfactant (alkyl chains with more than eight atoms) results in precipitation of

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a new compound, a catanionic surfactant, colloidally dispersed in solution and practically insoluble in water [41,43,60]. The term “catanionic surfactant” has been introduced in addition to the conventional classification based on the polar or ionic surfactant headgroup (cationic, anionic, nonionic, and zwitterionic). A catanionic surfactant is an amphiphilic compound that contains both cationic and anionic surfactants in an equimolar ratio with the counterions completely removed. The electrostatic interaction between oppositely charged headgroups neutralizes the surface charge through the formation of tight ionic pairs, forming compounds similar to those of double-chain surfactants. To our knowledge, there are only a few studies of solid-state transitions of symmetrical [62] and asymmetrical [63,64] catanionic surfactants. A.

Symmetrical Catanionic Surfactants

Symmetrical catanionic surfactants consist of anionic and cationic surfactants of the same chain length. Alkylammonium alkyl sulfates [such as decylammonium decyl sulfate (DeADeS), dodecylammonium dodecyl sulfate (DDADDS), and tetradecylammonium tetradecyl sulfate (TDATDS)] are prepared by mixing equimolar solutions of alkylammonium chloride and the corresponding alkyl sulfate. The reaction can be represented as (1) X-ray diffraction reveals a bilayered structure in agreement with the behavior of other amphiphilic compounds with n-alkyl chains [62]. The double headgroup layer is separated by two paraffinic layers composed of an equimolar mixture of cationic and anionic surfactants with saturated portions of chains mostly in the trans configuration with a high degree of molecular parallelism. The trans conformation of chains is indicated by the constant increment (~2.5 Å) in the long spacing of successive even members of the homologous series, which corresponds to the distance between Cn and Cn+2 atoms in the alkyl chains [22,65]. Considering the length of fully extended hydrocarbon chains and the shortest distance of an ionic headgroup from the α-carbon atom as well as the value of the basic bilayer thickness, one can conclude that hydrocarbon chains are tilted with respect to the bilayer plane. The symmetrical catanionic surfactants exhibit complex thermal behavior characterized by several successive phase transitions. Three endothermic transitions are displayed by heating: the solid crystalline–solid crystalline, the solid crystalline– liquid crystalline, and the liquid crystalline–isotropic liquid phase. On cooling, all compounds reversibly undergo the isotropic liquid–liquid crystalline transition, while other transitions exhibit peculiar properties. There is no


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FIG. 1 Thermogram of decylammonium decyl sulfate (DeADeS) obtained by differential scanning calorimetry during heating (full line) and cooling (dashed line) scans. T 1 represents polymorphic transition, T m and T i represent the temperatures of melting and isotropization, while T d and T c represent the temperatures of deisotropization and crystallization. The lettering a–f denotes the temperatures of diffraction patterns shown in Fig. 3.

corresponding exotherm on the cooling run for the solid crystalline–solid crystalline transition of DeADeS (Fig. 1) or for the liquid crystalline–solid crystalline transitions of TDATDS. All transitions on cooling are located at lower temperatures than the corresponding transitions in the heating scans, indicating a temperature hysteresis. The thermodynamic parameters change almost linearly with the total number of carbon atoms in hydrocarbon chains. The enthalpy increments for transitions are comparable with those for homologous series of n-alkanes, sodium alkyl sulfates, and long-chain alkyltrimethylammonium bromides [22,29–32,66,67], while the entropy change of melting falls within the range of those for stable bilayers of all double-chain amphiphiles, including natural lipids [19]. The phase transition temperatures [the solid crystalline–solid crystalline transition (T1); solid crystalline–liquid crystalline transition (Tm); liquid crystalline–

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FIG. 2 Plots of ( ) the solid crystalline–solid crystalline and ( ) solid crystalline– liquid crystalline transition temperatures and ( ) the temperature of isotropization as a function of the total number of C atoms, 2n, in molecules of symmetrical alkylammonium alkyl sulfate.

isotropic liquid transition or isotropization (T 1) show a linear dependence (Fig. 2) with increasing n in alkylammonium alkyl sulfates: (2) (3) (4) The nature of the transition was studied by XRD and by polarizing microscopy. Characteristic parts of XRD patterns of one of the investigated catanionic surfactants, DeADeS at 293 K (a), 323 K (b), 350 K (c), and 363 K (d), plus immediately after cooling to 293 K (e) and after aging for 4 days at 293 K (f) are shown in Fig. 3. When heated from room temperature to 323 K, DeADeS undergoes the solid crystalline–solid crystalline phase transition. Two different crystalline phases are denoted as SC1 [room temperature phase (Figs. 3a,f)] and as SC2 [high temperature phase (Fig. 3b)]. A systematic shift of the 001 diffraction lines of the crystalline phase toward smaller Bragg angles—i.e., the increase of basic lamellar thickness and changes in positions and intensities of other diffraction lines—for the SC1 and SC2 phases reveal polymorphism. The sample


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FIG. 3 Characteristic parts of X-ray diffraction patterns of decylammonium decyl sulfate (DeADeS) obtained at different temperatures during heating (a–d) and cooling (e,f) cycles. (See text.) Phase ( ) SC1; ( ) phase SC2.

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FIG. 4 Basic lamellar thickness D (in angstroms) and tilt angle of the chains to the layer plane, α (in degrees) as a function of the number of C atoms in a single alkyl chain in molecules of symmetrical alkylammonium alkyl sulfate polymorph, ( ) SC1 and ( ) SC2.

is amorphous for XRD with traces of the SC2 phase at 350 K (Fig. 3c) and completely amorphous at 363 K (Fig. 3d). On cooling to room temperature, the sample is crystalline again, as a mixture of the two phases (SC2 is the dominant phase) (Fig. 3e). After 4 days of aging, only the SC1 phase is recorded (Fig. 3f). On cooling, both the SC1 and SC2 phases exhibit sharper diffraction lines than before heating (Figs. 3a vs. 3b and 3e vs. 3f), indicating a more ordered structure. DDADDS and TDATDS show a dependence of the structure on heating similar to that of the DeADeS sample, while on cooling, different kinetics for attaining the starting state are observed [62]. The SC2–SC1 phase transition for DeADeS is kinetically hindered, whereas TDATDS readily converts back to the SC1 phase when cooled to room temperature. After cooling to room temperature DDADDS shows the formation of a phase similar to the SC2 phase (structural parameters slightly different from the initial SC2 phase). The basic lamellar thicknesses D(in angstroms) calculated from XRD using 001 diffraction lines for the SC1 and SC2 phases are shown in Fig. 4. The linear dependence of D(D1 for the SC1 phase and D2 for the SC2 phase) versus the number of C atoms in a single alkyl chain can be expressed by the equations (5)


465

and (6) If alkyl chains are in the trans form, the difference between the basic bilayer thicknesses in the SC1 and SC2 phases can be explained by the different tilt angles (α) of the chains with respect to the layer plane. The α value in the lamellae of the SC2 phase (α2)is somewhat higher than in the lamellae of the SC1 phase (α1) (Fig. 4). The linear dependence of α vs. n for the two phases is observed to follow the equations (7) and (8) Observation by polarizing microscopy shows typical textures of the smectic A phase between Tm and Ti for all samples. Clearing and transformation to the isotropic liquid are observed approximately 2–7 K above the melting points. The temperature interval within which the liquid crystalline phase exists, ∆T, is narrow, and this interval decreases linearly as the chain length of catanionics increases, according to the equation (9) A transparent liquid exists up to the temperature at which decomposition begins (~478 K). On cooling from the isotropic liquid phase, all samples display the focal conical texture of the liquid crystalline phase before crystallization. Nuclear magnetic resonance studies show [68] that the thermotropic transition from the solid to the liquid state in hydrocarbon compounds, which proceeds through intermediate states, results from increased molecular rotation and/or oscillation in the chains at elevated temperatures. The factors determining these phase changes are the state and packing of the chains governed by the balance between cohesive forces and thermal agitation [69]. The transition from the solid to the liquid state includes continuous and discontinuous modifications in packing during thermal expansion. The electrostatic forces in the ionic layer of catanionic lamellae are very strong compared to the van der Waals forces in the hydrocarbon layer, causing the segregation of ionic and hydrophobic parts. As the alkyl chains take on an ordered arrangement owing to weak intermolecular forces, molecular motions within the chains increase gradually as temperature increases until, at a characteristic temperature, a considerable increase in the molecular motion takes place, causing the formation of various polymorphs. By changing the tilt angle, the organization of the terminal CH3 groups and packing of the chains are altered [70]. It is possible to rationalize the structure of various polymorphs by taking

466


into account a change in the organization and packing of chains due to the increase in the tilt angle. As temperature approaches the melting point, a two-dimensional disordering of the ionic layers from the solid crystalline to the liquid crystalline organization takes place [13]. High values of enthalpy and entropy changes corresponding to the melting [62] imply the disordering of the hydrocarbon chains from an all-trans configuration to the liquid crystalline organization (a more disordered organization; i.e., a gauche configuration [71]). An undercooled state is observed in the cooling process; i.e., the time to recovery of the original state depends on chain length. B.

Asymmetrical Catanionic Surfactants

Asymmetrical catanionic surfactants consist of anionic and cationic surfactants with different chain lengths. Similar to Eq. (1), the formation of asymmetrical catanionic surfactants from hexadecyltrimethylammonium bromide (CTAB) and an anionic surfactants such as sodium alkyl sulfate (the numbers of carbon atoms per chain being 10, 12, and 14) can be represented as (10) Thermograms of a series of asymmetrical catanionic salts—hexadecyltrimethylammonium decyl sulfate (CTADeS), hexadecyltrimethylammonium dodecyl sulfate (CTADDS), and hexadecyltrimethylammonium tetradecyl sulfate (CTATDS)—are presented in Fig. 5. Different numbers of endothermic peaks during heating and exothermic peaks during cooling are obtained as the number of carbon atoms in the alkyl sulfates increases. A common feature of all thermograms are transitions corresponding to the solid crystalline–liquid crystalline (T m) and liquid crystalline– isotropic liquid (T I) transitions in the heating cycle and the isotropic liquid–liquid crystalline (Td) and liquid crystalline–solid crystalline (Tc) transitions in the cooling cycle. All liquid crystalline phases show characteristic textures of smectic phases. The temperature interval between the T m and T i points increases with increasing number of carbon atoms in the anionic surfactants. Transparent liquid phases exist up to the temperatures at which decomposition has begun. TGA reveals that the decomposition of CTADeS starts at ~445 K, that of CTADDS at ~465 K, and that of CTATDS at ~463 K. Almost all endothermic peaks have corresponding exothermic peaks at lower temperatures, indicating a temperature hysteresis. The exceptions are a small endothermic peak for CTADeS and a transition below T m for CTADDS; i.e., they do not have corresponding exotherms in the cooling cycle. The phase transition parameters, transition temperatures, and changes in enthalpy derived from DSC heating scans are listed in Table 1, indicating peculiar


467

FIG. 5 Thermograms of hexadecyltrimethylammonium decyl sulfate (CTADeS), hexadecyltrimethylammonium dodecyl sulfate (CTADDS), and hexadecyltrimethylammonium tetradecyl sulfate (CTATDS) obtained by differential scanning calorimetry during heating (full line) and cooling (dashed line) scans.

468


TABLE 1 Transition Temperatures (T) and Enthalpy Changes (∆ H ) of Hexadecyltrimethylammonium Alkyl Sulfate

Heating Sample CTADeS

CTADDS

CTATDS

T (K) 348 361 396 406 426 437 342–348 409 422 443 448 338 362 399 418 447

Cooling

∆H (kJ/mol)

T (K)

∆H (kJ/mol)

22.7 0.5 2.9 1.0 11.0 1.0 16.6 12.9 3.2 6.8 1.6 2.6 21.8 8.8 11.1 1.5

312

–2.2

339

–12.1

407 417 326 389

–6.7 –1.1 –11.9 –8.6

441 444 341 349 388 407 413

–6.1 –1.4 –13.1 –1.6 –11.1 –4.0 –0.5

properties of the solid crystalline–solid crystalline transitions for each sample. Obviously, the difference in cationic and anionic surfactant hydrocarbon chain lengths differently influences the number and kinetics of the solid crystalline–solid crystalline transitions. Detailed analyses of the nature of phase transitions obtained by X-ray diffraction and polarizing microscopy are given elsewhere [63,64]. Changes in the positions and relative intensities of the hk0/hkl diffraction lines of all homologs with the change of temperature indicate rearrangements in the crystal lattice, changes in conformation, and/or reorientation of crystal grains, i.e., polymorphism. All polymorphs exhibit a bilayered structure. The changes in the basic lamellar thickness D with the number n of C atoms in sodium alkyl sulfate for different temperatures are presented in Table 2. The variation of the basic lamellar thickness of the room temperature polymorph (SC1 phase) (D 1) and of the polymorph formed after the first endothermic transition (SC2 phase) (D2) with n follows the linear equations (11)

Sample CTADeS CTADDS CTATDS

a b c

Heating cycle 293 K 35.3(2) a 293 K 38.2(2) a 293 K 39.3(2) a

323 K 35.5(2) a 333 K 38.5(3) a 348 K 40.1(3) a

373 K 38.0(3) b 363 K 40.6(3) b 373 K 42.4(3) b

Cooling cycle

408 K 42.7(3) b

373 K 38.2(2) b 358 K 40.6(3) b 403 K 42.7(3) b

323 K 37.6(2) a 38.2(2) a 373 K 42.4(3) b

293 K 35.9(2) c 293 K 350 K 40.0(3), a 42.3(3) b

293 K 39.5(4) a


TABLE 2 The Long Spacing,a D (Å), of Hexadecyltrimethylammonium Alkyl Sulfates at Selected Temperatures

The numbers in parentheses are estimated standard deviations to the least significant digit. D value for the low temperature solid crystalline phase. D value for high temperature solid crystalline phase.

469

470


and (12) The constant increment of ~0.1 nm in the long spacing of successive members of the homologous series corresponds to half the difference in chain length between Cn and Cn+2 and indicates that there is probably no trans conformation of alkyl sulfate chains in hexadecyltrimethylammonium alkyl sulfates. Additionally, X-ray diffraction patterns of hexadecyltrimethylammonium alkyl sulfates in the heating cycle display a superposition of rather sharp diffraction lines on diffuse amorphous maxima, indicating the presence of two phases. One phase is the three-dimensionally ordered crystalline phase, and the other is a disordered one, indicating some kind of a two-dimensionally ordered liquid crystalline phase. The presence of a disordered phase in addition to the ordered phase is not observed in the symmetrical catanionic surfactants [62]. Obviously, there are two parallel mechanisms during the heating cycle: the structural transition of a two-phase system (the appearance of additional periodicity) and the solid crystalline–liquid crystalline transition. The order of appearance of different structures as temperature increases is usually consistent with the gradual breakdown of the long-range molecular order upon heating. As the temperature approaches the melting point, the long-range order gradually decreases. In the cooling cycle, the fraction of the three-dimensionally ordered phase increases, while the fraction of the disordered phase decreases. The kinetics of phase transitions on cooling is different from that on heating. A number of different bilayer phases coexist. In spite of the observed advanced ordering in the crystal lattice, a disordered phase is present again at room temperature. It seems that some thermal activation processes necessary for the transition are kinetically blocked due to steric hindrance. The assumed steric hindrance may occur via molecular conformation changes of the bulky aliphatic chains, rearrangements of the methyl end groups at the lamellae/lamellae interface, and so on. The comparison of the results obtained for asymmetrical and symmetrical catanionic homologs shows that the thermal properties are closely correlated with the extent of symmetry of surfactant molecules. There are two factors contributing to the bilayer stability: the electrostatic interactions between ionic headgroups and the state of packing of the surfactant chains. Since the electrostatic interactions play a significant role in bilayers formed from symmetrical and asymmetrical catanionics, the difference between the chain lengths of the cationic and anionic parts of a catanionic molecule leads to a different packing and to more complex thermal behavior. The same chain length of both tails in a symmetrical catanionic bilayer allows denser molecular packing than in a bilayer of asymmetrical catanionic surfactant; i.e., surfactant tails are more ordered in bilayers of symmetrical surfactants. As the difference between the lengths of the tails increases, a poorer hydrophobic match in the bilayer is attained.


471

Planar bilayers may undergo strong thermally induced out-of-plane undulations controlled by the bending elasticity. The bending elasticity can be described by the bending modulus, which is, in the case of uncharged bilayers, determined by molecular packing constraints [72]. This is in accordance with the demonstration [73] that the free energy required for bending a bilayer is the sum of the bending and stretching work. The hydrophobic moiety formed by two asymmetrical chains causes successive conformational changes and the formation of several polymorphs in the solid state. The presence of a disordered phase gives some peculiar properties to the asymmetrical catanionic surfactant. IV. DOUBLE-CHAIN SURFACTANTS Synthetic double-chain surfactants have been extensively studied [35,74–89] because they can serve as model systems for the study of natural lipid bilayers, i.e., biological membranes. The hydrophilic group of these surfactants may be cationic (ammonium and sulfonium), anionic (sulfonate, phosphate, and carboxylate), nonionic (polyoxyethylene), or zwitterionic. Double-chain cationic surfactants with a dimethylammonium headgroup are the most extensively studied, but many anionic double-chain surfactants [89] and nonionic oxyethylene oligomers [35] have also been investigated as model bilayer membrane compounds. The essential structural characteristics of synthetic surfactant membranes are very similar to those of biomembranes; the bilayer is formed only when the alkyl chain length exceeds 10 carbon atoms, and its thickness is 3–5 nm depending on the hydrocarbon chain length [79]. A number of double-chain surfactants have been synthesized as analogs of natural lipid molecules, and their thermal behavior in aqueous systems has been examined. Synthetic double-chain surfactants frequently form micelles at very low concentrations, with lower aggregation numbers and a higher degree of counterion dissociation than single-chain surfactants. In general, these surfactants form a lamellar phase as a first liquid crystalline phase. The lamellar phase usually borders on an isotropic phase in the phase diagrams of systems based on such surfactants, whereas for single-chain surfactants the lamellar phase is restricted to a rather small concentration range near the surfactant–water side of the corresponding phase diagrams [90]. Dialkyldimethylammonium bromides (which may be considered as a prototype of double-chain surfactants) were prepared by Okuyama et al. [88]. They are the first single crystals of a synthetic bilayer compound that were amenable to X-ray structural analysis. The most important aspect in this structure is bending of molecules at the hydrophilic group. This bend usually occurs in such a way that the straight pairs of the chains become unequal in length, thus often causing tilting of the molecule relative to the crystal planes. The chain tilting caused by

472


the balance between the molecular cross sections of the two hydrophobic chains and the hydrophilic headgroup displays the hairpin conformational structure [13]. A comparison of the layer thickness with the chain lengths suggests that the chains are tilted with respect to the bilayer surface by 32–47° depending on the alkyl chain length [35]. X-ray data of dioctadecyldimethylammonium chloride (DODMAC) show a typical structure of dialkylammonium salts [4]. Thermal analysis of dry DODMAC crystals reveals a reversible solid crystalline–solid crystalline phase transition at ~325 K; i.e., two equilibrium polymorphic forms exist. Melting at ~420 K is irreversible and is accompanied by chemical decomposition. Dioctadecylmethylammonium chloride (DOMAC) exhibits an extraordinary crystal structure with respect to both the conformational structure of the molecules and their packing within the crystal structure [4]. Both chains are extended away from the polar hydrophilic group in the crystal, and a curved midchain monolayer structure is formed. DOMAC forms at least one crystal tetrahydrate. Dioctadecylammonium cumene sulfonate (DOACS) is crystalline at low temperatures, showing a diffraction pattern with numerous diffraction lines [4]. X-ray studies reveal two phase transitions: solid crystalline to liquid crystalline at ~346 K and liquid crystalline to isotropic at ~395 K. This compound exhibits a very interesting chain structure change within the lamellar phase when it is heated. The coefficient of expansion is greater in some directions than in others. Another interesting feature is the increase of the crystal long spacing in passing from the crystal line phase to the liquid crystalline phase, but as temperature increases the thickness of the bilayer shrinks. The appearance of the long d-spacing line of the lamellar phase in the isotropic liquid phase indicates the persistence of the lamellar structural elements within the liquid phase. The unit cell of dioctadecyldimethylammonium bromide (DODAB) is triclinic, with two molecules in the unit cell [87]. An interdigitated packing in which {001} plane polar headgroups alternate with terminal methyl groups is proposed. In pure DODAB, the polar layer melts at ~360 K, producing a narrow domain of the fluid liquid with the texture of an inverse hexagonal mesophase. The transition point at ~373 K corresponds to the isotropic phase formation. On cooling, an unusual texture appears. On a slightly cloudy, scarcely birefringent background, many strongly birefringent golden structures with the shape of twin needles are obtained. Interaction of long-chain n-alkylammonium halides with a halide of a divalent metal leads to the formation of salts of the general formula (RNH3) 2MX4 with peculiar phase changes in the solid state [65]. Bis(n-alkylammonium)bromo zincates with n = 10–16 display two reversible high entropy solid crystalline–solid crystalline phase transitions and a solid crystalline–liquid crystalline (smectic phase) transition up to at least 450 K. In general, changes in the length and structure of the long chain influence the


473

thermal behavior. Long-chain potassium dialkylphosphate salts are solid crystals at room temperature, but when heated above their melting temperature a cubic mesophase followed by a columnar mesophase of hexagonal symmetry is observed [91]. The stability range of the cubic mesophase decreases significantly when the length of the alkyl chains increases. Introduction of a double bond lowers the temperature of phase transition [35]. The replacement of hydrogen by fluorine atoms generally results in a decrease in the enthalpy changes, while the effect on the temperature of transition is rather complicated [92]. The nature of the headgroup plays a crucial role in determining the phase transition, for two main reasons. One is the electrostatic interaction among headgroups at the bilayer surface, which may differently affect the stability of the bilayer structure. The other is the influence of the headgroup on the alignment of the hydrocarbon chains. For example, protonated pyridinium salts show a simple single phase transition from the solid crystalline state to an isotropic liquid, while methylated pyridinium salts exhibit solid crystalline–solid crystalline, solid crystalline–liquid crystalline, and liquid crystalline–isotropic liquid transitions [77]. An excellent example of counterion influence is the quite different thermal behavior of double-chain 1-methyl-3,5-bis(n-hexadecyloxycarbonyl)pyridinium ion in crystals with iodide or chloride as counterion [4]. The iodide salt revealed three phase transitions: solid crystalline–solid crystalline at ~326 K, solid crystalline– liquid crystalline at ~358 K, and liquid crystalline–isotropic liquid at ~378 K. The X-ray diffraction pattern of the liquid crystalline phase could be best rationalized in terms of a smectic-H phase. The chloride anion could be unfavorable for liquid crystalline behavior because of its smaller ionic radius relative to the iodide anion. Less shielding of the positive charges of the pyridinium rings by the chloride counterion leads to increased electrostatic repulsion between headgroups. Alkali metal salts of dihexadecylphosphoric acid heated above the melting temperature display columnar mesophases with lithium and sodium as counterions, whereas potassium, rubidium, and cesium as counterions show a cubic phase between the solid crystalline phase and the columnar mesophase [93]. Thermal behavior of double-chain surfactants shows complex phase transitions from the solid state to the isotropic liquid. The correlation between thermal behavior and molecular structure of synthetic double-chain surfactants can be generalized as follows: 1. The entropy change of the phase transitions falling within the range of 60–220 J/K mol indicates that all phase transition processes are closely related (chain melting). 2. The temperature of transition and enthalpy and entropy changes mainly increase with increasing lengths of tails.

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13 Thermal Behavior of Foods and Food Constituents ALOIS RAEMY and PIERRE LAMBELET Nestlé Research Center, Nestec Ltd., Lausanne, Switzerland NISSIM GARTI Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel I.

Introduction

478

II.

What Are Foods?

478

III.

Thermal Analysis and Calorimetric Techniques of Interest

479

IV.

Thermal Behavior of Food Constituents A. Water B. Lipids C. Carbohydrates (glucides) D. Proteins E. Minor constituents

480 480 481 485 489 490

V.

Thermal Behavior of Raw and Reconstituted Foods A. Phenomena related to food composition B. Interaction between food constituents C. Biological processes

492 492 493 494

VI.

Self-Heating, Self-Ignition, and Safety Aspects A. Self-heating, self-ignition, and rise in pressure B. Simulation of process conditions

494 494 495

VII. Other Thermodynamic Parameters A. Specific heat B. Heats of combustion C. Heat conductivity and thermal diffusivity D. Heats of solution

496 496 497 497 497

477

478

Ramey et al.

VIII. Related Techniques

497

IX.

Conclusion

498

References

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I. INTRODUCTION Chocolate bars should melt in the mouth and not in the hand, and the heating of oil should not lead to a kitchen fire. Based on such common examples, we may understand the interest in studying the thermal behavior and properties of foods. In the investigation of foods by thermal analysis and calorimetric techniques, many effects can be observed in the temperature range between –50°C and 300°C. These thermal phenomena may be either endothermic processes (such as melting, denaturation, gelatinization; and evaporation) or exothermic processes (such as crystallization and oxidation). Through precise knowledge of such effects, optimal conditions for safe storage or processing of foods can be defined. The main operations concerned are summarized in the following table. Below 0°C Around 70°C Around 100° Around 140°C Above 140°C

Freezing and freeze-drying Pasteurization, solid–liquid extraction Drying, cooking Ultrahigh temperature sterilization (of milk products) Frying, roasting (of coffee and coffee surrogates)

Thus, the thermal and also, more generally, the physicochemical properties of foods are of particular interest to the food technologist. To introduce the subject, we first present some general aspects of food constitution and of the most useful calorimetric techniques in this context. Because the thermal behavior of foods depends strongly on their composition, we concentrate at first on the thermal characteristics of food constituents—of water, lipids, glucides, proteins, and minor constituents—and then consider composite and reconstituted foods. Aspects of process safety are also considered. II. WHAT ARE FOODS? Foods are materials in a raw, processed, or reconstituted form that are consumed by humans or animals for their growth, health, and satisfaction (or even pleasure). Enteral and parenteral solutions are also foods, as are fruits, fruit juices, milk, milk powders, meat, and animal (pet) food.

Foods and Food Constituents

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Chemically, foods are mainly composed of water, lipids, glucides, and proteins. In addition, they contain comparatively small proportions of some minerals and various organic substances. Minerals are often analyzed globally as ash. The organic substances can be vitamins, emulsifiers, acids, antioxidants, pigments, polyphenols, or flavors. In some cases, foods contain physiologically active substances, such as caffeine or theobromine, and even toxic substances, such as natural toxins in mushrooms or, toxins produced by microorganisms. The main constituents just referred to are responsible for the physical properties (structure, texture, and color) as well as the flavor of foods. Sometimes, specific natural or synthetic ingredients (such as salt or antioxidants) are added to improve the food properties [1–3]. III. THERMAL ANALYSIS AND CALORIMETRIC TECHNIQUES OF INTEREST Differential scanning calorimetry (DSC) is the main approach used today for studying thermal properties of foods (phase transitions, reactions, and specific heats). Older systems, such as containers fitted with sensors that follow the rising temperature of a heating bench, autoclaves with additional pressure sensors, or (high pressure) differential thermal analysis (DTA) instruments, are still useful. Modulated DSC is also applied today to food studies [4–9]. However, the trend is toward the use of microcalorimeters (in the isothermal or scanning mode) with high sensitivities, especially for a more sensitive observation of the weak thermal phenomena that occur between 0°C and 100°C [10–13]. Parameters such as the heat of solution may also be of interest, so the use of solution calorimeters or of heat flux calorimeters with stirring devices is also recommended for studying certain food systems [14]. Instruments such as power compensation DSC, heat flux DSC, or intermediate systems have proved their worth in the study of foods and food constituents. The most important criteria for selecting the appropriate instrument for a specific problem are temperature range, sample size, and the sensitivity and resolution of the instrumentation. When studying food constituents, analysis of small samples gives a better resolution of thermal effects; this can be important for studying the polymorphism of fats and is a necessity for purity determinations. In contrast, large samples represent better the bulk material for composite foods; heat flux calorimeters with large crucibles (sometimes fitted with pressure sensors or pHmeters) are therefore often preferred [14]. This criterion is particularly important in the field of process safety, especially for adiabatic calorimeters [15]. Moreover, experiments with large samples must be performed at low heating rates.

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Complementary data on food and food constituents are obtained by other thermal analysis techniques, such as thermomanometry, thermogravimetry (TG), thermomicroscopy or hot stage microscopy (HSM), differential mechanical (thermal) analysis (DMA or DMTA), titration calorimetry, and microwave dielectric measurements during temperature scan. Adiabatic bomb calorimeters or isoperibolic calorimeters are used to determine the heat of combustion of foodstuffs. Although the values may be important in the context of process safety, they are mainly used to calculate caloric values of food for human nutrition or when foods (usually oils) are used as energy sources for engines. IV. THERMAL BEHAVIOR OF FOOD CONSTITUENTS A.

Water

Water is present in most natural foods, at levels up to 90–95% w/w in some fruits (oranges) and vegetables (tomatoes). Most beverages contain high proportions of water. Water exists in foods in various forms: free water, water droplets, water adsorbed on a surface, chemically bound water, crystal water, and composition water. Often water is removed from processed foods to improve their keeping quality or to reduce their weight and volume. In most cases, however, part of this water is extremely difficult to remove, so even dehydrated foods may contain 2– 3% residual water. The physics of water, as a pure substance and as part of biological systems, has been studied by many workers [16–18]; the basic phenomena are described in a volume edited by Franks [19]. As shown in Fig. 1, water has three phase transitions in the temperature range of interest: crystallization on cooling (or ice melting on heating), vaporization (or vapor liquefaction), and sublimation. Relatively high enthalpy values accompany melting and vaporization (334 J/g at 0°C and 2250 J/g at 100°C, respectively, under atmospheric pressure). Thus, these two endothermic phenomena are easily observed when studying foods by calorimetric techniques. Sublimation (freezedrying) takes place only under high vacuum, so this phenomenon is more difficult to detect [18]. A large number of studies have dealt with the behavior of water below 0°C (e.g., supercooling of water-in-oil emulsions) and determinations of free and bound water, around 0°C [20–25]. The crystallization enthalpy of water depends on temperature (see Ref. 19), which may be important in supercooled emulsions. Moreover, the difference in the specific heats of ice [2.05 J/(g · K)] and water [4.18 J/(g · K)] may introduce some error. Around 100°C, thermal analysis measurements with open crucibles distinguish among adsorbed, absorbed, and crystal water. Thus, DSC curves, TG curves, or microwave dielectric measurements give information on water content or on the


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FIG. 1 Phase diagram of water indicating the course of two different drying processes. Tp, triple point; Cp, critical point; a, air-drying; f, freeze-drying.

state of drying of foods [26–29]. The peak due to water vaporization in calorimetric curves often masks other phenomena of interest, such as the crystallization or decomposition of carbohydrates. To observe such effects, analyses have to be performed on samples in sealed crucibles (or under pressure). In such cases, however, it is important, for reasons of safety, to remember that the water vapor pressure increases rapidly with temperature, especially above 150°C. At 300°C, the water vapor pressure already amounts to 85 bars! B. Lipids The physical properties of edible fats and oils are closely related to those of triglycerides, which constitute the major part of lipids (molar ratio higher than 90%). The occurrence of more than one crystalline form (polymorphism) is a general characteristic of lipids or triglycerides in the solid state. A fat’s ability to undergo polymorphic changes is important, mainly because of its effect on food texture and appearance. It has been proved that DSC, in combination with X-ray diffraction, is one of the most efficient techniques for the study of the phase changes of lipids, including solid–liquid (melting), liquid–solid (crystallization), and solid–solid transitions [30–36]. The temperature range between

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FIG. 2 (A) Heating curves of DL-α,β-distearin, showing the melting of the stable polymorphic form (at 70°C) during the first run (——) and the melting (at 60°C) of a less stable polymorphic form during the second (—--—) and third (---) runs (superimposed). (B) Cooling curve (— · —) of DL-α,β-distearin, showing crystallization at 55°C. Instrument: DSC 7. (Courtesy of Perkin-Elmer Corp.)

–50°C and 80°C is of special interest; melting enthalpies are between 100 and 200 J/g. In the context of quality control, such calorimetric curves can be used as fingerprints for the considered fats. As examples, Figs. 2 and 3 present the thermal polymorphism of two glycerides, distearin and tristearin, as displayed by a power compensation DSC instrument. The influence of composition, processing parameters, thermal history, and aging can be clearly described by means of DSC investigations on lipid polymorphism. Contamination (adulteration) of fats can also be detected in calorimetric curves recorded during the crystallization [37] or melting [38] of lipid mixtures. In the same way, the solid fat index (SFI) representing the ratio of solid to liquid in a partially crystallized lipid at a given temperature can be obtained from the calorimetric melting curve by sequential peak integration [31,39,40]. SFI values are currently used in the fat industry for quality control and for monitoring processes such as interesterification, fractionation, hydrogenation, and tempering.


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FIG. 3 Calorimetric curves of tristearin showing, during the first heating (solid curve), the melting of the stable polymorphic form around 75°C and, during the second heating, (—--—), the melting of two less stable forms around 55°C and 70°C, with partial crystallization around 65°C. Instrument: DSC 7. (Courtesy of PerkinElmer Corp.)

They are determined from the equation

(1)

where T 0 is the onset temperature of melting, T 1 is the end temperature of melting, and H(T) is the enthalpy at the selected temperature. Lipid oxidation is an exothermic phenomenon that can be followed, at least at elevated temperatures, by DSC or (preferably) by isothermal calorimetry [41 – 44]. Measurements can be performed under a static air atmosphere or, better, under oxygen flow or oxygen pressure. In the isothermal mode, induction times can be defined according to published procedures using other techniques (see Fig. 4). Figure 5 compares the oxidative stability at 130°C of three very different oils (safflower, blackcurrant seed, and Nujol). Induction time values can be used

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FIG. 4 Determination of induction times A and B. A is the time lag between the start of oxidation and the start (extrapolated onset) of exothermic heat flow. B is the time lag between the start of oxidation and the maximum of exothermic heat flow. (Adapted from Ref. 41.)

FIG. 5 Calorimetric curves of three oils with different stabilities, oxidized at 130°C under oxygen flow. (...) Safflower oil; (——) blackcurrant seed oil; (---) Nujol. Instrument: Setaram DSC 111, isothermal mode. (From Ref. 41.)


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to determine the oxidative stability of lipids [41,42] or the efficiency of food antioxidants [41,43]. Thermal data on most triglycerides and lipids are compiled in handbooks [45]. In addition, DSC and microcalorimetry are very often used to study transitions in biological membranes, because lipids are major constituents of living cells. C. Carbohydrates (Glucides) During heating of (crystalline) carbohydrates, one generally observes first fusion and then exothermic decomposition (pyrolysis), which often immediately follows melting [46–48]. Other effects may also be detected: vaporization of water in hydrated carbohydrates, glass transitions and crystallization of amorphous sugars. Figure 6 presents the calorimetric curves of amorphous sucrose and amorphous cellobiose (both heated in sealed crucibles) between 70°C and 270°C. The onset temperatures of the exothermic decomposition observed on heating these carbohydrates in sealed vessels varied between 100°C and 230°C [46]; the corresponding enthalpies ranged from 300 to 800 J/g. The onset temperatures of fusion were found to be between 60°C and 220°C, with enthalpies from about 40 to 330 J/g. All values given here should be considered as approximate. With open containers the temperature range of thermal effects is much higher, probably because various hot gases are released during the decomposition [47,48]. It has long been known that amorphous carbohydrates have a glass transition around 50°C [49]. Glass transitions and crystallization studies by thermal analysis techniques are very

FIG. 6 Calorimetric curves of amorphous sucrose and cellobiose (both heated in sealed crucibles); c, Crystallization; f, fusion; d, decomposition. Instrument: Setaram C80. (From Ref. 46.)

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current [50–54], and even subzero temperature glass transitions have been detected for aqueous solutions [55]. In most food powders obtained by industrial (fast) drying techniques such as freeze-drying or spray-drying, the carbohydrates (sucrose, lactose, etc.) are not crystalline but amorphous. At ambient temperature and low water activity, they are in the amorphous glassy state. If temperature and/or water activity increases, they change to an amorphous rubbery state. The temperature at which this happens is called the glass transition temperature, T g. However, this phenomenon is observed over a temperature range, and, depending on the measuring conditions (annealing, thermal history), an overshoot called relaxation is observed as shown in Fig. 7. Glass transition as well as the following crystallization phenomena depend strongly on water activity and moisture content, as shown in the calorimetric curves of Fig. 8, and on the molecular weight of the carbohydrates, as shown in the graph presented in Fig. 9. Even if the food products are not perfectly stable below the glass transition, for storage it is very important in most cases to stay below this critical tempera-

FIG. 7 DSC curves of galactose (a) at first rewarming and (b, c) after annealing at 14°C for (b) 1 h and (c) 24 h. Cooling and heating scanning rates: 10°C/min. (From Ref. 51 with permission from Technomic Publishing Company, Inc.)


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FIG. 8 Calorimetric curves of amorphous sucrose showing the variation of the glass transition and crystallization temperatures at different water activities A w. Instrument: Setaram Micro-DSC. (From Ref. 52 with permission from the editors of J Thermal Anal.)

FIG. 9 Effect of water activity on glass transition temperatures of disaccharides and maltodextrins with various molecular weights (M values in daltons). (From Ref. 54 with permission from Elsevier Science.)

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ture. Glass transition is also a basic concept for the understanding of processing, especially drying, agglomeration, and encapsulation. Glass transition is also observed for proteins in powder form. For extrusion or similar cooking and texturization processes, many workers study in particular the endothermic gelatinization of starches and other carbohydrates (e.g., carrageenans) in the presence of water as well as the retrogradation of the gelatinized products [56–67]. Starch gelatinization is defined as the collapse (disruption) of molecular order within the starch granule, as shown by irreversible changes in its properties such as granular swelling, native crystalline melting, loss of birefringence, and starch solubilization [68]. In a calorimetric curve (see Fig. 10), gelatinization is observed as a peak around 60°C (depending in particular on the salt content), together with a change in the specific heat. Enthalpies of about 10–20 J/g dry matter (DM) are measured when the moisture content is about 50%. Starch retrogradation is defined as a process that occurs when gelatinized starch molecules begin to reassociate in an ordered structure; under favorable conditions, a crystalline order appears [68]. The heat slowly released by the recrystallization of the gel can be detected by means of a microcalorimeter [69] (see Fig. 11). However, most workers follow the retrogradation indirectly by observing the melting of the microcrystals formed after a given storage period. The corresponding broad melting peak is found in the calorimetric curves between 40°C and 80°C; the measured enthalpies are generally lower than 10 J/g DM and are often called retrogradation enthalpies. Retrogradation studies are of great importance to the understanding of such phenomena as the staling of bread.

FIG. 10 Gelatinization and specific heat change of native wheat starch (water solution of 40% dry matter). Instrument: Setaram Micro-DSC. (Adapted from Ref. 69.)


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FIG. 11 Retrogradation at 4°C of gels obtained from native wheat and potato starches (water solutions of 50% DM). Instrument: Setaram Micro-DSC, isothermal mode. (Adapted from Ref. 69.)

D. Proteins The functional properties (solubility, antigenicity, viscosity, capacity to form a gel or to emulsify lipids) of foods such as dairy products are essentially determined by their proteins. Heat treatments of proteins in water induce damage (denaturation) to the molecular structure [70,71]. Calorimetric techniques allow measurement of the energy changes that accompany conformational transitions in proteins. The methods of investigation as well as many results were first presented by Privalov [72,73]. The denaturation of proteins in aqueous solutions is seen as one or two endothermic phenomena encountered in the temperature range between 40°C and 160°C. The corresponding enthalpies are very weak; values between 1 and 20 J/g DM are generally observed. Calorimetric techniques have been used extensively to determine the conditions (pH, buffer, temperature, ionic strength, salt or carbohydrate content of the solution) that best maintain the physicochemical properties of proteins or promote flavor binding or release capacity [74–77] and to study whey proteins, especially βlactoglobulin (see Fig. 12) and α-lactalbumin, as well as soy proteins [78]. Similarly, the thermal denaturation of legume proteins such as legumin and vicilin [79], of egg white [80,81], and of meat [82], fish [83], and cereal proteins [84] has been studied with the help of DSC. DSC curves demonstrate the stabilizing effect of the binding of iron (or other metal ions) on protein (Fig. 13) [85]. The thermal denaturation of enzymes also gives information on their inactivation [86]. The loss of gel structure can be observed for meat gelatin by DSC around 30°C [87]. Although calorimetry of proteins is rarely performed on dry samples, this kind of analysis at least allows investigation of the glass transition and protein oxidation.

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FIG. 12 Calorimetric curves showing the heat denaturation of β-lactoglobulin in solution as a function of temperature at pH 3.5 (dashed line) and in the pH range 6.0 < pH < 8.0. Instrument: DuPont thermal analyzer 990. (From Ref. 75.)

E. Minor Constituents Physiologically active substances that are present in minor quantities in foodstuffs can be studied in their pure forms or in aqueous solutions. Crystalline caffeine has been studied extensively in the anhydrous or monohydrate form and in solution, particularly by calorimetric techniques [88–90]. Caffeine shows a solid–solid transformation around 140°C and melts at around 235°C, as shown in the calorimetric curve of Fig. 14.


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FIG. 13 Calorimetric curves showing the heat denaturation of ovotransferrin (conalbumin) in solution. (a) Apo-ovotransferrin; (b, c) ovotransferrin 39% saturated with iron; (d) ovotransferrin fully saturated with iron. The bar represents a heat flow of 500 µJ/s. Instrument: DuPont thermal analyzer 990. (From Ref. 85.)

FIG. 14 Calorimetric curve of pure β-caffeine. Instrument: DuPont thermal analyzer 990. (From Ref. 88.)

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V.

THERMAL BEHAVIOR OF RAW AND RECONSTITUTED FOODS

A.

Phenomena Related to Food Composition

Depending on the food composition, most of the main phenomena mentioned for the major constituents (carbohydrate melting excepted) are observed also with raw and reconstituted foods; however, the corresponding peaks in the calorimetric curves are broader. The effects due to minor constituents can be detected only in special cases. Around 0°C, the melting curves of water in high moisture foods such as ice creams introduce the differentiation between “bound” and “free” water. The amount of free water relative to the total amount of water (R) is given by the equation where S is the percentage of solute (or of dry matter), 1 – S is the percentage of water, ∆Hm is the measured fusion enthalpy (J/g) and ∆Hw is the fusion enthalpy of pure water (J/g). (2) Figure 15 presents calorimetric curves with ice melting peaks for various foods [91]. A detailed description of the low temperature behavior of many foods has been given by Riedel [92,93]. The enthalpy differences, with the zero enthalpy value at –60°C, have been compiled in tables or nomographs, which are very useful for chemical engineering calculations. Calorimetric cooling curves generally show freezing and supercooling very clearly; the temperature range of freezing is of particular interest in relation to freezing or cold storage. Around ambient temperature, the melting of fat can be observed in reconstituted foods and even in some raw foods such as cocoa beans. In the context of lipid research, modern instrumentation (DSC, microcalorimetry) allows the study of phase transitions, even in complex biological membranes [94–96]. Around 70°C, the gelatinization of finely divided flours (starches) mixed with water can be observed. Retrogradation, for instance bread staling, can also be studied [97]. Crystallization of amorphous sugars (e.g., crystallization of amorphous lactose in milk powders [98]) can be detected in reconstituted foods. However, protein denaturation is no longer detected clearly when studying liquid whole milk products containing lipids, lactose, calcium, etc. Around and above 100°C, the boiling of water is generally prevented by using sealed containers; this allows the detection of other phenomena such as carbohydrate decomposition. This is observed in the calorimetric curves of reconstituted foods such as milk powders and in the curves of raw foods such as coffee beans, chicory roots, and cereal grains [98–101].


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FIG. 15 Low-temperature calorimetric curves of carrots, reindeer meat, and white bread, showing ice melting. Instrument: Mettler DSC 30. (From Ref. 91.)

Lipid oxidation can be observed if the lipids are on the food surface and thus in contact with oxygen. This condition can be fulfilled for some processed foods and some reconstituted foods. The oxidation of minor constituents such as polyphenols is a possible cause of self-heating in hay, to temperatures above those normally reached during fermentation. To measure the heat released by these phenomena, specific calorimetric experiments have to be performed. B. Interaction Between Food Constituents In addition to the caloric phenomena due to each constituent alone, there are also interactions between food constituents. The corresponding thermal effects can be detected in model binary mixtures and sometimes, with more difficulty, in raw or reconstituted foods.

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Maillard reactions, the browning reactions between proteins and reducing sugars, are observed in the calorimetric curves of lactose–casein mixtures or in those of milk powders [98]. Maillard reactions are exothermic, take place above ambient temperature, and depend on the moisture content of the product. The corresponding enthalpies are not so important (less than 100 J/g DM). Phase transitions of starch–lipid complexes are also seen in calorimetric curves. These weak endothermic phenomena occur around 100°C and have enthalpies of less than 30 J/g DM [57]. Sometimes interactions between water and the foods or food constituents (dissolution, absorption, or desorption) in addition to interactions of cations and sugars in water are studied [102–104]. C. Biological Processes Many foods are obtained by fermentation. In this context, measuring the heat released during the fermentation process gives information relevant for dimensioning fermentors or for safety [105,106]. On the other hand, microorganisms can lead to spoilage of wet foods during storage. Calorimetric techniques are therefore also used to obtain a basic knowledge of the metabolic activities of bacteria, yeasts, and fungi [107]. A calorimetric method has been proposed to determine bacterial thermal death times [108].

VI. SELF-HEATING, SELF-IGNITION, AND SAFETY ASPECTS A. Self-Heating, Self-Ignition, and Rise in Pressure Fires and dust explosions are known hazards in many industries, including the food industry. Self-heating and self-ignition studies are thus often of interest to develop better defined safety conditions for high temperature processing operations when sufficient oxygen is available. Studies of spontaneous combustion of powders very often consider sample deposition on a heating plate or in a furnace heated to a known temperature. The data obtained by these tests are generally compiled as minimum ignition temperatures for dust layers [109]. Similar measurements of self-ignition temperatures can be performed by using differential thermal analysis (DTA) techniques with air or oxygen atmosphere. The sample can be heated under oxygen flow or oxygen pressure. The well-defined measuring conditions are an advantage, particularly the precise heating rates possible with thermal analysis instruments and the stepwise temperature increase of adiabatic calorimeters [110,111]. Figure 16 presents the DTA curves of cellulose heated and burned under 25 bars of oxygen.


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FIG. 16 DTA curves of cellulose heated and burned under 25 bars of oxygen. Highpressure DTA 404 H instrument from Netzsch. (From Ref. 112.)

Self-heating can lead to self-ignition of the food if sufficient oxygen is available. The main phenomena involved in thermal runaway of food products are fermentation, carbohydrate decomposition, lipid oxidation, and probably polyphenol and protein oxidation. However, other weaker exothermic effects such as Maillard reactions could participate in the initial temperature increase. If oxygen is in low concentrations, it is often the elevated pressure resulting from the rise in temperature in a closed medium that presents a risk (of bursting the autoclave, for example). Further dangers can come from degassing associated with fermentation or decomposition reactions; the gas emitted could lead to a rise in pressure (or be inflammable). B. Simulation of Process Conditions Sometimes thermal analysis techniques must be applied unconventionally if we are to be able to carry out the measurements under conditions close to those of the process being studied. Thus, for example, the calorimetric study of a sample in a sealed cell simulates what happens in a homogeneously heated autoclave. DTA or DSC measurements can also be carried out under a constant pressure of an inert gas or even under supercritical CO2 [112]. Figure 17 presents a scheme for a DTA experiment under supercritical CO2.

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FIG. 17 Scheme of a DTA experiment under supercritical CO 2 . High-pressure DTA 404 H instrument from Netzsch. (From Ref. 112.)

VII. OTHER THERMODYNAMIC PARAMETERS A.

Specific Heat

It is evident that calorimetric techniques are often used to determine the specific heats of foods. The methods, and a synthesis of the results, are presented in the literature [113]. The use of a standard such as synthetic sapphire simplifies the determination of specific heats. By measuring the standard, an empty cell, and the substance, the specific heat value C2 of the sample can be obtained directly by comparison. For a given temperature, (3)


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where m1 is the mass of the standard substance, m2 is the sample mass, C1 is the specific heat of the standard substance, and Q0, Q 1, and Q2 are the required heat quantities for the empty cell, the standard substance, and the sample, respectively. The values obtained vary between 0.9 J/(g · K) for very dry food products to 4.18 J/(g · K) for water. It is therefore evident that the moisture content of a food has a strong influence on its specific heat value. B. Heats of Combustion During the combustion of a food product, a large amount of energy is liberated. Values determined with calorimetric bombs or isoperibolic calorimeters correspond to about 39 kJ/g for fat, 23 kJ/g for protein, and 17 kJ/g for carbohydrate. C. Heat Conductivity and Thermal Diffusivity Other parameters such as heat conductivity or thermal diffusivity can be of interest to the food technologist and can, in some cases, be determined by calorimetry, by conducting special experiments. D. Heats of Solution The dissolution of ingredients, minerals, food constituents, or even foods in water or in other solvents can be observed by calorimetry. The data are determined in the isothermal mode. VIII. RELATED TECHNIQUES Some related thermal analysis techniques give mechanical and rheological rather than thermal information. These techniques include thermodilatometry (which is no longer of great interest for food studies), dynamic mechanical analysis (DMA), and dynamic mechanical thermal analysis (DMTA) [114]. Other techniques, such as X-ray diffraction, near-infrared (NIR) reflectance, low and high resolution nuclear magnetic resonance (NMR), microscopy, and light scattering, give information that characterizes a food before or after a thermal treatment. Low resolution NMR, for instance, is well known for rapidly giving SFI values of fats that correspond to those obtained by DSC [40]. X-ray diffraction can also be adapted, by temperature control of the sample, to follow the lipid phase transitions by recording the diffraction patterns versus temperature [115,116]. If the (lipid) sample is placed in a temperature-controlled cell, even microscopic techniques can be used to follow crystal growth or melting [117]. It is also worth noting that for caffeine solutions a thermodynamic parameter such as the enthalpy of dimerization of caffeine in water can be determined comparatively by dissolution calorimetry and by high resolution NMR [118,119].

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Thermal analysis techniques can also be coupled with the use of other instruments such as mass spectrometers or gas chromatographs to analyze the gases evolved during decomposition. Finally, mathematical models help in applying thermodynamic data to engineering problems. IX.

CONCLUSION

Other reviews of this type exist, and books have been published on the thermophysical properties of foods [120–126]. It should become clear from this review that calorimetry, (high pressure) DTA, and DSC give relevant, reproducible data that are of great importance in many fields of food technology, because this information characterizes the food globally. From the basics of food technology it is easy to understand that calorimetric techniques help in quality control, improvement of food characteristics, development of new operations, and process safety [127–134]. Many thermal effects that have been neglected until now, mainly because of experimental difficulties, remain to be studied. New technologies such as high hydrostatic pressure have recently promoted new DSC studies of proteins, lipids, and starches. Finally, food is sometimes used as a symbol, like the cheese in a fable of La Fontaine, to express things that are true in other fields. It is also true that many other fields, such as pharmaceuticals analysis, polymer physics or chemistry, materials and safety sciences, and semiconductor physics, have helped us to understand the thermal and more generally the physicochemical behavior of foods [135–140]. ACKNOWLEDGMENT We thank Dr. Ian Horman for reviewing the manuscript. This chapter is based on an earlier version published by A. Raemy and P. Lambelet [Thermal behaviour of foods. Thermochimica Acta 193: 417–439 (1991)] with permission from Elsevier Science. REFERENCES 1. 2. 3.

H Charley, C Weaver. Foods: A Scientific Approach, Merrill, Columbus, OH, 1998. VA Vaclavik, EW Christian. Essentials of Food Science, Chapman & Hall, New York, 1998. PM Gaman, KB Sherrington. The Science of Food, 4th ed., Butterworth/ Heinemann, Oxford, UK, 1996.

Foods and Food Constituents 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

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Index

Absorption, 494 Acridine, 139 Activation energy, 417 Active carbon, 169 Adhesion, 358 Adhesive interactions, 397 Adiabatic bomb calorimeters, 480 Adsorbate-adsorbent interactions, 163 Adsorbent, 365, 370, 375 Adsorption, 337, 398 capacity, 363, 365, 366, 375, 384 excess, 367–374, 384, 393 excess isotherms, 365, 377, 381 forces, 365 isotherms, 336, 349, 401, 433 layer, 363, 365–367, 372, 398 measurements, 401 of aerosil dispersions, 398 of binary liquid mixtures, 362 of surfactant, 335, 336 phenomena on fine powders, 343 volume, 365 Agglomeration, 488 Aggregate formation, 354 Aggregation, 155, 300 number, 2, 298, 305, 320 Aging, 415, 418, 434

α-lactalbumin, 489 Alcohol interactions, 94 Alkanephosphonic acid, 168 Alkyl chains, 392 Alkyl glucosides, 320, 321 Alkyl polyoxyethylenes, 353 Alkylammonium chain lengths, 385 Alkylbenzene polyoxyethylenes, 353 Alkylbenzyldimethylammonium bromides, 353 Alkyl-N-acetylamino saccharides, 216 Alumina oxide, 169 Alkylpyridinium chlorides, 353 Alkylsulfinylalkanols, 353 Alkyltrimethylammonium bromide, 138, 316 Alkyltrimethylammonium halides, 353 Amino acid, 440 Amorphous, 163 silica gel, 377 Antigenicity, 489 Antioxidants, 479 AOT, 3, 5, 8, 65, 91, 111, 141, 160, 161, 163, 166, 353, 432, 433, 438–440, 442, 444 Apolar solvents, 2, 3 Apo-ovotransferrin, 491

508 Aspartame, 438, 441–444 Asymmetrical catanionic surfactants, 466 Atomic force microscopy, 336 Attractive interactions, 305 Azobenzene, 457 Azoxybenzene, 457 Batch sorption microcalorimetry, 343 β-caffeine, 491 Bentonite, 353 Benzyldimethylhexadecylammonium chloride, 3 Bicontinuous structure, 6, 7 Bilayer, 284, 312, 321–324, 327, 330, 394, 452, 453, 460, 471 orientation of vermiculite, 394 stability, 470 structure, 453, 468 surface, 261 thickness, 465 Binary liquid mixtures, 359, 397 mixtures, 364 Bingham equation, 399 Biocatalysis, 12 Biochemical reactions, 17 Biological, 444 cells, 444 gels, 161 membranes, 8, 159, 321, 471, 485 mineralization, 444 process, 159 Biomembrane, 12, 256, 471 Biomineralization, 421, 429 Biphase transition, 136 Biphenyl, 457 Birefringence, 452 β-lactoglobulin, 489, 490 Block coploymer, 154, 156, 157 Bound crystal water, 443 water, 60, 93, 163, 249, 252,420, 480 Bovine corneas, 161 serum albumin, 169 Bridging orientation of vermiculite, 394 Bulk water, 161, 1661, 72, 270 Butanol, 79, 80, 96, 392–395, 397

Index Caffeine, 490 Calcium carbonates, 438 fluoride, 438 Calorimetric thermograms, 140 Calorimetry, 8, 86, 121, 131, 196, 201, 336–338, 497 Calorimetry of proteins, 489 Capacity to form a gel, 489 Carbohydrate decomposition, 495 Carrageenan, 488 Carrots, 493 Cascade nucleation, 26, 47 Cataionic surfactants, 459 Cationic surfactants, 136 Cellobiose, 485 Cellulose, 494, 495 Cereal proteins denaturation, 489 Cetyltrimethylammonium methacrylate (CTAM), 138 Chain ramification, 133 Characterization of inorganic compounds, 414 of organic compounds, 414 of the solid phase, 420 Chemical process, 159 Chocolate bars, 478 Cholesterol, 10, 137, 146, 325 Cholesteric liquid crystalline state, 455 Chromium nitrate, 103 Classification of calorimeters, 336 Classification of enthalpy isotherms, 375 Clausius-Clapeyron equation, 350 Clay minerals, 380 nonswelling mineral, 380 Cluster formation, 416 Clusters, 160 Coagel, 139 Coalescence, 184 Cocoa beans, 492 Coffee, 478 Coffee surrogates, 478 Colligative effects, 166 Colloidal dispersions, 409 particles, 377 Color, 479

Index Compact crystals, 415, 425 Complex, 214 liquid, 203 Composition of mixed liposomes, 152 Conalbumin, 491 Conductance, 6 Conductivity, 452 Confined regions, 159 Conformational rearrangements, 146 Control of crystal morphology, 428 crystallization, 429 by additives, 426 polymorphism, 438, 440 Cooking, 488 Copolymer, 154 Cosmetics, 24 Cosurfactant, 107, 223, 227 Coulomb attraction, 350 Critical micellar concentration, 430, 433 Critical supersaturation, 417, 434 Cross-linker, 104 Cryo-TEM, 94 Cryothermal electron microscopy, 94 Crystal growth, 415, 417, 419, 420, 422, 434 structure, 434, 454 water, 480 -crystal transition, 139 Crystalline dispersions, 413, 415, 418 hydrates, 142, 418 phase, 462 Crystallization, 134, 193, 195, 418, 423, 429–431, 434, 435, 437, 439, 442, 443, 481, 482, 483, 485, 487, 488, 492 of water, 161 enthalpy, 165, 480 in confined spaces, 434 in microemulsions, 437 of amorphous lactose, 492 of amorphous sugars, 485 of solutes, 439 of triglycerides, 435 phenomena, 486

509 [Crystallization] process, 445 rate, 134, 429 Crystalluria, 430 Crystal-mesophase, 140 D 2O, 65, 234, 242, 442 DDACl, 431, 432 DDADDS, 464 DeADeS, 464 Decaglycerol dioleate, 3 Decane, 235, 242 Decanephosphonic acid, 134, 136 Decomposition, 142, 485 reaction, 495 Decylammonium decyl sulfate, 460, 462 Decylmethylsulfoxide, 353 Degree of super saturation, 420 Degree of supercooling, 435 Dehydrated foods, 480 Dehydration, 322, 417, 420, 421, 424, 443, 444 of alcohols, 322 of Na + ions, 422 Demicellization, 296, 303–307, 309, 316, 317, 319 Denaturation, 478, 489, 490 Dendrites, 425 Dendritic crystals, 415, 417, 424 Depletion of solution concentration, 420 Deposition of solute ions, 422 Desorption, 494 Detergent, 312–315, 324, 326, 329, 330, 332 Diacylphosphatidylethanolamine, 256 Diacylphosphatidylglycerol, 256 Diacylphosphatidylcholine, 256 Didodecyldimethylammonium bromide, 3, 91, 98, 135, 136, 161 Dielectric spectroscopy, 215 Different modes of crystallization, 424 Differential interferometry, 342 molar enthalpies, 352 refractometer, 347 refractometry, 342

510 Dihexadecylphosphoric acid, 473 Diketopiperazine, 443 Dilatometry, 435 Dilinoleylphosphatidylethanolamine, 324 Dimerization of caffeine, 497 Dimethylaminoethanol, 89 Dimethyldecylphosphine oxide, 127–129 Dimethyldihexadecylammonium, 386 Dimyristoylphosphtidylcholine, 143, 151, 257 Dimyristoylphosphtidylethanolamine, 256 Dioctadecyldimethylammonium, 389, 390 Dioctadecyldimethylammonium bromide, 91, 98, 161, 472 Dioctadecyldimethylammonium chloride, 472 Dioctadecylmethylammonium chloride, 472 Dioleylphosphatidylcholine, 324 Dioleylphosphatidylglycerol, 324 Dipalmitoylphosphatidyl choline Dipalmitoylphosphatidylcholine, 132, 256 Dipalmitoylphosphatidylethaolamine, 256 Dipalmitoylphosphatidylglycerol, 256 Dipalmitoylphosphatidylcholine, 324 Diphenylamine, 139 Diphenylazomethine, 457 Dipole-dipole number, 2 Disodium n-decanephosphonate, 98, 103, 136 Dispersed solid particles, 362 Dissacharides, 487 Dissolution, 127, 494 calorimetry, 497 Distearin, 482 DMA, 497 DMPC, 257, 321, 322, 325 DMPE, 267, 268–271, 274–276, 281– 286, 288, 289, 291, 292 Dodecane, 61, 66, 96, 217, 227, 233, 236 Dodecanol, 78 Dodecylammonium dodecylsulfate, 460 Dodecylammonium propionate, 2 Dodecylammonium vermiculite, 392–397

Index Dodecyldiammonium vermiculite, 393, 395, 396 Dodecylpyridinium bromide, 139 Dodecylpyridinium iodide, 3 Double-chain surfactants, 471 DPPC, 258–267, 271, 275–281, 288, 289, 292, 324, 330 DPPE, 257 DPPG, 270, 272, 273, 291, 292 Droplet-droplet distance, 48 Drying process, 481, 488 Dynamic mechanical analysis, 497 Effect of hydrophobization, 375 Egg white denaturation, 489 Electrical conductivity, 70, 110, 111, 215, 241 double layer, 418 Electrolyte, 8, 419 Electron spin resonance, 62 Electrostatic interactions, 4, 470 Ellipsometry, 336 Emulsification boundary, 51 Emulsified microdroplets, 163 Emulsion, 157, 183, 194, 201, 415, 434–437, 443, 480 crystallization, 439 polymerization, 24 Encapsulation, 488 Endothermic transition, 156, 468 Energy barrier, 43, 45 of formation, 185 Enthalpic interaction, 343 Enthalpies of solidification, 192 Enthalpy, 154, 156, 162, 224, 252–254, 264, 228, 229, 231, 304, 325, 354, 385, 488, 268, 270, 274, 275, 296, 300, 314, 322, 324, 327, 328, 331, 336, 342, 345, 347, 359, 363, 364, 375, 376, 389, 414, 473 changes, 468 of freezing, 435 functions, 377 isotherms, 367, 372, 373, 376, 384 isotherms of diplacement, 350, 351

Index [Enthalpy] of crystallization, 200 of demicellization, 320 of displacement, 339, 340, 342, 349, 360–362, 368–373, 392 of immersion, 342 isotherms, 376 of melting, 217 of micelle formation, 303, 332 of micellization, 296, 299, 316 of octadecane, 136 of solution, 8 of water, 161, 162 of wetting, 379, 389 Entropy, 163, 165, 223, 239, 300, 392, 397, 414, 473 change, 154 Enzymatic activity, 438 ESR, 62 Ethanol, 96 Ethoxylated 20-sorbitan monolaurate, 436 alcohols, 76, 93 siloxanes, 77, 88 Eutectic composition, 139 melting, 139 point, 131 Evaporation, 128 Everett-Schay function, 363 Exothermic decomposition, 485 process, 478 Experimental observation, 45 Extraction processes, 12 Extreme viscosity, 160 Fermentation, 494, 495 Ferritin, 444 First hydration layer of bromide ion, 161 Fish denaturation, 489 Fish cut, 27 Flavor, 479 of food, 479 Flocculation, 415, 417, 418, 420, 434, 440

511 Flow sorption microcalorimetry, 346, 349, 393 Food antioxidants, 483 composition, 492 constituents, 477, 480, 497 industry, 494 properties, 479 Force balance technique, 336 Formation, 413, 419 and transformation of crystalline dispersions, 413, 415 and transformation of precursor phases, 420 of CTAM, 138 of diketopiperazine, 443 Fourier transform infrared spectroscopy, 414, 134, 167, 168 Fractionation, 482 Free energy, 32, 300, 416, 418, 419, 471 Free enthalpy of adsorption, 382, 395 of wetting, 363 Free water, 61, 87, 161, 162, 167, 480 Freeze-drying, 478, 480, 486 Freezing, 159, 478 Frying, 478 Functional properties, 489 Fusion, 128 temperature, 167 Galactose, 486 Gel, 148, 275, 281, 287, 288, 290, 488, 489 filtration, 86 mesophase, 145 transition, 148 phase, 137, 139, 262–264, 267, 268, 270–274, 277–280, 282, 283, 285–287, 290–292, 330 phase of lipid-water systems, 261 structure, 489 systems, 422 Gelatinization, 478, 488, 492 Gel-like structures, 420 Gel-liquid crystal transition, 132, 135

512 Gel-liquid crystalline phase transition, 137, 142, 147, 256 Gel-micellar solution transition, 139 Geophysical process, 159 Gibbs energy, 222, 239 equation, 403, 404 phase, 27, 42 Gibbs-Thompson relation, 416 Glass transition, 239, 240, 485–489 Glass-liquid transition, 240 Globular aggregates, 3 Glucitol, 317 Glucose, 317 Glycerides, 482 Glycerol esters, 87 Gradual decomposition, 138 Guar, 103 Hamaker constants, 398, 399, 401 HDP-illite, 382, 383 HDP-kaolinite, 384 HDP-montmorillonite, 386, 389 Headgroup area, 4 effect, 336 -headgroup interactions, 321 interactions, 474 network, 141 Heat capacity, 121, 127, 128, 129, 131, 163, 187, 207, 209, 210, 326, 336 conductivity, 497 denaturation, 491 evolution, 295 of bilayer-micelle phase transformation in mixtures of phospholipids and detergents, 312 evolution of micellization, 300 evolution of the self-assembly, 305 extraction, 396 flux, 338, 339 of combustion, 497 of demicellization, 305, 307 of evaporation, 302 of fusion, 162 of immersion, 359, 377, 401, 404, 407 of micelle formation, 154, 320 of micellization, 316, 328

Index [Heat capacity] of mixing, 162 of solution, 497 of transition, 316 of a triblock copolymer, 156 of wetting, 359, 377, 378, 386, 388 partitioning of amphipiles, 321 Heptane, 379, 398–401, 403–405, 407, 408 Heterogeneous nucleation, 418, 435 Hexadecane, 66, 79, 138, 158, 200, 201, 218, 221, 223, 224, 228, 229, 231, 232, 234, 235, 238, 436, 437 Hexadecylpyridinium, 388, 390, 386, 389 illites, 381 vermiculite, 392 cation, 387 Hexadecyltrimethylammonium alkyl sulfate, 468, 469 Hexadecyltrimethylammonium bromide, 466 Hexadecyltrimethylammonium decyl sulfate, 466, 467 Hexadecyltrimethylammonium dodecyl sulfate, 466, 467 Hexadecyltrimethylammonium tetradecyl sulfate, 466, 467 Hexagonal, 107 lattice, 453 mesophase, 136, 161, 472 symmetry, 473 Hexanol, 61, 66, 82, 96, 222, 224 High resolution NMR, 497 HLB number, 336 Homogeneous nucleation, 417, 418, 420, 423, 425, 435 phospholipid, 144 HPLC, 349 Hydrated decanephosphonic acid, 140 gel, 291 ion, 160 Hydration, 4, 251, 424 bonds, 13 layer, 171

Index [Hydration] number, 160 of DPPG bilayers, 271 of the gel phase, 274 of the nonionic surfactants, 172 of the solid phase, 350 of the surfactant molecule, 168, 350 shell, 163 water, 163, 443, 160 Hydrocarbon tail, 135 Hydrodynamic methods, 86 techniques, 86 Hydrogel, 103 membranes, 132 Hydrogen bonding, 153, 160, 257, 261, 350, 474 bonds, 134, 141, 142, 171, 257, 266, 300, 301, 303 Hydrogenation, 482 Hydrophilic enzymes, 438 headgroups, 3, 160 macromolecules, 8 Hydrophilicity of surfactant, 318 Hydrophobized motmorillonite, 387 Hydrosols, 378 Hydroxyapatite, 420, 421 Ice formation, 160 Ideal solution behavior, 163 Ill-defined in natural phospholipids, 132 Illite, 385 Immersion, 398 microcalorimetry, 341, 343, 359 Immersional wetting, 364 enthalpies, 385, 386 enthalpy isotherms, 376, 383 on nonswelling clay, 380 Impurity, 426, 435, 436, 439 Inclusion of cholesterol, 137, 324 Incorporation of hydrocortisone-21palmitate, 150 Indole, 139

513 Induced crystallization, 434 Industrial process, 159 Infrared spectroscopy, 62, 419, 456 Inhibition of dissolution, 434 Interaction with polyelectrolyte, 153 Interdigitated palisades, 137 Interesterification, 482 Interface-induced nucleation, 435 Interfacial area, 55 energy, 416, 425 energy of the germ, 185 layer, 365, 390–392 properties, 183 water, 165, 166, 169, 172 Interlamellar sorption, 386 space, 391 water, 270, 273, 280, 283, 285, 289, 292, 248, 253, 254, 257, 260, 261, 263, 264, 269 Interlayer composition, 392 Intermicellar interactions, 5, 7, 12 Interparticle attraction, 404 interactions, 358, 405, 407, 409 Interphasal water, 61, 80, 226, 228 Inverse microemulsions, 162 Ionic strength, 419, 489 surfactants, 4 Irreversible process, 240 Isooctane, 73, 87, 111, 223, 237, 242, 437, 444 Isoperiblolic calorimeters, 480, 497 Isothermal, 121 calorimetry, 483 titration calorimetry, 296, 313 Isotropic, 129 liquid, 127, 129, 452, 454, 473 liquid transition, 136, 461 ITC, 296, 297, 300, 305, 308, 310, 311, 332 Kalonite, 353, 385 Kidney stones, 423, 430

514 Kinetic of crystallization, 435 of diffusion, 201 of reactions, 445 of ripening, 197 of solution mediated phase transformation, 432 parameters, 456 transformation, 432 Kirchhoff ’s law, 135, 136 K-oleate, 222, 224 Krafft boundary, 123 eutectic point, 139 temperature, 139 L 2 transition, 40 Lactitol, 317 Lactose, 317, 486, 492 Lactose-casein mixtures, 494 Lamellar, 107 crystal, 455 interface, 470 liquid crystal, 455 mesophase, 129 morphology, 37 phase, 29, 35, 111, 471 structure, 456 thickness, 462, 464, 468 Laminar mesophase, 129, 136 Large unilamellar vesicles, 331 Laser Raman spectroscopic range, 137 Latent heat, 39, 42 Lecithin, 3, 5, 10 Legume protein denaturation, 489 Legumin, 489 Level of drug incorporation, 151 Light scattering, 497 Lipid -lipid interactions, 322 oxidation, 493, 495 transitions, 290 Liposomes, 143, 148, 150 Liquid crystal, 255, 281, 288, 290, 292, 452, 455 transitions, 140, 460, 470

Index Liquid crystalline behavior, 456 formation, 459 organization, 454, 466 phases, 107, 134, 137, 159, 167, 277, 287, 457, 458, 465, 470, 471 state, 455 Liquid -liquid separation system, 184 -solid transitions, 184 sorption, 357 sorption equilibrium, 390 Lithium ions, 160 Living cells, 485 Lowering of the melting point, 166 Lubricants, 24 Lyomesophases, 127 Lyospheres, 362 Lyotropic liquid crystals, 167 mesophases, 158, 232, 452 Maillard reactions, 494, 495 Maltodextrines, 487 Mass balance of surfactant, 156 Mass fraction of water, 158 Measurements of wetting, 408 Meat denaturation, 489 Mechanism of adsorption, 335 of crystallization, 444 of nucleation, 420 Melting enthalpy, 163, 250, 251 enthalpy of pure water, 162 of blends, 136 point, 161, 162, 163 Mesomorphism, 457, 458 Mesophase, 129, 140 Mesophase-isotropic liquid transition, 141 Meta-chloronitrobenzene, 436 Metastable ice, 163 Methyldodecanoic acid, 149 Methyl-3,5-bis(n-hexadecyloxcarbonyl) pyridinium ion, 473 Micellar catalysis, 163

Index Micellar solutions, 135, 136 Micellar swelling, 4 Micelle formation, 321 Micelles, 214, 300, 305, 312, 314, 315, 325, 326, 330, 332, 345 Micellization, 155, 300, 303, 316–320, 332 of block copolymer, 153 phenomena, 155 process, 155 Microcalorimetric measurements, 54, 342 Microcalorimetry, 54, 340, 386, 485, 492 Microemulsions, 5, 27, 158, 159, 214, 217–219, 220, 221, 223, 227, 233–237, 239, 240–243, 415, 434, 437–440, 442–444 as microreactor, 440 Microstructure, 121, 459 Microstructure surface, 132 Microstructure surface, 163 Microstructured fluids, 159 Microwave dielectric measurements, 480 Milk powders, 494 Milk products, 478 Mimetic systems, 12 Mineralization, 444 Mineralization of bone, 421 teeth, 421 Mixed bilayers, 331 Mixed emulsions, 183 Mixed micelles, 314, 316, 325, 326, 328, 459 Mixed vesicles, 148 Mixing-dimixing phenomena, 128 Mixtures of small copolymers, 155 Modified silicate surfaces, 392 Molar adsorption enthalpies, 383 Molar enthalpy, 314, 349, 350 Molar heat capacity, 156 Molar mass distribution, 155 Molecular diffusion, 47 Molecular motion, 239 Molecular structure, 438, 489 Monodisperse droplets, 44

515 Monolayer adsorption, 433 orientation of vermiculite, 394 structures, 453 Monosodium n-decanephosphonate, 98, 103, 136 Montmorillonite, 384, 386, 388 Mucopolysaccharides, 80 Multilamellar aqueous dispersions of phospholipid, 143 dispersions, 151, 248 structures, 151 vesicles, 292 Multiple emulsions, 183, 197 N,N-Dimethyldecylamine N-oxide, 352, 353 Na-kaolinite, 384 n-alkanophosphonic acid, 134, 136, 161 Na-montmorillonite, 384 Nanocontainers, 1 Nanoparticles 7, 12, 440 Nanoreactors 1, 17 Nanosized particles, 438 Nanosolvents, 1 Naphthylamine, 139 Natural toxins in mushrooms, 479 Near infrared spectroscopy, 456, 497 Nematic liquid crystalline state, 455 Neutron reflection, 336 Neutron scattering, 171 NMR, 62, 86, 90, 111, 172, 234, 248, 435, 442, 443, 458, 497 N-octylribonamide, 88 Nonaqueous dispersions, 357, 401 Nonfreezable interlamellar, 248 Nonfreezable water, 60, 86, 89 Nonfreezing water, 160 N-propionyl amine, 318 Nuclear magnetic resonance, 62 Nucleation, 26, 47, 186, 276, 415, 416, 422, 434–436 of molecular crystals, 434 of zeolites, 422 process, 43 Number of oscillations, 53

516 Octadecylammonium, 388, 389 Octadecyldimethylchlorosilane, 372 Octadecylpyridinium, 386 Octaethylene glycol mono n-dodecyl ether, 76, 168, 328 Octanol, 324 Octyl β-D-monoglucoside, 353 Octylglucoside, 319, 320, 325–328 Optical density of suspensions, 399 Organogels, 12 Organophilized hexadecylpyridinium, 380 Organosols, 357 Osmometry, 2 Ostwald ripening, 415, 418 Ostwald-de Izaguirre equation, 362, 365 Oxidation, 478, 484, 493 Oxidative stability, 483 Oxidative stability of lipids, 483 Palisade layer, 14 Parental solutions, 478 Particle formation, 440 size, 204 Particle-liquid interactions, 397, 398 Particle-particle interactions, 398 Pasteurization, 478 Pentane, 212 Peptides, 440 Percolation, 6, 12, 69, 241, 242, 244 transitions, 222 Perfluoropolyether, 216, 219, 239 pH, 346 Pharmaceuticals, 24 Phase diagram, 27, 129, 131, 214, 215, 313, 439, 481 separation, 43, 47, 107, 153, 155 transformation, 135, 415, 419 transition, 129, 201, 204, 221, 222, 236, 239, 275, 281, 332, 452, 456, 457, 472, 473, 480 of lipids, 287 of pyridinium salts, 458 Phenylalanine, 438, 441

Index Phosphate groups, 161 Phosphatidylcholine, 80, 111, 326, 327 Phosphatidylethanolamine, 145, 256 Phospholipid bilayer, 63, 247 Phospholipid vesicles, 321 Phospholipids, 146, 161, 256, 312, 324, 330 Physical adsorption, 367 process, 159 properties, 171 of edible fats, 481 Physicochemical behavior of foods, 498 properties, 161 of foods, 478 Pigments, 479 Planar bilayers, 166, 471 Platelets, 148 Polar headgroup, 132, 136, 146 interactions, 444 molecules, 8 Poloxamer, 157 Poly(4-hydroxystyrene) Poly(2-hydroxyethyl methacrylate), 103 Poly(ethylene glycol), 162, 169 Poly(methyl methacrylate), 132 Polyacrylic acid as a function of pH, 152 Polydimethylsiloxane, 83 Polyelectrolyte, 153 Polymerization of single-phase microemulsions, 438 solubilizates, 438 Polymethylsiloxanes, 103 Polymorphic transitions, 414, 454 Polymorphism, 452, 457, 458, 464, 468, 481 Polymorphism of fats, 479 Polymorphs, 418, 427, 428, 442, 465 of phenylalanine, 441 Polyoxyethylene, 66, 84 chains, 168 oleyl alcohol, 76 Polypeptide gramicidin, 151 Polyphenol, 479, 495 POPC, 325, 328, 330

Index Portion of the lipid molecule, 147 Potassium oleate, 61 Potato starch, 489 Precipitation kinetics, 420 Premicelles, 307 Presence of impurities, 419 Principles of biomineralization, 444 Properties of biominerals, 429 of emulsions, 183 of foods, 478 of precipitates, 419 of self assembling, 204 of the adsorption layer, 397 of water, 164 Propylene oxide, 154 Protein denaturation, 489 oxidation, 489, 495 surfaces, 169 Pyrolysis, 485 Quasi elastic light scattering, 215 Quenching, 163, 236 Radiotracer technique, 86 Rate of gas diffusion, 414 of heat transport, 414 of nucleation, 418 of precipitations, 419 Reconstituted foods Recrystallization, 415, 441 of diketopiperazine, 443 Redlich–Kister equations, 363, 381 Refractive index measurements, 398 Reindeer meat, 493 Retrogradation, 488, 489, 492 Reversed micelles, 1, 4, 5 Rewarming, 486 Rheological analysis, 399 data, 402 flow curves, 400, 401, 408 parameters, 405, 406 properties, 397, 407 of the suspension, 346, 409

517 Ripening, 201 Roasting, 478 Role of impurities, 436 Rotation of the head group, 146 Safety aspects, 494 Salinity, 346 Saturated phospholipid, 144 Scattering peaks, 107 Scattering vector, 108 Schay–Nagy classification, 375 SDS, 319, 320, 432 Secondary aggregation, 305, 306 Secondary hydration shell, 171 Second-order transition, 239 Self assembly, 2, 203, 295–297, 314, 331, 445 Self-aggregation, 296 Self-heating, 494, 495 Self-ignition, 494, 495 Semiconductor clusters, 438 Silica gel, 163, 169 Silver halides, 438 Single chain surfactant, 456 Single crystal diffraction, 456 Sludge dewatering, 159 Sludges, 159, 166 Small angle neutron scattering, 94, 160, 215, 359 Small angle X-ray scattering, 94, 359, 397, 407–409 Small unilamellar vesicles, 331 Smectic, 455, 457 Sodium, 4-(1-heptylnoyl)benzenesulphate, 168 Sodium alkylbenzene sulfonates, 354 Sodium alkylsulfates, 354 Sodium alkylxylenesulfonates, 354 betaines, 354 Sodium bis(2-ethylhexyl)sulfosuccinate, 3 Sodium cellulose sulfate, 103 Sodium cholate, 319, 431 Sodium deoxycholate, 319 Sodium dioctylphosphinate, 91, 103, 133, 161, 167 Sodium hexanoate, 354

518 Sodium-illite, 381–384 Sodium oleate, 354 Solid fat index, 482, 497 Solid state NMR, 456 Solid state transitions of surfactant crystals, 451 Solid/liquid adsorption layer, 361 Solid/liquid interactions, 383, 397 Solid/liquid interfaces, 359, 363, 380 Solid/liquid interfacial interactions, 362 Solid/liquid transformation, 436 Solid/solution interfaces, 335 Solidification processes, 190 Solidification transition, 189 Solid-liquid extraction, 478 cooking, 478 Solid-liquid interfacial interactions, 359, 362, 377 Solids in binary liquids, 367 Solid-solid transitions, 184 Solubility, 489 Solubilization, 331, 439 Solution-mediated phase transformation, 418, 422, 426, 427, 431 Solvates, 418 Solvation, 392 Solvent shell, 163 Sound absorption, 6 Soy proteins, 489 Specific heat, 31, 41, 46, 121, 189, 456, 488, 496 of foods, 496 Spectrophotometer, 347 Spectroscopic properties, 163 Spherulites, 444 Spongelike structures, 24 Spray drying, 486 S-Shaped excess isotherms, 372 Stability of aerosol dispersions, 397 Stability of disperse systems, 358, 397 Stability of emulsions, 183 Stable bilayers, 457 Stable sol, 415 Stable structures, 420 Starch, 488 Starch gelatinization, 488

Index Starch solubilization, 488 State of water in surfactant based systems, 159 Static permittivity, 6 Static viscosity, 12 Stearoylarachidonylphosphatidylcholine, 324 Stereochemistry, 336 Steroid content, 150 Stilbene, 140 Stoichiometric displacement, 340 Stokes-Einstein law, 47 Stretched water, 160, 171 Structural transitions, 67, 169 Structure, 479 Subgel phase, 275 Sublimation, 128, 480 Subzero temperature behavior, 59 Sucrose esters, 77 Sucrose monostearate, 87 Supercooled emulsion, 480 Supercooling, 435, 480 Supercritical CO 2, 495, 496 Supermolecules, 3 Supersaturation, 47, 416–420, 422, 428 Surface coverage, 387 diffusion, 422 layer composition, 391 structures of montmorillonite, 380 Surfactant adsorption, 353 Surfactant based microstructures, 163, 171 systems, 159 Surfactant crystals, 452 Surfactant monomer concentration, 155 Surfactant-surfactant interactions, 4, 5 Suspension, 7, 358, 400–407 SUV, 328 Swelling, 386, 389–391 clays, 343 of bentonites, 390 of hydrophobic Symmetrical catanionic surfactants, 460, 470 Synthetic phospholipid, 143

Index TDATDS, 464 Teflon powder, 349 Temperature, 121 Temperature dependence, 48, 52, 127 Tempering, 482 Tertiary oil recovery, 24 Tetrabutylammonium nitrate, 353 Tetradecane, 200 Tetradecylammonium tetradecylsulfate, 460 Tetradecylpyridinium, 386, 389 Tetraethylene glycol monododecylether, 3 Texture, 479 Texturization process, 488 Theoretical considerations, 297 Thermal behavior, 478 of different types of zeolites, 422 of food constituents, 480 of foods, 477 of raw foods, 492 of reconstituted foods, 492 of surfactant crystal, 453 Thermal characteristics of food constituents, 478 Thermal conductivity, 208, 212 denaturation of enzymes, 489 diffusivity, 497 microscopy, 414 properties of foods, 479 transitions, 132 Thermochemistry of organic, organometallic and inorganic compounds, 414 Thermodilatometry, 497 Thermodynamic properties, 124, 163 of crystallization, 439 Thermodynamic stability, 204, 241 Thermogravimetric analysis, 430 Thermogravimetry, 480 Thermomanometry, 480 Thermotropic liquid crystalline states, 455 Thickness of adsorption layer, 363, 407, 409 Titration sorption microcalorimetry, 344 Toxins produced by microorganisms, 479

519 Transformation of crystalline dispersions, 413, 415 Transformation temperature, 143 Transition temperature, 145, 162, 223 Transitions, 121 Transport phenomena, 452 Triblock copolymer, 155 Tricaprylin, 80, 87 Triglycerides, 485 Trimethylammonium bromide, 317 Trimethylammonium methacrylate, 138 Triphenylmethane, 140 Tristearin, 482, 483 Turbidity of suspension, 399 Tween-20, 436 Twin arrangement, 339 Two-dimensional nucleation, 417 Ultracentrifugation, 86 Ultrahigh temperature sterilization, 478 Ultrasonic velocity measurements, 435 Ultrasound velocity, 437 Unilamellar vesicles van der Waals forces, 350 van der Waals interactions, 301, 304, 398 van’t Hoff model, 151 Vapor liquification, 480 Vapor pressure, 161, 165 Vaporization, 142, 480 Vermiculite, 380, 390, 391 Vesicles, 143, 312, 314, 315, 325, 326, 331, 332, 444, 459 Vesicular assemblies, 289 Vicilin, 489 Vicinal water, 163 Vincent model, 398 Viscosity, 6, 86, 452, 489 Vitamins, 479 Wastewater treatment, 159 Water adsorbed, 480 behavior, 159, 247 distribution diagrams, 255 droplets, 480

520 [ Water] penetration into the interfacial region of the bilayers, 145 solubilization, 4 transport, 47 vaporization, 481 Water-in-oil emulsions, 200 Water-surfactant interactions, 61 Weaker hydration structure, 160 Wetting, 358 characteristics, 409 enthalpy, 385 properties, 398

Index Wheat, 489 Wheat starch, 488 White bread, 493 X-ray diffraction, 86, 92, 110, 248, 256, 386, 392, 414, 419, 425, 426, 430, 436, 442, 456, 458, 460, 462, 468, 470, 473, 481, 497 Zeolites, 169, 377, 378, 422, 423 Zwitterionic headgroups, 9 Zwitterionic surfactants, 80, 85, 157, 354

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