Introduction to Sol-Gel Processing 3030381439, 9783030381431

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Alain C. Pierre

Introduction to Sol-Gel Processing Second Edition

Introduction to Sol-Gel Processing

Alain C. Pierre

Introduction to Sol-Gel Processing Second Edition

Alain C. Pierre allée des écureuils Université Claude Bernard-Lyon 1 ROCHETAILLEE SUR SAONE, France

ISBN 978-3-030-38143-1 ISBN 978-3-030-38144-8 https://doi.org/10.1007/978-3-030-38144-8

(eBook)

© Springer Nature Switzerland AG 1998, 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Kaolinite gel network. Reproduced with permission from Pierre [1998, Kluwer edition of Introduction to Sol-Gel Processing]. Copyright Springer 1998

To Marie-Claude

Preface

Background Sol-gel processing has been known for a long time. The first silica gels were synthesized in 1845 by M. Ebelmen at the “Manufacture de Céramiques de Sèvres” in France. However, this processing technique has experienced a very important development, which drastically increased during the last two decades after the publication of the first edition of this book by Kluwer. This field of experimental science was addressed in several series of international conferences, among them: “International Workshops on Glasses and Ceramics from Gels,” “Better Ceramics Through Chemistry,” “Ultrastructure Processing of Ceramics, Glasses and Composites,” “International So-Gel conference,” “Sol-Gel Optics,” “Hybrid OrganicInorganic Materials,” and “Aerogels.” This list does not include many specialized sessions in other international or national conferences devoted to materials in general, such as the annual conference of the American Chemical Society or the American Ceramic Society. Sol-gel processes brought a new view in the domain of glass and ceramics fabrication, and they have enlightened the importance of chemistry along the complete fabrication lines of materials. The basic idea was initially to progressively create an oxide network by polymerization reactions of chemical precursors dissolved in a liquid medium. During the first decades, the presence of ceramic specialists was predominant in the field. But during the last two decades, chemistry and particularly organic chemistry took an increasing share in new developments, in particular regarding a new class of hybrid organic-inorganic gels and materials which did not exist in nature, but which offered very interesting new properties. The importance of sol-gel processing and its complexity is such that it deserves books and excellent ones, in particular Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics and Specialty Shapes edited by L. Klein (Noyes, Park Ridge, N.Y., 1985) and Sol-Gel Science. The Physics and Chemistry of Sol-Gel Processes by C.J. Brinker and G.W. Scherer (Academic Press, N.Y., 1990), appeared very ix

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early. The latter book definitely constituted an outstanding and complete reference on the subject at the time of its publication, which researchers are advised to consult first. But, a huge body of new information on sol-gel was more recently discovered, such that it deserved a huge Handbook of Sol-gel Science and Technology edited by Klein L, Aparicio M and Jitianu A (Springer 2016), plus a first Aerogels Handbook edited by Aegerter M.A, Leventis N, and Koebel MM (2011), followed by a re-edition under print edited by Steiner S, Leventis N, Koebel M, and Aegerter M. A (Springer).

Scope The subject of sol-gel has reached a level of being taught in universities, in conjunction with courses on inorganic chemistry, surface science, and ceramics processing or combinations of them. For this purpose, books less extensive on research developments than the handbooks previously mentioned, but also presenting the more basic theories underlying sol-gel technology, are needed. The present volume is an attempt in this direction. It presents the exact content of lectures which were progressively developed and taught, both at undergraduate and graduate levels, first at the University of Bordeaux in 1987 in France, then at the University of Alberta in Edmonton, Canada, and since 1995 at the University Claude BernardLyon 1 in France. A first shorter version was published in 1992 in French by the Publisher Septima in Paris, another one by Kluwer Academic Publishers in 1998, and the present version is an augmented version of the 1998 edition. The book is organized in such a way that each chapter actually corresponds to one of the main chronological order steps involved in sol-gel processing. The detailed developments in many sections are a consequence of the input of students. Other clarifications are certainly needed, as new ones appear necessary each year during the course of a teaching session and I would like to apologize for this to the reader. I will also be very grateful to all users of this book for further possible developments. Rochetaillee sur Saone, France

Alain C. Pierre

Acknowledgments

This book would not have been written without the strong initial encouragement of my students, all along my teaching experience. Challenging discussions with them over quite a few years have led to drastically modify the content of many sections. This present book edition is in part their fruit, and I am very thankful to them. I would also like to sincerely thank my research colleagues, whom I met either at sol-gel conferences or during research collaborations and more particularly E. Matijevic of Clarkson University, S. Sakka from the University of Kyoto, and J. Livage of the University of Paris-VI, who sent me some gel material photographs which I could incorporate in the various book editions. I would like especially to express my deep gratitude to L. Klein, Professor at Rutgers University, for her support and opportunity to publish the 1998 Kluwer edition, as well as for participation in the sol-gel handbooks previously mentioned. Regarding the present edition, I am very grateful to Prof. Aegerter who offered me the opportunity to participate in both editions of the Aerogels Handbook. I also wish to express my deepest sense of gratitude towards Prof. A. Rigacci, at Mines Paris Tech (France), for discussions with him in many occasions, for his encouragement, and for providing excellent photographs and granting permission to publish in this book. The technical support of the staff at Springer, in particular Cynthia Pushparaj, Brian Halm for the end index, and Arthi Kaliaperumal and co-workers to edit the book, were very helpful and I am very pleased to acknowledge their help. Finally, above all, I am very grateful and indebted to my wife, Marie-Claude, for her patience. She not only supported the time-consuming redaction of this book but also encouraged me.

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Contents

1

2

General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Short History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Scientific Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Colloids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 The Traditional Sol-Gel Processing of Ceramics . . . . 1.1.5 Recent Chemical Developments . . . . . . . . . . . . . . . . 1.2 Sols, Gels, and Gelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Sols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Gelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Xerogels and Aerogels . . . . . . . . . . . . . . . . . . . . . . 1.2.5 Gelatinous Precipitates . . . . . . . . . . . . . . . . . . . . . . 1.2.6 Sol-Gel Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Outline of Sol-Gel Processing . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Sol-Gel Processing Applications . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Advantages and Limitations of Sol-Gel Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 11 12

The Sol-Gel Chemistry of Oxides from Metal Salts . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Nonaqueous Solvents . . . . . . . . . . . . . . . . . . . . . . 2.3 Basis of Cation Transformations in Solution . . . . . . . . . . . . . 2.3.1 The Partial Charge Model . . . . . . . . . . . . . . . . . . . 2.3.2 Transformation Mechanisms of Complexes . . . . . .

15 15 16 16 19 21 21 25

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1 1 1 1 2 2 3 4 4 5 5 6 6 6 7 9 9

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2.4

Hydrolysis of Cations in Solution . . . . . . . . . . . . . . . . . . . . . 2.4.1 Ion Solvation in Water . . . . . . . . . . . . . . . . . . . . . 2.4.2 Hydrolysis of Cations in Aqueous Media . . . . . . . . 2.4.3 Hydrolysis of Hydrated Cations in Organic Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Polymerization by Condensation of Hydrolyzed Cations . . . . 2.5.1 Condensation by Olation . . . . . . . . . . . . . . . . . . . . 2.5.2 Condensation by Oxolation . . . . . . . . . . . . . . . . . . 2.5.3 Condensation and the Partial Charge Model . . . . . . 2.6 Complexation by Anions . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Complexation by Anions X and the Partial Charge Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Overall Complexation of a Metal M by Anions . . . . 2.6.3 Formation of a Solid Phase . . . . . . . . . . . . . . . . . . 2.7 Sol-Gel Behavior of Cations as a Function of Their Nature . . 2.7.1 Cations with Valence I . . . . . . . . . . . . . . . . . . . . . 2.7.2 Cations with Valence II . . . . . . . . . . . . . . . . . . . . . 2.7.3 Cations with Valence III . . . . . . . . . . . . . . . . . . . . 2.7.4 Cations with Valence IV . . . . . . . . . . . . . . . . . . . . 2.7.5 Cations with Valence V or Higher . . . . . . . . . . . . . 2.8 Metal Salt Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8.1 Modes of Cation Mixing in the Final Solid . . . . . . . 2.8.2 Complexation with Carboxylic Acids . . . . . . . . . . . 2.8.3 The Pechini Method . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

The Sol-Gel Chemistry of Oxides from Alkoxides . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Structure and Properties of Alkoxides . . . . . . . . . . . . . . . . . . 3.2.1 Chemical Nomenclature of Alkoxides . . . . . . . . . . 3.2.2 Physical and Structural Characteristics of Alkoxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Chemical Characteristics of Alkoxides . . . . . . . . . . 3.2.4 Silicon Alkoxides . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Hydrolysis of Alkoxides . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 The Main Parameters of Alkoxide Hydrolysis . . . . . 3.3.2 Formation of Hydroxo Ligands . . . . . . . . . . . . . . . 3.3.3 Formation of Oxo Ligands . . . . . . . . . . . . . . . . . . 3.4 Polymerization by Condensation from Hydrolyzed Alkoxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Condensation by Olation . . . . . . . . . . . . . . . . . . . . 3.4.2 Condensation by Oxolation . . . . . . . . . . . . . . . . . . 3.5 SolGel Behavior of a Few Homometallic Alkoxides as a Function of their Cation Nature . . . . . . . . . . . . . . . . . . . 3.5.1 Boron Alkoxides . . . . . . . . . . . . . . . . . . . . . . . . .

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27 28 29

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34 35 35 36 38 40

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41 44 45 49 50 50 51 55 59 61 61 62 62 64

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69 69 69 69

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70 72 73 75 75 75 77

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78 79 79

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3.5.2 Aluminum Alkoxides . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Titanium Alkoxides . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4 Zirconium Alkoxides . . . . . . . . . . . . . . . . . . . . . . . 3.5.5 Silicon Alkoxides . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Formation of Solid Phases from Alkoxides . . . . . . . . . . . . . . . 3.6.1 Boron Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.3 Titania . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.4 Zirconia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.5 Silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Alkoxysilanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 The Diversity of Alkoxysilanes . . . . . . . . . . . . . . . . 3.7.2 Organotrialkoxysilanes . . . . . . . . . . . . . . . . . . . . . . 3.7.3 Functionalization of Organotrialkoxysilanes . . . . . . . 3.7.4 Si Coordination Polyhedral Notation in Materials Derived from Alkoxysilanes . . . . . . . . . . . . . . . . . . 3.7.5 Polyhedral Oligomeric Silsesquioxane (POSS) . . . . . 3.8 Other Precursors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1 The Span of Precursors . . . . . . . . . . . . . . . . . . . . . . 3.8.2 Organometallics . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.3 Glycol-Modified Silanes (GMS) . . . . . . . . . . . . . . . 3.8.4 Polyhedral Oligometallasilsesquioxanes (POMS) and Other Non-Si Clusters . . . . . . . . . . . . . . . . . . . . 3.8.5 Other Metal-Organic Complexes . . . . . . . . . . . . . . . 3.9 Precursor Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.1 Mixing Two Alkoxides . . . . . . . . . . . . . . . . . . . . . . 3.9.2 Mixing an Alkoxide with a Metal Salt . . . . . . . . . . . 3.9.3 Mixing with Fine Solid Powders . . . . . . . . . . . . . . . 3.9.4 Cations Mixing with Silicon by the Glycol-Modified Silane (GMS) Method . . . . . . . . . . . . . . . . . . . . . . . 3.10 Non-hydrolytic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10.1 Non-hydrolytic Hydroxylation Reactions . . . . . . . . . 3.10.2 Aprotic Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

The Sol-Gel Chemistry of Non-oxides . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Chalcogenides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Deposition from a Chalcogenide Solution . . . . . . . . . 4.2.2 Sol-Gel Synthesis from Alkoxides . . . . . . . . . . . . . . 4.2.3 Sol-Gel Synthesis from Organometallics . . . . . . . . . 4.2.4 Sol-Gel Synthesis from Inorganic Precursors . . . . . . 4.3 Fluorides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 The Hydrolytic Route . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 The Trifluoroacetate Route . . . . . . . . . . . . . . . . . . . 4.3.3 The Fluorolytic Route . . . . . . . . . . . . . . . . . . . . . . .

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83 84 84 86 90 91 91 92 94 95 99 99 99 101 103 104 105 105 106 107 108 108 110 111 116 117 117 118 119 120 121 129 129 129 130 131 133 134 138 139 139 140

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4.4

Preceramic Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Carbides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Nitrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Organic Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Melamine-Formaldehyde and ResorcinolFormaldehyde Gels . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Cellulosic and Polyurethane-Based Gels . . . . . . . . . . 4.5.3 Other Synthetic Organic Hydrogels . . . . . . . . . . . . . 4.5.4 Hydrogels from Biopolymers . . . . . . . . . . . . . . . . . 4.6 Carbon and Graphene Gels . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Carbon Gels Derived from Organic Gels . . . . . . . . . 4.6.2 Graphene and Carbon Nanotube Gels . . . . . . . . . . . . 4.6.3 Carbon Nanotube and Graphene Gel Formation . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Nanoparticle Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Nucleation and Growth Versus Spinodal Decomposition . . . . 5.2.1 Relationship Between Hydrolysis, Condensation, and Formation of Solid Particles . . . . . . . . . . . . . . 5.2.2 Phase Transformation Modes According to Gibbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Nucleation of Solid Particles . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Gibbs Free Energy of a Spherical Particle . . . . . . . . 5.3.2 Gibbs Internal Free Energy Change, per Unit Volume, Due to Phase Transformation . . . . . . . . . . 5.3.3 Homogeneous Nucleation Rate . . . . . . . . . . . . . . . 5.3.4 Heterogeneous Nucleation . . . . . . . . . . . . . . . . . . . 5.3.5 LaMer Model, for the Growth of Monodisperse Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Crystalline Growth Mechanisms of Solid Particles . . . . . . . . . 5.4.1 Kinetics of Growth Controlled by the Fixation of New Complexes: Mononuclear Regime . . . . . . . 5.4.2 Polynuclear Growth Regime . . . . . . . . . . . . . . . . . 5.4.3 Kinetics of Growth Controlled by the Diffusion of Complexes in Solution . . . . . . . . . . . . . . . . . . . 5.4.4 Growth Regime Transition . . . . . . . . . . . . . . . . . . 5.4.5 Importance of Crystal Defects: Growth of Amorphous Particles . . . . . . . . . . . . . . . . . . . . . 5.4.6 Importance of Thermal Diffusion in the Growth Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Examples of Solid Particles Made by Nucleation and Growth from Precursor Solutions . . . . . . . . . . . . . . . . . . 5.5.1 Particle Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 Monodisperse Particles . . . . . . . . . . . . . . . . . . . . .

142 142 144 145 146 147 149 151 151 151 152 157 159

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5.5.3 Growth Termination . . . . . . . . . . . . . . . . . . . . . . . . 5.5.4 The Stöber Process . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.5 Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Other Techniques to Synthesize Solid Particles from a Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Hydrothermal Processing . . . . . . . . . . . . . . . . . . . . 5.6.2 Electrochemical Precipitation . . . . . . . . . . . . . . . . . . 5.6.3 Particle Growth in Aprotic or Non-hydrolytic Sol-Gel Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.4 Particle Nucleation and Growth Inside a Gel . . . . . . . 5.6.5 Use of Microemulsions . . . . . . . . . . . . . . . . . . . . . . 5.6.6 Exfoliation Methods . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Solid Particles Synthesized by More Physical Processes . . . . . . 5.7.1 Physical and Chemical Vapor Deposition . . . . . . . . . 5.7.2 Pyrolysis of Precursors . . . . . . . . . . . . . . . . . . . . . . 5.7.3 Spray-Drying Techniques . . . . . . . . . . . . . . . . . . . . 5.7.4 Freeze-Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.5 Liquid Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.6 Aerosol Hydrolysis . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.7 Advantages of Particle Synthesis by Sol-Gel Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Peptization of Colloidal Sols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Sols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Peptization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Kinetic Stability of a Sol . . . . . . . . . . . . . . . . . . . . 6.2.3 Main Interactions Involved in the Stability of a Sol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Van der Waals Interaction . . . . . . . . . . . . . . . . . . . 6.3.2 Adsorption of Ions and Electrical Double Layer . . . 6.3.3 Gouy-Chapman Model . . . . . . . . . . . . . . . . . . . . . 6.3.4 Debye-Hückel Approximation . . . . . . . . . . . . . . . . 6.3.5 Stern Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.6 Case of a Charged Spherical Particle . . . . . . . . . . . 6.3.7 Electrostatic Repulsion Force Between Two Charged Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.8 The Main Routes to Adjust the Electrostatic Repulsion Between Spherical Particles . . . . . . . . . . 6.3.9 Total Interaction Energy in Electrostatic Sols . . . . . 6.3.10 Coagulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.11 Effect of Ion Solvation . . . . . . . . . . . . . . . . . . . . . 6.3.12 Electrostatic Charge Reversal . . . . . . . . . . . . . . . .

. . . . .

189 192 193 197 197 197 197 199 199 199 199 200 200 201 202 202 202 203 203 209 209 210 210 210

. 211 . . . . . . .

211 211 215 221 224 225 225

. 230 . . . . .

237 237 239 240 242

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Contents

6.4

Coagulation Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Smoluchowski Derivation of Coagulation Rate . . . . 6.4.2 Reversibility of Coagulation . . . . . . . . . . . . . . . . . 6.5 The Steric Stabilization Theory . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Origin of Steric Stabilization . . . . . . . . . . . . . . . . . 6.5.2 Polymer Solutions . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Steric Interactions Between Colloidal Particles . . . . 6.5.4 Steric Interaction Energy . . . . . . . . . . . . . . . . . . . . 6.5.5 Mixed Steric and Electrical Interactions: Case of Surfactant Solutions . . . . . . . . . . . . . . . . . 6.5.6 Mixed Steric and Magnetic Interactions: Ferrofluids® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.7 Bridging Polymer Adsorption . . . . . . . . . . . . . . . . 6.6 Other Interactions Applying in Extended DLVO Theories . . . 6.6.1 Hydration Forces . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2 Hydrophobic Forces . . . . . . . . . . . . . . . . . . . . . . . 6.7 Potential of Mean Field (PMF) Simulations . . . . . . . . . . . . . 6.7.1 Limitations of the DLVO and Steric Theories . . . . . 6.7.2 The PMF Theory for Colloids . . . . . . . . . . . . . . . . 6.7.3 Main Results of the PMF Modelizations . . . . . . . . . 6.8 Other Phenomena in Sols . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8.1 Sol Demixion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8.2 Liquid Crystal-Like Sols . . . . . . . . . . . . . . . . . . . . 6.8.3 Aging Evolution of Sols . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

. . . . . . . .

244 244 245 247 247 247 250 251

. 252 . . . . . . . . . . . . . .

253 253 253 255 255 257 258 258 260 262 262 263 264 267

Gelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Percolation Models of Gelation . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Flory-Stockmayer Model . . . . . . . . . . . . . . . . . . . . . 7.2.2 Percolation Models . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Growth Models of Gelation . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Main Differences Between Percolation and Growth Models of Gelation . . . . . . . . . . . . . . . . 7.3.2 Example of Growth Models . . . . . . . . . . . . . . . . . . 7.4 Gelation and the DLVO Theory . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Experimental Critical Electrolyte Concentration for Gelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Electrostatic Conditions of Gelation . . . . . . . . . . . . . 7.4.3 Example of Gel Structure According to DLVO Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Experimental Study of Gelation . . . . . . . . . . . . . . . . . . . . . . . 7.5.1 Rheological Methods . . . . . . . . . . . . . . . . . . . . . . . 7.5.2 Vibrational Spectroscopy . . . . . . . . . . . . . . . . . . . . 7.5.3 Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . .

271 271 271 271 273 279 279 280 284 285 285 287 287 287 292 297

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7.5.4

Small-Angle X-Ray Scattering (SAXS) and Small-Angle Neutron Scattering (SANS) . . . . . . . . . 7.5.5 Nuclear Magnetic Resonance Spectroscopy (NMR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.6 Microscopic Techniques . . . . . . . . . . . . . . . . . . . . . 7.5.7 Other Experimental Techniques . . . . . . . . . . . . . . . . 7.5.8 Computer Calculation Methods . . . . . . . . . . . . . . . . 7.6 Gelation of Real Sols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.1 Gel Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.2 Gelation Theories as Frameworks of Experimental Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.3 Importance of the Cation Nature and Chemistry . . . . 7.6.4 Irreversible Gelation . . . . . . . . . . . . . . . . . . . . . . . . 7.6.5 Reversible Gelation . . . . . . . . . . . . . . . . . . . . . . . . 7.6.6 Gelation of Real Materials and the Percolation or Aggregation Models . . . . . . . . . . . . . . . . . . . . . . 7.6.7 Gelation of Multicomponent Systems . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Wet Gels and Their Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Network Structure and Classification of Gels . . . . . . . . . . . . . 8.2.1 Originality of Wet Gels as Materials . . . . . . . . . . . . 8.2.2 Gel Classifications . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Properties of Wet Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Solid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Transport Properties in the Liquid of a Gel . . . . . . . . 8.4 Reversible Swelling of Wet Gels . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Osmotic Swelling Theory of Covalent Organic Polymeric Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 Swelling of Inorganic Gels . . . . . . . . . . . . . . . . . . . 8.4.3 Donnan Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Syneresis of Inorganic Wet Gels . . . . . . . . . . . . . . . . . . . . . . . 8.6 Aging Wet Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.1 Chemical Evolution During Aging . . . . . . . . . . . . . . 8.6.2 Physical Evolution During Aging . . . . . . . . . . . . . . 8.7 Drying Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.1 Drying by Evaporation . . . . . . . . . . . . . . . . . . . . . . 8.7.2 Supercritical Drying . . . . . . . . . . . . . . . . . . . . . . . . 8.7.3 Ambient Pressure Drying . . . . . . . . . . . . . . . . . . . . 8.7.4 Subcritical Drying . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.5 Freeze-Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.6 Drying by Liquid–Liquid Extraction . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

297 299 301 301 302 305 305 306 306 307 310 314 317 318 323 323 323 323 324 327 327 331 331 331 333 336 337 341 341 341 344 344 352 355 356 357 357 358

xx

9

10

Contents

Dry Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Texture of Dry Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Pore Characterization Techniques . . . . . . . . . . . . . . 9.2.2 Mercury Porosimetry . . . . . . . . . . . . . . . . . . . . . . . 9.2.3 Adsorption Isotherms . . . . . . . . . . . . . . . . . . . . . . . 9.3 Structure of Dry Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Gel Fractal Structure . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 Gel Crystallographic Structure . . . . . . . . . . . . . . . . . 9.3.3 Gel Surface Structure . . . . . . . . . . . . . . . . . . . . . . . 9.4 Oxide Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Silica Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Borate Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.3 Alumina Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.4 Titania Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.5 Zirconia Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.6 Oxides Made by the Epoxidation Method . . . . . . . . . 9.4.7 Vanadium and Tungsten Oxide Gels . . . . . . . . . . . . 9.4.8 Mixed Oxide Gels . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.9 Oxide Gels Made by Non-hydrolytic Process . . . . . . 9.5 Non-oxide Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 Chalcogenide Gels . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.2 Organic Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.3 Carbon Aerogels . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Thermal Conduction and Mechanical Properties of Dry Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6.1 Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . 9.6.2 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

363 363 363 363 364 365 371 372 372 374 378 378 385 386 389 390 391 391 393 395 396 396 397 403

Hybrid Organic–Inorganic and Composite Materials . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Classes of Hybrid Organic-Inorganic Sol-Gel Materials . . . . . 10.2.1 Ormosils and Ceramers . . . . . . . . . . . . . . . . . . . . . 10.2.2 Class I and Class II Hybrids . . . . . . . . . . . . . . . . . 10.2.3 Hybrid Gel Architectures . . . . . . . . . . . . . . . . . . . 10.2.4 Hybrid Gels Versus Composite Materials . . . . . . . . 10.3 Examples of Class I Hybrid Architecture . . . . . . . . . . . . . . . 10.3.1 Class I Hybrids Made by Entrapment of Various Dispersed Components . . . . . . . . . . . . . . . . . . . . . 10.3.2 Class I Hybrid Made by Entrapment of an Organic Dye in Silica Gel . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.3 Class I Hybrid Made by Entrapment of Short Organic Polymers in an Oxide Gel, or of Oxide Clusters in a Polymer Gel . . . . . . . . . . . . . . . . . . .

421 421 422 422 422 424 425 426

. . . . . . . .

406 407 409 413

. 426 . 426

. 427

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10.3.4 10.3.5

Silica POSS Cluster Class I Hybrids . . . . . . . . . . . . Class I Hybrids Made by Gelation of Two Interpenetrating Gel Networks . . . . . . . . . . . . . . . . . 10.3.6 Class I Hybrids Made by Polymer Intercalation in Lamellar Inorganic Gels . . . . . . . . . . . . . . . . . . . 10.4 Examples of Class II Hybrid Architecture . . . . . . . . . . . . . . . . 10.4.1 Class II Ormosil Hybrids . . . . . . . . . . . . . . . . . . . . . 10.4.2 Class II CERAMER Hybrids . . . . . . . . . . . . . . . . . . 10.5 Sol-Gel Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.1 Composites Designed by Mixing of Constituents . . . 10.5.2 Carbon Nanotube (CNT) Aerogels/Sol-Gel Oxide Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.3 Composites Made by Spontaneous Phase Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Main Properties of Hybrid Gels . . . . . . . . . . . . . . . . . . . . . . . 10.6.1 Mechanical Properties of Hybrids . . . . . . . . . . . . . . 10.6.2 Other Properties of Hybrids . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Surfactant-Templated Sol-Gel Materials . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Solute Adsorption at a Liquid/Air or an Immiscible Liquid/Liquid Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1 Gibbs Adsorption Isotherm . . . . . . . . . . . . . . . . . . 11.2.2 Aqueous Solute Classification . . . . . . . . . . . . . . . . 11.3 Surfactants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.1 General Structure of Surfactant Molecules and Behavior Below a Concentration c.m.c. . . . . . . . . 11.4.1 Micelle Formation . . . . . . . . . . . . . . . . . . . . . . . . 11.4.2 Micelle Structure . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.3 Factors Influencing the c.m.c. . . . . . . . . . . . . . . . . 11.5 Solubilization of Organic Nonpolar Compounds in Water by Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5.1 Micellar Solutions . . . . . . . . . . . . . . . . . . . . . . . . 11.5.2 Micelle-Stabilized Microemulsions . . . . . . . . . . . . 11.5.3 State Diagrams of Ternary Solution Systems Made with Surfactants . . . . . . . . . . . . . . . . . . . . . 11.6 Microparticle Synthesis in Water-in-Oil (W/O) Microemulsions Stabilized by Surfactants . . . . . . . . . . . . . . . 11.6.1 Solid Microparticles and Microcapsules . . . . . . . . .

428 429 430 431 431 437 441 442 444 445 445 445 448 449

. 457 . 457 . . . .

457 457 460 462

. 462 . 463 . . . . .

465 466 466 467 469

. 472 . 472 . 472 . 473 . 475 . 475

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Contents

11.6.2

Core-Shell Microparticles Made by Stabilization of Colloidal Sols by a Surfactant . . . . . . . . . . . . . . 11.7 Application of Surfactants to Synthesize Ordered Mesoporous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.7.1 Importance of Micelles for Templating . . . . . . . . . . 11.7.2 Surfactant Templating and Sol-Gel Electronic Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.7.3 Surfactant Templating of Sol-Gel Silica . . . . . . . . . 11.7.4 Templating with Block Copolymer Surfactants . . . . 11.8 Some Characteristics of Surfactant-Templated Mesoporous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.8.1 Texture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.8.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.8.3 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

. 479 . 479 . 479 . 481 . 482 . 485 . . . . .

489 489 490 491 492

Phase Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Transformations in the Hüttig Range . . . . . . . . . . . . . . . . . . . 12.2.1 Types of Transformations in the Hüttig Range . . . . . 12.2.2 Gel Dehydration . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.3 Other Chemical Group Elimination . . . . . . . . . . . . . 12.2.4 Chemical Transformations of Non-oxide Gels . . . . . . 12.3 Transformations in the Lower Tammann Range . . . . . . . . . . . 12.3.1 Gel Network Transformation . . . . . . . . . . . . . . . . . . 12.3.2 Topotactic Crystallization . . . . . . . . . . . . . . . . . . . . 12.3.3 The Topotactic Formation of Transition Aluminas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4 Diversity of Topotactic Transition Phases in Sol-Gel Materials . . . . . . . . . . . . . . . . . . . . . . . . 12.3.5 Topotactic Phase Transformations in Multicomponent Oxides . . . . . . . . . . . . . . . . . . . . . 12.3.6 Gels Made by Polymerizable Complex Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4 Glass Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.1 Glasses, a Class of Amorphous Materials . . . . . . . . . 12.4.2 Experimental Characterization of the Glassy State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.3 Glass Formation Mechanism from Polymeric Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.4 Glass Formation from Gels Above Tg . . . . . . . . . . . 12.4.5 Glass Compositions Studied by Sol-Gel . . . . . . . . . . 12.4.6 Non-oxide Sol-Gel Glasses . . . . . . . . . . . . . . . . . . . 12.4.7 Differences Between Melt-Quenched Glasses and Sol-Gel Silica Glasses . . . . . . . . . . . . . . . . . . . . 12.5 Phase Transformations in the Upper Tammann Range . . . . . . .

497 497 499 499 499 504 507 508 508 510 511 513 514 517 518 518 519 524 525 526 528 528 529

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12.5.1 12.5.2

Spinodal Decomposition . . . . . . . . . . . . . . . . . . . . . Formation of the Stable Thermodynamics Phases by Nucleation and Growth . . . . . . . . . . . . . . . . . . . 12.5.3 Variation of the Specific Surface Area During Nucleation and Growth . . . . . . . . . . . . . . . . . . . . . . 12.5.4 Crystallization of Glasses . . . . . . . . . . . . . . . . . . . . 12.6 Conversion to Non-oxides by Chemical Reactions . . . . . . . . . . 12.6.1 Carbon Aerogels . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.6.2 Carbides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.6.3 Oxynitrides and Nitrides . . . . . . . . . . . . . . . . . . . . . 12.6.4 Borides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.6.5 Sulfides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

530 533 534 535 537 537 537 539 541 541 541

13

Sintering Sol-Gel Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Possible Texture Evolution . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.1 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.2 Textural Transformation Kinetics . . . . . . . . . . . . . . 13.2.3 Competition Between Grain Growth and Sintering . 13.2.4 Gel Network Transformation During Sintering . . . . 13.3 Atomic Transport Mechanisms Operating During Sintering . . 13.3.1 Atomic Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . 13.3.2 Viscous Flow Sintering . . . . . . . . . . . . . . . . . . . . . 13.4 Grain Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.1 Basic Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.2 Grain Growth Models . . . . . . . . . . . . . . . . . . . . . . 13.4.3 Grain Boundaries Pinning by Impurities . . . . . . . . . 13.5 Interaction of Pores with the Sintering Process . . . . . . . . . . . 13.5.1 Possible Pore Transformations . . . . . . . . . . . . . . . . 13.5.2 Action of Pores on the Grain Boundary Mobility . . 13.5.3 Abnormal Grain Growth . . . . . . . . . . . . . . . . . . . . 13.5.4 Pores Due to Initial Powder Packing . . . . . . . . . . . 13.6 Hot Pressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.7 Sintering Under an Electric Field . . . . . . . . . . . . . . . . . . . . . 13.7.1 Microwave-Assisted Thermal Treatments . . . . . . . . 13.7.2 Fast and Flash Sintering . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

551 551 552 552 553 556 557 560 560 564 568 568 568 569 570 571 573 575 581 584 587 587 588 593

14

Applications of Sol-Gel Processing . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 Health Hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3 Applications in the Sol or in the Gel State . . . . . . . . . . . . . . . . 14.3.1 Sols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.2 Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

597 597 598 598 598 599

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Contents

14.4

14.5

14.6

14.7

14.8

14.9

14.10

14.11

14.12

Coatings and Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.1 Functions of Sol-Gel Coatings . . . . . . . . . . . . . . . . 14.4.2 Fabrication Techniques . . . . . . . . . . . . . . . . . . . . . 14.4.3 Free-Standing Films . . . . . . . . . . . . . . . . . . . . . . . Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5.1 Main Compositions . . . . . . . . . . . . . . . . . . . . . . . 14.5.2 Fabrication Techniques . . . . . . . . . . . . . . . . . . . . . Monoliths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6.1 Gel Monoliths and Derived Ceramic Monoliths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6.2 Monoliths from Hybrids . . . . . . . . . . . . . . . . . . . . 14.6.3 Ambigel and Aerogel Monoliths . . . . . . . . . . . . . . 14.6.4 Monoliths from Sintered Sol-Gel Powder . . . . . . . . Filtration Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.7.1 Porous Membranes . . . . . . . . . . . . . . . . . . . . . . . . 14.7.2 Ceramic Membranes . . . . . . . . . . . . . . . . . . . . . . . 14.7.3 Sol-Gel Ceramic Membranes . . . . . . . . . . . . . . . . . Thermal and Acoustic Insulation . . . . . . . . . . . . . . . . . . . . . 14.8.1 Thermal Insulation . . . . . . . . . . . . . . . . . . . . . . . . 14.8.2 Acoustic Insulation . . . . . . . . . . . . . . . . . . . . . . . . Optical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.1 Optical Transparency of Silica Gels . . . . . . . . . . . . 14.9.2 Cherenkov Counters . . . . . . . . . . . . . . . . . . . . . . . 14.9.3 Luminescent Materials . . . . . . . . . . . . . . . . . . . . . 14.9.4 Optical Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.5 Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . Electrical, Dielectrical, and Other Electromagnetic Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.1 Electrical Conduction Applications . . . . . . . . . . . . 14.10.2 Electrodes and Batteries . . . . . . . . . . . . . . . . . . . . 14.10.3 Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . Applications as Immobilization Medium . . . . . . . . . . . . . . . . 14.11.1 Confinement Applications . . . . . . . . . . . . . . . . . . . 14.11.2 Environment Remediation Applications . . . . . . . . . 14.11.3 Capture of CO2 Gas . . . . . . . . . . . . . . . . . . . . . . . 14.11.4 Other Immobilization Applications . . . . . . . . . . . . Sol-Gel Catalysts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.12.1 The Catalytic Process . . . . . . . . . . . . . . . . . . . . . . 14.12.2 Synthesis of High-Value Organic Compounds . . . . 14.12.3 Protection of the Environment . . . . . . . . . . . . . . . . 14.12.4 Recent Sol-Gel-Made Catalysts . . . . . . . . . . . . . . . 14.12.5 Photocatalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.12.6 Sol-Gel Biocatalysts . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . .

600 600 603 605 606 606 607 609

. . . . . . . . . . . . . . . . .

609 610 611 612 614 615 616 618 623 624 627 627 627 628 630 631 636

. . . . . . . . . . . . . . . .

637 637 638 639 641 641 642 643 644 645 645 649 650 652 657 658

Contents

14.12.7 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Medical Applications and Biomaterials . . . . . . . . . . . . . . . . . 14.13.1 Biomaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.13.2 Drug Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.13

xxv

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659 661 661 664 664

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687

Chapter 1

General Introduction

1.1 1.1.1

Short History Scientific Basis

Sols and gels are two forms of matter which were known to exist naturally for a long time. They include various materials such as ink, clays, and a number of other substances such as the eye vitreous, blood, serum, and milk (Livage and Lemerle 1982). Sols and gels attracted the interest of scientist for a long time. The oldest sols prepared in a laboratory were synthesized with gold by Faraday (Faraday 1857). They were mentioned to be still stable nowadays (Matijevic 1987).

1.1.2

Colloids

Colloidal science is considered to have been founded by Graham (1861). Since then, the study of ceramic colloidal sols was slowly progressing, and laws governing the formation of sols and their behavior according to a number of different factors were progressively discovered. Later on, the size of colloid forming these sols could also be controlled, in particular by using inorganic salts to synthesize them (Roy 1956; Matijevic 1987). A good understanding of the nature of sols and of the laws explaining their behaviors was finally achieved and a major contribution in the understanding of sols’ physical chemistry came from the so-called Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory (Derjaguin and Landau 1941; Verwey 1941; Verwey and Overbeek 1948), also known as electrostatic theory. This theory was particularly the first one to distinguish a precipitate from a kinetically stable colloidal suspension.

© Springer Nature Switzerland AG 2020 A. C. Pierre, Introduction to Sol-Gel Processing, https://doi.org/10.1007/978-3-030-38144-8_1

1

2

1.1.3

1 General Introduction

Gels

As for gels, apart from some silica gels which exist naturally (Iler 1979), their synthesis was only achieved since the nineteenth century. Ebelmen (1846, 1847) produced the first silica gels and Cossa (1870) synthesized the first alumina gels by an electrolytic method. Since then, all kinds of inorganic gels were progressively synthesized and a technique such as the supercritical drying of Kistler (1931) was introduced. This technique permitted to produce the first materials termed “aerogels” of silica, alumina, zirconia, stannic, and tungsten oxides. Still in ceramics but outside the field of oxides, Stock et al. (1921) synthesized the first silazanes, polymeric precursors to Si3N4. Some oxide gels were more recently synthesized, such as the first borate gels, by Tohge et al. (1984). Overall, the number of publications on “gelatinous” and “colloidal” forms of ceramics kept however steadily increasing and some of the properties and structure of gels were in turn elucidated. The first historical details were summarized by Iler (1979) for silica and by Gitzen (1970) for alumina. The theoretical basis needed in order to understand the network structure of a gel and the kinetics of its formation and gelation was developed by Flory (1941). His original work addressed organic gels but was soon extended to inorganic ones. Shortly after, the theory of percolation of Hammersley (1957) explained the gelation process as a special case of the critical phenomena occurring in physics. The lace geometry that characterizes a gel network and the porous ceramic obtained at the beginning of densification were then described by the fractal geometry introduced by Mandelbrot (1977).

1.1.4

The Traditional Sol-Gel Processing of Ceramics

For a long time sols and gels were only of pure scientific interest. However, their extremely high specific area made them increasingly interesting in the field of catalysis. By the beginning of the 1960s, following the works on clays (Ford 1964) and nuclear fuel oxides in England, and those of Matijevic (1981) on the production of colloidal particles with controlled size and shape, new ceramics were also produced for more technical use, using inorganic sols and gels, giving name to the field as “sol-gel processing.” Since the 1970s, an increasing number of publications in the field of gels and inorganic colloids were published. This led to an increasing number of potentially interesting applications in high-technology ceramics and some of them begun to be commercialized. These new sol-gel processes were found to fulfill at least to some extent the current need for new and better products (Mazdiyasni et al. 1965; Wheat 1977). High-purity submicron powders, nuclear fuels, electronic and ionic conductors, and magnetic materials can now be produced by sol-gel techniques. Sol-gel processing is also very useful and important when the production of reproducible homogeneous complex ceramic materials is necessary.

1.1 Short History

3

A domain of importance for ceramists concerns the synthesis of ceramics of complex composition and a good homogeneity was often difficult to achieve. In this case, colloidal particles can be synthesized by sol-gel processing in a first step, and further treated by conventional ceramic processing techniques (cold pressing, hot pressing, sintering) to make a ceramic part in a second step. The colloidal size of each component implied shorter diffusion distances to achieve a homogeneous distribution of the different cations, which was the main interest of the sol-gel process. To avoid segregation of the different oxide components, the colloidal particles could also be dispersed within a stable organic sol further transformed to a gel before heat treatment, such as in the Pechini method addressed in Chap. 2. Sols and gels could also be spun into fibers or applied using various techniques to coat a substrate. It must also be noted that sol-gel processing is not the only route to synthesize ceramic materials at low temperature (Ohya 2016). Other types of techniques such as chemical bath deposition (CBD), successive ionic layer adsorption and reaction (SILAR), liquid-phase deposition (LPD), electroless deposition (ED), and film deposition on organic self-assembled monolayers (SAMs) were reviewed by Niesen and DeGuire (2001).

1.1.5

Recent Chemical Developments

During the last two decades, the sol-gel field has experienced a tremendous expansion. In a first period the synthesis of perfect gel monoliths, particularly SiO2 hydrophobic aerogel monoliths obtained using the supercritical drying technique (Chap. 8), required a more involved chemical adaptation of the wet gels, initially by grafting hydrophobic organic ligands on them. For this purpose, chemists and particularly organic chemists become increasingly involved to design “better ceramics through chemistry,” which was the title of a number of specialized conferences. In a second step, the organic functionalization of SiO2 gels led to conceiving of quite new products comprising hybrid organic-inorganic materials and also mesoporous structured materials. In practice, the bonding of organic molecules or polymeric macromolecules to an inorganic counterpart was developed, and a very large span of hybrid organicinorganic could be designed (Sanchez and Ribot 1994). Such materials are rather scarce in the nature: an example which can be mentioned is the material constituting the bones of living humans or animals where the inorganic part is hydroxyapatite, a hydrated calcium phosphate compound (Chap. 14). But, overall, these synthetic hybrid materials offered a very large variety of new properties considered as very interesting for a number of advanced technologic applications.

4

1 General Introduction

To these, one must moreover add materials comprising an ordered mesoporous structure of spherical, cylindrical, or lamellar pores, obtained by using surfactants during the sol-gel synthesis (Corma 1997). Sol-gel was also recently extended to non-oxide ceramics, comprising chalcogenides, fluorides, and carbon aerogels, the latter ones obtained either by calcination of organic aerogels or by binding graphene monolayer particles or carbon nanotubes, as described in Chap. 4. Even regarding oxides, a complex range of new chemical synthesis processing was developed and is presented in Chaps. 2 and 3.

1.2 1.2.1

Sols, Gels, and Gelation Sols

A sol can be defined as a stable suspension of colloidal solid particles within a liquid (Hiemenz 1977). For a sol to exist, the solid particles denser than the surrounding liquid must be small enough, so that the forces responsible for its dispersion are greater than those of gravity. Moreover, these particles must include a number of atoms macroscopically significant. In fact, if the particles were too small, then it would be more accurate to speak of molecules in solution. Originally, “colloidal” only referred to macroscopic particles that could not pass through a dialysis membrane. This definition, however, does not give accurate values of the size range of the particles which are concerned. Practically, particles in a colloidal sol must have a size comprised between 2 nm and 0.2 μm, which corresponds to 103–109 atoms per particle (Livage and Lemerle 1982). Particles in this size range can moreover be divided into three categories. They can be composed of subdivided parts of bulk matter (for example small particles of α-alumina), real macromolecules that are big enough to be colloidal (such as proteins), or small particles that can be considered as both macromolecules and tiny parts of macroscopic matter (such as lacey particles). In the case of subdivided parts of bulk material, two thermodynamic phases can be distinguished: one for the matter inside the particles, and another for the liquid in which they are dispersed. The sol can moreover be considered as either lyophobic (hence hydrophilic) or hydrophobic (hence lyophilic), depending on water, respectively, being or not being the main liquid-phase component. In the case of real macromolecules, only one thermodynamic phase is present and it is more appropriate to designate it as a hydrophilic or lyophilic solution. The small lacey particles are more difficult to characterize and can be observed, for instance, in some colloidal forms of silica of other lacey polymeric particles. Actually, the solvent most often used to disperse colloidal particles in a sol is either pure water or a solution composed mostly of water and an alcohol. Nevertheless, other liquid components may be used.

1.2 Sols, Gels, and Gelation

1.2.2

5

Gels

A gel can be defined as a porous three-dimensionally interconnected solid network that expands in a stable fashion throughout a liquid medium and is only limited by the size of the container. If the solid network is made of colloidal sol particles the gel is said to be colloidal. If the solid network is made of macromolecules initial in a polymeric solution, the gel is termed polymeric. A polymer, as defined by Flory (1974), is a macromolecule whose structure can be generated through “repetition of one or a few elementary units.” A great diversity of sols and gels exists and several classifications were proposed; the most simple of them maybe is the one given by Flory (1953) and presented in Chap. 8. The nature of gels is tied to an intricate contact and equilibrium coexistence between a very porous solid network and a fluid medium, either a liquid or a gas, filling its pores. In this type of equilibrium, the liquid impregnates the solid network mesh that composes the gel and constitutes the major part in volume%. Moreover it does not flow spontaneously out of this network which can reach a thermodynamic equilibrium with it. In Chap. 8, it is for instance described that a wet polymeric gel will undertake spontaneous and reversible swelling and shrinkage, depending on thermodynamics parameters such as the temperature or the liquid composition. If the liquid is mostly composed of water, the corresponding gel is often termed an aquagel or hydrogel. An aquagel is a soft material that can be easily cut with a knife. On the other hand, when the liquid phase is largely composed of an alcohol, the gel is then termed an alcogel. Finally, if most of the liquid is removed and only residual traces of it remain inside the gel, the dry form which is obtained, often a very brittle solid, is called either a xerogel or an aerogel, depending on the drying method.

1.2.3

Gelation

In practice, a gel is formed when the homogenous dispersion of colloidal particles or macromolecules present in the initial sol rigidifies the whole wet sol medium. This transformation, termed gelation, prevents the development of inhomogeneities within the material. The exact transition event from a sol or a solution to either a colloidal or a polymeric gel is known as the gel point (Flory 1974). Practically, at this point, the sol is abruptly transformed from a viscous liquid state to a gel, which behaves as a single solid monolith impregnated with liquid. This gel point and the properties of sols and gels near this point are now better characterized within the framework of the new “theory of critical phenomena” which is a branch of equilibrium thermodynamics.

6

1.2.4

1 General Introduction

Xerogels and Aerogels

The term “xerogel” is defined by IUPAC as an “open network formed by the removal of all swelling agents from a gel” (Alemán et al. 2007) but it was first introduced by Freundlich (1923) to designate “shrinking” (or swelling when shrinking is reversible) gels. As detailed in Chap. 8, drying a wet gel by evaporation of its mother liquid often induces an important contraction, for instance 30% or less of its initial volume (Brinker and Scherer 1990), under the action of capillary stresses. Hence, in this monography, the term “xerogel” is reserved for those gels which undertake an important shrinkage during drying. On the other hand, the term “aerogel” was first introduced by Kistler (1931, 1932) to designate gels in which the liquid was replaced with a gas, without any important shrinking of the gel solid network. As detailed in Chap. 8, Kistler achieved such a result by using a “supercritical drying” technique, according to which the liquid which impregnated the gels was evacuated after being transformed to a supercritical fluid, by heating above the fluid thermodynamic critical point. But this is not the only technique permitting to achieve such a result.

1.2.5

Gelatinous Precipitates

When the solid particles in a sol are heavy enough to precipitate, more or less slowly, a wet viscous solid-liquid mixture is deposited on the lower end of the sol container. Some authors called such precipitates “gel,” but it would be more accurate to describe them as gelatinous precipitates. The border line between gels and gelatinous precipitates can however be ambiguous, because as explained in Chap. 6, a precipitate is the result of the progressive formation of bigger aggregates of colloidal particles, so that a sol will more or less rapidly precipitate. Actually, while a gel can be thermodynamically stable, a sol can only be kinetically stable. On a time scale which depends on the material nature a sol always tends to precipitate, unless the formation kinetics of a gel 3D network expanding through the entire sol volume happens to be faster than the kinetics for dense aggregation of the colloidal particles. In details, these aggregates can really have a texture which can range from densely packed to very open, including all possible intermediate texture.

1.2.6

Sol-Gel Processes

Many definitions of sol-gel processes exist. For instance, Dislich (1983) considered that the sol-gel procedure only concerns multicomponent oxides which must be homogenized at the atomic level. This definition therefore did not include single-oxide materials (e.g., TiO2 gels), nor colloidal coprecipitates of hydroxides

1.3 Outline of Sol-Gel Processing

7

and oxyhydrates since they become homogeneous only by reaction at high temperature. Moreover in this definition, the term “sol-gel” processing was restricted to the gels synthesized from alkoxides. On the other hand, Segal (1984) defined “sol-gel” processing as the production of inorganic oxides, either from colloidal dispersion or from metal alkoxides. Since this time, sol-gel processing is no longer limited to oxides but it also includes non-oxide materials such as the nitrides (Seyferth and Wiseman 1984) and sulfides (Chap. 4), organic gels such as the hydrogels used in biomaterials (Chap. 4), or hybrid organic-inorganic materials which constitute a big new subfield of sol-gel processing (Chap. 10). In this book, a more general definition of sol-gel processes was therefore adopted. It is considered that a sol-gel process is a colloidal route used to synthesize any material with an intermediate stage including a sol and/or a gel state.

1.3

Outline of Sol-Gel Processing

Many variations can be brought to the sol-gel synthesis of materials. In fact, sol-gel processing does designate not only a unique technique, but also a very broad type of procedures which can be described according to a global scheme presented in Fig. 1.1. The first step of any sol-gel process always consists of selecting initial chemical compounds, termed precursors, from which the desired material will be synthesized. In most cases, these precursors are more or less complex chemical molecules, and their transformation by chemical reactions leads to the formation of any possible type of structures, from dense colloidal particles to polymeric gels with a very open macromolecular network. When the target material needs a combination of different chemical components, for instance several oxides of different cations (e.g., SiO2 and Al2O3), or an inorganic molecule plus an organic one, a variety of combinations of different precursors can be used and, depending on the chemical protocol selected, significantly different products in terms of phases formed, homogeneity, and texture can be obtained. A sol-gel synthesis scheme more in line with the recent developments must also comprise the possible use of non-hydrolytic solvents, or of colloidal carbon particle precursors: in detail carbon nanotubes and graphene or graphene oxide monolayer nanoparticles. The drying methods have also experienced a major development with ambigels, based on the grafting of hydrophobic groups on the pore surface of wet gels, which permit to dry them by simple evaporation of the solvent with minor drying shrinkage. In the last steps of a sol-gel processing scheme, the major progress concerned new good aerogel monoliths, either as ambigels or as aerogels dried by the supercritical method. On the other hand, gel coating or fiber drawing has not seen major new developments and the same is true regarding heat treatment and sintering: these steps were largely developed by ceramists before the introduction of more involved chemistry.

8

Fig. 1.1 Simplified chart of sol-gel processes

1 General Introduction

1.4 Sol-Gel Processing Applications

1.4 1.4.1

9

Sol-Gel Processing Applications Materials

The applications of sol-gel processing are in great expansion although their potentiality is still larger. Major fields of application concern thermal insulation and optical applications. SiO2 aerogel occupies a major place with products comprising translucent aerogel flakes, as well as transparent aerogel slabs and optically transparent insulating windows. Many optical sol-gel applications concern coating, such as in antireflective coatings with index gradation and optical or infrared absorbing coatings. To these, one must add electrically conductive coatings and protection coatings that work against scratch, oxidation, and erosion on all types of materials, including plastic and steel. Noteworthy success was also achieved in advanced fine-grain ceramics with ferroelectric, dielectric, piezoelectric, optical, or electro-optical properties. This success is due to the feasibility of better ultrafine ceramic powders (Mazdiyasni 1982). New interesting glasses and glass ceramics can now be synthesized from sol-gel monoliths as well as by the sintering or melting of sol-gel powders. Those glasses could not be obtained by any conventional processing. Moreover, sols and gels can themselves have particular properties which make them interesting for some specific applications, such as the coating of photographic films. Other examples of noteworthy recent achievements are the design of new organic-inorganic gels used in the embedment of photochromic and laser dyes (Sanchez and Ribot 1994), or new catalysts based on the synthesis of ordered pore structures from micellar surfactant solutions (Corma 1997).

1.4.2

Advantages and Limitations of Sol-Gel Processing

Sol-gel processing presents many advantages. First, it permits to synthesize materials with any oxide composition, but also new hybrid organic-inorganic materials which do not exist naturally. Another significant advantage concerns the purity of materials, which can be made very good given the nature of the chemical precursors which can be purified by distillation, crystallization, or electrolysis. Moreover, the chemical processes of the first steps are always carried out at low temperatures. By comparison with the classical high-temperature synthesis of conventional ceramics, this minimizes considerably the chemical interactions between the material and the container walls. Another advantage is the association of the solid colloidal state with a liquid medium, which permits to avoid any pollution by the eventual dispersion of dust. This explains why the biggest industrial application of sol-gel synthesis of ceramics is for nuclear fuels where control of the pollution is very critical.

10

1 General Introduction

There are other more fundamental advantages to sol-gel processing. For instance, the kinetics of the various chemical reactions can be easily controlled by the low processing temperature, the precursor nature and concentration of solution, and the solvent nature. The nucleation and growth of primary colloidal particles can also be controlled in order to obtain particles with a given shape, size, and size distribution. Typically, this size is submicronic which in turn permits sintering at temperatures currently lower by several hundred degrees, than by conventional processing (Zelinski and Uhlmann 1984). A lower sintering temperature can also be critical to form certain metastable phases, including some glasses, to avoid or limit fiber-matrix reaction in fiber composites or to densify some hybrid organic-inorganic materials. The structure of sol-gel ceramics can more easily be controlled by sol-gel processing than by conventional processing, in part due to the smaller primary sol-gel particles. An amorphous or semivitreous state is also easier to obtain and many new glass compositions could be synthesized by sol-gel, which were not feasible by a conventional quench technique. This is due to the fact that two problems encountered with the conventional quench techniques could be avoided by using sol-gel processing. The first one is the very high fluidity of the material liquidus which requires a very fast cooling rate to form a glass. The second one is the frequent existence of a miscibility gap in some domains of composition and temperature making it impossible to obtain a homogeneous glass by melt quenching. The distribution of pores and crystalline or amorphous phases in a crystalline material texture can also be tailored to a large extent. This is particularly true when a segregated phase can be controlled to be either present at grain boundaries or completely eliminated. Eliminating this phase can be important in some cases, such as for the ionic conductors composed of sodium and silicon (Nasicon) for which the segregation of ZrO2 at grain boundaries must be avoided. But the presence at grain boundaries only of segregated phase can be important to avoid abnormal grain growth and to permit full densification in some ceramics, such as Al2O3. Sol-gel processing offers the most outstanding advantages for mixed-oxide systems in which the chemical homogeneity of the various elements can be controlled down to the atomic level. This is the case of some lead lanthanum zirconium titanates (PLZT) (Haertling and Land 1972). This condition is virtually impossible to achieve when solid powders are mechanically mixed such as in the processing of bigger conventional powders, so that the optical transparency is not as high as that obtained by sol-gel processing. The greatest limitation to the synthesis of ceramic by sol-gel processing remains the cost of the precursors, especially that of alkoxides. Most of these alkoxides are nonetheless quite easy to make, especially if they do not tend to polymerize. A few of them such as Zr and Ti were early industrially used by the Schott company for coating applications (Dislich 1983) and are thus quite affordable. Moreover, alkoxides can also be mixed with much cheaper metal salts provided that a purification step is included in the procedure. The sol-gel synthesis of ceramics will never be able to compete for the mass production of some large-scale materials such as window glass for which the conventional processes can rely on much cheaper raw materials. Sol-gel processing becomes, however, much more interesting for highly advanced ceramics.

1.5 Organization of the Book

11

But sol-gel processing is not the only chemical route that leads to better ceramics. Another procedure includes the use of organometallic compounds in which an organic group is directly bonded to a metal without any oxygen atom intermediate. The chemistry of organometallics essentially concerns the synthesis of complex polymers, especially related to carbides and nitrides. But when this chemistry is carried out in a liquid medium, it can still be considered as a sol-gel process. Precipitation and coprecipitation techniques are also used and are sometimes even considered as a side branch of sol-gel processing. The chemical reactions concerned in this case are the same as those occurring in sol-gel synthesis. They often lead to the production of colloidal particles, but they can also be re-dispersed into a stable sol. Two other techniques are the thermal decomposition of precursors in the vapor phase (Mazdiyasni et al. 1965) and hydrothermal processing (Sapieszko and Matijevic 1980). The first one is also known as chemical vapor decomposition (CVD). Some CVD protocols use quite sophisticated nucleation and growth procedures such as heating by laser and, as in sol-gel processing, very pure products can be obtained depending on the CVD precursor used, which can be an alkoxide. The hydrothermal process is carried out in solutions placed in an autoclave and at higher temperatures than those required in sol-gel processing. This technique also produces crystals with a size of the order of a micrometer or larger. Hydrothermal synthesis is not within the scope of this book, although its wet chemistry aspect is essentially similar to that of sol-gel processing.

1.5

Organization of the Book

This book aims at offering a synthetic view of the various aspects and interest of the materials produced by sol-gel processing. These aspects are presented according to the scheme of sol-gel process illustrated in Fig. 1.1. The liquid medium chemistry is first discussed in Chap. 2 for metal salt precursors, in Chap. 3 for alkoxides, and in Chap. 4 for non-oxides (chalcogenide, fluorides, carbides and nitrides, simple organic gels, and carbon gels). Chapter 5 is devoted to the nucleation and growth of nanoparticles from these solutions and Chap. 6 describes their behavior, dispersion or coagulation, in a sol. The phenomenon of gelation is described in Chap. 7 and the gels themselves and their properties are the subject of Chap. 8 regarding wet gels (including their drying), and Chap. 9 regarding the dry gels (Chap. 5). Presentation of two recent families of sol-gel-derived materials is given in Chap. 10 for hybrid organic-inorganic materials and Chap. 11 regarding surfactant-templated materials. The phase transformations of gels at higher temperature and their sintering are the subjects of Chaps. 12 and 13, respectively. These chapters were only marginally modified in comparison with their equivalent from the first edition of this book. On the other hand, different applications were significantly developed and are presented in Chap. 14.

12

1 General Introduction

Overall, from molecules in an aqueous medium to porous ceramics undertaking sintering, a constant phenomenon is a competition between the formation of dense structures and of open ones. This book is a journey through the various stages of this competition.

References J. Alemán, A.V. Chadwick, J. He, M. Hess, K. Horie, R.G. Jones, P. Kratochvíl, I. Meisel, I. Mita, G. Moad, S. Penczek, R.F.T. Stepto, Pure Appl. Chem. 79, 1801–1829 (2007) C.J. Brinker, G.W. Scherer, Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing, vol 1990 (Academic Press, New York, 1990), p. 908 A. Corma, Chem. Rev. 97, 2373–2420 (1997) A. Cossa, Il Nuovo Cimento 3(3), 228–230 (1870) B.V. Derjaguin, L.D. Landau, Acta Physicochim. 14, 633–662 (1941) H. Dislich, J. Non-Cryst. Solids 57(57), 371–388 (1983) M. Ebelmen, Ann. Chim. Phys. 16, 129–166 (1846) M. Ebelmen, C. R. Acad. Sci. Paris 25, 854–856 (1847) M. Faraday, Philos. Trans. R. Soc. Lond. 147, 145–181 (1857) P.J. Flory, J. Am. Chem. Soc. 63(63), 3083–3100 (1941) J.P. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York, 1953) P.J. Flory, Disc. Faraday Soc. 57(54), 7–8 (1974) R.W. Ford, “Drying”, Institute of Ceramics, Textbook Series (MacLaren and Sons, London, 1964) H. Freundlich, Colloid and Capillary Chemistry (Dutton Ed., New York, 1923) W.H. Gitzen, Alumina as a Ceramic Material (The American Ceramic Society, Columbus, OH, 1970) T. Graham, Philos. Trans. R. Soc. Lond. 151, 183–224 (1861) G.H. Haertling, C.E. Land, Ferroelectrics 3, 269–280 (1972) J.M. Hammersley, Proc. Cambridge Phil. Soc. 53, 642–645 (1957) P.C. Hiemenz, Principles of Colloid and Surface Chemistry (Marcel Dekker, New York, 1977). Also: Hiemenz P.C. and Rajagopalan R. 3rd Edition Taylor and Francis (1997) R.K. Iler, The Chemistry of Silica (Wiley, New York, 1979) S.S. Kistler, Nature 127, 741 (1931) S.S. Kistler, J. Phys. Chem. 36, 52–64 (1932) J. Livage, J. Lemerle, Annu. Rev. Mater. Sci. 12, 103–122 (1982) B.B. Mandelbrot, Fractals: Form, Chances and Dimensions (Freeman, San Francisco, 1977) E. Matijevic, Acc. Chem. Res. 14, 22–29 (1981) E. Matijevic, in Monodisperse Colloids (Preparation, Properties and Applications), and Interactions in Mixed Colloidal Systems (Heterocoagulation, Adhesion and Microflotation). Conference Presented at the Université de Bordeaux I, France (9–10 June 1987) K.S. Mazdiyasni, Ceram. Int. 8, 42–56 (1982) K.S. Mazdiyasni, C.T. Lynch, J.S. Smith II, J. Am. Ceram. Soc. 48, 372–375 (1965) T.P. Niesen, M.R. DeGuire, J. Electroceram. 6, 169–207 (2001) Y. Ohya, Aqueous Precursors, in Handbook of Sol-Gel Science and Technology, ed. by L. Klein, M. Aparicio, A. Jitianu, (Springer, New York, 2016). (Chapters 2–10) R. Roy, J. Am. Ceram. Soc. 39, 145 (1956) C. Sanchez, F. Ribot, New J. Chem. 18, 1007–1047 (1994) R.S. Sapieszko, E. Matijevic, Corrosion 36, 522–530 (1980) D.L. Segal, J. Non-Cryst. Solids 63, 183–191 (1984) D. Seyferth, G.H. Wiseman, in Ultrastructure Processing of Ceramics, Classes and Composites, ed. by L. L. Hench, D. R. Ulrich, (Wiley, New York, 1984), pp. 265–271

References

13

A. Stock, K. Somieski, Silicon hydrides. X. Ber. Dtsch. Chem. Ges. 54, 740–758 (1921) N. Tohge, G.S. Moore, J.D. Mackenzie, J. Non-Cryst. Solids 63, 95–103 (1984) E.J.W. Verwey, Rec. Trav. Chim. 60, 625–633 (1941) E.J.W. Verwey, J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948) T.A. Wheat, J. Can. Ceram. Soc. 46, 11–18 (1977) B.J.J. Zelinski, D.R. Uhlmann, J. Phys. Chem. Solids 45, 1069–1090 (1984)

Chapter 2

The Sol-Gel Chemistry of Oxides from Metal Salts

2.1

Introduction

If inorganic sols and gels can be obtained by various methods, they are often directly synthesized from chemical reactants dissolved in a liquid medium. A chemical reactant which contains the cation M present in the final inorganic sol or gel is called a chemical precursor. Its chemical transformations are complex and involve a competition at the molecular level between the reactions responsible for the formation of open structures and those leading to dense solids. These same reactions are also responsible for the controlled dispersion of dense colloidal particles in a sol or their agglomeration into a gel or a precipitate. In sol-gel processing, many types of precursors can be used, provided that a solvent is available to dissolve them. In practice, two main groups are distinguished: the metallic salts and the alkoxides. The general formula of a metallic salt is MmXn where M is the metal, X an anionic group, and m and n stoichiometric coefficients. These precursors often have an ionic structure. They comprise chlorides such as aluminum chloride A1C13, but also sulfates, oxysulfates, nitrates, and organic salts such as acetates, citrates, and lactates (Ohya 2016). In this chapter, the focus is on the chemical reactions occurring in liquid medium for this type of precursors. The solids synthesized by sol-gel are mainly oxides. Hence water is usually present as a major reactant in order to bind oxygen atoms to the cations. Moreover it is also often the main solvent. Hence, the electronic properties of the water molecule are important to summarize, as they are largely linked to the chemical transformations of the precursors. At last a number of other reactants are important: acids, bases, solvents other than water, and various complexing agents. All these aspects and the main physical chemistry theory, the partial charge theory, which permits to some extent to predict or explain the molecular complexes which are formed, are reviewed.

© Springer Nature Switzerland AG 2020 A. C. Pierre, Introduction to Sol-Gel Processing, https://doi.org/10.1007/978-3-030-38144-8_2

15

16

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Fig. 2.1 Lewis representation of a water molecule

2.2

Solvents

It is necessary to consider water separately from the other solvents.

2.2.1

Water

The water molecule is, in the Lewis representation, V-shaped (Fig. 2.1). The oxygen atom is surrounded by four electron pairs; which comprise one covalent bond with each of the two hydrogen atoms, plus two unshared electron pairs. According to the valence shell electron pair repulsion (VSEPR) model, the oxygen therefore occupies the center position of a tetrahedron and the two hydrogen atoms occupy two of the d is 104.5 in the gaseous state, and varies tetrahedron corners. The angle θ ¼ HOH   from 118 to 120 in the liquid state. Such a configuration provides a permanent polarization to the water molecule, with a dipole moment defined as !

!

μ ¼ ðδqÞ d

ð2:1Þ !

In the physical representation, the distance vector d originates at the center of the negative charges (δq) on the unshared electron pair side of the oxygen atom, and ends at the center of the positive charges (+δq) of the H atoms. The magnitude of this dipole moment is |μ| ¼ 1.85 D (1D ¼ 1 Debye ¼ 3.336  1030 C m) (Atkins 1994). The water molecule belongs to the symmetry group C2v (Chabanel and Gressier 1991). The following theoretical calculations of the molecular orbitals of H2O can be made by linear combination of the 2s and 2p atomic orbitals of the oxygen atom and the 1s orbitals of the two hydrogen atoms. The electrons of the water molecule are therefore placed on the four molecular orbitals which have the following wave functions and energies:

2.2 Solvents

17

  Ψ w ð2a1 Þ ¼ 0:85Ψ 0 ð2sÞ þ 0:13Ψ 0 2pz þ 0:81ðΨ HA ð1sÞ þ Ψ HB ð1sÞÞ E ¼ 36 eV   Ψ w ð1b2 Þ ¼ 0:4Ψ 0 2py þ 0:78 ðΨ HA ð1sÞ  Ψ HB ð1sÞÞ   Ψ w ð3a1 Þ ¼ 0:46Ψ 0 ð2sÞ  0:83Ψ 0 2pz  0:33ðΨ HA ð1sÞ þ Ψ HB ð1sÞÞ E ¼ 14 eV Ψ w ð1b1 Þ ¼ Ψ 0 ð2px Þ

E ¼ 12 eV

ð2:2Þ E ¼ 19 eV

ð2:3Þ ð2:4Þ ð2:5Þ

In these equations Ψ w represents the molecular orbitals of a water molecule, while Ψ 0 designates atomic orbitals of the oxygen atom, and Ψ HA and Ψ HB the respective atomic orbitals of the two hydrogen atoms A and B. The corresponding energy diagram, as illustrated in Fig. 2.2 with a shape of the electron presence probability clouds, demonstrates that the 3a1 molecular orbital of water is largely delocalized outside the water molecule. This orbital is responsible for the Lewis base character of water. The molecule is therefore able to donate a pair of electrons to a ligand group and build a σ bond with it. On the other hand, the 1b1 molecular orbital is strictly nonbinding, and hence has a very weak π donor character. It is possible to estimate the partial electrical charge δq (thereafter simply termed δ) carried by each atom from the molecular orbital wave functions. Since the wave function Ψ M of a molecule AB is obtained by linear combination of Ψ A and Ψ B Ψ M ¼ aΨ A þ bΨ B

ð2:6Þ

The electronic charge density is obtained by integrating on the whole volume Ψ 2M ¼ a2 Ψ 2A þ b2 Ψ 2B þ 2abΨ A Ψ B

ð2:7Þ

The a2 coefficient gives the electron charge density contributed by the A atom only, and the b2 coefficient by the B atom only, and the overlap integral of 2abΨ AΨ B is attributed in equal proportion to the A and B atoms. The difference between the total charge density of the A atom in the molecule AB and in the isolated state gives an estimation of the partial charge δ(A) carried by the A atom. For the water molecule, this estimation gives a negative partial charge for the oxygen atom of δ(O) ¼ 0.4 and a positive partial charge δ(H) ¼ +0.2 for each hydrogen atom. Since its molecules are polarized, water is an excellent liquid medium in which to dissolve ionic solutes. This property is expressed by the following coulomb electrostatic force F between two electrical charges q and q0 :

18

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Fig. 2.2 Energy diagram and shape of the electron presence probability clouds for the molecular orbitals of water (adapted from Jorgensen and Salem (1973))

F¼

1 qq0 4πEr ε0 r 2

ð2:8Þ

in which ε0 ¼ 8.8542  1012 F m1 is the dielectric permittivity of vacuum and εr the relative dielectric constant which has no dimension. Water at 25  C has a relative dielectric constant of εr ¼ 78.4; consequently it largely attenuates the coulomb interaction between two electrical charges. As illustrated in Fig. 2.3, the polar structure of water molecules drives the formation of hydrogen bonds between oxygen and hydrogen atoms of different

2.2 Solvents

19

Fig. 2.3 Hydrogen bonding between two water molecules

molecules. In this type of bond, a hydrogen atom fluctuates by tunnel effect between two minimum energy positions only separated by a small energy barrier, of the order of 20–40 kJ mol1. Such bonds can also be formed with fluoride or nitrogen atoms instead of oxygen. A direct consequence of these bonds is that, according to molecular dynamic calculations (Stillinger 1980; Jolivet et al. 1994), very few water molecules can be isolated in the pure liquid state. Most water molecules are bound by up to four hydrogen bonds to neighboring molecules. Those random groups have an average lifetime of the order of 1010 s. Water molecules also auto-dissociate according to the equilibrium reaction: 2H2 O $ H3 Oþ þ HO

ð2:9Þ

K w ¼ ½H3 Oþ  ½HO  ¼ 1014 at 25∘ C

ð2:10Þ

with equilibrium constant

Hence water is a protic solvent. Furthermore, H3O+ and HO ions also associate themselves with other water molecules by hydrogen bonds, so that they actually exist in liquid water as [H9O4]+ and [H7O4]. The latter anion is the strongest possible base in aqueous solutions. As a consequence, O2 practically does not exist in water and, when a solid oxide is dissolved, it immediately undergoes an acidbase protonation reaction.

2.2.2

Nonaqueous Solvents

Apart for the molten salts, nonaqueous solvents are often polar with a molecular structure characterized by both a permanent dipole moment μ and a relative dielectric constant εr. εr not only depends on a permanent dipole moment μ, but also on the polarizability α of the molecule, which is itself defined according to the relation

20

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Table 2.1 List of some solvents with their dielectric properties Solvent Acetone C3H6O Acetic acid C2H4O2 Ammonia NH3 Benzene C6H6 Chloroform CHCl3 Dimethyl sulfoxide (CH3)2SO (CH3)(CH3)2SO Dioxane 1,4 C4H8O2 Water H2O Methanol CH3OH Ethanol C2H5OH Formamide CH3ON Dimethylformamide C3H7NO Nitrobenzene C6H5NO2 Tetrahydrofuran C4H8O Carbon tetrachloride CCl4 Diethylether C4H10O Pyridine C5H5N

εr 20.7 6.2 16.9 2.3 4.8 45 2.2 78.5 32.6 24.3 110.0 36.7 34.8 7.3 2.2 4.3 14.2

μ(D) 3.00 0.99–1.51 0.90 0.00 1.11 3.90 0.39 1.85 1.70 1.71 3.39 3.86 3.99 1.63 0.00 1.15 2.19

Type Aprotic Protic Protic Aprotic Aprotic Aprotic Aprotic Protic Protic Protic Protic Aprotic Aprotic Aprotic Aprotic Aprotic Aprotic

Adapted from Lagowski (1976)

μ ¼ αE

ð2:11Þ

μ defines the induced dipole moment which adds to the permanent dipole moment when the molecule is submitted to an electric field E. A high relative dielectric constant (εr > 40) is often due to the existence of a permanent dipole moment. Such molecules have good ionizing properties and can therefore dissolve other polar solute. On the other hand when the solvent’s relative dielectric constant is low (εr < 20), it has a weak ionizing property and can only dissolve less polar solute. A list of frequently used solvents with their relative dielectric constant and dipole moment is gathered in Table 2.1. Solvents are classified as protic when they can exchange a proton, and as aprotic when they cannot do so. They can also be classified as acidic, in the Brønsted sense when they are able to donate a proton or in the Lewis sense when they are able to accept a pair of electrons. Similarly, a base, according to Brønsted, is able to accept a proton, and according to Lewis to donate a pair of electrons. A solvent is amphoteric when it can behave both as a base and an acid. Amphoteric solvents include: – – – – –

Mineral acids (HCN, HX, HNO3, H2SO4, H2S) Carboxylic acids R-COOH Water, the first alcohols (CH3OH, C2H5OH, . . .), and phenol C6H5OH Ammonia NH3 and amines (RNH2, RR0 NH) Amides (R-CO-NH2, R-CO-NHR0 )

2.3 Basis of Cation Transformations in Solution

21

Organic solvents are frequently used in sol-gel processing as they permit to control the reaction of alkoxide precursors with water, and hence to direct with more flexibility the sol-gel product structure.

2.3 2.3.1

Basis of Cation Transformations in Solution The Partial Charge Model

Sol-gel precursors undergo chemical reactions both with water and with the other species present in the solution. One of the most efficient models used to predict those reactions is the partial charge model (PCM) which has been recently elaborated by Henry and Livage (Livage et al. 1988; Henry et al. 1990) after a principle developed by Sanderson (1971). It is based on the electrical interactions between the partial electric charges, δ, carried by each atom and molecule. Since the chemical potential of the electrons in an atom i or a molecule C depends on the partial electric charges δ(i) or δ(C) carried either by i or by C, and since the electronegativity χ(i) of i or χ(C) of C is directly related to this chemical potential, this model can also be expressed in terms of the particles’ electronegativity (Parr et al. 1978). The derivative of the function E ¼ f(ne) which associates the total energy E of an isolated atom to the number of electrons ne of this atom (Fig. 2.4) describes the influence of the electric charge carried by an atom on its electronegativity. The first ionization energy, I1, of an isolated atom is also a function of the first and second partial derivatives of f(ne) with respect to ne (Parr et al. 1978): 2

I 1 ¼ E ðz  1Þ  E ðzÞ   The electron affinity of this atom is

Fig. 2.4 First ionization and affinity energies of an atom (adapted from Chermette and Lissilour (1985))

∂E 1 ∂ E þ ∂ne 2 ∂ n2e

ð2:12Þ

22

2 The Sol-Gel Chemistry of Oxides from Metal Salts 2

A ¼ E ð z Þ  E ð z þ 1Þ  

∂E 1 ∂ E  ∂ne 2 ∂ n2e

ð2:13Þ

The electronegativity of an isolated atom is therefore defined as 1 ∂E χ a ¼ ðI 1 þ A Þ ¼  2 ∂ ne

ð2:14Þ

Since its hardness is defined as 2

1 1∂ E ηa ¼ ðI 1  AÞ ¼ 2 2 ∂ n2e

ð2:15Þ

and the chemical potential of the electrons in this atom is ∂E ∂ ne

ð2:16Þ

χ a ¼ μae

ð2:17Þ

μae ¼ we have

For any chemical transformation, equilibrium is achieved when all phases have the same chemical potential. In the same manner, the electrons of a molecule transfer from atom to atom until they all reach the same chemical potential or electronegativity. Each atom thus gains an electronic charge (δne). The definition of their hardness then leads to the following equation: μe ðiÞ ¼ μae ðiÞ  ηai ðδne Þ

ð2:18Þ

Since the electronegativity of an atom χ(i) is the opposite of the chemical potential of the electrons μe(i) this is equivalent to χ ðiÞ ¼ χ ai þ ηai ðδne Þ

ð2:19Þ

Electric charge transfer keeps proceeding until all atoms in all species reach an equilibrium where they all have the same electronegativity. Statistically, in order to reach such an equilibrium an ion such as H+ may leave a complex whenever its partial charge reaches the value δ(H) ¼ +1, an anion X if its partial charge reaches the value δ(X) ¼ 1, or a molecule HX if its total partial charge reaches the value δ(HX) ¼ 0. In this manner, the partial charge model provides the statistical thermodynamical basis needed to understand the possible evolution of a complex in solution.

2.3 Basis of Cation Transformations in Solution

23

Table 2.2 Allred-Rochow electronegativities

After Jolivet et al. (1994)

Several electronegativity scales exist. The absolute electronegativity χ ai and hardness ηai concern an isolated atom i. The Mulliken electronegativity χ M i and take into account the electronic state of an atom in its average valence hardness ηM i structure. At last, the Pauling electronegativity χ Pi and hardness ηPi involve the average structure configuration in which the atoms are engaged. It is therefore related to the binding enthalpies ΔHij between atoms i and j, ΔHii between two atoms i, and ΔHjj between two atoms j according to the relation h i1=2 1 χ Pi  χ Pj ¼ ΔHij  ΔHii þ ΔHjj 2

ð2:20Þ

The Pauling χ Pi and Mulliken χ M i electronegativities are linked by the following equation: χM i ¼

χ Pi þ 0:615 0:335

ð2:21Þ

The electronegativity usually taken as the reference in the partial charge model is the Allred and Rochow’s electronegativity χ 0i and the corresponding hardness η0i , because it takes into consideration both the valence state and the shape of an atom X in its average polarization state. These characteristics are reported in Table 2.2. Furthermore, in this scale the hardness and electronegativity are linked by the following relationship: η0i ¼ 1:36

qffiffiffiffiffi χ 0i

ð2:22Þ

24

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Let us consider in an aqueous medium and at a given pH a complex C such as [M (OH)y(H2O)Ny](zy)+. According to the partial charge model at equilibrium, the electronegativities are such that χ ðCÞ ¼ χ ðHþ Þ ¼ χ ðH2 OÞ

ð2:23Þ

This makes it possible to predict statistically which complex of a precursor M will exist in a solution, simply by calculating the electronegativities of all the possible complexes. Furthermore, for a simple atom i with a partial charge δi χ ðiÞ ¼ χ 0i þ η0i δi

ð2:24Þ

where χ 0i is the Allred-Rochow electronegativity and η0i the Allred-Rochow hardness. Hence the partial charge of atom i is δi ¼

χ  χ 0i χ  χ 0i pffiffiffiffiffi ¼ η0i 1:36 χ 0i

ð2:25Þ

In the case of a complex molecule Cz+ composed of several elements, we must consider its total charge z, or formal charge, which is defined as z¼

X

δ i i

ð2:26Þ

Since at equilibrium all atoms in C reach the same electronegativity, χ(i) ¼ χ(C) and hence χ ðC Þ ¼

P pffiffiffiffi0ffi χ þ 1:36z i Pi 1 pffiffiffi0ffi i

ð2:27Þ

χi

For water at pH ¼ 7, δ(H) ¼ +0.2 and δ(O) ¼ 0.4 (see Sect. 2.2). So that for water z¼

X

δ i i

¼ δðOÞ þ 2δðHÞ ¼ 0 pffiffiffiffiffiffi pffiffiffiffiffiffi 2 χ 0H þ χ 0O ¼ 2:491 χ ðH2 OÞ ¼ p2ffiffiffiffi0 þ p1ffiffiffiffi0 χH

ð2:28Þ ð2:29Þ

χO

For an acidic or basic solution, pH 6¼ 7 and the water molecules carry a partial charge δ(H2O) 6¼ 0 either positive or negative. This partial charge represents the average charge of the H+ and OH ions as if they were evenly shared between all H2O molecules. As mentioned in Sect. 2.2, this partial charge is actually a result of

2.3 Basis of Cation Transformations in Solution

25

the fast transformation of complex groups of water molecules bound to each other by hydrogen bonds. The Nernst equation then provides the expression of the chemical potential of a proton: μðHþ Þ ¼ μ0 ðHþ Þ  0:06 pH

ð2:30Þ

Finally, if considering that μ(H+) is proportional to μ(H+) and that χ(H+) takes the values 2.491 and 2.631 at pH ¼ 7 and pH ¼ 0, respectively, where H+ is statistically present in [H7O3]+ and [H9O4]+ species, the following formula can statistically be written as χ ðHþ Þ ¼ χ ðH2 OÞ ¼ 2:631  0:02 pH

2.3.2

ð2:31Þ

Transformation Mechanisms of Complexes

Various atomic or molecular groups called ligands can bind to a complex C or a cation M, either directly or by substituting to another ligand. The transformation mechanism depends on the partial charge of the different atoms in all complex species. Those ligands with a negative partial charge are nucleophilic, and those with a positive charge are electrophilic. Similarly, in a substitution reaction, the new ligand with the highest partial negative charge, Y, is the nucleophile while the group in the metal complex with the highest positive charge, X, is the leaving group. Direct addition of a new ligand to a complex C occurs when the coordination number of the cation in the complex is not fully satisfied. The mechanism then involved is a nucleophilic addition symbolized by AN which may be rather complex. Substitution of a ligand by another one occurs when the coordination number of the metal is already full. In this case the reaction is expressed as an exchange of a Lewis base by another one in order to form a Lewis acid. For instance in the following example, Cl substitutes H2O:  2þ  þ Cl þ CoðOH2 Þ6 ! CoClðOH2 Þ5 þ H2 O

ð2:32Þ

Three different substitution mechanisms exist: the dissociative, the associative, and the interchange mechanisms. In the first step of the dissociative substitution mechanism, enough thermal energy must be available in order to break the bond between the leaving group, X, and the complex. This X ligand then becomes labile, not very stable. Consequently, an intermediary complex in which the metal M has a reduced coordination number is formed and it can eventually be observed by analytical techniques such as NMR (Fig. 2.5a). In a second step the entering group, Y, completes again the normal coordination number of the cation M. Since the rate constant of such a reaction does not depend on the concentration of the

26

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Fig. 2.5 Substitution mechanisms of a ligand Y for A ligand X. (a) Dissociative SN1 mechanism; (b) associative SN2 mechanism; (c) interchange SN2 mechanism. After McMurry (1995)

entering Y ligand, this dissociative mechanism is a unimolecular nucleophilic substitution, designated by SN1. This is for instance the case of the substitution of H2O by a ligand L such as ammonia (NH3) or pyridine in [Ni(OH2)6]2+. Water is formed in the first step: 

NiðOH2 Þ6

2þ

 2þ ! NiðOH2 Þ5 þ H2 O

ð2:33Þ

while L enters in the second step:  2þ  2þ NiðOH2 Þ5 þ L ! NiðOH2 Þ5 L

ð2:34Þ

In the associative substitution mechanism, the entering group Y binds to the complex before departure of the other ligand. Therefore, in this first step, an intermediary complex is formed in which the cation M has an increased coordination number (Fig. 2.5b). This intermediate may also be observable by analytical techniques. The X leaving group separates from the complex only in a second step. As the rate constant of this mechanism depends on the concentration of both the

2.4 Hydrolysis of Cations in Solution

27

Fig. 2.6 Binding of a chelating ligand with a metal complex. An example of a bidentate chelating ligand: the acetylacetonato ion. After Shriver et al. (1994)

entering and the leaving groups, it is a bimolecular nucleophilic substitution, termed SN2. Some examples are given further on. Finally, in the interchange substitution mechanism no intermediary complex can be observed, in which the metal M has either an increased or a decreased coordination number. The reaction thus proceeds in only one step and as in a SN2 substitution (Fig. 2.5c). Various factors can influence the reaction mechanisms leading to the exchange of ligands. Steric strain on the reaction center, for instance, inhibits associative reactions in favor of the dissociative ones. Chelating ligands also have an important effect as they are polydentate. Hence they can bind to a metal atom by several bonds and become difficult to substitute. The acetylacetonato ion [CH3COCHCOCH3] is, for example, bidentate; if L is the chelating ligand, it can form a ring (LML) with the metal. The distance between the two binding points is the “bite distance” (Fig. 2.6). Table 2.3 gives a list of a few important chelating ligands.

2.4

Hydrolysis of Cations in Solution

In sol-gel processing, when metal salts are used as the cation precursors, they are often dissolved in an aqueous medium. A metal salt MX usually dissociates into ions which are dispersed in the solution, and the anions’ negative charge Xz is balanced by the positive charge of the metal cation Mz+. In this example, the cation and the anion then have the same absolute formal charge z. These anions are sometimes considered as impurities, in which case they must be eliminated in order to produce, for example, pure oxide ceramics. However, they can also be invaluable in channeling the chemical transformations within the solution. In any case, all ions first solvate with water molecules, a reaction due to the polar nature of water.

28

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Table 2.3 Typical chelating ligands (2: bidentate, 3: tridentate, 4: tetradentate, 6: hexadentate). The coordinating atoms are in parenthesis Name Acetylacetonato 2,2-Bipyridine

Formula [CH3COCHCOCH3]

Abbreviation acac bipy

Chelating type 2(0) 2(N)

Diethylenetriamine Ethylenediamine Ethyl acetoacetate Diethylenediamine-tetraacetato

NH(C2H4NH2)2 H2NCH2CH2NH2 CH3COCH2COCH2CH3

dien en etac EDTA

3(N) 2(N) 2(O) 6(N,O)

Glycinato Maleonitriledithiolato Nitrilotriaceto Oxalato Tetraazacyclotetradecane

N[NH2CH2C02]

gly mnt nta ox cyclarn

2(N,O) 2(S) 4(N,O) 2(O) 4(N)

trien

4(N)

2,20 200 -Triaminotriethylamine

N(CH2C02)3 C2O42

N(C2H4NH2)3

Adapted from Shriver et al. (1994) Fig. 2.7 Solvation of (a) a cation and (b) an anion

2.4.1

Ion Solvation in Water

When in solution in water, the positive charge z+ of a cation attracts the negative partial charge pole, that is, the oxygen atom, of H2O molecules (δO) < 0). Overall, a cation is therefore entrapped by a number N of water molecules which constitute the first solvation shell (Fig. 2.7). This shell is tightly bonded to the metal cation Mz+ so that the chemical formula of the complex formed by the solvated cation is [M (H2O)N]z+. The number N is fixed for a given type of metal; its value often ranges

2.4 Hydrolysis of Cations in Solution

29

from 4 to 8 and is frequently equal to 6, such as in [A1(H2O)6]3+. A water molecule also solvates the proton and Sect. 2.2 reported that the most frequent value of N for H+ is 4, which corresponds to the complex [H(H2O)4]+ also written as [H9O4]+. A second shell of water molecules surrounds this first solvation shell. Its oxygen atoms are turned towards the hydrogen atoms of the first shell. However this second shell is much less rigid than the first one and it does not have to be taken into consideration in the chemical evolution of the precursor. Anions are also solvated by water. In this case these molecules are turned the other way around with the hydrogen atoms oriented towards the anion (Fig. 2.7). Nevertheless, the solvation of anions is not as important as for cations. In fact, only the solvated cations need to be taken into consideration to explain the hydrolysis of metal salt precursors, a complex chemical transformation leading to the formation of oxides.

2.4.2

Hydrolysis of Cations in Aqueous Media

Hydrolysis is the deprotonation of a solvated metal cation. It consists of the loss of a proton by one or several of the water molecules which surround the metal M in the first solvation shell (Baes Jr. and Mesmer 1976). As a consequence, the aquo ligand molecule, H2O which is bonded to the metal center, is either transformed to a hydroxo ligand, OH whenever only one proton leaves, or to an oxo ligand, O2 whenever two protons leave (Schmidt et al. 1986).

2.4.2.1

The Formation of Hydroxo Ligands

A hydroxo ligand is formed when the solvated metal is an acid and when water therefore acts as a Lewis base (Baes Jr. and Mesmer 1976). This corresponds to the following reaction: 

zþ  ðz1Þ MðOH2 ÞN þ H2 O $ MðOHÞðOH2 ÞN1 þ H3 Oþ K 11 acid þ Lewisbase $ conjugated base þ conjugated acid

ð2:35Þ

K11 is the equilibrium constant of the first deprotonation reaction of a complex involving only one metal atom. This complex can undergo other successive deprotonations, globally described by the following reaction for h consecutive loss of protons: 

MðOH2 ÞN

zþ

 ðzhÞ þ hH2 O $ MðOHÞh ðOH2 ÞNh þ hH3 Oþ

ð2:36Þ

In [M(OH2)N] all the ligands are water molecules; it is therefore the most acidic form of the metal complex. On the contrary, [M(OH)h(OH2)Nh](zh)+ is a more

30

2 The Sol-Gel Chemistry of Oxides from Metal Salts

basic form of the metal complex. It is also an “aquo-hydroxo” complex since it contains both aquo (H2O) and hydroxo (OH) ligands. If the metal has an acidic oxide, the following equivalent deprotonation reaction (2.35) explains the formation of hydroxo ligands by addition of a base to the solution:  zþ  ðz1Þþ MðOH2 ÞN þ OH $ MðOHÞðOH2 ÞN1 þ H2 O

ð2:37Þ

The latter reaction proceeds according to the mechanism in reaction (2.38) (Livage et al. 1988; Jolivet et al. 1994):

ð2:38Þ

In this mechanism, a free OH nucleophilic anion attacks one of the hydrogen atoms of one of the water molecules in the first solvation shell of the metal M. Since this hydrogen carries a positive partial charge (δ(H) > 0), an electron charge transfer occurs between the incoming OH ion and the original metal complex. Consequently, the partial charge, δ(H2O), of the H2O group composed of the incoming OH ion and the attacked H atom increases until it becomes null, δ(H2O) ¼ 0. When this state is reached, an independent water molecule leaves the metal complex. Such deprotonation reactions occur as long as, for an H2O group ligand, δ(O)free water < δ(O)complex < 0. In this case, the deprotonation reaction can be written (Jolivet et al. 1994) as 

   MðOHÞz ðOH2 ÞNz þ H2 O $ MðOHÞzþ1 ðOH2 ÞNz1 þ H3 Oþ

ð2:39Þ

Actually, as indicated before, the H+ ion is also solvated by water. While the above metals which have acidic oxides form hydroxo ligands, those which have basic oxides are characterized by the formation of oxo ligands, O2. For such metals, a hydroxo ligand can still be produced with an acid by attack of a free H+ ion on the nucleophilic oxygen of an oxo ligand (Baes Jr. and Mesmer 1976; Jolivet et al. 1994). In the case of water, the reaction is the following one:

2.4 Hydrolysis of Cations in Solution



MOðOH2 ÞN1

ðz2Þþ

 ðz1Þþ þ H2 O $ MðOHÞðOH2 ÞN1 þ OH

Hþ þ OH

31

ð2:40Þ

The complex reacts with an acid in a similar reaction: 

MOðOH2 ÞN1

ðz2Þþ

 ðz1Þþ þ H3 Oþ $ MðOHÞðOH2 ÞN1 þ H2 O

ð2:41Þ

The corresponding mechanism is described in reaction (2.42):

ð2:42Þ

Such reactions keep proceeding as long as 0 < δ(H)complex < δ0 (H)water (Jolivet et al. 1994).

2.4.2.2

Formation of Oxo Ligands

As mentioned previously, an oxo ligand is an O2 anion bonded to a metal M within a complex. It is formed by the deprotonation of a hydroxo ligand according to the following acid-base reaction (Livage et al. 1988): 

ðz1Þþ  ðz2Þþ MðOHÞðOH2 ÞN1 þ H2 O $ MOðOH2 ÞN1 þ H3 Oþ Acid þ Lewis base $ conjugated base þ conjugated acid

ð2:43Þ

The product obtained, [MO(OH2)N1](z2)+, is an “aquo-oxo” complex since it contains both water and oxo ligands. Nevertheless, “oxo-hydroxo” and “oxohydroxo-aquo” complexes, with general chemical formula [MOx(OH)y(OH2)Nxy](zy2x)+, also exist. An example is the vanadium complex [VO(OH)2(OH2)3]+ (Jolivet et al. 1994).

32

2 The Sol-Gel Chemistry of Oxides from Metal Salts

2.4.2.3

Application of the Partial Charge Model to the Hydrolysis of Cations

According to the partial charge model, the electronegativity of any complex can be calculated from its formal charge and from the Allred and Rochow electronegativity of each atom present in the complex. The electronegativity of an aquo-hydroxo complex C ¼ [M(OH)h(OH2)N.h](zh)+ is for instance (Jolivet et al. 1994) pffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi χ 0M þ N χ 0O þ ð2N  hÞ χ 0H þ 1:36ðz  hÞ χ ðC Þ ¼ p1ffiffiffiffi0 ffi þ pNffiffiffiffi0 þ 2Nh pffiffiffiffi0 χM

χO

ð2:44Þ

χH

If the electronegativity of this complex, χ(C), is equal to the electronegativity of water, then χ ðHþ Þ ¼ χ ðH2 OÞ ¼ 2:631  0:02 pH ¼ χ ðCÞ

ð2:45Þ

which permits to derive the equation (Jolivet et al. 1994)  h¼

1 1 þ 0:014pH



2:621  0:02pH  χ 0M pffiffiffiffiffiffi  1:36z  N ð0:236  0:038pHÞ  χ 0M

! ð2:46Þ

For instance 2:621  χ 0M pffiffiffiffiffiffi χ 0M  0:836 2:341  χ 0M Þ pffiffiffiffiffiffi at pH ¼ 14; h ¼ 1:14z þ 0:25N  χ 0M at pH ¼ 0; h ¼ 1:36z  0:24N 

ð2:47Þ ð2:48Þ

Equation (2.46) can be used to estimate the number h of hydroxo ligands present in an aquo-hydroxo complex formed with a metal M. Likewise, other corresponding expressions exist for all types of complexes involving oxo ligands. The most acidic and the most basic forms of some metal cations as calculated by the partial charge model are reported in Table 2.4. The partial charge model also gives a basis to experimentally determine the pH domains in which pure aquo complexes [M(H2O)N]z+ and pure oxo anions [MOm](2mz) can, respectively, be formed. Those domains, which are represented in Fig. 2.8, are function of both the formal charge z of the cation M and the pH of the solution. This diagram reveals two extreme types of cations. Those with a low formal charge such as z ¼ l form very basic oxides and, when in solution, pure aquo cations;

2.4 Hydrolysis of Cations in Solution

33

Table 2.4 Most acidic and most basic complexes for some metal with formula [MONH2Nh](zh)+, together with the experimental and calculated value of h. The number h of hydroxo ligands is estimated by the partial charge model M Mn

z 7

Si

4

Fe

3

Li

1

Observed complexes Most acidic complex MnO3(OH) Most basic complex MnO4 Most acidic complex Si(OH)3(OH2)+ Most basic complex SiO2(OH)22 Most acidic complex Fe(OH)(OH2)52+ Most basic complex Fe(OH)4 Most acidic complex Li(OH2)4+ Most basic complex Li(OH)(OH2)3

h value 7 8 3 6 2 4 0 l

N 4 4 4 4 6 4 4 4

Calculated h 7.8 8.5 3.8 5.1 1.9 4 1.2 0.9

Adapted from Jolivet et al. (1994) Fig. 2.8 Domains of formation of pure aquo or oxo ligands in function of the formal charge z of the cation and of the pH of the solution (adapted from Jorgensen and Salem (1973))

this is the case of Li+ in [Li(OH2)4]+. On the other hand, those with a high formal charge such as z ¼ 6 produce very acidic oxides and, in solution, pure oxo anions. Sulfur, for instance, forms the acidic oxide SO3 and the oxo anion SO42. The electrostatic character of the hydrolysis mechanism, such as proposed by the partial charge model, justifies the correlation between the first deprotonation constant K11 of a cation M, its formal charge z, and the interatomic distance d between the metal and the oxygen atoms, M–O. This correlation, illustrated in Fig. 2.9, is well described by the following equation (Baes Jr. and Mesmer 1976): Log K 11 ¼ A þ 11:0

z d

ð2:49Þ

In this equation, the constant A is a function of the type of metal. In the periodic classification columns I and II, the metals are the most resistant to deprotonation and hydrolysis, and K11 has therefore a very low value: A ¼ 22. Transition metal cations such as Cu2+ are slightly less resistant to hydrolysis and A ¼ 20. As for the post-transition atom cations (e.g., Bi2+) which can undergo extensive hydrolysis, A has a higher value.

34

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Fig. 2.9 Correlation between log K11 and the ratio cations (adapted from Baes Jr. and Mesmer (1976))

2.4.3

Z d

of charge Z to M-O distance d for various

Hydrolysis of Hydrated Cations in Organic Solvents

Recently, the use of metal salts as sol-gel precursors was addressed with a renewed interest, because they can be hydrolyzed in solution in an organic solvent, in which a slow “proton scavenger” such as an epoxide was added (Gash et al. 2001). Gel and aerogel monoliths were obtained in this way with Cr, Fe, Al, Zr, and other cations, available as solid hydrated salts such as Y(NO3)3∙6H2O, in which the solvation is attached to the cation. This technique was further extended to a range of materials comprising Y2O3 (Eid et al. 2005), SnO2 (Baumann et al. 2005), Y2O3-stabilized ZrO2 aerogels (Chervin et al. 2005), aerogel thermites with dispersed Al nanoparticles (Gash et al. 2008), SiO2 aerogels with dispersed metal nanoparticles (Hund et al. 2004) or with CdS nanoparticles grown by lithography inside the aerogel (Bertino et al. 2004), and chitosan-SiO2 hybrid aerogels with dispersed gold particles (Kuthirummal et al. 2008). The hydrolysis reaction involves a nucleophilic attack on the epoxide secondary carbon by an anion, for instance a Cl anion which is a strong Lewis base, according to a mechanism illustrated in reaction (2.50). Consequently, the negative partial charge δ carried by the epoxide oxygen increases. In turn, the latter oxygen atom can attack and capture one proton from one coordination water molecule of the cation, which is transformed from an aquo to hydroxo ligand. Such a hydrolysis reaction by deprotonation is slow, and it largely depends on the nature of the anion in the metallic salt.

2.5 Polymerization by Condensation of Hydrolyzed Cations

35

ð2:50Þ

2.5

Polymerization by Condensation of Hydrolyzed Cations

Two mononuclear complexes of a metal M, each comprising only one metal atom M, can react with each other in a polymerization reaction to form a polynuclear complex comprising two metal atoms. Such a reaction, also called condensation, can, depending on the metal and the conditions, keep proceeding so as to produce bigger polynuclear species. Polymerization generally occurs if at least one hydroxo ligand (OH) is bonded to the cation M. This hydroxo ligand belongs either to an aquo-hydroxo complex of the type [M-(OH)(H2O)N.1](z1)+ or to an oxo-hydroxo complex [M-(OH)(O)N1](z2N +1)+1 . We often simply write it as M-OH. As indicated in Eqs. (2.35) and (2.40), those OH ligands can be obtained by adding to the solution either of a base, in the case of metals forming acidic oxides, or of an acid, for metals forming basic oxides. The condensation occurring afterwards is responsible for the formation of one of two types of bridge between the two metal atoms.

2.5.1

Condensation by Olation

The first step of any condensation reaction always includes the construction of an “ol” bridge in which a hydroxo ligand is linked to two metal atoms (Jolivet et al. 1994). For low-charge cations, this occurs through a dissociative SN1 mechanism: H2 O  M $ M  þH2 O and then

ð2:51Þ

36

2 The Sol-Gel Chemistry of Oxides from Metal Salts

M  OH þ M $ M  OH  M

ð2:52Þ

A nucleophilic addition reaction (AN) is also possible when the coordination number of the metal can be increased, such as for [A1(OH)4]. In this case M  OH þ M  OH $ M  OH  M  OH

ð2:53Þ

As for the transition elements the mechanism is, as detailed in (2.54), an associative SN2 one:

ð2:54Þ

The condensation of the solution keeps proceeding, either until reaching a complex [M(OH)h(OH2)Nh](zh)+ (with h < z) which cannot undertake condensation anymore or until unlimited polymerization leads to formation of solid. Table 2.5 gathers different types of “ol” bridges known to exist for a few cations.

2.5.2

Condensation by Oxolation (Jolivet et al. 1994)

Whenever condensation occurs by oxolation, an “ol” bridge is first established between the two metal atoms, as shown in (2.55), before transforming to an “oxo” bridge, by an SN2 mechanism. According to this mechanism, the maximum coordination number of the metal M is satisfied in the intermediate complex. And both acids and bases can catalyze this reaction. When the formation of oxo bridges is catalyzed by a base, an OH anion attacks the partially charged hydrogen atom, Hδ+, of a hydroxo ligand belonging to the metal complex, as illustrated in reaction (2.56). This in turn increases the negative partial charge of the oxygen atom of this ligand, which becomes more nucleophilic and binds to another solvated hydroxyl group. Two water molecules, together with an OH anion, then separate from the complex which is now composed of an “oxo” bridge. Similarly, when an acid catalyzes the condensation reaction (2.57), an H+ cation attacks the oxygen atom of a hydroxo ligand belonging to the metal complex.

2.5 Polymerization by Condensation of Hydrolyzed Cations

37

Table 2.5 Different types of “ol” bridges Type of “ol” bridges μ2–OH

General formula M–(OH)–M

2μ2–OH

Examples [M2(OH)(OH2)X with M2+ ¼ Be, Mn, Co, Ni, Zn, Cd, or Pb [Zr4(OH)8(OH2)16]8+ [A113O4(OH)24(OH2)12]7+ [M4(OH)6(NH3)12]6+ with M3+ ¼ Cr3+, Co3+

μ3–OH

[M4(OH)4(OH2)]4+ with M2+ ¼ Pb, Co, Ni, Cd [Pb60(OH)6(OH2)]4+ [M3(OH)4(OH2)N]2+ with M2+ ¼ Sn2+, Pb2+ with M3 + ¼ Sc3+,Y3+,La3+, Ce3+

3μ2–OH

[Co2(OH)3(NH3)6]3+

After (Livage et al. 1988)

The newly formed H2O ligand gains in turn a positive partial charge, δ+, and interacts with another OH ligand, creating an intermediate H3O+ ligand. The latter ion then leaves while the metal complex finally comprises an “oxo” bridge:

ð2:55Þ

38

2 The Sol-Gel Chemistry of Oxides from Metal Salts

ð2:56Þ

ð2:57Þ

A direct nucleophilic addition, as illustrated in reaction (2.58), is also possible when the coordination number of a metal can be increased: an example concerns [VO4]3: ½M  O  þ  M  OH ! ½M  O  M  OH

2.5.3

ð2:58Þ

Condensation and the Partial Charge Model

As previously mentioned, condensation by direct nucleophilic addition AN of an oxo M-O ligand to the metal M of another complex C can occur, when the coordination number of the metal M in this second complex is not fully satisfied. But many condensation reactions in sol-gel synthesis occur by substitution of ligands. In this

2.5 Polymerization by Condensation of Hydrolyzed Cations

39

Table 2.6 Electronegativity and partial charges of some aquo species χ ¼ 2.657 χ ¼ 2.756

[Mn(OH2)6]2+ [Cr(OH2)6]3+

δ(Mn) ¼ +0.59 δ(Cr) ¼ +0.68

δ(H2O) ¼ +0.23 δ(H2O) ¼ +0.39

After Jolivet et al. (1994) Table 2.7 Electronegativity and partial charges of some oxo species [MnO4] [CrO4]

χ ¼ 2.533 χ ¼ 2.055

δ(Mn) ¼ +0.52 δ(Cr) ¼ +0.27

δ(O) ¼ 0.38 δ(O) ¼ 0.0.57

After Jolivet et al. (1994)

case, the partial charge model offers an interesting global view of the conditions in which such type of reactions may occur. In practice, it states that three conditions must be satisfied: – An electron charge donor called the nucleophile: This is the atom or molecular group with the most negative partial charge δ. – An electron accepter, called the electrophile: This is the metal cation M with a positive partial charge, but it was experimentally shown that this partial charge actually applies when δ+(M) > 0.3. – An easily separable leaving group: This is the ligand of metal M with the highest partial charge δ+. A consequence of the above statements is that pure aquo species, whose formula is [M(OH2)N]z+, do not carry a nucleophile and hence they cannot undergo any condensation reaction in water. Some examples are given in Table 2.6. Similarly, in pure oxo species whose formula is [MON](2Nz), a strong π bond links the oxygen atom to the metal. Since no oxygen can leave, condensation cannot take place. Table 2.7 gives some examples of such pure oxo species. For those complexes which contain hydroxo ligands, such as aquo-hydroxo [M (OH)h(OH2)Nh](zh)+ or oxo-hydroxo, [M(O)Nh(OH)h](2Nhz) complexes, the hydroxo ligand partial charge is negative (δ(OH) < 0). Hence this hydroxo ligand can act as a nucleophile. Because the aquo-hydroxo complexes also comprise a leaving group, a water molecule with δ(H2O) > 0, an “ol” bridge can directly form through an SN1 mechanism (reaction 2.51). If the metal is a transition element, an SN2 mechanism rather applies as the H2O leaving group is very labile. For the oxo-hydroxo complexes, an “ol” bridge is first formed by attack of an oxygen from one OH ligand onto another M complex. A proton is then transferred from the “ol” bridge to a terminal OH. Hence a H2O group can depart and leave an oxo bridge between the 2M atoms. Overall, the mechanism is of the type SN2. These complexes cannot anymore undergo condensation by ligand substitution. As previously stated, it was experimentally determined that δ(M) must be >0.3 for condensation to occur. In fact, even though χ ¼ 2.533 and δ(O) ¼ 0.48 in [PO3(OH)], δ(P) ¼ +0.03, the partial charge of the metal is too low and there is no polymerization. This additional condition applies in particular to silicon which

40

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Table 2.8 Partial charge model characteristics of a few mononuclear complexes of Si of the type [SiO4H8h](4h)+

h¼6 h¼5 h¼4 h¼3

Complex [SiO2(OH)2]2 [SiO(OH)3] [Si(OH)]0 [Si(OH)3(OH2)]+

χ 2.10 2.37 2.8 2.74

δ(OH) 0.55 0.30 0.12 +0.03

δ(Si) +0.20 +0.35 +0.47 +0.56

After Jolivet et al. (1994)

undergoes condensation by oxolation. Table 2.8 reports a few mononuclear complexes of Si. The silicon complex for h ¼ 6 exists only in strongly basic medium (pH ¼ 12) and condensation is limited to the formation of dimers: 

SiOðOHÞ3



 2  3 þ SiO2 ðOHÞ2 ! Si2 O4 ðOHÞ3 þ H2 O

ð2:59Þ

In this dimer χ ¼ 2.183, δ(OH) ¼ 0.22, and δ(Si) ¼ +0.25 < 0.3. The partial charge of the metal is too low for condensation to continue. The h ¼ 5 Si complex can also make the following dimer by condensation:    2 2 SiOðOHÞ3 ! Si2 O3 ðOHÞ4 þ H2 O

ð2:60Þ

In this dimer χ ¼ 2.346, δ(OH) ¼ 0.33, and δ(Si) ¼ +0.34 > 0.3. In this case, the partial charge of Si is high enough for condensation to keep going on.

2.6

Complexation by Anions

The anions brought to the solution either with the metal salt or with other reagents are Lewis bases like in competition with water and the other organic additives. They are therefore also in competition with the hydroxo, oxo, and aquo ligands to participate in metal complexation. The stability and lifetime of the corresponding complexes depend on their nucleophilic strength. In some cases, such as for phosphates, chromates, and sulfates, the complex is very stable and the anion stays attached to the metal. In other frequent cases, if the anion may participate only temporarily to the metal complex, this may be long enough to orientate the future solid structure.

2.6 Complexation by Anions

2.6.1

41

Complexation by Anions X2 and the Partial Charge Model (Jolivet et al. 1994)

The complexation reaction of a solvated cation, [M(OH2)N]z+, with a monodentate anionic group X can be written as  zþ  ðz1Þþ M  ðH2 OÞN þ X $ M  XðOH2 ÞN1 þ H2 O  zþ  equivalent to M  ðOH2 ÞN1 X

ð2:61Þ

The metal complex containing the X anion group only forms when the algebraic partial charge of X is such that δðXÞ > 1

ð2:62Þ

Otherwise an anion X separates from the complex. This condition can be rewritten using electronegativity values: χ ðX Þ < χ



M  ðOH2 ÞN1

zþ

ð2:63Þ

For a molecular group HX, the complexation reaction is slightly different:  ðz1Þþ  ðz1Þþ þ HX $ M  XðOH2 ÞN1 M  ðOHÞðH2 OÞN2  ðz1Þþ equivalent to M  ðOHÞðHXÞðH2 OÞN2

ð2:64Þ

In this case the right-hand side product will form only if δðHXÞ < 0

ð2:65Þ

Otherwise an HX molecular group leaves the complex. Equation (2.65) can be reformulated using electronegativity numbers as follows: for HX to remain attached to the metal M, the electronegativity must be such that χ ðHXÞ > χ

 ðz1Þþ

M  ðOHÞðH2 OÞN2

ð2:66Þ

The molecular group leaves when it cannot keep its excess negative charge which enables it to bind to the metal M.

42

2 The Sol-Gel Chemistry of Oxides from Metal Salts

2.6.1.1

Example: Complexation of [Fe(OH)2(OH2)4]+ by Bidentate Anions (Jolivet et al. 1994)

A bidentate anion such as hydrogenocarbonate, HCO3, can replace two of the water molecules of the iron complex [Fe(OH)2(OH2)4]+. Such anions are a key factor to limit the hydrolysis of metal cations: they may sometimes constrain the metal complex to a specific coordination and induce the formation of a particular solid phase. Calling X a generic bidentate anion, the complexation reaction equivalent to (2.61) is  þ  0 FeðOHÞ2 ðH2 OÞ4 þ X $ FeXðOHÞ2 ðOH2 Þ2 þ 2 H2 O  þ equivalent to Fe  ðOHÞ2 ðOH2 Þ2 X

ð2:67Þ

As mentioned previously, X separates from the metal complex when χ ðXÞ > χ



Fe  ðOHÞ2 ðOH2 Þ2

þ

χX

ð2:68Þ

¼ 2:68 ¼ χ X

ð2:69Þ

The electronegativity limit to separation is given by χ ðXÞ ¼



Fe  ðOHÞ2 ðOH2 Þ2

þ

Similarly, considering a molecular group HX, the complexation reaction equivalent to (2.64) is 

0 Fe  ðOHÞ3 ðH2 OÞ þ HX

$

equivalent to



0 FeXðOHÞ2 ðOH2 Þ2  0 Fe  ðOHÞ3 ðH2 OÞ HX

ð2:70Þ

and the molecular group HX leaves the complex when χ ðHXÞ < χ



0

Fe  ðOHÞ3 ðOH2 Þ χ HX

ð2:71Þ

As for the X anion, the electronegativity limit to separation is given by χ ðHXÞ ¼ χ

 0

Fe  ðOHÞ3 ðOH2 Þ ¼ 2:53 ¼ χ HX

ð2:72Þ

Overall, the complexation of [Fe(OH)h(OH2)4.h](3h)+ with h ¼ 2 by a bidentate anion X such as HCO3 implies some conditions which are summarized in Fig. 2.10, altogether with the electronegativity of HCO3 (χ X) and H2CO3 (χ HX). As a consequence of Eqs. (2.68) and (2.71), the requirements for X and HX to

2.6 Complexation by Anions

43

Fig. 2.10 Necessary conditions for the complexation of [Fe(OH)2(OH2)4]+ by X ¼ HCO3 as implied by the partial charge model Table 2.9 X and HX electronegativity of different bidentate anionic groups together with the partial charge of X and HX in [FeX(OH)2(OH2)2] X χ(X) χ(HX) δ(X) δ(HX)

CH3COO 2.24 2.49 0.14 +0.07

H2PO4 2.49 2.71 0.64 0.38

HCO3 2.49 2.79 0.71 0.45

HSO4 2.64 2.88 0.94 0.65

NO3 2.76 3.08 1.10 0.80

ClO4 2.86 3.10 1.26 0.94

After Jolivet et al. (1994)

remain in the complex are fulfilled so that the [Fe(HCO3)(OH)2(OH2)2]0 complex can actually form. The pH of a solution monitors the electronegativity of its species. Thus, instead of comparing the electronegativities of χ(X) and χ(HX) with those of the metal complex, χ X and χ HX, it is easier to determine the pH range in which complexation occurs and whether the electrolyte HX permits in fact to reach this pH. The pH range corresponding to a complexation with H2CO3 is, for instance, pHx ¼ 1.5 < pH < 5.8 ¼ pHHX. Table 2.9 reports the partial charge and electronegativity of different X anionic groups. According to this table, no complex of the type [FeX(OH)2(OH2)2]0 can form with the acetate group (X ¼ CH3COO) because χ(HX) < 2.53 ¼ χ HX. In such a complex we would have δ(HX) > 0, so that the molecular group HX (CH3COOH) would leave. Similarly, no such complex can form with the anion groups NO3 and C1O4 since χ(X) > 2.68 ¼ χ X. In such a complex, we would have δ(X) < 1 so that the anion X would depart instead of the molecular group HX. Overall, only the anions with X ¼ H2PO4, HCO3, and HSO4 can form stable complexes with Fe for h ¼ 2. Similar calculations and reasoning can be made for all iron complexes of the type [FeX(OH)h(OH2)4.h](3h1)+, thus determining, for the different value of h, the anions that can indeed remain bonded to the metal.

44

2.6.2

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Overall Complexation of a Metal M by Anions

By repeating the previous derivations with all possible complexes, in order to determine the possible complexation of all possible bidentate anions, it is possible to predict which complexes could be formed when only one Xn anion substitutes for water molecules linked to a solvated metal cation of the type [M(OH2)N]z+. When such a complexation occurs, the general formula of the metal complex can be written as [MX(OH)h(OH2)Nα–h](z–n+h)+. For this purpose, it is necessary to compare the electronegativities both of [XHq](n–q)– with [M(OH)h+q(OH2)N–h–α–q](z–h–q)+ ¼ χ HqX and of Xn– with [M(OH)h(OH2)N.h](z–h)+ ¼ χ X so as to, respectively, establish whether [XHq](n–q)– or Xn– will leave the complex. Similar calculations can be applied to all metal complexes, even if the metal is a polynuclear species. For example, Fig. 2.11 shows the results obtained for Ti, which fully agree with the experimental data. Matijevic (1985), for instance, reported that anions such as SO42 and PO43 favor the formation of big polymeric metal complexes and, hence, of amorphous materials. On the other hand, Cl, NO3, and ClO4 favor small polymers with more crystalline structures. Since the complexes they form are the “building blocks” of the solid, the anions are, in fact, quite important to monitor the structure of a sol-gel-made solid. While anions offer a large diversity in the structure of sol-gel materials, they can however present some inconvenience. Nitrates, for example, usually crystallize during drying and may consequently destroy the material homogeneity achieved

Fig. 2.11 pH domains in which titanium complexes with various anions (adapted from Livage et al. (1990))

2.6 Complexation by Anions

45

during sol-gel processing (MacCarthy and Roy 1971). Furthermore, after hydrolysis, anions usually remain as impurities under the form of acids, such as HNO3 or HC1 (Segal 1984). The material must therefore be purified more or less efficiently by one of the following techniques. – Addition of a water-immiscible solution containing long-chain amines: The amines retain the hydrolytic acid while the anion-to-cation ratio can easily decrease down to 0.25. – Extensive washing of the gelatinous precipitate followed by its re-dispersion (its peptization): After re-dispersion with nitric acid, the anion-to-cation ratio can fall close to 0.2. This method is specially used with Al and Ce (Woodhead 1971). – Thermal treatment at a moderate temperature, e.g., 500  C (Hardy 1968): This lowers the anion-to-cation ratio down to 0.05, but with nitrates this may be a dangerous explosive treatment. After such purification treatment, a much smaller quantity of electrolyte will be necessary to re-disperse the powder into a colloidal sol.

2.6.3

Formation of a Solid Phase

Up to this point, the chemical transformations concerned metal complexes in solution. Yet, a solubility limit often exists, beyond which a solid phase will precipitate. This solid is formed by the complex in solution which first reaches its solubility limit. A simple example is the transformation of hydroxylated polynuclear complex into solid hydroxide according to reaction (2.73) xMðOHÞz ðsÞ þ ðxz  yÞHþ $ Mx ðOHÞy ðxzyÞþ þ ðxz  yÞH2 O

ð2:73Þ

The corresponding equilibrium constant is

K sxy ¼

h i Mx ðOHÞy ðxyzÞþ ½H þ 

xzy

ð2:74Þ

When two or more polynuclear complexes with different x and y coefficients react to form a solid hydroxide, the total metal concentration at saturation is msatd M ¼

X

xK sxy ½Hþ 

xzy

ð2:75Þ

This equation shows that, as was already mentioned, the pH of the solution is an important factor in the formation of a solid. Yet it is not the only factor. As was seen previously, the nature of the anion together with the temperature and the nature and

46

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Fig. 2.12 Relation between the equilibrium constants Kn and Ks10 of cations. The line corresponds to (K11)z Ks10 ¼ 105.6 (adapted from Baes Jr. and Mesmer (1976))

concentration of the metal cations are also significant parameters. In fact, the formation of metal complexes is often easier at higher temperatures. Precipitation of a solid itself is mostly due to electrostatic interactions between molecules and is described in more detail in a further chapter. But this electrostatic character is particularly well illustrated by the good correlation between K11, which is the constant of the first deprotonation reaction (2.35) and Ks10, the equilibrium constant of reaction (2.73) at saturation, for x ¼ l and y ¼ 0 (Fig. 2.12). These two reactions can be written as Mzþ þ H2 O $ ½MOHðz1Þþ þ Hþ

ð2:76Þ

with equilibrium constant 

K 11 and

 MOHðz1Þþ ½Hþ  ¼ ½Mzþ 

ð2:77Þ

2.6 Complexation by Anions

47

MðOHÞzðsÞ þ zHþ $ Mzþ þ zH2 O

ð2:78Þ

with the constant K s10 ¼

½Mzþ  z ½H þ 

ð2:79Þ

The correlation between these two constants follows the statistical equation K ¼ ðK 11 ÞZ K s10  105:6

ð2:80Þ

and the reaction corresponding to this new constant is MðOHÞzðsÞ þ ðz  1ÞMzþ $ z½MOHðz1Þþ

ð2:81Þ

With equilibrium constant K¼

 z MOHðz1Þþ z1

½Mzþ 



MOHðz1Þþ ½Mzþ 

!z  ½Mzþ 

ð2:82Þ

According to this equilibrium constant, it appears necessary to decrease the concentration of [Mz+] in order to increase the ratio of the concentrations of [MOH(z–1)+] to [Mz+] in solution, so as to increase the number of M complexes able to participate in condensation reactions while maintaining equilibrium with the solid phase. Globally, soluble hydrolyzed species form more favorably when the concentration of metal cation is low, and this low concentration depends on the metal M. According to Eq. (2.75), the total metal concentration at saturation msatrd M , of soluble species, decreases as the pH increases, until a saturation minimum is reached which depends on each mononuclear complex and pH. On the other hand, when the pH becomes high enough, the anions participate in the formation of the complexes and consequently increase again their solubility. Besides, the ionic force of the solution also increases, which induces the formation of dimers. Hydroxylated monomers and dimers in turn favor crystal growth in specific crystalline ionic materials. In practice, several soluble species generally react simultaneously to form a solid, so that it is often difficult to duplicate a given material with a specific structure. This difficulty often lies in the ability to add a base to the solution in an identical manner. As a matter of fact, the chemical reactions occurring around a basic drop change with an increasing distance from the drop. For instance, a drop of NaOH added to a solution of Fe(III) first deprotonates the aquo ligands of [Fe(OH2)6]3+ into hydroxo ones, and then, farther away, into an oxo ones. This example, illustrated in Fig. 2.13, corresponds to the following deprotonation reaction:

48

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Fig. 2.13 Reactions occurring at an increasing distance from an NaOH drop when added to an Fe (III) aqueous solution (adapted from Schneider (1984))

 ð3iÞþ FeðOHÞi ðOH2 Þ5i þ OH $



FeðOHÞiþ1 ðOH2 Þ4i þ H2 O

2i þ ð2:83Þ

During polymerization, the mononuclear species bind to each other so as to form polynuclear complexes. Different types of polynuclear complexes can therefore be produced depending on the initial monomers. In order to predict which complexes are formed, it is necessary to admit that deprotonation is a relatively fast reaction compared to polymerization. Furthermore, the deprotonation rate of the bigger polynuclear species is generally smaller than that of the monomers, so that the bigger ones often have a longer lifetime than the smaller ones. Practically, depending on the manner in which mixing is carried out, and hence on the size of the basic drops and on the distance separating them, three extreme cases of polymerization can be considered: (a) No polynuclear complexes are formed. (b) Polynuclear species are formed but in so small proportion, that they remain in solution.

2.7 Sol-Gel Behavior of Cations as a Function of Their Nature

49

Fig. 2.14 NaOH titration of an A1(NO3)3 solution at a concentration of 0.07 M (after Vermeulen et al. (1975))

(c) Polynuclear complexes are produced in large enough quantities to agglomerate into a solid. The above analysis explains that the manner in which NaOH was added was responsible for the formation of different kinds of iron products. Eventually, some complexes will lead to the formation of polymeric gels while others will transform to more or less hydrated colloidal particles (Magini 1977). Schneider demonstrated that, for instance, when a base was added very slowly to a solution of Fe(III), sols that were stable for months were produced. If the base was added rapidly, however, an amorphous precipitate may immediately form (Schneider 1984). As mentioned before, the anions are moreover as important as the mixing technique: a precipitate is   obtained more readily with SO2 4 than with NO3 and ClO4 (Segal 1980). The solubility limit of the polynuclear complexes also depends on the nature of the cation M and on the other complexing additives present in the solution. For example, when an aluminum nitrate salt is used, a buffer effect occurs during the titration of a base. The pH of the solution remains constant along a large plateau as the base is gradually added (Fig. 2.14). This buffer zone corresponds to the progressive formation of bigger aluminum polymers. When no more hydroxide can be formed, the pH again rises steeply.

2.7

Sol-Gel Behavior of Cations as a Function of Their Nature

Studies on the hydrolysis of cations were published by Baes Jr. and Mesmer (1976) and by Livage et al. (1988). Hydrolysis is a complex technique which, depending on the conditions, gives rise to a great variety of colloidal structures ranging from metals to hydroxides and including oxides and oxyhydroxides. Of those, the colloidal oxides are often so strongly solvated that the water molecules are tightly bonded

50

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Fig. 2.15 Charge versus electronegativity. This relation shows the nature of the species formed by cations in aqueous solutions (adapted from Henry et al. (1990))

to the complex and it is difficult to know the exact chemical formula of the particle. These solids are therefore simply referred to, in this text, as “hydrous oxides” regardless of their actual structure (Matijevic 1984). The behavior of cations in aqueous solutions can however be summarized according to their nature and with respect to their final type of ligands as in Fig. 2.15.

2.7.1

Cations with Valence I

These cations have a low charge, a low electronegativity, and an oxidation number of I. They are not hydrolyzed in solution but remain as solvated cations of the form [M(H2O)N]Z+. They form basic oxides which liberate OH anions when reacting with water. An example is Na.

2.7.2

Cations with Valence II

These cations have an oxidation number of II and a slightly higher charge and electronegativity than those with valence I. They consequently undergo condensation more extensively and precipitate in the form of hydroxides with formula M (OH)2. In solution, most of those cations (Mn, Co, and Ni) form compact tetramers which further transform into solid hydroxides with lamellar structures such as brucite, Mg(OH)2. Cu creates linear polymers which crystallize as Cu(OH)2 in a lamellar structure similar to that of boehmite, AIO(OH).

2.7 Sol-Gel Behavior of Cations as a Function of Their Nature

51

Gels are feasible, such as with ZnO by an aqueous sol-gel method using a zinc acetate-citric acid-ammonia system known as the Pechini method (Werde et al. 2002; Mondelaers et al. 2002). This complexation method is described in a further special paragraph. A sol could be obtained which gelled by heating.

2.7.3

Cations with Valence III

These cations having an oxidation number of III, such as Al, Fe, Cr, Se, Y, and rare earth elements, have a very rich aqueous chemistry. They easily polymerize to a variety of different polycations, at the origin of various solid phases, each more or less polymeric (Matijevic 1984). These phases are produced by a succession of olation and oxolation reactions which lead to the formation of several polynuclear complexes derived from various mononuclear species of the type [MOx(OH)h(H2O)N.h.2x](z–h–2x)+. These complexes later form oxyhydroxide solids. B(III) has a specific behavior (Jolivet et al. 1994). Contrary to most trivalent elements, it has a high electronegativity and hence produces oxolated species of the type [MOx(H2O)N.2x](z–2x)+ which later forms polynuclear molecules (Fig. 2.15). Its final hydrated solid oxide has a general formula MOz/2∙xH2O. Furthermore, boron presents two different monomers: the borate anion [B(OH)4] and boric acid B (OH)3 in which the metal, respectively, has a tetragonal and a trigonal coordination. Condensation in water can only occur if those two monomers are present and if the pH is in the range of 7 < pH < 11. The following reaction is a typical example of the corresponding condensation: 

BðOHÞ4



þ BðOHÞ3 !

  B2 OðOHÞ5 þ H2 O

ð2:84Þ

Dimers, trimers, as well as tetramers form only if those requisites are fulfilled. The polymers are then composed of rings comprising both tetragonal and trigonal boron atoms. At pH 3 are dimers consisting of a double-“ol” bridge. The mechanism of this dimerization condensation illustrated in (2.85) has for equilibrium constant K22 ¼ 1.12  107:

52

2 The Sol-Gel Chemistry of Oxides from Metal Salts

ð2:85Þ

This dimer is not detected by NMR technique, contrary to the corresponding trimer [A13(OH)4(H2O)9]5+. When formed, the trimer immediately loses one proton according to the following reaction: 

A13 ðOHÞ4 ðH2 OÞ9

5þ

!

 4þ A13 OðOHÞ3 ðH2 OÞ9 þ Hþ

ð2:86Þ

If in a basic environment, it then reacts to liberate three water molecules: 

A13 OðOHÞ3 ðH2 OÞ9

4þ

þ 3 OH !



A13 OðOHÞ3 ðO2 H3 Þ3 ðH2 OÞ3 þ 3 H2 O

þ ð2:87Þ

This reaction is necessary for the following polycondensation to occur. With increasing pH, other polynuclear complexes such as [Al6(OH)15]3+ and [Al8(OH)22]2 + are formed (Cotton et al. 1999). In a further step, at low concentration ( 80  C, the big polycation composed of 13 Al atoms remains stable. It later

54

2 The Sol-Gel Chemistry of Oxides from Metal Salts

transforms into a transparent layered gel with a structure similar to that of boehmite AIO(OH) (Fig. 2.16) (Nazar and Klein 1988; Nazar et al. 1988). In strongly basic medium, the aluminum is present in the solution as tetrahedral aluminate anions, [A1(OH)4] (Cotton et al. 1999). When an acid is added, the latter anion transforms into an aquo-hydroxo complex according to the following protonation reaction:    0 A1ðOHÞ4 þ H3 Oþ ! A1ðOHÞ3 ðH2 OÞ þ H2 O

ð2:89Þ

In a further step, this aquo-hydroxo complex transforms into the tetramer [A14(OH)12(H2O)5]0, which creates the necessary nucleus for growth of a boehmite gel. Anions can, of course, modify significantly this intricate chemistry. In particular, acetate, nitrate, chloride, and sulfate anions alter the chemical formula of the dimers (Akitt and Farthing 1981; Singh 1982). One consequence is that the rate of poly 2 merization decreases from NO 3 to Cl and SO4 .

2.7.3.2

Other Cations

Contrary to Al, Cr and Fe do not produce polycations containing 13 metal atoms. Their trimer only transforms to tetramers. In the case of Cr(III), [Cr(H2O)6]3+ initially present in the aqueous solution slowly transforms first into [Cr2(OH)2(H20)8]4+, then [Cr3(OH)4(H2O)9]5+, and finally [Cr4(OH)6(H2O)10]6+. When a base is added, the blue hydroxide Cr(OH)3(H2O)3 then precipitates. In a last step, oxo ligands are substituted for the aqua ligands in order to form the final tetramer, [Cr4O(OH)5(H2O)10]5+. This last complex produces green gels with a global composition CrO(OH) (Stuenzi and Marty 1983). With time, this chemical formula changes into Cr2O3. In the case of Fe(III), the oxo ligands enter the complex in a similar manner as with Cr(III) and the “gelatinous” precipitate obtained is called ferrihydrite. Its composition is variable but can be summarized by the general formula [FepOr(OH)q](3p–2r–q)+ (Schneider 1984). During aging, these gels transform either into α-FeO(OH), called goethite, or into α-Fe2O3, called hematite. When mixed Fe (II)/Fe(III) solutions are used, magnetite Fe3O4 gels with an inverse spinel-type structure are produced. Indium(III) oxide (In2O3) is an important component of transparent and electrically conducting indium tin oxide (ITO). A variety of In salts were investigated to prepare such films by sol-gel. These include the sulfate (In2(SO4)3∙6H2O) (Furusaki and Kodaira 1991), chloride (InCl3) (Kanbara et al. 1990; Perez-Maqueda et al. 1998), and nitrate (In(NO3)3) (Furusaki et al. 1994; Tahar et al. 1997). These precursors were hydrolyzed with aqueous ammonia or sodium hydroxide. In all cases, indium trihydroxide (In(OH)3) was precipitated and a sol was obtained by peptizing the precipitate with various acids (hydrochloric, nitric, acetic), and InCl3.

2.7 Sol-Gel Behavior of Cations as a Function of Their Nature

55

At last, the noble metals Ru, Rh, Pd, Pt, Ag, and Au which can make valence III compounds can be precipitated as metal colloids (Baes Jr. and Mesmer 1976).

2.7.4

Cations with Valence IV

These cations, such as Ti, Zr, and Hf, are only soluble in a very narrow pH range and build oxo-hydroxo complexes with a general formula MOx(OH)y (Fig. 2.15). Their stability decreases as the size of the cation increases. On the other hand, Si, Ge, Sn, and Pb form more covalent bond with the oxo ligands (Baes Jr. and Mesmer 1976; Jolivet et al. 1994). They are soluble only in strongly basic solutions in which they build oxo or oxo-hydroxo anions. Furthermore, their oxides are acidic and their hydroxides M(OH)4 unstable. They therefore spontaneously dehydrate and end in the formation of hydrated oxide MO2∙nH2O.

2.7.4.1

Case of Zr

As indicated above, Zr does not produce a hydroxide but an oxo-hydroxide (Cotton et al. 1999). Zr acetate is often used as the initial soluble salt precursor. The Zr4+ (aq) cation is only stable at low concentrations (~104 mol L1) and low pH and initially a solution of Zr(IV) does form the stable tetramer [Zr4(OH)8(H2O)16]8+ (Livage et al. 1992; Cotton et al. 1999; Geiculescu and Rack 2002) (Fig. 2.17). However, further condensation by slow oxolation reactions produces a white and gelatinous precipitate of formula ZrO2.x(OH)2x∙nH2O with varying n. The

Fig. 2.17 Schematic structure of [Zr4(OH)8(H2O)16]8+ ion (adapted from Cotton et al. (1999))

56

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Fig. 2.18 Formation of mixed “ol-anion” bridges with Ti cations

experimental conditions determine whether either cubic, tetragonal, or monoclinic ZrO2 is finally obtained. ZrOCl2∙8H2O has also been used to synthesize ZrO2 nanopowders by hydrothermal process, further peptized to a ZrO2 sol (Clearfield 1990; Julbe et al. 1993).

2.7.4.2

Case of Ti

Water-soluble titanium salts comprise halides such as TiCl4 or titanium oxysulfate TiO(SO4) which presents a structure made of polymeric Ti-O-Ti-O- chains (Cotton et al. 1999). Hydrolysis of the Ti4+ cations in a strongly acidic solution near the boiling point produces polymers consisting both of hydroxo and oxo bridges as in the octamer [Ti8O8(OH)12(H2O)2]4+ (Santacesaria et al. 1986). Complexes can also form with ligands other than OH. For example, sulfate produces with Ti the species Ti(OH)3(HSO4)(H2O)2 and [Ti(OH)2(HSO4)(H2O)2]+ (Fig. 2.18). Similar bridges are formed with chlorine anions such as in [Ti(OH)(H2O)Cl]4 and [Ti(OH)2Cl4]2 (Ciavatta et al. 1985). Further oxolation produces the rutile or anatase forms of TiO2 and a diagram of formation of these two crystalline forms was proposed by Yamabi and Imai (2002) (Fig. 2.19). At last, the peroxo anions [O–O]2 form water-soluble complexes characterized by an orange coloration with Ti4+ cations, but only in strongly acidic conditions (Cotton et al. 1999).

2.7.4.3

Case of Sn(IV)

Sn(IV) salts can be hydrolyzed to an amphoteric “α-stannic acid,” which is soluble in aqueous acid or base solutions, but slowly transforms to “β-stannic acid” or “metastannic acid.” The latter ones are insoluble in solutions of ordinary acids and bases, so that nanoparticles related to some form of hydrated crystalline rutile (Bailar et al. 1973) precipitate. However it is possible to peptize (see Chap. 5) such particles with ammonia at about pH 7 under ultrasonic vibration to obtain a transparent diluted sol (Ohya. 2016). It is also possible to modify the nanoparticle surface with additives such as β-alanine and NH2CH2CH2COOH or to use surfactants such as tetramethylammonium hydroxide under ultrasonication (Goebbert et al. 1999).

2.7 Sol-Gel Behavior of Cations as a Function of Their Nature

57

Fig. 2.19 Calculated “stability” diagram of the aqueous Ti4+ solution and experimental phase made by sol-gel (adapted from Yamabi and Imai (2002))

2.7.4.4

Case of Si

The synthesis of silica gels from aqueous sodium silicate (water glass: sodium metasilicate Na2SiO3) is itself a domain of interest, initially used for instance by Kistler (1932). This is a cheap precursor and an industrial process based on it was early developed by BASF (Broecker et al. 1986). A detailed review on the chemistry of alkaline silicate solutions, in which Na can be replaced by Li or K, was recently published in the Handbook of Sol-Gel Science and Technology by Vidal et al. (2016). To obtain such alkaline silicate solutions, alkali-silicate glasses are first prepared by reaction between silica and sodium carbonate or sodium sulfate (Iler 1979), or by silica fume in an alkaline solution (Steins 2014). The glass can be dissolved in water with the help of steam or pressure (Tognonvi et al. 2010). The alkaline silicate solutions which were obtained recently found applications as binder of sand (Talaghat et al. 2009; Vivier 2010) and as activation components in so-called geopolymers. These geopolymers are made by the dissolution of reactive natural aluminosilicate precursors (e.g., kaolin) in an alkaline solution at a temperature malic > oxalic ¼ succinic acid. It must however be noted that the carboxylate anions often remain in the solid product, precipitate, or gel, and must often be eliminated in a further step by thermal treatment. With easily hydrolyzable cations such as Ti, Nb, Ta, Zr, and Bi, it is possible to use other multidentate chelating agents, such as ethylenediaminetetraacetic acid (EDTA), to avoid precipitation of a hydroxide. This complexation method was applied to synthesize the Bi-2223 superconductor (Mao et al. 1996). Other watersoluble complexes investigated comprise citratoperoxotitanates (Kakihana et al. 2001), citratoperoxoniobate (Narendar and Messing 1997), and titanium lactate (Kakihana et al. 2004).

2.8.3

The Pechini Method

In 1967, Pechini developed a gel method known as the Pechini method (Pechini 1967) recently reviewed by Petrykin and Kakihana (2016). This method is a

2.8 Metal Salt Mixing

63

refinement of the carboxylic acid complexation route, as it rests on the chelation of metal cations with a carboxylic acid added in excess, such as citric acid (CA), except that a diol such as ethylene glycol (EG) is added as a solvent. Regarding the complexation scheme with citric acid, for instance, the middle carboxylic group (–mCOOH) of citric acid can very easily lose a proton H+ (pK1 ¼ 2.91) (Harris and Martell 1976) so that the pH of citric acid aqueous solution is usually in the range of 0–2 depending on the concentration. On the other hand, the terminal carboxylic groups (-tCOOH) are less acidic (pK2 ¼ 4.36 and pK3 ¼ 5.74) (Harris and Martell 1976) and the dissociation only becomes significant at higher pH. Finally, at very high pH the hydroxy group of citric acid may become deprotonated (pK4 ¼ 10.96) (Grigor’eva and Golubeva 1975). Moreover, hydrogen bonds can also easily form between carboxylic groups and hydroxy groups. So that stable five- and six-member rings may easily form in metal citrate complexes. A polyesterification of the citrate complex with ethylene glycol can next occur, which can be accelerated by heating at 100–130  C to also favor the esterification reaction of the remaining free citric acid and ethylene glycol (2.94). The metal complexes finally end up blocked in a plastic gel-like product from which the excess ethylene glycol can be removed by evaporation: (CH2tCOOH)(C(OH)mCOOH)(CH2tCOOH) + OH(CH2)2OH ® H2O + (CH2COOH)(C(OH)COOH)(CH2COOCH2)2OH

ð2:94Þ

This Pechini complexation method was studied in detail for the synthesis of BaTiO3, reviewed by Petrykin and Kakihana (2016). These authors indicate that alkaline earth citrate complexes are quite unstable and chelation by citric acid may only occur at high pH, while transition metals such as Ti form more stable chelate complexes. However, when both barium and titanium are mixed in a citric acid solution, they participate in the formation of the bimetallic complex BaTi(C6H5O7)3 (or more simply BaTi(CA)3), in which each CA group participates in the chelation of both Ba and Ti atoms (Hutchins et al. 1987; Kakihana et al. 1999). The stability of this complex is such that it can be separated in the pure form and a structure proposed by Petrykin and Kakihana is shown in Fig. 2.23. The method was extended to similar compounds in replacing Ba by Ca, Sr, or Pb, and Ti by Zr. For instance, Araujo et al. (1999) used a mixture of citric acid and ethylene glycol to complex nitrates derived from the oxide dissolved in nitric acid to synthesize PZT ceramics.

2.8.3.1

Possible Future Developments Regarding Cation Complexation

The possible range of interesting complex precursors is huge. To screen among the multiple synthesis variables, one approach is to use the so-called fractional factorial design, such as applied to find interesting electrode material synthesis protocols

64

2 The Sol-Gel Chemistry of Oxides from Metal Salts

Fig. 2.23 Molecular structure of BaTi(C6H5O7)3 complex (adapted from Petrykin and Kakihana (2016))

(Terezo and Pereira 2000; Rosario and Pereira 2002). This technique is useful when the number of possible synthesis parameters is large; it consists of the statistical planning of a matrix of synthesis experiments, to reduce the total number of these experiments. Another approach recently transferred from biochemistry to materials science is the sol-called combinatorial chemistry (Xiang et al. 1995). It screens through a very large range of composition ratio in a given complex system, by synthesizing a very large library of samples (up to 25,000) in the form of thin films made for instance by inkjet printing techniques, in a single experiment (Danielson et al. 1997). The main problem is then to choose the property which must be measured in this library, for instance a catalytic property. Such a combinatorial technique was applied for the Pechini synthesis of phosphor materials (Reichenbach and McGinn 2001; Kim et al. 2002). In a quite different field, an extreme case of very sophisticated cation complexation concerns the so-called metal-organic-framework (MOF) materials. These are one-, two-, or three-dimensional coordination compounds made by complexation of inorganic clusters with organic ligands. These ligands may have a structure such that an ordered network of regular pores is formed, rather than a random network of pores with a wide range of sizes as in gels. But this domain is outside the scope of this book. The interested reader is advised to focus on reviews of this field, such as the one published by Gangu et al. (2016).

References J.W. Akitt, A. Farthing, J. Chem. Soc. Dalton Trans., 1624–1628 (1981) E.B. Araujo, J. Bratusek, D. Garcia, J.A. Eiras, J. Mater. Sci. Lett. 18, 1961–1962 (1999) P. Atkins, Physical Chemistry, 5th edn. (W.H. Freeman & Company, New York, 1994) C.F. Baes Jr., R.E. Mesmer, The Hydrolysis of Cations (Wiley, New York, 1976) J.C. Bailar, H.J. Emeleus, R. Nyholm, A.F. Trotman-Dickenson, Comprehensive Inorganic Chemistry. 2 (Pergamon, Oxford, 1973), p. 64 T.F. Baumann, S.O. Kucheyev, A.E. Gash, J.H. Satcher Jr., Adv. Mater. 17, 1546–1548 (2005)

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Chapter 3

The Sol-Gel Chemistry of Oxides from Alkoxides

3.1

Introduction

Besides metallic salts, metal alkoxides constitute a major class of oxide sol-gel precursors. Their generic chemical formula can be written as M(OR)n, which indicates that they are a combination of a cation M with an alcohol group ROH. An example is aluminum ethoxide A1(OC2H5)3. The solution chemistry of these alkoxides is different from that of metal salts, mainly because water is now mostly a reactant added in a precise molar ratio to the precursor, while the solvent is usually an organic liquid which depends on the alkoxide, in part because the alkoxide and water both need to be soluble in this solvent. New non-hydrolytic processes even do not use any more water at all. Alkoxide precursors permit to generally avoid the presence of anions, which are mostly impurities to be eliminated when using metal salts. Hence more pure oxides can be synthesized. Moreover the diversity of alkoxides and derived precursors is extremely large, particularly for silicon. Besides, they can always be mixed with other metal salt precursors when needed.

3.2 3.2.1

Structure and Properties of Alkoxides Chemical Nomenclature of Alkoxides

In-depth reviews of these particular sol-gel precursors were published by Bradley et al. (2001), Turova et al. (2002), and Kessler (2016). The reader is advised to refer to these publications for a detailed and comprehensive review on these precursors. Because many different alcohols exist, a great variety of alkoxides can be produced for each metal. The nomenclature of the simplest alkoxides is summarized in Table 3.1, where a single alkoxy ligand is shown for each metal M, for simplicity.

© Springer Nature Switzerland AG 2020 A. C. Pierre, Introduction to Sol-Gel Processing, https://doi.org/10.1007/978-3-030-38144-8_3

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Table 3.1 Nomenclature of alkoxides Alkoxide Methoxide

Abbreviation for OR OMe

Ethanol C2H5OH

Ethoxide

OEt

1-Propanol (n-propanol) C3H7OH

1-Propoxide (n-propoxide)

OnPr

2-Propanol (isopropanol) C3H7OH

2-Propoxide (isopropoxide)

OiPr

1-Butanol (n-butanol) C4H9OH

1-Butoxide (n-butoxide)

OnBu

2-Butanol C4H9OH

2-Butoxide (sec-butoxide)

OsBu

2-Methyl-propanol (isobutanol) C4H9OH

2-Methyl propoxide (iso-butoxide)

OiBu

2-Methyl-prop-2-ol (tert-butanol) C4H9(OH)

Tert-butoxide

OtBu

Alcohol R(OH) Methanol CH3OH

3.2.2

Alkoxy ligand to the metal M

Physical and Structural Characteristics of Alkoxides

Many alkoxides are liquid or soluble in at least one organic solvent including, most of the time, their corresponding parent alcohol. But some alkoxides, including those of Cu, are solid polymers insoluble both in water and organic solvents. Much works have been devoted in the recent year to study the structure and reactivity of alkoxides. In many cases, their actual chemical composition was found to correspond to oxoalkoxides MOx(OR)y, rather than to M(OR)n (Kessler 2016). Alkoxides are also frequently polymerized. This is due to the oxygen of the alkoxy group (OR) which, when binding to a metal atom, can act as an electron pair donor for another metal. Contrary to the solvation of a metal by water, an alkoxy group can

3.2 Structure and Properties of Alkoxides

71

Fig. 3.1 A few known structures of aluminum alkoxides: (a) Al-isopropoxide, oligomers; (b) other Al alkoxides. (Adapted from Bradley et al. (1978) plus König et al. (2007))

directly build a bridge between different metal atoms even at the precursor level. This is especially the case if the solvent is the parent alcohol to the alkoxide. For instance, in dry methanol, the reaction of Mg metal with methanol is known to form tetrameric [Mg4(OCH3)8(CH4OH)8] oligomers which tend to crystallize as Mg (OMe)2∙3.55CH3OH (Wuttke et al. 2010). The case of Al isopropoxide solutions in isopropanol was investigated in detail by 27 Al NMR. The results indicated the presence of octahedral AlO6 sites (NMR chemical shift at 2.5 ppm) and tetrahedral AlO4 sites (chemical shift at 61.8 ppm), but also of pentagonal AlO5 sites (chemical shift at 32 ppm), supporting the existence of trimeric and tetrameric “AlO” oligomers such as those presented in Fig. 3.1, which are structures reported by Bradley et al. (1978) and more recently by König et al. (2007). The formation of such coordination sites was also confirmed by density functional theory (DFT) numerical computation (Kemnitz and Noack 2015). The existence of complex Al alkoxides in which several distinct alkoxy groups are bonded to a same Al coordination center is also shown in Fig. 3.1. For any given metal M, its alkoxides often present a great diversity of chemical and physical properties. This is particularly well illustrated for Zr alkoxides (Bradley and Wardlaw 1951). The primary alkoxides of Zr present a similar volatility and they all sublimate between 120 and 160
C under a 104 mm of Hg vacuum. However, Zr (OC5H11)4 is a viscous liquid while the tetra-methoxide and the tetra-ethoxide both form microcrystals. Similarly, among the secondary alkoxides, Zr(OsBut)4 is a gum while Zr(OiPr)4 is a viscous solid that decomposes between 100 and 125
C and Zr

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(OtBut)4 is a stable liquid with a vaporization temperature in the range of 190–210
C under atmospheric pressure (Mazdiyasni et al. 1965). Furthermore, while the secondary alkoxides may be either monomeric, dimeric, or trimeric, the tertiary ones are all monomeric.

3.2.3

Chemical Characteristics of Alkoxides

Alkoxides are compounds with chemical formula M(OR)n, which are the result of direct or indirect reactions between a metal M and an alcohol ROH, where R is an alkyl group. They can be made with virtually all the elements of the periodic table, except the radioactive ones. A non-limitative list comprises many metals such as Si, Al, Ti, Zr, Pb, La, Hf, Th, Y, Dy, Yb, Ba, Sn, Mg, Sb, and Ca (Mazdiyasni et al. 1965; Brown and Mazdiyasni 1972; Dislich 1983; Hayashi and Saito 1980) but also some nonmetals such as B (Gossink et al. 1975). Among them, Si alkoxides and their derivatives largely predominate and they are addressed in more detail in some of the next sections. Their chemical synthesis must be done in anhydrous solvents and under inert water-free atmosphere, and various protocols can be followed depending on the metal type. Besides, the homoleptic (alkoxide-only ligands) alkoxides of alkali, alkaline earth, and rare earth metals are very sensitive in solution to the presence of even very small traces of oxygen, which must be avoided. The hydrogen atom at the first carbon atom (α-carbon) connected to the alkoxide oxygen can form carbonyl compounds giving an intensive yellowish orange to the solutions (Turova et al. 2002). An extensive list of the various alkoxide synthesis techniques was reviewed by Kessler (2016). It comprises, for instance, direct reaction of a metal with an alcohol, eventually with the help of a catalyst; reaction of a metal with oxygen in alcohol; anodic oxidation of a metal in alcohol; reaction of a metal oxide or hydroxide with an alcohol; reaction of metal salts from weak or volatile acids with an alcohol in a hydrocarbon solvent; cation exchange by metathesis between a metal halide and an alkali alkoxide or amine; and alcohol-interchange reactions. The list of alkoxide-related precursors can moreover be expanded to related compounds partially comprising ligands other than alkoxy groups, such as β-diketonate, carboxylate, and amino groups. Homometallic alkoxides, which are alkoxides of a single cation, must also be distinguished from heterometallic alkoxides containing at least two different cations, the latter ones being often simply known as double alkoxides (Kessler 2016). In all cases, when alkoxides are dissolved in their corresponding parent alcohol, as previously mentioned, they build stable coordination complexes with the solvent, in which the alcohol oxygen gives an electron pair such as with zirconium so as to form a strong bond as shown in (3.1). As an example, in isopropanol, Zr(OPri)4 forms a stable complex Zr(COPri)4∙iPrOH. One advantage of alcohol-solvated alkoxides is that this usually makes them soluble in organic solvents (Kessler 2016):

3.2 Structure and Properties of Alkoxides

73

ð3:1Þ Most alkoxides are extremely reactive when in the presence of moisture, heat, or light (Mazdiyasni 1982). Unlike the metal salts, the impurities they create mainly come from the organic groups. In fact, the alkoxy group must sufficiently stabilize the alkoxide so that the M–OR or MO–R bonds are not broken during the alkoxide vaporization. The ionic character of the M–O bond mostly depends on the size and on the electronegativity of the metal atom. According to Pauling scale of electronegativity, a bond linking a metal to an oxygen is at least 50% covalent when the electronegativity difference between them is 0). This partial charge depends on the metal nature, as shown in Table 3.2 for a few extensively studied cations in ethoxide molecules. 2. The oxygen in the alkoxy group is a nucleophile (δ(O) < 0). 3. The partial charge of a complex group in an intermediate state in the nucleophilic attack, calculated as the partial charge sum of all its atoms, can reach a positive value. This group is then considered as a “leaving group” and can actually leave the complex as a neutral molecule. In most cases, this leaving group is either an alcohol (ROH with δ(ROH) > 0) or a water molecule (with δ(H2O) > 0). According to Table 3.2, the partial charge of Si in Si(OEt)4 is smaller than that of the other three metals in the corresponding ethoxides. It is therefore much more difficult, from a kinetics mechanism point of view, to hydrolyze the silicium alkoxides than the other ones. For tetravalent metal alkoxides M(OR)4, another reactivity indicator more simple than the cation partial charge is its unsaturation (N–z), where N is the usual coordination number of the metal M in compounds and z the formal electric charge

3.3 Hydrolysis of Alkoxides Table 3.3 Unsaturation of tetravalent metals in alkoxides (Livage et al. 1998)

77 Cation Si Sn Ti Zr Ce

N 4 6 6 7 8

N–z 0 2 2 3 6

of the corresponding cation. For instance, the value of (N–z) increases from Si to Ce for the cations reported in Table 3.3. Hence the hydrolysis reactivity increases in the order of cations Si  Sn < Ti < Zr < Ce (Bradley et al. 1978). In practice, the hydrolysis kinetics of Si alkoxides needs to be accelerated by a catalyst, usually either a strong electrophile such as H+ or a strong nucleophile such as OH. On the other hand, the alkoxides of alkaline and alkaline earth elements react violently with the slightest humidity. It is therefore safer to dissolve them in appropriate solvents to use them, such as in propanol for the propoxides (Mazdiyasni et al. 1967). Overall, some control on the hydrolysis reaction rate of an alkoxide can be obtained by adjusting various factors, of which two important ones are the water molar ratio and the nature of the alkoxy group. To achieve a slow hydrolysis reaction, hydrolysis can be carried out in a dry environment such as in a glove box. The reaction can also be slowed down by adding a quantity of water smaller than required according to stoichiometry. Regarding the nature of the alkoxy groups, breaking the O–R bond is more difficult when the alkyl R group is big, which decreases the hydrolysis reaction rate. Similarly, the substitution of OH for OR groups becomes more difficult beyond the first hydrolysis substitution.

3.3.3

Formation of Oxo Ligands

Lewis bases are strong nucleophiles, able to deprotonate the OH ligands of cations which form acidic oxides. Oxo ligands are then created according to the following general reaction (Mühlebach et al. 1970): M  OHþ þ : B ! ½M  O þ BHþ

ð3:4Þ

In this reaction, B is a Lewis base such as OH or NH3. Furthermore, Mazdiyasni et al. (1965) indicated that traces of water vapor can also hydrolyze metal alkoxides and transform them into oxyalkoxides. Such a hydrolysis follows a reaction of the type (3.5) MðORÞ4 þ H2 O ! MOðORÞ2 þ 2 ROH

ð3:5Þ

78

3 The Sol-Gel Chemistry of Oxides from Alkoxides

For instance, in the case of the ethoxide Ti(OEt)4, the formation of Ti8O6(OEt)20 (Day et al. 1991), Ti10O8(OEt)24 (Day et al. 1991), and Ti16O16(OEt)32 (Mosset and Galy 1988) was reported. If a tight synthesis reproducibility is required, the corresponding alkoxide sol-gel chemistry should be conducted under dry atmosphere and in dry solvents. Appropriate techniques of dry solvents were for instance described by Errington (1997). Microhydrolysis reactions can moreover lead to the formation of heterooxoalkoxide, such as the following with Bi and Ti (3.6): BiðORÞ3 þ 2TiðORÞ4 þ H2 O ! BiTi2 OðORÞ9 with R ¼ Et ori Pr

ð3:6Þ

The alkoxides of Zr, Hf, and lanthanide Ln solvated by solvents carrying O or N donor ligands L, of formula [Zr(OR)4L]2, [Hf(OR)4L]2, and [Ln(OR)3]mLn, also form oxoalkoxides when they are submitted to desolvation (Helgesson et al. 1991). As for the high-valence early transition elements, such as Mo, W, Re, and Nb, they often undertake spontaneous decomposition with formation of ether R2O (3.7) which may change their coloration: MðORÞn ! ðROÞn2 M ¼ O þ R2 O

ð3:7Þ

The above reaction is catalyzed by Brönsted acids (proton donors) and by heating, in particular above 200
C. Its rate also increases with the alkyl group in the order Me < Et  iPr  tBu (Turova et al. 2002; Gibson et al. 2002). At last for strongly electronegative high-valence metals such as V(V) (Kessler and Seisenbaeva 2000), Mo(VI) (Nabavi et al. 1991; Kessler et al. 1998a), rhenium (Hoffman et al. 1989), and precious metals, β-hydride or β-proton transfer can produce M–H metal hydride bonds and even elementary metal.

3.4

Polymerization by Condensation from Hydrolyzed Alkoxides (Stockmayer 1943; Aelion et al. 1950; Livage et al. 1990)

Condensation reaction can proceed via either olation or oxolation. In either case, for some alkoxides, the oxygen from the air may speed up the reactions to a point where it becomes necessary to work under a neutral argon atmosphere in order to control reproducible results. The CO2 coming from the air is also an important factor to control, especially with the alkali elements which tend to form hydrogen carbonate anions, possibly responsible for the formation of some undesired complex with the sol-gel oligomers, and hence alter the reproducibility of an experiment (Prassas et al. 1982).

3.4 Polymerization by Condensation from Hydrolyzed Alkoxides

3.4.1

79

Condensation by Olation

Condensation by olation is considered to follow an SN2 nucleophilic substitution mechanism in two steps, of which the first one always consists of a nucleophilic addition. In a second step, a leaving group will eventually separate from this complex. It can be either an alcohol molecule coming from a protonated alkoxy ligand, as in reaction (3.8), or a water molecule from a water-solvated alkoxide as in reaction (3.9), this water coming from a previous hydrolysis step:

ð3:8Þ

ð3:9Þ

When the leaving group is an alcohol molecule in acid catalysis conditions, the alkoxy ligand is first protonated according to reaction (3.10). In both cases before condensation may occur, the protonated alkoxy ligand or the solvated water molecule is linked to the metal atom by a shared electron pair:

ð3:10Þ

3.4.2

Condensation by Oxolation

Before condensation by oxolation of an alkoxide, an “ol” bridge is usually first established before it eventually transforms to an “oxo” bridge. The transformation

80

3 The Sol-Gel Chemistry of Oxides from Alkoxides

mechanism involves a transfer of the hydrogen from this “ol” bridge to a terminal alkoxy ligand or a terminal hydroxyl. Transfer of the H atom from the “ol” bridge to a terminal OR ligand is illustrated in reaction (3.11) and such condensation reaction is also termed alcoxolation:

ð3:11Þ

In the second case, transfer of the H to a terminal OH group according to reaction (3.12), the condensation reaction is simply termed oxolation. Oxolation can also be the result of a de-etheration as in reaction (3.13):

ð3:12Þ

M  OR þ RO  M ! M  O  M  þ ROR

ð3:13Þ

As with metal salt precursors, condensation by direct nucleophilic addition AN of an oxo M–O ligand to the metal M of another complex can occur, when the coordination number of the metal M in this second complex is not fully satisfied.

3.5 SolGel Behavior of a Few Homometallic Alkoxides as a Function of their Cation. . .

81

Fig. 3.3 (a) Tri-coordinated and (b) tetra-coordinated boron in alkoxides. (Adapted from Brinker and Scherer (1990))

3.5

SolGel Behavior of a Few Homometallic Alkoxides as a Function of their Cation Nature

3.5.1

Boron Alkoxides

3.5.1.1

Hydrolysis of Boron Alkoxides

The hydrolysis of boron alkoxides proceeds exactly as in reaction (3.2). But, as mentioned previously, the electronic configuration of B atoms differs from that of Si, since it can take either a coplanar sp2 or a tetrahedral sp3 hybridization form (Fig. 3.3): Boron atoms only carry three valence electrons 2s2 and 2p1 and no “d” electron, so that the trigonal sp2 coordination is normal. This configuration presents however an empty 2pz orbital accessible to other electrons, and hence its electrophilic character. To adopt the tetrahedral sp3 hybridization coordination, a donor atom such as an oxygen atom belonging to another chemical group must donate a full electron pair. But this tetrahedral coordination is quite unstable and only prevails in solutions (Edwards and Ross 1960). During hydrolysis, considering that the oxygen atom of a water molecules carries a negative partial charge (δ(O) < 0), trigonal boron can undertake a hydrolysis reaction with an H2O molecule, according to a SN2 mechanism illustrated in (3.14), which produces a transition complex in which boron is tetrahedrally coordinated:

82

3 The Sol-Gel Chemistry of Oxides from Alkoxides

ð3:14Þ

In this transition boron complex, two molecular groups may acquire the necessary positive partial charge to leave. One of them is the incoming H2O molecule: its departure corresponds to the reverse reaction. The second one, which actually occurs, is an alcohol ROH molecule. Trigonal boron can also undergo alcoholysis according to a similar mechanism in which a fourth alcohol molecule attacks the alkoxide. On the other hand, boron atoms in a tetrahedral alcohol coordination do not fix stable OH groups.

3.5.1.2

Condensation of Hydrolyzed Boron Alkoxides

Both tetrahedral and trigonal boron species are present in aqueous solutions, but they have a very different role. On the one hand, polymerization by condensation is insured by the presence of hydrolyzed trigonal boron, and on the other hand the relative stability of the polymers formed is insured by tetrahedral boron. This means that in all boron-derived oligomers, a tetrahedral boron must be linked to at least one trigonal boron atom, by oxo bridges. The hydrolytic stability of each of those polymers decreases according to the following order: ½ B  O  B  > ½ B  O  B ¼ > ½¼ B  O  B ¼

ð3:15Þ

Examples of a boron dimer, a trimer, and a tetramer are shown in Fig. 3.4.

3.5 SolGel Behavior of a Few Homometallic Alkoxides as a Function of their Cation. . .

83

Fig. 3.4 Borate polymers: dimer, trimer, and tetramer according to Edwards and Ross (1960)

3.5.2

Aluminum Alkoxides

3.5.2.1

Hydrolysis of Aluminum Alkoxides

Aluminum alkoxides are sufficiently stable to be vaporized without decomposition. The hydrolysis of Al(OsBu)3 was developed by Yoldas (1975) to produce boehmite sols in a large excess water at a temperature 85
C with a small addition of HNO3 for peptization (i.e., dispersion) of the colloidal particles formed. During hydrolysis, an alkoxy group (OR) is replaced by a hydroxo ligand (OH) according to the general reaction which, in that case, is written as (3.16) A1ðOs C4 H9 Þ3 þ H2 O ! A1ðOs C4 H9 Þ2 ðOHÞ þ C4 H9 OH

ð3:16Þ

Various pseudoboehmite preparations from the same precursor, of composition Al2O3∙xH2O with 1.0 < x < 2.0, were also designed to make alumina coatings (Assih et al. 1988; Vieira Coelho et al. 2008). The isopropoxide Al(OiPr)3 can also be used but it is not available as a liquid, e.g., Chen et al. (2000).

3.5.2.2

Condensation of Hydrolyzed Aluminum Alkoxides

The mechanistic behavior is similar to that presented in Chap. 2 for aluminum salt precursors. Double-“ol” bridges between two aluminum atoms are first created. This reaction (3.17), catalyzed in acidic conditions, is similar to the reaction (2.85) in Chap. 2 for the condensation of hydrolyzed Al cations from salt solutions:

84

3 The Sol-Gel Chemistry of Oxides from Alkoxides

ð3:17Þ

Further condensation forms polynuclear compounds equivalent to those produced from an initial aluminum salt solution, including, when in acidic conditions, the A113 cation (Bi et al. 2004). Depending on the temperature and pH, further condensation may lead to a variety of aluminum hydroxide structures, from monohydroxide such as boehmite γ-AlO(OH) presenting a layered structure, to trihydroxide such as bayerite Al(OH)3 (Pierre and Uhlmann 1984). On the other hand, partial chelation of Al(OsC4H9)3 with ethyl acetoacetate (etac), a β-diketonate which cannot be hydrolyzed during the sol-gel process, permitted to some extent to construct a random atomic network made from a mixture of Al(-O)2X and Al(-O)3, where X was the ethyl acetoacetate group (Pierre et al. 1999).

3.5.3

Titanium Alkoxides

Titanium alkoxides follow the general hydrolysis reaction (3.3). As for most other alkoxides, hydrolysis is not only faster than condensation but also much more exothermic (Karkamar and Ganguli 1985). A particularity of titanium alkoxides is that three of them, the ethoxide, Ti(OC2H5)4, isopropoxide, Ti(OC3H7)4, and butoxide, Ti(OC4H9)4, form peroxo complexes which, in solution, present a deep orange color. Ti(O2)(OH)aq(OC2H5) (where aq stands for aqua groups) is an example of those peroxo complexes. The mechanism leading to their formation is, however, not yet clarified (Mühlebach et al. 1970). More recently monolithic TiO2 aerogels were prepared from the normal butoxide Ti(OnC4H9)4 complexed by ethyl acetoacetate (etac) in solution in ethanol (Hirashima 2011).

3.5.4

Zirconium Alkoxides

The synthesis of ZrO2 gels and mainly aerogels, depending on various parameters comprising the precursor nature and concentration, water molar ratio, and acid concentration, was reviewed by Hammouda et al. (2011). Besides ZrO2 gels prepared from oxychlorides (Zhao et al. 2007) and zirconyl nitrate (ZrO(NO3)2∙5H2O) (Zhang et al. 2006), the use of zirconium alkoxides was reported by several groups. Zirconium alkoxides, such as the zirconium n-butoxide, were early used to prepare zirconia gels and aerogels by controlled hydrolysis in various nonaqueous solvents (Vicarini et al. 1970; Bedilo and Klabunde 1997; Stocker and Baiker 1998). Sui et al.

3.5 SolGel Behavior of a Few Homometallic Alkoxides as a Function of their Cation. . .

85

Fig. 3.5 Hydrolysis of Zr tetra-tertiobutoxide. (After Mazdiyasni et al. (1965))

(2006) performed hydrolysis directly under CO2 supercritical conditions with acetic acid as a complexation reagent. Hammouda et al. (2011) reported that the reactivity of zirconia alkoxides with water is such that, when a stoichiometric amount of water in alcohol with acid catalyst is directly added to the alkoxide solution, localized condensation about the added water drops induces the formation of opaque gels or precipitates. To obtain transparent homogeneous gels, it is necessary to acidify the alkoxide solution before adding water. Unlike most other alkoxides, the alkyl groups are replaced by either oxo or aqua ligands when zirconium undergoes hydrolysis, not by hydroxo ligands. The corresponding reaction is therefore a de-alcoholation of the following type: ZrðORÞx ðOHÞy ! ZrOx x1 ðORÞxl ðOHÞy xþxl þ ðx  x1 ÞROH

ð3:18Þ

The accepted mechanism proposed by Mazdiyasni et al. (1965) for the hydrolysis of Zr(OsBu)4 consists, as illustrated in Fig. 3.5, of four main steps. In the first one, an OH ligand substitutes an OR molecular group as in any typical hydrolysis substitution reaction. Yet, in the following step, this new hydroxo ligand separates from the complex altogether with another alkoxy group, hence permitting the creation of a

86

3 The Sol-Gel Chemistry of Oxides from Alkoxides

first Zr¼O double bond. Those two first steps are repeated for the last two OR groups of the initial alkoxide so that the final product, ZrO2, is a pure oxide. Because the first step is the slowest, the total reaction rate only depends on the initial alkoxide concentration.

3.5.5

Silicon Alkoxides

3.5.5.1

Hydrolysis of Silicon Alkoxides (Brinker et al. 1990)

The hydrolysis of Si alkoxide can be catalyzed either by bases which carry strong negative charges (e.g., OH) including strong Lewis bases such as F ions, or by acids (e.g., H+) and the reaction mechanisms are completely different depending on the type of catalyst. A large range of acids were shown to be useful catalysts, including HCl (Venkateswara Rao and Haranath 1999; Nicolaon and Teichner 1968), HF (Einarsrud et al. 2001; Zhou et al. 2007; Soleimani and Abbasi 2008), or carboxylic acids (Nicolaon and Teichner 1968; Moner-Girona et al. 2003; Venkastewara Rao et al. 2006), and under acidic catalysis, the hydrolysis rate is much faster than condensation. The hydrolysis of silicon alkoxides creates Si–OH groups termed silanol, in which a hydroxo ligand is bonded to a silicon atom. As already mentioned, this is a very slow process, and this is one of the reasons explaining that silicon alkoxides, especially tetraethoxysilane (or TEOS of formula Si(OC2H5)4 and tetramethoxysilane (or TMOS of formula Si(OCH3)4, are probably the most studied alkoxides. The hydrolysis condensation chemistry of TEOS largely depends on the pH. In fact, when the pH of an aqueous solution is 2.5, the silicate oligomeric clusters formed are not electrically charged. However, when the pH 2.5, the silanol groups are deprotonated according to reaction (3.21). They build siloxane bridges by another SN2 mechanism which involves two intermediary complexes with pentacoordinated silicon. This corresponds to reaction (3.23) proposed by Swain et al. (1949). When pH >4, the condensation rate is proportional to the concentration of OH anions, but it also becomes faster than hydrolysis. Furthermore, since the silicon polymer reticulation is more developed than in acidic catalysis conditions, denser solids are obtained:

3.5 SolGel Behavior of a Few Homometallic Alkoxides as a Function of their Cation. . .

89

ð3:23Þ

Basic catalysts, including Lewis bases, accelerate condensation and alcohol molecules are better leaving groups than water. Aqueous NH3 is the basic catalyst most frequently used (Mezza et al. 1967; Dieudonne et al. 2000; Venkastewara Rao et al. 2006) but Lewis bases such as dimethylaminopyridine (DMAP), n-Bu4NF, NaF, or NH4F present some advantages (Corriu et al. 1984, 1988). In particular NaF and NH4F are efficient with precursors such as MTMS (El Rassy et al. 2003; Suh et al. 1999). However condensation is an equilibrium and hence reversible reaction. Practically, the siloxane bridges Si–O–Si which are built during condensation can be dissolved back by alcohols at a pH ranging from pH 3 to 8, in the presence of OH catalyst. This corresponds to reaction (3.24). As a possible consequence, newly condensed monomers can be redissolved and again condensed with another dimer so as to form a trimer (reaction 3.25): OH

ROH þ ðROÞ3 Si  O  SiðORÞ3 $ SiðORÞ4 þ SiðORÞ3 ðOHÞ SiðORÞ3 ðOHÞ þ ðROÞ3 Si  O  SiðORÞ3 $ ðROÞ3 Si  O  SiðORÞ2  SiðORÞ3 þ ROH

ð3:24Þ ð3:25Þ

Overall in the case of silicon alkoxides, three reactions, hydrolysis, condensation, and redissolution, are in competition with each other. The final equilibrium silicon oligomer distribution in solutions depends on the relative kinetics of these reactions, which themselves vary according to the pH as reported in Fig. 3.6. The oxo bridges linking the different silicon atoms to each other are constantly redistributed among monomers and polymers (3.26), which explains the formation of spherical particles in basic conditions:

90

3 The Sol-Gel Chemistry of Oxides from Alkoxides

Fig. 3.6 Rates of hydrolysis, condensation, and redissolution of TEOS. (Adapted from Brinker (1988))

2 dimers

3.6

OH

$ 1 trimer þ 1 monomer

ð3:26Þ

Formation of Solid Phases from Alkoxides

For all alkoxides, hydrolysis and condensation both keep proceeding simultaneously, to gradually build up a tridimensional network which, at the end, often forms a solid phase. This process is accelerated by heat because the reaction rate of both reactions increases with the temperature (Kamiya et al. 1986). Since the kinetics of hydrolysis and condensation depends on the pH, the type of polymers formed also depends on the pH. Overall, a great variety of materials with different textures and structures can be obtained from linear polymers to dense colloidal particles, including intermediate textures with more or less weakly bonded colloidal particles made of variably cross-linked clusters of polymers. Apart from Si alkoxides, all alkoxides hydrolyze and condense so fast that the actual reaction rates are not yet determined. Although this is quite controversial, it is generally admitted that linear polymers form more favorably when hydrolysis is slower than polymerization. This can explain, again to the exception of silicon, that the hydrolysis rate of alkoxides must be attenuated with the help, for instance, of a chelating agent in order to form a gel, characterized by more linear polymeric structure than dense particles. This is also consistent with success in making new gels by a new slow hydrolysis technique of hydrated metal salts, developed by Gash et al. (2001). When the rate of hydrolysis is not reduced, a solid powder with denser reticulation of hydroxides or oxides usually precipitates. Moreover, the alkoxides of some elements, such as alkaline and alkaline earth, do not condense. With these elements, no gel can possibly form. Instead, dense colloidal hydroxidic or oxidic particles are obtained according to the following two reactions (Colomban 1985):

3.6 Formation of Solid Phases from Alkoxides

91

MðORÞZ þ zH2 O ! MðOHÞz þ zROH

ð3:27Þ

MðOHÞz ! MOz=2 þ z=2 H2 O

ð3:28Þ

For elements for which it is possible to make gels from alkoxides, relatively larger monoliths can more easily be formed when using an excess of water for hydrolysis. The oxide content of the materials obtained increases when a greater proportion of water is used for hydrolysis, so that more extensively cross-linked and stronger monoliths are formed (Partlow and Yoldas 1981; Yoldas 1982). A brief review of the solids formed for a few oxides according to the cation nature is presented next. The gel structure and properties are reviewed in further chapters (Chaps. 8 and 9).

3.6.1

Boron Oxides

Sol-gel boron oxide made from boron alkoxides mainly concerns borosilicate glasses, which have an excellent chemical durability, a low thermal expansion coefficient (~3.3 106
C1), and hence a good resistance to thermal shock (Xiang and Jiasong Zhong 2016). Glasses in this system also have the property to phase separate by spinodal decomposition (Chap. 12) during heat treatment, permitting to design porous materials with an open network of pores, obtained when dissolving in HF-type solvents one on the decomposed phases. The application of the sol-gel method to the synthesis of borosilicate glasses was reviewed by Xiang and Jiasong Zhong (2016). Sol-gel processing permits to easily entrap nanoparticle comprising various metal nanoclusters (Au, Ag, Cu, Pb, etc.) (Pei et al. 2014; Xiang et al. 2015), and various inorganic or organic quantum dots, e.g., CuInS2 (Xiang et al. 2012). Sol-gel synthesis from boron alkoxide precursors was initiated by Tohge et al. (1984) and further developed by Brinker et al. (1986a); Klein (1994); Prasad (2004); Sakka (2005); and Speranza et al. (2009). It was reported that formation of Si–O–B bonds in the gel could be promoted by using organoalkoxysilanes Rn–Si(OR)4-n, where R is an organic group (Soraru et al. 1999).

3.6.2

Alumina

Aluminum alkoxides produce, depending on the pH, either trihydroxides, A1(OH)3, or oxohydroxides—also called monohydroxides, AIO(OH), solids. Each of them can exist under different structures. For example, if the reactions are achieved in acidic conditions, the solid obtained after evaporation is a gel with a structure similar to layered structured boehmite, γ-AIO(OH) (Pierre and Uhlmann 1984). Moreover, with the polymerization reaction being fully reversible, the gel completely redissolves when replaced in water. In order to obtain an irreversible polymerization

92

3 The Sol-Gel Chemistry of Oxides from Alkoxides

of a gel able to remain monolithic after supercritical drying, the reactions need to be made in an organic solvent after the complexation of the alkoxide by a chelating agent such as ethyl acetoacetate or acetic acid (Pierre et al. 1999).

3.6.3

Titania

In the case of titanium, the final solids obtained are, according to Matsuda and Kato, either metatitanic acid TiO(OH)2 or orthotitanic acid Ti(OH)4 (Matsuda and Kato 1983). Yet, Barringer and Bowen demonstrated that some alkoxy groups always remained in the solid phase even when the hydrolysis water ratio rw was >3, so that the final product was never purely composed of those two acids (Barringer and Bowen 1982). As for all other alkoxides, the hydrolysis and condensation of Ti alkoxides can be controlled by two parameters: the concentration of reactants and the hydrolysis ratio rw (Komarneni et al. 1985). These two factors modify not only the reaction rates but also the degree of hydrolysis (Boyd 1951). For instance, for the isopropoxide if a ratio is rw < 1 soluble linear polymers are formed which still carry some lateral alkoxy ligands. This corresponds to reaction (3.29). With a hydrolysis ratio of rw < 2, the solutions are suitable for the creation of fibers by the spinning technique:

ð3:29Þ

Two other important factors also determine the structure of the polymer: the nature of the alkyl group and the catalyzer. The nature of alkyl group action depends on the length of their polymer chains; bigger groups slow down the diffusion of species in solution. Hence they can reduce the rate of hydrolysis to the point that only small polymers are produced by condensation. Regarding the catalyzer, as demonstrated by Yoldas, only two acids, HNO3 and HCl, permit to obtain clear solutions, provided that the molar ratio of [acid]/[alkoxide] is 7, they are no longer permanently interconnected, so that stable colloidal sols are observed. The OH anions are responsible for the formation of such stable sols because they tend to adsorb on the particle surface and, when they are present in excess concentration in the solution, they maintain the particles in a dispersed state controlled by electrostatic forces, as presented in details in Chap. 6. On the opposite, when pH Et2Zn > –But2Zn. β-ZnS white precipitates or ZnS whiskers, depending on the chemical protocol, were obtained from a series of organometallic precursors comprising Zn(SR)2 (R ¼ Et, Ph), Et2Zn, and EtZnSR, by thiolysis with H2S or (RS)2S (R ¼ Bz, Ph, tBu, nPr, Et) in aqueous medium or in an organic solvent under neutral atmosphere (Guiton and Pantano 1988). However, a red-orange gel was obtained by reaction of excess dibenzyl trisulfide (BzS)2S with Et2Zn, where Bz denotes the benzoyl (C6H5C(O)) group. Enhanced linear polymerization occurred via the formation of polysulfide bridges, according to (4.13). The approximate dry gel composition was Zn0.8S and it transformed to a glass at ~125  C: Et2 Zn þ ðBzSÞ2 S ! ½BzS  S  Zn  S  SBz þ 2EtSBz

ð4:13Þ

Besides H2S, liquid organopolysulfides such as thioacetamide (CH3CSNH2) and thiourea (NH2CSNH2) can be used as the sol-gel sulfur precursors (Almeida and Xu 2016). Such precursors were applied to the synthesis of ZnS, TiS2, and GeS2. As in alkoxide sol-gel processing, the reactions involved comprise thiolysis of the metal precursor, followed by condensation of the thiolyzed molecules, in agreement with reactions (4.14) and (4.15) where the sulfur precursor is represented by the general formula Y2S: MR0n þ xY2 S ! MR0x ðSYÞnx þ xR0 Y MR0x ðSYÞnx

ð4:14Þ 0

! MSn=2 þ ðx  n=2ÞY2 S þ ðn  xÞR Y

4.2.4

Sol-Gel Synthesis from Inorganic Precursors

4.2.4.1

Sol-Gel Synthesis by Linking of Chalcogenide Zintl Clusters

ð4:15Þ

The discovery of the so-called Zintl clusters dates back to initial work by Joannis (1891, 1892) who found that intense colored solutions could be made upon dissolving Pb metal in an alkali metal-ammonia solution. It was later shown that a plumbide salt was first formed, which was further dissociated in ammonia to produce polyanionic Pb94 clusters, of size ~1 nm (Kraus 1907). These species were later termed “Zintl” ions after a chemist who made important contributions to the field (Zintl et al. 1931; Zintl and Kaiser 1933). Such clusters can be made with many elements, in particular group 14 and 15 elements (e.g., Ge, Sn, Pb, As, Sb), by various synthesis techniques described by Aiken III and Finke (1999). They can also be separated from the solutions in

4.2 Chalcogenides

135

which they are made, and crystallized, by using sequestering agents such as polycyclic ligands termed cryptands (Dietrich et al. 1969; Lehn et al. 1970). These Zintl clusters can be used as precursors of very small and uniform nanoparticles (size 0.5%) had to be eliminated during the reaction to avoid gelation: CH3 COOH þ C2 H5 OH ! CH3 COOC2 H5 þ H2 O

ð4:25Þ

On the other hand, when the Mg precursor was the methoxide Mg(OCH3)2, which can be made by direct reaction of Mg metal with methanol, no water was liberated (4.26). It was then reported that a turbid sol containing 150 nm MgF2 particle agglomerates was first formed, which naturally peptized to a clear sol of 10 nm nanoparticles in a second step (Kemnitz 2016): MgðOCH3 Þ2 þ 2HF ! MgF2 þ 2CH3 OH

ð4:26Þ

The Mg ethoxide is not normally soluble in ethanol or methanol, but Kemnitz (2016) used the property that it becomes soluble when CO2 is passed through the solution, because of the formation of a soluble alkylcarbonate Mg(ROCO2)2 (R ¼ CH3, C2H5) (4.27):

4.3 Fluorides

141 EtOH

MgðC2 H5 OÞ2 þ 2CO2 ! ! MgðC2 H5 OCO2 Þ2

ð4:27Þ

The fluorolytic reaction of this compound then formed MgF2 and liberated the alkylcarbonate groups which decomposed to ethanol plus CO2 (4.28). In this reaction, CO2 acted as a Lewis acid able to break the strong oxo-bridges in the solid ethoxide Mg(OEt)2: MgðEtOCO2 Þ2 þ 2HF ! MgF2 þ 2EtOH þ 2CO2

ð4:28Þ

In an alternative protocol, MgCl2 and Mg(OEt)2 can be mixed in ethanol. MgCl2 is soluble and it rapidly reacts with HF by fluorolytic transformation, to produce HCl plus some MgF2. HCl then acts as an acid catalyst, similarly to CO2, and breaks the oxo-ethoxide groups. MgF2 is then directly formed without requiring an alkylcarbonate intermediate. Other Mg alkoxides were successful and powders with a higher specific surface area were made when the Mg precursor was magnesiumtert-butoxide (Kemnitz 2016). The technique can be adapted to other cation carboxylates and inorganic salts (Rüdiger et al. 2005, 2007; Kemnitz et al. 2010). For instance CaF2 was made from Ca lactate and AlF3 from aluminum isopropoxide (Kemnitz et al. 2003). For AlF3, a possible chemical mechanism was proposed by Kemnitz (2016). It comprises a fluorolysis step schematically illustrated in Fig. 4.4a, followed by a fluorolytic condensation step illustrated in Fig. 4.4b, similar to the hydrolysis and oxo-condensation mechanism of oxide sol-gels. The direct linkage of F atoms to an Al center could be proved by 19F NMR spectroscopy characterized by the occurrence of two chemical shifts at δiso ¼ 147 ppm and δiso ¼ 156 ppm

Fig. 4.4 The induction of the first fluorination step by electrophilic protonation of a metal alkoxide oxygen atom (adapted from Kemnitz (2016))

142

4 The Sol-Gel Chemistry of Non-oxides

(Chupas et al. 2003). Supplementary details, brought by density functional theory (DFT) computation on tetrameric Al(OiPr)3 oligomers, by Kemnitz and Noack (2015), were presented in the review by Kemnitz (2016). The mechanism involves Al atoms in coordination 4 (tetrahedral) and 6 (octahedral) but also 5 (pentagonal) in intermediate steps. As in oxide sol-gel, the solvent is important regarding its polarity and the precursor solubility. The polarity has an effect on the initial protonation of an M-OR group and, in turn, on the nucleation rate of the solid fluoride and its agglomeration via residual organic groups. A low-boiling-point solvent facilitates its elimination by evaporation in the end. The temperature mainly acts on the supersaturation limit of the fluoride nanoparticles, and hence on the precursor concentration which may be used without inducing precipitation.

4.4

Preceramic Polymers

Sol-gel preceramic polymer chemistry mostly concerns precursors which already comprise Si-C or Si-N bonds at the wet sol-gel chemistry level. Their main interest is that they can be transformed to various ceramics in the system Si(O)C or Si(C)N after pyrolysis in a temperature range from 800 to 1000  C, somewhat lower than the direct reaction temperature of SiO2 with carbon or nitrogen, typically well above 1000  C (Wei et al. 1984; White et al. 1987; Baney 1984). An early review of SiC and Si3N4 ceramics synthesized from siloxanes, silanes, and silazanes was made by Wills et al. (1983). Verbeek and Winter (1973) studied polysilanes and polysilazanes, and Yajima et al. (1976) polymethylsilane [(CH3)2Si]n, polycarbosilanes, and borodiphenylsiloxane (Yajima et al. 1977). Mazdiyasni et al. (1978) studied hexaphenylcyclotrisilazane and polymethylphenylsilane. The whole field was recently reviewed by Sorarù et al. (2016).

4.4.1

Carbides

The sol-gel chemistry of SiC preceramic polymer was studied by a few authors comprising Yajima et al. (1978), Riedel et al. (1992), Colombo et al. (2010), and Eckel et al. (2016). The preceramic polymer precursors of SiC are polycarbosilanes, which carry a periodic chain of Si and C atoms. Such precursors can be made from silanes of the type R1R2-Si(Cl)2, such as (CH3)2Si(Cl2), by a Wurtz-type reaction with Na metal (4.29) in solution in a hydrocarbon, at a temperature >100  C. With the latter silane, a poly(dimethylsilane) polymer with direct Si-Si bonds is produced, in a first time:

4.4 Preceramic Polymers

143

ð4:29Þ

Thermal treatment at a temperature rc the particle is termed a nucleus and this stage is termed growth. The free energy of a critical nucleus which corresponds to the maximum ΔGc, is

5.3 Nucleation of Solid Particles

4 16πγ 3 ΔGc ¼ πr 2c γ ¼ 3 3ðΔGv Þ2

5.3.2

169

ð5:7Þ

Gibbs Internal Free Energy Change, per Unit Volume, Due to Phase Transformation

In sol-gel processing, solid particles are made from a solution. Hence, they have a composition which is different from the surrounding initial phase. The Gibbs free energy change per unit volume ΔGv, due to internal phase transformation ΔGin, can be estimated from a free energy diagram such as shown in Fig. 5.3. However, because the solution keeps changing composition as nucleation and growth proceed, ΔGv also keeps changing. In particular, two different extreme values of ΔGv can be distinguished, as illustrated in Fig. 5.3, and explained after: – A final ΔGv,f which can be used when the particles are well developed, because the final system (solid particles + remaining liquid) has the same average composition as the initial liquid medium – An initial ΔGv,n which should be used at the beginning of the transformation, that is to say, during nucleation

5.3.2.1

Derivation of ΔGv,f for the Growth Stage of Homogeneous Nucleation

The final free energy change ΔGv,f, which applies to the growth stage corresponds to the transformation

Fig. 5.3 ΔGv,n for nucleation and average ΔGv,f for growth, during a phase transformation due to a changing liquid composition (adapted from Kingery et al. (1976b))

170

5 Nanoparticle Formation

Fig. 5.4 Linear relationship between an average free energy and the free energy of the two phases

Initial solution ! Final solution þ particles

ð5:8Þ

In the initial solution, the solute concentration is C0 while in the final solution, the solute concentration is Cs, and the solute concentration in the particles is Cβ. Cs and Cβ are located on the common tangent to the free energy curves of the liquid solution and of the solid. The solution solute average concentration cannot fall below Cs; otherwise the overall free energy would increase and, for the same reason, the solid solute concentration cannot exceed Cβ. Hence, ΔGv,f can be deduced from the change in free energy per unit volume, from G(C0) per unit volume in a liquid of composition C0, to the average solid-liquid mixture free energy Gv,f per unit volume once the solid has been formed, according to the following equation: ΔGv,f ¼ Gv,f  GðC0 Þ

ð5:9Þ

The average final composition of the “remaining liquid plus solid formed” is unchanged at C0, because no product is lost. Hence the average free energy per unit volume of “remaining liquid + solid formed” Gv,f, corresponds to point M in Fig. 5.3. Gv,f is a weighted value of the final solution and solid particles’ free energies per unit volume, themselves corresponding to points A and B, respectively, in Fig. 5.3. These three points A, M, and B are aligned and they are again represented in Fig. 5.4 where the corresponding compositions and free energy are more simply termed CA, CM, and CB and GA, GB, and GM, respectively. The slope of the straight AMB line is slope ¼

GM  GA GB  GA ¼ CM  CA CB  CA

ð5:10Þ

That is to say, GM  GA ¼ ðC M  CA Þ

GB  GA CB  CA

ð5:11Þ

5.3 Nucleation of Solid Particles

171

GM ¼ GA þ ðC M  CA Þ

GB  GA CB  CA

  CM  CA C  CA GM ¼ GA 1  þ GB M CB  CA CB  CA GM ¼ GA

CB  CM C  CA þ GB M CB  CA CB  CA

ð5:12Þ ð5:13Þ ð5:14Þ

The latter formula can be used to derive ΔGv,f. It can also be transformed to the following form which is, later on, useful to derive ΔGv,n: GB ¼ GM þ ðCB  C M Þ

GM  GA CM  CA

ð5:15Þ

Returning to Fig. 5.3 and replacing CA, CM, and CB, respectively, by Cs, C0, and Cβ, it comes Gv,f ¼ GðCs Þ


C  Cs Cβ  Co þ G Cβ o Cβ  Cs Cβ  Cs

ð5:16Þ

That is to say,
C  Cs Cβ  Co þ G Cβ o  GðC 0 Þ Cβ  Cs Cβ  Cs


G Cβ  GðC s Þ ¼ G Cβ  GðC 0 Þ  Cβ  C 0 Cβ  Cs

ΔGv,f ¼ GðCs Þ ΔGv,f

5.3.2.2

ð5:17Þ ð5:18Þ

Derivation of ΔGv,n for the Homogeneous Nucleation Stage

To evaluate the free energy per unit volume ΔGv,n which must be taken into consideration during nucleation, it is necessary to focus first on the nature of the initial equilibrium state of the solution. The solute concentration Cs used in the previous equations and shown in Fig. 5.3 is the saturation concentration in equilibrium with macroscopic solid particles. If we consider a solid spherical particle with a very small radius r, corresponding to a nucleus, the equilibrium solute concentration Cs(r) drastically increases with r, in agreement with the Thomson-Freundlich equation (5.19):

172

5 Nanoparticle Formation

Fig. 5.5 Free energy of a fluctuation in a solution

C s ðr Þ ¼ Cs exp

2γV m RTr

ð5:19Þ

where γ is the solid particle surface tension, Vm the molar volume of the complexes which constitute the solid, and R the universal gas constant. Actually, a thermodynamic equilibrium is a statistical equilibrium state and nucleation is a problem of thermodynamic statistical fluctuations about an average state. An equilibrium state with solute concentration C0 and Gibbs free energy G(C0) is really an average state. It corresponds to previous point M, also reported in Fig. 5.5, which is located on the free energy curve of the solution, as shown. Within this equilibrium state, local fluctuations in composition and Gibbs free energy constantly occur around point M, due to permanent Brownian motion of species in solution. One such fluctuation can be described as follows: inside a very small local solution volume, the solute concentration is CB, while the remaining solution has composition CA. The corresponding fluctuation point B in Fig. 5.5 is not located on the free energy curve of the solution, because this is not an average state. This is contrary to point A which also virtually corresponds to a huge solution volume, and hence to an equilibrium state. But the three points A, M, and B remain on a same straight line, as in previous Fig. 5.4. B can also be very far from point M, but with a probability described by Boltzmann statistics, which rapidly decreases as the distance from M increases. On the other hand, a fluctuation responsible for nucleation is of so small size that the volume of the remaining solution is virtually the same as the total solution volume. So CA and GA are virtually identical to the average equilibrium state values CM and GM of the solution. That is to say, for nucleation, the straight line AM to consider virtually coincides with the tangent at point M to the solution free energy curve (Fig. 5.5). And the free energy of all fluctuations participating in the statistical equilibrium state at point M is described by the full tangent at this point M. For instance, the free energy of a fluctuation of

5.3 Nucleation of Solid Particles

173

composition CB, about equilibrium M in the liquid, is described by point “B, fluctuation” in Fig. 5.5. An expression for the free energy of this fluctuation, GB,F as a function of CB, can be provided by previous equation (5.16), and be written as GB,F ¼ GM þ ðC B  CM Þ

GM  GA CM  CA

ð5:20Þ

Since, to describe thermodynamic fluctuations, the straight line AM must
be ∂G A replaced by the tangent at point M, it comes that GCMM G C A must be replaced by ∂C A and (5.20) becomes GB,F

  ∂G ¼ GM þ ðCB  C M Þ ∂C A

ð5:21Þ

Finally, CB and CM can be, respectively, replaced by C0 and Cβ, so that the fluctuation free energy is  GB,F ¼ GðC 0 Þ þ ðC B  C 0 Þ

∂G ∂C

 ð5:22Þ C0

No overall free energy change is involved in the appearance of this fluctuation, because this local fluctuation free energy is part of the equilibrium state itself. It is balanced by other fluctuations of opposite sign, so as to maintain a constant average solution free energy GM. The nucleation fluctuation occurred in the liquid state. Hence to complete the nucleation stage, it is moreover necessary to transform this liquid-state fluctuation with solute concentration Cβ, to a solid particle with the same solute concentration Cβ. The corresponding free energy change involved is (5.23) ΔGv,n ¼ GB,solid  GB,F

ð5:23Þ

Since, per definition, GB,solid ¼ G(Cβ) is the free energy of the solid phase, and considering (5.22), it comes that  

∂G ΔGv,n ¼ G C β  GðC0 Þ  C β  C 0 ∂C C0

ð5:24Þ

Overall, nucleation corresponds to the transformation Initial solution ! ðvirtually identicalÞ Initial solution þ ðvery smallÞ particles

ð5:25Þ

174

5 Nanoparticle Formation

Fig. 5.6 Nucleation and growth of a spherical particle for two values of the supersaturation S ¼ CC0s

When the solute concentration C0 in the liquid solution increases (Fig. 5.3),
the at solute supersaturation defined by S ¼ CCos (Fig. 5.3) increases and the slope ∂G ∂C C 0 point M increases very fast, so that ΔGv,n also quickly increases. Consequently, according to (5.7), ΔGc and rc decrease. The free energy of formation of a particle, as a function of its radius r, is modified as shown in Fig. 5.6. That is to say, nucleation becomes easier. Eventually, spontaneous precipitation may occur.

5.3.3

Homogeneous Nucleation Rate

Nucleation is due to statistical thermodynamic fluctuations, in agreement with the Boltzmann statistics. Bimolecular collisions responsible for nucleation become more probable with solution ageing, heating, and participation of chemical ligands. Aging gives more time for bigger fluctuations to occur. Heating accelerates all chemical steps and renewal rate of fluctuations. The ligands reviewed in Chap. 2 modify the saturation limit of complexes from which nucleation may occur. For ionic precursors, the nucleation rate often depends on the metal cation concentration with a reaction order of 4–10, although the detailed kinetics largely depend on the nature of each cation (Matijevic 1985). From the theoretical point of view, the rate of nucleation per unit volume and per second Iv is proportional to: – The probability P(ΔGc) that a thermodynamic fluctuation of Gibbs free energy amplitude ΔGc may occur, given by Boltzmann statistics: PðΔGc Þ ¼ exp 



ΔGc kT



ð5:26Þ

– The number of molecules per unit volume n0 which can be used as nucleation centers

5.3 Nucleation of Solid Particles

175

– The rapidity of fluctuation modifications, described by the so-called successful atomic jump frequency Γ from one site to another one: This term is also of Boltzmann statistical nature:  Γ ¼ ν0 exp 

ΔG kT

 ð5:27Þ

In this equation ν0 is the natural atomic vibration frequency and ΔG is the activation energy for diffusion per atom. This activation energy is related to the variation of the diffusion coefficient D of the complexes in solution, and to the temperature T, by D ¼ D0 exp 

  ΔG kT

ð5:28Þ

where D0 is a constant. So that,     ΔG ΔGc exp  I ν ¼ n0 ν0 exp  kT kT

ð5:29Þ

Equivalent laws can be obtained by replacing Γ by the viscosity of the solution η, according to Eq. (5.30), or by the diffusion coefficient according to Stokes Eq. (5.31): Γ¼

kT 3πλ3 η

ð5:30Þ

D¼

kT 3πλη

ð5:31Þ

where λ is the diameter of a complex solute molecule. The term ΔGC in Eq. (5.29) is only due to a particle size effect. It does not take into account an activation energy term due to the olation or oxolation chemical reactions, such as the SN2 mechanisms examined in Chap. 2. If this polymerization activation energy is termed ΔGp, then Eq. (5.29) must be replaced by I ν ¼ n0 ν0 exp 

    ΔGc þ ΔGp ΔG exp  kT kT

ð5:32Þ

Catalysts which are useful to accelerate the reactions of polymerization can decrease significantly ΔGP and hence accelerate nucleation.

176

5.3.4

5 Nanoparticle Formation

Heterogeneous Nucleation

Any foreign surface modifies the surface-to-volume ratio in a nucleus. Hence, in heterogeneous nucleation, ΔGc must be replaced by ΔGch ¼ ΔGc f ðθÞ

ð5:33Þ

where θ is the equilibrium contact angle between the nucleus and the foreign surface and f(θ) is a function of θ which depends on the geometry of the surface. For a planar foreign surface (Fig. 5.7) f ðθ Þ ¼

ð2 þ cos θÞð1  cos θÞ2 4

ð5:34Þ

In this case, the nucleation rate per unit foreign surface area Is is Is 

n0s n0

    ΔG ΔGch exp  exp  kT kT

ð5:35Þ

where n0s is the number of molecules which are in contact with a unit foreign surface area.

5.3.5

LaMer Model, for the Growth of Monodisperse Particles

Very often, nucleation and growth occur simultaneously and they produce a polydisperse population of particles. In particular, when two liquids are suddenly mixed, strong local variations of the reagent concentrations occur and lead to the formation of an irregular distribution of particles. To obtain a monodisperse population, which is composed of particles with a very narrow size distribution, it is necessary to first determine at least qualitatively the growth and nucleation kinetics (Matijevic 1978). This knowledge can be used to nucleate first one single burst of simultaneous nuclei, Fig. 5.7 Heterogeneous nucleation (adapted from Kingery et al. (1976c))

5.3 Nucleation of Solid Particles

177

Fig. 5.8 Variation of the nucleation and growth rates with the solute concentration (after Haruta and Delmon (1986))

and then to stop nucleation while letting growth proceed. The most common protocols of homogeneous nucleation used to synthesize monodisperse particles comprise forced hydrolysis, according to a term introduced by Matijevic; controlled release of anions; and controlled release of cations (Matijevic 1987).

5.3.5.1

Thermodynamics of the LaMer Model

The control of homogeneous nucleation rests on successive steps illustrated in Fig. 5.8, according to a model by LaMer (1952). The growth rate G and the nucleation rate N are reported as a function of the concentration C in solute species. This solute can be any complex in the solution, resulting from hydrolysis and condensation of the precursors. The growth rate is positive above the solubility limit Cs, while nucleation requires a minimum supersaturation concentration Cnu min > Cs to occur (Fig. 5.8). Depending on the solution composition and on the nature of complexes which may each be characterized by a different rate of formation rate and a different limit supersaturation for nucleation, the growth and nucleation rates may have a different magnitude with respect to each other. In Fig. 5.8, nucleation and growth both occur in region II. However, if the growth rate is relatively low by comparison with the nucleation rate, it is possible to maintain C above Cnu min for an appreciable amount of time so that more nuclei can form while they do not grow appreciably. If the relative magnitude of these rates is inverted, it is necessary to let the nucleation proceed only during a very short time. To stop nucleation and let only growth proceed, it is possible to decrease the solute concentration below C nu min but maintain it above Cs. In practice several synthesis protocols may be applied.

178

5 Nanoparticle Formation

Fig. 5.9 Simplified evolution of the solute concentration with time, during the homogeneous nucleation of particles. The domains I, II, and III are the same as in Fig. 5.8 (after Haruta and Delmon (1986))

5.3.5.2

Forced Hydrolysis

The technique of forced hydrolysis, according to a term introduced by Matijevic, consists of letting enough time for nucleation to occur spontaneously in a solution containing a given initial concentration of precursors. When one type of complex, designated after as the solute, reaches its minimum concentration Cnu min for nucleation, nuclei appear and they immediately begin to grow (Fig. 5.9). The solute concentration automatically levels out once complexes are captured by the growing particles, and it eventually starts decreasing. When the solute concentration falls below Cnu min , only growth can keep proceeding. The initial precursor concentration must be selected so that nucleation can only operate during a short time and all nuclei will virtually grow simultaneously. Very often, to synthesize oxide particles, the precursors are metal salts and the complexes responsible for the nucleation and growth of particles are formed by hydrolysis and condensation. Their nature depends on the anions: for instance with cobalt, only the acetate anions make it possible to obtain monodisperse particles (Sugimoto and Matijevic 1979). Not all complexes enter in the composition of particles. As an example, for chromium hydroxide and basic ferric sulfate, it was shown that only selected solute complexes, out of a large variety, participate in nucleation and growth (Bell and Matijevic 1975). Depending on whether growth is carried out from polymeric metal complexes, or from smaller ionic complexes, amorphous or crystalline particles form. Overall, the final structure can be modified in a wide range, by modifying the anions and the ionic strength of the solution.

5.3 Nucleation of Solid Particles

5.3.5.3

179

Controlled Release of Anions or Cations

A controlled release of anions makes it easier to tailor a precise size distribution. For instance, bimodal size distributions can be created by monitoring the appearance of two bursts of nuclei at different times as illustrated in Fig. 5.10. A similar result can be reached by controlling the release of cations. The appropriate ions can be released from chemical reagents playing the role of a reservoir, such as chelated complexes made with citrates or formaldehyde. Water is an OH reservoir, and thioacetamide a S2 reservoir. The release of desired species from a reservoir can be achieved by chemical reactions, for instance adding an appropriate reagent or modifying the pH or the temperature. LaMer (1952) used a method of this type to synthesize sulfides by continuous decomposition of thioacetamide. Referring to Fig. 5.9, the release of the S2 anions was monitored so as to be above the minimum concentration for nucleation C nu min in stage II, but below this minimum in stage III. In the synthesis of MoS3 by Haruta et al. (1984), the precursor was ammonium heptamolybdate, thioacetamide was the H2S reservoir, acetic acid was used to maintain pH 4 so as to avoid polymerization of Mo complexes before their reaction with H2S, and hydrazine N2H4 was used to accelerate the hydrolysis of thioacetamide to induce a nucleation burst. The main soluble molybdenum species was MoS42. When a small population of nuclei was formed, bigger particles were grown, and their diameter varied inversely with the degree of supersaturation S ¼ CCs : The standard deviation of the powders obtained in this example was about 15%.

5.3.5.4

Modification of the Temperature

To synthesize CdS particles, Matijevic and Wilhelmy (1982) modified the temperature T so as to modify the saturation concentration Cs of the complexes in solution. The reactor was first placed at a temperature T1 such that the solute concentration C was above CS1 but below C nu min 1 for nucleation at this temperature. In a next step,

Fig. 5.10 Nucleation and growth sequence of a bimodal distribution of particles (after Matijevic (1987))

180

5 Nanoparticle Formation

the temperature was lowered to a value T2 < T1, which induced the nucleation of particles. Once the desired concentration of nuclei was reached, the temperature was again raised to T1 so as to stop particle nucleation and accelerate the growth of nuclei formed at temperature T2.

5.3.5.5

Use of Separate Reactors

Another method consists of using successively two separate reactors. In a first reactor, the solute concentration is C > C nu min and in the second reactor the solute and Cs. Particles are made to nucleate in concentration is comprised between C nu min the first reactor, from where they are transferred to the second reactor so as to let them grow without any further nucleation. This technique can possibly be adapted to design a continuous flow process.

5.4

Crystalline Growth Mechanisms of Solid Particles

Once solid particles have nucleated, their growth may actually proceed according to several kinetic mechanisms. Mainly, growth can be controlled by the diffusion of additional species towards the surface of a particle, or by the fixation onto the surface of this particle (Matijevic and Wilhelmy 1982). Moreover in this second case, two different sub-regimes must be considered. In mononuclear growth each new crystalline layer on the particle is completed before another one can nucleate and start growing on top of it. On the other hand in polynuclear growth, a crystalline layer need not be completed before another can nucleate on top of it, as shown in Fig. 5.11. The “nucleation” which is concerned in this section is a “surface nucleation,” as the particle already exists.

Fig. 5.11 The various growth regimes for particles of a new phase

5.4 Crystalline Growth Mechanisms of Solid Particles

181

Table 5.1 Compared effects of the three growth mechanisms on the surface roughness of particles Growth regime Atomic scale surface Macroscopic scale surface

Mononuclear growth Smooth (crystallographic planes) Rough (faceted)

Polynuclear growth Rough

Diffusion controlled Rough

Smooth

Smooth

The effect of these three growth mechanisms on the surface roughness of the particles is summarized in Table 5.1.

5.4.1

Kinetics of Growth Controlled by the Fixation of New Complexes: Mononuclear Regime

When new complexes which must be added to a particle move by diffusion in the liquid medium, and this diffusion step is faster than bonding of the complexes to the existing solid surface, the particle growth rate is controlled by the surface fixation of new complexes. Moreover, in the mononuclear regime, the bonding of a first new complex to initiate a new crystalline layer is much slower than the completion of this layer. That is to say, each new crystalline layer needs to nucleate before it can spread onto the particle. Once this first bonding has been achieved, completion of the crystalline layer is made easier and faster, because further complex attachment may occur on several sides in steps of the solid surface (Fig. 5.11). Overall, growth proceeds layer by layer. This generally corresponds to welldefined geometrical shapes where the particle faces are the most dense atomic planes. Surface nucleation is increasingly probable when the particle size increases, so that the growth U rate of a particle is proportional to its surface area, as described by (5.36) (Nielsen 1964) U¼

dr ¼ k mðCÞ r 2 dt

ð5:36Þ

In this equation km(C) is a constant which depends on the solute concentration C. For two particles with an initial radius difference δro, the relative radius difference δr r increases with time as δr r

¼

r δr o ro ro

ð5:37Þ

This growth regime is not favorable to the formation of monodisperse particles. It was shown to occur when the entropy change per unit volume ΔSV, which is associated with the phase transformation from the liquid solution to the solid phase, satisfies (5.38) where R is the universal gas constant:

182

5 Nanoparticle Formation

ΔSV > 4R

5.4.2

ð5:38Þ

Polynuclear Growth Regime

When polynuclear growth occurs, the surface nucleation of a new crystalline layer is faster that in the previous mononuclear mechanism, although it remains slower than the transport of new complexes towards the solid by molecular diffusion in the liquid. Practically, the main difference with the mononuclear regime is that a new crystalline layer does not have the time to be completed before a second one nucleation occurs on top of it. This growth regime is also termed normal growth, because the growth rate U does not depend neither on the particle size, nor on the time (Williams et al. 1985). It was shown that U depends on the temperature T and on ΔGV the Gibbs free energy associated to phase change from the liquid solution to the solid, according to Eq. (5.39): U¼

  dr ΔGv ¼ k pðCÞ λΓ 1  exp  dt kT

ð5:39Þ

In this equation, Γ is the successful atomic jump frequency which was previously
v defined for nucleation, 1  exp  ΔG represents the probability to create a surface kT nucleus, and kp(C) is a constant which depends on the solute concentration. As in mononuclear growth, each surface nucleus provides steps where new v molecules can add up and easily fix to a layer. When ΔG kT is small, the normal growth rate can be expressed by replacing Γ with an equivalent expression depending on the diffusion coefficient: U¼

kp ðCÞ D ΔGv kT λ

ð5:40Þ

The value of ΔGv for growth which must be used in these equations is the average final ΔGv,f value illustrated in Fig. 5.3. This value can also be estimated from the solute supersaturation S ¼ CCs by ΔGv,f ¼

RT LnS Vm

ð5:41Þ

The particles rather take on a spherical shape and their radius grows linearly with time according to (5.42) (LaMer 1952) r ¼ r0 þ kp t

ð5:42Þ

5.4 Crystalline Growth Mechanisms of Solid Particles

183

In this equation kp is a constant. For two particles with an initial radius difference δro, the relative radius difference δr r attenuates slowly with time according to (5.43) δr r

5.4.3

¼

r o δr o r ro

ð5:43Þ

Kinetics of Growth Controlled by the Diffusion of Complexes in Solution

When new complexes which must be added to a particle move by diffusion in the liquid medium, and this diffusion step is slower than bonding of the complex to the existing solid surface, mathematical modeling gives a growing rate U of the radius r of particles in agreement with the following differential equation (Nielsen 1964): U¼

dr DðC  Cs ÞV m ¼ dt r

ð5:44Þ

In this equation, D is the diffusion coefficient of the complexes and Vm is the molar volume of the material constituting the particle. By solving this differential equation the following growth law can be obtained (Matijevic 1987): r 2 ¼ k D t þ r 20

ð5:45Þ

where kD is a constant which depends on the diffusion coefficient D of the complexes which are added to the particles. For two particles with an initial radius difference δro the relative radius difference δr decreases as time increases, according to (5.46) r  2 δr r δr 0 ¼ 0 r r r0

ð5:46Þ

This relative size difference attenuation is faster than in the previous polynuclear growth regime. This is therefore a growth regime favorable to the achievement of monodisperse particles. Moreover, since there is no limitation to the growth kinetics by the nucleation of a new crystalline layer on the particle, growth occurs by random fixation of new complexes on the existing particle surface, which favors a macroscopic spherical shape, exactly like in polynuclear growth (Fig. 5.11).

184

5.4.4

5 Nanoparticle Formation

Growth Regime Transition

From a comparison of these three mechanisms, it appears that the mononuclear growth regime dominates when the particles begin growing. As their size increases, the surface they offer to form surface nuclei increases. Hence, a transition from a mononuclear to a polynuclear regime is likely to occur. The diffusion of new complexes in the solution towards the particles becomes rate limiting when the particles are bigger, and the solute concentration which remains in the solution has decreased. The conditions according to which each mechanism predominates, as a function of the particle size and the solute concentration, are illustrated in Fig. 5.12 for ZnS particles synthesized by Williams et al. (1985).

5.4.5

Importance of Crystal Defects: Growth of Amorphous Particles

Crystalline packing defects may provide permanent steps where new solute complex molecules can easily fix to a solid particle. An example of such defects is screw dislocations illustrated in Fig. 5.13, which helps growing big monocrystals, such as silicium monocrystals by crystallization from the melt. With such defects, a distinction between mononuclear and polynuclear growth can no longer be made and the kinetics are similar to those observed in normal growth. The growth rate U is constant, independent of the particle size. However, it can still be controlled by

Fig. 5.12 Domains of occurrence of the three growth regimes of ZnS particles as a function of the particle diameter as a function of the supersaturation S: (1) mononuclear, (2) polynuclear, and (3) diffusion limited. The dark line indicates the experimental growth trajectory of ZnS particles (adapted from Williams et al. (1985))

5.5 Examples of Solid Particles Made by Nucleation and Growth from Precursor. . .

185

Fig. 5.13 Normal growth due to a screw dislocation

the diffusion of new complexes. In the case of amorphous particles, many steps are always available for growth. Hence the growth regime is often of the normal type.

5.4.6

Importance of Thermal Diffusion in the Growth Process

Up to this point, no mention was made of the influence of thermal diffusion on the growth of particles. When a liquid material such as a metal solidifies, the difficulty in evacuating the heat of solidification is often responsible for the growth of dendrites. Since many hydrolysis and condensation reactions of oxide precursors are also exothermic, the bonding of molecular complexes to a growing particle may certainly involve similar heat evacuation effects. As the oxide bonds are difficult to melt, it is possible that the local condensation heat accelerates the local condensation reactions, as well as the local diffusion of solutes. Hence, the formation of dendrites may also be possible, but this effect is not well documented.

5.5 5.5.1

Examples of Solid Particles Made by Nucleation and Growth from Precursor Solutions Particle Shape

In the present state of knowledge of the complex chemistry of inorganic material precursors in solution, it is not possible to predict which kind of particle shape may be obtained as a function of the nature of cations. The particle size, shape, and

186

5 Nanoparticle Formation

composition largely depend on the anion type and ionic strength. Besides, it is possible that complexes different from the first complexes reaching supersaturation induce after some time the nucleation of more stable particles different from the particles initially formed, due to a slower kinetics of formation although with a more stable thermodynamic structure. Overall, the type of particles obtained, for instance amorphous or crystalline, largely depends on details of the chemical protocol selected and all the precursors mentioned in Chaps. 2–4 may be used. However, an extensive amount of experimental results on hydrous oxide particles of uniform size and shape was gathered, in particular by Matijevic and Scheiner (1978). A very limited list of particles made from metal salts is provided in Table 5.2, but many other particles were made. To illustrate the variety of results such particles comprise spindle-shaped hematite particles by Matijevic and Cimas (1987) as illustrated in Fig. 5.14 but also disklike hematite (α-Fe2O3), and crystals of magnetite (Sapieszko and Matijevic 1980a), polyhedral copper oxide, rodlike crystals of zinc oxide, vanadium pentoxide leaflets and elemental nickel spherulites (Sapieszko and Matijevic 1980b), A1(OH)3 particles with a color due to a chelating ligand (Tentorio et al. 1980), stabilized ZrO2 particles (Uchiyama et al. 1987), and antimony-doped SnO2 particles for gas sensors (Seiyama et al. 1983). The technique is not limited to oxides. Mixed PbS-xCdS and ZnS-xCdS particles could be grown by mixing a solution containing CdS nuclei in solutions of PbS or ZnS precursors (Wilhelmy and Matijevic 1985). Cubic PbS particles obtained by Wilhelmy and Matijevic (1985) are shown in Fig. 5.15, while the variety in shape and composition of particles obtained by Ishikawa and Matijevic (1988) from CoSO4 solutions with sodium phosphate NaH2PO4 and urea is reported in Fig. 5.16. Many other particles were grown from alkoxides, such as in the mixedoxide powders made by Mazdiyasni (1982). Very often the particle shape is extremely complex to describe. For instance, ZnS particles synthesized by Rowell et al. (1968) or by Williams et al. (1985) appear to be faceted at low magnification. However, at a higher magnification, these facets show a fibrous structure. Actually, the particles which can be observed in microscopy are often agglomerates of smaller ones. For instance the TiO2 particles made by Santacesaria et al. (1986) or by Barringer and Bowen (1982) are well described by a double-size distribution: a first one for crystallites which can be determined by X-rays (6–8 nm) and a second one for the full particles observed under an electron microscope (0.2–0.5 μm).

5.5.2

Monodisperse Particles

Monodisperse particles have attracted much interest and a limited list of such particles is given in Table 5.3. Some of them have a complex oxide composition. A typical example of monodisperse particles is the ZnS particles made by Wilhelmy and Matijevic (1985). Their average size was 0.22 μm and their size distribution is reported in Fig. 5.17. They showed an effect known as the higher

Matijevic and Cimas (1987) and Ozaki and Matijevic (1985) Sapieszko and Matijevic (1980a) Watson et al. (1962)

Spindle

ZrO2 SiO2

Rutile TiO2

CeO2

CrOOH

Spherical

Spherical

Matijevic et al. (1977), Visca and Matijevic (1979), and Barringer and Bowen (1982) Blesa et al. (1985) Shimohira and Tomuro (1976)

Matijevic (1986)

Demchak and Matijevic (1969)

Regazzoni and Matijevic (1983) Brace and Matijevic (1973) Scott and Matijevic (1978)

Spherical

Ni ferrites

Spherical Layered spherical Spherical

Sugimoto and Matijevic (1979) and Ishikawa and Matijevic (1988) Regazzoni and Matijevic (1982)

Cubic

Ni-Co ferrites Amorphous A1OOH A1OOH

Sugimoto and Matijevic (1980) Matijevic et al. (1975)

Spherical

Disk Rod

References Ozaki et al. (1984) Matijevic and Scheiner (1978) Hamada and Matijevic (1981)

Shape Ellipsoidal Spherical Cubic

Fe3O4 Fe3(SO4)2(OH)5∙2H2O alunite Co3O4

β-FeOOH

Particles Hematite Fe2O3

Table 5.2 Particles made by nucleation and growth from metal salt solutions

Spherical Spherical Spherical Spherical

GdC Au metal Ni metal

Spherical

Spherical

Cubic

Spherical

Spherical

Whiskers Cubic

Spherical Spherical

Spherical

Shape Rods Leaflets Polyhedral

CdCO3 PbS-xCdS ZnSxCdS Al phosphate Fe phosphate AgI

CdS

PbS

PbS

Th (OH)2SO4 CuS ZnS

Particles ZnO V2O5 Cu(I)O

Ayame et al. (2011) and Kobayashi et al. (2013) Kobayashi et al. (2012) Faraday (1857) and Hayat (1989) Sapieszko and Matijevic (1980b)

Katsanis and Matijevic (1982)

Matijevic and Wilhelmy (1982)

Matijevic and Wilhelmy (1982) and Gobet and Matijevic (1984) Janekovic and Matijevic (1985) Wilhelmy and Matijevic (1985) Wilhelmy and Matijevic (1985)

Chiu and Meehan (1974)

Chiu (1977) Chiu (1981) and Wilhelmy and Matijevic (1984) Czekaj et al. (1988) Wilhelmy and Matijevic (1985)

References Sapieszko and Matijevic (1980b) Sapieszko and Matijevic (1980b) Sapieszko and Matijevic (1980b) and McFayden and Matijevic (1973) Milic and Matijevic (1982)

5.5 Examples of Solid Particles Made by Nucleation and Growth from Precursor. . . 187

188

5 Nanoparticle Formation

Fig. 5.14 Spindle-shaped hematite particles made at 100  C from FeCl3 (a) seen under an electron transmission microscope and (b) seen under a scanning electron microscope (reprinted with permission from Matijevic and Cimas (1987). Copyright 1987 Springer Nature)

Fig. 5.15 PbS particles made from thioacetamide and lead nitrate (reprinted with permission from Wilhelmy and Matijevic (1985). Copyright 1985 Springer Nature)

5.5 Examples of Solid Particles Made by Nucleation and Growth from Precursor. . .

189

Fig. 5.16 Transmission electron microscope micrographs of CoSO4 particles made at 80  C in the presence of urea and sodium phosphate NaH2PO4. Composition: (a, b) CoCO3∙xH2O; (c) Co (NH4)PO4∙xH2O; (d) Co3(PO4)2∙xH2O (reprinted with permission from Ishikawa and Matijevic (1988). Copyright 1988 Springer Nature)

order Tyndall effect (HOT) which is a diffraction of visible monochromatic wavelengths. They also had stoichiometric ZnS composition and they were well crystallized. However, their B.E.T. specific surface area 66 m2 g1 indicated an internal structure composed of primary crystallites with a size of 3–10 nm (Johnson et al. 1986). Another example of monodisperse particles concerns silica nanoparticles which were grown from propylene glycol-modified silane (PGMS), complexed with ice-cooled NH3,aq (Yokoi et al. 2009). In these conditions, the size was much smaller than in the previous example, centered at ~8.5 nm, as illustrated in Fig. 5.18.

5.5.3

Growth Termination

Another interesting phenomenon is the termination of growth at a given particle size. The anions seem to have an effect not only on the structure and shape of the particles, but also on their size. As an example, the size of aluminum hydroxide spherical powders was reported to be a function of the proportion of SO2 ions to Al in 4 solution (Matijevic 1984). In studies on CdS (Fojtik et al. 1984) and MnO2 (Lume-

190

5 Nanoparticle Formation

Table 5.3 Particles made by nucleation and growth from alkoxide solutions Particles from alkoxides TiO2

SiO2

Ref. Barringer and Bowen (1982) Fegley and Barringer (1984) Fegley and Barringer (1984) Stöber et al. (1968)

SiO2-B2O3

Jubb and Bowen (1987)

ZnO

Heistand II and Chia (1986) Ogihara et al. (1986) Brown and Mazdiyasni (1970) Rhodes and Haag (1970)

ZrO2 ZrO2-Al2O3

Ta2O5 HfO2 (Y doped) ZrO2 (Y doped)

Fig. 5.17 Particle size distribution of a ZnS sol as determined by electron microscopy (histogram) and by light scattering (dashed lines) (adapted from Wilhelmy and Matijevic (1984))

Complex particles NiFe2O4

Ref. Economos (1959)

(Mg, Mn)Fe2O4

Gallagher and Schrey (1964) Morgan (1974)

Li2TiO3 Pb1xLax(ZryTix)1x/ 4 O3 HfTiO4 BaTiO3

Brown and Mazdiyasni (1972) Mazdiyasni and Brown (1970) Mazdiyasni et al. (1969)

SrTiO3 SrZrO3

Smith II et al. (1970) Smith II et al. (1970)

Mullite 3Al2O3∙2SiO2 Ba1xLaxFe12O19

Mazdiyasni and Brown (1972) Higuchi et al. (1986)

5.5 Examples of Solid Particles Made by Nucleation and Growth from Precursor. . .

191

Fig. 5.18 Size distribution of colloidal silica nanoparticles synthesized from propylene glycolmodified silane (PGMS). Synthesis reactant concentrations: [NH3] ¼ 1.6 M, [PGMS] ¼ 10 mM, T ¼ 353 K, 24 h (adapted from Kobayashi et al. (2016))

Pereira et al. 1985) particles, growth stopped at a very precise final size which depended on the fabrication parameters (ion concentration, pH, solvent). With alkoxides, the amount of water for hydrolysis was also found to be an important parameter to determine the final particle size. An excess of water usually resulted in finer powders. A possible explanation to these phenomena rests on different hydrolysis kinetics for different ligands. In particular, chelating ligands have a profound effect. With titanium alkoxides, the half-time life of OR ligands is typically of the order of 20 s, while it is of the order of 2.5 h for substituted diketonato groups such as acac (Sanchez and Ribot 1994). Consequently, olation  becomes less prominent than oxolation as the complexation ratio x ¼ ½acac ½M  increases. Kinetically, a system behaves as if x ¼ 0 at the beginning of hydrolysis because the uncomplexed alkoxide group is first hydrolyzed, so that solid TiO2 particles can start to form. Then, more and more complexed alkoxides are mixed in the condensation product which attach onto the particles. These particles end up being capped by acac groups, so that their growth terminates. However, the process does not stop there. During aging, some acac groups are slowly eliminated from the particle surface and condensation can again slowly operate between surface OH groups of neighbor particles to produce colloidal gels. A behavior similar to that of Ti was reported for the tetravalent metals Zr, Ce, Ti, and Sn and even for trivalent Al. TiO2 sols could be made stable at pH 0 or 0 or 0 or 0 Φ ¼ βDx6 βD > 0 Φ ¼ βLx6 βL > 0 Φ ¼ δx7 δ>0 Φ ¼ ξx12 ξ>0

Effect Attraction or repulsion depending on the ion charges Attraction or repulsion depending on the ion sign and dipole orientation Attraction or repulsion depending on the dipole orientation Attraction, by rotation of dipoles

Name Coulomb

Attraction

Debye

Attraction

London

Attraction

Casimir and Polder

Coulomb Coulomb Keesom

Repulsion

Adapted from Hiemenz (1977)

X A

¼ ξx12  βx6

ð6:2Þ

In this equation, ξ and β are numerical coefficients. The term ξx12 corresponds to a repulsion force which dominates at hard contact between two molecules, when their external electronic orbitals begin to interpenetrate. If x > νc (c velocity of light, ν vibration frequency of the dipoles) the term βx6 must be replaced by a term δx7 (δ, a numerical coefficient) which corresponds to a modified attraction term known as the retarded effect. It is due to a time lag in the transmission of dipole vibrations between two molecules and only becomes significant at distances large enough, practically when x > 10 nm (Casimir and Polder 1948). As a good approximation, except at hard contact, the overall van der Waals interaction energy between two molecules can be approximated by the relationship X A

6.3.1.2

¼ βx6 with β > 0

ð6:3Þ

Van der Waals Interaction Between Colloidal Particles

To derive van der Waals interaction between two macroscopic particles placed in a liquid medium, the molecular interactions as expressed in Eq. (6.3) must be summed up for all pairs of molecules composed of one molecule in each particle, as well as

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

213

for all pairs of molecules with one molecule in a particle and one molecule in the solvent. Important contributions to this field were made by Hamaker (1936) for discrete molecules, and by Lifshitz (1956) who replaced the discrete atoms by a continuous medium. Integration of ∑A over two spherical particles of radius r separated by a distance S0 (Fig. 6.2) gives the interaction energy (Hiemenz 1977):    S20 þ 4rS0 A 2r 2 2r 2 ΦA ¼  þ þ ln 2 6 S20 þ 4rS0 S20 þ 4rS0 þ 4r 2 S0 þ 4rS0 þ 4r 2

ð6:4Þ

A is a positive constant termed the Hamaker constant, which depends on the polarization properties of the molecules in the two particles as well as in the medium which separates them. The Hamaker constant Ai of a medium i has the dimension of an energy and typical values are in the range from 3.5 to 8  1020 J. A few values are provided in Table 6.2. If A1 designates the Hamaker constant for the matter inside a particle 1, A2 for the matter inside the liquid which separates two particles, and A3 for the matter inside a particle 3, the Hamaker constant A123 for particles 1 and 3 separated by a liquid medium 2 which carries no permanent dipole contribution of molecular origin (hence not water) can be estimated by (Masliyah 1994)

Fig. 6.2 Pair of particles used to derive van der Waals interaction

Table 6.2 Hamaker “unretarded” (previous δx7 term ignored) constants Ai for a few common materials Materials Metals Gold Oxides A12O3 MgO SiO2 (fused) SiO2 (quartz) Ionic crystals Calcite

Ai (1020 J) 16.2–45.5 45.3 10.5–15.5 15.4 10.5 6.5 8.8 6.3–15.3 10.1

Adapted from Masliyah (1994)

Materials Polymers Polyvinyl chloride Polyethylene oxide Water Acetone Carbon tetrachloride Chlorobenzene Ethyl acetate Hexane Toluene

Ai (1020 J) 6.15–6.6 10.82 7.51 4.35 4.20 4.78 5.89 4.17 4.32 5.40

214

6 Peptization of Colloidal Sols

pffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffi A1  A2 A1  A3

A123 ¼

ð6:5Þ

A123 can actually be a positive or a negative constant. In the latter case, a repulsion occurs between the two particles. This formula also gives the Hamaker constant A121 for two particles 1 dispersed in the liquid medium 2 (except for permanent dipolar molecules such as water): A121 ¼

pffiffiffiffiffi pffiffiffiffiffi2 A1  A2

ð6:6Þ

In this case the Hamaker constant is always positive, and an attraction between the two particles always occurs. For a separation S0 between the external surfaces of the particles such that Sr0 < 1, a good approximation of Eq. (6.4) is (Overbeek 1977) ΦA ¼ 

AL 12S0

 1þ2

     S0 S0 15 S0 2 3 S0 3 ln   16 L 32 L L L

ð6:7Þ

where L ¼ R þ 3S40 . A simplified expression of this van der Waals interaction, valid when Sr0  1, is ΦA ¼



Ar 12S0

ð6:8Þ

Other simple expressions of van der Waals attraction are provided in Table 6.3.

Table 6.3 Simple formulas for van der Waals attraction between two particles Particles Two spheres of same radius r Two spheres with unequal radii r1 and r2 Two parallel plates with thickness δ Interaction per unit area Two blocks Interaction per unit area Two cylinders crossed at 90 Cylinder near a flat surface Two parallel cylinders

ΦA

Conditions r  S0

Ar 12S 0 1 r2 6S0Ar ðr1 þr 2 Þ A 12π



1 S20

1 þ ð2δþS

0Þ

2

þ ðδþS1

A 12πS 2 0

pffiffiffiffiffiffi A r r  6 S10 2 pffi  pAffiffi r 3=2 12 2 S0 pffiffiA 3=2 12 2 S0



Adapted from Hiemenz (1977) and Leite et al. (2012)



r 1 r2 r1 þr 2

1=2

0Þ

 2

r1 and r2  S0

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

6.3.2

215

Adsorption of Ions and Electrical Double Layer

When solid particles are dispersed in a liquid medium which contains an electrolyte, some specific ions are often preferentially adsorbed on the surface of the particles. That is to say, the surface of these particles carries a fixed electrical charge density, σ 0, and is brought to an electrical potential Ψ 0. The ions which are adsorbed on the particles are termed electric potential-determining ions.

6.3.2.1

Zero-Point Charge “z.p.c.”

For oxide particles, in most cases, these potential-determining ions are H+ and OH, so that it is possible to adjust Ψ 0 by modifying the pH. A consequence is that each oxide is actually characterized by a particular pH for which the particles carry no net charge, with pH known as the “zero-point charge” or z.p.c. At pH >z.p.c. the particles adsorb more OH anions than H+ ions, so that they are negatively charged. On the other hand at pH 9.4 alumina particles are negatively charged. For pH Li+

Li+ > Cs+ Li+ > Cs+

550

ZrO2 FeOOH β-MnO2 ZnO Cr2O3 Fe2O3 Al2O3 MgO

Ease of adsorption of cations Cs+ > Li+ Cs+ > Li+ Cs+ > Li+ Cs+ > Li+ Cs+ > Li+

Li+ > Cs+ Li+ > Cs+ Li+ > Cs+ Li+ > Cs+ Li+ > Cs+

650 532 773

μ¼

V ðV velocity, E electric fieldÞ E

z.p.c. (reference) 0.5 (Weiser 1935) 1–2 (Weiser 1935) 1.5 (Stumm et al. 1970) 2.5 (Hunter 1981) 3.7 (Malati and Estefan 1971) 3.2 (Depasse and Warlus 1976) 4.5 (Hunter 1981) 6 (Tadros and Lyklema 1969) 6 (Berube and De Bruyn 1968) 6.7 (Blesa et al. 1985) 6.7 (Hunter 1981) 7.3 (Stumm et al. 1970) 8 (Blok and De Bruyn 1970) 8.4 (Hunter 1981) 8.6 (Hunter 1981) 9 (Hunter 1981) 12 (Hunter 1981)

ð6:10Þ

The isoelectric point (i.e.p.) is defined as the pH for which the mobility of the particles is zero, that is to say, when ζ ¼ 0. In practice the i.e.p. and the z.p.c. are often considered as synonymous. Values for oxides have been investigated by Parks (1965), Yoon et al. (1979), and Hunter (1981); a list is gathered in Table 6.4. Parks showed that the adsorption of aqua groups H2O or hydroxo groups OH on the particles lowers the z.p.c. by approximately 2 units. A better crystallized oxide particle also has a lower z.p.c. than an amorphous or poorly crystallized particle. The relationship between the z.p.c., the hydration energy, and the order of adsorption of cations is discussed in a further paragraph.

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

6.3.2.4

219

Surface Electric Potential Ψ 0 of a Particle as a Function of the pH

Several models have been developed to describe the electric potential Ψ (x) in the liquid which surrounds a colloidal particle (Hiemenz 1977). In the most frequent applications of the electrostatic theory, the electric potential Ψ 0 at the surface of the charged particle is considered to be constant, for a given pH. If the activity coefficients of the protons adsorbed on the particle surface can be considered independent of their surface concentration, this surface potential can be simply related to the pH according to thermodynamics considerations, by the Nernst equation: Ψ0 ¼

2:303 RTððz:p:c:ÞÞpHÞ F

ð6:11Þ

where F is the Faraday (96,487 C), R is the universal gas constant (8.3143 J K1 mole1), and Ψ 0 is in volt. At 25  C Ψ 0 ¼ 0:06 ððz:p:c:ÞÞ  pHÞ

ð6:12Þ

More generally for an oxide, the two following charge formation reactions can be considered, with their equilibrium constants (Jolivet 1994):   ½MOH Hþ 0 $ MOH þ ¼  MOHþ 2  þ  ½MO H0  MOH $ MO þ Hþ 0 K0 ¼ ½MOH

MOHþ 2

Hþ 0

Kþ 0

ð6:13Þ ð6:14Þ

  designates the proton concentration near the surface of the particle. where Hþ 0 According to Boltzmann statistics 

Hþ 0



    eΨ 0 ¼ Hþ exp 1 kb T

ð6:15Þ

  where Hþ 1 is the proton concentration far from the surface of the particle. Hence Kþ 0 and

    ½MOH Hþ e Ψ 0 0 þ  ¼  exp ¼ K kb T MOHþ 2

ð6:16Þ

220

6 Peptization of Colloidal Sols

K 0

  ½MO Hþ 0 ¼ ½MOH

¼ K exp

  e Ψ 0 kb T

ð6:17Þ

where   ½MOH Hþ 1  K ¼  MOHþ 2

ð6:18Þ

  ½MO Hþ 1 K ¼ ½MOH

ð6:19Þ

þ

and 

K+ and K are intrinsic constants which characterize the acidity of the surface groups when the surface potential Ψ 0 ¼ 0. The difference in magnitude between these intrinsic constants is ΔpK ¼ pK  pKþ ¼ log 10

½MOH 2   ½MO MOHþ 2

ð6:20Þ

ΔpK can also be expressed as ΔpK ¼ log 10

1  2θ θ

ð6:21Þ

where θ¼ ¼

 þ

  MOHþ 2 þ ½MOH þ ½MO



½MO þ ½MOH þ ½MO

MOH2

MOHþ 2

ð6:22Þ

When ΔpK > 2, the fraction of charged adsorption sites is low and the concept of a zero-point charge is valid. This is the case with most oxides and the z.p.c. is given by z:p:c ¼

pK þ pKþ 2

ð6:23Þ

+  From this expression of the z.p.c. and from the expressions of Kþ 0 , K0 , K , and K, in (6.16) to (6.19), it is possible to derive the following expression of the surface electric potential Ψ 0:

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

½MO 2:303 1  RT ðz:p:c:Þ  pH þ log 10  Ψ0 ¼ F 2 MOHþ 2

221

! ð6:24Þ

On the other hand, the fraction of ionized sites is high when ΔpK < 2 and in this case the concept of i.e.p. is more useful than that of z.p.c.

6.3.3

Gouy-Chapman Model

6.3.3.1

Electric Potential Ψ (x) at a Distance x from a Planar Surface (Hiemenz 1977; Masliyah 1994)

According to Poisson’s equation, the electric potential profile Ψ is the solution to the differential equation: ∇2 Ψ ¼  2

2

ρ εr ε0

ð6:25Þ

2

where ∇2 Ψ ∂∂xΨ2 þ ∂∂yΨ2 þ ∂∂zΨ2 , ρ is the electric charge density at position (x, y, z), 1 εo is the dielectric permittivity of the vacuum (4π in u.e.s.c.g.s. units, 12 1 8.854  l0 Farad.nr in the international system), and εr is the relative dielectric constant of the liquid medium (78.4 for water at 25  C). For a charged planar surface with its face perpendicular to the x-axis, this equation simply becomes d2 Ψ ρ ¼ εr ε0 dx2

ð6:26Þ

In the Gouy-Chapman model, the counterion layer is considered to be entirely diffuse (Fig. 6.5) and the local charge density at x is ρ¼

X i

ðni zi eÞ

ð6:27Þ

where ni designates the local concentration (number of ions per m3) of ionic species i with charge number zi (positive for a cation and negative for an anion) and e is an electron charge (1.60209  1019 C). The summation is carried over all ion types i. According to Boltzmann statistics ni ¼ ni ð1Þ exp

zi eΨ kb T

ð6:28Þ

where ni(1) is the concentration of ion species i (number of ions per m3) far from the surface (on a molecular scale), kb is Boltzmann constant (1.38054  1023 J K1),

222

6 Peptization of Colloidal Sols

Fig. 6.5 Gouy-Chapman and Stern models for the electrical double layer

e is the electronic charge (1.60209  1019 C), and T is the temperature in K. In practice ni(1) corresponds to the average concentration of each electrolyte added in the liquid medium. If the electrolyte in the liquid medium where the particles are dispersed is a “z:z” electrolyte (cations and anions with the same charge number z), Ψ is the solution to the differential equation d2 Ψ ¼ dx2

P

i ðni ð1Þzi

εr ε0

eÞ



    zeΨ zeΨ þ exp exp kb T kb

for which the boundary conditions are

ð6:29Þ

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

Ψ ¼ Ψ 0 at x ¼ 0   dΨ ¼ 0 at x ¼ 1 Ψ ¼ 0 and dx 1

223

ð6:30Þ ð6:31Þ

Actually this equation could be exactly integrated by Gouy and Chapman. The solution is the following function of the distance x from a planar surface: Ψ ð xÞ ¼

1 þ Γ 0 exp ðκxÞ 2kb T ln e z 1  Γ 0 exp ðκxÞ

eΨ0 z kb T  2 1= 2e nð1Þ z2 2 κ¼ εr ε0 k b T

with Γ 0 ¼ tanh

ð6:32Þ ð6:33Þ ð6:34Þ

In the above formula, kTb can be replaced by FR in which R is the universal gas constant and F a Faraday. In spite of the fact that the electric potential gradually attenuates as the distance x increases, κ1 gives a measure of the rapidity of this attenuation. This parameter has the dimension of a distance and is termed the electrical double-layer thickness or the Debye-Hückel length. For an electrolyte which has different charge numbers on its ions, Eq. (6.34) becomes κ¼

 2 P 2 1=2 e i ni z i εr ε0 k b T

ð6:35Þ

where the sum is on all the ionic species i in solution. At large distances x when Γ 0 exp(κX) is small, (6.32) can be approximated by Ψ ð xÞ ¼

4kb T Γ exp ðκX Þ e z 0

ð6:36Þ

A more simple expression for the electrical double-layer thickness κ 1 is κ1 ðnmÞ ¼

0:304 pffiffiffiffi z C

ð6:37Þ

where C is the electrolyte concentration in mol L1 (or molarity). A few values of κ 1 for z ¼ 1 are given in Table 6.5: The surface charge σ 0 (in C m2) on the particle can be derived by considering that it must be exactly balanced by the excess counterions in the diffuse layer. Hence

224

6 Peptization of Colloidal Sols C (mol L1) 106 104 102

Table 6.5 Electrical doublelayer thickness for a few concentrations of a “1:1” electrolyte

Z σ0 ¼ 

1

Z ρdx ¼ 

0

1

εr ε0

0

d2 x dx ¼ εr ε0 dx2

κ 1 (nm) 304 30.4 3.04



dΨ dx



 1



dΨ dx

  ð6:38Þ 0

Considering the boundary conditions (6.31)  σ 0 ¼ εr ε0

6.3.4

dΨ dx



  zeΨ 0 ¼ 2½2εr ε0 k b Tnð1Þ sinh 2kb T 1=2

0

ð6:39Þ

Debye-Hückel Approximation (Hiemenz 1977; Masliyah 1994)

In the Debye-Hückel approximation zeΨ  1 kb T

ð6:40Þ

d2 Ψ ¼ κ2 Ψ dx2

ð6:41Þ

Ψ ¼ Ψ 0 exp ðκxÞ

ð6:42Þ

So that

and

In the case of a positively charged surface (Ψ 0 > 0), the coion and counterion concentration profiles are illustrated in Fig. 6.6 and given by the following functions:   zeΨ Coions nþ ¼ nð1Þ exp  kb T   zeΨ Counterions n ¼ nð1Þ exp kb T The surface charge density is

ð6:43Þ ð6:44Þ

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

225

Fig. 6.6 Distribution of the counterions and coions as a function of the distance x from a positively charged surface

σ0 ¼

6.3.5

ze Ψ 1 ½2εr ε0 kb Tnð1Þ =2 ¼ εr ε0 κΨ 0 kb T

ð6:45Þ

Stern Model (Hiemenz 1977; Masliyah 1994)

In the Stern model (Fig. 6.5), the counterion layer is itself divided into an external diffuse part plus an inner compact layer called the Stern layer. In this case the preceding formulas for the diffuse layer can be applied by replacing Ψ 0 by the Stern potential Ψ δ, while the distance x must be measured from the Stern surface instead of from the particle surface. The Stern potential Ψ δ is actually different from the zeta potential ζ. However for the most practical cases, these two potentials are very close to each other.

6.3.6

Case of a Charged Spherical Particle (Masliyah 1994)

6.3.6.1

Electric Potential Ψ (x) Created by a Spherical Particle

For a charged spherical particle, the differential equation which relates the electric potential Ψ to the distance x from the center of the sphere is

226

6 Peptization of Colloidal Sols

2 dΨ

  2eznð1Þ 1 d x dx zeΨ ¼ sinh εr ε0 dx kb T x2

ð6:46Þ

with Ψ ¼ Ψ 0 at x ¼ r (the particle radius). Let X xΨ . In the Debye-Hückel approximation where kzeΨ  1, the differential bT equation (6.46) becomes d2 x ¼ κ2 X dx2

ð6:47Þ

The solution of the above equation is of the type X ¼ Aeκx þ Beκx ¼ xΨ

ð6:48Þ

The condition Ψ 1 ¼ 0 gives B ¼ 0. If the double layer is much thicker than the particle radius, i.e., κr  1, that is to say, κ is very small (mathematically when κ ! 0), the electric potential around the particle is given by the potential around an isolated electric charge. Hence lim k!0 Ψ ¼

Q0 Q0 which gives A ¼ 4πεr ε0 x 4πεr ε0 x

ð6:49Þ

Hence Ψ¼

Q0 eκx 4πεr ε0 x

ð6:50Þ

Let x ¼ rζ be the radius corresponding to the shear surface where the ζ potential is measured. A large value of κ1 (i.e., a small value of κ) corresponds to a dilute solution. In this case the shear surface is very close to the surface of particle, that is to say, r can be replaced by rζ and (6.50) gives ζ¼

Q0 Q0 exp ðκr ζ Þ  exp ðκr Þ 4πεr ε0 r ζ 4πεr ε0 r

ð6:51Þ

rζ exp ðκðx  r ÞÞ x

ð6:52Þ

and Ψ¼ In conditions where κr  1

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

ζ

Q0 4πεr ε0 r

227

ð6:53Þ

and     dΨ 1 þ κr ¼ ζ dx x¼r r

ð6:54Þ

The surface charge density on the shear surface is therefore  σ ζ ¼ εr ε0

dΨ dx

 ¼ εr ε0 x¼r



 1 þ κr ζ r

ð6:55Þ

Considering again that κr  1 σ ζ  εr ε0

  1 ζ r

ð6:56Þ

So that Qζ ¼ 4πr 2 σ ζ ¼ 4πεr ε0 rζ ¼ Q0

6.3.6.2

ð6:57Þ

Electrophoretic Mobility of a Spherical Particle (Hiemenz 1977; Masliyah 1994)

Equation (6.46) makes it possible to determine an expression for the electrophoretic mobility of a spherical particle in the case of a thick double layer (κr  1) (Fig. 6.7). If Qζ is the total charge of the sphere composed of the particle plus the part of the Fig. 6.7 Electrophoretic mobility of a charged sphere with a thick double layer (adapted from Masliyah (1994))

228

6 Peptization of Colloidal Sols

electrical double layer inside the shear radius, the electrophoretic mobility of this core-shell sphere is μ¼

V Eapp

ð6:58Þ

where V is the velocity of the sphere and Eapp is the electric field applied to it. The electric force Fe acting on the sphere is F e ¼ Qζ Eapp ¼ 4πr 2 σ ζ E app

ð6:59Þ

If σ ζ is replaced by its expression from (6.57) F e ¼ 4πr 2 εr ε0

  1 ζEapp ¼ 4πrεr ε0 rζE app r

ð6:60Þ

At constant velocity, according to Stokes equation F e ¼ 6πηVr

ð6:61Þ

where η is the liquid medium viscosity. Hence, the electrophoretic mobility is μ¼

2εr ε0 ζ 3η

ð6:62Þ

In the case of a thin double layer (κr  1) (Fig. 6.8), the Navier-Stokes relationship gives η

d2 V x ¼ ρEapp dy2

ð6:63Þ

If this expression is combined with Poisson’s equation (6.26) d2 V x d2 Ψ ¼ ε ε E r 0 app dy2 dy2

ð6:64Þ

dV x dΨ þ C1 ¼ εr ε0 Eapp dy dy

ð6:65Þ

η A first integration gives η

dΨ x Since dV dy ! 0 and dy ! 0 as y ! 1, then C 1 ¼ 0 A second integration gives

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

229

Fig. 6.8 Electrophoretic mobility of a charged particle with a thin electric double layer (adapted from Masliyah (1994))

ηV x ¼ εr ε0 Eapp Ψ þ C 2

ð6:66Þ

Since dVx ! 0 and Ψ ! 0 as y ! 1, then C2 ¼ 0, Vx(y ¼ 0) ¼ V, and Ψ (y ¼ 0) ¼ ζ so that V¼

εr ε0 Eapp ζ η

ð6:67Þ

εr ε0 ζ η

ð6:68Þ

And the electrophoretic mobility is μ¼

230

6 Peptization of Colloidal Sols

6.3.7

Electrostatic Repulsion Force Between Two Charged Surfaces

6.3.7.1

Case of Parallel Planar Surfaces (Hiemenz 1977; Masliyah 1994)

This is a one-dimensional problem where the only dimension x is perpendicular to the planar surfaces. In this case, the repulsion force FR between two plates transcribes to the creation of a local hydrostatic overpressure p, which depends on the abscissa x, in the solution which surrounds the plates. This overpressure is itself due to an overconcentration of counterions, since from (6.43) and (6.44) and for positively charged plates      ze Ψ ze Ψ n  nþ ¼ nð1Þ exp  exp  kb T kb T

ð6:69Þ

  ze Ψ Δn ¼ n  nþ ¼ nð1Þ sinh kb T

ð6:70Þ

or

This gradient in excess counterions induces a gradient in the osmotic pressure π of the solvent, so that this solvent is dragged in the electric double layer and creates a local hydrostatic overpressure. In turn, the gradient in local hydrostatic pressure itself induces a local hydrostatic force (Fig. 6.9): Fig. 6.9 Balance of forces in the liquid between two parallel plates carrying positive surface charges

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

F h ¼ ½pðx þ dxÞ  pðxÞ ¼ 

∂p dx ∂x

231

ð6:71Þ

Moreover, the local ions at x in a slab of volume (1. dx), that is to say, of unit surface area (“1”) and thickness dx, are submitted to an electric force Fe given by F e ¼ ρ:l:dx:Ex

ð6:72Þ

where Ex ¼  dΨ dx is the local electric field at x. At equilibrium, the two forces Fe and Fh must balance each other (Fig. 6.9), so that dp dΨ þρ ¼ 0 dx dx

ð6:73Þ

If ρ is replaced by its expression given in (6.26) dp d2 Ψ dΨ  εr ε0 2 ¼0 dx dx dx

ð6:74Þ

By integration, this leads to the repulsive force per unit area between the two plates:  2 εr ε0 dΨ p ¼ constant ¼ F R dx 2

ð6:75Þ

This equation indicates that the particles’ repulsion is exactly balanced by the local hydrostatic overpressure pm in the solution at mid-distance between the two

particles because dΨ dx mid ¼ 0. In the Debye-Hückel approximation, the general solution to (6.40) is of the form Ψ ¼ C cosh ðκðx  So =2ÞÞ þ C 0 sinh ðκðX  S0 =2ÞÞ

ð6:76Þ

where C and C0 are two constants which must be selected to fit the boundary conditions. For two plates with different surface electric potentials Ψ 10 and Ψ 20, with external closest surfaces separated by a distance S0 C¼

Ψ 10 þ Ψ 20 Ψ 10  Ψ 20 C0 ¼ 2 cosh ðκS0 =2Þ 2 sinh ðκS0 =2Þ

ð6:77Þ

Moreover, in the case where the two plates have an identical surface electric potential Ψ 0

232

6 Peptization of Colloidal Sols

Fig. 6.10 Variation of the surface charge at constant surface potential, when two plates come closer to each other

Ψ¼

Ψ0 cosh κðX  S0 =2Þ cosh ðκS0 =2Þ

ð6:78Þ

In this symmetrical case, considering that the excess counterions in the liquid between the two plates are exactly balanced by the positive charge on the plates, the relation (6.39) which defines the surface charge density σ 0 remains valid, so that when the distance S0 between the two planar surface decreases and the surface potential Ψ 0 remains unchanged (no modification in the adsorbed ions) the surface charge σ 0 on the plates decreases as illustrated in Fig. 6.10. Next, Eq. (6.74) can be transformed to dp ¼ ρdΨ

ð6:79Þ

or, for a z:z electrolyte, according to (6.70) dp ¼ zeΔndΨ   zeΨ dp ¼ 2nð1Þze sinh kb T This overpressure differential integrates to

ð6:80Þ ð6:81Þ

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

  zeΨ 1 p ¼ 2nð1Þkb T cosh kb T

233



ð6:82Þ

and for zeΨ kb T  1  p ¼ nð1Þkb T

zeΨ kb T

2 ð6:83Þ

Making use of the Debye-Hückel solution for Ψ and dΨ dx and reporting them in (6.75), the repulsion force between the particles, when the separation distance S0 is small by comparison with the double-layer thickness, that is to say, when κS0  1, is e2 z2 nð1Þ 2 1 Ψ 0 ¼ εr ε0 κ2 Ψ 20 kb T 2

ð6:84Þ

4 e2 z2 nð1Þ 2 κS0 ¼ 2εr ε0 κ2 Ψ 20 eκS0 Ψ 0e kb T

ð6:85Þ

FR ¼ When κS0  1 FR ¼

At a large distance x when Γ 0 exp(κX) is small and Ψ (x) is given by (6.36) F R ¼ 64nð1Þk b TΓ 20 eκS0 In the case of two plates with different electric surface potentials Ψ 10 and Ψ 20 e2 z2 nð1Þ 2Ψ 10 Ψ 20 cosh κS0  1 FR ¼ kb T ð sinh κS0 Þ2

! ð6:86Þ

The electrostatic interaction energy is Z ΦR ¼

S0

1

 F R dS

ð6:87Þ

In the case κS0  1, Eq. (6.84) gives ΦR ¼ 2εr ε0 κ 2 Ψ 20 eκS0

ð6:88Þ

At a large distance x when Γ 0 exp(κX) is small and Ψ (x) is given by (6.36)

234

6 Peptization of Colloidal Sols

ΦR ¼

6.3.7.2

64nð1Þkb T 2 κS0 Γ0 e κ

ð6:89Þ

Electrostatic Interaction Between Spherical Particles (Hiemenz 1977; Masliyah 1994)

The electrostatic interaction between two particles is due to the electric charges adsorbed on the particles, which can be attenuated to a variable extent by the double electric layer. This is illustrated in Fig. 6.11, which shows that when two particles are far from each other, the counterion layers around each particle do not overlap. Hence, each particle has a virtually complete double electrical layer so that it roughly behaves as a neutral core-shell sphere (Fig. 6.11a). In these conditions, the interaction energy between two particles is ΦR  0.

Fig. 6.11 Conditions for the occurrence of electrostatic repulsion between colloidal particles

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

235

Fig. 6.12 Approximations made to derive the electrostatic interaction energy ΦR between the two spheres (adapted from Hiemenz (1977))

As the particles come sufficiently close to each other, their counterion layers start to overlap. That is to say, the excess counterion concentration at mid-distance is higher than what it would be from a single particle at the same distance. This increased ion concentration induces an increased osmotic flow of the solvent which itself induces a local hydrostatic overpressure in the solution between the spheres. Hence, a positive interaction energy ΦR > 0 appears which corresponds to a repulsion force between the two particles (Fig. 6.11b). Several models have been successively developed to describe this electrostatic interaction energy ΦR (Hiemenz 1977). As mentioned previously, it is often assumed in the mathematical derivation of ΦR that the electric potential at the surface of the particle remains a constant, Ψ 0, when the particles come close to each other. However, similar derivations have been made with the hypothesis that the surface charge density of the particles remains a constant, σ 0. For spherical particles which have a same radius r, if the electric double-layer thickness κ 1 is small by comparison with the nearest distance S0 between the surfaces of the particles, only the tails of the diffuse double layers overlap. Moreover, if r is large enough by comparison with κ1 (Fig. 6.12), the electric repulsion force between the two spheres can be estimated as the sum of elementary repulsion forces between parallel plates separated by a distance S such that pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S  S0 ¼ r  r 2  h2 2

ð6:90Þ

2h dh dS ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 2  h2

ð6:91Þ

Hence

236

6 Peptization of Colloidal Sols

Only the central region of the spheres significantly contributes to the repulsion between the spherical particles, so that dS ¼

2hdh r

ð6:92Þ

The corresponding repulsion force between the two elementary planar rings of the spheres is dF RS ¼ F R 2πhdh

ð6:93Þ

In this equation, FR can be replaced by the repulsion force between parallel planes previously calculated for κS  1 (thin double layer), which implicitly follows the Gouy-Chapman model and the Debye-Hückel approximation. This leads to dF RS ¼ 2εr ε0 κ2 Ψ 20 eκS 2πhdh ¼ 2εr ε0 κ2 Ψ 20 eκS πrdS

ð6:94Þ

Because the term eκS drastically attenuates the contributions to the repulsion force which do not come from the central part of the spheres, an approximate integration can be done by varying S from S0 to 1: Z F RS  πr

1

S0

2εr ε0 κ 2 Ψ 20 eκS πrdS

ð6:95Þ

which integrates to F RS  2πεr ε0 κ2 Ψ 20 eκS0

ð6:96Þ

The electrostatic interaction energy ΦR between the two spheres can then be derived by carrying the integration of FRS as this was done for plates in Eq. (6.87): ΦR ¼ 2πεr ε0 ρΨ 20 eκS0

ð6:97Þ

For unequal spheres having radii r1 and r2 and surface electrical potentials Ψ 10 and Ψ 20, the general expression for the electrostatic interaction energy is often referred to as the HHF expression (Hogg et al. 1966; Masliyah 1994): ΦR ¼

πεr ε0 r 1 r 2 r1 þ r2

   2

1 þ exp ðκS0 Þ 2  2Ψ 10 Ψ 20 Ln þ Ψ 10 þ Ψ 20 Ln½1  exp ð2κS0 Þ 1  exp ðκS0 Þ ð6:98Þ

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

6.3.8

237

The Main Routes to Adjust the Electrostatic Repulsion Between Spherical Particles

Equation (6.97) shows that the electrostatic repulsion between two particles can be experimentally modified in several ways. One method consists of modifying Ψ 0, by changing the concentration of potential-determining ions, that is to say, the pH when the potential-determining ions are H+ or OH. This action is necessary to realize the peptization of colloidal particles made from alkoxides. A second important method consists of modifying the electric double-layer thickness κ1 around the particles, so as to modify the screening effect due to the counterion layer. This can be done by adjusting the concentration n(1) of a non-potential determining electrolyte, such as Na+Cl for an oxide sol. This comes from the fact that n(1) is an important parameter in Eq. (6.34). As n(1) increases, κ increases and the electric doublelayer thickness κ 1 decreases, so that particles can come closer to each other without any significant increase of their electrostatic interaction. It is important to note that all ions in the liquid medium where colloidal particles are dispersed, whether or not they are potential determining, participate in the diffuse layer. For instance at pH ¼ 7, alumina particles are charged positively. If some NaCl is added to the solution, neither Na+ nor Cl modifies the electric potential since they are not adsorbed. However both participate in the construction of the electric diffuse layer, as well as H+ and OH. A third method consists of changing the valence z of an electrolyte which is dissolved in the liquid medium, for instance by replacing a chloride bringing Cl 3 anions by a sulfate bringing SO2 4 anions or a phosphate bringing PO4 anions. As the charge number z increases, Eq. (6.35) shows that κ drastically increases, and hence the electric double layer κ1 drastically decreases, so that colloidal particles can come much closer to each other without being submitted to a significant repulsion. This is a big effect which is at the root of the success of the DLVO theory.

6.3.9

Total Interaction Energy in Electrostatic Sols (Hiemenz 1977; Masliyah 1994)

According to the DLVO theory, the dispersion of colloidal particles in a stable sol depends on a combination of the electrostatic and van der Waals interactions, described by the total interaction energy: Φ ¼ Φ A þ ΦR

ð6:99Þ

This total interaction energy depends on the separation distance between particles, as illustrated in Fig. 6.13. Globally, van der Waals attraction always dominates at small and large separation distance S0 between the particles. The electrostatic repulsion may dominate only in some instances at intermediate separation distances,

238

6 Peptization of Colloidal Sols

Fig. 6.13 Variation of the total interaction energy Φ between two spherical particles, as a function of the closest separation distance S0 between their surfaces, for different double-layer thicknesses κ 1 obtained with different monovalent electrolyte concentrations. The electrolyte concentration is C (mol L1) ¼ 1015 κ2 (cm1) (adapted from Overbeek (1977))

which depend on the double-layer thickness κ 1, and hence on the concentration n (1), and the charge z of the ions composing the electrolyte is of great importance. When this is the case, Fig. 6.13 shows the existence of an energy barrier Φmax, opposing to the contact between two particles, which depends on the value of κ. If this energy barrier is high by comparison with the Brownian thermal agitation energy of the particles, for instance when Φmax > 30 kbT for κ1 ¼ 10  106 cm in Fig. 6.13, aggregation of the particles will not occur; the sol is kinetically stable. On the other hand, when this energy barrier is not too high by comparison with the Brownian motion energy of the particles, for instance Φmax  10 kbT for κ1 ¼ 106 cm in Fig. 6.13, this barrier can be statistically overcome by Brownian motion, as described by Boltzmann statistical law. In this case, the particles will slowly aggregate, which may correspond to the formation of colloidal gel as presented in Chap. 7. At last when the electrostatic repulsion never dominates,

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

239

even at intermediate distances, this barrier disappears and the particles rapidly aggregate. This phenomenon is known as flocculation or coagulation in the DLVO theory.

6.3.10 Coagulation (Overbeek 1977; Hiemenz 1977; Masliyah 1994) Globally, to achieve coagulation, it is possible to modify van der Waals interaction ΦA, generally with very limited flexibility for a given system. As indicated previously, it is more efficient to modify ΦR by monitoring the concentration of an electrolyte. This can be done with either a potential determining electrolyte which modifies the particle’s electric potential Ψ 0, that is to say, in most cases an acid or a base which modifies the pH, or a non-potential determining electrolyte such as NaCl or any other electrolyte which modifies the electrical double-layer thickness κ1. In the latter case, coagulation occurs for a critical coagulation concentration, designated by Cc in this book and by C.C.C. in other publications, which strongly depends on the counterion valence z. For parallel plates, Eq. (6.89) for ΦR and the appropriate formula for ΦA in Table 6.3 give Φ ¼ ΦR ¼

64 nð1Þkb T 2 κS0 A Γ0 e  κ 12π S20

ð6:100Þ

and when Ψ 0 is high, Γ 0  1. A simple way to consider when coagulation will occur is to consider the simplified condition such that Φmax  0

ð6:101Þ

dΦ ¼0 dS0

ð6:102Þ

64nð1Þk b T 2 κS0 A ¼ Γ0 e κ 12πS20

ð6:103Þ

while Φmax is itself defined by

This gives, respectively,

and

240

6 Peptization of Colloidal Sols

Table 6.6 Critical coagulation concentrations of A12O3 sols Valence z of counterions 1 2 3 4

Experimental values (mol L1) (Overbeek 1952) Cc(z) Cc(z)/Cc(z ¼ l) 1 5.2  102 6.3  104 1.2  102 5 0.8  10 1.5  103 5 5.3  10 10  104

64nð1Þk b T Γ 20 eκS0 ¼

A 6πS30

Theory (Hiemenz 1977) Cc(z)/Cc(z ¼ l) 1 1.56  102 1.37  103 2.44  104

ð6:104Þ

which when combined give Aκ A ¼ 12πS20 6πS30

ð6:105Þ

or κðS0 Þmax ¼ 2

ð6:106Þ

Substituting this result in Eq. (6.104) 64 nð1Þkb TΓ 20 e2 ¼

Aκ 3 48π

ð6:107Þ

Hence nð1Þ Cc  κ 3  z6

ð6:108Þ

This value of n(1) can actually be considered as an expression of the critical coagulation concentration Cc. This result is the most outstanding success of the DLVO theory because it shows that Cc is proportional to z6, in global agreement with experimental data. This is an effect of large magnitude and previously known, experimentally, as the Schulze-Hardy rule. In the case of A12O3 experimental data from Overbeek (1952) and calculated values are compared in Table 6.6.

6.3.11 Effect of Ion Solvation A study on Fe2O3 precipitates made from Fe(NO3)3 precursor (Dumont et al. 1976) has shown firstly that the critical coagulation concentration Cc depends on the volume fraction occupied by the particles, and secondly that positively charged particles (pH below the z.p.c.) are more stable than those negatively charged (pH above the z.p.c.). The latter result cannot be explained by a simple change in

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

241

the electrostatic repulsion, since the absolute magnitude of the zeta potential is the same for symmetrical pH values with respect to the z.p.c. However, it can be explained by a change in the structure of the electrical double layer due to solvation by water molecules. Structuration of water occurs with many materials. In Chap. 2, the solvation of ions by water molecules was presented. Actually, charged solid particles are themselves solvated by water molecules. Therefore, a slightly different effect of counterions on coagulation can be expected, depending on the relative strength of these counterions and the solid particles, to promote self-solvation by water. As an example, Fe2O3 particles themselves are strong structure promoters in water, as shown by a high hydration energy in Table 6.4. Small anions such as IO 3 and F are also known as strong “structure promoters” in water, and in practice they tend to form slightly more packed double layer close to the colloidal particles, than the larger size anions. Hence the electrical double layer is thinner and the critical coagulation concentration Cc is lower with these small-size anions. That is to say, they enhance coagulation.  On the other hand, larger size anions such as NO 3 and ClO4 are not much solvated by H2O dipoles. Hence, they are rejected by a material such as Fe2O3 which tends to be surrounded y a thick solvation water shell. The concentration of these anions is slightly lower immediately close to the particles, the electrical double layer is thicker, and the critical coagulation concentration Cc is higher. They favor the peptization of a sol. In summary, with strong water structure promoter particles such as Fe2O3 dispersed in acidic medium (positive charges on the particles), the amount of anions adsorbed decreases (and Cc increases), in the order known as the Hofmeister series (Hofmeister 1888; Dumont and Watillon 1971):     IO 3 > F > CH3 COO > CH2 ClCOO > BrO3 > SCN >       CHCl2 COO > Br > NO3 > ClO3 > Cl > ClO 4 I

ð6:109Þ

In basic conditions (negatively charged particles), a similar series occurs with cations in the order Liþ > Naþ > Kþ  Csþ

ð6:110Þ

In Table 6.4, this order is summarized by Li+ > Cs+. The z.p.c. of these colloidal particles is relatively high. With particles which are not strong structure promoters of water, the order of adsorption of anions and cations is reversed, as indicated in Table 6.4. A consequence of solvation is that experimental z.p.c. data reported for a given material are often scattered in a significant range of values, depending on the type of anions or cations in the liquid medium where the colloidal particles are dispersed, and hence on their fabrication method. Very cautious work is necessary to determine the z.p.c. of pure colloids without any adsorbed foreign anions or cations. An

242

6 Peptization of Colloidal Sols

example of such a study was made by Blesa et al. (1985) on ZrO2 particles made by hydrolysis of ZrOCl2∙8H2O and they found a z.p.c. of 6.7 for pure ZrO2.

6.3.12 Electrostatic Charge Reversal (Masliyah 1994) Let us consider two plates 1 and 2, each carrying positive charges but having a positive electrical surface potential Ψ 10 > 0 and Ψ 20 > 0, such that Ψ 20 > Ψ 10. The electrostatic force between these two plates is a repulsion at large separation distance S0. However it may become an attraction at close separation distance according to Eq. (6.86). This corresponds to an electric potential profile as shown in Fig. 6.14 when the two surfaces are closest to each other [6], such that the electric surface charge of plate 1 is reversed and becomes negative. However this view is questionable. It supposes that the electrical charges on the surface of the particle 1 can actually be reversed. With actual planar particles such as kaolinite, experimental behavior usually led to retaining of the hypothesis that the surface electric charge σ 0, rather than the electric potential Ψ0, is a constant (Newman 1987). Hence, repulsion always occurs between the two particles. For oxides where the surface charge is due to the adsorption of specific ions such as H+ and OH, charge reversal would mean that the [OH] concentration in the liquid close to particle 1 is such that the pH passed on the other side of the z.p.c. In this case particle 2 must be of a different nature from particle 1; otherwise it would also undertake charge reversal since it has the same z.p.c. This in turn led to

Fig. 6.14 Charge reversal for two plates with a different surface potential at close separation distances

6.3 The Classical Derjaguin, Landau, Verwey, Overbeek (DLVO) Stabilization Theory

243

Fig. 6.15 Transmission electron micrographs of (a) hematite particles and (b) hematite particles partly covered with Co3O4 particles (reprinted with permission from Ishikawa and Matijevic (1988). Copyright 1988 American Chemical Society)

examining of interactions between particles of a different nature. Matijevic has established 3-dimensional diagrams, depending on the concentration of two components and of the pH, which show behaviors not observable with a single component. Different fields of these diagrams correspond to the possible occurrence of several types of behavior: selective coagulation of one component; heterocoagulation in which one type of particles first coat the second type of particles; mixed sol formation in which the two types of particles are randomly dispersed; and sol demixion with separation in two liquid domains, each containing a different component. Heterocoagulation implies the formation of flocs which comprise the two types of particles. It usually occurs when particles of opposite charge are mixed (Matijevic 1978). Moreover, mixing these two components can be realized in various ways such as (1) two sols in a nascent state; (2) one sol with well-grown colloidal particles and one sol in a nascent state; and (3) two sols, each with well-grown colloidal particles. Each situation can lead to quite different coagulation or dispersion behaviors. When the particles of one component are much smaller than particles of the second component, they can adsorb on this second component and change its apparent charge as well as its coagulation conditions. For instance spindle-shaped well-grown Fe2O3 particles partly covered by smaller spherical Co3O4 particles are illustrated in Fig. 6.15. When hydrolyzable metal cations are added to a sol made with a different cation, three types of global z.p.c. corresponding to the three cases mentioned above can be observed (James and Healy 1972; Shaw and Pethica 1986). They are the following: 1. The z.p.c. of the colloidal particles in the absence of foreign metal cations, when the added cations remain in solution 2. The z.p.c. of a hydroxide from the added foreign cations, when these have led to the nucleation and growth of smaller new articles of a different nature, on top of the bigger initial sol particles

244

6 Peptization of Colloidal Sols

3. A z.p.c. intermediate between the two previous ones, when partial adsorption of colloidal particles formed by the foreign cations occurs For instance, when Mg2+ cations are dissolved in a Si3N4 sol, Mg(OH)2 colloidal particles have an opposite charge to the Si3N4 particles at most pH. The hydroxide Mg(OH)2 can moreover precipitate on the Si3N4 particles and eventually induce heteroflocculation. The adherence of colloidal particles to a preexisting solid substrate follows the same rules. Depending on the pH where precipitation is performed, the substrate and the particles may be of opposite charge (e.g., boehmite sol and the walls of a silica, Becher), in which case the adherence is favored. On the other hand, the inverse occurs when the electrical charges are of same sign on the two different materials.

6.4 6.4.1

Coagulation Kinetics Smoluchowski Derivation of Coagulation Rate

Thermodynamically, the specific surface area of a powder has a tendency to decrease and coagulation is one of the possible paths to achieve this evolution. The theory of Smoluchowski makes it possible to calculate a rate of fast coagulation, resulting from the Brownian motion when no energy barrier opposes to the contact between particles, such as when κ1 ¼ 0.1 in Fig. 6.13. In this case the number n of particles per unit volume of sol decreases with time according to (Overbeek 1977) dn ¼ kf n2 dt

ð6:111Þ

The half-life time, which is the time to decrease the number of particles by half, is t 1=2,f ¼

3η 4kf Tn0

ð6:112Þ

in which η is the viscosity of the sol and n0 the initial number of particles. When an energy barrier Φ exists, coagulation is slower. The half-life time can be written as t 1=2,S ¼ where

t 1=2,f α

ð6:113Þ

6.4 Coagulation Kinetics

245

1 ¼W ¼2 α

Z



1

exp 2r

 Φ dr kb T r2

ð6:114Þ

The efficiency of such an energy barrier to slow down coagulation increases as kΦb T increases. Practically for kbΦT > 15, a sol remains indefinitely stable (Verwey and Overbeek 1948).

6.4.2

Reversibility of Coagulation

When a sol has coagulated, a practical question is to know if this coagulation is irreversible, or if re-peptization can again be achieved. Actually, re-peptization appears to be feasible in the case of steric coagulation, described in the next section, not in the case of electrostatic case (Overbeek 1977). Indeed, according to the DLVO electrostatic theory, as illustrated in Fig. 6.16, the distance between two particles is large before coagulation, and it can for instance correspond to the shallow minimum in (a). On the other hand, the distance between particles is short after coagulation, and it corresponds to the deep minimum in (b). If after coagulation the electrolyte concentration is modified to obtain in (c) the same energy profile as in (a), a deep energy barrier has to be overcome to again reach the shallow minimum, and hence to re-disperse the sol, which does not appear to be feasible. However, experiments show that re-peptization is more frequent than exceptional. To explain such a behavior, Overbeek has proposed that a solvent layer of thickness 2δ remains between the particles, after coagulation. This solvent layer may eventually correspond to the Stern layer. For instance in the case of a negative AgI

Fig. 6.16 Potential interaction energy diagrams for a pair of particles corresponding to (a) a stable sol; (b) coagulation; and (c) irreversible coagulation after restoration of the original peptization conditions (adapted from Overbeek (1977))

246

6 Peptization of Colloidal Sols

Fig. 6.17 Energy versus distance diagrams similar to those in Fig. 6.16 showing the conditions where re-dispersion from a coagulated state (a) is impossible (b) or possible (c) (adapted from Overbeek (1977))

sol coagulated with the electrolyte KNO3, the Stern layer is composed mainly of monovalent solvated K+ cations. If an electrolyte such as Ba(NO3)2 is dissolved after coagulation, the Ba2+ ions will replace more slowly the K+ ions in the Stern layer than in the diffuse layer. Hence the charge on the particles is not immediately modified. That is to say, the interactions between particles which were derived at constant electric surface potential before and during coagulation must be replaced by interactions derived at constant surface charge for re-peptization, at least in a transitory stage. As the new counterions in the diffuse layer have a valence of 2, the hypothesis of constant surface charge results in a higher ζ potential of the Stern layer. In these conditions, as shown in Fig. 6.17, the interaction energy profile passes directly from (a) to (c), where the lower energy barrier is favorable to re-dispersion of the particles. After a longer time, Ba2+ ends up replacing K+ in the Stern layer also, so that the surface is modified and the sol ends up in the situation illustrated in Fig. 6.16a, which corresponds to a stable sol. If the order of electrolyte substitution were reversed, that is to say, first flocculation with Ba(NO3)2 followed by redissolution with KNO3, the sol would pass directly from the situation in Fig. 6.17a to the situation in Fig. 6.17b, because the decrease in counterion valence could not produce a momentary increase of ζ. Hence, no transitory stage permitting re-dispersion would be possible.

6.5 The Steric Stabilization Theory

6.5

247

The Steric Stabilization Theory

6.5.1

Origin of Steric Stabilization

Steric interactions occur when polymeric macromolecules are adsorbed on colloidal particles by only one of their end. Core-shell structures are formed in which each nanoparticle is covered with a polymer shell. Coagulation or stabilization of a sol will occur depending on the interactions in between the polymer chains, versus between the polymer chains and the solvent. These interactions govern the interpenetration or the repulsion of the polymer shells of neighbor nanoparticles. They are themselves a consequence of the interaction between the polymer macromolecules and the solvent. Hence, mathematical derivation of the steric interaction energy rests on the oldest theory for polymer solutions derived by Flory and Huggins (Flory 1942; Huggins 1942). Steric stabilization is widespread in aqueous as well as nonaqueous colloidal systems (Jekel 1986). It is also often treated as one extension of the so-called expanded DLVO theory. But, they offer to the experimentalist some flexibility in choosing the nature of the adsorbed polymer, and the temperature. Hence steric stabilization deserves a separate treatment.

6.5.2

Polymer Solutions

6.5.2.1

The Flory-Huggins Theory

The behavior of an organic polymeric solute in a solvent is driven by two types of phenomena. On the one hand, the Brownian motion makes each polymer macromolecule to extend in the solvent but there is a limit to this extension due to the finite length of each polymeric chain and its elasticity. On the other hand, interactions such as van der Waals interaction occur between the atoms inside a given polymeric chain, as well as between the atoms in neighbor polymeric chains and between the polymeric chains and the atoms in the solvent. These interactions are summarized by the affinity of the polymeric solute, for the solvent. In the Flory-Huggins theory, the total Gibbs free energy of mixing ΔGM of a polymer (2) in a solvent (1) is (Flory 1942; Huggins 1942)   ΔGM ¼ kb T n1 ln ðl  ϕ2 Þ þ n2 ϕ2 þ χ 1 n1 ϕ22

ð6:115Þ

In this equation n1 and n2 are the number of solvent and polymer molecules, ϕ1 1  ϕ2 and ϕ2 are their respective volume fraction in the solution, and χ 1 is a dimensionless parameter. In this solution, the molar chemical potential of the solvent can be written as

248

6 Peptization of Colloidal Sols

  h i 1 μ1  μ01 ¼ RT ln ðl  ϕ2 Þ þ 1  ϕ2 þ χ 1 ϕ22 x

ð6:116Þ

where x is the molar volume ratio VV 21 of the polymer solute to the solvent. Regarding the coefficient χ 1, Flory and Krigbaum (1950) distinguish a molar contribution of enthalpic nature h1 and a contribution of entropic nature s1 related to the partial enthalpy and entropy of dilution by ΔH 1 ¼ RT h1 ϕ22

ð6:117Þ

ΔS1 ¼ Rs1 ϕ2

ð6:118Þ

These contributions are related to χ 1 by χ1 

  1 θ ¼ h1  s 1 ¼ s 1 1  2 T

ð6:119Þ

In the latter equation, θ is a characteristic of a given couple of solvent-polymer. θ has the dimension of a temperature and it is termed the Flory-Huggins theta temperature. A large value of χ 1 corresponds to a large increase of the free energy of mixing so that the solvent behaves as a “bad” solvent for the polymer. On the other hand, a low value of χ 1 can give a negative free energy of mixing and the solvent behaves as a good solvent for the polymer. The transition between the two situations occurs for a critical value χ 1c. When χ 1 > χ 1c a separation of the solution in two liquid phases occurs. For endothermic solutions (ΔH1 > 0), χ 1 decreases as the temperature increases, which favors mixing. The temperature is an important parameter to modify χ 1. When T ¼ θ there is no net interaction between the polymeric solute and the solvent. When T > θ, mixing is favored. The polymeric solute macromolecules prefer to extend in the solvent so as to maximize polymer-solvent contact. That is to say, the solvent behaves as a good solvent for this polymer. On the contrary, when T < θ, the polymer chains tend to contract themselves and agglomerate with each other, so as to minimize polymersolvent contacts. The solvent behaves as a bad solvent for the polymer. Instead of modifying the temperature, it is also possible to modify the solute proportion. There exists a critical value of solute volume proportion ϕ2c such that phase separation occurs when ϕ2 > ϕ2c. Expressions ϕ2c and χ 1c can be calculated from the relations dμ1 d2 μ1 ¼ ¼0 dϕ2 dϕ22 which leads to

ð6:120Þ

6.5 The Steric Stabilization Theory

249

Fig. 6.18 Liquid/liquid phase diagrams for polymer solutions showing an upper critical solution temperature (adapted from Carpenter (1970))

1 pffiffiffi 1þ x

ð6:121Þ

1 1 1 þ pffiffiffi þ 2 2x x

ð6:122Þ

ϕ2c ¼ χ 1c ¼

Such results indicate the existence of an “upper critical” temperature (Fig. 6.18). For high-molecular-weight polymeric solutes x  1, 1 ϕ2c ¼ pffiffiffi x

ð6:123Þ

A comparison between the observed phase diagrams and those calculated is only qualitative but it makes it possible to globally understand the behavior of polymers in solution.

6.5.2.2

The State Equation Theory

A more elaborate theory, known as the “state equation theory,” has also been established by Flory (Carpenter 1970). It rests on a derivation of the thermodynamic state equation of the solution from a general statistical thermodynamics partition function. It requires to determine experimentally seven independent parameters. This theory presents the advantage to incorporate the individual characteristics of the components in the solution and to explain qualitatively the possible occurrence of a lower critical solution temperature in some systems. However, the agreement between the theory and the experiments remains only qualitative.

250

6.5.3

6 Peptization of Colloidal Sols

Steric Interactions Between Colloidal Particles

Steric interactions operate when polymeric macromolecules of polymeric solute are adsorbed on the colloidal particles. These steric interactions are a consequence of the interaction of polymer-solvent examined before, when the adsorbed polymer can only anchor by one end to a sol particle. Depending on the actual temperature T in the sol, with regard to the θ Flory temperature of the polymeric solute-solvent couple, repulsion or attraction between the colloidal particles can indeed occur (Fig. 6.19). When T > θ, the polymer macromolecules prefer to extend in the solvent so as to favor a good contact of polymer-solvent. If these polymers have one end of their chains adsorbed on a colloidal particle, they make a swollen polymer shell around the particle. An osmotic diffusion flow of the solvent penetrates in between the polymer macromolecules to maintain them in the swollen state. If two colloidal particles happen to collide, the polymer in both shells tends to avoid interpenetration to maximize the contact of solvent-polymer. Hence the particles remain dispersed. In

Fig. 6.19 Steric interactions between colloidal particles

6.5 The Steric Stabilization Theory

251

terms of interaction energy, the polymeric solute is responsible for an effective repulsion between the particles (Fig. 6.19a). On the other hand, when T < θ, the polymer chains contract and agglomerate with each other, so as to minimize polymer-solvent contacts. If two colloidal particles with adsorbed polymers happen to collide, the polymer chains in both shells tend to favor contact with each other, so that the particles remain agglomerated. The polymer shells act as a cement. In terms of interaction energy, the polymers are responsible for an effective attraction between the particles (Fig. 6.19b). In summary, swelling of the adsorbed polymer shell and repulsion of the particles are favored by an increasing temperature T. It occurs when T > θ, where θ is FloryHuggins characteristic temperature of the solvent-polymer couple. Contraction of the polymer shell, and hence attraction of the particles, occurs when T < θ.

6.5.4

Steric Interaction Energy

The treatment of polymer solutions by the initial Flory-Huggins theory does not apply directly to the calculation of the steric interaction energy between particles. This is because in steric stabilization, at least one end of the polymer chains is fixed on the particles, while in the Flory-Huggins theory both ends of a polymer are free. This has led Flory and Krigbaum (1950) to develop an extension of the initial polymer solution theory, appropriate for adsorbed polymers. In this theory, the incremental free energy of mixing d(ΔGM) in an incremental volume element containing dn1 solvent molecules can be estimated by dðΔGM Þ ¼ kb T ½ ln ðl  ϕ2 Þ þ χ 1 ϕ2 dn1

ð6:124Þ

So that, after integration to the full volume, the partial molar free energy of dilution of the solvent becomes ΔG1 ¼ RT

  1  χ 1 ϕ22 2

ð6:125Þ

If two colloidal particles are now considered, it is possible to select incremental volumes of same magnitude dV, in the polymer shell of a first colloidal particle where the polymer density is ρj, and in the polymer shell of a second particle where the polymer density is ρk. The free energy of mixing of the polymers in the solvent increases when these two volume elements happen to merge and an expression of this increase is dðΔGM Þ ¼ 2k b T

  1 dV  χ 1 ρj ρk V 2s 2 V1

ð6:126Þ

252

6 Peptization of Colloidal Sols

where Vs represents the volume of one polymer segment and V1 is the solvent molar volume. The total interaction energy between the two particles on which the polymers are adsorbed, when their polymer shells start to overlap, is then   Z θ V 2S Φs ¼ ΔGM ¼ 2kb Ts1 1  ρ ρ dV T V1 V j k

ð6:127Þ

The integration must be made on the complete volume where interpenetration of the polymer chains occurs. The most simple solution obtained by this method was by Ottewill et al. (1968). For two spheres of radius r, which have adsorbed a polymer layer of thickness δ, where S0 is the shortest distance between the particle surface, the steric interaction was found to follow the law:      4πC 2 θ S0 2 S0 Φs ¼ k b T δ S1 1  3r þ δ þ T 2 2 3V 1 ρ22 

ð6:128Þ

In this equation, C is the polymer concentration in mol L1 in the adsorbed layer and ρ2 the polymer density. When T > θ, these calculations show that the steric interaction energy is >0. This corresponds to repulsion between the colloidal particles, which increases very rapidly as S0 decreases.

6.5.5

Mixed Steric and Electrical Interactions: Case of Surfactant Solutions

When surfactants are dissolved in the liquid medium where a sol is dispersed, they can have an effect which is both of steric and electrostatic nature. For instance, cationic surfactants can reduce the charge of negatively charged sols and even reverse it such as in AgI sols (Glazman and Blashchuk 1977). They can also be responsible for the occurrence of a complex sequence of sol stabilization, due to the occurrence of both steric and electrostatic interactions dominating in different conditions such as when octadecyl-ether and polyethylene-glycol are added to AgI sols (Nakao and Kaeriyama 1986). Similar phenomena were also reported when anionic surfactants are mixed in positively charged As2S3 sols (Ottewill and Rastogi 1960).

6.6 Other Interactions Applying in Extended DLVO Theories

6.5.6

253

Mixed Steric and Magnetic Interactions: Ferrofluids®

The Ferrofluids® are special sols made of magnetic materials in which the colloidal particles have a small size (~10 nm), much smaller than that of other magnetic clutch materials, typically ~1 μm. The ferrofluid particles are sufficiently small to be composed of one single magnetic domain, so that their sols are super-magnetic with a high magnetic saturation field (4πMs ¼ 600 G), and without any remanent field. In terms of composition, they comprise transition metals or rare earths (Fe, Co, Ni, Gd, Dy) as well as ferrites containing Mn, Co, Cu, and Mg cations. They were prepared for the first time in 1938 by Elmore at the Massachusetts Institute of Technology, by grinding ferrites for weeks with steel balls in oleic acid (Elmore 1938). Ferrofluids® can also be prepared by precipitation of Fe3O4 particles from ferric or ferrous salt solutions, followed by extraction of the particles from the precipitate with a solution of oleic acid in a nonpolar liquid. In other methods, a gelatinous precipitate is first obtained with ammonia, and re-peptized by modifying the pH (Massart 1981). In ferrofluids, a coating layer consisting of long polar chain is adsorbed on the magnetic particle and prevents them from agglomerating by steric interaction (Elmore 1938; Papell 1965). Moreover, the magnetic interaction between these particles is so important that they can move altogether in the same direction, when they are submitted to a magnetic field, and they carry along with them the surrounding liquid medium, so that they can be used as transmission fluids.

6.5.7

Bridging Polymer Adsorption

Bridging between colloidal particles can be due to polymer chains able to adsorb on solid surfaces by their two ends. When this is possible, they may therefore establish bridges between different nanoparticles. The adsorption may also be physical or chemical and in the latter case the bonding between nanoparticles can be very strong (Butt et al. 2003). Such an adsorption behavior leads to the formation of a hybrid organic-inorganic gel, a field addressed in Chap. 10.

6.6

Other Interactions Applying in Extended DLVO Theories

Experimental measurements of the forces acting in colloidal systems, by various techniques such as surface force apparatus (SFA), atomic force microscope probe techniques, or quartz crystal microbalances, showed that forces other than the electrostatic and van der Waals forces should be added to the classical DLVO theory, to explain a number of classical DLVO theory limitations. This led to the

254

6 Peptization of Colloidal Sols

Fig. 6.20 Schematic principle of operation of a quartz crystal microbalance (adapted from Chen et al. (2016))

development of the extended DLVO theory (Rabinovich et al. 1982; Christenson and Claesson 1988; Ishida et al. 2000; Leite et al. 2012). The extended forces comprise repulsive hydration forces and attractive hydrophobic forces, plus the repulsive or attractive steric forces and attractive polymer bridging forces which were addressed in Sect. 6.5 (Butt et al. 2003; Chen et al. 2016). Chen et al. (2016) have recently given a comprehensive review of the experimental results obtained with quartz crystal microbalance with dissipation monitoring (QCM-D), plus a list of empirical bonding force formulas between a spherical nanoparticle and a planar surface. For instance, a quartz crystal microbalance (QCM) is composed of a piezoelectric quartz crystal disk, on which the two planar faces have been coated with a thin metal layer, such as gold, as illustrated in Fig. 6.20. When an alternating electric potential difference is applied between the two metal-coated faces, the crystal vibrates in a shear mode. The vibration frequency is very sensitive to the crystal mass which in turn depends on the mass of nanoparticles deposited on one face. This tool permits first to determine experimentally a coagulation rate of nanoparticles. Moreover, the damping mode, when the piezoelectric excitation is stopped, permits to quantify the “softness” of a colloid deposited on one of the surfaces. Hence it gives information

6.6 Other Interactions Applying in Extended DLVO Theories

255

on the bonding energy and permits to compare hydrophobic, hydrophilic, and polymer bonding energy.

6.6.1

Hydration Forces

The hydration forces are important for strongly hydrated nanoparticle surfaces. They are the result of interactions of water dipolar molecules with solid surfaces, when these are stronger than among water molecules. A consequence is that an increased energy is necessary to remove these water molecules from the solid surface, in order to permit a closer approach of two solid surfaces, even in the case of a very thin electrical double layer favorable to solid-to-solid contact. It is sometimes considered that the water dipoles take an orientation perpendicular to a hydrophilic solid surface, at least for the water layer not in contact with the hydrophilic surfaces. A possible illustration of the water organization according to Donaldson Jr. et al. (2015) is illustrated in Fig. 6.21a. But the exact action mechanism of these forces could not be really determined, neither experimentally, nor by statistical thermodynamics simulations. On silica, clay, and lipid systems they were found to decay exponentially on a length typically ranging from 0.4 to 4 nm. Solids which carry ionic surface groups or of biomolecular origin (e.g., proteins and polysaccharides) are often highly hydrated and they display strong hydration forces.

6.6.2

Hydrophobic Forces

The hydrophobic forces operate in between hydrophobic surfaces in water. Their exact nature is a subject of controversy, but they are stronger than classical van der Waals force and act on a longer range (Israelachvili and Pashley 1982, 1984; Fig. 6.21 Compared possible organization of water molecules in between two planar surfaces: (a) case of two hydrophilic surfaces; (b) case of two hydrophobic surfaces (adapted from Donaldson Jr. et al. (2015))

256

6 Peptization of Colloidal Sols

Fig. 6.22 Creation of a water vapor bridge between mica particles coated with polydimethylsiloxane (PDMS), e.g., of size S0 ~ 300 nm, and diameter ~23 mm (adapted from Donaldson Jr. et al. (2015))

Rabinovich and Yoon 1994a, b; Xu and Yoon 1989, 1990). The most classical view is that water molecules favor water-to-water molecular contact, so as to maximize the density of hydrogen bonds which they can establish in between them, to decrease the system free energy, as illustrated in Fig. 6.21b. With hydrophobic surfaces at close separation distances, water molecules can no longer establish such hydrogen bonds, so that they fluctuate and may even undertake a liquid–vapor phase transition. Water vapor nanobubbles without any air, and hence under partial vacuum, may even be created by dewetting as illustrated in Fig. 6.22. Various empirical equations were proposed to quantify them, based on exponential or power law decay expressions (Christenson et al. 1987; Rabinovich and Yoon 1994a; Ishida et al. 1999). The attractive mechanism on which they rest comprises (1) capillary Laplace forces due to the formation of vapor nanobubbles in between two hydrophobic surfaces; (2) solvation of water molecule reordering between two approaching hydrophobic surfaces; and (3) van der Waals correlations between the nanoparticle surface charges and dipoles. Next to reviews of experimental data, Donaldson Jr. et al. (2015) recently proposed a general formula to simultaneously quantify the hydrophilic and hydrophobic interactions, which per unit area of flat surface and a separation distance S0 is (6.129) ΦðS0 Þ ¼ 2γ i H y exp ðS0 =DH Þ

ð6:129Þ

6.7 Potential of Mean Field (PMF) Simulations

257

Fig. 6.23 Approximative interaction energy of couples of hydrophilic and hydrophobic surfaces, by comparison with van der Waals attraction (adapted from Donaldson Jr. et al. (2015))

In this equation, DH  0.3–2 nm is an experimental decay length, which applies for both hydrophobic and hydrophilic interactions. Hy is a nondimensional “hydra” parameter, which applies to both hydrophobic and hydrophilic interactions between extended surfaces. Hy ¼ 1 for two fully hydrophobic surfaces, Hy > 0 for partially hydrophobic surfaces, and Hy < 0 for partially hydrophilic (hydrated) interfaces such as mica, silica, and lipids. γ i is the interfacial tension of the interacting surfaces. As can be seen in Fig. 6.23, this interaction potential is much stronger than the traditional van der Waals interaction, with oscillation characteristics only observed in between rigid surfaces, related to the water molecule size. For anionic solid surfaces on which cations are adsorbed, such as mica, the hydration forces also take into account the energy required to dehydrate these cations, and it largely depends on the cation exchange property of the solid surface.

6.7

Potential of Mean Field (PMF) Simulations

The DLVO theory, along with its application to spherical, cylindrical, or lamellar colloids and its limitation, was discussed in a review by Hansen and Löwen (2000) and more recently by Dahirel and Jardat (2010) and Sogami et al. (2015). The former authors also introduced the more general theoretical framework of the density functional theory.

258

6.7.1

6 Peptization of Colloidal Sols

Limitations of the DLVO and Steric Theories

The DLVO and steric theories were successful in explaining the role of basic parameters on the peptization or the coagulation of colloidal sols. They also offered a global analytical formulation to embrace at once the salient features of the field. However, they failed to really explain a number of secondary experimental facts. The most outstanding of them regards the observed attraction due to the electrostatic contribution of colloidal particles of same charge in the presence of multivalent ions (Dijkstra 2001), in particular for very small colloidal particles ( rs, i.e., Cs(rL) < Cs(rs). Consequently, the solute concentration in the liquid medium of a sol is maintained at an average Cs(Liq) value that Cs(rL) < Cs(Liq) < Cs(rs). Dynamically, as shown in Fig. 6.25, the smaller particle keeps dissolving to try raising the solute concentration to a value Cs(rs) > Cs(Liq) near its surface. On the other hand, the solute precipitates on the larger particle to try reaching a solute concentration Cs(rL) < Cs(Liq) near its surface. Hence, a gradient in solute concentration is established in the liquid, so that this solute undertakes a diffusion from the smaller towards the larger particles. This

Fig. 6.25 Ostwald ripening mechanism

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J.T.G. Overbeek, in Colloid Science, ed. by H. Kruyt, vol. 1, (Elsevier, Amsterdam, 1952) J.T.G. Overbeek, J. Colloid Interface Sci. 58, 408–422 (1977) S.S. Papell, Propellant Containing Magnetic Particles. U.S. Patent 3,215,572 (2 Nov 1965) G.A. Parks, Chem. Rev. 65, 177–198 (1965) Y.I. Rabinovich, B.V. Derjaguin, N.V. Churaev, Adv. Colloid Interface Sci. 16, 63–78 (1982) Y.I. Rabinovich, R.H. Yoon, Langmuir 10, 1903–1909 (1994a) Y.I. Rabinovich, R.H. Yoon, Colloids Surf. A Physicochem. Eng. Asp. 93, 263–273 (1994b) M.N. Rahaman, Y. Boiteux, C. DeJonghe, Am. Ceram. Soc. Bull. 68, 1171–1176 (1986) A.E. Regazzoni, E. Matijevic, Corrosion 38, 212–218 (1982) A.E. Regazzoni, E. Matijevic, Colloid Surf. 6, 189–201 (1983) W. Schneider, Comments Inorg. Chem. 3, 205–223 (1984) T.M. Shaw, B.A. Pethica, J. Am. Ceram. Soc. 69, 88–93 (1986) I.S. Sogami, T. Shinohara, M. Tanigawa, K. Ito, J. Yamanaka, Int. J. Microgravity Sci. Appl. 32(2), 320202 (2015) W. Stumm, C.P. Huang, S.R. Jenkins, Croat. Chem. Acta 42, 223–245 (1970) T. Sugimoto, E. Matijevic, J. Colloid Interface Sci. 74, 227–243 (1980) T.F. Tadros, J. Lyklema, J. Electroanal. Chem. Interfacial Electrochem. 22, 9–17 (1969) F.W. Tavares, D. Bratko, H.W. Blanch, J.M. Prausnitz, J. Phys. Chem. B 108, 9228 (2004) E.J.W. Verwey, Rec. Trav. Chim. 60, 625–633 (1941) E.J.W. Verwey, J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948) V. Vlachy, Annu. Rev. Phys. Chem. 50, 145 (1999) H.B. Weiser, Inorganic Colloid Chemistry, in Hydrous Oxides and Hydroxides, vol. 2, (Wiley, New York, 1935) J.Z. Wu, D. Bratko, J.M. Prausnitz, Proc. Natl. Acad. Sci. U. S. A. 95, 15169 (1998) Z. Xu, R.H. Yoon, J. Colloid Interface Sci. 132, 532–541 (1989) Z. Xu, R.H. Yoon, J. Colloid Interface Sci. 134, 427–434 (1990) B.E. Yoldas, J. Appl. Chem. Biotechnol. 23, 803–809 (1973) R.H. Yoon, T. Salman, G. Donnay, J. Colloid Interface Sci. 70, 483–493 (1979) H. Yukawa, Proc. Phys. Math. Soc. Jap. 17, 48 (1935)

Chapter 7

Gelation

7.1

Introduction

Gelation is a process according to which a sol, or a solution, transforms to a gel. It consists of establishing links between sol particles, or solution molecules, so as to form a 3-dimensional solid network. However, this is very different from the solidification of a melt, since the solid structure remains completely impregnated with mother liquid of the sol, or solution. This is also a very general type of transformation and it is often considered that any solid material can be transformed to a gel. From the theoretical point of view, two types of approaches permit to understand the fundamental aspects of such a phenomenon; they are addressed in the first two parts of this chapter. The first one calls for a global description which can be presented within the framework of the thermodynamics of critical phenomena. The second one consists of a kinetic approach which rests on growth models. A third part of this chapter summarizes the methods which permit to study gelation, while a few gelation mechanisms known to operate with inorganic materials are reviewed in the last section.

7.2 7.2.1

Percolation Models of Gelation Flory-Stockmayer Model

The thermodynamics understanding of gelation is the oldest. It results from developments by Flory (1941, 1953) and Stockmayer (1943) and first concerned organic materials. In these first studies, gelation designates the transformation of a liquid, by chemical reactions, to a material presenting the characteristics of a solid but still fully impregnated by a liquid. Considering monomers with a © Springer Nature Switzerland AG 2020 A. C. Pierre, Introduction to Sol-Gel Processing, https://doi.org/10.1007/978-3-030-38144-8_7

271

272

7 Gelation

functionality Z > 2, mathematical derivations by Flory have shown that the condensation of monomers yields an infinitely large polymer structure, in a mathematical sense. Practically, the solid is limited in extent only by the size of the container where the reaction is performed, but it remains fully impregnated by the mother liquor from which it was generated.

7.2.1.1

Gel Point

Gelation occurs when the extent of polymerization reactions ξ reaches a critical value ξc. This precise critical stage, when for the first time a polymer of infinite size (in a mathematical sense) is formed, by comparison with the molecular scale, defines the gel point (GP). In a practical manner, at this point, the product resulting from polymeric condensations transforms suddenly from an increasingly viscous liquid to a material with elastic properties. In the liquid state a viscosity can be measured and its value increases towards infinity (in the mathematical derivation) when coming near the gel point. Experimentally, in the solid state, an elastic modulus can be measured and its value starts from zero at the gel point. In this model of gelation, called the Flory-Stockmayer model (or FS model), the infinite polymer is built by the successive addition of branches, all of which are constructed from the initial monomers (Fig. 7.1).

7.2.1.2

Characteristics of the Flory-Stockmayer Model

The FS model explains well the main characteristics of gelation. However, instead of describing a given local aggregate, it focuses on general thermodynamic parameters

Fig. 7.1 (a) Flory-Stockmayer model (adapted from Flory (1941)). (b) Bethe lattice (adapted from Fisher and Essam (1961))

7.2 Percolation Models of Gelation

273

which characterize macroscopically a polymer solution, such as the functionality Z and the extent of reaction ξ. It is therefore not surprising that it can be described in a more abstract fashion within the framework of critical phenomena in thermodynamics, in particular by the percolation theories.

7.2.2

Percolation Models

The development of the percolation theories was initiated by Hammersley (1957). Since that time, a large number of percolation models have been studied and applied to the description of many phenomena in physics, chemistry, and life sciences. They range from theoretical models as in the works of Stauffer et al. (1982) to computer simulations such as by Leung and Eichinger (1984).

7.2.2.1

Site and Bond Percolations

The simplest percolation models are isotropic, such as the bond percolation and the site percolation. In these models, either a bond is established or a site is occupied, with a probability p, in a completely random fashion throughout a geometrical network, as illustrated in Fig. 7.2, on a planar square network.

Fig. 7.2 Site percolation and bond percolation on a square bidimensional network

274

7.2.2.2

7 Gelation

Percolation Threshold, Critical Exponents, and Scaling Laws

These percolation theories show first the existence of a critical probability pc, termed the percolation threshold, such that if p > pc an infinite continuous cluster of bonds, or of sites, exists. The threshold corresponds to the GP in the case of gelation, but its significance is more general. Moreover, the mathematical formalism of percolation theories introduces some mathematical functions of the probability p which diverge mathematically when p comes close to the GP. The divergence of these functions is equivalent to that of viscosity and elastic modulus in a gel, but with a stiffness mathematically described by well-defined critical exponents. More precisely, when coming close to the percolation threshold from the p < pc side, which is the equivalent of coming close to the GP in a sol, two characteristic properties can be defined (Fig. 7.3): – The average mass of clusters, defined as the number of connected sites in one cluster, or of connected bonds, diverges towards infinity as p comes close to pc according to the scaling law (7.1), where γ is a numerical exponent:

Fig. 7.3 Variation with the fraction p of established bonds, of characteristic properties of bond percolation on a 3-dimensional cubic lattice: normalized conductivity σ( p) after Kirkpatrick (1973); percolation probability P( p) after Frisch et al. (1962); average cluster mass Mave( p) and average radius Rave(P) (adapted from Zallen (1983))

7.2 Percolation Models of Gelation

275

M ave ðpÞ  ðp  pc Þγ

ð7:1Þ

– The average value of any characteristic distance, such as the diameter of a circle in which the cluster can be fitted, diverges towards infinity as p comes close to pc according to the scaling law (7.2), where ν is a numerical exponent: Rave ðpÞ  ðp  pc Þν

ð7:2Þ

When p comes close to the percolation threshold pc from the p > pc side, that is to say, on the gel side in the case of gelation, two other characteristic properties can be defined (Fig. 4.3): – The probability P( p) that a bond, or site, belongs to the mathematically infinite cluster and hence participates in the elastic or conduction properties of a gel. It is given by the scaling law (7.3), where β is a numerical exponent: PðpÞ  ðp  pc Þβ

ð7:3Þ

– Any transport property of this cluster, such as its elastic shear modulus G( p), or its electric conductivity σ( p) when the bonds conduct electricity, is a function of p given by Eq. (7.4), where t is a numerical exponent: GðpÞ  σ ðpÞ  ðp  pc Þt

ð7:4Þ

At last, at the percolation threshold where p ¼ pc, which is the equivalent of the GP in the case of gelation, two more important characteristics are the following: – The probability P(M) for a cluster to have a mass M: It is given by Eq. (7.5), where τ is a numerical exponent. This is due to the fact that, at the percolation threshold, a whole population of clusters exists, but only one is mathematically infinite in size: PðM Þ  M τ

ð7:5Þ

– The geometry of the unique infinite cluster is such that, starting from any site or bond, the mass inside a radius R follows Eq. (7.6), where f is a numerical exponent: RðM Þ  M 1=f

ð7:6Þ

The exponent “f” is termed the fractal, or mass fractal, or Hausdorff dimension. It was introduced by Mandelbrot (1977). It provides a mathematical description of the lace geometry of the solid gel network. It is also possible to relate the radius R of an aggregate to its surface S by a relationship of the type (7.7): RðSÞ  M 1=f s

ð7:7Þ

276

7 Gelation

where fs is the surface fractal dimension. If an aggregate is such that fs > 2, this is a surface fractal aggregate. Each of the exponents f, t, τ, β, ν, and γ has the important property that they only depend on the Euclidean dimension d of the space in which the critical phenomenon occurs. They are termed “critical exponents.” The Euclidean dimension is d ¼ 3 for actual gelation and all 3-dimensional percolation models, and d ¼ 2 for all planar percolation models. It is possible in theory to consider percolation inside Euclidean spaces with dimensions other than 2 or 3. The corresponding critical exponents as a function of d are plotted in Fig. 7.4. This remarkable mathematical result has permitted to define the notion of a “universality class,” which gathers all the phenomena described by the same critical exponents, and for which the main characteristic properties obey the same mathematical laws. For instance, the theories of percolation and gelation in a 3-dimensional space belong to the same universality class and the equivalence between the various functions is gathered in Table 7.1. Fig. 7.4 Variation of the critical exponents for percolation, as a function of the Euclidean space dimension d (adapted from Zallen (1983))

Table 7.1 Comparison of bond percolation and gelation Bond percolation – Network coordination number Z – Bond connectedness probability p – Percolation threshold pc – Percolation probability P – Mean cluster radius Rave – Mean cluster mass Mave – Network conductivity σ – Bethe lattice Adapted from Zallen (1983)

Gelation – Polymer functionality Z – Extent of reaction ξ – Gel point – Proportion of monomers belonging to the gel, or gel fraction P(x) – Mean polymer radius Rave – Mean polymer mass Mave – Shear modulus G (elasticity) or electrical conductivity σ – Flory-Stockmayer model

7.2 Percolation Models of Gelation

7.2.2.3

277

Mean Field or Effective Medium Theory

Figure 7.4 shows the existence of a Euclidean dimension d beyond which the critical exponents level out to a constant value. This dimension is called the marginal dimension. For percolation and gelation d ¼ 6. In this special case, all mathematical laws coincide with those resulting from another type of mathematical modeling known as the “mean field” theory, also called “effective medium” theory, which was independently developed by Bruggeman (1935). In this model, the environment around a given polymer (around a given site in percolation) is described by replacing all other solvent or polymer molecules (all other occupied or unoccupied sites in percolation), by identical “fictitious” molecules with properties intermediate between the properties of the solvent and those of the polymers (equivalent to “partially occupied” sites in percolation). The percolation theories demonstrate, therefore, that provided that the dimension d of a Euclidean space is sufficiently high, each site is surrounded by a large number of neighboring sites, so that the details of occupied or unoccupied sites are unimportant: only the average occupancy matters. Actually, the FS model previously examined corresponds to a bond percolation model on a lattice known as a Bethe lattice (Fisher and Essam 1961). This is a lattice in which each node is connected to Z other nodes, without making any closed loop, as shown in Fig. 7.1b where Z ¼ 3. This coordination number Z in this model plays exactly the same role as the functionality Z in the FS model and the probability p to establish a bond is equivalent to the extent of reaction ξ. However, it was mathematically demonstrated that a Bethe lattice cannot be indefinitely extended in a Euclidean space of finite dimension d, because sooner or later an overcrowding problem will occur. An infinite Bethe lattice can only exist in a Euclidean space of dimension d ¼ 1, a very abstract space only mathematically conceivable. Such a value is therefore higher than the marginal dimension d ¼ 6. As a result, the FS model is both a special percolation model and an “effective medium” theory model, and it has the same critical exponents as the latter model. In particular, its fractal dimension is f ¼ 4, instead of f  2.6 for all percolation models in the Euclidean space d ¼ 3.

7.2.2.4

Other Critical Parameters in Percolation

In addition to the universal critical exponents introduced before, the percolation threshold probability pc is another important critical parameter. However its value depends, in addition to the Euclidean dimension d, either on the coordination number Z in the case of a regular site network or on the volume fraction ϕ occupied by the sites if they are replaced by hard spheres positioned in a random fashion. For the Euclidean space d ¼ 3 for instance, Fig. 7.5 shows that a quasi-linear relationship exists between pc and either Z or ϕ. The latter relationship has not been mathematically demonstrated but it was found by computer simulations.

278

7 Gelation

Fig. 7.5 Empirical correlation between the percolation threshold and the lattice coordination for various 3-dimensional structures (adapted from Zallen (1983))

Therefore, while these percolation models have in common some universal characteristics, they also differ from each other by many aspects. The FS is one of the simplest models; its critical probability pc is related to the coordination number (or functionality) Z by (7.8) Pc ¼ ξc ¼

1 ð Z  1Þ

ð7:8Þ

Its main default is to neglect the formation of closed loops, contrary to what occurs in real gelation.

7.2.2.5

Other Percolation Models

A more accurate description of gelation in a real system requires percolation models more complex than a simple site or bond percolation. For instance a gelation model for silica should involve the different functionality Z ¼ 4 for the silicon and Z ¼ 2 for the oxygen. In many cases of heterogeneous gelation, reagents of a different nature are necessary to build the gel network such as an alkoxide and a binding agent such as water in a third solvent. In this case, a special percolation model termed site-bond percolation has been developed. It combines sites, occupied by the species to link, and bonds which take the place of the binding agent. For each concentration of one species, one critical concentration for the other species exists. Hence a line of GP exists which is a function of the concentrations of both species.

7.3 Growth Models of Gelation

279

Moreover in many experimental cases, one has to consider colloidal particles which are no longer spherical but which can be small fibers or plates, a shape very difficult to take into account in theoretical developments. Computer simulations and experimental studies on the conductivity of such systems (Carmona et al. 1980) have shown that the percolation threshold can be reached with volume fraction of the order of 3% for fibers, therefore much lower than for spheres (of the order of 25%). Furthermore, it is not known whether the critical exponents keep the same universal values as in isotropic percolation. The derivation of mathematical models remains therefore an open research domain.

7.3 7.3.1

Growth Models of Gelation Main Differences Between Percolation and Growth Models of Gelation

Instead of forming a gel by a uniform phase change inside a fluid, it is quite possible to obtain a gel structure by the successive addition of sol particles (or of polymeric molecules in solution) to an initial particle (or an initial polymer molecule). Gelation studies which have adopted this point of view give up a macroscopic description of the sample to favor the local study of one aggregate. Such an approach presents two advantages. First, it uses models in which the parameters can be progressively changed. For instance, they can show that in some conditions the chemical species or colloidal particles dispersed in a liquid can associate to build dense aggregates, while they build much more open structures in other conditions. Dense aggregates correspond to particles such as examined in Chaps. 5 and 6, but with a more complex internal structure. On the other hand random open structures are typically of gels. The transition between both situations may be quite progressive. Secondly, when open structures are obtained, they are the result of kinetics processes which are of kinetics nature, not of equilibrium thermodynamics nature. It is still possible to measure their fractal dimension, but the values differ from those indicated by the theory of critical phenomenon. In common with percolation models, most growth-gelation models describe the liquid medium by a site network. However, each site is occupied by a chemical species which keeps moving with time, according to an algorithm which can be freely modified in a computer simulation. This is indeed a kinetic approach and typical examples are described in the following sections.

280

7 Gelation

7.3.2

Example of Growth Models

7.3.2.1

Polymerization Model by Manneville and de Seze (1981)

In this description, some sites of a network are attributed to monomers with a functionality of 2, other sites to monomers of functionality 4, and the remaining sites to solvent molecules. The proportions of each type of sites are, respectively, C2, C4, and CS ¼ 1  C2  C4 (Fig. 7.6). Next a fraction CI of chemical species acting as bonding initiators is initially distributed on the monomer sites, and they are let free to move by an algorithm which simulates a random walk from their initial position. Several events can then occur. Each time an initiator jumps from a site occupied by a monomer to another site occupied by a monomer, the two monomers are considered to be bonded to each other and they form a dimer. When the initiator jumps to a solvent site, no bonding occurs. At last, when two initiators jump on the same site they annihilate each other. The process stops when all sites available to the initiators are either monomers which have reacted or solvent molecules. Fractal aggregates with critical exponents different from those of percolation were then obtained.

7.3.2.2

Invasion Percolation Growth Model

In the invasion-percolation growth model by Chandler et al. (1982), a random number in the range from 0 to 1 is attributed to each site. Next, one site is selected as the initial nucleus and growth consists of adding the perimeter site with the lowest random number to this nucleus, at each step. Hence the focus is on the growth of one particular aggregate, rather than on the average growth of all aggregates such as in percolation. However, the aggregates which are formed in this process have the same fractal dimension as in a classical bidimensional percolation, that is to say, f ¼ 1.89.

7.3.2.3

Eden Model and Other Non-mass Fractal Growth Models

Not all random growth models produce mass fractal aggregates. In the “Eden” or “cancer growth” model (Eden 1961; Peters et al. 1979), growth also proceeds from Fig. 7.6 Addition polymerization model (adapted from Manneville and de Seze (1981))

7.3 Growth Models of Gelation

281

Fig. 7.7 Eden’s cancer growth model (adapted from Stanley et al. (1985))

one initial site which is selected as the initial nucleus. The sites which are added to this nucleus are then selected at random among all the perimeter sites of this nucleus. The resulting structures have holes as illustrated in Fig. 7.7 (Stanley et al. 1985), but their mass fractal dimension is identical to the Euclidean dimension ( f ¼ d ). They are therefore compact non-fractal structures. However they are surface fractal aggregates. Other growth models which produce compact solids have been developed. One of them is the ballistic model (Bensimon et al. 1983) where the particles which are added to a nucleus arrive in straight line. Another one is the multiple aggregation model (Witten Jr. and Sander 1981; Voss 1983) which consists of the simultaneous aggregation of a finite density of particles.

7.3.2.4

Rikvold Crystallization Model (Rikvold 1982)

This model is a modification of the cancer growth model, in which a new peripheral site added to a nucleus can diffuse on a length Ld along the cluster perimeter, so as to simulate surface diffusion. The results have shown that, starting from a low value Ld (negligible diffusion) which produces compact structures, the growth figure becomes more and more ramified with increasing Ld (Fig. 7.8).

282

7 Gelation

Fig. 7.8 Examples of aggregates in the Rikvold crystallization model for different values of the diffusion length parameter Ld. N designates the number of sites (adapted from Rikvold (1982))

7.3.2.5

The “Electric Breakdown” Model

This model, studied by Sawada et al. (1982), simulates the electric breakdown of capacitors. It is derived from the cancer growth model by weighing the perimeter sites with a factor F when they are close to a tip of an aggregate. These aggregates remain compact if F  35, but become ramified if F  35.

7.3.2.6

Diffusion-Limited Aggregation Model (DLA Model) (Witten Jr. and Sander 1981; Deutch and Meakin 1983)

The sites at a given distance from the original nucleus are allowed to walk randomly according to an appropriate algorithm, so as to simulate the Brownian motion of the particles in a sol. They may therefore either avoid meeting a nucleus or reach one of them and participate in its growth. As soon as some branches of the aggregate statistically start to grow around this nucleus, the possibility for sites to diffuse up the corridors without hitting a side branch becomes low. These branches therefore have a tendency to keep growing so that the aggregates become fractal structures

7.3 Growth Models of Gelation

283

Fig. 7.9 Bidimensional aggregates on a square lattice with different fractal dimensions: (a) aggregate near the percolation threshold in site percolation, redrawn sketch from Stanley et al. (1976), and (b) diffusion-limited aggregation cluster comprising 3600 particles (adapted from Witten Jr. and Sander (1981))

even more ramified than in the percolation models. The fractal dimensions are 1.67 for DLA and 1.89 for percolation bidimensional models, and, respectively, 2.5 (DLA) and 2.6 (percolation) for tridimensional models. The characteristics of the corresponding aggregates are illustrated in the sketch of Fig. 7.9. A refinement of the DLA model (Meakin 1983a; Kolb et al. 1983; Witten Jr. and Meakin 1983) considers several nucleation centers. Each nucleus grows by diffusion and simultaneously slowly itself diffuses, by Brownian motion. Hence, primary fractal DLA aggregates grow and finally aggregate themselves in a more open structure. It is possible to combine this double-diffusion system with a probability for aggregates to remain linked after contact. The results showed that when linkage between the primary aggregates was the rate-limiting step, the fractal dimension of such hierarchical DLA, also termed “cluster-cluster,” was f ¼ 1.4 for bidimensional aggregates and f ¼ 1.80 for tridimensional ones. On the other hand, when diffusion of the primary aggregates was rate limiting, f ¼ 2.09 in tridimensional models.

284

7 Gelation

Fig. 7.10 Hierarchical generation of aggregates in a powder (adapted from Onoda and Toner (1986))

7.3.2.7

Onoda and Toner Hierarchical Model

The preceding hierarchical DLA model has in common a hierarchical algorithm with a model by Onoda and Toner (1986). According to this model, a population of primary spherical particles with identical size aggregate to form a secondary spherical particle. The packing ratio p, defined as the volume fraction of the secondary sphere which is occupied by the primary spheres, and the ratio sphere radius S ¼ secondary primary sphere radius are fixed. The secondary particles themselves aggregate in tertiary spherical particles, characterized by the same packing ratio p and radius ratio S. This operation can be repeated several times (Fig. 7.10) and it can be shown that fractal structure is built with a fractal dimension given by (7.9) f ¼dþ

ln p ln S

ð7:9Þ

As an example for S ¼ 10, p ¼ 0.5, and d ¼ 3, f ¼ 2.7.

7.3.2.8

Other Mathematical Models

All previous growth models have in common the possibility to be studied by Monte Carlo simulation algorithms on a computer. Other pure mathematical analytic studies in continuous media have been attempted, although they have not been very successful (Meakin 1983b; Sander 1984).

7.4

Gelation and the DLVO Theory

Ramified structures such as described in the previous paragraphs can be observed when a large number of primary particles have aggregated. At a scale of a few particles, it is not obvious to make a difference between compact agglomerates and

7.4 Gelation and the DLVO Theory

285

fractal aggregates. However, a linear bonding between colloidal particles may be possible in some conditions as soon as the first contacts occur and this phenomenon can be described within the DLVO theory framework, presented in Chap. 6.

7.4.1

Experimental Critical Electrolyte Concentration for Gelation

In fact it has been known that the gelation of sols obeys the experimental SchulzeHardy rule which concerns the influence of the concentration of a non-potential determining electrolyte on the coagulation of a sol. In Chap. 6, the existence of a critical electrolyte concentration Cc for the occurrence of rapid coagulation was introduced. The existence of a critical concentration for gelation Cg has also been known for a long time (Prakash and Dhar 1929). If the concentration C of non-potential determining electrolyte is C < Cg, a sol is stable. If Cg < C < Cc, the sol slowly gels. At last if C > Cc, rapid coagulation occurs instead of gelation.

7.4.2

Electrostatic Conditions of Gelation

An increasing concentration of non-potential determining electrolyte decreases the energetic barrier which must be overcome by Brownian motion to realize the aggregation of two particles. As shown in Chap. 6, if C < Cg, the energy barrier to overcome is too high, and no linkage can kinetically occur within a normal observation time. However, for Cg < C < Cc, the energy barrier which opposes coagulation is still significant, but not as high as when C < Cg. Hence a low but non-negligible probability to overcome this barrier exists. With time, contacts between particles occur and they form pairs of particles which already present a linear architecture, in a first step. In some conditions, DLVO computations also show that a third particle has a smaller energy barrier to overcome to add up “rather” linearly (i.e., not exactly in straight line) to a two-particle aggregate, than to add up laterally (i.e., contact with both particles). This is even amplified for two bi-particles which have little chance to pack flat on each other. Hence, an open structure made of branched strings of particles may start to slowly build up from the very beginning of the coagulation process, which per nature constitutes a nascent gel (Fig. 7.11). At last, if the concentration of non-potential determining electrolyte is C > Cc, the energy barrier which a third particle has to overcome to link with a two-particle aggregate is low. It can occur at random laterally as well as linearly, and hence the coagulation of dense, randomly packed aggregates occurs. Globally, the conditions to form a gel according to the DLVO theory are reached when the thickness of the electric double layer κ1 (Chap. 6) is of the same order as the diameter of the colloidal spherical particles. In this case, a noticeable population

286

7 Gelation

Fig. 7.11 Conditions for the formation of (a) a stable sol; (b) gelation; and (c) coagulation, as a function of the non-potential determining electrolyte C Fig. 7.12 Smoothed electric potential around a string of colloidal particles with a thick double electrical layer (adapted from Pierre (1992))

of counterions is excluded from the volume occupied by two adjacent spheres in a string of particles. Moreover, the electric double layers of these adjacent spheres partly cover each other (Thomas and McCorkle 1971) (Fig. 7.12). With respect to electrostatic repulsion, a chain of colloidal spherical particles is therefore roughly perceived as a smooth cylinder by a free spherical particle which approaches the chain on its side. In these conditions, the hydrostatic overpressure which builds up by osmotic diffusion in between the coming particle and the existing chain of particles is strong on a larger front for a lateral approach than for a linear approach. Computation by the method of Derjaguin actually showed that the electrostatic repulsion was stronger pffiffiffi for a lateral approach than for a linear approach, by a coefficient of the order of 2, while the van der Waals interaction was modified in a much lower ratio (Pierre 1992). Hence, linear

7.5 Experimental Study of Gelation

287

Fig. 7.13 Possible structure of a gel obtained by electrostatic destabilization (adapted from Pierre (1992))

strings of particles should tend to keep growing rather linearly. Lateral linkage can statistically occur with a lower probability than linear linkage, which insures the formation of branches and cross-linking between the chains of spheres.

7.4.3

Example of Gel Structure According to DLVO Theory

A possible example of structure is the following: let us consider some primary particles of diameter 1 nm, with a surface electric potential of 27.5 mV at pH 3, in a material with z.p.c. 2.5 (i.e., silica). The energy barriers to overcome are 2.85 and 4 kbT, respectively, for linear and for lateral approach. These two values are much lower than 15 kbT; therefore they can easily be overwhelmed by Brownian motion and the primary particles agglomerate in relatively compact spherical secondary particles (Fig. 7.13). When the secondary particles reach a diameter of 5 nm the linear and lateral energy barriers become, respectively, 15 kbT and 21 kbT. In these conditions, linear linkage becomes much more probable than lateral linkage; it is a slow process which constructs chains made of these secondary spherical particles. The overall hierarchical structure illustrated in Fig. 7.13 is very similar to that actually admitted for silica gels (Fricke 1988).

7.5

Experimental Study of Gelation

7.5.1

Rheological Methods

7.5.1.1

Steady Flow Curves

The simplest and very qualitative method to determine gelation consists of tilting a sol and its container. Before gelation, the sol flows. After the gel point, the container can be turned upside down and the sample does not flow.

288

7 Gelation

Fig. 7.14 Schematic representation of the steady-state shear viscosity and of the equilibrium elastic modulus of a polymer during a sol-gel transition (adapted from Winter and Chambon (1987))

Otherwise the most traditional manner to study a sol-gel transition makes use of a viscometer (Winter and Chambon 1987). Before the gel point, a sol or a solution is submitted to a shear flow. The viscosity is measured as a function of time, which is itself directly related to the extent of the chemical reaction, until the limit of the apparatus is reached. Above the gel point, a gel behaves as a solid: it is submitted to a torsion strain and the steady-state shear modulus is measured as a function of time. The gel point itself is only accessible by extrapolation (Fig. 7.14). Such a method has been applied to colloidal boehmite sols (Pierre and Uhlmann 1987), to SiO2 polymeric solutions, and to other systems, including multicomponent systems for instance comprising the elements Si, Al, B, Ba, and Na (Mukherjee 1979). The measurements are tedious, but they can provide an estimation of a critical exponent, as the viscosity η is closely related to the average aggregate mass Mave (Flory 1943), by Eq. (7.10): Ln ðηÞ  A ðM ave Þm

ð7:10Þ

In the case of linear growth which should prevail in the first stage of aggregation according to the above DLVO theory, this equation can be transformed to (7.11) (Bechtold et al. 1968; Pope and Mackenzie 1988):  m 2M 0 =β M0 η¼A þ α 1α 1α

ð7:11Þ

in which the constant A is related to the monomer mass M0, and its viscosity in the initial solution η0 by

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289

A ¼ η0 =M 0

ð7:12Þ

β is related to the functionality f of the polymerizing species by β ¼f 2

ð7:13Þ

α ¼ t=t g

ð7:14Þ

and α is the reduced gelation time:

For nearly linear growth, β  1 and Eq. (7.11) can be simplified to 

2M 0 =β η¼A α 1α

m ð7:15Þ

In the case of fractal gelation such as in the percolation model, it can be established that (Pope and Mackenzie 1988) ηs ¼

QL exp ½ð3  f Þk R t  ρ0

ð7:16Þ

where f is the fractal dimension of aggregates, L is a geometrical shape constant which for a sphere is 2.5, ρ0 is the initial aggregate density, and kR is the radius R exponential growth rate constant from (R0 initial radius) R ¼ R 0 ek R t

ð7:17Þ

h i Q ¼ ηs ρ0 ðR0 =RÞ3f =L

ð7:18Þ

and

As an example, an analysis of viscosity data regarding the gelation of SiO2 from TEOS, by Pope and Mackenzie, is illustrated in Fig. 7.15. In the linear region II of Fig. 7.15, the experimental values of m and f were, respectively, 0.625 and 2.350, corresponding to a fractal growth regime, while in the linear region III they were, respectively, 0.900 and 3.56, interpreted as a hierarchical fractal growth mechanism.

7.5.1.2

Oscillatory Shear Flow (Winter and Chambon 1987)

Another rheological technique consists of applying an oscillatory shear, of small amplitude and of frequency ω, to a sample during gelation (Winter and Chambon 1987). The instantaneous shear modulus is recorded. For a given frequency ω, it is a

290

7 Gelation

Fig. 7.15 Reduced viscosity plotted as on a logarithm scale as a function of the time, in the gelation of HF-catalyzed SiO2 from TEOS (adapted from Pope and Mackenzie (1988))

periodic function G(t) of time which has the same frequency ω as the oscillatory shear, but which is not in phase with it. Hence, the instantaneous shear modulus can be considered as a complex modulus and decomposed in a component G0 (ω) termed the storage modulus which is in phase with the oscillatory shear modulus, and a component G00 (ω) termed the loss modulus which is out of phase with the oscillatory shear. The storage and loss modulus can be obtained by applying the following Fourier transforms: 0

Z

1

G ð ωÞ ¼ ω

Gðt Þ sin ðωt Þdt

ð7:19Þ

Gðt Þ cos ðωt Þdt

ð7:20Þ

0

G00 ðωÞ ¼ ω

Z

1

0

This method was for instance applied to the sol-gel precursor polydimethylsiloxane. It was shown that during gelation the storage modulus increased faster than the loss modulus with increasing time and that a crossing point existed at gel point (Fig. 7.16). The time necessary to reach the intersection depended on the oscillation frequency ω (Tung and Dynes 1982). However, this frequency could be modified by a factor up to 105 without affecting the following equality at gel point:

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291

Fig. 7.16 Evolution of the storage modulus (G0 ) and loss modulus (G00 ) of a polymer during gelation, when submitted to an oscillatory shear of frequency (adapted from Winter and Chambon (1987))

G0c ðωÞ ¼ G00c ðωÞ

ð7:21Þ

Therefore, this intersection could be used to define the experimental gel point. Moreover, if the temperature was modified within a large range from 50 to +180  C, all intersection data points for G0c and G00 C could be gathered on a single curve on which they were plotted as a function of kTω, where the coefficient kT was a function of the temperature only. At last it was possible to define a characteristic constant C for each material, which was independent of the temperature T and of the frequency ω, such that G0c ¼ G00c ¼ Ck T ω

ð7:22Þ

Moreover, this definition of the gel point was not contradictory with the previous traditional definition which corresponds to an oscillatory frequency ω ¼ 0. It could be shown that the viscosity ηc and shear modulus Gc at the gel point could be deduced from the loss and storage moduli according to Eqs. (7.23) and (7.24). As shown in these two equations, they take values which are in agreement with the characteristic values of the viscosity and shear modulus at the percolation threshold:  00    Gc ηc ¼ lim ω!0 ¼ C kT lim ω!0 ω½ ¼ 1 ω     Gc ¼ lim ω!0 G0c ¼ C k T lim ω!0 ω½ ¼ 0

ð7:23Þ ð7:24Þ

According to percolation theories it could be shown that, near the gel point,

c can G and G0 follow the laws (7.25) and (7.26) (de Gennes 1976), in which pp pc

tt g be replaced tg (Gauthier et al. 1987; Lin et al. 1991; Mallin et al. 1991): 00

292

7 Gelation

Fig. 7.17 Dependence of Ln(G0 ) and Ln(G00 ) with Ln [(t  tg)/tg] for suspensions containing different SnO2 concentrations of 1.4 and 1.6 M. The straight lines correspond to bond percolation simulations with μ ¼ 1.94 and κ ¼ 0.75, in Eqs. (7.25) and (7.26), in the vicinity of the gel point (adapted from Santos et al. (1999))

 κ pc  p for p < pc pc  μ p  pc for p > pc G0 ðpÞ  pc

G00 ðpÞ 

ð7:25Þ ð7:26Þ

An analysis of data by Santos et al. (1999) regarding the gelation of SnO2 colloidal sols is illustrated in Fig. 7.17. It shows that for t/tg < 0.2 and Cc, the bonding between particles is not linear from the beginning; hence random dense agglomerates are immediately formed (Fig. 8.10).

8.6 Aging Wet Gels

8.6

341

Aging Wet Gels

The structure of the wet gel also keeps transforming without shrinking, when stored for a long time in a liquid medium, and this evolution is known as aging. The type of transformations which may occur during aging can be chemical and/or textural.

8.6.1

Chemical Evolution During Aging

A gel has no reason to be composed of the most stable chemical species when it is formed for the first time, as a result of the hydrolysis-polymerization reactions occurring in liquid medium. A critical supersaturation of intermediate chemical complexes leading to gelation may indeed be due to intermediate species which are not the most stable, provided that they are first to reach supersaturation. The anions in the solution are well known to have a marked influence on the first colloidal and gel formed. But they can be slowly expelled from a gel by redissolution on longer timescales, which explains a possible chemical evolution of a wet gel with time. However, no universal mechanism can explain the aging evolution of a gel. With Al precursors in acidic conditions for instance, a pseudoboehmite monohydroxide gel network easily forms, which comprises ol bridges and oxo bridges, as shown in Chaps. 2 and 3. However this boehmite is metastable. Aging, especially in basic conditions, helps to transform the monohydroxide AIO(OH) gel to a more stable trihydroxide A1(OH)3 structure (Marboe and Bentur 1961). But anything which prevents the deprotonation of hydroxy groups in the monohydroxide, such as the adsorption of glycerol or ethanediol, prevents its aging transformation to bayerite. A similar aging evolution occurs in the case of tungsten oxide gels (Lemerle and Lefebvre 1977) which are known to be unstable and crystallize after a few days. But they can also be stabilized by foreign colloids such as MoO3. Even silicic acid gels, which always show an amorphous X-ray diffraction pattern have a tendency to crystallize after aging in dehydrating conditions (Hermans 1952). The reverse can also be true: crystalline zirconia immersed in water undergoes a surface hydrolysis modification yielding a thin gel-like coating (Blesa et al. 1985). In the case of Fe(OH)2 gels, dissolution followed by recrystallization during aging let individual Fe3O4 monocrystals grow after some time (Haruta and Delmon 1986) (Fig. 8.11).

8.6.2

Physical Evolution During Aging

The origin of the physical aging evolution is the same as in syneresis: it is the high specific surface area of the solid gel network which any evolution tends to slowly

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8 Wet Gels and Their Drying

Fig. 8.11 Aging evolution of Fe(OH)2 gels. Adapted from Haruta and Delmon (1986)

Fig. 8.12 Adsorption-desorption isotherms on silica gels after various aging times. Adapted from Van Bemmelen (1898), Hermans (1952), and Iler (1979)

decrease. In silica gels at low pH the polymer species which make the gel network are not very soluble, so the network is “frozen in”; no significant modification occurs during aging (Brinker et al. 1982). However, at higher pH, colloidal silica gel slowly transforms to coarser structures, as indicated by the evolution of water vapor adsorption desorption isotherms of these gels (Fig. 8.12). These isotherms show a displacement of the hysteresis loops towards higher pore sizes. That is to say, both the pores and the gel network become coarser and the specific surface area decreases as the aging time increases.

8.6 Aging Wet Gels

343

Fig. 8.13 Permeability of silica wet gels before drying, as a function of HF concentration in the aging bath composed of ethanol or ethyl acetoacetate containing 3 vol% water. Adapted from Strøm et al. (2007)

This type of evolution explains why silica gels are often aged via different processes before drying. The aim of this step generally is to mechanically reinforce the tenuous solid skeleton generated during the sol-gel process and was largely addressed in studies dedicated to these strengthening treatments by Einarsrud et al. (1998, 2001). These researchers showed that wet silica gels were strengthened by the new deposition of silica in the necks linking the nanoparticles constituting the solid network, when these wet gels were aged in alkoxide/alcohol solutions (Hæreid et al. 1994). Similarly, to improve the gel strength, it can be rewarding to enhance the syneresis mechanism as well as the Ostwald ripening mechanism, presented in Chap. 6, Sect. 6.8, by adjusting the composition of the liquid contained in gel pores. Adding water (Hæreid et al. 1997) and/or monomeric alkoxysilanes like TEOS (Einarsrud et al. 1998, 2001; Suh et al. 1999; Venkateswara Rao et al. 2004; Smitha et al. 2006; Estella et al. 2007; Strøm et al. 2007) can significantly enhance surface reactions and primarily those involving the residual hydroxy/alkoxy groups. Such additions induce supplementary condensation reactions which favor the dissolution/re-precipitation of silica. The associated kinetics depends on the pH and the nature of the solvent. Generally, the particle “neck” area, the average pore size, and the apparent density of the gel increase through aging treatments. The permeability and mechanical properties of silica aerogels can also be increased by adding large precursor molecules, such as polyethoxydisiloxanes, in the aging solution (Einarsrud et al. 2001) or by adding a simple dilute HF solution (Strøm et al. 2007) (Fig. 8.13). It was also shown that monitoring of the temperature and thermal aging protocol of a wet gel in water can be a key factor to decrease the gel microporosity before drying (Reichenauer 2004; Jensen et al. 2004). In gels other than SiO2, some completely different textures may develop during aging. An example concerns gelatinous ZrO2 precipitates made from Zr propoxide in cyclohexane by Kindu and Ganguli (1986), where coalescence of the colloidal particles into rods occurs, with a periodic swelling along the length of a rod.

344

8.7

8 Wet Gels and Their Drying

Drying Gels

A number of different techniques can be applied to dry a wet gel. They can be more or less complex to perform but they can have very different effects on the gel shrinkage during drying and its porous texture.

8.7.1

Drying by Evaporation

Evaporation of the gel liquid matrix is the simplest drying technique. It is known for clay (Ford 1964), boehmite (Pierre and Uhlmann 1987), and in a more controversial fashion silica (Hench and Wilson 1990) that the drying rate per unit contact area of gels with air or vacuum follows two successive regimes: a “constant-rate” period, followed by a “falling-rate” period (Fig. 8.14a, b). The transition between these two regimes occurs at a very sharp point named the “critical point” (Kingery and Francl 1954) or “leather-hard point” (Ford 1964) depending on authors. The main mechanisms proposed to explain these dual regimes are based on capillary liquid flow and were summarized by Hermans (1952).

Fig. 8.14 Evolution of the drying rate per external unit area of wet gel as a function of the liquid volume proportion VL: (a) and (b) experimental graphs; (c) graph when the drying rate was proportional to the relative surface of menisci

8.7 Drying Gels

345

Fig. 8.15 Capillary mechanism. Adapted from Pierre (2019)

8.7.1.1

The Capillary Mechanism

The capillary mechanism explains correctly the reproducible adsorption hysteresis curves of water in silica gels. This mechanism has been summarized as follows by Hermans (Fig. 8.15): 1. Evaporation creates a liquid vapor meniscus at the exit of pores in the gel. 2. This induces a hydrostatic tension in the liquid, which is balanced by an axial compression on the solid. 3. The latter compression makes the gel shrink. 4. As a result of shrinkage, more liquid is fed to the menisci at the exit of the gel pores, where it is evaporated and so on. One consequence of capillarity is also the existence of a hysteresis loop on adsorption-desorption isotherms, for instance of silica gels (Fig. 8.16). This comes from the fact that the equilibrium vapor pressure pv above a meniscus of principal radii r1 and r2 is given by the Kelvin equation (8.17):     1 1 þ pv ¼ p0 exp γ V m RT r1 r2

ð8:17Þ

where p0 is the vapor pressure above a planar surface and Vm is the molar volume of the liquid. Branch IC in Fig. 8.16a corresponds to the initial drying of the gel. At point C, the meniscus is as in Fig. 8.16b. Further on, it penetrates inside the gel pores which stop shrinking. Along CD, the meniscus is deeper inside the pores (Fig. 8.16c), but for a cylindrical pore this is a spherical meniscus with two radii of curvature 2 equal to the radius of the pore rpor. Its curvature is therefore rpor . From D to S, only a thin layer of water remains on the cylindrical walls of the pores. The cylindrical configuration of point S maintains if water is re-adsorbed in the gel and the curve SDF is followed during re-adsorption. At point F, the gel pores are again full of water. Finally, along FC, during the second desorption cycle, a spherical meniscus is formed again.

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8 Wet Gels and Their Drying

Fig. 8.16 Adsorption-desorption isotherms of water vapor in a silica gel. Adapted from Van Bemmelen (1898) and Hermans (1952)

Detailed calculations according to the capillary mechanism have been made by Scherer (1989). The equilibrium meniscus radius rm at any instant is given by the compressive stress that the solid network of the gel can support. The contact wetting angle at the liquid–solid–vapor interface is undetermined along a sharp solid edge. Higher stresses are required for higher compression states of the solid, which requires a higher hydrostatic tension in the liquid. It follows therefore that the menisci are sharper and sharper (smaller radius rm) when contraction increases. This keeps a gel shrinking until the meniscus radius rm reaches the pore radius rpor. The latter event defines the critical-point drying. Beyond this critical point, capillary stresses cannot increase the compressive stresses anymore on the solid network. For instance, for a cylindrical pore of radius rpor and cross section Apor: Apor ¼ πr 2

ð8:18Þ

The hydrostatic tension σ T in the pore liquid increases when rpor decreases as (8.19) σ T ¼ 2γ

cos θ r por

ð8:19Þ

where θ is the wetting angle of the liquid over the solid and γ is the surface tension in the liquid. For a perfect wetting (θ ¼ 0):

8.7 Drying Gels

347

σT ¼

2γ r por

ð8:20Þ

However, the tensile force decreases as (8.21) F T ¼ σ T Apor ¼ πγr por

ð8:21Þ

Hence the compressive force on the gel decreases so that the gel contraction stops at some moment. For a higher liquid surface tension γ, the gel reaches a higher shrinkage at the critical point, which is in agreement with data by Kingery and Francl (1954). The capillary mechanism is not able to explain in a straightforward fashion the existence of a “constant-rate” regime. A mathematical model by Suzuki and Maeda (1968) has shown that the rate of drying could be constant when evaporation occurs from menisci, even when these menisci only occupy a minor relative proportion AL of the gel external surface. A possible explanation is that the solvent vapor transport from the menisci is the slowest step and controls the kinetics of drying. However, an experimental study has shown that the drying rate falls drastically as soon as menisci appear, before reaching a constant regime while the menisci penetrate the inner part of a gel (Castro et al. 1988). It is also possible to argue that the heat transfer to vaporize the liquid can control the kinetics of drying. In this case the drying rate should, in a first approximation, be proportional to AL. As long as a gel is full of liquid, this is a random two-phase composite material. In these conditions, it is known (Kingery et al. 1975) that the proportion of each phase (liquid L and solid S), along a cutting line (respective linear proportions LL, LS), in a cutting plane (respective area proportions AL and AS), or in volume (respective volume proportions VL and VS) is independent of the determination mode: LL ¼ AL ¼ V L

ð8:22Þ

Ls ¼ AS ¼ V S

ð8:23Þ

Hence the drying rate per unit area should decrease linearly with the liquid content VL (Fig. 8.14c). The experimental existence of a “constant-rate” period before the critical point is therefore generally interpreted as being due to the evaporation of a continuous liquid film, which covers the entire surface of the gel. Obviously the existence of such a film can be related to the affinity of oxides for water, which largely depends on the nature of the oxide. In the case of boehmite and montmorillonite, this affinity is very high. The latter gels are able to swell back in water and the constant rate can account for up to 80% of the gel volume shrinkage.

348

8.7.1.2

8 Wet Gels and Their Drying

Drying by Evaporation and the DLVO Theory

To explain both the constant-rate regime and the behavior at the critical point, a mixed osmosis capillarity can be proposed (Pierre 1990). It takes into account the structuration of monomolecular water layers around a solid particle, which is well known to occur in clays, boehmite, and other oxides (cf. Chap. 2). Recent studies by Livage (1988) on V2O5 gels have shown that the number of water layers of this type can be very important. This structuration is a consequence of both steric and electrostatic interactions. For instance, in the case of the electrostatic interactions between two parallel and planar surfaces according to the DLVO theory (Chap. 6), the hydrostatic pressure P inside a pore of colloidal size is not uniform; it is a function of the distance x from the nearest pore surface which is given by (8.24) (Fig. 8.17)  2 E0 E dΨ Px ¼ PM þ 2 dx

ð8:24Þ

where M is the mid-distance point inside the liquid and Ψ is the electrical potential. During drying, when a meniscus is created at the end of a pore, the liquid is placed under hydrostatic tension (PM < 0) in the middle of the pore, so that the liquid-air meniscus just above the mid-distance point is concave. However the hydrostatic tension Px increases algebraically (is negative and decreases in magnitude) as the distance x from the nearest particle decreases. At a close distance x, it can even Fig. 8.17 Modification of the capillary mechanism by electrostatic osmosis according to the DLVO theory. Adapted from Pierre (1990)

8.7 Drying Gels

349

become a compression so that the meniscus profile becomes convex and insures continuity with a liquid film which covers the solid. An inflexion point exists in the meniscus profile, which corresponds to a null hydrostatic tension in the liquid. Actually, the capillary and osmotic theories constitute two approximations of the above colloidal view. The traditional capillary theory applies well when the pores have a diameter well above the colloidal dimensions; it approximates a solid–liquid interface by a sharp transition described by a surface tension γ SL. The osmotic theory applies well to molecular solutions or truly polymeric gels: the solid–liquid interface loses all significance and the solvent structuration is replaced by an average effect in the solvent. The structuration at the liquid–air interface is traditionally neglected and replaced by a sharp interface characterized by a surface tension γ w, which actually summarizes this interface structuration phenomenon. If pm hyd designates the hydrostatic tension in the middle of the meniscus, the meniscus curvature is maximum at this point and given by (8.25) rm ¼

γw pm hyd

ð8:25Þ

This radius of curvature is smaller; hence the curvature is more marked, when γ w is lower. During drying, the continuous solvent film above the solid becomes less thick, while the maximum curvature of the meniscus increases. This evolution can end when the film disappears, so that drying and shrinkage of the gel keep going with a decreasing rate (Fig. 8.17b). This is actually the case when the meniscus radius reaches the pore radius and penetrates inside the gel, so that shrinkage of the gel suddenly stops. This exactly corresponds to a behavior such as the critical-point drying (Fig. 8.17c). The influence of the liquid surface tension γ w on the critical point has been studied. If the chemical affinity of the liquid for the solid is maintained at a constant value, for instance by keeping water as the main liquid, it is possible to modify the water surface tension by adding a small amount of surfactant. This was done by Kingery and Francl (1954) in the kaolinite-water system. Their results are in agreement with the predictions of the mixed model, concerning the decrease in the water content of the gel after the critical point when the surface tension increases (Fig. 8.18). Instead of modifying the surface tension γ w and keeping the chemical affinity constant, the opposite can be done. A comparison has been made between the different drying behaviors of boehmite sols hydrolyzed in the same conditions, and then diluted in excess solvents of a different nature (Pierre and Uhlmann 1986). The solvents comprised of formamide, ethylene glycol, and water in which various surfactants were added so as to compare the drying behavior with formamide and ethylene glycol for a same surface tension. The results have shown that the drying behavior changed drastically depending on the solvent. With formamide,

350

8 Wet Gels and Their Drying

Fig. 8.18 Effect of surface tension on the critical-point drying and maximum constant drying rate of kaolin clay. Adapted from Kingery and Francl (1954)

the critical point roughly coincided with the gel point and it reached a total liquid volume much larger than that with a water-surfactant liquid having the same surface tension. Also, the volume at gel point increased linearly with the formamide initial volume. A similar behavior of different magnitude was observed with ethylene glycol. These results can only be explained by a different chemical affinity of boehmite for each solvent. During the constant-rate regime, two parameters influence in an opposite direction the observed evaporation rate. One is the surface area of the evaporation front, per unit cross-section area of drying gel. Because of roughness on the evaporation surface due to nascent menisci, the surface area of this evaporation profile increases slowly during drying and hence it tends to increase the drying rate. On the contrary, the water vapor pressure decreases both over the nascent menisci and above the adsorbed layer, which tends to decrease the drying rate. Actually, these effects become measurable only when the liquid surface tension is high and close to the critical-point drying. In these conditions, water evaporates from a film which follows more closely the particle contour and the increase in the evaporation surface becomes non-negligible. Data of Kingery and Francl (1954) showed that the drying rate per unit cross-section area of gel first increased briefly, before falling down suddenly at the critical point (Fig. 8.14b). That is to say, the increase in drying surface area outweighed the opposite decrease in water vapor pressure.

8.7.1.3

Stresses Developed in a Gel During Drying by Evaporation

To obtain a monolith, it is necessary to minimize the internal stresses due, on the one hand, to differential volume change inside a gel and, on the other hand, stresses of capillary origin.

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351

Internal stresses due to differential volume change were investigated by Cooper (1978) and Scherer (1989). Cooper assumed that drying gels were submitted to a plastic flow behavior similar to that in glasses. This approach showed that a gel slab of thickness 2w, dried by evaporation from its two flat sides with an evaporation rate j, was submitted at time t to a tensile stress σ(w,t) which increased with w. An approximate relation often numerically valid is (8.26) σ ðw, t Þð1  νÞ jw ¼ 9Dw E ðw, t Þ

ð8:26Þ

where E(w,t) is the Young’s modulus of the slab and ν its Poisson’s ratio, which both depend on the average local liquid content. This formula shows that to avoid fracturing a gel monolith, the drying rate j must be decreased in inverse proportion to the monolith thickness. This explains that the most appropriate application of gels is for coatings. The relationship between stresses developed during drying and presence of capillary pores in a gel was investigated by Zarzycki et al. (1982) and by Scherer (1989). According to Eq. (8.19), a larger pore radius decreases the capillary stresses and makes it easier to synthesize an unfractured gel monolith, as shown for SiO2 by Shoup (1976) and for A12O3 by Yoldas (1975). The size and pore distribution in a gel can be modified in particular by choosing a different chemical synthesis procedure, such as modifying the hydrolysis water ratio rw (Astier and Sing 1980) or the nature of a solvent (Cormack et al. 1980). Hydrolysis with a high water proportion produces a gel with a strong tridimensional cross-linking, which is less prone to cracking (Sakka 1982). With a low water proportion, a gel tends to crack in a powder as this is often the case with mixed alkoxide chemistry (Zelinski and Uhlmann 1984). In gels where no surface treatment such as surface silylation (Schwertfeger et al. 1998) or no aging treatment (Einarsrud et al. 1998) is applied more dense (e.g., ρ > 0.25 g/cm3 (Allié et al. 2006)) and very often cracked xerogel monoliths are obtained. A gel drying behavior also depends on its degree of crystallinity (Zelinski and Uhlmann 1984). To decrease the effect of capillary stresses, for a given gel structure, various solvent extraction techniques can be used, in particular freeze-drying; drying in a humid atmosphere; heating in a microwave oven (Higuchi et al. 1986); adding a surfactant; slow drying; and supercritical drying. The three latter techniques were compared by Zarzycki et al. (1982) on silica gels. The most efficient to make uncracked monoliths was supercritical drying which is examined in the next section. Slow evaporation was applied to make uncracked silica gel monolithic disks with a diameter of 65 mm and 10 mm thickness. The time necessary to avoid cracking was of the order of 1 month (Klein and Garvey 1982). During this process, the weight loss was 50% and the radial shrinkage 25% (Brinker et al. 1982). Shrinkage is also less important when drying is made in a humid atmosphere (Lanutti and Clark 1984). Drying in a controlled humidity atmosphere (up to 100% relative humidity) made it possible to attenuate cracking both during and after

352

8 Wet Gels and Their Drying

drying of ThO2 gel spheres, made by Yamagishi and Takahashi (1987). Similarly, when the main solvent is not water but for instance methanol, control over cracking and gel turbidity can be improved by controlling the solvent vapor pressure (Yamane et al. 1978). Gel monoliths can also crack because of restraint by adherence to the container. This effect can be limited by using material containers in Teflon®, or by performing gelation over a layer of non-water-miscible liquid (e.g., heavy oil or mercury).

8.7.2

Supercritical Drying

Supercritical drying, also named hypercritical drying, can be viewed as an application in an extreme case of the drying laws presented in the previous paragraphs. It corresponds to a case when the surface tension of the liquid cancels out (γ w ¼ 0). In this condition Eq. (8.25) gives a meniscus radius rm ¼ 0. Hence a meniscus radius reaches at once the radius of the pore where it penetrates. No constant-rate regime can be observed. All pores are emptied altogether with a very moderate contraction, due to possible fluid exchange flow inside the gel when such an intermediate exchange must be performed before supercritical drying, in agreement with experimental observations. The dry gels obtained are termed “aerogels.” The supercritical drying technique was first investigated on silica gels made of sodium silicate by Kistler (1932). To maintain a monolithic character during supercritical drying, the wet gels were actually dialyzed to replace water by ethanol, so Kistler initiated supercritical drying in this alcohol. Kistler also deposited several patents; one of them was assigned to the Monsanto Chemical Company which made the first industrial production of silica aerogels, commercialized under the name of Santocel® (Kistler 1941). Besides, Kistler also patented the first hydrophobic silica aerogels made by silylation with trichloromethylsilane, for use as water repellents (Kistler 1952). The latter technique is at the basis of the so-called ambient pressure drying method which produces aerogel-like materials, sometimes termed “ambigels.” Hence, Kistler initiated most of the directions in which aerogels were later developed. The supercritical drying technique consists of heating a gel at temperatures and pressures exceeding the critical point of the liquid which impregnates the wet gel. This liquid in a supercritical state can next be slowly evacuated by flushing the autoclave with dry argon. Supercritical drying was applied to SiO2 as well as to A12O3 and TiO2 by Teichner et al. (1976), to binary systems (SiO2–B2O3; SiO2–P2O5, NiO–Al2O3, Fe2O3–Al2O3) and ternary systems (SiO2–B2O3–P2O5) (Woignier et al. 1984), and to many gels since that time. Several heating schedules can be used, such as the one illustrated in Fig. 8.19. In this example, the autoclave is first partly filled with the solvent. Then it is closed and heated. The solvent evaporates first and its pressure increases altogether with its temperature. If a sufficient quantity of solvent were added in the autoclave, the pressure goes over the solvent critical point value Pc and the temperature over

8.7 Drying Gels

353

Fig. 8.19 (a) Illustration of the type of autoclave used in a HOT SCD process (ethanol- or methanol-impregnated gel) and (b) schematic temperature and pressure pathway. Adapted from Pierre and Pajonk (2002) Table 8.1 Critical point parameters of common fluids

Fluid Water Carbon dioxide Freon® 23 Freon® 116 Ammonia Acetone Benzene Nitrous oxide Methanol Ethanol 1-Propanol 1-Butanol

Formula H2O CO2 CHF3 CF3-CF3 NH3 (CH3)2O C6H6 N2O CH3OH C2H5OH C3H7OH C4H9OH

TC ( C) 374.1 31.0 25.9 19.7 132.5 235.0 288.9 36.4 239.4 243.0 263.5 289.7

Pc (MPa) 22.04 7.37 4.82 2.97 11.27 4.66 4.89 7.24 8.09 6.38 5.17 4.39

Adapted from Matson and Smith (1989)

its critical point temperature Tc, before menisci could be formed at the exit of the gel pores. This permits to avoid that the gel begins losing its liquid by evaporation. The supercritical solvent can then be evacuated as a gas, very slowly at the beginning to not decrease the autoclave temperature below Tc. A slow depressurization rate permits to minimize adiabatic cooling of the gel, and hence to inadvertently cross the liquid-gas coexistence line; otherwise menisci would again form. Once the pressure is sufficiently lower than Pc, while the temperature is still above Tc, depressurization and cooling can be accelerated. Supercritical drying remains the technique most frequently used to obtain aerogels (Leventis 2007; Dorcheh and Abbasi 2008; Chen et al. 2014; Maleki et al. 2014a, b, 2015a, b), although this is a slow process. This technique can be implemented with gel impregnated with fluids, of which a partial list with their critical parameters is given in Table 8.1.

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As this table shows, supercritical drying is difficult with water because of the high critical pressure and temperature, although water is not flammable. It is more feasible with methanol and ethanol, and easy with carbon dioxide (Tewari et al. 1986). In practice, high-temperature supercritical drying (or HOT SCD) in alcohol is distinguished from low-temperature supercritical drying (COLD SCD) in CO2, as applied with success by Tewari et al. (1985), next to a first unsuccessful attempt previously mentioned by Kistler, on rubber. The low-temperature CO2 supercritical drying processing is applicable to hydrogels prepared from natural polymers, such as pectin aerogels (Rudaz et al. 2014; Veronovski et al. 2014; Maleki 2016), contrary to the HOT SCD techniques. However, carbon dioxide does not dissolve water and is not an outstanding solvent for methanol and ethanol, while it is a much better solvent for acetone. Hence aqueous liquids in wet gels are often exchanged first for acetone, and second for liquid CO2 by dialysis. When the exchange is made in the normal liquid state, before supercritical drying in CO2 (Wagh et al. 1999), it may induce some moderate shrinkage. However, exchange of alcohol for CO2 can also be made with CO2 in the supercritical state (van Bommel and de Haan 1995). This is because the interdiffusion of CO2 with methanol or ethanol is significantly accelerated when CO2 is in its supercritical state (Novak et al. 1999; Wawrzyniak et al. 2001). Various detailed procedures regarding the drying protocol, such as the heatingpressurization path, initial atmosphere above the samples, and duration of each step, were investigated. In particular a low gel permeability results in rather slow CO2 washing and vessel depressurization steps (Scherer 1994; Woignier and Scherer 1994), in particular for thick gel plates. To speed up the CO2 washing, simple molecular diffusion must be assisted by forced convection, for example by integrating compression-decompression cycles into the process (Lee and Begag 2001). However if an accelerated depressurization is required, gels must be significantly strengthened prior to drying. Otherwise, they will experience cracks even at low depressurization rates (Pierre and Rigacci 2011). These parameters, summarized by Pajonk (1994), are important to control during the drying process, in order to minimize differential stresses. The solvent characteristics were also investigated and it was shown that they could induce important textural effects in the final dry aerogel. Overall, relatively large dry silica aerogel monoliths with 84–91% porosity and a specific area which can reach up to 800 m2 g1 could be produced by COLD supercritical drying (Fricke 1988). Currently, to try solving the fluid exchange difficulties associated with the standard supercritical CO2 route, one of the challenges investigated concerns the direct synthesis of the silica gel in supercritical CO2 by a water-free process (Moner-Girona et al. 2003; Loy et al. 1997; Sharp 1994). During the last decade, to accelerate the drying process, a new rapid supercritical extraction (RSCE) method was also experimented, where the sol-gel precursors were themselves brought to a supercritical state inside a pressurized mold under “HOT” supercritical conditions (Poco et al. 1996; Gross et al. 1998; Scherer et al. 2002; Gauthier et al. 2004; Roth et al. 2008). Even though successful in the case of small samples, this technique did not yet permit to elaborate large crack-free, low-density monolithic silica aerogels.

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Fig. 8.20 Photographs of aerogel A dried by COLD CO2 supercritical drying of xerogel X, synthesized from tetramethoxysilane (TMOS) with HCl catalysis in excess water in identical conditions. Reprinted with permission, from Favre et al. (2011) Copyright Springer Nature 2011

Examples of dry gels and aerogels will be illustrated in Chap. 9, but the difference in shrinkage between a xerogel and an aerogel dried by a COLD SCD is illustrated in Fig. 8.20, regarding initially similar SiO2 wet gel monoliths.

8.7.3

Ambient Pressure Drying

Ambient pressure drying necessitates modifying the wet gel surface to make it more hydrophobic, so as to largely decrease the magnitude of the capillary stresses in ambient temperature and pressure conditions. Such progress in the sol-gel chemistry permitted to synthesize materials also known as “ambigels,” which are similar to aerogels and often termed aerogels, except that they are obtained without any use of a supercritical drying autoclave, as described by Land et al. (2001). Ambient pressure drying was developed for silica aerogels by the Brinker team (Prakash et al. 1995a, b) and further applied to organic or organic coated-type aerogels (Leventis et al. 2005; Yang et al. 2010; Duraes et al. 2013; Schwan and Ratke 2013; Maleki et al. 2015b). In practice, this is a faster, less expensive, and more suitable technique for industrial production of aerogels (Maleki et al. 2015b; Zuo et al. 2015). The ambient pressure drying method was also extended to aerogels obtained from sodium silicate (Bangi Uzma et al. 2009). In the simplest approach, organic compounds can be added in the liquid where gelation is performed, to decrease the capillary drying stresses. These additives, in particular glycerol, formamide, dimethylformamide, oxalic acid, tetramethylammonium hydroxide, polyethylene glycol (PEG), polyvinyl alcohol (PVA), and surfactants, are also known as “drying control chemical additives” (DCCA) (Zarzycki et al. 1982;; Reetz et al. 1996; Anderson et al. 1998; Nakanishi et al. 1998; Pierre et al. 2000; Martin et al. 2001; Venkastewara Rao and Kulkarni

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2003). Depending on their polar or apolar and protic or aprotic characteristics, they interfere with the hydrolysis products of the SiO2 precursors and permit to control the pore size and pore volume as well as their size distribution. DCCA permitted to obtain uncracked dry monoliths with a relative pore volume as high as 97.4% (Hench 1986). Large molecular surfactants are interesting very special additives which are focused in Chap. 10, regarding templated materials. Besides, various silylation procedures permit to hydrophobize the surface of gel pores after its synthesis. But SiO2 silylated sol-gel precursors presented in Chap. 3, such as methyltrimethoxysilane (MTMS), can be used to synthesize a gel (Venkastewara Rao et al. 2006). A consequence of such hydrophobic surface groups is that a gel is no longer submitted to strong capillary contraction stresses during solvent evaporation. Moreover the Si–X functionalities (X hydrophobic group) make the formation of new siloxane Si–O–Sibonds impossible by condensation (Schwertfeger et al. 1998), during syneresis. In turn this explained that, in a study by Smith et al. at the Sandia National Laboratory, a shrinking gel during evaporation sprung back to 96.9% of its wet volume when the solvent front retreated and capillary stresses were released (Bisson et al. 2003). By comparison, an equivalent unsilylated dry xerogel occupied 30.1% of the initial wet gel volume (Smith et al. 1995). A density below 0.1 g cm3, for a total specific pore volume sometimes larger than that of CO2-dried samples, could be obtained. To conclude, after some trial and error, ambient pressure drying was applied with great success to the synthesis of silica aerogels from alkoxides (Deshpande et al. 1992; Land et al. 2001; Parvathy and Pajonk 2005), as well as from water glass (Venkateswara Rao et al. 2004; Schwertfeger et al. 1998), and is today the most promising manufacturing technique for SiO2 aerogels.

8.7.4

Subcritical Drying

Drying can also be done slightly below the solvent critical point, according to the subcritical drying method, for instance at pressure and temperature slightly below those of the critical points, where the liquid surface tension is low (Wang et al. 1992; Haereid et al. 1995; Maleki 2016). To facilitate application of this technique, the aqueous matrix of wet gel may be replaced by a solvent with a lower surface tension, such as ethanol or acetone. Also, very slow drying by evaporation according to the “pinhole technique” also permits to give more time for a gel network, mainly silica, to resist shrinkage by forming new siloxane Si–O–Si  bonds between network solid branches, at the beginning of the shrinkage process (Tabata et al. 2010; Adachi et al. 2011). Besides, lightweight monolithic silica ambigels could be obtained without surface silylation or DCCA addition, via “forced aging” by finely tuning the sol formulation. For instance, Scherdel and Reichenauer (2015) demonstrated that a two-step TEOS-based synthesis route, using low water concentration in a first step and a high amount

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of ammonia in a second step, permitted to obtain highly porous ambient-dried silica aerogels, mainly macroporous with apparent density as low as 0.15 g cm3. At last, recently, a novel drying process in subcritical conditions based on dielectric heating was investigated (Bonnardel and Chausson 2015). The energy transfer provided by electromagnetic radiations can significantly reduce the drying time as well as the energy consumption. Some blanket-type silica-based aerogels with excellent thermal insulation properties were already synthesized this way (Nocentini et al. 2018).

8.7.5

Freeze-Drying

Freeze-drying necessitates to bypass the triple point of the gel liquid matrix. In the technique developed by several groups (Klvana et al. 1989; Pajonk 1989; Tabata et al. 2010; Adachi et al. 2011), gels or solutions of their precursors are dried by sublimation of the frozen wet gel liquid, under vacuum. The dry gels obtained are termed cryogels and showed a maximum porosity of 80%, with only half of the surface area of the supercritical or ambient pressure dried aerogels (Pajonk et al. 1990; Zuo et al. 2015). The main problem with this technique was that the nucleation and growth of solvent crystals eventually destroyed or at least distorted the gel network, to produce very large pores (Kocklenberg et al. 1998). Except in some rare cases (Pons et al. 2012), freeze-drying led to cracked pieces or even powderlike products (Egeber and Engel 1989). This problem was attenuated by using solvents with a low expansion coefficient and a high sublimation pressure and also by applying rapid freezing in liquid nitrogen, also known as flash freezing, at cooling rates over 10 K s1. Many small crystals are then nucleated and separate crystallization of the various components is prevented (Tretyakov and Shlyakhtin 1999). SiO2 and Al2O3 powders with a texture close to those of aerogels were obtained using this technique, by Pajonk et al. (1990). The freeze-drying technique is also very useful to dry hydrogels which cannot withstand HOT supercritical drying conditions (e.g., cellulose, PI, PVA, pectin), in particular for medical applications (Chen et al. 2013, 2014b, c; Wicklein et al. 2014).

8.7.6

Drying by Liquid–Liquid Extraction

This technique is based on water extraction by osmosis, for instance in acetone, and the mechanism which describes it best is osmosis. As discussed in a previous section, the gel solid network plays the roles of both a solute and a porous membrane. The osmotic mechanism corresponding to drying can be described in a manner similar to swelling and is illustrated in Fig. 8.21. In practice, a gel can be made to shrink by immersion in another solvent than water, such as acetone, and in this case the definition of a water-acetone meniscus at the exit of pores is not really adequate because the two fluids are miscible.

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Fig. 8.21 The osmotic shrinkage mechanism: (a) separate gel and solvent; (b) creation of an overpressure inside the gel; (c) shrinkage of the gel

The osmotic mechanism involves first the creation of a dissymmetry between a gel and a new solvent (Fig. 8.21b). In the second step, water diffuses through the gel network (equivalent to a porous membrane) and creates a hydrostatic tension in the liquid of the gel. This tends to re-establish an identical total free energy, of chemical plus mechanical origin, in the gel solvent and in the solvent outside the gel. In a third step, this hydrostatic tension in the gel liquid makes the gel network shrink (Fig. 8.21c). Consequently, the liquid free energies of chemical origin come close to each other in the liquid inside and outside the gel. Simultaneously the difference in hydrostatic pressure decreases until it reaches an equilibrium value, balanced by the compressive stress in the gel network.

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S.J. Van Der Gaast, J.H.F. Jansen, T.C. Simonton, Clay Clay Miner. 33, 471–472 (1985) A. Venkastewara Rao, M.M. Kulkarni, Mater. Chem. Phys. 77, 819–825 (2003) A. Venkastewara Rao, S.D. Bhagat, H. Hirashima, G.M. Pajonk, J. Colloid Interface Sci 300, 279–285 (2006) A. Venkateswara Rao, A. Parvathy Rao, M.M. Kulkarni, J. Non-Cryst. Solids 350, 224–229 (2004) A. Veronovski, G. Tkalec, Z. Knez, Z. Novak, Carbohydr. Polym. 113, 272–278 (2014) C. Von Nàgeli, Pflanzenphysiologische Untersuchungen (F. Schulthess, Zurich, 1858) P.B. Wagh, R. Begag, G.M. Pajonk, A. Venkateswara Rao, D. Haranath, Mater. Chem. Phys. 57, 214–218 (1999) A.T. Walter, J. Polym. Sci. 13, 207–228 (1954) S.H. Wang, F. Kirkbir, S.R. Chauduri, A. Sarkar, P. Soc. Photo-Opt. Ins. 1758, 113–124 (1992) P. Wawrzyniak, G. Rogacki, J. Pruba, Z. Bartczak, J. Non-Cryst. Solids 285, 50–56 (2001) B. Wicklein, A. Kocjan, G. Salazar-Alvarez, F. Carosio, G. Camino, M. Antonietti, L. Bergström, Nat. Nanotechnol. 10, 277–283 (2014) E.J. Witzemann, J. Am. Chem. Soc. 37, 1080–1091 (1915) and 39, 25–33 (1917) T. Woignier, G.W. Scherer, J. Sol. Gel Sci. Technol. 3, 141–150 (1994) T. Woignier, J. Phalippou, J.J. Zarzycki, Non-Cryst. Solids 63, 117–130 (1984) S. Yamagishi, K.J. Takahashi, Nucl. Mater. 144, 244–251 (1987) M. Yamane, S. Aso, T.J. Sakaino, Mater. Sci. 13, 865–870 (1978) J. Yang, S.K. Li, L.L. Yan, J.X. Liu, F.C. Wang, Micropor. Mesopor. Mater. 133, 134–140 (2010) B.E.J. Yoldas, Mater. Sci. 10, 1856–1860 (1975) B.E.J. Yoldas, Mater. Sci. 21, 1087–1092 (1986) J. Zarzycki, M. Prassas, J. Phalippou, J. Mater. Sci. 17, 3371–3379 (1982) B.J.J. Zelinski, D.R.J. Uhlmann, Phys. Chem. Solids 45, 1069–1090 (1984) L.Z. Zuo, Y.F. Zhang, L.S. Zhang, Y.E. Miao, W. Fan, T.X. Liu, Materials 8, 6806–6848 (2015)

Chapter 9

Dry Gels

9.1

Introduction

It was shown in Chap. 8 that the drying of wet gels could lead to a range of dry gels from xerogels to aerogels, characterized by a very variable volume reduction depending on the drying technique applied. The next section of this chapter is focused on the porous texture of these dry gels, in terms of pore size and size distribution such as mainly studied by nitrogen adsorption. Their fractal structure is a result of the gelation process itself and was largely addressed in Chap. 7, but it is worth being revisited for real dry materials. A significant variety of dry gels, silica, alumina, silicates, titania, zirconia, sulfide, organic gels, carbon nanotubes, and graphene aerogels, are illustrated. Carbon gels derived by carbonization of organic gels are briefly described for completeness of the dry gel fields, but they are also addressed in Chap. 12 focused on the evolution of gel texture and structure during thermal treatments. All dry gels also have in common some important properties, although they are mainly studied for silica. This is essentially the case of their thermal conduction properties and mechanical properties, which are reviewed in the last section of this chapter. Other properties, regarding either gels of a particular nature or requirement of a specific shaping technique, such as thin antireflective coatings, are gathered in the last chapter on the applications of sol-gel processing.

9.2 9.2.1

Texture of Dry Gels Pore Characterization Techniques

One of the best classical ways to characterize the solid network in porous materials such as gels consists of describing their porosity. According to the most classical convention of pore according to their size (IUPAC 1994), pores in gels are © Springer Nature Switzerland AG 2020 A. C. Pierre, Introduction to Sol-Gel Processing, https://doi.org/10.1007/978-3-030-38144-8_9

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traditionally divided into micropores of size 50 nm. The data most usually available to characterize these pores are the apparent density ρa, determined by immersion in a liquid which does not wet the solid network, and hence does not penetrate the pores; the true density (or solid network density) ρt which can be determined in a fluid such as helium which penetrates into the smallest open micropores; and the specific surface area Sa and pore size distribution by adsorption of a gas such as nitrogen, when the porous solid is maintained at the classical thermodynamic equilibrium condensation temperature of this gas over a flat liquid–gas interface. These data make it possible to determine the specific pore volume Vpor and a mean colloidal particle radius rpar of the gel, according to the following formulas: 1 V por ¼ ρ1 a  ρt

ð9:1Þ

r par ¼ 3ðρt Sa Þ1

ð9:2Þ

As for the pore radius rpor, it can be determined provided that a shape is assumed. For cylindrical pores this is
1 1 Sa r por ¼ 2 ρ1 a  ρt

9.2.2

ð9:3Þ

Mercury Porosimetry

It is possible to force mercury intrusion inside the pores by applying an isostatic overpressure on mercury. The mercury meniscus diameter Rm at the exit of pores is related to the applied isostatic pressure by the Young–Laplace equation (Young 1805; Laplace 1805), also known as the Washburn equation when applied to determine the pore radius (Washburn 1921), which for a cylindrical pore shape is Rm ¼ 


2γ 2γ cos θ  cos θ assuming Ppore  0 Piso  Ppore Piso

ð9:4Þ

where γ is the mercury surface tension, Piso the isostatic pressure applied to mercury, and θ the mercury wetting angle, which is >90 degrees for a non-wetting liquid, so that cos θ is negative and Rm is positive. Considering cylindrical pores with sharp exit corners for simplicity, the contact angle θ at the pore exit can take a full range of value, because the solid surface is reduced to a point, and the meniscus radius Rm is only fixed by Piso (Fig. 9.1). Rm keeps decreasing as Piso increases. However, there is a lower limit, reached when

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365

Fig. 9.1 Mercury meniscus radius Rm as a function of the isostatic pressure Piso applied to mercury

the angle θ with the cylindrical pore surface reaches the equilibrium wetting angle θHg,cyl of mercury with this surface. As long as this does not occur, mercury does not intrude the pores. However, tenuous materials such as aerogels may easily be compressed and densified, before mercury can intrude the pores (Pirard et al. 1995). In particular, 3-dimensional gel networks made by rather linearly aggregated colloidal particles commonly undertake a progressive hierarchical collapse, characterized by a decreasing sample volume. Mercury only intrudes the pores when θ reaches θHg,cyl and intrusion/extrusion isotherms always show a mixture of nonintrusive compression, and pore intrusion as illustrated in Fig. 9.2 for a silica xerogel isotherm. In practice, a correct model and its associated equation are necessary to describe the collapse mechanism and its volume variation as a function of the pressure. In turn, this model equation permits to derive a reliable volume distribution as a function of pore size, such as in the case of polyurethane gels by Pirard et al. (2003). An example of data for a silica aerogel is illustrated in Fig. 9.3.

9.2.3

Adsorption Isotherms

Adsorption isotherms of a gas in a gel can be determined by adsorbing a number of possible gases termed the adsorbate (e.g., argon, nitrogen, xenon, water), in the adsorbent, which is the gel. The most frequent adsorbate is actually nitrogen which can often be physically, hence reversibly, adsorbed on the pore surface by adsorption (Reichenauer and Scherer 2001). An adsorption isotherm is obtained by recording the amount of gas adsorbed on the pore surface of a gel, as a function of the gas

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Fig. 9.2 Mercury intrusion/extrusion curves for a TEOS-based silica xerogel. The extrusion curves reveal an irreversible deformation of the samples upon intrusion. Adapted from Pirard et al. (1998) Fig. 9.3 Pore size distribution of a 0.15 g cm3 silica aerogel obtained by nonintrusive mercury porosimetry on samples synthesized in alcohol via a two-step process with TEOS (using a buckling constant kf of 28 nm MPa1/4). Adapted from Pierre and Rigacci (2011)

pressure in equilibrium with the gel, when the latter and the adsorbate are both maintained at the thermodynamic equilibrium condensation temperature of this gas with the liquid adsorbate over a flat liquid-gas interface (e.g., 77.36 K for nitrogen) (Lowell and Shields 1991). A complete hysteresis isotherm is usually recorded by also measuring the gas volume desorbed from the gel, as a function of the gas pressure. The frequent existence of a hysteresis loop comes from the fact that, as this was illustrated in Fig. 8.16 (Chap. 8) in the case of cylindrical pores, the gas is adsorbed by condensation as thin cylindrical films covering the pore walls, while it is

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desorbed from initially liquid full pores, where the liquid-vapor interfaces at the pore exit are spherical cap menisci. Various analytical computation methods using the Kelvin equation (8.17—Chap. 8), which relates the equilibrium adsorbate vapor pressure to the equilibrium meniscus radii, permit to derive pore size distribution histograms, showing the contribution to pore volume according to the pore size. Two of them are, for instance, the Barrett, Joyner, and Halenda (BJH) method (Barrett et al. 1951) and the Robert’s method (Roberts 1963). The reader interested in detailed presentation of adsorption techniques and the porous characteristics which can be derived from them can find many information in the book by Lowell and Shields (1991), for instance.

9.2.3.1

Examples of Nitrogen Adsorption Isotherms

In Fig. 9.4, nitrogen adsorption isotherms are reported for similar silica wet gels, which were partially dried by evaporation during increasing times before final supercritical drying in CO2. Xerogels are defined by IUPAC as “open networks formed by the removal of all swelling agents from a gel” (Alemán et al. 2007) but it was first introduced by Freundlich (1923) to designate “shrinking” as well as swelling gels. Hence an important shrinkage during drying justifies the appellation of xerogel. And indeed, the capillary stresses previously mentioned may contract a wet silica gel down to Fig. 9.4 Nitrogen adsorption isotherms of silica gels after increasing drying times by evaporation before final drying by the supercritical CO2 method. Adapted from Maury et al. (2001)

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30% or less of its initial volume (Brinker and Scherer 1990), hence to a much lower value than in aerogels (Brinker and Scherer 1990). In Fig. 9.4, these isotherms were of type IV both for the aerogel A and for the AX gel first dried by evaporation for 24 h, according to the classification by the IUPAC (Sing et al. 1985). The nitrogen volume adsorbed when nearing full filling of the gel with liquid nitrogen gives a first appraisal of the shrinkage supported by the gel during drying. It may be noted that a moderate shrinkage by evaporation (24 h) slightly reinforced the gel solid network, which could resist a little better to the moderate contraction due to fluid exchange, necessary for CO2 supercritical drying. On the other hand, when the drying time by evaporation increased to 144 h before supercritical drying, the isotherms transformed to a type IV with a marked hysteresis loop of type H2 according to the classification by Brunauer et al. (1940). Such hysteresis loops are characterized by a long quasi-horizontal section in the desorption branch, which terminates with a sharp vertical drop for a relative pressure P/ P0  0.43, where P0 designates the equilibrium vapor of the gas adsorbate over a flat liquid-gas interface of this adsorbate. The latter value corresponds to the Kelvin limit (radius of the order of ~2 nm), usually explained as the moment when the capillary tension in the liquid inside the pores exceeds the intermolecular forces of liquid nitrogen, so that the pores are all suddenly emptied (Gregg and Sing 1982). Finally, after 120 days of evaporation before supercritical drying, the hysteresis loop disappeared and the isotherms transformed to a reversible type I isotherm, corresponding to a silica xerogel. It must however be noted that, in the case of aerogels, the above adsorption isotherms are inadequate to analyze the contribution of the largest pores, of size >20 nm, to the pore volume. This is because their contribution to the specific surface area is minor, although their contribution to specific pore volume is high. For instance the above silica aerogel monoliths obtained after 0- or 24-h evaporation drying displayed an apparent specific volume of 8 cm3 g1, much higher than that observed from the data of their nitrogen adsorption isotherms near P/P0  1 (20 nm contributed to ~80% of the real total pore volume and could not be evaluated by nitrogen adsorption, which is consistent with previous reports (Schuck et al. 1986; Brinker and Scherer 1990).

9.2.3.2

Determination of the Specific Surface Area

The adsorption isotherms also permit to determine a porous specific surface area. The two best known theoretical adsorption theories which can be used for this purpose are the Langmuir model and the Brunauer, Emmett, and Teller (BET) model (Lowell and Shields 1991). The Langmuir mechanism mostly applies to microporous materials, while the BET mechanism is best fitted to gels containing a full range of micropores, mesopores, and possibly macropores. In the Langmuir model, all adsorption sites are equivalent and only a single monolayer can be adsorbed. The weight of gas adsorbed W as a function of the equilibrium gas pressure P is given by the formula

9.2 Texture of Dry Gels

369

P 1 P ¼ þ W KW m W m

ð9:5Þ

where K is a constant, and Wm the weight of a full adsorbed monolayer. When the Langmuir model applies, the plot of WP versus P is a straight line, which permits to determine K and Wm. The pore specific surface area per unit mass of dry gel Sa is then given by Sa ¼

W m N A σ ad M ad

ð9:6Þ

where N A is Avogadro’s number, σ ad is the cross-sectional area of one adsorbed molecule (16.2  1020 m2 for nitrogen), and Mad is the molecular weight of this adsorbate. In the BET model, multilayer condensation occurs, somewhat qualitatively as in the diffusion-limited growth model of solid nanoparticles (Chap. 5). In this case, the first gel surface sites to be covered by adsorbate molecules are the more energetic ones, while adsorption on further layers is less energetic. In this case, the weight of gas adsorbed W as a function of the equilibrium gas pressure P is given by the formula 1 1 C1 P0 ¼ þ W W mC C m W P 1



P P0

 ð9:7Þ

where P0 is previously defined and C is a constant which characterizes the nature of the adsorbent and its affinity for the adsorbate. When this model applies, a plot of P10 versus PP0 , in a PP0 range from 0.05 to W ½ P 1 0.35, is a straight line. For instance, regarding the isotherms in Fig. 9.4, the specific surface area of the aerogels obtained after 0- or 24-h preliminary drying by evaporation, before supercritical drying, had a total specific surface area Asp  850 m2 g1. In these samples, the pores were also mostly in the mesoporous range, as illustrated by the high contribution to the specific pore volume Vsp,Kel and specific surface area Sa,Kel, of pores with a size higher than the Kelvin limit (Fig. 9.5). Remarkably, the final xerogel submitted to 144 h of evaporation before supercritical drying displayed a specific surface area of ~600 m2 g1, only moderately lower than that of the aerogels, although an important shrinkage had occurred. This indicates that a high number of pores did not disappear. They simply shrunk in the microporous range below the Kelvin limit (Fig. 9.5), so that their contribution to the specific surface area remained high. Overall, the pore texture depends to a large extent on the drying method. The pore volume percent can be extremely high in an aerogel, up to 98% in silicate gels hydrolyzed in an excess of solvent and dried in supercritical conditions

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Fig. 9.5 Evolution with the number of drying days by evaporation of AX gels of the contribution of pores above the Kelvin limit to Sa and Vsp. Adapted from Maury et al. (2001)

(Woignier et al. 1984), and additives named “drying chemical control additives” (DCCA) examined in Chap. 8 can be used to obtain similar results. The adsorption characteristics are also related to the surface fractal structure (Pfeifer et al. 1984). The mass w adsorbed at low pressure follows a law of the type: ðf s,a =2Þ w  σ ad

ð9:8Þ

where fs,a is the surface fractal dimension for adsorption of an adsorbate with crosssectional area σ ad. Also, the volume Vp(R) of pores of size 0.5% by mass had a marked effect on the pore texture as illustrated in Fig. 9.6. A finer description of the porous network texture can moreover beneficiate from techniques complementary to the BET method, such as scanning or transmission electron microscopy (Tewari et al. 1986; Lampert and Mazur 1986), small-angle X-ray scattering (SAXS) (Hunt and Berdahl 1985), or light scattering (Fricke and Caps 1988). The results of all these techniques can make it possible to propose a geometrical model for the pore network and to compare the resulting specific area and pore volume with the experimental data measured on a real gel. The high specific surface area of gels induces many interesting properties, such as a higher chemical reactivity than conventional powders or porous solids. For this reason, a number of gels present important catalytic properties which will be reviewed in Chap. 14 (Teichner et al. 1976). Also, their high chemical reactivity is responsible for original phase transformation and sintering behavior which are, respectively, reviewed in Chaps. 12 and 13.

9.3

Structure of Dry Gels

The structure of dry gels was studied using the various techniques mentioned in Chap. 7 (Sect. 7.5) about the gelation process. Globally, several structural characteristics can be distinguished and the subjects being addressed in this section concern their fractal structure, their solid crystallographic structure, and their pore surface structure.

372

9.3.1

9 Dry Gels

Gel Fractal Structure (Reichenauer 2011)

Gel networks present a fractal architecture, as examined in Sect. 7.5 and described by Mandelbrot (1977), only in a limited scale range from 1 nm to hundreds of nm which depends on the exact type of the gel or aerogel. Besides, theoretically a true fractal structure can only exist near the gel point. At macroscopic dimensions, any gel can be described by a “uniformly dense material” characterized by an apparent constant density. The fractal architecture was particularly well studied for silica gels, for instance by Vacher in Montpellier (Vacher et al. 1989) and Schaefer et al. at the Sandia Laboratories in New Mexico (Schaefer et al. 1987), and the favorite technique was small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS). These experimental results led to propose various theoretical fractal models summarized by Brinker and Scherer (Kolb et al. 1983; Brinker and Scherer 1990). Silica aerogels made by Einarsrud et al., for instance, had a fractal network in the microporous range with an average mass fractal exponent f  1.9 consistent with a “diffusion-limited cluster aggregation” (DLCA) model (Einarsrud et al. 2001). Directly observing a gel fractal architecture under an electron microscope is a difficult task to achieve. First, the gel may undertake a local solid-phase transformation when it is heated by the electron beam. Secondly, in the case of light element oxides such as SiO2, the electronic contrast between the solid phase and the pore is relatively low. The electronic contrast is improved when the cations in an oxide have a higher atomic mass. Examples of the network observed in a SiO2 aerogel with a transition electron microscope (TEM) and of an aluminosilicate clay gel (montmorillonite) with a scanning electron microscope (SEM) are illustrated in Fig. 9.7. SEM observation of the montmorillonite gel was possible because the montmorillonite particles were colloidal in their thickness, but micrometer sized in their flat lamellar extent. Much better micrographs could be made for colloidal gold gels in which the gold particles were linked by the intermediate of organic molecules. These gels did not phase transform in the electron beam and they offered a high electronic contrast in a microscope (Weitz and Huang 1984). In this example, electron micrographs made it possible to actually observe the fractal characteristics of a solid gel network, which is illustrated in Fig. 9.8. It can be observed that in size scales ranging from 50 to 500 nm, the network architecture keeps the same relative geometry, which is typical of resembling figures which can be seen when the microscope magnification is increased.

9.3.2

Gel Crystallographic Structure

Dry gels often appear as amorphous or very poorly crystallized solids, according to their X-ray diffraction patterns (Dislich 1983). For instance, in the case of silica, a

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373

Fig. 9.7 (a) TEM micrograph of a SiO2 aerogel made from 80% TMOS and 40% methyltrimethoxysilane, dried by the CO2 supercritical method. Reprinted from Pierre (2011), with permission from Springer. Copyright Springer 2011. (b) Solid network texture of a montmorillonite gel dried by the CO2 COLD SCD process. Reprinted from Pierre (2019), with permission from Springer, copyright Springer 2019

powder amorphous X-ray diffraction pattern can be recorded which differs from the X-ray pattern of silica glassy state by the presence of a central peak, due to the presence of pores smaller than 10 nm (Fig. 9.9). This is possible because the random (Si–O–Si) network is similar to that in glass, but not all oxygen atoms are bridging. A large number of them terminate in hydroxyl groups (Si–OH), or in alkoxy groups (Si–OR) where R can be any alkyl group. Compared to the wet gel, some modifications were however observed during drying. For instance the tri-siloxanes observed in the surface of wet gels were absent and replaced by cyclic tetra-siloxanes during drying (Brinker et al. 1986). In Fig. 9.9, the relationship between the SAXS spectra and a classical model fractal structure of a SiO2 aerogel is also outlined. SAXS data and ultrasmall-angle X-ray scattering (USAXS) as well as SANS data can also be used to provide an estimation of the specific surface area, from a different source than nitrogen adsorption isotherms. The results generally give larger values than their Brunauer, Emmett, and Teller (BET) analogues. In some samples, SAXS spectra permit to possibly observe ordered mesopores and macropores in surfactantor polymer-templated sol-gels with diffraction peaks at scattering angle 2θ < 10 degree, as presented in Chap. 11 (Beck et al. 1992). These results can also be combined with other useful physical characterizations comprising for instance solidstate NMR spectra. All oxide gels are not really amorphous, but simply very poorly crystallized such as the alumina gels made by the Yoldas method (Yoldas 1975) which really consist of poorly crystallized boehmite AlO(OH) (Fig. 9.10).

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Fig. 9.8 Representative electron micrographs of clusters of colloidal gold gel at different scales. Reprinted from Weitz and Huang (1984), with permission from Elsevier. Copyright Elsevier 1984

9.3.3

Gel Surface Structure

The surface structure of pores was mostly investigated in silica gels. The pore surface of unsilylated silica wet gels are covered by residual alkoxy groups (Si– OR) and silanol groups (Si–OH) with a density of typically 4–6 groups per nm2, according to Fourier transformed infrared spectra (FTIR) (Calas 1997). Although some of these silanol groups undertake condensation during drying by evaporation, the corresponding xerogels, as well as aerogels dried by COLD CO2 supercritical technique, present a hydrophilic character. On the other hand, HOT supercritical drying induces reesterification of the silanol functionalities which makes these aerogels more hydrophobic. Otherwise, oxide surface can be hydrophobized using various treatments.

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375

Fig. 9.9 X-ray diffraction pattern of (a) cristobalite from X-ray File RUFF R060648; (b) silica gel adapted from Pierre (2011); and (c) silica glass, adapted from Warren and Biscoe (1938) Fig. 9.10 X-ray powder diffraction patterns of a boehmite gel made by the Yoldas method (Yoldas 1975). Adapted from Pierre and Uhlmann (1984)

The hydrophilic or hydrophobic characteristic of a solid surface can be determined from the contact angle θ of a water droplet with this solid surface, as illustrated in Fig. 9.11. When this angle is 0, and when this angle is >90 degree cos θ is 1000  C) carbonization of either organic gels or carbon nanotube (CNT) gels and graphene gels in which the bonding between the CNT and the graphene nanoparticles, described in Sect. 4.6, is insured by an organic gel. This aspect of sol-gel transformation is addressed in Chap. 11 but, to provide a complete view of the variety of gels described in this section, their structure and texture are briefly presented in this chapter. One of their outstanding characteristics is that some carbon aerogels now hold the record lowest density material (0.2 mg cm3), record previously held by some silica aerogels (1 mg cm3) (Sun et al. 2013).

9.5.3.1

Carbon Gels Derived from Organic Gels

Next to the precursor work of Pekala et al. (1990), carbon gels derived from resorcinol-formaldehyde (RF) gels were abundantly studied and constitute the main synthesis route of carbon xerogels and aerogels. These carbon aerogels are characterized by a high specific surface area (400–800 m2 g1), a large specific mesopore volume (>0.55 cm3 g1), and isotherms with a hysteresis loop very similar to that of their parent organic aerogel (Zhang et al. 1999; Tamon et al. 1999). In the case of activated carbon aerogels, values in excess of 3000 m2 g1 were reported (Baumann et al. 2008). Those aerogels pyrolyzed below 1000  C are largely microporous (Bock et al. 1998; Petricevic et al. 1998), while at higher pyrolysis temperature these micropores are replaced by mesopores and macropores (Reichenauer et al. 1998; Kuhn et al. 1998; Maldonado-Hodar et al. 2000). Most RF-derived carbon aerogel did not present any fractal structure, with the exception of some carbon aerogels derived from RF gelled in acetone (Barbieru et al. 2001). An illustration of RF gels and carbon gels derived from them is reproduced in Fig. 9.42.

9.5.3.2

Graphene Gels

As explained in Section 4.6, very weak physical graphene gels without any organic bonding can be obtained by freeze-drying. But most graphene gels consist of bonding of these graphene or graphene oxide sheets with RF gels. The carbon gel network observed after pyrolysis at high temperature can be considered as being very close to that of room-temperature RF/graphene composite gels. It consists of a 3D architecture of randomly oriented wrinkled sheetlike structures with a planar dimension ranging from hundreds of nanometers to several microns as illustrated in Fig. 9.43 (Yoo et al. 2008; Worsley and Baumann 2018; Wang and Ellsworth 2009; Tang et al. 2010; Xu et al. 2010).

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Fig. 9.42 Resorcinol-formaldehyde (RF) and carbon aerogels. (a) RF gel before drying; (b) RF aerogel after direct CO2 supercritical drying; (c) carbon aerogel derived from the RF aerogel in (b) by pyrolysis at 1050 C under nitrogen gas flow; (d) transmission electron micrograph of the carbon aerogel in (c). Reproduced from Pierre (2011). Courtesy of Dr. Berthon-Fabry S., MINES ParisTech, PERSEE Sophia Antipolis, France. With permission from Springer. Copyright Springer 2011

Fig. 9.43 SEM images of the graphene aerogels with (a) 4 wt%, (b) 2 wt%, and (c) 0 wt% initial RF content. Reprinted with permission from Worsley et al. (2011). Copyright 2011 American Chemical Society

The X-ray diffraction patterns of the weak physical graphene aerogels show a completely amorphous structure displaying no other peak than the small-angle central peak when they are made without any RF bonding gel (Worsley et al. 2011). On the other hand, when made from graphene oxide (GO) and bonded with RF gel, a very broad peak can be observed in the 2θ range from 8 to 20 (with Cu Kα X-ray radiation) due to GO (McAllister et al. 2007), plus a sharp peak at ~28 due to the RF initial gel (Takai et al. 2003). X-ray absorption spectroscopy shows a predominance of sp2 hybridized carbon atoms and 98% of them are directly bonded to another carbon atom in the graphene aerogel without any RF gel bonding (Stöhr 1992). On the other hand sp3 hybridization appears when RF is added, and is transformed to sp2 during pyrolysis (Al-Muhtaseb and Ritter 2003). The nitrogen adsorption isotherms of all graphene aerogels are of type IV corresponding to a mesoporous material, with hysteresis loop of type 3 (IUPAC 1994; Alemán et al. 2007), corresponding to a sheetlike structure. Their shape and

9.5 Non-oxide Gels

405

Fig. 9.44 Graphene aerogel texture: (a) Nitrogen adsorption/desorption isotherms and (b) normalized pore size distribution plots. Adapted from Worsley et al. (2011)

relative pore size distribution are illustrated in Fig. 9.44. This corresponds to a bimodal pore distribution, a specific surface area which can be as high as 1199 m2 g1 and pore volume as high as 6.4 cm3 g1 in a study by Worsley et al. (2011). As a general fact, the specific surface area of graphene aerogels often exceeds 1000 m2 g1. More mechanically robust graphene aerogels with a high specific surface area were prepared from GO gels made under basic conditions with NH3,aq. (Worsley et al. 2012), followed by carbonization at high temperature (cf. Chap. 11).

9.5.3.3

Carbon Nanotube Gels

As for graphene aerogels, very weak carbon nanotube (CNT) aerogels made without any organic additive were dried by freeze-drying by Bryning et al. (2007). But much stronger gels can be made by bonding these CNT with a small ratio (e.g., wt1%) of RF gel. The full carbon gel network observed after pyrolysis at high temperature consists of a 3D architecture of rigid nanotubes glued to each other, at cross points, by a RF-derived carbon gel. The structure of such aerogels is illustrated in the scanning electron micrographs (SEM) as shown in Fig. 9.45, which show interconnected filament-like particles with diameters of ~5 to ~40 nm and lengths of ~500 to ~1000 nm (Worsley et al. 2009). For CNT xerogels, the specific surface area is mostly due to pore size 12) are perpendicular to these layers (Fig. 10.5) (Adler et al. 1978). Vanadium also presents redox properties, so that it can induce an oxidative polymerization of the organic components, in particular of conducting polymers such as polyaniline, polypyrrole, or polythiophene.

10.4

Examples of Class II Hybrid Architecture

431

Fig. 10.5 Intercalation of organics in V2O5 xerogels of alkylammonium C n H2nþ1 NHþ 3 with different n and polyethylene oxide POE. Adapted from Sanchez and Ribot (1994)

10.4

Examples of Class II Hybrid Architecture

In these hybrid materials, the bonding between the organic and inorganic components is of the covalent or partly covalent (i.e., polar-covalent) type. In some cases, such hybrids can be formed in a sequential manner, for instance when an inorganic gel network of oxopolymers is first formed. If these oxopolymers comprise organic functionalities, these functionalities may be able to cross-link with an organic network in a second step. In other cases both networks can also form simultaneously from monomers comprising organic and inorganic functionalities. An important sub-domain of class II hybrids is based on silica as the inorganic component, which deserves a more extensive description, in the next sections.

10.4.1 Class II Ormosil Hybrids In ORMOSILs, strong bonding is made possible by the availability of an abundant list of Si-alkoxides functionalized with organic groups, as described in Chap. 3, Sect. 3.7. These groups may themselves be able to copolymerize so as to build a 3-dimensional network in which both the inorganic and the organic components participate. For this purpose, various techniques can be used such as achieving

432

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Hybrid Organic–Inorganic and Composite Materials

polymer cross-linking in an appropriate solvent or self-assembling with the help of surfactants as presented in Chap. 11. Phase separation of the copolymers formed by siloxane cross-linking may also occur. Besides, polysilsesquioxane can also be copolymerized with other silica or other oxide precursors, to produce a larger variety of materials fitting in the family of organosilicates or ormosils (Lim and Stein 1999). For instance, polysilsesquioxanes were mixed with success to at least 25% tetramethoxysilane or tetraethoxysilane (Schwertfeger et al. 1994). The 3-dimensional gel network was then made by interconnection of branched or cyclic polysilsesquioxane structures, and the pores were in the mesoporous size range from 2 to 50 nm (Loy 2016). Several main families of network architecture can be distinguished, as described next.

10.4.1.1

Ormosils Based on Silica Gel Carrying Pendant Organic Groups

Class II ormosils can have a 3-dimensional network insured by a silica gel carrying pendant-side organic or bioinorganic groups. Such pendant organic groups were already described in Chap. 3 regarding alkoxysilanes and functionalization of silicon alkoxides. The gels produced by hydrolysis condensation of these monomers constitute hybrid ormosil materials belonging to the subfamily of polysilsesquioxanes. The pendant groups can eventually be relatively big, such as encapsulated enzymes covalently linked to the gel network. Or they can be nanoparticles, for instance silica nanoparticles in silica-silsesquioxane copolymers (Loy 2016). Typically, trifunctional alkoxysilanes R’Si(OR)3 are particularly well fitted to construct such inorganic network carrying big organic groups. On the other hand bifunctional alkoxysilanes R0 R00 Si(OR)2 where R0 and R00 are methyl or phenyl groups do not normally produce 3-dimensional networks. In practice, however, organotrialkoxysilanes only gel in basic catalysis conditions when they carry small organic ligands themselves able to participate in the formation of 3D gel network (Loy 2016). Hence this synthesis route is mostly limited to H3C–Si(OMe)3 and H3C–Si(OEt)3 which form transparent hybrid gels (Loy et al. 2000). Many pendant organopolysilsesquioxanes do not gel but only lead to the formation of solid particles. This is for instance the case when the pendant groups are mercaptopropyl, phenyl, styryl, and methacryloxypropyl (Arkhireeva et al. 2004). Solid particles can also then be made by the Stöber process or by emulsion polymerizations (Loy 2016). In acid catalysis conditions, organotrialkoxysilanes carrying vinyl-, ethyl-, cyanoethyl-, and chloromethylphenyl-ligands are white opaque in appearance. This is also true with organotrialkoxysilanes carrying dodecyl-, hexadecyl-, and octadecyl-ligands, except that these gels are thermoreversible: they can be liquefied by heating and they are soluble in hydrocarbon solvents. Thermoreversible rubberlike gels are obtained with amine-functionalized ligands (Sanchez and Loy 2001). As for phenyl and mercaptopropyl ligands, they only form solid particles, themselves soluble and which can be melted at low temperature (Arkhireeva et al. 2004).

10.4

Examples of Class II Hybrid Architecture

10.4.1.2

433

Class II Ormosils Based on Polymer-Bridged Silica Clusters

This type of class II ormosils comprises hybrids in which the polymer is not simply a pendant lateral group on a silica cluster, but participates as a bridge in between siloxane-based units. Examples of hybrids of this type comprise bridged polysilsesquioxanes as described by Loy (2016). Such bridged ormosils can be achieved by using either a silica precursor containing an organic group directly bonded to Si (silane bond) (Iswar et al. 2018; Zu et al. 2018) or a coupling agent. For instance in the case of organotrialkoxysilanes carrying an organic group R larger than a methyl group, in which building a 3D siloxane network becomes difficult as mentioned before, it is possible to achieve gelation, when the organic pendant groups are themselves able to undertake polymerization reactions. Figure 10.6 shows several examples comprising isocyanate (Fig. 10.6a), alkyl halides (chloride, bromide, or iodides) (Fig. 10.6b), and epoxy groups (Fig. 10.6c), which react with monomers carrying a nucleophilic functionality such as an amine group (Meador et al. 2005). This is also the case of pendant groups terminated by an alkene group, which can react under exposition to light with another pendant group terminated by a thiol (Fig. 10.6d), or of pendant groups carrying ligands such as amines able to chelate a metal ion (Fig. 10.6e). Besides, as reported by Loy (2016), a large number of bridged polysilsesquioxane monomers are now commercially available. A few examples of bridges on which they are constructed are illustrated in Fig. 10.7. Most of them gel relatively rapidly at concentrations well below 1 M L1. These bridging organic groups facilitate

Fig. 10.6 A few possible bridging reactions between pendant silsesquioxanes. Adapted from Loy (2016)

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Fig. 10.7 A few type of bridges available in commercial polysilsesquioxane monomers. Adapted from Loy (2016)

the growth of a network via siloxane bonds. Hence, gels can easily be formed without adding any supplementary oxide precursors. Their optical aspect depends on the monomer, catalyst, and solvent used. Loy (2016) indicates that while alkylene-bridged gels are frequently opaque, arylene-bridged gels are more often transparent. They also often undertake a significant syneresis in a time range from a few minutes to hours, after gelation. Bridging can also be obtained with the help of an intermediate coupling agent. Two examples are glycidoxypropyltrimethoxysilane (GPTMS) which carries an epoxy ring and three methoxysilane groups able to react with polymers containing –OH, –COOH, or –NH2 side groups, and 3-aminopropyltriethoxysilane (APTES) (NH2(CH2)3–Si(OCH3)3) (Ren et al. 2002; Sugino et al. 2008; Valliant and Jones 2011; Mahony et al. 2010; Koh et al. 2011; Poologasundarampillai et al. 2012). For instance, hybrids with polymer cross-linking based on SiO2 with polymer bridging were recently studied in the systems SiO2-epoxy and SiO2polystyrene to improve the mechanical properties of SiO2 aerogels (Meador et al. 2009; Nguyen et al. 2009). In the SiO2-resorcinol formaldehyde (RF) system, acid-catalyzed co-gelation of RF and TEOS produced two interpenetrating gel networks, with some strong Si-O-C bonding (Chen et al. 2012). More recently, lightweight and flexible blankets were made by cross-linking resorcinolformaldehyde (RF) with the amine-carrying silica precursor (3-aminopropyl) triethoxysilane (APTES), plus MTMS or MTES (Berthon-Fabry et al. 2016, 2017). The type of blanket obtained and its microstructure are illustrated in Fig. 10.8. In the case of phenylene-bridged polysilsesquioxanes, a mesophase liquidcrystal-type structure was observed to form in the precursor solution, before gelation, by π stacking of the phenyl bridges. A relatively strong gel with an ordered mesoporous structure was then obtained (Ben et al. 2000). Another interesting case of bridged structure concerned SiO2-functionalized fullerene carbon nanoclusters (Patwardhan et al. 2002).

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Fig. 10.8 Optical and scanning electron microscopy views of a RF-silica blanket obtained by reaction between resorcinol (R), formaldehyde (F), and APTES. Reproduced from Berthon-Fabry et al. (2016) with permission from Elsevier. Copyright 2016 Elsevier

10.4.1.3

POSS-Organic Polymer Class II Hybrids

This is a subclass of class II ormosils which deserves a separate treatment. Polyhedral oligomeric silsesquioxanes (POSS) were presented in Chap. 3, Sect. 3.7. They gather siloxane clusters which can be covalently linked to an organic polymer so as to make class II strong hybrid composites (Jennings et al. 2016). In more detail, they can be linked as lateral pendant clusters, as clusters which participate linearly to hybrid polymer chains, also termed “bead copolymers,” or as cross-linking sites between at least three linear polymer segments, as illustrated in Fig. 10.9. Pendant POSS hybrid structure can be made when each POSS carries a single reactive functionality. The techniques used comprise copolymerization with the organic component, grafting the POSS after its functionalization, or reacting a grafting agent with all the available silanol groups of a polymer, according to an end-capping technique. Various reactive side groups were studied, comprising: – Vinyl reactive groups which can be copolymerized with propylene or ethylene using various molecular catalysts (Tsuchida et al. 1997). – Epoxy groups which can polymerize to epoxy resins with difunctional epoxides (Lee and Lichtenhan 1998; Lee et al. 2000). – Norbornyl groups which can link to norbornene by a ring-opening metathesis polymerization (ROMP): The POSS-polynorbornene nanocomposites obtained have a higher glass transition temperature Tg than pure polynorbornene (Mather et al. 1999).

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Fig. 10.9 Various POSS copolymer architectures. Adapted from Jennings et al. (2016)

– Styryl groups which can be copolymerized with styryl-functionalized monomers by a radical polymerization process using azobisisobutyronitrile (AIBN) (Haddad and Lichtenhan 1996). – Methyl methacrylate functional groups to prepare functionalized POSS monomer which can in turn copolymerize by a radical “reversible addition-fragmentation chain transfer” (RAFT) with various monomers (e.g., acrylamide) or block copolymers (Ramirez et al. 2013). Fluorinated POSS functionalized by such ligands permitted to form superhydrophobic and oleophobic coatings. – Azide groups that were used to end-cap polystyrene-block-poly(ethylene oxide) polymers with fluorinated POSS (Dong et al. 2015): It was also observed that end-capped tethered block copolymers could undertake a self-assembling behavior in complex lamellar structures, somewhat like some surfactants (Chap. 11). In “bead POSS-organic hybrid” composites, each POSS is linearly linked to the organic polymer branches by two strong bonds. These bonds can be siloxane bonds in which the Si atom which participates in the siloxane bond carries various side groups (Fig. 10.9) (Mantz et al. 1996). For instance, a complex linear POSS bead copolymer, resistant to oxygen erosion, was studied by Wang et al. (2015). It consisted of incompletely condensed POSS functionalized with diacylchloride,

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followed by copolymerization with terephthaloyl chloride (TPC) and a tertbutyldimethylsilyl-functionalized 4,6-diaminoresorcinol (DAR) monomer. To be used as cross-linkers, POSS must be functionalized on at least three reactive ends. An example is commercially available vinyl-functionalized POSS used as cross-linker with 1,6-hexanedithiol and a vinyl-functionalized porphyrin, for the preparation of fluorescent films (Ma et al. 2015). In another example, octa-functional POSS with methacrylate or epoxy-reactive side groups were used to cross-link methacrylate and/or epoxide polymers (Lungu et al. 2016). Amine-terminated POSS materials were used as cross-linkers of polyimides and these hybrid nanocomposites showed a better thermal stability than pure polyimides (Raaijmakers et al. 2014). Vulcanized silicone rubber with an improved thermal stability was also prepared by cross-linking partially condensed POSS with hydroxyl-terminated polydimethylsiloxane (Shi et al. 2014).

10.4.1.4

Hybrids Based on Coupling Silica with Hydrogels

A number of studies concerned the design of new biomaterials, by coupling an inorganic component with hydrogels such as polysaccharides (Kramer et al. 1987) or cellulosic materials (Monchâtre 1984). Poly(ε-caprolactone) (or PCL) diol, which is insoluble, was functionalized with isocyanatopropyl triethoxysilane (IPTS) (Rhee et al. 2004). The cyanate group of IPTS could react with the OH groups of PCL and bond with the SiO2 network by hydrolysis of its ethoxysilane groups. Shorter PCL polymers permitted a higher density of coupling bonds and a better control of the biodegradability. When each mer of the polymer carried side groups which permit coupling, the cross-linking degree was independent of the polymer molar weight. This was the case of type 1 collagen, which contains many –NH2 and – COOH side groups available for functionalization (O’Brien et al. 2004) and gelatin (Ren et al. 2010; Deguchi et al. 2006). A direct cross-linking of gelatin was made with SiO2 derived from (3-glycidopropyl) trimethoxysilane (GPTMS), via a ring-opening mechanism of the GPTMS epoxy groups followed by a nucleophilic attack on the NH2 side groups of the gelatin chains, as illustrated in Fig. 10.10. Other organic-bioinorganic hybrids made by co-gelation of silicic acid and pectin showed drastically improved mechanical properties, due to the disappearance of necks between colloidal silica particles and the formation of strong Si–O–CH2 bonds (Zhao et al. 2015).

10.4.2 Class II CERAMER Hybrids 10.4.2.1

Inorganic–Organic Polymer Class II Hybrids Containing Other Cations than Si

Besides silicon, a number of organic macromonomers carrying reactive functionalities and their copolymerization were studied regarding titanium precursors:

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Fig. 10.10 Illustration of coupling between a SiO2 gel network and polymers, by the intermediate of GPTMS or APTES. Adapted from Pierre (2016)

titanium alkoxides, titanium acetylacetonates, and triethanolamine titanium chelates. The properties of such hybrid materials and their homogeneity depend on many parameters, including the nature of each component, their relative proportion, their functionalities, hydrolysis ratio, solvent, temperature, and catalysts. Copolymerization of diethoxydimethyl silane with alkoxides of Ti, Zr, AI, and V was studied by Babonneau et al. who showed that mixed M-O-Si bonds were established (Dire et al. 1992; Sanchez et al. 1994). The coordination number of an alkoxide such as Ti(OR)4 is unsaturated. It is electrophilic and undergoes fast alcoholysis with R’OH solvents and with hydroxyl-terminated short OH-PDMS

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(polydimethoxysilane) chains so as to form Ti(OR)4-x-y(OR0 )x(OPDMS)y species. Overall, Ti(OR)4 catalyzes the condensation of siloxane units all along the PDMS chains. The products obtained can be used to make thick uncracked coating (Dire et al. 1992b). Oxo clusters such as Ti6O4(OEt)8(OMe) and (Zr10(μ4-O)2(μ3-O)4(μ3-OH)4(μ2-OPrn)8(OPrn)10 where the complexing ligands are located at the periphery of the clusters (Schubert et al. 1992; Sanchez et al. 1992) are very sensitive to hydrolytic cleavage below a certain size. Their polymerization must be performed in an organic solvent. Other TiO2-based hybrids could be made stable towards hydrolysis, by complexation of Ti(OR)4 with cinnamic acid (C6H5–CH¼CH–COOH) and methacrylamidosalycilate (MASA), or by chelation with acetoacetoxyethylmethacrylate (AAEM) (Sanchez and In 1992). Strong hybrid oxide-organic aerogels were also developed for instance in the isocyanate vanadia system (Luo et al. 2008) and CuO resorcinol-formaldehyde (Leventis et al. 2009).

10.4.2.2

Inorganic–Organic Polymer Class II Hybrids Made by the Pechini Method

As presented in Chap. 2, the Pechini method rests on esterification reactions between carboxylate metal complexes, excess carboxylic acid, and a diol such as ethylene glycol in which they are dissolved. The materials which are obtained are organic-inorganic hybrids. This reaction usually occurs in a temperature range from 100 to 130  C. It is illustrated in Fig. 10.11 for citric acid (CA),

Fig. 10.11 Possible polymerization reaction between citric acid, ethylene glycol, and BaTi(CA)3 complex mentioned in Chap. 2, inspired from Petrykin and Kakihana (2016)

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ethylene glycol (EG), and the BaTi(CA)3 complex mentioned in Chap. 2 from Petrykin and Kakihana (2016). With time, the viscosity increases drastically during mixing, at a rate which depends on the ratio CA/EG and on the nature of the metal chelates. The phenomenon looks experimentally like gelation, although this esterification is reversible and it is not clear whether a true gelation phenomenon occurs, or whether the viscosity tends towards a high maximum value (Arima et al. 1996; Kakihana et al. 1997). Hence, according to Petrykin and Kakihana (2016) the process should rather be termed “inspissation,” in so far as it may simply consists of a thickening of the solution. However, we may also consider the gel as a thixotropic one, so that the term “gelation” is retained in this monography, which conforms with the literature on the subject as the latter authors actually did. The term “gel” then designates the material obtained, which has the function to retain the chelated metal complexes uniformly dispersed. The ratio CA:EG is important. A high CA content increases the gel viscosity and is more appropriate to prevent segregation of the metal complexes during thermal decomposition of the polymer. It can also be noticed that water is produced during the esterification reaction, but it can easily be eliminated with an excess of EG vapor. In his initial study, Pechini used a CA:EG ratio of 1:4. But next to a study by Tai and Lessing (1992a, b), Petrykin and Kakihana (2016) suggest that a ratio in the range from 4:5 to 6:4 would be more appropriate for multicomponent oxide gels. A number of Cu-containing high-critical-temperature (Tc) superconductors, of perovskite structure, were made by the Pechini method and obtained as clear gels. This is the case of Ba3Cu3(C6H5O7)412H2O (Karen and Kjekshus 1994), YBa2Cu3O6+x (Choy et al. 1991), and (Pb2Cu)Sr0.9La1.1 CuO6+x (Kato et al. 1996). Petrykin and Kakihana (2016) also pointed out that some problems can also be encountered in the Pechini method. First, a precipitate may form before or during gelation, especially by hydrolysis when some water is present. To solve this problem, any progress in the design of new soluble metal complexes may be beneficial. Secondly, a redox reaction may occur between the organic compound and the metal cations. This is the case when preparing high-Tc cuprates, where interaction between the copper ions in the solution and ethylene glycol results in the formation of Cu2O and even metallic Cu precipitates.

10.4.2.3

Inorganic–Organic Polymer Class II Hybrids Made by a Polymeric Gel Precursor Method

The Pechini technique was extended to other similar methods which rest on the formation of stable metal complexes in polymerizable organic solutions. The aim was also to preserve an atomic scale homogeneity of metal cationic complexes, to further obtain complex ceramic phases after calcinations of the gel (Kakihana 1996; Kakihana and Yoshimura 1999). The hybrids obtained by these techniques do not present an interest in themselves; they are only an intermediate stage in ceramic synthesis by chemical processing.

10.5

Sol-Gel Composites

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Chelated metal cations can indeed be combined with hydrogels such as polyvinyl alcohol (PVA), polyethyleneimine (PEI), or polyethylene glycol (PEG). These metal cations can eventually promote the gelation kinetics by cross-linking with the dissolved polymer (Gülgün et al. 1995). This type of route was selected for instance by Mandai and Ram (2003) to synthesize PZT powders. Glycol-conjugated phosphate can also be used in this so-called polymerizable complex gel precursor method to prepare complex phosphates. For instance Eu2+-doped KSrPO4 homogeneous and transparent hybrid gels could be made by mixing ethylene glycol (EG-P)- or polyethylene glycol (PEG)-conjugated phosphates, presented in Chap. 2, KNO3, Sr(NO3)2, and Eu(NO3)3 chelated with citric acid plus polypropylene as the inorganic polymeric ligand. After thermal treatment at 1173 K under argon, a single-phase Eu2+-doped KSrPO4 phosphor was obtained (Kobayashi et al. 2016). Similar result using PEG-P as the glycol-polymerizable source was obtained with phosphors of composition Eu2+-doped LiCaPO4. (Kim et al. 2014). Polymers obtained by a free radical mechanism can also be dissolved in water to maintain the metal salt cations dispersed in aqueous solutions. This is the case of acrylamide (Gator et al. 1993; Rao et al. 1995; Sin et al. 2000, 2002) or acrylic acid (Mani et al. 1992). In the case of acrylamide, free radicals initiating the polymerization are created by hydrogen peroxide or azobisisobutyronitrile and gelation occurs by reaction between acrylamide and N-N ¼ methylene-bisacrylamide. Of course the metal salt cations may alter this polymerization process. This is the case of Cu, and in such cases it is still possible to add some EDTA (Sin et al. 2000) or citric acid (Gator et al. 1993; Rao et al. 1995) to chelate the metal. By comparison with the Pechini method, the polymer formation is irreversible, which permits to better control the gelation process.

10.5

Sol-Gel Composites

Composite materials constitute a vast field of materials science which is outside the scope of this monography, except in cases when the composite matrix can be made by sol-gel processing. When one component is organic (e.g., the matrix) and the other component is inorganic (e.g., dispersed particles or short fibers), these materials are close enough to the above hybrids. The main difference, already mentioned, is that the dispersed component of composites consists of nano- or micro-domains of an identified organic or inorganic thermodynamic phase, of macroscopic dimension by comparison with molecular dimensions. The gel matrix itself can be organic or inorganic (Liu et al. 2012; Chin et al. 2014; Xiong et al. 2015). A special recent case concerns carbon nanotube (CNT) aerogels/sol-gel oxide composites, where both components are made by sol-gel processing. This sol-gel-related field of composites is briefly reviewed below.

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10.5.1 Composites Designed by Mixing of Constituents Sol-gel composites can be designed to provide additional properties, such as magnetic or photocatalytic, to gels. These composites can be divided into particulate composites, short fiber composites, and long fiber ones. For each type of composite, sol-gel processes can be used to synthesize the dispersed phase, or the matrix. In the latter case, the dispersed component may be particles and powders (Kuhn et al. 1995; Santos et al. 2008), fibers (Li et al. 2013), nanofibers (Wong et al. 2015), nanotubes (Menshutina et al. 2017), or polymers (Kulkarni et al. 2006). For instance, recently, composites were made by impregnating RF-bonded single-wall carbon nanotubes (SWCNT) with poly(dimethylsilxane) (PDMS), or by coating the inner network of RF-bonded SWNT gel, with SiO2, SnO2, and TiO2 by sol-gel process (Worsley and Baumann 2016; Kucheyev et al. 2005; Baumann et al. 2005). Such composites are not necessarily of a hybrid type. They can also be made by sol-gel in mixed silica-based oxides (Vicarini et al. 1970; Cao et al. 2008; Lermontov et al. 2017). For instance, a precursor of the nanodomains can be mixed in a SiO2 sol before gelation, such as made with Cu or CuO nanoparticles (Li et al. 2011). Or the nanoparticle precursors can be added by diffusion inside the gel after gelation, eventually even after drying the gel, via a gaseous phase (Marzouk et al. 2004; Zhang et al. 2015b) or a supercritical fluid (Smirnova et al. 2004). A component can also be deposited by chemical vapor infiltration (Lee et al. 2000) or chemical vapor deposition (Boday et al. 2009). Composites and nanocomposites can also be elaborated by sol impregnation of macroporous materials and structures such as foams and honeycombs (Berkefeld et al. 2017) or fibrous networks (Zhao et al. 2015b, c). Examples of such composites comprise side-chain liquid crystal (SCLC) polyacrylate-silica aerogel where the SCLC was photopolymerized after liquid impregnation (da Silveira et al. 2009), and SiO2 aerogel-cellulose with improved mechanical resistance, by forced impregnation of an ultraporous cellulosic matrix by a SiO2 sol (Gavillon and Budtova 2008; Demilecamps et al. 2015). Other composites were made by forming silica μm-sized particles by sol-gel from sodium silicate, inside an ultraporous cellulose network (Demilecamps et al. 2014). Many different types of composite aerogels involving an organic or carbon aerogel matrix were studied. The aerogel texture could be tailored either by freeze-drying, such as in the systems polyaniline/ cellulose (Liang et al. 2015), polyaniline/phytic acid (Zhang et al. 2015b), and various types of composites with graphene (Ji et al. 2015; Zhang et al. 2015a), gelatin/chitosan (Dou et al. 2016), or gelatin/silica (Xie et al. 2015; Zhao et al. 2015), or by CO2 supercritical drying (Blanchard et al. 1983; Sun et al. 2014; Ye and Feng 2014; Wu et al. 2015). Recently, SiO2 aerogel-short cellulosic fiber composites with good flexible properties were also investigated (Markevicius et al. 2017; Jaxel et al. 2017). Nanocrystalline particles made by non-hydrolytic sol-gel process can be easily dispersed in an organic medium. For instance zirconia nanoparticles

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could be dispersed to design organic matrix composites which were completely transparent (Garnweitner et al. 2007). Polymer nanocomposites were similarly made by dispersing TiO2 nanofillers in epoxy and polymethacrylate (PMMA) resins (Koziej et al. 2009; Morselli et al. 2012a, b). Other composites, made by dispersed magnetite nanocrystals in epoxy, showed interesting superparamagnetic properties (Sciancalepore et al. 2015). Very stable amorphous silica-based sols could also be made in CH2Cl2 and used to design composites in a hydrophobic organic polymer (Aboulaich et al. 2009). Gels in the wet state can be used in the same manner as thermosetting or thermoplastic polymers to make composites with short or long fibers. After heat treating at high temperature to transform the gel to a ceramic, a ceramicceramic composite is obtained. A very special application was used regarding the synthesis of thermal protection tiles for the NASA space shuttle. A gel made from TEOS was used to bind silica or mullite fibers altogether. Then, this gel was converted to silica by thermal treatment. For structural applications, a ceramic-ceramic composite with a strength of 630 MPa was made by the company Babcock & Wilcox. It was synthesized by infiltrating SiC Nicalon® fibers weaving with a mullite sol-gel, followed by sintering (Roy 1969). Other studies were undertaken on systems comprising an alumina matrix made by sol-gel and SiC or alumina fibers. The results were not up to the level of expectations (MacCarthy et al. 1971; Mukherjee et al. 1976) but more progress may be anticipated with further research. The so-called transformation-toughened ceramic, which consists of tetragonal zirconia particles dispersed in a ceramic matrix, constitutes an interesting class of particulate ceramic composites, used for instance as abrasives. Other abrasives were made with particles synthesized by carbothermal or aluminothermal reductions of sol-gel materials and they presented properties superior to those of abrasives made by conventional methods. Examples of such materials are TiC/TiB2/Al composites used in cutting and grinding tools and ZrB2/SiC/C, ZrB2/Al/Al2O3, and TiB2/Al2O3/Al composites which can resist oxidation at high temperature (Sane 1984). To these particulate composites, one must add special applications for which sol-gel glasses are well suited. Among them, one can mention composites in which a glass matrix can encapsulate radioactive wastes to avoid radioactive pollution (Lackey et al. 1980). Hollow glass spheres with a diameter of 80–100 μm and a wall with a thickness of 1 μm could be made by inflating gel particles with the gases originating from the gel. These hollow spheres can be used to store nuclear fusion products such as deuterium and tritium (Carturan et al. 1982). Sol-gel-made nanoparticles can constitute the dispersed phase in an organic polymer matrix. This is the case of metal fluoride nanoparticle sols dispersed in a polymer matrix to make transparent hybrid organic-inorganic composite materials. They permitted to adjust the refractive index of transparent polymer to the desired value and to increase the polymer hardness (Noack et al. 2013), while the polymer matrix was able to maintain them dispersed (Kemnitz. 2016). Complex glass– ceramics were also made with nanofluoride particles dispersed in a complex silicate glass matrix (Campostrini et al. 2002).

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10.5.2 Carbon Nanotube (CNT) Aerogels/Sol-Gel Oxide Composites New composites based on CNT aerogels or xerogels were recently developed (Worsley et al. 2009, 2011). They can be made by impregnation of these CNT gels with various inorganic or organic matrices, according to a technique by Wang et al. (1993). As an example, CNT/SiO2 composite aerogels were made in which SiO2 was derived from polydimethylsiloxane (PDMS) (Thostenson et al. 2001). The elastic Young’s modulus measured by indentation showed an increase from 4.4 MPa for the material made from PDMS only to 14 MPa for the composite (Worsley and Baumann 2016; Dyke and Tour 2004). It also showed an excellent electrical conductivity over 1 S cm1 (Winey et al. 2007; Mathur et al. 2008). CNT/oxide composites in which the oxide was sol-gel SiO2, SnO2, orTiO2 were recently reviewed by Worsley and Baumann (2016) with more focus on SiO2/CNT composites, themselves also developed by a number of researchers (Ding et al. 2009; Shin et al. 2007; Hernadi et al. 2003; Fu et al. 2002). It was important to use a very low concentration of inorganic precursors to promote the growth of the condensed oxide phase primarily on the surface of CNT aerogel nanotubes, while avoiding the formation of an oxide gel in the free pore volume of the CNT aerogel. In these conditions, it was shown that the high electrical conductivity of the native CNT aerogel was maintained in the composite, while the elastic Young’s modulus was considerably increased. In more details, SiO2 was deposited on the CNT nanotubes as amorphous nanoparticles (Fig. 10.12), SnO2 as crystalline nanoparticles of size 3–5 nm, and TiO2 as amorphous nanoparticles which could be converted to anatase after treatment at 320  C.

Fig. 10.12 SEM images of CNT/SiO2 composite aerogel (at low and high magnifications). The SiO2 sol was prepared by one-step base-catalyzed hydrolysis of TMOS, in weight proportion: TMOS (4.1 g), water (1.5 g), aqueous ammonia (30%, 200 mL), and methanol (24 g). Reprinted with permission from Worsley et al. (2011). Copyright 2011 American Chemical Society

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Main Properties of Hybrid Gels

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10.5.3 Composites Made by Spontaneous Phase Separation With functionalized PDMS and PTMO, phase separation between the organic and the inorganic components generally occurs on a micrometer scale, and the interface between the two components plays an important role in improving the mechanical properties of the composite. With the silicates, no phase separation was observed. With the polyimides, phase separation between the organic and inorganic components is frequent. However, hybridization could be achieved by pre-binding Ti(OEt)4 or Si(OEt)4 to the carboxylic sites of polyamic acid according to the reaction in (10.2) (Nandi et al. 1991). Imidization occurs at 300  C and the water which is liberated hydrolyzes the alkoxide or can react with an ethoxysilyl-functionalized polyimide. Up to 70% silica could be incorporated by reaction of TEOS with the ethoxysilyl-functionalized polyimide macro-monomer shown in Fig. 3.15 (Chap. 3, Sect. 3.7), in solution in dimethylacetamide. Phase separation between silica and polyimide occurs but the size of silica particles can be monitored down to the nanometer range.

ð10:2Þ

10.6

Main Properties of Hybrid Gels

10.6.1 Mechanical Properties of Hybrids The main advantage of hybrid gels and aerogels can be considered to be their mechanical properties, as these materials can be made much less brittle and more flexible than their pure inorganic component gels (Jaxel et al. 2017). Such superhydrophobic and flexible aerogels were made from methyltrimethoxysilane (MTMS) and methyltriethoxysilane (MTES), with oxalic acid and ammonium hydroxide as the catalysts and drying by the HOT supercritical method in methanol, by Venkateswara Rao et al. (2011). The elastic behavior depended on the methanolðMeOHÞ to-MTMS or -MTES molar ratio rmeth ¼ ðMTMS or MTESÞ . With MTMS, the elastic Young’s modulus in compression E decreased from 1.4  105 to 3.4  104 Pa as

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Fig. 10.13 Photographs showing the maximum possible bending of aerogels prepared from MTES with rmeth ratio of (a) 6.45, (b) 12.96, and (c) 19.35. Reproduced with permission from Venkateswara Rao et al.(2011) with permission from Springer. Copyright 2011 Springer

rmeth increased from 21 to 35, while for MTES the Young’s modulus E decreased from 1.5  105 to 3.9  104 as rmeth increased from 6.45 to 19.35. The maximum bending, before breaking, of aerogel cylinders made with MTES as a function of rmeth is illustrated in Fig. 10.13. The flexibility was made possible by a siloxane ¼ RSi–O–SiR ¼ coordination limited to 3 by to the non-hydrolyzable ligand r (i.e., Me or Et), contrary to an upper coordination of 4 with usual alkoxides. The mechanical properties of hybrid organic-inorganic aerogels were investigated by numerical simulation as a function of their organic content (Morales-Florez et al. 2009), and more recently reviewed as a function of the network morphology and cross-linking chemistry by Leventis and Lu (2011). In particular, the latter authors examined class II silica aerogels made from aminopropyltriethoxysilane (APTES) cross-linked with a di-isocyanate or a tri-isocyalante (Desmodur N3300A® from Bayer) (Mizushima and Hori 1994; Leventis et al. 2002; Yim et al. 2002). The cross-linking bonds were of polyurea nature, obtained by reaction of the isocyanate groups with terminal amine groups from the silica precursor. These inorganic crosslinkers were introduced after silica gelation, and hence coated the silica gel network, to form an architecture similar to that described in Fig. 10.2c at the beginning of this chapter. Typical load deflection data in three-point bending tests according to ASTM D790 Procedure A (flexural properties of unreinforced and reinforced plastics and electronic insulating materials) showed an increased fracture stress, elastic flexural modulus M, and fracture energy with the cross-linker content, by comparison with the native silica aerogel, as illustrated in Fig. 10.14. This behavior was attributed to the thickness of the organic coating on silica native network. The authors also suggested that the most outstanding materials in terms of mechanical properties could be made if only the organic component were used, while keeping the global texture morphology. Di-isocyanate reinforcement was also reviewed by Meador (2011), on silica gels made from APTES and co-gelled with various combinations of TMOS, TEOS, 1,6-bis(trimethoxysilyl) hexane (BTMSH), vinyltrimethoxysilane, bis(trimethoxysilylpropyl)amine (BTMSPA), or tri-isocyanate Desmodur N3300A® from Bayer. Stressstrain data in compression on styrene-reinforced aerogel cylinders showed that only ~50% out of a 0.25 strain was recovered when releasing the stress, when no hexyl

10.6

Main Properties of Hybrid Gels

447

Fig. 10.14 Breaking stress in three-point bending tests, as a function of the aerogel density, for silica aerogels made from TMOS in base catalysis conditions, of initial density 0.2 g cm3, cross-linked with various amounts of di- or tri-isocyanates. Comparison with TMOS-only-derived silica aerogels of various densities. Adapted from Leventis and Lu (2011)

group from BTMSH was present, while virtually the total strain was recovered when hexyl-linked BTMSH was added. More simply, short cellulosic fibers were mixed in concentration above their percolation threshold in silica sols, to reinforce silica aerogels. Perfect monoliths could be obtained either by ambient pressure drying or by CO2 supercritical drying, while the flexural modulus and fracture stress determined by three-point bending were increased by a factor of ~4 by comparison with the native silica aerogels (Markevicius et al. 2017; Jaxel et al. 2017). It is also possible to do the opposite, which is to impregnate a cellulose aerogel with a silica sol, before drying. This was done for instance by Demilecamps et al. (2015, 2016) on ultraporous cellulose aerogels, which permitted to improve their mechanical properties as illustrated in Fig. 10.15. CNT/sol-gel oxide aerogel composites deserve themselves a special mention. Their elastic Young’s modulus E could be explained by a good SiO2 bonding in between the CNT nanotubes. It scaled with the aerogel composite density ρ with an exponent of 2.7, instead of 3.7 for pure SiO2 aerogels (Woignier et al. 1998); hence according to the law (10.3) E  ρ2:7

ð10:3Þ

Typical E values for the CNT/SiO2, CNT/SnO2, and CNT/TiO2 for a CNT content of 1 vol% were, respectively, 7.3  0.4 MPa, 1  0.2 MPa, and 17.3  1.7 MPa (Worsley et al. 2011).

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Fig. 10.15 Stress-strain uniaxial compression curves of cellulose-silica composite aerogel (a), aerocellulose (b), and silica aerogel (c). Adapted from Fig. 6 in Demilecamps et al. (2015)

Fig. 10.16 Compared nitrogen adsorption/ desorption isotherms of a CNT/SiO2 aerogel composite and the native CNT aerogel. Adapted from Worsley et al. (2011)

10.6.2 Other Properties of Hybrids 10.6.2.1

Specific Surface Area of Hybrids

The specific surface area of hybrid silica aerogels depends on the hybrid, but it can be extremely high. For instance, ormosils made from those organopolysilsesquioxanes which could be gelled such as silica-silsesquioxane (Schwertfeger et al. 1994), from bridged polysilsesquioxane aerogels (Loy et al. 1992), and more recently from those pendant polysilsesquioxanes which could be gelled (Venkateswara Rao et al. 2006) produced materials presenting among the highest specific surface area: 1900 m2 g1, for a density of 0.05 g cm3 for arylene-bridged polysilsesquioxanes. Regarding CNT/SiO2 aerogel composite, their nitrogen adsorption isotherms illustrated in Fig. 10.16 are close to those of a pure SiO2 aerogel, very different

References

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from that of the native CNT aerogel, due to a very different specific surface area, respectively, 742 m2 g1 and 670 m2 g1, compared to 162 m2 g1 for the native CNT aerogel (Zhang et al. 2010; Worsley and Baumann 2016).

10.6.2.2

Thermal Conductivity of Hybrids

The thermal conductivity of hybrid silica-organic aerogels depends on the material, but globally it remains of the same order of magnitude as silica aerogels at room temperature. This is for instance the case of silica aerocellulose hybrids (Kim and Jang 1991; Demilecamps et al. 2015; Demilecamps et al. 2016), or of silica aerogel/short cellulosic fiber composites, in which a very low thermal conductivity (0.017  0.001 W m1 K1) similar to that of pure silica aerogel was maintained (Markevicius et al. 2017; Jaxel et al. 2017). Other superinsulating ormosil aerogels were designed by Zu et al. (2018) from a single organically modified silica-based precursor (CH2CH(Si(CH3)O2/2))n.

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Chapter 11

Surfactant-Templated Sol-Gel Materials

11.1

Introduction

Besides hybrid organic-inorganic materials, the use during the last decades of new macromolecular additives known as “surfactants” has permitted to design very new mesoporous gel textures, such as ordered array of mesoporous cylindrical pores. These textures could be achieved, first in the aluminosilicate systems, by directing the architectural sol-gel network formation resulting from chemical hydrolysis and condensation reactions, with the help of long polymeric chain surfactant molecules, or of organic copolymers comprising a more or less ordered sequence of different functional groups, both presenting amphiphilic properties. The most emblematic types of such materials, which are ordered mesoporous materials made using surfactant liquid crystal templates, display a very high specific area. They were for instance reviewed by Corma (1997). This chapter is devoted to a description of the structure of these advanced sol-gel materials and to some of their general original properties, essentially their mechanical properties. Their achievement results from an understanding of the organization of various solutes in a liquid solution, either at the liquid/air (or gas) interface or at the liquid/ liquid interface which separates two immiscible liquids. Hence, it is necessary to first briefly understand the various types of solutes, with respect to their behavior at an interface.

© Springer Nature Switzerland AG 2020 A. C. Pierre, Introduction to Sol-Gel Processing, https://doi.org/10.1007/978-3-030-38144-8_11

457

458

11.2

11 Surfactant-Templated Sol-Gel Materials

Solute Adsorption at a Liquid/Air or an Immiscible Liquid/Liquid Interface

11.2.1 Gibbs Adsorption Isotherm (Hiemenz 1976; Hiemenz and Rajagopalan 1997) Gibbs adsorption isotherms concern the behavior of any solute at an interface between a liquid solution, containing the solute, and another fluid medium which can be air or another liquid immiscible with the first liquid solution (e.g., an organic nonpolar oil immiscible with a water solution). If we consider for simplicity an aqueous solution, in contact with air via a flat interface (Fig. 11.1), the solution can be described as composed of a solvent and a solute, respectively, designated by the labels 1 and 2. Actually, the solvent and solute concentrations change progressively across a thin layer between the solution and air. For instance if each component concentration is measured along an axis x perpendicular to the interface between the two medium, as illustrated in Fig. 11.1, the solvent concentration C1x progressively decreases from its average solution concentration C1 in the solution, far from its interface with air, to a value ¼ 0 at an abscissa xE. This is because the solution is spontaneously structured so as to decrease its interface energy with air, which may imply a lower solvent concentration when nearing the interface (or a higher solvent concentration depending on the solute). Naturally, an opposite similar gradation prevails regarding the solute concentration C2. It is desirable to replace this actual progressive composition interface by a more simple representation which consists of a well-defined surface at abscissa x ¼ xs, and to approximate the solvent concentration profile by a Heaviside-type discontinuous profile such that C1x ¼ C1 for x < xs and C1 ¼ 0 for x > xs. When doing this, a missing solvent mole number n 1 is neglected for x < xs and a surplus solvent mole is neglected for x > xs (Fig. 11.1). This can be accounted for by number nþ 1 attributing an excess solvent mole number ns1 to the surface at x ¼ xs, defined by

Fig. 11.1 Possible solvent concentration profile at an interface between an aqueous solution and air, and definition of the solvent Gibbs surface excess

11.2

Solute Adsorption at a Liquid/Air or an Immiscible Liquid/Liquid Interface  ns1 ¼ nþ 1  n1

459

ð11:1Þ

Let A designate the area in m2 of the surface at x ¼ xs. The solvent Gibbs surface excess for the solvent is defined as Γ1 ¼

ns1 A

ð11:2Þ

For the same abscissa x ¼ xs, the Gibbs surface excess for the solute is similarly described by Γ2 ¼

ns2 A

ð11:3Þ

According to the thermodynamics Gibbs-Duhem relationship 0 ¼ SdT  VdP þ Adγ þ n1 dμ1 þ n2 dμ2

ð11:4Þ

where S is the entropy, T the temperature, A the surface area, γ the surface tension, n1 the number of moles of the solvent 1 and μ1 its chemical potential, and n2 the number of moles of the solute and μ2 its chemical potential. In constant T and P conditions, this equation can be simplified for the interface defined by a surface at x ¼ xs, to 0 ¼ Adγ þ ns1 dμ1 þ ns2 dμ2

ð11:5Þ

which transforms, using the Gibbs surface excess defined in Eqs. (11.2) and (11.3), to the so-called Gibbs adsorption equation: dγ ¼ Γ 1 dμ1  Γ 2 dμ2

ð11:6Þ

Per convention, it is next convenient to choose the interface position x, such that Γ 1 ¼ 0, in which case dγ ¼ Γ 2 dμ2

ð11:7Þ

The chemical potential of the solute μ2 in the solution can also be related to its chemical activity a2, and a reference state μ02 classically defined by its chemical potential when its concentration is 1 mol L1, by μ2 ¼ μ02 þ RT Ln a2 which permits to transform Eq. (11.7) to

ð11:8Þ

460

11 Surfactant-Templated Sol-Gel Materials

dγ ¼ Γ 2 RT

da2 a2

ð11:9Þ

For a so-called thermodynamics “ideal” dilute solution, the solute activity can be replaced by its average concentration C2 so that dγ ¼ Γ 2 RT

dC 2 C2

ð11:10Þ

11.2.2 Aqueous Solute Classification (Hiemenz 1976; Hiemenz and Rajagopalan 1997) Equation (11.10) indicates that the surface tension γ 0 of a pure solvent is modified by addition of a solute. Hence the solution surface tension γ can be written as γ ¼ γ0  π

ð11:11Þ

where π is a modification of the solvent surface tension, termed the film pressure. This film pressure is due to the solute and the concentration profiles of both the solvent and the solute at the interface with air (or an immiscible liquid). However π Force is not a real pressure: it has the dimension of Length . The real film pressure in Pascal unit is P¼

π τ

ð11:12Þ

where τ is the interface thickness. The film pressure π depends on the solute concentration C2 and for a small concentration it can be approximated by a linear expression π ¼ mC 2

ð11:13Þ

where m is a simple numerical coefficient. The numerical value of m permits, in turn, to classify the various aqueous solutes in three classes, depending on their effect on the solution surface tension γ. As illustrated in Fig. 11.2, m is slightly negative for aqueous electrolytes. That is to say, the solution surface tension slightly increases with C2. On the other hand, for many organic solutes m > 0: the solution surface tension slightly decreases as C2 increases. At last for a third class of organic solutes termed surface-active solutes (or agents), more commonly termed surfactants, γ first rapidly decreases as C2 increases until a critical concentration termed the “critical micellar concentration” or c.m.c. is reached. Beyond the c.m.c., γ keeps a constant value of low magnitude.

11.2

Solute Adsorption at a Liquid/Air or an Immiscible Liquid/Liquid Interface

461

Fig. 11.2 Effect of different solutes on the surface tension of a solution

These surfactants comprise molecules characterized by an amphipathic behavior able to interact with both polar (e.g., water) and nonpolar solvents (e.g., organic water immiscible liquids). In so far as m can be considered as a numerical constant, a simple mathematical derivation from the linear approximation Eq. (11.13) followed by combination with Eq. (11.10) gives m¼

dπ dγ Γ RT ¼ ¼ 2 dC 2 dC2 C2

ð11:14Þ

After replacing again m by its expression taken from Eq. (11.13), the following equation can be obtained: π Γ RT ¼ 2 C2 C2

ð11:15Þ

π ¼ Γ 2 RT

ð11:16Þ

π A ¼ ns2 RT

ð11:17Þ

That is to say

or

The latter equation looks like the ideal gas equation. It is actually the equivalent of this ideal gas equation, which prevails in 3-dimensional real gases, but for a 2-dimensional gas, which prevails in a surface. Equation (11.17) indicates that at low concentration, the solute behaves in the solution interface with air as a perfect bidimensional gas.

462

11.3

11 Surfactant-Templated Sol-Gel Materials

Surfactants (Berthod 1983)

11.3.1 General Structure of Surfactant Molecules and Behavior Below a Concentration c.m.c. (Hiemenz 1976; Hiemenz and Rajagopalan 1997; Mittal 1979; Perron 1979; Mittal and Fendler 1982; Berthod 1983)

11.4.1 Micelle Formation As C2 increases in an aqueous liquid medium, π increases and σ decreases according to Eqs. 11.19 and 11.20. At the c.m.c., σ reaches a value σ 0 which is the minimum area necessary to place a surfactant molecule in the interface (Fig. 11.4). Beyond the c.m.c., the surfactant Gibbs surface excess defined by Eq. (11.3) remains a constant dγ ¼ 0. and dC 2 The surfactant film has reached a compact and almost uncompressible bidimensional liquid-like film state. All supplementary surfactant molecules added to the solution will participate neither in the surface film, nor in the solution, as individual molecules. They actually phase separate and build colloidal aggregates termed micelles, dispersed in the liquid solution volume. The formation of a micelle from m amphipathic molecule S can be represented by the chemical reaction (Berthod 1983) mS $ Sm

micelle

Fig. 11.4 Free area about a surfactant molecule in an aqueous medium/air interface film

ð11:28Þ

11.4

Behavior of Surfactants at a Concentration >c.m.c.

467

11.4.2 Micelle Structure (Berthod 1983; Mittal 1979; Perron 1979; Mittal and Fendler 1982) Several micelle structures are possible and they depend on the surfactant concentration C2. As C2 keeps increasing, the structure is transformed from spherical-like to rodlike and finally to lamella. The surfactant shape parameter g defined by g¼

V tail Ahead Ltail

ð11:29Þ

where Vtail is the volume of the hydrophobic tail, Ltail its maximum effective length, and Ahead the hydrophilic head area also permits to predict the shape of micelles more prone to be formed (Israelachvili 1985, 1987). Spherical micelles tend to form more readily when g < 1/3, cylindrical micelles when 1/3 < g < 1/2, and lamellar structures for higher g values. Besides, micelles can be formed in aqueous polar liquids as well as in nonpolar organic solvents, except that their structure in organic polar liquids is inverse to that prevailing in a polar aqueous liquid medium. That is, their hydrophilic head and hydrophobic tail just exchange their position. In the next paragraphs, the focus is mostly on the micelle structure in aqueous liquid media.

11.4.2.1

Spherical Micelles

For a concentration just above the c.m.c., the excess surfactant molecules in solution form spherical micelles with a structure illustrated in Fig. 11.5. Their polar head is turned towards the aqueous medium, while their hydrophobic tails avoid water contact by covering the inside wall of the micelles. A suspension of spherical Fig. 11.5 Spherical micelle

468

11 Surfactant-Templated Sol-Gel Materials

ionic surfactant micelles (often termed micellar solution) actually behaves in an aqueous solution as a typical colloidal sol, with an electrical double-layer structure which can be described by the Gouy-Chapman model.

11.4.2.2

Rodlike Micelles

As C2 keeps increasing, the spherical micelles merge in cylindrical rods (Fig. 11.6) which can comprise several thousands of surfactant molecules. The radius of such micelles is typically from 1 to 3 nm. For higher surfactant concentrations, these rods moreover take on an ordered parallel hexagonal packing orientation (Fig. 11.7), which is characteristic of some liquid crystals.

11.4.2.3

Lamellar Micelles

For still higher concentrations, the micelle shape changes again and consists of lamellar micelles (Fig. 11.8).

11.4.2.4

Inverse Micelles in an Organic Liquid

At last if the surfactant is added in an organic nonpolar liquid, inverse micelles with a hydrophobic tail turned outside the micelles are formed. A small volume ratio of immiscible water can also be added and it occupies the hydrophilic heart of spherical micelles (Fig. 11.9). Fig. 11.6 Cylindrical rod micelle

11.4

Behavior of Surfactants at a Concentration >c.m.c.

469

Fig. 11.7 Liquid crystal structure made by hexagonal packing of cylindrical micelles Fig. 11.8 Lamellar micelles

11.4.3 Factors Influencing the c.m.c. 11.4.3.1

Chemical Composition

The nature of a surfactant molecule has an important effect on the c.m.c., in particular the number of carbon atoms Nc of the hydrophobic chain. For a homologous series of surfactants (Israelachvili et al. 1976):

470

11 Surfactant-Templated Sol-Gel Materials

Fig. 11.9 Inverse micelles

log 10 c:m:c ¼ a þ bN c

ð11:30Þ

where a and b are some positive constants. Regarding the hydrophilic head, the most important parameter is the charge of the head counterions in solution, exactly as for colloidal sols (Chap. 6), but not the exact head nature itself. In the case of anionic surfactants the c.m.c. decreases as the formal charge z+ of the cationic counterions increases (Lindman and Wennerstrom 1980). Hence, the c.m.c. of divalent counterions such as Ca2+, Mg2+, Pb2+, and Zn2+ is lower than that of the monovalent cations Na+ or K+. Similarly, for cationic surfactants, the valence of the anionic counterions is important: the c.m.c. is lower for     SO2 4 than for NO3 , Br , Cl , and F . This result is the same as that already presented for solid particle colloids, in Chap. 6. Overall, the c.m.c. decreases as the ionic strength I increases in the case of ionic surfactants. When a concentration Cc of non-potential determining electrolyte is added to a surfactant solution, the c.m.c. follows an empirical relationship of the type (Berthod 1983) Ln ðc:m:c:Þ ¼ αLn ðc:m:c: þ Cc Þ þ β

ð11:31Þ

11.4

Behavior of Surfactants at a Concentration >c.m.c.

471

where α and β are positive constants which depend on the surfactant and the electrolyte. The addition of an electrolyte favors the formation of cylindrical micelles.

11.4.3.2

Temperature

The solubility of an ionic surfactant rapidly increases as the temperature T increases (Krafft and Wiglow 1895). The main temperature characteristic of an ionic surfactant solution is its Krafft point K. This is a particular temperature which depends on the surfactant. For T < K, the surfactant solubility is low and due to monomers. On the other hand for T > K, solubility occurs by the formation of micelles, unless the temperature is too high and the micelles are destroyed. The size of cylindrical micelles decreases as the temperature increases, an effect which is very moderate on spherical micelles. The qualitative effect of temperature is summarized in the graph in Fig. 11.10. The counterion valence has a significant influence, for instance K(Ca2+) > K(Na+), which explains that soap is precipitated in hard water. Nonionic surfactants are not characterized by a Krafft point, but by a cloud temperature which depends on the surfactant concentration. When a solution is heated above the cloud temperature, its phase separates into two solutions with a different micellar concentration. The c.m.c. of nonionic surfactants is much lower than that of ionic ones, and it is very moderately affected by electrolytes. It decreases as T increases. The ionic strength I of an electrolyte solution has little influence in the case of nonionic surfactants. Fig. 11.10 Structure of a surfactant solution as a function of temperature and surfactant concentration. Adapted from Berthod (1983)

472

11.5

11 Surfactant-Templated Sol-Gel Materials

Solubilization of Organic Nonpolar Compounds in Water by Micelles (Robb 1982; Berthod 1983)

The solubility of many compounds moderately or not soluble in water can be improved with the help of micelles, by techniques which are quite useful in the pharmaceutical and detergent industries, but also to synthesize template sol-gel materials.

11.5.1 Micellar Solutions Nonpolar organic compounds of smaller size such as hydrocarbons, toluene, and cyclohexane can be solubilized with the help of micelles to make micellar solutions. These molecules are dispersed in the heart of micelles made by the hydrophobic tails of the surfactant molecules (Fig. 11.11a). Hence, their solubility increases with the size of the micelles and with the length of the surfactant hydrophobic tails. However a solubility limit exists beyond which an emulsion is formed as this is discussed further on. Besides, polar compounds may also participate in the structure of micelles and form mixed micelles, as this occurs in particular with alcohol molecules (Fig. 11.11b).

11.5.2 Micelle-Stabilized Microemulsions An emulsion is a dynamic two-phase liquid mixture, formed by forced mixing of two liquids not, or only partially, soluble in each other. Mixing can be performed by mechanical agitation or with ultrasonic vibrations. Just after mechanical dispersion of the two liquids, the least abundant liquid phase is dispersed as fine droplets inside the most abundant liquid phase. Normally an emulsion is not stable; it readily transforms to a simple two-phase layered separation, either by flocculation followed by coalescence or by flotation followed by coalescence.

Fig. 11.11 Solubilization of (a) nonpolar and (b) polar compounds by micelles. Adapted from Mukerjee (1979)

11.5

Solubilization of Organic Nonpolar Compounds in Water by Micelles

473

Fig. 11.12 Micellar emulsion

Fig. 11.13 Oil-water (O/W) and water-oil (W/O) emulsions

On the other hand in a microemulsion, dispersed microdroplets can be kinetically stabilized when they are embedded inside surfactant micelles (Fig. 11.12). An emulsion can be of the O/W (oil in water) type when the oil is localized inside the micelle, or of the W/O (water in oil) inverse micelle type when water is inside the inverse micelle (Fig. 11.13). The size of the droplets typically ranges from 10 nm to 0.2 μm. In the first case an emulsion is transparent while in the second case it is bluish and can display the same Tyndall effect as sols of similar nanoparticle size.

11.5.3 State Diagrams of Ternary Solution Systems Made with Surfactants Ternary systems, composed of an organic liquid medium, an aqueous liquid medium in which sol-gel precursors are dissolved, and a surfactant, permit to design the templating sol-gel oxide materials: from spherical nanoparticles to ordered array of cylindrical mesopores, or lamellar structures. For this purpose, it is necessary to describe which type of micellar structures are formed, depending on the ternary system composition. The state of a ternary system composed of water (compound W), an organic liquid (compound O), and a surfactant (compound T) can be represented in an equilateral triangle diagram as illustrated in Fig. 11.14. In such diagrams the

474

11 Surfactant-Templated Sol-Gel Materials

Fig. 11.14 Ternary-state diagram representation

Fig. 11.15 Ternary diagram in the water-hexanol-cetyltrimethylammonium bromide (CTAB) system. Adapted from Ekwall et al. (1969)

percentage of each compound can be read by drawing lines parallel to the sides of the triangle. For instance in Fig. 11.14, the composition of system M is 55% W, 32% 0, and 13% T. In such state diagrams, it is possible to indicate whether spherical micelles (O/W, W/O, or both types), cylindrical micelles, or surfactant precipitation occurs, as in Fig. 11.15. Another classification by Winsor (1954) considers the number and nature of phases formed (Fig. 11.16). A Winsor I system comprises a W/O emulsion phase and an oil solution on top of it. A Winsor II system comprises a water solution and an O/W emulsion on top of it. In a Winsor III system we have three phases: a water solution, a O/W emulsion, and an oil solution. In a Winsor IV system, only an emulsion phase exists.

11.6

Microparticle Synthesis in Water-in-Oil (W/O) Microemulsions Stabilized by. . .

475

Fig. 11.16 Winsor classification in the ternary system of water + NaCI (3 g L1)-dodecaneparaoctylbenzene sodium sulfonate (SOBS) + pentanol. Adapted from Bellocq et al. (1981)

11.6

Microparticle Synthesis in Water-in-Oil (W/O) Microemulsions Stabilized by Surfactants

11.6.1 Solid Microparticles and Microcapsules As previously mentioned, any aqueous sol-gel precursor solution can be dispersed in an organic liquid to make a microemulsion (Nagy et al. 1983; Lufimpadio et al. 1984) and the process is not limited to the synthesis of oxide precursors. Recently, the size of aqueous droplets dispersed in water-in-oil (W/O) emulsions stabilized by surfactants could be controlled in a range from 70% were obtained.

13.3.1.2

Atomic Diffusion in Sol-Gel Materials

It is possible to question whether transport mechanisms such as atomic diffusion can be extrapolated from the conventional ceramics to the colloidal sizes. Atomic transport by diffusion in the vapor phase rests on an evaporation condensation process due to differences in the equilibrium vapor pressure near a solid surface, depending on the local surface curvature. According to Kelvin’s equation, the equilibrium vapor pressure is lower near a neck between two particles where the solid surface is essentially concave, than far from a neck, at atomic scales. The resulting vapor pressure gradient induces a vapor-phase diffusion which keeps feeding the neck. It modifies the pore shape but does not induce densification which in a gel often occurs between 900 and 1200  C. At these temperatures, the equilibrium vapor pressure of oxygen is very low for an oxide. On the other hand, the residual hydration water usually absent in conventional ceramics is much more volatile at relatively low temperatures. Hence, this mechanism cannot be completely rejected for the sol-gel processes, as water is known to be a general sintering aid. Surface atomic diffusion also does not induce densification. However, it is likely to operate at a lower temperature than usual, because of the extremely high specific area of sol-gel and also because of the special nature of the gel surface which easily adsorbs water molecules or OH groups. Overall, atomic transport mechanisms able to transform the pore shape to a spherical one, without producing any densification, are likely to be common in sol-gel materials. If this is the case, these mechanisms can be strongly modified by tailoring the nature of a sol-gel solid surface, for instance by adsorbing hydrophobic molecules. Hence the liquid sol-gel chemistry can have a marked influence on the sintering behavior. As seen previously, lattice atomic diffusion can actually increase the density of a material, depending on the source from where the atoms originate. In a crystalline material such as an oxide, this mechanism begins to significantly operate when the atomic mobility of oxygen atoms is high enough, that is to say, at high temperatures. It requires the presence of atomic point defects such as vacancies, interstitials, or dislocations. However gels are far from being very well crystallized. Gels have at best very small grains with a high defect density. Consequently, depending on the compound, lattice diffusion can often operate at a much lower temperature than in conventional ceramics. Actually, a distinction between the different atomic diffusion paths, such as on a surface, inside a lattice, along dislocations, or along grain boundaries, may be difficult in sol-gel materials, in so far as it becomes difficult to distinguish between dislocations, grain boundaries, and surfaces. It would seem more appropriate to consider a global diffusion process through a very disordered gel or transition-phase structure.

562

13.3.1.3

13

Sintering Sol-Gel Ceramics

Sintering and Crystallization in Sol-Gel Ceramics

In so far as densification can be considered to occur in sol-gel ceramics by global atomic diffusion, the corresponding diffusing species are also likely to enhance the crystallization by nucleation and growth of the most thermodynamically stable crystalline phase, as presented in Chap. 12. Hence densification of sol-gel ceramics often occurs concurrently with their crystallization (Uhlmann et al. 1975). Even in compounds where sintering occurs at a relatively low temperature, the crystallization of a stable phase usually occurs at a slightly lower but very close temperature to the sintering temperature. Besides, the sintering ease largely depends on the sol-gel powder preparation conditions, including milling and calcinations, as this was shown for alumina powders prepared by sol-gel process (Tsai and Shih 1993; Sathiyakumar and Gnanam 1999), because these conditions have an influence on the type of “impurity” additives, that is to say, dopants, present in the powder. Sol-gel zirconia is a typical material where densification is easy: it often begins at 800  C (Yoldas 1986). The crystalline monoclinic zirconia structure which is stable at this temperature also forms at low temperature, often at 500  C. Moreover, densification is faster at higher temperatures but it reaches a maximum rate in the temperature range of 1300–1400  C and it slows down again when transformation to the tetragonal phase occurs. It was also shown, in Y2O3-stabilized ZrO2, that atomic diffusion along grain boundaries dominated the initial-stage sintering. In agreement with this view, Herring’s scaling law correctly predicted that using smaller size particles was beneficial to sintering (Rhodes 1981; Yamagishi and Takahashi 1987). Water vapor also enhances the sintering process. For instance, ThO2 gel spheres could be densified up to 99% of their theoretical density by sintering them in air containing up to 99.7% humidity (Fig. 13.8). Simultaneously, the grain size drastically increased (Daniels and Wadsworth 1965). A similar phenomenon was observed in UO2 pellets (Stuart and Adams 1975). The proposed mechanism rested on the formation of non-stoichiometric compounds UO2+x and ThO2x which was consistent with a dark-gray coloration of the materials (Banister 1975). Sol-gel ceramics can themselves be quite effective sintering additives. Sol-gel ZrO2 was used with non-oxide powders such as carbides and borides, and made it possible to obtain dense particulate composites (Davidge and Woodhead 1984). With a nitride such as Si3N4 made by reaction of SiCl4 with liquid ammonia, according to a sol-gel-type process, alkoxide sol-gel additives such as Y(OH)3 and Mg(OH)2 also made it possible to improve the sintering behavior (Shaw and Pethica 1986), and the final density could be increased from 2.85 to 3.2 g/cm3. Similarly to ZrO2, sol-gel TiO2 can crystallize and sinter at a relatively low temperature (Komarneni et al. 1985). Powders with an average grain size of 0.08 mm made from titanium isopropoxide could reach a density up to 99% of their theoretical density at 800  C (Barringer and Bowen 1982). However, a good density can also be achieved by other techniques than true sol-gel processing. For instance

13.3

Atomic Transport Mechanisms Operating During Sintering

563

Fig. 13.8 Density of ThO2 spheres with 0.5 mm diameter sintered in air-steam atmospheres. Adapted from Yamagishi and Takahashi (1987)

TiO2 coating was also prepared by thermal decomposition of titanium alkoxides on a hot substrate at 600  C and sintered directly at this temperature to produce a hard thin transparent TiO2 layer (Mazdiyasni et al. 1965). In contrast with the previous materials where densification was enhanced by the sol-gel state, the poor sintering performance of sol-gel Al2O3 was already mentioned. A recent exception concerns dense Al2O3 glass films obtained from Al lactates by He et al. (2019) at a few hundred  C. In all other synthesis protocols, densification was actually beginning in the same range of temperature where the stable-phase α-alumina was observed to crystallize, above 1100  C. Moreover, the pores were not completely eliminated. A final pore distribution remained trapped inside large grains, a result which again illustrates the complex competition between densification, grain growth, and influence of pores on these transformations. In order to sinter compounds which comprise several cations, such as mullite 3Al2O32SiO2, the interdiffusion of cations is necessary. Hence, as for simple oxides, crystallization often occurs simultaneously with sintering. Sol-gel processing makes it possible to obtain powders which sinter at somewhat lower temperature because of a smaller diffusion distance in which the various cations have to migrate, due to the small size of the sol-gel particles. By comparison, in conventional ceramic processing, lengthy grinding times are necessary to make small-size particles so as to lower the temperature where diffusion can efficiently operate (Colomban 1985). Sol-gel mullite could be sintered at 1200  C instead of 1400  C by conventional processing (Ghate et al. 1973; Mazdiyasni and Brown 1972). Other examples concern spinel MgAl2O4 which could be densified between 600 and 800  C (Livage and Lemerle 1982) and lead zirconium titanates, or PLZT, which could be densified in oxygen at 1175  C (Brown and Mazdiyasni 1972; Colomban 1976). For the latter compound, sintering between 860 and 1150  C

564

13

Sintering Sol-Gel Ceramics

proceeded with the help of a liquid phase composed of PbO, TiO2, and ZrO2 in which the solid particle packing could easily reorganize their packing. At higher temperature and up to 1300  C, dissolution recrystallization occurred and induced the growth of large grains. Finally, at still higher temperatures, evaporation-condensation was the main densification mechanism and it required a low PbO vapor pressure. Other important technological titanates and zirconates made by the sol-gel process, in which a good densification could be achieved, include BaTiO3, prepared by mixed alkoxide techniques by Mazdiyasni et al. (1969) and sintered at 1300  C to dense translucent bodies, as well as SrTiO3, SrZrO3 (Smith II et al. 1970), and 6% (by mole) Y2O3–ZrO2 powder which could be sintered to dense transparent ceramics at a temperature of the same order (Mazdiyasni et al. 1967). All parameters in a sol-gel hydrolysis-condensation protocol can have an effect on the sintering rate (Yoldas 1986), in the same way as they are responsible for a large variability in the nature of the first phases which crystallize.

13.3.2 Viscous Flow Sintering Instead of moving individually by diffusion, atoms can also move by a cooperative displacement known as viscous flow, in particular when the intermolecular bonding presents a relatively strong covalent character. This kinetic process is well known to operate in silicate glasses made by quenching of melted oxides and it also operates largely in the densification of sol-gel glasses. It makes it possible to densify SiO2 polymeric gels to glasses at 1000  C, instead of melting them at 2000  C. The main difference between gels and glasses is that during the initial stages of densification, at least, the viscosity of gels is much lower than that of bulk glasses and hence densification is faster (Brinker and Scherer 1984). This property is due to the presence of residual OH. After some time, an increase in viscosity is observed, due to dehydration and also due to a more dense polymeric structure achieved by progressive polymer relaxation. This explains that, for thin coatings, the densification is relatively slower than for bulk gels, because the contraction of the gel is impeded and modified by the substrate. The viscous flow mechanism was well studied for the silicate systems, in particular by Sakka and Kamiya (1978), Yamane et al. (1979), Brinker and Mukherjee (1980), and Scherer (1977a, b). But viscous flow models were also applied to nonsilicates, such as monolithic gels obtained from a double alkoxide of Pb and Ti by Blum and Gurkovich (1985). Viscous flow densification models take implicitly into account that gels such as silica gels are non-Newtonian fluids and viscoelastic materials able to keep their monolithic shape. When submitted to a mechanical stress, they first show an immediate elastic response, then a delayed elastic response in a second step, and finally a viscous deformation. Densification is itself almost entirely caused by viscous flow and the densification rate depends on the morphology, composition, and chemical reactivity.

13.3

Atomic Transport Mechanisms Operating During Sintering

13.3.2.1

565

General Description of Viscous Flow Sintering

The Gibbs free energy decreasing rate, due to the surface energy γ in a porous material, can be derived from the decreasing rate of its specific surface area Sa according to dG dS ¼γ a dt dt

ð13:8Þ

For a material cylinder of volume V and radius r, this rate of energy dissipation can also be related to the strain rates dε dt and stress σ i where i ¼ r, θ, or z in cylindrical coordinates by
 dG dEr dEθ dEz ¼ V σr þ σθ þ σz dt dt dt dt

ð13:9Þ

In the hypothesis that a gel behaves as a glass in terms of atomic transport by viscous flow and, for more simplicity, if it can be considered to behave as a Newtonian liquid with a high viscosity η flowing in direction z, it is possible to show that (Kingery et al. 1976) dEr γ ¼ 3ηr dt

ð13:10Þ

which indicates that the importance of viscous flow increases for fine gel networks.

13.3.2.2

Sintering Models

More detailed laws to describe the viscous sintering of a gel depend on the geometrical model used to describe the network. The simplest model which was applied to gels was by Frenkel (1939). It simply describes the merging of spheres of radius r by viscous flow. The viscous flow lines are illustrated in Fig. 13.9.

Fig. 13.9 Viscous flow lines in the densification model of spheres of Frenkel. Adapted from Scherer (1983)

566

13

Sintering Sol-Gel Ceramics

Any linear dimension L(t) in the network was shown to decrease linearly with time according to Lð t Þ 3γt ¼1 8ηr Lð0Þ

ð13:11Þ

Frenkel’s model was modified by Mackenzie and Shuttelworth (1949) to address the final stage of densification. For this purpose, interconnected spherical particles were replaced by spherical and closed pores. A more elaborate model was developed by Scherer. It described a gel network by cylindrical solid rods placed along the edges of cubes, so that the pores formed a very open network during the initial stage of sintering (Scherer 1977a) (Fig. 13.10). This model was generalized to include a distribution of pore sizes (Scherer 1977b) and it was applied to colloidal silica gels (Scherer 1983). The results could be expressed with reduced variables, by functions of the type ρ γ ¼f ρth η r0

!
1=3 ρth ðt  t 0 Þ ρ0

ð13:12Þ

in which f() designates a function of the complex variable in between the parenthesis, termed the reduced time. In this equation, ρ0 is the initial apparent density, ρ is the apparent density at time t, ρth is the theoretical solid density, and r0 is the initial pore size. For n identical pores per unit volume, this model gives
1=3  ρ γn t ¼f ρth η

Fig. 13.10 Gel network for Scherer’s densification model by viscous flow. Adapted from Scherer (1983)

ð13:13Þ

13.3

Atomic Transport Mechanisms Operating During Sintering

567

Fig. 13.11 Relative density as a function of the reduced time for the cubic model in Fig. 13.10. Adapted from Scherer (1983)

This gives a graph of the reduced density ρρ as a function of the reduced time, th of sigmoidal shape, by opposition with Frenkel’s model (Fig. 13.11).

13.3.2.3

Densification of Gels Depending on Their Structure

Colloidal silica gels begin to densify at a temperature above 900  C, higher than with polymeric gels, because of a coarser network structure (Brinker et al. 1982). For instance, colloidal silica gel made by Nogami and Moriya (1980), which consisted of spheres with a diameter of 20 nm and a low density of 0.9 g/cm3, followed Frenkel’s viscous flow model above 1050  C with the same activation energy as that of fused silica (40.7 kJ/mol). Compacts of sol-gel silica powders sintered to translucent glass at 1150  C (Sakka 1982). The type of network built by the particles is important. Densely agglomerated particles densify more easily and at lower temperatures than gels with linearly interconnected particles. Large pores with a size comparable to the size of agglomerates slow down the viscous flow densification process exactly as for the mechanisms by atomic diffusion. On the other hand, silica aerogels dried in hypercritical conditions could be densified below 1100  C, in spite of their extremely open structure. In this case, the pore radius was extremely small so that sintering could begin at 525  C according to a viscous flow mechanism (Fricke 1988). The chemical composition has an important influence on the densification behavior. In particular, when the concentration of residual OH groups remains high after drying, e.g., >3000 ppm, a gel may start to foam at 1200  C. Such problems can be avoided by treating gels in Cl2, which eliminates the OH but somewhat raises the densification temperature. Residual organics and entrapped CO2 must also be eliminated at intermediate temperatures. As mentioned previously, the viscosity of gels keeps increasing with time during densification because their chemical composition keeps changing, in particular due to the loss of residual OH.

568

13.4

13

Sintering Sol-Gel Ceramics

Grain Growth

13.4.1 Basic Mechanism As previously mentioned, grain growth is also associated with a decrease in interfacial energy, originating in the grain boundaries. For a curved grain boundary such as illustrated in Fig. 13.12, Laplace’s equation indicates that a greater mechanical pressure exists at point A, that is to say, on the side of the grain boundary located towards the curvature center, than at point B on the opposite side:
pA  pB ¼ γ gb

1 1 þ r1 r2

 ð13:14Þ

where γ gb is the grain boundary interfacial energy and r1 and r2 the two main curvature radii of this grain boundary. The relative compression at A and tension at B can simultaneously be released by moving some atoms from the grain on the A side to the grain on the B side. This just requires a moderate atomic displacement or more precisely a realignment of these atoms. Overall, grain B grows while grain A shrinks and the grain boundary moves towards its center of curvature. Another practical consequence is that a planar interface should not move.

13.4.2 Grain Growth Models The simplest model for grain growth is based on atomic diffusion across the grain boundary, which corresponds to atoms jumping from grain A to grain B in Fig. 13.12. This results in a parabolic growth law:

Fig. 13.12 Motion of grain boundaries and their pinning by inclusions. Adapted from Kingery et al. (1976)

13.4

Grain Growth

569

r 2  r 20 ¼ 2

Dgb γ V m t RTw

ð13:15Þ

where Dgb is the diffusion coefficient for atomic jumps across a grain boundary of thickness w. A more accurate model by Hillert (1965) made a distinction between the grains of size larger than a critical size rcr, which did grow, and the smaller grains which shrunk. The critical grain size increased with time according to the equation  dr 2cr Dgb γ V m ¼ dt 2RTw

ð13:16Þ

and the grain size evolution was given by dr V γ ¼ M 0b m dt w




1 1  r cr r

 ð13:17Þ

In the previous equation M 0b is the grain boundary mobility which is related to its displacement velocity Vb when submitted to a force Fb, by M 0b ¼

Vb Fb

ð13:18Þ

13.4.3 Grain Boundaries Pinning by Impurities Impurities, such as atoms or particles, induce lattice stresses when they are introduced in a host lattice. The corresponding mechanical energy adds up to the free energy of the system. It can be released by moving the impurities to the grain boundaries where the atoms are less tightly packed. Consequently, some energy is required to separate the grain boundaries from the impurities, when these boundaries move during grain growth. Practically, the displacement of grain boundaries can be slowed down by foreign inclusions (Fig. 13.12), an effect which increases as the foreign inclusion size decreases (Brook 1969). The impurities exert a drag force F db and the total force necessary to move a grain boundary is F total ¼ F 0b ¼ F db ¼ b

Vb þ F db M 0b

ð13:19Þ

570

13

Sintering Sol-Gel Ceramics

Fig. 13.13 Force to move a grain boundary with segregated impurities, as a function of the grain boundary velocity

When the impurities can diffuse fast enough to keep up with the grain boundary, the conditions are such that the drag force exerted by the impurities can fully operate. However, if the grain boundary displacement velocity Vb becomes larger than the time τ for an additive to diffuse a unit distance, this additive starts to separate from the grain boundary and its drag force decreases (Fig. 13.13). Pores themselves can play a role similar to the additives with respect to grain boundary migration. This is the reason why grain growth often occurs during the last stages of sintering, when the number of pores able to slow down the migration of grain boundaries decreases. Pores must be eliminated during densification, but the way they interfere with the sintering process is very complex. Some aspects of this interaction are examined in the next section.

13.5

Interaction of Pores with the Sintering Process

According to Laplace’s equation, a spherical pore of radius rp introduces a tensile mechanical stress in the atoms near point A in the pore surface, given by σ t ¼ pA ¼

2γ b rp

ð13:20Þ

To release these mechanical stresses, pores tend to segregate at the grain boundaries. Pores can also move, disappear, merge with each other, or remain stable. These properties of pores are first addressed below, and their consequences for the grain growth and densification evolutions are examined in a further section. The effect of particular pore distributions such as due to the formation of agglomerates or packing of particles with unequal sizes is reviewed last.

13.5

Interaction of Pores with the Sintering Process

571

13.5.1 Possible Pore Transformations 13.5.1.1

Kinetic Stability of a Pore

The shape of a pore is an important characteristic. It is determined by the number N of grains which surround the pore and the dihedral angle ϕ derived from the grain boundary surface tension γ gb and pore surface tension γ s, by (Fig. 13.14) γ gb ¼ 2γ s cos

ϕ 2

ð13:21Þ

When ϕ becomes equal to the dihedral angle θ of the regularly inscribed polyhedron, for a pore located at the junction between several grains, this pore happens to have planar surfaces and densification stops (Kingery and François 1967). As an example, the polyhedron is a tetrahedron with a dihedral angle θ ¼ 70.5 , for a pore at the junction between four grains. When the angle θ is larger than this value, the pore grows, and for a smaller θ angle the pore shrinks. Planar surfaces are naturally present in boehmite platelet particles such as made in the sol-gel process of alumina, which can explain the difficulty to sinter this material.

13.5.1.2

Mobility of a Pore

A pore can move by the transport of matter which can diffuse in the surface, in the lattice, or in the gas phase inside the pore (Fig. 13.15). For each transport mechanism, it is possible to derive an expression for the pore mobility, which is defined as the ratio of the pore velocity to the force which makes it move: Mp ¼

Vp Fp

ð13:22Þ

Different expressions for the mobility of a pore could be derived, depending on the transport mechanism which operates (Shewmon 1964). Fig. 13.14 Dihedral configuration and curvature of a pore

572

13

Sintering Sol-Gel Ceramics

Fig. 13.15 Possible transport mechanisms for the migration of a pore

For surface diffusion, in a thin surface layer of thickness δs, with the diffusion coefficient Ds in a material with molar volume Vm xM SD p ¼

Ds δs V m RTπr 4p

ð13:23Þ

where R is the universal gas constant. For lattice diffusion with the diffusion coefficient DL M Lp ¼

DL V m RTπr 3p

ð13:24Þ

For diffusion in the vapor phase when the mean free path of the gas molecules is controlled by the gas pressure pv and the diffusion coefficient is Dg M gp ¼

13.5.1.3

Dg pv V m ðRT Þ2 2πr 3p

ð13:25Þ

Pore Coarsening

In Fig. 13.16a, a grain boundary comprising two spherical pores with a different radius is illustrated. The radii are rpS for the small pore and rpL for the large one. The tensile mechanical stress in the matter at the surface of the pores is larger in absolute magnitude (i.e., more negative for a tensile stress) near the small pore at point S than near the large pore at point L, because 2γ s 2γ s < r pS r pL

ð13:26Þ

13.5

Interaction of Pores with the Sintering Process

573

Fig. 13.16 Coarsening of pores by (a) Ostwald ripening and (b) grain growth

To release the tension gradient between points L and S, atoms will diffuse from point L towards point S. Consequently, the small pore will shrink while the bigger pore will grow. This mechanism is known as Ostwald ripening when it concerns the growth of solid particles at the expense of other smaller solid particles. Presently it occurs with pores, which globally tend to grow, a phenomenon also termed pore coarsening. The phenomenon of coarsening also concerns grains, as the larger grains tend to grow at the expense of the smaller ones. This is illustrated in Fig. 13.16b where the small center grain slowly disappears and induces a coarsening of the pores located at the border between three grains. These pores will merge with each other when the small center grain will disappear. Overall, in spite of the sintering process, pores tend to grow and therefore to become less mobile.

13.5.2 Action of Pores on the Grain Boundary Mobility (Brook 1969) The displacement velocity Vb of a grain boundary which drags a population of N pores per unit surface area can be written as   V b ¼ M 0b F b  NF p

ð13:27Þ

where Fb is mechanical force exerted onto the grain boundary due to its curvature, and Fp is the drag force necessary to move one pore (Fig. 13.17). When pores located at a grain boundary and the grain boundary move together V b ¼ V p ¼ MpFp

ð13:28Þ

574

13

Sintering Sol-Gel Ceramics

Fig. 13.17 Dragging force exerted by pores on a grain boundary

By equating the two expressions in Eqs. (13.27) and (13.28) for Vb, it is possible to extract an expression for Fp as a function of Fb and to report it in Eq. (13.25). This leads to Vb ¼ Vp ¼

M 0b F b 1þN

M 0b Mp

¼ M pb F b

ð13:29Þ

where M 0b is the effective mobility of the grain boundary with its pores. Two extreme situations can then be considered. On the one hand, when many pores are present, each with a mobility much lower than that of the grain boundary M 0b  M p

ð13:30Þ

then the effective mobility of the grain boundary is M pb 

Mp N

ð13:31Þ

That is to say, the pores control the grain growth and coarsening process. On the other hand when the pores are more scarce and with a much higher mobility than that of the grain boundary M 0b  M p

ð13:32Þ

then the effective mobility of the grain boundary is practically identical to its mobility without pores:

13.5

Interaction of Pores with the Sintering Process

575

Fig. 13.18 Distinction of the domains where pores retain or do not retain the grain boundary migration

M pb  M 0b

ð13:33Þ

In this case, the migration of atoms across the grain boundary controls the coarsening which is not strongly affected by the pores. An approximate borderline between these two extreme situations is given by M 0b N ¼ M p

ð13:34Þ

In a diagram where the grain size rg is plotted as a function of the pore size rp, this corresponds to a line of equal mobility of the pores and grain boundaries, which separates a domain where the pores control grain growth by slowing down the motion of grain boundaries, and a domain where the pores do not control grain growth but remain at the grain boundaries (Fig. 13.18). The position of this line depends on the most efficient displacement mechanism of the pores.

13.5.3 Abnormal Grain Growth (Brook 1969) As densification proceeds, residual pores become bigger but globally they slowly disappear, so that the drag force they can exert on the motion of grain boundaries gradually decreases. Hence, at a sufficiently advanced stage of densification, pores are eventually no longer able to limit grain growth. When this occurs, three cases must actually be considered. A first possibility is that the residual pores remain small enough and are enough mobile to keep up with the grain boundaries. In this case, they simply do not control grain growth anymore and this was addressed in the previous section. However a second possibility is that these residual pores are bigger and their mobility has decreased too much to keep up with the grain boundaries. In this case, the pores separate from the grain boundaries and remain trapped inside the grains. A third possibility is that pores which are separated from the grain boundaries could catch up again these grain boundaries, if the grain boundary mobility starts again to slow down after some time.

576

13.5.3.1

13

Sintering Sol-Gel Ceramics

Pore Separation from Grain Boundaries

After separation, no drag force is exerted on the grain boundaries so that some grains start to grow very fast, a regime known as abnormal grain growth or recrystallization (Fig. 13.19). In this case the grains grow linearly with time according to a law of the type: r g  r g0 ¼ kt

ð13:35Þ

where k is a constant and rg0 the average grain size when abnormal grain growth begins. Such a phenomenon occurs when the grain boundary velocity with its pores reaches the maximum pore velocity. At the moment of separation Vb > Vp

ð13:36Þ

Replacing Vb and Vp by their respective expressions in Eqs. (13.29) and (13.28) M 0b F b

> M p Fp

ð13:37Þ

M pFp þ N Fp M 0b

ð13:38Þ

M0

1 þ N M bp or

Fb >

In practice, pore separation can occur in conditions when Eq. (13.30) in the previous section prevails, that is to say, when M 0b  Mp. In this case, Eq. (13.38) simplifies to F b > NFp

ð13:39Þ

For instance if a grain boundary moves by atomic diffusion across the grain boundary, with the diffusion coefficient Dgb the grain boundary mobility is Fig. 13.19 Abnormal grain growth

13.5

Interaction of Pores with the Sintering Process

M 0b ¼

Dgb RT

577

ð13:40Þ

If the distance between pores dpp is proportional to the grain size rg a

ð13:41Þ

a2 r 2g

ð13:42Þ

dpp  Then the pore density is N

The local curvature of the grain boundary between two pinning pores can be 2 estimated to be ar2 so that the driving force Fb to move the boundary according g

to Laplace’s equation is Fb 

2γ sb a2 rg

ð13:43Þ

The dragging force Fp applied to a pore by a grain boundary is (Fig. 13.17) F p ¼ 2πr p γ gb sin θ cos θ

ð13:44Þ

F p, max ¼ πr p γ gb

ð13:45Þ

Its maximum value is

If Fp, Fb, and N are reported in the inequality (13.39), this gives rg >

13.5.3.2

π rp 2

ð13:46Þ

Pores Catching Up Grain Boundary

In this phenomenon, the grain boundaries have already separated from the pores but they themselves begin to slow down sufficiently, so that the pores which can still move, but more slowly by lattice diffusion of vacancies, could again join them. This last event occurs especially when impurities also contribute to slow down the motion of grain boundaries. In this case the mobility of the free grain boundary would be lower than that of a grain boundary with pores:

578

13

Mp > M 0b N

Sintering Sol-Gel Ceramics

ð13:47Þ

In this case Eq. (13.38) becomes Fb
70 MPa was found to induce no beneficial effect (Rhodes 1981).

582

13

Sintering Sol-Gel Ceramics

Besides, in sol-gel materials, grain growth occurs in the same time as agglomeration, so that it becomes difficult to discriminate experimentally between the so-called primary particles, which consist of small grains or crystallites, and the secondary particles which are agglomerates of the primary particles (Mazdiyasni 1982). As reported in Chap. 12, the specific surface area of sol-gel ceramics begins to slightly decrease in the temperature range where transition phases are formed. It then accelerates when the stable phases begin to crystallize. Globally, the specific surface area decreases in the same time as grain growth begins. For instance, in a study on HfO2Y2O3, the initial crystallite size was extremely small (1 nm). It increased to 30 nm after thermal treatment between 550 and 600  C (Mazdiyasni and Brown 1970). In the rare earth oxides Gd2O3, Dy2O3, Er2O3, and Y2O3, the drastic decrease of the specific surface area upon calcinations at 800  C coincided with a grain growth from a few nm to several tens of nm (Mazdiyasni and Brown 1971). A similar result was found for BaTiO3 (Brown and Mazdiyasni 1969). Even for a non-oxide material such as ZnS powder made by thiolysis of Et2Zn in a H2S-saturated toluene solution, the grain size increased from 0.02 to 0.1 μm during heat treatment at 800  C under vacuum (Johnson et al. 1986). It seems, therefore, that grain growth first affects the primary particles, until each secondary particle becomes one single grain. Regarding complex oxide compositions, the gel methods based on a polymerizable complex solution such as the Pechini method often produced agglomerated particles which needed to be ball milled before sintering to dense bulk ceramics. This was for instance the case of Y2O3 (Duran et al. 2002a), yttria-stabilized zirconia (YSZ) (Laberty-Robert et al. 2002), Y(Ni, Mn)O3 (Moure et al. 2003), LaCrO3 (Suda et al. 2002), and BaTiO3 (Duran et al. 2002b). To try solving this problem, Petrykin and Kakihana (2016) suggested to rather form “soft agglomerates” using short-chain hydroxylic acid as an additional reagent as reported by Hernandez and Gonzalez (2002) and to increase the citric acid/ethylene glycol (CA/EG) ratio (Hernandez and Gonzalez 2002; Laberty-Robert et al. 2002).

13.5.4.2

Monodispersed Powder Packing

Sol-gel processing is the first powder synthesis technique which made it possible to easily prepare particles with a monodisperse size distribution (Chap. 5), and hence to study the effects of such monodispersion on green powder packing and sintering. The experimental results showed that perfectly monosized spheres pack in perfectly ordered “colloidal” domains, which also displayed defects similar to the dislocations and vacancies observed in usual atomic crystals (Fig. 13.22). Each colloidal domain, or grain, could correctly be densified. However, a macroscopic sample generally comprised a large number of such colloidal grains limited by grain boundaries and Liniger and Raj (1987) showed that these grain boundaries opened during the sintering process to form flaws which were difficult to eliminate further on. Overall, monodispersed particles made it difficult to achieve a monodispersed

13.5

Interaction of Pores with the Sintering Process

583

Fig. 13.22 Ordering of monosize silica spheres made by the Stöber process (Stöber et al. 1968) and defects created. Reprinted with permission from Pierre (1998). Copyright Springer 1998

pore size distribution in the ceramic, which is the important characteristic for a good sintering behavior. Liniger and Raj also showed that these packing artifacts could be eliminated by replacing monodisperse powders by appropriate polydisperse powders as explained after.

13.5.4.3

Polydisperse Powder Packing

It would seem at first that packing small particles in the interstitial sites located between larger particles would decrease the size of the pores to be eliminated, and hence would accelerate densification. However, the situation is more complex than expected. If two types of powders with a different particle size are mixed with each other and one powder has much smaller particles than the other one, the smaller particles fit well in between the larger particles. However they densify much faster than the larger particles and they introduce sharp flaws which finally hinder the complete sintering of a green part. A large magnitude difference in the size of particles here again is responsible for the formation of an uneven pore size distribution (Fig. 13.23). On the other hand, Liniger and Raj (1987) studied the influence of the size ratio and the number ratio of bimodal sphere distributions (two sizes of spheres), on their packing distribution and densification. They found that the best theoretical packing should be realized for a radius ratio of 0.26 (Frost and Raj 1982). However, when they attempted to make such packing from spherical particles dispersed in a liquid, the mobility of the small spheres was too high in comparison with the mobility of the

584

13

Sintering Sol-Gel Ceramics

Fig. 13.23 Packing obtained with bidisperse spheres having a large size difference

Fig. 13.24 Packing obtained when mixing 50% spheres of 7 μm diameter, with 50% spheres of 5 μm diameter. Adapted from Liniger and Raj (1987)

large ones so that the two types of spheres segregated by diffusion within the liquid used for dispersion. Experimentally, they found that the best sintering packing was achieved for a radius ratio of 5/7. Moreover, when varying the number ratio of each type of spherical particles from 0 to 100%, they found that the previously mentioned “monocrystalline” packing defects observed for each extreme number ratio had disappeared for a 50–50% mixture of the two types of spheres. With the latter number proportion, a complete random liquid-like packing was formed without any grain boundaries and dislocations (Fig. 13.24). The pore size distribution of such packing was monodisperse and it densified very well.

13.6

Hot Pressing

Hot pressing is a technique which is especially useful for materials in which the coarsening rate is high. Generally, the densification rate increases with the applied pressure Pa as Pna , where the magnitude of the exponent n ranges from 1 for diffusion to more than 3 for viscous deformation. When the grain size rg increases, the densification rate decreased as r m where m ¼ 2 for atomic transport by lattice g diffusion and m ¼ 3 for grain boundary diffusion.

13.6

Hot Pressing

585

In order for hot pressing to be efficient, it is necessary to apply a pressure higher than the driving force necessary to make the pores shrink. That is to say: Pa 

2γ r por

ð13:51Þ

For industrial applications, the most efficient hot pressing technique is hot isostatic pressing, in which a uniform hydrostatic pressure is applied on all sides of a part to densify. This part needs to be previously enveloped in a metal foil, and the isostatic pressure is achieved with a gas under pressure. This is an expensive technique but it can be scaled up and makes it possible to eliminate most processing flaws. In sol-gel materials, hot pressing was first applied to silicate systems because they were prone to viscous flow densification. For instance, it was applied to alumino-borosilicate glass disks made from sol-gel powders, at a temperature ranging from 650 to 700  C (Dislich 1971). The viscous flow sintering model of Mackenzie and Shuttleworth was modified to take into account the applied pressure Pa. The results were that the relative density D(t) ¼ ρρ followed a s densification law expressed by ln ðl  Dðt ÞÞ ¼ ln ð1  D0 Þ þ

3Pa t 4η

ð13:52Þ

This model was further modified by Decottignies et al. (1978) to take into account the evolution of viscosity η with time, that is to say, the heating rate. Actually, the viscosity may change by an important extent during heating, as this was mentioned before and as illustrated in Fig. 13.25. Vasilos (1960) showed that the densification of glass powders by hot pressing between 1100 and 1200  C obeyed Murray’s law (Murray et al. 1954):

Fig. 13.25 Evolution of the viscosity as a function of the heat treatment time in a silica gel. Adapted from Decottignies et al. (1978)

586

13

d ð1  Dðt ÞÞ 3Pa 1 ¼ dt 4η dT dx

Sintering Sol-Gel Ceramics

ð13:53Þ

where dT dx is the heating rate. This result was confirmed by further hot pressing investigations on SiO2, La2O3– SiO2, and B2O3–SiO2 (Decottignies et al. 1978; Mukherjee and Zarzycki 1979; Jabra et al. 1979). Silica gels derived from alkoxides were reported to densify more easily than gels derived from hydrosols and fused glass (Fig. 13.26). Globally, the sintering temperature of multicomponent glasses made from gel was significantly lower than that of conventional processing, because the components were already mixed on a very fine scale. For instance, Dislich could make transparent pyrex® plates by hot pressing under 2800 atm between 650 and 700  C, instead of 1600  C by conventional techniques (Dislich 1971). The behavior of mullite sol-gel powders was somewhat more difficult. Performing hot pressing under vacuum was necessary to produce samples with a density of 99 to 99.5% of the theoretical density, and the final materials were not transparent (Mazdiyasni and Brown 1972). In nonsilicate systems, the application of high pressures at a given temperature improved densification to some extent. Haertling and Land (1972) studied the case of the lanthanum-modified lead zirconate ceramics, also known as PLZT. Hot pressing was applied at a temperature increasing from 900  C at the beginning of densification up to 1200  C at the end. The final material displayed a good optical transparency on dimensions of the order of 1.3 cm in height and 3 cm in diameter. Hot pressing is necessary with the non-oxide ceramics such as the carbides (e.g., SiC), even when the powder is made by sol-gel from a carbon precursor in a SiO2 gel. Some improvement could be achieved with the sol-gel powder

Fig. 13.26 Pressing time to make dense sample under a pressure of 42.6 MPa, as a function of temperature, for three types of silica powders. Adapted from Decottignies et al. (1978)

13.7

Sintering Under an Electric Field

587

since 99.5% of the theoretical density was reached after hot pressing at 2000  C when adding 0.6% BN as the dopant (Segal 1984), instead of 96% of theoretical density with conventional powder (Wei et al. 1984). Overall, many studies remain to be done to understand the hot pressing behavior of nonsilicate gels.

13.7

Sintering Under an Electric Field

13.7.1 Microwave-Assisted Thermal Treatments The technique rests on the interaction between a high-frequency alternating electric field and the dipoles present in a material. The various types of dipole materials tend to align with the changing direction of the electric field. This requires the displacement of microstructural charges for the so-called space dipoles (charges on grain boundaries, pore surface, and particle surface), the rotation of molecules with permanent dipoles and their deformation (e.g., water), the displacement of ions for ionic solids, and the dissymmetric displacement of the electron cloud about each atom for the electronic dipoles (atomic polarization) (Fig. 13.27). The ease with which each type of dipole can change direction depends on their nature

Fig. 13.27 Dependence of the real ε0 and imaginary ε00 components of the dielectric permittivity of materials, on the microwave frequency and the type of dipoles. Adapted from Kingery et al. (1976)

588

13

Sintering Sol-Gel Ceramics

and frequency of the microwave radiation to which they are submitted. These displacements induce the dissipation of heat directly inside the material, and in turn may favor mainly its crystallization at a temperature significantly lower than classical thermal treatments. Moreover, when this microwave frequency ν keeps increasing, each type of dipole will show an increasing difficulty to align with the new electric field direction at some frequency range. When such a lag occurs, the material dielectric permittivity ε can then be described by a complex permittivity, comprising an in-phase real component ε0 and an out-of-phase imaginary component ε00 . Beyond this frequency range, the corresponding dipoles stop reorienting and do not participate anymore in dielectric heating. The range of frequency where each type of dipoles stops operating is illustrated in Fig. 13.27. For instance, to help the crystallization of ionic solids, a frequency of the order of 108 Hz permits to take advantage of most type of dipoles, including the molecular dipoles from residual polar solvents for instance. For instance, in the review by Garadkar et al. (2016), a microwave oven of power 900 W and frequency 250 MHz was used. The first report on using this technique was by Gedye et al. (1986). Several teams have since used the technique to design new structures in sol-gel-derived materials, mainly oxide nanomaterials (e.g.: Bi et al. 2009; Wang et al. 2012; Nehru and Sanjeeviraja 2014; Kadam et al. 2014; Vijayalakshmi and Sivaraj 2015). A review was recently published by Garadkar et al. (2016), who detailed a number of examples, for instance ZnO nanorods with a length of the order in μm and nanoparticles in the nm range which were sintered at 500  C, by Farbod and Jafarpoor (2012). By comparison with conventional heating by heat transfer in a furnace, microwave heating is fast, the diffusion of atoms are enhanced, and hence all kinetics, crystallization, sintering, and grain growth, are accelerated. The final material microstructure is more uniform and achieved in a shorter time (Galema 1997; Macario et al. 2010; Chen et al. 2012).

13.7.2 Fast and Flash Sintering In these techniques, electrodes are pasted on each face of a material solid sample (e.g., compact green powder) to be densified, and an electric voltage difference is directly applied to the material, itself placed inside a furnace. Hence an electric current is directly passed through the material and its temperature increases. This electric current can be a continuous current, induced by a DC voltage. It can also be due to an alternating current induced by an AC voltage. In both cases, the electric current itself gradually heats the sample whose temperature TS increases and the sample heat is evacuated towards the furnace whose temperature TF increases according to a controlled heating schedule, hence which is itself reduced because of the heat internally produced inside the sample by the electric current. Overall the electric conduction in the sample contributes to internal heating of this sample, which in turn accelerates its sintering while requiring less external furnace heating, so that sintering can proceed at a lower furnace temperature.

13.7

Sintering Under an Electric Field

589

However, a major difference was observed depending on the strength of the electric field (DC as well as AC) applied to the material. For a moderate electric field, sintering is just accelerated and the technique is termed FAST sintering. But for high electric fields, a critical sample temperature TS corresponding to a critical measured furnace temperature TF can be reached where the heat internally produced in the sample by the electric current becomes so high that it cannot be dissipated, even by black-body radiation, in the furnace. Regulation of the electric current by applying a constant voltage must then be stopped and it is necessary to directly control it through the electric current intensity I itself, passing across the sample. This electric power internally produced in the sample diverges: it drastically increases as shown in Fig. 13.28, while TF remains constant. The electric current must be stopped when reaching the highest acceptable intensity. This technique is then termed FLASH sintering and was initiated by Cologna et al. (2010). The mechanism of this phenomenon is controversial, but a reasonable explanation is that a “thermal runaway” occurs at the FLASH point: as stated above, the material produces more heat energy than it can evacuate by any mean (including radiation). The phenomenon was well described for instance by Zhang et al. (2015), who listed a large number of ceramics to which flash sintering was applied. The technique can really be applied to ionic type ceramics which comprises charge anions and cations such as in Al2O3 or ZrO2. In more covalent ceramics (SiO2, SiC), it is necessary to mix some of these ionic additives. For instance, Zhang et al. (2015) applied a constant DC voltage corresponding to a constant electric field of 300 V cm1, in ZnO- and Bi2O3-doped ZnO samples heated at a rate of 5  C min1 up to 500  C. As illustrated Fig. 13.28, FLASH sintering occurred both in ZnO monocrystals and ZnO ceramic powder packing, but at a much lower furnace TF temperature for a powder packing, proving that surfaces such as particle surface and grain boundaries were important actors in the electrical conduction phenomenon.

Fig. 13.28 Measured electric power dissipation vs. furnace temperature curves for the flash sintering of pure and 0.5 mol.% Bi2O3-doped ZnO powder specimens (assuming no changes in the specimen volume in calculating electric power dissipation for simplicity) and ZnO single crystals. Adapted from Zhang et al. (2015)

590

13

Sintering Sol-Gel Ceramics

The electrical conductivity, and in turn sintering versus grain growth, is actually not directly insured by these ions, which are too tightly packed in a crystalline packing, but by the so-called charged point defects. These point defects are briefly described below with their so-called Kröger and Vink (1956) notation. They comprise atom vacancies, atom interstitials, foreign atom dopants, electrons in the conduction band of the ceramic termed “free electron,” and missing valence electrons termed “free holes.” A few of them are illustrated in Fig. 13.29. In the case of ZnO flash sintering experiments by Zhang et al. (2015), it was proposed that at the anode (+ electrode), free electrons e’ are accumulated. ZnO grain boundaries near the anode make it possible to have these free electrons react with oxygen gas from the furnace atmosphere, to create normal O site in crystalline ZnO, and Zn vacancies according to the reactions 1 2e0 þ O2 ðgasÞ $ OxO þ V 00Zn K T 2

ð13:54Þ

where KT is a thermodynamic equilibrium constant, at a given temperature T: KT ¼

00

V Zn 1=2

PO2 n2

ð13:55Þ

where n (e0 )0 is the free electron concentration. Hence, to tend reaching thermodynamic equilibrium, zinc atom vacancies are created in increasing concentration near ZnO free surfaces and grain boundaries, as free electrons keep being fed at the anode, according to

1=2 V 00Zn ¼ K T PO2 n2

ð13:56Þ

According to Zhang et al. (2015), the ZnO grain boundaries then become deficient in Zn atoms (presence of Zn vacancies), contrary to bulk ZnO which prevails inside each ZnO grain and is known to be metal excess oxide, of formula Zn1+xO (x « 1) (Tuller 1999). This in turn may explain that grain growth (coarsening) is observed close to the anode. The opposite prevails near the cathode ( electrode), which would explain that no grain growth was observed, rather a fine grain densification. A sharp transition was also observed inside the sample, from the coarsening side near the anode to fine microstructure side near the cathode. However, the types of point defects which predominate in an ionic oxide depend on the conditions, so that in some other studies grain growth was observed near the cathode side, instead of the anode side (Kim et al. 2011). The flash sintering effect was well illustrated by Charalambous et al. (2019) on 3% yttria-stabilized zirconia (3YSZ). The temperature reached inside a sample, for a given furnace temperature of 110  C, was estimated by X-ray determination of the crystalline lattice parameter. Three different values of the limit intensity were compared. The flash effect took the same time to burst (Fig. 13.30), but the

13.7

Sintering Under an Electric Field

591

Fig. 13.29 A few examples of atomic point defects and their Kröger-Vink notation

power dissipation limit achieved increased with the selected limit current density. The corresponding sample temperature according to lattice parameter data were ~1400  C, ~1800  C, and ~2000  C for respective current densities of 10, 20, and 30 A cm2. At the temperature above 1800  C, it was moreover known that abnormal grain growth occurred in this material, which was consistent with the

592

13

Sintering Sol-Gel Ceramics

Fig. 13.30 Lattice expansion and corresponding power dissipation for current limits, J ¼ 10, 20, and 30 A cm2 in 3YSZ powder ceramics for a furnace temperature, T ¼ 1100  C. Adapted from Charalambous et al. (2019)

results achieved in the flash experiments with the highest current density. The lower current density of 10 A cm2 was necessary to achieve densification with a fine microstructure. In Na2O–CaO–SiO2 glasses, the Na+ cations occupy empty holes inside the SiO2  glass networks. They can be considered as interstitial Nai atoms. Experiments on such small glass beams showed that these interstitials migrated towards the cathode under the electric field, leaving a sodium-depleted zone near the anode altogether with a localized voltage drop (Pinter et al. 2018). In turn this induced a strong electric arc flash near the anode, observable by an asymmetric luminous photoemission, much stronger near the anode, as illustrated in Fig. 13.31. Experiments on colloidal SiC powder packing, in which 5–20 wt% Y3Al5O12 (YAG) was added, were carried out by Candelarioa et al. (2017). Application of a flash sintering method resulted in a sintering mechanism via a liquid phase in a furnace operated at 900  C, but the final ceramic was porous. The use of finer particle additives also helped the liquid-phase sintering mechanism. Similarly, the technique was successfully applied to MgO–SiO2–Al2O3 glasses. But pure SiO2 glasses containing some Al2O3 never showed the flash event (Biesuza and Sglavoa 2017).

References

593

Fig. 13.31 (a) Pictures taken every 10 s using a digital camera and (b) temperature profiles along the glass beam length, relative to these images, determined with an IR thermo-camera. Time ¼ 0 s corresponds to the instant application of a DC power of 200 V, with limit current intensity of 50 mA, in furnace isothermal conditions at TF ¼ 700 10  C in a glass with weight% composition 72.2SiO2–14.3Na2O–1.2K2O–6.4CaO–4.3MgO–1.2Al2O3–0.3SO3. Photograph (a) reproduced with permission from Pinter et al. (2018). Copyright Elsevier 2018. Graph (b) adapted from Pinter et al. (2018)

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E. Liniger, R. Raj, J. Am. Ceram. Soc. 70, 843–849 (1987) J. Livage, J. Lemerle, Ann. Rev. Mater. Sci. 12, 103–122 (1982) R.L. Macario, M.L. Moreira, J. Andres, E. Longo, Cryst. Eng. Comm. 12, 3612–3619 (2010) J.K. Mackenzie, R. Shuttelworth, Proc. Phys. Soc. B 62, 833–852 (1949) K.S. Mazdiyasni, Ceram. Int. 8, 42–56 (1982) K.S. Mazdiyasni, Am. Ceram. Soc. Bull. 63, 591–594 (1984) K.S. Mazdiyasni, L.M. Brown, Am. Ceram. Soc. 53, 585–589 (1970) K.S. Mazdiyasni, L.M. Brown, J. Am. Ceram. Soc. 54, 479–483 (1971) K.S. Mazdiyasni, L.M. Brown, J. Am. Ceram. Soc. 55, 548–552 (1972) K.S. Mazdiyasni, C.T. Lynch, J.S. Smith II, J. Am. Ceram. Soc. 48, 372–375 (1965) K.S. Mazdiyasni, C.T. Lynch, J.S. Smith II, J. Am. Ceram. Soc. 50, 532–537 (1967) K.S. Mazdiyasni, R.T. Dolloff, J.S. Smith II, J. Am. Ceram. Soc., 52523–52526 (1969) C. Moure, D. Gutierrez, J. Tartaj, P. Duran, J. Eur. Ceram. Soc. 23, 729–736 (2003) S.P. Mukherjee, J. Zarzycki, J. Am. Ceram. Soc. 62, 1–4 (1979) P. Murray, E.P. Rodgers, A.E. Williams, Trans. Br. Ceram. Soc. 53, 474–510 (1954) L.C. Nehru, C. Sanjeeviraja, J. Adv. Ceram. 3, 171–176 (2014) K.H. Nii, Z. Metallkde 61, 935–941 (1970) M. Nogami, Y. Moriya, J. Non-Cryst. Solids 37, 191–201 (1980) V. Petrykin, M. Kakihana, Chemistry and applications of polymeric gel precursors, in Handbook of Sol-gel Science and Technology, ed. by L. Klein, M. Aparicio, A. Jitianu, (Springer, Cham, 2016), p. 4 G. Petzow, H.E. Exner, Z. Mettalkde 67, 611–618 (1976) A.C. Pierre, Introduction to Sol-Gel Processing (Kluwer, Boston, 1998) L. Pinter, M. Biesuz, V.M. Sglavo, T. Saunders, J. Binner, M. Reece, S. Grasso, Scr. Mater. 151, 14–18 (2018) W.H. Rhodes, J. Am. Ceram. Soc. 64, 19–22 (1981) W.H. Rhodes, R.M. Haag, High purity fine particulate stabilized zirconia (Zyttrite), Report No. AFML-TR-70-209 Prepared by Avco Systems Division for the U.S. Air Force Materials Lab., Wright-Patterson AFB, OH (1970) J.W. Ross, W.A. Miller, G.C. Weatherly, Acta Met. 30, 203–212 (1982) S. Sakka, Gel method for making glass, in Treatise on Materials Science and Technology, vol. 22, ed. by M. Tomazawa, R.H. Doremus (Academic Press, New York, 1982), pp. 129–167 S. Sakka, K. Kamiya, Preparation of compact solids Iron metal alkoxides, in Proc. Int. Symp. Factors in Densification and Sintering of Oxides and Nonoxide Ceramics (Tokyo Institute of Technology, Tokyo, 1978), pp. 101–109 M. Sathiyakumar, F.D. Gnanam, Br. Ceram. Trans. 98, 87–92 (1999) G.W. Scherer, J. Am. Ceram. Soc. 60, 236–239 (1977a) G.W. Scherer, J. Am. Ceram. Soc. 60, 243–245 (1977b) G.W. Scherer, Glastech. Ber-Glass 56, 834–838 (1983) G.W. Scherer, T.J. Garino, J. Am. Ceram. Soc. 68, 216–220 (1985) D.L. Segal, J. Non-Cryst. Solids 63, 183–191 (1984) T.M. Shaw, B.A. Pethica, J. Am. Ceram. Soc. 69, 88–93 (1986) P.G. Shewmon, Trans. AIME 230, 1134–1137 (1964) J.S. Smith II, R.T. Dolloff, K.S. Mazdiyasni, J. Am. Ceram. Soc. 53, 91–95 (1970) W. Stöber, A. Fink, E. Bohn, J. Colloid Interface Sci. 26, 62–69 (1968) C. Stosiek, H. Ludwig, U. Reichel, G. Scholz, E. Kemnitz, J. Ceram. Sci. Technol. 2, 31–38 (2011) W.I. Stuart, R.B. Adams, J. Nucl. Mater. 58, 201–204 (1975) E. Suda, B. Pacaud, T. Seguelong, Y. Takeda, Solid State lonics 151, 335–341 (2002) M.T. Tsai, H.C.A. Shih, J. Mater. Sci. Lett. 12, 1025–1027 (1993) H.L. Tuller, J. Electroceram. 4, 33–40 (1999) D.R. Uhlmann, L. Klein, P.I.K. Onorato, R.W. Hopper, The formation of lunar breccias: sintering and crystallization kinetics, in Proc. 6th Lunar Sci. Conf., ed. by R. B. Merril, vol. 1, (Pergamon Press, New York, 1975), pp. 693–705

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T. Vasilos, J. Am. Ceram. Soc. 43, 517–519 (1960) K. Vijayalakshmi, D. Sivaraj, RSC Adv. 5, 68461–68469 (2015) Z. Wang, J. Zhu, W. Xu, J. Sui, H. Peng, X. Tang, Mater. Chem. Phys. 135, 330–333 (2012) G.C. Wei, C.R. Kennedy, L.A. Harris, Am. Ceram. Soc. Bull. 63, 1054–1061 (1984) P.W. Davidge, J.L. Woodhead, Ceramic materials by sol-gel route, U.S. Patent 4,429,051—U. K. Atomic Energy Authority (31 Jan. 1984) S. Yamagishi, K. Takahashi, J. Nucl. Mater. 144, 244–251 (1987) M. Yamane, S. Aso, S. Okano, T. Sakaino, J. Mater. Sci. 14, 607–611 (1979) M.F. Yan, R.M.J. Cannon, H.K. Bowen, I.L. Chowdry, Mater. Sci. Eng. 60, 275–281 (1983) X. Yang, A.C. Pierre, D.R. Uhlmann, J. Non-Cryst. Solids 100, 371–377 (1988) B.E. Yoldas, J. Mater. Sci. 21, 1080–1086 (1986) Y. Zhang, J.-I. Jung, J. Luo, Acta Mater. 94, 87–100 (2015)

Chapter 14

Applications of Sol-Gel Processing

14.1

Introduction

Sol-gel processes are interesting from a scientific point of view as well as for new or potential industrial applications. Within this large materials science domain, aerogels have for instance become sufficiently interesting to deserve special symposia (Fricke 1986, 1992; Vacher et al. 1989; Pekala and Hrubesh 1995; Phalippou and Vacher 1998; Ashley et al. 2001) and reviews (Fricke and Emmerling 1992, 1998; Burger and Fricke 1998; Hrubesh 1998; Schmidt and Schwertfeger 1998; Husing and Schubert 1998; Chen et al. 2014; Alotaibi and Riffat 2014; Stergar and Maver 2016). In some rare examples, sols or gels can be used as final products. In many cases, however, they must be transformed to an appropriate ceramic phase with interesting technical properties, and in many cases they must be densified. In detail, a sol-gel fabrication process follows a synthesis protocol including a post-gelation treatment which depends on the end product. The products more specifically addressed in this chapter are sols and gels as final materials, coatings, fibers, monoliths, hybrid organic-inorganic materials for various applications, high specific surface area products such as filtering membranes and catalysts, and more sophisticated products such as made by templating techniques (Husing and Schubert 2002). Besides, the solid surface of these products can also be grafted with various chemical functionalities, either during sol-gel chemical synthesis (Rodembusch et al. 2005) or after gelation (Smith et al. 1992). On the other hand, powders and glasses are usually intermediate products for the applications just mentioned before. They were largely addressed in Chaps. 12 (Sect. 12.4) and 13 (Sect. 13.3) and they are not reconsidered in this chapter. The practical applications encompass a large span of fields. Some of them imply large-scale products such as in thermal insulation, while others are more involved in niche domains, such as in electronic or piezoelectric materials, in antireflective coatings, in catalysis, or in biomedical implants. This chapter does not pretend to be exhaustive. More detailed reviews have addressed all these fields, for instance in © Springer Nature Switzerland AG 2020 A. C. Pierre, Introduction to Sol-Gel Processing, https://doi.org/10.1007/978-3-030-38144-8_14

597

598

14

Applications of Sol-Gel Processing

the huge handbook of sol-gel chemistry (Klein et al. 2016), or in the aerogel handbook (Aegerter et al. 2011). But giving a flavor of all these applications brings much interest to sol-gel processing and mainly to its possible future developments.

14.2

Health Hazards

Studies on possible health hazards of sol-gel products are very limited. Such hazards probably depend on the gel’s chemical composition. However, the potential health hazards due to silica aerogels were summarized by the Aspen Company (Aspen Aerogels 2017a, b, c). The most outstanding outcome is that inhalation of amorphous silica aerogel dust does not present the dramatic risk of silicosis as occurs with crystalline silica powder, but it may induce allergy and some respiratory irritation. Regarding the biocompatibility of SiO2, it must be mentioned that this oxide is toxic for the human body when introduced under a crystalline form, responsible for lung silicosis. Nevertheless, this is a minor component in solution in blood and urine (0.6 μg mL
1 for serum and 41 μg mL
1 for muscle) so that a human body is known to contain about 7 g of SiO2 (Iler 1979; Viitala et al. 2008; Jones 2013). Contrary to the crystalline forms, porous sol-gel SiO2 carries a high density of silanol Si–OH which makes it prone to elimination through urine as silicic acid (He et al. 2008; Lu et al. 2010).

14.3

Applications in the Sol or in the Gel State

14.3.1 Sols One important application of ceramics as finished products in the sol state concerns essentially the Ferrofluids®, commercialized by the Ferrofluid® corporation, and mentioned in Chap. 6, Sect. 6.5. These products were developed around the year 1960 by NASA to control the flow of rocket fluids in zero-gravity environment (Elmore 1938; Charles and Popplewell 1980). Ferrofluid sols comprise magnetic colloidal particles such as Fe3O4 which can move when an appropriate magnetic field is applied to the sol. Because a sol is kinetically stable, the fluid in which the magnetic colloidal particles are dispersed moves altogether with these particles, and hence they can be used as transmission fluids in non-gravity. In a very different domain, mentioned in Chap. 2, alkaline silicate solutions are used as a binder of sand and of natural geological material (e.g., clay) in the so-called geopolymers, commonly applied as fireproof materials in industry such as foundry (Vidal et al. 2016).

14.3

Applications in the Sol or in the Gel State

599

14.3.2 Gels 14.3.2.1

Wet Gels

A typical application of wet gel concerns V2O5, as coating, because of the special semiconducting properties of this oxide (Michaud et al. 1976; Livage et al. 1988). This gel can be deposited as some paint in thin layers on large areas, with a thickness of 50–1000 nm. The semiconducting properties of the V2O5 gels are due to the two different valence states, +4 and +5, that vanadium can adopt, which makes it possible to transfer electrons between the corresponding energetic levels by optical (Colton et al. 1978) or by thermal (Murawski et al. 1979) activation. The mechanism of electrical conduction is typical of small polarons. These gels were patented for antistatic coatings on the dorsals of photographic films (Guestaux 1978). They are appreciated for their lower sensitivity to humidity. V2O5 gels can also be applied in electrical switching devices (Fritzsche 1974). When a voltage higher than a critical voltage Vt is applied to the device, the electrical resistance of a gel layer is low and the switch is in the “ON” state. On the other hand, the electrical resistance is high and the switch is in the “OFF” position when V < Vt. The switch also returns to the “OFF” position when the electrical current falls below a threshold Ih. For such applications, a gel layer thickness is typically of the order of 1 μm, the threshold current Ih is >50 mA, and the value of Vt ranges from 10 to 20 V depending on the (V4+) concentration. The relative proportion of tetravalent vana½V4þ  dium to total vanadium concentration ðVÞ is comprised between 0.01 and 0.04. The lowest relative (V4+) proportion corresponds to the highest Vt values. For a 50 Hz AC current, the gel characteristics were found to remain stable for at least several days. At last it is possible to intercalate organic molecules between the V2O5 atomic layers and to modify the gel properties (Fritzsche 1974; Adler et al. 1978, 1980; Aldebert et al. 1981: Livage et al. 1988). Lamellar WO3nH2O (n ¼ l or 2) gels present similar properties. In “ON” state the gel is transparent and in the “OFF” state the gel is blue (Morineau et al. 1983). Hence these gels can also be used in optical displays. Multilayer coatings could be made from such gels; they keep behaving well after many cycles and their memory is durable (Judeinstein et al. 1988). In a different domain, wet SiO2 gels found an application as media for the growth of crystalline particles (Raman et al. 1986), as mentioned in Chap. 5, Sect. 5.6. Liquid chromatography is another application in which gels with well-defined porous structure and pore surface polarity are important. For such applications, monodisperse particles were made from bridged organopolysilsesquioxane gels by emulsion polymerization (O’Gara and Wyndham 2006). They were able to support the high pressures used in modern liquid chromatographic systems. Other porous polysilsesquioxanes prepared for the same type of application were made by sol-gel spinodal phase separation, surfactant templating techniques (Guo et al. 2013), or molecular imprinting (Lofgreen et al. 2011).

600

14

Applications of Sol-Gel Processing

A special mention must also be given to random hybrid siloxane oligomers or hybrid silica gels containing Tn POSS clusters in their network (T-gels), which are considered for high-temperature lubricant applications (Jennings et al. 2016).

14.3.2.2

Dry Xerogels and Aerogels

Aerogels are generally characterized by a very high specific surface area, e.g., commonly of the order of 800 m2 g
1 (Fricke 1988). This property makes them outstanding thermal and acoustic insulation materials (Caps et al. 1989; Gronauer et al. 1986). Hence, a major domain of applications concerns the development of efficient thermal insulators (Zhang et al. 2005; Randall et al. 2011; Baetens et al. 2011; Ochoa et al. 2012; Sabri et al. 2014). SiO2 aerogel monoliths can moreover be made very transparent, and hence they are being investigated for insulation windows although their cost remains prohibitive when made by supercritical drying. The cost can however be drastically decreased when similar materials are made by drying with surfactants, which offers a real potential for such applications. Monolithic SiO2 aerogels are used in Cherenkov counters in high-energy physics (Poelz 1986a, b), because they make it possible to cover a continuous range of refractive index from 1.015 to 1.06. Before, such refractive indices were achieved with gases and liquids and aerogels are much more convenient. Tiles of appropriate dimensions, such as 20 cm  20 cm  3 cm, could relatively easily be made by supercritical drying. These types of applications above are more developed in further sections of this chapter. But more targeted different types of applications also exist, as colloidal abrasives. Such aerogel particles show for instance some insecticide properties because they remove the protecting lipid layer on insects (Loschiavo 1988).

14.4

Coatings and Thin Films

This is presently the domain where sol-gel processing is the most used, because drying stresses can be easily overcome in thin coatings.

14.4.1 Functions of Sol-Gel Coatings Sol-gel coatings can have many functions. The most frequent ones are optical, because oxides are transparent to visible light wavelengths. They can transmit, absorb, or reflect radiations with a wavelength in the visible range. They can also be used to protect a substrate against corrosion, abrasion, or scratch, and can be chemically and thermally stable or even stable against some radiation.

14.4

Coatings and Thin Films

601

The chemical applications include the possibility to improve the chemical durability of surfaces, for instance glass surfaces, by coating them with β-Al2O3 or αAl2O3 (Schroeder 1964; Partlow and Yoldas 1980). Sol-gel CeO2 coatings can also be made to protect gas-cooled reactors (Bennett et al. 1981). Some sol-gel glass coatings are used to protect against hydrolysis of special glasses sensible to water, used for instance in laser filters. A multicomponent oxide glass made by sol-gel and corresponding to reaction (14.1) was early commercialized, for the latter application (Dislich 1983): mSiðOMeÞ4 þ nAlðOBus Þ3 þ aP2 O5 þ pMgðOMeÞ2 ) Sim Aln Pa Mgp Oð4mþ3nþ5aþ2pÞ=2 ðH2 O, TÞ

ð14:1Þ

Sol-gel coatings can constitute protection barriers in both directions, for instance by stopping alkali migration towards the surface of glass sheet made by the float process. Protection barriers against the alkalis were made from the butoxide of Sb, B, Ti, and Al and deposited inside electric bulbs. SiO2–GeO2 coatings made it possible to protect non-oxide ceramics against oxidation at high temperature, by adjusting their thermal expansion to that of the substrate. The oxidation resistance of stainless steels could be improved by superposition of silica and ceria layers in which alumina colloidal particles were added (Nelson et al. 1981). The coating thickness was from 0.1 to 2 μm. Efficient sol-gel ZrO2 coating on steel was also designed (Izumi et al. 1990). Another type of oxide sol-gel-derived coating concerns ZrO2 sol made from Zr acetate hydroxide and doped with Y2O3, for coating Y2O3-stabilized ZrO2 singlecrystal substrate. Such coatings can be further crystallized to a single-crystal layer by epitaxial growth (Miller and Lange 1989; Seifert et al. 1993). Indium tin oxide (ITO), which is a transparent and electrical conductor, could also be prepared by sol-gel to coat glass panels (Werde et al. 2002; Mondelaers et al. 2002, 2003). Polysilsesquioxane gels and templated sol-gel materials were studied to make thin dielectric coatings (Castricum et al. 2014; Herzog et al. 2013; Zhang et al. 2016). Overall, sol-gel coatings can be deposited on substrates other than ceramics, such as plastics and metals, and another non-negligible advantage is that they are economical at least on simple shapes such as plates or tubing. A summary of possible functions of sol-gel coatings, depending on the substrate nature, is gathered in Table 14.1. Plastic sheets with an appropriate surface treatment gave the best results in terms of thickness, homogeneity, and bending strength. A partial list of oxide coating studied by sol-gel from alkoxides is also reported in Table 14.2. The Pechini and related polymer entrapping methods were also largely studied for the fabrication of thin films and coatings of complex oxides. Petrykin and Kakihana (2016) gave a list comprising dielectric materials for microwave and dynamic random access memory (DRAM) devices (Bianco et al. 2001; Gusmano et al. 2002), yttria-stabilized zirconia (Gorman and Anderson 2002), transparent conducting electrodes for display applications (Bernardi et al. 2002), electrochromic electrodes of Nb2O5 (Rosario and Pereira 2001, 2002a, b; Djaoued et al. 2002),

602 Table 14.1 Thin-film coatings made from alkoxides

14

Applications of Sol-Gel Processing

Substrate Glass

Metal

Plastic

Function of coatings Chemical durability Alkali resistance Mechanical strength Reflectivity control Coloring electrical conduction Corrosion resistance Oxidation resistance Insulation Surface protection Reflectivity

Effects of thin-film coatings made from alkoxides. Adapted from Sakka (1982)

Table 14.2 Partial list of sol-gel coatings made from alkoxides Composition TiO2 SiO2 SiO2 + 20% (Cu, Co, Ni, Ce) TiO2SiO2 TiO2SiO2 + 20% (Cu, Co, Ni, Fe) TiO24SiO2 88% SiO2, 5% B2O3, 2.6% Al2O3, 3.7% Na2O, 0.7% K2O 60% SiO2, 25.2% Al2O3, 0.02% MgO, 9% P2O5, 2.6% B2O3, 0.1% As2S3 62% SiO2, 30% PbO, 8% Na2O 80% SiO2, 10% Al2O3, 10% Na2O ZrO24SiO2 Al2O34SiO2 0.5% Al2O3, 93.5% SiO2

Reference Schroeder (1964) Schroeder (1964) Sakka (1982) Schroeder (1969) Sakka (1982) Nogami and Moriya (1977) Dislich (1971) Dislich (1971) Dislich (1971) Dislich (1971) Nogami and Moriya (1977) Nogami and Moriya (1977) Shinbo and Tanzawa (1976)

counter electrodes for electrochromic devices (Rosario and Pereira 2002b), dimensionally stable anodes (DSA) (Forti et al. 2001), luminescent materials (or phosphors) (Yu et al. 2003), high-Tc superconductors (von Lampe et al. 2001), catalytic coatings (Kozhukharov et al. 2003), and electrocatalytic films (Ronconi and Pereira 2001). Such films were made as self-supported films or as coating on a large variety of substrates: single crystals, metals, polycrystalline ceramics, and fine photocatalyst particles used for co-deposition. Complex shapes could also be coated, such as honeycomb catalyst monoliths (Isupova et al. 2002) or gas sensors (Yu and Choi 2002). The film deposition techniques comprised classical spin coating or dip coating, but also soft lithography such as for rare reath doped LaPO4 and YVO4 by Yu et al. (2002, 2003). A more involved coating route rests on the self-assembling of oxide nanoparticles made by non-hydrolytic sol-gel process in mesocrystals, which opens the road to the

14.4

Coatings and Thin Films

603

design of oriented films, and patterned coatings (Vioux and Mutin 2016), including monolayers. For instance, evaporation-induced self-assembly (EISA) of ultrasmall (~3 nm size) and highly soluble anatase nanoparticle sols to which a Pluronic surfactant was added permitted to deposit mesoporous titania coatings which could be converted to anatase at 450  C (Szeifert et al. 2010). Such coatings appeared to be very promising for Li-ion batteries because their structure combined an accelerated insertion of Li ion, with a high maximum capacitance. Other coatings made from non-hydrolytic sols comprise crystalline SnO2 nanoparticles with a cubic-like array of large mesopores (~20 nm) (Ba et al. 2005), tungsten oxide nanobundle coatings on alumina showing promising gas-sensing properties (Polleux et al. 2006), homogeneous metal ferrite films on flat or curved glass substrates (Bilecka et al. 2011), and transparent conducting films of ZnO and Sn:ZnO nanoparticles (Luo et al. 2013a, b), the two latter cases under microwave heating. Hybrid sol-gel materials can also provide interesting new porous membranes. As an example, polyamide-silica transparent hybrid selective membranes with a controlled pore size and hydrophilic/hydrophobic balance could be made by co-condensing polyoxazoline macromolecules and TEOS (Chujo et al. 1991). Hybrid POSS-based composite also offers some new possibility. For instance, fluorodecyl POSS-poly(methyl methacrylate) (PMMA) composites were electrospun on various surfaces to hydrophobize them (Mabry et al. 2008). At last some Si–O–C ceramics derived from preceramic polymer could also be deposited by sol-gel processing as coatings (Colombo et al. 1997).

14.4.2 Fabrication Techniques Several different techniques can be used to produce coatings from solutions, or colloidal sols. The main ones are the following (Schroeder 1969): – Dip coating, which consists of dipping the part to coat in a precursor solution, and then pulling it out: The object to be coated can also be immobilized and the solution container is moved successively up and down (Loy 2016). – Spin coating, which consists of spreading a film of the precursor solution on the part to coat which is spun: This technique applies well to cylindrical surfaces and disks (Zhang et al. 2016). – Spraying a solution on the surface to coat: However, it is a little more difficult to maintain a uniform film thickness in the desired range by this technique. But coating made by this technique and simple drying by evaporation (Castricum et al. 2014) with eventual electrochemical assistance (Herzog et al. 2013) was used for the self-assembling of templated mesoporous polysilsesquioxane gels (Loy 2016). The most frequently used technique is dip coating: it was applied on 12 m2 plates by the Schott Company (Dislich 1971). Hydrolysis was performed in an atmosphere with controlled humidity once the plates were pulled from the sol. Next, they were

604

14

Applications of Sol-Gel Processing

heat treated at a temperature ranging from 400 to 500  C. It was necessary to control the diffusion, first of the incoming water used for hydrolysis, and second of the outcoming condensation products, in order to achieve uniform, homogeneous, and dense coatings. The sol or solution in which the part to coat is dipped can consist of a polymeric solution derived from alkoxides, a solution of metal salts with volatile anions in an organic solvent, or a colloidal sol. For a good control of the process, it is desirable to choose a precursor solution with the following qualities: a high solubility of the precursors, a good fluidity, constant properties in time, a good wetting property on the substrate to be coated, a gelation behavior without heterogeneous precipitation, and a transformation to an oxide film with a good adherence to the substrate. In some cases, the coating solutions can be made by dissolution of a solid. Chalcogenide glasses such as As2S3, As2Se3, and GeSe2 are soluble in lowmolecular-weight amines (Almeida and Xu. 2016; Chern and Lauks 1982, 1983; Santiago et al. 1987) and they can be sprayed or dip coated on substrates under a dry inert atmosphere to avoid the incorporation of O or OH ligands. Other sulfide solutions made by this method comprised molybdenum disulfide (MoS2) by Pütz and Aegerter (1999) and antimony sulfide Sb2S3 made by a similar method from SbCl3 complexed with tartaric acid (O’Brien and McAleese 1998) or glacial acetic acid (Grovzdanov et al. 1994). But colloidal sols are often used as coating fluid media. This was for instance the case with colloidal sols made from GeCl4 thiolyzed with H2S in toluene, used to deposit GeSx films by Xu and Almeida (2000a, b). Other sulfide colloidal sols studied for waveguide coatings comprised As, Cd, and Sb sulfides (Guiton and Pantano 1988; Tomas et al. 1995; Grovzdanov et al. 1994; Desai and Lokhande 1995; Xu and Almeida 2000a, b; Almeida and Xu 2000). The surface to be coated must be cleaned and a constant pulling rate must be maintained. A coating operation is usually implemented at a temperature, 10 nm

1–100

A few nm

Adapted from Burggraaf et al. (1989)

Fig. 14.7 Schematic representation of a membrane reactor for syngas production and possible ionic conduction mechanism in the YSZ electrolyte. Adapted from Guizard et al. (2016)

Important domains of application of catalytic sol-gel membranes concern membrane reactors (MR) applied to perform chemical reactions or energy conversion. In these processes, the reactions involved directly occur inside the membrane which must be designed to display a best catalytic activity (Julbe et al. 2001). The complex oxides involved, feasible by sol-gel, comprise oxygen ionic conductors with a perovskite structure, such as lanthanum cobaltites, or fluorite-structured zirconia and bismuth oxides, applied in ceramic ion conductive membranes (CICM), which permit to separate oxygen from air for small-scale oxygen production equipments as well as large-scale production of oxygen-enriched air. A first important domain concerns the partial oxidation of light hydrocarbons, such as the synthesis of the so-called syngas which is a mixture of CO + H2 obtained by transformation of methane CH4 (Kilner et al. 1997), with membrane designs such as illustrated in Fig. 14.7. Another even more important domain of application concerns fuel cells. These can be of the type “solid oxide fuel cells” (SOFC), for which yttria-stabilized zirconia (YSZ) is a favorite electrolyte membrane material (Fig. 14.8a). Or they can

14.8

Thermal and Acoustic Insulation

623

Fig. 14.8 Schematic principle of fuel cells: (a): Solid oxide fuel cell (SOFC); (b) direct methanol fuel cell (DMFC). Adapted from Guizard et al. (2016)

be based on proton-conducting membranes, such as proton- and lithium-conducting hybrid membranes (Popall and Du 1995; Depre et al. 2000; Honma et al. 2002) (Fig. 14.8b) or complex perovskite oxides of composition SrCe1–xYbxO3 and BaCe1–xYxO3 (Iwahara et al. 1981).

14.8

Thermal and Acoustic Insulation

The acoustical properties of silica aerogels are closely related to their thermal insulation properties. They are mainly due to the high porosity of these materials.

624

14

Applications of Sol-Gel Processing

14.8.1 Thermal Insulation Expensive transparent and thermal insulating SiO2 aerogel monoliths were studied for window insulation. Transparent window glazing, derived from sintered aerogel with enhanced mechanical properties, was also proposed (Gao et al. 2015). As a consequence of their transparency and refractive index close to that of air, SiO2 aerogel coatings on solar cells permitted also to attenuate the Fresnel scattering losses and to improve their efficiency (Hrubesh and Poco 1995). Similarly, cladding films with a thickness of the order of 20 μm on optical fibers permit to increase the light trapping fraction by a multiplication factor of 4 (Sprehn et al. 1997). The thermal conductivity of silica aerogels, which can be as low as ~0.013 W m
1 K
1 (Baetens et al. 2011), is significantly lower than the conductivity of air under the same conditions (~0.025 W m
1 K
1) or of various traditional insulating materials such as fiberglass, cellulose, polystyrene, and polyurethane (from 0.020 to 0.050 W m
1 K
1 with occluded gas for some of them), although they remain higher than that of standard vacuum insulation panels (VIP) (0.004–0.008 W m
1 K
1) (Alotaibi and Riffat 2014). However, when evacuated at a pressure under 50 mbar and when opacified to limit radiative transfer, silica aerogels can be produced with thermal conductivities as low as 0.004 W m
1 K
1. Silica aerogels can also be made highly transparent in the solar spectrum. Provided that they can be mechanically reinforced, the combination of this characteristic with a low thermal conductivity opens to silica aerogels amazing applications for transparent insulating components and daylighting devices, such as in windows illustrated in Fig. 14.9 and solar collector covers, translucent roofs, building facades, or translucent solar walls, as illustrated in several architectural experiments (Wolff et al. 1989; Quenard et al. 1998; Baetens et al. 2011; Riffat and Qiu 2013; Saboktakin and Saboktakin 2015; Kieran Timberlake 2017; Kalwall 2017; Souayfane et al. 2018). Regarding granular aerogels, the thermal conductivity depends on the granule compression. Typical values range from 0.024 W m
1 K
1 for an aerogel packing density of 88 kg m
3 to 0.013 W m
1 K
1 for a density of 150 kg m
3 (Neugebauer et al. 2014). Thus, silica aerogels are among the best known thermal insulating materials (Yoldas et al. 2000). Besides, silica aerogels are nonreactive and nonflammable (TAASI Aerogel 2017). Commercial products were classified as a class B-s1, d0 material, regarding reaction to fire in compliance with the European norm EN 13501-1 (LNE Laboratoire de Trappes 2012). The most common aerogel insulation products are blankets or granules. An inexpensive aerogel powder made from sodium silicate (water glass) and termed Basogel® was developed by BASF (Herrmann et al. 1995) and an expandable product used to insulate pipes and termed “nanogel” by Cabot Aerogel (Massachusetts, USA). Various aerogel granules are also available with a higher density up to 180 kg m
3 and a thermal conductivity as low as 0.012 W m
1 K
1 (Fortlan Dibi 2017; Souers et al. 1975; Aktarus Group 2017; Aspen Aerogels 2017b; Cabot 2017). An example of aerogel granules is shown in Fig. 14.10. Granules can be packed inside the cavity

14.8

Thermal and Acoustic Insulation

625

Fig. 14.9 Large monolithic silica aerogel monoliths integrated in demonstration window prototypes. Reproduced from Pierre and Rigacci (2011). Courtesy of K.I. Jensen and J.M. Schultz, DTU, Lyngby, Copenhagen, with permission from Rigacci. Copyright Springer 2011. See also similar photographs in Jensen et al. (2005) Fig. 14.10 View of silica aerogel granules. Courtesy of Rigacci A. (MINES ParisTech, PERSEE, Sophia Antipolis, France). Reproduced with permission from Rigacci. See also Pierre and Rigacci (2020 to be published)

of double-glazed windows to substantially reduce the thermal transmittance for a multilayer wall without excessively affecting their visible transmittance (Berardi 2015; Gao et al. 2015; International Organization for Standardization 2017) as well as bricks (Wernery et al. 2017). Silica aerogel granules are now quite intensely studied for the development of brand new rendering systems for building retrofitting (Stahl et al. 2011; Ibrahim et al. 2014, 2015; Wakili et al. 2018).

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14

Applications of Sol-Gel Processing

Blankets made by impregnation of nonwoven textiles with aerogels, which remain flexible after drying, were developed by Aspen Aerogels (2017c). As silica is amorphous, these blankets do not present health risks by inhalation such as crystalline species (Baetens et al. 2011). Rolls and panels of aerogels for buildings have a practical density of 70–150 kg m
3, a thermal conductivity of 0.012–0.015 W m
1 K
1 which is much lower than traditional materials, and a water vapor resistance factor “μ” of 5.0–5.5 (Baetens et al. 2010; Schiavoni et al. 2016). However, presently, these aerogel products are only under test (Jelle 2011; Mitchener 2014). Aging and long-term performances must now be carefully studied (Nosrati and Berardi 2017). In selective solar energy collectors, silica aerogel can be used as a selective transmitter layer, able to transmit the sunlight to an absorber while reducing infrared thermal losses (Reim et al. 2004; Weinstein et al. 2015). Silica aerogel finds further applications in various clothing, designed to work at low temperatures (e.g., cold storage rooms in the food industry), in clothing for diving, as part of aeronautical and aerospace gear, and also in firefighter suits, which have to be resistant to very high temperatures (Qi et al. 2013; Shaid et al. 2014). They can also be applied to thermally insulated cooling or heating systems, including piping (Husing and Schubert 1998). Besides, they find ever-increasing use as thermal insulator in the military, aeronautical, or aerospace domains, for maintenance of temperatures in a wide temperature range (from
78 to 650  C) (Fesmire and Sass 2008; Randall et al. 2011; Sabri et al. 2014). They were for instance used in the recent PATHFINDER MARS mission to insulate the Sojourner Mars Rover. During the mission, the nocturnal temperature dropped down to –67  C while a stable inside temperature of 21  C was maintained. This permitted to protect the Rover’s very sensitive electronics from damage by the cold. For a similar program termed European Retrieval Carrier (EURECA) satellite, the use of aerogels was also investigated (Tsou 1995). Other minor applications concern new furnace crucible aerogel, which permits a better control of the temperature gradient required to grow monocrystalline metals or semiconductors (Tscheuschner and Ratke 1999) or simply metal-casting molds (Steinbach and Ratke 2007). New aerogel materials are currently being tested and developed in order to improve the thermal insulation and to simplify their production and handling, as reported in an example by Hayase et al. (2014). Besides SiO2 aerogels, polyacrylonitrile (PAN) (Gouerec et al. 1999) or polyisocyanate (Biesmans et al. 1998) gels are very interesting for practical applications. They can be turned into heavily cross-linked polyurethane (PUR), polyurea, polyurethane imine, or polyisocyanurate (PIR) aerogels and provide new thermal insulation material with good insulation characteristics both under evacuated and ambient conditions. At last, instead of insulating from heat sources, more complex aerogel compositions were designed to do the opposite. This is the case of thermites able to produce heat by an exothermic reaction (Gash et al. 2008).

14.9

Optical Applications

627

14.8.2 Acoustic Insulation The acoustic propagation in aerogels depends on the interstitial gas nature and pressure, the aerogel density, and more generally the texture (Forest et al. 1998; Putselyk et al. 2003). Silica aerogels are indeed excellent acoustical insulators. The propagation of an acoustic wave is attenuated both in amplitude and in velocity because the wave energy is progressively transferred from the gas to the aerogel solid network, over the entire aerogel piece thickness (Conroy et al. 1999). The longitudinal acoustic velocity is typically of the order of 100 m s
1 and can be as low as 90 m s
1 (Sai et al. 2013; Schiavoni et al. 2016; Gross and Fricke 1992; Chen et al. 2014), which makes silica aerogels suitable for applications in acoustical devices (Venkataraman et al. 2014; Wang et al. 2010a, b; Buratti et al. 2014). In details, studies on 3He-filled aerogel at different pressures showed that the sound transmission mode in aerogel was complex and depended on the pressure and temperature (Putselyk et al. 2003). Aerogels and alcogels also display different acoustical behaviors: in alcogels, the longitudinal wave velocity is similar to that in alcohol, significantly lower than the velocity of air. On the other hand, the sound propagation in both alcogels and aerogels can be quantitatively described by Biot’s model in terms of velocity and qualitatively in terms of absorption, when the aerogel is filled with a gas other than air. This model takes into account the solid, fluid, and skeletal contributions (Forest et al. 1998).

14.9

Optical Applications

14.9.1 Optical Transparency of Silica Gels The transparency of SiO2 aerogel was already reported in the preceding Sect. 14.7 regarding thermally insulating transparent windows. But the nature of this transparency deserves more description. In spite of their high porosity, aerogels can be quite transparent because their texture is composed of solid colloidal particles and pores which have a size smaller than the visible light wavelengths. A first review of this subject was published by Pajonk (1998). More recent works comprise those of Buzykaev et al. (1999), Danilyuk et al. (1999), Venkateswara Rao et al. (2001), Jensen et al. (2004), Schultz et al. (2005), and Adachi et al. (2005). However, silica aerogels tend to scatter the transmitted light to some extent, which reduces their optical quality (Duer and Svendsen 1998). The Rayleigh scattering due to the solid gel network heterogeneities in the nanometer range is responsible for a yellowish coloration of silica aerogel observed in transmission, and a bluish coloration when observed in reflection mode against a dark background. The scattering due to heterogeneities in the micrometer range is responsible for a blurred deformation of optical images (Husing and Schubert 1998).

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14

Applications of Sol-Gel Processing

Fig. 14.11 Hemispherical (τh) and diffuse (τd) normal transmittances of 1 cm thick plates of silica aerogels synthesized by a two-step process, from prepolymerized P750 silica precursors made by PCAS, Longjumeau, France, with a precursor volume fraction in a solution of 0.5, dried by a supercritical CO2 method. Adapted from Pierre and Rigacci (2011)

An efficient technique to improve this optical transparency for use in optical devices is the so-called two-step procedure mentioned in Chap. 3: acid-catalyzed hydrolysis followed by base-catalyzed condensation (Venkateswara Rao et al. 1998) (Fig. 14.11). Typically, aerogels made from TMOS in methanol can be obtained with an optical transmittance ratio up to 93% (for ~1 cm thick aerogels) at a wavelength of 900 nm (Tajiri and Igarashi 1998; Venkateswara Rao et al. 1998) and typically up to 90% together with specific extinction coefficient of the order of 15 m
1 (Rigacci et al. 2001) can be obtained with 1 cm thick aerogels synthesized with prepolymerized precursors. It permitted to tune their refraction index in a range from 1.01 to 1.03, very convenient for applications in Cherenkov counters, by the Teichner group (Cantin et al. 1974).

14.9.2 Cherenkov Counters Cherenkov counters constitute another case where monolith transparent SiO2 aerogels brought some significant improvement. This is due to the fact that the

14.9

Optical Applications

629

refractive index “n” of silica aerogels increases with their density ρ (kg m3) according to Eq. 14.10 (Sumiyoshi et al. 1998): n
1 ¼ 2:1  10
4 ρ

ð14:10Þ

Hence, given the very light density of SiO2 aerogels, n can be very close to 1 in these materials (Poelz and Riethmueller 1982) which makes them excellent to be applied in the radiator of Cherenkov counters (Yokogawa and Yokoyama 1995) such as in the type illustrated in Fig. 14.12. The synthesis of silica aerogel monoliths for Cherenkov counters was already mentioned above in the section on aerogel monoliths. In such counters, the radiator is a low-density medium such as an aerogel slab, in which electrically charged elementary particles travel with a velocity “v” higher than the velocity of light “c” and from where they radiate (emit) photons. An analysis of these photons can therefore be used to derive the velocity of the particles and hence their nature. This was one of the well-known historical uses of silica aerogels. Kharzheev published a recent review on the use of silica aerogels, for this type of application, with a description of their optical and physical characteristics (Kharzheev 2008). Moreover, a summary of the operational experience from 1998 to 2007, with silica aerogel tiles used in RICH-type Cherenkov counters, for the HERMES experiment at the DESY-HERA facility, was published by De Leo (2008). The aerogel optical quality was characterized by its light attenuation wavelength Λ at 400 nm. This characteristic is defined as the distance into an aerogel, where the probability that a photon having this wavelength will not be absorbed has dropped by 1/e (where e ¼ 2.71828). Clearly, this property depends on the aerogel density and it increased historically from Λ  1 cm in the 1980s to 2 cm in the early 1990s, to reach ~4.5 cm in recent larger aerogel tiles (20  20  4 cm3). Fig. 14.12 Principle of an aerogel Cherenkov counter with wavelength shifter readout. Adapted from Poelz (1986b)

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14

Applications of Sol-Gel Processing

Cherenkov counters entered in a very active applied use during the last decade. Tens of publications were dedicated to the results obtained with such counters. For instance, Tabata et al. (2016) developed the massive production of large-area (18 cm  18 cm  2 cm), high refractive index (n ~ 1.05) hydrophobic and transparent silica aerogel tiles, dried by the CO2 supercritical method, for use as Cherenkov radiators in the Belle II experiment at the Japanese High Energy Accelerator Research Organization (KEK).

14.9.3 Luminescent Materials When, in a material, electrons are excited to a higher energy level than their initial energy level by a method other than heat, these excited electrons may spontaneously emit a photon when falling back to their lower energy. The corresponding emitted light is termed luminescence and the material is generally termed a phosphor. In luminescence, the excitation step may be caused by various means: chemical reactions, electrical energy, subatomic motions, or stress on a crystal. When this is caused by heat, the phenomenon is termed incandescence. In details, luminescence gathers two types of different phenomena: phosphorescence and fluorescence. In phosphorescence, the emitted light intensity decays relatively slowly (in >1 ms), while in fluorescence the emitted intensity decays much faster (tens of ns). Phosphorescence is mostly used in radar screens and fluorescent materials in cathode ray tube (CRT), plasma video display screens, fluorescent lights, sensors, and white LEDs. The Pechini method was used to synthesize high-luminescence-intensity phosphor materials in which dopants could be uniformly dispersed (Harada et al. 2001; Lima et al. 2002; Serra et al. 2000). Yttrium aluminum garnet (YAG) for laser applications was also made by this technique. Eu2+-doped BaZrSi3O9 phosphor materials made from 1,3-butanediol-modified silane (1,3-BGMS) showed photoluminescence spectra with an internal quantum efficiency (IQE), which is the ratio of photons hitting and being absorbed by the phosphor surface that produce electrons, of 66.1% and external quantum efficiency (EQE), which is the ratio of total photons hitting the phosphor surface that produce electrons, of 52.9%, under excitation at 300 nm (Kobayashi et al. 2016). Complex green-emitting phosphors of Ce3+-doped Ca3Sc2Si3O12 (CSS) were also made by a similar process. Efficient phosphors were also made by a polymerizable complex method, using glycolconjugated phosphates and cations chelated by a carboxylic acid, such as Eu2+doped KSrPO4 and Eu2+-doped LiCaPO4 (Kim et al. 2013, 2014). Fluorides made by a fluorolytic sol-gel process present a great interest for a number of important technical applications in optics. These include solid-state lasers, luminophores, scintillators, optical amplifiers, and optoceramics, besides antireflective coatings which were mentioned before (Kemnitz 2016). A high concentration of rare earth elements can be dissolved in heavy-metal fluoride and oxyfluoride glasses. The doping of fluoride sols made by fluorolytic sol-gel processing with a high ratio of rare earth was therefore studied and it permitted to

14.9

Optical Applications

631

achieve excellent luminescent properties. For instance fully transparent sols of crystalline rare earth-doped (Eu3+ and Tb3+) CaF2 nanoparticles showed a whole range of coloration, from green to red, depending on the rare earth and its concentration, when illuminated under a radiation of 366 nm (Ritter et al. 2014). Fluorides are moreover characterized by a low phonon energy, which in turn favors an increased amplification and upconversion of lasers. Hence these glasses appear as an excellent host of such dopants for application in lasers. The combination of a high specific pore volume with some specific cases in a relatively resistant solid SiO2 network can also be advantageously used to encapsulate a very large span of molecules, such as photoluminescent dopants (Charlton et al. 1992; Bockhorst et al. 1995; Shen et al. 1998; Leventis et al. 1999; Zhou et al. 2000; Barnik et al. 2000) for applications in optical display equipment or lanthanides for lasers (Tillotson et al. 1994). However, fluorides have a lower chemical stability than oxyfluorides and they are difficult to be made as mixed thin sol-gel films in SiO2, because of a fast gelation of the silicate component catalyzed by the F
. To try solving this problem, the synthesis of transparent glass ceramics with fluoride nanoparticles in a silica matrix was studied (Fujihara 2016). This is the case of Er3+–Yb3+-co-doped SiO2-LaF3 glass-ceramics prepared by the TFA method, which appears to be very promising as a UV laser source for optical data storage and compact disk industry (Biswas et al. 2003). Efficient upconversion emissions at 379, 407, 450, 490, 520, 540, and 660 nm were observed under the 973 nm excitation. Ba2+ and Eu2+ ions have similar ionic radii and the same configuration of their outermost electrons (5s2 5p6). Hence inorganic fluoride compounds containing barium are good host materials for luminescent Eu2+ ions, which is possible by applying the trifluoroacetic acid (TFA) technique which permits to reduce Eu3+ to Eu2+ by appropriate thermal treatments. Strong blue-violet photoluminescence (PL) under UV excitation at 290 nm using a Xe lamp could be achieved, for instance in BaMgF4:Eu2+ films, as shown in Fig. 14.13. Strong photoluminescent red phosphor thin films of LaOF, SmOF, ErOF, Sm4O3F6, or Er4O3F6 doped with Eu3+, very transparent in the visible spectra, were also prepared by the TFA sol-gel route. They are very interesting for coating application of optoelectronic devices such as flat-panel displays and solidstate white lighting (Fujihara 2016). At last other types of material such as core-shell CdSe/ZnS gels showed a high photoluminescence emissivity even when excited under UV (Brock and Yu 2011).

14.9.4 Optical Coatings The application of sol-gel as coatings was summarized in Sect. 14.4. But many of these coatings were for optical applications, which deserve to be examined in more details (Schroeder 1964, 1969; Dislich et al. 1982; Dislich and Hussman 1981; Segal 1984; Zelinski and Uhlmann 1984). A partial list of single-oxide films with their optical absorption characteristics is given in Table 14.8 and it includes the chemical precursor from which they were made.

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14

Applications of Sol-Gel Processing

Fig. 14.13 Photoluminescence spectra (excitation and emission) of Eu2+-doped BaMgF4 blue phosphor thin film prepared by the trifluoroacetate-based sol-gel method. Adapted from Fujihara (2016)

Table 14.8 Optical characteristics of single metal oxide coatings Oxide A12O3 CeO2 HfO2 In2O3 La2O3 Nd2O3 PbO Sb2O4 SiO2 SnO2 Ta2O5 ThO2 TiO2 Y2O3 ZrO2

Favored precursor A1(NO3)39H2O Al(OBus)3 Ce(NO3)36H2O HfOCl28H2O In(NO3)3 La(NO3)3 Nd(NO3)3 Pb(CH3COO)2 SbCl5 Si(OR)4 SnCl4 TaCl5 ThCl4 Th(NO3)4 TiCl4 Ti(OR)4 Y(NO3)3 ZrOCl2

Adapted from Schroeder (1969)

Refraction index n 1.62

Absorbing below (nm) 250

Structure Amorphous Crystalline Crystalline Crystalline Crystalline

2.11 2.04 1.95 1.78 Inhom. Inhom. 1.90 1.455 Inhom. 2.1 1.93

400 220 420 220 380 340 205 350 310 220

Amorphous Crystalline

2.3

380

Crystalline

1.82 1.72

300 340

Crystalline

Amorphous

Crystalline

14.9

Optical Applications

633

For instance, TiO2 coatings are valuable as solar shields on glass (Yoldas and O’Keefe 1979; Zelinski and Uhlmann 1986). TiO2 is a well-known semiconductor which can absorb UV radiations due to its band gap: 3 eV and 3.2 V, respectively, for rutile and anatase, which corresponds to absorption edges at 413 nm and 388 nm, respectively. Its electrons can absorb UV and be excited to the above band gap, creating a pair of free electrons-holes. These excited electrons and holes can further be captured by other holes or electrons, for instance in the materials which surround TiO2, a mechanism which explains both the UV absorption characteristics and photocatalytic activity, examined later on (Yang et al. 2004). Besides TiO2, bulky chromophores were also incorporated in the gel network of polysilsesquioxanes, such as porphyrin-bridged monomers, to design surfactanttemplated photovoltaic thin films (Li et al. 2013a, b). Monomers used in commercial sunscreens to absorb ultraviolet light were also made by modifying reactive coupling agents with nucleophilic substituents. Coupling of the sunscreen reactive component to the gel network can impede this component from migrating into the human body and the sunscreen component also gains a much longer lifetime (Tolbert et al. 2016). In the applications of sol-gel to make antireflective films, the film thickness can be correctly adjusted by the technique of dip coating presented further on, while the sol composition makes it possible to monitor the refractive index. It is possible to adjust the visible light absorbency without changing the antireflective qualities by embedding palladium in TiO2. The TiO2–SiO2 system was also well studied (Brinker and Harrington 1981): such materials have been used by the “Deutsche Spezialglas AG” company to make coatings, since 1964. More recently, the Sandia and Westinghouse companies applied them to silicon solar cells, while the Battelle Institute applied them on laser lenses to control nuclear fusion (Dislich 1971). The coatings made by sol-gel are even more resistant to bombardment than the previous coatings and their resistance to alkalis can be increased by incorporating some ZrO2, itself made from alkoxide. The first wide-band antireflective coatings from multicomponent oxides were made in the SiO2–Na2O–B2O3 system where phase separation occurred. The most soluble phase was leached out with the help of an acid. The final microporous material was outstanding to concentrate high-power laser beams in nuclear fusion experiments and could withstand a laser bombardment of 21 J m
2 instead of 5 J m
2 for similar materials made by conventional techniques. Similar results were achieved with the composition SiO2–Al2O3–CaO–MgO–Na2O, by the Schott Company (Dislich 1983). Brinker and Pettit (1983) also quoted the composition BaO–Al2O3–B2O3–SiO2. Antireflective sol-gel laser coatings were also developed in France, by the CEA society. They were made of porous silica monolayer coatings with a thickness of 4λ or of two-layer coatings comprising a methyl silicone layer and a porous silica layer (Floch et al. 1989). Tin-doped indium oxide coatings (or ITO) can also be made by sol-gel (Dislich and Hussman 1981). They are very transparent to visible solar radiation but they reflect the long-wave infrared radiation. Consequently, they can be used in heat mirrors. They let the visible solar light enter through a glass window but they keep

634

14

Applications of Sol-Gel Processing

the heat inside. Their thickness was 1 μm at most and the sol-gel processes make it possible to prepare them more simply and more rapidly than other techniques. Other valuable optical coatings made by sol-gel include PLZT films for optoelectronic applications and transparent electrically conductive films of Cd2SnO4, made from Cd acetate and Sn alkoxide. The sol-gel technique made it possible to avoid the formation of phases such as SnO2, CdO, and CdSnO3, which limit the conductive properties. The formation of these phases cannot be avoided in conventional techniques, including the technique of cathodic sputtering. To the above oxides, we must add discrete POSS considered for application in optics (Hartmann-Thompson 2011), in particular ladderlike POSS as optical fiber coating (Xie and Zhang 1997; Zhou et al. 2008) and polymethylsilsesquioxane coatings (Dislich and Jacobsen 1973; Baney et al. 1995). Oxide sol-gel materials are not the only materials considered for applications as optical coating. Fluorides are chemically stable, mechanically strong, and highly transparent over a broad spectral range from the UV to IR. Hence they found various applications in optical devices. In particular, AlF3, MgF2, and CaF2 are among the inorganic materials with the lowest refractive indices. Their fluorolytic sol-gel synthesis permitted to make thin homogeneous antireflective films, even better than the dense fluorides, in part also due to their microporosity (Noack et al. 2012; Hegmann and Löbmann 2013). The refractive index of a transparent polymer matrix in which they were dispersed could be tailored in some range by selecting an appropriate nanoparticle content, as illustrated in Fig. 14.14. Solid metal fluorides are characterized by an optical transparency in a broad window (0.3–7 μm), from infrared (IR) to ultraviolet (UV) (Fujihara 2016). They are also ionic conductors due to the fluorine anions. Hence they find important technological applications in infrared (IR) optical components, ultra-low-loss optical fibers, high-power lasers, sensors, and solid electrolytes (Gan 1995; Poulain 1995). They are also interesting as ferroelectrics, magnetic materials, semiconductors, and catalysts (Fujihara 2016). In particular, alkaline earth fluorides (MgF2, CaF2, SrF2, and Fig. 14.14 Refractive indices of thin-film coatings based on magnesium and aluminum fluoride with different filler contents in a matrix of poly (1,4-BDDMA) determined by ellipsometry. Adapted from Noack et al. (2013)

14.9

Optical Applications

635

Fig. 14.15 Illustration of an AR coating on an optical component

BaF2), rare earth (RE) fluorides (LaF3, NdF3, GdF3, etc.), and rare earth oxyfluorides (REOF) are very interesting materials for optical applications in luminescent materials or as solid electrolytes (Nakajima et al. 2000). The principal application of sol-gel-made glassy fluorides and oxyfluorides is in the optical field, mainly as antireflective (AR) coatings. CaF2 altogether with SiO2 can provide very important optical coating in the ultraviolet (UV) spectra, including deep ultraviolet (DUV) and vacuum ultraviolet (VUV), for instance for high-power laser systems (Gogoll et al. 1996; Mizuguchi et al. 1998; Wang 2000; Liberman et al. 1999). For a single-layer AR coating illustrated in Fig. 14.15, complete antireflection is attained under the following conditions in Eq. (14.11): n21 ¼ n0 n2 and n1 d ¼

λ 4

ð14:11Þ

In this equation, n0, n1, and n2 are the refractive index of the air, the coating, and the coated component, respectively, while d is the coating thickness and λ is the wavelength of incident light (Pulker 1999). For example, to coat SiO2 glass (n2 ¼ 1.51) or CaF2 single crystal (n2 ¼ 1.47) for a KrF laser emitting at λ ¼ 248 nm, it is necessary to select coating materials with a refractive index n1 < 1.22 (Nikogosyan 1997). To reach such a low refractive index n1, it is necessary to produce a porous coating which only the sol-gel technique is able to achieve, because the refractive index of materials decreases as the porosity increases according to the extended Lorentz–Lorenz formula (Brinker and Scherer 1990):  1
p¼

n2dense þ 2 n2dense
1

 

n2porous
1 n2porous þ 2

 

ð14:12Þ

636

14

Applications of Sol-Gel Processing

Sol-gel porous thin films of SiO2–BaMgF4 transparent glass ceramics doped with Eu2+ were also made by the TFA process. The BaMgF4 nanocrystallites could be selectively and homogeneously doped with Eu3+ by in situ fluorination with dimethyl fluoride (DMF), added in the solution. These films exhibited a blue emission centered at 420 nm under UV excitation at 290 nm and they are considered for application as phosphors for solid-state white lighting (Fujihara et al. 2003). Chalcogenide glasses constitute another class of materials presenting interesting optical transmission properties in the infrared domain. The main compounds involved comprise As2S3 and GeS2 optical films for application in planar waveguides, optical interconnects, and “dense wavelength division multiplexing” (DWDM) devices for optical communications with silica fibers (Almeida et al. 1999; Orignac et al. 1999; Almeida and Xu 2016). Such sulfides also present a high solubility of rare earth dopants, lower vibrational energies, high refractive indices which results in high radiative transition rates, and large emission cross sections (Lucas et al. 1996; Marchese et al. 1996; Ballato et al. 1997). In an example, porous GeS2 films were prepared by spin coating GeCl4 thiolyzed sols by Xu and Almeida (2000a, b). Their thickness was in the range from 20 nm to 1.31 μm and their refractive index at 633 nm in the range of ~1.9–2.8. Their exact characteristics depended on their final porosity and residual oxide content. ZnS is another important optoelectronic material finding applications in infrared window and, when doped, as a phosphor and component of light-emitting diodes (LEDs) (Almeida and Xu 2016). Pt2(Ge4S10) Zintl cluster aerogels themselves present IR optical transmission in the visible to infrared spectrum (Brock and Yu 2011).

14.9.5 Nonlinear Optics Hybrids comprising polymers weakly bonded to an amorphous oxide sol-gel matrix can be made transparent, colorless, and homogeneous and with good mechanical properties and a controlled hydrophilic/hydrophobic balance (Chujo and Saegusa 1992). Their porosity is moreover adapted to the embedding of optical active molecules such as rhodamine 6G, rhodamine 640 and coumarin 4, photochromic spiropyrans, or nonlinear optics (NLO) molecules such as phthalocyanine, to provide new optical properties (Avnir et al. 1984; Dunn and Zink 1991). The synthesis of hybrid materials with NLO properties can be achieved for instance by the technique of simultaneous gelation of a modified silicon alkoxide plus an organic monomer. For instance, polyimide-SiO2 composites made by reaction of TEOS with the polyimide macromonomer also gave hybrids with good NLO properties, altogether with good mechanical properties (Raaijmakers et al. 2014). Besides the design of NLO devices, these hybrids are often applicable in other domains, such as luminescent solar concentrators or dye lasers.

14.10

Electrical, Dielectrical, and Other Electromagnetic Applications

14.10 14.10.1

637

Electrical, Dielectrical, and Other Electromagnetic Applications Electrical Conduction Applications

The sol-gel materials which present the most interesting electric conductivity are the various carbon aerogels, including graphene and carbon nanotube (CNT) aerogels. The electrical conductivity σ of carbon aerogels of density follows a scaling law of the type (Worsley and Baumann 2016): σ ¼ k ρn

ð14:13Þ

where k is a constant and n is an exponent ~1.55. However, for a 30 wt% carbon content, the constant k is about three times higher for a CNT aerogel, than for a conventional RF carbon aerogel. This difference is due to the contribution of the carbon nanotubes which are made of fully hexagonal sp2 carbon walls. The intrinsic conductivity σ strut of these nanotube walls can be defined by σ strut ¼ σ



σ strut=ρ

1:55

ð14:14Þ

CNT xerogels have a much higher electrical conductivity than the corresponding aerogels, e.g., ~60 times higher for a similar wet gel before drying, made by poly (dimethylsiloxane) (PDMS)/RF-bonded carbon nanotube composite containing 1.2 wt% CNT, in an example reported by Worsley and Baumann (2016). The bulk electrical conductivity of graphene aerogel can be as high as 100 S m
1, a value consistent with carbon junctions cross-linking between graphene sheets (Worsley et al. 2010). For isotropic graphene xerogel made by direct cross-linking via the oxidation sites of graphene oxide (GO), without adding any RF, an electrical conductivity of 1750 S cm
1 was observed (Worsley and Baumann 2016). Cyclic voltammetry (CV) data also showed that graphene aerogels can have a capacitance up to 165 F g
1, a maximum power density approaching 10 kW kg
1, and very fast charge/discharge capability (Worsley et al. 2012). Besides carbon gels, hybrid materials with new electrical properties could be tailored (Kramer et al. 1992). Ordered weakly bonded hybrids made by intercalation of organic conductive layers in between semiconducting V2O5 layers provided mixed electronic-ionic conductors, although their conduction properties were rather poor (Kanatzidis and Wu 1989). More interestingly, several hybrid materials are being investigated for their ionic conduction properties. As an example, Si–O–PEG (polyethylene glycol) hybrids can solvate small cations such as Li+, although they slowly deteriorate during aging (Ravaine et al. 1986). AMINOSILS is made by condensation of Si(OR)3R0 precursors where R0 ¼
(CH2)n-NH2 can solvate anions such as CF3SO
3 and give good proton conductors. The conductivity can reach a value of 1.4  10
5 S cm
1 in materials based on Si(OR)3(CH2)3NH2,

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Applications of Sol-Gel Processing

(CF3SO3H)0.1. Poly-(benzylsulfonic acid) siloxane (PBSS) hybrids have a high proton conductivity up to 10
2 S cm
1 and are stable up to 300  C (Sanchez et al. 1993). Electrochromic devices can be made by incorporating transition metal oxides in these hybrid materials but the oxide layer has a tendency to deteriorate due to the high acidity. The most stable hybrid ionic conductor is so far a three-component complex material comprising a solvating polymer, a proton source, and a proton vacancy inducer. All organic groups are anchored to trialkoxysilanes and the conductivity is of the order of 10
5 S cm
1. Trifunctional alkoxysilanes R0 Si (OR)3 where R0 is a vinyl, epoxy, or methacrylate group can form hybrids with special mechanical, optical, or electrical properties. For instance, N-3 trimethoxysilyl-propyl-pyrrole yields transparent sols which transform by polymerization of pyrrole to black xerogels with electronic conduction properties (Sanchez et al. 1994a, b).

14.10.2

Electrodes and Batteries

A number of different sol-gel materials present some interest for electric applications. In particular, carbon aerogels were investigated for applications as electrodes in supercapacitors, capacitive deionization units, and fuel cells (Owens et al. 1999; Long et al. 2008). Because of their high specific surface area, they can also store more electrical energy than conventional capacitors. A large amount of small ions such as Li+ can be stored in conductive polymer-derived aerogels for hightemperature electrical batteries of high capacity (Husing and Schubert 1998; Passerini et al. 1999; Long et al. 2008; Zhao et al. 2016). A proportion of Ru > 50 wt% could also be deposited inside the gels, which increased the specific capacitance of the carbon aerogels to values greater than 250 F/g (Miller and Dunn 1999). This energy could moreover be released very rapidly to provide a high instant power (Gouerec et al. 1999). Similarly, graphene aerogels display an original combination of high electrical conductivity and superior thermal, chemical, or electrochemical stability. Hence they are useful in electrode and energy storage equipment, such as for electrical batteries and actuators (Li and Kaner 2008; Novoselov et al. 2006). Quite different materials comprise ionogels made by non-hydrolytic reaction of silicon alkoxides with carboxylic acids in an ionic liquid solvent, potentially applicable as temperature-resistant electrolytes for energy storage devices, for instance in thin-film electrochemical double-layer capacitors (Horowitz and Panzer 2012). Rare earth oxyfluorides (REOF) of formula M2M0 2O3F6 where M can be Nd or La, and M0 Eu or Gd, are excellent solid electrolytes, besides being luminescent materials (Fujihara 2016). They crystallize in the fluorine structure in which F
and O2
anions can substitute for each other, which makes the O2
anions mobile charge carriers (Takashima and Kano 1987). To these materials, one must add titanium disulfide TiS2 which can be prepared by sol-gel as a useful intercalation cathode material of lithium in Li batteries (Jones et al. 1994; Almeida and Xu. 2016). Some

14.10

Electrical, Dielectrical, and Other Electromagnetic Applications

639

Si-O-C ceramics derived from preceramic polymer chemistry present interesting properties for application in semiconductivity (Dalcanale et al. 2014).

14.10.3

Superconductors

The synthesis of high-critical-temperature Cu-based superconductors by the Pechini method was extensively studied (Mazaki et al. 1991; Kakihana et al. 1992; Karen and Kjekshus 1994; Peng et al. 1998), including Ru–Sr–Gd–Ce–Cu–O ferromagnetic superconducting materials (Petrykin et al. 2002). Besides, the polymerizable route with hydrogel was also well applied to produce high-temperature superconductor powders, films, and fibers (Goto 1995, 2000; Goto and Torii 1996). To achieve a high critical temperature Tc, it is important to avoid the presence of a very small concentration of defects in the conducting CuO2 planes, and to control the homogeneous incorporation of dopants in the material (Kakihana et al. 1989).

14.10.3.1

Dielectric Applications

The relative dielectric constant of silica aerogels can be as low as 1.1 (Kawakami et al. 2000). Hence, thin-film silica aerogels could be used and are being considered as super-low dielectric constant material for integrated circuits in computers or in microwave equipment (Ullah et al. 2015; Sui et al. 2015). Siloxane-based ladderlike POSS themselves present some interest for applications as dielectric coatings (Xie and Zhang 1997; Zhou et al. 2008). Sol-gel polysilsesquioxane, in particular surfactant-templated silica-silsesquioxanes and bridged polysilsesquioxanes, has a dielectric constant κ lower than silica. Such materials in the form of coatings are needed to prevent electronic cross talk between circuits and to reduce power consumption and they also have excellent mechanical properties in film form. The most recent developments for such applications concern polyhydridosilsesquioxane, methylsilsesquioxane, and methylene-bridged polysilsesquioxane coatings (Hatton et al. 2006). It is also possible to modify the surface of silica aerogel and organic aerogels to obtain good electret materials (i.e., materials which produce a permanent external electric field) (Cao et al. 1998).

14.10.3.2

Piezoelectric Applications

For ultrasonic applications in gases, porous piezoelectric transducers with a low acoustic impedance are required. The acoustic impedance Z is itself related to the density of a material by the equation

640

14

Z ¼ ρc

Applications of Sol-Gel Processing

ð14:15Þ

where ρ is the medium density and c the sound velocity. Developing piezoelectric materials with a low density ρ is therefore necessary and, for this purpose, lead-zirconia-titania (PZT) aerogel monoliths were developed, for instance with a composition PbZr0.53Ti0.47O3 and porosity up to 90 vol% (Sinko et al. 2000). Actually, the technique most largely applied to the synthesis of ferroelectric, piezoelectric, and dielectric materials of general formula MTiO3, where M is a divalent metal such as Ca, Sr, Ba, and Pb, was the Pechini method (Kakihana et al. 1997, 1998). This route was also applied to the synthesis of “colossal magnetoresistant” (CMR) manganites (Fawcett et al. 1998; Lisboa et al. 2003), ferromagnetic spinels (Guaita et al. 1999; Verma et al. 1999; Uekawa and Kaneko 1999; Lisboa et al. 2000), and ferroelectric materials in the Bi–La–Ti–O system (Chu et al. 2002). Hydrogels were themselves used to synthesize leadzirconate-titanate (PZT) powders (Mandai and Ram, 2003). To these materials, one must add various other aluminates and components of Portland cement (Lee and Kriven 1998a, b; Lee et al. 1999; Guelguen et al. 1999; Nguyen et al. 1999). Besides, it is actually difficult to directly propagate an acoustic wave from a dense piezoelectric ceramic to air. An aerogel layer can improve considerably such transmission, by selecting an appropriate aerogel low density ρ, and layer thickness. This explains why SiO2 aerogels find acoustic applications in ultrasonic transducers (Nagahara et al. 2006), range finders, speakers (Gerlach et al. 1992) and anechoic chambers (Forest et al. 1998; Wang et al. 2010a, b; Buratti et al. 2014; Venkataraman et al. 2014), acoustic delay lines, and piezoactive antireflective acoustic coatings of thickness 4λ . In these applications, they can be used as a “matching layer,” using the principle of “acoustic impedance matching” to transmit and receive acoustic wave with high efficiency. It must also be noted that some Si– O–C ceramics derived from preceramic polymer chemistry (Sect. 4.4) also present interesting properties for application in piezoresistivity (Zhang et al. 2008). A quite different type of gel, polypyrrole/graphene oxide aerogel, exhibits improved absorption of electromagnetic radiation (Wu et al. 2015) and polypyrrole aerogels display a reversible change in resistance under pressure changes (Lu et al. 2014). Graphene aerogels are themselves considered for strain-sensing purposes, as actuators for soft robotics applications, flexible displays, and haptic devices which are used to recreate the sense of touch by applying forces, vibrations, or motions to a user. In all these applications, graphene aerogels were reported to be easier to prepare and superior to 2D graphene-based materials and to carbon nanotube-based 3D architectures (Nardecchia et al. 2013).

14.11

Applications as Immobilization Medium

14.11

641

Applications as Immobilization Medium

These applications cover different domains, comprising the confinement of dangerous wastes such as radioactive materials, the absorption of various liquids, and the immobilization of various additives from molecules to biomolecules for catalytic applications. The catalytic applications constitute a vast domain, which deserves to be reviewed in a further section.

14.11.1

Confinement Applications

Silica aerogels are excellent confinement media of liquid deuterium and tritium in fusion experiments (ICF) and hollow silica aerogel droplets were proposed as the immobilization medium (Kim et al. 1988; Jang et al. 1990 Kim and Jang 1991), as the target in fusion experiments under a powerful laser. The droplets were generated by a double-nozzle reactor. They were stable under radiation and could be wetted by deuterium and tritium. In aerogels, the gel network acts as an impurity for the fluids which strongly interact with the solid surface. Hence large fluid NMR signals with long polarization lifetimes can be recorded, revealing a very weak specific wall relaxation (Tastevin et al. 2000). This effect can be used to study either the gel itself or the entrapped fluid. The gel network was for instance studied by impregnation with liquid 131Xe near its critical temperature (Tc of approximately 289 K). Magnetic resonance images were obtained which made it possible to differentiate between aerogels of different densities and hydration levels (Pavlovskaya et al. 1999). Such confinement also opened the road to new fundamental studies on the ordering of smectic liquid crystals (da Silveira et al. 2009), or the interactions in superfluids such as 3He-4He mixtures near their critical temperature, because the aerogel high specific surface area induces strong perturbations in the fluids (Ma et al. 1993; Nakagawa et al. 2007; Li et al. 2013b). The interaction between superfluid 3He or solid 4He and the silica aerogel network was early reviewed by Halperin et al. (Halperin et al. 2003) but this subject was the focus of many publications during the last decade (Zhelev et al. 2014; Lauter et al. 2011; Fomin 2016; Matsuda et al. 2016). The solid network introduces disorders which interfere with the coupling interaction between electrons and molecules, so that an ordered state with continuous symmetry, such as occurring in superconductors or liquid crystals, can become unstable. Besides, such disorder can be modified by submitting the aerogel to various mechanical stresses. In a high-porosity aerogel, the liquid crystal long-range order can be destroyed, the superfluid transition temperature can be suppressed, and a nematic liquid crystal can be transformed to a glassy state (Feldman 2000), as this was predicted regarding 3He which can be transformed to a superfluid glass (Li et al. 2013b). For more practical applications, silica aerogels constitute good confinement medium of radioactive waste, in particular for long-life actinide wastes because

642

14

Applications of Sol-Gel Processing

they are chemically very stable with time on stream and they possess a very large relative pore volume (Hrubesh 1998; Buzykaev et al. 1999; Reynes et al. 1999; Woigner et al. 2004). They can also easily be converted to dense vitreous silica at a relatively low temperature (~1000  C) after a short heat treatment (Woignier et al. 1998; Reynes et al. 2001). The experiments also showed that these aerogels were able to store the waste much longer than the conventional borosilicate glass. Silica aerogels also constitute nonflammable cryogenic hydrogen storage equipment for hydrogen-consuming engine (Kabbour et al. 2006; Begag et al. 2008; Tian et al. 2009, 2013), an application field for which graphene aerogels seem also to have a superior capability (Li and Shi 2012; Nardecchia et al. 2013; Kotal et al. 2014; Fang et al. 2015a, b). Hydrogen can be stored in the form of hybrid nanoparticles, e.g., MgH2 or NaAlH4, with improved hydrogen sorption and storage cycling kinetics due to nanoconfinement (Stephens et al. 2009). Other rocket fuels (Gesser and Goswani 1989) or even water (Julio and Ilharco 2014) can also be stored and transported in such media. Partially sintered aerogels, which are mechanically stronger to resist capillary stresses, are convenient to store or transport liquids such as rocket fuel (Gesser and Goswani 1989). Hazardous liquids such as red fuming nitric acid and unsymmetric 1,1-dimethyl hydrazine (UDMH), both used as rocket fuels, have been stored with silica aerogels (Pajonk and Venkateswara Rao 2001).

14.11.2

Environment Remediation Applications

Hydrophobic SiO2-based gels can be used as water repellent (Latthe Sanjay et al. 2009) or to purify wastewater or gases (Perdigoto et al. 2012; Matias et al. 2015; Emmerling et al. 1990) from volatile organic compounds by absorbing them (VOC) (Reynolds et al. 2001a, b; Hrubesh et al. 2001; Goel et al. 2006; Wu et al. 2006; Standeker et al. 2007, 2009; Maldonado-Hodar et al. 2007; Fairen-Jimenez et al. 2007; Yang et al. 2007, 2008; Lee et al. 2009; Quevedo et al. 2009; Wang et al. 2010b; Bi et al. 2013; Lei et al. 2013; Hayase et al. 2013; Chen et al. 2014; Maleki 2016). The performance of aerogels for the purification of air inside building was analyzed by Buratti and Moretti (2011, 2012a, b). VOC comprise chemicals such as benzene, toluene, ethylbenzene, and xylene, also known as “BTEX,” which are serious air pollutants released in the atmosphere by industries or motor vehicle exhausts. For such purposes the aerogel can be placed in gas filtration membranes (Emmerling et al. 1990). To withdraw organic contaminants from water, hydrophobic silica aerogels are more adequate. These contaminants comprise light and heavy hydrocarbons, lubricants and cutting fluids, emulsified or non-emulsified oils (e.g., greases), and plants’ and animals’ fat (Wang et al. 2010b; Hayase et al. 2013; Maleki 2016). Silica aerogels can adsorb several times their weight of ethanol, toluene, chlorobenzene, or trichloroethylene (Hrubesh et al. 2001; Standeker et al. 2007; Liu et al. 2009) and

14.11

Applications as Immobilization Medium

643

3.5 times their weight of crude oil (Reynolds et al. 2001a, b). Hybrid silica-cellulose aerogel which combines hydrophobicity and a better mechanical compressibility was also studied (Sai et al. 2013). On the other hand, hydrophilic silica aerogels are more efficient to adsorb watersoluble organic compounds (Liu et al. 2009). Hydrophilic SiO2 gels can moreover be used to purify water by adsorbing heavy ions (Goel et al. 2006) or pesticides (Chevallier et al. 2008). A few bridged polysilsesquioxane sol-gel materials and templated bridged polysilsesquioxane were also investigated to absorb metal ions from aqueous solutions (Vlasova et al. 1989; Wu et al. 2010) or organic compounds from air (Borghard et al. 2009). To these, one must add chalcogenide aerogels (Bag et al. 2007) and V2O5/TiO2-based aerogels (Woignier and Phalippou 1989; Wu et al. 2007), also investigated to remove heavy metal ions or to decompose H2S (Kim et al. 2006). Brock and Yu (2011) reported that sulfide gels are known to preferentially adsorb heavy metal ions, such as Hg2+, over lighter ones such as Zn2+. Alumina aerogels were investigated to eliminate pyridine (Khaleel et al. 2002), MgO aerogels (Jeevanandam and Klabunde 2002), and chitosan-based aerogels (Chang et al. 2008) to remove surfactants from water. Carbon aerogels appear interesting for applications as capacitive deionization units (Pekala et al. 1998). They can be used to capture a large amount of ionic compounds such as NaCl or other aqueous pollutants (Fricke and Emmerling 1998; Pekala et al. 1998) by electrolytic methods. Because of their combined high mechanical strength and specific surface area and pore volume, graphene aerogels are themselves considered for application as absorbents for water treatment (Sun et al. 2015a, b).

14.11.3

Capture of CO2 Gas

An interesting application of SiO2 aerogels is to capture CO2 from flue gas (Santos et al. 2008; Maleki 2016). The conventional CO2 capture techniques rest on using liquid amine scrubbing or membrane separation. However, these technologies are highly energy consuming and highly corrosive for the equipment while the amines are prone to an oxidative degradation resulting in the formation of toxic by-products (Kong et al. 2014a, b, 2015; Maleki 2016). To avoid this problem, the pore surface of SiO2 aerogels can be functionalized with amine moieties such as monoethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA) (Pierre and Pajonk 2002; Maleki et al. 2014; Rechberger et al. 2014; Wang et al. 2014). It is known that these amine moieties possess a strong affinity towards molecular CO2. They can selectively and reversibly react with upcoming CO2 gas molecules at ambient temperature and pressure, in the presence of moisture, to mainly form carbamate intermediates according to reaction of the following type:

644

14

Applications of Sol-Gel Processing

CO2 þ 2RNH2 $ RNHCOO þ RNH3 þ

ð14:16Þ

Releasing the CO2 simply requires a moderate-temperature treatment (~100  C) in the presence of moisture. The amine functionalization of SiO2 aerogel can be achieved via physical interactions in class I sorbents, or stable chemical bonds in class II sorbents (Maleki et al. 2014). Typical class II aerogel sorbents can be made by linking a silane such as aminotrialkoxysilanes onto the silica pore surface or by co-condensing such aminosilanes with tetraalkoxysilanes (Araki et al. 2009). Several well-known silanes were explored to functionalize CO2 aerogel sorbents (Cui et al. 2011; Wormeyer et al. 2012; Begag et al. 2013; Maleki et al. 2014; Wang et al. 2014; Kong et al. 2014b; Minju et al. 2015). Linneen et al. (2013, 2014) could for instance achieve a CO2 adsorption performance of 7.9 mmol g
1 under simulated flue gas conditions (in pre-humidified 10% CO2). These studies showed that both the aerogel textural characteristics and the amine loading were important parameters. But the capture efficiency also depended on the CO2 partial pressure, the aerogel particle size, the gas/solid equipment design, and the temperature. The CO2 sorption kinetics is usually slow at low temperature (Nguyen et al. 2013), while the presence of a low water vapor pressure in the gas flow increases the sorbent stability by avoiding the formation of urea during the regeneration process (Maleki et al. 2014). Some aerogel coating on reusable Al2O3 membranes was also investigated to facilitate the CO2 transfer through the membrane pores (Lin et al. 2013, 2014, 2015). At last, Brock and Yu (2011) also suggested that aerogels based on Zintl ions/Pt2+ systems could be efficient for the separation of H2 gas from CO2.

14.11.4

Other Immobilization Applications

In a different domain, the encapsulation of water droplets in super-hydrophobic water glass aerogel particles was proposed (Julio and Ilharco 2014). Silica aerogels impregnated with CaCl2, LiBr, and MgCl2 salts were tested as water sorbents for heat storage at low temperature (Aristov et al. 2000). Their energy storage ability E measured by differential scanning calorimetry (DSC) could reach 4.0 kJ/g, which is much higher than for common sorbents such as zeolites and un-impregnated silica gels. In spite of their low density and brittle characteristics, the mechanical properties of silica aerogels are also quite promising for some other rare but specific applications. As an illustration, their good compressibility can be advantageously used for absorbing the kinetic energy involved in a compressive shock (Holmes et al. 1984; Buzykaev et al. 1999). Silica aerogels are useful low-shock impedance materials, to confine few eV plasmas, to capture frozen states of minerals generated under high

14.12

Sol-Gel Catalysts

645

shock pressures, or as a medium to study the mixing of fluids requiring X-rayinduced shocks (Holmes et al. 1984; Amendt et al. 1997; Buzykaev et al. 1999). The applications of silica aerogels in space were reviewed by Jones (2006). In particular, they were used as shock energy absorbers to collect comet dust (Tsou 1995; Guise et al. 1995) or aerosol particles (Guise et al. 1995). The most recent project, Stardust, successfully returned to earth in January 2006. This mission provided samples of a recently deflected comet named Wild-2. They can also be applied to protect space mirrors or to design tank baffles (Hrubesh 1998; Schmidt and Schwertfeger 1998) more generally to design parts able to absorb the energy involved in shock compression (Holmes et al. 1984).

14.12

Sol-Gel Catalysts

Of the order of 90% of the industrial chemical processes use a catalyst (Haggin 1990). Sol-gel ceramics have characteristics which make them good materials for such applications and review papers have been published on this subject (Pajonk 1991; Cauqui and Rodriguez-Izquierdo 1992; Ward and Ko 1995). Sol-gel-derived ordered mesoporous materials offer themselves interesting applications. The synthesis of catalysts is an important domain of sol-gel processing which deserves special consideration. The catalysts comprise a range of materials of very different nature: metals, semiconducting oxides, insulator oxides, solid acids, immobilized molecular catalysts including immobilized enzymes, and carbon and graphene aerogels. They can be prepared as bulk solids or as colloidal particles which are dispersed on a support and it is possible to find examples of preparation of all these types of catalysts by sol-gel process (Cauqui and Rodriguez-Izquierdo 1992; Li and Kaner 2008). The large surface area and very open porous texture of aerogels facilitate the diffusion of ions and molecules. Hence, aerogel-supported catalysts are interesting to design chemical or biochemical sensors (Plata et al. 2004; Zhang et al. 2013; Ren and Cheng 2013; Fang et al. 2015b; Peng et al. 2015; Sun et al. 2015b).

14.12.1

The Catalytic Process (Satterfield 1990)

14.12.1.1

Activity and Selectivity of a Catalyst

In terms of kinetics, the efficiency of a catalyst can be characterized by its selectivity for a given product and its activity (Satterfield 1990). The activity of a catalyst refers to the rate at which it makes a reaction proceed towards chemical equilibrium. It can reactedÞ be expressed in several ways such as ððmolecules timeÞðactive siteÞ the turnover number given by

646

14

Turnover number ¼

Applications of Sol-Gel Processing

ðmolecules reactedÞ ðtimeÞðactive siteÞ

ð14:17Þ

Turnover numbers depend on many conditions such as the temperature and pressure and they are not often provided in publications. Instead, it is often more convenient to indicate the temperature for which a given percent of reactant molecules is converted, for a given feed composition and pressure. For instance, T10 represents the temperature where 10% conversion occurs. On the other hand, the selectivity measures the extent to which a catalyst accelerates the formation of a given product. It is defined as the percentage of the desired product formed among all products formed. Depending on the type of reaction considered, a catalyst may be useful for its activity, its selectivity, or both. If several products can possibly be formed, the selectivity is often the most important property.

14.12.1.2

Oxide Active Sites

Most sol-gel materials are oxides and in terms of catalysis mechanisms the important aspects such as their surface sites which participate in the catalysis reaction, termed active sites, are very subtle, controversial, and subject to important changes due to apparently minor modifications in the material preparation methods. This is due to the fact that heterogeneous catalysis is essentially governed by local conditions around the active sites, which largely depend on the material preparation procedure. An oxide catalyst may participate in a chemical transformation by acid-base reactions: in this case its acid or basic sites are important. An acid site may be of the Brönsted or of the Lewis type and its origin in materials is subject to controversy. Pure silica gels have a very weak surface acidity while pure alumina is amphoteric with both acidic and basic properties. Surface terminal hydroxo M–OH or aquo groups M–H2O can liberate a proton and hence they can be Brönsted acid sites. Hydroxo and oxo M–O groups can capture a proton and act as basic Brönsted sites. On the other hand, terminal metal atoms can have missing electron pairs and constitute Lewis acid sites, while terminal oxo groups have unshared electron pairs which make them Lewis basic sites. Different types of Brönsted or Lewis acid sites may exist in a catalyst. According to Pauling, the acidity of a catalyst can largely be tailored by adding cations with a different valence state to a host oxide. For instance, if a trivalent Al3+ cation substitutes for a tetravalent Si4+ cation in SiO2, in such a way that it occupies a tetrahedral Si site, a net negative charge is created which must be balanced by a nearby positive charge. This can be an H+ cation from water molecules which dissociate to fix a hydroxyl OH on the A13+ cation. In terms of Kröger-Vink notation the overall reaction is written as in Eq. (14.18). The resulting structure corresponding to the right-hand side of Eq. (14.18) may behave as a Brönsted acid as it can give up

14.12

Sol-Gel Catalysts

647

a proton according to reaction 14.19 or it may transform to a Lewis acid by losing a water molecule according to reaction 14.20: ð14:18Þ

ð14:19Þ

ð14:20Þ

An acid site can itself react with a hydrocarbon to form a carbenium ion of the type RCH+CH3 which is adsorbed on the Al site (Satterfield 1990). The latter one can either give a proton as a Brönsted acid to RCH¼CH2 or fix a H
anion from RCH2CH3 on an electrophilic Al atom. The strength of an acid site can be increased by replacing a hydroxyl group by halogen anions, such as fluoride or chloride anions or by sulfate anions. The acid strength of a solid can be determined by its ability to change a neutral organic base B adsorbed on the solid into its conjugate acid form BH+, in the case of Brönsted acidity. This acid strength is determined by the Hammett indicator H0 (Hammett and Deyrup 1932; Hammett 1940) defined as H0 ¼ pKa þ log

½B for a Br€onsted acid ½BHþ 

ð14:21Þ

½B  for a Lewis acid ½AB

ð14:22Þ

H0 ¼ pKa þ log

where pKa is derived from the usual equilibrium dissociation constant of the acid, (B) is the organic base concentration in equilibrium on the solid surface, (BH+) is its conjugate acid concentration for the Brönsted case, and (AB) is the compound formed with the base for the Lewis case. The lower the H0, the more acidic the solid surface. An oxide may also participate in redox catalysis reactions, especially when it contains transition metal oxides linked to oxygen atoms which can easily be

648

14

Applications of Sol-Gel Processing

transferred out of the structure to produce a non-stoichiometric oxide. For the oxidation of a hydrocarbon R, the mechanism involves two steps: first oxidation of the hydrocarbon R by the catalyst oxygen Eq. (14.23), and second re-oxidation of the catalyst by oxygen gas molecules Eq. (14.24): Cat‐O þ R ! RO þ Cat

ð14:23Þ

2Cat þ O2 ! 2 Cat‐O

ð14:24Þ

The catalyst oxygen can be network oxygen for an oxide, or chemisorbed oxygen for a metal.

14.12.1.3

Special Characteristics of Sol-Gel Oxides

The definition of the turnover number points out to the importance of increasing the number of active sites, and hence the specific surface area of a catalyst. Gels and particularly aerogels have a very high porosity, for instance a specific surface area up to 1000 m2 g
1 for alumina aerogels, which corresponds to a pore volume of up to 98% of a sample volume, and an apparent density as low as 0.03 g cm
3 and currently of the order of 0.5 g cm
3. Moreover their texture presents a good stability at relatively high temperature, at least in the lower Tammann range according to the terms used in Sect. 12.3, sometimes even in the presence of water vapor. Their application in catalysis concerns two large domains: the synthesis of commercial organic products with a high added value and the protection of the environment. In both domains, sol-gel materials can participate in catalysis at two levels, either as catalytic active materials themselves or as support of a catalytically active phase. Very often this active phase is a noble metal such as Pt, Pd, or a transition metal element. An active phase must remain dispersed as much as possible, and hence the action of sol-gel is as catalyst support. A support with a large specific surface area maximizes the contacts between the reactants and the active phase, in so far as the active phase can be maintained finely dispersed at the atomic scale. Sol-gel processes can eventually hinder the sintering of this active phase by blocking it in an original fashion on the support. An interactive effect between the support and the active phase, such as an active metal, can also enhance the activity of this active phase. The interaction can be textural, that is to say, it modifies the types of pores and solid surfaces on which the active phase can be adsorbed, or structural due to the formation of a particular support phase such as a transition phase in alumina. For instance, amorphous or crystalline transition phases always tend to be more active than stable crystalline phases. Moreover, we mentioned before that the acidity of an oxide can be increased by dissolving cations with a different valence in the sites of the host cation oxide: sol-gel processes offer the potential to realize such substitutions without inducing phase segregation much more easily than conventional processes.

14.12

Sol-Gel Catalysts

14.12.2

649

Synthesis of High-Value Organic Compounds

For this type of applications, catalysts usually need to operate at a temperature T < 400  C, which is the Hüttig temperature range (Sect. 12.2) where aerogels keep a high specific surface area. Aerogels are particularly interesting to magnify all catalytic reactions because of their very high surface area. They are often better than the xerogels because either the active phase is better dispersed or the textural properties are better developed.

14.12.2.1

Types of Chemical Reactions Catalyzed

The types of chemical reactions involved include partial oxidation, nitroxidation, and hydrogenation. Examples are provided in Table 14.9 with the nature of the aerogel catalyst and the selectivity, that is to say, the percent of the desired compound formed, among all compounds formed other than the reactants. Sol-gel materials often have a high selectivity. However their activity is usually much lower. Table 14.9 Types of chemical reactions catalyzed by sol-gel Reactant Compound formed Selective oxidation Isobutylene Methylacroleine Isobutylene Acetone Isobutane, Acetone propane Nitroxidation Hydrocarbons Nitriles Selective hydrogenation Cyclopentadiene Cyclopentene Toluene Methylcyclohexane (storage of H2 for vehicles) Benzene Cyclohexane Nitrobenzene Aniline CO and CO2 (Fischer-Tropsch) methanol

Selective reduction N2 + 2H2O NO + NH3

Polymerization Ethylene

High-molecular-weight polyethylene

Aerogel catalyst

Selectivity (reference)

NiO–Al2O3 NiO–Al2O3 NiO–SiO2– Al2O3

67% (Astier et al. 1976) 25% (Astier et al. 1976) 100% (Matis et al. 1976)

NiO–Al2O3

80–90% (Pajonk 1991)

Cu–Al2O3 Ni–SiO2

100% (Taghavi et al. 1979) 100% (Klvana et al. 1988)

Ni–MoO2 Pd-Al2O3 Fe2O3– SiO2 Fe2O3– Al2O3

Astier et al. (1980a, b) 100% (Armor et al. 1985) 300  (unsupported Fe2O3) (Blanchard et al. 1982, 1983)

Fe2O3– Cr2O3– Al2O3

Willey et al. (1991)

TiCl4– Al2O3

Fanelli et al. (1989)

650

14

Applications of Sol-Gel Processing

Both single and mixed oxides of the transition elements present selective oxidation properties. On the other hand, selective hydrogenation is typically due to metal catalysts and sol-gel materials are mostly efficient as supports. Nitroxidation reactions correspond to the formation of nitriles (A or ϕ)-C(fx) N, where A designates an aliphatic hydrocarbon such as propene, isobutylene, isobutane, or propane and ϕ an aromatic hydrocarbon such as toluene, xylenes, and monotolunitriles. These nitriles are obtained by reaction of alkenes with NH3 plus O2, or of hydrocarbons with NO. In this case Ni2+ surface cations blocked in a spinel NiAl2O4 environment seem to be the active centers, and basic oxide additives such as MgO improve the catalyst activity. In the last example of Table 14.9, NH3 is adsorbed on Fe3+- and Cr3+oxidized sites which are partially reduced and NO2 is chemisorbed and decomposed on these sites.

14.12.3

Protection of the Environment

The most important research in this field concerns reactions of the following: – Air depollution, in particular the elimination of nitrogen oxide exhaust gases according to the reaction: 1 x NOx ! N2 þ O2 2 2

ð14:25Þ

Aerogels investigated for this purpose were studied in the systems Fe2O3-SiO2, Fe2O3/Cr2O3/Al2O3, MgO/Fe2O3, and Cr2O3/Al2O3 (Willey et al. 1991; Wojciechowska and Lomnicki 1999; Fabrizioli et al. 2002). – Clean catalytic combustion of hydrocarbons, so as to only reject CO2 and H2O. For instance with methane: CH4 þ 2O2 ! CO2 þ 2 H2 O

ð14:26Þ

Important catalysts for the oxidation of CO to CO2, or the decomposition of organic compounds, comprise Pt nanoparticles supported on carbon aerogels (Wojciechowska and Lomnicki 1999; King et al. 2008, Padilla-Serrano et al. 2005), Co-promoted Pt catalysts supported on SiO2 aerogels (Choi et al. 2008), V2O5–TiO2 aerogels (Choi et al. 2006), Au/TiO2-coated SiO2 aerogels (Tai and Tajiri 2008), and Al2O3 aerogels (Khaleel and Dellinger 2002). – Catalytic post-combustion depollution of automobile exhaust gases, known as three-way catalysis to simultaneously eliminate CO, NOx, and HC. – Catalytic combustion of diesel engine soot.

14.12

Sol-Gel Catalysts

651

The catalysts which are needed often operate at a high temperature from T  900 to 1200  C. At these temperatures, most aerogels lose their high specific surface area. In particular their sintering is promoted by H2O present in engine exhausts. Chemical reactions between the supports and active phase also commonly occur, as well as poisoning of the active sites. Consequently, the benefits of sol-gel materials in comparison with conventional materials are not obvious. However, as sintering can be accelerated by selecting the appropriate initial pore texture or additives, it should also be hindered by selecting other appropriate additives or initial pore texture. Hence research keeps going on in this field and some significant success was achieved with transition alumina phases which have a structure derived from a cubic close packing of oxygen anions. These transition alumina are also the single-oxide materials able to keep the highest specific surface at the highest temperature, over 100 m2 g
1 up to 1000  C. A significant success was achieved with materials derived from the hexaaluminate BaAl12O19 doped with Mn, Cr, Fe, Ni, or Co by Machida et al. (1986, 1987). This compound has a structure derived from cubic spinel where densification is attenuated by the formation of lamellar structures. A few properties of such compounds are given in Table 14.10, including T10 and T90 which are the temperatures where the clean combustion of, respectively, 10% and 90% of methane is achieved. Other additives were reported to enlarge the existence range of θ-Al2O3 towards higher temperature and hence to increase the high-temperature specific surface area of Al2O3-based material. For instance, yttrium could increase the residual specific surface area to 88 m2 g
1 at 1200  C (Ponthieu et al. 1993). Also, the resistance to sintering and transition to α-alumina seems to be improved by selecting a sol-gel process with organic complexing additives which produce a somewhat different initial pore texture as well as exotic transition alumina phases (Elaloui et al. 1997).

Table 14.10 Properties of hexaaluminate catalysts in the combustion of methane 

Temperature ( C) 1200  C 1300  C 1600  C

T10 ( C) ignition T90 ( C) complete combustion Data from Machida et al. (1986, 1987)

Specific surface area (m2 g
1) BaAl12O19 BaMnAl11O19 50 13.7 11 Catalytic combustion of CH4 BaAl12O19 BaMnAl11O19 700 490 760 750

652

14

14.12.4

Recent Sol-Gel-Made Catalysts

14.12.4.1

Aerogel Catalysts

Applications of Sol-Gel Processing

As previously stated, simple oxide aerogels are generally not active materials, so they are used as supports (Nicolaon and Teichner 1968; Teichner 1986; Bali et al. 2009; Gasser-Ramirez et al. 2008). However they enhance the activity of a catalyst by a controversial mechanism known as spillover. This consists, for instance, of a creation of active hydrogenation sites when in a H2 atmosphere, by transfer of hydrogen from the active phase to the support. Spillover by oxygen transfer is also possible. Silica is one of the most important supports because of its inertness. Alumina is widely used in catalysis because of its acidic properties and as support of other active phases in bifunctional catalysts. Zirconia is interesting because it develops both redox and acid-base functions, and hence it is used as a catalyst and as a support (Paal and Menon 1988). Superacid sulfated zirconia aerogel catalysts were studied for isomerization reactions (Mejri et al. 2006). Titania is a reducible support used in photocatalysis (Paal and Menon 1988). A third oxide component can eventually be added to develop new functionalities. Active metal particles supported on oxide aerogels can be prepared by impregnation of aerogels with a metal salt or by direct fabrication of a multicomponent aerogel (Lacroix et al. 1981). To obtain the metal particles, supercritical drying must be performed in a reducing environment, that is to say, either in alcohol or by replacing N2 with H2 before heating the autoclave or by flushing the autoclave with H2 at 200  C. In these conditions, NiO, CuO, PbO, and V2O5 are reduced to fine metal particles with a size of a few nm. A list of such supported metal particles made in situ in aerogels is given in Table 14.11. To be used industrially, aerogels can be encapsulated in honeycombs, Raschig rings, screens, mineral wool, boiling stones, and glass or metal tubes. The reactant gases can be forced to flow through a catalyst-fluidized powder bed (Fig. 14.16). Aerogel powders behave as type C beds as illustrated in Fig. 14.16a. In the packed state represented in this figure, reactant gases do not pass easily. They can either push the powder bed as a plug illustrated in Fig. 14.16b or pass through channels as Table 14.11 Supported metal particles in aerogels made by in situ reduction of oxide aerogels Metal–aerogel Pt–Al2O3 Ni–SiO2 Ni–Al2O3 Ni–SiO2–Al2O3 Ni–MoO2 Cu–Al2O3

Specific surface area at 20  C (m2 g
1) Total Metal 450 120 620 356 150–650 7–53 480–730 5–68 1–15 0.7–15 660 30

Adapted from Pajonk (1991)

Reference Lacroix et al. (1981) Klvana et al. (1988) Gardes et al. (1976) Gardes et al. (1976) Astier et al. (1980b) Pajonk et al. (1975)

14.12

Sol-Gel Catalysts

653

Fig. 14.16 Types of behavior of aerogel powders in a fluidized bed. Adapted from Pajonk (1991)

in Fig. 14.16c. A fluidized bed type of type A is reached for a much higher reactant laminar velocity than with conventional powders, because strong van der Waals attraction keeps the aerogel particles together. This fluidized bed state is illustrated in Fig. 14.16d. It corresponds to a break of the initial powder pack into clusters of aerogel powders with a size of the order of 1 mm.

14.12.4.2

Catalysts Made by Non-hydrolytic Sol-Gel Process

Non-hydrolytic sol-gel processing was applied to the synthesis of homogeneous mesoporous and/or mixed oxide catalysts (Debecker and Mutin 2012; Debecker et al. 2013). The focus was on mixed SiO2-based materials, but also on TiO2–V2O5 (Mutin et al. 2006) or Ag–Nb2O5–Al2O3 (Petitto et al. 2013). These materials could be calcined up to temperatures where the bulk diffusion of all atoms remained moderate, a property sometimes summarized in the low Tammann temperature range of the solid. And they were tested for the same span of reactions as similar oxide catalysts made by different techniques. For instance, Vioux and Mutin (2016) quoted the case of SiO2–TiO2 mixed oxides made by the ether route, which could be heat treated up to temperatures of the order of ~500  C without any significant diffusion of both the cations and anions. In these conditions, the Ti cations participated in mixed Si–O–Ti bonds and they remained well dispersed, while the specific surface area remained high. These catalysts were reported to be very efficient in the mild oxidation of organic compounds (Lafond et al. 2002; Cojocariu et al. 2010).

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14

Applications of Sol-Gel Processing

Other non-hydrolytic SiO2–TiO2 xerogels showed a good catalytic activity in the epoxidation of cyclohexene with cumyl hydroperoxide (Skoda et al. 2015a), while mesoporous SiO2–ZrO2 catalysts obtained by the templated acetamide elimination route were found to be promising for Meerwein–Ponndorf–Verley reduction reactions or aminolysis reactions (Skoda et al. 2015b). In other cases, the cations did migrate first towards the solid surface, at relatively low temperature. This was the case of aluminosilicates doped with MoO3 or Re2O7. A high concentration of well-dispersed Mo or Re cations was then observed to segregate in the surface, a texture found to be efficient in the metathesis of ethene and butene to propene (Debecker et al. 2009; Bouchmella et al. 2013).

14.12.4.3

Ordered Mesoporous Catalysts

Large-pore mesoporous materials presented in Chap. 11, Sect. 11.7 and mesoporous polysilsesquioxane sol-gel materials can be used as supports for catalytic active phases such as heteropolyacids, amines, transition metal complexes, and oxides. It is possible to introduce Brönsted acid sites on the pore surface (Shylesh et al. 2008) or transition metals so as to make redox catalysts. Eventually, new bifunctional acid/ metal oxide catalysts can be designed. By exchanging the alkaline cations for the Brönsted acid-site protons, the basicity of the conjugated base can also be increased. In summary, these mesoporous materials extend the catalytic possibilities of zeolites to larger molecules. Catalytic groups such as the sulfonic acid groups can be built inside the mesoporous material or added after its formation (Jones et al. 1998; Nakajima et al. 2005). Metal catalysts can be attached to pendant ligands (Dufaud and Davis 2003; Sharma and Singh 2014), grafted on the mesopore gel surface (Naeimi et al. 2015), attached as ligands to bridging groups (Gruening et al. 2014), or be part of bridging ligands (Borah et al. 2012). Organic catalysts can be attached to polysilsesquioxane mesoporous gel by ligands (Borah et al. 2015). For instance, chiral catalysts for hydrogenations were designed using chiral bridging groups (Wahab and Beltramini 2015). As acid catalysts, mesoporous type materials could be used for cracking or precracking of large gas-oil molecules (Corma et al. 1996), in association with zeolites. However the thermal stability, and more particularly the hydrothermal stability, during steaming regeneration at T  800  C of these MCM-type materials is low, an inconvenience which can be attenuated by making pores with thicker walls. On the other hand, MCM-type materials appear to be good acid catalysts for reactions requiring a lower hydrothermal stability, such as hydroisomerization, diesel production in mild hydrocracking reactions (MHC), demetallization, and olefin oligomerization. NiMo supported on MCM-41-based catalysts performed better than zeolites from the point of view of hydro-desulfurization (HDS), hydrodenitrogenation (HDN), and MHC (Corma et al. 1995a, b). A three-component NiW/MCM-41/zeolite was also developed for deep hydrocracking (Reddy and Song 1996). A NiW/MCM-41 could be used to hydrocrack heavy waxes into lubrication oils (Apelian et al. 1993). MCM-41-supported bifunctional catalysts were useful for

14.12

Sol-Gel Catalysts

655

the isomerization of normal paraffins into isoparaffins (Del Rossi et al. 1993). MCM-41-based catalysts were also studied to upgrade the disproportionation of larger olefins such as propylene. The most promising domain of applications of ordered acid mesoporous catalysts is in the field of organic synthesis of fine chemicals. Friedel-Crafts alkylation and acylation are of general use for the production of fine chemicals. In traditional processes, these reactions are catalyzed by stoichiometric proportions of AlCl3, which induce waste disposal problems and must now be replaced by solid acids. MCM-41-type catalysts appear to be very efficient (Armengol et al. 1995). Such applications concern in particular the synthesis of fragrances and pharmaceuticals which involve the acylation of aromatic ketones (Gunnevegh et al. 1996). Other mild acidic reactions are the acetalyzation of large-size aldehydes (Climent et al. 1996), the Beckmann rearrangement of cyclohexane oxide (Aucejo et al. 1986), and aldol condensation (Corma 1997). Regarding basic catalysts, much work needs to be done with the alkalineexchanged MCM-41 materials. The Na-exchanged ones were reported to be active in the Knoevenagel condensation of benzaldehyde with ethyl cyanoacetate (Kloetstra and Van Bekkum 1995). As redox catalysts, Ti-MCM-41 is more efficient than Ti-zeolites to catalyze the epoxidation of large olefin molecules by reactions with H2O2, because these molecules can diffuse in the large mesopores of the MCM-based material (Corma et al. 1994). Organic hydroperoxides can also be used as oxidants. Ti mesoporous materials made with a nonionic surfactant, termed Ti-HMS, appeared to be good in the liquid-phase peroxide oxidation of methyl methacrylate, styrene, and 2,6-di-tertbutylphenol (Iglesia et al. 1993). The oxidation of amines, interesting in some chemical and pharmaceutical synthesis, can also be catalyzed by Ti-MCM-41 and Ti-HMS materials (Sakane et al. 1993). A Ti-MCM-41 catalyst containing both TiIV oxidation sites and acidic H+ ones associated with AlIV sites was shown to be able to achieve at once the oxidation of linalool to cyclic furan and hydroxy ethers by using tert-butyl hydroperoxide (Corma et al. 1995b). When compared to TiO2–SiO2 aerogels, it appeared that the activity was higher per Ti atom in a Ti-MCM-41 than in an aerogel. However the aerogel contained more TiIV centers and, having a more open mesoporous texture, was globally more active with bulky olefins and organic hydroperoxides than the Ti-MCM-41 materials. Other catalyzed reactions include the ring-opening polymerization of lactic acid in Sn-HMS molecular sieves, synthesized with a nonionic surfactant. The Sn atoms were incorporated in the catalyst network instead of being mixed in the final products, which eliminated toxicological problems (Abdel-Fattah and Pinnavaia 1996). Gontier and Tuel (1996) also prepared ordered mesoporous silicas where the silica was amorphous and incorporated Zr cations. The obtained Zr-MS materials were active and selective for the oxidation of a large variety of substrates. As supports, ordered mesoporous materials can be used to make stronger solid acids and bases. In particular heteropolyacids (HPA) such as H3PW12O40 can be chemisorbed and used for reactions such as paraffin isomerization and isobutane/ butene alkylation (Kozheunikov et al. 1994). Strong basic catalysts can also be made

656

14

Applications of Sol-Gel Processing

by dispersion of amines in MCM-41. Such supported catalysts are useful to prepare monoglycerides from 2,3-epoxy alcohols and fatty acids (Brunel et al. 1995). Noble metals such as Pt or Pd could also be finely dispersed by using a neutral Pt(NH3)2Cl2 precursor which goes in the hydrophilic part of the micelle (Junges et al. 1995). The obtained catalyst performed well in the hydrogenation of benzene, naphthalene, phenanthrene, and olefins. A modified MCM-41 material containing Fe and Pd permitted to control the formation of NOx, CO, and hydrocarbon emissions generated by oxygen-rich combustion processes (Beck et al. 1992). Selective oxidation catalysts can also be obtained by grafting organometallic complexes on the inner walls of mesoporous MCM-41, or by functionalizing surface silanol groups with silanes followed by anchoring of a transition metal complex. Such procedures were used to obtain Ti-containing or Mn-containing active sites (Maschmeyer et al. 1995; Burch et al. 1996). The catalysts obtained showed good enantioselective properties, that is to say, they catalyzed the formation of a certain chiral form of a compound (Corma et al. 1991).

14.12.4.4

Application of POSS in Catalysis

Discrete POSS and POMS oligomers (Sects. 3.7 and 3.8) were studied in homogeneous or heterogeneous catalysis reactions as catalyst supports (Abbenhuis 2000). In particular, they were considered as tools for modeling the chemical transformations occurring on silica surfaces (Kung et al. 2014). This is the case of partially condensed POSS carrying terminal silanol groups (Feher et al. 1989; Herrmann et al. 1994). Other POMS clusters comprise Ti-containing POMS as catalysts for the epoxidation of alkenes (Crocker et al. 1997) or of cyclooctene (Wada et al. 2012), Mo-containing POMS for the metathesis and polymerization reactions of alkynes (Cho et al. 2006), and germanium-ruthenium POMS complexes in coupling reactions with styrene and olefins (Frackowiak et al. 2015).

14.12.4.5

Sol-Gel Fluoride Catalysts

Metal fluorides made by fluorolytic sol-gel processing exhibit high surface areas (200–400 m2 g
1).They are also among the strongest Lewis acids (Murthy et al. 2006; Krahl et al. 2007). Their Lewis acid activity is such that they can realize a silylationlike surface functionalization of AlF3 via AlF3–H–Si(C2H5)3 hydrogen bonding and catalyze the synthesis of methane CH4 from CH3F, CH2F2, and CHF3 at room temperature (Kemnitz and Coman 2016). It is also possible to adjust a Lewis-toBrønsted acid site ratio, by controlled partial fluorolytic transformation of an Al alkoxide (Kemnitz 2015).

14.12

Sol-Gel Catalysts

14.12.5

657

Photocatalysis

Another field of application of aerogel catalysts for the protection of the environment concerns photocatalysis under UV radiation, designed to decompose and eliminate organic pollutants. Since an early work on the photocatalytic properties of TiO2 able to split the water molecule (Fujishima and Honda 1972), the main photocatalytic materials comprise TiO2 aerogels (Tomkiewicz et al. 1994), SiO2–TiO2 aerogels (Yoda et al. 2001; Ismail et al. 2004; Liu et al. 2008), or TiO2–graphene aerogels (Xiong et al. 2015). TiO2 aerogel-supported Pt catalysts showed improved catalytic efficiency in the hydrogen production by methanol-assisted water splitting (D’Elia et al. 2011). TiO2 aerogel-TiO2 nanowire composites were also synthesized by dispersion of the nanowires in a TiO2 gel prior to gelation. These aerogel composites were mesoporous and characterized by a high specific surface area (e.g., 427 m2 g
1) (Tursiloadi et al. 2006; Suzuki et al. 2008). In all cases it appeared important that TiO2 crystallized in anatase nano-domains (Cao et al. 2006, 2007). Other new classes of photocatalysts could be synthesized at low temperature. These compounds, essentially perovskite-type oxides, can exchange alkaline cations for H+ and insert water molecules in between their perovskite blocks, while their band gap edges are favorably positioned with respect to the redox potential of water (Kudo 2001). The generic name of perovskite derives from the mineral compound CaTiO3. Many other complex materials such as BaTiO3 or the derived perovskite structures such as BaTi4O9 crystallize with the same type of atom packing. For such complex oxides comprising several cations, conventional ceramics processing needs high-temperature heat treatment, which favors an important ceramic grain growth and destroys their catalytic activity. This is not the case of these low-temperature gel-related methods in which soluble cation complexes can be homogeneously dispersed. They require lower heat treatment temperatures than by conventional methods, and hence induce very limited grain growth of their nanoparticles. Their photocatalytic activity was reported to be up to one order of magnitude higher than powders prepared by conventional techniques. For such materials, an efficient technique is the Pechini or polymerizable complex method, reviewed by Schaak and Mallouk (2002) and Kakihana and Domen (2000). Excellent photocatalysts such as Ba3Ta4Si4O24 were also synthesized by the polyalcohol-modified silane precursor route (Yanagisawa et al. 2010). At last, POSS clusters are also considered for application in photocatalysis to hydrophobize the photocatalysts. For this purpose, nanofibers made by mixing hydrophobic fluorinated POSS, poly(vinylidene fluoride) (PVDF), and TiO2 nanofiber composites were designed (Ragesh et al. 2014).

658

14.12.6

14

Applications of Sol-Gel Processing

Sol-Gel Biocatalysts

Enzymes are the natural molecular catalysts of the living world. They are extremely efficient, but each enzyme is very specific on one type of biochemical reaction. To apply them in industry, it is desirable to immobilize them on a support so that they can easily be recycled. For this purpose, the encapsulation or entrapment of enzymes inside silica gel was investigated by many researchers and several reviews were published (Avnir et al. 1994; Dave et al. 1994; Lin and Brown 1997; Gill and Ballesteros 2000; Livage et al. 2001; Jin and Brennan 2002; Pierre 2004; Livage and Coradin 2016). The first report on sol-gel encapsulation of enzymes dates back to Dickey (1955) who immobilized urease, catalase, and muscle adenylic acid deaminase in silica gel made from sodium silicate. Later on, Johnson and Whateley (1971) encapsulated trypsin in similar sol-gel materials, while Carturan et al. (1989) embedded enzymes in thin silica gel layers deposited on a glass slide. By applying a two-step sol-gel route in order to adjust the chemical environment to the enzymes, Brinker’s team extended it to enzymes comprising glucose oxidase, horseradish peroxidase, and glucose-6-phosphate dehydrogenase and to biomolecules in general (Bhatia et al. 1998, 2000; Brinker et al. 2002). Liu and Chen patented another process to encapsulate catalase in silica gel made from colloidal silica particles (Liu and Chen 2001). Nevertheless, the silicate method suffers from a lack of flexibility for adjusting the hydrolysis and condensation reaction rates to the desired level so as to tailor the texture of a gel, and the functionalities present on the surface of the gel pores. Hence, the favored precursors now are alkoxides Si(OR)4, or alkoxysilanes of the type XSi (OR)3 in which X designates an organic group and R an alkyl group. The first use of such precursors was by Venton et al. (1984) to encapsulate antiprogesterone antiserum, and by Glad et al. (1985) to encapsulate the enzymes glucose oxidase, horseradish peroxidase, trypsin, and alkaline phosphatase. Subsequently, the field began to expand, with work by Braun et al. (1990) on alkaline phosphatase, chitinase, aspartase, and β-glucosidase and Zink and coworkers (Ellerby et al. 1992; Yamanaka et al. 1992) on copper-zinc superoxide dismutase, glucose oxidase and peroxidase, as well as the metalloproteins cytochrome c and myoglobin (Reetz 1997; Gill and Ballesteros 1998; Livage et al. 2001). In particular, the team of Reetz (Reetz et al. 1995, 1996: Reetz 1997; Gill and Ballesteros 1998) achieved very high activity in esterification-transesterification reactions in organic solvents with lipases entrapped in silica xerogels having the proper hydrophobic–hydrophilic balance. In this case, hybrid organic-silica gels were really used and these gels were really ambigels, i.e., gels similar to aerogels but where the surface functionalities permitted to largely avoid shrinkage during drying. Other hybrid gels were also investigated, based on dextran-SiO2 gel (Gulcev et al. 2002), chitosan-SiO2 gel (Miao and Tan 2001), or cellulose acetate fiber-ZrO2 gel (Nakane et al. 2001). At last, more recently, enzymes encapsulated in hydrogel and xerogel quantum dots (QD) were developed to be used as building blocks of functional architectures such as QD biosensors, as summarized by Yuan et al. (2013). In particular tyrosinase was

14.12

Sol-Gel Catalysts

659

encapsulated in CdTe gel QD which showed to be efficient for the biosensing of dopamine. Aerogels themselves could successfully be used to entrap biomaterials (Yin and Rubenstein 2011), including enzymes such as lipases as shown by Antczak et al. (1997), and by Pierre and collaborators (Pierre et al. 2000; Pierre and Ricacci 2011; Buisson et al. 2001). These authors described the in situ encapsulation of the Pseudomonas cepacia lipase into a hydrophobic silica aerogel on which they tested various enzyme-catalyzed esterification and transesterification reactions. They also observed that the biocatalytic activity could be significantly higher than the enzyme in solution. Because of the larger pore size, each lipase molecule was indeed able to operate as a free isolated molecular catalyst, while agglomeration of the catalyst was made impossible by dispersion in the aerogel network.

14.12.7

Sensors

Sensors designate tools to determine the presence of target chemicals, known as “analytes,” using an easy, accurate, and low-cost technique, which can be applied to a small quantity or a low concentration of medium to analyze. Chemical sensors exist for many pollutants (CO2, CO, NOx, SO2, SO3, O3). Some sol-gel ceramics can also directly be used as the sensing component. This is for instance the recent case of Si–O–C sol-gel ceramics derived from preceramic polymer chemistry, which present interesting properties for application in toxic gas sensors (Karakuscu et al. 2013). But very often, in recent sol-gel sensors, a chemical-sensing additive must be integrated in a sol-gel support, itself directly connected or integrated to a physical transducer, which itself provides a signal depending on the analyte concentration. A recent review regarding sol-gel-based sensors was presented by Villegas et al. (2016). Among these sensors, a noteworthy development concerned biosensors, in which the sensing element is itself of biological nature, often an enzyme able to transform a small quantity of substrate analyte to a product. This field was addressed in a number of articles (Audebert et al. 1991: Braun et al. 1990; Ellerby et al. 1992: Wang 1999; Cullum and Vo-Dinh 2000; Power et al. 2001; Carroll and Anderson 2011; Casero et al. 2016). Practically, a biosensor is composed of a biological recognition system, termed a bioreceptor, and a transducer which must convey the information provided by the bioreceptor. This information is provided as some signal, when the bioreceptor meets the analyte to be identified and interacts with it. These bioreceptors must be immobilized on the transducer, in particular in a sol-gel component of this transducer. These bioreceptors comprise a very large variety of biomolecular species, including microorganisms (bacteria, fungi). Antibodies, which can bind with very specific antigen analytes, as well as these antigens themselves, have particularly become favorite bioreceptors. Among them, a large number of enzymes are available, summarized by Casero et al. (2016). As an example, the presence of glucose can be determined using the enzyme glucose

660

14

Applications of Sol-Gel Processing

oxidase (GOx) (Yamanaka et al. 1992; Audebert et al. 1993) which can efficiently catalyze the reaction: β‐D‐glucose þ O2 $ D‐gluconic acid þ H2 O2 GOx

ð14:27Þ

The signal is provided by H2O2. Overall, the nature of a signal can be optical electrochemical or mass sensitive. Optical transducers are practical. They can be analyzed by spectroscopic techniques: absorption, fluorescence, phosphorescence, Raman spectroscopy, refraction, and dispersion spectroscopy. Analysis by fluorescence is the most frequent method. In this case, the receptor-analyte system can be naturally fluorescent, or fluorescent ligands must be tagged either to the analyte or to the bioreceptor. Electrochemical transducers are useful when the analyte-bioreceptor system is not fluorescent, or when labeling with a fluorescent tag is tedious. A conducting hydrogel (Isola et al. 1998) or a conducting polymer deposited on a graphite felt or a carbon paste (Huang et al. 1998) or SnO2 electrodes (Okawa et al. 1999) can be used as the transducers. The mass sensitive techniques can for instance make use of vibrating piezoelectric crystals, e.g., in quartz crystal microbalance (QCM) which comprises a quartz crystal coated with gold on which a monolayer of receptors has been immobilized. The crystal vibration frequency is very dependent on any mass increase, due to the binding of the analyte to the bioreceptor (Su et al. 2000). A type of mass device even more sensitive consists of micro-cantilever sensors, where the sensitive tip surface can be as small as 10
5 cm2 (Fagan et al. 2000). The principles of a few types of transducer are illustrated in Fig. 14.17. They can for instance be mixed with silica sol-gel precursors and placed in the wells of an enzyme-linked immunosorbent assay (or ELISA) plate where they are rapidly entrapped by gelation. The medium to be tested just needs to be added in the wells, which results in the emission of some signal, transmitted by the transducer. In recent studies, these gels comprise organic materials, oxides, fluorides (Kemnitz. 2016), and graphene aerogels. The latter ones are particularly interesting because they are electrical conductors and they carry a high density of oxygencontaining functional groups and conjugated domains available for grafting (Li and Kaner 2008; Li and Shi 2012; Nardecchia et al. 2013; Kotal et al. 2014; Fang et al. 2015a, b). As an example, Power et al. (2001) described a biosensor under the form of an aerosol composed of aerogel dust particles, containing Escherichia coli and the green fluorescent protein (GFP) obtained from the jellyfish Aequorea victoria. When a virus, like the bacteriophage T7 polymerase promoter also under the form of an aerosol, contacted the bacteria, a green fluorescent light was emitted. Besides biological macromolecules, living organisms such as bacteria can also be trapped inside xerogel, e.g., yeast cells (Carturan et al. 1989) and even aerogels, such as in biosensors under the form of an aerosol composed of aerogel dust particles, containing Escherichia coli and the green fluorescent protein (Power et al. 2001). The team of Livage showed that such new-type hybrids could keep a good activity provided that a sol-gel chemistry adapted to the cells was selected (Livage et al. 2001; Livage and Coradin 2016).

14.13

Medical Applications and Biomaterials

661

Fig. 14.17 Principle of a few biosensors. (a) Micro-cantilever biosensor. Adapted from Fagan et al. (2000). (b) Optical nanofiber biosensor. Adapted from Tan (1998). (c) Biosensor chip. Adapted from Wadkins et al. (1998). (d) ELISA-type microtitration plate. Adapted from Goldsby et al. 2003. (e) Chromatograph column. Adapted from Waters et al. (1999)

14.13 14.13.1

Medical Applications and Biomaterials Biomaterials (Pierre 2016)

The American National Institute of Health defines biomaterial as “any substance or combination of substances, other than drugs, synthetic or natural in origin, which can be used for any period of time, which augments or replaces partially or totally any tissue, organ or function of the body, in order to maintain or improve the quality of life of the individual” (Bergmann and Stumpf 2013). Biomaterials must be biocompatible; for instance a good biomaterial should limit the release of deleterious metal ions, free radicals, and reactive oxygen species (ROS) which play a significant role in chronic inflammation diseases. A classical biomaterial is the mineral hydroxyapatite (HA). It belongs to the family of apatites of general formula Ca5(PO4)3(OH,F,Cl) in which the anions (OH
, F
; Cl
) can freely substitute for each other. HA corresponds to the case when the hydroxyl ions predominate. Its use is common for coatings of dental and orthopedic implants (Hayashi et al. 1994; Moroni et al. 2005). Given the nanotexture of HA in bone, the most extensive studies on HA synthesis aimed at producing nanocrystals, by techniques which are part of the sol-gel processes, except that only a

662

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Applications of Sol-Gel Processing

sol is produced, not a gel. Instead of gelation, a sol made of HA nanocrystals is induced to coagulate in bigger precipitates (Alves Cardoso et al. 2012). Typical precursors of HA sols involve a reaction of Ca(NO3)24H2O with (NH4)2HPO4, or H3PO4 with Ca(OH)2 or CaCl22H2O. Nano HA particles are obtained with CaCl2 in the presence of triethanolamine as a complexing agent as in the work of Puvvada et al. (2013). More recently, class II hybrids in which the Si and Ca atoms were homogeneously distributed could be achieved in the system SiO2 (from GPTMS)Ca-cPGTA by using a calcium salt of poly(c-glutamic acid) (cCaPGTA), in which Ca was chelated by the polymer component (Valliant et al. 2013). Competitor materials comprise the so-called bioactive glasses discovered in 1969 by Hench’s group (Hench et al. 1971; Hench 1991; Hench 2006). A detailed review by Jones was recently reprinted (Jones 2013). The first commercial reference patented 45S5 Bioglass® and, in clinical use since 1985, was made with the composition (in mol%) 46.1 SiO2, 24.4 Na2O, 26.9 CaO, and 2.6 P2O5 close to a ternary eutectic in the Na2O-CaO-SiO2 diagram. Sol-gel glasses with a composition close to the 45S5 Bioglass® were synthesized in the simpler systems SiO2CaOP2O5 or SiO2CaO, without any Na2O, by Hench’s group (Li et al. 1991; Siqueira et al. 2011). The sol-gel synthesis permits to avoid several drawbacks of melt-quench bioglasses, in particular crystallization during sintering. The solid network of both sol-gel and melt-quench bioglasses is made of siloxane Si–O–Si chains. The ions Na+, Ca2+, and PO43
do not participate in the network. They are dispersed in the network interstices and are termed “modifiers”. A schematic illustration of a SiO2 gel network containing some calcium was illustrated in Fig. 9.35 (Sect. 9.4). These biomaterials are bioactive because, in a biological liquid medium, natural HA is formed by a dissolution-reprecipitation mechanism from the bioglass. To favor bone implants, the presence of large channels inside the biomaterial is important, so as to offer pathways to the natural growth of bone cells after implantation. Such porous bioglass scaffolds containing large macropores (e.g., 300–600 μm pores and a porosity of 82 vol%) can be produced by adding a surfactant during sol-gel synthesis (Jones et al. 2010), or a polymer which is sacrificed in the end, for instance by calcination (Wang and Jain 2010). Overall, bioactive sol-gel-made scaffolds with an appropriate channel texture could be synthesized, which displayed a similar compressive strength to cortical bone (Fu et al. 2011). But they remained brittle and not fitted for implants working under cyclic load. Hydrogels are particularly interesting for this purpose. The texture of a hybrid gelatin-SiO2 sol-gel scaffold, with 90% porosity, is illustrated in Fig. 14.18 (Mahony et al. 2014). Other interesting sol-gel oxides for biomaterial applications are TiO2 and SiO2TiO2 sol-gel biomaterials (Advincula et al. 2006; Areva et al. 2007; Wang et al. 2012), studied as coatings on metallic Ti-based implants. The TiOH gel terminal groups can deprotonate to give negatively charged TiO
surface groups which can, in turn, respectively, attract Ca2+ cations and phosphate anions PO43
to form a bone-like CaP deposit (Viitala et al. 2008). They can also directly bond with an oxidized metal implant, by the intermediate of M-O-Ti bonds in which M is the implant metal (Kizuki et al. 2010). At last, aluminosilicates (Habazaki et al. 2014),

14.13

Medical Applications and Biomaterials

663

Fig. 14.18 SEM micrograph of a hybrid gelatin-SiO2 scaffold, made with 60 wt% gelatin. Reproduction of part of Fig. 2 from the OPEN ACCESS reference of Mahony et al. (2014), distributed under the terms of the Creative Commons Attribution 4.0 International License (http:// creativecommons.org/ licenses/by/4.0/). With permission from Springer Science+Business Media

ZrO2 and SiO2/ZrO2 mixed oxides (Śmieszek et al. 2014) were also studied as coatings for stainless steel implants. The brittleness of oxide bioceramics can be solved by designing hybrid organicinorganic biomaterials (Livage et al. 2004; Jones 2013; Miyazaki 2013; Carraro and Gross 2014), in particular with hydrogels as the organic components. The most widely used biodegradable polymers are PLA, PGA, and their copolymers (PLGA). These simple hydrogels, altogether with protein aerogels, are applied for tissue engineering and wound care application, such as to grow breast epithelial cell and tissue inserts for corneal implant (Pal et al. 2009; Mehling et al. 2009; GarciaGonzalez et al. 2011, 2015; Betz et al. 2012; Mikkonen et al. 2013). Class I hybrid scaffolds were studied in the systems SiO2-PVA (Gomide et al. 2012), SiO2–PEG (Catauro et al. 2015), and SiO2–PCL (Catauro et al. 2016). Regarding SiO2–PCL class I hybrids, the latter authors addressed the biocompatibility problems due to reactive oxygen species (ROS) coming from the implants. For this purpose quercetin, a naturally occurring antiradical flavonoid, was entrapped in the hybrids. Class II hybrids comprise ORMOSILS (e.g., Tsuru et al. 2004). The silane-carrying precursors include polydimethylsiloxane (PDMS), poly(tetramethyleneoxide) (Si-PTMO) terminated with 3-isocyanatopropyltriethoxysilyl ((C2H5O)3Si (CH2)3NHCOO–((CH2)4O)n–CONH(CH2)3Si(OC2H5)3), methacryloxypropyltrimethoxysilane (CH2 ¼ CCH3COO(CH2)3–Si(OCH3)3), mixed with TEOS plus a calcium precursor (Chen et al. 2001; Kamitakahara et al. 2001; Miyata et al. 2002; Yabuta et al. 2003). The elastic modulus and deformability of these hybrids were similar to those of human bones. At last, more recently, some siloxane-based POSS clusters were also investigated for application in biomaterials (Ghanbari et al. 2011).

664

14.13.2

14

Applications of Sol-Gel Processing

Drug Carriers

Another important field for applications of the above biomaterials, partly covered in the preceding section, is as pharmaceutical drug carriers which were addressed in many articles and reviews (Guenther et al. 2008; Mehling et al. 2009; GarciaGonzalez et al. 2011, 2012, 2013, 2015; Alnaief et al. 2012; Giray et al. 2012; Del Gaudio et al. 2013; Valo et al. 2013; Maleki et al. 2014; Marin et al. 2014; Ulker and Erkey 2014a, b; Colilla et al. 2015; Veres et al. 2015; Stergar and Maver 2016). In particular, the biomedical applications of SiO2-based aerogels for the controlled release of medical drugs were recently reviewed by Stergar and Maver (2016). It must be noted that hydrophilic SiO2 aerogels with a high specific surface area are biocompatible and slowly biodegradable because they can be slowly hydrolyzed, contrary to crystalline silica nanoparticles which are very dangerous, being responsible for the disease silicosis (Smirnova et al. 2004a, b; Murillo-Cremaes et al. 2013; Wang et al. 2015). The controllable pore size and high specific pore volume of silica aerogels make them ideal candidates for releasing medical drugs or agriculture chemicals (fungicides, herbicides, pesticides) (Brinker and Scherer 1990; Bernik 2007; Smirnova et al. 2004b; Maleki et al. 2014) in a controlled fashion. Hydrophilic silica aerogels can be loaded with chemicals during the sol-gel synthesis process or by posttreatment of dried aerogels (Smirnova and Arlt 2004). Hybrid aerogels, which combine an organic biodegradable component with silica, increase the range of available biodegradable aerogels (Ree et al. 1995; Alnaief et al. 2012; Giray et al. 2012; Wang and Jana 2013; Ulker and Erkey 2014b).

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Index

A Abnormal grain growth, 576 Acetone, 356 Acidic gels, 387 Acoustic impedance matching, 640 Acoustic insulation, 627 Action of dopants and pores, 579 Aerogel layer, 640 Aerogels, 2, 5, 6, 500, 501, 509, 537, 538, 540, 600 alumina, 388, 389 carbon, 403, 404 cellulose, 398, 402 elastic properties, 410 graphene, 404, 405, 412 HILIT project, 380 HR-SEM, silica aerogels, 380 mechanical properties, 412 organic gels, 398 polyurea, 401 pore size distribution, 366 pore texture, 369 RF gels, 399, 400 silica, 372 specific surface area, 369 sulfide, 396 superhydrophobic silica, 375 texture, 399 thermal conductivity, 408 thermal properties, 407 zirconia, 390 Aerosol hydrolysis, 202 Aging chemical evolution, 341, 342 physical evolution, 341, 343

© Springer Nature Switzerland AG 2020 A. C. Pierre, Introduction to Sol-Gel Processing, https://doi.org/10.1007/978-3-030-38144-8

Aging evolution Ostwald ripening, 266, 267 solid-phase recrystallization, 265, 266 Alkaline silicate solutions, 57 Alkanes, 487 Alkoxides, 10, 15, 191 aluminum ethoxide, 69 chemical characteristics, 72, 73 condensation reaction olation, 79 oxolation, 79, 80 hydrolysis hydroxo ligands, 75–77 oxo ligands, 77, 78 parameters, 75 non-hydrolytic processes, 69 oxide sol-gel precursors, 69 physical and structural characteristics, 70–72 silicon, 73–75 solid phases alumina, 91, 92 boron oxide, 91 elements, 90, 91 linear polymers, 90 polymerization, 90 titania, 92, 93 zirconia, 94, 95 Alkoxysilanes diversity, 99 organotrialkoxysilanes, 99, 100 Alumina, 91, 92 gels, 386–388 powders, 562 Aluminosilicate systems, 457

687

688 Aluminum, 51, 52 Aluminum alkoxides, 83, 84 Ambient pressure drying method, 352, 355, 356 Ambigels, 355, 376, 397 American Ceramic Society, 609 The American National Institute of Health, 661 3-Aminopropyl trimethoxysilane (APMS), 194, 195 Ammonia, 539, 540 Ammonium persulfate (AMPS), 149 Amorphous solid phases, 497 Amphiphilic copolymer templating, 457, 485 Amphoteric surfactants, 464, 488 Anionic surfactants, 463 Anions, 179 bidentate anion, 42, 43 metal M, 44, 45 solid phase chemical transformations, 45 electrostatic interactions, 46 equilibrium constant, 45, 46 iron products, 49 polymerization, 48 polynuclear complexes, 45, 49 soluble species, 47 statistical equation, 47 Antireflective (AR) coatings, 635 Aqueous hydrophilic liquid, 482 Aqueous solute classification, 460, 461 Aquo-hydroxo complex, 54 Aromatic ketones, 655 Aspen Company, 598 Atomic configuration, 528 Atomic diffusion, 576 crystallization, 562–564 ionic solids, 560 sintering, 562–564 sol-gel materials, 561 Atomic transport mechanisms, 561 Attenuated total reflection (ATR), 293 Avrami equation, 522 Azobisisobutyronitrile (AIBN), 106

B Barrett, Joyner and Halenda (BJH) method, 367, 382 Batteries, 638 “Bead POSS-organic hybrid” composites, 436 Bimolecular collisions, 174 Bimolecular nucleophilic substitution, 27 Bioactive glasses, 662 Biological recognition system, 659

Index Biomaterials, 661–663 Bioreceptors, 659 Bite distance, 27 Block copolymers, 485–487 Boehmite gels, 328, 500, 502–504, 512 Boltzmann statistics, 172 Book organization, 11 Borate gels, 385 Borides, 541 Boron alkoxides hydrolysis, 81, 82 Brönsted acid-site protons, 654 Brownian motion, 332 Brunauer, Emmett and Teller (BET) model, 368 Bulk electrical conductivity, 637

C Capillary mechanism, 345–347 Capillary stresses, 351 Carbides, 537, 538 Carbon aerogels, 129, 145, 151, 537 Carbon gels, 129 Carbon nanotube (CNT) gels, 129, 152, 157, 403, 537, 637 aerogels/sol-gel oxide composites, 441, 444 elastic mechanical properties, 413 freeze-drying, 405 graphene, 153, 155, 157, 158, 403 with RF-derived gel bonding, 412 SEM, 406 xerogels, 405 Carbon xerogels, 129 Carboxylic acids, 62, 396 Catalysis mechanisms, 646 Catalytic active phases, 654 Catalytic groups, 654 Cathode ray tube (CRT), 630 Cationic surfactants, 463 Cations, 179 Cellulose acetate aerogels, 402 Cellulose gels, 148, 401 Ceramer description, 422 hybrid architectures (see Hybrid architectures) Ceramic ion conductive membranes (CICM), 622 Ceramic membranes, 616–618 Ceramics, 2, 3 Cherenkov counters, 628–630 Chalcogenides, 129 aerogel, 135

Index gels, 138, 396–398 glasses, 604, 636 nanoparticles, 137 sulfide solutions, 130 xerogels, 137 Zintl clusters, 134, 135 Chemical homogeneity, 10 Chemical precursor, 15 Chemical transformations, 15, 646 Chemical vapor deposition (CVD), 11, 157, 199, 200 Chemical water, 499, 500 Chlorides, 15 Citric acid (CA), 63 Clay, 393 Clay/boehmite gels, 326 Clay-water systems, 334 CO2 supercritical method, 537 Coagulation kinetics re-peptization, 245–246 Smoluchowski derivation, coagulation , rate,244 Cocamidopropyl betaine (CAPB), 488 Coions, 216 Colloidal gelation, 306 Colloidal suspension, 209 Colossal magnetoresistant (CMR), 640 Combinatorial chemistry, 64 Compact hexagonal array, 483 Composite materials “bead POSS-organic hybrid”, 436 gel matrix, 441 and hybrid gels, 425 POSS, 429 sol-gel hybrids, 421 sol-gel processing (see Sol-gel composites) Computer calculation methods DFT, 302, 303 force field, 303, 304 mesoscale and coarse-grained, 305 reactive bond, 304 Conventional quench technique, 10 Coprecipitation mechanism, 61 Counterions, 216 Critical coagulation concentration (C.C.C.), 239 Crystalline materials, 561, 608 Crystalline packing, 184 Crystalline quantum dots (CQDs), 196 Crystallization, 521, 535, 536 Cu(I)-catalyzed azide and alkyne cycloaddition (CuAAC), 102, 103

689 Cyclic voltammetry (CV), 637 Cylindrical channels, 488 Cylindrical pore shape, 364

D Darcy’s law, 336 Debye-Hückel approximation, 224, 225 Debye-Hückel length, 223 Deep ultraviolet (DUV), 635 Demixion, 486 Dense colloidal particles, 15 Dense wavelength division multiplexing (DWDM) devices, 636 Densification atomic diffusion, 554, 556, 557 gel network, 566 grain growth, 555, 556 impurities, 579 packing distribution, 583 sol-gel materials, 561 viscous flow, 564, 585 zirconia, 562 Density functional theory (DFT), 71, 142, 302 Derjaguin, Landau, Verwey and Overbeek (DLVO) theory, 1, 209, 306, 348–350 coagulation, 239–240 Debye-Hückel approximation, 224, 225 effect of ion solvation, 240–242 electric potential Ψ (x), 219–221 electrophoretic mobility, 217 electrostatic charge reversal, 242–243 electrostatic repulsion force (see Electrostatic repulsion force) flocculation/coagulation, 239 Gouy-Chapman model (see Gouy-Chapman model) isoelectric point (i.e.p.), 218 non-determining ions, 216, 217 Stern model, 225 total interaction energy, 237 Van der Waals interaction (see Van der Waals interaction) zero-point charge (z.p.c), 215 and easy-to-adsorb cation, 218 zeta potential ζ, 217 Deutsches Elektronen-Synchrotron (DESY), 611 Dielectric applications, 639 Dielectric properties, 20

690 Differential scanning calorimetry (DSC), 520, 529, 644 Differential thermal analysis (DTA), 302, 499, 500, 519, 520 Diffuse reflectance IR Fourier transformed spectroscopy (DRIFTS), 293 Di-isocyanate reinforcement, 446 Dimethyldiethoxysilane, 74 Dimethyl fluoride (DMF), 636 Dip coating, 603 Dissolution-recrystallization, 513 Divinylbenzene (DVB), 144 Donnan equilibrium theory, 334, 336, 337 Double liquid–solid composition, 323 Double-nozzle reactor, 641 Drug carriers, 664 Dry gels adsorption isotherms analytical computation methods, 367 gas, 365 hysteresis isotherm, 366 nitrogen adsorption isotherms, 367, 368 porous specific surface area, 368–371 alumina gels, 386–388 borate gels, 385 epoxidation method, oxides, 391 gel chemical nature, 406 mechanical properties, 409–413 mercury porosimetry, 364, 365 mixed oxide gels silicate, 393–395 titanate, 395 network texture, 379 non-oxide gels (see Non-oxide gels) oxide gels (see Oxide gels) pore characterization techniques, 363, 364 structure gel crystallographic structure, 372, 373, 375 gel fractal structure, 372, 373 gel surface structure, 374, 375 hydrophobization, oxide gels, 375–377 texture, 363, 369, 370 thermal conductivity, 406–409 titania gels, 389 tungsten oxide gels, 391 vanadium, 391, 392 zirconia gels, 390 Drying control chemical additives (DCCA), 355, 611 Drying gels ambient pressure, 355, 356 evaporation

Index capillary mechanism, 345–347 DLVO theory, 348–350 stresses development, 350–352 freeze-drying, 357, 358 subcritical, 356, 357 (see Supercritical drying) Drying methods, 7 Dynamic random access memory (DRAM) devices, 601

E Efficient thermal insulators, 600 Elastic property, 328–330 Electric conduction, 328 Electric field fast and flash sintering charged point defects, 590 electrical conductivity, 590 electric conduction, 588 electric current, 588 electrodes, 588 limit intensity, 590 liquid-phase sintering mechanism, 592 thermal runaway, 589 thermodynamic equilibrium constant, 590 X-ray determination, 590 ZnO flash sintering experiments, 590 microwave-assisted thermal treatments, 587, 588 Electrical conduction, 599, 637, 638 Electrical conductors, 660 Electrical field, 332 Electrical resistance, 599 Electrochemical precipitation, 197 Electrochemical transducers, 660 Electrodes, 638 Electron charge donor, 39 Electron diffraction, 521 Electronegativity, 22, 23, 32, 42, 43 Electronic paramagnetic resonance (EPR), 302 Electrons, 16, 17 Electrophile, 39 Electrophilic protonation, 141 Electrostatic character, 33 Electrostatic repulsion force interaction between spherical particles, 234–236 changing the valence z, 237 potential-determining ions, 237 parallel planar surfaces, 230–234

Index Electrostatic theory, 1 Emulsion polymerization, 599 Energy-dispersive X-ray (EDX) detector, 301 Environment remediation applications, 642, 643 Enzyme glucose oxidase (GOx), 659 Enzyme immobilization capture, CO2 gas, 643, 644 confinement applications, 641, 642 environment remediation applications, , 642, 643 low density and brittle characteristics, 644 silica aerogels, 644, 645 water droplets, 644 Enzyme-linked immunosorbent assay (ELISA), 660 Epitaxial growth, 601 Equilibrium thermodynamics, 323, 517 Ethanol, 356 Ethylene glycol (EG), 63 Ethylenediaminetetraacetic acid (EDTA), 62 European Centre for Nuclear Research (CERN), 611 European Retrieval Carrier (EURECA) satellite, 626 Evaporation-induced self-assembly (EISA), 603 Experimental Schulze-Hardy rule, 285 Extended DLVO theories hydration forces, 255 hydrophobic forces, 255–257 QCM, 254 QCM-D, 254 repulsive hydration forces, 254 schematic principle, 254 SFA, 253 External quantum efficiency (EQE), 630

F Fabrication techniques coating thickness, 604 dip coating, 603 parameters, 604, 605 spin coating, 603 spraying, 603 viscosity, 605 Ferrihydrite, 54 Ferrofluid sols, 598 Fibers compositions, 606, 607 fabrication techniques, 607, 608 Fibrillar structure, 324

691 Filtration membranes ceramic membranes, 616–618 molecular diffusion, 614 porous membrane, 615, 616 Fine solid powders, 117 Flory-Huggins theory, 332 dimensionless parameter, 247 endothermic solutions, 248 Gibbs free energy, 247 molar contribution, 248 organic polymeric solute, 247 polymer chains, 248 upper critical temperature, 249 Flory-Stockmayer model, 271, 329 characteristics, 272 GP, 272 Fluoride glass, 528 Fluorides, 129, 138, 139, 507, 508, 630, 631, 634 Fluorine-doped tin dioxide (FTO), 139 Fluorolytic reaction, 141 Force field methods, 303 Forced hydrolysis, 178 Fourier transformation (FT), 293 Fourier transformed infrared spectra (FTIR), 374, 500 Fractional factorial design, 63, 64 Free energy contribution, 334 Free-standing films, 605, 606 Freeze-drying, 202, 357, 358 Frenkel’s model, 566

G Gelatinous precipitates, 6 Gelation, 5 colloidal vs. polymeric gels, 307 computer calculation methods (see Computer calculation methods) DLVO theory critical electrolyte concentration, 285 electrostatic conditions, 285, 286 gel structure, 287 kinetic approach, 271 light scattering, 296, 297 multicomponent systems, 317–318 NMR, 299–301 physical and chemical, 307 polymer solutions, 306 sol/solution, 271 Gel classifications chemical nature, 326, 327 colloidal vs. polymeric, 326

692 Gel classifications (cont.) drying technique, 326 organic and inorganic gels, 324 solid network and comprises, 324, 325 wet medium evolution, 326 Gel dehydration adsorbed water, 501 chemical water, 499 dissolution-recrystallization, 501 hydrolysis, 499 structural water, 501–504 Gel-derived glasses, 529 Gel network transformation effect of unsymmetrical particles, 558 particle distribution, 559, 560 spherical particles, 557 strings of particles, 558 Gel point (GP), 272 Gels, 5, 443 Geopolymers, 57 Gibbs adsorption isotherms, 458–460 Gibbs internal free energy activation energy, 175 final composition, 170 fluctuations, 172, 173 growth stage, 169 homogeneous nucleation, 171 linear relationship, 170 thermodynamic fluctuation, 174 transformation, 173 Glasses, 91 Glass formation amorphous materials, 518, 519 crystallization, 535, 536 gels above Tg, 525, 526 melt-quenched, 520, 528, 529 non-oxide sol-gel glasses, 528 polymeric gels, 524, 525 sol-gel, 526, 527 sol-gel silica, 528, 529 traditional experimental study, 519–521 TTT diagrams, 521–523 X-ray diffraction patterns, 523, 524 Glass formers, 519 Glycidoxypropyltrimethoxysilane (GPTMS), 434, 437, 438 Glycol-modified silanes (GMS), 107, 108, 117, 118 Goethite, 54 Gouy-Chapman model Boltzmann statistics, 221 boundary conditions, 222 counterions, 223 Debye-Hückel length, 223

Index electric potential profile Ψ, 221 planar surface, 223 Grain boundary mobility, 573–575 Grain growth densification, 575 grain boundaries, 575–578 impurities, 569, 570 mechanism, 568 models, 568, 569 prevention, 579 sintering maps, 578, 579 sol-gel ceramics, 580, 581 Graphene, 153, 155, 537, 637 Graphene aerogels, 640 Graphene gels, 403–405 Graphene oxide (GO), 156, 157, 637 Graphene quantum dots (GQDs), 196 Graphene xerogel, 412 Green fluorescent protein (GFP), 660 Growth mechanisms diffusion, 183, 184 effects, 181 mononuclear, 181, 182, 184 new phase, 180 polynuclear, 182, 184 solid particles, 180 Growth termination, 189

H Hamaker constant, 213 Hardness, 22, 23 Hazardous liquids, 642 Hematite, 54 Herring’s scaling laws, 553 Heterogeneous catalysis, 646 Heterogeneous gelation, 278 Heterogeneous nucleation, 176 Heterometallic alkoxides, 111–113 Heteropolyacids (HPA), 655 High-energy physics, 611 “Highly Insulating and Light Transmitting Aerogel Glazing for Windows” (HILIT) project, 380 High-temperature supercritical drying (HOT SCD), 354 Homogeneity, 536 Homogeneous nucleation, 171, 174, 178 Hot pressing, 584–587 Hybrid architectures class I dispersed components, 426 inorganic and organic sol-gel precursors, 429, 430

Index organic dye in silica gel, 426, 427 oxide gel with organic precursor solution, 430 polymer intercalation, lamellar inorganic gels, 430 short organic polymers, oxide gel/oxide clusters, 427 silica POSS cluster (see Polyhedral oligomeric silsesquioxane (POSS)) class II ceramer hybrids diethoxydimethyl silane with alkoxides, 438 Pechini method, 439, 440 polymeric gel precursor method, 440–441 polymerization, 439 titanium precursors, 437 class II ormosil hybrids coupling silica with hydrogels, 437 polymer-bridged silica clusters, 433, 434 polysilsesquioxane, 432 POSS-organic polymer, 435–437 silica gel, pendant organic groups, 432 3-dimensional network, 431 hybrid ormosil architectures, 424 Hybrid gels mechanical properties, 445–447 specific surface area, 448 thermal conductivity, 449 Hybrid organic-inorganic materials gels, 421 sol-gel materials class I and class II hybrids, 423, 424 hybrid gel architectures, 424, 425 hybrid gels vs. composite materials, 425 ormosils and ceramers, 422 3-dimensional gel network, 421 Hybrid ormosil architectures, 424 Hydration forces hydrophilic surfaces, 255 planar surfaces, 255 water molecules, 255 Hydrogels, 151, 400–402 Hydrogen, 642 atom, 19 bonds, 502 Hydrolysis, 351, 603 anions, 27 aqueous media hydroxo ligand (OH), 29–31 oxo ligand, 31 PCM, 32, 33 water molecules, 29

693 chemical transformations, 27 condensation reaction hydroxo ligand (OH), 35 metal atoms, 35 olation, 35–37 oxolation, 36–38 PCM, 38–40 ion solvation, water, 28, 29 organic solvents, 34 Hydrolytic sol-gel process, 139 Hydrophilic-lipophilic balance (HLB), 465, 466 Hydrophilic/lyophilic solution, 4 Hydrophobic forces attractive mechanism, 256 interaction energy, 257 liquid–vapor phase transition, 256 water vapor bridge, 256 Hydrophobic process, 197 Hydrotalcites, 62 Hydrothermal process, 197 Hydrous oxides, 50 Hydroxide precipitates, 510 Hydroxo ligand, 29–31 Hydroxyapatite (HA), 661, 662

I Imperial Chemical Industries (ICI) company, 606 Impurities, 569, 570 Indium tin oxide (ITO), 601 Infrared (IR), 292 Inorganic gels, 430 Inorganic sol-gel precursors, 483 Internal quantum efficiency (IQE), 630 Ionic solids, 560 Irreversible gelation, 307–309 Irreversible transformations, 323 Isocyanates, 148 Isoelectric point (i.e.p.), 218 Isogel, 324 Isotropic percolation, 279

J Japanese High Energy Accelerator Research Organization (KEK), 630

K Kaolinite, 242 Kelvin’s equation, 561 Kinetic properties, 529

694 L LaMer model, 176, 177 anions/cations, 179 forced hydrolysis, 178 monodispersed particles, 177 separate reactors, 180 temperature modifications, 179 thermodynamics, 177 Laplace’s equation, 568 Laser filters, 601 Lead lanthanum zirconium titanates (PLZT), 10 Lewis acids, 656 Lewis base, 29 Ligands, 25 Light-emitting diodes (LEDs), 636 Liquid chromatography, 599 Liquid crystals, 457, 468, 469 Liquid drying, 202 Liquid–liquid extraction, 357, 358 Liquid–solid–vapor interface, 346 Lorentz–Lorenz formula, 635 Low-density medium, 629 Low-temperature supercritical drying (COLD SCD), 354

M Magnetic nanoparticles (MNP), 478 Magnetic resonance images, 641 Martensitic transformations, 514 Matching layer, 640 Melamine-formaldehyde (MF), 146 Membrane reactors (MR), 622 Mesocrystals, 198 Mesopore architecture, 483 Mesoporous methyltrimethoxysilane (MTMS), 487 Mesostructured films, 483 Metal-organic-framework (MOF), 64 Metal salts anions (see Anions) carboxylic acids, 62 chemical precursor, 15 hydrolysis (see Hydrolysis) inorganic sols and gels, 15 modes, 61, 62 nonaqueous solvents, 19–21 PCM, 21, 22, 24, 25 Pechini method, 62–64 transformation mechanism, 25, 26, 28 water, 16, 17, 19 Metastannic acid, 56 Methyltriethoxysilane (MTES), 73

Index Methyltrimethoxysilane (MTMS), 73, 356 Micelle formation, 466 Microcapsules, 475, 477, 478 Microemulsion, 475 Microparticle synthesis colloidal sols, 479 microcapsules, 475, 477, 478 Microwave-assisted thermal treatments, 587, 588 Microwave devices, 601 Microwave heating, 484 Mixed alkoxide techniques, 564 Mixed steric and electrical interactions Ferrofluids®, 253 surfactants solutions, 252 Mobil Oil Company (MCM), 480 Molecular weight cutoff (MWCO), 615 Monodispersed particles, 165, 176, 186, 189 Monohydroxide, 341 Monoliths aerogel, 611, 612 ambigel, 611, 612 gel and derived ceramic, 609, 610 hybrids, 610, 611 sol-gel powders ceramics, 614 complex titanate synthesis, 612, 613 sintered, 612 Monomers, 633 Mononuclear growth, 182 Monosized particles, 165 Monsanto Chemical Company, 352 Multicomponent oxides, 514–516 Multilayer coatings, 599

N Nernst equation, 25 Network consolidation, 508, 509 Nitrides, 144, 145 Nitrogen, 539, 540 N-methyl-pyrrolidone (NMP), 155 Non-bridging oxygen (NBO), 58 Non-hydrolytic processes aprotic reactions, 120, 121 hydroxylation reactions, 119 liquid organic component, 118 mixed oxides, 118 oxide nanoparticles, 118 Non-hydrolytic sol-gel process, 395, 396 Nonionic amine, 488 Nonionic surfactants, 464 Nonlinear optics (NLO) molecules, 636

Index Non-oxide gels carbon aerogels carbonization, 403 CNT, 403 graphene gels, 403–405 from organic gels, 403 chalcogenide gels, 396–398 hydrogels, 400–402 organic gels, 397, 398 RF gels, 399, 400 Non-Si clusters, 108 Normal growth regime, 523 Nuclear magnetic resonance spectroscopy (NMR), 299–301 Nucleation, 166 alkoxide solutions, 190 fluctuation, 173 growth rate, 177 growth sequence, 179, 498, 510, 516, 519, 529, 531, 533–536 homogeneous rate, 174 magnification, 186 metal salt solutions, 187 nanoparticles, 199 particle shape/size, 186 phase transformation, 168 spherical particle, 167, 168 supersaturation, 174 Nucleophile, 39

O Olation/oxolation, 175 Optical applications Cherenkov counters, 628–630 luminescent materials, 630, 631 nonlinear optics, 636 optical coatings (see Optical coatings) silica gels, 627, 628 Optical coatings antireflective films, 633 conductive properties, 634 conventional techniques, 633 monomers, 633 oxide sol-gel materials, 634 polysilsesquioxanes, 633 principal application, 635 single metal oxide coatings, 632 single-oxide films, 631 technological applications, 634 TiO2, 633 transparent polymer matrix, 634 Optical transducers, 660

695 Ordering phenomena aging evolution (see Aging evolution) crystalline-like transitions, 263–264 sol demixion, 262–263 Organic aerogels, 129, 145 Organic catalysts, 654 Organic gels, 397–399 Organic hydroperoxides, 655 Organic/inorganic monocrystals, 331 Organic solvents, 21 Organometallics, 106, 107 Organotrialkoxysilanes, 99, 100, 432, 433 CuAAC, 102, 103 enzymes/DNA fragments, 101 POSSs, 104, 105 Si coordination polyhedra, 103 thiol-ene click reactions, 101 Ormosil, 422 Osmosis, 334 Osmotic free energy, 335 Osmotic swelling behavior, 329 Osmotic swelling theory, 331–333 Ostwald ripening, 266, 267, 343 Oxide gels, 333, 338 as colloidal, 378 hydrophobization, 375–377 non-hydrolytic process, 395, 396 silica from functionalized alkoxides, 383–384 simple alkoxide-derived gels, 378–383 Oxo-fluorides, 140 Oxo ligands, 31, 77, 78 Oxyfluoride glass, 528 Oxygen atom, 16

P Partial charge model (PCM), 21, 22, 24, 25, 32, 33, 38–40 Particle nucleation, 197 growth in gel, 199 PbS particles, 188 Pechini method, 51, 62–64, 439, 440, 506, , 517, 630 Percolation models bond/site, 273 critical parameter, 277, 278 Euclidean dimension, 276 vs. gelation, 276 mean/effective medium theory, 277 solid gel network, 275 threshold, 274 transport property, 275

696 Periodic mesoporous organosilica (PMO) materials, 480 Phase transformations, 167 atoms, 498 chemical evolution, 497 chemical group elimination residual anions, 506 residual organics, 504, 506 chemical transformations, 507, 508 chronological evolution, 498 gel network transformation, 508, 509 growth, 533, 534 Hüttig range, 498 (see also Gel dehydration) types, 499, 500 Hüttig temperature, 498 lower Tammann range, 508 melting temperature, 498 multicomponent oxides, 514–516 non-oxide ceramics, 499 nucleation, 533, 534 PG, 517, 518 sol-gel chemistry, 513 solid network, 497 specific surface area, 535 spinodal decomposition, 530, 532, 533 stable thermodynamics phases, 497, , 533, 534 Tammann temperature, 497, 498 topotactic (see Topotactic crystallization) zirconia, 513, 514 Phenylene-bridged polysilsesquioxanes, 434 Photocatalysis, 657 Photographic films, 9, 599 Physical chemistry theory, 15 Physical vapor deposition (PVD), 199, 200 Piezoelectric applications, 639, 640 Pinhole technique, 356 Planar surfaces, 571 Polyacrylamide gels, 149, 151 Polycarbosilane, 536 Polydisperse particles, 176 Polyethoxydisiloxanes, 343 Polyethylene glycol (PEG), 60, 108 Polyethylene glycol-conjugated phosphates (PEG-P), 60 Polyfunctional alkoxysilanes, 610 Polyhedral oligomeric silsesquioxanes (POSSs), 104, 105, 505 amine-terminated materials, 437 bead copolymers, 435, 436 “bead POSS-organic hybrid” , composites,436 “blended composites”, 429

Index copolymer architectures, 436 description, 428 fluorinated, 429 reactive side groups, 435 vinyl-functionalized POSS, 437 Polyhedral oligometallasilsesquioxanes (POMS), 108 Polyhedral oligosilsesquioxane nanocrystals (POSS), 100 Polyhydroxybutyrate (PHB), 478 Polymer dots (PDs), 196 Polymer solutions Flory-Huggins theory, 247–249 state equation theory, 249 Polymeric gels, 524, 525 Polymerizable complex (PC) method, 506, , 517, 518 Polynuclear growth, 182 Polypropylene glycol (PGMS), 309 Polysilsesquioxanes, 601, 621, 633 Pore texture evolution, 509 Pore transformations coarsening, 572, 573 grain boundary mobility, 573–575 kinetic stability, 571 Laplace’s equation, 570 mechanical stresses, 570 mobility, 571, 572 properties, 570 Porous membrane, 615, 616 Positive temperature coefficient (PTC), 613 Potential of mean field (PMF), 304 anisotropic shape, 261 charge discreteness modeling, 260 divalent counterions, 261 DLVO theory, 258, 259 Hofmeister series, 262 Monte Carlo/molecular dynamic, 260 primitive model, 260 statistical mechanics approach, 258 steric theory, 258 Potential of mean force (PMF), 209 Powder packing case of agglomerates, 581, 582 monodispersed, 582, 583 polydispersed, 583, 584 Preceramic polymers, 142, 143, 145, 610 Precursors fine solid powders, 117 GMS, 117, 118 GSM, 107, 108 heterometallic alkoxides, 111–113 hydrolysis rate, 114–116

Index metal-organic complexes, 108–110 metal salt, 116, 117 non-Si clusters, 108 organometallics, 106, 107 POMS, 108 simultaneous hydrolysis, 113, 114 sol-gel powder particles, 110 span of, 105, 106 Propylene glycol-modified silane (PGMS), 191 Proton scavenger, 34 Pyrolysis methods, 200, 201

Q Quantum dots (QD), 165, 193, 658 carbon, 195 colloidal particles, 194 heterogeneous nucleus, 195 sol-gel precursors, 196 types, 194 Quartz crystal microbalance (QCM), 254, 660 Quartz crystal microbalance with dissipation monitoring (QCM-D), 254 Quasi-hexagonal pattern array, 488

R Rapid supercritical extraction (RSCE) method, 354 Rare earth oxyfluorides (REOF), 638 Reactive bond modeling, 304 Reactive oxygen species (ROS), 663 Recrystallization, 576 Re-peptization DLVO electrostatic theory, 245 energy versus distance, 246 potential interaction energy, 245 steric coagulation, 245 Stern layer, 245 transitory stage, 246 Resorcinol-formaldehyde (RF) gels, 146, 399, 400 Retarded effect, 212 Reversible gelation, 310–312 Reversible transformations, 323 Rheological methods oscillatory shear flow, 289–292 steady flow curves, 287–290 Ring-imaging Cherenkov (RICH), 611

S Sandia National Laboratory, 356 Scaling law, 554 Scanning electron microscope (SEM), 301

697 Scherer’s densification model, 566 Schulze-Hardy rule, 240 Secondary ion mass spectroscopy (SIMS), 215 Selective oxidation catalysts, 656 Sensors, 659, 660 Shrinkage, 323, 326, 331, 334, 337, 338, 347, 349, 351, 354, 356 Side-chain liquid crystal (SCLC), 442 Silane precursors, 538 Silazanes, 145, 540 Silica aerogels, 624, 642 Silica communication fibers, 609 Silica gels, 430, 500 alkoxide-derived gels alkoxide-derived silica aerogels, 380 experimental laws, 379 HR-SEM, silica aerogels, 380 as polymeric, 379 polymerization, 378 relaxation process, 383 SAXS data, 380 synthesis parameters, 379 TMOS with HCl catalysis, 381 two-step acid-base catalysis process, 379 xerogels, 379 from functionalized alkoxides, 383–385 Silicate method, 658 Silicate mixed oxide gels, 393–395 Silicon alkoxides, 73–75, 86–90 chemical nature, 96 clusters, 95 composite materials, 95 hybrid materials, 95 ionic solvents, 98 OH anions, 95 oligomer chain, 95 silica oligomers, 99 siloxane bonds, 95 sonolysis, 97 texture of gels, 95 tri-siloxane and tetra-siloxane units, 96 two-step hydrolysis condensation process, 97 Siloxane bonds, 338 Single-oxide glasses, 529 Sintering sol-gel ceramics crystalline phases, 551 electric field (see Electric field) gel network transformation (see Gel network transformation) Gibbs free energy, 551 hot pressing, 584–587 porosity, 551 pressure, 551 temperature, 551

698 Sintering sol-gel ceramics (cont.) textural transformation kinetics (see Textural transformation kinetics thermodynamics, 552, 553 transformation, 551 Site-bond percolation, 278 Small-angle neutron scattering (SANS), 297 Small-angle X-ray scattering (SAXS), 297–299, 371–373, 380, 381, 397 Smectic liquid crystals, 641 Sojourner Mars Rover, 626 Sol demixion bad solvents, 262 electrostatic stabilization theory, 263 good solvents, 262 liquid-gas coexistence, 262 numerical simulations, 263 thermodynamics, 263 Sol-gel behavior aluminum, 51, 52 case of Si, 57–59 case of Zr, 55 chain-structured phosphates, 60 charge vs. electronegativity, 50 ferrihydrite, 54 hydrolysis, 49 oligomers, 60 Sn(IV) salts, 56 titanium salt (Ti), 56 valence I, 50 valence II, 50, 51 valence III, 51 Sol-gel catalysts activity and selectivity, 645, 646 aerogel catalysts, 652, 653 biocatalysts, 658, 659 bulk solids, 645 characteristics, 645, 648 chemical reactions, 649, 650 colloidal particles, 645 design chemical/biochemical sensors, 645 fluoride catalysts, 656 high-value organic compounds, 649 industrial chemical processes, 645 non-hydrolytic, 653, 654 ordered mesoporous catalysts, 654–656 oxide active sites, 646–648 photocatalysis, 657 POSS, 656 protection, environment, 649–651 sensors, 659, 660 Sol-gel ceramic membranes asymmetrical ceramic membrane, 619

Index capillary tension, 619 catalytic, 621–623 colloidal hydroxide, 620 filtering layer, 619 filtering membrane, 619 hydrous oxide, 620 membrane thickness vs. deposition time, 620 mesoporous, 621 microporous, 621 multilayered membranes, 619 POSS clusters, 621 self-supported, 618 structural properties, 618 surfactants/block copolymers, 621 ultrafiltration, 619 Sol-gel composites CNT aerogels/xerogels, 444 gel matrix, 441 metal fluoride nanoparticle sols, 443 mixing of constituents, 442–443 phase separation, 445 transformation-toughened ceramic, 443 Sol-gel materials, 561 Sol-gel processing, 169, 529 advantages, 9–11, 203 applications, 598–600 catalysts, 597 ceramics, 2, 3 chemical components, 7 chemical developments, 3, 4 colloids, 1 definitions, 6 drying methods, 7 filtering membranes, 597 functions alkoxides, 601, 602 chemical applications, 601 complex shapes, 602 films, 602 hybrid, 603 metals, 601 monolayers, 603 multicomponent oxide glass, 601 oxidation resistance, 601 plastics, 601 protection barriers, 601 gelatinous precipitates, 6 gelation, 5 gels, 2 health hazards, 598 limitations, 9–11 macromolecular network, 7

Index materials, 9 non-hydrolytic solvents, 7 non-oxide materials, 7 powders and glasses, 597 scientific basis, 1 simplified chart, 8, 11 solid surface, 597 supercritical method, 7 synthesis protocol, 597 thermal insulation, 597 type of procedures, 7 Sol-gel synthesis alkoxides, 131, 133 carbides, 142–144 chalcogenides, 129 gels, 138 nanoparticles, 137 colloidal sols, 136, 137 fluoride molecules, 140–142 fluorides, 138, 139 hydrolytic sol-gel process, 139 nitrides, 144, 145 organic gels, 145, 146 biopolymers, 151 cellulosic gels, 147, 148 MF/RF, 146, 147 polyacrylamide gels, 149, 151 organometallic compounds, 133, 134 preceramic polymer, 142 sulfides, 130, 133 TFA, 139 Zintl clusters, 134, 135 Sol-gel transition, 305, 306 Solid metal fluorides, 634 Solid network, 641 Solid oxide fuel cells (SOFC), 622 Solid properties elastic, 328–330 plastic, 327, 328 Solid-phase recrystallization, 265, 266 Sols, 4 interaction forces, 211 kinetic stability, 210 peptization, 210 Space dipoles, 587 Spin coating, 603 Spindle-shaped hematite particles, 188 Spinodal decomposition, 498, 529, 530, 532, 533 Spray-drying technique, 201 Stable-phase domains, 530 Stable thermodynamics phases, 533, 534 α-Stannic acid, 56

699 β-Stannic acid, 56 State equation theory, 249 Steric interaction energy, 251–252 Steric stabilization theory, 210 between colloidal particles, 250, 251 bridging polymer adsorption, 253 origin, 247 polymeric solution (see Polymeric solutions) Steric strain, 27 Stöber process, 192 liquid components, 193 microparticles, 192 oxides, 192 siloxane-condensed droplets, 193 Structure promoters, 241 Sulfate anions, 647 Sulfides, 541 Sulfidolysis, 133 Superconductors, 639 Supercooled liquid, 520 Supercritical drying, 600, 611 aerogels, 352, 353, 355 carbon dioxide (CO2), 354 dry gels, 355 fluid exchange flow, 352 fluids, 353 heating schedules, 352 hypercritical drying, 352 liquid, 352 monolithic character, 352 pressure, 352, 353 technique, 6 Supercritical method, 7 Surface acoustic wave (SAW) technique, 489 Surface atomic diffusion, 561 Surface force apparatus (SFA), 253 Surface nucleation, 180 Surfactant solutions aluminosilicate systems, 457 amphoteric, 464 anionic, 463 application sol-gel electronic interactions, 481 template, 479, 480 aqueous solute classification, 460, 461 block copolymers, 485–487 cationic, 463 characteristics mechanical properties, 491 structure, 490, 491 texture, 489 factors

700 Surfactant solutions (cont.) chemical composition, 469–471 temperature, 471 Gibbs adsorption isotherms, 458–460 HLB, 465, 466 mesoporous cylindrical pores, 457 micellar solutions, 472 micelle formation, 466 micelle-stabilized microemulsions, 472, 473 micelle structure inverse, 468 lamellar, 468 rodlike, 468 spherical, 467, 468 molecules and behavior, 462, 463 nonionic, 464 silica, 488 sol-gel silica mechanism of formation, 481–484 polysilsesquioxane sol-gel precursors, 484, 485 surfactant-related synthesis techniques and structures, 486, 487 ternary systems, 473, 474 Swelling, 323, 324, 326, 329, 334–336, 338, 343, 357 Syncrystallization mechanism, 61

T Tammann temperature, 497 Tetrabromoethane, 606 Tetrabutylammonium hydroxide (TBAOH), 199 Tetraethyl orthosilicate (TEOS), 192 Tetramethoxysilane (TMOS), 373, 377, 381–383, 385 Tetramethylammonium hydroxide (TM), 94 Tetramethylethylene diamine (TEMED), 149 Tetramethyl-tetravinyl-cyclotetrasiloxane (TMTV), 144 Tetravinylsilane (TVS), 144 Textural transformation kinetics grain growth, 556, 557 Herring’s scaling laws, 553 influence, 555, 556 mechanisms, 555 scaling law, 554 sintering, 556, 557 Thermal diffusion, 185 Thermal insulation blankets, 624, 626 cladding films, 624 cooling/heating systems, 626

Index granules, 624 mechanical properties, 624 selective transmitter layer, 626 silica aerogels, 624 window insulation, 624 Thermodynamics, 552, 553 equilibrium, 172 parameters, 5 Thermogravimetric analysis (TGA), 302, 500 Thermo-structural applications, 608 Thin-film silica aerogels, 639 Thiolysis, 132 Thiophenol-complexing molecules, 192 Thixotropic gels, 328 Thomson-Freundlich equation, 171 Time-consuming computations, 209 Tin-doped indium oxide coatings (ITO), 633 Titanate mixed oxide gels, 395 Titania, 92, 93, 389 Titanium alkoxides, 84 Titanium tetraisopropoxide (TTIP), 478 Topotactic crystallization characteristics, 510, 511 transition aluminas (see Transition aluminas) Transformation mechanism, 25, 26, 28 Transformation, time, temperature (TTT) diagrams, 511 Transformation-toughened ceramic, 443 Transition aluminas mechanism, 512, 513 TTT diagram, 511 Transition electron microscopy (TEM), 215 Transition phases, 497, 510, 511, 513, 516, 534 Transmission electron microscope (TEM), 301 Transmission/scanning electron microscopy, 326 Transport properties, 331 Transverse optical (TO), 294 Trifluoroacetate gels, 139 Trifluoroacetic acid (TFA), 139, 507, 631 1,3,5-Trimethylbenzene (TMB), 487 Tungstite nanostructures, 198

U Ultrasmall-angle X-ray scattering (USAXS), 373

V Vacuum insulation panels (VIP), 624 Vacuum ultraviolet (VUV), 635

Index Valence shell electron pair repulsion (VSEPR) model, 16 Vanadium, 430 Van der Waals interactions between colloidal particles, 212–215 molecular levels, 211, 212 Vibrational spectroscopy, 292–293 IR, 293–294 Raman, 294, 295 Viscous flow sintering densification of gels, 567 description, 565 intermolecular bonding, 564 kinetic process, 564 mechanical stress, 564 models, 565–567 monolithic gels, 564 property, 564 V2O5 gels, 430 Volatile organic compounds (VOC), 642

W Washburn equation, 364 Water, 16, 17, 19 molecules, 15, 29 vapor, 562 Water-in-oil (W/O) emulsion, 199 Wet gels, 599, 600 covalent polymeric organic gels, 331–333 Donnan equilibrium, 336, 337 materials, 323, 324

701 solid properties (see Solid properties) swelling, inorganic gels, 333–336 syneresis, 337, 338, 340

X Xerogels, 5, 6, 501, 600 definition, 367 graphene, 412 hybrid polysilsesquioxanes, 384 octylene-bridged polysilsesquioxane, 384 silica, 365, 379 silica-titania, 395 texture, 384 transparent titania xerogel monolith, 389 X-ray diffraction patterns, 521, 523, 524 X-ray photoelectron spectroscopy (XPS), 215, 302

Y Young’s modulus, 610 Yttria-stabilized zirconia (YSZ), 622 Yttrium aluminum garnet (YAG), 630

Z Zero-point charge, 215 Zintl clusters, 134, 135 Zirconia, 94, 95, 390, 513, 514, 652 Zirconia nanoparticles, 442 Zirconium alkoxides, 84, 85