Structure-Performance Relationships in Surfactants

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STRUCTUREPERFORMANCE RELATIONSHIPS IN SURFACTANTS Second Edition, Revised and Expanded edited by

Kunio Esumi Minoru Ueno Tokyo University of Science Tokyo, Japan

MARCEL

MARCEL DEKKER, INC.

Copyright © 2003 by Taylor & Francis Group, LLC

NEW YORK • BASEL

ISBN: 0-8247-4044-0 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 Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-260-6300; fax: 41-61-260-6333 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 # 2003 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 Copyright © 2003 by Taylor & Francis Group, LLC

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 Department of Chemical Engineering

ERIC W. KALER Department of Chemical Engineering

Massachusetts Institute of Technology Cambridge, Massachusetts

University of Delaware Newark, Delaware

S. KARABORNI Shell International Petroleum Company Limited London, England

CLARENCE MILLER Department of Chemical Engineering Rice University Houston, Texas

LISA B. QUENCER The Dow Chemical Company Midland, Michigan

DON RUBINGH The Procter & Gamble Company Cincinnati, Ohio

JOHN F. SCAMEHORN Institute for Applied Surfactant Research

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

University of Oklahoma Norman, Oklahoma

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

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JOHN TEXTER Strider Research Corporation Rochester, New York

1. Nonionic Surfactants, edited by Martin J. Schick (see also Volumes 19, 23, and 60) 2. Solvent Properties of Surfactant Solutions, edited by Kozo Shinoda (see Volume 55) 3. Surfactant Biodegradation, R. D. Swisher (see Volume 18) 4. Cationic Surfactants, edited by Eric Jungermann (see also Volumes 34, 37, and 53) 5. 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, edrted 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 byAyao Kitahara andAkira 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 Nairn 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 /. B. Ivanov 30. Microemulstons 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 Copyright © 2003 by Taylor & Francis Group, LLC

32. Interfacial Phenomena in Coal Technology, edited by Gregory D. Botsaris and Yuli M Glazman 33. Surfactant-Based Separation Processes, edited by John F. Scamehom 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, edrfed 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. Gratzel and K Katyanasundaram 39. Interfacial Phenomena in Biological Systems, ectted by Max Bender 40. Analysis of Surfactants, Thomas M. Schmiti (see Volume 96) 41. Light Scattering by Liquid Surfaces and Complementary Techniques, edited by Domimque Langevin 42. Polymeric Surfactants, Irja Piirma 43. Anionic Surfactants: Biochemistry, Toxicology, Dermatology. Second Edition, Revised and Expanded, edited by Christian Gloxhuberand Klaus Kunstler 44. Organized Solutions: Surfactants in Science and Technology, edited by Stig E Friberg and Bjom 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 Dobias 48. Biosurfactants: Production • Properties • Applications, ecWed by Nairn 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 Bergstrom 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. Scamehom 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 Sjdblom 62. Vesicles, edited by Morion Rosoff 63. Applied Surface Thermodynamics, edited by A. W. Neumann and Jan K Spelt 64. Surfactants in Solution, edited byArun K. Chattopadhyay and K. L. Mittat 65. Detergents in the Environment, edited by Milan Johann Schwuger Copyright © 2003 by Taylor & Francis Group, LLC

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 S0rensen 80. Interfacial Phenomena in Chromatography, edited by Emile Pefferkom 81. Solid-Liquid Dispersions, Bohuslav Dobias, Xueping Qiu, and Wolfgang von Rybinski 82. Handbook of Detergents, editor in chief: Uri Zoller Part A: Properties, edited by Guy Broze 83. Modem 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. Silicons 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 Mafaorzata Bordwko 90. Adsorption on Silica Surfaces, eoVted by Eugene Papirer 91. Nonionic Surfactants: Alkyl Polyglucosides, edited by Dieter Balzer and Harald Luders 92. Fine Particles: Synthesis, Characterization, and Mechanisms of Growth, edited by Tadao Sugimoto 93. Thermal Behavior of Dispersed Systems, ectted by Nissim Garti 94. Surface Characteristics of Fibers and Textiles, edited by Christopher M. Pastore and Paul Kiekens 95. Liquid Interfaces in Chemical, Biological, and Pharmaceutical Applications, edrtedbyA/exanderG. Volkov Copyright © 2003 by Taylor & Francis Group, LLC

96. Analysis of Surfactants: Second Edition, Revised and Expanded, Thomas M. Schmitt 97. Fluorinated Surfactants and Repellents: Second Edition, Revised and Expanded, Erik Kissa 98. Detergency of Specialty Surfactants, edited by Floyd E. Fried// 99. Physical Chemistry of Polyelectrolytes, edited by Tsetska Radeva 100. Reactions and Synthesis in Surfactant Systems, edited by John Texter 101. Protein-Based Surfactants: Synthesis, Physicochemical Properties, and Applications, edited by Ifendu A. Nnanna and Jiding Xia 102. Chemical Properties of Material Surfaces, Marek Kosmulski 103. Oxide Surfaces, edrfed by James A. Wingrave 104. Polymers in Particulate Systems: Properties and Applications, edited by Vincent A. Hackley, P. Somasundaran, and Jennifer A. Lewis 105. Colloid and Surface Properties of Clays and Related Minerals, Rossman F. Giese and Caret J. van Oss 106. Interfacial Electrokinetics and Electrophoresis, edited by Angel V. Delgado 107. Adsorption: Theory, Modeling, and Analysis, edited by Jdzsef T6th 108. Interfacial Applications in Environmental Engineering, edited by Mark A. Keane 109. Adsorption and Aggregation of Surfactants in Solution, edited by K. L Mittal andDineshO. Shah 110. Biopolymers at Interfaces: Second Edition, Revised and Expanded, edited by Martin Malmsten 111. Biomolecular Films: Design, Function, and Applications, edited by James F. Rusting 112. Structure-Performance Relationships in Surfactants: Second Edition, Revised and Expanded, edited by Kunio Esumi and Minoru Ueno

ADDITIONAL VOLUMES IN PREPARATION

Liquid Interfacial Systems: Oscillations and Instability, Rudolph V. Birikh, Vladimir A. Briskman, Manuel G. Velarde, and Jean-Claude Legros Novel Surfactants: Preparation, Applications, and Biodegradability: Second Edition, Revised and Expanded, edited by Krister Holmberg Colloidal Polymers: Preparation and Biomedical Applications, edited by Abdelhamid Elaissari

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Preface

Surfactant molecules can self-assemble in water, in oil, and in oil–water or solid–liquid mixtures to give a large variety of colloidal structures. Structure–performance relationships in surfactants are of great importance in nearly all fundamental studies and practical applications of surfactants. Six years ago, the ﬁrst edition of this book was published as Volume 70 in the Surfactant Science series. Its aim was to examine properties and performance of surfactants at various interfaces, such as air–liquid, liquid–liquid, and solid–liquid. Research on new surfactants has been intense in recent years. Now, greatly expanded interest and additional important work in this ﬁeld have led us to update the book to reﬂect current trends. This volume has 18 chapters, which can be classiﬁed into three parts: theoretical studies of surfactants (Chapter 1 and 2), physicochemical properties of surfactants at the air–liquid interface and in solutions (Chapters 3 through 14), and surfactant behavior at the solid–liquid interface (Chapters 15 through 18). In Chapter 1, Nagarajan presents the quantitative approach to predicting the aggregation properties of surfactants and surfactant–polymer mixtures. Chapter 2, by Koopal, reviews the thermodynamic models for micellization/adsorption and discusses the self-consistent-ﬁeld lattice model (SCFA) for association and adsorption of surfactants. Aratono, Villeneuve, and Ikeda’s discussion in Chapter 3 focuses on the surface tension and adsorption behaviour of spontaneously vesicle-forming surfactants. In Chapter 4, Ueno and Asano outline the mixed properties of bile salts and some nonionic surfactants and give examples for application of these systems. In Chapter 5, Ishigami describes the molecular design and characterization of biosurfactants, along with applications of multifunctional structure of biosurfactants. Chapter 6, by Koide and Esumi, deals with the physicochemical properties of ring-structured surfactants, including those of crown ether type, those of polyamine type, cyclodextrin, and Copyright © 2003 by Taylor & Francis Group, LLC

calix[n]arene. Zana’s Chapter 7 discusses the physicochemical properties of dimeric surfactants, such as adsorption at the air–solution and solid–solution interfaces, micelle formation, solubilization, micelle size and shape, rheology, phase behavior, and some applications. In Chapter 8, Yoshino compares the synthesis and properties of two series of double chain–type ﬂuorinated anionic surfactants. One of these is a series of surfactants with two ﬂuorocarbon chains in their molecules; the other is a series of hybrid-type surfactants having both ﬂuorocarbon and hydrocarbon chains in one molecule. Chapter 9, by Yoshimura and Esumi, describes the physicochemical properties of telomer-type surfactants having several hydrophobic groups and several hydrophilic groups; these surfactants often exhibit properties of both polymer-type and conventional surfactants. In Chapter 10, Hoﬀmann analyzes various types of viscoelastic surfactant systems, describing rheological properties and presenting models for understanding the diﬀerent ﬂow behaviors based on the diﬀerent microstructures. Kato’s Chapter 11 presents the micelle structure of nonionic surfactants in dilute, semidilute, and concentrated solutions and discusses the thermodynamic models for micellar solutions and the phase transitions in liquid crystal phases. In Chapter 12, Imae reviews the amphiphilic properties and association behavior of concentric dendrimers and hybrid copolymers. Chapter 13, by Zana, describes how polymer hydrophobicity and the surfactant head group aﬀect polymer–surfactant interactions; the chapter also addresses microstructural aspects, solubilization, and dynamic behaviors of polymer–surfactant aggregrates. In Chapter 14, Uddin, Kunieda, and Solans describe the preparation and properties of highly concentrated cubic phase-based emulsions, as well as the correlation between D-phase emulsiﬁcation and cubic phase-based emulsions. In Chapter 15, Treiner outlines the adsolubilization and related phenomena at solid–solution interfaces and presents some applications. Esumi’s Chapter 16 focuses on the adsorption of polymers and surfactants from their binary mixtures on oxide surface, also discussing the conformation of polymers adsorbed on particles. Chapter 17, also by Esumi, deals with the dispersion of particles by surfactants as well as the properties of surfactant-adsorbed layers. In Chapter 18, Fujii reviews the AFM techniques for the study of surfactant molecules, especially those relating to the morphology of the surfactant aggregations on solid–liquid interfaces. We would like to thank the authors who participated in this eﬀort, and we are indebted to Anita Lekhwani, Joseph Stubenrauch, Michael Deters, and Elissa Ryan of Marcel Dekker, Inc., for their assistance in preparing this volume. Kunio Esumi Minoru Ueno Copyright © 2003 by Taylor & Francis Group, LLC

Contents

Preface Contributors Part I

Theoretical Studies of Surfactants

1. Theory of Micelle Formation: Quantitative Approach to Predicting Micellar Properties from Surfactant Molecular Structure R. Nagarajan 2. Modeling Association and Adsorption of Surfactants Luuk K. Koopal Part II Physicochemical Properties of Surfactants at the Air–Liquid Interface and in Solutions 3. Adsorption of Vesicle-Forming Surfactants at the Air–Water Interface Makoto Aratono, Masumi Villeneuve, and Norihiro Ikeda 4. Physicochemical Properties of Bile Salts Minoru Ueno and Hiroyuki Asano 5. Characterization and Functionalization of Biosurfactants Yutaka Ishigami 6. Physicochemical Properties of Ring-Structured Surfactants Yoshifumi Koide and Kunio Esumi 7. Dimeric (Gemini) Surfactants Raoul Zana

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8. Fluorinated Surfactants Having Two Hydrophobic Chains Norio Yoshino 9. Surface-Active Properties of Telomer-Type Surfactants Having Several Hydrocarbon Chains Tomokazu Yoshimura and Kunio Esumi 10. Viscoelastic Surfactant Solutions Heinz Hoffmann 11. Microstructures of Nonionic Surfactant–Water Systems: From Dilute Micellar Solution to Liquid Crystal Phase Tadashi Kato 12. Association Behavior of Amphiphilic Dendritic Polymers Toyoko Imae 13. Polymer/Surfactant Systems Raoul Zana 14. Highly Concentrated Cubic Phase-Based Emulsions Md. Hemayet Uddin, Hironobu Kunieda, and Conxita Solans Part III

Surfactant Behaviors at the Solid–Liquid Interface

15. Adsolubilization and Related Phenomena Claude Treiner 16. Adsorption of Polymer and Surfactant from Their Binary Mixtures on an Oxide Surface Kunio Esumi 17. Dispersion of Particles by Surfactants Kunio Esumi 18. Arrangement of Adsorbed Surfactants on Solid Surfaces by AFM Observation Masatoshi Fujii

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Contributors

Makoto Aratono, Ph.D. Department of Chemistry, Faculty of Sciences, Kyushu University, Fukuoka, Japan Hiroyuki Asano, Ph.D. Research Laboratories, Nippon Menard Cosmetic Company, Ltd., Nagoya, Japan Kunio Esumi, Ph.D. Department of Applied Chemistry, Tokyo University of Science, Tokyo, Japan Masatoshi Fujii, Ph.D. Department of Chemistry, Tokyo Metropolitan University, Tokyo, Japan Heinz Hoﬀmann, Prof.Dr. Department of Physical Chemistry, University of Bayreuth, Bayreuth, Germany Norihiro Ikeda, Ph.D. Department of Environmental Science, Fukuoka Women’s University, Fukuoka, Japan Toyoko Imae, Ph.D. Research Center for Materials Science, Nagoya University, Nagoya, Japan Yutaka Ishigami, Ph.D. Tokyo Gakugei University and Meisei University, Tokyo, Japan, and Dong-Woo Fine-Chem Co. Ltd., Kyunggi-do, South Korea Tadashi Kato, D.Sc. Department of Chemistry, Tokyo Metropolitan University, Tokyo, Japan

Copyright © 2003 by Taylor & Francis Group, LLC

Yoshifumi Koide, Ph.D.y Department of Applied Chemistry Biochemistry, Kumamoto University, Kumamoto, Japan

and

Luuk K. Koopal, Ph.D. Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Wageningen, The Netherlands Hironobu Kunieda, D.Eng. Graduate School of Environment and Information Sciences, Yokohama National University, Yokohama, Japan R. Nagarajan, Ph.D. Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania, U.S.A. Conxita Solans Institute of Chemical and Environmental Research, CSIC, Barcelona, Spain Claude Treiner, Ph.D. Laboratoire Liquides Ioniques et Interfaces Charge´es, Universite´ Pierre et Marie Curie, Paris, France Md. Hemayet Uddin Graduate School of Environment and Information Sciences, Yokohama National University, Yokohama, Japan Minoru Ueno, Ph.D. Department of Applied Chemistry and Institute of Colloid and Interface Science, Tokyo University of Science, Tokyo, Japan Masumi Villeneuve Japan

Faculty of Science, Saitama University, Saitama,

Tomokazu Yoshimura, Ph.D. Department of Applied Chemistry, Faculty of Science, Tokyo University of Science, Tokyo, Japan Norio Yoshino, Ph.D. Department of Industrial Chemistry and Institute of Colloid and Interface Science, Tokyo University of Science, Tokyo, Japan Raoul Zana, Ph.D.

y

Institut C. Sadron, CNRS, Strasbourg, France

Deceased

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1 Theory of Micelle Formation Quantitative Approach to Predicting Micellar Properties from Surfactant Molecular Structure R. NAGARAJAN The Pennsylvania State University, University Park, Pennsylvania, U.S.A.

I.

INTRODUCTION

The numerous, practical applications of surfactants have their basis in the intrinsic duality of their molecular characteristics, namely, they are composed of a polar headgroup that likes water and a nonpolar tail group that dislikes water. A number of variations are possible in the types of the headgroup and tail group of surfactants. For example, the headgroup can be anionic, cationic, zwitterionic, or nonionic. It can be small and compact in size or an oligomeric chain. The tail group can be a hydrocarbon, ﬂuorocarbon, or a siloxane. It can contain straight chains, branched or ring structures, multiple chains, etc. Surfactant molecules with two headgroups (bola surfactants) are also available. Further, the headgroups and tail groups can be polymeric in character, as in the case of block copolymers. This variety in the molecular structure of surfactants allows for extensive variation in their solution and interfacial properties. It is natural that one would like to discover the link between the molecular structure of the surfactant and its physicochemical action so that surfactants can be synthesized or selected speciﬁc to a given practical application. Pioneering contributions to our understanding of the general principles of surfactant self-assembly in solutions have come from the early studies of Tanford [1–3], Shinoda [4], and Mukerjee [5–9]. Utilizing their results, we have focused our eﬀort in the last 25 years, on developing quantitative molecular thermodynamic models to predict the aggregation behavior of surfactants in solutions starting from the surfactant molecular structure

Copyright © 2003 by Taylor & Francis Group, LLC

and the solution conditions. In our approach, the physicochemical factors controlling self-assembly are ﬁrst identiﬁed by examining all the changes experienced by a singly dispersed surfactant molecule when it becomes part of an aggregate [10–16]. Relatively simple, explicit analytical equations are then formulated to calculate the contribution to the free energy of aggregation associated with each of these factors. Because the chemical structure of the surfactant and the solution conditions are suﬃcient for estimating the molecular constants appearing in these equations, the free energy expressions can be used to make completely a priori predictions. In this chapter we describe in detail our quantitative approach to predicting the aggregation properties of surfactants from their molecular structures. In Section II we present the general thermodynamic equations that govern the aggregation properties of surfactants in solutions. Many conclusions about the aggregation behavior can be drawn from such analysis without invoking any speciﬁc models to describe the aggregates. In Section III we summarize the geometrical relations for various shapes of aggregates including spherical, globular, and rodlike micelles and spherical bilayer vesicles, consistent with molecular packing considerations as had been discussed many years ago by Tartar [17]. These considerations lead us to the concept of the packing parameter proposed by Israelachvili et al. [18] that has been widely cited in the literature. The molecular packing model, as it is currently used, is built on the free energy model of Tanford [1]. We examine its predictive power and then show that the model neglects some tail length-dependent free energy contributions; if these are included, they will lead to signiﬁcantly diﬀerent predictions of the aggregation behavior. In Section IV the molecular theory of micelle formation is described. The central feature of the theory is the postulation of explicit equations to calculate the free energy of formation of diﬀerent types of aggregates invoking phenomenological concepts. We suggest how the molecular constants appearing in these equations can be estimated and describe the computational approach suitable for making predictive calculations. We then demonstrate the predictive power of the molecular theory via illustrative calculations performed on a number of surfactant molecules having a variety of headgroups and tail groups. This molecular theory presented in this section is the point of departure for all subsequent models described in this chapter and also for other aggregation phenomena involving solvent mixtures, solubilization, microemulsions, etc. that have been described elsewhere [19]. In Section V we extend the molecular theory to binary mixtures of surfactants and demonstrate its predictive ability for a variety of ideal and nonideal surfactant mixtures. The model is then applied to surfactants in the presence of nonionic polymers in Section VI. How the nonionic polymer changes the aggregate morphology, in addition to the critical concentrations Copyright © 2003 by Taylor & Francis Group, LLC

and aggregate microstructures, is explored in this section. The extension of the free energy model to block copolymers is done in Section VII, where the polymeric nature of the headgroup and the tail group of the molecule is taken into consideration in constructing the free energy expressions. The analogy between low-molecular-weight conventional surfactants and the block copolymer amphiphiles is discussed in this section. The last section presents some conclusions.

II. THERMODYNAMIC PRINCIPLES OF AGGREGATION A. Aggregate Shapes Figure 1 illustrates the shapes of surfactant aggregates formed in dilute solutions. The small micelles are spherical in shape. When large rodlike micelles form, they are visualized as having a cylindrical middle portion and parts of spheres as endcaps. The cylindrical middle and the spherical endcaps are allowed to have diﬀerent diameters. When micelles cannot pack any more into spheres, and if at the same time the rodlike micelles are not yet favored by equilibrium considerations, then small, nonspherical globular aggregates form. Israelachvili et al. [18] have suggested globular shapes generated via ellipses of revolution for the aggregates in the sphere-to-rod transition region, after examining the local molecular packing requirements for various nonspherical shapes. The average surface area per surfactant molecule of the ellipses of revolution suggested by Israelachvili et al. [18] is practically the same as that of prolate ellipsoids, for aggregation numbers up to 3 times larger than the largest spherical micelles,. Therefore, the average geometrical properties of globular aggregates in the sphere-to-rod transition region can be computed as for prolate ellipsoids. Some surfactants pack into a spherical bilayer structure called a vesicle that encloses an aqueous cavity. In the outer and the inner layers of the vesicle, the surface area (in contact with water) per surfactant molecule, and the number of surfactant molecules need not be equal to one another and the thicknesses of the two layers can also be diﬀerent. In addition to the variety of shapes, it is also natural to expect that surfactant aggregates of various sizes will exist in solution. The size distribution can be represented in terms of a distribution of the number of surfactant molecules constituting the aggregate (i.e., the aggregation number g).

B. Size Distribution of Aggregates Important results related to the size distribution of aggregates can be obtained from the application of general thermodynamic principles to surfactant solutions. The surfactant solution is a multicomponent system conCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 1 Schematic representation of surfactant aggregates in dilute aqueous solutions. The structures formed include spherical micelles (a), globular micelles (b), spherocylindrical micelles (c), and spherical bilayer vesicles (d).

sisting of NW water molecules, N1 singly dispersed surfactant molecules, and Ng aggregates of aggregation number g, where g can take all values from 2 to 1. (The subscript W refers to water, 1 to the singly dispersed surfactant, and g to the aggregate containing g surfactant molecules.) All shapes of Copyright © 2003 by Taylor & Francis Group, LLC

aggregates are considered. Each of the aggregates of a given shape and size is treated as a distinct chemical component described by a characteristic chemical potential. The total Gibbs free energy of the solution G, expressed in terms of the chemical potentials i of the various species i, has the form G ¼ Nw w þ N1 1 þ

g¼1 X

N g g

ð1Þ

g¼2

The equilibrium condition of a minimum of the free energy leads to g ¼ 1 g

ð2Þ

This equation stipulates that the chemical potential of the singly dispersed surfactant molecule is equal to the chemical potential per molecule of an aggregate of any size and shape. Assuming a dilute surfactant solution, one can write a simple expression for the chemical potential of an aggregate of size g (for all values of g including g ¼ 1) in the form: g ¼ 0g þ kT ln Xg

ð3Þ

where 0g is the standard state chemical potential of the species g and Xg is its mole fraction in solution. The standard states of all the species other than the solvent are taken as those corresponding to inﬁnitely dilute solution conditions. The standard state of the solvent is deﬁned as the pure solvent. Introducing the expression for the chemical potential in the equilibrium relation [(Eq. 2)], one gets the aggregate size distribution equation: ! ! 0g g01 g0g g g Xg ¼ X1 exp ¼ X1 exp ð4Þ kT kT where 0g is the diﬀerence in the standard chemical potentials between a surfactant molecule present in an aggregate of size g and a singly dispersed surfactant in water [1]. If an expression for 0g is available, then from Eq. (4), the aggregate size distribution can be calculated. From the aggregate size distribution, all other important and experimentally accessible solution properties can be computed as described below.

C. Calculating CMC, Micelle Size, and Aggregate Polydispersity 1. Critical Micelle Concentration (CMC) The critical micelle concentration can be calculated from the P aggregate P size distribution by constructing a plot of one of the functions X , X , gXg , 1 g P 2 or g Xg (which are proportional to diﬀerent experimentally measured Copyright © 2003 by Taylor & Francis Group, LLC

properties of the surfactant solution such as surface tension, electrical conductivity, dye solubilization, Plight scattering intensity, etc.) against the total concentration Xtot ð¼ X1 þ gXg Þ of the surfactant in solution [1,20–22]. In all cases, the summation extends from 2 to 1. The CMC can be identiﬁed as that value of the total surfactant concentration at which a sharp change in the plotted function (representing a physical property) occurs. The CMC has also been estimated as that value of X1 for which the concentration of the singly dispersed surfactant is equalPto that of the surfactant present in the form of aggregates, namely, X1 ¼ gXg ¼ XCMC ½23. For surfactants in aqueous solutions, the estimates of the CMC obtained by the diﬀerent methods mentioned above are usually close to one another, though not identical [20].

2. Average Micelle Size From the size distribution one can compute various average sizes of the aggregates based on the deﬁnitions P P 2 P 3 gXg g Xg g Xg P P gn ¼ ; gw ¼ ; gz ¼ P 2 ð5Þ Xg gXg g Xg where gn, gw, and gz denote the number average, the weight average, and the z average aggregation numbers, respectively, and the summations extend from 2 to 1, as mentioned earlier. The diﬀerent average aggregation numbers correspond to those determined by diﬀerent experimental techniques; for example, gn is obtained via membrane osmometry, gw via static light scattering, and gz via intrinsic viscosity measurements. If the summations in Eq. (5) extend from 1 to 1 (i.e., include the singly dispersed surfactant molecules), then one obtains apparent (as opposed to true) average aggregation numbers gn,app , gw,app, and gz,app.

3. Aggregate Size Polydispersity For nonionic and zwitterionic surfactants, the standard state free energy diﬀerence 0g appearing in Eq. (4) is not dependent on the concentration of the singly dispersed surfactant X1 or on the total concentration of the surfactant. Consequently, by taking the derivative of the size distribution relation with respect to X1 , one obtains [24–26]: i X 1 hX @ ln Xg ¼ P gXg @ ln X1 ¼ gn @ ln X1 Xg i X 1 hX 2 g Xg @ ln X1 ¼ gw @ ln X1 @ ln gXg ¼ P ð6Þ gXg hX i X 1 g3 Xg @ ln X1 ¼ gz @ ln X1 @ ln g2 Xg ¼ P 2 g Xg Copyright © 2003 by Taylor & Francis Group, LLC

where the average aggregation numbers deﬁned by Eq. (5) have been introduced. Equation (6) shows that the average aggregation numbers gn and gw depend on the concentration ðXtot X1 Þ of the micellized surfactant as P follows (note that gXg ¼ Xtot X1 ): X gn @ ln gXg @ ln gn ¼ 1 gw ð7Þ X gz @ ln gw ¼ 1 @ ln gXg gw The variances of the size dispersion 2 ðnÞ and 2 ðwÞ are deﬁned by the relations: P ðg gn Þ2 Xg g P ¼ g2n w 1 2 ðnÞ ¼ gn Xg ð8Þ P 2 ðg gw Þ gXg 2 2 gz P ðwÞ ¼ ¼ gw 1 gw gXg Combining Eqs. (7) and (8), we can relate the variance of the size distribution to the concentration dependence of the average aggregation number as follows: 1 ðnÞ 2 gw @ ln gn @ ln gn P P ¼ 1¼ 1 1 gn @ ln gXg @ ln gXg gn ð9Þ ðwÞ 2 gz @ ln gw P ¼ 1¼ gw @ ln gXg gw Equation (9) states that the average aggregation numbers gn and gw must increase appreciably with increasing concentration of the aggregated surfactant if the micelles are polydispersed ½ðnÞ=gn and ðwÞ=gw are large]; the average aggregation numbers must be virtually independent of the aggregated surfactant concentration if the micelles are narrowly dispersed. For ionic surfactants, 0g is dependent on the ionic strength of the solution (discussed in Section IV.A) and thus on the concentration of the surfactant, making Eq. (6) inapplicable to them. However, it has been shown that Eq. (9) derived for nonionic and zwitterionic surfactants based on general thermodynamic considerations is valid also for ionic surfactants [25,26].

D. Sphere-to-Rod Transition of Micelles Micelles having spherical or globular shapes are usually small and narrowly dispersed. A diﬀerent micellization behavior is, however, observed when Copyright © 2003 by Taylor & Francis Group, LLC

large rodlike micelles are generated [5–9]. These aggregates are visualized as having a cylindrical middle part with two spherical endcaps as shown in Fig. 1. The standard chemical potential of a rodlike aggregate of size g containing gcap molecules in the two spherical endcaps and (g gcap ) molecules in the cylindrical middle can be written [5–9,16,18,27] as 0g ¼ ðg gcap Þ0cyl þ gcap 0cap

ð10Þ

where 0cyl and 0cap are the standard chemical potentials of the molecules in the two regions of the rodlike aggregate, respectively. Introducing the above relation in the aggregate size distribution [Eq. (4)] yields " ! #g ! 0cyl 0cap 0cyl exp gcap Xg ¼ X1 exp ð11Þ kT kT where 0cyl and 0cap are the diﬀerences in the standard chemical potentials between a surfactant molecule in the cylindrical middle or the endcaps of the spherocylindrical micelle and a singly dispersed surfactant molecule. Equation (11) can be rewritten as " !# 0cyl 1 g Y ¼ X1 exp Xg ¼ Y ; ; kT K ! ð12Þ 0cap 0cyl K ¼ exp gcap kT where K is a measure of the free energy advantage for a molecule present in the cylindrical portion compared to that in the spherical endcaps. The possibility of occurrence of rodlike aggregates at a given concentration X1 of the singly dispersed surfactant molecules is indicated by the proximity of the parameter Y to unity. The average aggregation numbers deﬁned by Eq. (5) can be computed on the basis of the size distribution Eq. (12), by performing the analytical summation of the series functions [5–9,18]: Y Y 1 ; gw ¼ gcap þ 1þ gn ¼ gcap þ 1Y 1Y Y þ gcap ð1 YÞ ð13Þ The total concentration of surfactant present in the aggregated state can be also calculated analytically [5–9,18] and is given by the expression g X 1 gcap Y cap Y gXg ¼ 1þ ð14Þ K 1Y gcap ð1 YÞ Copyright © 2003 by Taylor & Francis Group, LLC

Equation (13) shows that for values of Y close to unity, very large aggregates are formed. In the limit of Y close to unity and gcap ð1 YÞ 1, Eqs. (13) and (14) reduce to X

2 1 1 ; gXg ¼ K 1Y

Y gn ¼ gcap þ ; 1Y

Y gw ¼ gcap þ 2 1Y ð15Þ

P Noting that gXg ¼ Xtot X1 , the dependence of the average aggregation numbers on the surfactant concentration is obtained:

1 ¼ gcap þ ðKðXtot X1 ÞÞ1=2 1Y 2 gw ¼ gcap þ ¼ gcap þ 2ðKðXtot X1 ÞÞ1=2 1Y gn ¼ gcap þ

ð16Þ

It is evident from Eq. (16) that the weight average and the number average aggregation numbers must substantially deviate from one another if rodlike micelles form (i.e., gn, gw gcap ), indicating large polydispersity in the micellar size. The polydispersity index gw/gn is close to 2 at suﬃciently large surfactant concentrations. Further, the sphere-to-rod transition parameter K must be in the range of 108 to 1012, if the rodlike micelles are to form at physically realistic surfactant concentrations [5–9,18,27]. The critical micelle concentration is calculated from Eq. (12) with the recognition that Y is close to unity:

X1 ¼ XCMC

0cyl ¼ exp kT

! ð17Þ

The thermodynamic results obtained so far are independent of any speciﬁc expression for the standard free energy change 0g associated with aggregation and constitute general theoretical principles governing the aggregation behavior of surfactants. However, to perform quantitative predictive calculations of the aggregation behavior, speciﬁc expressions for 0g are needed. In the following section, we will introduce the expression for 0g formulated by Tanford [1–3] on a phenomenological basis and use it to examine the molecular packing model of aggregation that is widely cited in the literature on self-assembly. Copyright © 2003 by Taylor & Francis Group, LLC

III. MOLECULAR PACKING MODEL A. Packing Constraint and Packing Parameter The notion of molecular packing into various aggregate shapes has been recognized in the early work of Tartar [17] and Tanford [1-3], as can be seen, for example, from Figure 9.1 of Tanford’s classic monograph (1). However, only after this concept was explored thoroughly in the work of Israelachvili et al. [18], taking the form of the packing parameter, has it evoked wide appreciation in the literature. We start by recognizing that the hydrophobic domain of a surfactant aggregate contains the surfactant tails. If the density in this domain is equal to that in similar hydrocarbon liquids, the surfactant tails must entirely ﬁll the space in this domain. This implies that, irrespective of the shape of the aggregate, no point within the aggregate can be farther than the distance ‘S from the aggregate–water interface, where ‘S is the extended length of the surfactant tail. Therefore, at least one dimension of the surfactant aggregate should be smaller than or at most equal to 2‘S [1–3,17,18]. The volume of the hydrophobic domain is determined from the number of surfactant molecules g in the aggregate and the volume vS of the surfactant tail. The molecular packing parameter is deﬁned as vS =a‘S , where vS and ‘S are the volume and the length of the surfactant tail and a is the surface area of the hydrophobic core of the aggregate expressed per surfactant molecule constituting the aggregate (hereafter referred to as the area per molecule). As we will see below, the concept of the molecular packing parameter allows a simple and intuitive insight into the self-assembly phenomenon.

B. Geometrical Relations for Aggregates For aggregates of various shapes containing g surfactant molecules, the volume of the hydrophobic domain of the aggregate, Vg , the surface area of contact between the aggregate and water, Ag, and the surface area at a distance from the aggregate–water interface, Ag , are listed in Table 1. Also given in the table is a packing factor P, deﬁned in terms of the geometrical variables characterizing the aggregate. Note that P is slightly diﬀerent from the packing parameter vS =a‘S introduced above. The area Ag is employed in the computation of the free energy of electrostatic interactions between surfactant headgroups, while the packing factor P is used in the computation of the free energy of tail deformation, both discussed later in this chapter. From the geometrical relations provided in Table 1, it can be seen that, given any surfactant molecule, the geometrical properties of spherical or Copyright © 2003 by Taylor & Francis Group, LLC

globular micelles depend only on the aggregation number g. In the case of rodlike micelles, the geometrical properties are dependent on two variables—the radius of the cylindrical part and the radius of the spherical endcaps. For spherical bilayer vesicles, any three variables, such as the aggregation number g and the thicknesses ti and to of the inner and outer layers of the bilayer, determine the geometrical properties.

C. Packing Parameter and Predicting Aggregate Shapes If we consider a spherical micelle with a core radius RS, made up of g molecules, then the volume of the core Vg ¼ gvS ¼ 4R3S =3 and the surface area of the core Ag ¼ ga ¼ 4R2S ; and from these simple geometrical relations we get RS ¼ 3vS =a. If the micelle core is packed with surfactant tails without any empty space, then the radius RS cannot exceed the extended length ‘S of the tail. Introducing this constraint in the expression for RS, one obtains, 0 vS =a‘s 1=3, for spherical micelles. Similarly for cylindrical or bilayer aggregates made up of g surfactant molecules, the geometrical relations for the volume Vg and the surface area Ag are given in Table 1. These geometrical relations, together with the constraint that at least one dimension of the aggregate (the radius of the sphere or the cylinder, or the half-bilayer thickness) cannot exceed ‘s, lead to the following well-known [18] connection between the molecular packing parameter and the aggregate shape: 0 vS =a‘s 1=3 for sphere; 1=3 vS = a‘s 1=2 for cylinder; and 1=2 vS =a‘S 1 for bilayer. Therefore, if we know the molecular packing parameter, the shape and size of the equilibrium aggregate can be readily identiﬁed as shown above. This is the predictive sense in which the molecular packing parameter of Israelachvili et al. [18] has found signiﬁcant use in the literature. For common surfactants, the ratio vS/‘S is a constant independent of tail length, equal to 21A 2 for single tail and 42A 2 for double tail (1). Consequently, in the packing parameter vS =a‘S , only the area a reﬂects the speciﬁcity of the surfactant.. The area per molecule a is a thermodynamic quantity obtained from equilibrium considerations of minimum free energy and is not a simple variable connected to the geometrical shape and size of the surfactant headgroup. To estimate a, Israelachvili et al. [18] invoked the model for the standard free energy change on aggregation pioneered by Tanford [1]. In the framework of Tanford’s free energy model, the area a is inﬂuenced directly by the surfactant headgroup interactions. Hence, the accepted notion in the surfactant literature is, given a headgroup, a is ﬁxed—which then, determines the packing parameter vS =a‘S —thus, the headgroup controls the equilibrium aggregate structure. Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 1

Geometrical Properties of Surfactant Aggregates

Spherical micelles (radius RS ‘S Þ: Vg ¼

4R3S ¼ gvS 3

Ag ¼ 4R2S ¼ ga Ag ¼ 4ðRS þ Þ2 ¼ ga P¼

Vg v 1 ¼ S ¼ Ag RS aRS 3

Globular micelles (semiminor axis RS ¼ ‘s , semimajor axis b 3‘S , eccentricity E): Vg ¼

4R2S b ¼ gvS 3 "

# " 2 #1=2 sin1 E RS ¼ ga; E ¼ 1 Ag ¼ 1þ 1=2 2 b Eð1 E Þ " # " #1=2 sin1 E RS þ 2 2 Ag ¼ 2ðRS þ Þ 1 þ E ¼ 1 ¼ ga ; bþ E ð1 E2 Þ1=2 1=3 Vg 3Vg v 1 P 0:406; Req ¼ P¼ ¼ S ; Ag RS aRS 4 3 2R2S

Cylindrical part of rodlike micelles (radius RC ‘s , length LC Þ: Vg ¼ R2C LC ¼ gvS Ag ¼ 2RC LC ¼ ga; P¼

Ag ¼ 2ðRC þ ÞLC ¼ ga

Vg v 1 ¼ S ¼ Ag RC aRC 2

Endcaps of rodlike micelles (endcap radius RS ‘S , cylinder radius RC ‘S Þ: H ¼ RS ½1 f1 ðRC =RS Þ2 g1=2 " # 8R3S 2 2 H ð3RS HÞ ¼ gvS Vg ¼ 3 3 Ag ¼ ½8R2S 4RS H ¼ ga Ag ¼ ½8ðRS þ Þ2 4ðRS þ ÞðH þ Þ ¼ ga P¼

Vg v ¼ S Ag RS aRS

Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 1 Continued Spherical vesicles (inner/outer radii Ri , Ro ; inner/outer layer thickness ti , to ‘s Þ; Vg ¼

4½R3o R3i ¼ gvS ; 3

g ¼ go þ gi

Vgo ¼

4½R3o ðRo to Þ3 ¼ go vS 3

Vgi ¼

4½ðRi þ ti Þ3 R3i Þ ¼ gi vS 3

Ago ¼ 4R2o ;

Agi ¼ 4R2i

Ago ¼ 4ðRo þ Þ2 ¼ go ao Agi ¼ 4ðRi Þ2 ¼ gi ai

D. Estimating Equilibrium Area from Tanford’s Free Energy Model In his phenomenological model Tanford suggests that the standard free energy change associated with the transfer of a surfactant molecule from its inﬁnitely dilute state in water to an aggregate of size g (aggregation number) has three contributions:

0g ¼ 0g Transfer þ 0g Interface þ 0g Head

ð18Þ

The ﬁrst term, ð0g ÞTransfer , is a negative free energy contribution arising from the transfer of the tail from its unfavorable contact with water to the hydrocarbonlike environment of the aggregate core. The transfer free energy contribution depends on the surfactant tail but not on the aggregate shape or size. The second term, ð0g ÞInterface , provides a positive contribution to account for the fact that the entire surface area of the tail is not removed from water but there is still residual contact with water at the surface of the aggregate core. This is represented as the product of a contact free energy per unit area (or an interfacial free energy) and the surface area per molecule of the aggregate core, a. The third term, ð0g ÞHead , provides another positive contribution representing the repulsive interactions between the headgroups that crowd at the aggregate surface. Because the repulsion would increase if the headgroups came close to one another, Tanford proposed an expression with an inverse dependence on a. Thus, Copyright © 2003 by Taylor & Francis Group, LLC

the standard free energy change per molecule on aggregation proposed by Tanford has the form 0 0 ð19Þ g ¼ g Transfer þa þ =a where is the headgroup repulsion parameter. Starting from the free energy model of Tanford, the equilibrium aggregation behavior can be examined either by treating the surfactant solution as consisting of aggregates with a distribution of sizes or by treating the aggregate as constituting a pseudophase [1–3,15]. If the aggregate is viewed as a pseudophase, in the sense of small systems thermodynamics, the equilibrium condition corresponds to a minimum in the standard free energy change ð0g Þ. The minimization can be done with respect to either the aggregation number g or the area per molecule a, since they are dependent on one another through the geometrical relations given in Table 1. In this manner one obtains the equilibrium area per molecule of the aggregate: 1=2 @ 0 g ¼ 0 ) 2 ¼ 0 ) a ¼ ð20Þ @a a The critical micelle concentration (CMC, denoted as XCMC in mole fraction units) in the pseudophase approximation is obtained from the relation ! ! 1 0g 0g ð21Þ ln XCMC ¼ þ aþ ¼ kT kT kT kT a Transfer

where the area a now stands for the equilibrium estimate given by Eq. (20). In Tanford’s free energy expression [Eq. (19)], the ﬁrst contribution, the tail transfer free energy, is negative. Hence, this contribution is responsible for the aggregation to occur. It aﬀects only the CMC [as shown by Eq. (21)] but not the equilibrium area a [as shown by Eq. (20)]. Hence it does not aﬀect the size and shape of the aggregate. The second contribution, the free energy of residual contact between the aggregate core and water, is positive and decreases in magnitude as the area a decreases. A decrease in the area a corresponds to an increase in the aggregation number g, for all aggregate shapes, as shown by the geometrical relations in Table 1. Hence, this contribution promotes the growth of the aggregate. The third contribution, the free energy due to headgroup repulsions, is also positive and increases in magnitude if the area a decreases or the aggregation number g increases. Hence, this contribution is responsible for limiting the growth of aggregates to a ﬁnite size. Thus, Tanford’s model clearly identiﬁes why aggregates form, why they grow, and why they do not keep growing but remain ﬁnite in size. Copyright © 2003 by Taylor & Francis Group, LLC

E. Predictive Power of Molecular Packing Model The packing parameter vS /a‘S can be estimated using the equilibrium area a obtained from Eq. (20). One can observe that a will be small and the packing parameter will be large if the headgroup interaction parameter is small. The area a will increase and the packing parameter will decrease if the interfacial free energy per unit area decreases. These simple considerations allow one to predict many features of surfactant self-assembly as summarized below. 1. For nonionic surfactants with ethylene oxide units as the headgroup, the headgroup parameter can be expected to increase in magnitude if the number of ethylene oxide units in the headgroup increases. Therefore, when the number of ethylene oxide units is small, is small, a is small, vS /a‘S is large, and bilayer aggregates (lamellae) are favored. For larger number of ethylene oxide units, increases, a increases, vS /a‘S decreases, and cylindrical micelles become possible. When the number of ethylene oxide units is further increased, a becomes very large, vS /a‘S becomes small enough so that spherical micelles will form with their aggregation number g decreasing with increasing ethylene oxide chain length. 2. Comparing nonionic and ionic surfactants, the headgroup interaction parameter will be smaller for nonionics than for ionics, because one has to also consider ionic repulsions in the latter case. Therefore, a will be smaller and vS /a‘S will be larger for the nonionics compared to the ionics. As a result, nonionic surfactants would form aggregates of larger aggregation number compared to ionic surfactants of the same tail length. 3. For a given surfactant molecule, the headgroup repulsion can be decreased by modifying the solution conditions. For example, adding salt to an ionic surfactant solution decreases ionic repulsions; increasing the temperature for a nonionic surfactant molecule with an ethylene oxide headgroup decreases steric repulsions. Because decreases, a will decrease and vS /a‘S will increase. Thus, one can achieve a transition from spherical micelles to rodlike micelles, and possibly to bilayer aggregates, by modifying solution conditions that control headgroup repulsions. 4. If single-tail and double-tail surfactant molecules are compared, for the same equilibrium area a, the double-tail molecule will have a packing parameter vS /a‘S twice as large as that of the single-tail molecule. Therefore, the double-tail molecule can self-assemble to form bilayer vesicles while the corresponding single-tail molecule aggregates into only spherical or globular micelles. 5. If the solvent is changed from water to a mixed aqueous-organic solvent, then the interfacial tension parameter decreases. For a given surfactant, this would lead to an increase in the equilibrium area per mole-

Copyright © 2003 by Taylor & Francis Group, LLC

cule a and, hence, a decrease in vS /a‘S . Therefore, on the addition of a polar organic solvent to an aqueous surfactant solution, bilayers will transform into micelles, rodlike micelles into spherical micelles, and spherical micelles into those of smaller aggregation numbers including only small molecular clusters. All the above predictions are in agreement with numerous experiments and are by now well established in the literature. One can thus see the evidence for the predictive power of the molecular packing parameter model and its dramatic simplicity.

F. Neglected Role of the Surfactant Tail From the previous discussion, it is obvious that the equilibrium area a has become closely identiﬁed with the headgroup of the surfactant because of its dependence on the headgroup interaction parameter . Indeed, a is often referred to as the ‘‘head-group area’’ in the literature. This has even led to the erroneous identiﬁcation of a as a simple geometrical area based on the chemical structure of the headgroup in many papers, in contrast to the actuality that a is an equilibrium parameter derived from thermodynamic considerations. For the same surfactant molecule, the area a can assume widely diﬀerent values depending on the solution conditions like temperature, salt concentration, additives present, etc.; hence, it is meaningless to associate one speciﬁc area with a given surfactant. While the role of the surfactant headgroup in controlling self-assembly is appreciated in the literature, in marked contrast, the role of the surfactant tail has been virtually neglected. This is because the ratio vS /‘S appearing in the molecular packing parameter is independent of the chain length for common surfactants and the area a depends only on the headgroup interaction parameter [Eq. (20)] in the framework of Tanford’s free energy model. However, as discussed below, it is necessary to consider an extension to Tanford’s free energy expression to account for the packing entropy of the surfactant tail in the aggregates. When this is done, the area a becomes dependent on the tail length of the surfactant and also on the aggregate shape. In formulating and evaluating his free energy expression, Tanford had already noted [1] that the transfer free energy of the tail has a magnitude diﬀerent from the free energy for transferring the corresponding hydrocarbon chain from aqueous solution to a pure hydrocarbon phase. He had correctly surmised that the diﬀerence arises from the packing constraints inside the aggregates that are absent in the case of a bulk hydrocarbon liquid phase. He took account of this factor empirically, as a correction to the transfer free energy, independent of the aggregate size and shape. Such an Copyright © 2003 by Taylor & Francis Group, LLC

empirical expression for the tail packing free energy, independent of the aggregate size and shape, was employed in our early treatments of micelle and vesicle formation [11–13]. Subsequently, detailed chain packing models to estimate this free energy contribution were developed following diﬀerent approaches, by Gruen [28– 30], Dill et al. [31–35], Ben-Shaul et al. [36–38], Puvvada and Blankschtein [39–41], and Nagarajan and Ruckenstein (16). The inclusion of this free energy contribution obviously leads to the surfactant tail directly inﬂuencing a, and hence the packing parameter, size, and shape of the equilibrium aggregate. This is discussed in detail in Ref. [42]. The molecular theory of micellization outlined in the next section is strongly inﬂuenced by Tanford’s work. Various contributions to the free energy of aggregation are identiﬁed phenomenologically. Explicit expressions to estimate these free energy contributions are then developed in molecular terms, involving only molecular constants that are readily estimated from knowledge of surfactant molecular structure and solution conditions. This allows a truly predictive approach to the phenomenon of surfactant self-assembly.

IV. THEORY OF MICELLIZATION OF SURFACTANTS A. Free Energy of Micellization 1. Contributions to the Free Energy of Micellization From our previous discussion, it is evident that at the heart of the theory of micellization is the formulation of an expression for the standard free energy diﬀerence 0g between a surfactant molecule in an aggregate of size g and one in the singly dispersed state. Once such an expression is available, all solution and aggregation properties can be a priori calculated. Tanford’s phenomenological model [1] has already suggested the essential components of this free energy change. One can decompose 0g into a number of contributions on the basis of phenomenological and molecular considerations [11,13,16]. First, the hydrophobic tail of the surfactant is removed from contact with water and transferred to the aggregate core, which is like a hydrocarbon liquid. Second, the surfactant tail inside the aggregate core is subjected to packing constraints because of the requirements that the polar headgroup should remain at the aggregate–water interface and the micelle core should have a hydrocarbon liquidlike density. Third, the formation of the aggregate is associated with the creation of an interface between its hydrophobic domain and water. Fourth, the surfactant headgroups are brought to the aggregate surface, giving rise to steric repulsions between them. Finally, if the headgroups are ionic or zwitterionic, then electrostatic Copyright © 2003 by Taylor & Francis Group, LLC

repulsions between the headgroups at the aggregate surface also arise. Explicit analytical expressions developed in our earlier studies [11,13,16] are presented in this section for each of these free energy contributions in terms of the molecular characteristics of the surfactant.

2. Transfer of the Surfactant Tail On aggregation, the surfactant tail is transferred from its contact with water to the hydrophobic core of the aggregate. The contribution to the free energy from this transfer process is estimated by considering the aggregate core to be like a liquid hydrocarbon. The fact that the aggregate core diﬀers from a liquid hydrocarbon gives rise to an additional free energy contribution that is evaluated immediately below. The transfer free energy of the surfactant tail is estimated from independent experimental data on the solubility of hydrocarbons in water [43,44]. On this basis, the transfer free energy for the methylene and methyl groups in an aliphatic tail as a function of temperature T (in 8K) is given by [16] ð0g Þtr 896 36:15 0:0056T (for CH2 Þ ¼ 5:85 ln T þ T kT ð0g Þtr 4064 44:13 þ 0:02595T (for CH3 Þ ¼ 3:38 ln T þ T kT

ð22Þ

For surfactant tails made up of two hydrocarbon chains, the contribution to the transfer free energy would be smaller than that calculated based on two independent single chains, because of intramolecular interactions. Tanford [1] has estimated that the second chain of a dialkyl molecule contributes a transfer free energy that is only about 60% of an equivalent single chain molecule, and this estimate is used for calculations involving double chain molecules. For ﬂuorocarbons, using the work of Mukerjee and Handa [45], we estimate the transfer free energy to be 6.2kT for the CF3 group and 2:25kT for the CF2 group, at 258C. The temperature dependencies of the transfer free energies for ﬂuorocarbons are presently not available.

3. Packing and Deformation of the Surfactant Tail Within the aggregates, one end of the surfactant tail, which is attached to the polar headgroup, is constrained to remain at the aggregate–water interface. The other end (the terminal methyl group) is free to occupy any position inside the aggregate as long as a uniform density is maintained in the aggregate core. Obviously, the tail must deform locally, that is, stretch and compress nonuniformly along the tail length, in order to satisfy both the packing and the uniform density constraints. The positive free energy contribution resulting from this conformational constraint on the surfactant tail is referred to as the tail deformation free energy. Diﬀerent methods for Copyright © 2003 by Taylor & Francis Group, LLC

estimating this contribution have appeared in the literature [28–41] that involve either complex expressions or extensive numerical calculations. In constructing our theory, we have followed the method suggested for block copolymer microdomains by Semenov [46], and have developed a simple analytical expression by integrating the local tail deformation energy over the volume of the aggregate. In this manner, we obtain [16] the following expression for spherical micelles: ð0g Þdef 9P 2 ¼ kT 80

!

R2S NL2

! ð23Þ

where P is the packing factor deﬁned in Table 1, RS is the core radius, L is the characteristic segment length for the tail, and N is the number of segments in the tail (N ¼ ‘S =L, where ‘S is the extended length of the tail). As suggested by Dill and Flory [31,32], a segment is assumed to consist of 3.6 methylene groups (hence, L ¼ 0:46 nm). L also represents the spacing between alkane molecules in the liquid state, namely, L2 ð¼ 0:21 nm2 Þ is the cross-sectional area of the polymethylene chain. Equation (23) is employed also for nonspherical globular micelles and the spherical endcaps of rodlike micelles. For inﬁnite cylindrical rods, Eq. (23) is still applicable, but with the changes that the coeﬃcient 9 is replaced by 10, the radius RS is replaced by the radius RC of the cylinder, and the packing factor P ¼ 1=2. For spherical bilayer vesicles, the molecular packing diﬀerences between the outer and the inner layers must be accounted for. Consequently, when Eq. (23) is applied to spherical bilayer vesicles, the radius RS is replaced by the half-bilayer thickness to for the molecules in the outer layer, and ti for the molecules in the inner layer, and the coeﬃcient 9 is replaced by 10 and the packing factor P ¼ 1, as for lamellar aggregates. For surfactant tails with two chains, the tail deformation free energy calculated for a single chain should be multiplied by a factor of 2. The segment size L mentioned above for hydrocarbon tails is employed, also for ﬂuorocarbon tails because most calculations involving ﬂuorocarbons have been done for hydrocarbon– ﬂuorocarbon mixed surfactants, and lattice models that allow for two different sizes for sites on the same lattice become mathematically complicated. For pure ﬂuorocarbon surfactants, one can perform predictive calculations taking L ¼ 0:55 nm consistent with the cross-sectional area of about 0.30 nm2 of a ﬂuorocarbon chain.

4. Formation of Aggregate Core–Water Interface The formation of an aggregate generates an interface between the hydrophobic domain consisting of surfactant tails and the surrounding water medium. The free energy of formation of this interface is calculated as the Copyright © 2003 by Taylor & Francis Group, LLC

product of the surface area in contact with water and the macroscopic interfacial tension agg characteristic of the interface [11,13,16]: ð 0g Þint agg ¼ ð24Þ ða ao Þ kT kT Here, a is the surface area of the hydrophobic core per surfactant molecule, and ao is the surface area per molecule shielded from contact with water by the polar headgroup of the surfactant. For spherical bilayer vesicles, the area per molecule diﬀers between the outer and inner layers and the area a in Eq. (24) is replaced with ðAgo þ Agi Þ=g. Expressions for the surface area per molecule corresponding to diﬀerent aggregate shapes and sizes are provided in Table 1. The area ao depends on the extent to which the polar headgroup shields the cross-sectional area L2 of the surfactant tail (2L2 for a double chain tail). If the headgroup cross-sectional area ap is larger than the tail cross-sectional area, the latter is shielded completely from contact with water and ao ¼ L2 (or 2L2 for double chains) in this case. If ap is smaller than the crosssectional area of the tail, then the headgroup shields only a part of the cross-sectional area of the tail from contact with water, and ao ¼ ap . Thus, ao is equal to the smaller of ap or L2 (2L2 for a double chain). The aggregate core–water interfacial tension agg is taken equal to the interfacial tension SW between water (W) and the aliphatic hydrocarbon of the same molecular weight as the surfactant tail (S). The interfacial tension SW can be calculated in terms of the surface tensions S of the aliphatic surfactant tail and W of water via the relation sw ¼ s þ w 2:0 ðs w Þ1=2

ð25Þ

where is a constant with a value of about 0.55 [47,48]. The surface tension S can be estimated to within 2% accuracy [16] using the relation s ¼ 35:0 325M 2=3 0:098ðT 298Þ

ð26Þ

where M is the molecular weight of the surfactant tail, T is in 8K, and S is expressed in mN/m. The surface tension of water [49] can be calculated using the expression [16] w ¼ 72:0 0:16ðT 298Þ

ð27Þ

where the surface tension is expressed in mN/m and the temperature in 8K. For ﬂuorocarbon surfactants, agg is taken equal to the experimentally determined interfacial tension of 56.45 mN/m at 258C between water and perﬂuorohexane [45]. The temperature dependency of this interfacial tension can be approximated by a constant coeﬃcient of 0.1 mN/m/8K, in the absence of available experimental data. Copyright © 2003 by Taylor & Francis Group, LLC

5. Headgroup Steric Interactions On aggregation, the polar headgroups of surfactant molecules are brought to the surface of the aggregate, where they are crowded when compared to the inﬁnitely dilute state of the singly dispersed molecules. This generates steric repulsions among the headgroups. If the headgroups are compact, the steric interactions between them can be estimated as hard-particle interactions, using any of the models available in the literature. The simplest is the van der Waals approach, on the basis of which the contribution from steric repulsion at the micelle surface is calculated as [11,13,16] ap ð0g Þsteric ¼ ln 1 kT a

ð28Þ

where ap is the cross-sectional area of the polar headgroup near the micellar surface. This equation is used for spherical and globular micelles as well as for the cylindrical middle and the spherical endcaps of rodlike micelles. For spherical bilayer vesicles, the steric repulsions at both the outer and the inner surfaces must be considered, taking into account that the area per molecule is diﬀerent for the two surfaces. Noting that go and gi surfactant molecules are present in the outer and the inner layers, respectively, one can write g g ap ap ð0g Þsteric i ln 1 ð29Þ ¼ o ln 1 kT g g Ago = go Agi = gi The above approach to calculating the headgroup interactions using Eqs.(28) or (29) is inadequate when the polar headgroups are not compact, as in the case of nonionic surfactants having polyoxyethylene chains as headgroups. An alternate treatment for headgroup interactions in such systems is presented later in this section.

6. Headgroup Dipole Interactions If the headgroup has a permanent dipole moment as in the case of zwitterionic surfactants, the crowding of the aggregate surface by the headgroups also leads to dipole–dipole interactions. The dipoles at the surface of the micelle are oriented normal to the interface and stacked such that the poles of the dipoles are located on parallel surfaces. The dipole–dipole interaction for such an orientation provides a repulsive contribution to the free energy of aggregation. The interaction free energy is estimated by considering that the poles of the dipoles generate an electrical capacitor and the distance between the planes of the capacitor is equal to the distance of charge separation d (or the dipole length) in the zwitterionic headgroup. Consequently, for spherical micelles one gets [11,13,16] the expression Copyright © 2003 by Taylor & Francis Group, LLC

ð 0g Þdipole 2 e2 RS d ¼ kT "a kT RS þ þ d

ð30Þ

where e is the electronic charge, " the dielectric constant of the solvent, RS the radius of the spherical core, and the distance from the core surface to the place where the dipole is located. This equation is also employed for globular micelles and the endcaps of rodlike micelles. For the cylindrical part of the rodlike micelles, the capacitor model yields ð 0g Þdipole 2 e2 RC d ¼ ln 1 þ ð31Þ kT "a kT RC þd þ where RC is the radius of the cylindrical core of the micelle. For vesicles, considering the outer and inner surfaces, one can write [12,13] gi 2 e2 Ri ð 0g Þdipole go 2 e2 Ro d d ¼ þ ð32Þ kT g " ao kT Ro þ þ d g " ai kT Ri d where the areas ao and ai are deﬁned in Table 1. The dielectric constant " is taken to be that of pure water [49] and is calculated using the expression [16] " ¼ 87:74 expð0:0046ðT 273ÞÞ

ð33Þ

where the temperature T is in 8K.

7. Headgroup Ionic Interactions If the surfactant has an anionic or cationic headgroup, then ionic interactions arise at the micellar surface. The theoretical computation of these interactions is complicated by a number of factors such as the size, shape, and orientation of the charged groups, the dielectric constant in the region where the headgroups are located, the occurrence of Stern layers, discrete charge eﬀects, etc. [1,4,50,51]. The Debye–Hu¨ckel solution to the Poisson– Boltzmann equation is found to overestimate the interaction energy approximately by a factor of 2 [1,15]. An approximate analytical solution to the Poisson–Boltzmann equation derived [52] for spherical and cylindrical micelles is used in the present calculations. This free energy expression has the form 8 9 8 ! 9 ! 0 < = < 2 1=2 = 2 1=2 ðg Þionic S S 4 S ¼ 2 ln þ 1þ 1þ 1 ; S: :2 ; kT 4 4 8 9 ð34Þ ! < 2 1=2 = 4C 1 1 S ln þ 1þ ; S :2 2 4 where Copyright © 2003 by Taylor & Francis Group, LLC

S¼

4 e2 " a kT

ð35Þ

and is the reciprocal Debye length. The area per molecule a is evaluated at a distance from the hydrophobic core surface (see Table 1), where the center of the counterion is located. The ﬁrst two terms on the right-hand side of Eq. (34) constitute the exact solution to the Poisson–Boltzmann equation for a planar geometry, and the last term provides the curvature correction. The curvature-dependent factor C is given by [16] C¼

2 ; RS þ

2 ; Req þ

1 RC þ

ð36Þ

for spheres/spherical endcaps of spherocylinders, globular aggregates (with an equivalent radius Req deﬁned in Table 1), and cylindrical middle part of spherocylinders, respectively. For spherical bilayer vesicles, the electrostatic interactions at both the outer and inner surfaces are taken into account [12,13]. For the molecules in the outer layer, the free energy contribution is calculated with a replaced by ao and C ¼ 2=ðRo þ Þ. For the molecules in the inner layer, a is replaced by ai and C ¼ 2=ðRi Þ. The reciprocal Debye length is related to the ionic strength of the solution via !1=2 8 n0 e2 ðC þ Cadd Þ NAv n0 ¼ 1 ð37Þ ; ¼ "kT 1000 In the above equation, n0 is the number of counterions in solution per cm3, C1 is the molar concentration of the singly dispersed surfactant molecules, Cadd is the molar concentration of the salt added to the surfactant solution, and NAv is Avogadro’s number. The temperature dependence of the reciprocal Debye length arises from both the variables T and " present in Eq. (37).

8. Headgroup Interactions for Oligomeric Headgroups For nonionic surfactants with polyoxyethylene chains as headgroups, the calculation of the headgroup interactions using Eq. (28) and (29) for the steric interaction energy becomes less satisfactory since it is diﬃcult to deﬁne an area ap characteristic of the oligomeric headgroups (13,16) without ambiguity. For suﬃciently large polyoxyethylene chain lengths, it is more appropriate to treat the headgroup as a polymeric chain when estimating the free energy of headgroup interactions. The treatment developed in our earlier work (16) is based on the following conceptual approach. In a singly dispersed surfactant molecule, the polyoxyethylene chain is viewed as an isoCopyright © 2003 by Taylor & Francis Group, LLC

lated free polymer coil swollen in water. In micelles, the polyoxyethylene chains present in the region surrounding the hydrophobic core (referred to as shell or corona) can be viewed as forming a solution denser in polymer segments compared to the isolated polymer coil. The diﬀerence in the two states of polyoxyethylene provides a contribution to the free energy of aggregation, which is computed as the sum of the free energy of mixing of the polymer segments with water and the free energy of polymer chain deformation. As the polyoxyethylene chain length decreases, the use of polymer statistics becomes less satisfactory. Two limiting models of micellar corona are considered. One assumes that the corona has a uniform concentration of polymer segments. The maintenance of such a uniform concentration in the corona is possible for curved aggregates, only if the chains deform nonuniformly along the radial coordinate. This model may be appropriate when the number of ethylene oxide units in the headgroup is small. The second model assumes a radial concentration gradient of chain segments in the corona consistent with the uniform deformation of the chain. This model may be more appropriate for headgroups with large number of ethylene oxide units. For either of the above models, in order to calculate the mixing free energies, one has to choose some polymer solution theory. Because of its simplicity, the mean-ﬁeld approach of Flory [53], which requires only the polyoxyethylene–water interaction parameter WE for calculating the free energies, is used here. Usually, it is necessary to consider the composition and temperature dependencies of the interaction parameter WE in order to accurately describe the thermodynamic properties of polymer solutions [54– 56]. Even with such dependencies incorporated, it has not been possible to satisfactorily describe the properties of a polyethylene oxide–water system, indicating the inadequacy of the polymer solution theory to quantitatively represent the aqueous polymer solution. Nevertheless, we have carried out calculations based on the Flory model and taking WE to be a constant, with the justiﬁcation that the model provides at least an approximate accounting of the mixing free energy needed for our purposes and no better model with comparable simplicity is available. For both uniform concentration and nonuniform concentration models, the free energy of the steric interactions is calculated using Eq. (28) or (29), but taking ap equal to L2 to describe the steric repulsions between neighboring surfactant tails at the sharp interface separating the core from the corona.

9. Headgroup Mixing in Corona Region For a polyoxyethylene chain containing EX oxyethylene units, the number of segments NE is given by NE ¼ EX vE =L3 , where vE is the volume of an oxyethylene unit and the characteristic segment volume is retained to be L3. Copyright © 2003 by Taylor & Francis Group, LLC

Based on available density data [57] at 258C, vE ¼ 0:063 nm3. The volume VS of the micellar corona, having a thickness D, is calculated from the geometrical relations given in Table 2. In the uniform concentration model, the volume fraction of the polymer segments in the corona is Eg ¼

g Ex vE g NE L3 ¼ VS VS

ð38Þ

In the nonuniform concentration model, the polymer concentration in the corona is determined from the requirement that the polymer chains be uniformly deformed over the thickness D. The radial variation of polymer concentration in the corona is thus found to be (16) ! 3 g NE L ðrÞ ¼ ð39Þ D 4 r2 for spherical aggregates and ! 3 g NE L ðrÞ ¼ D 2r LC

ð40Þ

TABLE 2 Corona Volume of Micelles with Polyoxytheylene Headgroups Spherical micelles: VS Vg ¼ g g Globluar micelles: VS Vg ¼ g g

"

" 1þ

D 1þ RS

D RS

#

3

1

2 1þ

# D 1 b

Cylindrical part of rodlike micelles: " # VS Vg D 2 1 ¼ 1þ g g RC Spherical endcaps of rodlike micelles: " # VS Vg 8ðRS þ DÞ3 2ðH þ DÞ2 ¼ f3ðRS þ DÞ ðH þ DÞg 1 g g 3gvS 3gvS

Copyright © 2003 by Taylor & Francis Group, LLC

for a cylinder of length LC containing g molecules. The polymer concentration ’R at the micellar core–water interface (at r ¼ R) reduces for both spheres and cylinders to ! 3 NE L R ¼ ð41Þ Da where a is the surface area of the micellar core per surfactant molecule. In the corona each polyoxyethylene chain experiences a potential U(r) because of the interactions between the segments of a single molecule and the segments of all the other molecules. This potential is taken in the meanﬁeld approach to be proportional to the total segment density arising from all the molecules of the micelle. The inﬂuence of the solvent is also incorporated in this mean potential via the excluded-volume factor [53,58]. The potential is written [16] as UðrÞ ¼ kTðrÞð12 wE Þ

ð42Þ

where ’(r) is the segment density of polyoxyethylene in the corona at the radial position r. For the uniform concentration model, ’(r) is a constant equal to ’Eg. Therefore, the mixing free energy of the headgroup in the corona with respect to that in an isolated, free polymer coil is given by [16] the expression ð ð 0g Þmix;E 1 1 RþD UðrÞ 1 2 r 4 ðrÞ dr ¼ ð43Þ ¼ N E Eg wE kT g L3 R kT 2 Here, R ¼ RS for the spherical micelles. This equation is used to calculate the headgroup mixing free energy for globular aggregates and endcaps of rodlike aggregates, as well. For the cylindrical part of the rodlike micelles, with R ¼ RC , one gets [16] ð ð 0g Þmix;E 1 1 RþD UðrÞ 1 2r ¼ ð44Þ ðrÞ dr ¼ N L C E Eg wE kT g L3 R kT 2 For the nonuniform concentration model, using the radial concentration proﬁle given by Eqs. (39)–(41), the headgroup mixing free energy in spherical micelles is obtained to be [16] ð ð 0g Þmix;E 1 1 RþD UðrÞ 1 1 2 r ¼ 4 ðrÞ dr ¼ N E R wE 3 kT gL R kT 2 ð1 þ D=RÞ ð45Þ This equation is also used for the globular aggregates and the endcaps of spherocylinders, with R denoting the radius of the globular aggregate or of Copyright © 2003 by Taylor & Francis Group, LLC

the spherical endcaps. For the cylindrical part of the spherocylinders, with R ¼ RC , one gets [16] ð ð 0g Þmix;E 1 1 RþD UðrÞ ¼ ðrÞ 2r LC dr 3 gL R kT kT ð46Þ 1 R lnð1 þ D=RÞ ¼ NE R wE 2 D

10. Headgroup Deformation in Corona Region For the uniform concentration model, the elastic deformation of the segments is nonuniform along the length of the polymer molecule. An expression for this nonuniform deformation free energy of the polyoxyethylene chains in the corona region of the micelle is obtained by employing the approach of Semenov [46] mentioned earlier. One can calculate the free energy contribution arising from the headgroup deformation in the corona from the expression [16] ð 0g Þdef;E 3 L RS D ¼ kT 2 a Eg RS þD

ð47Þ

for spherical and globular micelles and the endcaps of rodlike micelle and from ð 0g Þdef;E 3 L RC D ¼ ln 1 þ ð48Þ 2 a Eg kT RC for the cylindrical part of the rodlike micelle. In the nonuniform concentration model, the polymer chain has been assumed to deform uniformly along the chain length. Using Flory’s [53] rubber elasticity theory to estimate the deformation free energy of a chain, one obtains " # ð 0g Þdef;E 1 D2 2 NE1=2 L 3 ð49Þ ¼ þ 2 NE L2 D kT which can be employed for all aggregate shapes.

11. Formation of Core–Corona Interface The interfacial free energy contribution ð 0g Þint is calculated using Eq. (24) but recognizing that agg is now diﬀerent from SW since the interface in these aggregates is that between a domain of surfactant tails and a solution of polyoxyethylene segments in water. agg is calculated using the Prigogine theory [59,60] for the surface tensions of solutions. This involves determining the surface phase composition ’S for a given bulk solution composition Copyright © 2003 by Taylor & Francis Group, LLC

by equating the chemical potentials of the surface and bulk phases. The surface phase composition, in turn, determines the interfacial tension. agg is thus dependent on the concentration of the polyoxyethylene segments in the micellar corona and the surfactant tail–polyoxyethylene interfacial tension SE in addition to the surfactant tail–water interfacial tension SW. In the uniform concentration model, the micellar corona has a bulk concentration ’Eg. Correspondingly, the concentration ’S of polymer segments at the interface is determined [16] by solving the implicit equation " # ðS =Eg Þ1=NE ð SE Þ 2=3 ln vS ¼ SW kT ð1 S Þ=ð1 Eg Þ 3 1 þ WE ½ð1 Eg Þ Eg WE ½ð1 S Þ S 4 2 ð50Þ Once ’S is determined, the interfacial tension agg is calculated [16] from the explicit equation ! 1 S NE 1 agg SW 2=3 ðS Eg Þ vS ¼ ln þ kT 1 Eg NE ð51Þ 1 S2 3 2 þ WE ð Þ ðEg Þ 2 4 The interfacial tension SE between polyoxyethylene and surfactant tails is calculated in terms of the surface tension S of the surfactant tails and the surface tension E of polyoxyethylene using the relation SE ¼ S þ E 2:0 ðS E Þ1=2

ð52Þ

The constant is taken to be ¼ 0:55 as for the surfactant tail–water system in Eq. (25) because of the polar nature of the polyoxyethylene group [47,48]. The surface tension S is calculated using Eq. (26). The surface tension of polyoxyethylene with EX oxyethylene units is estimated (in mN/m) on the basis of the information given in Ref. [61] using the equation E ¼ 42:5 19EX2=3 0:098ðT 298Þ

ð53Þ

where T is in 8K. For the nonuniform concentration model also, the free energy of formation of the core–corona interface is calculated using Eqs. (50) and (51), but with the concentration ’R replacing ’Eg in both equations. Copyright © 2003 by Taylor & Francis Group, LLC

B. Computational Approach The equation for the size distribution of aggregates, in conjunction with the geometrical characteristics of the aggregates and the expressions for the diﬀerent contributions to the free energy of micellization, allow one to calculate the various solution properties of the surfactant system. In Eq. (4) for the aggregate size distribution, ð0g Þ is the sum of various contributions: ð 0g Þ ¼ð 0g Þtr þð 0g Þdef þð 0g Þint þð 0g Þsteric þð 0g Þdipole þ ð 0g Þionic

ð54Þ

where the contribution ð0g Þdipole is included if the surfactant is zwitterionic, the contribution ð0g Þionic is included if the surfactant is ionic, and neither of the two contributions is relevant when the surfactant is nonionic. For surfactants with polyoxyethylene headgroups, one has to include the contributions ð0g Þmix;E and ð0g Þdef;E associated with the mixing and deformation of the headgroups in the corona of the aggregate. Explicit equations for calculating each of these contributions have been discussed above. Using them, the various surfactant solution properties are calculated as follows.

1. Calculations Using Complete Size Distribution An obvious and direct approach to calculating the aggregation behavior of surfactants is based on calculating the entire size distribution of aggregates as a function of the independent variables and then performing the necessary summations to obtain the CMC, average aggregate size, and the variance of the size distribution as described in Section II.C. In contrast to a typical experiment where the total surfactant concentration is ﬁxed and the aggregation behavior is determined, in doing the predictive calculations, it is convenient to calculate the size distribution at a speciﬁed value of the singly dispersed surfactant concentration X1 and then obtain the total surfactant P concentration by the summation, as Xtot ¼ X1 þ gXg .

2. Calculations Using the Maximum-Term Method The approach based on the calculation of the aggregate size distribution is not complicated but is time-consuming. Instead, a simpler approach based on the maximum-term method [62] is employed in our calculations as described below. The simpler approach is built on the recognition that for spherical or globular micelles and spherical bilayer vesicles, the size dispersion is usually narrow. The concentrations of aggregates other than that corresponding to the maximum in the size distribution are relatively small. Because the average properties of the solution are strongly inﬂuenced by the Copyright © 2003 by Taylor & Francis Group, LLC

species present in the largest amount, the number average aggregation number gn can be taken as the value of g for which the number concentration Xg of the aggregates is a maximum (¼ XgM ) , and the weight average aggregation number gw can be taken as the value of g for which the weight concentration gXg of the aggregates is a maximum ½¼ ðgXg ÞM . These average aggregation numbers are very close to one another and are practically the same as those obtained by calculating the size distribution of aggregates [62]. As mentioned before, only the aggregation number g is the independent variable in the case of spherical or globular micelles; the aggregation number g as well as the inner and outer layer thicknesses ti and to are independent variables in the case of spherical vesicles. Further, for polyoxyethylene surfactants, one has to include the corona thickness D as an additional independent variable. One can obtain quantitative estimates of the variance of the size distribution, also by the maximum-term method. Approximating the derivatives in Eq. (9) by diﬀerences, we can write ðwÞ 2 @ ln g ln gw ¼ P w ¼ @ gXg lnðgXg ÞM gw ðnÞ 2 @ ln gn ln gn P ¼ ¼ @ ln gXg lnðgn XgM Þ gn

ð55Þ

In the above equation, the average aggregation numbers gn and gw are P taken gXg is as those corresponding to the maximum in Xg or (gXg), the sum approximated by the maximum term gn XgM or ðgXg ÞM , and the derivatives have been replaced by the diﬀerence terms denoted by the symbol . One can determine the maximum in Xg (or in gXg) for two slightly diﬀerent values of X1 and the two sets of values for gn and XgM or gw and (gXg)M can be introduced in Eq. (55) to calculate the variance in the size distribution. The CMC is estimated by plotting any one of the variables [X1 , XgM , ðgXg ÞM , gn;app , gw;app ] as a function of the total surfactant concentration Xtot and determining the surfactant concentration at which the plotted variable displays a sharp transition in values. It can also be calculated as the value of X1 for which the amount of surfactant in the micellized form P is equal to that in the singly dispersed form, namely XCMC ¼ X1 ¼ gXg ¼ gn XgM ¼ ðgXg ÞM . The predicted average aggregation numbers reported in this chapter correspond to those at the CMC, unless otherwise stated.

3. Calculations for Rodlike Micelles In the case of rodlike micelles, the size distribution Xg [Eq. (12)] is monotonic and does not have a maximum. In this case, by minimizing ð0cyl Þ for Copyright © 2003 by Taylor & Francis Group, LLC

an inﬁnitely long cylinder, the equilibrium radius RC of the cylindrical part of the micelle is determined. Given the radius of the cylindrical part, the number of molecules gcap in the spherical endcaps is found to be that value which minimizes ð0cap Þ. Given gcap, ð0cyl Þ, and ð0cap Þ, the sphere-torod transition parameter K is calculated from Eq. (12), the average aggregation numbers at any total surfactant concentration from Eq. (16), and the CMC from Eq. (17). For polyoxyethylene surfactants, one has to include the corona thickness D as an additional independent variable, and the equilibrium value of D is determined for the cylindrical middle part and the spherical endcaps via the minimizations of ð0cyl Þ and ð0cap Þ, respectively. The search for the parameter values that maximize the aggregate concentration Xg (or gXg) or minimize the standard free energy diﬀerences ð0cyl Þ and ð0cap Þ was carried out using the IMSL (International Mathematical and Statistical Library) subroutine ZXMWD. This subroutine is designed to search for the global extremum of a function of many independent variables subject to any speciﬁed constraints on the variables. This subroutine has been used for all the calculations described in this chapter.

C. Estimation of Molecular Constants For illustrative purposes, calculations have been carried out for a number of nonionic, zwitterionic, and ionic surfactants. Examples of molecules employed in these calculations are shown in Fig. 2. The molecular constants associated with the surfactant tail are the volume vS and the extended length ‘S of the tail. For the headgroup, one needs the cross-sectional area ap for all types of headgroups, the distance from the core surface where the counterion is located in the case of ionic headgroups, the dipole length d, and the distance from the core surface at which the dipole is located, in the case of a zwitterionic headgroup. All these molecular constants can be estimated from the chemical structure of the surfactant molecule. There are no free parameters, and the calculations are therefore completely predictive in nature. Some examples of how the molecular constants are estimated are given below. The molecular constants characterizing the headgroups of surfactants considered in this chapter are listed in Table 3.

1. Estimation of Tail Volume vS The molecular volume vS of the surfactant tail containing nC carbon atoms is calculated from the group contributions of (nC 1) methylene groups and the terminal methyl group vS ¼ vðCH3 Þ þ ðnC 1ÞvðCH2 Þ Copyright © 2003 by Taylor & Francis Group, LLC

ð56Þ

FIG. 2 Chemical structure of surfactant molecules considered in this chapter and the symbols used to refer to them in the text. Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 3 Molecular Constants for Surfactant Headgroups Surfactant headgroup -Glucoside Methyl sulfoxide Dimethyl phosphene oxide -Maltoside N-methyl glucamine Sodium sulfate Sodium sulfonate Potassium carboxylate Sodium carboxylate Pyridinium bromide Trimethyl ammonium bromide N-betaine Lecithin

ap (nm2 )

ao (nm2 )

(nm)

d (nm)

0.40 0.39 0.48 0.43 0.34 0.17 0.17 0.11 0.11 0.34 0.54 0.30 0.45

0.21 0.21 0.21 0.21 0.21 0.17 0.17 0.11 0.11 0.21 0.21 0.21 0.42

— — — — — 0.545 0.385 0.60 0.555 0.22 0.345 0.07 0.65

— — — — — — — — — — — 0.5 0.62

These group molecular volumes, estimated from the density versus temperature data available for aliphatic hydrocarbons, are given [16] by the expressions vðCH3 Þ ¼ 0:0546 þ 1:24 104 ðT 298Þ nm3 vðCH2 Þ ¼ 0:0269 þ 1:46 105 ðT 298Þ nm3

ð57Þ

where T is in 8K. For double-tailed surfactants, vS is calculated by accounting for both the tails. For the ﬂuorocarbon tails, using the data available [63–65] for 25oC, we estimate that vðCF3 Þ ¼ 1:67vðCH3 Þ and vðCF2 Þ ¼ 1:44vðCH2 Þ. Extensive volumetric data are not yet available to estimate the temperature dependence of the molecular volumes of CF3 and CF2 groups. As an approximate estimation, the ratio between the volumes of the ﬂuorocarbon and the hydrocarbon groups is assumed to be the same at all temperatures.

2. Estimation of Extended Tail Length ‘S

The extended length of the surfactant tail ‘S at 2988K is calculated using a group contribution of 0.1265 nm for the methylene group and 0.2765 nm for the methyl group [1]. Given the small volumetric expansion of the surfactant tail over the range of temperatures of interest, the extended tail length ‘S is considered as temperature-independent. Therefore, the small volumetric expansion of the surfactant tail is accounted for by small increases in the cross-sectional area of the surfactant tail. The extended length of the ﬂuorocarbon chain is estimated using the same group contributions as for hydroCopyright © 2003 by Taylor & Francis Group, LLC

carbon tails, namely, 0.1265 nm for the CF2 group and 0.2765 nm for the CF3 group.

3. Estimation of Headgroup Area ap The headgroup area ap is calculated as the cross-sectional area of the headgroup near the hydrophobic core-water interface. The glucoside headgroup in -glucosides has a compact ring structure [5] with an approximate diameter of 0.7 nm, and hence, the eﬀective cross-sectional area of the polar headgroup ap is estimated as 0.40 nm2. For sodium alkyl sulfates, the crosssectional area of the polar group ap has been estimated to be 0.17 nm2. For the zwitterionic N-betaine headgroup, ap has been estimated to be 0.30 nm2. The area per molecule a0 of the micellar core that is shielded by the headgroup from having contact with water, is the smaller of ap or L2, as discussed earlier.

4. Estimation of and d

For ionic surfactants, the molecular constant depends on the size of the ionic headgroup, the size of the hydrated counterion, and also the proximity of the counterion to the charge on the surfactant ion. Visualizing that the sodium counterion is placed on top of the sulfate anion, we estimate ¼ 0:545 nm for sodium alkyl sulfates and 0.385 nm for sodium alkyl sulfonates. For alkyl pyridinium bromide the surfactant cation can approach very near the hydrophobic core, and we estimate = 0.22 nm. For zwitterionic surfactants we need the molecular constant d, which is the distance of separation of the charges on the dipole (or the dipole length), and also the constant , which is the distance from the hydrophobic core surface at which the dipole is located. The computations in this chapter are based on an estimate of d ¼ 0:5 nm and ¼ 0:07 nm, for N-alkyl betaines, and d ¼ 0:62 nm and ¼ 0:65 nm, for the lecithin headgroup.

5. Estimation of WE For nonionic surfactants with a polyoxyethylene headgroup, we need the polyoxyethylene–water interaction parameter WE. This can, in principle, be estimated using the thermodynamic properties of polyoxyethylene–water solutions (such as the activity data or the phase behavior data). The activity data [54] represented in the framework of the Flory–Huggins theory indicate that WE is dependent on the composition of the polymer solution (55). The phase behavior exhibits both a lower critical solution temperature and an upper critical solution temperature [54–56] indicating that WE ﬁrst increases and then decreases with increasing temperature. Further, the headgroup of the surfactant contains a functional group (such as a hydroxyl) that terminates the polymer chain; the presence of this terminal group may also aﬀect the value of WE when compared to the estimate based on highCopyright © 2003 by Taylor & Francis Group, LLC

molecular-weight polyoxyethylenes. The dependence of WE on polymer concentration, temperature, polymer molecular weight, and the terminating functional group is, however, not known. Because water is a good solvent for polyoxyethylene, values for WE smaller than 0.5, namely WE ¼ 0:1 and 0.3, have been chosen for the illustrative calculations.

D. Illustrative Predictions for Surfactants 1. Inﬂuence of Free Energy Contributions on Aggregation Behavior Figure 3 presents the calculated free energy contributions ð0g Þ expressed per molecule of surfactant, for cetyl pyridinium bromide in water, as a function of the aggregation number g. Whereas the magnitude of ð0g Þ

FIG. 3 Contributions to the standard free energy diﬀerence between a surfactant molecule in the micellized state and one in the singly dispersed state calculated as a function of the aggregation number g of the micelle for cetyl pyridinium bromide in water at 258C. Subscripts refer to the following: total (total of all contributions), transfer (transfer free energy of tails), deform (deformation free energy of tails), interface (interfacial free energy), steric (headgroup steric interactions), and ionic (headgroup ionic interactions). Refer to text for detailed discussion. Copyright © 2003 by Taylor & Francis Group, LLC

inﬂuences the CMC, the functional dependence of ð0g Þ on g determines the shape and size of the equilibrium aggregates. Of all the contributions to ð0g Þ, only the transfer free energy of the surfactant tail is negative. Therefore, it is responsible for the aggregated state of the surfactant being favored over the singly dispersed state. The transfer free energy contribution is a constant independent of the micellar size and hence has no inﬂuence on the structural characteristics of the equilibrium aggregate. All the remaining free energy contributions to ð0g Þ are positive and depend on the aggregate size. It is clear from the geometrical relations for aggregates (see Table 1) that as the aggregation number g increases, the area per molecule a decreases. Consequently, the free energy of formation of the aggregate core–water interface decreases with increasing aggregation number. This free energy is thus responsible for the growth of aggregates to large sizes and is said to provide the positive cooperativity of aggregation. All remaining free energy contributions (namely, the surfactant tail deformation energy, the steric repulsions between the headgroups, the dipole–dipole interactions between zwitterionic headgroups, and the ionic interactions between ionic headgroups) increase with increasing aggregation number. These free energy contributions thus provide the negative cooperativity of aggregation and are responsible for limiting the aggregate growth to ﬁnite sizes. All the free energy contributions aﬀect, however, the magnitude of the CMC. The calculated size distributions for cetyl pyridinium bromide are presented in Fig. 4 for two values of the molar concentration C1 ð¼ 55:55X1 Þ of the singly dispersed surfactant. As expected, near the CMC, a small variation in C1 gives rise to a large variation in the total aggregate concentration, Ctot. The average aggregation number is, however, practically the same at these two concentrations. This implies [see Eq. (9)] that the size dispersion of the aggregates is narrow, which can be seen also from the ﬁgure. Various size-dependent solution properties calculated using the model are plotted in Fig. 5 as a function of the total concentration of cetyl pyridinium bromide in water. The concentration at which any one of these properties shows a sharp change in behavior can be taken as the CMC. All four properties plotted in the ﬁgure yield CMC values that are very close to one another.

2. Inﬂuence of Tail Groups and Headgroups on Aggregation Behavior The CMC values predicted at 258C, for nonionic alkyl -glucosides, zwitterionic N-alkyl betaines, and ionic alkyl sodium sulfates are presented in Fig. 6 as a function of the length of the surfactant tail. The CMC decreases with an increase in the chain length of the surfactant, as a consequence of the increase in the magnitude of the tail transfer free energy. The incremental variation in CMC is roughly constant for a given homologous family of surfactants. The Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Calculated size distribution of cetyl pyridinium bromide aggregates in water at 258C at two values of the total surfactant concentration Ctot and the singly dispersed surfactant concentration C1. (a) C1 ¼ 0:54 mM and Ctot ¼ 0:68 mM; (b) C1 ¼ 0:57 mM and Ctot ¼ 5:89 mM.

experimentally measured CMCs [66–71] are in reasonable agreement with the predicted values. For a given surfactant tail length, the CMC is smaller for a nonionic surfactant than for an anionic surfactant. This is a consequence of the strong repulsive interaction between ionic headgroups compared to the weaker steric interactions between nonionic headgroups. The predicted average aggregation numbers at the CMC are plotted as a function of the tail length in Fig. 7 for some zwitterionic and anionic surfactants. For the cases considered, the micelles are spherical or globular and are narrowly dispersed in size. For the zwitterionic alkyl N-betaines, the predicted aggregation numbers are in reasonable agreement with the measured values [70,71]. The aggregation number increases with an increase in the chain length of the surfactant tail. The equilibrium area per molecule of the aggregate changes with a change in the tail length, but the range of values assumed by a is small. Consequently, given an equilibrium area per molecule, Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Calculated size-dependent solution properties of cetyl pyridinium bromide in water as a function of the total surfactant concentration (expressed as mole fraction). gw,app is the apparent weight average aggregation number, gn,app is the apparent number P average aggregation number, X1 denotes the monomer concentration, and gXg is the total concentration of the surfactant in the form of aggregates. All concentrations are expressed in mole fraction units.

the aggregation number of a spherical or globular micelle must increase with increasing tail length, as dictated by the geometrical relations. For anionic sodium alkyl sulfates with chain lengths smaller than dodecyl, a large number of experimental data have been reported in the literature [72–75], from which we select for plotting in Fig. 7 those that show the largest deviation from the predicted values. For tetradecyl and hexadecyl chains, aggregation numbers mentioned in Ref. [76] have been plotted, although in the work of Tartar [72], which is cited as the source of these experimental data, no report of these experimental aggregation numbers is found; therefore, the reported aggregation numbers for these two surfactants should be discounted. For alkyl sulfates the predicted aggregation numbers do not show a signiﬁcant increase Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 6 Dependence of the critical micelle concentration on the number of carbon atoms in the surfactant tail for nonionic alkyl -glucosides (triangles), zwitterionic N-alkyl betaines (circles), and anionic sodium alkyl sulfates (squares). The lines represent the theoretical predictions while the points are experimental data. (From Refs. 66–71.)

with increasing length of the surfactant tail and remain practically constant for the longer tail lengths. These results can be understood by noting that the CMC for the surfactant with the smaller tail length is large, and for this reason the ionic strength is larger. This decreases the headgroup ionic repulsion, thus leading to a smaller equilibrium area per molecule in the aggregate. In contrast, for surfactants with longer tail lengths, the CMCs are low, the ionic strengths smaller, and hence, the equilibrium area per molecule in the aggregate larger. This increase in the equilibrium area per molecule with increasing tail length is responsible for the relatively small changes in the aggregation number with increasing tail length, in contrast to the behavior exhibited by the zwitterionic surfactant.

3. Inﬂuence of Ionic Strength on Aggregation Behavior The headgroup ionic interactions at the micelle surface are weakened by the addition of salt to the surfactant solution. Figures 8 and 9 present the predicted dependence of the CMC (Figure 8) and the average aggregation number (Figure 9) of sodium dodecyl sulfate, on the amount of added NaCl Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 7 Dependence of the weight average aggregation number of micelles at the CMC, on the chain length of the surfactant tail for sodium alkyl sulfates (squares) and N-alkyl betaines (circles). The points are experimental data. (From Refs. 70–76.) The dotted line shows predicted values for sodium alkyl sulfates while the continuous line describes the predictions for N-alkyl betaines. See text for comments about the reported experimental aggregation numbers for sodium alkyl sulfates with C14 and C16 surfactant tails.

electrolyte. For the range of ionic strengths considered, only narrowly dispersed spherical or globular micelles are formed. With decreasing ionic repulsion between the headgroups, the predicted CMC decreases and the average aggregation number of the micelle increases, in satisfactory agreement with experimental measurements (74,75).

4. Inﬂuence of Temperature on Aggregation Behavior The temperature dependence of the CMC and the average aggregation number of the micelle have been calculated for a number of surfactants. Figure 10 compares the predicted CMC values with the experimental data [70,71] for the zwitterionic surfactants N-alkyl betaines for three diﬀerent alkyl chain lengths. In Fig. 11, the predicted CMCs of the anionic sodium dodecyl sulfate have been plotted for two diﬀerent concentrations of added NaCl electrolyte and compared with experimental data [77]. Calculated and experimental [78] CMCs are presented in Fig. 12 for the homologous family of sodium alkyl sulfonates. In all cases, the predictions show reasonable Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 8 Inﬂuence of added NaCl concentration on the CMC of sodium dodecyl sulfate micelles. The lines denote the predicted values while the points are the experimental measurements at 258C. (From Refs. 74 and 75.)

FIG. 9 Inﬂuence of added NaCl concentration on the average aggregation number of sodium dodecyl sulfate micelles. The lines denote the predicted values while the points are the experimental measurements at 258C. (From Refs. 74 and 75.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10 The dependence of CMC on temperature for N-alkyl betaines having C10, C11 and C12 chains as surfactant tails. The lines are predictions of the present theory while the points are experimental data. (From Refs. 70 and 71.)

FIG. 11 The dependence of CMC on temperature for sodium dodecyl sulfate in water and in a 0.0125M solution of NaCl. The lines are predictions of the present theory while the points are experimental data. (From Ref. 77.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 12 The dependence of CMC on temperature for sodium alkyl sulfonates having C10, C12, and C14 chains as surfactant tails. The lines are predictions of the present theory while the points are experimental data. (From Ref. 78.)

agreement with experiment. One may note that the experiment indicates some increase in the CMC as the temperature is decreased below about 258C, while the predicted values show a monotonic decrease of the CMC with decreasing temperature. It has been suggested [5] that the hydration state of the ionic headgroup in the micelles may be diﬀerent from that in the singly dispersed state as the temperature is lowered below 258C. A free energy contribution accounting for such an eﬀect is not included in the theory since it cannot be calculated with any precision at the present time.

5. Transition from Spherical to Rodlike Micelles The predicted results for nonionic alkyl -glucosides indicate that large, polydispersed rodlike micelles form. For octyl glucoside the aggregation numbers are still not very large, but for longer chain lengths very large rods form. The predicted weight average aggregation number is used to compute the hydrodynamic radius of the micelles using the expression RH ¼

3 gw vS 1=3 þ ‘p 4

Copyright © 2003 by Taylor & Francis Group, LLC

ð58Þ

where ‘p is the length of the polar headgroup. For the ring structure of the -glucoside, ‘p has been estimated [5] to be 0.7 nm. The computed hydrodynamic radius as a function of surfactant concentration is presented in Fig.13. The two predicted lines correspond to two marginally diﬀerent values of the parameter ap describing the headgroup of the surfactant. One may note from Eq. (12) that the sphere-to-rod transition parameter K [which determines gw as per Eq. (16)] can be dramatically altered by small changes in the free energy diﬀerence ð0cap Þ ð0cyl Þ, since gcap, which appears in the deﬁnition of K, is quite large. For example, assuming a typical value of 90 for gcap, a small change of 0.05 kT in the free energy diﬀerence ð0cap Þ ð0cyl Þ will cause a change in K of e4:5 ¼ 90, which, in turn, can change the predicted value for gw by a factor of about 10. Therefore, the predicted average aggregation numbers are very sensitive even to small changes in

FIG. 13 The dependence of the micellar size (expressed as the hydrodynamic radius) on the concentration of the surfactant for octyl glucoside. Both lines correspond to predicted values but for marginally diﬀerent values of the molecular con 2 line corresponds to a ¼ 40A while the dotted line stant ap. The continuous p corresponds to ap ¼ 39A 2 . The squares denote the reported experimental data. (From Ref. 68.) The circles correspond to modiﬁed experimental data if the reported hydrodynamic radius had included one layer of water. See text for discussion. Copyright © 2003 by Taylor & Francis Group, LLC

the free energy estimates when rodlike micelles form. This is illustrated by the calculations carried out for two slightly diﬀerent values of the parameter ap, which aﬀects the magnitude of the headgroup steric interaction energy. The predictions are compared with the data provided by dynamic light scattering measurements [68]. It is not clear whether the reported hydrodynamic radii correspond to the dry or hydrated aggregates. Therefore, both the reported hydrodynamic radii and the radii obtained by subtracting the diameter of a water molecule are plotted in Fig. 13. Given the sensitivity of K to the free energy estimates, the agreement between the measured and predicted aggregate sizes is satisfactory. For anionic sodium alkyl sulfates with NaCl as the added electrolyte, an increase in ionic strength beyond that in Fig. 9 is expected to contribute to a transition from globular micelles to large spherocylindrical micelles. As already noted, the ability to predict ln K with deviations of about 4.5 or less from the measurements can be considered satisfactory. The predicted values for the sphere-to-rod transition parameter K for sodium dodecyl sulfate are plotted in Fig. 14 against the added concentration of NaCl as the electrolyte

FIG. 14 The dependence of the sphere-to-rod transition parameter K for sodium dodecyl sulfate on the concentration of added electrolyte NaCl. The points are from light scattering measurements (from Ref. 50) and the line represents the predictions, both at 258C. Copyright © 2003 by Taylor & Francis Group, LLC

and are compared with light scattering measurements [79]. The largest deviation between predicted and experimental value of ‘nK is about 2, at the highest ionic strength. The predicted radius of the cylindrical part of the aggregate is smaller than the fully extended length of the surfactant tail. It increases from 1.45 nm to 1.49 nm as the electrolyte concentration is increased from 0.45 M to 1.25 M at 258C. For this range of ionic strengths, the radius of the endcaps remains unaltered and is equal to the extended length of the surfactant tail. The predicted CMC, as deﬁned by Eq. (17), decreases from 0.38 mM to 0.204 mM over this range of added salt concentration. The temperature dependence of the parameter K has been calculated for sodium dodecyl sulfate for two concentrations of the added NaCl electrolyte. The predicted values of K are plotted in Fig. 15 along with the experimental estimates based on dynamic light scattering measurements [79]. The largest deviation in ‘nK is about 4.5, and the theory predicts a somewhat stronger dependence on the temperature than that observed experimentally. Figure 16 presents the predicted values of K as a function of the added electrolyte concentration for the homologous family of sodium alkyl sulfates

FIG. 15 Inﬂuence of temperature on the sphere-to-rod transition parameter K of sodium dodecyl sulfate in solutions containing 0.45M and 0.80M added NaCl electrolyte. The lines denote the predicted values while the points are experimental data. (From Ref. 79.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 16 The dependence of the sphere-to-rod transition parameter K on the surfactant tail length and on the concentration of added electrolyte NaCl for sodium alkyl sulfates. The lines are predictions obtained from the present theory while the points denote the experimental data (from Ref. 79), both at 308C. The predicted lines are labeled with the surfactant tail lengths, and the corresponding experimental data are indicated by circles, squares, triangles, and diamonds, respectively.

with 10 to 13 carbon atoms in their hydrophobic tails. The ﬁgure shows that even the largest deviation in ln K between the predicted and the experimental values [79] is smaller than 2 for C11, C12, and C13 sodium sulfates and is about 4 for the C10 sodium sulfate. Given the sensitivity of the parameter K to the free energy estimates, the ability of the theory to predict K accurately as a function of the ionic strength, temperature, and tail length for sodium alkyl sulfates is remarkable. However, when the calculations are repeated for alkyl sulfates with other counterions such as Li, K, etc., the predicted K values signiﬁcantly deviate from the measurements [79]. As mentioned before, this is not surprising given the sensitivity of K. In contrast, the prediction of the CMC and micelle size is quite satisfactory in the presence of various counterions, when only spherical or globular micelles form. Therefore, improved accounting of the counterion eﬀects beyond what is considered in the approximate analytical solution to the Poisson–Boltzmann equation is necessary for predicting accurate values of K. Such treatment of counterion eﬀects remains to be developed. Copyright © 2003 by Taylor & Francis Group, LLC

6. Formation of Bilayer Vesicles The aggregation behavior of the anionic dialkyl sodium sulfate at an ionic strength of 0.01 M has been calculated. Because of the presence of two tails, these surfactants can form spherical vesicular structures provided the length of the surfactant tail is large enough and the ionic strength is not too small. The predicted aggregation number, the inner and the outer radii, the thicknesses of the inner and the outer layer, the numbers of molecules of surfactant present in the two layers, and the CMC are all listed in Table 4. The inner and the outer layers diﬀer somewhat in thicknesses, with the inner layer more compressed than the outer. The thicknesses are much smaller than the extended lengths of the tails and are also smaller than the radii of spherical and cylindrical micelles formed of single-tailed sodium alkyl sulfates, discussed before. The equilibrium areas per surfactant molecule are substantially diﬀerent from one another for the molecules in the two layers. The vesicles are not too large and the aggregation number increases with increasing chain length of the surfactant. As one may anticipate, the CMC is small because of the larger magnitude of the tail transfer free energy in case of the dialkyl tail. Calculated results for dialkyl lecithins with phosphotidylcholine headgroup are also presented in Table 4 for alkyl chain lengths varying from 12 to 18. The vesicles formed of lecithins also have inner and outer layers of diﬀering thicknesses. However, the radii of the lecithin vesicles and, hence,

TABLE 4 Ri (nm)

Predicted Structural Properties of Vesicles ti (nm)

to (nm)

ai (nm2)

ao (nm)

gi

go

Xcmc

di-Cn SO4 Na þ 0:01M NaCl 12 4.63 6.68 0.98 14 5.30 7.57 1.09 16 5.83 8.31 1.20 18 6.36 9.04 1.30

1.07 1.08 1.28 1.38

0.5825 0.6065 0.627 0.646

0.771 0.805 0.836 0.865

462 580 684 787

727 893 1041 1185

7:67 108 1:07 109 1:46 1011 1:92 1013

di-Cn -lecithin 12 20.90 22.67 14 20.11 22.09 16 19.61 21.80 18 19.30 21.70

0.92 1.03 1.14 1.25

0.796 0.813 0.828 0.842

0.794 0.82 0.845 0.869

6929 6260 5855 5577

8163 7490 7086 6822

1:58 109 2:01 1011 2:49 1013 3:04 1015

nC

Ro (nm)

0.846 0.95 1.05 1.15

Note: i refers to the inner layer of the bilayer and o to the outer layer, R is the radius at the hydrophobic domain–water interface, t is the layer thickness, a is the area per surfactant molecule, and g is the number of surfactant molecules.

Copyright © 2003 by Taylor & Francis Group, LLC

the aggregation numbers are much larger than those formed of dialkyl sodium sulfates. Consequently, the areas per molecule in the inner and outer layers are closer to one another. The vesicle radius deceases slightly with an increase in the chain length of the surfactant. The diﬀerences between the two types of molecules can be traced to the decrease in the headgroup repulsions in the case of the zwitterionic lecithin headgroups compared to that in the case of anionic sodium sulfate headgroups. In all cases listed in Table 4, the aggregates are narrowly dispersed.

7. Inﬂuence of Polyoxyethylene Headgroups The predicted CMC values for a surfactant C12Ex with dodecyl hydrocarbon tail and 6 to 53 oxyethylene units are presented in Fig. 17 for both the uniform concentration model and the nonuniform concentration model

FIG. 17 Dependence of the CMC on the length of the polyoxyethylene headgroup of nonionic surfactants C12Ex. The points refer to measured values while the lines denote predictions from the present model, both at 258C. The continuous lines represent the results from the nonuniform concentration model while the dotted lines denote the predictions based on the uniform concentration model. Calculated results are shown for two diﬀerent values of the polyoxyethylene–water interaction parameter WE . The circles refer to commercial polyoxyethylene glycol ethers (from Refs. 81–84), triangles represent commercial samples where the distribution of oxyethylene chain lengths is reduced by molecular distillation (from Ref. 85), and squares correspond to puriﬁed polyoxyethylene methyl ethers (from Ref. 86). Copyright © 2003 by Taylor & Francis Group, LLC

and for WE ¼ 0:1 and 0.3. As mentioned before in Section IV.A.8, the uniform concentration model may be appropriate for small values of Ex and the nonuniform concentration model may be more suitable for larger Ex. The experimental data used for comparison are for polyoxyethylene glycol ethers [80–85] and polyoxyethylene methyl ethers [86]. The considerable scatter in the measured CMCs is a consequence of the heterogeneity of some of the surfactant samples that have been used, the samples containing a range of polyoxyethylene chain lengths distributed around the reported mean value. Figure 18 presents the predicted as well as measured CMC data for a surfactant C16Ex with a hexadecyl hydrocarbon tail and 8 to 63 oxyethylene units. The experimental data are for polyoxyethylene glycol ethers [87–90] and polyoxyethylene methyl ethers [86]. The smaller scatter in the experimental data of Fig. 18 compared to that of Fig. 17, is primarily due to the fewer measurements available for the C16Ex surfactants.

FIG. 18 Dependence of the CMC on the length of the polyoxyethylene headgroup of nonionic surfactants C16Ex. The points refer to measured values while the lines denote predictions from the present model, both at 258C. The continuous lines represent the results from the nonuniform concentration model while the dotted lines denote the predictions based on the uniform concentration model. Calculated results are shown for two diﬀerent values of the polyoxyethylene-water interaction parameter WE . Circles denote polyoxyethylene glycol ethers (from Refs. 87–90) while the squares represent puriﬁed polyoxyethylene methyl ethers (from Ref. 86). Copyright © 2003 by Taylor & Francis Group, LLC

The predicted aggregation numbers based on the nonuniform concentration model are plotted in Figs. 19 and 20 for C12Ex and C16Ex surfactants, respectively. Measured aggregation numbers [81,87–90] are also included for comparison. The calculated aggregation numbers are in qualitative agreement with the experimental values. The predicted aggregation numbers are larger when a larger value is taken for WE. The agreement between the predicted and measured aggregation numbers is satisfactory even from a quantitative point of view. The predicted thickness D of the micellar corona region is plotted in Figs. 21 and 22, respectively, for the C12Ex and C16Ex surfactants, on the basis of the non-uniform concentration model. The experimental shell thicknesses are those estimated by Tanford et al. [91] from intrinsic viscosity measurements [87–90]. As expected, the shell thickness D calculated assuming a smaller value for WE ð¼ 0:1, implying a better solvent) is larger than that based on a larger value (=0.3, implying a relatively poorer solvent). The predicted aggregation numbers based on the uniform concentration model are presented in Figs. 23 and 24 for C12Ex and C16Ex surfactants. The

FIG. 19 Inﬂuence of the polyoxyethylene headgroup size on the average aggregation number of micelles for surfactants with dodecyl hydrophobic tail. The points are experimental data at 258C (from Refs. 80 and 87-90) and the lines represent the predictions of the present theory. The calculated results are based on the nonuniform concentration model. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 20 Inﬂuence of the polyoxyethylene headgroup size on the average aggregation number of micelles for surfactants with hexadecyl hydrophobic tail. The points are experimental data at 258C (from Refs. 80 and 87–90) and the lines represent the predictions of the present theory. The calculated results are based on the nonuniform concentration model.

FIG. 21 Inﬂuence of the polyoxyethylene headgroup size on the shell thickness of the micelles for the C12Ex surfactants. The points are experimental data at 258C (from Ref. 91), and the lines represent the predictions of the present theory. The calculated results are based on the nonuniform concentration model. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 22 Inﬂuence of the polyoxyethylene headgroup size on the shell thickness of the micelles for the C16Ex surfactants. The points are experimental data at 258C (from Ref. 91), and the lines represent the predictions of the present theory. The calculated results are based on the nonuniform concentration model.

predicted shell thicknesses based on the uniform concentration model are presented in Figs. 25 and 26 for C12Ex and C16Ex surfactants. The predicted dependence of the micelle aggregation numbers on the polyoxyethylene chain length is in reasonable agreement with the experimental data, but the calculated aggregation numbers are smaller than the experimental values. Figures 25 and 26 show that the model predicts much smaller values for the corona thickness D than that estimated from intrinsic viscosity measurements [91]. The temperature dependence of the aggregation behavior of surfactants with polyoxyethylene headgroups is expected to diﬀer from that of ionic and zwitterionic surfactants because of the way the interactions between polyoxyethylene headgroups depend on temperature. For ionic and zwitterionic surfactants, the various contributions to the free energy of micellization display a temperature dependence that leads to a lowering of the aggregation number with increasing temperature. These temperature-dependent eﬀects are, however, overshadowed by the temperature-dependent WE, which governs the interactions between the polyoxyethylene headgroups and water in the micellar shell region. As suggested by the observed phase behavior of the polyoxyethylene–water systems [54–56], the interaction Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 23 Inﬂuence of the polyoxyethylene headgroup size on the average aggregation number of micelles. The surfactants contain dodecyl hydrophobic tails. The points are experimental data at 258C (from Refs. 80 and 87–90), and the lines represent the predictions of the present theory. The calculated results are based on the uniform concentration model.

FIG. 24 Inﬂuence of the polyoxyethylene headgroup size on the average aggregation number of micelles. The surfactants contain hexadecyl hydrophobic tails. The points are experimental data at 258C (from Refs. 80 amd 87–90), and the lines represent the predictions of the present theory. The calculated results are based on the uniform concentration model. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 25 Inﬂuence of the polyoxyethylene headgroup size on the thickness of the micellar shell for the C12Ex surfactants. The points are experimental data at 258C (91) and the lines represent the predictions of the present theory. The calculated results are based on the uniform concentration model.

FIG. 26 Inﬂuence of the polyoxyethylene headgroup size on the thickness of the micellar shell for the C16Ex. surfactants. The points are experimental data at 258C (from Ref. 91), and the lines represent the predictions of the present theory. The calculated results are based on the uniform concentration model. Copyright © 2003 by Taylor & Francis Group, LLC

parameter WE ﬁrst increases as the temperature is increased (giving rise to the lower critical solution temperature, LCST), passes through a maximum, and then decreases with increasing temperature (giving rise to the upper critical solution temperature, UCST). Thus, for temperatures smaller than the LCST (which is the temperature range for which the aggregation behavior is examined), the interaction parameter WE should increase with increasing temperature. The calculations presented above show that the aggregation numbers increase with increasing WE if none of the other variables is changed (Figs. 19 and 20 or 23 and 24). Consequently, for polyoxyethylene surfactants, the headgroup interactions with water promote aggregate growth with increasing temperature. The remaining free energy contributions favor a decrease in the aggregation number with increasing temperature. It is interesting to note that an increase in WE with increasing temperature promotes both the phase separation of the polymer solution (LCST) and also the growth of the micelles to large aggregation numbers [92,93]. The calculated results show that for nonionic surfactants with polyoxyethylene headgroups, the predictions from the nonuniform concentration model are in somewhat better agreement with experiments than those from the uniform concentration model. However, improved agreement between predicted and experimental micellar properties should await a more satisfactory treatment of polyoxyethylene–water solutions than presently available. Alternately, a modiﬁed treatment of headgroup interactions, considering the headgroups to be oligomers rather than polymers, is necessary. It is important that the general validity of any model for nonionic polyoxyethylene surfactants be tested by comparing experimental and predicted results for all the micellar characteristics, namely the CMC, the aggregation number, and the shell thickness over an extended range of polyoxyethylene chain lengths. Although these surfactants are among the most commonly used in practical applications, a comprehensive prediction of their solution properties remain to be developed despite many papers that have appeared in the literature.

V. THEORY OF MICELLIZATION OF SURFACTANT MIXTURES A. Size and Composition Distribution of Micelles The thermodynamic treatment and illustrative calculations presented in this section focus on binary mixtures of surfactants for which many experimental results are available. The approach, however, can be readily extended to a mixture of three or more surfactants. A molecular theory of mixed micelles Copyright © 2003 by Taylor & Francis Group, LLC

was ﬁrst proposed in our earlier work [94], which was later improved by incorporating a better treatment of molecular packing in mixed micelles [95]. This latter model constitutes the basis of this section. We consider a solution of surfactant molecules A and B and denote by g the aggregation number of the mixed micelle containing gA molecules of A and gB molecules of B. At equilibrium, in analogy with Eq. (4), one obtains [94–96] for the aggregate size and composition distribution, the equation ! ! ! 0g gA 01A gB 01B g0g g0g gA gB Xg ¼ X1A X1B exp ; ¼ kT kT kT ð59Þ Here, 0g is the standard chemical potential of the mixed micelle, while 01A and 01B are the standard chemical potentials of the singly dispersed A and B molecules, respectively; 0g is the diﬀerence in the standard chemical potentials between gA =g molecules of surfactant A plus gB =g molecules of surfactant B present in an aggregate of size g and the same numbers of molecules present in their singly dispersed states in water; X1A and X1B are the mole fractions of the singly dispersed surfactants A and B, while Xg is the mole fraction of aggregates of size g in the solution. The mole fraction Xg is dependent not only on the size g but also on the composition of the micelle. We deﬁne the solvent-free composition of the singly dispersed surfactant mixture, the mixed micelle, and the total surfactant mixture by the relations X1A X ¼ 1A ; X1A þ X1B X1 gA gA ; ¼ ¼ gA þ gB g P X1A þ gA Xg P ¼ ; X1 þ gXg

X1B X ¼ 1B X1A þ X1B X1 gB gB ¼ ¼ gA þ gB g P X1B þ gB Xg P ¼ X1 þ gXg

1A ¼

1B ¼

gA

gB

tA

tB

ð60Þ

In the deﬁnition for the total surfactant composition, the summation is over two independent variables, namely, the aggregation number g = 2 to 1 and the micelle composition gA ¼ 0 to 1. One may note that for spherical bilayer vesicles, the compositions of the inner and the outer layers need not be the same. Therefore, we deﬁne the composition variables gAi and gBi for the inner layer and gAo and gBo for the outer layer, similar to the deﬁnitions given above for the overall composition of the aggregate. From the size and composition distribution one can compute the average sizes of Copyright © 2003 by Taylor & Francis Group, LLC

the aggregates via Eq. (5). The average composition of the mixed micelle can be calculated from gA ¼

X

ðgA =gÞ Xg =

X

Xg ;

gB ¼

X

ðgB =gÞ Xg =

X

Xg

ð61Þ

The geometrical relations for various micellar shapes have been presented in Table 1. In these relations, the tail volume vS is now given by vS ¼ ðgA vSA þ gB vSB Þ, where, vSA and vSB denote the volumes of the hydrophobic tails of surfactants A and B.

B. Free Energy of Formation of Mixed Micelles Expressions for the standard free energy diﬀerence between the surfactant molecules A and B present in a mixed micelle and those present in the singly dispersed state in water are obtained by a simple extension of the equations developed in Section IV for single-component surfactant systems. Only the modiﬁcations necessary for the treatment of surfactant mixtures compared to the analysis of pure surfactant behavior are described below.

1. Transfer of the Surfactant Tail For a mixed micelle having the composition ðgA ; gB Þ, the transfer free energy per surfactant molecule is given by [94,95] ð0g Þtr ð0g Þtr;A ð0g Þtr;B ¼ gA þ gB kT kT kT

ð62Þ

The transfer free energy contribution can be estimated as described in Section IV.A.2 using the group contributions. The transfer free energy calculated from Eq. (62) does not include contributions arising from the mixing of the A and the B tails inside the micellar core, which are accounted for separately.

2. Deformation of the Surfactant Tail When surfactants A and B have diﬀerent tail lengths, segments of both molecules may not be simultaneously present everywhere in the micellar core. Let us assume that surfactant A has a longer tail than surfactant B, ‘SA > ‘SB. If the micelle radius R is less than both ‘SA and ‘SB, then even the shorter tail can reach everywhere within the core of the micelle. If ‘SA > RS > ‘SB , then the inner region of the micellar core, of dimension ðRS ‘SB Þ, can be reached only by the A tails. Taking into account the diﬀerent extent to which the A and the B tails are stretched for the two situations described above, one obtains [95] the expression Copyright © 2003 by Taylor & Francis Group, LLC

" # ð0g Þdef Q2g R2S ¼ Bg gA þ gB ; kT NA L2 NB L2

9P2 Bg ¼ 80

Qg ¼ RS if RS < ‘SA ; ‘SB ; Qg ¼ ‘SB ¼ NB L if ‘SA > RS > ‘SB

! ð63Þ

This equation is used for spherical and globular micelles and for the spherical endcaps of rodlike micelles. NA and NB stand for the number of segments in the tails of surfactants A and B, respectively, and P is the packing factor deﬁned in Table 1. Because the innermost region of the micelle is not accessible to surfactant B, the micelle must contain a suﬃcient number of A surfactant molecules to completely ﬁll up the inner region. This packing condition is satisﬁed if the radius RS is less than the composition averaged tail length, RS ð A ‘SA þ B ‘SB Þ, where A and B are the volume fractions of surfactant tails in the micellar core. In all the calculations reported here, the upper limit of RS is taken to be this composition averaged tail length [95]. For the cylindrical part of the rodlike micelles, the coeﬃcient 9 in Bg is replaced by 10, the radius RS is replaced by the radius RC of the cylindrical core, and the packing factor P ¼ 1=2. For spherical bilayer vesicles, the coeﬃcient 9 in Bg is replaced with 10, the radius RS is replaced by the layer thickness ti for the molecules in the inner layer and by the layer thickness to for the molecules in the outer layer, and P ¼ 1, as for lamellar aggregates. For ﬂuorocarbon chains, as mentioned in Section IV.A, the calculations are performed retaining the deﬁnition for the segment length L to be 0.46 nm.

3. Formation of Aggregate Core–Water Interface The free energy associated with the formation of the hydrophobic core– water interface is given for the case of binary mixtures by the expression [94,95] ð 0g Þint agg ¼ a gA aoA gB aoB kT kT

ð64Þ

Here, aoA and aoB are the areas per molecule of the core surface shielded from contact with water by the polar headgroups of surfactants A and B. Because the interfacial tension against water of various hydrocarbon and ﬂuorocarbon tails of surfactants are close to one another, the aggregate core–water interfacial tension agg is approximated by the micelle composition averaged value: agg ¼ A AW þ B BW Copyright © 2003 by Taylor & Francis Group, LLC

ð65Þ

where AW and BW are interfacial tensions between water and the tails of A and B surfactants. For spherical bilayer vesicles, the area per molecule diﬀers for the inner and the outer layers, and a in Eq. (64) is replaced by ðAgo þ Agi Þ=g.

4. Headgroup Steric Interactions Extending the expression used for single surfactant systems to binary surfactant mixtures, one can write [94,95] for mixed micellar aggregates gA apA þ gB apB ð0g Þsteric ¼ ln 1 ð66Þ kT a For spherical bilayer vesicles, we take into account the composition variation between the inner and the outer layers. Equation (29) for a single surfactant is now extended to the form gAo apA þ gBo apB ð0g Þsteric go ¼ ln 1 kT g Ago =go ð67Þ gAi apA þ gBi apB gi ln 1 g Agi =gi

5. Headgroup Dipole Interactions The dipole–dipole interactions for dipoles having a charge separation d and located at a distance from the hydrophobic domain surface can be computed for spherical and globular micelles and the spherical endcaps of rodlike micelles from [94,95] ð0g Þdipole 2 e2 RS d ¼ ð68Þ kT " adipole kT RS þ þ d g;dipole For the cylindrical part of the rodlike micelles, one can write ð0g Þdipole 2 e2 RC d g;dipole ¼ ln 1 þ kT " adipole kT RC þd þ

ð69Þ

In the above relations, g,dipole is the fraction of surfactant molecules in the aggregate having a dipolar headgroup. If both A and B are zwitterionic surfactants with the same headgroup, then g;dipole ¼ gA þ gB ¼ 1; adipole ¼ a

ð70Þ

If surfactant A is zwitterionic and surfactant B is nonionic or ionic, then a g;dipole ¼ gA ; adipole ¼ ð71Þ g;dipole Copyright © 2003 by Taylor & Francis Group, LLC

The dipole–dipole interactions may be relevant even when the surfactants do not possess zwitterionic headgroups. Such a situation occurs when the surfactant mixture consists of an anionic and a cationic surfactant. The two oppositely charged surfactants may be visualized as forming ion pairs. Depending on the location of the charges on the two surfactant headgroups, these ion pairs may act as dipoles. The distance of charge separation d in the zwitterionic headgroup, now refers to the distance between the locations of the anionic and the cationic charges, measured normal to the micelle core surface. Thus, for such systems, g;dipole ¼ the smaller of adipole ¼

a

g;dipole

;

ðgA ; gB Þ 2

d ¼ jA B j

ð72Þ

The factor 2 in the expression for g;dipole accounts for the fact that a dipole is associated with two surfactant molecules, treated as a pair. A and B represent the distance normal to the hydrophobic core surface at which the charges are located on the A and B surfactants. For spherical bilayer vesicles, Eq. (32) is extended to binary surfactant mixtures taking into account the composition variation between the two layers. Noting that the numbers of surfactant molecules in the two layers are go and gi and go,dipole and gi,dipole are the fractions of surfactant molecules in the outer and the inner layers having a dipolar headgroup, one gets ð0g Þdipole go 2e2 Ro d ¼ kT g "ao;dipole kT Ro þ þ d go;dipole ð73Þ gi 2e2 Ri d þ g "ai;dipole kT Ri d gi;dipole The areas per molecule ao,dipole and ai,dipole and the fractions of surfactant molecules that are dipolar go,dipole and gi,dipole, are evaluated by applying Eqs. (70) to (72) for both the inner and the outer layers.

6. Headgroup Ionic Interactions The ionic interactions that arise at the aggregate surface are calculated using Eq. (34), in conjunction with the curvature factor C given by Eq. (36), with the modiﬁcation that S is now given by S¼

4 e2 " a;ion kT

ð74Þ

If both A and B are ionic surfactants with the same kind of charged headgroups, then Copyright © 2003 by Taylor & Francis Group, LLC

g;ion ¼ gA þ gB ¼ 1;

a;ion ¼ a ;

¼ gA A þ gB B

If A is ionic while B is nonionic or zwitterionic, then a a;ion ¼ ; g;ion ¼ gA ; ¼ A g;ion If A and B are both ionic but of opposite charge, then a a;ion ¼ ; g;ion ¼ gA gB ; ¼ gA A þ gB B g;ion

ð75Þ

ð76Þ

ð77Þ

For spherical bilayer vesicles, the electrostatic interactions at both the outer and the inner surfaces are taken into account. For the molecules in the outer layer, a is replaced with ao , g;ion with go;ion , and the curvature factor C ¼ 2=ðRo þ Þ. For the molecules in the inner layer, a is replaced with ai , g;ion with gi;ion , and the curvature factor C ¼ 2=ðRi Þ. The fraction of charged molecules go;ion and gi;ion is calculated by applying Eqs. (75) to (77) to both the outer and the inner surfaces of the vesicle.

7. Free Energy of Mixing of Surfactant Tails This is the only contribution that is not present in the free energy model for single-component surfactant solutions. This contribution accounts for the entropy and the enthalpy of mixing of the surfactant tails of molecules A and B in the hydrophobic core of the micelle, with respect to the reference states of pure A and pure B micelle cores. Any available solution model can be employed to calculate the entropy and the enthalpy of mixing. Consistent with our use of the Flory–Huggins model in various cases considered before (because of its relative simplicity), we retain the same model here as well: ð0g Þmix H 2 ¼ gA ln A þ gB ln B þ ½gA vSA ðH A mix Þ kT H 2 þ gB vSB ðH B mix Þ =kT

ð78Þ

H where H A and B are the Hildebrand solubility parameters of the tails of surfactants A and B and H mix is the volume fraction averaged solubility parameter of all the components within the micelle core, H mix ¼ H

A H þ . B B A

8. Free Energy Model and Mixture Nonideality The free energy change on the formation of a mixed micelle can be written in terms of the free energies of formation of the two pure component micelles, the ideal entropy of mixing of surfactants inside the mixed micelle, and an excess free energy that is responsible for all nonidealities. This implies that if the free energy of formation of the mixed micelles, excluding the ideal entropy of mixing, is a linear function of the micelle composition, then Copyright © 2003 by Taylor & Francis Group, LLC

the excess free energy is zero and the mixed micelles are said to behave ideally. Any nonlinear dependence on the micelle composition is thus a signature for the nonideal behavior of the mixed surfactant system. In the framework of the molecular theory outlined in this section, the transfer free energy is a linear function of the micelle composition. All other contributions have a nonlinear dependence on micelle composition because they are dependent nonlinearly on the micelle core radius or the area per molecule. Further, these structural parameters are themselves dependent nonlinearly on the micelle composition if the tail lengths of the surfactants are diﬀerent from one another. Depending on the quantitative importance of these nonlinear contributions, the mixed surfactant system displays small or large deviations from ideal behavior, as we will discuss below.

C. Predictions for Surfactant Mixtures 1. Estimation of Molecular Constants and Computational Approach The molecular constants needed for the surfactants have been discussed before in Section IV.C, and the constants characterizing various surfactant headgroups are listed in Table 3. The only additional molecular constant needed for calculations involving surfactant mixtures is the Hildebrand solubility parameter for the hydrocarbon and ﬂuorocarbon tails of the surfactants. This can be estimated using a group contribution approach based on the properties of pure components [97–99]. For hydrocarbon tails, the solubility parameters can be estimated in units of MPa1/2 (1 MPa ¼ 1 J/cm3) from the relation H ¼

0:7 þ 0:471ðnC 1Þ MPa1=2 Þ; vS in nm3 vS

ð79Þ

The solubility parameter for the ﬂuorocarbon tail of the surfactant sodium perﬂuoro octanoate (SPFO) estimated using the group contribution approach yields 12.3 MPa1/2. Since the solubility parameters estimated in this manner have been found inadequate for the quantitative description of hydrocarbon–ﬂuorocarbon mixture properties, Mukerjee and Handa [45] have estimated group contributions to the solubility parameters by ﬁtting the critical solution temperature of the hydrocarbon–ﬂuorocarbon mixtures. On the basis of these group contributions, one can calculate the solubility parameter of the SPFO tail to be approximately 9.5 MPa1/2. Computed results for hydrocarbon–ﬂuorocarbon surfactant mixtures are presented later, utilizing both of these estimates. The predictive computations have been carried out using the maximumterm method described in Section IV.B.2. For the binary mixtures, the Copyright © 2003 by Taylor & Francis Group, LLC

concentration of the singly dispersed surfactant mixture X1 (¼ X1A þ X1B ) and the composition of this mixture 1A are used as inputs and the aggregation number g of the equilibrium aggregate and the composition gA of the equilibrium aggregate are obtained by ﬁnding the maximum in the aggregate size distribution. For spherical bilayer vesicles, one has to determine the thicknesses of the inner and the outer layers and the compositions of each layer as well. The critical micelle concentration is estimated using the results based on the maximum-term method calculations as described earlier in Section IV.B.

2. Nonionic Hydrocarbon–Nonionic Hydrocarbon Mixtures The calculated aggregation properties of binary mixtures of decyl methyl sulfoxide (designated as C10SO) and decyl dimethyl phosphene oxide (designated as C10PO) at 248C are presented in Figs. 27 and 28. In Fig. 27 the CMC is plotted against the composition of the micelles and the composition of the singly dispersed surfactants. One can practically equate the composition of the singly dispersed surfactant to the composition of the total surfactant, when the total surfactant concentration is equal to the CMC since

FIG. 27 The CMC of C10PO þ C10SO binary mixture as a function of the composition of micelles (dashed line) and that of singly dispersed surfactants (solid line) at 248C. The points are experimental data from Ref. (100). Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 28 The average aggregation number of C10PO þ C10SO mixed micelles at the CMC as a function of the composition of micelles (solid line) and that of the singly dispersed surfactants (dashed line) at 248C.

the amount of surfactant present as micelles is small. Figure 27 contains also the experimental data obtained by Holland and Rubingh [100] on the basis of surface tension measurements. Figure 28 presents the average aggregation numbers predicted by the theory as a function of the composition of the mixed micelle and that of the monomers. No experimental data are, however, available for comparison. The size of the mixed micelle varies approximately linear with the composition. It has been shown that the CMC of this binary surfactant system can be calculated from the CMC values of the individual surfactants by assuming the mixture to be ideal [100]. In the framework of the molecular theory presented here, nonidealities in this binary mixture can arise even when the two surfactants have somewhat diﬀerent headgroup cross-sectional areas while possessing identical tails [94,95]. Because there are no volume diﬀerences between the hydrophobic tails of the two surfactants, for any aggregation number, the area per molecule of the mixed micelle is independent of the micelle composition. However, the steric interaction between headgroups at any aggregation number is a nonlinear function of the micelle composition. This constitutes a source of mixture nonideality. However, because of the small magnitude of the steric repulsion free energy, the deviaCopyright © 2003 by Taylor & Francis Group, LLC

tion from ideal mixing is rather small. For this reason, the ideal mixed micelle model can satisfactorily predict the mixture CMC.

3. Ionic Hydrocarbon–Ionic Hydrocarbon Mixtures The predicted CMC of mixtures of two anionic surfactants sodium dodecyl sulfate (SDS) and sodium decyl sulfate (SDeS), which diﬀer from one another in their hydrocarbon tail lengths, is plotted against the composition of the singly dispersed surfactant in Fig. 29. The ﬁgure also contains the experimental data obtained by Mysels and Otter [101] based on conductivity measurements, and the data of Shedlowsky et al. [102] based on e.m.f. measurements. The predicted mixed micelle composition as a function of the composition of the singly dispersed surfactants is compared in Fig. 30 with the data obtained by Mysels and Otter [101]. In these binary mixtures, one of the sources of nonideality arises from the volume diﬀerences between the hydrophobic tails of the two surfactants. Consequently, at any given aggregation number, the area per molecule of the mixed micelle is a nonlinear function of the micelle composition and, hence, nonlinearity is reﬂected in all the free energy contributions. Another source of nonideality is the change in

FIG. 29 The CMC of SDS þ SDeS mixtures as a function of the composition of singly dispersed surfactants. (The experimental data shown by circles are from Ref. 101 and those shown by triangles are from Ref. 102.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 30 The composition of SDS þ SDeS mixed micelles as a function of the composition of singly dispersed surfactants. (The experimental data shown by circles are from Ref. 101.)

ionic strength of the solution as the composition is modiﬁed. In the absence of any added salt, the ionic strength is determined mainly by the concentration of the singly dispersed surfactants. This concentration changes with the composition of the mixed micelle and thus modiﬁes the ionic interactions at the micelle surface nonlinearly as a function of the micelle composition. Given the importance of the ionic interactions to the free energy of micellization, the nonideality is more perceptible in these binary mixtures. Similar behavior is exhibited by the mixtures of cationic surfactants, dodecyl trimethyl ammonium bromide (DTAB), and decyl trimethyl ammonium bromide (DeTAB). This mixture is similar to the SDS-SDeS mixture as concerns the tail lengths of the two surfactants. However, the trimethyl ammonium bromide headgroup has a larger area ap compared to that of the anionic sulfate headgroup. The predicted CMC as a function of the micelle and the monomer compositions is presented in Fig. 31, which also contains the experimental CMC data obtained by Garcia-Mateos et al. [103] using electrical conductivity measurements. One can observe large CMC changes for the DTAB-DeTAB mixture as the composition is altered, which also inﬂuences the ionic strength of the solution. The predicted aggregation numbers do not show much growth beyond the size of the pure component Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 31 The CMC of DTAB þ DeTAB mixtures as a function of the composition of the micelles (dashed line) and that of singly dispersed surfactants (solid line). (The points are experimental data from Ref. 101.)

micelles. In contrast, for SDS-SDeS mixtures, the mixed micelles are larger than the pure component micelles. This diﬀerent behavior is a consequence of the larger steric repulsion for these cationic surfactants with a bulky headgroup, when compared to the sulfate headgroups of SDS-SDeS. To explore the eﬀect of diﬀerent chain lengths of the hydrophobic tails, we have computed the micellization behavior of mixtures of anionic potassium alkanoates, namely, potassium tetradecanoate (KC14)–potassium octanoate (KC8) and potassium decanoate (KC10)–potassium octanoate (KC8) at 258C. The calculated CMC and micelle composition are plotted in Figs. 32 and 33 as a function of the composition of the singly dispersed surfactant, together with the experimental CMC data [104] obtained by Shinoda using dye solubilization measurements. One can observe from Fig. 33 that the less hydrophobic KC8 is almost completely excluded from the micelles in KC8 þ KC14 mixtures because of the much stronger hydrophobicity of KC14. The singly dispersed surfactants contain almost exclusively the less hydrophobic KC8 molecules. Such exclusion of KC8 from the mixed micelles is reduced in case of the KC8 þ KC10 mixtures, where the chain length diﬀerence between the surfactants is smaller. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 32 The CMC of mixtures of potassium alkanoate (KCn) surfactants, KC8 þ KC10 mixtures, and KC8 þ KC14 mixtures as a function of the composition of singly dispersed surfactants. (The experimental data [circles and triangles] are from Ref. 104.)

4. Ionic Hydrocarbon–Nonionic Hydrocarbon Mixtures The mixture of anionic sodium dodecyl sulfate (SDS) and nonionic decyl methyl sulfoxide (C10SO) at 248C, in the presence of 1-mM Na2CO3, is taken for illustrative calculations. The calculated CMC is plotted in Fig. 34 as a function of the composition of the singly dispersed molecules. The experimental CMC data based on surface tension measurements [100] are also included in the ﬁgure. The results show that this binary mixture exhibits considerable nonideality. The CMC of the mixed system is substantially smaller than that anticipated for the ideal mixed micelle. The two surfactants diﬀer somewhat in their hydrophobic tail lengths and in the sizes of the polar headgroups. Similar diﬀerences occurred in the case of nonionic–nonionic mixtures considered before, but they did not give rise to signiﬁcant nonidealities. However, in the present case, one component is ionic while the other is nonionic. Therefore, the area per charge at the micelle surface and the ionic strength are strongly aﬀected by the composition of the micelle. This results in a large variation in the ionic interaction energy at the micelle Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 33 The composition of KC8 þ KC10 mixed micelles and KC8 þ KC14 mixed micelles as a function of the composition of singly dispersed surfactants.

FIG. 34 The CMC of SDS þ decyl methyl sulfoxide (C10SO) mixtures as a function of the composition of singly dispersed surfactants. (The experimental data [circles] are from Ref. 100.) Copyright © 2003 by Taylor & Francis Group, LLC

surface as the micelle composition is changed. This free energy contribution is mostly responsible for the nonideal behavior exhibited by this system. The predictions for binary mixtures of the anionic sodium dodecyl sulfate (SDS) and nonionic -dodecyl maltoside (DM) are now compared with the experimental data obtained by Bucci et al. [105] in Figs. 35 to 37. In this system the two surfactants have identical hydrophobic chains, and hence the nonideality arises from the diﬀerences in the size and charge of the two headgroups. The calculated average aggregation numbers and those estimated from neutron scattering measurements [105] are plotted in Fig. 35 with and without added salt. The average aggregation number and the average micelle composition are estimated at a total surfactant concentration of 50 mM and at 258C. Figures 36 and 37 present the CMC and micelle composition as functions of the composition of the singly dispersed surfactants at two concentrations of added electrolyte, NaCl. They show that the nonionic DM molecules are preferentially incorporated in the micelles over most of the composition range. In the absence of any added electrolyte, this

FIG. 35 The average aggregation number of SDS þ dodecyl maltoside (DM) mixed micelles as a function of the total surfactant composition at a total surfactant concentration of 50 mM. (The experimental data are from Ref. 105, where the circles refer to micelle sizes in the absence of any added salt while the triangles correspond to a 0.2M concentration of added NaCl.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 36 The CMC of SDS þ DM mixtures as a function of the composition of monomers. The conditions correspond to those in Fig. 35.

FIG. 37 The composition of mixed micelles of SDS þ DM as a function of the composition of monomers. The conditions correspond to those in Fig. 35. Copyright © 2003 by Taylor & Francis Group, LLC

preference is stronger since this decreases the positive free energy contribution due to the presence of the anionic SDS in micelles. Obviously, in the presence of NaCl, the electrostatic repulsions between ionic headgroups are reduced, and hence a larger number of SDS molecules is incorporated into the mixed micelles.

5. Anionic Hydrocarbon–Cationic Hydrocarbon Mixtures When present together, the anionic and cationic surfactants are expected to form ion pairs with no net charge; this decreases their aqueous solubility and results in precipitation [106,107]. These surfactant mixtures can also generate mixed micelles or mixed spherical bilayer vesicles in certain concentration and composition ranges. As noted earlier, depending on the location of the charges on the anionic and the cationic surfactants, one can associate a dipole moment with each ion pair. Consequently, these surfactant mixtures can behave partly as ionic single chain molecules and partly as zwitterionic paired chain molecules. We have calculated the aggregation characteristics of binary mixtures of decyl trimethyl ammonium bromide (DeTAB) and sodium decyl sulfate (SDeS). The calculated and experimental [100] CMC values are presented in Fig. 38, while information regarding the micelle

FIG. 38 The CMC of SDeS þ DeTAB mixtures as a function of the composition of singly dispersed surfactants. (The points are experimental data from Ref. 100.)

Copyright © 2003 by Taylor & Francis Group, LLC

composition is provided by Fig. 39. The calculations show that rodlike mixed micelles are formed over most of the composition range. The micelle composition data show that the mixed micelles contain approximately equal numbers of the two types of surfactants over the entire composition range. The small deviation from the micelle composition value of 0.5 arises because of the diﬀerent sizes of the polar headgroups. Some binary mixtures of anionic and cationic surfactants have been observed to give rise to spherical bilayer vesicles in aqueous solutions [108–111]. In these mixtures, the surfactant tails have appreciably diﬀering lengths. Here, we have calculated the solution behavior of binary mixtures of cationic cetyl trimethyl ammonium bromide (CTAB) and anionic sodium dodecyl sulfate (SDS), in the presence of 1-mM NaBr as electrolyte, to explore the formation of micelles versus vesicles in such mixtures. Figure 40 shows the calculated critical aggregate (micelle or vesicle) concentration as a function of the composition of the aggregate. The lower the critical concentration for the formation of a given kind of aggregate, aggregates of that type are favored at equilibrium. In CTAB-poor systems, for CTAB mole fractions in the aggregates g;CTAB less than 0.2, only micelles are generated. For CTAB compositions in the region 0.2 < g;CTAB < 0.29,

FIG. 39 The average composition of SDeS þ DeTAB mixed micelles as a function of the composition of monomers. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 40 The critical micelle (or vesicle) concentration of CTAB þ SDS mixtures as a function of the composition of the aggregates. Squares denote micelles and triangles refer to spherical bilayer vesicles. The lines simply connect the calculated results. The dashed line near the composition region between 0.29 and 0.57 corresponds to a precipitated surfactant phase of lamellar aggregates.

spherical bilayer vesicles are predicted to form. In CTAB-rich systems, again for g;CTAB > 0.57, only micelles are present in solution. In the narrow composition region of 0.565 < g;CTAB < 0.567, vesicles are formed in solution. For a wide range of CTAB composition 0.29 < g;CTAB < 0.565, the calculations indicate the formation of lamellar aggregates rather than spherical bilayer vesicles. This may correspond to the formation of a precipitating surfactant phase. Figure 41 presents the calculated average aggregation numbers of the micellar and vesicular aggregates. The micelles correspond to spherical or globular aggregates. The smallest vesicles formed are not very much larger than the larger micellar aggregates. The vesicles (corresponding to the results shown in the ﬁgure) have outer radii in the range of 3 to 14 nm. The inner and outer layers of the bilayer vesicles have diﬀering compositions. In CTAB-poor vesicles the inner layer is enriched somewhat with CTAB, while in CTAB-rich vesicles the inner layer is somewhat depleted of CTAB. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 41 The aggregation number of mixed micelles and mixed vesicles formed of CTAB þ SDS mixtures as a function of the composition of the aggregates. Squares denote micelles and triangles refer to vesicles. The lines simply connect the calculated results. The dashed line near the compositions 0.29 and 0.57, which extend vertically, suggest the formation of inﬁnite lamellar aggregates in that region corresponding to the precipitation of a surfactant phase.

6. Anionic Fluorocarbon–Nonionic Hydrocarbon Mixtures The aggregation behavior of mixtures of nonionic alkyl-N-methyl glucamines (MEGA-n) and anionic sodium perﬂuoro octanoate (SPFO), studied experimentally by Wada et al. (112) was investigated using the present model. In such mixtures the nonideality associated with the mixing of hydrocarbon and ﬂuorocarbon surfactant tails is superimposed on the nonideality associated with the mixing of anionic and nonionic headgroups. For hydrocarbon surfactants with these polar headgroups, the results presented earlier revealed considerable negative deviations from ideality (i.e., the free energy of mixed micelle formation is lower than the composition averaged sum of the free energies of the pure component micelles) [94,95]. For mixtures of hydrocarbon and ﬂuorocarbon tails one can anticipate strong positive deviations from ideality. Thus, for the mixtures under study, both negative and positive deviations from ideality occur, which partially compensate for one another. As a result, these binary mixtures exhibit reduced nonideality. Figures 42 and 43 present Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 42 The CMC of MEGA-8 þ SPFO mixtures as a function of the composition of singly dispersed surfactants. The calculated results are presented for two alternate estimates of the solubility parameter of the SPFO tail. (The experimental data [circles] are from Ref. 112.)

FIG. 43 The average composition of MEGA-8 þ SPFO mixed micelles as a function of the composition of monomers. The conditions correspond to those described in Fig. 42. Copyright © 2003 by Taylor & Francis Group, LLC

the calculated CMC and the composition of the mixed micelles as a function of the composition of the singly dispersed surfactant for MEGA-8SPFO mixtures. Similar results for the MEGA-9-SPFO mixtures are presented in Figs. 44 and 45. The calculations have been performed for two diﬀerent values of the solubility parameter of SPFO, one determined from the properties of pure ﬂuorocarbons (12.3 MPa1/2), and the other determined from the properties of ﬂuorocarbon–hydrocarbon mixtures (9.5 MPa1/2). Both MEGA-8-SPFO and MEGA-9-SPFO mixtures display the same qualitative behavior. The miscibility between the two surfactants is promoted by the headgroup interactions, which lead to a single kind of mixed micelles in solution. As shown by the data presented in Figs. 43 and 45, there is no demixing of micelles for the MEGA-8-SPFO and MEGA-9SPFO mixtures.

7. Anionic Hydrocarbon–Anionic Fluorocarbon Mixtures The micellization behavior of sodium perﬂuoro octanoate (SPFO) and sodium decyl sulfate (SDeS) mixtures is plotted in Figs. 46 and 47. The

FIG. 44 The CMC of MEGA-9 þ SPFO mixtures as a function of the composition of singly dispersed surfactants. The calculated results are presented for two alternate estimates of the solubility parameter of the SPFO tail. (The experimental data [circles] are from Ref. 112.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 45 The average composition of MEGA-9 þ SPFO mixed micelles as a function of the composition of monomers. The conditions correspond to those described in Fig. 44.

FIG. 46 The CMC of SDeS þ SPFO mixtures as a function of the composition of micelles (dashed line) and that of singly dispersed surfactants (solid line). (The experimental data [circles] are from Ref. 112.) The experimental and calculated results indicate the coexistence of two micelle populations. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 47 The average aggregation number of SDeS þ SPFO mixed micelles as a function of the composition of micelles. A single type of mixed micelle exists in the SDeS-rich and SPFO-rich mixtures, while for intermediate compositions, two distinct micelle sizes corresponding to the two coexisting micelle populations are indicated.

CMCs are compared with available experimental data [112] in Fig. 46, which also provides the composition of the mixed micelle. There are positive deviations in the CMC in contrast to the negative deviations observed in the binary mixtures examined previously. This positive deviation is a direct consequence of the interactions between the hydrocarbon and ﬂuorocarbon tails. This positive deviation, which was also present in SPFOMEGA-n mixtures, was partially compensated for there by the negative deviations due to headgroup interactions. Such compensating eﬀects are, however, absent in the SPFO-SDeS mixtures since the headgroups of both surfactants are anionic. The calculations show the interesting feature that over a certain composition domain, two types of micelles coexist. One is hydrocarbon-rich and the other one is ﬂuorocarbon-rich, with average compositions gA ¼ 0:32 and 0.79, respectively. The predicted average aggregation numbers of the mixed micelles are plotted in Fig. 47. The

Copyright © 2003 by Taylor & Francis Group, LLC

ﬂuorocarbon- and hydrocarbon-rich micelles that coexist have diﬀerent aggregation numbers.

VI. MICELLIZATION OF SURFACTANTS IN THE PRESENCE OF POLYMERS The interactions between surfactant molecules and synthetic polymers in aqueous solutions are of importance to many applications in detergents and personal care products, chemical, pharmaceutical, mineral processing, and petroleum industries. In general, the mutual presence of polymer and surfactant molecules alter the rheological properties of solutions, adsorption characteristics at solid–liquid interfaces, stability of colloidal dispersions, the solubilization capacities in water for sparingly soluble molecules, and liquid–liquid interfacial tensions [113–117]. The ability of the surfactant and the polymer molecules to inﬂuence the solution and interfacial characteristics is controlled by the state of their occurrence in aqueous solutions, namely whether they form mixed aggregates in solution and, if so, the nature of their microstructures.

A. Polymer–Surfactant Association Structures Various morphologies of polymer-surfactant complexes can be visualized [118–121] depending on the molecular structures of the polymer and the surfactant and on the nature of the interaction forces operative between the solvent, the surfactant, and the polymer. A schematic view of these morphologies is presented in Fig. 48. Structure A denotes only the polymer, implying that no polymer–surfactant association occurs. This would be the case when both the polymer and the surfactant carry the same type of ionic charges. This could also occur when the polymer is relatively rigid and for steric reasons does not interact with ionic or nonionic surfactants. It could also be the situation when both the polymer and the surfactant are uncharged and no obvious attractive interactions, promoting association, exist between them. Structure B denotes a system where the polymer and the surfactant carry opposite electrical charges. Their mutual association is promoted by electrostatic attractions. These cause the creation of a complex with reduced charge and, hence, reduced hydrophilicity. Indeed, this eventually leads to the precipitation of these complexes from solution. Structure C also occurs in systems containing surfactant and polymer possessing opposite charges. In this case, the surfactant promotes intramolecular bridging within a polymer molecule by interacting with multiple sites on one molecule or intermolecular bridging by interacting simultaneously with sites on diﬀerent polymer molecules. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 48 Schematic representation of association structures involving surfactant and polymer molecules. A. Polymer molecule does not interact with surfactants for electrostatic or steric reasons. No surfactant is bound to the polymer. For example, the surfactant and the polymer are both anionic or both cationic. B. The polymer and the surfactant are oppositely charged. Single-surfactant molecules are bound linearly along the length of the polymer molecules. C. The polymer and the surfactant are oppositely charged. A single-surfactant molecule binds at multiple sites on a single-polymer molecule, giving rise to intramolecular bridging. Alternatively, it binds to more than one polymer molecule, allowing intermolecular bridging. D. The polymer is an uncharged random or multiblock copolymer. The surfactant molecules orient themselves at domain boundaries separating the polymer segments of diﬀerent polarities. E. Polymer is hydrophobically modiﬁed. Individual surfactant molecules associate with one or more of the hydrophobic modiﬁers on a singlepolymer molecule or multiple-polymer molecules. F. Polymer is hydrophobically modiﬁed. Clusters of surfactant molecules associate with multiple hydrophobic modiﬁers on a single-polymer molecule. G. Polymer is hydrophobically modiﬁed. Clusters of surfactant molecules associate with each of the hydrophobic modiﬁer on a single-polymer molecule. H. The polymer segments partially penetrate and wrap around the polar headgroup region of the surfactant micelles. A single polymer molecule can associate with one or more surfactant micelles. Copyright © 2003 by Taylor & Francis Group, LLC

Structure D depicts a situation when the polymer is a random copolymer or multiblock copolymer with relatively short blocks. In this case, the polymer molecule assumes a conformation in solution characterized by segregation of dissimilar segments or blocks of varying polarity. Depending on whether the polymer is a random copolymer or a block copolymer, the segregation in the polymer can take diﬀerent forms, including the formation of polymeric micelles. In either case, one can imagine the surfactant molecules to locate themselves at the interfaces between the segregated regions. Structures E, F, and G pertain to hydrophobically modiﬁed polymers. In this case the size of the hydrophobic modiﬁer, its grafting density along the polymer, and the relative concentrations of the surfactant and the polymer all inﬂuence the nature of the association structure. In general, at low surfactant concentrations, structure E may be obtained with single-surfactant molecules or very small surfactant clusters (dimers, trimers, etc.) interacting with one or more hydrophobic modiﬁers, without causing any conformational changes on the polymer. When the surfactant concentration is increased, somewhat larger surfactant clusters form co-aggregates with multiple hydrophobic modiﬁers belonging to the same polymer molecule, causing the polymer conformation to change signiﬁcantly. At larger surfactant concentrations, it is possible to obtain structure G, where surfactant aggregates are formed around each of the hydrophobic modiﬁer. Structure H denotes a complex consisting of the polymer molecule wrapped around surfactant micelles with the polymer segments partially penetrating the polar headgroup region of the micelles and reducing the micelle core–water contact. Such a structure can describe a nonionic polymer interacting with surfactant micelles. Such a structure can also be imagined in the case of an ionic polymer interacting with oppositely charged micelles. For each type of polymer molecule such as those depicted in Fig. 48, including the nonionic polymer, charged polymer, hydrophobically modiﬁed polymer, star polymer, random or block copolymer, some of the unique features of the polymer molecule will have to be invoked in developing quantitative models of polymer–surfactant association. Given the widespread use of nonionic polymers, in this paper we explore the association of surfactants with such polymers. The general ideas of molecular aggregation and the formation of competitive association structures discussed in this paper are applicable to the various types of polymers mentioned above, but the details of the modeling would have to be modiﬁed in each case to account for the particularities of the polymer molecule. Copyright © 2003 by Taylor & Francis Group, LLC

B. Modeling Nonionic Polymer–Surfactant Association The model presented below follows our earlier thermodynamic analysis of polymer-micelle association [121]; a somewhat diﬀerent approach has been presented by Ruckenstein et al. [122]. We have extended the model also to treat the association of nonionic polymers with rodlike micelles and vesicles [123] and various types of microemulsions [124]. We visualize a polymer–surfactant association complex (Structure H in Fig. 48) as consisting of fully formed surfactant aggregates interacting with the polymer segments. In the polymer-bound aggregates, the polymer segments are assumed to adsorb at the aggregate–water interface, shielding a part of the hydrophobic domain of the aggregate from being in contact with water. The physicochemical properties of the polymer molecule determine the area of mutual contact between the polymer molecule and the hydrophobic surface of the aggregate. A characteristic parameter apol is deﬁned to represent this area of mutual contact per surfactant molecule in the aggregate. Although it is not very realistic to anticipate that the polymer molecule can provide a uniform shielding of the aggregate surface from water by the amount apol per surfactant molecule, this area parameter is deﬁned in the mean-ﬁeld spirit to serve as a quantitative measure of the nature of polymer–aggregate interactions.

C. Free Energy of Micellization in the Presence of Polymer 1. Modiﬁcation of Free Energy Contributions Due to Polymer The various contributions to the standard free energy of formation of micelles or vesicles have been summarized in Eq. (54), and detailed expressions to calculate each of these contributions are described in Section IV.A. For an ionic surfactant, the free energy of micellization has the form ð 0g Þ ð 0g Þtr ð 0g Þdef ð 0g Þint ð 0g Þsteric ð 0g Þionic ¼ þ þ þ þ kT kT kT kT kT kT ð80Þ where the ﬁve terms respectively account for the transfer free energy of the surfactant tail, the deformation free energy of the tail, the free energy of formation of the micelle–water interface, the steric repulsions between the headgroups at the micelle surface, and the electrostatic repulsions between the ionic headgroups. The last term is absent for nonionic surfactants and is replaced by the dipole interaction free energy term for zwitterionic surfactants. The standard free energy of formation of aggregates bound to the nonionic polymer molecule can be written in a similar form, with modiﬁcations to account for the presence of polymer segments at the aggregate– Copyright © 2003 by Taylor & Francis Group, LLC

water interface. As mentioned above, we assume that the polymer segments shield the hydrophobic domain from water by an area apol per surfactant molecule. This gives rise to three competing contributions to the free energy of aggregation. First, a decrease in the hydrophobic surface area of the aggregate exposed to water occurs. This decreases the positive free energy of formation of the aggregate–water interface and thus favors the formation of polymer-bound aggregates. Second, steric repulsions arise between the polymer segments and the surfactant headgroups at the aggregate surface. This increases the positive free energy of headgroup repulsions and thus disfavors the formation of the polymer-bound aggregates. Finally, the contact area apol of the polymer molecule is removed from water and transferred to the surface of the aggregate, which is concentrated in the surfactant headgroups. This alters the free energy of the polymer and can favor or disfavor the formation of the polymer-bound micelles depending on the type of interactions between the polymer segments and the interfacial region rich in headgroups. Taking these factors into account, one may write ð0g Þ ð0g Þtr ð0g Þdef agg þ þ ða ao apol Þ ¼ kT kT kT kT ap þ apol ð0g Þionic pol apol ln 1 þ a kT kT

ð81Þ

The ﬁrst two terms and the ﬁfth term are identical to those appearing in Eq. (80). The modiﬁed third term accounts for the enhanced shielding of the micellar core from water provided by the polymer. The modiﬁed fourth term accounts for the increase in the steric repulsions due to the presence of the polymer. The sixth term is new and represents the change in the interaction free energy of the polymer molecule. This interaction free energy is written as the product of an interfacial tension and the area of the polymer that is removed from water and brought into contact with the micellar surface. Here, pol is the diﬀerence between the macroscopic polymer-water interfacial tension and the interfacial tension between the polymer and the aggregate headgroup region. The factor pol is obviously aﬀected by both the hydrophobic character of the polymer molecule and its interactions with the surfactant headgroups that are crowded at the interface. One may expect pol to be positive and larger for more hydrophobic polymers and for polymers that may have attractive interactions with surfactant headgroups. Given the above free energy equation, the equilibrium aggregation number, the surface area per surfactant molecule of the bound micelle, and the CMC are calculated as described in Section IV.B.2 by ﬁnding the maximum in the aggregate size distribution. Copyright © 2003 by Taylor & Francis Group, LLC

2. Estimation of Molecular Constants Two new molecular constants, apol and pol, that depend on the type of the polymer are necessary for predictive calculations. At present, there are no a priori methods available for estimating apol, while pol can, in principle, be determined from interfacial tension measurements as suggested by Ruckenstein et al. [122]. Consequently, a reasonable and simple way to estimate both these parameters is by ﬁtting the measured CMC and aggregation number of any one surfactant that forms spherical or globular micelles to the model; the ﬁtted parameters can then be used to make a priori predictions for any other surfactant and for systems forming not only globular micelles but those forming rodlike micelles, vesicles, and microemulsions as well. For the illustrative calculations discussed below, we take apol ¼ 0:20 nm2 and pol ¼ 15, 0, or 15 mN/m. The three values for pol allow the investigation of the subtle role this contribution plays in governing the formation of polymer-bound aggregates. One may note that pol aﬀects only the CMC and not the aggregation number since the polymer interaction free energy contribution is a constant independent of the aggregation number g.

D. Interaction of Polymer with Globular Micelles The equilibrium aggregation number, the area per molecule of the micelle, and the CMC calculated for the anionic surfactant—sodium dodecyl sulfate (SDS)—and the nonionic surfactant—decyl dimethyl phosphene oxide (C10PO)—are given in Table 5. In polymer-free solutions the anionic SDS micelles are small, only marginally larger than the largest spherical micelle possible, and the CMC is approximately 7.85 mM. In the presence of the polymer, the CMC is substantially decreased (2.45 mM, 1.2 mM, and 5.0 mM for pol ¼ 0, 15, and 15 mN/m, respectively), corresponding to a lower free energy for the formation of polymer-bound micelles. Therefore, polymer-bound globular micelles will be favored over free micelles in this case. The aggregation number of the polymer-bound micelles are smaller than those of the free micelles. Results for the nonionic surfactant C10PO are also given in Table 5. In the absence of the polymer, small ellipsoidal micelles (slightly larger than the largest spheres that are geometrically allowed) are formed and the CMC is approximately 0.386 mM. In the presence of the polymer, the CMC is signiﬁcantly decreased (0.18 and 0.088 mM) if pol ¼ 0 or 15 mN/m. Therefore, micelles that are bound to the polymer will be favored over free micelles. The aggregation number of the polymer-bound spherical micelles are substantially smaller compared to that of the free micelles. The CMC of 0.368 mM calculated for pol ¼ 15 mN/m is closer to but still smaller than that in the polymer-free solution, Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 5 Polymer Association with Surfactant Aggregates at 258C Surfactant

CMC (mM)

a (nm2 )

g

K

Shape

C10 PO C10 PO þ P* C12 SO4 Na C12 SO4 Na þ P C12 PO C12 PO þ P C12 SO4 Na þ 0:8M NaCl C12 SO4 Na þ 0:8M NaCl þ P di-C12 SO4 Na þ 0:01M NaCl

0.386 0.18 7.85 2.45 0.243 0.128 0.313 0.057 4:26 103

Globular Sphere Sphere Sphere Rod Sphere Rod Globular Vesicle**

2:61 103

52 20 56 29 — 28 — 88 462 727 60

— — — — 5:6 109 4:5 102 6:0 104 6:1 104 —

di-C12 SO4 Na þ P þ 0:01M NaCl

0.584 0.789 0.629 0.781 0.582 0.795 0.477 0.561 0.583 0.771 1.065

—

Globular

*P refers to polymer-bound aggregates, the corresponding CMCs listed are for pol ¼ 0 mN/m. These CMCs should be multiplied by 0.49 if pol ¼ 15 or by 2.043 if pol ¼ 15 mN/m. **The two values listed for both a and g correspond to the inner and the outer layers of vesicle.

Copyright © 2003 by Taylor & Francis Group, LLC

suggesting that polymer-bound micelles will be formed in this case as well. But a further decrease in pol (say, 16.5 mN/m) will result in the CMC for polymer-bound micelles being larger than the CMC for the polymer-free micelles. Therefore, a preference for free micelles over bound micelles would be predicted. Evidently, subtle free energy diﬀerences associated with the hydrophobicity of the polymer and its interactions with the surfactant headgroups can tilt the equilibrium favoring free micelles over bound micelles, or vice versa. The contrasting behavior of anionic and nonionic surfactants can be interpreted in the framework of the present thermodynamic model. If the polymer associates with the micelle, the presence of the polymer segments increases the equilibrium area per surfactant molecule. For nonionic surfactants, this incremental increase in the equilibrium area a is roughly comparable to the polymer-micelle contact area apol (see Table 5). Correspondingly, the negative increment in the free energy of shielding of the micellar core from water by the polymer segments is close in magnitude to the positive increment in the free energy of steric repulsions at the aggregate surface. If only these two eﬀects are considered, then the CMC values for the formation of bound and free micelles are always very near one another, with the free micelles generally favored over the bound micelles. The tail deformation free energy decreases for the polymer-bound micelles because of their reduced size, thus favoring the bound micelles over the free micelles. The polymer interaction free energy provides a positive or negative contribution to the formation of the polymer-bound aggregates, depending on the polymer hydrophobicity and the polymer–surfactant headgroup interactions. This factor decreases further the CMC when pol > 0 and tilts the balance more in favor of bound micelles. On the other hand, when pol < 0 and has a suﬃciently large magnitude, this factor inhibits the occurrence of binding. The calculated results for the anionic surfactants are diﬀerent from the above behavior of nonionic surfactants. In the case of anionic surfactants, the increase in the equilibrium area per molecule of the aggregate due to the presence of the polymer is generally smaller than the polymer–aggregate contact area apol. This is because of the importance of the electrostatic headgroup interaction term in determining the equilibrium area of the aggregate. Therefore, the negative increment in the free energy of shielding of the aggregate core from water by the polymer segments more than oﬀsets the positive increment in the free energy of steric repulsions at the micellar surface. More importantly, there is a negative increment in the free energy of electrostatic interactions at the aggregate surface because the equilibrium area in the presence of the polymer is somewhat larger. These free energy contributions dominate over the polymer interaction free energy with the Copyright © 2003 by Taylor & Francis Group, LLC

result that the polymer-bound anionic micelles are always favored over free micelles. It has been reported that cationic surfactants do not bind with a nonionic polymer such as polyoxyethylene [117–121]. This diﬀering behavior compared to anionic surfactants must thus come because pol < 0 and has a suﬃciently large magnitude than that considered, for example, here. Such a situation can arise because of the weakly cationic nature of the ether oxygens in polyoxyethylene [118–121] and may lead to a larger CMC if polymer-bound aggregates are to form; hence binding does not occur in these cases.

E. Interaction of Polymer with Rodlike Micelles The general thermodynamic analysis of rodlike micelles was discussed in Section II.D. Given Eqs. (80) and (81) for the free energy of micellization, the sphere-to-rod transition parameter K and the CMC can be calculated as described in Section IV.B. We again note that the radius of the cylindrical middle part of the micelle and that of the spherical endcaps are allowed to diﬀer from one another and are determined by the equilibrium conditions. The calculated results are included in Table 5 for the surfactant solution containing the anionic SDS in the presence of 0.8M NaCl. In the absence of the polymer, large polydispersed rodlike micelles are formed in solution as shown by the large value for K. When the polymer molecules are present, the magnitude of K is dramatically reduced. Consequently, only small globular micelles are formed. The CMC corresponding to the formation of the polymer-bound globular micelles (0.057, 0.028, and 0.116 mM for pol ¼ 0, 15, and 15 mN/m, respectively) is lower than that for the formation of polymer-free rodlike micelles (0.313 mM). Therefore, the equilibrium favors the formation of the smaller ellipsoidal micelles in the presence of the polymer. Thus, a rod-to-globule transition is induced by the addition of the polymer. In the case of the nonionic surfactant dodecyl dimethyl phosphene oxide (designated as C12PO), large rodlike micelles are formed in polymer-free solutions as reﬂected in the large value for K and at a CMC of 0.243 mM. In the presence of the nonionic polymer, K is dramatically decreased and the allowed aggregate is a small ellipsoid. The calculations show that if pol ¼ 0 or 15 mN/m, the CMC is 0.128 or 0.063 mM in the presence of the polymer. This implies that equilibrium will favor the formation of small polymerbound ellipsoidal micelles. In contrast, if pol ¼ 15 mN/m, the CMC corresponding to the polymer-bound micelles is larger (0.262 mM) than the CMC corresponding to the polymer-free micelles. In such a case, the binding with polymer does not occur and polymer-free rodlike micelles coexist with free polymer molecules in solution. One can also visualize Copyright © 2003 by Taylor & Francis Group, LLC

situations when pol assumes values such that the CMCs corresponding to both polymer-free and polymer-bound micelles are comparable. This condition will lead to the coexistence of both large rodlike and small polymer-bound ellipsoidal micelles.

F. Interaction of Polymer with Vesicles The free energy of aggregation is still given by Eqs. (80) and (81), with the understanding that the headgroup interaction free energies and the free energy of formation of the aggregate–water interface should be written for both inner and outer layers of the bilayer vesicle, the areas per molecule at these two layers can diﬀer from one another, and the layers can have diﬀerent thicknesses. The polymer molecules are assumed to be present at both inner and outer surfaces of the spherical bilayer vesicle. Calculations have been carried out for didodecyl sodium sulfate (designated as di-C12 SO4Na), and the results are included in Table 5. In the absence of the polymer, calculations show (see also Table 4) that di-C12 SO4Na forms small spherical bilayer vesicles. The inner and the outer radii of the hydrophobic shell are 4.63 nm and 6.68 nm, respectively. The volume of the aqueous core per surfactant molecule is approximately 0.350 nm3, whereas the volume of the polar headgroup of di-C12 SO4Na is less than 0.100 nm3. When the polymer molecule is present, the formation of the vesicular structure is not predicted. Calculations to examine the formation of closed aggregates have been carried out for the aggregate geometries described in Table 1. The results show that small globular micelles are favored (see Table 5). Thus, the addition of polymer to the solution containing vesicles can lead to a disruption of the vesicle structure and the generation of smaller closed aggregates.

VII. MICELLIZATION OF BLOCK COPOLYMERS A. Aggregation of Block Copolymers in Selective Solvents Block copolymer molecules exhibit self-assembly behavior similar to conventional low molecular-weight surfactants. The diﬀerent blocks of the AB copolymer can have diﬀering aﬃnities for the solvent: the A block being solvophobic and the B block being solvophilic. The two blocks thus resemble the tail and the head of a conventional low-molecular-weight surfactant. As a result, the block copolymer forms micelles in a variety of solvents that are selective to one block and nonselective to the other block (Fig. 49). In these micelles, the solvophobic blocks constitute the core and the solvophilic blocks constitute the corona or the shell region of the micelle. For BAB triblock copolymers, the A block has to bend back and form a loop so as to Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 49 Schematic representation of a micelle formed of AB diblock copolymers in a solvent selective for the B block. The thick lines denote the solvophobic blocks constituting the core of the micelle while the thin lines denote the solvophilic blocks forming the corona region of the micelle. A signiﬁcant amount of solvent is present in the corona region

ensure that the two B blocks are in the corona; similarly, in the case of an ABA copolymer, the B block has to form a loop and bend back so that the two A blocks can be inside the core. The micellization tendency of block copolymers may be viewed as more general compared to that of low-molecular-weight surfactants in the sense that aggregation of block copolymers is achievable in almost any solvent by selecting the appropriate block copolymer, whereas for low-molecularweight surfactants, water constitutes the best solvent for promoting aggregation [125–127]. Further, in the case of block copolymers, because of the large size of the solvophobic block, the CMC is often too small to be measurable when compared to the CMCs of low-molecular-weight surfactants. The block copolymer aggregates can assume a variety of shapes such as spheres, cylinders, and bilayers including vesicles. Theoretical treatments of block copolymer micelles have been pioneered by de Gennes [128], Leibler et al. [129], Noolandi and Hong [130], and Copyright © 2003 by Taylor & Francis Group, LLC

Whitmore and Noolandi [131]. de Gennes [128] has analyzed the formation of a diblock copolymer micelle in selective solvents by minimizing the free energy per molecule of an isolated micelle with respect to the aggregation number or core radius. The micelle core was assumed fully segregated and devoid of any solvent. The free energy of formation of the core–corona interface and the elastic free energy of stretching of the core blocks control the micellization behavior. Leibler et al. [129] have treated the problem of micelle formation of a symmetric diblock copolymer in a homopolymer solvent. In their study and in de Gennes’ work, the interface is taken to be sharp. Noolandi and Hong [130] and Whitmore and Noolandi [131] have formulated mean-ﬁeld models taking into account the possibility of a diﬀuse interface between the core and corona regions. The ideas of chain deformation and corona mixing eﬀects discussed in these studies have been applied to the treatment of micelles formed of nonionic surfactants with polyethylene oxide headgroups in Section IV. A. In this section the thermodynamic treatment of aggregation is presented for AB diblock and BAB triblock copolymers, and one can observe the close similarity between the model for low-molecular weight surfactants and that for the high-molecular-weight block copolymers.

B. Aggregate Shapes and Geometrical Relations Before developing a free energy model, we will ﬁrst deﬁne the geometrical relations connecting aggregate shapes to the molecular size properties of the block copolymer. The shape of the aggregate and the assumption of incompressibility lead to the geometrical relations summarized in Table 6 for diﬀerent morphologies. We denote the molecular volumes of the A and the B segments and the solvent by vA, vB, and vW, respectively. The characteristic lengths of the A and the B segments are denoted by LA (¼ v1=3 A ) ). The variables N and N refer to the number of segments and LB (¼ v1=3 A B B of block A and block B for the AB diblock as well as the BAB triblock TABLE 6 Geometrical Properties of Spherical, Cylindrical, and Lamellar Block Copolymer Aggregates Property Vc Vs g a ’B

Sphere

Cylinder

Lamella

4R3 =3 Vc ½ð1 þ D=RÞ3 1 Vc ’A =ðNA vA Þ 3NA vA =ðR’A Þ ðNB vB =NA vA Þ’A ðVc =Vs Þ

R2 Vc ½ð1 þ D=RÞ2 1 Vc ’A =ðNA vA Þ 2NA vA =ðR’A Þ ðNB vB =NA vA Þ’A ðVc =Vs Þ

2R Vc ½ð1 þ D=RÞ 1 Vc ’A =ðNA vA Þ NA vA =ðR’A Þ ðNB vB =NA vA Þ’A ðVc =Vs Þ

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copolymers, implying that the BAB triblock copolymer has two terminal blocks of size NB/2 attached to a middle block of size NA. We use the variable R to denote the hydrophobic core dimension (radius for sphere or cylinder and half-bilayer thickness for lamella), D for the corona thickness, and a for the surface area of the aggregate core per constituent block copolymer molecule. The number of molecules g, the micelle core volume VC, and the corona volume VS all refer to the total quantities in the case of spherical aggregates, quantities per unit length in the case of cylindrical aggregates, and quantities per unit area in the case of lamellae. The core volume VC is calculated as the volumes of the A blocks, VC ¼ gNA vA . The concentrations of segments are assumed to be uniform in the core as well as in the corona, with ’A standing for the volume fraction of the A segments in the core (’A = 1), and ’B for the volume fraction of the B segments in the corona. If any two structural variables are speciﬁed, all remaining geometrical variables can be calculated through the relations given in Table 6. For convenience, R and D are chosen as the independent variables.

C. Free Energy of Micellization of Block Copolymers An expression for 0g is formulated by considering all the physicochemical changes accompanying the transfer of a singly dispersed copolymer molecule from the inﬁnitely dilute solution state to an isolated micelle, also in the inﬁnitely dilute solution state. First, the transfer of the singly dispersed copolymer to the micellar core is associated with changes in the state of dilution and in the state of deformation of the A block. Second, the B block of the singly dispersed copolymer is transferred to the corona region of the micelle, and this transfer process also involves changes in the states of dilution and deformation of the B block. Third, the formation of the micelle localizes the copolymer such that the A block is conﬁned to the core while the B block is conﬁned to the corona. Fourth, the formation of the micelle is associated with the generation of an interface between the micelle core made up of A blocks and the micelle corona consisting of solvent W and B blocks. Further, in the case of a BAB triblock copolymer, folding or loop formation of the A block occurs, ensuring that the B blocks at the two ends are in the aqueous domain while the folded A block is within the hydrophobic core of the micelle. This provides an additional free energy contribution. The overall free energy of micellization can be obtained as the sum of the above individual contributions: ð0g Þ ¼ ð0g ÞA;dil þ ð0g ÞA;def þ ð0g ÞB;dil þ ð0g ÞB;def þ ð0g Þloc þ ð0g Þint þ ð0g Þloop ð82Þ Copyright © 2003 by Taylor & Francis Group, LLC

One may observe that many of the above free energy contributions are analogous to those considered in Section IV.A for conventional surfactants. The A block dilution contribution is equivalent to the tail transfer free energy. The A block deformation is identical to the tail deformation energy. The B block dilution and deformation contributions are equivalent to headgroup repulsions. The interfacial free energy is the same for both kinds of surfactants. Only the localization and looping free energy contributions are additions that had not been considered before. These two contributions are found to be less important relative to the other contributions. In essence, the free energy model for the block copolymer remains essentially the same as that for all self-assembling systems treated in this chapter. Expressions for each of the contributions appearing in Eq. (82) are formulated below.

1. Change in State of Dilution of Block A In the singly dispersed state of the copolymer molecule in solvent, the A block is in a collapsed state, minimizing its interactions with the solvent. The region consisting of the collapsed A block with some solvent entrapped in it is viewed as a spherical globule, whose diameter 2R1A is equal to the endto-end distance of block A in the solvent. The volume of this spherical region is denoted by V1A . The chain expansion parameter A describes the swelling of the polymer block A by the solvent W. 1=3 4 R31A 6 A ¼ ; 2 R1A ¼ A NA1=2 LA ; NA1=6 1=3 V1A ¼ A1 3 ð83Þ where ’A1 (¼ NA vA =V1A ) is the volume fraction of A segments within the monomolecular globule. The ﬁrst equality in Eq. (83) follows from geometry, while the second equality is based on the deﬁnition of the chain expansion parameter A, taking (NA1=2 LA ) as the unperturbed end-to-end distance of block A. The third equality is obtained by combining the ﬁrst two in conjunction with the deﬁnition for ’A1. Applying the suggestion of de Gennes [58], the volume fraction ’A1 is calculated from the condition of osmotic equilibrium between the monomolecular globule treated as a distinct phase and the solvent surrounding it. lnð1 A1 Þ þ A1 þ AW 2A1 ¼ 0

ð84Þ

In Eq. (84), AW is the Flory interaction parameter between the pure A polymer and solvent. In the micelle, the A block is conﬁned to the core region where it is like a pure liquid. The diﬀerence in the dilution of block A from its singly dispersed state to the micellized state makes a free energy contribution given by the relation Copyright © 2003 by Taylor & Francis Group, LLC

ð0g ÞA;dil v 1 A1 v ¼ NA A lnð1 A1 Þ þ A ð1 A1 ÞAW kT vW A1 vW ! 1=2 2 L 6NA AW A kT A

ð85Þ

The ﬁrst two terms account for the entropic and enthalpic changes associated with the removal of A block from its inﬁnitely dilute state in the solvent to a pure A state. These terms are written in the framework of the Flory [53] expression for an isolated polymer molecule. The last term accounts for the fact that the interface of the globule of the singly dispersed A block disappears on micellization. This term is written as the product of the interfacial tension ( AW) between pure A and solvent W, the surface area of the globule (4R21A2 ), and the factor ’A1 (volume fraction of the polymer A in the globule) to account for the reduction in the contact area between the block A and solvent W caused by the presence of some solvent molecules inside the monomolecular globule. If the interfacial tension AW is not available from direct measurements, it can be estimated using the relation AW ¼ ðAW =6Þ1=2 ðkT =L2 Þ, where L ¼ v1=3 W . Such a relation is usually employed for the calculation of polymer–polymer interfacial tensions [132,133].

2. Change in State of Deformation of Block A In the singly dispersed state of the copolymer, the conformation of the A block is characterized by the chain expansion parameter A, which is the ratio between the actual end-to-end distance and the unperturbed end-toend distance of the polymer block. The free energy of this deformation is written using the Flory [53] expression derived for an isolated polymer molecule. Within the micelle the A block is stretched nonuniformly, with the chain ends occupying a distribution of positions within the core while ensuring that the core has a uniform concentration. The free energy contribution allowing for nonuniform chain deformation is calculated using the analysis of chain packing pioneered by Semenov [46] and discussed earlier in detail in Section IV.A. In the case of a BAB triblock copolymer, the A block deformation is calculated by considering the folded A block of size NA to be equivalent to two A blocks of size NA/2. On this basis, one obtains " # ! 2 ð0g ÞA;def p 2 3 2 R 3 ¼ q ð 1Þ ln A ð86Þ kT 80 ðNA =qÞ L2A 2 A where q ¼ 1 for an AB diblock copolymer and q ¼ 2 for a BAB triblock copolymer having a middle hydrophobic block. The parameter p is dependent on aggregate shape and has the value of 3 for spherical micelles, 5 for Copyright © 2003 by Taylor & Francis Group, LLC

cylinders, and 10 for lamellae (see Section IV.A). In Eq. (86), the ﬁrst term represents the A block deformation free energy in the micelle while the second term corresponds to the deformation free energy in the singly dispersed copolymer.

3. Change in State of Dilution of Block B In the singly dispersed state of the copolymer, the polymer block B is swollen with the solvent. As mentioned before, NB denotes the size of the B block for the AB diblock copolymer, while for a symmetric BAB triblock copolymer, the end blocks are of equal size NB/2. We consider this swollen B block to be a sphere whose diameter 2R1B is equal to the end-to-end distance of isolated block B in the solvent. The volume of this spherical region is denoted by V1B , while ’B1 ½¼ ðNB =qÞvB =V1B is the volume fraction of B segments within the monomolecular globule; V1B ¼

4 R31B ; 3

2 R1B ¼ B ðNB =q Þ1=2 LB

ð87Þ

The second equality in Eq. (87) is based on the deﬁnition of the chain expansion parameter B, which can be estimated using the expression developed by Flory (53). In the Flory expression for B, Stockmayer (134) has suggested decreasing the numerical coeﬃcient by approximately a factor of 2 to ensure consistency with the results obtained from perturbation theories of excluded volume. Consequently, one can estimate B as the solution of 5B 3B ¼ 0:88ð1=2 BW ÞðNB =q Þ1=2

ð88Þ

where BW is the Flory interaction parameter between the B block and water. In the micelle, the B blocks are present in the corona region of volume VS. This region is assumed to be uniform in concentration with ’B (¼ gNB vB =VS ) being the volume fraction of the B segments in the corona. The free energy of the corona region can be written using the Flory [53] expression for a network swollen by the solvent. Therefore, the diﬀerence in the states of dilution of the B block on micellization provides the following free energy contribution: ð0g ÞB;dil v 1 B v ¼ NB B lnð1 B Þ þ B ð1 B ÞBW kT vW B vW ð89Þ v 1 B1 v NB B lnð1 B1 Þ þ B ð1 B1 ÞBW vW B1 vW The ﬁrst two terms in Eq. (89) describe the entropic and enthalpic contributions to the free energy of swelling of the B block by the solvent in the Copyright © 2003 by Taylor & Francis Group, LLC

corona region of the micelle, while the last two terms refer to the corresponding contributions in the singly dispersed copolymer molecule.

4. Change in State of Deformation of Block B In the singly dispersed state the B block has a chain conformation characterized by the chain expansion parameter B. In the micelle the B block is stretched nonuniformly over the micelle corona so as to ensure that the concentration in the corona region is uniform. Semenov [46] has shown that the estimate for the chain deformation energy assuming that the termini of all B blocks lie at the distance D from the core surface is not very diﬀerent from that calculated assuming a distribution of chain termini at various positions within the corona. This has already been applied to the case of surfactants with oligomeric ethylene oxide headgroups in Section IV. We use that expression here also: ð 0g ÞB;def 3 LB R 3 2 3 ¼ q P q ðB 1Þ ln B kT 2 ða=qÞ B 2

ð90Þ

where a is the surface area per molecule of the micelle core, q ¼ 1 for AB diblock and 2 for BAB triblock, as mentioned before, and P is a shapedependent function given by P ¼ ðD=RÞ=½1 þ ðD=RÞ for spheres, P ¼ ln½1 þ ðD=RÞ for cylinders, and P ¼ ðD=RÞ for lamellae. The ﬁrst term in Eq. (90) represents the free energy of deformation of the B block in the micellar corona, while the second term denotes the corresponding free energy in the singly dispersed copolymer molecule.

5. Localization of the Copolymer Molecule On micellization, the copolymer becomes localized in the sense that the joint linking blocks A and B in the copolymer are constrained to remain in the interfacial region rather than occupying all the positions available in the entire volume of the micelle. The entropic reduction associated with localization is modeled using the concept of conﬁgurational volume restriction [135]. Thus, the localization free energy is calculated on the basis of the ratio between the volume available to the A–B joint in the interfacial shell of the micelle (surrounding the core and having a thickness LB) and the total volume of the micelle: ð 0g Þloc d LB ¼ q ln kT Rð1 þ D=R Þd

ð91Þ

Here, d refers to the dimensionality of aggregate growth and is 3 for spherical micelles, 2 for cylinders, and 1 for lamellae. Copyright © 2003 by Taylor & Francis Group, LLC

6. Formation of Micellar Core–Solvent Interface When a micelle forms, an interface is generated between the core region consisting of the A block and the corona region consisting of the B block and the solvent W. The free energy of formation of this interface is estimated as the product of the surface area of the micellar core and an interfacial tension characteristic of this interface. The appropriate interfacial tension is that between a pure liquid of block A in the micelle core and a solution of block B and solvent W in the micellar corona. Because the corona region is often very dilute in block B, the interfacial tension can be approximated as that between the solvent W and the A block in the micelle core. Denoting the polymer A–solvent W interfacial tension by AW, the free energy of generation of the micellar core–solvent interface is calculated from ð 0g Þint agg ¼ a; kT kT

agg ¼ AW

ð92Þ

7. Backfolding or Looping in Triblock Copolymer The backfolding of the middle block in a BAB triblock copolymer contributes an entropic term to the free energy of solubilization. This contribution is absent for the case of a diblock copolymer. Jacobson and Stockmayer [136] show that the reduction in entropy for the condition that the ends of a linear chain of N segments are to lie in the same plane or on one side of a plane is proportional to ln N. Therefore, the assumption that the backfolding of the middle block in the micelle follows the same functional form is made. Hence, the backfolding entropy makes the following contribution in the case of a BAB copolymer: ð 0g Þloop 3 ¼ lnðNA Þ kT 2

ð93Þ

Here is an excluded volume parameter that is equal to unity when the excluded-volume eﬀects are negligible and larger than unity when these eﬀects become important. In our calculations, is taken to be unity. The diﬀerence in the estimate for in the case of ABA and BAB triblock copolymers may be important for explaining any observed diﬀerences between these two kinds of triblock copolymers having the same overall molecular weight and composition.

D. Predicted Aggregation Behavior of Block Copolymers Illustrative calculations have been carried out for the diblock copolymers, polystyrene-polyisoprene (PS-PI) and polyethylene oxide-polypropylene Copyright © 2003 by Taylor & Francis Group, LLC

oxide (PEO-PPO, denoted EXPY), and for the triblock copolymer PEOPPO-PEO (denoted EXPYEX). One may note that for PS-PI block copolymers, the micellization is examined in n-heptane, which is a selective solvent for the PI blocks and is a nonsolvent for the PS block. For the other two block copolymers, the calculations have been done in water as the solvent with PEO being the hydrophilic and PPO the hydrophobic blocks.

1. Estimation of Model Parameters To facilitate quantitative calculations, the values of molecular constants appearing in the free energy expressions are needed. The molecular volumes (vA and vB) of the repeating units appearing in the diﬀerent polymer blocks are 0.1612 nm3 for styrene, 0.0943 nm3 for butadiene, 0.01257 nm3 for isoprene, 0.0965 nm3 for propyleneoxide, and 0.0646 nm3 for ethyleneoxide [135]. The molecular volume of water is 0.030 nm3 and of n-heptane is 0.2447 nm3. Given the molecular weight M of the copolymer and the block composition (MA/M), the number of repeating units NA and NB in blocks A and B can be calculated, knowing the segmental molecular weights. The characteristic length L is calculated knowing the molecular volume of the solvent. For polyisoprene–heptane the solvent is practically a theta solvent at 258C and, correspondingly, the interaction parameters BW is taken to be 0.5 [130]. For polystyrene–heptane the solvent is a very poor solvent. The interaction parameter at 258C is taken to be AW ¼ 1:9 [130]. The corresponding interfacial tension between pure polystyrene and n-heptane is estimated from to be 5.92 mN/m [135]. For polyethyleneoxide–water and polypropyleneoxide–water systems, the interaction parameters were estimated from the experimental activity data available in the literature [54]. These data display a concentration dependence for the interaction parameters. Because the corona region is a dilute solution of polyethyleneoxide in water, the value for BW is taken from the dilute concentration region of the activity data. Correspondingly, BW ¼ 0.21. Because the core region is made of pure polypropyleneoxide, the value for AW is taken from the concentrated region of the activity data. For this condition AW ¼ 2.1. The corresponding value for the interfacial tension between water and polypropyleneoxide is calculated to be 25.9 mN/m. The estimation of these molecular constants are discussed in detail in Ref. [135].

2. Inﬂuence of Free Energy Contributions The role of various free energy contributions in inﬂuencing micelle formation can be understood from their dependence on the aggregation number. The formation of micelles in preference to the singly dispersed state of the copolymer occurs because of the large negative free energy contribution

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arising from a change in the state of dilution of the solvent incompatible A block. This free energy contribution is a constant independent of the size of the micelle and hence does not govern the aggregation number of micelle. The contribution favorable to the growth of the aggregates is provided by the interfacial energy. The geometrical relations dictate that the surface area per molecule of the micelle decrease with an increase in the aggregation number. Consequently, the positive interfacial free energy between the micellar core and the solvent decreases with increasing aggregation number of the micelle, and thus this contribution promotes the growth of the micelle. The changes in the state of deformation of the A and the B blocks and the change in the state of dilution of the B block provide positive free energy contributions that increase with increasing aggregation number of the micelle. Therefore, these factors are responsible for limiting the growth of the micelle. The free energy of localization and the free energy of backfolding or looping (in the case of BAB triblock copolymers) are practically independent of g and thus have little inﬂuence over the determination of the equilibrium aggregation number. The net free energy of formation of the micelle per molecule is negative and shows a minimum at the equilibrium aggregation number.

3. Predicted Micellization Behavior For the PS-PI copolymer, the calculated results have been compared against the measurements of Bahadur et al. [137] in Table 7. The tabulated experimental data have been derived from photon correlation spectroscopy and viscosity measurements, assuming that the micelle core is completely devoid of any solvent. The values for g, R, and D estimated from the measurements in this manner are compared against the model prediction and show reasonable agreement. Experimental observations using electron microscopy indi-

TABLE 7 Micellization Behavior of Polystyrene— Polyisoprene in n-Heptane at 258C

M 29,000 36,000 39,000 49,000 53,000

MA =M 0.31 0.45 0.49 0.59 0.62

g R (A ) D=R (Experiments)* 94 119 141 194 240

1.77 1.31 1.13 0.96 0.92

248 278 386 666 1113

*Source: Ref. 137.

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R ðA Þ D=R g (Predictions) 85 128 144 193 211

1.77 1.24 1.12 0.87 0.80

187 352 422 672 778

cated that the micelles are practically monodispersed [137], which is also in agreement with the predictions. Computed results for diblock copolymers of PEO-PPO are summarized in Table 8. The core radius, the corona thickness, the micelle aggregation number, and the calculated CMC (expressed as volume fraction CMC in water) are all listed. The calculations have been carried out keeping the size MA of the PPO block constant, the size MB of the PEO block constant, the composition of the block copolymer MA/M constant, and the overall molecular weight of the polymer M constant. In general, the PPO block plays a dominant role in determining the dimension of the core radius R, and hence the aggregation number g of the micelle, while the inﬂuence of the PEO

TABLE 8 Micellization Behavior of PEO–PPO Diblock Copolymers in Water M

MA =M

R ðA Þ

D=R

g

ln CMC

Results for constant 4,750 0.79 8,250 0.45 12,500 0.30 14,000 0.27 15,750 0.24

MA ¼ 3750 113 0.38 89 1.56 80 2.72 78 3.09 76 3.49

976 475 342 318 296

74.1 67.2 63.9 63.2 62.4

Results for constant 10.750 0.19 14,250 0.39 17,250 0.49 20.750 0.58 28,750 0.70 43,750 0.80

MB ¼ 8750 52 3.86 105 2.17 144 1.65 186 1.32 275 0.92 424 0.60

173 528 884 1354 2610 5491

38.8 85.3 116.7 148.3 208.8 298.1

Results for constant 2,000 0.30 7,000 0.30 20,000 0.30 35,000 0.30 50,000 0.30

MA =M 29 58 103 140 169

101 234 461 656 818

17.0 42.6 88.1 127.6 160.8

Results for constant 12,500 0.75 12,500 0.63 12,500 0.50 12,500 0.40 12,500 0.20

M ¼ 12,500 189 0.58 152 0.99 122 1.50 100 2.02 59 3.79

1808 1143 736 512 208

132.4 114.2 95.7 80.3 46.0

¼ 0:30 1.79 2.39 3.03 3.43 3.71

Copyright © 2003 by Taylor & Francis Group, LLC

block on R and g is comparatively smaller. The PEO block dominantly controls the corona dimension D, while the PPO block has only a marginal inﬂuence over it. In all cases the CMC is negligibly small because of the large size of the hydrophobic part of the block copolymer. The relative importance of the PEO block (the headgroup) and the PPO block (the tail group) is quite diﬀerent from that of conventional surfactant micelles. As seen in Section IV, the headgroup has a much more signiﬁcant eﬀect on the micellar properties for small surfactant molecules. This is because the headgroup interaction free energy is much more signiﬁcant compared to the tail deformation free energy in the case of small surfactant molecules. Hence, the eﬀect of the headgroup is dominant. In contrast, the tail deformation free energy can be comparable, if not larger, than the headgroup interaction energy in the case of block copolymers, depending on the relative sizes of the two blocks. Therefore, one sees the dominant role of the hydrophobic group in controlling the micelle size in the case of block copolymers.

4. Aggregate Shape Transitions To investigate how the size and composition of the block copolymer aﬀect the transition from one aggregate shape to another in the case of block copolymers, we have computed the aggregation properties of the family of Pluronic triblock copolymers, EXPYEX. The calculated results are summarized in Table 9. The aggregate shape that yields the smallest free energy of aggregation is taken to be the equilibrium shape. Also given are the dimensions of the core (R) and the corona (D), and the aggregation number (g) in the case of spherical aggregates. The numerical values within brackets are some available experimental data (see details in Ref. [138]). The calculations show that lamellar aggregates are favored when the ratio of PEO to PPO is small, whereas spherical aggregates are favored when the PEO to PPO ratio is large. Typically, for block copolymers containing 40 or more wt % PEO, only spherical aggregates form at 258C. For block copolymers containing 30 wt % PEO, cylindrical aggregates are possible. Block copolymers containing 20 or less wt % PEO generate lamellae. This is analogous to the behavior of small-molecular-weight surfactants where the reduction in headgroup repulsions can cause a transition from spherical micelles to rodlike micelles and then to bilayers. In this sense the formation of block copolymer micelles is entirely analogous to the formation of conventional surfactant micelles. One important diﬀerence that should be noted is connected to the tail transfer free energy contribution, which is negative and is the driving force for aggregation of surfactants and block copolymers. In Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 9

Aggregation Behavior of PEO–PPO–PEO Triblock Pluronic Copolymers in Water

Name

Structure

L62 L63 L64 L65 F68 P84 P85 F88 F98 P103 P104 P105 F108 P123 F127

E6 P35 E6 E9 P32 E9 E13 P30 E13 E19 P29 E19 E77 P29 E77 E19 P43 E19 E26 P40 E26 E104 P39 E104 E118 P45 E118 E17 P60 E17 E27 P61 E27 E37 P56 E37 E133 P50 E133 E20 P70 E20 E100 P64 E100

R (nm) 0.75 1.45 3.41 3.07 2.13 4.22 3.63 2.5 2.67 3.86 5.1 4.39 2.83 4.21 3.75

(3.8 to 4.6) (2.5) (3.7)

(2.5)

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D (nm) 1.92 1.39 1.66 (3.7 to 4.4) 2.21 5.1 (5.3) 2.25 2.83 (3.6) 6.39 7.03 2.15 2.98 3.73 7.66 (15.0) 2.44 7.02

g for Spheres — — 57 43 15 75 53 17 18 — 94 65 20 — 35

(39 to 70) (22) (57, 37 to 78)

(13) (15 to 45, 30)

Shape Lamellae Lamellae Sphere Sphere Sphere Sphere Sphere Sphere Sphere Cylinder Sphere Sphere Sphere Cylinder Sphere

the case of conventional surfactants the negative free energy associated with the transfer of the tail is signiﬁcant when water is the solvent and diminishes in magnitude when water is replaced by other polar organic molecules such as alcohols, glycerol, or formamide [139,140]. Therefore, the aggregation tendency is diminished when water is replaced by other solvents in the case of small-molecular-weight surfactants. In contrast, for block copolymers, the core-forming block can be incompatible with a wide variety of solvents, and therefore the tail transfer free energy contribution remains negative at appreciably large magnitude. Hence, signiﬁcant aggregation of block copolymers is possible in a number of solvents. The aggregation phenomenon where entropy changes (hydrophobic eﬀect) are important as in the case of conventional surfactants is replaced by an aggregation process where enthalpy eﬀects are also very important in the case of block copolymer aggregates.

VIII. CONCLUSIONS A quantitative approach to predicting micellar properties from the molecular structure of surfactant has been described in this chapter. No information derived from experiments on surfactant solutions is required for the predictive calculations. The approach combines the general thermodynamic principles of self-assembly with detailed molecular models for the various contributions to the free energy of micellization. Explicit analytical equations are developed for calculating each of these free energy contributions as a function of temperature. Methods for obtaining the few molecular constants appearing in these equations have been illustrated. A simple approach to calculating the aggregation properties via the maximum-term method, without having to perform detailed micelle size distribution calculations, is described. The quantitative approach is illustrated via predictive calculations performed on numerous surfactants, binary surfactant mixtures, and mixtures of surfactants with nonionic polymer. Surfactants having one or two tail groups, those possessing nonionic, anionic, cationic or zwitterionic headgroups, surfactants with ﬂuorocarbon tails, and mixtures of hydrocarbon and ﬂuorocarbon surfactants have been considered for the illustrative calculations. The formation of spherical micelles, globular micelles, rodlike micelles, and spherical bilayer vesicles have been investigated. The quantitative approach has been extended also to block copolymer aggregates taking into account the polymeric nature of both the headgroups and the tail groups of the block copolymer. The behavior of block copolymers is seen as analogous to that of surfactants, but with broader aggregation capabilities in a variety of solvent systems. The quantitative approach Copyright © 2003 by Taylor & Francis Group, LLC

described in this chapter has a broad scope as demonstrated by its extension to treat other self-assembly phenomena such as micellization in polar nonaqueous solvents [139,140], solubilization of hydrocarbons in micelles [16,19], the formation of droplet-type and bicontinuous-type microemulsions [141], and micelle formation at solid–liquid interfaces [142,143]. An approach similar to that discussed in this chapter for calculating the aggregation behavior of surfactants and surfactant mixtures, but with some variations in the free energy expressions, has been discussed in a number of papers by Blankschtein and co-workers [39–41,144–147].

ACKNOWLEDGMENTS Professor Ruckenstein has collaborated in many parts of the work discussed here as can be inferred from the cited references. The author has beneﬁted from numerous discussions with him.

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2 Modeling Association and Adsorption of Surfactants LUUK K. KOOPAL Netherlands

I.

Wageningen University, Wageningen, The

INTRODUCTION

The most characteristic property of surfactants is their strong amphipolarity caused by the primary structure of the molecules: a polar headgroup linked to an apolar hydrocarbon or ﬂuorocarbon tail. The spacial separation between headgroup and the apolar tail and the chemical diﬀerences between both parts of the molecule give surfactants their speciﬁc properties. With the headgroups a ﬁrst distinction can be made between ionic and nonionic surfactants. With the nonionic surfactants the headgroup consists of a sequence of hydrophilic or polar segments. For the ionic surfactants the headgroup is charged and coulomb interactions come into play. The speciﬁc nature of the headgroup can be emphasized by adhering speciﬁc (i.e., noncoulomb) properties to the headgroup in relation to the solvent and the surface. The tail segments of both the ionic and nonionic surfactants are apolar (hydrophobic). For the apolar tail the number of aliphatic or ﬂuorocarbon segments and aromaticity and branching are important. Due to their primary structure, surfactants form micelles. In aqueous solution there are surfactant aggregates with an apolar core surrounded by a corona of hydrated headgroups. The micelles are formed at a speciﬁc solution concentration, the critical micelle concentration, or CMC. The detailed structure of the surfactant—and, in particular, the size and shape of the headgroup as compared to the size and shape of the tail—determine the geometry of the micelles [1,2]. Surfactants with a large headgroup as compared to their tail form spherical micelles, weakly conical surfactants form cylindrical micelles, and surfactants with a cylindrical shape form lamellar aggregates. Copyright © 2003 by Taylor & Francis Group, LLC

Surfactants also have a strong tendency to adsorb on surfaces. With liquid–liquid and liquid–gas interfaces the primary structure of the surfactant determines the adsorption behavior. At solid–liquid interfaces the surface properties and the detailed structure of the surfactant determine the adsorption. In general, adsorption of surfactants at various interfaces starts at concentrations much below the CMC and it reaches a pseudosaturation value at the CMC. The fact that a pseudoplateau is reached, rather than a typical surface saturation value, is due to the fact that the concentration of free surfactant molecules hardly changes above the CMC. Provided the surfactant solution remains dilute, the ‘‘pressure’’ on the surfactants to go to the interface remains above the CMC the same. Similarly as in solution, at surfaces aggregated structures can also be present [3–14]. The structure of the surfactant will also in this case aﬀect the size and shape of the aggregates [15]; however, for solid surfaces the surface-surfactant aﬃnity also plays an important role. Both their behavior in solution and that at interfaces have led to a large variety of technical applications of surfactants. Solubilization of components in the micelles is one of the older applications of micelles [16]. At present, micelles are also used as, for instance, microdomains for chemical reactions or for micellar-catalyzed reactions [17–20] and in micellar chromatography [21,22] and micellar-enhanced (ultra) ﬁltration [23,24]. In liquid–liquid systems surfactants can be used to stabilize both normal and microemulsions [25,26]. Adsorption of surfactants to solid surfaces is of technical importance because at concentrations up to the CMC surfactants can cause both stabilization and destabilization of solid–liquid dispersions [27] and they can drastically modify wetting of solids [27–29]. Apart from these applications at relatively low surfactant concentrations there is a world of applications at high surfactant concentrations [30]. In all these applications the primary structure of the surfactant determines the general behavior, whereas the detailed structure gives rise to speciﬁc behavior. To present a review of applications and practical studies of surfactant micellization and adsorption is an almost impossible task. In order to gain understanding and to be able to further explore surfactant applications, good physical insight is required. Such insight can be obtained from modeling studies on both micellization and adsorption. In primitive models of surfactant behavior the primary structure is not even made explicit. For instance, micellization can be described on the basis of the mass action law describing the situation that n monomers form a micelle [31,32], and similarly adsorption can be described as accumulation of (interacting) monomers on a surface [33]. Such models may be able to describe the behavior phenomenologically, but they are not suited to give insight in surfactant behavior in relation to their structure. Copyright © 2003 by Taylor & Francis Group, LLC

One step better is the introduction of the head and tail group in the modeling, so that at least the primary structure is emphasized. However, in order to be able to investigate the eﬀect of the structural characteristics of a surfactant in detail, the precise structure of both the hydrophilic and hydrophobic parts of the molecule has to be considered. It will be clear that such models are far more complex than the models that treat surfactant molecules as simple monomers or amphiphilic entities. Although the sophisticated models are complex, they have the advantage that detailed insight in the surfactant behavior in solution and near interfaces can be obtained. Besides thermodynamic models, molecular dynamic (see e.g., [34–37]) and Monte Carlo simulations [38,39] can also be useful for a better understanding of surfactant behavior. In Chapter 1 Nagarajan [40] discusses the theory of micelle formation. A slightly older overview of the theory of micellization has been presented by Nagarajan and Ruckenstein [41]. Very recently, Hines [42] has presented a current opinion on theoretical aspects of micellization. Several reviews have appeared in the ﬁeld of surfactant adsorption at ﬂuid interfaces. Lu et al. [43] review the use of neutron reﬂectometry to study the structure and composition of surfactant layers at the air–water interface and critically assess the results by comparing them with information obtained with other methods. Fainerman et al. [44] have discussed adsorption isotherms and equations of state for ideal and nonideal surface layers in relation to experimental results. Old and new equilibrium surface tension models have been evaluated by Prosser and Franses [45]. Aratono and Ikeda [46] discuss in Chapter 3 adsorption at the gas–liquid interface on the basis of the Gibbs equation for mixed systems. Dynamic aspects of surfactant adsorption on ﬂuid interfaces have also attracted quite some attention. Several reviews have appeared; these are concerned partly with adsorption kinetics at static interfaces [47,48] and partly with dynamic interfaces [49–51]. Old reviews on surfactant adsorption at solid–liquid interfaces are those of Hough and Rendall [52] and Clunie and Ingram [53]. Rosen [54] has presented a practical review on synergism in mixtures of surfactants both in solution and at interfaces. Kronberg [55] has discussed mixed surfactant systems and advances in the understanding of surfactant mixtures at surfaces. Tiberg et al. [56] have discussed adsorption mechanisms and interfacial structures derived from modern measurement techniques. Manne and Gaub [57] have expressed a current opinion on imaging of surfactant micelles at surfaces and liquid ﬁlms by atomic force microscopy. Cox et al. [58] discuss self-assembled surfactant patterns on solid surfaces in relation to nanolithography. The ﬁrst part of the present paper presents a review of the thermodynamic models that have been used for the description of micellization and/or Copyright © 2003 by Taylor & Francis Group, LLC

adsorption. The review on micellization is kept brief because the theory of micellization is discussed in detail in Chapter 1. Fainerman et al. [44] and Prosser and Franses [45] have recently reviewed modeling aspects of adsorption at static ﬂuid interfaces. No recent reviews have appeared on modeling of surfactant adsorption at solid surfaces. The main attention will therefore be given to adsorption at solid surfaces. The second part of the paper is devoted to the self-consistent-ﬁeld lattice model for association and adsorption of surfactants [59–70]. This model is brieﬂy indicated by the acronym SCFA. In the SCFA model the surfactants are treated as chains of segments in solution that may adsorb at an interface and/or form micelles. Due to the number of parameters involved in such a detailed model the primary aim of this type of modeling is to study the eﬀects of the headgroup and tail structure on the micellization and adsorption behavior and to gain further understanding of surfactant behavior. The calculated results will be compared with experimentally observed trends in micellization and adsorption. Fitting of experimental data has not been the aim of most SCFA calculations. The emphasis in the SCFA section is also on micellization and adsorption on solid–liquid interfaces. The theory is well suited to cope with ﬂuid interfaces, but only a limited number of SCFA studies have been made on liquid–liquid [34,69] or liquid–vapor [70] interfaces.

II. MODELING MICELLIZATION A. General Classical models of micelle formation can be divided into two broad categories: the pseudophase separation models and the mass action models [71]. The range of insight that can be obtained with the pseudophase separation models as compared to the mass action models is limited. However, the relative simplicity of pseudophase models is a great advantage for their use in practice. A relatively new branch of theory is that of the self-consistent-ﬁeld models. In these models the conformations of the surfactant chains in a micelle are considered in the potential ﬁeld exerted by the presence of the surfactant molecules in that micelle [63].

B. Pseudophase Separation Models Phase separation models assume that the micelles are a separate pseudophase. The pseudophase commences at the CMC, which represents the saturation concentration for monomeric surfactants. The presence of the micellar phase is assumed but not explained; consequently no independent information can be obtained regarding the size, shape, or structure of the Copyright © 2003 by Taylor & Francis Group, LLC

micelles. To be able to describe the distribution of reactants between the solution phase and the micellar pseudophase, the chemical potentials of the reactants in the micellar phase have to be equated to those of the reactants that are dispersed in the aqueous phase. By introduction of a model for the chemical potentials of the components in both the aqueous and the micellar phases (e.g., assuming that the phases may be considered as regular solutions or be treated as solutions of solvent molecules and chain molecules that can be described by the Flory–Huggings theory), several features of micellization and solubilization in micelles can be investigated. With ionic surfactants electrostatic (1) eﬀects can be included in the activity coeﬃcients or (2) an electrical potential is given to the micellar pseudophase together with an adjustable parameter that accounts for counterion binding and electrochemical potentials are used instead of chemical potentials. The degree of complexity of the pseudophase models is directly related to the models used for the (electro)chemical potentials. Details and a discussion of the pseudophase models can be found in [25,71–76].

C. Mass Action Models Mass action models consider surfactant aggregates that are in equilibrium with surfactant monomers in a dilute aqueous solution. In the most simple models the surfactant monomers are in equilibrium with a micelle that has a certain average size (aggregation number) and shape. The more sophisticated multiple equilibrium mass action models consider stepwise association reactions of monomers and account for polydispersity eﬀects of micelles. The association of monomers to dimers, trimers, etc. up to n-mers now takes place under the condition that the chemical potential of the surfactant monomer in solution is equal to the chemical potential per molecule of an aggregate of any size and shape. The changes that a surfactant monomer (or a solubilizing species) in a dilute (electrolyte) solution undergoes if it is transferred to a surfactant aggregate dispersed in the same solution can be used to formulate the contributions to the standard Gibbs energy of micellization. As a result the standard free energy of the micellization reaction is related to a standard state in which the reactants (surfactants, salt ions, solubilizing species) are dispersed at inﬁnite dilution. With this type of modeling the micelle formation is predicted from basic principles; it is reversible, and the aggregate size, aggregate polydispersity, and, depending on the model, micellar shape can be calculated. If the surfactant molecules are ions, it is often necessary to introduce counterion binding using an adjustable parameter to model the ‘‘surface’’ charge or ‘‘surface’’ potential of the micelles. Copyright © 2003 by Taylor & Francis Group, LLC

The ‘‘ﬂexibility’’ of the mass action models is related to the selection of the contributions to the standard Gibbs energy of micellization. Common contributions are (1) the Gibbs energy to transfer the surfactant hydrophobe to the micellar interior, (2) the interaction related to the extent of shielding of the micellar core from exposure to the aqueous solution, (3) the steric and conformational interactions related to transferring a surfactant (chain) molecule from the standard solution to the micellar phase, (4) the electrostatic interaction, and (5) the Gibbs energy of mixing. The expressions for the ﬁrst four contributions are dependent on the geometry of the micelles. By introducing constraints related to the structure of the surfactant and considering diﬀerent geometries it is possible to predict the preferred geometry of an aggregate. Chapter 1 [40] explains the multiple mass action models in more detail and refs. [71,72,77] review these models, with emphasis on mixed surfactant systems. References [41,78–80] can be consulted for some illustrative advanced treatments.

D. Self-Consistent-Field Models Since about 1980 several authors have used self-consistent-ﬁeld (SCF) molecular thermodynamic models to gain further insight in micellization and especially the micellar structure [59–61,81–85]. Similarly as in the advanced mass action models, the detailed structure of the micelles is predicted. Special attention is given to the packing and conformations of the surfactant chains in the micelles and the relation between the molecular architecture and the micellar structure and size. Surfactant chains in a micelle are generated by a statistical step-weighted walk procedure. Each step of the walk is weighted with a Boltzmann factor that accounts for both the enthalpic and entropic (excluded volume) interactions that the segment experiences in the micelle. Similar types of interactions are taken into account as in the advanced mass action models. However, instead of applying analytical expressions for the various contributions to the standard Gibbs energy, only the interaction parameters (FH type) and the volume constraints have to be speciﬁed. The detailed equilibrium distribution of surfactant segments within the micellar structure, i.e., within a potential ﬁeld exerted by the presence of the surfactant molecules themselves, is calculated by an iterative minimization of the Gibbs (Helmholtz) energy of the system. At equilibrium the segment density distribution and the potential ﬁeld exerted by the segments are fully in accordance with each other. The CMC and the micelle size are found by using arguments from the small system thermodynamics as Copyright © 2003 by Taylor & Francis Group, LLC

introduced by Hill [86] and worked out for surfactant micellization by Hall and Pethica [87]. In the early treatments the surfactant hydrophobe was assumed to be ﬂexible and the walk was started at the plane ﬁxing the positions of the headgroups [81–83,88–90] and hence assuming (implicitly) the geometry of the micelle. The alignment of the surfactant headgroups in one plane is a severe simpliﬁcation when the aim is to describe not only the interior of the micelle but also the surface structure or ‘‘roughness’’ [91,92]. Gruen [84] and Szleifer et al. [85] relaxed this constraint in later studies but still used the ‘‘surface’’ density of the headgroups as an input parameter. The ﬁrst molecular thermodynamic treatment in which these constraints were completely avoided is the SCFA theory, developed by Leermakers and Scheutjens [59–61] and applied to membrane and micelle formation. The schematic representation of a spherical micelle in the SCFA theory is shown in Fig. 1. Subsequently Van Lent and Scheutjens [93] used the SCFA model to describe micellization of block copolymers and Bo¨hmer and Koopal [62] applied it for the modeling of micellization of nonionic surfactants. After Bo¨hmer et al. [94] and Barneveld et al. [95] had shown how electrostatic interactions could be incorporated in the SCFA theory, Bo¨hmer et al. [63] have used it to model micellization of ionic surfactants. The detailed theoretical background of the SCFA model is discussed in Section IV of this chapter. Predicted results for nonionic micelles are presented in Section V, and those for micelles of ionic surfactants in Section VII.

FIG. 1 Schematic representation of a section of a spherical micelle in the SCFA treatment. Copyright © 2003 by Taylor & Francis Group, LLC

III. MODELING ADSORPTION A. Adsorbed Layers, Surface Micelles, Hemimicelles, and Admicelles In relation to the models for micelles, most adsorption models can be classiﬁed as a kind of mass action models in which many diﬀerent expressions are used for the standard Gibbs energy of adsorption. An important aspect of the adsorption models is the assumed structure of the adsorbed layer. A distinction can be made between models that treat the adsorbed layer as ‘‘smeared-out’’ and models that consider ‘‘local aggregates’’ at the surface. In principle, the best models are those that do not make any a priori assumption at all about the adsorbed layer structure, but ﬁnd this structure in a self-consistent way. This kind of modeling is scarce; at present only some results obtained with the SCFA model for nonionic surfactant adsorption on a homogeneous surface are available. The smeared-out layer models can be subdivided into ‘‘monolayer’’ and ‘‘bilayer’’ models. With the local aggregate models various types of aggregates are assumed to describe the ‘‘surface micelles.’’ In the present text a distinction will be made between ‘‘surface micelles,’’ ‘‘hemimicelles,’’ and ‘‘admicelles,’’ see Fig. 2. In order to avoid confusion about the terminology, these terms will be explained ﬁrst. Surface micelles are surface bound micellarlike structures in general, and more speciﬁcally the term is used when the primary structure of the surfactant plays an important role in the description of the surface aggregates. In the older literature the term hemimicelles is used for surface aggregates in general. At present, it is more common to deﬁne hemimicelles as the speciﬁc class of monolayer-type local aggregates in which the surfactants are adsorbed either with their headgroup in contact with the surface (head-

FIG. 2 Schematic representation of hemimicelles, admicelles, and surface micelles on a hydrophilic (top) and a hydrophobic surface. Copyright © 2003 by Taylor & Francis Group, LLC

on adsorption on mineral surfaces) or with their tail in contact with the surface (tail-on adsorption on apolar surfaces). With this restricted deﬁnition the hemimicelle structure is strongly dominated by the attraction between the anchoring group and the surface. The shape of the hemimicelles is not necessarily comparable to the micellar structure that may occur in solution. The hemimicelle approximation can be compared with the monolayer approximation in the smeared-out case. Admicelles are bilayer-type local aggregates, i.e., some of the headgroups are in contact with the surface, other headgroups point toward the solution. Admicellar aggregates can be compared with bilayer adsorption in the smeared-out case. Hemimicelles on mineral surfaces (head-on adsorption) may become admicelles near the CMC, but they are not necessarily the precursor for the admicelles. At mineral surfaces smeared-out monolayer-bilayer models have often been used, in combination with the generally accepted knowledge that local aggregates may occur, to make predictions on the existence of hemimicelles or admicelles. In general, it should be realized that the attraction between the surfactant and a solid surface is an important variable that does not occur with micellization. This makes the modeling of surfactant adsorption to solid surfaces considerably more complex and more diverse than that of surfactant micellization.

B. Trends in Surfactant Adsorption on Solid Surfaces The area of surfactant adsorption to solid surfaces can be divided into subareas as indicated in Fig 3. The division is based on the type of surface, the type of surfactant, and the surfactant concentration. Broadly speaking, two types of solids and two types of surfactants can be distinguished: the surface is hydrophilic or hydrophobic and the surfactant is ionic or nonionic. The distinction between hydrophilic and hydrophobic surfaces is directly related to the distinction between the hydrophilic surfactant headgroup and the hydrophobic surfactant tail. The distinction between ionic and nonionic surfactants is important because of the special treatment required for the coulomb interactions (long-range). With adsorption on hydrophilic surfaces and low surfactant concentrations the driving force for adsorption is the attraction between the surfactant headgroup and the surface. Therefore, the surfactant adsorbs at low surfactant concentrations with its headgroup in contact with the surface. For both nonionic and ionic surfactants the attraction will have a shortrange (speciﬁc) contribution depending on the type of headgroup and the type of surface. Besides this speciﬁc attraction ionic surfactants will experiCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 3 Subareas of surfactant adsorption on solid surfaces. From left to right the drawings give a schematic representation of the state of adsorption with increasing surfactant concentration. The important variables are shown in the middle of the ﬁgure: T (temperature), c (surfactant concentration), I (ionic strength), and pH (as indicator for the surface charge).

ence a generic electrostatic (coulomb) interaction. This interaction will be attractive if surface and surfactant are oppositely charged and repulsive when surfactant and surface carry the same charge sign. In the latter case adsorption only occurs if the speciﬁc attraction is stronger than the coulomb repulsion. In general, the coulomb interactions depend on the valency of the surfactant, the magnitude of the surface charge (pH), the ionic strength (I), and the extent of surfactant adsorption. At intermediate surfactant concentrations the hydrophobic attraction between the surfactant tails that protrude into the solution promotes further adsorption. Initially the adsorption may continue in a monolayer or be monolayerlike (hemimicelles) with the headgroup still in contact with the surface. At a certain concentration the orientation of the molecules will reverse in order to screen the hydrophobic tails from contact with the aqueous solution and a bilayer or bilayer-type aggregates (admicelles) will be formed. The concentration at which the bilayer-type adsorption starts depends on the tail and headgroup characteristics. For ionic headgroups bilayer-type adsorption is, in general, favored if the charge of the surface Copyright © 2003 by Taylor & Francis Group, LLC

groups is compensated by the adsorbed surfactant charge. For nonionic surfactants the cross section (size) of the surfactant headgroup as compared to that of the tail is important for the concentration at which the transition occurs. Depending on the eﬀective size of the headgroups as compared to the tail size and length, either the bilayer structures will grow upon a further increase of the surfactant concentration into complete bilayers or they will form surface micelles. The shape of the surface micelles (roughly spherical or cylindrical) will depend on the surfactant structure and the surfactant–surface interactions (distortion of the shape to pinned micelles). The top of Fig. 2 indicates the main structure of the adsorbed layer on hydrophilic surfaces as a function of the surfactant concentration. For hydrophobic surfaces the situation is simpler than on hydrophilic surfaces. With hydrophobic surfaces the adsorption at low surfactant concentration is driven by the hydrophobic attraction between the surfactant tail and the surface sites. The surfactant molecules screen the unfavorable interactions between the surface and the aqueous solution. By increasing the surfactant concentration the lateral hydrophobic attraction between the surfactant tails comes into play and a submonolayer- or monolayer-type local surfactant aggregates (hemimicelles) may form. At surfactant concentrations near the CMC the monolayer structures may gradually transform into a complete monolayer or become larger hemimicellar aggregates. Again the type of structure that will be formed depends on the surfactant characteristics and the surfactant–surface interactions. The main diﬀerence with the hydrophilic surfaces is that no bilayer-type structures are formed. The bottom part of Fig. 2 gives a schematic representation of the adsorbed structures on hydrophobic surfaces. Surfactant adsorption on aqueous LG and LL interfaces will follow a similar trend as that on hydrophobic solid surfaces, with air or the oil phase taking the position of the solid surface. The role of the ionic strength is most important for ionic surfactants; its main action is to screen the electrostatic interactions. This screening leads in the ﬁrst place to lower values of the CMC. With its inﬂuence on the adsorption it should be realized that screening has a ‘‘normal’’ and a ‘‘lateral’’ component. The ‘‘normal’’ screening applies to the headgroup–surface interaction (which can be attractive or repulsive depending on the charge signs) and the ‘‘lateral’’ screening to the headgroup–headgroup repulsion. For nonionic surfactant adsorption on charged surfaces the ionic strength will aﬀect the surface charge. Surface charge and ionic strength will together aﬀect the speciﬁc interactions between the surfactant headgroup and the surface sites. The role of the surface charge is often synonymous with the role of the pH, because for many surfaces protons and hydroxyl ions act as chargedetermining ions. Copyright © 2003 by Taylor & Francis Group, LLC

The eﬀect of the temperature is important for all the interactions. However, its eﬀect on the hydrophobic interactions is most important. For hydrophilic surfaces a ﬁrst indication of the magnitude of this eﬀect can be obtained by considering the eﬀect of temperature on the CMC of the surfactants [96]. For hydrophobic surfaces not only the surfactant hydrophobe but also the extent of hydrophobicity of the surface will play a role. With the discussion of surfactant adsorption that follows a distinction will be made between nonionic and ionic surfactants and between smearedout models and local aggregate models. Most attention will be given to hydrophilic surfaces. In order not to confuse the discussion too much, ﬁrst some general remarks will be made on surface heterogeneity eﬀects in relation to surfactant adsorption. In the other sections surface heterogeneity is largely neglected.

C. Surface Heterogeneity and Surfactant Adsorption Surface heterogeneity plays a prominent role in the discussion about the shape of surfactant adsorption isotherms and heat of adsorption curves [97– 99]. In general, solid surfaces are heterogeneous, which is reﬂected by the fact that diﬀerent types of surface sites have diﬀerent interactions with the surfactant. With surface heterogeneity the length scale of the topography of the surface is important in relation to the length scale of the lateral interactions. Classically a distinction is made between random (molecular-length scale) and patchwise (large length scale) heterogeneity. For random surfaces the lateral interactions are averaged over the entire surface; for patchwise surfaces the lateral interactions are assumed to be ‘‘active’’ per patch only and interactions crossing the patch boundaries are mostly neglected. For nonionic surfactants the length scale of the lateral interactions is generally of the order of the size of the molecules, and the distinction between a random and a patchwise treatment can be based on the scale of the surface heterogeneity. For surfaces with a random heterogeneity the isotherm may have a somewhat lower slope than for homogeneous surfaces, but with progressive adsorption heterogeneity eﬀects will be largely masked by the strong lateral attractions between the surfactant molecules. At low surfactant concentrations and low surface coverage, lateral attractions are absent or weak and surface heterogeneity eﬀects may be noticeable by an initial slope of the log–log adsorption isotherm that is smaller than unity [100]. At intermediate and higher surface coverage the lateral hydrophobic attraction will most probably dominate the behavior. This is certainly the case with bilayer-type adsorption or adsorption in admicelles. Therefore, neglecting the heterogeneity may well be a reasonable approximation in Copyright © 2003 by Taylor & Francis Group, LLC

this case. Arguments based on the initial part of the isotherm to introduce heterogeneity in adsorption models are correct, but the way in which this heterogeneity aﬀects the rest of the adsorption depends strongly on the model for the local isotherm (i.e., the model for adsorption on a homogeneous surface). Hence, the eﬀect of heterogeneity on the adsorption can only be fully understood when a consensus is reached about the adsorption on homogeneous surfaces. In the case of patchwise surface heterogeneity, the nonionic surfactant isotherms may be seriously aﬀected by the heterogeneity. Each patch can be considered as a homogeneous surface and the overall adsorption is the sum of the local adsorption contributions. For instance, for well-deﬁned large patches, with suﬃciently diﬀerent aﬃnities for the surfactant, stepwise isotherms may be predicted, especially when the adsorption is plotted as a function of the logarithm of the surfactant concentration. For a wide distribution of surface heterogeneity a continuous aﬃnity distribution should be used, and the overall adsorption equation is an integral equation based on the local isotherm and the distribution function. In this case heterogeneity will lower the slope of the semilogarithmic isotherm (adsorption versus log c), in the same way as for random heterogeneous surfaces. Plotting the isotherm double logarithmically can make a distinction between lateral attraction and heterogeneity eﬀects. With pure surface heterogeneity the initial slope should be smaller than unity and the slope should decrease with increasing coverage. An increase in the slope of the isotherm or a slope larger than unity always points toward lateral (hydrophobic) attraction. In the case of a repulsive (coulomb) lateral interaction it is not possible to make a distinction between heterogeneity and lateral eﬀects. Only for simple local isotherm expressions, such as the Langmuir or Frumkin– Fowler–Guggenheim (FFG) equation, and a few speciﬁc distribution functions do analytical solutions exist for the overall isotherm [100]. In general, a numerical solution is required and the outcome depends on both the chosen local isotherm and the chosen distribution function. It will be clear that many possible solutions exist in this case and that this type of treatment is poorly suited to gain insight into the adsorption process and/or the structure of the adsorbed layer. Only in the case that the surface–surfactant aﬃnity distribution can be derived (approximately) from independent measurements is there a possibility to obtain insight into the adsorption process from the overall surfactant adsorption isotherm. For ionic surfactants the most important lateral interaction in relation to the scale of the surface heterogeneity is the coulomb repulsion between the surfactant ions. The Debye length, which is inversely proportional to the square root of the ionic strength, gives the length scale of the coulomb interactions. In practice, the Debye length may vary from a few tenths of Copyright © 2003 by Taylor & Francis Group, LLC

an nm at high salt concentrations to several hundreds of nm in the absence of added salt. For random heterogeneous surfaces the large scale of the lateral interactions is a good reason to neglect surface heterogeneity as a ﬁrst-order approximation. For patchwise surfaces the characteristic dimension of the patch has to be several times the Debye length; otherwise the surface may be considered as random heterogeneous and the heterogeneity eﬀect is relatively small. For a surface with a patchwise heterogeneity of not too large a scale, it may be necessary to treat the heterogeneity as random (and hence neglect it) at low salt concentrations but as patchwise (and take it into account) at high salt concentrations. In many treatments involving the adsorption of ionic surfactants on patchwise heterogeneous surfaces, this aspect is poorly recognized because the coulomb interactions are accounted for in too primitive of a way [98,99,101–103]. With today’s state of the art in surfactant adsorption modeling, the understanding of surfactant adsorption will merely improve by a better understanding of what occurs on a homogeneous surface and how the detailed structure of a surfactant aﬀects the adsorption behavior [15]. Once this issue is settled a more detailed discussion on surface heterogeneity may follow. Eﬀects of surface heterogeneity on adsorption isotherms are, in general, known. As indicated above, for surfactant adsorption the eﬀects will be relatively small for random-type surfaces and for patchwise surfaces they will either give steps in the isotherm (few large patches) or decrease the slope of the isotherm (wide distribution of patches). Only when independent evidence is present that the surface is composed of patches and that the isotherms predicted on the basis of surface homogeneity are too steep is it appropriate to introduce surface heterogeneity. But even then the question remains, especially in the case of ionic surfactants, of which local isotherm equation should be used. Fitting of isotherms or heats of adsorption data on the basis of surface heterogeneity and a too-simple local isotherm will not improve our understanding of the adsorption process. For the moment these arguments are a good reason to concentrate on the diﬃcult task of improving the description of surfactant adsorption at homogeneous surfaces. The heterogeneity issue can be settled when agreement is found on the isotherm equation for the homogeneous surface.

D. Adsorption of Nonionic Surfactants 1. Adsorbed Layers A simple mean-ﬁeld model that has been used to describe the adsorption of nonionic surfactants is the regular behavior model [104]. In this model the surfactant structure is completely denied and the adsorption is restricted to a smeared-out monolayer; however, nearest-neighbor contacts are taken into Copyright © 2003 by Taylor & Francis Group, LLC

account. For adsorption from dilute solution, a situation normally found for surfactants up to the CMC, the regular behavior model simpliﬁes to the Frumkin–Fowler–Guggenheim (FFG) [105,106] equation 1 ¼ x1 K12 exp 12 1 1 1

ð1Þ

In the case of surfactant adsorption 1 is simply the ratio between the adsorption and the adsorption at the CMC; x1 is the surfactant mole fraction (or concentration) in solution; K12 is the adsorption constant, being a measure of the preference of the surface for the surfactant with respect to the solvent; and ij is the so-called Flory–Huggins (FH) interaction parameter. The expression for ij is ij ¼

NA Z

"ij 0:5 ð"ii þ "jj Þ RT

ð2Þ

with NA Avogrado’s number, z the number of nearest neighbors to a central molecule, and "ii , "jj , and "ij the pairwise interaction potentials (Gibbs energies) [107]. Note that according to its deﬁnition ii ¼ jj ¼ 0. Because "ii , "jj , and "ij are generally of negative sign, ij is positive if like contacts are preferred over unlike contacts and negative if unlike contacts are favored. For surfactant adsorption K12 and 12 should be considered as adjustable parameters expressing the aﬃnity for the surface and the lateral interactions in the adsorbed layer, respectively. In order to arrive at a more realistic model for surfactant adsorption, Kronberg [108] and Koopal et al. [109,110] have used ideas expressed in polymer adsorption theories to incorporate the chain characteristics of the surfactants in the modeling. In this case volume fractions should be used rather than mole fractions and the adsorption is not restricted to a monolayer, but the surfactant segment density near the interface has a block proﬁle. Koopal et al. [110] have shown that for dilute solutions, an equation similar to Eq. (1) results: 1 b m Wm Km exp rm 1 r ¼ 1 ð1 1 Þ r

ð3Þ

where 1 is the volume fraction of the surfactant in the adsorbed phase and b1 that in bulk solution, Km expresses the aﬃnity, Wm is the loss in conformation entropy, r is the surfactant chain length, and m is an eﬀective FH interaction parameter in the adsorbed layer. Km , Wm , and m are dependent on the number of segments, m, in direct contact with the surface. Although Eq. (3) is more ‘‘ﬂexible’’ than Eq. (1), the structure of the adsorbed layer is still largely neglected. A complication of Eq. (3) is that m will depend on the adsorption itself so that Km , Wm , and m will only be constant over a limited Copyright © 2003 by Taylor & Francis Group, LLC

range of adsorption values. In principle m can be found by minimizing the Gibbs energy of the system at a given composition. Narkiewicz-Michalek et al. [102] give an expression that can be used to ﬁnd m as a function of 1 . The equation given by Kronberg is somewhat diﬀerent and used in practice [108,111,112] more than Eq. (3), but for dilute solutions the diﬀerences are not essential; see [110]. Huinink et al. [113] have presented a semi-thermodynamic (ST) model for adsorption of nonionic surfactants in cylindrical hydrophilic pores based on smeared-out adsorption layers. The adsorption is treated as a transition between a dilute gaslike phase and a bilayer phase. An expression similar to the Kelvin equation has been derived to describe the inﬂuence of pore curvature on the phase transition. The eﬀect of curvature on the phase transition increases with increasing aﬃnity of the surfactant bilayer for the surface. The higher the aﬃnity is, the more the formation of a bilayer in the pore is promoted as compared to that on a ﬂat surface. Because the model is based on a sharp phase transition, it holds best if the headgroup repulsion is weak (small headgroups).

2. Adsorbed Layers: SCFA Theory Koopal et al. [62] have used the SCFA model to describe the adsorption of nonionic surfactants. For details of the SCFA theory we refer to Section IV of this chapter. For nonionic surfactants on hydrophilic surfaces the SCFA theory predicts for molecules with a small headgroup a phase transition from a dilute layer to a condensed bilayer, provided the headgroups are not too long. For small headgroups the 2D transition is from a gaslike layer to the condensed bilayer; for an intermediate headgroup size a fairly ﬂat layer is formed before the 2D condensation to a bilayer takes place. For large headgroups the condensation step is absent. On hydrophobic surfaces surfactants with a small or intermediate headgroup undergo a phase transition from a gaslike layer to a condensed monolayer at low concentrations. For surfactants with a large headgroup a strong increase in adsorption is observed at low concentrations, but there is no phase transition. At both hydrophobic and hydrophilic surfaces the adsorption at the CMC increases with decreasing headgroup size. More details are presented in Sections VI.A and B. Huinink et al. [114,115] have extended the SCFA model to allow for adsorption of nonionic surfactants with a small headgroup on porous or rodlike hydrophilic surfaces. The phase transition that occurs on ﬂat surfaces also appears for the curved surfaces. On porous surfaces the transition occurs at lower and on rod-shaped surfaces at higher concentrations than on ﬂat surfaces. The prediction for the porous surface is in accordance with the results obtained with the ST theory [113]. The adsorbed amount decreases Copyright © 2003 by Taylor & Francis Group, LLC

with decreasing pore radius, and the phase transition is shown to depend on the molecular architecture and adsorption energies. The surface tension of the bilayer can be related to the surfactant structure and the curvature constant of the bilayer.

3. Surface Aggregates Zhu and Gu [116,117] have presented a very simple model for adsorption of nonionic surfactants. They assume that the adsorbed layer is composed of surfactant aggregates. A surfactant aggregate is formed on the surface before stable aggregates are formed in solution; the aggregate is stabilized by the interaction with the surface. By applying a simple mass action model Zhu arrives at the following equation: 1 ¼ cn1 K 1 1

ð4Þ

where 1 is the adsorption divided by the adsorption at the CMC, c1 is the surfactant concentration, and n is the number of monomers in the surface micelle. Zhu uses the word ‘‘hemimicelle,’’ but in the present text this term is used in a more restricted sense. Equation (4) is also known as the Hill or Freundlich equation; it reduces to the Langmuir equation for n ¼ 1. When values of n < 1 are found with nonionic surfactants, there is good reason to believe that the surface heterogeneity is important. Equation (4) is well suited to describe cooperative adsorption and S-shaped isotherms. The main advantage of this model is that it emphasizes in a very simple way that the adsorbed layer may be composed of aggregates stabilized by the presence of the surface. In Fig. 4 adsorption data for two nonionic surfactants on silica are shown, together with the isotherms calculated with Eq. (4). Equation (4) is a simpliﬁed form of a two-stage mass action model for surface aggregate formation proposed by Zhu et al. [117–119] and used by these authors for ionic surfactants. The general model is based on the following assumptions: (1) isolated surfactant molecules adsorb at the surface according to the Langmuir model and (2) the adsorbed monomers are nuclei for the formation of surface micelles composed of in total n monomers according to the mass action law. This leads to the following equation that can be used to describe a variety of shapes of adsorption isotherms: 1 þ k2 c1n1 k1 c1 n ð5Þ 1 ¼ 1 þ k1 c1 1 þ k2 cn1 1 In Eq. (5) 1 is the adsorption relative to that at the CMC, c1 is the monomer concentration, k1 is the aﬃnity of the monomer for the surface, k2 is the aggregation constant, and n is the ﬁnal aggregation number, or the coCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Adsorption isotherms of octylmethylsulfoxide (x) and decylmethylsulfoxide (~) on narrow pore and wide-pore (DEMS, ~) silica gels. (Redrawn from Ref. 116 with permission of Elsevier Science-NL, Amsterdam, The Netherlands.)

operativity. The value of k1 determines the initial part of the isotherm; it can give the isotherm a Langmuirlike (L) ﬁrst step at low concentrations. The value of k2 determines the second step. In the presence of a two-step isotherm (LS type) n represents the ratio of adsorption levels of the two steps. S-shaped isotherms will occur when k2 is larger than k1 . The model also allows for the derivation of the fraction of the adsorption present in monomers and that present in surface micelles. Moreover, the 2D equation of state can be obtained [120]. The model gives no further information on the structure of the surface micelles; it is merely a convenient tool to describe the adsorbed state. An older, somewhat similar model is the three-stage adsorption model of Klimenko [121,122]. Another treatment that describes surface micelles is due to Israelachvili [15]. In this elegant treatment Israelachvili extends his ideas for the relations between the structural properties of the surfactant molecules and the micellar structure (three-dimensional or 3D situation) to the 2D situation of surfactant aggregates at ﬂuid interfaces. The result is given as a nonideal 2D equation of state, and it is shown that due to the limited size of the aggregates the surface-pressure-area curves have nearly horizontal parts rather than a strictly horizontal part as expected for the 2D condensation of an inﬁnitely large aggregate or adsorbed layer. Both the size and shape of the 2D aggregate are shown to be dependent on the surfactant structure. In principle, the treatment can be extended to adsorption at solid surfaces using the Gibbs equation to convert the 2D equation of state in the corresponding adsorption isotherm. For solid surfaces the treatment will only be Copyright © 2003 by Taylor & Francis Group, LLC

realistic when obstruction eﬀects caused by the solid are small. This will be the case for low-energy solids. A far more complicated model that describes surface micelles is that of Levitz [123]. In this model a mass action type of approach is used with several contributions to the standard Gibbs energy in order to relate the structure of the surface aggregates to the structure of the surfactant molecules. Also in this model the aggregates are formed at the surface before they form in solution due to the interactions of the monomers with the surface. When the interaction with the surface is weak, the aggregate structure is determined by the primary structural parameters of the surfactant, just like in solution. For strong surface–surfactant interactions the surface properties become important for the structure of the surface aggregate. Rudzinski and co-workers [98,99] have also developed models to account for surfactant aggregates on surfaces. In the ﬁrst model monomers in solution are in equilibrium with a mixture of disklike or oblate aggregates of various dimensions [98]. In the second model the monomers are in equilibrium with hemimicelles and admicelles of variable size that are simultaneously present at the surface [99]. The latter model is inspired by the work of Scamehorn et al. [103] and Harwell et al. [124] on hemimicelles and admicelles, and it is suited to discuss whether at a given surfactant concentration hemimicelles or admicelles are present. In both models the scaled particle theory is used for the intermicellar (excluded-area) interactions, but the interactions with the surface and within the micelles are kept simple. The adsorption aﬃnity and the lateral interaction have to decrease with increasing adsorption; otherwise the 2D surface aggregation occurs in an inﬁnitely large aggregate at a concentration below the CMC. In Drach et al.’s most recent contribution [125] the intermicellar excluded-area interactions are complemented with short-range lateral interactions, and detailed attention is given to a quantitative analysis of calorimetric eﬀects accompanying the adsorption of nonionic surfactants. A disadvantage of these models is that the structures of the aggregates and the decrease of the lateral attraction are assumed, instead of explained on the basis of the structural properties of the surfactant molecules. For the description of the isotherms of nonionic surfactants on silica (see, e.g., Fig. 3) the models of Levitz [123] and Rudzinski et al. [98,125] are not better than the simple equations of Zhu [117]. However, Rudzinski et al. also consider heats of adsorption and Levitz’s model relates the structure of the aggregate to the surfactant structure.

4. Aggregates: SCFA Theory For nonionic surfactants also isolated local aggregates on hydrophilic surfaces have been described with the SCFA theory [67]. For this purpose the Copyright © 2003 by Taylor & Francis Group, LLC

inhomogeneity of the ﬁeld has to be considered in two directions (2D SCFA theory); see Section IV.C. The resulting adsorption isotherm for surfactants with a small headgroup is very similar to that observed with the 1D SCFA calculations. For surfactants with large headgroups the adsorbed amount is considerably larger than that observed with the 1D SCFA calculations. The reason for this is that now local 2D condensation occurs and ‘‘pinned’’ micelles are formed. Section VI.C presents the detailed results. Huinink et al. [126] have considered the behavior of rodlike surfactant aggregates at surfaces by modeling polydispers rectangles with endcaps on a square lattice. The treatment goes back to the model of Taylor and Herzfeld [127]. The molecular parameters needed for the model can, in principle, be calculated from the 2D SCFA approach [67]. The aggregates grow with increasing chemical potential. If the caps become more unfavorable, the average length of the rods increases. In the adsorption isotherms this leads to an increase of the cooperativity. Above a certain rod length a second-order transition occurs from an isotropic to a nematic phase. The nematic ordering promotes the further growth of the aggregates.

D. Adsorption of Ionic Surfactants 1. Adsorbed Layers For ionic surfactants the situation is more complicated than for the nonionics; besides speciﬁc interactions, the coulomb interactions are important. Due to the physical discreteness of the charges, an adsorbing ionic species experiences an electrostatic potential that can be thought of as composed of a mean ‘‘smeared-out’’ potential, a , and a self-atmosphere potential, a . In principle, both a and a depend on the magnitude of the surface charge and the adsorbed layer charge. However, in practice it is often assumed that the self-atmosphere potential is constant. In this case self-atmosphere potential eﬀects can be incorporated into the speciﬁc aﬃnity constant and only the smeared-out potential is considered explicitly. Now a Boltzmann factor including the smeared-out potential can be added to the expression for the standard Gibbs energy of adsorption or aggregate formation to account for the coulomb interactions. Equations (1) and (3) can thus be adapted for the description of the adsorption of ionic surfactants by adding such a Boltzmann factor, and Eq. (1) becomes

1 1 F a ¼ x1 K12 exp 12 1 ð6Þ 1 1 RT where a is the mean electrostatic potential in the adsorbed monolayer and 1 is the valency (sign included) of the surfactant ion. As a ﬁrst-order approximation, and in the absence of speciﬁc adsorption of salt ions to Copyright © 2003 by Taylor & Francis Group, LLC

either the surface or the surfactant, a can be equated to the electrokinetic or potential [128]. The potential of the adsorbent particles can be measured as a function of the surfactant adsorption or surfactant concentration. In the older literature on surfactant adsorption [129,130] Eq. (6), or reduced forms of Eq. (6), have been used frequently in combination with potential measurements to gain qualitative understanding of ionic surfactant adsorption on charged surfaces. Equation (6) can also be used in combination with a double-layer model such as the Gouy–Chapman or the Debye–Hu¨ckel model [131], to show that in the absence of speciﬁc adsorption of salt ions a is related to the surface charge, s , the charge due to the adsorbed surfactant, 1 , and the ionic strength [33]. The advantages of the simple Debye–Hu¨ckel (DH) model are that charge and potential are directly proportional to each other and that the equation that results from a combination of Eq. (6) and the DH model is simple and illustrative: 1 ð þ 1 Þ 1 F ¼ x1 K12 exp 12 1 s ð7Þ 1 1 "0 "r RT where "0 is the permittivity of vacuum, "r the permittivity of the solution, and the inverse Debye length that is proportional to the square root of the ionic strength. Although Eq. (6) is based on the Debye–Hu¨ckel approximation ( a < 50 mV), it has the advantage over Eq. (5) that it clearly shows how speciﬁc and coulomb interactions aﬀect the adsorption. All speciﬁc interactions (including the self-atmosphere potential) between surface and surfactant are included in K12 . Speciﬁc and hydrophobic lateral interactions between the surfactant molecules are incorporated through 12 . The coulomb interactions are governed by the surface charge, s , the adsorbed surfactant charge, 1 , the valency of the surfactant, 1 , and the square root of the ionic strength, . In general, the surface charge depends on (1) the concentration of surface charge-determining ions (mostly pH) [97], (2) the ionic strength, and (3) the surfactant adsorption. Only for low potentials, constant-equilibrium pH, constant ionic strength, and when it is assumed that the surface charge is ﬁxed or that it adapts to the adsorbed surfactant charge in a linear manner is it possible to simplify Eq. (7) to an FFG equation (in which K and have a compounded character) [33]. On the one hand, this illustrates that surfactant isotherms measured at constant-equilibrium pH and ionic strength will be easier to understand than when these conditions are not controlled. On the other hand, it follows that a whole range of conditions has to be fulﬁlled in order to arrive at an FFG-type adsorption isotherm for ionic surfactants. The advantage of Eq. (7) is that it already shows that the presence of the coulomb interactions has important consequences for surfactant adsorption. Copyright © 2003 by Taylor & Francis Group, LLC

When surface and surfactant carry the same charge sign, the adsorption is strongly and progressively inhibited. Only when the speciﬁc aﬃnity is larger than the coulomb repulsion does the adsorption start. With hydrophobic surfaces the tails form the anchoring groups and the headgroups will point to the solution; with hydrophilic surfaces either very limited or no adsorption will occur. When the surfactant and the surface are oppositely charged, the coulomb interaction promotes the adsorption as long as the surface charge is not yet compensated by the surfactant charge; see Eq. (7). The charged headgroups of the surfactant will prefer contact with the surface (head-on adsorption), also because there is mostly a speciﬁc contribution to the headgroup surface attraction. In the iso-electric point (or iep) the surfactant charge just compensates the surface charge (provided absence of speciﬁc adsorption of salt ions) and the coulomb attraction vanishes. In the case of superequivalent adsorption the coulomb interaction is repulsive and the charged headgroups tend to stay away from the surface (head-out adsorption) because it is easier to compensate the headgroup charge at the solution side of the adsorbed layer than at the surface side. The main driving force for further adsorption is now the hydrophobic attraction between the surfactant tails. For surfactant adsorption on an oppositely charged surface the surfactant orientation tends to go with increasing adsorption from ‘‘head-on’’ to ‘‘head-out,’’ with the iep as the turning point. In general, this applies to both hydrophilic and hydrophobic surfaces. The above trend can be rephrased as follows: below the iep (local) ‘‘monolayer’’ adsorption will prevail, whereas above the iep (local) ‘‘bilayer’’ adsorption starts. Moreover, below the iep the coulomb interactions promote adsorption, whereas above the iep these interactions inhibit adsorption. Therefore, screening of the coulomb interactions by salt addition will lead below the iep to a decrease and above the iep to an increase in adsorption. At the iep the coulomb interactions are absent and salt addition has no eﬀect on the adsorption. The conclusion has to be that at high salt concentrations the adsorption starts at higher surfactant concentrations, but the slope of the isotherm is steeper than at low salt concentrations. As a consequence, surfactant isotherms measured at diﬀerent salt concentrations should intersect when super equivalent adsorption occurs, and the common intersection point (or cip) should correspond with the point where the coulomb interactions are absent, i.e., the iep. The ﬁrst veriﬁcation of these trends has been made by De Keizer et al. [132], who also provide the thermodynamic interpretation. De Keizer et al. show that the adsorption isotherms of sodium nonyl-benzenesulfonate on positively charged rutile and that dodecyl-pyridinium chloride and dodecyltrimethylammonium bromide on kaolinite, measured at constant-equiliCopyright © 2003 by Taylor & Francis Group, LLC

brium pH and three diﬀerent salt concentrations, all show a cip corresponding to the iep that was obtained by microelectrophoresis. Figure 5 gives an illustration. The phenomenon of the cip has been a focus point for further investigations by Koopal et al. [64,65,68]. A similar cip has been observed by Bitting and Harwell [133] for the adsorption of dodecylsulfate on Al2O3 in the presence of 0.15 M of diﬀerent monovalent electrolytes. In this case the behavior is due to speciﬁc eﬀects, but the explanation of the phenomenon is the same. The stronger the screening ability of an ion is, the weaker are the coulomb attraction (low adsorption) and repulsion (high adsorption). In the cip the screening ability is unimportant and the isotherms for the diﬀerent ions cross each other. Koopal et al. [109,110] have also discussed Eq. (3) extended with the Boltzmann factor for the coulomb interactions in relation to the adsorption

FIG. 5 Adsorption isotherms of dodecyl trimethylammonium bromide on kaolinite (a) and electrophoretic mobility of kaolinite (b) at pH ¼ 5 and diﬀerent NaCl concentrations. (Redrawn from Ref. 132 with permission of Elsevier Science-NL, Amsterdam, The Netherlands.) Copyright © 2003 by Taylor & Francis Group, LLC

of ionic surfactants. A main problem of this more complicated treatment as compared to Eq. (6) or (7) is that decisions have to be made (1) about the location of the headgroups in the adsorbed layer and (2) about the distribution of the salt ions in the surfactant layer. A more general relation between a and the surfactant charge, the surface charge, and the ionic strength in the case that not all headgroups are located at one plane is discussed in Refs. [97,109]. For a qualitative understanding of surfactant adsorption behavior, Eq. (7) is, due to its elegant simplicity, however, equally well suited. Narkiewicsz-Michalek et al. [102] have discussed Koopal’s approach and generalized it for the case of adsorption on a heterogeneous surface. As part of the discussion an expression has been derived that allows for the calculation of m as a function of 1 . Also, a simple extension is presented for the description of bilayers with this model. According to Narkiewicsz-Michalek both Koopal’s equation and the generalized form for a heterogeneous surface predict a strong 2D condensation to occur. It should be noted, however, that the actual shape of the isotherms is determined by the values of the parameters, and by making a diﬀerent choice the 2D condensation is not so strong. Koopal (unpublished results) has calculated isotherms for diﬀerent values of m in combination with a Gibbs energy minimization to ﬁnd the correct value of m at a given value of 1 numerically. These calculations, with FH parameter values commonly used for the SCFA, show a more detailed isotherm composed of a Henry region and a 2D condensation step followed by a gradual increase of the adsorption. In the ideal case the results of calculations based on Eq. (3), extended with coulomb interactions, should give results compatible to those observed with the SCFA calculations (see Section VIII.B, Fig. 22) because the underlying model is the same. Cases and co-workers [101] use the FFG Eq. (1) by assuming that the aﬃnity (K12 ) and lateral interaction parameter ð12 Þ also account for the coulomb interactions. As has been indicated above with the discussion of Eq. (7) this is only approximately correct for low potentials and when both salt concentration and pH are kept constant. Cases et al. [134] also assume that the net lateral attraction parameter for surfactant chains with 8 or more CH2 groups is so large that strong 2D surface condensation occurs, so that the isotherm can be replaced by a step function. The fact that, in general, experimental surfactant isotherms increase stepwise or gradually is now entirely explained by patchwise surface heterogeneity. Although the stepwise nature of some of the isotherms as measured by Cases et al. [101] indeed may point toward surface heterogeneity, the arguments used cannot be applied in general. For a ﬁrm conclusion that heterogeneity indeed determines the shape of the isotherm, a more advanced form of local isotherm is required. Copyright © 2003 by Taylor & Francis Group, LLC

In order to ﬁnd out whether the adsorbed layer is hemimicelle-like or admicelle-like, Scamehorn et al. [103] extend the approach of Cases et al. [101] by considering bilayer formation on the basis of a BET-type extension of the FFG equation, without treating the coulomb interactions explicitly. In this model the aﬃnities of the surfactant for the ﬁrst and second layer diﬀer, but the lateral interactions are assumed to be the same. For a homogeneous surface (patch) and their choice of parameters the model predicts a strong 2D phase transition at low surfactant concentrations. Based on these results the authors conclude that a bilayer rather than a monolayer will form at the 2D phase transition. Following Cases et al. the shape of experimental isotherms is entirely explained by assuming that surfaces are patchwise heterogeneous. The size of the patches determines the size of the local aggregates. In a follow-up of the work of Scamehorn, Harwell et al. [124] introduce the ‘‘admicelle’’ concept and use a pseudophase model to describe the admicelles. In this model both hydrophobic and coulomb interactions are included, but the electrostatic interactions are treated with an overdose of detail as compared to the speciﬁc interactions. Again the limited size of the admicelles in this treatment is due to the surface heterogeneity. Yeskie and Harwell [135] have addressed the issue of whether hemimicelles or admicelles will be present at the surface in more detail, using the same model. According to Yeskie et al. there is a range of conditions under which hemimicelles are preferred over admicelles due to a strong repulsion between the headgroups present at the solution side of the adsorbed layer. Admicelles will form only at fairly high salt concentrations. In the section on the SCFA model, we will return to this issue. Mehrian et al. [136] have reconsidered the bilayer FFG model of Scamehorn et al. [103] by arguing that in the case of coulomb interactions not only the aﬃnities for the ﬁrst and second layer should be diﬀerent, but also the lateral interactions. In view of the discussion of Eq. (7) given above it will be clear that the bilayer FFG model is only suited for the description of experiments done at constant pH and constant salt concentration. Mehrian et al. [136] have shown that under these conditions surfactant adsorption on kaolinite could be ﬁtted with the bilayer model without the introduction of surface heterogeneity. Wilson et al. [137–139] have presented several models for surfactant adsorption in which the lateral interactions have been introduced on the basis of the ‘‘quasichemical’’ approximation [137] instead of with the mean-ﬁeld or Bragg–Williams approximation used for the FFG-type equations. Coulomb interactions are accounted for on the basis of the Poisson– Boltzmann equation assuming a ﬂat surface and taking into account the ﬁnite volume of the ions [139]. Wilson and Kennedy [138] have also derived an equation for bilayer adsorption. The disadvantage of these models is that Copyright © 2003 by Taylor & Francis Group, LLC

some aspects are treated in great detail and others very crudely. Combination of the regular solution model for charged surfactants, Eq. (6), with either the Debye–Hu¨ckel or the Gouy–Chapman double-layer model is much simpler and leads to an equally good semiquantitative understanding. Wa¨ngnerud and Jo¨nsson [140,141] have proposed two theoretical models for adsorption of ionic surfactants on oppositely charged surfaces, one for very low surfactant concentrations, the other for concentrations close to the CMC [140]. In the model for low concentrations dimerization of the surfactant molecules in bulk solution is assumed. Due to this association the charge number of the surfactant ions becomes higher than that of the ions of the background electrolyte. This leads to a larger coulomb attraction and to preferential adsorption of the surfactant dimers over the other counterions. In the model for concentrations close to the CMC [141] it is assumed that a close-packed (bi)layer is formed at a certain surfactant concentration. The model takes into account the eﬀects of hydrophobic, electrostatic, solvation, and steric interactions. The thickness of the layer increases with increasing surfactant concentration in solution.

2. Adsorbed Layers: SCFA Theory Koopal et al. [64–66,68,142–144] have extensively used the SCFA model to describe the adsorption of ionic surfactants. For details of the SCFA theory consult Section IV of this chapter. With ionic surfactants it has been possible only to study adsorbed layers; modeling of the coulomb interactions of (interacting) axially symmetric aggregates of an unidentiﬁed shape is rather complicated. The calculations apply to ionic surfactant adsorption on hydrophilic surfaces with a charge opposite that of the surfactant molecules. The main emphasis has been given to eﬀects of the ionic strength and surface charge on (the shape of) the isotherm. The FH parameters given to the segment–solvent interactions in bulk solution are obtained from modeling micellization of the surfactants [63]. In most calculations the speciﬁc interaction between a headgroup segment and the surface has been given an attractive value, whereas for all other species the FH parameters are put equal to zero. This implies that tail segments have an aﬃnity for the surface because they dislike the solution and that the ions of the background electrolyte are indiﬀerent. The ﬁrst calculations have been made for surfaces with a constant charge [64]. This approximation may hold for plate surfaces of clays when the plates do not contain impurities. As purely constant surfaces are scarce, further calculations have been made for constant potential surfaces [65,66,142–144]. These surfaces adjust the surface charge upon surfactant adsorption in order to keep the surface potential constant. The constant surface potential approximation is a reasonable approximation for mineral Copyright © 2003 by Taylor & Francis Group, LLC

oxide surfaces [97]. Both for constant-charge and constant-potential surfaces surfactant isotherms have a complex shape composed of a Henry region, a 2D condensation step, a gradual increase of the adsorption beyond the condensation step, and an adsorption pseudosaturation value at the CMC. Isotherms calculated at diﬀerent values of the ionic strength show a common intersection point in agreement with experimental results as presented in Fig. 5. The segment distribution proﬁles indicate that beyond this point bilayer-type adsorption occurs. The adsorption at constant-charge surfaces diﬀers from that at a constant-potential surface by the fact that after compensation of the surface charge a considerable hesitation occurs before the adsorption continues. Next to the calculations for constantcharge and constant-potential surfaces some calculations were also done on charge- and potential-regulating surfaces, in order to mimic the adsorption of surfactants on silica. Qualitatively the same trends are found as for the constant-charge surfaces, but the 2D condensation step in the isotherm is much smaller or absent. The overall conclusion that can be derived from the SCFA studies is that the isotherms of ionic surfactants on oppositely charged homogeneous surfaces are far from being a simple 2D condensation phenomenon. A more detailed comparison of the calculated and experimental results can be found in sections VIII.A, B, and C.

3. Surface Aggregates Although the hemimicelle–admicelle issue has been discussed on the basis of the models mentioned in the previous section, real aggregates could not be described; only the monolayer or bilayer character of the adsorption could be discussed. Models speciﬁcally developed to describe surface aggregates are those of Chander et al. [145], Zhu et al. [117–119], Rudzinski et al. [98,99], and Li and Ruckenstein [146]. Chander et al. [145] have derived a model comparable to the simple model of Zhu as described in the nonionic section. In this model the electrostatic interactions are considered by realizing that the standard Gibbs energy has two contributions—one speciﬁc, the other electrostatic (coulomb)—but the treatment is rather primitive. Zhu et al. [117–119] have applied the family of models presented in Section III.C (surface aggregates of nonionic surfactants) also to describe the adsorption of ionic surfactants. The disadvantage of this practice is that the electrostatic interactions are not taken into account explicitly. This means that for every pH and or ionic strength a new parameter set is required. Although a good ﬁt of separate experimental results can be achieved by parameter ﬁtting, the model is not suited to make predictions. The physical interpretation of the parameter values is quite complicated, if not impossible. In principle, the monomer aﬃnity will be aﬀected by the Copyright © 2003 by Taylor & Francis Group, LLC

degree of surface charge neutralization, the adsorbed micelles will repel each other more strongly when the surface density of micelles is increasing, and all electrostatic interactions are a function of the ionic strength. These aspects are hidden in the ﬁtted values of all three parameters. The oblate and hemimicelle and admicelle models derived by Rudzinski et al. [98,99] and discussed in Section III.C (nonionic surface aggregates) have also been used by Rudzinski et al. to describe the adsorption of ionic surfactants. Figure 6 gives a schematic picture of the surface phase and the description of the adsorption of dodecyl trimethylammonium bromide on silica. In the model the interactions between the headgroup and the surface and lateral interaction between the monomers in the aggregates are both linearly decreasing with adsorption density. To some extent this could be due to the coulomb interactions, but it will be a realistic approximation only when the potentials are suﬃciently low and the experiments are carried out at constant-equilibrium pH and salt concentration. The interaction between the aggregated structures is neglected in the model except for the excluded volume eﬀect. Because of the electrostatic repulsion between the aggregates, this excluded volume is likely to be given by the Debye length at low salt concentrations and at high salt concentrations by the size of the aggregates (excluded area). Hence, we may not expect the model to be very accurate for ionic surfactants. By introduction of surface heterogeneity, as done by Rudzinski et al., all eﬀects not properly accounted for will show up as heterogeneity. In relation to this aspect it should be realized that an underestimation of the coulomb repulsion leads to too steep an isotherm; increasing this repulsion may lead to a similar improvement as by invoking

FIG. 6 Schematic diagram of the surface phase composed of monomers, hemimicelles, and admicelles (panel a) and the contributions of hemimicelles (- - - -) and admicelles (— — —) to the total (——) adsorption of trimethylammonium bromide on silica (*) (panel b). (Redrawn with permission from Ref. 99. Copyright 1996 American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

heterogeneity. In any case, models that take into account the coulomb interactions implicitly or very poorly are not very well suited to make ﬁrm conclusions about the role of surface heterogeneity. It may be clear that the above models for the adsorption of surface micelles composed of ionic surfactants are still very primitive and not likely to provide detailed information on the surfactant aggregation behavior. They merely served as ﬁrst steps on the way to model surface aggregation of ionic surfactants. A much more advanced surface aggregation model for ionic surfactants on oppositely charged hydrophilic surfaces that takes the coulomb interactions explicitly into account is the model by Li and Ruckenstein [146]. This model has much in common with the description of micellization of ionic surfactants in bulk solution as done by Nagarajan and Ruckenstein [41], but it also reﬂects the scaled particle theory of Rudzinski et al. [98,99]. Similarly as in the model by Rudzinski et al. the surface is covered by solvent molecules, surfactant monomers, and monolayer- and bilayer-type surfactant aggregates of various sizes. The competition between the enthalpic and entropic contributions to the Gibbs energy in the adsorbed phase is responsible for the composition of the adsorbed phase. Similarly as done by Nagarajan and Ruckenstein [41] the standard Gibbs energy change in going from the solution to the surface aggregates is calculated by considering ﬁve contributions: hydrophobic, conformational, electrostatic, steric, and interfacial. The electrostatic contributions are treated within the framework of the Poisson–Boltzmann equation for ﬂat plates. Calculated results of the model, based on reasonable estimates of the parameter values, are compared with experimental results obtained on mineral surfaces. Figure 7 shows a typical example of the good quality of the prediction. From Fig. 7 a similar conclusion can be drawn as from the results of the SCFA theory: the isotherm for ionic surfactants adsorbing in surface aggregates on an oppositely charged homogeneous surface is not a simple step function. Also, the present model predicts that the isotherm is composed of four regions. So far, Li et al. have not taken into account the surface charge adjustment, nor has attention been paid to the eﬀect of the ionic strength and the common intersection point.

E. Conclusion The general conclusion of the section on adsorption of ionic surfactants is that both the SCFA result for adsorbed layers and the surface micellization model of Li and Ruckenstein [146] show very similar trends. The isotherm starts at low concentrations with a Henry region. The 2D condensation step that occurs in the SCFA results above the Henry region shows up in the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 7 Comparison between the isotherms predicted with the model of Li and Ruckenstein and measured adsorption isotherms for sodium alkylbenzenesulfonates on aluminum oxide at pH 7.7 and 0.171 mol/L NaCl. The results are plotted in a double logarithmic plot. (Redrawn from Ref. 146. Copyright 1996 American Chemical Society.)

results of Li and Ruckenstein as a steep but not vertical increase. This corresponds very well with the fact that with the SCFA theory the aggregate is inﬁnitely large, whereas the surface aggregates in the model of Li and Ruckenstein have a limited size. In both models the third region of the isotherm increases less steeply than the second region and beyond the CMC a pseudoplateau is reached. In both models also a monolayer-tobilayer transition takes place. This gives faith to the results of both models, and although the SCFA theory is not capable of describing local surfactant aggregates, it will still give a very good representation of the trends in surfactant adsorption, especially if it is realized that the steepness of the second region is overestimated. Therefore, in the second part of this review more detailed attention is paid to the SCFA theory and a more detailed comparison is made between calculated SCFA results and experimental ﬁndings.

IV. SCFA THEORY A. General Outline The SCF theory was originally developed by Scheutjens and Fleer [147,148] for polymer adsorption and is reviewed and discussed in relation to other Copyright © 2003 by Taylor & Francis Group, LLC

polymer adsorption treatments in a recent monograph [149]. In the last decades gradually other applications [34,59–61,69,70,93–95,150–152] appeared, and Koopal et al. [62–68,142–144] have used the model for a systematic investigation of the adsorption of both nonionic and ionic surfactants. The acronym SCFA for the theory is not widespread but is used in the surfactant applications. The SCFA theory involves a kind of ab initio treatment. Starting from system characteristics such as the number of diﬀerent types of molecule and the amount of each of them, together with molecular properties such as numbers of segments per molecule ð 1Þ, structure and charge of the molecules, and the interactions between the various segments, the equilibrium distribution of molecules is calculated. The theory involves a lattice that is completely ﬁlled with the molecules (and possibly vacancies) present in the system. The theory is an extension of the theory of polymer solutions by Flory [107] to systems that have inhomogeneities in one direction (1D SCFA), i.e., perpendicular to the surface or the center of the lattice, or in two directions (2D SCFA), i.e., perpendicular to the surface and in concentric rings parallel to the surface. The layers are numbered z ¼ 1 for the layer in the center of the lattice (spherical and cylindrical lattice) or that closest to the surface (ﬂat lattice) to z ¼ M. At the outer boundary of M a reﬂecting mirror is placed. The rings in the 2D system are numbered starting from R ¼ 1 in the central ring. At the outer boundary of the last ring a second reﬂecting mirror is placed. In the 1D SCFA option a mean-ﬁeld approximation is used in every lattice layer around to the center of the lattice or parallel to the surface. In the 2D case the mean-ﬁeld approximation is used in every ring. The contact interactions are incorporated in the SCFA theory similarly as in the Flory theory. The electrostatic interactions are calculated using a multiplate condenser model. The conformational statistics of the chains are evaluated using Boltzmann statistics. Basically the theory calculates, by minimizing the free energy of the system, iteratively, the equilibrium distribution of segments in a potential ﬁeld excerpted by the presence of the segments themselves. Once this is done the structure of the aggregates or that of the adsorbed layer and the thermodynamic properties of the system can be obtained. The advantage of the SCFA theory is that both surfactant micellization and adsorption can be considered. When micellization is predicted with a certain set of parameters, the same set of parameters should be used to predict the adsorption. The only new parameters for the adsorption calculation are those that describe the interactions of the segments with the solid surface. Copyright © 2003 by Taylor & Francis Group, LLC

B. One-Dimensional SCFA 1. Volume Fractions of Free Segments To study the shapes of the aggregates in bulk solution the 1D SCFA theory is used with a ﬂat, a cylindrical, or a spherical lattice. For adsorption studies a ﬂat lattice is considered. Let us ﬁrst consider the 1D case. In a ﬂat lattice the fraction of contacts of a lattice site in layer z with sites in layer z 1, denoted as 1 , equals the fraction of contacts with sites in layer z þ 1, denoted as 1 . These fractions are independent of z. In spherical and cylindrical lattices the number of lattice sites is not the same in every lattice layer; therefore, 1 , 0 , and 1 will be functions of z. These functions have been given elsewhere [93,153]. For spherical and cylindrical symmetries the layers will be numbered starting from the center of the lattice. To each segment of type x, in each layer z a volume fraction x ðzÞ is assigned. This implies that only inhomogeneities in the direction perpendicular to the lattice layers are considered. The calculated aggregate is in equilibrium with the bulk solution, where the volume fractions of molecules i are denoted by bi . As the volume fractions in the layers z are not the same as those in the bulk solution, a Helmholtz (or Gibbs) energy diﬀerence per segment (or potential of mean force), ux ðzÞ, exists for every type of segment with respect to the bulk solution. The expression for ux ðzÞ follows from statistical thermodynamics [94,153]: ux ðzÞ ¼ u 0 ðzÞ þ kT

X

ð< y ðzÞ > by Þxy þ vx e ðzÞ

ð8Þ

y

Three terms contribute to ux ðzÞ, u 0 ðzÞ quantiﬁes the local hard-core interaction with respect to the bulk solution and must be the same for every segment type in layer z. u 0 ðzÞ is related to the conformational entropy of the aggregate or adsorbed layer. As no explicit expression for u0 (z) is available, it has to be numerically adjusted to ensure that the sum of the volume fractions equals unity [153]. Physically, u 0 ðzÞ equals þ1 or 1 if the sum of the volume fractions in a layer is not unity. The second term on the right-hand side contains the contact interactions: xy is the FH parameter between segments x and y; < y ðzÞ > is the contact volume fraction of y in layer z, which has contributions from layers z 1, z, and z þ 1. The last term in Eq. (8) covers the electrostatic interactions: vx is the valency of segment x, ðzÞ is the electrostatic potential in layer z, and e is the elementary charge. From ux ðzÞ, segment-weighting factors, Gx ðzÞ, are calculated: Gx ðzÞ ¼ exp ½ux ðzÞ=kT Copyright © 2003 by Taylor & Francis Group, LLC

ð9Þ

The Boltzmann factor Gx ðzÞ indicates the probability to ﬁnd an unbound segment x in layer z relative to ﬁnding it in a layer in homogeneous equilibrium solution. In the case of a molecule containing just one segment in equilibrium with the bulk solution the volume fraction xz of a segment of type x in layer z is calculated from its bulk volume fraction bi and the segment-weighting factor: x ðzÞ ¼ bx Gx ðzÞ

ð10Þ

2. Volume Fractions of Segments Belonging to a Chain To obtain the volume fractions of segments belonging to chain molecules, one must take into account that the segments of the chain are connected to each other. Several types of chain statistics can be applied to arrive at the segment distribution of chain segments. The simplest form used in the SCFA theory is ﬁrst-order Markov statistics, where the chain segments follow a step-weighted walk and backfolding is not forbidden. For shortchain molecules, such as surfactants, a rotational isomeric state (RIS) scheme [60,61] is also used. This RIS method precludes backfolding in a series of ﬁve consecutive segments of a chain and allows for a distinction between trans and gauche conformations. The application of RIS results in a decrease of chain ﬂexibility compared to ﬁrst-order Markov statistics. This is important if a CH2 unit is considered as one segment, because these groups are too small to be regarded as statistical chain elements. To calculate the volume fractions of segments s of chains i containing ri segments, the so-called chain segment-weighting factor, Gi ðz; s j1 : rÞ, is required [94]. The chain segment-weighting factor combines two chain end-segment distribution functions. One describes a walk starting at segment 1 located at an arbitrary position in the system. The start value is given by G1 ðzÞ (the subscript 1 refers to segment 1, which is of type x), and it ends at segment s in layer z after a walk of s 1 steps along the chain—the index 1 in Gi ðz; s j1 : rÞ refers to this walk. The other chain end-segment distribution function starts at the other chain end, i.e., segment ri , where Gr ðzÞ is the start value. This walk ends at the same segment s in layer z after a walk of r s 1 steps along the chain. The index r in Gi ðz; s j1 : rÞ refers to this starting point. In each step of the walk along the chain a Boltzmann factor Gr ðzÞ appears. If the RIS method is applied, the chain segment-weighting factor, Gi ðz; s j1 : rÞ, of segments s of chains i containing ri segments depends not only on ux ðzÞ and the positions of the neighboring segments of a chain, but also on the orientation of the bonds between these segments. End-segment distribution functions have to be calculated for every orientation [60,61]. The RIS procedure has been generalized to branched chains [60]. Copyright © 2003 by Taylor & Francis Group, LLC

From the chain segment-weighting factors the volume fractions of segments s, belonging to chain i, can be calculated, using the analog of Eq. (10) for free chain segments [94,153]: i ðz; sÞ ¼ Ci Gi ðz; sj1 : rÞ

ð11Þ bi =ri

or, more generally, i =ri Gi ðrj1Þ, The normalization constant Ci equals where i is the total amount of chain i and Gi ðrj1Þ is the sum of the chain end-segment-weighting factors for segment ri , over the total number of layers, deﬁned as M. Equating Ci to bi =ri is equivalent to taking a special case of i =ri Gi ðrj1Þ, because in a homogeneous bulk solution i ¼ M bi and Gi ðrj1Þ = M 1 . The volume fraction, i ðzÞ, that each molecule type i has in layer z can be obtained by a summation of i ðz; sÞ over all segments that this molecule type has in layer z: i ðzÞ ¼

r X

i ðz; sÞ

ð12Þ

s¼1

The volume fractions of segments of type x, belonging to molecules i, xi ðzÞ can be obtained if the sum is restricted to segment s of type x. Because of the use of volume fractions instead of number of segments (or molecules), the deﬁnition of the total amount, i ; in the system is not entirely straightforward. For spherical geometry the number of lattice sites per layer, LðzÞ, can be calculated from the diﬀerence between volume V(z) and volume V(z 1), where V(z) equals 4 z3 =3 and the total amount is most conveniently expressed as X i ¼ LðzÞi ðzÞ ð13aÞ z

For lattices with cylindrical geometry only the relative change in the number of lattice sites with layer number is known, and not the total number of lattice sites, since the cylinder has an inﬁnite length. The volume of a disk with the thickness equal to the length of one lattice site is given by VðzÞ ¼ z2 . In Eq. (13a) we now use for L(z) the diﬀerence in volume of disks with radius z and z 1. For ﬂat geometry the amount i is deﬁned per unit cross section of a lattice site and is thus simply given by X i ¼ i ðzÞ ð13bÞ z

3. Electrostatic Interactions The uneven distribution of charged molecules leads to the development of electrostatic potentials. These potentials are calculated using a multiplate Copyright © 2003 by Taylor & Francis Group, LLC

condenser model and depend on the net charge and the electrostatic capacitance in each layer [94,154]. The charge is assumed to be exclusively located on the midplanes of the lattice layers, as shown schematically in Fig. 8. The charge density in each layer, ðzÞ, follows directly from X vx ex ðzÞ=as ð14Þ ðzÞ ¼ x

where as is the cross section of a lattice site. For the permittivity of layer z, "ðzÞ, the density weighted average can be used as an approximation: "ðzÞ ¼

X

"x x ðzÞ

ð15Þ

x

FIG. 8 Schematic representation of an electrostatic potential proﬁle in a ﬂat lattice. The lattice consists of z layers, the electrostatic charges, s, are located on the midplanes in each lattice layer. For the calculation of the electrostatic potentials, , the charges, s, the distance, l, between the midplanes, and the average permittivity, "ðzÞ, in each layer have to be known. For l a value of 0.31 nm is chosen and the distance from the surface is now measured by (nm). A discontinuous change in the ﬁeld strength occurs at the midplanes where the charge is present and at the boundary planes between two lattice layers where "ðzÞ change. (Reprinted with permission from Ref. 64. Copyright 1996 American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

where "x is the permittivity of species x ("x ¼ "0 "r;x ). The ﬁeld strength E as a function of the distance may change discontinuously at the midplanes of the lattice layers, which are separated by a distance l, located at z ¼ 1; 2; . . . ( ¼ 1=2l; 3=2l; . . .) due to the presence of charge and at z ¼ 1=2; 3=2; . . . ð ¼ 0; l; . . .) due to a change in permittivity; see Fig. 8. In addition, in curved lattices a continuous decrease of Eð Þ exists due to the divergence of the electric ﬁeld. The ﬁeld strength at distance from the central point (spherical), line (cylindrical), or plane (ﬂat) geometry of the lattice follows Þ from Gauss’s law, EdAs ¼ q=", where q is the charge and As the area. Application to the diﬀerent geometries yields: flat:

intð =lþ X 2Þ 1 ðz 0 Þ Eð Þ ¼ "ð Þ z 0 ¼1

ð16aÞ

cylinder:

intð =lþ2Þ X 1 Eð Þ ¼ Lðz 0 Þðz 0 Þ 2 "ð Þ z 0 ¼1

ð16bÞ

sphere:

intð =lþ2Þ X 1 Lðz 0 Þðz 0 Þ Eð Þ ¼ 2 4 "ð Þ z 0 ¼1

ð16cÞ

1

1

1

The upper boundary of the summation is the Entier function of =l þ 1=2 indicated as intð =l þ 1=2Þ. Because the charges are located on the midplanes of the lattice layers, only the potentials on these midplanes are relevant for the calculation. The potential diﬀerence between two neighboring midplanes at z þ 1 and z is given by

¼ðzþ1=2Þl ð

ðz þ 1Þ ðzÞ ¼

Eð Þd

ð17Þ

¼ðz1=2Þl

Using Eq. (17) we obtain for the three geometries: X z l 1 1 þ ðz 0 Þ ð18aÞ flat: ðz þ 1Þ ¼ ðzÞ 2 "ðzÞ "ðz þ 1Þ z 0 ¼1 " 1 1 z 1 ln cylinder: ðz þ 1Þ ¼ ðzÞ þ 2 "ðzÞ z 1=2 "ðz þ 1Þ # X z z þ 1=2 ln Lðz 0 Þðz 0 Þ z z 0 ¼1 ð18bÞ Copyright © 2003 by Taylor & Francis Group, LLC

1 1 ðz þ 1Þ ¼ ðzÞ 8l "ðzÞðz 1=2Þz X z 1 þ Lðz 0 Þðz 0 Þ "ðz þ 1Þzðz þ 1=2Þ z 0 ¼1

sphere:

ð18cÞ

In all geometries there is a contribution of layer z where the permittivity is "ðzÞ and a contribution of layer z þ 1 where the permittivity is "ðz þ 1Þ. In the middle of layer z the distance to the center of the lattice is ðz 1=2Þ ; this causes the ðz 1=2Þ-term and the absence of a ðz þ 1)-term in Eqs. (18b) and (18c). Except for cylindrical geometry the distance between two midplanes, l, has to be quantiﬁed to obtain the potential diﬀerence. For uncharged systems this distance is arbitrary. To calculate the potentials with respect to the bulk solution a starting point at layer M is needed; for this purpose the electroneutrality condition has to be used [94].

4. Self-Consistent Solution The circular deﬁnition of in terms of u, which in itself is deﬁned in terms of , makes it necessary to iterate to ﬁnd a solution to the set of equations that describe the system. When a set of fux g is obtained that generates a set of fx g, which is used to ﬁnd the same set of fux g (within the desired numerical precision), a self-consistent solution is obtained. Because only equilibrium potentials can be calculated, only equilibrium systems can be described.

5. Excess Free Energy for the Creation of a Micelle and Excess Amounts In the SCFA theory thermodynamic data are readily available. The derivation of the equations has been presented by Bo¨hmer et al. [94] and by Evers et al. [153]. In the case of micellization an important quantity is the excess free energy for the creation of a micelle with a given aggregation number and a ﬁxed position: Am

¼ kT

X z

( LðzÞ

X

x ðzÞ ln Gx ðzÞ

x

X i ðzÞ bi i

ri

h i 1XX xy x ðzÞ < y ðzÞ > by bx y ðzÞ by 2 x y ) ðzÞ ðzÞ þ 2 þ

Copyright © 2003 by Taylor & Francis Group, LLC

ð19Þ

The segment density proﬁles are used to calculate the excess amount of molecules in either the aggregate or the adsorbed layer. For the adsorbed layer the excess amount of molecules per surface site equals i Xh nexc ¼ i ðzÞ bi =ri ð20Þ i z

The excess number of molecules i in the system with respect to the equilibrium solution, due to the presence of a micelle, is h i X b ¼ LðzÞ ðzÞ nexc ð21Þ i i i z

may diﬀer from the The number of aggregated molecules in a micelle, nagg i excess number of molecules in the system because in layers adjacent to the micelle a depletion of surfactant molecules can occur. To calculate the aggregation number of a micelle, Eq. (21) can be used for layers where ½i ðzÞ bi is positive: h i h i X nagg ¼ LðzÞ i ðzÞ bi for i ðzÞ bi > 0 ð22Þ i z

C. Two-Dimensional SCFA The lattice used for the 2D SCFA calculations is shown schematically in Fig. 9. The number of lattice sites in a ring, L(R), varies as a function of R [155]. Within every ring the mean-ﬁeld approximation is applied and the volume fraction of segment x is now a function of both z and R : x ðz; RÞ. The sum of the volume fractions of the segments in each ring (z, R) is again unity. Just as in the case of the 1D SCFA theory the Gibbs energy per segment, ux ðz; RÞ, which is now also a function of R, has to be calculated: X ux ðz; RÞ ¼ u 0 ðz; RÞ þ kT xy ð< y ðz; RÞ > by Þ ð23Þ y

In this equation u 0 ðz; RÞ is independent of the segment type and it ensures the complete ﬁlling of ring ðz; RÞ. The angular brackets (<>) indicate a weighted average of the volume fraction, which has contributions from the volume fractions in neighboring rings: ðz 1; R 1Þ, ðz 1; RÞ, and ðz 1; R þ 1Þ from the previous layer; ðz; R 1Þ, ðz; RÞ, and ðz; R þ 1Þ from layer z; and ðz þ 1; R 1Þ, ðz þ 1; RÞ, and ðz þ 1; R þ 1Þ from the next layer. As the number of lattice sites varies with R, so does the weight of the contributions from the neighboring rings. The ux ðz; RÞ function is calculated with respect to the bulk solution, where the equilibrium volume fraction of x is bx . Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Representation of the 2D, cylindrical, symmetrical lattice. The layers contain concentric rings. The hatched plane represents the surface. (Reprinted with permission from Ref. 67. Copyright 1996 American Chemical Society.)

The weight of each conformation is calculated using a step-weighted walk procedure as discussed above, i.e., each step depends on the position of the previous segment and is weighted with the segment-weighting factor, Gx ðz; RÞ: Gx ðz; RÞ ¼ exp½ux ðz; RÞ=kT

ð24Þ

For monomers and chain molecules the volume fractions can be calculated from the segment-weighting factors by using the equivalents of Eq. (10) and Eq. (11), respectively. Also in this case the solution of the set of equations can only be found numerically. Copyright © 2003 by Taylor & Francis Group, LLC

From the equilibrium volume fraction proﬁle the excess adsorbed amount of molecule i with chain length ri can be calculated using XX ¼ LðRÞ i ðz; RÞ bi =ri ð25Þ nexc i z

R

In bulk, surfactant molecules associate in micelles. For concentrations higher than the CMC, bx in the above equations represents the bulk volume fraction of free molecules. It is therefore necessary to know the CMC, which can be calculated with the 1D SCFA theory.

D. Thermodynamics of Small Systems Using the SCFA theory one can calculate the equilibrium structure of a single micelle. In combination with the thermodynamics of small systems [59,93,86,87] the composition of a micellar solution, consisting of a number of identical micelles, can be found. To this end, the solution is divided into a number of subsystems with volume Vs , where every subsystem contains one micelle, with volume Vm . To distinguish between the equilibrium volume fraction of i in homogeneous bulk solution, bi , and the average volume fraction of i in both the system and each subsystem, the latter is denoted exc by i . The excess free energy of the subsystem, As consists of two parts: the translational entropy of the micelle, k lnðVm Vs Þ (micelles may move freely in the solution) and the excess free energy for creation of a micelle with a given aggregation number and a ﬁxed position, Am ; hence: Aexc ð26Þ s ¼ Am þ kT lnðVm Vs Þ For micelles in equilibrium with a homogeneous solution Aexc is zero. s for a given value of V and Am . As Equation (26) allows calculation of V s m k lnðVm Vs Þ is always negative, micelles can only exist if Am is suﬃciently positive. To obtain Vm for a charged micelle a cutoﬀ distance for the electrostatic interactions between the micelles has to be chosen. A quite common choice for the eﬀective range of the electrostatic interactions is the distance at which the electrostatic potential has dropped to 1/e of its maximum value. Consequently, the potential decay depends on the ionic strength and so does the chosen cutoﬀ distance. Once Vm is determined, Vs can be calculated with Eq. (26), and i follows from i ¼

nexc i r þ bi Vs

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ð27Þ

Contrary to small spheres, structures like inﬁnitely long membranes and cylinders have a negligible kinetic energy. Therefore, for these geometries the translational entropy term can be neglected so that for equilibrium membranes and cylinders Am ¼ 0.

E. General Parameter Values In principle, there is no limit to the number of diﬀerent molecules and segment types that can be handled in an SCFA calculation. For practical reasons the molecular structures and interaction parameters to model the surfactants in aqueous solutions and near interfaces are chosen as simple as possible. Only the main interactions involved in micellization and adsorption have been incorporated. The surfactants are modeled as An Bm chains, where A represents an aliphatic segment and B a hydrophilic segment. Water is modeled as a monomer W. The contact interactions, including the hydrophobic interaction, are modeled through the values of the parameters. With these parameters the properties of surfactants in water, such as their capability of forming micelles, should be reproduced. Temperature eﬀects are not considered; all results refer to room temperature. Ion speciﬁcity, hydration of ions, and size diﬀerences between the salt ions have been neglected, too; they are regarded as second-order eﬀects. The parameter AW should reﬂect the poor solubility of segments A in water W. Unless stated otherwise each CH2 group is considered as an A segment and AW = 2. The parameter BW depends on the type of headgroup and should reﬂect that water is a good or moderately good solvent for B. In the case of ionic surfactants BW ¼ 0, for ethylene oxide- (EO) type surfactants the measured value [156] BW ¼ 0:4 is used. The interaction between the hydrophilic segments B and the hydrophobic segments A should be repulsive. In general, a value AB ¼ 2 is chosen to ensure spatial separation of headgroup segments and tail segments, which is necessary for the formation of micelles. This set of parameters, in combination with our choice to treat one CH2 group as a segment, enables a correct prediction of the change in CMC with aliphatic chain length for nonionic surfactants. An alternative way to obtain the AW value is to calculate the partition equilibria for homologous series of alkanes between a water and an oil phase for which experimental data were reported by Tanford [157] with the multicomponent Flory equations [93]. This yields an only slightly higher value, AW ¼ 2:3. The segment-surface xS parameters will be speciﬁed with the results. It should be noted that the adsorption is a displacement process in which a segment x replaces a fraction 1 of its contacts with the solvent for contacts with the surface so that xS is not the ‘‘adsorption energy.’’ The ‘‘adsorption Copyright © 2003 by Taylor & Francis Group, LLC

energy’’ or, more correctly, the free energy of displacement, dðxÞ , of a water molecule by a segment of type x is deﬁned as dðxÞ ¼ 1 ðxS xW WS þ WW Þ

ð28Þ

Equation (28) shows that xS WS is important rather than each of these parameters. By using WS ¼ 0, dðxÞ is determined by xS xW because WW = 0, by deﬁnition.

V. SCFA AND MICELLIZATION OF NONIONIC SURFACTANTS A. Aggregate Shape To study the association behavior of nonionics, calculations have been performed for a series of A10 Bn molecules in lattices with spherical and ﬂat geometry [62]. B segments are used as a model for EO units, whereas the A segments mimic CH2 groups. It is obvious that an EO unit is much bigger than a CH2 group; nevertheless, one segment of type A for a CH2 group and one segment of type B for an EO unit have been used in the ﬁrst calculations. Three segments for an EO unit would overestimate the chain ﬂexibility, and 3 CH2 groups in one A segment require a very large positive value of AW which leads to large lattice artifacts. First-order Markov statistics are used for the chain statistics. Results for the series A10 Bn as a function of n are shown in Fig. 10. The volume fraction divided by the total chain length of the surfactant is a measure for the surfactant concentration. The concentration where phase separation occurs can be calculated using the extended Flory–Huggins theory [93]. Figure 10 shows that phase separation takes place when the number of B segments is smaller than 3. If the number of B segments is more than 3, the concentration at which micelles are formed is lower than the concentration required for membrane formation, so that micelles are preferred over membranes. Phase separation occurs at much higher concentrations. Due to the conical structure of the surfactant molecules the spherical geometry is the preferred shape of the aggregate. With increasing length of the headgroup the steric hindrance between the headgroups in an aggregate increases. This eﬀect is especially evident from the growing difference between the critical membrane concentration and the critical micelle concentration with increasing length of the B block. The CMC increases approximately linearly with the number of segments of type B. This agrees with experimental results for octylphenol polyoxyethylenes [158,159] and decyl polyoxyethylenes [160]. With the interaction parameters chosen the increase in the CMC with increasing length of the headgroup Bn is well predicted for octylphenol polyoxyethylenes: the CMC Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10 Equilibrium volume fractions of A10Bn molecules, for phase separation, membrane formation, and micelle formation, as a function of the B block length. (Reprinted with permission from Ref. 62. Copyright 1996 American Chemical Society.)

doubles if the number of headgroup segments increases from 12 to 30. For small B blocks the calculated slope is somewhat smaller than that found experimentally for monodisperse decyl polyoxyethylenes.

B. Structure of the Micelles In Fig. 11 the segment density proﬁles of the A and B segments in A10 B6 and A10 B40 micelles are shown at the same overall concentration (=r is 0.5103 ) of surfactant. The segments of type A are in the center of the micelle while the B segments are on the outside. Some solvent is still present in the interior of the micelle (not shown in the ﬁgure), which is due to the poor model used for water: a monomer without a preferential orientation. The hydrophobic core of the micelles formed by the A10 B6 molecules is much larger than that formed by the A10 B40 amphiphiles. Steric hindrance between the hydrophilic B blocks prevents the formation of large micelles of A10 B40 . The number of molecules per micelle at a constant overall concentration (=r is 0:5 103 ) decreases sharply for n < 10 and gradually for large n; see Fig. 12. This trend compares well with the experimental trend in the aggregation numbers measured for octylphenol polyoxyethylenes [158,159] using pyrene solubilization. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 11 Volume fraction proﬁles for A10 B6 (a) and A10 B40 (b) micelles. The volume fractions for segments of type A and type B are indicated. The overall concentration =r is 5 104 . (Reprinted with permission from Ref. 62. Copyright 1996 American Chemical Society.)

FIG. 12 The aggregation number of A10 Bn micelles at a constant overall concentration of 5 104 as a function of the number of B segments in the molecule. (Reprinted with permission from Ref. 62. Copyright 1996 American Chemical Society.)

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VI. SCFA AND ADSORPTION OF NONIONIC SURFACTANTS A. Adsorption Layers on Hydrophilic Surfaces 1. Adsorption Isotherms Adsorption isotherms have been calculated for the same homologous series of surfactants as used with the micellization study [62]. In general, the hydrophilic segments will have a relatively strong interaction with the surface and the hydrophobic a weak interaction. It is assumed that BS ¼ 6 and that the other FH parameters with the surface are zero. In this case the ‘‘adsorption energy’’ for a B segment is 1.6 kT and that of an A segment 0.5 kT, see Eq. (28). Results are presented in Fig. 13 for six diﬀerent values of n. The adsorption is presented as nexc , the excess number of molecules per lattice site. On the horizontal axis the overall concentration is given as =r. The CMCs are indicated with an asterisk. For a B block considerably longer than the A block (i.e., A10 B30 and A10 B40 ) the adsorption reaches a near-saturation value before the CMC is reached, and the shape of the isotherms is similar to that of a homopolymer of type B. The small irregularities in the adsorption isotherms are caused by layering transitions, a kind of lattice artifacts. At very low-volume fractions the aﬃnity increases with increasing length of the B block since chains with more B segments have a higher adsorption energy. With increasing volume fraction the cooperativity of the adsorption

FIG. 13 Calculated adsorption isotherms for a series of amphiphilic chain molecules on a hydrophilic surface. The CMC values are indicated with an asterisk. (Reprinted with permission from Ref. 62. Copyright 1996 American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

becomes important and the adsorption increases with decreasing B block size. The increase in adsorption is due to unfavorable interactions between A segments and solvent: the A segments associate to reduce the number of contacts with the solvent. The association is more pronounced if the A/B ratio increases, a trend comparable with the inﬂuence of the A/B ratio on the CMC. The A/B ratio also aﬀects the maximum adsorption; see Fig. 13. The higher the A/B ratio is, the higher is the adsorption at the CMC. For short B blocks the isotherm shows a 2D phase separation in the adsorbed layer, due to association of the A segments, and a surfactant bilayer is formed. If the B block is long, steric hindrance prevents such bilayer formation. This compares well with the fact that the diﬀerence between the critical micelle concentration and the critical membrane concentration increases if the B block becomes longer (Fig. 10).

2. Structure of the Adsorbed Layer The volume fraction proﬁles, x ðzÞ, in the plateau of the isotherm are given in Fig. 14 for segments of type A and type B for A10 B6 and A10 B40 . For A10 B6 a thick bilayer is formed: B segments are present both at the surface and at the solution side, spatially separated from each other by a layer of segments of type A. For A10 B40 no maximum in the volume fraction of B segments at the solution side is found, no bilayer is formed. Adsorbed and

FIG. 14 Volume fraction proﬁles of A10 B6 (a) and A10 B40 (b) in the adsorbed layer at the plateau of the isotherm on a hydrophilic surface. The volume fractions of segments of type A and of type B are indicated. (Reprinted with permission from Ref. 62. Copyright 1996 American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

free surfactant bilayers become more and more unfavorable as the number of B segments rises. The trends observed from the calculated isotherms compare well with experimental results by Levitz and Van Damme [158,159], Partyka et al. [161], and Tiberg et al. [162,163] for adsorption of a series of alkylphenol polyoxyethylenes on hydrophilic silica. Also for other nonionic surfactants, like decyl methylsulfoxide, adsorbed onto silica similar isotherms were found [164]. Levitz [158,159] also studied the structure of the adsorbed layer of octylphenol polyoxyethylenes, using pyrene as a ﬂuorescent probe. Pyrene solubilization was found to occur for all chain lengths studied, indicating that nonpolar domains exist in the adsorbed layer. For surfactants with small headgroups a homogeneous adsorbed layer may be formed near the CMC. For surfactants with longer headgroups aggregates were formed on the surface with sizes comparable to the sizes of micelles. These results, together those obtained with neutron reﬂection [67] and the fact that Fig. 10 shows that bilayers are not likely when the A=B ratio is small, all strongly suggest that the 1D SCFA calculations for the adsorbed layer are not adequate. We will return to this issue when the 2D SCFA calculations are discussed.

B. Adsorption Layers on Hydrophobic Surfaces In the study the adsorption of A10 Bn molecules on hydrophobic surfaces, SA is set to 4 and SB = 0 [64]. In this case the free energy of displacement of a water molecule on the surface by an A segment is 1.5 and that of a B segment 0.1 kT. The adsorption of A10 Bn versus a linear concentration axis approximates the L-type for all values of n studied ð6 n 40Þ. However, plotting the results semilogarithmically reveals that this is not the case: as soon as some material is present at the surface a strong increase in the adsorption occurs due to the association of the hydrophobic chains. The increase in adsorption with concentration levels oﬀ before the CMC is reached and saturation adsorption is reached around the CMC. The adsorption plateau decreases with increasing B block size. These trends agree with experimental isotherms of a series of nonylphenol polyoxyethylenes on polystyrene and poly(methyl methacrylate) [112,165].

C. Aggregates on Hydrophilic Surfaces 1. Parameter Values In order to investigate the problem of local aggregate formation in more detail, the adsorption of two surfactants, C12 ðEOÞ6 and C12 ðEOÞ25 , and an EO oligomer, EO22, have been studied experimentally and the results were compared with calculations using both the 1D and 2D SCFA theory [67]. In Copyright © 2003 by Taylor & Francis Group, LLC

these calculations a somewhat diﬀerent choice of segments has been made. The C 12 ðEOÞ6 and C12 ðEOÞ25 are modeled as A4 B6 and A4 B25 , i.e., one A segment is composed of 3 CH2 groups and each EO unit equals a B segment. The EO oligomer is modeled as a chain of 25 B segments. The present choice leads to a more realistic size ratio between a B and a A segment and makes it possible to perform the 2D calculations (fewer segments). With these large aliphatic segments a value AW ¼ 4:3 is required to reproduce approximately the correct change in CMC as a function of aliphatic chain length. For the 2D calculations a lattice with 16 layers and 10 rings has been used. This is rather small with respect to the chain length of the surfactant, but to deal with the problem a large number of equations have to be solved. At the time of the calculations this was the maximum size of the system that could be handled. For the B segments that are assumed to adsorb on the surface a value BS ¼ 3 is used rather than 6 as done above. The latter choice gave rise to high-aﬃnity isotherms for surfactants with long headgroups, which is not in agreement with the experimental ﬁndings. For the interaction between A and S a repulsive value AS ¼ 4:3 is chosen. This value equals AW , and it ensures that no preferential adsorption of A occurs on the surface, because the interaction of A with the surface is just as unfavorable as the interaction of A with W.

2. Comparison of 1D and 2D SCFA Calculations The adsorption isotherms of A4 B6 , A4 B25 , and B25 calculated with the 1D SCFA theory are shown in Fig. 15. An arrow indicates the CMC, beyond which no further increase in adsorption occurs. For A4 B6 (Fig. 15a) the initial adsorption is very low; just before the CMC a phase separation takes place in the adsorbed layer, leading to a large condensation step. The dashed curve is the calculated isotherm; the full curve indicates the condensation step. Layering transitions are especially evident because high x-values are used. For A4 B25 , Fig. 15b, a more gradual increase in adsorption is found and a much lower plateau value is reached than for A4 B6 (note the scale diﬀerence with Fig. 15a). The diﬀerences between A4 B25 and B25 are much smaller than observed experimentally for C12 ðEOÞ25 and the ðEOÞ22 oligomer. Due to the diﬀerent choice for the A segments and the diﬀerent parameter values, the shapes of the isotherms have changed slightly; compare Figs. 13 and 15. The A4 B6 isotherm starts to increase sharply at a concentration close to the CMC, whereas the A10 B6 isotherm in Fig. 13 increased well below the CMC due to the higher value of BS . For the surfactant with long headgroup the high-aﬃnity isotherm has disappeared, in agreement with experimental work [158,159]. The diﬀerence in plateau values of the two isotherms Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 15 Calculated 1D SCFA adsorption isotherm of A4 B6 (panel a). The dashed curve represents the calculated points; the full curve, which coincides with the dashed curve at high coverage, shows the phase separation. The results for A4 B25 and B25 are given in panel b. An arrow indicates the CMC. (Reprinted with permission from Ref. 67. Copyright 1996 American Chemical Society.)

and the volume fraction proﬁles of the A and B segments at the CMC are, however, very similar for the two sets of parameters. As indicated above, with the very long headgroup of A4 B25 as compared to the tail, it is unlikely that a homogeneous A4 B25 bilayer will form. Most likely the A segments will form hydrophobic clusters in the adsorbed layer. This eﬀect can be studied using the 2D SCFA theory. For A4 B6 the adsorption isotherm calculated with the 2D SCFA theory is given in Fig. 16a. Due to the aforementioned layering transitions the shape of the isotherm is not perfect and small irregularities should be neglected, but the ﬁrst condensation loop is realistic. It is clear that the instability region has become much smaller than with the 1D calculations. This is due to the fact that a critical concentration in a certain layer is no longer needed to get local phase separation. This critical concentration is needed in just one ring. The adsorption isotherm increases almost vertically, close to the step in the 1D adsorption isotherm. A drawback of the 2D calculations is that at present only a fairly small aggregate and its growth with bulk solution concentration could be studied. In the case of A4 B6 and high amounts of surfactant in the system, the surfactant molecules also start to accumulate near the system boundaries (near ring 10) and then the calculated volume fraction proﬁle depends strongly on the number of rings used. Because of this behavior the calculated isotherm is truncated at nexc ¼ 0:3. As the 2D isotherm follows about Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 16 Calculated 1D and 2D SCFA adsorption isotherms of A4 B6 (panel a), A4 B25 , and B25 (panel b). (Reprinted with permission from Ref. 67. Copyright 1996 American Chemical Society.)

the condensation step in the 1D isotherm it may be concluded that the local aggregates have to be very large bilayer structures (double ‘‘pancakes’’). For A4 B25 the diﬀerence between the 1D and 2D isotherms is quite signiﬁcant; see Fig. 16b. Again only the ﬁrst (and largest) instability in the isotherm is realistic; irregularities for nexc > 0:025 are layering transitions and should be neglected. The adsorbed amount calculated with the 2D theory is much higher than that with the 1D theory. Moreover, the adsorption is much higher than that of B25 . These diﬀerences and the high adsorption values indicate that strong association must have taken place.

3. Surface Micelles The calculated structure of the surfactant aggregate is illustrated in Fig. 17, where the volume fraction proﬁles of the adsorbed aggregate of A4 B25 at nexc ¼ 0:1 are shown. The B segments are located at the surface and on the outside of the core formed by the A segments. The aggregate consists of about 30 molecules. Note that in layer 10 and ring 1 a signiﬁcant volume fraction of B segments is still present. The shape of the isotherm C12 ðEOÞ25 is in agreement with experimental work [67,158,159,163]. From theory bilayer formation on a hydrophilic surface is evident. Experimentally a complete bilayer of C12 ðEOÞ25 on the surface is not found [8,9,67,163,166], but the large condensation step in the isotherm indicates that fairly large bilayer fragments are present. For A4 B25 the 2D SCFA theory predicts the formation of aggregates on the surface. The presence of these aggregates is responsible for the large adsorbed Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 17 Volume fraction proﬁles of B and A segments of A4 B25 for an adsorbed aggregate near the CMC. (Reprinted with permission from Ref. 67. Copyright 1996 American Chemical Society.)

amounts in comparison with those for the polymer B25 . These diﬀerences were also found experimentally between C12 ðEOÞ25 and ðEOÞ22 [67]. Assuming that the diﬀerence between the 1D and 2D isotherm is due to aggregation and that all aggregates are equal in size, an estimate can be made of the minimum aggregation number. The maximum aggregation number follows from the 2D isotherm. The obtained numbers range from 10–15 at low surfactant concentration to 26–34 near the CMC. The aggregation number of the adsorbed aggregate of A4 B25 at the CMC is about the same as that for A4 B25 micelles, calculated at high surfactant concentrations. This was also found experimentally by Levitz et al. [123,160] for surfactants with long EO chains adsorbed on silica, using pyrene excimer Copyright © 2003 by Taylor & Francis Group, LLC

formation. For a surfactant with an ðEOÞ13 headgroup Levitz et al. found a growth in aggregate size with the concentration. Calorimetric data of Denoyel et al. [167] with the same systems show two domains: at low adsorbed amounts the heat eﬀect is exothermal, and the contacts between surface and surfactant segments are enthalpically favorable. At higher adsorption values an endothermal eﬀect is observed, with a molar enthalpy of the same order of magnitude as the molar enthalpy of micellization, indicating the role of hydrophobic lateral interaction. With an increase in EO length the heat eﬀect at low coverage is enlarged, whereas at higher coverages the endothermic eﬀect is diminished. These trends are in agreement with the present calculations, where also two domains in the adsorption isotherm are found. The ﬁrst part is dominated by the adsorption of B segments on the surface, whereas the second part stems from the accumulation of A segments. In general, it may be concluded that a satisfactory agreement between 2D SCFA calculations and experimental data is observed.

VII. SCFA AND MICELLIZATION OF IONIC SURFACTANTS A. Parameter Values In the study of the ionic surfactants, the surfactants have been treated as chains consisting of series aliphatic segments, A, and three sequential headgroup segments B: An B3 [63–66,142,143]. The headgroup is considered to be about three times as large as a CH2 or A segment. A slightly diﬀerent choice of the number of headgroups segments (2 or 4) did not change the results signiﬁcantly. RIS statistics are used for the chain conformations. The energy diﬀerence between a trans and a gauche conformation in the chain is taken to be 1 kT. The nonelectrostatic interaction parameters between the A segments and the other segments in solution are set to AW ¼ AB ¼ AC ¼ AD ¼ 2. The remaining -values are 0. The valency of the headgroup, B3 , equals 1, or 1/3 charge per B segment. Cations and anions ðC; DÞ are modeled as monomers with a valency of +1 and 1, respectively. Because segments B, C, and D are deﬁned as charged segments, their charge is not indicated. The relative permittivity of the segments of type A is 2 and that of water and all other segments is 80. Salt ions only diﬀer from the solvent by their charge. Apart from the fact that salt ions and solvent have a volume, this situation is comparable to that in diﬀuse double-layer theories such as the Gouy Chapman theory. The distance l between two midplanes of lattice layers, which must be quantiﬁed in the computation in the case of electrostatic interactions, is 0.31 Copyright © 2003 by Taylor & Francis Group, LLC

nm and the cross section of a lattice site is assumed to be l2. Using l3 as the volume of a lattice site, this choice leads to 55.5 moles of lattice sites per dm3, i.e., every monomer is assumed to have the size of a water molecule. This size of a lattice site corresponds approximately with the volume of a CH2 group as calculated from the bulk density of alkanes. However, the length of a C–C bond is overestimated.

B. Aggregate Shape and Structure of the Micelles To obtain information on the preferred aggregate shape, calculations for spherical, cylindrical, and ﬂat lattices have been compared for various model surfactants [63]. The eﬀect of chain length of a homologous series of An B3 on the equilibrium volume fractions of aggregate formation for spherical aggregates (near the theoretical and practical CMC, i ¼ 0:01), inﬁnitely long cylinders, and inﬁnite membranes, all at a salt concentration of 0.1 M CD, is presented in Fig. 18. Because the spherical structures are in equilibrium with lower bulk volume fractions than the cylinders and the membranes, the ﬁrst-formed aggregates are spherical for all chain lengths studied. The equilibrium volume fractions for aggregate formation decrease with increasing chain length with a slope that is hardly diﬀerent for the diﬀerent aggregate shapes.

FIG. 18 Equilibrium bulk volume fractions as a function of the number, n, of aliphatic segments, A, of spherical, cylindrical, and ﬂat structures formed by AnB3 molecules, with a valency of 1 on the B3 headgroup (1/3 per B) in a univalent symmetrical electrolyte (C+ and D) solution with cs ¼ 0:1 M, solvent W. (Redrawn with permission from Ref. 63. Copyright 1996 American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

This slope is mainly dependent on the choice of the Ay parameter and the segment size. The calculated slopes correspond to that measured for a homologous series of ionic surfactants at high ionic strength [157], indicating an appropriate combination of parameter values. As n increases the equilibrium volume fractions at which cylinders and spheres (i = 0.01) are formed approach each other. In this situation it is to be expected that deviations from the spherical shape will occur and intermediate forms, such as ellipsoids, may be present and the aggregates will be polydisperse. The salt concentration also aﬀects the CMC and aggregation number. In Fig. 19 the CMC (panel a) and nagg (panel b) of spherical micelles are shown as a function of the aliphatic tail length, in the absence and presence of 0.1 M indiﬀerent salt. For both situations the CMC decreases and the aggre-

FIG. 19 Eﬀect of the chain length on the cm (panel a) and the aggregation number (panel b) at i = 0.01 at cs = 0 and cs = 0.1 M for AnB3 molecules. The calculated values are indicated with markers; the drawn lines are ﬁts through the calculated points. (Redrawn with permission from Ref. 63. Copyright 1996 American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

gation number increases with increasing chain length, but the eﬀects are larger in the presence of salt. In the absence of added electrolyte, the ionic strength is determined by the surfactant. A surfactant with a longer aliphatic tail has a stronger tendency to associate than one with a short tail due to the stronger hydrophobic interactions. This leads to a lower CMC. At this low CMC, however, the repulsion between the headgroups is strong because the ionic strength, determined by the CMC, is low. This repulsion counteracts the hydrophobic attraction and an increase of the chain length with one CH2 segment has a relatively small eﬀect on the CMC and the aggregation number. In the presence of 0.1M electrolyte the ionic strength is not signiﬁcantly aﬀected by the surfactant; the headgroup repulsion is relatively small and independent of the surfactant chain length. An increase in chain length manifests itself exclusively in the increase of the hydrophobic attraction and much larger micelles are formed and their size more strongly increases with n. These trends are in reasonable agreement with experimental data [157,168–171]. Volume fraction proﬁles, i.e., x as a function of z, the distance to the center of the micelles, for a spherical A12 B3 micelle in the absence of added electrolyte, are plotted in Fig. 20. In panel a the results are plotted on a linear scale and in panel b on a logarithmic scale. The proﬁles show that the aliphatic segments form the core of the micelle and that the headgroup segments are located on the outside of the aggregate. The interface between the hydrophobic segments A and the aqueous

FIG. 20 Volume fraction proﬁles of W, A, B, and C for an A12 B3 spherical micelle in the absence of added electrolyte. In panel a a cross section through a micelle is plotted on a linear scale; in panel b the same on a logarithmic scale (starting from the center of the micelle). (Redrawn with permission from Ref. 63. Copyright 1996 American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

phase W is rather sharp: it drops from about 0.9 to less than 0.1 over only 3 lattice layers (1 nm). This distance is in agreement with MD simulations [92,172–174]. The charged headgroups are located on the outside of the aggregate. The headgroup distribution is less sharp than the ‘‘A=W interface’’; it extends over about ﬁve lattice layers. Calculations performed for other headgroup sizes ðB; B2 ; B4 Þ gave almost identical results. The width of both the A=W interface and the headgroup distribution is hardly aﬀected by the salt concentration. The volume fraction proﬁle of the counterions is barely visible on the linear scale, but a clear picture results from the logarithmic plot. The counterions, C, accumulate mainly in the same layers as the charged headgroups. This implies an eﬀective partial neutralization of the micelle. To a good approximation micelles behave as spheres with a constant net charge density. Upon a tenfold increase of the salt concentration, the electric potential in the headgroup region is decreased in absolute value by about 59 mV to maintain this charge density. This result corresponds with experimentally obtained surface potentials as a function of the salt concentration [175]. Outside the micelle, at about z ¼ 12 a diﬀuse ionic layer has developed. In the diﬀuse layer the counterions are positively adsorbed and the surfactant anions are depleted. The diﬀerence between B and C at large distance is due to the fact that each B segment has a charge of 1/3 and each ion C a unit charge.

C. Chain Branching and Micellization Besides the chain length, branching of surfactants is also known to aﬀect the shape of the micelles, the CMC, and the aggregation number. Some results have been obtained for an isomeric series of A12 B3 surfactants for which the segment of attachment of aliphatic chain to the headgroup is varied [63]. The results are presented in Figs. 21 and 22. For all surfactants the tail is connected to the third of the three headgroup segments. A linear chain is obtained when the ﬁrst segment of the aliphatic chain, with segment ranking number SB =1, is connected to the headgroup. The longest branch length is attained when the segment with SB = 6 is attached to the headgroup. The results in Fig. 21 show that the CMC increases and that nagg decreases with increasing branch length. For the most strongly branched molecule, with SB ¼ 6, the CMC is about twice as high as for linear A12 B3 and nagg decreases from 37 to 26. The reason for this behavior is that for molecules with a thick but short hydrophobic part the packing into a spherical micelle is more diﬃcult than for long and thin molecules. The calculated shifts are in agreement with experimental ﬁndings for isomers of sodium alkylbenzene sulfonates [176], but for sodium alkyl sulfates the eﬀect of branching is more pronounced [177]. Calculations where the surfactant Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 21 Eﬀect of branching on the cm (panel a) and aggregation numbers at i = 0.01 (panel b) of molecules with 12 A segments, no salt added. The segment number to which the headgroup is attached, SB, is given on the horizontal axis. The calculated values are indicated with markers; the drawn lines are ﬁts through the calculated points. (Redrawn with permission from Ref. 35. Copyright 1996 American Chemical Society.)

was modeled as A12 B with a charge of 1 on the B headgroup showed a more pronounced eﬀect of branching. The eﬀect of branching and salt concentration on the shape of the micelles is shown in Fig. 22, where the equilibrium volume fractions for spherical micelles (near the CMC, and at i ¼ 0:01), cylindrical micelles, and ﬂat membranes are compared for A12 B3 with SB ¼ 1 and SB ¼ 6. For the linear chains and low salt concentrations, spherical micelles are favored over cylindrical aggregates and membranes. At higher salt concentrations, the equilibrium bulk volume fractions for spheres (i = 0.01), cylinders, and membranes are rather close to each other. Spherical micelles are still preferred at low concentrations but at higher overall concentrations the system may be very polydisperse because the equilibrium volume fractions for spheres and cylinders are hardly diﬀerent.

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FIG. 22 Comparison between aggregates of diﬀerent shapes. Eﬀect of the salt concentration on the equilibrium volume fraction of linear A12B3 (panel a) and branched A12B3 with SB = 6 (panel b). Equilibrium volume fractions at the CMC and i = 0.01 for spheres are shown together with those for cylinders and membranes. (Redrawn with permission from Ref. 63. Copyright 1996 American Chemical Society.)

For the branched isomer (A12 B3 , SB = 6) spherical aggregates are preferred at low salt and surfactant concentration, i.e., the micelles ﬁrst formed are spherical. If more surfactant is added, globular micelles remain preferred at low salt concentration. However, at higher salt concentration, about 0.2 M in this case, membranes and cylinders are preferred over spherical micelles: a transition from a spherical to a cylindrical shape occurs as function of salt or surfactant concentration. The calculated results are in agreement with data for alkylbenzene sulfonate micelles [178] that reveal that in the absence of salt the branched isomers have lower aggregation numbers than linear molecules. At high salt concentrations the aggregation numbers of the branched surfactants increase to very high values, while the aggregation number of the linear alkylbenzene sulfonate shows a limited increase. Copyright © 2003 by Taylor & Francis Group, LLC

VIII.

SCFA AND ADSORPTION OF IONIC SURFACTANTS

Adsorption calculations have been made for constant-charge [64], constantpotential [65,66,142,143], and charge-regulating surfaces [68]. All bulk parameters are the same as in the micellization study. For the constant-charge and constant-potential case, the noncoulomb interactions with the surface are expressed by BS ¼ 10 and xS ¼ 0 for all other segments. For the A and B segments this leads to a displacement free energy per segment of 0.5 kT and 2.5 kT, respectively. For the other segments the ‘‘adsorption energy’’ is zero. For the regulating surface (representing silica) the surface interaction parameters will be speciﬁed later.

A. Adsorption on Constant-Charge Surfaces 1. Adsorption Isotherms and Structure of the Layer Calculated adsorption isotherms of A12 B3 on a surface with a ﬁxed charge of 0.1 charges per lattice site (0.17 C/m2) and at three salt concentrations are shown in Fig. 23 [64]. To show the low coverage part more clearly, the isotherms are also plotted on log–log scales. The excess number of surfactant molecules per surface site is plotted as a function of the overall volume fraction, , of surfactant. The point where the CMC is reached is indicated with an asterisk. At low and intermediate salt concentrations the adsorption isotherms show two distinct steps, but at a salt concentration of 0.1 M the stepwise nature of the isotherm has almost disappeared. At low surfactant and low salt concentrations the initial adsorption is higher than at a high salt concentration. At high surfactant concentrations the situation is reversed, i.e., the adsorption is larger at high than at a low salt concentration. Due to this behavior the isotherms at diﬀerent salt concentrations intersect. The intersection point of the three isotherms marks the point where the surface charge is compensated by the adsorbed surfactant (iep). This behavior was already predicted on qualitative grounds by Eq. (7). The strong increase in adsorption, just before the ﬁrst plateau is reached, is due to hydrophobic attraction. This interaction is already substantial at rather low adsorption values. The second step in the isotherm occurs at about 0.1 of the CMC; this rise in the adsorption is also due to hydrophobic attraction, but this time a ‘‘bilayer’’ is formed. Experimentally this type of two-step isotherms has been found for surfaces such as mica [179], polystyrene [52], biotite [180], and spheron [52]. In cases where the adsorption was studied as a function of the salt concentration, the two-step shape disappeared at high salt concentrations [52]. Also for surfactant adsorption on silica a two-step isotherm has been found [181],

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FIG. 23 Theoretical adsorption isotherms of A12 B3 on a surface with a ﬁxed charge density of 0.1 charges per lattice site at three salt concentrations. The CMCs are indicated with an asterisk. Isotherms are plotted in two ways: log–log (a) and lin–log (b). (Redrawn with permission from Refs. 64 and 144. Copyright 1996 American Chemical Society.)

but silica is not a constant-charge surface and the conclusions drawn in [64] with respect to silica should be regarded as premature. In the section on adsorption on charge-regulating surfaces, the silica behavior will be discussed in more detail. The structure of the adsorbed A12 B3 layer on the constant-charge surface followed from the calculated volume fraction proﬁles [64]. At submonolayer coverage the surface charge is mainly compensated by the salt ions. After the ﬁrst step, in the plateau region, the surface charge is almost exclusively compensated by surfactant ions. The A segments are accumulated at the solution side of the adsorbed layer, so that the particles have become hydrophobic. At coverages above nexc = 0.1, a (partial) surfactant bilayer is present on the surface. Due to the presence of headgroups at both sides of the adsorbed layer the system becomes hydrophilic again. In general, the bilayer is asymmetric: the headgroups near the surface are distributed over three layers, whereas at the solution side the headgroup distribution is much wider Copyright © 2003 by Taylor & Francis Group, LLC

and it closely resembles the headgroup distribution in a micelle. This similarity is also reﬂected in the electrostatic properties of the bilayer: a low and approximately constant net charge density occurs in the outer headgroup region. The potential in this region strongly depends on the salt concentration. For a detailed discussion on the charge and potential distribution, consult Ref. [64]. Besides the electrostatic, the speciﬁc or contact interactions between B segments and A segments with the surface determine the shape of the adsorption isotherm. Some typical examples to illustrate this for a charge density of 0.1 charges per site and a salt concentration of 103 M can be found in Ref. [64].

2. Remarks on the SCFA Model Finally, a remark should be made with respect to the failure of the 1D SCFA theory to model surface aggregates. In the case of constant-charge surfaces where the charges are most probably distributed fairly regular over the surface (due to the electrostatic repulsion), the errors made with the 1D SCFA theory might be small, especially at high-surface-charge densities and strong noncoulomb interactions between the headgroup and the surface. In this case the charges at the surface act as initial nuclei for the surfactant adsorption, and this would result in a smeared-out (sub) monolayer of surfactants. Once the nuclei start to grow substantially, the aggregates formed may interact and form a bilayer. For low-charge densities and weak noncoulomb interactions with the surface, independent aggregates may be formed and the calculations should be considered with some reservation.

B. Adsorption on Constant Potential (Variable-Charge) Surfaces 1. Adsorption Isotherms Many metal oxide surfaces can be regarded, to a ﬁrst-order approximation, as constant-potential surfaces, provided the pH in solution is ﬁxed [97,183]. Theoretical investigations of these systems are therefore quite relevant. Adsorption isotherms of A12 B3 on a surface with a potential of 100 mV have been calculated [65,66,142,143]. Except for the surface charge and potential, all parameters are the same as for the constant-charge case. Results are shown in Fig. 24, where the excess number of surfactant molecules per surface site is plotted versus the overall volume fraction of surfactant. Three common ways of presentation are used. The log–log isotherms, presented in panel a, strongly emphasize the lower part of the isotherms. They show four regions, in qualitative agreement with Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 24 Theoretical adsorption isotherms of A12 B3 on a surface with a ﬁxed potential of 100 mV at three CD concentrations. The isotherms are plotted in two ways: log–log (a) and lin–log (b). (Redrawn with permission from Refs. 65 and 144. Copyright 1996 American Chemical Society.)

experimental results [28,65,66,142,143]. In region I the slope is unity (Henry region) and the adsorption decreases with increasing salt concentration. Region II shows a phase transition indicating that two coexisting phases are present at the surface at a given volume fraction. The condensation step occurs at all salt concentrations. Region II starts at a coverage of a few percent of the adsorbed amount at the CMC and ends at about nexc = 0.2. Region III has a slope much smaller than region II and the adsorption increases with increasing salt concentration. Above the CMC, in region IV, the adsorption reaches a plateau value. The lin–log plot of the isotherms (panel b) give equal weight to all adsorption values and show the eﬀects in the upper part of the isotherm more clearly than the log–log plots. In the lin–log plot the four regions of Copyright © 2003 by Taylor & Francis Group, LLC

the isotherm can also be distinguished. Region II ends when the surface charge can no longer adapt to the surfactant adsorption. The lin–lin plots are not shown, because they are rather featureless and the information at low-surfactant concentrations is lost. Comparison of the adsorption isotherms on a constant-potential surface (panel b) with those on a constant-charge surface (Fig. 23) shows that the behavior is rather diﬀerent: in the constant-potential case at low-surfactant concentration a strong phase transition occurs, the ﬁrst plateau is absent, and the adsorption increases more gradually to its value at the CMC in the second part of the isotherm. Moreover, the surface charge increases upon surfactant adsorption from below 0.05 to about 0.2 charge units per site, depending on the salt concentration. The fact that the surface responds to the surfactant adsorption explains why the ﬁrst plateau is missing: the coulomb interaction with the surface remains attractive much longer due to the fact that new charges are formed at the surface. The common intersection point of the three isotherms is located at nexc ¼ 0:1 (see Fig. 24), and it corresponds with the iep. After the iep is reached, the surface still increases its charge with increasing surfactant adsorption in order to screen the charges of the head-on adsorbed surfactant molecules. However, a part of the surfactant molecules adsorbs in the bilayer, and this adsorption gives the particles a net (negative) charge.

2. Structure of the Adsorbed Layer The volume fraction proﬁles in each of the four regions of the isotherm are presented in Fig. 25 for a salt concentration of 0.01 M [65]. In region I, panel a, the molecules adsorb fairly ﬂat on the surface, the tails are squeezed out of the water, and the headgroups adsorb strongly due to speciﬁc and coulomb attraction. The surface charge is screened by both surfactant and salt ions. In region II, at the end of condensation step (nexc ¼ 0:2), panel b, the aliphatic segments on the surface are displaced by B segments; head-on adsorbed surfactant is present on the surface and the surface is hydrophobized by the A segments at the solution side of the adsorbed layer. The volume fraction of B segments at the solution side is still very low. In region III (nexc ¼ 0:3, panel c) the second layer grows signiﬁcantly and the solution side of the layer becomes gradually more hydrophilic. This process stops when the CMC is reached, region IV. For adsorption values above the cip (iep) the hydrocarbon core of the bilayer separates two net uncharged parts. In regions III and IV the headgroup charges at the solution side are partly compensated by accumulation of counterions in between the headgroups, partly by the diﬀuse double layer. Again the outside of the bilayer is very similar to the outside of micelles. Some accumulation of counterions occurs at the surface side of the bilayer. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 25 Adsorbed layer structure for A12 B3 on a constant-potential surface at three diﬀerent coverages corresponding with regions I, II, and III of the isotherm. Volume fraction proﬁles of A, B, C, and D are shown (lin–lin and log–lin plots). The volume fractions of C and D are best shown in the log–lin plots. (Redrawn with permission from Refs. 65 and 144. Copyright 1996 American Chemical Society.)

In general, the calculations show that head-out adsorption starts after the cip has been reached [142,143]. Before the cip head-on adsorption is exclusive, after the cip both head-on and head-out adsorption occur, but the head-out adsorption increases more strongly. Increasing the salt Copyright © 2003 by Taylor & Francis Group, LLC

concentration favors head-out adsorption due to screening of the lateral repulsion. Above the cip head-on adsorption is discouraged by salt addition because of the enhanced screening of the coulomb headgroup surface attraction. Below the cip the head-on adsorption is hardly aﬀected in the case that BS ¼ 10.

3. Chain Branching and Adsorption The eﬀects of branching on the adsorption isotherms of three A12 B3 isomers are presented in Fig. 26 [66]. In the log–log plot, panel a, diﬀerences between the adsorption isotherms show up mainly in region I. Through the choice of AW the tail segments have some aﬃnity for the surface. The isomers with longer side chains will have less initial adsorption, because the entropy loss for a branched molecule to lie ﬂat on the surface will be larger than for a linear one. As expected, region II of the calculated adsorption isotherms shows a phase transition. The trends in the upper part of the isotherms are more clearly shown in the lin–log plot; see panel b. The diﬀerences in the adsorbed amounts show that packing of the molecules becomes more diﬃcult when the chains are strongly branched.

FIG. 26 Eﬀect of branching on the adsorption of A12B3 molecules on a surface with potential of 50 mV. The results are given on a log–log (a) and a log–lin (b) scale. The CMC values are indicated with an asterisk. (Reprinted with permission from Ref. 66. Copyright 1996 American Chemical Society.)

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4. Anionic Surfactant Adsorption on Metal Oxides Adsorption isotherms of anionic surfactants on positively charged metal oxide surfaces have been investigated in numerous studies [3,28,65,66, 103,124,129,133,135,142,143,145]. The general shape of the isotherm is well established. A typical result is shown in Fig. 27, where the adsorption of sodium nonylbenzene sulfonate on rutile is plotted in three diﬀerent ways [65]. The experimental isotherms are in qualitative agreement with the theoretical results. In both cases a four-region isotherm is found; along the isotherm an inversion of the salt eﬀect is observed and a common intersection point is present. The predicted trend that the adsorption increases slightly with increasing salt concentration in region IV also corresponds with experimental ﬁndings [65,132,133]. A qualitative agreement between 1D SCFA

FIG. 27 Four-region isotherm. Adsorption of sodium nonylbenzene sulfonate (SNBS) on rutile at pH ¼ 4.1 at three NaCl concentrations. The isotherms are plotted in two ways: log–log (a) and lin–log (b). The arrows indicate the CMC values. (Redrawn with permission from Refs. 65 and 144. Copyright 1996 American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

calculations and experimental results also exists with respect to the eﬀects of chain length and branching of the surfactant on adsorption [66]. Moreover, the calculated shifts of the isotherms for diﬀerent surface potentials compare well with experimentally measured shifts of isotherms obtained at diﬀerent pH values [65,142]. Qualitatively the calculated volume fraction proﬁles relate closely to experimentally observed maximums in the hydrophobicity [28] and ﬂotation recovery [183] of particles as a function of surfactant concentration: at low adsorbed amounts the particles are hydrophobized, whereas at high adsorbed amounts the particles are hydrophilic again. Around the iep the colloidal stability will be at its minimum, not only because the particles carry no net charge, but also because they are hydrophobized.

5. Surface Charge and Surfactant Adsorption An important feature of constant-potential surfaces is that the surface charge is adapted when speciﬁcally adsorbing ions, such as surfactant ions, are present. Due to the noncoulomb attraction, surfactant ions screen the surface charge better than the indiﬀerent ions present in the diﬀuse layer. The surface charge adjustment upon surfactant adsorption has been investigated in detail [65,142,143]. Results of the theoretical calculations are shown in Fig. 28. The surface charge, expressed in number of charges per lattice site, is plotted versus the surfactant concentration for two salt concentrations and one surface potential. The initial surface charge for all conditions is very low (<0.05 charges per site), but due to surfactant adsorption the surface charge adjusts strongly to neutralize the adsorbed surfactant charge. At higher coverages, but well before the CMC, the adjustment of the surface charge levels oﬀ and reaches a plateau. In general, the plateau value of the surface charge decreases slightly with decreasing surface potential. There is a small dependence on the salt concentration due to the incorporation of positive salt ions between the head-on adsorbed surfactants. The calculated results on charge adjustment can be compared with experimental results. Some typical data, referring to SNBS adsorption on rutile, are shown in Fig. 29. The qualitative agreement is obvious, apart from the instability loop that has been discussed before. Moreover, the calculated absolute values of the surface charges in the presence of surfactant are much higher than the experimental ones for SNBS. For other systems, such as, e.g., SDS on alumina [133], higher plateau adsorptions have been reported than for SNBS on rutile and then the surface charge may also be higher. The discrepancy is partly due to our choice of parameters. Probably an improvement can be achieved by modeling the surface as a charge- and potential-regulating surface with a limited number of chargeable sites (see the section on regulating surfaces). Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 28 Adsorption of A12 B3 and surface charges (0 as =e) as function of the A12 B3 volume fraction, both expressed in the same units. The surface potential and the salt concentration are indicated. (Reprinted with permission from Ref. 65. Copyright 1996 American Chemical Society.)

6. Anionic and Cationic Surfactant Adsorption on Rutile The theoretical results predict that the behavior of anionic surfactants on a positive constant-potential surface should be mirror images of the behavior of cationic surfactants on a negative constant-potential surface. Experimental results for the adsorption of nonylbenzene sulfonates and alkyl pyridinium surfactants on positive and negative rutile conﬁrm this [142,143]. However, the experimental results are not a perfect mirror image of each other, because the speciﬁc interactions of the two surfactant headgroups are quite diﬀerent. The sulfonate headgroup adsorbs much more strongly than the pyridinium group. Due to the weak interaction of the pyridinium group with the surface, also the cip in the isotherms measured at three diﬀerent salt concentrations does not coincide with the iep Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 29 Surface charge of rutile and adsorption of SNBS as a function of the SNBS concentration. The pH value and NaCl concentrations are indicated in the ﬁgures. (Reprinted with permission from Ref. 65. Copyright 1996 American Chemical Society.)

and the equivalence point (surface charge equivalent to the adsorbed surfactant charge) any more. The co-ions of the surfactant also contribute to the positions of these characteristic points [143]. Again the calculated results are in qualitative agreement with the experimental data, but there are fairly large quantitative diﬀerences.

7. Remarks on the SCFA Model The ability of the 1D SCFA theory to predict the four-region isotherm is gratifying. Except for the theory of Li [146], no other theory could do this unless ad-hoc assumptions were made about surface heterogeneity and the structure of the adsorbed layer. Nevertheless, some typical diﬀerences with the experimental isotherms appear. Notably region II is predicted incorrectly: the association starts and ends at too-high coverages as compared to the experimental situation. The model overestimates the 2D condensation behavior. As the calculated region II is too large, the slope of region III is Copyright © 2003 by Taylor & Francis Group, LLC

too low. Nevertheless, a signiﬁcant increase in adsorption in region III is predicted. The main reason for the discrepancy between theory and experiments is that for each layer z a mean-ﬁeld approximation is used. In practice, the aliphatic tails attract each other, so that in the layers parallel to the surface the volume fraction of A segments will not be the same everywhere. Due to local accumulation of segments, local condensation will occur at bulk solution volume fractions of surfactant much lower than those at which the 1D SCFA theory predicts condensation. In the mean-ﬁeld theory the phase separation is postponed as compared to reality, and it shows up in an exaggerated manner once it occurs. In reality, the transition is related to the architecture of the surfactant and corresponding with an optimal size of the local aggregates [15]. Further theoretical evidence for the structure of the adsorbed layer can in principle be obtained from 2D SCFA calculations, but such calculations are not available.

C. Adsorption on Charge- and Potential-Regulating Surfaces 1. General Considerations and Parameter Values The constant-charge and constant-potential cases discussed above are extreme limits of the more general case of charge- and potential-regulating surfaces. The ‘‘regulating surface’’ approaches the constant-charge surface when all the surface groups are, for instance, strongly acidic and fully dissociated at all pH values. It approaches the constant-potential case when the site density of the chargeable surface groups is very high [97,182]. Recent advances in the 1D SCFA theory make it possible to calculate surfactant adsorption on a regulating surface. A regulating surface is modeled by considering the proton association–dissociation equilibrium of the surface groups. The parameter characterizing this equilibrium is the proton aﬃnity constant, KH . A good example of a regulating surface is the silica surface. Practical and theoretical investigations have shown that the charging of silica surfaces is quite diﬀerent from that of the crystalline metal oxide surfaces [182]. This is due to the fact that the silica surface is acidic (hydrophilic silanol groups) and partially hydrophobic (siloxane groups). Apart from the eﬀect on the charge and potential characteristics of silica, the hydrophobic siloxane groups also aﬀect the surfactant adsorption directly. On silica the aliphatic surfactant tails can interact favorably with the surface, whereas on the more hydrophilic metal oxides this is not the case. Strong evidence for the presence of surface–surfactant tail interactions is derived from surface charge measurements of silica in various electrolyte solutions in the absence and presence of cationic surfactants [184]. Copyright © 2003 by Taylor & Francis Group, LLC

To a reasonable approximation the charging of a silica surface can be described with one proton aﬃnity constant [182,185,186]. The density of surface segments that can become charged can be regulated by composing the surface layer of two types of segments that are equal except for the fact that part of them can become charged and the other part does not have this possibility. The surface charge density can be obtained as the fraction of the surface sites that is actually dissociated. As the charges in the 1D SCFA model are located at the midplane of each lattice layer, the permittivity of the surface layer also has to be speciﬁed. By adjusting this value the slope of the charge-pH curves can be modiﬁed to improve the resemblance with the experimental charge-pH curves of silica. A value of 40"0 , in combination with 5.2 active surface sites per nm2 with a pKH value of 7.8, gives a satisfactory agreement with experimental charging data for silica [182,185,186]. The calculations show that both the surface charge and the surface potential of silica are a function of pH and salt concentration. The adsorption behavior of the linear A12 B3 molecule is modeled using the same bulk solution parameters as before (see Section VII.A). The surface-aliphatic segment parameter AS is taken as 1 kT, which indicates that the aliphatic tail has a speciﬁc interaction with the surface. The interaction of the B segment with the surface BS is assumed to be zero, indicating that there is no speciﬁc interaction between headgroup and surface. To check the eﬀect of AS and BS on the adsorption, some calculations have been done with other values.

2. Adsorption Isotherms Calculated adsorption isotherms of A12 B3 at three salt concentrations are shown in Fig. 30 (panel a shows the log–log isotherms, while panel b shows the lin–log isotherms) [68]. The log–log isotherms show similar behavior as before. It should be noted, however, that the slope of region II is very sensitive to the salt concentration. At low salt concentrations the slope of region II is smaller than that in region I, but at high salt concentrations it is steeper than the slope in region I. The slope in region II is indicative for the cooperativity of the adsorption process. At low salt a negative cooperativity appears, showing that surfactant association does not occur in region II, whereas at high salt concentrations a weak hydrophobic cooperativity points to lateral association. The lin–log isotherms are at all salt concentrations S-shaped, but the slope increases strongly with salt addition. Similarly as for the constant-charge and constant-potential case, the initial adsorption decreases with an increase of the salt concentration, whereas at high adsorption values this eﬀect is reversed. The distinction between the two regions is indicated by the cip of the isotherms. In this point adsorbed surfactant molecules neutralize the surface charge. Further Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 30 Calculated adsorption isotherms for the surfactant A12 B3 on a ‘‘regulating’’ surface at pH 7 and three salt concentrations. (Redrawn with permission from Ref. 68. Copyright 1996 American Chemical Society.)

adsorption occurs because the tail segments of adsorbing molecules may decrease the number of contacts with water by association with already adsorbed surfactant molecules.

3. Surface Charge Adjustment In Fig. 31 the calculated adsorption isotherms of A12 B3 at two salt concentrations and pH 7 are combined with the calculated surface charge isotherms. At low salt concentrations (panel a) the surface charge isotherms show two regions. In the ﬁrst region the surface charge follows the surfactant adsorption. At volume fractions between 5 105 and 2 103 nearly every adsorbed headgroup creates an opposite charge on the surface and the surface charge almost completely balances the adsorbed surfactant charge. Further adsorption near the CMC only causes a weak surface charge adaptation. At the CMC the surfactant adsorption is somewhat larger than surface charge: the hydrophobic attraction is only slightly larger than the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 31 Adsorption of A12 B3 and the surface charge (0 as =e) as function of the A12 B3 volume fraction at pH 7 and two salt concentrations. Adsorption and the surface charge are both expressed in the same units. (Redrawn with permission from Ref. 68. Copyright 1996 American Chemical Society.)

electrostatic repulsion. At high salt concentrations (panel b) the surface charge is hardly adjusted. Surfactant ions have to compete with salt ions. As a result the surface charge adaptation vanishes; adsorption is an ion exchange process driven by the hydrophobic attraction. The eﬀective screening of the headgroup repulsion leads to a much higher ﬁnal surfactant adsorption than at low salt concentrations, but the surface charge does not follow. As will be shown below, the calculations are in good agreement with both measured isotherms and charge adaptation curves. This is largely due to the choice of the surface–segment interaction parameters AS ¼ 1 and BS ¼ 0. These values ensured speciﬁc binding of the aliphatic tails to the surface rather than speciﬁc headgroup binding. To investigate how the values of interaction parameters between surfactant segments and the surface aﬀect the shape of adsorption and surface Copyright © 2003 by Taylor & Francis Group, LLC

charge isotherms, some other calculations have been made [68]. Decreasing AS to 2 kT shifts the beginning of the adsorption isotherms to lower volume fractions. At low salt concentrations the surface charge adjusts itself to the surfactant adsorption, but the aﬃnity of the tail segments to the surface is so strong that near the CMC aliphatic segments replace the headgroup segments from the surface. As a result the surface charge decreases at high coverages. At high salt concentrations the adjustment of the surface charge is rather weak, but also here the tail segments replace the head segments in the last part of the isotherm. For AS = 0 and BS ¼ 5 (strong aﬃnity of the headgroup for the surface), large instability loops occur near the CMC in the lin–log isotherms, indicating phase separation in the adsorbed layer. The adsorbed molecules form a condensed bilayer just before the CMC. Also, the process of the surface charge adaptation is very strong up to the CMC. Apparently, either a strong AS or a strong BS interaction does not lead to the experimentally observed behavior.

4. Structure of the Adsorbed Layer The volume fractions of the surfactant segments and salt ions as a function of the layer number z are shown in Fig. 30 for two adsorbed amounts of surfactant and a salt concentration of 103 M [68]. To see the proﬁles of simple salt ions more clearly, the results are plotted using both a linear and a logarithmic volume fraction scale. From Fig. 32 it follows that the orientation of the adsorbed molecules on the surface is always relatively ﬂat. Due to the aﬃnity of the surfactant tail for the surface the volume fraction of A segments on the surface is considerably higher than the volume fraction of headgroup segments. The hydrophobic attraction for the entire tail competes favorably with the coulomb attractions between headgroups and surface. The enrichment is most clearly observed in the ratio A =B at the surface. At low coverage this ratio equals 7 to 8 in the ﬁrst layer, and at high coverage it is 10 to 12 as compared to the bulk ratio of 4. At the low surface coverage (nexc ¼ 0:01) the headgroup segments are almost all located in the ﬁrst three layers in order to be able to compensate the surface charge. The ions C and D hardly contribute to the charge compensation. Further adsorption leads to an increase of number of surfactant segments in all layers near the surface and to an increase of layer thickness. At high surface coverage a weak maximum in B occurs in layer 2. This is an indication for the presence of a bilayer. Headgroups at the surface compensate the surface charge; the other headgroups are located at the solution side of the adsorbed layer. Hence, close to the CMC the adsorbed layer has a bilayer structure. The overcompensation of the surface charge leads to a reversal of the salt ion adsorption: D is excluded and Cþ is adsorbed. For high salt concentrations very similar proﬁles are found. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 32 Volume fraction proﬁles of the A and B segments and the ions C+ and D near a ‘‘regulating’’ surface in a 0.001 M CD solution at two values of nexc . The results are presented both as lin–lin and log–lin plots. (Redrawn with permission from Ref. 68. Copyright 1996 American Chemical Society.)

5. Alkyl Pyridinium Surfactant Adsorption on Silica Adsorption isotherms for both dodecyl and cetyl pyridinium surfactants (DPC and CPC) on silica have been measured at various pH values and salt concentrations [68,144,184]. A typical result is shown in Fig. 33. Two scales of presentation have been used: log–log in panel a and lin–log in panel b. The relatively low slope of region II in the log–log plot corresponds with the ﬁrst adsorption step in the lin–lin isotherms [181,187,188]. In general, in the log–log isotherms four regions can be distinguished, similarly as for the isotherms on metal oxides. The slope of the plot in region I is close to unity, pointing toward a constant aﬃnity. Similarly as in the calculated isotherms, the slope in region II is strongly dependent on the salt concentration. At low salt concentrations the slope is less than unity, indicating a continuing decrease in aﬃnity. Further adsorption in this region is progressively more diﬃcult due to either or both the crowding of the hydrophobic surface sites or the poor screening of headgroup repulsion. The surfactant concentration has to be increased signiﬁcantly before progressive adsorption starts Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 33 Isotherms of DPC adsorption on Aerosil OX50 at pH 7 and two salt concentrations. (Redrawn with permission from Ref. 68. Copyright 1996 American Chemical Society.)

in region III. The behavior in region II is quite diﬀerent from that of DPC on rutile [142,143]. At high salt concentrations an S-type isotherm is observed and in region II the slope is larger then unity; this indicates a continuing increase in overall aﬃnity. Due to the eﬀective screening of the headgroup repulsion, the hydrophobic attraction is relatively strong. The resemblance of the isotherm with that of DPC on rutile is now much closer [142,143]. The slope of region III hardly depends on salt concentration. Region IV is reached at the CMC. In general, the isotherms show a cip that corresponds with the measured iep [68]. At the cip the electrostatic contribution to the free energy of adsorption vanishes and the salt eﬀect disappears. For both DPC and CPC the cip is dependent on the pH; the farther the system is away from the pzc, the higher the surface coverage is at which the cip occurs [68]. Comparison of adsorption isotherms with surface charge isotherms (see below) shows that cip also corresponds with the equivalence point. The correspondence of cip, iep, and the equivalence point indicates that speciﬁc adsorption of the background electrolyte is weak or absent in the present case. The cip is the Copyright © 2003 by Taylor & Francis Group, LLC

turning point for the coulomb interactions and the surfactant orientation. Below the cip the attractions between headgroup and the surface are important. Above the cip coulomb repulsion occurs and, additionally, adsorbing molecules are predominantly oriented with their headgroups toward the solution and a bilayer is formed.

6. Surface Charge of Silica and Surfactant Adsorption To show the eﬀect of surfactant adsorption on the surface charge, DPC adsorption isotherms and surface charge isotherms at a given salt concentration are compared in Fig. 34 [68,184]. To facilitate the comparison, the surface charge is expressed as 0 0 =F, where F is the Faraday constant.

FIG. 34 Adsorption of DPC and surface charge (s0) of Aerosil OX 50 at 0.001 M (a) and 0.1 M KCl (b) as a function of the DPC concentration at pH 7. The corresponding contact angle, , at a silica plate is also shown. (From Ref. 27.) Copyright © 2003 by Taylor & Francis Group, LLC

At low salt concentrations the maximum change in surface charge occurs at low surfactant concentrations, where the adsorption and surface charge isotherms almost coincide. This indicates that in this region practically all adsorbed surfactant ions have their headgroups close to the surface. After the equivalence point the surface charge becomes almost independent of the increasing surfactant adsorption. As the eﬀect of surfactant adsorption on the surface charge is small, adsorption in a second layer starts with the headgroups directed to the solution. The orientation of the surfactant can also be inferred from the measured contact angle [27]. For pure silica the contact angle is zero; immediately after surfactant addition, the contact angle increases and reaches a broad maximum in the region where the surface charge and adsorbed surfactant charge nearly match each other. Close to the CMC the contact angle decreases again, pointing to bilayer formation. For CTAB on silica very similar wetting behavior is found [189]. At high salt concentrations screening of the surface charge is eﬀective and relatively large values of the initial surface charge occur. The changes in surface charge due to the surfactant adsorption are much less than at low salt concentrations; only a weak but steady increase of the surface charge results. Initially it is diﬃcult for a surfactant ion to start adsorption, but once the surfactant adsorption starts it increases very strongly over a narrow concentration region, causing a sharp intersection point with the surface charge isotherms. Correspondingly, the maximum in the contact angle is very sharp, indicating that the change from head-on adsorption to head-out adsorption occurs over a very narrow concentration range. These observations correspond very well with the calculated surface charge curves and the information included in the volume fraction proﬁles. Further experimental evidence for the presence of bilayer structures on silica surfaces at concentrations around the CMC has been obtained from neutron reﬂection results [14] and ﬂotation studies [190].

7. Remarks on the SCFA Model In general, it can be stated that the 1D SCFA calculations are in qualitative agreement with experimental results obtained for cationic surfactant adsorption on silica, a charge-regulating surface. The SCFA theory gives fairly realistic information about the main driving forces for the adsorption and about the structure of adsorbed layer. At low salt concentrations the surface charge increases due to surfactant adsorption, but this surface charge adaptation does not promote the aggregation process in adsorbed layer, as follows from the low slope of region II of the logarithmic isotherms. Surfactant molecules are adsorbed on the surface with their headgroups and tails close to the surface. For this type of adsorption the 1D Copyright © 2003 by Taylor & Francis Group, LLC

SCFA theory is well suited. At the concentrations close to the CMC the adsorption increases again due to lateral hydrophobic attraction. This time the increase in adsorption might be due to the formation of a ﬂat bilayer or local aggregates in the form of large, ﬂat admicelles. The 1D SCFA model is probably not very incorrect, and valuable information can still be obtained from the calculations. At high salt concentrations the adsorption increases steeply due to the relatively large hydrophobic attractions. The 1D SCFA theory has no diﬃculty in predicting this behavior, but most likely large, ﬂat local aggregates are formed. Nevertheless, the molecular orientation in these aggregates is probably similar to the orientation in the bilayer predicted by the 1D SCFA model.

IX. FUTURE In general, the combination of experimental results on surfactant adsorption at speciﬁed conditions—such as constant-equilibrium pH and salt concentration—with calculations based on the SCFA theory has oﬀered good possibilities to investigate surfactant adsorption in detail. Most calculations have been based on the 1D SCFA theory; although this theory does not allow conclusions on local aggregate formation, it has still been rather valuable. For nonionic surfactants some calculations have been made using the 2D SCFA model, and the results are very promising. The continuous increase of computational possibilities allows at present 2D SCFA calculations for larger systems, and this opportunity should be exploited in the future to investigate self assembly of nonionic surfactants at surfaces in more detail. For the ionic surfactants the problem of the modeling of the long-range coulomb interactions near local aggregates has to be tackled and solved. This may still take some time; both the fundamental problems (the image charge of an aggregate of unspeciﬁed form in the solid phase) and the practical problems (can the system be made large enough to handle the long-range coulomb forces?) have to be solved. Yet, it seems that the possibilities for further development of the 2D SCFA theory are, at the moment, at least as promising as, for instance, the possibilities of Monte Carlo simulations for charged aggregates on charged surfaces.

Acknowledgment The cooperation with Marcel Bo¨hmer, Ellen Lee, Tanya Goloub, and, last but not least, Frans Leermakers has not only been very valuable, but was also a great pleasure to me. Copyright © 2003 by Taylor & Francis Group, LLC

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3 Adsorption of Vesicle-Forming Surfactants at the Air–Water Interface MAKOTO ARATONO MASUMI VILLENEUVE NORIHIRO IKEDA

I.

Kyushu University, Fukuoka, Japan Saitama University, Saitama, Japan

Fukuoka Women’s University, Fukuoka, Japan

INTRODUCTION

The performance of surfactant molecules at the interfaces depends strongly not only on the chemical structure of them and the nature of the interfaces but also on the environmental conditions such as temperature, pressure, pH, the added materials, and so on. In the previous version of this series [1], the structure performance of adsorption properties has been summarized on the emphasis of the experimental results of the surface and interfacial tensions and their analysis according to the fundamental thermodynamic equations, eﬀects of chemical structures of the hydrophobic and hydrophilic groups, eﬀects of circumstances, and the structure of adsorbed ﬁlms from the scattering techniques. Basically the review itself is still quite useful to understand various interfacial and colloid chemistries. Surfactant molecules form a variety of aggregates with diﬀerent geometries in their aqueous solutions [2–4]. Micelles are most typical in rather dilute solutions and have been investigated with various experimental and theoretical tools. The surface tension measurement is one of the convenient and beneﬁcial experiments not only to determine the critical micelle concentrations but also to examine the state of adsorbed ﬁlms of micelle-forming surfactants. Because the adsorbed ﬁlms at interfaces are usually in equilibrium with aggregates in the aqueous solutions above the critical aggregate concentrations, the change of surface tension with various variables such as chemical structure of surfactants, the concentration, temperature, pressure, pH, additives, and so on, are inﬂuenced to a greater or lesser extent by the states of not only surface but also Copyright © 2003 by Taylor & Francis Group, LLC

aggregation behavior. Hoﬀmann has reported the correlation between the surface and interfacial tensions and the type of micelles that are formed in the surfactant solutions [5]. Lately, the adsorption behaviors of new chemical compounds, e.g., ﬂuorocarbon [6], sugar-based [7], protein-based [8], and novel surfactants [9], and that correlated to complex aggregation processes in solution, e.g., microemulsion [10] and vesicle formation [11], have attracted considerable attention. Here we are focused on the surface tension and adsorption behavior of spontaneously vesicle-forming surfactants.

II. ADSORPTION OF VESICLE-FORMING SINGLE-SURFACTANT SYSTEMS The vesicle is one of the typical types of aggregates formed in aqueous surfactant solutions. Because unilamellar or multilamellar surfactant ﬁlms have to be closed to form vesicles and then the inner and outer ﬁlms have a diﬀerent curvature from each other, it has been believed that an external energy like sonication or solvent extraction is required to prepare vesicles, and therefore vesicles are peculiar metastable state of matters. Nevertheless, the direct evidence of the spontaneous vesicle formation of didodecyldimethylammonium hydroxide at a rather high pH condition, ranging from 11 to 13, was revealed by cold-stage electron microscopy by Talmon et al. [12]. Since then, the spontaneous vesicle formation has been extensively investigated mainly from the viewpoints of the phase behavior and phase structures of the aqueous mixtures of such vesicle-forming surfactants. Also several reports are focused on the adsorption behavior of spontaneously vesicle-forming substances because the adsorbed ﬁlms and vesicular solutions are in a true equilibrium in these cases and thus the usual statistical mechanics and thermodynamics of adsorption and interfaces are applicable to them. The systems of spontaneous vesicle formation may be classiﬁed into four groups: (1) a single ionic surfactant like ðR1 R2 Þþ X , called a double-tailed surfactant, where ðR1 R2 Þþ is surface-active; (2) a single ionic surfactant like þ Rþ 1 R2 , called an ion-pair surfactant, where both R1 and R2 are long-chain surface-active ions; (3) a cationic and anionic surfactant mixture like þ Rþ 1 X þ M R2 , called a catanionic surfactant, where both surfactants are micelle-forming ones; and (4) a cationic and cationic-surfactant mixture like Rþ X þ ðR1 R2 Þþ X , called a bicationic surfactant, where the former is micelle-forming and the latter vesicle-forming surfactants, respectively. Here the recent reports on the adsorption behavior of these systems will be introduced one by one. Copyright © 2003 by Taylor & Francis Group, LLC

A. Double-Tailed Surfactants ðR1 R2 Þþ X It is known that some synthetic double-tailed surfactants spontaneously form vesicles without introducing an external agitation such as the usual sonication or solvent extraction. However, there are both negative and positive theoretical views for the spontaneous vesicle formation from a pure single surfactant. The negative is that the stability consideration from the free energy may exclude the formation of vesicles from a pure single surfactant because opposite nonzero curvatures cannot be reached spontaneously in such a case [13,14]. On the other hand, the positive is that under certain conditions the formation of a closed spherical bilayer becomes more favorable both energetically and entropically than that of inﬁnite planer bilayers, i.e., in a closed bilayer the energetically unfavorable edges are eliminated at a ﬁnite, rather than inﬁnite, aggregation number [15]. Talmon et al. have reported that dialkyldimethylammonium hydroxide surfactants are highly soluble in water and form spontaneous stable vesicles at a higher pH and that spontaneous vesicle formation was a consequence of strong hydration forces that are not necessarily limited to the hydroxide ions [12]. The spontaneous vesicle formations have been also reported with respect to didodecyldimethylammonium bromide (DDAB) [16–18], dialkyldimethylammonium bromides having alkyl chain lengths of 8, 10, 12, and 16 [19], a double-tailed biological amphiphile with a saccharidic headgroup ganglioside GM 3 [20]. Among them, Svitova et al. have studied the selfassembly in dialkyldimethylammonium bromides having alkyl chain lengths of 8, 10, 12, and 16 especially in their dilute aqueous solutions by using the surface and interfacial tension measurements as well as the static light scattering, densitometry, and freeze-fracture electron microscopy [19]. Here we introduce a part of their studies. Figure 1 shows the phase diagram of the DDAB–water system determined by visual observation with the crossed polarizers and freeze-fracture electron microscopy. Four regions on the phase diagram are identiﬁed: (1) molecular solution; (2) vesicular solution with small unilamellar vesicles having the mean diameter of 33 nm (L1 phase); (3) two-phase region where small vesicles and large multiplayer aggregates (L3 phase) coexist; and (4) a random lamellar phase (L3). To know the correlation between the solution structure and the surface adsorbed ﬁlms, the surface tension of the aqueous solutions of dialkyldimethylammonium bromide (diCnBr, n ¼ 8, 10, 12) was measured. The results are shown in Fig. 2. The critical vesicle concentration (CVC) determined from the breakpoints were C ¼ 1: 57 102 (log C ¼ 1:80Þ, 7:4 104 (log C ¼ 3:13Þ, 3:5 105 (log C ¼ 4:45Þ mol l1 for n ¼ 8, 10, 12, respectively.

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FIG. 1 Phase diagram of the DDAB–water system. L3 indicates a random lamellar phase. (From Ref. 19.)

The adsorption amounts and headgroup areas (average area per double long chain) A were estimated from the linear parts of the isotherms by applying the Gibbs equation for 1:1 electrolytes: ¼ 7:1 mmol m2 and A ¼ 0:235 nm2 for n ¼ 12, while ¼ 2:1 mmol m2 and A ¼ 0:78 nm2 for n ¼ 8 and 10, respectively. Taking into account that the cross-sectional area of one hydrocarbon chain is about 0:160:18 nm2 and then even the closest packing yields about 0:320:36 nm2 , A ¼ 0:235 nm2 for DDAB is too small for the adsorbed ﬁlm to be a monolayer and thus has no physical reality. Then the multilayer adsorption at the air–water interface was suggested for DDAB. The surface tension isotherm in the presence of KBr (molar ratio of KBr to DDAB was about 10) was found to be shifted to the lower concentration region and have a steeper slope compared to the isotherm in the absence of KBr. The headgroup area was further reduced to even 0.1 nm2, and thus the more multilayered ﬁlm is expected. The Langmuir balance studies of the spread monolayer of DDAB yielded the minimum area of about 0.68 nm2, which is a reasonable value for the monolayer. Thus these ﬁndings suggest that the multilayer formation happens only when DDAB molecules are adsorbed from the bulk solution. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 2 Surface tension versus concentration curves at 228C: (a) DDAB; (b) didecyldimethylammoium bromide; (c) dioctyldimethylammonium bromide. (From Ref. 19.)

The interfacial tension of the aqueous DDAB solution–octane system was also measured and is given in Fig. 3. The shape of the isotherm is essentially similar to each other: taking account of the phase diagram shown in Fig. 1, the breakpoints at log C ¼ 4:5 and 3.1 correspond to the transition from the monomer to the unilamellar vesicular solution and that from the vesicular solution to the vesicle + lamellar two-phase region, respectively. It should be noted that the interfacial tension is the ultralow value of 0.015 mN m1 at the higher concentrations (log C ¼ 3.1 – 2). The authors suggest that such a low interfacial tension was connected with the so-called surfactant or third-phase formation at the DDAB L3-phase– octane interface. This was conﬁrmed by the temperature dependence of the interfacial tension at the given DDAB concentration of log C ¼ 2:1: the ultralow value of the L3 phase at lower temperatures, where the third phase is formed at the surface, was abruptly increased at about 358C to about 1 mNm1 of the two-phase region at higher temperatures, where no third phase formation was not observed. Thus it was insisted that the structure Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 3 Interfacial tension versus concentration curve of the aqueous solution of DDAB–octane system. (From Ref. 19.)

changes in the bulk solution accompany the change of the interfacial tensions at the aqueous solution–air or –oil systems. Hoﬀmann has demonstrated from the simple calculation that the interfacial tension is a good measure for the curvature of an interface and the very low value of 102 –103 mN m1 corresponds to a structure formation of a planar interface like in a lamellar phase [5]. However, it should be mentioned that there are still controversial reports on the solution states, phase diagram, and the CVC values of the aqueous DDAB mixture [18,21–25]. B. Ion-Pair Surfactants Rþ 1 R2

þ Cationic and anionic surfactant mixtures like Rþ 1 X þ M R2 , called catanionic surfactants, form vesicles spontaneously and have been investigated most extensively mainly from the viewpoint of their structures in their aqueous solutions, although there is a view that such vesicles are not equilibrium ones from the thermodynamic points of view [26]. The driving force for this vesicle formation is an electrostatic one and the resulting ion pair having a double long chain has a suitable critical packing parameter for the vesicle formation. Very recently, the surfactant mixtures forming the mixed cationic/anionic vesicles have been collected thoroughly and classiﬁed into two categories by Tondre and Caillet [27]. One is a simple mixture of a cationic and an anionic þ surfactant like Rþ 1 X þ M R2 , and the other is an ion-pair amphiphile þ like R1 R2 , in which the counterions X and Mþ are removed from þ Rþ 1 X þ M R2 , respectively. Removing the counterions is accompanied

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by an increase of the Debye screening length, and thus the attractive electrostatic interaction between two surfactant ions should be stronger. This gives rise to a change of the total area occupied by the ion-pair heads and, as a result, to that of the tendency toward forming vesicles. Furthermore, vesicles are usually obtained in the presence of an excess of Rþ X or þ Mþ R in the mixture Rþ 1 X þ M R2 , whereas at equimolar condition in þ the R1 R2 system. Therefore, they emphasize that the comparison of mixed surfactant system and ion pair is not always straightforward. As will be described minutely in Section III.A, the adsorption behavior of þ the Rþ 1 X þ M R2 -type mixture of sodium decyl sulfate (SDeS) and decyltrimethylammonium bromide (DeTAB) was investigated by surface tension measurement [28]: it was shown thermodynamically that vesicles are formed spontaneously and coexist with micelles within a limited total concentration range and mixing ratio of the surfactants. Furthermore, no precipitates but vesicles were formed even in the equimolar mixture in the dilute region. These ﬁndings motivated us to investigate the vesicle formation of the Rþ 1 R2 -type surfactant, decyltrimethylammonium decyl sulfate (DeTADeS) [29]: the surface tension was measured as a function of temperature and the concentration to obtain the thermodynamic information on the vesicle formation from the viewpoints of the equilibrium in the monomer-vesicle, vesicle-adsorbed ﬁlm, and adsorbed ﬁlm-monomer. The information on the ﬂat adsorbed ﬁlm may provide interesting information on the curved bilayer ﬁlms of vesicle particles. Furthermore, the eﬀect of equimolar salt to DeTADeS on the vesicle formation and surface adsorption was investigated [30]. First the vesicle formation of the DeTADeS system is shown here and that of the decryltrimethylammonium bromide (DeTAB) + sodium decyl sulfate (SDeS) mixture in Section III.A. In Figure 4, the surface tension is demonstrated as a function of the molality of surfactant m^ at constant temperature. Here m^ is the total concentration of the surfactant ions deﬁned by m^ ¼ m1þ þ m1 ¼ 2m1

ð1Þ

where m1þ , m1 , and m1 are the molalities of the cationic decyltrimethylammonium ion DeTA+, the anionic decyl sulfate ion DeS , and the molality of the salt DeTADeS, respectively. The -value decreases very steeply with increasing m^ and becomes absolutely constant after the breakpoints. The shape of the curves is not diﬀerent from that of normal micelle-forming surfactants. However, spherulites with characteristic Maltese crosses were observed in the solutions by the optical microscope with crossed polarizer. Therefore, it was concluded that the aggregates were not micelles, but multilamellar vesicles (MLV) and then the breakpoints were the critical vesicle concentration, CVC. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Surface tension versus molality curves of the decyltrimethylammonium decyl sulfate (DeTADeS) system at constant temperature: (1) T ¼ 290.65 K; (2) 293.15; (3) 295.65; (4) 298.15; (5) 300.65; (6) 303.15; (7) 305.65; (8) 308.15; (9) 310.65. (From Ref. 29.)

Because both surfactant ions are surface-active and thus the adsorption of surfactant ^ is deﬁned appropriately by ^ ¼ 1þ þ 1 ¼ 21

ð2Þ

where 1þ , 1 , and 1 are the surface excess number of moles of DeTA+, DeS , and DeTADeS, respectively, and the electroneutrality condition requires 1þ ¼ 1 ¼ 1 ^ was evaluated by applying the equation Copyright © 2003 by Taylor & Francis Group, LLC

ð3Þ

FIG. 5 Surface density versus molality curves of the DeTADeS system at constant temperature: (1) T ¼ 290.65 K; (2) 293.15; (3) 295.65; (4) 298.15; (5) 300.65; (6) 303.15; (7) 305.65; (8) 308.15; (9) 310.65; (10) the curve of the DeTAB + SDeS equimolar mixture at 298.15 K. (From Ref. 29.)

^ ¼ ðm^ =RTÞð@=@m^ ÞT;p

ð4Þ

to the curves shown in Fig. 4 at concentrations below the CVC. The results are plotted against m^ at constant temperatures in Fig. 5. It should be noted from the ^ -values that the average molecular area per surfactant ion of DeTADeS is about half the usual single-chain micelle-forming surfactants. This undoubtedly comes from the almost neutral ion-pair formation due to the strong electrostatic attractive interaction between DeTA+ and DeS ions. Usually the ^ -value is diminished due to increasing thermal motion Copyright © 2003 by Taylor & Francis Group, LLC

of adsorbed species with increasing temperature at a given bulk concentration. For example, ^ of the dodecyltrimethylammonium chloride decreases from about 6 mmol m2 at 288.15 K to 4.4 mmol m2 at 308.15 K [31,32], and thus the decrement is about 0.08 mmol m2 K1 . However the much smaller decrement of 0.02 mmol m2 K1 was estimated for the DeTADeS system. This also substantiates the very strong electrostatic attraction in the ion-pair surfactant. It is expected that the electrostatic interaction is diminished by an addition of inorganic small ions. Curve 10 in Fig. 5 is the adsorption isotherm of the equimolar mixture of SDeS and DeTAB at 298.15 K. It evidently sits very low in the ^ region compared to curve 4 at the same temperature. This clearly shows that the inorganic ions shields the respective opposite charges and then reduces the electrostatic interaction between cationic and anionic surfactant ions. As mentioned above, the maximum adsorption of the DDAB system was about 7.1 mmol of double long chain, i.e., 14.2 mmol of single long chain, per square meter and thus the multilayer formation was suggested. However, the maximum adsorption of the DeTADeS system is about 6 mmol of single long chain per square meter and then the adsorbed ﬁlm is a normal monolayer. The adsorption behavior of ion-pair surfactants has been investigated by several workers, but independently of vesicle or aggregate formation in the aqueous solutions. The pioneering work may be the one about the DeTADeS solution by Corkill et al. that shows that the solution interface had an equimolar composition with respect to the two surface-active ions, and the limiting area per alkyl chain was 0.3 nm2 [33]. Furthermore, the radiotracer technique showed that when the long-chain cation and anion have the same chain length, an equimolar surface composition was obtained, whereas if the ions have diﬀerent chain lengths, the longer chain ion is preferentially adsorbed to give an asymmetric surface layer [34]. Recently the adsorption behavior of n-hexylammonium n-dodecylsulfate was studied by neutron reﬂection measurements as well as by the surface tension [35]. The average area per long-chain was about 0.22 nm2. This is close to the cross-sectional area of the hydrocarbon chain as mentioned above and suggests that the monolayer is rather closely packed. This estimation from the surface tension measurement was further conﬁrmed by the neutron scattering study, which also showed that the composition of the monolayer was 1:1. The adsorption behavior was further examined from the viewpoints of the entropy and energy of adsorption. The derivative of with respect to temperature at concentrations below the CVC gives the entropy change associated with the adsorption of the surfactant from the monomer states s ð1Þ: Copyright © 2003 by Taylor & Francis Group, LLC

sð1Þ ¼ ð@=@TÞp;m^ ;

m^ < CVC

ð5Þ

On the other hand, the derivative at concentrations above the CVC provides the entropy change associated with the adsorption from MLV to the surface sðVÞ: sðVÞ ¼ ð@=@TÞp;m^ ;

m^ CVC

ð6Þ

It was found that sð1Þ was negative and therefore concluded that the entropy of the monomer surfactant in the aqueous solution is larger than that of the surfactant in the adsorbed ﬁlm on the basis of the detailed analysis in terms of the partial molar entropies. On the other hand, it was found that sðVÞ was deﬁnitely positive and that the mean molar entropy of DeTADeS in the adsorbed ﬁlm is larger than the corresponding one in the MLV. Furthermore, the energy change per mole of surfactant associated with adsorption from MLV was found to be positive. Then it is said that the geometry of the ion pair of DeTA+ and DeS energetically favors the curved MLV more than the planar adsorbed ﬁlm. The diﬀerence in the hydration of the polar headgroups of surfactant ions between the monolayer of the adsorbed ﬁlms and the stacked multiple bilayer of the vesicles is also one of the inﬂuential factors. Here it is beneﬁcial to understand the diﬀerence between the micelle and vesicle formation from the thermodynamic point of view to compare the thermodynamic quantities associated with the aggregate formation. For example, the entropy of aggregate formation per mole of surfactants is illustrated for three normal micelle-forming ionic surfactants as well as the vesicle-forming surfactants in Fig. 6. The entropies of micelle formation M W s of decyltrimethylammonium bromide and sodium decyl sulfate, which are mother surfactants of decyltrimethylammonium decyl sulfate, decrease from a positive to a negative value. It should be noted that they are much larger than the entropy change associated with vesicle formation V W s of the DeTADeS system. Taking notice of the corresponding enthalpies is respectively given by M M W h ¼ TW s;

V V W h ¼ TW s

ð7Þ

It is said that micelle formation is driven mostly by entropy, whereas MLV formation of the DeTADeS system is driven by enthalpy.

III. ADSORPTION OF VESICLE-FORMING BINARY SURFACTANT MIXTURES Since the pioneering work of Kaler et al. on the cetyltrimethylammonium tosylate + sodium dodecylbenzene sulfonate system [36], the spontaneous Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 6 Entropy of micelle formation and that of vesicle formation versus molality M curves: (1) M W s of decyltrimethylammonium chloride; (2) W s of sodium decyl M V sulfate; (3) W s of sodium dodecyl sulfate; (4) W s of DeTADeS. (From Ref. 29.)

þ vesicle formation of catanionic surfactants Rþ 1 X þ M R2 has been studied extensively and mainly by examining the phase behavior and then constructing the phase diagrams by means of optical and electron microscopies, light and neutron scatterings, NMR, and so on. The inventories of vesicular systems of catanionic surfactants as well as that of ion-pair surfactants were gathered quite thoroughly together with the investigated properties [27]. Despite the fact that many papers have been published on the spontaneous vesicle formation of catanionic surfactants, there are only several reports from the standpoints of the surface tension’s and the solution surface’s being equilibrium with the vesicle particles [28,37–40]. Here we review

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ﬁrst our recent work on a simple model of the molality versus mole fraction diagram of aggregate formation and the spontaneous vesicle formation of the decyltrimethylammonium bromide (DeTAB) + sodium decyl sulfate (SDeS) mixture [28] and then the work on the dodecylammonium chloride (DDACl) + sodium dodecyl sulfate (SDS) mixture of Filipoviæ-Vincekoviæ et al. [38]. Furthermore, as described above in detail, double long-chain cationic surfactants, e.g., didodecyldimethylammonium bromide (DDAB), are known to spontaneously form vesicles by themselves. Therefore, it is expected that the mixture of a usual micelle-forming surfactant with ðR1 R2 Þþ X may also spontaneously form vesicles within a certain mixing ratio. There are several papers from this point of view [22,24,25,41]. Next the surface tension study of Viseu et al. [25] will be introduced. A strong synergistic action of catanionic surfactants has been studied also independently of vesicle formation. Figure 7 demonstrates the surface tension versus the total concentration curves of the SDS + DTAB mixtures obtained by Lucassen-Reynders et al. [42]. They point out the two main

FIG. 7 Surface tension versus concentration curves of the sodium dodecyl sulfate (SDS) + dodecyltrimethylammonium bromide (DTAB) mixture at constant surfactant mole fraction. Mixing ratio SDS/DTAB is shown nearby the corresponding curves. (From Ref. 42.) Copyright © 2003 by Taylor & Francis Group, LLC

features: ﬁrst, the large and almost parallel shift of the isotherms of the mixtures with respect to the individual surfactants over several decades in the surfactant concentration; and second, the equality of the adsorption of both cationic and anionic surfactant ions over the entire range of the mixing ratios. The ﬁrst observation shows the strong synergism and the constant total adsorption of surfactant ions, which is derived by applying Eq. (17) (see below). The second was veriﬁed because the slope of the log CNa R versus log CRþ Br plot at constant surface tension was 1. They refer to the formation of precipitate and its relation to the micelle formation, but do not notice the spontaneous vesicle formation.

A. Simple Model of the Molality Versus Mole Fraction Diagram of Aggregate Formation Aggregates such as micelles and vesicles are not macroscopic phases in the thermodynamic sense, because they never exist separately from the aqueous solution of surfactants. However, when their thermodynamic quantities are deﬁned properly in terms of the excess ones, the thermodynamic theory of micelle formation, in which micelle particles are treated as if they are macroscopic ones, has been successful in understanding the micelle formation [43,44]. Developing this idea further into vesicular systems and using the mass balance equation, we can construct a diagram of the total molality versus mole fraction of surfactant from which the micellar, vesicular, and their coexisting regions can be identiﬁed. In an anionic–cationic surfactant system such as SDeS + DeTAB, each pure surfactant does not form vesicles, but the mixture does in a rather wide range of the mole fraction, because the strong and attractive electrostatic molecular interaction between the two surfactant ions synergistically produces ion pairs having a double long chain and an advantageous critical packing parameter for vesicles. Thus the concentration of aggregate formation C (CMC or CVC) is decreased steeply from their respective pure CMC values, C10 and C20 , by adding the other component. Figure 8 illustrates an example of such C versus X2 behavior: the three curves are connected at two breakpoints at C t s and X2t s at which the vesicle–micelle transition is assumed to take place. On the other hand, the compositions of surfactant in micelles and vesicles can be estimated from the C versus X2 curves by using the thermodynamic equations previously developed [44]. The mole fraction of the second component in the micelle X2M is evaluated by applying X2M ¼ X2 ðX1 X2 =C M Þð@C M =@X2 ÞT;p

Copyright © 2003 by Taylor & Francis Group, LLC

ð8Þ

FIG. 8 Total molality versus mole fraction diagram predicted: (—— ) CM versus X20 at 0 X2 X2t and X2t X2 1, CV versus X2 at X2t X2 X2m and X2m X2 X2t ; (.......) C M versus X2M at 0 X2M X2Mt and X2Mt X2M 1; (- - - -) CV versus X2V at X2Vt X2V X2m and X2m X2V X2Vt ; (– –) mI versus X2 , (– – ) mII versus X20 .

to the critical micelle concentration C M versus X2 curves, and similarly the mole fraction of the second component in the vesicle X2V is evaluated by applying X2V ¼ X2 ðX1 X2 =C V Þð@CV =@X2 ÞT;p

ð9Þ

to the critical vesicle concentration C V versus X2 curves. The C M versus X2M and C V versus X2V are schematically shown also in Fig. 8, where X2Mt and X2Vt are the mole fractions in the micelle and vesicle, respectively, at the vesicle–micelle transition point. In the coexistence region of vesicles and micelles in the solution, the mass balance relations for the total surfactants and surfactant 2 are respectively given by m ¼ C t þ mM þ mV Copyright © 2003 by Taylor & Francis Group, LLC

ð10Þ

and mX2 ¼ C t X2t þ mM X2Mt þ mV X2Vt

ð11Þ

Here we assume that the monomer concentration is equal to C t and the mole fractions in vesicle and micelle are equal to X2Vt and X2Mt , respectively, and that they do not change as the total concentration is further increased because vesicle and micelle are assumed to be a kind of macroscopic phase. By way of example, let us examine the right-hand part of the diagram of Fig. 8. At the composition region X2Vt < X2 < X2Mt < X2t , the total molality mI at which micelle formation starts in the vesicle solution is obtained by putting mM ¼ 0, as mI ¼ Ct ðX2t X2Vt Þ=ðX2 X2Vt Þ

ð12Þ

At the composition region X2Vt < X2Mt < X2 < X2t , on the other hand, the total molality mII at which the vesicle disappears is obtained by putting mV ¼ 0, as mII ¼ C t ðX2t X2Mt Þ=ðX2 X2Mt Þ I

ð13Þ II

Therefore, the m versus X2 and m versus X2 curves are predictable once the values of X2t , X2Mt , and X2Vt are experimentally obtained. Taking account of the relation mI CV ¼ C t ðX2t X2Vt Þ=ðX2 X2Vt Þ C V > C V ðX2t X2 Þ=ðX2 X2Vt Þ > 0

ð14Þ

we note that vesicle formation takes place in preference to micelle formation in the vesicle–micelle coexistence regions within the present simple model. The change of with m at a given X2 can be predicted qualitatively by using the diagram given in Fig. 8. Figure 9 schematically illustrates the prediction with the respect to the right side of Fig. 8 (X2m < X2 ), where X2m is the mole fraction at the minimum of the C versus X2 curve. Curve 1 (pure second surfactant X2 ¼ 1) has one breakpoint—at the CMC—and the surface tension is practically constant above the CMC. Curve 2 (X t2 < X2 < 1) has one break, at the CMC, and the surface tension increases with the molality due to the change of the micelle and monomer compositions. Curve 3 (X2Mt < X2 < X t2 ) has three breakpoints, at C V , mI , and mII . It is expected that the surface tension at the concentrations between mI and mII is constant due to the vesicle–micelle coexistence. The changes of the surface tension before and after the constant-surface tension show the changes of vesicle and micelle compositions with m. On curve 4 (X2Vt < X2 < X2Mt ), vesicles and micelles start to coexist at mI and vesicles never vanish even at high m; therefore, the surface tension is constant at concentrations above Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Surface tension versus total molality curves predicted: (1) X2 =1, (2) X2t < X2 < 1, (3) X2Mt < X2 < X2t , (4) X2Vt < X2 < X2Mt , (5) X2m < X2 < X2Vt . (From Ref. 28.)

mI . Finally, curve 5 (X2m < X2 < X2Vt ) has only one break, corresponding to the CVC. The shape of the curves at X2m < X2 is qualitatively similar to that at X2 < X2m . The qualitative behavior predicted by this simple model will be compared to the one obtained from the thermodynamic analysis of the experimental results. Let us apply this simple model to the SDeS + DeTAB system and examine the spontaneous vesicle formation of the system. þ 1. Catanionic Surfactant Rþ 1 X þ M R2

The sodium decyl sulfate (SDeS) + decyltrimethylammonium bromide (DeTAB) system is one of the typical vesicle-forming catanionic surfactants, where the respective pure surfactants do not form vesicles but micelles. The surface tension of the mixture was carefully measured as a function of the total molality m at the ﬁxed mole fraction of DeTAB X2 deﬁned by m ¼ m1 þ m1þ þ m2þ þ m2 ¼ 2m1 þ 2m2

ð15Þ

and X2 ¼ ðm2þ þ m2 Þ=m ¼ m2 =ðm1 þ m2 Þ Copyright © 2003 by Taylor & Francis Group, LLC

ð16Þ

respectively [28]. Here m1 , m1þ , m2þ , m2 , m1 , and m2 are the molalities of DeS , Na+, DeTA+, Br , SDeS, and DeTAB, respectively. The molality at the critical micelle concentration (CMC) C M and that at the critical vesicle concentration (CVC) C V were determined from the versus m curves. Figure 10 shows the surface tension versus total molality curves at the mole fractions of the DeTAB-rich region [28]. It is seen that the variation of with m at low molalities and at X2 below 0.98 looks like that of a usual micelle-forming surfactant mixture: the surface tension decreases very rapidly with increasing m and is almost constant above a breakpoint. As mentioned above with respect to Fig. 8, we cannot determine whether the breakpoint corresponds to the CVC or CMC without other information. In the present case, the dynamic light scattering measurement suggested the existence of much larger aggregates than micelle particles with the average radius of approximately 500 nm. Furthermore, the vesicle particles were observed by using the optical microscope at some X2 and also in the TEM image of freeze-fracture replicas. Thus it was concluded the ﬁrst breakpoints on these versus m curves are referred to as the critical vesicle concentration C V .

FIG. 10 Surface tension versus total molality curves of the SDeS + DeTAB system at constant mole fraction: (1) X2 ¼ 0.7012, (2) 0.8004, (3) 0.9000, (4) 0.9700, (5) 0.9800, (6) 0.9990, (7) 0.9996, (8) 0.9997, (9) 0.9999, (10) 1. (From Ref. 28.) Copyright © 2003 by Taylor & Francis Group, LLC

By examining the curves more closely and taking account of the results of the visual and optical observations, we have concluded that four regions exist on each curve: the example at X2 ¼ 0:9700 is illustrated in Fig. 11. Region 1 corresponds to the monomer solution and the surface tension decreases steeply within a very narrow concentration range. In region 2, the surface tension increases slightly but deﬁnitely with m. The solutions were turbid and slightly bluish, although the bluish color disappeared completely by freezing them, followed by thawing and birefringent at some total molalities. It was expected from the turbidity that the aggregates have a size of micrometer order and, in fact, a doughnutlike shape with a size of a few micrometers was observed by diﬀerential interference microscope. Furthermore, the aggregates formed in the birefringent solution may have lamellar structures because a sheetlike structure was vaguely observed with the diﬀerential interference microscope. It should be noted that the surface tension falls on the same curve despite the changes in the structures. In region 3, the surface tension is constant and solution is observed to be bluish and transparent. It should be pointed out that the appearance of the solution and the -values were not changed by freezing the solution followed by

FIG. 11 Surface tension versus total molality curves of the SDeS + DeTAB system at X2 ¼ 0.9700: (1) monomer, (2) monomer + vesicle, (3) monomer + vesicle + micelle, (4) monomer + micelle. (From Ref. 28.) Copyright © 2003 by Taylor & Francis Group, LLC

thawing it, and the solution appeared to be bluish and transparent even at the highest total molality of this region. Judging from the appearance of the solution and the fact that vesicles were barely observed by optical microscopy, the size of vesicles in this region is probably around 100 nm or less. In region 4, it is important to note a new observation, which is not found in the ordinary mixed micelle systems—that the -value starts to increase again with m. The solutions become completely clear and colorless. This suggests the absence of vesicle particles. Curves 1 to 5 in Fig. 10 are similar in their shapes. Comparing the versus m curves obtained from the experiments to that from the simple theory given in Fig. 9, we note the fairly good correspondence between them. Thus in region 1, the surfactant monomers are dispersed in the solution, and vesicles of the surfactant mixture are formed spontaneously at CV . In region 2, the vesicles and monomers are dispersed in the solution. The composition of the vesicle is diﬀerent from that in monomer states. In region 3, micelles of the surfactant mixture appear at mI and then the vesicles, micelles, and monomers are dispersed in the solution. Judging from the experimental ﬁnding that the surface tension is constant in this region, it is probable that the aqueous solution system behaves as if it has three kinds of macroscopic phases, that is, monomer solution, micelles, and vesicles. The molality is further increased up to mII , vesicle particles disappear, and then micelle particles and monomer are dispersed in the solution in region 4. Now, let us evaluate the mole fraction of DeTAB in vesicles X2V by applying Eq. (9) to the CV versus X2 curve given by the open circles on the solid line. The results are drawn by the chained line in Fig. 12. The C V versus X2 and the C V versus X2V diagram is called the phase diagram of vesicle formation. It is very important to note that the X2V -values are close to 0.5 at most of bulk compositions: a vesicle particle contains almost equal numbers of surfactant cations and anions irrespective of the bulk compositions even when the monomer solution is in equilibrium with the vesicle particles and are only 0.01 mol% surfactant anions. mI - and mII -values from the experiments are plotted against X2 . Here the expected C M versus X2M curve is also shown, which was not obtained because of its experimental diﬃculty but is anticipated from the present results. The broken lines are the asymptotes of the mI and mII versus X2 curves suggested by the simple theory mentioned above. We note the good correspondence of the experimental results given in Fig. 12 to the prediction from the simple theory illustrated in Fig. 8. Thus the spontaneous vesicle formation and vesicle–micelle transition are well described by our thermodynamic method developed for mixed micelle formation: the concentration versus composition diagram can predict the critical vesicle and micelle concentrations, the concentration region of the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 12 Total molality versus mole fraction diagram of the SDeS + DeTAB system: (1) asymptote of the mI versus X2 curve; (2) asymptote of the mII versus X2 curve. (From Ref. 28.)

vesicle–micelle coexistence. Furthermore, the changes of surface tension with total molality as well as with the composition X2 can be predicted by using the concentration versus composition diagram. Here let us introduce the work on the dodecylammonium chloride (DDACl) + sodium dodecyl sulfate (SDS) mixture of FilipoviæVincekoviæ et al. They have studied the precipitate formation of the alkylammonium chloride + sodium alkyl sulfate systems with the chain length Copyright © 2003 by Taylor & Francis Group, LLC

from 10 to 14 by measuring the surface tension, surface potential, and conductivity [38,45,46]. The surface tension and the corresponding surface potential curves are illustrated with respect to the sodium dodecyl sulfate (SDS) and dodecylammnonium chloride (DDACl) mixtures in Fig. 13. The strong synergism was clearly observed, and the breakpoint between the steeply descending and fairly constant branch of the surface tension curve for the mixture corresponds to the precipitation of the ion-pair surfactant, dodecylammonium dodecyl sulfate. The data analysis according to the regular solution theory [47] showed the equimolar mixed monolayer formation with very low activity coeﬃcients of about 0.004 and with a high negative interaction parameter of about 22.1 in the monolayer. The similar syner-

FIG. 13 (a) Surface tension and (b) surface potential versus concentration curves of the sodium dodecyl sulfate (SDS) + dodecylammonium chloride (DDACl) system: (*) DDACl; (~) SDS; (&) equimolar mixture. (From Ref. 38.) Copyright © 2003 by Taylor & Francis Group, LLC

gism was also observed for the hexadecyltrimethylammonium bromide + sodium dodecyl sulfate mixtures [39]. The notable ﬁnding in the surface potential curve is that the potential of the adsorbed ﬁlm of the equimolar mixture has even higher positive values than that of the pure DDACl, despite that one may expect the behavior of a nonionic surfactant for a 1:1 adsorbed ﬁlm. This experimental ﬁnding indicates that the negative groups are embedded in the bulk solution and thus they do not dominate the surface potential; on the average, DDA+ ions are closer to the surface than DS ions due to a strong tendency of the negative sulfate group to orient itself deeper into water compared to the positive ammonium group due to the diﬀerences in their geometry and size, solubility and/or binding of the counterions in the underlying layer [38].

B. Bicationic Surfactants Rþ X þ ðR1 R2 Þþ X Viseu et al. have studied the spontaneous vesicle formation of the aqueous mixtures of DDAB and normal micelle-forming surfactant dodecyltrimethylammonium chloride (DTAC) by means of the cryogenic transmission electron microscopy (cryo-TEM) and dynamic light scattering (DLS): the bicationic amphiphile mixtures have two striking diﬀerences from catanionic surfactant: (1) that a precipitate is absent even around equimolar surfactant ratios and (2) the asymmetric sequences of phases [25]. However, the cryo-TEM method may accompany an artifact in the process of the thinﬁlm preparation, and also the DLS is not sensitive to the concentration but only to the sizes of aggregates. Thus they were not able to give the exact boundaries between the various phases. Then the conductivity and the equilibrium surface tension measurements were employed to determine the critical concentrations corresponding to the transition between monomer and micelles, and that between micelles and vesicles, together with the static light scattering [25]. The surface tension was measured for the respective pure surfactants and the mixture with DDAB mole fractions of 0.10 and 0.20. The results are drawn in three ways in Fig. 14: versus the total concentration of the mixture C0 in 14a; versus the DDAB concentration [DDAB] in 14b; and versus the DTAC concentration [DTAC] in 14c at the constant mole fraction xDDAB , respectively. The pure DTAC shows the inﬂection due to the CMC at about 22.4 mM and the pure DDAB due to the critical aggregate formation CAC at about 0.18 mM. The authors concluded that the aggregates were probably metastable vesicles, not equilibrium ones, in contrast to the conclusion of Svitova et al. [19]. It is evident from Fig. 14 that the curves of the mixtures have three distinct breakpoints. There are two minimum points at about 30 mN m1 Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 14 (a) Surface tension versus total concentration, (b) surface tension versus DDAB concentration, and (c) surface tension versus DTAC concentration curves of the didodecyldimethylammonium bromide (DDAB) + dodecyltrimethylammonium chloride (DTAC) system: (~) pure DTAC; (&) pure DDAB; (*) xDDAB ¼ 0.1; (~) xDDAB ¼ 0.2. (From Ref. 25.) Copyright © 2003 by Taylor & Francis Group, LLC

and one maximum point at about 50 mN m1 , respectively. The ﬁrst minimum was assigned to the critical vesicle concentration (CVC) as follows. In the versus [DDAB] plots given in Fig. 14b, it is said that the data at concentrations below the ﬁrst breakpoints sit on one curve of the pure DDAB system even at the mole fractions of 0.1 and 0.2, and also the breakpoints of the mixture (0.2–0.3 mM) are close to the CVC of the pure DDAB system (0.18 mM). These ﬁndings suggest that the surface properties of the mixtures below the ﬁrst breakpoint are determined mainly by DDAB molecules and thus the CVC at the ﬁrst break is responsible for the pure DDAB vesicle formation. According to the thermodynamic consideration, we have three equations corresponding to the combinations of the concentrations employed in Figs. 14a–c, respectively: d=RT ¼ ð=C0 ÞdC0 þ ð=xDTAC xDDAB ÞðyDDAB xDDAB ÞdxDDAB ð17Þ ¼ ð=CDDAB ÞdCDDAB ðDTAC =xDTAC xDDAB ÞdxDDAB

ð18Þ

¼ ð=CDTAC ÞdCDTAC þ ðDDAB =xDTAC xDDAB ÞdxDDAB

ð19Þ

Here the surface excess densities (adsorption) are respectively deﬁned by DTAC ¼ DTAþ þ Cl , ¼ DDAþ þ Br þ DDAB ¼ DDAþ þ Br , DTAþ þ Cl , and the mole fraction of DDAB in the adsorbed ﬁlm yDDAB is deﬁned by yDDAB ¼ DDAB =. Then the slope of the respective curves gives the same quantity, that is, the total surface excess of the surfactant mixture , as RT ¼ ð@=@ ln C0 ÞxDDAB ¼ ð@=@ ln CDDAB ÞxDDAB ¼ ð@=@ ln CDTAC ÞxDDAB ð20Þ Therefore, the almost equal slope of the curves of the mixture at concentrations below the CVC except the pure DTAB implies that the total surface excess is not altered very much by adding DTAC molecules into the pure DDAB solution, and then DTAB molecules are not adsorbed at the surface at least above the mole fraction of DDAB of 0.1. This is also in accord with the observation shown in Fig. 14b, i.e., DTAC ¼ ðxDTAC xDDAB =RT Þð@=@xDDAB ÞC0 0

ð21Þ

Despite the fact that the surface tension of the pure DDAB system still decreases with increasing DDAB concentration at concentrations above the CVC, Fig. 14b clearly demonstrates that the surface tension Copyright © 2003 by Taylor & Francis Group, LLC

of the mixture increases greatly from about 30 mN m1 to about 50 mN m1 at concentrations between the CVC and second breakpoint (CMCL). This behavior may be understood as follows. At the concentrations above the CVC of the mixture, the vesicular state mixed with DTAB molecules is energetically more favorable for DDAC molecules compared to the adsorbed ﬁlm. Thus DDAC molecules in the adsorbed ﬁlms are desorbed to spontaneously form the vesicles with DTAC molecules. The presence of the mixed vesicles having smaller size compared to the pure DDAB vesicles were veriﬁed by using of a phase-contrast microscopy. At the concentration above the CMCL, the surface tension again decreases with increasing DDAB and also DTAC concentrations. Judging from the results of the static light scattering measurement that vesicles and micelles coexist in this concentration range, the mixed micelle formation from mixed vesicles probably starts from this CMCL. The authors concluded that this decrease appears to be correlated to the onset of DTAC adsorption at the interface because of the similarity of the slope of this region to that of the pure DTAC in Fig. 14c. However, it should be noted that the slope of the mixture does not give the surface excess concentration directly under the presence of the aggregates such as micelles and vesicles and that, even when it does, the slope does not gives the surface excess of DTAC DTAC but the total surface excess , as Eq. (19) insists it do. The change of the monomer composition due to the transition of the aggregate from the vesicle to the micelles and the resulting change of the composition of adsorbed ﬁlm may be mainly responsible for this surface tension decrease. The third breakpoint, CMCU, was attributed to the end of the mixed micelle formation from vesicles because the solution became transparent and the scattering intensity of the light was almost zero above this breakpoint. The existence of the three breakpoints on the surface tension curves of the DDAB–DTAC mixture is apparently the same for the DeTAB + SDeS system mentioned above, although the shape of the curves is considerably diﬀerent from each other at concentrations above the CVC. This ﬁnding insists that the surface tension measurement is highly sensitive to the structure change happening in the bulk solution. Also the DDAB–dodecyltrimethylammonium bromide (DTAB) mixture was studied by surface tension measurement in detail [48]. Although the only diﬀerence from the DDAB– DTAC system is the counteranion of DTAB, the shape of the surface tension curves was found to be quite diﬀerent from each other even at the concentrations below the CVC and at the compositions very near to the single-chain surfactant, but it was found to be similar to the DeTAB–SDeS mixtures. Copyright © 2003 by Taylor & Francis Group, LLC

IV. CONCLUSION The adsorption behavior of vesicle-forming surfactants was reviewed with respect to the four typical classes: double-tailed, ion-pair, catanionic surfactants, and bicationic mixtures. In all cases, it is seen that the surface tension isotherms provide the onset and end of the structure changes in the aqueous solutions as a break or an inﬂection point and therefore are useful to determine the points of the structure transition. The thermodynamic analysis of the isotherms oﬀers important information on the relation between the adsorption behavior and the structure in the aqueous solution such as a possibility of formation of a multilayer adsorbed ﬁlm, very strong synergistic interaction both in the adsorbed ﬁlm and in the solution, the adsorption and desorption accompanied by the structure changes in the solution, and so on.

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4 Physicochemical Properties of Bile Salts MINORU UENO

Tokyo University of Science, Tokyo, Japan

HIROYUKI ASANO Nagoya, Japan

I.

Nippon Menard Cosmetic Company, Ltd.,

INTRODUCTION

Bile salts as biosurfactants frequently have been developed as solubilizers, emulsiﬁers, and dispersion agents for water-insoluble substances in many ﬁelds such as cosmetics, medicinals, and chemicals. Many papers and reviews concerning the colloidal and surface properties of aqueous solutions of bile salts have been published. These bile salts show common colloidal and surface properties; they have bulky, hydrophobic steroidal rings and one carboxyl group at the end of an alkyl chain (R) on a position 17 carbon atom of a ring in the molecule (Fig. 1); but their properties depend remarkably on the number and conﬁguration of hydroxyl groups bound to the ring, which are diﬀerent from those of ordinary surfactants with a linear hydrocarbon chain. The main bile salts are listed in order of increasing numbers of and by the position of the hydroxyl groups together with kinds of alkyl chains (R) and animal sources in Table 1 [1]. In this chapter, the unique structures of bile salts and their reﬂection in fundamental colloid and surface properties will be discussed.

II. CHEMICAL AND COLLOIDAL PROPERTIES OF BILE SALTS IN VITRO A. Single Bile Salt Systems 1. Chemical Structures Most of bile acids biosynthesized in the liver are represented by Fig. 1 [2]. The cholesterol molecule that is a starting material for biosynthesizing bile Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 1 Molecular structure (a) and the scheme of amphipathic structure (b) salts. R: side chains of glycine and taurine; C: cholate; DC: deoxycholate; CDC: deoxycholate; UDC: ursodeoxycholate; LC: lithocholate. (From Ref. 2.)

acids is a 3b-monohydroxy C27 sterol with a steroid nucleus containing 19 carbon atoms and a branched side chain containing 8 carbon atoms, as shown in Fig. 2. The cholesterol’s A, B, C, and D rings of its steroid nucleus have transformation extending like a stick, and the conformation of the hydroxyl group in the 3 position in the cholesterol molecule is the b position. Bile acids are carboxylic acids consisting of a cyclopenetnophenanthrene nucleus with a branched side chain having from three to nine carbon atoms ending in the carboxyl group. The A, B, C, and D rings of bile acids have a curved cis formation, and the hydroxyl groups of each bile acid bond to the steroid ring as follows. Cholic acid has the hydroxyl groups at the 3, 7, and 12 positions on the same concave side of the molecule. Deoxycholic acid has hydroxyl groups at both the 3 and 12 positions on the concave side. Lithocholic acid has an equatorial hydroxyl group at the 30e position. Lithocholic acid, as represented in Fig. 1b, is reabsorbed from the intestine and then resecreted as sulfate conjugates into the intestine; this is harmful to human beings, as it is the cause of hepatocirrhosis. However, combining with enteric bacterias in the intestine, most of lithocholic acid molecules are, fortunately, excreted and diﬃcult to reabsorb. Furthermore, both chenodeoxycholic acid and ursodeoxycholic acid, which are used as dissolution agents for cholelithiasis, have hydroxyl groups

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TABLE 1

Main Bile Salts In Vivo of Animals Positions of hydroxyl

Names

3

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

Lithocholic (LC) -Hyodeoxycholic (-HDC) -Hyodeoxycholic ( -HDC) Chenodeoxycholic (CDC) Ursodeoxycholic (UDC) Deoxycholic (DC) -Phocach ( -PHC) Hyocholic (HC) Cholic (C) -Muricholic (-MC) -Muricholic ( -MC) !-Muricholic (!-MC) Ursocholic (UC) 25-D-Coprostanic 25-L-Coprostanic Trihydroxyhomocholan Stimunol Pentahydroxy buphostan

6

7

12

23

24

*

e: — CH2 ðCH2 Þ2 CH3 , f:

g: — CH2 CH2 ðOHÞðCH3 ÞCðOHÞðCH3 Þ2 Source: Ref. 1. Copyright © 2003 by Taylor & Francis Group, LLC

R

Animals

*

a a a a a a b a a a a a a c d e f g

Man, cow, rabbit, pig Pig, boar Pig Mammal, bird, ﬁsh Bear Mammal Seal, sea lion, fur seal Pig Mammal, ﬁsh Mouse, rat Mouse, rat Mouse, rat Intestine, catabolism Frogs, crocodile Frogs Frogs Shark Frogs

*

R¼ a: — CH2 CH2 COOH, b: — CH2 CHðOHÞCOOH, c: d:

25

FIG. 2 The structure of cholesterol. (a) Position of each carbon; (b) steric conﬁguration.

at the 30e and 12 positions; however, the 12 hydroxyl group of the former is an axial () position and that of the latter is an equatorial ( ) position, as shown in Fig. 3. Accordingly, ursodeoxycholic acid, ﬁrst isolated in crystalline form from bear bile in 1927 [4], is identiﬁed as the 7 -epimer of chenodeoxycholic acid.

FIG. 3 Epimeric structures of (a) chenodeoxycholic acid (CDCA) and (b) ursodeoxycholic acid (UDCA). Copyright © 2003 by Taylor & Francis Group, LLC

2. Krafft Point Kraﬀt points, often called CMTs, of a number of monohydroxy and dihydroxy bile salts have been measured since the 1960s. Hofmann et al. [5] report that the CMT of unsubstituted sodium cholanate was above 1008C and that CMT values of most monohydroxy bile salts were in the range from 40 to 808C. Also, many investigators indicate that the natural bile salts have CMT values below the freezing point of water and are excellent coldwater surfactants. Accordingly, this low CMT of the common bile salts has little relevance to humans or other homeothermic vertebrates, as the body temperature of these vertebrates remains in the range from 32 to 388C. Furthermore, conjugations of glycine or taurine do not appear to have any major eﬀect on the CMT for bile salts [6].

3. Surface Tension Bile salts (which are alkaline metal salts) are very soluble, and surface tensions for various bile salts have been investigated by many workers in order to obtain critical micellar concentration (CMC) and other physicochemical parameters. If plots of surface tension in mN/m versus the logarithmic concentration are made, the surface tension curve shows one breakpoint corresponding to the CMC, and the adsorption at the surface and the area per molecule at surface saturation are calculated from the values of the surface tension and the concentration up to the CMC. The surface tensions for various bile salts, namely, sodium cholate (NaC) [7,8], sodium deoxycholate (NaDC) [7,8], sodium glycocholate (NaGC) [9], sodium glucodeoxycholate (NaGDC) [9], sodium glycochenodeoxycholate (NaGCDC), sodium glycoursodeoxycholate (NaGUDC), sodium taurocholate (NaTC) [10], and sodium taurodeoxycholate (NaTDC) [10], with high purity have been measured by the Wilhelmy vertical plate method using glass plates. Figure 4 shows surface tensions for various bile salts in TrisHCI buﬀer solutions (pH 9.0, ionic strength 0.026) versus logarithm of total concentrations of bile salts [7–l5]. The values of surface tensions for dihydroxylated bile salts are seen to be generally lower than those for trihydroxylated bile salts, and the values for bile salts conjugated by taurine are lower than those for the unconjugated bile salts. Furthermore, the CMC values are 6.93 mmol dm3 for NaC, 3.16 mmol dm3 for NaDC, 6.34 mmol dm3 for NaGC, 4.33 mmol dm3 for NaTC, and 2.98 mmol dm3 for NaTDC; and the CMC values for dihydroxylated or taurine-conjugated bile salts tend to be lower, in analogy with the surface tension results. This may be due to the high hydrophobicity of the dihydroxylated bile salts and to the hydrous water around the taurine group. On the other hand, the area occupied per bile salt molecule for NaC, NaDC, and NaGC, which is calculated from adsorption data at the air– Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Curves of surface tension at 258C versus logarithm of total concentration for various bile salts.

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FIG. 4

Continued

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liquid interface, is in the range from 0.9 to 1 nm2/molecule [l6]. This fact suggests that bile salt molecules orient horizontally on the surface, where each side of a bile salt molecule looks toward the air for the convex side as the hydrophobic part and toward the bulk phase for the concave side as the hydrophilic part.

4. Micelle Formation Properties of bile acids diﬀer from those of classical surfactants, because bile acid molecules have a hydrophobic surface that is the convex side of the steroid nucleus and a hydrophilic surface that is the polyhydroxylated concave side of this steroid nucleus. These molecules of bile acids form a molecular aggregation called ‘‘micelle’’ in the narrow concentration range from 0.6 to 5 mmol dm3 , and this concentration corresponds to the CMC. Micelles of bile acids above the CMC are called primary micelles, as shown in Fig. 5 [17]. A driving force of this micellar formation is interaction among the hydrophobic faces of bile acids, and this primary micelle is considered to be a spherical micelle consisting of bile acid molecules in the molecular number range from 2 to 15. Under higher concentrations of bile acids, and especially in the case of high ionic strength of the aqueous

FIG. 5

Structures of primary and secondary bile salt micelles. (From Ref. 17.)

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solutions, the primary micelles aggregate further because of hydrogen bonding among their hydrophilic faces, and then redlike secondary micelles are formed as shown in Fig. 5 (see Section II.A). Furthermore, as the polar lipids in vivo, for example, Iecithin, fatty salts, and monoglycerides, form liquid crystal aggregates in aqueous solutions, bile salt micelles solubilize these polar lipids at or above a 2:1 bile salt:lipid ratio [17–20]. Micellar sizes for these mixed micelles of bile salts and the lipids range from 6 to 40 nm. With excess lecithin, the mixed micelles form disk-shaped micelles of bimolecular layer as shown in Fig. 6 [17,20]. However, when the amount of lecithin is less than that of bile salts, the mixed micelles tend to form spherical micelles, as shown in Fig. 7 [21]. In the human gallbladder and intestine, both spherical and disk-shaped mixed micelles are thought to occur.

FIG. 6 Proposed molecular arrangement of the bile salt–lecithin–cholesterol micelles. (A) Small’s model (from Ref. 12); (B) Carey model (from Ref. 20).

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FIG. 7 The mixed micelles consisting of bile salts and lecithin. Disk: excess lecithin; sphere: excess bile salts. (From Ref. 21.)

5. Effects of pH Most bile salts precipitate as insoluble bile acids in the stomach or colon. The reason is that values of precipitation pH (ppt PH) for bile salts are higher than the pH value in the intestine [17,22]. When bile ﬂows backward Copyright © 2003 by Taylor & Francis Group, LLC

to the stomach, bile salts conjugated by glycine precipitate in gastric juice; however, the taurine conjugates never precipitate. Also, bile salts that leave the enterohepatic circulation in the colon become unconjugated bile salts (free bile salts), and these unconjugated bile salts then precipitate due to the rise of pKa. In the case of a lithocholic salt, the reason for precipitation is also the high Kraﬀt point value for a lithocholic salt [17]. In general, if pH values of aqueous solutions of bile salts decrease until about the pKa values of bile acids, the bile salts change to insoluble bile acids in the solutions, and then some of these bile acids are solubilized into micelles of bile salts. If an intramicelle of bile salts is supersaturated by bile acid molecules and the ppt pH of the solutions is about 1 higher than the pKa of bile acid, the precipitation of these bile acids in the solutions takes place. Appearance pKa values of these bile acids are shown in Table 2. As mentioned above, the pKa values of free bile acids are higher than those of the conjugated bile acids, and the amount of acid required to induce precipitation is much less for the free bile salts than for the conjugate. Furthermore, the pKa values of bile acids increase with their concentrations, and the diﬀerences in pKa below and above their CMCs are clearly seen in Table 2. This suggests a possibility of the hydrolysis of bile salts on the surfaces of their micelles. Accordingly, if a solution of free bile salts is prepared with a concentration and a pH similar to those present in the small intestine (10 mmol dm3 , pH 6.3), their acids will precipitate from solution. In contrast, both glycine and taurine conjugates soluble at the pH 5.5–7 are generally present in small intestinal content.

6. Aggregation Number The aggregation number (number of molecules per micelle) of bile salt micelles has been studied by many investigators, and these studies have given aggregation numbers for bile salts from 1 to 1000 associated molecules. However, these aggregation numbers are not clear due to lack of control of pH, temperature, counterion concentration, and bile salt concentration. Therefore, small apparent aggregation numbers of bile salts, deduced using equilibrium centrifugation and light scattering, are reported under the experimental conditions described in Table 3 [17]. In very dilute salt concentrations or in water, the aggregation numbers of bile salts do not vary with bile salt concentration. In water at 208C, most bile salts form dimmer aggregates over a wide range of bile salt concentrations. However, when the NaC1 concentration is increased, bile salt aggregation numbers tend to increase. In particular, aggregation numbers of dihydroxy bile salts abruptly increase with NaC1 concentration, and these bile salts also show a marked increase in micelle size. Furthemore, although decreasCopyright © 2003 by Taylor & Francis Group, LLC

TABLE 2 pKa Values of Free and Conjugated Bile Acids Bile acida Free bile acid CA

DCA

CDCA

Glycine conjugates GCA

GDCA

GCDCA Taurine conjugates TCA TDCA

Bile salt concentration (mM)

pKa

2 (CMC) 80 (>CMC) 2 (CMC) 101 (>CMC)

4.98 5.21 5.5 5.3 6.21 6.3 5.88 6.18 6.53

1.8 (CMC) 86 (>CMC) 2.1 (CMC) 20.0 (>CMC) 1.5 (CMC)

3.95 3.80 4.09 4.69 4.84 4.77 4.23 4.34

18.5 37.0 19.0 38.0

1.85 1.85 1.93 1.95

(>CMC) (>CMC) (>CMC) (>CMC)

a CA: cholic acid; DCA: deoxycholic acid; CDCA: chenodeoxycholic acid; GCA: glycocholic acid; GDCA: glycodeoxycholic acid; GCDCA: glycochenodeoxycholic acid; TCA: taurocholic acid: TDCA: taurodeoxycholic acid. Source: Ref. 1.

ing the pH of trihydroxy bile salt solutions has little eﬀect on the aggregation number, the aggregation numbers of dihydroxy bile salts, especially free bile salt and glycine conjugates, increase with decreasing pH. Aggregation numbers of most bile salts are not aﬀected by temperature variation. However, as the temperature is increased, the sizes of micelles of dihydroxy bile salts having aggregation numbers greater than 10 decrease because of the destruction for hydrogen bonds among bile salt molecules. Copyright © 2003 by Taylor & Francis Group, LLC

7. Solubilization Bile salt micelles can solubilize amphipathic substances of biological importance. In particular, their micelles solubilize cholesterol, lipovitamin, lecithin, fatty salts, and monoglycerides, which are water-insoluble substances, and then bile salt molecules form mixed micelles with these lipids [18]. Furthermore, bile salt micelles can solubilize insoluble bile acids in the form of their mixed micelles (see Section II.A.5). (a) Solubilization of Cholesterol. In general, bile salt micelles are thought to solubilize few cholesterol molecules, as polar lipids such as lecithin are not solubilized into the micelles. However, cholesterol monohydrate, the solubility of which in pure water is about 1 mmol dm3 [ 23], is solubilized in an aqueous solution of 200 mmol dm3 of NaDC, and the amount of the solubilized cholesterol monohydrate is 10 mmol dm3 , 10 million times that in pure water [24]. When lecithin is added to this aqueous solution of NaDC, the amount of solubilized cholesterol monohydrate is thought to become about 3 times that for NaDC alone. Although the micelles of the ordinary bile salts have the ability to solubilize cholesterol molecules in this manner, the solubilizing power of the micelles of the conjugates is inferior to that of free bile salts. In particular, the taurine conjugates do not solubilize more cholesterol than glycine conjugates [24]. Bile salt molecules form mixed micelles with lecithin, as mentioned in Section II.A.4. The solubilizing power of these mixed micelles with respect to cholesterol is 3 to 10 times that of micelles of bile salt alone. This solubilizing mechanism is viewed as follows. At ﬁrst, cholesterol molecules are captured by polar groups on the micellar surface; then, the captured cholesterol molecules are solubilized almost instantly into liquid hydrocarbon portions of the intramicelles [20,2l]. At this point, sizes of these mixed micelles solubilizing cholesterol molecules become larger, from 0.2 to 0.3 nm; however, micellar shape and the structure of the mixed micelles do not change. Then, how can sizes of mixed micelles of bile salts and lipids grow to about 40 nm? Because the conditions for the solutions of bile salts and polar lipids change as follows. The mixed micellar solutions are diluted in the intestine to the extent that the ratio of bile salts and lipids in the mixed micelles does not change, or the micellar solutions are added, swelling amphipathic substances. Under the above conditions, the sizes of the mixed micelles abruptly increase, and at last monolayer vesicles or liposomes are formed in the mixtures after the collapse of the mixed micelles [27–30]. Human bile contains 50 wt % lecithin, and this concentration of lecithin corresponds to the saturated state. Also, human bile contains saturated or supersaturated cholesterol. In particular, as the concentration of bile salts in

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TABLE 3 Apparent Aggregation Numbers of Bile Salt Micelles Bile salta NaC

Temperature (8C)

Solvent

pH

Aggregation number

20

H2 O 0.01 M NaCl 0.05 M NaCl 0.15 M NaCl 0.15 M NaCl 0.3 M NaCl 1.0 M NaCl 1.0 M NaCl H2 O 0.05 M NaCl 0.15 M NaCl 0.15 M NaCl 0.3 M NaCl 0.05 M NaCl 0.15 M NaCl 0.15 M NaCl 0.3 M NaCl 0.1 M NaCl 0.15 M NaCl 0.3 M NaCl 1.0 M NaCl 3.0 M NaCl 0.01 M NaCl 0.01 M NaCl 0.05 M NaCl 0.15 M NaCl 0.15 M NaCl 0.3 M NaCl 0.15 M NaCl 0.15 M NaCl 0.15 M NaCl 0.15 M NaCl H2 O 0.05 M NaCl 0.15 M NaCl 0.15 M NaCl 0.3 M NaCl 0.5 M NaCl 0.5 M NaCl 0.15 M NaCl 0.15 M NaCl 0.15 M NaCl

8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 8–9 7.3 7.3 7.85 7.85 8–9 8–9 8–9 8–9 8–9 8–9 8–9 4.9 6.2 7.2

2.0 2.8 3.8 4.8 4.8 5.8 7.2 7.3 1.9 5.0 5.8 5.6 7.0 4.2 4.6 4.5 6.0 3.6 4.0 5.2 9.0 16.0 4.3 3.8 8.9 15.2 13.3 29.2 551.9 13.5 16.8 13.3 2.0 11.7 19.4 16.2 36.9 63.9 46.6 2184.0 21.4 18.3

36 20

NaGC

36 20

NaTC

36 20 20 36 20 4 20

NaDC

20 36 20 36 20

NaGDC

36 20 36 20

36 20 36 20

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TABLE 3 Continued Bile salta

Temperature (8C)

Solvent

pH

NaTDC

20

0.01 M NaCl 0.05 M NaCl 0.15 M NaCl 0.15 M NaCl 0.3 M NaCl 0.5 M NaCl 0.15 M NaCl 0.15 M NaCl 0.15 M NaCl 0.05 M NaCl 0.15 M NaCl 0.15 M NaCl 0.3 M NaCl 0.15 M NaCl 0.15 M NaCl 0.05 M NaCl 0.15 M NaCl 0.15 M NaCl 0.3 M NaCl 0.15 M NaCl 0.15 M NaCl 0.15 M NaCl 0.15 M NaCl 0.3 M NaCl

8–9 8–9 8–9 8–9 8–9 8–9 1.6 3.6 6.5 8–9 8–9 8–9 8–9 7.00 7.05 8.0 8.0 8–9 8–9 8–9 8–9 8–9 8–9 8–9

36 20

NaCDC

20 36 20

NaGCDC

20

NaTCDC

36 20 20 36 4 20

Aggregation number 6.2 11.3 21.8 18.0 29.1 46.8 25.8 21.9 21.2 6.5 11.3 10.9 20.2 18.8 17.5 10.6 20.6 18.2 28.4 9.5 19.5 15.2 25.5 29.0

a

NaC: sodium cholate; NaGC: sodium glycocholate; NaTC: sodium taurocholate; NaDC: sodium deoxycholate; NaGDC: sodium glycodeoxycholate; NaTDC: sodium taurodeoxycholate; NaCDC: sodium chenodeoxycholate; NaGCDC: sodium glycochenodeoxycholate; NaTCDC: sodium taurochenodeoxycholate. Source: Ref. 1.

hepatic bile is smaller than that in gallbladder bile, cholesterol is solubilized in the supersaturated state [14]. The excess cholesterol in the supersaturated state does not exist in the micelles, but it forms stable microemulsion in the size range from 30 to 40 nm with lecithin [31]. However, in gallbladder bile, most excess cholesterol is in the micelles. (b) Absorption of Solubilized Vitamin E. Vitamin E (d--tocopherol, VE) is known to be absorbed in a state solubilized or emulsiﬁed by various bile salts in the small intestine. Some studies have reported the effects of bile salts on the intestinal absorption of VE [32,33]. Gibaldi and Feldman [34] indicate that the rate of drug transfer across biological membranes Copyright © 2003 by Taylor & Francis Group, LLC

was inﬂuenced by the surfactant micelles in two possible ways: a change in the physicochemical properties of the drug by the interaction with the micelle, and via an alteration in the permeability of the membrane by the direct action of the surfactant. Imai et al. [35] suggest that the intestinal absorption ratio of VE correlates with the micellar size and net water ﬂux in the intestinal lumen. However, the relationship between the intestinal absorption of VE and the particle sizes of micelles or emulsions containing VE was sufﬁciently conﬁrmed in either case. Therefore, we tried to clarify the absorption on the basis of the micellaar properties of bile salts and the absorption ratio of VE into the small intestine of a rat during 100 min of recirculating the saturated micellar solutions of VE solubilized with various concentrations of bile salts [36]. These micellar solutions of bile salts were prepared by sodium glycocholate (NaGC), sodium glycodeoxycholate (NaGDC), sodium glycochenodeoxycholate (NaGCDC), sodium taurocholate (NaTC), sodium taurodeoxycholate (NaTDC), and the mixed system. (The bile salt ratio of the mixture was 30:20:29:13:9 of NaGC, NaGDC, NaGCDC, NaTC, and NaTDC, respectively.) The results of this experiment were as follows. The amount of solubilized VE generally increased with the concentration of bile salts in micellar solutions above CMCs, and the micelles of dihydroxy bile salts solubilized more VE than trihydroxy bile salts. However, the mean aggregation numbers of bile salt micelles were virtually independent of the saturated amounts of solubilized VE. On the other hand, the absorption of VE for most bile salt systems was found to depend on the concentration of bile salts, but not on the kinds of bile salts. Also, the intestinal absorption of VE seems to be related to certain interactions of bile salts with the intestinal membrane, and independent of the micellar sizes. As hydrophobic bile salts such as NaGDC and NaGCDC would have strong aﬃnity for lipids in the surface of the intestinal lumen, VE solubilized into the micellar solutions of NaGDC and NaGCDC would appear to be absorbed through the intestinal membrane more easily than VE solubilized into micellar solutions of NaTC and NaGC.

B. Binary Mixtures of Epimer Bile Salts and Octaoxyethylene Glycol-n-Decylether (C10E8) As mentioned above, bile salt micelles diﬀer from the micelles found in solutions of classical surfactants, because their molecules have a lipophilic surface that is the convex side of the steroid nucleus and a hydrophilic surface that is the polyhydroxylated concave side of this steroid nucleus [17,25,26,37–40]. Accordingly, the micelles of bile salts are rigidly formed by the hydrophobic interaction and hydrogen bonding between the molecules of each bile salt. Copyright © 2003 by Taylor & Francis Group, LLC

On the other hand, octaoxyethylene glycol mono n-decyl ether (C10E8), a nonionic surfactant, is known to show typical properties of surface tension, critical micellar concentration (CMC), adsorption, and aggregation. In particular, C10E8 molecules form loosely packed micelles in solution and the CMC value of C10E8 is 1 mmol dm3 , which is convenient for the various theoretical calculations. Therefore, the unusual properties of bile salts, for example, NaC, NaDC, NaGC, NaTC, and NaTDC, have been studied by the addition of C10E8. In this section, we want to describe the properties of aqueous binary mixtures of bile salts and C10E8 from the viewpoints of surface tension, hydrophobicity, aggregation number, and conﬁguration in mixed micelles.

1. Surface Tension Figure 8 shows the surface tension versus logarithm of total surfactant concentration for aqueous binary solutions of the NaC–C10E8 system, the NaDC–C10E8 system, the NaGC–C10Es system, the NaGDC–C10E8 system, the NaGCDC–C10E8 system, the NaGUDC–C10E8 system, the NaTC– C10E8 system, and the NaTDC–C10E8 system. The measured mole fractions of bile salts for each mixed system are 0.00 (C10E8 alone), 0.25, 0.50, 0.75, 0.90, and 1.00 (bile salt alone). All curves for all systems show only one breakpoint, corresponding to the CMC, and these CMC values are listed in Table 4. From these CMC values, we calculated the compositions of a mixed micelle on the basis of chemical potentials in micelles and solutions [41] and the excess thermodynamic quantities of Motomura [42], and then we investigated the mixed states in micelles of each system. The compositions of the mixed micelles vary with increasing mole fraction of each bile salt in the solutions, and if the mixed states of bile salts and nonionic surfactant were ideal, the variation of the mole fraction of each bile salt in a mixed micelle, XMideal would be given by [40] M ¼ ðXbile CMCnonion Þ=ðXbile CMCnonion þ ð1 Xbile ÞCMCbile Þ Xideal

ð1Þ

where Xbile is the mole fraction of bile salt in the solution, and CMCnonion and CMCbile are the CMCs for the nonionic surfactant and bile salt alone, respectively. In most cases, however, the mixed states of these surfactants are known to be nonideal. The deviation from ideal mixing can be conﬁrmed by analyzing the relationship between the CMC and the mole fraction of bile salts from the theoretical treatment of excess thermodynamic quantities by Motomura [42]. As his theory is not inﬂuenced by the kinds of surfactants or the nature of their counterions, this should give the actual composition of the mixed micelles in the binary mixtures of bile salt and C10 E8 . Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 8 Curves of surface tension for bile salt–C10 E5 systems at 258C versus logarithm of total surfactant concentration with various mole fractions of bile salts.

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FIG. 8

Continued

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TABLE 4 The Values of CMC and X M excess for Each Bile Salt— C10 E8 System Mole fraction of bile salt in the solution, Xbile System CMC NaC–C10 E8 NaDC–C10 E8 NaGC–C10 E8 NaGDC–C10 E8 NaGCDC–C10 E8 NaGUDC–C10 E8 NaTC–C10 E8 NaTDC–C10 E8 M Xexcess NaC–C10 E8 NaDC–C10 E8 NaGC–C10 E8 NaGDC–C10 E8 NaGCDC–C10 E8 NaGUDC–C10 E8 NaTC–C10 E8 NaTDC–C10 E8

0.00

0.25

0.50

0.75

0.90

1.00

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.17 1.11 1.16 1.06 1.04 1.29 1.17 1.09

1.53 1.25 1.65 1.13 1.09 1.86 1.53 1.28

2.28 1.63 2.20 1.42 1.30 3.31 2.04 1.57

4.28 2.42 4.04 1.66 1.60 7.48 2.72 2.00

6.93 3.16 6.34 2.02 2.03 30.00 4.33 2.98

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.03 0.11 0.03 0.14 0.14 0.010 0.06 0.10

0.09 0.20 0.06 0.30 0.27 0.013 0.17 0.21

0.13 0.42 0.12 0.58 0.53 0.017 0.37 0.43

0.40 0.74 0.38 0.81 0.79 0.203 0.66 0.72

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Accordingly, the equations for calculation of the mole fraction of bile salt in M ) are as follows: a mixed micelle (Xexcess 6 ¼ 2Xbile =ðXnonion þ 2Xbile Þ Xbile 6 CMCmix ¼ Xnonion þ 2Xbile 6 6 Xnonion ¼ 1 Xbile M 6 6 6 6 6 ¼ Xbile ðXnonion Xbile =CMC6 Xexcess mix ÞðCMCmix =Xbile Þ

ð2Þ ð3Þ ð4Þ ð5Þ

where Xnonion is the mole fraction of nonionic surfactant in the solutions and CMCmix is the CMC for the mixed system of bile salts and nonionic surfactant. Xbile, Xnonion, and CMC6 mix are deﬁned as the variables considering the complete dissociation of the bile salt (instead of the variables Xbile, Xnonion, and CMCmix, respectively). M The values for XM ideal and Xexcess can be determined from experimental data and theory using a computer, and the XM excess -values for each system are listed in Table 4. Copyright © 2003 by Taylor & Francis Group, LLC

M Figure 9 shows the values of XM ideal as the dashed curve and Xexcess as the curve versus Xbile for aqueous binary solutions of the NaC–C10E8 system, the NaDC–C10E8 system, the NaGC–C10E8 system, the NaGDC–C10E8 system, the NaGCD–C10E8 system, the NaGUDC–C10E8 system, the M -values NaTC–C10E8 system, and the NaTDC–C10E8 system. The Xexcess M . for each system deviated negatively from each dashed curve for Xideal These facts suggest that these aqueous binary mixtures of each bile salt and C10E8 are nonideal and that C10E8-rich micelles are formed in these mixed binary solutions. However, the mixed systems between the dihydroxy bile salt and C10E8 or between the taurine conjugate and C10E8 show the small extent of deviation M M curve from the Xideal curve. Also as shown in Table 4 the of the Xexcess M Xexcess -values for the NaDC–C10E8 system, the NaTC–C10E8 system, and the NaTDC–C10E8 system are larger than those of the NaC–C10E8 system and the NaGC–C10E8 system. As mentioned, pKa values for the acid of the taurine conjugates were much lower than those for the other bile salts, and the taurine conjugates have higher solubility in the aqueous solutions because of the hydrated water around the taurine group. In contrast, C10E8 has the hydrated water around the polyoxyethylene chain. M is that the miscibility between Therefore, the reason for the order of Xexcess taurine conjugates and C10E8 is superior than that between NaC or NaDC and C10E8. On the other hand, the dihydroxy bile salts have strong hydrophobic interaction and easily form their micelles in the solutions. Accordingly, this may be due to the strong aﬃnity between NaDC or NaTDC and C10E8.

2. Hydrophobicity The hydrophobicity in the mixed micelles can be estimated from measurements of the ratio of the ﬁrst to the third vibronic peak, I1 =I3 , in a monomeric ﬂuorescence emission spectrum of pyrene [43–45]. In the case of low Il =I3 -values, the microenvironment of the solubilized pyrene is polar or hydropohobic as in hydrocarbon solvents. For example, it is about 0.6 for n-hexane. On the other hand, for more polar or hydrophilic microenvironments, the values are higher: 1.23 for ethanol, 1.83 for H2O. Figure 10 shows plots of I1 =I3 for various mole fractions of bile salts at a constant total surfactant concentration of 100 mmol/L as a function of the mole fraction of bile salt; these values are listed in Table 5. I1 =I3 -values for each single system of bile salts were 0.69 for NaC, 0.62 for NaDC, 0.74 for NaGC, 0.64 for NaGDC, 0.65 for NaGCDC, 0.96 for NaGUDC, 0.78 for NaTC, and 0.65 for NaTDC. These values indicate that the solubilized pyrene is located in micelles of bile salts with a microenvironment that is Copyright © 2003 by Taylor & Francis Group, LLC

nearly as nonpolar as in hydrocarbon solvents. Furthermore, the order of bile salt hydrophobocity is NaDC > NaGDC > NaGCDC NaTDC NaC > NaGC > NaTC > NaGUDC. From these results, the most important factor inﬂuencing the hydrophobicity in bile salt micelles is considered to be the deoxydation of bile salt molecules. In contrast, the taurine conjugation of the free bile salts inﬂuences the increase of polarity of hydrophilicity in bile salt micelles because of the higher polarity of the taurine group. On the other hand, the value for the single system of C10E8 was 1.05,

M M FIG. 9 Curves of Xideal and Xexcess versus Xbile for bile salt–C10E8 system.

Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9

Continued

close to the value for polar solvents. This means that pyrene molecules are solubilized into the palisade layer of C10E8 micelles, as C10E8 molecules form loose-packed micelles. For each mixed system, the I1 =I3 -values decreased slightly with increasing mole fraction of bile salt and showed a breakpoint at the mole fraction of 0.75 for the NaC–C10E8 system, 0.57 for the NaDC–C10E8 system, 0.68 for the NaGC–C10E8 system, 0.50 for the NaGDC–C10E8 system, 0.50 for the NaGCDC–C10E8 system, 0.82 for the NaGUDC–C10E8 system, 0.72 for the Copyright © 2003 by Taylor & Francis Group, LLC

NaTC–C10E8 system, and 0.54 for the NaTDC–C10E8 system. Above these mole fractions. I1 =I3 -values, except for the NaGUDC–C10E8 system, decreased more steeply. The I1 =I3 -value above the breakpoint for NaGUDC–C10E8 system showed an increasing tendency diﬀerent from that of the other systems.

FIG. 10 Plots of 11/13 versus mole fraction of bile salts at 258C. Total surfactant concentration for each of the solutions is 100 mmol dm3 . Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10

Continued

In general, nonionic surfactants form spherical micelles in the dilute solution, whereas bile salt molecules aggregate among the hydrocarbon backs of the steroid nucleus and form lamellar micelles, so-called back-toback micelles, as shown by Small [17]. Therefore, these breakpoints in each

Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 5 The Values of I1 =I3 and n for Each Bile Salt—C10 E8 System Mole fraction of bile salt in the solution, Xbile System I1 =I3 NaC–C10 E8 NaDC–C10 E8 NaGC–C10 E8 NaGDC–C10 E8 NaGCDC–C10 E8 NaGUDC–C10 E8 NaTC–C10 E8 NaTDC–C10 E8 n NaC–C10 E8 NaDC–C10 E8 NaGC–C10 E8 NaGDC–C10 E8 NaGCDC–C10 E8 NaGUDC–C10 E8 NaTC–C10 E8 NaTDC–C10 E8

0.00 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 69 69 69 69 69 69 69 69

0.25

0.50

1.00 0.99 1.03 0.98 0.97 1.01 0.99 0.98 37 37 36 41 38 43 33 40

0.94 0.91 0.98 0.91 0.91 0.97 0.94 0.90 29 30 32 32 33 33 27 30

0.75 0.90 0.77 0.90 0.77 0.77 0.93 0.89 0.79 23 25 23 26 27 29 22 23

0.90 0.77 0.65 0.82 0.69 0.69 0.93 0.83 0.69 16 21 18 21 21 25 18 19

1.00 0.69 0.62 0.74 0.64 0.65 0.96 0.78 0.65 15 18 14 16 18 13 15 16

curve suggest that these mixed micelles change from the C10E8-rich to the bile salt-rich ones and that below and above each breakpoint micellar shapes change from spherical to lamellar. I1 =I3 -values for the mixed systems from bile salt mole fraction to each breakpoint are near 1.05, which is that of pure C10E8 micelles. Thus, the hydrophobicity inside the mixed micelles resembles that of C10E8 in this range of the mole fraction; and above the mole fraction corresponding to each breakpoint, the hydrophobicity inside the mixed micelles approaches that of the single micelle of bile salts. As the mole fraction corresponding to the breakpoint for the NaGUDC–C10E8 system is larger than that for the NaGCDC–C10E8 system, the mixed micelle formation for the NaGUDC-C10E8 system is more diﬃcult than in the case of the NaGCDC-C10E8 system, and the diﬀerent behavior of I1 =I3 for this epimer suggests that the NaGUDC-rich micelles become loosely packed due to the spacing around the 7--hydroxyl group in the bile salt molecules. The mole fraction of bile salts corresponding to the I1 =I3 breakpoint for each mixed M system coincides with the Xexcess breakpoint obtained from theoretical calculations. Copyright © 2003 by Taylor & Francis Group, LLC

In addition, as shown in Fig. 10, the values of the mole fraction corresponding to the breakpoint for the dihydroxy bile salt–C10E8 systems were smaller than those for the trihydroxy bile salt–C10E8 systems. As the dihydroxy bile salts without a 7--hydroxyl group have high hydrophobicity, they easily aggregate among themselves in the mixed solutions. Therefore, although the C10E8 -rich micelles are formed in the low mole fraction of bile salts, the mixtures of dihydroxy bile salts and C10E8 tend to form the bile salt-rich micelles even from the lower mole fractions, compared with mixtures of trihydroxy bile salts and C10E8.

3. Aggregation Number The mean aggregation number of micelles is obtained from luminescence quenching measurements [46–48]. Assuming that both the probe molecule (P) and the quencher molecule (Q) are solubilized into micelles and obey the Poisson distribution among micelles, and that P is luminescent only in micelle free from Q, the measured ratio of luminescence intensities, I=I0 , in the presence of Q to that in the absence of Q is given by I=I0 ¼ expð½Q=½MÞ

ð6Þ

where [Q] is a concentration of quencher, and [M] is an unknown micelle concentration that can be related to the mean aggregation number, n , using the measurable concentration of the surfactant, [Surf], that is, ½M ¼ ð½Surf ½free monomerÞ=n . Since the free monomer concentration is approximately equal to the CMC, Eq. (6) can be rewritten using the relationship among n , [Surf], and CMC in the form ln I0 =I ¼ ½Qn =ð½Surf CMCÞ

ð7Þ

Accordingly, from the slope of plots of lnðI0 =IÞ against [Q], the mean aggregation number can be obtained for each concentration of surfactants. We measured the mean aggregation numbers, n for all mixed systems at the constant total surfactant concentration of 50 mmol dm3 by using the above method. Figure 11 shows plots of n -values for all systems as a function of the mole fraction of bile salts, and the n -values are listed in Table 5. In all mixed systems, abrupt decreases of n were observed in the range of bile salt mole fraction from 0 to 0.25. Because bile salt molecules have a bulky structure, for forming the mixed micelles, many molecules of bile salt or C10E8 are not required. Accordingly, even if only a few molecules of bile salts are mixed into C10E8 micelles, the n -values of the mixed micelles decrease abruptly.

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4. Molecular Orientation of NaGCDC and NaGUDC in Micelles Estimated by 1H NMR Measurements 1

H NMR of bile salts in the mixed micelle was measured in deuterium oxide (D2O) containing 10 mL sodium deuterium (NaOD) per 15 mL of D2O. The solutions were prepared for 100 mmol dm3 of C10E8 and bile salt alone, and

FIG. 11 Plots of the mean aggregation number, n , versus mole fraction of bile salts at 258C. Total surfactant concentration for each of the solutions is 50 mmol dm3 . Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 11

Continued

their mixtures, in an atmosphere of nitrogen and were investigated by Fourier transform (FT) NMR (400 MHZ JEOL JNM-EX400) at 238C. 1 H chemical shifts were referred to internal sodium 2,2,3,3-tetradeuteri0-3(trimethylsilyl) propionate, TSP (Aldrich), assigning zero value. Some spectra were recorded in the chemical shift range from 0 to 10 ppm for 1H NMR. A series of 1H relaxation times were measured automatically with the STACKI program of JEOL JNM-EX400 stack ﬁles. 1H spin-lattice relaxation times (T1) were measured for variation of the parameter PI1 (pulse interval, ) by using the inversion recovery method (180 90 Acq:) with a pulse delay time (PD) longer than 5Tl. T1 -values were determined by a nonlinear procedure after accumulating and Fourier-transforming FID (free induction decay) signals for PI1 values (ms) 50, 100, 150, 200, 250, 300, 350, 400, 500, 600, 700, 800, 900, 1000, 2000. 1 H spin-spin relaxation times (T2) were measured for variation of the parameter LOOPI (times of 180 pulse, n) by using the CPMG (Carr– Purcell–Meiboom–Gill) pulse sequence [90x ð 180y Þn Acq:]. The value of PI1 was ﬁxed at 1 ms, and PD was set over 5T1. T2 values were determined by a linear procedure after accumulating and Fouriertransforming FID signals of spin echoes that were collected for each LOOPI. Figure 12 shows the 1H NMR spectra for solutions of NaGCDC and NaGUDC single systems of 100 mM in D2O. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 12

Spectra of 400 MHZ IH NMR for bile salts in D20. (a) NaGCDC; (b) NaGUDC.

Copyright © 2003 by Taylor & Francis Group, LLC

The resolved signals assigned to methyl group proton positions (hereafter abbreviated as Mel8, Mel9, and Me21) in molecular structures of NaGCDC and NaGUDC did not overlap with signals in the spectrum of C10E8, except for the Me21 signal of NaGUDC. T2-values were measured using the CPMG technique [44] to estimate molecular rearrangements of bile salt molecules in the mixed micelles [45]. Figure 13 shows plots of 1H spin-lattice relaxation rates (1/T 1) and 1H spinspin relaxation rates 1/T1 for the NaGCDC–C10 E8 system as functions of the mole fraction of bile salts. 1/T1-values for Me21 were kept constant in all ranges of the mole fraction, but for Me18 they became fast in the lower mole fractions of bile salts and for Mel9 they became slow. On the other hand, 1H spin-spin relaxation rates (1/T1) showed nearly similar tendencies to those of 1/T1. Figure 14 shows 1/T1 and 1/T2 curves for NaGUDC as functions of the mole fraction. Values for both Mel8 and Mel9 remained nearly constant. In general, the relaxation rates depend on the emotional behavior of the surfactant molecules in an aqueous solution. When the surfactant molecules aggregate to form the micelles, their motions become slowed down, and the rates become faster. Accordingly, the decrease of 1/T1 - and 1/T2 -values for Mel9 in the lower mole fraction of NaGCDC suggests that Mel9 becomes free from hydrogen bonding formed by back-to-back contact between two

FIG. 13 Plots of 1H relaxation rates versus mole fraction of NaGCDC. (a) 1H spinlattice relaxation rates (1/T1 ); (b) 1 H spin-spin relaxation rates (1/T2 ). NaGUDC– C10E8 system. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 14 Plots of 1H relaxation rates versus mole fraction of NaGUDC. (a) 1H spinlattice relaxation rates (1/Tl); (b) 1H spin-spin relaxation rates (1/T2 ).

NaGCDC molecules in the mixed micelles. In contrast, the motion of Me18 is restricted at the lower mole fraction of NaGCDC, as shown in Fig. 13. These results suggest that the -plane of the NaGCDC molecule orients toward the water phase, and the -plane orients together with Mel9 toward the center of the core in the mixed micelle; Mel8 in the NaGCDC molecule is thus located near the boundary between ethylene oxide and the hydrocarbon chain of the nonionic surfactant molecule in the mixed micelle, as shown in the schemes of Figs. 15a and b. In the case of NaGUDC, as the 7--hydroxyl group is ﬁxed by hydrogen bonding to ethylene oxide near the boundary between ethylene oxide and the hydrocarbon chain of the nonionic surfactant molecule in the mixed micelle, and as the motions of Mel8 and Me19 are located and restricted near the boundary, the NaGUDC molecule may orient slightly obliquely near the boundary compared with the position of the NaGCDC molecule, as shown in the schemes of Figs. 15a and b.

5. Solubilization As discussed in Sections II.B.1–3, the mixed micelles consisting of bile salts and C10E8 show characteristic properties with regard to micellar composition, hydrophobicity, mean aggregation number, and conformation. Therefore, cholesterol solubilization behavior in aqueous binary mixed solutions of bile salt–C10E8 systems is expected to be inﬂuenced by the properCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 15 (a) Schematic orientation of bile salt molecules in the mixed micelle of NaGCDC and NaGUDC with C10E8; (b) scheme of the mixed micelles of the two systems versus mole fraction of bile salts.

Copyright © 2003 by Taylor & Francis Group, LLC

ties of the mixed micelles. In this section, we describe the cholesterol solubilities in the mixed micelles for the NaC–C10E8 and NaDC–C10E8 systems at various temperatures on the basis of the results for mixed micelles and the data from the enzyme assay [51,52], and then we investigate the relationship between the properties of these mixed micelles and the cholesterol solubilities in these systems. (a) Dependencies of Cholesterol Solubilization with Respect to Total Surfactant Concentration at 25 and 378C. Figure 16 shows the saturated amounts of the solubilized cholesterol, Cch , in the aqueous binary solution of NaC and C10E8 at 25 and 378C as functions of total surfactant concentration. Similar Cch curves for the NaDC–C10E8 system at 25 and 378C are shown in Fig. 17. The Cch -values for C10E8 alone at 25 and 378C increase linearly with total C10E8 concentration, and the slope of the Cch values at 378C was far larger than that at 258C. In general, the polyoxyethylene part of C10E8 is dehydrated by the rise in temperature and so the hydrophobicity of C10E8 micelles becomes greater. Accordingly, this suggests that the Cch -values in the C10E8 solution are strongly inﬂuenced by the rise in temperature. On the other hand, the Cch -values for NaC and NaDC alone at 25 and 378C also increase linearly with total NaC or NaDC concentration, respec-

FIG. 16 Curves of the saturated amounts of solubilized cholesterol at 258C (a) and 378C (b) for the NaC–C10E8 system versus the total surfactant concentration with various mole fractions; mole fraction of NaC is indicated by key on ﬁgure. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 17 Curves of the saturated amounts of solubilized cholesterol at 258C (a) and 378C (b) for NaDC–C10E8 system versus the total surfactant concentration with various mole fractions; mole fraction of NaDC is indicated by key on ﬁgure.

tively. However, the slopes for each system are far lower than that for C10E8, and the diﬀerences in the Cch -values between 25 and 378C at each total concentration of NaC or NaDC alone are less than those for C10E8. These are reasons that the molecules of bile salts tend to form a rigid micelle by their strong cohesion, as bile salt molecules lack a polyoxyethylene chain. Furthermore, the Cch -values for NaDC alone at each temperature are larger than those of NaC alone. As mentioned in Section II.B.2, NaDC molecules, without a 7--hydroxyl group, would form more hydrophobic micelles in the solutions than would NaC molecules, with a 7--hydroxyl group, on the basis of the pyrene ﬂuorescence data. Accordingly, this large Cch -value of NaDC alone may be due to the high hydrophobicity of NaDC micelles. In the case of the mixed NaC–C10E8 and NaDC–C10E8 systems, each curve of the Cch -values at 25 and 378C also increased with total surfactant concentration. And the Cch -values at 378C for each mole fraction of bile salts in both the NaC–C10E8 and NaDC–C10E8 systems were larger than those of 258C, because of the dehydration of C10E8 molecules in the mixed micelles. The values of Cch for the NaDC–C10E8 system were also larger than those for the NaC–C10E8 system because of the high hydrophobicity of NaDC micelles. Interestingly, for both mixed systems, these curves tended toward a straight line for C10E8 alone near the CMC and became logarithCopyright © 2003 by Taylor & Francis Group, LLC

mic at low total surfactant concentrations. As mentioned in Section II.B.1, mixed micelles consisting of bile salts and C10E8 form C10E8-rich micelles near the CMC. Accordingly, this phenomenon is attributed to the C10E8rich micelles at low total surfactant concentration. (b) Dependencies of Cholesterol Solubilization with Respect to Mole Fraction of Bile Salts. The Cch -values at 25, 29, 33, and 378C in micellar solutions, of ﬁxed total surfactant concentration 25 mmol dm3 , as a function of the mole fractions of bile salts are shown in Fig. 18a for the NaC–C10E8 system and in Fig. 18b for the NaDC–C10E8 system. These values are listed in Tables 6 and 7. The Cch -values of NaC and NaDC alone at each of these four temperatures were considerably smaller than those of C10E8 alone. This reason is that the solubilization of cholesterol into bile salt micelles is hindered by the rigid micelles and the low aggregation numbers of bile salts. However, the Cch -values of NaDC alone at each temperature were larger than those of NaC alone, because of the high hydrophobicity of NaDC molecules.

FIG. 18 Plots of the saturated amounts of solubilized cholesterol at various temperatures for the NaC–C10E8 system (a) and the NaDC–C10E8 system (b) versus mole fraction of NaC or NaDC, respectively. Total surfactant concentration of each system is ﬁxed at 25 mmol dm3 . (a) Mole fraction of bile salt. (b) Mole fraction of bile salt. Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 6 Saturated Amount of Cholesterol and the Values of Various Thermodynamic Parameters in the Solution of the NaC–C10 E8 System at Total Surfactant Concentration of 25 mmol dm3 Mole fraction of NaC in the solution, XNaC

Saturated amount of cholesterol Cch (mmol/L)

258C

298C

338C

378C

258C

298C

338C

378C

Enthalpy of solubilization, HS!M (kJ/mol)

0.00 0.25 0.50 0.75 0.90 1.00

0.831 0.481 0.280 0.140 0.071 0.044

1.093 0.607 0.348 0.172 0.082 0.050

1.458 0.791 0.424 0.195 0.092 0.056

1.965 1.020 0.534 0.242 0.098 0.061

8.547 9.872 11.20 12.91 14.60 15.78

7.996 9.433 10.81 12.57 14.41 15.66

7.402 8.899 10.45 12.42 14.34 15.59

6.776 8.379 10.00 12.02 14.35 15.55

52.55 47.22 40.51 33.86 24.46 19.93

Free energy of solubilization GS!M (kJ/mol)

TABLE 7 Saturated Amount of Cholesterol and the Values of Various Thermodynamic Parameters in the Solution of the NaDC–C10 E8 System at Total Surfactant Concentration of 25 mmol dm3 Mole fraction of NaDC in the solution, XNaDC

Saturated amount of cholesterol Cch (mmol/L)

258C

298C

338C

378C

258C

298C

338C

378C

Enthalpy of solubilization, HS!M (kJ/mol)

0.00 0.25 0.50 0.75 0.90 1.00

0.831 0.560 0.379 0.264 0.226 0.198

1.093 0.731 0.487 0.327 0.268 0.244

1.458 0.978 0.605 0.409 0.333 0.299

1.965 1.240 0.793 0.504 0.407 0.341

8.547 9.500 10.46 11.34 11.72 12.06

7.996 8.976 9.974 10.96 11.45 11.69

7.402 8.375 9.564 10.55 11.06 11.33

6.776 7.895 9.009 10.15 10.70 11.15

52.55 49.52 45.88 41.06 37.58 35.12

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Free energy of solubilization GS!M (kJ/mol)

The Cch -values at each temperature, 25, 29, 33, and 378C, in both mixed systems decreased abruptly with the increase of mole fraction of bile salts, and these curves resembled the plots of the variation of mean aggregation numbers of the mixed micelles for bile salt–C10E8 systems as a function of the mole fraction, as shown in Fig. 11. These facts indicate that the Cch -values depend considerably on the mean aggregation number of the micelles. Furthermore, in both systems, the more the mole fraction of bile salts decreased, the larger the Cch -values grew with a rise in temperature, for each mole fraction of bile salts. This may be due to the increase of the hydrophobicity of C10E8 caused by the dehydration at the polyoxyethylene portion. (c) Thermodynamic Analysis of Cholesterol Solubilization. The standard free energy (Gs!M ) and the enthalpy (Hs!M ) of the solubilization, considered as the transfer of cholesterol from the solid state to the micellar environment, have been calculated from the Cch -values in order to discuss thermodynamically the cholesterol solubilities into the micelles of the NaC–C10E8 and NaDC–C10E8 systems [53,54,63,64]. Gs!M values of each mole fraction of bile salts and each temperature are given by Gs!M ¼ RT ln Xch

ð8Þ

where R is the molar gas constant, T is the absolute temperature, and Xch is the mole fraction of cholesterol in the solutions. Figure 19a shows plots of Gs!M -values for the NaC–C10E8 system at 25, 29, 33, and 378C versus mole fractions of bile salts. Similar curves for the NaDC–C10E8 system are shown in Fig. 19b. Gs!M -values for C10E8 alone were lower than those for bile salt alone. Gs!M for each mixed system increased with increasing mole fraction of bile salts, and the curves of the Gs!M -values in the low-mole fraction range of bile salts deviated downward with rising temperature. These facts suggest that C10E8 micelles are easier to solubilize the cholesterol into than micelles of bile salts, and the ability of C10E8 to solubilize cholesterol depends strongly on the rise in temperature. Furthermore, the Gs!M -values of NaDC alone at each temperature are lower than those of NaC alone. This suggests that the micelles of NaDC molecules without a 7--hydroxyl group tend to solubilize cholesterol more easily than those of NaC, and this may be due to the high hydrophobicity of an intramicelle of NaDC. The Gs!m -values for each system in Fig. 19 are positive, and this indicates that the solubilization of cholesterol from the solid state to the micellar environment is not spontaneous. This is because the cholesterol is little dissolved in water, and the standard free energy of cholesterol’s dissolution, considered as the transfer from the solid state to the water phase, Gs!w , is enormous (Gs!w at 258C is 30.5 kJ/mol [51]). Accordingly, one must consider a saturated amount of the solubilized cholesterol from the solid Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 19 Plots of the free energy of solubilization, considered as the transfer of cholesterol from the solid state to the micellar environment at various temperatures for the NaC–C10E8 system (a) and the NaDC–C10E8 system (b) versus mole fraction of NaC or NaDC, respectively. Total surfactant concentration of each system is ﬁxed at 25 mmol dm3 .

state to water phase (in the absence of a surfactant), and calculate the standard free energy of the solubilization of cholesterol considered as the transfer from the water phase to the micellar environment (Gw!M ). Consequently, the GW!M -values of each system at 258C were calculated, as shown in Table 8. From these results, the transfer of cholesterol from the water phase to the micellar environment in both systems is seen to be a natural process thermodynamically. On the other hand, the HS!M -values were calculated using HS!M ¼ R

d ln Xch dð1=TÞ

ð9Þ

As the saturated amount of the dissolved cholesterol in water was negligibly small, the HS!M -values were calculated without consideration of the cholesterol’s transfer from the solid state to the water phase. Plots of HS!M for both the single and the mixed micellar systems of NaC–C10E8 and NaDC–C10E8 versus mole fraction of bile salts are shown in Fig. 20. All HS!M -values for both systems are positive, and so the cholesterol solubilizations in both the NaC–C10E8 and NaDC–C10E8 systems are endothermic reactions. Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 8 The Free Energy of the Solubilization of Cholesterol Considered as the Transfer from the Water Phase to the Micellar Environment, GW!M , at 258C Mole fraction of bile salts in the solution, Xbile 0.00 0.25 0.50 0.75 0.90 1.00

Free energy of solubilization GW!M (kJ/mol) NaC–C10 E8 system

NaDC–C10 E8 system

21:97 20:65 19:32 17:61 15:92 14:74

21:97 21:02 20:06 19:18 18:80 18:46

For each mixed system, the HS!M -values decreased with increasing mole fraction of bile salts and showed breakpoints around the mole fraction of 0.75 for the NaC–C10E8 system and 0.60 for NaDC–C10E8. Above these mole fractions, HS!M decreased more steeply. These variations of

FIG. 20 Plots of the enthalpy of the solubilization of cholesterol, considered as the transfer from the solid state to the micellar environment, for the NaC–C10 E8 system (a) and the NaDC–C10 E8 system (b) versus mole fraction of bile salts. Total surfactant concentration of each system is ﬁxed at 25 mmol dm3 . Copyright © 2003 by Taylor & Francis Group, LLC

HS!M -values for each system are similar to that of 1/33 values discussed in Section II.B.2, and so the analyses of the micelles for both systems by ﬂuorescence measurements are considered to be related to the analysis of cholesterol solubilization by the thermodynamic evaluation of HS!M values. The I1 =I3 -value is known to be an excellent index of the polarity for the intramicelles in the probe microenvironment [43–45], and moreover, the micellar shape of the binary mixture is presumed to change from C10E8rich micelles to bile salt-rich micelles at each breakpoint mole fraction. These facts suggest that cholesterol solubilization in solutions of the NaC–C10E8 and NaDC–C10E8 systems is inﬂuenced by the hydrophobicity of the mixed micelles and the change of the micellar shape from C10E8-rich to bile salt-rich micelles. Comparing the NaC–C10E8 and NaDC–C10E8 systems, the HS!M values of NaDC alone are higher than those of NaC alone, and the diﬀerence in the slopes of the straight lines before and after the breakpoint for the NaDC–C10E8 system is smaller than that of the NaC–C10E8 system. From the results of analyses for the mixed micelles, NaDC molecules, without a 7-hydroxyl group, are considered to form the more hydrophobic and rigid micelles than NaC molecules and to be easier to mix with C10E8 molecules. These facts suggest that rigid micelles of NaDC molecules have been loosened by the rise in temperature, so that the cholesterol molecules are more easily solubilized into NaDC micelles.

2. Binary Mixtures of Epimer Bile Salts and ,!Ditetraethyleneglycoldodecyl Ether (C12 2E4 ) 1. Properties of Binary Mixed Micelles of ,!-Ditetraethylene. Glycol Dodecyl Ether(C122E4) and Bile Salts: Comparison with the Mixed System of Octaethylene Glycol Mono-n-Decyl Ether (C10E8). The conformation change of the mixed micelle is suggested to be due to the differences in the orientation of hydroxyl groups and in the conjugation of the terminal group. When an ,!-type surfactant [61] such as C122E4 [62], instead of ordinary nonionic surfactant C10E8, having a homogeneous polyoxyethylene oxide chain (EO) at both ends of a linear hydrocarbon chain is mixed in the bile salt solution, the properties of the mixed micelles are expected to be different from those of the conventional nonionic surfactants. In this paper, surface tension, polarity of intramicelles, mean aggregation number, hydrodynamic radius, and 1H NMR were measured for the following four mixed systems of bile salts and nonionic surfactants: C122E4 supplied from Nikko Chemicals was puriﬁed by gel chromatography (Wakogel C200, Wako Chemicals) with mixed solvents of acetone/n-hexane (1/1) and methanol/chloroform (1/1) [8–11], respectively. The structural formulas of C122E4 and C10E8 are shown in Fig. 21. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 21

Structural formulas of C10E8 and C122E4.

Figures 22a and b show the plots of the surface tension versus total surfactant concentration in the mixed surfactant systems of NaGCDC– C122E4, NaGCDC–C10E8, NaGUDC–C122E4, and NaGUDC–C10E8, respectively. These curves show a breakpoint corresponding to the CMC. CMC values for NaGCDC, NaGUDC, C122E4 and C10E8 were for about 2, 30, 2 and 1 mM, respectively. This means that NaGCDC, C122E4, and C10E8 molecules form micelles more easily compared with NaGUDC having a large CMC value since the NaGUDC molecule is hydrophilic. The CMC values for mixtures of bile salts and C122E4 did not change with the mole fraction of bile salt, but those for mixtures of bile salts and C10E8 changed largely. These CMC values were deviated from those of the ideal state, and the interaction parameter, , calculated from these CMC values by using regular solution theory [36] was about 0.9, 0.8, 3.0, and 0.8 for mixed systems of NaGCDC–C122E4, NaGCDC–C10E8, NaGUDC–C122E4, and NaGUDC–C10E8, respectively. Equilibrium surface tension for each system is plotted against the mole fraction of bile salt as shown in Fig. 22c. The values for the mixtures of bile salts and C122E4 were higher than those of the mixtures for C10E8. This means that the surface activity for the mixtures of bile salts and C122E4 was lower than those of the mixtures for C10E8. Further, the tendency for change of the equilibrium surface tension in lower ranges of mole fraction of bile salt is diﬀerent from in higher ranges, except for the system of NaGUDC–C122E4. It suggests that the micellar shape in lower ranges of mole fraction of bile salt is diﬀerent from in higher ranges. Moreover, the surface excess for each system on the water surface calculated by applying the Gibbs adsorption isotherm equation is plotted against the mole fraction of bile salt as shown in Fig. 22d. Surface excess in higher ranges of bile salts, except for the system of NaGUDC–C10E8, abruptly increased with the increase of mole fraction of bile salt. As with the case of equilibrium surface tension, it suggests that the micellar shape in lower ranges of mole fraction of bile salt is diﬀerent from in higher ranges. Figure 23 shows the plots of I1 =I3 -values for the four Copyright © 2003 by Taylor & Francis Group, LLC

systems versus the mole fractions of bile salts at constant total surfactant concentrations of 100 mM. Each curve for three mixed systems showed a distinct breakpoint, except a curve for the NaGUDC–C122E4 system, which has a slight breakpoint. The breakpoint means the transition point of intramicellar polarity. At the point, the micellar composition changes from nonionic surfactant-rich to bile salt-rich, and also the micellar shape probably changes from spherical to lamellar. These results coincide with those of surface tension. Two curves for NaGCDC–nonionic systems in Fig. 23 showed a breakpoint, and above the points, I1 =I3 -values for both curves decreased steeply. A11 I1 =I3 -values for the mixture of NaGCDC and C10E8 were lower than those for the mixture of NaGCDC and C122E4. This suggests that intramicellar environments of NaGCDC and C10E8 are more hydrophobic than those of NaGCDC and C122E4 mixtures. On the other hand, two curves for NaGUDC–nonionic systems in Fig. 23 showed diﬀerent tendency from those for NaGCDC–nonionic systems. I1/I3-values for the NaGUDC–C10E8 system decreased abruptly up to the breakpoint and increased suddenly above the point, whereas I1 /I3 -values for the NaGUDC–C122E4 system decreased gradually up to the breakpoint and decreased slightly above the breakpoint. All I1 /I3 -values for the NaGUDC–C122E4 system were above 0.95 and were higher than those of NaGCDC, having a small value of about 0.6. The intramicellar polarities for the mixed systems of NaGUDC are considered to be higher than those of NaGCDC. The reason why these diﬀerent phenomena appear above and below the breakpoints can be estimated as follows. First, there is an epimer relationship between NaGCDC and NaGUDC. Second, the molecular structure of C122E4 is diﬀerent from C10E8; their compactnesses in micelles are diﬀerent from each other. Figure 24 shows the mean aggregation number for the four mixed surfactant systems versus the mole fractions of bile salts at constant total surfactant concentrations of 50 mM. The mean aggregation numbers for each micelle of bile salts, C122E4 and C10E8, were about 15, 30, and 70, respectively. The values for mixed micelle of bile salts–C10E8 systems abruptly reduced by the slight addition of bile salts and then kept on decreasing, moderately. Compared with the case of bile salts–C10E8 mixed systems, the mean aggregation number for bile salts–C122E4 mixed systems slightly changed. On the other hand, those of bile salts–C122E4 were almost constant, from 30 to 13, in all ranges of mole fraction of bile salt because the values of C122E4 were almost the same as those of bile salts. Hydrodynamic radii of C122E4 and C10E8 were about 2.0 nm and 2.8 nm, respectively. Furthermore, the radii of mixed micelles of bile salts and nonionic surfactants steeply decreased with the increase of the mole fraction of bile salts. Copyright © 2003 by Taylor & Francis Group, LLC

(These data are not shown in the ﬁgure.) These results showed the same tendency as those of the aggregation number. Compared with the case for the mixed system of C10E8 and bile salts, the mixed micelle of C122E4 and bile salts have a small aggregation number regardless of these large hydro-

Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 22 Curves of the surface tension versus total surfactant concentration with various mole fractions of bile salts. (a) NaGCDC–C122E4 system; (b) NaGCDC– C10E8 system. Mole fraction of bile salt: * 0, ! 0.25, & 0.5, ~ 0.75, * 0.9, ^ 1.0; (c) Equilibrium surface tension versus mole fraction of bile salts. Systems: * NaGCDC–C122E4, ! NaGCDC–C10E8, & NaGUDC–C122E4, ~ NaGUDC– C10E8; (d) Surface excess versus mole fraction of bile salts. Systems: * NaGCDC–C122E4, ! NaGCDC–C10E8, & NaGUDC–C122E4, ~ NaGUDC– C10E8. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 23 Plots of I1 /I3 -values versus mole fraction of bile salts. Systems: * NaGCDC–C12 2E4 , ! NaGUDC–C10 E8 , & NaGUDC–C12 2E4 , ~ NaGUDC– C10 E8 .

FIG. 24 Plots of mean aggregation numbers versus mole fraction of bile salts. Systems: * NaGCDC–C12 2E4 , ! NaGCDC–C10 E8 , & NaGUDC–C12 2E4 , ~ NaGUDC–C10 E8 . Copyright © 2003 by Taylor & Francis Group, LLC

dynamic radii. Thus, the mixed micelle of bile salts–C122E4 mixed systems is considered to be loose while the mixed micelle of C10E8 and bile salts is rigid. Table 9 shows the longitudinal and transverse relaxation times of protons for bile salts assigned as shown in Fig. 21. Correlation times (c ) of these protons were calculated from longitudinal and transverse relaxation times under the hypothesis that the relaxation of 1H nuclei arises predominantly by dipole–dipole interaction [55–59] as reported previously [14,15]. Figure 25a–d shows the plots of c -values for assigned proton as shown in Fig. 21 versus the mole fraction of bile salts in the total concentrations of mixed surfactant systems for NaGCDC–C122E4, NaGCDC–C10E8, NaGUDC– C122E4, and NaGUDC–C10E8 of 100 mM, respectively. In the mixed systems of NaGCDC and nonionic surfactants, as shown in Fig. 25(a) and (b), all c -values of bile salt protons decreased by the addition of nonionic surfactant in higher ranges of the mole fraction of bile salt. This means that the rigid micelle of NaGCDC becomes loosely packed by the

TABLE 9 Longitudinal and Transverse Relaxation Times for Protons of Bile Salts in the Four Mixed Systems Mole fraction of bile salts system NaGCDC–C12 2E4

NaGCDC–C10 E8

NaGUDC–C12 2E4

NaGUDC–C10 E8

0.25 proton 7 23 21 19 18

T1

0.5

T2

505

0.9

1

T1

T2

T1

T2

T1

T2

T1

T2

561 394 54 378 53 464 55 484

88 63 61 60 60

596 436 396 487 509

85 70 57 56 57

598 440 417 500 516

69 64 52 52 53

622 468 443 526 540

58 59 46 45 45

69 42 49 43

597 434 405 519

72 61 54 51

594 436 416 517

69 67 51 51

622 468 443 540

58 59 46 45

546 181 352 452 471

0.75

7 23 21 18

368 501

79 554 388 44 394 37 515

23 21 18

412 475

400 59 71 439 69 72 508 68

422 64 446 62 519 62

442 62 461 55 537 55

484 53 494 47 574 47

23 21 19 18

373 443 496

396 42 48 410 51 53 480 55 51 544 52

435 400 485 549

454 443 483 559

484 494 494 574

Values in milliseconds.

Copyright © 2003 by Taylor & Francis Group, LLC

55 52 55 54

62 51 54 53

53 47 47 47

addition of nonionic surfactant. These tendencies in the NaGCDC systems are similar to the case in the NaGUDC systems as shown in Fig. 25 (c) and (d). Furthermore, T-values of the protons of the hydrophobic convex side of the

FIG. 25 Plots of correlation times versus mole fraction of bile salts. (a) NaGCDC– C12 E4 system; (b) NaGCDC–C10 E8 system; (c) NaGUDC–C12 2E4 system; (d) NaGUDC–C10 E8 system. Positions of protons: * 7, * 23, ! 21, & 19, * 18. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 25

Continued

NaGCDC molecule (Me18 and/or Me19) in the micelle of C122E4 were almost constant in lower ranges of the mole fraction of the NaGCDC. On the contrary, these values in the micelle of C10E8 increased. This suggests that the mobility of NaGCDC molecule in the micelle of C122E4 is higher than in the case of C10E8. Moreover, c -values of the protons of the hydrophobic convex Copyright © 2003 by Taylor & Francis Group, LLC

side of the NaGUDC molecule in the micelle of C122E4 decreased further in lower ranges of the mole fraction of NaGUDC, but those for C10E8 were almost constant. As with the case of NaGCDC, the mobility of the NaGUDC molecule in the micelle of C122E4 is considered to be higher than in the case of C10E8. In the range of lower mole fractions of bile salts, c -value of Me18 in the NaGCDC–C10E8 system became larger and the tendency was more remarkable compared with those in the NaGUDC–C10E8 system. The mobility of the hydrophobic convex side of the steroid in the NaGCDC molecule is considered to be more restricted than in the NaGUDC molecule. It is estimated that the NaGCDC molecule exists as dimer in the C10E8 micelle, while the NaGUDC molecule exists as monomer. Furthermore, the c -value of the protons of the hydrophilic side chain of bile salt (Me23) in the mixed system of bile salt and C10E8 became larger in lower ranges of mole fraction of bile salt compared with those in the mixed system of bile salt and C122E4. It implies that the interaction of the hydrophilic side chain in bile salt molecule with the polar group in the C10E8 molecule is stronger than that with the polar group in the C122E4 molecule. In the mixed system of NaGCDC and nonionic surfactant, the c -value of the proton of the hydrophilic concave side of NaGCDC (Me7) became smaller by the addition of nonionic surfactant. This suggests that the hydrogen bondings between bile salts decrease with an increase of the mole fraction of the nonionic surfactant, and as the hydrophilic concave sides of bile salt are away from polar moieties of nonionic surfactant molecules, their interactions are weak. Consequently, the schematic models for the mixed micelle of bile salt and nonionic surfactant as shown in Fig. 26 are supported by these results. The properties of binary mixed micelles of the NaGCDC–C122E4 system, NaGCDC–C10E8 system, NaGUDC–C122E4 system, and NaGUDC–C10E8 system are concluded as follows: (1) the behaviors of all four binary mixed systems are nonideal; (2) polarities in the mixed micelles containing C122E4

FIG. 26 Schematic models of the nonionic surfactant-rich micelles when the mole fraction of bile salt is below the breakpoint. (a) NaGCDC–C122E4 system and NaGUDC–C122E4 system; (b) NaGCDC–C10E8 system; (c) NaGUDC–C10E8 system. Copyright © 2003 by Taylor & Francis Group, LLC

are more hydrophilic than in the case of the mixed micelle containing C10E8, also, the components of the mixed micelles of all four mixed systems change from nonionic surfactant-rich to bile salts one, with the increase of the mole fraction of bile salts; (3) C122E4 molecules make the mixed micelles loose, and on the contrary, C10E8 forms more rigid mixed micelles than in the case of C122E4; (4) the possible schematic models of micelles as shown in Fig. 26 are concluded by mobilities of protons of bile salts in the micelles.

III. APPLICATIONS OF BILE SALTS A. Solubilities of Cholesterol Gallstones 1. Solubility in Micellar Solutions Dissolution of gallstone in vitro has been studied via cholesterol disk models [65–67]. Cholesterol is regarded as cholesterol monohydrate in bile, and so the dissolution of the cholesterol monohydrate is often discussed by comparison with that of the anhydrate. Recently, interesting results on the cholesterol dissolution mechanism have been reported. When cholesterol forms mixed micelles with both the conjugated bile salt (sodium glycochenodeoxycholate and sodium glycoursodeoxycholate) and lecithin, the amount of the dissolved cholesterol is very small. However, if mixed micelles consisting of cholesterol, the conjugate, and lecithin form a liquid crystal, the amount of dissolved cholesterol becomes large. Therefore, cholesterol gallstone is considered to be dissolved by forming this liquid crystal [68,69].

2. Solubility in Organic Solvents Ursodeoxycholic acid (UDCA) and chenodeoxycholic acid (CDCA), known as dissolving agents of cholesterol gallstone in humans, have been used extensively so far for clinical treatment. However, their solubilities and dissolution rates for gallstones have been reported to be lower than those of artiﬁcial dissolving agents. In the 1970s, monooctanoin (glyceryl-l-monooctanoate, MO) and d-limonen were found to have better dissolving ability than bile acids [57–61]; however, these were known to have some problems with dissolving abilities and side eﬀects. To look for the dissolving agents with superior dissolving ability to those of MO and d-limonen, we tried to measure the dissolution rates of a cholesterol monohydrate (ChM) disk as a model cholesterol gallstone in other organic solvents in vitro. The dissolution rates of a ChM disk in organic solvents were calculated by the Nernst equation [73] applied to the diﬀerence between the concentration of solute in bulk phase (Cb) and that of the saturated solution (Cs) as follows: J ¼ AðCs CbÞ=ðh=DÞ Copyright © 2003 by Taylor & Francis Group, LLC

ð10Þ

where J and A are the dissolving rate and the surface area of the ChM disk, respectively; h and D are, respectively, the Nernst diﬀusion layer thickness and diﬀusion coeﬃcient. Under a sink condition [74], Cs » Cb, Cb is negligible (Cb = 0) and Eq. (10) becomes ðJ=AÞ ¼ ðDCs=hÞ ¼ DCs=R

ð11Þ

where R is the total resistance to the diﬀusion controlled dissolution. Accordingly, the dissolution rates of a ChM disk per unit area ( f =A) are obtained by calculating an initial slope of the curve of time dependence of the dissolution of the ChM. These J=A-values of each organic solvent at 378C are listed in Table 10. From the results of J=A-values, we obtained some important conclusions [77–79]. Terpene derivatives were much better solvents for a ChM disk than MO. For molecules with the same functional group, a decrease in chain length tends to increase the J=A-values. For the same number of isoprene units, the following order of eﬀectiveness was observed: ketone derivatives > ester derivatives > alcohol derivatives. In the series of polyol derivatives, the J=A-value for the ethyleneglycol monooctanoate, EMO, was highest, and J=A-values for monoesters were higher than those for diesterin for molecules with the same functional group. Furthermore, in the case of methyl t-butyl ether, MTBE, the f =A-value for MTBE alone was 450 times of that for MO, and so MTBE was a much better solvent for a ChM disk. Also, MTBE emulsion, which was prepared by nonionic surfactants as a emulsiﬁer to avoid side eﬀects on gallbladder and other human tissue, was found to be as eﬀective as MTBE solvent for the dissolution of gallstones.

B. Calciﬁcation of Cholesterol Gallstones Treatment with glycoursodeoxycholic acid (GUDCA), well known as a dissolution agent for cholesterol gallstones, has been reported to be responsible for calciﬁcation on the surface of the gallstones in a gallbladder, sometimes preventing further dissolution of the stones [78,79]. In general, in the presence of egg lecithin (EL), the sodium salt of GUDCA is also known to produce the mesophase during a dissolution of ChM in vitro, and then the amount of the dissolved ChM increases because of the mesophase formation. On the other hand, treatment with glycochenodeoxycholic acid (GCDCA) is not responsible for calciﬁcation. Accordingly, this mesophase formation was expected to cause the calciﬁcation, and so we elucidated the mechanism or relation between mesophase formation and calciﬁcation by measuring the calcium carbonate solubility in varying aqueous mixtures of sodium glycochenodeoxycholate (NaGCDC), sodium glycoursodeoxycholate (NaGUDC), and EL in the range of pH from 7.5 to 9.0 in vitro and Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 10 J=A-Values of a ChM Disk in Various Solvents

Solvent MO (monooctanoin)

J=A (mg/cm2 /s)

Number of isoprenes or carbons

1.15

—

2.18 3.34 3.63 7.77 8.75 9.05 26.73 32.93 33.04 74.20

— 4 — 3 3 3 2 2 2 1

Terpene series 1. Alcohol derivatives DHT (dihydro--terpineol) GL (geranyllinallol) -T (-terpineol) PA-15 (dihydronerolidol) FOL (farnesol) ND (nerolidol) GOH (geraniol) LL (linallol) NR (nerol) POH (prenol) 2. Ester derivatives FAG (geranyl farnecylacetate) FAM (methyl farnecylacetate) LA (linalylacetate) PA (prenylacetate) 3. Ketone derivatives SK-18 (farnecylacetone) GA (geranylacetone) MH (methylheptenone)

4.89 14.95 26.72 82.67

5 3 2 1

11.00 42.35 158.26

3 2 1

Polyol derivatives series DC (diglyceryl C8-10 ester) TC (triglyceryl C8-10 ester) EMO (ethyleneglycol monooctanoate) EDO (ethyleneglycol dioctanoate) EM2EII (ethyleneglycol mono-2-ethyl hexanoate) ED2EM (ethyleneglycol di-2-ethyl hexanoate) PDH (propyleneglycol dihexanoate) PMO (propyleneglycol monooctanoate) PDO (propyleneglycol dioctanoate) PDD (propyleneglycol didecanoate) PMOL (propyleneglycol monooleate) PM2EH (propyleneglycol mono-2-ethyl hexanoate) PD2EH (propyleneglycol di-2-ethyl hexanoate) DDO (dipropyleneglycol dioctanoate) MTBE (methyl t-butyl ether)

3.14 4.23 17.40 12.41 13.64 11.06 15.92 14.72 9.80 4.73 2.00 11.23 9.16 3.51 516.52

8 8 8 16 8 16 12 8 16 20 18 8 16 16 —

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observing the surface of the ChM fragments and disks dipped in the solution [80]. In this section, we will describe the results for calcium carbonate solubility and dissolution of ChM in the NaGCDC–NaGUDC–EL–ChM systems. We prepared the various solutions as follows: 32mM EL was dissolved with total concentration of NaGCDC and NaGUDC of 100 mM in six diﬀerent ratios (NaGDCD:NaGUDC ¼ 0:5, 1:4, 2:3, 3:2, 4:1, 5:0), adjusting pH with Tris-HCl buﬀer. The ChM disk as the gallstone model and excess calcium carbonate were added to the solutions. After N2 gas had been sealed in the glass bottles containing the samples, these were incubated for 6 months at 378C in the agitated water bath. After 6 months, the amounts of calcium ion dissolved in the solutions were measured by the ﬂame absorption spectrometer, and the presence or absence of the liquid crystal was determined by polarized microscopy and roentgenogram to conﬁrm the deposition of calcium salt on the surface of the ChM disks. Figure 27 shows the pH dependencies of the amounts of calcium ion in the solutions. The amounts of calcium ion decreased with increasing pH. This suggests that the possibility of calciﬁcation on the surface of ChM disks under high pH is larger than that under low pH. From the results of the measurements of the solubility of ChM disks and the precipitation of calcium salts shown in Table 11, the precipitation of calcium salts for the samples of pH 7.5 was not observed on the ChM disks, and the ChM

FIG. 27 Calcium salt solubility in mixed systems of NaGCDC–NaGUDC–EL with ChM disk dipped in, as a function of pH after 6 months’ incubation Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 11 The Solubility of ChM Disks and the Precipitation of Calcium Salts Sample no. (pH 7.5) Precipitationa

1b

2c

3d

4c s

5f s

6g s

7h s

Sample no. (pH 8.0) Precipitation

8

9

10

11

12

13 þ

14 þ

Sample no. (pH 8.5) Precipitation

15

16

17

18

19 þ

20 þ

21 þ

Sample no. (pH 9.0) Precipitation

22

23

24

25 þ

26 þ

27 þ

28 þ

a +: The precipitation of calcium salts was observed. : The precipitation of calcium salts was not observed. s: The ChM disk was soluble. b Nos. 1, 8, 15, 22: blank (buffer—ChM disk). c Nos. 2, 9, 16, 23: NaGCDC 100 mM, NaGUDC 0 mM, EL 32 mM, ChM disk. d Nos. 3, 10, 17, 24: NaGCDC 80 mM, NaGUDC 20 mM, EL 32 mM, ChM disk. e Nos. 4, 11, 18, 25: NaGCDC 60 mM, NaGUDC 40 mM, EL 32 mM, ChM disk. f Nos. 5, 12, 19, 26: NaGCDC 40 mM, NaGUDC 60 mM, EL 32 mM, ChM disk. g Nos. 6, 12, 20, 27: NaGCDC 20 mM, NaGUDC 80 mM, EL 32 mM, ChM disk. h Nos. 7, 14, 21, 28: NaGCDC 0 mM, NaGUDC 100 mM, EL 32 mM, ChM disk.

disks from samples no. 4 to no. 7 were completely dissolved. However, precipitation for samples of pH 8.0, 8.5, and 9.0 were observed on the ChM disks of no. 13 and no. 14 at pH 8.0, no. 19, no. 20, and no. 21 at pH 8.5, and no. 25, no. 26, no. 27, and no. 28 at pH 9.0. Also, the gelation took place on the surface of most of the calciﬁed ChM disks, and in particular, as shown in Table 12, the results of the calciﬁcation on the ChM disks TABLE 12 Mesophase Formation in the Mixed Systems of NaGCDC–NaDUDC–EL–ChM Sample no. (pH 7.5)a Mesophase formationb

1

2

3

4

5 þ

6 þ

7 þ

Sample no. (pH 8.0) Mesophase formation

8

9

10

11 þ

12 þ

13 þ

14 þ

Sample no. (pH 8.5) Mesophase formation

15

16

17

18 þ

19 þ

20 þ

21 þ

Sample no. (pH 9.0) Mesophase formation

22

23 þ

24 þ

25 þ

26 þ

27 þ

28 þ

a

See Table 10 for composition of samples. þ: The mesophase formation was observed. : The mesophase formation was not observed. b

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resembled the observations of mesophase formation in the mixed systems of NaGCDC–NaGUDC–EL–ChM. Accordingly, the calciﬁcation on the surface of the gallstone is considered to be caused by the low solubility of calcium ion and this mesophase formation in bile [81,82].

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

World Encyclopaedia. Heibonsha, 14:561, 1967. A. Hofmann and K. Mysels. Colloids Surf., 30:145–173, 1988. M.C. Carey. In I. Arias, H. Popper, D. Schachter, and D.A. Shafritz, eds. The Liver. New York: Raven Press, 1982. T. Hoshita, S. Nagayoshi, and T. Kazuno. J. Biochem., 54:369, 1963. A.F. Hofmann and H.S. Mekhjian. In P.P. Nair and D. Kritchevsky, eds. The Bile Acids. New York: Plenum Press, Vol. 2, 1973, p 103. M.C. Carey, S.F.J. Wu, and J.B. Watkins. Biochim. Biophys. Acta, 575:16, 1979. M. Ueno, Y. Kimoto, Y. Ikeda, H. Momose, and R. Zana. J. Colloid Interface Sci., 117:179, 1987. H. Asano, K. Aki, and M. Ueno. Colloid Polym Sci., 267:935, 1989. H. Asano, A. Murohashi, and M. Ueno. J. Am. Oil Chem. Soc., 67:1002, 1990. H. Asano, M. Yamazaki, A. Fujima, and M. Ueno. J. Jpn. Oil Chem. Soc., 40(4):293, 1991. H. Asano, C. Izumi, Y. Sano, Y. Tabata, and M. Ueno. J. Am. Oil Chem. Soc., 70:693, 1993. M. Ueno, K. Suzuki. S. Nakagawa, K. Tateiwa, H. Asano, and Y. Tabata. J. Jpn. Med. Soc. Biol. Interface, 24:28, 1993. M. Ueno, K. Suzuki, S. Koyama, K. Takata, H. Asano, and S. Nagatome. J. Jpn. Med. Soc. Biol. Interface, 25:19, 1994. K. Suzuki, T. Hasegawa, Y. Takamura, K. Takahashi, H. Asano, and M. Ueno. Langmuir, 12:5536, 1996. Y. Takamura, S. Nakagawa, K. Suzuki, K. Takahashi, H. Asano, G. Sugihara, and M. Ueno. Colloid Surf. B, 7:239, 1996. M. Ueno, M. Obata, and Y. Kimoto. J. Jpn. Med. Soc. Biol. Interface, 15:45, 1982. D.M. Small. In P.P. Nair and D. Kritchevsky, eds. The Bile Acids, New York: Plenum Press, Vol. 1, 1971, Ch. 8, p 249. M.C. Carey and D.M. Small. Am. J. Med., 49:590, 1970. M.C. Carey and D.M. Small. J. Clin. Invest., 61:998, 1978. N.A. Mazer, G.B. Benedek, and M.C. Carey. Biochemistry, 19(4):601, 1980. K. Muller. Biochemistry, 20:404, 1981. H. Igimi and M.C. Carey. J. Lipid Res., 21:72, 1980. H.Y. Saad and W.I. Higuchi. J. Pharm. Sci., 54:1205, 1965. H. Igimi and M.C. Carey. J. Lipid Res., 22:254, 1981.

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K. Akasaka and T. Imoto. Pulse and Fourier Transform NMR. Kyoto: Yoshioka, 1976, p 61. S. Lusse and K. Arnold. Macromolecules, 29:4251, 1996. W.R. Carper and C.E. Keller. J. Phys. Chem. A, 101:3246, 1997. R. Kimmich. NMR Tomography Diﬀusiometry Relaxometry. Berlin: Springer-Verlag, 1997, p 102. J. Zhao and B.M. Fung. Langmuir, 9:1228, 1993. E.D. Barton. Measurement of Suspended Particles by Quasi-Elastic Light Scattering. New York: John Wiley and Sons, 1983, p 3. M. Ishikawa, K. Matsumura, K. Esumi, K. Meguro, W. Binana-Limbele, and R. Zana. J. Colloid Interface Sci., 151:70, 1992. M. Ueno, et. al. J. Jpn. Oil Chem. Soc., 49(1), 2000. Y. Moroi, H. Noma, and R. Murata. J. Phys. Chem. 87:872, 1983. J.G. Weers. J. Am. Oil Chem. Soc., 67:340, 1990. K.M. Feld and W. Higuchi. J. Pharm. Sci., 70:717, 1981. K.M. Feld and W. Higuchi. J. Pharm. Sci., 70:723, 1981. M. Vadnere and S. Lindenbaum. J. Pharm. Sci., 71:875, 1982. O.I. Corrigan, C.C. Su, W.I. Higuchi, and A.F. Hofmann. J. Pharm. Sci., 69:870, 1980. H. Igimi, S. Asakawa, D. Watanabe, and H. Shimura. Gastroenterologia Japonica, 18:93, 1983. J.L. Thistle, G.L. Carlson, A.F. Hofmann, and V.K. Babayan. Gastroenterology, 72:1141, 1977. T.R. Gadacz. Surgery, 89:527, 1981. J.L. Thistle, G.L. Carlson, A.F. Hofmann, N.F. Larusso, R.L. Maccarty, G.L. Flynn, W.I. Higuchi, and V.K. Babayan. Gastroenterology, 78:1016, 1980. T.R. Gadacz. J. Surg. Res., 26:378, 1979. J.L. Thistle, G.L. Carlson, N.F. Larusso, and A.F. Hofmann. Gastroenterology, 74:1103, 1980. W. Nernst and E. Brunner. Z. Phys. Chem., 47:52, 1904. K.W. Kwan, W.I. Higuchi, A.M. Molokhia, and A.F. Hofmann. J. Pharm. Sci., 66:1094, 1977. M. Ueno, K. Fukuda, and K. Seaki. J. Jpn. Oil Chem. Soc., 35:182, 1986. M. Ueno, K. Fukuda, and K. Seaki. J. Jpn. Med. Soc. Biol. Interface, 17:34, 1986. M. Ueno K. Seaki, H. Nakata, F. Fukuda, N. Yamashita, K. Yamamoto, R. Tsuchiya, and K. Matsumoto. J. Jpn. Med. Soc. Biol. Interface, 19:19, 1988. R. Raedsch, A. Stiehl, and P. Czygan. Lancet, Dec. 5, 1981. H. Igimi, M. Tamesue, Y. Ikejiri, and H. Shimura. Life Sci., 21:1373, 1977. M. Ueno, H. Asano, N. Inoue, and K. Kamisaka. J. Jpn. Med. Soc. Biol. Interface, 16:6, 1985.

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5 Characterization and Functionalization of Biosurfactants YUTAKA ISHIGAMI Tokyo Gakugei University and Meisei University, Tokyo, Japan, and Dong-Woo Fine-Chem Co. Ltd., Kyunggi-do, South Korea

I.

INTRODUCTION

Synthetic chemicals from petroleum origins are now coming at a turning point for their hazardous problems to living organisms. Concerns about environmental protection and the safety for health have introduced an interest in developing biomaterials such as naturally occurring surfactants (biosurfactants), biodyes, biopolymers, and ﬁne chemicals [1,2]. It is historically signiﬁcant that many naturally occurring surfactants of animal and plant origins have contributed to daily lives. Biomembranes present a prosperous museum of natural amphiphiles [3]. Some part of them have been industrially produced as chemicals. However, their supplying volume sometimes has been unstable depending on the unusual climate and natural calamity. It has been reported in the R & D studies of single-cell proteins since 1969 that some part of hydrocarbon-assimilating bacteria excrete surface-active substances. These microbial surfactants are classiﬁed as biosurfactants—microbial biosurfactants, bioemulsiﬁers, and so on [4,5]. The merits of microbial production processes include (1) the ease of cultivation due to the establishment of fermentation industry, (2) the higher growth rate of microbes, (3) the eﬃcient production rate of biosurfactants, and (4) the expectation of ﬁnding new functional materials. The items in (3) and (4) are now being developed [6]. Characterization of biosurfactants is described in the ﬁrst edition of this book [7].

II. STRUCTURAL FEATURES OF BIOSURFACTANTS Examples of biosurfactants are shown in Table 1. Biosurfactants have proper chemical structures diﬀerent from ordinary synthetic surfactants in Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 1 1.

2. 3. 4. 5. 6.

7.

8. 9.

Naturally Occurring Surfactants

Bile acid (cholesterol derivatives) [8] Absorption enhancers of lipid nutrients through mammalian intestines on the basis of their emulsifying action Gastric juice of the Crustacea (N-acylhydroxyproline-taurine etc.) [9] Emulsifying action Lung surfactant (complex of phospholipids and proteins) [8] Forming alveolar lining layer and lubricating respiratory action Cornea surface amphiphile (mucopolysaccharides) [10] Spreading of aqueous tear layer on cornea surface Amphiphile on mucous membrane of middle ear (phospholipids) [11] Control of ear pressure Milk fat globule membrane (MFGM, complex of lipoprotein and phospholipids) [12] Stabilization of milk fat by capsulation and adsorption Amphiphile of soapﬁsh (peptide derivative) [13] Surface tension lowering at the gills of small ﬁshes for escaping from bigger ﬁshes Saponin (glycyrrhizin, quillaia saponin, aescin, etc.) [14] Microbial biosurfactants [7] Enhancement of taking-in and assimilation of hydrocarbons by microorganisms

both hydrophilic and hydrophobic portions as surfactants (Fig. 1). This is ascribed to their structural features as shown in Table 2. Such features seem to bring about both bulky molecular and multifunctional chemical structures (Fig. 2). It may be expected that the proper structures of biosurfactants produce new functions.

III. PRODUCTION OF BIOSURFACTANTS Natural surfactants such as rosin, saponins, and phospholipids are commercially available. Shellac is from insects, and lanolin is from wool, and others are listed in Table 1. Table 3 shows production procedures of biochemicals and biomimetic surfactants as hybrids of natural raw materials [15]. Microbial biosurfactants are produced by the bioindustry process using growing cells or enzymes from hydrocarbons as the carbon source, sometimes from ethanol, glycerol, glucose, and so on. It is noted that major biosurfactants are produced Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 1 Correlation between the structural factors of surfactants and their properties and actions. (From Ref. 7.)

by hydrocarbon-assimilating bacteria. Table 4 is an example of the comparison of the production eﬃciency and the selectivity of homologous rhamnolipids. Resting cells produce the largest yield compared with growing cells and immobilized ones [16]. Otherwise, hydrocarbon-assimilating bacteria can take oil droplets via hydrophilic cell surface by diﬀusion/active transport inside the cell under the support of biosurfactants [17]. The details of production of typical biosurfactants are described [18], and biosurfactants are listed [19]. Enzymatic syntheses of biosurfactants are carried out using resting cells of producible microbes and their isolated enzymes [20,21]. A typical biosurfactant production procedure of corynomycolic acid is shown in Fig. 3.

IV. DEVELOPMENT OF BIOSURFACTANTS Recent development of biosurfactants is described individually here in addition to in the preceding publication [7].

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TABLE 2

Structural Features of Naturally Occurring Surfactants

Hydrophobic moieties 1. Acyl Hydroxyfatty acids Peculiar fatty acids Fatty acids Saturated $ Unsaturated Even number $ Odd number Linear alkyl chain $ Branched 2. Steroid 3. Isoprenoid Hydrophilic moieties 1. Ions 2. Hydroxyl 3. Glycerides 4. Glycerylether 5. Saccharides Trehalose Sophorose Glucose Glucosamine Lipopolysaccharides 6. Lipoamino acids 7. Peptides 8. Tricarboxylic acid cycle

Corynomycolic acids, lipid A Mycolic acid

alkyl chain Phytosterol, bile acid conjugates, saponin Saponin Anion, cation, ampholyte Phospholipids, H13A biosurfactant Archebacteria Microbes, insects Sophorose lipid Glucose lipid, acylglucose Chitin, hyaluronic acid, emulsan Thigloyl tetraglucose, saponin Peptide lipids, surfactin Spiculisporic acid, agaricic acid

Source: Ref. 7.

A. Spiculisporic Acid Spiculisporic acid, (4S,5S)-4,5-dicarboxy-4-pentadecanolide, is a polyfunctional fatty acid from microbial origin as shown in Fig. 4. Tabuchi et al. [23,24] realized a high-yield production (110 g/l culture broth) from glucose as the sole carbon source using Penicillium spiculisporum Lehman No. 10-1. Spiculisporic acid (abbreviated as S-acid below) is excreted from the microbes and is accumulated into the culture broth in a lower pH medium as 60% carbon recovery compared with the carbon content of glucose. Neutralized and saponiﬁed products of spiculisporic acid comprise polyfunctional anionic surfactant homologues. About the neutralization of the two carboxylic moieties, the 4-positioned carboxylic moiety of spiculisporic acid is most susceptible to neutralization, competing with the 5-positioned one according to 13 C NMR spectroscopic results [25]. Its lactone ring Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 2 Comparison of the chemical structure of biosurfactants with synthetic oligosoap and polysoap. (From Ref. 7.)

TABLE 3 Production of Biochemicals and Biomimetic Surfactants Methods

Procedure

Bacterial

Fermentation

Enzymatic

Hydrolysis

Transfer Synthesis

Solvent

Fractionation

Chemical

Hydrolysis Ester exchange Synthesis Modiﬁcation

Biochemicals Xanthan gum, polysaccharide AX Cardiolipin Cyclodextrin Protein hydrolysate Lysolecithin Lysophosphatidic acid Transphosphatidylated lecithin Sugar ester N-acyl amino acid Leucine SDS-gelatin Mono or diacylglycerol Proteose-peptone Fractionated lecithin Phytoglycolipid Protein hydrolysate, lysolecithin Mono or diacylglycerol Soap, sugar ester Acetylated lecithin Acetylated protein Hydroxylated lecithin

Source: Ref. 15.

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TABLE 4 Rhamnolipid Formation by Pseudomonas spec. DSM 2874. Inﬂuence of Different Reaction Conditions on the Conversion Yield (g product/g carbon substrate) and Product Composition Product composition (%) Conversion yield (g/g)

R1

R2

R3

R4

Growing cells No limitation N limitation

0.04 0.18

50 65

— —

50 35

— —

Resting cells C-source: n-alkanes, 308C C-source: glycerol, 308C C-source: n-alkanes, 378C

0.23 0.10 0.23

42 22 57

15 15 —

41 62 43

2 1 —

Immobilized cells C-source: glycerol, 308C

0.11

22

15

62

1

Reaction conditions a

b

c

R1 and R3 are the same as R1 and R3 in Fig. 9. R2, which has sole 3-hydroxydecanoic moiety, is an analog of R1 prepared by the b and c procedures. R4, which has sole 3-hydroxydecanoic moiety, is an analog of R3 prepared by the b and c procedures. Source: Ref. 17.

FIG. 3 A typical time course of biosurfactant production (corynomycolic acid) using the growing cells of Corynebacterium lepus in a 1 kL-tank scale. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Spiculisporic acid (abbreviated as S-acid) and its lactone-ring cleaved acid (open ring acid, O-acid).

cleaves on heating in aqueous media. Trisodium salt of spiculisporic acid, trisubstituted sodium salt of 4-hydroxy-1,3,4-tetradecanetricarboxylic acid (abbreviated as O-acid), is hydrophilic and shows buﬀering and metal sequestration actions [25], a considerable hard-water tolerance in spite of anionic surfactant [26]. Its monosodium salt is more surface-active than diand tri-sodium salt, having a mild pH of 6.1 in the 0.1% solution and an emulsiﬁer for the emulsion polymerization of ethyl acrylate and methyl methacrylate [27]. It was found that alkylamine salts had a large surface activity in smaller HLB values by balancing the hydrophilicity and lipophilicity of spiculisporate [28]. Alkylamine salts are more surface-active than sodium salts, as shown in Fig. 5. Di-neutralized n-hexylamine salt of spiculisporic acid (S-2n-HA) showed the largest surface tension lowering capacity of all, and the cmc (surface tension at critical micelle concentration) was reached at 27 mN/m. Monosubstituted n-hexylamine salt (S-1n-HA) and disubstituted 2-ethylhexylamine salt of O-acid (O-2EHA) exhibited an excellent emulsifying action for cotton seed oil (required HLB 10) and kerosene (required HLB 12.5) as shown in Table 5, and dispersing action for phthalocyanine blue) and carbon black in water as summarized in Table 6 [28]. Such large capacities may be attributed to their vesicle formation (0.1– 10 mm in the size by TEM) in water [29] for the enhancement of the entrapment of oils and dispersoids inside the increased hydrophobic domains. Sodium spiculisporate is used as the ingredient of the coloring material for the concrete surface design in contact with the surface on the concrete Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Surface tension versus concentration plots of alkylamine salts of spiculisporic acid and open ring acid at 308C. (From Ref. 28.) S-2cHA: dicyclohexylamine salt of S-acid, S-2n-HA: di-n-hexylamine salt of S-acid, O-2-n-HA: di-n-hexylamine salt of O-acid, O-2EHA: di-2-ethylhexylamine salt of O-acid.

placing [30]. In detail, a mixed aqueous solution of spiculisporate and ﬂuorocarbon-type surfactant contributes to painting, but also stains its surface layer. Spiculisporate exerts the dispersing action of dyes and pigments in a higher pH region, while a ﬂuorocarbon-type surfactant has strong penetrating and dispersing actions. There are many proposals to the neutralized and saponiﬁed derivatives of spiculisporic acid for potential application to antistatic and antirusting agents [31], emulsiﬁers [31,32], thickeners [33], rhodamine-type dye [34], surface-active ﬂuorescent dye for monitoring the hydrophobicity and ﬂuidity of the environment where the surface layer of coatings is [35], detergent [36], geling agent [37], and biodegradable polyesters [38]. Spiculisporic acid N-methyl formamide provides an electrolytic solution more stable in a range of 55 to þ1258C than the conventional compound of maleic acid N-methyl formamide [39]. Spiculisporic acid tetCopyright © 2003 by Taylor & Francis Group, LLC

TABLE 5 Emulsifying Action of Alkylamine Salts of Spiculisporic Acid Emulsifying capacity*

S-1 n-HA S-1 n-HA S-1 n-HA S-2 n-HA S-2 n-HA S-2 c-HA S-2 EHA O-2 n-HA O-2 EHA O-2 EHA O-2 EHA SDS NP-9 NP-15

Concn. (%)

Cotton seed oil

Kerosene

Dimethylphthalate

0.1 0.5 1.0 0.5 1.0 0.5 0.5 0.5 0.1 0.5 1.0 0.5 0.5 0.5

0 75 77 13 67 0 43 55 68 41 29 72 87 78

17 77 89 0 0 0 97 30 78 60 36 61 84 72

8 0 0 0 0 0 4 0 0 29 0 0 7 8

Source: Ref. 28. *Emulsifying capacity was measured by observing oil, emulsion, and water layers with time (5–120 min.) at 908C using stoppered 30-ml volumetric test tube containing the emulsion prepared by mixing a sample solution (3 ml) and oil (2 ml). Emulsifying rate (%) was calculated by (emulsiﬁed area of oil layer/2 ml oil layer) 100 from the height of emulsifying layer vs. time (5–120 min.) plot. (From Ref. 65.)

ramethylammonium salt can produce an electrolytic solution for operating an electric condenser with a larger capacity for voltage endurance in comparison with conventional maleic acid tetraethylammonium salt [40]. In electrophotography where latent electrostatic images are obtained by exposure to an electrostatically changed optical semiconductor and are developed with toner particles for electrostatic printing and information record [41]. Spiculisporic acid 1-n-hexylamine and monosodium salts, diethyl spiculisporate, and spiculisporic acid anhydride were eﬀective surfactants in the preparation of an aqueous rolling agent with corrosion inhibiting action [42], curing agent for cross-linking epoxy resins [43], and an oxygen supply enhancer from hemoglobin [44]. The Pt(II) complex of spiculisporic acid (Fig. 6) was found to act as anticancer drug [45]. N-alkylamide and isocyanate adducts of spiculisporic acid were prepared for cosmetic formulations

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TABLE 6

Dispersing Capacity of Sodium Salt of Rhamnolipids (RA-Na and RB-Na) Stability of dispersion**

Stability of dispersion**

S-1 n-HA S-1 n-HA S-2 n-HA S-2 n-HA S-1 c-HA S-2 c-HA S-2 c-HA S-2 EHA NP-9 A. OT Water

Conc. (%)

Dispersing Capacity (%)*

0.1 0.5 0.1 0.5 0.1 0.1 0.5 0.05 0.1 0.1

29 53 66 50 13 7 19 0 56 46 7

4h

24 h

17.5 30.0 27.0 28.3 6.1

17.0 24.8

Concn. (%)

Dispersing Capacity (%)**

4h

24 h

28.3

O-1 O-1 O-2 O-2

n-HA n-HA n-HA n-HA

0.1 0.5 0.1 0.5

0 0 24 48

6.2 28.2

28.0

22.0 22.3

O-2 O-2 O-2 O-2

c-HA EHA EHA EHA

0.5 0.05 0.1 0.5

0 62 67 69

30.0 30.0 30.0

30.0 30.0 30.0

6.5 23.8 24.3

Biosoap

Source: Ref. 28. *aSumitomo cyanine blue HB, Av. 2.0 m. *Suspensions containing dispersoid were allowed to stand for 4 h after mixing the aqueous sample solution with dispersoid. The degree of dispersing capacity was evaluated from the turbidity of the solution at 445 nm. **The stability of dispersion was determined by the height of the sedimented boundary of suspension at the scale of the 30-ml volumetric test tube after standing 4 and 24 h. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 6

Pt(II)-spiculisporic acid complex.

[46]. Spiculisporic acid anhydride (Fig. 7) is easily prepared on heating spiculisporic acid in vacuum. This shows a good metal sequestration action for Ca2þ , Cu2þ , and Zn2þ [47] and absorbs on the surfaces of inorganic materials such as titanium dioxide [48].

B. Sophorolipids Sophorolipids (Fig. 8) have been expected to develop their industrial and housefold applications in addition to the current cosmetic formulation, as they will be supplied in reasonable prices as a kind of ﬁne biochemical. There appear new proposals of high-yield production procedures of sophorolipids having 320 g/l culture broth from the combination of glucose and ethylesters of long-chain fatty acids as the carbon sources using Candida bombicola [49] and having attained 700 g/l [50]. The major components are 17-hydroxyoctadecanoic acid and its corresponding lactone. Sophorolipids are a waxy substance at room temperature and consists of more than eight homologous compounds on the basis of sophorose backbone skeleton. Chromatographically puriﬁed sophorolipids are less water-soluble (70 mg/l), are more surface-active (cmc ¼ 36 mN=m, cmc ¼ 10 mg/l), and have a stronger cytotoxity LC50 ¼ 15 mg/l) than crude ones [51]. Sophorolipids showed the action of the growth enhancer of hydrocarbon-assimilating microbes [52] and the eﬀectiveness for the improvement of the texture aging of bread and the baking volume of bread rolls in bakery products [53,54]. There are eﬀorts to get well-deﬁned pure sophorolipids analogs by

FIG. 7

2-(2-carboxyethyl)-3-decyl maleic anhydride.

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FIG. 8 Sophorolipid homologues.

chemical synthesis [55] and enzymatic synthesis [56] for the evaluation of the surface activity and the biological activity. Chemical modiﬁcations of sophorolipids are ordinary procedures for applications: deacetyl-, lactonering cleaving, esters with C1C10 alcohol [57,58], acid amide [59], propylene oxide adducts [58]. They are also useful as surfactants for the decontamination process of soil that is polluted by waste oils [60,61]. Sophorolipids are applied now in the cosmetic formulation in the propylene oxide adducts [57] and as a detergent for the dishwasher which has low foaming and biodegradable properties as an alternate to pluronics [62].

C. Rhamnolipids There are two kinds of rhamnolipid analogs with rhamnolipid A and B (abbreviated as RA and RB) and without deconoate residue, rhamnolipid 1 and 2 (abbreviate as R1 and R2 below), as shown in Fig. 9. The CPK model of RB is illustrated in Fig. 10, which is understandable by taking into account the bulkiness of the RB molecule in comparison with conventional surfactants. The yield of the bioindustry process was 14 g/l culture broth in the total of RA and RB [63], and 118 g/l in R1 and R2 [64], respectively. RA and RB have both anionic (carboxylic moiety) and nonionic (rhamnose residues) characters and show strong surface activities especially in alkaline media. The cmc values were around 105 M and cmc attained 28 mN/m in the PBS buﬀer (pH 7.35). The interfacial tension at the 0.1% aqueous solutions and kerosene was 0.2 mN/m (RA) and 3.2 mN/m (RB) in pH 7.35. RA and RB formed vesicle (pH 5.8–4.3) and lamella (pH 6.5–6.0) in lower pH conditions [65]. The micelle aggregation number was 56 (RA) and 8.5 (RB) in PBS buﬀer (pH 7.35). In this manner, RA and RB morphologically changed their aggregation structure depending on the environmental Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Rhamnolipid homologues.

pH values. The emulsifying and dispersing actions were good even in the lower concentration region around 0.01% because of the low cmc values, as shown in Table 7 [66]. Ishigami et al. [67] prepared methylester of RB from the aspect of the ordering character of the hydrophobic and hydrophilic portions of RB and compared with the surface activity of RB with that of RB methylester (nonionics). RB methylester was larger for the hydrophobic aﬃnity than RB in decreasing the interfacial tension lowering and increasing the wetting actions as shown in Table 8, while the hemolytic action of RB methylester was reduced. The wetting actions of RB and RB methylester (RB-Me) are shown in Fig. 11. A coproduction procedure of RA and RB and pyocyanine was proposed from the viewpoint of an intensive biochemical production [68]. Rhamnolipids are also utilized as a source of L-rhamCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 10 CPK model of rhamnolipid B (RB) compared with sodium dodecylsulfate (SDS). (From Ref. 7.)

TABLE 7 Dispersing Action of RA-Na and RB-Na (-Cu phthalocyanine blue) Surfactant

0.10%

0.01%

44 75 33 71 7

36 46 23 37 7

A-Na B-Na SDS NP-11 Water

(Carbon black) 0.10%

0.01%

30 23 4 89 2

14 23 3 8 2

A-Na B-Na SDS NP-11 Water Source: Ref. 66.

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TABLE 8 Surface Activity of Rhamnolipid B Sodium Salt (RB-Na) and Rhamnolipid B Methylester (RB-Me)

cmc interfacial tension for octane cmc (ANS ﬂuorometry)

Rhamnolipid B (RB-Na)

Methyl ester of rhamnolipid B (RB-Me)

28.0 mN/m 3.5 mN/m (0.1%) 3:15 104 M (0.026%)

30.6 mN/m 0.1 mN/m (0.01%) 4:95 104 M (0.040%)

Source: Ref. 67.

nose [69] for an intermediate of a food ﬂavor and ﬁne chemicals. Zhang et al. [70] report that R2 methylester enhanced hexadecane degradation by hydrocarbon-assimilating microbes that had high cell surface hydrophobicity, much more than that of R2. It was also reported that R1 showed big dispersing action for octadecane as the result of the vesicle and lamella formation of R1 for the remediation of waste oil treatment [71]. It was found that R1 and R2 containing a crude medium (0.3–0.5%) enhanced the removal of hydrophobic compounds like naphthalene, anthracene, and octadecane, etc. into aqueous phase from soil (sandy loam, silt one)

FIG. 11 Wetting action of RB-Na and RB-methylester (RB-Me) for ﬁve kinds of polymer surfaces having diﬀerent c -values. PE, polyethylene; PS, polystyrene; PMMA, polymethyl methacrylate; PE, polyethylene terephthalate. (From Ref. 67.) Copyright © 2003 by Taylor & Francis Group, LLC

by solubilization and mobilization [72,73,74] as well as the solubilization of pesticides [75]. Nakata et al. [76] propose a total system of spilled oil treatment using rhamnolipids (R1 and R2) as an eﬀective emulsiﬁer for the mousse oil production and for the bioremediation process by environmental hydrocarbon-assimilating bacteria. A selected Pseudomonas aeruginosa (rhamnolipid-producing bacterium) for bioremediation and waste oil treatment was patented as an example [77]. Tan et al. [78] further found the complexation capacity of rhamnolipids with heavy metals such as cadmium for the environmental remediation. In detail, 92% of Cd2þ (0.72 mM) was complexed by 7.3 mM rhamnolipids, and the maximum complexation capacity of the rhamnolipids was 0.2 Cd2þ /rhamnolipid on a molar basis.

D. Trehalose Lipids Trehalose lipids (Fig. 12) seem to be given attention in relation to the current interest in trehalose as an antifreeze for foods and biotechnological purposes. Furthermore, chemical analyses of trehalose derivatives are capable by learning the specialties of the microbially produced trehalose lipids. There are a variety of reports about trehalose lipids such as freeze-tolerance of baker’s yeast [79], prolonged storage of bacteria with trehalose monocorynomycolate [80], dried vesicle for artiﬁcial red blood cells [81], hair growth [82], pimple inhibition or skin fat control [83], pharmaceuticals like adjuvant [84] and diﬀerentiation action of succinoyl trehaloselipids for promyelocytic leukemia cells [85], and an emulsiﬁer and a dispersant [86]. Buﬀering action and metal ion complexation of sodium salts of trehalose esters of monosuccinoyl difatty acid and disuccinoyl difatty acid (NaSTL) are shown in Tables 9 and 10 [86].

E. Surfactin Surfactin (Fig. 13) is produced by Bacillus subtilis in a lower yield as it is kept inside the bacterial cell without the excretion from the cell. High yield was attained at 3 g/l from an original of around 200 mg/l [87]. It is notable

FIG. 12

Trehalose lipid.

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TABLE 9 Buffering Capacity of Sodium Succinoyl Trehalose Lipids (NaSTL and S-2Na) Buﬀering capacity* dB/dpH (ml)

Initial pH

0.45 0.83 0.35 0.15

6.7 6.9 — —

NaSTL S-2Na CMC** Itaconate

Source: Ref. 86. *(dB/dpH) was obtained from the initial slope of the titration curve, where B was the titrated volume (ml) of 0.00628 N HCl to the 0.1% sample solution (50 ml). (From Ref. 65.) **Carboxy methyl cellulose.

that surfactin shows strong surface activities of cmc ¼ 28 mN/m and the CMC ¼ 12 mg/l [88] and organizes the secondary structure of -sheet micelle [89]. Furthermore, an ionophoric action for Ca2þ and Rb+ [90], Zn2þ and Cu2þ [91], an inhibitor of red blood cell clogging [92], were found. The detail of the formation of ion channel and secondary structure has been described [7].

TABLE 10 Qualitative Test Result of the Complex Formation of Sodium Succinoyl Trehalose Lipids (NaSTL) and S-2Na with Metal Ions

NaSTL S-2Na SDS

Cu2þ 300 ppm

Ca2þ 150 ppm

Zn2þ 300 ppm

Co2þ 300 ppm

Mg2þ 300 ppm

z þ

z þ

Source: Ref. 86. z: Remarkable scum formation. þ: Scum formation. : Negative.

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FIG. 13

Surfactin.

F. Aescin Saponins are natural surfactants that are extracted from plants. Many kinds of saponins have been used in chemicals and pharmaceuticals. It is recorded that quillaja saponin (food emulsiﬁer, immunostimulative complex), glycyrrhizin (sweetener, anti-inﬂammatory eﬀect), glycyrrhetinic acid (antivirus agent, emulsiﬁer), digitonin (solubilizer for physiologically active proteins), soyasaponin (decrease in blood cholesterol content), and mukurossi saponin (cosmetic ingredient). It is notable that the supplying volume of natural surfactants is nearly unstable. However, special interests for such ecological chemicals will be capable of their increased supply by biotechnological developments. Aescin (Fig. 14) is a kind of saponin extracted from the

FIG. 14

-Aescin.

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horse chestnut from marronnier [93] and has been used as a traditional surfactant (carpet shampoo), astringent in cosmetics, and a medicine [94]. There is special interest in the swelling decrease eﬀect of aescin on foot edema, which is interpretable physicochemically [95]. On the other hand, such biodegradable natural surfactants seem to be applicable in the environmental remediation as attractive alternatives to synthetic surfactants. It was shown that mukurossi saponin showed large aqueous solubilities of hydrophobic contaminants such as hexachlorobenzene and naphthalene for soil washing [96]. Remediation of a soil contaminated with Cd2þ and Pb2þ was successfully carried out by a soil washing process using aescin [97]. Cd2þ and Pb2þ in a model soil matrix migrated to the 30-mM aescin solution in 41% of Cd2þ (pH 7.8) and 25% of Pb2þ , respectively, as shown in Figs. 15 and 16. It was made clear that 1 mol of of aescin formed complexes with 2 mol of Cd2þ and 3 mol of aescin with Pb2þ from the addition eﬀect of Cd2þ and Pb2þ on the electrical conductivity of aqueous solutions of aescin. The carboxylic moiety of aescin complexed with the divalent cations. One more hydrophilic moiety of a saccharide of aescin may play an important role of remaining aescin molecules in the aqueous phase for soil washing. Furthermore, the enhancement of the emulsiﬁcation capacity of aescin was found on the addition of shorter members of alcohols for the purpose of applying the treatment of spilled marine oil [98]. It is convenient that the surface activity is enhanced at the pH of the seawater is around 8.1, as shown in Fig. 17. Otherwise aescin

FIG. 15 Addition eﬀect of cadmium ion (3 mM) on the electrical conductivity of the aescin solution. (From Ref. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 16 Addition eﬀect of lead ion (3 mM) on the electrical conductivity of the aescin solution. (From Ref. 96.)

precipitates in a lower pH region. Then we can use aescin in alkaline conditions and recover it in the lower pH region to repeat the procedure. Surface tension lowering action and the emulsiﬁcation capacity of aescin were enhanced under the coexistence of cosurfactants (C1C8 alcohols) or 3M urea in water and seawater. The seawater solutions of aescin were more surface-active than those of pure water. Especially coexistence of iso-amyl

FIG. 17 Eﬀect of diﬀerent solution media on the surface tension of aescin solutions: *, water; &, 3M urea; ~, 3M glucose; !, seawater. (From Ref. 97.) Copyright © 2003 by Taylor & Francis Group, LLC

alcohol improved most the emulsiﬁcation of aescin for liquid paraﬃn as a model of oil phase. Tannic acid was also eﬀective for the recovery of Cd2þ and Pb2þ from polluted water [99]. Tea seed saponin was used for the purpose of extracting heavy metals of lead (recovery 100%), copper (60%), Cr (40%), Zn (50%) from MSW incinerator ﬂy ash [100].

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6 Physicochemical Properties of Ring-Structured Surfactants YOSHIFUMI KOIDE KUNIO ESUMI

I.

Kumamoto University, Kumamoto, Japan

Tokyo University of Science, Tokyo, Japan

INTRODUCTION

Inclusion compounds having a cage, such as cyclodextrin [1,2], crown ether [3–5], and calix[6]arene [6–9], have received much attention as new functional materials in recent years because they possess a ring structure and form highly stable complexes with guest molecular compounds. More eﬀective inclusion abilities should be induced by introducing a long alkyl group to these compounds, since the amphiphilic compounds are densely condensed at the interface, in micelle, or in a limited amount of organic layer, together with the guest molecules [10–13]. In addition, polyalkylated amphiphilic compounds with a ring structure have been developed and investigated as a selective complexing reagent for speciﬁc guest molecules such as uranyl ion [6–9,14], saccharide [11], and others. Moreover, they have been applied to removal of ions [15], transportation of ions [16,17], and other functions [1–13]. In this chapter, the physicochemical properties and applications of ringstructured surfactants will be discussed.

Deceased.

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II. TYPICAL SURFACTANTS BEARING RING-STRUCTURED HYDROPHILIC GROUPS Polyalcohols of sugar, imidazole ring, pyrrolidone, and pyridine are well known as typical hydrophilic groups with a ring structure [18–20]. Alkanoic esters and alkane ethers of ring-structured polyalcohols, such as sorbitol, polysaccharides, and biosurfactants from glycolipids, are nonionic surfactants. Polyoxyethylenation of sorbitol gives a wide range of solubility and hydrophilic–lipophilic balance to the products (e.g., Span and Tween). The sorbitol esters are useful for food and pharmaceutical emulsiﬁers (e.g., soluble vitamins). Alkanoic esters (C10,C12) of polysaccharides (sugar esters) show wetting, foaming, detergency, and biodegradation properties. Alkylpolyglycosides are highly soluble in solutions of electrolytes and sodium hydroxide and do not show a cloud point. They are recommended for liquid dishwashing and hard surface cleaners. It should be mentioned [21] that the alkylpolyglycosides break down into glucose and long-chain alcohol under acidic condition, while on the alkaline side, even at very high pH, they are stable to hydrolysis. The imidazole ring shows cationic properties at low pH. These properties are discussed in the literature [18–20]. N-alkylpyrrolidone is a nonionic surfactant with a ring structure. The Ndodecyl compound depresses surface tension to about 26 mNm1 at a conCopyright © 2003 by Taylor & Francis Group, LLC

centration of 0.002%, and the N-octyl compound is a low foaming wetting agent [18–20]. Vinylpyrrolidone can be polymerized to telomer-type surfactants, which act as builders of detergency in hard water containing Ca2+, Mg2+, and the like. N-alkylpyridinium halide is a cationic surfactant, and hexadecyl pyridinium bromide is used in oral antiseptics and other applications [18–20]. Cationic polysoap derived from vinylpyridine is widely used in technical applications, and amphiphilic vinylpyridine telomer (telomer-type surfactant) is used as a catalysis; the Cu2+ complex of telomer shows catalytic properties for the oxidative polymerization of 2,6-xylenol (polyphenylene oxide resins) [22].

III. SURFACTANTS OF ALICYCLIC HYDROPHOBIC GROUPS Sterol and other alicyclic compounds can oﬀer a molecular structure that in some respects resembles the structure of nonylphenol. The ring structure, sometimes with several unsaturated bonds, together with a branched hydrocarbon tail, appears in both sterols and rosin acids. The formation of micelles has been investigated using many steroid derivatives [23]. The number of the aggregated molecules in micelle is 4–8 mol for deoxycholate, 9–13 mol for cholate, and more for both in the presence of salts.

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Relatively little has been reported regarding polyoxyethylene sterols, as compared to other polyoxyethylene surfactants. The surface activity of polyoxyethylene derivatives of diﬀerent sterols has been studied by only a few workers [24–26]. Table 1 shows thermodynamic parameters of polyoxyethylene cholesterol with 30 oxyethylene units [27]. In addition, the data for aggregation behavior of three diﬀerent sterol derivatives are also given: cholesterol with an average number of 25 and 30 oxyethylene units (ChlEO25 and Chl-EO30) and hydrogenated cholesterol with 30 oxyethylene units (DHC-EO30). The critical micelle concentration (CMC) values as well as the thermodynamic parameters are similar to those reported for other nonionic surfactants. It can be said that the cholesteryl groups have a hydrophobic character similar to that of the dodecyl or nonylphenyl groups. Furthermore, it has been observed that despite the similarities in the geometric form of the lipophilic group, the cholesterol ethers behave very diﬀerently to cholic acids and their conjugates. Surface activities of nonionic surfactants consisting of a fundamentally alicyclic structure are shown in Table 2. Their solutions show excellent surface tension lowering abilities, and the CMC becomes higher than that of the linear alkyl groups.

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TABLE 1 Thermodynamic Parameters of Polyoxyethylene (30) Cholesterol: CMC Values, Micellar Weight, and Aggregation Numbers of Polyoxyethylene Cholesteryl Ethers in Water Temp. (8C) 15 25 35

CMC (M)

G8m (J/mol)

h8m (J/mol)

s8m (J/kmol)

(mol/cm2 )

A (nm2 /molecule)

1:17 104 1:12 104 0:79 104

21:7 22:6 22:2

14.6 15.7 16.7

126 128 133

1:8 1010 1:7 1010 1:2 1010

0.92 1.00 1.40

Surfactant

CMCa (M)

Micellar weightb

Aggregation numberb

Chl-EO30 Chl-EO25 DHC-EO30

1:12 104 1:15 104 0:79 104

1:5 105 — 8:1 105

90 — 470

a

At 258C. At 238C. Source: Ref. 27.

b

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TABLE 2 Surface Activities of Alicyclic Polyoxyethylenes Surfactant

a

R12 EO7.3 R12 EO9.4 C12 EO7.2 C12 EO9.2 C16 EO11.9 ADMEO7.2 SDS

CMC (mN m1 )

CMC 104 (mol dm3 )

Areab (nm2 )

33.6 39.5 35.5 35.5 35.3 40.9 40

0.85 0.94 13 15 0.32 43 82

0.54 0.62 0.71 0.86 0.65 0.65

Cpc (8C)

Carbon suspended (mg 100 cm3 )

68 35 52

70.7 16d

380 840 —

a

R12 : n-dodecyl group; C12 : cyclododecyl group; ADME: adamanthyl group; SDS: sodium dodecylsulfate; EO7.3: 7.3 mol of polyoxyethylene. b Area: area per molecule. c Cp: cloud point. d Krafft point. Source: Refs. 18–20 and 28.

IV. CROWN ETHER-TYPE SURFACTANTS Amphiphilic crown ethers have been prepared by many investigators [3–5]. The oxygen atom in crown ether binds with alkali metal ions or links with NH4+ by hydrogen bonding [29]. These complexes have been examined as phase transfer catalysis [3] and speciﬁc reagents [3–5]. Some aspects of their surface activities are shown in Table 3. Crown- and monoazacrown-type surfactants ( Rn-m, Rn-Nm) show a high ability to lower the surface tension of their solutions. The CMC of Rn-Nm is higher than that of Rn-m, and the cloud point of Rn-Nm is also higher than that of Rn-m.

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TABLE 3 Surface Activities of Crown- and Monoazacrown-Type Surfactants Surfactant R8 -15 R8 -18 R10 -18 R10 -21 R12 -18 R12 -21 R8 -N15 R8 -N18 R10 -N18 R10 -N21 R12 -N18 R12 -N21

a

CMC (mN m1 )

CMC 104 (mol dm3 )

Areab (nm2 Þ

Cp (8C)

39.4 39.2 33.0 33.0 34.7 34.6 34.0 34.0 34.0 35.6 33.0 34.6

25 18 3.3 3.5 0.21 0.23 8.6 19 8.0 13 3.8 6.0

0.53 0.55 0.56 0.63 0.56 0.64 0.47 0.53 0.53 0.60 0.54 0.57

13 28.5

3.0 33.5 42.5 29.0

a -15, -18, -21, -N15, -N18, -N21: total atomic number in crown or monoazacrown. b Area: area per molecule. Source: Refs. 3–5 and 30.

The properties change markedly in the presence of alkali metal ions because of selective complex formation (Table 4). The CMCs of R10-18 and R8-15 are high in the presence of K+ but not Na+, whereas the CMC of R8-15 is high in the presence of Na+ but not K+; the CMCs in the absence of both ions are 2530 104 mol dm3 for R8-15, 3:03:3 104 mol dm3 for R10-18, and 8:09:5 104 mol dm3 for R10N18. Cloud points of these surfactants are similarly high in the presence of metal ions where a complex is formed. Amphiphilic crown ethers have been applied to transportation through a liquid membrane as a model of cell membranes in vital organs (see Section V.B) [32] or as phase transfer catalysis [33].

V. CYCLIC POLYAMINE-TYPE SURFACTANTS A. Surface Activity High selectivity is usually a matter of great importance in separation. Cyclic polyamine can capture heavy metal ions, and the dianion-type cyclic dioxopolyamine forms an uncharged complex with cyclic divalent metal ions [34]. Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 4 Surface Activities in the Presence of Salts Surfactant R10 -18 R10 -18 R10 -18 R10 -18 R8 -15 R8 -15 R10 -N18 R10 -N18

Salt

Concn (mol dm3 )

CMC (mN m1 )

CMC 104 (mol dm3 )

KCl KCl NaCl NaCl KCl NaCl KCl NaCl

0.1 0.5 0.1 0.5 0.5 0.5 0.5 0.5

32.0 33.1 32.7 32.2 32.0 31.0 36.6 34.5

4.4 4.2 2.5 2.7 23 45 12 10

Source: Refs. 30 and 31.

Amphiphilic cyclic dioxopolyamine (RndoN4, RndoN5) forms uncharged complexes with Cu2+ and Ni2+, although the stability constants (log K) are smaller than those of the polyamine-Cu2+ complexes [35,36].

Amphiphilic RndoN4 and RndoN5 lower the surface tension to nearly 30–40 mNm-1. Surface tensions of the RndoN4 solution in the presence of Cu2+ are shown in Table 5. The lowering of gCMC by R12doN4 is better at pH 10 than that at pH 4; the CMC at pH 4 is not observed in concentrations below 3.8 10-4 mol dm3 . However, the gCMC at pH 4 is low when Cu2+ is added to the R12doN4 solution, and similar lowering is observed at pH 4 Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 5 Surface Tensions of Rn doN4 Solution in the Presence of Cu2þ pH 4

R12 doN4 R12 doN4 þ Cu2þ R18 doN4 R18 doN4 þ Cu2þ a

pH 10

CMC (mN m1 )

CMC 104 (mol dm3 )

Areaa (nm2 )

CMC (mN m1 )

CMC 104 (mol dm3 )

Areaa (nm2 )

<39 35 45 <39

>3.8 2 0.3 >1.3

0.82 0.66 0.77 0.67

32 36

1 0.5 –Insoluble– 0.3

0.57 0.46

40

0.48

Area: area per molecule, at 208C.

and 10. R18doN4 is hardly soluble in the alkali solution, but the addition of Cu2+ to the R18doN4 solution at pH 10 makes the surface tension lower. Also, Ni2+ lowers the surface tension as much as the Cu2+ over the pH range of 4–10 [37]. Surface tension curves of RndoN5 are located in higher concentrations, and the CMC is larger than that of RndoN4. Alkylated[14]aneN4(R12N4) is cationic at pH 4–10, and the gCMC is 40 mNm1 at pH 10 (CMC 104 mol dm3 ). Addition of Cu2+ to the R12N4 solution reduces the surface tension and the CMC a little. Polyalkylated[18]aneN6(2.4R-N6) and a telomer containing 6.8 units mol of [18]aneN6(Ls6.8N6) also show the ability to lower surface tension; gCMC is 34–37 mNm1 for 2.4R-N6 and 43 mNm1 for Ls6.8N6. Area per molecules, calculated from the Gibbs adsorption isotherm [38], may lead to a small error, but it is reasonable to estimate the relative areas in connection with the pH. RndoN4 is cationic at pH 4 but not at pH 10 [35,36] so that the electrostatic repulsion and the solvating would make the area wider at pH 4 than that at pH 10. The areas in the presence of Cu2+ are smaller because of the complexation; the charged Cu2+ complexes at pH 4 are 0.66–0.67 nm2, and the neutralized complexes with OH at pH 10 are 0.46–0.48 nm2 [37]. The area of cationic R12N4 is 0.95 nm2 at pH 4 and 0.66 nm2 at pH 10, whereas that of the Cu2+ complex is 0.48–0.53 nm2 at pH 4 and 0.40 nm2 at pH 10.

B. Transportation and Flotation R14doN4 forms an uncharged complex with divalent metal ions [34] and has been used as a carrier of Cu2+ in transportation of liquid membrane [34,39] where Cu2+ is transported selectively according to the stability constant. Copyright © 2003 by Taylor & Francis Group, LLC

Selectivity in ion ﬂotation diﬀers considerably from that in extraction or transportation. The Cu2+ and Ni2+ in a mixture of four metal ions (Cu2+, Ni2+, Fe3+, Zn2+) are separated as a scum by ion ﬂotation using RndoN4 or RndoN5 [15]. The ﬂoatable complex should be hydrophobic and slightly surface-active, but the complex of extracted metal ions is merely oleophilic.

VI. AMPHIPHILIC CYCLODEXTRIN A. Surface Activity Polyalkylated amphiphilic compounds with a ring structure can orient at a surface or an interface [1,2], and such compounds are regarded as a new type of surfactant. Amphiphilic cyclodextrins are prepared by the alkylation of -, -, and -cyclodextrin ( has a 6-, a 7-, and an 8-membered ring). Primary OH groups of -cyclodextrin are replaced with either dodecylthio, dodecylsulﬁnyl, or dodecylamine groups, and secondary OH groups are left free. Surface-active properties at pH 5.6 for 6-alkylamine derivatives of cyclodextrin are shown in Table 6 [1,2]. 6-Alkylsulﬁde derivatives of cyclodextrin-2-sulfonate show less ability to lower surface tension [1,2]. The CMC at pH 6 is 44 mNm1 (CMC 2:5 103 mol dm3 ) for the butylsulﬁde derivatives and 48 mNm1 (2:6 103 mol dm3 ) for the octylsulﬁde derivative. Amphiphilic cyclodextrins are also prepared [40] by conjugation of oligo(ethylene oxide) units at the secondary side of heptakis(6-alkylthio)- cyclodextrins, with alkyl ¼ ethyl, dodecyl, and hexadecyl, respectively. The oligo(ethylene oxide) substitutes are introduced by reaction with ethyCopyright © 2003 by Taylor & Francis Group, LLC

TABLE 6

Properties of 6-Alkylamine Derivatives of -Cyclodextrin at pH 5.6

R

mpa (8C)

½D

C4 H9 C8 H17 C12 H25

212 204 206

121 98 95

a b

b

Solubility

CMC (mN m1 )

CMC (mol dm3 )

— 3.56 37

— 6 105 2 105

mp: decomposition. ½D in CHCl3 .

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H2 O/mol dm 4 103 2:6 103 1:0 104

3

MeOH

CHCl3

Benzene

þþþ þþ —

þ þþþ þþþ

þ þþ

lene carbonate in the presence of potassium carbonate at elevated temperature. These amphiphiles are highly soluble in water and form various lyotropic phases including micelles and vesicles, depending on the alkyl chain length, concentration, and temperature. The grafting of a cholesterol derivative onto a methylated cyclodextrin through a spacer arm produces an amphiphilic compound exhibiting high solubility in water [41]. An analysis of its behavior in aqueous solution proves that it self-assembles into monodisperse spherical micelles with an average aggregation number of 24. The micelles can be described as two-shell objects, the cyclodextrin moieties being exposed to the aqueous medium, making them prone to include guest molecules in the cavities. LB ﬁlms are formed by using the cyclodextrin-type surfactants. The isotherms curves between surface pressure and area per molecule in the condensed monolayer show that the cylinder sizes of the 6-octadecylsulﬁde derivatives of -, -, and - cyclodextrin are consistent with the outer sizes of -, -, and -cyclodextrin [1,2]. Amphiphilic per (2,3-di-O-alkyl)- and -cycloodextrins and hexakis(6-deoxy-6-thio-2,3-di-O-pentyl)-cyclodextrin show from the surface pressure-mean mol. area isotherms that they are capable of forming a stable monolayer at the air–water interface where the monolayers correspond to typical solidlike ones [42]. In addition, mixed monolayers of per-6-ammonium-per-6-deoxy-per-O2,O3hexyl- -cyclodextrin (I) and per-O2,O3-hexanoyl- -cyclodextrin (II) are studied at the air–water interface [43]. The mixed monolayers show a nonideal mixing with formation of a 3:2 complex between I and II. The interactions between amphiphilic cyclodextrins and drugs or proteins have also been investigated [44,45].

B. Solubilization of Dye Salts Two dye salts, methyl orange (MO) and ammonium salts of 8-anilino-1naphthalenesulfonic acid (ANS), are eﬀectively extracted into a CHCl3 layer with the lipophilic 6-dodecylamine derivative of -cyclodextrin [2]. The high solubilization is brought about by host–guest complexation in addition to the large partition based on the lipophilicity.

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VII.

CALIX[N]ARENE AND CALIX[4]RESORCINARENE WITH ALKYL SIDE CHAINS

A. Surface Activity Many kinds of calix[n]arene derivatives have been developed, and amphiphilic calix[n]arene are used as an extractant for uranyl ions [6–9], a coat of SnO2 electrode for ribose [46,47], a membrane material for gas separation [48–51], and so on. Water-soluble and conformationally immobilized calix[4]arene, cone and 1,3-alternate conformations have been prepared [52], in which the para position of each phenyl unit is an Me3N+CH2 + group or an Meþ 3 (CH2)nOCH2 group. The cone Me3N CH2 derivative aggregates into small micellar particles in water, but the 1,3-alternate isomer does not. In Meþ 3 (CH2)nOCH2 derivatives, both the cone and 1,3-alternate isomers form aggregates in water; the cone isomers (n ¼ 4, 6, and 11) always give critical aggregation concentration values (CAC) lower than the 1,3-alternate isomers [52], as seen in Table 7. The cone isomers of calix[4]arene containing amphiphiles are intermolecularly cohesive based on the cone-shaped hydrophobic surface, and they favorably form a globular micelle, whereas the 1,3-alternate isomers with a cylindrical hydrophobic surface favorably form a two-dimensional lamella and stable vesicular aggregates detectable by an electron microscope. Thus, the aggregation properties can be controlled by the conformational structure diﬀerence in the calix[4]arene core. Amphiphilic calix[4]resorcinarene with four alkyl chains substitutes, [4]Ar-Rn, is prepared by the condensation of resorcinol with alkyl aldehyde

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TABLE 7 Surface Tension and CAC of Polyalkylated Calix[4]arene Cone Calix[4]arene p-Me3 Nþ CH2 p-Meþ 3 ðCH2 Þ4 OCH2 p-Meþ 3 ðCH2 Þ6 OCH2 p-Meþ 3 ðCH2 Þ11 OCH2

1,2-Alternate

CMC (mN m1 )

CAC (mol dm3 )

Particle size (nm)

41 39 32 41

1:0 105 5:0 105 1:0 105 5:5 107

3 76 68 115

a

CMC (mN m1 )

CAC (mol dm3 )

Particle sizea (nm)

72 28 36 35

— 3:0 103 1:0 103 3:0 105

— 42 93 146

Particle size was determined by a dynamic light scattering method at 308C; concentration: 1 102 mol dm3 , p-Meþ 3 ðCH2 Þ11 OCH2 : 1 104 mol dm3 . a

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(alkanal) [53–55]. The shape of [4]Ar-Rn resembles a table with four legs. [4]Ar-Rn has the ability to lower the surface tension, but the lowering speed of the orientation is slow because of the crowded chains [13]. Their surface tensions are shown in Fig. 1. The CMC of [4]Ar-Rn (n ¼ 6, 8) reaches about 30 mNm1 in a time over 4 h, and the CMCs increase with decreasing alkyl chain length. The cross-sectional areas of [4]Ar-Rn per molecule, calculated from the Gibbs adsorption isotherm at 258C, are 0.69 nm2 for [4]Ar-R4, 0.45 nm2 for [4]Ar-R6, and 0.32 nm2 for [4]Ar-R8 at pH 13. [4]Ar-R2 and [4]Ar-R12 have little ability to lower the surface tension, for example, 57 mNm1 at the CMC for [4]Ar-R12. Mixed aqueous properties of [4]Ar-Rn (n ¼ 4, 6, and 8) and a cationic surfactant, dodecyltrimethylammonium bromide (DTAB), have been investigated by surface tension and ﬂuorescence measurements [56]. It is found that the mixtures of [4]Ar-Rn and DTAB show considerably lower mixed CMCs, similar to other oppositely charged surfactant systems, and the

FIG. 1 Surface tensions of [4]Ar-Rn solutions. *: [4]Ar-R4 ; &: [4]Ar-R6 ; *: [4]ArR8 ; ~: [4]Ar-R12 . Temperature 258C. The pHs of the solutions were adjusted to 13 with NaOH. Copyright © 2003 by Taylor & Francis Group, LLC

interaction parameter for the mixed micelles, calculated using the modiﬁed regular solution theory, increases from 25.2 to 10.4 with increasing side chain length of [4]Ar-Rn. In addition, the ﬂuorescence results show that the micropolarity of mixed micelles of [4]Ar-R6/DTAB is higher than that of [4]Ar-R8/DTAB.

B. Recovery of Cs+ Alkali metal ions and ammonium compounds combine with calix[4]arene or calix[4]resorcinarene to form their complexes [16,17,54,55]. The amphiphilic [4]Ar-Rn can be used as an extractant for the alkali metal ions (Na+, K+, Rb+, and Cs+) in a pH range of 9.5–12.5. The extraction for a mixture of alkali metal ions is shown in Table 8. [4]Ar-Rn is functionally capable of capturing Cs+, and the selectivity in extraction (Cs+ Rb+ > K+ > Na+ > Li+) is consistent with the stability of calix[6]arene [16,17]. Scheider et al. conﬁrmed the formation of the hydrogen bonds by the proton signals at 8.8–9.6 ppm in the NMR spectra and by the absorption at 3100 cm-1 in the IR spectrum [11,54,55]. The Cs+ must be included in the composition of 1:1 in the networks of intramolecular hydrogen bonds between the four hydroxyl groups and the four oxido groups. The surface-active [4]Ar-Rn have the competence to ﬂoat Cs+ with the aid of bubbles as the foam ﬁlm (adsorbates) when short-chain [4]Ar-Rn (n ¼ 48) are used for foam fractionation, and as the scum when longchain [4]Ar-Rn (n ¼ 816) are used for ion ﬂotation [13]. The eﬀects of [4]Ar-Rn on foam fractionation of Cs+ and foaming ability are shown in Fig. 2. Foam fractionation is correlated with foaming ability, and the optimum pH regions of foaming ability and ﬂoatability shift to high pH with increasing chain length. The Cs+ is ﬂoated selectively from a mixture of alkali metal ions by using [4]Ar-R4 and [4]Ar-R6. Ion ﬂotation (scum ﬂotation) is more favorable than foam fractionation, with respect to easy treatment. The eﬀect of pH on the Cs+ ﬂotation in the Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 8 Extraction from a Mixturea of Alkali Metal Ions pH adjustment

Extractability

[4]Ar-Rn

pH

Reagent

Cs /%

Rbþ /%

Kþ /%

Naþ /%

[4]Ar=R6

11 11 12 12 11 11 12 12

NaOH KOH NaOH KOH NaOH KOH NaOH KOH

74 65 68 9 81 82 79 83

29 13 24 5 24 16 18 11

16 — 18 — 17 — 8 —

— 0 — 1 — 7 — 2

[4]Ar-R12

þ

Mixture: ½Csþ ¼ ½Rbþ ¼ ½Kþ ¼ 7:5 105 mol dm3 , or ½Csþ ¼ ½Rbþ ½Naþ ¼ 7:5 105 mol dm3 , 60 cm3 ; [4]Ar-Rn : ﬁvefold molar amount of [Mþ ] 20 cm3 of benzene. a

FIG. 2 Eﬀects of [4]Ar-Rn on foam fractionation and foaming ability. Foam fractionation (left scale): Csþ ¼ 10 ppm (7:5 105 mol dm3 ), 200 cm3 . *: [[4]Ar-R4 ]/ [Csþ ¼ 5; ^:[[4]Ar-R6 =½Csþ ¼ 5; ~: [[4]Ar-R8 =½Csþ ¼ 5. Foaming ability (right scale): foam height in glass cylinder of 1-cm diameter, with lapse of 1 min after shaking 10 cm3 of [4]Ar-Rn solution. [4]Ar-R2 ( Þ ¼ 2 104 mol dm3 ; [4]Ar-R4 (*) ¼ [4]Ar-R6 ; (^) ¼ [4]Ar-R8 ; (~) ¼ 104 mol dm3 . Copyright © 2003 by Taylor & Francis Group, LLC

presence of 0.1 mol dm3 Na+ (½Naþ =½Csþ ¼ 1:33 103 ) is shown in Fig. 3 (left). The Cs+ is ﬂoated eﬀectively by using [4]Ar-R12 or [4]Ar-R16, and the ﬂoatabilities rise up to 80–85% by the addition of a ﬁvefold molar amount of [4]Ar-R16, as shown in Fig. 3 (right). Moreover, the Cs+ is ﬂoated selectively from a mixture of Na+, K+, and Rb+. This system is considered to be available to meet the demand for rapid Cs+ recovery from, for example, contaminated cooling water in the atomic industry [57,58].

C. Emulsiﬁcation Water can be emulsiﬁed in toluene, kerosene, and cyclohexane by using [4]Ar-Rn, and the water–oil (W/O) emulsion of toluene is the most stable among them. The emulsiﬁcation for toluene–water (0.1 mol dm3 HCl solution) mixture is shown in Fig. 4. [4]Ar-Rn bearing four alkyl chain emulsiﬁes more than four times molar of 4-dodecylresorcinol ([1]M-R12) or two times molar of dimer ([2]D-R12) [59]. Because the emulsion produced by [4]Ar-R8

FIG. 3 Ion ﬂotations of Csþ . Eﬀect of pH (left): ½Csþ ¼ 10 ppm (7:5 105 mol dm3 ), ½Naþ ¼ 0:1 mol dm3 ; 200 cm3 . *: ½½4Ar-R12 =½Csþ ¼ 1, 2; ~: [[4]Ar-R16 =½Csþ ¼ 1. Eﬀect of amount of [4]Ar-Rn (right): ½Csþ ¼ 10 ppm ð7:5 105 mol dm3 ); 200 cm3 . *: [4]Ar-R12 at pH 11.5, ~: [4]Ar-R16 at pH 12.5. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Emulsiﬁcation of [4]Ar-Rn for toluene. Toluene:HCl solution (0.1 mol dm3 ) ¼ 6 cm3 : 6 cm3 , 208C. [4]Ar-R8 ¼ ½4Ar-R12 ¼ ½1M-R12 ¼ 2 104 mol.

is stable at room temperature but unstable at 908C, the desired emulsiﬁcation can be set by regulating the temperature. The alkyl chain length of [4]Ar-Rn also aﬀects the emulsiﬁcation. The eﬀective alkyl chain length is 6 for the emulsion of toluene–HCl solution (95% after 20 h), 8 for that of cyclohexane, and above 10 for that of kerosene. Emulsiﬁcation is closely related to interfacial tension. The interfacial tensions of the toluene–water (0.1 mol dm3 HCl solution) are shown in Fig. 5. The CMC of [4]Ar-R6 is 2 mNm1 , and the magnitude of tension lowering is [4]Ar-R6 > [4]Ar-R4 > [4]Ar-R8 > [4]Ar-R12, whereas [1]MR12 lowers the interfacial tension little at the low concentrations. The cross-sectional areas per molecule calculated from the slopes of lowering curves are 0.99 nm2 for [1]M-R12 and 1.98 nm2 for [4]Ar-R12. [4]Ar-R12 is composed of four times molar of [1]M-R12 units, so that the [4]Ar-R12 covers an interfacial area narrower than that (0:99 4 ¼ 3:96 nm2) of four times molar of [1]M-R12. [4]Ar-Rn of bundle structure can orient densely at the interface and hold the highly stable emulsion because of the steric and electrical barriers to coalescence of the dispersed phase; the ﬁlm consisting Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Interfacial tension between toluene containing [4]Ar-Rn and an HCl solution. Toluene:HCl solution (0.1 mol dm3 Þ ¼ 20 cm3 : 25 cm3 , 198C.

of surfactants at the interface is strengthened by depressing the static repulsion of hydrophobic groups and the adducts of water. [4]Ar-Rn becomes hydrophilic in an alkali solution because of the dissociation of the hydroxyl groups. Interfacial tension between toluene and a 0.01 mol dm3 NaOH solution is 4 mNm1 for [4]Ar-R6, 5 mNm1 for [4]Ar-R8, and 6 mNm1 for [4]Ar-R16.

D. Liquid Surfactant-Membrane Transportation through a liquid surfactant-membrane of water/oil/water (W/O/W) emulsion has been developed by Li [60] and Nakashio and coworkers [61,62]. The transportation usually requires an emulsiﬁer and a carrier of target material. The process consists of four steps: (1) W/O emulsiﬁcation of inner aqueous solution; (2) transportation of the target material from an outer aqueous solution through the W/O/W membrane; (3) separation into the W/O emulsion and the outer aqueous solution; (4) deemulsiﬁcation of the W/O emulsion (Fig. 6). The interfacial areas of both sides of

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FIG. 6 Process of transportation.

the emulsiﬁed membrane are very wide, and the thickness is thin; thus, the rate of transportation is very rapid. However, the opposite function, deemulsiﬁcation, should be satisﬁed for the emulsiﬁer in the deemulsiﬁcation step. Bifunctional [4]Ar-Rn as an emulsiﬁer capable of complexing with Cs+ makes the transportation easy, since a stable W/O/W emulsion is formed by pouring the W/O emulsion of toluene–water (inner HCl solution) into water. The emulsiﬁed membrane remains hardly broken for a long time at room temperature. The Cs+ in an outer aqueous solution is transported through the emulsiﬁed membrane into the inner HCl solution, while the H+ in the inner solution is transported reversibly. After the deemulsiﬁcation by heating at 90oC, the Cs+ is reported reversibly. The eﬃciencies of transportation are aﬀected by the alkyl chain length of [4]Ar-Rn, as shown in Fig. 7. [4]Ar-R6 is the most eﬀective emulsiﬁer capable of carrying Cs+ of the [4]Ar-Rn. Excess Cs+ is transported repeatedly through the toluene membrane in about 8–11 min per cycle by using [4]Ar-R6, and the amount of Cs+ in the inner solution is ultimately nine times as much as the [4]Ar-R6, at 100 min, when the initial amount of Cs+ in the outer solution is 10 times molar to that of [4]Ar-R6 (Fig. 8); the turnover number of [4]Ar-R6 is 9. The oriented [4]Ar-R6 in toluene should form the Cs+ complex at the outer interface of the NaOH solution, and the complex should dissociate at the inner interface of the HCl solution. Furthermore, the Cs+ is transported selectively from a mixture of alkali metal ions (Cs+, Na+, and K+).

E. Solubilization Considerable research on surfactants has been devoted to the solubilization of organic compounds and oily soil in ﬁber [63]. Organic compounds and Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 7 Relation between alkyl chain length of [4]Ar-Rn and transportability of 10 ppm Csþ . Outer aqueous solution: 10 ppm Csþ at pH 12.0; inner aqueous solution: 0.1 mol dm3 HCl. [4]Ar-Rn ¼ 2 104 mol.

oils can be dissolved in micelles of the surfactants or as the O/W microemulsion. The table-type [4]Ar-Rn, [4]Ar-Ph of tetraphenyl substituent, and [4]Ar-N of tetranaphthyl substituent can solubilize some organic compounds and oils, since they include these compounds in the large cavity as well as incorporating them into the micelles. The solubilization is great, and the capacities are in the order [4]Ar-R6 > [4]Ar-R8 > [4]Ar-R10. Figure 9 shows the relation between the concentration of [4]Ar-R6 and the solubilization capacities for some compounds. The capacity is large for hexanol, and it decreases with increasing size of the solubilizates as hexanol > benzene > toluene > t-butylbenzene; for example, 0.3 g of 1-heptanol is dissolved into 100 cm3 of 2 104 mol [4]Ar-R6 (8 mol/l mol [4]Ar-R6), and 0.4 g of t-butylbenzene in 100 cm3 of 5 104 mol [4]Ar-R6 (6 mol/l mol of [4]Ar-R6). Hexane is less soluble than hexanol, benzene, or toluene. [4]Ar-Ph and [4]Ar-N have solubilization capacities about one third to one ﬁfth that of [4]Ar-Rn, whereas [1]M-R12 has a smaller capacity in the range above the CMC (0:1 103 mol dm3 ).

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FIG. 8 Turnover number of [4]Ar-R6 for the transportation of Csþ . Outer aqueous solution: excess Csþ at pH 12.0 (initial amount of Csþ to [4]Ar-R6 ¼ 2, 4, 6, 10); membrane: 2 104 mol [4]Ar-R6 in toluene; inner aqueous solution: 0.1 mol dm3 HCl.

The surface tension of [4]Ar-Rn reaches about 30 mNm1 at pH 12–13 (Table 9), and [4]Ar-Ph also lowers the surface tension (42 mNm1 at pH 11), in spite of the bulky aromatic side chains [13]. The presence of a small amount of hexane and benzene makes the surface tension a little lower, and the solubilization capacities are consistent with the order of the CMCs in the Copyright © 2003 by Taylor & Francis Group, LLC

Q

FIG. 9 Relation between the concentration of [4]Ar-R6 and the solubilization capacities for some compounds. *: hexanol; *: toluene; ~: hexane; & þ (4-square): tbutylbenzene; *: dodecanol solubilized by [1]M-R12 ; #: CMC in presence of the compounds; CMC of [1]M-R12 . The capacity was determine by the absorbance of 700 nm in the ultraviolet (UV) spectrum of the compound (solubilizate).

TABLE 9

Surface Tension of Polyalkylated Calix[4]resorcinarene

CMC c /mN m1 [4]Ar-R6 [4]Ar-R8 [4]Ar-N CMCc /mol dm3 [4]Ar-R6 [4]Ar-R8 [4]Ar-N

[4]Ar-Rn a

+Hexanolb

+Benzeneb

+Hexaneb

30 28 42

25

28 27

22 25 41

3 105 5 106 3 105

9 105

1:0 104 2:5 104

1:3 104 1:6 104 2:8 104

a

Conditions: 208C, pH 12–13. Seven-fold molar of hexanol, benzene, and hexane was added to 3 103 mol dm3 [4]Ar-Rn (or [4]Ar-N) solution, and the mixture was diluted for the measurement of surface tension. c CMC of [1]M-R12 : 30 mN m1 , CMC: 1:0 104 mol dm3 . b

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presence of hexane or benzene. A pair of [4]Ar-Rn forms 1:1 aggregates by overlapping each other with their polyalkylside chains [64]. The solubilization based on aggregation should become eﬀective with the aid of these solubilizates, and the solubilizates must be dissolved in the aggregation [65] (Fig. 10). [4]Ar-R6 is the most eﬀective solubilizer among the [4]Ar-Rn, [4]Ar-Ph, and [4]Ar-N; 11-fold molar of hexanol is dissolved by 2 103 mol dm3 [4]Ar-R6. Moreover, long-chain alcohol is most solubilized by the [4]Ar-Rn bearing alkyl side chains of the same chain length. The agreement of both chains allows the incorporation of the chain alcohol into the polyalkyl side chains of [4]Ar-Rn as for a mixed micelle. The 1H NMR data of [4]Ar-R6 at concentrations above the CMC are shown in Table 10 [66]. The -values based on the proton in the alkyl side chains of [4]Ar-R6 are appreciably diﬀerent from those in the presence of benzene, whereas nearly the same values are observed on the calix[4]resorcinarene skeleton. The presence of hexane gives similar shifts in -values in the alkyl side chains of [4]Ar-R6. This implies the dissolution of solubilizates in the polyalkyl side chains. Moreover, the diﬀerences based on the alkyl side chains after 0.5–1 h are far larger than those in Table 10 (after 24 h). Because [4]Ar-Rn shows excellent ability to lower interfacial tension ([4]Ar-R6; about 2 mNm1 ) and great emulsiﬁcation, the large diﬀerences about 0.5–1 h would imply high solubilization based on the formation of an O/W microemulsion.

FIG. 10

Location of the organic compound in [4]Ar-Rn .

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TABLE 10 Benzene

1

H NMR of [4]Ar-R6 Solutions Containing Added benzeneb

0 mm3

A

B

[4]Ar-R6 a

/ppm

/ppm

Diﬀerencec

/ppm

Diﬀerencec

Ar–Ha Ar–Hb >CH– –CH2 – –(CH2 Þ3 – –CH3

6.950 5.886 4.202 2.127 1.386 0.965

6.951 5.868 4.204 2.112 1.368 0.952

0:001 þ0:018 0:002 þ0:015 þ0:018 þ0:013

6.951 5.868 4.204 2.118 1.352 0.939

0:001 þ0:018 0:002 þ0:009 þ0:034 þ0:026

a

Proton in [4]Ar-R6 :

A: 5 mmol dm3 [4]Ar-R6 D2 O-solution prepared with the solvent NaOD/D2 O saturated with benzene (contains 15.8 mmol dm3 benzene). B: 5 mmol dm3 [4]Ar-R6 D2 O-solution satured with benzene (contains 40.6 mmol dm3 benzene). c Shift value from the data of the [4]Ar-R6 D2 O-solution (ref: TSP-d4 ). Source: Ref. 66.

b

F. Dispersion Surfactants are used as dispersing agents for solid particles in liquid media. Hydrophilic particles such as Fe2O3 and SiO2 are aggregated by adding an amphiphilic surfactant below the CMC and then are dispersed above the CMC, whereas hydrophobic particles such as carbon are dispersed near the CMC [67]. The polyalkylated [4]Ar-Rn should adsorb stably onto the surface of particles (the hydrophilic particle is double layer, and the hydrophobic particle is monolayer), and they function as a dispersing agent in water. [4]Ar-R4 is soluble in water, but [4]Ar-R6 of longer chains is insoluble. Figure 11 shows the dispersion of Fe2O3 by addition of [4]Ar-R4 and SDS. [4]Ar-R4 at neutral pH shows high dispersion of the Fe2O3 particles at [4]Ar-R4 concentrations above the CMC (CMC < 1 104 mol dm3 at Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 11 Dispersion of Fe2 O3 particles by [4]Ar-R4 or SDS. Fe2 O3 particles: 200 mg ðd ¼ 4:2 mm); *: [4]Ar-R4 1 104 mol dm3 ; &: SDS 1 104 mol dm3 (*: 1 102 mol dm3 ); pH 8. Dispersion was determined from the absorbance (turbidity) of the Fe2 O3 particle solution at 700 nm in the UV spectrum

pH 8). On the other hand, the same concentration of sodium dodecyl sulfate (SDS) (below the CMC) does not disperse the Fe2O3 particles. The dispersing capacity of [4]Ar-R4 is great, as much as 100-fold molar of SDS or [1]M-R12. Dispersion by [4]Ar-R4 must be eﬀected by the strong interaction (association) of the polyalkyl side chains between both layers, in addition to the cooperative adsorption of a bundle of hydroxyl groups onto the Fe2O3 particles.

VIII. PHOSPHATE ESTERS OF C-UNDECYLCALIX[4]RESORCINARENE A. Surface Activity Functionalized C-alkylcalix[4]resorcinarene, [4]ArmX-Rn, has been prepared by introducing chelating groups to [4]Ar-Rn (mX means the number Copyright © 2003 by Taylor & Francis Group, LLC

(m) of phosphates (P), carboxylic acid (Ac), or hydroxamic acid (Hx), respectively) [68–70], and the structures of aryloxyphosphinoyloxy derivatives have been investigated by V.I. Kal’chenko and co-workers [71]. [4]ArmX-R12 is easily soluble in water of neutral pH, and the solution shows surface activity. [4]ArmP-R6 and [4]ArmP-R8 have foaming properties, but [4]Ar6.3P-R12 and [4]Ar8.0Ac-R12 are too hydrophobic to foam. Surface tension ( CMC) is 35 mNm1 for [4]Ar5.6PR6, 32 mNm1 for [4]Ar6.3-R8, 52mNm-1 for [4]Ar6.3P-R12, 42 mNm1 (CMC 5 103 mol dm3 ) for [4]Ar8.0Ac-R7, 42 mNm1 (CMC 1:6 104 mol dm3 ) for [4]Ar8.0Ac-R12, and 48 mNm1 for [4]Ar5.1Hx-R12 solution. Thus, [4]ArmX-R12 bearing longer side chains do not lower the values of CMC very much, but they do show excellent ability to lower the interfacial tension between toluene and water—for example, 3 mNm1 for [4]Ar8.0AC-R12 above the CMC (CMC 2:5 104 mol dm3 ).

In addition, the physicochemical properties of [4]Ar5P-Rn (n ¼ 6, 8, and 12) in aqueous solutions have been characterized by several techniques including surface tension and NMR [72]. It is found that the CMCs of [4]Ar5P-Rn are insensitive against the alkyl side chain length, whereas the polarity of aggregates depends remarkably on the alkyl side chain length. From static light scattering and NMR measurements it is suggested that the shapes of aggregates of [4]Ar5P-Rn are not globular and the alkyl side chains of [4]Ar5P-Rn gather loosely in the aggregates. The mixed properties of [4]Ar5P-R12 and hexaethyleneglycol dodecylether have also been investigated. The mixed CMCs are considerably greater than those of the respective surfactant CMCs, and the interaction parameter calculated using a modiﬁed regular solution theory is +2.7. This result indicates that the repulsive interaction occurs in the mixed micelles. Copyright © 2003 by Taylor & Francis Group, LLC

B. UO2þ 2 Recovery UO2þ 2 in an aqueous solution is extracted with CHCl3 containing [4]Ar6.3PR12, [4]Ar8.0Ac-R12, or [4]Ar5.1Hx-R12. [4]Ar6.3P-R12 is more eﬀective than [4]Ar5.1Hx-R12 or [4]Ar8.0Ac-R12, and the number of phosphate groups aﬀects the uranium recovery. The surrounding phosphates in the cavity of [4]Ar6.3P-R12 would cooperatively form a UO2 complex of 1:1 composition. The UO2þ 2 can be also ﬂoated as a scum with [4]Ar6.3P-R12, [4]Ar8.0AC-R12, or [4]Ar5.1Hx-R12 by air bubbling. The ﬂoatability of UO2þ 2 is nearly 100% by using [4]Ar6.3P-R12, but the [4]ArmP-Rn bearing short chains (-R4,-R6) are ineﬀective for the scum ﬂotation. Moreover, [4]Ar6.3P-R12 can recover uranium from seawater, as shown in Table 11. The ﬂotation is more eﬀective than the extraction. Uranium in the 450 cm3 of seawater is ﬂoated about 68–94% by using 1–10 mg of [4]ArmP-R12, whereas the eﬃciency of P-R12 bearing 2 mol of phosphates is about one quarter. [4]Ar5.1Hx-R12 and [4]Ar8.0Ac-R12 bring about lower ﬂoatabilities than [4]ArmP-R12.

C. Solubilization and Dispersion [4]ArmX-Rn in water of neutral pH can function as a solubilizer and as a dispersion agent. The solubilization and the dispersion are great, similar to those of [4]Ar-Rn in pH above 10. Hydrophilic Fe2O3 particles are aggregated by adding [4]Ar6.3P-R12 (or [4]Ar8.0Ac-R12) up to the CMC and then dis-

TABLE 11 Seawatera

Recoveries of Uranium from Extractionc

Collector

b

[4]Ar-R12 [4]Ar6.3P-R12 [4]Ar6.3P-R12 [4]Ar6.3P-R12 [4]Ar8.0Ac-R12 [4]Ar5.1Hx-R12

Flotation

%

mg/g-col

%

mg/g-col

0 48 — — 0 16

0 0.06 — — 0 0.02

0 94 76d 75e 50 60

0 0.13 0.27d 0.44e 0.07 0.09

a

Seawater: 450 cm3 . Collector: 10 mg. c Extraction: CHCl3 20 cm3 . d Flotation: seawater þ 5 ppb U. e Flotation: seawater þ 10 ppb U. b

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perse above the CMC, whereas hydrophobic carbon particles are dispersed near the CMC. The abilities of [4]Ar6.3P-R12 bearing longer side chains are better than those of monomeric P-R12 and hydrophilic [4]Ar6.3P-R6. When gold particles are prepared in aqueous solutions in the presence of [4]Ar6P-Rn (n ¼ 8 and 12), very stable gold nanoparticles having a mean diameter of 4–6 nm are obtained. This result indicates that [4]Ar6P-Rn operates as an eﬀective dispersing agent.

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7 Dimeric (Gemini) Surfactants RAOUL ZANA

Institut C. Sadron, CNRS, Strasbourg, France

GLOSSARY a: surface area occupied by one surfactant at the air–solution interface cmc: critical micelle concentration m: number of carbon atoms in the surfactant alkyl chain m-s-m: alkanediyl-,!-bis(alkyldimethylammonium bromide) dimeric surfactants s: number of carbon atoms in the alkanediyl spacer of m-s-m surfactants nT: total number of carbon and oxygen atoms in the spacer of dimeric surfactant with a poly(ethylene oxide) spacer (see surfactant A3 in Table 1) C: surfactant concentration DTAB, CTAB: dodecyl, hexadecyltrimethylammonium bromide SANS: small angle neutron scattering TRFQ: time-resolved ﬂuorescence quenching : surface excess concentration

I.

INTRODUCTION

Dimeric surfactants are made up of two identical amphiphilic moieties connected at the level of the headgroups, or of the alkyl chains but still very close to the headgroups, by a spacer group, which can be of variable chemical nature (Figs. 1a and b). The ﬁrst studies of dimeric surfactants, by Bunton et al. in 1971 [1] and Ul’berg et al. [2,3] in 1974, dealt with surface properties and critical micelle concentrations (cmc) of alkanediyl-,!bis(alkyldimethylammonium bromide) surfactants. These surfactants were referred to as ‘‘bisquaternary ammonium’’ [1–4], ‘‘gemini’’ [5], ‘‘dimeric’’ [6], and ‘‘siamese’’ [7] surfactants. Other surfactants of similar structure, with a hydrophobic or hydrophilic, ﬂexible or rigid spacer, were later synthesized and investigated. Still later, the synthesis of this type of surfactants was extended in three directions: Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 1 Schematic representation of dimeric surfactants with the spacer group connecting the two headgroups (a) or the alkyl chains at points close to headgroups (b). Surfactant (c), where the spacer connects the two amphiphilic moieties at points on the alkyl chains close to the chain ends, is a bolaform surfactant with a branched alkyl chain.

1. Surfactants made up of more than two amphiphilic moieties connected at the level or close to the headgroup, called oligomeric surfactants [8,9] 2. Dimeric surfactants where the two amphiphilic moieties are diﬀerent and that can be referred to as heterodimeric surfactants [10,11] 3. Dimeric surfactants with mixed ﬂuorinated-hydrogenated alkyl chains, such as C8F17C4H8 [12] In this chapter ‘‘dimeric’’ refers to surfactants made up by the covalent binding of two moieties, which are conventional amphiphiles (made up of one hydrophilic headgroup and one hydrophobic moiety, which may include more than one alkyl chain). It is essential that the spacer, whichever its nature, be located very close to the headgroups. When a fully hydrophobic spacer (polymethylene chain or aromatic group) connects the amphiphilic moieties far from the headgroups, somewhere in the second half of the alkyl chains, the dimeric surfactant is then simply a bolaform surfactant with a branched alkyl chain (Fig. 1c), characterized by a high cmc and poor performances [13]. The results may be worse with a hydrophilic spacer. The ﬁrst reports on dimeric surfactants did not generate much interest in the surfactant community. Starting in 1976, Devinsky et al. initiated new studies of quaternary ammonium dimeric surfactants, from the physicochemical viewpoint and for an assessment of their biological activity [14–22]. Anionic, cationic, and nonionic dimeric surfactants were later synthesized in a great variety of chemical structures and their properties investigated. In general, the properties of dimeric surfactants are Copyright © 2003 by Taylor & Francis Group, LLC

superior to those of comparable conventional monomeric surfactants [23]. Thus, their cmc values are at least one order of magnitude smaller [5,6,19,21–23]. Their values of C20, the surfactant concentration at which the surface tension of water is decreased by 20 mN/m, are much lower [23] and the values of cmc (surface tension at the cmc) for dimeric surfactants are equal to or lower than those for the corresponding conventional surfactants [23]. Also, they appear to have better solubilizing property [21] as well as better wetting, foaming, and lime-soap dispersing properties [24–27] than conventional surfactants. These properties are commonly used to evaluate surfactant performances. Besides, the Kraﬀt temperatures of dimeric surfactants with hydrophilic spacers are generally very low [23– 27], giving these surfactants a wide temperature range of utilization. Last, some dimeric surfactants show remarkable rheological properties (viscoelasticity, geliﬁcation and shear-thickening) at relatively low concentration, which cannot be obtained with conventional surfactants with the same alkyl chain, in the absence of additives [28]. It is therefore not surprising that physicochemical studies of dimeric surfactants and the assessment of their performances are presently a topic of activity in academic as well as industrial laboratories. In 1993 M.J. Rosen [23] stated that dimeric surfactants had ‘‘the potentials for being the next generation of surfactants— surfactants for the nineties.’’ This statement may have been premature but seems to be coming closer to reality. Indeed the German Company Sasol (formerly Condea) is now selling formulations based on dimeric surfactants under the trademark Ceralution. The alkanediyl-,!-bis(alkyldimethylammonium bromide) CsH2s-,!bis(CmH2m+1(CH3)2N+Br) have been by far the most extensively investigated dimeric surfactants. This chapter refers often to these surfactants, abbreviated as m-s-m, s and m being the carbon numbers of the alkanediyl group (spacer) and of the alkyl chain of the amphiphilic moieties. These surfactants are formally the dimers of the quaternary dimethylammonium surfactants with two unequal alkyl chains of carbon numbers m and s/2, Cs/2Hs+1(CmH2m+1N+(CH3)2 Br), thus the name dimeric surfactants. In this chapter, ‘‘conventional surfactants’’ and ‘‘monomeric surfactants’’ are given the same meaning. Chemical structures of dimeric surfactants are presented in Section II. The behavior at interfaces is considered next. Sections IV and V deal with micellization and micelle size, respectively. Microstructure of aqueous solution of dimeric surfactants, rheology of these solutions, and mixed micellization are considered in Sections VI, VII, and VIII, respectively. The phase behavior of dimeric surfactant–water mixtures is reviewed in Section IX. A last section deals with miscellaneous aspects.

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II. CHEMICAL STRUCTURES OF DIMERIC SURFACTANTS Dimeric surfactants have been synthesized in a great variety of chemical structures, particularly by the groups of Okahara in Osaka and Menger in Atlanta. In most instances the hydrophobic moieties are CmH2m+1 alkyl chains. Dimeric surfactants where the hydrophobic moieties are mixed ﬂuorinatedhydrogenated alkyl chains, as, for instance, C8F17C4H8 [12], have been synthesized. The diversity in structure is obtained by acting on the nature of the headgroup and spacer group and is illustrated in Table 1 [5,6,10,12,19,2950]. Thus, anionic, cationic, and nonionic headgroups have been used. Spacer groups, hydrophilic as well as hydrophobic, both rigid and ﬂexible for the latter, have been used. In Table 1, surfactants A and D are cationic; B, C, and E are anionic; F– H are nonionic with sugar or ethoxylated headgroup. I is half-anionic and half-nonionic. J and K are zwitterionic. L is a trimeric surfactant that can be referred to as 12-3-12-3-12 (generalizing the abbreviation introduced in the introduction for m-s-m surfactants). The tetrameric surfactant 12-3-12-4-123-12 has also been synthesized [51]. Surfactants A1–A3, B1, C, E, G, and I have a ﬂexible spacer. A4, A5, B2, and B3 have a rigid spacer. In many of these surfactants (A1, A4, A5, B1–B3, and C) the spacer is hydrophobic while it is hydrophilic in A3, E, and I. Surfactants similar to A with arylalkyl groups as hydrophobic moieties have been reported [20]. Surfactants A7 [12] and C [38] have mixed ﬂuorocarbon–hydrocarbon alkyl chains.

III. BEHAVIOR AT INTERFACES A. Air–Solution Interface The early studies of dimeric surfactants all involved surface tension measurements with the dual purpose of investigating their behavior at the air– solution interface (measurement of surface area a occupied by one surfactant molecule at the interface) and determining the cmc values. The surface areas a were obtained from the variation of the surface tension with the surfactant concentration, C, using the Gibbs expression of the surface excess concentration : ¼ ½d=d ln C=nRT

ð1Þ

where R is the gas constant and T the absolute temperature. n is a constant that takes the value 3 for 2-1 or 1-2 ionic surfactants (case of the ionic dimeric surfactants A–E in Table 1), in the absence of a swamping electrolyte. a is then obtained as (NA)1 , NA being Avogadro’s number. The value Copyright © 2003 by Taylor & Francis Group, LLC

n ¼ 2 has been used in some studies of dimeric surfactants on the basis that one of the two charged headgroups is neutralized by a bound counterion [18,19,22,52]. Other studies used the value n ¼ 3 [5,32,53–56]. Neutron reﬂectivity studies of several 12-s-12 surfactants concluded that the dimeric surfactant ion binds one bromide counterion at concentrations below the cmc [57]. This conclusion was not supported by an electrical conductivity study of the same surfactants [58]. Ion pairing cannot be excluded at concentration close to the cmc, for dimeric surfactants with large cmc values, that is, small m values (see Section IV.A). At any rate, the value used for n does not aﬀect the conclusions drawn from the values of a for series of homologous surfactants as these values are all aﬀected by the same constant factor. Note that this problem does not occur in the presence of a swamping electrolyte, where n ¼ 1. It is generally observed that dimeric surfactants are more eﬃcient than the corresponding monomeric surfactants in lowering the surface tension of water. Indeed, the values of the surface tension at the cmc, cmc, are close for monomeric and dimeric surfactants. However, because the cmcs of dimeric surfactants are much lower than those of monomeric surfactants, the former are more eﬃcient surface-active agents. Likewise, the values of the surfactant concentration C20 for which is lowered by 20 mN/m are much lower for dimeric than for monomeric surfactants. This is, of course, extremely important for utilization purposes. The large number of available data sheds light on the behavior of dimeric surfactants at the air–solution interface. The most important results are summarized below. 1. Surface activity is favored by ﬂexible spacers such as polymethylene or poly(ethylene oxide) chains. Bulky headgroups [59] or rigid aromatic spacers [5] result in larger values of cmc. Aging eﬀects (time-dependent surface tension) have been noted for surfactants with rigid spacers [5]. 2. The eﬀect of the carbon number m of the dimeric surfactant alkyl chain on a is generally small when m is not too large, up to say 12–14 [18,19]. For some dimeric surfactants, however, at higher values of m, premicellar association sets in and results in larger values of cmc and smaller apparent values of a [5,29,32,60,61]. 3. For surfactants A1 with the spacer (CH2)iY(CH2)i the value of a depends on the nature of the chemical group Y and increases in the order S (0.84) < N(CH3) (1.08) < CH2 (1.14) < O (1.28) [17]. The values in parentheses are those of a in nm2. 4. The variation of a with the spacer length (spacer carbon number s for m-s-m surfactants A1; total number nT of oxygen and carbon atoms in the spacer connecting the two charged groups for poly(ethylene oxide) spacers, as with surfactants A3 or E) is unusual. Figure 2 shows typical results for Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 1 Examples of Dimeric and Oligomeric Surfactants

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Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 2 Surface area a occupied by one dimeric surfactant at the air–water interface. Variation with the spacer carbon number s for the 12-s-12 surfactants A1 (*, data from Refs. 53 and 62); and with the total number nT of oxygen and carbon atoms in the spacer connecting the two charged headgroups for surfactants A3 with m ¼ 12 (&; nT ¼ 3z þ 2; from Ref. 31) and for surfactants [C10H21OCH2CH(OCH2CO 2, Na+)(CH2)]2O(CH2CH2O)z (*, data in the presence of 0.1 M NaCl; nT ¼ 9 þ 3z; from Ref. 63).

three series of dimeric surfactants [31,53,62,63]. For the m-s-m surfactants A1 (hydrophobic spacer) a is a maximum at a value of s around 10–12 [53,62]. A similar maximum in a at about the same value of s appears to occur for the bolaform surfactants [N+(CH3)3, Br]2(CH2)s [64]. Likewise, a maximum was observed for the dimeric surfactants derived from arginine and that also contain a hydrophobic spacer [40]. However, Figure 2 shows only a rather slow increase of a with nT for the two series of surfactants with a short poly(ethylene oxide) hydrophilic spacer [31,63]. Such behavior is expected from the increased volume and, thus, surface of the spacer group, which remains located on the water side of the interface. For the m-s-m surfactants with a hydrophobic spacer the maximum of a was explained in terms of a change of location of the polymethylene chain upon increasing s [62]. At s < 10, the chain has little ﬂexibility and lies ﬂat with a fairly linear conformation at the air–solution interface. This is suggested by the rapid initial increase of a with s in Fig. 2 and is supported by X-ray scattering studies of the lamellar and hexagonal phases in the water/12-s-12 surfactant mixtures [65]. At s > 10 the spacer becomes too hydrophobic to remain in contact with water and moves to the air side of the Copyright © 2003 by Taylor & Francis Group, LLC

interface, where it adopts a looped (wicketlike) conformation [62,64]. This results in an overall decrease of a. That eﬀect may be enhanced by a change of orientation of the alkyl chains with respect to the interface as s increases. The absence of a maximum for dimeric surfactants with a hydrophilic spacer also supports the above explanation. The maximum observed for dimeric surfactants with a hydrophobic spacer was accounted for theoretically by statistical-mechanical calculations [66]. The spacer conformational entropy and the attractive and repulsive interactions between surfactant molecules were found to be the main factors that determine the variation of a with s. Monte Carlo simulations were also performed to understand the behavior of dimeric surfactants at the air–solution interface [67,68]. Neutron reﬂection was used to investigate the structure of the layer of surfactant F with m ¼ 6 adsorbed at the air–solution interface [69]. The average thickness remained constant in the concentration range between 0.003 CMC and the CMC. The surface roughness was similar to that for other surfactants. The alkyl chains were normal to the surface at very low concentration (0.002 CMC) but showed an angle of tilt of about 358 at the CMC. The kinetics of adsorption of dimeric surfactants was found to be quite dependent on the nature of the surfactant. Two reports that concern anionic [70] and cationic A2 0 and A5 [71] dimeric surfactants indicated a diﬀusioncontrolled adsorption of the investigated surfactants. Dimeric surfactants with a ﬂexible spacer depressed the surface tension of water faster than dimers with a rigid spacer. At the diﬀerence of the preceding results a very large barrier to adsorption was found to exist for cationic dimeric surfactants derived from disulfur betaine [54]. The nonionic dimeric surfactants F showed a mixed behavior: diﬀusion-controlled adsorption at low surface coverage, but slower than this limit at the end of the process [72].

B. Liquid–Solution Interface Some results are available for the behavior of dimeric surfactants at the hexadecane–solution interface [29]. The occurrence of premicellization makes the analysis of the interfacial tension data diﬃcult. The results for the surfactant A2 with Y ¼ O and m ¼ 12 for which premicellization eﬀects are negligible show that the value of a at the air–solution interface is larger than at the hexadecane–solution interface.

C. Solid–Solution Interface Much progress has been achieved concerning the understanding of the adsorption of dimeric and oligomeric surfactants at solid–solution interfaces in the past 5 years. The adsorption isotherms of the cationic dimeric surfacCopyright © 2003 by Taylor & Francis Group, LLC

tants 12-s-12 on macroporous amorphous silica have been determined [73– 75]. As for conventional surfactants the mechanism of adsorption involves two steps [73–75]. The ﬁrst step takes place at very low concentration. It involves the binding of individual dimeric surfactants on charged sites on the silica surface by an ion exchange mechanism. The second step occurs at a concentration slightly below the cmc and corresponds to the formation of surface aggregates. The shape of the adsorption isotherm and the maximum amount of adsorbed surfactant, max, depend much on the state of the silica, raw or washed with HCl [75], as seen in Fig. 3. max decreases as the spacer carbon number s increases (see Fig. 4). This variation reﬂects changes of structure of the surface aggregates. An atomic force microscopy (AFM) study of the adsorbed layer of dimeric surfactants on the mica surface showed that 12-2-12 adsorbs as a ﬂat bilayer, whereas 12-4-12 and 12-612 adsorb under the form of parallel cylindrical aggregates [76]. The same study showed that a surfactant with a low packing parameter adsorbs under the form of spherical surface aggregates. The maximum amount of adsorbed surfactant is expected to decrease as the structure goes from a ﬂat bilayer to parallel cylinders and to spheres, thereby explaining the decrease of max upon increasing s seen in Fig. 4. AFM also showed a strong dependence of

FIG. 3 Adsorption isotherms of 12-2-12 on raw silica (*, SiNa) and on HClwashed silica (o, SiH) at 258C ( ¼ amount of adsorbed surfactant in micromole of surfactant per gram of silica; Ce ¼ concentration of surfactant in the equilibrated supernatant in the presence of silica). The arrows indicate the CMC of the surfactant in the presence of silica. (Reproduced from Ref. 75 with permission of Academic Press.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Variation of the maximum amount of adsorbed 12-s-12 surfactant on HClwashed silica with the spacer carbon number s at 258C. (Reproduced from Ref. 74 with permission of Academic Press.)

the shape of the surface aggregates on the nature of the solid surface. Thus 12-2-12 and 12-4-12 surfactants both adsorb on the cleavage plane of graphite under the form of half-cylindrical aggregates [76]. A recent study of the adsorption of 12-s-12 surfactants on amorphous silica involved the detailed chemical analysis of the equilibrated supernatant [77]. The results showed that the binding of 12-2-12 on the silica surface in the ion exchange step involves the two headgroups of this surfactant. The binding of 12-s-12 surfactants with a long spacer (s ¼ 10) involves only one headgroup. Intermediate situations occur with intermediate values of s. The adsorption behaviors on silica of the conventional surfactant dodecyltrimethylammonium bromide (DTAB), its dimer 12-3-12, trimer 12-3-123-12, and tetramer 12-3-12-4-12-3-12 have been compared. The eﬃciency of adsorption on silica at a given surfactant concentration below the CMC increased with the degree of oligomerization but the maximum amount adsorbed, expressed in gram of surfactant per gram of silica, varied little [51,73,78]. The microviscosity of the surface aggregates of 12-2-12 and 12-212-2-12 was shown to be larger than for the monomer DTAB [73]. The adsorption of various dimeric surfactants on titanium dioxide [79,80] and on laponite [81–83], and of m-4-m on montmorillonite, limestone, and sand [84,85], was investigated. In most of these studies the adsolubilization of model compounds by the surface aggregates was also investigated. Copyright © 2003 by Taylor & Francis Group, LLC

IV. MICELLE FORMATION AND SOLUBILIZATION A. Critical Micelle Concentration A large number of CMC values are available, and the most important features are as follows. 1. The CMCs of dimeric surfactants are much smaller than those of the corresponding monomeric surfactants, by at least one order of magnitude. Thus, the CMCs of the 12-2-12 and of DTAB are 0.81 mM and 15 mM, respectively [6]. As pointed out above, this is one reason for the current interest in dimeric surfactants. This important decrease of CMC may look surprising because a dimeric surfactant and the corresponding monomeric surfactant have nearly the same HLB number. This decrease is well explained in terms of the free energy change upon micellization. Indeed, the relationships between the free energy of micellization per alkyl chain, GoM , the CMC in mole of alkyl chain per liter, and the fraction of charges of micellized surfactant not neutralized by bound counterions (micelle ionization degree) are respectively given by for monomeric and dimeric ionic surfactants [86]: GoM ¼ RTð2 Þln CMC GoM ¼ RTð1:5 Þln CMC

ð2aÞ ð2bÞ

and

These equations yielded equal values of GoM for DTAB and 12-2-12, within the experimental error that is mainly due to the uncertainty on the value of [51]. Thus the low CMC values of dimeric surfactants simply arise because two alkyl chains are simultaneously transferred from water to the micelle pseudophase, instead of one for a conventional surfactant. 2. For the homologous series of surfactants A1–A3 (Table 1) with the ﬂexible hydrophobic spacer (CH2)2Y(CH2)2 the CMC depends little on the nature of the chemical group Y. Thus, the CMCs have been found to be [19] — N(CH3), O, CH2, and S, respectively. 1.2, 1.1, 1.0, and 0.84 mM for Y — 3. The variation of the CMC with the carbon number m of the alkyl chain has been determined for several series of dimeric surfactants with diﬀerent spacer groups. Figure 5 shows the variation of CMC with m for the three closely related series A1 with (CH2)5 and (CH2)6 spacers, and A5 with the (CH2C6H4CH2) spacer, in a semilogarithmic representation. The results for the ﬁrst two series (ﬂexible hydrophobic spacer) are nearly coincident and show a linear variation of ln CMC with m, as for the corresponding monomeric surfactants. The use of Eq. (2b) yields the value of the free energy of transfer from water to the micellar pseudophase per mole of CH2 group, GoM (CH2) ¼ 3.2 0.3 kJ/mol, a value close to that for alkyltrimethylammonium bromides [86]. The behavior of the third series with a rigid Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Variation of the CMC of surfactants A1 with the alkyl chain carbon number m for the m-5-m series (*, from Ref. 19) and m-6-m series (!, from Refs. 6 and 7), and the surfactant series A5 with the rigid spacer CH2C6H4CH2 series (*, from Ref. 5 at 508C).

hydrophobic spacer is very diﬀerent. The plot is linear, with a smaller slope than for the other two series, up to m 16, a value at which it goes through a minimum. This minimum was attributed to alkyl chain self-coiling and to premicellar aggregation [5]. Other series of dimeric surfactants showed a minimum or a departure from linearity in the variation of ln CMC with m at m 16 that were attributed to premicellar aggregation [29,32,58,60,61]. An increase of CMC upon increasing m was reported for a series of anionic trimeric surfactants and also attributed to premicellar aggregation [87]. Note that in some studies the values of the CMC measured by surface tension were found to be very diﬀerent from those obtained by other methods [5,87]. 4. Figure 6 shows that for three series of m-s-m surfactants A1 the CMC goes through a maximum upon increasing s at about s ¼ 56, irrespective of the value of m [6,18]. This maximum has been attributed to a change of the spacer conformation and its resulting eﬀect on headgroup hydration [18] and alkyl chain orientation [5]. In the semilogarithmic representation used ln CMC decreases nearly linearly upon increasing s, at s > 1012, that is when the spacer becomes hydrophobic enough to be located in the micelle core. Figure 6 also shows that for short hydrophilic poly(ethylene oxide) spacers the CMC increases slowly with nT. 5. For surfactants A3 with m ¼ 12 and a short poly(ethylene oxide) spacer, the CMC increased from 0.80 to 1.23 mM as the number z of Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 6 Variation of the CMC with the spacer carbon number s for the 10-s-10 surfactants A1 (*, from Ref. 20), 12-s-12 (!, from Ref. 6) and 16-s-16 (*, from Refs. 6 and 91); and with the total number nT of oxygen and carbon atoms in the spacer of A3 surfactants with m ¼ 12 (, from Ref. 31).

ethylene oxide units increased from 1 to 5 (see Fig. 6) [31]. Recall that for conventional surfactants the CMC decreased upon intercalation of ethylene oxide units between the alkyl chain and the charged group [88]. 6. The existence of two CMCs has been reported for some m-s-m surfactants [2,7,30]. For instance, the plots of the electrical conductivity versus concentration of solutions of 8-3-8 and 8-6-8 clearly showed two changes of slope [7]. However, micelles were present in the solution only at concentrations above the second break [7]. The ﬁrst change of slope is due to ion pairing between one dimeric surfactant ion and one counterion [58]. The results suggest that ion pairing becomes signiﬁcant only in the range between about CMC/2 and CMC. This does not justify the use of the value n ¼ 2 in the analysis of surface tension data by means of Eq. (1) (see Section III.A).

B. Micelle Ionization Degree The reported values of the ionization degree of micelles of ionic dimeric surfactants were obtained from the variation of electrical conductivity, K, with the surfactant concentration C, taking ¼ ðdK=dCÞC>CMC = ðdK=dCÞC
shown to yield too-large values of . The values of for 12-s-12 micelles have been recalculated [98] by applying the method proposed by Evans [97] to the same conductivity data. This new set of values of is certainly more accurate than the previously reported ones [6,89]. The results show a signiﬁcant increase of with s for the m-s-m surfactants A1 with a hydrophobic spacer: 10-s-10 [92,93]; 12-s-12 [6,89,98]; 16-s16 [91,94], and for the surfactants B1 with m ¼ 16 and phosphate headgroups [96]. The so-called chemical trapping method showed a decrease of the interfacial concentration of bromide ions upon increasing s, at the surface of 12-s-12 micelles, as expected from the results of SANS and conductivity [99]. SANS studies of a series of cationic dimeric surfactants A3, with a hydrophilic poly(ethylene oxide) spacer group and m ¼ 16, showed little variation of with the spacer length [95,96]. Note, however, that another SANS study of surfactants A3 with m ¼ 12 showed a large increase of with the spacer length [31]. The reason for the diﬀerence between the two studies is unknown.

C. Thermodynamics of Micellization Values of the free energy of micellization GoM have been reported for many dimeric surfactants [17–19,22,34]. Unfortunately, in most of these studies the values of GoM were obtained by inserting the CMC value into Eq. (2a) with or without the correcting -term, whereas Eq. (2b) should have been used. This procedure resulted in errors diﬃcult to evaluate since the values of are not known. o , of the dimeric surfactants A1 The enthalpies of micellization, HM [98,100–102] and A6 [35] have been determined calorimetrically. The results for the surfactants A1 are represented in Fig. 7. The two sets of represented data show important diﬀerences in numerical values, but the variation with the spacer carbon number is qualitatively the same with the presence of a shallow minimum around s ¼ 5–6. This value is the same as that for which the CMC of m-s-m surfactants is a maximum (see Fig. 7). The values of GoM , calculated from the reported values of the CMC and o permitted the calculation of the of , and the calorimetric values of HM o entropies of micellization, SM [98]. These values indicated that the micellization of 12-s-12 surfactants is entropy-driven [98]. 0 , were measured for cationic Volume changes upon micellization, VM 0 was about twice larger than dimers. For the short-chain dimer 8-6-8, VM for the corresponding surfactant monomer [7]. More recently the values of 0 VM were determined for several 12-s-12 surfactants [89]. The results repre0 sented in Fig. 7 show that VM goes through a shallow minimum at about Copyright © 2003 by Taylor & Francis Group, LLC

o FIG. 7 Variation of the enthalpy of micellization HM (*: from Ref. 98; &: from o (*, from Ref. 89) for Ref. 101) and of the volume change upon micellization VM the 12-s-12 surfactants A1 at 258C.

o o 0 the same s-value as HM . The minimum in the values of HM and VM has been assigned to a conformational change of the 12-s-12 molecule occurring at s ¼ 4–6 as the spacer carbon number is increased [98]. A study of surfactants A6 with m ¼ 12 concluded on the basis of measure0 o and HM that the two alkyl chains of the dimers are partially ments of VM associated in the premicellar range of concentration [35]. However, this conclusion was partly based on measurements performed at concentrations below 1 mM, where errors on the partial molal quantities are very large.

D. Solubilization Data on the solubility of water-insoluble compounds in micellar solutions of dimeric surfactants are scarce. Devinsky et al. [21] studied the solubilization of trans-azobenzene, a typical aromatic molecule, by micellar solutions of ms-m surfactants A1. The solubilizing capacity Sc, calculated from the reported data and expressed in moles of solubilized trans-azobenzene per mole of micellized m-6-m surfactant, increased nearly linearly with m at constant s. This result is similar to that for conventional surfactants, reﬂecting the nearly linear increase of volume of hydrophobic pseudophase with m. The eﬀect of the spacer carbon number at constant m is more interesting, with a maximum in the solubilizing power around s ¼ 6 (see Fig. 8). Again, Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 8 Solubilizing capacity of micellar solutions of m-6-m surfactants A1 for trans-azobenzene as a function of the spacer carbon number s. (Prepared from the results in Ref. 21. Surfactant concentration: 20 mM).

this value is close to that for which the cmc is a maximum. This result was interpreted in terms of spacer ﬂexibility and micelle structure [21]. A study of the solubilization of styrene by micellar solutions of 12-s-12 surfactants did not conﬁrm the eﬀect of the spacer length reported in Ref. [21]. The solubilization capacity of the solution increased progressively as s was increased from 2 to 12 (see Fig. 9) and showed a strong temperature dependence [103]. However, the solubilization capacity of surfactants A3 with m ¼ 12 and a hydrophilic poly(ethylene oxide) spacer was a maximum for z ¼ 1 or nT ¼ 5 (see Fig. 9), i.e., when the spacer length was close to that for the surfactant 12-5-12 [31]. Dam et al. [104] compared the solubilizing capacities of conventional and m-s-m surfactants for toluene and n-hexane. The dimeric surfactants showed a larger solubilizing capacity than the corresponding conventional surfactants and solubilized more toluene than n-hexane.

V. MICELLE SIZE AND SHAPE The size and polydispersity of dimeric surfactant micelles have been extensively investigated using time-resolved ﬂuorescence quenching (TRFQ) [8,51,105] and SANS [31,44,45,90–96]. SANS gives access to the micelle diameter from which the micelle aggregation number N (number of surfactants per micelle) can be calculated. TRFQ gives direct access to N. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Variation of the solubilization capacity of micellar solutions of 12-s-12 surfactants A1 (*) and of surfactants A3 with m ¼ 12 (*) for styrene with the spacer carbon number s for 12-s-12 surfactants A1 and with the total number nT of oxygen and carbon atoms in the spacer for A3, at 608C. The surfactant concentration is around 120 mM. (Figure prepared from results reported in Refs. 31 and 103.)

The variation of the micelle aggregation number N with the surfactant concentration C is illustrated in Fig. 10 for the 12-s-12 surfactants. Very similar variations were reported for the 10-s-10 surfactants [92,93]. The two sets of data showed remarkable similarities. In each series, the diﬀerent N versus C plots converged to the same value of N at zero concentration of micellized surfactant. For each surfactant series this value was close to that for the maximum spherical micelle formed by conventional surfactants with m ¼ 10 or 12. This behavior reveals that the m-s-m micelles are nearly spherical at very low concentration, close to the CMC. Also, the increase of N with C becomes steeper as s is decreased, indicating an increased tendency to micelle growth. For 12-2-12 and 12-3-12 growth results in threadlike micelles, which have been visualized by transmission electron microscopy at cryogenic temperature (see Section VI) [106]. The analysis of the N versus C results for the 10-s-10 surfactants [92,93] in terms of the ladder model for micellar growth [107,108] yielded the free energy diﬀerence G0SC between N0 dimeric surfactants packed in a part of a cylindrical micelle and in the maximum spherical micelle of aggregation number N0. Figure 11 shows that G0SC becomes less negative as s increases, as expected from the data in Fig. 10 and Refs. [92,93]. The decrease of the N-value upon increasing s was also evidenced with 16-s-16 surfactants [91,94] and for the anionic (phosphate) surfactants B1 Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10 Variation of the micelle aggregation number N with the surfactant concentration for 12-s-12 surfactants A1 at 258C: (^) 12-2-12; (&) 12-3-12; (&) 12-4-12; (*) 12-5-12; (*) 12-6-12; (s) 12-8-12; (~) 12-10-12; and (^) DTAB. For DTAB the aggregation number and the concentration have been divided by 2 to permit a direct comparison with the results for the dimeric surfactants. (Adapted from Refs. 8 and 105.)

FIG. 11 Variation of the free energy diﬀerence G0SC between N0 dimeric surfactants packed in a part of a cylindrical micelle and in the maximum spherical micelle, with the spacer carbon number s for 10-s-10 surfactants at 258C. (Reproduced from Ref. 46 with permission of Spinger-Verlag.) Copyright © 2003 by Taylor & Francis Group, LLC

[96]. Surfactants A3 with a hydrophilic poly(ethylene oxide) spacer and m ¼ 12 also showed a decrease of N upon increasing length (nT) of the spacer group [31]. The eﬀect of the spacer conformation on the aggregation of dimeric surfactants can be important. This eﬀect was investigated in the case of surfactants A5 with the rigid phenylenedimethylene spacer group having the ortho, meta, or para structure and with m ¼ 8 [90]. At a concentration of 2.5 wt % the ortho compound formed micelles, whereas the meta and para compounds gave rise to small premicellar aggregates (aggregation number: 3–4). Substitution of the bromide counterions by chloride counterions resulted in a signiﬁcant decrease of N, as in the case of conventional surfactant [8,105]. The size and shape of the dichained-diglucamide sugar surfactant F (Table 1) have been investigated by SANS [44]. This surfactant forms elongated micelles even at fairly low concentration, for instance, 14 nm long at 16 mM. Some indication on the polydispersity of micelles of dimeric surfactants was obtained in TRFQ studies of 12-s-12 surfactants [105]. A very small polydispersity was evidenced for the 15-mM solution of 12-3-12 and for the 50-mM solutions of 12-5-12 and 12-6-12, where the values of N indicate the presence of quasispherical micelles. Such behavior is in agreement with the theoretical prediction that spherical micelles are nearly monodisperse [109]. Signiﬁcant micelle polydispersity was evidenced in the 55-mM 12-3-12, 102mM 12-4-12, and 253-mM 12-5-12 solutions. This is in line with the larger values of N in those systems, all above 50 (that is, 100 dodecyl chains) and indicating nonspherical micelles [105]. Thus, as the dimeric surfactant micelles grow, the micelle shape changes and the micelle polydispersity increases.

VI. MICROSTRUCTURE OF AQUEOUS SOLUTIONS OF DIMERIC SURFACTANTS Transmission electron microscopy at cryogenic temperature (cryo-TEM) has been extensively used to investigate the microstructure of solutions of m-s-m surfactants A1, and of surfactants A3. The reported results show that at least for short spacers dimerization always results in the formation of aggregates that are less curved than those formed by the corresponding monomeric surfactants. The growth of micelles in aqueous solutions of 12-2-12 with increasing surfactant concentration has been investigated in detail [110]. The micrographs show spherical micelles at 0.26 wt % (Fig. 12A). Threadlike micelles Copyright © 2003 by Taylor & Francis Group, LLC

appeared already at 0.5 wt %, coexisting with spherical micelles (Fig. 12B). As the concentration was increased from 0.26 to 1 wt %, the fraction of surfactant under the form of threadlike micelles increased rapidly, while the number of spherical micelles per unit volume decreased (Figs. 12C and D). At 1 wt % branched threadlike micelles as well as closed-ring cylindrical micelles were observed (Fig. 12E). At 1.5 wt % the micrograph showed a network of connected cylindrical and closed-ring micelles with few isolated spherical and closed-ring micelles (Fig. 12F) [110]. The improved cryo-TEM resolution allowed the authors to show that the diameter of the endcaps of the threadlike micelles was larger than the diameter of the cylindrical part of the micelles, in agreement with theoretical predictions (inset in Fig. 12D) [110]. Entangled threadlike micelles extending over the whole micrograph, i.e., several microns long, are present in the 20-mM 12-2-12 solution (Fig. 12F). The presence of such micelles is responsible for the peculiar rheological behavior of these solutions (see Section VII). The micrograph of the 110mM 12-3-12 solution also showed threadlike micelles, although much shorter, but a 30-mM solution of this surfactant showed only spheroidal micelles [105]. Recall that DTAB, which approximately represents the monomer of 12-2-12 and 12-3-12, forms only spherical micelles even at fairly high concentrations [111]. The micrographs for the solutions of 12-4-12, 128-12, and 12-12-12 showed only densely packed spheroidal micelles [105]. This trend is in agreement with the results in Fig. 10. With 12-16-12 and 1220-12, the micrographs revealed vesicles, often doubly lamellar for the latter. The corresponding monomers of these dimeric surfactants also form vesicles at higher concentrations. In summary, the sequence of structures resulting from the self-assembly of 12-s-12 surfactants upon increasing s-value is elongated micelles ! spheroidal micelles ! vesicles For the 16-s-16 series, the electron micrographs revealed vesicles, bilayers membrane fragments, and threadlike micelles for the 16-3-16 surfactants and entangled elongated micelles for 16-4-16. The micelles were still slightly elongated for 16-6-16 but spheroidal for 16-8-16. SANS showed the 16-1216 micelles to be spheroidal [94]. Recall that hexadecyltrimethylammonium bromide (CTAB), which can be considered as the monomer of 16-3-16, forms elongated micelles at high concentrations [111]. Thus, as for 12-s-12 surfactants, dimerization results in aggregates of lower curvature for short spacers. The sequence of structures for 16-s-16 surfactants upon increasing the spacer carbon number is vesicles þ elongated micelles ! elongated micelles ! spheroidal micelles

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Vesicles are expected to form with 16-s-16 surfactants with s 12, but such surfactants have not been investigated yet. Cryo-TEM showed that the surfactants A3 with a poly(ethylene oxide) spacer and m ¼ 12 form spheroidal micelles for nT ¼ 14 (that is, z ¼ 4) and

FIG. 12 Cryo-TEM images of 12-2-12 solutions at 258C. (A) 0.26 wt %: the dark dots are spherical micelles; a few short cylindrical micelles are observed. (B) 0.50 wt %: longer cylindrical micelles in larger number than in (A). (C) 0.62 wt % and (D) 0.74 wt %: the density of spheroidal micelles has signiﬁcantly decreased and the length of the elongated micelles has much increased. The inset in (D) shows that the endcaps have a larger diameter than the cylindrical part of the micelles. (E) 1 wt %: very few spheroidal micelles and endcaps are still present. Existence of branching points (arrows) and closed rings (arrowheads). (F) 1.5 wt %: network of branched (arrows) cylindrical micelles. (G) 1.5 wt %: many closed-ring micelles in addition to normal branching points. (Reproduced from Ref. 110 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 12

Continued

wormlike micelles for nT ¼ 5 (that is, z ¼ 1) [31], whereas 12-s-12 micelles are spherical for s ¼ 5. The diﬀerence between surfactants A3 and 12-s-12 at s ¼ nT ¼ 5 can be explained on the basis of the results in Fig. 2. The surface area per surfactant is lower for the A3 than for the 12-s-12 surfactants. Thus aggregates of lower curvature are expected with the former, as indeed observed. The dimeric surfactants m-2-m,T, where T is an L- or D-tartrate ion, are soluble in many organic solvents, such as toluene, xylene, pyridine, CH2Cl2, CHCl3, and Cl2CHCHCl2. The solutions are low viscous at above 408C but turn into gels at room temperature [112,113]. Examination of the gels by transmission electron microscopy revealed long and strongly entangled helical ﬁbers (see Fig. 13). The mechanism of formation of these structures was discussed [113]. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 13 Transmission electron microscopy images of the gel formed by the surfactant 12-2-12,L-tartrate in CHCl3 (A) and of an individual helix formed by 12-2-12,Ltartrate in water (B). (Reproduced from Ref. 112 with permission of Wiley-VCH Verlag GmbH.)

Molecular dynamics has been used to simulate the association behavior of dimeric surfactants in aqueous solution [114]. The change of structure from elongated to spheroidal micelles upon increasing the spacer carbon number was accounted for. The calculation also predicted the formation of branched threadlike micelles. These structures were not observed in the early cryo-TEM studies of 12-s-12 surfactants [105,106] but were observed with the triquaternary ammonium surfactant 12-3-12-3-12 [9]. Later on, improvements brought to the cryo-TEM technique permitted the observation of branched threadlike micelles of 12-2-12 [110]. Dimeric and oligomeric surfactants are capable of forming such structures because the diﬀerent alkyl chains in a given oligomeric surfactant ion can take diﬀerent relative orientations [114]. Copyright © 2003 by Taylor & Francis Group, LLC

VII.

RHEOLOGY OF AQUEOUS SOLUTIONS OF DIMERIC SURFACTANTS

The reported studies concerned solutions of 12-2-12 and 12-3-12 [28,51]. Figure 14 illustrates the rheological behavior of these surfactants in the absence of added salt. At low surfactant volume fraction , the zero shear viscosity increases ﬁrst relatively slowly with . This increase becomes very steep above a certain volume fraction , interpreted as the onset of fast micellar growth and of the semidilute concentration range. is seen to be greatly increased in going from 12-2-12 to 12-3-12, that is, upon increasing the spacer carbon number. The maximum in the versus plot has been attributed to a true decrease of micelle length [28] caused by the theoretically predicted increase of micelle ionization degree with the surfactant concentration for cylindrical micelles [115,116]. In turn, this increase of micelle charge can cause a decrease of magnitude of the free energy diﬀerence G0SC (see Section V). Self-diﬀusion studies of various dimeric surfactants conﬁrmed the importance of these eﬀects [117]. Nevertheless, the molecular dynamics simulations suggested an alternative explanation in terms of formation of branched threadlike micelles [114]. The analysis of the frequency-dependent loss and storage moduli was based on the theory for ‘‘living polymers’’ [118,119]. The time for micelle breakdown (average time after which an elongated micelle breaks into two

FIG. 14 Variation of the zero shear viscosity of solutions of 12-2-12 () and 12-312 (*) with the surfactant volume fraction at 208C. (Reproduced from Ref. 51 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 15 Eﬀect of the shear rate on the viscosity of a 1 wt % solution of 12-2-12 in D2O. (Reproduced from Ref. 123 with permission of the American Chemical Society.)

smaller ones) was thus evaluated and found to fall in the range between 10 and 0.1 s [28]. The study of the linear and nonlinear viscoelastic properties of 12-2-12 solutions in the presence of salt [120] suggested that they depend on electrostatic interactions between micelles. These interactions are long-range and result in the occurrence of a pronounced correlation peak in the SANS spectra of the solutions [121]. Salt-free dilute solutions of 12-2-12 show shear-induced structure at a concentration ranging between 0.7 and 1.5 wt %. Above a certain shear rate the viscosity increases rapidly and the solution becomes anisotropic. The viscosity then goes through a maximum and decreases [122,123]. This behavior is illustrated in Fig. 15. Cryo-TEM observation revealed that the shear induced an aggregation of the threadlike micelles [123]. This explanation was supported by a time-resolved SANS study [124] that also showed that the shear-induced structures had long lifetimes. Recent theoretical calculations appear to support this explanation [125].

VIII. MIXED MICELLIZATION Studies of mixed micellization of dimeric surfactants with conventional surfactants were performed with the hope of observing synergistic eﬀects that would render even more attractive the use of dimeric surfactants in formulating commercial detergents. Copyright © 2003 by Taylor & Francis Group, LLC

Anionic dimeric surfactants comicellize with zwitterionic and nonionic polyoxyethylated conventional surfactants [126,127]. Synergism in micelle formation was observed with the zwitterionic surfactants but not with the nonionic surfactants used. However, synergism in surface tension reduction eﬀectiveness was observed. The mixed micellization of four series of cationic dimeric surfactants A1, A2, and A2 0 , diﬀering by the nature of the spacer, and of conventional sugar surfactants (alkylglucoside and alkylmaltoside) has been investigated [128]. All mixtures of cationic dimeric surfactants with the conventional sugar surfactants showed synergism in surface tension reduction eﬃciency. Synergism was not observed with the mixtures of conventional cationic surfactants and the same sugar surfactants. The cryo-TEM study of the comicellization of 12-2-12 with its corresponding monomer, DTAB, revealed that the threadlike micelles formed by the former are rapidly transformed into spheroidal micelles, already at a DTAB mole fraction of 0.3 [106]. A variable contrast SANS study showed a rather uniform DTAB distribution in the threadlike micelles and no detectable accumulation of DTAB in their hemispherical endcaps [129]. Cryo-TEM showed that additions of the spherical micelle-forming surfactants DTAB and 12-10-12 to vesicular suspensions of 12-20-12 result in the progressive transformation of the 12-20-12 vesicles into mixed spheroidal micelles [130]. No intermediate structures, such as bilayer membrane fragments and/or threadlike micelles, usually formed during such a transformation, were observed [130]. A very diﬀerent behavior was noted upon addition of the threadlike-forming surfactant 12-2-12 to vesicular suspensions of 12-20-12 [131]. The vesicle size ﬁrst increased at very low 12-2-12 content. The vesicles then broke up into smaller ones. This was followed by the formation of disklike micelles, then of ringlike micelles and short threadlike micelles. At a still higher 12-2-12 concentration, the threadlike micelles became longer. The ﬁnal structure was that of a network of connected threadlike micelles containing a few isolated closed-ring micelles as in Figs. 12F and G. Metastable ribbonlike structures were evidenced in the intermediate range of 12-2-12 content. The equilibrium structure in this range was reached only after several weeks. Additions of the dimeric anionic surfactant B2 with m ¼ 12 and a hydrophobic rigid spacer to a solution of CTAB has been reported to result in the formation of so-called cross-linked micelles [132]. Very large particles were detected by light scattering at values of the mole ratio [dimeric surfactant]/ [CTAB] as low as 0.05–0.07 [132]. The eﬀect of additions of a dimeric disulfate surfactant with a hydrophilic poly(ethylene oxide) spacer to a CTAB solution under experimental conditions identical to those in Ref. [132] was investigated [133]. Cryo-TEM and TRFQ showed that these additions resulted in a simple growth of the CTAB micelles and, at the highest Copyright © 2003 by Taylor & Francis Group, LLC

content of dimeric surfactant, in the presence of membrane fragments [133]. The latter probably corresponds to the large particles seen in Ref. [132]. These new results do not support the existence of crossed-linked micelles. The size of mixed micelles of dimeric and conventional surfactants was investigated by TRFQ and SANS. The size and the extent of micellar growth in mixtures of CTAB and 16-s-16 surfactants were shown to be modulated by the fraction of dimeric surfactant in the mixture. The composition of the mixed micelles followed that predicted for an ideal mixture [134]. The microviscosity of the mixed micelles showed a continuous increase with the fraction of dimeric surfactant [134]. In several instances the micelle aggregation number of mixed micelles of anionic or cationic dimers and conventional surfactants, cationic or nonionic, varied monotonously from the value for the conventional surfactant to that for the dimeric surfactant, as the dimer mole fraction was increased [135,136]. In some cases, the aggregation number was a minimum at some intermediate composition, but there appeared to be no correlation between the existence of this minimum and synergism in micelle formation [135,136]. These diﬀerent behaviors are illustrated in Fig. 16, which compares the variations of the total number of alkyl chains per micelle in the systems DTAB/C12E8 and 123-12/C12E8 [136].

FIG. 16 Variations of the total aggregation number with the mole fraction of ionic surfactant in the mixtures DTAB/C12E8 (A, total concentration 100 mM) and 12-312/C12E8 (B, total concentration 20 mM), at 258C (*), 408C (~), and 558C (&). The solid lines are guides to the eyes. (Reproduced from Ref. 136 with permission from Academic Press.) Copyright © 2003 by Taylor & Francis Group, LLC

IX. PHASE BEHAVIOR The phase behavior of the 12-s-12 surfactant–water mixtures has been systematically investigated [65]. Lyotropic mesophases occurred in a concentration range that narrowed as the spacer carbon number increased and completely disappeared for s ¼ 10 and 12. For these surfactants the micellar range extends to concentrations as high as 90 wt %. The corresponding monomeric surfactants, C12H25(Cs/2Hs+1)N+(CH3)2 Br with s/2 ¼ 5 and 6, showed a similar behavior [137]. This may be of considerable interest in the use of these surfactants. Lyotropic mesophases occur again for s 16. The observed mesophases have the texture of the conventional lamellar and cylindrical phases. The alkyl chains are inside the cylinders of the cylindrical phase, and the octanediyl spacer lies nearly ﬂat and almost fully extended on the core–water interface in both the lamellar and cylindrical (hexagonal) phases. The 12-s-12 surfactants showed no thermotropism, contrary to the corresponding monomers. Geometric constraints on the headgroup arrangement associated to the presence of the spacer were held responsible for this behavior [65]. The 16-s-16 surfactants were shown to form intermediate and/ or bicontinuous cubic phases, in addition to lamellar and hexagonal phases [138]. The eﬀect of the alkyl chain carbon number m was found to be relatively unimportant for the m-6-m series with m ¼ 8, 10, and 12 [139]. The dissymmetric surfactants m-2-m 0 (A9 in Table 1) showed a phase behavior rather diﬀerent from that of conventional surfactants. Thus, upon increasing concentration, the elongated micelles turned into multilayered structures (stacks of bilayers with no water layer in between) and then into an inverted hexagonal phase (see Fig. 17) [10,11]. On the contrary, the phase diagrams of the dimeric surfactant sodium-1,2-bis(N-dodecanoyl -alanate)-N-ethane did not diﬀer much from that of the corresponding monomeric surfactant sodium N-dodecanoyl-N-methyl -alanate [140]. The dimeric surfactant (CH2)6-1,6-bis[NCPhPhO(CH2)5N+(CH3)2, Br], which is chemically similar to the preceding ones, forms no cylindrical phase but gives rise to two lamellar phases under appropriate temperature and concentration [141]. The dimeric sugar surfactant F (Table 1) showed the phase sequence hydrated crystals ! lamellar (L) ! cubic (V1) ! hexagonal (H1) ! micellar (L1) with decreasing surfactant concentration, similarly to conventional surfactants [44]. The addition of KBr to a solution of threadlike 12-2-12 micelles brought about the formation of a lamellar phase followed by phase separation into a salt-rich dilute surfactant phase and a salt-poor lamellar phase [142]. The latter was shown to contain highly curved defects that were identiﬁed as water-ﬁlled holes crossing the lamellae. The eﬀect of KBr on the phase

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FIG. 17 Phases observed in aqueous solutions of m-2-m 0 surfactants A9 as a function of m and m 0 . The concentrations of the investigated solutions were between 0.1 and 10 wt %. Transition temperatures are indicated whenever a phase transition was observed. The diﬀerent types of threadlike micelles diﬀer by their overlap concentrations: lower than 0.5 wt % for the longest micelles, between 0.5 and 2 wt %, and between 2 and 10 wt %. (Reproduced from Ref. 10 by permission of Royal Society of Chemistry.)

behavior of 12-2-12 conﬁrmed the tendency of this surfactant and of similar ones to form stacks of collapsed bilayers [143].

X. MISCELLANEOUS A. Dynamics of Micelles of Dimeric Surfactants Chemical relaxation methods have been used to investigate the kinetics of exchange of dimeric surfactants between micelles and intermicellar solution in micellar solutions of m-s-m surfactants A1. For the short alkyl chains surfactants 8-3-8 and 8-6-8, the reaction of entry of one surfactant into its micelle is nearly diﬀusion-controlled, whereas the rate of dissociation (exit) depends strongly on the hydrophobicity of the surfactant [7]. However, for the longer alkyl chain surfactants 12-s-12, the rate of entry of a surfactant into its micelle is considerably slower than for a diﬀusion-controlled process, by a factor of over 100 [144]. The entry-rate constant increases with the Copyright © 2003 by Taylor & Francis Group, LLC

spacer carbon number. The residence time of the 12-s-12 dimeric surfactants in their micelles is much longer than that for the corresponding monomeric surfactants [144]. The kinetics of micelle formation/breakup for the dimeric surfactants 12s-12 was investigated by pressure-jump [144]. The variation of the relaxation time associated to this process with the surfactant concentration suggests that, at concentrations close to the cmc, micelle formation/breakup occurs via stepwise entry/exit of one dimeric surfactant at a time into/from its micelles. The results also indicate that the 12-s-12 micelles can have very long lifetimes, up to tens of seconds. Long-chain dimeric surfactants (14-2-14, m-2-m 0 surfactants A9 with m þ m 0 > 28, and surfactants A7 with C8F17C4H8 alkyl chains and s ¼ 2) were investigated using NMR [12,145]. This study revealed a slow exchange of the surfactant between micelles and intermicellar solution on the NMR time scale. These results support the trend noted in the pressure-jump study discussed above [144]. Rheological investigations of fairly concentrated solutions of 12-2-12 threadlike micelles [28] provided an estimate of the time for the breakup of a threadlike micelle into two daughter micelles. This time was found to range between 10 and 0.1 s.

B. Oligomeric Surfactants Oligomeric surfactants are made up of x amphiphilic moieties connected at the level of the headgroups by x 1 hydrophilic or hydrophobic spacers. They constitute a natural extension of dimeric surfactants. The cationic trimeric surfactants 12-3-12-3-12 and 12-6-12-6-12 (with the notations used in Section I) have been synthesized and their self-association behavior in water investigated [8,9,51]. Anionic trimeric surfactants [88] and the tetrameric cationic surfactant 12-3-12-4-12-3-12 have also been synthesized [51]. The cmc decreases in a somewhat hyperbolic manner as one goes from the monomer DTAB to the dimer 12-3-12, trimer 12-3-12-3-12, and tetramer 12-3-12-4-12-3-12 (see Fig. 18) [51]. The largest decrease of cmc is obtained in going from DTAB to 12-2-12 or 12-3-12. The tendency to micelle growth upon increasing surfactant concentration follows the sequence 12-3-12-3-12 12-2-12 > 12-3-12 12-6-12-6-12 [8,9,51]. This sequence reveals a subtle compensation between the eﬀect of the spacer carbon number and that of the degree of oligomerization. Cryo-TEM studies showed that 12-3-12-3-12 forms branched threadlike micelles [9] while the solutions of 12-3-12-4-12-3-12 contain a signiﬁcant amount of surfactant under the form of closed-ring micelles [51,146]. Interesting rheological properties were also observed [51,147]. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 18 Variation of the CMC of cationic surfactant oligomers of the type 12-s-12s-12 . . . with the number of dodecyl groups at 258C: (*) s ¼ 3; (*) s ¼ 6. (Reproduced from Ref. 51 with permission of the American Chemical Society.)

C. Interactions Between Dimeric Surfactants and WaterSoluble Polymers Surfactant-based formulations often contain water-soluble polymers that improve the formulation properties. The study of the interaction of dimeric and oligomeric surfactants with water-soluble polymers is therefore important in view of a future use of such surfactants in formulations. The reported studies concern m-s-m dimeric surfactants and varied watersoluble polymers [148–152]. Hydroxypropylguar (HPG) and its hydrophobically modiﬁed derivative, HMHPG, were used as neutral polymers [148]. The 12-s-12 surfactants were found to interact weakly with HPG and strongly with HMHPG. The corresponding monomer, DTAB, hardly interacted with HPG and only weakly with HMHPG. The interaction between these polymers and the trimeric surfactant 12-3-12-3-12 was stronger than with the dimers [148]. Thus the oligomerization results in increased interactions with a given polymer. The interaction between m-s-m surfactants and oppositely charged polyelectrolytes, copolymers of disodium maleate and alkylvinylether [149] and sodium hyaluronate [150,151] showed that as for neutral polymers, dimeric surfactants interact more strongly than monomeric surfactants with polymers. As for conventional surfactant/polyelectrolyte systems, the strength of the m-s-m–sodium hyaluronate interaction could be modulated by addition of salt [150,151].

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The interaction between 12-2-12 or DTAB and poly(amidoamine) dendrimers with surface carboxyl groups was investigated [152]. The results showed that the presence of the dendrimer decreased the DTAB concentration but increased the 12-2-12 concentration at which the surfactant aggregates. The last result is very surprising.

D. Speciﬁc Uses of Dimeric Surfactants We have pointed out in the introduction that dimeric surfactants are generally superior to conventional surfactants in properties such as surface tension lowering, solubilization (Section IV.D), wetting, foaming, and lime-soap dispersing ability. Some uses of dimeric surfactants are now brieﬂy mentioned. Dimeric surfactants are capable of various biological eﬀects such as an inhibitory action on bacterial activity [14,16,17,153] and on photosynthesis [4]. Dimeric surfactants have been found to achieve much better separation than sodium dodecylsulfate, for instance, in electrokinetic chromatography [154,155]. m-s-m and m-s-m 0 surfactants have been systematically used for the synthesis of organized mesoporous silica of cubic [156] and hexagonal symmetry [156,157]. Cationic dimeric surfactants, when used as phase transfer catalysts in alkylation reactions, showed a better extractive activity than compounds generally used for this purpose [158]. Micellar solutions of 16-s-16 surfactants were used to modify the rate of various types of chemical reactions: nucleophilic substitution [1], decarboxylation [159,160], and cyclization [161,162]. Dimeric surfactants A1 [103] and A3 [31] with m ¼ 12 have been used for generating styrene/water/dimeric surfactant oil-in-water microemulsions and for polymerizing styrene in these systems. With microemulsions based on 12-s-12 surfactants the molecular weight of the synthesized polystyrene was a maximum at s ¼ 6 in the absence of a cross-linker and at s ¼ 10 in the presence of a cross-linker, at 258C. No maximum was observed at 608C. Some correlation appeared to exist between the extent of the microemulsion domain and the molecular weight of the polymer [103]. Micellar solutions of 12-2-12 have been used to prepare colloidal metal particles of gold from AuHCl4 [163]. The particles were polyhedral or ﬁbrous depending on the HAuCl4 content of the UV-irradiated solution (see Fig. 19). Colloidal silver and gold particles were prepared from a solution of the nonionic dimeric surfactant Surfynol 465, with a yield 10 times larger than when using other methods of preparation [164,165]. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 19 Morphology of the colloidal gold particles generated in an HAuCl4 solution containing 2 wt % 12-2-12, after a 4-h UV irradiation. [HAuCl4] ¼ 1 mM (a); 5mM (b); 10 mM (c); and 40 mM (d). (Reproduced from Ref. 164 with permission of Academic Press.)

Cationic surfactants have been adsorbed on various solids and the treated solids used for removing model pollutants from aqueous media. Esumi et al. [79–83] and Rosen et al. [166,167] show that dimeric surfactants are more eﬃcient than the corresponding monomeric surfactants for this purpose.

XI. CONCLUSIONS This chapter has considered several aspects of the dimeric or gemini surfactants. The interest of these surfactants lies mostly in their low cmc and in their high eﬃcacy in lowering the surface tension of water and in adsorbing at interfaces, as compared to conventional (monomeric) surfactants. These properties are very important when considering possible uses of these surfactants. Additionally, dimeric surfactants interact more strongly with water-soluble polymers than the corresponding monomeric surfactants, and their micelles have long lifetimes. These two aspects may be useful in speciﬁc applications. Finally, dimeric surfactants with a short spacer show interesting rheological properties. Copyright © 2003 by Taylor & Francis Group, LLC

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8 Fluorinated Surfactants Having Two Hydrophobic Chains NORIO YOSHINO

I.

Tokyo University of Science, Tokyo, Japan

INTRODUCTION

Carbon atoms in hydrocarbon molecule are in a reduced state because they bind to hydrogen atom of an electronegativity of 2.1, and the C–H linkage has a moderately high bond energy of 415 kJ mol1 while those in ﬂuorocarbon molecule are highly oxidized, more oxidized than those binding to an oxygen atom of an electronegativity of 3.6 since they are bound to a ﬂuorine atom with an electronegativity of 4.0, thereby making the ﬂuorocarbon molecule very stable against oxidation. Halogen atoms are in general strongly electronegative, and the bond strength between halogen and carbon atoms is high; in particular, the F–C bond has a high bond energy of 484 kJ mol1 . Moreover, the ﬂuorine atom is very small in size, the second smallest next to the hydrogen atom, and its van der Waals and covalent radii are merely 10% larger than those of the hydrogen atom. Nevertheless, this small diﬀerence in size makes the ﬂuorocarbon chain a rigid, rodlike shape with a twist period of 13 carbon atoms, whereas the hydrocarbon chain takes a ﬂexible structure. Fluorine atoms of the ﬂuorocarbon chain densely cover the carbon skeleton inside the chain, forming a ﬂuorine sheath. Fluorine compounds alter the surface characteristics of solids and liquids to a great extent, in addition to their thermal resistivity, chemicals resistivity, weather resistivity, and electroinsulativity, and form an extremely low free energy surface. Because of this low surface free energy, ﬂuorine compounds develop a remarkable surface tension lowering activity, water and oil repellency, dirt preventing activity, low friction, nonadherability, etc. Introduction of ﬂuorine atoms into medicines (e.g., 5-ﬂuorouracil, an anticancer agent) and pesticides (e.g., 2,6-diﬂuorobenzoylurea derivatives with a ﬂuorinated aromatic ring) gives these compounds a speciﬁc physiological activity. Because the ﬂuorine atom is only slightly larger in size than the Copyright © 2003 by Taylor & Francis Group, LLC

hydrogen atom, the body can take up ﬂuorinated compounds derived from original compounds by replacing hydrogen with ﬂuorine atoms as well as the original ones (mimic eﬀect). These ﬂuorinated compounds can keep their pharmacological activity for a relatively long time because the bond energy of the C–F bond is large, thereby inhibiting their metabolism through oxidation and other reactions. As mentioned above, ﬂuorinated surfactants with a perﬂuoroalkyl group as their hydrophobic group greatly lower the surface tension of water, exhibit a high surface activity at low concentrations, are heat- and chemicalsresistant, and develop a surface activity even in organic solvents. Surfactants having a ﬂuorocarbon chain in their molecule can ﬁnd many applications based on their properties. Thus, C7F15COONH4 is used as an emulsiﬁer in emulsion polymerization for ﬂuororesins and C8F17SO3K as an additive to etching and plating baths because of its chemicals resistance and surface activity in strongly acidic and basic media. The surfactants are also used as an oil ﬁre extinguisher and a wax on account of their surface tension lowering action and oil and water repellency, in paints and inks due to their low surface tension and high penetrability, and as an additive to enhance the anticlouding and antifogging ability of agricultural ﬁlms. The present review article is concerned with the synthesis and some properties of two series of double chain-type ﬂuorinated anionic surfactants. One is a series of surfactants with two ﬂuorocarbon chains in their molecules and a strong adsorbability and a high ﬂocculating-dispersing action on magnetite particles in water. The other is a series of hybrid-type surfactants having both ﬂuorocarbon and hydrocarbon chains in one molecule and the ability of emulsifying three component systems composed of hydrocarbon, water, and ﬂuorinated oil.

II. SYNTHESIS AND APPLICATIONS OF FLUORINATED DOUBLE CHAIN-TYPE SURFACTANTS (I) [1–4] The surface of inorganic substances is generally hydrophilic and incompatible with organic solvents. In order to prepare stable dispersions of inorganic ﬁne particles in organic solvents such as paints, surfactants are often necessary to make the particle surface organophilic. If ﬂuorinated oils are used instead of organic solvents, the particle surface should be compatible with the oils. Oils or resins with ﬂuorocarbon chains, as represented by polytetraﬂuoroethylene, are oil- and water-repellent and constitute a class of speciﬁc compounds with many characteristics including incombustibility, high lubricativity, chemical inactivity, low toxicity, high electroinsulativity, and good viscosity-temperature performance. Copyright © 2003 by Taylor & Francis Group, LLC

Fluorinated polymers have a low surface energy as compared with hydrocarbon polymers, and so the binding force between the surfaces of polymer and ﬁller (inorganic ﬁller) is insuﬃcient even though compounding seems to be a shortcut to allow these polymers to develop those functions such as magnetism which they don’t have while making good use of their characteristics. This review describes the synthesis and dispersion-ﬂocculation ability of new ﬂuorosurfactants that eﬀectively cover the surface of magnetite particles with ﬂuorocarbon chains, thereby giving them high dispersibility and ﬂocculability. The surfactants synthesized are double chain-type ﬂuorosurfactants with two ﬂuorocarbon chains like a pine needle. The method of their synthesis is shown below. Typical chemical reactions are as follows:

A. Synthesis of Intermediates Bis(polyﬂuoroalkyl)maleates 1. Synthesis of F(CF2)8(CH2)2OCOCH=CHCOO(CH2)2(CF2)8F 1H,1H,2H,2H-heptadecaﬂuoro-1-decanol [F(CF2)8(CH2)2OH, bp 88–908C/ 500 Pa (133 Pa ¼ 1 mmHg)] (30.1 g, 6.2 mmol), maleic anhydride (3.10 g, 31.6 mmol), and p-toluenesulfonic acid monohydrate (1.18 g, 6.2 mmol) were reﬂuxed under magnetically stirring in 120 cm3 of toluene for 15 hr at the boiling point of the mixture (1108C). This is an esteriﬁcation reaction, and the byproduct of water was removed out of the reaction system by azeotropy. The reaction mixture was cooled down to 708C and washed thoroughly with water to remove p-toluenesulfonic acid, catalyst, and unreacted maleic acid anhydride when the amount of water formed was 90% of the theoretical value. Fractional distillation of the toluene solution after dehydration with anhydrous sodium sulfate gave bis(1H,1H,2H,2H-heptadecaﬂuorodecyl)maleate (bp 195–1978C/400 Pa, mp 62–638C) as a white solid. The amount obtained and the yield were respectively 27.1 g and 86.8%. Copyright © 2003 by Taylor & Francis Group, LLC

Other bis(polyﬂuoroalkyl)maleates were synthesized in a similar way. Table 1 summarizes the boiling points and yields of the compounds synthesized. With the exception of bis(1H,1H,2H,2H-heptadecaﬂuorodecyl)maleate, all other compounds were colorless transparent liquids.

B. Synthesis of Double Chain-Type Fluorosurfactants 1. Synthesis of F(CF2)8(CH2)2OCOCH2CH(SO3Na)COO(CH2)2 (CF2)8F Bis(1H,1H,2H,2H-heptadecaﬂuorodecyl)maleate (5.00 g, 5.1 mmol) was dissolved in 85 cm3 of 1,4-dioxane and an aqueous sodium hydrogensulﬁte solution [NaHSO3 (0.7 g, 6.7 mmol) dissolved in 35 cm3 water] was added to the dioxane solution at 508C. The mixed solution was reﬂuxed at 1018C and ﬂuorosurfactant began to form in 10–15 hr with a large number of bubbles. The temperature was lowered to 988C at this moment and heating was continued while preventing boiling and bubbling of the solution. After the solution was heated at this temperature further for 30–40 hr, white precipitates formed were ﬁltered out with a glass ﬁlter and washed with 50 cm3 of 1,4-dioxane at 508C on the ﬁlter to remove the unreacted bis(1H,1H,2H,2H-heptadecaﬂuorodecyl)maleate. Crude ﬂuorosurfactant thus obtained was dispersed in 50 cm3 of water with an ultrasonic homogenizer, the resultant colloidal dispersion was centrifuged (10,000 rpm, 10 min), and the supernatant liquid was discarded. This procedure was repeated three times to remove excess sodium hydrogensulﬁte. The ﬁnal product was obtained after dispersing the washed solid in tetrahydrofuran (noncolloidal dispersion) to remove water, separating the solid by ﬁltration with a glass ﬁlter, and drying it. The amount obtained and the yield of the product were 4.7 g and 86.0%, respectively. The melting point was 2908C. Other double chain-type ﬂuorosurfactants were synthesized in a similar manner and obtained as white solids. Table 2 shows their melting points and yields. TABLE 1

Boiling Points and Yields of Bis(polyﬂuoroalkyl)maleates

Bis(polyﬂuoroalkyl)maleate

Bp (8C/Pa)

Yield (%)

FðCF2 Þ8 ðCH2 Þ2 OCOCH=CHCOOðCH2 Þ2 ðCF2 Þ8 F FðCF2 Þ6 ðCH2 Þ2 OCOCH=CHCOOðCH2 Þ2 ðCF2 Þ6 F FðCF2 Þ4 ðCH2 Þ2 OCOCH=CHCOOðCH2 Þ2 ðCF2 Þ4 F HðCF2 Þ8 CH2 OCOCH=CHCOOCH2 ðCF2 Þ8 H HðCF2 Þ6 CH2 OCOCH=CHCOOCH2 ðCF2 Þ6 H HðCF2 Þ4 CH2 OCOCH=CHCOOCH2 ðCF2 Þ4 H

195–197/400 133–135/10 114–115/10 129–131/27 126–127/13 109–110/40

86.8 80.6 61.5 38.4 36.9 38.2

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TABLE 2 Melting Points, Yields, Krafft Points, and CMCs of Synthesized Surfactants Surfactant FðCF2 Þ8 ðCH2 Þ2 OCOCH2 CHðSO3 NaÞCOOðCH2 Þ2 ðCF2 Þ8 F FðCF2 Þ6 ðCH2 Þ2 OCOCH2 CHðSO3 NaÞCOOðCH2 Þ2 ðCF2 Þ6 F FðCF2 Þ4 ðCH2 Þ2 OCOCH2 CHðSO3 NaÞCOOðCH2 Þ2 ðCF2 Þ4 F HðCF2 Þ8 CH2 OCOCH2 CHðSO3 NaÞCOOCH2 ðCF2 Þ8 H HðCF2 Þ6 CH2 OCOCH2 CHðSO3 NaÞCOOCH2 ðCF2 Þ6 H HðCF2 Þ4 CH2 OCOCH2 CHðSO3 NaÞCOOCH2 ðCF2 Þ4 H

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Mp (8C)

Yield (%)

Kraﬀt point (8C)

CMC (mol l1 )/8C

290 278 270 228 219 201

86.0 60.5 61.5 48.3 56.1 87.9

72 26 <0 52 28 <0

1:0 105 =73 4:5 105 =30 7:2 104 =30 1:0 105 =53 9:0 105 =30 1:1 102 =30

Surfactants with a single ﬂuoroalkyl chain were synthesized using the reaction of the corresponding carboxylic acids with sodium carbonate in tetrahydrofuran and used to compare their properties with those of double chain-type ﬂuorosurfactants. Magnetite particles to be used to measure the ﬂocculating-dispersing action of the surfactants were synthesized by the coprecipitation method [5], in which an aqueous sodium hydroxide solution was added to an aqueous mixed solution of ferrous sulfate (I) and ferric sulfate (II), and the precipitates were dried after washing with water. The mean size of magnetite particles thus obtained was determined to be 109A˚ by the light scattering method.

C. Surface Modiﬁcation of Magnetite Particles with Double Chain-Type Fluorosurfactants 1. Flocculating-Dispersing Action on Magnetite Particles of Fluorosurfactants The following experiment was performed after conﬁrming that ultrasonically (200 W, 20 kHz, 15 min) dispersed magnetite particles (1.00 g) in water (50 cm3) remain stable for 3 days with almost no sign of sedimentation. Magnetite (0.10 g) was placed in each of the sample bottles, to which various concentrations of aqueous ﬂuorosurfactant solution (40 cm3) were added, and each bottle was exposed to an ultrasonic wave for 15 min. Ultrasonic irradiation was done to prevent particle ﬂocculation and enhance surfactant adsorption. After the sample dispersions were allowed to stand for 24 hr at room temperature, the ﬂocculating-dispersing action on magnetite particles of the surfactants was measured. The results obtained are shown in Fig. 1. Flocculation was observed in the area indicated by a rectangle in the ﬁgure for each surfactant. The arrow in the ﬁgure corresponds to the surfactant that causes no deﬂocculation of magnetite particles even at the highest concentration, beyond which it separated from solution to make measurement impossible. Figures 2 and 3 are the ﬂocculation-dispersion states of the particles in solutions of a double chain-type ﬂuorosurfactant that gave a high ﬂocculation-dispersion ability and a conventional single chain-type ﬂuorosurfactant. These ﬁndings demonstrate a high ﬂocculation-dispersion ability of double chain-type ﬂuorosurfactants having relatively long ﬂuorocarbon chains with a CF3 group at their terminals. Figure 4 shows schematically the two opposing phenomena, ﬂocculation and dispersion (deﬂocculation), by double chain-type ﬂuorosurfactant. Magnetite particles are positively charged in aqueous dispersion. Addition of the surfactant causes monolayer adsorption of surfactant molecules with their negatively charged groups (–SO 3 or Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 1 Comparison of ﬂocculating-dispersing action among ﬂuorinated surfactants using magnetite particles. Rfa and Rfb are for RfaCH2OCOCH2CH(SO3Na) COOCH2Rfa and RfbCOONa, respectively.

COO ) directing to the positively charged surface and hydrophobic ﬂuoroalkyl groups directing outwards, thereby covering magnetite particles. The particle surface then becomes hydrophobic to produce particle ﬂocculation and sedimentation. Further addition of the surfactant brings about adsorp-

FIG. 2 Flocculation-dispersion of magnetite particles by double chain-type ﬂuorinated surfactants. Flocculation begins at 3 wt % and redispersion starts at 15 wt %. Flocculation range is narrow.

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FIG. 3 Flocculation-dispersion of magnetite particles by single chain-type ﬂuorinated surfactants. Flocculation begins at 20 wt % and slight redispersion starts at 420 wt %. Flocculation range is wide and dispersing action is weak.

FIG. 4

Schematic representation of ﬂocculation-redispersion of magnetite.

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tion of surfactant molecules with their hydrophilic charged groups directing outwards, forming a bimolecular layer on the modiﬁed hydrophobic particle surface through the interaction between the hydrophobic groups. Magnetite particles thus covered with a bimolecular layer of surfactant molecules turn out to be hydrophilic and dispersible in water.

2. Measurement of Adsorbed Amount of Fluorosurfactant on Magnetite Surface The amount of ﬂuorosurfactant adsorbed on magnetite particles was calculated on the basis of the electroconductometrically determined surfactant concentrations in the supernatant solutions just after the start of ﬂocculation and just before the start of deﬂocculation. Table 3 shows the data for the double chain-type and single chain-type ﬂuorosurfactants that gave the highest ﬂocculation-dispersion ability.

3. ESCA Analysis of Neighborhood of Magnetite Surface Modiﬁed with Fluorosurfactant ESCA measurements were conducted on magnetite particles modiﬁed with double chain-type and single chain-type ﬂuorosurfactants that exhibited the highest ﬂocculation-dispersion ability to analyze the immediate vicinity of the particle surface. Samples of modiﬁed magnetite particles were taken from the middle part of the ﬂocculation region. The results revealed that the ratios of iron to ﬂuorine are respectively 1:7.53 and 1:4.26 for magnetite particles modiﬁed with the double chain-type and single chain-type ﬂuorosurfactants. Based on these values, the molar ratios of magnetite (Fe3O4) to surfactant were calculated to be 1:0.66 and 1:0.85 for the particles modiﬁed with the double chain-type and single chain-type surfactants, respectively.

TABLE 3 The Highest Flocculating-Dispersing Action Surfactant

Adsorption Amounts (mg/g-magnetite)

FðCF2 Þ8 ðCH2 Þ2 OCOCH2 CHðSO3 NaÞCOOðCH2 Þ2 ðCF2 Þ8 F After ﬂocculation Before redispersion

29.5 109

F(CF2 Þ7 COONa After ﬂocculation Before redispersion

176 440

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4. Twenty-Five Times Higher Adsorbability The initial molar concentration ratio for both types of surfactants used to modify magnetite particles for ESCA measurement is (double chaintype:single chain-type =) 1:33 and the molar ratio for the adsorbed surfactants is 0.66:0.85, as estimated above. Then, the ratio of adsorbability for both types of surfactants becomes (double chain-type):(single chain-type) ¼ (0.66/1):(0.85/33) ¼ 25:1. Thus, the double chain-type surfactant is 25 times more adsorbable than the single chain-type commercially available surfactant.

5. Water Repellency of Magnetite Surface Modiﬁed with Fluorosurfactant Measurements of the contact angle of water were carried out on the surface of modiﬁed magnetite taken from the middle part of the ﬂocculation region and pelletized with a tabletting apparatus for IR spectrum measurement. The contact angle for unmodiﬁed magnetite was assumed to be zero because it absorbed water quickly. The results of measurement are shown in Table 4. High contact angle values were obtained on the surface modiﬁed with surfactants having long ﬂuorocarbon chain(s) with a terminal CF3 group

TABLE 4 Contact Angle of Water on Magnetite Surface Modiﬁed with Fluorinated Surfactant Surfactanta Unmodiﬁed Rfa =FðCF2 Þ8 CH2 Rfa =FðCF2 Þ6 CH2 Rfa ¼ FðCF2 Þ4 CH2 Rfa =HðCF2 Þ8 Rfa =HðCF2 Þ6 Rfa =HðCF2 Þ4 Rfb =HðCF2 Þ7 Rfb =HðCF2 Þ8 Rfb =HðCF2 Þ6 Rfb =HðCF2 Þ4

Contact angle 0 125 102 75 106 80 65 119 95 71 64

a

RfaCH2OCOCH2CH(SO3Na)COOCH2Rfa, RfbCOONa

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and the surfaces covered with double chain surfactants did not necessarily give high contact angle. The reason why double chain-type ﬂuorosurfactants have a high ﬂocculation-dispersion ability at low concentrations would be due to their high adsorbability and high magnetite surface coverage.

III. SYNTHESIS AND APPLICATIONS OF FLUOROSURFACTANTS (II) [6] The characteristic structure of surfactants is that both hydrophilic and hydrophobic groups are present in one molecule. This causes their molecules to adsorb on the surface (interface) of various substances, thereby altering its properties. Surfactants sometimes have two or more hydrophilic and hydrophobic groups in one molecule, and such surfactants are highly functional. For instance, natural double chain-type surface-active substances (e.g., phospholipids) and synthetic double chain-type surfactants form micelles at their low concentrations, have a high solubilization capacity, and yield liposomes (vesicles) that have attracted attention as a drug carrier in drug delivery systems. The double chain-type surfactants used so far are those with two hydrocarbon or ﬂuorocarbon chains in their molecule. From the viewpoint of surface activity (function), a mixed surfactant system is said to be superior to a single surfactant system. Although attempts have been made to obtain micellar systems with a higher functionality by mixing mutually compatible hydrocarbon surfactant and ﬂuorocarbon surfactant, both having the same hydrophilic group, many of these attempts have yielded heterogeneous micelles [7–10]. Guo et al. [11] of Oklahoma University synthesized a homologous series of hybrid-type surfactants with diﬀerent kinds of hydrophobic groups, i.e., a hydrocarbon chain and a ﬂuorocarbon chain, in one molecule, represented by C7F15CH(OSO3Na) C7H15, in 1992. However, these surfactants were easily hydrolyzed through moisture absorption and had to be stored in a dry desiccator at 258C because of their very poor stability. Then, measurements of their properties had to be completed in 20 hr and so they were hardly used in practice. Meanwhile, we have succeeded in synthesizing novel hybrid-type surfactants with a high hydrolysis and heat resistance. The present section deals with synthesis of hybrid-type anionic surfactants with a hydrocarbon chain and a ﬂuorocarbon chain as the hydrophobic groups and a sulfonic acid group as the hydrophilic group in one molecule and describes part of their properties.

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A. Synthesis of Hybrid-Type Surfactants The reaction scheme is as follows:

1. Acylation of Iodobenzene [12] Synthesis of Intermediate I–C6H4–COC3H7. Anhydrous aluminum chloride (31.0 g, 232 mmol) was dispersed in 100 cm3 of carbon disulﬁde in a 500-ml ﬂask and butanoyl chloride (24.8 g, 232 mmol) was added dropwise to the dispersion from a dropping funnel in 1 hr while stirring magnetically at 08C in a nitrogen atmosphere. After adding iodobenzene (47.5 g, 233 mmol) was added dropwise to this reaction system in 2 hr, the system was reﬂuxed for 16 hr at 468C and poured into 100 cm3 of ice water. The organic layer was then washed with water after adding 25 cm3 of conc. HCl and stirring the system. If the organic layer was colored orange, it was treated with 10% sodium thiosulfate for decoloration and washed again with water. The product was a white solid (44.1 g, bp 948C/ 40 Pa, mp 58.58C) with a 69.3% yield. Other acylated iodobenzenes were obtained in a similar manner. Table 5 shows the properties and yields of the iodobenzenes synthesized.

2. Perﬂuoroalkylation [12] Synthesis of Intermediate C4F9–C6H4–COC3H7. A dispersion consisting of perﬂuorobutyl iodide (C4F9I) (27.8 g, 80.5 mmol), I–C6H4–COC3H7 Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 5 Properties and Yields of Acylated Iodobenzenes Acylated iodobenzene

Appearance

Bp (8C/Pa)

Mp (8C)

Yield (%)

IC6 H4COC3 H7 IC6 H4COC5 H11 IC6 H4COC7 H15

white-solid white-solid white-solid

94/40 83.5/25 113.5/39

58.5 62.3 64.0

69.3 73.2 71.9

(19.9 g, 72.7 mmol), copper-bronze powder (24.8 g, 390 mmol), and DMSO (120 cm3) was heated with stirring at 1258C for 16 hr in a nitrogen atmosphere. Excess copper-bronze powder was removed by ﬁltration and 50 cm3 each of water and ethyl ether were added to the ﬁltrate to transfer the product into the ether layer. After the ether layer was washed with water three times to remove DMSO, the ether was distilled out under reduced pressure to yield a colorless transparent liquid (18.0 g). The yield and the boiling point were 68.3% and 58.58C/24 Pa, respectively. Other aromatic ketones including a perﬂuoroalkyl chain at the paraposition of the benzene ring were obtained in a similar way, and Table 6 summarizes the properties and yields of the compounds synthesized.

3. Synthesis of Hybrid-Type Surfactants Synthesis of C4F9–C6H4–COCH(SO3Na)C2H5 (F4H2). A complex, SO3/ 1,4-dioxane, was synthesized beforehand in the following way. Addition of 1,4-dioxane (38.8 g, 441 mmol) at 08C to an SO3 (35.3 g, 441 mmol) solution in 1,2-dichloroethane (100 cm3) produced precipitation of a SO3/ 1,4-dioxane complex as a white solid. The solid complex was stored in a refrigerator (< 08C) and used when needed. A solution of C4F9–C6H4– COC3H7 (7.33 g, 20.0 mmol) in 1,2-dichloroethane (15 cm3) was added to a dispersion of SO3/1,4-dioxane complex (3.93 g, 23.4 mmol) in 1,2-dichloroethane (6 cm3) and the mixture was stirred for 30 min at 08C. After TABLE 6 Properties and Yields of Perﬂuoroalkylated Ketones Perﬂuoroalkylated ketone C4 F9C6 H4COC3 H7 C4 F9C6 H4COC5 H11 C4 F9C6 H4COC7 H15 C6 F13C6 H4COC3 H7 C6 F13C6 H4COC5 H11 C6 F13C6 H4COC7 H15

Appearance

Bp (8C/Pa)

Mp (8C)

Yield (%)

colorless, liquid colorless, liquid colorless, liquid white, solid white, solid white, solid

58.5/24 72.5/27 72.2/20 88.5/49 86.5/21 102/27

— — — 36.6 43.5 49.7

68.3 66.3 50.0 86.1 70.1 67.0

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further stirring for 3 hr at room temperature, C4F9–C6H4–COCH (SO3H)C2H5 (not separated) thus formed was extracted 2–3 times with 50 cm3 of water. When the water layer was neutralized with 0.5M aqueous NaOH solution and then water was removed, a white solid yielded. Puriﬁcation of the solid by ethanol extraction gave the desired hybrid-type surfactant (5.09 g) with a yield of 54.4%. Similarly, other hybrid-type surfactants (white solids) were obtained. Table 7 gives the abbreviations and yields of the surfactants synthesized. The compounds obtained are stable against water. Thus, for example, even when F6H6 (0.500 g) is exposed to the air for a week, it absorbs only 0.002 g of water and is not hydrolyzed. Because the compound, C7F15CH(OSO3Na)C7H15, synthesized by Guo et al. is a sulfate ester with a C–OSO3Na linkage next to the electrophilic ﬂuoroalkyl group, it is sensitive to water and easily hydrolyzed. On the contrary, the hybrid-type surfactants we synthesized have a much higher resistance to hydrolysis because they take a stable structure in which a benzene ring and carbonyl group in their molecule are in resonance with each other and possess a C–SO3Na bond.

B. Properties and Applications of Hybrid-Type Surfactants Thermogravimetric measurements (TG) performed in a nitrogen atmosphere to examine the thermostability of the hybrid-type surfactants synthesized revealed that the surfactants show no sign of thermal decomposition below 250–2608C though the decomposition temperature slightly diﬀers among the surfactants depending on their carbon chain length and ﬂuorocarbon chain length. This temperature range lies 50–608C higher than that for conventional hydrocarbon surfactants, and the hybrid-type surfactants are thus expected to exhibit excellent properties in their practical applications. How high their solubility is in solvent is important for surfactants since they are usually used in the form of solution (mainly aqueous). The TABLE 7 Abbreviations, Yields, Krafft Points, CMCs and Surface Tension Values at the CMC of Hybrid-Type Surfactants Hybrid-type surfactant

Yield Kraﬀt CMC cmc Abbr. (%) pt. (8C) (mol l1 Þ=8C ðmN m1 Þ

C4 F9C6 H4COCHðSO3 NaÞC2 H5 C4 F9C6 H4COCHðSO3 NaÞC4 H9 C4 F9C6 H4COCHðSO3 NaÞC6 H13 C6 F13C6 H4COCHðSO3 NaÞC2 H5 C6 F13C6 H4COCHðSO3 NaÞC4 H9 C6 F13C6 H4COCHðSO3 NaÞC6 H13

F4H2 F4H4 F4H6 F6H2 F6H4 F6H6

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54.4 75.0 58.5 63.8 85.8 79.3

<0 <0 20 <0 15 48

8:2 103 =25 3:5 103 =25 1:2 103 =25 8:3 104 =25 2:3 104 =25 5:5 105 =50

24.0 22.5 18.9 21.5 20.4 16.2

solubility of a surfactant is evaluated by its Kraﬀt point (melting point of hydrated solid) on the low-temperature side and its cloud point (solid deposition due to dehydration) on the high-temperature side. Since the hybrid-type surfactants we synthesized have no such hydrophilic group that causes dehydration due to temperature rise, the Kraﬀt points of F4H2, F4H4, and F6H2 were found to be below 08C, showing their rather good solubility in water. With an increase in length of both hydrocarbon and ﬂuorocarbon chains, the Kraﬀt point increases and the values for F6H6 and similarly synthesized F8H6 are about 48 and 988C, respectively. Table 7 also summarizes the measured Kraﬀt points, cmcs, and surface tension values at the cmc for the hybrid-type surfactants synthesized. The water surface tension lowering is one of the important surface chemical actions of surfactants. The surface tension of water generally decreases with an increase in the dissolved surfactant concentration and shows a constant value above the cmc. The value is in general around 35 mN m1 for surfactants with a hydrocarbon chain and about 25 mN m1 for those with a ﬂuorocarbon chain. By contrast, for the hybrid-type surfactants we synthesized, the surface tension lowered down to 18.9 (258C) and 16.2 (508C) mN m1 for F4H6 and F6H6 at their cmc, respectively, as shown in Fig. 5, demonstrating their highest water surface tension lowering ability among all of the surfactants available at present.

FIG. 5 Relationship between surface tension and concentration for solutions of hybrid-type surfactants (CmF2m+1–C6H4–COCH(SO3Na)CnH2n+1. The subscripts m and n denote the carbon atom numbers in ﬂuorocarbon and hydrocarbon chains, respectively. Copyright © 2003 by Taylor & Francis Group, LLC

This indicates their superb usefulness as a dispersing agent and detergent. For instance, they easily dispersed hardly water-soluble ﬂuorinated polyether oils in water (Fig. 6, left). When 0.02 g of F6H4 was added to a mutually immiscible system consisting of octane (1.00 g), water (22.98 g), and DEMNUM S-20 (1.00 g) and the system was exposed to ultrasound in an ultrasonic homogenizer (200 W, 20 kHz, 3 min), the resultant emulsion remained stable for more than 3 days (Fig. 6, right). DEMNUM S-20 is a commercially available ﬂuorinated polyether oil with a composition of F(CF2CF2CF2O)n–CF2CF3 (mean mol. wt. 2700). Moreover, after the emulsion was once formed, no oil was separated though the droplets gradually sedimented. Thus, these hybrid-type surfactants can disperse two quite diﬀerent kinds of oils in water to form a stable emulsion without no additive. The ﬂuorinated polyether oil used here is employed in such ﬁelds where a high performance is required and soluble in only ﬂuorinated solvents such as Fleons known as an ozone layer destroyer. Because the hybridtype surfactants can emulsify ﬂuorinated polyether oils, the oils will become applicable in many ﬁelds.

FIG. 6 Center: octane (upper), water (middle), and ﬂuorinated oil (lower) layers. Left: ﬂuorinated oil dispersed in water to form emulsion. Right: emulsion composed of the above three components with aid of hybrid-type surfactant. Copyright © 2003 by Taylor & Francis Group, LLC

Hybrid-type surfactants are also interesting scientiﬁcally. As shown in Fig. 5, the series of hybrid-type surfactants reduce the surface tension of water even above their cmc while ordinary surfactants cause the surface tension to level oﬀ beyond their cmc. This would be brought about by a change in the micellar structure with an increase in surfactant concentration. The reason for this is under study. There has been an increasing tendency in recent years to avoid the use of organic solvents for paints because of concerns about air pollution and workers’ health condition, and conversion of organic solvents to water is a global demand. Because hybrid-type surfactants are suitable for preparation of aqueous dispersion of ﬂuorinated paints, they are expected to greatly contribute to the prevention of environment pollution. They are also expected to be applicable in unexplored ﬁelds such as those of detergent and refrigerant. Our papers [13–27] on the related subjects are referrable.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

16.

N. Yoshino, N. Komine, J. Suzuki, Y. Arima, and H. Hirai. Bull. Chem. Soc. Jpn., 64:3262, 1991. N. Yoshino. Polyﬁle, 29:48, 1992. N. Yoshino. Material Technology, 12:26, 1994. N. Yoshino, M. Morita, A. Ito, and M. Abe. J. Fluorine Chem., 70:187, 1995. J. Shimoiizaka. Powder and Powder Metallurgy, 13:263, 1966. N. Yoshino, K. Hamano, Y. Omiya, Y. Kondo, A. Ito, and M. Abe. Langmuir, 11:466, 1995. M. Abe, T. Yamaguchi, Y. Sibata, H. Uchiyama, N. Yoshino, K. Ogino, and S.D. Christian. Colloids and Surfaces, 67:29, 1992. S.J. Burkitt, R.H. Ottewill, J.B. Hayter, and B.T. Ingram. Colloid Polym. Sci., 265:628, 1987. S.J. Burkitt, B.T. Ingram, and R.H. Ottewill. Prog. Colloid Polym. Sci., 76:247, 1988. N. Funasaki and S. Hada. J. Phys. Chem., 87:342, 1983. W. Guo, Z. Li, B.M. Fung, E.A. O’Rear, and J.H. Harwell. J. Phys. Chem., 96:6738, 1992. V.C.R. McLoughlin, J. Thrower. Tetrahedron, 25:5921, 1969. A. Ito, K. Kamogawa, H. Sakai, Y. Kondo, N. Yoshino, and M. Abe. J. Jpn. Oil Chem. Soc., 45:479, 1996. A. Ito, H. Sakai, Y. Kondo, N. Yoshino, and M. Abe. Langmuir, 12:5768, 1996. M. Abe, K. Tobita, H. Sakai, Y. Kondo, N. Yoshino, Y. Kashihara, H. Matsuzawa, M. Iwahashi, N. Momozawa, and K. Nishiyama. Langmuir, 13:2932, 1997. A. Ito, K. Kamogawa, H. Sakai, K. Hamano, Y. Kondo, N. Yoshino, and M. Abe. Langmuir, 13:2935, 1997.

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17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

K. Tobita, H. Sakai, Y. Kondo, N. Yoshino, M. Iwahashi, N. Momozawa, and M. Abe. Langmuir, 13:5054, 1997. K. Tobita, H. Sakai, Y. Kondo, N. Yoshino, K. Kamogawa, N. Momozawa, and M. Abe. Material Technology, 16:202, 1998. K. Tobita, H. Sakai, Y. Kondo, N. Yoshino, K. Kamogawa, N. Momozawa, and M. Abe. Langmuir, 14:4753, 1998. Y. Kondo, E. Yokochi, S. Mizumura, and N. Yoshino. J. Fluorine Chem., 91:147, 1998. Y. Kondo, M. Hamasaki, K. Tobita, H. Sakai, M. Abe, and N. Yoshino. J. Jpn. Oil Chem. Soc., 48:7071, 1999. M. Hisatomi, M. Abe, N. Yoshino, S. Lee, S. Nagadome, and G. Sugihara. Langmuir, 16:1515 (2000). M. Abe, Y. Kondo, M. Sagisaka, H. Sakai, Y. Morita, C. Kaise, and N. Yoshino. Shikizai, 73:53, 2000. M. Abe, K. Tobita, H. Sakai, K. Kamogawa, N. Momozawa, Y. Kondo, and N. Yoshino. Colloids and Surfaces, 167:47, 2000. M. Abe, A. Saeki, K. Kamogawa, H. Sakai, Y. Kondo, N. Yoshino, H. Uchiyama, and J.H. Harwell. Ind. Eng. Chem. Res., 39:2697, 2000. A. Saeki, K. Kamogawa, A. Ito, Y. Kondo, N. Yoshino, H. Sakai, and M. Abe. Material Technology, 18:158, 2000. A. Saeki, H. Sakai, K. Kamogawa, Y. Kondo, N. Yoshino, H. Uchiyama, J.H. Harwell, and M. Abe. Langmuir, 16:9991 2000.

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9 Surface-Active Properties of TelomerType Surfactants Having Several Hydrocarbon Chains TOMOKAZU YOSHIMURA and KUNIO ESUMI Science, Tokyo, Japan

I.

Tokyo University of

INTRODUCTION

Surfactants having several hydrophobic groups and several hydrophilic groups have been developed and their achievements have become a center of attraction. A study of gemini (or dimeric) surfactants is being continued steadily by many workers; they show unusual physicochemical properties, such as better water solubilities, much lower critical micelle concentrations (CMCs), and more eﬃciencies in lowering surface tension of water and interfacial tension at the oil–water interface than conventional monomeric surfactants having one hydrophobic group and one hydrophilic group [1–10]. There are very few papers about synthesis and properties of trimeric [11–14] and tetrameric [15–17] surfactants since it is diﬃcult to introduce several alkyl chains in a molecule. Polysoaps are known as a type of surfactant having multihydrophobic groups and multihydrophilic groups. A great number of types of polysoaps have been synthesized, and many of them are excellent dispersants or ﬂocculants, although they give much higher surface tension than conventional surfactants [18,19]. It indicates that the orientations of hydrophobic groups of polysoaps are limited due to blocking and steric hindrance caused by the main polymer chains. It is necessary to control the balance of hydrophobic and hydrophilic groups in order to enhance the interfacial orientations of surfactants having multihydrophobic groups and multihydrophilic groups. Telomers (or oligomers) are known as a type of polymer with degree of polymerization (Pn) of 5 to 20. They are obtained by polymerizing vinyl monomers in solvents with large chain transfer constants such as alkanethiol or alkyl alcohol [20,21]. Telomer-type surfactants have the properties of Copyright © 2003 by Taylor & Francis Group, LLC

both polymer-type surfactants and those of the conventional surfactants. In addition, it is expected that telomers enhance the interfacial orientation due to the increase of the functional groups’ freedom. In general, telomer-type surfactants have one hydrophobic group and several hydrophilic groups. It is very interesting to study surface-active properties of telomer-type surfactants having several hydrophobic groups and several hydrophilic groups. Such telomer-type surfactants are obtained by introducing several alkyl chains to functional groups or by polymerizing the monomer with a hydrophobic group. Figure 1 shows the schematic representation of the background in this study. In this chapter, the surface-active properties of some telomer-type surfactants having several hydrophobic groups and several hydrophilic groups are discussed.

II. LIPID–LYSINE TELOMERS Molecular devices of nanoscopic scale can be useful in various ﬁelds. The understanding of assembly mechanisms has been challenged by using some speciﬁc molecules [22–24]. Soluble surfactants usually self-assemble into micelles in aqueous solutions above their CMC, but insoluble or poorly soluble surfactants form vesicles [25]. Telomers of alternating -amino tetradecanoic acid and lysine having positively charged groups and lipid chains

FIG. 1

Background of this study.

Copyright © 2003 by Taylor & Francis Group, LLC

(n ¼ 2), as shown in Fig. 2, are insoluble in water and diluted acid solutions, but those with larger n are soluble in acid conditions and poorly soluble in alkaline ones [26]. Hence, in one series, one can conduct experiments both on the determination of micelle formation and on spread monolayer behavior. The CMCs of the telomers in 0.1-mM HCl shift to high concentration with an increase of n and the surface tensions are 53 and 48–50 mN m1 at their CMC for the telomers with n ¼ 3 and those with n ¼ 4–6, respectively. The surface areas occupied per molecule of the telomers are 0.44–0.65 nm2 molecule1 , showing close packing at the surface. From the data of surfacepressure-area isotherms, the telomers with n ¼ 2 and n ¼ 3 aggregate or form multilayers at the air–water interface. The ﬂuorescence intensity ratio of the third to ﬁrst band in the emission spectra of pyrene as a function of the telomer concentrations demonstrates that the telomers with n ¼ 3 have fewer accessible hydrophobic sites for pyrene and the forces of the repulsion between the charged headgroups are crucial on the formation of micelles. Supramolecular ﬁberlike structures are observed by transmission electron microscopy (TEM) in aqueous solutions only when the telomers are with n ¼ 3. Cryogenic TEM observation of the solutions also reveals that the micelles may elongate to form long cylindrical or ﬁbrous structures. The diameter of these structures is estimated to be 6.0–13 nm, although their length varies. These lipid–lysine telomers are expected as new supramolecular carrier systems for drugs.

III. QUATERNARY AMINO SILOXANE TELOMERS Quaternary amine derivatives of siloxanes have been reported to show the surface-active properties and excellent binding to primarily negatively charged substrates such as hair and fabrics. They can be used as emulsiﬁer, hair and skin conditioning agents, and textile softeners [27,28]. Siloxane chains are known to have high ﬂexibility due to the easy rotation of Si–O–Si and Si–C bonds, resulting in improved ﬁlm-forming properties at the air–water interface. The oleﬁnic quaternary amino siloxane-type telomers, as shown in Fig. 3 (left), show excellent surface activities [29].

FIG. 2

Chemical structures of lipid–lysine telomers.

Copyright © 2003 by Taylor & Francis Group, LLC

The lowering in surface tension depends upon the number of siloxane units, and the telomers give the surface tension of 22 mN m1 . The corresponding monomeric quaternary amino siloxanes associate at low concentration and form micelle at 7 mmol dm3. On the other hand, the telomers do not appear to form micelles. In fact, they show lower surface tension even at very low concentrations, and the aggregation occurs at a concentration of 0.6 mmol dm3. The high molecular weight and ﬂexibility of the –Si–O–Si– backbone is explained as a result of linear spreading of the siloxane molecule at the air–water interface, resulting in low surface tension. Amino siloxane telomers quaternized with several dodecyl chains, as shown in Fig. 3 (right), also give the surface tension of 26 mN m1 , showing high surface activity [30].

IV. MALEIC DERIVATIVE ANIONIC TELOMERS Maleic acid derivatives are widely investigated compounds since they are easily prepared from maleic anhydride, which is a cheap and quite available substance [31]. Maleic anhydride and its derivatives are known to homopolymerize, and the polymerization gives polymers with low polymerization degree [32–34]. Telomer-type anionic surfactants of maleic acid alkyl ester (xRn Ma; x is the total number of alkyl chains, n is the main alkyl chain length) and N-alkyl maleamic acid (xRnMaAm) are prepared by the telomerization of the corresponding monomers (RnMa, RnMaAm), which are synthesized by the reaction of maleic anhydride with alkyl alcohol [35,36] or alkylamine [37,38], in the presence of alkanethiol as a chain transfer agent. Figure 4 shows the structures and the abbreviations.

FIG. 3 Chemical structures of quaternary amino siloxane telomers. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Structures and abbreviations of maleic derivative telomers and monomers.

A. Surface Tension Figure 5 shows surface tension curves of xRn Ma telomers in aqueous solutions at pH 9–10 as a function of the logarithm of telomer concentration [39]. The surface tensions of telomers decrease with an increase of the concentration of the aqueous solutions reaching clear breakpoints, which are taken as CMC. Figure 6 shows the relationships between the alkyl chain length and the logarithm of the CMC, the surface tension at CMC ( cmc), and the occupied areas per molecule (A) of xRn Ma and xRn MaAm telomers as well as RnMa and RnMaAm monomers [39,40]. The CMCs of xRn Ma and xRn MaAm telomers are from 1/110th to 1/14th and from 1/142th to 1/42th of those of the corresponding RnMa and RnMaAm monomers, respectively. It is also noteworthy that the CMCs of the telomers are much lower than those of the conventional anionic surfactants such as sodium n-octanoate (3.6 mmol dm3 at 208C) and sodium n-dodecanoate (0.26 mmol dm3 at 258C) [41]. The telomers have large hydrophobicities due to the several alkyl chains along with the skeletal hydrocarbon chains, showing the low CMCs. The CMCs of RnMa with the ester group are slightly lower than those of RnMaAm with the amide group, while the diﬀerence is not seen for xRn Ma and xRn MaAm telomers. xRn Ma and xRn MaAm telomers show higher eﬃciencies in lowering the surface tension than RnMa and RnMaAm monomers and sodium n-dodacanoate (37 mN m1 at 258C) [41]. The increase of alkyl chains and Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Relationship between logarithm of concentration and surface tension of xRn Ma telomers. pH 9–10, 258C. ~: 3.3R6Ma, *: 3.1R8Ma, ^: 3.2R10Ma, &: 2.8R12Ma, *: 2.9R14Ma. (From Ref. 40 with permission of AOCS Press.)

carboxylate groups reduces the surface tension. The cmcs of xRn MaAm with amide groups are lower than those of xRn Ma with ester groups. It is probably due to the strong hydrogen bonds among the amide groups of the telomers. Surface excess concentration () at the air–water interface can be calculated by applying the Gibbs adsorption isotherm equation [42]: ¼ ð1=iRTÞðd=d ln CÞ where R is the gas constant (8.31 J mol1 K1 ), T is the absolute temperature, is the surface tension, and C is the concentration of surfactant. Here, i is taken as x þ 1 for xRn Ma and xRn MaAm, since these telomers are dissociated into several positive ions and several negative ions. i is also taken as 2 for RnMa and RnMaAm. The occupied area per molecule (A) can be calculated from the following equation: A ¼ 1=N where N is Avogadro’s number. The values of A of the telomers, which are calculated from the linear portion of the plots below CMC in the relationship between concentration and surface tension, are much greater than those of the monomers, while the occupied areas per one alkyl chain of telomers are smaller than those of the monomers. An increase from decyl to dodecyl and tetradecyl in the hydrophobic chain length of the telomers gives the small occupied areas due to the interactions between several alkyl chains. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 6 Relationships between alkyl chain length and (a) logarithm of concentration, (b) surface tension ( cmc), and (c) occupied area per molecule (A) of Rn Ma, Rn MaAm, xRn Ma, and xRn MaAm. pH 9–10, 258C. &: Rn Ma, *: Rn MaAm, &: xRn Ma, *: xRn MaAm. (From Ref. 40 with permission of AOCS Press.)

The telomers are adsorbed at the air–water interface with wide occupied areas; oriented themselves, they indeed lower the surface tension. Some anionic surfactants are known to form solid salts in hard water containing Ca2þ or Mg2þ , while the telomers are easily soluble in hard water containing 300 ppm of Ca2þ due to the several carboxylate groups. Figure 7 shows the relationships between the alkyl chain length and the logarithm of the CMC and the cmc of xRn Ma and xRn MaAm telomers in hard water [39,40]. The CMCs of the telomers in the presence of Ca2þ are lower than those of the telomers in the absence of Ca2þ . In general, the amide and the carboxylate groups eﬃciently chelate the divalent cations Ca2þ . In the presence of Ca2þ , the interactions between the amides or the carboxylates and Ca2þ ions reduce their electrostatic repulsion, resulting in the decrease of the CMC. However, the addition of Ca2þ shows diﬀerent behaviors in the cmc of the telomers; the cmcs of the xRn Ma in the presence of Ca2þ are almost Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 7 Relationships between alkyl chain length and (a) logarithm of concentration and (b) surface tension ( cmc) of Rn Ma and xRn MaAm telomers in hard water containing 300 ppm of Ca2þ as well as in water. pH 7–8, 258C. ^: xRn Ma, in water, ^: xRn Ma, in hard water, ~: xRn MaAm, in water, ~: xRn MaAm, in hard water. (From Ref. 40 with permission of AOCS Press.)

the same as those of xRn Ma in the absence of Ca2þ , while those of xRn MaAm in the presence of Ca2þ are rather higher than those of xRn MaAm in the absence of Ca2þ .

B. Foaming Property The foaming property is determined by the height of the foaming volume after shaking of surfactant solutions (0.2 wt %) for 3 min with a Shaker machine at 258C. Figure 8 shows the foaming abilities and the foam stabilities of xRn Ma and xRn MaAm telomers in water as well as in hard water [39,40]. The foaming properties are inﬂuenced by the number of alkyl chains, the alkyl chain length, and the nature of ester or amide groups, in a similar manner to the surface tension. RnMa and RnMaAm monomers with n ¼ 6 and n ¼ 8 do not have the ability to form the foam. Those with n ¼ 10–14 give the foaming abilities, while the foam volumes reduce to less than one half the initial value after 60 min of standing. The telomers show higher foaming abilities and higher foam stabilities than the monomers. It is noteworthy that some telomers having several short alkyl chains give the foam stabilities. The foam stabilities of the telomers are kept at the level of 70–90% of initial volume. These foaming properties are derived from the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 8 Foaming abilities and foam stabilities of xRn Ma and xRn MaAm telomers in water as well as in hard water containing 300 ppm of Ca2þ . 0.2 wt %, 258C. (From Ref. 40 with permission of AOCS Press.)

enhancement of the interfacial density of the telomers having several alkyl chains and several carboxylate groups. The addition of 300 ppm of Ca2þ to the aqueous solutions of the telomers results in lowering of the foaming properties. The foaming ability and the foam stability of 3.2R12MaAm in the presence of Ca2þ are about one half of those in the absence of Ca2þ . The other telomers give the poor ones in hard water. The telomers seem to less easily orient themselves at the interface due to the high hydrophobicities caused by the interactions between the carboxylates and Ca2þ ions in the presence of Ca2þ .

C. Emulsiﬁcation Power Emulsiﬁcation power is determined by the height of the emulsion layer after shaking of cotelomer solutions (0.3 wt %) and organic solvent with a Shaker Copyright © 2003 by Taylor & Francis Group, LLC

machine at 258C. The mixtures of toluene and aqueous solutions of telomers form emulsion. Figure 9 shows the percentage of emulsion phases of Rn MaAm monomers and xRn MaAm telomers at elapsed time [39]. The stabilization of emulsions is aﬀected by the number of alkyl chains and the alkyl chain length. R6MaAm and R8MaAm monomers do not form the emulsions due to the high hydrophilicity. The emulsions formed by using Rn MnAm with n between 10–14 dramatically decrease after 20 min, while xRn MaAm with n of 6–10 and x of 3.0–3.2 keep the high emulsions for a while. The degrees of emulsiﬁcation of the telomers were kept at the level of 60–70% after 24 h. The emulsions formed by xRn MaAm with n of 6–12 are separated only into aqueous solution phase, while those formed by 3.0R14MaAm are separated into 35% toluene phase and 30% aqueous solution phase after 10 h. 3.0R14MaAm, which has several longer alkyl chains, dissolves in toluene due to the enhancement hydrophobicity, giving low emulsion stabilities. The degrees of emulsiﬁcation of xRn MaAm with amide groups are also higher than those of xRn Ma with ester groups [40]. Emulsions, which are produced with the telomers dissolved in water, lead to oil-in-water-(o/w) type emulsions. As observed for the surface tension, the telomers reduce interfacial tension between the aqueous solution and toluene. The interfacial tension of water and toluene is 36 mN m1 at 208C. The interface between the aqueous solutions of 2.9R6MaAm,

FIG. 9 Relationship between elapsed time and degree of emulsiﬁcation between aqueous solutions of Rn MaAm or xRn MaAm and toluene. Solutions of monomer or telomer: 0.3 wt %, 258C. !: R10MaAm, &: R12MaAm, ^: R14MaAm, ~: 2.9R6MaAm, *: 3.0R8MaAm, ^: 3.0R10MaAm, &: 3.2R12MaAm, *: 3.0R14MaAm. (From Ref. 39 with permission of Japan Oil Chemists’ Society.) Copyright © 2003 by Taylor & Francis Group, LLC

3.0R8MaAm, 3.0R10MaAm, 3.2R12MaAm, and 3.0R14MaAm and toluene gives the interfacial tension of 6, 5, 5, 4, and 4 mN m1 , respectively. The CMCs of xRn MaAm telomers are 0.26–0.42 mmol dm3 at their interface. xRn MaAm telomers give a lower CMC and a lower interfacial tension at the aqueous solution–toluene interface than Rn MaAm monomers (2– 60 mmol dm3 , 8–10 mN m1 ). Except for 3.0R14MaAm, the telomers with high emulsion stabilities of toluene and water give a higher eﬃciency at reducing the interfacial tension at their interface. Emulsions of organic solvents are formed by shaking with the aqueous solutions of the telomers. The degrees of emulsiﬁcation are in the orders of toluene > n-dodecane > kerosene. The degrees of emulsiﬁcation for alkane of n-octane and n-hexadecane are as high as those for n-dodecane. The highly o/wtype emulsion is formed by using 3.0R8MaAm for toluene or kerosene as an oil phase and by using 3.0R10MaAm for n-dodecane. The increase of the alkyl chain length of the telomers decreases the emulsion. The interfacial orientations of telomers having several longer alkyl chains are less easy than those having several shorter alkyl chains.

V. ALKYL ACRYLATE–ACRYLIC ACID ANIONIC COTELOMERS Surface activities of conventional surfactants are known to be inﬂuenced by the nature of hydrophobic groups, such as alkyl chain length, branching, unsaturation, and the presence of an aromatic nucleus [42]. Cotelomer-type anionic surfactants of alkyl acrylate and acrylic acid (xRn A-yAA; x is the number of hydrophobic groups, y is the number of hydrophilic groups) are prepared by the cotelomerization of n-hexyl acrylate (R6A), n-octyl acrylate [R8(No)A], 2-ethylhexyl acrylate [R8(Eh)A], 2-phenylethyl acrylate [R8(Pe)A], or n-dodecyl acrylate (R12A) and acrylic acid (AA) in the presence of 2-aminoethanethiol hydrochloride as a chain transfer agent. Figure 10 shows the structures and the abbreviations.

A. Surface Tension Surface tensions in aqueous solutions at pH 9–10 decrease with increasing concentration of the cotelomers reaching clear breakpoints, which are taken as CMC [43–45]. As to the aqueous solutions of the cotelomers at the concentration above CMC, it takes 10–50 h for the surface tension to reach equilibrium. Below CMC, the surface tension of the cotelomers reaches the equilibrium within 10–20 h. Table 1 summarizes the values of the CMC, the cmc, and A of some cotelomers. The CMCs shift to lower Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10

Structures and abbreviations of alkyl acrylate–acrylic acid cotelomers.

concentration with an increase of alkyl chain length and number of alkyl chains in xR6A-yAA, xR8(Eh)A-yAA, and xR12A-yAA series. The CMC of conventional surfactants is known to decrease with an increase in the number of carbon atoms in the hydrophobic groups [42]. One can regard telomer molecules as bundles of sodium alkanoate, a conventional anionic surfactant. Hence the CMCs of the cotelomers are compared with those of sodium alkanoate. Their CMCs are in the order of sodium n-octanoate >

TABLE 1 CMC, cmc , and Occupied Area per Molecule (A) of xRnA-yAA CMC (mmol dm3 )

cmc (mN m1 Þ

A (nm2 molecule1 Þ

1.1R6 A-3.9AA 2.3R6 A-3.0AA 2.9R6 A-2.3AA 3.2R6 A-6.5AA

1.5 0.69 0.54 2.1

32.3 28.6 27.7 28.1

6.21 5.38 5.58 6.43

5.0 3.9 4.8 5.3 5.1 4.7

2.1R8 (No)A-1.2AA 1.1R8 (Eh)A-2.8AA 1.9R8 (Eh)A-2.9AA 2.8R8 (Eh)A-2.5AA 3.3R8 (Eh)A-1.8AA 1.6R8 (Pe)A-3.0AA

0.22 1.0 0.71 0.072 0.45 2.5

32.3 28.8 27.3 29.7 29.9 41.1

1.20 5.32 8.70 2.84 3.87 6.25

5.7 5.6 7.2 9.5

2.3R12 A-3.4AA 2.7R12 A-2.9AA 3.2R12 A-4.0AA 5.1R12 A-4.4AA

0.018 0.018 0.012 0.011

41.1 37.8 45.3 42.2

1.85 1.75 1.78 1.09

C11 H23 COO Naþ

0.26

37

0.92

Pn

Cotelomer

5.0 5.3 5.2 9.7

Source: Refs. 43 and 44.

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2.3R6A-3.0AA > 2.9R6A-2.3AA > sodium n-dodecanoate > 2.8R8(Eh)A2.5AA > sodium n-hexadecanoate > 2.3R12A-3.4AA > 2.7R12A-2.9AA > 3.2R12A-4.0AA. The CMCs of xR12A-yAA with Pn 5–10 are from 1/24th to 1/14th of that of sodium n-dodecanoate. xR12A-yAA having 2–5 dodecyl chains gives a lower CMC than sodium n-hexadecanoate, which has a longer alkyl chain. In the case of 8 carbon atoms, the CMCs are in the order of 1.6R8(Pe)A-3.0AA > 1.9R8(Eh)A-2.9AA > 2.1R8(No)A-1.2AA; they decrease with a decrease of the hydrophile-lipophile balance (HLB). The cmcs of xR6A-yAA, xR8(Eh)A-yAA, and xR12A-yAA are 28–32, 27– 30, and 38–45 mN m1 , respectively. The increase of the hydrophobic chain length renders the cotelomers less surface-active. The cotelomers having several hexyl or ethylhexyl chains show higher eﬃciencies in lowering the surface tension than sodium n-dodecanoate, a conventional anionic surfactant. The cmcs of 2.9R6A-2.3AA and 1.9R8(Eh)A-2.9AA are lower than those of 1.1R6A-3.9AA and 1.1R8(Eh)A-2.8AA, respectively; the increase of the hydrophobic chains reduces the surface tension. The values of A of xR6A-yAA, xR8(Eh)A-yAA, and xR12A-yAA are 5.40–5.60, 2.80–3.90, and 1.70–1.90 nm2 molecule1 , respectively. These values are greater than that of sodium n-dodecanoate (0.92 nm2 molecule1 at 258C) [41]. In the case of the cotelomers, they adsorb at the air–water interface by orienting their alkyl chains along with skeletal hydrocarbon chains to air, enlarging their occupied areas per molecule. Thus, xR6A-yAA, which has several shorter alkyl chains, and xR8(Eh)AyAA, which has several branched alkyl chains, are considered to be adsorbed at the air–water interface with wide occupied areas and to orient themselves so as to cause eﬀective surface activities due to a good balance between hydrophobic and hydrophilic groups. xR12A-yAA, which has longer multialkyl chains, is considered to be packed so densely at the air– water interface that it gives rise to the poor surface activities. The presence of aromatic nucleuses in the hydrophobic group renders the cotelomers less surface-active due to their bulky structures.

B. Foaming Property Figure 11 shows the foam stabilities of some cotelomers and sodium ndodecanoate in water as well as in hard water containing 300 ppm of Ca2þ [43–45]. The foam abilities of 2.9R6A-2.3AA, 2.8R8(Eh)A-2.5AA, and 2.7R12A-2.9AA in water are as high as that of sodium n-dodecanoate. 2.9R6A-2.3AA gives high foam stability, while 2.8R8(Eh)A-2.5AA gives a poor one. The cotelomers having branched alkyl chains seem to orient themselves at the interface less easily than those having a straight alkyl chains. The foam stabilities of the conventional surfactants having a Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 11 Foam stabilities of xRn A-yAA in water as well as in hard water containing 300 ppm of Ca2þ . 0.2 wt %, 258C. 2.9R6A-2.3AA: & (water), & (hard water), 2.8R8(No)A-2.5AA: ! (water), ! (hard water), 2.7R12A-2.9AA: ^ (water), ^ (hard water), C11H23COO-Na+: * (water). (From Ref. 43 with permission of Japan Oil Chemists’ Society.)

branched alkyl chain are known to be lower than those of the surfactants having a straight alkyl chain. The foaming properties of the cotelomers are also signiﬁcantly inﬂuenced by the alkyl chain length and the number of hydrophobic and hydrophilic groups. In the case of the xR6A-yAA series, the foam stabilities after 60 min of standing decrease in the order of 2.9R6A2.3AA > 2.3R6A-3.0AA > 1.1R6A-3.9AA > 3.2R6A-6.5AA. xR8(Pe)-yAA also shows low foaming properties. The cotelomers having 2–3 straight alkyl chains and 2–3 hydrophilic groups form the closely packed small-bubble foams; those having branched alkyl chains, aromatic nucleuses, or high hydrophilic groups produce the loosely packed large-bubble ones. In the presence of 300 ppm of Ca2þ , the foaming abilities of the cotelomers having straight and branched alkyl chains are almost equal to those in the absence of Ca2þ . However, the cotelomers having straight alkyl chains give high foam stabilities, while those having branched alkyl chains give poor ones. The cotelomers having aromatic nucleuses show low foaming abilities and low foam stabilities.

C. Emulsiﬁcation Power Emulsiﬁcation of toluene is inﬂuenced by the alkyl chain length, the number of alkyl chains, and the nature of hydrophobic groups, in a similar manner Copyright © 2003 by Taylor & Francis Group, LLC

to the surface tension and the foaming property [43–45]. The highly stable o/ w-type emulsions are formed by using xR6A-yAA, xR8(No)A-yAA, xR8(Eh)A-yAA, and xR12A-yAA having 2–3 alkyl chains and xR8(Pe)AyAA, and the degrees of emulsiﬁcation are kept at the level of 60–70% after 10 h of standing. Emulsion of organic solvents is formed by shaking with the cotelomer solutions. The degrees of emulsiﬁcation are in the order of toluene > hexane > octane > kerosene > ligroin > chloroform. xR8(No)AyAA, having straight alkyl chains, gives much lower emulsions of octane and water than xR8(Eh)A-yAA having branched alkyl chains and xR8(Pe)A-yAA having aromatic nucleuses, indicating a less easy orientation of xR8(No)A-yAA at the octane–water interface. As observed for the surface tension, the cotelomers reduce the interfacial tension at the toluene–water or octane–water interface. For example, aqueous solutions of 2.1R8(No)A-1.2AA, 1.9R8(Eh)A-2.9AA, and 1.6R8(Pe)A3.0AA give the interfacial tension of 4, 8, and 1 mN m1 , respectively, for the interface with toluene and 5, 7, and 9 mN m1 , respectively, for that with octane. Close aﬃnity of the phenyls of 1.6R8(Pe)A-3.0AA for toluene orients the cotelomers in orderly packing to give rise to the eﬀective interfacial activities at the toluene–water interface. In the case of 2.1R8(No)A-1.2AA using octane as an oil phase, there is no correlation between the emulsion stability and the interfacial tension. It adsorbs strongly at the octane–water interface as an oriented interfacial ﬁlm, lowering the interfacial tension. However, it gives the poor emulsion stability for octane and water.

VI. N-(a-CARBOXYALKYL)ACRYLAMIDE ANIONIC TELOMERS N-(-Carboxyalkyl)acrylamide telomer-type anionic surfactants (xRn AmAc; x is the total number of alkyl chains) are prepared by the telomerization of the monomers, which is synthesized by the reaction of -aminoalkanoic acid with acryloyl chloride [46,47], in the presence of alkanethiol as a chain transfer agent. Figure 12 shows the structures and the abbreviations.

FIG. 12

Structure and abbreviation of N-(-carboxyalkyl)acrylamide telomers.

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A. Surface Tension Figure 13 shows the relationships between the polymerization degree and the logarithm of the CMC and the cmc of the telomers [48]. The CMCs of the telomers shift to lower concentration with increasing alkyl chain length, and those of the telomers with n ¼ 8–12 shift to lower concentration with increasing from about 2 to 9 in the Pn. The CMCs of xRn AmAc with x of more than 9 increase or remain unchanged with increasing polymerization degree. A number of alkyl chains to the telomers render them less surfaceactive. In addition, the increase of the polymerization degree renders the telomers less surface-active. It is found that the telomers having several alkyl chains have the strong hydrophobicities, showing the high surface tensions. Figure 14 shows the relationship between the polymerization degree and the occupied areas per molecule of the telomers. The values of A of the telomers become greater with increasing polymerization degree and are much greater than 0.90–1.10 nm2 molecule1 of Rn AmAc monomers. The areas of the telomers with n ¼ 10 and n ¼ 12 are smaller than those of the telomers with n ¼ 6 and n ¼ 8, probably due to the interactions among several long alkyl chains. Thus, over the range of repeat units investigated there is a linear

FIG. 13 Relationships between polymerization degree and (a) logarithm of CMC and (b) surface tension ( cmc) of xRn AmAc telomers. pH 9–10, 238C. &: xR6AmAc, ~: xR8AmAc, *: xR10AmAc, &: xR12AmAc. (From Ref. 48 with permission of AOCS Press.) Copyright © 2003 by Taylor & Francis Group, LLC

dependence of the surface area per molecule with the polymerization degree and a weak dependence of the CMC and the surface tension. In the presence of 2.6 mmol dm3 of Ca2þ , the cmcs of the telomers are higher than those of the telomers in the absence of Ca2þ , whereas the CMCs of the telomers are lower than those of the telomers in the absence of Ca2þ due to the interactions between amides or carboxylates and Ca2þ ions. The surface activities of surfactants can be correlated with the HLB [49]. The HLB of the telomers are calculated by the Oda equation [50,51]. The values of HLB of the telomers are 21.0–23.1, 15.7–17.7, 13.1–15.3, and 10.5– 12.4 for xR6AmAc, xR8AmAc, xR10AmAc, and xR12AmAc, respectively. Figure 15 shows the relationship between the values of HLB and the cmc of the telomers. The cmc of the telomers has the minimum value at HLB of 14.5. To obtain the high surface activities it is important to control the balance of hydrophobic groups and hydrophilic groups in the telomers.

B. Foaming Property Figure 16 shows the foam volume of aqueous solutions of xRn AmAc telomers immediately and after 60 min of standing [48]. The foaming properties are inﬂuenced signiﬁcantly by the alkyl chain length as well as the polymerization degree of the telomers. The telomers with n ¼ 6 and n ¼ 12 do not have the ability to keep the foam after 60 min of standing, while the foam volume of the telomers with n ¼ 8 and n ¼ 10 reduces to 62–75 and 77–96% of initial volume, respectively. Of the telomers, xR8AmAc with x ¼ 9.2–13.1 gives the highest foaming abilities and foam stabilities. Further, the foam properties of the telomers are correlated with the HLB; the foam volume of the telomers has the maximum value at HLB of 16–18.

FIG. 14 Relationship between polymerization degree and occupied area per molecule (A) of xRn AmAc telomers. pH 9–10, 238C. &: xR6AmAc, ~: xR8AmAc, *: xR10AmAc, &: xR12AmAc. (From Ref. 48 with permission of AOCS Press.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 15 Relationship between HLB and surface tension ( cmc) of xRn AmAc telomers. (From Ref. 48 with permission of AOCS Press.)

FIG. 16 Relationships between polymerization degree and (a) foaming abilities and (b) foam stabilities after 60 min of standing of xRn AmAc telomers. 0.2 wt %, 238C. &: xR6AmAc, ~: xR8AmAc, *: xR10AmAc, &: xR12AmAc. (From Ref. 48 with permission of AOCS Press.) Copyright © 2003 by Taylor & Francis Group, LLC

C. Emulsiﬁcation Power xRn AmAc with n ¼ 6 and n ¼ 8 forms highly stable o/w-type emulsions and the degrees of emulsiﬁcation are kept at the level of 30% for xR6AmAc and 58–67% for xR8AmAc after 100 min of standing [48]. xRn AmAc with n ¼ 10 and n ¼ 12 forms the highly stable emulsions until 3–5 min of standing, while the emulsions are separated completely into 50% aqueous solution phase and 50% toluene phase after 100 min. The interfacial orientations of the telomers having several decyl or dodecyl chains are less easy than those of the telomers having several hexyl or octyl chains. There seems to be an optimum chain length for foam and emulsion stabilities at about n ¼ 8. Further, as shown in Fig. 17, the highly stable emulsion formations of the telomers are observed at values of HLB of 16–18; they cause the eﬀective interfacial activities at the toluene–water interface. The addition of 2.6 mmol dm3 of Ca2þ to the mixtures of the aqueous solutions of the telomers and toluene decreases the emulsion stability and the degrees of emulsiﬁcation are 50–55% for xR8AmAc with x ¼ 9.2–13.1 and 0–10% for the other telomers. xR8AmAc also results in the formation of water-in-oil-(w/o) type emulsions. This is ascribed to the reduction of the electrostatic repulsion due to the interactions between the carboxylates or the amides and Ca2þ ions and the decrease of the hydrophilic properties of the telomers, resulting in the inversion from o/w to w/o. If the addition of Ca2þ causes phase inversion, this suggests that the addition of smaller amounts lowers the interfacial tension. If a concentration could be found

FIG. 17 Relationship between HLB and degree of emulsiﬁcation after 100 min of standing of xRn AmAc telomers. (From Ref. 48 with permission of AOCS Press.) Copyright © 2003 by Taylor & Francis Group, LLC

that is near the critical point, this could lead to some highly eﬀective cleaning agents.

VII. PARTIALLY QUATERNIZED 2- OR 4-VINYLPYRIDINE CATIONIC TELOMERS Partially quaternized 2-vinylpyridine or 4-vinylpyridine telomer-type cationic surfactants (xRn -2VPQ, xRn -4VPQ; x is the total number of alkyl chains) are prepared by the telomerization of 2-vinylpyridine or 4-vinylpyridine in the presence of alkanethiol as a chain transfer agent and then the quaternization of the obtained telomers with alkyl bromide. Figure 18 shows the structures and the abbreviations.

A. Surface Activity The surface activities in aqueous solutions at pH 2 are found to be inﬂuenced by the polymerization degree, the number of alkyl chains, the alkyl chain length, and the conﬁguration of alkyl chains of the telomers [52–54]. Figure 19 shows the relationship between the number of dodecyl chains and the surface tension at CMC of xR12-2VPQ with Pn 11 and xR12-4VPQ with

FIG. 18 Structures and abbreviations of partially quaternized 2-vinylpyridine and 4-vinylpyridine telomers. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 19 Relationship between number of alkyl chains and surface tension ( cmc) of the telomers with Pn 10–11. pH 2, 258C. *: xR12-2VPQ with Pn 11, &: xR12-4VPQ with Pn 10. (From Ref. 52 with permission of Japan Oil Chemists’ Society.)

Pn 10. The surface tensions attain 33–35 mN m1 for xR12-2VPQ with x ¼ 3.2–9.5 and 37 mN m1 for xR12-4VPQ with x ¼ 3.2. However, upon increasing the dodecyl chains, lowering the surface tension of xR12-4VPQ is less eﬀective than that of xR12-2VPQ. It is clear that xR12-2VPQ orients densely at the air–water interface and shows great surface activities, because the chains of xR12-2VPQ orient in the nearly same direction to the skeletal hydrocarbon chains and the orientations are eﬀective, while those in xR124VPQ orient reversely. The surface tensions are inﬂuenced by the polymerization degree of the telomers. The cmcs of 1.9–4.5R12-2VPQ with Pn 20 and 2.9–13.7R12-4VPQ with Pn 19 are 44–48 and 54–59 mN m1 , respectively. xR12-2VPQ with Pn 20 shows higher eﬃciencies in lowering the surface tension than xR12-4VPQ Pn 19, while these telomers with Pn 19–20 are less eﬀective than those with Pn 10–11. The surface tensions of polysoaps of the quaternized 2-vinylpyridine with Pn 560 are 57 mN m1 at a concentration of 0.5% and 52 mN m1 at a concentration of 1% [55,56]. The telomers with Pn about 20 show less eﬀective surface activities due to the bending of the skeletal hydrocarbon chains, like polysoaps. On the other hand, the telomers with Pn about 5 show excellent surface activities. They are also inﬂuenced by the alkyl chain length of the telomers. Table 2 shows the values of the CMC and the cmc of xR12-2VPQ with Pn 4–6 in aqueous solutions at pH 2. In the case of an alkyl chain length of 12, upon increasing the dodecyl chains, the telomers reduce the surface tension and the CMCs shift to lower Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 2 CMC, cmc , and Occupied Area per Molecule (A) of xRn -2VPQ with Pn 4–6 Pn

Telomer

3.9 3.9 3.9

R6 -2VP 2.1R6 -2VPQ 3.0R6 -2VPQ

5.8 5.8 5.8 5.8

R8 -2VP 2.1R8 -2VPQ 3.0R8 -2VPQ 3.9R8 -2VPQ

5.2 5.2 5.2

R12 -2VP 2.5R12 -2VPQ 3.4R12 -2VPQ C12 H25 Pyrþa

cmc (mN m1 )

A (nm2 molecule1 )

31.7 33.2 32.9

0.77 0.88 1.01

8.5 0.65 0.34 0.022

32.9 32.4 29.1 28.6

0.67 1.35 1.26 0.73

0.63 0.25 0.015

39.4 30.1 28.1

0.71 1.28 0.78

32.9

0.50

CMC (mmol dm3 ) 45 11 3.9

11.4

a N-dodecylpyridinium bromide. Source: Ref. 53.

concentration. In particular, the CMC of 3.4R12-2VPQ is 1/760th of that of N-dodecylpyridinium [42], a conventional cationic surfactant. The telomers having 2–3 octyl or dodecyl chains orient by both one terminal alkyl chain and introduced alkyl chains, giving large occupied areas, and those having 3– 4 octyl or dodecyl chains orient densely by the introduced alkyl chains due to the interactions between their chains, giving small ones. The aggregation number of the telomers is determined by static light scattering measurement [57]. From the Debye plots the aggregation numbers of the telomers at their CMCs are about 4 1 for 2.1R8-2VPQ with Pn 6, 45 10 for 2.5R12-2VPQ with Pn 5, and 11 1 for 3.4R12-2VPQ with Pn 5 (neutral pH). The aggregation number of 2.1R8-2VPQ is very small, probably due to the short hydrophobic chain length of the telomers. The aggregation of the hydrocarbon chains of 3.4R12-2VPQ seems to be hindered by the vinyl chains, giving an extremely small aggregation number. Thus, the number of chains and the alkyl chain length of the telomers aﬀect the micellar properties in aqueous solution. Emulsiﬁcation is also aﬀected by the number of alkyl chains as well as the polymerization degree. The eﬀect of the number on emulsiﬁcation of toluene and aqueous solutions of xR12-2VPQ with Pn 11 or xR12-4VPQ with Pn 10 after 5 and 100 min of standing is shown in Fig. 20 [52]. The highly stable o/w-type emulsions are formed by xR12-2VPQ having 3.2–6.2 dodecyl Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 20 Relationship between number of alkyl chains and degree of emulsiﬁcation after 5 and 100 min of standing of the telomers with Pn 10–11. Solutions at pH 2– toluene, 258C. *: xR12-2VPQ with Pn 11, after 5 min, *: after 100 min, &: xR124VPQ with Pn 10, after 5 min, &: after 100 min. (From Ref. 52 with permission of Japan Oil Chemists’ Society.)

chains and 3.2R12-4VPQ. In the same manner as lowering of the surface tension, xR12-2VPQ is more eﬃcient than xR12-4VPQ, and xR12-2VPQ with Pn 5–11 makes the emulsiﬁcation more stable than that with Pn 20.

B. Dispersion The adsorption behavior of the telomers at the solid–liquid interface is discussed using silica particles [57]. Because silica particles are negatively charged at neutral pH, it is expected that adsorption of the telomers occurs mainly due to an electrostatic attraction force between negatively charged sites of silica and quaternary pyridinium groups of the telomers as a ﬁrst adsorption step. It is apparent that the adsorbed amounts of the telomers increase sharply at very low concentrations and reach a plateau, suggesting that the interaction between the telomers and the surface of silica is appreciably strong. At low telomer concentrations, the telomer molecules adsorb on the negatively charged silica surface by orienting their hydrocarbon chains to the aqueous solution so that the surface of silica becomes hydrophobic. With a further increase of the telomer concentration, a bilayer adsorption will occur. These adsorption behaviors reﬂect the changes in the -potential of silica. The -potential of silica in the absence of the telomers is negative, but it increases rapidly with Copyright © 2003 by Taylor & Francis Group, LLC

increasing telomer concentration. This alteration from negative to positive in the -potential supports the formation of a bilayer. Because the areas occupied by the telomer adsorbed (the surface area of silica/the saturated amount of telomer adsorbed, 10.7 nm2 molecule1 for 2.1R8-2VPQ with Pn 6, 10.3 nm2 molecule1 for 2.5R12-2VPQ with Pn 5, and 7.5 nm2 molecule1 for 3.4R12-2VPQ with Pn 5) at the saturation level are quite large compared to those at the air–aqueous solution interface, it is conceivable that patchlike bilayers are sparsely formed even at high telomer concentrations. The sedimentation rate of silica by adsorption of the telomers is signiﬁcantly aﬀected by the change of potential; it increases rapidly at low telomer concentrations, reaches a maximum, and then decreases with further increase of the telomer concentration. The maximum sedimentation rate corresponded to the almost-zero potential, where the rates are the order of 3.4R12-2VPQ > 2.5R12-2VPQ > 2.1R82VPQ. This indicates that the chain length and the number of hydrocarbon chains, along with the pyridinium group and the main hydrocarbon chains of the telomers, play an important role in the ﬂocculation of silica. Thus, the silica suspensions show a dispersion–ﬂocculation–redispersion sequence with the telomer concentration, which is very similar for oppositely charged systems of surfactants and particles [58,59].

C. Binary Property with Cationic Gemini Surfactant Mixed surfactants, rather than individual surfactants, are used in most practical applications. Mixtures of diﬀerent types of surfactants often exhibit synergism, which is the condition when the properties of the mixtures are better than those attainable with the individual components by themselves [60,61]. Although many mixed surfactant systems have been extensively studied, there are few reports for the behavior of mixtures of cationic and cationic surfactant systems [62,63]. Cationic gemini surfactant of 1,2bis(alkyldimethylammonio)ethane dibromide (2Rn enQ) is known to show unusual physicochemical properties [1–7]. Here, the properties of mixtures of xRn -2VPQ with Pn about 5 and 2Rn enQ as well as xRn -2VPQ with Pn about 5 and alkyltrimethylammonium bromide (1Rn Q) are discussed by surface tension, foaming, and emulsiﬁcation measurements [64].

1. Surface Tension The surface tensions of xRn -2VPQ/1Rn Q and xRn -2VPQ/2Rn enQ mixture systems at various mole fractions of xRn -2VPQ () decrease with increasing total surfactant concentration and then reach clear breakpoints, which are taken as a CMC of the mixed systems. In the case of an alkyl chain length of 10, the mixed CMCs are intermediate between the CMC of xR10-2VPQ and that of 1R10Q or 2R10enQ. It is reported that the mixed CMCs of two Copyright © 2003 by Taylor & Francis Group, LLC

cationic surfactants are intermediate between the respective surfactants’ CMCs [62, 63]. The mixed surfactants at ¼ 0.50 show the highest eﬃciency at reducing the surface tension. The cmcs of the mixtures with the other mole fractions ( ¼ 0.20–0.33 and 0.67–0.80) are slightly higher than those of 2R10enQ or 2.0R10-2VPQ. Similar trends in the CMC and the lowering abilities of the surface tension are observed for 2.1R8-2VPQ/ 2R8enQ, 2.1R12-2VPQ/2R12enQ, and 1.9R14-2VPQ/2R14enQ systems. These results indicate that the equimolar cationic mixed surfactants having several alkyl chains are adsorbed at the air–water interface and orient themselves so as to cause eﬀective surface activities. However, in the case of xRn 2VPQ/1Rn Q systems, the mixtures at ¼ 0.33 show the lowest surface tension. This suggests that the number of alkyl chains of quaternary ammonium salt has an eﬀect on the surface activities. Further, the logarithm of the CMC of the mixed systems decreases linearly with increasing alkyl chain length of the binary surfactants, like the pure-component monomeric surfactants [42]. The mixed CMCs of the xRn -2VPQ/2Rn enQ system are also lower than those of the xRn -2VPQ/1Rn Q system. Figure 21 shows the relationship between the alkyl chain length and the cmc of xRn -2VPQ/1Rn Q ( ¼ 0.33) and xRn -2VPQ/2Rn enQ ( ¼ 0.50) systems. The 2.0Rn -2VPQ/ 2Rn enQ system shows higher eﬃciencies at reducing the surface tension than the xRn -2VPQ/1Rn Q system. The surface tension is also inﬂuenced by the alkyl chain length of the mixed surfactants; the mixtures having decyl chains

FIG. 21 Relationship between alkyl chain length and surface tension ( cmc) for xRn -2VPQ, 1Rn Q, 2Rn enQ, xRn -2VPQ/1Rn Q ( ¼ 0.33) and xRn -2VPQ/2Rn enQ ( ¼ 0.50) systems. pH 2, 238C. *: 1Rn Q, &: 2Rn enQ, ~: xRn -2VPQ, *: xRn 2VPQ/1Rn Q ( ¼ 0.33), &: xRn -2VPQ/2Rn enQ ( ¼ 0.50). (From Ref. 64 with permission of Japan Oil Chemists’ Society.) Copyright © 2003 by Taylor & Francis Group, LLC

give the maximum ability to lower the surface tension. Thus, it is found that the equimolar mixtures of the cationic telomers having several decyl chains and the cationic gemini surfactant having two decyl chains show the high surface activities due to the interactions between decyl chains of two surfactants and the weak electrostatic repulsion of nitrogen ions.

2. Foaming Property In general, most conventional cationic surfactants do not have foaming properties [42]. 1Rn Q does not have foaming abilities, while 2Rn enQ (n ¼ 10–14) and xRn -2VPQ (n ¼ 8–14), having several alkyl chains, show foaming properties. The cationic mixed surfactants of xRn -2VPQ/1Rn Q and xRn -2VPQ/2Rn enQ systems give foaming properties, and the stabilities are signiﬁcantly inﬂuenced by the mole fraction of xRn -2VPQ and the alkyl chain length of binary surfactants. Figure 22 shows the relationship between the mole fraction of xRn -2VPQ and the foam volume after 60 min of standing for xRn -2VPQ/2Rn enQ systems. xRn -2VPQ/2Rn enQ systems show higher foam stabilities than the pure-component surfactants with the same alkyl chain length. xRn -2VPQ/2Rn enQ systems give the maximum foam stabilities at ¼ 0.50 which are higher than those of xRn -2VPQ/1Rn Q systems. These results suggest that the foaming properties are derived from the enhancement of the interfacial density due to the interactions between several alkyl chains of 2-vinylpyridine telomers and bis-quaternary ammonium salt. Further, the foam stabilities of the mixed surfactants are

FIG. 22 Relationship between mole fraction of xRn -2VPQ and foam volume after 60 min of standing for xRn -2VPQ/2Rn enQ system. pH 2, 238C. *: R8, &: R10, ~: R12, !: R14. (From Ref. 64 with permission of Japan Oil Chemists’ Society.) Copyright © 2003 by Taylor & Francis Group, LLC

correlated with the lowering abilities of the surface tension. The maximum foaming stabilities are known to be obtained at approximately the same mole ratio of the two surfactants that produced maximum synergism in surface tension reduction [65].

3. Emulsiﬁcation Power Vigorous shaking of the mixtures of the aqueous solutions of xRn -2VPQ/ 1Rn Q or xRn -2VPQ/2Rn enQ systems and toluene forms o/w-type emulsions. Figure 23 shows the relationship between the mole fraction of xRn 2VPQ and the degree of emulsiﬁcation after 180 min of standing for xRn 2VPQ/2Rn enQ systems. Most xRn -2VPQ/2Rn enQ systems show higher emulsion stabilities than the pure-component surfactants. Except for the mixture system with n ¼ 14, the highest emulsion stabilities of the mixed surfactants with the same alkyl chain length are observed at ¼ 0.50. In the case of the mixed surfactants with the alkyl chain length of 14, the degrees of emulsiﬁcation decrease dramatically with increasing mole fraction of xR142VPQ. The maximum emulsion stabilities of xRn -2VPQ/2Rn enQ systems are also higher than those of xRn -2VPQ/1Rn Q. It is found that the highly stable emulsions are formed by the equimolar mixtures of two cationic surfactants having several decyl chains. Thus, surface activities of the mixed surfactants of xRn -2VPQ and 1Rn Q or 2Rn enQ are signiﬁcantly inﬂuenced by the alkyl chain length of the binary surfactants, the mole fraction of xRn -2VPQ, and the number of alkyl chains

FIG. 23 Relationship between mole fraction of xRn -2VPQ and degree of emulsiﬁcation after 180 min of standing for xRn -2VPQ/2Rn enQ system. 238C. *: R8, &: R10, ~: R12, !: R14. (From Ref. 64 with permission of Japan Oil Chemists’ Society.) Copyright © 2003 by Taylor & Francis Group, LLC

of quaternary ammonium salt. In particular, the equimolar mixed surfactant of 2.0R10-2VPQ/2R10enQ shows the greatest surface activities such as surface tension, foaming properties, and emulsiﬁcation power. The reason why the mixed system of 2.0R10-2VPQ/2R10enQ provides the greatest surface activities can be interpreted as follows; the mixed surfactants having several octyl chains seem to show weak interactions between octyl chains and electrostatic repulsions between nitrogen ions due to a short alkyl chain length of 2.1R8-2VPQ and 2R8enQ, resulting in the reduced surface activities. On the other hand, those having several dodecyl or tetradecyl chains seem to give poor surface activities due to strong cohesion by the several hydrophobic chains of xRn -2VPQ and by the several alkyl chains of 2Rn enQ. In the case of the mixed system having several decyl chains, compact mixed micelles can be formed due to strong hydrophobic interactions between several decyl chains of xR10-2VPQ and two decyl chains of 2R10enQ as well as less electrostatic repulsions between hydrophilic groups of xR10-2VPQ and 2R10enQ.

VIII. PARTIALLY QUATERNIZED 4-VINYLPYRIDINE–SODIUM ACRYLATE ZWITTERIONIC COTELOMERS Zwitterionic surfactants are adsorbed onto both negatively charged and positively charged surfaces without changing the charge of the surface signiﬁcantly, since they carry both positive and negative charges. They exhibit pH-dependent behavior and are less irritating to skin and eyes than many anionic and cationic surfactants [66]. Because of these useful characteristics, zwitterionic surfactants are often combined with anionic or cationic surfactants in many consumer products, such as shampoos and detergents [67]. Cotelomer-type zwitterionic surfactants (R6S-zR6VPQ-wVP-yAA; w and y are the number of 4-vinylpyridine and sodium acrylate unit, respectively, z is the number of hexyl chains) are prepared by the quaternization and the hydrolyses of the cotelomers (R6S-xVP-yMA), which are prepared by the cotelomerization of 4-vinylpyridine and methyl acrylate in the presence of hexanethiol as a chain transfer agent. Figure 24 shows the structures and the abbreviations.

A. Surface Tension The corresponding cationic cotelomers prepared (R6S-zR6VPQ-wVP-yMA) are easily soluble in water, while the zwitterionic cotelomers prepared are slightly soluble in water. The surface tensions of the cationic cotelomers and the zwitterionic cotelomers decrease with increasing concentration of the aqueous solution reaching clear breakpoints, which are taken as CMC [68]. Figure 25 shows the relationships between the number of hexyl chains Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 24 Structures and abbreviations of cationic and zwitterionic cotelomers derived from 4-vinylpyridine–methyl acrylate cotelomers.

and the logarithm of the CMC and the cmc of the cationic and zwitterionic cotelomers in R6S-4.0VP-2.3MA series. The CMCs of the zwitterionic cotelomers shift to lower concentration with increasing number of hexyl chains, while those of the corresponding cationic cotelomers shift to higher concentration. In the present cationic cotelomers, the number of pyridinium groups increases with an increasing number of hexyl chains, which have weak hydrophobic properties. Hence the cationic cotelomers are inﬂuenced by the hydrophilic properties of the pyridinium groups. The zwitterionic cotelomers give lower CMCs than the cationic cotelomers, and the CMC of the zwitterionic cotelomers having 3.8 hexyl chains is 1/110th of that of the corresponding cationic cotelomers. This indicates that the interactions between the carboxylates and the pyridiniums enhance the hydrophobicities of the cotelomers. The CMCs of the zwitterionic cotelomers are also lower than those of the conventional zwitterionic surfactants such as N-octylbetaine (250 mmol dm3 at 278C) [69] and N-dodecylbetaine (1.8 mmol dm3 at 238C) [70], which have longer alkyl chains than the present cotelomers. Except for R6S-1.4R6VPQ2.6VP-2.3AA, the cmcs of the zwitterionic cotelomers are higher than those of the cationic cotelomers. The increase of hexyl chains of the cationic cotelomers reduces the surface tension, in a similar manner to cationic vinylpyridine-type telomers xRn -2VPQ and xRn -4VPQ, while that of the zwitterionic cotelomers renders them less surface-active. This is ascribed to the interactions between the carboxylates and the pyridiniums in the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 25 Relationships between number of hexyl chains and (a) logarithm of CMC and (b) surface tension ( cmc) of R6S-zR6VPQ-wVP-2.3MA(AA) with Pn of 6.3. 238C. &: cationic cotelomer of R6S-zR6VPQ-wVP-2.3MA with Pn 6.3, *: zwitterionic cotelomer of R6S-zR6VPQ-wVP-2.3AA with Pn 6.3. (From Ref. 68 with permission of Japan Oil Chemists’ Society.)

FIG. 26 Relationship between number of hexyl chains and degree of emulsiﬁcation of water and chloroform solutions of R6S-zR6VPQ-wVP-2.3AA with Pn of 6.3. Solutions of telomers: 0.5 wt %, 238C. *: after 2 min, &: after 10 min, ^: after 30 min, ~: after 100 min, !: after 200 min, *: after 360 min. (From Ref. 68 with permission of Japan Oil Chemists’ Society.) Copyright © 2003 by Taylor & Francis Group, LLC

cotelomers as mentioned for the CMC. The zwitterionic cotelomers of R6SzR6VPQ-wVP-2.3AA series have the pyridiniums of z as cationic parts and the carboxylates of 2.3 as anionic parts. Hence the zwitterionic cotelomers with z of 3–4 have a weak hydrophilic property, showing high surface tension.

B. Emulsiﬁcation Power The zwitterionic cotelomers are added to chloroform or toluene and the solutions obtained are shaken well with water, giving o/w-type emulsions [68]. The degrees of emulsiﬁcation of chloroform and toluene in the presence of R6S-3.0R6VPQ-0.5VP-2.1AA are 56 and 11%, respectively, after 24 h of standing. Figure 26 shows the relationship between the number of hexyl chains and the degree of emulsiﬁcation of water and the chloroform solution containing R6S-zR6VPQ-wVP-2.3AA cotelomers after 2, 10, 30, 100, 200, and 360 min of standing. The degrees of emulsiﬁcation are inﬂuenced by the number of hexyl chains, in a similar manner as surface tension. All the zwitterionic cotelomers give highly stable emulsions until 10 min of standing. After 30 min, the emulsions decrease with the number of hexyl chains. The degrees of emulsiﬁcation of the cotelomers having 2–3 hexyl chains are kept at the level of 60–70% after 360 min, while those of the cotelomers having hexyl chains of 4–5 rapidly decrease. The increase of hexyl chains reduces the interfacial activities in a similar manner to the surface tension. It is probably due to the lack of ﬂuidity of the cotelomers having several hexyl chains, which have weak hydrophilic properties. The zwitterionic cotelomers contain the partially quaternized pyridiniums as cationic parts and the carboxylates as anionic parts. It is interesting to examine the ability of the mixtures of cationic cotelomer R6S-2.1R6VPQ-1.9VP-2.3MA and anionic cotelomer 2.9R6A-2.3AA having 2.9 hexyl chains and 2.3 sodium acrylate to cause emulsion. A chloroform–water mixture is shaken in the presence of the mixtures of cationic and anionic cotelomers. No emulsion is observed after 1 min of standing. The mixtures give low emulsions due to the interactions between the carboxylates and the pyridiniums of intermolecular of the cotelomers. The zwitterionic cotelomers reduce the interfacial tension at the chloroform or toluene–water interface. For example, the interfacial tensions of R6S-3.0R6VPQ-0.5VP-2.1AA using chloroform and toluene as an oil phase are 3 and 4 mN m1 , respectively. Figure 27 shows the relationship between the logarithm of the concentration of the cotelomers in chloroform solutions and the interfacial tension for R6S-zR6VPQ-wVP-2.3AA series, along with the data of mixtures of cationic cotelomer of R6S-2.1R6VPQ1.9VP-2.3MA and anionic cotelomer of 2.9R6A-2.3AA. R6S-zR6VPQ-wVP2.3AA with z ¼ 1.4–3.8 gives the interfacial tension of 2–4 mN m1 at the concentrations of 0.0052–0.0057 mmol dm3 , while the equimolar mixtures Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 27 Relationship between logarithm of concentration of cotelomers in chloroform solutions and interfacial tension. 238C. *: R6S-1.4R6VPQ-2.6VP-2.3AA, !: R6S-2.1R6VPQ-1.9VP-2.3AA, &: R6S-3.0R6VPQ-1.0VP-2.3AA, ^: R6S-3.8R6 VPQ-0.2VP-2.3AA, &: equimolar mixtures of R6S-2.1R6VPQ-1.9VP-2.3MA and 2.9R6A-2.3AA (From Ref. 68 with permission of Japan Oil Chemists’ Society.)

of R6S-2.1R6VPQ-1.9VP-2.3MA and 2.9R6A-2.3AA give the interfacial tension of 8 mN m1 with the CMC of 0.062 mmol dm3 . The zwitterionic cotelomers with the anionic carboxylates and the cationic pyridiniums in the molecule are adsorbed at the chloroform–water interface and orient themselves so as to cause the eﬀective interfacial activities. In addition, the interfacial tensions of the zwitterionic cotelomers and the mixtures of cationic cotelomer and anionic cotelomer are correlated to the emulsion abilities.

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10 Viscoelastic Surfactant Solutions HEINZ HOFFMANN

I.

University of Bayreuth, Bayreuth, Germany

INTRODUCTION

In numerous applications of surfactants the rheological behavior of their aqueous solutions is of great practical importance. Surfactant systems can have very complex ﬂow properties. For example, concentrated solutions of certain surfactants are Newtonian liquids and their viscosities are only slightly higher than that of pure water. On the other hand, solutions of other surfactants have viscosities that are 106 to 107 times higher than the water viscosity although the surfactant concentration is still below 1 wt %, and such systems are also highly elastic. The viscosities of such samples can be varied within 6 orders of magnitude by only a small change of diﬀerent parameters like surfactant concentration, ionic strength, temperature, or concentration of additives [1]. This diﬀerent rheological behavior of the solutions of various surfactants is due to the types of aggregates present in the solutions. Spherical micelles are present in systems with low viscosities, and the ﬂow behavior of such liquids is similar to that of normal dispersions in which the particles are not connected. On the other hand, long cylindrical micelles are present in solutions with a high viscoelasticity. These micelles can be described as worm-, thread-, or rodlike. They form temporary entanglement networks in the solutions; that means that the network points have only a ﬁnite lifetime, which can, however be rather long, with values in the range of up to a few hundred seconds. As a consequence, these solutions show elastic properties in all experiments that are shorter than the lifetime of the network. In long time experiments the systems do not show elasticity, but they behave like normal liquids and do not possess a yield stress value. This can be demonstrated by a simple experiment: air bubbles entrapped in the solutions recoil elastically after swirling of the samples and the bubbles seem to be stationary on observation for several minutes. On standing for longer periods, however, the bubbles rise slowly and the solutions are free of bubbles Copyright © 2003 by Taylor & Francis Group, LLC

after standing for some days. Such viscoelastic surfactants solutions have been known for a long time, and considerable progress has been made in the theoretical understanding of those systems [2–5]. Recently, another type of viscoelastic surfactant solutions has been found that has completely diﬀerent rheological properties. Such solutions often contain mixtures of surfactants and cosurfactants in a mixing ratio around 1:1. Such samples contain vesicles and classical lamellar phases [6–10]. These phases show shear thinning behavior with increasing shear rates. Many such vesicle or lamellar phases do not show elasticity, but other systems show the same recoil eﬀect of entrapped air bubbles like the viscoelastic solutions with entangled rodlike micelles. Quantitative rheological measurements furthermore show that the shear moduli of both types of viscoelastic surfactant solutions are in the same range; it could thus be concluded that both systems should have the same rheological properties. The simple experiment described above already shows that this is not the case; the air bubbles in viscoelastic lamellar phases do not rise even on standing for months. That clearly proves that these samples have a yield stress value [11]. They behave as soft matter as long as an applied shear stress is smaller than the yield stress value, but they ﬂow like liquids at higher shear stresses. There is a third type of surfactant solutions with a viscoelastic behavior under shear that has the most fascinating properties. At low concentrations these phases contain small rodlike micelles at rest, i.e., the rods are far apart from overlap. As expected, the solutions are isotropic and have low zero shear viscosity values without elasticity as long as an applied shear gradient remains below a characteristic threshold value. If a shear rate is applied to the systems which is above this threshold value, the systems show shear-induced phenomena [12–16]; their viscosity, their normal stress, and their birefringence increase with increasing shear rate until a plateau value is reached. This shear-induced change is completely reversible; when the ﬂow of the solutions is stopped, the values relax again to their original states. The experiments show that these shear-induced phenomena are due to a reversible growth of the small rods under the inﬂuence of the shear gradient to very long rods, which are completely oriented in the shear gradient; this can be concluded from the extinction angle in ﬂow birefringence experiments, which drops to zero when the threshold shear rate is crossed over. At rest, the long rods decay again to the small original aggregates. In this article we discuss and compare all the various types of viscoelastic surfactant systems. Their rheological properties are described and models are presented for the understanding of the diﬀerent ﬂow behavior of the three systems on the basis of the diﬀerent microstructures. Copyright © 2003 by Taylor & Francis Group, LLC

II. VISCOELASTIC SOLUTIONS WITH ENTANGLED RODS A. General Behavior Surfactant solutions containing globular micelles are generally Newtonian liquids with a low viscosity that increases linearly with the volume fraction of the particles according to Einstein’s law [17,18]

¼ s ð1 þ 2:5Þ

ð1Þ

Here s is the viscosity of the pure solvent and is an eﬀective volume fraction that also takes into account the hydration of the molecules; it can be twice to three times higher than the true volume fraction. But also in this case the viscosity of a 10 wt % surfactant solution is only about twice as high as the solvent viscosity. The same is true if anisometric micelles are present in the solutions as long as their rotational volumes do not overlap. On the other hand, many surfactant solutions are highly viscous even at low concentrations in the range of 1 wt %. From this observation it can be concluded that the micellar aggregates in these solutions must organize themselves into a kind of supermolecular network. The viscosity of such systems greatly depends on parameters like surfactant concentration, temperature, ionic strength, or concentration of additives. The solutions also often have elastic properties because the zero shear viscosity 0 is caused by a transient network of entangled rods that is characterized by a shear modulus G0 and a structural relaxation time according to

0 ¼ G 0

ð2Þ

In this case the shear modulus is determined by the number density of entanglement points G0 ¼ kT

ð3Þ

The networks of entangled cylindrical micelles could be made visible by cryo-electron microscopy by Talmon and co-workers [19]. These pictures clearly show the shape and the persistence length of the rods, but they do not reveal their dynamic behavior. According to Eq. (2), the viscosity is the result of structure, which is selected in G0 , and dynamic behavior, i.e., the structural relaxation time . It depends on many parameters and can vary by many orders of magnitude for the same surfactant if, for instance, the counterion concentration is changed [20,21]. This is shown in Fig. 1, where 0 for several cetylpyridiniumchloride (CPyCl) concentrations is plotted against the sodiumsalicylate (NaSal) concentration [22]. With increasing amounts of NaSal, the viscosity passes over a maximum, then through a minimum, and ﬁnally over a second maximum. This behavior is Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 1 Double logarithmic plot of the zero shear viscosity 0 for three diﬀerent CPyCl concentrations against the concentration of added NaSal at 258C. (From Ref. 22.)

due to a corresponding dependence of on the NaSal concentration while G0 is independent of this parameter for a constant CPyCl concentration. Similar results have been observed for many systems by various groups. The viscosity of a 1 wt % surfactant solution can be anywhere between the solvent viscosity and values 106 times as high. Figure 2 shows a cryo-TEM micrograph of a network of rodlike micelles [22]. It is generally assumed that the crosslinks of the network that cause the elastic behavior are entanglements [23]. However, this is not always true. Adhesive contacts between the micelles or a transient branching point like a many-armed disklike micelle can act as crosslinks [24,25]. Some experimental evidence for both possibilities have been observed. The entangled thread or wormlike micelles have typical persistence lengths between a few 100 to a few 1000 A˚, and they may or may not be fused together at the entanglement points. The cylindrical micelles have an equilibrium network conformation. They always undergo translational and rotational diﬀusion processes and also break and reform. If the network is deformed or the equilibrium conditions are suddenly changed, it will take some time until the system reaches equilibrium again. If a shear stress p21 is applied to a network solution in a much shorter time than the equilibration time, the solution behaves like a soft material that obeys Hooke’s law p21 ¼ G0 Copyright © 2003 by Taylor & Francis Group, LLC

ð4Þ

FIG. 2 Image of a vitriﬁed specimen of 0.62 wt % of the gemini surfactant dimethylene-1,2-bis(dodecyldimethylammonium bromide), showing branched threadlike micelles coexisting with spheroidal micelles. The sample was quenched from 258C. (By Y. Talmon/Tel Aviv.)

with the spring constant G0 and the deformation . On the other hand, if the stress is applied for a longer time, the system ﬂows like a Newtonian liquid p21 ¼ 0 _

ð5Þ

with the zero shear viscosity 0 and the shear rate _ . A mechanical model for a viscoelastic ﬂuid is the so-called Maxwell model, which consists of a spring with the constant G0 and a dashpot with the viscosity 0. The zero shear Copyright © 2003 by Taylor & Francis Group, LLC

viscosity of such a system can be expressed by the product of G0 and according to Eq. (2). Both quantities can be determined by oscillating rheological measurements [26]. Many viscoelastic surfactant solutions can be described in a large-frequency range by the Maxwell model with a single shear modulus G0 and a single structural relaxation time constant [27]. This is shown in Fig. 3a [22]. However, there are surfactant solutions that behave in a completely diﬀerent manner as can be seen from Fig. 3b [22]. The systems do not

FIG. 3 (a) Double logarithmic plot of storage modulus G 0 , loss modulus G 00 , and complex viscosity j j against frequency f for a solution with 100-mM CPyCl and 60mM NaSal at 258C. The solution behaves like a Maxwell ﬂuid with a single shear modulus G0 and a single structural relaxation time t. (b) The same plot for a solution with 80-mM C14DMAO, 20-mM SDS, and 55-mM C6OH. The solution does not behave like a Maxwell ﬂuid. Note the diﬀerences to Fig. 3a: G 00 does not pass over a maximum; G 0 does not show a plateau value, but increases with f after the intersection with G 00 with a constant slope of 0.25. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

show a frequency-independent plateau value of the modulus, and the viscosity cannot be expressed by a single G0- and a single -value. In such situations the shear stress after a rapid deformation relaxes according to a stretched exponential function [28] t ð6Þ p21 ¼ p^ 21 exp Figure 3b shows that the loss modulus G 00 increases again with the frequency f. This increase can be related to Rouse modes of the cylindrical micelles. On the basis of a theoretical model [29], the minimum value of G 00 can be expressed by the storage modulus G 0 , the entanglement length le, and the contour length lk of the cylindrical micelles according to G00min ¼ G 0

le lk

ð7Þ

B. Results on Various Viscoelastic Surfactant Systems Rodlike micelles from ionic surfactants are usually formed at high ionic strengths, with strongly binding or hydrophobic counterions or with large hydrophobic groups like double chain or perﬂuoro surfactants [30]. Solutions of such surfactants become highly viscous and viscoelastic with increasing concentration. Some results are shown in Fig. 4 [22] in a double logarithmic plot of the viscosity against the concentration [31–34]. All these surfactants show a concentration region where the slope of the graph is the

FIG. 4 Double logarithmic plot of zero shear viscosity 0 against concentration c for several solutions of charged surfactants. Note that all diﬀerent systems show the same power-law exponent within a limited concentration range above c . (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

same and in the range of 8.5, which is very high by any comparison. The viscosity starts to rise abruptly at an overlap concentration c* and follows the scaling law within a certain concentration region c x ð8Þ

0 / c The exponent for all systems is the same and about 8.5 þ 0.5 in spite of the diﬀerent chemistry of the surfactants. The power-law exponent must therefore be controlled by the electrostatic interaction in the solutions. The slope is much greater than the value of 4.5 þ 0.5, which is expected for large polymer molecules that do not change their size with increasing concentration. It can be concluded from the large exponent that the rodlike micelles continue to grow with concentration above c ; this has been postulated by McKintosh and co-workers [35,36]. Figure 5 shows a plot of log ¼ f ðlog cÞ for the system CPyCl þ NaSal [37,38]. This system can be described by the Maxwell model with one G0and one -value above the ﬁrst viscosity maximum, Fig. 1. The complicated viscosity behavior is due to the concentration dependence of , while G0 steadily increases with concentration. Furthermore, it was found that is controlled by the kinetics of breaking and reforming of the micelles [39]; these processes are faster than the reptation of the rods under the given experimental conditions. As already mentioned, the same is true for the system with a constant CPyCl concentration with increasing amounts of NaSal, which is shown in

FIG. 5 Double logarithmic plot of zero shear viscosity 0 against concentration c of CPyCl þ NaSal for solutions at the ﬁrst maximum (*) viscosity, at the second maximum (!), and at the minimum (&) at 258C (see Fig. 1). (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

Fig. 1. The dependence of the viscosity on the counterion concentration is controlled by a corresponding behavior of , while G0 is independent of the NaSal concentration. The viscosity is therefore a result of the dynamics of the system and not of its structure. This can be proven by cryo-electron microscopy on the system [19]. In all four concentration regions no diﬀerences between the structure of the micelles can be seen in the electron micrographs. This is very remarkable because the micelles are diﬀerently charged in the concentration regions. Below the ﬁrst maximum of the viscosity they are highly and positively charged, at the minimum they are completely neutral, and at the second maximum they carry a negative charge. The power-law behavior in the diﬀerent concentration regions is also completely diﬀerent, as can be seen from Fig. 5. The exponent at the ﬁrst maximum is 8, at the minimum 1.3, and at the second maximum 2.5. Figure 6 [22] shows a plot of logð Þ ¼ f ðlog cÞ for zwitterionic alkyldimethylaminoxide surfactants (CxDMAO) [24]. The data again show a power-law behavior over extended concentration regions. Some results show a break in the curves, which indicates that uncharged systems can also undergo a switch of the relaxation mechanism when the concentration changes. At the lowest concentration region in which a power-law behavior is observed, the slope is the highest and close to the slope that is observed for polymers. This is somewhat surprising because it could be expected that the length of the micellar rods increases with increasing concentration, which should lead to a higher exponent of the power law.

FIG. 6 Double logarithmic plots of zero shear viscosity 0 against concentration c for solutions of alkyldimethylaminoxide surfactants with various chain lengths at 258C. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

It is therefore likely that the dynamics of the systems are already inﬂuenced by kinetic processes under these conditions. For higher concentrations, a lower exponent is observed. Obviously a new mechanism is operating under these conditions that is more eﬀective in reducing a stress than the mechanism in the low-concentration region. Generally, a mechanism can only become determining with increasing concentrations if it is faster than the one at low concentrations. The moduli increase with the same exponent in the various concentration regions. Figure 6 furthermore shows that the absolute value of 0 for C16DMAO and ODMAO (Oleyl) diﬀer by an order of magnitude even though the slope is the same in the high-concentration region. This is due to the fact that in the kinetically controlled region the breaking of the micelles depends very much on the chain length of the surfactant. Cosurfactants can be regarded as surfactants with a small headgroup. According to the theory of micelle formation, addition of cosurfactants to surfactant solutions leads to a transition of spherical micelles to rods or to a growth of rodlike micelles [40]. As a consequence, the viscosity of a surfactant solution increases with increasing cosurfactant concentration. This is shown in Fig. 7 for the system of 100-mM C14DMAO with various cosurfactants [22]. The viscosity ﬁrst increases and then passes over a maximum. The situation is similar as that shown in Fig. 1. It is likely that the micelles still grow steadily with increasing cosurfactant concentration, but the system switches from one mechanism on the left side of the maximum to a faster

FIG. 7 Semilogarithmic plot of zero shear viscosity 0 of a 100-mM solution of C14DMAO against the concentration c of added cosurfactants at 258C. Note that all curves pass over a maximum. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

mechanism on the right side. The reason for the switch is probably that the rods become more ﬂexible with increasing cosurfactant concentration. The diﬀerent mechanisms become obvious in Fig. 8, where log( 0) is plotted against log(c) for C14DMAO with diﬀerent amounts of decanol (C10OH) solubilized in the micelles [22]. The plot shows that the slopes of mixtures at the left side of the maximum are the same while the mixture with the highest cosurfactant/surfactant ratio has the lowest slope of 1.3. This value is equal to the one for CPySal at the viscosity minimum. Systems with similar low slopes from the literature [41,42] are shown in Fig. 9 [22]. The chemistry and also the viscosity values for these systems are diﬀerent, yet the slope is the same. The shear moduli for these systems are very similar for given surfactant concentrations, and they also scale with the same exponent. The low exponent for the viscosity therefore comes about by the structural relaxation time, which scales with an exponent of 1 according to c 1 ð9Þ / c

C. Mechanisms for the Different Scaling Behavior All studied surfactant systems show the same qualitative behavior. The viscosity rises abruptly at a characteristic concentration c , which is lower the longer the chain length of the surfactant. c is the concentration at which

FIG. 8 Double logarithmic plots of zero shear viscosity 0 of a mixture of C14DMAO and C10OH with diﬀerent molar ratios of cosurfactant/surfactant against the concentration of C14DMAO at 258C. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Double logarithmic plot of zero shear viscosity 0 against the total surfactant concentration for several surfactant systems with the same power-law exponent of 1.3. (From Ref. 22.)

the rotational volumes of rodlike micelles start to overlap and form a network. This network can be an entanglement network as in polymer solutions or the micelles can be fused together or can be held together by adhesive contacts. All these types of networks have been proposed, and it has been shown that they really exist [43]. In the theoretical treatment it is assumed that the cylindrical micelles are wormlike and ﬂexible. This can be the case for some of the presented systems, but it is certainly not so for the binary surfactant systems. For example, C16DMAO and ODMAO have very low c -values, and if the micelles were ﬂexible, they would have to be coiled below c . But both electric birefringence and dynamic light scattering results show that at c c , the lengths of the rods are comparable with the mean distances between them. Hence, the rods must be rather stiﬀ with persistence lengths of several thousand A˚. Similar results have been obtained by electron micrographs. The abrupt increase of 0 at c is diﬃcult to understand for stiﬀ rods even if further growth of the rods with increasing concentration is taken into account. Many systems with rodlike particles show that the rotational time constant for the rods is aﬀected very little around c and the solutions do not become viscoelastic above c . We therefore have to assume that other interactions than just hard-core repulsion between the rods must Copyright © 2003 by Taylor & Francis Group, LLC

exist that are responsible for the formation of the network at c . It is conceivable that the rods form adhesive bonds or that they actually form a connected network of fused rods, as has been proposed by Drye and Cates [44]. In such situations two diﬀerent types of networks have to be distinguished, namely saturated and interpenetrating networks. In the ﬁrst case the mean distance between the knots or entanglement points is equivalent to the mesh size; in the second this distance can be much larger than the mesh size between neighboring rods. The viscosities above c increase abruptly with the power law of Eq. (8) with an exponent x > 3:5, while the exponent of the power law for the shear modulus is always about 2.3. This behavior has been treated in detail by Cates and co-workers [45]. The structural relaxation times are aﬀected both by reptation and by bond-breaking processes. Cates treats three diﬀerent kinetic mechanisms. The ﬁrst consists of the break of a rod with the formation of two new endcaps. In the recombination step the rods have to collide at the ends in order to fuse into a new rod. In the second mechanism the endcap of one rod collides with a second rod, and, in a three-armed transition state, a new rod and a new endcap are formed. In the third mechanism two rods collide and form two new rods through a four-armed transition state. These mechanisms lead to somewhat diﬀerent power laws for the kinetic time constant according to c x / ð10Þ c But in all cases x is between 1 and 2. Mechanism 3 is probably less likely in systems with low c -values and stiﬀ rods. For this argument it is likely that mechanism 2 or 3 is eﬀective in the more concentrated region of the pure CxDMAO solutions. For solutions of C16DMAO and ODMAO the slope of the logð 0 Þ logðcÞ plots suddenly changes at a characteristic concentration c . For both regions the same scaling law for the shear modulus with an exponent of 2.3 is found, while the power exponent for the relaxation times changes from 1 to zero. From the constant exponent for G0 it can be concluded that the structures in both concentration regions are the same. The change in the slope must therefore be due to a new mechanism that becomes eﬀective above c . The independence of of the concentration makes it likely that in this region the dynamics are governed by a pure kinetically controlled mechanism and a reptation process is no longer possible. This situation has not yet been treated theoretically. Cates mentions however, that there might be situations where the reputation loses its importance. The more eﬀective mechanism in this range could be the bond interchange mechanism. Copyright © 2003 by Taylor & Francis Group, LLC

For the C14DMAO solutions with C10OH and the CPySal system at the minimum viscosity the extremely low power-law exponent of 1.3 for the viscosity and an exponent of 1 for the structural relaxation times are found. The explanation for this behavior could be that the cylindrical micelles for systems with such low exponents are very ﬂexible. In such a situation the persistence length would be much shorter than the contour length between two neighboring entanglement points. Furthermore, the persistence length should be independent of the concentration. The diﬀusion of the rods can therefore be described by a constant diﬀusion coeﬃcient D. In order for two arms to collide, they have to diﬀuse a distance x. In order for two neighboring rods to undergo a bond exchange process, they have to diﬀuse at least for the average distance x between two arms. The time constant D for the diﬀusion should be proportional to x2 =D. Because the mesh size x decreases with the square root of the concentration, one obtains for the structural relaxation time the observed law 1=Dc, which is identical to Eq. (9). We can therefore conclude that for systems with the low exponent 1.3 the viscosity is controlled by a diﬀusion-controlled bond interchange mechanism. The absolute values of 0 and can still vary from system to system because the persistence length lp of the rods should depend on the particular conditions of the systems. With increasing chain length lp should decrease and D should increase. For such situations we would expect to measure the lowest activation energies for the viscosity. A similar mechanism could be based on the assumption of connected or fused threadlike micelles as crosslinks. These crosslinks could be visualized as disklike micelles from which the rods extend. This means that the transient intermediate species in the various bond interchange mechanisms are now assumed to be stable. In this situation all end caps could be connected. The resulting network could be in the saturated or unsaturated state. The crosslink points could then slide along the threadlike micelles, which can be described as a one-dimensional diﬀusion process with a concentration-independent diﬀusion coeﬃcient. A knot can be dissolved if two network points meet on their random path. If the structural relaxation time is determined by this random movement, a similar equation— / 1=c—can be derived. Both models can describe the low exponent of 1.3 for the scaling law for 0, and for both models reptation is no longer necessary for the release of stress. The mechanisms could probably be distinguished by the concentration dependence of the self-diﬀusion coeﬃcients Ds of the surfactant molecules. In a solution with a connected network a surfactant molecule should be in the same situation as in an L3 phase for which it has been shown that Ds is independent of the surfactant concentration [46]. As Kato et al. [47] showed that the Ds -values increase with concentration for a corresponding Copyright © 2003 by Taylor & Francis Group, LLC

system with rods, a diﬀusion-limited bond interchange mechanism is more likely for the explanation of the scaling law of the structural relaxation time than the assumption of connected networks of threadlike micelles.

D. Rheological Measurements on Viscoelastic Solutions in the kHz Range From electric birefringence measurements it is known that surfactant solutions like those of tetraethylammoniumperﬂuorooctanesulfonate show several time constants from microseconds up to some seconds [33,48,49]. The shortest one, 1, is attributed to the free rotation of rodlike micelles and amounts to 105 to 106 s. It can be found in almost the whole concentration range. The second one, 2, the birefringence of which has a diﬀerent sign, is in the range of 104 s and can only be detected in the narrow concentration region where the rods begin to overlap. The longest time constant, 4, the value of which is about some seconds, represents the structural relaxation time and can be found in both electric birefringence and rheological measurements at suﬃciently high concentrations when a network is formed. The remaining time constant, 3, in the range of milliseconds, cannot yet be detected by rheological measurements because the frequency range of commercial rheometers typically ends at frequencies of about 10 Hz due to inertial forces. Therefore, it is not possible to determine rheological time constants shorter than about 0.01 s. In order to overcome this problem it was necessary to extend the frequency range for the dynamic rheological measurements. For this purpose a dynamic rheometer (HF rheometer) with a frequency range from 1 Hz up to 1 kHz was used. For samples with a high modulus (G 1 kPa) the measurements can even be extended to 2 kHz [50]. This HF rheometer is based on a prototype that was developed in the group of Pechhold at the University of Ulm [51,52]. The sensitivity of the apparatus could be notably improved by numerous technical modiﬁcations. Solutions of tetraethylammoniumperﬂuorooctanesulfonate [C8F17SO3 N(C2H5)4] were studied with the HF rheometer. A typical rheogram is shown in Fig. 10 [50]. The measurement was carried out on a 90-mM solution with the 50-mm gap in the frequency range above 10 Hz. Below 10 Hz, a Bohlin CS 10 rheometer with a cone plate geometry was employed. In the lower-frequency range the samples show Maxwell behavior. G 0 rises with the slope 2, G 00 with slope 1. At frequencies above the crossover of G 0 and G 00 , G 0 reaches a plateau value while G 0 decreases and increases´ again after passing through a minimum. At high frequencies both G 0 and G 00 increase. Even though a second plateau value of G 0 at high frequencies could Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10 Dynamic rheogram of a 90-mM solution of C8F17SO3N(C2H5)4 at T ¼ 208C. Below 10 Hz, the measurement was performed with a Bohlin CS 10 rheometer, above 10 Hz with the HF rheometer and the 50-mm gap (with 1% deformation). (From Ref. 50.)

not be found, it was possible to ﬁt the data by a Burger model (four-parameter Maxwell model): !2 42 !2 32 þ G 2 1 þ !2 42 1 þ !2 32 !4 !4 þ G2 G 0 ð!Þ ¼ G1 1 þ !2 42 1 þ !2 32

G 0 ð!Þ ¼ G1

.

and ð11Þ

The structural relaxation times 4 (the indices have been chosen for correspondence to previous results) decrease with increasing concentration from 25 ms (70 mM) to 0.2 ms (300 mM); the short time constants 3 decrease from 0.35 ms (70 mM) to 0.1 ms (250 mM). Therefore, they correspond well with the time constants determined by dynamic electric birefringence measurements. For each concentration the minimum value of G 00 is about a factor of 2.5 lower than the plateau value of G 0 . According to a theory of Granek and Cates [53] this yields a value of 2.5 for the ratio of the mean contour length of the micelles to the entanglement length [Eq. (7)]. A decrease of the mean Copyright © 2003 by Taylor & Francis Group, LLC

micellar length with a rising concentration can be concluded on the basis of this value and from the decreasing structural relaxation times. Furthermore, mixtures of tetraethylammoniumperﬂuorooctanesulfonate and the pure perﬂuorooctanesulfonic acid (C8F17SO3H) were studied with the HF rheometer. In Fig. 11 a rheogram of 150-mM solution with a salt– acid ratio of 7:3 is shown [50]. From a qualitative point of view the rheogram does not diﬀer too much from that represented in Fig. 3a. It can be noticed, however, that, after substitution of salt by acid, the minimum of G 00 is more pronounced. This means a larger ratio of the mean contour length to the entanglement length (here 4) that can be calculated according to Eq. (7). Generally one observes that until a mole fraction of 40% of the acid the structural relaxation times 4 increase by a factor of 10 (from 7 ms to 70 ms). From these results a growth of the micellar aggregates can be concluded. The short time constants 3 are not notably changed and amount to about 0.1 ms. At a molar ratio of more than 50% of the acid, the viscosity breaks down due to a decreasing length of the micelles. In this case it is no longer possible to measure the samples with the HF rheometer. The high-frequency increase of the moduli can be interpreted on the basis of the following models: 1. In addition to the continuous network there also exist unentangled shorter rods due to the equilibrium distribution of the micellar lengths. These shorter aggregates do not signiﬁcantly inﬂuence the rheological

FIG. 11 Dynamic rheogram of a 150-mM solution of C8F17SO3N(C2H5)4/ C8F17SO3H ¼ 7:3 at T ¼ 218C. The deformation was again 1%. The minimum of G 00 is deeper than in the case of the pure C8F17SO3NEt4. (From Ref. 50.) Copyright © 2003 by Taylor & Francis Group, LLC

behavior of the samples at lower frequencies; at higher frequencies, however, they contribute to the moduli. 2. At angular frequencies higher than the reciprocal value of the Rouse time of a chain segment of the entanglement length, these segments can no longer relax by Rouse diﬀusion [54].

E. SANS Measurements on Viscoelastic Surfactant Solutions Under Shear Small-angle neutron scattering (SANS) is a method particularly suited for the study of self-aggregating colloids since its spatial resolution is typically in the range of 10–1000 A˚, which is exactly the size range of micellar aggregates. Shear cells are available [55] that allow for SANS experiments under shear. This has the advantage that one can align anisometric aggregates in the shear ﬁeld, and from the scattering curves of the aligned particles one can deduce more detailed information regarding their structure and their dynamic behavior in the shear ﬁeld. In addition, systems can be studied that exhibit shear-induced structures, i.e., systems that are very interesting since they show drag-reducing behavior. Anisometric micelles can be oriented by shear if _ > 1 and this allows for a more detailed study of the micellar structure as well as of the dynamic process of alignment. One such system that has been studied is cetylpyridiniumsalicylate at 20-mM concentration (in 20-mM NaCl D2O solution). The system contains rodlike micelles of 21.5-A˚ radius and a length of more than 750 A˚ [55,56]. Under shear an anisotropic scattering pattern is observed that relaxes to the isotropic pattern after switching oﬀ the applied shear ﬁeld. Time-resolved measurements (time resolution of 250 ms) showed that the scattering curves during this relaxation process can be described by one single parameter, the rotational diﬀusion coeﬃcient Drot. It was observed that Drot is time-dependent and decreases with time, an eﬀect due to the interaction between the charged rodlike aggregates, i.e., at the beginning the aligned rods have the largest electrostatic repulsion, giving a large driving force for the disorientation (since for this aligned arrangement the electrostatic potential energy has its highest value). The less aligned the system, the smaller this driving force becomes (since the electrostatic interaction becomes weaker) and correspondingly the rotational diﬀusion coeﬃcient becomes smaller [57]. The orientation of these rodlike aggregates in the shear ﬁeld can be described by a model that explains the experimental scattering curves by an orientation distribution function of the rods that depends on the applied shear gradient [58]. Under the experimental conditions the product of shear gradient _ , and structural relaxation time (which increases with the length Copyright © 2003 by Taylor & Francis Group, LLC

of the aggregates) was always much larger than 1 and therefore a high orientational ordering was achieved because under this condition the ordering force becomes stronger than the diﬀusive force. In general, all anisometric aggregates can become oriented in the shear ﬁeld. Systems with shorter relaxation times require higher shear gradients. The eﬀect of the shear rate has been studied with the system C16C8DMABr at 50-mM concentration. Here the unsheared solution shows a correlation ring that upon application of shear becomes increasingly anisotropic (compare with Fig. 12, where the scattering patterns for various shear gradients are shown [59]). In addition a higher-order peak becomes visible. Finally, for shear rates above _ ¼ 2000 s1 , the scattering pattern hardly changes any more. In this system not only do the relatively short rodlike aggregates become weakly aligned but, in addition, in the shear ﬁeld a second type of micelle is formed, where their relative concentration increases with rising shear rate. Therefore, in this system a shear-induced transformation of micellar aggregates is observed [59]. A more detailed analysis of the system tetradecyltrimethylammoniumsalicylate (C14TMASal) [60] indicates that the sharp peaks that occur upon applying the shear are due to a hexagonal array of cylindrical

FIG. 12 SANS scattering patterns of C16C8DABr in D2O (50 mM) for various shear gradients (the momentum transfer is given in units of nm1): (a) _ ¼ 0 s1 ; (b) _ ¼ 100 s1 ; (c) _ ¼ 400 s1 ; (d) _ ¼ 2000 s1 . The neutron beam is perpendicular to the direction of shear. (From Ref. 57.) Copyright © 2003 by Taylor & Francis Group, LLC

micelles, i.e., again now two types of micelles are present: the originally present short rodlike micelles and very long rodlike aggregates that are formed in the ﬂow ﬁeld [61]. This lattice-type array is formed within about 2 min, as could be seen from time-resolved shear experiments [61] where this result also agrees well with ﬂow birefringence experiments. At a given shear rate an equilibrium between the short rodlike micelles (that normally are only weakly aligned) and the long rodlike aggregates is present. This equilibrium depends on the shear rate—the higher the shear rate, the more the equilibrium is shifted in favor of the long aggregates [62].

F. Overview and General Remarks on Viscoelastic Solutions from Surfactants The discussed results clearly show that viscoelastic surfactant solutions in the L1 phase contain networks of entangled threadlike micelles. As a consequence of the networks, the phases have a shear modulus like any other soft material. The value of the shear modulus is determined by the entanglement points in the system. It scales in the same way as for polymer solutions. Its absolute value is mainly determined by the surfactant concentration and is practically independent of the type of surfactant. The network points are not of a permanent nature. Due to the dynamic behavior of the network, they open and close. If the network is therefore strained, the resulting stress will relax with a certain time constant, the structural relaxation time s. This time constant depends very much on the speciﬁc chemistry of the system. For seemingly similar conditions and the same total concentration, it can vary between a few msecs and thousands of seconds. As a consequence the zero shear viscosity of the system ( 0 ¼ G0 s ) can vary between several mPas and several thousand Pas. Because the mesh size of the network is usually much larger than the diameter of small hydrated ions, the conductivity of the system is little aﬀected by the presence of the network. The structural relaxation time can be both entanglement or kinetically controlled. In the second case it is inﬂuenced by the breaking and reforming of the long, threadlike micelles. As a consequence of the large structural relaxation times, viscoelastic surfactant solutions can show large normal stress diﬀerences in shear ﬂow and a large Weissenberg eﬀect. The normal stress can become much larger than the shear stress. The systems can also show the recoil eﬀect. This eﬀect occurs when the frequencies of the mechanical modes of the viscoelastic samples are higher than the reciprocal relaxation time. These frequencies are determined by the shear modulus, the density, and the dimension of the samples. In semidilute viscoelastic systems it is very diﬃcult to determine experimentally the contour length of the threadlike micelles if the micelles are Copyright © 2003 by Taylor & Francis Group, LLC

longer than the persistence length. As a consequence there are no exact experimental values of the contour length and the length distribution available. Cryo-TEM micrographs show, however, that in some systems the micelles can be at least several mm long. It also is clear from such micrographs that the radius of the endcaps of the cylindrical micelles is larger than the radius of the cylinders [63]. Furthermore, available micrographs show that three- and four-armed branching points do indeed occur as ﬁrst had been postulated [64]. On the basis of scaling laws for the diﬀerent relaxation mechanism it is now possible to explain the complicated concentration dependence of the rheological properties of viscoelastic surfactant solutions. It is still remarkable and surprising, however, that the structural relaxation times for cationic systems with the same chain length but diﬀerent counterions can vary by many orders of magnitude when the systems are in the entangled region and controlled by kinetic processes. One would imagine that the rate constant for the breaking process of a cylindrical micelle should not depend so much on the type of counterion but should mainly be determined by the cross section of the micelle and hence on the chain length of the surfactant. The structural relaxation times for systems with hydrophilic counterions, however, in general are much shorter than with hydrophobic counterions. On the basis of these results today’s explanations should be sometimes questioned even though the experimental data can be quantitatively explained with the available theories and assumptions. There might be other models that can also ﬁt the data. In this context it is necessary to point out that in the presently available theories on the dynamic behavior of the entangled micellar solutions there is no mention of sticky contacts between micelles. In colloid science, in general, such contacts are considered and the binding energy of such contacts plays a critical role for macroscopic properties of the systems. In view of the diﬀerent surfaces of diﬀerent micelles it is easy to imagine that a lifetime for a contact could vary by many orders of magnitude. Systems with extremely long structural relaxation times usually have hydrophobic headgroups and hydrophobic counterions. When two such micelles come into contact they should form a hydrophobic bond, even though the micelles carry a weak charge. The time constant should be proportional to expðA=kTÞ, where A is the bond energy. Such a bond energy could easily amount to 10 kT and thus explain the large structural relaxation times. At present the available evidence seems to agree that all viscoelastic L1 phases can have a very long but ﬁnite structural relaxation time. In eﬀect this means that all L1 phases have a zero shear viscosity and not a yield stress value. In the latter situation entrapped bubbles in an L1 phase would not rise to the surface and would remain entrapped for a long time. There Copyright © 2003 by Taylor & Francis Group, LLC

are, however, indications that systems with bulky hydrophobic counterions may even have a yield stress value. While earlier investigations were mainly concerned with the understanding of viscoelastic systems at equilibrium, more recent papers are concentrated more on nonlinear conditions in shear ﬂow [65]. It was shown that the reptation–reaction model yields a nonlinear constitutive equation that shows a nonmonotonous dependence of stress and shear rate. This leads one to expect ﬂow instabilities with shear-banded ﬂow [66]. Evidence for such situations has actually been observed [53,67,68]. Other recent papers have been concerned with new viscoelastic systems [69–73] with the behavior of viscoelastic L1 phases under elongational ﬂow [74] and, in particular, with highly charged systems without salt screening, which show a maximum in the viscosity with increasing concentration [75]. The authors convincingly show that the phenomenon is mainly due to the fact that the mean length of the micelles is passing over a maximum with increasing concentration. This again is a consequence of a switch of the relaxation mechanism from being entanglement-controlled to kinetically controlled. A similar behavior is often observed in charged viscoelastic systems when the excess salt concentration is increased [76].

III. VISCOELASTIC SOLUTIONS WITH MULTILAMELLAR VESICLES A. The Conditions for the Existence of Vesicles Thermodynamically stable vesicles have been found recently in many solutions with various types of surfactants [6–10,77–82]. Such vesicles occur especially in ternary systems of zwitterionic or nonionic surfactants, aliphatic alcohols as cosurfactants, and water. The vesicles are due to the low spontaneous curvature of the micellar surface, which is continuously lowered with increasing amounts of the cosurfactant because of their small headgroup area [83]. The systems try to come as close as possible to the spontaneous mean curvature without causing much bending energy by adjusting the two main curvatures on the micellar aggregates. As a consequence, the micellar system undergoes several phase transitions with increasing cosurfactant concentration. The vesicle phase occurs within a wide range of the total surfactant and cosurfactant concentration, but only within a small range of the molar ratio of cosurfactant surfactant around 1:1; this is shown, for example, in Fig. 13 [10]. If the surfactant bilayers are charged by the addition of an ionic surfactant, the phase diagram becomes somewhat simpler because some mesophases are suppressed by the charge. As can be seen from Fig. 14, the vesicle phase is still Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 13 Section of the phase diagram of the ternary system C14DMAO/C6OH/ water in the water-rich corner at 258C (see also Fig. 14). (From Ref. 10.)

FIG. 14 Section of the pseudoternary phase diagram of the quaternary system consisting of 100-mM (C14DMAO þ C14TMABr)/C6OH/water at 258C. (From Ref. 10.) Copyright © 2003 by Taylor & Francis Group, LLC

found under these conditions, but it is shifted toward higher cosurfactant concentrations [10]. Thermodynamically stable vesicles have also been found in ternary systems of nonionic alkylpolyglycol surfactants, cosurfactants, and water [84] and also in the binary system of the double chain surfactant didodecyldimethylammoniumbromide (DDMABr) and water [85].

B. Freeze-Fracture Electron Microscopy The vesicles can be made visible by freeze-fracture transmission electron microscopy (FF-TEM). Figure 15 [22] shows the vesicles in a system of 90-mM C14DMAO, 10-mM tetradecyltrimethylammoniumbromide (C14TMABr), 220-mM n-hexanol (C6OH), and water; the cationic surfactant can also be replaced by the anionic surfactant SDS without causing a change of the vesicles or of the rheological properties. From this electron micrograph it is possible to recognize some general features that are of relevance for the properties of the systems. The vesicles have a rather high polydispersity; some seem to be rather small unilamellar vesicles while others consist of about 10 bilayers. The interlamellar spacing is fairly uniform and is in the range of 800 A˚. The vesicles are very densely packed and the whole volume of the system is completely ﬁlled with them. They have a

FIG. 15 Electron micrograph of the vesicles in the system of 90-mM C14DMAO, 10-mM C14TMABr, 220-mM C6OH, and water (the bar represents 1 mm). (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

spherical shape even though the outermost shell can have a radius of several thousand A˚. Some of them do not consist of concentric shells, but have defects. The larger vesicles have typical sizes in the range of 1 mm, and the wedges that result from the dense packing are completely ﬁlled with smaller vesicles. Thus, each vesicle is sitting in a cage from which it cannot escape by a simple diﬀusion process without deformation of its shells. Therefore, the system must have viscoelastic properties.

C. Rheological Properties of the Vesicle Solutions In Fig. 16 [22] the viscoelastic properties of a vesicle phase with 90-mM C14DMAO, 10-mM C14TMABr, and 220-mM C6OH are demonstrated by plots of the storage modulus G 0 , the loss modulus G 00 , and the magnitude of the complex viscosity | *| as a function of the oscillation frequency f. G 0 is much larger than G 00 and independent of f in the whole frequency range. The system behaves like a soft solid and must have a yield stress value. This can be seen from a plot of the shear rate, _ , as a function of the applied shear stress s in Fig. 17 [22]. Both the shear moduli G0 (equal to the frequencyindependent value of G 0 ) and the yield stress values sy increase with increasing total surfactant concentration as can be seen from Fig. 18 [22]. Both quantities disappear at total concentrations below 1 wt %. This means that the vesicles are no longer densely packed. Hence, they can move around

FIG. 16 Double logarithmic plot of storage modulus G 0 , loss modulus G 00 , and the magnitude of the complex viscosity | | against frequency f for a vesicle phase of 90mM C14DMAO, 10-mM C14TMABr, 220-mM C6OH, and water at 258C. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 17 Plot of the shear rate _ against applied shear stress for the same vesicle phase as in Fig. 16. (From Ref. 22.)

FIG. 18 Plot of shear modulus G0 and yield stress y against the total surfactant concentration for a vesicle phase of C14DMAO and C14TMABr with a molar ratio of 9:1 and C6OH at 258C. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

each other easily under shear ﬂow. For higher concentrated systems sy varies linearly with G0 and is about 10 times smaller than G0. This means that the vesicles must be deformed by about 10% until they can pass each other under shear. Similar results are obtained for the vesicles in the binary system of DDMABr and water. Figure 19a and b demonstrate the inﬂuence of charge density on the bilayers on G0 [22]. The moduli increase with increasing amounts of ionic surfactant and saturate around 10 mol% of the ionic compound (Fig. 19a). On addition of electrolyte, the moduli decrease again linearly with the square root of the ionic strength (Fig. 19b). The eﬀect of the chain length of the surfactant compound can be seen from Fig. 20 [22]. The moduli steadily increase for systems with the same concentrations with increasing chain length from C10 to C16 and seem to decrease again for C18; that means that the modulus is not determined only by the electrostatic repulsion between the bilayers, but it depends on the thickness of the bilayers, too. The headgroup of the surfactant in the vesicle phase has only a moderate eﬀect on rheological properties. For example, a vesicle phase of 90-mM C12E6, 10-mM SDS, and 250-mM C6OH shows a very similar behavior as the corresponding phase of 90-mM C14DMAO, 10-mM C14TMABr, and 220-mM C6OH, and also the absolute values of G 0 , G 00 , and | *| are very similar for both systems. The same can be found for systems in which the concentration of the cosurfactant (Fig. 21) or the chain length of the cosurfactant is changed (Fig. 22) [22]. The ﬁgures show that the moduli and the yield stress values increase slightly with the cosurfactant concentration and the chain length of the cosurfactant, but this increase is only small in comparison to the strong dependence of these values on the concentration and the chain length of the surfactant compounds. The temperature has only a very small eﬀect on both G0 and sy between 108C and 608C. An interesting eﬀect is shown in Fig. 23, where the shear viscosity as a function of the shear rate _ , and the magnitude of the complex viscosity | *| as a function of the angular frequency o are compared for two vesicle phases [22]. The diagram shows the important diﬀerence to viscoelastic solutions of threadlike micelles [86] that the Cox–Merz rule— for all values of _ has the same value as | *| at the corresponding value of o in the shear thinning region [87]—is not fulﬁlled for the vesicle phases under all conditions. At low shear rates or frequencies both viscosities have the same value, while at higher shear rates (_ ) is larger than | *|(o = _ ). The curve for the zwitterionic system shows two breaks at characteristic shear rates. It is likely that for shear rates above these characteristic values the multilamellar vesicles undergo transformations to new structures, as has recently been proposed by Roux et al. [88,89]. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 19 (a) Plot of shear modulus G0 against the concentration of the ionic surfactant C14TMABr for a vesicle phase with a total concentration of 100-mM C14DMAO þ C14TMABr and 220-mM C6OH at 258C. (b) Plot of shear modulus G0 against the square root of the concentration of added NaCl for a vesicle phase with 85-mM C14DMAO, 15-mM C14TMABr, and 300-mM C6OH at 258C. (From Ref. 22.)

Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 20 Double logarithmic plot of storage modulus G 0 against frequency f for vesicle phases of 90-mM CxDMAO, 10-mM C14TMABr, and 220-mM C6OH at 258C with various chain lengths x of the zwitterionic surfactant. (From Ref. 22.)

FIG. 21 Plot of storage modulus G 0 , loss modulus G 00 , and yield stress y against the cosurfactant concentration for a vesicle phase of 90-mM C14DMAO, 10-mM SDS, and varying amounts of C6OH at 258C. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 22 Double logarithmic plot of storage modulus G 0 against frequency f for a vesicle phase of 90-mM C14DMAO, 10-mM C14TMABr, and 160-mM CnOH for cosurfactants with various chain lengths at 258C. (From Ref. 22.)

D. Model for the Shear Modulus In previous publications the shear modulus for the multilamellar phases was considered to be the result of the interactions of hard sphere particles [22,90,91]. In this picture each charged multilamellar vesicle is considered a hard sphere. The theoretical treatment of the samples would then be similar as for latex systems. The modulus of the systems depends on the chain length of the surfactants that are used for the preparation of the systems when all other parameters like the charge density, the salinity, and the concentrations of surfactant and cosurfactant are kept constant. It can be argued that the diﬀerences of the moduli could be a result of a change of the number density of the vesicles. These values for diﬀerent systems are not known exactly. The similar conductivities for the systems that diﬀer in chain length indicate that the number density is also the same and should not be the reason for diﬀerent shear moduli. Furthermore, the birefringence of the samples with diﬀerent chain lengths looks the same, too. The birefringence should increase if the number density of the vesicles is decreasing and the mean size of the vesicles is increasing. This is not the case. The diﬀerent moduli must therefore have a diﬀerent origin. Consequently, we propose a diﬀerent model for the explanation of the magnitude of the shear moduli. This model has actually already been proposed for the treatment of multilamellar vesicle phases and L phases by van der Linden and Dro¨ge [92]. To our knowledge the theory has not yet Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 23 Double logarithmic plot of shear viscosity against shear rate _ and of the magnitude of the complex viscosity | | against angular frequency ! for two diﬀerent vesicle phases at 258C. (From Ref. 22.)

been applied to experimental results. van der Linden assumes that multilamellar vesicles (droplets) are deformed in shear ﬂow from a spherical to an elliptical shape. Turning into the deformed state the energy of closed shells is shifted because both their curvature and the interlamellar distance D are changed. Due to the interaction of the bilayers expressed by the bulk compression modulus B, the inner shells are deformed in a way that the total deformation energy E of the lamellar droplet is minimized. Assuming that the volume of a droplet is not modiﬁed by the deformation, the surface A must consequently increase. It is therefore possible to deﬁne an eﬀective surface tension eff ¼ E=A. van der Linden obtains eff ¼ 12ðKBÞ1=2

ð12Þ

where K is the bulk rigidity, which is correlated to the bilayer’s bending constant k by K ¼ k=D. We can relate this eﬀective surface tension to the shear modulus G of a vesicle with radius R. Using the identity G ¼ 2eff =R yields 1=2 k B ðKBÞ1=2 D ¼ ð13Þ G¼ R R Copyright © 2003 by Taylor & Francis Group, LLC

Both the bulk compression modulus and the bending constant depend on the charge density of the bilayers and the shielding of the charges with excess salt. Strictly speaking, van der Linden’s theory results in a calculation of the geometrical average of the compression (EB) and bending energy (EK) per unit volume. Expression (13) can be squared to k B D G2 ¼ ð14Þ R2 With n ¼ R=D, which denotes the number of bilayers in a vesicle, we obtain G2 ¼

nk B ¼ Ek EB R3

ð15Þ

Now we can try to ﬁnd adequate expressions and values for the quantities B and K by other theories. For the bending constant as a function of the charge density we can use the following expression, which has been given by Lekkerkerker [93]: kB T ðq 1Þðq þ 2Þ ð16Þ 2Q ðq þ 1Þq pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ with q ¼ p2 þ 1 and p ¼ 2Qj j=e. kB is Boltzmann’s constant, T the absolute temperature, Q the Bjerrum length, the reciprocal Debye length, and s the surface charge density. For the bulk compression modulus we can use the expression that is often used to describe the interaction between two charged particles: Kel ¼

K ¼ fa fs np 2 d 2 VðdÞ

ð17Þ

where VðdÞ is the energy of interaction between a pair of spherical particles: z2 e2 expðaÞ 2 expðdÞ ð18Þ VðdÞ ¼ 4" ð1 þ aÞ d where d denotes the separation of particles and a their radius. fa and fs are numerical factors [94]. There is a further possibility to get an expression for the compression modulus B. This quantity may be simply given by the osmotic pressure between the bilayers. According to a theory of Dubois et al. [95] we have calculated the osmotic pressure from the equation ¼ cm kT

ð19Þ

where cm is the number concentration of ions at the midplane between the bilayers calculated by resolving the Poisson–Boltzmann equation for the Copyright © 2003 by Taylor & Francis Group, LLC

current conditions. In a previous paper we have discussed the possibility to identify the shear modulus directly with the osmotic pressure. This seemed to be obvious because the osmotic pressure qualitatively increases in the same way with the charge density of the bilayers as the shear modulus and decreases also on addition of salt. Nevertheless, this attempt has failed since the calculated values in the order of several thousand Pascals were much too high. In the current context it looks reasonable, however, to identify the osmotic pressure with the compression modulus B in Eqs. (12) and (13). Now there is a concept available that is appropriate to reproduce the characteristic features of our experimental results: the inﬂuence of the charge density and the inﬂuence of salinity on the shear modulus. The growth of the shear modulus with the charge density can mainly be attributed to the increase of the bending constant and the osmotic pressure with the charge density while the decrease with the salinity seems to come from the pair potential VðdÞ for small salinities and the linear decrease at higher salinities from the bending constants. However, we should keep in mind that for both changes the vesicular structures do not remain constant but change also. At present it is therefore not possible to give a complete quantitative interpretation of the experimental results and ﬁt the data precisely on an exact theoretical model. At the end of this paragraph we would like to check whether formula (13) for the modulus gives reasonable results combined with our primary data. We assume the following values: Interlamellar distance: d ¼ 80 nm Radius of a vesicle: R ¼ 0:5 mm Charging degree: 10% i.e. a surface charge density on the bilayers of 2 e0 =500 A ðe0 is the elementary charge) Electrical contribution of the bending modulus calculated according to Eq. (16): k ¼ 0:56 kB T (see Ref. [77]) Compression modulus calculated according to Eq. (19): B ¼ ¼ 3000 Pa (see Ref. [76]) With these data Eq. (13) yields G0 18 Pa for the shear modulus. This value is very close to the measured one and demonstrates a probably correct approach to a theoretical description of the rheological properties of the solutions.

E. Recent Results During the last few years we have experienced many investigations on dilute L phases that contain multilamellar vesicles. These phases can already be Copyright © 2003 by Taylor & Francis Group, LLC

highly viscoelastic when they contain as little as a few percent of surfactant and sometimes cosurfactants. It is clear now that these phases can be prepared by many combinations of surfactant and cosurfactants. Typical combinations are catanionic systems [96], mixtures of surfactants and cosurfactants [91], nonionic surfactants at a certain temperature region [84], and mixtures of Ca salts of ionic surfactants with zwitterionic surfactants [97], and very recently it was found that vesicles can even be prepared by protonation of oleyldimethylaminoxid [98]. Under the condition that the micellar structures are charged and there is no excess salt present to shield the ionic charges on the bilayers the macroscopic properties, in particular the rheological properties, are very similar and independent of the particular chemistry. The systems behave like weak gels and have a yield stress value. This property makes the systems very useful as ﬂuids to stabilize dispersions and emulsions. The yield stress value is usually large enough to prevent upcreaming and sedimentation. For larger shear stresses, the phases behave like other shear thinning ﬂuids. The phases, in general, are transparent. Sometimes they are optically isotropic; sometimes they show birefringence that is the result of stress birefringence, but no birefringence from liquid crystalline domains. The size of the vesicles, their polydispersity, and the number of shells depend on the shear history of the samples. It actually has been shown recently that the vesicles in these L phases are the result of shear forces to which the samples have been exposed during the preparation, that is, during the mixing process of the individual components [98]. When the samples are prepared by a special route in which the micellar structures are not exposed to shear, one usually obtains normal stacked L phases without vesicles (Fig. 24) [99]. These phases have diﬀerent macroscopic properties; for example, they have a much lower shear modulus than the MLV phases. On applying shear stress, the L phases are transformed to vesicle phases. The transformation is accompanied with shear thickening (Fig. 25) [100]. Charged systems remain in the vesicle state, while uncharged systems usually relax back to normal L phases. The transformation has been followed by many diﬀerent physicochemical methods like conductivity measurements in a Couette cell (Fig. 26), SANS (Fig. 27), rheological cryo-TEM (Fig. 28), and NMR measurements (Fig. 29) [101]. The transformation of a multidomain L phase in a vesicle phase proceeds in several steps, shown in Fig. 30 [102]. While the diﬀerent steps have been demonstrated by several groups on diﬀerent systems, a quantitative explanation on ﬁrst principles is not available [103]. Very puzzling is the observed behavior that under shear the bilayers ﬁrst orient parallel to the wall and than orient perpendicular to the wall in the shear-gradient-ﬂow plane before they break up in vesicles. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 24 FF-TEM micrograph of a stacked L phase of the system 100-mM C14DMAO/250-mM hexanol/10-mM methylformiate in the presence of 20% glycerol in water; this state was observed after 1 h of hydrolysis.

FIG. 25 The apparent viscosity against the elapsed time of shear for the system 100-mM C14DMAO/250-mM hexanol/10-mM oxalic acid diethyl ester/water at various constant shear rates. The original L phase is transformed to a vesicle phase. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 26 The speciﬁc conductivity as a function of the evolving time after turning on a constant shear rate of 10 s1 for a sample of 100-mM C14DMAO/250mM hexanol/10-mM oxalic acid diethyl ester in water. The conductivity was measured separately in the direction of the shear gradient (x), the ﬂow (y), and the vorticity (z).

The virgin L phases that are not exposed to shear during the formation can be prepared by a chemical reaction that proceeds in a sample that is at rest. A catanionic system can be prepared from a micellar L1 phase from zwitterionic surfactant and an anionic surfactant by protonation of the zwitterionic surfactant [104]. The necessary proton can be produced by the hydrolysis of a small ester molecules that can be added to the L1 phase. Similarly, L phases can be prepared from L3 phases by ionically charging the bilayer with protons that are released from a chemical reaction.

IV. SHEAR-INDUCED PHENOMENA IN SURFACTANT SOLUTIONS A. General The interaction energy between micellar structures in surfactant solutions is an important part of the Gibbs free energy of the system. In equilibrium the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 27 Radially averaged SANS scattering intensity of the system 90mM C14DMAO/10-mM C14TMABr/220-mM 1-hexanol as a function of the scattering vector q for various shear rates.

FIG. 28 FF-TEM micrograph of the system 90-mM C14DMAO/10-mM C14TMABr/220-mM 1-hexanol after applying a shear rate of 4000 s1. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 29 2H-NMR spectra of the system 200-mM C14DMAO/450-mM hexanol-d2/ 20-mM methylformate/H2O; (a) sponge phase just before adding methylformiate; (b) a randomly aligned lamellar phase, 24 h after adding methylformiate; (c) a lamellar phase that developed from the sponge phase in a magnetic ﬁeld; (d) a vesicle phase that was prepared from the lamellar phase by applying a shear gradient of 4000 s1.

system adjusts this energy to a minimum that results in equilibrium values for micellar aggregation numbers, size distributions for rods, and so on. In shear ﬂow with shear gradients in the bulk phase these equilibrium parameters are changed because diﬀerent structures have to pass each other,

FIG. 30 Schematic representation of an L phase under constant shear gradient with time. In the third state, the bilayers are oriented perpendicular to the walls of the Couette cell. This state can clearly be seen by SANS measurements. Copyright © 2003 by Taylor & Francis Group, LLC

become oriented, and might even collide with each other. The interaction forces between particles due to shear can become very much larger than for forces due to Brownian motion. Shear ﬂow is therefore an important thermodynamic variable for micellar structures. One is generally aware that temperature, ionic strength, concentration, and cosurfactants can change micellar structures and, hence, the properties of surfactant solutions. One should also be aware that shear can change and inﬂuence micellar structures and even mesophases [105]. It has been observed that micellar solutions can be transformed into liquid crystalline phases, [106] and single clear-phase solutions become turbid and biphasic under shear. On the other hand, biphasic solutions can turn into a single phase under shear. A very striking example of a shear-produced transition is the transformation of a dilute L3 phase into an L phase with bright irridescent colors [16]. All these eﬀects are based on the fact that the shape and size of the micelle depend to some degree on the intermicellar interaction energy, which itself depends on the mutual orientation of the micelles [107]. When the interaction energy is changed, the system responds with a change of structure and properties. These changes can be unexpected and large. They can, however, be used to advantage. In this section we discuss a remarkable and puzzling phenomenon that, because of its complicated nature, is not yet completely understood. The phenomenon has, however, considerable potential for technical applications where it is necessary to control the ﬂow behavior of aqueous solutions. In all applications where large amounts of water have to be circulated for cooling or heating purposes, the energy expense for the pumping is a major economic factor. Usually, one is also interested in pumping as fast as feasible, and the ﬂow in the water pipes is generally in the turbulent ﬂow region. Under these conditions, it is possible to reduce the friction coeﬃcient by polymer additives or by drag-reducing surfactants (Fig. 31) [108–111]. In recycling operations, polymers have the big disadvantage that they deteriorate under shear because the molecules break under shear forces. Surfactants do not have this disadvantage because the micellar structures that produce this eﬀect are self-healing. Pilot operations have been running for months without loss of eﬃciency. The energy costs have been cut to less than half.

B. Under What Conditions Do We Find Drag-Reducing Surfactants? Drag reduction often occurs in surfactant solutions in which small, rodlike micelles are formed that have a charge that is not screened by excess salt [108,112]. Many surfactant systems have been found in which such condiCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 31 Plot of the pressure drop against the ﬂow velocity in a capillary in the laminar and turbulent ﬂow regions for water (solid line) and for a drag reducing surfactant solution (750-ppm C14TMABr þ NaSal at 27.58C, dashed line). (From Ref. 82.)

tions exist. Typically the length of the rods is smaller than the mean distance between them. From this point of view, the micellar solutions can be considered dilute even though there is repulsive interaction between the rods. Because of this repulsion the micelles try to be as far away from each other as possible and set up what is called a nearest-neighbor order. The result of this order is a correlation peak in scattering experiments. In typical conditions the surfactant concentration is a few mM ( 0.1–0.2 wt %), the rods are a few hundred A˚ long, and their mean separation is somewhat larger. Because there is no steric hindrance between the rods, they can undergo more or less free Brownian rotations with rotation times of a few microseconds. Such conditions can easily be set up when charged surfactants are mixed with zwitterionic surfactants. Usually 1 to 3 ionic surfactants in 10 uncharged surfactant molecules are favorable for the eﬀect. These features of the micelles are the necessary prerequisites for the eﬀect to occur. They are, however, not the only ones, as will become clear later. In shear measurements one expects the described solutions to behave like normal Newtonian aqueous solutions. This is, in fact, the case for small shear rates, as is shown in Fig. 32, where the shear viscosity measured in a capillary viscometer is plotted against the shear rate [15]. One observes a sudden rise of the viscosity at a characteristic shear rate _ c and for _ > _ c Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 32 The shear viscosity against the shear rate _ for mixtures of C14DMAO:SDS ¼ 6:4 with various total concentrations in a capillary viscometer at 258C. (From Ref. 15.)

the solutions now show some shear thickening behavior. Obviously something dramatic has happened to the micelles in the solutions. Some conclusions about what has happened can be drawn from ﬂow birefringence measurements. Some typical results of ﬂow measurements from a Couette system are shown in Fig. 33 [15]. We note a sudden increase of the ﬂow birefringence at a critical shear rate. For _ > _ c , no ﬂow birefringence could be detected. In Fig. 34 viscosity and ﬂow birefringence measurements for other surfactant systems with shear-induced structures are shown [37]. In these experiments a constant shear rate above the threshold value was abruptly applied in the solution at rest; this shear rate was kept constant for a certain time and then suddenly dropped to zero. Under these conditions the viscosity and the ﬂow birefringence increase with characteristic time constants to their corresponding plateau values at which the viscosity passes over a maximum; both quantities relax with characteristic relaxation times to their original value when the shear rate dropped to zero. In ﬂow experiments, besides the birefringence it is also easy to measure the angle of extinction, which is the angle between the direction of ﬂow and the mean orientation of the rods. In normal ﬂow orientation this angle Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 33 The ﬂow birefringence n against the shear rate _ for the same solutions as in Fig. 32. (From Ref. 15.)

decreases smoothly from 458 to zero with increasing ﬂow rate because the rods become more and more aligned. In the drag-reducing solution the situation is very diﬀerent. In the Newtonian region for _ < _ c , the solution remains isotropic and no preferential alignment can be detected. When _ > _ c , however, the angle of extinction is close to zero. This experimental

FIG. 34 The shear viscosity at a shear rate _ of 50 s1 for a solution of 0.9-mM CPySal at 208C (a) and the ﬂow birefringence n at a shear rate of 10 s1 for a solution of 20-mM C10F21CO2N(CH3)4 at 308C (b) as a function of the time t (_ jumped from 0 s1 to the corresponding value and dropped after a certain time again to zero). (From Ref. 37.) Copyright © 2003 by Taylor & Francis Group, LLC

fact tells us that the new structures that are produced by the shear are completely aligned. Obviously the new-found structures must be much larger than the original small rods that were not aligned. Figure 35 shows this situation for a selected surfactant system together with the viscosity, the ﬁrst normal stress diﬀerence, and the ﬂow birefringence as functions of the shear rate [16]. It is now believed that the small, rodlike micelles undergo collisions in the shear ﬂow, and their interfacial properties are such that they stick together for some time. In this way long necklace-type structures are formed under shear which at the same time become aligned in the shear ﬂow. This situation is schematically sketched in Fig. 36 [16]. These neck-

FIG. 35 The zero shear viscosity and the complex viscosity j *| (a), the ﬁrst normal stress diﬀerence p11–p22 (b), the ﬂow birefringence n (c), and the extinction angle (d), as functions of the shear rate _ or the oscillation frequency !, respectively, for a solution of 5-mM C14TMASal at 208C. (From Ref. 16.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 36 Model to explain shear-induced micellar structures: The small rodlike micelles can form long necklace-type structures under shear. (From Ref. 16.)

lace-type structures act like high-molecular-weight polymers and give rise to drag reduction. One may ask why the small rods stick together under shear while they do not in the solution at rest. It is conceivable that the reason lies in a sheardependent equilibrium constant K for the aggregation equilibrium A1 þ A1 Ð A2 ½A2 K¼ ½A1 ½A1 where A1 are the small rods. The situation could be comparable to the micelle formation from monomers. If the situation is such that K A1 < 1, where the A1 are now the monomers, there are practically no micelles in the solution. When, however, K is increased somewhat so that K A1 > 1, then micelles will form because the micellar concentration is proportional to A1 ðK A1 Þn , where n is an aggregation number. If the necklace-type aggregates become large enough, they will then be completely aligned because the product of rotation time and shear rate became larger than 1 ( _ > 1). The Copyright © 2003 by Taylor & Francis Group, LLC

stability of the necklace-type aggregates could lie in the chemical composition of the micellar interfaces. All the known systems that give rise to shearinduced structures (SIS) formation form small rods on which the micellar surfaces are covered with methyl, ethyl, or other hydrophobic groups. The surfaces are thus hydrophobic even when they are charged. It is likely that if such two surfaces collide and make contact, they should form a sticky contact even though the total interaction energy between the particles is repulsive. Support for this model has recently been found. It was shown that if the surface of the small rods was modiﬁed by hydrophilic groups that protrude from the micellar interphase and a contact of the two surfaces was no longer possible, the shear-induced structures were no longer observed [113]. These results explain nicely why micellar systems where the micelles have hydrophilic surfaces do not form SIS. In a shear rate range just above the critical shear rate _c , the ﬂow birefringence increases with _ before it becomes constant. This is an indication that not all the surfactants above the CMC are involved in the SIS and that there are still small rods in equilibrium with the SIS. The scattering anisotropy of SANS measurements under shear points out the same. Phenomenologically the situation is similar as for ﬁrst-order phase transitions when a thermodynamic equilibrium parameter is varied. The systems changes then from a single-phase to a two-phase and ﬁnally again to a onephase situation. In this respect, it was shown recently that the systems not only behaves in this way but the systems in the two-phase region separates actually macroscopically in ﬂow in a Couette system. The steady state in the two-phase region is characterized by two coexisting states separated by a cylindrical interface. Near the inner cylinder viscous SIS were observed, while near the outer cylinder, a much less viscous ﬂuid similar to the original micellar solution was observed [114]. It furthermore was shown in this work that for much higher shear stresses the SIS can break again and the system switches back to the original state. Furthermore, it was shown that the system does not only form two macroscopic separate phases but several rings and periodic structures that change with time. This can lead to periodic oscillations in the birefringence [115]. In many systems the lifetime of the SIS is so short that it disappears as soon as the shear is stopped. For longer chain length surfactants, the SIS can still be present after the shear has been turned oﬀ. For such a situation the SIS have recently been made visible by FF TEM [116–118].

C. SANS Measurements on Shear-Induced Structures The growth process of the large micellar structures (which are strongly aligned) has been studied in more detail by transient SANS experiments Copyright © 2003 by Taylor & Francis Group, LLC

where the shear rate for the samples was raised stepwise from zero to a certain ﬁnite value. These experiments showed that the large micelles grow according to the Avrami law cðtÞ ¼ cinf ½1 expðkt Þ

ð20Þ

that originally was used to describe nucleation and growth in metals and alloys. For the system C14TMA-Sal the exponent was found to be 2–2.5 [119]. The exponent should be i þ 1 for i-dimensional growth, which means that the growth process observed here is close to unidimensional as should be expected since the micelles just grow in length without otherwise changing their dimensions. Such SIS are an interesting phenomena in particular for self-aggregating systems like micelles, where the equilibrium structure often depends very subtly on small energetic changes. These structural changes have a profound inﬂuence on the properties of these systems, especially on their ﬂow behavior. The scattering patterns of the SANS experiments exhibit a strong anisotropy. This shear-induced eﬀect will already occur at _ rot 1 ( rot ¼ rotational time constant of the small type of micelles), i.e., in a range where the shear ﬁeld should not be able to orient the small rodlike aggregates signiﬁcantly. This means that the observed anisotropy is not due to the orientation of these originally present micelles but that instead larger oriented micellar aggregates have to be present in the solutions. So far the mechanism for formation of the shear-induced state is not fully understood, and several diﬀerent mechanisms have been postulated [120–122]. One particular system—a mixture of tetradecyldimethylaminoxide (C14DMAO) and sodiumdodecylsulfate (SDS)—has been studied in much detail. This system shows a pronounced SIS formation around a molar mixing ratio of 7:3 for C14DMAO/SDS [15]—and it might also be noted here that for this composition the nematic phase that is found for that systems extends to the lowest surfactant concentration [123]. In order to ﬁnd relations between the macroscopic behavior of the system and the structure of the micellar aggregates present, a SANS study was performed [124]. Here by changing the contrast condition in the micellar aggregate by using both hydrogenated and deuterated SDS, detailed information regarding the structure of the micelles could be obtained. The SANS experiments show that at the mixing ratios where SIS is observed, elongated micelles are present that are best described by a three-axes prolate ellipsoid, and where the length of these aggregates reduces with increasing SDS content. From a contrast variation experiment using both deuterated and hydrogenated SDS, it could be concluded that the buildup of these micelles is homogeneous and no internal segregation of the surfactant molecules within the aggregate could be deduced [124]. Such an internal segregation by having an Copyright © 2003 by Taylor & Francis Group, LLC

enrichment of SDS at the endcaps (here the relative area per molecule is necessarily larger because of the larger curvature and one could imagine that the SDS with its larger hydrophilic headgroup would preferentially be located at this position) would have been conceivable and, of course, such a buildup that would contain two more highly charged ends would have been an important factor to consider for the explanation of the SIS. However, this evidently is not the case, and SIS formation has to be explained starting from originally short, homogeneously charged, elongated aggregates.

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11 Microstructures of Nonionic Surfactant–Water Systems From Dilute Micellar Solution to Liquid Crystal Phase TADASHI KATO

I.

Tokyo Metropolitan University, Tokyo, Japan

INTRODUCTION

Surfactant systems exhibit a variety of phase behaviors. When one of these phases is transformed into another phase, not only the arrangement but also the shape of building block itself is changed. This makes it diﬃcult but fascinating to clarify the mechanism of the phase transition in surfactant systems. Variation in the shape of building block occurs even far from the transition point. So the equilibrium structure near the phase boundary should be elucidated to clarify the mechanism of the phase transition. It is, however, very diﬃcult to determine the structure uniquely at one point in the temperature–concentration diagram due to the complex structure. Thus variation in structures with concentration and temperature should be investigated systematically. Moreover, a variety of techniques is necessary to observe the structures from diﬀerent length scales. From these points of view, the author studies polyoxyethylene surfactant–water systems in a wide concentration and temperature range by using scattering techniques and pulsed-gradient spin echo (PGSE). Polyoxyethylene surfactants are used because (1) the hydrophilic-lipophilic balance of molecules can be systematically changed, (2) theoretical treatment is much simpler than in ionic systems in the sense that it is unnecessary to take into account electrostatic eﬀects, (3) various types of phase transitions can be observed merely by changing temperature, and (4) the transverse relaxation time of 1H is much longer than that of ionic surfactants due to the fast motion of the oxyethylene groups; this is very important for the PGSE measurements.

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In Section II, we discuss the problems encountered in the determination of micelle size by using conventional techniques. A novel method is then described that gives information on intermicellar interactions and micelle size distribution separately. Finally, thermodynamic models for micellar growth are discussed based on the concentration and temperature dependence of micelle aggregation number obtained from light scattering measurements in extremely dilute solutions where eﬀects of intermicellar interactions can be neglected. Section III covers the structure and dynamics of semidilute and concentrated solutions. After the analogy with polymer solutions is described, dynamical aspects of entangled wormlike micelles are discussed based on the surfactant self-diﬀusion coeﬃcient and the structural relaxation time obtained by using PGSE and dynamic light scattering, respectively. In the last part of this section, the gradual transformation from entangled wormlike micelles to a three-dimensional network with a stable connection with increasing concentration and temperature is demonstrated. Variation in the structure occurs also in the lamellar phase, as is shown in Section IV. We discuss correlations among the structures of the concentrated micellar phase, the lamellar phase, and the bicontinuous cubic phase as well as relations with phase behaviors. Finally, our recent studies on eﬀects of shear ﬂow and adding fatty acid on the structure of the lamellar phase are brieﬂy described.

II. DILUTE SOLUTIONS A. Micellar Growth with Increasing Temperature The most fundamental properties of micellar solutions may be the critical micelle concentration (CMC) and the mean aggregation number of micelles. For determining the latter, static light scattering is one of the most useful methods because it does not need any probe molecules. However, the light scattering intensity depends on not only the aggregation number but also the intermicellar interactions. For globular micelles, the eﬀects of intermicellar interactions can be eliminated by extrapolating data to the CMC because the aggregation number depends on the concentration only slightly. In the case of elongated micelles, however, the aggregation number usually depends on the concentration and so it is diﬃcult to separate these two contributions (see below). In nonionic surfactant systems, light scattering intensities increase with increasing temperature above a certain temperature. From the reason described above, this does not always indicate the increase in the aggregation number with temperature, because they usually have the lower critical Copyright © 2003 by Taylor & Francis Group, LLC

solution temperature, that is, attractive interactions between micelles (or the critical eﬀects) may aﬀect the light scattering intensity. Corti and Degiorgio [5] pointed out this problem for the ﬁrst time. After their work, various studies have been performed in order to elucidate the inﬂuence of critical eﬀects [1,3]. Among them are important the studies using techniques that are less aﬀected by the critical eﬀects such as NMR self-diﬀusion [6–8], ﬂuorescence decay [9], dynamic neutron scattering [3,10], light scattering from semidilute solutions [11,12], and so on. From the results of these studies (summarized by Lindman and Wennerstro¨m [13]), it can be concluded that micellar growth actually occurs, but the extent of micelle size variation depends strongly on the speciﬁc surfactants in question. This conclusion has been conﬁrmed by cryo-TEM (for C16E6) [14] and small-angle neutron scattering (SANS) using direct analysis by Fourier transformation (for C12E5) [15] and generalized indirect Fourier transformation (for C8E3, C8E4, C8E5, C10E4, C12E5, and C12E6) [16].

B. Intermicellar Interactions 1. Virial Coefﬁcients Obtained from Conventional Methods Usually, thermodynamic arguments for interparticle interactions are developed on using the virial coeﬃcients obtained from the osmotic pressure, , or the light scattering intensities. For micellar solutions, the absolute intensity of the scattered light (Rayleigh ratio) extrapolated to the zero scattering vector, R(0), can be expressed as follows [3,17]: Rð0Þ ¼ R0 ð0Þ þ HMðc c0 ÞSð0Þ 42 2 @ 2 H 4 NA @c T;P

ð1Þ

where M is the weight-averaged micellar weight, c is the weight concentration (g cm3 ) of surfactant, c0 is the CMC in g cm3 , R(0) and R0(0) are the Rayleigh ratios at zero scattering vector at c and c0, respectively, is the wavelength in vacuum, is the refractive index of solution, NA is Avogadro’s number, and S(0) is the structure factor at zero scattering vector. In dilute solutions, S(0) can be related to the second virial coeﬃcient, A2, through the equation Sð0Þ1 ¼ 1 þ kðc c0 Þ þ

ð2Þ

where k 2A2 M. Substitution of Eq. (2) into Eq. (1) gives Hðc c0 Þ 1 1 1 ¼ ½1 þ kðc c0 Þ þ ¼ þ 2A2 ðc c0 Þ þ ¼ Rð0Þ R0 MSð0Þ M M ð3Þ Copyright © 2003 by Taylor & Francis Group, LLC

In the case where the micellar weight is independent of concentration, the second virial coeﬃcient can be obtained from the slope of the Debye plot, that is, H(c c0)/[R(0) R0(0)] versus c c0. However, situations become complicated when the micellar weight depends on concentration. As a typical example, we consider the case where intermicellar interactions can be neglected and the concentration dependence of M is expressed as M ¼ M0 ½1 þ kM ðc c0 Þ þ

ð4Þ

From Eqs. (3) and (4), we obtain Hðc c0 Þ 1 1 ¼ ¼ ½1 þ ðk kM Þðc c0 Þ þ Rð0Þ R0 MSð0Þ M0

ð5Þ

Therefore, the apparent second virial coeﬃcient, k kM, becomes smaller than the ‘‘true’’ one, k, and so it is no longer possible to discuss intermicellar interactions on the basis of light scattering data. Concentration dependence of the micellar weight also aﬀects the collective (or mutual) diﬀusion coeﬃcient (Dc) obtained from dynamic light scattering, which can be expressed as [18] kT Sð0Þ C 1 1 ¼ ½1 þ kC ðc c0 Þ þ

C 6 0 r0

DC ¼

ð6Þ ð7Þ

where 0 is the solvent viscosity, r0 is the hydrodynamic radius of micelles, and kc represent hydrodynamic interactions between micelles. Substituting Eq. (2) into Eq. (7), we obtain DC ¼

kT ½1 þ ðk þ kc Þðc c0 Þ þ 6 0 r0

ð8Þ

Therefore, the concentration dependence of Dc is dominated by both the micelle size term, r0, and the interaction term, k + kc, when the micellar weight depends on concentration.

2. Information Obtained from the Ratio of Mutual Diffusion to Self-Diffusion Coefﬁcient As expressed in the following equation, the surfactant self-diﬀusion coeﬃcient (DS) also depends on intermicellar interactions although the eﬀect of it is much smaller than that of Dc. Copyright © 2003 by Taylor & Francis Group, LLC

kT

S 1 1 ¼ ½1 þ kS ðc c0 Þ þ &s 6 0 r0

DS ¼

ð9aÞ ð9bÞ

On the other hand, the ratio Dc/Ds can be expressed as DC 1 &S ¼ ¼ 1 þ k0 ðc c0 Þ þ DS Sð0Þ &C k0 k þ kC kS

ð10aÞ ð10bÞ

As the relation k ðkc ks Þ usually holds [8], the coeﬃcient k 0 is dominated by k. Then we can discuss intermicellar interactions on the basis of k 0 at least qualitatively; k 0 is positive/negative when repulsive/attractive interactions are dominant. It should be noted, however, that k 0 depends on concentration. When the aggregation number increases with concentration, the size distribution becomes broad, which also aﬀects the ratio Dc /Ds . In this case, the following equation can be used instead of Eq. (10) (see below): DC =DS ¼ 1 þ k0 ðc c0 Þ þ lim DC =DS

ð11Þ

c!c0

Figure 1b shows temperature dependence of k 0 for C12E5, C12E6, and C12E8 systems obtained by using dynamic light scattering and PGSE [19]. One sees that below Tc 30K, k 0 depends on temperature only slightly, which is consistent with the fact that micelles remain small in this temperature range [see the apparent hydrodynamic radii RH in Fig. 1a obtained from DS through the relation Ds ¼ kT=ð6t RH Þ. Above Tc 30K, k 0 increases with temperature and takes a maximum at about Tc 15K. The increase in k 0 indicates that repulsive interactions becomes strong as the temperature increases. This appears to be an unexpected result because attention has been paid to only attractive interactions in nonionic systems. If micellar growth actually occurs, however, the increase of k is a natural consequence. It is well known that S(0)1 or the second virial coeﬃcient increases as the particle shape deviates more and more from a sphere under a constant volume fraction of particles [19–22]. If the particle is hemispherocylinder, for example, k can be expressed as " # ðL=Þ2 k ¼ 8 g 1 þ ð12Þ 8=3 þ 4ðL=Þ

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FIG. 1 Temperature dependence of the apparent hydrodynamic radii (a), intermicellar interaction parameter k 0 in Eq. (10) (b), size distribution parameter in Eq. (13), and line width of the main proton NMR signals for the methylene groups (d) for D2O solutions of C12E5 (*), C12E6 (~), and C12E8 (!). (From Ref. 8, 19, and 20.)

where g is the speciﬁc volume of micelles (cm3 g1) and L and s are the length and diameter of the cylinder part, respectively. As particles are elongated, L/s increases, which results in an increase of k. The decrease in k originates from the rapid increase in attractive interactions (i.e., increase in critical concentration ﬂuctuations) and/or the decrease in the excluded volume eﬀects. We discuss these two factors in turn.

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(a) Decrease in the Excluded Volume Effects. The decrease in the excluded volume effects can be attributed to (1) change in micellar shape from rod to disk and/or (2) increase in ﬂexibility of elongated micelles. Interpretation (1) is consistent with the prediction of Tiddy and co-workers based on systematic studies on phase behaviors of polyoxyethylene surfactants–water systems [23]. On the other hand, interpretation (2) is supported by NMR data of Nilsson and co-workers [6]. They have observed the line width v1=2 of the main proton NMR signal for the methylene groups of C12E5 and found that the line width takes a maximum at 10– 158C. They have noted that the increase of v1/2 arises from micellar growth, whereas the decrease of v1/2 is due to ﬂuctuations in aggregate size and shape. As these measurements have been performed at relatively high concentrations (about 50 g dm3 ), the author and co-workers have measured the line widths of the same signals at 6 g dm3 . The results are shown in Fig. 1d, where the line width of C12E6 at 15 g dm3 is also presented. As can be seen from this ﬁgure, k and v1/2 reach maxima at almost the same temperature, namely about Tc 15K. (b) Critical Effects. Figure 1c demonstrates also that k 0 becomes negative above Tc ð3 5ÞK. This cannot be explained by the decrease in the excluded-volume effects alone. As these systems have the LCST, attractive interactions should increase with increasing temperature. Even if the excluded-volume effects continue to increase, rapid increase in attractive interactions may result in decreasing k 0 . Claesson and co-workers [24] have directly measured the force between two surfaces coated with C12E5 in water as a function of surface separation in the temperature range 15– 378C. They have shown that at 158C the interaction is repulsive at all separations. Above 208C, however, an attractive minimum appears and the attraction increases rapidly with temperature. Note that the temperature range 15–208C, where interactions are changed from repulsive to attractive, is close to the temperature that gives a maximum for k 0 , Tc 15K. This may support a rapid increase in attractive interactions above this temperature. However, a deﬁnite conclusion cannot be drawn until such direct measurements of surface force are performed for other homologues. Thus, at this stage, we cannot distinguish between these two eﬀects. In either case, however, the most important result in Fig. 1c is that k 0 is positive below Tc ð3 5ÞK. In other words, net interactions are not attractive until the temperature increases up to a few degrees below Tc, contrary to the ordinary recognition. This speciﬁc temperature where k changes from positive to negative corresponds to the y temperature in polymer solutions. Note that if the conventional method is applied to these systems, the y temperature is obtained about Tc 30K, as previously described.

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The above result that the temperature is close to Tc is conﬁrmed by the scaling analysis in semidilute region (see Section IV) and the following studies. Wilcoxon and Kaler [25,26] have made precise measurements of the angular distribution of scattered light from the C12E6 system and obtained the temperature dependences of the osmotic compressibility and the static and dynamic correlation lengths. They show that in the range Tc 4K to Tc , these quantities lie reasonably close to the predicted results for critical scattering. Similar conclusions have been obtained for the same system by Brown and co-workers [7,27] and Strey and Pakusch [28].

C. Micelle Size Distribution Figure 1b shows the limiting value for Dc /Ds as c ! 0. As the CMC is much lower than the concentration range studied, the limiting value corresponded to Dc /Ds , not for the inﬁnitely dilute solution (only monomers exist) but for the solution where intermicellar interactions can be neglected. Thus, we obtain [8] P P 2 DC mn D < m >D m m nm D i = Pm m m ¼ ¼ P ð13Þ lim 2 c!0 DS < m >W m m nm = m mnm where nm is the number of micelles having aggregation number m and diﬀusion coeﬃcient Dm. As Dm decreases with increasing m, the limiting value for Dc /Ds is always equal to or smaller than unity. If size distribution becomes broad, therefore, the limiting value decreases. See also the discussion by Brown and co-workers [7]. One sees from Fig. 1c that the limiting value is close to unity below about Tc 30K, indicating a narrow distribution of micellar size. This is consistent with the existence of globular micelles in this temperature range. Figure 1c demonstrates also that the limiting value decreases with increasing temperature above Tc 30K and then becomes almost constant (about 0.5 for C12E5 and 0.55 for C12E6). This suggests that micelle size distribution becomes broad. As shown in Ref. [8], the limiting value becomes 0.5 if stepwise selfassociation and rodlike micelles are assumed. The results for the C12E5 and C12E6 systems in the higher temperature range are consistent with this model.

D. Mean Aggregation Number in Extremely Dilute Solutions and Thermodynamic Models for Micellar Growth 1. Concentration and Temperature Dependence of Mean Aggregation Number in Extremely Dilute Solutions As emphasized before, light scattering intensity depends on not only the aggregation number, but also the intermicellar interactions, and so it is Copyright © 2003 by Taylor & Francis Group, LLC

diﬃcult to obtain the aggregation number of elongated micelles from light scattering measurements. However, there is a way to obtain the aggregation number as a function of concentration: perform measurements in the extremely dilute region, where the eﬀects of intermicellar interactions can be neglected. Such a measurement is diﬃcult because of weak scattering intensities. In fact, most of the measurements have been made at concentrations above about 103g cm3 , which are much higher than the CMC for most elongated micelles. Table 1 summarizes available light scattering data on C12E6, a typical nonionic surfactant. The author reported light scattering intensities from this system (C12E6) at concentrations as low as 105 g cm3 , which is two orders of magnitude lower than those of published data [33]. Figure 2 shows double logarithmic plots of light scattering intensity against concentration. The breakpoint in the plot at 258C is close to the CMC determined by the surface tension measurement. The ﬁgure demonstrates that the CMC decreases with the elevation of temperature as is expected from the published data [34]. To the author’s knowledge, however, light scattering data around the CMC have not yet been reported for the C12E6 system or for any surfactant solution with the CMC as low as that of C12E6. In Fig. 2, the data of Balmbra and co-workers [29] are also included. They report that the plot of the excess turbidity against concentration is linear below 2 102g cm3 but intersects the concentration axis at about 5 104 cm3, which is about 10 times higher than the CMC. From these results, they propose that there is secondary aggregation of spherical micelles. Figure 2 demonstrates that such a discussion based on the data in a range much higher than the CMC is meaningless. However, it can be

TABLE 1 Light Scattering Data on Dilute Solutions of C12E6 Concentration (103 g cm3 Þ 2–20 1–15 3–20 2–10 3–10 4–10 12.5 0.01–10 0.01–2.5

Temperature (8C)

Ref.

15,25 35,45 5 10–45 25 5–45 24.8–49.9 15,25 35,45

29 29 30 7 31 32 5 33 33

Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 2 Double logarithmic plots of the Rayleigh ratio against concentration for aqueous solutions of C12E6. Open and closed symbols are the data of the author (from Ref. 33) and Balmbra et al. (from Ref. 29), respectively. Solid lines indicate least-square ﬁttings based on Eq. (16) (from Ref. 35). (From Ref. 33.)

seen from the ﬁgure that the slope of the plot begins to increase at a certain concentration cSP, which decreases with increasing temperature in the range 15–358C (cSP seems very close to the CMC at 458C). As the concentration increases further, the Rayleigh ratio becomes proportional to c3/2. Such results cannot be seen from the data of Balmbra and co-workers. It should be noted that their measurements are made down to a concentration that is the lowest for any published data (see Table 1). As S(0) in Eq. (1) is unity in the concentration and temperature range studied (see the discussion in Refs. [33] and [35], the light scattering intensity at the zero scattering vector can be expressed as Rð0Þ ¼ R0 ð0Þ þ HM1 ½c1 þ hmiw ðc c1 Þ R0 ð0Þ þ HM1 hmiw ðc c0 Þ

ð14Þ

where R 0 (0) is the Rayleigh ratio for the ﬂuctuations other than the concentration ﬂuctuation, M1 is the molecular weight of surfactant monomers, c1 is the weight concentration of monomers, and hmiw is the weight-averaged aggregation number of micelles. In the second relation of Eq. (14), the monomer concentration is assumed to be equal to the CMC and so R0 ð0Þ ¼ R 0 ð0Þ þ HM1 c0 . Thus, we can determine hmiw at each concentration from R(0) by using Eq. (14). In Fig. 3, observed hmiw is plotted against the square root of the mole fraction of the surfactant molecules forming micelles. It can be seen from the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 3 Concentration dependence of weight-averaged aggregation number of micelles obtained from the Rayleigh ratio for aqueous solutions of C12E6. X is the mole fraction of surfactant and Xcmc is the CMC expressed by the mole fraction. The solid lines represent theoretical values obtained from the least-square ﬁtting for the light scattering intensity based on Eq. (16) shown in Fig. 2. (From Ref. 33.)

ﬁgure that hmiw at the CMC is small ( 110) and depends on temperature only slightly. According to the results around the critical composition (cC 102 g cm3 ) described in the previous section, micelles are globular below about TC 30K (or TC 35K) and grow with increasing temperature above this speciﬁc temperature. Figure 3 demonstrates that this does not hold true in the extremely dilute region (note that the speciﬁc temperature just mentioned is 15–208C in the case of C12E6). As the concentration exceeds a certain concentration (cSP), hmiw becomes proportional to (X XCMC)1/2 X1/2 / c1/2, as can be expected from the concentration dependence of R(0) in Fig. 2 and Eq. (14).

2. Thermodynamic Models for Micellar Growth The light scattering data for the C12E6 system at extremely low concentrations enable us to choose an appropriate model for micellar growth. The author calculated concentration dependence of light scattering intensity using various thermodynamic models for micellar growth and compared these results with the observed one. The most simple and frequently used model for rodlike micelles may be the ‘‘stepwise aggregation model’’ (or ‘‘ladder model’’). In this model (referred to as model A), it is assumed that a rodlike micelle of aggregation number m is constructed from two hemispherical endcaps (each cap is formed by s/2 monomers) and a cylindrical region. The thermodynamic Copyright © 2003 by Taylor & Francis Group, LLC

states for the surfactant molecules in two endcaps and in the cylindrical part are the same as that in the spherical micelle of aggregation number s and the rodlike micelle of inﬁnite aggregation number, respectively. Then the standard chemical potential of the surfactant molecules in rodlike micelles of aggregation number m, g0m , is expressed as [36] g0m ¼

s 0 ms 0 s gs þ g1 ¼ g01 þ ðg0s g01 Þ m m m

ð15Þ

where g0s and g01 are the standard chemical potentials for spherical micelles of aggregation number s and rodlike micelles of inﬁnite aggregation number, respectively. According to this model, the mean aggregation number of micelles is proportional to the square root of concentration of surfactant molecules forming micelles except for the concentrations near the CMC [36,37]. As can be seen from Fig. 3, the data at 458C in the C12E6 system can be explained by this model. At 258C and 358C, however, the slope of the observed plot abruptly increases at a certain concentration, Csp, which decreases as the temperature increases from 258C to 358C (at 458C, Csp may be further decreased and become close to the CMC). This model cannot explain these features. Such a tendency can be seen more clearly in the double logarithmic plot of hmiw versus c shown in Fig. 4. The limitation of this model is that ‘‘immediate environment of a monomer in the more or less hemispherical ends of a big micelle is just the same as the one encountered by the monomer in the small globular micelle of minimum size’’ [38]. Note that the radius of the cylindrical part is not always equal to that of the hemispherical end, and so there may exist a junction zone between them [39]. Moreover, the micelle of minimum size is not always spherical [39–42]. Thus, the above assumption may be doubtful, as pointed out by Porte and co-workers [38]. The apparent success of this model reported for various systems comes from the fact that the concentration range of the observed data is much higher than the CMC. Second, calculations were made for the model where a rodlike micelle is assumed to be formed by the secondary aggregation of p small (probably spherical) micelles of aggregation number s [43–46], that is, only rodlike micelles of aggregation number ps coexist with the small micelle of aggregation number s. This model (referred to as model B) can explain the observed results at 258C and 358C in the sense that hmiw increases abruptly at a certain concentration. However, the calculated hmiw is not proportional to the square root of the concentration for any parameter values and converges to q in the higher concentration limit. These features are diﬀerent from the observed concentration dependence at 458C. A model that can explain the observed data in the entire concentration and temperature range with the least ﬁtting parameters was found to be that Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Double logarithmic plots of the weight-averaged aggregation number of micelles against concentration for aqueous solutions of C12E6. The solid lines represent theoretical values obtained from the least-square ﬁtting for the light scattering intensity based on Eq. (16) shown in Fig. 2. The arrows indicate the CMC at 15, 25, 35, and 458C from left to right.

where the chemical potential diﬀerence g0m g01 in Eq. (15) changes above a certain aggregation number, q, that is, s g0m ¼ g01 þ ðg0s g0q Þ for s m q ð16aÞ m i sh 0 qs 0 ðgs g0q Þ þ ðgq g01 Þ for q m ð16bÞ g0m ¼ g01 þ m m Least-square ﬁtting based on this model was performed not for hmiw obtained from Eq. (14) but for the light scattering intensity (see the solid lines in Fig. 2) because we need not replace the monomer concentration by the CMC. The calculated hmiw and distribution of aggregation number for the best-ﬁt parameters are shown in Figs. 3–5. It has been found from the ﬁtting procedure that the q-value is relatively close to s, the aggregation number of the small (globular) micelle (ﬃ 110) formed at the CMC, as can be seen from the distribution of the aggregation number shown in Fig. 5. This suggests that micellar shape changes signiﬁcantly when globular micelles begin to grow into rodlike micelles. Such early steps of the elongation process have been previously suggested by Porte and co-workers [47,48] using magnetic birefringence and viscosity data for concentrated solutions Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Distribution of aggregation number for aqueous solutions of C12E6 calculated from the least-square ﬁtting for the light scattering intensity based on Eq. (16) shown in Fig. 2. (From Ref. 35.)

of a cationic surfactant. However, the author’s study is the ﬁrst one that analyzes the experimental data quantitatively without any problems concerning treatment of intermicellar interactions. The results are considered to become the basis of more detailed thermodynamic theory taking into account intermicellar interactions [49–53]. Eriksson and Lunggren [54,55] have developed a more detailed thermodynamic theory for rodlike micelles formed by ionic surfactants. They consider that the radius of the spherical micelle is signiﬁcantly larger than the corresponding radius of the cylindrical micelle and so there should be a junction zone. It is also possible that the change of g0s g01 described above comes from the existence of such a junction zone. Even if the system being studied is limited to the nonionic micelles, the mechanism of micellar growth has not yet been established. Most investigators use model A or model B for analyzing their experimental data obtained in a limited range of concentration or temperature. As shown in the previous section, the results in the higher temperature range (458C in the C12E6 system) can be explained by model A, whereas model B can explain the results in the lower temperature range (258C). Balmbra et al. [29] as described in Section III.E propose the secondary aggregation of spherical micelles on the basis of light scattering data on the C12E6 system in the concentration range much higher than CMC. Copyright © 2003 by Taylor & Francis Group, LLC

Funasaki et al. [46] have investigated the aggregation properties of C12E6 at 258C in the concentration range 1.7–50 mM (7:6 103 2:3 102 g cm3 ) by gel ﬁltration chromatography (GFC). Computer simulations of the GFC data reveal strong evidence of the coexistence of small micelles with large micelles. From this, they have considered that model B is more favorable. As described before, our data at 258C can be explained by model B. However, this model cannot explain the data at higher temperatures. Strey and Pakusch [28] have measured the relaxation time of temperature jump experiments on the same system (C12E6). They found that a plot of the reciprocal relaxation time against the square root of (c CMC)/CMC becomes a straight line intersecting the abscissa at ﬁnite concentrations; the higher the temperature, the lower the concentration. The intersection has been regarded as the crossover concentration between globular and large micelles. Also, they consider the possibility of both models A and B. The author’s results are not inconsistent with theirs. In fact, the Csp-value at each temperature is not much diﬀerent from the value of the intersection at the corresponding temperature. However, note that these measurements were performed above about 103 g cm3 , which is still 20–50 times higher than the CMC.

III. SEMIDILUTE AND CONCENTRATED SOLUTIONS A. Analogy with Polymer Solutions Exhibiting Critical Demixing During the 10 years after 1985, applications of the scaling theory for entangled polymers to semidilute solutions of surfactants had been reported [11,12,56–63]. According to this theory, the correlation length of concentration ﬂuctuations, , and the osmotic compressibility, @=@c, follow the power laws above the overlap concentration c at which polymer chains begin to entangle with each other [64,65]: / c =ð13 Þ @ / c1=ð3 1Þ @c

ð17aÞ ð17bÞ

where c is the concentration of the polymer and is 0.5 and 0.588 for solvent and good solvent, respectively. Candau and co-workers [56–59] have applied this theory to micellar solutions for the ﬁrst time. They show that light scattering data on aqueous KBr solutions of cetyltrimethylammonium bromide (CTAB) can be explained by Eqs. (17a) and (17b). Copyright © 2003 by Taylor & Francis Group, LLC

The osmotic compressibility is related to the scattering intensity at the zero scattering vector as @ RTHðc c0 Þ RT ¼ ¼ @c Rð0Þ R0 ð0Þ mapp MSð0Þ mapp

M1

ð18aÞ ð18bÞ

where mapp is the apparent aggregation number, which becomes equal to the weight-averaged aggregation number if intermicellar interactions can be neglected. Combining Eqs. (17b) and (18a), we obtain mapp / c1=ð13vÞ

ð19Þ

Figure 6 shows double logarithmic plots of mapp against c for D2O solutions of C12E5 [12]. This ﬁgure demonstrates that the data at 17.9, 25.0, and 27.08C above c can be ﬁtted by a straight line that breaks at a certain concentration, c . From the slope of the log–log plots, -values can be obtained using Eq. (17). The -values obtained from the data below and above c are close to those for good solvent and solvent, respectively. When the concentration exceeds about 150 g dm3 , the log–log plots deviate

FIG. 6 Double logarithmic plots of the apparent aggregation number obtained from light scattering intensities against surfactant concentration for D2O solutions of C12E5. (From Ref. 12.) Copyright © 2003 by Taylor & Francis Group, LLC

from these straight lines. Similar results have been obtained for C16E7 [66], C14E6 [67], and C14E7 [67] systems. Daoud and Jannink [68] have deduced a temperature–concentration (T– C) diagram of a ﬂexible polymer solution that exhibits phase separations. They have divided the one-phase region into four diﬀerent subregions: dilute region (region I); dilute region (region I 0 ); semidilute region (region II); and semidilute region (region III). Experimental determination of these regions has been performed by Cotton and co-workers [69]. The above regions are characterized by the -value; 0.588 for regions I and II and 0.5 for regions I 0 and III. Therefore, c and c for the C12E5 system may correspond to the crossover concentration between regions I and II and that between regions II and III, respectively. In polymer systems, the temperature exists between Tc and the temperature at which region II disappears. In the C12E5 system, TC is equal to 30.5 0.58C and region II disappears above 278C [12]. So it can be inferred that there exists the temperature at 27–308C, which is in good agreement with that obtained from the ratio Dc =Ds in dilute solutions (see Section II.B), i.e., TC ð3 5Þ8C. These results conﬁrm the analogy between semidilute solutions of nonionic surfactants and entangled solutions of ﬂexible polymers that exhibit the critical demixing. It should be noted that the results below about TC 15K cannot be explained by the scaling theory. Also, the C12E8 system does not show analogy with polymer systems in all temperature ranges. These results are also reasonable because micelles are not so elongated to entangle each other under these conditions. The existence of the crossover concentration c in surfactant systems has been reported by Imae [61,62] for nonionic surfactant systems with salt. She has also calculated c - and c - values by using the theory of Ying and Chu [70]. Agreement with experimental results is good for c , whereas calculated values of c are much smaller than the observed ones. The scaling theory assumes monodisperse polymers, whereas wormlike micelles have broad distribution in aggregation number and, equivalently, molecular weight, or length. Ohta and co-workers [71,72] have developed conformation space renormalization theory of entangled polymers in good solvent taking into account the polydispersity. Schurtenberger and co-workers [73–75] have applied the results of this theory to wormlike micelles taking into account the increase in the micelle aggregation number with concentration by assuming a power law Nw / c . From the least-square ﬁtting of the apparent micellar weight [proportional to mapp in Eq. (18)] in dilute and semidilute regions (104–102 g cm3 ), they have obtained ¼ 1:2 for the C16E6 system, which is much larger than that found in extremely dilute solutions, 0.5, described previously. Copyright © 2003 by Taylor & Francis Group, LLC

Other interpretations of light scattering data than the scaling analysis have been reported. Brown and co-workers [27,76] have investigated C12Em (m ¼ 5; 7; 8) in the concentration range 0.05–15% by using static and dynamic light scattering and PGSE. They have noted that mixture of micelles and loose clusters of micelles is formed for C12E7 and C12E8 systems. For the C12E5 system, however, they have noted that such clusters are not formed even at temperatures close to the cloud point and that micellar growth occurs. Richtering et al. [77] have studied a C14E8 system by measuring viscosity, static and dynamic light scattering, and PGNMR. From the analysis of the friction coeﬃcient, the second virial coeﬃcient, and the osmotic compressibility, they have concluded that small micelles aggregate to random percolation clusters.

B. Self-Diffusion Processes in Entangled Wormlike Micelles The results described in the previous section suggest that static properties of semidilute solutions of surfactants show similar behavior to that observed in semidilute solutions of ﬂexible polymers in a certain concentration and temperature range. On the other hand, dynamical properties of wormlike micelles are expected to be diﬀerent from those of polymers. For ionic surfactant systems, in fact, such a discrepancy has been reported mainly for viscoelastic behaviors. At present, however, a theoretical treatment for the dynamical aspects of entanglement has not yet been established. The surfactant self-diﬀusion coeﬃcient is a useful property for discussing dynamics of entanglement from the ‘‘microscopic’’ point of view, because it gives direct information on the translational motion of surfactant molecules forming micelles themselves; this will be shown later. Measurement of the self-diﬀusion coeﬃcient of the ionic surfactant in the semidilute region by PGSE is rather diﬃcult because of a very short transverse relaxation time (T2) due to the restricted motion of the hydrophobic chain. For surfactants of polyoxyethylene type, on the other hand, the polyoxyethylene chain can move more freely than the hydrophobic chain does and so gives longer T2. In this section, self-diﬀusion behaviors in entangled nonionic micelles are described after a brief review of dynamical properties for other systems.

1. Self-Diffusion Behaviors in Entangled Polymers and Ionic Micelles In the case of entangled polymers, the self-diﬀusion coeﬃcient follows the power law [64,65,78] D / N 2 cð 2Þð3 1Þ Copyright © 2003 by Taylor & Francis Group, LLC

ð20Þ

where N is the number of monomers per chain. In micellar solutions, N corresponds to the aggregation number and so increases with concentration. If we assume the stepwise aggregation model (model A in Section II.D), the concentration dependence of N can be written as N / c1=2

ð21Þ

for the concentration range much larger than CMC. Combining Eqs. (20) and (21), we obtain D / cx

ð22Þ

where x ¼ 2:85 and 4 for ¼ 0:588 and 0.5, respectively. Cates [79,80] has proposed a theoretical model (‘‘living polymers’’) taking into account chain breakage and recombination. In his theory, the survival time of a chain before it breaks into two pieces, break, is introduced in addition to the classical reptation time, rep. In the case where break rep, he obtains the exponent x in Eq. (19) to be 1.6 for ¼ 0:6 and ¼ 0:5. Messager and co-workers [81] have measured the self-diﬀusion coeﬃcient of the photobleaching dyes dissolved in micelles for KBr solutions of cetyltrimethylammonium bromide (CTAB) by using the technique of ﬂuorescence recovery after fringe-pattern photo bleaching (FRAP). They have shown that x varies from 1.57 to 4.6 depending on the salinity. Safran and co-workers [82,83] have attributed this variation of x to an increase in the ionic strength with surfactant concentration. Such eﬀects can be neglected for ionic surfactants in water at high salinity, ionic surfactants in organic solvent, and nonionic surfactants. Ott and co-workers [84] have performed a self-diﬀusion study on reverse micelles of lecithin in isooctane with a very small amount of water by using FRAP. They obtained x ¼ 1:32 and 1.35 for w0 ¼ 1 and 2, respectively, where w0 is the water-to-lecithin molar ratio. These results indicate that the exponent depends on conditions such as salinity, which cannot be explained by the living polymer theory.

2. Self-Diffusion Behaviors in Nonionic Surfactant Systems Figure 7 shows the self-diﬀusion coeﬃcients of C16E7 obtained by using PGSE at the concentrations and temperatures where entanglement of micelles is suggested from the light scattering results [66,85,86]. In the lower concentration range, the self-diﬀusion coeﬃcient decreases with concentration, and the slope was found to be gentler than for polymers, as was observed in the CTAB system. As the concentration increases further, however, the diﬀusion coeﬃcient increases after taking a minimum. Such selfdiﬀusion behavior is completely diﬀerent from the prediction of the theories for polymers and even for the ‘‘living polymers.’’ Similar results have been obtained for C14E6 and C14E7 systems [85]. Also, it has been found that the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 7 Self-diﬀusion coeﬃcient of C16E7 in D2O obtained by using pulsed-gradient spin echo. (From Ref. 86.)

slope in the higher concentration range tends to approach almost the same value, that is, about 2/3, regardless of the temperature and surfactants. The existence of the minimum in the concentration dependence of the self-diﬀusion coeﬃcient was found ﬁrst for the C12E5 and C12E8 systems by Nilsson and co-workers [6] before the scaling analyses of light scattering results were performed by the author in these systems. They deduced that the increase in the self-diﬀusion coeﬃcient is due to the enhanced exchange of surfactant monomers between diﬀerent micelles. The author has conﬁrmed the existence of intermicellar migration by measuring the dependence of the self-diﬀusion coeﬃcient on diﬀusion time; it has been found that surfactant molecules migrate to another micelles in the diﬀusion time (0.1–0.3 s). Subsequently, a diﬀusion model for entangled wormlike micelles has been proposed [66,85]. In this model, it is assumed that (1) a surfactant molecule diﬀuses in a micelle along its contour during the time m and then migrates to adjacent micelles at one of the entanglement points (see Fig. 8a) and (2) m satisﬁes the condition R2g =DL m , where Rg is the radius of gyration of wormlike micelles, DL is the intramicellar (lateral) diﬀusion coeﬃcient, and is the diﬀusion time. Then the mean-square displacement Copyright © 2003 by Taylor & Francis Group, LLC

of surfactant molecules for the time much longer than m can be estimated by random walks where a jump of length d is performed at each time m (see Fig. 8b), which gives the surfactant self-diﬀusion coeﬃcient as D ¼ DM þ hdi2 =ð6m Þ

ð23Þ

where DM is the self-diﬀusion coeﬃcient of micelles, hdi is the mean distance between the centers of mass of adjacent micelles. As hdi3 is inversely proportional to the number density of micelles, hdi can be expressed in terms of the surfactant concentration (c) and the mean aggregation number of micelles (hmi) as hdi / ðc=hmiÞ1=3 / cð1Þ=3

ð24Þ

In the second relation of Eq. (24), the power law for the mean aggregation number, hmi / c , is assumed. Equation (24) indicates that hdi depends on the concentration only slightly; hdi / c1=6 for ¼ 1=2. On the other

FIG. 8 Diﬀusion model taking into account intermicellar migration of surfactant molecules (from Ref. 66). (a) A surfactant molecule diﬀuses in a wormlike micelle along its contour for the time m (the white line indicates the path) and migrates to adjacent micelles at one of the entanglement points (see the solid circle). The dotted circles indicate the region where the surfactant molecule exists for the time m . (b) If m satisﬁes the condition R2g =DL m (Rg is the radius of gyration of wormlike micelles, DL is the intramicellar (lateral) diﬀusion coeﬃcient, and is the diﬀusion time), the mean-square displacement of surfactant molecules for the time much longer than m can be estimated by random walks where a jump of length d is performed at each time m . Copyright © 2003 by Taylor & Francis Group, LLC

hand, m is expected to decrease as the concentration increases (see later). Thus, the second term of Eq. (23) increases with increasing concentration. In dilute solutions (but still much higher than the CMC where contributions from the monomer diﬀusion can be neglected), the self-diﬀusion coeﬃcient is dominated by the ﬁrst term of Eq. (23), DM . As the concentration increases, DM decreases rapidly due to the entanglement of wormlike micelles, whereas the second term of Eq. (23) increases. Thus, we can explain the existence of the minimum in the plot of D versus c by using this model. By assuming power laws for the concentration dependence of hmi and m, we succeeded in reproducing the observed concentration dependence of D [85]. At almost the same time as the author’s study was published, Cates and co-workers modiﬁed the living polymer theory where ‘‘bond interchange’’ and ‘‘end interchange’’ reactions are taken into account as well as the reversible scission [87]. The bond interchange reactions occur when the two chains come into contact and react at some point along the arc length, chosen at random. When the end of one chain ‘‘bites into’’ a second chain at a random position along its length, the end interchange reactions occur. They have calculated the scaling of the stress relaxation time, the zero shear viscosity, and the monomer diﬀusion coeﬃcient. However, their theory predicts only a monotonous decrease of the diﬀusion coeﬃcient with increasing concentration because neither lateral diﬀusion nor intermicellar migration of surfactant molecules is taken into account. After the author’s study, several models have been reported taking into account these processes including more general cases [88–90].

C. Structural Relaxation and Self-Diffusion Processes As described in the previous section, the observed concentration dependence of the surfactant self-diﬀusion coeﬃcient can be explained by the author’s model if appropriate power laws are assumed for the concentration dependence of hmi and m. However, this does not always indicate the validity of these power laws (note that the thermodynamic models for micellar growth described in the previous section do not always hold when micelles are entangled [73], as described in Section III.A). This motivated the author to perform dynamic light scattering measurements paying attention to the slow mode that may give information on m [86,91,92]. Figure 9 shows time correlation functions of the scattered ﬁeld at diﬀerent scattering angles for the C16E7 system [91]. One sees that the relaxation is bimodal and that the correlation time s of the slow relaxation is independent of the scattering angle. Such behaviors were not observed for dilute solutions (<0.1 wt %) where entanglement does not occur. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Time correlation function of scattered ﬁeld for the C16E7–D2O system (6.4 wt % at 358C) at diﬀerent scattering angles. (From Ref. 86.)

Observation of the slow mode for wormlike micelles has been reported for solutions of cetyltrimethylammonium bromide (CTAB) in the presence of organic/inorganic salt [93–95]. In these studies, it has been shown that s is equivalent to the terminal time of stress relaxation observed by using a conventional rheometer, that is, structural relaxation time. The theoretical explanation is also reported based on dynamic coupling between stress and composition in polymer systems [96]. Such equivalency is useful especially for nonionic micelles because the structural relaxation time is too short to be measured by using a conventional rheometer. For ionic micelles, on the other hand, it is usually very diﬃcult to perform PGSE measurements because of short transverse relaxation time. By using PGSE and dynamic light scattering, therefore, we can obtain both the surfactant self-diﬀusion coeﬃcient and the structural relaxation time for nonionic micelles. Figure 10 shows concentration dependence of the correlation time of the slow mode obtained from dynamic light scattering for the C16E7-D2O system [91] (log–log plots). At 358C, s slightly increases in the lower concentration range and then levels oﬀ. When the concentration exceeds 20 wt %, s increases rapidly. Figure 11 shows the phase diagram of the C16E7-D2O system [97–99]. It can be seen from the ﬁgure that the point (20 wt %, 358C) corresponds to the boundary between the micellar phase and the nematic phase. So the anomalous behaviors of s may be a result from pretransition from micellar to nematic phase. This slowing down enabled us to perform Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10 Correlation time of the slow mode obtained from dynamic light scattering for the C16E7–D2O system. (From Ref. 86.)

rheological measurements in this range and it was conﬁrmed that s is equal to the structural relaxation time [92]. As described previously, Cates and co-workers [79,80,87] have proposed a ‘‘living polymer’’ theory taking into account the ‘‘scission and recombination,’’ ‘‘end interchange,’’ and ‘‘bond interchange.’’ However, these models cannot explain our results because all of them predict monotonous increase of s with increasing concentration, as can be expected from the fact that they fail to explain the self-diﬀusion results in the same system. Shikata and co-workers [100] measured the rheological relaxation time for CTAB micelles in the presence of sodium salicylate. They propose a model to explain the dependence of the relaxation time on the concentration of salicylate ions. According to their model, two diﬀerent micelles can go through like a ghost to relax the stress applied to the entangled network (see Fig. 12a). The model proposed by Porte and co-workers [101], on the other hand, considers sliding of a crosslink (see Fig. 12b). These two models may explain the decrease of the relaxation time with increasing surfactant concentration although explicit expression has not been reported except for a preliminary attempt by Hoﬀmann [102]. However, it is still diﬃcult to deterCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 11 Phase diagram of the C16E7–D2O system (from Refs. 97–99,108). L, lamellar phase; V1, cubic phase; H1, hexagonal phase; Nc, nematic phase; L1, isotropic micellar phase; and W þ L1, coexisting liquid phases. The dotted lines in the L1 phase indicate constant contours of the activation energy for self-diﬀusion processes (from Ref. 97). Filled and open triangles indicate the presence and absence of the broad component, respectively (from Ref. 108). The dotted lines in the L phase are constant contours of the volume fraction of the water-ﬁlled defects in the hydrophobic layer, fw (from Ref. 108). The shaded line indicates the speciﬁc temperature range where the structure varies from that of the usual lamellar phase, that is, ﬂat bilayers without any defects.

mine which model is more appropriate for the structural relaxation time alone. Figures 7 and 9 demonstrate the strong correlation between D and s in the concentration range of 2–20 wt % except for 358C. In fact, the product D s is almost constant in this range. This indicates that self-diﬀusion and structural relaxation are dominated by the same kinetic process. According to the author’s diﬀusion model, D is inversely proportional to the time m , which reﬂects the frequency of intermicellar migration. If we consider that surfactant molecules migrate to another micelle through a transient connection at an entanglement point (see Fig. 12a), the formation rate of such a Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 12 Models for stress relaxation; ghostlike crossing (a) and sliding of connection (b) proposed by Shikata and co-workers [100] and Porte [101], respectively. These two models can explain the concentration dependence of the relaxation time of the slow mode observed by dynamic light scattering ( s ) shown in Fig. 10. However, the strong correlation between s and D (Fig. 7) in the C16E7 and C14E6 systems can be explained only by model (a) because surfactant molecules can migrate to another micelle only when the transient connection is formed in model (a), whereas the sliding of the connection itself does not aﬀect the self-diﬀusion coeﬃcient very much.

transient connection should dominate both self-diﬀusion and structural relaxation. In other words, m should be nearly equal to s . So we have calculated the average spacing hdi from Eq. (23) by using observed D and s and then compared it with that obtained from static light scattering. The results indicate that the relation m ﬃ s holds true for these systems. From these results, we can infer that entangled micelles form a transient connection whose lifetime is of the order of 103 s, depending on concentration and temperature, and that surfactant molecules migrate to other micelles through such a transient connection.

D. Three-Dimensional Network Formed by Connections of Wormlike Micelles When the temperature exceeds a certain value (about 458C in the C16E7 system), the concentration and temperature dependencies become very different from those described previously. In Fig. 13, the self-diﬀusion coeﬃcient of C16E7 is plotted semilogarithmically against the reciprocal temperature [97]. Note that in the hexagonal phase the direction of each rod may be random. The ﬁgure shows that in the lower temperature range Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 13 Logarithm of surfactant self-diﬀusion coeﬃcient versus reciprocal temperature. The concentrations for the micellar solutions are indicated in the ﬁgure (in wt %). (From Ref. 97.)

the self-diﬀusion coeﬃcient in the micellar phase is much lower than those in the liquid crystal phases. As the temperature is increased, the self-diﬀusion coeﬃcient in the micellar phase rapidly increases. Above about 608C, the self-diﬀusion coeﬃcient depends on concentration only slightly and falls into the line obtained by extrapolating the plot in the cubic phase to higher temperatures (see the dashed line in Fig. 13). From these plots, the activation energy for the self-diﬀusion processes (ED) was obtained. It was found that below about 458C the activation energy in the micellar phase ( 165 kJ mol1 ) is much larger than that in the cubic phase ( 30 kJ mol1 ). Note that the activation energies in the hexagonal phase and in the pure liquid are nearly equal to that in the cubic phase, as can be seen from Fig. 13. As the temperature is raised above about 458C, however, ED in the micellar phase decreases rapidly and approaches the value in the liquid crystal phase. These results suggest that the diﬀusion processes at higher temperatures may be diﬀerent from those described in the previous section. A possible mechanism is connection of wormlike micelles [101–107]. When wormlike micelles are connected to each other, surfactant molecules can diﬀuse over a large distance by lateral diﬀusion alone. Such a situation is, in fact, encountered in the liquid crystal phases. In particular, the bicontinuous cubic phase Copyright © 2003 by Taylor & Francis Group, LLC

resembles such a connection picture although the regularity disappears in the micellar phase. If connection occurs, therefore, the self-diﬀusion coeﬃcient and the activation energy in the micellar phase are expected to be close to those in the bicontinuous cubic phase. These considerations suggest that the activation energy for self-diﬀusion processes can be regarded as the measure of the connectivity. Figure 11 includes the lines where the activation energy is constant. Below the line corresponding to 160 kJ mol1, there exists no connection except for transient one with a lifetime of m . Above this line, the connectivity increases with increasing temperature and concentration. To conﬁrm these conclusions, the author has measured small-angle X-ray scattering (SAXS) in the same concentration and temperature range [98]. The repeat distance in the micellar phase was found to approach that calculated for the ‘‘cubic phase-like’’ structures, which is consistent with the self-diﬀusion results.

IV. LAMELLAR PHASE A. Variation in Structures of Lamellar Phase with Concentration and Temperature The foregoing results may be not surprising because the micellar phase is connected to the cubic phase as can be seen from the phase diagram. At higher temperatures, however, the micellar phase connects to the lamellar phase. The lamellar phase consists of bilayer sheets, and so the mechanism of the transition from micellar to lamellar phase is quite interesting. This led the author to investigate the structure of the lamellar phase [108]. Figure 14 shows double logarithmic plots of the repeat distance in the lamellar phase versus weight concentration of C16E7. When bilayer sheets of constant thickness are stacked, the repeat distance d can be related to the volume fraction (hc) and the thickness (2hc) of the hydrophobic layers as d ¼ 2hc 1 hc

ð25Þ

At 758C, a plot of log d versus log hc (not shown but similar to Fig. 14) gives a straight line with a slope of 1 as expected from Eq. (25). When the temperature is reduced from 708C down to 358C, however, the absolute value of the slope rapidly decreases from unity to about 0.65. In the region denoted as ‘‘L ’’ in the phase diagram shown in Fig. 11, only ﬁrst-order and second-order reﬂections were observed in the positional ratio 1:2. Also, the 2 H NMR spectra observed in this region consist of only one doublet, indicating that the possibility of coexistence with other phases can be excluded. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 14 Double logarithmic plot of the repeat distance d versus weight concentration of the C16E7 for the lamellar phase of the C16E7–D2O system. (From Refs. 99 and 108.)

The above discussion is based on the assumption that hc is constant. If hc depends on the concentration, the slope of the log d versus log hc plot may deviate from 1 even if Eq. (25) holds true. To determine the thickness hc, the line shape of SAXS has been analyzed. If we assume that layer displacement ﬂuctuations are independent of the transverse position, the scattering intensity can be written in terms of the form factor of a membrane P(q) and the structure factor S(q) as [109] IðqÞ ¼ ð2=dÞPðqÞSðqÞ=q2

ð26Þ

In the calculation of P(q), the membrane was assumed to be composed of three layers: one hydrophobic layer and two hydrophilic layers [108]. Then I(q) can be expressed as a function of hc and a parameter correlated with the layer displacement ﬂuctuations. These parameters have been determined by the least-square ﬁtting of q4I(q) because I(q) is inversely proportional to q4. Figure 15 (left) shows examples of observed q4I(q) and least-squares ﬁts Copyright © 2003 by Taylor & Francis Group, LLC

[110]. It has been found that the hc-value thus obtained depends on concentration and temperature only slightly [108], suggesting that the deviation of the slope from 1 is not due to the variation of hc but due to the change in the structure itself. It has been reported that the bilayer sheets in the lamellar phase contain water-ﬁlled defects under speciﬁc conditions depending on the molecular structure of the surfactants and additives as well as concentration and temperature. Holmes and co-workers [111–113] have investigated binary solutions of water and nonionic surfactants C16E6, C22E6, and C30E9 using optical microscopy, 2H NMR, and SAXS. In the C16E6 system, the following phase sequence is observed; lamellar (L), defected lamellar (LH ), mesh intermediate (Int.), Ia3d cubic (V1), and hexagonal (H1) or hexagonal plus gel biphase (H1 þ L ) on cooling while H1 or H1 þ L , V1, LH , and L on heating. The mesh intermediate phase, appearing only on cooling, has a rhombohedral structure assigned the space group R3 m. If water-ﬁlled defects exist, the repeat distance can be expressed as d ¼ ð1 fw Þð2hc Þ1 hc

ð27Þ

where fw is the volume fraction of the defects. As the concentration increases, fw is expected to decrease, and so the repeat distance decreases more gently than that for fw ¼ 0 [Eq. (25)], which is consistent with the results in the lower temperature range (see Fig. 14). By utilizing hc-values at 80 wt % (at this concentration hc depends on temperature only slightly, and so the structure is expected to be not anomalous) and the observed repeat distance, we have calculated fw at each concentration and temperature. Figure 12 contains the lines where fw is constant. The results demonstrate that the fraction of the defects increases with decreasing concentration and temperature. Figure 15 (right) shows the temperature dependence of SAXS patterns at 48 wt %; logarithm of the scattering intensity versus scattering vector q. Note that a broad component is superimposed on the ﬁrst diﬀraction peak at 55 and 608C. The ﬁlled and open triangles in Fig. 11 indicate the presence and absence of the broad component, respectively. It can be seen from the ﬁgure that the broad component is observed in the region where fw is relatively large. The observation of such a broad component has already been reported for the C16E6 system by Holmes and co-workers [111], who assign it to the reﬂection from the water-ﬁlled defects. This assignment is consistent with the strong correlation between fw and the appearance of the broad component in the present system. Imai and co-workers [114] have measured SAXS by using an oriented sample with the thickness of about 50 mm. They have shown that the broad component corresponds to the diﬀraction along the direction of membranes, also consistent with the interpretation of Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 15 Examples of SAXS patterns. Left: Least-squares ﬁts of q4I at 758C (40, 51, and 55 wt % from the bottom). Right: Logarithm of the SAXS intensity at 48 wt % (55, 60, 65, 70, and 758C from the bottom). (From Ref. 108 and 110.)

Holmes and co-workers. Even if the water-ﬁlled defects do not exist, the decrease in the absolute value of the slope of the log d versus log hc plot indicates the increase in the mean curvature of the interface for aggregates [115,116]. Such a variation in interfacial curvature has been conﬁrmed by measurements of quadrupolar splitting of 2H2O ( ) [108]. Taking into account the temperature dependence of , the constant contour of fw, and the observation of the broad component in the SAXS pattern, the speciﬁc temperature range has been drawn in Fig. 11 as a shaded line where the structure deviates from that of the usual lamellar phase, that is, ﬂat bilayers without any defects. As described in Section III.D, the L1 phase is composed of a three-dimensional network in the vicinity of the ‘‘L’’ and V1 phases. On the other hand, bilayer sheets with water-ﬁlled holes can be regarded as a two-dimensional network (see Fig. 11). In the lower concentration range in the ‘‘L’’ phase, a gradual transition into such a structure occurs by the reduction of temperature (note that fw increases toward the boundary with L1 and V1 phases). Then the structures of the ‘‘L’’ and L1 phases become similar as the temperature decreases. Moreover, the ‘‘L’’ þ L1 two-phase coexistence region Copyright © 2003 by Taylor & Francis Group, LLC

becomes rapidly narrow with decreasing temperature in the range 65–688C, which corresponds to the speciﬁc temperature range (shown as a shaded line in Fig. 11) in the lower concentration limit. Figure 11 also demonstrates that above the speciﬁc temperature range, the existence region of the lamellar phase suddenly extends to the lower concentrations, suggesting that the lamellar phase can swell distinctly only when defects disappear.

B. Effects of Shear Flow In recent years, eﬀects of shear ﬂow on the structure of lamellar phase by using small-angle neutron and light scattering, NMR, and microscopy have been reported [117–124]. In these studies, attention has been paid to the formation of multilayered vesicles (onion phase) by shear ﬂow and the orientation of the sample for structural analyses. The author and co-workers [99,125,126] have measured small-angle neutron scattering (SANS) on the C16E7-D2O system in the range of shear rate _ = 103–102 s1 [127], much lower than those for other studies reported so far. Shear rate dependence of the position and intensity of the ﬁrst reﬂection has been measured in ﬂow, gradient, and vorticity directions. At lower shear rates less than 0.1 s1 , the peak intensities for both directions decrease with increasing shear rate. In the range 0.1–1 s1 , the lamellar spacing (d) suddenly decreases. As _ increases further, d increases and then levels oﬀ. At the same time, the peak intensities in gradient and vorticity directions increase with the increase of _ whereas that in ﬂow direction does not change very much. The abrupt decrease in the lamellar spacing d has been observed at two diﬀerent concentrations, 48 and 55 wt % at 708C; d decreases from 7.2 nm down to 5.1 nm at 48 wt % and from 6.5 nm down to 5.1 nm at 55 wt %, respectively. Note that the minimum values of d for these two concentrations are the same in spite of the diﬀerence of d-values at rest. From the line shape analyses of SAXS described in the previous section, the total thickness of bilayers is obtained to be about 5.1 nm. This indicates that the water layer between bilayers is excluded by shear ﬂow.

C. Effects of Adding Fatty Acid In the past 15 years, highly swollen lamellar phases have been found for various kinds of surfactant systems. Such phases may be formed even in a binary system such as water–C12E5 [128] that does not contain any ionic species, indicating that the dominant component of forces between widely separated bilayers is the undulation force proposed by Helfrich [129]. Copyright © 2003 by Taylor & Francis Group, LLC

The eﬀects of adding ionic surfactants on phase behaviors and properties of nonionic bilayers such as the bending modulus have been investigated by several groups [130–136]. These studies suggest that a weak charge suppresses undulations of bilayers and so reduces the spacing distance. Compared to ionic surfactants such as SDS, fatty acid is considered to be an interesting additive in the sense that the solubility for water is very small, and so almost all the molecules are incorporated to bilayers, and that hydrophobicity of the molecule is much higher than that of ionic surfactants and so novel phase behaviors can be expected. The author and co-workers [137] have investigated phase behaviors and light scattering patterns for a water– C12E5–lauric acid system. Figure 16 shows the inﬂuence of lauric acid on phase behaviors for xa ¼ 0–0.175 and ctot ¼ 1.4 wt %, where xa is the mole fraction of lauric acid in the total mixed solute and ctot is the concentration of the total mixed solute. As xa increases, the L/L3 transition temperature ﬁrst increases rapidly. After the L3 phase disappears, the high-temperature boundary of the L phase takes a maximum and then gradually decreases. On the other hand, the low-temperature boundary of the L phase decreases monotonously as xa increases. Thus the existence region of the L phase profoundly increases with increasing xa.

FIG. 16 Partial phase diagram of C12E5–lauric acid–water system where the mole fraction of lauric acid in the total mixed solute (xa) is varied while the concentration of the total mixed solute (ctot) is kept at 1.4 wt %. 1, micellar phase; 2, coexistence of two isotropic phases; L, lamellar phase; L3, sponge phase. (From Ref. 137.) Copyright © 2003 by Taylor & Francis Group, LLC

Figure 17 shows eﬀects of lauric acid on light scattering patterns at 588C. For binary solutions of water and C12E5, only a very weak peak has been observed as indicated by closed circles. When 5% of C12E5 was replaced by lauric acid, on the other hand, a very strong and sharp diﬀraction peak was observed. This sharp peak is substantially decreased again by adding only 104 M NaCl. These results suggest that the very weak charge of lauric acid enhances the growth of the lamellar grain. The spacing distance obtained from the peak position (around 250 nm) slightly decreases as xa increases from 0 to 0.175, where ctot is kept constant (1.4 wt %). The results have been compared to the electrostatic theory of de Vries [138] that takes into account the interplay between thermal undulations and electrostatic repulsion for salt-free lamellar phase [137].

V. CONCLUDING REMARKS Figure 18 shows a variation in structures of a polyoxyethylene surfactant– water system with concentration and temperature. As described in the introduction, the systematic study of such a structural change in the single-phase region is important to clarify the mechanism of the phase transition (see Ref. [114] for example). In the concentration and temperature range where micellar, lamellar, and bicontinuous cubic phases are closely located, the structures of these three

FIG. 17 Inﬂuence of lauric acid on light scattering patterns at 588C. The pattern for xa ¼ 0 corresponds to a binary system of water and C12E5. Concentration of the total mixed solute is kept at 1.4 wt %. (From Ref. 137.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 18 Variation in structures of self-assembly formed in a polyoxyethylene surfactant–water system with concentration and temperature.

phases are similar: three-dimensional random networks (micellar phase); two-dimensional random networks (lamellar phase); and three-dimensional regular networks (bicontinuous cubic phase). On the other hand, structures of micellar and lamellar phases in the higher temperature range are completely diﬀerent. Nevertheless, the phase transition from micellar to lamellar phase occurs by elevation of temperature within a few seconds [139]. The mechanism of the phase transition at this point is therefore very interesting. Line-shape analyses of time-resolved SAXS is considered to be a powerful technique for this purpose. Dynamical aspects of ﬂuctuations in the equilibrium structures are also important. As described in Section III, dynamic light scattering and PGSE give information on macroscopic and microscopic dynamics, respectively, and so are useful to choose appropriate kinetic models for wormlike micelles. The exclusion of water layers by shear ﬂow in the lamellar phase described in Section IV may be a result from suppression of undulations of bilayers. So the speciﬁc shear rate is considered to be strongly correlated with the time scale of undulations. To conﬁrm this relation, direct measurements of the relaxation time for undulations by using neutron spin echo (NSE) are necessary. NSE is also useful for investigating the bending motion of entangled wormlike micelles [140]. Work along these lines is in progress. Copyright © 2003 by Taylor & Francis Group, LLC

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12 Association Behavior of Amphiphilic Dendritic Polymers TOYOKO IMAE

I.

Nagoya University, Nagoya, Japan

INTRODUCTION

The main characteristics of amphiphilic molecules such as surface activity and association behavior originate in their unique chemical structure, which consists of hydrophilic and lipophilic moieties. Traditional low-molecularweight surfactants are typical amphiphilic molecules and have a hydrophilic head and a hydrophobic alkyl chain tail. Such a structural character is dominant to associate into micelles, vesicles, microemulsions, liquid crystals, and other self-assemblies. These aggregates are utilized for huge industrial, cosmetic, and pharmaceutical purposes. AB-type block copolymers are also a kind of amphiphiles, since every block in the copolymers has diﬀerent aﬃnities to solvents. Those are associated into micelles, but the micellar sizes are usually larger than the sizes of traditional surfactant micelles. Then polymer micelles create large hydrophilic and lipophilic domains, which are superior as a solubilization reservoir and a microreaction matrix. Amphiphilic (AB)n-type block copolymers form unimolecular micelles, where blocks familiar to solvent are in the periphery of micelles. However, unimolecular polymer micelles are destroyed, like surfactant micelles, depending on conditions such as temperature, additives, and solvents. Recently, novel polymers, dendrimers, are focused on as nanomolecules and expected as covalent-bonded ‘‘unimolecular micelles’’ or ‘‘dendritic boxes’’ for the encapsulation of small molecules and the chemical reaction [1–8]. Dendrimers are prepared from a functional core through the successive repeating synthesis of a spacer and a branching part (divergent method) or from a conjugation at the conic center of dendrons, units of a dendrimer (convergent method). When two steps are needed for the extension of a repeating unit, each step is called a half-generation. While structures of dendrimers at low generations are opened and asymmetric, the Copyright © 2003 by Taylor & Francis Group, LLC

structures become concentrated and spherical during the increase of the generation. In the process of the stepwise synthesis, it is possible to modify the central core, spacer, branch, and terminal group, and a variety of functional moieties are conjugated in dendrimers. Amphiphilic character could be introduced by designing the diﬀerent generations or layers to be either hydrophilic or hydrophobic. On the other hand, hybrid copolymers with linear polymers and dendrimers (or dendrons) are synthesized. Such copolymers with a speciﬁc chemical structure may also possess unique characteristics such as amphiphilicity besides intrinsic dendritic and polymeric characters. Then, the amphiphilic concentric dendrimers and hybrid copolymers could be applied to many nanoscopic smart materials including drug deliveries, diagnostics, and segregations, as well as reaction catalysts, transport agents, and molecular recognitions. In this section, the up-to-date investigations concerning the characteristic covalent-bonded structures of concentric dendrimers and hybrid copolymers are reviewed. Especially, their amphiphilic properties and association behavior are examined. Amphiphilic nanomolecules can make supramolecular architectures as self-assemblies in solutions and monolayers or thin ﬁlms at interfaces between water and immiscible organic solvent, at air–water interfaces, and on solid substrates. The formation of architectures is discussed in relation to the structures of dendrimers and copolymers.

II. AMPHIPHILIC DENDRIMERS HAVING A CONCENTRIC STRUCTURE When, during the stepwise synthesis of dendrimers, generations or terminal groups are modiﬁed by diﬀerent chemical units, the dendrimers carry the amphiphilicity on the concentric layers. The terminal groups of poly(amido amine) dendrimers have been substituted by lactose and maltose derivatives [model (a) in Fig. 1] [9]. These globular dendrimers, called ‘‘sugar balls,’’ are three-dimensional architectures of artiﬁcial glycoconjugates as mimics of natural multiantennary oligosaccarides. Sugar moieties with a wellcontrolled geometric arrangement in those sugar-substituted layer-block copolymers possess the function as molecular recognition sites. Funayama et al. [10] have investigated the segment distribution and the water penetration in a sugar-terminated poly(amido amine) dendrimers and compared them with those in a hydroxyl-terminated poly(amido amine) dendrimer and a hydroxyl-terminated poly(trimethylene imine)/mono (amido amine) dendrimer. Bulky sugar terminals distribute in the periphery of dendrimers, while some hydroxyl terminals direct to the interior. In the case of a poly(trimethylene imine) dendrimer, the segment distribution Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 1

Schematic models of amphiphilic dendritic polymers.

increases from the interior to the periphery. The water penetration is not necessarily dependent on the segment distribution but relates to the aﬃnity of the dendrimer-constituting units for the solvent. The encapsulation of small molecules, depending on the dendrimer species, implies the selective doping ability of dendrimers, which allows us the application of dendrimers as dendritic boxes. Poly(amido amine) dendrimers have been coupled with D-glucono-1,5lactone, and the solubilization of pyrene and aromatic ketones in water has Copyright © 2003 by Taylor & Francis Group, LLC

been investigated [11]. The solubility of hydrophobic molecules is increased, depending on the microcavities of dendrimers. This indicates the behavior of dendrimers like surfactant micelles. Glucose-substituted dendrimers aggregate through hydrogen bonding. The size of aggregates is 100–2000 nm in diameter. Radially layered copolymers containing a hydrophilic poly(amido amine) dendrimer interior and a hydrophobic organosilicon exterior have been synthesized by Dvornic et al. [12]. Although the solubility and glass transition temperature of the copolymers are inﬂuenced by their chemical compositions and molecular architectures, their thermal and thermooxidative stability is mostly determined by the presence of the less stable poly(amido amine) component. Ponomarenko et al. [13] have synthesized a carbosilane liquid crystal dendrimer with cyanobiphenyl mesogenic groups. Molecular organization on ﬁlms of the dendrimer was studied. The modiﬁcation of the terminal groups of hydrophilic poly(propylene imine) dendrimers with hydrophobic alkyl chains has been carried out by Stevelmans et al. [14], and the guest–host properties as an inverted unimolecular dendritic micelle have been examined. The terminal groups of poly(propylene imine) dendrimers of the ﬁrst to ﬁfth generations have been modiﬁed with long hydrophobic (palmitoyl) chains [15]. These amphiphilic dendritic surfactants aggregate at the air–water interface and in the solution. Dendrimerlike star-block copolymers with a radial geometry [model (b) in Fig. 1] has been synthesized from a hexahydroxyl functional core by the living ring opening polymerization of e-caprolactone producing a hydroxylterminated six-arm star polymer [16]. The copolymers have concentric structures with generations or layers of diﬀerent components, which are comprised of high-molecular-weight linear polymers emanating from a functional core. A star-shaped dendrimer has been synthesized by radial-growth polymerization of sarcosine N-carboxyanhydride initiated with poly(trimethylene imine) dendrimer [model (c) in Fig. 1] [17]. Polysarcosine chains linked with terminal groups of the dendrimer are shrunk in an aqueous solution. Core-shell copolymers, where the shell is formed from rigid, conductive ionic polyacetylene arms and an initiator interior is spheroidal aliphatic ply(amido amine) dendrimer, have been synthesized by Balogh et al. [18]. The thermal stability of the dendrimer improves dramatically as a result of copolymer formation. Kimura et al. [19] have synthesized the dendrimerbased multiarm copolymers as a temperature-sensitive nanoscopic capsule for catalysts. The catalytic activity of the poly(propylene imine) dendrimer with poly(N-isopropylacrylamide) arms is controlled in response to the change in polymer conformations. Copyright © 2003 by Taylor & Francis Group, LLC

As an approach for forming dendritic monolayers, dendritic amphiphiles of the ﬁrst to third generations have been synthesized from a tripeptide with dioctadecylamino tails at the C-terminal and an acetyl head at the Nterminal [20]. The molecular area in the condensed phase on the surfacepressure-area isotherm is comparable to the total area of the alkyl chain cross sections, although the packing behavior somewhat depends on the generation. This approach provides a well-deﬁned two-dimensional arrangement of the hydrophobic tails and polar heads with desirable sequences and combinations. Poly(propylene imine) dendrimers with both hydrophilic triethylenoxy methyl ether chains and hydrophobic octyl chains at every terminal [model (d) in Fig. 1] have been synthesized by Pan and Ford [21]. The dendrimers converted to quaternary ammonium chlorides are soluble in both organic solvents and water and solubilize lipophilic compounds in aqueous solutions. The limiting solubility in quaternized cationic dendrimers is one pyrene per dendrimer molecule. The rates of the decarboxylation of 6-nitrobenzisoxazole-3-carboxylic acid in aqueous solutions of the cationic dendrimers are up to 500 times faster than in water alone. Amphiphilic dendrimers having the concentric but asymmetric structure [model (e) in Fig. 1] have been constructed. Both hemispheres in these dendrimers, which are called surface-block dendrimers, have diﬀerent chemical structures. Fre´chet and his collaborators [22] have synthesized a carboxyl- and phenyl-terminated dendritic diblock copolymer and its analogs, where the interior is composed of benzyl ether pendant groups. The liquid membrane of amphiphilic dendrimers is aligned at the interface between water and an immiscible organic solvent. AB-type surface-block dendrimers have also been synthesized by the divergent/convergent joint approach or divergent/divergent approach with a half-protected initiator core, as shown in Scheme 1 [23]. Amphiphilic ABtype surface-block dendrimers display characteristic surface activity. Surface tension versus dendrimer concentration curves for aqueous solutions of Nacetyl-D-glucosamine/n-hexyl and hydroxyl/n-hexyl terminated poly(amido amine) dendrimers show the remarkable decrease with increasing the dendrimer concentration and reach the constant value through a two-step decrease. The CMCs obtained are listed in Table 1. The two-step process of surface tension decrease, where the ﬁrst CMC is one order lower than the second, implies the existence of a precursor like a dimeric aggregate before the formation of regular micelles. The cmcs increase with increasing the generation of the dendrimer, although those are not sensitive to the change of hydrophilic surface groups from N-acetyl-D-glucosamine to hydroxyl. This is attributed to the increase of the hydrophilicity/lipophilicity balance due to the fractional increase of amido amine moieties. Copyright © 2003 by Taylor & Francis Group, LLC

Scheme 1 Synthesis process of surface-block poly(amido amine) dendrimers. (From Ref. 23b.)

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TABLE 1 Critical Micelle Concentration (CMC) of Amphiphilic Dendritic Polymers at 258C First CMC (104 M)

Second CMC (104 M)

Occupied area (A2 /terminal)

N-acetyl-D-glucosamine/n-hexyl terminated poly(amido amine) dendrimer

2.0 3.0 4.0

0.27 0.82 1.8

1.8 5.2 19

Hydroxyl/n-hexyl terminated poly(amido amine) dendrimer

3.0

0.87

6.3

Methyl ester-terminated poly(amido amine) dendrimer-blockpoly(2-methyl-2-oxazoline)

3.5 4.5 5.5

Generation

19 — 1.2

24 36 55

Source: Refs. 23 and 28.

Nierengarten et al. [24] have synthesized a globular diblock dendrimer, where a dendron conjugated C60 units in the branching shell and peripheral long alkyl chains is attached to a poly(benzyl ether) dendron with ethylene glycol terminal chains. The resulting dendrimer with hydrophobic chains on one hemisphere and hydrophilic ones on the other forms stable Langmuir ﬁrms with perfect reversibility in successive compression/decompression cycles and well-ordered multilayer Langmuir–Blodgett ﬁrms. This unique approach suggests that the nonamphiphilic molecules such as fullerenes attached in an amphiphilic structure can be eﬃciently incorporated in thin ordered ﬁlms.

III. AMPHIPHILIC HYBRIDS OF DENDRIMERS WITH LINEAR CHAINS One group of amphiphilic dendritic polymers is a head-tail block copolymer where a linear polymer is attached to a focal point of a dendron or a functional site of the core in a dendrimer. Polystyrene has been combined with poly(propylene imine) dendrimers [model (f) in Fig. 1], and the solution properties of the head-tail diblock copolymers as amphiphiles have been investigated [25]. The resulting amphiphilic macromolecules have the chemical structure composed of a hydrophilic head and a lipophilic tail as well as traditional surfactants. Copyright © 2003 by Taylor & Francis Group, LLC

Fre´chet and his collaborators [22b,26] have synthesized an amphiphilic dendritic-linear diblock copolymer with a hydrophobic poly(benzyl ether) dendron head and a hydrophilic poly(ethylene oxide) tail. It should be noticed that the solvent aﬃnity of head and tail blocks in this copolymer is inverse to that in traditional surfactants. The stability and conformation of poly(benzyl ether) dendrons with linear oligo(ethylene glycol) tails have been studied by Kampf et al. [27]. Aoi et al. [28] have synthesized two dendritic-linear diblock copolymers. One is a surface-N-hexylamide-type poly(amido amine) dendrimer/polysarcosine [poly(N-methylglycine)] diblock copolymer, and another is a methyl ester-terminated poly(amido amine) dendrimer-block-poly(2-methyl-2-oxazoline) (Scheme 2). Both are a hydrophobic dendrimer-hydrophilic linear polymer hybrid identical to Fre´chet’s hybrid. These copolymers display surface activity as proved by the surface tensiometry: the surface tension of aqueous solutions of the latter diblock copolymer decreases with increasing copolymer concentration until the cmc, as seen in Fig. 2. The CMCs lower with increasing the generation of hydrophobic dendritic block (Table 1). This aspect is due to the increasing rigidity of the dendritic block occurring from the increase of generation, which is consistent with the increase in occupied area per terminal group, as seen in Table 1. The aggregation number of a diblock copolymer of generation 5.5 in an aqueous solution is about 103. Figure 3 illustrates an adsorption model of poly(amido amine) dendrimer/polysarcosine diblock copolymer at the air–water interface. Solution properties of linear-dendritic diblock copolymers with a linear poly(ethylene oxide) block and a methyl ester-terminated dendritic poly (amido amine) block have been investigated by Iyer et al. [29]. Copolymers with a longer poly(ethylene oxide) chain length possess the unimolecular micellelike structure. Johnson et al. [30] have linked a linear poly(ethylene oxide) block to a dendritic poly(amido amine), where the amino terminal groups are functionalized with stearic acid to make the dendritic block hydrophobic. The structure of monolayers formed from the resulting macroamphiphile has been investigated at the air–water interface. Amphiphilic AB-type diblock copolymers consisting of hydrophilic linear poly(ethylene oxide) and hydrophobic dendritic carbosilane have been synthesized by Chang et al. [31]. Their amphiphilic nature is highly dependent on the size of the hydrophobic dendron block: the ﬁrst and second generations of dendritic carbosilane blocks form micelles in aqueous solutions. The average diameters of the micelles are 120 and 170 nm, respectively, which are one order larger than those of traditional surfactant micelles. Both terminals of hydrophilic linear polymers, poly(ethylene glycol)s or poly(ethylene oxide)s, have been replaced by hydrophobic poly(benzyl Copyright © 2003 by Taylor & Francis Group, LLC

Scheme 2 Synthesis process of poly(amido amine) dendrimer-block-poly (2-methyl-2-oxazoline). (From Ref. 28a.)

ether) dendrons [model (g) in Fig. 1] [26,32]. These ABA-type hybrids change the conformation from the extended structure to the coiled one during an increase of hybrid concentration and form mono- and multimolecular micelles depending on the dendron generation, hybrid concentration, and solvent. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 2 Surface tension () of aqueous solutions of dendritic-linear diblock copolymers, methyl ester-terminated poly(amido amine) dendrimer)-block-poly(2-methyl2-oxazoline), as a function of logarithmic copolymer concentration (C) at 258C. Generation: &, 3.0; *, 4.5; ~, 5.5. (From Ref. 28b.)

FIG. 3 An adsorption model of a surface-N-hexylamide-type poly(amido amine) dendrimer/polysarcosine [poly(N-methylglycine)] diblock copolymer of 2.5 generation at the air–water interface. (From Ref. 28b.) Copyright © 2003 by Taylor & Francis Group, LLC

Two poly(amido amine) dendrimers have been linked with aliphatic methylene chains from 2 to 12 [33]. A hybrid with a long aliphatic chain (C ¼ 12) shows the ability to host the hydrophobic dye in an aqueous solution. This result implies a strong tendency of dye probe to associate with methylene chains. Moreover, the interactions of these hybrids with anionic surfactants generate supramolecular assemblies. The ‘‘dumbbellshaped’’ triblock copolymers based on a linear oligothiophene and poly(benzyl ether) dendrons have been synthesized, and their aggregation behavior in solutions has been investigated [34]. Five to six molecules are assembled in aggregates. Amphiphilic dendritic-linear block copolymers with a variety of AxBxtype topologies have been prepared [model (h) in Fig. 1] [35]. The A blocks are composed of the ﬁrst- through third-generation dendrons from 2,2bis(hydroxymethyl)-propionic acid, while the B blocks are poly("-caprolactone) chains. The macromolecules are amphiphilic polymer surfactants with polar hydrophilic heads and nonpolar hydrophobic tails. Four-arm star poly(ethylene oxide) has been linked, at the periphery, with poly(benzyl ether) dendrons [model (i) in Fig. 1] [26,36]. Amphiphilic starlike hybrid copolymers with dendritic groups behave as the stimuliresponsible hybrid macromolecules for organic solvents.

IV. AMPHIPHILIC POLYDENDRIMERS Side chains of linear polymers were modiﬁed by dendrons. Kaneko et al. [37] have synthesized polydendrimers by polymerizing dendritic phenylacetylene monomers [model (j) in Fig. 1], which are produced by the repetitive coupling reaction of 3,5-dibromo-1-(3-hydroxy-3-methylbutynyl)benzene with [4-(trimethylsilyl)phenyl]acetylene as a starting peripheral group. The polyacetylene-substituted polydendrimers with the well-deﬁned dendritic and rodlike structure indicate the good membrane-forming ability and may possess additional properties such as electrical conductivity, nonlinear optics, and magnetism. The oxygen separation ability of the membrane of the ﬁrst-generation polydendrimer is higher than that of the zeroth generation, aﬀording potential application to a highly selective polydendrimer membrane. Poly(phenylenevinylene)s substituted with dendritic side chains have been synthesized by using methyl-3,4,5-trihydroxybenzoate as a starting material [38]. These polymers self-order in the solid state and yield thermotropic nematic phases. Polystyrenes with 3,4,5-tris[4-(n-tetradecan-1-yloxy)benzyloxy]benzoate or 3,4,5-tris[3 0 ,4 0 ,5 0 -(n-dodecan-1-yloxy)benzyloxy]benzyl ether side groups have been synthesized by Prokhorova et al. [39]. The monodendron-jacketed Copyright © 2003 by Taylor & Francis Group, LLC

linear polystyrenes are visualized as wormlike cylinders. The conformational change and ordering of these polydendrimers depending on the branching density have been investigated. The positional and orientational order of the adsorbed wormlike cylinders is explained by the speciﬁc interaction of the alkyl substituents of the monodendrons with the highly oriented pyrolytic graphite surface used. However, if the substitution of the monodendrons by the alkoxy groups is too dense, regular adsorption of alkyl tails is embedded. The conducting polythiophene, which is functionalized exclusively with aliphatic ether convergent dendrons as solubilizing groups, has been prepared from a dendrimer-oligothiophene hybrid monomer [40]. Both the dendrimer size and the dendrimer-to-thiophene unit ratio were varied in order to obtain an optimum solution-processable conducting polymer. Conductivities measured for iodine-doped thin ﬁlms of the polythiophene with six thiophene repeating units for each third-generation dendron is as high as 200 S/cm. Wormlike polydendrimers consisting of ﬂexible and noninteracting segments have been synthesized by a stepwise chemical modiﬁcation of a poly(methylhydrosiloxane) through alternating sequences of hydrosilylation and alkylation reactions on every monomer unit of the polymer [41]. The polysiloxane backbone is stretching out, upon carrying carbosilane dendrons, from the Gaussian random conformation for the zeroth generation to the almost fully extended rodlike conformation for the second generation, depending on the overcrowding of the branches at the periphery. However, even fully extended polymethylsiloxane polydendrimers prove incapable of the orientation and the liquid crystal formation because of their dynamic ﬂexibility. Dendrimers are also used for chemical modiﬁcation of chitosan, which is a polysaccharide composed of mainly -(1-4)-2-amino-2-deoxy-D-glucopyranose repeating units [42]. The sialic acid-bound chitosan-dendrimer hybrids have the potential for biological purposes because of nontoxic and biodegradable properties of chitosan and of biopharmaceutical advantages of dendrimers. Grayson and Fre´chet [43] have reported the divergent grafting of aliphatic polyester dendrons from a poly(p-hydroxystyrene) backbone. Wyatt et al. [44] have synthesized optically active polydendrimers by the polymerization of binaphthyl poly(benzyl ether) dendrimers. The energy migration from dendritic side chains to the conjugated polybinaphthyl main chain was observed. The increase in dendron generation inﬂuences the thermal transition of the polybinaphthyls. Poly(para-phenylene)s with hydrophobic and hydrophilic pendant moieties have been synthesized as a prototype of an amphiphilic cylinder with the potential to segregate lengthwise [45]. Monomers equipped with unlike Copyright © 2003 by Taylor & Francis Group, LLC

dendrons or combinations of hydrophilic dendron-hydrophobic linear chain and hydrophobic dendron-hydrophilic linear chain were polycondensed with diboronic acid [models (k) and (l) in Fig. 1]. The surface-pressurearea isotherms provide the evidence that these hybrid polymeric amphiphiles segregate lengthwise into hydrophobic and hydrophilic domains. Diblock copolymers composed of polydendrimer and linear styrene polymer [model (m) in Fig. 1] have been synthesized by Sivaniah et al. [46]. In the polydendrimer, the semiﬂuorinated alkane mesogens are attached as threearm monodendrons to the isoprene backbone. The surface topology was reported. Imae et al. [47] have synthesized methacrylate-acrylate diblock copolymers with unlike side chains, where the poly(methacrylate) block is modiﬁed by poly(benzyl ether) dendrons and the side chains of poly(acrylate) block are perﬂuorooctylethers. Copolymers form spherical aggregates with various sizes in solutions and thin ﬁlms at the air–water interface. Further characterization is presently underway.

V. AGGREGATES OF AMPHIPHILIC DENDRITIC POLYMERS Some dendrimers and hybrid copolymers are associated into various molecular assemblies due to their amphiphilic characters. The molecular arrangement of poly(benzyl ether) dendrimer at the air–water interface has been investigated by Saville et al. [48]. The dendrimer forms a bilayer structure. The molecules in the layer next to the water subphase are ellipsoidal in structure due to compression and contain water (about 25% in volume fraction), while the molecules in the layer next to air are spherical and contain no water. Poly(propylene imine) dendrimers, where the terminal groups are modiﬁed with palmitoyl chains, form stable monolayers at the air–water interface [15]. Those adopt a cylindrical shape at the air–water interface: hydrophobic chains are aligned perpendicularly to the interface and the dendritic poly(propylene imine) interior faces the water subphase. In aqueous solutions at pH ¼ 1, dendritic surfactants are self-assembled into small spherical aggregates with the bilayer structure. It was shown from the theoretical calculation of molecular volumes that the dendritic surfactants have the highly asymmetric conformation and the shape of the dendritic poly(propylene imine) interior is distorted within monolayer at the air–water interface and within the aggregates in the solution. These results indicate the high ﬂexibility of the poly(propylene imine) dendrimers. Spreading of a carbosilane dendrimer containing hydroxyethyl terminal groups has been investigated at the air–water interface [49]. The carbosilane dendrimer forms a monolayer, which shows a sharp transition presumably Copyright © 2003 by Taylor & Francis Group, LLC

into the bilayer structure, while the hyperbranched polymer of an identical chemical composition does not show any transition. The monolayer stability and molecular conformation at the air–water interface have been studied for Langmuir ﬁlms formed from dendritic-linear diblock copolymers, poly(benzyl ether) dendrons with linear oligo(ethylene glycol) tails [27]. The copolymers with third- and fourth-generation dendrons form stable Langmuir ﬁlms, but the ﬁfth-generation dendron does not. Longer hydrophilic tails increase the stability of the Langmuir ﬁlms. The molecular area of the dendrons at the air–water interface increases linearly with the molecular weight. It was certiﬁed that the dendritic blocks take a vertically elongated shape at the air–water interface and become ﬂatter as the generation increases. The monolayers of a linear poly(ethylene oxide) block linked to a poly(amido amine) dendron, where terminal groups are modiﬁed with stearic acid, have been investigated by Johnson et al. [30]. The hybrid diblock copolymer intermixes the linear blocks with the poly(amido amine) dendrons at low surface pressure, while it forms the stable, distinct monolayers with a linear block resting in the subphase and stearate groups extending into the air at high surface pressure. Stearate groups form a distinct ordered layer separating from the third-generation poly(amido amine) dendron, whereas those are intermixed with the fourth-generation poly(amido amine) dendron due to the surface curvature of the higher-generation dendron. Moreover, the poly(ethylene oxide) block is intermixed with the water subphase after being kept for at least 10 h. Liebau et al. [50] have recently synthesized dendritic multisulﬁdes of the ﬁrst to ﬁfth generations by the modiﬁcation of poly(propylene imine) dendrons with dialkyl sulﬁde chains. At the air–water interface, the dendritic multisulﬁdes form stable Langmuir monolayers with densely packed alkyl chains pointing to the air and dendron exposed to the water subphase. Langmuir–Blodgett ﬁlms transferred onto a gold surface remain the original densely packed structure. Diﬀerent surface architectures of the same compounds are prepared by solely varying the preparation procedure. Selfassembly of the dendritic multisulﬁdes from a solution onto a gold surface leads to a ﬂattened orientation of the dendrons on it. The formation of the surface-spread dendritic structure can be attributed to the adsorption onto the gold surface of not only the sulﬁde moieties in the alkyl chains but also the tertiary amines in the dendron. The aggregation behaviors of dendrimers and dendritic-linear diblock copolymers as amphiphiles in solutions have been examined. Percec et al. [51] have reported the synthesis and characterization of hyperbranched dendrimeric polyethers with the spacers of alkyl chains and the alkylated phenol chain terminals. The copolymers present the thermotropic transCopyright © 2003 by Taylor & Francis Group, LLC

formation between isotropic phase and enanthiotropic nematic liquid crystalline mesophase. Generation-dependent aggregation of amphiphilic diblock copolymers of polystyrene with poly(propylene imine) dendrimers have been reported by van Hest et al. [25]. The morphological change of aggregates depends on the generation of hydrophilic dendrimer and the pH of solution: block copolymers composed of poly(propylene imine) dendrimers of 4.0, 3.0, and 2.0 generations form spherical micelles, micellar rods, and vesicles, respectively, which are similar in shape but diﬀerent in size than those of traditional surfactant molecules. The block copolymer of the lowest generation shows the inverted micellar behavior. Microphase separation of diblock copolymers consisting of linear polystyrene and carboxylic acid-functionalized poly(propylene imine) dendrimers has been reported by Roma´n et al. [52]. The copolymers are spontaneously self-assembled into microdomains. By increasing the dendrimer generation, the microlattice morphology changes from hexagonally packed cylinders with styrene matrix to lamellar phase. The dendritic structure is sometimes modiﬁed in order to control the morphological behavior. Donnio et al. [53] have functionalized the terminal groups of poly(amido amine) and poly(propylene imine) dendrimers by mesogenic units, which are derived from salicylaldimine bearing one, two, or three terminal aliphatic chains. The compounds exhibit liquid crystalline properties, correlating with the number of terminal chains grafted on the peripheral mesogenic units. The existence of one chain per mesogenic unit makes favorable the parallel arrangement of the molecules and induces smectic mesomorphism. On the other hand, molecules with two or three aliphatic chains take radial dispersion, leading to the formation of columnar structures. Organized ﬁlms of carbosilane liquid crystalline dendrimer with cyanobiphenyl mesogenic groups have been examined at diﬀerent temperatures and ﬁlm thicknesses [13]. Rectangular and hexagonal lattices are found in the single layer. With increasing ﬁlm thickness, smectic layers are formed and, then, domains consist of aggregates of ﬂat-on lying. Edge-on standing smectic layers are found in thick ﬁlms. The domains exhibit the layered structure of diﬀerent thicknesses and orientations. Height variation of domains caused by anisotropic changes of lattices of the smectic layers occurs with the change of temperature. The isotropization temperature increases with increasing the generation. The surface topology has been investigated for diblock copolymers composed of linear polystyrene and polydendrimer that have semiﬂuorinated alkane mesogens attached as three-arm monodendrons to the isoprene backbone [46]. The amphiphilic macromolecules in the smectic phase separate Copyright © 2003 by Taylor & Francis Group, LLC

into diblock copolymer microstructures. There are periodic surface structures, so-called domes that arise from the arrangement of the semiﬂuorinated mesogens at the polymer surface. Imae et al. [54] have reported the formation of organized adsorption layers by amphiphilic surface-block poly(amido amine) dendrimers composed of two hemispheres with hydroxyl and n-hexyl terminals. On solid substrates, unlike which the adsorption ﬁlm of a symmetric poly(amido amine) dendrimer is rather ﬂat, the surface-block dendrimer displays the layer texture, indicating the formation of bilayers and their accumulation, as shown in Fig. 4. The bilayer is formed by pairing between hydrophobic terminals of two dendrimers (see Fig. 5). The surface of the adsorption ﬁlm takes hydrophilic character, suggesting that the hydrophilic hydroxyl terminals face the solution. The adsorption is more abundant by the third-generation dendrimer than by the fourth-generation dendrimer, in

FIG. 4 Atomic force microscopic images and their section analyses of 15 min adsorption ﬁlms on mica surface from aqueous 0.01 wt % solutions of the thirdgeneration surface-block poly(amido amine) dendrimers. Left, hydroxyl/n-hexyl terminated dendrimer; right, N-acetyl-D-glucosamine/n-hexyl terminated dendrimer. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 A schematic model of coupled adsorption ﬁlm of a surface-block hydroxyl/ n-hexyl terminated poly(amido amine) dendrimer on substrate

agreement with the generation dependence of the cmc as seen in Table 1. Similar adsorption behavior is also observed by a surface-block poly(amido amine) dendrimer with amino and n-hexyl terminals but not by a dendrimer with N-acetyl-D-glucosamine and n-hexyl terminals (see Fig. 4). Dendrons are focused as building blocks of supramolecular or selfassembled architectures. The role for controlling the architectural shape through the self-assemblies from tapered and conical nanodendrons has been reviewed [55]. Tapered nanodendrons are associated into cylinders and then hexagonal columns, that is, hexagonal liquid crystal, while conical dendrons form spheroidal assemblies in dilute solutions and cubic phase in concentrated solutions. Poly(benzyl ether) dendrons with a carboxylate anionic focal point are self-assembled through central trivalent lantanide cations (Er3+, Tb3+, and Eu3+) [56]. This self-assembly is applicable in the design of energy-harvesting devices and ampliﬁers for ﬁber optics. The complexes show the dependence of luminescence activity on the size of the dendritic shell. The observed luminescence enhancement is attributed to the large antenna eﬀect and the site isolation eﬀect of poly(benzyl ether) dendron framework for a lantanide cation within a dendritic sphere, preventing the mutual interaction of lantanide cations and decreasing their rate of self-quenching. Characteristic and functional dendrimers can be also achieved by the molecular assemblies of simple dendrimers. A novel architecture of dendrimers, a core-shell tecto-(dendrimer), has been synthesized [57]. In the tecto-(dendrimer), a poly(amido amine) dendrimer molecule as a core is covalent-bonding with a shell of other poly(amido amine) dendrimers. The dimensions increase as a function of the sum of core-shell tecto-(dendrimer) generation.

VI. CONCLUSIONS Dendrimers, named after their dendritic structure, are highly branched polymers, which have the strictly controlled chemical structure and geoCopyright © 2003 by Taylor & Francis Group, LLC

metric arrangement of layer moieties. The main characteristics of the dendritic structure are microcavity for encapsulating small molecules and the large number of terminal groups for acting as functional sites. Dendrimers may be conspicuous by these characteristics for the many applications in industrial, cosmetic, and pharmaceutical ﬁelds. In addition, the utilization of dendrimers as a building block for organized architectures is possible by the introduction of amphiphilicity in their chemical structure. In this section, the structures and properties of amphiphilic dendritic polymers were reviewed. The amphiphilicity is accomplished by the derivation of unlike blocks in concentric dendrimers. Copolymers of dendritic blocks with linear polymers are also amphiphilic. Many investigations have reported the synthesis and characterization of amphiphilic dendritic polymers and the architectures by them in solutions, at the air–water interface, and on the solid surfaces. Some applications of amphiphilic dendritic polymers were also reported. The dendritic amphiphiles behave and are associated like traditional surfactants and linear block copolymers. However, we expect that future research will demonstrate more the predominance of dendritic amphiphiles over traditional surfactants and linear block copolymers. Especially, the water-soluble and nontoxic dendronized amphiphilic compounds are useful for biomedical applications, and studies must be carried out for determining their applicability.

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13 Polymer/Surfactant Systems RAOUL ZANA

Institut C. Sadron, CNRS, Strasbourg, France

GLOSSARY ( 0 ) ¼ ionization degree of a free (polymer-bound) micelle. P ¼ neutralization degree of a poly(acid). cac: critical aggregation concentration. cmc: critical micellization concentration. C 2: concentration at which the polymer is saturated by bound surfactant. Cf ðCb Þ ¼ concentration of free (polymer-bound) surfactant. Cm EOx: nonionic monoalkylether ethoxylated surfactant; x ¼ number of ethylene oxide units in the headgroup; m ¼ alkyl chain carbon number. DeTAB, DTAB, TTAB, CTAB, OTAB: decyl, dodecyl, tetradecyl, hexadecyl, and octadecyl trimethylammonium bromides. DTAC, CTAC: dodecyl and hexadecyltrimethylammonium chlorides. DPC: dodecylpyridinium chloride. EHEC, HM-EHEC: ethylhydroxyethylcellulose, hydrophobically modiﬁed EHEC. HEC, HM-HEC: hydroxyethylcellulose, hydrophobically modiﬁed HEC. I1 =I3 ¼ pyrene polarity ratio. N: number of surfactants making up a micelle or a polymer-bound aggregate. NaPP, NaPAA, NaPSS: sodium poly(phosphate), poly(acrylate), poly(styrenesulfonate). PAA, PMA: poly(acrylic acid), poly(methacrylic acid). PDADMAC: poly(diallyldimethylammonium chloride). PEO, PPO: poly(ethylene oxide), poly(propylene oxide). PNIPAM: poly(N-isopropylacrylamide). PSX: poly(maleic acid-alt-alkylvinylether) copolymer; X ¼ alkyl chain carbon number. PVP: poly(vinylpyrrolidone). SDS: sodium dodecylsulfate.

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I. INTRODUCTION Surfactants and water-soluble polymers are present together in many formulations and industrial processes in order to boost the properties of the surfactant by the added polymer, or vice versa (synergism), and also in order to produce properties that neither the surfactant nor the polymer possesses when used alone. The applications and uses of polymer/surfactant systems are numerous: rheology control, solubilization, separation, control of surfactant mildness, drug delivery, surface conditioning, etc. and have been reviewed [1]. Besides, interesting changes of properties of both the polymer and surfactant often occur when these two types of compounds are used together. This, of course, has greatly stimulated the interest of academic circles in polymer/surfactant systems. It should therefore not come as a surprise that the study of polymer/surfactant interactions is a very actual topic in surfactant science. Papers on mixed polymer/surfactant systems are being published at a high rate and this ﬁeld has been recently reviewed. The volumes edited by Goddard and Ananthapadmanabhan [2], and Kwak [3] on polymer/surfactant systems, are highly recommended for gaining a good introduction in the ﬁeld. Due to the large number of available water-soluble polymers and surfactants, the number of polymer/surfactant systems that can be investigated is nearly inﬁnite. This chapter considers only systems where interaction between surfactant and polymer means that the surfactant binds noncovalently (by electrostatic or hydrophobic interactions) to the polymer, i.e., only associative systems are considered, when using the terminology introduced by Picullel and Lindman [4]. There are indeed a number of systems where the interaction is repulsive, of the segregative type [4]. Such systems at some point separate into two phases, one concentrated in surfactant, the other in polymer. The early studies of polymer/surfactant systems seemed to indicate that neutral polymers mostly interact with anionic surfactants, their interaction with nonionic and cationic surfactants being very weak or altogether negligible, irrespective of the surfactant chain length, i.e., hydrophobicity. Likewise, for polyelectrolyte/surfactant systems, the early results indicated the absence of interaction between polyelectrolytes and surfactants of like charge due to the strong electrostatic repulsion between the two species. The advent of water-soluble hydrophobically modiﬁed polymers and the extension of the investigations to systems containing such polymers modiﬁed this simple picture. Thus, it was found that neutral polymers could be hydrophobically modiﬁed to an extent that they interact more or less strongly with all types of surfactants, the hydrophobic interaction between polymer hydrophobes and surfactant alkyl chains then being predominant. Copyright © 2003 by Taylor & Francis Group, LLC

Likewise polyelectrolytes can be hydrophobically modiﬁed to an extent that they bind surfactants of like charge, the attractive hydrophobic interaction then overcoming the electrostatic repulsion. A very large number of parameters can be acted upon when studying polymer/surfactant systems. Some of these parameters concern the polymer: nature (ionic, nonionic, zwitterionic), structure of the repeat unit, molecular weight, and hydrophobicity. Several other parameters concern the surfactant: nature of the headgroup (ionic, nonionic, or zwitterionic) and of the counterion for ionic surfactants, length of the alkyl chain, structure of the surfactant: conventional or dimeric (Gemini). There are also a number of external parameters, the two most important ones being the ionic strength (especially important in the case of systems involving charged polymers) and the temperature [in the case of polymers containing poly(ethylene oxide) segments]. A survey of the literature and the content of the next section show that the polymer hydrophobicity is the most important parameter in determining the properties of polymer/surfactant systems. The natures of the polymer repeat unit and that of the surfactant headgroup (charged or uncharged) come next. As illustrated below, the polymer hydrophobicity determines whether the polymer interacts at all with a given surfactant and, in the case of interaction, aﬀects the nature of the interaction (cooperative or noncooperative). On the other hand, the electrical charge on the polymer repeat unit and on the surfactant headgroup largely determines the strength of the interaction, that is, the thermodynamics of the binding. A large number of studies dealing with polymer/surfactant systems have been reported since the publication of Kwak’s volume in 1998 [3]. To keep this chapter to a reasonable length, its content has been restricted to papers and results that illustrate the diﬀerent types of behaviors reported in the literature. Some important aspects of polymer/surfactant systems that have been well covered in the recent literature are not examined here, such as, for instance, phase diagrams that have been much studied by the group at Lund [5]. Protein/surfactant systems are also not included in this chapter. This topic has been recently reviewed [6,7]. However, this chapter examines several aspects of polymer/surfactant systems that have yet to be reviewed. The chapter is organized as follows. After this Introduction comes a section on the eﬀect of the polymer hydrophobicity on polymer/surfactant interactions, which is the most important part of this chapter. The eﬀect of the surfactant headgroup (in the case of hydrophilic polymers) is considered in Section III. Section IV reviews the microstructural aspects of polymer/ surfactant solutions. Sections V, VI, and VII examine solubilization in polymer-bound surfactant aggregates, dynamics of polymer-bound surfactant aggregates, and polymer/surfactant interactions at interfaces. Section VIII reviews structural aspects of polyelectrolyte/oppositely charged surfactant Copyright © 2003 by Taylor & Francis Group, LLC

complexes in both the gel and the solid states. Indeed mesomorphic ordering and precipitation often occur in polymer/oppositely charged surfactant systems. In fact, precipitation is a major obstacle when studying these systems. Nevertheless, the mesomorphic order observed in many polymer/surfactant systems in the gel state and in the solid state is extremely interesting and represents a whole new ﬁeld of investigation. Only a small fraction of the reported papers is reviewed in each section in order to keep this chapter to a reasonable length. The papers reviewed have been selected in order to illustrate the diﬀerent types of behavior reported in each section. Preference has been given to recent studies to provide easier access to previous investigations. Nevertheless, the views of the author may have biased the selection process. Apologies are presented to the authors of the many papers that are not cited.

II. POLYMER–SURFACTANT INTERACTIONS: EFFECT OF THE POLYMER HYDROPHOBICITY The study of the eﬀect of the polymer hydrophobicity implies the availability of series of homologous water-soluble polymers where, for instance, the repeat unit contains an alkyl chain whose length is progressively increased, without any other change of the polymer chemical structure. Such series are not easily found with homopolymers. Possible polymer series are the poly(2alkylacrylic) acids or the poly(alkylene)oxides. Unfortunately, with the second series only poly(ethylene oxide) (PEO) and low-molecular-weight poly(propylene oxide) (PPO) are water-soluble. Copolymers where one monomer bears a hydrophobic group of adjustable size oﬀer more possibilities. However, the distribution of the hydrophobic monomer along the polymer chain (at random or by short or long sequences) becomes an additional parameter as it can aﬀect the binding. Alternating copolymers avoid this diﬃculty. The most comprehensive studies of the eﬀect of the polymer hydrophobicity on polymer/surfactant interactions used the alternating copolymers poly(maleic acid-alt-alkylvinylether) (see Scheme 1; PD ¼ polymerization degree.) The hydrophobicity can be ﬁnely tuned by adjusting the neutralization degree P of the maleic acid moiety (P ¼ 1 when the two acidic functions of the maleic acid are neutralized) and/or the carbon number X of the alkylvinylether moiety. This section is largely based on results reported for these copolymers, which are referred to as PSX. The value of the pyrene polarity index I1/I3, ratio of the ﬂuorescence intensities of the ﬁrst and third peaks in the ﬂuorescence emission spectrum of pyrene, provides an easy way to characterize the environment of pyrene in polymer solutions. Values of I1 /I3 close to that in water, i.e., 1.8–1.9, are Copyright © 2003 by Taylor & Francis Group, LLC

Scheme 1

indicative of strongly hydrophilic polymers that do not interact with pyrene [8–14]. Values between 1.1 and 1.4 are typical for pyrene solubilized in micelles of conventional surfactants [8]. They also characterize strongly hydrophobic polymers (polysoaps) capable of forming micellelike hydrophobic microdomains in solution and in which pyrene can be solubilized [9–14]. Intermediate values of I1 /I3 correspond to polymers of intermediate or low hydrophobicity that can bind pyrene on their hydrophobic moiety [12,13]. This may possibly result in the formation of hydrophobic microdomains. Pyrene ﬂuorescence probing showed that PS1, PS2, and poly(acrylic acid) (PAA), even at aP ¼ 0.0, and PEO are strongly hydrophilic [9–14], whereas PSX with X 6 are strongly hydrophobic [9,11,13]. PS4 [11–13] and poly(methacrylic acid) (PMA) [14] show an intermediate behavior, being able to form hydrophobic microdomains at low pH or P and behaving as strongly hydrophilic polymers at high pH or P. A survey of the reported results shows that as the polymer hydrophobicity increases the interaction between polymer and surfactant becomes stronger (larger binding constant of the surfactant to the polymer). Besides, the nature of the binding changes from strongly cooperative for strongly hydrophilic polymers to anticooperative or noncooperative for strongly hydrophobic polymers. As is shown below this has an enormous impact on many properties of the systems. We shall successively examine how the binding isotherm of a surfactant to a polymer, the surfactant critical aggregation concentration (CAC), the surfactant aggregation number, and the microviscosity of the polymer-bound aggregates are aﬀected by the hydrophobicity of the polymer.

A. Binding Isotherms The binding isotherms represent the variation of the amount of surfactant bound to the polymer with the concentration of free surfactant, Cf. The amount of bound surfactant is expressed in mole of surfactant per mole Copyright © 2003 by Taylor & Francis Group, LLC

of polymer repeat unit or in mole of surfactant per gram of polymer. The shape of the binding isotherm depends on the nature of the binding process (cooperative or anticooperative). The analysis of the binding isotherm with an appropriate theory yields the values of the binding constant and of the cooperativity parameter [3].

1. Strongly Hydrophilic Polymers Figure 1 shows that the shape of the binding isotherms of dodecyltrimethylammonium chloride (DTAC) to PS1, i.e., a polyelectrolyte/oppositely charged surfactant system, is independent of the polymer degree of neutralization, P. [12]. The binding starts at a surfactant concentration above the critical aggregation concentration (CAC) and the amount of bound surfactant increases rapidly with Cf. This rapid increase is indicative of a cooperative binding, i.e., meaning the surfactant binds to the polymer under the form of micellelike aggregates. At higher values of Cf the amount of bound surfactant levels out, indicating a saturation of the polymer. For the system in Fig. 1 the binding isotherm is nearly independent of P, except for the two extreme values 0.0 and 1.0. The cac is much smaller than the surfactant

FIG. 1 Binding isotherms for the PS1/DTAC system at polymer degree of neutralization P ¼ 0 (*); 0.1 (!); 0.2 (&); 0.4 (!); and 1.0 (~) from potentiometric measurements using a surfactant ion-speciﬁc electrode ( ¼ Cb =iCP ; i ¼ ionization degree of the polymer; CP ¼ polymer concentration in acid equivalent per liter ¼ 4 meq; T ¼ 258C.. (From Ref. 12 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

cmc (0.7–0.8 mM against 20 mM) [12], due to a strong electrostatic interaction between PS1 and DTAC. Figure 2 shows that the binding isotherm of sodium dodecylsulfate (SDS) to the neutral polymer PEO, i.e., a neutral polymer/ionic surfactant system, is also cooperative [16]. At high concentrations of free surfactant, the isotherm shows a decrease in the amount of bound surfactant because the experiments were performed in the absence of a swamping electrolyte [16,17]. In the presence of salt, which suppresses the Donnan eﬀect, this decrease is replaced by a leveling out [18]. The polymerization degree PD of the polymer has very little eﬀect on the binding isotherm as long as PD remains high enough [19,20]. However, at very low PD, the cac increases (see below) and the cooperativity decreases as the PD decreases [19–21]. This is illustrated in Fig. 3 for the sodium polyphosphate (NaPP)/dodecylpyridinium chloride (DPC) system [19]. The slope of the binding isotherm is seen to decrease with the PD, indicating a lower binding cooperativity. The cooperativity of the binding is explained by modeling the polymer as a succession of binding sites that are free or occupied by one bound surfactant. An oncoming surfactant has a stronger tendency to bind to a free site adjacent to an occupied site than to a free site adjacent to free sites. Indeed, in the ﬁrst case it interacts with the polymer and with the bound surfactant. This results in a larger decrease of free energy and in the formation of micellelike aggregates of surfactant on the polymer.

FIG. 2 Binding isotherm for the PEO/SDS system from equilibrium dialysis experiments (y ¼ concentration of bound SDS in mM per gram of PEO. (From Ref. 16 with permission of the American Chemical Society.)

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FIG. 3 Binding isotherms for the NaPP/DPC system from potentiometric measurements in the presence of 10-mM NaCl, using a surfactant ion-speciﬁc electrode, for NaPP of diﬀerent degrees of polymerization as indicated in the inset ( : same deﬁnition as in Fig. 1; the DP of the Kurol polymer is of several tens of thousands; T ¼ 308C. (From Ref. 19 with permission of Springer-Verlag GmbH.)

2. Strongly Hydrophobic Polymers Figure 4 shows the binding isotherms of DTAB to the strongly hydrophobic PS6, PS10, and PS16 [11]. The binding is strong and nearly quantitative even at the lowest concentration of surfactant investigated. The CAC is no longer seen, and the isotherm shape indicates a noncooperative or anticooperative binding. This behavior is due to the fact that the PSX in Fig. 4 are capable of forming hydrophobic microdomains in the absence of surfactant. Thus an oncoming surfactant cannot distinguish whether a given microdomain contains one or no bound surfactant and binds to any microdomain. This results in a loss of the binding cooperativity. Figure 4 shows that the strength of the binding increases with the PSX alkyl chain length, i.e., with the tendency of the polymer to form microdomains.

3. Polymers of Intermediate Hydrophobicity The results are illustrated with three types of systems. 1. The ﬁrst example concerns a neutral copolymer/ionic surfactant system and a hydrophobically modiﬁed polymer/ionic surfactant system where binding is cooperative or noncooperative depending on the surfactant concentration. Figure 5 shows the variations of the fraction of SDS bound to Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Binding isotherms of DTAB to PS6 (~), PS10 (*), and PS16 (*), in the presence of 5-mM KBr at 258C from potentiometric measurements ( : same deﬁnition as in Fig. 1; P ¼ 1.0; same polymer concentration as in Fig. 1. (From Ref. 11 with permission of the American Chemical Society.)

FIG. 5 Variation of the fraction of SDS bound to EHEC (*) and to HM-EHEC (^,^), with the total SDS concentration from potentiometry with surfactant ionspeciﬁc electrode and NMR self-diﬀusion. (From Ref. 22 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

ethylhydroxyethylcellulose (EHEC) and to hydrophobically modiﬁed EHEC (HM-EHEC) against the total concentration of SDS [22]. The binding to EHEC is cooperative with a cac value of about 1 mM (cmc ¼ 8 mM). The binding to HM-EHEC is seen to be noncooperative at low SDS concentration and cooperative at high SDS concentration. In fact, the two binding curves become coincident at a concentration of about 3 mM. A similar behavior has been observed for the poly(vinyl alcohol-co-vinyl acetate)/CTAB system where the vinyl acetate repeat units are hydrophobic [23]. The binding is noncooperative or slightly cooperative at low concentrations of bound surfactant, Cb, and becomes highly cooperative at higher values of Cb. 2. The second example is that of a polyelectrolyte/oppositely charged surfactant system where the nature of the binding is adjusted by changing the polyelectrolyte degree of neutralization. Figure 6 shows the binding isotherms of DTAB to PS4. Binding is noncooperative for P 0.25 and cooperative for larger values of P. Recall that this polymer forms microdomains up to a value of P close to 0.25 [9]. This result is very important because it directly relates the nature of the binding to the presence or absence of microdomains in the polymer solution, in the absence of surfactant. 3. The third type of system is similar to the second one but it involves a series of fully neutralized copolymers, the poly(sodium acrylate-sodium alkylacrylate), and the change of cooperativity is achieved by increasing the length of the alkyl group [24]. Sasaki et al. showed that the binding of

FIG. 6 Binding isotherms for the system PS4/DTAB at polymer degree of neutralization P ¼ 0 (*); 0.25 (!); 0.50 ( ); 0.75 (~); and 1.0 () from potentiometric measurements using a surfactant ion-speciﬁc electrode ( ¼ same deﬁnition as in Fig. 1; T ¼ 258C; polymer concentration same as in Fig. 1, in the presence of 5-mM KBr). (From Ref. 11 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

DPC to poly(sodium acrylate-sodium methylacrylate) and poly(sodium acrylate-sodium ethylacrylate) was strongly cooperative. The binding to poly(sodium acrylate-sodium propylacrylate) was weakly cooperative. The binding to poly(sodium acrylate-sodium butylacrylate) was anticooperative. Two additional remarks must be made. The ﬁrst remark concerns the surfactant concentration C2 where the binding isotherm levels out. Other methods such as surface tension and conductivity also permit the determination of C2. This concentration is often interpreted as corresponding to that where free micelles start forming in the system. In fact, several reports have shown that free micelles can already form at a concentration lower than C2 [17,25–28]. The second remark concerns the analysis of the binding isotherms. The available theories have been reviewed by Shirahama [29] and are not considered here. It is only recalled that in many instances the binding isotherms were analyzed using Satake and Yang’s treatment [30], which only considers nearest-neighbor interactions between surfactants bound to sites on the polymer. The analysis of the data yields the values of the binding constant K of a surfactant to an empty site and of the cooperativity parameter u. This parameter is related to the free energy gained by the system when a surfactant binds to a site adjacent to an occupied site with respect to that when it binds to a site adjacent to empty sites.

B. Critical Aggregation Concentration The cmc is probably the most important characteristic of a surfactant. The CAC is also an extremely important characteristic of a polymer/surfactant system. It gives information on the strength of the polymer/surfactant interaction, i.e., the aﬃnity of the surfactant for the polymer. Measurements of CAC are, of course, restricted to systems with hydrophilic or weakly hydrophobic polymers. Surface tension, conductivity, and potentiometry with surfactant ion-speciﬁc or counterion-speciﬁc electrodes can be used for this purpose, depending on the nature of the polymer and surfactant. A suﬃcient but not necessary condition for the existence of interaction between a polymer and a surfactant is that CAC < CMC [2,3]. For a few neutral polymer/nonionic surfactant systems where interactions have been shown to occur, the cac was found to diﬀer very little from the cmc [31]. This behavior has been explained on a theoretical basis [32]. In the vast majority of the systems where the surfactant binds to the polymer the condition CAC < CMC is fulﬁlled. Nevertheless, the diﬀerence between CAC and CMC can be rather small. The CAC is independent of the polymer degree of polymerization except for very low value of the PD [19–21]. This is illustrated in Fig. 3 for the polyelectrolyte/oppositely charged surfactant system NaPP/DPC, and in Copyright © 2003 by Taylor & Francis Group, LLC

Table 1 for the neutral polymer/ionic surfactant system PEO/SDS. For polyelectrolyte/oppositely charged surfactant systems the CAC increases upon addition of a salt having the same counterion as the surfactant. This can be viewed as a result of a competition between surfactant ions and coions of the added electrolyte for the polymer binding sites. Thus for a given ionic surfactant the variations of the CAC and of the CMC with the concentration of added salt are opposite. It is noteworthy that the addition of salt to a polyelectrolyte/oppositely charged surfactant system may in some instances prevent the precipitation of a polymer/surfactant complex and therefore permit the study of the system. The CAC increases with the concentration of the polyion [33,34]. The variations of the CAC and of the CMC with the surfactant alkyl chain length are quantitatively very similar, yielding the same value of the free energy increment for the transfer of a surfactant from the aqueous phase to the micelles, whether free or polymer-bound [35,36]. This result indicates that the surfactant alkyl chains are in contact with each other much in the same manner in free and polymer-bound aggregates [35,36]. These points are reviewed in Ref. [3] and are not discussed further here. Table 1 lists the CAC and CMC values of a number of polymer/surfactant systems [12,21,37–39]. As expected, the ratio CAC/CMC is much lower

TABLE 1 Values of the CMC of Surfactants in the Absence of Polymer, of the CAC in Several Polymer/Surfactant Systems, and of the Free Energy of Interaction Surfactant Polymer C12 EO6 C12 EO8 SDS SDS SDS SDS DTAC DTAC SDeSulc

PAA at low pH PAA at low pH PEO (MW ¼ 20,000)a PEO (MW ¼ 6,000)a PEO (MW ¼ 1,000)a PAA at pH ¼ 2:4b PS1 at P ¼ 1:0 PS4 at P ¼ 1:0 PMeVPCc

CMC (mM) CAC (mM) Gint (kJ/mol) Ref. 0.07 0.08 7.9 7.9 7.9 1 16 16 32

0.05 0.063 4.3 4.7 5.8 2 0:8 0:2 0.29

0:85d 0:60d 2:7e 2:3e 1:4e 7:1e 13:2e 19:3e 20:7e

[37] [37] [21] [21] [21] [38] [12] [12] [39]

MW ¼ polymer molecular weight. In the presence of 0.01M NaCl. c SDeSul ¼ sodium decanesulfonate; PMeVPC ¼ poly(1-methyl-4-vinylpyridinium chloride). Results in the presence of 0.0212M NaCl. d Calculated using Eq. (1). e Calculated using Eq. (2) with ¼ 0 ¼ 0.25. a

b

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for polyelectrolyte/oppositely charged surfactant systems than for neutral polymer/ionic surfactant systems due to the strong electrostatic interaction present in the ﬁrst type of system. Equations (1) and (2) give the expressions of the energy of interaction Gint for polymer/nonionic surfactant and polymer/uni-univalent ionic surfactant systems, respectively. Gint ¼ RT logðCAC=CMCÞ

ð1Þ

and Gint ¼ RTð2 0 Þ log CAC RTð2 Þ log CMC

ð2Þ

In Eq. (2) and 0 are the values of the ionization degree of free and polymer-bound micelles, respectively. It is therefore, at least in principle, possible to obtain the values of Gint from those of the CMC, CAC, and ionization degrees. Unfortunately, the ionization degrees are rarely known with suﬃcient accuracy. Some values for systems with neutral polymers have been obtained from potentiometric measurements with a counterion-speciﬁc electrode [17,26–28] and conductivity [40]. The results in Fig. 7 for the PVP/SDS system show that the bound aggregates are more ionized than the free micelles and that 0 decreases rapidly as the surfactant concentration is increased [17]. The variation of 0 with the surfactant concentration is larger for slightly more hydrophobic polymers such as EHEC or PPO [26]. This behavior reﬂects the smaller size and, thus, the larger ionization degree of the bound aggregates at surfactant concentrations above the cac but still close to

FIG. 7 Variation of the ionization degree of polymer-bound surfactant aggregates in the PVP/SDS system from potentiometric measurements using a Na+-speciﬁc electrode. (From Ref. 17 with permission of the Royal Society of Chemistry.) Copyright © 2003 by Taylor & Francis Group, LLC

this value (see Section II.C). These variations of 0 are extremely important with regards to the details of the process by which surfactant aggregates form on polymers: progressive growth of many aggregates or successive formation of fully grown aggregates one at a time. This problem is discussed in Section II.C. Ionization data for polyelectrolyte/oppositely charged surfactant systems are rather scarce. However, it has been shown by means of ﬂuorescence probing that the surfactant counterions are completely excluded from the surface of polyelectrolyte-bound surfactant aggregates [12,41]. In view of the rapid variations of 0 with the surfactant concentration, the values of the free energy of interaction Gint listed in Table 1 were all calculated assuming ¼ 0 ¼ 0:25 [17,26–28,40]. As expected, the magnitude of Gint is smaller for systems with neutral polymers than with charged polymers, the diﬀerence being mainly due to the electrostatic interactions present in the second type of systems. The diﬀerence in values of Gint for the PS1/DTAC and PS4/DTAC systems is remarkable. It reﬂects the hydrophobic interactions between the surfactant dodecyl chains and the butyl chains of PS4.

C. Aggregation Number (Size) of Polymer-Bound Surfactant Aggregates Many reports deal with the aggregation number of the bound surfactant aggregates—that is, the number N of surfactants making up a bound aggregate. Steady-state and time-resolved ﬂuorescence quenching techniques (SSFQ and TRFQ, respectively) [42] were used in most of these studies. Indeed, the systems are complex and interactions often too strong for applying scattering techniques. Fluorescence quenching techniques require the solubilization of a ﬂuorescent probe and a quencher in the surfactant aggregates [42]. Several conditions must be fulﬁlled for obtaining reliable values of N. The conditions are more stringent for SSFQ than for TRFQ. A recent discussion points out some of the diﬃculties associated with such measurements [43,44]. An additional diﬃculty may arise with polymer-bound surfactant aggregates. It is associated with the small value of the quenching rate constant of the probe ﬂuorescence by the quencher within the aggregates, caused by the high microviscosity of the bound aggregates (see Section II.D). Last, the measurements must be restricted to the range where the investigated system contains only bound aggregates and no free micelles; that is the surfactant concentration must be below the critical value C2. Indeed, if this condition is not met, the measured aggregation number is a complex average between the N-values of free and bound micelles and has little meaning. Unfortunately, it is diﬃcult to know whether the required conditions were fulﬁlled in many of the reported studies. Copyright © 2003 by Taylor & Francis Group, LLC

A survey of the literature shows that the reported values of N depend mostly on the hydrophobicity of the polymer and on whether the polymer is neutral or electrically charged.

1. Strongly Hydrophilic Polymers (a) Neutral Polymer/Surfactant Systems. Several neutral polymer/ionic surfactant systems have been investigated [21,45–50], the PEO/SDS [21,48–50] and PVP/SDS [21,47,48] systems being the most investigated ones. All investigations yielded N-values that are smaller for polymerbound aggregates than for free micelles. They also show for the bound aggregates an increase of N with increasing surfactant concentration and decreasing polymer concentration. However, Gilanyi and Varga [49] showed that the dependence of N on the polymer concentration disappears when N is plotted against the concentration of free surfactant. This is illustrated in Fig. 8 for the PVP/SDS system [49]. This observation is explained qualitatively on the basis of the known dependence of the free energy of micelle formation on the ionic strength, the latter being determined by the amount of free ions (free surfactant ions and counterions) [49]. The increase of N with the surfactant concentration explains the decrease of the ionization degree of the polymer-bound aggregates upon increasing surfactant concentration seen in Fig. 7. The results in Figs. 7 and 8 suggest that in a neutral polymer/ionic surfactant system, such as the PVP/SDS

FIG. 8 PVP/SDS system: variation of the aggregation number of the polymerbound aggregates with the concentration of free surfactant at polymer concentration 0.2 % (,&); 0.4 % (*); 0.6 % (þ); and 0.8 % (&). (From Ref. 49 with permission of the American Chemical Society.)

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system, many polymer-bound aggregates form on the polymer above the CAC and grow simultaneously as the surfactant concentration is increased. Two studies concern nonionic polymer/nonionic surfactant systems: the PAA/C12EOx [51] and the agarose gel/C12EOx [52] systems with x ¼ 6, 8, 10. In both instances the values of N were found to be equal to or smaller than those for free micelles. The value of N was found to be the same for C12EO8 in the presence and absence of PEO (MW ¼ 20,000) up to a temperature of 658C [53]. However, light scattering detected large clusters of micelles of C12EO8 sited within the polymer coil when using a PEO of very high molecular weight (about 600,000) [54]. (b) Polyelectrolyte/Oppositely Charged Surfactant Systems. These systems have also been much investigated. The errors affecting the N-values can be rather large, because of the fairly low values of the maximum polymer and surfactant concentrations used in the experiments in order to avoid precipitation. Results concerning the reported values of N are summarized below. 1. N has been found to be independent of the concentration Cb of bound surfactant [12,33,55–57]. This behavior is illustrated in Fig. 9 for the PS1/DTAC system in the whole range of P-values and/or the PS4/ DTAC system at P 0.5, when PS4 behaves as a hydrophilic polyelectrolyte. The constancy of N indicates that the surfactant binding to hydrophilic polyions results in the formation of aggregates of constant composition and, thus, involving a constant length of polyion chain, the number of aggregates increasing with Cb. This behavior suggests that once a surfactant has become bound to a polyelectrolyte site, it acts as a nucleus for the formation of a full surfactant aggregate. In other words, the aggregates would form one after the other. This behavior is very diﬀerent from that for the neutral polymer/ionic surfactant systems. It may reﬂect diﬀerences in the cooperativity parameter in the two types of systems. An increase of N with P was also reported for the PAA/TTAB system [55]. The N-values were much larger than expected from the analysis of the surfactant binding isotherms on the basis of Satake and Yang’s treatment [30]. The authors conclude that conformational eﬀects, not taken into account in this theory, may be involved. 2. The diﬀerence in behavior for the PS1/DTAC and PS4/DTAC systems was attributed to the hydrophobic interaction between the butyl chain of PS4 and the surfactant dodecyl chain [12]. The bound surfactant aggregates in the PS4/DTAC system are similar to mixed micelles of two surfactants, one with a dodecyl chain and the other with a butyl chain. 3. The N-values for polyelectrolyte-bound aggregates increase with the surfactant chain length as in polymer-free systems [56]. However, they

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FIG. 9 Variation of the aggregation number of the polymer-bound surfactant aggregates in the PS1/DTAC system (top) and in the PS4/DTAC system (bottom) at diﬀerent neutralization degrees P of the polymer as indicated in the ﬁgure, with the concentration of bound surfactant at 258C. (From Ref. 12 with permission of the American Chemical Society.)

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increase with temperature [58] and are independent of the nature of the surfactant counterion [33,56] and of the concentration of added salt [57]. All these results are in contrast with those for pure (polyelectrolyte-free) surfactant solutions. 4. The bound aggregates are relatively polydisperse with /N-values ranging between 0.3 and 0.7 ( ¼ standard deviation of the distribution of aggregation numbers) [56,58,59]. 5. The values of the aggregation number of the bound aggregates available for a variety of systems show an important eﬀect of the polyelectrolyte nature (charged group, pendant chain, and backbone). They permit a comparison of values of N for polymer-bound aggregates and free micelles [12,33,55–60]. Thus, the N-values in the PS1(P ¼ 1.0)/DTAC [12], NaPAA/DTAB [33,56], sodium hyaluronate/DTAB [59], and sodium carboxyamylose/CTAB [60] systems are all close to those for free micelles. The polyelectrolytes in these systems are all highly hydrophilic. On the contrary, the N-values in the PS4(P ¼ 1.0)/DTAC [12] and NaPSS/DTAB or CTAB [33] are smaller than in the absence of polyelectrolyte. PS4(P ¼ 1.0) and NaPSS do behave like hydrophilic polyelectrolytes. Nevertheless, they already show some hydrophobicity, which is due to the presence of the butyl chain [12] and phenylene group [61,62], respectively. A partial penetration of the polymer chain in the micelles would result in lower N-values [58]. Last, the N-values in the sodium polyvinylsulfate/DTAB and sodium dextransulfate/DTAB systems are larger than for pure DTAB micelles [41,58]. This result was interpreted as reﬂecting the speciﬁc nature of the sulfate group [58], similarly to the way the counterion nature can strongly aﬀect micelle aggregation numbers. Indeed, in polymer-bound surfactant aggregates the surfactant counterions are expelled from the aggregate surface and replaced by polyelectrolyte charged groups, that act as counterions [12,41]. 6. In the NaPAA/DTAB or CTAB systems, addition of salt brings about phase separation in two liquid phases [33]. The values of N in the two phases were almost equal, and the eﬀect of the surfactant counterion and chain length was the same as in monophasic systems. 7. Two other studies relate to aggregation numbers in polyelectrolyte/ surfactant systems. For the NaPSS/DTAB system crude measurements yielded rather low values of N, between 7 and 10 [63]. N-values of 100– 120 were reported for the NaPMA/DeTAB system [64]. The concentration of free surfactant was not accounted for in this study. The correction would reduce the measured aggregation number to about 50–60, a value comparable to that for free DeTAB micelles. 8. All the above studies concerned polyanion/cationic surfactant systems. Two examples illustrate the behavior of the polycation/anionic surCopyright © 2003 by Taylor & Francis Group, LLC

factant systems. The poly(trimethylammonioethylacrylate chloride)/SDS system [65] showed a behavior diﬀerent from that of polyanion/cationic surfactant systems. The value of N was very large, close to and above 200 (as compared to 60 for free SDS micelles) and increased with the salt content. The N-values for the random poly(acrylamide-co-cationic monomer)/ SDS system were larger than for free SDS micelles [66]. Substituting acrylamide by the more hydrophobic isopropylacrylamide resulted in N-values much lower than for free SDS micelles [66]. 9. Some studies have used gelled polyelectrolytes. The values of N in the NaPAA gel/DTAB system were only slightly larger than in water and increased nearly linearly with the ratio of the molar concentrations of SDS and NaPAA [67]. The N-values in the system -carrageenan/C12EO8 were the same as in water, whereas they were larger than in water in the system -carrageenan/C12EO6 [68]. 10. There is an increasing interest in the DNA/cationic surfactant systems for achieving DNA compaction and tranfection. The phase diagrams of the DNA/alkyltrimethyammonium bromide systems have been investigated [69]. The type of binding of such surfactants to DNA is still open to question [70].

2. Strongly Hydrophobic Polymers Strongly hydrophobic polymers are often referred to as polysoaps. Most studies involved charged polymers in order to ensure solubility in water. Polysoaps are capable of forming hydrophobic microdomains, intramolecularly and/or intermolecularly, that have been visualized by transmission electron microscopy at cryogenic temperatures [71]. The electron micrographs of PS16(P ¼ 1.0) showed long, threadlike micelles resulting from end-to-end association of several PS16 polymer chains [71]. Besides, the cmc of polysoaps is extremely small and is usually taken as zero, i.e., microdomains exist at any concentration, however small [72]. The number of polymer repeat units per microdomain has been evaluated and found to increase with temperature [10,13,73]. Also, the microdomains are usually much more rigid (microviscous) than conventional surfactant micelles [13,73]. (a) Polysoap/Oppositely Charged Surfactant Systems. The ability of polysoaps to form microdomains strongly affects the association of the surfactant. Figure 10 shows that for the PS12(P ¼ 1.0)/DTAC and PS16(P ¼ 1.0)/DTAC systems the surfactant aggregation number N increases linearly with the concentration of bound surfactant, Cb. This behavior is very different from that for hydrophilic polyelectrolytes (see Fig. 9). The fact that the N versus Cb plots extrapolate to the origin has been interpreted as indicating that the bound surfactants simply swell the polysoap hydrophobic microdomains preexisting the addition of surfactant, Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10 Variation of the aggregation number of the polymer-bound surfactant aggregates in the PS12/DTAC and PS16/DTAC systems at 258C and P ¼ 0.50 (!) and 1.00 (~), with the concentration of bound surfactant. (From Ref. 13 with permission of the American Chemical Society.)

without creation of new microdomains [13]. A titration calorimetry study of the interaction between poly(sodium acrylate-co-alkylmethacrylate) or poly(acrylamide-co-alkylmethacrylate) and single-tail surfactants, including DTAB, conﬁrmed the noncooperative binding of surfactants to polysoaps [74]. The fact that poly(acrylamide-co-alkylmethacrylate) is nonionic shows the general character of the results. (b) Polysoap/Surfactant of Like Charge Systems. There appears to be no report of surfactant aggregation numbers in such systems. Nevertheless, some results show that the hydrophobic interaction between polysoap Copyright © 2003 by Taylor & Francis Group, LLC

and surfactant alkyl chain can overcome the electrostatic repulsion between surfactant and polymer-charged groups and result in the binding of the surfactant. Fluorescence probing showed that SDS binds to polysoaps of like charge such as poly(potassium maleate-alt-1-alkene), with 1-alkene ¼ 1-decene, 1tetradecene, and 1-octadecene [75,76]. Direct evidence has been obtained for the binding of SDS to PS16(P ¼ 1.0) [77,78]. The viscoelasticity of pure PS16(P ¼ 1.0) solutions disappeared and the solution viscosity decreased upon addition of SDS or of the nonionic surfactants C10EO6 and C12EO6 [77,78]. Self-diﬀusion measurements showed that only a small fraction of the added SDS was bound to the polymer [78]. This result was interpreted as indicating a preferential binding of the surfactant at the junctions between PS16 chains, resulting in their easy breakup.

3. Polymers of Intermediate Hydrophobicity This section concerns polymers of intermediate hydrophobicity where hydrophobic microdomains are extremely small or not present but about to occur. Typical polyelectrolytes of intermediate hydrophobicity are those showing a polysoap/polyelectrolyte transition when their degree of neutralization P is increased (see below). PS4 and NaPSS are examples of partially hydrophobic polymers. Their interaction with cationic surfactants indeed results in surfactant-bound aggregates of an aggregation number that can be lower than for free micelles [13,63]. The N-value in the PS4(P ¼ 0.25)/DTAC system varied little with the surfactant concentration as for hydrophilic polyelectrolytes [13]. However, the values of N were quite low, as a result of the mixed micellization of the surfactant dodecyl chains and of the copolymer butyl chains. The results suggest the presence of a small number of microdomains prior to surfactant addition, thus a noncooperative binding, and the formation of additional microdomains upon surfactant binding [13]. The poly(acrylic acid-co-ethylmethacrylate) copolymers show a polysoap/polyelectrolyte transition upon neutralization of the acrylic acid moieties and the transition pH increases with the ethylmethacrylate content [79]. Additions of cationic surfactants such as DeTAB result in the formation of hydrophobic microdomains at DeTAB concentrations decreasing upon increasing ethylmethacrylate content. The measured aggregation number of polymer-bound surfactant aggregates decreased upon increasing hydrophobicity of the copolymer [79], as expected on the basis of the results reviewed above. More examples are available with cellulose derivatives such as EHEC [16, 80–83], hydroxypropylcellulose (HPC) [84,85], poly(N-isopropylacrylamide) (PNIPAM) [86–89], and PPO [53,90–94]. These polymers interact with any Copyright © 2003 by Taylor & Francis Group, LLC

type of surfactant, irrespective of the nature of its headgroup, and the polymer-bound aggregates have aggregation numbers smaller than the free micelles. The so-called water-soluble associating polymers (WSAP) are also polymers of intermediate hydrophobicity. These polymers include a few percent of a strongly hydrophobic comonomer, or of a grafted hydrophobe. In aqueous solution the hydrophobic moieties self-associate intramolecularly and/or intermolecularly. This explains the use of WSAP as thickeners [95]. As other polymers of intermediate hydrophobicity, WSAP can interact with any type of surfactant [96–101]. Surfactant aggregation numbers have been determined in a few WSAP/surfactant systems. Magny et al. [96] report on the aggregation number of DTAC bound to sodium polyacrylate hydrophobically modiﬁed by 1 to 3% dodecyl or octadecyl groups. The total number of surfactant ions and polymer side groups was only slightly larger than the aggregation number of the free DTAC micelles. Dualeh and Steiner [102] investigated the binding of SDS to EHEC hydrophobically modiﬁed by dodecyl groups. The measurements yielded surfactant aggregation numbers only slightly lower than for free SDS micelles, increasing with the SDS concentration at constant hydrophobe concentration, and independent of the hydrophobe content at constant SDS concentration. Low aggregation numbers were found for various surfactants interacting with a hydrophobically modiﬁed PNIPAM [89].

D. Microviscosity in the Polymer-Bound Surfactant Aggregates Several studies concluded that surfactant aggregates bound to hydrophilic polyelectrolytes are less ﬂuid (or more rigid) than free micelles of the same surfactant [12,55,56,59,103]. For instance, Fig. 11a shows that the values of the microviscosity, i , of the bound aggregates relative to that of free DTAC micelles in the PS1/DTAC system range between 2 and 12 [12]. The large microviscosity of polymer-bound aggregates relative to free micelles is responsible for the smaller quenching rate constants measured in these systems [12]. It probably also results in smaller rate constants for all bimolecular reactions performed in polymer-bound aggregates relatively to free micelles. This may be an advantage or an inconvenience when using polymer-bound surfactant aggregates as microreactors, depending on the type of chemical reaction performed in the aggregate and on the result one is trying to achieve. Figure 11a also shows that i is independent of the DTAC concentration. This result supports the conclusion that the aggregate composition is independent of the bound surfactant concentration, in line with the constant aggregation number measured for the aggregates (see Fig. 9). Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 11 Variations of the relative microviscosity of the polymer-bound surfactant aggregates with the surfactant concentration. (Top) PS1/DTAC systems at P ¼ 0 (*), 0.10 (!), 0.20 (&), 0.40 (!), and 1.0 (~). (Bottom) PS16(P ¼ 1.0)/DTAC (~) and PS10(P ¼ 1.0)/DTAC (*) systems. Temperature: 258C. i ¼ 1 corresponds to the free DTAC micelles. (From Refs. 12 and 13 with permission of the American Chemical Society.)

The eﬀect of surfactant binding on the microviscosity in polysoap/surfactant systems is very diﬀerent from that of hydrophilic polyelectrolyte/ surfactant systems. Indeed, an important feature of the hydrophobic microdomains formed by strongly hydrophobic polymers (polysoaps) in the Copyright © 2003 by Taylor & Francis Group, LLC

absence of any added surfactant is their high microviscosity relative to that of free surfactant micelles [13,75,76,104–107]. Thus the microviscosity of PS16(P ¼ 1.0) microdomains relative to free DTAC micelles is about 30 [13]. These high microviscosity values are responsible for the low quenching rate of pyrene by alkylpyridinium ions in these systems [10,13,73,108]. This high microviscosity arises because the motion of any alkyl chain in a microdomain requires that of part of the polysoap main chain and of some adjacent alkyl chains. The microviscosity of the PS16(P ¼ 1.0)/DTAC aggregates relative to that of free DTAC micelles decreases as the concentration of bound surfactant increases (Fig. 11b) [13]. Indeed, the microdomains of PS16(P ¼ 1.0) now contain surfactant alkyl chains that can move independently from the polysoap alkyl chains, thereby increasing the overall ﬂuidity of the microdomains. The decrease of microviscosity upon binding of surfactants by long-chain polysoaps explains the observed decrease of the pyrene ﬂuorescence lifetime in aerated systems, as the quenching of the pyrene ﬂuorescence by molecular oxygen is then facilitated [13,57]. It also explains the observed increase of the intra-aggregate quenching rate constant. PS16(P ¼ 1.0) represents an extreme case of polysoap where most alkyl chains are under the form of microdomains [72]. A polysoap such as PS10(P ¼ 1.0) where only part of the chains forms microdomains [72] shows a nearly constant microviscosity upon DTAC binding (Fig. 11b). Indeed, upon binding of surfactant (decreasing i), some free repeat units of the PS10(P ¼ 1.0) become incorporated in the growing microdomains or in newly formed microdomains (increasing i ). These two opposite eﬀects leave i nearly unchanged but still fairly high. The binding of SDS to poly(potassium maleate-alt-1-octadecene), a polysoap of like charge, apparently also results in a decrease of microviscosity [75,76].

E. Models of Binding of Surfactants to Polymers of Varying Hydrophobicity The results reviewed in Sections II.A–D led to the binding models represented in Figs. 12–14 for strongly hydrophilic, strongly hydrophobic, and weakly hydrophobic polymers, respectively.

III. POLYMER/SURFACTANT INTERACTIONS: EFFECT OF THE NATURE OF THE SURFACTANT HEADGROUP This section considers only hydrophilic polymers as it focuses primarily on the occurrence or absence of interactions between polymers and surfactants Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 12 Schematic representation of a surfactant aggregate bound to an oppositely charged hydrophilic polyelectrolyte. (, *, ____) and (, *, - - - - ) represent a polymer-charged group, a surfactant-charged group, and a polymer chain or a surfactant alkyl chain above and below the plane of the page, respectively. Only a few surfactant alkyl chains and one bound aggregate are represented, for sake of clarity.

and on the strength of the interaction. This strength is characterized by the CAC/CMC ratio, even if this quantity gives only a semiquantitative idea of the interaction. For ionic surfactants the nature of both the charged headgroup and the counterion has a strong impact in determining the occurrence and the strength of the interaction between a polymer and a surfactant. The same is true for the nature of the surfactant headgroup in the case of uncharged (nonionic, zwitterionic) surfactants. The systems containing the polymers that have been used the most in such studies, namely PEO or PVP, are considered to illustrate what has been just stated. It has been shown that at room temperature these polymers interact with all anionic surfactants investigated: SDS [17,18,46,48,49], sodium n-decylphosphate [109], sodium dodecylbenzenesulfonate [110], sodium alkylcarboxylates [111], sodium di(ethylhexyl)phosphate [112], lithium perﬂuorooctanesulfonate [113], sodium perﬂuorononanoatate [114], AOT [115], potassium 2-alkylmalonates [116], etc. However, their interaction with the nonionic surfactants CmEOx [53], with surfactants having a sugar headgroup (glucoside, thioglucoside) [31,117], with zwitterionic surfactants such as the dodecyldimethylammoniopropanesulfonate [118], and with cationic surfactants of the alkyltrimethylammonium bromide type [53,119] is extremely weak or not present, at least at room temperature. Note, however, that a slight increase of the temperature is suﬃcient to bring about interactions in the case of the PEO/alkyltrimethylammonium bromide systems due to the increased hydrophobicity of PEO at high temperatures [53,120,121]. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 13 Model for the binding of a cationic surfactant to an anionic polysoap which forms intramolecular hydrophobic microdomains. The polymer-charged groups are located close to the surfactant-charged groups replacing the surfactant counterions at the aggregate surface, while the surfactant alkyl chains swell the microdomains. (From Ref. 13 with permission of the American Chemical Society.)

Likewise, the more hydrophobic PPO interacts with alkyltrimethylammonium bromides [53] and sugar surfactants [117]. A survey of the reported results shows that the polymer/surfactant interaction depends in a subtle manner on the nature of the counterion and of the headgroup. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 14 Model of binding of a cationic surfactant to a weakly hydrophobic polyelectrolyte, such as PS4 at P 0.25, capable of forming very few and small microdomains (most repeat units are free). (A): Swelling of a preexisting microdomain by the bound surfactant with incorporation of free repeat units; (B) generation of an additional microdomain upon further surfactant binding. (From Ref. 13 with permission of the American Chemical Society.)

1. Starting with cationic surfactants, PEO does not interact with DTAB, TTAB, CTAB, and DTAC (no change of CMC) but does interact with CTAC (small decrease of the CMC) at 258C [119]. 2. For cationic surfactants (CTAC, CTANO3, and CTAClO3) the larger the CMC, the larger the eﬀect of the polymer (PPO) in decreasing the CMC [94]. Copyright © 2003 by Taylor & Francis Group, LLC

3. For anionic surfactants the strength of the interaction also depends on the nature of the surfactant counterion and on its valency, judging from the values of the ratio CAC/CMC listed in Table 2 for diﬀerent systems. The strength of the interaction of PEO or PVP with dodecylsulfate surfactants decreases following the sequence: Na+ > Cs+ > tetramethylammonium ion TMA+ > tetraethylammonium ion TEA+ [122]. No interaction was noted between tetrapropylammonium or tetrabutylammonium dodecylsulfates (TPADS or TBADS) and PEO or PVP [122]. Likewise, the interaction of X(DS)2, X being a divalent counterion, with PVP or PEO is weaker than for SDS (see Table 2) [15,25,123,124]. In general, when considering a series of surfactants with diﬀerent counterions of the same valency, in the presence of a given polymer, the lower the surfactant CMC, the closer to 1 the value of the CAC/CMC ratio (i.e., the weaker the polymer–surfactant interaction). 4. For ionic surfactants the nature of the surfactant headgroup can also aﬀect the interaction with a polymer [119,125]. Thus PEO does not interact with DTAC, but an interaction was evidenced with dodecylammonium chloride (DAC), a surfactant with a smaller headgroup [119]. The above results are well explained by considering the pair interactions occurring in the systems: micelle–counterion, micelle–polymer, and counterion–polymer. For instance, if the counterion is modiﬁed as to have a weaker micelle–counterion interaction, the polymer–surfactant interaction will be enhanced as in results 1 and 2. In these examples changing the counterion leaves the polymer–micelle unchanged and the counterion interacts little or not at all with the polymer. In result 3 the counterions are cations that are known to interact with PEO. If the PEO–counterion interaction is assumed to decrease or remain constant upon increasing counterion valency or radius, an increase of either of these two parameters increases the micelle–counterion interaction and, thus, reduces the polymer–surfactant interaction. Result 4 is explained by the fact that the reduced size of the surfactant headgroup may enhance the polymer–micelle interaction, an eﬀect that may more than compensate for the increased micelle–counterion interaction. Recall that for cationic surfactants the sequence of CMC values and of the strength of the counterion–micelle interaction follows the Hoﬀmeister series. Results 1–4 deal with neutral polymers and ionic surfactants. Examples can also be given of neutral hydrophilic polymer–nonionic surfactant systems. The occurrence or absence of polymer–surfactant interactions in such systems is then completely conditioned by the nature of the surfactant headgroup and the nature of the polymer functional group. For instance, no interaction was evidenced in the poly(acrylamide)/SDS system [126] and in the PEO/C12EO8 system [53]. However, interaction exists in the PAA, low pH (nonionized)/SDS system [38], and in the PAA, low pH (nonCopyright © 2003 by Taylor & Francis Group, LLC

TABLE 2 Values of the CMC of Dodecylsulfate Surfactants with Monovalent and Divalent Counterions in Water and in Water þ 0.1 wt % PEO and Water þ 0.1 wt % PVP at 258C

SDS CsDS (308C) TMA-DS TEA-DS TEA-DS (408C) TPA-DS TBA-DS Cd(DS)2 Mg(DS)2 c (358C) Cu(DS)2 a b

CMC in water (mM)

CAC in water +0.1 wt % PEO (mM)

CAC/CMC (0.1 wt % PEO)

CAC in water +0.1 wt % PVP (mM)

CAC/CMC (0.1 wt % PVP)

Ref.

8.0 6.2 5.4 3.65 3.8 2.15 1.15 1.19 1.20 1.20

4.5 4.1 4.7 3.6 3.6 2.3 1.15 0.95a 1.00a 0.96

0.56 0.66 0.87 0.99 0.95 1.06 1.00 0.80 0.83 0.80

2.3 4.5 4.9 — — 2.15 — 0.80b 0.80b 0.80

0.29 0.72 0.90 — — 1.0 — 0.67 0.67 0.67

122 122 122 122 122 122 122 15 15 25

In the presence of 0.17 wt % PEO. In the presence of 0.50 wt % PVP. Copyright © 2003 by Taylor & Francis Group, LLC

ionized)/CmEOx or alkylphenylethoxylate surfactant such as Triton X100 systems [37,127]. The situation can be extremely complex with charged polymer/ionic surfactant systems. Indeed the system may now contain up to four components (two counterions, the surfactant ion, and the polyion) and ﬁve pair interactions must be considered, assuming no interaction between the two types of counterions. This complexity is well illustrated by the reported study of the inﬂuence of added salt on the interaction between dextransulfate and the DTAB [128] or sodium hyaluronate and TTAB [129]. The eﬀect of the nature of the counterion and of the co-ion is well demonstrated, particularly in Ref. [129]. The eﬀect of the surfactant headgroup is still present [125]. The PEO/anionic surfactant systems are probably the ones that have been the most investigated. Diﬀerent explanations have been put forward for the origin of the binding of SDS to PEO and have been reviewed by Dubin et al. [130]. These authors state, ‘‘It has thus been variously proposed that the PEO/SDS complex is stabilized by hydrophobic interactions between the methylene units of the polymer and those of the surfactant alkyl chain, by interactions between polymeric ether groups and sulfate groups, or by eﬀects more closely related to the nature of the micellewater interface’’ and conclude that ‘‘none of the foregoing proposals has been clearly substantiated and that the driving force for the binding of SDS to PEO is open to debate.’’ In this paper the authors investigate the eﬀect of the nature of the surfactant counterion on the PEO–dodecylsulfate micelle interaction. They conclude that the surfactant cation plays a direct role in the stabilization of the PEO/dodecylsulfate complex [130]. The cation would interact simultaneously with the dodecylsulfate micelle via electrostatic interactions and with the PEO via coordination complexation. The results in Table 2 support this explanation. Nevertheless, this explanation is not always accepted. In a recent study the interaction between nonionic polymers and anionic surfactants has been explained in terms of an excludedvolume eﬀect of the polymer [131]. The system investigated is the PVP/ sodium alkylsulfonate (alkyl ¼ octyl, decyl, undecyl). The CAC was equal to or only slightly smaller than the CMC. However, the surfactant alkyl chain was too short to validate the proposed explanation. At the end of this section it should be noted that studies of polymer/ surfactant systems have also been performed using polymers of special structures: star-shaped or of the dendrimer type. Little diﬀerence was found between linear and star-shaped PEO in terms of its interaction with SDS [132]. The two types of systems had the same CAC values, but the capacity of binding was lower with the star-shaped PEO. With the dendrimer-type polymers used [poly(1,4-diaminobutane [133] or the sugar– Copyright © 2003 by Taylor & Francis Group, LLC

persubstituted poly(amidoamine) [134]] the binding was found to start at very low surfactant concentrations and not to be cooperative. It became cooperative at higher surfactant concentration [133]. The behavior of these dendrimer/surfactant systems is thus similar to that of polymers of intermediate or weak hydrophobicity discussed in Section II.A.3. This is not surprising when considering the rather hydrophobic interior of the investigated dendrimers.

IV. MICROSTRUCTURES IN POLYMER/SURFACTANT SOLUTIONS This section reviews the microstructures of polymer/surfactant systems in solution. Transmission electron microscopy at cryogenic temperature (cryoTEM) has been very eﬀective in visualizing these microstructures. Such studies have provided direct evidence for some of the results described above and support for some of the models postulated for polymer/surfactant systems. Starting with hydrophilic or weakly hydrophobic polymers, cryo-TEM has directly visualized the transformation of the threadlike micelles present in CTAB/sodium salicylate solutions into globular micelles upon addition of PPO or PVME (polyvinylmethylether) [135]. In other cryo-TEM studies the same transformation was visualized upon addition of 1.5 wt % PEO to a solution of 2 wt % SDS þ 0.6 M NaCl at 408C [136] and upon addition of PEO or PPO to a solution of potassium oleate containing threadlike micelles [137]. These results explain the enormous decrease of viscosity and the loss of viscoelasticity of the corresponding surfactant solutions upon addition of polymer. They also conﬁrm the eﬀect of the polymer in reducing the size of the micelles, a conclusion inferred from ﬂuorescence quenching measurements. Cryo-TEM conﬁrmed the absence of interaction in NaPSS/CmEOx systems as well as in PPO or PVME/C12EO5 systems [135]. Also PAA at low pH (nonionized) did not aﬀect CmEOx threadlike micelles until a polymer– surfactant complex precipitated out [135]. Turning to polysoaps, very interesting microstructural changes have been observed in PS16(P ¼ 1.0)/surfactant systems. PS16(P ¼ 1.0) forms very long plurimolecular threadlike micelles by end-to-end association of several polymer chains, and these micelles have been visualized by cryo-TEM [71]. This technique was used to visualize the progressive breakup of these micelles into isolated microdomains made up of one polymer chain, upon addition of SDS, a surfactant of like charge [77,78], or C10EO6 and C12EO6 [78]. Cryo-TEM has also been used to visualize structural changes in polymer/mixed surfactant systems. The system HM-HEC/(DTAB þ SDS) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 15 Cryo-TEM micrographs of a mixture of 30-mM SDS þ DTAC (DTAC mole fraction ¼ 0.23. (Top) No polymer added: the micrograph shows spheroidal micelles. (Bottom) 1 wt % HM-HEC added: existence of the cell-like structure. Frost particles are denoted by f. (From Ref. 138 with permission of the American Chemical Society.)

[138] showed micelles appearing like ‘‘threads on a string’’ arranged in a cell-like pattern (see Fig. 15). This network was not present in the absence of the polymer. Its formation required an average number of polymer hydrophobes per mixed micelles of 3–5. Another cryo-TEM investigation concerned the PDADMAC/(SDS þ Triton X100) system [139]. The micrographs (see Fig. 16) showed regions rich in micelles, presumably corresponding to domains of polymer chains. The size of these aggregates grew with the polymer concentration. This growth was attributed to the involvement of several polymer chains per aggregate. Cryo-TEM was also used to investigate the interaction of the cationic cellulose derivatives JR400 (homopolymer) and Quatrisoft LM200 (JR400 with grafted dodeCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 16 Dense concentrated micellar domains present in the PDADMAC/ (SDS þ Triton X100) system at 258C. Bar ¼ 100 nm. (From Ref. 139 with permission of Academic Press-Elsevier Science.)

cyl chains) with the catanionic vesicles present in the mixed surfactant SDS þ didodecyldimethlammonium bromide (DDDMAB) [140]. The interaction JR400–vesicles was found to give rise to faceted vesicles and disklike micelles in the composition range where the solution was bluish, located at compositions below those where the system phase-separates. The interaction with Quatrisoft LM200 gave rise to faceted vesicles and to clusters of vesicles. The transformation of vesicles into disklike micelles noted with JR400 corresponds to an increase of the surfactant assembly curvature upon binding of the polymer. The opposite transformation, i.e., from micelle to vesicle, was shown to occur in a freeze-fracture electron microscopy study of partially hydrolyzed poly(acrylamide)/cationic surfactant system [141]. Indeed, in this system the binding of the anionic polymer to a cationic micelle resulted in a lowering of the micelle charge and, in turn, in an increase of surfactant packing parameter and in the observed micelle-to-vesicle transformation. With the JR400/ (DDDMAB þ SDS) system the cationic polymer may remove some dodecylsufate ions from the mixed vesicles, thereby increasing the overall vesicle charge and resulting in their breakup into smaller disklike micelles. The last two examples illustrate well the versatility of the eﬀect that polymer–surfactant interactions can have on the microstructure of surfactant solutions. Copyright © 2003 by Taylor & Francis Group, LLC

V. DYNAMICS OF POLYMER-BOUND SURFACTANT AGGREGATES Micelles are not frozen objects. They are in dynamic equilibrium with the surrounding solution, constantly incorporating/losing surfactants (exchange process) and forming/breaking up. The kinetics of the surfactant exchange and of the micelle formation/breakup have been well investigated in micellar solutions in the absence of polymer by means of chemical relaxation methods and the topic has been reviewed [142]. These studies have been extended to polymer-bound surfactant aggregates. Chemical relaxation techniques such as ultrasonic absorption, T-jump, and stopped ﬂow as well as NMR were used for this purpose. A fast exchange of the surfactant between free and polymer-bound states was inferred in a 1H NMR study of hydrophobically modiﬁed poly(acrylamide)/sodium alkylbenzenesulfonate systems [143]. The most extensive studies of the kinetics of the surfactant exchange for polymer/surfactant systems were performed for the PVP/SDS system, by means of the ultrasonic absorption relaxation technique. Less comprehensive studies have been also performed on other systems. Rather diﬀerent results have been reported by Wyn-Jones et al. [17,144,145] and La Mesa et al. [146–148] for the kinetics of the surfactant exchange between the free state and the polymer-bound aggregated state. For instance, the ultrasonic relaxation frequency associated with the exchange process was reported to increase linearly with the surfactant concentration by Wyn-Jones et al. [17,144,145] and to be independent of the surfactant concentration, C, in the binding range, that is for CAC < C < C2 by La Mesa et al. [146–148]. This diﬀerence may reﬂect the fact that the concentration ranges investigated in the two studies were not identical. Also, the ultrasonic absorption data were not analyzed in exactly the same way. Nevertheless, the values of the relaxation frequencies measured for the exchange process in the two series of studies are comparable. The papers of Wyn-Jones et al. [17,144,145] are reviewed in some detail now because these authors complemented their ultrasonic relaxation studies by electrochemical measurements of the concentration of free surfactant. Such data are necessary for a more precise analysis of the results. Besides, their analysis used the phenomenological theory developed by Hall et al. [149] which circumvents some of the diﬃculties associated with the classical theoretical treatment of micellar kinetics [142]. Values of the ratio k =N ðk ¼ rate constant for the exit of one surfactant from a polymer-bound aggregate of aggregation number N) around 9 104 s1 were reported for several PVP/SDS systems [17]. Assuming an aggregation number of about 30 for the bound surfactant aggregates and using the reported value of the concentration of free surfacCopyright © 2003 by Taylor & Francis Group, LLC

tant [17] yields for k+, the rate constant for the association of one surfactant to a polymer-bound aggregate, values around 109 M1 s1 . Such high values indicate that the association process is nearly diﬀusion-controlled. A similar conclusion was reached in studies of other polymer/surfactant systems [144,145]. Recall that the association of a surfactant to its micelle is also diﬀusion-controlled in the absence of polymer [142]. Some studies showed at a low surfactant concentration, below the CAC, a relaxation of small amplitude. This relaxation is also present in the absence of polymer but is then much less pronounced. This eﬀect may be associated to the formation of very small premicellar surfactant aggregates [147–150]. Both the p-jump and the T-jump techniques were used to study the eﬀect of polymers on the kinetics of micelle formation/breakup. In SDS solutions the value of 1/ 2, the reciprocal of the relaxation time associated to the micelle formation/breakup process, increased much upon addition of PEO [151] or PVP [152] (Fig. 17). This eﬀect is reminiscent of that of alcohols on the kinetics of micelle formation/breakup [142]. On the basis of the classical treatment of micellar kinetics, this behavior indicates that polymer-bound aggregates have a much shorter lifetime than free micelles. The smaller aggregation number of the bound aggregates with respect to free micelles and the shape of the distribution curve of the bound aggregates probably both contribute to the observed eﬀect.

VI. SOLUBILIZATION IN POLYMER-BOUND SURFACTANT AGGREGATES Polymer-bound surfactant aggregates can solubilize chemicals that are sparingly soluble in water. Such studies, even though tedious, are important when using systems where surfactants and polymers are simultaneously present and interact with each other. The reported studies concern many aspects of the solubilized systems; here the polymer-bound surfactant aggregates that contains a solubilizate: locus of solubilization, amount of solubilized material, partitioning of chemicals between polymer-bound aggregates and bulk phase, eﬀect of the solubilizate on the binding of the surfactant to the polymer. The most signiﬁcant results are summarized below. 1. For a given surfactant the locus of solubilization in polymer-bound surfactant aggregates appears to be the same as in free micelles. Thus aromatic ring currents show that in the PS4/DTAB system, aromatic molecules such as benzene, naphthalene, acridine, or pyrene are solubilized near the surfactant headgroups, just as in the case of micellar solutions of DTAB [153]. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 17 Eﬀect of addition of (+) PEO to a 70-mM SDS solution at 258C [151] and of (*) PVP to a 100-mM SDS solution at 208C [152] on the relaxation time associated to the micelle formation/breakup.

2. Dyes that aggregate in water (R6G, proﬂavine, acridine orange) are solubilized in the monomer form in the surfactant aggregates present in polyelectrolyte/oppositely charged surfactant systems, just as in free micelles [127,154–157]. The dissociation of the dye into monomers can give rise to interesting spectral properties. 3. A correlation was shown between solubilization capacity and degree of cooperativity of surfactant binding to a polyanion [158–160]. A model of cooperative binding of the dye and surfactant to the polyanion was proposed [158]. 4. The amount of solubilized material increases nearly linearly with the amount of polymer-bound surfactant, just as for micellar systems in the absence of polymer [127,161,162]. Copyright © 2003 by Taylor & Francis Group, LLC

5. The solubilizing power SP, the macroscopic quantity equal to the ratio of the number of micellar solubilizate per micellar surfactant, is often found to be larger for polymer-bound surfactant aggregates than for free micelles [160–162]. For instance, the solubilizing power of the polymerbound aggregates in the sodium poly(vinylsulfate)/alkyltrimethylammonium bromide systems is two to three times larger than that of free alkyltrimethylammonium bromide micelles for Orange Yellow, but somewhat lower for 1-pyrenecarboxaldehyde [161]. Also, the solubilizing power of the polymer-bound aggregates in PSX/DTAB [10] and PEO/SDS [162] systems is larger than that of the corresponding free micelles. 6. One study compared the solubilization capacity SC of polymerbound surfactant aggregates and of the corresponding free micelles [162]. SC is a microscopic quantity deﬁned as the average number of molecules solubilized in a single aggregate at saturation. For pyrene solubilized in the PEO/SDS system, the value of SC was found to be very close to those measured for free micelles even though the bound aggregates had smaller aggregation numbers than free micelles. The interaction of pyrene with PEO may explain this result. Besides, SC was found to be more sensitive to ionic strength for bound aggregates than free micelles [162].

VII.

POLYMER–SURFACTANT INTERACTIONS AT INTERFACES

This aspect of polymer–surfactant interaction is very important as it relates to practical uses of these complex systems. Indeed, the presence of the polymer can enhance or diminish the adsorption of the surfactant, and vice versa, with consequences on the properties of the surface on which adsorption occurs.

A. Air–Solution Interface Synergism in surface activity and an aging eﬀect were observed with polymer–surfactant systems at the air–solution interface. For instance, with the EHEC/SDS system at a concentration below the CAC, the reduction of surface tension depends on the concentration of SDS in the bulk phase and on the number of polymer segments in actual contact with the surface [163]. Above the CAC, addition of SDS brings about an increase of the amount of adsorbed polymer, due to the formation of an EHEC/SDS complex at the air–water interface. The observed aging eﬀect was attributed to a progressive ordering of the complex [163]. A study by neutron reﬂection has yielded detailed information of the mixed PVP/SDS layer at the air–solution surface [164]. At SDS concentraCopyright © 2003 by Taylor & Francis Group, LLC

tions below the cac, the adsorption of SDS was increased by the presence of the polymer (synergism). This result was interpreted as indicating the existence of an interaction between PVP and SDS at concentrations below the cac in the bulk phase. This interaction would be diﬃcult to detect by other methods because of the low amount of SDS being bound to PVP below the cac. A simple method was proposed to obtain qualitative evidence of a polymer–surfactant interaction at the air–solution surface [165]. Talc is sprinkled on the solution surface and an air current blown tangentially at the particles for 1–2 s, then stopped. A motion of recoil of the particles provides evidence of surface viscoelasticity and of the formation of polymer–surfactant complexes at the interface. The occurrence of surface viscoelasticity is taken as strong evidence for a synergistic adsorption of the surfactant and polymer at the interface.

B. Solid–Solution Interface Polymer–surfactant interactions occur at solid–solution interfaces only if they also occur in the bulk phase [166]. Several studies of polymer/surfactant systems at solid–solution interfaces showed competition or synergism in adsorption of the polymer and surfactant. For instance, SDS does not adsorb on the negatively charged surface of silica but adsorbs if PEO is pre-adsorbed on this surface [167]. Likewise, a silica surface loaded with EHEC or HM-EHEC adsorbs SDS as well as CTAC. The adsorption of SDS brings about a considerable expansion of the adsorbed layer that probably results from the electrostatic repulsion between polymer-bound surfactant aggregates in the layer [168]. When the silica surface was hydrophobized, the SDS could replace EHEC but some HM-EHEC remained adsorbed. In another study the pre-adsorbed layer of the HM-cationic hydroxyethylcellulose Quatrisoft LM200 on mica and silica was progressively removed by the addition of SDS. Complete removal occurred at SDS concentrations larger than the cmc [169]. The amount of adsorbed HEC on the positively charged surface of alumina was largely increased in the presence of SDS, while the amount of adsorbed SDS was unaﬀected [170]. A similar trend was observed when replacing HEC by an HM-HEC. In all cases the stability of the alumina dispersion was enhanced [170]. The cationic surfactant TTAB adsorbed on a hydrophobized gold surface permitted the adsorption of several anionic polymers: PAA, NaPSS, poly(maleic acid-alt-ethylene) [171]. Surface force measurements have been greatly used to study the polymer– surfactant interaction at the mica–solution interface. Thus the repulsive force between two mica surfaces coated with the cationic cellulose derivative Copyright © 2003 by Taylor & Francis Group, LLC

JR400 turned into an attractive force upon addition of SDS. Indeed, the surfactant adsorption resulted in a hydrophobic attractive force between the two surfaces [172]. The properties of an adsorption layer on a mica surface in contact with a polymer–surfactant solution may depend on the experimental pathway by which the mixed layer is generated. For instance, the components can be successively adsorbed or the adsorption may be realized directly from a solution containing both the polymer and the surfactant. The adsorption layer can be trapped in a quasi-equilibrium state that may take a long time to transform into the true equilibrium state [173]. AFM has permitted studies of the structure of the mixed polymer/surfactant layer adsorbed at solid surfaces. The adsorbed layer from the PVP/ SDS system on graphite has been investigated [174]. Nonequilibrium structures of the adsorbed layer consisting of micrometer-sized domains of ordered aggregates rich in surfactant separated by disordered domains rich in polymer were seen (Fig. 18, top). Higher-resolution AFM images showed hemicylindrical SDS micelles with polymer globules at the grain boundaries (Fig. 18, bottom). The ordered domains grew with time and occupied the whole layer only after several hours. This long equilibration time was said to have important implications regarding colloid stability. AFM was also used to study the adsorption layer from the PDADMAC/ CTAB or CTAC systems onto silica [175]. A preadsorbed layer of surfactant hindered the adsorption of the polymer. The adsorption layer of polymer alone was featureless and did not desorb upon rinsing. The AFM images obtained after exposing this layer to a CTAC solution at a concentration larger than the cmc were similar to those when CTAC alone was adsorbed on silica. This result suggests a polymer desorption by the surfactant.

VIII. STRUCTURAL ASPECTS OF POLYMER/SURFACTANT SYSTEMS IN THE GEL STATE AND IN THE SOLID STATE A. Structure of Polymer/Surfactant Complexes in the Gel State The binding of ionic surfactants to oppositely charged hydrophilic polyelectrolytes is a highly cooperative process (see Section II.A). This high cooperativity was maintained when the polyelectrolyte was cross-linked by an appropriate agent that did not aﬀect the overall hydrophobicity of the polymer [176–178]. In some instances the binding cooperativity was reduced by the cross-links [179]. The surfactant associated inside the gel network at concentrations that were much lower than the cmc, just as with polyelecCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 18 AFM deﬂection images of the adsorption layer from the PVP/SDS system on graphite. Top: low-resolution image showing the nonuniform coverage. The smooth-looking domains are rich in polymer; the rough-looking domains are rich in surfactant. Bottom: high-resolution image of a rough domain:the hemicylindrical SDS micelles deﬁne grains at the boundaries of which are located globules of PVP. (From Ref. 174 with permission of the American Chemical Society.)

trolytes that are not cross-linked. Large amounts of surfactant brought about a collapse of the polyelectrolyte gel. An examination of the polyelectrolyte gel/oppositely charged surfactant systems by X-ray showed the existence of a long-range order [180,181]. Many similar studies followed. The binding of DPC to a network of poly[2-(acrylamido)-2-methylpropanesulfonic acid] yielded a system with a cubic structure [181]. Gels of higher charge densities led to better-deﬁned structures [182,183]. Gels Copyright © 2003 by Taylor & Francis Group, LLC

of cross-linked PDADMAC in the presence of SDS at a concentration well below the cmc gave rise to a hexagonal structure with a high degree of order [183,184]. A cubic structure was also observed with this system [185]. The degree of cross-linking had apparently little or no eﬀect on the structure [186]. Lamellar [187] and cubic [188] structures were also obtained with other polyelectrolyte gel/oppositely charged surfactant systems.

B. Structure of Polymer/Surfactant Complexes in the Solid State When mixing a solution of ionic surfactant and a solution of oppositely charged polyelectrolyte, one often observes the formation of a precipitate that is an electrically neutral polyion/surfactant ion complex containing no small ions. This precipitation explains that most studies of polyelectrolyte/ oppositely charged surfactant systems were performed at very low concentrations of both components. Some of the solid polyelectrolyte/surfactant complexes are soluble in organic solvents such as dimethylformamide, tetrahydrofuran, ethanol, or isopropanol [189,190] and even in n-alkanes or xylene [191–193]. These solutions have been cast into ﬁlms and examined using X-ray diﬀraction. Films of NaPSS/alkyltrimethylammonium bromide complexes showed highly ordered mesophases that changed gradually with the surfactant chain length [189,190]. This observation prompted many authors to study polyelectrolyte/surfactant complexes in the solid state, as powders or in the form of cast ﬁlms. These investigations often revealed mesomorphic order, similar to that found for surfactants alone as well as new phases. Highly ordered mesophases of the lamellar type were observed [189,194–196], in particular an undulating lamellar phase, called the egg-carton phase, with undulations of high amplitude [194–196]. Such structures appear to be of general character since they were observed with other polyion/surfactant ion complexes: poly(2-acrylamido-2-methyl-1-propanesulfonic acid-co-octadecylacrylamide) at diﬀerent ratios of the two monomers/CTAB [194], and PDADMAC/natural lipid [195,196]. Some other examples are now presented where the stoichiometric complexes were isolated and investigated as powders. Hexagonal and cubic structures were seen with NaPSS, NaPAA, and NaPMA complexes with alkylpyridinium chlorides [197]. Various polyelectrolyte/ﬂuorinated surfactant complexes were investigated. All showed mesomorphous order. Columnar liquid crystallinelike structures were observed in some of these systems [198,199]. A thermotropic phase transition from lamellar to hexagonal was observed with an NaPAA/(mixed cationic þ zwitterionic surfactant) system [200]. Smectic and cubic mesophases were evidenced in Copyright © 2003 by Taylor & Francis Group, LLC

complexes of a polyvinylsulfonate of low polymerization degree and various alkylammonium surfactants [201]. Interesting results were obtained with the complexes of sodium poly(-L-glutamate) and alkyltrimethylammonium bromides [202]. All complexes were of a lamellar structure. The surfactant alkyl chains were disordered for the DTAB- and CTAB-based complexes. They crystallized in a hexagonal lattice for the OTAB. To close this section we now cite some studies that somehow refer to the use of polymer/surfactant complexes. Electroluminescent mesostructured polyelectrolyte/surfactant complexes have been prepared using the water-soluble poly(1,4-phenyleneethylenecarboxylate) and dialkyldimethylammonium or alkylpyridinium surfactants [203]. Mesostructured PDADMAC/SDS complexes were used as hosts for the polymerization of difunctional monomers, resulting in the formation of unusually shaped polymer particles [204]. The addition of lead nitrate and sodium sulﬁde to an aqueous soluble PEO/SDS complex resulted in the formation of colloidal lead sulﬁde particles directly on polymer-bound aggregates (see Fig. 19). Aging of the system yielded long (5-mm) and thin (100-nm) rodlike colloidal aggregates with a layered structure [205]. This represents a new organic/inorganic hybride material. The method used can be extended to other systems.

FIG. 19 Particles observed ﬁve days after starting the precipitation reaction of lead acetate and sodium sulﬁde in the PEO/SDS systems. (a) Low-resolution image; (b) closeup of one of the particles showing adsorbed polymer chains. (From Ref. 205 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

IX. CONCLUSIONS This review has considered several aspects of polymer/surfactant systems. Some of the behaviors reviewed are summarized in Table 3. A qualitative understanding of these behaviors has now been reached. The importance of the hydrophobicity of the polymer in determining the properties of the systems—shape of the binding isotherm, cac, aggregation number, and microviscosity of the surfactant aggregates—has been clearly demonstrated. The nature of the surfactant headgroup and of its counterion in the case of ionic surfactants are also extremely important in determining whether an interaction takes place. Nevertheless, several other aspects of polymer/surfactant systems deserve further research. First, the studies should be extended to systems containing polyampholytes. Only one such study has been reported [206]. Also, the interactions between polymers and dimeric (gemini) surfactants should be investigated. Preliminary studies showed that the interaction between a given polymer (charged or neutral) and a dimeric surfactant is much stronger than with the corresponding monomeric (conventional) surfactant [207,208]. Another aspect concerns the microstructure of the polymer/surfactant systems in solution. More systematic studies should be performed using modern visualization techniques such as cryo-TEM, where one parameter at a time is progressively varied. Studies of solubilization described in Section VI and of the behavior of polymer/surfactant systems at interfaces (Section VII) should be greatly extended. Indeed, such studies are important in terms of the use of polymer/surfactant systems in formulations. Another direction of future research concerns polymer/surfactant complexes in the gel phase and in the solid state. Reported studies have uncovered a rich variety of structures with long-range order. More structures remain to be discovered in view of the variety of polyelectrolyte/surfactant systems. New materials may possibly be synthesized using polymer/surfactant complexes (see Ref. [205], concerning the SDS/PEO systems in the presence of lead and sulﬁde ions). In fact, it is likely that polymer–surfactant interactions are important for the explanation of the formation of mesostructured materials such as silica, or alumina in the presence of surfactants [209]. For instance, the acidiﬁcation of a solution of sodium silicate in the presence of CTAB results in the precipitation of a mesostructured siliceous material. It has recently been proposed that this material results from the interaction between the growing silica polymers and the CTAB present in the system, and its precipitation when the size of the polymerized silica/CTAB complex is large enough [210]. Also, much work remains to be done to characterize the interactions between surfactants and biological polymers such as proteins and nucleic acids. Cationic surfactants interact with DNA, but the Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 3 Some Characteristics of Polymer/Surfactant Systems Polymer

Nature of binding and binding model

CAC/ CMC

Aggregation number N

Aggregate microviscosity

1

Independent of [bound surfactant]

Higher than for free micelles

Bind all surfactants noncooperatively. Swelling of polysoap microdomains (Fig. 13)

0

Increases linearly with [bound surfactant]

Higher than for free micelles

Moderately hydrophobic polyelectrolytes

Noncooperative binding. Swelling of preexisting microdomains and creation of additional ones (Fig. 14)

1

Nearly constant

Unknown

Nonionic polymers (PEO, for instance)

Cooperative binding of anionic surfactants. Bind cationic surfactants only when suﬃciently hydrophobic. (i.e., PEO at high temperature, PPO) Necklace and beads model.

0.1–1

N smaller than for free surfactant micelles, decreases with increasing polymer hydrophobicity and concentration, increases with [bound surfactant]

Probably higher than for free surfactant micelles

Strongy hydrophilic polyelectrolytes

Bind only oppositely charged surfactants cooperatively. Necklace and beads model (Fig. 12)

Strongly hydrophobic polyelectrolytes

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structure of the complexes is still unknown although a cryo-TEM investigation showed very special features [211]. Two important aspects of polymer/surfactant systems have not been dealt with in this review: the theoretical aspects and the rheology of these systems. Both topics are being actively investigated and much progress achieved. Both topics deserve speciﬁc reviews.

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14 Highly Concentrated Cubic PhaseBased Emulsions MD. HEMAYET UDDIN and HIRONOBU KUNIEDA National University, Yokohama, Japan

Yokohama

CONXITA SOLANS Institute of Chemical and Environmental Research, CSIC, Barcelona, Spain

I.

INTRODUCTION

An emulsion is an opaque, heterogeneous system of two or more immiscible liquids (‘‘oil’’ and ‘‘water’’) generally stabilized by a third component, surfactant or other emulsiﬁers, where one of the liquids is dispersed as droplets of microscopic or colloidal size in the other [1]. High internal-phase volumeratio or highly concentrated emulsions are designed with the volume fraction of a dispersed phase, which exceeds Ostwald’s critical volume fraction (0.74) for the closest packing spheres [2–4]. Due to their high viscosity and gellike consistency, they are also called gel emulsions. The gel emulsions have received particular interest for speciﬁc applications as formulations such as gelled fuels, emulsion explosives, cosmetics, pharmaceuticals, etc. and novel reaction media for polymerization reactions [5,6]. Highly concentrated emulsions have been studied earlier, usually consisting of two isotopic liquid phases, which are formed in either water- or oil-rich regions of water– surfactant–oil systems [7–16]. In the oil-rich region oil droplets are dispersed in a small amount of aqueous micellar solution phase (O/W or O/Wm emulsions), whereas in the water rich-region, water droplets are dispersed in the oil-swollen reverse micellar solutions (W/O or W/Om emulsions). In both cases of emulsions, since a large amount of internal phase (maximum up to 99+%) is dispersed in a very small amount of continuous phase, each droplet touches closely to another and cannot move, and hence they are often very viscous. However, since the droplets are covered by a ﬂexible surfactant monolayer, these emulsions are rather fragile against coalescence, although the stability of W/O-type concentrated emulsions increases upon Copyright © 2003 by Taylor & Francis Group, LLC

addition of inorganic salt. Other types of emulsions are also known although their structures are not completely known [17,18]. Surfactants form a variety of liquid crystals with water or other solvents. Liquid crystals have been used as a continuous medium to stabilize emulsions in the ﬁeld of applications [19,20]. In contrast to conventional emulsions, thick surfactant layers of liquid crystals cover emulsion droplets and prevent their coalescence. High viscosity of liquid crystals also improves the emulsion stability. Lamellar liquid crystals (L) are mainly used to stabilize the emulsions, although reverse hexagonal liquid crystals (H2) are able to stabilize W/O-type emulsions [21]. However, studies on other types of liquid crystals-based emulsions are scarce. Recently, it was found that a stable and viscous high internal-phase-ratio emulsion or highly concentrated emulsion can be produced by using either micellar cubic (I1) or reverse micellar cubic (I2) liquid crystals [22,23]. The aim of this chapter is to review new experimental ﬁndings regarding these highly concentrated cubic phase-based emulsions. The cubic phase-based emulsions are mainly described in conventional poly(oxyethylene)-type surfactant systems. Other types of surfactants such as polyglycerol-type and suger-type surfactants are also used to form the concentrated emulsions. There are many methods or formulations to produce ﬁne emulsions. Among them, there is a well-known method called D-phase emulsiﬁcation on which a polyol-nonionic surfactant–oil gel is based [17]. This gel is also related to the present cubic phase-based emulsions. We also mention the correlation.

II. CUBIC PHASE-BASED EMULSIONS: GENERAL AND STRUCTURAL ASPECTS The cubic phases are stiﬀ (extremely viscous), optically isotropic, and structurally ordered in three dimensions. According to their underlying structure, the cubic phases can be divided into two families: micellar cubic phases and bicontinuous cubic phases [24]. The micellar (or reverse micellar) cubic phase consists of discrete micelles (or reverse micelles) packed in cubic symmetry. The normal (oil-in-water) micellar cubic phase (I1 ) is normally found between the aqueous micellar solution phase (Wm) and the normal hexagonal phase (H1 ), and the reverse (water-in-oil) micellar cubic phase (I2 ) is found between the reverse hexagonal phase (H2 ) and the reverse micellar solution phase (Om) in the phase diagram [25,26]. The bicontinuous cubic phase has two polar labyrinths separated by an apolar ﬁlm (bilayer), or vice versa, where the bilayer midplane can be modeled as a minimal surface. The bicontinuous cubic phase (V1 or V2 ) is normally found between the hexagonal phase (H1 or H2 ) and the lamellar phase (L) in the phase diagram Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 1 Schematic drawing of cubic phases: (a) normal micellar cubic (I1 ) (primitive lattice), (b) normal bicontinuous cubic (V1 ) (space group Ia3d), (c) reverse bicontinuous cubic (V2 ) (space group Ia3d), (d) reverse micellar cubic (I2 ) (primitive lattice).

[27]. The apparently complete phase sequence, Wm I1 H1 V1 L V2 H2 I2 Om is usually observed in some water–surfactant or water– copolymer–oil systems [28,29]. The schematics of the cubic structures are represented in Fig. 1. The cubic structures can be divided into three main families: primitive (P), body-centered (bcc), and face-centered (fcc), belonging to diﬀerent crystallographic space groups with diﬀerent symmetries. The simple primitive, bcc, and fcc contain 1, 2, and 4 micelles (or reverse micelles) per unit cell, respectively. Space groups with larger number micelles per unit cell, e.g., Pm3n having 8 micelles and Fd3m having 24 micelles, are also observed in surfactant, lipid, or block copolymer systems [24–27,29,30]. Commonly observed bicontinuous cubic belongs to the Ia3d space group where the bilayer channel structure can be associated with the so-called Gyroid (G) minimal surface; less common structures are the primitive Pn3m and the body-centered Im3m, the associated minimal surfaces are the Diamond (D) and the Schwartz (P) surfaces, respectively [24,25,31]. The types of self-organized structures formed in a given system mainly depend on the hydrophile-lipophile property of the surfactant. Hydrophilic surfactants such as long polyoxyethylene-chain nonionic surfactants tend to form discontinuous micellar cubic phase (I1 ) in water [32–34]. In the case of ionic surfactants, only few surfactants form the I1 phase in water [35]. The hydrophilicity of surfactant decreases with increasing surfactant concentration because the counterion concentration also increases. Hence, in most ionic surfactant systems, a hexagonal phase appears following the formation of an aqueous micellar solution. However, in both nonionic and ionic surfactant systems, the formation of the I1 phase is enhanced upon addition of oil, especially a long saturated hydrocarbon. A small amount of oil can be solubilized into the lipophilic core of micelles forming the I1 phase. Beyond the solubilization limit of the I1 phase, oil is separated as an excess phase Copyright © 2003 by Taylor & Francis Group, LLC

(O). Under some circumstances a large amount of oil can be incorporated or trapped into the I1 phase, forming a stable emulsion. The volume fraction of the incorporated or dispersed oil into the continuous I1 phase sometimes exceeds Ostwald’s critical volume fraction, c ¼ 0:74, of the most compact arrangement of uniform, undeformed spherical droplets. Consequently, the droplets in these emulsions are deformed and/or polydisperse. Because of the high internal-phase volume, oil droplets are covered by a thin viscous I1 phase, these emulsions are designated as highly concentrated O/I1 emulsions. Similarly, it is also possible to prepare a highly concentrated W/I2 emulsion. Long lipophilic-chain nonionic surfactants form reverse micellar cubic phase (I2 ) in water or oil [36,37]. A small amount of water can be solubilized in the polar core of the reverse micelles, forming the I2 phase. However, under some conditions a large amount of water can also be incorporated into the I2 phase to form the W/I2 highly concentrated emulsions in the I2 þ W regions. In both the O/I1 and W/I2 emulsions systems, the internal phase (oil or water) has a high volume fraction and external phases are comprised with the extremely viscous I1 or I2 phase and are schematically shown in Fig. 2a and b. Although the emulsions are thermodynamically unstable systems, they are often very stable because of the presence of a highly viscous external (I1 or I2 ) phase. The physicochemical properties of these emulsions are consistent with the previously found gel emulsions consisting of two isotropic phases. So the emulsions could be also named as the cubic phase-based gel emulsion. The stability of such an emulsion is correlated to the stability of the external cubic phase. In the following sections, methods of preparation, and some cubic phasebased emulsions forming water–surfactant–oil systems are presented, followed by a discussion of the conditions of formations, stability, and its correlation with the phase behavior. The structure of the external phase

FIG. 2 Schematic drawing of (a) O/I1 and (b) W/I2 gel emulsions. Copyright © 2003 by Taylor & Francis Group, LLC

and translucency of the gel emulsions are also discussed. The structure of the cubic phase both in the homogeneous phase region and in the nonequilibrium region as the external phase of gel emulsion were determined by small-angle X-ray scattering (SAXS) measurements.

III. METHODS OF PREPARATION The cubic phases (I1 or I2 ) are usually thermally stable. In the case of the I1 phase formed in water–surfactant binary system, swelling of long-chain hydrocarbon oil in micelles increases the thermal stability of the I1 phase and reaches its maximum. Upon addition of more oil, turbid viscous phase appears and ﬁnally the I1 phase is dispersed in a large amount of ﬂuid phase (oil). However, the maximum melting temperature of the I1 phase remains almost unchanged all over the composition (Fig. 3a). Similarly, the melting temperature of the I2 phase formed in the water–surfactant or surfactant–oil systems increases upon addition of water and reaches the maximum, which remains the same in the (I2 þ W) whole regions (Fig. 3b) [36]. In order to prepare a cubic phase-based emulsion whether it is O/I1 or W/I2 , the cubic phases (I1 or I2 ) should be melted above their maximum melting temperatures to enable an adequate mixing during the emulsiﬁcation process. As the mixture is agitated, the oil or water incorporates gradually in the surfactant phase and ﬁnally a gel (O/I1 or W/I2 ) is obtained by cooling the sample. Since the oil or water droplets are bounded by an extremely viscous cubic phase, the emulsions are very stable.

IV. CUBIC PHASE-BASED EMULSION-FORMING SYSTEMS A. O/I1 Emulsions Highly concentrated O/I1 emulsions generally occur in the oil-rich region of a ternary water–hydrophilic surfactant–oil system. A micellar cubic phase (I1 ) has been found in many systems, such as polyoxyethylene dodecyl or oleyl ethers, and so forth [28,32–34]. When the polyoxyethylene (EO) unit number is 8 or more, dodecyl ethers form the I1 phase in water. With increasing EO units the surfactant forms the I1 phase over a wide range of compositions and temperatures in a binary water–surfactant system. It is also reported that adding long-chain alkanes facilitates the formation of a normal micellar cubic phase to hydrophilic ionic or nonionic surfactant– water systems [38–40]. Hence, it is possible to form a stable concentrated O/ I1 emulsion in the hydrophilic surfactant–water–oil systems. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 3 (a) Phase diagram of water–C12EO25–n-decane system showing the Tmax of the I1 phase. The surfactant–water weight ratio is 50 : 50. I1 , Wm, and O indicate normal micellar cubic, aqueous micellar solution, and excess oil phases, respectively. (b) Phase diagram of binary water–Si14C3EO7.8 system forming the I2 phase. I2 , Om, W, and II represent reverse micellar cubic, a surfactant liquid phase containing small amounts of water, excess water phase, and a two-phase region, respectively. (From Ref. 36.) Copyright © 2003 by Taylor & Francis Group, LLC

1. Water–C12EO25–Oil System Figure 4 shows the phase diagram of a representative O/I1 gel emulsionforming system, water–polyethyleneglycol dodecyl ether (C12EO25)/decane at 258C [22]. In the water–C12EO25 binary axis, normal discontinuous cubic of the sample shows liquid crystal (I1 ) is observed. An pﬃﬃﬃX-ray pﬃﬃﬃ pﬃﬃdiﬀractogram ﬃ the spacing peak ratios: 1 : 1= 2 : 1= 3 : 1= 4, which corresponds to a body-centered cubic structure [24,41]. A small amount of oil can be solubilized into the lipophilic core of the micelle, forming the I1 phase. Upon addition of oil in the system, an excess-oil phase is separated beyond the solubilization limit of the I1 phase. Although the solubilization of oil in the I1 phase is small, it was found that a considerable amount of oil (up to 90 wt % decane) can be incorporated in the I1 þ O region in transparent or translucent gellike emulsions having an I1 phase as the external phase. These emulsions are quite stable, since coalescence and creaming are prevented by the extremely high viscosity of the external phase. A picture of a transparent gel emulsion formed at a water–surfactant weight ratio equal to 50 : 50 containing 90 wt % decane is shown in Fig. 5. A photomicrograph of the same gel emulsion, obtained by video-enhanced microscopy (VEM), is also represented in Fig. 6. To increase the contrast, a trace amount of water-soluble dye is incorporated in the sample. The emulsion is polydisperse and some of the droplets are polyhedral, since the volume fraction of the internal phase (hydrocarbon) exceeds the maximum value for a packing

FIG. 4 Partial phase diagram of a water–C12EO25–n-decane system at 258C. Wm, micellar solution; I1 , discontinuous cubic phase; S, solid present region; O, an excessoil phase. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Photograph of a transparent cubic phase-based emulsion containing 90 wt % n-decane. The C12EO25–water weight ratio is 50 : 50 in this sample. (From Ref. 22.)

of spheres, 0.74. The gel emulsion can be diluted with water to form normal emulsions with a small droplet size (1–10 mm). The stability of emulsions is related to the stability of the external cubic phase. In the case of decane, the thermal stability of the cubic phase increases upon the addition of a very small amount of oil (Fig. 3a). The

FIG. 6 VEM photomicrograph of the cubic phase-based emulsion described in Fig. 5. Water-soluble dye was added to enhance contrast. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

melting temperature of the cubic phase, that is, the phase-transition temperatures from the viscous cubic phase to a ﬂuid micellar solution phase, increases sharply with the incorporation of oil in the micelles forming the cubic structure until the phase separation occurs. Both the thermal-stability enhancing eﬀect and the solubility of oil in the cubic phase decrease as the molar volume of the oil increases, from decane to squalane, as shown in Fig. 7. The samples in the I1 þ O regions are heated to melt at a temperature above the maximum temperature of the I1 phase (Fig. 7), then the ﬂuid mixtures are adequately mixed by a vortex mixture. Finally, a stable gel emulsion is obtained by quenching the system. The structure of the external phase is identiﬁed experiments. pﬃﬃﬃ bypSAXS p ﬃﬃﬃ ﬃﬃﬃ Judging from the spacing peak ratios, 1 : 1= 2 : 1= 3 : 1= 4 obtained from SAXS data of the sample in the oil-swollen I1 region, the body-centered cubic structure in the water–C12EO25 binary system is preserved in oilpresent systems even in the I1 þ O regions. Hence, it is considered that the external (or continuous) phase of emulsions also consists of a body-centered cubic phase. Crossing the boundary between the I1 and I1 þ O regions (Fig. 4) the samples look either transparent (at water–C12EO25 ¼ 1 : 1) or gradually introduce turbidity with the oil content. Therefore, it is diﬃcult to determine the phase boundary by visual observation only. The interlayer

FIG. 7 Eﬀect of added oils on the melting temperature of cubic phases in C12EO25– water systems. The surfactant–water weight ratios are 50 : 50: (&) n-decane, (*) nhexadecane, (&) squalane, (~) TEH. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

spacing d of the cubic phase was measured as a function of increasing decane content, keeping the water–C12EO25 ratio constant at unity, and the results are shown in Fig. 8. Because oil is incorporated in the micelle core, micelles grow and d increases until an excess-oil phase separates. Hence, the phase boundary between the I1 and I1 þ O regions can be determined by the inﬂection point in the d curve. As mentioned above, along the water–C12EO25 ratio 1 : 1, the samples in the I1 þ O region also look transparent and ﬁnally a transparent gel emulsion is obtained at a high concentration of decane ( 90 wt % in the system). Searching for the reason for the transparency of gels, we carried out refractive index measurements on the cubic phase. Figure 9 shows that the values of the refractive index of the cubic phase and oil are very similar when the water–surfactant ratio is 50 : 50, which gives an explanation for the transparency of the isogels. In fact, gels became turbid when 40 : 60 and 60 : 40 surfactant–water ratios were used. Perfume molecules are hydrophobic organic compounds, usually insoluble in water and hence they have been solubilized in many water-based formulations by using surfactant. Figure 10 shows the phase behavior of the water–C12EO25– -ionone (IN) system examined at 258C [42].

FIG. 8 Change in inter layer spacing, d, in the I1 phase as a function of O or L þ O in a water–C12EO25–n-decane system at 258C. The C12EO25–water weight ratio is 50 : 50. (From Ref. 22.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Refractive index as a function of surfactant concentration in a C12EO25– water system. The dashed line indicates the refractive index of decane. (From Ref. 22.)

FIG. 10 Phase diagram of the water–C12EO25– -ionone system at 258C. Notations are as follows: I1 , discontinuous cubic phase; H1 , hexagonal phase; L, lamellar phase; V1 , bicontinuous cubic phase; D1, sponge phase; Wm, micellar solution phase; Om, reversed micellar solution phase; O, an excess-oil phase; II, two-phase region. (From Ref. 42.) Copyright © 2003 by Taylor & Francis Group, LLC

Solubilization of a synthetic perfume, IN, in the Wm and I1 phases is low. Upon further addition of IN, an excess-oil (O) phase separates from the phase boundaries of the single Wm and I1 regions. However, it was found that a large amount of IN (up to 80 wt %) can be incorporated into the I1 þ O region in O/I1 concentrated emulsions. Due to the large diﬀerence between the refractive index of pure water–C12EO25 cubic phase (1.41 when the water–surfactant mass ratio is unity) and that of dispersed IN (1.52), the emulsions are not translucent. It is reported that no stable emulsion could be formed in the oil-rich (Wm þ O) region [42]. From Fig. 10 it is observed that the normal hexagonal and lamellar liquid crystals can solubilize a considerable amount of -ionone. But the samples in these liquid crystals regions are not so viscous and when they are kept in an open vessel the perfume molecules evaporate. On the other hand, the O/I1 emulsion not only contains a large amount of perfume but also is rather stable against the evaporation of perfume molecules, since in this emulsion system perfume droplets are covered by the extremely viscous I1 phase. A large amount of other synthetic perfumes such as d-limonene can also be incorporated as a stable O/I1 highly concentrated emulsion.

2. Correlation Between D-Phase Emulsiﬁcation and Cubic Phase-Based Emulsions Sagitani et al. [43] found a new method called D-phase emulsiﬁcation to obtain ﬁne O/W emulsion. First, nonionic surfactant is mixed with polyol, oil, and a small amount of water to form a transparent or translucent gel. Then a ﬁne O/W emulsion can be obtained by diluting the gel with water [17,43]. The gel in the D-phase emulsiﬁcation is highly related to cubic phase-based concentrated emulsion. Figure 11 represents the phase diagram of a C12EO8–water–decane system at 258C [44]. In the water–binary axis, Wm and H1 phases are observed and there is no I1 phase at this temperature, since the I1 phase is formed below 208C [45]. Upon addition of decane to the aqueous system, the maximum temperature of the I1 phase is increased and the I1 phase appears in the ternary phase diagram as is shown in Fig. 11. The hexagonal liquid crystal is also changed to the I1 phase by adding decane. The rod micelles in the H1 phase are changed to spherical micelles in the I1 phase upon addition of oil at constant temperature. The oil-induced H1 –I1 transition is observed in many surfactant systems [46]. For example, to form a spherical micelle, the sectional area should be large by packing parameter theory; the critical packing parameter CP ¼ vL =aS l should be lower than 1/3, where vL is the volume of lipophilic chains, l is their eﬀective length, and aS is the interfacial area per surfactant molecule. aS is almost unchanged by the solubilization of long-chain hydrocarbon. Upon a small addition of the oil, l increases because it makes an oil pool inside aggregates. Hence, the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 11 Phase diagram of water–C12EO8–decane system at 258C. Wm is an aqueous micellar solution phase. I1 , H1 , V1 , and L indicate discontinuous micellar cubic phase, normal hexagonal phase, normal bicontinuous cubic phase, and lamellar phase, respectively. Om is a surfactant liquid or reverse micellar solution phase. O is an excess-oil phase. S is a solid present phase. (From Ref. 44.)

aggregate shape tends to the spherical in the presence of the oil. Because the I1 phase is present between the Wm phase and the H1 phase, it is considered to p beﬃﬃﬃ a discontinuous pﬃﬃﬃ pﬃﬃﬃ cubic phase (I1 ). Judging from the SAXS peak ratios, 1= 3 : 1= 4 : 1= 8, the I1 phase has a face-centered cubic structure (Fm3m). The interlayer spacing in the I1 phase increases with increasing oil content, as shown in Fig. 12. Beyond the solubilization limit of the I1 phase an excess-oil phase (O) is separated and two-phase regions (I1 þ O) are formed. Stable, very viscous, and gellike emulsions of the O/I1 type were formed in the I1 þ O region. A highly concentrated emulsion with the composition 7.6 wt % C12EO8–12.4 wt % water–80 wt % decane has been reported in which the shape of emulsion droplets is not spherical but polyhedral [44]. The appearance of this emulsion is similar to that of the gel emulsion obtained in the D-phase emulsiﬁcation [47]. The highly concentrated O/I1 gel emulsion looks turbid because the diﬀerence between the refractive indices of the I1 phase and the dispersed oil phase is large. Upon addition of alkyl polyol such as glycerol or 1,3-butanediol, the transparency of the emulsion in the I1 þ O region increases because the diﬀerCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 12 Change in interlayer spacing, d, in the I1 phase as a function of decane content in water–C12EO8–decane system at 258C. The C12EO8–water weight ratio is ﬁxed at 62 : 38. (From Ref. 44.)

ence in refractive index between the I1 phase and excess oil is decreased. The change in refractive index of the I1 phase as a function of alkyl polyol content in water is shown in Fig. 13. By increasing the alkyl polyol content, the refractive index approaches that of decane (1.4094). As shown in Fig. 14, the stable gel emulsion becomes translucent upon addition of glycerol. The maximum temperature of the I1 phase decreases with increasing polyol content [22]. Consequently, the addition of alkyl polyols is not crucial to form O/I1 gel emulsions in an oil-rich region. However, the addition of alkyl polyol is very eﬀective in increasing the refractive index of the I1 phase and consequently in preparing translucent O/I1 gel emulsions. Most nonionic surfactants used for commercial products are usually mixtures of surfactants, which have a distribution in hydrophilic chain length and often contain unreacted alcohol. For most of the systems for D-phase emulsiﬁcation, commercial poly(oxyethylene)-type nonionic surfactants have been used. The gel-phase regions are limited in oil-rich regions, and there is no cubic phase observed in phase diagrams. To understand the eﬀect of mixing surfactants on a cubic phase region, a phase diagram of water–C12EO4:8–decane system at 258C is shown in Fig. 15 [44]. C12EO4:8 is an equal-weight mixture of C12EO8 and C12EO3. It is evident that polyoxyethylene dodecyl ether does not form an I1 phase below the EO unit number 8. Consequently, there is no single I1 phase region in the phase diagram. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 13 Change in refractive indices of I1 (open symbols) and Wm (ﬁlled symbols) phases as a function of glycerol (&, &) or 1,3-butanediol (*, *) concentrations in water þ alkyl polyol at 258C. The (water þ polyol)–C12EO8–decane weight ratio is ﬁxed at 58:9 : 36:1 : 5. (From Ref. 44.)

FIG. 14 Eﬀect of added glycerol on the appearance of O/I1 concentrated emulsions or gel based on the I1 phase. The glycerol concentrations in water þ alkyl polyol are 0 (a), 0.20 (b), and 0.40 (c). The (water þ polyol)–C12EO8–decane weight ratio is ﬁxed at 18:6 : 11:4 : 70. (From Ref. 44.) Copyright © 2003 by Taylor & Francis Group, LLC

Instead, there is a two-phase region of I1 þ O in the oil-rich region. With increasing oil content, a fraction of the surfactant monomer is dissolved in oil and the solubility of a short EO-chain lipophilic surfactant (C12EO3) is much larger than that of a hydrophilic one (C12EO8). Then, the fraction of hydrophilic surfactant at the interface of aggregates dominates and hence the structures are characterized by the hydrophilic surfactant. Consequently, although the I1 phase is not observed in the oil-poor region, the I1 þ O twophase region appears (Fig. 15) as a gel in an oil-rich region. The presence of the I1 þ O region is conﬁrmed and discussed elsewhere in details [44]. Consequently, the O/I1 highly concentrated emulsion corresponds to a gel in the D-phase emulsiﬁcation although a single I1 phase is not observed in commercial surfactant system.

3. Water–Polyglycerol Fatty Acid Ester–Oil systems Polyglycerol fatty acid esters are biocompatible environmental-friendly surfactants. They are widely used as formulations of foods, cosmetics, and toiletries. Because the polyglycerols have a wide distribution of chain lengths and degree of esteriﬁcation, commercial polyglycerol fatty acid esters are usually a mixture of compounds. Phase diagrams of polyglycerol fatty acid esters, 10G*0.7L and 20G*1L in a water–decane system are shown in Fig. 16a and b, respectively at 258C [48]. 10G* and 20G* indicate the average polymerization degree of polyglyceryl chain as 10 and 20,

FIG. 15 Phase diagram of water–C12EO4:8–decane system at 258C. C12EO4:8 is an equal-weight mixture of C12EO8 and C12EO3. (From Ref. 44.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 16 Phase diagrams of (a) water–10G*0.7L–decane; (b) water–20G*1L–decane systems at 258C. Wm, H1 , I1 , Om, and O indicate an aqueous micellar phase, a hexagonal liquid crystalline phase, a discrete micellar cubic phase, a reverse micellar phase, and an excess-oil phase, respectively. (From Ref. 48.)

Copyright © 2003 by Taylor & Francis Group, LLC

respectively. 0.7L and 1.0L mean the average number of dodecanoic (or lauric) acid residues attached to poly(glycerol) chain. Neither 10G*0.7L nor 20G*1L forms a cubic phase in water at 258C, but each forms cubic phase with the addition of a small amount of decane. Because the cubic phases are found between the micellar solution (Wm) and the normal hexagonal (H1 ) phase (Fig. 16a), and adjacent to the Wm phase (Fig. 16b), it is considered to micellar cubic phase (I1 ). The SAXS peak pﬃﬃbe ﬃ a discontinuous pﬃﬃﬃ ratios 1 : 1= 2 : 1= 3 indicate that the I1 phase consists of either a face- or body-centered cubic lattice. The thermal stability of the I1 phase is increased with an increase in the solubilization of decane. An excess-oil phase coexists with the I1 phase beyond the solubilization limit of the I1 phase and the oil phase could be dispersed in the I1 as emulsion droplets. A highly viscous and stable gel emulsion containing 80 wt % decane has been obtained; obviously the oil droplets are polydispersed and polyhedral [48]. Sucrose alkanoates are biocompatible surfactants used for food, cosmetics, medicines, etc. The hydrophile-lipophile property of the surfactant can be varied by changing the number of attached lipophilic alkanoates tails. The phase diagram of a hydrophilic surfactant, L-1695–water–d-limonene (LN) at 258C is shown in Fig. 17 [49]. L-1695 (the mixture of 83.6% sucrose monododecanoate, 15.2% didocanoate, and 1.2% tridodecanoate) forms Wm and H1 phases in water. Upon addition of a hydrocarbon-type perfume, LN, perfume molecules swell into the core of cylinder in the H1 phase, change the interfacial curvature toward more positive (here, positive means the curvature is concave toward the lipophilic chain), and an H1 –I1 phase transition occurs. The I1 phase solubilizes a small amount of perfume and coexists with an excess-oil (LN) phase beyond the solubilization limit. O/I1 gel emulsion could be prepared in the oil-rich region of the I1 þ O phase. Instead, polar perfume such as linalool (LL) molecules penetrate into the palisade layer of the lipophilic chains of the surfactant, changes the interfacial curvature toward zero or negative, and H1 –L–Om phase transitions occur [49]. Consequently, an O/I1 -type gel emulsion could not be found in the L-1695–water–linalool (LL) system, that is, the formation of cubic phase as well as cubic phase-based gel emulsion is also highly dependent on the types of oil used for the formulations.

B. W/I2 Emulsions Water-in-oil-type highly concentrated emulsions can be formed based on the discontinuous reverse micellar cubic phase (I2 ). However, the I2 phase has been found only in a few systems, such as lecithin, polyoxyethylene-polyoxypropylene copolymer, sugar-related surfactant systems, and so forth [50– 53]. Recently, we have found that long lipophilic chain polyoxyethyleneCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 17 Phase diagram of the water–L-1695–d-limonene system at 258C. Notations are as follows: Wm, micellar solution phase; H1 , hexagonal liquid crystalline phase; L, lamellar liquid crystalline phase; I1 , normal micellar cubic phase; O, an excess-oil phase. (From Ref. 49.)

type silicone surfactants (or copolymers) form a reverse micellar cubic phase in water and/or oil even in the absence of solvent [54]. Silicone surfactants have unique surface-active properties, and they ﬁnd application in the production of polyurethane foams, textiles, cosmetics, agricultural adjuvants, paints, and so forth. Nonionic A-B-type silicone surfactants are ﬂuid even at high molecular weights due to the ﬂexibility of the lipophilic moiety; therefore, both hydrophilic EO-chain and lipophilic siloxane-chain lengths can be changed and hence diﬀerent mesophases, in which surfactant-layer curvature changes from negative to positive, are observed. The ﬂexibility of siloxane chains and the amphiphilicity of high-molecular-weight silicone surfactants are suitable for the formation of reverse aggregates. The phase diagram of poly(oxyethylene) poly(dimethylsiloxane) surfactants (copolymer) (Me3SiO-(Me2SiO)m-2-Me2SiCH2 CH2 CH2 -O-(CH2 CH2 O)nH, abbreviated SimC3EOn) in water as a function of the EO chain length or the volume fraction of EO chain to the total surfactant is shown in Fig. 18 at 258C [54]. From Fig. 18 it is evident that Si25C3EO5-19 forms I2 phase in water, which coexists with excess water (W) beyond the solubilization capacity of the I2 phase. An unstable emulsion can be produced in the I2 +W Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 18 Phase diagram of water–Si25C3EOn systems as a function of the EO chain length at 258C. f is the volume ratio of EO chain to the surfactant. I2 , H2 , L, and Om indicate reverse micellar cubic, reverse hexagonal, lamellar and surfactant liquid, or reverse micellar solution phase, respectively. W indicates excess water phase and S indicates solid present phase. (From Ref. 54.)

region. However, a stable W/I2 emulsion can be obtained in the oil-present system.

1. Water–SimC3EOn–Oil System Highly concentrated W/I2 emulsions generally occur in the water-rich region of the water–lipophilic surfactant–oil ternary phase diagram. Figure 19 shows a representative phase diagram of W/I2 emulsions forming the system water-Si25C3EO15.8-D4 (octamethylcyclotetrasiloxane) at 258C [23]. There are two single phases, namely an isotropic cubic phase and an oil-swollen reverse micellar solution phase (Om). The cubic phase is considered to be a reverse micellar cubic phase (I2 ) since it is located between the H2 phase and Om phase (Fig. 18). The structure of the I2 phase was determined by means Copyright © 2003 by Taylor & Francis Group, LLC

of a synchrotron radiation SAXS spectrometer. Figure 20 shows a representative SAXS pattern of a bulk (undiluted) Si25C3EO15.8 sample at 808C. A total of eight brag peaks was identiﬁed which can be indexed as the 110, 220, 311, 400, 331, 333, 440, and 533 reﬂections of the face-centered space group Fd3m (Q227). The Om phase can solubilize small amounts of water up to a maximum of about 15 wt % (Fig. 19). A considerably large reverse micellar cubic phase region is found at the surfactant corner of the phase diagram solubilizing a maximum of 28 wt % water (on the water–surfactant binary axis). An excess-water phase separates beyond the solubilizaton boundary of each Om and I2 phase. Just crossing the phase boundary from I2 to I2 þ W the samples are still viscous and become a little turbid, making it diﬃcult to determine the phase boundary between I2 and I2 þ W phases only by visual observation. To ascertain the phase boundary, the interlayer spacing (d) of the samples at constant Si25C3EO15.8/D4 weight

FIG. 19 Phase diagram of the water–Si25C3EO15.8–D4 system at 258C. I2 , reverse micellar cubic phase; Om, reverse micellar solution or surfactant liquid phase; W, an excess-water phase; S, solid present phase; II, two-phase region; III, three-phase region. SAXS measurements were performed to determine the phase boundary between I2 and I2 þ W regions along Si25C3EO15.8–D4 weight ratios of 80 : 20 and 70 : 30 indicated by lines A and B, respectively. (From Ref. 23.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 20 SAXS diﬀraction pattern obtained from a bulk (as received) Si25C3EO15.8 sample at 808C. The arrows indicate reﬂections corresponding to the Fd3m space group; q is the scattering vector. (From Ref. 23.)

ratios of 80 : 20 and 70 : 30 was measured by using SAXS, and the results are shown in Fig. 21 as a function of increasing water content. d increases as the micellar size increases upon solubilization of water into the reverse micellar core and becomes ﬂat after reaching the solubilization limit of the I2 phase. Hence, the inﬂection point of the d-curve clearly indicates the phase boundary between the homogeneous I2 phase and an excess water region. Although the solubilization amount of water in the I2 phase is not very much, a large amount of water (up to 90 wt %) can be incorporated as water droplets in the I2 þ W region, forming a turbid gellike emulsion having the I2 phase as the external continuous phase. Water incorporation in the stable emulsions can be increased (up to 96 wt % of water) in oil-present systems. In other binary water–Si25C3EO12.2, –Si25C3EO7.8, and –Si14C3EO7.8 systems, the maximum incorporation of water was around 40–50 wt % in the viscous I2 þ W phases; beyond this concentration water is separated out as an excess phase. However, in all the surfactant systems, in the presence of silicone oil (D4) more than 90 wt % of water can be incorporated in gellike emulsions. The presence of oil molecules into the surfactant palisade layer induces the change in curvature and Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 21 Variation of d in the I2 phase in the water–Si25C3EO15.8–D4 system as a function of water content at 258C. Lines A and B indicate the weight ratios of Si25C3EO15.8–D4 of 80 : 20 and 70 : 30, respectively. (From Ref. 23.)

ﬂexibility of the surfactant layer that allows higher amounts of water to be incorporated in the stable gel emulsions. The emulsions are quite stable, and excess water cannot be separated out even by centrifuging the samples for at least 12 h over 4000 rounds per min at room temperature, because coalescence and creaming could not take place because of the extremely high viscosity of the external I2 phase. The emulsions are also thermally stable and cannot be diluted with a lot of excess water because the I2 phase exists as an external phase. However, the gel emulsions can be diluted with D4 to form normal emulsions with a small droplet size (1–10 mm). It can be noted that very stable emulsions are not found in the water-rich Om +W region. The W/I2 gels look turbid over the entire range of compositions in which they can be produced, because of the diﬀerence in the values of refractive indices of the cubic phase and water. The refractive index of the continuous I2 phase is higher than that of the dispersed water phase. Replacing water partially with glycerol increases the refractive index of the dispersed phase. Figure 22 shows the refractive index of water þ glycerol as a function of glycerol concentration. The dashed line (Fig. 22) indicates the refractive index of the I2 phase of the composition Si25C3EO15.8/D4 ¼ 1 : 1. So it is observed that the refractive indices of the I2 phase and dispersed phase match each other when the water–glycerol weight ratio is 1 : 1. A photograph of a transparent W/I2 gel emulsion of the composition 90 wt % aqueous phase (water–glycerol ¼ 45 : 45) 10 wt % I2 phase (Si25C3EO15.8/ Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 22 Refractive index of water þ glycerol as a function of glycerol concentration. The dashed line indicates the refractive index of the I2 phase of composition 50 wt % Si25C3EO15.8–50 wt % D4.

D4 ¼ 5 : 5) is shown in Fig. 23. A photomicrograph of the gel emulsion containing 96 wt % water dispersed into 4 wt % I2 phase (Si25C3EO15.8/ D4 ¼ 2 : 2), obtained by video-enhanced microscopy (VEM), is shown in Fig. 24. The emulsion droplets are polydisperse and some of the droplets are polyhedral, since the volume fraction of the internal phase (water) is quite large (C > 0:74).

V. CONCLUSIONS Highly concentrated cubic phase-based gel emulsions, O/I1 and W/I2 , occur in the oil-rich and water-rich regions, respectively, of a ternary water–nonionic surfactant–oil system. Polyoxyethylene alkyl ether, polyglycerol fatty acid ester, and sucrose alkanoate surfactants form an O/I1 gel emulsion. On the other hand, long silicone chain surfactant or copolymer forms a W/I2 gel emulsion. The O/I1 emulsion corresponds to a gel in the D-phase emulsiﬁcation. The formation and stability of cubic phase-based gel emulsions are Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 23 A photograph of a transparent emulsion containing 90 wt % dispersed aqueous phase (water–glycerol ¼ 45 : 45) and 10 wt % I2 phase (Si25C3EO15.8–D4 weight ratio is 5 : 5).

FIG. 24. VEM photomicrograph of a reverse cubic phase-based emulsion containing 96 wt % water. The Si25C3EO15.8–D4 weight ratio is 50 : 50. Bar = 50 mm. (From Ref. 23.) Copyright © 2003 by Taylor & Francis Group, LLC

highly correlated to the conditions of formation and stability of the external (continuous) cubic phase. The thermal stability of cubic phase and hence that of the gel emulsion is enhanced upon addition of long-chain hydrocarbon oil and is decreased by adding polyols. The translucency of gel emulsion can be improved by partially replacing water with polyol. The emulsion droplets are polydisperse and polyhedral of shape. The O/I1 and W/I2 gel emulsions can be diluted with water and oil, respectively, to form normal emulsions with a small droplet size.

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

B.P. Binks. Modern Aspects of Emulsion Science. Cambridge, UK: The Royal Society of Chemistry, 1998, Ch. 1, pp 1–55. K.J. Lissant. J. Colloid Interface Sci. 22:462–468, 1966. H.M. Princen. J. Colloid Interface Sci. 71:55–66, 1979. H. Kunieda, C. Solans, N. Shida, and J.L. Parra. Colloids Surf. 24:225–237, 1987. E. Ruckenstein. Adv. Polym. Sci. 127:3, 1997. N.R. Cameron and D.C. Sherrington. Adv. Polym. Sci. 126:165, 1996. C. Solans, F. Comelles, N. Azemar, J. Sanchez Leal, and J.L. Parra. J. Cosm. Esp. Deterg. 17:109, 1986. C. Solans, N. Azemar, and J.L. Parra. Prog. Colloid Polym. Sci. 76:224–227, 1988. C. Solans, J.G. Dominguez, J.L. Parra, J. Heuser, and S.E. Friberg. Colloid Polym. Sci. 266:570–574, 1988. H. Kunieda, N. Yano, and C. Solans. Colloids Surf. 36:313–322, 1989. H. Kunieda, D.F. Evans, C. Solans, and M. Yosida. Colloids Surf. 47:35–43, 1990. R. Pons, C. Solans, M.J. Stebe, P. Erra, and J.C. Ravey. Prog. Colloid Polym. Sci. 89:110–113, 1992. C. Solans, R. Pons, S. Zhu, H.T. Davis, D.F. Evans, K. Nakamura, and H. Kunieda. Langmuir 9:1479–1482, 1993. R. Pons, P. Erra, C. Solans, J.C. Ravey, and M.J. Stebe. J. Phys. Chem. 97:12320–12324, 1993. R. Pons, J.C. Ravey, S. Sauvage, M.J. Stebe, P. Erra, and C. Solans. Colloids Surf. A. 76:171–177, 1993. R. Pons, I. Carrera, P. Erra, H. Kunieda, and C. Solans. Colloids Surf. A 91:259–266, 1994. H. Sagitani. J. Dispersion Sci. Technol. 9:115, 1989. A. Tsugita,Y. Nishijima, and T. Sasaki. Yukagaku 29:227, 1980. S. Friberg, L. Mandell, and M. Larsson. J. Colloid Interface Sci. 29:155–156, 1969. T. Suzuki, H. Takei, and S. Yamazaki. J. Colloid Interface Sci. 129:491–500, 1989.

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21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.

Y. Suzuki and H. Tsutsumi. Yukagaku 36:588, 1987. C. Rodriguez, K. Shigeta, and H. Kunieda. J. Colloid Interface Sci. 223:197204, 2000. Md.H. Uddin, C. Rodriguez, K. Watanabe, A. Lopez-Quintela, T. Kato, H. Furukawa, A. Harashima, and H. Kunieda. Langmuir 17:5169–5175, 2001. K. Fontell. Colloid Polym. Sci. 268:264–285, 1990. G. Lindblom and L. Rilfors. Biochim. Biophys. Acta 988:221–256, 1989. S.T. Hyde. J. Phys. Chem. 93:1458–1464, 1989 K. Fontell. Mol. Cryst. Liq. Cryst. 63:59, 1981. H. Kunieda, K. Shigeta, K. Ozawa, and M. Suzuki. J. Phys. Chem. B 101:7952–7957, 1997. P. Alexandridis, U. Olsson, and B. Lindman. Langmuir 14:2627–2638, 1998. V. Luzzati, R. Vargas, A. Gulik, P. Mariani, J.M. Seddon, and E. Rivas. Biochemistry 31:279–285, 1992. D.A. Hajduk, P.E. Harper, S.M. Gruner, C.C. Honeker, G. Kim, E.L. Thomas, and L.J. Fetters. Macromolecules 27:4063–4075, 1994. K.L. Huang, K. Shigeta, and H. Kunieda. Prog. Colloid Polym. Sci. 110:171– 174, 1998. K. Shigeta, M. Suzuki, and H. Kunieda. Prog Colloid Polym. Sci. 106:49–51, 1997. C. Rodriguez, Md.H. Uddin, H. Furukawa, A. Harashima, and H. Kunieda. Prog. Colloid Polym. Sci. 118:53-56, 2001. O. So¨derman, U. Olsson, and T.C. Wong. J. Phys. Chem. 93:7474–7478, 1989. H. Kunieda, Md.H. Uddin, M. Horii, H. Furukawa, and A. Harashima. J. Phys. Chem. B 105:5419–5426, 2001. C. Rodriguez, Md.H. Uddin, K. Watanabe, H. Furukawa, A. Harashima, and H. Kunieda. J. Phys. Chem. B 106:22–29, 2002. H. Kunieda, K. Ozawa, and K.L. Huang. J. Phys. Chem. B 102:831–838, 1998. K. Shigeta, C. Rodriguez, and H. Kunieda. J. Disp. Sci. Technol. 21:1023– 1042, 2000. X. Li and H. Kunieda. Langmuir 16:10092–10100, 2000. P. Sakya, J.M. Seddon, R.H. Templer, R.J. Mirkin, and G.J.T. Tiddy. Langmuir 13:3706–3714, 1997. Md.H. Uddin, N. Kanei, and H. Kunieda. Langmuir 16:6891–6897, 2000. H. Sagitani, Y. Hirai, K. Nabeta, and M. Nagai. Yukagaku 35:102–107, 1986. H. Kunieda, M. Tanimoto, K. Shigeta, and C. Rodriguez. J. Oleo. Sci. 50:633–639, 2001. D.J. Mitchell, G.J.T. Tiddy, L. Waring, T. Bostock, and M.P. McDonald. J. Chem. Soc. Faraday Trans. 1 79:975–1000, 1983. H. Kunieda, G. Umizu, and K. Aramaki. J. Phys. Chem. B 104:2005–2011, 2000. H. Sagitani, T. Hattori, K. Nabeta, and M. Nagai. J. Chem. Soc. Japan 1399– 1404, 1983.

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48. 49. 50. 51. 52. 53. 54.

H. Kunieda, K. Aramaki, T. Nishimura, and M. Ishitobi. Nihon Yukagaku Kaishi 49:617–624, 2000. N. Kanei and H. Kunieda. Nihon Yukagaku Kaishi 49:957–966, 2000. R. Angelico, A. Ceglie, U. Olsson, and G. Palazzo. Langmuir 16:2124–2132, 2000. J.M. Seddon. Biochemistry 29:7997–8002, 1990. P. Alexandridis, U. Olsson, and B. Lindman. Langmuir 12:1419–1422, 1996. H. Minamikawa and M. Hato. Langmuir 14:4503–4509, 1998. Md.H. Uddin, Y. Yamashita, H. Furukawa, A. Harashima, and H. Kunieda. Prog. Colloid. Polym. Sci. Accepted.

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15 Adsolubilization and Related Phenomena CLAUDE TREINER

I.

Universite´ Pierre et Marie Curie, Paris, France

INTRODUCTION

Surfactants may be deﬁned as chemical compounds that spontaneously form aggregates of a few dozens monomers in aqueous solutions above a critical concentration. The simplest aggregation that occurs in solution is the micelle. Such aggregates may incorporate poorly soluble molecules and therefore increase their solubility limit: this is the basis of the micellar solubilization eﬀect. However, surfactants may associate to form aggregates at solid–water or polymer–water interfaces as well. Such aggregates may also incorporate hydrophobic molecules or other chemical species as the result of their poor interaction with the aqueous media. This phenomenon has been called adsolubilization. The literature on surfactant adsorption at the solid–water interface is extremely voluminous, and various reviews and books have adequately covered the diﬀerent aspects of this subject [1–3]. Thus, only some basic information on the adsorption of surfactants that could be useful for the discussion of the adsolubilization phenomenon will be recalled here. Ever since the concept of the hemimicelle was put forward [4], it has been recognized that surfactant monomers may form structural aggregates of various geometries as they adsorb on solid surfaces. These geometries depend on the surfactant concentration, the pH of the system, the presence of salts, the properties of the surfactant, and that of the solid surface in terms of charge, chemistry, and porosity. Modern techniques of investigation that have been applied to these systems such as neutron scattering, ellipsometry, or atomic force microscopy (AFM) have provided new pictures that could not have been imagined before. Thus, it seems established that cationic surfactants form half-cylinders on crystalline hydrophobic substrates, full cylinders on mica, and spheres on amorphous silica [5]. Note,

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however, that ellipsometry and AFM study the organization of surfactants on solid plates whereas most of the systems that will be discussed in this chapter are dispersed ﬁne particles. It is not clear today how cylinders, for example, can ﬁt into the geometry of very small particles. Furthermore, AFM investigations apply above the equilibrium critical micelle concentration (CMC); thus, the assumed geometries of surfactant aggregates that have been suggested below the CMC (hemimicelles, admicelles)—that is, below full coverage—rely mostly on indirect evidence. Discussions on the adsorption of surfactants are often based on the proﬁle of the adsorption isotherm as displayed in Fig. 1. In very broad terms this proﬁle in the case of a cationic surfactant adsorbed on hydrophilic mineral oxide particles [6] (which is the substrate most often discussed in this chapter) may be interpreted along the following lines.

FIG. 1 Adsorption isotherm of cetylpyridinium chloride on a porous silica at pH ¼ 6.5 in the presence of 1.0 102 NaCl: CMC ¼ 2:4 104 mol=l1 . Copyright © 2003 by Taylor & Francis Group, LLC

In region I isolated molecules lie ﬂat onto the solid surface. In region II small aggregates are formed that should be able to incorporate hydrophobic molecules. These aggregates grow in size as the surfactant concentration increases until they form some type of identiﬁable geometry: micelles, bilayers, half-cylinders, or cylinders. One of the questions that will arise in the following is to what extent the geometry of the aggregates inﬂuences the quantity of incorporated solute. Region III sometimes coincides with the solid isoelectric point. Some repulsion between the neighboring surfactant headgroups slows down the path toward full surfactant coverage. Region IV begins around (sometimes above) the surfactant equilibrium CMC; beyond that point, the quantity of surfactant adsorbed remains constant if the conditions for surfactant multilayers are not met. Evidently all the physicochemical parameters recalled above may considerably inﬂuence this oversimpliﬁed view of surfactant adsorption at solid–water interfaces. For most systems, ionic surfactants adsorb on solid surface sites of opposite charges: the most common mineral oxides used are silica [isoelectric point (iep) ¼ 2.5], alumina (iep ¼ 9.1), and titanium dioxide (iep ¼ 5.8). The solid surfaces are predominantly negatively charged above the iep. Thus, cationic surfactants are usually adsorbed on silica and anionic surfactants on alumina. However, cationic surfactants may be adsorbed on alumina above the iep, and titanium dioxide can be used for both types of ionic surfactants. The term adsolubilization has been coined to describe an eﬀect akin to micellar solubilization, i.e., to the incorporation of a hydrophobic solute, usually a small molecule, to surfactant aggregates in an aqueous solution. A recent review article presents some aspects of the adsolubilization phenomenon [7]. The present chapter will embrace the incorporation to solid–water interfaces of various molecules that do not adsorb spontaneously to such interfaces, but can be incorporated through some type of interaction with an adsorbing surfactant molecule. This concerns classically poorly water-soluble hydrophobic molecules. However, the ionized form of some of these molecules may become water-soluble. The latter case cannot be ignored as the pH is an essential parameter for the characterization of the solid surface properties. A pH change modiﬁes at the same time the number of the solid charged surface sites, the quantity of adsorbed surfactant, and, in the case of ionizable solutes, the charge of the solute and therefore the electrostatics of the system. Furthermore, surfactants or hydrophilic polymers that do not adsorb spontaneously from solution to a solid surface can be incorporated to the solid–water interface by the formation of mixed aggregates with an adsorbing surfactant and will be considered as related to the adsolubilization eﬀect. However, because the polymer–surfactant interaction at surfaces Copyright © 2003 by Taylor & Francis Group, LLC

is discussed extensively in a speciﬁc chapter of this volume, only some typical examples are provided in the present chapter. The phenomenon known as elutability (the displacement of adsorbed compounds such as proteins from a solid–water interface by the addition of surfactants) is mentioned here only for the sake of completeness [8]. Likewise, molecules used as probes for the investigation of the properties of adsorbed surfactant aggregates: pyrene for static or time-resolved ﬂuorescence, 12-doxylstearate for ESR experiments, and others may be considered as adsolubilized in the surfactant aggregates. Their behavior will not be discussed. Other terms have been used to describe the same phenomenon: surface solubilization, sorption, coadsorption, surfactant mediated adsorption. It is of the interest to all scientists in the ﬁeld to use the same term if only for an easy usage of computerized literature searches. It seems that ‘‘adsolubilization’’ is recognized by an increasingly large number of experts as the most suitable one. It will be used as deﬁned above even for the description of results that were presented under other equivalent terms. The phenomenon as deﬁned above will be described separately under three diﬀerent headings: small molecules, surfactants, and neutral hydrophilic polymers. Some applications of the adsolubilization phenomenon will also be presented in the areas of thin-ﬁlm preparation, environment, and pharmacy.

II. EARLY WORKS Before the systematic investigations on adsolubilization as it developed in the 1980s, some scattered interesting studies may be found in the literature which describe experiments very much related to adsolubilization although the word was proposed only years later. Stigter and co-workers [9] were apparently the ﬁrst authors to describe this phenomenon in a remark in a paper otherwise devoted to the determination of the diﬀusion constant of ionic micelles in water using dyes as probes. They note that when the anionic dye Orange OT is used in conjunction with the cationic surfactant cetylpyridinium chloride (CPC), 50% of the dye was adsorbed by the walls of the glass; the same eﬀect was not observed in the presence of SDS. They correctly interpret this observation as the result of the cationic surfactant forming a bilayer on the negatively charged glass promoting the binding of the anionic dye on its surface. They call this eﬀect a surface solubilization. There are some hints in the medical area that this eﬀect was used for practical purposes. Thus, the cationic surfactant under the general name of benzalkonium chloride, a mixture of dimethylbenzylalkylammonium chlorides of varying hydrocarbon chain lengths, was used as an anchor of the antithrombotic heparin, a negatively charged polysaccharide, on graphite [10]. Later, the same surfactant was used, which, upon adsorption on the polymer Copyright © 2003 by Taylor & Francis Group, LLC

polytetraﬂuoroethylene, bound negatively charged antibiotic molecules such as penicillin G, cephalothin, and cefoxithin as a device for the protection against infections of vascular prostheses by Staphylococcus aureus [11]. The adsorption of the cationic surfactant although physisorbed on the polymer was suﬃciently strong so that repeated washing with water at low or high pH did not induce desorption of the surfactant and hence ensured some in vivo stability to the device. The optimum conditions for this approach were thoroughly investigated [12] in the case of double and triple hydrocarbon chains adsorbed on the polymers Teﬂon and Dacron. The technique used was ESR with various spin probes. The Russian group of Klimenko also performed adsolubilization experiments of 1-naphthol-phtaleine [13] and naphthalene [14] on acetylene black using nonionic surfactants. The similarity of the adsolubilization and micellar solubilization eﬀects was recognized in these early papers. It was pointed out that the adsolubilization capacity of 1-naphthol-phtaleine and naphthalene is larger than the solubilization one; an observation will be made repeatedly for ionizable molecules. It was also recognized that the presence of surfactants in the environment may inhibit the uptake of pollutants by activated carbon. Thus, the adsolubilization of 2-naphthol was studied on activated carbon in the presence of adsorbed SDS [15]. It was shown that the kinetics of adsolubilization may be increased by the presence of the surfactant, but the competition between the solute and the surfactant for adsorption results in an inhibition of the incorporation of the former in favor of the latter molecule at the solid–water interface. Color change observations as the result of the adsolubilization of a cationic dye, pinacyanol hydrochloride, at the alumina–water interface using an anionic surfactant were reported in 1982 [16]. Rupprecht, a pharmacologist, with his group at Regensburg University in Germany investigated the question of adsolubilization as a means for the development of drug delivery systems [17–19]. However, the systematic investigation of adsolubilization started with the classical study by Harwell and his group at the University of Oklahoma at Norman who introduced the term ‘‘adsolubilization’’ [20].

III. ADSOLUBILIZATION BEHAVIOR OF POORLY SOLUBLE MOLECULES A full typical adsolubilization proﬁle has been displayed in Fig. 2 for 2naphthol, a commonly used solute in adsolubilization studies, adsolubilized with CTAB at a silica–water interface. The surfactant adsorption isotherm is also displayed in this graph [6]. 2-Naphthol does not adsorb on the solid surface in the absence of surfactant. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 2 Adsorption isotherm of CPC at a silica–water interface * (left scale) at pH ¼ 3.6 (NaCl ¼ 1.0 102). Adsolubilization of 2-naphthol * (right scale).

The concentration of the solute is kept constant, below its solubility limit, and the surfactant concentration is varied in a large concentration domain. As the surfactant concentration is increased, the solute is incorporated (adsolubilized) in the adsorbed aggregates that are formed onto the solid surface. The adsolubilization increases with the amount of surfactant adsorbed up to the region of the surfactant CMC. As the surfactant concentration is further increased and free micelles are formed, the solute is partitioned between the adsorbed and the free micelles until, at still-higher concentrations, the solute molecules may be considered as desorbed from the adsorbed aggregates and solubilized in the free micelles. Thus, adsolubilization occurs below the CMC, adsolubilization and micellar solubilization compete for incorporation of the solute molecules above the CMC, and only micellar solubilization is observed at still-higher surfactant concentration. A few exceptions to this general behavior will be considered below. The case of naphthalene is somewhat diﬀerent, as this solute adsorbs somewhat onto the silica surface (Fig. 3). Nevertheless, as the equilibrium CMC is attained, naphthalene molecules partition between the free micelles and the adsorbed aggregates as in the case of 2-naphthol. The investigation of the micellar solubilization phenomenon has from almost the beginning made use of a partition coeﬃcient to describe the strength of the interaction between the solute and the surfactant aggregates. Thus, literally hundreds of partition coeﬃcients are available for numerous solutes in anionic, cationic, or nonionic surfactant solutions. This has Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 3 Adsorption isotherm of CTAB * at pH ¼ 3.6 (NaCl ¼ 1:0 102 ) on a porous silica (left scale); * adsolubilization of naphthalene (right scale).

enabled theoretical calculations as well as correlation approaches to be performed which have led to a better understanding of the physicochemical parameters responsible for the incorporation of solutes to free surfactant aggregates. The same approach has not been systematically used for the adsolubilization phenomenon. The ﬁrst review on adsolubilization appeared in 1995 [21]. However, it is essential in view of the apparent similarity between the incorporation of a solute to a free aggregate or to an adsorbed one to compare whenever possible the corresponding partition coeﬃcients.

A. Calculation of Partition Coefﬁcients from Adsorption Batch Experiments The partition coeﬃcient of a neutral species between the surfactant aggregates, considered as a pseudophase, and the aqueous media may be performed using two experimental procedures: (1) at constant solute concentration and variable surfactant concentration, or (2) at constant surfactant concentration and variable solute concentration. Both procedures have been employed, depending on the problem at stake. If, for example, the focus is on the optimum conditions for adsolubilization, i.e., the conditions beyond which solute desorption occurs, then method 1 will be preferred [22,23]. If the solute is suﬃciently water-soluble, the second method may

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be employed [24–27]. In both cases a partition coeﬃcient may be calculated from the relation KS=W ¼ 55:5

s Cads surf Cws Cads

ð1Þ

c surf where Cads , Cws and Cads are, respectively, the concentrations of coadsorbed solute, free solute, and adsorbed surfactant. If the partition model is valid at c over Cws constant initial solute concentration, a plot of the ratio of Cads surf versus Cads should be linear crossing the origin and the slope is equal to KS=W . Such a plot is shown in Fig. 4 for three steroids, namely, progesterone, testosterone, and hydrocortisone, adsolubilized with CPC on silica [28]. c Alternatively, at constant initial surfactant concentration, a plot of Cads s versus Cw should be linear. If the adsolubilization process occurs as the result of a speciﬁc interaction such as ion binding between the surfactant and the solute, neither of these plots is linear and a Langmuir plot may be

FIG. 4 Determination of KS/W for progesterone *, testosterone ^, and hydrocortisone * on a nonporous silica–water interface in the presence of CPC below the CMC (NaCl ¼ 0.15 mol l1); see Eq. (1). Copyright © 2003 by Taylor & Francis Group, LLC

applied at constant surfactant and variable solute concentration from the classical relationship 1 1 1 þ s ¼ Cs s s C Cads K b ads;max Ceq ads;max

ð2Þ

s where Cads;max is the maximum solute adsolubilization and Kb the binding constant for the reaction.

B. Solute Concentration Effects on Adsolubilization Most literature data on the solubilization of poorly soluble solutes in micellar solutions provide a single partition coeﬃcient corresponding either to the saturation conditions or to supposedly inﬁnitely dilute solutions. However, using a ﬂuorescence technique as applied to the micellar solubilization of alkanols in SDS solutions, above the CMC [29] it was shown that the partition coeﬃcient of n-hexanol and n-heptanol between SDS solutions and water decreases as the solute mole fraction in the micelles increases above a mole fraction of 0.5 to a constant lower value corresponding to the saturation conditions. The decrease of KS/W for the n-alkanols studied was of a factor of 3 between the dilute and the saturated partition coeﬃcient value. The same behavior was observed [30] for 1-pentanol in SDS micellar solutions as deduced from a head-space gas-chromatographic method. The value of KM/W varied from 750 (mole fraction scale) to 400 as the mole fraction of the alcohol in the micelles increased from 0.03 to 0.50. This trend could be predicted theoretically [31]. The activity coeﬃcient of both solutes and surfactants for a number of systems was found using a very sensitive vapor pressure method from which absolute solubilization constants were determined [32,33]. The trend of the variation of KM/W with solute occupancy was shown to depend upon the surfactant charge, the solute hydrophobicity of the solute, and the concentration of the two chemicals. For example, the solubilization constant of benzene in CTAB micelles decreases with solute occupancy but increases by a factor of 2 for cyclohexane within a solute mole fraction in micelles of 0.3 while the opposite trend is observed for n-butanol. Likewise for phenol, it is shown using a semiequilibrium dialysis method that KM/W decreases with increasing solute occupancy in CPC micelles [34]. Thus, it may be safely concluded that for polar solutes, the micellar solubilization constant decreases with increasing solute occupancy. The same wealth of information has not been gathered for the adsolubilization eﬀect. It has been shown that for linear alkanols coadsorbed with SDS on alumina [35] the adsorption is relatively larger at small surfactant coverage than at larger ones. This is at variance with the micelCopyright © 2003 by Taylor & Francis Group, LLC

lar solubilization ﬁndings. The interpretation of this observation is based upon a two-site model where alcohol molecules are adsorbed predominantly in the polar palisade admicellar layer and to a much lesser extent within the hydrocarbon core of the surfactant aggregates. The former mode of adsorption would decrease as the surfactant surface coverage increases and as the admicelles merge to form a bilayer. The same interpretation was suggested for 2-naphthol adsolubilized with SDS on alumina where KS/W was also found to decrease as SDS adsorbed concentration increases, i.e., as the solute mole fraction in the aggregates decreases [25]. Again this is in opposition with the micellar constant variation with solute occupancy. The same observation has been made indicating that for 2naphthol on laponite clay with cationic surfactants solute incorporation is larger at small surfactant coverage (high solute mole fraction) and decreases as the surfactant coverage increases [36]. Likewise, for naphthalene and phenanthrene adsolubilized by SDS and Tween 80 on Kaolinite, KS/W decreases as the solute/surfactant ratio decreases below the CMC [37]. However, for naphthalene adsolubilized with SDS on alumina, the partitioning seems to be independent of the solute occupancy, at least in the concentration range investigated, an observation that may be looked upon as a conﬁrmation of the suitability of the two-site model suggested for polar molecules [35]. A three-site model has also been suggested for the interpretation of apparently nonlinear adsolubilization behavior of aromatic molecules such as naphthalene, anthracene, and 1-naphthol as a function of surfactant concentration on a precipitated silica chromatographic column [38]. This model is based on the various assumed structural changes of CTAB aggregates on that solid surface upon surfactant covering. Thus, it seems that the available results for solute concentration eﬀects on adsolubilization constants are in opposition to the micellar solubilization ﬁndings. Thus, a nonambiguous comparison between the adsolubilization and the micellar solubilization constants is hampered by the fact that solutes may be adsolubilized even at small surfactant coverage (region I of the adsorption isotherm) as the solid particles become hydrophobic, whereas in the case of micellar solubilization, solute uptake by surfactants is hardly noticeable below the CMC. Thus, the micellar solubilization eﬀect should, in principle, only be compared to the adsolubilization eﬀect above the equilibrium CMC. However, at that concentration, the adsolubilization begins to decrease because of the formation of free micelles. In conclusion, the surfactant as well as the solute concentrations range at which micellar solubilization and adsolubilization results can be rigorously compared appears rather narrow.

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C. Comparison Between Admicellar and Micellar Partition Coefﬁcients It is often assumed in the literature that adsorbed aggregates and free micelles present many common features. If this was the case also for the adsolubilization and the micellar solubilization phenomena, it would be of the utmost interest as partition coeﬃcients of solubilization are available by the hundreds in many surfactant solutions. These data could thus be readily used for the prediction of the behavior of a considerable number of diﬀerent solutes in adsorbed aggregates on various solid–water interfaces and under very diﬀerent solution conditions. Such assumptions have been made, for example, for the simulation of phenanthrene adsolubilization and removal from soil by a biosurfactant, rhamnolipid [39]. Micellar solubilization constants have been derived using a number of diﬀerent techniques: vapor pressure, conductivity, microcalorimetry, spinecho NMR, ﬂuorescence, solubility, and micellar liquid chromatography (MLC). The number of methods applied to the determination of adsolubilization constants is not as large. Essentially the batch method and the MLC method have been used. Micellar solubilization constants may also be derived from adsolubilization experiments performed above the CMC, using the deﬁnition of a solubilization coeﬃcient as KM=W ¼ 55:5

Cws ðc

s Cmic CMCÞ

ð3Þ

s where C is the total surfactant concentration and Cmic is the concentration of solute solubilized in the micelles. Combining Eqs. (1) and (3), one can deduce the following relation [26]:

s Cads ¼

Cts surf 1 þ ½ð1 þ KM=W ðc CMCÞ=ðKS=W Cads;max ÞÞ

ð4Þ

where Cts is the total solute concentration introduced in the system. Knowing KS/W from the adsolubilization experiments below the CMC as presented in Fig. 4, the only unknown in Eq. (4) is KM/W, the micellar solubilization constant whose value can be deduced from a ﬁtting of the decreasing portion of the full adsolubilization curve as shown in Fig. 5 for progesterone adsolubilized on silica with CPC [28]. Now that all the parameters in Eq. (4) are known, we can calculate the surfactant concentration for which 95% of the solute is solubilized in micelles. In the case of Fig. 5, it is about 100 times the CMC. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Adsolubilization of progesterone with CPC at a silica–water interface. Continuous curve: ﬁtting of KM/W using Eq. (4). The arrow indicates the equilibrium CMC.

1. Systems Calculated from Batch-Type Experiments Some authors have compared adsolubilization and micellar solubilization constants. Usually the techniques were diﬀerent for either thermodynamic constant, and as discussed above, comparison between these may be fruitless if the experimental conditions do not meet the same criteria. An attempt will be made in the following to present such a comparison in a few examples. Figure 6 presents a correlation between log KS/W and log KM/W for various solutes on CPC adsorbed on hydrophilic silica [40]. The continuous line was drawn as the bisectrix of the ﬁgure. The data were obtained from the same technique at the same pH value, under the same experimental conditions, and the constants calculated were from Eqs. (1)–(4) with the same assumptions. Table 1 provides some additional information on some of the systems presented in Fig. 6. At the pH of the experiments (pH ¼ 6.5) these were all undissociated molecules. One observes that for ionizable species (phenols or amines) KS/W constants values are systematically larger than KM/W by a factor of 3 [23,26], whereas KS/W-values are equal to KM/W for nonionizable ones (alkyl and aromatic alcohols) [23,26] or hydrocortisone, progesterone, or testosterone [28,41]. As the observation applies to acidic as well as basic molecules, one may suggest that the charge is not responsible for this additional adsolubilization eﬀect when compared to the behavior of neutral molecules. Other examples are provided below. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 6 Correlation between KS/W and KM/W for various solutes with CPC on silica at pH ¼ 6.5 (NaCl ¼ 1:0 102 ). * Nonionizable molecules, in increasing order: 2phenoxyethanol < hydrocortisone < 3-phenoxypropanol, 1,4-benzoquinone < 1,4naphthoquinone < testosterone < progesterone < 2-naphthaleneethanol. * Ionizable molecules: 1,4-nitroaniline, 1-naphthylamine < 2-naphthol < 1,4-salicylic acid < 2,4,6-trichlorophenol.

For phenol and 4-chlorophenol adsolubilized with CTAB on silica, KS/W is also larger than KM/W by a factor of 3 [42]. The limiting partition coeﬃcients KS/W for 2-naphthol adsolubilized on SDS-coated alumina are essentially equal to that of KM/W. However, for naphthalene, KS/W is larger than KM/W [25]. For phenanthrene adsolubilized with the nonionic Tween 80 on kaolinite, KS/W ¼ KM/W. However, with SDS at pH ¼ 6.5, KS/W was 10 times larger than KM/W. Furthermore, KS/W decreased signiﬁcantly with increasing pH for SDS, while this eﬀect was very small for Tween 80 [37]. The adsolubilization of -Tocopherol (a component of Vitamin E) and its analogs was determined with a nonionic surfactant, Tween 80, on a hydrophilic silica. KS/W is systematically larger than KM/W, although the eﬀect is relatively small (typically of the order of 30%) [43,44]. In such a case, the method of calculation could be partially responsible for the diﬀerences observed. For naphthalene and phenanthrene with petroleum sulfonate-oil surfactants (petronates) coadsorbed on a soil–water interface (Oshtemo BHorizon containing 89% sand, 6% clay, and 5% silt), KM/W was slightly larger than KS/W. Note, however, that instead of a micellar phase, KM/W refers to an emulsion phase [45]. Again [46] for naphthalene or phenanCopyright © 2003 by Taylor & Francis Group, LLC

TABLE 1 Solute Partition Coefﬁcients of Adsolubilization and of Micellar Solubilization (Molar Scale) at 258C Surfactant

Solid

pH

Medium

log KS=W

log KM=S

Ref.

Hydrocortisone

CTAB

SiO2

6.5

2.02

1.88

28

Testosterone

CTAB

SiO2

6.5

2.59

2.52

28

Progesterone

CTAB

SiO2

6.5

3.16

3.19

28

HNaa

CTAB

SiO2

6.5

3.71

3.44

41

2-Naphthalene-ethanol 1-Naphthylamine 2-Naphthalene-ethanol 2-Naphthalene-ethanol 1-Naphthylamine 1-Naphthylamine 2-Naphthol 2-Naphthol

CTAB CTAB CTAB CTAB CTAB CTAB CPC CPC CTAB CPC CTAB CPC CTAB

SiO2 SiO2 Al2 O3 TiO2 Al2 O3 TiO2 SiO2

NaCl 0.15 M, ethanol 10% NaCl 0.15 M, ethanol 10% NaCl 0.15 M, ethanol 10% NaCl 0.15 M, ethanol 10% NaCl 0.01 M NaCl 0.01 M NaCl 0.01 M NaCl 0.01 M NaCl 0.01 M NaCl 0.01 M NaCl 0.01 M

3.38 3.23 3.42 3.51 3.33 3.27 3.68 4.01

3.29 2.92 3.29 3.29 2.92 2.92 3.22 3.22 3.26 3.22 3.29 3.22 3.29

26 26 26 26 26 26 6 6

Solute

2-Naphthol 2-Naphthalene-ethanol 2-Naphthol 2-Naphthalene-ethanol a b

SiO2 SiO2 SiO2 SiO2 SiO2

6.5 6.5 10.0 9.0 10.0 9.0 3.6 6.5 6.5 6.5 3.6 6.5

NaCl NaCl NaCl NaCl NaCl

0.01 M 0.01 M 0.01 M 0.01 M 0.01 M

3.37 3.43

Hydrocortisone 21-hemisuccinate (sodium salt). The isoelectric points of alumina, silica, and titanium dioxide were, respectively, equal to 9.1, 2.5, and 5.8.

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6 26 6 26

threne coadsorbed with anionic surfactants on alumina, KM/W > KS/W, but for CCl4 the two constants are equal. The latter data vary with most of the other results. It is stressed above that in order for the comparison to be valid, limiting micellar solubilization and adsolubilization constants should be measured under the same experimental conditions. This is usually not possible. However, the following conclusions may be suggested: 1. KS/W and KM/W decrease as the solute/surfactant ratio decreases. 2. The most general observation seems to be that for polar solutes adsolubilized with ionic surfactants on silica, alumina, or kaolinite, KS/W is larger than KM/W. For most nonpolar solutes (which means essentially naphthalene and phenanthrene), KS/W ¼ KM/W. This result may be looked upon as a consequence of the ﬁnding by AFM that on silica, surfactants form micelles as in bulk solutions. It remains to explain the reason for the inequality of KS/W and KM/W for polar solutes. It could be the consequence of the diﬀerent variation of the solute activity coeﬃcient with solute occupancy in micellar and admicellar solutions: one observes experimentally that solute adsolubilization begins at a very high solute/surfactant ratio, whereas micellar solubilization begins as the ﬁrst micelle appears, which means de facto a much lower solute/surfactant ratio. This activity coeﬃcient eﬀect would be larger for a polar solute than for a nonpolar one as in the classical case of solute distribution between two-phase systems. It could also be the consequence of the two-site model [35]. However, such tautological remarks could only be considered as a reasonable ad-hoc hypothesis. 3. The state of the solid, which has a large inﬂuence on the quantity of surfactants adsorbed, has a negligible inﬂuence on the adsolubilization constants. This is because of the linear correlation between the quantity of adsorbed surfactant and adsolubilized solute as inferred by Eq. (1) and shown in Fig. 2.

2. Partition Coefﬁcients as Deduced from Micellar Liquid Chromatography (MLC) In 1980 a new chromatographic method was introduced that enables us in principle to determine, from a single experimental run, the two constants KS/W and KM/W. [47,48]. It was shown that the separation of solutes and their dosage could be performed as the result of the interplay of a mobile phase (a micellar phase) and a stationary phase (the chromatographic column, whose surface is covered by the same surfactant). KS/W is in principle an admicellar solubilization constant that should depend on the type of surfactant structure formed at this interface, which in turn depends on the material of the column. In a chromatographic experiment the column is surfactant-saturated and corresponds to region IV of the adsorption isoCopyright © 2003 by Taylor & Francis Group, LLC

therm. The KM/W-values should be equal to that obtained with any classical method of determination of micellar partition coeﬃcients, keeping in mind the concentration condition of the solute molecules. This method as applied using a reversed-phase HPLC method for a series of alkylbenzene in the presence of the nonionic ethoxylated surfactants Brij22 and Brij-35 indicated that KS/W ¼ KM/W [49]. The method was applied to the determination of partition constants of a number of polar and nonpolar solutes with SDS, CTAB, and the nonionic Brij-35 (C12E23) using the same type of hydrophobic columns. Solutes ranged from weak acids such as 2naphthol to weak bases such as 1-naphthylamine and neutral molecules like naphthalene or phenylacetonitrile. The total solute concentration was equal to 2.0 105 mol/L. It was found in all cases that KM/W > KS/W, in opposition to the previous observations outlined above. In another investigation, using Hypersil columns with SDS and CTAB and various polar solutes (caﬀeine, toluene, benzoic acid), it was also shown that KM/W > KS/W [51]. In conclusion, the experimental conditions of the MPC method are such that a single distribution constant can be obtained corresponding to an inﬁnitely dilute solution, in either micellar or admicellar systems. It has been noted above that these conditions provide numbers that correspond to opposite behaviors: largest KS/W-values for micellar solutions, lowest values for admicellar aggregates. It must be kept in mind that for a proper comparison between KM/W and KS/W, the value of the volume surfactant phase adsorbed on the stationary phase should be known—a diﬃcult parameter to obtain [52]. However, the most serious diﬃculty for comparing numbers from MLC or bath methods is that in most cases the MLC column is made of silica with a grafted C18 hydrocarbon chain. The surface is therefore hydrophobic. The ionic surfactants should form a monolayer on such a surface with the headgroups turned toward the bulk solution. Thus, the structure of the adsorbed aggregates may play an important role in the values of the partition constants, and a better knowledge of these structures will be necessary for a clearer understanding of the reasons for the above discrepancies.

3. Effect of Surfactant Aggregate Structures on the Partitioning of Solutes As noted in the Introduction section, the image of surfactant aggregates adsorbed on ﬂat solid surfaces has changed since the advent of AFM. Many of the assumptions made to interpret various surface eﬀects linked to structural changes will eventually be readapted to the new ﬁndings. However, most adsolubilization investigations have been performed on dispersed solid particles. The extent to which the AFM ﬁndings apply to small

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particles is not known today. Thus, in the examples recalled below the classical surfactant structures terminology is used throughout. Solutes such as benzene, phenol, and aniline were adsolubilized on zeolites modiﬁed by CTAB [53]. At constant and neutral pH, the adsolubilization increased with surfactant addition up to a concentration that corresponded to a surfactant monolayer. Beyond that concentration, where an assumed bilayer forms, the solute distribution coeﬃcient remained approximately constant at all pH values except for aniline, where a decreased adsolubilization is observed. These concentrations are below the equilibrium CMC of the surfactant. In the case of 2-naphthol adsolubilized on SDS aggregates on alumina it was observed [54] that the decrease of adsolubilization as the surfactant concentration increases does not coincide with the CMC—as others have stressed—but begins below the CMC. This observation is interpreted as the consequence of a change in the surfactant structure on the alumina particles with surfactant concentration. Again, the adsolubilization would be larger for an SDS monolayer than for the bilayer that forms at higher surfactant concentrations. This result may mean that anionic and cationic surfactants that adsorb on widely diﬀerent solid substrates structures induce diﬀerent adsolubilization capabilities. In eﬀect, most data showing a solute decreased adsolubilization starting around the CMC concern cationic surfactants adsorbed on silica, alumina, or clay minerals. Note, however, that for 2naphthol on hydrophobically modiﬁed TiO2 [55] the decrease of adsolubilization begins at the CMC of the cationic surfactant used. The observation was made in the case of 2-naphthol adsolubilized with tetradecyltrimethylammonium bromide and its mixtures with polyacrylamide on kaolinite [56]. One may also note that the CMC of a surfactant does not always coincide with the onset of the adsorption plateau as the general picture implies. In some cases the surfactant adsorption continues to increases above the CMC. The two phenomena—decrease of adsolubilization below the CMC and increase of surfactant adsorption above the CMC—might be related. The linear relationship between solute adsolubilization and surfactant concentration below the CMC as displayed in Fig. 4 was not observed for a number of aromatic solutes such as 1,2-dichlorobenzene, 2,3-dimethylphenol, and 4-chlorophenol, which were adsolubilized with CTAB on silica columns as deduced using a chromatographic method [57]. Depending on the surfactant coverage and the pH of the system, diﬀerent KS/W-values were therefore calculated. This was interpreted in terms of changing surfactant aggregate structures. As outlined before, it seems that at the present stage such an eﬀect on the adsolubilization phenomenon should be considered with some care.

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4. Surfactant Concentration Effect Above the Equilibrium CMC on Adsolubilization Constants As the surfactant concentration increases beyond the CMC, at constant pH and ionic strength, one observes a decrease of adsolubilization. This observation has been made for a number of adsolubilization systems; to name just a few: toluene with SDS on ferryhydrite [58]; 2-naphthol with DoTAB and CTAB on clays [59]; 2-naphthol and naphthalene with CPC on silica [6]; 2naphthaleneethanol and 1-naphthylamine with CTAB on alumina and titanium dioxide above their iep [26]; hydrophobic steroids with CPC on silica [28]; 2-naphthol with SDS on quaternized titanium dioxide [60]; and phenanthrene with rhamnolipid on soils [39]. Thus, whatever the solute, the surfactant, or the solid, in most cases the adsolubilization decreases above the CMC. Exceptions to this general rule where the decrease begins below the CMC have been noted above. The decrease is the consequence of the presence of the surfactant pseudophase and of the distribution of the solute between the constant adsorbed aggregates and the increasing concentration of free aggregates. Equation (4) has been used to determine a micellar solubilization constant, and it has been repeatedly shown that for neutral solutes KM/W ¼ KS/W. This result was taken as evidence that the decreasing portion in Figs. 2 or 3 is the sole consequence of the micellar solubilization eﬀect. It is clear, therefore, that immobilization or, on the contrary, the migration of adsolubilized solute molecules (surfactant-enhanced remediation) may be achieved by the control of the surfactant concentration, which must be precisely known.

5. Salt and pH Effects on the Adsolubilization Partition Constants of Neutral Solutes (a) Salt Effects. The effect of the addition of a salt with no speciﬁc interaction of either the solid substrate or the surfactant on adsolubilization is the consequence of its effect both on the surfactant adsorption and on the solubility (the activity) of the solute molecule in the medium. As noted before, the addition of a salt decreases the CMC of an ionic surfactant. Hence the adsorption starts at a smaller surfactant concentration. The effect of the salt also increases the amount of surfactant adsorption as the screening of the surfactant charges will be more efﬁcient (effect I). However, the former effect is quantitatively larger than the latter. As a direct result, if the solute concentration is kept constant, the solute activity coefﬁcient effect discussed above will be larger as the solute mole fraction in the aggregates will be larger. The addition of the salt will have an effect on the solubility of the solute. Most inorganic salts induce a salting-out effect. As a consequence, the fraction of solute molecule in the adsorbed

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surfactant aggregates will increase (effect II). The addition of salt may be used to improve the conditions for the formation of thin ﬁlms by the adsolubilization method. The ﬁnal consequence of the salt eﬀect on adsolubilization partition constants depends on the range of surfactant concentration investigated. At low surfactant coverage, the addition of salt will increase both the adsorbed surfactant concentration (eﬀect I) and the adsolubilization (eﬀect II). It has been shown that under such circumstances the adsolubilization constant, which is essentially the ratio of these two quantities, remains almost constant. It was the case for an aromatic alcohol adsolubilized with CPC on silica. The value of KS/W is approximately constant as the added NaCl varies from 0.01 to 0.2 mol/L [61]. However, if the surfactant coverage is already high in the absence of salt, the surfactant increase will be small with salt addition and the value of KS/W will decrease as only eﬀect II remains operative. (b) pH Effects. Increasing the pH above its isoelectric point (for silica, for example) increases the number of ionic sites on the solid and therefore the adsorption of most ionic surfactants. The pH change has no effect on the CMC of surfactants (the zwitterionic group is an exception). In the case of neutral molecules, solute incorporation into surfactant aggregates increases also so that, as with the effect of salt, KS/W remains approximately constant. It was the case, for example, for 1-phenoxy-2-propanol adsolubilized with CPC on silica whose KS/W-value is equal to 130 in the pH range from 4.2 to 8.5 [61]. However for phenanthrene adsolubilized with SDS on kaolinite, KS/W was found to decrease with increasing pH, as recalled above [37]. However, the experiments were performed below and above the point of zero charge (PZC) of the kaolinite sample, whereas the above data concern a pH range above the silica isoelectric point, i.e., for a negatively charged solid surface. In the former case the change of the electric charge at the PZC certainly induces a repulsion effect that is absent with silica, hence the decrease of KS/W. Finally, it has been noted in the Introduction section that in most investigations, cationic surfactants are adsorbed on silica and anionic surfactants on alumina. An investigation was undertaken on the adsolubilization of two neutral molecules, 2-naphthaleneethanol and 1-naphthylamine, on CTAB using the three substrates silica (at pH ¼ 6.5), alumina (at pH ¼ 10.0), and titanium dioxide (at pH ¼ 9.0) at such pH values that the solid surfaces were all negatively charged [26]. The results of Table 1 show that the KS/Wvalues obtained are equal regardless of the type of substrate: only the quantity of surfactants adsorbed and the hydrophobicity of the solutes control the partitioning of the solutes between the adsorbed surfactant aggregates and the aqueous solution.

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6. Salt and pH Effects on the Adsolubilization Partition Constants of Ionized Solutes It has been stated in the Introduction section that the competitive interaction of ions and surfactants for surface sites is beyond the scope of the present review. However, there is a large class of weak acids and weak bases that are not adsorbed on mineral oxide surfaces but are incorporated to the interface via surfactants. Their incorporation at the silica–water interface will depend heavily on their degree of ionization. In eﬀect, a pH change in a system will induce a change of surfactant adsorption as shown above as well as introducing new charges in the system via the ionized molecules. Furthermore, it has been indicated above that ionizable solutes, at pH values remote from their pK, display nevertheless a speciﬁc behavior in that KS/W > KM/W at variance with nonionizable solutes. Finally, it must be stressed that, in general, the behavior of ionizable molecules between immiscible phases is studied under the condition that the solutes are neutral. This is the case of the partitioning of chemical species in the n-octanol/water system, for example, which is often used for correlation purposes. The knowledge of some information on the distribution of totally or partially ionized molecules between immiscible phases (liquid–liquid or solid–liquid) should be of the utmost interest. Some adsolubilizations experiments have been performed at several pH values. It is the case of pentachlorophenol that has been adsolubilized on montmorillonite clay modiﬁed by CTAB [62]. These authors have shown that the adsolubilization of the ionized (deprotonated) form decreased as the pH was increased. The adsolubilization of phenol and aniline on a zeolite modiﬁed by CTAB was dependent on the pH [53]. A maximum coadsorption was observed closed to the pK for the phenol but not for aniline. Also, as stated previously, the eﬀect of pH on phenol adsorption was greatest at the largest CTAB concentration, when a bilayer was formed, but the reverse was observed for aniline; i.e., the adsorption was largest for the CTAB concentration corresponding to a monolayer. The general adsolubilization behavior of ionized solutes in the whole surfactant concentration domain at a constant pH and salt concentration is very similar to that of nonionized (neutral) solutes under the same experimental conditions. Figure 7 shows the adsolubilization behavior of sodium salicylate with CPC with silica at a constant pH value of 6.5 [40]. Two observations may be pointed out: (1) the incorporation of the salicylate ion begins in region I of the surfactant isotherm, i.e., in a region where the surfactant monomers adsorb ﬂat on the solid surface; (2) the decrease of adsolubilization begins at the surfactant equilibrium CMC as with a neutral compound. The general adsolubilization proﬁle for sodium

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FIG. 7 Adsorption isotherm of CPC * on a nonporous silica (left scale). at pH ¼ 4.2. Adsolubilization of sodium salicylate * (right scale) (c ¼ 4:0 104 mol l1 Þ: The arrow indicates the equilibrium CMC.

salicylate at three pH values in the presence of CPC on silica at a constant salt concentration is presented in Fig. 8 and Table 1 [27]. For the sake of clarity the adsorption isotherm of CPC was not reported on this graph. The salicylate ion (pK ¼ 3.0), being negatively charged, does not adsorb spontaneously on the silica surface. As the surfactant concentration increases, the salicylate ion is incorporated to the silica–water interface through an electrostatic interaction with the cetylpyridinium ion up to the CMC, forming a hydrophobic ion pair. It is known that this interaction is very strong, leading to the formation of rods in bulk solutions with viscoelastic properties [63]. As free micelles are formed above the CMC, the salicylate ions are distributed between the adsorbed CPC aggregates and the free micelles. At higher CPC concentrations as more free micelles are created, the equilibrium is shifted from the coadsorbed ions to the micellar ones until, at high concentrations, the salicylate ions are completely washed out from the silica–water interface. The three adsolubilization curves correspond to three diﬀerent KS/W- or Kb-values, because the adsorption concentration of CPC is a function of the system’s pH. However, the curves merge Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 8 Adsolubilization of sodium salicylate with CPC on silica at three pH values: * pH ¼ 4.4; * pH ¼ 6.5; ~ pH ¼ 8.5.

at the CMC because, above this value, the salicylate ions are distributed in the CPC micelles, whose properties are pH-independent. Therefore, three KS/W-values may be deduced below the CMC and a single KM/W-value above the CMC. The KS/W decrease as the pH increases. This was interpreted as follows: as the pH increases at a constant CPC concentration, more negatively charged sites are created on the solid surface. This induces an electrostatic repulsion that prevails over the favorable interaction between the surfactant and the salicylate ions; hence the continuous decrease of adsolubilization of the aromatic ion. In order to make the behavior of the ionized and the unionized forms more apparent, a series of experiments was performed with various weak acids and weak bases [64]. The weak acids (2,4,6-trichlorophenol, 4-nitrophenol, 2-naphthoic acid, 4-aminosalicylic acid) were adsolubilized with a cationic surfactant, CPC on silica, and the weak bases (1,10-phenanthroline, 1-naphthylamine, 4-toluidine) were adsolubilized with the anionic surfactant sodium octylbenezenesulfonate (p-OBS) on alumina. Figures 9 and 10 present an example of each class of solutes: 2,4,6-trichlorophenol for the former case and 1,10-phenanthroline for the latter. Neither of these solutes adsorbs on the naked mineral oxide surfaces. The concentration of adsorbed surfactant was low and constant in the whole pH domain investigated, i.e., from 3 to 10. The adsorption of the solutes in the absence of surfactant was again very low. This case is shown for 2,4,6trichlorophenol on silica. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Variation of the ratio of adsorbed to free 1-naphthylamine with pH at a constant sodium octylbenzenesulfonate and 4-toluidine concentration on alumina. The arrow indicates the pK of the base.

FIG. 10 Variation of the ratio of adsorbed to free 2,4,6-trichlorophenol with pH at a constant CPC concentration ^; in the absence of surfactant ~. The arrow indicates the pK of the acid.

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A maximum adsolubilization is observed with the particularity that, as shown by the arrows on Figs. 9 and 10, the maximum systematically coincides with the pK of the solute. The pKs are equal, respectively, to 3.92 for the base and 6.0 for the acid. The same observation was made for all the solutes cited above. Another example of the same sort is discussed below. An adsolubilization maximum was also observed [53] for phenol and aniline on a zeolite loaded with CTAB although the maximum did not seem to coincide with the pK of the solute (at least in the case of the aniline). In order to interpret such results in a more quantitative way, a simple model was devised [64] that describes the solute in its unionized form using a partitioning model and the ionized form by a Langmuir-type model. Taking the example of the phenol: CPþ þ A , ACP where A is the conjugated form of the acid. Then one has Kb ¼

ðACPÞ þ ðCPads ÞðA Þ

ð6Þ

Using the binding site model, one can write: e ðA Þ ¼ Ceq exp þ b kT

ð7Þ

b is the electrical potential created by the ionic sites on the solid surface corresponding to a Stern potential. K, e, and T have their usual meanings. Hence, the binding constant can be written as Kb ¼

s Cads s Cads;max Ceq

exp

eb kT

ð8Þ

The same approach may be used for 1,10-phenanthroline, changing only the sign of the exponential. Introducing the deﬁnition of the pK, the ﬁnal result for the acid is s Kb Cads;max þ KS=W Cads 10 Cads s ¼ Ceq 1 þ 10pHpK surf

surf

pHpK

ð9Þ

where KS/W is obtained from experiments performed below the CMC (see reference 64 for details). The same model is applied to the base. Next, one assumes Kb ¼ A expðBpHÞ where A and B are ﬁtting parameters. The continuous lines in Figs. 9 and 10 are calculated from the model. The maximum adsolubilization at the pK of Copyright © 2003 by Taylor & Francis Group, LLC

the solutes is recovered. The value of KS/W may also be obtained from the ratio of Cads/Caq at the low pH values for the acid and at the high pH values for the base. The following physical interpretation may be suggested. At high pH the ionized negative form of the phenol is desorbed from the silica–water interface as the result of the strong repulsive interaction with the anionic sites. In turn, at a low pH the protonated amine is desorbed by the strong repulsion interaction with the positively charged alumina surface. In both cases the repulsion interaction dominates over the favorable interaction between surfactant and ionized solutes at extreme pH values. The maximum arises from the favorable interaction between solute and surfactant at intermediate pH values, from which the repulsion interaction is not strong enough to overcome the favorable one between the species of opposite charges. Finally, both solutes in their neutral form are distributed between the adsorbed surfactant aggregates and the solution as in the classical situation. A case related to the eﬀect of pH and added salts on adsolubilization is worth recalling [41]. It concerns the behavior of the sodium salt of hydrocortisone 21-hemisuccinate and of the closely related prednisolone 21-succinate on CTAB with silica. Figure 11 presents the molecular structure of the sodium salt of hydrocortisone 21-hemisuccinate. First, the adsolubilization behavior of these two salts with CTAB on hydrophilic silica particles is presented in Fig. 12. The proﬁle of the two steroids is qualitatively similar to that of all other chemical species studied. The decreasing portion of the

FIG. 11

Structure of the sodium salt of hydrocortisone 21, hemisuccinate.

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FIG. 12 Adsolubilization of the sodium salts of hydrocortisone 21, hemisuccinate * and prednisolone 21, hemisuccinate * at a silica–water interface in the presence of CTAB concentration. The arrow indicates the equilibrium CMC.

curves can be treated in a slightly diﬀerent manner from that of Eq. (4), taking into account the charge on the molecule. One can then extract the solute apparent binding constants to adsorbed aggregates from the increasing portion of the curve and the binding to the free micelles from the decreasing portion. In the present case, one ﬁnds, respectively, Km ¼ 5075 l mol1 and 2750 l mol1. Thus, the strength of the binding is larger with the adsorbed aggregates than with the free micelles, as with the other ionizable compounds studied. Figure 13 shows the adsolubilization proﬁle of one of the acidic steroids, namely, hydrocortisone 21-hemisuccinate, with CTAB on silica as a function of pH in the presence of various concentrations of NaCl. The solute and the surfactant concentrations are kept constant at low surface coverage. The presence of the surfactant increases the extent of the incorporation of the steroid anion to the silica–water interface. However, the adsolubilization decreases with added salt. This is the result of the screening of the charge of the steroid’s ionized form by the added NaCl, an eﬀect that decreases the value of Kb as expected. Although this steroid adsorbs on the naked silica in the absence of surfactant below a pH of 4.5, it is noteworthy that the maximum adsolubilization in the presence of CTAB occurs at a pH that Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 13 Eﬀect of salt on the variation of the ratio of adsorbed to free hydrocortisone 21-hemisuccinate, sodium salt with pH at constant CTAB concentration: solute concentration is constant at 4:4 104 mol l1 (CTAB concentration is equal to 6:0 104 mol l1 ). Succinic acid: pK ¼ 4.2. ^ No added salt; * NaCl ¼ 1:0 102 mol l1 ; * NaCl ¼ 1:0 101 mol l1 .

is equal to the pK of succinic acid, i.e., at 4.2, in agreement with the prediction of the above derivation. Thus, the apparent pK of weak acids or bases could be deduced from adsolubilization experiments. Another important aspect from such adsolubilization experiments is displayed in Figs. 8–10 and 13. The ionized solutes may be completely desorbed from the solid– water interface without removing the surfactant from the interface; at high pH for a weak acid, at low pH for a weak base. Some caution should be exercised, however, in the physicochemical interpretation of some of these adsorption versus pH proﬁles. The adsorption of weak bases as a function of pH may present the same apparent behavior at solid–water interfaces in the absence of surfactants. It is the case, for example, for aniline and various toluidines adsorbed on a bentonite clay [65]. The maximum adsorption occurs around the pK of the weak bases. As is well known, the faces of crystal clays are negatively charged, but the edges are of opposite sign. A maximum adsorption has been observed for a pH value close to the pK for a weak acid, benzoic acid, adsorbed on kaolin [66]. Here, the negatively charged anion is adsorbed on the positive kaolin sites. The situation is, however, diﬀerent from adsolubilization because in the above experiments, for example, the protonated weak bases adsorb directly on the Copyright © 2003 by Taylor & Francis Group, LLC

negatively charged bentonite sites, whereas in the surfactant case, the adsolubilization is obtained as the result of the opposite electric charges of the surfactant and of the ionized solute molecules. Nevertheless, another apparent similarity between the two systems can be found. The maximum aniline or toluidine adsorption on bentonite decreases with the addition of inorganic salts. The reason is the same as that suggested above for the sodium salt of hydrocortisone 21-hemisuccinate, i.e., the screening of the charges of the ionized molecules by the added ions, with, as a direct consequence, the decrease of the favorable interaction between the ionic surfactant and the ionized solute.

7. Cross Adsorption/Desorption Effects of Surfactant and Solute at the Solid–Water Interface As shown above, increasing the surfactant concentration increases the incorporation of hydrophobic solutes up to the CMC. Above this concentration, most solutes, either neutral or charged, are desorbed from the solid–water interface and solubilized in the free micelles. Adding the solute at a constant initial surfactant concentration may increase or decrease surfactant adsorption. The addition of linear alcohols to an SDS/alumina system increases surfactant concentration [35]. The mixed surfactant/alcohol aggregates may contain up to 90% alcohol and 10% surfactant. The alcohol concentrations added above were up to 0.1 mol/L of alcohol. In the chemical system of n-butanol/SDS/alumina, the alcohol concentration was increased to 0.80 mol/L. It was shown that surfactant adsorption at the saturation plateau decreased and 1-butanol adsolubilization increased upon n-butanol addition [67]. Likewise, the addition of large concentrations (up to 0.3 mol/L) of benzylalcohol decreases the adorption of CPC on silica [68] although the decrease of the latter is much less than the increase of the former compound. The same observation was made for phenol coadsorbed with CPC on silica [24]. In all these cases, the surfactant plateau appears at a lower concentration as the solute concentration is increased. The decrease of the CMC upon the addition of solutes that are solubilized in micelles had been recognized long ago for micellar solutions. In general, the more hydrophobic the solute, the larger the CMC decrease, the magnitude of which is directly related to the solute partition coeﬃcient. The same overall eﬀect is observed in the presence of the solid phase, although the two-site model [35] seems to be applicable only above a critical alcohol chain length as deduced from an investigation on n-alkanol’s adsolubilization with sodium decylsulfonate on alumina [69]. The conclusion that can be drawn from the relatively small number of studies available is that the surfactant is desorbed from the solid–water interface if the added solute (generally an alcohol) is adequately water-soluble so that the water Copyright © 2003 by Taylor & Francis Group, LLC

structure is partially destroyed. Under all other circumstances, surfactant adsorption is increased.

8. A Case of Adsolubilization: 2-Naphthol Contrary to the case of micellar solubilization for which a large variety of solutes may be found in the literature, the adsolubilization eﬀect has been studied for a relatively small number of solutes. Among these, 2-naphthol is the molecule that has attracted the largest number of investigations. Table 2 provides a short bibliography for this compound.

III. APPLICATIONS OF ADSOLUBILIZATION FOR SMALL MOLECULES Although the adsolubilization eﬀect concerns, in principle, all domains of surfactants usage, applications have been found and recognized as such in TABLE 2 Adsolubilization of 2-Naphthol as Induced by Adsorbed Surfactants at Solid–Water Interfaces: A Bibliography Solids

Surfactant systems

Speciﬁcities

Methods

TiO2 TiO2 TiO2 Alumina Alumina Alumina

SDS SDS Cationics SDS SDS SDS+PVP, SDS+AOT SDS+nonionics Cationics SDS Cationics

— Cu2þ , pH KS=W — KS=W —

Batch, ESR, Batch Batch Batch Batch Batch, UV

60 70 55 54 25 71

— — — KS=W

72 73 74 59

— — — KS=W , pH KS=W KS=W

Batch Batch Batch, X-ray, Batch, kinetics, X-ray Heats, X-ray Batch, Batch, ESR, Batch Batch Chromatography

75 56 76 26 23 50

KS=W

Batch

77

—

Batch

15

Alumina Laponite Hydrotalcite Montmorillonite Illite, kaolinite Kaolinite Silica Silica Silica Silica Activated carbon Activated carbon

Cationics TTAB+polymer Cationics CPC CPC SDS, CTAB, Brij-35 SDS, CTAB, NP8 SDS

¼ zeta potential measurements.

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Ref.

essentially three domains: pharmaceuticals, thin-ﬁlm formation, and the environment. Of these three, the last one is certainly the most promising.

A. Pharmaceuticals Some early uses of surfactants for anchoring drugs at solid–water interfaces are listed in the Introduction section. This is, in fact, the main application of the adsolubilization eﬀect for medical purposes. Nonionic surfactants below the CMC were used to promote the adsolubilization of pilocarpine salts on cyanoacrylate particles [78]. The same eﬀect (which was then called mediated adsorption) was applied to anionic drugs incorporated with alkylpyridinium surfactants on silica [19]. The inﬂuence of surfactants on drug release from acrylic matrices was also investigated [79]. The rate of drug release was found to increase following the incorporation of surfactants at the solid–water interfaces. The increased loading of the steroid hydrocortisone on albumin nanoparticles due to the presence of adsorbed nonionic surfactants for inﬂamed and healthy eyes was also investigated [80]. The strong binding of the drug to the particle/surfactant system was suggested to be responsible for the decreased rate release. Model propellant systems have also made use of the adsolubilization of drugs on microparticulate systems using surfactants [81]. Steroids (progesterone, testosterone, hydrocortisone) were used as model compounds for the comparison between micellar solubilization and adsolubilization, as recalled earlier [28].

B. Ultrathin Films Formation Many processes can be employed for the formation of thin ﬁlms on surfaces. Among these, the one based upon the adsolubilization eﬀect is, if not the most eﬃcient one, a simple and elegant approach. A procedure based on the ability of some compounds such as styrene or pyrrole to polymerize in the presence of an initiator was proposed [20]: styrene is dissolved in ethanol in order to obtain a reasonably concentrated solution. A solution of SDS is prepared below the CMC in order to prevent the formation of free micelles, which would incorporate some styrene molecules. Both solutions are poured over an alumina plate. Sodium chloride is added to the system in order to induce a salting-out eﬀect, which will increase the adsolubilization of styrene in the surfactant aggregates that are formed on the alumina plate. Finally, an initiator, e.g., sodium persulfate, is added to the system, which is equilibrated for 48 h. The alumina plates are then rinsed with water and heated at 60–708C to initiate the polymerization process. The polymer (polystyrene) is extracted from the solid surface using tetrahydrofuran. The thickness of the ﬁlm is, in principle, equal to that of the surfactant double layer in which the solvent monomer has been adsolubilized. Essentially the same procedure Copyright © 2003 by Taylor & Francis Group, LLC

was employed with some modiﬁcations for the diﬀerent systems displayed in Table 3. The case of the conductive polypyrrole ﬁlm is particularly interesting as its properties can be monitored by simple electrical methods. One direct application of this approach was used for the improvement of the performance of rubber compounds using precipitated silica as a reinforcing ﬁller [88].

C. Environment The remediation of contaminated soils and the investigations on the transport or the migration of chemicals in groundwaters have made a large use of surfactants as mobilizing or immobilizing agents of chemicals adsorbed on soils depending on the practical situation encountered [89,90]. Although this important domain is by no means conﬁned to the use of surfactants, the largest number of recent publications on adsolubilization, whether the term is actually used or not, concerns environmental problems. It is beyond the scope of this review to provide even an overview of the work performed in this area. However, some additional examples are presented below that illustrate the remarkable similarities of the adsolubilization behavior of widely diﬀerent chemical systems. One of the main diﬀerences between the more fundamental investigations recalled above and the environmentally oriented studies is that in the former case the solid substrates are simple mineral oxides such as silica or alumina whereas in the latter case a large variety of more complex substrates is used:

TABLE 3 Ultrathin Film Formation Using the Adsolubilization Method Monomer

Polymer

Surfactant

Styrene

Polystyrene

SDS

Pyrrole

Polypyrrole

SDS

Styrene

Polystyrene

CTAB

Tetraﬂuoroethylene

PTFE

Styrene, isoprene

Polystyrene

Sodium perﬂuoroheptanoate CTAB

Styrene

Polystyrene

CTAB, nonionics

Styrene

Polystyrene

CPC, DTAB

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Surface

Ref.

Alumina plate Alumina powder Precipitated silica Alumina powder Precipitated silica Precipitated silica Glass ﬁbers

20 82 83 84 85 86 87

clays such as kaolinites and bentonites (Na+-montmorillonites), zeolites, or natural soils. This state of aﬀairs may complicate the comparison between diﬀerent systems, although such investigations have been attempted as in the case of kaolin, alumina, and montmorillonite in the presence of sodium dodecylbenzenesulfonate adsolubilized with isomers of tricresylphosphate [91]. Furthermore, many of these materials need to be chemically treated before use, which again introduces ambiguities. The type of solutes adopted as model compounds fall into the general term of HOC (for hydrophobic organic compounds): naphthalene, phenanthrene, and halogenated analogs are among the most studied molecules. Most surfactants used for adsolubilization investigations are the same as those used in the more fundamental studies with the exception of some biosurfactants, called natural surfactants, which are only employed in environmental situations. For example, a surfactant obtained from Sapindus mukurossi was used for soil-ﬂushing of naphthalene and hexachlorobenzene [92], a rhamnolipid was obtained from Pseudomonas aerogonosa UG2 to solubilize the pesticides atrazine, truﬂurin, and coumaphos [93]; glycolipids were produced from Rhodococcus for the solubilization (mobilization) of naphthalene derivatives [94]. Another notable diﬀerence with the simpler systems analyzed above is that the surfactants are often incorporated to the solid phase through an ion exchange or coating procedure, i.e., that after exposure to the surfactant solution, the solid phase is separated, dried, and mechanically ground with a mortar before use [95,96]. The KS/W-values are deﬁned for such systems usually as suggested by Eq. (1), where the amount of organic material present on the solid substrate (the so-called organic content) may be a surfactant, a humic acid, or any organic component of any origin as long as it can be determined analytically. Even though natural systems used in environmental studies are more complicated than those described previously, the main characteristics remain. For example, tetrachloroethylene was adsolubilized with the nonionic surfactants, octylphenolethoxylates, on a natural aquifer sediment quarried from Pleistocene lacustrine deposits [97]. The solute uptake is observed up to the equilibrium CMC of the surfactant and decreases to zero as micellization occurs. The maximum adsolubilization does not occur exactly at the equilibrium CMC but below that concentration. However, for phenanthrene adsolubilized with the nonionic Tween 80 on kaolinite [37], the decreased incorporation of the solute beyond the CMC was apparently not observed. A maximum adsolubilization of phenol and aniline with CTAB on zeolites was observed as a function of pH [53]. This maximum does not coincide with the pK of these solutes, as was observed for phenols and amines for the Copyright © 2003 by Taylor & Francis Group, LLC

silica/CPC system. These examples point out again similarities in the behavior of widely diﬀerent solute molecules adsolubilized on diﬀerent surfactant/solid surfaces although diﬀerences may reveal interesting speciﬁcities as in the case of phenanthrene mentioned above. Evidently, diﬀerences may be observed between chemical systems based on speciﬁc properties of surfactant and solute, concentration, or pH. The inhibition or, on the contrary, the synergy of adsorption of either the surfactant or the solute due to competition for adsorption is an important topic under natural environmental conditions. For example, the adsorption capacity of activated carbon for solutes and surfactants is aﬀected by both solute and surfactant; hence, the inhibition of adsorption of the pesticide atrazine is twice as large with CTAB than with SDS, respectively, 45% and 23%. The same observation was made with the same solid/surfactant system for another classical pesticide, diuron with respectively 27% and 16% inhibition [98]. Recall that an increase of SDS adsorption on alumina is induced by the addition of alkanols [35]. In the case of the adsolubilization of herbicides [96] it was shown that organic cations such as benzyltrimethylammonium chloride, which is not a surfactant but may be considered as the lowest analog to the benzalkonium surfactant series, could considerably improve the adsolubilization of alachlor, metolachlor, norﬂuorazone, or montmorillonite. This shows that the adsolubilization concept may have greater universality than originally considered.

IV. PHENOMENA RELATED TO ADSOLUBILIZATION Some surfactants and hydrophilic polymers that do not adsorb to solid– water interfaces may be incorporated to these interfaces using an adsorbing surfactant. Although diﬀerent from the adsolubilization eﬀect, this situation is related to it, as in all these cases adsorbed surfactant aggregates incorporate these chemical species by the same mechanisms whether hydrophobic or electrostatic. The term incorporation will be used, reserving the term adsolubilization for the incorporation of small molecules.

A. Nonadsorbing Surfactant Incorporation at Solid–Water Interfaces by Adsorbing Ones One of the most obvious diﬀerences between bulk micellization and adsorption of surfactants at solid–water interfaces is that in the former case, the appearance of the phenomenon depends only on the concentration of the component, whereas in the latter case, some kind of favorable interaction between the surfactant and the solid is often necessary for the Copyright © 2003 by Taylor & Francis Group, LLC

eﬀect to develop. Thus, generally ionic surfactants do not adsorb on solid surfaces of opposite charges. Nonionic surfactants, which are often ethoxylated compounds, scarcely adsorb on alumina but do adsorb readily on silica. Here the electrostatic charges play a minor role. Exceptions to these general rules have been studied: for example, an anionic surfactant may adsorb on a negatively charged surface as the result of chemisorption interaction. There may be practical reasons to favor the adsorption of a nonionic surfactant using an ionic one on a solid–water interface. The CMC is lower for nonionic surfactants, which is always a favorable situation; however, ionic surfactants cannot be replaced by nonionic ones in a number of situations where the solid electrical charge has to be cancelled or counterbalanced (ﬂotation experiments). Besides, the Kraﬀt point (for ionic surfactants) or the cloud point (for nonionic surfactants) are important parameters that control the applicability of any surfactant for a practical purpose. Therefore, it may be useful to form mixed micelles of diﬀerent surfactants in order to get more freedom in the choice of the most suitable surfactant system to be employed in a given situation: hence, the Kraﬀt point of an anionic surfactant may be decreased or even suppressed by the addition of a nonionic component, whereas the cloud point of a nonionic surfactant may be considerably increased by adding an anionic component. Thus, in so far as the incorporation of one component to a solid–liquid interface is induced by the adsorption of a surfactant at that interface, the adsorption of mixed surfactants from solution onto solids deﬁnitely belongs to the adsolubilization area. The formation of mixed micelles has been an important ﬁeld of investigation for many years. A number of physicochemical models can be employed to predict parameters such as the CMC of any binary surfactant system, their degree of interaction, and the mixed micelles aggregation number. Using what may be called the Clint–Rubingh approach of mixed surfactant systems [99,100], we may draw the following decreasing order of interactions between classical surfactants using Rubingh’s ¼ w=RT ﬁtting interaction coeﬃcient as a rough guideline: anionic=cationic > anionic=zwitterionic > anionic=nonionic > cationic=nonionic > nonionic=nonionic One may expect that the same order of decreasing interaction at solid–water interfaces will prevail when one of the surfactant pair adsorbs signiﬁcantly to the solid surface. Some representative results are presented below for selected mixtures.

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1. Incorporation of an Anionic Surfactant by a Cationic One at a Solid–Water Interface The adsorption of cationic surfactants on silica (DoTMAB, DoPyCl) is increased by the addition of the adsorbing anionic surfactants (SDBS, SDS) [101]. The excess of adsorbed cationic surfactant is equal to the added anionic surfactant concentration, which demonstrates that the latter compound is adsorbed as a mixed ion pair onto the solid surface. This is in line with the highly negative -value of the binary surfactant solutions. SDS adsorption on the positive charges of the edges of laponite clay seems not to be signiﬁcant [102]. SDS is incorporated to the clay surface by preadsorbed CPC. The concentration of SDS goes through a maximum close to its CMC and decreases as free micelles are formed. This is the same phenomenon as the one discussed above for smaller, nonsurfactant molecules. However, the cationic surfactant adsorption also decreases. This is because mixed micelles are formed in solution. As the experiments were performed at constant CPC concentration, the strength of the anionic–cationic interaction induced the desorption of both surfactants from the clay surface. The same eﬀect is not observed in the presence of preadsorbed dioctadecyldimethylammonium chloride (DiDoTMACl), i.e., no mixed micelles are formed with the poorly soluble double chain surfactant, which, as a result, does not desorb from the clay surface and, therefore, SDS monomers are retained at the solid surface. Alternatively, one may suggest that the interaction between DiDoTMACl and the clay negative sites is much stronger than with the anionic surfactant.

2. Incorporation of an Anionic Surfactant by a Nonionic One to a Solid–Water Interface These are the most studied binary systems although they may apply to quite diﬀerent purposes: coadsorption of an anionic surfactant by an adsorbing nonionic one in the case of a negatively charged silica, and coadsorption of a nonadsorbing nonionic surfactant by an anionic one in the case of a positively charged alumina. (a) Incorporation of an Anionic Surfactant by a Nonionic Surfactant to a Silica–Water or a Clay–Water Interface. Several studies deal with silica as the solid surface [103–106]. In the ﬁrst of these investigations it is shown that the formation of mixed aggregates of the nonionic Triton X100 with SDS at the silica surface decreases the adsorption plateau of the nonionic component as the result of the repulsion induced by the negative sites on the incorporation of SDS. The same conclusions were brought about by the so-called displacement enthalpies as well as adsorption isotherms for mixed surfactants of Triton X-100 with p-OBS [107]. The

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coadsorption of the p-octylbenzenesulfonate ion on silica was obtained [108] via the addition of the adsorbing nonionics C12E8, C8PhE10, or C8PhE40. The zeta potential of silica particles in the presence of the sole added C12E8 changes from 45 mV to about 10 mV at the density plateau along a sigmoid curve. However, when both nonionic and anionic surfactants are adsorbed at the particle surfaces, the zeta potential remains constant with concentration at about 45 mV. The self-desorption of C12E9 and SDS from a silica–water interface at a surfactant concentration about 100 times the CMC was observed [106] (see Fig. 14). This is interpreted as the result of the repulsion interaction of the dodecylsulfate anion and the negatively charged silica sites, keeping in mind the behavior of bulk mixed micelles. It has been shown both experimentally and theoretically that as the total concentration of mixed surfactant is increased at a constant ratio above the CMC the composition of the aggregates changes from nonionic-rich to the stoichiometric composition. If the same concept is applied to surface aggregates, this means that as the total concentration is increased above the CMC, the mixed aggregates become richer in the anionic component, which above a critical composition triggers the

FIG. 14 Global adsorption isotherms of three nonionic/ionic surfactant mixtures; * r ¼ C12E9/SDS at silica–water interfaces: ratios r ¼ 0.3; 0.5; 0.7. The higher the SDS content in the mixture the smaller the surfactant concentration for surfactant self-desorption. & r ¼ 0:7=0:3; * r ¼ 0:5=0:5; ~ r ¼ 0:3=0:7. Copyright © 2003 by Taylor & Francis Group, LLC

repulsion interaction and the desorption of both surfactants from the silica surface. The coadsorption of C12E8 with SDS on kaolinite has been investigated [109]. A positive synergistic eﬀect is observed below the mixed CMC. The adsorption enhancement of SDS is assumed as due to the favorable interaction of the anionic surfactant with the positively charges edges of the clay as well as from mixed micelle formation. Above the CMC, SDS adsorption is decreased with increasing C12E8 composition. The maximum adsorption plateau is observed for a 1/1 mixed micelle composition. When the adsorption experiments were performed at constant SDS concentrations and variable C12E8 concentration, i.e., at changing surfactant ratio, a maximum SDS adsorption is observed close to the CMC [110] (Fig. 15). This is most certainly due to the same phenomenon discussed above for the adsolubilization of small molecules: the mixed admicelles formed below the CMC incorporate the anionic component as the total concentration increases.

FIG. 15 Adsorption isotherm of sodium dodecylsulfate on kaolinite from mixtures with C12E8 at two constant initial SDS concentrations and variable nonionic surfactant concentrations: pH ¼ 5.5; NaCl concentration equals 3:0 102 mol l1 . The arrow indicates the CMC. * SDS ¼ 1:03 103 mol l1 ; ~ SDS ¼ 0:43 103 mol l1 . Copyright © 2003 by Taylor & Francis Group, LLC

(b) Incorporation of a Nonionic Surfactant to an Alumina–Water Interface by an Anionic Surfactant. It has already been recalled that nonionic surfactants of the ethoxylated type do not adsorb spontaneously to any great extent on alumina. As below the iep of 9.1, this mineral oxide is positively charged, the adsorption of an anionic component may help to incorporate the nonionic one onto the alumina surface, through mixed micelle formation. The most studied systems are SDS with NPE10 [111], p-OBS with C12E8 [104], and SDS with Triton X-100 [112]. In all cases, mixed micelle formation has induced the incorporation of the nonionic surfactant to the alumina–water interface, with a strong decrease of the the critical adsorption concentration (CAC), as expected. An attempt has been made to apply the Clint–Rubingh regular solution approximation to the mixed admicelle formation [113]. The theory incorporates in a single parameter all nonideal features of the free energy of mixing. It enables us to calculate the actual composition of the mixed aggregates and its variation with total surfactant concentration as well as the concentration of free monomers in equilibrium with the mixed micelles. Such parameters would be very interesting to be used at the solid–water interface. It was shown that the Clint–Rubingh approximation reproduced the CMC of the mixed SDS+NPE10 binary well, but when applied to the adsorbed mixture replacing the CMC by the CAC the model did not reproduce the experimental data well. The adsorption of the nonionic component on alumina by mixed micelle formation may increase the adsorption of the anionic surfactant [104]. This is due to the screening of the repulsion interaction between the anionic headgroups by the nonionic component, an eﬀect that is also responsible for the decrease of the CAC. However, if the ratio of anionic to nonionic is large then the repulsion interaction between headgroups overcomes the positive synergism induced by the mixed micelle formation. These ﬁndings were conﬁrmed [112] in a recent study that also suggests a three-dimensional representation of the binary surfactant adsorption isotherms, taking into account the solution and the surface concentrations of both surfactants of the mixtures. (c) Incorporation of a Cationic Surfactant to a Silica–Water or Clay– Water Interface by a Nonionic Surfactant. A cationic surfactant such as DoTMACl adsorbs spontaneously on kaolinite as does the nonionic C12E8 [109]. Mixed micelle formation increases the adsorption of both surfactants, exhibiting the same features as the SDS/C12E8 system studied by the same authors. Mixtures of CTAB with NP20 on silica were studied [114]. Here also the two surfactants adsorb spontaneously on the solid surface. Below the CMC their adsorption is mutually increased as noted for other ionic/nonionic systems. Above the CMC, as free micelles are Copyright © 2003 by Taylor & Francis Group, LLC

formed, the adsorption of the cationic component decreases while that of the nonionic one remains essentially constant. The adsorption of TTAC þ NP15 on alumina was investigated above the iep of that mineral oxide, i.e., at a pH value of 10, where the solid particles are negatively charged [115]. The adsorption of the cationic surfactant incorporates the nonionic one to the alumina–water interface. The same situation has been investigated in the case of the adsolubilization of small molecules such as 2-naphthol with CTAB on alumina at pH ¼ 10 [26]. The eﬀect of the presence of NP15 at the alumina–water interface is to lower the mixed CMC and therefore the concentration at which the saturation plateau occurs. The regular solution approximation was used to calculate the individual monomer concentrations. (d) Incorporation of Mixed Surfactants of Like Charges on an Alumina– Water Interface. For the sake of completeness one may mention mixtures of both adsorbing or nonadsorbing surfactants. This situation has been investigated in the case of mixtures of anionic surfactants adsorbed on alumina and mixtures of nonionic surfactants adsorbed on silica. However, in both cases, the surfactants adsorb spontaneously on the solid surfaces. This situation does not correspond to the extended adsolubilization effect as deﬁned in the Introduction and therefore is not considered further. (e) Adsolubilization by Mixed Surfactants. The adsolubilization of 2naphthol by a mixture of two surfactants, sodium dodecylsulfate and hexaoxyethylenedodecylether, adsorbed on alumina has been investigated [54]. As the nonionic surfactant hardly adsorbs on alumina, the addition of SDS induces the incorporation of the solute at the alumina–water interface. Some synergy is observed: 2-naphthol uptake is larger with the mixed surfactants than with SDS adsorbed alone on the solid surface. In that respect the adsolubilization behavior is opposite to that of micellar solubilization, where surfactant mixing is usually unfavorable to the solubilization of polar molecules [116].

B. Incorporation of Hydrophilic Polymers at Solid–Water Interfaces by Added Surfactants It has been repeatedly shown in the literature that neutral hydrophilic polymers such as poly(oxyethylene) (POE), poly(vinylpyrolidone) (PVP), and hydroxyethylcellulose (HEC) interact with surfactants S in aqueous solutions forming what many describe as complexes. The situation resembles that encountered above in the case of mixed surfactants. The strength of the interaction (at room temperature) follows the order polymer þ anionic-S > polymer þ cationic-S > polymer þ nonionic-S Copyright © 2003 by Taylor & Francis Group, LLC

The similarity with mixed surfactants goes even one step further. Because these hydrophilic polymers are ethoxylated nonionic compounds, they do not adsorb spontaneously on alumina but do so, for example, on silica. Thus, these compounds may be incorporated to a given solid–water interface by choosing the proper surfactant. As the subject of the surfactant þ polymer interaction is covered extensively in other chapters of this volume, only a few examples are provided here in order to illustrate the eﬀect of the polymer þ surfactant interaction on the incorporation of such polymers to various solid–water interfaces as induced by adsorbed surfactants. Suﬃce it to recall for the present purpose that either anionic or cationic surfactants form small aggregates of the micellar type on the backbone of hydrophilic polymers. In the presence of solid particles, both types of compounds may either compete for adsorption or favor the adsorption of one species by the other [117]. The following examples illustrate standard behaviors of such systems.

1. Adsolubilization per se The anionic surfactant SDS adsorbs with PVP on a positively charged alumina [118]. PVP is scarcely adsorbed on alumina in the absence of surfactant but is coadsorbed with SDS (negatively charged) as the result of the PVP–SDS favorable interaction much as in the case of mixed surfactants. An increase of PVP adsorption is observed with no change of SDS adsorption at low concentrations followed by a decrease in adsorption at higher surfactant concentrations. At larger surfactant concentrations, the formation of mixed PVP/SDS complexes in solution compete with the mixed adsorbed aggregates, hence the PVP desorption from the alumina surface.

2. Competitive Adsolubilization The cationic surfactant dodecyltrimethylammonium chloride (DoTACl) is adsorbed with PVP on a negatively charged silica [119]. Competitive adsorption occurs, which results in a decrease of adsorption of PVP (at constant polymer concentration) and an increase of that of the cationic surfactant. Another similar example is provided by the cationic surfactant CTAB as it adsorbs with quaternized HEC cationic polymers of various molecular weights on a negatively charged silica [120]. The competitive adsorption that is observed depends to a large extent on the molecular mass of the cationic polymer: smaller molecules adsorb preferentially onto the solid surface, preventing the adsorption of larger ones. The situation is reminiscent of that of polydispersed surfactants adsorbed on silica as described above.

3. Adsolubilization by a Mixed Surfactant/Polymer System Just as mixed surfactants were used for the adsolubilization of 2-naphthol, the same phenol was chosen as a model compound for adsolubilization in Copyright © 2003 by Taylor & Francis Group, LLC

mixtures of the cationic surfactant tetradecyltrimethylammonium bromide with a hydrophobically modiﬁed polyacrylamide, both coadsorbed on Nakaolinite [56]. 2-Naphthol hardly adsorbs onto the clay in the absence of the surfactant. Under the same conditions, adsorption of the polymer is small. The adsorption of both of these compounds increases dramatically in the presence of the added cationic surfactant. Some adsolubilization synergy is observed at low surfactant concentrations in the presence of the adsorbed polymer, but the maximum adsolubilization of 2-naphthol is not much enhanced by the presence of the added polymer. Above the CMC, 2naphthol is partitioned between the mixed polymer/surfactant free and adsorbed aggregates, as in the case of single adsorbed surfactant systems. As noted previously, the decrease of adsolubilization begins somewhat below the CMC of the mixed surfactant þ polymer binary.

V. CONCLUSIONS The adsolubilization phenomenon presents many characteristics of the classical micellar solubilization eﬀect to the extent that for most neutral molecules, adsolubilization and micellar solubilization constants are equal within experimental errors as the result of a common driving force for the escaping tendency of poorly water-soluble molecules from the aqueous media toward surfactant aggregates. Most experiments show that the delicate changes of aggregate structures with surfactant concentration on mineral oxides do not introduce important numerical diﬀerences between the two processes. The situation is diﬀerent with ionizable solutes, where in addition to the hydrophobic eﬀect, electrostatic forces intervene where the solid surface charge plays an important role. Under the same experimental conditions, the adsolubilization constants are systematically larger than the micellar solubilization by a factor between 2 and 3. Within this context of ionized solute, the pH has a marked eﬀect on the adsolubilization proﬁle: the interplay between the opposite (or like charges) of the solid surface, the surfactant (when ionic), and the solute results in an adsolubilization maximum around the pK of the solute molecule. The adsolubilization proﬁle displays other speciﬁcities. For some systems the decrease of solute adsolubilization as the surfactant concentration increases beyond the CMC begins at the equilibrium CMC, as free micelles are formed in solution; for others, the decrease begins below the CMC. For one system at least, no decrease is observed. It should again be pointed out that contrary to the micellar solubilization situation, the number of adsolubilized systems thoroughly investigated is small: 2-naphthol, naphthalene, and phenanthrene represent by far the majority of molecules studied. Adsolubilization and micellar solubilization are closely linked phenomena. Copyright © 2003 by Taylor & Francis Group, LLC

The importance of the equilibrium CMC cannot be overemphasized in applications, as the appearance of free micelles in solution decreases the quantity of adsolubilized material. The adsolubilization phenomenon plays a major role in all aspects of surfactant science wherever a solid surface is present. Various types of chemical species may eventually concentrate at a solid–liquid interface. Understanding the behavior of chemicals in the environment is an important aspect of such research, but the formulation of chemical specialties from pesticides to pharmaceuticals also depends on the way chemicals interact with solid surfaces in the presence of surfactants. Many questions need to be resolved, however: desorption is one of them. The rate of desorption of surfactants under various experimental conditions certainly controls to a large extent the rate of desorption of adsolubilized molecules. The relation between the two phenomena is not known. Molecules may be incorporated to a solid–water interface using other compounds than surfactants. The term adsolubilization would still be adequate in that situation, which is worthy of thorough investigation. A thermodynamic theory of adsolubilization is needed. Adsolubilization begins at a high solute/surfactant ratio. Thus, the probability of solute + solute interactions in the small aggregates that are initially formed is high. This interaction may result in a nonideal behavior that could be described either by an activity coeﬃcient as in the case of micellar solubilization or by structural modeling. Until this question is settled, the relation between thermodynamic adsolubilization and surfactant aggregate structure should be considered with caution.

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16 Adsorption of Polymer and Surfactant from Their Binary Mixtures on an Oxide Surface KUNIO ESUMI

I.

Tokyo University of Science, Tokyo, Japan

INTRODUCTION

Interactions between polymers and surfactants in aqueous solutions have been intensively investigated by many techniques [1–4]. The strength of interactions depends on the kinds of polymer and surfactant. It has been shown that the binding of ionic surfactants to neutral polymers occurs mainly by hydrophobic interactions, whereas a combination of electrostatic and hydrophobic interactions is involved in the binding of oppositely charged polymers and surfactants. Studies of interactions between polymers and oxide surfaces have been given attention due to the numerous technological and industrial applications as well as the importance of the fundamental standpoint. Several reviews have been reported through theoretical and experimental descriptions [5–14]. Polymers in solution accumulate at an interface, which is called ‘‘adsorption,’’ and polymers adsorbed at the interface can take various conformations such as a tail, loop, or train. Such a conformation often aﬀects the stability of colloidal dispersions [15,16]. Although there are several theories of the adsorption of neutral polymers, some work is still needed for theoretical studies of polyelectrolytes and copolymers. Further, polymer adsorption on oxide surfaces is often inﬂuenced by other factors including surface properties of the oxides [17–19] and some additives such as surfactants. Adsorption of surfactants on solid particles also controls many interfacial processes, such as stabilization of solid dispersions, selective ﬂoatation of minerals, detergency, protection of metal surfaces, and lubrication. Surfactant adsorption at the solid–liquid interface is a major event in Copyright © 2003 by Taylor & Francis Group, LLC

which the molecules of the surfactant can interact with the solid surface. Several adsorption models for a large number of studies have been proposed. The reverse orientation model suggested by Somasundaran and Fuerstenau [20] has been successful in describing anionic surfactant adsorption on alumina and titania. The bilayer model has been presented by Harwell et al. [21] for mainly anionic surfactant adsorption on alumina. Gu and Huang [22] have proposed a much diﬀerent model from the former two models; this model involves adsorption of small surface micelles and applies for cationic surfactant adsorption on silica. In addition, the selfconsistent ﬁeld lattice theory (SCFA theory) utilized by Bo¨hmer and Koopal [23] does not require any assumptions about the adsorbed layer structure, and results obtained with the SCFA theory show the shape of the adsorption isotherm to be quite complex and diﬀerent for constant charge and constant potential surfaces. Striking atomic force microscopy (AFM) images from a number of laboratories over the past few years have changed the surfactant adsorbed structures developed from theoretical adsorption isotherms; the emerging picture of the surfactant adsorbed layer on solid substrates consists of micellelike aggregates such as spheres and cylinders [24–26]. The adsorption and orientation of polymers and surfactants from binary mixtures, however, have not been extensively studied at the solid–liquid interface, although these phenomena are important for understanding the mechanisms of stabilization and ﬂocculation in dispersions and emulsions. Further, these systems have been used in many industrial ﬁelds. Also, adequate information on the conformation of nonionic polymers adsorbed on particles in the presence of surfactants is not suﬃciently available, whereas the conformation of polymers alone adsorbed at the solid–liquid interface has been studied using many methods including neutron scattering, neutron and X-ray reﬂectivity, internal reﬂection spectroscopy, electron spin resonance, NMR, and various other techniques [27]. The objective of this chapter is to describe the interaction between polymers and surfactants on solid particles—in particular, oxide surfaces in aqueous solution. In addition, the conformation of polymers adsorbed on particles in the presence of surfactants is also discussed.

II. CHARACTERIZATION OF OXIDE SURFACE Before discussing adsorption of polymers and surfactants on oxide surfaces from aqueous solution, it is necessary to provide a description of the oxide– liquid interface. When an oxide such as Al2O3, TiO2, or Fe2O3 is immersed in an aqueous solution, the surface tends to coordinate water molecules and Copyright © 2003 by Taylor & Francis Group, LLC

any further dissociation of water molecules leads to a fully hydroxylated surface. Then the electrical double layer develops since charged species will migrate across the oxide–water interface, and the oxide surface will acquire a charge with respect to the aqueous phase. In many cases the electrical double layer plays an important role in the adsorption of polymer and surfactant. The excess charge ﬁxed at the oxide surface is exactly balanced by a diﬀuse region of equal but opposite charge on the liquid side. The surface charge and the diﬀuse region constitute the electrical double layer. Figure 1 is a schematic of the structure of the electrical double layer at the solid–water interface. The formation of a charge on

FIG. 1 Schematic representation of the structure of the electrical double layer at the solid–water interface. Copyright © 2003 by Taylor & Francis Group, LLC

an oxide in aqueous solution occurs by a number of mechanisms including chemisorption, preferential dissociation of surface ions, selective adsorption of ions, and oxide lattice substitution. The surface charge of an oxide is determined in part by the pH of the solution ion in which it is immersed. For such systems the H+ and OH ions are potential-determining ions: 0 ¼ FðHþ OH Þ where Hþ and OH are adsorption densities of Hþ and OH, 0 is the surface charge, and F is the Faraday constant. Two important parameters describing the electrical double layer of an oxide are the point of zero charge (pzc) and the isoelectric point (iep). The pzc can be deﬁned as the concentration of the potential-determining ion with the surface charge of an oxide ¼ 0, while the iep is the concentration of potential-determining ion at which the zero potential ¼ 0 can be calculated from electrokinetic measurements. The surface potential ð 0 Þ is determined by the activity of potentialdetermining ions in solution: 0

¼ RT lnðaþ Þ=zFðaþ pzc Þ

where z is the valence of the potential-determining cation in solution, aþ is the activity of the potential-determining cation in solution, and aþ pzc is its activity when the surface charge is uncharged. The pzc of an oxide is an essential parameter to describe electrical-layer phenomena at the oxide–water interface. The importance of the pzc can be understood that the surface charge has a major eﬀect on the adsorption of all ions, including polyelectrolytes. The acid-base behavior of the surface hydroxyl groups can be determined by the electron distribution in the surface O–H bond, which is dependent on the electronegativity of the surface metal atom. In the case of a predominantly ionic bond such as in MgO the electron pair is close to the oxygen atom, which results in a stronger attraction for the proton. However, for an oxide with an increased character of covalent bond such as SiO2, the proton will not be strongly bound to the oxygen, and therefore this type of hydroxyl group is expected to be acidic. Al2O3 has a more covalent character of Al–O bond than Mg–O, but at the same time it is more ionic compared to SiO2. Thus, SiO2 has stronger Bro¨nsted acid sites than Al2O3. Such an acid-base character of an oxide surface may also play an important role for adsorption of a polymer such as a nonionic polymer. Copyright © 2003 by Taylor & Francis Group, LLC

III. EFFECT OF SURFACTANT ON POLYMER ADSORPTION A. Polymer–Surfactant Interaction The adsorption of the polymer and surfactant on particles will be inﬂuenced by the nature of interactions between various species in the bulk and at interfaces [28–32]. It is now well established that ionic surfactants interact with nonionic polymers and that the resulting polymer-surfactant complexes behave as polyelectrolytes [33–52]. The nature of these complexes has been investigated using viscosity [33–39,45,47–51], surface tension [45,48–50], conductivity [45,47], dye solubilization [33–36,48–50], dialysis [51], electrophoresis [37–39], ion activity [40,43], and NMR [53,54] measurements. The surface charge characteristics of the solid substrate will also play a key role in determining the adsorption properties of both polymer and surfactant. In particular, interactions between polymer and surfactant profoundly inﬂuence their adsorption behaviors. These interactions are discussed in the following. Polymer and surfactant interactions can be aﬀected mostly by (1) the changes in the solvent power of the medium and (2) interactions in the bulk or at interfaces as a result of electrostatic, hydrogen, and hydrophobic bonding between polymer and surfactant. Interactions due to changes in the solvent power of the medium are studied by surface tension measurements. The surface-active nature of the complex itself is also investigated by surface tension measurements. Furthermore, complex formation due to the aforementioned bondings is identiﬁed by viscosity measurements. Figure 2a shows the eﬀect of poly(vinylpyrrolidone) (PVP) on the surface tension of aqueous solutions of lithium dodecyl sulafte (LiDS) [55]. There are two transition points, which are breaking points in the presence of PVP; one is located below and the other above the critical micelle concentration (CMC) of LiDS. The ﬁrst transition point, T1, is considered to be the concentration at which association of LiDS and PVP in the bulk phase begins. The second one, T2, corresponds to the concentration at which PVP is saturated with LiDS for complex formation. At concentrations greater than T2, the regular micelles of LiDS and the PVP–LiDS complex coexist in the bulk phase. T1 is constant, 1.4 mmol dm3 , and the concentration is independent of that of PVP. A similar result is obtained in the PVP–LiFOS (lithium perﬂuorooctane sulfonate) system (Fig. 2b). However, T1 for the PVP–LiFOS system is 0.1 mmol dm3 , which is considerably diﬀerent from T1 for the PVP–LiDS system, although the CMC of LiFOS is almost the same as that of LiDS. It would appear that PVP inﬂuences the behavior of aqueous solutions of LiFOS to a much greater extent than that of aqueous solutions of LiDS. The fact that T1 for the PVP–LiFOS system is much lower than that for the PVP–LiDS system implies that the polymer– Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 2 Eﬀect of PVP on surface tension of aqueous surfactant solutions: (a) PVP– LiDS system; (b) PVP–LiFOS system. (Reproduced from Ref. 55 with permission of JAOC.)

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surfactant aggregate is a more favorable energy state for LiFOS than for LiDS. The variation of relative viscosity as a function of LiDS concentration in the PVP–LiDS system is shown in Fig. 3a. The relative viscosity of aqueous solutions of LiDS containing PVP increases with an increase of LiDS concentration. Such an increase in the viscosity occurs in the vicinity of 1 mmol dm3 of LiDS, which is T1 for this system. This result clearly implies the conformational change of PVP associated with LiDS. Alternatively, the increase in the viscosity is due to an expansion of the polymer coils on association with the charged surfactant. In the PVP–LiFOS system (Fig. 3b), an increase in the relative viscosity occurs at a concentration near T1, 0.1 mmol dm3 , which is due to a combination of electrical charging and attendant conformational eﬀects. However, in the PVP–LiFOS system a signiﬁcant change in the relative viscosity, which shows a maximum at a certain concentration of LiFOS, is recognized by comparison with the PVP– LiDS system. A marked high viscosity at a low concentration of LiFOS in this system can be probably be attributed to a rigidity of the ﬂuorocarbon chain of LiFOS. Similar behavior has been observed in poly(sodium-4-styrenesulfonate)-cationic hydrocarbon surfactant–ﬂuorocarbon surfactant systems [56]. Thus, the interaction can be described in terms of an association of the surfactant to the polymer. Another description can be represented as the pearl-necklace model (Fig. 4) [57]. This model, with the surfactant forming discrete micellarlike clusters along the polymer chain, has received wide acceptance for the case of mixed solutions of ionic surfactants and homopolymers. The micelle sizes are similar in the presence and in the absence of polymer, and the aggregation numbers are slightly lower than those of micelles in the absence of polymer.

B. Linear Nonionic Polymer–Surfactant Adsorption Figure 5 shows the adsorption of PVP and lithium dodecylsulfate (LiDS) on Al2O3 from their mixed aqueous solutions at feed concentrations of PVP (0.2 and 0.5 g/dm3) as a function of LiDS concentration [58]. The amount of PVP adsorbed increases markedly with LiDS concentration, achieves a maximum, and then decreases for both feed concentrations of PVP. On the other hand, the adsorption of LiDS also increases with LiDS concentration and reaches a plateau in the absence of PVP; in the presence of PVP, the amount of LiDS adsorbed is less than that for LiDS only. This result can be explained by a view that PVP-surfactant complexes are formed on Al2O3. Because it is known that a nonionic polymer and an ionic surfactant can form a polyelectrolytelike complex by hydrophobic interaction in aqueous solution [55], it is postulated that the same interaction takes place and a type Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 3 Variation of relative viscosity in PVP–surfactant aqueous solutions: (a) PVP–LiDS system; (b) PVP–LiFOS system. (Reproduced from Ref. 55 with permission of JAOC.)

Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4

Pearl-necklace model of a surfactant–polymer association.

FIG. 5 Adsorption of LiDS and PVP on alumina from PVP–LiDS mixed aqueous solution containing ﬁxed initial concentrations of PVP (0.2 and 0.5 g dm3 ) as a function of LiDS concentration. (Reproduced from Ref. 58 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

of surface complex of PVP and surfactant forms at the solid–liquid interface. The anionic surfactant (below the CMC) adsorbs much faster on the alumina surface than PVP, due to its smaller size and the electrostatic attraction force between the negatively charged hydrophilic groups of the surfactant and the positively charged sites on Al2O3. The hydrophobic chain of the surfactant extends toward the aqueous solution. Then PVP attaches to the hydrophobic chain of the adsorbed layer of the anionic surfactant. This model also applies to surfactant concentrations greater than its CMC, but instead of a bilayer of PVP-surfactant attachments, there might also be patches of hemimicelles to which PVP attaches. As a result, PVP and the surfactant adsorbed on Al2O3 can combine with each other by hydrophobic binding, so that more PVP is adsorbed. With increasing concentration of LiDS, the adsorption of PVP rapidly decreases because PVP-anionic surfactant complexes formed in the bulk are relatively surface-inactive and scarcely adsorb at the alumina–solution interface. The formation of a surfactant bilayer on Al2O3 may also prevent the formation of a PVP-anionic surfactant complex on Al2O3. The formation of a PVP-anionic surfactant complexes in aqueous solutions has been conﬁrmed by surface tension [55] and NMR [53,54] measurements. Using a spin-labeled PVP, the conformation change of PVP with adsorption of anionic surfactant on Al2O3 has also been investigated. Generally, the conformation of adsorbed polymers can be classiﬁed into three segments: loops, tails, and trains. The fraction of bound segments (i.e., trains) is usually denoted as p. Figure 6 shows the plots of p-values against LiDS concentration. The values of p steeply increase with increasing LiDS concentration and then become constant. This probably occurs because the PVP-surfactant complexes formed by the interaction between PVP and hydrophobic chains of LiDS on Al2O3 become more rigid. Then, although the adsorbed amount of PVP decreases remarkably, the values of p remain constant with their segments in trains. The value of p is larger in 0.2 g/dm3 than in 0.5 g/dm3 at the maximum PVP adsorption. This diﬀerence in the p correlates with the bound ratio of PVP and LiDS adsorbed: the bound ratio of LiDS to PVP in the presence of 0.2 g/dm3 is greater than that in the presence of 0.5 g/dm3. The adsorption of PVP on Al2O3 in the presence of an anionic ﬂuorocarbon surfactant such as lithium perﬂuorooctane sulfonate (LiFOS) shows a similar behavior to that of the PVP–LiDS system. However, the p-values in the PVP–LiFOS system are higher than those in the PVP–LiDS system, probably due to a rigidity of the ﬂuorocarbon chain of LiFOS. The interaction of PVP with SDS on Al2O3 has been studied using a calorimetric method [59]. One of the interesting results is that the enthalpy change upon PVP addition to SDS adsorbed on Al2O3 is endothermic. This observation would mean that an SDS monolayer is present with Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 6 Plots of p-values against LiDS for the PVP–LiDS–alumina system. The initial polymer concentrations are 0.2 and 0.5 g dm3 . (Reproduced from Ref. 58 with permission of the American Chemical Society.)

the hydrophobic alkyl chain pointing toward the solution. This mechanism is supported by the change of p-value for the PVP–LiDS system. The additive eﬀect of a double chained anionic surfactant such as sodium bis(2-ethylhexyl) sulfosuccinate (AOT) on the adsorption of PVP on Al2O3 has also been studied [60]. The adsorption of PVP is signiﬁcantly enhanced at low concentrations of AOT, but the amount of PVP adsorbed decreases gradually at higher AOT concentrations. Interestingly, below the CMC of AOT, p-values are greater for the PVP–AOT system than for the PVP–LiDS system. These large p-values suggest that the PVP–surfactant complexes formed by the interaction between PVP and the hydrophobic chain of AOT on Al2O3 become more immobile than those formed between PVP and LiDS. It is likely that since the strength of the interaction between PVP and AOT on Al2O3 is stronger than that between PVP and LiDS, the train portion of PVP for the former system is larger than that for the latter system. The adsorption of PVP on Fe2O3 is also considerably enhanced in the presence of sodium dodecyl sulfate [61]. It has been shown that PVP adsorption exhibits a strong aﬃnity with SiO2, diﬀerent from a weak aﬃnity with Al2O3. The eﬀect of anionic surfactant on PVP adsorption on hydrophilic silica is shown in Fig. 7 [62]: the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 7 Adsorption of LiDS and PVP on silica from single and mixed aqueous solutions containing a ﬁxed initial concentration of PVP (1.0 g dm3 ) as a function of surfactant equilibrium concentration. (Reproduced from Ref. 62 with permission of Elsevier Science–NL.)

adsorption of PVP increases and shows a maximum, then decreases with increasing LiDS concentration. However, the enhancement in the adsorption of PVP on SiO2 is small in comparison with that on Al2O3. It is very important to conﬁrm the relationship between the polymer conformation adsorbed (values of p) and the thickness of the adsorbed layer (). Most frequently the photon correlation spectroscopy (PCS) technique is used to measure the size of both core particles and adducts, and the thickness of the adsorbed layer is found from the diﬀerence between the two. For polydisperse samples of unknown distribution, the technique is less suitable, as it only provides values for the average diameter together with a polydispersity index. Because larger particles scatter light more strongly than ﬁne particles, even minor contaminations by particles larger than the average tend to shift the average size toward larger values without noticeably aﬀecting the measured polydispersity. By introducing a sedimentation ﬁeld ﬂow fractionation separation step [63,64] prior to the PCS sizing of the adsorbate, it is possible to improve the accuracy in these size measurements. It is reasonable to Copyright © 2003 by Taylor & Francis Group, LLC

assume that determined in this process is more reliable. Figure 8 shows the layer thickness and the values of p for the PVP–LiDS–SiO2 system at a feed concentration of PVP ¼ 1:0 g/dm3. The layer thickness has been obtained using a sedimentation ﬁeld ﬂow fractionation and PCS technique. The adsorption layer thickness of PVP alone on SiO2 (not shown in the ﬁgure) has suggested that the molecules would be adsorbed ﬂat on the surface in a very low concentration region, having a thinner layer. When the PVP concentration increases, the adsorption layer rapidly becomes thicker because larger loops and tails are formed. Adsorption layer thickness in the range of 5–10 nm is known from the literature. Furthermore, from segment density proﬁles calculated with the Scheutjens–Fleer adsorption theory, the variation of hydrodynamic layer thickness of adsorbed polymer layers with coverage is known to come from long tails that extend far into the solution. Thus, the thicker layer could be attributed to the conformation of polymer adsorbed in the tail. In Fig. 8 a remarkable decrease in the thickness of the adsorbed layer occurs with increasing LiDS and becomes constant, while the value of p increases and then becomes constant, indicating that the conformation of PVP adsorbed on SiO2 signiﬁcantly aﬀects the thickness of the adsorbed layer. Thus, a good relationship between the layer thickness and

FIG. 8 Relationship between the thickness of the adsorbed layer and p-values for the PVP–LiDS–silica system. (Reproduced from Ref. 62 with permission of Elsevier Science–NL.) Copyright © 2003 by Taylor & Francis Group, LLC

the value of p is obtained. Such a relationship is also obtained for the PVP– LiDS–hydrophobic silica system. The enthalpy of replacement has been measured for the PVP–SDS–silica system while changing the SDS concentration and keeping the PVP concentration constant. It has been reported [65] that the enthalpy of displacement ﬁrst increases with SDS and reaches a maximum, and then decreases with a further increase of SDS concentration. This behavior suggests that the adsorption of the polymer–surfactant associate is more favorable than that one of the neat polymer and that the macromolecules lie ﬂat on the solid surface in the presence of SDS. The conformation change of poly(ethylene glycol) on silica by addition of SDS has been conﬁrmed using photo correlation spectroscopy [66]. In the absence of surfactant, the thickness of poly(ethylene glycol) adsorbed is close to 10 nm and the addition of a small amount of SDS results in a substantially thinner layer. At an SDS concentration higher than the critical micelle concentration, the adsorbed layer recovers approximately the thickness observed for the neat polymer. It may suggest that polymer chains are stretched by wrapping around SDS micelles. The adsorption of hydroethylcellulose and hydrophobically modiﬁed hydroethylcellulose and SDS on Al2O3 has been investigated [67]. In both systems the amount of polymers adsorbed increases by twice as much as that without SDS. On the contrary, the adsorption of SDS increases with SDS concentration and reaches a plateau in the absence of the polymer. Further, the addition of hydroethylcellulose hardly alters the amount of SDS adsorbed, but the addition of the hydrophobically one reduces the amount of SDS adsorbed to some extent. In the two cellulose systems alone, the values of p are almost zero, indicating that the polymer chains extend considerably in the bulk solution. By addition of SDS, the values of p are in the range from 0.2 to 0.6 and increase slightly with increasing SDS concentration, where the p-values in the hydrophobically modiﬁed cellulose are slightly higher than those in the hydroethylcellulose. Coadsorption of an amphiphilic triblock copolymer poly(ethylene oxideb-propylene oxide-b-ethylene oxide), Pluronic F108, and SDS on silica has been studied [68]. F108 adsorbs appreciably on the silica surface in the absence of SDS and is irreversible. The presence of SDS in solution controls both the extent and reversibility of F108 adsorption. For coadsorption of F108 with varying SDS concentration and varying NaCl concentration, a surfactant concentration above which no adsorption occurs can always be found. As the surfactant concentration is decreased from this level, the adsorbed amount increases until the critical aggregation concentration is reached. The interactions of nonionic polymers and cationic surfactants in aqueous solutions are usually weaker than those between nonionic polymers Copyright © 2003 by Taylor & Francis Group, LLC

and anionic surfactants so that the adsorption of nonionic polymers on particles would show a competitive adsorption with cationic surfactant when the polymer and surfactant have aﬃnity to the particle surfaces. Such a case is the PVP–dodecyltrimethylammonium chloride (DTAC)– SiO2 system [32]. Figure 9 shows the competitive adsorption of PVP and DTAC from their mixed solution in the presence of PVP (0.2, 1.0, and 1.8 g/dm3). At the highest concentration of PVP studied, the adsorption of PVP decreases gradually with increasing DTAC concentration, whereas the amount of DTAC adsorbed increases, but the magnitude of the increase in the adsorption is lower than that in the absence of PVP. A similar result is obtained at low concentrations of PVP. Thus, the replacement of PVP on SiO2 by DTAC occurs. Because the interaction between PVP and cationic surfactants in aqueous solutions has been observed to be nonexistent or very weak, in contrast to the case of anionic surfactants, it is readily understood that competitive adsorption between PVP and DTAC on SiO2 takes place. Figure 10 shows the change in p-values as a function of DTAC concentration for the PVP–DTAC–SiO2 system. The p-value decreases gradually with increasing DTAC concentration in the presence of higher concentrations of PVP, whereas p shows an almost-constant, high value in the presence of a lower PVP concentration. This change in the p-value correlates well with the stability of silica dispersion: the dispersion stability of SiO2 increases with decreasing p-value. This suggests that the dispersion stability of SiO2 is dominated by the steric repulsion force, that is, the fraction of segments in loops or tails. The competitive adsorption on SiO2 between nonionic surfactants and PEO has been investigated as a function of polymer chain length [69]. For low-molecular-weight PEO, a preferential adsorption of the surfactants is observed. However, at higher-molecular-weight PEO, a competitive adsorption between PEO and the surfactant takes place. It is assumed that there is a competition on the silica surface between surfactant surface aggregates whose molecular weight would range between 80,000 and 130,000 and adsorbed PEO.

C. Linear Ionic Polymer–Surfactant Adsorption The adsorption of anionic polymers such as sodium poly(styrene sulfonate) (PSS) and polyacrylamide including 3 mol% sulfonate groups (PAMS) on oxide surfaces has been inﬂuenced by the addition of anionic surfactants. In the case of the PSS–sodium dodecyl sulfate (SDS)–Al2O3 system [70], the amount of PSS adsorbed decreases with increasing adsorption of SDS, suggesting that the adsorbed PSS is replaced by SDS with increasing SDS concentration. A decrease in the adsorption of PAMS on Fe2O3 is also Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Competitive adsorption of PVP and DTAC on silica. The initial polymer concentrations are (a) 0.2, (b) 1.0, and (c) 1.8 g dm3 . (Reproduced from Ref. 32 with permission of the American Chemical Society.)

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Figure 9 continued

FIG. 10 Change in p-values as a function of DTAC concentration for the PVP– DTAC–silica system. The initial polymer concentrations are indicated by symbols on the ﬁgure. (Reproduced from Ref. 32 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

obtained by addition of sodium dodecylsulfonate [71]. However, no signiﬁcant change in sodium dodecylsulfonate adsorption on Fe2O3 is reported by adsorption of PAMS. When oppositely charged polymer and surfactant are mixed in aqueous solutions, precipitation often occurs due to the formation of a complex from hydrophobic as well as electrostatic attractive forces. A typical case is a combination between PSS and hexadecyltrimethylammonium chloride (HTAC) [70]. Figure 11 shows the adsorption of PSS and HTAC on positively charged alumina from the mixed solution at a ﬁxed initial concentration of PSS (0.4 g/dm3). The amount of PSS adsorbed increases gradually and then sharply, accompanied by a similar sharp adsorption of HTAC with increasing HTAC concentration. Because there are an electrostatic attraction force between oppositely charged PSS and HTAC in aqueous solution and a hydrophobic force between them, it is reasonable to assume that such a complex forms on the surface of Al2O3, resulting in the enhancement of PSS adsorption. A similar coadsorption of PSS and hexadodecyltrimethyl ammonium bromide (HTAB) on SiO2 has been studied from mixed solutions by attenuated total reﬂection techniques [72]. The adsorbed amount of PSS and HTAB is highly dependent on both pH and the order of addition of both

FIG. 11 Adsorption of PSS and HTAC on alumina from their mixed aqueous solutions. The ﬁxed initial concentration of PSS is 0.4 g dm3 . (Reproduced from Ref. 70 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

species. Figure 12 shows a schematic representation of the proposed surface and solution species formed at various pHs for the sequential addition of HTAB and PSS to SiO2. At pH 2, although the amount of HTAB adsorbed is small, the hydrophobic nature of the HTAB-coated silica surface facilitates adsorption of PSS. When the solution pH is raised to 7.0, the polyelectrolyte desorbs due to electrostatic repulsion between the silica surface and PSS. As the solution pH is increased to 9.7, a large rise in the amount of HTAB

FIG. 12 Schematic representation of the proposed surface and solution species formed at pH 2.0, 7.0, and 9.7 for the sequential addition of HTAB (5:5 105 M) and PSS (100 ppm) to silica. (Reproduced from Ref. 72 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

adsorbed is observed. Surfactant removal from the polyelectrolyte to the surface can be understood in terms of the increased electrostatic attraction between HTAB and the highly negatively charged surface at pH 9.7. Anionic polyacrylamide (PAMS) adsorption on positively charged hematite at pH 2.4 has also been investigated by the addition of dodecylamine [71]. At this pH the amine is fully cationic. The adsorption of PAMS is enhanced compared with that for PAMS alone. This increase is also explained by the associative interaction between the two oppositely charged species. The adsorption of cationic polymers on oxides has been investigated by the addition of anionic or cationic surfactants. From a study of adsorption of SDS and of JR400 (water-soluble cellulose ether polymer containing quaternary nitrogens grafted onto its backbone) on Al2O3 [73], it is found that synergistic adsorption occurs under certain conditions (e.g., at pH 6 and relatively low ratios of SDS to JR400), whereas under diﬀerent conditions either component can inhibit the adsorption of the other one. In the case of simultaneous adsorption of three cationic polymers (JR polymer) and hexadecyltrimethylammonium bromide on SiO2, the polymers are competing with small molecules; the number of adsorbed groups per molecule is an important factor. Here, the order of the molecular weight of the JR polymer is as follows: JR30M > JR400 > JR125. Figure 13 indicates that the diﬀusion of polymers to the surface before surfactant adsorption is important, as is the number of adsorbed groups per polymer. The amount of polymer adsorbed increases in the order of JR125 < JR30M < JR400, suggesting that the amount of polymer adsorbed is determined by two factors: (1) the weight of polymer that can diﬀuse to the surface; and (2) the number of segments each polymer chain has on the surface at equilibrium. The larger the polymer, the greater the weight that would be attached to the surface at the start of adsorption, although the slower the diﬀusion to the surface. In competition with the surfactant, JR125 has the lowest weight adsorbed, probably because of too few contacts with the surface. JR400 may have been adsorbed to a greater extent than JR30M because of its faster diﬀusion while having suﬃcient contacts with the surface. The eﬀect of hexadecyltrimethylammonium bromide (HTAB) on the conformation of the adsorbed copolymer (a copolymer of dimethyldiallyl ammonium chloride and acrylic acid) on SiO2 has been studied [74]. The ESR spectra obtained indicate that the polymer adsorbed takes a ﬂat conformation at a lower HTAB concentration, whereas at a higher HTAB concentration the spectra are narrower, suggesting that the polymer adsorbed in the form of loops and tails extending out into solution. When the surfactant concentration increases, HTAB adsorbs on SiO2 and its competition for the surface sites causes the polymer to adopt a more extended conformation. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 13 Eﬀects of surfactant on JR polymer adsorption on silica: (a) JR 125; (b) JR 400; (c) JR 30M. (Reproduced from Ref.73 with permission of the Royal Society of Chemistry)

Coadsorption of poly-L-lysine hydrobromide and HTAB onto silica surfaces has been carried out [75]. In the absence of added salt, polylysine has a modest inhibitory eﬀect on HTAB adsorption to silica, whereas the qualitative form of the HTAB adsorption isotherm is preserved. In the presence of 10 mmol dm3 KBr, polylysine eﬀectively eliminates admicelle adsorption below the CMC, indicating that the primary role of the polylysine is to disrupt the surfactant’s capacity for interfacial self-assembly.

IV. CHARACTERIZATION OF ADSORPTION A. Dendrimer Adsorption Dendrimers are three-dimensional, globular, highly branched macromolecules made of a central core surrounded by repetitive units all enclosed by a terminal group. They can be synthesized with a highly controllable size determined by the core type, extent of branching, and nature of the end groups, in the range from a few to several tens of nanometers in diameter [76–81]. Dendrimers have become the subject of extensive studies because their functional groups and speciﬁc shape have unique properties compared with those of conventional linear polymers. For example, poly(amidomaiCopyright © 2003 by Taylor & Francis Group, LLC

ne)dendrimers with surface carboxylic groups in the earlier generations interact weakly with cationic surfactants, but the later generations of the dendrimers induce cooperative interactions among bound surfactant molecules [82,83]. Furthermore, dendrimers have the ability to form organized superstructures at the interfaces; thus, it is very important to characterize adsorption behaviors at various interfaces [84–92]. Figures 14–16 show adsorption isotherms of poly(amidoamine)dendrimers on particles [93,94]. In Fig. 14 the amount of poly(amidoamine)dendrimers with surface carboxyl groups adsorbed on alumina at pH 5 increases sharply at low concentrations and then attains a saturation with an increase of the dendrimer concentrations, where the amount in weight of dendrimers adsorbed becomes larger with an increase of the generation of dendrimers. Comparison of the adsorption of G5.5 dendrimer (molecular weight ¼ 52,852) and poly(acrylic acid) (molecular weight ¼ 50,000) on alumina shows that the adsorption of G5.5 dendrimer is about 3 times that of poly(acrylic acid). This diﬀerence probably comes from the diﬀerent molecular structures of poly(acrylic acid) and dendrimers adsorbed; at pH 5 poly(acrylic acid) adsorbs predominantly as train segments and G5.5 dendrimer is suggested to be adsorbed as globular, orienting with only a few carboxyl groups to positively charged sites on the alumina. It is found that the occupied areas of dendrimers increase with an increase of the generation

FIG. 14 Adsorption isotherms of G (n.5) dendrimers on alumina. (Reproduced from Ref. 93 with permission of Academic Press, Inc.) Copyright © 2003 by Taylor & Francis Group, LLC

from 0.5 to 5.5, and they are considerably smaller compared with the corresponding cross-sectional areas for all the dendrimers studied. This result suggests the possibilities for compression of dendrimers adsorbed. Actually, it has been reported that dendrimers are highly compressed along the ﬂat solid surface [87]. In addition, it has been demonstrated that dendritic macromolecules within Langmuir monolayers at the air–water interface can be easily squeezed in the lateral direction even by modest compression [89]. To determine the eﬀect of surface charge on the interaction of the nonionic ester dendrimer, poly(amidomaine)dendrimers with surface methylester groups (G-ME), the adsorption of G-ME dendrimers has also been performed. The amount of G-0.5ME dendrimer adsorbed is almost the same as that of corresponding G0.5 dendrimer, but those of G-3.5ME and G5.5ME dendrimers are considerably smaller than those of the corresponding G3.5 and G5.5 dendrimers. The interactions between poly(amidoamine)dendrimers with surface amino groups and negatively charged silica particles have also been examined at pH 5 [94]. Because the estimated pKNH2 is about 9.7, it is expected that the amino groups of dendrimers are proton-donated, resulting in positively charged NH3þ , and that the electrostatic attraction forces are operated between the dendrimers and silica particles. Figure 15 shows the adsorption isotherms of dendrimers on silica. The amount of dendrimer

FIG. 15 Adsorption isotherms of G (n.0) dendrimers on silica. (Reproduced from Ref. 94 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

adsorbed on silica increases gradually with an increase of dendrimer concentration for G0 and G1, while the adsorption increases at low concentrations of dendrimer and reaches a plateau for G2–5 dendrimers. The saturated amount in weight of dendrimer adsorbed increases with an increase of the generation from G0 to G3, and those for G4 and G5 dendrimers are very similar. This adsorption is probably due to electrostatic attractive interactions between cationic amino groups of dendrimers and negatively charged sites on silica surface. Furthermore, the adsorption isotherms suggest that the aﬃnity between the surface of silica and dendrimer is relatively low for G0 and G1 dendrimers but is high for G2–5 dendrimers. The occupied areas obtained from the saturated amount of dendrimer adsorbed and the speciﬁc surface area of silica are very large and are almost 3–4 times that of the cross-sectional areas of the corresponding dendrimers. Figure 16 shows adsorption isotherms of sugar-persubstituted poly(amidoamine)dendrimers (sugar ball, SB) on alumina at pH 3.5 [95]. Sugar balls have been synthesized by the reaction of the amine-terminated poly(amidoamine) dendrimers with an excess amount of aldonolactone [96]. The adsorbed amounts of SB3 and SB5 increase with an increase of SBn con-

FIG. 16 Adsorption isotherms of sugar balls on alumina. (Reproduced from Ref. 95 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

centration and then reach a plateau. The calculated occupied areas by SB3 and SB5 at the saturation are about 50 nm2. Because the extended areas of SB3 and SB5 are expected to range from 38–70 nm2, a monolayer adsorption is suggested at the saturation. The driving force for the adsorption of SBn seems to be hydrogen bonding due to the interaction between hydroxyl groups of alumina surface and hydroxyl groups of SBn.

B. Dendrimer–Surfactant Adsorption Figure 17 shows the simultaneous adsorption of dendrimers (G1.5,G5.5) and SDS on alumina at pH 5 [97]. Because aqueous properties of solutions generally inﬂuence adsorption on solids, it is important to note that the interaction between SDS and poly(amidomaine)dendrimers with surface carboxyl groups is very weak in aqueous solution because they have the same negatively charged sites and the surface tension values of SDS with and without the dendrimers are almost unchanged. The simultaneous adsorption has been performed by changing SDS concentration under a constant feed concentration of the dendrimers. Two diﬀerent feed concentrations have been employed: a half and a quarter of the respective saturation amounts of the dendrimers adsorbed. The amounts adsorbed of both dendrimers decrease gradually with an increasing amount of SDS adsorbed; the rate in the decrement of adsorption of G1.5 is much higher than that of G5.5. This result suggests a competitive adsorption between the dendrimer and SDS. In particular, a larger dendrimer prevents the adsorption of SDS more, because it occupies several sites for the adsorption on the alumina surface. To compare the eﬀect of SDS concentration on the competitive adsorption, ‘‘adsorption selectivity’’ can be deﬁned as A ¼ ðd =Cd Þ=ðs =Cs Þ whered and s are the adsorbed amounts of the dendrimer and SDS, respectively. Cd and Cs are the equilibria concentrations of the dendrimer and SDS in bulk, respectively. The larger the A-values, the more favorable adsorption of the dendrimer than SDS occurs. Figure 18 shows the variation of A as a function of SDS concentration. It is seen that the A-values increase with the SDS concentration for all the systems where they are greater for the SDS/G5.5 system than those for the SDS G1.5 system. This diﬀerence between G5.5 and G1.5 is easily understood by a view that the earlier generations of dendrimers behave as ordinary electrolytes, while the later ones behave as an anionic surfactant or polyelectrolytes. Figure 19 shows a simultaneous adsorption of a cationic surfactant, dodecyltrimethylammonium bromide (DTAB), and poly(amidoamine) dendrimer Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 17 Adsorption of dendrimers and SDS from their mixed aqueous solutions on alumina: (a) SDS–G1.5 system; (b) SDS–G5.5 system. The initial ﬁxed concentrations of dendrimers are 0.2 and 0.4 g dm3 . (Reproduced from Ref. 97 with permission of the American Chemical Society.)

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FIG. 18 Plots of adsorption selectivity with SDS concentration for the dendrimer– SDS–alumina system. (Reproduced from Ref. 97 with permission of the American Chemical Society.)

with surface amino groups on silica at pH 5 [98]. Here feed concentrations of dendrimers are 0.2 and 0.4 g dm3, respectively. The amount of the dendrimer adsorbed decreases with DTAB concentration, while the amount of DTAB adsorbed increases gradually and then sharply with DTAB concentration. The decrease in the adsorption of G0 occurs remarkably at above 6 mmol dm3 DTAB, while that of G5 occurs gradually. At high DTAB concentrations the complete replacement of the dendrimers by DTAB is attained. Thus, the results show that DTAB is preferably adsorbed and G5 adsorbs on silica much more preferentially than G0 against DTAB. A similar competitive adsorption of the dendrimers with surface amino groups and a cationic gemini surfactant on silica has also been observed. In the dendrimer– DTAB–silica system, the adsorption selectivity, A, ranges between 1 and 8 below 10 mmol dm3 DTAB. Also, a comparison between the dendrimers shows that G5 is preferentially adsorbed rather than G0 because G5 has many surface groups that can be adsorbed on the surface of silica. On the other hand, the behavior of simultaneous adsorption of sugar balls and SDS on alumina is quite diﬀerent from those of the systems described above. Figure 20 shows a simultaneous adsorption of SB3 and SDS on Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 19 Adsorption of dendrimers and DTAB from their mixed aqueous solutions on silica: (a) DTAB–G0 system; (b) DTAB–G5 system. The initial ﬁxed concentrations of dendrimers are 0.2 and 0.4 g dm3 . (Reproduced from Ref. 98 with permission of the Japan Society of Colour Materials.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 20 Adsorption of SB3 and SDS from their mixed aqueous solutions on alumina: (a) SDS adsorption; (b) SB3 adsorption. The initial ﬁxed concentrations of SB3 are 0.10 and 0.25 g dm3 . (Reproduced from Ref. 95 with permission of the American Chemical Society.)

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alumina at pH 3.5 [95]. Here the feed concentrations of SB3 are ﬁxed at 0.10 and 0.25 g dm3 , respectively. It is very interesting to note that the amount of SB3 adsorbed increases markedly at low SDS concentrations, shows a maximum, and then decreases with an increase of SDS concentration, while the amount of SDS adsorbed in the presence of SB3 is greater than that in the absence of SB3. Such an enhancement in the adsorption of SB3 is probably due to the interaction between SDS and SB3 on the alumina surface. The result that the surface tension of SB3 alone in aqueous solution is high and is almost the same as that of water, but decreases markedly by the addition of SDS, and shows about 30–35 mNm1 in the SDS range between 0.4 and 8 mmol dm3 (Fig. 21) suggests a formation of some complex of SDS and SB3. The hydrophilic groups of SDS might be adsorbed on the residue of glycoside of SB3, resulting in the orientation of the hydrocarbon chain of SDS to aqueous phase [99,100]. When the mixtures of SDS and SB3 consisting of their complexes and SDS monomer contact with alumina particles, SDS monomer adsorbs at ﬁrst, orienting its hydrocarbon chain to aqueous phase, followed by adsorption of SDS–SB3 complex on the surface. As a result, adsorption of SB3 is enhanced at low SDS concentrations. With an increase of SDS concentration, a competitive adsorption between SDS

FIG. 21 Surface tensions of SDS alone and SDS–SBn mixed aqueous solutions. The initial concentration of SBn is 0.25 g dm3 . (Reproduced from Ref. 95 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

monomer and SDS–SB3 complex against SDS-covered alumina surface occurs, and at the same time the state of the SDS–SB3 complex changes from monolayer coverage to bilayer coverage of SDS on the SB3 surface. Then adsorption of SB3 on alumina will decrease. The enhancement in the adsorption of SB3 by SDS is clearly observed when the feed concentration of SB3 is higher. An enhancement in the adsorption of SB5 by SDS at low SDS concentrations on the alumina has also been observed. For the two systems of SDS–SB3 and SDS–SB5, no clear diﬀerence is observed in the adsorption characteristics. A similar adsorption enhancement of a linear polymer, poly(vinylpyrrolidone), by the addition of SDS on alumina has been already described [58] in which the surface tension of the poly(vinylpyrrolidone)– SDS complex is higher than that of SDS alone.

VII.

CONCLUSIONS

This chapter has described adsorption of polymers and surfactants on oxide surfaces from their mixed aqueous solutions. The adsorption of polymers and surfactants is aﬀected by many factors such as chemical structures of polymer-surfactant in solution and the surface conditions of oxides. Several examples show interesting adsorption behaviors of polymers and surfactants on oxides, which may be useful for some applications. In addition, the use of atomic force microscopy or surface force apparatus can provide new insight for elucidating interactions between polymers-surfactants with oxide surfaces [101–104].

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17 Dispersion of Particles by Surfactants KUNIO ESUMI

I.

Tokyo University of Science, Tokyo, Japan

INTRODUCTION

Adsorption of surfactants on solid surfaces controls many interfacial processes, such as stabilization of solid dispersions, selective ﬂoatation of minerals, detergency, protection of metal surfaces, and lubrication. Surfactant adsorption at the solid–liquid interface is a major event in which the molecules of surfactant can interact with the solid surface. Most solids have heterogeneous surfaces, and their surface properties depend on their history of exposure to various conditions. They are likely to contain some high-energy or low-energy sites. In certain cases polar and nonpolar sites can coexist in the same solid. Thus, many diﬀerent types of solid surfaces are available for studying adsorption of surfactants. Adsorption of surfactants on solids is the result of several contributing forces, including covalent bonding, Coulombic interaction, ion exchange, hydrogen bonding, hydrophobic interactions, and van der Waals interactions. In this chapter the eﬀect of the characteristics of the solid surface and the surfactant on the various interaction forces are described. In addition, dispersion of solid particles by surfactants is discussed.

II. THERMODYNAMIC ASPECTS OF ADSORPTION A. Adsorption Isotherms Information on the thermodynamics of surfactant adsorption can be obtained from experimentally determined adsorption isotherms, which display the amount adsorbed as a function of the equilibrium concentration. Adsorption of surfactants at the solid–liquid interface is usually described by the Stern–Graham equation, which can be written in the form [1,2] =ð1 Þ ¼ Ce =55:5 expðG0ads =RTÞ Copyright © 2003 by Taylor & Francis Group, LLC

ð1Þ

where is the fraction of surface sites occupied, Ce is the equilibrium concentration of surfactant, and G0ads is the standard free energy of adsorption. Equation (1) can also be written in the form ¼ Ce =½ð1= Þ þ Ce

ð2Þ

where ¼ 1=55:5 expðG0ads =RTÞ Equation (2) is similar to a Langmuir-type isotherm. At very low surface coverage, 1, Eq. (1) reduces to ¼ Ce

ð3Þ

which is an expression of Henry’s law. Equation (3) can also be written in the form s ¼ zrCe expðG0ads =RTÞ

ð4Þ

where s is the adsorption density (surface excess) in the Stern plane, z is the valency of the surfactant, and r is the eﬀective radius of the adsorbed species. Modiﬁcation of Eq. (4) has been proposed to include electrostatic interactions as well as lateral interactions between hydrocarbon chains [3,4]: s ¼ zrCe expð2F s n=RTÞ

ð5Þ

where F is the Faraday constant, cs is the electrokinetic potential at the adsorption plane, n is the number of CH2 groups in the surfactant, and is the cohesive energy per mole of CH2 groups. In general, the contributions to the total free energy of adsorption in Eq. (4) can be divided into several diﬀerent components as follows: G0ads ¼ G0el þ G0chem þ G0CH2 þ G0solv þ G0el

G0chem

ð6Þ

is the electrostatic contribution, is the possible chemical where interactions such as covalent bond formation, G0CH2 is the contribution derived from the lateral interaction between the adsorbed hydrocarbon chains, and G0solv indicates the change in free energy derived from the changes in solvation of the surface and surfactant species upon adsorption. For a given solid–surfactant system, as described above, one or more of these forces can be responsible for adsorption, depending on the nature and concentration of the surfactant, the chemical composition of the solid, and properties of the medium such as ionic strength and pH. Several models have been developed to describe adsorption on homogeneous and heterogeneous solid surfaces. In the models for ionic surfactants [5–9], the headgroups are assumed to form the boundary of the adsorbed layer on the solid side, the solution side, or both sides of the adsorbed layer. Copyright © 2003 by Taylor & Francis Group, LLC

On the other hand, in models of nonionic surfactants, a homogeneous adsorbed layer [9,10] or a three-stage adsorption process [11] is assumed. Based on the two-step adsorption model, a general adsorption isotherm equation has also been derived [12]. Additionally, the self-consistent ﬁeld theory has been used to study adsorption of nonionic surfactants on hydrophilic and hydrophobic surfaces [13].

B. Thermodynamics of Adsorption of Surfactants on Solids The fundamental thermodynamic concepts for the adsorption of surfactant at a solid–liquid interface are expressed by the Gibbs adsorption equation, which relates the interfacial tension between the solid and liquid to the absolute temperature T of the system, the chemical potential of the various species in bulk, i, and the surface excess or adsorption density of the surfactant at the interface, i. At constant pressure this equation is equivalent to the familiar Gibbs–Duhem equation and has the form [14] d ¼ Ss dT Si di

ð7Þ

where Ss is the surface entropy per square meter. For an adsorption process, the free energy change Gads of the system is given by Gads ¼ Hads TSads

ð8Þ

where Hads is the enthalpy change and Sads is the entropy change upon surfactant adsorption. Gads is negative if the process occurs spontaneously. This is the case for exothermic adsorption systems or if the adsorption process is accompanied by a large entropy increase. Generally, there will be an entropy decrease due to the more ordered structure of surfactant ions or molecules at the interface. However, there may be a signiﬁcant increase in entropy due to the release of structured water molecules from the solid– liquid interface. The standard free energy of adsorption, G0ads , can also be written using the equilibrium constant K: G0ads ¼ RT ln K

ð9Þ

In principle, the enthalpy of the adsorption, for a certain surface coverage y, can be obtained using the Gibbs–Helmholtz relation: Hads =T ¼ ½dðG0ads =TÞ=dT

ð10Þ

However, it is diﬃcult to apply Eq. (10) because the state of hydration of surfactant molecules varies with temperature. This situation is especially true for nonionic surfactants [15]. The most reliable method for obtaining the heat of adsorption is a calorimetric technique [16]. The method involves Copyright © 2003 by Taylor & Francis Group, LLC

the measurement of the heat changes accompanying the injection of successive small volumes of concentrated surfactant solution into a stirred suspension of the solid. Since the concentration of surfactant solution injected is usually well above the critical micelle concentration (CMC), the process in the calorimeter involves demicellization in addition to adsorption on the solid surface. Consequently, the heat of demicellization should be taken into consideration in obtaining the heat of adsorption.

III. CLASSIFICATION OF SURFACTANTS AND SOLIDS A. Surfactants Surfactants have basically a characteristic molecular structure consisting of a lyophobic group that has very little attraction for the solvent and a lyophilic group that has strong attraction for the solvent. This is known as an amphipathic structure. In an aqueous solution of a surfactant, the presence of the lyophobic (hydrophobic) group in the interior of the water may cause distortion of water structure, resulting in an increase of the free energy of the system. As a consequence, the surfactant concentrates at the surface. On the other hand, the presence of the lyophilic (hydrophilic) group prevents the surfactant from being expelled completely from the water. The surfactant therefore orients at the surfaces with its hydrophilic group anchoring in the aqueous phase and its hydrophobic group directed away from it. As well as adsorbing at interfaces, surfactants form micelles at the CMC in the solution. The chemical structures of grouping suitable as the lyophobic and lyophilic portions of the surfactant molecule vary with the nature of the solvent and the conditions of use. In a highly polar solvent such as water, the lyophobic group may be a hydrocarbon, ﬂuorocarbon, or siloxane chain of proper length, whereas ionic or highly polar groups such as an oxyethylene chain may act as a lyophilic group. Because the hydrophobic group usually consists of a long-chain hydrocarbon, surfactants are classiﬁed according to the diﬀerence in the nature of the hydrophilic group: 1. Anionic: the lyophilic portion of the molecule bears a negative charge, þ e.g., RCOO Naþ , ROSO 3 Na . 2. Cationic: the lyophilic portion bears a positive charge, e.g., RNHþ 3 Cl . 3. Zwitterionic: both positive and negative charges are present in the surfactant molecule, e.g., RNH2CH2COO . 4. Nonionic: the lyophilic portion of surfactant bears no apparent ionic charge, e.g., R(OC2H4)xOH. Copyright © 2003 by Taylor & Francis Group, LLC

B. Solids In studying the adsorption of surfactants at the solid–liquid interface, it is important to consider various surface properties of solids. The surface properties are dependent on the types and the strength of forces exerted from the surface onto the surrounding medium, as well as chemical groups on the surface, which may give rise to speciﬁc adsorption or chemisorption. Heats of immersion studies [17] provide the enthalpy change accompanying the immersion of a solid in a liquid which is directly correlated with thermodynamic quantities. The nature of a solid surface is often aﬀected by its history and preparation. Carbon, for example, can have varying amounts of oxygen complexes on the surface, which can be removed by heat treatment. Also, the removal of hydroxyl groups from the surface of silica renders an initially hydrophilic surface hydrophobic. The surface area of the solid, which is often determined by adsorption of nitrogen molecules, is also important for adsorption studies. Gas adsorption data, if determined under appropriate conditions, may also be used to provide an assessment of the pore size distribution in the solid. In addition, useful information may be obtained concerning the chemical nature of the solid surface by the analysis of the gas–solid interactions that control the adsorption process. ‘‘Hydrophilicity’’ [18] of a solid can be obtained as the ratio of the surface area determined by water adsorption to that by nitrogen adsorption. Note that the surface area available to nitrogen molecules may not be equally available to much larger surfactant molecules if the solid is microporous.

1. Hydrophilic Solids In the class of hydrophilic solids, solids with a high concentration of hydrophilic groups on the surface can be included. Examples are metal oxides, silica, clay, polyamide, and so on. They show high heats of immersion values. Most solids of this class have charged groups and show zero net charge at their isoelectric points, but they possess highly charged surfaces at pHs above and below their isoelectric points. The isoelectric point is an important property, since the adsorption of ionic surfactants depends on the concentration of potential-determining ions.

2. Hydrophobic Solids Common members in the class of hydrophobic solids include graphite, polyethylene, and polystyrene, which have low-energy surfaces and essentially no ionizable groups on the surfaces. They show small heat of immersion values, indicating that the solid–liquid interaction is mainly by van der Waals forces. We will also include in this class organic pigments such as phthalocyanine blue and quinaqulidone. Copyright © 2003 by Taylor & Francis Group, LLC

IV. ADSORPTION OF SURFACTANTS A. Adsorption on Hydrophilic Solids From the experimental evidence in several adsorption systems, it has been found that ionic surfactants do not adsorb onto solids of the same charge but do adsorb in appreciable amounts onto oppositely charged solids. Figure 1 shows the adsorption isotherm of sodium dodecyl sulfate (SDS) on positively charged alumina [19]. The isotherm consists of three distinct modes of adsorption. In region I adsorption has been attributed to simple exchange of surfactant ions, since the charge density of the solid remains almost constant. In region II there is a marked increase in adsorption, resulting from interaction of the hydrophobic chains of oncoming surfactant ions with those of previously adsorbed surfactant. This aggregation of the hydrophobic groups, which may occur at concentrations below the CMC of the surfactant, has been called a hemimicelle [20]. In this region the original charge of the solid is neutralized by the adsorption of oppositely charged surfactant ions. In region III the slope of the isotherm is reduced, but the original charge of the solid is reversed. Finally, adsorption is usually complete in region IV. Here the surface is covered with a bilayer of the surfactant that has been called an admicelle [8].

FIG. 1 Adsorption isotherm of sodium dodecyl sulfate on alumina. (Reproduced from Ref. 19 with permission of Academic Press, Inc.) Copyright © 2003 by Taylor & Francis Group, LLC

The adsorption isotherms obtained for dodecyltrimethylammonium bromide on precipitated silica at a pH of 8 and 9 are shown in Fig. 2. [21] The results show a clear visible knee in the isotherm. When the charge on the surface is increased by raising the pH, the amount adsorbed at the knee is also increased. The point of zero electophoretic mobility also occurs in the knee region, at the beginning of the ﬁrst plateau on the isotherm. As the amount of surfactant adsorbed increases, the bromide adsorption occurs parallel to the surfactant adsorption. At low concentrations of surfactant, the cationic headgroups interact with negative sites on the silica surface and are oriented with the hydrocarbon chains parallel to the surface. As the concentration increases, the hydrocarbon chains reorient into a vertical position. As the second plateau is approached, a bilayer is formed, where the packing of the surfactant is enhanced by the adsorption of bromide ions. Adsorption of cationic gemini surfactants (surfactants containing two hydrophilic and two hydrophobic groups in the molecule) on silica [22– 24] has been investigated, whose adsorption mechanism is very similar to that of single chained cationic surfactants. The adsorption of nonionic surfactants, such as those of alkylpoly(oxyethylene) and alkylphenol(oxyethylene) types, at the solid–liquid interface has also been the subject of much experimental and theoretical research [12,13,16,25–28]. Generally, the adsorption of nonionic surfactants leads to an increase in the colloidal stability of the particles. However, the aﬃnity of nonionic surfactants for most solids is lower than that of ionic surfactants; the bonding energy between the hydrophilic groups and the solid is weak. The adsorption of nonionic surfactants also depends on their chemical structure [29–32]. Figure 3 shows the adsorption isotherms of the nonionic surfactants with three diﬀerent ethylene oxide numbers but the same alkyl chain length on silica [33]. Clearly, the slopes of the ascending parts of the isotherms decrease with increasing ethoxylation. However, the extent of adsorption in the ascending part at low concentrations is greater for the surfactants with higher ethoxylation than for those with lower ethoxylation. This trend is reversed at high concentrations. A linear relationship between the packing area and the ethoxylation number is obtained, with the slope giving a packing area of 0.092 nm2. This is comparable with the value of 0.085 nm2 for the Triton series surfactants. Because the nonionic surfactants do not have ionic and chemisorbing components, hydrogen bonding mechanisms may be considered as the initial driving force for adsorption. Hydrogen bonding is the mechanism also proposed for the adsorption of polyethylene oxide on silica. In low-concentration regions, the higher uptake of surfactants with larger ethylene oxide numbers is due to stronger cumulative hydrogen bonding interaction of long ethylene oxide chains with the silica surface. In higher-concentration Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 2 Adsorption isotherms of dodecyltrimethylammonium bromide on precipitated silica: (a) pH 8; (b) pH 9. (*) Surfactant ion; (&) Br adsorption. (Reproduced from Ref. 21 with permission of Academic Press, Inc.)

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FIG. 3 Adsorption isotherms of nonylphenoxyethoxylated alcohols on silica: (&) (EO)10; (~) (EO)20; (*) (EO)40. (Reproduced from Ref. 33 with permission of Academic Press, Inc.)

regions, hydrophobic chain–chain interactions between the adsorbed surfactants may become more signiﬁcant. Microcalorimetric experiments have shown [34] that for low coverage exothermic eﬀects are prevalent due to the interaction between the oxyethylene chains of the surfactant and the solid surface, but at higher surface coverages the lateral interactions between the hydrophobic chains lead to endothermic eﬀects. Commercial surfactants used in various processes usually consist of mixtures of compounds that may have a marked eﬀect on the interfacial behavior of the system. In general, surfactant mixtures [35] do not behave like single surfactants, so that it is important to characterize adsorption from surfactant mixtures. In particular, mixtures of ionic and nonionic surfactants have shown large surface activity and their adsorption behavior signiﬁcantly deviates from ideal behavior [36–42]. Figures 4 and 5 show the adsorption of 1:1 SDS and CnEO8 (n ¼ 10,12,14,16) mixtures on kaolinite [43]. It is interesting to note from Fig. 4 that the isotherms for the adsorption of SDS are identical when the hydrocarbon chain length of the nonionic surfactants is equal to or longer than that of SDS. When the hydrocarbon chain length of the nonionic surfactant is shorter (C10E8) than that of SDS, however, a diﬀerent isotherm is obtained. The presence of SDS is seen to Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 4 Eﬀect of nonionic surfactant hydrocarbon chain length on the adsorption of sodium dodecyl sulfate (SDS) from 1:1 SDS/CnEO8 (n ¼ 10,12,14,16) mixtures. 0.03M NaCl, pH 5, 25oC. (Reproduced from Ref. 43 with permission of Elsevier Science-NL.)

enhance the plateau adsorption of the nonionic CnE8, and the isotherms are shifted to lower-concentration regions. A schematic illustration of surfactant mixture adsorption is shown in Fig. 6. When the hydrocarbon chain length of the nonionic surfactant is equal to or longer than that of SDS, the hydrocarbon chains of SDS are equally shielded from the hydrophilic environment by the hydrocarbon chains of the coadsorption nonionic surfactant. Accordingly, the ideal residing environment leads to a common isotherm for SDS adsorption on kaolinite. However, when the hydrocarbon chain of the nonionic surfactant is shorter than that of SDS, part of the SDS hydrocarbon chain is exposed to the hydrophilic environment. The environment for the SDS hydrocarbon chain is, in this case, less hydrophobic and, therefore, the isotherm is shifted less into the low-concentration region. Similarly, the adsorption from mixed solutions of hexadecyltrimethylammonium bromide and ethoxylated octyl phenol on silica gel exhibits a synergistic eﬀect at low concentrations and an antagonistic eﬀect at high concentrations [39]. In addition, adsorption of like surfactant mixtures [44–48] such as nonionic–nonionic, anionic–anionic, and cationic–cationic has been reported. Note that more than 250 types of nonionic surfactants exist [49], and freCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Eﬀect of nonionic surfactant hydrocarbon chain length on the adsorption of CnEO8 from 1:1 SDS/CnEO8 (n ¼ 10,12,14,16) mixtures; 0.03M NaCl, pH 5, 25oC. (Reproduced from Ref. 43 with permission of Elsevier Science-NL.)

FIG. 6 Schematic presentation of the eﬀect of nonionic surfactant hydrocarbon chain length on the adsorption of the anionic sodium dodecyl sulfate (SDS): (a) nonionic surfactant hydrocarbon chains longer than that of SDS; (b) nonionic surfactant hydrocarbon chain length equal to that of SDS; (c) nonionic surfactant hydrocarbon chain length shorter than that of SDS, partially exposing SDS hydrocarbon chains to the aqueous solution or the hydrophilic ethoxyl chains of the nonionic surfactant. (Reproduced from Ref. 43 with permission of Elsevier Science-NL.) Copyright © 2003 by Taylor & Francis Group, LLC

quently materials of interest are heterogeneous mixtures. However, only a few studies have focused on the mixed adsorption of both cationic and anionic surfactants on solids [50–55]. The buildup of successively adsorbed bilayers of anionic and cationic surfactants can be carried out on positively charged solids such as iron oxide or titanium dioxide [53]. The surfactant adsorption from aqueous solution of an anionic–cationic mixed surfactant system on negatively charged silica [54] or clay [55] has also been reported.

B. Adsorption on Hydrophobic Solids Adsorption isotherms for anionic and cationic surfactants are similar on Graphon and are of Langmuir type (Figs. 7 and 8) [56]. The surface saturation occurs in the vicinity of the CMC of the surfactant. At low concentrations the orientation of the surfactant initially may be parallel to the surface of the solid or slightly tilted with the hydrophobic chain to the surface and the hydrophilic group oriented toward the aqueous solution. As adsorption continues, the adsorbed surfactants may become oriented increasingly toward the perpendicular to the surface with hydrophilic heads oriented toward the solution. In some cases the adsorption isotherm shows an inﬂec-

FIG. 7 Adsorption isotherm of sodium dodecyl sulfate on Graphon from aqueous solution. (Reproduced from Ref. 56 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 8 Adsorption isotherm of dodecyltrimethylammonium bromide on Graphon from aqueous solution. (Reproduced from Ref. 56 with permission of the American Chemical Society.)

tion point (Fig. 7), which has been ascribed to a change in orientation of the surfactant from parallel to perpendicular. Typical results are shown in Fig. 9 for the adsorption of polyoxyethylene alkyl phenols from C9PhE5 to C9PhE30 on carbon black [57]. All the isotherms give Langmuir-type adsorption. The adsorption saturation level decreases with an increase of the length of the oxyethylene chain of the surfactant. This indicates that the cross-sectional area of the molecule at the interface increases with increasing length of the oxyethylene chain [58]. Figure 10 shows the adsorption isotherms of alkyl ethoxylates on graphitized carbon black [15]. Here the alkyl chain length is varied while the ethoxylate chain is kept constant at E6. The hydrophilic group itself shows some tendency to adsorb, as seen by the adsorption of hexaoxyethylene glycol. As the area per molecule for E6 is about 1.50 nm2, the molecules may lie ﬂat to the Graphon surface. The saturation adsorption level increases with increasing alkyl chain length for a ﬁxed headgroup. As the alkyl chain length increases, the orientation of the adsorbed molecules may become increasingly oriented toward the perpendicular to the Graphon surface, with the hydrophilic groups oriented toward the water. A similar adsorption isotherm has been reported for nonionic surfactants on hydroCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Adsorption isotherms of nonylphenoxyethyoxylated alcohols on carbon black from aqueous solutions: (~) (EO)5; (&) (EO)7; (*) (EO)9; (^) (EO)10; (~) (EO)15; (&) (EO)21; (*) (EO)30. (Reproduced from Ref. 57 with permission of Springer-Verlag.)

phobic silica [59]. Mixed adsorption of nonionic and ionic surfactants has also been reported on hydrophobic silica [39] and carbons [60,61].

C. Characterization of the Adsorbed Surfactant Layer Among the methods used for studying the adsorbed surfactant layer, conventional adsorption experiments have provided useful basic information on the surface coverage by surfactants on various solids. However, certain changes in the adsorbed layer structure will not be directly detected by adsorption experiments. Structural properties such as polarity, microviscosity, and surfactant aggregation numbers of the adsorbed surfactant layer on solids have been studied using ﬂuorescence [19,62–65], electron spin resonance [66–69], excited state resonance Raman spectroscopy [70], neutron reﬂectometry [26,71], ellipsometry [72], NMR [73–76], and atomic force microscopy [77,78]. The pyrene ﬂuorescence ﬁne structure has been found to depend markedly on the solvent polarity: the intensities of the ﬁrst (I1) and the third (I3) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10 Adsorption isotherms of nonionic surfactants CxE6 on graphitized carbon black Graphon: (~) x ¼ 0; (*) x ¼ 6; (^) x ¼ 8; (~) x ¼ 10; (*) x ¼ 12. (Reproduced from Ref. 15 with permission of the Royal Society of Chemistry.)

vibronic bands at 373 and 383 nm, respectively, are sensitive to the solvent polarity. Actually, I1/I3 for pyrene changes from 1.8 in water to 1.0 in hydrocarbon media. Pyrene has been widely used as a polarity probe in the study of surfactant micelles, since pyrene is selectively solubilized in micelles due to its hydrophobic nature [79]. The extent of excimer as a measure of the local probe mobility has been used to determine the viscosity eﬀect of microenvironments such as micelles. In addition, the ﬂuorescence decay method developed for the determination of the micellar aggregation number [19,62] has been extended to the adsorbed surfactant layer on solids. Figure 11 shows the I1/I3 of pyrene in SDS-alumina slurries [19]. The adsorption isotherm is given in Fig. 1. The I1/I3-value changes abruptly in the local polarity of the probe from an aqueous environment to a relatively nonpolar, micelle-type environment, which occurs in a region well below the CMC of SDS. This change approximately corresponds to the transition in the adsorption isotherm from region I to II. Between regions II and IV, the I1/I3-values are relatively constant, suggesting the existence of solubilization sites for pyrene on the surface that are formed by micellelike association of hydrocarbon chains. From the emission spectra of the intramolecular excimer-forming probe, dinaphtylpropane, and the calibration in ethanol–glyCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 11 I1/I3, ﬂuorescence parameter of pyrene in SDS–alumina slurries. (Reproduced from Ref. 19 with permission of Academic Press, Inc.)

cerol mixtures of known viscosities, the adsorbed layer viscosity is estimated to be 90–120 cP, whereas that of micelle is 8 cP. The high microviscosity in the adsorbed layer may suggest that the surface phase is highly structured and almost rigid. Figure 12 shows the surface aggregation number as a function of adsorption density [19]. In region II, when the surface is positively charged, relatively uniform-sized aggregates (12–130) are measured on the surface. As the positive charge on the alumina is neutralized, the growth of existing aggregates may occur rather than the formation of new aggregates (region III). A similar behavior has been observed for the adsorption of lithium perﬂuorooctane [80] on positively charged alumina: the I1/I3value of pyrene in the adsorbed changes ﬁrst with increasing adsorption density and then keeps a constant value of 1.5, which is considerably greater than that of SDS. This diﬀerence in the micropolarity may arise from different solubilized sites of pyrene in the adsorbed layer. The structure of a nonionic surfactant (Triton X100) layer on a hydrophilic silica has also been characterized using ﬂuorescence decay spectroscopy. The parallel determination of the average aggregation number and aggregate numerical density in the fragmented-phase domain [62] shows three distinct regimes: (1) a growth regime, from = 0 to 0.17 ( being the apparent surface coverage), where the size of the surface aggregates Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 12 Surfactant aggregation number as a function of adsorption density for SDS–alumina system (average number at each adsorption point shown along isotherm). (Reproduced from Ref. 19 with permission of Academic Press, Inc.)

increases at constant number density; (2) a self-repeating regime, from ¼ 0.17 to 0.5, where the number density increases while the size of the aggregates remains constant; (3) a growth regime, up to a point ( ¼ 0:8) where the adsorbed phase can be described as an assembly of surface micelles in close packing. Electron resonance spectroscopy has normally been employed in studying the micellar environment. This technique has also been applied to study the environmental properties in the adsorbed surfactant layer. Information on the micropolarity and microviscosity of the environment can be obtained by measuring the hyperﬁne splitting constant, AN, and the rotational correlation time. A particular feature in the case of spin probes [67] is that the carboxylates of 5-, 12-, and 16-doxyl stearic acids bind tightly to the alumina surface in such a way that the nitroxide moieties sense environments corresponding to diﬀerent distances from the alumina surface. The SDS–alumina layer varies in ﬂuidity within the hemimicelle as a function of distance from the alumina surface: the closer to the surface the nitroxide is, the more viscous the environment it senses. This situation is shown schematically in Fig. 13 [67]. In addition, 2,2,6,6-tetramethylpiperidinyl-1-oxy (TEMPO) has also been employed as a spin probe [80]. Figure 14 shows the rotational Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 13 Schematic representation showing the SDS hemimicelle ﬂexibility diﬀerences in two probe positions. (Reproduced from Ref. 67 with permission of the American Chemical Society.)

correlation time of TEMPO for the lithium dodecyl sulfate–alumina and lithium perﬂuoroocatane sulfonate–alumina systems together with their adsorption isotherms. The rotational correlation time for both systems increases with increasing surfactant adsorbed, and the rotational correlation time for the lithium perﬂuorooctane sulfonate–alumina system is much greater than that for the lithium dodecyl sulfate–alumina system. This may suggest that TEMPO molecules sense the environmental change in the adsorbed layer. Opposite behavior in the rotational correlation time has been observed [48] in systems of cationic surfactants such as hexadecylpyridinium chloride and bis(hydroxyethyl) (heptadecaﬂuoro-2-hydroxyundecyl)methylammonium chloride and silica: the rotational correlation time for the hydrocarbon surfactant–silica system is larger than that for the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 14 Rotational correlation time of TEMPO for the (a) lithium dodecyl sulfate– alumina and (b) lithium perﬂuorooctane sulfonate–alumina systems together their adsorption isotherms. (Reproduced from Ref. 80 with permission of the American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

ﬂuorocarbon surfactant–silica system. This diﬀerence may result from the diﬀerence in compactness of the adsorbed layers of the surfactants. Time-resolved resonance Raman spectroscopy has been applied to study SDS micelles and SDS–alumina using tris(2,2-bipyridine)ruthenium(II) chloride as a Raman probe. The intensities of some Raman lines [70] trace the shape of the adsorption isotherm, reﬂecting its ability to report changes occurring in the adsorbed layer. Neutron reﬂectometry [81] as a technique for determining structures of adsorbed layers has been used mainly for the liquid–air interface, although a number of experiments have involved solid–liquid interfaces. The three most readily available materials for the neutron reﬂection experiment are silicon, and crystal and amorphous quartz. Because under normal circumstances silicon is covered with an oxide layer, each of the solids will have approximately the same silica surface. The reﬂectivity data for the hexadecyltrimethylammonium bromide–silica system [82] indicate that adsorption of the surfactant on silica occurs as a thick layer with headgroups at both the silica surface and adjacent to the bulk solution, even at concentrations well below the CMC. The amount of surface covered with this type of aggregate varies with concentration. The structure of layers of hexaethylene glycol dodecyl ether (C12E6) adsorbed at the quartz–water interface [83] has also been determined: the surfactant is in the form of a defective bilayer or ﬂattened micelles. In addition, the reﬂectivity has been measured for adsorption of C12E5 on a self-assembled undecenyl trichlosilane (UenTS) layer on silica or on unreacted and hydroxylated (U(OH)TS) samples [71]. Figure 15 shows a schematic representation of the C12E5 adsorption on the two types of surface: the conformation of the surfactant molecules is with the hydrocarbon chain pointing toward the UenTS and the oxyethylene chain pointing outwards, while both the alkyl chain and the ethylene glycol chains lie ﬂat on the hydroxylated surface because the thickness of the adsorbed layer is always 0.4 0.1 nm. Useful data have also been derived from the silica–water colloidal system using a small-angle neutron scattering technique [84]. The nature of layers of a series of poly(oxyethylene glycol) alkyl ethers (CnEm) adsorbed on silica surfaces has been investigated by means of null ellipsometry [72]. The mean optical thickness is relatively independent of the number of ethylene oxide groups in the surfactant but almost linearly dependent on the length of the hydrocarbon tail. It is suggested that the adsorbed layer is built up of disperse surface aggregates, or micelles, with dimensions resembling those observed in bulk solution. 2 H NMR and 13C NMR have been used to probe the molecular dynamics and structures of surfactant adsorbed on solids. The 2H NMR results for SDS adsorbed on positively charged alumina at the adsorption plateau of Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 15 Schematic diagram of the adsorbed layers of C12E5 on (a) the UenTS and (b) the U(OH)TS. No attempt has been made to represent the penetration of the alkyl chain into the self-assembled monolayer in (a). (Reproduced from Ref. 71 with permission of the American Chemical Society.)

the isotherm suggest that SDS does not form homogeneous, ﬂat bilayers or prolate micellar aggregates, but long ribbonlike aggregates, oblate micelles, or a densely porous bilayer [73]. By using 13C NMR on ionic surfactants adsorbed onto charged solid surfaces, it has been found that ionic surfactants show similar chemical shifts in the micellar state and in the adsorbed state, regardless of the sign of the formal charge of the headgroup [75]. This indicates that the state of surfactants adsorbed onto solid surfaces is similar to the micellized state from a chain conformational point of view. The morphology of surfactant molecules adsorbed onto hydrophobic and hydrophilic substrates has been directly observed by atomic force microscopy (AFM). AFM images from a number of laboratories over the past few years have suggested that laterally unstructured adsorbed layers are the exception—and the adsorbed micelles are the rule. These results have Copyright © 2003 by Taylor & Francis Group, LLC

pointed out the importance of aggregate curvature or surfactant packing [85] in determining the adsorbed layer structure. The direct imaging for cationic [86], anionic [87], zwitterionic [88], and nonionic [89,90] surfactants with alkyl chains of 12 or more carbons onto graphite yields very straight, parallel stripes, which have been interpreted as hemicylinders. Images of adsorbed-layer structures on hydrophobically modiﬁed substrates have been obtained. On diethyloctylsilanated silica [91] a variety of nonionic surfactants show no lateral structure. On the other hand, on trimethylsilanated silica [92] cationic, anionic, zwitterionic, and nonionic surfactants are shown to form globular structures consistent with hemispherical adsorbed micelles. The double-tailed cationic surfactant forms a laterally featureless ﬁlm, consistent with an adsorbed monolayer. Hydrophilic substrates for surfactant adsorption by AFM imaging are mainly muscovite mica and oxidized silicon. Surfactant adsorbed layer structures on silica have been found to closely parallel micellar self-assembly morphologies, whereas surfactants forming spherical micelles in aqueous solution tend to form cylinders onto mica [77].

V. DISPERSION OF SOLID PARTICLES BY SURFACTANTS Dispersion of solid particles in liquid media is essential in many products and processes. Suspensions of ﬁnely divided solid particles in liquid are commonly used for paints, pharmaceutical preparations, pigments, dyestuﬀs, and so forth. In the preparation of a dispersion of solid particles in liquid media, the solid particles are ﬁrst wetted by the liquid. Mechanical work is then applied to break down aggregates and agglomerates or comminute the particles in order to reduce the particle size. Finally, the particles must be stabilized against ﬂocculation. Surfactants are necessary materials in the preparation of a stable dispersion. Recently, from the standpoint of environmental pollution and conservation of resources, water-based dispersions have become attractive, compared with organic-based dispersions. This situation requires the preparation of a stable aqueous dispersion of solid particles. Many types of surfactants have been utilized as dispersants for this purpose. Two interactions between solid particles lead to the dispersion of solid particles by surfactants: electric repulsion due to a double layer formed on the particle, and steric hindrance due to an adsorbed layer. Before discussing the interactions between solid particles and surfactants from the standpoint of particle dispersions, we must review the forces between particles. Copyright © 2003 by Taylor & Francis Group, LLC

A. Interaction Forces Between Particles When two similar particles encounter each other in a liquid medium, there are two types of interparticle forces: attractive and repulsive. According to Derjaguin–Landau–Verwey–Overbeek (DLVO) theory [93,94], a balance between repulsive and attractive potential energies of interaction of the particles is to be assumed. Repulsive forces are due to the similarly charged electrical double layers surrounding the particles. When the surfaces of the particles approach closely enough so that the two double layers begin to overlap, the concentration in the overlapping region exceeds that in the bulk solution so that an osmotic pressure, which causes solvent to move into the overlap region, produces a repulsive force between the particles. Attractive forces are the van der Waals forces due to interactions between ﬂuctuations within the electron distribution of individual atoms or molecules. To disperse the particles, the repulsive forces must overcome the attractive forces. The total potential energy (VT) operating between two particles is the sum of the potential energies of attraction (VA) and of repulsion (VR): VT ¼ VA þ VR

ð11Þ

The potential energy of attraction for two spherical particles, of radius a, suspended in a medium is given approximately by the expression [95] VA ¼ Aa=12H

ð12Þ

where H is the nearest distance between the surfaces of the particles and A is the Hamaker constant for the particles interacting through the medium. As the particles and medium become increasingly similar, A becomes smaller, resulting in a smaller attractive potential energy between the particles. When there is an adsorbed layer of surfactant on both particles, the attractive forces are changed if the Hamaker constant of the layer is diﬀerent from that of the original particle [96]. The potential energy of repulsion for two spherical particles is given by the approximate equation VR ¼ ""0 20 =2 ln½1 þ expðkHÞ

ð13Þ

where " is the dielectric constant of the medium, "0 is the permittivity of free space, and 0 is the surface potential on the particles. The parameter k is known as the Debye–Hu¨ckel reciprocal length and is an approximate measure of the thickness of the electrical double layer. As k increases with increasing electrolyte concentration, the double layer becomes compressed, and the electrostatic repulsion is decreased. Obviously, ionic surfactants will contribute more to electrostatic repulsion than nonionic ones. When adsorption of surfactant ions results in an increase in the potential of the particle at Copyright © 2003 by Taylor & Francis Group, LLC

the Stern layer, the stability of the dispersion is increased; when it results in a decrease in that potential, the stability of the dispersion is decreased. Because the range of thermal energies for dispersed particles may go as high as 10 kT, an energy barrier of greater than 15 kT is usually necessary to obtain a stable dispersion. The DLVO theory is very useful in predicting the eﬀect of ionic surfactants on electrical barriers in order to understand the dispersion stability. However, the DLVO theory is insuﬃcient to account for the very large increase in stability produced by many nonionic surfactants, even when nonionic surfactants change the Hamaker constant. Surfactants that are polymeric or have long polyoxyethylene chains may form nonelectrical steric barriers, which may increase the stability of dispersion, even when electrical barriers are reduced or absent. The steric repulsion has two eﬀects [97]. One is that when the adsorbed layer is very closely packed and the two layers approach each other, the groups from each layer are unable to interpenetrate, resulting in a steric repulsion. The other eﬀect is due to solvent– chain interactions. When the solvent–chain interaction is stronger than the chain–chain interactions, the free energy of the system is increased when the extended portions of the adsorbed molecules overlap, and an energy barrier to closer approach is produced from local osmotic pressure. Forces between surfaces have been directly measured using AFM or surface force apparatus. The link between traditional electrokinetic measurements and forces measured with the AFM comes from incorporation of data from electrokinetic measurements into calculations of the force of interaction between surfaces. This work utilizes the concept that the measured force is the sum of attractive van der Waals and repulsive electrostatic contributions. There is an extensive literature on the measurement of forces using the AFM and good correlation of potentials calculated from the force of interaction between surfaces and either electrokinetic studies or calculated interaction forces [98–104]. Analysis of the force proﬁle provides some molecular-scale information.

B. Interaction Among Some Lyophobic Sols and Surfactants Ferric oxide sol is well known to be a positively charged sol [105]. Such a ferric oxide sol is coagulated upon addition of sodium alkyl sulfates, such as sodium butyl sulfate (SBS), sodium octyl sulfate (SOS), and SDS. This sort of coagulation phenomenon is called hydrophobic coagulation. The variation of coagulation behavior of ferric oxide sol with the alkyl chain length of coagulators is shown in Table 1. The conclusion from these data are as follows: (1) the longer the alkyl chain length of the coagulator, the smaller Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 1

Coagulation Behavior of Ferric Oxide Sol by Different Surfactants Conc. of surfactant (mol dm3 )

Surfactanta

5.0

2.0

1.0

0.5

0.2

0.1

0.05

0.02

0.01

0.005

0.002

0.001

0.0005

0.0002

0.0001

SBS SOS SDS

*b

*

yb

y

**b *

** * þb

** * *

** * *

** y *

yyb *

** *

** y

** yy

** *

*

a b

SBS: sodium butyl sulfate; SOS: sodium octyl sulfate; SDS: sodium dodecyl sulfate. *: coagulated; y: coagulated through turbid state; **: invariant; yy: turbid; þ: perfectly dispersed.

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is the coagulation value, which is a critical concentration required to coagulate the sol; (2) when the alkyl chain of the coagulator reaches C12 and the coagulator becomes a surfactant peptization, a redispersion of coagulated sol is observed in addition to the coagulation action. The precipitate of ferric oxide sol coagulated by SDS can be easily transferred into an organic phase, such as benzene, toluene, and chloroform, simply by shaking. The sol particles transferred into an organic phase disperse perfectly in the phase. It is observed that the precipitate of a ferric oxide sol coagulated by SDS is peptized again upon addition of a concentrated SDS solution. A similar peptization phenomenon can be observed with the addition of cationic or nonionic surfactants to this precipitate. Hydrophobic coagulation can be observed similarly in the combination of a negative sol, such as arsenic sulﬁde [106] or silver iodide [107], and a cationic surfactant, such as alkylpyridinium bromide. The model for hydrophobic coagulation and peptization is shown in Fig. 16. When an oppositely charged surfactant is added to a sol, the sol is coagulated (see the middle of Fig. 16). When an oppositely charged surfactant is added to a sol, the sol is

FIG. 16 Model for hydrophobic coagulation and peptization of negatively charged sol by surfactants: (*——) cationic surfactant; (*——) anionic surfactant; (vvv) nonionic surfactant. Copyright © 2003 by Taylor & Francis Group, LLC

coagulated (see the middle of Fig. 16). The coagulated sol is peptized by further addition of the same surfactant, a surfactant oppositely charged to the ﬁrst one, or a nonionic surfactant (right side of Fig. 16).

C. Effect of Surfactant on Aqueous Dispersion To elucidate the eﬀect of surfactant on the stability of particle dispersion, one must obtain a well-dispersed system. For example, a well-dispersed iron oxide suspension is obtained by suspending the particles in aqueous iron(III) chloride solution [108]. The & potential of the iron oxide becomes more positive and reaches a maximum value at some iron(III) chloride concentration where the particle size shows a minimum value. The positively charged iron oxide particles thus obtained are ﬂocculated by addition of a small amount of SDS. Figure 17 shows the eﬀect of nonionic surfactants on the redispersion of the iron oxide ﬂocs. The concentration of nonionic surfactants required for redispersion is shifted to lower concentrations with an increase of the ethylene oxide chain length. This result may indicate that the redispersion power by the nonionic surfactant is enhanced with an increase in the ethylene oxide chain length. Note that the iron oxide ﬂocs are

FIG. 17 Variation of the mean particle size of iron oxide in the presence of 0.5 mmol dm3 iron(III) chloride and of SDS by the addition of nonionic surfactants, polyoxyethylene cetyl ether: (*) (EO)20; (*) (EO)25; (~) (EO)30. (Reproduced from Ref. 108 with permission of Springer-Verlag.) Copyright © 2003 by Taylor & Francis Group, LLC

uncharged and the addition of the nonionic surfactant has no eﬀect on the potential. The adsorption of the nonionic surfactant occurs when a hydrocarbon chain-to-hydrocarbon chain interaction takes place with the ethylene oxide chain of the nonionic surfactant oriented toward the solution. These results suggest that the redispersion is due not to electric repulsion, but to steric hindrance caused by the adsorption of nonionic surfactant. The addition of a polyoxyethylene nonionic surfactant to an aqueous dispersion of particles that carry a small negative charge increases the stability of the dispersion against ﬂocculation by a polyvalent cation [109]. The stability increases sharply as adsorption of the nonionic surfactant on the particles approaches a close packed vertical monolayer, where the high stability may be attributed to the solvated polyoxyethylene chains. The diﬀerence in the properties between aqueous dispersions treated with oppositely charged surfactants containing a single hydrophilic group and hydrophobic group and those treated with oppositely charged surfactants containing two hydrophilic groups at both ends of the hydrophobic chain has been discussed [110,111]. The dispersions are, in all cases, ﬂocculated by the addition of the oppositely charged surfactant [107]. However, when the surfactant used has a single hydrophilic group, the ﬂocculated particles are easily dispersed into toluene. When the surfactant has two hydrophilic groups at both ends of the hydrocarbon chain, the ﬂocculated particles cannot be dispersed in toluene; rather, they form a ﬁlm at the toluene– water interface. In the latter case, each hydrophobic chain of the surfactant extending into the aqueous phase has a terminal hydrophilic group, which prevents the particles from becoming lipophilic. When bilayer-coated particles are diluted with water, the weakly adsorbed secondary surfactant is stripped from the particle surfaces, leaving the hydrocarbon tails of the primary surfactant exposed to the surrounding aqueous solvent. As a result, the stable dispersion of particles is lost. To prevent the destabilization of aqueous dispersion, polymerizable surfactants [112–117] have been applied to dispersions of solid particles. When polymerizable surfactants such as sodium 1-undecenoate and sodium 10-undecenyl sulfate are added to positively charged particles, a bilayer of the polymerizable surfactant is formed. The polymerization of the polymerizable bilayer adsorbed on particles has been carried out by UV irradiation. Figure 18 shows the eﬀect of UV irradiation, examined via the potential and the dispersion stability [118]. The potential of the dispersion decreases gradually with increasing irradiation time and then levels oﬀ after 6 h of irradiation, while the dispersion stability estimated by light absorbance increases with the irradiation time. During the polymerization, the mass transfer eﬀect from supernatant to bilayer on particles may be signiﬁcant, so that the surface charge density is enhanced. Then dispersion stability Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 18 Plots of potential and absorbance at 600 nm of irradiated alumina forming a bilayer of 10-undecyl sulfate. (Reproduced from Ref. 118 with permission of the Japan Society of Colour Materials.)

increases due to an increase in the electrostatic repulsion forces between the particles. Furthermore, it is crucial to elucidate how strongly the polymerized layer on particles is ﬁxed. After washing the polymerized dispersions, the potential and the percentage of retained surfactant have been determined. Without polymerization, the proportion of retained surfactant is only about 33%, whereas with irradiation of 6 h or more, the proportion of retained surfactant is more than 90%. These results indicate that the layer polymerized by UV irradiation enhances the ﬁxation of the bilayer. Similarly, -irradiation can be eﬀective in polymerizing oleﬁn-terminated surfactant bilayer coatings on magnetite nanoparticles [119]. When both layers consist of a terminally unsaturated surfactant such as 10-undecenoic acid, the irradiation process dramatically improves the stability of the magnetic ﬂuids against their agglomeration during dilution, as the polymerization process decreases the ability of stabilizing secondary surfactant to freely desorb from the particle surface.

D. Aqueous Dispersion by Oligomer Surfactants When the aqueous dispersion stabilized by a surfactant has been utilized for water-based paints, there are some deﬁciencies, such as poor ﬁlm formation Copyright © 2003 by Taylor & Francis Group, LLC

and sensitivity to water vapor after the ﬁlm is dried. To overcome these weak points of conventional surfactants, oligomer surfactants have been developed [120–123]. The chemical structure and analytical properties of the oligomer surfactants synthesized from some acrylic monomers [124,125] are given in Table 2. The aqueous dispersions of iron oxide are ﬂocculated by the addition of the oppositely charged oligomer surfactants. The ﬂocs formed upon addition of the oligomer surfactants can be easily suspended in toluene by shaking, indicating that the surfaces of the solids become hydrophobic by adsorption of the oligomer surfactants. In addition, redispersion of the ﬂocs also occurs by further addition of the oligomer surfactant. The mechanism of the ﬂocculation and redispersion processes using oligomer surfactants is also consistent with bilayer formation, similar to the case for conventional surfactants. A typical example of the dispersion behaviors using an oligomer surfactant is given in Fig. 19. To examine the eﬀect of diﬀerent compositions of oligomer surfactant on the dispersions of iron oxide, the maximum ﬂocculation and redispersion concentration values are plotted in Fig. 20 [125]. As the ionizable acrylic content in the oligomer surfactant molecule increases, the maximum ﬂocculation concentration decreases gradually, whereas the redispersion concentration decreases more steeply. These results suggest that the oligomer surfactant with a higher ionizable acrylic content adsorbs eﬀectively to the positively charged iron oxide, resulting in lowering of the maximum ﬂocculation concentration. However, because the oligomer surfactant with a lower ionizable acrylic content may be coiled more closely in the solution, compared with the oligomer surfactant with a higher ionizable acrylic content, the adsorption of a second layer due to hydrophobic–hydrophobic interactions may not occur eﬀectively. Also, the oligomer surfactant with a lower ionizable acrylic content would not contribute as strongly to electrostatic

TABLE 2 Chemical Structure and Composition of Oligomer-Type Surfactants

Oligomer

x

y

z

(I) (II) (III) (IV) (V)

0 3.6 6.8 6.5 11.9

9.5 7.0 2.8 5.7 4.5

3.8 2.2 11.4 2.0 2.9

MW Molecular weight

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1530 1325 1700 1320 1539

FIG. 19 Variation of potential and mean particle size of iron oxide by addition of an oligomer surfactant. (Reproduced from Ref. 125 with permission of the Chemical Society of Japan.)

FIG. 20 Variation of the maximum ﬂocculation concentration (*) and redispersion concentration (~) as a function of the acrylic content in oligomer surfactants. (Reproduced from Ref. 125 with permission of the Chemical Society of Japan.) Copyright © 2003 by Taylor & Francis Group, LLC

repulsion forces. Consequently, denser adsorption at the second layer is required to attain redispersion by adding an oligomer surfactant with lower ionizable acrylic content. Anionic oligomer surfactants have also been synthesized from the alternating cooligomers of dimethyl maleate and alkyl vinylether [126]. In the aqueous dispersions of copper phthalocyanine and carbon black, the anionic oligomer surfactants are probably used as an alternative dispersant to other functional agents such as conventional surfactants. The alkyl chain length in the structure of the oligomer surfactants is important to control the dispersibility of the solids. Other cationic oligomer surfactants have been synthesized, and their structures are shown in Fig. 21 [127]. The adsorption behavior of the oligomer surfactants at the solid–liquid interface has been studied using silica. Because silica is negatively charged at a neutral pH, it is expected that adsorption of the oligomer surfactants would occur mainly due to electrostatic attraction forces between negatively charged sites of silica and quaternary pyridinium groups of the oligomer surfactant as a ﬁrst layer. Figure 22 shows the adsorption isotherms of the oligomer surfactants on silica. It is apparent that the adsorbed amounts of the oligomer surfactants increase sharply at very low concentrations and reach a plateau, suggesting that the interaction between the oligomer surfactant and the surface of silica is

FIG. 21

Structures of cationic oligomers.

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FIG. 22 Adsorption isotherms and potential change for (a) 2.1R8–2VPQ–silica; (b) 2.5R12–2VPQ–silica; (c) 3.4R12–2VPQ–silica systems. (Reproduced from Ref. 127 with permission of Academic Press, Inc.)

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Figure 22

continued

FIG. 23 Maximum sedimentation rate against the number of alkyl chains of oligomers for the oligomer–silica systems: 2.1 for 2.1R8–2VPQ, 2.5 for 2.5R12–2VPQ, 3.4 for 3.4R12–2VPQ. (Reproduced from Ref. 127 with permission of Academic Press, Inc.) Copyright © 2003 by Taylor & Francis Group, LLC

appreciably strong. At low oligomer surfactant concentrations, the oligomer surfactant molecules adsorb on the negatively charged silica surface by orienting their hydrocarbon chains to the aqueous solution so that the surface of silica becomes hydrophobic. With a further increase of the oligomer surfactant concentration, a bilayer adsorption will occur. The potential of silica in the absence of the oligomer surfactants is negative, but it increases rapidly with increasing oligomer surfactant concentration. This alternation from negative to positive in the potential supports the formation of a bilayer. Because the areas occupied by the oligomer surfactants adsorbed are quite large compared to those at the air–aqueous solution interface, it is conceivable that patchlike bilayers are sparsely formed even at high oligomer surfactant concentrations. The sedimentation rate of silica by adsorption of the oligomer surfactants is signiﬁcantly aﬀected by the change of potential: it increases rapidly at low oligomer surfactant concentrations, reaches a maximum, and then decreases with a further increase of the oligomer surfactant concentration. The maximum sedimentation rate corresponds to the almost-zero potential, where the order of the rate is 3.4R122VPQ > 2.5R12-2VPQ > 2.1R8-2VPQ (Fig. 23). This indicates that the chain length and the number of hydrocarbon chains, along with the pyridinium group and the main hydrocarbon chains of the oligomer surfactants, play an important role in the ﬂocculation of silica. Thus, the silica suspension shows a dispersion–ﬂocculation–redispersion sequence with the oligomer surfactant concentrations that is very similar for oppositely charged systems of surfactants and particles. In this chapter adsorption of surfactants from aqueous solutions and aqueous dispersions have been discussed. However, nonaqueous dispersions are also important in many industrial ﬁelds [128,129].

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18 Arrangement of Adsorbed Surfactants on Solid Surfaces by AFM Observation MASATOSHI FUJII

I.

Tokyo Metropolitan University, Tokyo, Japan

INTRODUCTION

Surfactant molecules in aqueous solution form various shapes of self-assembly aggregates: spherical and cylindrical micelles, bilayer vesicles, planar bilayers, and inverted micelles. These shapes are produced by the balance between many kinds of interactions: between water molecules and surfactant molecules, between surfactant molecules and others. Many studies about the formation of the aggregates have proceeded in various approaches. On a solid surface in aqueous solution, the surfactant aggregates are in a diﬀerent situation from that in an aqueous solution. The surfactant molecules forming the aggregations are interacted not only with the surrounded solution molecules but also with the solid surface’s atoms. Thus, the shapes of the aggregates at the solid–solution interface are often greatly inﬂuenced by the properties of the solid surfaces. The properties of the solid surface adsorbed by the surfactant are very important for the usage of application. Many methods for investigating the aggregates on the solid surface have been applied: a thermotropic measurement [1–6], a neutron reﬂectometry [7,8], spectroscopy [9–11], ellipsometry [12–16], and others [2,17,18]. There are, however, a few methods to observe the real shape of the aggregates: electron microscopes of a freeze-fracture SEM [19] and cryo-TEM. The sample for electron microscopy, however, is not the same conditions in the solution, since a wet sample cannot be observed by an electron microscope directly. The microscope can only observe dry samples. Thus, morphology for surfactant molecule aggregates in aqueous solution cannot be observed this way. Recently, atomic force microscopy (AFM) [20] has been widely used to investigate morphology of various matters. There are many reasons for Copyright © 2003 by Taylor & Francis Group, LLC

AFM’s wide usage. One of the merits of AFM is that it can observe nonconductive materials. Most of the surfactant molecules are nonconductive, and so the aggregates are also nonconductive. Second, AFM can conduct under various atmospheres: in vacuum, in air, and in liquid [21]. Because the surfactant aggregates form various shapes in aqueous solutions, the true shapes can only be observed in the same aqueous solutions. These are the reasons AFM is a powerful tool that gets many interesting results about the aggregates of surfactant molecules. This chapter reviews the AFM techniques for the study of surfactant molecules, especially for the morphology of the surfactant aggregations on the solid–liquid interface.

II. ATOMIC FORCE MICROSCOPY A. Principles of Atomic Force Microscopy The atomic force microscope, AFM, was developed by Binnig et al. in 1986 [20]. The development of AFM was preceded by the development of the scanning tunneling microscope, STM [22]. Although the STM provides subAngstrom resolution, it is limited to adopting conductive and semiconductive samples. To image insulators as well as conductors, AFM picks up the change of applied force on the sample surface instead of the tunneling current the STM picks up. Monitoring the applied force, AFM operates not only on various kinds of samples regardless of their conductivity but also under various atmospheres, even in water. Since its development, AFM has been widely used as a convenient high-resolution microscope under atmospheric condition. The principles of how AFM works are brieﬂy explained as follows. AFM consists of a sharp tip on the end of a ﬂexible cantilever across a sample surface while maintaining a small constant force. The tips typically have an end radius of 2 nm to 20 nm, depending on the tip type. The scanning motion is conducted by a piezoelectric tube scanner, which scans the tip in a raster pattern with respect to the sample. The tip–sample interaction is monitored by reﬂecting a laser oﬀ the back of the cantilever into a split photodiode detector (Fig. 1). By detecting the diﬀerence in the photodetector output voltages, changes in the cantilever deﬂection are determined. Contact-mode AFM consists of scanning the probe across a sample surface while monitoring the change in cantilever deﬂection with the split photodiode detector. A feedback loop maintains a constant cantilever deﬂection by vertically moving the scanner to maintain a constant photo-detector diﬀerence signal. The distance the scanner moves vertically as each x, y data point is stored by the computer to form the topographic image of Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 1

Schematic diagram of AFM.

the sample surface. This feedback loop maintains a constant force imaging, which typically ranges between 0.1 to 100 nN.

B. Interpretation of Force Curve Force versus distance curves, known as force curves, are used to measure the vertical force that the tip applies to the surface while an AFM image is being taken [23]. This technique can also be used to analyze surface contaminants’ viscosity, lubrication thickness, and local variations in the elastic properties of the surface. A diagram of a typical force curve is shown in Fig. 2. The xaxis represents the distance by which the xyz translator and hence the sample surface move up and down. The sample surface approaches the tip when going to the left in the force curve. The y-axis represents the signal of the photo-detector, which is proportional to the distance of the cantilever and therefore the force of the cantilever spring constant. Deﬂecting the cantilever away from the sample surface means going upward in the force curve. Following a whole cycle in the force curve, we start at a large tip-sample separation in the nontouching regime. From there, with no or with only little deﬂection of the cantilever, the sample approaches the tip following along the horizontal line to the left in the force curve. At a certain point (jump-in point in the force versus distance curve) the transition from nontouching to touching occurs, i.e., the tip jumps onto the sample surface. Moving the sample still farther causes deﬂection of the cantilever for the same amount the sample is moved; this is represented by the diagonal line in Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 2 Diagrams of force-versus-distance curve and force-versus-separation curve.

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the left part of the force curve. Then retract the sample from the tip, i.e., go to the right in the force curve, and the cantilever moves ﬁrst again with the sample. It can even deﬂect toward the sample surface, going through the point of minimal force in the force curve. One deﬁnes the diﬀerence between this minimal force and the nontouching line as the pull-out force. At the jump-out point—the transition from touching to nontouching—the tip has completely lost contact with the surface or the adsorbed layers on the surface; the force curve returns to the nontouching line. The force curve can convert to a force versus tip-sample separation curve, known as the force-separation curve. To convert the curve, it is necessary to deﬁne zeros of both force and separation. In general, the zero force is chosen where the deﬂection is constant, and the zero of distance is chosen to occur when the cantilever deﬂection is linear with respect to sample displacement at high force [24]. At some point, the output of the photo signal becomes a linear function of the force curve: the regime of constant compliance. The relationship between sample displacement and photo signal in the region of constant compliance is used to convert the photo signal into the deﬂection of the cantilever. This conversion is used to determine changes in tip-surface separation; the separation is calculated by adding the distance of the force curve to the deﬂection of the cantilever. The force-separation curves involve a lot of information about the conditions of adsorbed surfactants at solid– solution interface, described in Sections III.C and IV.

III. AFM OBSERVATION OF ADSORBED SURFACTANTS ON SOLID SURFACES Ionic surfactants are favorably adsorbed on solid surfaces having opposite charge signs by electrostatic interaction; for example, cationic surfactants adsorbed on a negatively charged surface. If the surface charge sites regularly arrange on the surface, it is expected that the adsorbed surfactants are also arranged regularly. Muscovite mica, a typical layered silicate mineral, is thus exclusively used as a standard surface or a substrate for the Surface Force Apparatus (SFA) [25] and is also used as a reference surface and a substrate for AFM. The mica is easily cleaved, reproducibly gets an atomically smooth surface, and is purchased for a large single crystal. The cleaved surface of muscovite mica appears as hexagonally arranged potassium sites, which are easily ionexchanged by other cationic ions. The surface is observed as the periodic structural image of hexagonally arranged potassium sites under an atomic resolution. There are some techniques to measure an amount of adsorbed surfactants on ﬂat plates less than the monomolecular layer. Electron spectroscopy for Copyright © 2003 by Taylor & Francis Group, LLC

chemical analysis (ESCA) is one of the available tools to determine the number of cations adsorbed on the mica surface with an accuracy of 10% [26]. The occupied area of dihexadecyldimethylammonium (2C16DAþ ) adsorbed on a cleaved mica surface is 0.75 nm2/molecule by dipping the mica specimen in an adsorption bath of 258C for 30 min [27]. The molecular area of dioctadecyldimethylammonium (2C18DAþ ) is 0.5 nm2/molecule for 2C18DAB LB ﬁlm on mica [28]. The occupied areas of 2C18DAþ , C18TAþ , and 4C1Aþ on mica are 0.43, 0.24, and 0.2 nm2 , respectively, for their saturated adsorbed ﬁlms sunk in the aqueous solutions at 58C for 72 h [29]. The ESCA’s results, however, have neither enough accuracy nor adequate information about the surface arrangements.

A. Surfactant Molecules’ Arrangement on a Solid Surface The two-dimensional arrangement of surfactant molecules on a solid surface is diﬃcult to observe. Alkyl chains, hydrophobic group of surfactants, have weak reﬂectance for X-rays. Therefore, it needs to introduce atoms having large reﬂectance to detect the arrangement by X-ray diﬀraction patterns. Thus, the observed arrangement is not the true alkyl chain’s one. For an electron microscopy, the direct observation by the microscope also needs a special technique, since the alkyl chain is easily damaged by the high-energy electron beam. On the other hand, AFM can observe the direct arrangement of alkyl chains of surfactant molecules of a single crystal, not a reciprocal lattice pattern [30]. For the observation in molecular order, it is quite important to ﬁx the molecule to the substrate. Many images for the self-assembly monolayer, SAM, ﬁlms in molecular resolution have been reported [31,32], while images of LB ﬁlms are scarcely reported because the molecules are weakly adsorbed on the substrate [33–35]. Muscovite mica is a general substrate for AFM observation on an atomic scale. The mica has negative charges on the surface, so that the cationic surfactant, which was adsorbed on the negative surface, was frequently selected for studies of adsorption. Moreover, the cationic surfactant on the mica is adsorbed by an ion exchange process, which is strongly connected by electrostatic interaction. Thus, this system is proper to study in molecular order analysis by AFM observation.

1. Adsorption of Double Chained Cations on Mica Tsao et al. [36–38] have studied the adsorption of double chained cationic surfactants on mica surface. The surfaces were prepared by a dip in heated cyclohexane solutions. The AFM images were resolved up to the individual alkyl chain from which they have estimated the molecular areas for 2C16DAþ , 2C18DAþ , and 2C20DAþ to be 0.52, 0.51, and 0.47 nm2 , respecCopyright © 2003 by Taylor & Francis Group, LLC

FIG. 3 AFM image of (a) 2C16DAB, (b) 2C18DAB, and (c) 2C20DAB monolayer on mica in water at 258C. Alkyl chains remain in frozen or crystalline state on mica in water at 258C. (Reprinted with permission from Ref. 36. Copyright 1991, American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

tively (Fig. 3). The dependency of the chain length for the occupied area is explained by the fact that the two-dimensional arrangement of adsorbed surfactant molecules is solely determined by the packing of alkyl chains rather than by the ion exchange process of the headgroups. Figure 4a and b show the AFM images of 2C12DAB and 2C18DAB adsorbed on mica, which were prepared by being sunk in aqueous solution of 2C12DAB and 2C18DAB for 72 h at 58C [39]. Figure 4c is the image for a bare mica surface cleaved in pure water for comparison. The bright spots in the images are arranged hexagonally for all images obtained for other 2CnDAB (n ¼ 10, 12, 14, 16, 18). The distance between the two neighboring spots is about 0.5 nm, irrespective of the alkyl chain length. The symmetry and the spacing of the spots pattern resemble those observed for the bare mica surface shown in Fig. 4c. Two-dimensional Fourier transformation (FT) is a useful method to analyze AFM images statistically. Figure 5a–c show the FT patterns as derived from Fig. 4a–c, respectively. All FT patterns show a common hexagonal symmetry with the central angle of 608. The spotted pattern of the

FIG. 4 AFM micrographs of the surfaces modiﬁed with (a) 2C12DAB, (b) 2C18DAB, (d) C6TAB, (e) C18TAB, and (f) 4C1AC, and (c) freshly cleaved bare mica surface. The images were taken in water under constant force mode with a cantilever having elastic modulus of 0.38 N/m. The scan area was set at 10 nm 10 nm. Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 5 Fourier transform (FT) patterns derived from Fig. 4. The distorted region at the right margin of each images in Fig. 4 were cut oﬀ before the FT process. The eﬀective pattern areas are thus reduced to 9 nm 9 nm. Horizontal lines indicate the presence of random noise in each scan. Tiny extra FT spots observed should indicate the high regularity of the original pattern in that direction. The bright spot with satellite at top left and bottom right in pattern (f) should represent the double spot in the original real pattern, suggesting the closer arrangement of the spots.

AFM images can be well characterized by the distance and the angle of spots in the FT patterns. The average occupied area of the terminal methyl group is listed in Table 1 under diﬀerent cleavage conditions, either in air or in aqueous surfactant solutions, and diﬀerent imaging conditions, in air and in water. For double chained cations, the occupied areas of the spots correspond to the area for each alkyl chain of adsorbed 2CnDAB molecules. Thus, the molecular area for 2CnDAB is twice the area of the spot and ranges from 0.45 to 0.47 nm2 , regardless of the alkyl chain length. This value coincides with the area of an ion-exchangeable site on a cleaved mica surface, 0.47 nm2 , and with the packed area of the dialkyldimethylammonium group at an air–water interface. The agreements of the molecular area and the array patterns of the spots indicate the 2CnDAB molecules are epitaxially adsorbed by exchanging all the ion-exchangeable cations (Kþ or H3Oþ ions, etc.) originally present on the cleaved mica surface after a long adsorption time—more than 72 h at 58C. Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 1 The Average Occupied Area of Unit Spot for Double Chained Cations on Mica (Adsorption at 58C for 72 h) A(nm2 /spot) Cation 2C10 DAB 2C12 DAB 2C14 DAB 2C16 DAB 2C18 DAB Mica

I

II

III

0:231 0:006 0:232 0:003 0:227 0:004 0:233 0:006 0:224 0:005 —

0:235 0:009 0:230 0:005 0:233 0:004 0:239 0:005 0:236 0:002 0:234 0:005

0:228 0:006 0:226 0:007 0:227 0:005 0:229 0:007 0:233 0:002 0:232 0:004

I: Mica cleaved in solution/imaged in air. II: Mica cleaved in solution/imaged in water. III: Mica cleaved in air/imaged in air.

2. Adsorption of Other Ammonium Salts on Mica The AFM images of the ammonium ions adsorbed on the mica surfaces observed in water are shown in Fig. 4d–f for C6TAB, C18TAB, and 4C1AC, respectively. Much like the double chained cations (Fig. 4a and b), the twodimensional arrangements of the observed spots in all AFM images are hexagonal, and the distance between the two neighboring spots is also 0.5 nm. The arrangements patterns also resemble that of the mica substrate (Fig. 4c). Figure 5d and e show the FT patterns as derived from Fig. 4d and e, respectively. The average occupied areas of each spot, A, are listed in Table 2, and areas estimated under various imaging conditions are also listed. Because CnTAB has only one alkyl chain for each molecule, the occupied area for one CnTAB molecule ranges from 0.23 to 0.24 nm2. This area is half the area of ion-exchangeable cations, 0.47 nm2 , on a cleaved mica surface. That is, the adsorption density of a single chained cationic surfactant on a cleaved mica surface is twice as large as that expected from the electrical neutrality of the ion-exchangeable cations originally present on the mica surface.

3. Adsorption of Tetramethylammonium Chloride on Mica The shape of the 4C1AC molecule is much diﬀerent from other analogs 2CnDAB and CnTAB—it does not have long alkyl chains. The AFM images observed in water for a mica surface modiﬁed with 4C1AC (Fig. 4f) show a considerably diﬀerent appearance with respect to the arrangement of spots. Although the spots are aligned in three directions similar to the double and Copyright © 2003 by Taylor & Francis Group, LLC

single chained cations, however, the spots are aligned closer in one particular direction than the other two. In fact, the FT pattern of Fig. 5f transformed from Fig. 4f shows that the spots correspond to a shorter periodicity of 0.27 nm along the direction of closer alignment. The period along this direction is comparable to the calculated spacing of 0.248 nm between two methyl groups of 4C1AC as computed by the MM2 simulation program of molecular structure. The periods along the other two directions remain 0.45 nm. Accordingly, the observed spots in Fig. 4f should reasonably be assigned to each protruding methyl group of 4C1AC. In order to see the correspondence of the array of spots for modiﬁed and clean surfaces, the mica surface with adsorbed 4C1AC was exposed to 1N HCl for 4 h and then rinsed with water in an AFM ﬂuid cell. The in situ images of AFM obtained for the mica surface with adsorbed 4C1AC before and after the treatment with 1N HCl solution are shown in Fig. 6a and b, respectively. The FT patterns corresponding to Figs. 6a and b are also shown in Fig. 6c and d, respectively. These FT patterns show that the closely packed array of spots in Fig. 6c, top right and bottom left spots, diminished by acid treatment and the hexagonally arranged spots of base mica surface appeared instead. The arrays of the spots in other two directions in Fig. 6d are the same as Fig. 6c. The two methyl groups of adsorbed 4C1AC molecules should explain the observed double spots hexagonally arranged. The pattern of the arrangement is akin to the array of spots observed for a clean mica surface.

TABLE 2 Average Occupied Area of Unit Spot for Single Chained Cations on Mica (Adsorption at 58C for 72 h) A(nm2 /spot) Cation C6 TAB C8 TAB C10 TAB C12 TAB C14 TAB C16 TAB C18 TAB 4C1 AC

I

II

0:233 0:009 0:235 0:013 0:231 0:005 0:240 0:009 0:233 0:006 0:234 0:005 0:241 0:011 0:118 0:003

0:235 0:005 0:236 0:006 0:227 0:004 0:240 0:003 0:237 0:004 0:239 0:006 0:238 0:004 0:119 0:004

I: Mica cleaved in solution/imaged in air. II: Mica cleaved in solution/imaged in water.

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FIG. 6 In situ AFM micrographs of 4C1AB adsorbed surface (a) before and (b) after the injection of aqueous 1N HCl to the AFM ﬂuid cell, 5 nm 5 nm. (c) and (d) are Fourier transform (FT) patterns derived from (a) and (b), respectively. The eﬀective pattern areas are reduced to 4.5 nm 4.5 nm. The top right and bottom left spots in pattern (c) indicate the presence of double spots, which are not seen in pattern (d) due to the desorption of 4C1AB in acidic environment.

A similar arrangement of adsorbed 4C1AC molecules was also reported by Shindo et al. [40] for a cleaved K4NbO17 3H2O surface. They explain the observed molecular packing as formed by the orientation of 4C1AC: two methyl groups protruding upward and the rest downward. The two methyl groups of adsorbed 4C1AC were observed as a double spot with a separation of 0.25 nm whose periodicity agrees with that of Kþ ions in cleaved niobate crystal. The molecular area of 4C1AC adsorbed on mica corresponds to the occupied area of the double spot, which is about 0.23 nm2, the value close to that of CnTAB. The occupied area of methyl groups of adsorbed 4C1AC on mica is smaller than that of an ion-exchangeable site on the mica surface by a factor of 0.5, which means that the number of adsorbed 4C1AC molecules is twice as large as that expected from the electrical neutrality of surface sites. Copyright © 2003 by Taylor & Francis Group, LLC

B. Aggregation Morphology of Surfactant Molecules on Solid-Surface Ex Situ Conditions The adsorption of the surfactant molecule on a solid surface in aqueous solution does not proceed only by the molecule–surface interaction, but also by molecule–molecule interaction; the interaction induces the aggregation of molecules. The observation in atomic scale described in the previous section is useful to study the adsorption sites of surfactant molecules and the molecular arrangement. However, the observation in molecular scale cannot get enough information about the aggregation of molecules; the observation of a wide area is appropriate for this goal. Even in observing a wide area, AFM keeps a high resolution in the height direction, regardless of those of the lateral directions; this is one of the merits of AFM. Many AFM studies have been reported not only for surfactants aggregation but also for other selfassembly ﬁlms, OTS [41–44], OPA [45,46], and thiol [42], and two-dimensional phase separation of LB ﬁlms [47–50], and have revealed much new knowledge about the aggregations. The adsorbed aggregates on a solid surface in a wide area have been reported in a dry condition at ﬁrst. The solid plate was dipped in a surfactant solution and dried. Then, the surface was observed in atmospheric condition, an ex situ observation. In the ﬁrst ex situ observation of the adsorbed surface, the morphology of adsorbed cationic surfactant molecules, C16TAB, on mica changed according with the surfactant concentration of aqueous solution (Fig. 7) [51]. The adsorption of C16TAB on mica has been studied by many techniques [52]. From these investigations, it has been found that C16TAþ was adsorbed on a mica surface at a rapid initial stage (Fig. 8). The initial adsorption is driven by an electrostatic attraction between the solvated C16TAþ and negative lattice sites on the mica. From the AFM observation, adsorbed patches of surfactant molecules on the surface increase and grow with the increase of the surfactant concentration. At low concentrations adsorption takes place as sparse patches of surfactant molecules on the mica. An increase in surfactant concentration results in an increased number of patches or surfactant aggregates, which tend to combine to form a more continuous adsorbed micellar structure. The surfactant micelles seem to grow in the form of a continuous bilayer that forms a zigzag pattern across the substrate. Such features were also observed in in situ conditions, which is described in a later section. The aggregates of a longer alkyl chain surfactant, C18TAB, on mica were also investigated by AFM [46,53–55]. The Kraﬀt point of C18TAB (37.78C [56]) is higher than room temperature, while that of C16TAB is about 278C. Thus, the adsorption proceeds not only with the electrostatic interaction but also with a segregation process at room temperature for C18TAB.

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FIG. 7 AFM micrographs for surface topography at (a) 0.01-mM, (b) 0.1-mM, and 1-mM C16TAB adsorbed mica surface. (Reprinted with permission from Ref. 51. Copyright 1996, American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 8 Adsorption mechanism of bilayer from a micellar solution well above the CMC. (Reprinted with permission from Ref. 52. Copyright 1992, Academic Press, Inc.)

For 0.1-mM C18TAB aqueous solution at room-temperature adsorption (just below the cmc) [53], the surface images are featureless and exhibit subnanometer roughness, in the case of fewer than 24 h of exposure (Fig. 9). As the exposure time is over 48 h, small circular aggregates appear and the fractional surface coverage increases. The aggregate has a ﬂat top shape. The height of the aggregate is 1.7 0.3 nm, which is less than the length of C18TAB molecule, 2.5 nm. This characteristic shape indicates that the aggregate consists of the surfactant molecules gathered with a similar direction, Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 9 Series of ex situ contact-mode AFM images showing the surface topography of the coated mica surface as a function of the duration of exposure to a 0.10-mM C18TAB solution: (A) 1 h, (B) 24 h, (C) 48 h, (D) 72 h, (E) 120 h, (F) 168 h, and (G) 336 h. (H) shows a representative line scan through image (E). (Reprinted with permission from Ref. 53. Copyright 1998, American Chemical Society.)

perpendicular to the mica surface. After more than 300-h exposure, the aggregates connect to each other and the surface coverage reaches 0.9 [46, 53]. The observed morphology only refracts the outer layer of the adsorbed surface. Thus, it is diﬃcult to investigate the growth process of the aggregate layer. The inner structure of the aggregates can be also investigated by AFM observation after rinsing the surface little by little. Figure 10 shows the surfaces for 0.1-mM C18TAB at 58C for 72-h exposure after being rinsed with warm water (508C: higher than Kraﬀt point) [55]. There are various sizes and shapes of projections on the surface without rinse; see Fig. 10a [54]. The size of the projections is about 200 nm in width and from 2 nm to 8 nm in height; the heights of the projections are randomly distributed. After 5-min rinse, they are completely washed out. The asadsorbed mica is covered with not only the adsorbate but also the precipitate of C18TAB. Thus, the projections, which desorbed easily, are the precipitates of C18TAB attached on the surface and are not formed by regularly assembled molecules on the mica surface. After the projections were washed out, many islands appeared on the surface. The height of the islands in this case is lower than that for the room-temperature adsorption [53]. Comparing with the molecular length of C18TAB, 2.5 nm, the height of the island is less than half the molecular Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 10 Series of ex situ contact-mode AFM images showing the surface topography of the mica sunk in 0.10-mM C18TAB solution for 70 h at 58C. Surfaces were rinsed with 508C pure water. (a) Without rinse; (b) rinse for 5 min; (c) rinse for 10 min; and (d) rinse for 20 min. Z-range: 3.75 nm, (a) for 10 nm.

length. The molecules in the islands attached to the surface were considerably tilted. The thickness of the ﬂat layer under the islands is estimated to 1.5 nm; the hole in the images of the surface rinsed for 20 min, Fig. 10d, shows 1.5 nm in depth. Since the base layer has the same thickness as that of the island reported [53], the layer consists of arrayed structure of molecular assembly as that of the islands. An enlarged image, 700 nm, of the surface rinsed for 20 min shows a ﬂat surface with tiny holes randomly distributed (Fig. 11a). The particular structure in Fig. 10d reﬂects the tiny holes that cannot be distinguished in the wide image size. Figure 11b is an atomic-scale image, 10 nm, at the ﬂat area of the same surface. Although the quality of the image is very poor, the regularly arrayed spots can be observed. The base layer, thus, consists of regular packing molecules with some defective areas. It is diﬃcult to determine the chemical species exposed on the surface from the AFM observation only. Thus, it is important to characterize the adsorbed surface such that the observed morphology must be combined with other techniques, such as contact angle, IR, and ESCA measurements [29,46,53,57]. For example, the contact angle measurement can easily distinguish which end of the surfactant molecule is exposed to the surface. The time dependence of the contact angle is shown in Fig. 12. The contact angle for the surface without rinse shows a constant value of 808. For the surfaces rinsed with water, the contact angle decreases with the elapsed time of the observation. Because the surface without rinse has been experienced in the Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 11

Close-up view of Fig. 10d. Scan size: (a) 700 nm; (b) 10 nm.

solution for a long duration at a low temperature, the molecules assembled to a stable structure in the aqueous solution, i.e., hydrated solid [56]. Therefore, the adsorbate does not easily desorb to the water droplet, and the angle shows a stable value. The decrease of the contact angle for the rinsed surface shows that the surface is not washed completely with water.

FIG. 12 Contact angle of water on adsorbed surfaces sunk in 0.10-mM C18TAB solution for 70 h at 58C. Dependence of the contact angle on age of water drop on the surface. Copyright © 2003 by Taylor & Francis Group, LLC

The remaining molecules, which do not bind to the ion-exchangeable sites, gradually desorbed from the surface make the angle decrease.

C. Aggregation Morphology of Surfactant Molecules on Solid-Surface In Situ Observations The aggregation of surfactant forms various structures, but the structures keep only in the solutions. AFM can observe the morphology of the aggregations in the solution as in in situ observation. Therefore, the observation can clarify the true morphology of the aggregation at the solid–liquid interface; in addition, it can observe the growth process of the aggregation in situ.

1. Heterogeneous Growth of Adsorption Film Figure 13 shows a typical sequence of AFM images observed everywhere of a mica surface at the various lapse of times after the introduction of 0.1-mM aqueous C18TAB solution until the stable morphology is approached at 158 min. Figure 13a indicates the intact surface of mica observed in pure water. The range scanned was 2000 2000 nm. Figure 13b shows the emergence of numerous tiny islands of the diameter around 10–30 nm 6 min after the injection of the aqueous surfactant solution, which suggests the two-dimensional molecular aggregates of adsorbed surfactant. The image of Fig.13c, observed at 15 min, clearly shows that the small islands as observed in Fig. 13b grew into larger patches, which have a terrace structure. Figure 13d shows that the area of each island increased further with the elapse of time while the height of the island remained unchanged. Figure 13e–h show the occurrence of spontaneous fusion among those grown-up patches. The image of Fig. 13i at steady morphology was obtained by stop scanning after the observation of Fig. 13h and standing the surface in the solution until 158 min. The images for the sequences from 55 min to steady morphology at 158 min were not able to obtain the growth process as far as the mica surface was kept scanned with the AFM tip, suggesting that the perturbation induced by the scanning tip is preventing the growth process from proceeding. The images in Fig. 13g and h show that stroking the surface with the tip helped the bridge formation among the patches. The direction of the bridge agrees with that of scanning, while the islands or the patches at the early stage of adsorption are circular and are not elliptic. This seems to become evidence that the observed images are not measured under the severe inﬂuence of scanning tip [33,58] at the early stage of the adsorption. The vertical force as high as 10 nN, including an adhesion force, is optimal for these systems. This value is well below the collapse force of adsorbed ﬁlm and yet low enough to detect two-dimensional molecular aggregates without destroying them. The collapse pressure of the adsorbed Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 13 Series of in situ contact-mode AFM images showing the surface topography of the heterogeneous growth process of C18TAB bilayer on mica surface in 0.10mM C18TAB solution at room temperature. The adsorption time after the introduction of the solution: (a) 0 min, (b) 6 min, (c) 15 min, (d) 22 min, (e) 25 min, (f) 31 min, (g) 52 min, (h) 55 min, and (i) 158 min. Scan size: 2000 nm.

molecular layer is estimated to be 120 nN for the tip point having a similar curvature [59,60]. Although the sequence of the adsorption is similar to those of ex situ observation [53], which is described in the previous section, the formation of two-dimensional aggregates of C18TAB proceeds on mica surface much faster than the ex situ sequence. The reason probably lies on any disturbing eﬀect inevitably introduced in the ex situ condition of measurements.

2. Self-Repairing of Adsorbed Film The self-repairing process of the adsorbed ﬁlm in surfactant solution can be also analyzed by in situ AFM. The adsorbed ﬁlm of C18TAB on the mica surface, equilibrated for 3 h in 0.1-mM solution from the results of the growth experiment, was scratched over an area of 4000 nm 4000 nm by the AFM tip [34,35,61]. The vertical force applied to the tip for scratching Copyright © 2003 by Taylor & Francis Group, LLC

was 200 nN, which is larger than the collapse force of the adsorbed ﬁlm [59]. Figure 14 shows the typical repairing sequence observed for the damaged surface in surfactant solution. Applied tip pressure for this imaging was less than 10 nN. The central part of Fig. 14a shows the square damaged area, which is accompanied by numerous tiny pits surrounding the central square hole. Figure 14b–f show the successive self-repairing processes that occurred in 0.1-mM solution. The self-repairing of the surface ﬂaws seems to occur through the smoothing of the ragged periphery of the hole. It is interesting to note that the disappearance of the small islands in the hole accidentally formed on scratching (Fig. 14a and b) precedes the ﬁlling of small pits around the hole (Fig. 14b–d), for which some tentative explanations are made in the next paragraph. After about 218 min of healing, the original ﬂawless ﬁlm is restored.

3. Shape Factor of Two-Dimensional Aggregates The phenomena of island growth and the self-repairing of the adsorbed ﬁlm seem to occur through the processes of two-dimensional isothermal condensation and vaporization of the molecular aggregates at the mica–solution interface. The principal rate-determining factors for these processes other than a diﬀusion coeﬃcient of the molecules at the interface and in the bulk may be a line tension and a curvature of the peripheral part of the two-

FIG. 14 Series of in situ contact-mode AFM images showing the surface topography of the self-repairing process of C18TAB bilayer on mica surface in 0.10-mM C18TAB solution at room temperature. The 4000 4000 nm2 surface of adsorbed ﬁlm was scratched with the scanning tip. After scratched time (a) 0 min, (b) 42 min, (c) 58 min, (d) 78 min, (e) 204 min, and (f) 218 min. Scan size: 8025 nm. Copyright © 2003 by Taylor & Francis Group, LLC

dimensional aggregates, which induce two-dimensional Laplace pressure [62,63]. In the present studies the total peripheral length of islands, patches, pits, and holes observed for each image in Figs. 13 and 14 was estimated as well as the total adsorbed area to see if the eﬀect of the line tension actually inﬂuences the rate processes involved in these equilibria among the various two-dimensional phases. The surface coverage (island and repaired) and the total peripheral length of the aggregates (Pisland and Phole) for each image were measured for all images in Figs. 13 and 14. The coverage island is the ratio of total accumulated area of the islands Aisland to the total area scanned Atotal area scanned, which was 4.00 mm2. repaired shows the ratio of the area increased by the selfrepairing of the holes Arepaired to the initial area of the central hole Ainitial 2 area of hole, which was 17.08 mm ; the initial area does not include those of the tiny pits around the central hole, because of the restricted resolution of the images. They are expressed in Eqs. (1) and (2). The change of island and repaired with adsorption time are shown in Fig. 15 indicating the rapid growth of the islands while the self-repairing rate is moderate somehow, probably because of the ﬁrst ordered reaction’s nature. island ¼ Aisland =Atotal area scanned ¼ Aisland =4:00 mm2 repaired ¼ Arepaired =Ainitial area of hole ¼ Arepaired =17:08 mm Sisland ¼ Pisland =2ðAisland Þ Shole ¼ Phole =2ðAhole Þ

1=2

1=2

ð1Þ 2

ð2Þ ð3Þ ð4Þ

FIG. 15 Change of surface coverage of mica by adsorbed C18TAB molecules in aqueous solution. Estimated for both island growth (~) and self-repairing (*) processes in Figs. 13 and 14. Copyright © 2003 by Taylor & Francis Group, LLC

The total peripheral lengths of the islands Pisland and of the holes Phole are normalized by dividing each of them with the expected perimeters when all existing islands or holes coalesced to give a single circular patch or a hole as expressed in Eqs. (3) and (4) to introduce relative shape factors Sisland and Shole. What the authors meant by these shape factors is the instability factor of the proﬁle of two-dimensional molecular aggregates. The shape of molecular aggregates having the smallest S-value may be the ultimate contour to be attained for both islands and holes. Figure 16 shows the time dependence of the shape factors Sisland and Shole. The steep decrease of Sisland is observed, while Shole decreases gradually with time. At the early stage of the process, the small decrease of Shole should come partly from the neglect of the tiny pits surrounding the hole for the resolution of the image’s sake. The comparison of Figs. 15 and 16 seems to suggest that the two-dimensional Laplace pressure plays its role in the dynamic processes of twodimensional phase separation. The growth of the islands and the self-repairing of the holes may be understood from the line tension aspects as the counteracting processes at the peripheral part of the molecular aggregates having positive and negative curvatures as explained below. The surface pressure of adsorbed molecules, which is in equilibrium with islands having particular positive curvature, should be higher than that in equilibrium with the holes having negative curvature of the same radius. The disappearance of the tiny islands in the hole before the smoothing of the ragged edge of the hole occurs as observed in Fig. 14a and b may reasonably be understood as the phenomenon of two-dimensional isothermal distillation, as depicted by the simple analogy of the Laplace–Kelvin equation [62].

FIG. 16 The change of shape parameters Sisland (~) and Shole (*), deﬁned by Eqs. (3) and (4), respectively, with the lapse of adsorption time. Copyright © 2003 by Taylor & Francis Group, LLC

4. Surface Aggregation Shapes in Nanometer-Scale Observation Recently, Manne et al. [64] ﬁrst used AFM to obtain the microscopic evidence of the organization of C16TAB at the interface between graphite and aqueous solution under the double-layer repulsion imaging condition [65]. The images showed straight parallel stripes spaced apart by approximately twice the surfactant length (Fig. 17). Accordingly, the initially arranged monolayer with a head-to-head structure was proposed to serve as the template for the further formation of hemicylinders. In subsequent

FIG. 17 Images and proposed model of the adsorbate structure of C16TAB on graphite at a solution concentration of about 0.8 mM. The adsorbate structure is imaged as stripes that are spaced 4.2 0.4 nm apart, organized into two-dimensional domains in which all the stripes are parallel. (Reprinted with permission from Ref. 64. Copyright 1994, American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 3 Structure of Adsorbed Micelles and Nearest-Neighbor Spacing (nm) for Quaternary Ammonium Surfactantsa on Mica, Showing the Effect of Different Counterions Bromide Alkyl chain length C12 C14 C16

Me3

Et3

Rods 4:8 0:2b Rods 5.4 —

Spheres 5.0 Spheres 6.0 Rods 6.0

Chloride Pr3

Bu3

—

—

Spheres 5.7 Short rods 6.2

Soft layer

a

Excess salicylate

Me3

Me3

Et3

Spheres 5.4 Rods 5.7

Rods 5.1 Rods 5.4

Rods 4.8 Rods 5.4 Rods 5.4

Soft layer

Alkyl-trimethyl, Me3 , -triethyl, Et3 , -tripropyl, Pr3 , -tributyl, Bu3 , ammonium bromides. All listed spacings have an uncertainty of 0:2 nm. Source: Ref. 70. b

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Pr3

Bu3

—

—

Rods 5.4 Rods 5.1

Layer Layer

TABLE 4 Summary of Equilibrium Structures Above Krafft Temperature, TK , for Alkylammonium Bromide Surfactants on Silica, Mica, and Graphite Substrate Alkyl chain length

Equilibrium structure above TK

Comparison to bulk structure

Silica

14, 16 18, 20

Spherical Flat

Relatively unperturbed Flattened

Mica

12, 14

Cylindrical

16, 18, 20

Flat

All structures highly perturbed from solution due to closely spaced counterions on substrate

14, 16, 18, 20

Hemicylinders

Graphite

Source: Ref. 68.

TABLE 5 Effect of Monovalent and Divalent Anions on the Shape of CTAþ Aggregates on Silica Anion

Hard/Softa

Aggregate shape

Cl Ac Br HSO 3 HS SO2 4 S2 O2 3 CO2 3 CS2 3 SO2 3

Hard Hard Borderline Borderline Soft Hard Soft Hard Soft Borderline

Spheres (oblate) Spheres Cylinders Spheres Cylinders Spheres Cylinders/short cylinders Spheres Cylinders Spheres

a

J.E. Huheey, E.A. Keiter, R.L. Keiter. Inorganic Chemistry. New York: Harper Collins College Publishers, 1993, Ch. 9. Source: Ref. 75.

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Highly perturbed from solution because of alkyl substrate epitaxy

studies structures of a variety of diﬀerent surfactants adsorbed from aqueous solutions on many diﬀerent types of substrates were studied by this technique. Many observations have been reported about cationic surfactants aggregation at the solid–solution interface. AFM images for CnTAB aggregations on hydrophilic surface show full cylinders on mica [66–74] and spherical micelles on amorphous silica (Tables 3 and 4) [8,66,68,75–78]. The inﬂuence of coexistent ions to the shape of aggregates is also reported: counterions Cl, Br, Ac, divalent anions (Table 5) [8,67,69,75], and coions Hþ , Liþ , Naþ , Kþ , Csþ [67,69]. While the gemini surfactants [79], quaternary ammonium surfactants [70], and alkylpyridinium surfactants [80,81] aggregate at the solid–solution interface, they form diﬀerent shapes according to the size and shape of surfactant molecules. The anionic surfactant, SDS [82–84], and a ﬂuorocarbon anionic surfactant, LiFOS [85], show stripe patterns on the graphite surface. The zwitterionic surfactant (dodecyldimethylammonio)propanesulfonate (DDAPS) forms spherical micelles on mica [86–88], whereas DDAPS mixed with C12TAB changes the forms from spherical micelles to cylinder micelles on mica [86]. Hexadecyltrimethylammonium hydroxide and SDS forms halfcylinders on gold, and C14TAB forms full cylinders [79]. Nonionic surfactants CnEm, also form spherical micelles or cylinder micelles on amorphous silica or graphite surface (Table 6) [89–91]. Holland et al. suggest that the Nalkylmaltonamide nonionic diblock surfactants assembled into an ordered monolayer on graphite as a template for subsequent hemicylinder formation and the periodic banding structure [92]. Jaschke et al. report that cationic surfactant molecules adsorbed on the hydrophobic graphite form a layer parallel to the surface through relatively strong adsorption forces to give a solid ﬁlm as the ﬁrst layer, on top of which semicylindrical micelles are formed [79,93]. Sakai et al. propose that C14TAB molecules adsorbed on mica form the ﬁrst layer perpendicular to the surface and template the formation of cylindrical micelles [74]. Because mica adsorbs cationic surfactants by the ion exchange mechanism, the adsorbed ﬁrst-layer molecules are strongly attracted from mica and arranged according to mica structure, described in Section III.A, while the second-layer molecules are arranged by means of the interaction of alkyl chains. Molecular dynamics (MD) simulations showed that the monolayer arrangement of C16TAB on a hydrophobic surface was unstable and evolved into hemicylindrical-type aggregates [94] that supported the proposed model [64,66]. The growth process of rodlike micelles on a hydrophilic surface has also been studied with a two-dimensional mean-ﬁeld lattice model [95] and by Avrami’s theorem [96]. Copyright © 2003 by Taylor & Francis Group, LLC

TABLE 6 Aggregates Structure of Cn Em on Silica, Hydrophobic Silica, and Graphite Cn Em

CMC/mM

Conc/CMC

Silica

C10 E5 C10 E6 C12 E5 C12 E8 C14 E6 C16 E6

0.81 0.90 0.057 0.092 0.010 0.0017

5.3 2.2 1.9 2.0 5.0 2.0

Globular Globular Continuous/globular Globular Continuous/globular Globular

a

Not measured. Measured at the C16 E6 CMC. Source: Ref. 90.

b

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Hydrophobic silica —a Continuous Continuous Continuous Continuous Continuousb

Graphite Continuous Continuous/hemicylinders Hemicylinders — Hemicylinders —

IV. SURFACE FORCE MEASUREMENTS FOR SURFACTANT ADSORBED SURFACES Surface forces play important roles in many industrial and scientiﬁc processes. They determine the stability of suspensions and emulsions, the adhesion between surfaces, and colloidal particle interactions. An adsorbed layer of surfactant molecules can completely change the nature of the interaction between particles. The adsorption of surfactant can completely remove the repulsive interactions between particles and replace them with an attractive interaction. Two negatively charged surfaces repel each other electrostatically. The addition of a cationic surfactant results in monomer adsorption to reduce the surface charge by adsorbing to the negative sites of the surface. A reduction in the surface charge leads to a reduction in the repulsive force between the surfaces. At a particular surfactant concentration, the surfaces will be completely neutralized by surfactant molecules and only attractive interactions will be present between the surfaces. A further increase in the surfactant concentration can lead to the further adsorption of surfactant and the surface recharges. At very high surfactant concentrations, surfactant aggregates form in solution. The presence of these aggregates aﬀects the force between surfaces. Tabor and Winterton constructed an apparatus for measurement forces between mica surfaces [97]. This was modiﬁed—called the Surface Force Apparatus (SFA) by Israelachvili and Adams [25]—to allow measurements to be preformed in liquid. Many surfactant systems were investigated by the SFA and have revealed the adsorption states of surfactants on mica surface. However, SFA limits the kind of substrates as mica because of the determination of the separation between two surfaces as fringes of equal chromatic order (FECO) interferometry method. Thus, some other techniques have been proposed to adapt to the substrates other than mica: bimorph surface force apparatus for two colloidal systems [98,99]. AFM is a microscope that detects the force diﬀerence in the microscopic area and images the diﬀerence. Therefore, the precise force detection system for the microscopic local area is the main part of the AFM apparatus. For imaging soft matter, as for adsorbed aggregate in solution, it is important to set the tip pressure to a suitable value described in a previous section. Thus, there have been reports that AFM is used as a force measurement apparatus between the AFM tip and a sample plate in air and in solutions [21,100,101]. Because the shape of the AFM tip is diﬃcult to characterize, one cannot give a quantitative force measurement [102,103]. Thus, the AFM probe-attached colloidal sphere (Fig. 18), which is easier to characterize than the AFM tip, is used as the qualitative force measurement between a silica colloid surface and a planer surface system

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FIG. 18 SEM micrograph of colloid probe. A silica sphere is attached to the pyramidal Si3N4 tip with a small amount of glue. (Reprinted with permission from Ref. 115. Copyright 1993, American Chemical Society.)

[104,105]. The force measurement by AFM with the colloid probe method is available to study the interaction quantitatively. The interaction energy (W) between the colloid and the plate is calculated from the force (F) measured with colloid probe (R in radius) to W ¼ F=2R by Derjaguin’s approximation. Thus, one can estimate the surface and solution properties: surface potential; eﬀective ion concentration; and Hamaker constant by ﬁtting DLVO theory relationship [106,107]. The interactions were measured and analyzed between a silica colloid and a silica plate [24,108], a silica colloid and a hydrophobic silica [109], a stainless steel plate [110], or an -alumina plate [111] in aqueous inorganic electrolytes. The many kinds of colloids are also investigated: spherical ZnS [112,113], ZrO sphere [114], and polystyrene sphere [110]. The surface potential and the Debye length were well within experimental error. The technique for the surface force measurement has also been adapted to the surfactant systems. Rutland and Senden studied the surface force for adsorbed poly(oxyethylene) nonionic surfactant C12E5 on silica sphere and silica plate [115]. At a low concentration (one-third cmc), the force proﬁle simply obeys the double-layer repulsion calculated from the concentration of supporting electrolyte excluded from a short separation region. The repulsion was replaced at short separations by an attractive force, which pulled the surfaces into adhesive contact. At concentrations above the cmc, the proﬁle of the repulsive steric force changes depending on passed time Copyright © 2003 by Taylor & Francis Group, LLC

(Fig. 19). They present a tentative scheme for the C12E5 adsorption to the silica surface (Fig. 20). The surface force of adsorbed cationic surfactants has already been investigated by SFA [116–118], whose substrate was a negatively charged mica sheet. To investigate the inner structure of the adsorbed layer, however, one cannot apply the high pressure to disjoin the adsorbed layer. As for SFA, since the area of the contact region is in the macro range, the large contact area limits the applied pressure. While for AFM the contact area of the colloidal probe and the ﬂat surfaces is smaller than that of SFA, the adsorbed layer is easy to squeeze out between the surfaces, despite the similar pressure value. Johnson et al. observed the collapse of the adsorbed layer of C12TAB on a silica sphere and a ﬂat plate surface above the cmc [119]. There are dual step-ins just prior to the onset of the exponential diﬀuse double-layer potential decay in the force distance curve. Each stepin was about 3.5 nm. This can be compared with other measurements of the thickness of an adsorbed C12TAB bilayer [7,116–118]. Other cationic surfactants are also investigated. Bremmell et al. studied the adsorption of alkylpyridinium salt with a silica spherical prove and cleaved mica sheet [120], and the force proﬁles were changed from attraction to repulsion according to increasing the concentration the same amount as

FIG. 19 Force separation curve between a colloidal silica probe and oxidized silicon wafer in a solution of 0.1-mM C12E5 and 0.3-mM NaCl after an equilibration. The surfaces jump from 12.4 nm into a repulsive regime at 9.8 nm, from which they again jump into another repulsion 5 nm from constant compliance. The solid lines are a ﬁt of the DLVO theory to the data using a Hamaker constant of 1 1020 J, with the ﬁtting parameters ¼ 45 mV and 1 ¼ 17:5 nm. (Reprinted with permission from Ref. 115. Copyright 1993, American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 20 Adsorption scheme for C12E5 on silica. A small amount of adsorption takes place due to hydrogen bonding (I), then forms small aggregation (II, III). At concentrations about the CMC these aggregates have fused suﬃciently to form intercalated bilayer structure (IV). After equilibration a classical bilayer forms (V). (Reprinted with permission from Ref. 115. Copyright 1993, American Chemical Society.)

the other cationic surfactants on negative charged surfaces. Sakai et al. used [121] silica spherical probes whose surfaces were modiﬁed with quaternary ammonium groups bearing various alkyl chain lengths to investigate the adsorption of C12TAC. The driving force for the adsorption of C12TAC seems to be a hydrophobic interaction between the surfactant tails and the attached hydrophobic layer. The alkyl chain of the hydrophobic layer changes its conformation with the surfactant concentration. For anionic surfactants it is suitable to investigate the surface force by the colloid probe method rather than SFA because the substrate for SFA is usually used mica whose surface charge is negative and attracts anionic Copyright © 2003 by Taylor & Francis Group, LLC

surfactant. The adsorption of SDS was investigated by measuring the surface forces between either a positively charged or hydrophobic SAM-covered gold substrate over broad ranges of SDS concentration [122]. For the positively charged substrate, surface charge reversal occurred at an SDS concentration of about 1/1000 cmc, similar to a cationic surfactant on a negative charged surface. At the concentration near the cmc the surface was fully covered with bilayer or surface micelles, which was not compact and uniform, as estimated by the force proﬁles (Fig. 21). For a hydrophobic SAM substrate, the SDS adsorption behavior was found to be diﬀerent from the adsorption on a hemimicelle formed on the charged substrate. These results led to the conclusion that the formation of a compact and uniform SDS hemimicelle or bilayer on a charged surface did not occur (Fig. 22). Another anionic surfactant, sodium dodecylbenzenesulfonate, was also studied by the force proﬁles between silica colloid and mica sheet [120]. In this system the surfactant was scarcely adsorbed on the surfaces because of the same sign of charge. On the other hand, for the surfaces modiﬁed by alkyl chains [121] and cationic polyelectrolyte [123], alkylsulfate and alkylsulfonate ions were found to be adsorbed on the surfaces by the analysis of the surface force measurement.

FIG. 21 Force separation curve between a colloidal silica probe and positively charged gold substrate in aqueous solutions of diﬀerent SDS concentration at pH 5.0. The force curves correspond to SDS concentrations, from bottom to top, of 0, 104, 103, 5 103, 0.01, 0.1, 1 mM. (Reprinted with permission from Ref. 122. Copyright 1997, American Chemical Society.) Copyright © 2003 by Taylor & Francis Group, LLC

FIG. 22 Schematic of structures of adsorbed SDS aggregates on a positively charged gold substrate. (Reprinted with permission from Ref. 122. Copyright 1997, American Chemical Society.)

The analysis of the force proﬁles is also convenient for the investigation of the bulk properties of aqueous solution of surfactants. Tulpar et al. studied the force proﬁles for aqueous solutions of C12TAC and SDS [124]. They estimate the activity coeﬃcients and the degree of dissociations for the surfactant ions from the nonlinear Poisson–Boltzmann equation. Corrections to the nominal concentration using the degree of association in bulk solution from conductivity measurements or the activity are similar, and both provide good estimates of Debye lengths in surfactant solutions. The method of surface force measurements by AFM is a powerful technique to investigate the adsorption behavior of surfactants on various kinds of solid surfaces. Copyright © 2003 by Taylor & Francis Group, LLC

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