Nanocrystals Forming Mesoscopic Structures

Nanocrystals Forming Mesoscopic Structures Edited by Marie-Paule Pileni

Editor Prof. Marie-Paule Pileni University Pierre et Marie Curie Laboratoire LM2N, UMR CNRS 7070 4 Place Jussieu 75231 Paris France

& This book was carefully produced. Nevertheless,

editors, authors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de.  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Cover Design SCHULZ Grafik-Design, Fußgönheim Composition ProsatzUnger, Weinheim Printing betz-druck GmbH, Darmstadt Bookbinding Litges & Dopf Buchbinderei GmbH, Heppenheim Printed in the Federal Republic of Germany Printed on acid-free paper ISBN-13: 978-3-527-311705 ISBN-10: 3-527-31170-X

V

Contents List of Contributors 1

1.1 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.3 1.3.1 1.3.2 1.3.3 1.3.3.1 1.3.3.2 1.4 1.4.1 1.4.1.1 1.4.1.2 1.4.2 1.4.3 1.4.3.1 1.4.3.2 1.4.3.3 1.5 1.5.1

XIII

Self-Organization of Inorganic Nanocrystals 1 Laurence Motte, Alexa Courty, Anh-Tu Ngo, Isabelle Lisiecki, and Marie-Paule Pileni Introduction 1 Surface Modification of Nanocrystals and Interparticle Forces in Solution 2 Van der Waals Forces 4 Magnetic Dipolar Forces 4 Electrostatic Forces 5 Steric Forces 5 Solvation Forces 5 What is Required to Provide Highly Ordered Self-Assemblies? 6 Nanocrystal Size Distribution Effect 6 Substrate Effect 6 Capillary Forces 8 Solvent Evaporation Process 8 Application of a Magnetic or Electric Field During the Evaporation Process 9 Self-Assemblies in the Absence of External Forces 9 Control of the Interparticle Gap Via the Coating Agent 16 Silver Sulfide Nanocrystals 16 Silver Nanocrystals 17 Influence of the Substrate 19 Thermal and Time Stabilities 24 Crystallinity Improvement Related to the Atomic and Nanocrystal Ordering 24 A New Approach to Crystal Growth 27 Stability with Time 29 Self-Assemblies in the Presence of External Forces and Constraints 31 Fluid Flow 31

Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

VI

Contents

1.5.2 1.5.2.1 1.5.2.2 1.6

Application of a Magnetic Field 34 Applied Field Parallel to the Substrate 34 Applied Field Perpendicular to the Substrate 40 Conclusion 45 References 45

2

Structures of Magnetic Nanoparticles and Their Self-Assembly 49 Zhong L. Wang,Yong Ding, and Jing Li Introduction 49 Phase Identification of Nanoparticles 49 Core–Shell Nanoparticles 49 FePt/Fe3Pt Nanocomposites 55 Determining the Nanoparticle Shapes and Surfaces 58 The Shape of Fe3O4 Nanoparticles 59 The Shapes of FePt Nanoparticles 60 Multiply Twinned FePt Nanoparticles 61 Phase Transformation and Coalescence of Nanoparticles 65 Self-Assembled Nanoarchitectures of Fe3O4 Nanoparticles 69 Summary 72 References 73

2.1 2.2 2.2.1 2.2.2 2.3 2.3.1 2.3.2 2.4 2.5 2.6 2.7

3

3.1 3.2 3.2.1 3.2.2 3.3 3.4 3.5 3.6

4 4.1 4.2 4.2.1 4.2.1.1

Self-Organization of Magnetic Nanocrystals at the Mesoscopic Scale: Example of Liquid–Gas Transitions 75 Johannes Richardi and Marie-Paule Pileni Introduction 75 Simulation Studies of Liquid–Gas Transitions (LGT) in Colloids and Dipolar Systems 76 Liquid–Gas Transitions in Colloids 76 Liquid–Gas Transition in Dipolar Systems 77 Orientational and Structural Correlations in Dipolar Fluids 79 Mesoscopic Organization of Magnetic Nanocrystals in a Parallel Field 80 Mesoscopic Organization of Magnetic Nanocrystals in a Perpendicular Field 82 Conclusion 87 References 87 In Situ Fabrication of Metal Nanoparticles in Solid Matrices 91 Junhui He and Toyoki Kunitake Introduction 91 In Situ Fabrication of Metal Nanoparticles in Films 92 In Situ Fabrication of Metal Nanoparticles in Inorganic Films 92 In Situ Fabrication of Metal Nanoparticles in Mesoporous Inorganic Films 92

Contents

4.2.1.2 4.2.1.3 4.2.2 4.2.3 4.3 4.3.1 4.3.2 4.4 4.4.1 4.4.2 4.4.3 4.5

5 5.1 5.2 5.2.1 5.2.2 5.2.2.1 5.2.2.2 5.2.2.3 5.2.3 5.2.3.1 5.2.3.2 5.2.3.3 5.2.3.4 5.2.3.5 5.2.3.6 5.2.4 5.2.4.1 5.2.4.2 5.2.5 5.3 5.3.1

In Situ Fabrication of Metal Nanoparticles in Metal Oxide Ultrathin Films: the Surface Sol–Gel Process 95 In Situ Fabrication of Metal Nanoparticles in TiO2 Films Prepared from Anatase Sol by Spin-Coating 99 In Situ Fabrication of Metal Nanoparticles in Polymeric Films 101 In Situ Fabrication of Metal Nanoparticles in Layer-by-Layer Assembled Polyelectrolyte Thin Films 104 In Situ Fabrication of Metal Nanoparticles in Nonfilm Solid Matrices 106 In Situ Fabrication of Metal Nanoparticles in Inorganic Matrices 107 In Situ Fabrication of Metal Nanoparticles in Polymeric Matrices 110 Physicochemical Properties 112 Catalytic Properties 113 Optical Properties 113 Magnetic Properties 114 Summary and Outlook 115 References 115 Three-Dimensional Self-Assemblies of Nanoparticles 119 Sachiko Matsushita and Shin-ya Onoue Introduction 119 Mesoscopic Assembly of Inorganic Nanoparticles in Molecular Matrixes 120 Introduction 120 Random Assemblies of Inorganic Nanoparticles by Various Triggers 120 pH and Ions 121 Small Molecules and Polymers 121 Biological Components (Programmed Assemblies and Sensors) 121 Versatile Assemblies of Inorganic Nanoparticles Guided by Designable Templates: Superstructures and 1D and 3D Assemblies 123 Langmuir–Blodgett Films 123 Amphiphiles and Surfactants 124 Gels (Networks) 124 Polymer and DNA as a Template 124 Inorganic Templates 125 Others 126 Layer-by-Layer Assemblies Embedded with Inorganic Nanoparticles 126 Multifunctional Molecules and Polymers 127 Inorganic Molecules 127 “Key and Vision” for Future Development 128 Three-Dimensional Self-Assemblies via Nanoparticle Interactions 129 Liquid Colloidal Crystals 129

VII

VIII

Contents

5.3.1.1 5.3.1.2 5.3.1.3 5.3.1.4 5.3.2 5.3.2.1 5.3.2.2 5.3.2.3 5.3.2.4 5.3.3 5.3.3.1 5.3.3.2 5.3.4 5.3.4.1 5.3.4.2 5.3.4.3 5.3.5 5.4 5.4.1 5.4.2 5.4.3 5.4.4

6

6.1 6.2 6.3 6.4 6.5 6.6 6.7

Control of the Lattice Structure 130 Control of the Orientation 131 Overcoming the Mechanical Fragility 133 Self-Assembly Preparations for Complicated Structures 133 Solid Colloidal Crystals 135 Control of the Orientation 136 Control of the Lattice Structure 137 Overcoming the Slow Growth Rate 137 Self-Assembly Preparations for Complicated Structures 137 Two-Dimensional Colloidal Crystals 137 Various Preparation Methods 140 Control of the Lattice Structure 142 Processing of Self-Assembled Structures 143 Submicrostructures Formed by Reactive Ion Etching in 3D Self-Assembled Structures 143 Flexible Self-Assembled Structures 144 Freestanding Colloidal Crystals 144 Dissipative Process for Fabrication of 3D Self-Assembly 145 Applications of Three-Dimensional Self-Assemblies of Nanoparticles 145 Photonic Crystals 148 Sensing Materials 150 Optical Switches 150 Optical Memory Media 150 References 151 Dissipative Structures and Dynamic Processes for Mesoscopic Polymer Patterning 157 Masatsugu Shimomura Introduction 157 Formation of Dissipative Structures in Drying Polymer Solutions 159 Regular Pattern Formation of Deposited Polymers After Solvent Evaporation 160 Preparation of Honeycomb-Patterned Polymer Films 164 Processing of Honeycomb Patterns 166 Application of Regularly Patterned Polymer Films 167 Conclusion 169 References 169

Contents

7

7.1 7.2 7.2.1 7.2.2 7.3 7.3.1 7.3.2 7.3.3 7.3.3.1 7.3.3.2 7.3.3.3 7.3.4 7.3.5 7.3.5.1 7.3.5.2 7.4 7.4.1 7.4.2 7.4.3 7.5 7.5.1 7.5.2 7.5.3 7.6 7.6.1 7.6.2 7.6.3 7.6.4 7.6.5 7.7

8

8.1 8.2 8.2.1 8.2.2 8.2.2.1

Self-Assemblies of Anisotropic Nanoparticles: Mineral Liquid Crystals 173 Patrick Davidson and Jean-Christophe P. Gabriel Introduction 173 Basic Principles and Investigation Techniques 174 Basic Principles 174 Investigation Techniques 177 Nematic Phases 178 The Onsager Model 179 Rigid Rodlike Nanoparticles 180 Semiflexible Wires, Ribbons, and Tubules 181 Li2Mo6Se6 Wires 181 V2O5 Ribbons 182 Imogolite Nanotubules 189 Nanorods, Nanowires, and Nanotubes: A Wealth of Potential New MLCs 189 Disklike Nanoparticles 190 Clays 190 Gibbsite Nanodisks 193 Lamellar Phases 195 Numerical Simulations 195 “Schiller Layers” 196 Suspensions of H3Sb3P2O14 and HSbP2O8 Nanosheets 196 Columnar Phases 199 Numerical Simulations 199 Two-Dimensional Phases of Rodlike Particles 200 Hexagonal Phase of Disklike Particles 201 Physical Properties and Applications 202 Rheological Properties 202 Composite Materials 204 The Outstanding Magnetic Properties of Goethite Nanorods 205 Electric Field Effects 207 The Use of Mineral Liquid-Crystalline Suspensions for the Structural Determination of Biomolecules 207 Conclusion 209 References 210 Collective Properties Due to Self-Organization of Silver Nanocrystals 213 Arnaud Brioude, Alexa Courty, and Marie-Paule Pileni Introduction 213 Results and Discussion 214 Intrinsic Properties Due to “Supra” Crystal Formation 216 Dipolar Interactions 218 Absorption Spectroscopy 218

IX

X

Contents

8.2.2.2 8.2.2.3 8.2.2.4 8.3

Reflectivity Measurements 220 Polarized Electron Spectroscopy 225 STM-Induced Photon Emission 226 Conclusion 228 References 228

9

Scanning Tunneling Luminescence from Metal Nanoparticles Fabrice Charra Introduction 231 Mechanisms of Scanning Tunneling Luminescence 232 Electromagnetic-Field-Assisted Inelastic Tunneling 233 Local Plasmon Modes 234 Experimental Details 235 Tip-Formed Protrusions 236 Colloidal Silver Nanoparticles 238 Single-Particle Contact by STM 239 Collective Plasmon Modes 240 Individual-Site Dependence of Luminescence 243 Tip-Modified Luminescence 246 Conclusion 248 References 249

9.1 9.2 9.2.1 9.2.2 9.3 9.4 9.5 9.5.1 9.5.2 9.5.3 9.5.4 9.6

10

10.1 10.2 10.2.1 10.2.2 10.2.3 10.3 10.3.1 10.3.2 10.4 10.4.1 10.4.2 10.4.3 10.4.4 10.4.5 10.4.5.1 10.4.5.2

231

Collective Magnetic Properties of Organizations of Magnetic Nanocrystals 251 Christophe Petit, Laurence Motte, Anh-Tu Ngo, Isabelle Lisiecki, and Marie Paule Pileni Introduction 251 General Principles of the Magnetism of Nanoparticles: Theory and Investigation 252 Magnetocrystalline Anisotropy Energy and Blocking Temperature 253 Magnetic Characterization from the Hysteresis Curves 254 Demagnetizing Fields 254 Origin of the Collective Properties in Mesoscopic Structures of Magnetic Nanocrystals 255 Orientation of the Easy Magnetic Axes 255 Dipolar Interactions 256 Collective Magnetic Properties of Mesostructures Made of Magnetic Nanocrystals 256 Materials and Mesoscopic Structures 257 Bidimensional (2D) Organization of Cobalt Nanocrystals 257 Three-Dimensional (3D) Organizations of Cobalt Nanocrystals 259 Does the Internal Order Play a Role? 260 Does the Structure Play a Role? 263 Linear Chains of Cobalt Nanocrystals 263 Patterned 3D Film of Magnetic Nanoparticles 266

Contents

10.4.5.2.1 10.4.5.2.2 10.5 10.5.1 10.5.2 10.6

11

11.1 11.2 11.3 11.4 11.5 11.6 11.7

12 12.1 12.2 12.2.1 12.2.2 12.2.3 12.3 12.3.1 12.3.2 12.4 12.4.1 12.4.2 12.4.3 12.5

13

Surface-Structured 3D Film 267 Tubelike-Structured 3D Film: Effect of a Volumic Texturation 269 Towards Collective Magnetic Properties at Room Temperature 270 Cigar-Shaped Maghemite Nanocrystals Organized in 3D Films 270 Organization of Cobalt Nanocrystals with High Magnetic Anisotropy Energy 272 Conclusion 276 References 277 Exploitation of Self-Assembled Nanostructures in Optical Biosensors 279 Janos H. Fendler Introduction 279 Substrate Preparation 280 Preparation of Self-Assembled Monolayers 282 Monolayer-Protected Metallic Particles 284 Layer-by-Layer Self-Assembled Ultrathin Films 284 Surface Plasmon Resonance Spectroscopy and Transmission Resonance Surface Plasmon Resonance Spectroscopy 286 Gold-Nanoparticle-Enhanced Surface Plasmon Resonance Spectroscopy 289 References 292 Nano Lithography 295 Dorothée Ingert and Marie-Paule Pileni Introduction 295 Colloidal Lithography: Spheres Lithography 296 Ordered-Particle Arrays: Nanosphere Lithography (NSL) Nonorganized particle patterns 297 Applications 297 Colloidal Lithography: Copolymer Lithography 298 Block Copolymer Used as a Lithographic Mask 298 Hierarchical Pattern 299 Colloidal Lithography: Nanocrystals 300 Process 301 Mesoscale 301 Nanoscale 302 Conclusion 304 References 304 Shrinkage Cracks: a Universal Feature 307 Marie-Paule Pileni References 316 Subject Index 317

296

XI

XIII

List of Contributors Arnaud Brioude Laboratoire des Matériaux Mésoscopiques et Nanométriques LM2N, UMR-CNRS 7070 Université P. et M. Curie 4 Place Jussieu 75005 Paris France Fabrice Charra Service de Physique et Chimie des Surfaces et Interfaces Département de Recherche sur l’État Condensé, les Atomes et les Molécules Direction des Sciences de la Matière Commissariat à l’Énergie Atomique CEA Saclay 91191 Gif-sur-Yvette cedex France Alexa Courty Laboratoire des Matériaux Mésoscopiques et Nanométriques LM2N, UMR-CNRS 7070 Université P. et M. Curie 4 Place Jussieu 75005 Paris France

Patrick Davidson Laboratoire de Physique des Solides Bat. 510 Université Paris-Sud 91405 Orsay cedex France Yong Ding School of Materials Science and Engineering Georgia Institute of Technology Atlanta, GA 30332-0245 USA Janos H. Fendler Department of Chemistry and Center for Advanced Materials Processing Clarkson University Potsdam, NY 13699 USA Jean-Christophe P. Gabriel Nanomix Inc. 5980 Horton Street, Suite 600 Emeryville, CA 94608 USA

Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

XIV

List of Contributors

Junhui He Frontier Research System The Institute of Physical and Chemical Research (RIKEN) 2-1 Hirosawa,Wako Saitama 351-0198 Japan and Technical Institute of Physics and Chemistry The Chinese Academy of Sciences Chaoyangqu, Datunlu Jia 3 Beijing 100101 China Dorothe´e Ingert Laboratoire des Matériaux Mésoscopiques et Nanométriques LM2N, UMR-CNRS 7070 Université P. et M. Curie 4 Place Jussieu 75005 Paris France

Sachiko Matsushita Frontier Research System The Institute of Physical and Chemical Research (RIKEN) 2-1 Hirosawa,Wako Saitama 351-0198 Japan Laurence Motte Laboratoire des Matériaux Mésoscopiques et Nanométriques LM2N, UMR-CNRS 7070 Université P. et M. Curie 4 Place Jussieu 75005 Paris France Anh-Tu Ngo Université P. et M. Curie Laboratoire LM2N, Bat F, BP 52 4 Place Jussieu 75252 Paris cedex 05 France

Toyoki Kunitake Frontier Research System The Institute of Physical and Chemical Research (RIKEN) 2-1 Hirosawa,Wako Saitama 351-0198 Japan

Shin-ya Onoue Frontier Research System The Institute of Physical and Chemical Research (RIKEN) 2-1 Hirosawa,Wako Saitama 351-0198 Japan

Jing Li School of Materials Science and Engineering Georgia Institute of Technology Atlanta, GA 30332-0245 USA

Christophe Petit Laboratoire des Matériaux Mésoscopiques et Nanométriques LM2N, UMR-CNRS 7070 Université P. et M. Curie 4 Place Jussieu 75005 Paris France

Isabelle Lisiecki Université P. et M. Curie Laboratoire LM2N, Bat F, BP 52 4 Place Jussieu 75252 Paris cedex 05 France

List of Contributors

Marie-Paule Pileni Laboratoire des Matériaux Mésoscopiques et Nanomètriques, LM2N Université P. et M. Curie U.M.R 7070, BP 52 4 Place Jussieu 75005 Paris France Johannes Richardi Laboratoire des Matériaux Mésoscopiques et Nanométriques LM2N, UMR-CNRS 7070 Université P. et M. Curie 4 Place Jussieu 75005 Paris France

Masatsugu Shimomura Nanotechnology Research Center Research Institute for Electronic Science Hokkaido University and Spatio-Temporal Function Materials Research Group Frontier Research System RIKEN Institute and CREST, Japan Science and Technology Agency N21W10, Sapporo, 001-0021 Japan Zhong L. Wang School of Materials Science and Engineering Georgia Institute of Technology Atlanta, GA 30332-0245 USA

XV

1

1 Self-Organization of Inorganic Nanocrystals Laurence Motte, Alexa Courty, Anh-Tu Ngo, Isabelle Lisiecki, and Marie-Paule Pileni

1.1 Introduction

Self-organization of inorganic nanocrystals opens a new and challenging area in nanotechnology [1, 2]. We already know that nanomaterials are a new generation of advanced materials that are expected to exhibit unusual chemical and physical properties, different from those of either the bulk materials or isolated nanocrystals [3–5]. Engineering of nanophase materials and devices is of great interest in several domains such as electronics, semiconductors, optics, catalysis, and magnetism. During the past decade, nanocrystal research has been focused on two major properties of finite-size materials: quantum size effects and surface/interface effects [6, 7]. A new trend, however, has emerged in the past few years: the arrangement of the nanocrystals into two- and three-dimensional (2D and 3D) superlattices. It was found that inorganic nanocrystals are able to self-assemble in compact hexagonal networks [8], rings [9, 10], lines [11, 12], stripes [13], tubes [14, 15], columns and labyrinths [16–18], and in large “supra” crystals characterized by a face centered cubic (fcc) structure [8, 19–23]. The physical properties of such mesoscopic assemblies differ from those of isolated nanocrystals and from the bulk phase [1, 2]. Furthermore, the mesoscopic structure itself is also a key parameter in the control of the physical properties [11, 15, 24–26]. In the last five years, collective magnetic, optical, and transport properties were demonstrated [1]. They are mainly due to dipole–dipole interactions. Intrinsic properties due to self-organization also open a new research area, which concerns the physical, chemical, and mechanical properties of these assemblies. Recently it has been demonstrated that vibrational coherences of nanocrystals occur when they are organized in fcc structures [27]. These coherences could explain the change in the transport properties observed previously with silver nanocrystal self-organizations [28]. Similarly, a gentle annealing process (below 50 8C) produces large monocrystals like those observed under ultravacuum by epitaxial growth [29]. This opens a new approach in the crystal growth mechanism. The nanocrystals can also be used as masks for Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

2

1 Self-Organization of Inorganic Nanocrystals

nanolithography and their self-assemblies are then transferred onto a substrate, which is a completely new technique in this field [30, 31]. The nanocrystal stability in an annealing process is markedly improved by the self-organization [32]. All these new approaches make it possible to claim that self-organization of nanocrystals opens a large number of new research areas which involve many of the present research domains. Several groups have obtained 2D and 3D superlattices of various nanomaterials such as semiconductors (Ag2S, CdSe, PbSe) [8, 19, 33, 34], metals (Ag [20, 21, 27, 29, 35–46], Au [47–62], Pd and Pt [63, 64], Co [11, 13, 22, 23, 25, 26, 32, 65–70] etc.), and oxides (ferrites) [71, 72]. The most common crystalline structure of these organizations is hexagonal at 2D and fcc at 3D. The nanocrystal self-organization is induced by “internal” forces already present in the system. For nanometer-size particles, these forces are usually van der Waals interactions and capillarity forces. Furthermore, the 2D and 3D superlattices are most often obtained by evaporation of a size-selected nanocrystal solution on a substrate. Thus, the particle–particle and particle–substrate interactions have to be taken into account in their formation. Moreover, the solvent plays a role in the nanocrystal self-organization through wetting properties, and it interacts with the substrate and the nanocrystals via the capillarity forces. Other types of mesoscopic nanocrystal organizations such as rings [9, 10, 73, 74], chains and ribbons [11–15, 24–26, 75–82], columns and labyrinths [16–18] etc. are obtained by application of “external” forces (temperature gradient, magnetic field, pressure) during the solvent evaporation process. This chapter is divided into four major parts. In the first two parts, the various forces involved in nanocrystal self-organizations are described. In the third and fourth parts, the formation of 2D and 3D assemblies in the absence or presence of external forces, and the parameters controlling the ordering and/or the mesoscopic shapes of the nanocrystal assemblies are discussed.

1.2 Surface Modification of Nanocrystals and Interparticle Forces in Solution

To produce well-defined 2D and 3D superlattices of nanocrystals, highly stable materials are needed. Furthermore various forces have to be taken into account. Let us first list the various parameters involved in the nanocrystal self-assemblies. Due to van der Waals interactions, particles in the nanometer-size range have a strong tendency to agglomerate (Fig. 1.1). It is therefore important to develop synthetic methods by which the particles can be stabilized, i. e., where repulsive and attractive forces between particles balance each other. Mainly electrostatic and steric forces prevent agglomeration of nanoparticles. Electrostatic stabilization involves creation of an electrical double layer arising from ions adsorbed on the surface and associated counterions that surround the particle. Thus, if the electric potential associated with the double layer is sufficiently high, the Coulombic repulsions between the particles prevent their agglomeration (Fig. 1.2 A). Steric stabili-

1.2 Surface Modification of Nanocrystals and Interparticle Forces in Solution

Fig. 1.1 Uncharged particles are free to collide and agglomerate.

zation is achieved by adsorption of organic molecules containing suitable functional groups, such as –SH, –COOH, and –NH2, at the particle surface (Fig. 1.2 B). Indeed, the lengths of the alkyl chains are usually greater than the range over which the attraction forces between nanocrystals are active. In addition, dipolar magnetic interactions are to be taken into account for single-domain magnetic nanocrystals. Hence the stability of a colloidal solution is governed by the total interparticle potential energy Vtotal, which can be expressed as: Utotal ˆ UvdW ‡ Udd ‡ Uelec ‡ Usteric

…1†

where UvdW, Udd , Uelec , and Usteric are the attractive potential energy due to longrange van der Waals interactions between particles, the attractive potential energy

Fig. 1.2 Schematic illustration of the interaction potential energy and relevant length scales for (A) electrostatic and (B) steric contributions, where k–1 is the effective double-layer thickness and d the adlayer thickness.

3

4

1 Self-Organization of Inorganic Nanocrystals

due to long-range dipolar interactions between magnetic particles, the repulsive potential energy resulting from electrostatic interactions between like-charged particle surfaces, and the repulsive potential energy resulting from steric interactions between particle surfaces coated with adsorbed organic molecules, respectively. 1.2.1 Van der Waals Forces

UvdW exhibits a power-law distance dependence whose strength varies with the Hamaker constant and a geometrical factor [83, 84]. The Hamaker constant (Ap–o–p) depends on the dielectric properties of the interacting colloidal particles (p) and intervening solvent (oil) and it is higher for metallic materials than for semiconductors. The geometrical factor depends on the particle size and the contact distance between nanocrystals. For spherical particles (i, j ) of equal size, UvdW is given by the Hamaker expression: 8 !9 rij2 d2 = Ap o p < d2 d2   ‡ 2 ‡ 2 ln …2† UvdW ˆ ; 12 : r 2 d2 rij rij2 ij where Ap–o–p, d, and rij are the Hamaker constant, the particle diameter, and the distance between the particles (r = d + l with l the distance of separation), respectively. At the minimum separation distance, the l value is directly correlated to the surface coating agent and Uvdw scale as l –1 : UvdW ˆ

Ap o 24

p

  d l

…3†

1.2.2 Magnetic Dipolar Forces

The magnetic dipolar energy between spherical nanocrystals of equal size and with the same magnetic properties is expressed as [85]: 8 9
m2 4pm0 …d ‡ l†3

…5†

When this dipolar energy is larger than 3kT, it is expected that there will be a spontaneous organization of the nanocrystals in linear chains [86].

1.2 Surface Modification of Nanocrystals and Interparticle Forces in Solution

1.2.3 Electrostatic Forces

The electrostatic potential energy between charged particles, Uelec , exhibits an exponential distance dependence whose strength varies with the surface potential induced on the interacting colloidal particles and with the dielectric properties of the intervening medium [87]. Exact analytical expressions for the electrostatic potential energy cannot be given. Therefore, analytical approximations or numerical solutions are used. For equal-size spherical particles that approach one another under constant potential conditions, Uelec is given by: Uelec ˆ per e0 dC20 exp … kh†

…6†

where er, e0, C0, h, and 1/k are the dielectric constant of the solvent, the permittivity of vacuum, the surface potential, the minimum separation distance between particles, and the Debye–Hückel screening length, respectively. k is given by: 0 kˆ

@

F2

P i

Ni z2i

11=2 A

…7†

er e0 kT

where Ni and zi are the number density and valence of the counterions of type i, respectively, and F is the Faraday constant [88]. 1.2.4 Steric Forces

Steric stabilization provides an alternate route to controlling colloidal stability and is used in aqueous and nonaqueous solutions. In this approach, adsorbed organic molecules are utilized to induce steric repulsion. To be effective, the adsorbed layers must be of sufficient thickness and density to overcome the van der Waals attraction between particles and to prevent bridging flocculation. Such species should be strongly anchored to avoid desorption during particle collisions. Steric interactions occur when particles approach one another at a separation distance less than twice the adlayer thickness (d). Usteric is given by [89]:  Usteric ˆ p d2 NkT 1

rij

d d

  rij d‡d ln d rij

…8†

1.2.5 Solvation Forces

The use of appropriate solvents is required for high particle stabilization. The stabilizing agent has to possess high affinity with the solvent in order to solvate the particles and form an extended layer for screening the attraction between particles [90].

5

6

1 Self-Organization of Inorganic Nanocrystals

1.3 What is Required to Provide Highly Ordered Self-Assemblies?

Usually, self-assemblies of nanocrystals are obtained by evaporation of the solution containing nanocrystals on a given substrate. Various parameters play a role in the nanocrystals’ organization. 1.3.1 Nanocrystal Size Distribution Effect

The size distribution of nanocrystals is the key parameter to obtain ordered nanocrystal superlattices. This is well illustrated in Fig. 1.3, which shows TEM images of the various arrangements of cobalt nanocrystals characterized by various size distributions (s). (All the depositions are made in the same way, i. e., by deposition of a colloidal solution on an amorphous carbon grid [67]). The nanocrystals self-assemble in a 2D hexagonal network when s is equal to or lower than 13 %. The Fourier transform (insert in Fig. 1.3 E) made on a 200 × 200-nm array displays three orders of reflections and thus confirms the long-range hexagonal network. 1.3.2 Substrate Effect

The long-range order of the organization depends on the particle–substrate interactions. Hence, compact monolayers are produced on a large scale by deposition of silver nanocrystals [91] on a highly oriented pyrolytic graphite (HOPG) substrate (Fig. 1.4 B). Conversely, with amorphous carbon as substrate, the order is local and the monolayer shows vacancies (Fig. 1.4 A). The strength of the particle–substrate interaction depends on the Hamaker constant, A p–o–s, which takes into account the nature of the nanocrystals, the solvent (oil), and the substrate (s). It is given by the expression [83, 84]: UvdW ˆ

Ap

(

d

o s

2 rij

6

d
‡
‡ ln 2 rij ‡ d d

2 rij ‡ d 2 rij ‡ d


!)


…9†

where rij is the distance from the particle (i) center to the wall ( j). At the minimum separation distance, rij = d/2 + l and the interaction energy becomes: UvdW ˆ

Ap o 12

s

  d l

…10†

1.3 What is Required to Provide Highly Ordered Self-Assemblies?

Fig. 1.3 Transmission electron microscopy (TEM) images of 7.2-nm cobalt nanocrystals obtained at various size distributions (s: (A) 30 %, (B) 18 %, (C) 13%, (D) 12 %, (E) 12 %, (F) 8 %. Inset of (E): corresponding Fourier transform).

7

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1 Self-Organization of Inorganic Nanocrystals

Fig. 1.4 TEM images of 2D self-assemblies of silver nanocrystals (A) on amorphous carbon and (B) on HOPG substrates.

1.3.3 Capillary Forces

Capillary forces arise when, during the evaporation process, the thickness of the film reaches the particle diameter. They depend on the contact angle (f) of the solvent meniscus (surface tension g) between two neighboring particles of diameter d (Fig. 1.5). The capillary force [92] is: F ˆ 2 p dg cosf

…11†

When capillary forces act, their strengths are greater than those involving particle–particle and/or particle–substrate interactions. They induce the cohesion of the organization.

Fig. 1.5 Schematic illustration of capillary forces acting between nanocrystals.

1.3.3.1 Solvent Evaporation Process Removal of the liquid vehicle during the evaporation process can induce nanocrystal aggregation and film cracking (see Chapter 13). This is illustrated in Fig. 1.6. By increasing the amount of cobalt nanocrystals deposited on a substrate, 3D assemblies are obtained. When the evaporation [13] takes place in air (fast evapora-

1.4 Self-Assemblies in the Absence of External Forces

Fig. 1.6 Scanning electron microscopy (SEM) images of 3D assemblies of cobalt nanocrystals obtained by drying the colloidal solution in air (A) and in a quasi-“saturated” atmosphere of solvent (B).

tion process), nanocrystals tend to aggregate (Fig. 1.6 A, whereas on decreasing the evaporation rate a smooth film with cracks is observed (Fig. 1.6 B).

1.3.3.2 Application of a Magnetic or Electric Field During the Evaporation Process The application of a field (magnetic or electric) during the evaporation process involves dipolar interactions between nanocrystals. Coupled to van der Waals interactions, they can have a considerable influence on the nanocrystal organization. Hence, the drying process is a critical step in the formation of self-assemblies. It is a multistage process that involves, as well as fluid flow, evaporation processes, nanocrystal diffusion, nanocrystal interactions, etc.

1.4 Self-Assemblies in the Absence of External Forces

In 1995, large-scale arrays of semiconductor nanocrystals were produced simultaneously by French and American groups [12, 13]. Later on, a large number of groups succeeded in forming 2D networks of various materials: metallic as silver, gold, or cobalt, and oxide as ferrite etc. [14–20, 41, 42]. The nanocrystals are characterized by a low size distribution. Furthermore, their surfaces are passivated (with either thiol, carboxylic acid or phosphine) in order to prevent their coalescence. Usually, the 2D organizations are obtained after evaporation of a drop deposition of a diluted nanocrystal solution on a TEM grid. A typical hexagonal 2D nanocrystal organization is shown in Fig. 1.7 [93]. For any amount of material deposited on the substrate, the nanocrystals are always organized in a hexagonal network. Note that the organization occurs on larger scale when the amount of nanomaterial deposited is rather large (compare Fig. 1.7 A and B). Moreover, due to

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1 Self-Organization of Inorganic Nanocrystals

Fig. 1.7 TEM images of a monolayer of 5.8-nm Ag2S nanocrystals after evaporation of a colloidal solution containing (A) 3.6 × 1017 and (B) 6 × 1017 nano-crystals mL–1.

Fig. 1.8 TEM images at low magnification of monolayers (A–C) and at high magnification (D–F) for various Ag2S nanocrystals diameters: (A, D) 3 nm, (B, E) 4 nm and (C, F) 5.8 nm.

1.4 Self-Assemblies in the Absence of External Forces

van der Waals forces [94], the long-range ordering increases with increasing nanocrystal size (Fig. 1.8). By deposition of a concentrated solution, 3D superlattices are obtained in coexistence with monolayers (Fig. 1.9 A). A typical TEM pattern of 3D superlattices is shown in Fig. 1.9 B. The high-magnification image of an aggregate shown in Fig. 1.9 B exhibits a large degree of ordering of nanocrystals in fourfold symmetry (Fig. 1.9 C). This can be attributed to the [001] plane of an fcc lattice [19, 94]. The large aggregate (1 mm wide and 116 nm high) corresponds to a stacking of 20 layers (Fig. 1.9 D). The 3D arrays are very inhomogeneous in size and shape (Fig. 1.9 A). In order to obtain more regular 3D superlattices, also called “supra” crystals, control of the solvent evaporation rate is required. For this, the substrate is directly immersed in the colloidal solution and the solvent is allowed to evaporate. The evaporation rate is controlled by either the substrate temperature or the solvent saturation degree of the surrounding atmosphere. By using this deposition process, “supra” crystals made of silver [20, 21] (Fig. 1.10 A) or cobalt [22] (Fig. 1.10 B) nanocrystals form. They look like paving stones characterized by welldefined shapes and rims. The “supra” crystal thickness is about 10 mm with silver nanocrystals. This corresponds to the regular stacking of around 1000 monolayers whereas for cobalt nanocrystals, the number of monolayers is smaller by almost a factor of 2. The optimal temperatures to reach the highest-ordered “supra” crystals

Fig. 1.9 TEM images of 3D aggregates in coexistence with monolayers of Ag2S nanocrystals (A); high magnification of one aggregate (B, C); AFM image of one aggregate (D).

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Fig. 1.10 SEM images of “supra” crystals of silver (A) and cobalt (B) nanocrystals obtained by deposition on HOPG substrate at 35 8C. Scanning electron microscopy images of 3D amorphous assemblies of silver (C) and cobalt (D) nanocrystals obtained by deposition on HOPG substrate at 10 8C.

are around 35 and 45 8C for silver and cobalt nanocrystals, respectively. The ordering decreases with decreasing the substrate temperature to reach, at 10 8C, amorphous aggregates, highly polydispersed in size and shape, and forming a nonhomogeneous film. This is observed for silver [21] (Fig. 1.11 C) and cobalt [23] (Fig. 1.11 D) nanocrystals. Small-angle X-ray diffraction (XRD) measurements in a grazing incidence show, for silver [20, 21, 27] and cobalt [22, 23] “supra” crystals, an fcc packing. For cobalt “supra” crystals, nine spots are recorded (Fig. 1.11). Their coordinates, which are reciprocal distances, are in good agreement on conversion into d-spacing, with the calculated coordinates of diffraction spots assuming an fcc structure (Table 1.1). The XRD pattern of the amorphous aggregates described above shows a diffuse ring (insert Fig. 1.12 A). Hence the ordering of the “supra” crystals is tuned by controlling the substrate temperature. This is well demonstrated with cobalt nanocrystals where the Bragg reflections, typical of the (111) lying planes, become more and more intense whereas the diffuse ring intensity progressively decreases when the substrate temperature increases from 10 to 45 8C (Fig. 1.12 and Table 1.2). This behavior clearly indicates an increase in both size and out-of-plane ordering of the “supra” crystals. The center-to-center nanocrystal distance calcu-

1.4 Self-Assemblies in the Absence of External Forces

13

Fig. 1.11 X-ray diffraction pattern obtained in a grazing incidence geometry of a “supra” crystal of Co nanocrystals. The intensity is reduced by a factor of 20 in the central inset.

Table 1.1 Comparison of experimental and calculated coordinates of diffraction spots assuming an fcc structure; coordinates are expressed in d-spacings. Reflection label (see Fig. 1.11)

{h,k,l } indices

X X Y (measured) (calculated) (measured) [nm] [nm] [nm]

dhkl Y dhkl (calculated) (measured) (calculated) [nm] [nm] [nm]

1 2 * * 3 4 5 6 7 8 9+

1,1,–1 2,0,0 1,1,1 2,2,2 –1,3,1 1,1,3 2,2,–2 1,1,–3 4,0,0 3,3,1 4,2,0

25.15 12.89 8.54 4.24 8.53 5.12 13.22 26.09 6.38 3.67 4.31

9.04 9.04 0 0 5.22 9.04 4.52 4.52 4.52 9.04 5.22

25.56 12.78 8.52 4.26 8.52 5.11 12.78 25.56 6.39 3.65 4.26

9.05 9.19 0 0 5.24 9.51 4.52 4.47 4.55 10.10 5.44

8.52 7.48 8.52 4.24 4.46 4.51 4.28 4.41 3.70 3.45 3.38

lated from the stacking parameter is 10.75 nm, when the nanocrystals are ordered, against 11.75 nm for the disordered system. As expected, the packing of Co nanocrystals is less compact in the amorphous phase than in the “supra” crystal. Similar behavior with the substrate temperature was observed previously in the fabrication of “supra” crystals made of silver nanocrystals [21, 27]. The second-order Bragg reflection is observed from 22 8C and the interparticle distance is minimal at this temperature. At substrate temperatures above 22 8C, the “supra” crystal size increases [27]. The dependence of the structural organization upon the deposition temperature is mostly related to the nanocrystal diffusion on the substrate. At low temperature, this diffusion is limited; hence, nanocrystals rapidly

8.52 7.38 8.52 4.26 4.45 4.45 4.26 4.45 3.69 3.39 3.30

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1 Self-Organization of Inorganic Nanocrystals

Fig. 1.12 Diffractograms of cobalt films obtained from HOPG substrate immersed in a highly concentrated cobalt colloidal solution. The different substrate temperatures (T) are: (A) 10 8C, (B) 25 8C, (C) 35 8C, (D) 45 8C. Insets: diffraction patterns.

Table 1.2 Various parameters extracted from the diffraction patterns and the corresponding diffractograms in Fig. 1.12. Substrate temperature [ pC]

12

25

35

45

Inner ring distance [nm] d q1/2 [nm–1] Rint : Iref /Ihalo Dcenter–center [nm] Dinterpart. [nm]

9.60 0.19 1.6 1.75 4.55

8.80 0.050 11 10.80 3.60

8.80 0.035 87 10.80 3.60

8.70 0.034 674 10.65 3.45

d q1/2 : the half width at half maximum; Rint : the reflection intensity to the halo intensity ratio; Dcenter–center: center-to-center nanocrystal distance; Dinterpart. : border-to-border nanocrystal distance.

stick on the substrate which hinders their compact organization. Moreover, it is also possible that the coating “fluidity” plays a role during the organization step. On increasing the partial vapor pressure of the solvent during the evaporation process to close to 100 %, i. e., by slowing down the solvent evaporation rate, crackfree homogeneous cobalt nanocrystal “supra” crystals with terraces are obtained (Fig. 1.13). XRD measurements confirm that they are highly crystallized and have the same structural characteristics as the fcc “supra” crystals described above. The change in the “supra” crystal morphology is related to the variation of the surface

1.4 Self-Assemblies in the Absence of External Forces

Fig. 1.13 SEM image of “supra” crystal of cobalt obtained from HOPG substrate immersed in a highly concentrated cobalt colloidal solution. The solvent evaporation rate is very low.

tension arising during solvent evaporation. Similar behavior was previously observed with silver nanocrystals with well-defined “supra” crystals in quasi-saturated vapor with a high degree of ordering (Fig. 1.10 A), whereas a low extent of ordering and defects are found when the evaporation takes place in air (Fig. 1.14 A and B). Another growth technique to obtain 3D superlattices is based on slow diffusion of a nonsolvent in the bulk of a concentrated solution of nanocrystals in a solvent. By this method, 3D superlattices of CdSe [95] and Au [96] are obtained. The building blocks are also aligned in a regular fcc-like 3D superlattice. Recently, “supra” crystals made of mercaptosuccinic acid-coated Au nanocrystals have been obtained in aqueous solution. In this case, the crystalline structure corresponds to hexagonal close packing (hcp) [97]. The ability to make “supra” crystals provides a new horizon to study the physical (optical, magnetic, electron transport, etc.) collective properties due to the particle interactions [1]. Furthermore, for devices, it is important to obtain these different arrays on the required substrate. Therefore, it is crucial to control various parameters like the interparticle gap and particle crystallinity. Obviously, such mesostructures must be stable in time and must also be thermally stable, in the parti-

Fig. 1.14 SEM patterns at a 458 tilt and at different magnifications obtained by drying the silver colloidal solution on a hot substrate at 35 8C in air (A and B).

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cular case where a thermal treatment is necessary to improve the nanoparticle crystallinity. These various points are described below. 1.4.1 Control of the Interparticle Gap Via the Coating Agent

A large amount of data concern the 2D organization of nanocrystals surfacecoated with thiol molecules with different alkyl chain lengths. Self-organizations in 2D networks are produced with Ag2S [93] as well as Ag nanocrystals [91], coated with thiols with different lengths, with the number of carbon atoms, n, going from 8 to 14. For gold and palladium nanocrystals, n is between 6 and 14 [62] and between 6 and 16 [63, 64], respectively. This is related to the coating process as well as to the difference in the material–thiol headgroup bonding strength. However, the minimum and the maximum chain lengths making it possible to obtain 2D nanocrystal organizations differ with the nature of the materials.

1.4.1.1 Silver Sulfide Nanocrystals The TEM images of Ag2S nanocrystals coated with various alkyl chain lengths show nanocrystal self-organization in compact hexagonal networks (Fig. 1.15). The interparticle spacings change with the alkanethiol chain length. However, the edge–edge separation distances (dpp) do not correspond exactly to the distances one might expect from the alkyl chain lengths in trans zigzag conformation (dzigzag) (Fig. 1.15). The experimental dpp values are considerably shorter than twice the chain length. In the case of octanethiol and decanethiol, dpp is longer than the expected length of one chain. For dodecanethiol-coated nanocrystals, dpp is about equal to dzigzag . For C14-thiol-derivative particles, dpp is actually shorter than dzigzag . These trends are explained by the change in chain conformation and the various defects that depend on chain length [93]. Indeed, the number of gauche defects near the particle surface decreases as the alkyl chain length increases. However, the incidence of gauche defects near the terminal (methyl) end of the chain increases with chain length. Hence, the shortest chains (C6) behave almost as free alkanes, and are thus not prone to 2D organization or interdigitation. As the chain length increases, interdigitation between alkyl chains on adjacent particles occurs, leading to a dpp value that approaches the length of a single chain, dzigzag (C10- and C12-thiol systems). In the case of C14-thiol surface groups, the increase in gauche defects near the chain terminal end allows pseudorotational motion of the chain about the R–S bond axis. This explains why the dpp value is smaller than dzigzag for the C14-thiol system. Hence, the interparticle spacing, dpp, is dependent on chain length, and does not evolve linearly. However, very short-chain alkanethiol groups behave more as free alkanes and the 2D superlattices are not produced.

1.4 Self-Assemblies in the Absence of External Forces

Fig. 1.15 TEM images of monolayers of 4-nm Ag2S nanocrystals surfacecoated with (A) 1-octanethiol (C8), (B) 1-decanethiol (C10), (C) 1-dodecanethiol (C12), and (D) 1-tetradecanethiol (C14 ). (E) Experimental average interparticle gap (dpp) to theoretical alkyl chain length in trans zigzag comformation (dzigzag) ratio and evolution of the gauche defect with alkyl chain length for thiol molecules.

1.4.1.2 Silver Nanocrystals The mean interparticle distance remains more or less the same (1.8 nm) for any thiol alkyl chain length between C8 and C12 thiols [91], with an optimal interdigitation obtained with a C12 alkyl chain. Furthermore, the long-range order of the organization increases with the alkyl chain length (Fig. 1.16). Note that the interdigitation obtained for dodecanoic acid-coated cobalt nanocrystals [67] is not as pronounced (2.5 nm) as those obtained for Ag (1.8 nm) or Ag2S (1.8 nm) nanocrystals coated by dodecanethiol. Theoretically it has been found [60] that the ratio, r, of the capping ligand chain length, , to the metal core radius, R, controls the superlattice struc-

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Fig. 1.16 TEM images of 2D self-assemblies on HOPG substrate of silver nanocrystals coated by thiol alkyl chains with different lengths: (A) dodecanethiol, (B) decanethiol, (C) octanethiol.

ture: the packing in an fcc structure is favored for r < 0.69, whereas it evolved to a less compact structure like bcc for r > 0.69. Most of the coated nanocrystals used for fabricating 2D or 3D superlattices are in the scale range r < 0.69. As expected from these considerations, the crystalline structure of the 3D superlattices is usually fcc. This is illustrated with Ag2S nanocrystals coated with thiols with different alkyl chain lengths (Fig. 1.17). The nanocrystals coated with C8 and C10 thiols, and with the same average size, form well-faceted aggregates with fourfold symmetry, as observed for the C12-thiol-coated nanocrystals (Fig. 1.17 A–C). Conversely, C14-thiol-coated nanocrystals do not form well-defined supracrystals (Fig. 1.17 D). The difference in self-assembly behavior when C14 alkanethiols are used is related to the dpp edge-to-edge spacing parameter discussed earlier. For the alkyl chain lengths shorter than C14, the dpp value is either similar to (for example, n = 12) or slightly longer (8 ^ n ^ 12) than the calculated chain length assuming complete trans (zigzag) conformation. The interdigitation of alkyl chains in these systems leads to a dense packing of the nanocrystals, which in turn results in well-defined 3D lattices. In the case of the C14 alkyl chains, the small dpp value implies strong interparticle van der Waals attraction [Eq. (9)], in addition to the presence of a large number of gauche defects and poor interdigitation.

1.4 Self-Assemblies in the Absence of External Forces

Fig. 1.17 TEM images of 3D assemblies of Ag2S nanocrystals surface-coated with (A) 1-octanethiol (C8), (B) 1-decanethiol (C10), (C) 1-dodecanethiol (C12), (D) 1-tetradecanethiol (C14 ).

Similar results are obtained with thin superlattices made of silver nanocrystals [29] with different thiol alkyl chain lengths (C8 to C14). The average center-to-center nanocrystal distance for “supra” crystals of silver as well as cobalt nanocrystals is determined from XRD measurements. It is found to be larger than that determined by TEM for the monolayers. Such a difference is attributed to the presence of defects inside the “supra” crystals (cf. Fig. 1.10), which are also taken into account by the XRD technique. 1.4.2 Influence of the Substrate

The nature of the substrate used in the deposition of the nanocrystals markedly changes the nanocrystal organization. This has been well demonstrated with silver sulfide nanocrystals [98]. On HOPG, Ag2S nanocrystals self-organize in compact monolayers and form small microdomains over the entire surface (Fig. 1.18 A). The gray region in Fig. 1.18 A corresponds to Ag2S nanocrystal monolayers and the darkest is due to the bare substrate (designated hole). The brightest regions correspond to 3D faceted aggregates characterized by a thickness less than 1 mm and 4– 8 mm width (Fig. 1.18 B). Holes are found within the large monolayer regions as observed with atomic force microscopy (AFM; Fig. 1.18 C). The cross section (Fig. 1.18 C insert) along the line shows that the depth of a hole is about 6 nm, cor-

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Fig. 1.18 SEM (A, B) and AFM (C, D) images obtained by using HOPG as the substrate, showing 3D aggregates in coexistence with monolayers. Insert: cross section along the line.

responding to the average nanocrystal diameter and indicating a very dense monolayer, and the coated alkyl chain lines on the substrate surface. Figure 1.18 D shows, by high-resolution AFM, that Ag2S nanoparticles are organized in hexagonal networks with the same interparticle gap as that observed with TEM. By replacing HOPG with MoS2, the self-organization markedly differs with large interconnected domains of monolayers in coexistence with holes (Fig. 1.19 A). Furthermore, conversely to what is observed on HOPG substrate, aggregates build on the top of the monolayers (Fig. 1.19 B). They are small compared to those observed previously, around 2 mm width and 150 nm height. The AFM pattern shown in Fig. 1.19 C at a large scale confirms the data observed with SEM (Fig. 1.19 B): rather large holes are trapped inside the monolayer (Fig. 1.19 C). The high-resolution AFM pattern (Fig. 1.19 D) confirms the formation of small islands made of particles arranged in a hexagonal network. Hence, conversely to HOPG substrate, the monolayers on MoS2 are less dense and the aggregates grow on the top of the monolayers. These changes were correlated to the interparticle effects [Eq. (1)], particle– substrate interactions [Eq. (9)], and to solvent–substrate interaction (wetting).

1.4 Self-Assemblies in the Absence of External Forces

Fig. 1.19 SEM (A, B) and AFM (C, D) images obtained by using MoS2 as the substrate, showing 3D aggregates in coexistence with monolayers. Insert: cross section along the line.

Calculations of the Hamaker constant A p–o–p and A p–o–s indicate that, with HOPG substrate, the interactions between the nanocrystals are dominant compared to particle–substrate interactions. Moreover, the heptane solvent on HOPG forms a nonzero contact angle (5–108), which means that as evaporation occurs, the solvent film becomes unstable and droplets begin to form. The dynamics of these droplets play a key role in the evolution of the Ag2S nanocrystal assembly on HOPG (Fig. 1.20). Immediately after deposition of a drop of solution containing the nanocrystals, the solvent starts to evaporate (Fig. 1.20 A). The Ag2S nanocrystals themselves are fully solvated by the heptane, thus preventing their assembly into dense structures. As the droplets grow and begin to merge, some of the Ag2S nanocrystals (which are still mobile because of the thin solvent layer present on the HOPG surface) are expelled from the merge center (see arrows in Fig. 1.20 B). These coated nanocrystals form compact monolayer islands, whose density increases after all of the solvent evaporates and interdigitation of the alkyl chains on the Ag2S nanocrystal occurs. Other particles are caught in the center of the droplet merge point. The pressure exerted on these nano-

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Fig. 1.20 Sketch of formation of a monolayer and a multilayer on HOPG substrate.

crystals by the droplet menisci is large, and while a monolayer initially forms, continued droplet coalescence engenders the formation of a 3D structure (Fig. 1.20 C). This process may be viewed as analogous to the collapse of Langmuir films when the lateral pressure on the monolayer is too high. The sizes of the 3D aggregates of Ag2S are similar, which implies that the merge regions between growing solvent droplets are also similar in size. A key point implied by the scheme in Fig. 1.20 B and D is that the formation of monolayers and 3D aggregates occurs essentially simultaneously. With MoS2 as substrate, the Hamaker constant indicates that the particle–substrate interactions are higher than those between particles. This favors the sticking of the nanoparticles on the substrate. At this point, this random process induces a

1.4 Self-Assemblies in the Absence of External Forces

Fig. 1.21 Monolayers of 5-nm silver nanocrystals on (A) HOPG, (B) Au(111), and (C) silicon. These images were obtained by TEM in (A), constant-current mode STM (Vt = 2.5 V, It = 0.8 nA) in (B), and by SEM in (C).

nonordered monolayer. However, because of the surface diffusion and attractive particle–particle interactions (van der Waals and capillary forces), small islands of ordered particles are formed. Once monolayers are formed, the particle–substrate interactions do not play any role in the aggregate growth. Because the nanocrystals interact they tend to form small aggregates. This suggests a layer-by-layer growth following the monolayer formation. With silver nanocrystals, self-assemblies in a compact hexagonal network are obtained by using a rather large variety of substrates such as HOPG, gold, and silicon (Fig. 1.21) [36]. The vacancies observed in Fig. 1.21 C are probably due to the fact that not enough nanocrystals were deposited on the silicon. Similarly, “supra” crystals are produced with these substrates and also with Al0.7Ga0.3As (Fig. 1.22). X-ray diffraction measurements show reflectograms similar to those observed with HOPG (Fig. 1.11) and characteristic of fcc crystalline structures. All of these substrates are characterized by low-roughness surfaces that favor the particles‘ diffusion and their organization in 2D and thus in 3D structures.

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Fig. 1.22 SEM images of “supra” crystals made of silver nanocrystals deposited on different substrates: (A) HOPG, (B) gold, (C) silicon, and (D) Al0.7Ga0.3As.

1.4.3 Thermal and Time Stabilities

To be used, superlattices have to be highly ordered, and thermally and time stable.

1.4.3.1 Crystallinity Improvement Related to the Atomic and Nanocrystal Ordering The thermal stability of the arrays was specially studied in the case of cobalt particles coated either with dodecanoic acid [32, 68] or with oleic acid [69]. As expected, the annealing of cobalt nanocrystals improves their crystallinity. Native cobalt nanocrystals coated with dodecanoic acid, self-organized in 2D (Fig. 1.23 A) or in 3D (Fig. 1.23 D) superlattices, are made of poorly crystallized fcc particles (Fig. 1.23 B and C). The annealing of the monolayers at 300 8C (Fig. 1.23 E) does not change either the particle diameter (7.2 nm) or the average distance between their neighbors (3.55 nm). The 3D superlattices remain similarly ordered (Fig. 1.23 H). However, in both cases, the annealing process improves the crystallinity of the particles with formation of pure hcp nanocrystals

1.4 Self-Assemblies in the Absence of External Forces

Fig. 1.23 TEM images of 7.2-nm cobalt nanocrystals coated with dodecanoic acid and ordered in a compact hexagonal network: not annealed (A) and annealed at 300 8C (E). The corresponding high-resolution images (B, F) and electron diffraction patterns (C, G). Multilayers of cobalt nanocrystals: not annealed (D) and annealed at 300 8C (H).

(Fig. 1.23 F and G). Furthermore, by annealing cobalt nanocrystals coated with dodecanoic acid in powder form at 2758C, it is possible to redisperse them in a non-polar solvent and to obtain the same organization as those formed before annealing. In addition, the crystallinity is improved with formation of pure hcp nanoparticles [68]. It must be noted that when the annealed monolayers [32] are left in air for a few weeks, nanocrystals can be superficially oxidized (Fig. 1.24 B), whereas their organization remains unchanged (Fig. 1.24 A). When these oxidized nanocrystals are not implied in the array, i. e., when they are isolated, coalescence takes place (Fig. 1.24 C). Thus, it is concluded that selforganization of nanocrystals prevents coalescence. This claim is confirmed in Fig. 1.24 D where obviously the nanocrystals in the superlattice are protected from coalescence. This is one of the first intrinsic properties of the self-organization process. This fact can be explained in terms of collective entropy gained by nanocrystal ordering, which contributes a substantial amount of stabilization energy to the superlattice. Similarly, the annealing at 300 8C of monolayers of Co nanocrystals coated with oleic acid [69] does not alter the organization, but material oxidation is observed. With 3D superlattices, there is coalescence of the particles [69]. This is correlated to the removal of the oleic acid molecules during the annealing process. Note that the absence of coalescence in 2D organizations, expected after the coating agent removal, is explained by the absence of mobility of nanocrystals on the substrate, due to their interactions with the latter. In the same way, it has been reported that thin 3D superlattices of FePt [70] nanocrystals are stable up to 550 8C; above this temperature, the mixed coating made with oleic acid and oleyl amine evaporates, inducing again particle coalescence [70].

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Fig. 1.24 TEM images of 7.2-nm cobalt nanocrystals after annealing at 300 8C: ordered in a compact hexagonal network (A) and the corresponding electron diffraction pattern (B). The sample is examined a few weeks after its preparation. Individual dispersed cobalt nanocrystals (C) and the same sample having self-assembled and isolated nanoparticles (D).

As observed for 2D and thin 3D superlattices made of dodecanoic acid-coated cobalt nanocrystals, annealing at 300 8C of “supra” crystals does not change the ordering and keeps the fcc structure [32]. Furthermore, from the XRD patterns, the ordering of the “supra” crystals increases, with an increase in the Bragg peak of the (111) reflection to ring intensity ratio (insert Fig. 1.25 F ) and a decrease in the Bragg peak width (Fig. 1.25 F) compared to that of the native sample (Fig. 1.25 C and insert). Note that the interparticle gap decreases from 0.90 nm with increasing the temperature from 25 to 300 8C. Furthermore, cracks appear (Fig. 1.25 D) favoring the decrease of the constraints existing in the native superlattice. The reduction of the interparticle gap is due to the coating agent compaction. From this, it is concluded that thermal treatment of “supra” crystals induces,

1.4 Self-Assemblies in the Absence of External Forces

Fig. 1.25 SEM images of 7.2-nm cobalt nanocrystals ordered in “supra” crystals not annealed (A, B), annealed at 300 8C (D, E), and annealed at 350 8C (G, H). Corresponding diffractograms obtained by imaging plate scanning and corresponding to the X-ray diffraction patterns obtained in a grazing incidence geometry (insets C, F, I).

as in the bulk phase, an increase in the nanocrystal order. A further increase in the annealing temperature to 350 8C induces formation of small domains (Fig. 1.25 G) and breaks the “supra” crystal ordering with a shift of the Bragg peak towards a smaller angle in the XRD pattern (Fig. 1.25 I and insert). This indicates a dilatation of the (111) planes of about 0.8 nm compared to the “supra” crystal annealed at 300 8C.

1.4.3.2 A New Approach to Crystal Growth Another annealing process that totally differs from that presented above can be used to form large, flat, silver single crystals with a triangular shape [29]. A colloidal solution of coated silver nanocrystals is evaporated and kept for several days at 50 8C. Immediately after solvent evaporation the nanocrystals are organized in fcc 3D superlattices (Fig. 1.26 A). With time, the nanocrystals coalesce to give rise to

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Fig. 1.26 TEM and HRTEM images obtained by immersing HOPG substrate in a silver nanocrystal solution heated at 50 8C for 3 h (A) and for 6 days (B–D). (A) 3D fcc superlattices of silver nanocrystals; in insets, a higher resolution of part of the superlattices and the corresponding power spectrum. (B) Large triangular-shape silver single crystals. (C) HRTEM images of a single triangular particle and (D) the corresponding power spectrum.

large silver single crystals characterized by a regular triangular shape and an average size around 100 nm (Fig. 1.26B). HRTEM images and image processing by the square Fourier transform (power spectrum, PS; Fig. 1.26 C and D) show that these triangular particles are very well crystallized in an fcc structure and are very flat. The reflections observed in the PS correspond to 1/3 (422) reflections that are normally forbidden and indicate very thin particles, which has been confirmed by TEM weak field/dark field techniques. The nature of the substrate plays an important role in the nanocrystal growth. By replacing HOPG with amorphous carbon, small silver polycrystals (average size around 15 nm) are produced (Fig. 1.27 B–D). As the silver nanocrystals are not initially as well organized on amorphous carbon as on HOPG, this shows the

1.4 Self-Assemblies in the Absence of External Forces

Fig. 1.27 TEM observations of annealing-time effect on the crystal growth of silver nanocrystals deposited on a amorphous carbon grid: (A) after 3 h (in inset, the corresponding power spectrum); (B, C) after 6 days; (D) HRTEM images of Ag particles in (C).

key role of the nanocrystal organization in the crystal growth process. This feature gives rise to a new area of research in the crystal growth domain and shows a new intrinsic property of the self-organization of inorganic nanocrystals in a well-defined structure.

1.4.3.3 Stability with Time The stability with time of “supra” crystals is also a real challenge. After a few weeks, the silver nanocrystal monolayers are damaged [20]. The nanocrystals start indeed to coalesce. This finding indicates a desorption of the coating agent with time and thus its weak bonding with silver nanocrystals, which has been observed for various coating agents. Nevertheless, this aging has not been observed in the

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Fig. 1.28 SEM images obtained from HOPG substrate immersed in a highly concentrated colloidal silver solution (3 × 10–6 mol L–1), dried 9 h at 35 8C in a hexane vapor atmosphere and then left in air at room temperature for one month (A, B) and five months (C, D). In (B) and (D) the sample is tilted by 458.

case of monolayers made of cobalt nanocrystals coated by dodecanoic acid [22]. This is mainly due to the fact that the bonding of dodecanoic acid with cobalt atoms at the interface is covalent [99] whereas that of dodecanethiol with silver nanocrystals is weaker. After several months, the “supra” crystals of silver nanocrystals show cracks and holes on their surfaces (Fig. 1.28) and their edges are no longer well defined [20]. The roughness of the surface increases with aging (Fig. 1.28 B and D). From XRD patterns, the evaporation of the residual solvent with time reduces the mean distance between the nanocrystals with a less well-defined second-order peak as for the freshly prepared sample, indicating a decrease in the ordering inside the “supra” crystals. After five months‘ aging, the “supra” structure is totally destroyed. This is explained as follows: the evaporation of the residual solvent remaining inside the thick “supra” crystals induces the desorption of the alkyl chain used to coat the nanocrystals and thus their coalescence. This confirms the loss in the edge and very rough surfaces observed on the sample (Fig. 1.28 D). Conversely to cobalt nanocrystals, “supra” crystals remain stable in time [22].

1.5 Self-Assemblies in the Presence of External Forces and Constraints

1.5 Self-Assemblies in the Presence of External Forces and Constraints

2D hexagonal networks of nanocrystals and 3D fcc superlattices are the most commonly observed organizations with low-size-distribution nanocrystals. Furthermore, it was shown that the use of external force as in the Langmuir–Blodgett technique can improve the 2D hexagonal nanocrystal organization [100–103] and the monolayer is transferred on various substrates. Other external forces, such as convection modes in the liquid phase and application of a magnetic field, either parallel or perpendicular to the substrate during evaporation, induce the formation of new patterns. 1.5.1 Fluid Flow

The deposition method and the evaporation rate of the solvent used to disperse the nanocrystals are two parameters that can also strongly influence the 2D and 3D arrangements of the nanoparticles. Thus, when a droplet of diluted colloidal solution is deposited on a TEM grid maintained with an anticapillary tweezer, nanocrystal ring formations are observed (Fig. 1.29), depending on the solvent evaporation rate [9, 10]. In this deposition mode, the droplet remains on its support until the solvent is totally evaporated (solvent cannot escape from the grid). Ring formation has been observed with different nanomaterials like spherical silver (Fig. 1.29 A), silver sulfide (Fig. 1.29 B), cobalt (Fig. 1.29 C), maghemite (Fig. 1.29 D), nanocrystals and flat triangular CdS (Fig. 1.29 E), and cigar-shaped hematite (Fig. 1.29 F ) nanoparticles. This organization is obtained by using a highly volatile solvent as hexane. Both parameters, deposition mode and the solvent evaporation rate, are correlated. A fast evaporation process induces a high gradient temperature between the interface and the substrate, which results in an increase of the surface tension perturbation and convective flow. After complete evaporation of the solvent, the nanocrystal organization is the replica of this flow. By decreasing the evaporation rate (use of a low-volatility solvent, such as decane), the system equilibrates faster than the heat loss by the evaporation process and instabilities disappear. With nanocrystals having a low size distribution, the nanocrystals organized in rings are self-organized in a hexagonal array (Fig. 1.7); otherwise, they are randomly dispersed on the substrate. By increasing the particle concentration, more complex organizations [9, 10] such as honeycombs or chaotic structures are observed (Fig. 1.30 A and B) after evaporation of the solvent. Again, this result is obtained whatever the nature of the nanocrystals. These patterns are similar in shape to those observed in Bénard’s experiment with liquid films [104] and attributed to a Marangoni effect. In this case, the concentration gradient appearing during the evaporation favors a convective flux. The patterns observed after evaporation are a replica of the liquid flows and instabilities. This is confirmed by evaporation of a highly concentrated

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Fig. 1.29 TEM images of ring organizations of spherical silver (A), silver sulfide (B), cobalt (C), maghemite (D), nanocrystals and flat triangular CdS (E), and cigar-shaped hematite (F) nanoparticles.

nanocrystal solution on a substrate (Fig. 1.31). At the wetting front, during the droplet spreading, fingering instability is observed. An increase in the fingering periodicity is observed from 120 to 200 mm during the evaporation stage. When the solvent is totally evaporated, fingering patterns are still homogeneous in shape and periodicity (Fig. 1.31 C). Again, these instabilities reflect the migration of the solvent on a substrate and can be observed because it contains nanocrystals dispersed in the solution.

1.5 Self-Assemblies in the Presence of External Forces and Constraints

Fig. 1.30 Honeycombs (A) and chaotic structures (B) obtained after evaporation of a concentrated solution containing silver nanocrystals on a TEM grid.

Fig. 1.31 Fingering patterns obtained from a concentrated solution of silver nanocrystals dispersed in hexane. The images are obtained at different times during the spreading of the droplet (A, B) and after evaporation of the solvent (C).

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1.5.2 Application of a Magnetic Field 1.5.2.1 Applied Field Parallel to the Substrate Magnetic nanocrystals with dominant dipolar attractions tend to organize in chainlike structures. This was well demonstrated with iron [75] and magnetite [76] nanocrystals [Eq. (5)]. Similar organizations can be obtained with weakly dipolar nanocrystals by evaporation of the ferrofluid in a magnetic field applied parallel to the substrate. Such experiments were made with spherical cobalt ferrite [14], maghemite [12, 77, 78], and cobalt [13, 25] and with acicular nickel [79] and maghemite [80] nanocrystals. Two types of coating agent are used: an ionic agent like citrate ions, or alkyl chains like carboxylic acid. Then the stability of the ferrofluid is governed on the one hand by electrostatic interparticle repulsion (Fig. 1.2 A) and on the other hand by steric repulsion (Fig. 1.2 B). A polar solvent such as water is used to stabilize nanocrystals coated with citrate ions or with short alkyl chain length. An apolar solvent like hexane or cyclohexane is used for long alkyl chain lengths. Depending on the solvent, the deposition modes differ: with polar solvents, a drop of ferrofluid is deposited on the substrate; with apolar solvents, the substrate is dipped into the solution. Evaporation takes place in the presence or absence of a magnetic field. Conversely to ring and honeycomb formation, the deposition mode and solvent used are not key parameters for obtaining chainlike organizations. Using spherical 10-nm g-Fe2O3 nanocrystals [12, 77], surface-passivated with octanoic (C8), decanoic (C10), and dodecanoic (C12) acids, the TEM patterns markedly differ (Fig. 1.32) Without a magnetic field applied during the evaporation process, large spherical aggregates are produced with C8 nanocrystals (Fig. 1.32 A), whereas smaller ones are obtained with the C10 derivative (Fig. 1.32 B) and, finally, randomly dispersed nanocrystals with C12 (Fig. 1.32 C). When nanocrystals are deposited in a 0.59-T magnetic field, an evolution of the organization from chains to a random dispersion is observed (Fig. 1.32 E–G). Such a change in nanocrystal organization is correlated to the total interparticle potential energy which can be expressed as Utotal = UvdW + Udd + Usteric (see Chapter 3). The interaction between particles increases when the interparticle distance decreases [Eq. (3)]. The length of the alkyl chain used as coating molecule modulates this distance. Large van der Waals interactions (short interparticle distance) usually lead to spherical aggregations of particles. This is observed experimentally using C8 nanocrystals in the absence of a magnetic field. In this case the steric repulsion is not sufficient to overcome the van der Waals and dipolar interactions between nanocrystals. The application of a magnetic field during evaporation induces a total magnetic dipole in each aggregate, which is much larger than that of a single nanoparticle. Therefore, the aggregates attract each other and form a chainlike structure. Conversely, by increasing the alkyl chain length of the coating agent (C12 nanocrystals), the steric repulsion is active and particles are then randomly deposited due to a large size dispersion (s = 20 %). With a magnetic field, dipolar interactions between nanocrystals are too weak to induce chain formation (see Chapter 3). An intermediate behavior is observed for nanocrystals coated with C10 chains. This explanation is sup-

1.5 Self-Assemblies in the Presence of External Forces and Constraints

Fig. 1.32 TEM images of spherical g-Fe2O3 nanocrystals, deposited in the absence (A–D) and in the presence (E–H) of a magnetic field. Nanocrystals are surface-passivated with octanoic acid (A, E), decanoic (B, F), dodecanoic acid (C, G), and citrate ions (D, H).

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ported by Brownian dynamic simulations [12, 77]. Chainlike structures are also obtained with maghemite nanocrystals coated with citrate ions (Fig. 1.32 H). With no magnetic field, spherical aggregation is observed (Fig. 1.32 D). The structures observed with or without a magnetic field can be explained with the same process described for C8 nanocrystals. Of course, with citrate-coated nanocrystals, electrostatic repulsion has to be taken into account (Utotal = UvdW + Udd + Uelec). During evaporation, the overlap of the ionic double layer occurs and the Debye–Hückel screening length decreases. Large van der Waals interactions are expected, inducing aggregation in the absence of a magnetic field. Indeed, with a field, dipolar interactions between aggregates are sufficiently high to induce chainlike organizations. By increasing the amount of material deposited on the substrate, similar types of mesostructures are observed (Fig. 1.33). In this way, spherical maghemite nanocrystals [15, 77] coated with short chains (C8 nanocrystals) or with citrate ions organize in spherical highly compact aggregates (Fig. 1.33 A and D) without an applied magnetic field, and form long cylinders with a very regular structure in its presence (Fig. 1.33 E and H). By tilting the sample, it is seen that the structure corresponds to superimposed cylinders. Conversely, when nanocrystals are coated with long alkyl chain length acids (C12 nanocrystals), without a field, a dense film with a flat surface is observed (Fig. 1.33 C) and the application of a magnetic field induces only a slight undulation at the surface of the film (Fig. 1.33 E). An intermediate behavior is observed with C10 nanocrystals (Fig. 1.33 B and F). As in the case of diluted ferrofluids, such changes in the mesoscopic structure are correlated to interactions between nanocrystals (see Chapter 3) [12, 77]. Hence, the disappearance of structural organization for dodecanoic acid-coated nanocrystals is a result of the significant decrease in the interaction between nanocrystals due to the large interparticle distance. Cobalt nanocrystals coated with dodecanoic acid and deposited under an applied magnetic field show the formation of stripes (in concentrated systems) [13, 25]. This finding markedly differs from that observed with C12 maghemite nanocrystals. It is attributed to the difference in hardness of the magnetic materials (see Chapter 10, cobalt nanocrystals constitute a hard magnetic material while maghemite is a soft one) as well as to van der Waals interactions between the magnetic materials (see Chapter 3, the Hamaker constant of metallic cobalt is higher than that of oxide nanocrystals). The strength of the applied field and evaporation rate control the mesoscopic structure. Figure 1.34 shows that whatever the strength of the applied field, maghemite nanocrystals are aligned along the direction of the magnetic field in tubelike structures. However, the average width of the cylinders and the compacity increase with the strength of the applied field [15, 24]. Similar results are obtained with cobalt nanocrystals: the roughness decreases and the average distance between two adjacent stripes decreases linearly with the strength of the applied magnetic field [13]. The organization in the absence and presence of a magnetic field differs with the evaporation rate [13]. This is illustrated with cobalt nanocrystals coated with dodecanoic acid (Figs. 1.6 and 1.35). When evaporation takes place in air and in the absence of a magnetic field, a 3D film with high roughness is obtained (Fig. 1.35 A).

1.5 Self-Assemblies in the Presence of External Forces and Constraints

Fig. 1.33 SEM images of spherical g-Fe2O3 nanocrystals, deposited in the absence (A–D) and in the presence (E–H) of a magnetic field. Nanocrystals are surface-passivated with octanoic acid (A, E), decanoic (B, F), dodecanoic acid (C, G), and citrate ions (D, H).

High magnification (Fig. 1.35 E) shows that cobalt nanocrystals tend to aggregate in 70-nm-diameter spherical shapes. The application of a magnetic field induces formation of a linear structure (Fig. 1.35 B) made of these 70-nm spherical aggregates (Fig. 1.35 F). Under hexane vapor, such aggregates are not observed and a homogeneous film, with cracks, is observed without an applied field (Fig. 1.35 C and G); in its presence, long stripes corresponding to a highly compact film are seen (Fig. 1.35D and H). Hence, these changes in morphologies are related to eva-

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Fig. 1.34 SEM images obtained at various magnifications for spherical citrate-coated g-Fe2O3 nanocrystals, deposited in various magnetic field strengths: (A, B) 0.01 T; (C, D) 0.05 T, and (E, F) 0.59 T.

poration rate and again to nanocrystal interactions. A rapid evaporation favors the close approach between nanocrystals and attractive van der Waals and dipolar interactions between nanocrystals increase, inducing spherical aggregation. In a slow evaporation, the nanocrystals freely diffuse in solution leading to formation of homogeneous structures. The anisotropy shape of nanocrystals also plays a role in the mesoscopic structure. Chainlike structures are obtained with cigar-shaped maghemite nanocrystals coated with citrate ions [80] and having an average length, width, and aspect ratio of 325, 49, and 6.7 nm, respectively. Figure 1.36 A shows nanocrystals randomly deposited without an external magnetic field during evaporation. With a magnetic field (1.8 T ), the nanocrystals are aligned with their long axis along the field direction (Fig. 1.36 C). The applied field assembles the nanocrystals in chains and aligns their easy axes with their magnetic moments during evaporation. By in-

1.5 Self-Assemblies in the Presence of External Forces and Constraints

Fig. 1.35 SEM images of 3D films made of spherical cobalt nanocrystals, deposited in the absence (A, C, E, G) and in the presence (B, D, F, H) of a magnetic field. The evaporation takes place in air in 45 min (A, B, E, F) and under a saturated hexane atmosphere in 12 h (C, D, G, H).

creasing the amount of material deposited, similar morphologies are obtained. With no applied magnetic field, a thin magnetic film is obtained and the nanocrystals are randomly oriented (Fig. 1.36 B). The application of a magnetic field during evaporation induces the organization of the nanocrystals into ribbons (Fig. 1.36 D). The nanocrystals are mainly oriented with their long axis along the direction of the applied field.

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Fig. 1.36 TEM (A, C) and SEM (B, D) images of cigar-shaped g-Fe2O3 nanocrystals deposited in the absence (A, B) and in the presence (C, D) of a magnetic field.

From these data it is concluded that the mesoscopic structures markedly differ with the nanocrystal coating agent and the nature of the material, and are influenced by the strength of the magnetic field, the evaporation rate, and the extent of the nanocrystal anisotropy.

1.5.2.2 Applied Field Perpendicular to the Substrate Recently in our laboratory, solid mesostructures, such as columns or labyrinths of cobalt nanocrystals coated with dodecanoic acid, were produced by applying a magnetic field during the evaporation of the fluid containing magnetic nanocrystals dispersed in a nonpolar solvent. A transition from columns to labyrinths is shown in Fig. 1.37. However, a thick film of cobalt nanocrystals underneath such “supra” structures was observed. In this case, the applied magnetic field is rather high and is located in the nonlinear regime. By improving the synthesis mode of cobalt nanocrystals, the underlying layer disappeared with more or less similar structures remaining [16]. A theory is developed to understand the formation of these patterns (see Chapter 3). Taking into account the radius, the height of the cylinders, the magnetic phase to the total volume ratio, and the center-to-center distance between cylinders, and by using the model developed in ref. [105], the estimated interfacial tension deduced by the minimization of the total free energy is 5 × 10–5 N m–1. From this it is concluded that the formation of structures takes place in a concentrated solution of nanocrys-

1.5 Self-Assemblies in the Presence of External Forces and Constraints

Fig. 1.37 SEM images obtained by evaporating a concentrated solution of cobalt nanocrystals deposited in a magnetic field perpendicular to the HOPG substrate.The evaporation time is 12 h. The strength of the applied field is (A) 0.01 T; (B) 0.27 T; (C) 0.45 T; (D) 0.60 T, and (E) 0.78 T.

tals induced by a liquid–gas phase transition and not via a Rosenweig instability [89]. This is confirmed by a video recorded during the evaporation process. Dots appear 7 hours after the evaporation starts (Fig. 1.38 A). Figure 1.38 shows that the number of dots increases progressively and then they migrate in the solution to form a hexagonal array (Fig. 1.38 D). At the end of the evaporation a wave due to capillary forces induces the collapse of the columns (Fig. 1.38 E and F). This is confirmed by the SEM image recorded at the end of the evaporation process (Fig. 1.39). At this point a question arises: what process controls the formation of columns and/or labyrinths? To answer this we have to take into account the size distribution of nanocrystals with mainly the same average nanocrystal size. The SEM image shown in Fig. 1.40 (see page 43) is produced with nanocrystals having 5.7-nm average diameter and 13 % size distribution. Well-defined structures are produced with formation of dots (insert A, Fig. 1.40), collapsed columns (insert B, Fig. 1.40), and very few labyrinths. On replacing HOPG by TEM substrate, the columns are well defined (insert C, Fig. 1.40), and their ends are highly organized in fcc structures (insert D, Fig. 1.40). By increasing the size distribution to 18 % and keeping a similar average diameter (5.9 nm), the SEM pattern markedly differs with the appearance of labyrinths and flowerlike patterns (Fig. 1.41). Inserts a and b show that the flowerlike patterns are in fact the ends of fused columns and that they tend to form wormlike patterns and labyrinths, as shown in Fig. 1.41. By using the same procedure as that described above, the TEM image shows that the columns are not well defined (insert C) and their

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Fig. 1.38 Video microscopy image (A) obtained during the evaporation of a cobalt nanocrystal solution in a 0.25-T magnetic field at the instant when the columns appear. A silicon substrate is used. The ring in (B) encloses the columns, the arrows in (C) indicate the direction of column diffusion. (E, F) Images obtained at the end of the evaporation of a cobalt nanocrystal solution; the arrow indicates the direction of the wave created by the capillarity forces.

extremities are totally disordered (insert D). A careful examination of the labyrinthine structures shows that they are made of fused columns having more or less the same height (Fig. 1.42). From these data and those reported in refs. [17, 18, 106–108] we have quite good knowledge of the mechanism of production of mesostructures when magnetic nanocrystals are subjected to a rather large vertical applied field. It is concluded that the column growth in the concentrated liquid phase of cobalt nanocrystals is induced by a phase transition. They migrate inside the solution to self-

1.5 Self-Assemblies in the Presence of External Forces and Constraints

Fig. 1.39 SEM image obtained at the end of the evaporation process.

Fig. 1.40 SEM image of mesostructures made of 5.7-nm cobalt nanocrystals with 13 % size distribution The vertical magnetic field strength applied during the evaporation process is 0.25 T. Inserts (A) and (B) are magnifications of the SEM image; (C) and (D) are TEM images at two different magnifications, obtained with the same experimental procedure.

organize in a hexagonal network. Waves induced by capillary forces induce the collapse of most of these columns. Their rigidity is controlled by the ability of nanocrystals to self-organize in fcc structures. They can thus retain their integrity. Conversely, the disorder inside and at the edges of the columns, mainly due to the large size distribution of the nanocrystals, induces their fusion. However because the columns are formed in the solution, those having a similar size tend to attract

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Fig. 1.41 SEM images of mesostructures made of 5.9-nm cobalt nanocrystals with 18 % size distribution. The vertical magnetic field strength applied during the evaporation process is 0.25 T; silicon is used as substrate. Inserts (A) and (B) are magnifications of the structures in the SEM image. Inserts (C) and (D) are TEM images at two different magnifications, obtained with the same experimental procedure.

Fig. 1.42 SEM image of labyrinthine structures showing that they are made of fused columns.

each other by van der Waals interactions and to fuse. This makes it possible to produce rather homogenous wormlike structures or labyrinths. Furthermore, these mesostructures are independent of the strength of the applied field in the range of 0.1 to 0.8 T, because the experiments are carried out where there is nonlinear behavior of the magnetic field.

References

1.6 Conclusion

The last few years have seen extremely rapid advances in the preparation of very narrow size distributions of various types of nanomaterials. These advances have enabled many groups to prepare 2D and 3D nanoparticle superlattices. In the same way, organizations of nanoparticles in mesoscopic patterns such as rings, chains, and ribbons have also been developed. Some of these patterns require the presence of external forces to be formed. These various systems constitute an open research field and many exciting phenomena remain to be discovered. Such new materials could have a significant impact on future electronic, optics, and magnetic storage devices. Nevertheless, the optimization of their fabrication is still needed in order to obtain very regular and well-defined patterns. In this chapter, we have shown that many parameters are involved in the formation of these organizations.

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90 Israelachvili J., Acc. Chem. Res. 1987, 20, 415. 91 Pileni M. P., Lalatonne Y., Ingert D., Lisiecki I., Courty A., Faraday Discuss. 2004, 125, 251. 92 Adamson A. W., Gast A. P., Physical Chemistry of Surfaces, 6th ed.,WileyInterscience, New York, 1997. 93 Motte L., Pileni M. P., J. Phys. Chem. 1998, 102, 4104. 94 Motte L., Billoudet F., Douin J., Lacaze E., Pileni M. P., J. Phys. Chem. 1997, 101, 138. 95 Talapin D. V., Shevchenko E. V., Kornowski A., Gaponik N., Haase M., Rogach A. L., Weller H., Adv. Mater. 2001, 13, 1868. 96 Lin X. M., Sorensen C. M., Klabunde K. J., Chem. Mater. 1999, 11, 198. 97 Wang S., Sato S., Kimura K., Chem. Mater. 2003, 15, 2445. 98 Motte L., Lacaze E., Maillard M., Pileni M. P., Langmuir 2000, 16, 3803. 99 Wu N., Fu L., Su M., Aslam M., Wong K. C., Dravid V. P., Nano Lett. 2004, 4, 383. 100 Dabbousi B. O., Murrau C. B., Rubner M. F., Bawendi M. G., Chem. Mater. 1994, 6, 216. 101 Heath J.R., Knobler C.M., Leff D., J. Phys. Chem. B 1997, 101, 189. 102 Huang S., Tsutsui G., Skaue H., Shingubara S., Takahagi T., J. Vac. Sci Technol. B 2001, 19, 115. 103 Guo Q., Teng X., Rahman S.,Yang H., J. Am. Chem. Soc. 2003, 125, 630. 104 Benard H., Rev. Gen. Sci. Pure Appl. 1900, 11, 1261. 105 Germain V., Richardi J., Ingert D., Pileni M. P., J. Phys. Chem. B 2005, 109, 5541. 106 Richardi J., Ingert D., Pileni M. P., J. Phys. Chem. 2002, 106, 1521. 107 Richardi J., Ingert D., Pileni M. P., Phys. Rev. E 2002, 66, 46306. 108 Richardi J., Pileni M. P., Phys. Rev. E 2004, 69, 16304.

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2 Structures of Magnetic Nanoparticles and Their Self-Assembly Zhong L. Wang,Yong Ding, and Jing Li

2.1 Introduction

Nanoparticles represent the most popular nanomaterials that have applications ranging from catalysts, surface coatings and drug delivery systems to composites. Structural characterization of nanoparticles relies on X-ray diffraction, optical spectroscopy, electron microscopy and scanning probe microscopy. As of today, transmission electron microscopy and its associated techniques are still the most powerful techniques for characterizing the structures of nanoparticles, and particularly in determining their shapes, sizes, size distribution and surface structures. Previously, a few review articles have been made available for structure analysis of metallic nanoparticles and their self-assemblies [1–4]. In this chapter, we mainly focus on the structure analysis of magnetic nanocrystals. Using FePt and ferrites as examples, we illustrate the techniques for determining the phases and structures of nanoparticles, and the shape, phase transformation, surface structure and orientation ordering in self-assembly. Our analysis is based on the assumption that readers have substantial knowledge about high-resolution transmission electron microscopy (HRTEM); thus, our presentation mainly focuses on the results and data interpretation rather than the theory of the technique.

2.2 Phase Identification of Nanoparticles 2.2.1 Core–Shell Nanoparticles [5]

Core–shell structured nanoparticles are interesting because of their unique physical and chemical properties as well as technological applications [6–14]. The core–shell structured nanoparticles have the advantage of tuning and tailoring their physical properties by designing the chemical compositions as well as Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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sizes of the core and the shell. The wurtzite CdSe/CdS core–shell semiconductor nanoparticles, for example, show a comprehensively improved photostability, electronic accessibility and high quantum yield [8]. The ferromagnetic Co nanoparticles enclosed by an antiferromagnetic CoO shell provide an extra source of anisotropy induced by the exchange coupling at the interface between the two phases, leading to enhanced ferromagnetic stability beyond the “superparamagnetic limit” [12]. Fe58Pt42/Fe3O4 core–shell nanoparticles demonstrate interphase exchange coupling between core (magnetic hard phase) and shell (magnetic soft phase), which may lead to magnets with improved energy products [13]. The physical and chemical properties and performances of the core–shell nanoparticles strongly depend on their microstructure, which includes the structure of the core, the shell and their interface [6–8, 12, 14]. The interface is particularly important because its sharpness, lattice mismatch and chemical gradient are critical for electron transfer and coupling. An epitaxial orientation relationship between the core and the shell is favorable, but epitaxial growth is determined by their crystal structures [14]. The CoFe/Fe3O4 nanoparticles were obtained by coating iron species over a 4-nm CoFe2O4 core [15]. The coating was performed by mixing the CoFe2O4 particles with oleic acid, oleyl amine, phenyl ether, and Fe(CO)5 and heating the mixture to refluxing temperature. Based on the synthesis technique presented, we know that the most likely structures could be CoFe2O4 and Fe3O4, which have the spinel structure. This structure has two cation sites: the tetrahedrally coordinated A sites and octahedrally coordinated B sites. For Fe3O4, the A and B positions are occupied by Fe3+ and Fe2+ cations, respectively; for CoFe2O4, the A and B positions are equally occupied by Co and Fe cations. Fe3O4 and CoFe2O4 have almost the same lattice parameters: a = 8.3963 Å for Fe3O4 ; a = 8.39 Å for CoFe2O4. The mass densities for Fe3O4 and CoFe2O4 are almost identical. As a result of the very small difference in atomic number between Co and Fe and the identical crystal structure, the two phases can hardly be distinguished by either HRTEM or X-ray diffraction, especially with the shape-induced peak broadening. Figure 2.1 a shows a typical low-magnification TEM image of the nanoparticles, which clearly displays the core–shell morphology of 9–10 nm in size. Figure 2.1 b shows an enlarged TEM image revealing that the core–shell nanoparticles have a uniform shell, but the shell is composed of tiny nanocrystallites (so-called polycrystalline). In contrast to the expected result, the core shows a darker contrast than the shell, indicating that the core should have a higher projected mass density. This is impossible if the core is CoFe2O4 and the shell is Fe3O4. The question now is, what are the core and the shell? Firstly, HRTEM is applied to determine the structure of the larger-sized nanoparticles. Figure 2.2 a shows a typical HRTEM image and the corresponding Fourier transformations from the adjacent regions in the shell. The lattice spacing can be directly measured from the image, and the projected symmetry is revealed by the Fourier transformations. The image clearly shows the structure of the shell, but the core is unresolved due to a different crystal orientation. The symmetry of

2.2 Phase Identification of Nanoparticles

Fig. 2.1 (a) Low-magnification TEM image recorded from a monolayer of dispersed nanoparticles, showing a mixture of larger-sized core–shell structured nanoparticles and smaller single-phase nanoparticles. (b) Enlarged TEM image showing the polycrystalline shell structure. (Adapted from [5], with permission from ACS).

Fig. 2.2 HRTEM image and corresponding Fourier transforms of the image recorded from a large-size core–shell nanoparticle, showing the spinel structure of the shell. The shell is composed of nanocrystallites; the two that can be identified from the image are oriented along [125] and [114] of Fe3O4. (Adapted from [5], with permission from ACS).

the local image and the interplanar spacing of the shell fit well to the spinel structure. The shell shows two grains oriented along [114, 125]. Energy-dispersive X-ray spectroscopy (EDS) is applied to determine if the shell is Fe3O4 or CoFe2O4. By using a fine electron probe of ~3 nm, EDS spectra were acquired by positioning at different parts of the large-sized nanoparticle. Figure 2.3 shows a comparison of EDS spectra acquired by positioning the electron probe through only the shell and through the core and shell, respectively. The spectra are displayed for different energy ranges. The copper and carbon signals came from the TEM grid. It is apparent that Fe dominates in the shell, while the

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Fig. 2.3 Comparison of the EDS spectra (displayed for different energy ranges) acquired from (a, b) the shell and (c, d) the core of a core–shell nanoparticle. The core is significantly rich in Co, but poor in oxygen. (Adapted from [5], with permission from ACS).

core is rich in Co, suggesting that the shell of the large-sized nanoparticle may be Fe3O4. It is, however, uncertain if the core would be the CoFe2O4 phase, although the EDS data show both Co and Fe signals (see Fig. 2.3 c and d). Electron diffraction and HRTEM have been applied in conjunction to determine if the core is CoFe2O4. HRTEM images can provide important real-space structural information, but only the particles oriented along specific directions and the lattice planes that are large enough to be resolved by TEM can give rise to lattice fringes in the image. The electron diffraction pattern recorded from a large number of particles has a unique advantage in that all of the lattice planes are represented in the diffraction pattern, and we can fit a wide range of diffraction peaks to uniquely determine the structure. Figure 2.4 a shows an electron diffraction pattern recorded from an array of over 200 core–shell structured nanoparticles. Using the standard crystallographic data for Fe3O4, a set of diffraction rings (with the indexes) has been identified. But there are three additional diffraction rings that

2.2 Phase Identification of Nanoparticles

Fig. 2.4 (a) Electron diffraction pattern recorded from core–shell nanoparticles for identifying the spinel phase. (b) Electron diffraction pattern recorded from a standard sample of a-Fe nanocrystallites for identifying the four unknown diffraction rings, as labeled with arrowheads. (Adapted from [5], with permission from ACS).

remain to be identified, which are weak and noncontinuous and are labeled with arrowheads 1, 2 and 4. If the core is CoFe2O4 and the shell is Fe3O4, no additional diffraction would be observed in the diffraction pattern because both of them have almost identical crystal structure and lattice parameters. The presence of additional peaks may suggest that the core could have a structure different from spinel. The question now is, what is this phase? The EDS data shown in Fig. 2.3 b indicate that the core should contain both Co and Fe. From the binary Co–Fe phase diagram [16] we found that, in a composition range (at%) of 29–75 % of Fe, there exists a CoFe (a') phase with an ordered CsCl structure (body centered cubic, bcc), with space group Pm3¯m (221), and lattice parameter a = 2.857 Å. The CoFe structure is almost identical to the bcc-structured a-Fe (a = 2.86 Å). Therefore, we may use the diffraction data recorded from a-Fe available to us to identify the unknown phase. A careful comparison of the electron diffraction pattern from the core–shell sample (Fig. 2.4 a) with the diffraction pattern recorded from a-Fe nanoparticles (Fig. 2.4 b) under identical experimental conditions shows that the additional three diffraction rings from the sample match the {110}, {200} and {220} rings of the a-Fe phase, although the {220} ring of a-Fe is weak. It is also noticed that the {211} ring of the a-Fe phase matches the {642} ring of the Fe3O4 phase. For the Fe3O4 phase, the d-space of the {642} is 1.1214 Å, which is very close to the {211} d-space of the a-Fe phase (d{211} = 1.1676 Å). Therefore, it is reasonable to believe that the diffraction ring corresponding to {642} of Fe3O4 overlaps with the {211} of a-Fe. Finally, the {110}, {200}, {211} and {220} diffractions of the a-Fe match well to the unidentified diffraction rings labeled 1–4, respectively, in Fig. 2.4a. As we discussed above, because the lattice parameters of the a-Fe phase and CoFe (a') phase are almost identical, it is suggested that the nanoparticles contain the CoFe (a') phase. Due

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2 Structures of Magnetic Nanoparticles and Their Self-Assembly Table 2.1 Phase identification by electron diffraction data.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

d (A˚) (measured ± 0.05)

Miller indexes CoFe Fe3O4

d (A˚) (standard data) Fe3O4 CoFe

2.93 2.51 2.08 2.01a) 1.70 1.61 1.47 1.43a) 1.33 1.28 1.21 1.16a) 1.09 1.05 1.02a)

{220} {311} {400}

2.966 2.53 2.096 {110}

{422} {511} {440}

2.0202 1.712 1.614 1.483

{200} {620} {533} {444} {642} {731} {800}

{211}

{220}

1.4285 1.327 1.279 1.2112 1.1214 1.0922 1.0489

1.1664

1.0101

a) Additional diffractions corresponding to a'-CoFe phase.

to a very low volume fraction of the core, the {100} and {111} diffraction rings from the CoFe (a') are too weak to be observed. The interplanar distances measured from the electron diffraction pattern and the standard data are compared in Table 1. The data confirmed that the CoFe (a') phase exists in the nanoparticles, but its real space location has to be identified by imaging. HRTEM helps to identify whether the core is CoFe. As mentioned above, it is difficult to get a high-quality HRTEM image from the core because the cores are embedded in the polycrystalline shells. In many cases, the cores show lattice fringes with a d-space of 2.02 Å, which corresponds to the {110} planes of CoFe (a'). Figure 2.5 shows HRTEM images recorded from the cores. Fourier filtering was used to extract the lattice fringe information by suppressing noise. HRTEM images with the incident beam along [001] (Fig. 2.5 a, b) and [111] (Fig. 2.5 c, d) of the core are shown. The corresponding lattice planes are indexed to be the {110} type and their interplanar spacing matches well to those of CoFe. Therefore, the core has the CoFe (a') structure. On the other hand, because CoFe has a significantly higher volume density than that of Fe3O4, the core generates more scattering than the shell, resulting in darker contrast, as observed in Fig. 2.1. Based on a conjunction application of high-resolution TEM, EDS microanalysis and electron diffraction, the structure of CoFe/Fe3O4 core–shell nanoparticles can be determined. It indicates the importance of quantitative structure analysis for the composite nanoparticles. The procedures and methodology presented here can be extended to the analysis of general nanoparticles that have a complex phase structure.

2.2 Phase Identification of Nanoparticles

Fig. 2.5 HRTEM images and the Fourier-filtered images recorded from the cores of a core–shell nanoparticle that is oriented along (a, b) [001] and (c, d) [111]. The structure is identified as CoFe (a’). (Adapted from [5], with permission from ACS).

2.2.2 FePt/Fe3Pt Nanocomposites [17]

The iron–platinum (Fe-Pt) alloys have been investigated for several decades because of their important applications in permanent magnetism [18–20]. Depending on the Fe to Pt elemental ratio, these alloys can display a chemically disordered face centered cubic (fcc) phase (A1, Fm3¯m) or chemically ordered phases, such as (L12, Pm3¯m) for Fe3Pt, face centered tetragonal (fct) (L10, P4/mmm) for FePt and (L12, Pm3¯m) for Pt3Fe [21, 22]. These structure variations have a dramatic effect on the magnetic properties of the alloys. For example, the Fe3Pt material is paramagnetic [23], the Pt3Fe is antiferromagnetic, while the L10 structured FePt has a large uniaxial magnetocrystalline anisotropy (Ku h 7 × 106 J m–3) [24, 25], and shows strong ferromagnetic properties [26]. Various experimental results have revealed that the L10-type structure can be formed in FexPt1–x with x ranging from 0.35 to 0.60 [27]. The iron-rich L10-FePt alloy-based nanocrystal materials have shown excellent hard magnetic properties [20, 28, 29], and are expected to be a new generation of ultrahigh-density magnetic recording media [29–31].

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The research interest in FePt/Fe3Pt nanocomposites is due to the theoretical prediction that two-phase materials with exchange-coupled magnetically hard and soft phases may greatly enhance the energy products, and it is well known that FePt and Fe3Pt belong to, respectively, hard and soft magnetic phases. Quantitative EDS analyses were carried out with a beam size of ~3 nm for different nanocomposite samples. The main EDS results are as follows: (1) some of the aggregated larger particles have a composition of FePt, while some other aggregates are Fe-rich; (2) some of the small nanocrystallites with sizes < 10 nm within the large aggregates have the composition of the Fe3Pt phase. The L10 FePt phase has a chemically ordered fct structure with a = 0.3861 nm and c = 0.3788 nm; the Fe3Pt phase has a structure of either disordered fcc or ordered L12 with a = 0.3730 nm. These three kinds of structures have very close lattice parameters, although L10 (fct) FePt and L12 Fe3Pt have different ordered Fe

Fig. 2.6 Structure models of FePt (L10) and Fe3Pt (L12) and the corresponding projections of the structures along different zone axes. (Adapted from [17], with permission from American Institute of Physics).

2.2 Phase Identification of Nanoparticles

and Pt distributions in the unit cell, but they will have different [001] projected potentials with different composition modulation periodicities, while the fcc-structured Fe3Pt does not. Also, the L10 (fct) FePt has a layered Fe and Pt distribution for the [100] or [010] projection (see Fig. 2.6 and the insets in Fig. 2.7 a and b). For thin samples, the HRTEM image can be interpreted as a projected potential image of the sample under certain imaging conditions [32]. Thus, by using HRTEM images of <001> oriented particles, we will be able to identify and distinguish different phases. The typical objective lens defocus (Df ) values we have used are 250 to 50 nm; the typical sample thickness is in a range of 4–12 nm. Figure 2.7 a shows a typical HRTEM image of a [001] oriented L10 (fct) FePt particle with a strong composition modulation. Figure 2.7 b shows an HRTEM image of a [100]

Fig. 2.7 HRTEM images for different phases in FePt nanocomposites. (a) [001] L10 (fct) FePt particle, with the insets showing schematic [001] L10 structure projection and simulated HRTEM image (Df = –12 nm, thickness = 4.56 nm). (b) [001] fcc Fe3Pt particle, with insets showing schematic [001] fcc projection and simulated HRTEM image (Df = 0 nm, thickness = 5.7 nm). (Adapted from [17], with permission from American Institute of Physics).

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Fig. 2.8 HRTEM images of an FePt/Fe3Pt interface in FePt-based nanocomposites; FePt and Fe3Pt phases coexist within a common grain as domains. The inset shows the Fourier-filtered HRTEM images from the corresponding area, as marked by the rectangle. (Adapted from [17], with permission from American Institute of Physics).

oriented fcc Fe3Pt particle without composition modulation. The insets in Fig. 2.3 a and b also show simulated HRTEM images corresponding to the experimental images. The weak contrast of Fe atoms in the simulated images cannot be observed experimentally due to the limited resolution and the background from the amorphous carbon film. Figure 2.8 shows the FePt/Fe3Pt interface for the samples deposited onto TEM grids. The FePt and Fe3Pt phases are coexistent as domains within a single grain. Mostly, the FePt and Fe3Pt phases coexist as different domains with sizes <10 nm within a common grain (see Fig. 2.8), displaying an excellent magnetically hard/soft-phase nanocomposite. This microstructure is consistent with the measured magnetic properties from these samples [33]. The images also show that the FePt and Fe3Pt phases have the same orientation as defined by their fcc crystal structure, and that the interfaces between the FePt and Fe3Pt phases are completely coherent without misfit dislocation.

2.3 Determining the Nanoparticle Shapes and Surfaces

Surface energies associated with different crystallographic planes are usually different, and a general sequence may hold, g {111} < g {100} < g {110}, for fcc-structured metallic nanoparticles [34]. For a spherical single-crystalline particle, its surface must contain high-index crystallography planes, which possibly result in a higher surface energy. Facets tend to form on the particle surface to increase the

2.3 Determining the Nanoparticle Shapes and Surfaces

portion of low-index planes. Therefore, for particles smaller than 10–20 nm, the surface is a polyhedron. The most frequently observed shapes at the nanometer scale are tetrahedron, cuboctahedron, truncated octahedron, icosahedron, regular and round pentagonal, although some unusual and complex shapes have been found, such as Co nanoparticles [35]. By controlling the synthesis conditions, we can get truncated tetrahedral platelet, truncated octahedral, and octahedral Fe3O4 magnetic nanoparticles and cuboctahedron FePt nanoparticles. 2.3.1 The Shape of Fe3O4 Nanoparticles

The synthesis of magnetic iron oxide nanocrystals is of key scientific and technological interest in magnetic data storage, biological applications, drug delivery and ferrofluids [36, 37]. Recent syntheses on magnetite nanocrystals have focused on size and shape control [15, 38, 39]. A typical TEM image of a monolayer of Fe3O4 nanoparticles is shown in Fig. 2.9. The inserted selected-area electron diffraction (SAED) pattern confirms that these nanoparticles belong to the Fe3O4 cubic spinel structure. The ring features of the SAED pattern indicate the random orientations of the nanoparticles.

Fig. 2.9 Monolayer Fe3O4 nanocrystals; the inserted SAED pattern indicates that the orientation of the nanocrystals is random.

Figure 2.10 a, c and e show three HRTEM images of Fe3O4 nanoparticles taking the truncated tetrahedron, truncated octahedron and octahedron shapes, respectively. The clear lattice images indicate that the nanoparticles are well-crystallized. The truncated tetrahedron shape of the nanoparticle in Fig. 2.10 a can be easily distinguished from the dark-field image inserted in Fig. 2.10 b, which shows uniform contrast across its width, indicating uniform thickness. Thus, the exposed top/bottom surfaces are +{111} planes. The diagram of a truncated tetrahedron is depicted in Fig. 2.10 b, which is looking down from the [111] direction. The truncated octahedron shape in Fig. 2.10 c is looking down from the [100] direction,

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Fig. 2.10 HRTEM images of truncated tetrahedron (a), truncated octahedron (c) and octahedron (e) shaped Fe3O4 nanoparticles. The corresponding diagrams are depicted in (b), (d) and (f), respectively.

as indicated in the diagram in Fig. 2.10 d. The exposed surfaces are {100}, {110} and {111} planes. The octahedron in Fig. 2.10 e is looking down from the [110] direction, as indicated by the HRTEM image. The contrast variation from right to left corresponds to the thickness variation. The diagram of an octahedron is displayed in Fig. 2.10 f. 2.3.2 The Shapes of FePt Nanoparticles

FePt nanoparticles have been synthesized by a polyol reduction process [40]. Figures 2.11 a–y are HRTEM images of FePt nanoparticles projected along the <100> or <110> orientation. The particle sizes are approximately 2 nm. Careful examination of the HRTEM images reveals that the particles show good crystallinity, with many being single crystals and some possessing multiple twin boundaries within the particle. The crystal structure of the particles is chemically disordered fcc and the (100) lattice spacing is about 3.8 Å, which is consistent with the known fcc FePt structure. The octahedron shape can be clearly identified in Fig. 2.11 h and l, while the nanoparticles in Fig. 2.11 i, k, p, q and x take a truncated octahedron shape. The most popular exposed surfaces are {111}, then {100} and {110} planes.

2.4 Multiply Twinned FePt Nanoparticles

Fig. 2.11 (a–y) TEM images of as-synthesized ultrafine FePt particles.

2.4 Multiply Twinned FePt Nanoparticles [41]

Although the predominant shape of FePt nanoparticles is a truncated octahedron, some other shapes are also observed. Figure 2.12 a shows an HRTEM image of the as-synthesized FePt nanoparticle, in which the fivefold twinning-related domains are identified. In order to study the structure in detail, image processing is demonstrated by the Fourier-filtering technique [42]. Simply, a fast Fourier transform (FFT) is applied to a digitized HRTEM image for producing a power spectrum of the image. Then a Bragg filter is generated with circular “holes” at the positions of the Bragg spots of the periodic part of the image. The multiplication of the power spectrum with the filter is followed by a reverse FFT to produce a filtered image. A proper choice of the size of the holes is important to prevent artifacts in the image. Figure 2.12 d is an FFT of the image shown in Fig. 2.12 a, and Fig. 2.12 b is the corresponding filtered image. The dotted lines marked by OA,

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Fig. 2.12 (a) HRTEM image of the as-synthesized FePt nanocrystal with the Marks decahedron shape. (b) Fourier-filtered image. (c) Schematic polyhedron model. (d) FFT pattern of the image shown in (a). (Adapted from [41], with permission from Elsevier).

OB, OC, OD and OE in Fig. 2.12 b represent the positions of the twin boundaries. The twin boundaries are coherent and free from defects such as stacking fault, dislocation or micro-twin. The angle between two adjacent boundaries varies within 71.5–72.58. This feature can also be verified from the FFT pattern (Fig. 2.12 d), where reflections A, B, C, D and E are produced from the twin boundaries OA, OB, OC, OD and OE, respectively. The shape of the nanoparticle obviously is the so-called Marks decahedron [43], i. e., a truncated regular decahedron. Figure 2.12 c gives a schematic diagram of a regular decahedron OO1ABCDE, and the Marks decahedron is shown in shadow. Shown in Fig. 2.13 a is another FePt nanoparticle with a spherical shape. The corresponding Fourier-filtered image (Fig. 2.13 b) and FFT pattern (Fig. 2.13 d), however, illustrate that the nanoparticle consists of six domains with sixfold twins. The twin boundaries are indicated by dashed lines OF, OP, OL, OR, OI and OQ, as shown in Fig. 2.13 b, in which neither the twin boundary OF is parallel to the twin boundary OR, nor OQ to OL. The angles between OF and OR, and OQ and OL, are about 6˘, which is responsible for the split spots K and J, and H and G in

2.4 Multiply Twinned FePt Nanoparticles

Fig. 2.13 (a) HRTEM image of the as-synthesized FePt nanocrystal with icosahedron-related shape. (b) Fourier-filtered image. (c) Schematic polyhedron model. (d) FFT pattern of the image shown in (a). (Adapted from [41], with permission from Elsevier).

the FFT pattern (Fig. 2.13 d). In contrast, the twin boundary OI is parallel to that of OP. The corresponding reflections P and P' in Fig. 2.13 d, therefore, are not split although they are a bit diffuse. Figure 2.13 c gives a schematic model of the twins in the FePt. Multiply twinned particles are usually observed in fcc-structured small metal particle systems, which are mainly associated with either a decahedron or icosahedron. The decahedron can be regarded as being composed of five tetrahedra A-EOO1, B-AOO1, C-BOO1, D-COO1 and E-AOO1 by sharing faces, as shown in Fig. 2.12c. For the case of fcc stacking, a tetrahedron is enclosed by four {111} crystal planes with an including angle of 70832' between two neighboring planes. If five fcc stacked tetrahedra directly form a decahedron, a 7820' gap remains. The gap can be accommodated by straining the atomic lattice. If the strain is uniformly distributed in the decahedron, a disclination will form at the center of the decahedral particle [44]. That is just the case for the FePt nanoparticle shown in Fig. 2.12. The strain can also be relaxed by forming a stacking fault or micro-twin in the particle [45]. Several variants of the decahedron exist, such as star, round

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pentagonal and Marks decahedron. Among these the Marks decahedron is the most common shape since it contains extra {111} facets, resulting in remarkable stability [45]. Ino [46] and Allpress et al. [47] first proposed several models for the multiply twinned particles with shapes associated with an icosahedron. Shown in Fig. 2.14 a is one of the models. The multiply twinned particle is formed by nucleation of a tetrahedral atomic cluster O-ABC with its ABC plane facing on a substrate. Then three more tetrahedra, F-AOB, I-BOC and L-AOC, grow on three {111} planes of the nucleus AOB, BOC and AOC by sharing a face, respectively, thus forming primary twins. Following that, the six tetrahedra E-FAO, G-FBO, H-BIO, J-CIO, D-ALO and K-CLO grow on the surfaces of the primary twins to form secondary twins. The corresponding diffraction pattern is schematically shown in Fig. 2.14 c, where only the {111} reflections from the secondary twins are displayed. Comparing the diffraction pattern (Fig. 2.14 c) with the FFT pattern (Fig. 2.13 d), they are not matching because the reflections P and P' in Fig. 2.13 d are not splitting, whereas that occurs in Fig. 2.14c. This indicates that the model (Fig. 2.14 a) cannot be used to explain the structure of the multiply twinned nanoparticle displayed in Fig. 2.13. A modified model, therefore, is suggested (Fig. 2.14 b). The only difference between the modified model and the previous

Fig. 2.14 (a) The Ino model of icosahedron-related multiply twinned nanoparticles, and (c) the corresponding diffraction pattern. (b) A new model suggested in the present study, and (d) the corresponding diffraction pattern. (Adapted from [41], with permission from Elsevier).

2.5 Phase Transformation and Coalescence of Nanoparticles

model (Fig. 2.14 a) is that two {111} planes DAO and FAO are joined in parallel. As a result, the split reflections E and D (Fig. 2.14 c) overlap to form a reflection P, which reproduces the pattern of Fig. 2.13d.

2.5 Phase Transformation and Coalescence of Nanoparticles [48]

To fully understand the magnetics of the FePt-based nanomaterials, it is essential to synthesize monodisperse FePt particles with controlled size and composition and study the structure transformation within each particle after various thermal treatments. It will also be important to know the aggregation behaviors of these annealed nanoparticles. The synthesis has been attempted by various vacuum deposition techniques [49–52]. However, random nucleation in the process generally results in broad distributions of particle sizes, which complicates the observations on particle structure transformation and particle magnetics. Recently, monodisperse FePt nanocrystals with good control of particle size and composition were produced by a solution-phase chemical procedure [29]. These monodisperse FePt nanocrystals become ideal candidates for microscopic study on thermal-annealing-induced structure transformation. Previous thermal annealing experiments have shown that, for stoichiometric bulk FePt alloy, the A1 to L10 transformation temperature is 1300 8C [53], while for nanoscale FePt particles this temperature is lowered to within 500–700 8C, depending on the FePt stoichiometry and particle sizes [17, 29, 54]. Our transmission electron microscopy (TEM) studies show that A1 to L10 phase transformation occurs at 530 8C. The multilayered nanocrystal assemblies coalesce to form larger grains at 600 8C. We notice that the coalescence temperature of the nanocrystal monolayer assembly depends on the substrate used. On SiO2 substrate, the FePt nanocrystal monolayer can stand up to 700 8C without any obvious aggregation. The coalesced nanocrystals show a dominant {111} twin defect inside, while their surface and coalescent grain boundary consist of both {111} and (001) facets. The monodisperse FePt nanocrystals are synthesized by reduction of platinum acetylacetonate (Pt(CH3COCHCOCH3)2) and decomposition of iron pentacarbonyl (Fe(CO)5) in the presence of oleic acid and oleyl amine stabilizers [29]. The size and composition of the FePt nanoparticles can be readily controlled. Their composition is adjusted by controlling the molar ratio of iron carbonyl to the platinum salt. In the present study, the 6-nm FePt nanocrystals are synthesized by first growing 3-nm monodisperse FePt seed crystals and then adding more reagents to enlarge the seed crystals to the desired size under a 2 : 1 molar ratio of iron carbonyl to the platinum salt. These nanocrystals are isolated and purified by centrifugation after the addition of a flocculent (for example, ethanol) and can be redispersed in nonpolar solvents in a variety of concentrations. Shown in Fig. 2.15 a is a low-magnification TEM image of the as-synthesized monodisperse FePt nanocrystals. The size of the nanocrystals is about 6 nm in diameter. HRTEM observation of an individual nanocrystal (Fig. 2.15 b) indicates

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Fig. 2.15 (a) TEM image of the as-synthesized Fe52Pt48 nanocrystals and (c) the corresponding selected-area electron diffraction pattern. (b) HRTEM images of the as-synthesized individual Fe52Pt48 nanocrystals. TEM images of the Fe52Pt48 nanocrystals after annealing at 530 8C for 1 hour (d) and at 600 8C for 1 hour (e). Selected-area electron diffraction patterns of the Fe52Pt48 nanocrystals recorded in situ at 530 8C for 1 hour. (Adapted from [48], with permission from ACS).

very good crystallinity and a dominant truncated octahedral shape. The truncated octahedron is enclosed by the {100} and {111} crystal facets of the fcc structure, indicating that the as-synthesized FePt nanocrystals have a chemically disordered fcc (A1) phase of which the lattice parameter is a = 0.376 nm. The fcc structure feature of the as-synthesized FePt nanocrystals is also shown in their electron diffraction pattern. Figure 2.15 c is such a pattern from the selected-area diffraction of the nanocrystal assembly. The composition of the nanocrystals is determined to be very close to Fe52Pt48 by energy-dispersive X-ray spectroscopy (EDS). To study the phase transformation from the chemically disordered A1–FePt phase to the chemically ordered ferromagnetic L10-FePt phase, in situ thermal annealing is applied to the as-synthesized FePt nanocrystal assembly. At temperatures below 450 8C, no obvious assembly or structure change is observed. At temperatures beyond 450 8C, multilayered nanocrystal assemblies start to decay gra-

2.5 Phase Transformation and Coalescence of Nanoparticles

Fig. 2.16 (a) HRTEM image of an individual Fe52Pt48 nanocrystal after annealing at 530 8C for 1 hour. (b) An enlarged HRTEM image of the chemically ordered L10-FePt structure and (c) a Fourier transform of the corresponding HRTEM image. (d) Simulated electron diffraction pattern and (e) the corresponding simulated HRTEM image demonstrated under the conditions: 400 kV, Cs = 1.0 mm, thickness = 8 nm, defocus = –74 nm and beam divergence = 0.15 mrad. (Adapted from [48], with permission from ACS).

dually. Further annealing at 530 8C transforms the chemically disordered A1 phase to the chemically ordered L10 phase. The TEM image (Fig. 2.15 d) shows the morphology of FePt nanocrystals isothermally treated at 530 8C for 1 hour. It shows that most of the hexagonally packed monolayer nanocrystal assemblies are almost intact, while regular-arrayed multilayer assemblies are deteriorated by this thermal treatment. The corresponding electron diffraction pattern is shown in Fig. 2.15 f. Comparing the diffraction patterns shown in Fig. 2.15 f with those in Fig. 2.15 c, different reflection rings, such as {110}, {120}, {112}, etc., appear, indicating the occurrence of phase transformation from the chemically disordered A1

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fcc phase to the chemically ordered L10 fct phase. Continually heating the specimen at higher temperature results in the coalescing of these nanocrystals. Figure 2.15 e shows a TEM image taken from the specimen undergoing an isothermal treatment at 600 8C for 1 hour, after which most of the nanocrystals, especially in multilayer regions, coalesce with only some dots in the monolayer region staying intact. Figure 2.16 a is an HRTEM image of one of the intact FePt nanocrystals. Comparing this with the image shown in Fig. 2.15 b, an intensity modulation of image spots can be identified, as marked by arrowheads in Fig. 2.16 a, indicating the formation of the chemically ordered L10-FePt structure. To illustrate the detailed atomic arrangement within a single nanocrystal, an enlarged HRTEM image is shown in Fig. 2.16 b. FFT of such an atomic arrangement reveals distorted twofold symmetry, as shown in Fig. 2.16 c. This diffraction pattern matches well with that generated from theoretical simulations based on dynamic diffraction theory for the L10-FePt structure (Fig. 2.16 d) with the [110] beam and lattice parameters a = 0.3861 nm and c = 0.3788 nm. The HRTEM image of the atomic arrangement obtained from the simulation (Fig. 2.16 e) is identical to the image shown in Fig. 2.16 b, confirming the intensity modulation occurring along the c-axis of the L10-FePt Phase, along which Fe and Pt atoms stack alternately, i. e.,

Fig. 2.17 HRTEM images of coalescent Fe52Pt48 grains after annealing at 600 8C for 1 hour. (Adapted from [48], with permission from ACS).

2.6 Self-Assembled Nanoarchitectures of Fe3O4 Nanoparticles

the intensity change of image spots along the c-axis is due to chemical ordering (composition modulation) in the L10-FePt structure. The structure of the coalesced FePt nanocrystals has also been studied. Figure 2.17 shows two HRTEM images of typical coalescent large FePt grains. The grain shown in Fig. 2.17 a consists of three individual FePt nanocrystals and, in Fig. 2.17 b, is from two nanocrystals. Twinning is a characteristic feature of the microstructure of the coalescent grains. The dashed lines marked in Fig. 2.17 a and b represent twin boundaries in the coalescent FePt grains, which usually form a coherent or semicoherent interface between coalesced FePt nanocrystals. The composition modulation in the L10-FePt structure is indicated by black arrowheads in Fig. 2.17 a and b. The white arrowheads indicate the direction of the magnetic easy axis, i. e., the c-axis direction of L10-FePt.

2.6 Self-Assembled Nanoarchitectures of Fe3O4 Nanoparticles

By controlling the self-assembly process, the different shaped Fe3O4 nanoparticles can be separated to form different orientation-ordered superstructures. The superstructure self-assembled by the truncated tetrahedron-shaped Fe3O4 nanoparticles is shown in Fig. 2.18 a. The inserted high-magnification image shows the building

Fig. 2.18 (a) Low- and high-magnification TEM images showing the hexagonal superstructure built up by the truncated tetrahedral platelets (TTP) of Fe3O4 nanocrystals. (b) The SAED pattern. (c) HRTEM image of a single TTP nanocrystal. The model inserted between (c) and (d) shows the shape of the nanocrystal. (d) Top view of the superstructure.

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blocks taking the shape of a truncated tetrahedral platelet and having uniform size distribution. The amazing phenomenon is that the SAED pattern from the self-assembled nanoparticles (Fig. 2.18 b) shows the single-crystal type [111] zoneaxis pattern, which indicates the orientation ordering among the nanoparticles in the assembly. The truncated tetrahedral shape has been distinguished from the dark-field image inserted in Fig. 2.8 b, which shows uniform contrast across its width, indicating uniform thickness. The model of a nanoparticle is inserted in between Fig. 2.18 c and d; two {111} planes served as the top/bottom surfaces and six intersected {111} and {100} planes composed the side surfaces. Using the model as building block, the self-assembled superstructure is sketched in Fig. 2.18 d. The nanoparticles in plane tend to pack as closely as possible. In the perpendicular direction, the second plane tends to overlap right on the bottom plane without translation; this case can be justified from the holes in the multilayer area. Thus, the hexagonal superstructure is formed. The Fe3O4 truncated octahedral self-assembled superstructure is shown in Fig. 2.19 a. The high-magnification image from a multilayer area is inserted in Fig. 2.19 a. The corresponding SAED pattern is displayed in Fig. 2.19 b. As for the case in Fig. 2.15, the self-assembly is also orientation-ordered. The electron beam of the SAED pattern is parallel to [001]. The HRTEM image of a single truncated octahedral nanoparticle is shown in Fig. 2.19 c; the four edges correspond to {220} planes. The three-dimensional model and the two-dimensional projection of the

Fig. 2.19 (a) Low- and high-magnification TEM images showing the primitive cubelike superstructure built up by the truncated octahedral (TO) Fe3O4 nanocrystals. (b) The SAED pattern. (c) HRTEM image of a single TO nanocrystal. (d) The three-dimensional model and two-dimensional projection of the nanocrystal. (e) Top view of the superstructure.

2.6 Self-Assembled Nanoarchitectures of Fe3O4 Nanoparticles

truncated octahedral Fe3O4 nanoparticle are illustrated in Fig. 2.19 d. The self-assembled superstructure built by the truncated octahedral nanoparticles is sketched in Fig. 2.19 e. The second layer overlapped on the first layer without translation or twist, forming a simple cubelike superstructure. The image in Fig. 2.20 a displays the superstructure built up by the octahedral nanoparticles. From the inserted image, the overlap among the octahedra can be clearly observed. The SAED pattern in Fig. 2.20 b indicates that most of the building blocks take the same crystal orientation, which is [110]. The HRTEM image of a single nanoparticle in Fig. 2.20 c shows a well-faceted structure; the low contrast of the two horizontal corners is consistent with the projected thickness of the octahedron. The three-dimensional model is depicted in Fig. 2.20d. The top-view and side-view illustrations of the self-assembled superstructure are sketched in Fig. 2.20 e and f, respectively. The self-assembly can be approximated to a distorted body centered cubic superstructure. The fact that the observed three types of 3-D superstructures and their corresponding specific orientation ordering depend on the shapes of Fe3O4 nanoparticles ambiguously elucidates that the shape of nanoparticles plays a crucial role in determining both the structure and orientation of 3-D superstructures. As illustrated above, one can clearly see that the striking feature in the packing sequence is the face-to-face (facet-to-facet) mode in all three types of superstructures. Similar shape-related 3-D superstructures with preferential orientation have been re-

Fig. 2.20 (a) Low- and high-magnification TEM images showing the body centered cubic superstructure built up by the octahedral Fe3O4 nanocrystals. (b) The SAED pattern. (c) HRTEM image of a single octahedral nanocrystal. (d) The three-dimensional model the nanocrystal. (e) Top view and (f) side view of the superstructure.

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ported in truncated octahedral thiol-capped Ag nanoparticles, where face centered cubic (fcc) superstructures have orientation along the [110] direction [55]. Presumably, such oriented superstructure formation essentially originates from the energy balance between the van der Waals (vdW) attractive potential and repulsive potential among nanoparticles. In the case of faceted nanoparticles, theoretical studies point out that the orientation is mainly determined by the maximization of the vdW interactions between the facets of neighboring nanoparticles [56–59]. The face-to-face stacking mode gives rise to stronger vdW interactions than that of either edge-to-edge or corner-to-corner packing. The reason is that the vdW interaction energy for the face-to-face mode is inversely proportional to the square of the distance between the two faces, whereas for edge-to-edge packing, the vdW interaction energy is inversely proportional to distance [60, 61]. Consequently, the face-to-face stacking is the choice for maximizing the vdW interactions among nanoparticles, and our experimental results are in good agreement with such a theoretical predication.

2.7 Summary

Structure analysis is important for understanding the physical and chemical properties of nanoparticles. This chapter reviews the applications of TEM in determining the structures of magnetic nanoparticles, including particle phase, shape, surface structure, phase transformation and self-assembled arrays. This chapter should serve as the basis for understanding the structure of nanoparticles and their self-assemblies. Using the techniques illustrated here, readers can study a wide range of nanomaterials.

Acknowledgment

The work reviewed here was partially contributed by our collaborators Drs. Shouheng Sun, J. Ping Liu, Hao Zeng, Zurong Dai and Qing Song. Thanks go to NSF and DARPA for support.

References

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3 Self-Organization of Magnetic Nanocrystals at the Mesoscopic Scale: Example of Liquid–Gas Transitions Johannes Richardi and Marie-Paule Pileni

3.1 Introduction

The fabrication of structures at the nanometric and mesoscopic scale is one of the great challenges in nanotechnology. A promising approach is the use of self-organization of nanocrystals. In this, solid mesostructures of submicron dimensions are prepared by evaporation of nanocrystal solutions. When the nanocrystals are magnetic, the organization is markedly influenced by the direction of the magnetic field applied during the evaporation process. Thus, in a field parallel to the substrate the particles organize in chainlike structures [1–3], whereas a perpendicular field induces labyrinthine and hexagonal structures [4, 5]. Here, we show that the mesoscopic organization of magnetic nanocrystals is explained by a liquid–gas transition widely observed in colloidal systems [6]. The experimental preparation and deposition of magnetic nanocrystals is described in detail in Chapter 1 of this book. A colloidal solution of magnetic nanocrystals (ferrofluids) is regarded as a dipolar fluid [7]. The theoretical study of dipolar fluids has attracted much interest during the last few decades and many discoveries in this domain are of importance for the understanding of the organization of magnetic nanocrystals. Since 1990, the theoretical study of dipolar fluids has been divided into two major directions boosted by the progress in computer simulation. The first direction focuses on the orientational and structural correlations in dipolar liquids. The discovery of spontaneous magnetization at zero field [8] and the investigation of dipolar chaining [9] are examples of this evolution. The other field of great interest is the exploration of the phase diagram, in particular the liquid–gas transition, in dipolar systems [10]. This chapter is organized as follows. First, we review the literature on simulations of liquid–gas transitions in colloids and dipolar systems. Then, the simulation studies of the orientational and structural correlations in dipolar fluids are discussed. We show that these results are not sufficient to explain the organization of magnetic nanocrystals like those discussed above. Recent Brownian dynamics simulations are presented, which explain the chainlike structures Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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observed in a parallel field as a liquid–gas transition. Finally, a recently developed free energy theory of magnetic nanocrystal organization in a perpendicular field is described.

3.2 Simulation Studies of Liquid–Gas Transitions (LGT) in Colloids and Dipolar Systems 3.2.1 Liquid–Gas Transitions in Colloids

In analogy to the phase diagram of atomic and molecular systems, gas, liquid and solid phases are defined for colloids [6]. Diluted colloids in a liquid solvent correspond to the gas phase, while the liquid phase is a concentrated solution of the colloidal particles. A colloidal solid is, usually, a face-centered-cubic packing assembly [11]. The transitions between these phases in colloids have been widely studied and we present only a short introduction to this work, since an excellent review article was recently published [6]. Colloids with negligible attraction between the particles are often described as systems of hard spheres, which have no liquid–gas transition. Only a transition between fluid and crystalline phases at a volume fraction of about 0.5 is observed (Fig. 3.1 a). A minimum amount of attraction between the particles is obviously required to obtain a liquid–gas transition (Fig. 3.1 b). The LGT is usually observed at volume fractions considerably smaller than 0.5. When the interparticle attraction has a very short range, the gas–liquid equilibrium becomes metastable [11]. Colloids, such as nanocrystals, attract each other due to van der Waals and solvent-mediated interactions. Mixtures of colloids

Fig. 3.1 Phase diagrams of colloids: (a) Hard-sphere systems display only fluid (f) and crystal (s) phases. Above the so-called “freezing” volume fraction, Ff = 0.494, entropy favors that some particles form crystals. Above the so-called “melting” volume fraction, Fm = 0.545, only a solid phase should exist. (b) The addition of attraction leads to the appearance of a gas–liquid transition.

3.2 Simulation Studies of Liquid–Gas Transitions in Colloids and Dipolar Systems

and polymers are widely studied, since the addition of polymer produces an attraction between the particles due to depletion interactions [12]. Thus, the range and depth of interactions is tuned by the size and volume fraction of the polymer. It must be emphasized that the equilibrium diagrams only rarely predict the experimentally observed phases. Due to the slow dynamics of phase transitions, colloids often become undercooled, supersaturated or trapped in gel-like states. There has been a large volume of theoretical work on particle aggregation predicting the size distribution and fractal dimensions of clusters [13]. Recently, the nucleation and growth of a condensed phase from a gas phase has attracted much interest. The progress in computational technology enables the simulation of this phenomenon at a particle level [14, 15]. However, most work is concentrated on systems, such as hard spheres, where only a transition between fluid and solid phases exists. 3.2.2 Liquid–Gas Transition in Dipolar Systems

We only briefly review the literature on liquid–gas transition in dipolar systems. For more details, a review article has recently been published [16]. Most theoretical work focuses on interaction models without attraction, such as hard or soft spheres with dipoles. These systems are characterized by the reduced density, r* = rs3, and temperature, T* = 4 p m0 kT s3/m2, where s, m and k are the particle diameter, dipole moment and Boltzmann constant, respectively. The dipole moment is calculated from the bulk magnetization using m = p/6 s3m0 Ms , where m0 is the magnetic permittivity in vacuum. The thermodynamics of these systems was mainly studied by the Gibbs ensemble or constant-pressure Monte Carlo simulations. The central question was, can a liquid–gas transition be induced only by large dipole–dipole interactions? Initial simulations have shown that the usual LGT driven by the isotropic aggregation of particles is absent in dipolar fluids [10, 17]. Theories attributed this absence to the formation of chains, which only weakly interact [18]. Thus, there is only little energy to be gained by chain aggregation, which is the driving force for the formation of a liquid phase. Moreover, the formation of chains prevents the density of free unassociated particles from reaching the minimum necessary for a LGT [19]. However, from simulation [20] and theory [21], there is evidence for another type of phase transition in dipolar systems. It is interpreted as a coexistence of a low-density phase of chain ends and a phase dominated by Y chain junctions. However, to the best of our knowledge, this interpretation has not yet been confirmed by simulations. The estimated critical temperature (Tc* = 0.2) and density (r c* = 0.1) are unusually low compared to simple fluid values. These phase transitions were not observed by Gibbs ensemble Monte Carlo simulations, since these are apparently unreliable in the relevant system of temperature and density [20]. In an applied field, phase coexistence is also observed for highly dipolar particles, yet again not the usual LGT [22]. No significant structural differences are observed between the two coexisting phases. The critical parameters are very low. Tc increases with the field strength, while rc is field-independent.

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By an additional attractive energy between the particles, the usual LGT is restored. Several simulation studies investigated phase coexistence in Stockmayer fluids, which consist of point dipoles additionally interacting via an attractive Lennard–Jones (LJ) potential [23, 24]. The LJ system with no dipole interaction has a critical point at Tc* = 1.316 and r c* = 0.304 [25]. The critical density is not sensitive to the dipole strength. On the contrary, the critical temperature is a rapidly increasing function of this parameter [23]. Obviously, the presence of dipolar interaction favors the LGT transition. The influence of an external field on the LGT of Stockmayer fluids was also studied [23]. As for dipole particles without LJ potential, Tc increases with the field due to stronger dipole interactions, while rc only slightly changes. The study of the nucleation in supersaturated fluids of Stockmayer particles is of great interest for the understanding of mesoscopic organizations of magnetic nanocrystals [26, 27]. The nucleation is not induced by high concentration but by very low temperatures. Actually, the density is so low that without association the gas is ideal. The study is mainly interested in the influence of a high dipole moment on the nucleation. For highly dipolar particles the nucleation process is initiated by chainlike clusters (Fig. 3.2, left). When these clusters exceed a certain size, they condense to form compact dropletlike nuclei. However, the interface of these droplets has still a large fraction of chains (Fig. 3.2, right). The classical nucleation theory underestimates both the size of the critical nucleus and the height of the nucleation barrier, which is in agreement with the experiments on strongly dipolar fluids. Finally, the phase behavior of elongated dipolar particles without van der Waals interaction was also studied [28]. Due to the nonspherical shape, the strong aniso-

Fig. 3.2 Nucleation of highly dipolar particles. Initially, the clusters are chainlike (snapshot, left), but at a cluster size of 30 they collapse to compact spherical nuclei (snapshot, right). Images taken from [21].

3.3 Orientational and Structural Correlations in Dipolar Fluids

tropy of the dipolar interaction is overcome and the energies of the nose-to-tail and side-by-side arrangement become equal. Then, LGTs occur more easily and they retain the ability to cluster isotropically in three dimensions like Stockmayer fluids, even without van der Waals attraction.

3.3 Orientational and Structural Correlations in Dipolar Fluids

The structure of dipolar systems has been widely studied using Monte Carlo simulations, molecular dynamics and Brownian dynamics [29]. The organization of dipolar particles is determined by the ratio l of the dipolar to thermal energy: lˆ

m2 4 p m0 d3pp kT

…1†

where dpp = s + d is the center-to-center distance between particles (Fig. 3.3). For the models of dipolar hard and soft spheres, dpp = s and l = 1/T*.

Fig. 3.3 Sketch of two magnetic particles: s, d and m denote the particle diameter, spacing and magnetic moment, respectively.

In a pioneering work, Chantrell et al. [30] observed the formation of chains and rings for highly dipolar particles. The chainlike structures behave as “living polymers” breaking and recombining [31]. The onset of chain formation is usually observed at l > 4 [32, 33]. Chains appear already at very low densities (r* = 0.001) [34]. As a field is applied, the clusters break up to form chains aligned in the direction of the field [30]. The critical value of 4 for chain formation is only slightly decreased in the presence of a magnetic field [35]. Also, in two-dimensional systems, where the dipolar particles are confined in a plane, chains appear for l > 4 as in the 3D case [36]. The theoretical predictions are confirmed by experiments which show chains for large magnetic nanocrystals of iron [37] and cobalt [38]. The number of branching points between the chains increases with the density and a network is observed. As the density is raised further (r* > 0.6), the network structure is destroyed, to be replaced by a more normal dense liquid state [32, 33]. For large dipolar coupling (l > 6) and high densities (r* > 0.6), the systems become spontaneously polarized and a ferroelectric nematic state appears [39–41].

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In contrast, no evidence for ferroelectric ordering is observed in 2D dipolar systems [42]. Recently, the influence of the polydispersity on the structure of dipolar fluids has been studied [43]. It shows that chains of larger dipolar particles do not induce the aggregation of smaller particles in polydisperse systems.

3.4 Mesoscopic Organization of Magnetic Nanocrystals in a Parallel Field

The previous section shows that dipolar particles align in chains for l > 4. Assuming an edge–edge core spacing, d, of about 2 nm, a l value of 0.7 for 10-nm maghemite nanocrystals is obtained (Ms = 3.76105 Am–1) [3]. For cobalt nanocrystals, a l value of 0.4 is calculated using the experimentally measured d (3.2 nm), size (7.2 nm) and saturation magnetization (Ms = 76105 Am–1) [44]. Let us study the theoretical predictions for this kind of weakly dipolar nanocrystal. The evaporation process is studied at a particle level using Langevin dynamics [36, 45, 46]. The interparticle interaction is defined as the sum of the steric repulsion due to the coating molecules, the van der Waals attraction and the dipole–dipole term [30, 35, 36]. The attraction between the particles is markedly influenced by the thickness of the layer of the coating molecules. The double of this coating thickness is denoted by d, which is close to the interparticle separation, d, within this interaction model. Repulsive potentials describe the substrate and the gas– liquid interface at the bottom and the top of the simulation box [3]. The evaporation is modeled by a slow decrease of the gas–liquid interface. Due to the long range of dipolar forces, simulations with magnetic particles are usually carried out with large boxes. Therefore, 512 particles are used in the simulations presented below. Moreover, a comparison with simulations carried out with Ewald summation does not show significant differences. Initially, the solution of magnetic nanocrystals is stable, i. e., no particle aggregation occurs without and with a magnetic field (Fig. 3.4 a and b). After evaporation with no magnetic field, spherical clusters are observed for d = 1.2 nm (Fig. 3.4 c). This is due to a large interparticle attraction of about – 4.5 kT, mainly caused by the van der Waals term. This strong attraction leads to a transition from a nonaggregated (gaslike) to an aggregated (liquidlike) state during the evaporation. Spherical aggregates are actually experimentally observed for maghemite nanocrystals coated with small molecules, such as octanoic acid [3]. Fig. 3.4 d shows that the application of a magnetic field during the evaporation process induces chainlike structures. This is explained by the dipolar attraction between the clusters, which have considerably larger dipole moments than the isolated particles (Fig. 3.5). In good agreement with experiment, chainlike mesostructures made of maghemite or cobalt nanocrystals are observed by evaporation in a parallel magnetic field (Fig. 3.6). Obviously, the chainlike organizations of maghemite nanocrystals observed in spite of a small l value are related to the nucleation and growth of particle aggre-

3.4 Mesoscopic Organization of Magnetic Nanocrystals in a Parallel Field

Fig. 3.4 Snapshots of the configurations by the Langevin dynamics simulations. (a) For the coating layer thickness d = 1.2 nm before evaporation without, or (b) with an applied field, no significant aggregation of particles is observed. (c) After evaporation with no applied field, spherical clusters of particles are observed; (d) with an applied field elongated clusters of particles appear. (e, f) For a thicker coating (d = 1.6 nm), no particle aggregation is observed even during the evaporation when particles are subjected (f) or not (e) to an applied magnetic field.

Fig. 3.5 Sketch of the organization of magnetic nanocrystals with an applied field. The liquid–gas transition explains the formation of chainlike structures in spite of low dipolar coupling.

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Fig. 3.6 Transmission electron microscopy images of maghemite nanocrystals deposited with magnetic field parallel to the substrate [3]. The nanocrystals coated with octanoic acid organize in chainlike structures.

gates due to a gas–liquid transition during the evaporation. Then, an increase in the temperature pushes the system to a supercritical regime without a liquid–gas transition. Under these conditions, any mesostructure would disappear, if it was really due to a liquid–gas transition. The increase in temperature, which reaches the supercritical state, is not experimentally realistic, e. g., due to the low boiling temperature of the solvent. Instead, the interparticle attraction decreases by a variation of the particle contact distance, which is tuned by the thickness of the coating layer. Simulations show that, for d = 1.6 nm, no mesoscopic organization occurs in the absence and presence of a field (Fig. 3.4 e and f ). This is actually experimentally observed for nanocrystals coated with longer molecules [3]. This experiment confirms that the observed mesoscopic organization of nanocrystals is due to a gas–liquid transition. It is worth noting that a slow evaporation is necessary to correctly predict nanocrystal organization in the simulation. Thus, when we directly start from a concentrated random configuration to study the case of Fig. 3.4 d (d = 1.2 nm, field applied), the simulation leads to ambiguous structures: elongated and spherical aggregates of particles coexist [47].

3.5 Mesoscopic Organization of Magnetic Nanocrystals in a Perpendicular Field

As in the parallel case, mesostructures are also observed when a magnetic field perpendicular to the substrate is applied during the evaporation of a solution of magnetic nanocrystals. However, the morphologies of the submicron structures are quite different from the chainlike structures: labyrinthine patterns and hexagonal arrays of cylinders appear (Fig. 3.7). These kinds of structures occur in a large variety of systems such as type I superconductors subjected to a magnetic field, in micrometric films of ferromagnetic garnets, Langmuir monolayers, diblock copolymers and physicosorbed monolayers on solid surfaces [48]. Labyr-

3.5 Mesoscopic Organization of Magnetic Nanocrystals in a Perpendicular Field

Fig. 3.7 Scanning electron microscopy patterns of cobalt nanocrystals deposited with magnetic field perpendicular to the substrate [4]. The strength of the applied field was 0.27 T (left) and 0.78 T (right).

inthine patterns and hexagonal arrays of cylinders also arise, when a magnetic fluid is confined between two glass plates and a field perpendicular to the plates is applied [49–53]. Since this system is very similar to the one we are interested in [4, 54], the experimental data obtained for it are used to check the quality of our theoretical approach. With respect to our discussion of organizations in a parallel field in Section 3.4, a question arises: can the structures in Fig. 3.8 observed in a perpendicular field also be explained by a liquid–gas transition? Then, according to colloidal theory, the interfacial tension between the liquidlike and gaslike phases should be very small (10–5 Nm–1) [55]. The theoretical prediction of the pattern size depends on

Fig. 3.8 Dependence of the normalized stripe width, wf /L, in labyrinths on the external field H0 . Stars: accurate results; dotted line: uniform approximation; dashed-dotted line: constant approximation; dots: experimental data. The cell height and volume fraction are fixed at L = 0.9 mm and at F = 0.5. The experimental points were obtained from [50].

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the interfacial tension. This is determined by comparing the theoretical and experimental pattern sizes, and, thus, the hypothesis of a gas–liquid transition is checked. Therefore, a theory was developed which yields the pattern size (the cylinder radius r0 or the stripe width wf ) as a function of the external field, H0, the ratio of the magnetic phase to the total volume, F, and the cylinder height, L [56]. The labyrinth is described by a repeating pattern of infinitely long parallel stripes. The hexagonal pattern is idealized as a hexagonal array of cylinders consisting of the magnetic fluid. The pattern size is characterized by the stripe width, wf , or the cylinder radius, r0 , for the labyrinthine or hexagonal structure, respectively. In contrast to the structures obtained in a parallel field, the formation of structures in the perpendicular case is due to a competition between interfacial and magnetic energy. In the following [50, 57–59], the theoretical prediction of the pattern geometry is obtained by minimization of the total free energy per unit surface area: f ˆ

Fs ‡ Fm s

…2†

The surface energy, Fs, is characterized by the interfacial tension, s, between the two phases. The second term on the right-hand side of Eq. (2) represents the magnetic energy given by Z Fm ˆ

ZB dr

V

H0  dB0

0

m0 2

Z …3†

drH 20 V

where the magnetic induction is calculated from B = m0 (H + M). The magnetization M (r) at a point r within the pattern is calculated in a selfconsistent way from the equations:   Z 1 3 ‰M …ri †
…r ri †Š …r ri † dr M …r † …4† Hi …ri † ˆ i 4 p …r ri †3 …r ri †2 Vm

H …r† ˆ H0 …r† ‡ Hd …r†

with

Hd …r† ˆ

X

Hi …r

ri †

…5†

i

M …r† ˆ f …H …r††

…6†

where H and H0 are the total and external fields. Hd is the demagnetization field due to the fields Hi of the stripes or cylinders forming the patterns. f (H) is a nonlinear function given by the magnetization curve. For weak field strengths, Eq. (6) can be replaced by M = wH0, where w is the initial magnetic susceptibility. In order to investigate the influence of approximations on the theoretical predictions, we restrict ourselves first to the linear case. The asterisks in Fig. 3.8 show the accurate results for the labyrinthine stripe width as a function of the applied field. The theoretical values are in good agree-

3.5 Mesoscopic Organization of Magnetic Nanocrystals in a Perpendicular Field

ment with the experimental results, which were obtained for a magnetic liquid confined with an immiscible nonmagnetic fluid in a Hele–Shaw cell [50]. However, the accurate calculation is extremely time-consuming, in particular, the numerical integration in Eq. (4). Thus, the calculation of an energy value takes about one hour and several hundreds of values are needed to establish a curve such as that in Fig. 3.8. In order to reduce the computation time, three approximations have been proposed in the literature. In the following, we will discuss these approximations and study their influence on the theoretical results. Within the uniform approach [50], it is assumed that the demagnetization field within the ferrofluid is uniform and equal to that in the center of the stripes or cylinders. It was generally believed that this approximation has no marked impact on the calculated values, since Rosensweig et al. observed good agreement between experiment and theory [50]. We have recently shown [60] that this agreement was due to an error made in the calculation by Rosensweig et al. [50]. The correction of this error leads to values for the labyrinthine stripes which are markedly higher than the experimental data at high field strengths (see dotted curve in Fig. 3.8). The comparison with accurate results has shown two further shortcomings of the uniform approximation. First, this approach predicts field-induced transitions between hexagonal and labyrinthine structures [56]. Furthermore, within the uniform approximation, the appearance of patterns at small field strengths is a first-order transition accompanied by a hysteresis [61]. Both results cannot be confirmed by more accurate approaches [56, 61]. A second approximation is based on the assumption that the magnetization of the magnetic phase is constant during the formation of the structures [49, 57, 58]. Usually this assumption is not valid, since the demagnetization field and, therefore, the magnetization is changed due to the pattern formation. Nevertheless, this so-called constant approximation can give reliable results. The quality of this approach markedly depends on the way of calculating the magnetization. It is often computed from M = wH0 , thus neglecting the demagnetization field. The results obtained by this approximation (dashed-dotted line in Fig. 3.8) markedly deviate from the accurate values. We recently proposed to calculate the magnetization from its initial value observed before the pattern formation using the equation M = wH0/(1 + F) (dashed line in Fig. 3.9) [62, 63]. This markedly improves the agreement with the accurate results, which has been explained by establishing a relationship between the constant and accurate results. Thus, we have recently shown that the use of the constant magnetization calculated from the modified equation is a good approximation of the use of an average magnetization. The use of an average magnetization for the calculation of the demagnetization field in Eq. (4) is actually the third approximation studied. Figure 3.9 shows that the average approximation (line) does not affect the theoretical results. In ref. [62] the good agreement between the average and accurate approach is explained by a compensation of errors. Due to the use of an average magnetization for the calculation of the demagnetization field, the calculation of an energy value takes only a few seconds. This should be compared to the hours taken for the accurate calculations. Only the average approximation also enabled calculations for a nonlinear

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Fig. 3.9 Dependence of the normalized stripe width, wf /L, in labyrinths on the external field H0 . Stars: accurate results; dotted line: average approximation; dashed-dotted line: modified constant approximation; dots: experimental data. The same parameters as in Fig. 3.8 are used.

relationship between M and H, where many more energy values must be computed than in the linear case and an accurate calculation would have been very time-consuming. The use of Eq. (3) for the magnetic energies yields numerically instable values in the nonlinear case. To avoid this, Eq. (3) must be rewritten in the form [56]: Z ZB Fm ˆ

Z

H0
dB0 dr

m0 H0


Vm 0

Z Hd dr Vm

m0 H0


Mdr

Vm

m0 2

Z Hd
Mdr Vm

m0 2

Z H2d dr

…7†

Vm

By minimization of the free energy, we calculated the interfacial tensions, which are necessary to reproduce the experimentally observed cylinder radius taking the magnetic field, the measured pattern height and phase ratio into account. Very small values between 2 × 10–5 and 5 × 10–5 Nm–1 are obtained, which indicates a gas–liquid transition also in the perpendicular case [5]. It should be emphasized that we cannot exclude a direct gas–solid transition which is also consistent with a small interfacial tension. The free energy approach was also successfully used to study the parameters determining the size of the mesostructures. Due to the saturation effects at the high field strengths usually applied, the mesostructures do not vary with the field. However, theory and experiment show an increase in the reduced cylinder radius, r0/L, of hexagonal patterns with the phase ratio. The

References

Fig. 3.10 Comparison of the experimental and theoretical variation of the reduced radius as a function of the cylinder height. The theoretical results for three different phase ratios are shown. The experimental data are obtained from deposition of cobalt nanocrystals [5].

theory also correctly predicts that, for cylinder heights above 5 µm, the cylinder reduced radius varies only slightly with L (Fig. 3.10). For smaller pattern heights, the reduced radius drastically increases on decreasing L.

3.6 Conclusion

The comparison of theory and experiment shows that the organization of magnetic nanocrystals at the mesoscopic scale can be explained by a liquid–gas transition. Based on this assumption, Langevin dynamics simulations and free energy approaches predict the nanocrystal organizations in good agreement with experiments. Since the liquid–gas transition is usually caused by short-range attraction, varying the coating can strongly influence the patterns. Due to the long range of dipolar interactions, an applied magnetic field leads to a marked change in the structures, even for weakly dipolar nanocrystals.

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4 In Situ Fabrication of Metal Nanoparticles in Solid Matrices Junhui He and Toyoki Kunitake

4.1 Introduction

Nanoparticles of metals and semiconductors are attracting much attention, as they exhibit size- and shape-dependent characteristics due to quantum confinement and high surface area, and possess promise in photonic, nonlinear optical, electronic, magnetic, and chemical applications [1–5]. They are key building blocks towards higher-order architectures in the so-called bottom-up approach in nanotechnology. Nanoparticles are usually synthesized in solution by chemical, photochemical, radiolytic, and hydrothermal reactions. In most cases of practical applications, however, effective immobilization or organization of nanoparticles within or on the surface of matrices is required, and it becomes one of the major challenges in the fabrication of many functional materials. The physicochemical properties of nanoparticles depend not only on their size but also on their state of aggregation [6]. Solid matrices may provide suitable media for stabilization of individual nanoparticles better than colloidal dispersions, especially at elevated temperatures. The interaction between the nanoparticle and the matrix will also bring about alteration of electronic states, leading to changes of physicochemical properties, such as surface plasmon absorption and catalytic activity. On the other hand, the immobilization of nanoparticles can also enhance the functionalities (e. g., photocatalytic activity) of matrices themselves. Efforts have been dedicated to immobilization of nanoparticles in solid matrices. One important method is incorporation of preformed nanoparticles in solid matrices. As the preparation of nanoparticles in solution has seen rapid developments in recent years, it is now possible to obtain nanoparticles of various shape, size, and size distribution. Such preformed, well-defined nanoparticles were employed as building blocks to assemble functional thin films [7]. They were also incorporated into solid matrices either by direct incorporation in sol–gel precursors [8] or by uptake in mesoporous solid matrices [9]. The former requires good compatibility of nanoparticles with the components of the sol–gel reaction. In the latter, a so-called sieving effect, i. e., discrimination by particle size, was observed, Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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and even distribution of nanoparticles within solid matrices may not be easily achieved, which is important from the viewpoint of optical properties. Another important approach to immobilization of nanoparticles is their in situ fabrication in solid matrices. In this article, we will review recent developments along this direction. We will also briefly discuss the physicochemical properties of composites of metal nanoparticle and solid matrix and their potential applications.

4.2 In Situ Fabrication of Metal Nanoparticles in Films

Thin films consisting of nanoparticles are especially interesting and important as new functional materials, as many advanced applications are realized in the form of thin films. These composite thin films are promising in membrane-based separation, catalysis, sensors, and electronic and optical devices. 4.2.1 In Situ Fabrication of Metal Nanoparticles in Inorganic Films 4.2.1.1 In Situ Fabrication of Metal Nanoparticles in Mesoporous Inorganic Films Surfactant-templated mesoporous thin films of metal oxides have been the focus of many studies [10, 11]. In particular, a dip-coating method based on the sol–gel process has been developed for rapid film fabrication [11]. Size-controlled and ordered mesoporosity, unidimensional channels, and preferable orientation with respect to the supporting substrate are desirable for many applications, including nanoparticle systems. Plyuto and coworkers prepared a transparent mesoporous silica film on a Pyrex slide by dip-coating. By contacting the film with an aqueous solution of [Ag(NH3)2]NO3 followed by reduction in an H2–N2 (5 % H2) flow, they succeeded in fabricating Ag nanoparticles in the mesoporous thin film [12]. They observed two types of Ag nanoparticles (Fig. 4.1 a), i. e., ca. 3 nm and 6–7 nm in size, which further grew via consecutive contact with aqueous [Ag(NH3)2]NO3 and reduction (e. g., to ca. 5 and 11 nm by three consecutive processes) (Fig. 4.1 b). The authors attributed the formation of two different sizes of the Ag particle to the presence of defects, such as locally coalesced pores or walls. However, it was also speculated that the particle diameter was not limited by the pore size. Although ordering of Ag nanoparticles in the vicinity of the external surface was seen, the majority of Ag nanoparticles were randomly distributed in the mesoporous film. Similar results were obtained by Besson et al. (Fig. 4.2 a) [13]. They attributed random dispersion of Ag nanoparticles of large size distribution to the fast diffusion of Ag+ ions into the film. Grafting of hydrophobic Si(CH3)3 groups at the pore surface significantly slows down this Ag+ ion diffusion, anchoring small Ag clusters in micropores and leading to organized domains of Ag particles in mesopores with a narrower size distribution (Fig. 4.2 b and c).

4.2 In Situ Fabrication of Metal Nanoparticles in Films

Fig. 4.1 Transmission electron micrographs of the calcined mesoporous silica film observed in cross-sectional view after one (a) and three (b) contacts with an aqueous solution of [Ag(NH3)2]NO3 and subsequent reductive treatment at 400 8C.

Fig. 4.2 HRTEM image of a cross section of the silver particles in mesoporous silica films. Silver ions are directly reduced after impregnation in an ionic solution (a). The impregnated film is treated by hexamethyldisilazane (HMDS) before reduction (b, c). The inset in (c) is the power spectrum of the image showing the 3D hexagonal structure.

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In contrast to Ag nanoparticles, mesoporous silica films have been used as templates to prepare uniform nanoparticles of gold and platinum. In this case, the pore surface was not modified with hydrophobic groups [14]. Ordered arrays of uniform Au and Pt nanoparticles of 2.5-nm diameter were fabricated by in situ synthesis in pores of 2.7-nm diameter, as exemplified in Fig. 4.3. The Pt nanoparticles are packed in close vicinity to each other in the one-dimensional mesopores, and in some part the nanoparticle arrays show an ordered structure. It is clear that the nanoparticle size is defined by the pore size. In all the above-mentioned cases, the nanocomposite film contains a metal embedded in an insulating matrix. As the metal–semiconductor interaction would tune the different pathways for electrical conductivity, metal nanoparticles incorporated within a semiconductor matrix can give tunable electrical and optical properties controlled by the particle size and by the distribution of localized states at the metal–semiconductor junction. Such nanocomposites possess promise in electronic devices, solar cells, catalysis, and sensors. In this respect, Pérez et al. recently prepared TiO2 mesoporous films using a block copolymer ((PEO)106(PPO)70(PEO)106) as the template. Gold nanoparticles were then fabricated in situ in the mesoporous TiO2 films by electrodeposition. The Au/TiO2 nanocomposite films show electrochemical behavior typical of a gold electrode of high surface

Fig. 4.3 (a) TEM image of a cross section of Pt–film–Si. Scale bar: 50 nm. (b) TEM image of Pt–film.

4.2 In Situ Fabrication of Metal Nanoparticles in Films

area. The attenuation of Au surface plasmons due to electroadsorption and the existence of mixed localized states in these Au/TiO2 nanocomposites was observed by in situ spectroelectrochemistry [15].

4.2.1.2 In Situ Fabrication of Metal Nanoparticles in Metal Oxide Ultrathin Films: the Surface Sol–Gel Process [16] Recently, we developed a new ion-exchange method for incorporation of metal ions into metal oxide thin films, the thickness of which can be readily controlled with molecular precision [17]. A variety of metal ions can be introduced, and the number of metal ions incorporated is adjusted by the amount of template and the ion-exchange conditions. Incorporation of two or more metal species is also possible by simultaneous or sequential procedures. Such films are nanoporous, and can serve as a nanoreactor for the in situ synthesis of nanoparticles, as indicated by formation of noble metal nanoparticles, interconversion between metal and oxide moieties, and successful preparation of bimetallic nanoparticles. Firstly, in situ preparation of monometallic nanoparticles was explored [18]. The formation of Ag, Au, Pd, and Pt nanoparticles was confirmed by their surface plasmon absorptions, TEM observations (including selected area electron diffraction, SAED) and X-ray photoelectron spectroscopy (XPS) measurements. There are several parameters that affect the formation of metal nanoparticles: the period of H2 plasma irradiation, the power of the plasma, the template concentration, and reduction methods. As exemplified in Fig. 4.4, at a Mg(OEt)2 concentration of 10 mM, the obtained Ag nanoparticles have a mean diameter (d ) of 8.6 nm and a standard deviation (s) of 3.0 nm. In contrast, smaller Ag particles (d = 4.5 nm) of a narrower distribution (s = 1.1 nm) were obtained at a lower Mg(OEt)2 concentration of 1 mM. Among the reduction methods examined (NaBH4, UV irradiation, and H2 plasma), the wet chemical approach uses chemicals and solvents, and may cause undesired changes of ultrathin films (e. g., loss of metal ions). Light-induced reduction is a clean and dry method. However, the TiO2 matrix needs to be excited first by UV light in order to generate reducing free electrons as indicated by its mechanism. This brings about restrictions to this method since most other matrices do not have a similar photochemical property. The current H2 plasma approach is not only clean and dry, but is not subject to such limitations. An additional advantage of H2 plasma reduction is that organic species remaining in films during the surface sol–gel process are effectively removed. It is interesting that crystalline silver nanoparticles thus produced in TiO2 film are effectively transformed into amorphous silver oxide nanoparticles by O2 plasma (Scheme 4.1) [19]. This may open a door to the in situ preparation of metal oxide nanoparticles in thin films. If plasmas of other gases are employed, the present method might be extended to the in situ synthesis of other semiconductor nanoparticles. This transformation is reversible, and the conversion of nanoparticles of silver and silver oxide can be repeatedly conducted by applying O2 and H2 plasmas alternately (Scheme 4.1).

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Fig. 4.4 TEM images and histograms of Ag nanoparticles in TiO2 thin films prepared from precursor solutions containing Mg(OEt)2 of 1 mM (a) and 10 mM (b). Ti(O-nBu)4 : 100 mM.

Scheme 4.1 Schematic illustration of conversion of the silver moiety in TiO2 matrix.

Interestingly, the size distribution is reduced by this process, leading to formation of monodisperse metal and oxide nanoparticles (Fig. 4.5). Here the TiO2-gel film serves as effective nanoflasks for the in situ chemical transformation of nanosized materials. Such materials can be confined in the film without fusion, coagulation, and growth. The migration of atoms, ions, and small atomic clusters within the gel film is possible, as demonstrated by altered size distributions of silver and silver oxide nanoparticles during the reversible transformation. However, direct fusion of nanoparticles is not noticed in this matrix, since nanoparticles themselves are apparently not capable of penetration through the TiO2 network. The in situ transformation could become a useful tool for the preparation of nanosized materials that are not readily accessible by other means.

4.2 In Situ Fabrication of Metal Nanoparticles in Films

Fig. 4.5 (a) UV/visible absorption spectra of silver-ion-doped TiO2 film during alternate H2/O2 plasma treatments. Curves 1–6: after H2 plasma treatment; curves 1'–6': after O2 plasma treatment. (b–d) TEM images and histograms of silver nanoparticles after the first (b) (curve 1 in (a)) and seventh (d) H2 plasma treatment, and silver oxide nanoparticles after the sixth O2 plasma treatment (c) (curve 6' in (a)) in TiO2 film.

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Fig. 4.6 Schematic of preparation of Pd-on-Ag core–shell bimetallic nanoparticles in TiO2 thin film by sequential incorporation–reduction of Ag+ and Pd2+ ions, and the corresponding UV/visible spectra of the thin film: (a) after 4 h immersion in aqueous AgNO3 (10 mM); (b) after exposure to H2 plasma of 10 W for 150 s; (c) after 4 h immersion in aqueous Pd(NO3)2 (10 mM); and (d) after exposure to H2 plasma of 10 W for 5 s.

One of the unique properties of our approach is the regeneration of ion-exchange sites upon formation of nanoparticles. It provides an opportunity to sequentially introduce metal ions into thin films [20]. After formation of monometallic (e. g., Ag) nanoparticles, a second metal ion (e. g., Pd2+) was again incorporated by ion exchange. By applying H2 plasma, the Pd2+ ions can be converted to Pd atoms, which cover the surface of the Ag particle (Fig. 4.6). The Pd-on-Ag morphology of the bimetallic nanoparticle was confirmed by the corresponding absorption spectra [21] and XPS measurements. Figure 4.7 shows that both spherical and elongated bimetallic nanoparticles exist in the TiO2 matrix. The bimetallic nanoparticle has a mean diameter (d) of 4.5 nm and a standard deviation (s) of 1.2 nm. When the nanoparticle is observed at an enhanced magnification, dotlike structures of 1.0–1.5 nm are noticed on the surface of the bimetallic nanoparticle (Fig. 4.7, inset a). The outer shell layer appears not to be uniform in thickness,

4.2 In Situ Fabrication of Metal Nanoparticles in Films

Fig. 4.7 TEM image of Pd-on-Ag core– shell bimetallic nanoparticles in TiO2-gel film prepared by sequential incorporation–reduction of Ag+ and Pd2+ ions. Insets (a) and (b) are a magnified image and a simplified cross-sectional model, respectively.

and Pd clusters may be formed on top of the Pd shell. A model of the particle morphology based on these results is illustrated in Fig. 4.7, inset b). By assuming that the bimetallic nanoparticle is spherical, simple estimation indicates that three layers of Pd atoms cover the surface of the Ag nanoparticle. The catalytic activity of the Pd-on-Ag bimetallic nanoparticle was compared with those of the Pd monometallic nanoparticle and commercial Pd black in the hydrogenation of methyl acrylate. It was found that the bimetallic particle is 367 times more effective than the commercial Pd black and 1.6 times more effective than the monometallic Pd nanoparticle. The observed higher catalytic activity of the Pd-on-Ag nanoparticle is attributed mainly to the large fraction of surface Pd atoms. This is a general efficient method for the fabrication of nanoparticle-containing ultrathin films. The thickness of the thin film can be readily controlled at the nanometer scale. Such thin films are nanoporous and serve well as nanoreactors for formation of various nanoparticles and for their transformation. It must be emphasized that the reversible transformation is a unique tool for obtaining monodisperse nanoparticles directly in thin films. The success of in situ fabrication of Pd-on-Ag core–shell nanoparticles shows that the current approach is capable of preparation of very complicated nanostructures directly in thin films. Thus, it opens the door to fabrication of a variety of nanostructures by so-called nanodecoration: decoration of nano-objects at the nanometer scale and precision.

4.2.1.3 In Situ Fabrication of Metal Nanoparticles in TiO2 Films Prepared from Anatase Sol by Spin-Coating Naoi and coworkers prepared nanoporous films by spin-coating a diluted anatase sol on Pyrex glass substrates. After casting aqueous AgNO3 on the films and irradiation with UV light, Ag nanoparticles were formed in situ inside the film [22, 23]. The authors showed that diverse nanopores had been created, which acted as the molds for formation of diverse Ag nanoparticles (Fig. 4.8). This molding

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Fig. 4.8 Proposed model for the molding effect of a porous TiO2 thin film (a–c) and multicolored Ag/TiO2 film (d). (a) Ag+-adsorbed porous TiO2 film (film looks colorless). (b) Ag nanoparticles deposited by UV light (film looks brownish-gray). (c) Ag particles absorbing green light are photoelectrochemically oxidized to Ag+ by green light (film looks green). The blue, green, or red particle symbol represents a nanoparticle absorbing only blue,

green, or red light, respectively. (d) Each spot (6-mm diameter) was irradiated successively with blue, green, red, or white light. A xenon lamp and a UV cutoff filter (blocking light below 400 nm) were used with an appropriate bandpass filter (blue, 460 nm, 10 mW cm–2, 1 h; green, 520 nm, 11 mW cm–2, 30 min; red, 630 nm, 10 mW cm–2, 30 min) or without any bandpass filter (white, 480 mW cm–2, 10 min).

4.2 In Situ Fabrication of Metal Nanoparticles in Films

effect leads to multicolor photochromism of the Ag nanoparticle-containing TiO2 films. Here the semiconducting TiO2 is indispensable, as it can photocatalyze the formation of Ag nanoparticles. In contrast, Ag nanoparticles loaded in nanoporous ITO and silica films have exhibited no multicolor photochromism. 4.2.2 In Situ Fabrication of Metal Nanoparticles in Polymeric Films

Metal nanoparticles dispersed in polymeric matrices have recently been the subject of intense study aiming to develop inorganic–organic nanocomposite films. The potential advantage of such metal–polymer systems would be that the size and distribution of dispersed metal nanoparticles may be readily controllable, based on the thermoplastic properties of the host polymers. Kobayashi and coworkers fabricated metallic nanoparticles of Ag, Cu, and Pd in polyimide layers by ion implantation at different doses [24]. Unfortunately, the metal nanoparticles formed were not well defined and homogeneously distributed in the ion implantation direction. During the metal implantation, the irradiation also induced carbonization, and this may not be desired for fabricating inorganic– organic composite films. Alternatively, Akamatsu et al. modified the surface layer of polyimide by potassium hydroxide (KOH) treatment, cleaving the imide rings and forming homogeneously distributed carboxylic ion-exchange sites. After replacing the K+ ions with Cu2+ ions by ion exchange, the specimen was heated in a hydrogen atmosphere. The Cu2+ ions were reduced to Cu nanoparticles, while re-imidization produced heterocyclic imide rings (Scheme 4.2) [25]. The extent of surface modification depends on the time, concentration, and temperature of the KOH treatment: longer treatment time, higher KOH concentration, and elevated temperature promote surface modification. Copper loading by ion exchange is affected by the pH of the Cu2+ ion solution used, a decrease in pH resulting in a significant decrease in Cu2+ adsorption. The size of Cu nanoparticles increases with the temperature of heat treatment in a hydrogen atmosphere, as shown in Fig. 4.9. Shim and coworkers prepared iron (3–15 nm) and copper (30–120 nm) nanoparticles in cellulose acetate films by first mixing iron or copper complexes and cellulose acetate in tetrahydrofuran, followed by coating the mixture onto substrate and reduction of metal complexes to nanoparticles with H2 at elevated temperatures. These nanoparticle-containing cellulose acetate films demonstrated catalytic activity in the hydrogenation of olefins, CO oxidation, NO reduction, and the water–gas shift reaction under relatively mild conditions [26]. However, these polymer films are nonporous, and catalytic sites may not be fully accessible by guest molecules. In addition, the formation of large particles was apparently caused by aggregation of smaller metal particles. The decrease of particle sizes would significantly enhance catalytic activities. Micellar block copolymers are known to form microdomains in suitable solvents. When such solutions are cast on substrates, films of ordered microdomains are formed. These polymer films can be used as a scaffold or nanoreactor for the

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Scheme 4.2 Schematic diagram of the present synthesis process for composite polyimide layers containing monodispersed copper nanoparticles.

4.2 In Situ Fabrication of Metal Nanoparticles in Films

Fig. 4.9 Cross-sectional TEM images of polyimide films containing Cu nanoparticles and the corresponding size histograms of Cu nanoparticles. Samples were prepared by heat treatment of Cu2+-adsorbed resins at 250 8C (a) and 350 8C (b) for 30 min in a hydrogen atmosphere.

in situ fabrication of metal nanoparticles, resulting in patterned particle arrays. Saito and coworkers prepared films of lamellar phase separation using poly(styrene-b-2-vinylpyridine) (P(S-b-2VP)) (Fig. 4.10 a) [27]. By soaking the films in silver acetate solution, Ag+ ions were loaded into the poly(2-vinylpyridine) (P2VP) microdomain. After reduction, Ag nanoparticles were formed in the P2VP phase, producing a periodic pattern with Ag nanoparticles (Fig. 4.10 b and c). Later, the same research group also fabricated films of spherical P2VP microdomains with Ag nanoparticles [28]. More recently, Abes et al. prepared a solution of P(S-b-2VP) and Co2(CO)8 (dicobalt octacarbonyl). A film was formed by casting the solution on a substrate. After thermodecomposition, magnetic cobalt nanoparticles were fabricated in situ in the P2VP microdomains of different morphologies, depending on the polymer characteristics and the Co2(CO)8 concentration [29].

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Fig. 4.10 TEM micrographs of P(S-b-2VP) films. (a) After cross-linking with diiodobutane (DIB); the dark areas are segregated P2VP sequences crosslinked and stained with DIB. (b, c) After soaking in aqueous Na2S2O3 ; the gray areas are segregated P2VP sequences cross-linked with DIB, the white areas are PS phases, and the black areas are colloidal silver.

4.2.3 In Situ Fabrication of Metal Nanoparticles in Layer-by-Layer Assembled Polyelectrolyte Thin Films

As first described by Decher and coworkers, multilayer thin films of polyelectrolytes are constructed one polymer layer at a time using a simple layer-by-layer (LbL) processing scheme that involves alternate adsorption of oppositely charged polyelectrolytes [30]. The simplicity and versatility of this approach has made it possible to fabricate a wide variety of complex multilayer thin films comprised of such entities as light-emitting polymers, nonlinear optical polymers, conducting polymers, biologically active molecules, inorganic nanomaterials, fullerenes, and organic dyes [31]. Rubner et al. incorporated silver ions into LbL polyelectrolye films of poly (acrylic acid) (PAA) and poly(allylamine hydrochloride) (PAH) by ion exchange with carboxylic acid protons. The Ag+ ions were then reduced by H2, producing Ag nanoparticles, as illustrated in Scheme 4.3 [32]. The nanoparticle size and Ag concentration can be adjusted by the assembly pH of PAH/PAA-based multilayers and by the number of cycles of ion exchange and reduction. These authors also de-

4.2 In Situ Fabrication of Metal Nanoparticles in Films

Scheme 4.3 Schematic illustration of the metal-ion exchange and reduction process flow.

monstrated that the spatial location of in situ formed nanoparticles within the multilayer thin film could be readily controlled by employing two different types of bilayer building blocks (Fig. 4.11). The PAH/SPS (i. e., poly(styrenesulfonic acid)) combination tends to form fully ion-paired polymer chains, resulting in a bilayer in which essentially all of the sulfonic acid groups of SPS are ionically bound to the cationic group. Such bilayers will not support the growth of nanoparticles. Thus, metal ions will only be sequestered into the PAH/PAA multilayers of a heterostructural thin film, and metal nanoparticles are created and confined in these layers (dark areas in Fig. 4.11). Related to the above method, Bruening and coworkers reported the fabrication of nanoparticle-containing films through formation of a polyelectrolyte–metal ion complex, layer-by-layer adsorption of this complex and a polyanion, and postdeposition reduction of the metal ions (Scheme 4.4) [33]. The nanoparticle size can be

Fig. 4.11 Cross-sectional TEM image of a multilayer thin film comprised of PAH/PAA bilayer blocks alternating with PAH/SPS bilayer blocks on a coronatreated polystyrene substrate (final structure: polystyrene/[(PAH/PAA)11/ (PAH/SPS)30]2). Silver nanoparticles are created only within the two PAH/PAA bilayer blocks. Inset: a higher magnification of a region of the film showing the diffuse interfaces between the multilayers.

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Scheme 4.4 Schematic illustration of the fabrication of nanoparticlecontaining films by layer-by-layer adsorption of a polyelectrolyte–metal ion complex and a polyanion.

varied readily by changing the concentration of metal ions present during PEI/ PAA deposition. These nanoparticles are electrocatalytically active, accessible to analyte molecules, and electrically connected with the underlying electrode. The films also show antimicrobial properties. Later, the same research group extended this technique to spherical alumina particles of 150-mm diameter [34]. They synthesized Pd-containing catalysts by layer-by-layer deposition of PAA and PEIPd(II) on spherical alumina particles and subsequent reduction of Pd2+ ions. The polyelectrolyte matrix stabilizes the particles, introduces selectivity, and significantly decreases unwanted isomerization. PtCl2– 6 anions were also assembled directly with [tetrakis(N-methylpyridyl)porphyrinato]cobalt cations on a glassy carbon electrode through layer-by-layer adsorption, then electrochemically reduced to yield zero-valent Pt nanoparticles [35].

4.3 In Situ Fabrication of Metal Nanoparticles in Nonfilm Solid Matrices

Nonfilm solid matrices include monoliths, powders, fibers, and sheets. They are used in a variety of applications from conventional to advanced materials and devices. Fabrication of nanoparticle-containing nonfilm solid materials has also been attracting much attention of material scientists and chemists. Considering their more complex morphologies and possible diffusion problems encountered, in situ fabrication of nanoparticles in these solid matrices may be more challenging.

4.3 In Situ Fabrication of Metal Nanoparticles in Nonfilm Solid Matrices

4.3.1 In Situ Fabrication of Metal Nanoparticles in Inorganic Matrices

Mesoporous inorganic matrices have been frequently employed for the in situ fabrication of metal nanoparticles. For example, Schweyer and coworkers prepared magnetic metal nanoparticles in mesoporous silica xerogels and MCM-41 by impregnating a heterometallic cluster [NEt4][Co3Ru(CO)12] in these matrices, followed by thermal treatment under an inert atmosphere [36]. The particle size is controlled by the pore size but depends also on the temperature of thermal treatment. Growth of nanoparticles in outer pores is a frequently encountered drawback of the impregnation–calcination method. By cocondensation of 3-mercaptopropyltrimethoxysilane with tetraethoxysilane, Guari and coworkers synthesized SBA-15 materials containing mercaptopropyl groups. Gold precursors were chemically complexed within the pores of the functionalized mesoporous silica, and the growth of gold nanoparticles was achieved selectively within the pores by chemical reduction. The particles have a size less than the pore size and adopt a narrow size distribution. The particle size is only dependent on the pore size in the matrix [37]. Recently, Chen et al. demonstrated that platinum nanoparticles can be homogeneously confined in the mesopore channel of zirconia by simple ion exchange and subsequent in situ reduction using sucrose molecules as both the dispersive medium and reducing agent for PtCl2– 6 (Fig. 4.12) [38]. They also prepared a ceriadoped platinum-loaded mesoporous zirconia in the identical way. Low-temperature oxidation of CO and high conversion of CO + NO into CO2 + N2 can be achieved by catalysis with these materials. The combination of ion exchange and thermal treatment was also employed for selective synthesis of Pd nanoparticles in complementary micropores of SBA-15 [39]. Interestingly, Han and coworkers reported the in situ fabrication of metal nanoparticles in porous silica using an inclusion complex of cyclodextrin–organome-

Fig. 4.12 HRTEM image of Pt/M-ZrO2 sample and its selected-area diffraction pattern (inset). The amount of platinum loaded is about 0.5 at. %.

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Fig. 4.13 TEM images of Au nanoparticles in porous titania filaments: (a) as-prepared, (b) after annealing at 500 8C for 5 h (the arrow pointing to a small pore), (c) after additional annealing at 800 8C for 5 h, and (d) temperature dependence of particle mean diameter (.) and standard deviation (o).

tallic coordination compound as porogen that simultaneously acted as template and metal precursor [40]. In situ fabrication of metal nanoparticles in micro- and mesoporous silica was also carried out by using an ultrasound-assisted polyol method [41] and by using supercritical solvents [42]. Montmorillonite has a mesoporous lamellar structure and possesses high surface area. It was used as a solid matrix for the in situ synthesis of metal nanoparticles. Although the particle size of metal nanoparticles is still quite large in the reported work, and further efforts are needed to improve the fabrication processes, such nanometal–clay composites may find applications as bifunctional catalysts (metal + acid functions) [43]. Most porous matrices in the above-mentioned examples were prepared using ordered supramolecular assemblies as template. Recently, versatile biological struc-

4.3 In Situ Fabrication of Metal Nanoparticles in Nonfilm Solid Matrices

Fig. 4.14 TEM images of Au nanoparticles in porous zirconia filaments: (a) as-prepared, (b) after annealing at 500 8C for 5 h, (c) after additional annealing at 800 8C for 5 h, and (d) temperature dependence of particle mean diameter (.) and standard deviation (o).

tures, many of which are porous, were also used as templates for porous structures. Replication of bacteria, wood cells, and silk by inorganic materials has given materials of unique morphology and high porosity [44–46]. We further studied the in situ fabrication of metal nanoparticles in silk-templated nanoporous titania and zirconia by impregnation of metal ions and subsequent chemical reduction. The assynthesized gold nanoparticle (ca. 4 nm) in titania showed only a small increase (to ca. 6 nm) in particle size after annealing at 500 8C for 5 h, but it became much larger (~ 40 nm) at 800 8C (Fig. 4.13). Under otherwise identical conditions, amorphous zirconia matrix gave rise to a much smaller size increase (ca. 10 nm at 800 8C) (Fig. 4.14). The Au nanoparticle of 4–6 nm (melting point, 700–740 8C) is not molten at 500 8C, and naturally shows higher stability at this temperature. At

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800 8C, however, it is molten, and would show higher instability due to possible interparticle fusion. Crystal growth of titania at elevated temperatures would make the molten particle become exposed at least partially, and thus enhance its interparticle fusion. In contrast, zirconia can keep its amorphous morphology at elevated temperatures, which would more effectively suppress fusion of molten Au nanoparticles by isolating the particles from each other. Apparently, better physical isolation of the nanoparticle was attained for amorphous zirconia than for nanocrystalline titania. These findings point to better design and more appropriate application of heterogeneous catalysts. In another work of our laboratory, we immobilized preformed Au nanoparticles (5 + 1 nm) on titania nanotubes derived from cellulose templates [47]. After removal of the organic components by calcination at 450 8C for 6 h, Au nanoparticles with sizes as large as 20–30 nm were found on the outer surface of the titania nanotube. Some of the original Au nanoparticles apparently fused with their closely neighboring particles. When an additional five titania layers were applied to cover the immobilized Au nanoparticles, however, the particle stability was enhanced, indicating again the beneficial effect of physical isolation on the particle stability. 4.3.2 In Situ Fabrication of Metal Nanoparticles in Polymeric Matrices

Composites of nanoparticles and polymers are readily processable, and have potential applications in photonic and electronic devices. They are also applicable as catalysts in a variety of chemical reactions. However, in most of these cases, the polymers were merely used as a passivating reagent for encapsulating the particles [48], or as a sophisticated phase-segregating matrix (block copolymers), as described earlier in this review [27–29]. Recently, Corain and coworkers reported on the in situ synthesis of palladium nanoparticles inside nanoporous domains of gel-type resins [49–51]. As shown in Fig. 4.15, Pd2+ ions are homogeneously introduced using a THF solution of Pd(OAc)2 into a gel-type lipophilic polymer framework [poly(dodecyl methacrylate) (92 mol %)–4-vinylpyridine (4 mol %)–ethylene glycol dimethacrylate (4 mol %)]. Pd2+ ions are reduced to Pd atoms that aggregate in subnanoclusters. Finally, nanoclusters of 3-nm diameter are formed and immobilized inside the largest mesh present in that “slice” of polymer framework. The nanoparticle size is controllable by the matrix nanoporosity. Polymer matrices with functional groups that can form complexes with metal ions and other inorganic solids are appropriate as solid matrix for the in situ synthesis of nanoparticles. In fact, Uozumi et al. prepared an amphiphilic resin dispersion of palladium nanoparticles by formation of a polystyrene–poly(ethylene glycol) (PS-PEG)-supported bispyridine-palladium(II) complex followed by reduction of the complex by benzyl alcohol [52]. The amphiphilic resin dispersion combines high catalytic activity owing to the large surface area of the Pd nanoparticles and water-based reactivity provided by the amphiphilicity of the PS-PEG matrix, and catalytic oxidation of alcohols was achieved in water under an atmospheric

4.3 In Situ Fabrication of Metal Nanoparticles in Nonfilm Solid Matrices

Fig. 4.15 Model for the generation of size-controlled metal nanoparticles inside metalated resins. (a) Pd2+ is homogeneously dispersed inside the polymer framework; (b) Pd2+ is reduced to Pd0 ; (c) Pd0 atoms start to aggregate in subnanoclusters; (d) a single 3-nm nanocluster is formed and “blocked” inside the largest mesh present in that “slice” of polymer framework.

pressure of molecular oxygen using this catalyst. In another attempt, Weitz and coworkers synthesized Cu2O, CuS, CdS, and Ag nanoparticles in a polar polysulfone active matrix [53]. Biopolymers are an important category of macromolecules with diverse origins and wide applications. They must be attractive matrices for the in situ synthesis of nanoparticles, which is in fact the case. As recently demonstrated by us, noble metal (Ag, Au, Pt, Pd) nanoparticles of less than 10-nm diameter were readily fabricated in porous cellulose fibers under ambient conditions, which show different colors (Fig. 4.16), and monodisperse nanoparticles were obtained under an optimized concentration of the metal precursor solution [54]. The nanoporous structure and the high oxygen (ether and hydroxy) density of the cellulose fiber constitute an effective nanoreactor for the in situ synthesis of metal nanoparticles. The nanopore is essential for incorporation of both of metal ion and reductant into cellulose fibers, as well as for removal of unnecessary by-products from fibers. The

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Fig. 4.16 Cellulose specimens with (a) none, (b) Ag, (c) Au, (d) Pt, and (e) Pd metallic nanoparticles.

ether oxygen and the hydroxy group not only anchor metal ions tightly in cellulose fibers via ion–dipole interactions, but they also stabilize metal nanoparticles by strong bonding interaction with their surface atoms. Very interestingly, carbonization of Pt nanoparticle (5.7 + 2.2 nm)-containing cellulose matrices showed that the Pt nanoparticle can catalyze the carbonization process, producing composites of almost intact platinum nanoparticles (3.7 + 1.4 nm) and amorphous carbon films [55]. Apparently, the carbon matrix acted as an effective barrier against aggregation of Pt nanoparticles in the Pt-catalyzed carbonization process. This strategy can be extended to other nanoparticle–polymer systems; thus, it opens the door to a wide variety of nanoparticle-containing carbon materials that possess promise in many applications. As a related report, Baumann et al. prepared ordered macroporous carbons with metal nanoparticles of wide distribution (5–60 nm) by a templated sol–gel process followed by ion exchange and pyrolysis [56].

4.4 Physicochemical Properties

The physicochemical properties of composites of metal nanoparticles and solid matrices will be determined basically by both of the components. However, the major aspects will largely depend on the characteristics of the immobilized nanoparticles. In fact, composites of metal nanoparticles and inorganic (polymer) matrices show surface plasmon absorption, high catalytic activity, and magnetic properties that are specific to their quantum size effects and extremely large surface areas [57]. These properties will also be affected by the matrix and the spatial organization of the nanoparticles. Furthermore, matrices of the composites not only play the roles of passivating agent, carrier matrix, and support, but they also act as functional components. It is particularly true when these composites are prepared as catalysts. Both components may influence the catalytic properties of each other or act synergistically.

4.4 Physicochemical Properties

4.4.1 Catalytic Properties

Those reactions that can be catalyzed by isolated metal nanoparticles are similarly subject to catalysis by the nanoparticles immobilized in solid matrices. Such cases include a variety of chemical reactions, such as isomerization, the Heck reaction, hydrogenation, hydrocracking, water–gas shift reaction, hydrogenolysis, photooxidation, and photoreduction [58–63]. Here, we only discuss some of the very recent results in which metal nanoparticles were fabricated in situ within solid matrices. Noble metal nanoparticles were fabricated in mesoporous zirconia and silica, and showed catalytic activities in oxidation reactions [38, 41, 42]. Alcohols were catalytically oxidized in water under atmospheric oxygen by use of an amphiphilic resin dispersion of a nanopalladium catalyst [52]. We reported that Pt nanoparticles in cellulose fibers could catalyze carbonization of these carbohydrate materials to nanoporous amorphous carbon [55]. Ag–Pd bimetallic nanoparticles in TiO2 thin films showed much enhanced catalytic activities for hydrogenation compared with Pd monometallic nanoparticles and commercial Pd black [20]. Iron and copper nanoparticles in cellulose acetate polymer were examined for various chemical reactions [26]. The former showed catalytic activity in the water–gas shift reaction, CO oxidation, NO reduction, and hydrogenation of olefins; the latter showed catalytic activity in the hydrogenation of olefins and CH3CN, CO oxidation, and NO reduction, all under relatively mild conditions. Metal nanoparticles fabricated in situ in multilayer polyelectrolyte films are electocatalytically active and those of silver also show bactericidal activities [33]. Very interestingly, such polyelectrolyte multilayers not only stabilize immobilized Pd metal nanoparticles, but also introduce selectivity and significantly reduce unwanted isomerization [34]. On the other hand, metal nanoclusters, such as silver, were found to significantly enhance the photocatalytic activity of TiO2 particles for both oxidation and reduction [64, 65]. 4.4.2 Optical Properties

Metal nanoparticles show characteristic surface plasmon absorptions due to their electron quantum confinement. Such optical properties depend on the shape, size, and size distribution of particles, and are also related to particle–particle and particle–matrix interactions. Silver nanoparticles fabricated in situ within mesoporous silica pores show a large red-shift of the optical absorption edge that is attributed to the interband absorption of Ag metal and to dipole interaction between Ag particles [66]. The lack of a plasmon peak typical for Ag nanoparticles is attributed to a small particle size and interaction at the interfaces between Ag particles and pore walls. The position of the absorption edge is controllable across the whole visible region by the amount of Ag in silica. We developed a general method for the in situ fabrication of metal nanoparticlecontaining ultrathin films using a hydrogen plasma technique [17, 18]. This ap-

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proach has unique advantages. First, smooth and transparent ultrathin films containing metal nanoparticles can be readily assembled on flat surfaces and curved substrates. Second, reduction with low-temperature H2 plasma is clean and dry. The surface plasmon absorption disappears by treating the Ag nanoparticle-containing film with oxygen plasma, and reappears with H2 plasma [19]. The optical absorption band becomes narrower and enhanced by repeating these processes. Similar color changes of TiO2 films loaded with Ag nanoparticles also occur by light irradiation, leading to multicolor photochromism [22, 23]. The surface plasmon absorption also disappears upon coating Ag nanoparticles by palladium atomic layers [20]. Ag nanoparticles fabricated in situ in polyelectrolyte multilayers show enhanced surface plasmon absorption bands with a decrease in pH of the processing solution and an increase in the number of layers [32, 33]. Ag nanoparticles in multilayer composites were examined for surface-enhanced Raman scattering (SERS) spectroscopy and showed enhanced signals. The optical properties and SERS enhancement vary with the accumulation of immobilized Ag nanoparticles. The SERS enhancement is also related to the surface morphology of the substrate. Stronger SERS signals can be obtained from the substrate with addition of KCl solution [67]. 4.4.3 Magnetic Properties

It is well known that magnetic properties of particles strongly depend on their sizes. With a decrease in particle diameter, the nature of the magnetism changes: ferromagnetic particles become superparamagnetic and these properties are temperature-dependent. Jung and coworkers prepared nickel nanoparticles of 1–2 nm in an aluminosilicate with the MCM-41 structure by ion exchange and subsequent chemical reduction. The obtained composite shows superparamagnetic behavior with a blocking temperature of 5 K [68]. Iron nanoparticles were also fabricated by introduction of iron complexes into the channels of MCM-41 and subsequent pyrolysis in a nitrogen atmosphere. The silica channels affect nucleation and growth of the superparamagnetic Fe nanoparticle [69]. In contrast, metal nanoparticles prepared in mesoporous silica xerogel and MCM-41-type materials from heterometallic Co-Ru carbonyl clusters show ferromagnetic and superparamagnetic properties depending on the particle size [36]. In a recent effort using polymeric matrices, cobalt nanoparticles were selectively synthesized in situ inside the P2VP domains of P(S-b-2VP) block copolymer films, and patterned on the nanometer scale [29]. These particles are large enough to show ferromagnetic behavior.

References

4.5 Summary and Outlook

Solid matrices that contain metal nanoparticles are now attracting much attention from scientists and engineers in different fields. The in situ approach of nanoparticle fabrication is developing rapidly as one of the most promising methods. A variety of nanoparticle–matrix composites can be prepared using organic and inorganic films and nonfilm matrices as host materials. The size, size distribution, positioning, and ordering of nanoparticles can be controlled to a significant extent. It is clear that one must select a most appropriate method for a particular application. In the case of optical and magnetic applications, thin films may be more promising than nonfilm matrices. It is indispensable in this case to control the size, monodispersity, interparticle distance, and order of nanoparticles, while it may not be essential whether the films are porous or not. In contrast, in catalytic applications, such porous structures are essential to ensure efficient access of reagents to nanoparticle catalysts as well as ready release of products. The control of particle size is also critical in order to provide high particle surface areas. Although considerable progress has been made so far, more efforts are needed to develop better control over the above-mentioned parameters so that the physicochemical properties of the composites can be better defined. The shape of the nanoparticle is an important parameter that significantly affects its functions. However, the in situ fabrication of nanoparticles with desired shapes other than spheres is still a challenge. The design and fabrication of novel matrices (compositions and morphologies) would still be an additional challenge. Designed and unsigned interactions between nanoparticle and matrix are still another research frontier. We can expect that such interactions should be exploited to enhance the functionalities and efficiencies of the composite materials with better understanding. Further research is imminent, in view of the enormous potential in practical applications.

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5 Three-Dimensional Self-Assemblies of Nanoparticles Sachiko Matsushita and Shin-ya Onoue

5.1 Introduction

The spontaneous three-dimensional (3D) formation of various self-assembled structures inspires us to imagine how our lives are created [1–5]. The self-assembly science is profound: nanomaterial self-assemblies are related to the interfaces of solid, liquid, and gas phases [6, 7]; the size of nanoparticles/nanocrystals is in the range from a few nanometers to thousands of nanometers (Table 5.1) [8, 9], and thus nano-, meso-, and microscale sciences are all concerned with research on 3D self-assemblies; the nanoparticles and nanocrystals have many shapes, such as spherical, ellipsoidal, rodlike [10, 11], starlike, strawberry-like, fistlike, egglike [12], bowl-like, snowman-like [13], and so forth; additionally, the types of materials composed of the nanoparticles/nanocrystals also have a wide variation such as organic, inorganic, composite, and core–shell [12, 14] particles. Thus, in this chapter, we limit the contents to an introduction to the resulting self-assembled structures and their applications. We present two types of self-assembly. One is 3D self-assembly of nanocrystals utilizing the mesoscopic phenomena in a molecular matrix (e. g., phase separation of polymers). The other is the 3D self-assembly obtained via nanoparticle interactions. Many excellent reviews [8, 15–18] have been published on these latter selfassemblies. Table 5.1 The particle sizes used in the 3D self-assemblies of nanoparticles. Type of 3D self-assembly

Particle size

Liquid colloidal crystals

10 nm (metal) 518 nm (poly(methyl methacrylate)) [77] 88 nm (polystyrene) to 800 nm (silica) [91] 4 nm (FePt) [66] to 20 µm (polystyrene) [182]

Solid colloidal crystals Two-dimensional colloidal crystals

Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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5.2 Mesoscopic Assembly of Inorganic Nanoparticles in Molecular Matrixes 5.2.1 Introduction

Inorganic nanoparticles especially metals had been regarded as classical materials. However, during the last two decades, the science of all kinds of inorganic nanoparticles such as metals, metal oxides, and other semiconductors was well established and represents a wealth of knowledge of both fundamental and applied aspects of the subject [15, 19–25]. Particle sizes of current interest range from less than one nanometer to several hundreds of nanometers, in contrast to the larger polymer spheres [19, 20]. Therefore, nowadays they are considered as one of the most promising materials that can play an important role in future nanotechnology. The recently developed monolayer-protected nanoparticles are characterized by their extraordinary stability both in solution and in the solid state, which distinguishes them from most other types of nanometer-sized inorganic substances [19, 20]. Currently, functionalized inorganic nanoparticle applications include, for instance, catalysis, electronics including SET, data storage, color coatings, optical filters, and biomarkers or biosensors, etc. [15, 23–32]. As a novel aspect, the development of precise assembly methods of such stable inorganic nanoparticles in molecular components or matrixes should be an important research area for nanochemistry. However, it is still an uncultivated area. Given the breadth of these inorganic nanoparticles and the number of excellent reviews and edited collections available, this chapter focuses mainly on the recent mesoscopic assembly of inorganic nanoparticles [15, 23, 29, 30, 32]. These techniques will lead to new functions and open new fields of materials systems. 5.2.2 Random Assemblies of Inorganic Nanoparticles by Various Triggers

The compatibility of inorganic nanoparticles with solvents and matrixes is originally low and they readily aggregate and coagulate by themselves. This is one of the problems which must be overcome. At the same time, in the mesoscopic regime, the controlled assembly of inorganic nanoparticles induced by external factors is indispensable for materials systems. Herein, intentionally assembled inorganic nanoparticles with random and spherical mesoscopic shapes are examined, and classified by the initiator of assembly. In the case of dispersions of gold and silver nanoparticles with distinct optical characteristics, their original red and yellow colors change with the degree of aggregation. Thus, the control of aggregation of the inorganic nanoparticles will also give a good mechanism and well-amplified spectroscopic signals useful as sensors. The preparation, structural analysis, and functions of three-dimensional microcrystals constructed from small inorganic nanoparticles have been energetically investigated. Splendid research has been carried out chiefly by the groups of

5.2 Mesoscopic Assembly of Inorganic Nanoparticles in Molecular Matrixes

Wang and Whetten [33, 34], Pileni [35], Kimura [36–38], and Schmid [39]. However, the details are not given in this section.

5.2.2.1 pH and Ions Generally, aqueous inorganic nanoparticles are stabilized by the repulsion of negative or positive charges and steric effects of the stabilizer molecules attached to the surface of the nanoparticles. For example, rapid agglomeration of charged nanoparticles occurs in aqueous media by addition of salts. In many cases, using carboxylic acid-coated gold and silver nanoparticles, the behaviors of pH-dependent assemblies have been well examined by several groups [40–45]. The dissociation of the proton in aqueous media is induced by pH control, and the dispersion stabilities are dramatically changed between acid and alkaline conditions via the pKa. Carboxylate anions located on the particle surface can bind and recognize metal ions such as Li+ [43] and the heavy ions Hg2+, Pb2+, and Cd2+ [44]. Color changes based on the exchange of concentrations were clearly shown in Ref. [44]. It has also been shown that lipoic acid-capped gold and silver nanoparticles can recognize and discriminate between polyvalent cationic metal species (Cu, Fe, Zn, Mn, Ni, Cd) and their concentrations [45]. As target ions, such as K+ recognized by 15-crown-5 ether [46], several anions bound by amide moieties in the middle of stabilizer molecules [47] were reported on the basis of spectroscopic investigation. Furthermore, redox-active metallodendron-stabilized gold nanoparticles can specifically catch the phosphate or sulfate monoanions and ATP2– [48–50].

5.2.2.2 Small Molecules and Polymers Most controlled assemblies of inorganic nanoparticles in solution are based on supramolecular chemistry [51]. In this case, noncovalent bonding is a general strategy leading to well-assembled inorganic nanoparticles. Thus, approaches of supramolecular chemistry have been reported using hydrogen-bonding [52, 53] (Fig. 5.1), p–p [54], host–guest [55], van der Waals [56], electrostatic [57], and charge-transfer [56] interactions. The morphology of assembled structures of inorganic nanoparticles is likely to be spherical. A pseudo-rotaxane assembly was also achieved by Fitzmaurice et al. [58] at the surface of inorganic nanoparticles. This phenomenon is similar to the binding of a molecule by the receptor sites on a cell surface. In addition, a dialysis and reprecipitation method gave spherical aggregates. Small organic molecules and polymers are also sufficiently used as a trigger for the aggregation of inorganic nanoparticles.

5.2.2.3 Biological Components (Programmed Assemblies and Sensors) Color changes derived from the aggregation of inorganic nanoparticles such as gold and silver can give selective and sensitive detection for specific biological sub-

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Fig. 5.1 (a) Proposed mechanism for the polymer-mediated self-assembly of Thy-Au. (b) TEM image of polymer 1–Thy-Au aggregates formed at 23.8 8C. Inset: representative self-assembled microparticle. (Reprinted with permission from A. K. Boal, F. Ilhan, J. E. DeRouchey, T.-T. Albrecht, T. P. Russel, and V. M. Rotello, Nature 404, 746 (2000). Copyright 2000 by the Nature publisher).

stances via interactions between anchored stabilizer molecules and target molecules. In pioneering and fundamental research, extraordinary specific bindings, for example biotin–avidin binding, are used to evaluate the basic properties of color and spectroscopic change. Mann et al. succeeded in the aggregation of gold nanoparticles using antigen–antibodylike reactions such as DNP (dinitrophenol)– anti-DNP IgE and biotin–anti-biotin IgG [59]. Otsuka et al. described extremely stable and sugar-conjugated gold nanoparticles that exhibited selective aggregation with RCA120 lectin, a bivalent lectin specifically recognizing the a-d-galactose residue, inducing significant changes in the absorption spectrum with concomitant visible color change from pinkish-red to purple [60]. Aggregation of the gold nanoparticles by the RCA120 lectin was reversible, recovering the original dispersed phase and color by addition of excess galactose. This system could be utilized to quantify lectin concentration with nearly the same sensitivity as ELISA (Fig. 5.2). At present, new gold and silver colloidal assay systems are also examined not only in dispersions but also on the surface of biologically modified latex [59, 61]. It seems that the research in this field is accelerating more and more. Assembled structures of inorganic nanoparticles with DNA attached on the metal surface are not extensively described herein. The details are given in good reviews and books elsewhere (see splendid reference [23]).

5.2 Mesoscopic Assembly of Inorganic Nanoparticles in Molecular Matrixes

Fig. 5.2 Schematic representation of the reversible aggregation–dispersion behavior of Lac-PEGylated gold nanoparticles by sequential addition of RCA120 lectin and galactose with actual concomitant change in color from pinkish-redpurplepinkish-red. (Reprinted with permission from H. Otsuka, Y. Akiyama,Y. Nagasaki, and K. Kataoka, J. Am. Chem. Soc. 123, 8226 (2001). Copyright 2001 by the American Chemical Society).

5.2.3 Versatile Assemblies of Inorganic Nanoparticles Guided by Designable Templates: Superstructures and 1D and 3D Assemblies

In order to assemble small particles one-dimensionally or three-dimensionally, the use of a template is available and versatile. In this section, we introduce morphologically controlled mesoscopic assemblies of inorganic nanoparticles in 1D and 3D. Published papers are currently available with respect to the formation of 2D monoparticulate layers. We will not discuss them here.

5.2.3.1 Langmuir–Blodgett Films Charged surfaces of regularly layered amphiphiles have the ability to condense oppositely charged nanoparticles at the air/water interface. Assembled monolayers of nanoparticles can be readily piled up by the Langmuir–Blodgett (LB) method. Each monolayer of nanoparticles is basically separated by the length of the double layers of the amphiphiles used. Such LB film composites of gold and silver, magnetic nanoparticles (Fe3O4), and others were mainly produced.

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5.2.3.2 Amphiphiles and Surfactants Organic templates made by molecular assemblies such as amphiphiles, surfactants, gelators, and -conjugated compounds can form designable mesoscopic structures. The structures are fascinating: sheets, helixes, fibers, tubes, lamellae, globular aggregates such as liposomes, etc. Nanoparticle arrays obtained by mixing anionic bilayer membranes and cationic, quaternary ammonium-stabilized nanoparticles were immobilized densely into the hydrophilic interlayers of dispersed lamellar structures to form a quasi-1D structure [62]. Mann et al. described ordered chains of prismatic BaCrO4 nanoparticles formed using AOT microemulsions [63]. This was quite a unique feature (Fig. 5.3).

Fig. 5.3 TEM image showing ordered chains of prismatic BaCrO4 nanoparticles prepared in AOT microemulsions at [Ba2+]:[CrO42–] molar ratio = 1 and w = 10 (w = AOT/H2O). Scale bar = 50 nm. (Reprinted with permission from M. Li, H. Schnablegger, S. Mann, Nature, 1999, 402, 393.

5.2.3.3 Gels (Networks) The assembly of gold nanoparticles into 3D network structures by site-exchange reaction was demonstrated by Kimura et al. [64] (Fig. 5.4). The figure schematically illustrates the assembly of gold nanoparticles. First, a self-assembling gel is spontaneously formed through an intermolecular hydrogen bond. Gold nanoparticles accumulate on the fibrous assemblies by the site-exchange reaction. The accumulation around organic fiber assemblies creates three-dimensional network structures. Large network structures with gold nanoparticle arrays will open up new possibilities for the construction of optical and electronic nanodevices.

5.2.3.4 Polymer and DNA as a Template Recently, reports describing the one-dimensional arrangement of nanoparticles have increased by using polymer linearity. Carbon nanotubes, DNA and viruses

5.2 Mesoscopic Assembly of Inorganic Nanoparticles in Molecular Matrixes

Fig. 5.4 Schematic illustration for organization of gold nanoparticles around organic fibers. (Reprinted with permission from M. Kimura, S. Kobayashi, T. Kuroda, K. Hanabusa, and H. Shirai, Adv. Mater. 16, 335, 2004.

are suitable as templates of the inorganic nanoparticles. Several methods have been reported for DNA in particular (Fig. 5.5) [63].

5.2.3.5 Inorganic Templates Examples of a new class of three-dimensionally arranged inorganic nanoparticles have been prepared in the nanoscale pores of inorganic solid matrixes. Immobilization of the gold nanoparticles in alumina nanopores was achieved by a modification of the inner walls with alkoxysilanes bearing NH2 or SH functional groups, followed by anchoring of the particles by self-assembly onto the modified surface. This procedure provides tight and stable assemblies of gold nanoparticles on the walls. Hanaoka et al. revealed uniform and random gold nanoparticle dispersions

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Fig. 5.5 (a) TEM image of thiocholine bromide-stabilized gold nanoparticles and ë-DNA mixtures. (b) Enlarged image of (a). Nanoparticles were adsorbed on the side surface of a bundle of DNA molecules (c). The particles grew dramatically compared to their original size and fused with each other to form 1D wirelike structures. (Reprinted with permission from T. Yonezawa, S.-y. Onoue, and N. Kimizuka, Chem. Lett. 1172 (2002). Copyright 2002 by the Chemical Society of Japan).

on the walls in the form of submonolayers without any aggregation on TEM observation [64]. UV/Vis spectra of the filled membranes showed an absorption maximum at ca. 525 nm arising from an excitation of the plasmon resonance of the gold nanoparticles. The dimensions of the pores can be “tuned” and, given the diverse range of different gold nanoparticles available, routes to novel catalysts and sensors can be envisaged.

5.2.3.6 Others Herein, we show another type of preparation of mesoscopic architectures. Fluoro nanoparticles of silver were dispersible in fluorocarbon solvents, and casting of the dilute dispersion gave monolayers with highly regular hexagonal-packed structure (2D). On the other hand, casting of a concentrated dispersion under a humid atmosphere gave a highly ordered honeycomb structure over a wide area (3D) (Fig. 5.6) [65].These unique self-assembling features are characteristic of the dissipative hierarchy structure (DHS). Other honeycombs and rings based on the DHS were also reported. The details of formation of the honeycomb are explained elsewhere. 5.2.4 Layer-by-Layer Assemblies Embedded with Inorganic Nanoparticles

From the beginning of the 1990s, the layer-by-layer (L-by-L) method has been intensively developed especially, and independently, by the groups of Decher, Kunitake, and Rubner. L-by-L film assembly is the powerful procedure which can make functionally and sequentially designed smooth ultrathin films in the nanometer order via intermolecular interactions. Spherical protein and inorganic nanoparti-

5.2 Mesoscopic Assembly of Inorganic Nanoparticles in Molecular Matrixes

Fig. 5.6 SEM image of an ordered assembly of a microscopic honeycomb structure of fluorocarbon-stabilized Ag nanoparticles obtained by casting a concentrated HCFC-225 dispersion ([Ag] = 10 mM) at high humidity (75 %, 25 8C) on a HOPG substrate. Inset: Fourier-transformed image. Samples were examined in a Hitachi S-5000 TEM operating at 25 kV without any metal coating. (Reprinted with permission from T. Yonezawa, S.-y. Onoue, and N. Kimizuka, Adv. Mater. 13, 140–142, 2004).

cles such as metals, metal oxides, and other semiconductors are also regarded as one of the functional components. The layer-by-layer method is also applicable to the preparation of multilayers. Thin films with controlled thickness were formed via polymer-mediated self-assembly. Nanocrystals (4-nm FePt [66], 4-nm gold [67], and 300–1000-nm zeolite nanocrystals [68]) were used. Herein, we show the classes of components which are combined with the nanoparticle.

5.2.4.1 Multifunctional Molecules and Polymers This procedure is the simplest method to build up the film structure of inorganic nanoparticles. Willner et al. described the stepwise assembly of a three-dimensional array of palladium–bipyridine ‘square’ molecules and gold nanoparticles on a conductive ITO substrate (Fig. 5.7) [69].

5.2.4.2 Inorganic Molecules Yonezawa et al. succeeded in the preparation of thin films embedded with gold nanoparticles with uniformity and high density. They applied the sol–gel reaction to the L-by-L method using the combination of titanium tetra-n-butoxide [Ti(O(n-C4H9))4] and bis(11-hydroxyundecyl) disulfide-covered gold nanoparticles [70a, 70b]. In this case, since hydroxyl groups can coordinate to titanium, gold nanoparticles were stably introduced into thin films. Generally, the poor compatibility of nanoparticles in inorganic matrixes is well known. That is why this method is expected to be used for constructing thin films which are densely embedded with the nanoparticles.

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Fig. 5.7 Stepwise assembly of a three-dimensional array of palladiumbipyridine ‘square’ and gold nanoparticles on a conductive ITO substrate. (Reprinted with permission from M. Lahav, R. Gabai, A. N. Shipway, and I. Willner, Chem. Commun. 1937 (1999). Copyright 1999 by the Royal Society of Chemistry).

5.2.5 "Key and Vision" for Future Development

There are extensive and marvelous reports of research on the three-dimensional assemblies of inorganic nanoparticles elsewhere. We have to omit them here due to lack of space. Considering this whole research area, we can find one common point. It is “organic molecules and matrixes” such as solvents, mediators, templates, and stabilizers attached to the surface of inorganic nanoparticles. “Organic molecules and matrixes” seem to be an important key to controlling the precise assemblies. In the future, inorganic nanoparticles will form self-organized structures on the organic components, and highly dense and highly ordered structures of the inorganic nanoparticles will become possible. These are also expected to be one of the important technologies from the viewpoint of the development of fine processing based on the “building-up” method. Finally, we believe that precisely assembled structures of inorganic nanoparticles sufficiently fulfill the role as future device element. Moreover, they will also produce new chemical and physical phenomena.

5.3 Three-Dimensional Self-Assemblies via Nanoparticle Interactions

5.3 Three-Dimensional Self-Assemblies via Nanoparticle Interactions

Here, we introduce the 3D self-assemblies obtained via nanoparticle interactions. In the field of self-assembly science, nanoparticle/nanocrystal self-assembly has been studied as a convenient model system for fundamental studies of crystallization and fusion. The materials for the assemblies are suspensions. The self-assembled structures can be classified into three types: liquid colloidal crystals (also called “colloidal crystals”, “crystalline colloidal arrays” [70]), which result from crystallization via repulsive electrostatic interactions between particles (Fig. 5.8 a); solid colloidal crystals (also named “artificial opals”), which are selfassembled structures obtained via capillary forces and gravity by a dry process (Fig. 5.8 b); and two-dimensional colloidal crystals (also named “two-dimensional particle arrays”, “particle films”), which are formed at the air/liquid and liquid/liquid interfaces (Fig. 5.8 c). In the section concerning two-dimensional colloidal crystals, we will limit the contents to those that are applicable to multilayer preparations.

Fig. 5.8 Schematic of 3D self-assembled particle structures.

5.3.1 Liquid Colloidal Crystals

Particles/crystals are negatively charged in solution (even if there is a cationic base on the particle/crystal surfaces [71]). These highly charged colloidal spheres suspended in a dispersion medium can spontaneously organize themselves into a variety of crystalline structures. This process is driven by the minimization of electrostatic repulsive interactions. The periodic particle structure thus prepared is called a “liquid colloidal crystal” [72] or a “crystalline colloidal array” [70]. The maximum growth rate of the liquid colloidal crystal is 30 mm s–1, which is approximately the same as the growth rate of a snow crystal. When the spaces between particles are in the wavelength region of visible light, the crystal exhibits beautiful colors caused by the diffracted light (the color is called “iridescent” or “opalescent”) (Fig. 5.9) [73]. The periodicity is determined by the thickness of the electric double layers. Colloidal particles dispersed in a polar

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Fig. 5.9 Close-up color photograph of colloidal single crystals of 103-nm silica spheres [73]. (Reprinted with permission from T. Okubo, J. Colloid Interface Sci. 171(1), 55–62 (1995). Copyright 1995 by Elsevier).

solvent (alcohol, for example) are always surrounded by an electric double layer, which is extremely sensitive to the surrounding conditions [74]. Generally, the maximum thickness of the electric double layer is only 1 mm in water. When typical colloidal particles (0.1-mm diameter) have the electric double layer, their apparent diameters become 0.1 + 2 mm. As the particle diameter becomes smaller, the influences of the electric double layer on the interface phenomena (such as translation motion) become greater. Here, we present a review of the control of liquid colloidal crystals.

5.3.1.1 Control of the Lattice Structure The liquid colloidal crystal has either a body-centered-cubic (bcc) or a face-centeredcubic (fcc) structure, or both. The lattice constant and the crystal type of the liquid colloidal crystal are sensitive to additional fields such as gravitational force, electric field, centrifugal force, high pressure, temperature, and ion concentration (generally, the deionization of particles is necessary for the preparation of the liquid colloidal crystal [75]). We present an exploration of the control of the lattice structure.

By the thickness of the liquid colloidal crystal The observation of a series of structural transitions when the thickness of the liquid colloidal crystal layer changes has been reported (Fig. 5.10). The alternation of phases with triangular and square intraplanar orders has also been observed [76]. By microgravity The liquid colloidal crystal has only a bcc structure under the microgravity in a space shuttle [77]. This is because the fcc structure is preferable

5.3 Three-Dimensional Self-Assemblies via Nanoparticle Interactions

Fig. 5.10 Schematic image of the observation of the growth of liquid colloidal crystals [76]. M.O.: microscope objective. Photographs illustrating the thickness sequence of structures characteristic of the passage from two to three dimensions in a thin layer of the liquid colloidal crystals. The diameter of the polystyrene particles is 1.1 mm. (a) Formation of the monolayer. (b) When the number of particles is low the monolayer is disordered.

(c) The monolayer has triangular intraplanar order. (d) The bright and dark particles are situated at different heights. (e) One of the square-ordered layers. (f) The thickness of the gap increases from right to left; the transition is clear. (Reprinted with permission from P. Pieranski, L. Strzelecki, and B. Pansu, Phys. Rev. Lett. 50(12), 900–903 (1983). Copyright 1983 by the American Physical Society).

Fig. 5.11 (I) Experimental setup for pH gradient growth in gel [82]. (IIa) Side view and (IIb) cross-sectional view of a gelled crystal under pH gradient. Arrows show the growth direction. (Reprinted with permission from J. Yamanaka, M. Murai,Y. Iwayama, M. Yonese, K. Ito, and T. Sawada, J. Am. Chem. Soc. 126(23), 7156–7157 (2004). Copyright 2004 by the American Chemical Society).

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due to the difference in entropy between the fcc and bcc structures. Note that the volume fractions of the two structures have the same value of 74 % [78, 79].

5.3.1.2 Control of the Orientation Self-assembly processes always have thermodynamic fragility. Obtaining a well-oriented large single crystal has also been explored.

Colloidal epitaxy The slow sedimentation of colloidal particles onto a patterned substrate (or template) can guide the crystallization of bulk colloidal crystals, and so permit the control of the lattice structure, orientation, and size of the resulting crystals. Temperature gradient The nucleation and growth of hard-sphere nanocrystals were controlled via the utilization of temperature gradients. Single crystal size: 3 mm by poly(methyl methacrylate) (PMMA) 349-nm-diameter particles; 1 cm growth in approximately 50 days [81]. pH gradient A pH gradient formed by the diffusion of a weak base, pyridine, can prepare a novel one-directional crystal growth for colloidal silica dispersions (Fig. 5.11) [82]. Single crystal size: 0.5 × 5 × 5 mm with silica 110-nm-diameter particles; 1 cm growth in 5 hours. Shear flow A 1-cm-sized single-crystalline domain of a liquid colloidal crystal was instantaneously fabricated through a dynamic shear-flow process using polystyrene 173-nm-diameter particles (Fig. 5.12). Single crystal size: no description; 1 cm growth in 1 s [83, 84].

Fig. 5.12 Colloidal crystals formed by shear flow [83]. (a) Irregular texture produced by slowly pressing the syringe piston. (b) Uniform texture produced by quickly pressing the piston. The photograph was taken under indirect lighting. The cell is 8 cm long. (Reprinted with permission from T. Sawada, Y. Suzuki, A. Toyotama, and N. Iyi, Jpn. J. Appl. Phys. Part 2. 40(11B), L1226–L1228 (2001). Copyright 2001 by the Institute of Pure and Applied Physics).

5.3 Three-Dimensional Self-Assemblies via Nanoparticle Interactions

Electrorheological fluids When an electric field is applied across particle suspensions, they tend to exhibit an equilibrium body-centered-tetragonal (bct) phase and several nonequilibrium structures, such as sheetlike labyrinths and isolated chains of colloids. In this case, particles of 1–100 mm size are used. The concentration of the particles is 10–50 % volume fraction. The electric field could be used to switch between bct and fcc crystals. Induced dipolar interactions are also used to grow large fcc or bct single crystals, as well as crystal structures with part fcc and part bct layer stacking.

5.3.1.3 Overcoming the Mechanical Fragility A disadvantage of the liquid colloidal crystal is mechanical fragility. The crystal elastic modulus of a large single crystal is quite small (that of the 8-mm single crystal of SiO2 particles is less than 10–3 Pa, and that of sweet jelly is approximately 1000 Pa.). Thus, the crystal is distorted and broken by small mechanical vibrations. However, very interestingly, crystal formation is reversible; once formed, the structures can be broken by a slight mechanical shock and reformed in several hours [85]. Nature has overcome this weakness of mechanical fragility. Opal is a gem that is a self-organized crystal formed from high-concentration silica liquid. The silica liquid is concentrated, and monodispersed SiO2 particles are formed. The particles are self-assembly ordered, solidified, and form an opal in nature. This process takes more than a few million years [86]. Opal is often referred to as a typical solid colloidal crystal; however, natural opals are found which are liquid colloidal crystals solidified by the surrounded silica gel. The gels in these natural opals sometimes dehydrate and crack upon being dug out. This natural process has been mimicked and improved upon by researchers. Polymerized acrylamide hydrogel networks formed around liquid-like colloidal crystals permanently lock in the ordering [70, 87]. Poly(N-isopropylacrylamide) is well known as a polymer which has a temperature-induced volume-phase transition. Highly charged polystyrene spheres were formed into liquid colloidal crystals in an aqueous solution containing acrylamide monomer. Then, polymerization was photochemically initiated to create a colloidal crystal embedded in the acrylamide hydrogel film that was 125- to 500-µm thick. These polymerized crystals are not disordered by vibrations or by the addition of ionic impurities. The applications of these gelled colloidal crystals are presented in Section 5.4

5.3.1.4 Self-Assembly Preparations for Complicated Structures Here, we show two interesting examples which utilize the mobility of particles in solution:

Superstructures in binary mixtures of liquid-like colloidal crystals In some unusual gem opals, two kinds of silica particles of different sizes form a superstructure with a long period. The structures have been formed in a stable dispersion of

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Fig. 5.13 Patterns observed in a 550–310-nm particle mixture. (a) The pattern of the first plane, and (b) that of the second plane which lies about 400 nm above the first plane. Small particles in the first plane are at the centers of triangles of large particles, whereas those in the second plane lie at the midpoints of the lines connecting the blurred images of the larger particles. This is characteristic of a CaCu5-type alloy structure [85].

silica spheres and have then been condensed and dehydrated. Artificially, researchers have also succeeded in producing superstructures in mixtures of two monodisperse particles of different particle sizes, and have observed them microscopically in the stably dispersed state (Fig. 5.13) [85]. The superstructures are composed of polystyrene or silica [88] particles. The crystal growth is very slow; the ordered phase appears after 20–30 hours of growth. Several structures were found, including the alloy structures of NaZn13, CaCu5, AlB2, MgCu2, and compound types [89], which all belong to the group of so-called size-factor compounds. The range of particle diameters investigated in these studies is wide, from 85 to 1000 nm. The lattice constants of the alloy structure are from 500 to over 1000 nm. It has also been reported that the speed of crystal growth shows a 40–100 % increase under microgravity using polystyrene particles with 88- and 109-nm diameters (T. Okubo, personal communications). This is because of a decrease of the size effect under microgravity. Centrifugal compression Liquid-like colloidal crystals of polystyrene particles (85–173-nm diameter) are formed under centrifugal equilibrium (Fig. 5.14) [90]. By rotating a quartz glass disk containing a particle suspension, beautiful iridescent color bands due to Bragg diffraction appear in the observation cell, and centrifugal compression occurs for the lattice spacings of the crystal-like structures from the center. It was reported that the crystal was grown for 5–7 days at 3430 rpm, and the beautiful color thus formed was maintained one week after the cessation of centrifugal compression.

5.3 Three-Dimensional Self-Assemblies via Nanoparticle Interactions

Fig. 5.14 Photographs showing the rotating observation cell for centrifugal compression [90]. For a volume fraction of 0.0617, the photographs from obtuse (a) and acute (b) angle illumination are shown. For the volume fraction of 0.0820, a photograph from acute angle illumination is shown in (c). The observation cell on black-and-white paper is also shown in (d). (Reprinted with permission from T. Okubo, J. Am. Chem. Soc. 112(14), 5420–5424 (1990). Copyright 1990 by the American Chemical Society).

5.3.2 Solid Colloidal Crystals

When the particle suspension is dried out, the particles form periodic structures via gravitational force and capillary forces between the particles. This dried structure is called a “solid colloidal crystal” or an “artificial opal”. Numerous types of preparation method have been reported. The simplest approach to the formation of the solid colloidal crystal is sedimentation in a gravitational field [91]. This method involves multiple processes, such as Brownian motion, nuclear formation, and nuclear growth. When the sedimentation process is sufficiently slow, the particles concentrate at the bottom and form a three-dimensionally ordered structure. Both fcc and bcc structures are found to exist in the crystal. If the particle density is close to that of the dispersion medium, the particles will exist in a dispersed, equilibrium state and will rarely form periodic structures. Thus, monodispersed silica colloids are the most commonly employed particles for sedimentation due to the high density of amorphous silica.

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The sedimentation method for the preparation of solid colloidal crystals has been studied intensively, not only from the viewpoint of thermodynamic arguments [6] but also in terms of nonequilibrium processes [2]. For example, recent calculations which considered the role of solvent fluctuations show how the choices of solvent, nanoparticle size (and identity), and thermodynamic state give rise to the various morphologies of the final structures [92]. In general, the experimental parameters for the sedimentation method are the particle diameter, solvent, temperature, and moisture. Here, we introduce a number of developments in the preparation of solid colloidal crystals.

5.3.2.1 Control of the Orientation A solid colloidal crystal also has thermodynamic fragility like the liquid colloidal crystal. The obtaining of a well-oriented large single crystal of a solid colloidal crystal has also been explored intensively.

Evaporation control The low-velocity quasi-equilibrium evaporation of water from an aqueous particle solution enabled the preparation of a solid colloidal crystal without significant distortion of the lattice [93]. In a water suspension, polystyrene particles with 220-nm diameter were settled under a relative humidity of 95 %. The crystal growth rate is not reported; however, it can be assumed to be extremely slow. Oscillatory shear Controlled oscillatory shear with various amplitudes or frequencies was applied to fluid sediments of particles to find the “resonance” conditions under which the best ordering of particles was achieved. It may be expected that these experiments would have used liquid colloidal crystal; however, to accelerate the process of packing, the liquid medium was removed from the system [94]. This approach allows the relatively fast preparation of large-scale 3D self-assemblies. Control of the contact line In the conventional method, a ring-shaped solid colloidal crystal is usually formed at the edge (contact line) of the suspension on the substrate. The driving force for this ring formation is based on capillary flow in

Fig. 5.15 Conceptual scheme of the fabrication of artificial-opal films on glass substrates with and without covering liquid [95].

5.3 Three-Dimensional Self-Assemblies via Nanoparticle Interactions

the suspension from inside to outside because of the high evaporation rate at the contact line. By covering the suspension with hydrophobic silicone liquid, ring formation was suppressed and flat artificial-opal films were formed (Fig. 5.15) [95].

5.3.2.2 Control of the Lattice Structure The solid colloidal crystal has bcc, fcc, and tetragonal structures. For solid colloidal crystals, the control of the lattice structure is not easy. There have been attempts to control the lattice structure using a combination of lithographically patterned substrates. For example, a substrate with V-shaped groove patterns made the particles form into a pattern of fcc colloidal crystal parallel lines [96, 97]. The colloid samples consisted of 700- to 1200-nm-diameter polymer particles [97]; 840-nmdiameter SiO2 [96] particles were used.

5.3.2.3 Overcoming the Slow Growth Rate A disadvantage of solid colloidal crystals is the slow growth rate. To overcome this disadvantage, not only the gravitational field but also other additional fields are utilized for the particle assembly. Xia et al. have demonstrated an approach that allows the fabrication of colloidal crystals with a domain size as large as several square centimeters using a fluidic cell [98]. In a typical procedure, spherical colloids (with diameters ranging from ~50 nm to ~5 mm) were injected into a specially designed fluidic cell, and crystallized into a cubic-close-packed (ccp) 3D lattice under constant agitation from sonication or mechanical vibration. It was reported that colloidal crystals several square centimeters in area and tens of micrometers in thickness could be conveniently obtained within a few days.

5.3.2.4 Self-Assembly Preparations for Complicated Structures Here, we introduce interesting microstructured particles obtained through colloidal crystallization. Spherical, ellipsoidal, and donut-like microstructures have been synthesized by the growth of colloidal crystals in aqueous droplets suspended on fluorinated oil (Fig. 5.16) [99]. Crystallization in colloidal mixtures yields anisotropic particles of organic (polystyrene particles 270 to 630 nm in diameter) and inorganic materials (40-nm-diameter gold nanocrystals) that can, for example, be oriented and turned over by magnetic fields. The shape and size of the artificial opals can also be controlled by the selection of particles and the concentration of surfactants. The microstructures were formed within 12 hours. 5.3.3 Two-Dimensional Colloidal Crystals

Two-dimensional forces at the gas/liquid, liquid/solid, or liquid/liquid interfaces were also utilized for the preparation of 3D self-assemblies. In this case, the layers were stacked under two-dimensional forces and formed multilayers. The advantages

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Fig. 5.16 Schematic of the assembly method used for the class of microstructured particles through colloidal crystallization. Examples of anisotropic particles thus prepared are shown [99]. (A) Unoriented spherical assemblies incorporating regular (white) and magnetic (brown) latexes. (B) In the presence of a magnetic field originating from below, these particles immediately form an array with the white halves oriented upwards. If the magnetic field

gradient is reversed, the particles flip to form an array with the brown side up. (C, D) Two assemblies of complex shape obtained in the presence of small gold particles, as viewed from opposite faces. A metallic ring is deposited only on the side of the particle that was originally exposed to air. Scale bars, 500 mm. (Reprinted with permission from O. D. Velev, A. M. Lenhoff, and E. W. Kaler, Science 287, 2240–2243 (2000). Copyright 2000 AAAS).

of two-dimensional colloidal crystals are the controllability of the number of the layers and the ease of modification both chemically and physically. There are a number of special characteristics depending on the number of layers. For example, it was reported that anomalously strong diffraction was observed from a bilayer lattice of dielectric particles. It has been reported that the origin of the strong diffraction was

5.3 Three-Dimensional Self-Assemblies via Nanoparticle Interactions

its enhancement by specular resonance in constituent biparticles [100–103]. Because of these characteristics, beautiful fluorescent-light propagation patterns were observed in the multilayers of the composite two-dimensional colloidal crystals with mixtures of fluorescent and nonfluorescent polystyrene particles [104–106]. To show an example of the way these phenomena depend on the number of layers, we explain the beautiful patterns shown in Fig. 5.17. A fluorescence microscopic image of a hexagonal monolayer of two-dimensional colloidal crystal containing green and red fluorescent particles is shown in Fig. 5.17(I). Polystyrene particles (1000-nm diameter) are used. In addition to the bright fluorescence emitted from a fluorescing particle, emission is also observed at additional nearby spots in sixfold symmetrical patterns [104]. The emitted light propagates within the bulk of the particles and between particles at their points of contact, because of the difference between the refractive indices of polystyrene and air. The light propagation patterns of a tetragonal-packed structure in a triple layer are shown in Fig. 5.17(II). The optical microscopic image is also shown (d). As the focal

Fig. 5.17 Light propagation in a monolayer (I), a triple layer of tetragonalpacked (II), and a tetra layer of fccpacked (III) two-dimensional colloidal crystal of polystyrene particles (1-mm diameter) consisting of a mixture of green-fluorescing, red-fluorescing, and nonfluorescent particles [104–106]. As the focal point was moved from the bottom layer (a) to the top layer (c), the observed images changed. The phasecontrast microscopic image of (a–c) is also shown in (d).

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plane was changed from the bottom layer (a) to the top layer (c), the observed patterns also changed. In a tetra layer of fcc packing (Fig. 5.17(III)), beautiful triangular patterns were observed. Many methods for the two-dimensional ordering of particles have been reported from the various research fields. In this next section, we restrict ourselves to an introduction of the methods that can be used to prepare three-dimensional structures.

5.3.3.1 Various Preparation Methods Evaporation-driven self-assembly [17] (two-dimensional crystallization). In a thin film of coffee spread on the wall of a cup, coffee powders spontaneously form a ring. The two-dimensional crystallization method [107] (or evaporation-driven self-assembly) [108–110] utilizes this phenomenon. At the edge of the meniscus, the thickness of a liquid film becomes small. The meniscus between particles has an unstable form in the thin liquid film (Fig. 5.18) [111, 112]. There are strong attractive interactions among the colloidal particles because of this instability. This attractive capillary force is called the “lateral capillary force” [111, 113, 114]. The water evaporation rate is high where the particles aggregate because of the large surface area. As a result, water from the bulk suspension flows to the edge of the meniscus, and other particles in the suspension are driven toward this nu-

Fig. 5.18 Schematic image of the lateral capillary force caused by an unstable meniscus.

Fig. 5.19 Schematic image of evaporation-driven self-assembly.

5.3 Three-Dimensional Self-Assemblies via Nanoparticle Interactions

Fig. 5.20 Optical microscopic image of a monolayer of a two-dimensional colloidal crystal of polystyrene particles prepared by the evaporation-driven self-assembly technique.

cleus by the resulting convective transport (Fig. 5.19). By moving the substrate in the same direction and at the same speed as the suspension’s flow, we can obtain a two-dimensional highly ordered particle array [110, 115] (Fig. 5.20). Evaporation-driven self-assembly is one of the most promising techniques for practical use [116], because it is inexpensive, has a high throughput, and it is a suitable technique for both mono- and multilayer assemblies. Long-range-ordered, gold nanoparticle superlattices have been formed on silicon nitride substrates by the evaporation-driven self-assembly technique [117]. The advantage of evaporation-driven self-assembly is the ability to control the number of layers by varying the preparation conditions such as the contact angle, the height of the meniscus, or the translation speed of the substrate. This method is also useful for the preparation of binary structures by using a suspension with a mixture of particles with different diameters. Well-ordered single binary crystals with a stoichiometry of large (L) and small (S) particles of LS3, LS2, and LS were generated as a result of the templating effect of the first layer and the forces exerted by the surface tension of the drying liquid [118]. Electrophoretic deposition The lateral capillary force between nanoparticles/nanocrystals is very small, and thus it is difficult to form them into a two-dimensional colloidal crystal by the evaporation-driven self-assembly technique. However, there are a number of methods for forming nanosize particles into self-assembled structures. To order metal particle systems, a well-defined electrostatic or steric barrier, which is created at the metal particle surface to offset the large van der Waals attractive force between metal particles, was utilized. Alkenethiol was used to stabilize the gold metal surfaces. Gold nanoparticles (approximately 15-nm diameter) have been electrophoretically deposited onto carbon-coated copper grids by an applied voltage of less than 1 V cm–1. Increasing the applied voltage (for example, from 0.5 to 1.5 V) had unexpected effects. With a sufficiently strong current, the particles move toward one another across the electrode surface over very large distances (greater than five particle diameters). The ability to modulate this “lateral attraction” between particles, by adjusting the field strength or frequency, allows

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us to facilitate the reversible formation of two-dimensional fluid and crystalline colloidal states on the electrode surface. The method has also been used to form ordered monolayers of silica particles of 900-nm diameter [119], polystyrene particles of diameter 144, 365, 1696 [108], and 2000 nm [120, 121], and also bilayers of latex particles (475-nm diameter) [122]. Dynamic thin laminar flow. The dynamic thin laminar flow (DTLF) method involves reducing the particle electrostatic forces in a 5-mm-thick laminar flow driven by a rotating glass cylinder until adsorption occurs at the air/water interface [123, 124]. Multilayers were also formed by simply passing the mobile DTLF device back and forth over the same surface. The particle layers were amorphous and exhibited pseudoaggregation. Suspensions of 2697-, 821-, and 220-nm polystyrene particles [124] and cytochrome proteins [125] were used for demonstration; growth of 1-cm monolayer in 10 s. Spin-coating technique The spin-coating technique that is utilized in various industrial applications, such as photoresist coating and recordable compact disk fabrication, is one of the most well-known and widely used techniques. The spin-coating technique has been applied in the fabrication of nanoparticle assemblies. A dispersion of nanoparticles (Co [126], CdS [127], or CdSe [128] particles with 1.4–6-nm diameter) without a binder is spin-coated onto a solid substrate and dried out over a period of 1 [127] to 24 hours. Uniform nanoparticle assemblies with large areas (2-inch, 30×30 mm) on various kinds of substrates can be rapidly fabricated. However, generally, the ordering of the nanoparticles is unsatisfactory. Self-assembly of nanocrystal micelles Gold nanocrystal micelles are also arranged within a silica matrix in a face-centered-cubic lattice using the spin-coating technique [129]. The size of the nanocrystal in a micelle is from 1.0 to 3.3 nm and the lattice constant is ~10.2 nm. The lattice constants are adjustable through control of the nanocrystal diameter and/or the alkane chain lengths of the micelles or the surrounding secondary surfactants. Evaporation during the spin-coating drives the nanocrystal micelles into an ordered nanocrystal–silica mesophase.

5.3.3.2 Control of the Lattice Structure By patterned substrates. A grating substrate with a periodic one-dimensional height profile was used for the control of the lattice structure. It was shown that the lattice structures strongly depend on the ratio between the diameter of the particle and the period of the grating. The grating can control a centered-rectangular symmetry or a hexagonal symmetry [130]. The combination of the patterned substrates and evaporation-driven self-assembly enables us to form interesting self-assembly structures. Particles were selfassembled into complex aggregates under the physical confinement exerted by the holes patterned in a thin film of photoresist spin-coated onto the surface of a

5.3 Three-Dimensional Self-Assemblies via Nanoparticle Interactions

glass substrate [131]. Triangles, squares, pentagons, hexagons, tetrahedrons, octahedrons, and bi-square pyramids composed of spherical particles were spontaneously formed. Polystyrene particles (with diameters of hundreds of nanometers) were used. 5.3.4 Processing of Self-Assembled Structures 5.3.4.1 Submicrostructures Formed by Reactive Ion Etching in 3D Self-Assembled Structures The structures prepared by the self-assembly process do have an intrinsic disadvantage that precludes their widespread application. The permitted morphology of the structures is hexagonal high-density packing, which is governed only by the particles’ diameter. One simple technique for controlling the morphology of the two-dimensional self-assembled structure is by means of reactive ion etching [132–134]. Reactive ions can etch the surfaces of polystyrene and silica particles [135, 136]. Thus, a periodical nanostructure, in which the size of the nanostructure is related to the array pitch, can be formed. Not only monolayers, but also the complicated nanostructures in multilayers of two-dimensional self-assembled structures are formed [137]. The characteristic structures in the double layer of polystyrene 1-mm particle arrays after etching for 30, 60, and 90 s at 100 W using O2 reactive ion etching apparatus (SAMCO, BP-1) are shown in Fig. 5.21. The O2 pressure was 20 mPa. In each image, the glass substrate is shown in black, and the first and second layers from the glass substrate are shown in dark gray and gray, respectively. The gaps, where polystyrene particles did not exist in either the first or the second layer,

Fig. 5.21 Scanning electron micrographs of the double layer of two-dimensional fineparticle arrays after reactive ion etching for (a) 30, (b) 60, and (c) 90 s at 100 W. The diameter of the original latex particle is 1 mm. In each image, the glass substrate is shown as black, the bottom layer is shown as dark gray, and the top layer is shown as gray [137].

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were selectively etched in three directions (we can see the glass substrate through this gap as a black triangle in Fig. 5.21). These attractive structures are expected to expand the range of applications of self-assembled structures to include uses such as templates or masks.

5.3.4.2 Flexible Self-Assembled Structures The self-assembled particle structures are prepared on solid substrates. There have been a number of explorations of the preparation of physically flexible selfassembled particle structures utilizing a thermosetting resin [138–140]. A thermosetting resin, poly(dimethylsiloxane) (PDMS), was dripped onto polystyrene-particle structures and kept at a suitable temperature. The combined structure was immersed in water and peeled off gently from the glass substrate using tweezers. This type of self-assembled structure can be bent easily and repeatedly. It exhibits beautiful iridescent colors under illumination with white light because the Bragg diffraction depends on the periodic structure. Taking advantage of the flexibility and the Bragg diffraction, these flexible self-assembled structures have been applied as photonic papers [139, 140]. As the thermosetting resin was swollen by a liquid (e. g., a silicone fluid or an organic solvent such as octane), the lattice constant (and thus the wavelength of diffracted light) was increased. Polystyrene particles of 175-nm diameter were used for the demonstration.

5.3.4.3 Freestanding Colloidal Crystals Self-assembled structures are prepared on solid surfaces. Thus far, generally, we cannot ignore the influence of the substrates on the intrinsic characteristics of colloidal crystals. Matsushita et al. fabricated freestanding two-dimensional colloidal crystals using the photochemically activated linkage process [141]. A photoactivatable cross-linker, which can link together polymer strands with terminal amino groups under UV illumination (320–350 nm), was placed in water suspensions of NH2terminated polystyrene particles (220- and 1030-nm diameter). A two-dimensional colloidal crystal was prepared by evaporation-driven self-assembly with UV light illumination at the edge of the meniscus of the suspension. The crystal thus prepared was soaked in pure water for about 1 minute and was peeled off the substrate using tweezers; a freestanding colloidal crystal could be obtained. However, the photoactive cross-linker was piled up in the crystal; consequently, the original quality of the colloidal crystals was found to have deteriorated after the photocross-linking technique was applied. The other most popular method is the sintering technique. The sintering of colloidal crystals has a relatively long history when we consider the preparation of latex films from the 1970s [142]. Sintering processes of inorganic and organic materials are reproducible, controllable processes, and have been fully investigated both theoretically [143] and experimentally [144]. Freestanding monolayers of two-dimensional colloidal crystals of polystyrene spheres (1034- and 491-nm diameter) were

5.4 Applications of Three-Dimensional Self-Assemblies of Nanoparticles

prepared using the sintering technique [145]. The two-dimensional colloidal crystal was prepared on a glass substrate by evaporation-driven self-assembly, and the particles were connected with each other by the sintering process. The array was peeled off from the substrate softly and a freestanding two-dimensional colloidal crystal was formed. The fragility of the crystal depends on the sintering conditions. Utilizing the sintering method and patterned surfaces, fcc colloidal crystals are also formed into a pyramidal shape on an anisotropically etched silicon (100) and (110) substrate [97]. The freestanding colloidal crystal is expected to have a lot of applications; for example, the crystal was used to confirm a theoretical calculation [146] for photonic crystals which predicts that freestanding colloidal crystals have sharper transmission spectra than those of colloidal crystals on substrates [145]. 5.3.5 Dissipative Process for Fabrication of 3D Self-Assembly

Due to the limitations of space, we cannot introduce all of the methods used for the fabrication of 3D self-assembled structures here; for example, the dissipative process for fabricating self-assembled structures of nanocrystals/nanoparticles is also a very interesting and promising method. Please refer to the chapter on dissipative structures in this book.

5.4 Applications of Three-Dimensional Self-Assemblies of Nanoparticles

The structures introduced above are generally composed of monodispersed materials. Therefore, the materials are limited to silica particles, polystyrene particles, and proteins. Researchers are attempting to add further functions to these structures. In some cases, the trials may succeed through the transcription of the selfassembled structures to other functional materials. There are two means of achieving such transcriptions: (a) taking a mold of the self-assembled structures, and (b) using the self-assembled structure as a mask. Molds of the Self-assembled Structures The mold structure is now well known as an “inverse opal” [147]. A diverse range of 3D macroporous materials have been constructed by using colloidal crystals as 3D ordered scaffolds for the infiltration or synthesis of various materials: semiconductors [148–150], metals [151, 152], carbon and silicon [135, 147, 153], polymers [154–156], and gold–silica composites [157]. The colloid particles are subsequently removed by calcination or chemical means, yielding a periodic and open pore structure which is often termed an inverse opal. The dimensions of the pores can be extended to cover a wide range that spans from 10 nm to 10 mm, by varying the particle diameters. To the best of our knowledge, the first report of inverse opals was presented by Velev et al. [151] After that, many papers [148–150, 158–160] have been published on the topic of inverse opals. This great interest is related to the study of photonic

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Fig. 5.22 (a) Scanning electron microscopic images of a TiO2 inverse opal prepared using a two-dimensional colloidal crystal. (b) Silver, which was photodeposited onto the inverse opal, was observed as a white color in a backscattered electron image [148, 149].

crystals as described below; however, the inverse-opal structure has also attracted interest for use as a catalyst or a filter. The photocatalytic activity of TiO2 inverse opals (Fig. 5.22) was actually confirmed in the early days of research by the successful photoreduction of silver ions on textured surfaces [149]. Self-assembled Structures as Masks Self-assembled structures can be used not only as scaffolds but also as masks. A monolayer of colloidal particles is deposited in either a random or ordered array over the entire surface of a macroscopic substrate. Large-area random or ordered mosaic arrays of identical submicron microcolumnar structures are produced by using the colloidal particles as either an etching or deposition mask [161, 162]. Metals (silver, nickel, gold) were deposited in the spaces between the particles in self-assembled monolayers or double layers, and thus formed metal-dot arrays [163]. However, since a flat, clean, and hydrophilic surface is preferable for the purpose of generating a highly ordered array with a relatively large domain size, the substrate on which the metals are deposited is limited to such materials as glass slides or silicon wafers. Recently, some researchers have modified the surfaces of functional materials to make them suitable as substrates for the self-assembly technique. To obtain a hydrophilic surface, oxygen plasma, NaOH treatment, and ozone treatment have been examined. For example, Okuyama et al. fabricated periodic diamond-cylinder arrays on diamond surfaces using the evaporation-driven self-assembly method (Fig. 5.23) [135, 136]. Generally, the diamond surface has a high contact angle (40–608), and thus it is not suitable for use in the evaporation-driven self-assembly technique because the suspension cannot spread. To reduce the contact angle, Okuyama et al. carried out an oxygen plasma treatment (20 Pa, 70 W,

5.4 Applications of Three-Dimensional Self-Assemblies of Nanoparticles

Fig. 5.23 Schematic diagrams showing the preparation procedures for cylinder-like microstructured diamond films [135, 136].

15 s) of the diamond surface and obtained a much smaller contact angle (nearly 08), due to the convention of H termination to O termination on the diamond surface [136] (Fig. 5.24). Accordingly, SiO2-nanoparticle colloidal crystals were prepared on this diamond surface and utilized as a mask. These authors carried out further oxygen plasma etching (20 Pa, 150 W, 5–120 min) on the colloidal crystals and etched diamond using oxygen ions. As a result, cylinder-like diamond films were formed.

Fig. 5.24 Scanning electron microscopic images of the diamond cylinder surfaces observed at (a) 08 and (b) 908 from the surface normal [135, 136].

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One of the applications of these diamond cylinders is as an electron emitter array, and its capacity for electron emission has already been reported [136]. Here, we would like to introduce a number of the major application fields of the various related self-assembly structures. These are the fields of photonic crystals, sensing materials, optical switches, and memory media. 5.4.1 Photonic Crystals

A photonic crystal is a spatially periodic structure fabricated from materials having different refractive indices. The periodicity of the dielectric constant has an influence on the propagation of electromagnetic waves that is similar to the influence of a semiconductor on electrons [164–168]. Three-dimensional self-assembled structures, in which the periodicity is in the range of the photon wavelength, can also be photonic crystals. Before the concept of photonic crystals became well known, the photonic characteristics of self-assembled particle structures were discussed in terms of Bragg diffraction [74, 169–171]; currently, they are being reconsidered with respect to photonic crystal concepts (for example, recently, the first Bragg diffraction observed in the optical transmittance/reflectance spectra has been called the “optical stop band”) [139, 172–175]. There exists a bandgap that prevents the passage of photons of a specific frequency in some photonic crystals; this bandgap is called the “photonic bandgap”. The optical transmittance spectra of liquid colloidal crystals were measured by varying the incident angle of the light, and the photonic energy band was investigated experimentally. Moreover, it has been reported that the liquid colloidal crystals include some eccentric particles, which have different diameters or are composed of different materials and have dips in their photonic bandgaps. The dips occur according to the donor–acceptor states in the semiconductor. For the study of photonic crystals, many radiative materials such as fluorescent particles, CdS nanocrystals, CdSe nanocrystals, ZnS nanocrystals, dyes, and electroconductive polymers have been combined with self-assembled particle structures and inverse opals. The photonic characteristics of these combined structures are also interesting, but are beyond the scope of this book. The advantages of 3D self-assembled structures of nanoparticles are their convenient and inexpensive fabrication, the ease of 3D fabrication, and the ease of varying the position of the photonic bandgap. The disadvantages are the imperfect control of the structures (there is always thermodynamic fragility) and, generally, no full photonic bandgaps. However, there are a number of conditions under which self-assembled particle structures have full photonic bandgaps. Control of Pore Wall Thickness in Inverse Opals The control of pore wall thickness and the formation of structures with closed pores is also studied. Macroporous TiO2 and TiO2/SiO2 materials have been prepared by using assemblies of polystyrene colloidal spheres coated with polyelectro-

5.4 Applications of Three-Dimensional Self-Assemblies of Nanoparticles

lyte multilayers as templates. Titanium(IV) isopropoxide was infiltrated into the close-packed spheres and thereafter the colloidal cores and polyelectrolytes were removed by calcination [176]. The wall thickness of the resulting macroporous materials increases with the number of polyelectrolyte multilayers deposited onto the colloidal spheres. The preparation of inverse opals is convenient, versatile, and cost-effective. In essence, any material which can fill the spaces between the particles of 3D self-assembled structures can be tailored to the inverse-opal shape, except those materials which have significant volume shrinkage or which expand during the preparation procedure. Theoretically, the void space in inverse opals is 74 % of their total volume. Most studies on the formation of photonic crystals from colloids have utilized uncoated colloid spheres. However, surface-modified colloids have also been used [14, 177]. The optical bandgap of the colloidal crystals can be modulated by varying the thickness of the coated materials on the spheres. In essence, the position of the stop band is defined by the particle size and the effective refractive index of the colloidal crystal. This has been demonstrated for spheres coated with gold nanoparticle–polyelectrolyte layers, which were assembled to form metallodielectric colloidal crystals, and also for spheres coated with HgTe semiconductor nanocrystal–polyelectrolyate layers [176]. For the latter system, the photoluminescence properties of the HgTe semiconductor nanocrystals assembled around the colloid spheres are impacted by the stop band of the colloidal crystals, giving rise to a modification of their emission properties. This provides a means to combine electronic confinement, originating from the semiconductor nanocrystals, with photon confinement, due to the ordered dielectric structures, thus potentially opening new avenues in the design and construction of novel electrooptical devices based on photonic crystals. .

Theoreticians have pointed out that fcc structures of metal particles (e. g., silver) are expected to have a full photonic bandgap in the visible light range.

.

Theoreticians have also pointed out that the diamond structures of those particles, for which the refractive index is over two times larger than that of the ambient material, are expected to have full photonic bandgaps. Incidentally, diamond structures composed of particles can be prepared using a manipulation technique employing a scanning electron microscope [178].

.

Inverse opals which are infiltrated imperfectly are expected to have a full photonic bandgap.

Currently, the photonic energy bands of colloidal alloy structures have not been calculated theoretically. Further progress in this field is expected. Tunable Photonic Crystals By fixing liquid colloidal crystals in a polyacrylamide hydrogel matrix, photonic crystals were prepared whose diffraction peak wavelengths were tunable by the application of mechanical stress [82, 87].

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5.4.2 Sensing Materials Chemical Sensing Materials A liquid colloidal crystal of polymer particles (roughly 100 nm in diameter) polymerized within a hydrogel that swells and shrinks reversibly in the presence of certain analytes is demonstrated as a chemical sensor for the presence of metal ions and glucose. The diffracted color of the liquid colloidal crystal changes in response to a chemical signal. The hydrogel contains either a molecular-recognition group that binds the analyte selectively (crown ethers for metal ions), or a molecular-recognition agent that reacts with the analyte selectively. These recognitions cause the gel to swell due to an increase in osmotic pressure, which increases the mean separation between the particles and thus shifts the Bragg peak of the diffracted light [179]. Optical Affinity Biosensing The application of inverse opal structures to biological optical affinity sensing has also been explored. Solid colloidal crystals of polystyrene (350-nm diameter) were used as templates for the fabrication of biotinylated polymer inverse opal. The interaction between biotin and avidin is highly specific and has one of the largest known binding constants for noncovalently bound protein to a small ligand. Thus, the bioselective adsorption of avidin was expected to diminish the pore diameter and, as a result, to induce a bathochromic shift of the optical stop band peak position [180]. 5.4.3 Optical Switches Electrically Switchable The electrooptic response of liquid crystal–polymer composites with a conventional liquid colloidal crystal is used to achieve electrically switchable three-dimensional Bragg diffraction. Silica particles of 1.6-mm diameter were used [181]. Physical Pressure The liquid-like colloidal crystal of dyed particles embedded in a polyacrylamide hydrogel acts as a nanosecond optical Bragg diffraction switching device under temperature variation, since the hydrogel undergoes a volume phase transition between a swollen and a compact state at around room temperature [70]. 5.4.4 Optical Memory Media

Bright luminescent images are stored and then read out by excitation of the thin films of semiconductor nanocrystals, with blue or UV light [182].

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Acknowledgments

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6 Dissipative Structures and Dynamic Processes for Mesoscopic Polymer Patterning Masatsugu Shimomura

6.1 Introduction

Many regular patterns are around us [1], and they can be classified into three categories. One is artificially manufactured and the other two originate in the working of nature as biological and nonbiological phenomena. Lithography is a modern, convenient technology for the regular micro- and nanopatterning of materials. In the biological systems, regular patterns with the hierarchical structuring of molecular assemblies are formed by self-assembly with small energy consumption. Self-assembly is the fundamental principle that generates various structures spontaneously on all scales, from molecules to galaxies, including living organs. Regular patterns are formed by two types of self-assembly processes, static or dynamic. The static self-assembly is ordered-state formation in equilibrium without energy dissipation. Crystals are typical examples of static molecular self-assemblies. The dynamic self-assembly is defined as self-organization. The dissipative structure [2], a regular pattern formation requiring energy dissipation under chemical or physical conditions far from thermal equilibrium, is a typical example of self-organization. A Nobel laureate, Ilya Prigogine, coined the term dissipative structure. Some types of regular spatiotemporal patterns, such as spirals in Belousov–Zhabotinsky reaction systems and the honeycomb and stripes of Rayleigh–Bénard convection, are formed as dissipative structures. Some methods and principles for regular pattern formation are classified in Fig. 6.1. Various functions characteristic of the regular patterns are expressed. A typical example of the functional regular patterns formed in living organisms is a moth’s eye structure [3]. The moth’s eye is a compound eye of many small lenses. The surface of each small lens is not smooth and is covered with hexagonally arrayed protuberances, which are roughly 200 nm in height and spaced with centers approximately 300 nm apart. The regular surface pattern on the subwavelength scale provides a low-reflectance surface for light. Therefore the moth’s eyes absorb a high percentage of light, which is enough for their night flight. The moth’s eye structure is now industrially important, such as for antireflective coatings [4] on Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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Fig. 6.1 Classification of regular pattern formation.

optical lenses and polymer-film screens of liquid-crystal devices. Since the sizes of the elements on the antireflective coating are required to be on the order of 200 nm, conventional lithography processes are essential to produce microstructures imitating the moth’s eye structure. Lithography is a typical downsizing technology for fabricating micro- and nanopatterns from bulk materials. Compared with pattern formation in the natural systems, however, lithography requires high energy consumption and a large investment in equipment. Moreover, even with the latest lithographic techniques, the nanometer-scale processing is not so easy. Self-assembly is now focused as an innovative methodology supporting bottom-up nanotechnology. Supramolecular chemistry [5] is one of the new trends of bottom-up nanotechnology, which enables spontaneous ordered-structure formation by static molecular self-assembly. Recently, dynamic self-assembly, i. e., self-organization, attracted attention in the construction of large systems beyond molecular assemblies and toward the mesoscopic and macroscopic molecular systems [6, 7]. Here we describe the formation of various regular polymer patterns on the micrometer and submicrometer scales by using self-organization processes. We have utilized dissipative structures generated in casting polymer solutions for microand nanopatterning of polymer materials. The new methodology of our proposal is widely applicable to nano- and microfabrication without lithographic procedures, because the physical generality of dissipative structure formation provides us with a diversity of material selection.

6.2 Formation of Dissipative Structures in Drying Polymer Solutions

6.2 Formation of Dissipative Structures in Drying Polymer Solutions

A typical example of daily-life patterns is the convection seen in hot Japanese miso soup (Fig. 6.2). When a fluid is heated from the bottom, convection occurs as the fluid motion from bottom to top is induced by buoyancy with dissipation of heat energy. The patterned convection in miso soup is one example of Rayleigh– Bénard convection, which consists of cooperative regular hexagonal assemblies of many small convection cells. The convection pattern disappears on cooling the miso soup. Another example is the formation of periodic liquid stripes in a wine glass, called “wine legs” or “tear of wine”. Due to faster evaporation of ethanol, convection known as the Maringoni effect is induced by local surface tension changes in the thin liquid film of wine climbing the glass surface. The water-condensed liquid film forms small droplets on increasing its surface tension, and eventually the droplets crawl down as periodic stripes after breaking the balance of surface tension and gravity. The “wine legs” phenomenon is called a fingering instability in physics [8]. A third example of regular pattern formation in daily life is found in a left coffee cup. The periodic “coffee stain” stripes remaining in a coffee cup are formed by “stick–slip motion”, a term used in tribology and mechanical engineering. In the case of the coffee stain phenomenon, the stick–slip phenomenon means an intermittent movement of the solution edge by the successive

Fig. 6.2 Regular dynamic patterning in daily life and in casting polymer solution.

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repetition of coffee solutes deposition and viscosity increase by water evaporation. Finally, the periodic concentric layers of the deposited coffee stain the cup. The coffee ring formation is theoretically described [9–11] as a contact line pinning phenomenon [12, 13]. These regular structures are formed through dynamic processes involving the dissipation of energy or matter. Though the formation of a dissipative structure is a complicated phenomenon, it can be applied to material fabrication because of its physical generality. We have found that typical dissipative structures were formed in the casting process of dilute polymer solutions on solid surfaces. Figure 6.2 shows a fluorescence microscope image of the substrate/solution interface of a polymer solution droplet [14]. The brighter areas indicate condensation of polymer solutes, since the polymer is labeled with a fluorescent probe. The wine legs phenomenon can be seen near the solution edge, and Rayleigh–Bénard convections are observed as circular domains in the center of the droplet.

6.3 Regular Pattern Formation of Deposited Polymers After Solvent Evaporation

Dynamic regular structures formed in drying polymer solutions are fixed as regular patterns, stripes, and lattices, etc., after solvent evaporation. The key in the experiment was high dilution of evaporating solutions. Solutions were 100 to 1000 times more dilute than those used in creating ordinary continuous polymer film. Spreading of highly diluted solutions often results in areas of fragmentation due to dewetting, a phenomenon in which the solution is repelled by the substrate. This phenomenon is a well-known problem in the coating and film manufacturing industries. Once dewetting occurs in a homogeneous polymer film, randomly formed polymer aggregates are arranged to form irregular figures like the Voronoi pattern [15]. We have discovered, however, that regular dewetting can be created if the polymer concentration and other casting conditions are properly controlled. At the initial stage of drying, the contact line of a droplet edge recedes monotonically as the volume of the solution droplet decreases with solvent evaporation. The regularly aligned periodic stripes, running parallel to the direction of the contact line, are deposited from the periodically aligned wine legs, where the polymer solutes are locally condensed. Figure 6.3 shows snapshots of stripe formation from the periodically aligned “fingers”. The fingers are straightened as regular stripes concomitant with smooth receding of the contact line. Figure 6.4 shows three typical polymer patterns deposited on solid substrate after solvent evaporation. In the early phase of evaporation, periodic condensation of polymer solutes along the receding solution front, i. e., fingers, form a regular stripe pattern (area 1). However, at area 3, where the concentration increases as evaporation continues, stripes are formed perpendicular to the direction of the receding solution front. This phenomenon is identical to the “coffee stain” phenomenon. At the intermediate concentration the two phenomena occur simulta-

6.3 Regular Pattern Formation of Deposited Polymers After Solvent Evaporation

Fig. 6.3 Snapshots of stripe formation from the periodically aligned “wine legs”. Time (s) from the start of video recording is shown in the upper left of each shot.

Fig. 6.4 Pattern transition in cast polymer film.

neously, forming a gridlike structure (area 2). Finally, after complete evaporation of solvent, a thin polymer film remained as a continuous phase in the center of the drying droplet (area 4). Figure 6.4 clearly indicates that the polymer concentration is one of the definitive experimental factors of the self-organization events emerging at the receding contact line. To fabricate uniform polymer patterns, a continuous supply of polymer solution of constant concentration is essential. We have fabricated a new ap-

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Fig. 6.5 Experimental setup for continuous patterning and schematic illustration of sliding meniscus and pattern formation.

paratus composed of two moving substrate holders and a microscope system for in situ observation of the receding solution front [16]. Figure 6.5 a shows a photographic illustration of the instrumentation for continuous-film preparation. A glass plate for optical microscopy was fixed on a substrate holder, which smoothly moved with controlled velocity by a computer-controlled driving system. Another glass plate was set on the other substrate holder. Each glass plate was overlapped by 3–4 cm and spaced with a narrow gap of 200 mm (Fig. 6.5 b). To avoid the evaporation of the entire solution, the polymer solution was sandwiched between two glass plates. Gradually moving the top glass plate to form an interface with a constant concentration allowed continuous pattern formation. Optical micrographs and atomic force microscopy (AFM) images of patterned polystyrene films shown in Fig. 6.6 clearly indicate that polymer concentration dominates the mode of regular polymer patterns. A regular array of micron-sized polymer dots was formed when a 0.1 g l–1 polystyrene solution was deposited at a sliding speed of 50 mm s–1. The mean diameter of each microdot was 10 mm. AFM measurement shows that the height of the microdot ranged from 50 to 100 nm. The spacing between two dots was about 10 mm along the sliding direction and 2–5 mm perpendicular to the sliding direction. In the case of a higher concentration (0.5 g l–1), micron-sized periodic stripes were formed. The stripes were perpendicularly oriented to the sliding direction. AFM revealed that the width and

6.3 Regular Pattern Formation of Deposited Polymers After Solvent Evaporation

Fig. 6.6 (a) Optical (top row) and atomic force (bottom row) micrographs of patterned polystyrene. (b) Ladder-patterned polymer film on a glass plate and its laser diffraction pattern.

height of the microstripe were 10 mm and 100 nm, respectively, and the line spacing was 10 mm. Highly uniform ladderlike polymer patterns were formed when the 4.0 g l–1 solution was supplied for casting. These “ladder patterns” consisted of thick lines with 400-nm height along the sliding direction and thin lines with 100-nm height perpendicular to the sliding direction. The array of microdots perpendicular to the sliding direction converts to a single continuous line with increasing concentration. Further increasing the concentration yields new stripes parallel to the moving direction to form ladder patterns. At a sliding speed of 50 mm s–1, 0.3 and 1.0 g l–1 were the critical concentrations for stripe and ladder formation, respectively, because the coexistence of two patterns (dots and stripes, stripes and ladders) was found at these two concentrations. As shown in Fig. 6.6 b, glass plates coated with a patterned polymer film showed strong interference colors originating from the microstructures, especially from the ladder pattern. Periodic spots from diffraction of a laser beam by the ladder-patterned polymer film are also shown in Fig. 6.6b. The two periodic structures formed in the ladder pattern were indicated by two series of diffraction spots crossing each other. Diffraction spots arrayed horizontally were generated by

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stripes that ran parallel to the sliding direction of the glass plate. These diffractions, with a long spacing, reflect the regular arrangement of the stripes with a short repeating period formed perpendicular to the sliding direction. Another series of diffraction spots arrayed vertically, perpendicular to the former series, had a shorter spacing. They were diffracted from another stripe structure formed parallel to the sliding direction, with a long repeating period. This result clearly indicates that the micrometer-scale lattices in the ladder pattern are regular enough to serve as a grating. Thus, our sliding instrument without conventional lithographic techniques can easily prepare highly ordered periodic structures. These micropatterns can be used for optical waveguide arrays, diffraction gratings and photonic bandgap materials. Due to the physical generality of the self-organization phenomena, a remarkable advantage of our patterning method is versatility [17–23], not only of materials – organic, biological and inorganic – including nanoparticles [24], but also their application. Consideration of the underlying mechanism [25] and theory is another important approach to control regular pattern formation as well as the experimental trials. We have proposed a mathematical model [26] of the periodic precipitation from a droplet of solution by evaporation. In our simulations, precipitation takes place only in the vicinity of the contact line except for the very final stage of evaporation, as is observed in the experiments. Our model could reproduce striped patterns by taking supersaturation into account, which is essential for this kind of periodic precipitation. Actually, the pattern becomes irregular in the absence of supersaturation, since the precipitation occurs not only near the contact line but also inside the droplet.

6.4 Preparation of Honeycomb-Patterned Polymer Films

Some research groups [14, 27, 28] have independently found that microporous polymer films were prepared from water-immiscible solvent under humid casting conditions. The self-organization of water droplets condensed by evaporation cooling forms vaporizing templates of honeycomb-like structured porous polymer films. The formation mechanism of honeycomb-structured film is schematically shown in Fig. 6.7. Under highly humid conditions fine water droplets condensed on the surface of a polymer solution were eventually packed in a hexagonal regular array. Due to the homogeneous nucleation of water droplets on the solution surface, their size distribution curve is very sharp. Droplets formed in the center of the solution surface are transported toward the solution front, first by convection and then by capillary forces at the interface. Polymer molecules find their way into the narrow spaces between the droplets and remain after evaporation of the water droplets. The polymer molecules stabilize the water droplets from the coalescence. After complete water evaporation, a regularly porous polymer sheet is formed. Pore size can be widely regulated from several tens of microns to a few hundred nanometers. The size of the water droplets increases along with an in-

6.4 Preparation of Honeycomb-Patterned Polymer Films

Fig. 6.7 Schematic illustration of honeycomb pattern formation.

crease in humidity. The pore size is strongly dependent not only on humidity but also on the vapor pressure of the solvent. Benzene provides smaller pores than xylene. A larger casting volume of the polymer solution leads to a larger pore size of the film. Since the water vapor is constantly supplied to the evaporating solution, the longer it takes for the complete solvent evaporation, the larger the water droplets become. A larger amount of solvent requires a longer time for evaporation. Figure 6.8 clearly indicates the effect of solvent volume on the pore size. We have succeeded in creating a honeycomb-patterned polymer film with pores ranging in size from approximately 200 nm to 0.1 mm, with good reproducibility if we used a chloroform solution of the biodegradable polymer, e-caprolactone [29]. The formation mechanism of honeycomb-patterned films is general, so this method is widely applicable for many polymers: C60 [30], block copolymers [31–34], star polymers [35–38], inorganic polymers [39– 42], polyimides [43], celluloses [44, 45], conducting polymers [46–49], nanoparticles [50–52], and so on.

Fig. 6.8 Pore size control of the honeycomb-patterned polymer films. Biodegradable polymer, e-caprolactone, was dissolved in chloroform (4 mg ml–1).

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6.5 Processing of Honeycomb Patterns

Some examples of the structural versatility of the honeycomb pattern are shown in this section. The cross section of the honeycomb-patterned film is shown in Fig. 6.9 (center). The spherical shape of the pores reflects the shape of the template water droplets. The honeycomb-patterned porous film had a double-layered structure with pillars supporting the two porous layers on each vertex of the hexagons. A regularly arrayed pillar structure, like a “pincushion”, was formed when the honeycomb film was cleaved into halves by peeling with an adhesive tape. Each pillar was broken into two sharp pins, one on the surface of each layer, after

Fig. 6.9 Structure and preparation of pincushion structure from the honeycomb-patterned porous film.

Fig. 6.10 Plastic deformation of honeycomb-patterned films: (a) original hexagons, (b) elongated hexagons, (c) rectangles.

6.6 Application of Regularly Patterned Polymer Films

peeling. The regularly arrayed pillar structure showed superhydrophobicity, the so-called lotus effect, when the honeycomb film was formed from hydrophobic polymers including the fluorinated polymer [53]. Figure 6.10 indicates that the plastic deformation of the honeycomb-patterned films by stretching provides various shaped patterns, such as elongated hexagons, rectangles, etc. [54]. New regular patterns can be produced when the self-organized polymer films are used as molds. As shown in Fig. 6.11, the primary copy of the honeycomb mold provides regularly arrayed convexes [55, 56]. Furthermore, a regular concave array was prepared when the second molding was performed by using the primary copy as the mold. The molding method enables the regular patterning of water-soluble polymers. Incorporation of nanoparticles in the honeycomb holes is another example of the molding and structural modification of the honeycomb-patterned films, too. The composites are easily prepared by simple spreading of a water suspension of nanoparticles on the honeycomb-patterned polymer films [57–60].

Fig. 6.11 Regular pattern formation by using honeycomb pattern as a mold.

6.6 Application of Regularly Patterned Polymer Films

Regular polymer patterns prepared by self-organization processes, the dissipative process and water droplet template, are promising as novel functional materials [61]. The honeycomb-patterned films can be applicable to optical and photonic devices, as microlens arrays [56], e-papers and photonic crystals [62]. Biomedical application is another emerging requirement for the honeycomb-patterned polymer films [29, 54, 63–69], especially of biodegradable polymers. The honeycomb-patterned and normal cast films of e-caprolactone were used as a liver cell (Wistar rat hepatocytes) culture substrate. Liver cells cultured on normal cast film with no structure tend to flatten (Fig. 6.12 a) and do not express proper liver functionality,

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Fig. 6.12 Substrate effect on cultured cells: (a, b) hepatocytes, (c, d) hippocampus neural cells.

e. g., albumin secretion and urea synthesis. Conversely, liver cells cultured on the honeycomb-patterned film take on a spherical shape (hepatocytes spheroid) and are functional (Fig. 6.12 b). The shapes and functions of liver cells can be altered, depending on the size and shape of the pores and the materials used in preparing the honeycomb-patterned film. Figure 6.12 also indicates spheroid formation of neural cells (hippocampus neural cells) on the honeycomb-patterned film [70]. Different materials can be used and different sizes and shapes of pores can be formed on the film, which can be patterned in a self-standing manner [71], making it possible to culture cells under various conditions. It is possible to use both sides of the film at the same time to, for example, culture liver cells on one side and vascular cells or endothelial cells on the other side.

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6.7 Conclusion

The spatiotemporal structures originating from the dissipative structure and dynamic processes of water droplet organization in casting polymer solutions are frozen on solid surfaces as regular mesoscopic polymer patterns. Taking advantage of the physical generality of self-organized pattern formation, a new microfabrication technology without lithographic procedures is expected. It can be widely applicable for any materials, organic and inorganic, polymeric and low molecular weight, etc. Hierarchical structuring from the molecular to the micrometer scale can be achieved when nanostructured polymer materials, e. g., block copolymers, are chosen. Layer-by-layer fabrication of the honeycomb-patterned film provides a regular three-dimensional porous structure [72]. Another three-dimensional honeycomb structure can be fabricated when the polymer casting is performed on a patterned substrate fabricated by the conventional lithographic technique [73]. Many applications of meso- and nanoscopic regular polymer patterns as novel biomaterials, photonic and electronic devices, and so on are in full progress. References 1 P. Ball, The Self-Made Tapestry: Pattern Formation in Nature, Oxford University Press, Oxford, 1998. 2 G. Nicolis, I. Prigogine, Self-Organization in Nonequilibrium Systems, Wiley, New York, 1977. 3 E. Warrant, K. Bartsche, C. Guenter, J. Exp. Biol., 1999, 202, 497. 4 K. Kintaka, J. Nishii, A. Mizutani, H. Kikuta, H. Nakano, Opt. Lett., 2001, 26, 1642. 5 J. M. Lehn, Proc. Natl. Acad. Sci USA, 2002, 99, 4763. 6 M. Shimomura, T. Sawadaishi, Curr. Opin. Colloid Interface Sci., 2001, 6, 11. 7 G. Whitesides, M. Boncheva, Proc. Natl. Acad. Sci. USA, 2002, 99, 4769. 8 A. Cazabat, F. Heslot, S. Troian, P. Carles, Nature, 1990, 346, 824. 9 R. Deegan, O. Bakajin, T. Dupont, G. Huber, S. Nagel, T. Witten, Nature, 1997, 389, 827. 10 R. Deegan, Phys. Rev., 2000, E61, 475. 11 R. Deegan, O. Bakajin, T. Dupont, G. Huber, S. Nagel, T. Witten, Phys. Rev., 2000, E62, 756.

12 P. G. de Gennes, Rev. Mod. Phys., 1985, 57, 827; E. L. Decker, S. Garo, Langmuir, 1997, 13, 6321. 13 N. Maruyama, T. Koito, T. Sawadaishi, O. Karthaus, K. Ijiro, N. Nishi, S. Tokura, S. Nishimura, M. Shimomura, Supramol.Sci., 1998, 5, 331. 15 T. Stange, D. Evans, W. Hendrikson, Langmuir, 1994, 10, 1566. 16 H. Yabu, M. Shimomura, Adv. Funct. Mater., 2005, 15 (4), 575–581. 17 M. Shimomura, O. Karthaus, N. Maruyama, K. Ijiro, T. Sawadaishi, S. Tokura, N. Nishi, Rep. Prog. Polym. Phys. Jpn., 1997, 40, 523. 18 O. Karthaus, L. Grasjo, N. Maruyama, M. Shimomura, Thin Solid Films, 1998, 327–329, 829. 19 M. Shimomura, T. Koito, N. Maruyama, K. Arai, J. Nishida, L. Grasjo, O. Karthaus, Mol. Cryst. Liq. Cryst., 1998, 322, 305. 20 J. Hellmann, M. Hamana, O. Karthaus, K. Ijiro, M.Shimomura, M. Irie, Jpn. J. Appl. Phys., 1998, 37, L816. 21 O. Karthaus, T. Koito, N. Maruyama, M. Shimomura, Mol. Cryst. Liq. Cryst., 1999, 327, 253.

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6 Dissipative Structures and Dynamic Processes for Mesoscopic Polymer Patterning 22 O. Karthaus, T. Koito, N. Maruyama, M. Shimomura, Mater. Sci. Eng., 1999, C8–9, 523. 23 O. Karthaus, H. Yabu, T. Koito, K. Akagi, M. Shimomura, Mol. Cryst. Liq. Cryst., 2001, 370, 353. 24 T. Sawadaishi, K. Ijiro, M. Shimomura, Y. Shiraishi, N. Toshima, T. Yonezawa, T. Kunitake, Mol. Cryst. Liq. Cryst., 2001, 371, 123. 25 O. Karthaus, L. Grasjo, N. Maruyama, M. Shimomura, 1999, Caos, 9, 308. 26 M. Nonomura, R. Kobayashi, Y. Nishiura, M. Shimomura, J. Phys. Soc. Jpn., 2003, 72, 2468. 27 G. Widawski, M. Rawiso, B. François, Nature, 1994, 369, 387. 28 L. Govor, M. Goldbach, I. Bashmakov, J. Parisi, Phys. Lett., 1999, A261, 197. 29 M. Tanaka, M. Takebayashi, M. Miyama, J. Nishida, M. Shimomura, Bio-Med. Mater. Eng., 2004, 14, 439. 30 B. Francois,Y. Ederle, C. Mathis, Synth. Met., 1999, 103, 2362. 31 B. Francois, O, Pitois, J. Francois, Adv. Mater., 1995, 7, 1041. 32 S. Jenekhe, X. Chen, Science, 1999, 283, 372. 33 B. de Boer, U. Stalmach, H. Nijland, G. Hadziioannou, Adv. Mater., 2000, 12, 1581. 34 T. Hayakawa, S. Horiuchi, Angew. Chem. Int. Ed. Engl., 2003, 42, 2285. 34 M. Stenzel, Aust. J. Chem., 2002, 55, 239. 35 C. Barner-Kowollik, H. Dalton, T. Davis, M. Stenzel, Angew. Chem. Int. Ed. Engl., 2003, 42, 3664. 37 M. Jesberger, J. Polym. Sci. A, 2003, 41, 3847. 38 H. Lord, J. Mater. Chem., 2003, 13, 2819. 39 O. Karthaus, X. Cieren, N. Maruyama, M. Shimomura, Mater. Sci. Eng. C, 1999, 10, 103. 40 L. Govor, M. Goldbach, I. Bashmakov, I. Butylina, J. Parisi, Phys. Rev., 2000, B62, 2201. 41 L. Govor, I. Bashmakov, K. Boehme, J. Parisi, J. Appl. Phys., 2002, 91, 739. 42 L. Govor, J. Parisi, Z. Natur. A, 2002, 57, 757. 43 H. Yabu, M. Tanaka, K. Ijiro, M. Shimomura, Langmuir, 2003, 19, 6297.

44 L. Govor, I. Bashmakov, F. Kaputski, M. Pientka, J. Parisi, Macromol. Chem. Phys., 2000, 201, 2721. 45 W. Kasai, T. Kondo, Macromol. Biosci., 2004, 4, 17. 46 U. Stalmach, B. de Boer, C. Videlot, P. van Hutten, G. Hadziioannou, J. Am. Chem. Soc., 2000, 122, 5464. 47 L. Govor, I. Bashmakov, R. Kiebooms, V. Dyakonov, J. Parisi, Adv. Mater., 2001, 13, 588. 48 C. Yu, J. Phys. Chem., 2004, B108, 4586. 49 O. Karthaus, T. Koito, N. Maruyama, M. Shimomura, Mol. Cryst. Liq. Cryst., 1999, 327, 253. 50 T. Yonezawa, S. Onoue, N. Kimizuka, Adv. Mater., 2001, 13, 140. 51 I. Bashmakov, L. Govor, L. Solovieva, J. Parisi, Macromol. Chem. Phys., 2002, 203, 544. 52 P. Shah, Adv. Mater., 2003, 15, 971. 53 H. Yabu, M. Takebayashi, M. Tanaka, M. Shimomura, Langmuir, submitted. 54 T. Nishikawa, M. Nonomura, K. Arai, J. Hayashi, T. Sawadaishi,Y. Nishiura, M. Hara, M. Shimomura, Langmuir, 2003, 19, 6193. 55 T. Ohzono, N. Fukuda, T. Nishikawa, M. Shimomura, Int. J. Nanosci., 2002, 1, 569. 56 H. Yabu1, M. Shimomura1, Langmuir, in press. 57 T. Sawadaishi, M. Shimomura, Mol. Cryst. Liq. Cryst., 2003, 406, 159. 58 H. Yabu, M. Shimomura, Int. J. Nanosci., 2002, 1, 673. 59 S. Matsushita, N. Kurono, T. Sawadaushi, M. Shimomura, Synth. Met., 2004, 147, 237–240. 60 N. Fukuda, M. Shimomura, Int. J. Nanosci., 2002, 1, 551. 61 M. Shimomura, T. Koito, N. Maruyama, K. Arai, J. Nishida, L. Grasjo, O. Karthaus, Mol. Cryst. Liq. Cryst., 1998, 322, 305. 62 N. Kurono, R. Shimada, T. Ishihara, M. Shimomura, Mol. Cryst. Liq. Cryst., 2002, 377, 285. 63 R. Ookura, J. Nishida, T. Nishikawa, M. Shimomura, Mol. Cryst. Liq. Cryst., 1999, 337, 461.

References 64 T. Nishikawa, J. Nishida, R. Ookura, S. Nishimura, S. Wada, T. Karino, M. Shimomura, Mater. Sci. Eng., 1999, C8–9, 485. 65 T. Nishikawa, J. Nishida, R. Ookura, S. Nishimura, S. Wada, T. Karino, M. Shimomura, Mater. Sci. Eng., 1999, C10, 141. 66 T. Nishikawa, J. Nishida, K. Nishikawa, R. Ohkura, H. Ookubo, H. Kamachi, M. Matsushita, S. Todo, M. Shimomura, Stud. Surf. Sci. Catal., 2001, 132, 509. 67 T. Nishikawa, R. Ookura, J. Nishida, T. Sawadaishi, M. Shimomura, RIKEN Review, 2001, 37, 43. 68 J. Nishida, K. Nishikawa, S. Nishimura, S. Wada,T. Karino,T. Nishikawa,

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7 Self-Assemblies of Anisotropic Nanoparticles: Mineral Liquid Crystals Patrick Davidson and Jean-Christophe P. Gabriel

7.1 Introduction

The aim of this chapter is not to give the reader a complete and detailed review of the field of mineral liquid crystals (MLCs) because such reviews have been recently published [1]. Instead, we describe the main physical concepts and investigation techniques used in this field and we illustrate them with selected examples. Therefore, this book chapter is meant for the young chemists and physical chemists who want to engage in these studies. The quite ambiguous expression “liquid crystals” actually applies to intermediate states of matter observed between the usual liquid and crystalline solid ones. These intermediate phases, also called mesophases, appear for example upon variation of the temperature or the concentration of a system. The liquid-crystalline phases are anisotropic like crystals, which means that their properties depend on the direction in which they are considered. However, they are also fluids, like ordinary liquids, because they do not have any crystalline three-dimensional lattice at the molecular scale. A liquid-crystalline phase will therefore be defined as a state of matter that is both fluid and anisotropic [2]. In practice, a simple observation in polarized light is enough to check the phase fluidity and its birefringence (therefore its anisotropy). There are two types of liquid crystals: .

Thermotropic liquid crystals are usually pure organic compounds that show liquid-crystalline phases depending on temperature. Melting of their crystalline phase does not directly lead to an ordinary liquid but generates one or several mesophases. Such compounds are used for electro-optic applications like displays.

.

Lyotropic liquid crystals are compounds that show liquid-crystalline phases when they are dissolved or dispersed in a solvent. This is the case, for example, for surfactant molecules used by the detergent and cosmetic industries. In the following, we will only consider this type of liquid crystal.

Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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One of the most important features of liquid-crystalline entities, also called mesogens, is their shape. The mesophase anisotropy must indeed reflect that of its building blocks, at the molecular level. The simplest case is that of rigid rods dispersed in a solvent. For example, these rods can be rigid polymers or anisotropic crystallites but they can also arise from the aggregation of surfactant molecules into very elongated micelles. Other mesophases are formed of nanometric disks, ribbons or sheets. Therefore, in a very general way, a lyotropic liquid-crystalline phase is a dispersion in a solvent of anisotropic entities, regardless of their particular composition. Let us now dwell a moment on the chemical nature of the mesogens. We have already mentioned the case of surfactant molecules that form aggregates (elongated micelles, bilayers …) in a solvent like water. These molecular architectures find an extension in the family of block copolymers that find wide applications in industry. Besides, rigid or semiflexible polymers like DNA also display liquid-crystalline phases. In addition, biology provides a wealth of mesogenic compounds (cellulose, chitin, collagen, actin, phospholipids …). Altogether, about a hundred thousand liquid crystals, thermotropic and lyotropic, have been fed into databanks and one of their common features is that they are of organic or organometallic nature. In contrast, there are today only a dozen mineral liquid crystals even though the first of them, namely the aqueous suspension of vanadium pentoxide (V2O5), was discovered as early as 1925 by Zocher [3], a German physicist whom we consider as the founder of this field. The requirements for liquid crystallinity that we described above being very general, one may wonder about the possible reasons for this situation and whether it is possible to find other examples of mineral mesophases. Of course, the intuition of the chemist plays a crucial role here, but one of the aims of this chapter is to present and illustrate the chemical and physical principles that guide this approach. Moreover, we shall see that mineral liquid crystals have original specific properties and that some of them have already found applications.

7.2 Basic Principles and Investigation Techniques 7.2.1 Basic Principles

In order to obtain a mineral liquid-crystalline phase, it is necessary to stabilize a suspension of anisotropic nanoparticles of large enough concentration. The phases that we are interested in are essentially colloidal suspensions. The microscopic interactions that govern their stability depend on the nature of the solvent. In a polar solvent like water, the electrostatic interactions are very important because the repulsions between objects of like charges prevent flocculation. The surface charge density and the point of zero charge are very important properties in this respect. The pH, the ionic strength, and the solvent dielectric constant also

7.2 Basic Principles and Investigation Techniques

determine the range and intensity of the electrostatic repulsions and must be carefully examined. The suspension concentration also plays an important role because it determines the average distance between the particles in a homogeneous phase. Moreover, the van der Waals interactions, of electromagnetic origin, are most often attractive and lead to flocculation. The balance between electrostatic repulsions and van der Waals attractions is described by the classical theory, called DLVO (Deryaguin–Landau–Verwey–Overbeek), of colloidal stability [4, 5]. This theory provides us with a very efficient frame in order to understand the stability of aqueous systems, whatever the particle shape. However, the quantitative detailed description of these interactions between anisotropic particles is difficult and is still the subject of numerous studies. In a nonpolar solvent, it is necessary to devise other ways of countering the van der Waals attractions. The most common one consists in grafting polymers or surfactants in order to prevent the particles from approaching each other and sticking together. The grafting density and the polymer or surfactant size are important parameters and their influence may be estimated in a semiquantitative way. Note that hydrosoluble polymers may also be used to improve the colloidal stability of suspensions in water. Once colloidal stability is obtained, one may worry about liquid-crystalline order. The relevant theories are mostly based on the idea of “hard-core” interactions. The idea behind this is roughly that two particles may not be in the same place at the same time. One then considers that two particles undergo an infinite repulsion as soon as they touch each other, but have no interaction at all if they do not touch. For each particle, an “excluded volume” is defined into which the centers of mass of the other particles cannot enter. Interactions between particles of like charges or between grafted particles can approximately be treated in the same convenient way. Finally, the intensity of each interaction (including gravity for “large” particles) must be compared to thermal energy, measured in kT units, where k is Boltzmann’s constant. Let us now consider the different kinds of liquid-crystalline phases. They can be defined and classified according to their symmetries that characterize their degree of order. Two types of order should be distinguished: the orientational and positional orders. All mesophases have long-range orientational order. In other words, in a mesophase single domain, if the orientation of one particle is known, the orientation of all other particles will also be known (if we neglect possible fluctuations such as thermal fluctuations). When such a mesophase does not show any positional long-range order, the particles may freely diffuse in all directions, as in a usual liquid, and the phase is called “nematic” (Fig. 7.1). If long-range positional order appears in one direction, then there are layers and the phase is called “lamellar” or “smectic” (Fig. 7.1). If the positional order appears in two dimensions, the structure is made of columns and the phase is called “columnar” (Fig. 7.1). The column lattice can be hexagonal, square or oblique. Note that these different phases may be comprised of flat (i. e., disk-shaped) as well as elongated (i. e., rodlike) nanoparticles and that they are also observed in thermotropic systems. Liquid-crystalline phases can be identified by polarized-light optical micro-

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Fig. 7.1 Organization of the main liquid-crystalline phases illustrated with assemblies of rodlike and disklike particles.

scopy and by their X-ray scattering patterns, as will be described later in this chapter. Transitions between these different mesophases can sometimes be detected by varying the suspension concentration, and these transitions are represented in a phase diagram that summarizes our thermodynamic understanding of the system. From a physics point of view, one of the main interests of liquid crystals is indeed to provide model systems for the study of all kinds of phase transitions. Gelation is one of the problems often met when trying to obtain mineral liquid crystals. Several systems like aqueous suspensions of clay particles undergo a sol– gel transition when a given concentration is reached. Beyond this gelation threshold, the suspension becomes not only viscous but also elastic. The material does not flow any more; it keeps its shape over long times that can extend to years. This may be qualitatively assessed either by turning a test tube of the suspension upside down and observing that it does not flow even after a long time (hours, in practice) or by noticing air bubbles that remain trapped within the gel. These mechanical properties can be measured and studied quantitatively using rheology. The gels that we are discussing here are physical ones that do not involve covalent bonds and that do not reach thermodynamic equilibrium. This enormously complicates our understanding of the system because distinguishing the intrinsic or artifactual characters of the phase organization becomes very difficult. The influence of the solvent can sometimes go beyond its simple physical properties (polarizability, refraction index …) if it interacts strongly with the dispersed

7.2 Basic Principles and Investigation Techniques

particles. For example, as we shall see later on, some semiflexible mineral chains may have a coil conformation in DMF or a rodlike conformation in NMF. This is probably due to hydrogen bonds between the chain and the solvent. The rods selfassemble into a hexagonal columnar mesophase in NMF but the coils (and the phase) remain isotropic in DMF. 7.2.2 Investigation Techniques

Establishing a phase diagram is the first step in the study of a new mineral system that may show a liquid-crystalline phase. This is done by preparing samples, in test tubes, of variable compositions depending on concentration, ionic strength (by adding salt) or pH. Ideally, all samples will be prepared the same day so as to avoid possible problems of different sample histories. The appearance of the samples will be carefully recorded over time: single phase or biphasic, homogeneous or flocculated, transparent or opaque, sol or gel, and most importantly, isotropic or birefringent. This latter point may be assessed by examining the test tubes, if the samples are transparent enough, between crossed polarizers with the naked eye by use of a “magic box” (a strong enough white light bulb, a frosted screen for homogeneous illumination, two crossed polarizers before and after the sample). If the sample appears bright at rest, then it is birefringent and therefore anisotropic. It can be compared with a water sample that must appear dark between crossed polarizers. Moreover, if the sample is also fluid, then it is most likely liquid-crystalline. This identification must further be confirmed by the inspection of the optical texture in polarized-light microscopy. For this purpose, a little sample can be inserted between glass slide and cover slip or, even better, be sucked into a flat glass optical capillary (of thickness between 50 and 200 µm, depending on birefringence and absorption) that is flame sealed in order to be kept. Like ordinary crystals (except those of cubic symmetry) [6], liquid crystals interact with polarized light; they are birefringent. Therefore, they are bright when examined between crossed polarizers and their image in the polarizing microscope is called their “texture”. This texture arises from the organization of small domains separated by defects in which the ideal order of the mesophase prevails. The meaning of “texture” here is the same as in crystalline texture. Let us now examine the case where the sample is a single domain of the mesophase; such a single domain can often be obtained by applying a magnetic field. The texture will then be uniform under the microscope. If the phase has cylindrical symmetry (nematic phase, for instance), the sample will look uniformly bright, with maximum brightness when its symmetry axis lies at 458 from the directions of the polarizer and analyzer. It will look uniformly dark if its symmetry axis is either parallel to one of these two directions or parallel to the light beam. There again, the general rules of crystalline optics are obeyed [6]. In most cases, however, the sample is not a single domain but the texture displays many topological defects. These defects can be simple domain walls or “disclination” lines, which are

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the equivalent for liquid crystals of the dislocation lines of crystals. The careful examination of these defects allows experts to identify the mesophase types, but this requires a lot of experience and also checking by other techniques. The most dependable technique to determine the nature of a mesophase is X-ray scattering. This technique is very commonly employed for the study of usual liquid crystals and can also be adapted to the study of mineral liquid crystals. However, these systems have a few specific features. The particle size ranging from 1 to 100 nm, useful information must be retrieved at small scattering angles. Such experiments require small-angle X-ray scattering (SAXS) setups that can be found in some laboratories but more often at synchrotron-radiation facilities. An advantage of mineral particles is that they have a strong electronic-density contrast with the solvent. Then, the SAXS signals are intense and exposure times are short, which makes it possible to perform dynamic experiments to examine the behavior of a mesophase submitted to a mechanical stress or an external field. In addition to mesophase identification, X-ray scattering provides a lot more information: direction and degree of orientation (the so-called nematic order parameter) of the particles in the nematic phase, lamellar period and electron density profile in the smectic phases, nature and dimensions of the lattice in the columnar phases, etc. This approach is more efficient if applied to single-domain samples that can be produced by applying an external field or a shear stress thanks to special devices. Moreover, SAXS can be applied to dilute isotropic suspensions in order to determine the particles’ form factor and in turn their dimensions. Scanning or transmission electron microscopies and near-field microscopies can also be used to characterize the dimensions of nanoparticles and their polydispersity. Unfortunately, these techniques usually require elimination of the solvent, thus precluding the study of organization in the mesophases. There are nevertheless some rather sophisticated techniques (cryofracture, cryomicroscopy) that could prove efficient in this respect but that remain little used because of their complexity. The physical properties of mineral liquid crystals can be studied with many different experimental setups. For example, the mechanical properties (viscosity, elasticity) can be examined with a rheometer that can even be placed in an X-ray beam [7]. The magnetization and the magnetic susceptibility can be measured with a SQUID magnetometer, and it may sometimes be useful to freeze the solvent in order to prevent the reorientation of the liquid crystal in the field of the SQUID. Besides, there are specific devices that can be used to characterize the electric properties of these materials, for applications in display technology.

7.3 Nematic Phases

As we have already mentioned, the nematic phase has true long-range orientational order but only has short-range, liquidlike, positional order. Therefore, the anisotropic nanoparticles are aligned on average in the same direction but they

7.3 Nematic Phases

can easily diffuse in all directions. Experimentally, the phase transition between the nematic and the usual isotropic liquid is first-order. When the concentration is varied, a biphasic domain shows up where the two phases coexist. The observation of this biphasic domain proves that the samples have reached thermodynamic equilibrium. The average direction of the particles is called the “director” (usually labeled n) and the “nematic order parameter” is defined as S = <1/2 (3 cos2 y – 1)> where y is the angle between a particle and the director and < > represents a statistical average. S varies between 0 for an isotropic liquid and 1 for a nematic phase ideally aligned and devoid of any fluctuation. Mathematically speaking, S represents the second-order moment of the orientational distribution function that defines the probability that a given rod points in a direction at an angle y from the director (by reason of symmetry, all odd-order moments are null). 7.3.1 The Onsager Model

As early as 1949, Onsager published a statistical physics model aimed at understanding the nematic order of the suspensions of the tobacco mosaic virus (TMV) that constitute model suspensions of rodlike particles [8]. This model essentially describes a trade-off between two types of entropies: the orientational entropy of the rods and the packing entropy related to the excluded volume interactions. Qualitatively speaking, nematic ordering takes place because the loss in orientational entropy is more than compensated by the gain in packing entropy. We need not analyze this model in more detail here (see [9]) but, because of its importance, we shall now describe its assumptions and its main results. Onsager considered an assembly of rigid, very elongated, particles, of length L and diameter D, with L >> D. The ratio L/D is called the particle aspect ratio. The particles only experience excluded-volume interactions. Instead of concentration, physicists rather use the volume fraction f that is the total volume of the particles divided by that of the suspension. The predictions of the model are that: (a) the isotropic/nematic phase transition is first-order with phase coexistence; (b) the volume fractions fn and fi at the transition of the nematic and isotropic phases are respectively given by fn = 4.2 D/L and fi = 3.3 D/L; (c) the nematic order parameter at the transition is large: S = 0.8; (d) temperature has no effect on the transition, which directly results from the athermal character of the excluded-volume interaction. It is very important to notice that the volume fractions that must be reached in order to obtain the nematic ordering are inversely proportional to the particle aspect ratio. The Onsager model has inspired many theoretical developments and this class of models eventually accounts rather well for the experimental observations. In his original article, Onsager extended his model to the case where the particles undergo electrostatic repulsions rather than excluded-volume interactions. In a first approximation, the above formulas can still be used, provided that an effective diameter is used that more or less takes into account the counterion clouds. Khokhlov and Semenov have extended Onsager’s model to the case of semiflexible rods [10]; qualitatively speaking, their results remain similar to those

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described here. Finally, Onsager himself also considered in his article the case of disklike particles. Therefore, we have a theoretical frame to help us understand the nematic ordering of a suspension of anisotropic particles. 7.3.2 Rigid Rodlike Nanoparticles

The suspensions of boehmite (AlOOH) crystallites, also discovered by Zocher in 1960, provide a fairly good system to verify the predictions of the Onsager model. A very complete study of these phenomena was performed by the group of Lekkerkerker at the famous Van’t Hoff Laboratorium in Utrecht [11]. Nematic suspensions were obtained not only in water but also in nonpolar solvents by grafting the particles with a polymer layer. The isotropic/nematic transition is easily observed in this system. The nematic phase, which is birefringent and denser, sediments to the bottom of the cell whereas the dark isotropic phase floats to the top. In the biphasic domain, the proportion of nematic phase regularly increases with the overall volume fraction. The textures, observed by polarized-light microscopy, of freshly produced biphasic suspensions in capillary tubes (Fig. 7.2) show the for-

Fig. 7.2 Evolution over time (a–d) of the nematic phase from the isotropic one by the coalescence of birefringent droplets. (From Buining et al., J. Phys. Chem. (1993) 97 : 11510).

7.3 Nematic Phases

mation of small birefringent droplets of the nematic phase floating within the dark isotropic liquid. These droplets, also called tactoids in the literature, slowly grow and merge to form the nematic phase. Boehmite suspensions were also used to show that the particle polydispersity widens the biphasic gap. Moreover the polydispersity leads to a fractionation effect because the first nematic droplets are richer in longer particles. There are other suspensions of mineral rodlike particles that show very similar phenomena, for instance the suspensions of goethite that display very surprising magnetic properties. 7.3.3 Semiflexible Wires, Ribbons, and Tubules 7.3.3.1 Li2Mo6Se6 Wires The discovery of the liquid-crystalline phase of the one-dimensional compound Li2Mo6Se6 illustrates the “top-down” approach that can be used in this field. This compound is related to the famous family of the Chevrel–Sergent phases [12]. Li2Mo6Se6 crystals are comprised of infinite [Mo6Se6]2– chains organized on a two-dimensional hexagonal lattice. This crystal can be exfoliated into an assembly of molecular nanowires by using very polar solvents like NMF [13]. The small and highly polarizable Li+ ions ensure complete exfoliation. For comparison, the indium phase In2Mo6Se6 could not be exfoliated. Beyond a critical concentration of 10–2 mol l–1, the suspensions show a nematic phase [14]. These suspensions will now be used to illustrate the use of polarized-light microscopy (Fig. 7.3). The texture displays dark threads connected together by nodes. The nematic director is mostly parallel to the preparation plane (planar texture). Then, the dark threads simply correspond to the places where the director is parallel to the directions of the polarizer or the analyzer. The topological defects are actually disclination lines parallel to the light beam; they only appear as points (numbered on Fig. 7.3) [2]. These line defects are classified by their strength (taking most of the time the values –1, –1/2, 1/2, 1) related to the distortion that they

Fig. 7.3 Schlieren texture observed by polarized-light microscopy of a nematic suspension of Li2Mo6Se6 in NMF. Topological singularities (disclination lines of strength +1/2) labeled from 1 to 7 are clearly seen.

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create in the director field. It is possible to determine each defect strength by rotating the directions of the crossed polarizer and analyzer. Naturally, in this respect, mineral liquid crystals simply obey the general rules that apply to liquid crystals. Unfortunately, [Mo6Se6]2– chains are rather sensitive to oxygen, which makes them rather difficult to handle compared to other systems. From the liquid-crystal point of view, chain degradation appears in the following way. The nice homogeneous texture of Fig. 7.3 becomes slightly speckled, then very small dark domains appear and slowly grow within the birefringent liquid. These dark domains are little drops of the isotropic phase (sometimes called “atactoids” in the literature) that progressively invade the whole preparation. The nematic phase is completely destabilized with respect to the isotropic one. This observation finds a simple explanation in the frame of the Onsager model described above. The nanowires are randomly cut by oxygen so that their average length L regularly decreases. The volume fraction being fixed, at some point, it becomes smaller than the threshold fn that increases as L decreases. The system then enters the biphasic domain and isotropic droplets nucleate. As L further decreases, at some other point, the volume fraction becomes smaller than the other threshold fi and the system leaves the biphasic domain to enter the stability region of the pure isotropic phase; all birefringence is then lost. Finally, much later, the new products of the degradation reaction are formed and can easily be observed with the naked eye. This process is very unfortunate because the [Mo6Se6]2– chain is truly a beautiful molecular object, the structure of which strongly looks like an electrical wire with its “metallic” core and its “insulating” envelope. Besides, this nano-object has often been used in the field of nanoscience [15].

7.3.3.2 V2O5 Ribbons V2O5 suspensions make a good example of the “bottom-up” approach to mineral nano-objects. The synthesis of these ribbons results from the inorganic polycondensation of molecular precursors in a well-defined pH and concentration domain. This process has been studied in detail from the physical chemistry point of view [16]. The synthesis is achieved as follows: a 1 M sodium metavanadate solution is passed through a column filled with an ion-exchange resin. The Na+ ions are replaced by protons and the pH drops to about 2, in the stability domain of the ribbons (see Fig. 7.4). The solution is collected and fractionated in several vials and the intermediate fractions are the only ones that show the right concentration and pH conditions for ribbon formation. The appearance of the ribbons takes several hours and the gel evolution extends over a few days (the mechanical properties of the gels can even take several months to stabilize). Synchrotron small-angle X-ray scattering is a very powerful technique to follow such synthetic processes. Before the ribbons start interacting, the scattering is governed by the particle form factor that represents all interferences between photons scattered by the electrons of any given particle. The theoretical form factors of various objects of simple geometries (spheres, cylinders, disks, ribbons …) are well known [17]. They can be expressed as a function of q, the scattering vector

7.3 Nematic Phases

Fig. 7.4 Stability diagram of VV molecular species versus pH and vanadium molarity (courtesy J. Livage).

modulus given by: q = (4 p/l) sin y with 2 y the scattering angle and l the wavelength. The experimental scattered-intensity curve can be adjusted with these formulas and the nanoparticle dimensions can thus be derived at any time during the synthesis. Whatever the synthesis conditions and evolution time, 1-nm-thick objects are always obtained and this thickness is actually determined by the molecular structure of the ribbons. The width of the objects increases regularly during synthesis until it reaches limiting values of the order of 25 nm after about ten hours. To date, we do not understand the factors that control this width which is fairly constant, even when very different synthesis methods are used. The ribbon (overall) length L can reach several microns, as demonstrated by the TEM images of xerogels (dried gels), but the persistence length Lp (~ 300 nm) can be directly measured by light-scattering experiments directly in solution. The persistence length Lp is a very important property of flexible nano-objects; it is roughly the length over which the nanoparticle may be considered as rigid. If Lp is much smaller than L, the object will adopt a random-coil conformation whereas if Lp is much larger than L, the object will be essentially straight. When Lp is about the same as L, the description of the object becomes much more difficult, from a theoretical point of view. The most likely scenario that can be drawn from this study of the synthesis of nematic gels comprised of V2O5 ribbons is as follows. When the solution pH becomes acidic, VV ions adopt an octaedric coordination and a molecular precursor of formula VO(OH)3(H2O)2 appears in a transient way. This precursor quickly polymerizes in less than an hour, by olation reactions, to form a flexible polymer.

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These wires then assemble laterally through oxolation reactions, within a few hours, a bit like zippers. At this stage,V2O5 ribbons are formed and probably have their final dimensions; therefore, the suspensions acquire their viscoelastic properties that are typical of gels. Then, after a day, the SAXS patterns start displaying interferences between ribbons that modulate the form factor and show that the gels have liquidlike short-range positional order. Finally, after a few days, the material becomes birefringent, which demonstrates the nematic ordering. This example shows that all the degrees of freedom must not necessarily be frozen at the sol–gel transition because the nematic order does appear after gelation of the suspension. V2O5 suspensions provide a very good model system to investigate the numerous properties of mineral liquid crystals because they are cheap aqueous materials, chemically robust, and easy to synthesize in large amounts. These positive features easily outweigh their drawbacks, which are their ribbon rather than wire morphology and the existence of a gelation transition. For example, these suspensions will now be used to illustrate what happens when a liquid crystal is submitted to a magnetic field. Any liquid-crystalline phase is essentially anisotropic; its magnetic susceptibility w (i. e., the ratio of the induced magnetization to the magnetic-field intensity) is then also anisotropic and will be represented by a matrix instead of a scalar. By referring to a single domain of the mesophase, this matrix can be diagonalized and the diagonal elements (eigenvalues) need only be considered. In the case of a uniaxial mesophase, like the nematic one, the susceptibility parallel to the director, noted w//, is therefore different from the susceptibility in the perpendicular plane, noted wk. The difference between the two is noted Dw = w// – wk. Dw is very important because it governs the orientation properties of the mesophase when submitted to the field. When Dw is positive, which is the most common case, the mesophase minimizes its free energy by aligning its director parallel to the magnetic field. In contrast, when Dw is negative, the director aligns in the plane perpendicular to the magnetic field. The orientation is then degenerated because all the directions in this plane are allowed a priori. We have observed that V2O5 suspensions have a positive anisotropy of magnetic susceptibility [18]. Beyond a threshold field of 0.3 T, the ribbons all align on average along the magnetic-field direction. The defects observed by polarized-light microscopy vanish and the suspension texture becomes uniform (Fig. 7.5). Moreover, when the magnetic field is parallel to the directions of the polarizer or the analyzer, the sample is uniformly dark. Its brightness is maximum when the field is applied at 458 from these directions. Such observations demonstrate that the sample is actually a single domain. This process is very important because it is similar for liquid crystals to the process of growing single crystals. In this way, a large single domain can be obtained from a liquid-crystal “powder” (i. e., a random distribution of small liquid-crystalline domains). Through a purely external and noninvasive action,V2O5 ribbons can be rotated at will with the help of a rather modest field (easily produced by the permanent magnets found on closet doors). The origin of the magnetization of these phases still remains rather mysterious to date. In addition to diamagnetism and the demagnetizing fields re-

7.3 Nematic Phases

Fig. 7.5 Magnetic-field alignment of a nematic suspension of V2O5 ribbons. (a) Threaded nematic texture in zero field; (b) field-aligned sample set at 458 from the polarizer and analyzer directions; (c) the same aligned sample set parallel to the polarizer and therefore in extinction position.

lated to the ribbon intrinsic anisotropy, the influence of a possible paramagnetism due to small VIV amounts has also been suggested. The magnetic-field alignment could be further exploited: let us consider a sample aligned by a horizontal magnetic field applied in the plane of Fig. 7.6. When the magnetic field direction is suddenly reoriented along the vertical direction, vertical striations are observed. These striations are the walls of domains in which the director rotates from the horizontal direction to the vertical one, alternately clockwise and counterclockwise. This is a transient hydrodynamic instability, well known in the field of liquid crystals, which eventually disappears when the director is everywhere aligned along the vertical field. A similar instability takes place when the

Fig. 7.6 A nematic sample of V2O5 suspension, first aligned by a magnetic field applied horizontally in the plane of the figure, displays transient hydrodynamic instabilities when the field is suddenly reoriented either vertically in the plane of (a) or perpendicular to the plane of (b).

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magnetic field is suddenly reoriented from the initial horizontal direction to the direction perpendicular to Fig. 7.6. Such instabilities could be used as very cheap and convenient techniques to modulate the orientation of nano-objects with a period ranging from 5 to 50 µm, depending on field intensity and sample thickness. Since we know how to obtain a single domain of nematic phase, let us now try to understand its SAXS pattern (Fig. 7.7 a). This pattern displays two diffuse spots located symmetrically with respect to the origin of reciprocal space. Of course, no Bragg reflections can be observed because the ribbons have no positional longrange order, and diffuse scattering spots can only be observed because the nematic phase only has liquidlike positional order. The SAXS pattern is clearly anisotropic and the mesophase is indeed both fluid and anisotropic. For SAXS, in reciprocal space, the Ewald sphere can be approximated as a plane perpendicular to the incident X-ray beam. Because of the cylindrical symmetry of the nematic phase, the diffuse spots represent the intersection with the Ewald sphere of a diffuse revolution torus located in the reciprocal plane going through the origin and perpendicular to the director. These diffuse spots arise from interferences between rods (we assimilate here the ribbons to rods in order to keep

Fig. 7.7 (a) SAXS pattern of a nematic suspension of V2O5 ribbons aligned by a horizontal magnetic field. (b) Radial profile of the scattered intensity showing a maximum due to the liquidlike positional order. (c) Azimuthal profile of the scattered intensity showing the mesophase orientation, which allows one to deduce the nematic order parameter S.

7.3 Nematic Phases

this analysis as general as possible) in directions perpendicular to the director. A scan of the scattered intensity in the radial direction going through the maximum of the diffuse spots is displayed in Fig. 7.7b. The maximum, observed at the qmax position, is related to the average distance d between objects in the plane perpendicular to the director: qmax = 2 p/d. The spot width D (2 y ) gives us information about the range x of the liquidlike order by using Scherrer’s formula [19] l . Of course, these quantities depend on concentration; we shall D (2 y) = x cos ymax come back to this point later on. A scan of the intensity I (c) scattered along a section of circle centered on the origin and going through the maximum of the diffuse spots can be used to extract the orientation degree of the rods in the single domain, that is, the nematic order parameter S (Fig. 7.7 c). Thanks to a set of assumptions that will not be detailed here but are discussed in ref. [20], this intensity profile can be fitted by the following formula: I …c† ˆ C

p i erf … m cos c† m cos2 c p e 4 p erf …i m† cos c

where m is a fit parameter directly related to S, C is a fit parameter that depends on the conditions of the experiment (exposure time, incident beam intensity …), and erf is the error function. This seemingly barbarous formula is actually not very harmful. It is easy to program with mathematical software on a personal computer and usually describes the data fairly well. For example, the value S = 0.75+0.05 was obtained from the pattern in Fig. 7.7 a and because this pattern is that of the nematic phase at coexistence, this value agrees well with that predicted (0.8) by the Onsager model. Let us now examine the dependence with concentration, called “swelling law”, of the average distance d between ribbons. For infinite wires, this swelling is twodimensional and d varies like f–1/2 with volume fraction f. This dependence is usually rather well obeyed even though the objects are not infinite. In the case of the suspensions of V2O5 ribbons, this dependence is restricted to the dilute regime in which the ribbons are free to rotate around their long axis. However, when the distance d becomes comparable to their width w, the planes of the ribbons develop orientational correlations and become parallel. The positional order remains nevertheless liquidlike. The structure is locally lamellar and the swelling law shows a crossover to that of an assembly of sheets as d varies like f–1. This reminds us that V2O5 is a very good intercalation compound at large concentrations. The nematic order loses its uniaxial symmetry. This situation corresponds to the biaxial nematic phase or, more properly here, a biaxial nematic gel state, which can be proved by SAXS experiments with samples sheared in a Couette cell (i. e., between two concentric cylinders) [21]. Note that examples of a biaxial nematic phase are extremely uncommon, even in the wide field of organic liquid crystals. V2O5 suspensions have also been used to examine the influence of ionic strength by adding salt (NaCl). In systems of rodlike particles, such as the TMV suspensions, the nematic phase is destabilized with respect to the isotropic one as

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the ionic strength increases and the electrostatic interactions are screened. Indeed, the effective particle dimensions are then reduced to the bare dimensions. On the one hand, this effect increases the particle aspect ratio (L/D > (L + kk–1)/ (D + kk–1) where k is a coefficient that can be calculated) but, on the other hand, the effective volume decreases (LD2 < (L + kk–1)(D + kk–1)2). The latter effect usually dominates and the nematic phase may disappear upon salt addition. V2O5 suspensions are even more subtle, because experimental observations show that the nematic phase is actually stabilized compared to the isotropic one [22]. This surprising fact can be explained by considering van der Waals attractions that are often negligible in front of electrostatic interactions for organic liquid crystals. These attractions depend on the refraction-index contrast between the particles and the solvent and they can be rather strong for electron-rich mineral particles. Because these attractive interactions between anisotropic objects are quite directional, they can induce parallel alignment of the ribbons and favor the nematic phase. When the electrostatic forces are screened, it is quite possible that the van der Waals attractions play their part in stabilizing the nematic phase. Naturally, the colloidal suspension should ultimately flocculate, which is observed at even higher ionic strength. However, at intermediate ionic strength, the system gels, probably for the same reasons, which prevents the dispersion from collapsing into a floc (Fig. 7.8). We could quantitatively model these interactions and show that this explanation is likely. In order to conclude on this very rich system, let us mention deuterium NMR experiments performed with suspensions enriched in D2O [23]. The NMR spectra display a quadrupolar splitting, which is the sign of a fast exchange of the solvent between surface sites (“bound water”) and volume sites (“free water”). In the isotropic phase, a single sharp resonance line is observed. The fraction of bound

Fig. 7.8 Phase diagram of suspensions of V2O5 ribbons versus V2O5 and salt concentrations. The points located above the top oblique line correspond to flocculated systems; the points located above the horizontal gelation line correspond to gels.

7.3 Nematic Phases

water could be estimated by making assumptions about the geometry of water molecules adsorbed on the ribbons and by using the value of S determined by SAXS and the volume fraction. Besides, the value of the quadrupolar splitting was used to monitor the mesophase reorientation upon a sudden variation of the magnetic-field direction, and thus to derive information about the suspension’s viscoelasticity. This kind of NMR experiment is in fact very common in the field of liquid crystals.

7.3.3.3 Imogolite Nanotubules Imogolite is an aluminosilicate-type material that can be found in the ashes of some Japanese volcanoes but that can also be synthesized in the laboratory [24]. Electron microscopy experiments show that imogolite is comprised of nanotubules of 2.5-nm diameter and variable length (several microns). A group of Japanese scientists have recently investigated aqueous suspensions of imogolite and observed that they display a liquid-crystalline phase. With this system, they could verify the predictions of the Onsager model and examine the influence of polydispersity [25]. In addition, these researchers have exploited the fractionation effect mentioned above in order to decrease the polydispersity of the suspensions. The observation of textures by polarized-light microscopy and the images of the suspensions obtained by electron microscopy are somewhat contradictory as regards the mesophase structure. Although some nanotubule chirality was first suggested, an ordinary nematic organization now seems more likely. 7.3.4 Nanorods, Nanowires, and Nanotubes: A Wealth of Potential New MLCs

The advent of methods for preparing highly soluble and processable colloidal metallic, semiconductor, and magnetic nanocrystals with narrow size distributions [26] opened the way to the discovery of a wealth of new liquid-crystalline phases. As proposed in our previous reviews [1] and based on the results obtained with the first examples of such suspensions (a- and b-FeOOH), this field has a bright future as its potential for new discoveries is very high. When the phase is not available in large amounts, a first study of the self-assembly of anisotropic nanoparticles (for example, BaCrO4 nanorods and silver nanowires) as well as the observation of phase transitions can be performed in two dimensions, using the Langmuir–Blodgett technique [27]. Two-dimensional nematic and smectic phases have been produced with this technique that can be used in ultrasensitive, moleculespecific sensing applications using vibrational signatures. More recently, Alivisatos and coworkers studied the phase behavior of semiconductor nanorods such as CdSe. They showed that this behavior is very similar to that observed with boehmite suspensions and can be discussed in the framework of Onsager’s theory, although attractive interactions between the nanorods may also be important [28]. The very high aspect ratio and fairly rigid nature of carbon nanotubes, somewhat similar to those of Li2Mo6Se6 nanowires, had suggested long ago their self-assem-

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bly into a nematic phase. This intuitive idea was confirmed in a first theoretical study that reported, in 2001, a possible liquid-crystalline phase in suspensions of carbon nanotubes [29]. The self-assembly of carbon nanotubes in two dimensions has also been reported [30]. The major hurdle to be overcome in order to observe a phase transition was to reach a concentration of nanotubes high enough to allow for an Onsager transition to take place. This was first achieved by Windle and coworkers who used highly oxidized and charged multiwalled nanotubes. In their article, they reported the observation of Schlieren textures typical of a lyotropic nematic liquid crystal above a critical concentration of 4.8 % by volume [31]. Other reports of nematic ordering in suspensions of carbon nanotubes soon followed [32]. 7.3.5 Disklike Nanoparticles 7.3.5.1 Clays Langmuir observed the birefringence of clay suspensions as early as 1938 [33]. He had even observed a phase separation between an isotropic phase and a birefringent one, although he noted in the same article that the phase separation was not reproducible. Langmuir had not however fully explained the meaning of his observations because the understanding of liquid crystals was still shaky at this time. Aqueous clay suspensions that are produced through an exfoliation process have recently raised a renewed interest because they show a sol–gel transition, the origin of which is still hotly debated [34]. In contrast to V2O5 suspensions, clay suspensions undergo gelation at a concentration smaller than that where orientational ordering occurs. Upon increasing concentration from the dilute regime, these systems first form an isotropic liquid phase, then an isotropic gel phase, and finally a birefringent gel. This difference is crucial because a gel is not at thermodynamic equilibrium, but is instead kinetically trapped in some local minimum of the free energy. (This situation is also sometimes called a glass in the literature.). Then, the nonreproducible phase separation (at the macroscopic level) mentioned by Langmuir remains quite exceptional and the birefringence of these materials, although quite significant by its magnitude and its consequences, cannot be understood in terms of the Onsager model. Laponite gels, a synthetic clay of formula [(Na2Ca)x/2(LixMg3–x)(Si4O10)(OH)2 7 zH2O], have been studied in very much detail in order to understand their birefringence properties [35]. These gels are comprised of rather polydisperse and roughly circular nanodisks of diameter D = 30 nm and thickness L = 1 nm [36]. In addition, bentonite suspensions, a natural clay of formula [Nax(Al2–xMgx) (Si4O10)(OH)2 7 zH2O] have also been examined in this perspective. The gels are here comprised of semiflexible sheets of about 300-nm diameter and also 1-nm thick. The behaviors of these two rather different types of clays are strikingly similar. Figures 7.9 and 7.10 illustrate their birefringence properties and their textures observed by polarized-light microscopy One of the fundamental questions raised by these peculiar materials is the origin of their birefringence: is it due to a real nematic ordering or is it only a flow-

7.3 Nematic Phases

Fig. 7.9 Textures observed by polarized-light microscopy of aqueous clay gels. (a) Bentonite, 0.044 g cm–3 ; (b) bentonite (0.053 g cm–3), detail of a 1/2 singularity (arrow); (c) laponite (0.065 g cm–3), (d) laponite (0.034 g cm–3), detail of a 1/2 singularity (arrow).

Fig. 7.10 Photographs in polarized light of aqueous clay gel samples held in test tubes. (a) Bentonite, 0.043 g cm–3 ; (b) laponite (0.065 g cm–3); (c) flow birefringence of a bentonite suspension (0.019 g cm–3), (d) large aligned domain of laponite gel; (e) an initially isotropic (0.020 g cm–3) bentonite gel becomes birefringent when contacted with a brine (5 M) solution. (The arrow points at the gel–brine interface).

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induced phenomenon trapped by the gelation and of little magnitude or significance? Even though the Onsager model does not really apply to such systems, a number of experimental observations lead us to think that clay particles have a strong tendency to align parallel, in a cooperative way. For example, adding brine on top of an isotropic gel makes it birefringent in the absence of any flow. Note, by the way, that the orientational ordering is therefore improved by an increase of ionic strength. This result is quite unexpected because it contradicts the observations relative to the model TMV suspensions, discussed above. Nevertheless, this effect had been theoretically predicted for nematic suspensions of disks [37]. Moreover, isotropic gels can be left to concentrate very slowly, over weeks, in test tubes or in capillary tubes. Beyond a well-defined volume fraction that also corresponds to that of the phase diagram, the gel becomes not only birefringent but also a single domain in which all disks adopt, on average, the same direction, their normal being approximately parallel to the tube axis. In order to clear a confusion sometimes found in literature, let us stress here that the nematic ordering is no explanation at all for the gelation phenomenon. A simple proof of this is that there are clay gel samples that are completely isotropic and therefore devoid of any nematic correlations. In fact, very recent experiments with suspensions of size-fractionated clay particles have shown that gelation takes place at lower concentrations for less anisotropic particles, which contradicts most existing gelation models [38]. From the liquid-crystalline point of view, the sol–gel transition is merely an unexplained (but interesting) nuisance that prevents the systems from reaching the true phase coexistence that would have been described by the Onsager model. Interestingly, delamination of clays in silicone fluid has been reported and the suspensions obtained do not present a sol–gel transition [39]. It would be interesting to study whether a nematic phase can be observed in these suspensions. The influence of gravity on samples in test tubes was also examined and several strata could be detected differing by the type of order, the orientation of the particles, and the domain size [40]. The particle orientation was studied by wide-angle X-ray scattering, making use of the crystallographic intraparticle reflections. Let us now use the single domains described above in order to extract the nematic order parameter S [41]. The SAXS signals of these assemblies of aligned clay particles are mostly governed by their form factor; the interferences between particles can be neglected in the domain of scattering-vector modulus of our experiments. This situation is therefore the opposite of that which prevails for V2O5 suspensions for which we had implicitly assumed that interferences between particles were very strong and led to scattering peaks. In the present case, the SAXS patterns show an anisotropic diffuse halo whose intensity decreases regularly with q (Fig. 7.11). By considering the form factor of a cylinder of radius R and height L, given by the formula: F …q; g† ˆ K

sin …qL cos g† J1 …qR sin g† qL cos g qR sin g

7.3 Nematic Phases

Fig. 7.11 (a) SAXS pattern of an aligned sample of laponite gel; (b) simulation (iso-intensity curves) of the SAXS pattern with the model described in the text.

where K is a fit parameter, J1 is the first-order Bessel function, g the angle between a disk normal and q, and f (y) = Z1 exp (m cos2 y) the Maier–Saupe distribution function, that is classical for liquid crystals, the SAXS scattered intensity can be adjusted (Fig. 7.11) by the following formula: I …q† ˆ I …q; c† ˆ 2 K

2

R2p 0

p

dj

R2

f …y† F 2 …q; g† sin y d y

0

The value S = 0.55+0.05 of the nematic order parameter, directly obtained from this fit, is in no way negligible and actually corresponds to the typical values of thermotropic liquid crystals used in display technology. Very recent experiments with clay gels have demonstrated the existence of small submicronic domains, most probably formed by aligned particles [42]. The nematic ordering in these systems may therefore not fully take place because of the kinetic arrest brought about by gelation. Nevertheless, the large values of S and of the birefringence show that the tendency to cooperative alignment of clay particles must be considered in practice to reach a complete description of these materials. Besides, suspensions of spherical or simply less anisotropic (L/D ~3) particles do not display such orientation properties, which will be discussed later on in terms of applications.

7.3.5.2 Gibbsite Nanodisks The previous section has illustrated the difficulties met when a sol–gel transition occurs before the nematic ordering. In fact, more than half a century has elapsed between the predictions of Onsager, the first observations by Langmuir, and the recent results of the group of Lekkerkerker in Utrecht who managed to show a clear-cut On-

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sager transition for suspensions of mineral nanodisks in toluene [43]. The particles are hexagonal gibbsite (g-Al(OH)3) disks of 150-nm diameter and 10–15-nm thickness. Polyisobutene chains were grafted on the surface of the particles in order to disperse them in toluene. Then, in a thin domain of volume fractions between 0.16 and 0.17, the suspensions demix into an isotropic phase and a denser nematic phase. Moreover, the isotropic phase displays a strong flow birefringence (that vanishes at rest) and the nematic phase is truly a sol and not a gel. These experimental observations are rather well described by the Onsager model for disks, which proves that grafting particles with organic chains allows one to mimic a hard-core potential. More recently, the isotropic/nematic (I/N) phase separation was demonstrated with the same (ungrafted) gibbsite disklike particles in water (Fig. 7.12) [44].

Fig. 7.12 Increase of the proportion of nematic phase with increasing overall concentration in the biphasic domain of the suspensions of gibbsite nanodisks. (Courtesy David van der Beek).

This is the first time since Langmuir’s early work that the I/N transition was observed in an aqueous system for disklike particles. This result was obtained by adding aluminum chlorohydrate, an agent that forms Al13O4(OH)24(H2O)7+ 12 polycations that stabilize the suspension through a mechanism still mostly unknown. Understanding the exact nature of this mechanism would of course be very important. From a thermodynamic point of view, adding aluminum chlorohydrate seems to push the sol–gel transition to higher volume fractions, thus leaving a concentration range where the I/N phase separation could occur. In a subsequent work, the gelation line could be pushed even further, beyond the I/N biphasic gap, and fullynematic sol samples could be produced [45]. Besides, electrostatic repulsions are most probably dominant in these aqueous suspensions but, as we already mentioned, their detailed calculation is very complicated and is still an active subject of theoretical research [46]. Note also that aqueous suspensions of layered double hydroxide (LDHs) disklike particles were recently reported to display the isotropic/nematic phase transition, with a biphasic domain ranging from 16 to 34 % w/w [47]. This promising class of materials is presently under further investigation. Finally, aqueous suspensions comprised of both disks and rods have also been produced by

7.4 Lamellar Phases

the group in Utrecht [48]. These suspensions display a very rich polymorphism with up to five different mesophases, such as nematic phases respectively disk-rich or rod-rich. Moreover, the same group managed to devise a complete theoretical frame in order to understand this polymorphism. Unfortunately, we do not have space here to detail their very original findings any further.

7.4 Lamellar Phases 7.4.1 Numerical Simulations

Numerical simulations, performed with powerful computers, often help one to grasp the behaviors of complex systems that would be very hard to describe by analytical methods. Such simulations have been used a lot in the field of phase transitions, in particular for assemblies of spheres that can have liquid, solid, and glassy states, the stabilities of which have been thus determined. The hard-core potential is well-suited for numerical simulations of nano-object suspensions. The influence of several parameters, such as, most notably, the polydispersity, could be examined in detail. Anisotropic disklike or rodlike particles need to be considered in order to predict the appearance of liquid-crystalline phases. Several simulation principles and several geometric shapes (spherocylinders, truncated spheres …) have been used in these simulations [49]. Their results mostly agree and provide the schematic phase diagram displayed in Fig. 7.13.

Fig. 7.13 Prediction by numerical simulations of the existence of a lamellar phase (Sm) between a nematic (N) phase and an ordered three-dimensional solid (AAA) phase. (From Bolhuis and Frenkel, J. Chem. Phys. (1997) 106 : 666).

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The stability domain of the nematic phase is predicted for volume fractions that depend on the object aspect ratio. Moreover, these simulations show that rods, monodisperse in length, can assemble into liquid layers that stack and form a lamellar phase. This structure is precisely that of the smectic phases of thermotropic liquid crystals comprised of small organic molecules. We shall see below that there are colloidal mineral suspensions that are very similar to these smectic phases. 7.4.2 "Schiller Layers"

Aqueous colloidal suspensions of akaganeite (b-FeOOH, not to be confused with goethite, a-FeOOH, that we shall describe later on) nanoparticles have been first studied by Zocher, then by his student Heller, since the 1920s [50]. Both scientists had noticed that when these suspensions were left undisturbed for a very long time (up to years), iridescent layers (“schiller schichten” in German) sedimented at the bottom of the vials. They demonstrated that the iridescent layers must have a lamellar structure by studying the colors of light diffracted as a function of the angle of incidence. Recent studies have shown that akaganeite particles are rather large and monodisperse rods of 100-nm diameter and 500-nm length. These objects indeed seem a little too massive to show pure Brownian behavior and gravity probably plays a role in this phenomenon, which makes them difficult to qualify as liquid crystals, from a purely conceptual point of view. Nevertheless, the early ideas of Zocher and Heller were experimentally confirmed as atomic force microscopy studies, performed by Japanese scientists, have shown that akaganeite rods pack in layers that sediment to form the iridescent layers [51]. The layers can have two types of structures. The layers may only have positional liquidlike order (within the layers); the structure is then completely similar to that of the smectic A phase of usual thermotropic liquid crystals but at a length scale a hundred times larger. The layers may also be crystalline, which means that the rods remain at the nodes of a two-dimensional lattice and the phase is then comparable to some thermotropic smectic B phases that are close to crystals. The sediments remain at thermodynamic equilibrium with a supernatant because the rods can go from one phase to the other, not unlike the classical liquid–vapor phase equilibrium. There again, the formation and stability of these lamellar phases can be explained by resorting to the DLVO theory and excluded-volume interactions. The low rod polydispersity is a crucial feature to obtain this kind of mesophase. 7.4.3 Suspensions of H3Sb3P2O14 and HSbP2O8 Nanosheets

The aqueous suspensions of H3Sb3P2O14 and HSbP2O8 make another example of the exfoliation of low-dimensional solids. The synthesis of these lamellar materials is well documented and will not be described here [52]. In the presence of water, the solids swell and completely exfoliate to form birefringent or isotropic, fluid or gel suspensions, depending on volume fraction (Fig. 7.14) [53].

7.4 Lamellar Phases

Fig. 7.14 Samples of H3Sb3P2O14 suspensions held in test tubes viewed between crossed polarizers. (a) Lamellar gel (f = 1.98%); (b) lamellar fluid (f = 0.93%); (c) biphasic suspension (f = 0.65%); (d) biphasic suspension (f = 0.03%); (e, f) magnetic-field aligned sample; (g) sample (f = 0.75%), observed in natural light, showing a blue iridescence due to its 225-nm period.

In this section, we shall mostly focus on the phase obtained from H3Sb3P2O14, whose phase diagram is represented in Fig. 7.15. Luckily, the sol– gel transition occurs at a concentration much larger than that for which birefringence appears and a phase separation does take place, which is the sign that the system can reach thermodynamic equilibrium. This phase diagram immediately shows us a striking difference with those of the nematic phases discussed above. The biphasic regime seems to extend indefinitely as the suspensions are diluted: For a series of samples in test tubes, the proportion of birefringent phase decreases regularly with decreasing concentration but the mesophase does not suddenly vanish beyond some concentration threshold. Then, the Onsager model does not apply to this case and SAXS experiments tell us that the phase is not nematic.

Fig. 7.15 Phase diagram of the H3Sb3P2O14 suspensions versus volume fraction and salt molarity. (F: flocculated; B: biphasic; Lf : lamellar fluid; Lg : lamellar gel).

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A SAXS pattern of a shear-aligned sample of this mesophase is shown in Fig. 7.16. The diagram presents a row of sharp reflections that are due to the existence of a long-range positional order in one direction of space, that is a lamellar order. The period of this row in reciprocal space directly gives us the lamellar period d in direct space. The dependence of d versus volume fraction (the “swelling” law) displays two regimes. At large volume fraction, in the stability domain of the mesophase, the f–1 dependence is typical of the swelling of a lamellar system. This dependence directly gives the nanosheet thickness d = 1.05 nm. In contrast, the period levels to a constant value, d = 225 nm, in the biphasic domain. This corresponds to the maximum swelling beyond which solvent cannot be inserted any more between the mineral sheets. Then, the phase expels excess water and the system becomes biphasic. This maximum period probably results from a balance between the van der Waals attractions between the mineral sheets and their electrostatic repulsions. Moreover, adding salt decreases the maximum swelling and eventually induces flocculation of the suspension. The 225-nm period has an order of magnitude comparable to that of the wavelengths of visible light. Therefore, a sample of this “swollen” lamellar phase, held in a test tube, shows some blue iridescence. If the phase is very gently centrifuged, it will be slightly compressed at the bottom of the test tube and dilated at the top. Then, a rainbow can be observed in the test tube, which is a rather original effect of a transient nature because it relaxes as the phase recovers mechanical equilibrium.

Fig. 7.16 (a) SAXS pattern of an aligned sample of H3Sb3P2O14 suspension. (b) Intensity profile showing the lamellar reflections at small angles and the wide-angle diffraction lines (inset) due to the crystalline structure of the dispersed nanosheets. (c, d) Evolution of the lamellar period d versus 1/f, the inverse of the volume fraction. (The dashed line corresponds to the d = d/f swelling law where d is the nanosheet thickness).

7.5 Columnar Phases

The dilution behavior that we have just discussed is quite classical for a swollen lamellar phase and merely reproduces that observed for similar phases of surfactant molecules. However, the number of lamellar reflections observed at maximum swelling is unusually high. The number of reflections is known to get larger as the strength of the lamellar order increases and the fluctuations become limited [54]. This actually depends on the elastic constants of the mesophase and we see, therefore, that this mineral phase is a rather uncompressible stack of fairly rigid sheets. Besides, the X-ray scattering patterns display, at wide angles, diffraction lines that demonstrate that the crystalline structure of the nanosheets is preserved in solution. This point is confirmed by SAXS experiments performed with very dilute suspensions that gave a q–2 form factor typical of rigid sheets extending at least over 300 nm. The lamellar phase of H3Sb3P2O14 described here is therefore a stack of mineral covalent rigid sheets, 1-nm thick, with a continuously adjustable period up to 225 nm. Such a structure has no equivalent in the field of organic liquid crystals and illustrates the possibilities that mineral building blocks can bring to the physical chemistry of complex fluids. Let us now consider the case of the lamellar materials of HSbP2O8 formula that seem to behave similarly as the previous ones; they fully exfoliate in water to form birefringent fluids and gels that are aligned by shear flow. However, their SAXS patterns do not reveal a row of sharp reflections but several diffuse spots instead. Then, the positional order is not truly long-range, which points to a nematic phase rather than a lamellar one. To date, we do not really understand the origin of these different behaviors. Due to their molecular structures, it is very likely that the HSbP2O8 nanosheets are more flexible than the H3Sb3P2O14 ones, which might destabilize the lamellar phase. We shall examine the flow properties of these suspensions later on in this chapter. As proposed, in conclusion of our article about the phase diagram of H3Sb3P2O14 [53], the successful exfoliation of many oxides by Mallouk and coworkers has allowed for other liquid-crystalline phases based on nanosheets to be obtained. The first such example was based on the acid-exchanged K4Nb6O17 phase and the observation of a typical nematic behavior [55]. This was soon followed by others, such as HNb3O8 and HTiNbO5 [56].

7.5 Columnar Phases 7.5.1 Numerical Simulations

Computer simulations of assemblies of disklike particles submitted to excludedvolume interactions have suggested the existence, in addition to nematic phases, of columnar mesophases at high volume fractions (Fig. 7.17) [57]. For particles of moderate aspect ratio, a direct transition from the isotropic phase to a hexagonal columnar one was predicted. In contrast, simulations predict, for very anisotropic

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Fig. 7.17 Columnar phase predicted by numerical simulations for a suspension of disks of aspect ratio L/D, between a nematic phase and a three-dimensional solid. (From Veerman and Frenkel, Phys. Rev. A (1992) 45 : 5632).

particles, the sequence isotropic liquid/nematic phase/columnar phase upon increasing volume fraction. The two-dimensional phase is essentially comprised of stacks of disks assembled on a hexagonal lattice. Of course, the system may also be trapped in a glassy state at these high concentrations. 7.5.2 Two-Dimensional Phases of Rodlike Particles

The low-dimensionality material NaNb2PS10 is comprised of chains that fully exfoliate in polar solvents like NMF and DMF. These chains have a flexibility a priori intermediate between that of Li2Mo6Se6, which we have already discussed, and that of KPdPS4 which leads to a complex fluid of random coils in suspension [58]. The [Nb2PS10]– chains behave very differently in DMF and in NMF because they are structureless in the former, whereas they form nanotubules in the latter [59]. The nanotubule structure, most probably helicoidal, is perhaps stabilized by hydrogen bonds with the solvent; this point deserves to be clarified. The SAXS patterns of concentrated suspensions of [Nb2PS10] – chains in NMF display sharp diffraction lines at q values in ratios (1, M3, 2, M7, …), superimposed onto a diffuse halo. This is typical of a biphasic suspension involving a columnar mesophase and a more disordered phase that is probably isotropic. In the columnar phase, the nanotubules self-assemble on a hexagonal two-dimensional lattice but they can still diffuse along their axis. Unfortunately, these suspensions could not be concentrated enough to obtain the columnar phase pure (i. e., without any isotropic phase) and the biphasic mixtures are too viscoelastic to show phase separation. Nevertheless, let us mention that the columnar phase melts when submitted to shear flow in a Couette cell but readily reappears when shear is stopped. This phenomenon had only once been observed with hexagonal lyotropic phases of surfactant molecules [60]. The aqueous suspensions of goethite (a-FeOOH) nanorods, whose magnetic properties we shall detail later, also form a columnar phase of rectangular symmetry at high concentration [61]. This mesophase often grows in large domains with the lattice oriented perpendicular to the X-ray beam (Fig. 7.18), which is very help-

7.5 Columnar Phases

Fig. 7.18 (a) SAXS pattern of a single domain of the rectangular columnar mesophase of goethite suspensions. (The long axes of the nanorods are parallel to the beam that is perpendicular to the plane of the figure). (b) Schematic representation of the two-dimensional unit cell.

ful because the symmetry and structure can then be completely determined. The (two-dimensional) space group, c2mm, of the mesophase has glide mirrors and there are two particles per unit cell (Fig. 7.18). The cell dimensions decrease regularly upon increasing concentration. The mesophase has rectangular symmetry rather than hexagonal because the particles are not cylindrical but flattened. The two-dimensional mesophase is separated from the nematic one by a biphasic region because the nematic/rectangular phase transition is first order like the isotropic/nematic one. Domains of the columnar mesophase are easily observed in biphasic samples held in flat glass optical capillaries. Finally, applying a 1-T magnetic field clearly stabilizes the rectangular phase with respect to the nematic phase. This very surprising result remains to be explained from a theoretical point of view. 7.5.3 Hexagonal Phase of Disklike Particles

Ni(OH)2 disklike nanoparticles of about 90-nm diameter and 10-nm thickness have been produced by controlled precipitation [62]. These objects have then been stabilized in aqueous solvent by grafting a polyacrylate layer on their surface, which reduced their aspect ratio to D/L ~ 5. At fairly large concentration, the small-angle neutron scattering patterns (that can be interpreted almost in the same way as SAXS patterns) of these suspensions present two series of sharp diffraction lines. The first series of reflections has positions in ratios (1, M3, 2, M7, …),

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which is the signature of a two-dimensional hexagonal lattice, whereas the second series has positions in ratios (1, 2, 3 …) due to a one-dimensional positional order. These patterns imply that the disks stack in columns that self-assemble on a hexagonal lattice. The columns are not correlated in the direction perpendicular to the lattice and may therefore slide past each other, which ensures the mesophase fluidity. This interpretation has been confirmed by the oriented patterns obtained with samples aligned by shear flow in a Couette cell. Consequently, on a length scale of a hundred nanometers, this mineral columnar phase is completely analogous to the hexagonal mesophase of thermotropic discotic small molecules. This system also provides the opportunity to carefully tune the respective intensities of electrostatic and steric interactions by adjusting the ionic strength and polymer layer thickness. The suspensions of gibbsite (g-Al(OH)3) nanoparticles that we have already discussed above also display such a hexagonal columnar phase in addition to the nematic one [63]. In fact, the effective dimensions of the gibbsite particles can be varied by adjusting the ionic strength of the suspensions through salt addition. In very good agreement with the predictions of the numerical simulations, the suspensions showed an isotropic/nematic transition for large aspect ratios and an isotropic/columnar one for low aspect ratios [45]. Moreover, very interestingly, the effect of gravity on these rather large particles brought about a slow sedimentation phenomenon resulting in a three-phase equilibrium (isotropic/nematic/columnar, from the top to the bottom of a test tube). This unusual phenomenon could be simply accounted for with a simple and elegant model. Compared to the previous system, this one allows a better control of diameter and thickness polydispersities that are crucially important for the stability of the mesophases displaying positional order. For example, disks very polydisperse in thickness but not in diameter will more readily form a columnar phase, whereas rods very polydisperse in diameter but not in length will more readily form a lamellar phase. Note, by the way, that the polydispersities of coexisting phases may differ because of a fractionation effect, which may even result in very counterintuitive phenomena such as the coexistence of nematic and isotropic phases with the isotropic phase denser than the nematic one [64].

7.6 Physical Properties and Applications 7.6.1 Rheological Properties

The mesophase mechanical properties (viscosity, elasticity) are very important for applications; they are the subject of “rheological” studies performed with mechanical cells such as the Couette cell. In this cell, the sample is confined and sheared between two concentric cylinders that rotate with respect to each other with a given angular velocity. Using a rheometer equipped with a Couette cell, a

7.6 Physical Properties and Applications

constant angular velocity can be controlled and the shear stress arising between the cylinders can be measured. Conversely, the shear stress can be controlled and the angular velocity can be measured. Combining this kind of rheological study with a structural investigation technique can sometimes prove very useful. This is the reason why a rheometer can be found as an in situ sample environment at the ID02 SAXS beamline of the ESRF European synchrotron facility. We have recently examined the behavior of mineral liquid crystals under such conditions because mineral particles are robust under shear and show a good electronic contrast with the solvent, which makes them very good candidates to tackle rheophysical questions. Let us first examine the flow curve of the H3Sb3P2O14 lamellar gels (Fig. 7.19) that represents the relation between the shear stress and the shear rate. In the

Fig. 7.19 In situ rheoSAXS studies of lamellar H3Sb3P2O14 gels. (a) Curves of the elastic (squares) and viscous (lozenges) moduli versus alternating shear frequency. (b) Flow curve showing the existence of a yield stress, around 40–60 Pa, below which the gel does not flow. (c) Series of SAXS patterns showing that the yield stress actually lies between 35 and 40 Pa.

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case of an ideal fluid, this curve should be a straight line going through the origin (Newton’s law) whereas in the case of an ideal elastic solid, the stress should simply be proportional to the deformation (Hooke’s law). The flow curves of concentrated H3Sb3P2O14 suspensions are actually more complicated [65] because they show a “yield stress” below which the materials do not flow and because, when they start flowing, the shear stress does not depend linearly on the shear rate; the materials are then called “shear-thinning”. The existence of a yield stress is one of the typical features of a physical gel. Let us now compare this flow curve with the SAXS patterns recorded in situ. At rest, the mesophase displays an oriented SAXS pattern because it is extremely difficult to fill the cell without aligning the mesophase to some extent. Nevertheless, the mesophase orientation state does not change until the yield stress is reached. Then, the SAXS pattern suddenly changes as the phase reorients and the nanosheets align in the shear flow. Note that this scattering technique is a very accurate one (although quite expensive) to determine the yield stress. At lower concentration, the lamellar fluids of H3Sb3P2O14 nanosheets behave in a similar way except that they do not have a yield stress. The nematic phases of HSbP2O8 display a behavior quite comparable to that of the lamellar suspensions of H3Sb3P2O14 . From a liquid-crystalline perspective, these shear-thinning phenomena are quite natural. Due to its anisotropy, a liquid crystal has an anisotropic viscoelasticity and therefore has different viscosities, depending on the flow geometry. In order to minimize the flow dissipation, the material will then spontaneously align so that its lowest viscosity is involved. Intuitively, this will occur when the nanosheets slide past each other. Similar considerations can be suggested to explain the behavior of clay-based materials, either for the “soapy” layers in geophysics or for the lubricating fluids used in industry. Finally, let us mention that very similar phenomena have been observed with liquid-crystalline suspensions of rodlike particles. 7.6.2 Composite Materials

Trying to organize materials such as polymers or amorphous silica by exploiting the anisotropic structures of liquid crystals is a very attractive idea. Such approaches have been recently reported in the literature in order to obtain interesting mechanical properties or solids of high specific area. For example, flexible polymers like PVA (poly(vinyl alcohol)) or HPC (hydroxypropylcellulose) have been mixed with imogolite [66]. PVA is an amorphous polymer whereas HPC has a cholesteric phase. Improved mechanical properties could be obtained with HPC only. Besides, there have been very numerous studies of composite materials based on polymers and clays [67]. The influence of the orientational order of the clay particles on the mechanical properties of these composites should be carefully evaluated. The previously described [Mo6Se6]2– molecular wires have been dispersed and then recondensed with surfactant molecules whose nature determines the lamellar or hexagonal symmetry of the phases produced [68].

7.6 Physical Properties and Applications

Molecular precursors of silica could be dissolved in the aqueous nematic suspensions of V2O5 ribbons [69]. The mesophase could then be aligned by applying a magnetic field and the silica was polymerized in order to obtain monoliths of centimeter size. The ribbons could be eliminated liberating aligned mesopores. A very similar method has been used with suspensions of [Nb6O17] 4– nanotubules [70]. This approach leads to quite new nano-objects that can be used as structuring agents for the synthesis of mesoporous materials. 7.6.3 The Outstanding Magnetic Properties of Goethite Nanorods

Aqueous suspensions of goethite (a-FeOOH) nanorods can easily be synthesized by “chimie douce” techniques [71]. These rather polydisperse particles are about 150nm long, 25-nm wide, and 10-nm thick. The suspensions display a nematic phase at thermodynamic equilibrium in a well-defined concentration range [72]. Even though bulk goethite is a typical example of an antiferromagnetic material, these nanoparticle suspensions have very original magnetic properties for liquid crystals. For example, the field intensity required to align the nematic phase is only 20 mT (for a 20-µm-thick sample), which is about 50 times less than that required for the model TMV suspensions and about 20 times less than that required for the organic thermotropic liquid crystals used in displays. The nematic suspensions of goethite therefore seem to have record-breaking sensitivity to magnetic fields. Even better: for low values of magnetic-field intensities, goethite nanorods align parallel to the field but they reorient perpendicularly when the field intensity reaches about 350 mT, the field direction being kept fixed (Fig. 7.20). To the best of our knowledge, this is the only liquid crystal that shows such an intriguing behavior.

Fig. 7.20 SAXS patterns of nematic and isotropic suspensions of goethite submitted to small and large magnetic-field intensities.

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The isotropic phase also shows similar properties. It becomes strongly birefringent when submitted to a magnetic field. This effect is actually expected because the isotropic symmetry is broken by applying the field. Nevertheless, the magnitude of this effect is about a million times larger than that observed with the TMV suspensions. Beyond the same 350-mT intensity threshold, goethite nanorods also reorient in the plane perpendicular to the magnetic field. These quite unexpected phenomena had already been observed by Majorana in 1902 and Cotton and Mouton in 1905 with suspensions of mixed iron oxides. These scientists understood that such phenomena were due to the orientation of anisotropic nanoparticles in the magnetic field [73]. Even though they slowly fade with dilution, the suspension properties remain similar whatever the concentration and the phase. This suggests that their origin should lie in the individual properties of the nanorods. Magnetic measurements have shown that they bear a remanent magnetic moment of about m = 1000 mB that most probably arises from noncompensated surface spins. Moreover, the anisotropy of magnetic susceptibility Dw is negative. The magnetic free energy of a particle can be expressed as the sum of two terms: Em …y† ˆ

m B cos y

DwV 2 2 B cos y 2 m0

where V is the particle volume and y is its angle with the magnetic field B. The first term, linear in B, corresponds to the remanent magnetization of the nanorods; it leads at small fields and drives the parallel orientation. The second term quadratic in B corresponds to the induced magnetization. It leads at large fields and drives the perpendicular orientation. The value of the field at which these two terms are equal defines the reorientation threshold of the particles. This quite simple expression of the magnetic energy gives a proper qualitative description of the observations. Moreover, experiments in alternating fields confirm this interpretation. At frequencies larger than 400 Hz, perpendicular orientation only is observed. This is due to the fact that the remanent longitudinal moment cannot follow the variations of the magnetic field any more. The first term of the magnetic energy is then averaged to zero and the magnetic susceptibility–anisotropy term is the only one left. This model could be extended in a much more rigorous way by incorporating this magnetic free energy into the Onsager model, which allowed us to account quantitatively for the observed phenomena [74]. Let us examine the isotropic phase in more detail. At small field intensity, the nanorods align parallel to the field but with a still modest nematic order parameter (S = 0.05). The phase acquires the uniaxial symmetry of a common nematic phase and it is then called “paranematic”. In contrast, at high field intensities, the nanorods orient perpendicular to the field that remains a revolutionsymmetry axis for the phase. The nanorods seem here to “avoid” the magneticfield direction and align in the perpendicular planes. Such a kind of orientational order has already been considered, from a quite theoretical point of view, and has been called “antinematic” order. Goethite suspensions may be the first exam-

7.6 Physical Properties and Applications

ple of this organization. The amplitude of this effect is measured by the value of the nematic order parameter, S = – 0.35. Such a value is actually close to the maximum because S varies between 0 and – 0.5 in this unusual geometry. However, this original orientational ordering disappears when the magnetic field is switched off. 7.6.4 Electric Field Effects

Examining the influence of an electric field on mineral liquid crystals is quite natural because display technology is one of the major applications of liquid crystals. Unfortunately, applying an electric field to these systems can prove quite difficult because they are always lyotropic and therefore in the presence of a solvent. For example, aqueous suspensions often contain ions (due to pH for instance) that migrate to the electrodes and screen the field. An alternating high-frequency (100-kHz) electric field should be used and the electrodes should be passivated with a polymer coating in order to avoid these problems. These experiments therefore require the preparation of well-suited cells and a specific know-how. Under such conditions, the nematic phase (sol) of the suspensions of V2O5 ribbons could be aligned by using small voltages (a few volts) applied across samples of thicknesses ranging from 10 to 75 µm [75]. Starting from a planar texture (Fig. 7.21) for which the director is parallel to the preparation plane, the birefringence disappears when the electric field is applied because the nematic director aligns parallel to the field and therefore to the light beam (homeotropic texture). The director goes back to the preparation plane when the field is switched off so that these orientation phenomena are reversible. Then, birefringence cycles can be produced by alternating periods when the field is switched on and off, which is required to build a display device. However, two drawbacks severely limit the interest of such a device. Firstly,V2O5 suspensions have a strong purple color. Secondly, the response times of these suspensions comprised of rather large particles, compared to the usual liquid-crystal molecules, are of the order of a second. This is much too long to be useful for many applications that usually require microsecond response times. Nevertheless, applications for slow devices could be considered like display panels in train stations. Finally, nematic suspensions of goethite could also be aligned in an electric field. As in a magnetic field, they show different orientation directions depending on the electric-field intensity and frequency [74]. 7.6.5 The Use of Mineral Liquid-Crystalline Suspensions for the Structural Determination of Biomolecules

A quite unexpected application of mineral liquid crystals was found recently in the field of the structural determination of biomolecules by nuclear magnetic resonance (NMR). The determination of protein conformations in usual isotropic solutions by NMR classically suffers from a loss of information that is intrinsic to

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Fig. 7.21 Progressive evolution over time (a–d) of a nematic suspension of V2O5 ribbons submitted to an electric field applied in the direction perpendicular to the plane of the figure. The initially bright planar texture becomes homeotropic and therefore dark.

the technique. In order to solve this problem, specialists have resorted to anisotropic solutions that are therefore liquid-crystalline [76]. This new and quickly expanding approach has so far made use of micellar solutions, viruses or cellulose rod suspensions. Additional information is thus retrieved through dipolar residual couplings. Mineral suspensions are also very good candidates for such studies. Their volume fractions are usually lower than those of the other systems and can be adjusted in a wide range; their pH and ionic strength can also be controlled. A priori, these entities do not interact much with the biomolecules. Mineral mesophases can often be aligned in a magnetic field. Finally, these suspensions can be prepared in heavy water, so that they do not have any protons, carbon or nitrogen nuclei, which suppresses the usual need for isotopic labeling. The validity of this approach was recently illustrated with two systems [77]: nematic suspensions of V2O5 ribbons and the lamellar phase of H3Sb3P2O14 in which a nonlabeled polysaccharide, containing the LewisX motif, had been dissolved. In both cases, the polysaccharide structure could be determined. This approach demonstrates well how quite unexpected applications may arise from very fundamental progress.

Acknowledgments

7.7 Conclusion

Although it is about a century old and after it had almost disappeared, the field of mineral liquid crystals has lately found a renewed interest for several reasons. Most importantly, the development of “chimie douce” and the “nano” trend led to the synthesis of numerous suspensions of anisotropic nanoparticles all over the world. There are many systems that may have liquid-crystalline phases and they are fairly easy to synthesize. A nonexhaustive list of such candidates has been presented in a recent review [1 b]. Then, the typical properties of liquid crystals, fluidity and anisotropy, can be used to handle the mineral particles with very simple and cheap techniques like applying external fields or shear flows. Mineral mesophases can also be used to template materials and produce hybrids of original properties. A new step should now be considered in which chemical reactions would employ the partitioning of space induced by positionally ordered mesophases. For example, one may think of the polymerization of moieties within the interlamellar space of a smectic phase. From the point of view of the physics of complex fluids, suspensions of mineral nanoparticles make good systems to test the theoretical models of phase transitions and to check the predictions of numerical simulations, as these suspensions are generally more robust and simple than their organic counterparts. However, they are also much more polydisperse than suspensions of biological objects such as viruses. Nowadays, the most important kinds (nematic, lamellar, columnar …) of mesophases have been discovered in mineral suspensions and, in our opinion, the research thrust should rather focus on combining specific physical properties with liquid-crystalline order. The original magnetic behavior of goethite suspensions is completely unknown in the field of organic liquid crystals and provides a very good example of the perspectives open to anyone willing to take part in this scientific adventure.

Acknowledgments

We are indebted to too many people to thank them all here. We would only like to mention here the students, F. Camerel, X. Commeinhes, A. Garreau, B. Lemaire, O. Pelletier, L. Schoutteten, and D. van der Beek, who worked with us and P. Batail, H. Lekkerkerker, and J. Livage, who have persistently supported us in this new avenue of research.

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14 (a) Davidson P, Gabriel JC, Levelut AM, Batail P (1993) Europhys. Lett. 21 : 317; (b) Davidson P, Gabriel JC, Levelut AM, Batail P (1993) Adv. Mater. 5 : 665. 15 Fuhrer MS, Nygard J, Shih L, Forero M,Yoon Y, Mazzoni MSC, Choi H, Ihm J, Louie SG, Zettl A, McEuen PL (2000) Science 288 : 494. 16 Pelletier O, Davidson P, Bourgaux C, Coulon C, Regnault S, Livage J (2000) Langmuir 16 : 5295. 17 Guinier A, Fournet G (1955) SmallAngle Scattering of X-rays, J Wiley and Sons, New York. 18 Commeinhes X, Davidson P, Bourgaux C, Livage J (1997) Adv. Mater. 9 : 900. 19 Guinier A (1994) X-ray Diffraction in Crystals, Imperfect Crystals and Amorphous Bodies, Dover, New York. 20 Davidson P, Petermann D, Levelut AM (1995) J. Phys. II (France) 5 : 113. 21 Pelletier O, Bourgaux C, Diat O, Davidson P, Livage J (1999) Eur. Phys. J. B 12 : 541. 22 Pelletier O, Davidson P, Bourgaux C, Livage J (1999) Europhys. Lett. 48 : 53. 23 Pelletier O, Sotta P, Davidson P (1999) J. Phys. Chem. B 103 : 5427. 24 (a) Farmer C, Fraser AR,Tait JM (1977) Chem. Commun. 462; (b) Wada S-I, Eto A,Wada K (1979) J. Soil Sci. 30 : 347; (c) Wada S-I (1987) Clays Clay Miner. 35 : 379; (d) Barett SM, Budd PM, Price C (1991) Eur. Polym. J. 27 : 609; (e) US patents 4252779 and 4241035; (f ) Koenderink GH, Kluijtmans SGJM, Philipse AP (1999) J. Coll. Interf. Sci. 216 : 429. 25 (a) Kajiwara K, Donkai N, Hiragi Y, Inagaki H (1986) Makromol. Chem. 187 : 2883; (b) Kajiwara K, Donkai N, Fujiyoshi Y, Inagaki H (1986) Makromol. Chem. 187 : 2895; (c) Donkai N, Kajiwara K, Schmidt M, Miyamoto T (1993) Makromol. Chem. Rapid Commun. 14 : 611; (d) Donkai N, Hoshino H, Kajiwara K, Miyamoto T, Makromol. Chem. (1993) 194 : 559.

References 26 Pileni MP (1993) J. Phys. Chem. 97 : 1; (1999) Acc. Chem. Res. 32, special issue on Nanoscale Materials. 27 (a) Kim F, Kwan S, Akana J,Yang P (2001) J. Am. Chem. Soc. 123 : 4360; (b) Tao A, Kim F, Hess C, Goldberger J, He R, Yugang Sun, Xia Y,Yang P (2003) Nano Lett. 3 : 1229. 28 (a) Li LS,Walda J, Manna L, Alivisatos AP (2002) Nano Lett. 2 : 557; (b) Li LS, Alivisatos AP (2003) Adv. Mater. 15 : 408; (c) Liang-shi L, Marjanska M, Park GHJ, Pines A, Alivisatos AP (2004) J. Chem. Phys. 120 : 1149. 29 Somoza AM, Sagui C, Roland C (2001) Phys. Rev. B 63 : 081403. 30 (a) Shimoda H, Oh SJ, Geng HZ, Walker RJ, Zhang XB, McNeil LA, Zhou O (2002) Adv. Mater. 14 : 899; (b) Armitage NP, Gabriel JCP, Gruner G (2004) J. Appl. Phys. 95 : 3228. 31 Song W, Kinloch IA,Windle AH (2003) Nature 302 : 1363. 32 (a) Davis VA, Ericson LM, ParraVasquez ANG, Fan H,Wang YH, Prieto V, Longoria JA, Ramesh S, Saini RK, Kittrell C, Billups WE, Adams WW, Hauge RH, Smalley RE, Pasquali M (2004) Macromolecules 37 : 154; (b) Islam MF, Alsayed AM, Dogic Z, Zhang J, Lubensky TC, Yodh AG (2004) Phys. Rev. Lett. 92 : 088303. 33 Langmuir I (1938) J. Chem. Phys. 6 : 873. 34 (a) Mourchid A, Delville A, Lambard J, Lécolier E, Levitz P (1995) Langmuir 11 : 1942; (b) Mourchid A, Lécolier E, Van Damme H, Levitz P (1998) Langmuir 14 : 4718; (c) Pignon F, Piau JM, Magnin A (1996) Phys. Rev. Lett. 76 : 4857; (d) Pignon F, Magnin A, Piau JM (1997) Phys. Rev. Lett. 79 : 4689; (d) Pignon F, Magnin A, Piau JM, Cabane B, Lindner P, Diat O (1997) Phys. Rev. E 56 : 3281; (f ) Bonn D,Tanaka H, Wegdam G, Kellay H, Meunier J (1998) Europhys. Lett. 45 : 52; (g) Bonn D, Kellay H,Tanaka H,Wegdam G, Meunier J (1999) Langmuir 15 : 7534. 35 Gabriel JCP, Sanchez C, Davidson P (1996) J. Phys. Chem. 100 : 11139. 36 Balnois E, Durand-Vidal S, Levitz P (2003) Langmuir 19 : 6633.

37 Forsyth PA, Marcelja JS, Mitchell DJ, Ninham BW (1978) Adv. Coll. Interf. Sci. 9 : 37. 38 Michot L (2004) Personal communication. 39 Zhang LM, Jahns C, Hsiao BS, Chu B (2003) J. Coll. Interf. Sci. 266 : 339. 40 DiMasi E, Fossum JO, Gog T, Venkataraman C (2001) Phys. Rev. E 64 : 061704. 41 Lemaire BJ, Panine P, Gabriel JCP, Davidson P (2002) Europhys. Lett. 59 : 55. 42 (a) Bihannic I, Michot LJ, Lartiges BS, Vantelon D, Labille J,Thomas F, Susini J, Salomé M, Fayard B, (2001) Langmuir 17 : 4144; (b) Cousin F, Cabuil V, Levitz P (2002) Langmuir 18 : 1466. 43 Van der Kooij F, Lekkerkerker HNW (1998) J. Phys. Chem. B 102 : 7829. 44 Van der Beek D, Lekkerkerker HNW (2003) Europhys. Lett. 61 : 702. 45 Van der Beek D, Lekkerkerker HNW (2004) Langmuir 20 : 8582. 46 Aubouy M,Trizac E, Bocquet L (2003) J. Phys. A Math. Gen. 36 : 5835. 47 Liu S, Zhang J,Wang N, Liu W, Zhang C, Sun D (2003) Chem. Mater. 15 : 3240. 48 (a) van der Kooij FM, Lekkerkerker HNW (2000) Phys. Rev. Lett. 84 : 781; (b) Wensink HH,Vroege GJ, Lekkerkerker HNW (2001) J. Chem. Phys. 115 : 7319; (c) van der Kooij FM, Lekkerkerker HNW (2000) Langmuir 16 : 10144. 49 Bolhuis P, Frenkel D (1997) J. Chem. Phys. 106 : 666. 50 (a) Zocher H, Jacobsohn K (1929) Kolloid Beih. 28 : 167; (b) Heller W (1935) Compt. Rend. 201 : 831; (c) Heller W (1980) Polymer Colloids II, ed. E Fitch, Plenum Press, New York. 51 (a) Maeda Y, Hachisu S (1983) Colloids Surf. 6 : 1; (b) Maeda H, Maeda Y (1996) Langmuir 12 : 1446. 52 Piffard Y,Verbaere A, Lachgard A, Deniard-Courant S,Tournoux M (1986) Rev. Chim. Gen. 23 : 766. 53 Gabriel JCP, Camerel F, Lemaire BJ, Desvaux H, Davidson P, Batail P (2001) Nature 413 : 504. 54 Safinya C R et al. (1986) Phys. Rev. Lett. 57 : 2718.

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7 Self-Assemblies of Anisotropic Nanoparticles: Mineral Liquid Crystals 55 (a) Camerel F, Gabriel JCP, Batail P (2002) Chem. Commun. 1926; (b) Miyamoto N, Nakato T (2002) Adv. Mater. 14 : 1267; (c) Nakato T, Miyamoto N (2002) J. Mater. Chem. 12 : 1245; (d) Miyamoto N, Nakato T (2004) J. Phys. Chem. 108 : 6152. 56 Nakato T, Miyamoto N, Harada A (2004) Chem. Commun. 78. 57 Veerman JAC, Frenkel D (1992) Phys. Rev. A 45 : 5632. 58 Sayettat J, Bull LM, Gabriel JCP, Jobic S, Camerel F, Marie AM, Fourmigué M, Batail P, Brec R, Inglebert RL (1998) Angew. Chem. Int. Ed. 37 : 1711. 59 Camerel F, Gabriel JCP, Davidson P, Schmutz M, Gulik-Krzywicki T, Lemaire B, Bourgaux C, Batail P (2002) Nano Lett. 2 : 403. 60 Ramos L, Molino F, Porte G (2000) Langmuir 16 : 5846. 61 Lemaire BJ et al. (2004) Phys. Rev. Lett. 93: 267801. 62 (a) Brown ABD, Clarke SM, Rennie AR (1998) Langmuir 14 : 3129; (b) Brown ABD, Ferrero C, Narayanan T, Rennie AR (1999) Eur. Phys. J. B 11 : 481; (c) Brown ADB, Rennie AR (2001) Chem. Eng. Sci. 56 : 2999. 63 van der Kooij FM, Kassapidou K, Lekkerkerker HNW (2000) Nature 406 : 868. 64 (a) van der Kooij FM, van der Beek D, Lekkerkerker HNW (2001) J. Phys. Chem. B 105 : 1696; (b) Wensink HH, Vroege GJ, Lekkerkerker HNW (2001) J. Phys. Chem. B 105 : 10610 65 Camerel F, Gabriel JCP, Batail P, Panine P, Davidson P (2003) Langmuir 19 : 10028.

66 (a) Hoshino H,Yamana M, Donkai N, Sinigerski V, Kajiwara K, Miyamoto T, Inagaki H (1992) Polym. Bull. 28 : 607; (b) Hoshino H, Ito T, Donkai N, Urakawa H, Kajiwara K (1992) Polym. Bull. 29 : 453. 67 Biswas M, Ray SS (2001) Adv. Polym. Sci. 155 : 167. 68 Messer B, Song JH, Huang M,Wu YY, Kim F,Yang PD (2000) Adv. Mater. 12 : 1526. 69 Camerel F, Gabriel JCP, Batail P (2003) Adv. Funct. Mater. 13 : 377. 70 Camerel F, Gabriel JCP, Batail P (2002) Chem. Commun. 17 : 1926. 71 Hernandez J (1998) Thesis Université Paris 6. 72 Lemaire BJ, Davidson P, Ferré J, Jamet JP, Panine P, Dozov I, Jolivet JP (2002) Phys. Rev. Lett. 88 : 125507. 73 (a) Majorana Q (1902) C. R. Acad. Sci. 135 : 159; (b) Cotton A, Mouton H (1905) C. R. Acad. Sci. 141 : 317. 74 (a) Lemaire BJ et al. (2004) Eur. Phys. J. E 13 : 291; (b) Lemaire BJ et al. (2004) Eur. Phys. J. E 13 : 309. 75 Lamarque-Forget S, Pelletier O, Dozov I, Davidson P, MartinotLagarde P, Livage J (2000) Adv. Mater. 12 : 1267. 76 (a) Tjandra N, Bax A (1997) Science 278 : 1111; (b) Prestegard JH, Kishore AI (2001) Curr. Opin. Chem. Biochem. 5 : 584. 77 (a) Desvaux H, Gabriel JCP, Berthault P, Camerel F (2001) Angew. Chem. Int. Ed. 40 : 373; (b) Berthault P, Jeannerat D, Camerel F, Alvarez-Salgado F, Boulard Y, Gabriel JCP, Desvaux H (2003) Carbohydrate Res. 338 : 1771.

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8 Collective Properties Due to Self-Organization of Silver Nanocrystals Arnaud Brioude, Alexa Courty, and Marie-Paule Pileni

8.1 Introduction

During the last decade, due to the emergence of a new generation of high-technology materials, the number of groups involved in nanomaterials has increased exponentially. Mesoscopic structures of nanocrystals are nowadays a rapidly growing field of science where the efforts of chemists, physicists, material scientists and biologists have merged. A new field of research has recently emerged in the use of individual nanocrystals for growing 2D and 3D superstructures and investigation of the collective properties of these artificial quantum dot solids [1]. Fabrication of nanometer order at the mesoscopic scale is considered as the key for applications in data storage, functional devices, communications and technology. The nanostructures, which are randomly distributed, fluctuate in size and have an unchanged periodicity giving significant limitations to their applications. Hence, an ultimate challenge in materials research is now the creation of perfect nanometerscale crystallites, identically replicated in unlimited quantities and in a state that can be manipulated, which behave as pure macromolecular substances. Thus, the ability to systematically manipulate these crystallites is an important goal in modern materials chemistry. We first demonstrated self-organization of nanocrystals with the formation, on a mesoscopic scale, of a monolayer in a compact hexagonal network and in 3D superlattices [1–5]. Crystallization followed by the unambiguous determination of the exact position of each nanocrystal in the superlattice structures is the most suitable method of characterization [6, 7]. The physical properties of these superstructures [1] (optical, magnetic, transport) markedly differ from those of isolated nanocrystals and the bulk phase. They are mainly due to the close vicinity of nanocrystals, that is, to dipolar interactions. In this review we scan the various optical properties of 5-nm silver nanocrystals, self-organized in 2D or 3D superlattices. These properties are either intrinsic to the self-assembly or due to dipolar interactions induced by the close vicinity of the nanocrystals at fixed distance from each other. Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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8.2 Results and Discussion

To study these collective properties 5-nm silver nanocrystals coated with dodecyl alkyl chains are produced from reverse micelles [8]. The nanocrystals, characterized by a very low size distribution (10 %), are then dispersed in hexane. The resulting colloidal solution is characterized by a UV/visible absorption spectrum attributed to the well-known Mie resonance centered around 2.9 eV and interband transitions at larger energy [9]. This result is in good agreement with that deduced from numerical calculations [10, 11] on particles of isolated silver spheres, taking into account the surrounding media and the presence of dodecyl alkyl chains. The influence of the chemical environment on the optical response of nanocrystals has also been demonstrated for other systems [12, 13]. The theory used is an extension of the Mie theory and is the solution of Maxwell’s equation for an isotropic sphere. Surrounded by an infinite external medium (refractive index 1.3914), there are two concentric regions of dielectric material of specified thickness [14, 15]. This is known as the layered-sphere problem, and our calculation of the extinction cross section is done with a publicly available method called BHCOAT. Deposition of a drop of the solution on a highly oriented pyrolytic graphite (HOPG) substrate causes the silver nanocrystals to self-organize in a compact hexagonal network [9] (Fig. 8.1 A). The average distance between two adjacent nanocrystals is around 2 nm. The electron diffraction pattern shows concentric rings, which can be indexed (from the inside) as the (111), (200), (220) and (311) reflectance characteristics of a face centered cubic (fcc) structure [16]. Inside the concentric rings appear spots corresponding to various orientations of the nanocrystals. This clearly shows a good crystallinity of the nanocrystals. High-resolution transmission electron microscopy (HRTEM) images show three structures identified as multiply twinned particles (MTP) such as decahedra (Fig. 8.1 B), icosahedra (Fig. 8.1 C) and cuboctahedra (Fig. 8.1 D). From this structural investigation [16], Ag nanoparticles appear to be highly crystallized. However, it can be seen that the crystal structure of the silver nanoparticles does not always correspond to that of the bulk solid. This is in good agreement with what has been shown in the literature for such very small crystals [17]. In addition, it is known that the energies of these different types of crystals are so close that, in a given sample like here, it is expected that a statistical distribution of structures can be observed, especially in the case of smaller sizes [18]. On increasing nanocrystal concentration small aggregates characterized by a fourfold symmetry are observed by TEM, indicating an fcc structure [9]. On controlling substrate temperature (22 8C) and evaporation rate, large aggregates [19, 20] are formed with heights and widths of several hundreds of micrometers, respectively (Fig. 8.2 A). The diffraction pattern shows two strong reflections normal to the substrate [21]. The absence of further diffraction orders is due to a decrease in the structure factor for spherical nanocrystals. The width of the firstorder reflection is found to be nearly resolution-limited, indicating long-range ordering of the silver nanocrystals perpendicular to the surface. Other less intense

8.2 Results and Discussion

Fig. 8.1 (A) TEM image of silver nanocrystals with a mean diameter of 5 nm. (B–D) HRTEM images: (B) decahedron viewed along the fivefold axis; (C) icosahedron viewed along the threefold axis; (D) cuboctahedron in the [110] orientation.

Fig. 8.2 SEM images and (inserts) X-ray diffraction patterns of 5-nm silver nanocrystals. (A) Self-organized in fcc structure and forming a “supra” crystal; (B) forming a disordered assembly of nanocrystals.

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reflections are also observed. Furthermore, the diffraction pattern shows a weak ring with an intrinsic width nearly resolution-limited. This confirms a long-range ordering of the silver nanocrystals. On tilting the sample by 108, the diffraction pattern (insert Fig. 8.2 A) shows numerous additional diffraction spots revealing a 3D long-range ordering within supracrystalline domains. From these results, it appears that the ordered domains share a common crystallographic axis normal to the substrate and that their in-plane orientation is random. A comparison of observed and calculated diffraction spot coordinates leads to an fcc packing. At low substrate temperature (10 8C), compact islands formed by the stacking of several layers of nanocrystals (Fig. 8.2 B) with the appearance of defects and a very rough surface are observed. The diffraction pattern (insert Fig. 8.2 B) shows a broad diffusing ring typical of a disordered arrangement. In the following discussion we will describe the intrinsic properties due to the self-assembly of nanocrystals and collective properties due to dipolar interactions induced by the high ordering and vicinity of the nanocrystals. 8.2.1 Intrinsic Properties Due to "Supra" Crystal Formation [17]

As already described above with the same nanocrystals, it is possible to produce either “supra” crystals in the fcc structure or disordered aggregates. We will study the Stokes–anti-Stokes Raman spectra of nanocrystals forming these two assemblies (either disordered aggregate or “supra” crystals). Let us first consider disordered aggregates of highly crystallized nanocrystals. When incident light energy is in resonance with the energy of the electronic dipolar plasmon, scattering by cluster vibrations is observed. For spherical nanocrystals with sizes larger than 1 nm, the cluster vibrations are described by modeling the nanocrystal as a continuum nanosphere of a diameter D equal to the size of the nanocrystal, and using the longitudinal vl and transversal vt sound of velocities of bulk silver. The vibrations are characterized by the quantum numbers n and l, like those for spherical harmonics [22], and the vibrational frequencies are given by: vln ˆ

Sln vt D

…1†

where Sln depends on the ratio vl /vt. Figure 8.3 A shows the Stokes–anti-Stokes Raman spectrum of this assembly. The quadrupolar modes [23–25] appear as sharp intense lines. Because the nanocrystal assemblies are characterized by a size distribution [9] we would also expect a vibrational frequency distribution. The good agreement of the Stokes lineshape with the inverse size distribution demonstrates the intra-nanoparticle coherence, i. e., nanocrystallinity. This agrees with data published previously by Duval et al. [24] for silver nanocrystals dispersed in a polymeric matrix. The Stokes–anti-Stokes Raman spectrum of small “supra” crystals (dashed line) in the fcc structure (Fig. 8.3 B) is shifted toward low frequency while the quadrupo-

8.2 Results and Discussion

Fig. 8.3 Stokes–anti-Stokes Raman spectra of silver nanocrystals deposited on a substrate: (A) at 10 8C and forming a disordered assembly; (B) at 22 8C and forming fcc “supra” crystals.

lar line is narrowed compared to that obtained with a disordered assembly. From _ the calculation described in Ref. [21], the Raman vibration intensity I SD (v) for the scattering by the nanocrystals vibrating coherently in a small supracrystal is: 2 2 I …s† sc …v† ! I nc …v† v

…2†

This equation shows that in the case of small supracrystals, the coherence effect shows up as a narrowing of the Raman peak. Figure 8.4 compares the profile obtained with the “supra” crystals (solid line) with the square intensity of the profile of a disordered assembly multiplied by the square of the frequency (n2) (dotted line). The good match in Fig. 8.4 means that the average size of the supra crystals is smaller than the light wavelength. The shift to lower frequency is due to the effect of the local electric field in the fcc “supra” structure. The scattered intensity is proportional to the square of the local field. Such a situation differs from a uniformly disordered arrangement of nanocrystals having different sizes, where the local electric field has the same

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Fig. 8.4 Comparison of the Raman scattered intensity I(n) from silver nanocrystals. (a “supra” crystal) with the product I (n)n2 where I (n) is the Raman scattered intensity of a disordered assembly of nanocrystals.

mean value for all nanocrystals. Therefore, in a set of supracrystals where each of them is built with nanocrystals of the same size which differs from one supracrystal to another, the relatively strong Lorentz field EL at the plasmon resonance enhances the intensity of Raman scattering and induces a shift of the quadrupolar mode, as observed in Fig. 8.3B. 8.2.2 Dipolar Interactions

At this point we ask ourselves the following question: are there any collective properties, due to induced dipolar interactions, when nanocrystals are self-organized in a compact hexagonal network? To answer such an important question we study the same system by various techniques. 8.2.2.1 Absorption Spectroscopy [26] Let consider a cluster constituted of a several particles with hexagonal structure (Fig. 8.5). The interparticle distance (2 nm) is fixed and the particle diameter is 5 nm. The external medium dielectric constant of 2 is close to that of the alkyl chain used to coat the nanocrystals. The extinction cross section of the cluster expressed as its logarithm is calculated for the s- and p-polarizations, respectively, with the method given by Gerady and Ausloos [27]. The s-polarization spectrum presents a single peak (Fig. 8.6 A), while with p-polarization two peaks appear (Fig. 8.6 B). In s-polarization, the two components of the electric field are parallel to the substrate plane. Thus, this resonance at low energy has to be attributed to E//. In p-polarization, one of the components of the electric field is perpendicular to the substrate plane (Ek). As a consequence, the new resonance at high energy can be attributed to Ek. This is clearly the result of the optical anisotropy of the system [10, 22]. The experimental absorption spectrum of nanocrystals self-organized in a hexagonal network on a substrate [9] is recorded using a diffuse reflectance accessory. Compared to that obtained in solution (2.9 eV), the spectra of 2D and 3D self-orga-

8.2 Results and Discussion

Fig. 8.5 Cluster used in the calculation corresponding to the hexagonal structure.

Fig. 8.6 Extinction cross section for the cluster of Fig. 8.5; 2R = 6.60 nm, d = 8.45 nm, e = 2 for both s (A) and p (B) polarizations. In the latter case, the angle of incidence in degrees is indicated.

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nized systems show resonances at 2.73 and 2.6 eV, respectively [9]. This lowenergy shift of the optical response is due to the Lorentz field effect. In fact, due to the interaction between dipoles of those systems, the field really acting on one dipole depends on the orientation and on the position of the others. The local environment of one dipole differs when nanocrystals are isolated in solution or selfassembled at 2D or 3D on a substrate.

8.2.2.2 Reflectivity Measurements [22, 23] In order to study the influence of the Lorentz field effect, we have compared the optical response of two systems where particles are randomly deposited (Fig. 8.7 A) or self-assembled (Fig. 8.7 B) on a HOPG substrate. Let us first consider the reflectiv-

Fig. 8.7 On the left: (A) TEM patterns of disordered and coalesced particles on the substrate. (B) Reflectance spectra of these deposited particles obtained with s-polarization at 608 incident angle. (C) Reflectance spectra of the same particles obtained with p-polarization at 608 incident angle. On the right: (A) TEM patterns of spherical particles organized on the substrate. (B) Reflectance spectra of these deposited particles obtained with s-polarization at 608 incident angle. (C) Reflectance spectra of the same particles obtained with p-polarization at 608 incident angle.

8.2 Results and Discussion

ity spectra of nanocrystals randomly deposited on a HOPG substrate obtained for the two polarization states s and p, respectively, in Fig. 8.7 B and C. The angle of the incident light is fixed at 608. In this paper, as we discuss absorption resonances we will comment only on the minima of the reflectivity curves. In fact, the real probed quantity should be the so-called surface differential reflectance (SDR) [28–30]: DR R R0 ˆ R0 R where R0 stands for the substrate reflectivity and R for that of the particle-covered surface. Nevertheless, as the reflectivity of the HOPG substrate is constant in this energy range (Fig. 8.8), these experimental curves are quite sufficient for qualitative studies. Figure 8.7 A shows nanocrystals (type A) well isolated on the HOPG substrate and nanocrystals assembled in randomly shaped aggregates (type B). In s-polarization, the minimum of the curve at 3.75 eV cannot be attributed to a resonance because of the rise of the HOPG reflectivity (Fig. 8.8) between 3.5 and 4.5 eV. In p-polarization, a minimum is observed at around 2.9 eV. This value exactly corresponds to the resonance of silver particles in solution. Dipolar modes perpendicular to the surface, which can only be observed in p-polarization, usually tend to create a depolarization field on each particle that enhances the dipole oscillator strength. As a result, compared to the optical response of isolated particles, these modes should be high-energy shift. This probably means that there are no interactions between particles of type A and the substrate. Concerning the other particles of type B arranged in randomly shaped aggregates, the dipolar-mode resonances are too broad to be observed, whatever the polarization. In fact, the resonances of each aggregate clearly exist but the sum of their contributions is only revealed by the overall asymmetry of the curve at high energy.

Fig. 8.8 Calculated reflectivity spectra of the bare substrates: HOPG (solid line), silicon(short dashed line), AlxGa1+xAs (long dashed line), and Au (dots).

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Fig. 8.9 Experimental reflectivity spectra of silver nanoparticles monolayer on (A) HOPG, (B) gold, (C) silicon, (D) Al0,7Ga0,3As under p-polarized light and at incident angles of 608 (solid line), 458 (dashed line), 208 (dotted line).

The same study has been done on a self-assembled 2D array of particles on HOPG. In s-polarization, a minimum is observed at 2.4 eV. This is not surprising because the depolarization field associated with dipolar modes parallel to the surface reduces the frequency of the isolated case (2.9 eV), which can be explained as a low-energy shift. In p-polarization, this minimum still remains because one component of the electric field is parallel to the surface. The other component perpendicular to the surface is responsible for the other resonance at high energy (3.2 eV). In conclusion, we have shown that interactions between particles in a self-assembled 2D array deposited on a HOPG substrate are observed by reflectivity curves in the two polarization states of the electric field. The two dipolar resonances at low (2.4 eV) and high energy (3.2 eV) are respectively attributed to E// and Ek. In order to study the influence of the two polarization states of the electric field on the previously discussed dipolar resonances, we have repeated the above experiments but varied the angle of the incident light (Fig. 8.9). Under s-polarization, the reflectivity spectrum is independent of the incident angle y, which is not surprising, considering the fact that the two electric-field components are parallel to the surface whatever the value of y. Under p-polarization (Fig. 8.9 A), the reflectivity spectra markedly change. Decreasing the incident angle, we observed that the high-energy resonance around 3.4 eV (similar to that discussed at 3.2 eV) tends to vanish progressively. In fact, at low angle (208, dotted line), the electric-field vector along the particle film becomes predominant (Fig. 8.10). In this case, the reflectivity spectrum in p-polarization is very similar to that obtained under s-polarization, i. e., without any high-energy resonance. At high incident angles, the perpendicular electric-field component becomes much larger than the parallel one, which explains the presence of this high-energy resonance. We also notice that the low-energy resonance remains unchanged whatever the angle,

8.2 Results and Discussion

Fig. 8.10 Schematic representation of the spherical particles organized on a substrate under a polarized light with different incident angles.

since in the two polarization states, at least, one component of the electric field is parallel to the particle surface. To determine clearly the position of the plasmon resonances, the reflectivity spectrum of these systems has been simulated by the matrix method from Abeles’ theory of stratified media [31, 33]. The monolayer of nanocrystals is modeled as a homogeneous film made of 5-nm silver nanocrystals with a nearest-neighbor distance of 7 nm in a medium of dielectric constant 2 (Fig. 8.11). The effective dielectric function of the nanocrystal film is deduced from a slight modification of the theory developed by Barrera et al. [34]. The effective nanocrystal film polarization, characterized by an anisotropic dielectric function in an infinite surrounding medium, is assumed to be that of the overall nanocrystals forming the film and organized in a compact hexagonal network. The whole system is modeled by a stratified medium composed of a 2-nm layer of dielectric constant 2 representing the coating (dodecanethiol), a 5-nm layer of silver nanocrystals and another 2-nm layer representing the coating (Fig. 8.11).

Fig. 8.11 Schematic representation of the modeled system.

Calculations have been made for different substrates: HOPG (Fig. 8.12 A), gold (Fig. 8.12 B), silicon (Fig. 8.12 C) and Al0.7Ga0.3As (Fig. 8.12 D) with p-polarized light and at incident angles of 608 (solid line), 508, 408, 308 and 178 (dotted line). Whatever the substrate, similar behavior is observed with the appearance of the minimum around 3.5 eV already discussed. Nevertheless, the low-energy reso-

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Fig. 8.12 Calculated reflectivity spectra of silver nanoparticles monolayer on (A) HOPG, (B) gold, (C) silicon, (D) Al0,7Ga0,3As under p-polarized light and at incident angles of 608 (solid line), 508, 408, 308, 178(dotted line).

nance at 2.4 eV is only present in calculations with HOPG and gold substrates. The reflectivities due to the substrate and the film made of nanocrystals are both nonnegligible. The model used is limited to dipole–dipole interaction. In fact, the substrate could influence the optical response of the silver nanocrystal monolayer by image forces (Fig. 8.13), i. e., formation of image dipoles in the substrate induced by the dipoles in the nanocrystals subjected to an electromagnetic field. To introduce the image forces, the Barrera calculations described in Ref. [34] are used. If we consider that silver nanocrystals are not in direct contact with the substrate, calculated spectra are very similar to those obtained without image forces. But it is not so obvious that the dipole/image-dipole distance is sufficiently high to be negligible. Moreover, the incident roughness of the metallic substrate (gold) can act as an electromagnetic coupler under certain conditions (incident light direction, polarization) with the incident light, thus creating delocalized plasmons that interact with localized ones created close to the particles. From these data, it

Fig. 8.13 Schematic representation of the dipole image.

8.2 Results and Discussion

is concluded that the influence of the substrate is not clear, and has to be taken into account for a precise determination of the resonances observed. The experiments presented here have to be performed by introducing, for example, a transparent spacer layer (Langmuir–Blodgett) between the substrate and the nanocrystal film to avoid a dipole-force image. Work using nonabsorbing substrates in this range of energy is also in progress. To confirm the appearance of coupled plasmon modes, polarized electron photoemission spectroscopy is performed.

8.2.2.3 Polarized Electron Spectroscopy [35] Polarized electron photoemission spectroscopy on 5-nm silver nanocrystal self-assemblies in a hexagonal network on HOPG and gold substrates demonstrates a two-photon mechanism [35]. The electron photoemission spectra, measured at constant beam intensity under s-and p-polarization, show a marked change in the spectrum with the light polarization (Fig. 8.14). Under s- and p-polarizations, two wide-emission bands are observed. The bands are not well defined because there are few experimental points, due to the intrinsic laser wavelength interval. However, two well-defined peaks are always observed. Under s-polarization, the maximum at low energy is around 2.45 eV. Compared to the absorption data and the calculated reflectivity absorption spectrum a single resonance is expected. It is rather difficult to explain the presence of this high-energy peak. Under p-polarization, the electron emission intensity markedly increases with the appearance of two maxima at 2.4 and 3.2 eV. The increase in the electron emission yield under p-polarization cannot be attributed to the intrinsic increase observed when light is p-polarized. In fact the ratio of the relative intensity under p- and s-polarization shows a continuous increase in the electron emission (Fig. 8.15). Hence the increase in the electron emission yield under p-polarization is due to the optical ani-

Fig. 8.14 Photoemission spectra of silver nanocrystal films on HOPG (triangles) and gold (diamonds), under s (dashed line) and p (solid line) polarizations.

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Fig. 8.15 Polarization ratio spectra (Ie (p)/Ie (s)) of the silver nanocrystal film on gold (diamonds) and graphite (triangles). Lines are effective fitting curves of the experimental points. Insert: extinction spectra of a film of nanocrystals on glass obtained at direct incidence and at 608 under p-polarized light. Lines are effective fitting curves of the experimental points.

sotropy of the supported nanocrystal film. This permits us to conclude that the two electron emission peaks are related to the film made of self-organized nanocrystals. The low-energy peak is related to the longitudinal surface plasmon resonance (SPR) of the film (around 2.4 eV), whereas the high-energy peak is the transverse SPR mode. These data are in good agreement with those obtained by recording the absorption spectrum of the nanocrystal film deposited on a glass slide with one peak centered at 2.7 eV under s-polarization and two peaks at 2.78 and 3.5 eV under p-polarization (insert Fig. 8.15). These data are also in good agreement with the simulated absorption spectrum under s- and p-polarization of the same silver nanocrystals organized in a hexagonal network.

8.2.2.4 STM-Induced Photon Emission [3] STM-induced photon emission experiments were conducted on silver nanocrystals self-organized in a 2D superlattice on an atomically flat (111) gold surface. A light collection optic was adapted inside the UHV STM. Photon maps were acquired simultaneously with topographic maps, and the STM was operated in a constant-current mode. The topographic STM image of a silver nanocrystal monolayer acquired at 0.8-nA tunnel current and 2.3 V shows a hexagonal arrangement of nanocrystals. In Fig. 8.16, the topography (Fig. 8.16 A and B) and the photon map (Fig. 8.16 C and D) are recorded simultaneously. The same area is recorded at two different biases: VT = 2.1 V (Fig. 8.16 C) and VT = 2.5 V (Fig. 8.16 D). In both cases, the tunnel current is constant at IT = 3.5 nA. Even though the topography is quite the same, save for slight drift on the right, the photon maps exhibit a drastic change in the photon emission efficiency. At lower bias (Fig. 8.16 C) the light emission is below the detection limit when the tip is located above the top of the

8.2 Results and Discussion

Fig. 8.16 Simultaneously recorded STM topography (A, B) and photon map (C, D). Graphs (E) and (F) present a topography cross section which goes through the summit of the nanocrystal and junction between nanocrystals alternately following the dotted line in (A) and (B). The biases are VT = 2.1 V (A, C, D) and VT = 2.5 V (B, D, F) with the same IT = 3.5 nA.

nanocrystals, and appears gradually when the tip is moved toward the side. A maximum of emission is reached between the nanocrystals (Fig. 8.16 E). Conversely, when the bias is 2.5 V (Fig. 8.16 D), the maximum of photon emission is detected on the top of the nanocrystal. The emission decreases progressively when the tip is moved toward the side. The junction between nanocrystals is now the minimum of emission (Fig. 8.16 F). One can notice, however, that the emission rate measured at this minimum at 2.5 V is still as large as that measured at the same location at 2.1 V, where it is a maximum of emission. Since both set-point current and bias voltage are kept constant during the scan, variations in photon emission rate reflect changes in the quantum efficiency of photon emission through inelastic electron tunneling. These differences observed at various biases can be explained in terms of the nature of the plasmon modes excited [36]. The lowest bias (2.1 V) is similar to the lowest energy-couple mode involving the unperturbed modes polarized along the axis formed by the center of the nanocrystals oscillating in phase. The maximum field amplitude is in the region between the nanocrystals. At larger biases, the increase in the emission rate over the top of the nanocrystals is explained by excitation of the plasmon modes with vertically polarized electric fields. Then a minimum of emission rate between nanocrystals indicates a reduced electric field between the nanocrystals. These data clearly show the effects of local geometry on the photon emission process, with the appearance

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of a coupled plasmon mode of the hexagonal network of silver nanocrystals as a function of the excitation energy. The understanding of the collective excitations in such a system lead to a control of field distribution and finally of the optical and photophysical properties.

8.3 Conclusion

We first demonstrate that self-organization of silver nanocrystals in a compact hexagonal network induces collective properties with the appearance of coupled plasmon modes due to induced dipole–dipole interactions. Furthermore, the strength of the network produced with formation of fcc “supra” crystals induces vibrational coherence, which is an intrinsic property of self-organization. A local polarization electric-field effect is also observed.

Acknowledgments

The authors wish to thank their coworkers, Drs. M. Maillard, C. Petit, N. Pinna, V. Russier and A. Taleb, for their strong participation in this difficult project. Thanks are also due to Dr. F. Charra. References 1 M. P. Pileni, J. Phys. Chem., 2001, 105, 3358. 2 L. Motte, F. Billoudet, M. P. Pileni, J. Phys. Chem., 1995, 99, 16425. 3 M. Brust, D. Bethell, D. J. Schiffrin, C. Kiely, Adv. Mater., 1995, 9, 797. 4 S. A. Harfenist, Z. L. Wang, M. M. Alvarez, I. Vezmar, R. L. Whetten, J. Phys. Chem., 1996, 100, 13904. 5 L. Motte, F. Billoudet, E. Lacaze, J. Douin, M. P. Pileni, J. Phys. Chem. B 1997, 101, 138. 6 A. Courty, C. Fermon, M. P. Pileni, Adv. Mater., 2003, 13, 58. 7 I. Lisiecki, P. A. Albouy, M. P. Pileni, Adv. Mater. 2003, 15, 712. 8 M. P.Pileni, J. Phys. Chem., 1993, 97, 6961. 9 A. Taleb, C. Petit, M. P. Pileni, J. Phys. Chem. B, 1998, 102, 2214. 10 J. Peter Toennies, Optical Properties of Metal Clusters, U. Kreibig, M. Vollmer

11 12 13

14 15

16 17 18

19

(eds.), Series in Material Science, Vol. 25, Springer-Verlag, Berlin, 1993. B. N. J. Persson, Surf. Sci., 1993, 281, 153. P. Mulvaney, Langmuir, 1996, 12, 788. M. D. Malinsky, K. L. Kelly, G. C. Schatz, R. P. Van Duyne, J. Am. Chem. Soc., 2001, 123, 1471. A. L. Aden, M. J. Kerker, J. Appl. Phys., 1951, 22, 1242. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles,Wiley-Interscience, New York, 1983. A. Courty, I. Lisiecki, M P. Pileni, J. Chem. Phys., 2002, 116, 8074. J. Urban, H. Sack-Kongehl, K. Weiss, Z. Phys. D, 1993, 28, 247. M. José Yacaman, J. A. Ascencio, H. B Liu, J. Gardea-Torresdey, J. Vac. Sci. Technol. B, 2001, 19, 4. A. Courty, C. Fermon, M. P. Pileni, Adv. Mater., 2001, 13, 254.

References 20 A. Courty, O. Araspin , C. Fermon, M. P. Pileni, Langmuir, 2001, 17, 1372. 21 A. Courty, A. Mermet, P. A. Albouy, E. Duval, M. P. Pileni, in press. 22 Lamb, J. Proc. London Math. Soc., 1882, 13, 187. 23 B. Palpant, H. Portales, L. Saviot, J. Lermé, B. Prével, M. Pellarin, E. Duval, A. Perez, M. Broyer, Phys. Rev. B, 1999, 60, 17107. 24 H. Portales, L. Saviot, E. Duval, M. Fujii, S. Hayashi, N. Del Fatti, F. Vallée, J. Chem. Phys., 2001, 115, 3444. 25 E. Duval, H. Portales, L. Saviot, M. Fujii, K. Sumitomo, S. Hayashi, Phys. Rev. B, 2001, 63, 075405. 26 A. Taleb,V. Russier, A. Courty, M. P. Pileni, Phys. Rev. B, 1999, 59, 13350. 27 J. M.Gerardy, M. Ausloos, Phys. Rev. B 1982, 25, 4204. 28 R. Lazzari, I. Simonsen, J. Jupille, Europhys. Lett., 2003, 61, 541.

29 C. Beitia,Y. Borensztein, R. Lazzari, J. Nieto, R.G. Barrera, Phys. Rev. B, 1999, 60, 8, 6018. 30 R. Lazzari, S. Roux, I. Simonsen, J. Jupille, D. Bedeaux, J. Vlieger, Phys. Rev. B, 2002, 65, 235424. 31 N. Pinna, M. Maillard, A. Courty, V. Russier, M. P. Pileni, Phys. Rev. B, 2002, 66, 45415. 32 F. Abeles, Ann. Phys. (Paris), 1950, 5, 596. 33 J. Lekner, Theory of Reflection, Martinus Nijhoff, Dordrecht, 1987. 34 R. G. Barrera, M del Castillo-Mussot„ G. Monsivais, P. Villasenor, W. L. Mochan, Phys. Rev. B, 1991, 43, 12819. 35 M. Maillard, P. Montchicourt, M. P. Pileni, Chem. Phys. Lett., 2003, 107, 7492. 36 F. Silly, A. O. Gusev , A. Taleb, F. Charra, M. P. Pileni, Phys. Rev. Lett., 2000, 84, 5840.

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9 Scanning Tunneling Luminescence from Metal Nanoparticles Fabrice Charra

9.1 Introduction

The photonics properties of dense metal nanostructures are currently under intense investigation, from the viewpoints of both the mechanisms of elementary electronic and photonic processes and of possible applications. These properties are dominated by two phenomena: – the localization by noble-metal nanostructures of the so-called plasmon modes; – the transfer of energy between electrons and electromagnetic fields which produces luminescence. Plasmon modes are eigenmodes of the electromagnetic fields combined with collective electron oscillations. In the close vicinity of noble-metal nanostructures, such as nanoparticles, plasmon modes present local field enhancements by several orders of magnitude compared to a plane wave at the same frequency. A wellknown consequence is the appearance of increased optical absorptions forming peaks in the absorption spectra at plasmon resonance frequencies, which was first studied by Faraday in the nineteenth century [1]. The amplification role played by localization of plasmon-mode electromagnetic fields is now clearly established in many other photonic phenomena such as surface-enhanced Raman scattering (SERS) at rough noble-metal surfaces [2], inelastic fast-electron scattering by clusters of metal nanoparticles [3], amplification of nonlinear optical properties [4] or anomalously high light transmission through subwavelength apertures in noblemetal films [5]. The particular electronic properties of noble metals, specifically their high electron mobility, are at the origin of important luminescence phenomena. These are also further amplified by the increased electron coupling with local electromagnetic fields of plasmon modes, through a variant of the Purcell effect [6]. For instance, photoluminescence has been observed on gold island films with increased efficiency compared to bulk Au and with spectral changes reflecting intrinsic modification of gold film emission processes [7]. Light emission from a single Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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gold cluster [8], as well as a film of silver clusters linked by electron tunneling and excited electrically, have been observed and interpreted in terms of electron-gas heating [9]. Efficient electroluminescence from metal–oxide–metal devices involving one tunnel junction with rough interfaces has been observed and attributed to plasmon-mode-assisted inelastic electron tunneling [10]. Indirectly, silver nanoparticles can also increase the photoluminescence yields, for example in semiconductor quantum dots [11, 12]. Hence, dense assemblies of metal nanoparticles present numerous complex photonic processes resulting in extraordinary behaviors. The scanning tunneling microscope (STM) permits a well-controlled electrical addressing of a single nanoparticle out of a dense assembly deposited on a conductive atomically flat surface. This nanoscale tunnel junction constitutes a very interesting model system for gaining insights into the elementary electronic mechanisms [13]. It can also behave as a highly localized source of electromagnetic radiation at a frequency up to the quantum limit oC = e |VBIAS|/k, where VBIAS is the sample bias. For biases of ~1 V and above, this source has frequencies up to the optical domain, and can thus probe electronic and photonic properties with unparalleled spatial resolution. After its first observation with relatively high quantum efficiencies [14] scanning tunneling luminescence (STL) was shown to be suitable for imaging with molecular-scale resolution [15]. The possibility of achieving a chemical contrast through this technique has been demonstrated for carbon clusters on silicon [16] and tipinduced surface chemical modifications [17]. Despite the weakness of the emission, generally detected using photon-counting techniques, the optical nature of the detection permitted local spectroscopic studies of rough metal surfaces [18, 19] or single silver clusters [20].

9.2 Mechanisms of Scanning Tunneling Luminescence

In a classical framework, the sources of electromagnetic fields at frequency o are the spatial distribution of current density vector j (o, M) and charge density r (o, M) at point M. The electromagnetic fields radiated by j (o, M) can be determined through Maxwell equations; from the calculated electric field E (o, M) the rate of energy loss is: dW ˆ dt

Z 2Re

E  jd3 M

This expression is equivalent to the full quantum treatment of an optical transition which involves transition currents between quantum states (or transition dipoles for localized electron states) in place of the classical currents j (o, M) (or classical AC dipole moments). Then, the efficiency of radiation by a given source distribution will depend on the electromagnetic response and the geometry of the environment, often modeled as a local response described through a spatially vary-

9.2 Mechanisms of Scanning Tunneling Luminescence

ing dielectric constant e (o, M). In particular, the existence of electromagnetic eigenmodes at frequency o localized on sources, such as localized plasmon modes, will strongly enhance the efficiency of the emission [21]. Light emission from the junction of the STM thus depends both on local electronic properties through the source term j (o, M), which can be as localized as the DC tunnel current, and on local electromagnetic properties through the field E (o, M) at the location of the tunnel current. Schematically, compared with scanning near-field optical microscopy, which consists of a probe of local optical properties through a fixed secondary subwavelength optical source, in STL additional contrast contributions arise from variations of the source itself, which reflect local electronic properties. Hence, the first issue in interpretation of STL spectra or spatial contrasts is to discriminate between these two influences. In what follows we discuss how each term can reflect particular properties of the sample, in order to answer the question “what can one learn from STL?” 9.2.1 Electromagnetic-Field-Assisted Inelastic Tunneling

Two main mechanisms can be involved as the origin of the source term j (o, M) in STL, as sketched in Fig. 9.1. In one scheme, an electron tunnels inelastically from a filled state of the tip towards an empty state of the sample at lower energy, the excess energy being transferred simultaneously to an eigenmode of the electromagnetic field (see Fig. 9.1 a). The other scheme is a two-step process in which an elastic tunnel process generates an excited electron in the sample which subsequently recombines radiatively (see Fig. 9.1 b). The latter mechanism dominates in semiconductor samples, where the bandgap restricts inelastic tunneling to very few available hole states. In this case, the coherence may be lost between tunneling and radiative relaxation processes and the latter may occur at a variable time after tunneling and at a variable distance from the junction. Yet, if both tip and

Fig. 9.1 Energy scheme of the two possible mechanisms for luminescence in an STM junction: (a) one-step emission through inelastic tunneling from initial state i to final state f; (b) two-step emission from elastic tunneling followed by radiative relaxation of excited electron.

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sample are metallic, the case that we consider in the following, then rough estimations show that inelastic tunneling constitutes the most effective contribution to j (o, M) [22]. The localized DC tunnel current in a STM arises from the interaction between the evanescent wave functions of filled initial tip electronic state i with energy Ei and empty final sample state f at the same energy. However, each tip state interacts also with sample states at energies Ef different from Ei , giving rise to AC currents at frequency o = (Ei – Ef )/k as sketched in Fig. 9.1a. From a fully quantum point of view, the excitation of electromagnetic modes by these currents is analogous to a spontaneous emission process associated with transitions from i to f. The spectrum of j (o, M) is a function of the local densities of contributing i- and f-state energies and of the tunneling matrix element Tif between them in the tunneling Hamiltonian formalism [23]. If both density of states and matrix elements can be approximated as constants over the entire energy range thus defined, the spectrum is determined by the number of (i, f ) couples verifying o = (Ei – Ef )/k for each given frequency o, which is proportional to the difference VBIAS – (Ei – Ef ). Hence, the spectrum vanishes at the cutoff frequency oC = e |VBIAS|/k and increases regularly for decreasing frequencies. The lower limit is merely given by the detector. A deviation from this standard behavior can arise from a structured density of states, which may favor elastic tunneling paths compared to inelastic ones, or vice versa. For example, a spatial contrast in photon-emission yields can reflect specifically the wave functions of particular states, like surface states, involved either in elastic or inelastic tunneling. Similarly, spatial extensions of electron states of adatoms or of adsorbed molecules are able to change the branching ratio between elastic and inelastic processes. Finally, for nanostructured systems, charging effects can also influence j (o, M) by reducing locally the effective junction bias; STL constitutes then an optical probe of electrostatic potentials. 9.2.2 Local Plasmon Modes

As discussed above, the emission of photons also requires an efficient coupling of the source term j (o, M) with the electric field of the excited mode. For optical 1 modes localized in a volume V, the local field amplitude scales as V 2 . Since the tunnel current is localized in a volume much smaller than that of the optical mode, the rate of energy transfer scales as V–1 [22]. On metal surfaces, the tip itself strongly favors light emission efficiency through the formation of a tip-induced plasmon mode (also called “gap-mode”p [23]), highly localized at the tip–surface junction [24]. Its lateral extension is dR where d is the tip–sample distance and R the tip curvature [25], so that the confinement volume is V = d2R. In the example of a spherical tip apex and flat sample made of the same metal, the resonance frequencies o of these modes are implicitly given by the relation  r l 1 1 d = l‡ which involves the frequency-dependent dielectric cone …ol 2 2R stant of the metal e (o) and an integer mode index l = 0, 1, … For a metal described

9.3 Experimental Details

by a Drude model with plasmon frequency oP and in the case d << R, this equas   r 1 d tion gives explicitly: ol & oP . A better understanding of the natl‡ 2 2R ure of these modes can be gained by considering the coupled plasmon modes of two metal spheres [26]. The lowest-frequency l = 0 mode corresponds, by continuity when increasing d, to the coupled mode formed by combination of the two single-sphere dipolar modes oscillating in-phase along their common axis, as will be detailed later (see Fig. 9.8 below). When d is reduced down to d << R, it is shown that higher-order single-sphere modes become increasingly involved in order to form highly localized oscillations at the junction of the sphere, which then corresponds to a gap mode. Once a local mode is excited, the probability of detecting a photon in the far field is controlled by the balance between the far-field radiation rate of this mode and electromagnetic losses in the tip and sample materials. In the local-response model, these losses are described by the imaginary part of the dielectric constant. The gap mode of lowest frequency (l = 0) has the largest rate of radiation in the far field and is thus less affected by losses. Hence, it is usually the most effective path for photon generation in STL. In summary, the local geometry of the junction, together with electromagnetic parameters [Re (e (o, M))], control the rate of energy transfer from the tunneling electrons to electromagnetic fields, through the localization of the first (l = 0) gap mode. Then, electromagnetic losses, Im (e (o, M)), determine the ratio of gapmode excitations radiated in the far field. 9.3 Experimental Details

Because of low quantum yields and tunnel currents, the maximum rate of photon emission is usually of the order of a few 105 emitted photons per second. Hence, the main experimental difficulty is the high efficiency required both for collection and detection. In all the experiments reported below, a light collection optics has been adapted inside a UHV STM (Omicron, base pressure ~10–8 Pa). It consists of an f/0.6 lens corrected for spherical aberration. The detection axis was close to the grazing incidence, at about 758 from the surface normal. Accounting for the sample shadow, the detection solid angle was about 0.35 sr, with incidences between 908 (grazing incidence) and 358 from the surface normal. The emitted light was focused through a view port onto an avalanche photodiode (EGG, SPCM-AQ-15), operating in a photoncounting mode. The detector dark noise was 35 counts per second (cps), and it was sensitive in the optical wavelength range from 400 to 1000 nm. The extended infrared sensitivity of this detector compared with a photomultiplier permits the study of photoemission with lower biases, which is safer for the stability of surface quality. Photon maps were acquired simultaneously with topographic maps by recording photon counts at each pixel for a fixed acquisition time. The STM operated in a constant-current mode. Since the bias is also constant, photon counts map di-

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rectly the quantum efficiency of photon emission per tunnel electron. Defects in the regulation of the tunnel current to its set point, notably through a too-low response time of the feedback loop compared with scan speed, would cause instrumental artifacts in photon maps. To ensure that the regulation was well adapted, we systematically recorded photon counts acquired for both fast-scan directions, and checked that both photon maps were identical. Electrochemically formed Au tips were used, which were then cleaned and further sharpened in situ by electron bombardment, producing typical radii of no more than a few nanometers. Gold (111) substrates were formed on mica following a known procedure [27]. After epitaxial growth of the 100-nm-thick gold film on freshly cleaved mica plates, the substrates were submitted to argon-ion bombardment followed by annealing. This procedure yielded typically 200-nm-wide atomically flat terraces, as observed by STM. Despite the poor imaging capability of gold tips, we chose this noble metal both for tip and substrate because of its very low optical losses in the red to infrared optical range, of interest here, which ensures the highest photon emission rates.

9.4 Tip-Formed Protrusions

When voltage pulses are applied to an STM junction, atoms can be released from the tip and deposited on the surface. This process is especially effective when gold tips are used and can be exploited in the more or less controlled formation of nanoscale bumps on the surface. This has been demonstrated for the formation of regular lattices of gold bumps on a gold (111) substrate [28]. This offers the opportunity to study the STM-induced photon emission properties of such individual tip-formed protrusions. Gold bumps were formed highly reproducibly by application of 4-V, 100-µs bias pulses. Their height was ~1.0 nm whereas their width was ~10 nm. The STM images of one such bump and of the original surface are reproduced in Fig. 9.2. Contrary to the flat surface, no step structure is apparent on the bump surface, which indicates a low degree of crystallinity. The STL photon map

(a)

(b)

Fig. 9.2 (a) STM height-mode image of the Au(111) surface made with a gold tip, before application of a bias pulse; 100650 nm, IT = 1 nA,VT = 0.2 V. (b) The same image after application of a 4-V 100-µs bias pulse; a gold bump is formed of width 30 nm and height 4 nm. (c) Scanning tunneling luminescence map acquired with a set point IT = 1 nA and a bias VT = 1.5 V. The photon-rate color palette ranges from zero (black) to 2500 cps (white) [29].

(c)

9.4 Tip-Formed Protrusions

acquired with a set point IT = 1 nA and a bias VT = 1.5 V reveals strong variations in luminescence quantum yields above the bump and in its vicinity. Superimposed sectional views of topography and photon maps are presented in Fig. 9.3, for different values of the bias. In all photon map profiles, the photon yields are nearly constant on the flat surface, except in an area located within ~10 nm from the bump external limits, where the yield systematically decreases. This effect is especially visible for the largest biases where an angular point is clearly visible at the minimum of the photon rate. Accounting for the convolution with tip shape, topography profiles show that the minimum of photon emission corresponds to the sudden change of the location of the tunnel current, from the surface to the bump. Another clear feature of photon-emission profiles is an increase in efficiency near the maximum of the bump. This increase amounts to ~50 % of the flat terrace uniform emission, nearly independently of the bias. Since the terrace and the bump are made of gold, the source term j (o, M) and the local dielectric constants e (o, M) can be considered as uniform. Hence, the origin of the observed contrasts in STL can only be ascribed to changes in the geo-

Fig. 9.3 Cross sections of topography (lower curves with gray area) and profiles of photon emission yields (upper curves) acquired simultaneously for a scan line crossing the middle of a tip-generated gold bump. The set point is IT = 1 nA and the bias is: (a) VT = 1.9 V, (b) VT = 1.7 V, (c) VT = 1.5 V and (d) VT = 1.3 V. The dark-noise level of the photon detector is ~50 cps [29].

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metry of the junction, which influences the extension of the plasmon mode. The change in photon rate observed when the tip approaches the bump while the topographic profile is still flat shows that the photon-emission process “feels” the presence of the bump at a larger distance than electron tunneling. This proves that the spatial extension of the plasmon mode is much larger that that of the tunnel current. The decrease can be explained by an extension of the plasmon mode towards the bump where the tip–sample distance is reduced. As explained above, such an extension of the plasmon volume decreases the electron–plasmon coupling. This interpretation is further confirmed by the observation that the slope is reversed precisely at the point where the current flips towards the bump. Similarly, when the tip apex is located on top of the bump, the plasmon mode is better localized which significantly increases this coupling.

9.5 Colloidal Silver Nanoparticles

Nanochemistry permits the fabrication of nearly perfect nanosized metal spheres. Such nanoparticles self-assemble into hexagonal monolayers identically replicated with a long-range order [30, 31]. Such structures provide well-suited model systems to explore the original optical and electronic properties emerging at the nanometer scale and are especially well adapted to STL. Silver nanoparticles were synthesized following the procedure described in detail in Ref. [30]: water-solution droplets in hexane were stabilized by a monolayer of bis(2-ethylhexyl) sulfosuccinate (AOT) as a surfactant, forming so-called reverse micelles [31]. Two solutions with the same molar ratio W = [H2O]/[AOT] = 40, corresponding to 12-nm micelles [32], were mixed. One contained 30 % Ag(AOT) and 70 % Na(AOT) and the other was made with hydrazine, N2H4, as a reducing agent with an overall concentration of 7610–2 M. Silver particles (3.4 nm) were formed with a rather large size distribution (43 %). Dodecanethiol was then added (1 µl ml–1) and formed a monolayer at the Ag particle surface. Surfactant was removed by precipitation in ethanol. Repeated size-selective precipitation processes followed by centrifugation, as described in ref. [30], yielded a homogeneous clear hexane colloidal solution of 4-nm dodecanethiol-coated silver nanoparticles with a size distribution as low as 13 %. Size dispersity and self-assembling ability were controlled by transmission electron microscopy (TEM) [33]. The particles were then deposited on Au(111) substrates by applying one droplet of solution, and immediately reintroducing the sample into the UHV. A quantitative Auger-electron spectrum analysis confirmed that only Ag, C and S chemical elements were present on the treated surface with an S/C ratio corresponding to that of dodecanethiol.

9.5 Colloidal Silver Nanoparticles

9.5.1 Single-Particle Contact by STM

Two topographic STM images of a silver nanosphere monolayer acquired at a tunnel current IT = 0.8 nA and a bias of VT = 2.5 V are shown in Fig. 9.4. The hexagonal arrangement and the size homogeneity of the particles are visible. The lattice constant is 6.1 nm, consistent with the 4.3-nm diameter of spherical particles observed by TEM [33] with an additional 1.8-nm gap formed by the dodecanethiol layer. Although insulating, this gap does not appear directly in the STM image because of the convolution with the spherical tip shape.

(a)

(b)

Fig. 9.4 STM height-mode images of a monolayer of silver nanoparticles self-organized on a gold (111) substrate. Image size: (a) 3006300 nm and (b) 1306130 nm. Both images were acquired with a set point of IT = 0.8 nA and a bias of VT = 2.5 V.

Depending on the colloidal solution concentration, some area of the substrate remains uncovered, permitting one to measure a 5-nm height difference from the substrate to the top of the particles. Hence, the 4.3-nm particles are not in contact with the substrate, but are separated from it by the dodecanethiol chains. Thus, each particle is separated both from its neighbors and from the substrate by a dielectric and electrically insulating layer, which acts as an additional tunnel barrier. Through interaction with the scanning tip, some particles at a domain border can drift across the uncovered area from one domain to the other. This explains the horizontal bands observed in the uncovered areas of Fig. 9.4 a and demonstrates the weak bonding between particles and substrate, and the mechanical stabilization provided by the particle packing. The existence of a second tunnel barrier between particle and substrate is confirmed by comparison of the current versus voltage I (V) characteristics measured while the tip is located above the bare Au(111) substrate and those measured above a silver nanocrystal. The substrate has an almost linear I (V) relationship

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Fig. 9.5 Current–voltage STM junction characteristics measured along the vertical dotted line of the STM image shown in the inset. Dotted curve: averaged characteristics measured on the bare substrate. Solid curve: averaged characteristics measured near the middle of the particle. Both curves were measured for a height Z defined by a set point IT = 1 nA and a bias VT = 1.0 V, while the feedback was switched off. As expected, both curves meet at the set-point current for a voltage equal to the bias.

that becomes slightly superlinear above 1.0 nA (Fig. 9.5, dotted curve). With nanocrystals present, the I (V) relationship is characterized by a highly nonlinear behavior (Fig. 9.5, solid curve). The blocking in the –0.5 to +0.5 V bias range can be attributed to the existence of charging effects. 9.5.2 Collective Plasmon Modes

A close-up on a self-assembled domain is presented in Fig. 9.6. The topography and the photon map were recorded simultaneously. The two topography/luminescence couples were recorded on the same area successively using different biases VT = 2.1 V (left images) and VT = 2.5 V (right images). In both cases, the tunnel current was set to IT = 3.5 nA. The two photon maps exhibit a drastic change in the photon emission efficiency. At the lower bias, photon emission drops below our detection limit (35 cps) when the tip is located above the top of a particle and appears gradually when the tip is moved towards the side. A maximum of emission is reached exactly at the junction between two neighboring particles. In contrast, when a higher bias is applied, the maximum of photon emission is detected on the top of each particle. The emission decreases progressively when the tip is moved towards the side. The junction between particles is now a minimum of emission. One can notice, however, that the emission rate measured at this minimum at VT = 2.5 V is still as large as that measured at the same location at VT = 2.1 V, where it is a maximum of emission; so there is no decrease of emission efficiency with increasing bias. When the tip scans one particle, only the tip–particle junction is changed; since the current flows through the same particle during the scan, the particle–substrate junction is conserved. Hence, the observation of an intraparticle contrast shows

9.5 Colloidal Silver Nanoparticles

Fig. 9.6 STM height-mode images of a monolayer of silver nanoparticles self-organized on a gold (111) substrate (upper images) and corresponding maps of the simultaneously acquired scanning tunneling luminescence (lower images) for two different biases: VT = 2.1 V (left) and VT = 2.5 V (right). The image sizes are 26610 nm and the set point was IT = 3.5 nA. The topography cross sections and corresponding luminescence profiles, taken along the dotted lines, are also presented for easier comparison and in order to show the vertical scales [34].

that the tunnel current responsible for light emission is mainly that taking place between tip and particle. This indicates that the bias is mainly applied to this junction, the second one presenting a less pronounced barrier for electrons, corresponding to a lower resistance. This particular point will be further discussed in Section 9.5.3 below. Obviously, the variations of photon emission rates are correlated with the geometry of the system. Since a systematic correlation between geometry and particle composition is not conceivable, the contrast must be attributed to local plasmon effects. As in the case of tip-formed protrusions (see Section 9.4), the photon maps show that the emission rate is sensitive to the neighboring of the junction at a distance at least of the order of particle size, hence larger than the tunnel current extension. It should be noticed that that the lowest-energy unperturbed plasmon mode of an isolated silver sphere is of 2.9 eV [35], far larger than the excitation biases applied here of up to 2.5 V. We are thus led to consider coupled, or collective, plasmon modes. The full calculation of coupled plasmon modes in a 2D hexagonal network of particles including tip and substrate would require numerical computations. However, some insights can be gained by considering the simple model of the coupled plasmon modes of two spheres brought close together. Figure 9.7 presents the modes derived from the combination of the single-particle dipolar plasmon

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Fig. 9.7 Scheme of the two-particle plasmon modes derived from the two weakly coupled dipole plasmon modes of the single particles.

modes of each isolated particle. This picture is valid for weak coupling, that is, for relatively large distances. An exact calculation has been made for arbitrary interparticle distances in ref. [26]. As already discussed in Section 9.2.2, the lowest-energy mode corresponds to the combination of the two single-sphere dipolar modes oscillating in-phase along their common axis. The maximum field amplitude is in the region between the spheres. The next mode in energy involves the unperturbed modes polarized perpendicularly to the axis, oscillating out-of-phase, and thus forming a node of electric field in the region between the spheres. Although the generalization of this simple model to our complex system is not straightforward, when d is reduced the first mode is increasingly localized at the junction of the sphere, and becomes equivalent to a gap mode. The localization makes such modes more independent from one another, and justifies this model as a rough approximation even for densely-packed particle assemblies. Of course the presence of the tip perturbs this scheme, but its electromagnetic interactions with the sample follow this general trend, and yield increased mode localization when the tip is located above a junction between particles. These considerations explain the contrast observed at lower bias, when only the first low-energy mode is excited. At larger biases, we observe an increase of the emission rate over the top of the spheres, indicating that additional plasmon modes can then be excited. Consistently, the contrast is less pronounced. The maximum of luminescence when the tip is located on top of a particle is then similar to what is observed on tip-formed protrusions (see Section 9.4). Hence, the excited plasmon mode rather corresponds to a more standard gap mode, involving only one particle and the tip. Coupling between particles is thus less important.

9.5 Colloidal Silver Nanoparticles

9.5.3 Individual-Site Dependence of Luminescence

Figure 9.8 shows a large-scale view of the simultaneously recorded STM image and photon map on a gold substrate partially covered with silver nanoparticles. Both covered and uncovered regions emit photons when excited by the biased STM tip. However, the average emission efficiency of the nanocrystal layer (700 cps detected) is almost one order of magnitude lower than that of the bare substrate. This difference in photon emission efficiency can be explained either by the sample morphology or by the difference between optical properties of gold and silver. Surprisingly, another striking difference is the spatial inhomogeneity of photon emission on nanoparticle assemblies, whereas uncovered Au substrate produces quite a uniform photon map. In the uncovered area, lines corresponding to the tip-induced drift of particles (see Section 9.5.1) correspond to black lines in photon maps. This indicates a quenching of luminescence when the particles move from one covered region to the other. In contrast, light emission from the ordered nanocrystal monolayer exhibits large local variations on the scale of the particle network. More precisely, although most particles appear as emission spots on the photon maps, several (about 5 % depending on deposition conditions) correspond to completely dark, nonemissive sites. Hence, nonemitting sites are observed inside the monolayer made of nanocrystals and when particles move from one covered region to another.

(a)

(b)

Fig. 9.8 STM height-mode image of a monolayer of silver nanoparticles self-organized on a gold (111) substrate (a), and map of the simultaneously acquired scanning tunneling luminescence (b). The image size is 2056147 nm. The set point was IT = 1.8 nA and the bias VT = 2.5 V. The photon rate ranged from zero (black) to 3000 cps (white) [36].

Analyses of the STM image and photon map with an increased resolution over an area of 26626 nm comprising a nonemissive particle are presented in Figs. 9.9 and 9.10. The inhomogeneity in the photoemission process can be analyzed. The photon count in the dark area is less than 100 cps, which is close to the dark noise level, whereas the average photon rate in the image is about 1400 cps. It appears clearly in the photon map that the dark area corresponding to a nonemissive parti-

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(a)

(b)

Fig. 9.9 STM height-mode image of a monolayer of silver nanoparticles selforganized on a gold (111) substrate (a), and corresponding map of the simultaneously acquired scanning tunneling luminescence (b). The set point was IT = 1.8 nA and the bias was VT = 2.5 V. The image size is 26624 nm. The photon rate ranged from zero (black) to 1600 cps (white). One specific particle was nonemissive, with a rate below the dark noise level of the photon detector.

(a)

(b)

Fig. 9.10 Effect of the fast-scan direction of the tip on the measured location of the nanoparticles shown in Fig. 9.8. (a) Solid curves correspond to the right-to-left scan and superimposed dotted curves to the reverse motion on the same scan line. Five such typical dual cross sections are represented. Specific particles are labeled 1–7 to correlate with the topography (b). Only the particle in the site of quenched luminescence (label 4, see Fig. 9.8) fluctuates notably, both in position (approx. 1.0 nm) and in apparent size.

9.5 Colloidal Silver Nanoparticles

cle exhibits abrupt limits that strictly coincide with the contour of the sphere. This means that photon emission is quenched rigorously when the tunnel-current path involves this specific nanocrystal, independently of the exact location of the tip on the particle. Analysis of the two scan directions reported in Fig. 9.10 reveals specific behavior during the forward and backward scans. Superposition of these two images shows that only one particle position has a significant fluctuation amplitude of about 9 Å. This is clearly seen by recording different sections in the region around the particles labeled 1 to 7 in the STM topography given in Fig. 9.10. Comparison of the two fast-scan directions reveals a larger mobility of the nonemissive nanocrystal under the influence of the tip interaction. In contrast, the neighboring nanocrystals remain strongly anchored in their sites. This correlation between singleparticle luminescence quenching and the particle mobility has been confirmed for various examples and situations; further examples can be found in Section 9.5.4 below, where this property is exploited to control the luminescence through action of the tip. Several particles with similar geometrical parameters exhibit normal photon emission efficiencies. This shows that the extinction of the luminescence cannot be explained by a plasmon effect, like in previous examples. Here, similar geometrical and material environments result in highly dissimilar photon emission yields. We are thus led to consider possible variations of the source j (o, M) itself. As already mentioned in Section 9.5.2, this source is normally located at the tip– particle junction, whereas the extinction of luminescence appears abruptly when the current flow switches to a specific particle and thus seems linked with the underlying junction, between particle and substrate. This effect can thus be explained by a less efficient electrical contact between particle and substrate. As a matter of fact, an increased tunnel barrier between particle and substrate results in an increased voltage difference, VSUBSTRATE – VPARTICLE , at the corresponding junction and a decreased voltage drop,VPARTICLE __ VTIP , between tip and particle, since VT = VSUBSTRATE – VTIP . The available excess energy of the tunneling process at the tip–particle junction could then become insufficient for plasmon excitation, if e (VSUBSTRATE – VTIP) < koP . The increased mobility, which means a weaker interaction with substrate, is consistent with a weaker electrical contact. However, the situation is more complicated if we consider that the average particle size is smaller than the electron mean free path in bulk silver [37], which opens the possibility of a direct tip-to-substrate tunnel transition in one single step. Then the relaxation of the ballistic electron inside the particles would be a condition for the quenching of the photon emission. The coupling of a hot electron with surface-phonon modes and its role in the excitation relaxation in metal nanoparticles has been emphasized by ultrafast excitation-probe experiments [38, 39]. Particles that exhibit pronounced mobility are able to develop localized phonon modes, which could efficiently interact with ballistic electrons as well as hot electrons. Hence, loose particle anchorage could favor relaxation of the energy of tunneling electrons in the intermediate media (the particle), thus making the nonemissive two-step tunneling process more probable.

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9.5.4 Tip-Modified Luminescence

Despite the good ordering in a hexagonal network, we have seen that the quantum efficiencies of STM-induced luminescence of single nanoparticles appear highly dependent on the environment and thus on the adsorption site. We have noticed also that the mechanical interaction with the tip itself is able to induce a motion of single particles. Actually, manipulation and control of the nanoparticle assembly at the single-particle scale can be realized through direct mechanical interactions with the sharp STM tip. Such interactions increase on increasing the tunnelcurrent set point. A value of ~5 nA, for a bias of 2.5 V, which corresponds to a gap resistance of 470 MO, is sufficient to systematically provoke the removing of particles from the borders of self-assembled domains [40]. These observations suggest an opportunity for tuning single-particle luminescence by changing the particle location or environment through manipulation with the tip. A fortuitous observation of such an effect is reported in Fig. 9.11. The topography profiles and photon emission measured at different times on a given scan line that crosses a “dark” particle (site labeled 3) are plotted. Again, a clear correlation between emission quenching and nanocrystal particle mobility is observed on the first profiles (Fig. 9.11 a and d) where both scan directions are superimposed. This observation is identical to the case reported in Section 9.5.3 above. Yet here, the suc(a)

(b)

(c)

(d)

(e)

(f )

Fig. 9.11 Cross sections of topography (d, e, f) and profiles of photon emission rates (a–c) acquired simultaneously for the same scan line over a nanoparticle row (labelled 1–5) in a self-assembled monolayer at time intervals of 20 s. The reverse motion on the same scan line is superimposed as a dotted curve, as in Fig. 9.10. The set point was IT = 1.8 nA and the bias was VT = 2.5 V. The particle labelled 3 is both nonluminescent (a) and more mobile than its neighbors (d), like reported in Fig. 9.8. After scanning for 20 s this particle is removed, leaving a vacancy where the luminescence is restored (b, e). Then the site becomes occupied again and the luminescence disappears (c, f ) [29].

9.5 Colloidal Silver Nanoparticles

cessive scans show that the dark particle exhibits not only a mobility inside its site, but also a vertical mobility, that is, from the inside to the outside of the network. This tip-induced particle motion either restores the luminescence when the particle is removed or reversibly suppresses again the luminescence when a particle is inserted back into the vacant site. The particle present in the site labeled 3 in the lefthand plots is not necessarily the same as that observed 40 seconds later in this site. Control of particle removal by the tip is relatively easy by increasing the current set point. However, replacing deterministically a particle in that site is much more difficult, and was merely a random process in this example. We describe below a situation in which both onset and offset of the luminescence may be controlled. In Fig. 9.12, we report the combined topography and luminescence cross sections in the providential situation where a dark particle (site B) was bound to a vacant site (site A). Hence, when the scan axis crossed both sites and the current set point was increased to 5.3 nA, the particle could be pushed from one site to the other reversibly, depending on the direction scanned by the tip. As a consequence of a displacement towards site A, the luminescence of the particle was switched on, whereas it was nearly completely switched off again by moving the particle back to site B. The reproducibility of the result was checked by ten successive reversals between sites A and B spaced out by 0.656 s. Contrary to the case reported

(a)

(b)

(c)

(d)

Fig. 9.12 Cross section of STM height-mode topography and corresponding photon emission profile during three successive particle manipulations. The sample bias was VT = 2.5 V and set point was IT = 5.3 nA. One particle was alternately shifted through action of the STM tip between the luminescent site labelled A (light-gray area in (a) and (c)) and site labelled B (black area in (b) and (d)) where the light emission was quenched. The process was repeated reversibly several times [40].

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above (see Fig. 9.11), it is clear here that the same molecule is moved from one site to the other. This shows that the quenching of the luminescence is a property of a site and not of an individual particle itself. The controlled manipulation of an individual particle first requires a stabilization of its position on the substrate against thermal agitation. For isolated small adsorbates this is achieved by lowering the temperature. In a densely packed adsorbed monolayer, the interaction of each adsorbate with its nearest neighbors stabilizes its position so that the whole system appears stable even at room temperature. This interaction is repulsive at very short distances due to steric hindrance, but may be attractive at intermediate distances through Van der Waals forces. This attractive contribution is responsible for the formation of self-assembled close-packed islands in incomplete monolayers, as we observed, for example, in Fig. 9.4 above. The organically coated 4-nm gold nanoparticles experience a stabilization energy due to the interpenetration of several aliphatic chains, which is large enough compared with thermal energy to ensure a long-term stability of particles inside a site. A minimum energy is then required to break such links in order to move a particle to another site, thus forming a bistable system. One can notice that the delay in particle removal systematically observed for a motion from site A to site B does not appear for the reverse manipulation, that is, from site B to site A. Hence, the particle appears more efficiently tied to its neighbors in the “luminescent” site A than in the “dark” site B. This confirms again the correlation between particle mobility and STM luminescence efficiency. This nanoscale “flip-flop” device constitutes a luminescence switch, based on the combination of the ability of single-particle manipulation and a site-dependence of single-particle luminescence.

9.6 Conclusion

Scanning tunneling luminescence permits excitation of the luminescence of one individual metal nanoparticle out of a densely packed assembly in an adsorbed monolayer. Intraparticle features could even be observed, corresponding to resolutions of the order of 1 nm. In this process, the STM tip is used simultaneously as a tunnel-current probe to map the topography of the studied sample and as a highly localized excitation source generating luminescence. A third possible simultaneous action of the tip is the modification of the surface. We have illustrated this possibility here for the reversible reorganization of a self-assembled nanoparticle monolayer. The simultaneous influence of such tip-induced effects on both nanoscale topography and locally excited luminescence gives very valuable information on the fundamental photonic processes taking place at the nanometric scale. As compared to other surface characterization techniques, optical detection coupled to STM offers a very powerful local diagnostic tool through the possibility of various optical spectroscopies.

References

The next challenges comprise the excitation of individual quantum objects, such as semiconductor quantum dots or conjugated molecules, thus forming highly correlated nanoscale light sources, and the exploitation of the opportunities offered by optical detection in the study of phenomena like Coulomb blockades. The recent developments in time-resolved STL [41, 42] may offer very exciting new perspectives in both domains. References 1 M. Faraday, Experimental relations of gold (and other metals) to light, Phil.Trans. R. Soc. 147, 145, 1857. 2 M. Moskovits, Surface-enhanced spectroscopy, Rev. Mod. Phys. 57, 783, 1985. 3 P. E. Batson, A new surface plasmon resonance in clusters of small aluminum spheres, Ultramicroscopy 9, 277, 1982. 4 F. Hache, D. Ricard, C. Flytzanis, Optical nonlinearities of small metal nanoparticles: surface-mediated resonance and quantum size effects, J. Opt. Soc. Am. B3, 1647, 1986. 5 T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, Extraordinary optical transmission through subwavelength hole arrays, Nature 391, 667, 1998. 6 E. M. Purcell, Spontaneous emission probabilities at radio frequencies, Phys. Rev. 69, 681, 1946. 7 L. Khriachtcheva, L. Heikkila, T. Kuusela, Red photoluminescence of gold island films, Appl. Phys. Lett. 78, 1994, 2001. 8 J.I. Gonzalez,T.-H. Lee, M. D. Barnes, Y. Antoku, R. M. Dickson, Quantum mechanical single-gold-nanocluster electroluminescent light source at room temperature, Phys. Rev. Lett. 93, 147402, 2004. 9 S. A. Nepijko, R. D. Fedorovich, L. V. Viduta, D. N. Ievlev,W. Schulze, Light emission from Ag cluster films excited by conduction current, Ann. Phys. 9, 125, 2000. 10 J. Lambe, S. L. McCarthy, Light emission from inelastic electron tunneling, Phys. Rev. Lett. 37, 923, 1976.

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10 Collective Magnetic Properties of Organizations of Magnetic Nanocrystals Christophe Petit, Laurence Motte, Anh-Tu Ngo, Isabelle Lisiecki, and Marie-Paule Pileni

10.1 Introduction

The emergence of new methods and concepts for the organization of nanoparticles has rapidly induced great hope in the world of magnetism. In fact, the organization of nanoscale ferromagnetic particles opens a new field of technologies through the controlled fabrication of mesoscopic materials with unique magnetic properties [1]. In particular, these ferromagnetic nanoparticles are potential candidates for magnetic storage [2], where the idea is that each ferromagnetic particle corresponds to one bit of information [3]. Thin granular films of ferromagnetic particles formed by sputtering deposition are already the basis of conventional rigid magnetic-storage media. However, there are several problems remaining to be solved before their application to the storage industry becomes feasible. Devices based on magnetic nanocrystals are limited by thermal fluctuations of the magnetization: due to their reduced sizes, ferromagnetic nanocrystals become superparamagnetic at room temperature. The dipolar magnetic interaction between nanocrystals ordered in arrays is also an important limiting factor for their use in magnetic-storage media. A detailed understanding of the magnetic properties of assemblies of nanocrystals is therefore essential to the development of magnetic recording technology. Organized arrays of magnetic nanoparticles have been obtained for various metallic (Fe [4], Co [5–12]), ferrite (g-Fe2O3 [13, 14], Fe3O4 [15, 16], MFe2O4 (M=Fe, Co,Mn) [17, 18]) and alloy (AgCo [19, 20], CoPt [21–24], FePt [25–30]) nanomaterials. The most common organizations are the hexagonal network in 2D [4–11, 13–21, 24–26, 29–31] and the fcc packing in 3D [12, 22, 23, 27, 28]. These organizations are usually obtained by evaporation of a solution containing a low size distribution of magnetic nanocrystals on a substrate or by using the Langmuir–Blodgett technique (see Chapter 1). Strong magnetic dipolar interactions between nanoparticles induce their organization in 2D chains and rings [32]. For weak dipolar interactions, 1D chains, 3D cylinders, dots and labyrinths are obtained by applying a magnetic field during the deposition process (see Chapter 1). Collective magnetic Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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properties were reported. However there are still points, which are not clear in the magnetic properties of such particles, as to whether they are dispersed in the solvent or assembled in 2D and 3D mesostructures. One must distinguish the properties depending on the atomic-scale structure from those involving the interaction between the nanocrystals. On the other hand, the effect of the structure of the film on the collective magnetic properties has not been investigated. Especially, in the case of mesoscopic structures, as described above, a question arises: does the dipolar interaction between nanocrystals, the easy axes orientation or the anisotropic shape of the mesoscopic organization induce the change in magnetic behavior? In this chapter our aim is to focus on the collective magnetic properties induced by the organization of magnetic nanocrystals in mesostructures. Beyond the changes in the magnetic behavior due to the interactions between magnetic nanocrystals, we will focus on the different parameters, which can modify the general response. Especially, it is shown that, in some cases, it is possible to obtain a structural effect on the collective magnetic properties of such assemblies despite the long-range scale of the dipolar interactions. The organization itself induces intrinsic collective properties. In the first part, we present some general comments on the magnetization measurements used to determine the collective magnetic properties. We want to give the reader the minimum background required to understand the complexity of this field. In the second part, we present the evidence of collective magnetic properties due to the organization of uncoalesced magnetic nanocrystals in mesostuctures.

10.2 General Principles of the Magnetism of Nanoparticles: Theory and Investigation

It should first be recalled that a general feature characterizing single magnetic nanocrystals is their superparamagnetic behavior [1, 33]. This is clearly a finite size effect: bulk magnetic materials have a multidomain structure. They are divided into uniformly magnetized domains separated by Bloch walls in order to minimize the magnetostatic energy. By reducing the size of the materials, the size of the domains is also reduced. However, due to the cost in energy to create a Bloch wall there is a minimum size below which the particles are in a single domain. Typically it is below 20–100 nm depending on the material. It should also be noticed that in the very small nanocrystals, below 2 nm, the number of atoms at the surface is predominant and the superparamagnetic model is no longer valid. Nanocrystals deposited on a substrate forming an assembly tend to strongly interact, inducing a marked change in the magnetic properties. No correlation between the nanocrystals organization and the change in the magnetic properties is demonstrated. To our knowledge, the collective magnetic behavior of nanoparticle arrays was studied for 2D hexagonal networks and chains, 3D fcc supra crystals and cylinders. For such purposes, hysteresis curves and zero-field cooled/field cooled (ZFC/FC) susceptibility measurements are recorded and analyzed.

10.2 General Principles of the Magnetism of Nanoparticles: Theory and Investigation

10.2.1 Magnetocrystalline Anisotropy Energy and Blocking Temperature

The superparamagnetic limit has important implications in the thermal and time stability of devices made of magnetic nanoparticles. For a magnetic particle with volume V, the magnetocrystalline anisotropy energy in axial symmetry is expressed as: Eanis ˆ KV sin2 y

(1)

where y is the angle between the magnetization vector and the easy magnetic axis, and K is the magnetocrystalline anisotropy energy (MAE). In very small particles, the anisotropy energy barrier, Eb = KV, is usually of the same magnitude as the thermal energy. The magnetization vector fluctuates among the easy directions of magnetization. This process is called superparamagnetic relaxation. For a single-domain particle with uniaxial anisotropy, in the absence of an applied magnetic field, the relaxation time t at temperature T has an activation-like thermal dependence and is given by Néel’s expression [34]:  t ˆ t0 exp

KV kB T

 …2†

where t0 is a microscopic relaxation time, which is on the order of 10–9–10–11 s for ferro- or ferrimagnetic materials. This microscopic “trial” time depends in principle on the volume of the particle, on temperature and on the magnetic crystalline anisotropy energy, K [35]. The blocking temperature, Tb, for a particle of volume V is defined as the temperature for which the relaxation time t is equal to the timescale of the given measurement technique, tm : kB T b ˆ

KV   tm ln t0

…3†

In a classical magnetometer, such as a SQUID, this can be approximated as KV & 28 kBTb. For an assembly of small particles with a large size distribution at a given temperature, the distribution of relaxation times given by the equation is very broad, and extends over several orders of magnitude. As a first approximation, one may consider that the smaller particles, with a relaxation time smaller than the timescale tm of the measurement technique, behave as paramagnetic objects, whereas the larger ones, with t larger than tm, are “blocked”. Hence, in the case of a system of polydisperse particles, the volume V has to be replaced by an effective volume Veff proportional to the average volume,Veff = / [36].

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10.2.2 Magnetic Characterization from the Hysteresis Curves [37]

When a magnetic material is subjected to an increasing magnetic field, the spins within the material are aligned with the field. Its magnetization is increased and reaches a maximum value called the saturation magnetization, Ms . As the magnitude of the magnetic field decreases, spins cease to be aligned with the field, and the total magnetization decreases. In ferromagnets, a residual magnetic moment remains at zero field. The value of the magnetization at zero field is called the remanent magnetization, Mr . The ratio of the remanent magnetization to the saturation magnetization, Mr/Ms , is called the reduced remanence and varies from 0 to 1. The coercive field, Hc, is the magnitude of the field that must be applied in the negative direction to bring the magnetization of the sample back to zero. The shape of the hysteresis loop is especially of interest for magnetic recording applications, which require a large remanent magnetization, moderate coercivity, and (ideally) a square hysteresis loop at room temperature. Depending on the orientation of the measuring field, and the anisotropy of the particle and of the mesostructure, various shapes for hysteresis curves are expected. 10.2.3 Demagnetizing Fields [38]

If a finite-size body of a magnetic material is subjected to a magnetic field, free dipoles are induced on both its ends. This gives rise to a magnetic field in an oppo~ d, site direction to the magnetization. This field is called a demagnetizing field, H and is given by: ~d ˆ H

~ NM m0

…4†

~ and N are the permeability of vacuum, the magnetization and the dewhere m0, M magnetizing factor (dimensionless quantity), respectively. The demagnetizing factor, N, depends on the shape of the sample: for spheres, N is 1/3. For cylinders considered as infinite ellipsoids and subjected to an applied field parallel to the long axis c (c = !), the demagnetizing factor is 0. It is also 0 for infinite flat plates subjected to an applied field in the direction of one of the two long axes, whereas it is 1 in the direction of the short axis (normal to its surface). The effective field of ~ eff , is given by: the material, H ~ ex + H ~d ~ eff ˆ H H

(5)

~ d are the applied external and the demagnetizing fields, respec~ ex and H where H tively. Thus, depending on the orientation of the measuring field, it is necessary to take care of the demagnetizing effect. Hence, considering a thin film when the ap-

10.3 Origin of the Collective Properties in Mesoscopic Structures of Magnetic Nanocrystals

plied field is normal to the substrate, the hysteresis loop is smoother than that obtained when the applied field is parallel to the thin magnetic film. The reduced remanence decreases but the coercive field remains quite unchanged.

10.3 Origin of the Collective Properties in Mesoscopic Structures of Magnetic Nanocrystals

The collective magnetic properties of an assembly of magnetic nanoparticles are markedly influenced by the interactions. There are in fact three main types of interactions in an assembly of magnetic particles [39]: . .

.

dipolar interactions (which always exist); exchange interactions through the surface of the nanoparticles, which are in close contact; RKKY interactions through a metallic matrix in granular solids, when the particles are also metallic, or the superexchange interaction when the matrix is insulating.

Here, we limit our study to the magnetic properties of the organization of magnetic nanocrystals surrounded by an organic shell. Under such conditions, the nanocrystals are not in contact with each other and consequently the exchange interactions are neglected. Hence the dipolar interactions are the major parameter [33, 40, 41]. The orientation of the easy axes of nanocrystals during the formation of the mesoscopic arrays could also play a role. In the following, the theoretical backgrounds of these two approaches are described. 10.3.1 Orientation of the Easy Magnetic Axes

In the presence of a magnetic field H, the magnetic particle energy with uniaxial magnetic anisotropy is given by U ˆ KVsin2 y

mH cosa

…6†

where y and a are the angles between the magnetic moment, m and the easy magnetic axis, and the magnetic moment and the applied field, respectively. In the liquid state, the particles are free to rotate and the particle magnetic moments can be aligned along the applied magnetic field direction [42, 43]. For this, the Zeeman energy, mH, must be at least greater than the thermal energy, kBT. Moreover, if the anisotropy energy, KV, is greater than the thermal energy, the nanocrystals can rotate with their magnetic moment lying in the easy axes. A preferential orientation of the easy axes in the applied magnetic field direction is then expected.

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Let us assume a total alignment of the easy magnetic axes; from the Stoner– Wohlfarth model, the hysteresis loop measured when the applied field is parallel to the easy axes is expected to be rectangular with a reduced remanence of 1. In a perpendicular applied field, no hysteresis loop with 0 as reduced remanence is expected [44]. 10.3.2 Dipolar Interactions

The influences of the interaction between nanoparticles on the magnetic properties were studied theoretically for an assembly of Stoner–Wohlfarth particles, with a random distribution of the easy axes. In two-dimensional systems, the dipolar interactions have been modeled by a 2D random-field Ising model [40]. The magnetization in the direction of the applied field is calculated for an assembly of particles organized on well-defined two-dimensional lattices [45]. The surface plane is the (x, y) plane and the z axis is normal to the surface. The applied field is either normal or parallel to the surface plane. The particles are distributed on the plane surface with fixed positions and the easy-axes orientations ({n, k}) are randomly distributed. The particles are characterized by their saturation magnetic moment Ms, their anisotropy constant K, and their diameter D. For a perfect square lattice, with a lattice spacing d, the influence of these interactions is characterized by a coupling constant: ad ˆ (pM2s /12K) 6 (D/d)3

(7)

which is the ratio of the dipolar to the anisotropy energy. For sufficiently small values of the dipolar interaction, a mean-field-type approach, where only the demagnetizing field effect is taken into account, leads to a satisfactory approximation of the magnetization curve. The effect of the dipolar interactions can be estimated, at a quantitative level, by the change in the reduced remanence magnetization, Mr/Ms, in terms of ad for the two orientations of the external applied field. // Changes are measured by the ratio, g = (Mr/Ms)\/(Mr/Ms)//, where M\ r and Mr are the values of the remanence magnetization for the applied field normal and parallel to the surface, respectively. The decrease in g with increasing coupling constant ad implies a squarer hysteresis loop (in the parallel case, Fig. 10.1 A) which is smoother (in the normal case, Fig. 10.1 B) compared to that of the nanocrystals without interactions (Fig. 10.1 C).

10.4 Collective Magnetic Properties of Mesostructures Made of Magnetic Nanocrystals

In the following, we show the collective magnetic properties of mesostructures made of uncoalesced magnetic nanocrystals. Beyond the experimental evidence of the influence of the dipolar interaction, we want to show the different parameters

10.4 Collective Magnetic Properties of Mesostructures Made of Magnetic Nanocrystals

Fig. 10.1 Calculated hysteresis curve for Stoner–Wohlfarth magnetic particles. The high value of ad is a limiting case for the 8-nm cobalt nanocrystals presented here. (A) ad = 0.1: the applied field is parallel to the surface, (x, y) plane; (B) ad = 0.1: the applied field is perpendicular to the surface, z direction; (C) noninteracting particles (ad = 0): this corresponds to isolated particles in solution.

that can influence the magnetic response: the internal order, the shape or the texturation of the mesostructure, etc. 10.4.1 Materials and Mesoscopic Structures

Magnetic properties are studied of various mesoscopic structures made of spherical nanocrystals (cobalt [5, 6, 11, 45, 46] and maghemite [47–50]) and acicular maghemite nanocrystals [51–53]. These correspond to a soft (maghemite) and a hard (cobalt) magnetic material. The mesostructures are: linear (1D) chains [48, 54], 2D hexagonal [11] or disordered monolayers [5], 3D ordered fcc supracrystal [12, 55] or disordered films [56] and 3D textured films (stripes or cylinders) [47–49, 51, 57]. This gives us a general overview of the effect of the order, the shape and the structure of the film on the collective magnetic properties. These mesostructures are obtained by evaporation of the ferrofluid on HOPG (highly oriented pyrolytic graphite) substrate. During this process, a magnetic field is or is not applied parallel to the substrate plane. 10.4.2 Bidimensional (2D) Organization of Cobalt Nanocrystals

At room temperature, due to their superparamagnetic behavior, the magnetization of the cobalt nanocrystals dispersed in solution shows no hysteresis. The blocking temperature, as determined by ZFC/FC experiments [58], increases with the nanocrystal size (Table 10.1). This corresponds to a decrease in the magnetic anisotropy energy (MAE), as has been reported for magnetic nanocrystals [59]. For spherical nanocrystals, it is related to the increase in the surface anisotropy when the size decreases. Decreasing the temperature allows recovery of classical ferromagnetic behavior, characterized by a nonzero value of the remanent magnetization, Mr,

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10 Collective Magnetic Properties of Organizations of Magnetic Nanocrystals Table 10.1 Magnetic properties of Co nanocrystals depending on their organization: 0D (isolated in solutions), 1D (linear chains), 2D (monolayers). 1D a)

0D

Size (nm)

Ms (emu g–1)

5.8

110+5

Hc (T) Mr/Ms Tb 0.12 0.25 60

8

120+5

0.13

0.45

70

Hc (T) 0.13 (//) 0.10 (\) 0.14 (//) 0.10 (\)

Mr/Ms Tb 0.31 (//) – 0.19(\) 0.60 (//) 90 0.25(\)

2D b)

Hc (T) 0.12 (//) 0.12 (\) 0.13 (//) 0.13 (\)

Mr/Ms Tb 0.29 (//) 65 0.21(\) 0.52(//) 85 0.35(\)

a) (//) is for a field applied parallel to the chains and the substrates (x direction); (\) is for a field perpendicular to the chains but keeping the substrates parallel (y direction). b) (//) is for a field applied parallel to the substrates (x, y planes); (\) is for a field perpendicular to the x, y plane (z direction).

even when there is no applied field. At 3 K the thermal excitation vanishes, and the magnetization curves of the cobalt nanocrystals dispersed in hexane show a classical hysteresis. For isolated nanocrystals, the saturation magnetization, Ms, is not reached and is deduced from extrapolation (Table 10.1). The slight increase in Ms on increasing the size could be due to a relative decrease in the surface effect as the average size increases. Figure 10.2 shows the hysteresis loop of the cobalt nanocrystals having various average sizes (5.8 and 8 nm, Fig. 10.2 A and B, respectively), either isolated in solution (Fig. 10.2 C and D) or deposited as 2D monolayers on cleaved graphite (Fig. 10.2 E and F ). A typical monolayer of cobalt nanocrystals is shown in Fig. 10.3A. During the measurement at 3 K, the sample is kept parallel to the external applied field (x, y plane). For any size, the hysteresis loop is squarer than that for the same nanocrystals isolated in solution [45]. On the other hand, the reduced remanence increases (Table 10.1). This change is more pronounced for larger nanocrystals. Similarly, the blocking temperature increases when the nanocrystals are organized in 2D monolayers (Table 10.1). The hysteresis loop appears smoother when the sample is normal (z direction) compared to the same sample kept parallel to the external field (Fig. 10.3 B). As expected theoretically and shown in Fig. 10.1, this effect is attributed to the long-range dipolar interaction. This is quantified by the g value, defined as the ratio of the reduced remanence in normal and parallel geometry (g = (Mr/Ms)\/(Mr/Ms)//. This experimental value is compared to the theoretical one knowing the value of the coupling constant ad. Hence, from a coupling constant ad of 0.05 calculated for 8-nm cobalt nanocrystals, the theoretical ratio gth = 0.66, whereas it is 0.65 from experiment [45]. Similar and less pronounced behavior is obtained for 5.8-nm cobalt nanocrystals (Table 10.1). Thus, the good agreement obtained between the experimental and theoretical values of g confirms that the collective effects on the magnetic properties of the 2D monolayers made of cobalt nanocrystals are mainly due to the dipolar inter-

10.4 Collective Magnetic Properties of Mesostructures Made of Magnetic Nanocrystals

Fig. 10.2 TEM characterization (A, B) and corresponding hysteresis loops recorded at 3 K of cobalt nanocrystals either isolated in solution (C, D) or deposited as a monolayer on HOPG substrate with the field applied parallel (E, F). (A, C, E) 5.8-nm-diameter cobalt nanocrystals; (B, D, F) 8-nm-diameter cobalt nanocrystals.

action between adjacent nanocrystals. Similar behavior has also been reported since then for e-cobalt nanocrystals in hexagonal ordered monolayers, and again the collective properties were attributed to the dipolar interaction [8]. 10.4.3 Three-Dimensional (3D) Organizations of Cobalt Nanocrystals

3D thin films of cobalt nanocrystals can be obtained by slow evaporation (Fig. 10.3 C) [57]. The magnetic response, recorded in a parallel configuration, of these unorganized 3D films (Fig. 10.3 D) is similar to that of the 2D monolayers: the reduced remanence, Mr/Ms, is 0.51 instead of 0.52. Conversely, the coercive field increases: Hc = 0.25 T compared to that of isolated or 2D monolayers, 0.13 T. On the other hand, as for 2D organizations, the blocking temperature increases as a signature of the magnetic interaction. The change in the coercivity is attributed

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Fig. 10.3 TEM pictures showing 2D organization (A) and 3D organization (C) of cobalt nanocrystals. The corresponding hysteresis loop at 3 K is reported for each mesostructure: (B) for 2D monolayers the magnetic field is applied parallel to the substrate (x, y plane; solid line) or perpendicular to the substrate (z direction; dotted line); (D) for 3D film the magnetic field is applied parallel to the substrate (x, y plane).

to small ferromagnetic domains made of several adjacent particles having the same orientation of their magnetic moment. Thus, in these unorganized 3D films of nanocrystals, dipolar interactions exist and induce changes in the magnetic response. However, the behavior is quite similar to that of granular films or to the observed increase in the dipolar interaction by increasing the volume fraction of nanoparticles in solution [33, 41]. 10.4.4 Does the Internal Order Play a Role?

The structural order does not seem to be a crucial parameter; as a matter of fact, the 2D monolayers described above (Fig. 10.3 A) are rather highly disordered. This is confirmed by modeling. The hysteresis loop was calculated assuming two models: the real disordered model (Fig. 10.4 A) and a reference well-ordered model (Fig. 10.4 B). For this an effective coupling constant, aeff d , is determined, which

10.4 Collective Magnetic Properties of Mesostructures Made of Magnetic Nanocrystals

Fig. 10.4 Calculated hysteresis curves for 2D (D) and 1D (E) mesostructures made of uncoalesced magnetic nanoparticles. The corresponding structures are shown in (A) and (C), respectively. Dotted line: applied field in the x direction assuming a perfect square lattice as reference model (B); solid line: applied field in the z direction assuming a perfect square lattice with a similar density of nanoparticles. In each case, the exact calculations corresponding to the real structure correspond to the square (x directions) and to the circle (z direction). In the case of the linear chains there is a large discrepancy I if the magnetic field is applied in the x direction during the measurement. In (A– C), the length of the arrow corresponds to the projection of the magnetic moment in the x, y plane; there is no alignment of the magnetic moment due to the dipolar interactions.

takes into account the mean density of nanocrystals in the disordered monolayers [60]. The surface occupation fraction, F, is the ratio of the surface occupied by the nanocrystals, nspD2/4, to that of the lattices, l2. This determines the lattice spacing, d0, which is the average distance between adjacent nanocrystals and is related to the surface occupation fraction, F, of the layer as follows: (d0/D) ˆ (p/4F)1/2

(8)

with F = nspD2/4 l2 . Then, the effective coupling constant is aeff d ˆ

pMs2 12K



D d0

3 …9†

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10 Collective Magnetic Properties of Organizations of Magnetic Nanocrystals 2 where aM d = (pMs )/(12K) is the maximum value of the coupling constant defined eff above. ad is used to calculate the magnetization of the well-ordered reference model. Details of the calculation are given in ref. [60]. Figure 10.4 D shows no difference in the hysteresis loop for ordered and disordered monolayers. This is observed for the two orientations of the magnetic field. Hence, due to the long-range order of the dipolar interaction, the local structure of the monolayer is not important: a well-ordered reference model is suitable for calculating the hysteresis curve of an isotropic disordered monolayer, for any orientation of the applied field relative to the substrate. At this point a question arises: does ordering in 3D superlattices change the magnetic behavior? To answer this question the magnetic properties of 3D films, either highly ordered in an fcc structure or disordered, are compared. Let us first describe the system used: 7.2-nm-diameter cobalt nanocrystals with a low size distribution (12 %) are produced [11]. By adjusting the substrate temperature during the solvent evaporation process, it is possible to obtain either “supra” crystals characterized by a long-range fcc ordering of the nanocrystals (25 8C, Fig. 10.5 B) [12, 55] or a disordered 3D film (10 8C, Fig. 10.5 A) of uncoalesced cobalt nanocrystals, (cf. Chapter 1) [55]. From the small-angle X-ray diffraction study, we know that the ordering of particles induces a decrease in the interparticle gap of around 1 nm. In fact, this distance is 3.60 and 4.55 nm for the highly-ordered “supra” crystal and the amorphous film, respectively. The magnetization curves recorded at 3 K and with an applied magnetic field parallel to the substrate are shown in Fig. 10.5C. The hysteresis loop appears squarer when nanocrystals are ordered compared to the disordered systems [55]. For “supra” crystals, the saturation mag-

Fig. 10.5 (A) SEM image of disorganized 7.2-nm cobalt 3D film. (B) SEM image of superlattices made of 7.2-nm Co nanocrystals. (C) Corresponding hysteresis magnetization loops obtained at 3 K (inset, the ZFC/FC curves); amorphous assembly (dotted line), “supra” crystal (solid line).

10.4 Collective Magnetic Properties of Mesostructures Made of Magnetic Nanocrystals

netization is reached at 0.3 T whereas with an amorphous aggregate, it is around 1.5 T. In both cases, the saturation magnetization is 120 emu g–1 and the coercivity is 0.07 T. Moreover, the zero-field cooled and field cooled (ZFC/FC) curves, recorded with a 75 Oe field (inset Fig. 10.5 C) show a lower blocking temperature for an amorphous film (95 K) compared to that obtained for fcc “supra” crystals (115 K). Such differences can be explained by taking into account the structural results described above. The decrease in the average distance between nanocrystals of 1 nm, when they are organized, induces an increase in the coupling constant, ad, from 0.025 in the disordered case to 0.030 in the fcc superlattices. This change in the blocking temperature and the squareness of the hysteresis loop corresponds to an increase in the dipolar interaction. Hence, the internal order of 3D films plays a role in the collective magnetic properties via the increase in the coupling constant. 10.4.5 Does the Structure Play a Role? 10.4.5.1 Linear Chains of Cobalt Nanocrystals For magnetic nanocrystals in 1D chains (Fig. 10.4 C), it is no longer possible to model the magnetic behavior of linear chains (open squares, Fig. 10.4 E) made of uncoalesced nanocrystals by a well-ordered reference model (dotted line, Fig. 10.4 E), when the magnetic field is applied parallel to the chains and the substrate. An exact calculation taking into account the position of each particle in the 1D organization is necessary to obtain the hysteresis loop of a network of linear chains [60]. To show this more clearly, calculations have been made for a very high coupling constant (ad = 0.26) with the same nanoparticle density. The hysteresis loop appears squarer than that observed for a monolayer of nanoparticles (Fig. 10.6 A). Moreover, conversely to the isotropic monolayer, the magnetic response of the 1D chains changes drastically with the direction of the applied field parallel (x direction) or perpendicular (y direction) to the measured field, keeping the plane of the substrate parallel (Fig. 10.6 A). In fact, due to the dipolar coupling, the linear chains behave roughly as homogeneous wires with an effective easy axis in the direction of the chains, although individual nanocrystals have randomly distributed easy axes. In this case, the strength of the structural effect is estimated theoretically by comparing the reduced remanence in the two geometries. As previously, a ratio g'th = (Mr/Ms)\/(Mr/Ms)//, can be deduced for the linear chains oriented in the x direction from the two calculations corresponding to h = y and h = x, respectively. In the experiments, cobalt nanocrystals (8 nm) dispersed in hexane are subjected to an applied field (1 T) during the evaporation process. This produces linear chains of uncoalesced nanocrystals (Fig. 10.6 B). The average width is 300+50 nm and the interchain distance is 600 nm. A closer view of the chains indicates that they are formed by uncoalesced cobalt nanocrystals in mono- or bilayers, without any internal order [54]. Their magnetic properties differ markedly from those of the isotropic monolayers. When the measuring field is parallel to

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Fig. 10.6 (A) Magnetization for particles organized in chains: aeff d = 0.26. Solid squares: linear chains parallel to the applied field (x direction); open squares: linear chains perpendicular to the applied field (y direction). Solid lines correspond to a perfect square lattice. (B) TEM pictures of 1D organization of 8-nm cobalt nanocrystals.

the chain and thus also to the substrate plane, the hysteresis curve appears to be squarer than that of the isotropic 2D monolayer measured with a field parallel to the substrate (Fig. 10.7 A). The reduced remanence increases and the saturation is reached at a lower field. These changes increase with the coupling constant (i. e., with the size of the nanocrystals) (Table 10.1). On turning the chain by 908, the field remains in the plane but perpendicular to the chains and induces a smoother loop with a decrease in the reduced remanence (Fig. 10.7 B and Table 10.1). Similar and less pronounced behavior is observed for 5.8-nm cobalt nanocrystals (Table 10.1). For 8-nm cobalt nanocrystals the coupling constant is 0.05. Figure 10.7 C shows the theoretical change in the hysteresis loop with the orientation of the applied field with a ratio, g'th = (Mr/Ms)\/(Mr/Ms)//, equal to 0.77. From the experimental data (Fig. 10.7 B), g'exp = 0.42. Rather good agreement between experiments and calculated data is obtained. Obviously the experimental samples do not have the perfect chainlike structure introduced in the model (compare Figs. 10.6 B and 10.4 C). This probably explains the difference in magnitude between experiment and theory. On the other hand, an effect of the alignment of the easy axes during the deposition in a field cannot be totally excluded and could also explain the discrepancy between theory and experiment. Indeed, the results reported above appear to be mainly a structural effect on the collective magnetic properties in the 1D chains made of uncoalesced cobalt nanocrystal, as predicted theoretically. Due to the dipolar interactions, the chains behave like wires with an effective easy axis in the direction of the wire. Similar 2D monolayers [7] and linear structures have been reported for cobalt nanocrystals [61]. Again, collective magnetic properties due to the dipolar cou-

10.4 Collective Magnetic Properties of Mesostructures Made of Magnetic Nanocrystals

Fig. 10.7 (A) Hysteresis loop at 3 K for the 1D chains (solid line); the magnetic field is applied parallel to the substrate and to the chains (x direction). Comparison is made with the 2D monolayer (solid circle) and isolated in solution (dotted line). (B) Hysteresis loop, measured at 3 K, of aligned 8-nm cobalt nanocrystals. The applied field is either parallel (solid line) or normal (dotted line) to the directions of the chains, keeping the substrate parallel to the applied field. (C) Calculated hysteresis curve for linear chains made of 8-nm cobalt nanocrystals for aeff d = 0.06 with an applied field either parallel (solid circle) or normal (open circle) to the directions of the chains keeping the substrate parallel to the applied field.

pling have been observed but the structural effect has not been investigated. Hence, depending on the level of organization of the nanocrystals (0D, 1D, 2D), the magnetic response is strongly modified due to the dipolar interactions. This is clearly illustrated in Fig. 10.7A. Conversely to the 2D monolayers, in the case of 3D films the internal order plays a role as it reduces the interparticle distances. It is, in fact, an intrinsic effect on the magnetic response of the mesostructure (Fig. 10.5).

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10.4.5.2 Patterned 3D Film of Magnetic Nanoparticles We have seen previously that the transition from a 2D organization to a 1D organization induced a clear structural effect on the collective magnetic properties. Can we generalize this result to the patterned 3D films of nanocrystals? These mesostructures are obtained using the same process as that described previously for 1D chains, with concentrated solutions of cobalt, maghemite or cobalt–ferrite nanoparticles. With 8-nm-diameter cobalt nanocrystals coated by dodecanoic acid and dispersed in hexane, linear stripes are formed with a periodic structure for any applied field (Fig. 10.8). The structure appears like a corrugation of the surface of the 3D film. The order and compacity of stripes increase on increasing the applied field [57]. With 10-nm spherical g-Fe2O3 nanocrystals coated with citrate ions (insert Fig. 10.9 A) and with short alkyl chains, such as octanoic acid (insert Fig. 10.9 B), evaporation of the solvent in a magnetic field (0.59 T) produces tubelike structures [47, 49]. The average width of the tubes and their compacity increase with the strength of the field applied during the evaporation process (Fig. 10.10 A–C). By increasing the length of the alkyl chains using decanoic acid (insert Fig. 10.9 C) and dodecanoic acid (insert Fig. 10.9 D), the patterning of the films disappears continuously [49]. Hence, a dense film with a slight corrugation at the surface is

Fig. 10.8 Hysteresis loop (A) and SEM patterns of cobalt superlattices obtained by evaporating a solution of cobalt nanocrystals on HOPG with a magnetic field during the deposition process. (B) Deposition at 0.27 T, (C) deposition at 0.45 T, (D) deposition at 0.56 T, (E) deposition at 0.78 T. The squareness of the hysteresis loop increases with the strength of the deposition field. The interfringe distances (lc) are correlated to the increase in the reduced remanence (inset in A).

10.4 Collective Magnetic Properties of Mesostructures Made of Magnetic Nanocrystals

Fig. 10.9 Magnetization curves recorded at 3 K for citrate (A), octanoic (B), decanoic (C) and dodecanoic (D) coated maghemite nanocrystals with no (solid lines) and 0.59-T applied field during the deposition process, the measuring field being along the x (open circle) and y direction (solid circle).

obtained for dodecanoic acid as a coating agent, (insert Fig. 10.9 D). This structural change in the patterned film, from a tubelike organization to a smooth undulated surface, is correlated to a decrease in the Van der Waals interaction between the nanocrystals, when the interparticle gap increases (cf. Chapters 1 and 3). The difference between mesostructures obtained with cobalt and maghemite nanocrystals coated with dodecanoic acid and deposited at similar fields is due to the difference in hardness of the magnetic materials: Hc = 420 Oe for a 3D film of g-Fe2O3 and Hc = 2500 Oe for a 3D film of cobalt.

10.4.5.2.1 Surface-Structured 3D Film From the above, it is possible to obtain 3D patterned films with either a corrugation of the surface (cobalt or g-Fe2O3 nanocrystals coated with dodecanoic acid) or a volumic tubelike organization of g-Fe2O3 nanocrystals coated by citrate ions, or octanoic and decanoic acid. We can thus study the magnetic collective behavior of films structured either in surface or in volume. For this, the hysteresis curves are

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Fig. 10.10 SEM images obtained at various magnifications for citratecoated maghemite nanocrystals evaporated in various applied magnetic field strengths: (A) 0.01 T, (B) 0.05 T and (C) 0.59 T. Variation of the reduced remanence with the average width d of the “tubes” (D).

measured with an applied field parallel to the surface plane in the x and y directions. Concerning the 3D film of cobalt nanocrystals, the hysteresis loop (recorded in the x direction) is squarer with the strength of the magnetic field applied during the deposition process (Fig. 10.8 A). Moreover, the hysteresis loops recorded when the applied field is parallel and perpendicular to the stripes (x or y direction) are similar for all the samples. Furthermore, the reduced remanence increases with the reciprocal of the stripe characteristic distance (i. e., with an increase in the strength of the applied field during the deposition process; insert Fig. 10.8 A). Conversely, the hysteresis loops of 3D films made of g-Fe2O3 nanocrystals coated by dodecanoic acid deposited in the absence and in the presence of a magnetic field are similar for any orientation of the measuring field (Fig. 10.9 D). In both cases, a significant alignment of the easy axes is possible, from an energetic point of view. However this can be excluded because the hysteresis loops remain unchanged along the x and y directions. But the change in the reduced remanence with the characteristic distance observed with cobalt nanocrystals strongly supports the fact that small ferromagnetic domains could be formed in the mesostructure. Thus, collective magnetic properties are observed in the 3D corrugated-surface film, if the strength of the dipolar interaction between the na-

10.4 Collective Magnetic Properties of Mesostructures Made of Magnetic Nanocrystals

nocrystals is sufficiently high. The difference observed between the films obtained with these two materials must be related to the hardness of the magnetic materials (cobalt nanocrystals are a hard magnetic material while maghemite is a soft one). Changes in the van der Waals interaction (see Chapter 3) also have to be considered, as they are greater for cobalt than for maghemite. Because of this the surface texturation is higher for cobalt than maghemite and the magnetic behavior differs.

10.4.5.2.2 Tubelike-Structured 3D Film: Effect of a Volumic Texturation As for the linear chains made under a magnetic field, the structure of the 3D film can really play a role in the magnetic response. This is illustrated with the tubelike film of citrate-coated maghemite nanocrystals [49]. Now, conversely to the previous case, the hysteresis loops of samples made of tubelike structures markedly change with the orientation of the applied field (Fig. 10.9 A). When the field is applied along the direction of the long axis of the tubes, (x direction) the hysteresis loop is squarer than that observed when the applied field is along the short axis (y direction). Furthermore, in the x direction, the reduced remanence and the coercivity increase (0.52 and 480 Oe) compared to those observed with films obtained without an applied field (0.42 and 420 Oe) (Fig. 10.9 A). Conversely, the reduced remanence and coercivity decrease in the y direction. These effects are not due to the orientation of the easy axes of nanocrystals [49] even if it is energetically possible [47]. This has been well demonstrated through Mössbauer spectroscopy [49]. Such behavior is more marked with increasing the applied field strength during the deposition process [47, 49]. Figure 10.10 shows that the reduced remanence increases with the average width of the tubes, whereas in the perpendicular direction (y direction) it decreases (Table 10.2). These changes in the hysteresis loops are attributed to the mesoscopic structure. Hence, similar behavior is obtained with g-Fe2O3 nanocrystals coated with octanoic acid (Fig. 10.9 B). However, the amplitude of these changes decreases by reducing the length of the alkyl chains used to coat the nanocrystals (Fig. 10.9 C and D). This is related to the decrease in the ordering of the film. (see Chapters 1 and 3). Again tubes of g-Fe2O3

Table 10.2 Variation of the reduced remanence at 3 K for particles coated with citrate ions, deposited with no magnetic field and in a magnetic field of 0.01, 0.05 and 0.59 T during evaporation. For the oriented deposits, the measuring field is applied parallel to the substrate and is either (//) along the direction or (\) perpendicular to the aligned particles. Sample

0T

Mr/Ms Hc (Hc// – Hc\) (Oe)

0.42 0

0.01 T (//) 0.45

0.01 T (\) 0.37

50

0.05 T (//) 0.50

0.05 T (\) 0.30

50

0.59 T (//) 0.52

0.59 T (\) 0.31

90

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10 Collective Magnetic Properties of Organizations of Magnetic Nanocrystals

nanocrystals behave as magnetic nanowires with an effective easy axis parallel to the tube. Similar behavior is observed with tubelike structures made of citratecoated cobalt ferrite nanocrystals. Hence, it is unambiguously demonstrated that the structure of the 3D film can change the magnetic collective properties even if the easy axes of the individual nanocrystals are not oriented. This indicates also that our model of dipolar interaction is quite general and explains, at least qualitatively, the magnetic collective properties of the mesostructure made of uncoalesced magnetic nanocrystals, whatever their organization. Moreover, in spite of the long-range scale of the dipolar interaction, structural and intrinsic effects can be observed.

10.5 Towards Collective Magnetic Properties at Room Temperature

One of the major problems is to overcome the nanocrystals superparamagnetism. For any synthesis route to obtaining ferromagnetic particles at room temperature, postsynthesis processes are needed. Hence, it is possible to obtain soft magnetic or paramagnetic nanocrystals and recrystallize them to a harder magnetic phase. This has been illustrated with the transition of disordered fcc-FePt to fct-FePt at 560 8C [28, 62]. Similar thermal treatments are needed in CoPt nanoalloys [24, 63], but were also reported in the case of cobalt nanocrystals obtained by decomposition of organometallic compounds [64]. It has also been found that there is a transition of e-Co to hcp-Co for cobalt nanocrystals heated for several hours at 300 8C or to fcc if annealed at 500 8C [8]. However, this thermal treatment does not allow sufficient control of the organization and then of the interparticle distance, which is a key parameter for controlling the dipolar interaction. Moreover, these particles are far from ferromagnetic at room temperature. The situation is different for the Co–Pt or Fe–Pt nanoalloys: the nanocrystals are ferromagnetic at room temperature; however, the annealing temperatures are so high that it is impossible to collect the nanocrystals after annealing and often drastic coalescence takes place and the organization is lost. The annealing and postsynthesis treatment is not the only route for obtaining devices useful at room temperature. We can also use anisotropically shaped magnetic nanoparticles. However, this is always a challenge, not only to obtain such elongated nanocrystals but also to organize them in order to study their collective properties. 10.5.1 Cigar-Shaped Maghemite Nanocrystals Organized in 3D Films

Cigar-shaped maghemite (g-Fe2O3) nanocrystals coated with citrate ions are characterized by a high crystallinity and an average length and aspect ratio of 325 nm and 6.7, respectively (Fig. 10.11). Due to their large size and high shape anisotropy, these nanocrystals are ferromagnetic at room temperature [48]. These elon-

10.5 Towards Collective Magnetic Properties at Room Temperature

Fig. 10.11 SEM images of cigar-shaped maghemite nanocrystals (A) in the absence and (B) in the presence of a 1.8-T applied field. (C) Magnetization curves at 290 K for the nanocrystals deposited on HOPG with no applied field (dashed curves with circles) and with a nonzero applied field (1.8 T) during the deposition process. The magnetization is recorded with an applied field either parallel (x direction, solid curves with squares), perpendicular (y direction, dashed curves with triangles) or normal (z direction, solid curves with lozenge) to the ribbons direction.

gated nanocrystals are expected to be in a single domain with uniaxial anisotropy [65]. This is confirmed with the value of the reduced remanence, Mr/Ms = 0.5, of the isolated nanocrystals [44]. With no applied magnetic field during the deposition process, a thin magnetic film is obtained and the nanocrystals are randomly oriented on the substrate (Fig. 10.11 A). The magnetic properties are the same as those obtained for isolated nanocrystals (Table 10.3). By applying a magnetic field during the deposition process (1.8 T), the cigar-shaped nanocrystals are mainly oriented along the direction of the applied field and form ribbons (Fig. 10.11 B). The magnetic properties, recorded at room temperature, of these mesostructures markedly change with the orientation of the applied field. When the applied field

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10 Collective Magnetic Properties of Organizations of Magnetic Nanocrystals Table 10.3 Variation of the reduced remanence and the coercive field Hc at 290 K. The field is applied parallel to the film made of nanocrystals and is either (//) in the direction of or (\) perpendicular to the ribbons. The applied field is normal (\n) to the film made of nanocrystals. Sample nonoriented Mr/Ms (//) Hc (//) 0.50 425 Oe

Sample oriented Mr/Ms (//) 0.8

Hc (//) 425 Oe

Mr/Ms (\) 0.24

Hc (\) 225 Oe

Mr/Ms (\n) 0.11

Hc (\n) 225 Oe

is parallel to the substrate and parallel to the long axis of the elongated nanocrystals (x direction), the hysteresis loop (Fig. 10.11 C) is squarer than that obtained with a random distribution of the nanocrystals on the substrate. The reduced remanence markedly increases and the coercive field remains unchanged (Table 10.3). Turning the ribbons by 908 (y direction) induces a smoother hysteresis loop with a marked decrease in the reduced remanence and in the coercive field (Table 10.3). The change in the hysteresis loop with the field applied either along the long or the short axes of the cigar-shaped nanocrystals is due to the orientation of the easy magnetization axes in the ribbons direction [51–53]. The dipolar coupling between aligned nanocrystals cannot be observed because the applied measured field is always parallel to the substrate, i. e., to the film. Therefore, the demagnetizing factor for the film made of oriented nanocrystals remains unchanged and close to zero. To be convinced that the change in the hysteresis loop described above is not due to the film demagnetizing factor, let us apply the measured field normal to the surface of the film (z direction). In such a case, the applied field is always parallel to the short axis of the nanocrystals. Thus, the demagnetizing factor of the individual nanocrystals remains unchanged but the demagnetizing factor of the thin magnetic film varies from 0 to 1. The hysteresis curve (Fig. 10.11 C) is smoother, the reduced remanence decreases and the coercive field remains unchanged (Table 10.3). The hysteresis curve, corrected for the effect of the demagnetizing field, well reproduces that obtained with the field parallel to the film surface (y direction). Thus, the assembly of the cigar-shaped maghemite nanocrystals in thin 3D films induces a strong effect of the demagnetizing field normal to the film surface. This is again a collective magnetic behavior, but at room temperature. 10.5.2 Organization of Cobalt Nanocrystals with High Magnetic Anisotropy Energy

The cobalt nanocrystals obtained by soft chemistry and studied in Section 10.4, often have a low crystallinity. As an example, the corresponding selected-area electron diffraction (SAED) pattern shows only two diffuse rings at 2 and 1.25 Å, indicating a low degree of crystallinity for these 7-nm cobalt nanoparticles

10.5 Towards Collective Magnetic Properties at Room Temperature

Fig. 10.12 Magnetic and TEM characterization of cobalt nanocrystals. (A, B) Electron diffraction and TEM, respectively, of the as-synthesized nanocrystals. The corresponding ZFC/FC curves for particles either isolated or deposited as 2D monolayers on HOPG are in (C) and (F), respectively (solid line). (D, E) The SAED and TEM picture, respectively, of the same nanocrystals after annealing at 275 8C in nitrogen. The corresponding ZFC/FC curves are marked with circles in (C) (0D, isolated in solution) and (F) (2D monolayers).

(Fig. 10.12 A). A moderate annealing of the cobalt nanocrystals is undertaken in order to keep their ability to self-organize in 2D monolayers (Fig. 10.12 B). For this, a hexane dispersion of cobalt nanocrystals is evaporated completely in a glove box in nitrogen. The vessels with the remaining black film made of uncoalesced cobalt nanocrystals are then heated at 250 or 275 8C for 15 min in nitrogen. Then, after fast cooling at room temperature, the remaining black film is redispersed in hexane by sonication. The SAED patterns change drastically for the cobalt nanocrystals heated at 275 8C (Fig. 10.12 D). The diffraction shows only spots forming a pattern of rings corresponding to that of cobalt metal in the hcp phase. TEM measurements show that coalescence is avoided and monolayers with local organization are still obtained (Fig. 10.12 E). However, a slight change in the size distribution (from 17 to 15 %) and in the average diameter (from 7 to 6.8 nm) is observed. Hence, a phase transition occurs during the annealing, from low crystallinity to hcp cobalt nanocrystals. This induces a strong effect on the magnetic properties of the isolated nanocrystals. The ZFC/FC curve changes drastically depending on the annealing temperature (Fig. 10.12 C and F ). The as-synthesized nanoparticles and those annealed at 275 8C are characterized by blocking temperatures, Tb , of 65 and 215 K, respectively. This agrees with a transition from low

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crystallinity to a pure hcp structure of the nanocrystals. The magnetic anisotropy energy (MAE) is estimated from the ZFC/FC studies to be 1.35 × 106 and 4.50 × 106 erg cm–3, respectively, before and after annealing at 275 8C [58]. The first value is consistent with the previously reported value for cobalt nanocrystals with a low crystallinity [24, 46] or in the e phase [8]. The second value corresponds to the magnetic anisotropy of cobalt metal in an hcp structure (4.5 × 106 erg cm–3) [10]. Comparison of the magnetization curve at 3 K before and after annealing also shows drastic changes. For as-synthesized nanoparticles, the saturation magnetization Ms, not reached at 2.5 T, is estimated from M versus 1/H extrapolation to be 85+5 emu g–1. Conversely, it is reached at 2 T for annealed nanocrystals and markedly increases (145+5 emu g–1). The coercivity and reduced remanence are 0.18 and 0.35, respectively, for native nanoparticles whereas they are 0.13 and 0.42 for the annealed materials. Note that the reduced remanences are close to the theoretical value for nanocrystals having uniaxial anisotropy such as cobalt in the hcp form (Mr/Ms = 0.5). The major change between native and annealed nanocrystals is observed in the saturation magnetization value, which increases from 85 to 145 emu g–1. This is explained as follows: the native nanoparticle is made of small crystalline domains separated by amorphous materials of cobalt or cobalt/ boron. Each crystalline domain is characterized by its own magnetic moment. The total magnetic moment of the nanoparticle is the sum of these magnetic domains coupled by dipolar interactions. On annealing, nanocrystals are formed and these nanodomains disappear. A monocrystalline phase, characterized by a uniaxial moment, is produced. The saturation magnetization (145 emu g–1) is then close to that of the bulk phase (162 emu g–1). The slight difference between these two values is attributed to either the surface or a few boron inclusions. The magnetic properties of nanoparticles, annealed or not, and deposited on a HOPG substrate are compared (Fig. 10.12). As observed previously, due to the dipolar interactions, the blocking temperature always increases when the nanoparticles are deposited on a substrate compared to the same particles dispersed, at a low volume fraction, in a solvent. Figure 10.12 F shows the ZFC/FC curve of native particles and those annealed at 275 8C deposited on HOPG substrates. The blocking temperature increases from 85 to 275 K. Similarly, the hysteresis loop is squarer and the saturation magnetization is reached at a lower applied magnetic field with an increase in the reduced remanence (from 0.42 to 0.52). The saturation magnetization (145 emu g–1) and coercivity (0.13 T) remain unchanged. Because the saturation magnetization markedly increases by annealing we would expect, from the coupling constant ad = (pM2s /12K) × (D/d )3 (see Section 10.3), to observe a change in the magnetization loop. However, the increase in the crystallinity of nanocrystals induces an increase in the anisotropy constant, K, by a factor of 3.2. This compensates for the increase in the saturation magnetization and the coupling constant remains quite unchanged. It is 0.04 and 0.036 for native and annealed nanocrystals, respectively. Thus, highly crystallized cobalt nanoparticles can be obtained by fast and moderate annealing. This markedly improves the magnetic properties of the film made of uncoalesced cobalt nanocrystals. Murray et al. [8] report such a change from an e phase to an hcp phase for 9-nm cobalt

10.5 Towards Collective Magnetic Properties at Room Temperature

Fig. 10.13 Diffractograms of cobalt nanocrystals ordered in “supra” crystals: not annealed (A), annealed at 250 8C (D), annealed at 300 8C (G). Insets: diffraction patterns. (B, E, H) Corresponding SEM images. (C, F, I) Corresponding ZFC/FC curves.

nanoparticles heated at 300 8C. However, in our case the cobalt nanocrystals have a blocking temperature close to room temperature after fast annealing at 275 8C. The annealing mode allows us to build new mesostructures made of hard magnetic nanocrystals with a low coupling constant [66]. We have seen above (Section 10.4.4) that cobalt nanocrystals can organize in fcc superlattices (Fig. 10.13). Similar annealing processes have been carried out directly on the superlattices (see Chapter 1) and, as previously, a similar phase transformation from poorly crystallized fcc cobalt nanoparticles to hcp single crystals keeping the same size is observed [67]. Nevertheless, the fcc structures of the superlattices are retained. Furthermore, it is seen that the internal order increases with the annealing temperature, while the interparticle gap decreases. For any annealing temperature, the ZFC/FC curves (Fig. 10.13) show a drastic increase in the blocking temperature from 115 K (Fig. 10.13 C) for the native materials to 245 K (for a sample annealed at 300 8C, Fig. 10.13 I). This is mainly due to the increase in the MAE. However, similarly to the result shown in Section 10.4.4, the

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final value of Tb depends on the annealing temperature. This has to be related to both an increase in the internal order and a decrease in the interparticle gap, which produces an increase in the coupling constant and then the dipolar interaction. These results can have important consequences for the building of a magnetic device operating at room temperature and based on the organization of magnetic nanocrystals.

10.6 Conclusion

In this chapter, we demonstrated collective magnetic properties due to the self-organization of nanocrystals. For these mesostructures made of uncoalesced nanocrystals, the dipolar interactions are responsible for the collective behavior. The theoretical model presented here gives a general framework to explain, at least qualitatively, the magnetic collective properties. Furthermore, in spite of the longrange scale of the dipolar interaction, it has been shown that the structure of the organization of nanocrystals plays an important role in the magnetic response depending on whether they are in 0D, 1D, 2D or 3D. Beyond this, the internal order also changes the magnetic behavior and indeed these intrinsic properties can have an important role in the future. Moreover, the structure of the film depends also on the hardness of the magnetic materials and this also changes the magnetic response. Hence, if the general picture emerging of these magnetic collective properties appears to be quite easy to understand, there is a very complicated underlying behavior due to the various levels of organization.

Acknowledgments

We would like to thank Dr. G. Lebras and Dr. E. Vincent for providing us with SQUID facilities from CEA/DSM/DRECAM/SPEC.

References

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56 J. Legrand, C. Petit, M. P. Pileni, J. Phys. Chem. B 2001, 105, 5643. 57 C. Petit, J. Legrand,V. Russier, M. P. Pileni, J. Appl. Phys. 2002, 91, 1502. 58 The zero-field cooled/field cooled (ZFC/ FC) experiment is typical in the measurement of the magnetization of nanoparticles. The sample is initially cooled in a zero field to 3 K. A 75-Oe field is then applied and magnetization is recorded as the temperature is increased. This curve is called zero-field cooled. At a given temperature, called the blocking temperature, Tb, a maximum in the magnetization is observed. In the FC procedure, far above Tb, the sample is progressively cooled and the magnetization is recorded. In a system without interactions, the magnetization increases continuously by decreasing the temperature. In a strongly interacting system, the FC curve shows a plateau below Tb, more or less pronounced, depending on the strength of the interactions. 59 J. P. Chen, C. M. Sorensen, K. J. Klabunde, G. C. Hadjipanayis, Phys. Rev. B 1995, 51, 11527. 60 V. Russier, C. Petit, M. P. Pileni, J. Appl. Phys. 2003, 93, 10001. 61 M. Spasova, U. Wiedwald, R. Ramchal, M. Farle, M. Hilgendorff, M. Giersig, J. Magn. Magn. Mater. 2002, 240, 40. 62 B. Stahl et al. Adv. Mater. 2002, 14, 24. 63 M. Chen, D. E. Nikles, J. Appl. Phys. 2002, 91, 8477. 64 X. Nie, J. C. Jiang, E. I. Meletis, L. D. Tung, L. Spinu, J. Appl. Phys. 2003, 93, 4750. 65 A. H. Morrish, S. P. Yu. J.Appl. Phys. 1955, 26, 1049. 66 C. Petit, Z. L. Wang, M. P. Pileni, J. Phys. Chem. B (2005) to be published; Z. L. Wang, M. P. Pileni, J. Phys. Chem. B, in press. 67 I. Lisiecki, P. A. Albouy, C. Andreazza, M. P. Pileni, submitted for publication.

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11 Exploitation of Self-Assembled Nanostructures in Optical Biosensors Janos H. Fendler

11.1 Introduction

Biosensing consists of molecular recognition, signal amplification and detection. The relative ease of fabrication of optically transparent ultrathin films composed of size-quantized and shape-controlled semiconducting, metallic and magnetic nanoparticles with unique optical, electro-optical, plasmonic, electrical and magnetic properties has prompted the increasing interest in employing nanostructures as molecular recognition elements [1]. In the present review attention will be focused on molecular recognition elements composed of: (a) gold and silver nanoisland and thin films deposited onto optically transparent glass substrates; (b) thiol-functionalized monolayers, self-assembled onto gold and silver thin films on glass substrates (referred to as self-assembled monolayers, SAMs); (c) chemically stabilized gold and silver nanoparticles (those stabilized by thiol-functionalized monolayers are often termed monolayer-protected clusters, MPCs); and (d) gold (or silver) nanoparticles linked to gold and silver nanoisland and thin films, via appropriately functionalized SAMs. Gold (or silver) nanoparticles in the last system have been fruitfully employed for the amplification of the molecular recognition signal. Attention will be limited to optical detection methods, specifically to those based on propagating surface plasmon resonance (as employed in surface plasmon resonance, SPR, spectroscopy) and those that are governed by localized surface plasmon resonance (as employed in transmission surface plasmon resonance, T-SPR, spectroscopy). Substrate preparations will be surveyed in Section 11.2. Sections 11.3 to 11.5 will summarize the constructions of SAMs, monolayer-protected metallic particles and the layer-by-layer self-assembled ultrathin films. The principles of SPR and T-SPR will be delineated in Section 11.6 and gold (or silver) nanoparticle enhanced surface plasmon resonance spectroscopy (both SPR and T-SPR) will be discussed in Section 11.7.

Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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11.2 Substrate Preparation

Vacuum evaporation is the usual method of choice for depositing ultrathin (10– 200-nm-thick) gold or silver films onto glass substrates. Vacuum deposition or sputtering involves the condensation of atoms produced by evaporation of a metal shot placed on a heating element [2]. The thickness of the metal film is monitored in situ by a quartz crystal microbalance. Ultrathin (less than 10 nm nominal thickness) evaporated gold films have well-defined island structures and optical properties similar to those of colloidal gold nanoparticles [3–5]. Figure 11.1 shows typical TEM images of gold nanoislands obtained by the slow (0.0014–0.0028 nm s–1) evaporation of gold onto Formvar-covered, carbon-coated, 200-mesh copper grids [6].

Fig. 11.1 A typical TEM image of ultrathin gold nanoislands (2.5 nm nominal thickness), evaporated onto Formvar-covered, carbon-coated, 200-mesh copper grids at a rate of 0.0014–0.0028 nm s–1. The gold nanoislands were slightly elongated; therefore the two axes are shown separately in the inserted histogram. (Taken from [6] and reproduced with permission of the American Chemical Society).

Patterned deposition can be accomplished by electron-beam (EB) lithography. Figure 11.2 shows an array of elongated gold nanoparticles deposited by EB lithography [7]. It also shows the extinction spectra obtained by excitation with transverse (A) and longitudinal (B) polarizations. Typically, EB lithography involves the following steps: (a) spin coating of a conducting substrate (either an ITO glass or a glass slide coated by ca. 10-nm-thick gold film) with a 70–100-nm electron-sensitive resist, usually poly(methyl methacrylate) (PMMA); (b) forming the desired

11.2 Substrate Preparation

Fig. 11.2 Extinction spectrum of a regular array of gold elongated nanoparticles: major and medium axes of 175 and 126 nm, respectively, are parallel to the substrate (particle aspect ratio r = 1.39); particle height is 40 nm and the spacing between the particles is 461 nm. The spectrum is acquired by transmission under normal incidence in water. “A” denotes the transverse polarization and “B” the longitudinal polarization. Inset: scanning electron microscopic image of the nanoparticle array. (Taken from [7] and reproduced with permission of the American Institute of Physics).

pattern by EB lithography (which burns off the polymer and the thin gold film); (c) chemical development of the exposed PMMA; (d) thermal evaporation (at a rate of 1–2 nm s–1) of the gold (or silver) film; (e) removal of the remaining PMMA film by acetone (and the 10-nm gold film, if present, by etching with an aqueous solution of KI and I2 (4.0 and 1 g in 15 mL water)); and (f ) imaging the pattern by SEM and/or AFM [8–11]. Difficulty of scale-up, beyond a few microscopic slides at a time, and the expenses involved are the disadvantages of EB lithography. Electrochemical deposition of ultrathin metallic films and/or nanoislands is attractive since a high degree of control can be achieved by the judicious employment of Faraday’s laws (96,500 n coulomb results in the deposition of 1 g mol of material, where n is the number of electrons passed in depositing one mole of the deposit). Furthermore, composition, defect chemistry and shapes (along with thickness) are controllable at a reasonable cost. Anodic depositions are limited to metallic substrates since the process involves the electrolytic reduction of metal in the presence of the appropriate anions. Galvanic replacement reactions have been used for alloying and dealloying silver and gold nanoparticles as well as for preparing nanoshells [12]. Regardless of the method employed for deposition the careful cleaning and preparation of the substrate is vital. Glass slides are typically cleaned by piranha solu-

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tion, rinsed copiously with distilled water and dried by dry nitrogen. Peeling off the metallic film (or nanoislands) from the substrate surfaces presents a difficulty for constructing sensors for aqueous solutions. This difficulty can be overcome by the deposition of a few-nanometer-thick layer of chromium prior to the evaporation (or electrodeposition) of the metal or by postdeposition treatments (annealing, for example). It should be stated that SPR and T-SPR spectroscopies require different gold (or silver) coated substrates: an utrathin contiguous 50–150-nm-thick film for the former and 5–15-nm-thick nanoislands for the latter.

11.3 Preparation of Self-Assembled Monolayers

Self-assembled monolayers (SAMs), as the term implies, are spontaneously formed by the adsorption of long-chain alkane (or arene) thiols or disulfides from their alcoholic (or aqueous) solutions onto gold (or silver or platinum) substrates [13–18]. The kinetics of self-assembly have been extensively investigated and discussed in terms of a multistep process involving physisorption, chemisorption and restructuring [15]. Formation of strong Au–S bonds and hydrophobic attraction between the neighboring apolar chains of the thiols (or dithiols) govern SAM formation and are responsible for the reasonably uniform and defect-free coverage of the coinage metal surface. The extent of substrate coverage by SAMs (i. e., the extent of defects and pinholes) can be quantified by determining the faradaic response of a redox couple ([Fe(CN)6]3–/[Fe(CN)6]4–, for example) in aqueous solution employing a working electrode in the presence and absence of SAMs. The current peaks (using the uncoated working electrode) are completely suppressed in the presence of a defect-free SAM coating [19–21]. The most likely mechanism of SAM formation involves electron transfer; an anodic oxidation of alkane (or arene) thiols [22–24]: RS–H + Au RS–Au + Au + e–

(1)

and a cathodic reduction of dialkyl disulfides [23, 24]: RS–SR + e– RS–Au + RS–

(2)

In the case of Eq. (2), some of the thiolate ions (RS–) formed are adsorbed onto the gold surface by an anodic oxidation (analogous to Eq. 1): RS– + Au RS–Au + e–

(3)

and the rest diffuse away into the bulk solution where they are protonated (to RSH) and/or oxidized (back to RS–SR). An important corollary of Eqs. (3–5) is that more efficient SAM formation can be achieved under appropriate potential control. Due

11.3 Preparation of Self-Assembled Monolayers

care needs to be exercised, however, in applying a potential to adsorbed SAMs [25]. Potential-induced structural and chemical changes may include: an order-to-disorder phase transition, defect formation and hence increased ion permeabilities, desorption and readsorption of the SAM, chemical changes of the electroactive functional groups on the SAM, restructuring of the gold (or silver) substrate surface, and any combination (to a different extent) of all of the above. Great advances have been made on the in situ functionalization of SAMs [18]. Amino-, carboxylic acid-, anhydride-, hydroxyl- and cyano-terminated SAMs have been treated by surface reactions to obtain other desired functionalities (including those with electrochemical and photochemical activities). It should be pointed out, however, that standard organic reactions that proceed well in bulk solution often behave differently at SAM surfaces. It is desirable to select surface reactions with the highest possible yield, since the by-products (or reagents) may react with the substrate surface and/or with the SAM already present. Derivatization of SAMs is important, of course, in the construction of molecular recognition elements for biosensors. Formation of an SAM can be monitored in situ by electrochemical (quartz crystal microbalance, cyclic voltammetry, impedance spectroscopy) and optical (ellipsometry, surface plasmon resonance imaging, infrared reflection absorption spectroscopy) measurements. The structure of the SAM formed can be imaged ex situ by microscopic techniques (scanning electron and scanning force microscopies). Electron diffraction, X-ray diffraction, Fourier-transform infrared (FTIR) spectroscopy, scanning force microscopy, and computer simulations have established a hexagonal symmetry of sulfur atoms in surfactant thiolates with S–S distances of and the formation of a SAM on the Au(111) surface with a p0.497  pnm,  ( 3  3† R 308 overlayer with typical tilting of the alkyl chains of 308 with respect to the gold substrate (Fig. 11.3) [26]. In general, the tilt angle of alkane thiolates is smaller on silver than on gold substrates. However, rigid thiol SAMs behave differently; they have a relatively small tilt from the gold or silver substrate normal. Quantitative FTIR spectroscopy of 4'-substituted 4-mercaptobiphenyls established the tilting of the biphenyl planes from the surface to be 14, 20 and 128, and rotation around the 1,4 axis of the ring to be 30, 15 and 308 for the NO2 ,

Fig. 11.3 Cartoon showing the self-assembly on gold and silver surfaces.

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C(O)CH3 and CO2Et substituents, respectively, on gold substrates [27]. On silver substrates, tilt angles for the NO2 , C(O)CH3 and CO2Et 4'-substituted 4-mercaptobiphenyl SAMs were found to be 8, 21 and 118, respectively, while the rotation angles around the 1,4 axis of the ring were 30, 15 and 308. Using scanning tunneling microscopy (STM), a significant insight has been gained into self-assembly and into the structure of self-assembled films [28].

11.4 Monolayer-Protected Metallic Particles

Alkane (or arene) thiols or disulfides have also been self-assembled onto gold, silver, platinum and other metallic nanoparticle surfaces, which are sometimes referred to as monolayer-protected clusters (MPCs). Since they are stabilized by covalently linked molecules, which form a monolayer-thick capping, MPCs can be considered to be large macromolecules. Importantly, they can be isolated from their dispersions as solids and redispersed in a solvent without structural or chemical alteration. They can be functionalized and subjected to all the synthetic procedures (without breaking the metal–S bonds) known to chemists. The relative ease of preparation of MPCs in large quantities is useful, since it permits their characterization by such standard methods as elemental analysis, spectroscopy (visible, infrared, NMR, EPR), microscopy (TEM, SEM, scanning tunneling) and electrochemical methods in dispersion.

11.5 Layer-by-Layer Self-Assembled Ultrathin Films

Self-assembly of alternating layers of oppositely charged polyelectrolytes and nanoparticles (or nanoplatelets) is deceptively simple (see Fig. 11.4). Self-assembly is governed by a delicate balance between adsorption and desorption equilibria. In the self-assembly of nanoparticles, for example, the efficient adsorption of one (and only one) monoparticulate layer of nanoparticles onto the oppositely charged substrate surface is the objective of the immersion step. Desorption of nanoparticles forming a second and additional layers (and preventing the desorption of the first added layer) is the purpose of the rinsing process. The optimization of the self-assembly in terms of maximizing the adsorption of nanoparticles from their dispersions and minimizing their desorption on rinsing requires the judicious selection of stabilizer(s) and the careful control of the kinetics of the process. Forces between nanoparticles (or nanoplatelets) and binder nanolayers (polyions or dithiols, for example) govern the spontaneous layer-by-layer self-assembly of ultrathin films. These forces are primarily electrostatic and covalent (for selfassembled monolayers, SAMs, of dithiol derivatives onto metallic surfaces) in nature, but they can also involve hydrogen bonding, p–p interactions, van der Waals attractions, hydrophobic and epitaxial or other types of interactions. It is impor-

11.5 Layer-by-Layer Self-Assembled Ultrathin Films

Fig. 11.4 Schematics of layer-by-layer self-assembly.

tant to recognize that polyionic binders must have counterions which can be displaced in order to electrostatically bind them to the oppositely charged surface. The use of dithiols is only relevant with building blocks which incorporate accessible metal atoms, M (Au and Ag nanoparticles, for example), or semiconducting nanoparticles (MS and MSe, for example where M = Cd, Zn, Pb) in which covalent M–S bonds can be formed. The properties of the self-assembled multilayers depend primarily on the choice of the building blocks used, their rational organization and integration along the axis perpendicular to the substrate. Sequential adsorption of oppositely charged colloids was reported in a seminal paper [29]. Self-assembly was subsequently “rediscovered” and extended to the preparations of multilayers of polycations and phosphonate anions [30–32], as well as to the layering of polyelectrolyte [33]. Construction of electrodes coated by polyelectrolytes, clays and other materials often involved self-assembly [34, 35], albeit the method had not been called as such. Self-assembly is now routinely employed for the fabrication of ultrathin films from charged nanoparticles (metallic, semiconducting, magnetic, ferroelectric, insulating, for example) nanoplatelets, (clays or graphite platelets, for example), proteins, pigments and other supramolecular species [32, 36, 37]. Indeed, layer-by-layer self-assembly has been recognized as a subfield of colloid chemistry, and the exponentially increasing research publications are listed at a website [38]. The fact that a large variety of molecules, polyelectrolytes, nanoparticles and nanoplatelets, can be layer-by-layer adsorbed, in any desired order, is the greatest advantage of self-assembly. The oppositely charged species are held together by strong ionic bonds and form long-lasting, uniform and stable films which are often impervious to solvents. No special film balance is required for the self-assembly; indeed the method has been referred to as a “molecular beaker epitaxy” [39]. Furthermore, self-assembly is economical (dilute solutions and dispersions are

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used and the materials can be recovered) and readily amenable to scaling up for the fabrication of large-area, defect-free devices on virtually any kind and shape of surface.

11.6 Surface Plasmon Resonance Spectroscopy and Transmission Resonance Surface Plasmon Resonance Spectroscopy

It is important to differentiate between surface plasmon resonance (SPR) spectroscopy and transmission surface plasmon resonance (T-SPR) spectroscopy. Conventional SPR spectroscopy is based on propagating surface plasmons, which are charge-density oscillations at the interface of an ultrathin metallic (typically Au or Ag) film and a dielectric. Advantage is taken of localized surface plasmon (LSP) resonance in T-SPR spectroscopy. LSPs are charge-density oscillations confined to coinage-metal nanoparticles and nanoislands [40]. LSP resonance (unlike propagating surface plasmon resonance) manifests itself in highly intense extinction (i. e., transmission + scattering) spectra. An example of LSP resonance is provided by the well-known red color of gold nanoparticle dispersions in aqueous solutions. In SPR spectroscopy the propagating surface plasmons are excited by p-polarized light under certain experimental conditions (typically via a prism, arranged in the Kretschmann geometry, see Fig. 11.5). The SPR sensor typically contains ultrathin layers of materials (monolayer containing the molecular recognition element and analyte in the simplest case), deposited or self-assembled onto the gold substrate. These layers, along with the semi-infinite medium (air) and prism are

Fig. 11.5 Schematics of SPR spectroscopy using the Kretchmann configuration. On the right-hand side, plots of incident angle versus reflected light intensity are shown for a gold substrate in the absence (left top plot) and presence (right bottom plot) of a self-assembled monolayer.

11.6 Surface Plasmon Resonance Spectroscopy

modeled as four parallel plate layers (1 = air; 2 = prism; 3 = monolayer containing the molecular recognition elements; 4 = analyte) and the thickness and dielectric constants (real and imaginary) for each layer are calculated by relatively straightforward equations using the appropriate effective media approximation [41]. In a typical SPR experiment, the angle of the incident p-polarized light is scanned (at a range where total internal reflection occurs) and the relative intensity of the reflected light is measured. At a fixed wavelength, and at the incident angle corresponding to SPR, the reflectance goes through a minimum. This minimum is extremely sensitive to the refractive indices. Therefore, in the presence of an added layer (the monolayer containing the molecular recognition elements, for example) it will shift to a new value, often accompanied by a change in the shape of the angle of incidence versus intensity of reflected light curve. In practice, variations of incident angle versus intensity of the reflected light are sequentially determined for each stratified layer (layers 2, 3 and 4 in the cited simplest case, for example). Treatment of the SPR data involves the following steps: (a) construction of an appropriate model that describes the behavior of the experimentally probed sample well; (b) generation of plots of angle of incidence versus intensity of reflected light from the model for each layer; (c) experimental determination of angle of incidence versus intensity of reflected light plots for each layer; and (d) comparison of the theoretically obtained and experimentally determined plots for each layer, and recording the adjustable parameters (thickness and dielectric constants) used to obtain the best fit. Confidence in the approach is gained if the parameters obtained from the best fit agree well with known values for layers 1 and 2. In spite of having two adjustable parameters for each layer, quite satisfactory values for thickness and dielectric constants are routinely obtained for eight to ten layers of selfassembled monolayers. The high sensitivity of SPR (10–6 RIU) and the availability of a commercial, inexpensive, versatile dual-channel instrument (Texas Instruments Spreeta, Fig. 11.6) have made SPR sensors highly popular. The last ten years have seen a tremendous development of SPR use in bioanalytical applications, such as the measurement of DNA hybridization, enzyme–substrate interac-

Fig. 11.6 Photograph of the Texas Instruments Spreeta SPR sensor (with a quarter to gage its size) and the schematics of its dual-channel sensing element.

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tions, polyclonal antibody characterization, epitope mapping, protein conformation studies and label-free immunoassays [42]. The intensity and position of the surface plasmon absorption bands (generated by light at an incident wavelength where resonance occurs with the metallic nanoparticles or nanoislands) are characteristic of the type of material (typically, gold, silver or platinum) and are highly sensitive to the size, size distribution and shape of the nanostructures as well as to the environments which surround them. These are the precise properties which are exploited in T-SPR spectroscopy. The first systematic studies on the effects of adsorbed and self-assembled materials on the T-SPR spectrum of ultrathin gold nanoislands (evaporated onto quartz or mica) were reported in 2002 by the Rubinstein group [3]. This report was followed by several other publications of the same group [43, 44]. Van Duyne and coworkers reported an alternative approach in which advantage was taken of the high sensitivity of the LSP resonance of triangular silver nanoparticles to attached or adsorbed materials [45–50]. Triangular silver nanoparticle arrays were prepared by nanosphere lithography (silver was evaporated onto an optically transparent substrate through a mask of polystyrene nanobeads; subsequent removal of the mask left well-ordered two-dimensional triangular silver particles) [45]. The use of gold nanoislands or triangular silver nanoparticles for T-SPR spectroscopy has manifold advantages. First and foremost, the plasmon-resonant particles are ultrabright (an 80-nm-diameter particle has a scattering flux that corresponds to 106 fluorescein molecules [51]), which makes their optical detection highly sensitive. Second, the

Fig. 11.7 Schematics of T-SPR spectroscopy. A TEM image of the gold nanoislands and the shift of the surface plasmon absorption spectrum of the nanoislands in the presence a SAM are also shown.

11.7 Gold-Nanoparticle-Enhanced Surface Plasmon Resonance Spectroscopy

interparticle distances and the morphology of the metallic nanoparticles can be controlled (and reproduced). Third, since they are prepared by vacuum evaporation and immobilized on solid substrates, the metallic nanostructures do not contain any stabilizers and/or capping agents and can, therefore, be readily functionalized (via self-assembly of thiol-functionalized monolayers, for example) or indeed used for sensitive adsorption measurements in their pristine state. Fourth, adsorbed substances can be desorbed (and bound molecules be released) with concomitant recovery of the original T-SPR spectrum; thus, continuous sensing applications (in a flow cell, for example) can be readily set up. The requirements of T-SPR spectroscopy-based sensing are straightforward, and can be performed on miniaturized, robust, and inexpensive transmission spectroscopic equipment (using a fiber optics device based on commercially available components, from Ocean Optics, for example). The schematics of T-SPR spectroscopy are illustrated in Fig. 11.7.

11.7 Gold-Nanoparticle-Enhanced Surface Plasmon Resonance Spectroscopy

Silver and gold nanoparticles are known to amplify the optical signal of closely placed analytes. The well-established and documented examples of metallic-particle-enhanced Raman, infrared and fluorescence spectroscopies are outside the scope of the present review. We limit ourselves to the more recently described amplification of the propagating (SPR) and localized (T-SPR) surface plasmon resonance signals by gold (or silver) nanoparticles. Gold-nanoparticle-enhanced SPR immunosensing was reported in 1998 [52]. The SPR shift observed upon binding proteins to human immonoglobulin G (immobilized on the gold-film SPR sensor) was found to be enhanced by a factor of 25 if the protein was attached to gold nanoparticles [52]. The effect was rationalized in terms of complex interactions between the propagating and localized surface plasmons and simulated for the gold-nanoparticle-enhanced SPR signal of a 1,6-hexadecanethiol SAM by using a five-layer model (Fig. 11.8) [53, 54]. A simple

Fig. 11.8 Reflectivity R of a gold film measured as a function of the incident angle y of a probe laser beam in the ATR configuration. The symbols represent the measured reflectivities in air for the Au film (circles), for a layer of 1,6-hexadecanethiol (HDT) deposited on the Au film (triangles), and for a layer of Au nanoparticles deposited on the Au film–HDT system (squares). The solid lines through the circles and the triangles are calculated fits to the experimental data obtained in the absence of the Au particles. (Taken from [53] and reproduced with permission of the American Chemical Society).

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calculation showed up to 41-fold increased sensitivity of the SPR shift in the presence of gold (or silver) nanoparticles [41]. Similar gold-nanoparticle-enhanced SPR shifts were reported for detection of oligonucleotides [55, 56] and DNA hybridization [55]. We have pioneered the use of gold nanoparticles to enhance the sensitivity of gold-island-based T-SPR spectroscopy. In a recent communication considerable enhancement of the T-SPR shift (caused by the adsorption of double-stranded DNA onto gold nanoislands) by 12-nm-diameter gold nanoparticles attached to the complementary single-stranded DNA was reported (Fig. 11.9) [6]. In this work, gold nanoislands were evaporated onto well-cleaned microscopic glass slides. Depending on individual preparations, the T-SPR absorption maxima of the gold nanoislands were found to be between 570 and 630 nm and had absorbances of 0.12+0.05 (with respect to air). Introduction of 10 mM thiolated DNA into the TE buffer bathing the gold-nanoisland-coated glass slide caused a 12-nm shift of the absorption maxima, indicating the self-assembly of a submonolayer of DNA. Hybridization with the complementary thiolated oligonucleotide (subsequent to the self-assembly of mercaptohexanol spacer, to prevent the nonspecific

Fig. 11.9 Schematics of single-stranded DNA hybridization by its complementary DNA, which is functionalized by gold nanoparticles. T-SPR changes due to DNA hybridization. (Taken from [6] and reproduced with permission of the American Chemical Society).

11.7 Gold-Nanoparticle-Enhanced Surface Plasmon Resonance Spectroscopy

Fig. 11.10 (a) Schematics of the reversible pH-change-induced swelling of gold-nanoparticle-coated poly(2-vinylpyridine) (P2VP) brushes. (b) T-SPR spectra of gold nanoislands (containing poly(glycidyl methacrylate) (PGMA), P2VP polymer brushes and gold nanoparticles) at pH 2.0 and 5.0. (Taken from [57] and reproduced with permission of the American Chemical Society).

attachment of DNA to the gold surface) produced an additional 6-nm peak shift. Significantly, if the hybridization was carried out by complementary DNA which was labeled by 11.7+1.9-nm-diameter gold nanoparticles, the shift of the T-SPR absorption band (22 nm) was substantially greater than that in the absence of the gold nanoparticles (compare spectra 2 and 3 in Fig. 11.9 b). From the density of Au nanoparticles (approximately 400 particles in 1 mm2) the detection limit was estimated to be 4 × 107 oligonucleotides. Gold-nanoparticle-enhanced T-SPR spectroscopy was also employed for monitoring the swelling (and shrinking) of a responsive polymer brush, poly(2-vinylpyridine) (P2VP; Fig. 11.9), induced by changes in pH [57]. In the presence of gold nanoparticles, a 50-nm shift of the absorption maximum of the T-SPR spectrum of the supporting gold nanoislands was observed upon changing the pH from 5.0 to 2.0, corresponding to a swelling of the polymer brushes from 8.1+0.7 to 24.0+2.0 nm (see Fig. 11.10). In the absence of gold nanoparticles the corresponding shift was only 6 nm. Extreme simplicity, ease of operation, versatility and high sensitivity are the advantages of biosensors based on T-SPR spectroscopy. Depositing nanoislands of different composition and/or different shapes on distinct regions of the transparent substrate will open the door to the construction of massively parallel biosensors. This will require, of course, more sophisticated assembly and self-assembly of the appropriate nanostructures.

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12 Nano Lithography Dorothée Ingert and Marie-Paule Pileni

12.1 Introduction

Nanotechnology research is led by the demand for ever smaller device features that are required to improve performance and decrease costs in microelectronics, communication and data storage. Lithographic methods are in the center of this nanotechnology. Usually, the lithography process can be divided into two steps. The first is making the master. This is a structure that provides or encodes a pattern to be replicated. Thus, making the master is usually done by serial techniques such as writing with a focused beam. The second is the replication, where the pattern transfer should be done rapidly and with high accuracy. Generating patterned surfaces at the nanoscale is beyond the limits of standard lithography techniques. Indeed, very few methods provide the ability to work in the sub-50-nm scale [1–3]. In addition to well-established methods for the fabrication of nanometer-scale structures [2], such as electron- and ion-beam lithography, there is a need for alternative simple techniques in order to save processing time and costs [4]. This need has given rise to different kinds of approaches like, for example, the use of self-assembled monolayers (SAMs) [3, 5]. In this chapter we will focus on three techniques that can be called “colloidal lithography” : the major difference between these procedures is related to the type of mask used, while the standard techniques to pattern the substrate such as metal deposition or ion-plasma etching are kept similar. Let us list these three colloidal lithography techniques. The mask is: .

. .

a monodispersed-spheres template (typically polystyrene (PS) beads with an average diameter of 200 nm) – this is called nanosphere lithography; block copolymers; nanocrystals.

The resolution and limitations of these three techniques will be described and discussed.

Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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12.2 Colloidal Lithography: Spheres Lithography

One of the first colloidal lithography processes was nanosphere lithography, initially called natural lithography [6, 7]. The idea was to use a 2D deposition of polymer spheres (organized or not) onto a substrate to pattern surfaces. 12.2.1 Ordered-Particle Arrays: Nanosphere Lithography (NSL)

In 1981, Fischer and Zingsheim [6] proposed the use of a monolayer of spheres (about 300 nm). They evaporated a colloidal suspension onto a glass plate and obtained, in some regions, hexagonally packed spheres. After platinum deposition under vacuum conditions, they obtained triangular structures. One year later, Deckman and Dunsmuir [7] improved the technique in which spherical colloidal particles are used to define larger-area lithographic masks. The deposition is either random or with ordered arrays over the entire surface of a macroscopic substrate [8]. The coating procedure developed to produce microcrystalline arrays is based on a spin-coating process; they also used a Langmuir–Blodgett-based technique [9]. It is necessary that the colloids wet the substrate surface. Then, the substrates are either precoated with a surfactant layer or a surfactant is added to the colloidal solution. On the tens of micrometers scale, point defects and dislocations are present [7–9]; this is related to the formation of hexagonally closepacked arrays which is a two-step mechanism with nucleation and growth [10]. Then in the 1990s, Van Duyne explored the versatility of the technique, which was called nanosphere lithography [11, 12]. His group changed either the substrate (semiconductor, metal or insulator) or the deposition material (metal, organic semiconductor or insulator). They used two ways to deposit the nanospheres: spin coating or hand (drop) coating. The technique was then improved to control not only the shape of the resulting particles but also the shape of the periodic particle array [13]. To do this, colloids having different diameters and organized in a single or double layer as a mask are used. With single-layer nanosphere arrays, the final structure is made of triangular particles organized in a honeycomb structure. A schematic representation is given in Fig. 12.1. Indeed, the deposited material passes through the threefold triangular-shaped interstices

Fig. 12.1 Schematic representation of nanosphere lithography.

12.2 Colloidal Lithography: Spheres Lithography

in the mask. The double-layer nanosphere mask is prepared using higher colloid solution concentrations. In this case, the evaporated material passes through the sixfold hexagonal-shaped interstices in the mask. This leads to elliptically shaped particles organized in a hexagonal network. More recently, this group described a novel approach to tune the shape of the final particles. This approach, called angle-resolved nanosphere lithography [14], is a variant of the standard nanosphere lithography. This is accomplished by controlling the angle between the normal to the surface of the sample assembly and the propagation vector of the material deposition beam [14, 15]. This makes it possible to reduce the in-plane particle dimensions. Another very simple method to obtain a colloid monolayer is to deposit a droplet of a colloid solution on a glass plate and control the evaporation time and the temperature [16, 17]. Leiderer et al. developed a method to use almost any substrate [18–20]. The entire monolayer is transferred from the glass substrate onto a water surface. From there, it is transferred to the desired substrate by contacting it from above with a horizontally held substrate. 12.2.2 Nonorganized particle patterns

As described above, Deckman et al. [7] used random arrays of colloidal particles to texture surfaces. Random sphere arrangements are produced because polyballs adhere to the substrate after diffusing through the aqueous colloidal suspension close to the substrate surface. Indeed, when an electrostatic attraction is set up between a substrate and an aqueous suspension of charged polyballs, a randomly arranged monolayer-thick coating can be obtained. Charged spheres adsorb randomly onto an oppositely charged surface, and are arranged through electrostatic interactions. The randomness of the initial interactions of the colloids produces

Fig. 12.2 SEM images of 107-nm particle films with (A) coverage 0.12+0.01 with no added salt; (B) coverage 0.40+0.02 with 10 mM salt. (Reprinted with permission from P. Hanarp, PhD Thesis, Chalmers University, Sweden).

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uniformity over large surface areas. This can be an advantage compared to the hexagonally close-packed arrays where dislocations and points defects are common. In this case, the substrate coverage is controlled and, consequently, the average distance between colloids [21, 22]. This control is obtained by changing the colloid concentration or by adding salt to the colloidal solution (Fig. 12.2). With this deposition process, combined with a heat treatment leading to a shape modification of the beads, gold nanodisks have been formed [23]. 12.2.3 Applications

Colloidal lithography leading to nanostructured surfaces with defined roughness and periodicity finds several applications, for example, in optical studies, catalysis, magnetism or biological devices. Here, we will just mention a few of these. Van Duyne et al. [24, 25] made in-depth studies of the optical properties, the surface plasmon resonance, of periodic arrays of silver particles. Indeed, as described previously, the shape, size and particle spacings are tuned by nanosphere lithography. This was extended to surface-enhanced Raman spectroscopy (SERS) [26]. Another application is based on the understanding of catalytic processes. In the fabrication of a model catalyst the kinetic parameters, such as particle size and shape, interparticle distances or the influence of the substrate [27, 28], are controlled. To conclude this list of the applications of colloidal lithography, one of the very promising fields is biology. It has been demonstrated that arrays of metal particles can be used as nanosensors by binding biological molecules to them [29–31]. Another use could be the fabrication of implants where the nanostructuration plays a very efficient role [32].

12.3 Colloidal Lithography: Copolymer Lithography

Although block copolymers have been largely studied for several decades, it is only in the last few years that they have been used for nanotechnology [33]. Here, we briefly describe how they are used as lithographic masks and present some combined techniques to improve their potential applications. 12.3.1 Block Copolymer Used as a Lithographic Mask

Block copolymers are made of two chemically different chains bonded covalently. When the blocks are incompatible, they spontaneously self-assemble into microdomains which leads, at equilibrium, to an ordered structure. Owing to their mutual repulsion, dissimilar blocks tend to segregate into different domains, the spatial extent of the domains being limited by the constraint imposed by the chemical connectivity of the blocks. Parameters like the chemical composition of the differ-

12.3 Colloidal Lithography: Copolymer Lithography

ent blocks, their length or their molar mass control the microphase morphology, size or periodicity. This high adjustability enables the topography of the block copolymer pattern to be of interest for nanolithography masks [34–36]. Indeed, one block relative to another block of the copolymer has chemical or physical differences. This involves a selective process, e. g., the etching rate is different between the two blocks, leading to the formation of a template of either a porous network or arrays of dots [37–39]. Various methods were developed to enhance the etch selectivity. A common approach feature is to have one of the block phases containing suitable inorganic components [40–45]. This makes it possible to achieve etching contrast. This template is then used for pattern transfer, either by direct replication into the substrate through etching or as a growth matrix. Mansky et al. [34, 35] first demonstrated that monolayer films of diblock copolymer microdomains could potentially be used as masks for nanolithography, on the scale of a few tens of nanometers. Park et al. [37] obtained dense periodic arrays of holes and dots by spin coating diblock copolymer thin films. The final holes obtained were 20-nm across, hexagonally ordered, with 40-nm spacing and polygrain structure, yielding a pattern with approximately 1011 holes cm–2. 12.3.2 Hierarchical Pattern

The main limitation in using block copolymers as lithographic masks is that it is hard to control the order on the global scale, even if locally the self-assembled structure is very precise. Indeed, self-assembly of block copolymers leads to polygrain structures with defects such as grain boundaries and/or dislocations. Several techniques are developed to induce long-range order of the microdomains of block copolymers. They are based on achieving anisotropic properties of the polymer. The methods currently used in the polymer field are application of mechanical flow fields, temperature gradients, electric fields or solvent control [33]. Another way to provide better control of block copolymer microdomains is to use other lithographic techniques in order to prepattern the substrate. For example, self-assembled monolayers (SAMs) allow chemical modification of the surface pattern [46, 47]. This leads to a higher homogeneity of the interactions between the block copolymer and the substrate [48]. The substrates can also be patterned topographically. Micropatterning a substrate is done with a PDNS pattern, which can be generated by soft lithography and used as a mold for block copolymers [49, 50]. Standard lithography is used to fabricate grating substrates with, for example, microscale periodicity and various heights. Ordered arrays are formed in this way by spin casting a block copolymer over surfaces patterned with shallow grooves [51, 52]. An illustration of this is shown in Fig. 12.3, where the bands, patterned by interference lithography, control the nanostructure location. Dots that are organized in rings or stars are also achieved by a similar process, with prepatterning generated by photo or e-beam lithography [44]. This leads to a large variety of rather complex structures on the mesoscale, with dot arrays inside on the nanoscale.

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Fig. 12.3 Pattern transfer from an ordered PS/PFS 50/12 polymer to form an array of ordered silica nanostructures. (a) Side view of the PFS pattern in 240-nm-wide grooves. (b) Side view and (c) plan view of the pattern after it has been transferred into an underlying silica layer by reactive ion etching. The silica posts in (c) have the same spatial organization as the originating PFS features and aspect ratios exceeding 3. PFS: polyferrocenyldimethylsilane. (Reprinted with permission from J. Y. Cheng, C. A. Ross, E. L. Thomas, H. I. Smith, and G. J. Vancso, Applied Physics Letters, 81, 3657 (2002). Copyright 2002, American Institute of Physics).

Block copolymer lithography has led, by combination with standard semiconductor lithography techniques, to, for example, the fabrication of semiconductor capacitors. Another field in which this lithography is involved is the production of magnetic structures [43, 45]. For example, cobalt nanodot arrays have been prepared; they are small enough to be a single magnetic domain.

12.4 Colloidal Lithography: Nanocrystals

Here, we present nanocrystals as a very recent and new kind of lithographic mask. Indeed, as their size is nanometric, they potentially improve the resolution scale compared with the standard lithographic techniques. Moreover, they can also be organized in the mesoscale [53] with interesting geometries like rings [54, 55] or lines [56–59]; for these reasons they can be good candidates for this purpose.

12.4 Colloidal Lithography: Nanocrystals

12.4.1 Process

The technique used is based on a two-step reactive ion etching (RIE). A thin film of polymer is spin-coated onto a silica substrate. This “multilayer” substrate makes it possible to increase the etching depth. Ferrite nanocrystals are deposited onto the multilayer substrate. They are of great interest because, as they are oxides, they are O2-plasma resistant in the etching conditions; moreover, their organizations are substrate independent making it possible to obtain mesostructures even on a polymer film. Different nanocrystal deposition methods are used depending on the geometry of the desired mask. Rings or lines made of nanocrystals can be formed. Using anticapillarity tweezers to maintain the substrate during the deposition of a droplet of the nanocrystal solution leads to the formation of rings due to Marangoni instabilities [54, 55]. If the substrate is immersed in a nanocrystal solution and a magnetic field is applied during the evaporation process, lines made of nanocrystals are formed [56–59]. A first RIE (O2) etches the polymer leading to the formation of a premask. This makes it possible to increase the depth of the mask and thus reach the silica substrate. The second RIE step involves an SF6 plasma which will etch this substrate. 12.4.2 Mesoscale

Mesostructures made of ferrite nanocrystals are used as masks and the resolution of this technique in the hundred-nanometer-scale regime has been checked. Two mesostructure geometries have been used. The ring geometry is kept before and after etching (Fig. 12.4 A and B). Analyses (EDX and XRD) prove that the transferred ring pattern is made of SiO2. Hence, mesostructures are reproduced in a given substrate through a nanocrystal mesoscopic organization used as a lithographic mask [60]. This is the first example where the use of nanocrystals as masks is demonstrated. In the ring geometry, even if the diameter remains equivalent, a loss in the ring profile resolution is observed compared to that obtained before etching. This is explained by the inhomogeneity in the thickness of the pattern mask. In fact, a sinusoidal thickness profile of the mask induces the increase in the width of the etching replica [61]. Thus, this technique loses in resolution if the mask height is not homogeneous. Line geometry has the advantage of the same average height. After etching, the dimension and the resolution of the lines are retained (Fig. 12.4). The precision of the lines remains equivalent before and after etching. This indicates that the resolution transfer improves with increasing the regularity of the mask relief. As with rings, lines made of ferrite nanocrystals play a very efficient role in a transferring mask. This technique makes it possible to pattern a large surface area in a very short time. In this range (hundred nanometers), it gives good resolution if the mask relief is homogeneous.

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Fig. 12.4 (A, B) AFM images of a ring made of 10-nm maghemite obtained before and after the etching process, respectively, with the cross sections in inserts. (C, D) AFM images of lines before and after etching, respectively, with the cross sections in inserts.

12.4.3 Nanoscale

After employing mesostructures, an individual nanocrystal is used as a lithographic mask to reach a resolution of about 10 nm. The mask consists of hematite needles with a diameter of 40 nm and length of 280 nm. The transferred individual needles are very well defined. This means that it is possible to use nanocrystals with a smaller dimension of about 10 nm as lithographic masks. This is, to our knowledge, the first time that an individual nanocrystal has been used as a mask [62]. Nevertheless, it must be noted that although this method is good enough to pattern dimensions of about 10 nm, it is not satisfactory for lower dimensions (a few nanometers). When needles are packed in 2D, which means with

12.4 Colloidal Lithography: Nanocrystals

height homogeneity and separated by few nanometers, in the transferred pattern the outline is no more discernable. Thus, it seems that this technique reaches its spatial resolution at a few nanometers. To be able to determine precisely the accuracy of this method, the dimensions of the native nanocrystals are compared to the pattern observed after transfer. For the transferred patterns, the average width and height are 86 and 27 nm, respectively. The transfer takes place through 87 nm (60 nm poly(methyl methacrylate) and 27 nm silica). The needle width increases by approximately 8 nm with the etching. This means that on the side of the needles, a loss of 4 nm in resolution during the etching of a total height of 87 nm is observed. If a perfect perpendicular etching is considered, this is equivalent to having a deviation of 2.638. This difference in the width value shows the limitation of this precise technique that is efficient for masks in the tens of nanometers scale. From this result, a spacing between objects of less than 10 nm can be deduced. This means the average distance between nanocrystals is a crucial parameter for the transfer. In order to prove that this technique really achieves spacings smaller than 10 nm, field emission gun scanning electron microscopy (FEG-SEM) patterns are obtained. Figure 12.5 A shows clearly that the isolated needle is well separated from the “V” needle. The distance between them is 9.3 nm (Fig. 12.5 B) and clearly confirms that with the technique described here it is possible reach a spacing smaller than 10 nm. This is, to our knowledge, the first time that an individual nanocrystal has been used as a mask. The etching method (two-step RIE) gives very good results in the tens of nanometers scale with a spacing below 10 nm. The resolution reached is in the same scale as that of methods such as electron lithography, with a great difference in processing time and cost.

Fig. 12.5 FEG-SEM images of transferred needles with the smallest spacing: (A) tilted 108, (B) nontilted.

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12.5 Conclusion

In this chapter, we have presented three techniques that can be called “colloidal lithography”. Nanosphere lithography can pattern a rather large surface area with defined final particle shapes. The smallest spacing that has been attained with usual nanosphere lithography is about 50 nm. With block copolymer lithography, the dot/cylinder shape is most commonly obtained. The main limitation is to get well-resolved periodic arrays over a large area. The developments of this technique are mainly based on combining it with patterns obtained with standard lithography methods. In nanocrystal lithography, a resolution down to 10 nm can be reached which starts to be competitive with electron lithography. To reach the fewnanometer scale, individual nanocrystals or 2D organizations could be suitable masks but the patterning technique has to be changed. With these new alternative techniques, it appears that the present limitations in lithography, such as the production of particles differing in their sizes, shapes and interparticle spacings, can be overcome.

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42 R. G. H. Lammertink, M. A. Hempenius, J. E. van den Enk,V. Z. H. Chan, E. L. Thomas, G. J. Vancso, Adv. Mater., 2000, 12, 98. 43 J. Y. Cheng, C. A. Ross,V. Z. H. Chan, E. L. Thomas, R. G. H. Lammertink, G. J. Vancso, Adv. Mater., 2001, 13, 1174. 44 R. Glass, M. Möller, J.P. Spatz, Nanotechnology, 2003, 14, 1153. 45 D. G. Choi, J. R. Jeong, K. Y. Kwon, H. T. Jung, S. C. Shin, S. M. Yang, Nanotechnology, 2004, 15, 970. 46 A. Kumar, G. M. Whitesides, Appl. Phys. Lett., 2002, 1993, 63. 47 Y. Xia, G. M. Whitesides, Annu. Rev. Mater. Sci., 1998, 28, 153. 48 J. Heier, J. Genzer, E. J. Kramer, F. S. Bates, G. Krausch, J. Chem. Phys., 1999, 111, 11101. 49 T. Deng,Y. H. Ha, J. Y. Cheng, C. A. Ross, E. L. Thomas, Langmuir, 2002, 18, 6719. 50 D. G. Choi, H. K. Yu, S. M. Yang, Mater. Sci. Eng. C, 2004, 24, 213. 51 C. Park, J. Y. Cheng, M. J. Fasolka, A. M. Mayes, C. A. Ross, E. L. Ross, E. L. Thomas, C. DeRosa, Appl. Phys. Lett., 2001, 79, 848. 52 J. Y. Cheng, C. A. Ross, E. L. Thomas, H. I. Smith, G. J. Vancso, Appl. Phys. Lett., 2002, 81, 3657. 53 M. P. Pileni, J. Phys. Chem. B, 2001, 105, 58. 54 M. Maillard, L. Motte, M. P. Pileni, Adv. Mater., 2001, 13, 200. 55 M. Maillard, L. Motte, A. T. Ngo, M. P. Pileni, J. Phys. Chem. B, 2000, 104, 11871. 56 A. T. Ngo, M. P. Pileni, Adv. Mater., 2000, 12, 276. 57 A. T. Ngo, M. P. Pileni, J. Phys. Chem. B, 2001, 105, 53. 58 Y. Lalatonne, L. Motte, J. Richardi, M.P. Pileni, Phys. Rev. E, 2004, 71, 011404. 59 M. P. Pileni,Y. Lalatonne, D. Ingert, I. Lisiecki, A. Courty, Faraday Discuss., 2004, 125, 251. 60 D. Ingert, M. P. Pilen, J. Phys. Chem. B, 2003, 107, 9617. 61 C. J. Huang, X. P. Zhu, C. Li,Y. H. Zuo, B. W. Cheng, D. Z Li, L. P. Luo, J. Z Yu, Q. M. Wang, J. Cryst. Growth, 2002, 236, 141. 62 D. Ingert, M. P. Pileni, submitted.

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13 Shrinkage Cracks: a Universal Feature Marie-Paule Pileni

All of us have observed crack patterns inside and outside our laboratories with various materials. These cracks are part of our life and most of us never pay any attention to them. In fact they exist in both natural and man-made systems. They arise in materials that contract on cooling or drying. When the stress leading to such contractions exceeds the local tensile strength, the materials fracture. Natural polygonal crack networks are observed in a wide variety of rock types [1–5]. Müller studied 3D shrinkage crack patterns in starch–water mixture drying [4] and found they were very similar to those formed by the cooling of basaltic lava flows with polygonal cross sections. The water concentration in starch is analogous to the temperature in basalt; both quantities obey diffusion equations, water loss is equivalent to heat loss. This is rather surprising because there are large differences (chemical composition, grain form, porosity, desiccation and cooling processes, etc.) between a starch–water mixture and basalt. Other natural examples are observed in drying mud, in desert regions (Fig. 13.1 A) and in salt lakes. In addition to these short-lived crack systems, long-lived examples caused by desiccation and dehydration are also observed [6, 7]. Desiccation cracks are not restricted to nature. With tixogel, the primary component of porcelain (50 % kaolin, 25 % feldspar and 25 % quartz), paint and other protective coatings, cracks are produced which have some similarity to the first generation in starch. In laboratories, cracks are also observed by drying packed polystyrene beads [8], coffee–water mixtures [9], methacrylate colloids [10] and 13-nm alumina–water mixtures [11]. These studies indicate that cracks initially appear by nucleation of a few points. The formation of crack patterns is strongly influenced by drying gradients that in turn lead to stress gradients. Once the spacing of the primary cracks is established perpendicular to the planar front, no subsequent changes are observed. The length scale of the pattern is proportional to the layer thickness and increases when the bottom friction is reduced. For thick layers, polygonal patterns consisting mostly of straight cracks at 908 junctions are produced. As the thickness decreases, there is a transition with a large fraction of the junctions going to 1208 and wavy cracks appear. Several models [8, 12–15] have been used to study the geometrical properties of shrinkage crack pattern formation. Cracks appear in the Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

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13 Shrinkage Cracks: a Universal Feature

Fig. 13.1 Pictures of a desert (A) and a road in the sand (B).

middle of existing segments, so the length scale of the pattern decreases by a factor of 2 with each generation of cracks. This follows from the fact that, ideally, the stress in a fragment of the drying layer will be a maximum midway between two cracks. In thin layers, crack development can be slow enough compared to diffusion in that the layer is homogeneous over its thickness and the resulting crack pattern is effectively two-dimensional. Cracks tend to propagate in the direction of the drying gradient, following it as it moves through the material and leading to 3D crack patterns (Fig. 13.1 B). The formation and morphology of crack patterns are strongly influenced by drying gradients that lead to stress gradients. There have not been many studies of directional cracking in the presence of moving gradients in 2D and 3D. This was observed with a colloidal suspension between two glass plates [16] and with the alumina–water system [11]. Due to water evaporation, particles and ionic species accumulate near the surface and a gel forms and shrinks. In a confined geometry, the gel shrinkage leads to large stresses that are the cause of crack formation. For the 1D geometry used it was observed that the cracks are regularly spaced. The characteristic wavelength results from the competition between the stress relaxation due to crack opening and the stress increase due to the water loss. Most of the cracks described in the literature related to drying processes involve water molecules. Silica and most other inorganic gels shrink spontaneously while immersed in their liquid phase. In these materials, electrostatic and osmotic forces are relatively unimportant and shrinkage during evaporation is caused by capillary stresses. However, some systems expand when immersed due to strong affinity of the solid phase for water (adsorption forces) and electrostatic repulsion between particles. In such gels, osmotic pressure may play an important role in shrinkage during drying. In this chapter we demonstrate that cracks are also formed in the mesoscopic scale (micrometer range) with the same behavior as that observed in the larger scale, with similar changes in the pattern lengths and junction distribution with the layer thickness. Similar cracks are obtained with nanocrystals dispersed in water and in nonpolar solvents. The evaporation time does not seem to be a key parameter in crack formation. The crack behavior, i. e., the variation of surface area with thickness, seems to depend on the material used.

13 Shrinkage Cracks: a Universal Feature

Fig. 13.2 SEM pattern of 10-nm g-Fe2O3 nanocrystals coated with citrate ions and deposited on HOPG in the absence of a magnetic field.

Let us first consider 10-nm g-Fe2O3 nanocrystals [17] coated with citrate ions and solubilized in aqueous solution. Seven drops (10 µL) of solution containing 6.2 × 10–7 mol L–1 of nanocrystals are deposited consecutively on a HOPG (highly oriented pyrolitic graphite) substrate. The total solvent evaporation time is 8 hours. A thick film of g-Fe2O3 nanocrystals is produced with well-defined polygonal cracks (Fig. 13.2), as shown in the desert (Fig. 13.1 A). The crack areas are very small at the center of the substrate and increase progressively from the center to the periphery (Table 13.1). Similarly, the thickness of the film increases from 3+1 µm to 7+1 and 10+1 µm from the center, to the middle and at the periphery. Most of the polygons at the periphery are three-sided and the crack junction angles are close to 908 (insert A, Fig. 13.2), whereas at the center these are close to 1208 (insert B, Fig. 13.2). Similar behavior is observed on replacing citrate ions as the passivating agent with propanoic acid (called C3 nanocrystals) (Fig. 13.3 A). In both cases the g-Fe2O3 nanocrystals are dispersed in water. Coffee–water [9] or alumina–water [11] systems also show a decrease in the crack areas and a change in the crack junction angle with decreasing film thickness. The major differences between these systems and the present ones are that the crack behavior is observed at a smaller scale (more than two orders of magnitude). Furthermore, the change in the crack area with the film thickness is observed on the same pattern in the present case, whereas in others the thickness of the film varies from one sample to another. These data confirm that cracks behave as fractals and are obtained on various scales. To our knowledge, these cracks have always been obtained experimentally by evaporation of particles dispersed in water. At this point we have to ask if crack

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Fig. 13.3 SEM patterns of 10-nm g-Fe2O3 nanocrystals coated with (A) propanoic and (B) octanoic acids, called C3 and C8 nanocrystals, respectively, and deposited on HOPG in the absence of a magnetic field.

formation is related to the presence of water during the evaporation process. To answer this question, the coating of g-Fe2O3 nanocrystals is replaced by dodecanoic acid (C12 nanocrystals) and the nanocrystals are now dispersed in a nonpolar solvent like cyclohexane. Because the wetting properties on a substrate depend on the solvent, the nanocrystal deposition procedure differs from that described above. The substrate is directly dipped in a 200-mL of solution containing g-Fe2O3 nanocrystals coated with C12 and evaporation takes place in a quasi-saturated atmosphere. The evaporation time is 8 hours. The initial nanocrystal concentration is 6.2 × 10–6 mol L–1. As observed previously, cracks are formed with g-Fe2O3 nanocrystals coated with C12 (Fig. 13.4). Similarly as in aqueous solution (Figs. 13.2 and 13.3 A), the crack areas and film thicknesses are smaller at the center of the pattern than at the periphery, and the junction angle decreases from 1208 (insert B, Fig. 13.4) to 908 (insert A, Fig. 13.4), respectively. Similar behavior is observed with g-Fe2O3 nanocrystals coated with octanoic acid, called C8 nanocrystals (Fig. 13.3 B). On replacing cyclohexane with hexane or decane, i. e., by changing the evaporation time from 8 hours (for cyclohexane and hexane) to 6 days (for decane), similar cracks are produced indicating that crack formation does not depend on the evaporation rate. Similarly, it can be concluded that crack formation does not depend on the deposition mode and on the solvent in which the particles are dispersed. Water does not seem to be needed to produce cracks. However, g-Fe2O3 nanocrystals are prepared in aqueous solution and then coated with alkyl chains. Although traces of water molecules in solution and/or formation of a water layer at the nanocrystal interface cannot be excluded, it seems reasonable to conclude that water does not play a major role in crack formation, which is mainly related to the drying process. These cracks are analyzed as being the consequence of a critical stress condition [9], which is explained in terms of an increase in the nucleation likelihood of cracks from inhomogeneities in the material when the layer thickness becomes roughly the same size as the local inhomogeneities.

13 Shrinkage Cracks: a Universal Feature

Fig. 13.4 SEM pattern of 10-nm g-Fe2O3 nanocrystals coated with dodecanoic acid, called C12 nanocrystals, and deposited on HOPG in the absence of a magnetic field.

By applying a magnetic field (0.59 T) during the deposition process, the SEM pattern obtained by depositing g-Fe2O3 nanocrystals coated with C12 shows, over a long distance, straight-line cracks divided parallel and perpendicular to the applied field direction with the formation of uniform cells (Fig. 13.5). The distance between two cracks and the crack area increase from the center to the pattern border. The layer depth in the center is 3+1 µm whereas it is 10+1 µm at this border. Figure 13.6 shows a similar behavior for g-Fe2O3 nanocrystals with different coatings and dispersed either in water as with citrate ions (Fig. 13.6 A) or C3 (Fig. 13.6 B), or in cyclohexane as with C8 (Fig. 13.6 C). Furthermore, the crack junction angles are centered at 908 with a rather low angle distribution. It can thus be concluded that the application of a magnetic field during the deposition

Fig. 13.5 SEM pattern of 10-nm g-Fe2O3 nanocrystals coated with dodecanoic acid, called C12 nanocrystals, and deposited on HOPG subjected to an applied magnetic field (0.59 T) during the deposition process.

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Fig. 13.6 SEM patterns of 10-nm g-Fe2O3 nanocrystals coated with citrate ions (A), propanoic acid (B) and octanoic acid (C) and deposited on HOPG subjected to an applied magnetic field (0.59 T) during the deposition process.

process drastically changes the crack structures and their junction angles. Similar patterns were obtained when cracks were formed in the presence of moving gradients [11, 16, 18, 19], particularly when using a directional drying technique with colloidal solutions [11, 16]. These regular patterns are explained by the fact that the cracks are formed in the middle of existing segments where the stress is highest and the crack wavelength changes with the depth layer as d 2/3 [16]. The parallel cracks shown in Figs. 13.5 and 13.6 are due to the motion of nanocrystals subjected to a magnetic field. This could induce slight instabilities on the surface along the direction of the applied field. The nanocrystals at the top of the wave, i. e., near the open surface, accumulate, inducing an increase in the local viscosity. Capillary forces drain the solvent to prevent exposure to air of the nanocrystals, thus leading to shrinkage of the layer and inducing large stresses at the origin of the crack. The fact that directional cracks are observed for various coatings clearly indicates that they are mainly due to directional drying processes and not to magnetic interactions between nanocrystals. Let us consider another nanomaterial such as 5-nm silver nanocrystals coated with dodecanethiol and dispersed in hexane. The temperature of the deposition process is controlled. The HOPG substrate is horizontally immersed in 200 ml of a solution with an initial nanocrystal concentration of 3 × 10–6 mol L–1. Solvent evaporation takes place under a hexane vapor atmosphere close to saturation. The

13 Shrinkage Cracks: a Universal Feature

Fig. 13.7 SEM patterns on a very large area (around 50 mm2) of 5-nm silver nanocrystals coated with dodecanethiol and deposited on HOPG at various substrate temperatures: (A) 5 8C, (B) 10 8C, (C) 25 8C, (D) 35 8C.

evaporation time is around 9 hours and the substrate temperature is controlled from 5 to 35 8C. An overview of the substrate on the millimeter scale (around 50 mm2) shows, at low temperatures (5 and 10 8C), a total coverage of the substrate by nanocrystals (Fig. 13.7 A and B). On increasing the substrate temperature to 25 8C (Fig. 13.7 C) and 35 8C (Fig. 13.7 D), the overall film shrinks with a homogeneous coverage at the center. In the following, we consider patterns observed at the center of the substrate on a surface area of around 0.1 mm2. At low substrate temperature (5 8C), there is a rough surface with formation of compact islands formed by the stacking of several layers of nanocrystals and the appearance of defects, as shown in Fig. 13.8A. The increase in the substrate temperature to 10 8C induces cracks with nuclei on the

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13 Shrinkage Cracks: a Universal Feature

Fig. 13.8 SEM patterns, at the center of the substrate (around 0.1 mm2), of 5-nm silver nanocrystals coated with dodecanethiol and deposited on HOPG at various substrate temperatures: (A) 5 8C, (B) 10 8C, (C) 25 8C, (D) 35 8C.

13 Shrinkage Cracks: a Universal Feature

holes (Fig. 13.8 B). A further increase in the substrate temperature to 25 8C induces an increase in the film thickness to 10 mm with the appearance of well-defined cracks (Fig. 13.8 C). The crack areas (2100+600 mm2) are rather homogeneous all over the substrate and the crack junction angle is 115+508. In some pattern regions, the cracks are not perfectly defined. At a 35 8C substrate temperature, the thickness of the film increases (15 mm) and the cracks are very welldefined with an average area of 2500+600 mm2 and a junction angle of 97+318 (Fig. 13.8 D). Under these experimental conditions, “supra” crystals with an fcc structure are produced [20, 21]. Note that the hole area increases with the substrate temperature from 10 mm2 at 5 8C to 250 mm2 at 10 8C. In the latter case, by tilting the sample (458), the average height of the holes is found to be 3 mm. From this finding, it is concluded that the crack nuclei on the holes produced by the liquid recede into the interior, whereas the body is too thick to shrink leaving airfilled pores near the surface. The liquid becomes isolated in the pockets and the drying can proceed only by evaporation of the liquid within the body and diffusion of the vapor to outside. The results described above with 10-nm g-Fe203 nanocrystals and those obtained with 5-nm dodecanethiol-coated silver nanocrystals show some general behaviors like those previously observed with coffee–water [9] and alumina–water [11] systems, with an increase in the crack area and a change of the crack junction from 120 to 908 on increasing the film thickness. However, for the first time, this phenomenon is observed at scales several orders of magnitude smaller than those previously seen [9, 11]. For materials in the same nanosize range and forming cracks at the microscopic scale, some differences are observed: .

The increase in the crack area with the film thickness is more pronounced with g-Fe203 nanocrystals than with silver nanocrystals. Furthermore, for a given thickness, the areas markedly differ (Tables 13.1 and 13.2). For a given thickness (10 mm), the area is around 20 000 mm2 for g-Fe203 nanocrystals whereas it is around 2000 mm2 for silver nanocrystals (Table 13.2).

.

The change in the crack junction with the film thickness is not observed in the same thickness range. Tables 13.1 and 13.2 show that, for a 10-mm film thickness, the junction is close to 908 for g-Fe203 nanocrystals whereas it is 1208 for silver nanocrystals.

We do not have any hypothesis to explain these differences. Furthermore, it is also rather difficult to explain crack formation with similar behavior at various scale lengths. We next have to determine the physical parameters involved in crack formation. These results open a new research area and, because the systems are rather well-defined with nanocrystals having low size distributions, we could expect in the future to solve this problem.

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13 Shrinkage Cracks: a Universal Feature Table 13.1 Crack characteristics of 10-nm g-Fe203 nanocrystals coated either with citrate ions and dispersed in water or with octanoic acid (C8) and dodecanoic acid (C12) and dispersed in cyclohexane. Coating agent

Citrate

C8

C12

Average area (mm2)

Center Middle Periphery

2050+200 6700+1000 17600+3000

2400+200 6200+1000 22600+3000

1800+200 7200+1000 18000+3000

Thickness (mm)

Center Middle Periphery

3+1 7+1 10+1

3+1 7+1 10+1

3+1 7+1 10+1

Crack junction (8)

Center and Middle Periphery

112+58 96+29

118+26 94+28

108+32 89+18

Table 13.2 Crack characteristics of 5-nm silver nanocrystals deposited on HOPG substrate at various substrate temperatures. Temperature (8C) Average area (mm2) Crack junction (8) Thickness (mm)

5 – – 3

10 – – 3

25 2100+600 115+50 10

35 2500+600 97+31 15

References 1 Ryan, M. P.; Sammis, C. G. Geol. Soc. Am. Bull. 1978, 89, 1295. 2 De Graff, J. M.; Aydin, A. Geol. Soc. Am. Bull. 1987, 99, 605. 3 Budkewitsch, P.; Robin, P. Y. J. Volcanol. Geotherm. Res. 1994, 59, 219. 4 Müller, G. J. Geophys. Res. B 1998, 103, 15239. 5 Freund, L. B. Dynamic Fracture Mechanics, Cambridge University Press, New York, 1990. 6 Nelson, R. A. Am. Assoc. Petrol. Geol. Bull. 1979, 63, 2214. 7 Plummer, P. S.; Gostin,V. A. J. Sediment. Petrol. 1981, 51, 1147. 8 Skjeltorp, A. T.; Meakin, P. Nature 1988, 335, 424. 9 Groisman, A.; Kaplan, E. Europhys. Lett. 1994, 25, 415. 10 Egen, M.; Zentel, R. Chem. Mater. 2002, 14, 2176. 11 Shorlin, K. A.; de Bruyn, J. R.; Graham, M.; Morris, S. W. Phys. Rev. E 2000, 61, 6950.

12 Korneta,W.; Mendiratta, S. K.; Menteiro, J. Phys. Rev. E 1998, 57, 3142. 13 Andersen, J. V. Phys. Rev. B 1994, 49, 9981. 14 Hornig, T.; Sokolov, I. M.; Blumen, A. Phys. Rev. E 1996, 54, 4293. 15 Crosby, K. M.; Bradey, R. M. Phys. Rev. E 1997, 55, 6084. 16 Allain, C.; Limat, L. Phys. Rev. Lett. 1995, 74, 2981. 17 Pileni, M. P.; Lalatonne,Y.; Ingert, D.; Lisiecki, I.; Courty. A. Faraday Discuss. 2004, 125, 251. 18 Yuse, A.; Sano, M. Nature 1993, 362, 329. 19 Hayakawa,Y. Phys. Rev. E 1994, 49, R1804. 20 Courty A.; Fermon, C.; Pileni, M. P. Adv. Mater. 2001, 13, 254. 21 Courty A.; Araspin, O.; Fermon, C.; Pileni, M. P. Langmuir 2001, 17, 1372.

317

Subject Index a Abeles theory 223 absorption spectroscopy of Ag nanoparticles 218 agglomeration, rapid 121 aggregation – color changes derived from 121 – control 120 – small molecules 121 akaganeite 196 alkane thiols, anodic oxidation 282 alkyl chains 266 alumina nanopores, immobilization of Au 125 alumina particles, spherical 106 alumina-water – mixtures 307 – systems 309 aluminum chlorohydrate 194 amorphous carbon films 112 amphiphiles 124 amphiphilic resin dispersion 110 anatase sol 99 anisotropy constant 274 annealing process 275 antiferromagnetic cobalt oxide shell 50 antinematic 206 AOT microemulsions 124 AOT surfactant 238 approximation – average 85 – constant 85 aqueous inorganic nanoparticles 121 arene thiols, anodic oxidation 282 artificial opals 129 135 assembly – controlled 121 – layer-by-layer 126 f. – methods 120 – programmed 121

– versatile 123 assembly stepwise of Au nanoparticles 128 atactoids 182 atomic force microscopy (AFM) 19 – 3D aggregates 20 – maghemite after etching 302 – patterned polystyrene films 162 – using MoS2 as substrate 21 avalanche photodiode 235 b ballistic electron 245 barium chromate nanoparticles, prismatic 124 barium chromate nanorods 189 bathochromic shift 150 Belousov-Zhabotinsky reaction systems 157 bentonite suspensions 190 Bessel function 193 BHCOAT method 214 bias 226 bimetallic nanoparticles 95, 98 biopolymers 111 biosensing 279 – optical affinity 150 biosensors, optical 279 ff. biphasic suspension 197, 200 birefringent gel 190 birefringent liquid 182 birefringent phase 197 bis(2-ethylhexyl) sulfosuccinate 238 block copolymer 110, 165 – lithographic mask 298 – self-assembly of 299 blocking temperature 253, 273 boehmite crystallites 180 Boltzmann constant 175 bottom-up approach for mineral nanoobjects 182 bottom-up nanotechnology 158

Nanocrystals Forming Mesoscopic Structures. Edited by Marie-Paule Pileni Copyright # 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31170-X

318

Subject Index bound water 188 Bragg diffraction 134, 144 Bragg diffraction switching device 150 Bragg filter 61 Bragg peak 26, 150 Bragg reflections 12 Bragg spots 61 branching points 79 bridging flocculation 5 Brownian behavior 196 Brownian dynamics 79 – simulation 36 Brownian motion 135 bulk magnetization 77 bump 237 c cadmium selenide nanorods 189 cadmium sulfide, flat triangular 31 capillary force 8, 23 – lateral, schematic image 140 – waves induced 43 caprolactone 167 carbon film, amorphous 58, 112 carbon grid, amorphous 6 carbon nanotubes 189 – templates 124 carboxylic acid 34 cast polymer film, pattern transition 161 catalysts, Pd-containing 106 catalytic activity of metal nanoparticles 113 cellulose acetate films 101 cellulose fibers – in-situ synthesis of metal nanoparticles 111 – porous 111 cellulose templates 110 chainlike clusters 78 – ferromagnetic and supramagnetic 114 – heterometallic 107 chaotic structures 33 Chevrel-Sergent phases 181 chimie douce techniques 205 citrate ions 34 clays 190 coalescence 65 ff. coating agents 16 coating materials – octanoic 310 – oleic acid 50 – oleyl amine 50 coating procedure 296 cobalt film diffractograms 14

cobalt-iron – phase diagram 53 – structure 50, 53 cobalt-iron structure 53 cobalt nanocrystals 6 – annealing 25, 273 – bidimensional (2D) organization 257 – chainlike mesostructures 80 – coating 24 – crystallinity 25 – 3D organizations 259 – hysteresis loop 258 – labyrinthine structures 42 – linear chains 263 – magnetic and TEM characterization 273 – magnetic properties 258 – ordered in supra crystals 275 – thick film 40 – uncoalesced 263 – under applied magnetic field 36 – with high MAE 272 – with magnetic field perpendicular to substrate 83 – XRD pattern 12 cobalt nanoparticles – ferro- and antiferromagnetic 50 – ferromagnetic behaviour 114 – highly crystallized 274 cobalt-ruthenium carbonyl clusters – ferromagnetic 114 – superparamagnetic 114 cobalt supra crystals 12 coercive field 272 coffee-water mixtures 307 coffee-water systems 309 colloidal crystals – freestanding 144 – freestanding, 2D 144 – liquid 119 – metallodielectric 149 – orientation 131 – solid 119 – temperature gradient 131 – two-dimensional 119, 137 colloidal epitaxy 131 colloidal lithography 296, 300 ff. – applications 298 – nanocrystals as mask 301 colloidal particles, dispersed 129 colloidal solution 3 ff. colloidal stability 175 colloids – characterization 76 – liquid-gas transition 76

Subject Index – monolayer 297 – phase diagram 76 columnar phase 175 – numerical simulations 199 contact angle 8 continuous film preparation 162 copolymer lithography 298 ff. copper grids 141 copper nanoparticles 101 – catalytic activities 113 – cellulose acetate films 101 – composite polyimide layers 102 core-shell nanoparticles 49 – properties 50 Couette cell 187, 202 Coulombic repulsion 2 crack area 309, 311 crack characteristics – maghemite nanocrystals 316 – silver nanocrystals 316 crack junction angle 315 crack patterns – 1D geometry 308 – influence of magnetic field 311 – influences 307 – maghemite 309 f. crack systems – long-lived 307 – short-lived 307 crack wavelength 312 crystal growth 27 f. crystal structure of FePt 60 crystallographic planes, high-index 58 cubelike superstructure 70 current density vector 232 cyclohexane 310 d 1D arrangement using polymer linearity 124 2D crystallization 140 2D monolayer 265 2D organization of Co 257 2D particle arrays 129 2D phases of rodlike particles 200 2D superlattice 2 3D array of palladium bipyridine square 128 3D films 262, 265 f. – Co nanocrystals 268 – surface-structured 267 – tubelike-structured 269 3D microcrystals, preparation, structure analysis and function 120

3D organization of Co 258 ff. 3D self-assembly 119 ff. – applications 145 – dissipative process 145 – nanoparticle interaction 129 – particle sizes 119 – structures 143 f. 3D shrinkage crack patterns 307 3D superlattices 11 ff., 262 Debye-Hückel screening 36 – length 5 decahedral particle 63 decane 310 decanethiol 16 demagnetization factor 254, 272 demagnetization field 84 f. deposition – method 31 – self assemblies 11 Deryaguin-Landau-Verwey-Overbeek (DLVO) theory 175 dialkyl disulfides, cathodic reduction 282 diamond-cylinder arrays, periodic 146 dicobalt octacarbonyl 103 dielectric constant 223, 233, 237 diffraction pattern 64 diffraction rings 53 diffusion of nonsovent 15 diiodobutane (DIB) 104 dipolar fluids, structural correaltion 79 dipolar interactions 256 – Ag nanoparticles 218 dipolar particles, nucleation 78 dipolar systems – liquid-gas transition 76 f. dipole image, schematic representation 224 dipole-dipole interaction 1, 224 disklike nanoparticles 190 disklike particles, hexagonal phase 201 dissipative hierarchy structure (DHS) 126 dissipative structure 157 ff. DLVO, see Deryaguin-Landau-VerweyOverbeek DNA as template 124 DNA hybridization, single-stranded 290 dodecanethiol 17, 238, 312 – chains 239 – coating agent 223 dodecanoic acid 17, 30, 266 – coating material 24, 310 dodecyl alkyl chains 214 downsizing technology 158 drift of particles 243

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Subject Index drop coating 296 droplet nucleation 164 Drude model 235 drying polymer solution – dissipative structures 159 – dynamic regular structure 160 dual-channel sensing element, schematics of 287 dynamic thin laminar flow (DTLF)

evaporation rate 11 – solvent 31 evaporation-driven self-assembly technique 146 Ewald sphere 186 Ewald summation 80 extinction of luminescence 245 142

e easy axes 268 easy magnetic axes, orientation 255 EDS, see energy dispersive X-ray spectroscopy eigenmode 231, 233 eigenvalue 184 electric double layer 130 electric field effects on mineral liquid crystals 207 electrochemical deposition 281 electromagnetic losses 235 electromagnetic modes 234 electron-beam (EB) lithography 280 electron diffraction – data, phase identification 54 – determination of core-shell nanoparticles 54 – pattern 52 electron-plasmon coupling 238 electrophoretic deposition 141 electrorheological fluids 133 electrostatic forces 5, 188 electrostatic stabilization 2 energy dispersive X-ray spectroscopy (EDS) 51 – core-shell nanoparticles 54 – FePt composition determination 66 – microanalysis 54 – quantitative analysis 56 energy transfer rate 235 etching apparatus 143 etching method 303 evaporation – configuration of Langevin dynamics 81 – control of solid colloidal crystals 136 – crack formation 309 – patterns 41 – processes 8 – solvent 30, 160 – regular pattern formation of deposited polymers 160 – vacuum 280

f Faraday constant 5 Faraday law 281 far-field radiation 235 fast Fourier transform (FFT) 64 Fe nanoparticles, see also iron nanoparticles Fe3Pt structure models 56 Fe52Pt48 isothermally treated 67 FePt – crystal structure 60 – phase structure 68 – structure models 56 f. FePt alloys – magnetic properties 55 – phases 56 – structure variations 55 FePt nanocrystals – assembly 66 – composition analysis by EDS 66 – monodisperse 65 – phase transformation 66 – structure of coalesced 69 FePt nanoparticles – multiply twinned 61 – shapes of 60, 62 – synthesis 60 FePt/Fe3Pt nanocomposites 55 ff. FePt particles, ultrafine 61 ferrite nanocrystals 301 ferroelectric nematic state 79 ferrofluid 34, 75, 85 – diluted 36 ferromagnetic Co nanoparticles 50 ferromagnetic garnets 82 ferromagnetic nanocrystals 251 FFT, see fast Fourier transform field emission gun scanning electron microscopy (FEG-SEM) 303 film cracking 8 fingering instability 159 fingering patterns 33 fingering periodicity 32 flocculation bridging 5 fluid flow 31 fluorescein 288 fluoro nanoparticles 126

Subject Index Fourier filtering technique, imaging of FePt 61 Fourier transform 6 Fourier transformations 50 Fourier-transform infrared (FTIR) spectroscopy, quantitative 283 free water 188 freestanding colloidal crystals 144 f. freezing volume fraction 76 g gap-mode 234 gas-liquid transition (GLT), pattern size 84 gauche defects 16, 18 gel 124 – shrinkage 308 gelation 176, 190 Gibbs ensemble 77 gibbsite nanodisks 193 – nematic phase 194 gibbsite nanoparticles, hexagonal columnar phase 202 goethite 196 – electric field effects 207 goethite nanorods 200 – magnetic properties 205 gold bumps 236 gold colloidal assay 122 gold nanocrystals – coating agent for 16 – micelles 142 gold nanoparticles – alumina nanopores 125 – carboxylic acid-coated 121 – electrophoretic deposition 141 – elongated 281 – fabrication 94 – gels 124 – immobilized 110 – in porous Ti-filaments 108 – in porous Zr-filaments 109 – mercaptosuccinic acid-coated 15 – organization around organic fibers 125 – poly(2-vinylpyridine) coated 291 – poly(glycidyl methacrylate) coated 291 – redox-active metallodendron-stabilized 121 – stepwise assembly 128 – sugar-conjugated 122 – thiocholine bromide-stabilized 126 gold tips 236 gold-silica composites 145

h Hamaker – constant 4, 6, 21 f. – expression 4 hard magnetic phases 56, 58 Heck reaction 113 Hele-Shaw cell 85 hematite – cigar-shaped 31 – needles 302 heptane 21 heterometallic cluster 107 hexadecanethiol 289 hexagonal structure 82 hexagonal superstructure 70 hexamethyldisilazane (HMDS) 93 hexane 312 – coating material 310 – solvent 31 hierarchical pattern 299 highly oriented pyrolytic graphite (HOPG) 6, 214 – reflectivity 221 – substrate 20, 222, 309 high-resolution transmission electron microscopy (HRTEM) 49, 214 – Ag particles in mesoporous silica films 93 – coalescent Fe52Pt48 grains 68 – FePt nanocomposites 57 – HOPG substrate immersed in a Ag nanocrystal solution 28 – image of Pt/M-ZrO2 sample 107 – iron oxide 69 – larger-sized nanoparticles 50 HMDS, see hexamethyldisilazane homeotropic texture 207 honeycomb 33 – formation 34 – pattern formation 165 honeycomb-patterned films 164 ff. – applications 167 f. – plastic deformation 166 – preparation of pincushion structure 166 Hooke’s law 204 HRTEM, see high-resolution transmission electron microscopy hydrazine 238 hydrogel 150 hydrogen plasma 95, 114 – technique 113 hydroxypropylcellulose (HPC) 204 hysteresis curves 254

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Subject Index hysteresis loop 254 – coated maghemite nanocrystals 269 – Co nanocrystals 258, 263 – Co superlattices 266 i icosahedron shape 64 immobilized nanoparticles, physicochemical properties 112 imogolite nanocrystals – mixed with HPC 204 – mixed with PVA 204 imogolite nanotubules 189 in-situ fabrication 91 ff. – Au nanoparticles 94 – metal nanoparticles 91, 107, 110 – Pt nanoparticles 94 inelastic electron tunneling 227 – electromagnetic-field-assisted 233 Ino model 64 inorganic films 92 ff. inorganic matrices 107 ff. inorganic molecules 127 inorganic nanocrystals, self organizing 1 ff. inorganic nanoparticles – aqueous 121 – assembled structures with DNA 122 – biological conponents 122 – color changes 121 – guided by designable templates 123 – mesoscopic assembly 120 – random assembly 120 inorganic solid matrix 125 inorganic templates 125 interfacial tension 84 inverse opal 145 – biotinylated polymers 150 – pore wall thickness 148 – preparation 149 ion-plasma etching 295 iridescent layers 196 iron, see also Fe – coating 50 iron nanocrystals 34 ff. iron nanoparticles – cellulose acetate films 101 – superparamagnetic 114 iron oxide 69 – crystallogrphic data 52 – structure 50 iron oxide nanocrystals – monolayer 59

iron oxide nanoparticles – self-assembly 69 f. – shapes 59 – synthesis 59 iron pentacarbonyl 65 – as coating material 50 iron-platinum nanocrystals, thin 3D superlattices 25 iron-platinum nanocomposites, magnetic properties 55 isotropic/nematic phase separation 194 isotropic/nematic transition 202 ITO substrate 127 – stepwise assembly 128 k Kretchmann configuration 286 l labyrinthine patterns 82 ladder patterns 163 lamellar phase 175 – numerical simulations 195 – H3Sb3P2O14 199 – swelling 198 Langevin dynamics 80 – configurations during evaporation 81 Langmuir monolayers 82 Langmuir-Blodgett films 123 Langmuir-Blodgett technique 31, 189, 296 laponite gels 190 latex films 144 lattice parameters 68 lattice structure, control 142 layer-by-layer (LbL) adsorption 106 layer-by-layer (LbL) assembly 126 f. layer-by-layer (LbL) processing 104 f. layer-by-layer (LbL) method 127 layer-by-layer (LbL) self-assembly, schematic 285 layered double hydroxide (LDH) 194 Lenard-Jones potential 78 Lewis motif 208 LGT, see liquid-gas transition linear chains 263 ff. line geometry 301 liquid colloidal crystals 129 ff. – electrically switchable 150 – formed by shear flow 132 – lattice structure 130 – layer thickness 130 – mechanical fragility 133 – pH gradient 132 – properties 129

Subject Index liquid-crystalline phases 173 – classification 175 liquid crystal polymer, electrooptic response 150 liquid crystals – lyotropic 173 – thermotropic 173, 196 liquid-gas transition (LGT) 75 ff. – in dipolar systems 76 f. – simulation studies 76 liquid-like colloidal crystal – optical switch 150 – formed under centrifugal equilibrium 134 – superstructures in binary mixtures 133 lithium nanowires 189 lithography 295 ff. – colloidal 295 – copolymer 298 – interference 299 – nanosphere 296 – natural 296 – photo or e-beam 299 – regular micro- and nanopatterning of materials 157 – spheres 296 liver cells 167 localized surface plasmon (LSP) 286 local plasmon modes 234 Lorentz field 218 – effect 220 luminescence 246 f. – cross sections 247 – individual-site dependence 243 – switch 248 – tip-modified 246 lyotropic liquid crystals 173 m maghemite 31 – AFM images 302 maghemite nanocrystals 34, 36 – chainlike mesostructures 80 – cigar-shaped 270 – coated with citrate ions 309 – crack characteristics 316 – crack formation with different coatings 310 – magnetization curves 267 – magnetic field 82 – polygon cracks 309 – spherical aggregates 80 – tubelike film of citrate-coated 269

magnetic anisotropy 255 magnetic anisotropy energy (MAE) 253, 257 – Co nanocrystals 272 magnetic behaviour of metal nanoparticles 114 magnetic dipolar forces 4 magnetic energy 84, 86 magnetic field 34 ff., 255 – applications of 34 – nematic suspension 185 – vanadium pentoxide suspensions 184 magnetic free energy 206 magnetic hard phase 50 magnetic induction 84 magnetic moment, remanent 206 magnetic nanocrystals – chain structures 34 – collective magnetic properties 251 ff. – column growth 42 – mesoscopic organization 75 ff. – mesostructures 256 ff. – organization with applied field 80 ff. – perpendicular field 82 magnetic nanoparticles – organized arrays 251 – patterned 3D film 266 – self-assembly 50 ff. – structure 50 ff. magnetic soft phase 50 magnetic susceptibility 84 magnetism, permanent 55 magnetite nanocrystals 34 magnetization 84 f. – spontaneous 75 – vanadium pentoxide ribbons 184 magnetization curve 256 – maghemite nonocrystals with several coatings 267 magnetization factor 254 Maier-Saupe distribution 193 Marangoni effect 31, 159 Marangoni instability 301 Marks decahedron 64 – shape 62 masks, etching or deposition 146 Maxwell equations 214, 232 MCM-41 107 melting volume fraction 76 4-mercaptobiphenyls 283 mercaptohexanol spacer 290 3-mercaptopropyltrimethoxysilane 107 mercury semiconductor nanocrystals 149

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Subject Index mesophases 173 – columnar 201 – hexagonal 202 – identification techniques 178 – single domain 184 – single domain examination 177 – transition between 176 – types 175 – uniaxial 184 mesoporous films – from titanium dioxide 94 – silica 92 mesoporous zirconia 107 mesoscopic organization 80 ff. – magnetic nanocrystals 80, 82 mesoscopic polymer patterning 157 mesoscopic structures 1, 36, 257 – masks 301 – collective magnetic properties 255 ff. – size 86 metal deposition 295 metal nanoparticles – catalytic properties 113 – composites of 110 – fabrication in inorganic films 92 – ferromagnetic 114 – generation of size-controlled 111 – inorganic matrices 107 – in-situ fabrication 91 ff. – magnetic properties 114 – metal oxide ultrathin films 95 – monodispers 96 – non-film solid matrices 106 – optical properties 113 – physicochemical properties 112 – polyelectrolyte thin films 104 – polymeric films 101 – polymeric matrices 110 – shapes and surfaces 58 – TiO2 films 99 metallic particles, monolayer-protected 284 methacrylate colloids 307 micellar block copolymers 101 micelles, reverse 238 microdomains 19, 101 microgravity, control of lattice structure 130 micropatterns 164 mineral liquid crystals (MLC) 173 ff. – basic principles 174 – composites 204 – electric field effects 207 – investigation techniques 177

– physical properties 178 – rheological properties 202 – solvent influence 176 mold structure 145 molecular beaker epitaxy 285 molecular matrix 120 – nanoparticle assembly 120 molybdenum sulfide monolayers 20 monolayer-protected clusters (MPC) 279 – preparation 284 monolayers 21 – formation, sketch 22 monometallic nanoparticles 98 – in-situ preparation 95 monophase materials 1 Monte Carlo simulation 77, 79 montmorillonite 108 moth’s eye structure 157 Mössbauer spectroscopy 269 multicolor photochromism 101 multilayer 142 – thin films 104 f. multiply twinned particles 63 n nanoalloys 270 nanocomposite films 94 – inorganic-organic 101 nanocrystals – C3 309 – C8 310 – C12 310 – anisotropy shape 38 – arrangement 1 – coalescence 27 – interparticles forces in solution 2 – inorganic 1 ff. – magnetic, see magnetic nanocrystals – self-assemblies 6 – spherical 257 – surface modifications 2 – uncoalesced 263 nanodecoration 99 nanolithography 2, 295 ff. – masks 299 nanomaterials – alloy 251 – ferrite 251 – metallic 251 nanometal-clay composites 108 nanopalladium catalyst 113 nanoparticles – applications 49 – arrays 124

Subject Index – general principles of magnetism 252 – immobilization 91 – inorganic, see inorganic nanoparticles – iron 114 – monodisperse oxide 96 – palladium, see palladium nanoparticles – silver oxide, see silver oxide nanoparticles – structural characterization 49 nanoporous films 99 nanorods 189 nanosphere lithography (NSL) 296 ff. – angle-resolved 297 – applications 298 – ordered-particle arrays 296 – schematic representation 296 nanotubes 189 nanowires 182, 189 native Co nanocrystals, thermal stability 24 Neel expression 253 nematic director 179, 181 nematic gels, vanadium pentoxide ribbons 183 nematic order parameter 179 nematic phases 175, 178, 180 neural cells 168 Newton’s law 204 nickel hydroxide disklike nanoparticles 201 noble metal nanoparticles 113 nonfilm solid matrices 106 nonmagnetic fluid 85 nuclear magnetic resonance (NMR) – ribbon structures 188 – structural determination of biomolecules 207 nucleation, supersaturated fluids 78 o Ocean Optics 289 octahedron shape 59 octane 144 octanethiol 16 octanoic acid 266 oleic acid 65 oleyl amine 65 Onsager model 179, 182, 187, 194, 206 optical memory media 150 optical micrographs, patterned polystyrene films 162 optical stop band 148 optical switches 150 optical transmittance spectra 148 organic templates 124 oscillatory shear of solid colloidal crystals 136

osmotic pressure 150 oxygen plasma 95 – etching 147 p palladium-bipyridine square molecules 127 palladium nanocrystals, coating agent 16 palladium nanoparticles – monometallic 99 – resins 110 – synthesis in micropores of SBA-15 107 palladium on Ag bimetallic nanoparticles 98 palladium(II) complex, PS-PEG supported 110 paranematic 206 particle patterns 297 particle-substrate interaction, strength 6 particle-substrate junction 240 pattern – formation of deposited polymers 160 f. – geometry 84 – hierarchical 299 – size characterization 84 – transfer 300 patterned deposition, electron-beam (EB) lithography 280 patterned substrates for lattice structure control 142 phase diagram – investigation technique 177 – vanadium pentoxide 188 phase identification 49 ff. – electron diffraction data 54 – magnetic nanocrystals 52 f. phase separation – biphasic gap 194 – isotropic/nematic 194 phase transformation 65 ff. phenyl ether 50 photodiode, avalanche 235 photoemission spectra of Ag nanocrystal films 225 photon map 235, 240 – profiles 237 photonic bandgap 148 photonic crystals 148 – formation from colloids 149 – tunable 149 photooxidation 113 pincushion 166 Piranha solution 281 plasmon frequency 235

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Subject Index plasmon-mode-assisted inelastic electron tunneling 232 plasmon modes 231, 238 – collective 240 – coupled 241 – excited 242 – scheme of the two-particle 242 – single-particle dipolar 241 plasmon resonances 223 platinum acetylacetonate 65 platinum deposition 296 platinum nanoparticles – carbonization of 112 – fabrication 94 – inorganic matrices 107 – zero-valent 106 polarization ratio spectra of Ag nanocrystal film 226 polarized electron spectroscopy 225 polarized light, of spherical particles 223 polarized-light microscopy – aqueous clay gels 191 – images of birefringent droplets 180 – mineral system investigation 177 – nematic suspension of Li2Mo6Se6 181 polarizing microscope 177 poly(2-vinylpyridine) (P2VP) 291 – microdomain 103 poly(acrylic acid) (PAA) 104 poly(allylamine hydrochloride) (PAH) 104 polycrystalline shells 54 poly(dimethylsiloxane) (PDMS) 144 polyelectrolyte-metal ion complex 105 polyelectrolyte thin films 104 ff. poly(ethylene glycol) 111 polyimide 165 – films 103 – surface layer modification by 101 polyimide layers – Cu nanoparticles synthesis 102 – fabrication of metallic Ag, Cu, Pd nanoparticles 101 polyisobutene chains 194 poly(N-isopropylacrylamide) 133 polymer – brushes 291 – flexible 183 – fluorinated 167 – grafting 175 – hydrophobic 167 – hydrosoluble 175 – patterns 160 – template 124

– trigger for controlled assemblies 121 polymer films 101 f. – mold for regular patterns 167 – ladder patterns 163 – preparation of honeycomb-patterned 164 ff. polymer matrices 101, 110 f. – metal nanoparticles fabrication 110 polymer solutions, drying 159 poly(methyl methacrylate) (PMMA) 280, 303 polyol reduction process 60 polystyrene 111 – beads 307 – reactive ion etching 143 – spheres 144 – superstructures 134 polystyrene films – AFM images 162 – optical micrographs 162 polystyrene particles – fluorescent 139 – nonfluorescent 139 poly(styrene-b-2-vinylpyridine) (P(S-b-2VP)) 103 poly(styrenesulfonic acid) 105 poly(vinyl alcohol) (PVA) 204 porcelain 307 pore size control 165 potassium hydroxide 101 programmed assemblies 121 propanoic acid 309 protrusions, tip-formed 236 P(S-b-2VP), see poly(styrene-b-2-vinylpyridine) pseudoaggregation 142 pseudo-rotaxane assembly 121 Purcell effect 231 r Raman scattering 218 Raman spectroscopy 216 Rayleigh-Benard convection 159 reactive ion etching (RIE) 301 – two-step 303 reflectivity measurements 220 reflectivity spectra of Ag monolayer 224 regular dynamic patterning 159 regular pattern formation, classification 158 regular patterns – fabrication 157 – drying polymer solutions 160 regular polymer patterns, applications 167 regular stripe patterns 160

Subject Index relaxation 245 – times 253 remanence magnetization 254 – Co nanocrystals 259 – reduced 256 resin dispersion, amphiphilic 110 rheology, mineral liquid crystal 204 ribbons, vanadium pentoxide 182 ff. rigid rodlike nanoparticles 180 ring geometry 301 RKKY interactions 255 rodlike particles, 2D phases 200 Rosensweig instability 41 s SAED, see selected-area electron diffraction saturation magnetic moment 256 saturation magnetization 80, 254, 274 SBA-15 107 scanning electron microscopy (SEM) – 3D aggregates 20 – 3D films of spherical Co nanocrystals 39 – cigar-shaped maghemite nanocrystals 40 – coated maghemite nanocrystals 268 – Co nanocrystals 9 – labyrinthine structure 44 – mesostructures made of Co nanocrystals 43 – silver colloidal solution 15 – silver nanocrystals 215 – supra crystals of Ag and Co 12 – supra crystal of Co 15 – using MoS2 as the substrate 21 scanning electron microscopy (SEM) patterns – Ag nanocrystals coated withdodecanethiol and deposited on HOPG 313 – Co superlattices 266 – maghemite subjected to an applied magnetic field 311 scanning tunneling luminescence (STL) 231 ff. – mechanisms 232 – metal nanoparticles 227 – photon map 236 scanning tunneling microscopy (STM) 232, 284 – induced photon emission 226 – silver nanoparticle monolayer 243 – single-particle contacts 239 scanning tunneling microscopy (STM) junction 236

– current-voltage characteristic 240 – mechanisms for luminescence 233 Scherrer formula 187 Schiller layers 196 Schlieren texture 181 selected-area electron diffraction (SAED) 59 – pattern 272 – self assembled nanoparticles 70 self-assembled 2D array, reflectance on HOPG 222 self-assembled monolayer (SAM) 279, 282 f., 299 – formation monitoring 283 – in-situ functionalization 283 – preparation 282 – properties 282 – structure analysis 283 self-assembled structures 143 ff. – flexible 144 – processing 143 – solid surfaces 144 self-assembled superstructures 70 – 3D model 71 self assembly 31 f., 49 ff. – anisotropic nanoparticles 173 ff. – applications 285 – evaporation driven 140 – external forces 9, 31 – iron oxide nanoparticles 70 f. – multilayer preparation 285 – nanocrystal micelles 142 – preparation of multilayers 285 – solution deposition 11 self-assembly process – dynamic 158 – regular pattern fabrication 157 – static molecular 158 self-organization – Ag nanocrystals 213 ff. – inorganic nanoparticles 1 ff. self-evaporation technique 146 SEM, see scanning electron microscopy semiconductor nanocrystals, 149 semiflexible wires – Li2Mo6Se6 181 – molybdenum selenide ion chains 181 sensing materials – chemical 150 – optical 150 shapes of magnetic nanocrystals 58 shear rate of the H3Sb3P2O14 lamellar gels 203 shear stress of the H3Sb3P2O14 lamellar gels 203

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Subject Index shear-thinning 204 shrinkage – capillary stress 308 – cracks 307 ff. silica – reactive ion etching 143 – superstructures 134 silica colloids, monodisperse 135 silica films – cross section of silver particles 93 – mesoporous 92 – TEM of the calcinated mesoporous 93 silica xerogels, mesoporous 107 silicon – anisotropically etched, 145 – substrate in reflectivity measurements 223 silicone fluid 192 silver colloidal assay 122 silver nanocrystals 1, 171 ff., 213 ff. – coated with dodecyl alkyl chains 214 – coating agent 16 – collective properties 214 – crack characteristics 316 – crack patterns 312 – interparticle gap control 17 – photoemission spectra on Au and HOPG substrates 225 silver nanoparticles – by LbL polyelectrolyte films 104 – carboxylic acid-coated 121 – colloidal 238 – crystalline 95 – examined by SERS 114 – experimental reflectivity spectra 222 – fabrication 92 – fluorocarbon-stabilized 127 – formed in P2VP phase 103 – in-situ fabrication 99 – optical properties 113 – TiO2 film 95 – reflectivity spectra 224 – synthesis 238 – triangular 288 silver oxide nanoparticles, amorphous 95 silver-palladium bimetallic nanoparticles, catalytic activity 113 silver polycrystals 28 silver, spherical 31 silver sulfide nanocrystals 20 ff. – interparticle gap control 16 – substrate influence 19 sintering technique 144 size distribution effect 6

small-angle X-ray diffraction (XRD) 12 ff. small-angle X-ray scattering (SAXS) – mesophase investigation 178 – studies of lamellar H3Sb3P2O14 gels 203 small-angle X-ray scattering (SAXS) pattern – laponite gel 193 – nematic suspension of vanadium pentoxide ribbons 186 – goethite 201, 205 – H3Sb3P2O14 suspension 198 smectic B phases, thermotropic 196 smectic phases 175 – 2D 189 soft magnetic phases 56, 58 sol-gel reaction 127 sol-gel transition 176, 192 f. solid colloidal crystals 135 ff. – control of contact line 136 – control of orientation 136 – growth rate 137 – lattice structure 137 – preparation methods 140 – sedimentation method 136 solid matrices 91 ff. solvation forces 5 solvent – evaporation 8, 160 – evaporation rate 31 – migration 32 source term 237 spheres lithography 296 spherical harmonics 216 spin casting 299 spin coating 296, 301 – technique 142 SPR, see surface plasmon resonance spectroscopy sputtering 280 square Fourier transform 28 SQUID magnetometer 178 stacked tetrahedra 63 star polymers – conducting 165 – inorganic 165 starch-water mixture 307 steric forces 5 steric repulsion 5 steric stabilization 2 STM, see scanning tunneling microscopy Stockmayer fluids 78 Stokes-anti-Stokes, Raman spectroscopy 216

Subject Index – Ag nanocrystals 217 – small supra crystals 216 Stoner-Wohlfarth magnetic particles 257 Stoner-Wohlfarth model 256 structure – formation due to evaporation 41 submicrostructures by reactive ion etching 143 subnanoclusters 110 substrate – effect 6 – influence on deposition 19 – parallel applied field 34 – patterned, lattice structure control 142 – perpendicular applied field 40 – preparation 280 ff. sulfonic acid groups 105 superconductors type I 82 superlattices – Au and CdSe 15 – 2D and 3D 2, 11 ff. – of FePt nanocrystals 25 – TEM pattern 11 superparamagnetic limit 50, 253 superparamagnetic nanocrystals 252 superparamagnetic relaxation 253 superparamagnetism 270 superstructures 134 – self-assembled 70 – types 70 f. supra crystals 11 ff., 262, 315 – diffractograms of Co nanocrystals 275 – formation 216 f. surface charge density 174 surface differential reflectance (SDR) 221 surface energy 84 surface-enhanced Raman scattering (SERS) 114, 231 – applications 298 surface modification 101 surface occupation fraction 261 surface plasmon absorption bands 288 surface plasmon resonance (SPR) – applications 287 – longitudinal 226 – sensitivity 287 – transversal 226 surface plasmon resonance (SPR) spectroscopy 279, 286 – gold-nanoparticle-enhanced 289 ff. – immunosensing 289 – schematics 286 surface sol-gel process 95

surfactants 124 susceptibility measurements 252 swelling law 187 synchrotron small-angle X-ray scattering 182 t tactoids 181 TEM, see transmission electron microscopy tetraethoxysilane 107 tetrahedral atomic cluster 64 Texas Instruments Spreeta SPR sensor 287 thermal stability 24 thermotropic liquid crystals 173 time stability 24, 29 tip-formed protrusions 241 tip-particle junction 240, 245 tip-sample distance 234 tip-surface junction 234 titania nanotubes 110 titanium dioxide – films 95 ff. – macroporous 148 – mesoporous 148 – mesoporous films 94 titanium dioxide inverse opals, photocatalytic activity 146 titanium dioxide thin film 99 – model for molding effect 100 titanium(IV) isopropoxide 149 tobacco mosaic virus (TMV) 179 – suspensions 192, 205 top-down approach for mineral liquid crystals 181 total free energy 84 trans zigzag conformation 16, 18 transmission electron microscopy (TEM) – Ag nanocrystals 8 – Ag nanoparticle characterization 214 – AgS monolayer 10 – Au nanoparticles in porous titania filaments 108 f. – calcinated mesoporous silica film 93 – cigar-shaped maghemite nanocrystals 40 – cross sectional of polyimide films 103 – determination of core-shell nanoparticles 54 – 3D images of silver aggregates 11 – hexagonal superstructure 69 – high magnification 69 – Co nanocrystal 7 – Co nanocrystal multilayer 25 – imaging of ribbon synthesis 183 – low magnification 51, 69

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Subject Index – micrographs of P(S-b-2VP) films 104 – morphology of FePt nanocrystals isothermally treated 67 – Pd-on-Ag core shell bimetallic nanoparticles in TiO2 gel film 99 – phase transformation analysis 65 – ring organization of Ag, Co and maghemite nanocrystals 32 – spherical maghemite nanocrystals 35 – thiocholine bromide-stabilized Au nanoparticles 126 – ultrafine FePt 61 transmission electron microscopy (TEM) patterns – disordered and coalesced particles 220 – spherical particles 220 transmission surface plasmon resonance (T-SPR) spectroscopy 286 ff. – schematics 288 truncated octahedral shape of monodisperse FePt 66 truncated octahedral superstructure 70 truncated octahedral (TO) nanoparticles 70 truncated octahedron shape 59 f. truncated tetrahedral platelets (TTP) of Fe3O4 nanocrystals 69 truncated tetrahedron shape 59 tunable photonic crystals 149 tunnel barrier 239, 245 tunnel current 226, 234, 238 tunneling 233 tunneling Hamiltonian formalism 234 tunneling matrix element 234 tunneling process, non-emissive two-step 245 u UHV STM 235 ultrathin films 95 ff. – layer-by-layer self-assembled 284

колхоз 5/16/06

– metal oxide 95 – nanoparticle fabrication 99 – optically transparent 279 – spontaneous, LbL-self assembled 284 f. ultrathin gold nanoislands 280 v vacuum deposition 280 vacuum evaporation 280, 289 van der Waals attractions 80, 188, 198 van der Waals attractive potential 72 van der Waals forces 4, 23 van der Waals interactions 2, 9, 34, 175, 267 vanadium pentoxide ribbon 184 ff. – electric field effects 207 vanadium pentoxide solution 184 vibrational frequency 216 video microscopy image of Co nanocrystal solution 42 viruses as templates 124 volume fractions 179 Voronoi pattern 160 w water-gas shift reaction 101, 113 Wistar rat hepatocytes 167 wurtzite CdSe/CdS core-shell semiconductor nanoparticles 50 x X-ray diffraction (XRD) patterns – Ag nanocrystals 215 – Co supra crystals 13 XRD, see small-angle X-ray diffraction z Zeeman energy 255 zero-field cooled and field cooled (ZFC/FC) – curve 263, 273, 275 – experiments 257 zirconia, mesoporous 107