Nanostructured Soft Matter: Experiment, Theory, Simulation and Perspectives (NanoScience and Technology) (NanoScience and Technology)

NanoScience and Technology

NanoScience and Technology Series Editors: P. Avouris B. Bhushan D. Bimberg K. von Klitzing H. Sakaki R. Wiesendanger The series NanoScience and Technology is focused on the fascinating nano-world, mesoscopic physics, analysis with atomic resolution, nano and quantum-effect devices, nanomechanics and atomic-scale processes. All the basic aspects and technology-oriented developments in this emerging discipline are covered by comprehensive and timely books. The series constitutes a survey of the relevant special topics, which are presented by leading experts in the field. These books will appeal to researchers, engineers, and advanced students.

Applied Scanning Probe Methods II Scanning Probe Microscopy Techniques Editors: B. Bhushan and H. Fuchs

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Applied Scanning Probe Methods III Characterization Editors: B. Bhushan and H. Fuchs

Applied Scanning Probe Methods VII Biomimetics and Industrial Applications Editors: B. Bhushan and H. Fuchs

Applied Scanning Probe Methods IV Industrial Application Editors: B. Bhushan and H. Fuchs

Roadmap of Scanning Probe Microscopy Editors: S. Morita

Scanning Probe Microscopy Atomic Scale Engineering by Forces and Currents Editors: A. Foster and W. Hofer

Nanocatalysis Editors: U. Heiz and U. Landman

Single Molecule Chemistry and Physics An Introduction By C. Wang and C. Bai Atomic Force Microscopy, Scanning Nearfield Optical Microscopy and Nanoscratching Application to Rough and Natural Surfaces By G. Kaupp Applied Scanning Probe Methods V Scanning Probe Microscopy Techniques Editors: B. Bhushan, H. Fuchs, and S. Kawata

Nanostructures Fabrication and Analysis Editor: H. Nejo Fundamentals of Friction and Wear on the Nanoscale Editors: E. Gnecco and E. Meyer Lateral Alignment of Epitaxial Quantum Dots Editor: O. Schmidt Nanostructured Soft Matter Experiment, Theory, Simulation and Perspectives Editor: A.V. Zvelindovsky

A.V. Zvelindovsky

(Ed.)

Nanostructured Soft Matter Experiment, Theory, Simulation and Perspectives

With 261 Figures

Dr. A.V. Zvelindovsky (Ed.) Centre for Materials Science Department of Physics, Astronomy and Mathematics University of Central Lancashire Preston Lancashire PR1 2HE United Kingdom

Series Editors: Professor Dr. Phaedon Avouris

Professor Dr., Dres. h.c. Klaus von Klitzing

IBM Research Division Nanometer Scale Science & Technology Thomas J. Watson Research Center P.O. Box 218 Yorktown Heights, NY 10598, USA

Max-Planck-Institut für Festkörperforschung Heisenbergstr. 1 70569 Stuttgart, Germany

Professor Dr. Bharat Bhushan

University of Tokyo Institute of Industrial Science 4-6-1 Komaba, Meguro-ku Tokyo 153-8505, Japan

Ohio State University Nanotribology Laboratory for Information Storage and MEMS/NEMS (NLIM) Suite 255, Ackerman Road 650 Columbus, Ohio 43210, USA

Professor Dr. Dieter Bimberg TU Berlin, Fakutät Mathematik/ Naturwissenschaften Institut für Festkörperphyisk Hardenbergstr. 36 10623 Berlin, Germany

Professor Hiroyuki Sakaki

Professor Dr. Roland Wiesendanger Institut für Angewandte Physik Universität Hamburg Jungiusstr. 11 20355 Hamburg, Germany

A C.I.P. Catalogue record for this book is available from the Library of Congress

ISSN 1434-4904 ISBN 978-1-4020-6329-9 (HB) ISBN 978-1-4020-6330-5 (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands In association with Canopus Publishing Limited, 27 Queen Square, Bristol BS1 4ND, UK www.springer.com and www.canopusbooks.com All Rights Reserved © Canopus Publishing Limited 2007 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means,electronic,mechanical,photocopying,microfilming,recording or otherwise,without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

Preface

“The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.” Henri Poincar´e (1854 - 1912) The ancient Greeks, quite ingeniously, realised that all materials and their (now known as macroscopic) properties, including life itself, are due to a limited number of tiny, constantly moving building blocks and the connections (now called interactions) between these blocks. Receiving both scientific and non-scientific opposition, the idea faded and, despite some renaissance of atomistic ideas in the 17-19th centuries, it still took more than two thousand years, until the time of Einstein, for the idea of microscopic building blocks to be fully accepted. These ideas, begun during the golden age of physics in the 20th century, have led to a comprehensive understanding of such states of matter as gases and solids, which in turn have completely revolutionised everyday life in the developed world by introducing technological wonders such as modern cars, air traffic, semiconductor chips for computers and nuclear power. Another state of matter, fluids, appeared to be much more difficult to tackle, even in the case of simple liquids like liquid argon, a research favourite in the field. Legend tells that Lev D. Landau, Physics Nobel Laureate, was said to have commented that there could be no theoretical physics of liquids, as they have no small parameters. Nonetheless, as the 20th century advanced, it also became possible to treat even this most slippery of subjects due, in part, to the introduction of computers and the development of computer simulation methods like molecular dynamics. The 20th century brought yet another revolution: the industrial production of novel classes of materials, which simply did not exist before. For instance, almost every aspect of our everyday life would change immeasurably if plastics should disappear and life would turn “blind”, “deaf” and rather miserable without liquid crystals for computer screens or mobile phones. Such new materials were given the name complex fluids, and their building blocks are not simply atoms or small molecules, but include block copolymers, surfactants, amphiphiles, colloids, liquid crystals, biomacromolecules, such as proteins and DNA, and various composites of the above. Complex fluids possess features of both fluids (for instance, they can flow) and solids (they can have an internal structure often with various well

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Preface

resolved symmetry groups). These structures have a characteristic scale for their building blocks which is in the range of nanometers to microns, but the building blocks can be made (synthesised) with various degrees of complexity, so more than one size scale can be involved. Some structures can be formed spontaneously from a homogeneous mixture of the building blocks, a process referred to as self-assembly, which can be hierarchical and occur on various time scales depending on the complexity of the building blocks. Self-assembly is related to self-organization, which makes complex fluids similar to living matter, so they can serve as model systems for biological systems and bioinspired materials. In the last decades of the 20th century the term complex fluids started to be substituted by a more general one that is better suited to the overall concept of condensed matter: soft matter. The transition between millennia was marked by a burst of soft matter research, due, in part, to the fact that computers had then reached a level of power allowing the simulation of experimental size systems, thus enabling the very first “virtual experiments” of such complex systems to be performed. This development made the links between theory and experiment truly symbiotic. Nanostructured soft materials, even apart from future technological perspectives beyond our imagination, are fascinating and beautiful. This research field is growing so fast that there has been no single book that provided an overview of the many different perspectives on both fundamental concepts and recent advances in the field. A group of very enthusiastic contributors has now filled this gap; and the present book is the first comprehensive monograph on nanostructured soft matter. It covers materials ranging in size from short amphiphilic molecules to block copolymers to proteins and also discusses colloids, hybrids, microemulsions and bio-inspired materials such as vesicles. Each chapter is written by active world-class researchers in the field who offer the reader an interdisciplinary view from differing perspectives. They combine the experimental approaches of Chemistry and Physics, e.g. scattering techniques, electron and Atomic Force microscopy, with various Theoretical Physics, Mathematics and advanced computer modelling methods. We hope the book will be useful for both active and starting researchers as well as for undergraduate students; or, citing one of the anonymous referees of the original proposal for this book: “There is something for everyone in this book and it would represent a very useful text for those both operating at the forefront of nano-science and those entering the field . . . ” I wish to thank the publishers at Canopus for assistance in the production of this book. I also thank Drs. R. McCabe, S. V. Kuzmin and N. Kiriushcheva. My editorial effort is dedicated to Prof. A. V. Zatovsky (1942-2006), who first introduced me to the wonders of Soft Matter.

Preston, Lancashire, January 2007

AVZ

Contents

Preface A. V. Zvelindovsky (ed.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V

Part I Experimental Advances Microemulsion Templating W. F. C. Sager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

Nanofabrication of Block Copolymer Bulk and Thin Films: Microdomain Structures as Templates Takeji Hashimoto and Kenji Fukunaga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Characterization of Surfactant Water Systems by X-Ray Scattering and 2 H NMR Michael C. Holmes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Polyelectrolyte Diblock Copolymer Micelles: Small Angle Scattering Estimates of the Charge Ordering in the Coronal Layer Johan R. C. van der Maarel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Structure and Shear-Induced Order in Blends of a Diblock Copolymer with the Corresponding Homopolymers I. W. Hamley, V. Castelletto and Z. Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Electric Field Alignment of Diblock Copolymer Thin Films T. Xu, J. Wang and T. P. Russell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Control of Block Copolymer Microdomain Orientation from Solution using Electric Fields: Governing Parameters and Mechanisms Alexander B¨ oker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

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Structure and Dynamics of Cylinder Forming Block Copolymers in Thin Films Larisa Tsarkova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

Part II Mathematical and Theoretical Approaches

Mathematical Description of Nanostructures with Minkowski Functionals G.J.A. Sevink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Scaling Theory of Polyelectrolyte and Polyampholyte Micelles Nadezhda P. Shusharina and Michael Rubinstein . . . . . . . . . . . . . . . . . . . . . 301 The Latest Development of the Weak Segregation Theory of Microphase Separation In Block Copolymers I. Ya. Erukhimovich . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Coarse-Grained Modeling of Mesophase Dynamics in Block Copolymers Zhi-Feng Huang and Jorge Vi˜ nals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Effective Interactions in Soft Materials Alan R. Denton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

Part III Computer Simulations

Ab-initio Coarse-Graining of Entangled Polymer Systems J.T. Padding and W.J. Briels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 Computer Simulations of Nano-Scale Phenomena Based on the Dynamic Density Functional Theories: Applications of SUSHI in the OCTA System Takashi Honda and Toshihiro Kawakatsu . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 Monte Carlo Simulations of Nano-Confined Block Copolymers Qiang Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Understanding Vesicles and Bio-Inspired Systems with Dissipative Particle Dynamics Julian C. Shillcock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 Theoretical Study of Nanostructured Biopolymers Using Molecular Dynamics Simulations: A Practical Introduction Danilo Roccatano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555

Contents

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Understanding Liquid/Colloids Composites with Mesoscopic Simulations Ignacio Pagonabarraga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617

List of Contributors

Alexander B¨ oker (Germany) Physikalische Chemie II, Universit¨ at Bayreuth. Wim J Briels (The Netherlands) Computational Biophysics, Faculty of Science and Technology, University of Twente, Enschede. Valeria Castelletto (United Kingdom) Department of Chemistry, University of Reading. Alan R Denton (USA) Department of Physics, North Dakota State University, Fargo. Igor Erukhimovich (Russia) Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Moscow, and Physics Department, Moscow State University. Kenji Fukunaga (Japan) Polymer Laboratory, Ube Industries, Ltd., Chiba. Ian W Hamley (United Kingdom) Department of Chemistry, University of Reading.

Takeji Hashimoto (Japan) Advanced Science Research Centre, Japan Atomic Energy Agency, Ibaraki. Michael C Holmes (United Kingdom) Centre for Materials Science, Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston. Takashi Honda (Japan) Japan Chemical Innovation Institute, and Department of Organic and Polymeric Materials, Tokyo Institute of Technology. Zhi-Feng Huang (USA, Canada) Department of Physics and Astronomy, Wayne State University, Detroit and McGill Institute for Advanced Materials and Department of Physics, McGill University, Montreal. Toshihiro Kawakatsu (Japan) Department of Physics, Tohoku University, Sendai.

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List of Contributors

Johan R C van der Maarel (Singapore) Department of Physics, National University of Singapore.

Nadezhda P Shusharina (USA) Department of Chemistry, University of North Carolina at Chapel Hill.

Johan T Padding (The Netherlands) Computational Biophysics, Faculty of Science and Technology, University of Twente, Enschede.

Larisa A Tsarkova (Germany) Physikalische Chemie II, Universit¨ at Bayreuth.

Ignacio Pagonabarraga (Spain) Departament de F´isica Fondamental, Universitat de Barcelona.

Jorge Vi˜ nals (Canada) McGill Institute for Advanced Materials and Department of Physics, McGill University, Montreal.

Danilo Roccatano (Germany) School of Engineering and Science, Jacobs University Bremen. Michael Rubinshtein (USA) Department of Chemistry, University of North Carolina at Chapel Hill. Thomas P Russell (USA) Polymer Science and Engineering Department, University of Massachusetts, Amherst. Wiebke F C Sager (Germany) IFF-Soft Matter, Forschungszentrum J¨ ulich. G J Agur Sevink (The Netherlands) Leiden Institute of Chemistry, Leiden University. Julian C Shillcock (Germany) Theory Department, Max Plank Institute of Colloids and Interfaces, Potsdam.

Jiayu Wang (USA) Polymer Science and Engineering Department, University of Massachusetts, Amherst. Qiang Wang (USA) Department of Chemical and Biological Engineering, Colorado State University, Fort Collins. Ting Xu (USA) Department of Materials Science and Engineering, University of California, Berkeley. Zhou Yang (United Kingdom) School of Materials, The University of Manchester. Andrei V Zvelindovsky (United Kingdom) Centre for Materials Science, Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston.

Part I

Experimental Advances

Microemulsion Templating W.F.C. Sager Institute for Solid State Research (IFF)-Soft Matter, Forschungszentrum J¨ ulich, 52425 J¨ ulich, Germany

1 Introduction Surfactant molecules have for a long time been employed in stabilising finely dispersed matter since they have, due to their amphiphilic character, the tendency to adsorb at hydrophilic/hydrophobic interfaces such as water/air, water/oil or water/(hydrophobic) solid and oil/(hydrophilic) solid. In many inorganic or organic (colloidal) particle preparation routes, different types of surfactants have been added to stabilise the formed particles sterically or electrostatically against (irreversible) aggregation (and, if applicable, coalescence) processes. Apart from their stabilising properties, surfactants have progressively gained more attention because they may self-assemble under certain conditions in binary and ternary systems of surfactant(s), water and/or oil into thermodynamically stable nano-heterogeneous systems, with a variety of different morphologies. These self-assembled systems can in principle be used as a kind of micro- or better nanoreactor to separate and control nucleation and growth processes and as a template to direct growth and to control the morphology of the forming solid phase. Over the last two to three decades our knowledge of self-assembled surfactant systems has increased dramatically and a number of these systems have been thoroughly investigated for advanced materials synthesis [1–5]. Figure 1 shows in the central part a schematic phase diagram that displays the existence regions of a variety of morphologically different self-assembled surfactant phases together with their multi-phase equilibria that can principally form in a ternary system of water, oil and a medium- or long-chain surfactant around its balanced state [6]. The structural polymorphism ranges, at low surfactant concentrations, from spherical and cylindrical micellar surfactant aggregates via swollen micelles and oil-in-water (o/w) droplet microemulsions on the water rich side to water-in-oil (w/o) droplet microemulsions and inverted micelles on the oil rich side, whereby the polar head group of the surfactant is turned inside. At intermediate water/oil ratios bicontinuous microemulsions are stable, consisting of an interwoven network of

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Fig. 1. Schematic Gibbs triangle (central part) displaying self-assembling structure formation in binary and ternary surfactant systems, stabilised by a strong amphiphile close to its balanced state [6]. The existence regions of the different phases together with all corresponding two- and three-phase equilibria are presented. The compositions of the coexisting phases are indicated by the end points of the tie-lines in the two-phase regions, and by the corners of the three-phase triangles. More details about the phase diagram are given in Sect. 2.2. The outer part shows examples for solid phases of different morphologies that have been prepared from the indicated self-assembled surfactant phases and will be described in more detail in Sects. 3–5. Central part reproduced with permission from [6].

water and oil channels. At higher surfactant concentrations hexagonal or cubic phases are formed, consisting of micellar and reverse micellar aggregates packed into ordered crystalline arrays, as well as lamellar liquid crystalline phases that are built up by a stack of planar surfactant bilayer sheets separated by water and/or oil. The phase diagram and the general phase evolution in binary and ternary self-assembled surfactant systems will be discussed in detail in Sect. 2.2 and 2.3. The outer part of Fig. 1 shows a selection of solid phases with different morphologies that have been prepared from the indicated self-assembled surfactant systems. Besides thermodynamically stable surfactant self-assemblies, kinetically stabilised systems such as ordinary emulsions and uni- or multi-lamellar vesicles have been utilised. As can already be seen from these examples, self-assembled surfactant systems have successfully been employed in the synthesis of differently shaped organic and

Microemulsion Templating

5

inorganic nanoparticles and, more recently, of nanostructured or nanoporous (composite) materials [7]. Reflecting the changing demands in advanced materials science, emphasis has shifted from first preparing only (monodisperse) spherical particles to controlling the particle morphology and finally to manufacturing well-defined nanostructured materials. Since it has been realised that new developments in materials science synthesis are possible only if research efforts are not solely concerned with finding novel materials but also with the morphological tailoring of the desired materials, special attention has been paid toward the end of the last century to investigating new techniques for microstructural design. These efforts include the preparation of well-defined particles of low polydispersity and of increasingly small dimensions down to the nanometer scale, ordering of these particles into two- and three-dimensional arrays, directed growth, as well as hierarchical structuring and control from the nanoto the meso-scale. In most of these processes, solid phase preparation and precipitation in surfactant self-assemblies has played a substantial role. In the case of mono-sized nanoparticles, precipitation in reversed micelles or w/o microemulsions has often been the first successful route to prepare such small particles for different inorganic materials and has therefore been employed to study quantum size effects [8]. The preparation of ordered mesoporous materials such as silica by precipitation in crystalline surfactant phases opened a fast developing field in the area of hybrid inorganic–organic mesoporous solids and zeolites [2, 9]. The basic idea of using the internal (dispersed) phase of the (thermodynamically) stable systems as nanoreactors lies in the possibility of achieving a controlled compartmentalisation and well-determined structure of the reaction medium. Precipitation and thus formation of the solid phase can be better controlled since it takes place in a more or less isolated and (ultra-) small space as, e.g., the critical supersaturation of the dissolved solid phase precursor is reached. (Direct) templating by precipitation from the continuous medium onto the surface of preformed micellar structures can be obtained if the precursor species of the forming solid phase undergo interactions with the surfactant head groups. This allows (molecular) orientation and directed ordering. The principle of both the defined isolation of space and the structural templating has been adapted from nature. Natural examples include the preparation of magnetic particles in bacteria and biomineralisation processes in algae [10]. Precipitation in self-assembling systems has therefore increasingly been studied for biomimetic approaches and the development of novel preparation routes which are based on them [1, 10]. However, one should keep in mind that surfactant self-assembled systems are highly dynamic systems and that the precipitation processes taking place in them can be quite complex due to the large number of possible interactions between the mould and the templated structure. Preparation processes are therefore not always straightforward. To obtain solid phases that are commensurate in size and shape with the self-assembled surfactant system from which they are formed, detailed

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knowledge of the templating system as well as the precipitation reaction leading to the desired solid phase formation is a prerequisite. Generally, the final morphology of the solid phase depends on the reaction kinetics (material exchange and solid phase formation), the reorientation of the surfactant selfassembled system as well as the interactions between the surfactant and the precipitating solid. In the latter case surfactants may block oriented growth due to specific adsorption of the surfactant onto certain surfaces (crystal net plains) of a forming crystalline phase, or direct ordering and aggregation of nanosized particles into complex inorganic particle–surfactant assemblies that can reach mesoscopic length scales [2, 11, 12]. Since microemulsion templating has developed into a broad field and offers a rich playground for new materials synthesis routes, only a few examples (see Fig. 1) to explain the main strategies and principles have been selected for this contribution. The chapter is organised as follows: In Sect. 2 the microemulsion template will be introduced, wherein special attention is paid to explaining the conditions under which the different self-assembled surfactant phases form, allowing for a targeted morphological tailoring of the templating mould. Basic features and trends in the phase evolution and the tuning of the different morphologies will be explained within the concept of the curvature energy. Most emphasis is laid on the structural changes and (exchange) kinetics of droplet phases. Sect. 3 deals with the preparation of well-defined spherical and rod-like inorganic nanoparticles from single and aggregated w/o droplet phases. In Sect. 4, o/w (micro)emulsion droplet phases and bicontinuous microemulsions are discussed in view of the preparation of latex particles and polymer networks. Sect. 5 describes the basic ideas of employing different crystalline phases to prepare ordered mesoporous solids.

2 The Microemulsion Template Surfactant molecules can, due to their amphiphilic nature, stabilise a number of different microscopically heterogeneous systems. In the binary water– surfactant and oil–surfactant systems, surfactants self-assemble into normal (hydrophobic part inside) and reverse (hydrophilic part inside) micellar aggregates, respectively, with well-defined aggregation numbers. At high surfactant concentration different liquid crystalline phases are formed. The morphology of the micellar aggregates depends on the geometry and concentration of the surfactant molecules and external variables such as temperature or concentration of added salt. In the ternary water–oil–surfactant system, transparent and thermodynamically stable microemulsions can form under certain conditions. These microemulsion phases consist of structurally well-defined nanosized domains of water and oil, separated by a monomolecular surfactant film. The morphology and characteristic length depend on the water-to-oil ratio and the elastic properties (e.g., spontaneous curvature and rigidity constants) of the surfactant film. Generally, droplet phase microemulsions exist if either oil

Microemulsion Templating

7

or water is only present in small amounts, whereas bicontinuous microemulsions are found at comparable amounts of water and oil. The spontaneous or natural curvature of the interfacial surfactant film depends on the geometric properties of the hydrophilic and hydrophobic moieties of the surfactant molecule and these, in turn, on their interactions with water and oil, respectively. If the temperature and/or ionic strength of the aqueous phase is varied, a rich phase behaviour is generally revealed, whereby microemulsion phases can coexist with water and/or oil excess phases as well as liquid crystalline phases forming two- and three-phase equilibria. If two-phase systems, consisting of a microemulsion phase in coexistence with a water or oil excess phase formed at low surfactant concentrations are mechanically agitated, ordinary or macro-emulsions can be obtained with a milky appearance. In this case the excess phase has mechanically been dispersed into, generally, micrometer-sized droplets, that can be kinetically stabilised due to the adsorption of surfactants onto the newly formed interface. The interface is not saturated and the size of the droplets depends on the mechanical energy applied to prepare the emulsion and on the outcome of coalescence and coagulation processes as well as Ostwald ripening that finally lead to phase separation. In this section self-assembled as well as kinetically stabilised surfactant systems will be introduced in view of their application as precipitation media and as templates. Since microemulsion phases form at intermediate conditions between the (binary) micellar (nanometer scale) systems and macroemulsions (micrometer scale), they will be treated in this context. Sect. 2.1 starts with the binary systems, whereby surface activity, micelle formation and the factors that influence the morphology of the micellar phase formed are discussed. The latter will be performed within the framework of a geometrical model (packing parameter approach). For more details on the different classes of surfactants, micellar systems and a description of the structural evolution within the curvature energy concept, the interested reader is referred to more advanced textbooks such as [13–15] and [16]. Microemulsion systems will be introduced in the second part of Sect. 2.1 and their phase behaviour and structural evolution are described in Sect. 2.2. It has been found that the properties of the microemulsion phases are dominantly determined by properties of the interfacial surfactant film that separates the water and oil domains. Basic features of the microemulsion phases are described within the framework of the curvature free energy. This concept is based on the statistical mechanics of curved interfaces, whereby the main properties are described in terms of spontaneous curvature and the rigidity constants for mean and Gaussian curvature. Since a full theoretical treatment is not in the scope of this Chapter, emphasis is only placed on explaining the general trends in (i) the phase behaviour and (ii) the structural evolution of the microemulsion phases and (iii) the macroscopic interfacial tension between microemulsion phases and water and/or oil excess phases in the two- and three-phase equilibria observed. In this context, formulas are only derived for droplet phases. More information on the curvature free energy and its application to more complex (microemulsion) phases,

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e.g., isotropic and crystalline bicontinuous phases, can be found in [17, 18]. Further knowledge of microemulsions can be obtained from [15, 16] and [19]. To obtain a better understanding of the precipitation reactions performed in droplet phases, Sect. 2.3 deals with the stability and exchange kinetics of microemulsion droplet phases. A comparison with ordinary emulsion droplet systems is finally given in Sect. 2.4. 2.1 Surfactant Self-assembly, Micelles and Microemulsions

Fig. 2. Left: Schematic diagram of a typical adsorption isotherm for an aqueous surfactant solution: Surface tension σ plotted against the logarithm of the surfactant concentration cS . Reproduced from [20]. The sketched insets show the state of the surfactant molecules in the water phase (bulk) and at the water/air surface. Right: Surfactant parameter range for different surfactant aggregates. Reproduced from [13].

The Binary Water–Surfactant System: Surface Activity and Micelle Formation Amphiphiles are surface active molecules. If a surfactant is added to an aqueous solution, it will be distributed between the surface (water/air surface) and the bulk water phase. The distribution coefficient depends on the solubility of the surfactant molecules in water. Upon addition of surfactant, the surface tension decreases due to the presence of the surfactant molecules at the water/air surface. The surface pressure Π caused by the spreading of the surfactant molecules is given by Π = σ0 − σ where σ is the surface tension at a given surfactant concentration cS and σ0 the surface tension of the bare surface without added surfactant. Fig. 2 shows a schematic plot of the Gibbs adsorption isotherm, typically observed for surfactants in aqueous solution.

Microemulsion Templating

9

The surface excess Γ , excess concentration of surfactant in the interface, is given by   dσ 1 (1) Γ =− RT d ln cS T where R is the gas constant and T the absolute temperature. At a certain concentration, the so-called critical micelle concentration (cmc), it becomes energetically more favourable for the surfactant molecules to aggregate into micelles. The area of the surfactant in the saturated macroscopic flat interface can be calculated from the surface excess for surfactant concentrations close to the cmc [21]. Above the cmc the surface tension stays constant since all additionally added surfactant molecules form micelles in the bulk water phase and the surface excess concentration remains nearly constant. Plateau values for the surface tension (cS > ccmc ) lie for conventional surfactants typically in the range of 25–35 mN m−1 . The driving force for micellisation is the hydrophobic effect, which is mainly of entropic origin. The contribution to the free energy that favours micelle formation stems from a gain in entropy of the surrounding water molecules (hydrophobic or Tanford effect) [14,15]. The presence of the hydrocarbon tail in the molecular dispersed state (below the cmc) induces an increased ordering of the surrounding water molecules (water cluster formation), which is not the case if the hydrocarbon chains form the micellar core and are shielded by the polar head groups from the bulk water phase. Since the operating aggregation forces are opposed by the repulsion between the head groups, finite (self-assembled) micellar aggregates are formed with a well-defined number of surfactant molecules Np per micelle (Np ∼ 50–80). The size and shape of the micellar aggregates depend on the geometry of the surfactants. This dependence can be well described by a geometric model that is based on the (critical) packing parameter v/(al), where l and v correspond to the length and volume of the aliphatic tail and a corresponds to the effective head group area. Np can be determined by dividing the total volume of a given micellar aggregate by v or the total surface area by a. For spherical micelles, a packing parameter of v/(al) ≤ 1/3 is obtained if one assumes that the radius of the micelle Rmic cannot exceed l: 4 3 3 πRmic

2 v 1 4πRmic → ≤ . (2) v a al 3 Whereas for a saturated hydrocarbon chain, v and l can easily be calculated from the van der Waals radii, a depends not only on the size of the head group but also on pH, surfactant and electrolyte concentration for ionic surfactants [15]. Head group areas are usually determined from measured values of the size of the micelle and the number of surfactant molecules per micelle. The head group area is typically in the range of 55–70 ˚ A2 . For ionic surfactants, the effective head group area decreases if the ionic strength of the aqueous

Np =

, Np =

10

W.F.C. Sager

phase increases by addition of a salt. Due to screening of the electric charge at higher ionic strength, repulsion between the head groups of neighbouring surfactant molecules decreases and consequently the effective head group area is smaller. For commonly used nonionic surfactants that are composed of a hydrocarbon chain and a water-soluble ethyleneoxide chain (Ci Ej , where the subscripts denote the number of methyl Ci and oxyethylene Ej repeats), the head group area increases with j and decreases for given j with increasing temperature. Increasing temperature breaks the hydrogen bonds between the ethyleneoxide oxygen atoms and the surrounding water molecules and results in a smaller effective head group area. The different possible packing geometries of surfactant molecules are listed in the table within Fig. 2 together with the ranges of packing parameters and the structure of the aggregates they form. Generally, surfactants shaped in a manner where the effective head group takes more space than the tail region (v/al < 1/3) form spherical micelles. If v/al approaches 1, first cylindrical micelles and finally almost flat films form as they occur in vesicles (bilayers) and lamellar crystals. If v/al > 1, the surfactants are no longer soluble in water. When dissolved in an apolar solvent (oil) they form inverse micelles. In this case the head groups form the interior of the reverse micelle and are shielded by the apolar moiety from the bulk oil. Tuning from strongly curved micelles to flat surfactant sheets and even to oppositely curved aggregates (inverse micelles) can generally be achieved by either increasing the bulkiness (volume) of the hydrophobic moiety (e.g., double tailed instead of single tailed surfactants) and/or by decreasing the head group area. The latter can be realised by addition of salt in the case of ionic surfactants, decreasing j and increasing temperature in the case of nonionic surfactants and/or addition of long chain alcohols in multicomponent mixed systems. In the binary watersurfactant system micelles are generally formed at concentrations above the cmc. At high surfactant concentrations, different liquid crystalline phases may exist, including hexagonal, cubic and lamellar phases (see water-surfactant side of the Gibbs triangle in Fig. 1). With increasing surfactant concentration in water v/al may rise up to values of above 1. For a description of the different morphologies of micellar and crystalline structures in binary systems within the curvature free energy concept, the reader is referred to [18, 22]. The Ternary Water–Oil–Surfactant System: Microemulsions and (Multi)Phase Equilibria If a small amount of a third component barely miscible with water, such as a medium- or long chain alkane (oil), is added to micelles in water (or if water is added to reverse micelles in oil), this third component can be solubilised in the interior of (reverse) micelles. In the case of regular micelles, first swollen micelles and then o/w microemulsions are formed upon the addition of oil, while w/o microemulsions form from reverse micelles upon addition of water.

Microemulsion Templating

11

If a larger amount of the third component is added, a number of different (coexisting) phases may form and the phase diagram can become rather complex, especially at higher surfactant concentrations. Microemulsions are structurally well-defined self-organising mixtures of water, oil and surfactant(s) that can form a wide variety of thermodynamically stable (mainly transparent) phases. These comprise droplet phases that consist of more or less spherical nanosized (20–300 ˚ A) droplets of oil in water (o/w microemulsions or L1 -phase) and water in oil (w/o microemulsions or L2 -phase), as well as bicontinuous mono- and bilayer (L3 ) phases. The latter two consist of an interwoven network of water and oil channels, separated by a saturated (mono- or bilayer) surfactant film (see Fig. 3). If the temperature and/or ionic strength of the aqueous phase is varied, a rich phase behaviour is generally revealed, whereby microemulsion phases can coexist with water and/or oil excess phases as well as liquid crystalline phases forming two- and three-phase equilibria. The different phases and coexistence regions occurring in a three-component water, oil and surfactant system can be represented in a triangular phase diagram (Gibbs triangle). At each point in the diagram, the concentration of each species is determined by drawing a line parallel to the corresponding axis, lying along one edge of the triangle. The central part of Fig. 1 shows a Gibbs triangle displaying a variety of structurally different phases, which can principally form in a ternary system of a strong amphiphile close to its balanced state, together with their two- and three phase coexistence regions. At high surfactant concentrations the different liquid crystalline phases reach from the water-surfactant and oil-surfactant (inverse structures) sides into the triangle. These phases form two and three-phase equilibria at intermediate surfactant concentration with the microemulsion phases at lower surfactant concentrations (lower 1/3 of the diagram). At the balanced state of surfactant, the volumes of the hydrophilic and hydrophobic moieties are nearly equal (v/al ≈ 1) and the interfacial surfactant film is on average not curved. Therefore, bicontinuous microemulsions (and lamellar and bicontinuous crystalline phases at high surfactant concentrations) occur in the central part of the Gibbs triangle. Isotropic bicontinuous microemulsions exist only over a small surfactant concentration range at comparable amounts of water and oil. At lower surfactant concentrations, the amount of surfactant present is not high enough to form a bicontinuous structure over the whole sample. In this case the sample splits into a bicontinuous middle phase and almost pure water and pure oil excess phases. The compositions of the three coexisting phases are given by the corners of the three-phase triangle. According to the Gibbs phase rule, a three-component system can separate into a maximum of three coexisting isotropic phases at given temperature and pressure. The general phase behaviour and the structural evolution in microemulsion systems is described in Sect. 2.3. Microemulsions possess a huge internal interface since the size of the water and/or oil domains ranges from about 20–500 ˚ A. If one considers 10 g of a microemulsion that consists of, e.g., water droplets in oil and contains 1

12

W.F.C. Sager

g surfactant and 1 g water, the interfacial area formed by the surfactant film amounts to about 500 m2 . Such large internal interfaces can only be formed if the interfacial tension of the macroscopic water/oil interface has become very small. In these cases, the gain in entropy leads to a spontaneous microemulsion formation (spontaneous emulsification). Water/oil interfaces that are saturated with a surfactant (plateau values in Fig. 2) reach values of σ = 10−1 –10−3 mN m−1 . At these low interfacial tensions curvature effects start to play a dominant role. As will be shown in the following subsection (Sect. 2.2), this curvature energy is responsible for the rich phase behaviour displayed. Historically, the droplet phases are the first and also most studied microemulsion structures. The reason for this lies probably in the fact that their existence regions are larger and thus easier to find, if, e.g., the temperature or salt concentration is varied. The term “microemulsion” was originally coined by Hoar and Schulman [23] in 1943 and was applied to a transparent sample, prepared by emulsifying an oil in an aqueous surfactant solution wherein a fourth component, a so-called cosurfactant (generally an alcohol of intermediate chain length such as hexanol) has been added. Upon titrating the emulsion system with the alcohol, they observed a sudden decrease in turbidity and obtained finally a transparent o/w dispersion. They concluded that the size of the droplets must be smaller than the wavelength of visible light and thus microscopically small, without knowing that they are actually in the nanometer range. The type of the dispersion (o/w or w/o) follows in principle the Bancroft rule, which had been found earlier for ordinary emulsions [24]: The medium that forms the continuous phase of the dispersion is the one in which the surfactant is better soluble. The bicontinuous structure was first postulated by Scriven in 1976 [25]. A typical micrograph of a bicontinuous structure obtained by freeze fracture transmission electron microscopy is shown in Fig. 3. Best evidence of bicontinuous microemulsions is provided by NMR-self diffusion measurements when samples with differently deuterated compounds are used. For droplet phases, the dispersed phase and the surfactant display the same diffusion coefficient, that depends on the size of the droplets following Stokes’s law [15], while the diffusion coefficient for molecules of the continuous phase is much faster. For the bicontinuous structures, the diffusion coefficients for water and oil are of the same order while that of the surfactant is much lower, since it is located in the interface. 2.2 Phase Behaviour and Structural Evolution Curvature Energy Model and Phase Behaviour of Microemulsions Over the last two decades it has been realised that the structure and phase behaviour of microemulsion systems is, apart from the composition, determined by the elastic properties of the surfactant film that separates the water and oil domains. These have successfully been described using the presently

Microemulsion Templating

13

Fig. 3. Freeze fracture transmission electron micrographs (FF-TEM) of a bicontinuous microemulsion, containing 7 wt% C12 E5 , 37 wt% octane and 56 wt% water. The sample was prepared by rapid freezing, fracturing and subsequent deposition of a thin tantalum-tungsten coating to obtain a replica. Contrast between the oil and water domains occurs because the coating forms a mottled pattern on the oil regions. Reproduced from [26]. Copyright (1988) American Chemical Society.

well-established approach based on the statistical mechanics of curved interfaces that was introduced by Helfrich in 1973 [27]. The Helfrich free energy FH describes the bending energy of an arbitrarily shaped surface in terms of the spontaneous curvature, H0 , the rigidity constant associated with bending, κ, and the rigidity constant associated with Gaussian curvature, κ ¯,    2 FH = dA f0 + 2κ (H − H0 ) + κ ¯K . (3) The above form for the free energy is an expansion up to second order in curvature and features an integral over the whole surface area, A, of the mean curvature, H = 1/2(1/R1 + 1/R2 ), and Gaussian curvature, K = (1/R1 R2 ) with R1 and R2 the principal radii of curvature at a certain point on the surface A. The sign of the principal radii of curvature is generally taken as positive when the film curves toward oil and negative when it is curved toward water, see Fig. 4. In terms of R1 and R2 , FH can be written as  FH =



2κ dA σ − R0



1 1 + R1 R2



κ + 2



1 1 + R1 R2

2

 κ ¯ + , R1 R2

(4)

14

W.F.C. Sager

where R0 = 1/H0 is the radius of spontaneous curvature and σ is the surface tension of the planar surface. f0 is defined such that σ comprises all terms that are independent of curvature: σ = f0 + 2κH02 . At present the four parameters σ, R0 , κ and κ ¯ cannot be obtained from a molecular model allowing the direct input of the properties of the surfactant molecules and the interactions of the hydrophilic and hydrophobic moieties with water and oil, respectively. They can, however, be determined experimentally or simulated for simple model systems with well defined interaction potentials (e.g., a “surfactant” with Lennard-Jones interactions [28]). A global insight into the general phase behaviour can be gained by minimising the Helfrich free energy for the different phases. Phase boundaries or existence regions can then be obtained in terms of R0 and, e.g., κ ¯ /κ. It is therefore important to know how they are related to experimentally accessible variables, such as temperature or salt concentration. Since a complete treatment of microemulsion phases within the curvature energy concept is beyond the scope of this chapter, attention is only paid here to its manifestation in the general phase behaviour of microemulsion systems. In this context, formulas will only be derived for microemulsion droplet phases.

spontaneous curvature interfacial film curved toward (packing parameter v/al microemulsion type multiphase equilibria

H0 > 0 oil

H0 ∼ =0 no preferred curvaturebalanced state

H0 < 0 water

<1

1

> 1)

o/w (L1 -phase)

bicontinuous

w/o (L2 -phase)

Winsor I (2Φ)

Winsor III (3Φ)

Winsor II (¯ 2Φ)

Fig. 4. Curved surfactant monolayers at the water/oil interface, with the corresponding values for the spontaneous curvature H0 and the type of microemulsion formed in the single phase and in multiphase equilibria.

The spontaneous curvature, H0 , is defined as the curvature H a surfactant film will adopt when the film is totally unconstrained. In this case the film is in its lowest free energy state and thus ∂FH /∂H = 0 for H = H0 . H0

Microemulsion Templating

15

corresponds to the energetically most favourable packing configuration of the surfactant molecules in the interface. It can principally be compared with the packing parameters for micelles and depends on the molecular geometry of the surfactant and the solubilisation of the hydrophilic part in the aqueous phase and of the hydrophobic part in the oil. The latter depends in turn on formulation parameters such as temperature, (pressure), salt concentration in the aqueous phase, kind of oil used and type and concentration of cosurfactants (e.g., alcohol). Fig. 4 sketches the possible conformations of surfactant monolayers at a water/oil interface and gives the corresponding values for H0 and the type of microemulsion formed in the single phase and in multiphase equilibria. Positive and negative values for H0 favour the formation of droplets with spherical or cylindrical geometry. When H0 is zero (balanced state), the film will preferably form flat planar bilayers or bicontinuous structures with saddle shaped curvature for which R1 = −R2 . For a given surfactant, the spontaneous curvature can be tuned and adjusted by the aforementioned formulation variables. For nonionic surfactants of the Ci Ej type temperature has the strongest effect on H0 . Upon increasing the temperature the hydrogen bonds between the hydrating water molecules and the ether groups of the ethyleneoxide moiety Ej break, whereby the surfactant becomes increasingly less soluble in the aqueous phase. The interfacial surfactant film turns from being curved toward oil (H0 > 0) via its balanced state (H0 ∼ = 0) to become curved toward water (H0 < 0). The actual transition temperatures depend on the length of the ethylene Ci and ethylene oxide Ej blocks of the surfactant and the oil used. Smaller i, longer j and long chain aliphatic oils favour values of H0 > 0. For ionic surfactants the strongest influence is the salt concentration of the aqueous phase. If the salt concentration is increased the effective charge of the head group will be screened and the surfactant heads repel each other less which can lead to a change from H0 > 0 → H0 < 0. The temperature dependence of H0 is for an ionic surfactant film with H0 < 0 → H0 > 0 opposite to the salt dependence, since the Debye screening length is given by 1/κD = (εRT /2F 2 I)1/2 , where ε is the permittivity, F the Faraday constant, and I the ionic strength of the aqueous phase. The temperature dependence for nonionic and ionic surfactants is therefore opposite. For both kinds of surfactant, the addition of alcohols with more than four C-atoms stabilises structures which are curved toward water. Ionic surfactants with a strong head group (e.g., −SO− 3 or ), such as sodium dodecylsulfate (SDS), can only be brought into their −SO− 4 balanced state (or even curved toward water) if salt and a long chain alcohol are added, while films of a double tailed ionic surfactant, such sodium di(2-ethylhexyl)sulfosuccinate (AOT), are close to their balanced state. The (bending) rigidity constant or bending elastic modulus, κ, is, in principle, a measure of how easily an interfacial surfactant film can be bent and influences both the static and dynamic properties of microemulsions. κ is expressed in units of energy with values typically between 1-20 kB T , where kB is the Boltzmann constant. Experimentally, κ can be obtained from ellipsometric

16

W.F.C. Sager

measurements of fluctuating flat interfaces [29] or from electro-optical birefringence measurements of the form fluctuations of microemulsion droplets [30]. The persistence length of the interfacial film ξk describes the length over which the film is locally flat. High values of ξk indicate flat surfaces, whereas low values are found with highly curved surfaces. ξk is given by   2πκ (5) ξk = l exp kB T where l is a molecular length that corresponds to the length of the surfactant. If the bending elastic constant κ is of the order of kB T , ξk is microscopic and the interfacial film is flexible. Over a large volume fraction range (see Figs. 1 and 5), a bicontinuous structure will exist if the spontaneous curvature of the surfactant film is adjusted to be close to zero (H0 ∼ = 0) by, e.g., variation of T , salt and/or alcohol concentration. If κ is much larger than kB T , ξk is macroscopic and the film is rigid. In this case, the droplet structure exists up to very high volume fractions and phase inversion takes place preferably via a lamellar crystalline phase. Flexibility is increased when i) short chain hydrocarbon chains or cosurfactants are added, ii) double chain surfactants with unequal chain lengths are used and iii) short chain oils are employed, that can easily penetrate into the surfactant film, or iv) the salt concentration of the aqueous phase is increased. For the rigidity constant associated with Gaussian curvature or the saddle splay modulus, κ ¯ , few reliable measurements are available. The integral of the Gaussian curvature depends solely on the topology of the surface (Gauss–Bonnet theorem). Deformations of the film leave the integral over K thus unchanged. This value only changes if the film breaks due to the formation of holes or if two separated domains join. The typical trend is that κ ¯ is negative. The magnitude of it is usually smaller than that of κ for the same system. Experiments have shown that κ and κ ¯ are approximately constant over the temperature range encountered, but depend for ionic surfactant layers strongly on the salt concentration of the aqueous phase [31]. Generally, the interfacial layer is more stiff when no screening occurs with little or no salt added. Phase and Structural Evolution in Microemulsions Figure 5 shows a phase evolution typically observed for nonionic microemulsion systems with increasing temperature. The same trend can in principle be obtained for ionic microemulsion systems with increasing salt concentration in the aqueous phase, but focus will be placed only on the nonionic system. At low temperatures, the surfactant is preferably soluble in the aqueous phase and forms, at concentrations above the cmc, micelles that can take up only small amounts of oil. Within the central miscibility gap at low temperatures an o/w microemulsion is formed which is in equilibrium with an almost pure oil excess phase (all tie-lines decline toward the oil corner), which is classified as the Winsor I microemulsion system [32]. With increasing temperature,

Microemulsion Templating

17

Fig. 5. Phase evolution resulting in Winsor I-III-II microemulsion equilibria, as observed for microemulsions stabilised by a nonionic surfactant with increasing temperature and for microemulsions stabilised by an ionic surfactant with increasing salt concentration. The compositions ci of the coexisting phases are indicated by the end points of the tie-lines and the corners of the three phase triangle, whereby the subscripts l, m, or u stand for lower, middle or upper phase, respectively. The bars below and above the 2 in the two-phase systems indicate whether the microemulsion is formed in the bottom or top phase. These also indicate in which phase the surfactant is preferably soluble. The thick lines mark the critical tie-line out of which (at Te ) and into which (at Tμ ) the three-phase triangle develops and collapses, respectively. T0 is the temperature at which the three-phase triangle is isosceles.

the hydrophilic moiety becomes less soluble in water and the interfacial film becomes less curved toward oil (H0 > 0 → H0 ∼ = 0). When H0 approaches zero, the lower microemulsion phase of the Winsor I systems separates into a surfactant-rich, bicontinuous middle phase and a water-rich phase (Winsor III, which is also depicted in Fig. 1). The three-phase triangle develops out of a, so-called, critical tie-line, which is indicated as a thick line. At T = T0 the three-phase triangle is isosceles in shape. The concentrations of the three coexisting phases ci are given by the corners of the triangle, see Fig. 5. For samples that are prepared at overall concentrations within the three phase triangle, only the volumina but not the concentrations of the three coexisting phases differ. The degree of freedom, f , is given by the Gibbs phase rule: f = C − P at constant temperature and pressure, where C corresponds to the number of components and P to the number of phases [15]. For a system consisting of three components and three phases f = 0. Upon further increasing the temperature the surfactant moves via the middle phase into the oil phase, whereby the middle phase takes up an increasingly large amount of oil

18

W.F.C. Sager

and the upper, the originally almost pure oil phase, takes up more water and surfactant. cm moves clockwise around the central miscibility gap, while the bottom phase declines in oil and surfactant and c moves to the water corner. If the compositions of both upper phases become identical, they merge (H0 ∼ = 0 → H0 < 0) into a two phase system (Winsor II system), that is composed of a w/o microemulsion (upper phase) in equilibrium with an almost pure water phase (lower phase). In this case the tie-lines decline toward the water corner. In the Winsor I-III systems the curvature of the surfactant film in the different assemblies/structures formed is related to the spontaneous curvature H0 . At higher surfactant concentrations, enough surfactant is available to solubilise all excess water and/or oil in the corresponding microemulsion droplets or bicontinuous phases, respectively, to span the whole system and as a result single phase microemulsions are formed.

Fig. 6. Experimentally averaged mean curvature < H > (left) and characteristic length ξ (middle) obtained from FF-TEM and SANS for the system C12 E5 -water(n-octane). Around T¯ = 32.6◦ C, < H > changes sign and ξ is maximal. Interfacial tension (right) of the interface between the water-rich and oil-rich phases, indicated by σab , in the Winsor I, III and II systems for the same microemulsion system, obtained by spinning drop measurements. The interfacial tension shows a minimum when ξ is maximal. Reproduced with permission from [33].

The main trends found in microemulsions prepared from the H2 O-octaneC12 E5 system are summarised in Fig. 6. The data was collected by Strey and co-workers [33,34] using small angle neutron scattering (SANS) and FF-TEM to determine the characteristic sizes ξ and main curvatures of the water and oil domains as they evolve with temperature. In addition, spinning drop measurements were performed to determine the interfacial tension σab between the water-rich and oil-rich phases of the Winsor I, III, II systems. In the microemulsion region, the mean curvature varies linearly with temperature (H ∼ T − T0 ), while the characteristic length ξ shows a maximum at T = T0 , when the mean curvature passes through zero. Experimentally, it has been found that T0 lies close to the mean temperature T¯ of the threephase temperature interval that can be obtained from T¯ = (Tu + T )/2. Tu

Microemulsion Templating

19

and T are the temperatures at which the isotropic three-phase triangle appears and vanishes, respectively, in the Gibbs triangle (see Fig. 5). At high and low temperatures, both H and ξ level off to their limiting values of the corresponding (reverse) micellar systems. The interfacial tension σab shows a minimum when ξ is at a maximum. The minimum is more pronounced with higher amphiphilicity (amphiphilic strength) of the surfactant.

2 g

Fig. 7. Schematic phase diagrams performed at the indicated cuts through the phase prism. Left: fish-cut; right: one-phase-channel. The sketched structures within the one-phase regions display the structural evolution observed by different experiments, including small-angle scattering and FF-TEM. Reproduced with permission from [33].

The determination of all the (co)existence regions and phase boundaries within the Gibbs triangle is quite time consuming. If one is particularly interested in the temperature evolution, it is often sufficient to perform certain cuts through the phase prism constructed from the Gibbs triangle as base and temperature as ordinate. Two of the most instructive phase diagrams obtained in this way are displayed in Fig. 7. The left hand diagram shows schematically a phase diagram obtainable by measuring the phase boundaries occurring in samples with an equal amount of water and oil as a function of surfactant concentration γ and temperature. This is a cut through the prism that starts in the middle of the water–oil side of the triangle and heads torwards the surfactant corner (see inset in Fig. 7). In this way it cuts through the central miscibility gap and the three-phase triangle at temperatures between T and

20

W.F.C. Sager

Tu . At T < T Winsor I (2Φ) phase equilibria are formed within the central miscibility gap, while Winsor II phase (¯2Φ) equilibria form at T > Tu (see also Fig. 5). The three-phase region then shows up as a kind of “fish-head” shape, that is surrounded by the two-phase regions. At very low surfactant concentration γ, the surfactant is molecularly dispersed in the water or the oil phase, respectively, depending on in which medium it is preferably dissolved at a given temperature. At low temperatures (T < T¯), the surfactant is soluble in water. If micellar aggregates form at concentrations above the cmc, they contain a certain amount of oil that depends on the spontaneous curvature H0 at that temperature. Figure 7 also shows the cmc-lines that indicate from which surfactant concentration onward microemulsion droplets form in the water (cmcwater ) and oil phases (cmcoil ). Both lines decline toward the threephase region. The two-phase region in front of the “fish-head” corresponds to the two-phase region that surrounds the three-phase triangle in Fig. 5 along the water-oil side of the Gibbs triangle. At T = T¯ (balanced state of the surfactant) the surfactant molecules are most efficient and show the lowest solubility in a water-oil system. Above the three-phase region, the surfactant is preferably dissolved in the oil, and Winsor II microemulsion systems are formed with different droplet sizes, which depend on the temperature and thus H0 . If, at a given temperature more surfactant is added, more microemulsion droplets of the same size can be formed and the microemulsion phase takes up more of the excess phase. Considering, e.g., a Winsor I system at T < T , more oil becomes solubilised in the o/w microemulsion. If more surfactant is present more oil can be “encapsulated” in order to keep almost the same size. At a certain surfactant concentration all excess phase is taken up and a single o/w microemulsion is formed. When more oil is solubilised in the o/w microemulsion phase at temperatures closer to T¯, more oil is present at low surfactant concentrations and the 2Φ → 1Φ boundary is shifted to lower surfactant concentrations. The point at which the boundaries of the three-phase region and the one-phase region intersect γ˜ , corresponds to the corner of the isosceles three-phase triangle that indicates the composition of the middle phase cm (see Fig. 5). γ˜ marks the lowest surfactant concentration needed to prepare single phase microemulsions. In its balanced state the surfactant film can solubilise the highest amount of water and oil, the domain size is maximized and the surface tension between the excess phases is at a minimum. The sketched structures within the one-phase, “fishtail”-like region in Fig. 7 display the micro-structural evolution that is observed experimentally. Droplet phases form within the tail at high surfactant concentrations and T < T¯ (o/w) or T > T¯ (w/o). The transition from one droplet structure to the other can either occur continuously via cylindrical structures and bicontinuous phases or via a 1st order phase transition to the lamellar phase Lα that might intersect with the microemulsion phases at temperatures close to T¯ (see Fig. 1). The phase diagram on the right in Fig. 7 presents a cut through the phase prism at constant surfactant concentration, whereby the concentration is chosen such that at T¯ the bicontinuous one-phase microemulsion is just formed.

Microemulsion Templating

21

The surfactant concentration is thus chosen to be slightly higher than γ˜. In this way, a continuous one-phase microemulsion channel can be obtained that leads from the water to the oil side with a large bicontinuous region at intermediate water/oil ratios. The sketches of the structural evolution within the channel demonstrate nicely that the microemulsion morphology is governed by the composition and the properties of the interfacial surfactant layer. If the temperature is varied the latter is primarily determined by H0 . The Helfrich energy may be applied to derive expressions for the droplet radius and the interfacial tension in Winsor I and II droplet phases and to determine the 2Φ → 1Φ boundary, when only spherical droplets are considered. For spheres R1 = R2 = Rs and volume (Vs ) and surface area (As ) are given by Vs = (4/3)πRs3 and As = 4πRs2 . For a given sample of a droplet microemulsion phase in equilibrium with an oil (T < T¯) or water (T > T¯) excess phase, the surfactant concentration and thus the total surface area A can be assumed not to change with temperature, since almost all surfactant is situated in the droplet interfaces of the w/o or o/w microemulsion phases. The radius and the droplet volume increase in the direction of T¯. The total interfacial area A is given by A = Ns 4πRs2 , with Ns the number of spherical droplets. The Helfrich free energy for a spherical droplet phase, Fs , can be written as

2κ + κ ¯ 4κ Fs = Ns 4πRs2 σ − + . (6) R0 Rs Rs2 Minimisation of Fs can then be performed with respect to the droplet radius Rs and the number of droplets Ns under the condition of constant interfacial area and thus surfactant concentration. Minimisation with respect to Rs gives κ 2κ ∂Fs = 8πNs σRs − 16πNs =0→σ= . ∂Rs R0 R0 Rs

(7)

The interfacial tension between the droplet and the excess phases is in good approximation proportional to the square of the droplet radius. The expression for σ in (7) was first derived by de Gennes [35]. Minimisation with respect to Ns gives

4κ 4κ ∂Fs 2κ + κ ¯ 2κ + κ ¯ =0→σ= = 4πRs2 σ − + − ∂Ns R0 Rs Rs2 R0 Rs Rs2

(8)

and thus  Rs =

1+

¯ 1κ 2κ

 R0 .

(9)

Since the bending constant in the range considered depends only weakly on the temperature, the droplet radius in the Winsor I and II systems is pro-

22

W.F.C. Sager

portional to the radius of spontaneous curvature, which is tuned by the temperature. On approaching T¯ from high and low temperatures |R0 | increases, leading to an increase in Rs and a decrease in σ. To obtain the 2Φ →1Φ boundary, one has to determine when the droplet radius in the Winsor I and II systems becomes equal to the droplet radius in the neighbouring one-phase regions. The radius of the droplets in the onephase region is determined by the following argument. If there is no excess phase present, then not only the total surface area A but also the total volume Vtot = Ns (4/3)πRs3 is determined and consequently Rs = 3Vtot /A = 3ω. The phase boundary, which is normally referred to as the solubilisation limit, occurs at   ¯ κ ¯ 1κ ω 1 R0 → 2+ . (10) = Rs = 3ω = 1 + 2κ R0 6 κ So far, entropic effects have been neglected. Including translational entropy and a radial polydispersity for the droplets allows the droplet polydispersity to be calculated; this shifts the phase boundaries only slightly [36]. To obtain the complete picture not only spherical droplets but also cylindrical domains and interconnected cylinders have to be considered. For more information about the phase behaviour of nonionic and ionic surfactant–water-oil systems the reader is referred to review articles by the group of Kahlweit [37], (nonionic) [38], (ionic) [39]. 2.3 Statics and Dynamics of Droplet Phases One-phase w/o or o/w droplet microemulsions have been thoroughly investigated over the past three to four decades. They have mainly been studied as model systems to apply liquid state theories [40], to study dynamic percolation phenomena [41] and to investigate their exchange kinetics in view of their employment as reaction media [42]. Recently, the Helfrich energy has been used to describe shape fluctuations [43], droplet aggregation [44] and the formation of cylinders [36] and interconnected networks [45]. In this section, only results, most relevant for particle preparation, are briefly described. Droplet Phase Existence Regions, Droplet Aggregation and Cylinder Formation Within the one-phase region, the total area and total volume are fixed by the concentrations of surfactant and the dispersed phase. This imposes a constraint of area and volume conservation. Figure 8 shows schematically the existence region of a w/o microemulsion stabilised by an ionic surfactant, such as AOT. The phase diagram can be obtained by a cut through the phase prism as indicated in the inset. The cut is performed by varying the water/surfactant weight ratio, rw , at constant oil and thus droplet weight

Microemulsion Templating

23

Fig. 8. Schematic phase diagram showing the existence region of a w/o microemulsion stabilised by an ionic surfactant, such as AOT, as a function of the water/surfactant ratio and temperature. The cut through the phase prism is performed by variation of rw =(water/wt%)/(surfactant/wt%) at constant oil and thus droplet weight fraction.

fraction. Since the temperature dependence of ionic and nonionic surfactants is opposite, the lower phase boundary corresponds to the solubilisation limit boundary (see Fig. 7 for comparison). Close to the solubilisation limit, Rs /R0 equals 1 and spherical droplets are formed with a polydispersity of about 20%. Their radius depends linearly on the (molar) water/surfactant ratio, since Vtot = vw NA [water] and A = aNA [surfactant], with vw the molar volume of a water molecule, NA the Avogadro number and the concentrations given in mol L−1 . The smallest radii reached are those of the inverse micelles and the largest that of the corresponding radius at the solubilisation limit at a given temperature. If the temperature is increased, H0 → 0 and the interfacial film tends to be less curved towards the water phase. In the corresponding Winsor II system, the water volume is not fixed and fewer droplets with larger radii are formed. In the one-phase region, if Rs /R0  1 the system minimises its free energy by forming a certain amount of aggregated droplets or cylinders. Small angle x-ray or neutron scattering curves, measured for AOT stabilised w/o microemulsions at different temperatures and interpreted in terms of the sticky

24

W.F.C. Sager

hard sphere model [46] for the structure factor, have generally shown that the droplets become more attractive with increasing temperature. The degree of attraction depends on the oil used; at constant temperature, w/o emulsions prepared with long chain alkanes, such as decane and dodecane, show more attraction then systems with less hydrophobic oils as the continuous phase. Recently, the droplet→cylinder transition has been studied in detail, both experimentally [47] and theoretically [36]. Within the one-phase region spheres and cylinders coexist. When the cylindrical droplets start to form, they are of a certain minimal length that corresponds to a few multiples of their diameter. If one compares the radius of the spherical droplets at the lowest temperature with that of the cylinders, Rc , at the highest temperature measured, the geometrical limit of Rc = 0.67Rs is reached. The geometric limit is the point at which all spheres transform into cylinders. At temperatures close to the upper phase boundaries, the cylinders start to interconnect and form (bicontinuous) networks. The existence of these networks can best be demonstrated by conductivity measurements. If the temperature is increased the conductivity may show a steep increase over two to three orders of magnitude, reaching values of the same order as that of the aqueous phase [41]. At the upper phase boundary, either two coexisting oil-continuous microemulsions (low rw -values) form or the microemulsion coexists at high rw -values with a lamellar phase (Lα ). The transition from a microemulsion consisting of spherical droplets only to a lamellar phase can easily be determined by setting the contributions that stem from the curvature energy in the Helfrich free energy equal for both phases: Fs,curv = −

4κ κ ¯ 2κ + κ ¯ ω 1  2 + . + = F = 0 → = L ,curv α R0 Rs Rs2 R0 12 κ

(11)

Since the lamellar phase is composed of flat surfactant sheets their contribution to the curvature energy is equal to zero. In Fig. 8 both the solubilisation limit and the transition to the lamellar phase are given for phases consisting of infinitely long cylinders, which can be obtained in the same way as described above for spherical droplets using 1/R1 = 1/Rc and 1/R2 = 0. Vtot and A are then given by Vtot = Nc πRc2 L and A = Nc 2πRc L, with Nc the number and L the length of the cylinders. A full description including the coexistence of spheres and cylinders taking the radial and length polydispersity into account is given in [36]. Exchange Kinetics in Droplet Phases Micellar systems and microemulsions are highly dynamic systems. Surfactant molecules that are dissolved in the continuous phase exchange rapidly with those located at the interface of the assembled structures. Fast relaxation measurements have shown that exchange of monomeric surfactants between micelles or microemulsion droplets takes place with relaxation times of

Microemulsion Templating

25

τ1 = 10−6 -10−3 s. Relaxation times associated with the much slower formation or desintegration of entire micelles lie typically in the range of τ2 = 10−3 1 s [48]. In droplet microemulsions exchange of the dispersed phase also occurs. If, for example, two w/o microemulsions are brought together containing the same amounts of surfactant, aqueous phase and oil, but different types of solubilised species in the internal water pools, material exchange sets in immediately and leads to a redistribution of the two species over the entire dispersed droplet phase. Solubilisation of two reactants A and B that can undergo a chemical reaction to form C, can then be utilised to measure the exchange kinetics. It is now generally accepted that material exchange between droplets, necessary for particle formation, takes place via the formation of intermediate dimeric droplet aggregates. Dimers allowing free passage of the solubilised species were originally proposed by Fletcher et al. [49]. For AOT w/o microemulsions, exchange of solubilisate between the water pools of the microemulsion droplets occurs with a second order rate constant of kex = 106 –108 dm3 mol−1 s−1 ; thus two to four orders of magnitude slower than the droplet encounter rate as predicted from simple diffusion theory. This indicates that successful fusion events take place only in 0.01-1% of binary droplet collisions [49], [50]. For microemulsions stabilised by nonionic surfactants of the ethyleneoxide monoalkylether (Ci Ej ) type exchange rates of kex = 108 –109 dm3 mol−1 s−1 were measured [51]. Rate constants were found not to depend on the size of the solubilised species but on droplet size, temperature and factors influencing the rigidity of the interfacial surfactant film, such as the kind of surfactants and oil used, presence of cosurfactants (alcohol) and salt concentration of the aqueous phase [49]. The extent to which the interdroplet exchange rate is influenced by the presence of droplet aggregates and cylindrical droplets has so far not been investigated. Generally it has been observed that the exchange rate is low in droplet phases with rigid interfaces and high if water channels start to form. 2.4 Comparison Between Micro- and Macroemulsions (Macro)emulsions generally form when water and oil are vigorously mixed in the presence of a surface active compound. They are normally of milky appearance and display droplet sizes ranging from 10 μm down to 0.1 μm. The final size of the emulsion droplets depends on the mechanical energy applied in the preparation process and on their stability. The free energy ΔFemul to disperse a liquid of volume V with drops of radius R in another liquid is 3V . (12) ΔFemul = σ R If the freshly created droplet interfaces are not stabilised during the emulsification process, coagulation and coalescence processes cause a quick increase in droplet size and lead to rapid macroscopic phase separation. Employing surfactants in the emulsification process enables the surface tension and thus

26

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the mechanical energy required to be lowered and to stabilise the formed droplets electrostatically or sterically. Since macroscopic emulsions are only kinetically stabilised, their preparation, stabilisation and destabilisation resembles those of solid colloidal particles. Figure 9 shows schematically the destabilisation processes that can principally occur in, e.g., o/w emulsions. Flocculation and coagulation lead to (ir)reversible droplet aggregation, while the density difference between the water and oil phases causes creaming of the oil droplets. Coalescence processes and Ostwald ripening cause an increase in droplet size and lead eventually to phase separation. Ostwald ripening occurs only if molecules of the dispersed phase are slightly soluble in the continuous phase. Since the Laplace pressure is higher for more curved interfaces, small droplets display a higher tendency to dissolve. Since oil molecules inside the droplets are in equilibrium with those dissolved in the continuous phase, material transport occurs via molecular diffusion from small to large droplets. In this way, the larger droplets increase in size, while the smaller ones disappear.

Fig. 9. Processes that generally lead to a destabilisation of (o/w) emulsions. Creaming occurs normally before phase separation. The broken lines around the droplets indicate that the interfaces are not fully saturated.

Since emulsions are stabilised by surfactants, they combine the properties associated with colloidal particles and surfactant self-assembled systems. Within a certain water/oil ratio, the type of surfactant used as emulsifier determines the type of emulsion formed. Emulsions displaying long-term stabilities are normally prepared at surfactant concentrations higher than the cmc and formulation conditions adjusted in such a way that the surfactant is not in its balanced state (H0 = 0). At surfactant concentrations above the cmc the macroscopic interfacial tension remains constant (see Fig. 2) and micelles or microemulsion droplets, formed in the continuous phase, serve as a surfactant reservoir to stabilise the newly formed interface. The corresponding thermodynamic equilibrium phases for o/w and w/o macroemulsions are the Winsor I and II systems. To prepare the emulsions the water and oil phases do not necessarily have to be in equilibrium but they will finally phase-separate into the Winsor systems. If after the emulsification, micelles or microemulsion droplets are still present in sufficient concentration, they may introduce

Microemulsion Templating

27

flocculation by depletion [52]. The attractive depletion forces are caused by a difference in osmotic pressure. If two emulsion droplets approach each other by Brownian motion, the distance can become so small that no swollen micelles can come in between them. The osmotic pressure of the continuous phase is then much lower between the approaching droplets than in the surrounding phase, resulting in an attractive force that can lead to droplet aggregation. At the balanced state of the surfactant, the prepared emulsions are not stable and phase separate quickly. T¯ then corresponds to the phase inversion temperature PIT [53] of emulsions. Phase separation can thus also be induced by changing a formulation variable after the emulsion has been formed. Changes in temperature, salt or alcohol concentration that cause H0 → 0 destabilise the emulsion. For more information concerning the relatively broad field of emulsion preparation, stabilisation and emulsion breaking, the reader is referred to [15] and [54]. In order to obtain a better overview of the different emulsions systems employed in particle preparation routes, Table 1 lists important properties and characteristics of microemulsions when compared to ordinary macroemulsions.

3 Precipitation of (Inorganic) Nanoparticles in Droplet Phases Microemulsion droplet phases, e.g., water-in-oil microemulsions stabilised by ionic or nonionic surfactants or surfactant mixtures, have been extensively utilised over the past two decades as nano-reactors for the preparation of welldefined small spherical particles for a variety of different inorganic materials. These include metals, semiconductors, metal halides, as well as magnetic, ferroelectric, superconducting and ceramic precursor particles. Since the use of microemulsions has for the first time enabled the preparation of monodisperse particles of a few nanometres in diameter for some materials, a large number of investigations could focus on studying the optical, electrical and magnetic properties of the particles synthesised and on the study of quantum size effects [1, 55–60]. The advantages w/o microemulsions offer are directly linked to the easily performable tailoring of the compartmentalised reaction medium in terms of droplet size and concentration as well as the extremely small size of the aqueous cores. Compared to conventional methods using homogeneous reaction media, better control of the size and size distribution of the nanoparticles and an enhancement of the reaction rates have often been achieved. In recent years, interest has shifted from making monodisperse nanoparticles of mostly spherical shape of different materials to the control of particle morphology (anisotropic and high-axial-ratio particles), introduction of crystallinity and oriented growth [61,62] as well as the ordering of (spherical) nanoparticles into 2D or 3D structured arrays and superlattices [63, 64]. Microemulsions are both highly dispersed and highly dynamic systems, which makes them a good candidate for the precipitation of inorganic nanopar-

28

W.F.C. Sager Table 1. Main characteristics of (macro)emulsions and microemulsions

Stability

(Macro)emulsion kinetically stabilised

Microemulsion thermodynamically stable

•

•

•

•

Properties of the interfacial film

•

• •

Emulsion structure and domain size

• • •

• Surfactant (type and concentration)

• • • •

form only if (mechanical) energy is applied to the system. emulsion characteristics depend on the way the emulsion is formed and the amount of mechanical energy applied. occurrence of coagulation and coalescence processes as well as Ostwald ripening that lead to an increase in droplet size and finally to macroscopic phase separation.

• •

•

self-assembled systems that form spontaneously. properties do not depend on the preparation. domain structure and size are thermodynamically controlled; they depend on the composition and the elastic properties of the separating surfactant film and thus on H0 , κ and κ ¯. domain size does not change with time.

stable emulsions are formed if the • macroscopic (bulk water/ oil) interfacial tension is reduced by 10– 40 mN m−1 . the emulsion droplet interface is • not fully saturated. large internal interface. •

Winsor phase equilibria form when the interfacial tension between the water- and oil-rich phase σ = 5– 10−3 mN m−1 . the interfacial film is formed by a saturated surfactant mono- or bilayer. huge internal interface of up to 100 m2 g−1 .

•

the interfacial tension is comparable with κ. rich phase behaviour: droplet phases form if H0 = 0. For H0 ≈ 0 bicontinuous microemulsions form at low κ and Lα phases at high κ. characteristic length of 2–50 nm and low polydispersity. transparent.

interfacial energy is low but still larger than κ. the structure formed has the minimal surface/volume ratio. spherical droplets of oil (o/w) or water (w/o) with sizes of 0.1–10 μm and high polydispersity are formed milky appearance.

•

• •

water- (o/w) or oil-(w/o) soluble • surfactants. instable emulsions if the surfactant is at its balanced state. low surfactant concentrations. • stable emulsions form at surfac- • tant concentrations ≥ cmc: at concentrations a few times larger than the cmc flocculation occurs.

water- (o/w) or oil-(w/o) soluble surfactants; at the balanced state of the surfactants either bicontinuous microemulsions or Lα phases form. high surfactant concentrations. surfactant concentration > cmc up to 20–30 wt%.

Microemulsion Templating

29

ticles. The surfactant-stabilised cavities provide a cage-like effect that can control nucleation, growth and agglomeration. Particle nucleation and growth are governed by the occupation numbers of the reactants (solutes) in the aqueous droplet cores, the kinetics of the chemical reaction(s) leading to particle formation and the rate of solute exchange between the droplets. The final particle morphology is influenced by the properties of the microemulsion system, the chemistry of the precipitation reaction and specific interactions between surfactants and the solid phase being formed. The particles prepared can be of amorphous, quasi-crystalline or crystalline nature and the set of independently variable and intrinsic parameters determining this is quite large. Besides the increasing use of microemulsion systems in preparation routes for nanoparticles, much less systematic work has, however, been performed on the factors that control the size, shape and stability of the particles formed. To prepare (monodisperse) particles of a given size and material, the proper precipitation conditions have to be determined experimentally and the chemical reaction conditions have to be matched with the stabilisation criteria of the microemulsion system. Metal ions can be introduced to the microemulsion via the aqueous core or in the case of anionic surfactants as surfactant counterions. The reactant agent can then be brought in via the dispersed phase of a second microemulsion of the same composition or added directly to the microemulsion if it is soluble in the continuous phase. In any case, reactants and concentrations should be chosen such that phase separation leading to uncontrolled precipitation conditions is avoided. If the reactions that lead to the formation of the solid phase are much faster than the solute exchange between the droplets, the latter becomes the rate limiting step. The exchange kinetics then dominates nucleation and growth allowing us to establish general trends that can be used for the tailoring of spherical nanoparticles. The observed dependence of the size and distribution of spherical nanoparticles on compositional parameters and on the exchange rate will be described in Sect. 3.1. The morphology of the solid phase formed is not in all cases commensurate with that of the microemulsions from which they are formed. If only a few nuclei are formed, particle growth due to solute exchange can lead to particle sizes that are a few times larger than the droplet cores. Furthermore, secondary growth processes such as (uncontrolled) aggregation or reorganisation and (re)crystallisation might lead to complex inorganic-surfactant assemblies that can reach mesoscopic length scales. Recently, w/o microemulsion systems have also been investigated to prepare non-spherical particles such as nanorods and nanofibres. The underlying idea is to perform the precipitation in cylindrical aggregates or interconnected cylinder phases. However the extent to which the self-assembled surfactant systems can really serve as a mould for high-axial ratio particles has not yet been completely established. Conditions under which rod-like particles and fibres have been obtained are described in Sect. 3.2.

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W.F.C. Sager

3.1 Spherical Nanoparticles

Fig. 10. Schematic presentation of nucleation and growth processes occurring in the reduction of metal ions in w/o microemulsions. Metal ions M+ solubilised in the aqueous core become reduced when the reducing agent R enters the droplet interior. If the number of metal atoms is higher than the critical aggregation number n∗ , a metal cluster nucleus forms that grows due to the exchange of metal ions with other droplets.

The basic trends observed in the formation of nanoparticles in w/o microemulsions will be described in more detail, allowing a better insight into the nucleation and growth processes that are taking place. It has been found that under certain conditions the number density of microemulsion droplets and particles obtained can differ by up to three to four orders of magnitude, indicating the importance of interdroplet solute exchange [8, 65]. Let us for the sake of simplicity consider the reduction of a metal ion under the condition that the reducing agent is brought in via the continuous phase and that all chemical reactions involved are fast compared to the interdroplet exchange (see Fig. 10). Metal particle formation then involves the following

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31

steps: i) Diffusion of the reactant to the droplet interface, ii) instantaneous reduction of the metal ions, iii) metal particle nucleation and iv) growth via intramicellar attachment of metal atoms and intermicellar exchange of droplets. The final particle size depends on the population balances and the interdroplet exchange rate constant kex . Since diffusion into the reversed micelles proceeds faster than the interdroplet exchange process, the initial distribution of the metal ions equals that of the metal atoms. It has been found by fluorescence measurements that the ion distributions generally obey Poisson statistics. If the metal occupation number in the droplets is smaller than the critical nucleation number n∗ , nucleation can only occur after solute exchange between the droplets has taken place and n∗ has been reached. Nuclei formed grow via interdroplet exchange until all free metal ions are used up. The described situation allows the following trends to be predicted: In general, the more nuclei are formed then less free metal ions are left for particle growth. Low metal occupation numbers obtained at low metal salt concentrations and high droplet number densities lead to extended particle growth and low particle number densities. If kex is high, more nuclei can form due to faster exchange kinetics leading to smaller particles and higher particle number densities. The number of droplets Ns depends on the relative amounts of water and surfactant present, whereby Ns ∼[surfactant]3 /[water]2 . The fraction of particles having a particular size increases if n∗ is higher since more free metal atoms became available for growth. The polydispersity also becomes larger as n∗ is increased. This can be explained by the fact that for higher n∗ more free metal atoms are available for the formation of nuclei as well as for particle growth. The particles would therefore start gathering over wider ranges and larger sizes. Therefore, for systems in which n∗ is high, low and moderate salt concentrations are expected to give highly polydisperse particles. In Fig. 11 samples with silver particles that have been prepared in a waterC12 E5 -cyclohexane microemulsion system at different water/surfactant weight ratios rw are displayed [66]. The silver particles were prepared by mixing an Ag+ ion containing microemulsion with a microemulsion of the same composition that contains NaBH4 as reducing agent. The microemulsions were either prepared with a 0.1 M AgNO3 or a 0.1 M NaBH4 solution. Reduction occurs by exchange of Ag+ and BH− 4 between the droplets. The total amount and the quantity of surfactant plus aqueous phase were kept constant, for the cut through the phase prism (see the inset in Fig. 11). As can be seen from the particle size distribution, the radius passes a maximum as rw is increased. In this series the overall concentration of silver ions increases with rw , whereas the number of microemulsion droplets decreases. Both effects lead to higher occupation numbers, although the latter is much stronger than the former. Since nonionic and ionic surfactants show an opposing phase behaviour with respect to temperature, the upper boundary corresponds to the solubilisation limit and aggregation processes occur with decreasing temperature (H0 → 0) (see Fig. 8 for comparison). In this case the interdroplet exchange rate is expected to increase if the lower phase boundary is approached at high rw values.

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W.F.C. Sager

Fig. 11. Solutions and TEM-micrographs obtained by reduction of silver ions in w/o emulsions by varying the water/surfactant weight fraction rw at constant oil weight fraction (cw = 0.2) performed at 23◦ C [66]. The colour changes from yellow to red (from left to right), because both absorption and scattering depends on the size of the particles (Mie-scattering). The phase diagram shown has been performed for the system water-C12 E5 -cyclohexane along the cut indicated in the Gibbs triangle as a function of rw and temperature at cw = 0.2. Since for nonionic surfactant systems, temperature has a much larger effect on the phase behaviour than added salt, the phase boundaries change only slightly for the concentrations of AgNO3 and NaBH4 used for the precipitation. The arrow in the phase diagram marks the temperature at which the precipitation has been performed. In the Table the averaged radius and its standard deviation obtained from the TEM-micrographs are given in nanometres. Reprinted from [66]. Copyright (1992) with permission from Elsevier.

Thus the formation of more smaller particles is expected at high rw . If the number of droplets Ns present in, e.g., 3 g of microemulsion is estimated, then this number decreases from Ns ∼ 1020 at rw = 0.05 to Ns ∼ 1017 leading to average occupation numbers that are smaller than 10−2 at rw = 0.05 and about 25 at rw = 0.8. These values indicate that enormous growth takes place

Microemulsion Templating

33

for the very small droplets and explain the observed maximum in the radius if rw is increased. The polydispersity is increased at high occupation numbers.

Fig. 12. Particles of different morphology obtained by reduction of copper [67] in water-Cu(AOT)2 -(iso-octane) microemulsions (left) and mineralisation of BaSO4 [69] in water-Ba0.019 Na0.0962 AOT-(iso-octane) microemulsions (right) at different molar water/surfactant ratios w0 . Left: reproduced from [67]. Right: reproduced from [69]. Copyright (1997) American Chemical Society.

3.2 Nanorods and Filaments Figure 12 shows examples of nanorods and nanofilaments and fibres prepared from AOT w/o microemulsions. Pileni and co-workers have demonstrated that the system water-Cu(AOT)2 -(iso-octane) can be employed to prepare well defined spherical copper nanoparticles and nanorods [5, 67, 68]. Cu(AOT)2 was prepared by exchanging the Na+ counter-ion for Cu2+ and the reduction was performed by addition of hydrazine under nitrogen atmosphere at room temperature. If water is added to spherical inversed Cu(AOT)2 micelles at low molar water/Cu(AOT)2 ratio w0 , they first swell and thereafter elongate into cylinders that then form interconnected cylindrical networks. Mostly spherical Cu particles displaying polydispersities below 15% were obtained when spherical and cylindrical droplets were used as templates (w0 = 4). In this case the spherical Cu particles self-assemble into hexagonal arrays on the TEM-grid. As soon as the interconnected cylinders formed in the mould, mixtures of copper spheres and rods with up to 40% rods were obtained (w0 = 12). The rods were on average 18–25 nm long and 7–8 nm thick. Examples for both Cu nanospheres and nanorods are shown on the left side in Fig. 12. Further elongated rods could be obtained if NaCl or KCl were added. Both salts are known to inhibit growth along the [100] direction and favour that along the [110] direction.

34

W.F.C. Sager

The right hand picture of Fig. 12 shows barite fibers and filaments that were obtained by addition of Na2 SO4 to a water-Ba0.019 Na0.962 AOT-(isooctane) microemulsion system at different w0 -values. The crystallisation was performed within one week. At w0 = 10, a non-compact fibre formed, consisting of 2–20 μm long multiple filaments, while for 12 ≤ w0 ≤ 29 single highly ordered crystalline barrite filaments 1–100 μm long and 20–200 nm wide were obtained. All filaments formed in this w0 -range were found to be single crystalline and elongated predominately along the [010] crystallographic axis displaying a uniform thickness and aspect ratio of 1000. These results indicate that the final morphology is not determined by the microemulsion template. Extended oriented growth took place, which might have been induced by secondary growth processes influenced by the presence of surfactants in high concentrations [69, 70]. Studies of the time dependence in the formation of CaSO4 obtained from comparable systems showed that in most cases firstly spherical particles were formed that elongated into cylinders and finally into long fibres [71].

4 (Micro)Emulsion Polymerisation 4.1 Classical Emulsion Polymerisation Compartmentalisation has become more relevant for the preparation of polymer particles (latexes) by radical polymerisation on an industrial scale than for the synthesis of inorganic materials. Over the last 50 years this has developed into a broad field with an enormous variety of industrial and academic applications. In contrast to suspension polymerisation, where the monomer starts to nucleate in a suitable solvent (diluent) in which it is dissolved, classical emulsion polymerisation makes use of the low solubility of most common monomers in water. Monomers that contain (at least) one double bond are dispersed into micrometer-sized droplets in the water phase. The monomer molecules in the droplets are in equilibrium with monomer molecules dissolved in the water phase. When water-soluble initiators start the radical polymerisation, polymer chains grow until they become insoluble in the water-phase and form primary particles. In principle, polymer particles can form under homogeneous nucleation conditions and the formation of the critical nuclei can be described by homogeneous nucleation theory. For the nucleation process to be spontaneous, the energy ΔFspon required for creating the polymer-water interface has to be compensated. Energy is in this case gained by the aggregation of the hydrophobic parts of the growing chain, ΔFchain , so that the overall free energy of a growing chain is given by 4 ΔF = ΔFspon + ΔFchain = 4πR2 σpw − πR3 fv, (13) 3 where R is the radius of the incipient particle, σpw the interfacial tension between polymer and water and fv the free energy of condensation per unit

Microemulsion Templating

35

volume of the primary particle or nucleus. At very small sizes the first term dominates and prevents the formation of particles. With increasing R, the released condensation energy overcomes the surface energy requirement, and ΔF passes through a maximum. Beyond the maximum, the critical nucleus can grow further. Particle growth then takes place by diffusion of monomer molecules from the emulsion droplets, which serve as a reservoir for monomers. (Ionic) surfactants have been widely used to reduce σpw and to stabilise the particles formed against aggregation. Employing a micellar phase as continuous medium ensures surfactant concentrations high enough for particle stabilisation and may lead to heterogeneous nucleation conditions and thus to particle formation which is not restricted by surface energy requirements. The largest application of water-born latex particles is probably in the paint industry, however increasingly greater applications are found in floor coatings (polishes), printing inks, adhesives, paper overprint varnishes, carpet backing and paper making. Water-based paints consist of a dispersion of inorganic pigment and latex particles made of a polymer that possesses a sufficiently low glass transition temperature Tg . When the water evaporates from the applied paint, the particles coalesce to form a continuous paint film. Using emulsion polymerisation submicrometer-sized latex particles made of, e.g., acrylonitrile, butadiene, styrene and polymethacrylate have been prepared. Advantages compared to suspension polymerisation are that i) high molecular weight polymers can be prepared at rapid reaction rates due to the fact that the free radicals grow in relative isolation and that ii) heat transfer can easily be controlled during the polymerisation due to the low viscosity of the medium even at high solid contents. In some cases, latexes with an extremely narrow size distribution and a homogeneous charge density can be obtained, that can be employed as ideal model systems to study order-disorder phenomena in colloidal suspensions. Since it is not possible to explain the different processes involved in emulsion polymerisation in more detail within the scope of this chapter by discussing the different mechanisms proposed and the kinetic models applied, only a brief description of the different stages observed during emulsion polymerisation in the presence of micelles in the aqueous phase is given next. This allows a better comparison to polymerisation in microemulsion systems. For more information the reader is referred to recent text books or text book contributions on emulsion polymerisation such as [72–74]. Emulsion Polymerisation in the Presence of Micelles Free radical polymerisation proceeds generally via initiation and propagation followed by termination and chain transfer. The reaction is started by the induced dissociation of an added initiator into two radicals that can attack the monomer and form new radicals with added monomer units. A constant overall concentration of propagating free radicals can be obtained if the initial radicals are formed under steady state conditions. In this case they are generated at

36

W.F.C. Sager

the same rate as they disappear, which is the case when the initiator decomposition is much slower than the subsequent reactions. In Fig. 13 three different stages of emulsion polymerisation in the presence of micelles are sketched. Initially the continuous water phase may contain dissolved monomer, inactive monomer swollen micelles and the initiator I. Polymer latex particles are generated by two processes which may occur simultaneously. The first is the entry of the free radicals R• into the micelles (micellar nucleation). Despite their large size, the monomer droplets are greatly outnumbered by the small micelles which have a much larger total surface area. The radicals enter the micelles rather than the large monomer droplets. The second process involves nuclei formation in the continuous phase, whereby oligomeric radicals (homogeneous nucleation) are formed. If they increase in size they may be solubilised in the micellar core or the surfactant might adsorb onto the nucleus when the chain becomes insoluble. In both cases polymer particles surrounded by surfactant are formed. In this first interval particles grown are stabilised by adsorbing surfactants from surrounding micelles. By the end of interval I (at about 2–25% conversion), the micelles have either been nucleated to form new polymer particles or depleted to stabilise those particles formed. Most of the polymerisation occurs in interval II during which the nucleated polymer particles continue to grow due to diffusion of monomer molecules from the monomer droplets through the continuous medium and into the particles. The primary radicals which are formed in interval II enter the polymer particles. In particles which already have a growing polymer radical, termination occurs more or less rapidly depending on the particle size. After a short interval, another radical may enter the particle, and start a new chain. Thus, these single latex particles may at the end of the polymerisation contain a large number of polymer chains. It should be noted that termination between two growing polymer radicals, predominant in bulk, does not occur because the chains are isolated from one another in the heterogeneous solution. Finally, interval III is reached when all of the monomer in the monomer droplets is consumed and only the monomer in the still-swollen particles remains to be polymerised. 4.2 Polymerisation in Droplet and Bicontinuous Microemulsions Since 1980 microemulsions have been investigated in order to prepare latex particles within the nanosize range (< 50 nm), starting with o/w droplet phases. In this case, o/w microemulsions were prepared using a monomer, such as styrene or methyl methacrylate (MMA) as dispersed phase. Nucleation then takes place inside the droplets by diffusion of water soluble initiators into the droplet interior. The final droplet size is determined by the oil/surfactant ratio and the droplet exchange processes taking place. At too high monomer concentrations phase separation occurs during the polymerisation. Stable latex dispersions are generally obtained at surfactant/monomer ratios ranging from 1–5, which are quite high in comparison to emulsion polymerisation in which the surfactant/monomer ratio is usually smaller than 0.03. Additionally,

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Fig. 13. Schematic presentation of the different intervals taking place in emulsion polymerisation in the presence of (monomer swollen) micelles M in the continuous aqueous phase. The micelles are below 100 ˚ A while the monomer swollen polymer particles PP reach sizes of about 500 ˚ A (I and II) to about 1000 ˚ A (III). The monomer supply originates from the emulsified monomer droplets ED of about 10 μm.

w/o microemulsions can be employed to polymerise water-soluble monomers, such as acrylic acid and 2-hydroxyethylmethacrylate (HEMA). Generally the monomer was first dissolved in water and w/o microemulsions formed from the four components. Bicontinuous microemulsions were first studied to improve the interdroplet exchange rates and later to obtain interconnected polymer networks [75]. In templating the morphology of microemulsions, it has often been observed that the solid phase that nucleates in the microemulsion cavities (e.g., droplets or channels) finally grows out of these cavities. The solid structures thus formed are not commensurate in size, and even shape, with the template, especially in polymerising bicontinuous microemulsions. When the monomeric oil starts to polymerise, surfactant molecules may adsorb on the forming polymer, so causing the surfactant concentration in the remaining microemulsion to change. If the monomer continues to solidify while morphological changes or even phase inversion or separation processes occur, the final structure may even become homogeneous but will certainly differ in size and shape [76]. Bicontinuous microemulsions have only successfully been solidified, yielding porous polymeric films in the same size range, if the polymerisation reaction was sufficiently fast and the surfactant itself took part in the reaction. In this case the surfactant needs to possess the same polymerisable group as the monomer in its hydrophobic moiety. The first breakthrough in polymerising bicontinuous microemulsions was realised by Gan et al. [77, 78]. They obtained nanoporous polymeric materials by water-methylmethacrylate (MMA) microemulsions stabilised by a zwitterionic or a quaternary ammonium salt surfactant, possessing the same polymerisable group. Solidification took place only in a certain composition range (water and surfactant). The channel width

38

W.F.C. Sager

of the remaining water domains increased with decreasing surfactant or increasing water concentration. The resulting pore sizes could furthermore be decreased by the addition of a more water soluble monomer, which partly polymerised in the water phase and then precipitated onto the pore surfaces. In this way a continuous variation of the channel width from 4–60 nm could be obtained. A higher mechanical strength of the polymeric film was attained if a crosslinker was added. The polymerisation reaction was either initiated using UV light or a redox initiator at 50◦ C. Meanwhile, polymerisable nonionic surfactants and microemulsions could also be prepared which allow for copolymerisation with vinylbenzenesulfonate [79].

Fig. 14. TEM micrographs of a sample prepared of 30 wt% water, 32 wt% MMA, 38 wt% (((acryloyloxy)-undecyl)dimethylammino) acetate (AUDMAA), a polymerisable zwitterionic surfactant, and 2 wt% cross-linking agent (ethylene glycol dimethacrylate) during polymerisation. The reaction was photoinitiated at 35◦ C and samples were taken after 3–8 min and after 1 h. The polymeric phase is presented by the lighter contrast. Reproduced from [77]. Copyright (1995) American Chemical Society.

Figure 14 shows the network formation as a function of time in a sample prepared of 30 wt% water, 32 wt% MMA, 38 wt% (((acryloyloxy)undecyl)dimethylammino) acetate (AUDMAA), a polymerisable zwitterionic surfactant, and 2 wt% cross-linking agent (ethylene glycol dimethacrylate) [77]. Numerous nanoparticles can be seen from the TEM micrograph after 3 min of polymerisation, when the sample is still very fluid. A semigel formed

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39

after 6 min with polymer particles in the form of interconnected clusters with interdispersed pores and sizes smaller than 250 nm. The sample was totally gelled after 8 min. The obtained nanostructured network resembles that of the original bicontinuous microemulsion. The dimensions of the channels were in the range of 50–70 nm in width and 100–200 nm in length. The structure did not alter much even after polymerisation for 1 h when a transparent solid polymer was obtained as the final product.

5 Templating of Crystalline Phases The synthesis of inorganic mesoporous materials using ionic surfactant templates, first reported in 1992 [80, 81], led to the discovery of a novel family of molecular sieves called M41S (see Fig. 16) and opened up a new field of organised matter chemistry. The synthesis was performed by combining appropriate amounts of silica (and alumina) precursors, an alkyltrimethylammonium halide surfactant (e.g., cetyltrimethylammonium bromide, CTAB), a base and water. The inorganic phase is formed by hydrolysis of an alkoxide (e.g., tetramethylorthosilicate) that reacts with water followed by condensation. The mixture is then aged at elevated temperatures for 24–144 h, which results in a solid precipitate. The organic-inorganic mesostructured product is calcined A and a at about 500◦ C after washing. With well-defined pore sizes of 15–100˚ hexagonal symmetry, these first mesoporous (alumino)silicate materials break past the pore-size constraint (< 15 ˚ A) set by microporous zeolites. Surfactant– mediated synthesis has since been intensively investigated and employed to form a variety of mesoporous materials. The extremely high surface areas (> 1000 m2 g−1 ) and the precise tuning of pore sizes has made these materials highly attractive for applications in catalysis, membrane and separation technology, and molecular engineering. The M41S materials also ushered in a new approach in materials synthesis where, instead of the use of single molecules as templating agents, as in the synthesis of zeolites, self-assembled (molecular) surfactant aggregates or supramolecular assemblies are employed as the structure directing agents [82]. Recently, considerable attention has been focussed on tailoring the chemical composition of ordered mesoporous silicas for novel applications. The introduction of inorganic heteroatoms such as Al, Ti, or V into the silica framework, the synthesis of non-silica analogues (oxides of Al, Ti, V, W, Sb, Pb), and attachment of metallocene derivatives via pendant Si-O-H groups (to form Si-Θ metal linkages) have been explored as routes to the preparation of catalytically active, ordered mesophases. Furthermore, cocondensation of siloxane and organosiloxane precursors has been investigated to produce inorganic-organic networks. These organically functionalised, uniformly porous, ordered silica materials offer a high potential in applications in organometallic chemistry, catalysis and host-guest systems [83]. There is still some debate on the actual mechanism that leads to the formation of the mesoporous materials. In principle, two different paths are pos-

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sible, which are depicted in Fig. 15, for preparation of mesoporous materials with hexagonally ordered pores. In the original preparation route from 1992, the synthesis was performed at very low surfactant concentrations of about 1 wt%. This concentration is above the cmc but much too low to allow the formation of liquid crystalline arrays such as the hexagonal phase H1 that is built up of hexagonally ordered rodlike micelles. In this case, cooperative processes must be at work which require specific interactions between the soluble silicate species and the surfactant head group. The processes involved include specific binding of the silica precursor to the interfacial surfactant film, polymerisation of the silica at the interface and a kind of interfacial charge density matching that leads to the mechanism sketched in Fig. 15, depicting an ordering of the co-adapted micelles into a hexagonal array. Pattern replication then proceeds by further condensation and polymerisation of silica within the interstitial spaces of the coassembled template. Post synthesis removal of the organic phase affords an ordered mesoporous inorganic material with channel dimensions commensurate with the width of the rodlike surfactant micelles (for more insight into the mechanisms, see also [84]). Besides preparation via cooperative assembling, mesoporous silica has also been prepared by direct templating of a liquid crystalline phase, leading to a monolithic solid material that spans the whole sample.

Fig. 15. Two principally different paths to prepare mesoporous silica (MCM-41). The cooperative approach has been performed by adding a silica precursor to a surfactant solution at low surfactant concentration. Specific interactions between the silicate precursors and the surfactant molecules are necessary to obtain coassembly into a hexagonal array. The monolithic approach has been performed at high surfactant concentrations and employs direct templating of a hexagonal liquid crystal. Reprinted with permission from [82].

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Fig. 16. Mesoporous M41S silica obtained by direct templating of an H1 phase of C12 E8 (left) and of the Lα -phase of C16 E8 (middle) [85] together with schematic illustrations of the mesoporpous M41S materials of hexagonal (MCM-41, space group: p6m), cubic (MCM-48, space group: Ia¯ 3d) and lamellar (MCM-50, space group p2) structure [82]. Silica is presented by the lighter contrast. Left and middle: reproduced from [85]. Right: reproduced from [82].

Figure 16 shows mesostructured materials that have been synthesised by direct templating of the corresponding liquid crystalline phases (monolithic approach) [85]. The mesoporous silica with hexagonal symmetry was obtained from the H1 phase of C12 E8 . The silica was prepared by adding tetramethylorthosilicate (TMOS) in quantities of 0.25 mole equivalent with respect to water to an H1 phase of C12 E5 with a surfactant/water ratio of 50 wt% at pH = 2. Methanol released from the hydrolysis of TMOS was removed under mild vacuum, since it destroys the H1 phase, before the sample was left at room temperature for 18 h to allow the monolith to form. The TEM-micrograph on the left in Fig. 16 shows a hexagonal array of regularly sized holes of 28 ˚ A diameter separated by ∼ 12 ˚ A-thick silica walls. X-ray diffraction shows that the value for the lattice parameter decreased only slightly upon solidifying the H1 -phase. The monolithic approach could also be applied in templating cubic and lamellar liquid crystals. The central portion of Fig. 16 shows mesoporous silica with a lamellar structure obtained from the Lα -phase of C16 E8 . When the same nonionic surfactants used in the monolithic approach were employed in the cooperative approach at much lower concentrations, no mesostructured precipitate was formed, indicating that direct templating was responsible for the formation of the monolith rather than specific interactions. Acknowledgement. This chapter is part of the Lecture notes of the 33rd Spring School of the Institute of Solid State Research (IFF) on “Soft Matter: Complex Materials on Mesoscopic Scales” (Foschungszentrum J¨ ulich, 2002, ISBN 3-89336297-5. The author would like to thank S. Uhorczuk for her assistance with figure drawings.

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References 1. Fendler J. H. (1987) Chem. Rev. 87:877 2. Ozin G. A. (1992) Adv. Mater. 4:612 3. Mann S., Burkett S. L., Davis S. A., Fowler C. E., Mendelson N. H., Sims S. D., Walsh D., Whilton N. T. (1997) Chem. Mat. 9:2300 4. Capek I. (2004) Adv. Colloid Interface Sci. 110:49 5. Pileni M. P. (2003) Nat. Mat. 2:145 6. Davis H. T., Bodet J. F., Scriven L. E., Miller W. G. (1987). In: Meunier J., Langevin D., Boccara N. (eds) Physics of Amphiphilic Layers. Springer-Verlag, Berlin, p. p. 310-327 7. Sager W. F. C. (1998) Curr. Opin. Colloid Interface Sci 3:276 8. Pileni M. P. (1993) J. Phys. Chem. 97:6961 9. Ying J. Y., Mehnert C. P., Wong M. S. (1999) Angew. Chem. Int. Ed. 38:56 10. Wong K. K. W., Mann S. (1998) Curr. Opin. Colloid Interface Sci. 3:63 11. Stein A., Melde B. J., Schroden R. C. (2000) Adv. Mater. 12:1403 12. Soten I., Ozin G. A. (1999) Curr. Opin. Colloid Interface Sci. 4:325 13. Hamley I. W. (2000) Introduction to Soft Matter: Polymers, Colloids, Amphiphiles and Liquid Crystals. Wiley, New York 14. Israelachvili J. (1992) Intermolecular & Surface Forces, 2nd Ed. Academic Press, London, p. p. 341-381 15. Evans D. F., Wennerstr¨ om H. (1999) The Colloidal Domain: Where Physics, Chemistry, Biology and Technology Meet, 2nd Ed. Wiley-VCH, New York 16. Gelbart W. M., Ben-Shaul A., Roux D. (1994) Micelles, Membranes, Microemulsions and Monolayers. Springer-Verlag, Berlin 17. Safran S. A. (1994) Statistical Thermodynamics of Surfaces, Interfaces and Membranes. Addison-Wesley, Reading, MA 18. Hyde S., Andersson S., Larsson K., Blum Z., Landh T., Lidin S., Ninham B. W. (1997) The Language of Shape-The Role of Curvature in Condensed Matter: Physics, Chemistry and Biology. Elsevier Science B. V., Amsterdam 19. Degiorgio V., Corti M. (1985) Physics of Amphiphiles: Micelles, Vesicles and Microemulsions. North-Holland, Amsterdam 20. Overbeek J. Th. G. (1986) K. Ned. Akad. Wet. Ser. B 89:61 21. Hunter R. J. (1993) Introduction to Modern Colloid Science. Oxford University Press, Oxford 22. Seddon J. M. (1996) Ber. Bunsen. Phys. Chem. 100:380 23. Hoar T. P., Schulman J. H. (1943) Nature 152:102 24. Bancroft W. D., Tucker C. W. (1927) J. Phys. Chem. 31:1681 25. Scriven L. E. (1976) Nature 263:123 26. Jahn W., Strey R. (1988) J. Phys. Chem. 92:2294 27. Helfrich W. (1973) Z. Naturforsch. C 28:693 28. Goetz R., Gompper G., Lipowsky R. (1999) Phys. Rev. Let. 82:221 29. Kellay H., Binks B. P., Hendrikx Y., Lee L. T., Meunier J. (1994) Adv. Colloid Interface Sci. 49:85 30. Van der Linden E., Bedeaux D., Borkovec M. (1989) Physica A 162:99 31. Mitchell D. J., Ninham B. W. (1989) Langmuir 4:1121 32. Winsor P. A. (1954) Solvent Properties of Amphiphilic Compounds. Butterworths, London 33. Strey R. (1994) Colloid Polym. Sci. 272:1005

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Strey R. (1996) Curr. Opin. Colloid Interface Sci. 1:402 De Gennes P. G., Taupin C. (1982) J. Phys. Chem. 86:2294 Blokhuis E. M., Sager W. F. C. (2001) J. Chem. Phys. 115:1073 Kahlweit M., Strey R., Busse G. (1990) J. Phys. Chem. 94:3881 Kahlweit M., Strey R., Firman P., Haase D., Jen J., Schom¨ acker R. (1988) Langmuir 4:499 Kahlweit M., Strey R., Schom¨ acker R., Haase D. (1989) Langmuir 5:305 Koper G. J. M., Sager W. F. C., Smeets J., Bedeaux D. (1995) J. Phys. Chem. 99:13291 Kahlweit M., Strey R., Haase D., Kunieda H., Schmeling T., Faulhaber B., Borkovec M., Eicke H. F., Busse G., Eggers F., Funck T., Richmann H., Magid L., S¨ oderman O., Stilbs P., Winkler J., Dittrich A., Jahn W. (1987) J. Colloid. Interface Sci. 118:436 Fletcher P. D. I., Holzwarth J. F. (1991) J. Phys. Chem. 95:2550 Borkovec M., Eicke H. F. (1988) Chem. Phys. Lett. 147:195 Blokhuis E. M., Sager W. F. C. (1999) J. Chem. Phys. 111:7062 Tlusty T., Safran S. A. (2000) J. Phys.-Condens. Mat. 12:A253 Baxter R. J. (1968) J. Chem. Phys. 49:2270 Svergun D. I., Konarev P. V., Volkov V. V., Koch M. H. J., Sager W. F. C., Smeets J., Blokhuis E. M. (2000) J. Chem. Phys. 113:1651 Stokes R. J., Evans D. F. (1997) Fundamentals of Interfacial Engineering. WileyVCH, New York Fletcher P. D. I., Howe A. M., Robinson B. H. (1987) J. Chem. Soc. Faraday Trans. I. 83:985 Jain T. K., Casin G., Badiali J. P., Pileni M. P. (1996) Langmuir 12:2408 Fletcher P. D. I., Horsup D. I. (1992) J. Chem. Soc. Faraday Trans. 88:855 Binks B. P., Fletcher P. D. I., Horsup D. I. (1991) Colloids Surfaces 61:291 Shinoda K. (1967) J. Colloid. Interface Sci. 24:4 Becher P. (ed) (1983) Encyclopedia of Emulsion Technology, Vol. 1, Basic Theory. Marcel Dekker, New York Hou M. J., Shah D. O. (1988). In: Attia Y. A., Moudgil B. M., Chander S. (eds) Interfacial Phenomena in Biology and Materials Processing. Elsevier, Amsterdam, p. p. 443-458 Pileni M. P. (1993) J. Phys. Chem. 97:6961 Boutonnet M., Kizling J., Stenius P. (1982) Colloids Surfaces 5:209 Cushing B. L., Kolesnichenko V. L., O’Connor J. (2004) Chem. Rev. 104:3893 Burda C., Chen X., Narayanan R., El-Sayed M. A. (2005) Chem. Rev. 105:1025 Uskokovic V., Drofenik M. (2005) Surf. Rev. Lett. 12:239 Walsh D., Mann S. (1995) Nature 377:320 M¨ oller M., Spatz J. P. (1997) Curr. Opinion Colloid Interface Sci. 2:177 Fendler J. H. (1997) Curr. Opinion Solid State Materials Sci. 2:365 Pileni M. P., Motte L., Billoudet F., Mahrt J., Willig F. (1997) Mater. Lett. 31:255 Natarajan U., Handique K., Mehra A., Bellare J. R., Khilar K. (1996) Langmiur 12:2670 Barnickel P., Wokaun A., Sager W., Eicke H. F. (1992) J. Colloid. Interface Sci. 148:80 Tanori J., Pileni M. P. (1997) Langmuir 13:639 Pileni M. P. (2001) Langmuir 17:7476

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69. Hopwood J. D., Mann S. (1997) Chem. Mat. 9:1819 70. Li M., Mann S. (2000) Langmuir 16:7088 71. Rees G. D., Evans-Gowing R., Hammond S. J., Robinson B. H. (1999) Langmuir 15:1993 72. Lovell P. A., El-Aasser M. S. (1997) Emulsion Polymerisation and Emulsion Polymers. John Wiley, Chichester 73. Gilbert R. G. (1995) Emulsion Polymerisation. Academic Press, London 74. Fitch R. M. (1997) Polymer Colloids: A Comprehensive Introduction. Academic Press, San Diego 75. Chow P. Y., Gan L. M. (2005) Adv. Polym. Sci. 175:257 76. Antonietti M., Hentze H. P. (1996) Colloid Polym. Sci. 274:696 77. Gan L. M., Li T. D., Chew C. H., Teo W. K., Gan L. H. (1995) Langmuir 11:3316 78. Gan L. M., Chieng T. H., Chew C. H., Ng S. C. (1994) Langmuir 10:4022 79. Liu J., Teo W. K., Chew C. H., Gan L. M. (2000) J. Appl. Polym. Sci. 77:2785 80. Kresge C. T., Leonowicz M. E., Roth W. J., Vartuli J. C., Beck J. S. (1992) Nature 359:710 81. Beck J. S., Vartuli J. C., Roth W. J., Leonowicz M. E., Kresge C. T. , Schmitt K. D., Chu C. T. W., Olson D. H., Sheppard E. W., McCullen S. B., Higgins J. B., Schlenker J. L. (1992) J. Am. Chem. Soc. 114:10834 82. Ying J. Y., Mehnert C. P., Wong M. S. (1999) Angew. Chem. Int. Ed. 38:56 83. Mann S., Burkett S. L., Davis S. A., Fowler C. E., Mendelson N. H., Sims S. D., Walsh D., Whilton N. T. (1997) Chem. Mat. 9:2300 84. Flodstrom K., Wennerst¨ om H., Teixeira C. V., Amenitsch H., Linden M., Alfredsson V. (2004) Langmuir 20: 10311 85. Attard G. S., Glyde J. C., G¨ oltner C. G. (1995) Nature 378:366

Nanofabrication of Block Copolymer Bulk and Thin Films Microdomain Structures as Templates Takeji Hashimoto1 and Kenji Fukunaga2 1

2

Advanced Science Research Center, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, Japan Polymer Laboratory, Ube Industries, Ltd., Ichihara, Chiba 290-0045, Japan

1 Introduction and Background In this chapter we shall discuss applications of block copolymers (bcps) to nanotechnologies and nanosciences. Our objectives here are to explore the methods and principles concerning fabrications of ordered structures of bcps having various symmetries with nano-sized periodicity to create new materials with interesting structures and properties. We define this kind of fabrication as nano-fabrication. In other words we aim to control or manipulate selforganized microdomain structures of bcps, in both nonequilibrium and equilibrium states, and utilize them as templates for further nano-fabrication toward advanced devices and materials, such as tunable photonic crystals [1–4], quantum dots and nanowires [5–9], nanohybrids with inorganic materials and nanometal particles [10–12], photovoltaics and photoluminescence [13–16], etc. We shall present the bcp templates in both bulk (Sect. 2) and thin films (Sect. 3). 1.1 Bulk Before going into detailed discussion, it would be useful to review the basic physical factors which control the morphology of bcp microdomains as templates. Let us discuss the simplest bcp of A-b-B diblock copolymers (dibcps) in which one end of polymer A is covalently bonded with one end of polymer B. A-b-B dibcps in bulk are interesting two-component polymer systems. Without this covalent bond connecting A and B polymers, the two component system is a binary polymer mixture which can undergo a macrophase separation into two macrophases with a single interface at thermal equilibrium, as shown in part (a) of Fig. 1. Here important parameters are the short-range interactions between A-A, B-B, and A-B as also indicated in the legend of Fig. 1(a). On the other hand, with this covalent bond, the two component

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Takeji Hashimoto and Kenji Fukunaga

system becomes A-b-B dibcp which can undergo microphase separation and which can have multi-interfaces in bulk, as shown in Fig. 1(b). In this case, the bulk bcp is nothing other than an assembly of interfaces on which the chemical junctions between A and B exist. Here in addition to the short-range interactions, the long-range interactions play an important role as shown in the legend in Fig. 1(b). The long-range interactions arise from connectivity between two polymers A and B and their packing in the respective domains with a demand of incompressibility. Interplay of the short-range interactions and the long-range interactions is a key physical factor in bcp systems [17].

Fig. 1. Comparison of a self-assembled structure for a binary mixture of polymer A and B and that for a diblock copolymer A-b-B. Reprinted from [54]. Copyright (2005) The Chemical Society of Japan.

The long-range interactions involve conformational entropy of polymer chains (and hence elastic energy of polymer chains) as well as translational entropy of polymer chains (or junctions of A and B) along the interface. Thus the interplay of the short-range and long-range interactions is considered to be a competition between energetics and entropies. In the case when the short range van der Waals interactions between A and A and between B and B are stronger than those between A and B, A and B are subjected to net repulsive interactions, under which macro- and microphase separation can occur in the two component system. It is well known that various microdomain structures, including BCCSphere (sphere in body-centered-cubic lattice), Hex-cylinder (hexagonallypacked cylinders), a bicontinuous microdomain structure of the so-called double gyroid network structure with Ia¯3d space group symmetry, and alternating lamellae [18] can be tailored by changing the relative length of the two blocks as shown in Fig. 2. This is a tailoring based on chemistry. This is one of the consequences of the interplay of those two physical factors as described above.

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Fig. 2. Changes in the tailored microdomain morphology by increasing a chain length of A block chain relative to that of B block chain. Only the cases where A block chains are shorter than or equal to B block chains is shown.

We should note also the fact that bulk bcp usually have grains, as also shown in Fig. 2 for the lamella morphology for example, within which orientation of the ordered domain is consistent. The control of the grain size further requires a control of the ordering process of bcp, i.e., a tailoring based on physics. 1.2 Thin Films Let us now consider the case of thin bcp films. In this case, in addition to (i) the short range interactions of their own in bulk, there are (ii) short-range interactions of A and B with air and substrate surfaces as indicated in Fig. 3. The two kinds of the short-range interactions (i) and (ii) further interplay with each other. The long range interactions of their own in bulk interplay also with those arising from the confined space of the bcp in between the air surface and the substrate surface. The two kinds of the long-range interactions further interplay with each other. The interplay in the bcp thin film is therefore much richer than that in bulk, simply because there are competitions or interplays within and between each of these interactions. This enrichment further enriches manipulations of ordered microdomain structures as templates. We know that lamella-forming bcp thin films have parallel lamellae, in the case when their substrates and/or air surfaces have different interfacial ten-

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sions against A and B, as shown schematically in Fig. 3(a). If the substrate and air surfaces are neutral against A and B, the thin films have perpendicular lamellar orientation [19], as shown also in Fig. 3(b). The perpendicular lamellar systems may be more interesting than the parallel ones for use of them as a template for further fabrication.

Fig. 3. Parallel (a) and perpendicular orientation (b) of bcp microdomains in thin bcp films as a consequence of short-range interactions of block chains A and B with surface and substrate surface and of long-range interactions of block chains A and B in a confined space inherent in the thin film thickness. γAir (K) and γsubstrate (K) denote interfacial tension between air and block chain K (K = A or B) and that between substrate and block chain K, respectively.

In this chapter we shall deal with microdomain structures developed in both bulk films (Sect. 2) and thin films (Sect. 3). In the case of the thin films we shall focus on kinetic pathway along which the orientation and microdomain structure in thin films change towards equilibrium. The clarification of the pathway is crucial for the manipulation of the template structures in thin films for nanofabrication. In the case of bulk films, one of the microdomains in bulk bcps can be transformed into empty space (Sect. 2.1). When the microdomains are co-continuous in 3d space, such a fabrication as described above creates continuous phase of empty space. We shall also discuss a controlled alignment of metal nanopraticles into microdomain structures as templates in Sect. 2.2.

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2 Bulk Block Copolymers 2.1 Nanofabrication of Microdomains via Selective Chemical Degradation by Ozonolysis: Double Gyroid Networks Background We shall discuss here a nano-fabrication, which involves transformation of one of the microdomains A or B in A-b-B dibcp into vacant space by using a selective chemical degradation. Such fabrication may be applied to hexagonal cylinders, double gyroid network structure with Ia¯3d space group symmetry, and alternating lamellae of polystyrene-block -polyisoprene (PS-b-PI) and poly(2-vinyl pyridine)-block -polyisoprene (P2VP-b-PI). Ozonolysis selectively degrades only polyisoprene microdomains but does not essentially affect PS or P2VP microdomains in these bcps. The degraded compounds can be leached out from the domains by soaking the film in ethanol, which transforms the PI microdomains into empty space. We shall discuss an application of such a nano-fabrication as discussed above to the double gyroid network structure, a periodic co-continuous microdomain structure, which is formed in a very narrow composition range between those of cylinders and the lamellae (ca.33-36 vol % of network forming component in the case of PS-b-PI, [20, 21]). We can selectively degrade one of the “microphases” of double gyroid network structure. When the network phase is degraded and transformed into empty space, a set of two vacant network channels designated as “voided double-gyroid channel” is formed in the solid matrix of the major component (eg., PS or P2VP). On the other hand, when the matrix is selectively degraded, the free standing (doublegyroid-network) texture of PS or P2VP in vacancy is formed. The free standing texture may be stabilized by the existence of a grain boundary structure, which may be easily visualized in a simpler case of the free standing lamellae. Fig. 4 shows a grain boundary structure called Scherk’s first surface (part a) [22–24], which is made in the boundary of two orthogonal sets of lamellae (part b). The dark and bright lamellae in one grain are interconnected respectively to the dark and bright lamellae in another grain through the grain-boundary interface as shown in part (a). Even when one kind of the lamellar microdomains is transformed into empty space, the rest of lamellar system remains intact through this grain boundary structure. Degradation of Network Domains: Voided Double-Gyroid Channel A double gyroid network structure was prepared by casting a mixture of PSb-PI block copolymer and PS homopolymer (designated as SI in this section) with an overall volume fraction of PI component of 0.34 from toluene solution having total polymer concentration of ca. 5 wt% into petri dishes or by casting a mixture of P2VP-b-PI and PI homopolymer (designated as VI in

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Fig. 4. Scherk’s first surface (a) formed in the grain boundary between two orthogonal sets of lamellae (b). l1 and l2 designate unit vectors along the directions normal to the lamellar interface.

this section) with an overall volume fraction of PI of 0.4 from chloroform solution having total polymer concentration of ca. 5 wt%. The details of the bcps and homopolymers used can be found elsewhere [25, 26]. It is important to note that the molecular weight of the PS or PI homopolymer is so small compared with the molecular weight of the corresponding block that the homopolymer is always solubilized into the corresponding domain of the bcp. Film specimens of about 100-300μm thick were prepared by slowly evaporating the solvent over a week. The films thus obtained were further dried until a constant weight was attained. The obtained VI films were further treated with 1,4-diiodobutane (DIB) in order to crosslink the matrix phase of P2VP according to the method as detailed elsewhere [27, 28]. Fig. 5 represents a transmission electron microscopic (TEM) image for an ultrathin section of SI stained with OsO4 (part a) and that of VI crosslinked and stained with DIB (part b). In part (a) the PI microdomains (the gyroid networks) stained with OsO4 appear dark and gray, while the PS matrix unstained with OsO4 appears bright. On the other hand, in part (b) the PI microdomains (the gyroid networks) unstained with DIB appear bright and gray, while the P2VP matrix stained with DIB appears dark: consequently the contrast of the two images is reversed. Nevertheless the two images show a common characteristic of a periodic arrangement of a “double wave pattern” comprising a set of a small amplitude wave and a large amplitude wave. In part (a), the bright double wave pattern exists in the gray background, while in part (b), the dark double wave pattern exists in the gray background, as highlighted by the insets. The double wave appears to reflect the PS matrix in

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part (a) and the P2VP matrix in part (b), while the gray background appears to reflect the PI microdomains in both cases.

Fig. 5. TEM images for SI stained with OsO4 (part a) and for VI stained with diiodobutane (part b), both showing the periodic double wave pattern. From [26].

One can further observe a series of dark circles in part (a) or bright circles in part (b) along the double wave pattern. These circles are expected to be the PI microdomains oriented more or less normal to the ultrathin section. We shall discuss the morphological interpretations of this double wave pattern later in this section in conjunction with Fig. 7. It should be noted that the image in part (a) is somewhat distorted, probably due to deformation of the microdomain structure in the ultrathin-sectioning process. However the distortion is less noticeable in the image in part b, probably because hardening of the P2VP matrix by the DIB crosslinking suppressed the distortion. The same film specimens used for TEM were subjected to ozonolysis for 24 h at room temperature, followed by rinsing with methanol [25,26]. The treated specimens were then freeze-fractured in a liquid nitrogen bath, sputter-coated with platinum, and observed under a scanning electron microscope with a field-emission gun (FE-SEM). Fig. 6 presents a typical FE-SEM image for the SI sample. The image uniformly shows the ordered structure comprising the double wave pattern with the dark circles along the waves. In the SEM image, the bright region indicates undegraded PS matrix, while the dark and gray regions are the degraded vacant microphase corresponding to the PI microdomains before the ozone degradation. The dark circles indicate the vacant channel oriented nearly perpendicular to the surface of the freezefractured specimens. Similar FE-SEM patterns were also observed for the

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freeze-fractured surface of degraded VI specimens [26]. This SEM image is quite similar to the particular TEM images shown in Fig. 5 observed for the specimens before the degradation.

Fig. 6. FE-SEM image of freeze-fractured surface of ozone-degraded SI block copolymer having voided double-gyroid channel in the matrix of PS. The image exhibits facets between the two cleavage surfaces parallel to (211) plane with a step height difference. From [26].

Fig. 7 shows 3d computer graphics (CG) of one repeat unit of the double gyroid network structure with Ia¯3d space group symmetry. In part (a), only the double network phase shown in Fig. 2 is made empty in the solid matrix [25]. Therefore Fig. 7 (a) presents a CG for the voided double-gyroidchannel in the solid matrix, while Fig. 7(b) shows the 3d cross sectional view on a particular plane cut parallel to the (211) plane of the double gyroid network structure. The CG of 3d cross sectional image (part b) shows a double wave pattern with holes along the waves. Here the bright and gray regions certainly correspond to the matrix phase and the voided double-gyroid-channel, respectively. The CG pattern is exactly identical to that shown in the FE-SEM image in Fig. 6; This pattern should also explain the TEM images shown in Fig. 5(a) and (b), revealing that the TEM images reflect those obtained on ultrathin sections which happened to be cut parallel to the (211) plane of the double gyroid network. These results obtained in Figs. 5 to 7 illuminate that the double gyroid network of PI microdomains is successfully transformed into the vacant nanochannel by the nano-fabrication technique described here.

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Fig. 7. Computer graphics of one repeat unit of the double gyroid network structure with Ia¯ 3d space group symmetry. (a) The double network phase made empty in the solid matrix phase, and (b) 3d CG image obtained in a cross section of the structure in part (a) cut parallel to (211) plane.

The TEM images showed various kinds of patterns other than the double wave pattern, depending on the cutting direction of the ultrathin section with respect to the double gyroid network lattice, for example, the “wagon wheel” pattern observed when an ultrathin section is cut parallel to the (111) plane. Contrary to the TEM images, the FE-SEM images observed on the freeze-fractured surface after the ozonolysis exclusively show the double wave pattern, except for the “hexagonal doughnut” pattern as will be shown later in Fig. 8. Why do we observe only these two special patterns? The detailed analyses of the double wave pattern and the hexagonal doughnut pattern elucidated that the patterns reflect cleavages plane parallel to (211) plane and (110) plane, respectively [26]. The cleavage planes correspond to the planes which have the minimum area fraction of the matrix phase, i.e., 0.51 and 0.56 for the cleavage planes parallel to (211) and (110), respectively. Since the cross sectional area of the former is smaller than that of the latter, the double-wave type cleavage pattern appears more often than the hexagonal-doughnut type cleavage pattern. The hexagonal doughnut pattern found for the cleavage plane parallel to (110) plane is shown in Fig. 8 where part (a) shows the CG of the 3d cross sectional image cut parallel to (110) plane and part (b) shows a typical FE-SEM image. It should be noted that the two patterns (a) and (b) have common characteristics along the lines a, b, c, and d drawn as insets. The image (b) shows a facet between the two (110) cleavage planes with a step height difference. Across the facet, characteristic features of the pattern along the lines a to c are shifted to the lines a to c . The existence of the two special regular patterns, double wave pattern and hexagonal doughnut pattern, and evidence

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Fig. 8. Cross-sectional image showing hexagonal doughnut pattern. (a) 3d CG of cross-section cut at the particular planes parallel to (110) plane of the double gyroid network structure and (b) an FE-SEM image on the freeze- fractured surface of the SI films subjected to ozonolysis.

of these particular patterns reflecting the patterns on the cleavage surfaces unequivocally indicate existence of the double gyroid network structure with Ia¯ 3d space group symmetry in the real system. The special patterns of the facets shown in Fig. 6 also reinforce the above assessment, as will be discussed in detail elsewhere [26]. Degradation of Matrix Domains: “Free-Standing” Double-Gyroid Texture Films having the double gyroid network structure comprising P2VP block chains in the matrix of PI block chains were prepared by solution casting of mixtures of P2VP-b-PI (number average molecular weight Mn = 6.7×104 and weight fraction of PI block wP I = 0.39) and homopolyisoprene (Mn = 4×103 ) which contain a total PI volume fraction of 0.66. The mixtures were dissolved into ∼ 5 wt% total polymer concentration with benzene. Thin films about 1 mm thick were prepared from the solution in a petri dish by slowly evaporating solvent over approximately a month. The as-cast films were further dried under vacuum for about a week until constant weight was attained. The films thus prepared were exposed to 1.4-diiodobutane (DIB) vapor at 80o C for 72 h for selective crosslinking of P2VP double-gyroid-network phase. The DIB crosslinked films were soaked in heptane and the ozone was bubbled in heptane for 48 h at room temperature. The cleaved compounds were leached out from the films by soaking them in ethanol at room temperature for 24 h. Detailed analysis of the efficiency of the DIB crosslinking and ozonolysis

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can be referred to elsewhere [27]. Morphology of the as-cast film untreated with DIB was investigated under TEM with ultrathin sections stained with OsO4 . The observed images such as the wagon wheel pattern and the double wave pattern image confirmed that the films are definitely composed of large grains (of order of 10μms) of the double gyroid network structure, though the images are not shown here.

Fig. 9. Frequently observed FE-SEM images on freeze-fractured surfaces of films obtained after the nanofabrication described in the text. Based on [27].

The films subjected to the DIB crosslinking and the ozonolysis were freezefractured, and the fractured surfaces sputter-coated with platinum were observed under FE-SEM. Fig. 9 (part a and b) shows frequently observed EFSEM images [27]. Fig. 10(a) and (b) represent the numerically constructed computer graphics of 3d images of the texture cross-sectioned with the plane parallel to (100) and (110) plane, respectively [27]. The images illuminate topographical features of the texture around the cross-sectional planes. The 3d CG-SEM images shown in Fig. 10 and the FE-SEM images shown in Fig. 9 are quite similar, elucidating that the free-standing double gyroid texture is successfully obtained. With improved image quality the FE-SEM image would allow us to characterize topological features of the texture more precisely, which merits future studies. 2.2 Nanohybrids of Metal Nanoparticles and Polymers In this section we shall present various ways of creating hybrids of metal nanoparticles and polymers (hybrid #1 to #5). Hybrid Formation by Mixing BCP and Pd-BCP (Hybrid #1) Let us consider a self-assembly of mixtures of a small amount of Pd-(P2VPb-PI)’s, which are Pd nanoparticles coordinated and stabilized by P2VP-b-PI

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Fig. 10. 3d computer graphics of the free-standing double-gyroid texture crosssectioned with a plane parallel to (100) (a) and (110) plane (b). From [27].

bcps, and a large amount of P2VP-b-PI bcps (designated hereafter Tp-P2VPb-PI), which are free from Pd nanoparticles but which are a major component forming a microdomain as a template for an incorporation of Pd-(P2VPb-PI)’s. The amount of Pd-(P2VP-b-PI) has to be small in order to avoid macrophase separation between Pd-(P2VP-b-PI) and Tp-(P2VP-b-PI). It is important to note that the mixture involves generally the macrophase separation as well as the microphase separation [29]. We like to induce only the microphase separation so that one of the microdomains selectively incorporates Pd nanoparticles as a consequence of Pd-(P2VP-b-PI)’s being solubilized in the template microdomain formed by Tp-(P2VP-b-PI). We are concerned with a spatial distribution of Pd nanoparticles in the template microdomains. The template bcps Tp-(P2VP-b-PI) used in this section form by themselves alternating lamellae of P2VP block chains and PI block chains. The spatial distribution of Pd nanoparticles is intimately related to configurations of P2VP-b-PI incorporating Pd nanoparticles, i.e. Pd-(P2VP-b-PI). Pd nanoparticles obviously like P2VP more than PI as will be elucidated below. If Pd particles are heavily adsorbed by many P2VP block chains as illustrated in part a of Fig. 11, so that P2VP block chains are coating the particles and PI block chains emanate from the particles as brushes, then the Pd nanoparticles should be incorporated into PI lamellae rather than P2VP lamellae. In our experience this is not the case, at least for this system. Part (b) of Fig. 11 represents the case where the Pd nanoparticles adsorb only a small number of the bcp chains, e.g., only one chain here. The P2VP block segments are extensively adsorbed to the Pd nanoparticles so that the subchains of P2VP free from the particles are short and hence a PI block chain has a configuration such that one end of the PI chain is fixed to the Pd nanoparticle but the rest of it is free from the particle, because P2VP and PI chains repel each other. If this were the case, the particles would always

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align preferentially near the interface of P2VP lamellar nanodomains, simply because the PI block chains of Pd-(P2VP-b-PI) favors the PI lamellae and Pd coated by P2VP block chains may favor the P2VP lamellae. This is not the case found in our experiments either. If the Pd nanoparticles adsorb (i) only a small number of P2VP chains, (ii) only a small fraction of segments per single P2VP chains as shown in part (c), and (iii) furthermore uniformly any parts of the P2VP chains, at the free end, middle, and near the junction point as shown in part (d), then we anticipate that the Pd particles are arranged more or less uniformly in the P2VP domains.

Fig. 11. Possible configuration of P2VP-b-PI block copolymer chains adsorbed to Pd nanoparicles. Based on [30]. Copyright (2004) Materials Research Society of Japan.

Fig. 12 shows a typical TEM image of solution-cast film specimens of a mixture of Pd-(P2VP-b-PI) and Tp-(P2VP-b-PI), both having the same lamella-forming P2VP-b-PI. In the TEM image obtained on the unstained ultrathin sections (part (a)), the dark and bright lamellae are P2VP and PI lamellae, respectively, and the dark dots are Pd nanoparticles as sketched in part (b). Interestingly enough we found that Pd nanoparticles are more or less uniformly distributed across the lamella interface. This piece of evidence should infer that the models (c) and (d) in Fig. 11 are plausible models for configurations of P2VP block chain incorporating Pd particles. The model is also consistent with the AFM studies of visualization of isolated single Pd(P2VP-b-PI), as will be described below. Fig. 13 shows an AFM image and corresponding sketches for Pd-(P2VP-bPI), representing two chains with contour length of 380 and 400 nm adsorbed to a single Pd particle [31]. The bright object has a height of 6.1 nm and diameter of 21 nm. The height is very close to the average diameter (7 nm) of the Pd nanoparticles as observed under TEM [31, 32], suggesting that the object is a single Pd particle. The width is much larger than 6.1 nm, which is

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Fig. 12. Nanohybrids prepared through the self-assembly of a Pd-(P2VP-b-PI) / Tp-(P2VP-b-PI) mixture.

well-known to be due to a smearing effect induced by the finite size of the AFM probe tip. The string like object observed around the particle is believed to be the adsorbed block chain(s). The height analysis of the string shows a height value of 0.2 nm, consistent with the single block chain. The counter length of 500 nm measured for the block chain adsorbed to the particles is consistent with that of 799 nm calculated from the molecular weight of P2VP-b-PI.

Fig. 13. Tapping-mode AFM image for Pd-(P2VP-b-PI) (left) and its sketch (right). The two bcp chains are adsorbed by the Pd particle. Reprinted from [31]. Copyright (2003) American Chemical Society.

Here it is worth noting that the mixture of Pd-P2VP (the Pd nanoparticles coordinated by P2VP homopolymer) and Tp-(P2VP-b-PI) was found to give selective incorporation of Pd nanoparticles in the middle of the P2VP lamellar

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microdomains formed by Tp- (P2VP-b-PI). Those requiring further details are referred to [32]. In order to control physically (i.e., to tailor) the location of the particles across the interface, we can use the physics of bcp mixtures. Part (a) in Fig. 14 exaggerates the chain conformation of a small amount of larger-molecularweight bcp mixed in the matrix of a large amount of smaller-molecular-weight bcps, while part (b) exaggerates the chain conformation of a small amount of smaller-molecular-weight bcps mixed in the matrix of a large amount of largermolecular-weight bcps. In both cases, we assume that chemical junctions of the short and long block chains share the common interfaces and the block chains are microphase-separated in their respective domains, hence the short and long bcps satisfying the so-called cosurfactant criterion [17, 29, 33–37]. If a part of the minority chains shown by the thick lines are coordinating Pd nanoparticles with equal probability along the chains as shown in Fig. 11(d), then the Pd particles will be localized preferentially in the middle or near the interface in the case (a) and (b) in Fig. 14, respectively.

Fig. 14. Lamellar microdomain structures formed by mixtures of short and long symmetric bcps. The long and short bcps are minority components in parts (a) and (b), respectively. Reprinted from [30]. Copyright (2004) Materials Research Society of Japan.

Fig. 15 shows a histogram P (z) for the location of Pd nanoparticles across the interface for the three systems as indicated in the figure, where z indicates the location of Pd nanoparticles (defined by d) across the interface in the P2VP lamellae normalized by thicknesses of the P2VP lamellae (dP 2V P ), z ≡ d/dP 2V P . In the case when the P2VP blocks in Pd-(P2VP-b-PI) have a molecular weight much smaller than the matrix-forming P2VP blocks in Tp-(P2VP-b-PI), the Pd nanoparticles were found to be localized near the interface (part a). If the two P2VP blocks have the same molecular weights, the Pd nanoparticles were found to be more or less uniformly distributed

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(part b). More rigorous analyses with element spectroscopic imaging tend to show a weak bimodal distribution of Pd particles with small peaks at 0.15 and 0.85 [38]. If the P2VP blocks in Pd-(P2VP-b-PI) have a molecular weight much larger than the P2VP blocks in Tp-(P2VP-b-PI), the Pd nanoparticles were found to be localized in the middle of the P2VP lamellae (part c). Thus the models (c) and (d) in Fig. 11 are supported by these independent experiments. Moreover, the results shown in Fig. 15 are consistent with the AFM result shown in Fig. 13. Further details can be found in [39].

Fig. 15. Histograms showing position of Pd nanoparticles in P2VP lamellae in the solution-cast mixtures of Pd-(P2VP-b-PI) and Tp-(P2VP-b-PI). Pd-Xk-b-Yk / Zk-b-Wk in the figure legend designates weight-average molecular weights of P2VP and PI block chains in Pd-(P2VP-b-PI) being X and Y in units of thousands, respectively, and those of the P2VP and PI block chains in Tp-(P2VP-b-PI) being Z and W in units of thousands, respectively. Relative lengths of P2VP blocks coordinating Pd particles and those acting as microdomain templates are shown, respectively, by the relative length of the lines with and without the dark dot in the top section of the figure, respectively. The dark dots on the lines are designated Pd nanoparticles coordinated by the P2VP block chains. Reprinted from [30]. Copyright (2004) Materials Research Society of Japan.

In-situ Formation of Metal Nanoparticles in BCP Microdomains as Templates In this section we shall discuss hybrid formation via reduction of Pd ions, Pd(II), into Pd atoms, Pd(0), in the presence of bcp microdomains as templates. The reduction involves a selective incorporation of Pd nanoparticles in one of the domains (hybrids #2, #3 and #5 below) or on the interface between the two domains (hybrids #4 below).

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Self-assembly of Microdomain Templates and Pd Nanoparticles from bcp Solutions (Hybrid #2). We shall consider here a way to create nanohybrids by a single-step process as schematically illustrated in Fig. 16. In this case, P2VP-b-PI bcp (M n = 3.1 × 104 , volume fraction of P2VP block chain, φP 2V P = 0.4, Mw /Mn = 1.04 with Mw being weight average molecular weight) and palladium acetylacetonate, Pd(acac)2 , were dissolved into a dilute solution of benzyl alcohol and chloroform as a mixed solvent as shown in part (a). The solution is homogeneous and the bcps are in the disordered state. Chloroform was first evaporated at room temperature to obtain a concentrated solution of the bcp in benzyl alcohol in which the lamellar microdomain structures swollen with benzyl alcohol were already self-organized but the Pd ions were not yet reduced and uniformly distributed in both PI and P2VP lamellae as shown in part (b). Although Pd(II) appear as if they are localized in one of the lamellae in the figure, this is actually not true. They are confirmed equally partitioned in both P2VP and PI lamellae swollen with benzyl alcohol by means of small-angle X-ray scattering (SAXS) studies [40]. This is probably because Pd(II)’s are solvated, interacting more strongly with the solvent than the P2VP and PI blocks.

Fig. 16. A single step hybridization process of metal nanoparticles in bcp templates (hybrid #2). Based on [30]. Copyright (2004) Materials Research Society of Japan.

Then the temperature of the system was raised to 140˚C where Pd (II)’s were reduced into Pd(0)’s, the Pd(0)’s were aggregated into nanoparticles, and benzyl alcohol was simultaneously evaporated. In this way films in which Pd nanoparticles were selectively incorporated in P2VP nanodomain structures were obtained, because of specific interactions of Pd nanoparticles with P2VP. Fig. 17 shows a typical TEM image of the microphase-separated structure

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observed for an unstained ultrathin section of obtained films (part a) and its corresponding model (part b) confirmed by the TEM image obtained with the ultrathin sections stained with osmium tetraoxide [40], though the image is not shown here. The dark dots in part (a) are Pd nanoparticles. They are aligned in a row with a spacing of about 40 nm perpendicular to the row. The image obtained with the OsO4 stained specimen indicated dark lamellae composed of selectively stained PI phase and bright lamellae composed of unstained P2VP phase. The TEM image shows that Pd nanoparticles were selectively localized in the middle part of bright P2VP lamellae [40], as schematically shown in the inset at upper left corner of Fig. 17(b). The inset enlarges the part of the domain enclosed by the square in Fig. 17(b).

Fig. 17. Microphase-separated structure containing Pd clusters obtained by the single-step hybridization process as schematically shown in Fig. 16. Based on [30]. Copyright (2004) Materials Research Society of Japan.

In this way, we can create hybrids of metal nanoparticles and bcp template where nanoparticles are aligned selectively in a row in one of the lamellae with a controlled spacing between the rows. The metal nanoparticles are driven towards the middle of the nanodomain due to the (rubber-like) elastic force of the P2VP chains emanating from the lamellar interface. We can create denser nanoparticles with increasing concentration of Pd(II)’s [40]. Incorporation of Pd Nanoparticles in Free-Standing Double-Gyroid Texture (Hybrid #3). Earlier in Sect. 2.1 we presented the nanofabrication method for preparation of the free-standing double-gyroid texture made out of crosslinked P2VP chains. We can incorporate Pd nanoparticles into this texture which can be regarded as a porous template having pore volume of 67%. The porous membrane containing Pd nanoparticles may be useful for applications such as membrane reactors [43–46]. The double-gyroid texture prepared as described previously (p. 54) was soaked in a warm bath (85◦ C) made from a 50ml mixture of

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1-proponal and toluene (25:75). This mixed solvent contained 0.3 grams of Pd(acac)2 which has been shown to be reduced to Pd atoms by 1-propanol [32]. The amount of Pd(acac)2 added to the solvents was intended to give an initial ion concentration in excess of the total number of pyridine units in the system which are thought to have attractive interactions with Pd atoms and particles. It is expected that this reduction process will occur not only within the P2VP texture but also within the bulk solution itself. The immersion time was controlled and varied from 1 h to 4 days as part of the experimental strategy. Additionally the toluene was replaced with other solvents; benzene,14 dioxane, and acetone in order to investigate effects of the solvent used upon Pd nanoparticle growth. The microdomain structures of the samples prepared in this way were then examined by TEM. Ultrathin sections for TEM were obtained using a cryoultramicrotome. The size distribution of the Pd nanoparticles observed in the resulting micrographs was then analyzed by use of standard imaging software. This approach was endorsed by independent manual measurements on selected micrographs. Typically 300-400 particles were counted and measured within a 0.16μm2 area of the micrograph. Since the sampled area of the micrographs was constant, the number of particles found represents the particle number density, N. Fig. 18 (a) to (c) show representative TEM of the sample after reduction in a 1-propanol/toluene/Pd(acac)2 bath for a range of times [28]. The Pd particles, approximately spherical in shape, are visibly growing in size with the reduction time. Moreover in the final stages of the time scale shown in Fig. 18(c) the particle number density, N, is decreasing. It also seems that the Pd particles are to be found in the P2VP phase (stained dark by DIB) and not in the void areas. The fact that this is not immediately apparent is a testament to the three dimensional nature of the double gyroid texture. Pd particles that may seem (from the micrographs) to be within the void phase (bright phase) of the micrographs are more likely to be found at a lower or upper overlapping domain of the P2VP gyroid network in the ultrathin section used for the TEM observation. However it is unequivocally proved that the particles reside only in the P2VP microdomain by conducting similar experiments within a lamellar microdomain morphology. Fig. 18(d) shows just such a micrograph, where the processing described above has been applied to the pure PI-b-P2VP polymer forming a lamellar morphology and this degraded structure together with the double gyroid network texture, has been immersed in the same Pd(acac)2 bath for 48 h in order to ensure the two structures were being subjected to the same reduction condition. It should be noted that the P2VP lamellae (stained dark by DIB) and the degraded PI lamellae (existing as a void space and hence appearing bright) are oriented with their interfaces parallel to the electron beam within the ultrathin sections prepared for the TEM observation so that two sets of lamellae are not overlapping. TEM images of the double-gyroid texture samples, subjected to the reducing reaction in the Pd(acac)2 bath, were collected in order to obtain a

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Fig. 18. TEM images of Pd-nanoparticle loaded in the free-standing gyroid texture in air matrix after reduction in 1-propanol/toluene/Pd(acac)2 for different times at 85◦ C. (a) 13 h; (b) 24 h; (c) 48 h. The bright regions refer to the degraded PI domain (void space). The dark regions refer to the DIB stained P2VP phase. The darkest spots are the Pd nanoparticles. Part (d) represents TEM image of Pd-nanoparticle loaded into the free-standing P2VP lamellar microdomains in air. Pd nanoparticles are demonstrated to exist only in the dark P2VP lamellae. Reproduced from [28]. Copyright (2006) American Chemical Society.

quantitative measure of the nature of the particle growth mechanism. Particle analysis software allowed us to determine the population and size distribution as a function of time. Fitting the distributions with a normal Gaussian ¯ with time model, we can extract the growth of the mean particle diameter, D ¯ which goes as t1/6 (Fig. 19) [28]. There is a clear power low dependence for D (part a). At the same time we see that the number density, N , of particles appears to first rise quickly as a function of time before decaying at a slower rate (part b). It is worthwhile considering the various possible processes that

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are at work during immersion of the polymer within the reducing bath. Both inside and outside of the swollen double-gyroid texture, Pd(II)’s are being reduced to Pd atoms, and these atoms are subsequently aggregating into larger particles.

¯ vs time for the Pd reduction in 1Fig. 19. Experimental D propanol/toluene/Pd(acac)2 at 85◦ C extracted from particle analysis (filled circles). Also shown are the power law predictions from the diffusion and coalescence model (without hydrodynamic interactions); full line; and the LSW theory; dashed line. (b) The number of particles in a 0.16 μm2 area of the TEM micrograph as a function of time. Reproduced from [28]. Copyright (2006) American Chemical Society.

The number of these particles that make their way into the swollen P2VP polymer network will be a complex function of several parameters that depend on the relative interactions between the Pd(II), the Pd atom, the solvent, and the P2VP texture. The picture is slightly simpler if we consider only Pd(II)s that have diffused and adsorbed into the P2VP texture. This process is shown schematically in Fig. 20. The adsorbed ions will be reduced to Pd atoms in the presence of 1-propanol in the swollen cross-linked texture. These atoms quickly aggregate to small Pd particles (process 1). There may be an exchange of ions between the inside and the outside of the network (process 2). The number of Pd particles will increase with time as a consequence of the reduction and aggregation. These particles will then coalesce within the texture into larger particles (process 3a & 3b). As a consequence the particle number tends to decrease with time. However the precise nature of this latter stage is subject to speculation. There are two feasible dominant modes of particle growth. The first, often known as Ostwald ripening predicted by Lifschitz–Slyozov–Wagner (LSW) [47, 48], might occur by an evaporation/condensation mechanism of small Pd

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particles existing in the neighborhood of large Pd particles whereby Pd atoms from a smaller particle aggregate evaporate into the matrix, diffuse toward the large aggregate driven by the Gibbs–Thomson effect, and condense to the large particle (process 3a). The alternative model would be that of diffusion and coalescences of particles into a larger aggregate [49, 50](process 3b). ¯ as tn . Both models are characterized by a power law time dependence for D, The LSW model predicts n = 1/3. The diffusion and coalescence model has n = 1/6 and 1/3, respectively, in the absence and presence of hydrodynamic interactions [51]. These predictions are plotted in Fig. 19(a), and it is clear that the diffusion and coalescence model without hydrodynamic interactions has a very good agreement.

Fig. 20. A schematic of the various processes that will occur during the immersion of the gyroid network into the Pd reducing bath. The three processes highlighted are discussed in the text. Reproduced from [28]. Copyright (2006) American Chemical Society.

The coarsening process of metal particles via either of the two models mentioned were originally proposed to occur in hot melts of binary metal alloys, e.g., Oki et al. [52]. Whether or not such coarsening of Pd nanoparticles occurs in the swollen polymer network at low temperatures is not self-evident. We should note that the state of Pd atoms changes from gaseous state to liquid state and eventually to solid state. The coarsening process described above should occur when the particles are still in liquid state. The coarsening of particles via absorption of gaseous atoms would occur as long as their surfaces are still in the liquid state. There are other caveats to the use of coarsening models, since the exponents are based on theory where the total number of Pd atoms is conserved

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during the coarsening process. Since there is a bath of Pd(II) surrounding the texture and the atoms can constantly be fed into the system via diffusion and reduction of Pd(II), this will not necessarily be the case. We can argue that there is a given concentration of Pd(II) inside and outside of the P2VP texture immediately before the reduction of Pd(II) starts to occur. There may be an exchange or interdiffusion of ions between the inside and outside of the texture during the reduction, driven by osmotic pressure of ions, but the total ion concentration subject to reduction inside and outside of the texture will not be altered by the exchange of ions. The reductions of Pd(II) inside and outside the texture are effectively independent of each other, and the reduced atoms effectively stay in the same region, i.e., either within the texture or outside of it. In this way a quasi-conserved system might exist. Such a notion is corroborated by the behavior of N as a function of time. The initially fast increase in particle number density, N , could refer to the reduction of Pd(II) to atoms and the aggregation of atoms into particles as shown by process 1 in Fig. 20. The subsequent slower decay of N suggests that the large number of small Pd particles thus created grow into a smaller number of larger Pd particles via process 3a or process 3b. It is prudent at this stage to only show that we can control the size and distribution of Pd particles dynamically. Such control will be critical in the potential application of such materials. There are other factors that can influence the nature of Pd particle growth in the matrix, such as the degree of cross-linking achieved with DIB, and the nature of co-solvent that is used with 1-propanol. For further details the reader is referred to [28]. Incorporation of Metal Nanoparticles on the Surface of the Voided Double-Gyroid Channel (Hybrid #4). In Sect. 2.1 we described creation of the voided double-gyroid-channel in the matrix of PS blocks. We can introduce metal plating of the surface of the PS matrix by using commercial reagents for the non-electrolytic plating [25]. The metal plating should be essentially equivalent to the incorporation of metal particles on the surface of the channel. First the specimens with the vacant nanochannels were soaked in a “sensitizer” (an aqueous solution of SnCl2 ) so that the surface adsorbs Sn2+ . The sensitized films were then soaked in an “activator” (an aqueous solution of PdCl2 ) so that the surface adsorbs Pd0 through the reaction Sn2+ + Pd2+ → Sn4+ + Pd0 . Finally the activated films were soaked in a 1:4 mixture of “nickel A” (an aqueous solution of NiCl2 ) and “nickel B” (an aqueous solution of reductant) for the nickel plating. Pd0 was used as the catalyst for the reduction of Ni2+ . All the commercial reagents were diluted with water to avoid rapid clogging of the vacant nanochannel with the reduced nickel metal. Since the matrix phase of PS is not swollen with the aqueous medium, we expect that the reduced metal particles are preferentially localized in the interface between the voided nanochannel and the PS matrix.

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Fig. 21(a) shows a typical TEM image of the ultrathin section of the nickel plated nanochannel specimen obtained without staining. The nickel metal plated on the nanochannel surface gives a dark gray contrast in the TEM image. The PS matrix free from the metal plating appears bright and the vacant nanochannel with its surface plated with metal appears gray and dark. The bright PS matrix phase has the double wave pattern (with a series of dark circles along the waves as highlighted with a visual guide in Fig. 21(b)), though slightly distorted. The dark circles correspond to a part of the nanochannel oriented perpendicular to the thin section. The special pattern reflects the metal-plated nanochannel having the double gyroid network structure. The inset to Fig. 21(a) or (b) shows an enlarged image of the dark circles. The image highlights a deposition of metal particles on the channel surface, leaving an empty space in the center of the channels.

Fig. 21. (a) TEM image of nickel-plated voided double-gyroid nanochannel and (b) its visual guide for the double wave pattern. Based on [30].

Incorporation of Pd Nanoparticles in Thin BCP Films (Hybrid #5). In Sect. 3.3 later, we shall discuss control of lamellar microdomain orientation in spin-cast poly(styrene)-block -poly(methyl methacrylate) (PS-bPMMA) thin films. We found that the perpendicular or parallel lamellae can be obtained on substrates having reduced roughness parameter qs Rs larger or smaller than a critical value (qs Rs )c , respectively. Here qs and Rs are the characteristic wave number and root-mean squared amplitude of the surface roughness of the substrate, respectively. We can incorporate metal nanoparticles selectively into one of the lamellar nanodomains by reducing metal ions

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Fig. 22. Selective incorporation of Pd nanoparticles into thin films of PS-b-PMMA having perpendicular lamellae by sublimation of Pd(acac)2 complex at 200◦ C into the films and in-situ selective reduction in PS lamellae. Based on [54].

in the microdomain template. There are two methods of creating hybrids of metal nanoparticles in thin bcp films. The methods involve thermal reduction of metal ions into metal nanoparticles in the thin film templates. We designate here this type of hybrid as hybrid #5. One method involves spin-casting of PS-b-PMMA bcp solutions containing Pd(acac)2 into thin films on rough or smooth substrates and then heating of the thin films for reduction of Pd(acac)2 . The selective interactions of Pd(acac)2 to one of the domains in the as-spun films and/or the difference in the reduction rate in the two types of domain determine the selectivity in the incorporation of Pd nanoparticles into one of the domains. Another method involves spin-casting of thin films of PS-b-PMMA free from Pd(acac)2 and then sublimation of unreduced Pd(acac)2 complex into the spun-cast thin films where selective reduction occurs in-situ [53], as schematically shown in Fig. 22(a). Figs. 22 (b) and (c) show typical hybrids prepared on rough substrates of indium tin oxide, as observed by plan (through) view TEM and tapping mode AFM, respectively. The TEM image (b) indicates the perpendicular lamellae of PMMA (bright regions) and of PS (dark regions). The dark dots

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representing Pd nanoparticles are selectively localized into PS lamellae, presumably because the reduction rate is much faster in PS lamellae than in PMMA lamellae. Origin of the dark and bright contrast on the PS and PMMA lamellae is due to a selective abrasion of PMMA lamellae by electron beams. The AFM image in part (c) shows the surface structure on the same domain structure as observed in TEM. It is particularly interesting to note that the bright dots in AFM correspond to Pd nanoparticles which locate on the top surface of the thin films. The images (b) and (c) indicate that the particles exist on the surface of the thin films as well as in their interior. The hybrids are believed to have important applications as patterned media with a large magnetic memory density.

3 Thin Film Block Copolymer 3.1 Surface-Induced Alignment and Thickness Quantization As mentioned in Sect. 1, various very intriguing nano-structures have been found in bulk bcps. As well as in the bulk bcps, there is a growing interest in thin film bcps [55]. Thin films typically have a thickness less than about ten times of the microdomain spacing of the constituting bcp. In such thin films, as described in Sect. 1.2, the microphase-separated structures within the thin films are much more enriched than those in the bulk. The bcp component preferentially attractive to one surface develops the microdomains on this surface [56, 57]. In this section we shall consider lamella-forming bcps in bulk. In the case of a lamella-forming dibcp, the boundary surface gives rise to a lamella of the one component preferred by the surface. Thus the non-neutral surface generally generates a parallel lamellae structure (lamellar microdomains with their lamellar interfaces parallel to the substrate surface) throughout the entire film (called surface-induced alignment of microdomains) [58]. In this parallel lamellae structure, the film thickness should be restricted to some quantized values of the lamella spacing. When the substrate surface and the air surface prefer different components in the diblock copolymer (asymmetric boundary condition), the film thickness becomes a half-integer (n + 1/2) multiple of the lamella spacing d. When the initial film thickness is not commensurate with this quantization, lateral mass transport in the plane of the thin film is induced so that the local film thickness is adjusted to some quantized value (thickness quantization) and thereby the parallel lamellae are established in the entire film [59]. The substrate generally leads the parallel lamella formation, which is well known to be due to short range interactions. Recent studies, however, revealed some new aspects on the effects of the short-range interactions with the substrate: The short-range interactions of bcps with the substrates cause not only parallel lamella formation but also long range effects on microdomain

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formation in thin films. We shall highlight the long range effects of the substrate on the non-equilibrium microdomain formation process. A rich variety of the long-range effects arising from the substrate will be shown below. 3.2 Substrate Effect on Parallel Lamellae Formation For the lamella-forming bcp, the substrate surface is believed to determine which lamella constitutes the first layer on the substrate. However, there can be cases in which the morphology most preferred by the substrate surface is not the lamellar structure. An example was found on the substrate which has a very strong attractive interaction with one of the blocks in the lamella-forming bcp (case A). In this case, the conformations of the preferred block chains on the surface are considerably perturbed compared with those in the bulk, and thereby the substrate induces a perturbation of the lamella structure near the substrate [60]. Another example is the case of thin films of a lamella-forming triblock terpolymer on the substrate which is preferential to the middle block of the terpolymer (case B). In this case, the parallel lamella alignment is not expected near the substrate surface [61, 62]. In the above examples, the substrate induces a special structure which is never observed in bulk bcp. The problem was found to be most highlighted in the non-equilibrium process of bcp thin films. First, the non-equilibrium process will be presented in dibcp thin films on a substrate which has strong interactions to one block component (case A). Later the non-equilibrium process observed for the triblock terpolymer thin films on the substrate which preferentially adsorbs the middle block (case B) will be presented. Diblock Copolymer Thin Films on Substrate Which Strongly Adsorbs One Block Component As-Spun State Thin films of polyisoprene-block -poly(2-vinylpyridine) dibcps (PI-b-P2VP) (Mn = 67.9 × 103 , Mw /Mn = 1.31, volume fraction of PI φP I = 0.49, and bulk showing lamellar morphology with the lamella spacing D = 44 nm) were prepared by spin-cast from a solution in chloroform on hydrogen-terminated silicon (SiH) [60]. The initial film thickness z0 was about 25 nm, which is nearly equal to the half lamella thickness in the bulk. P2VP is preferentially adsorbed by the SiH substrate. On the other hand, PI has a lower surface free energy than P2VP and thereby tends to segregate toward the free surface. The thin film having half-lamella thickness is anticipated to form a monolayer of bcp brushes comprising PI-half-lamella on the free surface and P2VP-halflamella on the substrate surface, respectively, at thermal equilibrium.

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The as-spun film surface was explored with a Tapping Mode AFM [63]. The AFM height image (Fig. 23a) showed the objects slightly protruding (∼ 1 nm) from the surrounding area. They seem to form the close-packed hexagonal structure. In the AFM phase image of the same area (Fig. 23b), the protrusions appear as bright phase. Since the glassy (rubbery) phase appears bright (dark) in the phase image, the protrusion and the matrix are considered to be P2VP and PI microdomains, respectively. The glass transition temperature of P2VP is much higher than that of PI, and thereby the P2VP is vitrified earlier than the PI as the solvent evaporates during the spincast. After the vitrification of P2VP domains, the PI matrix further shrinks as the residual solvent evaporates, and hence it is depressed relative to the P2VP.

Fig. 23. AFM height (a) and phase images (b) of the as-spun PI-b-P2VP thin film of 25 nm thickness. The gray level of part a and b represents a height range of 8 nm and the phase shift range of 10 deg, respectively. Power spectral density of the phase image acquired in extended area (2μ × 2μ) is shown in the inset to part (b). The structure observed in the area indicated by the white circle in part a and b is schematically drawn in part c. In part c, the bright phase corresponds to P2VP domains protruded in part a and appearing harder in part b. Reproduced from [60]. Copyright (2006) American Chemical Society.

Formation of the laterally microphase-separated structure, rather than the parallel lamellae which are laterally uniform, may be a consequence of the strong interactions of P2VP block chains with the substrate. In order to clarify the influences of the substrate, it is very instructive to explore the structure

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of the first layer on top of the substrate surface. The strong adsorption of the thin films to the substrate makes it difficult to remove the thin films from the substrate for the preparation of TEM specimens. On the other hand, due to this strong adsorption, the PI-b-P2VP monomolecular layer film on the substrate, which should resemble the first layer structure developed in the half-lamella thickness films, can be obtained by simply soaking the PI-b-P2VP thin films on the SiH substrate as a whole in solvent [60]. The AFM height image of the obtained PI-b-P2VP monomolecular film is shown in Fig. 24a. This film surface shows small protrusions appearing bright, and the protrusions exhibit a short-range spatial order. The protrusions are considered to be condensed globules of PI bound to the monomolecular layer of P2VP preferentially adsorbed to the substrate surface. Part (b) shows the binarized AFM height image in order to highlight the spatial distribution of the PI globules. The binarization threshold was chosen so that the areas occupied by the PI globules appear white. The PI globules indicated by the round markers seem to form hexagons as specified by the solid white line (Fig. 24b). A schematic model of this monomolecular film is shown in part c. Although the spatial distribution of the PI globules have not attained a well-defined long-range order, they seem to show a locally ordered honeycomb-like pattern as schematically indicated by the broken line. The unit cell of this structure is indicated by the solid line in part (c) and is reproduced in part (d) together with the PI globules marked by the open circles. The length L0 of the unit cell defined in part c and d is about 63nm as determined from the AFM images. This value is larger than the bulk lamellar spacing. Now let us recall the as-spun film structure as already shown in Fig. 23; P2VP domains form the close-packed hexagonal structure. The hexagon resembles the grid of the PI globules on top of the P2VP monomolecular film (Fig. 24). The spatial distribution of the PI globules is determined by the configurations of the P2VP block chains adsorbed to the SiH surface, as schematically shown in Fig. 25 (see the layer α). The configurational changes have a high kinetic barrier due to the strong interactions between the P2VP and the SiH and hence due to the stiffness of the P2VP layer. In the PI-b-P2VP half-lamella thickness films too, the spatial distribution of the PI globules on top of the first P2VP layer (layer α) is believed to be almost the same as that observed in the monomolecular film. Therefore the following model (Fig. 25) may be considered for the structure of the as-spun thin films. The condensed PI globules G form on top of the physisorbed P2VP layer (the layer α in Fig. 25). Their spatial distribution on top of this first P2VP layer shows a short-range order with the unit cell as represented in Fig. 24d. In the second or higher molecular layer (the layer β in Fig. 25b), the P2VP chains are expelled from the positions occupied by the PI globules in the first molecular layer in order to minimize the unfavorable contact between PI and P2VP. As a result, the P2VP chains segregate into the complementary space in the second or higher layer with respect to the PI globule (G) (see Fig. 25b).

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Fig. 24. AFM height image of the monomolecular film surface (Part a). The image in part b is a zoom-in of the area indicated by dotted square in part a and is binarized such a way that the PI globules appear bright. Some of the PI globules are highlighted by the round markers in part b. Part c represents a schematic model for the structure of the monomolecular film which is composed of PI globules on the top of the P2VP layer adsorbed to SiH. Part d shows the unit cell (solid line) for the locally ordered PI globules on the monomolecular film surface. Open circles represent the positions of PI globules. Part e shows the unit cell of the as-spun thin film surface. Filled circles represent the P2VP domains whose position vectors are shown by u1 and u2 . L1 and L0 are anticipated to be identical and are actually found to be almost identical. Reproduced from [60]. Copyright (2006) American Chemical Society.

These positions for the centers of the P2VP domains, together with the unit cell of the PI globules array in the first molecular layer, are schematically indicated by filled circles in Fig. 24e. The centers of the P2VP domains are located in the vertexes of the unit cell of the PI globule array and thereby forms the close-packed hexagonal structure. In this model, the spacing L1 of the P2VP domains, which perforate the PI matrix and appear on the free surface, has to be almost identical to L0 (the unit cell size of the PI globule arrays, see Fig. 24c and d) on top of the first layer α. Indeed, the observed

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Fig. 25. Schematic model of the as-spun thin film structure (Part a). Part b displays a cross-sectional view of the model cut through the plane including the broken line and normal to the substrate shown in part a, which is parallel to vector u1 in Fig. 24e. In part b, α and β schematically designate the P2VP monomolecular layer and the second layer comprising PI and P2VP blocks on the top of the first molecular layer, respectively. Although the PI globules (G) are not in this cross-sectional plane, their projection on the same plane is represented. L0 and L1 represent the characteristic length for the unit cell of the PI globules and that of the P2VP domains defined in Fig. 24d and Fig. 24e, respectively. L1 ≈ L0 ≈ 63 nm was found experimentally in this system. Based on [60].

spacing L1 of the P2VP domains in the half-lamella thickness film is the same as the observed L0 of the PI globules in the monomolecular film. The P2VP domains observed in the as-spun film of the half-lamella thickness may be considered as the P2VP cylinders standing up with respect to the special layer α in Fig. 25. Non-Equilibrium Pathway Toward Monomolecular Brush Layer Parallel to Substrate. Upon thermal treatment, the kinetically trapped non-equilibrium structure in the as-spun thin films starts transforming into the equilibrium morphology. The as-spun films of PI-b-P2VP in the half-lamella thickness were annealed at 210˚C in vacuum. After this heat treatment for one day, the P2VP protrusions on the free surface seen in Fig. 23 disappeared [60]. This indicates a transformation of the microphase-separated structure into a new structure. The thin film structure was investigated by AFM after a stepwise removal of thin layers of polymer from the top of the thin films, since the strongly

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adsorbing rigid substrate inhibited the microtoming of the thin films necessary for the cross-sectional TEM observation [56, 57]. We concluded that the PI-b-P2VP surface can successfully be ablated by the UV-O3 treatment detailed elsewhere [60]. This method was applied to the samples after the heat treatment for one day and three days, respectively (Fig. 26a and b). After the UV-O3 treatment for various periods, the AFM height images were taken at the same lateral position of the sample. For the sample after the heat treatment for one day (part a), after removal of about 5nm of polymer from the sample surface (ex. image a1), the surface becomes non-uniform and shows protrusions with a short-range order in the AFM images. As the removed thickness, defined by Δz, increases to more than 10 nm, the short-range ordered morphology becomes more significant (see images a3 to a5). The surface, however, becomes again featureless when Δz exceeds 20 nm (ex. image a6).

Fig. 26. AFM height images of the PI-b-P2VP thin film after the UV-O3 treatment for various etching thickness. For each of the AFM images, the residual thickness after the etching is indicated by the solid lines, respectively, in the schematic drawing of the thin film shown in the center. The sample annealed at 210◦ C for one day and for three days prior to the UV-O3 etching procedure is shown in the left-hand part and in the right-hand part, respectively. The scale bar shown in the bottom left image applies to all the images. The shaded portion shown in the schematic drawing in part (c) represents the thickness range in which the short-range ordered morphology is observed on the surface after the UV-O3 treatment. Based on [60].

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In the case of heat treatment for three days (part b), the change in the surface topography along the progress of the UV-O3 etching shows a trend similar to what is shown in part (a): the initially featureless surface (image b1) turns to a corrugated surface with short-range order (image b2 and b3) and becomes featureless again (image b4 and b5). However, the thickness range in which short-range ordered structure is detected is reduced significantly as the annealing time increases: 6 nm ≤ Δz ≤ 20 nm for the sample after heat treatment for one day; 8 nm ≤ Δz ≤ 14 nm for the sample after heat treatment for 3 days. The disappearance of the surface corrugation seems to indicate formation of a laterally homogeneous layer on top of the thin film (see Fig. 27c). Since the surface energy of PI is lower than that of P2VP, the PI chains begin to cover the free surface of the thin film via diffusion of junction points between P2VP and PI along the interface as shown in Fig. 27b. Eventually a thin layer of PI covers the entire top of the P2VP domains. However, the microdomain interfaces perpendicular to the film surface still exist in the middle of the thin film. When the etched surface intersects the microdomain interfaces perpendicular to the film surface, the etched surface shows a laterally inhomogeneous topography. The reduction in the Δz range, in which the inhomogeneous surface topography is detected, indicates that the amplitude of the undulations of microdomain interfaces between PI and P2VP in the plane normal to the film surface decreases with extension of the heat treatment. Noting that the half-lamella thickness film of the PI-b-P2VP will most likely develop the parallel lamellae or bcp monolayer with the microdomain interface parallel to the substrate and air surface (PI-half-lamella on the free surface and P2VP-half-lamella on the substrate surface) in thermal equilibrium, the equilibration mechanism or process can be understood as shown schematically in Fig. 27. Through heat treatments for a prolonged time, the non-equilibrium microdomain structure as shown in Fig. 25 and in Fig. 27a is transformed to the parallel lamellae by way of decreasing the area of the microdomain interface perpendicular to the film surface. The process involves translational diffusion of chemical junctions of the bcps along the interface oriented perpendicular to the substrate surface toward the interfaces parallel to the substrate surface as shown by the gray and white arrows in Fig. 27b. This diffusion creates new PI layers in the free surface side and new P2VP layers on the top of the first layer α defined in Fig. 25. Since the surface area parallel to the substrate does not change with the heat treatments, the transformation process tends to decrease total interfacial area and hence stretches the block chains normal to the interface, which is a natural trend for the equilibration process.

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Fig. 27. This schematic diagram visualizes the transformation mechanism of the PI-b-P2VP thin film structure during heat treatment; (a) as-spun state, (b) intermediate state, and (c) the equilibrium state. The black dot on the microdomain interfaces schematically represents the junction point between the PI block and the P2VP block. After heat treatment, some of the junction points on the microdomain interfaces perpendicular to the substrate are moved on the interface parallel to and close to the substrate surface as indicated by the brighter arrows, and some of the junction points are moved on the interface parallel to and close to the free surface as indicated by the dark arrows. A depression of the parallel interface in the air side by the height d1 is compensated by an elevation of the parallel interface (in the substrate side) by the height d2 in such a way that volume conservation is satisfied. Eventually, the microdomain interfaces perpendicular to the film surface that have developed in the as-spun film are transformed into the interface parallel to the film surface. Reproduced from [60]. Copyright (2006) American Chemical Society.

Triblock Terpolymer Thin Films on Substrate Preferentially Adsorbing Middle Block In the above section, the interactions of the substrate and the bcps were shown to force the bcps to reconstruct the microphase-separated structure under the particular boundary condition set by the interactions between polymers and substrates and thereby form some special structure on top of the substrate. The results were presented in the context of the lamella-forming dibcp thin films. The substrate strongly affects the conformation of the chains adsorbed to the substrate, and the special structure formed on the substrate has significant influences on the non-equilibrium process in the thin films. This substrate

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effect appears to have a long-range effect on the entire thin film structure. This effect is more clearly and explicitly highlighted in thin films of ABC triblock terpolymers. In the case of ABC triblock terpolymers in bulk, the short-range interactions compete with each other among A, B, and C and so do the long-range interactions between A-B and B-C connectivities [17]. These enriched competitions give rise to an extremely rich variety of morphologies in bulk [17, 64]. Let us consider thin films of ABC triblock terpolymers which form a three phase co-existing lamella morphology in bulk. In thin films one should take into account short-range interactions with air and substrate surface and effects of a confined space on the long-range interactions as well. When the substrate preferentially adsorbs the middle block B, the lamellae expected for bulk have to be reconstructed to allow the B block chains to adhere on the substrate. As will be shown later, this constraint further enriches the microphase-separation in the thin films, and clearly represents the longrange substrate effect which has been partly shown in the previous section for the dibcp thin films. As-Prepared State Thin films of lamella-forming polystyrene-block -poly(2-vinylpyridine)-block poly(tert-butylmethacrylate) triblock copolymers, denoted as SVT terpolymer, where S, V, and T respectively denote polystyrene, poly(2-vinylpyridine), and poly(tert-butylmethacrylate), on SiOx or polyimide substrate were studied [62,65,66]. T block is the component having the lowest surface tension and is thereby expected to segregate to the free surface in the film. Moreover this segregation gives rise to a parallel lamellae morphology with T lamella on the free surface. On the other hand, both the SiOx and the polyimide substrate preferentially adsorb the middle V block. The thin films were prepared by using the dipping method with a solution of the SVT in THF as a common solvent. Fig. 28 a and b show the cross-sectional TEM image taken for the as-spun film on the SiOx and polyimide substrate, respectively. In the TEM images, S, V, and T domains appear bright, dark, and gray, respectively (the samples were stained by OsO4 vapor). Although the preparation procedure is the same for both substrates, the film thickness varies depending on the substrate (260 nm on SiOx , 200 nm on polyimide). This indicates the difference in the interactions between the substrate and the triblock terpolymer. The as-spun thin film on the SiOx substrate (part a) shows “sponge-like” structures in phase-separated polymer blends [67] with a short-range spatial order. Three microphases of S (bright), V (dark), and T (gray) appear to be continuous in space. The characteristic spacing of the sponge-like domains (e.g. spacing of the bright domains) is about 71 nm. The free surface of this thin film exhibits the undulation (not shown here) with a characteristic length equal to the aforementioned spacing of the sponge-like domains. On the other hand, the as-spun thin film on the polyimide substrate (part b) shows a texture of dark domains within a gray matrix. Although three

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Fig. 28. Cross-sectional TEM image of the as-spun film on SiOx (a) and polyimide (b). A zoom-in TEM image of the as-spun film on SiOx is shown in the right-hand part of part (a). A schematic model of the microphase-separated structure of the as-spun film on polyimide is shown in part (b). Based on [65, 66].

different microphases are not obviously distinguished, this structure can be understood as a core-shell cylinder model as schematically shown in part (b). In this model, T block forms the gray matrix, and S and V blocks are segregated to the core and shell, respectively, which appear as dark domains. The TEM contrast expected for this model coincided well with the observed contrast across the dark domain [66]. The core-shell cylinders are separated by a characteristic spacing of about 70 nm. The characteristic spacing of the microphase-separated morphology developed in the “bulk” of the as-spun thin films (middle portion of the as-spun thin films) seems identical for the two different substrates. However, the morphology itself seems somewhat different, depending on the nature of the substrates, despite the same selectivity of interactions between these substrates and the block components.

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Self-Assembly into Parallel Lamellae In the case of the SVT triblock terpolymers, thermal annealing does not provide a successful route for the system to achieve thermodynamic equilibrium. This is partly due to the high viscosity of the terpolymer melts and the rather narrow temperature window between the highest glass transition and the lowest thermal degradation temperature of the respective blocks. This is also due to a large kinetic energy barrier for a complex metastable structure formed during sample preparation processes to overcome in order to achieve its equilibrium structure. Therefore, swelling the terpolymer thin film with non-selective solvents, followed by drying of the thin film, is a method applied to the sample as an effective alternative route for “equilibration” [68–70]. Fig. 29 shows a series of cross-sectional TEM images of the SVT thin films on the SiOx substrate (part a) and those on the polyimide substrate (part b) as a function of time of the solvent vapor treatment. Fig. 29a-1 to a-3 shows the surface-induced formation of the lamellar microdomains like the case of thermally equilibrated thin films of symmetric dibcps [71]. After vapor exposure for 1 min (Fig. 29a-3), the lamellae are uniformly developed with their interfaces parallel to the surface of the thin film (defined as the “firststage” ordering process). After a further prolonged solvent-vapor treatment (Fig. 29a-4), a thickening of the lamellar microdomains was observed (defined as the “second-stage” ordering process). This second-stage ordering process is accompanied by macroscopic dewetting of the SVT thin films from the SiOx substrate (Fig. 29a-5). This dewetting process leaves the monomolecular film strongly adsorbed to the SiOx substrate in the dewetted area indicated by B in Fig. 29a-5. On the other hand, the self-assembly process of the SVT lamellae on the polyimide substrate is very different from what is observed on the SiOx substrate. The fragmented dark domains in the as-prepared film (Fig. 29b-1) tend to connect to each other, leading to a more continuous structure after the short solvent-vapor treatment (for 5 s, not shown here). After the solvent treatment for 10 s, the dark domain completely covers the substrate surface (Fig. 29b-2). Another laterally continuous dark domain (indicated by L in Fig. 29b-2) has developed on the air surface side from the initially discontinuous domains. Detailed analysis of this structure showed that the structure shown in part (b-2) is a mesh-like structure (see Figure 3b in [66], where the dark cylinders (C) perforate the gray matrix, thereby bridging between the dark layer (L) and the dark layer on the substrate). The intermediate structure in part (b-2) eventually transformed into a lamellar structure oriented parallel to the film surface after the solvent treatment for 1 min (Fig. 29b-3). After a further prolonged solvent-vapor treatment, the ordering of the lamellae is somewhat improved and all three phases become clearly distinguished in the TEM image (Fig. 29b-4). However, the spacing of the lamellae does not change, contrary to the case of the SiOx substrate. We therefore conclude that on the polyimide substrate the equilib-

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Fig. 29. (a) Cross-sectional TEM images showing the time-evolution of selfassembly in the thin SVT triblock terpolymer film on SiOx : as-prepared (a-1), after the THF-vapor treatment for 5 s (a-2), 1 min (a-3), and 3 days (a-4). Part (a5) represents AFM height images of the film after vapor treatment for 3 days. (b) Cross-sectional TEM images showing the time-evolution of self- assembly in the thin SVT triblock terpolymer film on polyimide: as-prepared (b-1), after the THF-vapor treatment for 10 s (b-2), 1 min (b-3), and 1 day (b-4). Part (b-5) represents AFM height images of the film after vapor treatment for 1 day. The black scale bar in (a-1) and (b-1) represents 100 nm and is common for all the TEM images. The triblock terpolymer film are in the portion P. In the right part of (a-4) and (b-4), the lamellae structure is represented schematically. Part (a-5) and (b-5) shows the SVT that dewets on both substrates after the long solvent treatment. Based on [65, 66].

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rium lamellae are formed in a one-step ordering process (no lamella thickening process). This reveals a remarkable difference to the case of SiOx substrates, where the equilibrium lamellae formed in the two-step ordering process. First Layer on Substrate Both SiOx and polyimide preferentially adsorb V component in the SVT terpolymer. However, the strength of the interaction of V is different in these two substrates. In the case of the SiOx substrate, soaking of the SVT thin film samples in THF left a monomolecular film of the SVT terpolymer, whereas, in the case of the polyimide substrate, the same procedure completely removed the thin films. It indicates that the SiOx substrate has stronger attractive interactions with the V block in the SVT terpolymer than the polyimide substrate. This difference in the interaction strength should be responsible for the observed difference in the non-equilibrium process. Like the PI-b-P2VP thin films presented in Sect. 3.2, the ultrathin films of the SVT terpolymer were explored to understand the substrate effect. The ultrathin films on SiOx were obtained by soaking the SVT terpolymer thin films on SiOx in the solvent, and its structure was unchanged after any heat treatment and/or solvent treatment. The ultrathin films on polyimide were prepared by partly dissolving the 200 nm thick SVT terpolymer thin films by THF [66]. The thickness of the remaining films ranged between 10 and 30 nm. In the case of the polyimide substrate, the films thus prepared will be referred to as ultrathin films. As seen in Fig. 30a, the as-prepared ultrathin film forms isolated V microdomains in a matrix of the other two blocks as schematically represented by black particles in the right-hand part. On the solvent-vapor treatment, the V blocks first form a layer completely covering the polyimide surface (Fig. 30b), indicating that the V chains are selectively attracted by the polyimide. Subsequently, as schematically shown in the right-hand side of Fig. 30b, S and T blocks microphase-separate on top of the V layer. This ultrathin film is supposed to be a monomolecular film. Figure 31 shows the structure of the monomolecular SVT film on the polyimide (a-1) after the vapor treatment and on the SiOx substrate (b-1), respectively. On the polyimide substrate (Fig. 31a-1), S and T blocks form periodic phase-separated domains across their common interfaces on top of the V layer as schematically shown in part (a-3). The height profile shown in part (a-2) indicates areas of two different height levels (A, and B). After the solvent-vapor treatment, S domains are vitrified later than T domains and thereby shrink more, since the solvent is preferential to S [61]. Furthermore, the radius of gyration of the T block is larger than that of the S block. Hence, in the monomolecular film, the T block is expected to be more protruded than the S block on top of the V layer, and the higher (A) and lower area (B) are therefore assumed to correspond to T and S microdomains, respectively. Part (a-3) displays schematically the chain configuration of the SVT on the

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Fig. 30. Cross-sectional TEM images showing the time-evolution of self-assembly in an ultrathin SVT film on the polyimide substrate: as-prepared (a), after THFvapor treatment for 1 min (b). The scale bar, common for all images, is shown in the bottom of the figure. As a visual-guide, the anticipated structures are schematically depicted on the right-hand side. In the schematic diagrams, the embedding resin, the substrate, the matrix comprising PS and PtBMA, and P2VP are represented by the dotted area, slashed area, gray area, and black area, respectively. In part (b), PS domains are explicitly depicted by the bright area in order to distinguish them from the PtBMA (gray) matrix [66].

polyimide substrate in order to highlight a comparison with that on the SiOx substrate (part b-3) to be discussed below. On the SiOx substrate, the SFM height image (part b-1) shows areas of three different height levels (A, B, and C). As in the case of the polyimide substrate, V blocks form the first layer on the SiOx substrate (part b-3). On the top of this V layer, the S and T blocks form microdomains, which do not seem to have common interfaces. Hence the height of the lowest level (C) in part (b-2) is expected to correspond to the top of the bare V layer. Noting that the gyration radius of the T block is larger than that of the S block, it is expected that the more protruded area A and the less protruded area B correspond to the T and S microdomains, respectively. The expected chain configuration is schematically depicted in part (b-3). From Fig. 30b, the thickness of the V layer (dV ) is estimated to be around 6 nm for the case

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of the polyimide substrates. This value is considerably larger than the one observed on SiOx substrates (the height of the level C in Fig. 31b-2 being only 1.3 nm). This finding indicates that on the polyimide the V block is less collapsed toward the substrate and less expanded parallel to the substrate compared to the situation on SiOx . The lateral spacing L of the condensed domains comprising S and T end blocks is smaller on polyimide substrates than on SiOx substrates. This means that the area density of junction points on top of the V layer is higher on polyimide than on SiOx . Therefore, the S and T domains are expected to be more extended in the direction normal to the V layer on polyimide than on SiOx .

Fig. 31. AFM image showing topography of a monomolecular SVT film on a polyimide substrate (part a-1) after the vapor treatment and on a SiOx substrate (part b-1). Part (a-2) and (b- 2) show height profiles along the white lines in part (a-1) and (b-1), respectively. Part (a-3) and (b-3) show schematically the chain configurations of the SVT on the polyimide substrate and on the SiOx substrate, respectively. Part (a-4) and (b-4) are blown-up TEM micrographs of the first layer on the polyimide substrate (B in Fig. 29b-4) and that on the SiOx substrate (B in Fig. 29a-4), respectively. Here, the bright phase (supposed to be PS) is indicated by the white dotted circles. The spacing of the bright domains on the SiOx substrate (part b-4) is larger than that on the polyimide substrate (part a-4). Based on [66].

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Substrate Effect on Self-Assembling Process On both the polyimide and the SiOx substrates, the non-equilibrium structure trapped in the as-prepared film is eventually transformed into a parallel lamella structure in the first-step of the ordering process as shown in Fig. 32a and b, respectively. However, the thicknesses of the lamellae formed in this step differ significantly on the SiOx and the polyimide substrates. The difference in the first layer structure formed on the two substrates is responsible for this difference. On the polyimide substrate, the density of the junction points in the first layer is rather high due to the weaker interactions between the V blocks and the substrate surface. The lamellae of equilibrium thickness are directly formed on the polyimide substrate in the one step ordering process (Fig. 29). However, on the SiOx substrate, thin lamellae are formed over several layers in this step. Here, due to extensive adsorption of V segments onto the polar substrate surface, the density of the junction points between S and V and between V and T in the first layer is lower than that on the polyimide substrate as discussed before. The small number density of junction points may be inherited over several interfaces on top of the first V layer, giving rise to a tendency toward formation of lamellae thinner than the equilibrium lamellae in the first-step ordering process. Therefore, the substrate-polymer interactions exert a long-range effect, influencing the lamellar spacing across the entire thin film. This trend was found to be applicable to thin films with thickness in the range from some 100 nm to some 1000 nm. The mobility of the V blocks on the SiOx surface is lower than that on the polyimide surface, which causes a slower equilibration of the junction density on the substrate and interfaces and hence of the lamellar thickness. 3.3 Effect of Surface Roughness of Substrate on Lamella Orientation Perpendicular Lamellae One recent issue is how to produce perpendicular lamellae (lamellar microdomains with their lamellar interfaces perpendicular to the substrate surface) which is attractive for expanding applications of the thin film structure. In the previous section, crucial effects of the substrate on the nonequilibrium process of forming the parallel lamellae was presented. The difference in the strength of the short-range interactions between the substrate and the constituent block chains was found to have a long-range effect on the self-assembled structure in the thin films mediated by the particular chain conformation of the preferential component on the substrate. Non-neutral substrates having flat surfaces generally formed parallel lamellae after thermal treatment and/or solvent treatment. So far, the ‘neutral’ surface [72], or the patterned surface with a laterally repeating chemical

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Fig. 32. Cross-sectional TEM images of three-phase coexisting SVT lamellae formed after THF-vapor treatment for 1min on polyimide (a) and on SiOx (b), respectively. Reproduced from [66]. Copyright (2003) American Chemical Society.

pattern that alternately attracted each component of the bcp [73, 74] were found to successfully develop perpendicular orientation in the lamella-forming bcp thin films. Imposing an external field that is stronger than the existing surface directed fields is another route to creating perpendicular orientations [41, 42, 62, 75–78]. In addition to the aforementioned methods utilizing elaborate manipulation of substrate surface or external fields, it should be emphasized that there is the possibility of forming perpendicular lamellae by choosing the roughness of substrate surface [79, 80]. The lamellar orientation in thin films of a symmetric poly(styrene)-block -poly(methyl methacrylate), PS-b-PMMA, on indium tin oxide (ITO) coatings and on polyimide replicas of these was explored in detail. Although the roughness of the ITO arose from crystallization of the ITO alloy during deposition, and the relationship between the roughness and the crystallization is not well defined, an ITO rougher than a certain critical roughness was found to produce perpendicular lamellae throughout the thin film, Fig. 33(a).

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Fig. 33. Cross-sectional TEM micrographs of thin PS-b-PMMA (38k-36.8k) film annealed at 230◦ C for 5 hours on two different ITO substrates (ITO1 and ITO2). The roughness characteristics of the two ITO substrates are given at the bottom of the respective images. R is the root-mean-square roughness, and qs is the wave number at the maximal power spectral density obtained from the height image of the ITO. Both parameters are schematically represented in the inset on top of the figure (λs is the characteristic wavelength of the surface roughness). ITO1 is rougher than ITO2. Although parallel lamellae are formed on ITO2 (part b), perpendicular lamellae are formed on ITO1 (part a).

Substrate with Various Surface Roughness A good starting point to assess the effect of the substrate roughness that dictates bcp orientation is to compare the main free energy penalties, ΔF , for each orientation, perpendicular (⊥) and parallel ( ), due to a rough substrate. The rough substrate will increase the free energy of a parallel lamellae through bending deformations of the lamellae (Fig. 34b). This cost of free energy may be circumvented by the perpendicular orientation (Fig. 34d). However, the perpendicular lamellae are accompanied by unfavorable contacts between the bcp components and the substrate. For a sufficiently rough substrate such comparison may lead to the perpendicular orientation being more energetically favorable. We assume a simplified substrate with a single sinusoidal surface topology, having an amplitude Rs and lateral periodicity λs (≡ 2π/qs ). Other simplifying assumptions are that the mean film thickness of both the parallel and perpendicular orientations is a multiple of lamellar periods, L, and that L is invariable, irrespective of lamellar orientation or position within the film.

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Fig. 34. Change in the interior lamellar structure of thin films with increasing reduced critical roughness parameter qs Rs . Parts (b) and (d) illustrate the models used to calculate the true critical roughness for parallel and perpendicular orientations, respectively. Part (a) depicts the reference state of the parallel lamellae on top of a flat substrate.

The film thickness is also considered sufficiently large so as to neglect the surface-normal compressive forces. Referring to the theoretical treatment for the free energy (ΔF|| ) of parallel lamellae on a sinusoidal modulated substrate of roughness qs Rs by [81–83], the critical roughness, (qs Rs )c , at which the ΔF|| exceeds the free energy of perpendicular lamellae (ΔF⊥ ) is given by [80]: 3 (qs Rs )c = (γPS,PMMA /δ2 ) − 3/4 δ2 is the spreading coefficient defined by (γ2,PMMA − γ2,PS ), where γ2,i is the interfacial tension between the substrate and the block i(i = PS or PMMA). This expression takes into account air surface neutrality. Let us apply this criteria to the experimental results shown in Fig. 33. Taking γPS,PMMA as 1 mN/m and δ2 for ITO and polyimide substrates as roughly 0.25 mN/m, (qs Rs )c is estimated as 0.92. Although the actual (qs Rs )c (0.4) seems to be smaller than this value (parallel lamellae are observed on the substrate of smaller qs Rs ), this criterion qualitatively explains the experimental results. The critical roughness was experimentally determined by using polyimide replicas of the ITO1 surface as a substrate. The polyimide surface made from biphenyltetracarboxylic-acid and oxydianiline was not deformed during the PS-b-PMMA film preparation process and the heat treatment around 200o C, while the roughness of this polyimide surface can be suppressed by heat treatment above the glass transition temperature of this polyimide (around 260 − 270◦ C).

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PS-b-PMMA (38k-36.8k) thin films (thickness 250 nm) were prepared on the polyimide substrates of various roughness; the samples were then annealed at 200o C for a range of times and their structures observed iteratively with AFM between anneals. During annealing, three types of bcp surface images were observed: The first is a perpendicular lamellae structure (see Fig. 35a) which is most frequently observed after the initial anneal on rough substrates. The second is the perpendicular lamellae with signs of surface roughening (see Fig. 35b). For a substrate with a given qs Rs , the perpendicular surface structure persisted for a time, tqs,Rs , after which the thin film surface structure began to show macroscopic roughening. The third is a stepped surface indicative of the establishment of parallel lamellae of a different stack number (Fig. 35c). Extended annealing of the sample then led to increased surface roughening, a disappearance of the perpendicular lamellae and the eventual development of terraced surface. It was observed that there was a longer lag time, tqs,Rs , before the thin films on higher qs Rs polyimide substrates showed signs of surface roughening. In the case of very high qs Rs substrates this transition did not occur at all and a perpendicular surface structure was observed over the timescale covered in the experiments. Fig. 36 summarizes this behavior for the polyimide replica substrates studied and indicates, at a given time, the roughness of the substrates upon which the PS-b-PMMA (38k-37k) thin film surface exhibits only perpendicular lamellae (filled symbols). The figure also shows the point at which each of these substrates, upon prolonged annealing, began to show signs of forming parallel lamellae (open symbols). The locus of the time at which the perpendicular lamellae start to transform to parallel lamellae (as a function of qs Rs ) is delineated by the broken line within the figure. This locus changes with time in the parameter space of qs Rs and the annealing time. It was found to become independent of time at a value of qs Rs around 0.4; this is identified as the critical roughness, (qs Rs )c , of the substrate for 38k-36.8k PS-b-PMMA on the polyimide substrate at 200o C. The experimentally determined (qs Rs )c is smaller than that expected from theoretical considerations (0.92) of this system as presented before. Here it should be noted the experimentally determined (qs Rs )c may be an underestimate of the true critical roughness of the substrate. With reference to Fig. 34c, the experimentally obtained critical roughness is redefined as the criterion below which, if parallel lamellae form on the substrate, they are able to grow until they reach the air surface. Beside (or above) this AFM observed critical roughness, there is a possibility that parallel lamellae form on the substrate but do not reach the free surface, Fig 34c. It has been shown that a sufficiently rough substrate can lead to perpendicular lamellar orientation of the block copolymer. There is a critical substrate roughness below which the parallel orientation of block copolymers is favored. Given this study, it is unsurprising that previous experiments with rough substrates did not report the means to produce perpendicular lamellae. The substrates used by [84] were not rough enough. A further experiment, which did

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Fig. 35. AFM images of PS-b-PMMA (38k-37k) bcps on a polyimide replica substrate that have been thermally smoothed to a qs Rs of 0.25. Images show the surfaces of the thin bcp films after annealing at 200◦ C for (a) 60min, (b) 70 min, and (c) 1 day. Reproduced from [80]. Copyright (2005) American Chemical Society.

use significantly rough substrates, also used poly(styrene)-block -poly(2-vinyl pyridine) as the model block copolymer [85]. However, this system has large differences in the attraction of its component blocks to the air and substrate surfaces. In PS-b-PMMA these differences are small and can be overcome by substrate roughness effects. Formation of Patterned Surface The perpendicular lamellae system found here can load metal nano-particles preferentially into the domains constituting of certain components [54]. Palladium nano-particles were loaded into the perpendicular lamellae film via sublimed vapor of Pd precursor (palladium acetyl-acetone complex) at elevated temperature (200◦ C). A high molecular weight PS-b-PMMA (106k-99k) was used in order to prevent disordering of the microphase-separated structure

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Fig. 36. Summary of AFM analysis of PS-b-PMMA (38k-36.8k) films annealed on an array of polyimide substrates having a range of qs Rs values. The filled and open symbols indicate surfaces found to be in a fully perpendicular (c.f. Fig. 35a) and mixed (c.f. Fig. 35b) surface state. The dotted lines indicate the locus of (qs Rs )c from one state to the other. Reproduced from [80]. Copyright (2001) American Chemical Society.

of PS-b-PMMA during the vapor exposure process and simultaneously proceeding thermal reduction of the Pd complex. The ITO1 substrate successfully developed perpendicular lamellae of this high molecular weight copolymer. As shown in Fig. 22 (Sect. 2.2), the thin film of PS-b-PMMA having perpendicular lamellar orientation selectively incorporates Pd nano-particles into the PS lamellae. The Pd nano-particles appear as the darkest spots and the brightest (most protruded) spots in the TEM micrograph (part a) and the AFM image (part b), respectively. The finding that a rough surface induces a perpendicular orientation in lamella-forming block copolymer films was also demonstrated in the SVT thin film. Fig. 37 shows an AFM height image of 200 nm thickness SVT thin film on polyimide substrate. The thin films was subjected to THF-vapor treatment and thereby the parallel lamellae as shown in Fig. 32a were already established in most areas of the sample. However, along a small scratch induced on the polyimide substrate before the film preparation (indicated by the arrow), a zone in which the perpendicular lamellae form is observed. Though the scratched area may expose functional groups different from those on the nonscratched area and thereby have altered surface energy, the orientation of the lamellae seems to be controlled by the mechanical scratch on the substrate.

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Fig. 37. The SVT triblock terpolymer film on the polyimide substrate. There is a scratched line on the substrate surface in the area marked by an arrow. Perpendicularly orientated lamellae are observed on top of the scratched area, while the parallel lamellar orientation was observed in the surrounding area having a flat substrate surface. Reproduced from [80]. Copyright (2005) American Chemical Society.

3.4 Remarks - Substrate and Thin Film Structure This section highlights the effects of the substrate surface (chemistry and geometry) on the self-assembling process in lamella-forming bcp thin films. First, it was shown that the strong short-range interactions between the substrate surface and the block segments appear as a long-range effect in the non-equilibrium process through the chain connectivity of the block copolymers. The strong interaction between the bcp and the substrate leads to a special structure on the substrate surface, and this seems to significantly influence the as-prepared (non-equilibrium) film structure. In this study, the flat substrate always led to parallel lamellae orientation in thermal equilibrium. The transformation process of the as-prepared film structure toward

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the parallel lamellae seemed to be determined by the special structure formed on the substrate. Using the lamella-forming triblock terpolymer and the substrate preferentially attracting the middle block, these findings (the long-range substrate effect) were highlighted. The discovery concerning the effects of substrates on kinetic pathways and time-scale to achieve equilibrium morphology may be quite important, since in many cases systems cannot attain equilibrium. The systems rather tend to be trapped in metastable states, and hence one must find methods to control non-equilibrium structures assisted by some basic principles of non-equilibrium phenomena to be further developed in future. Secondly, it was shown that the generally observed parallel lamellae can be switched into perpendicular lamellae by roughening the substrate surface. Here, added to the aforementioned effect from the substrate, geometrical constraints induced by the substrate surface topography influence the lamellar formation process. With the substrate having a roughness above the critical one, the bcp thin films were found to have an intriguing perpendicularly orientated lamellar structure which can be utilized in various applications. We hope the present work will contribute to some extent in nano-fabrication technology in various fields.

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Characterization of Surfactant Water Systems by X-Ray Scattering and 2 H NMR Michael C. Holmes Centre for Materials Science, Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston, PR1 2HE, United Kingdom

1 Introduction to Surfactant Water Systems Aqueous solutions of surfactants not only have important applications as detergents, in food and cosmetic products, in oil recovery and drug delivery [1] but are now becoming important as a medium for the templating of nanostructured materials [2–7]. Surfactants are molecules which possess two different moieties; a hydrophobic moiety and a hydrophilic moiety [8] and typically have dimensions in the range 1 to 10 nm. At very low concentrations in aqueous solution they exist as individual molecules but above the critical micellar concentration and Krafft temperature they self assemble to form micelles. At such low concentrations interactions between the micelles are negligible and generally they will have a spherical shape whose radius is determined by the length of the hydrophobic tail. However as the concentration of surfactant is increased, micelles can become non-spherical (rod or disk shaped) and the interactions between them become significant. In fact within these systems there are two important interactions determining structure; inter-molecular interactions (both head and tail groups) which to a large extent determine the aggregate size and shape and inter-aggregate interactions which can influence aggregate size and shape but more importantly can determine phase structure. These interactions can easily become strong enough to promote macroscopic order and can lead to the formation of a sequence of ordered mesophases having length scales in the range 3 to 200 nm typically. One of the key properties of these mesophases is that they divide space into two regions; hydrophobic and hydrophilic, making them ideal for templating media. The wide range of phases that can form have been reviewed elsewhere [1–9] but table 1 lists the wide range of types of phase and their space groups. Clearly there are phases with one, two and three dimensional positional order in addition to varying degrees of orientational order of the aggregates. One of the best ways of determining aggregate structure and determining the symmetry of a phase is using X-ray scattering.

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Table 1. Summary of nomenclature for lyotropic phases and for their intermediate phases. The subscripts 1 and 2 refer to normal (water continuous) and reversed (surfactant continuous) phases, modified from reference [9]. Details of the space groups can be found in reference [10] Phase

Symbols

Isotropic

Possible space groups L1 , L2 , L3 , L4 –

Micellar Cubic Nematic

I 1 , I2 Nc , N d

Hexagonal H1 , H2 Bicontinuous cubicV1 , V2 Lamellar Lα Ribbon Rb1 , Rb2 Mesh

Mh1 , Mh2

Bicontinuous

Bc1 , Bc2

Notes L3 , L4 refer to bicontinuous isotropic and vesicle phases

Pm3n, Fd3m –

Consisting of rod or disk shaped micelles p6mm Two-dimensional space group. Ia3d, Pn3m, Im3m – pm One-dimensional space group. c2mm, p2gg Two dimensional centred rectangular space groups. 0, I4mm, R3m 0 represents the random mesh whilst three dimensional space groups I4mm, R3m represent tetragonal and rhombohedral phases mesh respectively. ? No space groups identified to date.

In addition to the structural diversity these phases contain interfacial surfaces dividing the aqueous environment from the hydrophobic alkyl chain region. The curvature of this surface is determined by the strength of the interactions between the moieties and the volume fraction of the moieties and any associated solvents. Any surface curved in three dimensions can be described by two radii of curvature at each point,  Fig. 1. The curvature is de1 1 1 fined in two ways: the mean curvature, H = 2 rab + rcd and the Gaussian  curvature, K = r1ab r1cd . 2

H NMR is sensitive to the surface curvature in surfactant water systems and, in the case of 2 H NMR from solvent 2 H2 O it is also sensitive to the fraction of water molecules bound to the surfactant head groups. Since the surface curvature can change at a phase transition between two ordered phases, 2 H NMR can be used as a sensitive technique for establishing phase diagrams, and together with X-ray scattering can fully characterize the phases of a surfactant water system.

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Fig. 1. A region of interface whose curvature at each point can be described by two radii of curvature, rab and rcd with their respective arcs ab and cd shown.

2 Small Angle X-Ray Scattering (SAXS) There are many general works on X-ray scattering [11] and a few on scattering from specific mesophase structures, e.g. cubic phases [12, 13]. Many of the ideas given here were originally outlined in the pioneering work by Luzzati and coworkers, [13–19]. 2.1 Some Basic X-Ray Scattering Theory Scattering from a Single Electron X-rays are scattered by electrons in matter. They can be scattered both coherently and incoherently, i.e. the scattered X-ray can have the same wavelength as the incident X-ray and a fixed phase relationship to it or the wavelength can be different. The incoherent scattering arises from such effects as Compton scattering, fluorescence, photoelectron emission etc [11] and gives rise to background and noise. Coherent scattering arises when the electric field vector of the incident X-ray wave causes an electron to oscillate in a direction parallel to the electric field vector and then re-emit coherent X-rays in all directions. The intensity Ip of X-rays scattered to a point P a distance r from a single electron, mass m and charge e at point O is given by

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Ip = I0

e4 sin2 α r2 m2 c4

where I0 is the intensity of the incident X-ray and α is the angle between OP and the direction of acceleration of the electron at O. Notice that Ip ∝ 1/r2 i.e. the inverse square law is satisfied and Ip ∝ 1/m2 i.e. the scattering from the electrons is much stronger than that from the nucleus. This relationship, first proposed by J. J. Thomson [11] shows that the scattered intensity depends upon angle. In general we are interested in considering the scattering from atoms or collections of atoms which contain many electrons. Two Scattering Centres We start by considering the scattering from two electrons located at O and M and separated by a distance OM, Fig. 2.

Fig. 2. The geometry of X-ray scattering from a pair of electrons.

S 0 and S are unit vectors defining the directions of the incident and scattered radiation and λ the wavelength of the X-rays. The path difference between rays 1 and 2 is mMn and will determine the phase difference between rays 1 and 2. In turn this will determine whether constructive or destructive interference takes place and thereby the intensity of scattered X-rays in the direction 2θ. From Fig. 2 mM = S 0 .OM and M n = −S.OM . Thus the path difference between rays 1 and 2, is given by δ = −OM (S − S 0 ). The phase difference between rays 1 and 2 is given by φ=

(S − S 0 ) 2πδ = −2π OM . λ λ

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(S−S )

where λ 0 = s is the scattering vector. s is an important parameter in scattering theory since all scattering measurements can be reduced to determining the scattered intensity I(s). The modulus of s can be easily determined from fig. 2 to be 2 sin θ/λ. Scattering from a Single Atom For coherently scattered X-rays the amplitudes add so that the scattered intensity from a single atom I(s) is given by I(s) = f 2 (s)Ie (s)

(1)

Where Ie is the intensity scattered by a single electron, and f is the atomic scattering factor. The atomic scattering factor is defined as f=

amplitude of the wave scattered by an atom . amplitude of the wave scattered by one electron

The scattering factor is a function of both the scattering angle θ and the X-ray wavelength λ.

Fig. 3. The atomic scattering factor for fluorine, Z = 9.

When s = 0, f = Z, the atomic number of the atom and the total number of electrons in the atom. For a low density gas of well separated atoms of atomic scattering factor f the scattered intensity is given by (1) and is simply the square of the curve shown in Fig. 3. Scattering from a Group of Atoms Extending this to a group of n atoms such as a crystal, the scattering is the sum of the scattering from individual atoms modified by the interference

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between these components due to the spatial arrangement of those atoms. The scattered intensity from the group can be written

2

I(s) = F (s) where F (s) is the structure factor and is given by F (s) =

n 

fj exp(−2π is.r)

(2)

j=1

fj is the atomic scattering factor of the jth atom. F (s) and I(s) not only depend upon fj but also on the spatial arrangement of atoms through the term exp(−2πs.r). This will determine the phase difference between the scattering from different atoms and thereby the intensity of the scattering in a particular direction. Note that when s = 0, F (0) is equal to the total number of electrons in the group of atoms. F (s) will usually be a complex number containing information about the phases of X-rays scattered from different atoms in the group. When the square of F (s) is formed to give I(s) this phase information is lost. If the number of electrons is large (2) becomes  F (s) = ρ(r) exp(−2π is.r) dr (3) V

where ρ(r) is the electron density of the group of atoms and V is the volume of the atomic group. This has the form of a Fourier transform so that the electron density can be deduced from  F (s) exp(2π is.r)ds ρ(r) = V

Thus in principle the intensity may be related to the electron or atomic distribution via a Fourier transform and ρ(r ) is the structure in real space whilst F (s) is the structure in reciprocal space.

3 Scattering from Surfactant Water Systems The general principles developed in the previous section can now be applied to surfactant water phases. However, caution must be exercised. An old but seldom mentioned principle in X-ray scattering is Babinet’s Principle which states that complementary structures appear identical, ie holes in a screen appear identical to opaque spots of the same size. Thus the X-ray scattering from hexagonal, H1 and reversed hexagonal, H2 phase will generate reflections in the same ratio to each other. Other information such as the volume fraction of surfactant must be used to distinguish between these possibilities.

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A number of assumptions also need to be made about the organization of the structure before proceeding. These are summarized in the three protocols of Luzzati [14]. 1. Aqueous and lipid components occupy distinct regions and the interface between them is ‘smooth’. Generally the aggregate is assumed to have a simple symmetry i.e. the hexagonal phase is composed of circular rods although this may not always be the case; see for example figures 7 and 9 later in the chapter. 2. Some water molecules are strongly associated with the head groups in an interfacial region. 3. The water and head groups comprise the polar region. With surfactant water systems we may distinguish three different classes of situation. Firstly there are isotropic micellar and sponge phases, L1 , L2 , L3 , L4 which possess no long range order. Secondly there are phases that have long range positional order (i.e. more or less crystalline) in at least one direction. Examples of these phases are lamellar, Lα ; hexagonal, H1,2 : cubic, V1 and the so-called intermediate phases such as mesh phases, Mh1 (0). Finally there are nematic phases, Nc,d which consist of anisometric micelles possessing only long range orientational order. In studying surfactant water phases we are interested in structural units which consist of large aggregates of surfactant molecules for which an electron density distribution is the most appropriate form of the structure factor, (3). However these surfactant aggregates may be close enough for the scattering from individual aggregates to interfere. The observed intensity can therefore be defined as I(s) = F 2 (s)J(s) (4) where J(s) is a function which describes the interference between scattering objects. 3.1 Phases with no Long Range Order Scattering from Well Separated, Non-Interacting Particles For a simple, low density monatomic gas (4) gives a very simple result J(s) = 1 and I(s) = F 2 = f 2 /v where v is the average volume available per atom (i.e. v = V /N where V is the total volume and N is the number of atoms). Thus the scattering pattern is identical to f 2 . This is the same situation that is found in dilute micellar phases where the micelles are well separated and there is no interference between particles. For spherical micelles the scattering arises simply from the electron density distribution within a single micelle (assuming monodispersity) and leads to a scattering curve with the form of a Bessel function [11]. However polydispersity in the size and shape of the micelles means that the secondary maximum

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is often very difficult to observe. The equivalent functions for rod and disk shaped micelles are more complex mathematically. It is often difficult experimentally to distinguish the precise micellar shape. For the central peak of the scattering there is an exponential approximation for the scattered intensity [11],

4π 2 s2 R2 I(s) ∝ exp − 3 where R is the radius of gyration of the micelle. By plotting ln I(s)as a function of the scattering angle, it is possible to obtain an estimate for R. This assumes that the particles are identical, of low density and randomly orientated. Scattering from a Liquid-Like Structure As the density of the particles (whether single atoms or spherical micelles in an isotropic solution) increases, the interference function J(s) departs from unity and starts to reflect the increasing local positional order measured by the radial density function n(r), i.e. the number density of particles in a thin spherical shell of radius r and thickness δr.

Fig. 4. (a) A representation of a liquid formed by spherical particles. A thin spherical shell of radius r and thickness δr is shown. (b) The radial density function, n(r) as a function of r for three different number densities represented by the function a/v 1/3 .

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Because of the higher number density of particles, there is inter-particle interference expressed by [11]  1 J(s) = 1 + [n(r) − 1] exp(−2π i s.r)dr v V For spherical particles this becomes  2 [n(r) − 1] sin(2π s r)rdr J(s) = 1 + sv V Notice that increasing the density increases the extent of the long range order and the scattering pattern evolves to that of a liquid with a scattering maximum at about s = 1/a where a is the particle radius, Fig. 5.

Fig. 5. (a) I(s) as a function of s for increasing density of particles. (b) X-ray scattering from a micellar phase. Notice the appearance of a diffuse scattering ring arising from the short range positional order in the liquid.

For a dense liquid the scattering pattern shows a pronounced peak and we can write the inter-atomic interference as sin(2π sr) 1  J(s) = 1 + (number of pairs at distance r) × N 2π sr The first maximum for

sin(2π sr) 2π sr

occurs at

1.23 2 sin θm = λ rm For a hexagonal close packed solid the first diffraction peak occurs at  3 1 1.22 = sm = 2 rm rm Therefore it is tempting to associate the liquid maximum with the mean separation of particle. However, this should be treated with care particularly as the number density of the liquid decreases. sm =

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3.2 Phases with Long Range Positional Order Scattering from a Crystalline Solid In a crystalline solid the interference function is important and becomes a series of delta functions. The scattering power per unit cell for an infinite crystal can now be written: I(s) = F 2 (s)J(s) = F 2 (s)δ(r∗hkl − s)

(5)

where δ is the Dirac delta function and r∗hkl is defined by r∗hkl = ha∗ + kb∗ + lc∗ .

(6)

The integers h, k and l are the Millar indices of the crystal plane under consideration and a*, b* and c* are the vectors defining the reciprocal lattice, i.e. a* = a −1 b* = b −1 and c* = c −1 . Here a, b, and c are the lattice vectors of the crystal. Now put  ∗ (7) Fhkl = F (rhkl ) = ρ(r) exp(−2π ir∗hkl .r)dv 2 Then I(s) = Fhkl Peaks can only occur for s = r∗hkl or, according to the Bragg condition,

2dhkl sin θ = λ. Fig. 6 shows the progression of scattering patterns from a low density gas through to a crystalline solid. In fig. 6(b) notice that the intensity of the scattering peaks is modulated by the single particle scattering. Lamellar Phase: 1-Dimensional Positional Order The lamellar phase, Lα is the simplest ordered structure of a surfactant water system consisting of surfactant bilayers interspersed with water layers and positional order in one direction, Fig. 7. From (5) and (6) l s0 = r∗l = lc∗ = . d0 So there are a series of lines in the scattering pattern in the ratio 1:2:3 etc. Having determined d0 other important parameters can be determined from it by using the volume fraction φhc of hydrocarbon in the sample. This can be calculated  from −1 hc c where ξhc and ξw are the densities of hydrocarφhc = 1 + ξwξ(1−c) bon and water respectively and c is the concentration of hydrocarbon in the

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Fig. 6. Schematic diagrams of the scattering from (a) gas, liquid/dense gas and liquid states and (b) a crystalline solid.

Fig. 7. A schematic representation of the real space structure of the lamellar phase and the X-ray scattering pattern in reciprocal space for a powder and a single crystal sample. The graph on the right shows the scattered intensity profile as a function of s.

sample. The bilayer thickness is then calculated from dhc = φhc d0 . Notice that this equation provides a scaling relationship which can confirm that this phase is indeed a classical lamellar phase since dhc should remain constant as the water content changes at fixed temperature and therefore d0 ∝ φ−1 hc . It will be shown below that phases with other structures and symmetries have other scaling relationships.

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The surface area per surfactant molecule, sa at the interfacial surface can also be calculated knowing the volume of the hydrocarbon, vhc from sa = 2vhc /φhc d0 Returning to (3) , we see that whilst the position of the scattering lines depends upon d0 their intensity depends upon F 2 (s) which is determined by the electron density profile of the bilayer itself. Equation (3) becomes I(sz ) = F 2 (sz ) where sz is the scattering vector in the z direction parallel to the bilayer normal. Equation (7) becomes F (sz ) = [1/π sz (ρhc − ρw ) sin 2π sz tw ]+[1/π sz (ρhead − ρw ) sin 2π sz (tw + thead )] where tw is the half width of the water layer, thead is the thickness of the head group region and ρhc , ρhead and ρwater are the electron densities of the hydrocarbon, head group and water layers which typically have values of ρhc = 273 nm−3 , ρhead = 360 nm−3 and ρwater = 335 nm−3 for 2 H2 O. Fig. 8 shows a schematic representation of the electron density across the semi-bilayer section.

Fig. 8. A schematic representation of the electron density across the semi-bilayer section in the z direction. Terms are defined in the text.

Using the simplified electron density profile shown in figure 8, F 2 (sz ) can be calculated and compared to the intensity profile of the reflections from the lamellae.

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Hexagonal Phase: 2-Dimensional Positional Order With the hexagonal, H1 phase we progress to a system with 2-dimensional positional order and long range orientational order. Fig. 3.2 schematically shows the structure and scattering from both powder and single crystal samples.

Fig. 9. A schematic representation of the real space structure of the hexagonal phase and the X-ray scattering pattern in reciprocal space for a powder and single crystal sample orientated with the cylinder axis n ˆ in the same plane as s and with it parallel to the incident X-ray beam. a is the lattice vector of the 2-dimensional lattice on which the cylinders are packed and dhc here is the diameter of a cylinder.

From (5) and (6) scattering maxima occur when  (h2 + k 2 + hk) 2 ∗ shk = rhk = |a| 3

√ √ √ This √ generates reflections with s values in the ratio of 1, 3, 2, 7, 3, 12, 13 . . . . A common mistake is to assign the first and strongest reflection to the lattice parameter |a|. In fact the first reflection corresponds to the lowest √ |a| 3 values of Millar indices (1,0) and is d10 = 2 . The diameter of the hydrocarbon cylinders is now given by  √  2 3φhc 8φhc √ = d10 dhc = | a| π π 3 Notice that the scaling relationship between d10 and φhc is now d10 ∝ 1/φ0.5 hc . 2vhc 2π√ . Once again The surface area per molecule is given by sa = | a| φ 3 hc

the intensity of the scattering peaks will be determined by the structure factor

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of the cylinders. This time a one dimensional electron density profile will have to be replaced by a two dimensional map. Cubic Phases: 3-Dimensional Positional Order There are a number of phases with cubic symmetry [12, 13]. Micellar cubics comprise micelles, which may be slightly distorted into short cylinders located on lattices with cubic symmetry. In addition between lamellar and hexagonal phases there are three bicontinuous cubic phases in which both the water and hydrocarbon regions are continuous. These are illustrated in Fig. 10.

Fig. 10. The three bicontinuous cubic structures and their space groups. The distance a represents the lattice parameter. Reprinted from [12]. Copyright (1993) The Royal Society.

The structure of these phases is more complex however the same method of working applies. From (5) and (6) scattering peaks will occur when 1  2 h + k 2 + l2 . shkl = r∗hkl = |a| √ √ √ √ This √ generates reflections with s values in the ratio of 1, 2, 3, 2, 5, 6, 8, 3,... Not all reflections will necessarily be present, and will depend upon the particular symmetry and upon the structure factor from the electron density distribution. Cubic phases have been extensively reviewed by Seddon [12]. Calculating dhc and sa is possible provided the structure has been identified and a suitable structural model is used. Simple rod-box models can give reasonable estimates for these parameters (see below) however they must always

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be treated with a degree of caution. The scaling relationship for a cubic phase will be d10 ∝ 1/φ0.33 hc although practically it is often not very useful since these phases only have a narrow concentration range of only a few weight percent of surfactant. Mesh Phases: 1 or 3-Dimensional Positional Order Mesh phases are part of a group of phases known as “intermediates” since they occur between hexagonal and lamellar phases and have a number of structures and symmetries [20]. Mesh phases are essentially lamellar phases pierced by water filled pores and are analogous to hexagonally perforated phases of diblock copolymers. The random mesh phase, Mh1 (0) has the lamellae pierced by pores but these have a liquid-like arrangement and there is no correlation between the lamellae. By contrast the rhombohedral mesh, Mh1 (R3m) has pores which are arranged within the lamellae on a hexagonal lattice and are correlated from layer to layer with an ABC arrangement. Fig. 11 shows the evolution of the X-ray scattering from a lamellar phase, Lα to random mesh phase, Mh1 (0) and random mesh phase to rhombohedral mesh phase, Mh1 (R3m).

Fig. 11. (a) shows the evolution of the Mh1 (0) phase to the Lα in the C16 EO6 /2 H2 O system [21]. (b) Shows the evolution of the Mh1 (R3m) phase to Mh1 (0) in the tetramethylammonium perfluorodecanoate / water system as a function of temperature [22].

The difference between the scattering from Mh1 (0) and Lα phase is rather subtle. Both have 1-dimensional order and therefore produce the characteristic lamellar pattern with reflections in the ratio 1:2 etc. The Mh1 (0) phase differs by having a broad (and consequently weaker) liquid-like reflection labeled

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dh in Fig. 11(a). This comes from the pores within the lamellae. It should also be noticed that d0 (Mh1 (0)) < d0 (Lα ) since as the pores open up in the lamellae they are filled by water from between the lamellae reducing d0 . In Fig. 11(b) the Mh1 (0) phase is seen at 65◦ C whilst the Mh1 (R3m) phase is seen at lower temperatures. This latter phase has long range positional order in 3-dimensions and this is reflected in the sharp multi-line scattering which can be indexed to the R3m space group. Calculating dhc and sa is possible provided a suitable structural model is used. Two such models are shown in Fig. 12.

Fig. 12. (a) A mean curvature model of one lamellae of the Mh1 (R3m) phase and (b) the same constructed from a series of interconnected rods (shaded) and triangular boxes.

The simple rod-box model of Fig. 12 can give good estimates of the structural parameters in these phases [21]. For example, table 2 shows rhc the hydrocarbon region semi-thickness and sa calculated for four different phases in the C16 EO6 / water. What is noteworthy is that sa remains rather constant with phase structure but that rhc changes as the interface becomes more curved. Finally the scaling relationship for a mesh phase becomes much more like that of a hexagonal phase and d0 ∝ 1/φ0.5 hc . 3.3 Phases with Long Range Orientational Order Only Nematic Phases Lyonematics are composed of anisometric micelles, either rod shaped, Nc or disk shaped, Nd , and they usually occur between isotropic micellar phases and

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Table 2. Summary of the parameters for the 52 weight percentage C16 EO6 /water sample [23]. Model rhc (nm) Lamellar phase 0.89 Rhombohedral smoothed mesh 2.19 Cubic Ia3d 1.60 Hexagonal Phase 2.00

sa (nm2 ) 0.51 0.36 0.57 0.45

either hexagonal or lamellar phases respectively [24,25]. Typically these phases are found in short chain ionic surfactants often with an added cosurfactant or salt [24]. Both phases have a relatively low viscosity and can often be easily aligned either by an external magnetic field or by surface forces caused by the walls of the sample container and the shear flow on filling [26]. It is therefore relatively easy to obtain single crystal samples, Fig. 13.

Fig. 13. The structure of the Nd and Nc phases in real and reciprocal space shown schematically. n ˆ shows the mean orientation of the symmetry axis of the micelles (or liquid crystal director).

It is important to notice that disk shaped micelles are naturally monodispersed since the growth of the micelle is controlled by the need to increase the amount of highly curved edge, increasing its mean surface energy. In contrast rod micelles tend to be more polydispersed since after the hemispherical end caps are established the rod can continue to grow. It is for this reason that it is often impossible to observe d in the Nc phase. The scattering peaks from d in the Nd phase and d⊥ in the Nc phase are sharp relative to the scattering from an isotropic micellar solution and indicate some degree of positional

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order in those directions. In contrast d⊥ in the Nd phase is broad and comparable to that observed in the isotropic micellar phase. The value obtained for d⊥ from the maximum in the scattering peak can not be regarded as an exact value in the same way as the value obtained for d . However it is now possible to calculate the mean aggregation number for an Nd phase assuming the micelles are hexagonally arranged in layers with lattice parameter a where a = √23 d⊥ . √

The volume of a primitive cell, containing one disk, V = a2 23 d = 2 √ d2 d . 3 ⊥ The volume of one disk micelle is then = √23 d2⊥ d|| φhc and the mean aggregation number per micelle is given by 2 d|| d2⊥ φhc

n = √ 3 vhc The orientational order parameter for director, n ˆ fluctuations can be obtained from the angular spread of the peak associated with d . 3.4 Summary X-ray scattering is a powerful technique for investigating the phase structure of surfactant water systems. The scattered intensity from a system is made up of two components, the scattering from the individual objects and the inter-particle interference function. One or other of these may dominate. For most concentrated surfactant water phases the degree of positional order allows us to assume that the scattering is dominated by inter-aggregate interference. Hence, they may be treated as crystals in one or more dimensions and identified. With some simplifying assumptions structural information may be easily extracted. Some phases, concentrated micellar solution, nematic and mesh show liquid-like features where it is difficult to separate, the aggregate scattering and the inter aggregate interference. Scattering from dilute micellar solution where the individual particle scattering dominates, can give information about the mean radius of gyration but is rather insensitive to the shape and size distribution of the particles.

4 2 H NMR Nuclear magnetic resonance (NMR) is a very powerful technique for investigating chemical structure, phase transitions, molecular orientation and conformations, molecular dynamics and self diffusion in lyotropic liquid crystalline systems. Detailed reviews of these applications have been published elsewhere [27–29]. In this chapter the use of 2 H NMR will be considered simply as a technique for the identification and phase characterization of surfactant water mixtures.

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Some Basic NMR Theory The nucleus is composed of protons and neutrons which possess ‘spin’ or intrinsic angular momentum, I. Nuclei of spin I ≥ 1 may possess non-spherically symmetrical nuclear charge distributions, resulting in their having electric quadrupole moments, which can interact with the electric field gradient at the position of the nucleus so that a series of quantized energy levels are produced, even if there is no external magnetic field. When a quadrupolar nucleus is placed in a magnetic field, two energy terms need to be considered: the Zeeman and the quadrupolar contributions [30], that is 3m2I − I(I + 1) γh (3 cos2 θq − 1) (8) E = − mI B0 + e2 Qq 2π 8I(2I − 1) where γ, the magnetogyric ratio, is a constant characteristic of the particular nucleus, B0 is the externally applied magnetic field, and mI is the nuclear spin magnetic quantum number, which has values of mI = I, I −1, I −2, ..., −I. The first term in (8) is the Zeeman energy, and the second term is the quadrupolar contribution. eq is the electrical field gradient, eQ is the quadrupole moment, θq is the angle between B0 and the electric field gradient, and e2 qQ/h is the quadrupole coupling constant. For a deuterium nucleus with I = 1, (8) reduces to: EmI = −

γh 3m2I − 2 mI B0 + e2 Qq (3 cos2 θq − 1) 2π 8

(9)

If the nucleus is exposed to radio-frequency energy of the appropriate frequency, transitions will be induced between the levels given in (9) , and because the population of a lower state is slightly greater than that of an upper, there will be a net absorption of energy. A nuclear magnetic resonance spectrometer thus consists of a means of producing a strong magnetic field, a source of radio frequency power, and a means of detecting absorption of energy by the sample. Since mI in (9) possesses three values, -1, 0, +1, there are three energy levels given by γh 1 E1 = − B0 + e2 Qq (3 cos2 θq − 1) 2π 8 2 E0 = +e2 Qq (3 cos2 θq − 1) 8 γh 1 B0 + e2 Qq (3 cos2 θq − 1) E−1 = 2π 8 Applying the selection rule ΔmI = ±1, the 2 H NMR spectrum is a doublet with a splitting given by: (E−1 − E1 )/¯h = Δν =

Δν0 (3 cos2 θq − 1) 2

(10)

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where Δν0 = 3e2¯hQq . Fig. 14(a) shows the typical doublet spectrum from a sample with a single orientation for θq whilst fig. 14(b) shows the typical spectrum from a powder sample, i.e. where there is a spherical distribution of values of θq .

Fig. 14. (a) shows the typical doublet spectrum from a sample with a single orientation for θq whilst (b) shows the typical spectrum from a powder sample, i.e. where there is a spherical distribution of values of θq . This is known as a Pake powder pattern.

The two pronounced peaks in Fig. 14(b) arise from θq = 90o since in a spherical distribution this is the angle with the largest population. Measuring the peak to peak splitting from the Pake powder will give Δν =

Δν0 Δν0 (3 cos2 θq − 1) = − . 2 2

The minus sign simply refers to the fact that for θq = 90o the relative sizes of E−1 and E1 have been reversed. For practical purposes the sign can be ignored.

5 2 H NMR from Surfactant Water Systems Deuterium can be introduced into a surfactant system in two ways: either by specifically deuterating a protonated group on the surfactant molecule or by replacing the solvent water by 2 H2 O. The former type of experiment is more difficult to do but can provide information about the degree of orientational and motional order of the molecule or even a group on that molecule. The

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latter type of experiment is easy to achieve and can provide information on the orientational order and surface curvature of the surfactant aggregate and also on the fraction of water bound to the interfacial region. This information can lead to the identification and characterization of phase transitions within these systems. In the remainder of this chapter the information that can be obtained from the 2 H NMR of solvent 2 H2 O will be discussed although where appropriate results from specific deuteration will also be referred to. 5.1 Fraction of Bound Water The 2 H NMR spectra and quadrupolar splitting obtained from the 2 H of bound 2 H2 O molecules in lyotropic phases provides considerable information on their nature [31–33]. Rendall et al [31] have carried out a study of the concentration dependence of the quadrupolar splitting (Δν) recorded from 2 H2 O in non-ionic surfactants and concluded that its main component comes from the 2 H2 O bound to the first one or two ethylene oxide groups (EO) attached to the alkyl chain. Thus it may be considered that solvent 2 H2 O can effectively sit in two environments: one where they are associated with the aggregate water interface and one in free water. The bound molecules are in a dynamic exchange with the unbound molecules. If the exchange is fast, it will result in a smaller quadrupolar splitting, given by Δν = pf Δνf + pb Δνb where pi is the fraction of bound water at site i and the subscripts f and b refer to the free and bound sites for water. For free water Δνf is zero because of the rapid tumbling of the water molecule and Δν = pb Δνb . The measured splitting can be written Δν =

1 Δν0 p b (3 cos2 θq − 1) 2

(11)

5.2 Frames of Reference and Order Parameters The angle θq is not very convenient. There are three frames of reference and three associated angles which it is useful to use, Fig. 15. These are firstly the angle, θqi between the electric field gradient, eq and the normal to the interface, ˆi, secondly the angle, θin between the normal to the interface and the symmetry axis or director, n ˆ of the phase, and finally the angle, θnB between the director of the phase and the applied magnetic field, B 0 . In any experiment many water molecules are being considered and these will also be undergoing motional averaging so that (11) can be rewritten as 1 1 Δν = Δν0 p b Sqi (3 cos2 θin − 1) (3 cos2 θnB − 1) 2 2

(12)

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Fig. 15. Frames of reference and the associated angles used in the text.

where Sqi is the order parameter of the bound water molecules and is given by 1 Sqi = (3 cos2 θqi − 1) 2 In the case of a lamellar phase θin = 0◦ and (12) becomes 1 Δν = Δν0 p b Sqi (3 cos2 θnB − 1) 2 In contrast, for a hexagonal phase, where the director of the phase lies along the cylinder axes θin = 90◦ (12) becomes 1 Δν = −Δν0 p b Sqi (3 cos2 θnB − 1) 4 Notice therefore that there is a factor of two difference between Δν measured in the lamellar and hexagonal phases, all other parameters being equal. Where the phase has some intermediate structure, for example a mesh phase there will be diffusion of water molecules over the interfacial surface averaging the term 12 (3 cos2 θin − 1) and defining a new order parameter Sin which reflects the amount of curvature in the system and the degree of departure from a lamellar phase. Equation (12) becomes 1 Δν = Δν0 p b Sqi Sin (3 cos2 θnB − 1) (13) 2 For a lamellar phase Sin = 1 whilst for a bicontinuous cubic phase Sin = 0 and no powder pattern is observed, only a single line. A mesh phase will generally have 21 ≤ Sin ≤ 1.

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Finally in nematic phases the surfactant aggregate is small and is itself ˆ and B o motionally averaged about the B o axis. The relationship between n is well defined since n ˆ will align either parallel or perpendicular to B o [26]. The 2 H NMR spectrum shows well defined spectra such as, in the parallel case a single doublet or, in the perpendicular case a 2-dimensional powder pattern. Δν reflects the orientational order parameter of the aggregate itself, SnB defined by 1 SnB = (3 cos2 θnB − 1) 2 Equation (13) then becomes 1 Δν = Δν0 p b Sqi SnB (3 cos2 θni − 1) 2

(14)

In order to extract SnB assumptions must be made about the behavior of pb Sqi . The quadrupolar splitting Δν from a surfactant / 2 H2 O system reflects a number of factors; the degree of macroscopic order in the sample through the term (3 cos2 θnB − 1), the degree of surface curvature through Sin , and the hydration of the interface through pb . The technique is therefore useful not only to help determine phase structure but also to monitor changes of surface curvature and hydration with additives. It can also be used to investigate the macroscopic orientation of phases with the application of external fields such as electric, magnetic and shear fields. 5.3 Determination of Macroscopic Director Order The term (3 cos2 θnB −1) reflects the degree of director order in the sample and in all phases except nematic phases, this term is not motionally averaged. Fig. 16 shows some examples of 2 H NMR spectra taken from the C16 EO6 /2 H2 O system [34]. Fig. 16(a) shows a near perfect 3-dimensional Pake powder pattern; however notice that the θnB = 0◦ shoulders are slightly distorted indicating some departure from a true powder and probably reflecting partial ordering of n ˆ in this mesh phase along the field direction. In Fig. 16(b) there is a 2-dimensional powder pattern with pronounced peaks at the θnB = 0◦ positions. Fig. 16(c) shows a near perfect pattern with a single n ˆ orientation although there are weak θnB = 0◦ shoulders and also some infilling between the θnB = 90◦ peaks, denoting a second weaker external force e.g. surface orientation which is affecting a small percentage of the sample. Fig. 16(d) shows a poor 3-dimensional Pake powder pattern reflecting an intermediate state of director order probably caused by several conflicting external forces acting on n ˆ . It may also reflect the thermal history of the sample.

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Fig. 16. 2 H NMR spectra taken from the C16 EO6 /2 H2 O system [34]. (a) a 3dimensional Pake powder pattern, (b) a 2-dimensional powder pattern, (c) a pattern with a single n ˆ orientation and (d) a poor 3-dimensional Pake powder pattern reflecting an intermediate state of director order.

Determination of Phase Transitions 2

H NMR provides an excellent method for determining phase transitions; both their temperatures and type. Transitions from isotropic phases to ordered mesophases are easy to see from inspection of the spectra. It is also easy to see transitions between phases that are first order where there is a two phase region and the two phases coexist and change in proportion as the region is crossed, figures 17 and 18. In addition to the information provided by the spectra it is useful to plot the Δν taken from the inner peaks (θnB = 90◦ in (12) ) since that will reveal both first and second order phase transitions between mesophases. Fig. 19 shows Δν plotted as a function of temperature for the C16 EO6 / 2 H2 O system [23,34]. Starting at high temperature where SAXS shows there to be a lamellar phase, there is a slow increase in Δν with decreasing temperature reflecting the increasing hydration of the EO head groups through the term pb in (12) (see below). At 46◦ C Δν starts to decrease and SAXS measurements

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Fig. 17. 2 H NMR spectra taken from the C16 EO6 / 2 H2 O system [34] , at the following temperatures (a) 31◦ C, (b) 30◦ C, (c) 29◦ C, and (d) 27◦ C. The sample concentration is 51% by weight of C16 EO6 and the two phases present are the V1 (Ia3d) cubic phase (single isotropic line) and hexagonal phase (Pake powder).

Fig. 18. 2 H NMR spectra taken from the C16 EO6 / 2 H2 O system [34] , at the following temperatures (a) 24◦ C, (b) 27◦ C, and (c) 28◦ C. The sample concentration is 50% by weight of C16 EO6 and the two phases present are the gel phase, Lβ (outer doublet) and hexagonal phase (2-dimensional powder).

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Fig. 19. 2 H NMR spectra taken on cooling from the C16 EO6 / 2 H2 O system [34] with a sample concentration of 50% by weight of C16 EO6 . Closed points refer to the scale on the left, whilst open points refer to the scale on the right and are a replotting of the closed squares on an expanded scale to show details of the changes in gradient. Region A is a two phase region of V1 (Ia3d) cubic phase (single isotropic line) and Mh1 (R3m) phase. Region B is a V1 (Ia3d) cubic phase.

show there to be a random mesh phase, Mh1 (0). The transition from Lα to Mh1 (0) phase is virtually continuous and is likely to be second order or only very weakly first order. No two phase coexistence region is detected between the two phases. Similarly at 32.5◦ C where there is a transition from Mh1 (0) to Mh1 (R3m) phase, the transition is second order and not detectable by NMR. SAXS shows the transition is simply the ordering of already existing water filled pores into a positionally ordered structure. At 30◦ C the NMR clearly shows a two phase coexistence region (labeled A in Fig. 19) between Mh1 (R3m) and V1 (Ia3d) phases denoting a first order transition associated with the significant reorganization associated with the change in phase structure [21]. Notice that Δν for the Mh1 (R3m) phase is virtually constant in this region. In region B of Fig. 19 there is only a single isotropic line which agrees with the SAXS evidence of the V1 (Ia3d) phase. Finally below 25◦ C there is another two phase region composed of hexagonal phase, H1 and gel phase Lβ , again confirmed by SAXS. 2 H NMR is the best way of delineating the phase boundaries. Although it cannot definitively identify phases as can be done with SAXS, it can precisely fix the location of boundaries and two phase regions which can be difficult with SAXS. The two phase regions can also be useful in delineating boundaries of phases which exist at concentrations that are too high or are beyond the scope of the study. This is achieved using the lever rule and measuring the

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relative proportions of phases and how they change with concentration in regions which are experimentally accessible. 5.4 Determination of Order Parameters It is possible to extract information from Δν plotted as a function of temperature in Fig. 19 about the order parameter, Sin . At high temperature where SAXS shows there to be a lamellar phase, (12) becomes Δν =

1 Δν0 p b Sqi 2

(15)

and the slow increase in Δν with decreasing temperature reflects the increasing hydration of the EO head groups through the term pb . At 46◦ C Δν starts to decrease and SAXS measurements show there to be a random mesh phase, Mh1 (0). The decrease is driven by the increase in interfacial curvature around the water filled pores. Equation (12) is now Δν =

1 Δν0 p b Sqi Sin 2

(16)

The splitting Δν can be extrapolated from the lamellar phase to lower temperature. This assumes that all the temperature change comes from the increase in hydration, pb . The extrapolated values, Δν lam are the extrapolated values of Δν in the absence of a phase change. Taking the ratio between Δν and Δν lam gives a value for Sin and a measure of curvature in the mesh phase. From (15) and (16) Δν = Δν lam

1 2 Δν0 pb Sqi Sin 1 2 Δν0 pb Sqi

= Sin

(17)

Fig. 20 shows this for the results plotted in Fig. 19. The order parameter Sin , which is 1 in the lamellar phase, falls to about 0.7 in the Mh1 (0) phase reflecting the increase in surface curvature. In the hexagonal phase it has dropped to 0.6 which is slightly larger than the theoretical value of 0.5 (see above). This method rests on the assumption that pb is the only factor that changes with temperature in (15) and that this is approximately linear. In a recent paper Baciu et al [35] tested this hypothesis by also examining the behavior of α-deuterated surfactants. Sin determined by 2 H NMR from water or from the surfactant was found to be identical in both C12 EO5 and C16 EO6 systems. In the C12 EO5 system the minimum value of Sin in the mesh phase was again found to be about 0.65. 5.5 Summary 2 H NMR is able to provide an accurate method for the mapping of phase diagrams in surfactant water systems. It can identify first order phase transitions

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Fig. 20. The filled points show Δν as a function of temperature after Fig. 19. The heavy solid line is the extrapolation of Δν lam and the open points are the values of Sin calculated from (17) . Vertical lines represent the phase transitions after Fig. 19.

by the presence of two phase regions and also higher order transitions from the discontinuity in Δν when plotted as a function of temperature. Whilst the identification of the exact nature of phases from NMR can be ambiguous, its use in conjunction with X-ray scattering or optical polarizing microscopy can provide a powerful combination. NMR not only enables the mapping of phase diagrams but also allows the state of head group hydration and the interfacial curvature to be probed. This can be of particular value when investigating the effect of additives on the phase structure of these systems [36, 37].

6 Outlook Both of these techniques have been well used for many years for a wide variety of systems. However sometimes they are not used together. Recently there has been interest in using these systems as the basis for templating nanostructured materials. The addition of the metals or starting materials from which the templating takes place can disrupt the mesophase which is being used. It becomes important to be able to understand the variation of phase structure with additives which can be done easily with these techniques. A second area of interest may be the use of polar solvents and surfactants to act as templating media [38]. It will be interesting to see the development of the techniques for these novel systems.

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References 1. Fairhurst, C. E., Fuller, S., Gray, J., Holmes, M. C., Tiddy, G. J. T. In Handbook of Liquid Crystals, Demus, D., Gray, G. W., Goodby, J. W., Spiess, H. W., Vill, V., Eds., Wiley-VCH Verlagsgesellschaft mbH: Weinheim, Germany, 1998, pp 341-392. 2. Coleman, N. R. B., Attard, G. S. Microporous and Mesoporous Materials 2001, 44, 73-80. 3. Attard, G. S., Leclerc, S. A. A., Maniguet, S., Russell, A. E., Nandhakumar, I., Bartlett, P. N. Chem. Mater. 2001, 13, 1444. 4. Attard, G. S., Fuller, S., Tiddy, G. J. T. Journal of Physical Chemistry B 2000, 104, 10426-10436. 5. Attard, G. S., Edgar, M., Goltner, C. G. Acta Mater. 1998, 46, 751-758. 6. Fujii, H., Ohtaki, M., Eguchi, K. J. Am. Chem. Soc. 1998, 120, 6832-6833. 7. Yan, X. W., Chen, H. Y., Li, Q. Z. Acta Chim. Sin. 1998, 56, 1214-1217. 8. Tanford, C. The Hydrophobic Effect; Wiley: New York, 1973. 9. Holmes, M. C. Curr. Opin. Colloid Interface S. 1998, 3, 485-492. 10. International Tables For Crystallography; Fourth ed., Kluwer Academic: Dordrecht, Boston & London, 1995, Vol. A. 11. Guinier, A. X-ray Diffraction: In Crystals, Imperfect Crystals and Amorphous Bodies; Dover Publications: 1994. 12. Seddon, J. M., Templer, R. H. Phil. Trans. R. Lond. A 1993, 344, 377-401. 13. Luzzati, V., Tardieu, A., Gulik-Krzywicki, T., Rivas, E., Reiss-Husson, F. Nature 1968, 220, 485-488. 14. Luzzati, V. In Biological Membranes, Chapman, D., Ed., Academic Press: London and New York, 1968, pp 71-123. 15. Luzzati, V., Tardieu, A., Gulik-Krzywicki, T. Nature 1968, 217, 1028-1030. 16. Reiss-Husson, F., Luzzati, V. J. Phys. Chem. 1964, 68, 3504-3511. 17. Skoulios, A., Luzzati, V. Acta Crystallogr. 1961, 14, 278-286. 18. Luzzati, V., Mustacchi, H., Skoulios, A., Husson, F. Acta Crystallogr. 1960, 13, 660-667. 19. Husson, F., Mustacchi, H., Luzzati, V. Acta Crystallogr. 1960, 13, 668. 20. Holmes, M. C., Leaver, M. S. In Bicontinuous Liquid Crystals, Lynch, M. L., Spicer, P. T., Eds., CRC Press, Taylor & Francis Group, Boca Raton, 2005, pp 15-39. 21. Leaver, M. S., Fogden, A., Holmes, M. C., Fairhurst, C. E. Langmuir 2001, 17, 35-46. 22. Puntambekar, S., Holmes, M. C., Leaver, M. S. Liq. Cryst. 2000, 27, 743-747. 23. Fairhurst, C. E., Holmes, M. C., Leaver, M. S. Langmuir 1997, 13, 4964-4975. 24. Holmes, M. C., Charvolin, J., Reynolds, D. J. Liq. Cryst. 1988, 3, 1147-1155. 25. Holmes, M. C., Reynolds, D. J., Boden, N. J. Phys. Chem. 1987, 91, 5257-5262. 26. Boden, N., Radley, K., Holmes, M. C. Mol. Phys. 1981, 42, 493-496. 27. S¨ oderman, O., Stilbs, P. Prog. Nucl. Magn. Reson. Spectros. 1994, 26, 445-482. 28. Halle, B., Quist, P.-O., Fury, I. Liq. Cryst. 1993, 14, 227-263. 29. Lindblom, G., Oradd, G. Prog. Nucl. Magn. Reson. Spectros. 1994, 26, 483-515. 30. Harris, R. K. Nuclear Magnetic Resonance Spectroscopy; Longman Scientific & Technical: 1986. 31. Rendall, K., Tiddy, G. J. T. J. Chem. Soc. ,Faraday Trans. 1 1984, 80, 33393357.

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32. Rendall, K., Tiddy, G. J. T., Trevethan, M. A. J. Colloid Interface Sci. 1984, 98, 565-571. 33. Rendall, K., Tiddy, G. J. T., Trevethan, M. A. J. Chem. Soc., Faraday Trans. 1 1983, 79, 637-649. 34. Burgoyne, J., Holmes, M. C., Tiddy, G. J. T. J. Phys. Chem. 1995, 99, 60546063. 35. Baciu, M., Olsson, U., Leaver, M. S., Holmes, M. C. J. Phys. Chem. B 2006, 110, 8184-8187. 36. Baciu, M., Holmes, M. C., Leaver, M. S. J. Phys.Chem. B 2007, 111, 909-917. 37. Wang, Y., Holmes, M. C., Leaver, M. S., Fogden, A. Langmuir, 2006, 22, 1095110957 38. Warnheim, T. Curr. Opin. Colloid Interface S. 1997, 2, 472-477.

Polyelectrolyte Diblock Copolymer Micelles Small Angle Scattering Estimates of the Charge Ordering in the Coronal Layer Johan R. C. van der Maarel National University of Singapore, Department of Physics, 2 Science Drive 3, Singapore, 117542

1 Introduction Amphiphilic diblock copolymers with a polyelectrolyte block comprise two linearly attached moieties: a charged and a hydrophobic chain part. Owing to their specific properties and the increased need of water supported polymer materials, these copolymers have found widespread applications from the stabilization of colloidal suspensions, through encapsulation and delivery of bioactive agents, to the control of gelation, lubrication, and flow behavior [1,2]. Besides these technological applications, progress in this area also has implications for biophysics. Polyelectrolyte brushes are a model system for the external envelope of certain microorganisms (glycocalix) and are thought to play a role in, e.g., cell recognition and cushioning properties of synovial fluid [3, 4]. The hydrophobic attachment provides a mechanism for self-assembling of the copolymers into units of mesoscopic size, which are large compared to the molecular dimensions. Major factors controlling the self-assembled structures are solvent composition, charge, ionic strength, and chemical nature and the respective sizes of the blocks. For ionic diblocks of poly(styrene-block -acrylate) (PS-b-PA) with a polyelectrolyte (PA) block length smaller than the length of the polystyrene (PS) block, a multitude of different “crew-cut” structures has been observed by Eisenberg and coworkers [5–7]. These structures include hexagonal wormlike cylinders, lamellae, and (compound) vesicles (see Fig. 1). If the length of the core-forming block is comparable to or smaller than the length of the corona-forming block, it was observed that the copolymers associate to form spherical micelles with a hydrophobic core and a polyelectrolyte corona (Fig. 2). It should be noticed, however, that due to the high glass temperature (363 K) of the PS-block, the observed structures are in a frozen meta-stable state and they depend critically on how the samples are prepared. Once the structures are formed after cooling below the glass temperature, the functionality (i.e., aggregation number) and morphology are fixed. We can use this phenomenon however to our advantage, because the frozen structures

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provide excellent model systems to investigate the properties of the interfacial polyelectrolyte brush without complications related to copolymer rearrangements and concomitant changes in morphology.

Fig. 1. Asymmetric amphiphilic block copolymers in solution. Transmission electron micrographs reprinted from [7].

Fig. 2. A schematic drawing of a polyelectrolyte copolymer micelle. The polyelectrolyte corona surrounds the hydrophobic core. The ions are trapped in the coronal layer.

Here, we review our studies of spherical micelles of PS-b-PA polyelectrolyte diblock copolymers with degree of polymerization 20 and 85 of the PS and PA blocks, respectively. At ambient temperature, the PS core is in a glassy state,

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which results in micelles with fixed core size and functionality (the glass temperature of PS, Tg = 363 K). The PA corona charge is pH dependent and we will first show with infrared (IR) spectroscopy that the corona charge can be varied between almost zero and full (100%) charge where every monomer carries an ionized group. Transmission electron microscopy (TEM) will be used to verify the micelle morphology. Then we will move on to the investigation of the core and corona size and its relation to charge, screening, and counterion distribution with small angle neutron and X-ray scattering techniques (SANS and SAXS). The main results of these scattering studies are osmotic starbranched polyelectrolyte behavior, full corona chain stretching at high charge and minimal screening conditions, and robustness of the coronal layer against the salinity generated by the addition of salt [8–10]. This behavior is strikingly different from the situation for uncharged spherical polymer brushes and/or star-branched polymers, where the chains take a compact, coiled conformation [11–15]. At low degrees of ionization, the corona charges migrate to the outer micelle region due to the recombination/dissociation balance of the weak polyacid (charge annealing) [16]. We will show that the radial density profile of the counterions is very close to the one for the corona forming copolymer segments and that most, if not all counterions are adsorbed in the coronal layer [17, 18]. We will also review SANS and SAXS experiments on our model system up to concentrations where the coronas have to shrink and/or interpenetrate in order to accommodate the micelles in the increasingly crowded volume [19, 20]. In the latter studies, it is observed that, irrespective of ionic strength, the corona shrinks with increasing packing fraction. At high charge and minimal screening conditions, the corona layers eventually interpenetrate once the volume fraction exceeds a certain critical value. Finally, we will show that this interpenetration of the arms of the micelle has a profound effect on the fluid rheology.

2 Small Angle Neutron and X-Ray Scattering From intensities to structure factors. The structure factors describing the density correlations of the PS and PA copolymer blocks are obtained with SANS and contrast matching in water by variation of the H2 O/D2 O solvent composition. We will also review SANS experiments in which the structural arrangement of tetramethylammonium (TMA+ ) counterions in the coronal layer of PS-b-PA micelles (PS-b-TMAPA) is investigated. The use of TMA+ counterions instead of Na+ allows contrast variation by isotope labeling of the counterion. For this purpose, a fraction of the TMA counterions is labeled by deuteration, while the contributions to the scattering related to the PA-blocks are blanked by contrast matching in water. In the case of our SAXS experiments, we have neutralized the polyelectrolyte copolymer with CsOH. Since the Cs+ ion is much heavier (atomic number Z = 55) than the organic copolymer atoms, the scattering is dominated by the counterions in

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the coronal layer. Accordingly, the SAXS intensity is directly proportional to the counterion structure factor, but there is also a small contribution from the copolymer. For a diblock PS(NP S )-b-PA(NP A ) copolymer solution, with NP S and NP A the number of monomers of the PS and PA block, respectively, it is convenient to consider the blocks as the elementary scattering units [21]. Every PS block is attached to a PA block, and, hence, the macroscopic block concentrations exactly match the copolymer concentration ρP S = ρP A = ρ. The coherent part of the solvent corrected scattering intensity is given by  ¯bi¯bj Ni Nj Sij (q) (1) I(q)/ρ = i,j

where the summation runs over all structure factors Sij (q) pertaining to the density correlations among the solutes (i = j = PS, PA, and TMA; Sii is abbreviated as Si ) and solute pairs (i = j). The scattering length contrast vs , where the solute (i) and solvent (s) have scattering reads ¯bi = bi − bs v¯i /¯ lengths bi and bs and partial molar volumes v¯i and v¯s , respectively. Here, the contrast is matched either in water by variation of bs through the H2 O/D2 O solvent composition (PS and PA) or by variation of bi through deuteration of the counterion (TMA). Momentum transfer q is defined by the wavelength λ and scattering angle θ between the incident and scattered beam according to q = 4π/λ sin (θ/2). The partial structure factors Sij (q) are the spatial Fourier transforms of the density correlation functions  −1 ρ (q) = dr exp (−iq · r) ρi (0)ρj (r) (2) Sij V

In a selective solvent, the copolymers form spherical aggregates with a hydrophobic PS block core and a polyelectrolyte PA block corona. If the radial density of the corona is assumed to be invariant to fluctuations in inter-micelle separation, the structure factor Eq. (2) takes the form −1 Sij (q) = Nag Fi (q)Fj (q) Scm (q)

(3)

with the micelle aggregation number Nag , the form factor amplitude Fi (q), and the micelle center of mass structure factor Scm (q). In the absence of interactions between the micelles and/or at sufficiently high values of momentum transfer Scm (q) reduces to unity. The form factor amplitude Fi (q) can be expressed in terms of the radial core (i = PS) or corona (i = PA) density ρi (r)   dr exp (−iq · r) ρi (r) = drsin (qr)/(qr)4πr2 ρi (r) (4) Fi (q) = Vmicelle

The scattering amplitudes are normalized to Nag