Mesocrystals and Nonclassical Crystallization

Mesocrystals and Nonclassical Crystallization ¨ LFEN HELMUT CO Max-Planck-Institute of Colloids and Interfaces, Potsdam-...

Author: Helmut Cöelfen | Professor Markus Antonietti

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Mesocrystals and Nonclassical Crystallization ¨ LFEN HELMUT CO Max-Planck-Institute of Colloids and Interfaces, Potsdam-Golm, Germany MARKUS ANTONIETTI Max-Planck-Institute of Colloids and Interfaces, Potsdam-Golm, Germany

Mesocrystals and Nonclassical Crystallization

Mesocrystals and Nonclassical Crystallization ¨ LFEN HELMUT CO Max-Planck-Institute of Colloids and Interfaces, Potsdam-Golm, Germany MARKUS ANTONIETTI Max-Planck-Institute of Colloids and Interfaces, Potsdam-Golm, Germany

Copyright # 2008

John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (þ44) 1243 779777

Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxed to (þ44) 1243 770620. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. The Publisher and the Author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of fitness for a particular purpose. The advice and strategies contained herein may not be suitable for every situation. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. No warranty may be created or extended by any promotional statements for this work. Neither the Publisher nor the Author shall be liable for any damages arising herefrom. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Ltd, 6045 Freemont Blvd, Mississauga, Ontario L5R 4J3, Canada Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data Co¨lfen, Helmut. Mesocrystals and nonclassical crystallization / Helmut Co¨lfen, Antonietti Markus. p. cm. Includes bibliographical references and index. ISBN 978-0-470-02981-7 (cloth) 1. Colloidal crystals 2. Crystal growth. 3. Nanostructured materials. I. Antonietti, M. II. Title. QD549.2.C64C64 2008 548’.5–dc22 2008004950 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 978-0-470-02981-7 Typeset in 10/12 pt Times by Thomson Digital, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire

Contents Preface

ix

1

Mesocrystals and Nonclassical Crystallization 1.1 Introduction References

1 1 6

2

Physico-Chemical Principles of Crystallization 2.1 Classical Crystallization 2.2 Definition of a Crystal and Crystal Growth 2.3 Nucleation Theories 2.3.1 Classical Nucleation Theory 2.3.2 Experimental Tests of Nucleation Theories 2.4 Some Points towards a More Realistic View of Supersaturation and Crystallization 2.4.1 Concentration Fluctuations and ‘Spinodal Crystallization’ 2.4.2 Reduction of Supersaturation by the Formation of Clusters and Amorphous Intermediates 2.5 Thermodynamic and Kinetic Crystallization Pathways 2.6 Polymorph Control 2.7 Crystal Morphology and the Role of Additives and Selective Adsorption 2.7.1 Crystal Morphology 2.7.2 What Determines Adsorption of an Additive? 2.8 Properties of Single Crystals and Polycrystals 2.8.1 Electrical Polarization 2.8.2 Light Refraction and Birefringence 2.8.3 Mechanical Properties References

3

Examples of Crystals Challenging the Classical Textbook Mechanism 3.1 Some Biomineral Examples 3.1.1 Elongated Magnetite Nanocrystals in Magnetotactic Bacteria

7 7 9 15 15 19 19 19 21 22 25 28 30 36 39 39 43 44 47 51 51 52

vi

Contents

3.1.2

Calcite with Complex Form and Single Crystal Behavior in Foraminifera 3.1.3 Calcite with Complex Form and Single Crystal Behavior in Sea Urchin Spines 3.1.4 Calcite Single Crystals with Complex Form in Coccoliths 3.1.5 Morphological Complexity Develops with Time 3.2 From Biology to Biomimetics: In Vitro Mineralization Examples 3.3 Biomorphs 3.4 Other Synthetic Examples References

56 57 58 59 68 69 71

4

Nonclassical Crystallization 4.1 Amorphous Precursors 4.2 Liquid Precursors 4.3 Oriented Attachment 4.4 Mesocrystals References

73 75 78 83 96 98

5

Self-Assembly and Self-Organization References

103 106

6

Colloidal Crystals with Spherical Units: Opals and Colloidal Nanocrystals References

107 111

7

Mesocrystal Systems 7.1 Mesocrystals and Their Properties 7.2 Early Reports on Mesocrystals 7.3 One-Dimensional Mesocrystals 7.4 Two-Dimensional Mesocrystals 7.5 Mesocrystals in Biomineralization 7.6 Mesocrystals in Gels 7.7 Mesocrystals Formed without Additives 7.8 Mesocrystals Formed with Simple Ion Additives 7.9 Mesocrystals Formed with Polymer Additives 7.10 Mesocrystals in Nonaqueous Systems 7.11 Mesocrystals Formed via Solid-State Reactions 7.11.1 Solid Matrices for Mesocrystal Formation 7.11.2 Topotactic Reactions 7.12 Liquid Crystals, Tactoids, Somatoids, and Schiller Layers References

113 113 114 117 118 122 129 135 138 142 152 157 157 159 163 173

8

Mechanisms of Mesocrystal Formation 8.1 Principal Mechanisms Leading to Mesocrystals 8.2 Conditions for Mesocrystal Formation

179 179 186

53

Contents

Alignment by Colloidal Forces, Capillarity and Other Short-Ranged Physical Fields 8.3.1 Alignment by Capillary Forces 8.3.2 Alignment by Hydrophobic Forces and Interface Energies 8.3.3 Alignment by Minimization of the Interfacial Energy 8.3.4 Alignment by Additive Coding of Nanoparticles 8.3.5 Alignment by a Mechanical Stress Field 8.4 The Role of Magnetic Fields 8.5 The Role of Dipole and Polarization Forces 8.5.1 Polarization Forces 8.6 The Role of External Electric Fields 8.7 Self-Similar Assembly and Shape Constraints 8.8 Shaping of Mesocrystals 8.9 Mesocrystals as Intermediates in Single Crystal Formation References

vii

8.3

9

190 190 192 192 194 196 198 204 204 219 222 226 228 233

Analysis of Mesocrystals 9.1 Nucleation and Growth of Primary Nanoparticles 9.2 Rapid Aggregation and Formation of Randomly Oriented Aggregates 9.3 Mesocrystal Formation 9.4 Fusion of the Mesocrystal to a Single Crystal/Ripening and Ion-Mediated Recrystallization Towards an Outer Single Crystalline Shell 9.5 Analytical Techniques for Mesocrystals References

240 241 244

10

Tuning of Properties References

247 249

11

A Unifying Crystallization Mechanism References

251 255

12

Analogy between Oriented Attachment or Hierarchically Structured Crystals and Polymers 12.1 Analogy between Oriented Attachment and Polymerization 12.2 Structural Levels in Hierarchically Structured Crystals and Biopolymers References

263 264

Summary and Outlook 13.1 Summary 13.2 Outlook References

265 265 267 270

13

Index

237 238 239 239

257 259

271

Preface Crystallization is certainly among the most studied processes in science and also of great practical importance. This is because the properties of many solid bodies and materials depend on their crystal structure, the crystal shape and their mutual texture. In addition, crystallization is an elemental separation technique, one of the most simple self-assembly processes to create order from the atomic to the macroscopic scale. Finally, it creates beautiful objects of esthetical value, which fascinate humankind already for centuries. It is not astonishing that crystallization processes are already studied for a long time, beginning with alchemy (where crystallization was one of the ‘‘elemental operations’’), and in a systematic, scientific fashion since the end of the 18th century. One might think that a process of such scientific and technological importance is well known down to the finest details after such intense studies for more than a century, but this is not true. It is true that a ‘‘classical’’ picture of crystallization has been established, supported by a pleiora of experimental work. It describes crystallization as a layer-wise deposition of atom/ion/ molecules on the surfaces of a crystal nucleus, amplifying it within the constraints dictated by the crystal unit cell. Nevertheless, it is also well known that this classical model does not apply for many ‘‘real-life’’ crystallization processes (i.e. beyond conditions chosen which are especially good to observe the ‘‘classical’’ growth). It is still mostly not possible to quantitatively predict crystallization processes as well as the formed intermediates. Application of crystallization theories fails often even for most simple systems, and thus the modelling of crystallization processes. After 200 years of systematic scientific work, one might also state that the understanding of crystallization beginning from the atomar level is still rather restricted, as well as it is for the interface of a crystal with solvent and the other dissolved compounds. Apart and apparently separated from synthetic crystallization processes, crystalline biominerals have been analyzed, which have nothing in common with the conception of a single crystal, anymore. Despite physical single crystal properties, they exhibit curvature as a common feature, e.g. as sea urchin spines. Up to now, their precise formation is often still unknown. Such structures are a true challenge for the classical crystallization model, which simply by no means can explain the formation of such structures. Amorphous precursor phases as well as nanoparticle based crystallization pathways were recently identified to contribute to the formation processes of Biominerals, and this knowledge could be folded back to the growth of synthetic crystals. Reanalyzing the literature, this

x

Preface

turns out to be a ‘‘rediscovery’’, as it seems that many important original observations are meanwhile forgotten and hidden in the past literature, as they simply did not comply with the classical crystallization model. It is interesting to guess how crystallization processes were perceived in the early days. Natural scientists were quite universally trained and did not differentiate between biological and inorganic matter to an extent which is common nowadays. It was therefore ‘‘clear’’ to observe their scientific objects with an interdisciplinary view – a skill which is weak nowadays and indeed is worth to be rediscovered. As a tutorial exercise, we will start this book with the early descriptions of Biominerals and other crystals, which do not agree with the classical view on crystallization. These old papers already contain the keys towards a deeper understanding of crystal complexity – even if the analytical techniques to probe the assumptions made were often not yet developed. For example the philosopher and biologist Ernst Haeckel carefully observed the complexity of crystallization in the presence and absence of biomolecules and coined notations as ‘‘living crystal field’’ and ‘‘diseased crystals’’. These words do not sound as exact science in todays language, but in fact already indicate the importance of long-ranged physical fields or additives for crystallization processes. It was presumably the biggest challenge of this book that we seriously tried to gather all available information from historical colloid studies together, which are often only available in german language, and to refresh them for modern use. The early observations of crystallization pathways well beyond the classical crystallization model (which is much younger) were followed by experimental evidence from the last decade for nanoparticle based formation mechanisms of single crystals, and nowadays this evidence is literally exploding. An increasing number of densified concepts like ‘‘Oriented Attachment’’ or ‘‘Mesocrystal formation’’ as well as elucidation of the role of amorphous precursor particles, also in Biominerals, was following. This explosion of knowledge can certainly be attributed to the increasing interest in nanotechnology and colloid science, but is to our opinion mainly due to the improved analytical possibilities as compared to those available only 20 years ago. For example, tactoids, which are oriented nanoparticle assemblies, were described as early as 1925 by Zocher but could only be analyzed by light microscopy. A detailed analysis with modern methods would certainly have changed crystallization models as such. It is also the intention of this book to present the whole wealth of experimental observations available meanwhile, and to formulate mechanisms of non classical crystallization in an attempt to extend the classical textbook knowledge on crystallization. This is especially important in view of the fact that all more general textbooks, e.g. for physical chemistry, still only consider the classical atom/ion/molecule mediated crystallization pathway. In this book, we will try to summarize the classical and non classical crystallization pathways not only by experimental evidence but also with a comprehensive discussion of possible formation mechanisms and features of the various crystallization pathways as well as the necessary analytics. It is a go for a comprehensive treatment of modern crystallization science, and we know well that it is impossible at the present stage of knowledge to provide detailed and well backed up mechanisms for all non classical crystallization pathways which are discussed in this book. We nevertheless hope to provide the necessary toolbox for all scientists who work in the many areas related to modern crystallization to gain a better understanding of their systems; the book

Preface

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hopefully gives some guidelines how to deal with these often highly complex crystal systems. The emerging crystallization picture is a more open one where the borderlines between crystallization schemes leading to single crystals and polycrystalline aggregates as well as those between liquid crystalline systems and solid crystals vanish. There appears to be a unifying crystallization picture, which combines all well known observations of the past so far attributed to different mechanisms. A comprehensive treatment of classical and non classical crystallization will catalyze future progress in the field since it helps to identify mechanisms on the base of their typical features and by suitable analytical techniques. It is a special wish that also students and young researchers can confront themselves with the ‘‘self-organization’’ view of crystallization since up to now, there is no equivalent densified treatment of non classical crystallization. The expectations for the future are high: The gain of basic knowledge in the field of organized crystalline arrays will lead to highly sophisticated crystalline materials of the future, covering topics such as hierarchical organic-inorganic hybrid structures, better understanding of biomineralization processes, enhanced predictive tools of crystallization events, new morphosynthesis strategies, new hybrid materials combining the physical properties of different nanoparticles in a single crystalline material, and many more. We have structured our book into 12 chapters. After the introduction, we introduce the existing crystallization theory (Chapter 2), opposed by the presentation of crystals challenging this classical textbook view on crystallization (Chapter 3). Some non classical particle mediated crystallization pathways are presented afterwards. (Chapter 4). Their foundations are discussed with a treatment of self organization (Chapter 5), colloidal crystals (Chapter 6) as well as the mesocrystal concept and properties (Chapter 7). Formation mechanisms of mesocrystals are discussed in chapter 8, as well as the analytical tools to study such mesocrystals (Chapter 9). Possibilities for the tuning of mesocrystal properties are delineated in (Chapter 10). Finally, a unifying crystallization scenario combining classical and non-classical crystallization will be presented (Chapter 11), and the analogy between hierarchically structured crystals and biopolymers as well as oriented Aggregation and polymers will be discussed (Chapter 12). An outlook to the future with a short glance of what might be possible with an extended toolbox of crystallization will be given. We are deeply indebted to Annette Pape for her enduring assistance during the writing process of this book. We also thank Profs. Lennart Bergstro¨m, Stockholm and Shu Hong Yu, Hefei for the useful discussions on the content of this book. Finally we would like to acknowledge our families who have supported us through all the years of doing science, but especially during the two years of writing this book. It is clear that an active scientist has no time to write such book predominantly at the normal working hours, and many weekends and nights were sacrificed for the writing process. We are therefore extremely grateful to our wives Steffi and Sigrun as well as to our children for their patience to accept passionate science as it is. Potsdam March 2008

1 Mesocrystals and Nonclassical Crystallization 1.1 Introduction This chapter presents a history of observations that crystallization can go well beyond the simple ‘expected’ behaviour found in the salt cellar or when you buy a chemical. Biomorphs, crystal gardens, ‘crystal souls’, but also the remarkable pattern and structures of biominerals made researchers think that there is something beyond the concept of the bare three-dimensional regularity of molecules. This chapter introduces the beauty and diversity of ‘old knowledge’. Crystallization is the most elementary step in the handling of solid compounds. Crystallization is used for purification or isolation, but crystallization also creates order and beauty. It is presumably no exaggeration that the beauty of crystals has brought humankind to think in categories of substances and molecules. Although crystallization is well known, it is astonishing how little we know about this most elemental process between molecules, and their self-organization. Of course, there is a classical view on crystallization, presented in textbooks [1] and a plethora of scientific articles. But how much do we really know, and how many original observations have been forgotten in the effort to arrange and compact our knowledge, creating the classical crystallization theory? In the early days of chemistry, people were quite open in their views and differentiated little between biology and inorganic chemistry, and indeed many similarities have been observed. The first work on a chemical approach to address the morphological complexity of biominerals that we are aware of is the 1873 work of Peter Harting on the morphological complexity of calcium carbonate crystals synthesized in oyster marrow. His schematic drawings are shown in Figure 1.1, highlighting the absence of clear faces

Mesocrystals and Nonclassical Crystallization Helmut Co¨lfen and Markus Antonietti # 2008 John Wiley & Sons, Ltd

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Figure 1.1 Left: CaCO3 crystals obtained via a double diffusion experiment in Oyster marrow [2]. (P. Harting, Recherches de morphologie synthetique sur la production artificielle de quelques formations calcaire organiques, van der Post, Amsterdam, 1872). Right: CaCO3 synthesized in a double jet reactor in presence of 1 g/l (PEG-b-PEI-COC17H35 (CH2-COOH)n) [3]. (M. Sedlak and H. Co¨lfen, Macromolecular Chemistry and Physics, 2001, 202, 587).

and the appearance of curvature, properties that are classically not attributed to crystalline matter. We parallel this traditional drawing with an actual photograph, which depicts many of the described morphologies mimicked by synthetic processes, as they will be described later in the book. It is clear that the observation of such structures made people suspect that there were no clear borderlines between biology and dead inorganic matter. In his book Kristallseelen – Studien u¨ber das anorganische Leben [4], the philosopher and biologist Ernst Haeckel tried to approach the interplay between crystallography and biological structure formation. He carefully observed the complexity of crystallization with and without biomolecules and coined such notations as ‘living crystal field’ and ‘diseased crystals’, which (also from a modern view) hit the effects to be described in the very heart, but sound ‘nonscientific’ in today’s language. Haeckel was presumably the first to compile the evidence that the amazing complexity of biominerals can be, to some extent, mimicked in vitro with rather simple ingredients. The colloid chemist Herbert Freundlich devoted in his book [5] no less than two chapters on crystallization and its dependence on additives. Freundlich described nucleation agents and nucleation inhibitors, binodal crystallization and spinodal processes (the latter being long forgotten afterwards), as well as ‘little facts’ such as that dyes which are able to stain an inorganic crystal can also inhibit its crystallization. In the book, the first full synthetic experiments for synthesis of morphology (morphosynthesis) found entry, where the shapes of AgCl crystals were modified by adsorption of methylene blue [6]. The actual versions of all these experiments will be discussed in more detail later in this book; it is just amazing how similar the thinking and experimental approaches were in those days. The main improvement is not the mindset, but only the existence of much

Introduction

3

Figure 1.2 Various biominerals with complex forms. Left: Prosobranchia, center: Thalamophora, right: Acephala. (From Ernst Haeckel, Kunstformen der Natur, 1899 – 1904. http://www.zum.de/stueber/haeckel/kunstformen/natur.html. Copyright 1999, Kurt Stueber and Max-Planck-Institut fu¨r Zu¨chtungsforschung).

better analytical tools, which have enabled us to grab the details of these unconventional crystallization processes. Maybe better known in the English speaking world, the Scottish zoologist D’Arcy Thompson published his historic book, On Growth and Form [7], in 1917, referring actually to the extensive work of Haeckel. Thompson used his classical and mathematical training for an integrative approach to describe biological structural motifs, including biominerals. A point that influenced his book very seriously is that he was able to show that most biological complexity still follows very strict physico-chemical rules, partly given by the growth process, and partly driven by mechanical demands on the biomaterials that underlie evolutionary optimization pressure. It is the topic of this book to clarify how such complex crystallization processes can be controlled. Collected evidence will be presented that – beside classical crystallization treated in former textbooks – there is a second ‘reaction channel’ that works via parallel crystallization towards amorphous intermediates and then crystalline nanostructures, which act as material deposits or intermediates for arrangement and densification towards the final structure. This way, crystallization gains the freedom and possibilities to generate complex forms, but also mineral heterostructures, gradient materials, and organic/inorganic nanohybrids are brought to the hands of humankind. Due to the importance of organized self-assembly and the many formal similarities to the formation of organized mesophases, we will call these structures mesocrystals, as an abbreviation of mesoscopically structured crystal, and the process of parallel crystallization, colloidal assembly, and controlled structure formation, mesocrystallization. In this analysis, much has been and still can be learned from the processes of biomineralization, leading to those well-defined organic–inorganic hybrid materials with superior material properties, complex morphologies and hierarchical order [8–10]. Biominerals are often iso-oriented crystal structures with amazingly complex morphologies, like the hammer-shaped building units of coccoliths [11] or the skeletal plates of sea urchins [12]. Although it is known that organic templates, as in the case for

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coccoliths, play an important role [11], the actual crystallization mechanism of the inorganic phase in many biominerals remained largely unexplored. Recently, increasing evidence was found that biomineralization also takes place via the colloidal pathways of meso-crystallization. Amorphous precursor particles, for instance, as reported for sea urchin spines [13], allow the storage of large amounts of materials in metastable precursor particles, which are readily available to a crystallization event in a confined reaction environment. Advantages of this crystallization pathway are highly efficient mass fluxes independent of ion products, the coupled high crystallization speeds, and crystallization without changes in the pH and the osmotic pressure, key features for mineralization, especially in biological systems. This is set in strong contrast to the possibilities of classical crystallization, which postulates an ion-by-ion or single molecule attachment to a critical crystal nucleus and is therefore bound to solubility products and diffusion limitations. These particle mediated crystallization pathways are thus a nonclassical crystallization process involving mesoscopic transformation of self-assembled, metastable or amorphous precursor particles into nanoparticulate superstructures [14,15], as recently reviewed [16]. By mesoscale transformation, not only single oriented crystals with complex morphologies, but also superstructures of nanoparticles interspaced by organic additives can be formed. Their fusion leads to apparently single crystalline, isooriented structures with included organic additives as defects and sometimes also the leftovers of the prior amorphous phases. Support for this view comes from biomineral examples, which –although apparently single crystalline – often contain minor amounts of included biopolymers. This inclusion cannot be understood from the viewpoint of an ion-mediated crystallization process, as additives in this mechanism are generally considered to adsorb at edges and kinks in the developing crystal surface, stopping it from further growth [17]. (see also Figure 2.7). Mesocrystal formation and the process of mesoscale transformation are, however, not restricted to biominerals, thus motivating this book. It looks like Nature makes use of an advantageous physico-chemical construction principle, gaining speed and flexibility of construction. In synthetic systems, similar inclusions of additives up to 30 wt.% were observed in as-grown crystals, too [18–20]. Revisiting the older literature shows that comparable observations were made in synthetic inorganic chemistry much earlier, even in the absence of additives [21–24], and the relevant question arises as to which role precursor particles and their superstructures play – at least as intermediates – in crystallization in general. We also want to note that the term ‘‘mesocrystal’’ has been used before in the literature, but in the less restricted sense of a mutual three-dimensional translational ordering of various nanocrystals. As templates, pore systems of the MCM 41 type were used for the deposition of quantum sized BaTiO3 [25–27] or SrBi2Ta2O9. [26,28] Our definition is more restricted as it also involves, besides translational three-dimensional order, orientational order (vectorial alignment), and spontaneous self-assembly towards normally facetted microstructures. Besides the interesting scientific question of formation mechanisms and the superior properties of the resulting materials, it is admittedly also a big bonus for this field that mesocrystals are simply beautiful and esthetically appealing. The fascination for objects with complex shapes has always been an integral part of the cultural heritage of

Introduction

5

humankind and constitutes inspiration as well as a driving force in architecture, art and also science. The morphological diversity and complexity of naturally occurring forms and patterns has been a motivation for humans to copy Nature to achieve functional, esthetic, and societal value. [29] Although natural materials are often characterized by a finely carved appearance of remarkable aesthetical form, their formation is mostly directed by stringent selection processes, in order to provide efficiency and superior function [30]. Often, the non-classical nature of crystalline assemblies is not recognized, especially when they scatter X-rays and electrons like single crystals, which makes it difficult to assign mesocrystallization experiments described in the literature unequivocally. It is therefore the main task of this book to close this knowledge gap, to go beyond classical crystallization and to show that both crystallization pathways, particle-mediated and molecule-mediated, are in fact part of a common unifying crystallization scenario. Therefore, our book is structured into main chapters describing the classical crystallization theories and possibilities for crystal morphogenesis (Chapter 2), crystals challenging the classical textbook view on crystallization (Chapter 3), and nonclassical particle-mediated crystallization pathways (Chapter 4). Afterwards, we will give the foundations for the understanding of particle-mediated crystallization processes and mesocrystal formation. These include a treatment of self-organization processes (Chapter 5), colloidal crystals (Chapter 6), and the mesocrystal concept and properties (Chapter 7), including a description of the mesocrystals described so far sorted by their preparation and main occurrence. We will then try to capture the current existing knowledge about the formation mechanisms of mesocrystals (Chapter 8), as well as the analytical tools used to study mesocrystals (Chapter 9) and discuss the possibilities for the tuning of mesocrystal properties (Chapter 10). This will be summarized with the description of a unifying crystallization scenario combining classical and nonclassical crystallization (Chapter 11). This unifying crystallization scenario will allow, at least, for a phenomenological understanding of the crystallization phenomena described in this book. We will finally point out the analogy between hierarchically structured crystals and biopolymers, as well as oriented aggregation and polymers (Chapter 12) to show that a clear distinction between the living organic world and nonliving inorganic world cannot be made, which goes back to the initial views on this subject of people like Haeckel. Finally, we will end with a summary and outlook of possible future research directions (Chapter 13). We have structured each of the main chapters in such a way that a short summarizing introduction for the general reader is given at the beginning of each chapter. This will enable the fast pick up of the main ideas discussed in the specific chapter, although each chapter also contains detailed material for the specialist or those readers who want to obtain extended knowledge in the described area. The chapters will also give relevant primary literature for more in-depth study of the subjects. Although our book, in view of the rapid development of this research area, has obviously no chance to be really comprehensive, it has at least been tried to capture the most recent developments and current knowledge. It is therefore hoped that this book will further stimulate research in this new and very exiting area, especially in view of the huge scientific and industrial relevance of crystallization processes and their control.

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References 1. J. W. Mullin, Crystallization, 4th edn., Butterworth-Heinemann, Oxford, 2001. 2. P. Harting, Recherches de morphologie synthe´tique sur la production artificielle de quelques formations calcaires organiques, van der Post, Amsterdam, 1872. 3. M. Sedla´k and H. Co¨lfen, Macromolecular Chemistry and Physics 2001, 202, 587. 4. E. Haeckel, Kristallseelen: Studien u¨ber das anorganische Leben (Crystal Souls: Studies on Inorganic Life), 3rd edn., Kro¨ner, Leipzig, 1925. 5. H. Freundlich, Kapillarchemie: eine Darstellung der Chemie der Kolloide und verwandter Gebiete, 3rd edn., Akademische Verlagsgesellschaft, Leipzig, 1923. 6. W. Reinders, Zeitschrift fu¨r physikalische Chemie–Sto¨chiometrie und Verwandtschaftslehre 1911, 77, 677. 7. D. A. W. Thompson, On Growth and Form, abridged edn., Cambridge University Press, Cambridge, 1966. 8. H. A. Lowenstam and S. Weiner, On Biomineralization, Oxford University Press, New York, 1989. 9. W. Ba¨uerlein, Biomineralization, Progress in Biology, Molecular Biology and Application, 2nd completely revised and extended ed., Wiley-VCH, Weinheim, 2004. 10. S. Mann, Biomineralization, Principles and Concepts in Bioinorganic Materials Chemistry, Oxford University Press, Oxford, 2001. 11. M. E. Marsh, in Biomineralization, Progress in Biology, Molecular Biology and Application, 2nd completely revised and extended edition edn., Wiley-VCH, Weinheim, 2004, p. 197. 12. G. Donnay and D. L. Pawson, Science 1969, 166, 1147. 13. Y. Politi, T. Arad, E. Klein, S. Weiner, and L. Addadi, Science 2004, 306, 1161. 14. H. Co¨lfen and M. Antonietti, Angew. Chem. Int. Ed. 2005, 44, 5576. 15. H. Co¨lfen, in Biomineralization: From Paleontology to Materials Science, (eds. J. L. Arias and M. S. Fernandez), Editorial Universitaria, Universidad de Chile, Santiago, 2006. 16. H. Co¨lfen and S. Mann, Angew. Chem. Int. Ed. 2003, 42(21), 2350. 17. G. Wegner, P. Baum, M. Mu¨ller, J. Norwig, and K. Landfester, Macromolecular Symposia 2001, 175, 349. 18. S. H. Yu and H. Co¨lfen, J. Mater. Chem. 2004, 14, 2124. 19. L. Qi, H. Co¨lfen, and M. Antonietti, Ang. Chem. Int. Ed, 2000, 39, 604. 20. A. Taubert, D. Palms, O. Weiss, M. T. Piccini, and D. N. Batchelder, Chemistry of Materials 2002, 14, 2594. 21. H. Zocher and W. Heller, Zeitschrift fu¨r Anorganische und Allgemeine Chemie 1930, 186, 75. 22. W. Heller, Comptes Rendus Hebdomadaires des Seances de L’ Academie des Sciences 1935, 201, 831. 23. E. Matijevic and P. Scheiner, J. Coll. Interface Sci. 1978, 63, 509. 24. W. P. Hsu, L. Ro¨nnquist, and E. Matijevic, Langmuir 1988, 4, 31. 25. K. Yamada and S. Kohiki, Physica E 1999, 4, 228. 26. S. Kohiki, S. Takada, A. Shimizu, K. Yamada, H. Higashijima, and M. Mitome, J. Appl. Phys. 2000, 87, 474. 27. S. Kohiki, S. Takada, K. Yamada, Y. Adachi, A. Shimizu, M. Oku, and M. Mitome, Physica E 1999, 5, 161. 28. H. Higashijima, S. Kohiki, S. Takada, A. Shimizu, and K. Yamada, Appl. Phys. Lett. 1999, 75, 3189. 29. S. Mann, Angew. Chem. Int. Ed. 2000, 39, 3392. 30. C. Sanchez, H. Arribart, and M. M. Giraud Guille, Nat. Mater. 2005, 4, 277.

2 Physico-Chemical Principles of Crystallization Defining notations first is an enabling step for a scientific discussion of a distinct topic. This chapter introduces the physico-chemical background of crystallization processes and defines notations such as ‘supersaturation’, ‘crystal growth’,‘nucleation’ and ‘surface properties’. The expert reader may prefer to leave this chapter for later clarifications.

2.1 Classical Crystallization Before mesocrystal formation and nonclassical crystallization processes are discussed, it is necessary to introduce the picture of classical crystallization itself at a very basic level. Crystallization starts from dissolved atoms or molecules, or in case of salts from different ions. The thermodynamic driving force for crystallization is the supersaturation of the solution. The relative supersaturation S is defined as a dimensionless ratio of the actual concentration of the species c, divided by its equilibrium molecular solubility product ksp under the given set of conditions: c ð2:1Þ S¼ ksp In the case of multiple species involved in crystallization as, for example, in ionic crystals, c is the product of the concentrations of the individual components (or more correctly the activity product). Further, it is important to note that the definition of supersaturation preassumes a structure of the final precipitate. If a species, e.g. calcium carbonate, exists in five different polymorphs and at least one amorphous species, the same concentration can mean different supersaturations depending on which species is precipitated, as a result of the different solubilities of amorphous matter and different crystalline polymorphs. These


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differences in supersaturation can be, in selected cases, rather large, which will turn into an important tool for polymorph control. It must be also mentioned that the magnitude of supersaturation is not the only driving force in crystallization control. On the contrary, the Ostwald rule of stages teaches that it is usually the least dense species and therefore the most soluble species which precipitates first (see also Section 2.5, Thermodynamic and Kinetic Crystallization Pathways). Supersaturation is therefore only a first approach in handling the complex problem of crystallization from a thermodynamic viewpoint, as the supersaturation can be related to the change in the chemical potential and thus the free enthalpy (Equation 2.2) of the crystallization reaction by: m ¼ kT ln S

ð2:2Þ

where m is the change in the chemical potential, k is the Boltzmann constant and T is the thermodynamic temperature. Supersaturated solutions can be easily prepared by a temperature or pressure jump, by reactions generating the respective species, by adding nonsolvents under mixed solvent conditions, or – in the case of acids and bases – very conveniently by a pH jump. Figure 2.1 presents the classical 1950 La-Mer curve for the crystallization behavior of sulfur in ethanol [1]. Here a reaction is linearly increasing the amount of sulfur, until a critical supersaturation is reached, and particles spontaneously form thereafter. Due to that, the sulfur concentration decreases again, until finally S ¼ 1 or the equilibrium solubility is reached. If the time of the nucleation burst is short, crystal nuclei of uniform size can be obtained, which is often desired in colloid synthesis. Once supersaturated (i.e. S > 1), crystals can, in principle, grow in solution, but need a nucleus to grow from. In heterogeneous nucleation, surfaces or dispersed components, such as dust particles or crystal seeds, provide the starting point for the crystallization event. Heterogeneous nucleation is least demanding and becomes relevant when the other

Figure 2.1 Schematic representation of the concentration of molecularly dissolved sulfur before and after nucleation as a function of time. (Taken from V.K. LaMer, R.H. Dinegar, J. Am. Chem. Soc. 1950, 72, 4847. With permission of the American Chemical Society.)

Physico-Chemical Principles of Crystallization

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options are kinetically excluded. In homogenous nucleation, the nucleus forms spontaneously from the solution itself when a critical supersaturation is reached, however it is in a crystal-by-crystal fashion. The nucleation sites in this model can be treated independently. In addition, we will also introduce the concept of spinodal (homogeneous) nucleation, in which all crystals start to nucleate practically at the same time, i.e. the single nucleation events cannot be treated as thermodynamically independent, but are coupled via a joint concentration field.

2.2 Definition of a Crystal and Crystal Growth According to Wikipedia free encyclopedia (http://en.wikipedia.org/wiki/single_crystal, definition taken on 23.7.07), ‘a single crystal, also called monocrystal, is a crystalline solid in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries. The alternative to the presence of a single crystal sample is a polycrystalline sample, which is made up of a number of smaller crystals known as crystallites. Because of a variety of entropic effects on the microstructure of solids, including the distorting effects of impurities and the mobility of crystallographic defects and dislocations, single crystals of meaningful size are exceedingly rare in nature, and can also be difficult to produce in the laboratory under controlled conditions.’ In the classical view, a crystal is therefore a solid body with a rigid lattice of molecules, atoms or ions in a characteristic location for the crystal [2]. The smallest repeat unit of the crystal is its unit cell. Due to the regularity of its internal structure, a crystal has a characteristic shape with smooth surfaces parallel to atomic planes in the lattice. Therefore, defined angles exist between the external faces. This is expressed in the law of constant interfacial angles, stating that the angles between corresponding faces of all crystals of a given substance and polymorph are constant. A typical single crystal is displayed in Figure 2.2. This definition of a crystal expresses single crystals as solid bodies with a defined geometrical outer shape characterized by smooth surfaces. This definition excludes any curvature in the morphology of a single crystal. The flat surfaces of a crystal growing via layer-by-layer adsorption of solute atoms or molecules onto an existing crystal face was suggested by Volmer [3]. When an atom/molecule arrives at the crystal surface from solution, it is not immediately integrated into the crystal lattice, but is able to migrate on the crystal surface in two dimensions. These units form the so-called adsorption layer with a typical thickness of about 1 nm [2]. The migrating units on the crystal surface will get integrated into the crystal lattice at ‘active centres’ where the attraction of the moving units to the lattice is greatest. These are steps and kinks on the growth surface (Figure 2.3a). The attachment of a growth unit to a kink is the most favoured scenario, so that the kink moves along the step until it is completed and a new step is started. The nucleation of a new layer starts from surface nucleation of an island on the plane face (Figure 2.3c), which grows further by attachment of further atoms/ions to the steps and kinks of the new layer until the surface is completed (Figure 2.3b). This layer-bylayer growth mode of a crystal surface is expressed in the model of Kossel [4]. However, the growth of a surface is rarely perfect, and a number of imperfections exist in form of vacancies (Figure 2.4 E,F) and dislocations, screw dislocations being a

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Figure 2.2

Single crystal of calcite (CaCO3) with the typical rhombohedral morphology.

particularly important example. In addition, even at equilibrium, the steps have kinks due to thermally activated detachment of molecules from the steps onto either the step edges or the terraces or even back into solution [5–7]. Consequently the step edges are not static; molecules are constantly attaching and detaching, even at equilibrium [8,9]. As a consequence, growth steps are not as ideal, as implied by the Kossel model, but fuzzy (Figure 2.5). Growing crystal surfaces can nowadays be very favourably imaged by scanning force microscopy (SFM), while the growing layers can be depicted with high resolution (Figure 2.6). In a similar manner, the surface nucleation in form of islands (Figure 2.6c) can be imaged using SFM, and some typical scenarios are shown in Figure 2.7. The layer-by-layer growth of crystals has important consequences for the effect of impurities on the growth of a crystal face. Potential impurities are all substances other than

Figure 2.3 Ideal layer-by-layer crystal growth: (a) migration of a unit towards a kink on the surface; (b) completed layer; and (c) surface nucleation. (Reproduced from J.W. Mullin, Crystallization, 4th edn., Butterworth-Heinemann, Oxford, 2001, with permission of Butterworth-Heinemann).


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Figure 2.4 Kossel’s model of a growing crystal surface showing: (a) flat surfaces; (b) steps; (c) kinks; (d) surface adsorbed growth units; (e) edge vacancies; and (f) surface vacancies. (Reproduced from J.W. Mullin, Crystallization, 4th edn., Butterworth-Heinemann, Oxford, 2001, with permission of Butterworth-Heinemann).

Figure 2.5 AFM images of a step on a crystal of the protein canavalin showing the fuzziness of the step due to attachment and detachment of molecules. (Image reproduced from [10] with permission of Mineralogical Society of America.)

Figure 2.6 AFM images showing examples of two-dimensional nucleation at high supersaturation for (a) calcite and (b) canavalin. N - locations where islands have nucleated on top of other islands. s is the supersaturation in this image. (Image reproduced from [10] with permission of Mineralogical Society of America.)

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Figure 2.7 Sites for impurity adsorption on a growing crystal based on the Kossel model. (a) kink, (b) step and (c) surface after impurity adsorption. [11] Reproduced from [2] with permission of Butterworth-Heinemann at Oxford.

the crystallizing material, including even the solvent. Impurities can adsorb at various sites of the growing crystal as shown in Figure 2.7 and both lower the surface energy of the crystal face as well as inhibit step edges from further growth. The influence of an impurity on crystallization is therefore both thermodynamic and kinetic in character. The adsorption of impurities onto kinks or steps allows a tiny amount of an impurity to retard or even block the growth of a complete crystal face. The surface is ‘poisoned,’ which is often a desired effect to selectively block the growth of a certain face if an impurity is found which selectively adsorbs to this specific crystal face. This is further discussed in Section 2.7, Crystal Morphology and the Role of Additives and Selective Adsorption. One example of proteins adsorbing to the step edges of a growing calcite (104) surface is illustrated in Figure 2.8. It can be seen that the step edges become rounded, which is equivalent to a macroscopic habit modification of a crystal by additive adsorption. On the other hand, the additives can also nucleate the growth of new layers, as found for the protein perlucin (Figure 2.9) [13]. The nucleation of new layers will also modify the macroscopic crystal morphology.

Figure 2.8 (a) A calcite (104) surface without proteins. Light grey and dark grey lines are obtuse and acute step edges, respectively. Step edges are generally straight and smooth, with sharp corners. Some kinks are visible in the acute step edges in the upper right corner. (b) With proteins. Step edges have become rounded (suggesting an isotropic step edge speed) and more convoluted. The step edge appears highlighted, as by a raised lip of proteins. Strong white-andblack features (that are identical in (a) and (b)) are defects in the crystal that can act as barriers to step edge motion. (Reprinted from [12] with permission of the Biophysical Society.)


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Figure 2.9 AFM measurements of the interaction of perlucin with geological calcite (3 min interval between two images). (A–E) Consecutive AFM images of a (4-4-1) calcite surface immersed in deionized water. The calcite crystal slowly dissolves layer by layer (white and black arrowheads). (F–K) Consecutive AFM images of the growth of calcite (4-4-1) surface in saturated calcium carbonate solution. Note the growth of the molecular layers (white and black arrowheads). (L–T) Consecutive AFM images show a (4-4-1) calcite surface immersed in saturated calcium carbonate solution with perlucin (0.01 mg/mL). Note that perlucin nucleates small islands (e.g. R, S, light grey arrowheads) for the next molecular layer. As different layers (e.g. L to O, black arrowheads) merge without detectable defects (e.g. small arrowheads in P), it is reasonable to suggest that perlucin induces epitactic growth of new layers in the orientation of the crystal lattice. (Reprinted from [13] with permission of Blackwell Publishing Ltd.)

If the growth of the face is not completely blocked, the impurities are potentially incorporated into the crystal after they are overgrown by subsequent layers. This can be nicely demonstrated for the case of polymer latexes which are functionalized to adsorb onto certain crystal faces so that they get incorporated into the crystals [14]. Once removed from the crystal by dissolution or calcination, a porous crystal with a ‘swiss cheese’ morphology is obtained, as shown in Figure 2.10. The adsorption of additives onto crystal surfaces can be highly selective and even chiral surface textures can be produced with a chiral additive. An example is presented in Figure 2.11, which shows the effect of right-handed and left-handed aspartic acid on the shapes of growth hillocks and the resulting macroscopic crystals [16]. It is obvious that

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Figure 2.10 SEM images of CaCO3 particles with porous surface obtained by templating and THF extraction of P(St-MMA-AA) latex particles with a size of 380 nm. (Image reproduced from [15] with permission of the American Chemical Society.)

the shapes of the growth hillocks are dramatically altered and the symmetry about the calcite glide plane is broken, such that L-aspartic acid gives one chirality, while D-aspartic acid gives the opposite chirality. There are new step directions that can be altered from one side of the glide plane to the other when the amino acid enantiomer is switched from L to D. This observation is explained by changes in the step edge energies caused by the adsorption of the chiral additives.

Figure 2.11 Example of a system that exhibits behavior expected for addition of a growth modifying additive. AFM images of calcite grown in: (a) pure solution; (b) solution containing D-aspartic acid; and (c) solution containing L-aspartic acid. The shape changes dramatically and even shows a left–right shape dependence that corresponds to that of the additive. (d–f) show that the resulting crystal shape reflects these changes. Figure reproduced from [16] with permission from Nature publishing group.


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2.3 Nucleation Theories 2.3.1

Classical Nucleation Theory

Homogeneous Nucleation. Homogeneous nucleation phenomena have been studied for over 70 years, starting with the pioneering experiments of Wilson and the theoretical studies of Becker and Do¨ring [17] and Volmer [3]. Although spontaneous homogeneous nucleation is well studied, there are still major uncertainties concerning the nucleation mechanisms and their theoretical description. It is well known that the classical nucleation theory (CNT) [17], which is the most commonly found formalism to analyze nucleation phenomena, fails in predicting the temperature dependence and absolute values of the critical supersaturations of a number of substances including water, alcohols and high alkanes [18–23]. A large number of theories [24–28] to test against the experimental data have been reported in the literature in the last two decades, yet a major source of the discrepancies is not clearly identified. Classical nucleation theory considers the formation of a molecular cluster consisting of i þ 1 molecules by the attachment of a single vapor molecule (monomer) to an i-mer. The classical homogeneous nucleation (or barrier-crossing) rate J is given by a simple Boltzmann approach: Gi J ¼ K exp ð2:3Þ kT where k is the Boltzmann constant, Gi is the change in the Gibbs free energy associated with the i-mer formation, and K is the kinetic prefactor. The barrier height or change in the Gibbs free energy is expressed in the CNT as a sum of volume and surface terms: GCNT ¼ mi þ gAðiÞ i

ð2:4Þ

where (mi is the change in the chemical potential of the i-mer, A(i) is the surface area of the i-mer, and g is the surface free energy. The volume terms typically drive the reaction, as a new, more stable phase is formed (e.g. by the crystallization enthalpy), whereas the surface terms are usually positive and hinder the formation of a new phase. As the surface area of each nucleus is proportional to the square of the radius of the spherical cluster r2, whereas the volume is proportional to r3, there is a maximum of barrier height for a distinct cluster size r*, the so-called critical cluster size (see Figure 2.12). Compared to the speed of molecular processes, as described by the Boltzmann probability in Equation (2.3), the clusters rarely reach the size of a so-called critical crystal nucleus. At this point, the change in the free enthalpy of the system becomes negative upon further particle growth, and the gain in lattice energy overcompensates the loss in surface energy. The critical crystal nucleus is the smallest crystalline unit capable of continued further growth. Its existence separates the domain of nucleation from the domain of crystal growth. It is interesting to note that this critical cluster size was determined in a number of cases. For water, dependent on temperature, critical cluster sizes of 20–35 molecules were reported [20]. For pentanol as a model system, these numbers are between 24–36 [29]. However, the above sizes of the critical crystal nucleus do not only depend on the system, but also on the shape and structure of the nucleus [30]. This is not accounted for

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Figure 2.12 Change of GCNT with r. At a distinct particle radius r*, the bulk energy balances i the surface energy. GCNT at r* is the nucleation barrier. For r > r , GCNT becomes negative, i i particle growth is favoured.

in the CNT, which assumes a spherical solid cluster. Indeed, it was possible to follow the crystallization of 12 nm large apoferritin molecules with AFM in a ‘movie mode’, and a nonspherical, quasi planar shape of this particular critical crystal nucleus was demonstrated, consisting of 20–50 apoferritin units (see Figure 2.13) [31]. The Becker–Do¨ring theory expresses the nucleation rates, i.e. rates of events passing the critical barrier, as: 0:5 GCNT BD 2 2g i J ¼ Ni exp pM kT ð2:5Þ GCNT BD i ¼ K exp kT which gives Equation (2.3), where M is the molecular weight, Ni is the number of i-mers and is the molecular volume. The kinetic prefactor Ni2 ½2g=pM0:5 was later found to be inconsistent. Two different derivations of the classical nucleation rate performed using both the kinetic theory and constrained equilibrium approach [32,33] showed that the Becker–Do¨ring theory should be corrected by 1/S. Nevertheless, the Becker–Do¨ring theory, in its original form, remains the most common theory to analyze nucleation processes, probably because the application of the correction 1/S to Equation (2.5) makes the agreement with the experimental data even worse. In many contributions, the Becker–Do¨ring theory is even denoted as CNT. Nucleation rates in the kinetically consistent version of CNT are given by the following equation: 0:5 1 GCNT 1 CNT 2 2g i exp J ¼ N1 ð2:6Þ ¼ J BD pM S S kT


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Figure 2.13 A near-critical-size cluster on the (111) face of an apoferritin crystal at supersaturation S ¼ 1:1. (a)–(c) Molecules attach and detach from the cluster. Molecules that are missing in the next frame are highlighted in blue, those that have appeared after the previous frame was captured are highlighted in red; (d), (e) An advancing step pushes the cluster back into the solution. The step velocity is 0.6 nm/s, close to the fastest step velocity previously recorded for this supersaturation with apoferritin crystals. This indicates that the selected AFM imaging mode did not affect the monitored processes; (f) Diagram of (111) and (110) planes and < 110 > molecular rows in a face-centered cubic (f.c.c.) crystal lattice. (Image reproduced from [31] with permission of the Nature Publishing group.)

It has already been mentioned that even the corrected versions of CNT fail by orders of magnitude to predict the correct magnitude and parameter dependences of nucleation rates. In a set of papers, Strey and coworkers very carefully analyzed the experimental nucleation rates for a variety of systems and compared them with the Becker-Do¨ring theory [20,29,34]. Very systematically, the Becker–Do¨ring theory underestimates the real nucleation rate at low temperatures, whereas they are overestimated at high temperatures. Coincident overlap is just found at one single temperature, while the deviations can easily be as high as four orders of magnitude, for both the over- and underestimations (see also Figure 2.14 and the corresponding discussion). This difference indicates how much the free energy of formation has to be corrected dependent on the temperature. Neglected energy terms within the nucleation process are, in our opinion, manyfold and include: the volume work, entropy

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Figure 2.14 Ratio of the experimentally determined nucleation rates of pentanol from the gas phase (using Ar or He) as a carrier gas) to the calculated ones predicted by the Becker–Do¨ring theory in dependence of the temperature. (Figure reproduced from [29] with permission from the American Institute of Physics.)

effects and the role of hydration/solvation phenomena. But differences are also due to the disregard of molecular interactions between the single components and collective phenomena, such as concentration fluctuations. There are empirically corrected versions of CNT [35], however the reasons for the applied corrections remain physically unclear. Heterogeneous Nucleation. Heterogeneous nucleation occurs in very clean solutions along surfaces and interfaces (such as the container wall); in real systems it progresses on solid impurities (such as dust) or gas bubbles. It is well known in preparative chemistry that crystallization of a desired compound can be induced by scratching the wall of the crystallization vessel. Extending Equation (2.4) to heterogeneous situations, heterogeneous nucleation is always energetically more favored when the interface energy of the crystal being formed with the substrate is lower than the corresponding one with the free solution. This is especially the case when the impurities or seeds are chemically very similar to the crystal being formed. But even in case of favourable seeds, crystallization processes are usually controlled by different processes at the same time (e.g. [36]). This is mainly due to crystallization kinetics: the area of foreign particles or the container surface is always low, as compared to effective homogeneous seeds. This is why at low supersaturations, heterogeneous nucleation will be dominant, while at high supersaturation, homogeneous nucleation will be the prevailing process. For practical purposes, it should be mentioned that even heterogeneous nucleation is sometimes not easy to accomplish and can be quite effectively suppressed. To be miscible


19

soluble, molecules have to have a cohesion energy or polarity not too different from each other, and interface tensions between crystals and the mother liquor are usually rather low. Containers or impurities with very different cohesion energies from the solute are therefore not able to nucleate, or better: heterogeneous nucleation is even harder to obtain than homogeneous nucleation. For aqueous solutions, these non-nucleating surfaces are, for instance, hydrophobic polypropylene containers or Teflon1 stirring bars. On the other side, beyond sheerly providing favourable surface energies, surfaces can stimulate heterogeneous nucleation by enrichment of the crystallizing species within the surface double layer. This is, for instance, easily accomplished for ions, but also for all macromolecular or colloidal species which are attracted by surface forces. Such cases will be discussed in detail below and are one key to control crystallization in a spatially directed way. 2.3.2

Experimental Tests of Nucleation Theories

Starting from the early work of Wilson in 1897 [37], nucleation processes have also been studied in a quantitative fashion. Different techniques complementing each other are available for this purpose, such as cloud chambers [38,39], diffusion cloud chambers [40], nucleation pulse chambers [41], pulse expansion wave tubes [42], shock tubes [43], and supersonic nozzles [22,44]. With all these techniques, absolute nucleation rates covering no less than 20 orders of magnitude starting from nucleation rates of J ¼ 103 / cm3/s (one nucleation center per cm3 in a thousand seconds) to J ¼ 1017 /cm3/s can be covered. For further reading, this was nicely reviewed by Strey et al. [29]. These data were then collected, in one case even using a big experimental panel, and compared to classical nucleation theory. A typical result is presented in Figure 2.14 (from [29]). It can be seen that the experimental techniques support each other quite well, but that the real nucleation rates differ from the experimental ones by orders of magnitude, with a very systematic dependence on the crystallization temperature. This is because nucleation theories underestimate nucleation at low temperatures, while they overestimate the real behaviour at high temperatures. It has already been said that there are empirical functional factors to correct for these systematic experimental deviations [34,35], but the physical reasons to justify those empirical reasons remain unclear.

2.4 Some Points towards a More Realistic View of Supersaturation and Crystallization 2.4.1

Concentration Fluctuations and ‘Spinodal Crystallization’

The very big deviations between classical nucleation theories and the experimental findings, especially in regions far from the equilibrium, already indicate that the real crystallization scenario is more complicated than indicated by a description based on single molecules only. In another, more illustrative picture, supersaturation can be translated, on a molecular scale, into a thermodynamically derived attraction of molecules or ions which leads to a nonstatistical distribution of these primary building units. Very similar to the discussion of cooperativity in assembly behavior below (in fact, nucleation and cooperative assembly have strong similarities), this binary interaction is not necessarily strong

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enough to lead to the permanent adherence of two or a few species to a cluster, but lead to joint concentration fluctuations and coupled thermodynamic behavior. In fluctuation theory, increasing attraction between the moieties is expressed as the occurrence of increasing concentration fluctuations, i.e. the deviations from mean concentration are not damped out, but thermodynamically stimulated. This is described by the Cahn–Hilliard theory [45], which also defines the precise wavelength or spatial correlation length dependent on thermodynamic parameters. With crystallization ‘‘folded into’’ the concentration fluctuations, nucleation obviously becomes highly simplified into positive concentration fluctuations, due to the higher supersaturation. In such metastable situations, there is a critical concentration, above which concentration fluctuations do not relax, but spontaneously grow. Here, the systems become unstable, which is due to the change of the free energy of mixing GM ðcÞ with concentration (more precisely, the second derivative of GM ðcÞ becomes negative). For the formation of phases in such a second order scenario, (e.g. for the demixing of two components), this is called the spinodal region [46] and is shown in Figure 2.15. The notation ‘spinodal crystallization’ is somewhat ill defined, as crystals still have to nucleate one-by-one. More precisely, demixing is a second order phenomenon, but crystallization is still driven by the crystallization enthalpy and is a first order phase transition. However, the occurrence of crystallization is, at least apparently, coincident in the whole reaction system, and the individual crystallization events are seemingly coupled to each other via concentration fluctuations. A more correct description of ‘spinodal crystallization’ would have to consider supersaturation as a variable depending on time and spatial position.

Figure 2.15 Free energy of mixing GM (upper diagram) and demixing temperature (lower diagram) as a function of the solute volume fraction f2 for a partially miscible system. st ¼ stable region, m ¼ metastable region, u ¼ unstable region, b ¼ binodal, sp ¼ spinodal, T1 ¼ temperature for the validity of the upper diagram.


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It is important to note that even in the ‘binodal’ region, concentration fluctuations play a significant role in crystallization. They are damped, but can reach rather high amplitudes, which diverge approaching the spinodal line. This is why classical single site crystallization is also increasingly simplified with increasing proximity to the spinodal line, with concentration fluctuations supporting the critical level of supersaturation. Although nucleation is only a short, transient state in the life of a crystal, it determines the majority of properties. One legacy of the phase of nucleation is the crystal size and number, which is proportional to the relative rates of nucleation to growth. Some substances are notoriously hard to nucleate, and consequently, they usually form very big crystals. Ice is a good example of this type of behavior. Other particles nucleate very fast and only grow slowly, so that their usual appearance is that of very fine nanocrystalline powders. Synthetic anatase, but also dyestuff, belongs to this class of substances. 2.4.2 Reduction of Supersaturation by the Formation of Clusters and Amorphous Intermediates High supersaturation does not only lead to micro concentration fluctuations, but the attraction between the molecules can also lead to a physical or chemical binding situation between the singular entities. In the chemistry of oxides/hydroxides or ligand chemistry, this is quite a regular situation: Fe3þ, for instance, in neutral or even weakly acidic conditions does not exist as an ion, but as a charged, extended iron oxide polymer or cluster. A similar story could be told for Cu2þ and Cl, where the chlorides can bridge between different Cu centers, usually leading to oligoclusters, the size of which depends on concentration. It is obviously a question of the strength of pair attraction or specific chemical forces for an unfavourable solvent situation to lead to the formation of dimers, trimers, clusters, polymers, or even amorphous nanoparticles and colloids. The formation of such dimers is obviously promoted by the gain in chemical energy and not hindered by interface energy, i.e. occurs spontaneously in a reaction- or diffusion-controlled fashion. For weakly hydrated ions such as Ca2þ, the formation of clusters and amorphous intermediates can be driven by dehydration and the related entropy gain. Such a situation is not within a classical bonding scheme, as it is endothermic, but strongly spontaneous as the change in free energy is negative. If no significant activation barrier for formation of the cluster is involved, such processes occur spontaneously and are fully reversible. Indeed, we believe that all crystallization events involving Ca2þ, but also similarly weakly solvated species, do not take place from a supersaturated ‘molecular’ solution, but proceed via the formation of clusters and amorphous phases first. As with any crystal, these intermediates or phases are in equilibrium with the dissolved species. As the free energy of formation of amorphous phases is lower than the corresponding free energy of crystallization, the equilibrium concentration of free species is higher. For Ca2þ, this is experimentally easily accessed, e.g. with a Ca2þ-selective electrode, or by characterization of the ion product. It is very illustrative to compare these values for the technically highly relevant case of calcium carbonate, which exists in three different anhydrous polymorphs, but can also be prepared in the amorphous state. The three anhydrous polymorphs have different thermodynamic stabilities and therefore different ion products, with calcite being the most stable and having the lowest corresponding ion product. We can calculate the

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1E-3

1E-4

Ca

2+

concentration in solution

0.01

1E-5 Ámorphous

Vaterite

Aragonite

Calcite

Figure 2.16 Ca2þ concentrations in solution for different CaCO3 polymorphs. The circles are the Ca2þ concentrations calculated from the solubility product of the respective species, the squares are the Ca2þ concentrations where the respective polymorphs are found. The gray region is the region of ACC. Note the logarithmic concentration scale. Image reproduced from [48] with permission of Wiley-VCH.

Ca2þ concentrations from the solubility products Ksp of the different polymorphs ( log Ksp 25 C: ACC ¼ 6.4 [16], vaterite ¼ 7.91 [47], aragonite ¼ 8.34 [47], calcite 8.48 [47]. Amorphous calcium carbonate (ACC) is formed practically without an activation barrier and therefore lowers the supersaturation of almost any Ca2þ solution which exceeds its ion product, but provides by its dissolution equilibrium, a calcium concentration which is itself ‘supersaturated’ for all the crystal polymorphs. Experimental Ca2þ concentrations from which to start crystallization (squares in Figure 2.16) are therefore likely to be reduced to the value where amorphous intermediates and clusters form spontaneously. These solutions are, however, still supersaturated with respect to the formation of the crystalline polymorphs. This can be nicely visualized for the example of polymer controlled crystallization of all three CaCO3 polymorphs in one reaction system [48]. From the ion products of the different polymorphs and the different experimental starting concentrations for the different polymorphs (vaterite 5 mM, aragonite 1.25 mM, and calcite 10 mM), we can calculate S-values of 45 (vaterite), 18 (aragonite), and 173 (calcite) according to Equation (2.1) and neglecting the polymer influence. In this picture, only crystallization reactions with supersaturations below the ACC threshold are expected to progress without any amorphous intermediates. The actual supersaturations – considering the formation of amorphous clusters and the ion product of ACC as the starting concentration – are therefore much lower, namely 6 (vaterite), 9 (aragonite), and 10 (calcite).

2.5 Thermodynamic and Kinetic Crystallization Pathways The thermodynamic equilibrium considerations of crystallization are already quite complex and interdependent as shown in the above section. In addition, they are not always well suited to describe real, experimentally observed crystallization processes. In


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fact, most crystallization reactions follow a kinetic pathway, which is inherently difficult to predict and to describe with theoretical models. Kinetic control can express itself in crystal morphology and architecture which does not follow the rules of energy minimization, but is also relevant for the formation of polymorphs. We understand as polymorphism, that the crystal packing of many compounds can be accomplished in a number of nearly isoenergetic, but structurally distinct motifs. The so-called polymorphs usually have different thermodynamic stabilities, melting points, solubilities, and mechanical or electrical properties, i.e. act as different components. In general, kinetic polymorph control is based predominantly on the modification of the activation-energy barriers of nucleation, growth, and phase transformation (Figure 2.17) [49]. In such cases, crystallization is often a sequential process involving structural and compositional modifications rather than a single-step pathway [50–53]. The intermediate particles have multiple possibilities for further reaction including dissolution-recrystallization, aggregation, solid phase transformation, or other mesoscopic transformations delineated below. For crystallization in the presence of an additive, the situation gets really complex, as the additive can interact in multiple ways with all the amorphous or crystalline intermediates. This will be later discussed under the topic ‘nonclassical crystallization pathways’ The kinetic cascade displayed in Figure 2.17 is a manifestation of Wolfgang Ostwald’s ‘step rule’. This rule allows an empirical prediction of the formation sequence of phases in a crystallization event. Usually, the least dense phase is formed first and transforms to the

Figure 2.17 Simplified scheme of the crystallization pathways under thermodynamic and kinetic control. Whether a system follows a one-step route to the final mineral phase (pathway A) or proceeds by sequential precipitation (pathway B) depends on the free energy of activation associated with nucleation (n), growth (g), and phase transformation (t). (Reproduced from Ref. [50] with permission of Wiley-VCH.)

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Figure 2.18 Transformation of metastable vaterite spheres into thermodynamically stable calcite rhombohedra at pH 6.5 at room temperature. Reprinted from Ref. [54] with permission of Deutscher Verlag fu¨r Grundstoffindustrie.

next dense phase until finally, the densest (which is usually also the most stable phase) is formed. This illustrates that the activation energy of crystallization and transformation is connected with the magnitude of compression of the different phases, pointing to a previously not considered volume term in nucleation thermodynamics. Of course, the kinetic transformation sequence is strictly in order of increasing thermodynamic stability. It should also be mentioned that not all possible polymorphs show up along such lines. An experimental example for modification transformations following the Ostwald step rule is given in Figure 2.18 for CaCO3. Note that the third anhydrous polymorph, aragonite, is not observed along this sequence, as it is notoriously hard to nucleate. In most crystallization experiments, the thermodynamically most stable phase is rarely formed directly, but is generated via metastable phases, as shown in Figure 2.17. How far the metastable intermediates are stable or transform to the next stable species according to Ostwalds step rule, depends on the solubility of the minerals and on the free energies of activation of nucleation in different environments, all of which are strongly influenced by additives. The corresponding changes in composition and structure usually occur by dissolution– renucleation processes. If enough nucleation centers are provided on the dissolving metastable phase, it can be used for a template effect to nucleate the stable phase on a sacrificial metastable phase. One example are calcite hollow spheres grown on the surface of sacrificial vaterite spheres (Figure 2.19) [55].


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Figure 2.19 Hollow spherical metastable vaterite aggregates transform into hollow stable aggregates of calcite rhombohedra by a dissolution–recrystallization process in the presence of a block copolymer. [55] The growth sequence is the formation of vaterite nanoparticles (a), which form spherical aggregates (b). These aggregates partly dissolve, and calcite rhombohedra are nucleated on the surface of the vaterite aggregate. After the sacrificial vaterite aggregate is completely dissolved, a hollow sphere composed of calcite rhombohedra is formed. Reprinted from [55] with permission of the American Chemical Society.

Kinetic control of crystallization can be achieved by high supersaturation promoting a rapid particle nucleation of the kinetically favored crystal modification, according to Ostwalds step rule, or by modifying the interactions of nuclei and developing crystals with solid surfaces and soluble molecules [56]. Kinetically driven crystallization, especially at high supersaturations, most often involves an initial amorphous phase that may be nonstoichiometric, hydrated, and susceptible to rapid phase transformation. Amorphous calcium carbonate (ACC), for instance, is, in general, highly soluble, has a low density of almost half of the crystalline mineral, indicating a high hydration [57], and rapidly transforms to calcite, vaterite, or aragonite unless kinetically stabilized. For example, magnesium or polyphosphonate can inhibit CaCO3 crystallization completely, resulting in handleable ACC [58–61], and other literature sources report stabilization for months by suitable additives, like the highly phosphorylated phytic acid [62]. In biomineralization, a significant number of stabilized ACC biominerals has recently been documented in plant cystoliths [63,64], snail shells [65], aragonitic mollusk shells [66,67], Nacre [68], ascidian spicules [69–71], precursors of the carbonated apatite inner tooth layer of chitons [72], and crustacean exoskeletons [73] and likely, more biominerals belong to this list.

2.6 Polymorph Control Polymorphism has great technological significance, due to the dependence of materials’ behavior, such as hardness or optical properties, on solid-state structure. One of the

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long-standing challenges of crystallization is the ability to predict and control the occurrence of polymorphism. Traditional strategies for selection of polymorphs often involve changing solvents, temperature, and other growth conditions in an attempt to control crystal formation [74–76], but also polymer additives can be used for the selection of polymorphic forms [77–81]. In biomineralization, polymorph selection is a key issue for survival, again because of the material properties involved. Excellent examples of polymorphic control are found in diverse organisms, such as molluscs, that can selectively deposit a specific polymorph of CaCO3 (aragonite or calcite) under the control of biopolymers, always at about constant outer conditions [82]. For instance, aragonite, which is hard to synthesize otherwise under ambient conditions, but is beneficial because of its mechanical properties, could be nucleated in the presence of soluble proteins extracted from an aragonite nacre layer [83,84]. The same level of control has, up to now, not been achieved by chemists, although elegant examples of selective polymorph production using monolayers [85–87] or synthetic polymer additives [81,88,89] and references therein, have been demonstrated for special cases. Nevertheless, even for the biopolymers extracted from biominerals, the exact role for the polymorph control is not yet known, although their mixtures extracted from the respective region of the natural organism exhibit the targeted activity [83,84]. For instance, isolated and characterized biomineralization proteins like AP7 and AP24, which had been believed to be aragonite nucleating, turned out to be calcite inhibiting [90,91]. Despite the general pathway for polymorph control by specific biopolymer interactions deduced from natural model cases, the control of a crystal polymorph is so far mainly achieved in an empirical manner. Usually Ostwald’s step rule is employed to control the crystallization reaction along the kinetic pathway, as shown in Figure 2.17, stopping the reaction at the demanded derivative. The transformation into a more stable polymorph in contact with a solvent, usually occurs via dissolution–recrystallization as reported for stearic acid [92], magnesium phosphate hydrates [93] or L-histidine [94]. The transformation into a more stable polymorph, however, can also take place as a solid-state reaction. Usually, such solid-state transformations simply have higher activation energies and are therefore only found for systems with low cohesion energy in the crystal or slightly below the melting point. Solid-state transformations can therefore occur in mobile glasses, or, particularly common, for organic crystals at annealing temperatures close to their melting point [95]. Such transitions are already exploited on an industrial scale, e.g. in dyestuff pigment synthesis. Systematically valid conditions for a targeted quantitative and reproducible synthesis of metastable polymorphs have not yet been revealed. A first step towards this goal was reported for the polymer controlled crystallization of CaCO3, where all three polymorphs (calcite, aragonite and vaterite) could be selectively and reproducibly produced by a simple variation of the reactant concentrations [48]. All three polymorphs were not produced as the classical single crystals, but as defined superstructures of nanocrystals (see Figure 2.20). In addition, amorphous CaCO3 nanoparticles were found as precursors in all three cases. One important conclusion of this work is that in such cases, the classical calculation of molecular supersaturation S is irrelevant, as it is always lowered by the


27

Figure 2.20 Polymer controlled crystallization of CaCO3: [48] (a) Calcite, polymer: 1 g/L, [CaCl2] ¼ 10 mM; (b) vaterite 0.5 g/L, [CaCl2] ¼ 5 mM; (c) aragonite polymer, 0.1 g/L, [CaCl2] ¼ 1.25 mM. Image reproduced from Ref. [48] with permission of Wiley-VCH.

formation of amorphous precursor nanoparticles, which just differ in their number for the different applied experimental conditions (see also discussion of Figure 2.16). The identified selection criteria for the different polymorphs are: A high initial molecular supersaturation leads to the formation of amorphous precursor particles. Then, transformation reactions occur, both for calcite and vaterite, following the kinetic reaction cascade. Homogeneous nucleation as well as particle growth are essentially carried out by the amorphous nanoparticles as mass reservoir and depend on their concentration. A second consequence of the particle mediated reaction pathway is the appearance of the two polymorphs as complex structured ‘mesocrystals’ with well-defined morphology, where the primary tecton unit size reflects the size of the amorphous nanoparticles. Switching between calcite and vaterite can be obtained by a strong crystallization inhibiting additive and kinetic discrimination. For the highest inhibition, only the most stable and least soluble species, calcite, can nucleate, whereas for intermediary inhibition, vaterite nucleates according to the Ostwald rule of stages and is efficiently stabilized against recrystallization by the added polymer which then acts as a surface stabilizer. The relative inhibition and stabilization can be adjusted via the polymer concentration. At very low concentrations of amorphous nanoparticles (just slightly exceeding their equilibrium dissolution concentration), particle based nucleation pathways and homogeneous nucleation looses its kinetic importance. Here, a polar surface with a special physisorbed polymer allows for heterogeneous aragonite nucleation in the c direction. The discrimination of the other polymorphs presumably comes from the appropriate orientation of carbonate ions in the adsorption layer (discriminates vaterite) and the fact that the aragonite crystal symmetry allows growth in the c direction via an atomically rough, but almost neutral, face and ion-by-ion addition. This crystallization mode is – due to the neutral character of the growth face – not inhibited by the polymer additive, which blocks all other reaction channels. This example shows that the control of polymorphism is a complex interplay between thermodynamic and kinetic factors, the control of crystallization by additives, as well as the possible switch between ion/atom/molecule growth at low reactant concentrations and particle mediated crystallization pathways. As amorphous precursor phases can be

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generated for a number of crystalline systems – especially in the experimentally most relevant kinetic crystallization regime – the principles can be nevertheless transferred to other systems.

2.7 Crystal Morphology and the Role of Additives and Selective Adsorption Soluble macromolecules and organic as well as inorganic ions, such as Mg2þ, Liþ, or HPO42, have a marked effect on crystallization, particularly with regard to habit modification, as observed, for instance, for CaCO3 (see Figure 2.21) [96]. This is caused by the fact that different crystals can lower their surface energies by substitution of surface ions by foreign ions. Consequently, these faces are more expressed in the crystal morphology (for a more detailed consideration see Section 2.7.1, Crystal Morphology. For example, atomistic simulations showed a marked energetic preference of the {110} faces of calcite for Mg2þ, which becomes expressed in the obtained crystal morphology (Figure 2.21b). The substitution of Ca2þ ions with Liþ ions results in an effective negative charge, which can be compensated by the addition of an Liþ interstitial, or by incorporation into the crystal lattice [96]. Atomistic simulations showed that the highly charged (001) face becomes the most stable face after Liþ incorporation, while all neutral crystal faces become destabilized. Consequently, (001) becomes morphologically dominant

Figure 2.21 Predicted morphologies based on atomistic simulation of calcite surfaces in the presence of various additives: (a) {104} rhombohedral (no additives); (b) {100} faces stabilized by Mg2þ; (c) {001} tabular, stabilized with Liþ; (d) prismatic rhomb {1-10}/{104}, stabilized with HPO2 4 . The morphologies are in agreement with experimental results. Reprinted from [96] with permission of Elsevier.


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(Figure 2.21c). HPO42 replaces CO32 most favourably on the {100} faces, which then is expressed in the crystal morphology, complementing the {104} faces for the morphological construction [96]. Another well-known and educational case is the crystallization of common rock salt, NaCl. Rock salt is cubic and crystallizes as cubes, exposing the six primary faces. For powder handling and flow, cubes are suboptimal, as they can easily be tightly packed, with strong adherence of the faces to each other. It is medieval technology to add urea to the crystallizing brine to stabilize the {111} faces, thus resulting in salt octahedra, which show much better processability and flow. Such studies on crystal growth indicate that additives can act, in a classical and thus predictable way, as selective surface poisoning agents. This could be further supported by the results of functionalized latex adsorption onto growing crystals [14,97]. The latexes, as all additives, can even become occluded into a single crystal, which in the latex case can become an interesting porous material after latex removal [15,98]. Generally, the interface energy of a crystal surface results from its unsaturated, ‘dangling’ surface bonds, minus the interaction of the crystal surface with the surrounding medium, such as solvation, or hydration in the case of a liquid medium. As a rule of thumb and for isotropic structures, the surface ‘bond strength’ (summarizing, ionic, van der Waals and all secondary interactions without a detailed molecular picture) can be estimated from the cohesion energy of the material, as it is, for instance, revealed from the evaporation energy Evap or the Hildebrandt solubility parameter dðd2 Evap Þ. The surface tension g then can be approximately calculated from the molar cohesion energy by dividing with the area demand per molecule (derivation analogous to [99]): g¼

Evap 2NA Amol

ð2:7Þ

where NA is Avogadro’s number and Amol is the cross section per molecule. Surface tension is, in this picture, the strength of ‘dangling bonds’ per unit area. It is obvious that very polarizable and high melting substances, like ionic crystals, have a high surface tension, while bare van der Waals solids like organic crystals have a lower surface energy. The strength of dangling bonds can be compensated by secondary interactions with the solvent, which is especially strong for very polar surfaces and water as a solvent. Again, and analogous to the previous lines, the change of the surface energy g with a solvent or additive can be estimated from its molar free energy of adsorption Eads . g ¼

Eads NA Amol

ð2:8Þ

Molecularly, the adsorption process can also be illustrated as a partial saturation of the surface bonds of the crystal, e.g. by ions with the opposite charge or coordinative bonding in case of metals. If the heat of adsorption is equal to half of the heat of evaporation, the surface tension is zero, and the surface can be created at no energetic expense. If Eads > 0:5Evap , the formal surface energy is negative and the crystal would spontaneously disintegrate to allow more surface interactions, i.e. it would ‘dissolve’.

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Figure 2.22 (a) The DL-Alanine unit cell. C ¼ grey, O ¼ red, N ¼ blue, H ¼ white; (b) (001) surface cut of DL-alanine (yellow dashed line) showing that (001) is a charged face; (c) (010) surface cut of DL-alanine (yellow dashed line) showing that this face is hydrophobic, electrically neutral, but dipolar and polarizable.

This is of course a formal, nonmolecular, but illustrative picture of surface tension, which does not reflect the complexity and multiplicity of chemical bonding. In addition, effects such as surface reconstitution (i.e. formation of a structure deviating from the bulk structure) or surface roughness to minimize the mutual interactions are not considered. In the case of anisotropic structures (and all crystals are anisotropic by definition), faces and their surface behavior can be very different. For crystals, we can find ionic faces (with an excess charge), electrically neutral, but dipolar, faces, highly polarizable faces or simple hydrophobic faces, all of them having a different surface energy, potentially existing in one and the same chemical crystal system. This is demonstrated in Figure 2.22. Charged faces have, due to uncompensated Coulomb forces, such high interface energies that they cannot exist in real situations, except when their charge is counterbalanced by an additive. 2.7.1

Crystal Morphology

The micro- and macroshape of inorganic crystals is related to the intrinsic structure of the unit cell. Sometimes the crystal shape can be the outside embodiment of the unit cell replication and amplification. However, often, the crystal morphology varies significantly from the shape of the unit cell. From a thermodynamic viewpoint, the diverse crystal morphologies of the same mineral are due to the differences of the crystal faces in surface energy and their dependence on the external growth environment, as revealed early last century by Wulff [100]. Generally speaking, the growth rate of a crystal face is usually directly related to its surface energy if the same growth mechanism acts on each face. Faces that have high surface energies will grow fast, have small surface areas or vanish completely upon crystal growth to the final morphology, if a geometric construction avoiding them has less energy than one where these faces are exposed. Faces with low


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surface energy will grow slowly and dominate the final shape. This treatment assumes that the equilibrium morphology of a crystal is defined by its minimum energy, which can be calculated as the sum of the products of surface energy and surface area of all exposed faces (Wulff’s rule) [100]. X gi A i ¼ F S ð2:9Þ i

where gi is the surface energy of the surface i, Ai is the area of surface i, and FS is the surface free energy. It has already been mentioned before that the surface energy of a crystal face can be lowered by the adsorption of an additive and solvent, changing the Wulff construction. Due to the change of interface energy, the shapes of crystals can be affected by various additives, i.e., inorganic ions or organic additives, but also the solvent/solvent mixture itself. The anisotropic growth of the particles can then be explained by the specific adsorption of ions or organic additives to particular faces perpendicular to the growth direction. This strategy of crystal morphogenesis has been known for a long time and has even found industrial application, mainly based on empirical observations. An experimental manifestation of Wulff’s rule can be obtained from the dissolution– recrystallization of high-energy crystal faces in a good solvent. This can be shown for the case of calcite in water [101]. The calcite {001} and {012} faces are high-energy surfaces because they are the most polar calcite surfaces. Such faces can be generated with high quality with solid surface templates or soluble templates, but surface reconstruction is to be expected from the thermodynamic viewpoint, in the absence of surface stabilizing additives. Indeed, the surface reconstruction can be followed by scanning force microscopy (SFM) when the (012) surfaces are put into deionized water for different lengths of time (Figure 2.23 upper). The mean roughness of the surfaces at

Figure 2.23 (Upper): Time-dependent SFM-imaging of calcite (012) surfaces (1 1 mm2). Note that the zero point corresponds to the beginning of the measurement and not the beginning of exposure of the calcite surface to water. (Lower): Surface reconstruction of a calcite (012) surface observed with polarized light microscopy. (Reproduced from [101] with permission of the American Chemical Society.)

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the start of the experiment was 1.1 nm. It was found that after 30 min the mean roughness increased to 5.7 nm, while after 2 h the surfaces were very rough and composed of neutral (104) surface spikes with characteristic shape. Obviously, it is energetically more favourable to expose larger areas of a (104) sawtooth pattern than a flat (012) face (Figure 2.23 upper, surface roughness 95 nm). The presence of (104) faces could be demonstrated by adhesion force measurements for poly(glutamic acid) on the reconstructed calcite faces. The reconstruction of the (012) to the (104) faces is so pronounced that its final stages are visible with a light microscope (Figure 2.23 lower). If the same experiment is repeated in the poor solvent ethanol, no reconstruction of the (012) surface is observed, which shows that the surface reconstruction of high-energy faces is indeed a dissolution–recrystallization process. Furthermore, the (012) faces are stable for a long time when kept in a dry environment. It is well known that this purely thermodynamic equilibrium treatment does not predict the experimentally found crystal morphologies in all cases. This is because crystallization and the resulting morphologies are often kinetically dominated, and defect structures like screw dislocations or kinks have a special importance for the dynamics of crystal growth. Nevertheless, Wulff’s rule is a good basis for understanding additive mediated crystal morphology changes from the basic viewpoint, and it is especially helpful in explaining changes of crystal morphology if an additive is selectively adsorbed onto one crystal face only. Wulff’s rule has also some explanative power if all outer faces are the same or influenced by the additive in a similar fashion. As the growth rate is related to the surface energy of the system, the crystal growth rate is then reduced overall. Assuming unperturbed nucleation rates, this leads to much finer particles. This is why most recipes using strongly adhering additives, e.g. surfactants or ligands, result in stable nanoparticles, which can be accessed as such. Figure 2.24 shows the effect of additives upon the crystal morphology when selectively adsorbed onto only one crystal face. Only the uncovered faces with their higher surface energies will now grow (Figure 2.24a).

Figure 2.24 (A) Adsorption of an additive (filled circles) onto a crystal surface lowers its surface energy and thus its growth rate. The crystal predominantly grows at the uncovered faces. (B) If surfactants are used in aqueous solution, the surfactant covered particles will self organize to form surfactant assemblies (such as bilayers) for further energy minimization.


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If surfactants are used to adsorb on crystals in aqueous solution (Figure 2.24b), not only is the surface energy of the crystal minimized, but the hydrophobic tails can contribute to further energy minimization of the system by a surfactant-like assembly. This can be advantageously exploited to create superstructures by self-organization in aqueous solution. Some examples of this strategy will be given in Sections 7.3, One-Dimensional Mesocrystals and 7.4, Two-Dimensional Mesocrystals. The striking influence of small molecule additives on the shape and structures of inorganic crystals has been well documented. More sophistication is, however, generated when the additives are also more complex, polymeric or peptidic in nature, where they can even be designed to bind to specific crystal faces. Recent reports show that so-called double hydrophilic block copolymers (DHBCs) [80] are highly effective for stabilization of specific planes of some crystals, like Au [102], ZnO [103–105], calcium oxalate [80], PbCO3 [106] and BaSO4 [107]. A very illustrative case for the potential of special functional polymers with block structure is the controlled morphosynthesis of gold nanostructures in the presence of a PEO-b-1,4,7,10,13,16-hexaazacyclooctadecan (hexacyclen) ethyleneimine macrocycle [102]. A typical image (Figure 2.25) shows the very thin and thus electron transparent triangles, truncated triangular nanoprisms, and hexagons with high crystallinity, as confirmed by the selected area electron diffraction pattern. The results suggest that this polymer can stabilize the (111) faces of Au nanoparticles highly effectively, leading to the preferential exposure of this face and growth along the other directions due to the selective adsorption effects of the polymer. This results in the formation of the observed very thin plates. This preferential, selective, and strong

Figure 2.25 (a) TEM image and electron diffraction pattern of Au nanoparticles synthesized by self-reduction of 104 M HAuCl4 solution in the presence of the block copolymer PEO-b1,4,7,10,13,16-hexaazacyclooctadecan (hexacyclen) EI macrocycle. (b) Molecular modeling of the Au (111) surface and a hexacyclen molecule in vacuum, which shows the excellent match of this molecule to the hexagonal atom arrangement on Au (111). Yellow: Au; Blue: N; Gray: C; White: H. Figure drawn to scale. (Reprinted from [102] with permission of American Scientific Publishers.)

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polymer adsorption onto the (111) faces can be understood on the basis of molecular modeling results, which show a good geometrical match of the interacting nitrogens in the hexacyclen part to the Au hexagons on the (111) face, thus effectively minimizing surface energy. The span distance of the neighboring –NH2 matches quite well with the distance of the neighboring Au atoms within the (111) face, as shown in Figure 2.25b. It is obvious that in this way the free energy of adsorption and the related lowering of surface energy can be quite high. Such geometric considerations and model calculations are, however, hard to generalize, as interaction not only contains short range mutual bonding motifs, but also long range contributions and – most important – solvent entropy effects, which are the key to most supramolecular recognition events in water. Application of the same DHBC hexacyclen-b-PEO additive for CaCO3 crystallization did not result in crystal morphologies with predictable shape. The match of the hexacyclen molecule to those crystal faces which turned out experimentally to be exposed was bad [108]. Another remarkably illustrative case for face selective additive adsorption is the dyeing of crystals, such as KH2PO4 or poppy acid. Around 1900, Gaubert was the first to find out that organic dye molecules interact quite selectively with distinct growth zones of crystals [109]. For example, methylene blue recognized the {021} faces of phthalic acid and the {101} faces of poppy acid [110]. The dyes cannot only interact with the respective faces of the grown crystal; when present throughout crystallization, they get incorporated, modify the speed of crystallization, but also taint the whole growth sector. This is illustrated in Figure 2.26 for KH2PO4, containing Chicago sky blue, zinc phthalocyaninetetrasulfonate, cobalt phthalocyaninetetrasulfonate, sunset yellow and amaranth [111]. KH2PO4 tends to incorporate a whole number of anionic dyes only at the {101} faces, and it is speculated that this is because those faces are Kþ terminated [112]. For an excellent review on the whole field of dyeing crystals, we can only recommend [111]. As the dye molecules are clearly seen by optical microscopy or even the naked eye, we can follow their interaction with the crystal surfaces. Considering the multiplicity of different dye structures with very different sizes and the presence of extended aromatic structures onto ionic flat surfaces, it is hard to believe that this interaction is provided by epitactic recognition alone. In our opinion, dehydration entropy and polarization interactions will seriously contribute to the selectiveness of dye sorption. On the other

Figure 2.26 KH2PO4 crystals containing dyes in the {101} growth sectors. From left to right: Chicago sky blue, zinc phthalocyaninetetrasulfonate, cobalt phthalocyaninetetrasulfonate, sunset yellow and amaranth. Average height is 7 mm. View along [100] or [101]. Crystals prepared by J. A. Subramony [111]. Image reproduced from Ref. [111] with permission of the American Chemical Society.


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Figure 2.27 Lead acetate trihydrate crystals containing methylene blue in solution, inclusions confined to the (100) growth sector. View along [010]. Horizontal dimension: 9 mm [111, 113]. Reproduced from Ref. [111] with permission of the American Chemical Society.

hand, it is clear that the dyes are embedded in the crystal, while embedding probability obviously depends on the size of the crystal. This again speaks for long-range contributions (such as polarization forces), beyond sheer surface recognition, which enables the dye to ‘differentiate’ between different crystal sites. In extreme cases, the dyes are even incorporated as liquid bands, the periodicity and size of which again depends on crystal size. An excellent sample is lead acetate trihydrate, containing methylene blue dye (Figure 2.27, from [113]). Besides dye molecules, polar peptides and proteins are ideal to address interactions with specific faces. Laursen and DeOliveira showed an excellent example of using protein secondary structures to control the orientation of chemical functionality and thus protein binding to a targeted crystal face. An a-helical peptide (CBP1) with an array of aspartyl residues was designed to bind to the (1 10) prism faces of calcite [114]. The observation of the effect of CBP1 and other peptides on calcite crystal growth was skillfully done by adding the peptide to rhombohedral seed crystals growing from a saturated Ca(HCO3)2 solution. When CBP1 was added to seed crystals, as shown in Figure 2.28A, and growth was allowed to continue, the calcite crystals elongated along the [001] direction (c-axis) with rhombohedral {104} caps (Figure 2.28B). After washing the crystals with water and replacing the mother solution with fresh saturated Ca(HCO3)2 solution, a regular rhombohedron formed by a sort of repair process occurred, with subsequent growth on the putative prism surfaces (Figure 2.28C). CBP1 is only about 40% helical when the temperature is 25 C, leading to the formation of studded crystals by epitaxial growth perpendicular to each of the six rhombohedral surfaces (Figure 2.28, D, E). After washing these crystals and regrowing in fresh Ca(HCO3)2 solution, repair of the nonrhombohedral surfaces was again observed. On each face, a new rhombohedron was formed and thus six regular rhombohedra overgrew the original seed (Figure 2.28F). Another striking example of complex crystal morphologies, which can be obtained by selective polymer adsorption, is given by flower-like BaSO4 particles with a 10-fold

36


Figure 2.28 Left: The footprint of two a-helical peptide (CBP1) molecules binding to the (11 0) prism faces of calcite. The filled circles are Ca2þ ions, and open circles are CO32 ions. Large circles are ions in the plane of the surface and small circles are 1.28 A˚ behind this plane. The hexagons indicate that peptide carboxylate ions occupy CO32 sites on the corrugated surface. Right: SEM micrographs showing the effect of CBP1 on the growth of calcite crystals: (A) calcite seed crystals showing typical rhombohedral morphology; (B) elongated calcite crystals formed from seed crystals in saturated Ca(HCO3)2 containing ca. 0.2 mM CBP1; (C) ‘repair’ and re-expression of rhombohedral surfaces when crystals from (B) are allowed to grow in saturated Ca(HCO3)2 after removal of CBP1 solution; (D and E) respective earlier and later stages of growth of calcite crystals from rhombohedral seed crystals at 25 C in saturated Ca(HCO3)2 containing ca. 0.2 mM CBP1; (F) ‘repair’ and re-expression of rhombohedral surfaces when crystals from (E) are allowed to grow in saturated Ca(HCO3)2 after removal of CBP1. Reproduced in part from [114] with permission of the American Chemical Society.

symmetry. These structures can be produced by a multi-step growth process in the presence of a sulfonated PEO-b-PEI, as shown in Figure 2.29 [107]. For the formation of these particles, an elongated core nanocrystal formed by selective polymer adsorption was proposed, which has 10 dominant side faces (Figure 2.29b, 4 {022}, 4 {041} and 2 {002} family) [107]. This particle serves as a seed particle for the heterogeneous nucleation of 10 single crystalline petals, with the polymer selectively adsorbing onto (200) faces (these are overgrown in a later stage). Thus, a structure forms, which is single crystalline (the petals) but which does not violate the laws of crystal symmetry due to the primary particle with 10 side faces. This example implies that apparently ‘symmetry forbidden’ crystal structures are enabled in a polymer directed multi-step crystallization process, provided that face selective and targeted additive adsorption can be maintained. 2.7.2

What Determines Adsorption of an Additive?

The question of how to choose an additive or to predict its quality in crystallization control is of uttermost practical importance, but also one of the most disputed.


37

Figure 2.29 (a) SEM micrograph of BaSO4 single crystals with an unusual 10-fold symmetry precipitated in the presence of PEO-b-PEI-SO3H at pH 5. (b) The morphology of a primary crystal with 10 side faces. Reprinted from Ref. [107] with permission of the American Chemical Society.

To create a gain in free energy of adsorption for a surface/additive or surface/template pair, a number of potential contributions have been discussed. For repetition, the most prominent are:

Direct Coulombic interactions Dipole-dipole interactions Van der Waals forces/directional polarization forces Specific chemical interactions, such as metal–ligand interactions or hydrogen bridges Solvation forces, entropy changes by solvent interactions.

The ideal situation would be an exact complementary fit of the charge distribution and polarity patterns along the surface, i.e. the surface is stabilized by its exact negative. This is only obtained in perfection for the material itself, but for regular, and thus less perfect, fits this is the concept of epitaxy. In vacuum applications and gas phase syntheses, epitaxy is indeed the best way to minimize surface interactions and to direct ordered crystal growth. This is presumably the reason why epitaxial fit is also regularly discussed in solution processes, and crystallization processes below Langmuir monolayers and on self-assembled monolayers indeed prove sometimes astonishing similarity between the template and the nucleated phase [85,115,116]. In many, if not most, cases, there is, however, no resemblance between any possible packing of the soft template and the stabilized crystal faces. This is most obvious for the interactions between crystals and dyes, which can be highly specific [111], but where the dye molecules are obviously too big to fit to any direct regularity within unit cells. Such nonepitaxial control is to be expected when a possible alternative interaction is stronger than the complex pattern match; in the case of dyes, mostly dipole and polarization forces, which can be extraordinarily high. Another major weakness of transferring the concept of epitaxy to solution processes is that it does not consider any hydration or solvation effects, i.e. to match two faces epitaxially, both faces have to be completely dehydrated, which adds unfavourably to thermodynamic considerations.

38


We must actually ask ourselves how much we really know about the exact interface between a crystal surface and a solvent. It seems that the traditional treatment of a crystal surface as the ordered interface present in vacuum does not hold for the situation in solution – an assumption which is, however, often made for epitaxial considerations, whether an additive fits to a surface or not. Computational studies of the interface between a crystal and a solvent suggest an ordering of the solvent at the interface, as well as partial reconstitution of the crystal interface. One example is the orientation of the hydroxide ions of the apatite layer and the formation of several strongly ordered hydration layers on hydroxyapatite surfaces, as a result of electrostatic/hydrogen bonding [117]. Another published example is the predicted cluster formation of water on silver iodide surfaces [118]. Molecular dynamics simulations show that the water density ˚ from the neutral exhibits a damped oscillatory behavior up to a distance of at least 15 A (104) surface of a calcite crystal, indicating that interface effects reach out more in three dimensions than usually expected (Figure 2.30) [119]. In addition, the molecular dynamics simulations suggest that the relationship between the overall free energy of dissolution of an ion from the surface and the number of crystal bonds to be broken is not linear, as normally assumed in dissolution models, such as the solid-on-solid model [120]. This also hints at the point that a better understanding of the crystal–solution interface is needed to really become quantitative. The most critical point for the transfer of vacuum concepts at least to crystallization in water is the disregard of entropic effects, both in the structure of water (the ‘hydrophobic’ effect) as well as in the hydration shell of surface and additive. Calorimetric measurements on the pair CaCO3/polyacrylic acid copolymer (the commercially most important case of a ‘scale inhibition’ additive) indeed indicate that the strong interactions found are barely endothermic, that is that the binding of polymer to the surface is only driven by the entropy changes [121]. 7.5

2.5

2

1.5

2.5

0

1

Density Relative to Bulk Water

Density

5 (KJ mol-1)

Free Energy Difference

Free Energy

0.5

-2.5

0

-5 0

5

10 Distance (Å)

15

20

Figure 2.30 Water density and free energy profiles as a function of distance from the (104) calcite surface. The MD simulation was performed at 300 K and zero pressure. (Reproduced from [119] with permission of the Royal Chemical Society.)


39

The generally relevant entropy contribution of surface interactions makes a rational prediction or design of additives ‘from scratch’ practically impossible. Dehydration effects, however, are most strong for ‘hydrotropes’ and molecules exhibiting a strong ‘hydrophobic effect’. This fact explains the strong influence of many surfactants, but also, again, of dye molecules on crystallization events.

2.8 Properties of Single Crystals and Polycrystals Single crystals and polycrystals differ significantly in their properties due to their different size and also the orientation of the building units. The building units of a single crystal are atoms or molecules, whereas a polycrystal is built up from much larger crystalline particle blocks. The most evident difference is in their scattering behavior in X-ray or electron diffraction. A single crystal exhibits long-range translational order of its atomic building units and, therefore, it enables interference of diffracted X-rays or electrons, which results in the typical spot pattern of a single crystal. The spots permit the calculation of the lattice plane distance as well as the calculation of the orientation of the crystal lattice with respect to the beam axis. The polycrystalline aggregate, on the other hand, has the typical ring-like diffraction pattern of a crystalline powder, because the crystalline building units of the polycrystal have random orientations (see Figure 2.31). Nevertheless, the spacing of the diffraction rings from the center still permits the calculation of the lattice plane distances of the crystalline units, which build up the polycrystalline aggregate or powder (‘Bragg rings’). Experimentally, we find all types of transition states between a single crystal and a polycrystalline material, as the orientation of the nanoparticles in a polycrystalline aggregate can vary from random orientation to mutual crystallographic orientation. This is called the texture of a mineral, or a material. Many natural processes do change the crystallographic texture. In mineralogy, this is used to trace back tectonic or metamorphic processes. For technology, it is important that texture is a key parameter to adjust the anisotropic properties of crystalline materials to the demands of the application, as known from steel forging, ceramic processing, etc. The orientation of the crystalline subunits can advantageously be accessed by an electron or X-ray diffraction experiment and is directly evident from the diffraction pattern. There are a number of crystal properties that are tensorial, as crystals systems are not isotropic, and therefore critically depend on the texture. 2.8.1

Electrical Polarization

The electrical polarization of a crystal can be observed if the electrically nonconducting body (the so-called dielectric medium) is subjected to the influence of an external electrical field. Charged subunits (e.g. the constituting ions) of the crystal, as well as polarizable electrons, will be moved along the electrical field lines out of their equilibrium positions until the binding potentials balance the electric force. As positive and negative charges will be moved in opposite directions, the crystal will become polarized, and an electric dipole is generated in the interior of the crystal, diminishing the

40


Figure 2.31 Wide angle X-ray scattering of calcite. Upper left: typical spot diffraction pattern of a single crystal; Upper right: typical diffraction pattern of a polycrystalline powder; Lower center: Gandolfi mode image of the powder sample where the Goniometer axes o and f are permanently moved during exposure. This image demonstrates that the spots from a single crystal diffraction pattern form the rings of the polycrystalline sample. Experimental details: Stoe IPDS 2T, Mo LFF tube, 50 kV, 40 mA, collimator 0.5 mm, instrument offset 0 , detector distance 80 mm, 2y(min) ¼ 2.86 (border of the central black spot), 2y(max) ¼ 64.8 . All images were taken from the same single crystals, which were ground to obtain the powder. (Copyright by Dr. Friedemann Hahn, Stoe & Cie GmbH, Hilpertstr. 10, D-64295 Darmstadt, Germany. (Images reproduced with permission.)

outer electric field. The polarization of an anisotropic crystal with the components ~ Pi is a vector and can be expressed as: X ~ ~ ð2:10Þ weij~ Ej Pi ¼ e 0 j

where ~ weij is the electric susceptibility as a tensor combining the vectors i, j, ~ Ej are the components of the electric field strength, and e0 the vacuum dielectric constant. The equation indicates that the polarization of a randomly oriented polycrystal will differ greatly of that of an anisotropic crystal. Equation (2.10) shows that the induced polarization will vanish if the electrical field is removed. A high polarizability makes a crystal ‘polar,’ sometimes in a highly anisotropic fashion. High polarizability is also the basis for high surface tensions, high van der Waals forces or high Hamaker constants, i.e. highly polar crystals also attract other substances and molecules quite strongly.


41

Pyroelectricity. Some crystal structures with sufficiently low symmetry do not only have an induced polarizability, but also exhibit a permanent electric dipole moment. From all crystal symmetries, the 10 most primitive arrangements have a structure where the primary ion–ion dipoles do not compensate (no symmetry center). In such cases, the polarization does not vanish with the outer field, and special effects, such as ferroelectricity and pyroelectricity can be expected. Pyroelectricity is the change of the polarization or dielectric tensor with temperature. Usually, it arises from the change of dipole moment with thermal expansion, but especially nearby phase transitions with large structural transitions, pyroelectricity can be quite high. 1 K temperature change can result in a polarization corresponding to an electric field of 105 V/m near phase transitions. Vice versa, temperature gradients across a pyroelectric material result in a spontaneous separation of charges or the build-up of an electric field. This can be used to prove pyroelectricity. A quick qualitative test would be to put the crystal on a metal spoon into liquid nitrogen. If charges are generated, the crystal will stick to the spoon and the ice particles crystallized from the moisture in the air will arrange onto the crystal in such a way that they form lines in the direction of the electrical field lines. Ferroelectricity. For some crystal systems, the orientation of the permanent polarization can be reversed by the application of an external electrical field. This means that those parts of the crystal structure that cause the charge dissymmetry, can be arranged or switched. For example, in potassium dihydrogenphosphate, KH2PO4, the spontaneous polarization is caused by nonsymmetric hydrogen bonds, which can be switched by proton re-orientation in the crystal lattice. The effect on the effective electric field is shown in Figure 2.32. If the electric field is applied for the first time (point 0) and increased, the polarization increases from 0 to þP0 by orientation of the permanent electric dipoles in the field direction. If an electric field is applied to a negatively polarized crystal (point 1), the polarization reverses at a critical field strength (point 2), until þP0 is reached. Further

Figure 2.32 Hysteresis of the polarization P with respect to the electric field strength E for a ferroelectric substance.

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increase of the electric field does not change the polarization and the dipole orientation saturates (point 3). This process is symmetric with field inversion (points 4, 5 and 6) so that overall the hysteresis shown in Figure 2.32 is obtained. The formal analogy to the much better known case of ferromagnetism gave the name ferroelectricity to this phenomenon (iron is not ferroelectric). Piezoelectricity. Similar to temperature, the dimensions and therefore the polarization of a crystal can also be changed by mechanical deformation. The resulting coupling of pressure and electric properties is called piezoelectricity and is described by Equation (2.11). X ~ ~ Pi ¼ ð2:11Þ di; j; k~ sj;k i; j; k ¼ 1; 2; 3 j;k

where ~ di; j; k is the piezoelectric modulus or piezoelectric coefficient as a 3rd degree tensor and ~ sj; k is the stress tensor (2nd degree). Figure 2.33 illustrates the technically relevant case of quartz. If pressure is exerted in the x direction, the charge centers are compacted in this direction, which leads to the situation that a positive Si charge center is overcompensated by the nearby negative O charge centers, so that the overall surface charge becomes negative; the opposite is happening at the other end of the crystal (longitudinal piezo effect). Compaction of the crystal in the y direction has the opposite effect on the charge centers to that in the x-direction. They now become more separated, so that the surface charge will be negative at the end of the negative O charge center and positive near the positive Si-charge center. This is equivalent to a strain on the crystal in the x-direction (transversal piezo effect). Such a crystal cannot only sense pressure by the change of the electric polarization, it also works in the other direction: if an electric field is applied to a piezoelectric crystal in the respective direction, the crystal contracts or expands in this direction. This effect is applied for the very precise movement of components, like in an atomic force microscope, but is also the basis of the quartz resonator as a frequency standard.

Figure 2.33 Simplified structural model to demonstrate the piezoelectricity of quartz: (A) schematic detail of the quartz structure. The charge centers of the Si ions (þ) and the O ions () are projected onto the (0001) plane; (B) pressure in direction of the x-axis; (C) pressure in direction of the y-axis.


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Figure 2.34 (a) Huygens construction for the propagation of a wave in an isotropic medium. W0 ¼ wave front at time t ¼ 0, W1 ¼ wave front at time t ¼ t1 , N ¼ wave normal; (b) Huygens construction for the light refraction at a planar interface between two isotropic media. W1 ¼ incoming wave front, W2 ¼ refracted wave front, N1 and N2 ¼ wave normals.

Polycrystals of piezoelectric materials can also show a piezoelectric effect when they have an appropriate texture. Alternatively, crystal powders and films without orientation like the PZT ceramics Pb(Zr,Ti)O3 can be poled at high temperature in a strong electric field. This orientation remains after cooling as the re-orientation of the crystallites is hindered, and the film shows piezoelectricity. 2.8.2

Light Refraction and Birefringence

One important property of a crystal is the light refraction. If a crystal is isotropic, an electromagnetic wave proceeds according to the Huygens construction (1690), i.e. by superimposed spherical waves (see Figure 2.34a). If a wavefront hits a planar interface T between two isotropic optical media, the light is refracted. This is due to the different light velocities, v1 and v2 in the two media. The light is refracted according to Snell’s law of refraction (1610): sin i v1 n2 ¼ ¼ const: sin r v2 n1

ð2:12Þ

where n is the refractive index. As the refractive index is nothing but at the frequency of light polarization of a material, i.e. e n2 , it is clear that most crystals are not optically isotropic. As with polarization, the refractive index depends on the orientation of the crystal. The difference between the highest and the lowest refractive index in a crystal defines the birefringence. The most prominent example is the birefringence of calcite. The asymmetry of the calcite lattice (in all directions except the c-axis) splits light rays into two beams with mutually perpendicular polarizations (Figure 2.35), called the ordinary and the extraordinary rays. Observing an object through the crystal results in a double image. Analysis through a polarizer sheet shows that these images have axes of polarization at right angles to each other; rotating the polaroid makes the images alternately vanish. The double refraction of crystals is a simple means to characterize crystals with a polarization microscope, giving

44


Figure 2.35 Upper: birefringence for a calcite crystal; Lower: a calcite single crystal laid upon a paper with some letters showing the double refraction. (Lower image by H. Co¨lfen)

a picture under crossed-polarizers only if the substance is birefringent. The c-axis of calcite, for instance, can be identified between crossed polarizers when the crystal appears black. Orientations and orientation distributions in polycrystals can be determined in a similar fashion, while a textured calcite polycrystal with oriented subunits will behave optically like a single crystal. 2.8.3

Mechanical Properties

In addition to the anisotropic interaction of crystals with electromagnetic fields, the mechanical properties of crystals are also anisotropic as they are determined by the crystal structure. Elasticity. Hooke’s law describes the change of the length l respective the normalized strain e ¼ l=l in dependence of an applied mechanical stress s as: e¼

l ¼ ss l

resp: s ¼ E

l ¼ Ee l

ð2:12Þ

where s ¼ 1=E is the elasticity coefficient and E is the elastic modulus (extension modulus or Young modulus). The Young modulus is a measure of how hard or soft the material is in extension.


45

Figure 2.36 Elasticity modulus bodies of: (a) gold; (b) aluminium; (c) magnesium; (d) zinc. The displayed bodies are crystal class m-3m [(a) and (b)] with cube symmetry and class 6=mmm [(c) and (d)], which is rotational symmetric. (Image reproduced from [122] with permission of Oldenbourg Verlag.

Due to the anisotropy of crystals, Equation (2.13) has to be written as tensor: X ~ ~ sijkl skl i; j; k; l ¼ 1; 2; 3 ð2:13Þ eij ¼ kl

For a crystal, the elastic modulus can be plotted in the direction of the corresponding radius vector in each crystal plane. This leads to so-called elasticity figures in the respective crystal plane, which illustrate the anisotropy of the elastic response in this plane. This treatment can be extended into three dimensions, which yields elastic modulus bodies as shown in Figure 2.36. It is remarkable that the elasticity modulus bodies can differ significantly, even for the same structure type (see gold and aluminium, or magnesium and zinc in Figure 2.36. Elastic properties are sensitive to differences in the binding forces and electronic hybridization in a crystal. Hooke’s law, describing the reversible elastic deformation is only valid up to a certain stress. If this limiting stress is exceeded, plastic deformations can be observed, up to a maximum stress, called tensile strength, is reached, after which the sample will break (Figure 2.37).

Figure 2.37 Stress–strain diagram of a metal. Many crystals break when the linear region of Hooks law validity is exceeded and do not show much plastic deformation.

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Figure 2.38 Model of mechanical gliding by translation along gliding planes: (a) and (c) top view, (b) and (d) side view; (a) and (b) are before gliding by stress application, (c) and (d) after gliding by stress application; (e), (f), and (g) single crystal rods of metals after gliding deformation in a stress experiment; (e) b-tin, (f) bismuth and (g) zinc. Images (e), (f), and (g) reproduced from [122] with permission of Verlag Technik Berlin.

The plastic deformation of crystals is technologically important – especially in metal forming. It applies the fact that upon stress application, lattice planes can glide along each other although the crystal lattice itself remains intact, despite smaller defects (Figure 2.38 a–d). This suggests that only certain gliding planes exist for a crystal, which is experimentally confirmed. This gliding deformation sometimes becomes visible in the macroscopic bodies as shown in (Figure 2.38 f–g). It is evident that such plastic deformation can only be applied for a single crystal in a distinct orientation. Crystal Cleavage. The anisotropic lattice structure of crystals allows for the possibility of cleaving a crystal along certain lattice planes with mechanical forces. These cleavage planes are planar and can even be atomically flat over large regions. Therefore, the cleavage and fracture surface of a crystal is a good way to distinguish between a single crystal and a polycrystal. For a polycrystal, nanoparticulate grain boundaries become visible, leading to a rough surface, in contrast to the planar cleavage plane of a single crystal.


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As cleavage planes, mostly low index planes are found, which are densely occupied by atoms (net planes). Such faces are also often morphology determining as growth faces. Usually, the most densely packed lattice planes exhibit the largest distance between these planes in a crystal lattice, which leads to a minimum in the cohesion between these lattice planes. The cleavage planes are often very obvious. For example, layered crystals (graphite, layered silicates) have a perfect cleavability parallel to the planes, which is technically exploited in mica as an atomic flat surface, for example. For crystals with chain structures (pyroxenes, amphiboles), prismatic cleavage is found. All considerations in this chapter show that optical, electrical and mechanical experiments are suited to differentiate between polycrystals and single crystals. For some properties, like birefringence, a polycrystal can show the same properties as a single crystal, if its subunits are iso-oriented; for other properties, like mechanic characteristics, a single crystal always behaves differently to a multi-particulate polycrystalline structure. Many of the properties discussed above are therefore needed later in this book for the characterization of a crystal as a single crystal or a polycrystal, and whether the polycrystal subunits are oriented or not.

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3 Examples of Crystals Challenging the Classical Textbook Mechanism Although textbooks usually present a very simplified picture of the formation of a crystal and how crystallization has to occur, the evidence in the literature is indeed overwhelming that there must be much more to the story. This chapter collects both the early and the especially nice cases of crystallization processes where structure formation goes along different lines and leads to remarkably complex patterns, thus questioning any simplified truth of crystallization.

3.1 Some Biomineral Examples If one looks at the complex forms of biominerals, it becomes immediately obvious that the morphology of many of them are in disagreement with the classical definition of a crystal as they are often nonfacetted and exhibit curvature (see Section 7.5, Mesocrystals in Biomineralization and Figure 3.6). One possibility to explain the often-observed rounded forms would be to conclude the presence of an amorphous biomineral or a polycrystalline aggregate. Indeed, biogenic silica is amorphous, and the beautiful complex shapes of diatoms and other silica biominerals can be explained by the fact that amorphous silica can be moulded into any shape. On the other hand, there are also several examples of biominerals which show single crystalline behavior in scattering experiments and which have an unusual or complex morphology, often exhibiting curvature. Such biominerals challenge the classical view of the behavior of a single crystal. Considering such examples, it was assumed that organisms must have sophisticated tools to perfectly control the crystal morphogenesis process towards complex shape and function, deviating from the expected and energetically more favourable morphology of a single crystal. The existence of biogenic crystals with single crystal scattering, but sometimes the properties and morphologies of a Mesocrystals and Nonclassical Crystallization Helmut Co¨lfen and Markus Antonietti # 2008 John Wiley & Sons, Ltd

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polycrystal also raised thoughts on how far the existing models of crystallization need to be extended; in other words, if the formation of such structures can be mimicked and transferred to all fields outside biology, and more importantly, in the absence of specific biological activity. What is clear is that minerals, which are formed by an organism, undergo extensive processing, such as moulding processes, to achieve the complex shapes. Numerous examples can be found in the textbooks of biomineralization [1–5]. These observations and the increasing knowledge of the bioprocesses also raised many questions, however, as it seems disadvantageous, if not kinetically impossible, for a living organism to apply an ion-mediated crystallization process. The required supersaturations for crystallization would increase the ionic strength and the coupled osmotic pressure, while isotonic processing seemed previously mandatory for all biological operations. In addition, for biominerals, with their low solubility, large solvent volumes would have to be transported to accumulate enough precursor material for the formation of the mineral. Temporary formation of nanoparticles as mineral storage units and subsequent transport of the nanoparticles by carrier vesicles to the building site seems much more advantageous from this perspective. 3.1.1

Elongated Magnetite Nanocrystals in Magnetotactic Bacteria

Indeed, nanocrystals can be formed in vesicles, as demonstrated by magnetite in magnetotactic bacteria, which produce chains of elongated single crystals of magnetite (see Figure 3.1). This is a first and rather simple example of a single crystal with an unusual shape, which is formed in separated compartments called magnetosome vesicles [6]. The vesicles serve as a template for the mineralization process. Several of the elongated magnetite particles form an oriented chain structure called a magnetosome,

Figure 3.1 Section though a magnetotactic bacterial cell showing: (A) three mature magnetite crystals and three empty magnetosome vesicles (MV); (B) vesicles containing immature magnetite particles. Scale bar, 250 nm. (Figures reproduced from [2] with permission of Oxford University Press.)

Crystals Challenging the Classical Mechanism

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Figure 3.2 Morphological types of bacterial magnetite single crystals: (A) cubo-octahedral; (B) and (C) hexagonal prisms; and (D) elongated cubo-octahedral (E) Bullet shaped bacterial magnetite single crystal with side and end (111) faces. Scale bar, 10 nm. (Figures reproduced from [2] with permission of Oxford University Press.)

which is used by the organism as a detector for the geomagnetic field. What is special about the biogenic magnetite single crystals is their shape, which is unusual and often species-specific. The default morphology of magnetite in synthetic systems is cubooctahedral with a family of four equivalent [111] faces (see Figure 3.2 A) [6]. The elongated bacterial magnetite crystal in Figure 3.2 E is not in agreement with the symmetry of the crystal structure, as it is elongated only along one of the four possible and equivalent [111] axes. How the organism can break the symmetry and prefer one of the equivalent crystallographic directions ahead of the others is not yet clear. Meanwhile, a similar behavior was observed in fully synthetic systems and can be attributed to particle/particle alignment [7]. 3.1.2

Calcite with Complex Form and Single Crystal Behavior in Foraminifera

Another more complex example of a crystalline biosystem with single crystal diffraction but other properties challenging the laws of crystallization are foraminifera. Foraminifera are marine protozoans with a diversity of about 4000 different living species [8]. The planktonic foraminifera are very abundant and form a huge part of calcium carbonate sediments as their shells consist of calcite [9]. There are different types of shells with the radial shells being of special interest for this section, as they show a typical uniaxial interference figure in polarized light indicative of a single crystalline nature for the shell [10]. The cell walls of foraminifera are composed of mineral layers and layers of organic material and interestingly, the radial shells contain both high and low magnesium calcite (Figure 3.3) [10].

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Figure 3.3 Scanning electron micrograph of the fixed, etched, and critical point dried shell of the benthonic foraminifer, Heterostegina depressa, showing the lamellae separated by organic matrix layers. Note that the shapes of the crystals are very difficult to discern (magnification 2400, scale bar, 10 mm.) (Reproduced from [10] with permission.)

Crushed shells of foraminifera give a single crystal electron diffraction pattern [11] although the crystal boundaries are very irregular, suggesting a penetration of adjacent crystals into each other [10]. In addition, the crystal sizes vary greatly – even within a single lamella in the foraminifera shell – between ca. 200 nm up to several mm [12]. This is also expressed in the rough external appearance of foraminifera shells (Figure 3.4).

Figure 3.4 Radial shell of Patellina corrugata Williamson, D 500 mm. [13], http://palaeoelectronica.org/paleo/2002_2/guide/issue2_02.htm. (Copyright: Palaeontological Association. 28 March 2003.)


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Figure 3.5 (1) Scanning electron micrograph of Patellina corrugata secondarily overgrown with calcite crystals; (2,3) An individual of Patellina corrugata viewed in polarized light with crossed-nichols and a gypsum plate. Both views are extinction positions at right angles showing maximum (2) and minimum relief (3); (4) Buerger precession X-ray photograph showing the single crystal pattern from Patellina corrugata. (Reproduced from [14] with permission of the Cushman foundation.)

Although the foraminifera shells are clearly polycrystalline, the subcrystallites are mutually aligned, which can be demonstrated by various tests for single crystal behavior shown in Figure 3.5. Polarization microscopy reveals maximum and minimum reliefs in the radial shell of Patellina corrugata (Figure 3.5, 2 and 3) indicative of a single crystal, which is confirmed by the single crystal spot diffraction pattern (Figure 3.5, 4). Overgrowth experiments with calcite yield mutually oriented calcite rhombohedra, which demonstrate the polycrystalline nature of the shell, but simultaneously also the mutual alignment of the crystallites building up the shell. From this

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Figure 3.6 SEM images of a sea urchin spine from Anthocidaris crassispina (Images by Rona Pitschke, MPI C & I, Potsdam-Golm).

experiment, it is even possible to assign the crystallographic axes for the shell, although the morphology of the shell would not enable any direct assignment of an axis, as it has a completely different morphology from a classical calcite single crystal (compare Figure 3.6 and Figure 3.4). Little is known about the formation process of these oriented arrays of crystallites, but the classical picture of crystal growth in an ionmediated crystallization reaction certainly has difficulties in explaining the generation of such an elaborate structure. 3.1.3 Calcite with Complex Form and Single Crystal Behavior in Sea Urchin Spines Sea urchin spines are another biomineral that behaves like a single crystal in polarization microscopy or scattering experiments, but exhibits a ‘glassy’ chonchoidal fracture surface. The morphology of a sea urchin spine also challenges the classical expectation for the habit of a single crystal, as it shows no crystal faces at all, is highly curved and has


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an overall sponge-like, very complex, inner structure (Figure 3.6). Sea urchin spines form via amorphous precursors [15]. Amorphous precursors are also applied in the repair of a spine tip [16]. The final crystalline phase is calcite, as in the case of foraminifera, and cleavage planes show nanoparticulate subunits evidencing the polycrystalline character of the spicule. This will be discussed in detail in section 7.5, Mesocrystals in Biomineralization (see also Figure 7.9 and the corresponding discussion). Here, it is sufficient to set these complex and beautiful structures against classical single crystal morphologies. 3.1.4

Calcite Single Crystals with Complex Form in Coccoliths

An example of single calcite crystals with complex form can be found in coccoliths, which build up a hollow sphere of interlocked oval-shaped plates. This hollow sphere is called a coccosphere and forms the exoskeleton of marine algae like Emiliana huxleyi (Figure 3.7 a) [2]. What is amazing about this structure is its hierarchical assembly of a hollow sphere from interlocked oval plates (Figure 3.7 b), with each of the plates again built up from 30–40 subunits (Figure 3.7 c), which themselves have a complex hammer-head shape (Figure 3.7 d). Each of the primary units is a single crystal with various structural features deviating strongly from ordinary crystals (Figure 3.7 d).

Figure 3.7 (a) Coccosphere of Emiliana huxleyi; (b) Coccolith scale viewed approximately side-on. The scale consists of a ring of about 30 hammer-headed calcite crystals that together produce a double-rimmed structure. Scale bar ¼ 1 mm; (c) Drawing of coccolith based on an elliptical array of discrete structural units; (d) Individual structural unit from a coccolith plate showing a calcite single crystal with various growth elements. (Figures reproduced from [2] with permission of Oxford University Press.)

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The part of the subunit that is most reminiscent of a crystal is the base plate (proximal shield element), which has two well defined end faces: a large (108) and a small (104) face. Electron diffraction shows that each of the coccolith subunits has a defined crystallographic alignment with the c-axis aligned along the direction of the hammerheaded extension of the distal shield elements (Figure 3.9 a) [2]. The c-axis also bisects the large (108) from the small (104) face, which makes the primary subunit of the coccolith chiral [17]. The complex shape of each of the coccolith subunits is thought to be templated by a pre-formed shaped vesicle, arranged around the rim of an organic base plate. The initial calcite rhombohedral crystal is nucleated in a precisely oriented fashion. The growth in a shaped organic environment allows for the development of the finally observed complex single crystal shape. Different from the above two examples of foraminifera and sea urchin spicules, this crystal lacks evidence of an internal polycrystalline nature and distinct grain boundaries are absent. Nevertheless, it is obvious that the classical laws of crystallization such as the Wulff rule cannot explain such morphological complexity. 3.1.5

Morphological Complexity Develops with Time

In some of the above mentioned cases, it was possible to follow the development of the biological complexity throughout animal or algae growth. In many cases, the initial nucleating nanocrystals have the habit of a single crystal, as can be seen in the protococcolith ring of Emiliana huxleyi (Figure 3.8 a) or in the initial rhombohedral calcite crystal of the sea urchin larval spicule (Figure 3.8 b).

Figure 3.8 (A) Proto-coccolith ring of Emiliana huxleyi. Scale bar, 500 nm; (B) 20 h embryo sea urchin larval spicule of Paracentrotus lividus with an initial rhombohedral calcite crystal and three radii starting to grow; (C) Triradiate spicule (25 h embryo); (D) Fully developed pluteus spicule (48 h embryo) composed of the central triradiate portion and three rods growing roughly in the c-axis direction. (Figures reproduced from [2] with permission and [15] with permission.)


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Figure 3.9 Time-dependent changes in biomineral morphology: (a) coccolith crystal; (b) larval sea urchin spicule.

This means that the crystallographic alignment in three-dimensional biological space is already achieved by orienting the crystal nucleus accordingly (see also Figure 3.6 for the macroscopic example). Upon further growth in a spatially constrained reaction environment, like a shaped vesicle in the coccolith example or in a membrane-delineated compartment (called a syncytium formed by specialized mesodermal cells, in case of the sea urchin), the initial geometric shape is lost and complexity in morphology is generated (Figure 3.9). Interestingly, in the example of the sea urchin larvae, during the next stage of spiculogenesis, two of the radii in the initially triradiate particle change their growth direction by 90 , forming so-called rods growing along the c-axis of calcite [15]. This is also the final long axis in sea urchin spicules. It is remarkable that in the sea urchin case, a significant amount of amorphous CaCO3 was traced (ca. 90% after 48 h) which decreased with time due to the crystallization of calcite [15]. The ACC might give a hint how the complex morphology can be obtained, as an amorphous phase can be moulded before it subsequently crystallizes with shape preservation. The presence of ACC may reflect the fact that the mineral is delivered into the spicular cavity in this form through vesicles, as suggested by the presence of electrondense calcium-rich granules in spicule-forming cells [18]. In summary, the complexity in crystal shape develops with time. On the nanoscale for the primary nanoparticles, the classical laws of crystallization are still valid, and single crystal nanoparticles, with their geometric shapes determined by the crystal symmetry, are obtained. However, what follows next in the complex biomineralization process is a highly interesting lesson on how to generate complexity, which is not yet covered by the textbook knowledge on crystallization. Obviously, a large diversity of scenarios is active in biology to form the finally observed complex crystal morphology, including single crystalline, textured polycrystalline, and weakly ordered polycrystalline species.

3.2 From Biology to Biomimetics: In Vitro Mineralization Examples In the previous chapter, several examples of biominerals allowed us to reveal some of the additional tools that enable the formation of the delicate biomineral structures beyond the behavior of classical single crystals. Those tools include the application of templates and

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confined reaction environments, spatially controlled mineral deposition, the presence of soluble additives as crystallization modifiers, inhibitors or nucleation agents, and the vectorial alignment of smaller crystalline subunits. These strategies are also very attractive for the bottom up synthesis of advanced materials with optimized properties in nonbiological synthesis, using biominerals as source of inspiration and as archetypes for future materials. Based on the above ideas, a rapidly developing research field has evolved, which could be summarized as bio-inspired or biomimetic materials chemistry [19,20]. Bio-inspired morphosynthesis provides an important and environmentally friendly route to generate materials with controlled morphologies by using self-assembled organic superstructures, inorganic or organic additives, and/or templates with complex functionalization patterns. During the past decade, exploration, as well as application, of these bio-inspired synthesis strategies have resulted in the generation of complex materials with specific size, shape, orientation, composition, and hierarchical organization [21–29]. It is no surprise that the application of biomimetic mineralization principles has led to similarly complex crystal morphologies, as found in biominerals, including curvature. From the very many examples for such structures from biomimetic mineralization experiments we can just select a few representative examples in this book. More extensive discussion of this subject can be found in various reviews [19,20,30–38]. One very successful biomimetic mineralization strategy towards single crystals with complex shape is the application of templates, as they allow the structure of the formed single crystal to be predefined. The most elemental way towards two-dimensional patterned single crystals is the application of patterned self-assembled monolayers (SAMs) as a nucleating zone. If SAMs are patterned, all features of oriented crystallization on a SAM can be carried out in a spatially organized way, and remarkable control over particle assembly can be achieved, as recently summarized by Aizenberg [29]. Patterned SAMs were successfully used by Aizenberg et al. for the direct fabrication of large micropatterned calcite single crystals (Figure 3.10) [39], which can be considered to be a rough mimic of the oriented single crystal calcite microlens arrays in brittlestars [40]. First, photoresist micropatterns were formed on a glass surface by photolithography. Then, the surface was coated with Au or Ag., and a localized nanoregion of a polar alkanethiol was deposited on the surface, with an AFM tip serving as a single nucleation center for calcite with a known orientation. Afterwards, the remainder of the metal surface was coated with alkanethiols with varying lengths and functionalities, which created a disordered surface and favored the formation of amorphous calcium carbonate (ACC). In the course of the reaction, a mesh of metastable ACC filled the interstices of the framework, followed by site specific nucleation of a calcite single crystal at the deposited nucleation spots. This crystal, at the expense of the surrounding ACC, finally led to a micropatterned single crystal, as could be evidenced by polarization microscopy. The micropatterned surface was found to serve for the release of stresses, water, and impurities during the formation of the final crystal. Figure 3.10c clearly shows the curvature of the single crystal on the mm scale and demonstrates that the two-dimensional ACC precursor phase could essentially be moulded into any shape, which was then adopted by the subsequently formed single crystal. This example shows that the generation of complex, single crystal morphologies can be achieved via site specific nucleation of amorphous precursor phases and their subsequent crystallization to the final calcite single crystal.


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Figure 3.10 (A) Preparation of templates with micropatterns for mineral deposition. Photoresist micropatterns were formed on a glass slide by standard photolithographic procedures. The micropatterned substrate was coated with a transparent, 5 to 10 nm thick film of gold or silver. A nanoregion (red circle) of a SAM of HS(CH2)nA (A ¼ OH, CO2H, SO3H), which induces the nucleation of calcite in a controlled orientation, was deposited on Au (Ag) by the tip of a scanning force microscope. The remainder of the surface was derivatized with a mixture of alkanethiols of different lengths terminated with phosphate, methyl, and hydroxyl groups to create a disordered organic surface that suppresses the nucleation of calcite and favors the formation of ACC. The functionalized substrate was covered with a thin, gas-permeable polymeric film, such as polydimethylsiloxane (PDMS); (B) Calcium carbonate deposition; (C) SEM of a sample micropatterned single calcite crystal fabricated as described in (A) and (B); Inset: Large-area TEM diffraction, showing that the section is a single crystal oriented along the c-axis; (D) The calcite single crystal rotated under crossed polarizers. (Reproduced from [39] with permission of the American Association for the Advancement of Science.)

Amorphous precursors can also form crystalline films with oriented texture, which scatter like single crystals, but have a polycrystalline morphology in microscopy images. Kato and co-workers [41] have reported the formation of uniaxially oriented CaCO3 thinfilm crystals (Figure 3.11) on chitin matrices by using a natural peptide (CAP-1) isolated

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Figure 3.11 (a) SEM image of CaCO3 crystals grown on a chitin matrix in the presence of CAP-1 for 20 h (3:0 103 wt%); (b) Magnified image of the crystal surface in (a); (c) TEM image; and (d) the corresponding selected-area electron diffraction image of the uniaxially oriented crystal grown on a chitin matrix in the presence of CAP-1. (Reproduced from [41] Copyright & 2006, Wiley-VCH.)

from the exoskeleton of a crayfish. This film was formed in patches of ca. 10 mm and 1 mm thickness and was composed of an assembly of ca. 20 nm calcite nanocrystals (Figure 3.11 b). The peptide used, CAP-1, is thought to exhibit several functions: (1) binding of CaCO3 to the surface, because CAP-1 has a binding domain to the oriented a-chitin fibrils; (2) arrangement of its acidic groups through specific interaction with chitin; and (3) stabilization of amorphous CaCO3. Synergetic combinations of these functions led to the formation of the uniaxially oriented CaCO3 patches in the films. The uniform texture could be clearly confirmed by an electron diffraction pattern (Figure 3.11 d). It has to be noted that the crystalline patches have a different crystal orientation, but each patch consists of iso-oriented calcite nanocrystals, as could be revealed by polarization microscopy. Other work demonstrated that a so-called hard-template strategy could be used to produce complex three-dimensional curved structures of calcite, which shows the typical rhombohedral morphology under default crystallization conditions (see Figure 3.6). First, a sea urchin plate was replicated into a polymer structure by polymerization of a monomer within the original sea urchin structure, then removing the original template by dissolution. If these polymer replicas of sea urchin skeletal plates are again used as a template in a double diffusion experiment (slow CaCO3 crystallization at low ion concentrations), CaCO3 crystals similar to the original complex structure of the sea urchin skeletal plate


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Figure 3.12 Templated CaCO3 single crystal in a polymeric replica of a sea urchin skeletal plate. (Reprinted with permission from [42] Copyright & 2002, Wiley-VCH.)

could be formed [42]. (Figure 3.12). Again, the curvature on the micrometer scale is remarkable. These crystals were not grown via an ACC precursor phase, demonstrating that ACC is not a necessary prerequisite for the formation of curved crystalline morphologies [43]. This templating strategy could also be transferred to other crystal systems, like SrSO4, PbSO4, PbCO3, NaCl and CuSO4 5H2O, demonstrating that the generation of complex morphologies by suitable hard templates is quite versatile [44]. Single crystalline systems with a complex morphology can also be obtained in a multistep growth mechanism. Striking examples of such growth pathway are flower-like BaSO4 particles with a ‘forbidden’ 10-fold symmetry, which can be produced in presence of a sulfonated poly(ethylene oxide)-block-poly(ethylene imine) (PEO-b-PEI) as shown earlier in Figure 2.29 a [45]. For the formation of these particles, an elongated primary nanoparticle formed by selective polymer adsorption was proposed, that has 10 side faces (Figure 2.29 b) [45]. This particle serves as a seed for the heterogeneous nucleation of 10 single crystalline petals, which are overgrown in the final stage. Thus a structure forms which is single crystalline (the petals), but which does not violate the laws of crystal symmetry due to the primary particle with 10 side faces. Crystalline systems with apparent unicrystalline orientation can also be formed by self-assembly processes (for a more detailed discussion of the underlying principle and more examples, see Section 4.3, Oriented Attachment). One example is the single crystalline BaSO4/BaCrO4 fiber bundles and cones (Figure 3.13), which can be generated by a particle-mediated polymer-controlled crystallization process [46–54]. or via nanoparticles generated in a reverse microemulsion [55]. These species are composed of defect-free single crystalline fibers, which are selfassembled into the complex self-similar bundle structures. A thin cut perpendicular to the fiber bundle axis shows individual single crystalline fibers, which are interspaced by a polymer layer due to the preparation process. These fibers are generated by

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Figure 3.13 Complex forms of BaSO4 fiber bundles produced in the presence of 0.11 mM sodium polyacrylate (M ¼ 5100 g/mol), at room temperature, [BaSO4] ¼ 2 mM, pH ¼ 5.5, 4 days. (Reproduced from [56] with permission of the Materials Research Society (left and center). The right figure is reproduced from [47].)

heterogeneous nucleation from aggregates of amorphous precursor particles via oriented attachment of nanoparticles with subsequent nanoparticle fusion to the single crystalline nanowires, and simultaneous assembly into complex bundles and cones (see Section 4.3, Oriented Attachment for further details). Fiber structures were also reported for complex nested whisker structures composed of hydroxyapatite, which were synthesized in the presence of poly(ethylene oxide)-balkylated poly(methacrylic acid) (PEO-b-PMAA-C12) as an additive [57]. This polymer, with the functional carboxy groups as direct neighbours to the hydrophobic chains, undergoes a weak aggregate formation in water [57]. These loose aggregates sequester Ca2þ ions and thus serve as localized mineralization centers in the precipitation reaction of hydroxyapatite. Delicate mesoskeletons of interconnected calcium phosphate nanofibers with star-like, neuron-like, and more complex nested forms can be produced, as displayed in Figure 3.14. The complex structures result from a feedback loop between selective polymer adsorption on all faces parallel to the hydroxyapatite c-axis and the deformation of the polymer aggregates by the polymer adsorption onto the growing filaments. Removing the three C12 alkane chains of the hydrophobically modified derivative and mineralizing, with the pure parental DHBC, resulted in different mesostructures, compact spherical colloids with inner structure, underlining how subtle changes of the DHBC functional block can have a big effect on the crystallization process as such. The above example also shows that the three-dimensional aggregation structure of the crystallization additives, prior to mineralization, provide a further variable for the control of crystal morphogenesis by polymers, which resembles again natural protein systems localized in their biological networks. It is remarkable that the hydroxyapatite nanofibers in Figure 3.14 with only 2–3 nm diameter show branching, in contrast to the single crystalline nanofibers shown in Figure 3.13. This can be explained by the differences between ion- and nanoparticle-mediated crystal growth, as further discussed in Section 4.3, Oriented Attachment and Figure 4.21. The combination of crystallization control by polymer and self-assembly of surfactants in an aqueous environment can produce another remarkably beautiful class of crystal


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Figure 3.14 TEM images of calcium phosphate block copolymer nested colloids: (a) Star-like form at an early stage at pH 4.5; (b) later stage showing a complex central core, and very long and thin (2–3 nm) filaments; (c) neuron-like tangles produced at pH 5; (d) packing view of calcium phosphate along the c-axis. ((a), (b), and (c) reprinted with permission from [57] Copyright & 1998, Wiley-VCH; (d) from [31], Copyright RSC.)

constructions, as is reported for simple polyelectrolyte/surfactant mixtures as crystallization additives. Elegant featherlike morphologies up to 50 mm in length of the binary oxide compound BaWO4 (BaO WO3) were prepared under mild conditions via a multistep growth process by combination of both catanionic reverse micelles (undecyl acid and decylamine) and the block copolymer poly(ethylene oxide)-block-poly(methacrylic acid) (PEO-b-PMAA) [58]. Numerous nearly parallel single crystalline barbs (length ca. 2.5–4.5 mm, diameter ca. 3.5 nm) stand perpendicular on both sides of a polycrystalline central shaft (d ¼ 200–400 nm) with their c-axis as the long axis, showing that rather special template effects can be realized in a certain experimental window (Figure 3.15) [58]. These structures could be varied from star-like structures to a single shaft by a simple variation of the polymer concentration. The growth mechanism was found to be quite complex [59]. There are two subsequent growth steps (Figure 3.16). First, c-axis oriented shuttle-like particles of about

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Figure 3.15 TEM image of penniform BaWO4 nanostructures grown in the presence of 0.5 g/L PEO-b-PMAA after aging for 8 h in a reverse micelle system. (Reprinted with permission from [58] & 2003, American Chemical Society.)

80–200 nm in length are formed, which are grown controlled by the applied PEO-bPMAA block copolymer. These primary nanoparticles attach to each other along the [001] direction by ‘oriented attachment’ and then crystallographically fuse to form the shaft (Figure 3.16). This mechanism will be discussed in detail in Section 4.3, Oriented Attachment. The second stage, the formation of the [001] oriented nanowires on the central shaft, is controlled by the added surfactants, which form bilayers and adsorb to the faces parallel

Figure 3.16 Schematic illustration of the detailed formation of penniform BaWO4 nanostructures. (Reprinted from [59] with permission of the American Chemical Society.)


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to the c-axis. Changing the molar ratio of the anionic and the cationic surfactants r could be applied to change the growth from pendant nanowires to nanobelts, growing perpendicular to the central shaft. It is also possible to apply face selective adsorption of additives to control the anisotropy of crystal tectons for subsequent self-assembly. Helices composed of nanorods can be ‘programmed’ by face selective adsorption of a stiff polymer and subsequent selfassembly of nanoparticle building units. This has recently been successfully achieved for the formation of BaCO3 helices by programmed self-assembly of the elongated orthorhombic BaCO3 nanorod subunits using a racemic phosphonated DHBC (polyethyleneglycol-b-[(2-[4-dihydroxyphosphoryl]-2-oxabutyl) acrylate ethyl ester] (PEG-b-DHPOBAEE)) for crystallization (Figure 3.17) [60]. The involvement of the polymer in two processes results in this tectonic arrangement via coded self-assembly. The adsorption of the stiff DHBC onto the favorable (110) faces is the first stage, resulting in a staggered arrangement of aggregating nanoparticles that are controlled in helix direction after the aggregation of the first three particles. Secondly, a particle approaching an aggregate in the perpendicular direction is presented with favorable and unfavorable adsorption sites. Favourable adsorption sites are those where only a match to

Figure 3.17 (a) Helical BaCO3 nanoparticle superstructures formed by a programmed selfassembly of elongated nanoparticles at room temperature using PEG-b-DHPOBAEE as template. [Polymer] ¼ 1 g/L, [BaCl2] ¼ 10 mM, starting pH 4; (b) Magnified SEM image showing the helical structure; (c) The primary nanocrystalline witherite building block in vacuum not representing observed face areas in solution, but just illustrating the orientation of the relevant faces; (d) Proposed formation mechanism of the helical superstructure. (Reproduced with permission from [60]. Copyright 2005 Nature Publishing Group.)

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a (011) face in the existing aggregate is required and the unfavourable adsorption sites require a match of (020) and (011) faces. This leads to a twist in the particle aggregate. The overlay of these two processes leads to the formation of a helical superstructure, as shown in Figure 3.17. The above examples already show, that ‘bio-inspired mineralization’ is not only the reproduction of biominerals or their structural features, but is furthermore able to significantly extend the options of Nature. Chemistry is able to apply a much wider pH range for crystallization than possible in biology, can transfer the principles to minerals, which do not occur as biominerals because they are not broadly available, and can also apply an almost unlimited number of additives from the large chemical toolbox.

3.3 Biomorphs Biomorphs are self-assembled silica-carbonate composite materials, which are usually obtained by performing a (carbonate) mineralization reaction in the presence of a solidifying silica gel. Due to the simltaneously occurring crystallization and gelation reactions, structural complexity is generated by self-organization processes [61–63] Biomorphs were, to our knowledge, first observed by Herrera in 1912 [64], and belong to the oldest non-explained observations in structural crystallization. Also, biomorphs demonstrate that inorganic abiotic materials can display a wide range of curved morphologies which are usually considered to be exclusively for the biological world. This includes complex helical structures, flower-like spherulithic objects, orchid-like cones, coral-like bended plates, trumpets, mushroom bundles, etc. A remarkably nice growth sequence of spherical BaCO3 objects is depicted in Figure 3.18, which also indicates that structural complexity is here the result of a self-organized, dynamic growth program. Obviously, and as evidenced by excellent detailed microscopy observations [65], the mineral first crystallizes as nanocrystals, the mutual alignments of which are controlled by the chemistry and by mechanical interactions with the soft, solidifying silica gel. The perfection of the mutual alignment of the primary nanocrystals towards curved objects in the absence of any organic molecule or biological action can be followed by all the techniques introduced in the previous chapter, for instance polarized light microscopy.

Figure 3.18

Growth sequence of floral spherulites, taken from [62] with permission of Elsevier.


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Figure 3.19 Optical micrograph of a sheet viewed under crossed polarizers. The extinction pattern is indicative of radial orientational ordering of the optically anisotropic witherite nanocrystals within the sheet [62]. Reproduced with permission of Elsevier.

Figure 3.19 depicts a snail like structure, grown from a helical stem. It can be clearly seen that the crystal superstructure perfectly follows the radial assembly program, which is reflected in the colours due to the birefringence of witherite (BaCO3). The mechanisms of formation are manifold and have been partly analyzed in great detail [65]. Practically all structures start their life as little, ca. 10–50 nm sized nanoparticles which also constitute the pathway of material transport. Usually these primary blocks aggregate first to an embrional microsphere, which then grows, presumably by field effects from the crystallizing superspheres, in a countable number of distinct directions. Helix formation, for instance, can be categorized into different stages: (1) growth of an initial globular aggregate, which extrudes a tongue; (2) the curling of the edges of the tongue in different directions; (3) the continued growth of a double helix; and (4) the development of a worm-like aggregate on the pre-exisiting double helix. The fact that the helix keeps its diameter constant throughout the growth process indicates that matter is only added in the growth zone, i.e. the tip of the helix. Besides directional transport, the found structures also strongly support the possible influence of mechanical stress fields and dipolar interactions. The role of the soft silica gel seems to be the suppression of turbulences and – via the sol fraction – stabilization of primary nanoparticles until they can interact and adhere. In any case, the original gel structure on the nanoscale is broken throughout growth of the biomorphs.

3.4 Other Synthetic Examples It is interesting to note that even crystals precipitated in the ‘ordinary’ way without any additives can be in disagreement with the classical expectations for crystal formation.

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One particularly interesting example of this kind is the formation of porous BaSO4 crystals. Porous BaSO4 crystals with a sponge-like structure and an average pore size of 3 nm were reported decades ago, and an aggregation-based mechanism was suggested for the formation of the crystals [66]. However, their formation mechanism, based on nanoparticle aggregation was only revealed in a recent study where they were precipitated at high supersaturations in a batch reactor or with a free jet technique using a Y-mixer, thus allowing demanding sampling and cryo TEM techniques to study the early reaction stages [67]. In Figure 3.20 left, a typical BaSO4 crystal is shown, as obtained at the applied high supersaturations. The remarkable feature of this crystal is the appearance of pores with an increasing pore size towards the center of the particle. A closer examination (Figure 3.20 center) of one ca. 15 nm pore reveals the individual Ba2þ ions in a regular crystal lattice of an apparent monocrystal, despite the pore, which shows curved features even down to the scale of a few nm.

Figure 3.20 (Left) TEM micrograph of a BaSO4 crystal (on the right) showing its characteristic internal structure (S ¼ 1000). In the left of the picture is depicted the polymer film which extends between the copper grid and which serves as a substrate for the particles; (Center) Detailed picture of a cavity which shows also the crystal lattice with regularly stacked Ba2þ ions; (Right) Electron diffraction pattern of an apparently monocrystalline particle generated at S ¼ 2500. (Image reproduced from [67] with permission of Elsevier.)


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Not surprisingly, this crystal also shows a spotted electron diffraction pattern, formerly interpreted as the presence of a single crystal (Figure 3.20 right). The pictures also indicate the continuity of crystal lattice planes around the curved pores. The size of the pores depends on the applied supersaturation and increases with increasing supersaturation. These results can certainly not be explained by the classical mechanism of a layerby-layer growth of a single crystal via ion addition, as it cannot account for the formation of pores. The finding that the pores are filled with a solution containing the counter ions of the precipitation process hints at an aggregation-based mechanism of superstructure formation. This will be introduced in the following chapters.

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4 Nonclassical Crystallization This chapter describes a second pathway of crystallization via nanoparticulate intermediates, called ‘nonclassical’ crystallization (to complement the ‘classical’ crystallization. This concept contains a number of novel steps, which, however, have carefully been evidenced in some hundreds of original contributions. Beside the formation of amorphous clusters and particles as intermediates, this is the multiple, parallel formation of nanoparticles and their oriented alignment towards mesocrystals Nonclassical crystallization is a concept that has been more or less developed in the last few years; for a review, see [1]. It was driven by the experimental evidence that several crystallization cascades can obviously not be understood on basis of the classical crystallization schemes. The long list of case studies in the previous chapters already shows that instead of simple nucleation and growth, crystallization can also precede along particle-based reaction channels. These reaction channels have in common that molecular supersaturation is first lowered by the formation of clusters or small primary (usually amorphous) nanoparticles, which serve as an intermediate deposit of material and are the carriers of mass transport and growth. The nanoparticle aggregation, self-organization and final mesoscopic transformation nicely complements the classical picture of crystal growth via ions, atoms or molecules. As mesoscale transformations we want to understand all local restructuration processes that take place on the mesoscale, say between 1–1000 nm. In the meantime, a number of steps or options within nonclassical crystallization mechanisms have been identified. These are: Formation of intermediary clusters or phase separation to liquid precursors as the primary building blocks Crystallization via amorphous intermediates involving transient amorphous building blocks, which can undergo mesoscopic transformations


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Oriented attachment of nanoparticulate building blocks, i.e. the directed aggregation of nanoparticles with possible subsequent crystallographic fusion of high-energy crystal faces. Mesocrystallization involving the three-dimensional self-organization of nanoparticles in a crystallographic register to a highly ordered mesostructure. This list is likely far from being complete, as science is just starting to understand particle-based crystallization pathways. ‘Nonclassical crystallization’ in the following context describes processes which involve parallel, multiple nucleation events to form nanoparticles, which then form a superstructure (in stark contrast to a single nucleation event to form a single crystal). Nonclassical crystallization involves self-assembly of preformed nanoparticles to an ordered superstructure, which then can fuse to a single crystalline structure. These crystallization pathways or phenomena especially apply to systems far from equilibrium, even for very ‘classical’ crystallization processes, which have so far been considered to proceed via tradional pathways. Figure 4.1 schematically illustrates these processes. Each of the steps will be discussed below in more detail under the respective headings. From Figure 4.1, it becomes clear that several products of nonclassical crystallization mechanisms have a transient character and change via mesoscopic transformation. These newly developed concepts not only expand our view on crystallization in general, they furthermore extend the toolbox of crystallization as one of the base operations of chemistry and material synthesis. The particle-mediated nonclassical crystallization path makes crystallization practically independent of ion products or molecular solubility, it can occur without pH or osmotic pressure change in the crystallization medium, and opens new spatiotemporal strategies for crystal morphogenesis. This is possible because the precursor particles can be formed independently even at different locations (i.e. in a different flask), can be stored and transported to the locus of mineralization/crystallization, keeping this site unaffected from precipitation effects (elevated ion concentrations or pH changes). It is obvious that these benefits make nanoparticle-mediated nonclassical crystallization especially relevant for biological systems. However, the precursor structures of the particlemediated nonclassical crystallization pathways are difficult to detect, as they are often only of a transient nature. Nanoparticles can undergo self-assembly to superstructures even long after the molecular supersaturation has dropped to one so that no crystallization is to be expected, according to the classical nucleation picture. An example for this was reported for BaSO4 fibers synthesized in the presence of poly(acrylate), which continue to grow further by particle attachment, although the supersaturation as detected via the changes in the pH value had dropped to one [2,3] (Figure 4.2). In the figure showing the timedependent supersaturation (Figure 4.2 a), three zones are evident. In zone I crystallization is essentially inhibited, but amorphous precursor particles are nucleated, which form micron sized aggregates visible by light microscopy (Figure 4.2 b). Once crystallization and formation of crystalline nanoparticles sets in, the supersaturation drops by further particle nucleation, and particle growth. In addition, the formation of fiber bundle superstructures by oriented attachment is observed (zone II in Figure 4.2 a). In the light micrographs, this is evidenced by the higher particle number, as well as their size (Figure 4.2 c and d). For a more detailed electron micrograph of the final structures, see Figure 3.13.

Nonclassical Crystallization

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Figure 4.1 Schematic representation of classical and nonclassical crystallization. Pathway (a) represents the classical crystallization pathway, where nucleation clusters form and grow until they reach the size of the critical crystal nucleus growing to a primary nanoparticle, which is amplified to a single crystal. The primary nanoparticles can also arrange to form an isooriented crystal, where the nanocrystalline building units can crystallographically lock in and fuse to form a single crystal (oriented attachment, path (b)). If the primary nanoparticles are covered by a polymer or other additive before they undergo a mesoscale assembly, they can form a mesocrystal (path (c)). Note: Mesocrystals can even form from pure nanoparticles. There is also the possibility that amorphous particles are formed, which can transform before or after their assembly to complicated morphologies (symbolized by the question mark in path (d)).

Even long after the supersaturation has dropped to one and thus the primary thermodynamic driving force for crystallization has completely vanished, new microparticles are formed and also grow (Figure 4.2e). This clearly shows that the microparticle formation must take place via nanoparticles as building units, as the ion pool for the crystallization according to the classical crystallization mechanism is exhausted. Furthermore, this is an experimental demonstration of the advantage that nonclassical crystallization events can take place quite rapidly at ionic strengths as low as the solubility product of the mineral under consideration.

4.1 Amorphous Precursors Maybe the first step in most nonclassical crystallization pathways is the formation and transformation of amorphous precursor nanoparticles [4] (see Figure 4.1 d). This strategy

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Figure 4.2 Time-dependent measurement during BaSO4 crystallization from a mixture of BaCl2 (1.92 mmol/L) and Na2SO4 (1.92 mmol/L) in the presence of 0.56 g/L of poly(acrylic acid) sodium salt. Note the different zones: I ¼ crystallization inhibition, II ¼ crystallization and III ¼ equilibration. (a) The supersaturation of the mixture; (b) – (e) light microscopy of the same area in solution after (b) 80 min (Zone I), (c) 420 min (zone II), (d) 780 min (zone II) and (e) 1440 min (zone III). Scale bar 10 mm. (Reproduced from [2] with permission of the American Chemical Society.

is especially capable of generating complex crystal morphologies, because amorphous precursors can be moulded and formed into any shape, as in pottery or in glass blowing. Amorphous precursor particles are favored to form as the first species at high supersaturations, as, according to the Ostwald rule of stages, the least stable and least dense modification also has the lowest activation barrier of formation. It is meanwhile experimentally well established that in ionic solutions with concentrations far above the saturation level, the formation of amorphous clusters and droplets is practically unavoidable, see also the discussion in Section 2.5, Thermodynamic and Kinetic Crystallization Pathways. [5,6] Quite generally, the supersaturation relaxes much faster than the presence of crystals can be detected. This was also nicely illustrated for amino acid solutions where – after a crystallization inducing pH jump – the conductivity due to dissolved amino acid molecules collapsed practically immediately, while turbidity and the presence of crystals was found to occur at the timescale of minutes to hours.[7] Amorphous particles, however, can only be formed at concentrations above their dissolution threshold, which is – due to the laws of phase thermodynamics – significantly higher than the corresponding value of the crystalline species (see also Section 2.6. Polymorph Control). This ensures a certain experimental window (between the equilibrium dissolution concentrations of crystalline and amorphous species) where only classical ionmediated crystallization can be found, e.g. as it is needed for the formation of large, single crystalline objects. The higher the supersaturation, the more amorphous clusters are formed, thus promoting their role in the following structure formation processes. Another rule of thumb is that the lower the solubility or solubility product of a component, the more probable is it to find amorphous precursor stages and nonclassical


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crystallization. This is simply due to the fact that a lower solubility automatically increases the apparent supersaturation even at moderate molarities, but also kinetically stabilizes the amorphous nanostructures against redissolution. As amorphous nanoparticles can also be involved in a classical crystallization reaction, but only as a material depot for subsequent dissolution and recrystallization, it has to be carefully checked mechanistically if the amorphous particles redissolve as the crystalline species is generated. Amorphous nanoparticles are difficult to detect, as they are usually a transient species and often highly unstable. One way to distinguish between redissolution of amorphous precursors and their mesoscopic transformation is the combination of analytical techniques, which are able to detect ions and supersaturation on-line in solution (pH, conductivity etc.), with those able to detect the amorphous nanoparticle character (TEM with electron diffraction or WAXS). If for example, amorphous particles are detected and particle superstructures still grow, although the supersaturation has decreased to one, the occurrence of nonclassical crystallization via mesoscopic transformation of amorphous precursor particles can be assumed. (see Figure 4.2 and associated discussion) The role of amorphous nanoparticles as intermediates was first identified as such in 2001, [8] but the observation of amorphous precursor phases as such is older[9,10]. In synthetic bio-inspired mineralization systems, amorphous precursor particles are now found to be omnipresent,[11] as they most often constitute the early nanoparticle phase. In this situation, it is an interesting proof-of-concept to apply the isolated and identified tools of biomimetics back to biomineralization. As one example, the retrosynthesis of nacre is given. In this model system, a demineralized insoluble matrix of nacre was remineralized with amorphous CaCO3 nanoparticles, which were formed in the presence of mg/ml amounts of polyaspartic acid in a different ‘synthetic’ container. [12] The amorphous precursors were able to completely fill the compartments of the insoluble organic matrix with CaCO3. Calcite was obtained instead of the natural aragonite, and the single crystalline domains were found to be smaller than for the natural archetype (Figure 4.3). Besides that, the retrosynthesized nacre was indistinguishable from its natural archetype by bare observation techniques, e.g. electron microscopy (SEM & TEM), as shown in Figure 4.3. This experiment suggests that natural nacre can indeed be built up from amorphous precursor particles, and no specialized active protein biofunctions are needed to achieve the generation and transport of precursor material to the mineralization site – a simple polyelectrolyte function is sufficient. In a recent study, Tremel et al. applied amorphous precursor particles in a related bio-inspired mineralization approach using a self-assembled monolayer (SAM) as a mimic for the insoluble polymer matrix in biominerals and poly(acrylic acid) (PAA) as a mimic for the soluble additives, which can adsorb onto the SAM. [13] Amorphous calcium carbonate (ACC) nanoparticles attach to the PAA/SAM and, subsequently, vaterite nanowires are formed by cooperative action of the PAA/SAM. These nanowires are themselves aggregates of nanoparticles being nucleated from the ACC nanoparticles on the PAA backbone. We have to be aware that similar mineralization problems and their control are also a part of our daily technical world. Scale inhibition is a key issue for water piping or laundry cleaning, and technical aids to avoid scale, both of a physical and a chemical nature, are omnipresent and megascale products of industry. It is enlightening that the function of some of these devices, e.g. the application of electric fields to soften water, can only be understood when their target of action are indeed the amorphous

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Figure 4.3 Nacre retrosythesized in the insoluble organic matrix of a Haliotis laevigata shell via transformation of amorphous precursor particles. The upper pictures show the comparison of the SEM morphology of natural and synthetic nacre, the lower line the corresponding transmission electron micrographs (TEM) of microtomed samples. (a) Synthetic nacre; (b) synthetic nacre in higher zoom; and (c) electron diffraction pattern taken in this region and showing an almost single crystalline calcite domain; (d) TEM thin cut of natural nacre. (Reprinted from [12] with permission of the American Chemical Society.)

intermediates of scale. Similar to that, it was long thought that polymer antiscale additives, such as Sokalan1, only sequester ions. In fact it turned out that such polymers stabilize amorphous ACC nanoparticles and keep them from adhering to the fabric or the metal, thus developing a much higher efficiency. [6,14]

4.2. Liquid Precursors A slight, but relevant variation of the amorphous precursor phases are liquid presursors. All amorphous materials have a glass transition, which, depending on composition, additive content or solvent/water content can be below the temperature of the experiments. In this case, the precursor is not only disordered, but also liquid. It is obvious that the two cases are not clearly separated, but exhibit a continuum between them. Liquid/liquid phase separation is a general effect when two components become nonmiscible with each other, e.g. salts and water. The decomposition always leads to a solvent-rich and a solvent-poor phase (see also and Figure 4.5 below), the composition of which are very similar to each other near the critial demixing point, but become increasingly phase pure in one of the components, the deeper the quench in the


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nonmiscible region becomes. This means that near the critical demixing point, liquid/ liquid phase separation is the default case. It can be observed as an undesirable effect during protein crystallization from solution, [15] but is also already known for mineral salts such as CaCO3 as a phenomenon for more than a century. [16–18] If such a liquid phase is used as a precursor phase for a subsequent crystallization process, crystal morphologies with complex shapes, molten appearance, or crystalline coatings with flexible geometry can be realized. Wegner et al. postulated a liquid/liquid phase separation with a lower critical solution temperature (LCST) point at about 10 C in a saturated CaCO3 solution without additives, and postulated a ‘virtual’ phase diagram in a coordinate system spanned by temperature and CO2 concentration. [19,20] The term virtual here means that CaCO3 crystallization as a natural consecutive process towards the more stable phase, was not considered in this phase diagram, applying the thermodynamic description of phase behavior to a kinetic, metastable phase. For this kinetic metastability, the postulated liquid phase could not directly be experimentally proven. Nevertheless, the proposed virtual phase diagram shows that under isothermal conditions and constant Ca2þ concentration, addition of CO2 first leads to spherical, hydrated ACC particles (experimentally proven) of the postulated liquid character from point B (Figure 4.4). Up to the spinodal decomposition point C, the droplets have to be nucleated, i.e. form at surfaces or along impurities, only. From C to D, spontaneous and simultaneous formation of a highly concentrated CaCO3 phase in solution occurs (spinodal domain), while still increasing CO2 concentrations lead to a more stable, binodal situation again (region D–E, ‘over-carbonated’ droplets). Finally, very high CO2 concentrations lead to a one phase region, again, as can be seen in Figure 4.4. In case of CaCO3, such a liquid precursor phase separated from the saturated crystallization solution can be induced by addition of tiny amounts (mg/mL range) of polyelectrolytes like PAsp or PAA, which obviously increase the water content of the salt-containing phase. Gower et al. used the term ‘polymer-induced liquid-precursor (PILP) process’ for the formation process of such liquid precursors. [21] They can be

Figure 4.4 Proposed schematic virtual phase diagram that explains the formation of spherical particles by liquid/liquid phase segregation. (Reproduced from [19] with permission of Wiley-VCH.)

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Figure 4.5 Left: Light microscopy of CaCO3 PILP droplets in a crystallization solution of 20 mM CaCl2 þ 20 mg/ml PAsp on a glass plate. CO2 is slowly added via the gas phase; Right: TEM and TEM/SAED pictures of a PILP solution after shock freezing in N2 and subsequent freeze drying show the amorphous character. (Image by Dr. Nicole Gehrke.)

observed as little droplets in the crystallization solution by light microscopy (Figure 4.5) and lead to polycrystalline aggregates with complex shape after crystallization. Such liquid precursor droplets were independently observed for CaCO3, when anionic dextran sulfate was used as an additive. [22] The role of the polymer appears to be the sequestering and enriching of the calcium ions in a still rather water-rich environment, while simultaneously delaying crystal nucleation and growth within the droplets to form an, at least, metastable emulsion. [23,24] The PILP droplets were shown to generate with sizes in the range of about 100 nm and then grow to microscopic size by subsequent aggregation and fusion as evidenced by laser light scattering experiments. [25] PILPs do not necessarily contain both ions in the correct composition, as in amorphous phases electroneutrality can also be accomplished by inclusion of ternary counterions and the additive itself. For illustration, a CaCO3 –PILP can be ‘overcarbonated’ or ‘undercarbonated,’ meaning that for complete crystallization a certain supply of ions from the continuous phase is still needed. Experimentally, undercarbonation of CaCO3 –PILPs was revealed and the carbonate transport was the rate limiting step for formation of the crystalline CaCO3 from the PILP precursor, once a critical level of carbonate was reached for crystallization. [26] Furthermore, the composition of a PILP will, due to the demixing transition involved, sensitively depend on reaction conditions; these are all the reactant concentrations, temperature, but – without equilibration – also the sequence of reactant addition and the mixing geometry. Crystalline products generated from these PILPs may essentially keep the outer shape of the PILP phase or – when small – the droplet shape, as an envelope of a crystal superstructure. This will be discussed in more detail below. The crystallization itself however may also deform the flexible phase, and nonequilibrium morphologies can be generated (see Figure 4.6) Amazing spherulitic vaterite aggregates containing helical extensions with spiral pits were obtained, and it was suggested that they grew from the


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Figure 4.6 Left: A CaCO3 helix formed in the presence of polyaspartate. The helix has been fractured, revealing an outer membrane and polycrystalline core. The helices were fractured using a micro-manipulator on an optical microscope. Bar ¼ 10 mm. Right: Hollow CaCO3 helices fractured by micro-manipulation. The fracture is different from that of the solid structures shown in the left side. Bar ¼ 10 mm. (Reprinted from [21] with permission of Elsevier Science Publishers.)

deposited CaCO3 films controlled by the polymer. Those structures are quite similar to those found in some biogenic minerals, such as the otoliths (ear stones) of fishes. [27] Here, spherulitic growth is induced by nucleation sites distributed along a surface, and the aragonite or vaterite crystals grow with their c-axes approximately perpendicular to the surface. [28] So far, the most intensely studied system possessing liquid precursors is CaCO3. If PILP droplets are deposited on a substrate, they coalesce and form a coating, which subsequently transforms into patched calcite films with different single crystalline domains via crystallization. [23] Particles, or even emulsion droplets, can be coated as well [29] by PILPs. Gower et al. were also able to synthesize calcite nanofibers via a PILP process, in a deposition mechanism termed a solution-precursor-solid (SPS) mechanism. [30] Calcite seed rhombohedra were overgrown with fibers with rounded tips. CaCO3 PILPs were also found to mineralize collagen, where the PILP precursors were, amazingly, even able to enter the nm sized gap zones of collagen resulting in a structure partly resembling that of bone. [31] These results suggest that bone mineralization might also proceed via a PILP precursor stage. The authors suggested a paradigm that all Ca-based biominerals form via a PILP stage [24] although the current evidence is still based on CaCO3 only. PILP precursors can also be used to deposit an amorphous precursor film, which is composed of 20–30 nm ACC nanoparticles and PAA on a substrate. This film, composed of amorphous nanoparticles, transforms into a partially crystalline film by drying at room temperature for several days. [32] Heating to 400 C for ca. 2 h yields a completely crystalline film with a structure of crystalline patches with differing crystallographic orientations and typical domain sizes between 50–200 mm, as revealed by polarization microscopy (see also Figure 4.7). Overgrowth of the polycrystalline patchwork film with CaCO3 without polymer resulted in single and multiple layers of highly oriented multicrystalline calcite crystals within one domain grown on top of the polycrystalline

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Figure 4.7 Scheme of a three-step procedure for the morphosynthesis of nacre-type laminated CaCO3 coatings. In the first step, an amorphous, highly hydrated CaCO3 thin film is deposited on a glass substrate. Upon heating, this precursor film is transformed into a polycrystalline thin film consisting of a mosaic of flat single-crystalline calcite domains. In the last step highly oriented single and multiple layers of calcite crystals are grown epitaxially on the underlying polycrystalline thin film. (Reproduced from [32] with permission of Wiley-VCH.)

patchwork film, finally leading to a laminated CaCO3 coating (Figure 4.7). The crystal domain texture changes abruptly at the borderline between different domains, but stays constant within each individual domain, supporting a mechanism of epitaxial overgrowth. The multilayered structure within the domains is reminiscent of the nacre architecture, although the present films have a simpler structure. The coatings nevertheless show iridescence indicating that the multilayers of highly parallel calcite tablets exhibit periodicity in the range of the wavelengths of visible light of a few hundred nm, so that the presented route is an interesting low cost and bio-inspired pathway towards photonic materials. [32]. In addition, the platelet thickness in the nm range and the polycrystalline nature of the template film suggests that each domain with a single crystalline behavior in polarization microscopy is, in fact, a mosaic structure of almost perfectly aligned nanocrystals. So far, the existence of PILPs has been mainly established for CaCO3 systems. Interestingly, PILP processes could also be revealed for organic crystals, as recently demonstrated for various acidic and basic amino acid systems, which formed PILPs upon addition of the countercharged polycation respective polyanion (PAA and PEI). [33] Organic crystal systems have the advantage that they have a much lower lattice energy compared to their inorganic, ionic counterparts. Consequently, the chance to observe or stabilize metastable precursor phases is much higher for organic crystals, as the driving force for crystallization is lower as an effect of the lower lattice energy. In addition, amino acids have the advantage that their solubility can be tuned via simple pH changes, making supersaturation jumps rather immediate. For this system, a direct proof of the liquid PILP character was possible by centrifugation, which resulted in isolation and observation of a very viscous PILP fluid. (Figure 4.8 c). The crystallization of the PILP droplets resulted in porous microspheres composed of nanoplates (see Figure 4.8), where the envelope of the crystal superstructure essentially


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Figure 4.8 (a) DL-glutamic acid crystals obtained from a concentrated PILP precursor phase with PEI; (b) zoom in of (a) showing the porous structure and the nanoplate building units; (c) experimental proof of the liquid character of a DL-glutamic acid PILP phase after centrifugation and removal of the supernatant aqueous phase; (d) L-histidine crystals obtained from a concentrated PILP precursor phase with PAA; and (e) L-lysine crystals obtained from a concentrated PILP precursor phase with PAA. The insets show the default crystals without additives. Scale bars: (a) 10 mm; (b) 200 nm; (d) 20 mm; (e) 3 mm. (Figure reproduced from [33] with permission of Wiley VCH.)

reflects the droplet shape and distribution of the parental PILP phase, while the relative mass density within the porous spheres is a measure of the original amino acid concentration within the viscous droplet. As porous spherical crystal superaggregates are, meanwhile, quite regularly found as a result of complex crystallization processes, it is a good guess that they have experienced a PILP phase along their synthesis pathway. To summarize this section, the formation of PILPs enables the production of complex polycrystalline nonequilibrium morphologies and coatings by liquid processing from a fluid-like precursor state. PILPS can, in principle, be printed, sheared, deformed, and moulded, thus giving a certain flexibility of outer shape to the hands of scientists. Additional benefits, such as the adjustment of different polymorphs (as crystallization is nucleated from a high salt-containing phase different from dilute solution) or the adjustment of porosity by adjusting the concentration of the PILP phase, have up to now not been exploited, but are expected in near future.

4.3 Oriented Attachment Classically, crystal coarsening has been described in terms of growth of large particles at the expense of smaller particles (Ostwald ripening). The driving force for this process,

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from a thermodynamic viewpoint, is the lowering of the surface energy. Ostwald ripening is a dominant process for all cases with a sufficiently high molecular solubility in the continuous phase, and a high interface energy of the crystal, which enables both sufficient thermodynamic driving force, as well as a sufficient speed of recrystallization. However, when the surface energy is low (e.g. by the addition of additives) or the solubility of material weak, other reaction channels can open up. The first experimental observations of unconventional coarsening behavior and morphology evolution of nanocrystalline titania prepared under hydrothermal conditions [34,35] has stimulated many other observations and finally led to the formulation of a new mechanism of crystal growth – so called oriented attachment. This mechanism, which, kinetically, is second order in the number of primary particles, [36,37] describes the spontaneous selforganization of adjacent particles with a common crystallographic orientation, followed by joining of these particles at a planar interface. The process is particularly relevant in the nanocrystalline regime with relatively high specific surface areas, where bonding between the particles allows the system to win a substantial amount of energy by eliminating two high-energy surfaces by crystallographic fusion [38,39] as well as entropy by the release of previously surface-attached molecules by crystallographic fusion. Oriented attachment was first found for TiO2 particles generated in a hydrothermal process. [34] Chains of nanoparticles fused in a crystallographic register were found, and the fusion surfaces were identified to be the highest energy surfaces of the nanoparticles (see Figure 4.9). There are, in principle, two main possible ways to achieve the mutual orientation. One is an effective collision of particles with mutual orientation, the second is coalescence induced by particle rotation in weakly coagulated samples where the nanoparticles still have rotational freedom. [40] This fusion process can happen in an appropriate intermediate interaction region. The colloidal stabilization of the particles has to be so weak that two nanoparticles can approach each other within the primary minimum where they mutually attract by van der Waals forces. However, the flexibility and dynamics must be still high enough to rearrange to the low-energy configuration represented by a coherent particle–particle interface. [38] This ‘weak attraction’ leads to crystallographic fusion of the two particles, eliminating the two high energy surfaces.

Figure 4.9 TEM micrograph of a single crystal of anatase that was hydrothermally coarsened in 0.001 M HCl, showing that the primary particles align, dock, and fuse to form oriented chain structures. (Reproduced from [34] with permission of Elsevier.)


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Figure 4.10 (a) TEM image of wire-like nanostructures composed of trizma-functionalized anatase nanoparticles; (b, (c) HRTEM image of a part of such a nanoparticle assembly and Fourier transformed image showing the single crystalline character of the nanostructure. (Images taken from [41] with permission of Wiley-VCH.)

This appropriate metastability of colloidal particles cannot only be adjusted by reaction conditions, but also by appropriate additive concentrations, i.e. insufficient addition of stabilizer or controlled aggregation agents, so-called ‘assemblers’. A step in this direction was reported for the surface functionalization of previously stable titania nanoparticles with low molecular weight ligands (the ‘assemblers’), which predetermine the assembly behavior of the nanoparticles. Anatase nanoparticles with diameters of about 3 nm were coated with various multidentate ligands. [41,42] Upon redispersion in water and reversible deprotection of specific surfaces by refluxing at elevated temperatures, the nanoparticles self-organized into pearl-necklace structures several hundreds of nanometers in total length (Figure 4.10 a). Interestingly, these nanowire-like arrangements were composed of a continuous string of precisely ordered nanoparticles. HRTEM investigations gave evidence that the nanoparticles assemble along the [001] direction via oriented attachment, exhibiting monocrystal-like lattice fringes (Figure 4.10 b). Experimental data indicate that the anisotropic assembly is a consequence of the water-promoted desorption of the organic ligand selectively from the {001} faces of the crystalline nanosized building blocks, together with the dissociative adsorption of water on these crystal faces. The use of polydentate and charged ligands to functionalize the surface of titania nanoparticles thus provides a versatile tool to control the nanoparticle arrangement at the nanoscale. An illustraton of this oriented ‘polymerization process’ of nanoparticles is given in Figure 4.11: the anatase particles possess a truncated octahedral shape, with the two ligands representing remainders of benzylalcohol and the ligand trisma which had to be added to provide water solubility. These ligands only bind weakly to the flat tips (the [001] direction), which makes the whole system undergo polymerization in the c direction. Other interesting examples of oriented attachment include the synthesis of ZnO nanorods [43] and MnO multipods [44] (Figure 4.12).

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Figure 4.11 Oriented attachment of titania nanoparticles along the [001] direction after selective desorption of ligands from the {001} faces. (Image reproduced from [42] with permission of Wiley-VCH.)

In the case of ZnO, in a first step, quasi-spherical nanoparticles were prepared, followed by an increase of particle concentration by evaporation of solvent. A final heating step under reflux conditions induced the oriented attachment of the nanoparticles into pearl-chain-like structures, with perfectly aligned lattice planes (Figure 4.12 a, b, c and d), finally resulting in the formation of single crystalline nanorods (Figure 4.12 e, f). Bottle necks between adjacent particles were presumably filled up by the conventional mechanism of dissolution and growth of monomers. [43]

Figure 4.12 (a)–(d) HRTEM images of ZnO nanoparticle assemblies; (e) TEM image of ZnO nanorods; (f) HRTEM image of a part of such a rod; (g) TEM overview image of MnO multipods; (h) TEM of a MnO hexapod; ( i) TEM image of a MnO pentapod. (Images (a)–(f) taken from [43] with permission of Wiley-VCH. Images (g)–(i) taken from [44] with permission of the American Chemical Society.)


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The MnO multipods were achieved in a non-hydrolytic sol-gel process in a mixture of different surfactants. [44] TEM micrographs show predominantly hexapods (Figure 4.12 g and h), however bi-, tri-, quadro- or penta-pods (Figure 4.12 i) were found in the sample, too. The cores of the pods, as well as the pods themselves, are uniform in size and each arm is terminated by an arrow-like shape. Selected area electron diffraction (SAED) from isolated multipods proved their single-crystalline nature. Considering the cubic rocksalt structure of MnO, anisotropic crystal growth is unexpected, but any aggregation inherently generates anisotropy. To explain the found behavior, the authors proposed a two-step mechanism involving nucleation of truncated octahedra or cubes, followed by oriented attachment of the nanoparticles into the final pod morphology. As a matter of fact, nanoparticles matching the size of the tetrapod building blocks with a truncated octahedral shape were found in the earlier stages of reaction or by decreasing the reaction time. Other examples of the one-dimensional assembly of nanoparticles are discussed in the recent review by Tang and Kotov. [45] Nanoparticles can also arrange into ring structures by oriented attachment. [46] For this, a system with intrinsic hexagonal symmetry like CdS (wurtzite) can be applied. After selectively stabilizing the {001} planes with a suitable additive, hexagonal building units with six equal chances of attaching to neighboring crystallites are obtained. They can arrange to ring patterns by oriented attachment of the side faces of the hexagonal platelet by one of the possibilities outlined in Figure 4.13, which is certainly an idealized figure, but the corresponding rings of all three types were indeed observed experimentally. [46] These rings show the typical single crystalline diffraction pattern indicating the perfect orientation of the building units. This suggests that oriented attachment can also be used in a defined way for multifunctional building units. Such a strategy was recently applied to synthesize hollow cones via oriented attachment of ZnO in a hydrothermal process. [47] The formation process starts with the assembly of a hexagonal base ring followed by an upward growth, which constructs the sloped wall and finally a top closure is added to the tube structure, resulting in a hollow cone with one open end. Oriented attachment can also be combined with a template to direct the oriented attachment process, as recently reported by Yu and coworkers. [48] Reduction of SeO2 with ethylene alcohol in the presence of cellulose acetate in a solvothermal reaction yielded selenium rods, which resulted from adsorption of reduced Se on the cellulose acetate fibers followed by directed anisotropic Se growth and oriented attachment along the fiber template to the finally observed novel raft-like organic–inorganic superstructures containing very crystalline Se nanowires. Illustrative examples were also reported for the case of surfactants as additives. Oriented attachment was observed throughout the synthesis of BaSO4 in a reverse microemulsion of AOT, resulting in long fibers. [49,50] BaSO4 or the isomorphous BaCrO4 is a rather well-examined model system for nonclassical crystallization, as its equilibrium solubility over a wide range of pH conditions is very low, thus suppressing molecular redissolution/crystallization events. The presence of polymers clearly improves the quality of oriented assembly, as the nanoparticle surfaces are obviously ‘coded’ by the selective polymer adsorption for subsequent oriented attachment. An impressive example is the formation of BaSO4 or BaCrO4 fibers of about 30 nm in diameter, which are, however, defect free up to hundreds

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Figure 4.13 Schematic illustration of three novel self-tuning mechanisms for ring formation (viewed along the [0001] axis of the wurtzite CdS crystal): (i) a circular ring arrangement formed from hexagonal nano building blocks with alternative crystal plane segments of the {10-10} and {11-20} families; (ii) a hexagonal ring bound with low-Miller-index crystal planes of the {10-10} family; and (iii) a hexagonal ring bordered with higher-Miller-index crystal planes of the {11-20} family. Some of the inner or outer crystal planes are indicated to show correlations among the structures. (Image reproduced from [46] with permission of the ACS.)

of mm in length. These primary fibers further assemble to hierarchical fiber bundles and cones (Figure 4.14). Here, the sodium salt of polyacrylic acid serves as a very simple structure-directing agent for the room temperature synthesis of highly ordered cone-like crystals [8] or very long, extended nanofibers of BaCrO4 or BaSO4 with hierarchical and repetitive growth patterns. [52] Temperature and concentration variation allow the control the finer details of the architecture, namely length, axial ratio, opening angle, and mutual packing. [53] The observed [210] growth axis implies that the polyanion adsorbs onto all parallel faces to this axis on the nucleated nanoparticles, just leaving the negatively charged (210) faces free for direct interaction. This makes them the highest energy faces, which fuse together by oriented attachment to form the fibers. Such pictures make it obvious that the nanoparticle alignment has many similarities to a controlled ‘polymerization’ process, where the defined nanoparticles take the role of the organic monomers. Controlled nucleation or initiation in a short period of time sets the basis of a process that is terminated by the depletion of material or external stimuli, such as electric fields, or curvature or stress fields. In this way, monodisperse aggregates and superstructures can be created. This similarity between controlled assembly and


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Figure 4.14 Complex forms of BaSO4 fiber bundles produced in the presence of 0.11 mM sodium polyacrylate (M ¼ 5100 g/mol), at room temperature, [BaSO4] ¼ 2 mM, pH ¼ 5.5, 4 days. (Reproduced from [51] with permission of the Materials Research Society.)

controlled polymerization has also been stressed by other authors [37,54] (see also Section 12.1). The kinetics of formation of such structures have been studied in detail. At the early experimental stages, the polymer forms complexes with Ba2þ ions, which serve as ion depot for the subsequent crystallization. As a next step, amorphous nanoparticles and aggregates thereof can be observed, which occasionally attach to a polar surface and heterogeneously nucleate. [2,3] Further fiber growth occurs by attachment of nanoparticles to the (210) faces of the fibers, even if the supersaturation has already dropped to one, meaning that no further particles are nucleated (Figure 4.2). This is clear experimental proof for the nanoparticle- mediated crystal growth process. Interestingly, at least three different formation steps could be identified. At the early experimental stages and thus high concentration of building material, the fiber bundles nucleate with their broad tips on the polar surface, whereas at later stages, the bundles are nucleated from a single nucleation spot. At the end of the reaction and the lowest concentration of building material, striation patterns are observed, which indicate a simultaneous self-limiting growth of several fibers in a bundle (Figure 4.15). This example demonstrates how complex a nanoparticle-mediated crystallization reaction can be. Figure 4.16 shows another of these fibrous, self-organized superstructures composed of densely packed, highly ordered, almost parallel nanofibers of BaCrO4, which can be obtained with a phosphonated DHBC. [53] Also, BaCrO4 possesses a very low equilibrium solubility and is therefore apt to undergo particlemediated crystallization. A selective area electron diffraction pattern taken from such an

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Figure 4.15 BaSO4 fibers nucleated in presence of polyacrylate.: (a) – (c) Light microscopy images; (d) – (f) SEM images; (a), (d) Early stages of the experiment, S > 2, fiber bundles nucleate on the surface from their broad ends; (b), (e) Intermediate experimental stage, S ¼ 1:02–2.0, fiber bundles nucleate on the surface from a single spot; (c), (f) Final experimental stage, S ¼ 1, fiber bundles nucleate from a single point and show striations at their broad ends. ((a), (c), (d), and (f) reproduced from [3] with permission of the American Chemical Society.)

oriented planar bundle, as shown in Figure 4.16, confirms that the whole structure scatters as a well-crystallized single crystal where scattering plane-of-view is along the [001] direction and the fibers are elongated along the [210] direction, suggesting a perfect mutual two-dimensional order of the nanofibers. The atomic surface structure modeling data for the surface cleavage of the BaCrO4 crystal (hashemite) shows that the faces (1 22), (121), (120), (120), which are parallel to the [210] axis, contain barium ions slightly elevated from the surface. It is reasonable to assume that the negatively charged –PO3H2, –COOH groups of the PEO-b-PMAAPO3H2 block copolymer preferentially adsorb on these faces by electrostatic condensation and block these faces from further growth. In contrast, the surface cleavage of the (210) face shows no addressable barium ions on the surface (red lines); meaningful cuts are always rich in chromate, as shown in Figure 4.16. The negatively charged functional polymer group will certainly not favorably adsorb on this face, making the (210) face bare and exposed, and thus favorable for further growth by oriented attachment. The resulting nanoparticle fusion finally results in the defect-free fibers oriented along [210]. The very low solubility product of barium chromate (Ksp ¼ 1:17 1010 ), together with the already high speed of formation of these structures, are perfect indications that the superstructures do not really grow from a supersaturated ion solution, but by aggregation/transformation of the primary clusters. The whole mechanism of controlled assembly relies on the absence of flow, which would disturb the directed aggregation. Indeed, no fiber bundles or cones are obtained


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Figure 4.16 (a) TEM image of highly ordered BaCrO4 nanofibers obtained in the presence of PEO-b-PMAA-PO3H2, pH 5; (b) Electron diffraction pattern taken along the zone, showing the fiber bundles are well-crystallized single crystals and elongated along [210]; (c) Plot of the BaCrO4 crystal structure, as calculated with the Cerius2 software, viewed perpendicular to the [210] axis (indicated by the white dashed arrow). Blue ¼ Ba, Red ¼ O, light brown ¼ Cr. (210) faces (red lines) are always rich in negative chromate, while the top face is terminated by elevated Ba2þ -ions. ((a) and (b) reprinted from [53], and (c) from [55] with permission of Wiley-VCH.)

when the solutions are stirred continuously at room temperature after mixing the reactants. Instead, only irregular and nearly spherical particles are obtained. [8,52]. It is a relevant question to ask what type of particles can undergo aggregation, as, in principle, two scenarios can be envisaged (Figure 4.17) Most growth processes presumably start with the formation of amorphous nanoparticles, which are – as long as no precipitation is observed – colloidally stable. Small nanocrystals are homogeneously nucleated afterwards, which – due to their regular inner structure and the coherent addition of polarization and dipole moment – certainly have a higher Hamaker constant and a coupled lower colloidal stability than their amorphous precursors. With decreasing colloidal stabilization (either by concentration, reaction conditions, or the consumption of stabilizer), crystal–crystal addition will occur at first, as this is the colloidal species with the highest mutual attraction (Figure 4.17 a). After two crystals have been added, anisotropy has been generated, and it is a question of interaction energy where the next particle will add. If the addition is dipole controlled, the next particle will certainly add along the long axis of the particle, thus also explaining the formation of rods for systems with cubic crystal symmetry. [44] For the formation of multipods, it is the availability of faces only, i.e. each face of the center particle can add one nanoparticle branch. The second option, based on weaker interactions or higher

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Figure 4.17 (a) Crystallization of an amorphous nanoparticle and addition of this nanocrystal to a high-energy surface of an existing nanocrystal in a crystallographic register; or (b) addition of an amorphous precursor nanoparticle to a high-energy surface of a nanocrystal with subsequent crystallization (epitaxial crystallization).

destabilization, is the addition of an amorphous intermediate to a crystalline particle (Figure 4.17 b). Such a situation becomes relevant when the number of crystalline structures is simply too low to make binary crystal–crystal interactions very probable, or – in case of heterogeneous nucleation, if simply no free crystals are present in solution. Most of the above delineated very long nanofiber cases are based on very rare nucleation and extended growth processes, i.e. in most cases heterogeneous surface nucleation. Here, only amorphous nanoparticles can add to the growth center, and are then ‘directionally polymerized’, i.e. added at the tip of the fiber and recrystallized in an oriented fashion along the primary crystalline template pattern. In certain domains of reaction conditions with appropriate balance of reactant concentrations, both addition mechanisms can be observed, resulting, however, in different superstructure morphologies. Crystallization of vaterite in the presence of ammonium ions results in the formation of thin, sheet-like hexagons with exposed {001} faces. [56] In the first phase of reaction, only these hexagons undergo aggregation, leading to a stack-of-pancakes-like morphology (Figure 4.18 a–e). With progressing reaction and increasing size, the interaction potential of these superstructures increases (note that van der Waals interactions, as well as dipolar interactions, increase with the size of the object), until amorphous nanoparticles can also be added to the aggregate. Starting from this point of reaction, a curved outer shape with a coarse surface structure is obtained, determined by the nanoparticle aggregation probability and size. The recrystallization of the amorphous nanoparticles at the position of aggregation, however, still results in an apparent single crystalline scattering (Figure 4.18 f). Another example of the direct crystallization of amorphous precursor nanoparticles onto the surface of a crystal is vaterite formed in presence of an N-trimethylammonium derivative of hydroxyethyl cellulose. [57] In this case, vaterite hexagons can be produced that show single crystal diffraction patterns in SAED, although they show a rough surface, indicative of adsorbed nanoparticles. As ED proves that hexagons with a rough


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Figure 4.18 TEM pictures of hexagonal vaterite crystals formed from a 0.02 M CaCl2 solution after 18 h by adsorption of NH4þ onto the polar vaterite (001) face (a); and selected area electron diffractions of the upper (b) and lower (c) particles, respectively. Both are characteristic of the vaterite structure confirmed by the HRTEM image (d) and the power spectrum (e) of the upper particle. (f) SEM images showing the lens-shaped crystals of vaterite from a 0.02 M CaCl2 sample aged 18 h and a higher magnification showing the surface roughness (inset). (Reprinted from [56] with permission of American Chemical Society.)

surface are still composed of pure, single-crystalline vaterite, the growth of the superstructure seems likely to occur by the aggregation of the colloidal amorphous precursors onto the surface and their subsequent crystallization along the vectorial reference system of the superstructure (Figure 4.17 b). The vaterite hexagons themselves also grow from amorphous precursor particles, as shown below in the time-resolved sequence (Figure 4.19). These examples show that oriented attachment is an important step or tool for crystallization, which especially offers the advantage to produce very long, defect free one-dimensional single crystals. This is certainly of interest in materials science. Oriented attachment offers the possibility of making single crystalline fibers, which can be hundreds of micrometers long. The question whether these secondary fibers

Figure 4.19 Vaterite formed in the presence of N-trimethylammonium-modified hydroxyethyl cellulose. TEM, HRTEM, and ED patterns of samples obtained at the early formation stages. [Ca2þ] ¼ 10 mM, [polymer] ¼ 1 g/L. The reaction times are: (a) 0.5 h; (b) 2 h; and (c) one day. (Reprinted from [56] with permission of Wiley-VCH.)

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Figure 4.20 BaSO4 nanofibers formed in the presence of 0.11 mM sodium polyacrylate, [BaSO4] ¼ 2 mM, pH¼ 5.8 after 4 days. (a) and (b) Very long BaSO4 fibers with linear character formed at room temperature. (Reprinted from [52] with permission of the American Chemical Society.)

continue to aggregate to ternary fiber bundles is one of stabilization and interaction of the side faces by the polymer. Provided there is sufficient polymer concentration and stabilization power, completely disaggregated fiber morphologies can be synthesized, too (Figure 4.20). Similar fibers, much smaller in size, however, and less perfect, can also be produced by classical crystallization and face-selective polymer adsorption. This is demonstrated by the example of hydroxyapatite (HAP) fibers, which grow controlled by aggregates of special block copolymers, adsorbing to all faces parallel to the c-growth axis (Figure 4.21). [58] Thin and long crystalline HAP fibers were obtained (the single crystalline nature of the fibers could not be shown due to their small diameter of only 2–3 nm), being, in this case, potentially interesting for bone and tooth repair materials. The fibers clearly show occasional branches, which can be attributed to a noncontinuous polymer layer, so that branching can occur at the noncovered sites on the crystal, as result of the ion-based classical growth mechanism. Nanoparticle adsorption on a fiber is less prone to defects in the adsorbed polymer layer for simple size and interaction reasons. Here, the advantages for the control of the particle-based growth mechanism compared to the ion-based one become directly obvious. All these examples nicely illustrate the potential of oriented attachment for the preparation of anisotropic single crystalline nanostructures. However, this strategy is only successful if the attachment process can be performed in a controlled manner, that is uncontrolled aggregation or flocculation has to be suppressed; the primary particles have to be ‘weakly destabilized’. The list of clearly identified cases of oriented attachment is getting longer and longer and comprises a variety of chemical systems, such as TiO2[9] FeOOH, [60–62] Co3O4, [63] CuO, [64,65] CoOOH, [66] SnO2, [40] CeO2, [67,68] Ag, [69] ZnO, [43] ZnS, [36,70] CaCO3, [56,57] PbSe, [71] and Pt [72] Cd(OH)2/CdO. [73] This list is far from


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Figure 4.21 Classical (a) vs. nonclassical crystallization (b), (c): (a) Crystallization of Hydroxyapatite (HAP) fibers from block copolymer aggregates, [58] where the block copolymers adsorb onto all faces parallel to the HAP c-growth axis, resulting in whisker structures with occasional branches (see arrows). (b), (c) Formation of single crystalline and defect-free BaSO4 [210] oriented fiber bundles by the process of oriented attachment, in experiments described in [8,52,53] (Figure reproduced from [1] with kind permission of Editorial Universitaria, Universidad de Chile, Santiago, Chile.)

being complete, as the number of examples is rapidly increasing. However, a large body of examples was recently summarized in review papers. [37,74,75] Very recently, oriented attachment was reported for the case of heterostructures of the crystallographically similar SnO2 and TiO2 systems. [76] This example shows that the oriented attachment mechanism is not limited to assembly of crystallographically homogeneous nanoparticles, as long as the nanoparticles are crystallographically similar. This possibility opens up a number of possibilities for the synthesis of new hybrid materials – especially semiconductors, as these are suitable for the assembly of low dimensional structures by the oriented attachment mechanism. It is also possible to produce core-shell structures via a combination of classical crystallization and oriented attachment, as reported for PbSe nanowires produced by oriented attachment, which were subsequently coated by PbS by classical growth. [77] Here are certainly a large number of further exciting possibilities for the application of the oriented Attachment mechanism. Oriented attachment is not only described for the zero- to one-dimensional case (Figure 4.22 a), [43,59] and the one-dimensional case (Figure 4.22 b), [78] but can also occur in two-dimensional (Figure 4.22 c) [43,56,79] and three-dimensional cases (Figure 4.282 d and e), [64,80] as exemplified above and shown in Figure 4.22. The three-dimensional case of oriented attachment directly leads to the mesocrystal concept, as is described in the next section.

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Figure 4.22 Various organizing schemes for self-construction of nanostructures by oriented attachment. (Image taken from [80] with permission of Wiley-VCH.)

4.4 Mesocrystals As this book will describe mesocrystals in detail in several dedicated chapters, the current section only introduces some basic principles and the most important properties of mesocrystals. The notation ‘mesocrystal’ is an abbreviation for ‘mesoscopically structured crystal.’ We define mesocrystals as colloidal crystals that are built up from individual nanocrystals and are aligned in a common crystallographic register (see also Figure 4.1 c). A mesocrystal usually scatters X-rays like a single crystal. [81] It can be molded into any outer shape, including novel engulfing symmetries or even curvature. This definition of a mesocrystal is somehow too strict, as we will see later, as a continuous transition between a mesocrystal and a polycrystalline aggregate with disordered building units can be observed. The above mesocrystal definition is nevertheless very useful to cover most of the known mesocrystals. A good model case for a mesocrystal from biominerals is the sea urchin spine presented in Section 3.1, Some Biomineral Examples, but mesocrystals also exist in many other fields, apart from biominerals. Mesocrystals in technology are, on the broader scale, available via different strategies like crystallization in gels, in the presence of


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Figure 4.23 Calcium carbonate crystals precipitated from a solution containing 1 mM Ca and PEO22-PNaStS49 at a concentration such that the [Ca]:[S] molar ratio was 1.25:1. (Image kindly supplied by Dr. Fiona Meldrum, School of Chemistry, University of Bristol. For further details about these mesocrystals, see [82])

polymer additives, via solid-state reactions, by guiding electric or magnetic fields, but also by kinetically ‘extremely fast’ precipitations in the absence of additives. Figure 4.23 depicts a nice example of a calcite mesocrystal, which appears to be composed of two twinned tetrahedra slotted into each other. It is obvious that such morphology cannot be generated for a calcite single crystal, with its typical rhombohedral shape (see Figure 2.2). The rough surfaces already show the nanoparticle building units, which are all aligned in a crystallographic register. In Nature, there are, however, other packing and interaction rules than just placing primary units in a regular, translational invariant, periodic three-dimensional order, leading to facetted mesocrystals. The joint primary fields can be bent or toroidal (especially when electric or magnetic interactions are involved), and also the structures resulting from those addition rules show all the characteristic features of mesocrystals, except three-dimensional translational invariance and the resulting single crystal properties (see Figure 4.24). In the following, we will also name these mesoscopically ordered, but not mesoscopically crystalline structures as ‘mesocrystals’ (alternative ‘bent or splayed mesocrystals’ although the notation might be conflicting per se, as the structures do not follow Euclidian geometry. Mesocrystals can, in principle, not only be formed as a stabilizer/nanocrystal twophase system, but also from any other two-phase system, where one phase is the mutually oriented crystalline nanoparticle phase. The other phase can be any other type of phase – the most important and relevant being an amorphous phase in between the aligned nanoparticle crystals. The existence of such thin and stable amorphous layers between tectonic crystals was recently proven by a HRTEM study of synthetic aragonite [84] and of Haliotis Laevigata

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Figure 4.24 Example of a crystalline BaSO4 mesostructure, the so-called dumbbell. [83] Left: TEM thin cut; Right: SEM image. All tectonic nanocrystals are organised, but the geometry is not Euclidian. This means that such structures, although highly ordered, will not show the scattering of a single crystal. (Images reproduced from [83] with permission of the American Chemical Society.)

gastropod nacre. [85] It was suspected that this layer was formed by accumulation of impurities throughout zone crystallization, which prevents further crystallization, in analogy to the zone melting process in metallurgy. A composite material between aligned single crystalline nanoparticles embedded in an amorphous layer containing the impurities and including polymers therefore seems to be an intriguing hypothesis for biominerals, such as sea urchin spines, which scatter like single crystals (the aligned nanocrystal phase), but fracture like an amorphous glass (the interparticle phase). Probably, mesocrystals are much more common than assumed so far, but it is difficult to detect them, as they may be misinterpreted as single crystals due to their single crystal scattering properties and their well facetted appearance. [81] Additionally, if the surface of the nanocrystals is not sufficiently stabilized, a mesocrystal can easily transform to a single crystal by crystallographic fusion (Figure 4.1), as the nanoparticle units are already crystallographically aligned so that a crystallographic fusion is thermodynamically favored. Therefore, literature evidence for mesocrystals is mainly indirect, and in many cases mesocrystals are not recognized as such in the literature or named differently.

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5 Self-Assembly and Self-Organization As a critical feature in structure formation seems to be ‘self’-processes, this chapter tries to introduce these ‘soft’ notations in a cohesive manner. Similarities between parallel crystallization and micelle formation or liquid crystalline transitions, which are also ‘cooperative’ and characterized by the spontaneous emergence of order are underlined. An important aspect of mesocrystal formation are so-called self-processes, which are spontaneously occurring events leading to structure formation. The notations ‘selfassembly’ and ‘self-organization’ can be used in a variety of ways [1–6] and are sometimes even used interchangeably. We understand self-assembly as a structure-generating process of a chemical system near a local equilibrium state; usually self-assembly sets in with a certain set of chemical conditions or physico-chemical parameters. Self-assembly can occur between components of the same type (homo-assembly), but also between components of different type (hetero-assembly). A good example for the first case is micelle formation, for the second the pairing between two nucleotide strands. In many cases, self-assembly can follow a sequence and a hierarchy of assembly steps, as the first assembly structure (which did not exist before assembly) shows a more amplified tendency towards specific interactions, thus spontaneously leading to a cascade of structure formation steps. This is the general case in mesocrystal formation, but also in many other examples of hierarchical structures. Self-organization is understood to be a dynamic phenomenon, involving transport and reactions. Self-organization is found for chemical systems that are capable of generating structure and order along reaction pathways or reaction coordinates, and such systems are usually dynamically metastable. Contrary to self-assembly, self-organization can also generate temporal structure and order. A good model case for self-organization is the spatial–temporal patterns generated by the Belousov–Zhabotinsky reaction. Supramolecular chemistry or colloid chemistry has reached a level where selfassembly can be encoded and predicted by many of the primary components; self-organization under simultaneous formation of meaningful structures is, in our Mesocrystals and Nonclassical Crystallization Helmut Co¨lfen and Markus Antonietti # 2008 John Wiley & Sons, Ltd

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opinion, however, still out of the reach of the hands of chemists. Numerous biological structures result from self-assembly, and a living system offers the ultimate in self-organization. They provide inspiration for chemists and physicists, hopefully enabling the mimicking of biology in the hierarchical aspects of chemical systems (‘biomimetic molecular systems’). There also has to be a – admittedly sometimes diffuse – borderline between mere aggregation (e.g. as found by the homo-aggregation of milk proteins in the formation of cheese) and self-assembly. An accepted way to differentiate aggregation from assembly is the principle of cooperativity. This principle was introduced for surfactant micelles and mesophases [7], but could also be nicely extended to the process of ionic self-assembly [8]. Cooperativity is usually identified by analyzing a system near the critical aggregation/ assembly transition, which can be driven by concentration, temperature, or another adjustable parameter. The parameter b denotes the fraction of component bound to the assembled structure: b is therefore zero below the assembly transition, whereas it goes to one well above the transition. Cooperativity is now identified as the steepness of the b-curve against the variable parameter. This is exemplified for the case of selfassembling surfactant dye complexes (ionic self-assembly ISA), which are illustrative model cases for cooperativity beyond micelle formation (Figure 5.1). The cooperativity u is now determined, using the Satake–Yang approach [9] from the slope at b ¼ 0:5 as: ðdb=d ln Cf Þx¼0:5 ¼ u1=2 =4

ð5:1Þ

Cooperativities can easily be as high as 1000, translating into the fact that no less than 1000 components self-assemble to an organized superstructure at the same critical point! In the given ISA case, the system AR27 (a charged dye)/dodecyltrimethylammonium exhibits a cooperativity of 600–800, underlining the spontaneous formation of rather extended structures at this distinct concentration. As the variable parameter is, in many cases, an in situ reaction coordinate, such curves are not always straightforward to determine. However, they nicely illustrate the concept of cooperativity. 1.0

AR27/DTA

0.8 OG/DTA

0.6 ß

0.4 0.2 0.0 0.0

0.2 0.4 0.6 0.8 Free Surfactant / mM

1.0

Figure 5.1 Two cooperative binding curves of the amount of bound surfactant b against surfactant concentration. The dye AR27 shows the immediate onset of surfactant binding at a distinct concentration in reversible fashion. The dye OG, on the other hand, undergoes cooperative structure formation, coupled with crystallization casting a slight hysteresis.

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In many cases, cooperative behavior also comes with a so-called closed aggregate structure, i.e. the system just exists either as the monomer or as the aggregate, usually being composed of at least the number of components identified by the cooperativity parameter. Especially dimers, trimers, or other small oligomer species are not stable in such cases and can be excluded from kinetic and thermodynamic considerations. This originates from the fact that the free energy gain of aggregation is not based on the binary interaction potential of two components, but in the formation of the collective ensemble. It is obvious that self-assembly is closely related to the formation of a new phase from another, and this is why it is sometimes also called ‘microphase formation.’ The question of whether micelle formation is a first-order or a second-order phase formation process is controversial, but as a heat of formation is not needed, at least some second-order character can be assumed. This is why fluctuation theory (discussed below in more detail) can at least explain how hundreds of molecules ‘spontaneously’ meet and form a new structure; slightly before the critical point of structure formation, inhomogeneous concentration distributions are stable. These stable concentration fluctuations are important for cooperative structure formation as such. Controlled structure formation by self-assembly and self-organization is set in stark contrast with classical aggregation. Aggregation of components or colloids sets in when the stability, expressed usually by a DLVO type binary interaction potential, does not provide sufficient repulsion to keep two objects separated, i.e. it is mainly based on binary interactions. Figure 5.2 depicts such binary interaction potentials, one for a stable system, the other for a weakly unstable system.

Figure 5.2 Binary DLVO interaction potentials (solid lines): (1) for a stable system; (2) for a weakly unstable system. Particles are forced to move to the position of minimum energy. For the unstable situation, this results in contact pairs or weakly separated particles (the first minimum).

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As a result, fractal aggregates are usually formed [10], which are rather badly ordered and also broadly distributed in their structure. In a binding curve, as depicted in Figure 5.1, aggregation would be identified as a very broad process without a clearly defined onset. For particles with an anisotropic interaction potential, introduced, for instance, by anisotropic polarization interactions of a crystal, the stabilization can fail face-by-face or direction-by-direction, thus leading to directed aggregation. It is also common sense in colloidal science that near critical stability may depend on size, i.e. while smaller particles are still stable, the attraction of larger entities can become too large so that they act as localized centers of instability. This nucleated aggregation is well known as a failure mechanism of emulsions, but is valid for crystalline systems in the same way. Near a critical stability, it needs only a few bigger species to destabilize a formerly completely stable nanocrystal dispersion.

References 1. J.-M. Lehn, in Supramolecular Chemistry, VCH Verlagsgesellschaft mbH, Weinheim, 1995, pp. 161. 2. H. Wennerstro¨m and D. F. Evans, The Colloidal Domain where Physics, Chemistry, Biology and Technology meet, VCH Publishers, Inc., New York, Weinheim, Cambridge, 1994. 3. C. Faul and M. Antonietti, Adv. Mater. 2003, 15, 673. 4. I. Satake and J. T. Yang, Biopolymers 1976, 15, 2263. 5. D. W. Schaefer, Science 1989, 243, 1023.

6 Colloidal Crystals with Spherical Units: Opals and Colloidal Nanocrystals The organization of well-defined nanosized objects into regular arrays – although via nondirectional forces – is well known and leads to opals (naturally) or colloidal crystals (in vitro). As there are many similarities, but also certain differences, between colloidal crystals and mesocrystals, this chapter shortly summarizes the formation and structural features of colloidal crystals. Mesocrystals are a special case of colloidal crystals. Opals, 3D-colloidal crystals with spherical subunits (Figure 6.1 a), have been catching human attention from the beginning of civilization, as the colours depend on the viewing angle and give the ornaments luster and a ‘meta-appearance’. The formation of natural opal is quite straightforward from its inner construction: silica sols with nanoparticle diameters in the optical range are formed in water, are separated by hydrodynamic forces and flows in lakes and rivers into monodisperse particle fractions deposited at certain locations, which later on densify and crystallize into the ordered arrays. As the regularity of these crystals is in the optical range, colour specific reflectance can be expected, according to Bragg’s law. For the mechanistic understanding of opal formation, extensive work has been performed on monodisperse latex dispersions to learn about the conditions of crystallization (e.g., see [2,3]). Contrary to mesocrystals, the best colloidal crystals are obtained in the absence of interactions, at a distinct volume fraction, and order formation is predominantly due to gain in entropy of the overall system, very similar to the Onsager theory of liquid crystallinity. Opals and their replicas, inverse opals, have received considerable attention in recent years, as these superlattices exhibit new and exiting properties, like photonic band gaps [4] or altered electronic and optical properties as in semiconductors [5]. Besides colloidal Mesocrystals and Nonclassical Crystallization Helmut Co¨lfen and Markus Antonietti # 2008 John Wiley & Sons, Ltd

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Figure 6.1 Example of colloidal crystal in Nature: A high value natural opal, a 3D cubic structure of spherical silica nanoparticles.

crystals made from silica as a convenient model case, the colloidal crystallizations of semiconductor and metal nanoparticles have been intensively investigated, due to their electronic and optical applications [6–10]. The latter systems can be regarded as spherical core–shell nanoparticles, with an inorganic or metal core and an organic surfactant/ligand shell, both playing a role for the crystallographic symmetry of the superlattice. Even colloidal crystals from two different nanocrystal systems can be prepared [10]. The control of these structures has meanwhile reached amazing sophistication, as demonstrated in Figure 6.2 for the binary colloidal crystals made of PbSe and Au nanoparticles. Such colloidal structures can, in principle, combine the properties of its constituents. If inorganic and slightly prolate building units like CdSe are used, an almost perfect crystallographic alignment of the nanocrystals with respect to their internal structure is detected [5] – a feature which is also observed in mesocrystals. As these colloidal crystals are sufficiently different from the mesocrystals presented here, and certainly worth a separate monograph, we can only direct the interested reader to some excellent available reviews on their formation and properties, and also the binary systems [11–13]. Contrary to the mesocrystal formation described below, all these colloidal crystals are generated by (partly highly sophisticated) drying processes at high volume fractions, while mesocrystals can easily form at concentrations as low as 0.2 g/L. For colloidal crystals, there are no long-range attractive interactions driving structure formation, but sheer optimization of packing and the coupled entropy gain. This is why colloidal crystals teach a lot about structural features and potential applications, but not how mesocrystals form.

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Figure 6.2 TEM micrographs of Binary Nanoparticle Superlattice (BNSL) isostructural with AuCu formed by 7.6 nm PbSe and 5.0 nm Au nanoparticles: (a) TEM overview of the (001) projection; (a, inset), small-angle ED pattern of the (001) plane; (b) as in (a) but at high magnification; (c) TEM overview of the (100) plane. TEM micrographs of AuCu-type BNSL formed by 6.2 nm PbSe and 5.0 nm Au nanoparticles: (e) 3D sketch of the AuCu unit cell (SG 123, P4/mmm). (f), (h) Depictions of the (001) and (100) planes, respectively; (g), (i) Depictions of the minimum number of layers in the (001) and (100) planes, respectively, leading to the formation of patterns identical to those observed; Inset in (i), small-angle ED pattern measured from the (100) plane; (k) TEM micrograph of the (100) projection of AuCutype BNSL formed by 5.8 nm PbSe and 3.4 nm Ag NPs; (l), (m) TEM images of the (100) projection containing nanoparticle ‘antiphases’; (n) Depiction of an antiphase boundary. (Taken from [11] with permission of the American Chemical Society.)

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The importance of control throughout slow drying of a colloidal dispersion to force nanoparticle self-organization was illustrated in a series of original contributions. A common problem is the so-called ‘coffee stain effect’ which gives the well-known rings at the perimeter of an evaporating droplet where the solvent evaporates fast, as well as the material accumulation in the center. As one example, a fast, uniform material deposition in a regular array by simple drying of a droplet was recently proposed by Bigioni et al [14,15]. This method ensures rapid crystallization of nanoparticles into a single monolayer-thick two-dimensional film. If the interparticle interactions allow for rotation and alignment of the nanoparticles into a crystallographic register, two-dimensional mesocrystals can be readily formed. For the fast formation of nanoparticle monolayers, a high evaporation rate, as well as a finely tuned interface stickiness are crucial [15]. When the solvent molecules evaporate faster from the top surface of a concentrated dispersion drop than the remaining nanoparticles at the now concentrated surface, layers can diffuse into the droplet interior, a steep concentration gradient is formed and the nanoparticles begin to segregate at the droplet–air interface. Addition of a trace amount of surfactant makes the droplet–air interface sticky for the nanoparticles resulting in an enrichment of the nanoparticles in the interface region. In the presence of an attractive particle–interface interaction, rapid early-stage evaporation dynamically produces a two-dimensional arrangement of nanoparticles at the liquid–air interface, from which nanoparticle islands nucleate and grow. Once a two-dimensional island is crystallized, surrounding nanoparticles will attach to the already existing nucleus forming a two-dimensional crystal. This self-assembly mechanism produces monolayers with exceptional long-range ordering that are compact over macroscopic areas, despite the far-from-equilibrium evaporation process. Ordering of the nanoparticles into a crystallographic register leads to colloidal crystal formation over larger areas of several mm2, as shown in Figure 6.3.

Figure 6.3 Micrograph of a typical monolayer produced by drop-casting 10 ml of a solution of dodecanethiol-ligated 6 nm gold nanocrystals onto a 3 mm 4 mm substrate. The upper left inset schematically shows the arrangement of two neighbouring nanocrystals in the monolayer. The lower right inset is a fast Fourier transform of the image. (Image reproduced from [14,15] with permission of Nature Publishing Group.)

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Figure 6.4 An express route to two-dimensional colloidal crystallization of nanoparticles from solution. The solvent from a droplet of dilute nanoparticle solution, freshly cast on an Si3N4 wafer, begins to evaporate. This leads to (a) enrichment of the slowly diffusing nanoparticles everywhere along the droplet’s receding surface; and (b) culminates in two-dimensional supersaturation when the interfacial layer is slightly sticky, enhanced by trace (100 ppm) of surfactant molecules; (c) Lateral diffusion generates nanoparticle nucleation and reversible growth of ‘monolayer islands’, as monitored continually by optical microscopy; (d) The nanoparticles settle into a single, wrinkle- and stain-free sheet that, after prolonged drying, can be identified as a monolayer covering the substrate. Note, for clarity, the dodecanethiolate groups covering the nanoparticles are not shown. (Image reproduced from [15] with permission of Nature Publishing Group.)

The whole structure formation mechanism is illustrated in Figure 6.4 and consists of four steps. This method should be a fast and versatile method for the production of large area twodimensional colloidal crystals after fine tuning of a high evaporation rate with the interface stickiness of the nanoparticles.

References 1. J. V. Sanders, Philosoph. Mag. A Phys. Condensed Matter Struct. Defects Mech. Prop. 1980, 42, 705. 2. A. van Blaaderen and P. Wiltzius, Adv. Mater. 1997, 9, 833. 3. K. P. Velikov, C. G. Christova, R. P. A. Dullens, and A. van Blaaderen, Science 2002, 296, 106. 4. H. Higashijima, S. Kohiki, S. Takada, A. Shimizu, and K. Yamada, Appl. Phys. Lett. 1999, 75, 3189. 5. C. B. Murray, C. R. Kagan, and M. G. Bawendi, Science 1995, 270, 1335. 6. C. P. Collier, T. Vossmeyer, and J. R. Heath, Ann. Rev. Phys. Chem. 1998, 49, 371. 7. C. B. Murray, C. R. Kagan, and M. G. Bawendi, Ann. Rev. Mater. Sci. 2000, 30, 545.

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8. C. B. Murray, S. H. Sun, W. Gaschler, H. Doyle, T. A. Betley, and C. R. Kagan, IBM J. Res. Devel. 2001, 45, 47. 9. H. Weller, Phil. Trans. R. Soc. Lond. A 2003, 361, 229. 10. F. X. Redl, K. S. Cho, C. B. Murray, and S. O’Brien, Nature 2003, 423, 968. 11. E. V. Shevchenko, D. V. Talapin, C. B. Murray, and S. O’Brien, J. Am. Chem. Soc. 2006, 128, 3620. 12. Y. Yin and A. P. Alivisatos, Nature 2005, 437, 664. 13. E. V. Shevchenko, D. V. Talapin, N. A. Kotov, S. O’Brien, and C. B. Murray, Nature 2006, 439, 55. 14. T. P. Bigioni, X. M. Lin, T. T. Nguyen, E. I. Corwin, T. A. Witten, and H. M. Jaeger, Nature Mater. 2006, 5, 265. 15. R. L. Whetten, Nature Mater. 2006, 5, 259.

7 Mesocrystal Systems This chapter describes the central objects of the book, the mesocrystals. It summarizes some general features and properties of mesocrystals. In addition, it lists some model cases where mesocrystals have previously been found, either in synthetic one-, two-, or three-dimensional alignment, but also in biomineralization. These case studies also give the collected evidence we need to elaborate the general mechanisms and conditions affecting mesocrystal formation.

7.1 Mesocrystals and Their Properties Mesocrystals are a very interesting generalization of colloidal crystals, as they extend from the currently known colloidal crystals with monodisperse and spherical tectons, to those with nonspherical building units and sometimes larger polydispersity in size and structure, which offer new possibilities of superstructure formation. It is clear that nonspherical nanoparticle building units with structural multiplicity should provide additional opportunities for self-assembly, like LEGO1 – a kit with more than one structural element simply has a higher flexibility of construction. Some of the characteristic properties have already been mentioned: mesocrystals show the typical three-dimensional scattering patterns of a single crystal in electron diffraction and WAXS, and tensorial optical properties (such as birefringence) like those of almost perfectly aligned crystal domains can be detected. The mechanical properties are unusual: mesocrystals exhibit fracture surfaces like glasses, but are more ductile and tough than the corresponding single crystalline material. This is why they are so favourably exploited in biominerals. Figure 7.1 shows a mesocrystal made of DL-alanine without any additives, presenting some of the typical features, such as single crystalline scattering, but rough surfaces and fracture, internal porosity and grain boundaries. For potential applications, the inherent porosity of mesocrystals is also worth consideration. The closed, intracrystalline porosity is good for thermal and dielectric Mesocrystals and Nonclassical Crystallization Helmut Co¨lfen and Markus Antonietti # 2008 John Wiley & Sons, Ltd

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Figure 7.1 DL-alanine mesocrystals obtained in supersaturated solution at 15 C for 2 h with the pH of the solution at 6.2: (a) SEM image of a fracture surface showing the inner nanoparticular mesostructure; (b) typical image of a single crystal XRD analysis. (Images reproduced from [1] with permission of the American Chemical Society.)

insulation, while the accessible open pore porosity of some systems of up to 400 m2/g enables their use as sorption materials or medical delivery systems. Finally, the combination of two very different materials on the mesoscale (which would never mix on the nanoscale) will result in multifunctional hybrids where, for instance, magnetic and optical properties can be combined in one system, or dielectric dissipation and mechanical toughness in one film. The borderline between organic and inorganic materials can be further disintegrated, as, for instance, dye molecules within inorganic crystals are more stable and more efficient pigments, and one might list many other similar opportunities for application. It is simply that mesocrystals offer a new principle for chemistry, allowing bonding of very different systems to occur on the mesoscale, and at the same time having the advantages of a spontaneous, highly reproducible and simple process.

7.2 Early Reports on Mesocrystals In general, although particle aggregates have been observed since the dawning of crystallization experiments, particle aggregates with defined morphology and size were much less reported. For a review by one of the pioneers in this field, Egon Matijevic, see [2]. A list of early mesocrystal reports, however, cannot be complete, as it is very difficult to trace mesocrystals in the literature – especially in the older literature. At best, they are found under headings such as ‘topotactic reaction fabric,’ in cases where they were derived from a topotactic solid-state reaction [3], ‘Schiller layers’ [4–6] or described as ‘tactoids’ [7]. Tactoids were initially defined as droplets of a nematic liquid crystalline phase that under suitable conditions form in dispersions of elongated colloidal particles [8]. Rediscovery of mesocrystal systems in the literature is therefore a matter of luck, because, usually, the mesocrystals are only intermediates in the formation pathway of a single crystal, or are misinterpreted as single crystals deduced from their diffraction properties.

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Figure 7.2 Electron micrographs of rodlike Ce(IV) basic sulfate particles obtained by aging 2:5 109 mol/dm3 Ce(SO4)2, 4.5mol/dm3 H2SO4 and 0.45 mol/dm3 Na2SO4 at 90 C for 12 h. (Figure reproduced from [12] with kind permission of the American Chemical Society.)

One early indication for the existence of mesocrystals (in this paper named tactoid-like aggregates of nematic symmetry) was deduced from the toothed nanoparticle contours of tungstic acid particles, but was not proven by further analysis [9,10]. More early evidence of mesocrystal intermediates was deduced from the porous internal structure of BaSO4, [11] which – according to the classical crystallization theory – should crystallize to a monolithic single crystal. However, the analytical possibilities for the observation of the mesocrystal structure, such as high quality electron microscopy, were limited those days. A very illustrative early study of mesocrystals, although not exhibiting flat external faces, was reported by Matijevic et al., who, in a synthetic study on various Ce(IV) compounds, analyzed the structural patterns in the absence of any organic additives [12]. Figure 7.2 shows some of the resulting rod-like superstructures. These structures are obviously oriented nanoparticle aggregates without a wellfacetted external morphology. Nevertheless, the single rod- or plate-like nanoparticles mutually align with high positional and vectorial precision towards a reproducible superstructure. Also, Hsu reported on superstructure formation of the same compound [12]. For CuO, the aggregation from primary nanoparticles could be revealed in a kinetic study [13]. This paper already indicates the general self-assembly mechanism for mesocrystals, although a common faceting of the nanocrystal aggregates is predominately lacking (Figure 7.3 right). For CeO2, a two-dimensional hexagonal platelet has formed from not too homogeneous and not too well-defined globular nanoparticles. Obviously, the cooperative minimization of mutual interaction forces drives the single nanoparticles to form a super-hexagon. It is remarkable that CeO2 possesses a primitive triclinic unit cell, i.e. it has no hexagonal

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Figure 7.3 (Left) Magnified TEM of a minor part of CeO2 precipitates obtained by aging 1:5 103 mol/dm3 (NH4)2Ce(NO3)6, 6:4 102 mol/dm3 in H2SO4 and 1:6 102 mol/ dm3 in Na2SO4 pH 1.4 at 90 C for 12 h. (Figure reproduced from [12] with kind permission of the American Chemical Society.) Right: CuO particle aggregates obtained via double jet precipitation [13] reproduced with permission of Academic Press Inc.

symmetry axis. It will turn out below that this is a rather general observation for mesocrystals; very often they have a higher symmetry than their constituting tectons. In these early experiments, the hexagon superstructure, however, just represented a minor part of the precipitates, and its formation mechanism remained as unclear as for the rods in Figure 7.2. It was, however, an early observation of crystalline superstructures with an external structure and symmetry differing from that of the nanoparticle building units. The structures are usually very well ordered within each nanoparticle and on the overall scale, but are not too well ordered and full of inclusions and pores on the scale of the primary nanoparticles and slightly above. For CuO, elliptical mesocrystals were reported (Figure 7.3 right) [13], which interestingly have the shape of the tactoids first described by Zocher [4,6]. (see also Section 7.12, Liquid Crystals, Tactoids, Somatoids and Schiller layers). For the sake of completion, it should be mentioned that very similar observations on the oriented aggregation of CuO were just recently republished [14], although with a more precise analysis of the ongoing phenomena. In 1986, mesocrystals with even higher definition were reported for CaCO3 made in silica gels [15]. Here, fibers built from a set of cleaved calcite rhombohedra arranged along their c-axis were reported. Although each fiber was an aggregate of crystalline subunits, the observed behavior by polarization microscopy was that of a single crystal, indicating the high orientational alignment of the subunits in this one-dimensional mesocrystal [15]. Interestingly, these mesocrystal fibers were only an outer part of a hierarchical structure, the so called ‘sheaf of wheat’ morphology [15]. From different sheaves, mesocrystal fibers with a very different morphology splayed out radially from the sheaf center. Again, the mesocrystals behaved like single crystals in polarization microscopy, but exhibited a complicated morphology (Figure 7.4). The reason for this unusual aggregate morphology remained unexplained, although the morphogenesis process was assumed to be of importance.

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Figure 7.4 CaCO3 formed in a silica gel. Upper left: SEM view of a set of serrated fibers and a diagram of one. Upper right: Enlarged view of the left image showing a morphological unit formed by two domes. Lower: Diagrammatic representation of a morphological unit of the structures shown in the upper figure, revealing the orientation of the aggregating rhombohedra. PS ¼ planar surfaces, KS ¼ kinked surfaces, SS ¼ stepped surfaces. (Reprinted from [15] with permission of Elsevier Science publishers B.V.)

Other early reports on crystal mesostructures can be found in the area of topotactic solid-state reactions [16]. Lotgering described the formation of mesocrystals of hexagonal ferrites by a topotactic solid-state reaction of ferromagnetic starting oxides, which were oriented by magnetic fields (see also Section 7.11. Mesocrystals Formed Via SolidState Reactions for more details) [16]. These topotactic reactions are advantageous for mesocrystal formation, because they are solid-state reactions, which preserve the crystal orientation of the initial phase. Therefore, a number of topotactic reactions leading to mesocrystals are reported, which can be found in the literature under ‘topotactic (micro) structures’ or ‘topotactic reaction fabrics.’ Examples are the pseudomorphic topotactic reaction of brucite Mg(OH)2 to periklas MgO mesocrystals [17,18], the formation of Eu3O4 by a topotactic solid-state reaction of LiEu3O4, [19,20], the formation of maghemite Fe2O3 by thermal dehydration of lepidocrite g-FeO(OH) and controlled oriented deposition inside the matrix of the needle-like educt [21,22], and the oxidation of Mn(OH)2 to b-MnO(OH) mesocrystals [23].

7.3 One-Dimensional Mesocrystals One- and two-dimensional particle arrays were reported by Li and Mann. The authors used a surfactant microemulsion-mediated approach. Here, presumably, a combined action of nanoparticle crystallization and surfactant interactions led to the self-assembly

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Figure 7.5 TEM image showing ordered chains of prismatic BaCrO4 nanoparticles prepared in a reverse microemulsion. Scale bar ¼ 50 nm. (Reproduced from [24] with kind permission of Nature Publishing Group.)

of remarkable structures with one-dimensional character. A surfactant-mediated mechanism was suggested for the growth of these structures, as shown in Figure 7.5 [24]. It was speculated that part of the ordering comes from the face selective surfactant adsorption onto BaCrO4, followed by the formation of surfactant bilayers in between the prismatic nanoparticles. It was suggested that the BaCrO4 growth occurs in association and concurrent with the self-organization of stacked micellar aggregates and not through sequential attachment of individual nanoparticles. Another approach towards one-dimensional mesocrystals without application of any additives was reported for the assembly of Mn-doped PbSe mesocrystals, which assembled in a high temperature reaction via face-to-face or edge-to-edge assembly of octahedral nanocrystalline building units [25]. Figure 7.6 shows typical electron micrographs of the one-dimensional mesocrystals formed at early stages, revealing a [001]-oriented array structure with single crystalline scattering behavior, as typical for mesocrystals. It is remarkable that no defects were observed and that the one-dimensional mesocrystals showed a uniform thickness and assembly pattern of the nanocrystal building units. From Figure 7.6 d–g, it becomes obvious that in the early stages the particles assemble in a face-to-face manner via the {111} family of octahedral faces. The underlying assembly mechanism will be further discussed in Section 8.7.

7.4 Two-Dimensional Mesocrystals The formation of mesocrystalline arrays can also be restricted to two dimensions, as long as the mutual interactions drive such an arrangement. The structures shown in Figure 7.7 quite nicely illustrate some of the building principles of mesocrystals in two dimensions:

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Figure 7.6 Morphologies and structural characteristics of Pb0.996Mn0.004Se corrugated nanoarrays after 5 min of growth. (a) and (b) SEM micrographs, indicating that these corrugated nanoarrays were self-assembled by uniform-sized nanocrystals according to specific stacking modes; (c), (e), and (f) TEM images, displaying arrays of stacked nanocrystals with side-facets which expose periodical zigzag corrugated side-surfaces; (d) TEM micrograph and electron diffraction pattern, showing a single-crystal structure based on an array composed of over 20 nanocrystals; (g) HRTEM image, revealing the faceted shape of the nanocrystal and the welldefined crystallographic planes and demonstrating that the surface of the nanocrystal is clean without amorphous contamination. (Image reproduced from [25] with permission of the American Chemical Society.)

the primary crystalline building blocks are mutually aligned, but constantly interspaced by a surfactant stabilizer, following common crystallographic coordinates. The mesostructure in itself is not exactly crystalline, as minor differences in length or size are obviously tolerated and taken up in the structure by undulation and bending, and

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even larger vacancies can be overplayed and heal back on a longer scale. It is a mutual self-organization principle of crystalline building blocks, which can tolerate structural and lattice defects. These mesocrystals show some features both from crystals and liquid crystals, and their physicochemistry can be understood to be in between the two cases. This is one example of the continuous transition between mesocrystals, with their usually solid character, and liquid crystals, which is discussed in further detail in Section 7.12, Liquid crystals, Tactoids, Somatoids and Schiller layers. A similar two-dimensional ordering of nanoparticles to a mesocrystal can also be observed with other surfactant stabilized nanoparticle systems like oleylamine stabilized monodisperse Pt particles with octapod shapes, which form mesocrystal lattices with single crystal electron diffraction pattern upon drying (Figure 7.8) [26]. The crystalline order of these two-dimensional mesocrystals is even higher than those shown in Figure 7.7, as

Figure 7.7 Left: TEM image showing a rectangular superlattice of BaCrO4 nanoparticles prepared in a reverse microemulsion. Scale bars ¼ 50 nm. Inset, the electron diffraction pattern gives the superimposition of reflections from zone axes approximately parallel to the [100] direction. Right: Proposed model for the surfactant-induced self-assembly of nanoparticle chains and superlattices. (a) Surfactant-coated prismatic BaCrO4 nanoparticles synthesized by controlled crystallization in microemulsion water droplets. For clarity, only one face is shown with associated surfactant molecules; (b) Interdigitation of the surfactant monolayers induced as the crystal faces develop in shape and size, resulting in preferential aggregation normal to both the prism long axis (crystallographic axis) and the largest side face; (c) Aggregation in two dimensions proceeds as the chains develop in length and number. (Reproduced from [24] with kind permission of Nature Publishing Group.)

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Figure 7.8 Monodispersed platinum nanocubes formed with high precursor concentrations. (a) and (b) Low-resolution TEM image of self-assembled highly monodispersed filled octopod nanocubes. Inset is a SAED pattern; (c) High-resolution TEM image of a faceted platinum nanocube. Inset is an FFT of the particle image. (Image reproduced from [26] Copyright & American Chemical Society.)

evidenced by the SAED pattern; the mesocrystal structure tolerates defects like missing nanoparticles or slightly undulated nanocrystal layers. Other two-dimensional mesocrystal systems formed by drying of a dispersion of stable monodisperse metal nanoparticles in organic solvent are also reported for silver, such as hexagonal close packing of icosahedral or dodecahedral silver particles passivated by a dodecanethiol surface monolayer [27], two-dimensional mesocrystal formation with an fcc lattice of truncated octahedral silver nanoparticles, also stabilized by dodecanethiol [28] or a lattice of the same system with 2m symmetry, but tetrahedral silver nanocrystals [29]. The interaction between the interdigitated surfactant tails was also identified as a driving force for the self-organization. As the surfactant tails are short (ca. 1.5 nm) only the nearest neighbors surrounding a nanoparticle can be bound. In addition, the length of the adsorbed molecules is a controllable parameter, making the ratio of particle size to interparticle distance an adjustable parameter that sensitively tunes the interparticle interaction coupling and resulting collective properties [30]. The structural analysis issues of two-dimensional mesocrystals, their formation, the interparticle binding and defect structures of the mesocrystals (slip planes, twins and stacking faults or distorted structures), as well as the growth mechanism, are discussed in detail in the review by Wang [31], and the interested reader can find further details on metal two-dimensional arrays there.

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These examples show that one- or two-dimensional mesocrystals can form by self-assembly, which can take place directly in solution, or which can be induced by slow drying of a dispersion. Prerequisite are rather monodisperse nanoparticles to ensure the crystallographic order of the nanoparticle building units without too many defects.

7.5 Mesocrystals in Biomineralization As indicated in Section 3.1, Some Biomineral Examples, there exists a number of biominerals with amazing morphological features that simply do not ‘behave’ as expected from a single crystal. Many questions remain – especially the question about the orientation of organic templates, but more importantly orientation of the inorganic crystals [32]. This article highlights the precise crystal orientation, which up to now is still the big mystery of biomineralization. In 1972, it was stated: ‘The single most important feature of almost all mineralized tissues . . . is not so much the shape or even the mineralogy of the inorganic phase but rather its crystallography. The crystallographic preferred orientation, the ordered arrangement of crystallographic axes is of paramount concern’ [33]. Therefore, it is also important for biomineralization to learn about factors of mutual orientation of nanocrystalline building units. For us, there is a very good probability that biology simply learned to handle and employ mesocrystallization at a very early stage of evolution. Indeed there are several recent reports about mesocrystals in biomineralization, and it has already been suggested that nanocluster crystal growth, induced by organic matrices, is a basic characteristic of biomineralization that enables the production of composite materials with elaborate morphologies [34]. In fact, the number of reports on biominerals, which appear to be mesocrystals or at least involve a transient mesocrystal intermediate state, is starting to steadily increase. These findings are supported by the recognition of the advantages of particle-based crystallization pathways over the classical ion-mediated crystallization for a living organism. The sparingly soluble biominerals would require the transport of large solution volumes for the formation of the biomineral, local enrichment of ions would cause osmotic stresses harmful to cells, as well as other local changes in the crystallization environment needed to create a local supersaturation of ions. Instead, particle-mediated crystallization pathways have the advantage of providing a large amount of readily available building material, as well as the nearly complete independence of pH, ionic strength, and the associated osmotic forces. Consequently, it is not astonishing that in recent years, a number of amorphous precursor phases were discovered in biominerals, so that they can also be considered as a common precursor species in biomineralization processes (e.g., see [35]). However, the fate of the amorphous precursors is, as yet, largely unknown. In principle, they could dissolve and recrystallize towards a larger single crystal via the classical ion-mediated mechanism. The second possibility is a direct solid-state transition of the amorphous precursor into the crystalline material. Extended X-ray absorption fine structure (EXAFS) studies on biogenic calcium carbonate have shown that the amorphous phase is not completely disordered. Instead, a short-range order around the calcium ions exists, which resembles the crystalline calcite or aragonite phase into which the amorphous phase later transforms [36,37]. This local order indicates the feasibility of a solid-state transition of ACC to the crystalline phase. This solid-state

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transition can be seen in addition to the crystallization of an amorphous particle on the ordered surface of a crystal, which was discussed in Section 4.3, Oriented Attachment. Amorphous nanoparticles can be formed and stored in regions away from the mineralization site and then be transported, via vesicles, on demand [38]. Such a scenario implies a brick-by-brick ‘prefabricated’ construction mechanism for a biomineral. Nanoparticles were indeed suggested as building units of biominerals in combination with a brick-bybrick formation mechanism [39,40]. This mechanism is consistent with the mesocrystal picture in Figure 4.1. Indications for the formation of mesocrystals in biomineralization have existed for a long time. For 60 years, data indicating that Echinoderm calcite may be a mesocrystal instead of a single crystal were reported [41–49]. From the observation of polycrystalline material on the surface of single crystalline material in Echinoderm skeletal plates, Towe suggested the single crystal formation by fusion of oriented polycrystals – in other words a mesocrystal to single crystal transformation under shape preservation (see also Section 8.9, Mesocrystals as Intermediates in Single Crystal Formation) [46]. Nevertheless, detailed and targeted research on the topic of mesocrystals in biomineralization has just recently started [49,50]. Similar to the synthetic systems, this is possibly the result of previously missing concepts and analytical possibilities. In this context, the investigation of the sea urchin spicule is a good example (Figure 7.9 a). It consists of calcite and shows single crystalline behavior in polarization microscopy and

Figure 7.9 SEM images of: (a) sea urchin spicule from Anthocidaris crassispina; (b), (c), (d) conchoidal fracture surface at various magnifications. (Figures (a) and (b) reproduced from [51] with permission of the Royal Society of Chemistry.)

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Figure 7.10 Single crystal diffraction pattern of a sea urchin spicule from Anthocidaris crassispina roughly taken along the c-axis. (The image is courtesy of Prof. U. Schilde, University of Potsdam, Germany.)

scattering experiments. However, the fracture surface of the spine does not show the typical cleavage planes of a single crystal, but instead a chonchoidal fracture surface, which is typical of an amorphous body (Figure 7.9 b). If this fracture surface is further magnified, nanoparticles can be clearly seen, which is supportive of the presence of a mesocrystal rather than a single crystal, which would have cleavage planes (Figure 7.9 c and d). In case of calcite, these would be the (104) planes. Nevertheless, the scattering/diffraction behavior is that of a perfect single crystal elongated along the c-axis (Figure 7.10), and single crystal analysis reveals a calcite unit cell. As in the case for the foraminifera, these findings can only be explained by a perfect mutual alignment of the nanoparticles in a crystallographic register or a crystallographic bridging connection of the individual nanoparticles. These apparently contradicting results were the subject of debate for decades as to whether the spine is in fact a single crystal [52] or not [41–45]. In addition, the coexistence of single crystalline parts next to polycrystalline regions was discussed [46]. Evidence for the presence of a mesocrystal was reported recently [49,59]. Higher magnification SEM images of the skeleton unequivocally characterized the alignment of the building blocks as well as their nanoparticulate morphology and single crystal diffraction pattern (Figure 7.11). The mesocrystal structure of the sea urchin spine can well explain the ‘glassy’ fracture behavior combined with single crystal diffraction behavior as a mesocrystal does not have cleavage planes due to its nanoparticle inner structure. This is consistent with the findings of O’Neil et al. who found that rapid fracture led to smooth and glassy surfaces, whereas stress relaxation before fracture revealed the texture of calcite nanocrystals [43].

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Figure 7.11 FESEM (a)–(c) and FETEM (d) images of the nanobricks and their assembly in an Echinoderm skeleton: (a) A sponge skeletal structure exhibiting a fractured surface; (b) the radial assembly of the nanobricks on the fractured surface; (c) magnified FESEM image clearly showing that the spongy skeletal architecture consists of nanobricks; (d) the assembly of the nanobricks and the corresponding SAED pattern (inset). (Figure reproduced from [49] with permission of Wiley-VCH.)

Aligned nanoparticle building units were also found in sponge spicules consisting of calcite (Figure 7.12) [34]. Similar to the sea urchin spine, the scattering behavior was that of a single crystal (Figure 7.12 d), although various microscopy studies (AFM, HRTEM, see Figure 7.12 b and c) clearly revealed the nanoparticulate building units of the sponges, which is consistent with the definition of a mesocrystal. Combined highresolution and energy-filtering transmission electron microscopy revealed carbon enrichments located in between crystal domain boundaries, strongly pointing to the presence of an intercalated network-like protein-rich organic matrix between the nanocrystal building units of the mesocrystal [34]. Furthermore, mutually aligned nanoparticulate building units were also found in the crystalline tablets of nacre. Up to now, the aragonite tablets were believed to be aligned single crystals, with c-axis orientation perpendicular to the interspacing organic sheets.

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Figure 7.12 (a) Fractured spicule actine of the calcareous sponge Pericharax heteroraphis with conchoidal fracture pattern (FESEM); (b) AFM height image of a conchoidal fracture surface, revealing the nano-cluster structure of the spicule material; and (c) HRTEM image of the fracture pattern in relation to the crystal texture. The trace of fracture is clearly influenced by crystal domain boundaries (arrows). The black line represents a rounded fracture trace, which may clarify the structural relation between crystal domains and cluster units as displayed in (b); (d) selected area electron diffraction pattern of a Pericharax spicule (polished, ionmilled, and carbon coated). (Figure reproduced from [34] with permission of Elsevier.)

However, Dauphin [60], Chang et al. [61], Oaki and Imai [40], and Rousseau et al. [50,62] found that these tablets also consist of aligned nanoparticles. Moreover, the ca. 45 nm particles in the platelet were recently found to be interspaced by a continuous organic framework, which is at least partly crystalline [50]. The nanograins were identified to be important for energy dissipation in nacre [63], which is 3000 times more fracture resistant than aragonite alone. The required energy dissipation was found to happen via nanograin rotation and deformation, while the biopolymer spaced between the nanograins facilitates the grain rotation process (Figure 7.13). This result can also explain the deformability of individual ductile aragonite platelets [61]. They do not break upon nanoindentation, as would be expected for a brittle single crystal, but show extensive plastic deformation with a clear residual indent and surrounding pileup instead, further supporting the inorganic nanograin structure being embedded in a plastic, partially organic matrix [64].

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Figure 7.13 SEM images of a nacre fracture surface: (a) The brick mortar architecture is shown; (b) Nanoscale asperities on the aragonite platelet surface are readily observed; (c)The organic biopolymer is found to serve as adhesive to hold aragonite platelets, as indicated by the arrow; (d) and (e) Schematics of grain rotation and deformation mechanisms in an aragonite platelet. Dashed lines denote the original width of the platelet; (d) Closely packed nanograins without external applied strain/stress; (e) Grain rotation, grain deformation, and biopolymer spacing between the grains under external applied strain/stress. Arrows denote the rotation direction of grains. D in the figure denotes grain deformation. The arrows under the pictures denote the tensile direction. (Images (a), (b), and (c) reproduced from [61] and (d) and (e) from [63] with permission of the American Chemical Society.)

The irregularity of the nanograin structure in the mesocrystal also ensures that layers of nanocrystals cannot slide along each other upon mechanic load, which would lead to the exposure of sliding planes and poor mechanical properties. Instead, the interlocked, but nevertheless flexible, structure maintains energy dissipation and absorption during crack propagation upon fracture and therefore high fracture resistance. This is not only valid for a single nacre platelet, but also for the entire nacre structure (Figure 7.13 a), which shows asperities on the surface of each superplatelet (Figure 7.13 b); the gluing of these rough surfaces by adhesive biopolymers (Figure 7.13 c) makes interfacial sliding of platelets upon shear more difficult [64]. This example shows in an impressive manner, that the mesocrystal architecture of a biomineral does not only improve synthesis, but also makes much sense in terms of the improved mechanical properties obtained. The classical crystallization toolbox would not allow for such fine tuned hierarchical engineering of composite hybrid materials.

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Beside nacre, the calcitic prism of Pinna nobilis was also found to exhibit mesocrystalline order, as shown in Figure 7.14 [65]. It can be shown that the prisms are not compact structures, but are composed of oblique and elongated crystallites (Figure 7.14 G–H), the width of which varies from 150 to 180 nm. These crystallites are subdivided into smaller rounded units with distinct boundaries in AFM height and phase images, suggesting that they are surrounded by organic envelopes (Figure 7.14 I). Nevertheless, the prisms behave like a single crystal under crossed polarizers (Figure 7.14 F).

Figure 7.14 Microstructures and nanostructures of the calcitic prisms of Pinna nobilis.:(A) Vertical fracture in the outer layer showing the long parallel regular prismatic units. No pattern is visible on the outer surface of the prisms; (B) Transverse polished, fixed, and etched section showing the thick organic walls (w); (C) Vertical polished and etched section showing the thick interprismatic walls (w) and the regular growth lines; (D) Transverse polished, fixed, and etched section showing the interprismatic wall (w) and a pattern of parallel crests; (E) Inner surface showing the same pattern of parallel crests and the walls (w); (F) Thin section observed in transmitted light (cross-nicols) showing the walls (w) and the monocrystalline extinction of each prismatic unit; (G) Vertical polished and etched section showing the aligned acicular crystallites; (H) Detail of the same; (I) Tranverse polished and etched section of the prisms showing the small crystallites surrounded by an organic thin layer. Detailed preparation procedures, see original literature [65]. (Figure is reproduced from [65] with permission of the American Society for Biochemistry and Molecular Biology, Inc.)

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Another example of mesocrystals in biomineralization is fibrous subunits in corals, which show apparently single crystalline domains in the polarization microscope, but are composed of nanoparticles interspaced by organic matrix, which separates the nanograins [66]. Oaki et al. recently summarized a large amount of the biomineral mesocrystal examples [48] for nacre, coral, echinoderm stereoms, foraminifera and eggshells, as shown in Figure 7.15. Regardless of their macroscopic shape (Figure 7.15 a1–a5), all displayed biominerals have a nanoparticle substructure, which can be directly seen on fracture surfaces or the powdered samples (Figure 7.15 b1–b5 (SEM) and c1–c5 (TEM)). The TEM images in Figure 7.15 reveal the nanoparticle bricks in the mesocrystals (c1–c5). Further magnification reveals that each of the nanoparticle bricks is a facetted single crystal (Figure 7.15 d1–d5 and e1–e5) with typical sizes of 10–80 nm for calcite and 20–180 nm for aragonite [48]. These examples show that some biominerals, which were traditionally considered to be single crystals (like the calcite sea urchin spicules and the aragonite tablets in nacre), are presumably formed via a nonclassical nanoparticle-based crystallization process. The revealed nanoparticle subunits in a variety of biominerals imply at least the presence of mesocrystalline intermediates in the biomineralization process, if not also the presence of stable superstructures with mesoscale order, as this seems to be coupled with favourable mechanical properties [67] and the option for composition tolerant construction of gradient materials.

7.6 Mesocrystals in Gels Crystallization in gels appears to be well suited to the generation of mesocrystals, as crystal growth in gels takes place under very high supersaturation [68] which can lead to increased nucleation of small clusters – the building units for the mesocrystals. Simultaneously, convection or turbulence throughout crystallization can be suppressed, thus allowing the mutual interaction potentials to dominate the mutual alignment of particles. In addition, the diffusion of the mesocrystal building units is significantly lowered in gels, which leads to a slower growth process and therefore the possibility of observing the time-resolved structure formation process. Also, gels can be made as inert structures without interacting moieties for the crystals and just providing diffusion control (for example poly(acrylamide) gels) or be equipped with chemical functions for interaction with the forming crystal structures. These are the reasons why many of the most defined mesocrystals are indeed observed in gels. One of the most investigated synthetic mesocrystals so far is the hexagonal prismatic seed crystal of fluoroapatite, formed in a gelatine gel, which further grows to spherical particles via dumbbell intermediates (Figure 7.16) [69–71]. The morphogenesis process from rods, via dumbbells, to spheres, shown in Figure 7.16, is already highly interesting, as it follows the rules of self-similarity and is also observed for many other systems in solution with and without additives. In terms of mesocrystal formation, however, the hexagonal seed crystal is of most interest. The hexagonal seed crystal shows all typical features of a mesocrystal and is thus a nice example to demonstrate the basic properties of a mesocrystal and also the problems in identifying it (Figure 7.17 a). The hexagonal seed crystal was not directly recognizable as a mesocrystal, as it showed a well-facetted,

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single crystal-like morphology (Figure 7.17a). Even X-ray diffraction showed features of a fluoroapatite single crystal oriented along the c-axis [72], due to the very high vectorial order of its nanoparticulate building units (Figure 7.17 a). This example illustrates the difficulties in recognizing mesocrystals and the danger of erroneously considering such crystals as single crystals. Although the hexagonal crystals contain ca. 2 wt.% intracrystalline gelatine, the polymer does not modulate the crystal structure, so that an adaptation of the gelatine to the fluoroapatite structure was concluded [72]. It was to the credit of this group that they elucidated the radial inner structure by a hexagonal cross section perpendicular to the seed axis, disproving the presence of a classical single crystal (Figure 7.17c) [69]. It was concluded that the hexagonal seed crystal with single crystalline appearance and scattering behavior is a hierarchically ordered inorganic–organic composite superstructure with periodic orientation of hexagonal primary apatite nanocrystals [73], or in other words, a mesocrystal. After gelatine cross linking and apatite removal, the polymer distribution inside the crystal could be visualized replicating the structure of the former dumbbell-shaped hybrid particle (Figure 7.17 b). The internal structure of the hexagonal seed crystals (Figure 7.17 c) revealed a radial pattern and a superstructure periodicity of 10 nm, in good agreement with a primary nanoparticle size of about 10 nm [74]. The hexagonal pattern, already known from X-ray diffraction [72,75], was also found in high resolution TEM micrographs with subsequent fast Fourier transform (FFT) analysis (Figure 7.18 left). Electronic filtering and enhancing this image revealed structural defects, which were attributed to a collagen triple helix strand (white circle Figure 7.18 right) [74], the memory of the former grain boundaries stabilized by organic material. Also, self-similar nano-subunits nucleated by gelatine were detected [76]. Furthermore, TEM of a focused ion-beam milled sample showed pores and channels at the grain boundaries containing an amorphous phase [77], giving final evidence for the mesocrystalline nature of the well-facetted hexagonal superstructure. On the basis of this evidence, a growth model for the observed radial outgrowth in the hexagonal seed was developed (Figure 7.17 d). It agrees with the mesocrystal scheme presented in Figure 4.1 c, but with hexagonal building units. The stiffness of the gelatine molecules tunable by interaction with Ca2þ or PO43 was found to have a pronounced influence on the morphogenesis scenario following the formation of the hexagonal seed mesocrystal [78]. Whereas gelatine gels can be considered to interact with inorganic crystals at least via their charged groups, poly-acrylamide gels can be considered to be essentially inert. The growth of CaCO3 in the latter gels led to remarkable pseudo-octahedral calcite mesocrystal morphologies built up of rhombohedral primary nanocrystallites, as shown in Figure 7.19

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Figure 7.15 The summarized FESEM (a), (b) and FETEM (c)–(e) images of the biominerals investigated: (a1)–(a5) The macroscopic appearance (inset) and the FESEM images of the characteristic morphologies; (b1)–(b5) The magnified FESEM images on the fractured surface, indicating the presence of nanoscopic structures; (c1)–(c5) The corresponding FETEM images on the same scale as the panels in (b); (d1)–(d5) The FETEM images of each nanocrystal exhibiting a specified facet; (e1)–(e5) The high-resolution FETEM images of the nanocrystals, showing that each nanocrystal is a single crystal. (From [48] with permission of Wiley-VCH.)

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Figure 7.16 Selected sequence of SEM images of progressive stages of self-assembled (hierarchical) growth of fluorapatite aggregates in a gelatine gel (morphogenesis): from an elongated hexagonal-prismatic seed (top left) through dumbbell shapes to spheres; the surface of a just closed sphere also consists of needle-like units (bottom right) following the general principles of self-similarity. Intrinsic electric fields were suggested control factors for the rod– dumbbell–sphere fractal growth. (Picture reproduced from [69] with kind permission of WileyVCH Weinheim.)

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Figure 7.17 Fluoroapatite grown in a gelatine gel: (a) SEM of the hexagonal prismatic seed together with the corresponding diffraction pattern. The arrow indicates the direction of the incident X-ray beam; (b) Gelatinous residue of the composite; (c) SEM image of the fracture area of a central seed; (d) Arrangement of hexagonal nanoparticles forming a superstructure. The lines and arrows indicate preferred cleaving directions. ((a), (b), and (d) are reproduced from [72] with permission of Wiley-VCH; (c) is reprinted from [74] with permission of the Royal Society of Chemistry.)

[79,80]. The external faces of the superstructure could be indexed and a growth model based on hierarchical aggregation of rhombohedral subunits was proposed [80]. As already found for the fluorapatite hexagonal seeds, the crystallographic orientation of the subcrystallites is almost perfect, and the organic matrix appears to be interspaced between individual crystallites (Figure 7.19) [80]. However, whereas the fluoroapatite diffraction pattern was that of a single crystal [72], the calcite mesocrystals indicate a slight orientational distortion of the diffraction spots (Figure 7.19) corresponding to an average mosaic spread of 3:9 1:1 degrees. This nevertheless still confirms a high orientational order of the subunits in the mesocrystal [80]. We attribute this to symmetry differences between the calcite and the fluoroapatite system, as the calcite system contains many vacancies and is potentially twinned (to allow construction of an octahedron from rhombohedra), whereas the Kniep particles possess a higher symmetry and are obviously rather tightly packed. Varying the polyacrylamide hydrogels by copolymerization with charged acrylamidopropanesulfonate (AMPS) to give polyacrylamide-co-acrylamidopropanesulfonate

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Figure 7.18 (Left) High resolution electron micrograph of a composite seed (fast ion bombardment (FIB) preparation) viewed along [001]. The FFT (inset bottom right) is characterized by hexagonal symmetry. Structural disorder of the composite (defects, mosaic structure) is indicated by diffuse reflections and by the disappearance of higher order peaks; (Right) Filtered and enhanced view of the white frame area of the left image. The inset represents the mask used for the filter process (reflections observed). The overall hexagonal pattern is significantly broken inside the area of the white circle. (Reproduced from [74] with permission of the Royal Society of Chemistry.)

(PAAm-co-PAMPS), the morphology of the calcite mesocrystals could be tuned from pseudo-octahedral [80] towards a cubo-oactahedral morphology, with increased amounts of the charged AMPS in the copolymer gel (Figure 7.20) [81]. The substructure of the mesocrystals from aligned smaller crystals could be nicely visualized (Figure 7.20 lower images). One important conclusion of this study was that the alteration of the functional groups in the hydrogel did not change the mesocrystal formation as such, but the morphogenesis process, shedding some light onto the question why mesocrystals exhibit defined outer faces and how they can be influenced [363].

Figure 7.19 (Left) SEM-image of a calcite mesocrystal grown in a poly-acrylamide gel with characteristic pseudo-octahedral morphology; (Center) TEM image of the microstructure of a poly-acrylamide-grown mesocrystal showing alignment of individual crystallites. An electron diffraction pattern of an individual calcite crystal is inserted; (Right) Single crystal-like diffraction pattern of the calcite mesocrystal. (Reprinted from [80] with permission of the American Mineralogical Society.)

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Figure 7.20 Pseudo-cubo-oactaedral calcite mesocrytals grown in a PAAm-co-PAMPS hydrogel containing 10 mol% of sulfonate group-bearing monomers. Upper left: SEM micrograph. Upper right: Schematic illustration of the pseudo-cubo-octaedral morphology. Lower left: Flattened vertices of pseudo-cubo-octahedral particles showing calcite rhombohedral faces; Lower right: Orientation of rhombohedral subcrystals on aggregate faces. The lower images clearly show the substructure of the mesocrystal. (Figure reproduced from [81] with permission of Wiley-VCH.)

7.7 Mesocrystals Formed without Additives Mesocrystals can also be formed without any additive. Although the application of additives is advantageous to temporarily stabilize the primary particles and thus prolong the lifetime of mesocrystal intermediates and the mesocrystals themselves, additives are not a necessary prerequisite for the formation of mesocrystals. This was demonstrated for a number of examples. We have already discussed the model case of the precipitation reaction of BaSO4 crystallization at high supersaturations, where mesocrystals were observed as short-lived

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intermediates in the formation process of a single crystal [82]. See also Section 8.9, Mesocrystals as Intermediates in Single Crystal Formation. It is, however, difficult to detect the mesocrystals if they are short-lived intermediates [82] and this is the reason why they can be overlooked. Another example for mesocrystals formed directly from solution without any additive is the case of (NH4)3PW12O40 [83–87]. In the observed crystals, nanocrystals were unidirectionally aligned and epitaxially connected to form dodecahedral mesocrystals. As in the above BaSO4 example, the mesocrystals were found to be porous [86]. Comparison of the cesium and ammonium salts precipitated at different temperatures showed a variation of the degree of order in the mesocrystals [88]. The solubility of the salts was considered to be responsible for the control of the microstructure morphology with the higher solubility favoring the regular polyhedral shape [88]. Mesocrystal formation is also regularly observed for Zeolites [89,90]. In these experiments, the zeolite first forms ‘nanoslabs’ containg 2, 6, 12, or 48 zeolithic unit cells, which then vectorially align into larger structures. TEM, however, clearly reveals that those bigger units are composed of the smaller building blocks, with all the textures and defects typical of mesocrystals. Cobalt oxalate dihydrate can form remarkably structured mesocrystals [91]. However, their structure changes with time, as they are intermediates. As for copper oxalate, the crystals are composed from nanometer building units, according to WAXS, and AFM revealed strings of nanodomains oriented along the principal axis of the particle (Figure 7.21) revealing that the lateral and basal faces of the precipitate are composed of stacked nanoparticle layers with a thickness of 5–7 nm. A time-resolved HRSEM study revealed the formation mechanism of the mesocrystal (Figure 7.21) [91]. Poorly crystalline primary particles (10 nm) first aggregate to form secondary particles (23 nm).The latter subsequently aggregate to form polydisperse elongated particles. These elongated particles also aggregate at the ends and center of a growing particle (Figure 7.21 right) building the mesocrystal. Afterwards, there is a

Figure 7.21 (Left) AFM image of a CoC2O4*2 H2O particle aged 1 h in suspension. (Right) LVHRSEM micrograph of cobalt oxalate dihydrate mesocrystal formed from secondary particle aggregates. (Figure reproduced from [91] with permission of the American Chemical Society.)

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layer-by-layer growth by aggregation of primary particles onto the lateral external faces. Thus the mesocrystal is a core–shell particle or core–shell mesocrystal, where the core is quite disordered due to the polydispersity of the nanoparticle building units [91]. The presence of steps and kinks on the external faces is reminiscent of the classical crystallization models – except that the atoms or molecules are replaced by nanoparticles. The evolution of supersaturation and thus ionic strength, closely associated with the colloidal stability of nanoparticles, was suggested to play a predominant role in the ordering process of the nanocrystals to a mesocrystal. The nanoparticles building up the mesocrystal do not necessarily need to be formed by a homogeneous precipitation reaction, but can also be formed in emulsion droplets. Such an example was reported by Taden et al. for dyes with an anisotropic polarizability [92]. Amorphous particle precursors were made in a size-controlled fashion by cooling the liquid nanodroplets of a mini emulsion, and spontaneous rearrangement of many nanodroplets to well-defined linear mesocrystal aggregates was observed. This was accompanied by significant color changes of the dye superstructures. These rod-like particles could be ripened to larger three-dimensional mesocrystals retaining the almost perfect molecular orientation in the nanoparticle aggregate, which became obvious when turning the ripened mesocrystals under crossed polarizers (Figure 8.22). Sugimoto et al. also found a proof for an aggregative growth model for hematite mesocrystals based on the observation that their pseudo-cubic hematite particles are polycrystals consisting of smaller ‘subcrystals’ of the order of 2.5 nm [93]. They proposed that the polycrystalline structure is formed by ‘the stacking of ultrafine crystallites epitaxially grown from their two-dimensional nuclei but strictly restricted in their growth and mutual fusion’. More evidence for an aggregation-based process was reported for ellipsoidal hematite particles obtained by homogeneous precipitation from ferric salt solutions [94]. To study the changes in the characteristics of the precipitated particles, the authors performed a time-dependent TEM study (Figure 7.22). After four days of aging the solution at 100 C, small anisotropic hematite nanoparticles about 30–40 nm in length were formed, which started to aggregate in a highly ordered fashion (Figure 7.22 a) finally forming ellipsoidal particles (Figure 7.22 b). High resolution TEM images gave evidence for their internal composite nature, i.e., aggregates of smaller subunits with surface defects and internal interfaces. However electron diffraction showed that the mosaic crystal behaved like a single crystal with a spot pattern characteristic of hematite [94]. Iron oxide seems to be a material that is particularly well suited for mesocrystal formation. The hydrothermal treatment of a hexanuclear iron-polyolate complex led to relatively monodisperse hematite particles with a disc-like shape, about 1 mm in diameter and 250 nm in thickness (Figure 7.23 a) [95]. Obviously each particle consists of many plate-like crystallites, which can mutually penetrate without influencing the size and shape of the particles (Figure 7.23 b). This observation was confirmed by TEM measurements on one particle (Figure 7.23 c). The HRTEM image clearly gives evidence for the internal composite nature of the particles (Figure 7.23 d). Small crystallites are perfectly aligned, and a hexagonal pattern of dark spots can be seen in the whole region. Selected area electron diffraction performed on the particle displays a spot pattern characteristic of the hexagonal lattice of a single crystalline hematite particle (Figure 7.23 e) [95].

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Figure 7.22 TEM images of hematite particles in different states of aggregation, aged at 100 C for: (a) four days; and (b) six days (final particles). (Images taken from [94] with permission of Elsevier Science Publishers.)

Figure 7.24 provides two more examples of mesocrystals that are formed without additives: three-dimensional aggregates of CuO (Figure 7.24 a) [96] and cube-like SrTiO3 [97]. To explain the ellipsoidal particle shape of the CuO aggregates, the authors suggested an anisotropic agglomeration rate in the following order of directions: ½010 > ½100 > ½001 (Figure 7.24 b), which is different from the classical crystal growth of CuO nanowires, which usually occurs along the [111] direction. In the case of SrTiO3, the spherical crystallites, in the size range of 4–5 nm, self-assemble into cube-like particles, depicted from a vertex of the cube in Figure 7.24 c [97]. The HRTEM image shows the parallelism of the lattice fringes, proving that all the nanocrystals are aligned along the same crystallographic direction (Figure 7.24 d), which is additionally confirmed by the electron diffraction pattern (Figure 7.24 c, inset). However, differences in the contrast between the crystallites points to the presence of nanopores, defects and dislocations.

7.8 Mesocrystals Formed with Simple Ion Additives Ions can also serve as additives to selectively address crystal faces by adsorption and to induce and control mesocrystal formation. However, the ion concentration is related to the colloidal stability of electrostatically stabilized colloidal particles, which is true for most nanoparticle precursors to mesocrystals. Therefore, too high an ion additive concentration will lead to uncontrolled aggregation, due to the destabilization of the primary nanoparticles without the possibility of re-orienting into a crystallographic register. Nevertheless, selective ion adsorption with subsequent mesocrystal formation is possible. One example is the pseudo-cubic hematite (a-Fe2O3) particle, which can be obtained by a gel-sol method in presence of Cl ions [98–101]. The type of crystal morphology and structure varies markedly in the presence of ions. Whereas Cl produced the

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Figure 7.23 (a) SEM image of hematite colloids; (b) side view on interpenetrated particles; (c) TEM top view image of one particle; (d) HRTEM image of the edge of one particle; (e) selected area electron diffraction of one particle along the c-axis. (Images taken from [95] with permission of the American Chemical Society.)

pseudo-cubic particles, SO42 or PO43 produced ellipsoidal- or peanut-shaped polycrystalline microparticles [100,102,103]. The pseudo-cubic hematite particles show the typical high orientational alignment of the nanoparticle subunits in a mesocrystal, which is already obvious from the spot patterns in the electron diffraction images and furthermore from the iso-aligned nanoparticle building units (Figure 7.25) [101]. It was noted that the adsorption of anions plays an important role in the morphology and internal structure control and Cl was suggested to remain in the mesocrystal interior [101]. Cl was reported to adsorb onto the faces of the {012} family.

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Figure 7.24 (a) TEM image of CuO nanoparticles assembled into larger agglomerates; (b) schematic illustration of such a single-crystalline assembly; (c) TEM image of a SrTiO3 particle along the diagonal axis of the cube-like morphology; Inset: Electron diffraction pattern of the whole particle; (d) HRTEM image of the edge of such a particle. (Images (a) and (b) taken from [96] with permission of Wiley-VCH; images (c) and (d) from [97] with permission of the American Chemical Society.)

This becomes understandable when Figure 7.26 is considered. (012) exposes only highly charged surfaces, e.g. exclusively Fe ions, which can complete their coordination sphere by the coordination of anions like Cl, SO42 or PO43. Such ion adsorption will then effectively block such surfaces from further growth and will change the surface charge, which in case of Cl coordination leads to elongated primary nanoparticles. However, the elongated nanoparticle subunits are not arranged in a perfectly parallel way. On the larger scale, a radial alignment of the elongated subcrystals (Figure 7.27) becomes visible. This means that the high mutual crystallographic orientation of the nanoparticle subunits is only realized in the first integration step or for smaller parts of the microparticle, which, as a whole, has lost its single crystalline spot pattern in electron diffraction (see electron diffraction pattern in Figure 7.27 a). It is noteworthy that these mesocrystals were reported not to be formed by an aggregation process of pre-formed nanoparticles (like most other mesocrystals), but by dissolution–recrystallization of metastable precursor phases (in this case by dissolution of metastable b-Fe2O3 and recrystallization of the stable a-Fe2O3) [93]. This was concluded from the tremendous increase of the phase transformation upon seeding with hematite

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Figure 7.25 Hematite (a-Fe2O3) mesocrystals: (Left) Transmission electron micrograph of a thin section and electron diffraction patterns obtained from the parts E, F, and G; (Right) lower left is the transmission electron micrograph of a section around a corner of a pseudo-cubic particle; large photois the high-resolution electron micrograph of the area indicated by an arrow in the lower left inset; Upper left is the Fourier diffractogram of the insets. (Figure reproduced from [101] with permission of Academic Press.)

(a-Fe2O3) particles [93]. From the reported results, in our opinion no conclusion can be taken as to whether the species forming the mesocrystals are ions or clusters/particles. Especially Fe3þ is known to be, at least partly, polymerized and forms clusters even at a low pH [104]. A mesocrystal formation by aggregation of those clusters seems more likely. The formation of a-Fe2O3 nanoparticles from the b-Fe2O3 precursor particles can equally well explain the effect of seeding on the phase transformation, as clusters/nanoparticles

Figure 7.26 Atomic surface cut of a hematite (012) surface (Cerius2, Accelrys). The surface (yellow dashed line) exposes positively charged Fe atoms (brown; oxygen, red). It is obvious that the (012) surface can only expose uniform charges of high density (either only positive or only negative).

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Figure 7.27 Hematite (a-Fe2O3) mesocrystals: (Left) Transmission electron micrograph of a thin section together with the corresponding HRTEM pictures as insets. The star notes the position where the electron diffraction was taken; Right: TEM micrograph of a thin section of a pseudo-cubic particle. An arrow indicates a subcrystal separated from the solution. (Figure reproduced from [101] with permission of Academic Press.)

attaching to a mesocrystal are removed from the solution phase in analogy to ions attaching to a single crystal. Obviously, in analogy to the fact that heterogeneous nucleation is favored over homogeneous nucleation in classical crystallization, there is an acceleration of mesocrystal growth in the presence of appropriate seeds, i.e. mesocrystals can also be heterogeneously nucleated, although with a process on the mesoscale.

7.9 Mesocrystals Formed with Polymer Additives Compared to ions or other low molar mass additives, polymers are especially well suited to induce and control mesocrystal formation due to five main properties: (1) Polymers can control nanoparticle nucleation and store material in precursor complexes or metastable precursor phases resulting in material depots for the immediate transformation into the nanoparticles forming the mesocrystal. (2) They can temporarily stabilize (steric or electrosteric stabilization) the primary nanoparticles preventing their uncontrolled aggregation before they can mutually align into a crystallographic register and mesocrystal formation can take place. (3) They can selectively adsorb onto defined crystal faces and thus ‘code’ the nanoparticles for their mutual alignment. (4) Polymers have multiple adsorption sites and can therefore bind more strongly compared to their low molar mass counterparts (5) Polymers usually get, at least partially, occluded into the mesocrystal and thus prevent the crystallographic fusion of the aligned nanoparticles to single crystals. This is often the only reason why mesocrystals can be observed, as otherwise, only time-resolved investigations can reveal the mesocrystal intermediates (see Section 8.9, Mesocrystals as Intermediates in Single Crystal Formation).

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It is therefore not surprising that the best mesocrystal examples so far were reported for polymer additives (including gels). One such example is DL-alanine mesocrystals obtained in the presence of a block copolymer with a neutral water-soluble poly(ethylene oxide) block as a steric stabilizer, and a charged butyric acid functionalized block for selective adsorption onto crystal surfaces. Organic crystals have the advantage that they are molecular crystals, where a dipole moment as well as an anisotropic polarizability can already be encoded in the molecule. Mesocrystals made up from nanoparticles consisting of dipolar molecules are particularly well suited for learning about the mechanism of mesocrystal formation. For example, DL-alanine is dipolar and has the dipole axis along the c-axis of a needle, which is also the default morphology of DL-alanine (see Figure 7.28 upper left). It therefore has one positively and one negatively charged tip. Adsorption of the negatively charged polymer block onto the positive (001) face of DL-alanine hinders further growth along the high-energy (001) direction and creates platelets with a dipole moment along the c-axis (Figure 7.28 upper right). The important faces of the platelet can be deduced, from X-ray diffraction experiments, to be the {001} faces (green) and {210} face family (red), which make up the edges of the mesocrystal towards a small (200) face (white), and which are visible in the SEM micrographs (Figure 7.28 center). The resulting dipole moment is aligned along the c-axis of the platelets and results in a secondary stacking of the nanoplatelets due to dipole–dipole attraction. This finally results in a superstructure shown schematically at the bottom of Figure 7.28 [105]. In the mesocrystal, the individual building units are interspaced by the adsorbed polymer in layers along the c-axis. In the other directions, this is not the case, and therefore, the crystals can crystallographically fuse in this plane once they are crystallographically oriented and their (100) and (210) faces come into close contact (shown in the lower sketch of Figure 7.28). Only at the (010) face, do the edges made up of the (210) faces of the platelets become visible, as shown in the micrographs in Figure 7.28 center. The layer-like structure and mutual orientation of the crystalline platelets in this figure is remarkably perfect. Inorganic crystals built up from ions do not have the advantage of a large anisotropy of their smallest building blocks. Anisotropy of nanoparticles, which is necessary for their crystallographic alignment and mesocrystal formation, must therefore be induced by additives, if it is not already encoded in the crystal lattice itself. This is possible in an elegant way by selective polymer adsorption. A very detailed study on mesocrystal formation directly in solution and subsequent fusion to iso-oriented crystals was reported for copper oxalate in presence of hydroxymethylpropylcellulose (HPMC) [106,107]. Here, nanoparticles were found to arrange almost perfectly to a mesocrystal that could be influenced in terms of morphology by HPMC (Figure 7.29). This polymer can selectively interact with the more hydrophobic lateral (110)/(1 1 0) e-faces of an [001] elongated nanocrystal, as compared to the hydrophilic (001) a-face, which lowers the surface energies of the respective faces [106]. However, besides face selective adsorption, the polymer influences nucleation, nanocrystal growth, and aggregation, which is an example of the multiple roles polymers can play during the various stages of mesocrystal formation. Increasing polymer concentration led to the formation of more, but smaller, nuclei due to the decrease of the interfacial tension between nuclei and solution. The specific HPMC

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Figure 7.28 DL-alanine mesocrystals through crystallization of a supersaturated solution (from 65 C to 20 C): (Upper left) default experiment without additive; (Upper right) Suggested mesocrystal subunit by addition of 1.0 wt.% anionic block copolymer and selective adsorption onto (001) (green {001}, red {210}, white {200}; (Center left) High resolution SEM of DL-alanine crystals through crystallization by addition of 1.0 wt.% block copolymer (scale bar ¼ 2 mm); (Center right): Different cut of the same structure revealing the high orientational order of the nanocrystalline platelets (scale bar ¼ 3 mm); (Bottom): Schematic drawing of the self-structuring of a primary crystal to a mesocrystal for DL-alanine, with an outline of the externally exposed faces. Note that the rough face is (010), which exposes the nanocrystal platelet tips. Along the a and b directions, partial particle fusion occurs by oriented attachment. For simplicity, the polymer is not shown. (Figure reproduced from [105] with permission of Wiley-VCH.)

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Figure 7.29 SEM micrographs of copper oxalate powders prepared: (a) without (HPMC); (b) with 0.005 g/l HPMC; (c) 0.0195 g/l HPMC; (d) 0.156 g/l HPMC; (e) 0.625 g/l HPMC; and (f) a higher magnification of (e) showing the mesocrystal structure. (Figure reproduced from [106] with permission of Academic Press.)

adsorption to the lateral e-surfaces of the growing nanocrystals, once a sufficient HPMC concentration was reached, led to the formation of anisotropic shapes. Upon aggregation of these nanocrystals, a mesocrystal is formed as an intermediate, but is apparently not stable due to the low repulsive electrostatic and steric forces. Depletion flocculation of the weakly adsorbed polymer layers was suggested to be the reason for the vanishing of the polymer from the inner mesocrystal surfaces, resulting in subsequent nanoparticle fusion towards an iso-oriented crystal [106]. This iso-oriented crystal was proven to be not single crystalline, as line width analysis in WAXS revealed the nanometer size of the primary building units, which gets smaller with increasing HPMC concentration. This means that the crystal is still built up from brick-like nanoparticle subunits. As typical for mesocrystals, electron diffraction indicated a minor, but detectable orientational disorder, here along the [001] direction, also supporting the nanoparticle aggregation-based mechanism of mesocrystal formation (Figure 7.30).

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Figure 7.30 (a) TEM micrograph of copper oxalate precipitated in presence of 0.0195 g/l HPMC with a square rod shape; and (b) Electron diffraction pattern of the smallest particle on the micrograph, zone axis [1–10]. (Figure reproduced from [106] with permission of Academic Press.)

Figure 7.31 illustrates the whole mesocrystal formation process [106]. Here, the role of the polymeric additive in nucleation, growth, and organized aggregation to a mesocrystal is delineated, and a coding of the mesocrystal morphology, by tuning the surface energies of the nanocrystal building units and thus the nanocrystal morphology, is suggested. It becomes clear that already comparatively small polymer amounts can lead to remarkable differences in the final mesocrystal morphology. It is remarkable to note that the copper oxalate mesocrystals retain their morphology and nanometric substructure throughout thermal decomposition into copper oxide [108]. In a later and more detailed study on the copper oxalate system, also without the HPMC [109–111] the ‘brick-by-brick’ aggregation mechanism could be revealed in a time-resolved study [109,111]. Here, the mesocrystal core parallel to the [110] direction showed poor organization, while the order and the nanoparticle size increased towards the particle surface. The particle density was higher at the hydrophobic e-surfaces than at the hydrophilic a-surface. Kinetic studies revealed a fast nucleation, growth, and onset of agglomeration towards primary mesocrystals with relatively disordered structure, followed by a much slower but also organized growth, via controlled aggregation as the predominant growth mechanism, amplifying the mesocrystal morphology with a gradient of order. Secondary particle nucleation was found as a concurring event. Upon extended ripening, likely by dissolution-recrystallization, high-energy surfaces were eliminated [109,111]. This study supports our view that a mesocrystal – when badly stabilized – is more a kinetic, metastable intermediate than a thermodynamically stable product. In a series of studies, Oaki and Imai reported on various mesocrystal systems. In these examples, so called ‘mineral bridges’ between the individual nanoparticle building units are discussed as a tool to induce crystallization and orientation [112]. (see also Section 8.1, Principal Mechanisms Leading to Mesocrystals and Figure 8.1) These bridges are a plausible explanation for a perfect crystallographic alignment of the building units, because they can transfer the crystal orientation from one nanocrystal to the next, but their existence is experimentally extremely difficult to prove. This building principle is schematically outlined in Figure 7.32. The soft and adhesive PAA polymer serves as mortar between the

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Figure 7.31 Schematic representation of copper oxalate precipitation. Influence of HPMC on the three major steps of particle formation. (Figure redrawn from [106] with permission of Academic Press.)

Figure 7.32 Schematic illustration of sequential growth of calcite bricks covered with PAA. Nanoscale calcite bricks are formed by competitive growth of the crystal with adsorption of PAA. An oriented architecture is achieved by the sequential growth through mineral bridges. (Reproduced from [113] with permission of the American Chemical Society.)

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inorganic nanobricks. For example, acute calcite morphologies could be produced on a surface in the presence of PAA using this principle [113]. PAA was selected as a versatile polymer for the production of mesocrystals. This concept was demonstrated for both inorganic and organic crystals [112,114], and was identified by the authors as much more versatile than previously thought. A very remarkable example of a mesocrystal produced by this concept was reported for the K2SO4–PAA system [114]. In this case, no less than six hierarchical levels of structure formation were observed from the nm scale to the scale of several hundreds of mm. This is a typical feature of biominerals and was so far only rarely reported for a synthetic system (see Figure 7.33) [114]. The superstructure design at each level is controllable by changing the polymer concentration, and the observed hierarchy can be attributed to the interaction between crystals and polymers [114]. On the lowest structural level, the polymer interlayer between individual nanoparticles can be accessed by tainting with dye molecules, which themselves can form J-aggregates (Figure 7.33 tier 6). These nanoparticles then form a mesocrystal subunit (Figure 7.33 tier 4, 5), which stacks with other subunits to form a plate unit (Figure 7.33 tier 3). The plate units themselves stack in a columnar way (Figure 7.33 tier 2), and the columns themselves finally order to a lattice in a microscopic body (Figure 7.33 tier 1). The structuring on the level of a microscopic body by self-organization is extraordinary, because transport of units in the size range of tens of mm is not promoted by diffusion; such big inorganic particles will sediment as a result of their density and size. This means, in turn, that the microscopic structure in Figure 7.33 tier 1 must have been built up by self-organization of nanoparticle building units at the microscopic construction site itself, the complete sophisticated structure formation by self-organization is encoded in the primary nanoparticles, and no secondary processes are involved here. A similar hierarchical system was recently found for potassium hydrogen phthalate and PAA. Again, plate-like units were composed of aligned crystalline nanocrystals [112]. A similar structure sequence that was analyzed over a wider range of conditions was obtained when CaCO3 was precipitated in the presence of a double hydrophilic block copolymer poly(ethylene oxide)-block-poly(styrene sulfonate) (PEO22-PNaStS49) [115]. Ca-concentrations of 10 mM (Figure 7.34 a) and 5 mM (Figure 7.34 b) generated defined, rounded polycrystalline structures. The emergence of a triangular bended top face at 5 mM indicates that the crystals are not uniaxially aligned, but follow a joint field

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Figure 7.33 Overview of the hierarchical architecture in the K2SO4–PAA system and its schematic illustrations at six different size scales (cPAA ¼ 10 g/l): (a), (b) Field emission scanning electron microscopy (FESEM) image and a schematic representation of the macroscopic lattice architecture consisting of large thin plates and columns (tier 1); (c), (d) Columnar assembly between plates (tier 2); (e), (f) Units in the columns (tier 3); (g), (h) Subunits inside a unit (tier 4); (i), (j) Field-emission transmission electron microscopy (FETEM) image and schematic representation of crystallites with the same orientation in a subunit (inset: corresponding selected area electron diffraction (SAED) patterns taken along the [010] direction (tier 5); (k), (l) Energy-filtered TEM (EF-TEM) image and schematic illustration of the organization of dye molecules in a nanostorage space (tier 6). (Figure reproduced from [114] with kind permission of Wiley-VCH.)

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orientation. A Ca concentration of 2.5 mM (Figure 7.34 c) results in the previously described rounded mesocrystals with sixfold symmetry: The constituent crystalline units are, due to a lower relative Ca concentration, significantly smaller, leading to somewhat smoother surfaces. At a Ca concentration of 1 mM (Figure 7.34 d), the particles already possess well-defined rhombohedral morphologies with significantly roughened faces, modified with the characteristic corner and edge truncations due to the presence of the adsorbed polymer. Morphologies similar to single crystals were observed at low Ca concentrations. Rhombohedral calcite particles with remarkable corner and edge truncations were produced at 0.5 mM (Figure 7.34 e) and 0.1 mM (Figure 7.34 f) Ca, with the

Figure 7.34 Calcium carbonate crystals precipitated from a solution containing Ca and PEO22–PNaStS49 at a fixed [Ca]:[S] molar ratio of 1.25:1 and Ca concentrations of: (a) 10 mM; (b) 5 mM; (c) 2.5 mM; (d) 1 mM; (e) 0.5 mM; and (f) 0.1 mM. (Reprinted from [115] with permission of the American Chemical Society.)

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particle faces produced at 0.1 mM being almost entirely smooth. From these pictures one cannot safely state if these particles also form via an aggregation-based mechanism; the outer shape is, however, typical, but with smaller building units, for a locally recrystallized mesocrystal, which usually follows the outer envelope of the preceding structure. Calcite recrystallized by a solution-redissolution process would exhibit both corners and edges, which should be attained extrapolating to low Ca and copolymer concentrations. As the final product morphology is often indistinguishable from a single crystal formed by ion-by-ion growth, identification can only be achieved by time-resolved analysis of the formation mechanism or by analysis of the internal nanostructure of the particles. Microfocus XRD experiments performed on individual crystals reveal further insight into the inner order in these crystals/crystalline aggregates. The [Ca] ¼ 2.5 mM particle, despite showing a rounded profile and rough surfaces (Figure 7.34 c), diffracts like a single crystal, showing only a few isolated spots in the diffraction pattern (Figure 7.35 a). The apparently spherical [Ca] ¼ 10 mM particles (Figure 7.35 a), in contrast, showed powder rings with strong texturing, indicating a substantial degree of preferred orientation for these crystallites (Figure 7.35 b), i.e. the primary units are not random, but aligned along a bend, with joint orientation, as it is typical for liquid crystals. These two examples show that particles that are obviously composed of many subcrystals can exhibit different types of supercrystalline order. The first case with its rough surfaces and identifiable polycrystallinity is a classical mesocrystal, while the more spherical structures are obviously constructed from parabolic or hyperbolic lattice lines and therefore show no translational invariance (thus leading to typical sickle like smearing of the peaks. The occurrence of bent or splayed mesostructures in organized crystal superstructures is a quite common observation and will be discussed below in the context of dipole fields (Section 8.5, The Role Of Dipole and Polarization Forces). As the particle in Figure 7.34 c already diffracts like a single crystal, the following

Figure 7.35 Selected microbeam diffraction patterns from single calcium carbonate particles precipitated from a solution containing Ca and PEO22-PNaStS49 at a fixed [Ca]:[S] molar ratio of 1.25:1 and Ca concentrations of: (a) 2.5 mM (corresponding to Figure 7.35 c); (b) 10 mM (corresponding to Figure 7.35 a). The reflections seen in (a) and (b) correspond to calcite. (Reprinted from [115] with permission of the American Chemical Society.)

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single crystalline scattering behavior of the higher-ordered particle aggregates in Figure 7.34 d–f is not surprising. Very recently, the first spherical mesocrystals were reported for ZnO synthesized in DMF in the presence of poly(vinyl pyrrolidone) (PVP) in a hydrothermal reaction [116]. The spherical mesocrystal structure built from highly anisotropic building units is very unusual, because, for all spherical polycrystalline structures, the nanoparticles normally exhibit an orientation distribution. A good example is the fluorapatite structures formed in a gelatine gel as displayed in Figures 11.1 and 12.1. The spherical final product exhibits the typical rings for polycrystals in the scattering pattern (Figure 11.1). However, the spherical ZnO particles with a pronounced equatorial notch (Figure 7.36) diffract like a single crystal, as shown in Figure 7.36 a and are composed of aligned nanoparticles (Figure 7.36 c). A fractal growth, as observed for fluorapatite in gelatine, leading to an orientational distribution of the building units in the sphere (Figure 11.1) can therefore be excluded. The spherical particles themselves are constructed from two mesocrystalline hemispheres with incorporated PVP, and c-axis oriented ZnO nanoparticles. ZnO has the peculiar property of being noncentrosymmetric along the [001] direction, which results in a positively charged (001) face and a negatively charged (00-1) counterface. Therefore, the (00-1) juncture is considered as a symmetric plane between the upper and lower mesocrystal hemisphere. The formation mechanism of these unusual spherical mesocrystals is largely unknown as yet. It is speculated that a cationic thermal DMF hydrolysis product could stabilize the negative (00-1) surface, whereas the positive (001) surface interacts with PVP as revealed by FTIR [116]. However, what leads to the c-axis orientation of the ZnO nanocrystallites and their very unusual self-organization into a hemisphere with subsequent fusion of the two hemispheres, is yet unknown.

7.10 Mesocrystals in Nonaqueous Systems Although the predominant number of crystallization reactions is performed from ions and therefore in water, mesocrystal formation is not restricted to this solvent. On the contrary, organic solvents even allow the observation of orientation effects free of charges and Coulombic monopole interactions. On the other hand, as dielectric constants of organic solvents are usually much smaller than water, all other interactions (dipole-dipole interactions, polarization forces and dispersive forces) are much stronger in organic solvents, making them even more suited to observing orientation effects. An elegant route to highly crystalline, defect-free, high-purity nanoparticles is the synthesis via nonaqueous sol-gel chemistry, where non-toxic solvents act as reactant as well as control agent for particle growth, thereby allowing the synthesis of high-purity metal oxide nanoparticles [117–119]. It is a remarkable feature of these processes that the as-synthesized nanoparticles exhibit a wide variety of particle morphologies, including spheres [120–122], ellipsoids [123], cubes [124], platelets [125,126], wires [127], and hybrids [128]. Despite the various morphologies, within the same reaction system the particles are characterized by high homogeneity with respect to particle size and shape.

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Figure 7.36 (a) TEM image of a ZnO/PVP sphere and (b) its SAED patterns along the [0001] zone; (c) HRTEM image of a sphere viewed along the c-axis; (d) FESEM image of a ZnO/PVP sphere (side-view). (Image reproduced from [116] with permission of the ACS.)

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Nonaqueous sol-gel processes are typically performed in a temperature range of 50 to 200 C. These moderate conditions are a prerequisite for the organic species in the reaction mixture to fulfil its complex role as reactant and crystal growth modifier. For systems with sufficient anisotropy and interactions, the solvent also acts to support organized assembly of the particles, and dissolution of additional, face-selective ligands (‘assemblers’) even refines the textural organization, analogous to biomimetic processes [129]. The synthesis of tungsten oxide nanoparticles and nanostructures constitutes an illustrative example of how precursors, solvents, and additional ligands influence crystallite size, shape, and assembly behavior [130]. The reaction of tungsten chloride with benzyl alcohol yields tungstite nanoplatelets with a relatively broad size distribution of 30 to 100 nm (Figure 7.37 a) [130]. Addition of the bioligand deferoxamine mesylate, a siderophore, changes the particle morphology completely from a pseudotwo-dimensional shape to one-dimensional nanowire bundles (Figure 7.37 b). These nanowires are single-crystalline and exhibit a uniform diameter of 1.3 nm (Figure 7.37 c) [130]. If a small amount of 4-tert-butylcatechol is added to the tungsten chloride–benzyl alcohol mixture, anisotropic rod-like architectures with diameters between 35 and 40 nm are observed (Figure 7.37 d) [131]. The rods consist of a highly ordered, lamellar

Figure 7.37 TEM or SEM images of various tungsten oxide nanoparticles and nanostructures: (a) nanoplatelets; (b) nanowire bundles; (c) nanowires (HRTEM image); (d) columns of stacked nanoplatelets (inset: separated individual nanoplatelets); (e) laterally assembled columns of stacked nanoplatelets; (f) nanowire ribbons (inset: separated individual nanowires). (Images (b)–(c) taken from [130] with permission of the American Chemical Society.)

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organic–inorganic hybrid nanostructure, where the lamellae are stacked in one crystallographic register with high precision. The only slightly corrugated sides of the rods prove the good monodispersity of the nanoparticulate building blocks. No individual or isolated nanoparticles are found in the sample washed in chloroform, whereas many discs and platelets with round corners are detected upon drying and redispersing the brown powder in water (Figure 7.37 d, inset). This finding clearly gives evidence that the inorganic platelets interact only weakly, i.e., the superstructure is built up by secondary interactions of the organic phase, only; no crystal bridges are formed. The reaction between tungsten chloride and 4-tert-butylbenzyl alcohol (instead of benzyl alcohol) results in the formation of a fibrous network. The TEM image reveals ribbon-like structures consisting of parallel columns of nanocrystals with uniform diameters of about 4 nm (Figure 7.37 e) [131]. Each nanocolumn is composed of selfaligned nanoplatelets about 1 nm thick and facing each other along the entire length of the nanostack. The individual nanostacks are nearly monodisperse in diameter as a consequence of the uniformly sized platelets, which leads to an outstanding alignment on two levels of hierarchy. It is intriguing to follow the tremendous difference in crystal growth and in the assembly of the tungsten oxide building blocks, although 4-tertbutylbenzyl alcohol and benzyl alcohol differ only in the presence of a tert-butyl group. If the precursor is changed from tungsten chloride to tungsten isopropoxide, tungsten oxide nanowire bundles are obtained in benzyl alcohol without the use of any additional structure-directing templates (Figure 7.37 f) [132]. The nanowires are kept together by intercalated benzaldehyde molecules that are formed in situ during the synthesis. The bundles can be split up into individual nanowires of 1 nm diameter by the addition of formamide to a dispersion of the nanobundles in ethanol (Figure 7.37 f, inset). The high surface-to-volume ratio combined with the high purity of the material makes these nanowire bundles ideal candidates for gas-sensing devices. Preliminary results confirm this assumption, as these nanowires show an extraordinarily good sensitivity to NO2 concentrations in the ppb range [132]. Mesocrystallization, in these special cases, regularly involves more than one level of hierarchy. Careful analysis of the plates forming the extended stacks in Figure 7.37 d (which can be exfoliated using different solvents) indicates that they are not single crystals, but superstructures themselves (Figure 7.38). As clearly evidenced by the detectable grain boundaries, about 100–200 nanoparticles form a mosaic-like pattern towards one joint mesocrystal, which is only one nanoparticle layer thick. The vectorial organization of the primary units, in spite of the grain boundaries and rounded corners, is nevertheless about perfect. Ordered nanoparticle assemblies in nonaqueous solvents were also observed during the crystallization process of indium tin oxide (ITO) nanoparticles, but with a very uncommon superstructure (Figure 7.39) [133]. In an intermediary phase of reaction, and directly after onset of crystallization (when the particles are still sufficiently small), the system forms large extended nanostripes of matter, which are obviously composed of one layer of nanoparticles aligned in a striated line pattern.

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Figure 7.38 More detailed analysis of the ‘beer mat particles’ forming the stacks shown in Figure 7.37 d: (a) overview of the non-stacked particles; (b) higher magnification of one particle indicating rounded corners; (c) corresponding electron diffraction picture indicating apparent single crystal character; (d) high magnification of the same particle indicating that the plate is an oriented mosaic pattern of primary particles ca. 5 nm in size, i.e. a mesocrystal. (Images (a)–(e) taken from [131] with permission of the American Chemical Society.)

Although the 4 nm sized nanoparticles are nearly perfectly position-aligned into those striated two-dimensional arrays, the lattice fringes of the individual nano building blocks are not oriented with respect to each other. Obviously, the anisotropic interactions in ITO are only weakly related to the crystal orientation. We speculatively related the order to polarization of the mobile electron plasma within those conducting particles, which is indeed the case for cubic particles independent of orientation. Those superstructures can also extend in three dimensions, as observed by scanning electron microscopy. Regarding future work on the controlled assembly of nanoparticles into complex structures, it is a central question how these nanoparticles can align to extended arrays without any mutual orientation of the crystal lattices.

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Figure 7.39 Ordered nanoparticle films found as an intermediate in the nonaqueous synthesis of ITO nanoparticles. The nanoparticles form extended lines, which again pack to thin stripes. In this case, a rotational orientation of the single particles is not observed, although translational order is quite high. (Pictures reproduced from [133] with permission of Wiley-VCH.)

7.11 Mesocrystals Formed via Solid-State Reactions Mesocrystals can also be formed via solid-state reactions. Here, either a solid matrix can serve as a template or steric stabilizer, which keeps the nanocrystal building units of the mesocrystal apart and thus prevents crystallite fusion, or the mesocrystals are formed by a chemical reaction from a crystalline precursor phase by keeping the crystal orientation or other boundaries of the initial phase. 7.11.1

Solid Matrices for Mesocrystal Formation

A crystallization reaction starting from an amorphous precursor phase can be performed in such a way that the crystals within the solid matrix are oriented to produce mesocrystals. This is nicely shown by model experiments based on a binary sequence of amorphous layers, where only one of the two layers is able to crystallize and the other

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acts as a solid matrix or separating scaffold, as was demonstrated for the formation of Si mesocrystals in an amorphous matrix of SiO2 [134]. The nm thick amorphous Si (a-Si) layers were deposited by magnetron sputtering with controllable size in the nm range followed by plasma oxidation, which produces a 3 nm thick SiO2 layer [135,136]. Then the next a-Si layer is deposited, surface oxidized, and so on. The crystallization of Si nanocrystals between the SiO2 layers can be achieved in two steps by rapid thermal pulse annealing and slow ramp-up furnace annealing [134]. This leads to Si mesocrystals in an amorphous SiO2 matrix separating the nanocrystallites, as shown in Figure 7.40. The thickness of the layers with the Si crystals is important for the shape of the crystals, as can be seen in Figure 7.40. A 4.2 nm nanocrystalline Si layer consists of only spherical and elliptical nanocrystals with huge variations in their shape (Figure 7.40 a), whereas in the 8.5 nm Si layer consists of square-shaped nanocrystals (Figure 7.40 b) and the 20 nm Si layer of well-defined brick-like nanocrystals (Figure 7.40 c, d). Polarized Raman spectroscopy of the 20 nm thick layer in Figure 7.40 d reveals the [111] orientation of the nanocrystallites in the mesocrystal, with less than 5% deviation in the layer stack [134]. The orientation of the Si nanocrystals between the amorphous SiO2 layers can be discussed as a result of the constrained vertical growth of the Si nanocrystals and the

Figure 7.40 Transmission electron microscope micrographs showing examples of nanocrystalline Si superlattices with different thicknesses of nc-Si layers: (a) 4.2 nm; (b) 8.5 nm; (c) 20.0 nm; and (d) the enhanced image of a brick-shaped Si nanocrystal with 20.0 nm and 50.0 nm vertical and lateral dimensions respectively. Note that crystallization is performed under identical conditions for all samples. (Image reproduced from [134] with permission of Nature Publishing Group.)

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significant growth rate differences in the different crystallographic directions of Si, leading to an alignment of the nanocrystals [137]. It is nevertheless interesting that the layers exhibit mutual orientation, although the amorphous separator phase does not support epitaxy as an orientation mechanism. This speaks either for a field-based crosscommunication between the layers or – as stated by the authors – by a dynamic discrimination of directions via growth speed. These effects make the presence of ‘crystal bridges,’ as discussed in some other publications, a supportive but unnecessary precondition of oriented crystallization. 7.11.2

Topotactic Reactions

Mesocrystals can also be formed by a topotactic solid-state reaction. The term topotaxy (Greek; ‘topos’: ‘space’ and ‘axis’: ‘in ordered manner’) describes all solid-state reactions that lead to a material with crystal orientations which are correlated with crystal orientations in the initial product [16]. Such mesocrystals were actually the first for which the single crystalline scattering behavior in X-ray or electron diffraction was observed together with a peak broadening due to the small size of the primary building units [21,138]. The first introduction of the term ‘topotaxy’ was by Lotgering in 1959 [16]. Topotaxy shows an essential difference from epitaxy. Epitaxy is a kind of interface between a thin film and a substrate. The term epitaxy (Greek; ‘epi’: ‘above’ and ‘taxis’: ‘in ordered manner’) describes an ordered crystalline growth on a (single-) crystalline substrate. It involves the growth of crystals of one material on the crystal face of another (heteroepitaxy) or the same (homoepitaxy) material. The lattice structure and orientation or lattice symmetry of the thin film material is identical to that of the substrate on which it is deposited. Most importantly, if the substrate is a single crystal, then the thin film will also be a single crystal. Consequently, the final product of an epitaxial process is an intergrowth of the new phase and the substrate. In case of topotaxy, the substrates disappear completely as they react in a solidstate reaction and the final products consist of only the newly formed pure phase. If the product of a topotactic transformation is denser than the educt, the product will contain pores due to the volume contraction associated with the transformation. The crystallographic orientation relations between educt and product crystals usually do not originate from the homogeneous transition of the educt crystal into the product crystal. Instead, the educt crystal matrix serves as a heterogeneous nucleation surface for the induced nucleation of a large number of product nuclei, which are crystallographically oriented in the three-dimensional educt crystal matrix. The growth of the nuclei happens by diffusion processes, which are typical for solid-state reactions at elevated temperatures. During the growth process, the product crystals keep their orientations and a mesocrystal is formed. One very illustrative notation for the resulting product crystal system is ‘topotactic reaction fabric.’ [3] The orientation relations between educt and product of a large number of known topotactic reactions are no group and subgroup relations between the different crystal structures, but originate from the equality of minimal energy considerations for the smallest regions in the crystal, where the product phase is nucleated. This means the product crystal orientation is determined by the crystal lattice of the educt because that way the nucleation barrier is lowest, but the space group of the nucleated phase must not

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be related to the environment. For example, the topotactic reaction of brucite Mg(OH)2 to periklas MgO mesocrystals [17,18] via thermal dehydration leads to a topotactic reaction fabric with anions forming a cubic densest sphere packing of the periklas product while the brucite educt has a hexagonal densest sphere packing. These structures are not related by a group–subgroup relation. The topotactic transformations of the above kind are often also denoted as pseudomorphous transformations, as the external morphology of the educt crystal can be kept, although the product crystal, as such, should exhibit a different geometry. According to Strunz [139] pseudomorphosis can be classified as:

Para-morphosis or transformation pseudo-morphosis of polymorphs Demixing pseudo-morphosis of mixed crystals Depletion pseudo-morphosis Peri-morphosis or overgrowth pseudo-morphosis Filling pseudo-morphosis.

Depletion pseudo-morphosis is the most common pseudo-morphosis reaction found in mesocrystals formed by topotactic transformations. A large number of pseudo-morphosis reactions and topotactic transformations are reported in the literature. In the following, we will discuss some topotactic transformations leading to mesocrystals. One example is the oxidation of pyrochroite Mn(OH)2 to feitknechtite b-MnO(OH), as reported in [23]. Figure 7.41 a shows the thin hexagonal platelets of the starting product, which are oxidized to hexagonal b-MnO(OH) (Figure 7.41 b). A closer look (Figure 7.41 c) reveals the porous structure of the hexagonal platelets and very fine nanoparticles, indicating that the hexagonal platelets consist of nanoparticles and show multiple defects in the form of pores.

Figure 7.41 Topotactic oxidation of pyrochroite Mn(OH)2 to feitknechtite b-MnO(OH) in air with controlled water vapor pressure leading to b-MnOOH mesocrystals: (a) Mn(OH)2 starting product (80 000 ); (b) b-MnOOH product (80 000 ); and (c) Zoom in of a b-MnOOH nanoparticle (700 000 ) showing the existence of pores and smaller nanoparticles. (Images reproduced from [23] with permission of Consiglio Nazionale delle Ricerche Roma.)

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The oxidation of the Mn(OH)2 educt was found to progress from the edges of the platelets, growth steps, and overgrown little crystals on the particle surface in a direction parallel to the layers (001). As the trigonal-hexagonal scalenohedral (a scalenohedral is a crystalline body, see http://www.mineralienatlas.de/smorf/smorf.php?mineral¼ Skalenoeder) Mn(OH)2 (space group: P 3m1) with a density of 3.26 g/ml is less dense than the hexagonal b-MnO(OH) (Space group Unk) with a density of 3.8 g/ml, the formation of pores upon the topotactic reaction becomes understandable (data taken from http://www.webmineral.com/). If the reaction is monitored by electron diffraction (Figure 7.42), the transformation of the single crystalline Mn(OH)2 platelets to the b-MnO(OH) mesocrystals can be nicely followed. In all cases, the diffraction pattern is that of a single crystal. However, the initial Mn(OH)2 platelet shows sharp diffraction spots (Figure 7.42 a), indicative that each nanoplatelet is a single crystal, whereas that of the b-MnO(OH) mesocrystals is broadened (Figure 7.42 c) indicating the small size of the primary nanoparticles making up the mesocrystal. This observation supports the direct imaging in Figure 7.41 c. The intermediate stage (Figure 7.42 b), where only parts of the educt have reacted to the product, shows this very clearly as the diffraction pattern is an overlay of the educt single crystal and the product mesocrystal, composed of small nanocrystallites. The authors of the original publication [23] noted more than 40 years ago: ‘It is noteworthy how highly oriented the products described occur during the whole range of transformations from Mn(OH)2 to b-MnO(OH) to d-MnO(OH) to Mn3O4 and MnO, the first two

Figure 7.42 Electron diffraction pattern for the topotactical oxidation of pyrochroite Mn(OH)2 to feitknechtite b-MnOOH in air with controlled water vapor pressure leading to b-MnOOH mesocrystals: (a) Mn(OH)2 starting product showing single crystal diffraction; (b) intermediate product of topotactic assembly of Mn(OH)2 and b-MnOOH, showing single crystal diffraction and superposition of the individual diffraction patterns of both single crystals. Note the broadened diffraction spots of b-MnOOH indicating their small particle size; and c) diffraction pattern of orthorhombic pseudohexagonal b-MnOOH. (Images reproduced from [23] with permission of Consiglio Nazionale delle Ricerche Roma.)

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produced in a liquid film, the second two within the electron microscope under high vacuum.’ Another classic example of orientation relations between educt and product of a topotactic solid-state reaction is the thermal dehydration of lepidocrite (g-FeO(OH)) to maghemite g-Fe2O3 [21,22]. In this experiment, the maghemite (isometric – tetartoidal, space group P 213, r ¼ 4.9 g/ml) mesocrystal is formed in an oriented way inside the matrix of the lepidocrite needles (orthorhombic dipyramidal, space group Amam, r ¼ 4 g/ml, data taken from http://www.webmineral.com/). Again, the product density is considerably higher than that of the educt, and the diffraction patterns show the typical superposition of educt and product diffraction throughout the course of reaction. As typical for this kind of solid-state reaction, the building units of the mesocrystals are small nanocrystals, as evidenced by their typical broadened diffraction spots. A further example is the formation of Eu3O4 by a topotactic solid-state reaction of LiEu3O4 by heating [19,20]. Again, the product is more dense than the educt and the diffraction data show a superposition of Eu3O4 and LiEu3O4 diffraction patterns, where the symmetry directions of the rhombohedral unit cells of Eu3O4 and LiEu3O4 are superimposed, so that the a, b and c axes of educt and mesocrystal product have exactly the same orientation [19]. Initially, the product diffraction spots are rather diffuse indicating the small particle size of the primary nanoparticle units of the mesocrystal. Upon annealing, the diffraction spots become sharper, which indicates an increasing size in the crystallographically coherent units e.g. a mesocrystal to single crystal transition (see also Section 8.9, Mesocrystals as Intermediates in Single Crystal Formation). Characteristic for many topotactic reactions leading to mesocrystal-type textures are several features: (1) The density of the mesocrystal product is higher than that of the single crystalline educt. This leads to fine pores in the mesocrystal, which is still held together by mineral connections between the individual nanocrystals. The pore formation maintains the reaction progress into the educt single crystal interior. (2) Time-resolved diffraction patterns show sharp spots for the educt at the start of the reaction, which are subsequently overlaid by the diffraction pattern of the product mesocrystal, revealing the orientational relation between the two crystals. (3) The high nucleation speed of induced heterogeneous nucleation on/in the educt single crystal matrix, but comparatively slow growth, lead to the formation of the nanocrystal building units of the mesocrystal, which become evident as broadened spots in diffraction patterns. Ripening to larger single crystalline domains can be revealed by sharpening of the diffraction spots. Mesocrystal themselves are ideal starting materials for transformation by a topotactic reaction. One elegant example is the topotactic reaction of dicalcium phosphate dihydrate (DCPD) to dicalcium phosphate (DCP) by dehydration and then further conversion to hydroxyapatite (HAP) by rapid DCP hydrolysis with NaOH solution [140]. As already discussed in Section 7.6, Mesocrystals in Gels, a gel can be advantageously applied for the synthesis of mesocrystals because a high supersaturation can be maintained without the rapid mixing of the mineral forming ions. Using this

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strategy, the precipitation of calcium phosphate in a gelatine gel was found to lead to DCPD with ca. 2% gelatine incorporated into a hydrated layer parallel to the (010) plane. Dehydration of the DCPD to DCP at 60 C in air kept the macroscopic crystal morphology (Figure 7.43 a), but led to a dramatically different laminated microstructure (Figure 7.43 b, c). The laminated DCP architecture was found to consist of rectangular units (2–5 mm in length and 100–200 nm width, Figure 7.43 d). These building units themselves are composed of DCP nanoparticles with a size of ca. 50 nm, which are mutually crystallographically oriented to a mesocrystal along the [100] and [001] directions (Figure 7.43 e, f). In this way, a complex mesocrystal structure is obtained with hierarchical organization. FTIR investigations suggested that the nanocrystals are covered by gelatine and that the hierarchical structure is organic–inorganic in nature. Gelatine plays a dual role in the structure formation process: (1) It provides a gel matrix for the formation of gelatine-incorporated DCPD precursor crystals. These crystals grow slowly with the inclusion of gelatine molecules due to a specific gelatine interaction, and rapid mixing of the ions is prevented by the gel matrix. (2) Gelatine assists and promotes the phase transition of DCPD to DCP by dehydration at 60 C, and a specific interaction with the (100) and (001) DCPD faces restricts the DCP growth during the phase transition. This leads to lattice structures with rectangular units mainly exhibiting (010) faces and the emergence of a hierarchical structure. Rapid hydrolysis of the DCP structure to HAP at 95 C and pH 13.6 preserves the delicate hierarchical architecture, as the conversion can be carried out in a topotactic way. The fast growing HAP c-axis is parallel to the surface of the formed nanoplate units (ca. 20 nm in size), which make up the hierarchical mesocrystal structure. Indeed, the laminated structure is preserved and similar to that in Figure 7.43. The structural details are, however, smaller, due to the smaller HAP building units (Figure 7.44). The topotactic conversion is assessed to be successful because the size of the nanocrystals making up the mesocrystal structure in educt and product is similar, and the lattice angle of the laminated structure remains unchanged. The gelatine inclusions in the hierarchical crystals are important for the formation of the hierarchical mesocrystal structure, as a similar HAP structure cannot be obtained when performing the same reaction cycle on commercial DCPD crystals. This remarkable reaction sequence shows that topotactic reactions can be used advantageously to produce hierarchically organized mesocrystal structures by simple chemical reactions. The whole sequence is schematically illustrated in Figure 7.45.

7.12 Liquid Crystals, Tactoids, Somatoids, and Schiller Layers In the discussion of mesocrystal systems, the relation between mesocrystals and order phenomena in classical liquid crystalline systems becomes obvious. Whereas the mesocrystal systems discussed so far have a solid phase, which interspaces the aligned nanocrystals (polymer, surfactant) or the nanocrystals are crystallographically connected

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Figure 7.43 Appearance of DCP crystals dried at 60 C: (a) an optical micrograph ; (b), (c) and (d) SEM images; and (e) and (f) TEM images. The inset of (e) is an electron diffraction pattern for the rectangle area. The laminated structure made up from rectangular mesocrystals is clearly visible. (Figure reproduced from [140] with permission of the American Chemical Society.)

via mineral bridges, in liquid crystals, the building units are interspaced by a liquid, thus allowing fluidity. Liquid crystals are indeed known for having anisotropic nanoparticles as building blocks, as well as for molecular building units, which exhibit a rigid and anisotropic unit (mesogen).

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Figure 7.44 Appearance of HAP crystals formed by topotactic reaction from the DCP structures in Figure 7.43: (a) an optical micrograph; (b) and (c) SEM images; and (d) a TEM image. (Figure reproduced from [140] with permission of the American Chemical Society.)

Figure 7.45 Schematic illustration of the overall process from precursor DCPD (a) to nanostructured HAP (c) through nanotextured DCP (b). Precursor DCPD (a) was prepared in gelatine gel containing phosphate ions. Nanotextured DCP (b) was obtained by the dehydration of precursor DCPD. Nanoscale structures of HAP consisting of textured particles (c-1) and fibers (c-2) were formed by hydrolysis at pH 13.6 and 10.0, respectively. (Figure reproduced from [140] with permission of the American Chemical Society.)

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The most obvious difference is the fact that liquid crystals are liquid, meaning that their building units can become displaced with respect to each other. This is not observed for the solid mesocrystals. The second difference is that the order in liquid crystals is usually lower than the almost perfect order usually observed in mesocrystals. The order in liquid crystals is expressed by the order parameter S, which is defined as: S¼

3 cos2 y 1 2

ð7:1Þ

where y ¼ the angle between the mesogen molecule axis and the local director (which is the average ‘preferred direction’ in a liquid crystal sample). For a completely random and isotropic sample, S ¼ 0, whereas for a perfectly aligned sample S ¼ 1. For a typical liquid crystal sample, S is of the order of 0.3 to 0.8, and generally decreases when the temperature is raised. The transition between highly ordered mesocrystals (S 1) and poorly ordered liquid crystals (S 0:3) is obviously continuous. Similar order transitions – fixed the the solid state – have, in fact, already been observed for mesocrystals [115]. (Figure 7.34, Chapter 11). In this case, the order can also vary from S ¼ 1 (perfect mesocrystal) to S ¼ 0 (unoriented polycrystalline aggregate). As traditional liquid crystals are discussed in various textbooks, it is beyond the scope of this book to treat them in great detail here. Nevertheless, some work closely related to the mesocrystal concept will be discussed here. The liquid crystalline analogs to mesocrystal microparticles are the so-called ‘tactoids.’ Tactoids are a particular form of concentrated colloidal suspension dispersed within a more dilute suspension of the same colloidal nanoparticles. (For a review on tactoids and Schiller layers, see [141].) A tactoid usually consists of two phases, one of which is dispersed in the other, i.e. they are lyotropic liquid crystals. The tactoid-forming particles can be either organic or inorganic in nature, and their nanoparticle building units possess an anisotropic shape typical for mesogens (fiber, needle, plate). In a tactoid, the building units are mutually oriented in a quasi parallel manner, whereas in the surrounding dilute phase, they are randomly oriented. Tactoids were first described as early as in 1925 by H. Zocher for the dyes benzopurpurin 4B and chrysophenin, as well as aged vanadium pentoxide and iron hydroxide sols [6]. The shape of the tactoids is usually a prolate ellipsoid or in form of layers as shown in Figure 7.46, differing from the usual droplets with a spherical shape (see also Section 4.2, Liquid Precursors). This is the expression of the minimization of an anisotropic surface energy tensor. All tactoids show uniform orientation of their subunits as evident by their uniform double refraction between crossed polarizers. The vanadium pentoxide tactoids still showed Brownian motion of their building units indicative of their weak interaction and the fluid interspacing. These tactoids could be destroyed by mixing, and formed again, i.e. they are equilibrium structures. Very similarly, iron hydroxide colloids formed so-called ‘Schiller layers’ (schillernd (German) ¼ iridescent), where the layer distances are of the order of the wavelength of light, leading to the observed iridescence by Bragg reflection. These Schiller layers consist of b-FeOOH (akagenite) [142] and are, so far, the most investigated tactoid

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Figure 7.46 The first reported examples of tactoids [6] observed with the light microscope: Benzopurpurinosol in (a) polarized light and (b) between crossed Nichols prisms; demixed vanadium pentoxide sol in (c) polarized light and (d) between crossed Nichols prisms; aged iron hydroxide sol (Schiller layer) in (e) polarized light and (f) between crossed Nichols prisms. PP and AA are the polarization directions. (Image reproduced from [6] with permission of Wiley-VCH.)

system. Interestingly, the analogy of these liquid crystals to butterfly wings has been drawn, as both of them are photonic structures. Later, Zocher called the Schiller layers ‘supercrystals’ [141]. Brownian motion of the subunits was also evidenced in the Schiller layers. Zocher also explored the role of magnetic and electric fields, as well as mechanic shear onto the structure of the tactoids. Magnetic fields and shear-generated anisotropy not only align, but also stretch large tactoids along their axis, as shown in Figure 7.47. This is an effect of the anisotropy in magnetic susceptibility [143]. The effect of magnetic fields on such structures has already been investigated via detection of the birefringence in magnetic fields caused by the alignment of the plateshaped building units [144,145]. Interestingly, electric fields change the layer distance and therefore the colour [6]. The early work of Zocher contains, not only the description of this type of ordered liquid crystal composed of nanocrystals, but also ways to modify the internal structure. Zocher also reflected on ‘ordered or parallel coagulation’ as the reason for the oriented assembly of the tactoids. A balance between attractive molecular and repulsive electrostatic forces was identified for the ordering of nanoparticles. If the interparticle distances are high, the interaction is weak, and Brownian motion of the nanoparticles can be observed, as in the example of the Schiller layers. For small interparticle distances, the binding interactions in the tactoids are so strong that particle motion is suppressed [6]. Interestingly, Schiller layers can be dried without structural collapse as long as a slow

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Figure 7.47 (a) The orientation of tactoids in a magnetic field. The direction of the field is given on top of the figure, demonstrating that the tactoids align with their long axis in direction of the magnetic field; (b) A tactoid in the absence of a magnetic field: and (c) the same tactoid stretched along its axis by the magnetic field. (Image reproduced from [143] with permission of MAIK ‘Nauka/Interperiodica.’)

drying process is maintained. As the liquid between the charged nanoparticles is now missing, we would assign the dried structure mesocrystal character, where interparticle binding is so weak that the structures can be reswollen. Indeed, reanalysis of these classical studies shows a way in which prolate and oblate mesocrystals could be assembled. In case of the iron oxyhydroxide tactoids, electrolyte addition decreases the interparticle distance, as evidenced by the change in colour. These are considerations of colloidal forces and the balance between attractive and repulsive forces, which are discussed in more detail in Chapter 8. The given reason that an elongated nanoparticle also exhibits a nonspherical, anisotropic ion cloud, which leads to parallel orientation of the nanoparticles, is valid and also relevant for crystallographic orientation in mesocrystals. Later on, the Schiller layer forming b-FeOOH tactoids, as well as their formation mechanism were characterized in more detail and their mesostructural character revealed [146]. The nanocrystals forming the Schiller layers were found to be elongated nanoparticles with a quadratic cross section (Figure 7.48 b, d) and rounded edges (Figure 7.48 a), in stark contrast to the plate-shaped nanoparticles assumed by Zocher in

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Figure 7.48 (a) Unsectioned whole crystals of b-FeOOH ( 50 000), scale bar ¼ 100 nm; (b) Cross section of an orthogonal array of crystals ( 90 000), scale bar ¼ 100 nm; (c) an approximately longitudinal section of a group of b-FeOOH crystals ( 40 000). This section is inclined somewhat toward the diagonal of the orthogonal crystals so that their apparent widths (58 nm) are somewhat larger than they would be if they had been sectioned parallel to a side (55 nm).;(d) A crystal sectioned at an angle significantly less than 90 showing lines parallel to the sides ( 280 000); (e) Crystal sectioned obliquely through the tip of a crystal ( 280 000); and (f) sectioned as a thin fragment ( 326 000). (Images reproduced from [146] with permission of the American Chemical Society.)

the initial work [6]. Even more, it turned out that the nanocrystals forming the Schiller layers are themselves already a mesocrystalline structure composed of primary rod-like nanoparticles with an interlayer distance of 3 nm. The mesocrystal building units of the Schiller layers (Figure 7.48 a) are remarkably uniform, with square sides of 55 3 nm (Figure 7.48 c,d) These results again reveal a hierarchical structural theme of mesocrystals demonstrating well-developed ordering of the structural units over several length scales, according to different organizational mechanisms. It is also interesting to note that the Schiller layers were already called a colloidal crystal. In the higher resolved TEM micrographs (Figure 7.48 d–f), the substructure of the primary nanoparticles forming the Schiller layers becomes evident, revealing that these particles themselves are mesocrystals with parallel-aligned subunits. These rod-like subunits have a cross section of 3 3 nm separated by 3 nm (Figure 7.48 d–f). The pore

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Figure 7.49 A drawing to illustrate the probable structure of the primary crystals in a Schiller layer with a mesocrystal structure. (Image reproduced from [146] with permission of the American Chemical Society.)

size of 3 nm was confirmed by nitrogen adsorption measurements, further revealing the porous mesocrystal structure [147,148]. The structural model of these crystals, which could be developed on the basis of these findings (Figure 7.49) is very similar to the schematic drawing of a mesocrystal in Figure 4.1. In this case, the light regions in Figure 7.48 d–f) are the spacings between the electron dense rod-like building units. The initial contradiction of the small interparticle distances of only 3 nm reported by Watson [146] with the much larger layer distances in the range of the wavelength of light reported by Zocher [6] was only resolved 60 years after the original work and 20 years after the more detailed Watson study. Maeda et al. suggested a smectic-like arrangement of elongated rods, which themselves have a mesocrystal structure composed of primary nanoparticles. This hierarchical mesocrystalline-smectic structure of the Schiller layers is shown in Figure 7.50 a according to the model presented by Maeda and Hachisu [149]. This model was confirmed by SEM results, as shown in Figure 7.50 b and also by AFM [150]. This impressive image indeed shows the large perfected smectic layers of the oriented mesocrystals, but also some obvious defects are found, as typical for mesostructures. Mesocrystals are indeed error tolerant and accept larger voids and orientational defects, keeping the overall order scheme. It must be underlined that Schiller layers, however, can only develop when the primary nanoparticle arrangement forms monodisperse rod-like superstructures, as a polydispersity in the rod length would cause local undulations in the smectic layers leading to layer roughening and, finally, packing breakdown. A layer undulation was later observed by AFM [150]. This speaks for the fact that mesocrystallization and the following smectic packing are not independent, but dynamically crosscoupled processes. The V2O5 tactoids first described by Zocher [6] (see Figure 7.46 c, d) were later also investigated more systematically to reveal their formation mechanism and the transformation of tactoids with time [152]. In this case, very small ( Ua;b , and the a- or b-axis is aligned parallel to the magnetic field. This means that the c-axis of a particle is aligned, in all directions, perpendicular to the imposed magnetic field. Both cases are visualized in Figure 8.17. These considerations show that a mesocrystal can only be obtained for case (a), so that a consideration of the directionally dependent magnetic susceptibilities of a given crystal system can already reveal whether mesocrystal formation can be expected by magnetic field alignment or not. Even then, the alignment along one axis, as shown in Figure 8.17 a is not yet sufficient to form a mesocrystal, because the other two magnetic axes remain unaligned, and a three-dimensional orientation in a crystallographic register is not yet obtained. This alignment can be achieved by the shape of the crystallites leading to a

Figure 8.16 A schematic view of hexagonal crystal with magnetic anisotropy. (Figure reproduced from [47] with permission of Elsevier.)

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Figure 8.17 Schematic view showing the alignment of nanoparticles in a magnetic field. (Figure reproduced from [47] with permission of Elsevier.)

mutual particle orientation when the particles come into close proximity, which can be achieved by slow drying of the dispersion. Another effective way to three-dimensionally align a magnetic crystallite using a magnetic field is the combination of a static magnetic field, which aligns the easy magnetization axis, and a rotating magnetic field, which aligns the hard magnetization axis. Here, the rotation must be performed with a nonconstant velocity, as the constant rotation would only lead to the uniaxial alignment of the hard magnetization axis. As the magnetic fields that are required for the alignment are high and usually in the range of a few Tesla, it is more practical to rotate the sample in a static magnetic field [58]. Mesocrystal formation by this method was recently demonstrated for L-alanine crystallites, by applying a special frequency modulated sample rotation program in a magnetic field (Figure 8.18) [58]. This special sample rotation scheme in the magnetic field ensures that the angular velocity o is slow (o1 ) when the local sample x’-axis passes through the x-axis of the laboratory coordinate system (direction of the magnetic field) and high (o2 ) when the x’-axis passes the y-axis of the laboratory coordinate system, which is perpendicular to the magnetic field. This leads to an alignment of micron sized L-alanine crystallites to a mesocrystal in a resin, which can be fixed by photopolymerization [58]. A high ordering of the crystallites was achieved in all three perpendicular directions and only a slight rotational spread of ca. 3 half width was observed in the single crystal diffraction pattern, as shown in Figure 8.19. These results suggest a quite universal possibility for the production of mesocrystals. This method was applied to align Somasif, a synthetic mica, which then aligned intercalated guest dye molecules of Rhodamine B [59]. The alignment by a magnetic

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Figure 8.18 Diagram illustrating the frequency modulated sample rotation. The x-, y-, and z-axes are laboratory coordinates; the x- and y-axes are on the horizontal plane and the z-axis is on the vertical plane. The x’-, y’-, and z’-axes are imbedded in the sample that is rotated around the z’-axis (the z-axis coincides with the z’-axis). The rotation is performed nonuniformly so that o1 (5 rpm) < o2 (25 rpm). The x-axis coincides with the direction of the magnetic field. (Reproduced from [58] with permission of the American Chemical Society.)

field can, however, only occur when the crystal size d of the precursor particles is large enough that the magnetic energy exceeds the thermal energy. For a particle with its magnetic axis aligned with the external field, the critical size d can be estimated according to: 2kTm0 1=3 d¼ ð8:3Þ jwa jB2 where k ¼ the Boltzmann constant and wa ¼ the anisotropic magnetic susceptibility. This has the consequence that, for practical purposes, the nanoparticles should be bigger than 10–100 nm in order to align them by available magnets [59]. Another option is to dry the dispersion slowly in order to continuously reduce the possibility of Brownian motion of the nanoparticles. If the nanoparticles are superparamagnetic or ferromagnetic, like magnetite or maghemite, the applied magnetic fields can be lower. Organization of 10 nm maghemite nanopartices by a magnetic field of 0.59 T was reported experimentally and described theoretically [60–62]. Another prerequisite for the orientation of nanocrystals to a mesocrystal by magnetic fields is that the nanoparticles are well dispersed and not aggregated, which would prevent them from rotating into their magnetic-field aligned position. Such dispersions can be slip cast onto a substrate and the orientation of the nanoparticles be fixed by subsequent sintering [47]. This has been applied for a number of ceramics, such as TiO2,


203

Figure 8.19 X-ray diffraction patterns obtained for an L-alanine mesocrystal sample. Contrasts are different between left and right halves. Patterns in (a), (b), and (c) were obtained with the alignment of the a, b, and c axes, respectively, perpendicular to the X-ray beam with an automatic crystal axis alignment system. (d) Shows the sample without alignment by a magnetic field. (Reproduced from [58] with permission of the American Chemical Society.)

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Al2O3, ZnO, hydroxyapatite and Si3N4 [63–68]. With all these lowly magnetic ceramics, the alignment is not perfect. Instead, a relative facial angle (RFA) yF relative to the cplane can be observed [47]. P ðIhkl yhkl Þ P yF ¼ ð8:4Þ Ihkl where yhkl ¼ the facial angle between the (hkl) and (00n) planes and Ihkl ¼ the intensity of (hkl) as obtained from the XRD pattern. yF has a value of zero if the crystals are aligned along (001) and 90 if they are aligned along (100) or (010). The difference of the experimentally determined RFA and that calculated from the JCPDS card is called the relative rotation angle (RRA). The orientations of the nanocrystals in a mesocrystal is shown for several materials in Table 8.1. Among the first examples of crystal orientation by a magnetic field in a polycrystal is the report of Lotgering, who formed oriented crystals of ferromagnetic particles by a topotactic reaction after particle orientation in a static magnetic field [69]. A mixture of BaFe12O19 and Fe3O4 was pressed to a pellet in a magnetic field resulting in the orientation of the BaFe12O19 crystals with their c-axes oriented parallel to the magnetic field, whereas the weakly anisotropic Fe3O4 was not oriented. Heating the mixture in a suitable gas atmosphere leads to a topotactic reaction. BaFe12 O19 þ 2 Fe3 O4 ! BaFe18 O27

ð8:5Þ

The crystals in the polycrystalline product were found to be oriented because they retained the texture and orientation of the initial BaFe12O19 crystals. This topotactic reaction of a strongly anisotropic ferromagnetic compound, which is oriented in a magnetic field, with a second unoriented compound opens a solid-state reaction pathway for the synthesis of mesocrystals. This is especially advantageous if materials of low anisotropy are oriented in a magnetic field, as they cannot be directly oriented. This was demonstrated for a number of solid-state reactions [69].

8.5 The Role of Dipole and Polarization Forces Dipole and polarization forces can be directional forces that can align nanoparticles to form mesocrystal structures. While dipole forces are directional in nature if the dipoles in a crystal are arranged in a parallel fashion, polarization forces are not, unless an anisotropic crystal is considered, with different constituent populations of the different faces. In such a case, the polarization forces can be directed, which can also be exploited for mesocrystal formation. 8.5.1

Polarization Forces

Practically all interactions between molecules are based upon the electron polarizability and dipole interactions. Whereas the classical London interactions just consider the attraction of two molecules proportional to the ease they shift electrons in their structure, as expressed by their polarizability a (as two molecules are involved, the attraction is

Table 8.1 The relative facial angle (RFA) and relative rotation angle (RRA) of different ceramic systems composed of aligned nanocrystals in a high magnetic field of 10 T [47], The magnetic field direction Pa means parallel direction to the slip casting direction; Pe, the perpendicular direction. Materials Crystal structure

TiO2 Tetragonal system wc > wa;b Spherical Pa D ¼ 30 nm

RFA obtained under magnetic field of 10 T

ytop ¼ 28:3

RFA calculated from JCPDS card RRA

y ¼ 63:2

Magnetic susceptibility Shape of the powders Magnetic field direction Length (L) and diameter (D) of the particles

yside ¼ 80:2

ytop ¼ 34:8 yside ¼ þ17:1

Rod Pe L ¼ 1:68 mm

Al2O3 Trigonal system wc < wa;b Spherical Pa D ¼ 0:15 mm

Si3N4 Hexagonal system wc < wa;b Spherical Pa D ¼ 0:7 mm

HAp Hexagonal system wc > wa;b Spherical Pa D ¼ 2:17 mm

ZnO Hexagonal system wc > wa;b Rod Pa L ¼ 50 nm

D ¼ 0:13 mm ytop ¼ 83:6

ytop ¼ 13:2

ytop ¼ 79:5

ytop ¼ 70:5

D ¼ 25 nm ytop ¼ 81:7

yside1 ¼ 81:1 yside2 ¼ 26:8 y ¼ 63:2

yside ¼ 86:2

yside ¼ 63:4

y ¼ 57:6

y ¼ 68:8

ytop ¼ 19:5 yside 1 ¼ 17:9 yside 2 ¼ 36:4

ytop ¼ 44:4 yside ¼ þ28:6

ytop ¼ þ10:7 ytop ¼ 10:9 ytop ¼ þ24:3 yside ¼ 5:4 yside ¼ 15:5

yside ¼ 41:9 y ¼ 59:6

y ¼ 57:4

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proportional to a2 ), van der Waals interactions also consider the dipole–dipole interactions, as expressed by the permanent dipole moments of the molecule m, and the interactions between static and induced dipole moment, as all of them are proportional to the sixth exponent of distance r. Without going into too much detail (which can be found in appropriate textbooks of physical chemistry) it is said that all three contributions can have similar importance for the cohesion of matter, in which the role of the electron polarizability is usually underestimated. There is a whole range of intermolecular forces with similar distance scaling and dielectric behavior that are sub-summarized as van der Waals forces. Assuming that two interacting units have the polarizability a1;2 and the permanent electric dipole moment m1;2 , these are: 1. The dipole-dipole interaction (Keesom’s interaction): EDD ¼

m21 m22

1 r 3 ð4peeo Þ k T 6 2

ð8:6Þ

m1 m2 (if the dipoles are not aligned, i.e. ð4pe 3 < kT). 0 Þr 2. The electrostatic polarization force, which comes from the fact that a dipole in one unit can polarize the electrons in the other:

EDA ¼

m21 a2 þ m22 a1 1 ð4pee0 Þ2 r 6

ð8:7Þ

3. The classical dispersion force (London Interaction): EAA ¼

3 a1 a2 1 I 1 I 2 2 ð4pee0 Þ2 r 6 ðI1 þ I2 Þ

ð8:8Þ

where I1=2 are the ionization energies. As all these components behave similarly with respect to distance and permittivity, they are sub-summarized to the van-der-Waals force, i.e. E¼

CvdW r6

ð8:9Þ

With CvdW ¼ constant. Usually, even for polar molecules, the role of dipole-dipole interaction is overestimated, and the dispersion interaction is at least as high. All these equations are valid in vacuum, while crystallization usually takes place in solvents. Here, some type of ‘buoyancy’ argument holds true, i.e. the interactions of particles with the solvent have to be subtracted from the particle–particle interactions. The dispersion force can, for instance, be completely screened by using an isorefractive solvent, thus balancing the individual polarizablilities. This is, however, not valid for the complete van der Waals force, as long as permanent dipole moments are involved. It should also be stated that the dipole–dipole interactions – due to thermal averaging – contain a temperature dependence, which can give attraction and related order formation a strong temperature component. This is usually disregarded.


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For isotropic colloids without a permanent dipole moment, all the elemental polarizabilities sum up to the so-called Hamaker constant AH , which is constant for a material and quantifies the van der Waals attraction between two colloids: AH ¼ 0:75p2 N 2 a2 h0

ð8:10Þ

where N ¼ the number of atoms/molecules per unit volume, h ¼ the Planck constant and 0 ¼ the limiting electron frequency. In practical life, molecules with low polarizability are hydrophobic, show a lower colloidal attraction and are therefore easier to stabilize, while colloids with high dipole moments and high electron mobility (such as dyes or metals) show high Hamaker constants and are more difficult to stabilize. It is obvious that the whole context becomes very complicated when the colloid or nanoparticle is a single crystal. Due to the alignment of molecules, dipole moments may add up or compensate each other, and, especially, polarizabilities will sum up in a constructive fashion, not to mention the potential development of a joint electron plasma which adds to the polarizability in a highly nonlinear fashion. Due to the directionality of crystals, the Hamaker constant then becomes a Hamaker tensor, with some of the elements in the direction of maximal polarizability being very large, i.e. expressing coherent summation of polarizabilities or a ‘super-Hamaker’ interaction. This, of course, can be a stable base for mesocrystal formation. A remarkably nice case for such a process was reported for crystallization from a dye mini-emulsion [2]. Mini-emulsions are stable, nanoscopic dispersions of one liquid in another [70], and if dye molecules or other functional organic molecules are hydrophobic and have a melting point below 100 C, they can be dispersed as nanodroplets above their melting point in water. The model character of this experiment is that transport over the continuous phase or nucleation from the water phase can be excluded: each droplet can just crystallize itself, and the maximal size of the primary nanocrystal is given by the droplet size. The concept of such a crystallization experiment is shown in Figure 8.20; the amount of materials crystallized can be very high and can easily reach 10–30 wt% of the whole solution in the vessel. The stability of this mini-emulsion is given with respect to the liquid state: once such a droplet is crystallizing, its Hamaker constant changes, and the colloidal stability will break down in a directional fashion, because of the development of ‘super van der

Figure 8.20 Crystallization of oil soluble dyes from mini-emulsions. From left to the right: the dye is molten, here with the aid of some added chloroform. Then, by addition of an appropriate surfactant, the liquid dye droplets are mini-emulsified to nanodroplets. Crystallization of those nanodroplets results in colloidally unstable entities, which undergo mesocrystallization to form uni-dimensional nanoparticle arrays. (Figure modified from [2].)

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Figure 8.21 (a) Crystallization sequence of Oil Blue, as perceived by the naked eye; (b) Corresponding SEM texture of needle-like dye mesostructures, sometimes with bent tips; the thickness of the needles corresponds to the previous nanodroplet size; (c) Scheme to illustrate the directed mesoscale aggregation of dye nanoparticles. The formed primary nanocrystals – caused by the symmetry of the unit cell – show different polarizabilities along different planes. As is typical for van der Waals forces, similar polarizabilities attract each other optimally (‘attraction of the same’), here, schematically, the bright faces with the highest polarizability giving the strongest van der Waals force. As a result, aggregation and mesocrystal formation occurs only in this direction. (Taken from [2] with kind permission of the American Chemical Society.)

Waals forces’ due to the high directional polarizability of dyes. This is indeed observed: the crystallizing Oil Blue emulsion immediately becomes unstable and develops a strong pleiochromism, which gives such a dye dispersion a metallic-like texture (Figure 8.21). Scanning electron microscopy reveals the structural background of this optical effect: fiber-like crystalline mesostructures with a length of about 5 microns are formed, the diameter of which corresponds to the primary droplet size. As transport over the water phase (due to the extremely low solubilty) can be excluded, fibers only can grow via particle–particle assembly. It is worth underlining that not a single primary particle has been left, the structure after this crystallization time is composed of monodisperse needles, only.


209

Figure 8.22 Series of polarization tilts of a selected large mesocrystal of oil blue (Scale bar ¼ 20 mm). (Figure reproduced from [2] with permission of the American Chemical Society.)

Due to the optical properties of dyes, it can also be decided which type of interaction has broken up the colloidal stability in an anisotropic fashion. For that, a larger, longer crystallized mesocrystal was put under the polarization microscope (Figure 8.22). The practically perfect alignment of the single dye molecules within the crystal is nicely revealed by the almost perfect pleiochromism (the crystal is transparent in one direction while highly tinted in the other). As the dipole moment of such dyes is along the molecular axis and coupled to the maximum color, we can directly see that the dye is oriented perpendicular to the main growth direction. This clearly proves that the crystal did not grow in the direction of the dipole moment, but in direction of the maximal dye polarization force (which are orthogonal to each other). For the expert, this is not surprising: dipole moments usually compensate in a crystal structure, while polarizabilities sum up. Therefore, these experiments clearly reveal tensorial differences in the polarizability of various nanocrystal faces as the driving force for mesocrystal formation with the observed high orientational order. Whether or not the nanocrystalline building units in the mesocrystals fuse together after oriented attachment [71] to form a single crystal has not yet been revealed.

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Another model case of mesocrystal formation in organic molecules is the analysis of the crystallization behavior of amino acids, discussed above on a number of occasions (see Sections 7.9, Mesocrystals Formed With Polymer Additives and 8.1, Principal Mechanisms leading to Mesocrystals. For the unit cell representation of DL-alanine, see Figure 2.22). All amino acids are zwitterionic components and carry an inherent dipole moment in their structure, also known from their polymers, peptide helices, or ß-sheets. Interestingly, in many amino acid crystals these dipoles do not compensate in the unit cell, making amino acid nanocrystals inherently strong dipoles. This is exemplified in Figure 2.22 showing the unit cell of DL-Alanine, which obviously expresses a strong dipole moment in the c direction. Indeed, mesocrystal growth mostly occurs in the c direction, making the strong dipole–dipole interactions between the primary nanocrystals responsible for the breakdown of colloidal stability and oriented attachment (see Sections 7.7, Mesocrystals Formed Without Additives and 8.1, Principal Mechanisms Leading to Mesocrystals as well as Figures 7.28 and 7.1). Crystals with a low enough symmetry to preserve the molecular dipole moments are therefore especially suited to undergo mesocrystal formation. Excitingly, not only systems with low crystal symmetry, but also highly symmetric unit cells with otherwise compensating molecular dipoles can express a macroscopic dipole moment at the nanoscale. The general effect of spontaneous dielectric symmetry breaking is already long known from the piezoelectricity of bone. Bone is strongly piezoelectric [72], while the material it is essentially made of, hydroxyapatite, exhibits mirror planes in its crystal structure and is too symmetric to exhibit a permanent dipole moment and therefore piezoelectricity. This spontaneous breaking of dielectric symmetry turned out to be adaptable to other systems and was – for instance – also observed for simple calcite, presumably the model system of biomimetic crystallization control examined in the most detail. It has already been stated [73] that certain anionic polyelectrolytes and anionic block copolymers allow for discrimination of the c-axis of calcite. Another remarkable example of a mesocrystal system with such c-axis discrimination is the CaCO3 mesocrystal formed in the presence of poly(styrene sulfonate) (PSS) [5,74]. These mesocrystals are formed by selective adsorption of the polyanion onto the highly polar calcite (001) nanoparticle faces [5,74]. For this system, it is remarkable that the morphologies and particle superstructures can be varied over a wide range in a systematic way by simply adjusting the two reactant concentrations (Figure 8.23). At the lowest polymer concentration and CaCO3 supersaturation, crystals which resemble the default rhombohedral calcite single crystals are found (Figure 8.23 a). Selective PSS adsorption onto the (001) face of calcite upon increase of polymer and Ca2þ concentrations leads to the formation of nanoparticles with dissimilar charge on the opposite {001} faces. The nanoparticles then form a mesocrystal by controlled arrangement of the nanoparticle subunits (Figure 8.23), which will be discussed in detail further below. Variation of the CaCO3 / PSS ratio results in very systematic variations of the mesocrystal morphology, including a whole family of highly defined rounded structures. Higher PSS concentrations lead to increasing exposition of the highly polar (001) face, as shown in Figure 8.24, finally resulting in a multi-curved convex–concave structure with broken symmetry along the [001] direction at high Ca2þ and PSS concentrations. These


211

Figure 8.23 Typical SEM images of calcite mesocrystals obtained on a glass slip by the gas diffusion reaction after 1 day in 1 mL of solution with different concentrations of Ca2þ and polystyrene-sulfonate: (a) [Ca2þ] ¼ 1.25 mmol/L, [PSS] ¼ 0.1 g/L; (b) [Ca2þ] ¼ 1.25 mmol/L, [PSS] ¼ 0.5 g/L; (c) [Ca2þ] ¼ 1.25 mmol/L, [PSS] ¼ 1.0 g/L; (d) [Ca2þ] ¼ 2.5 mmol/L, [PSS] ¼ 0.1 g/L; (e) [Ca2þ] ¼ 2.5 mmol/L, [PSS] ¼ 0.5 g/L; (f) [Ca2þ] ¼ 2.5 mmol/L, [PSS] ¼ 1.0 g/L; (g) [Ca2þ] ¼ 5 mmol/L, [PSS] ¼ 0.1 g/L; (h) [Ca2þ] ¼ 5 mmol/L, [PSS] ¼ 0.5 g/L; (i) [Ca2þ] ¼ 5 mmol/L, [PSS] ¼ 1.0 g/L. (Figure taken from [5] with kind permission of Wiley-VCH.)

Figure 8.24 Left: Cerius2 model of truncated trigonal calcite structure viewed upon the 001 face (white). Grey scales ¼ (104); Right: The corresponding assembly motif according to Figure 8.23 [5]. (Figure taken from [5] with kind permission of Wiley-VCH.)

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mesocrystals are highly porous, with surface areas well exceeding 100 m2/g, but show their common mutual high orientation, as indicated by the rather perfect tensorial birefringence under crossed polarizers [74]. Note that calcite is highly birefringent except when observed from the [001] direction. This enables a more detailed understanding of the mesoscale assembly process. The c-axis of calcite has hexagonal symmetry and is usually not exposed, as it is constituted by either pure cationic or anionic sites and is thus the most polar calcite surface. The corresponding Cerius2 representation of this face is shown in Figure 8.25. It is straightforward to understand why specifically this surface is stabilized by the anionic polyelectrolyte PSS: the multiple cationic sites can bind the negative polyelectrolyte, and a low energy surface is obtained. The involved multiple binding of a polyelectrolyte onto the (001) surface also explains the very high binding efficiency and stability of the nanoparticle assembly at comparably low concentrations: the free energy of binding is known to be very high for such Coulombic multi-binding events [75]. After Ca2þ complexation by the polymer, the very high Ca2þ supersaturation results in fast nucleation of very small, thin platelets. The highly positive, pure Ca-exposing (001) face is ideal for the adsorption of PSS, making this face energetically very favourable. It must, however, also be underlined that PSS presumably can bind only on one side of such a c-exposed platelet: due to electrostatic fields within the crystal, the structure cannot tolerate two positive faces at too close a distance, as they would repel each other strongly, thus lowering the free energy of the system. Because of that, each platelet is presumably balanced by Ca2þ and CO32 ions. One (001) face of the platelet, due to the high charge density is stabilized by PSS and the adsorption side is determined by the adsorption of the first PSS molecules, which will block this surface from further growth, but nevertheless maintain the overall cationic character of this ‘frozen in’ face. On the other hand, as the thin crystal is a dielectric, this cationic face hinders the attachment of further cations to the (00-1) face. The counter-face, at least for nanosized platelet crystals, now has to be a CO32 ion terminated (00-1) face, as two positive planes in such proximity would repel each other throughout the crystal. For high Ca2þ supersaturations, a rough estimate of the single platelet thickness on the base of the HRSEM

Figure 8.25 Cerius2 presentation of the calcite (001) surface, which is indicated by the yellow dashed line. Ca2þ ¼ blue, C ¼ grey, O ¼ red. Left: Side view; Right: Top view of a 3 3 2 unit cell arrangement; the hexagonal ion arrangement on this surface is clearly visible. (Figure taken from [5] with kind permission of Wiley-VCH.)


213

Figure 8.26 HRSEM images of typical convex–concave structure (inset) of calcite mesocrystals at early crystallization times, and the detailed surface structure composed of nanoparticles. Samples were obtained on a glass slip by the gas diffusion reaction after 7 hours in 5 mL of 5 mmol/L Ca2þ solution with different PSS concentrations: (a) 0.5 g/L; (b) 0.1 g/L. (From [5] with kind permission of Wiley-VCH.)

data (Figure 8.26) gives ca. 40 nm. A simple calculation based on Coulomb’s law shows that the repulsive electrical energy Er on the other side of the crystal is of the order of 0.2 kT (thermal energy ET ¼ 4:12 1021 J at 25 C) per charge unit on the counterplane. Taking the Coulomb equation for z elementary charges: FC ¼

ze2 4per e0 d2

ð8:11Þ

and multiplying by the distance between the charges gives the repulsive electrical energy Er where z ¼ charge unit ¼ 1; e ¼ elementary charge ¼ 1:602 1019 C; er ¼ dielectric constant of the CaCO3 crystal ¼ 8 6:1 9:1, according to [76], e0 ¼ dielectric constant of vacuum ¼ 8:854 1012 A s V1 m1 and d ¼ distance between charges ¼ thickness of the nanocrystal. d ¼ 40 109 m gives 0:72 1021 J per charge at 25 C. As a result, no further Ca2þ and PSS layers can adsorb on a counterface of a highly charged surface (say with 100 charge units), as this is charge-forbidden. The entire mechanism of mesocrystal formation is depicted in Figure 8.27. Such a dissymmetry of surface ions, however, is a source of a permanent dipole moment. Although the structure of calcite is not dipolar at all, it is the dissymmetric surface termination of its nanostructures that makes such structures highly dipolar. Consequently, this dissymmetry in the c direction is expressed and amplified throughout further particle growth. A time-dependent SEM study revealed that there is a morphology change (Figure 8.28): at an early stage, after 3 h, ca. 600 nm large, biconvex particles are formed, which, upon further growth, develop an asymmetric convex–concave morphology oriented along the c direction. This is indicative of continued nanoparticle attachment to an existing, initially symmetric particle, which, however, has different surface properties on the two opposite sites.

Figure 8.27 Mechanism of final morphology change in calcite crystals due to selective adsorption of PSS to one (001) face and the resulting build up of an inner dipole moment within the crystal in the c direction. The primary crystals are asymmetric, as they bind the polymer only onto one side. These primary blocks assemble into flat, pseudo-symmetric mesocrystal structures. Over a certain size, not only primary platelets, but also amorphous intermediates are attracted. By recrystallization of those species, bent crystalline structures without translational order can develop. The same mechanism applies if the opposite side of the primary nanoparticles binds the polymer. (Image reproduced from [5] with kind permission of Wiley-VCH.)


215

Figure 8.28 SEM images of calcite mesocrystals at different crystallization times: (a) 3 hours; (b) 6 hours from solution with the same concentration of 5 mmol/L Ca2þ and 1 g/L of PSS. Samples were obtained on a glass slip by the gas diffusion reaction from 1 mL solution. (From [5] with kind permission of Wiley-VCH.)

The higher the Ca2þ and polymer concentrations, the more pronounced the asymmetry and the more bent the structures are, until a central hole on one side is finally formed. This morphology is contradictive to all classical pictures of crystallization, where such a hole should immediately vanish by Ostwald ripening, and where symmetry is encoded in the primary unit cells and thermodynamics, as described by Wulff’s law of crystal growth [77]. Such a hole (¼ no effective mass transport) with a pile (¼ increased effective mass transport) on the opposite side strongly supports the picture of dipolar long-range interactions controlling the growth and mesoscale assembly of such structures. Wulff’s law only considers short-range interface energies (i.e. energies in the plane) as the driving force, but consideration of long-range energy contributions might indeed explain the different mesocrystal morphologies. As both sides of the primary platelet (Figure 8.27, red) are charged (with different species, however), such a structure is colloidally stable with respect to direct charge interactions and carries the typical electrostatic double layer (Figure 8.27, blue). The created dipole increases with the thickness of the crystal, i.e. the double layer, with its 2 nm thickness (under the applied conditions) cannot compensate for the charge separation over the ca. 40 nm thick (Figure 8.26) calcite platelet. This argument of repulsion of equally charged species throughout the crystal reveals a new possible source of dipolar fields associated with highly symmetric ionic nanocrystals that are otherwise nonpolar, as discussed above. Previous reports in the literature have just considered the specific binding of a polymer to a distinct crystal surface [78] or surface dipole fields ranging into the solution, [79,80], which, however, are known to be weak, and screened by the ionic strength of the solution. Our view is based on the natural dissymmetry of a nanocrystal with highly charged splitting planes, with the surfacecharge generated electric field being strong and long-ranged throughout the crystal. It is important to repeat that ionic crystals possess a rather low dielectric constant (usually e 8), and that the nonscreened Coulomb law holds within the structure (instead of the screened Coulomb law in solution). Therefore, electric fields are much stronger and more long-ranged throughout nanocrystals than through the aqueous environment surrounding them.

216


The resulting nanoplatelets possess a dipole moment perpendicular to the (001) plane, based on the different surface structures. Such dipolar platelets will align in three dimensions to minimize their mutual interaction energy, thus, however, promoting the build-up of an even larger dipole moment in the growing stack. Above a critical size, due to the linear dependence of dipole moment on thickness, a new effect sets in. The inner dipole moment is getting so large that not only the dipolar nanoplatelets (as for the first set of morphologies), but also polymer-stabilized amorphous intermediates are attracted. As these small particles have, due to the polyelectrolyte component, a homogeneous surface charge of one type (presumably negative), the potential of also attracting amorphous intermediates defines the moment where the mesostructures spontaneously develop curvature and dissymmetry: the one, similarly charged pole in the middle of one mesocrystal (001) face repels all intermediates from further crystal growth (and a hole is formed), whereas the other, oppositely charged, pole attracts the particles. As there is a continuous change from attractive to repulsive interaction from pole to pole, the continuous variation of aggregation probability leads to the finally observed, nicely curved concave–convex particle morphology. The existence of strong dipole fields in the final mesostructure is also proven by their nonstatistical orientation along the substrate: we were unable to find a single mesostructure (out of some thousands) of this type that was positioned with the hole or cavity towards the (usually negatively charged) substrate. Additional experimental evidence for the organization scheme of the convex–concave assembly structure could be obtained by polarization light microscopy, where the images show a dark spot in the center of the structures, indicative of the calcite (001) orientation. Time-dependent experiments (Figure 8.29) show that the principal (001) orientation of the growing mesostructures is kept throughout the whole process of crystallization,

Figure 8.29 Polarized light microscopy of calcite mesocrystals after different crystallization times: (a) 4 hours; (b) 1 day. Polarization angle was about 90o. The mesocrystals were prepared on a glass slip by the gas diffusion reaction after 1 day in 1 mL solution with concentrations of [Ca2þ ] ¼ 5 mmol=L and [PSS] ¼ 0:5 g=L. Note that the particle center, 001 face, is not birefringent, and the centres of the particles were kept as (001) faces although they have different sizes during the crystallization process, indicating the good orientation and specific interaction of the primary crystals during the growth process of the mesocrystals. (From [5] with kind permission of Wiley-VCH.)


217

although the structure develops the bended rims without register to the c-axis at the end of the crystallization process. To illustrate the analytical procedure, we will also give the final proof of the dipolar character of the convex–concave mesocrystals, which can be obtained by staining experiments with charged dyes. If a positively charged dye (fast dark blue) is added to the final convex–concave crystals, only the top is stained (Figure 8.30), whereas the addition of a negatively charged dye (Congo red) selectively stains the sides of the mesocrystals. As these mesocrystals are concavely bent, staining of the bottom of the mesocrystals is visible, as staining of the sides as observed in Figure 8.30 b for the negative dye. This means that, in our case, the tops of the mesocrystals are negatively charged, the bottoms positively. It should be underlined that Kniep et al. proposed the existence of a dipolar field quite some time ago to explain some of the structural features of the rod–dumbbell–sphere transition found for fluoroapatite crystallization in gelatine gels [79,80]. A striking direct experimental proof for the importance of dipole fields in this system was recently reported by Kniep et al.; [81] see Figure 7.17 and Figure 7.18 and corresponding text. Using electron holography, it was possible to detect the phase of the image in vacuum, which contains information about the electric field around the hexagonal seed particle (Figure 8.31 a, b). The results could be compared with computer calculations for a dipole field aligned along

Figure 8.30 Optical microscopy images of calcite mesocrystals obtained on a glass slip by the gas diffusion reaction after 1 day in 1 mL of solution with 5 mmol/L of Ca2þ and 0.5 g/L of polystyrenesulfonate, corresponding to Figure 8.23h in paper stained with: a) positively charged dye: Fast Dark Blue (chemical structure as (c)); or (b) negatively charged dye: Congo Red (chemical structure as (d))

218


Figure 8.31 Hexagonal-prismatic fluorapatite–gelatine nanocomposite seed: (a) Conventional TEM micrograph; (b) retrieved phase image of an electron hologram (amplified eight times, composed of four single images), showing the electric potential distribution around a seed. Color code denotes a phase shift of 2p from grey to grey. Fresnel fringes of the interferograms appear as striation patterns at the corners of the phase images. The observed projected potential corresponds to a mesoscopic dipole. Inset: The phase profile reveals a phase increase of about 1 rad per 300 nm; (c) Simulation of the phase image around a nanocomposite seed based on an ideal arrangement of nanodipoles. The model is constructed of triple helices in parallel orientation along [001] within the seed. Triple helices represent dipoles and are depicted as arrows. For further details see text. The contour plot of the phase shift shows a good qualitative agreement with the electron holographic experimental data in (b). (Reprinted from [81] with permission of Wiley-VCH.)


219

the c-axis of the seed (Figure 8.31 c). Although the absolute agreement between measurement and calculation was not good, due to various uncertainties in the calculation (pH-dependent gelatine charge, length and spacing of the helices etc.), the qualitative agreement between prediction and experiment was good, as displayed in Figure 8.31. The model calculations show that the tendency for branching at the ends of the elongated seed is caused by an orientation energetically favored for further material to be added to the hexagonal c-axis direction. Therefore, the role of intrinsic dipole fields for the structuring of inorganic crystals could be experimentally revealed for the first time, even if the situation in a gel may differ from the investigated vacuum environment [81]. The authors attribute the dipolar character of the seed to the collagen triple helices included in the crystal, while we prefer asymmetric surface termination as the source of dipolarity. Further experiments are certainly needed to reveal the real reason for the spontaneous dipolar symmetry break, and the answer might even be system specific. The constant thickness observation: The considerations made on the unscreened Coulomb force inside a CaCO3 nanoparticle building unit of a mesocrystal above (Equation (8.11)) can also explain another interesting observation in the field of bio- and biomimetic mineralization. Many of the superstructures found have a rather constant size of building units between 20–50 nm. A good example of such structures are the above shown CaCO3 mesocrystals with 40 nm thickness, or the BaSO4 fibers with about 30 nm diameter (see Figures 4.15 and 4.16). With a typical dielectric constant of 8 for a crystal of CaCO3 (6.1– 9.1) and 11 for BaSO4 (11.4) according to [76] the repulsive electrical energy resulting from the unscreened Coulomb force throughout a 20–50 nm thick nanocrystal is about 0.15–0.35 kT for CaCO3 and 0.05–0.25 kT for BaSO4, but will be much higher for thinner nanocrystals. If a crystal nucleated and grew ion-by-ion, this would restrict the growth as soon as a polymer adsorbed, which should be statistically equally as possible as for the thicker crystals. Therefore, thinner platelets should also be observable, which is not usually the case. Instead, aggregates of amorphous precursor nanoparticles (10–30 nm) are detected prior to mesocrystal formation [74]. If these nanoparticles crystallize, the crystal plate thickness will already be in the observed size order of the observed mesocrystal building units. If the thickness of a dipolar nanocrystal is too thin, attraction and crystallization of further amorphous material can decrease the unscreened Coulomb force inside the nanocrystal until the observed energy level of 0.2–0.5 kT per charge is reached. However, ionic growth is not possible for these cases. Similar considerations apply for the 30 nm BaSO4 fibers (0.15 kT), where amorphous nanoparticle precursors are also observed [82]. Although the fibers form by fusion of primary nanoparticle units, their thickness is constant, which is related to the same considerations. Therefore, the unscreened Coulomb force inside a crystal can regulate the crystal thickness in the case of non classical crystallization.

8.6 The Role of External Electric Fields Polarization forces and permanent dipole moments have already been discussed in Section 8.5. In this Section, we want to further reveal the importance of electric fields, while focusing attention on externally applied electric fields.

220


Electric fields can be very advantageously used to order anisotropic nanoparticles with high electron polarizability. One possibility is induced polarization by an alternating electric field, which could be used to align metal nanorods on microelectrodes [83] or between two electrodes, as shown for Au nanorods [84]. External electric fields can also be used to align nanoparticles with permanent dipole moments, like CdS or CdSe nanorods, into a crystallographic register to form a mesocrystal. This can be achieved by the combination of nanoparticle alignment and controlled slow solvent evaporation [85]. The electric field rotates the nanorods and aligns them along the electric field lines, whereas the evaporating solvent confines the aligned nanorods in an array. The experimental set-up for such experiments is shown in Figure 8.32. Mesocrystal formation is observed on the substrate grid, and the degree of positional ordering is higher, the slower the solvent evaporates. In absence of an electric field (Figure 8.33 a, b), a nanorod array is formed with the center rods oriented perpendicularly to the substrate in a two-dimensional hexagonal array. The outer layers of nanorods progressively tilt with increasing distance from the center, and are oriented parallel to the substrates at the edges of the nanorod array (Figure 8.33 a, b). Application of the electric field leads to perpendicular orientation of the 5 30 nm CdS nanorods, with a noncentrosymmetric Wurtzite structure for the substrate, due to the alignment of the ca. 220 Debye dipole along the parallel electric field lines (Figure 8.33 c, d). The electric field can also induce a dipole along, but also perpendicular to, the long axis of the nanorods. The nanorods are interspaced by interdigitated ligand layers, which prevent fusion of the nanoparticles. Figure 8.33 e shows the alignment of the CdS nanorods over a larger area and the Fourier transform image confirms the single crystalline behavior of the defect-poor mesocrystal (stacking faults could be occasionally observed). It is remarkable that the rods are not only aligned along their long axes, but also azimuthally along their {100}

Figure 8.32 Schematic of electrode assembly for nanorod alignment: (a) Three-dimensional drawing. Each electrode measures 35 mm 15 mm 5 mm and is separated by a distance of 1.2 mm. The electrode assembly in a horizontal orientation is placed in a glass vial with 1 mL of toluene to create a saturated atmosphere; (b) Two-dimensional close up of trapped meniscus. The substrate (carbon-coated electron microscopy grid or silicon nitride membrane window) is placed between the electrodes, and 50 mL of nanorod toluene solution is deposited, forming a meniscus between the upper and lower electrode. (Figure reproduced from [85] with permission of the American Chemical Society.)

Figure 8.33 TEM images of perpendicularly aligned nanorod superlattices: (a) Section of CdS nanorod (30 nm 5 nm) domain in the absence of an electric field, scale bar 30 nm; (b) Magnified section of (a), showing parallel to perpendicular alignment from edge to center (scale bar 15 nm); (c) CdS nanorods aligned under a field of 1 V=mm (d) Azimuthal alignment of the nanorods; (e) 30 nm CdS nanorod superlattice with domain size > 0:5 mm2 ; inset: Fourier transform of image showing electron diffraction from hexagonally ordered two-dimensional array. Maxima highlighted from [01-10] and [02-20] diffraction planes with remaining planes [10-10], [1-100], [0-110], [-1010], [-1100] and [20-20], [2-200], [0-220], [-2020], [-2200] clockwise from these positions, respectively. (Image reproduced from [85] with permission of the American Chemical Society.)

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Figure 8.34 (a) Three-dimensional superlattice of CdS nanorods 30 5 nm (scale bar ¼ 10 nm); (b) Schematic showing the top down view of perpendicular arrangement of nanorods with AB stacking. (Image reproduced from [85] with permission of the American Chemical Society.)

and {111} crystal faces, as can be seen in (Figure 8.33 d). This azimuthal alignment of the hexagonal nanorods implies a dynamic addition/removal of individual nanorods to/ from the mesocrystal lattice, which facilitates a correction mechanism for the maximum interaction between the individual nanocrystals in the mesocrystal. It is not only possible to create two-dimensional mesocrystals by this approach, but also three-dimenaional mesocrystals at high nanoparticle concentrations. When the evaporation of the solvent is very slow, high ordering and also orientational correction mechanisms are supported. The incoming nanorods selectively deposit on the interstitial spacing between the nanorods in the underlying layer, which leads to an AB layered mesocrystal. Again, high ordering of the nanorods is observed in all dimensions (Figure 8.34). The above example clearly demonstrates that electric fields can play a key role in mesocrystal formation. The size of experimentally accessible outer electric fields can be of the order of 106 V/m. Internal electric fields on the nm scale can be much higher and can reach the order of 109 V/m. Local electric fields can therefore certainly cause a mutual alignment of nanoparticles. However, as a prerequisite of ordering, a dipolar crystal structure is not generally sufficient, as demonstrated for the above CdS example. Instead, charged surfaces are often needed to create local electric fields, which can then be utilized for nanoparticle organization.

8.7 Self-Similar Assembly and Shape Constraints The formation of mesocrystals according to shape constraints is schematically presented in Figure 8.1c. While the anisotropic shape can already lead to particle alignment by anisotropic capillary forces (see discussion in Section 8.3), the mere presence of a geometric constraint on the orientation of a growing particle can be sufficient for nanoparticle orientation into a crystallographic register. On the other hand, self-similar growth of well-defined polyhedral building units can also lead to mesocrystals; this is a growth process, which relies on the shape of the


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primary building units, plus some elementary connection rules. For instance, the construction of the mesocrystal can be provided by geometric packing of the building units, which mutually orient by edge-to-edge or face-to-face contacts. The driving force for the geometrical alignment is the minimization of the interface mismatch energy, by forming a coherent interface and reducing the exposed surface area, which is closely related to the strategies reported in Section 8.3. Self-similar growth was demonstrated for the spontaneous self-assembly of ca. 5 mm sized octahedral silica crystals [86] on glass surfaces. These crystals are formed by the {111} faces of the cubic phase and can selfassemble in an oriented manner due to the capability of edge sharing (Figure 8.35). As the primary building blocks are very well defined in size, as well as the contact edges to the next particles, a self-similar growth process is induced, which leads to a mutual crystallographic orientation of the primary particles and thus to the formation of a mesocrystal. A large variety of arrangements are possible, as the initially formed mesocrystal units can themselves assemble into higher-order structures (Figure 8.35 e, f). Because of the octahedral structure of the primary building units, these mesocrystals have porosity due to the structural voids. Larger pores are formed by packing defects and larger cage formation (Figure 8.35 b). The above principle of octahedral edge sharing is learnt from some crystals built from atoms [87] and also nanoparticles [88], thus showing that the same building principles can be applied regardless of the size of the building units, which is the basis for self-similarity even within one structure.

Figure 8.35 Schematic illustrations of edge-sharing stacking: (a) primary octahedral units, face-on configurations; (b) quartet-octahedron model for the secondary structure; (c) tertiary structure with filled corners; (d) tertiary structure with unfilled corners; (e) a high-order structure from primary octahedra; (f) a high-order structure from tertiary units. (Reproduced from [86] with permission of Wiley-VCH.)

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Figure 8.36 SEM images of the obtained trigonal calcite mesocrystals, with triangle capped particles, in the presence of PS-MA: (a) Overall product morphology; (b), (c), and (d) high magnification SEM images showing the basal faces of elongated microparticles; (e) and (f) SEM images showing the lateral faces along the c-axis; (g) a modelled calcite morphology of a combination of {001} and {011} forms constructed by the Cerius2 software. Gray lines and face indices are those at the back. Polymer: 0.1 g/L, [CaCl2] ¼ 1.25 mM. (Image reproduced from [89] with permission of Wiley-VCH.)


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Sharing of interfaces instead of edges in a crystallographic register reduces the surface energy significantly, as discussed as a driving force for oriented attachment in Section 4.3, Oriented Attachment. Edge sharing is therefore promoted by a reduction in the amount of dangling unsaturated bonds along the edge, which have an inherently high chemical energy. Besides the self-similar assembly strategy for mesocrystals, the crystallographic orientation of the nanoparticles building up the mesocrystal can also be achieved by spatial constraints in an already existing mesocrystal, as shown schematically in Figure 8.1 c. However, the distinction between spatial constraints and self-similar assembly is not easy to make on the basis of the final mesocrystals, and only a timeresolved investigation is able to reveal how the mesocrystals are formed. A very recent example of the self-similar assembly of a calcite mesocrystal is shown in Figure 8.36. In this case, calcite nanoparticles with a characteristic shape aligned to a mesocrystal with a shape resembling that of the primary nanoparticles, with triangular tip structures [89]. The sample consists of a large number of elongated calcite particles with well-defined faces and edges (Figure 8.36 a, b, e). The elongation direction of each microparticle is along the c-axis, as marked in Figure 8.36 e. The high-magnification SEM images show that the microparticles appear to be mesoporous superstructures themselves (Figure 8.36 d), formed by aggregation of the primary nanoparticles. The size of those nanoparticles determined from SEM images is ca. 23–30 nm, in agreement with the XRD measurement. There are, in total, eight faces for each microparticle. Two basal faces of each elongated microparticle have a three-fold symmetry (the equilateral triangular crystal planes (Figure 8.36 b, c) have three angles of 60 , that is, the crystallographic planes of each end surface belong to the {001} family), corresponding to the (001) and (001) faces [90,91]. By comparing the measured interfacial angles with the theoretical angles of six lateral faces, it can be concluded that these six lateral faces are (101), (101), (111), (111), (011), and (011) (Figure 8.36 e, g). For example, the isosceles triangular crystal planes (Figure 8.36 e) have angles of 76 1 and 28 1 , that is, the crystallographic planes of this surface (and the opposite face parallel to it) are ascribed to the {011} family (Figure 8.36 e, g). All eight faces are clearly displayed in Figure 8.36 g, which is a modeled calcite morphology constructed by the Cerius2 software. In fact, the modeling morphology (Figure 8.36 g) for a set of {001} and {011} faces is quite similar to the calcite morphology grown (Figure 8.36 a, e). Usually, calcite is not able to expose the {001} faces, as these faces are composed of only CO32 or Ca2þ ions in a hexagonal orientation, respectively, and therefore are highly charged faces, as discussed above in Figure 8.25. Such highly charged faces exhibit very high surface energies and cannot be exposed in the absence of growth modifiers. The fact that this face now becomes dominant can again be ascribed to multiple Coulomb binding of the negatively charged poly(styrene -alt-maleic acid) (PS-MA) copolymer to the positively charged (001) plane. The side faces from the {011} family are neutral faces, which align according to their surface ion pattern. The oriented self-assembly of subunits toward larger, singlecrystalline superstructures (Figure 8.36) can be seen in the framework of self-similar growth of a mesocrystal from particulate subunits. This observation indicates that an overall crystallographic relationship exists among the nanocrystallites that constitute the

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Figure 8.37 Proposed formation mechanism of hierarchical self-similar calcite mesocrystals made of triangular calcite subunits: (a) Nearly spherical CaCO3 nanoparticles formed in the initial reaction stage; (b) Crystallization of calcite nanoparticles exposing{011} and {001} faces, and their aggregation; (c) Further aggregation of the nanoparticles into an aggregate with the shape of its subunits; (d) Formation of large calcite three-dimensional mesocrystals consisting of triangular calcite building blocks via mesoscale transformation. (Image reproduced from [89] with permission of Wiley-VCH.)

whole three-dimensional mesocrystals. The SEM depicts the formation of a hierarchical structure. This structural hierarchy indicates that both the primary units and the pre-assembled intermediates can undergo further oriented attachment, with the larger structures also being able to support larger pores while packing towards the superstructure. The scattering behavior is of a single crystal because the triangle-capped subunits are arranged with the same crystallographic orientation (three edges of each triangle are parallel to those of other triangles). This is schematically visualized in Figure 8.37. The above example gives clear evidence that mesocrystals can self assemble even from complicately shaped sub units via edge or face energy minimization.

8.8 Shaping of Mesocrystals It has already been mentioned above that mesocrystals do not necessarily exhibit a morphology with external faces. Despite curvature, a mesocrystal can virtually adapt to any shape, if it is molded by a suitable external template. In this respect Oaki and Imai compared the macroscopic mesocrystal morphology to a nanoscale LEGO# construction kit, because it has no restrictions in its external shape [7]. The example in Figure 7.34 shows that self-organization of the mesocrystal subunits can lead to complex structures. One simple example of the shaping of a mesocrystal by an external template is the production of a calcite mesocrystal film formed on a glass substrate by pouring a precursor solution containing Ca2þ and PAA into a plastic vessel and placing a glass slide vertically into this solution before the carbonate is slowly added [7]. This results in a mesocrystal film with the calcite c-axis oriented perpendicular to the glass slide. It is also remarkable that a mesocrystal can be produced with polymers originally occluded in a natural biomineral [7]. This was demonstrated for sea urchin spines, from which the external organic matter was removed. Then, the CaCO3 biomineral was


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dissolved producing a Ca2þ solution containing the initially occluded biopolymers. Reprecipitation of CaCO3 after carbonate addition to exactly this mixture resulted in the formation of calcite mesocrystals, as shown in Figure 8.38. The nanoparticle substructure of the mesocrystal becomes obvious in the higher-magnification SEM images (Figure 8.38 b), while TEM experiments confirm a polycrystalline, but oriented mesocrystal structure with the typical electron diffraction pattern of a single crystal (Figure 8.38 c). Higher magnification shows that each calcite nanocrystal of ca. 20 nm size is a single crystal (Figure 8.38 d, e). This example demonstrates quite nicely the similarity of synthetic tools and reaction conditions between biomineralization and synthetic (or here biomimetic) mesocrystallization. Although the delicate sponge-like shape of sea urchin spine mesocrystals was not reproduced (see Figures 3.6, 7.9, and 7.11), because no outer shape donating template

Figure 8.38 The nanoscopic architectures in the reproduction of sea urchin spine: (a) The FESEM images of the macroscopic morphology: (b) The magnified FESEM image of the nanoscopic structure; (c) The FETEM and the corresponding SAED pattern (inset); (d) FETEM image of bridged nanocrystals ca. 20 nm in size; (e) HRTEM image, showing that each nanocrystal is a single calcite crystal. Reproduced from [7] with permission of Wiley-VCH.)

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was applied on the micron scale, the nm structure of the mesocrystal was nicely mimicked in this synthesis. This result demonstrates that: 1. The mesocrystal structure on the nm scale is controlled by polymer additives. 2. The shape on the micron scale cannot be reproduced without the application of a template acting as a scaffold for the mesocrystal assembly. In an extreme case, a mesocrystal can, although vectorially quite perfectly aligned with respect to its subunits, completely lose any macroscopic crystalline appearance and can exhibit other geometric morphologies. An illustrative example is BaCO3 the case of BaCO3 helices, which were formed after selective encoding of special faces of the orthorhombic primary nanoparticle building units by a stiff and shape-persistent polymer (see Figure 8.39) [92]. The helical arrangement of the elongated primary nanoparticles into helices with about the same amount of left- and right- handedness can be explained by steric constraints of the polymer, which is selectively adsorbed onto the caps of the nanoparticles and thus leads to a staggered aggregation pattern (For further details, see [92]). Not only is the high alignment of elongated nanoparticles in these helices remarkable, but also the obvious ‘communication’ between the two helices. Identical morphologies and irregular helix pitch strongly indicate ordering physical fields beside the constraints exerted by the face-selective polymer adsorption.

8.9 Mesocrystals as Intermediates in Single Crystal Formation The reason why mesocrystal formation is often overlooked is, in our opinion, due to the fact that their nanoparticle subunits can fuse together to form a single crystal, as they are already in a crystallographic register. This happens especially if the nanoparticles do not carry an adhered surface layer that can prevent them from fusion, thus stabilizing the

Figure 8.39 SEM image of helical BaCO3 fibers formed in presence of a stiff phosphonated block copolymer. (Reproduced from [92] with permission of Nature Publishing Group.)


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mesocrystal intermediate. It is very difficult to study mesocrystal intermediates in a crystallization reaction with a final ‘single crystalline’ product, as the mesocrystal intermediates can be very short-lived, with lifetimes < 1 s. One successful characterization of such an aggregation-based crystallization reaction for the formation of a single crystal was reported for BaSO4 [13]. The early reaction products could be captured with a sophisticated sampling technique for cryo TEM, which shows the mesocrystal formation process with high time-resolution in the ms range (Figure 8.40). Already as early as 6 ms after mixing, spherical particles with a size of 5–10 nm and without internal structure are observed. This size is already ten times the estimated size of the critical crystal nucleus; the species formed can be considered as the primary particles building up the mesocrystal. Only 5 ms later, the primary particles have already aggregated into irregularly shaped particles with 50 nm mean diameter, but some primary particles and smaller aggregates are still observed. After 26 ms, the aggregates have grown to 100 nm. The further growth of the apparently unstructured aggregates is captured in Figure 8.40, which describes the next growth steps until the final particle size of about 1 mm is reached. Electron diffraction of the aggregate after 72 ms shows the typical spot pattern of a single crystal with slight misorientations. (Note that the diffraction of the BASO4 is overlayed with that of ice from the cryo preparation,

Figure 8.40 Time-resolved observation of mesocrystallization for BaSO4 precipitated at S ¼ 2500. Upper row from left to right: 6 ms; 11 ms; 26 ms after nucleation. Lower row from left to right: 48 ms and 72 ms after nucleation and electron diffraction pattern of the particle 72 ms after nucleation. The dark stripes in the upper left figure are web-like ice structures, which are located in front or beneath the focal plane. (Figures reproduced from [13] with permission of Elsevier.)

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(Figure 8.40)). The single crystalline diffraction pattern of BaSO4 remains upon heating the sample to room temperature. This diffraction pattern, in combination with the obviously polycrystalline aggregate showing a corrugated surface, reveals the mesocrystal intermediate in a crystallization process. Finally, well-facetted, but porous single crystals are obtained (see Figure 3.20). The transformation of the mesocrystal aggregate to a porous single crystal follows two mechanisms. One is the crystallographic fusion of the nanoparticles, which are already in a crystallographic register in their mesostructure, but a dissolution–recrystallization mechanism due to Ostwald ripening for final structural optimization cannot be excluded. It is hard to distinguish between a solid-state fusion of the primary nanoparticles and a solution based dissolution-recrystallization mechanism. However, in the present BaSO4 example, the more-or-less spherical pore structure in the final crystals with rather flat pore walls implies only ‘polishing’ by a dissolution-recrystallization mechanism, which allows for the minimization of the pore surface and thus the adaptation of a spherical morphology. The whole structure formation mechanism is shown in Figure 8.41. The dissolution time of the primary nanoparticles in the mesocrystal can be estimated with an equation given by Nielsen and Mullin [93,94]. t¼

RTd3 2 D c 8gSL Vmol AB 1

ð8:12Þ

where DAB ¼ diffusion coefficient, c1 ¼ the solubility of a flat surface, d ¼ particle diameter, Vmol ¼ molecular volume and gSL ¼ the solid–liquid interfacial tension.

Figure 8.41 Proposed growth mechanism for BaSO4 single crystal formation via mesocrystal intermediates by Judat and Kind. After nucleation, small nanocrystallites are produced, which are responsible for the aggregative growth. The observed aggregation-based crystallization mechanism was revealed at high supersaturation, whereas the classical ion-mediated crystallization pathway was observed at low supersaturations. (Figure reproduced from [13] with permission of Elsevier.)


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The dissolution due to Ostwald ripening can be very fast; a 5 nm BaSO4 nanoparticle – following this formula – dissolves in only 13 ms. Thus, a local dissolution-recrystallization of the mesocrystal to a single crystal, with the observed pores originating from packing defects in a mesocrystal, is possible within ms. This shows in an impressive manner, how short-lived mesocrystals usually are if not stabilized by additional measures. This is especially valid for inorganic minerals, with their high interfacial energies. Organic mesocrystals can have a longer lifetime and transform on the timescale of hours, as the lattice energy of molecular crystals is much lower than the lattice energy of ionic crystals. This is only valid if the single crystal is formed by nanoparticle fusion, as the driving force of this process is the energy gain of the system by elimination of two faces, whereas a dissolution-recrystallization process is determined by the physicochemical parameters in the solution, as expressed in Chapter 4. A model example for an organic mesocrystal that transforms to a single crystal by fusion of the nanoparticle subunits, is DL-alanine. Figure 7.1 shows a fracture surface of a DL-alanine mesocrystal needle, revealing the nanoparticle subunits. As usual, this mesocrystal scatters like a perfect single crystal. With time, the nanoparticles of the mesocrystal fuse to give a single crystal. This can be observed by small angle neutron scattering (SANS) [95]. Neutron scattering from at least mm size particles showed Q3 power law behavior in the beginning and later a transition to Q4 behavior (Figure 8.42). Q3 power law behavior is characteristic for porous structures with surface roughness, while Q4 behavior is characteristic for a two-phase system with sharp interfaces. Thus, this transition detected for the inner structure of the mesocrystal reveals the already discussed elimination of grain boundaries and the flattening of the pore walls on the way to the final (porous) single crystal.

Figure 8.42 Scattering pattern of DL-alanine in D2O just before (!) and just after () the transition from Q3 to Q4 power law, which was about 2.5 hours after starting the experiment (for exact times see Figure 8.43). (Figure reproduced from [94] with permission of the American Chemical Society.)

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Figure 8.43 (a) Intensity at Q ¼ 5 103 /A˚ and (b) P3 and P4 amplitudes versus time. Crystallization starts after less than 1 hour, with the increase of P3 and the transition from P3 and P4 after about 2.5 hours. The open symbols (b) correspond to an independent experiment; the amplitude P3 starts to grow after 7 hours and no transition to P4 was observed within 12 hours. (Figure reproduced from [95] with permission of the American Chemical Society.)

This transition can be quantified by measuring the corresponding amplitudes P3 and P4, where P4 directly relates to the interface area of the particles (Figure 8.43). The crystallization data represented by the solid symbols shows that mesoscopic porous crystals with rough and ill-defined surfaces are present immediately after initiation of the reaction. The increase in the scattering intensity (Figure 8.43 a) points to the particles starting to gain interface area or grow in number up to about 50 min crystallization time. After about 2.5 hours, the interfaces are flattened, and sharp two-phase boundaries between solution and crystal have developed, as indicated by the transition from P3 to P4 (Figure 8.43 a, b). The marked increase in P3 shows the formation and growth of the porous crystalline particles, which are formed from the amorphous (and therefore less scattering) precursor nanoparticles. After transition to crystals with sharp surface structures, a further increase of the total surface area is indicated by a further increase in P4. This speaks for the fact that densification of the crystal, e.g. by elimination of grain boundaries, goes on for the next 12 hours, thus resulting in additional pores within the single crystalline structure. The open symbols in Figure 8.43 b correspond to a repetition of the crystallization under the same experimental conditions, showing exactly the same level of scattering intensity, but a delayed process, leading to the formation of the porous mesocrystals only without dissolution–recrystallization sharpening of the pore walls or the elimination of grain boundaries. In this set, only the early P3 behavior is observed, which is constant over 6 hours from initiation. The onset of growth to the more perfected structures seems to set in after 6 hours, but is far from being complete within the experimental time of 12 hours. This shows that the compaction of a mesocrystal to a single crystal can have very different time frames, even if the experiment is repeated in an identical manner. This missing reproducibility of the time of transition is characteristic for phase transitions of first order, which rely on nucleation.


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Figure 8.44 Transformation of a mesocrystal to a single crystal: (a) by a dissolution– recrystallization process (Ostwald ripening) and (b) by crystallographic fusion.

Overall, the above two examples suggest two different mechanisms for the transformation of a mesocrystal into a single crystal (see Figure 8.44). The first is crystallographic fusion of the mutually oriented nanoparticles under elimination of surfaces, which gains energy for the system. The second mechanism is the Ostwald ripening and thus partial dissolution of the nanoparticles with subsequent recrystallization to a single crystal with flat surfaces. Characteristic for this process are the formation of almost spherical pores (instead of clefts and interstitial pores), which result from a surface minimization process upon recrystallization and a rather slow kinetics on the timescale of hours.

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9 Analysis of Mesocrystals The occurrence of mesocrystals is a process that covers size ranges and timescales over many orders of magnitude. Depending on these, appropriate techniques need to be chosen to analyze the formation and transitions of mesocrystalline structures. This chapter repeats the different characteristic steps of mesocrystal formation and discusses appropriate analytical techniques to follow or verify each step. It is always the case that a combination of techniques covering several of the size ranges and timescales is needed to reveal the mechanistic details of this self-assembly process. It has already been the subject of discussion that mesocrystals are notoriously difficult to analyze. One problem is their usually intermediate nature in the formation process of a single crystal (see also Section 8.9, Mesocrystals as Intermediates in Single Crystal Formation). Therefore, a mesocrystal intermediate can often only be concluded from a final porous single crystalline structure, despite no pore-forming additives being applied, as observed for the example of BaSO4 [1] or (NH4)3PW12O40 [2]. A second analytical challenge is that each formation process of a mesocrystal is a multi-step process consisting at least of two elementary steps: (a) nanoparticle nucleation and (b) mesocrystal assembly. Often, there are more steps involved, like the formation of amorphous precursors, the formation of mineral bridges between the nanoparticles in a mesocrystal, or the fusion of the crystallographically aligned nanocrystals to single crystalline domains. Therefore one has to face the problem of analyzing a time-dependent process, which starts from molecules and ions in solution and usually ends at the micron scale. Therefore, the relevant particle size range spans five orders of magnitude from 10 9–10 4 m, which is a challenge for a single analytical technique. The corresponding timescales of interest are even broader, spanning from the sub ms range, for primary particle formation [3,4], to the many hours of structural ripening, as exemplified in the (NH4)3PW12O40 example discussed above [2]. This spans at least eight orders of magnitude in time, from (10 3–105 s). With this in mind, it becomes clear that a combination of analytical techniques has to be applied that consists of imaging techniques, kinetic techniques, techniques sensitive Mesocrystals and Nonclassical Crystallization Helmut Co¨lfen and Markus Antonietti # 2008 John Wiley & Sons, Ltd

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Figure 9.1 Schematic representation of the precipitation mechanism of copper oxalate formation from the initial stage to the final particle as a function of time, with the applied analytical techniques for the different time and size regimes. (Based on results in [5].)

to dissolved species, and techniques sensitive to the structure of the mesocrystal. This will be illustrated by the investigation of the growth mechanism of copper oxalate mesocrystal intermediates, which was revealed in an elegant way by the combination of a number of analytical techniques, illustrating the above issue of complementing timescales and size ranges [5]. The particle growth mechanism of this particular crystal, with a mesocrystal intermediate, can be described in four stages: (1) initial nucleation and growth of primary particles; (2) rapid aggregation to give a core of randomly oriented primary particles or crystallites; (3) a period of ordered attachment of crystallites giving an inner shell of well-aligned nanocrystals; (4) a slow approach towards equilibrium with the solution, where high-energy surfaces are eliminated and an outer shell of larger well-cemented crystallites envelopes the initially formed particles. The schematic diagram in Figure 9.1 shows that in this particular example, a timescale from the ms range up to two weeks and a size range from nanocrystals to microcrystals had to be monitored.

9.1 Nucleation and Growth of Primary Nanoparticles The very early stages of particle formation can be monitored with synchrotron SAXS in a fast-mixing stopped-flow chamber. This technique detects the formation of nanoparticles after only milliseconds, and the fast growth to nanoparticles exceeding 100 nm can be monitored. Therefore, SAXS with high time resolution is very well suited for the study of the very early species in a nucleation event. Alternatively, a free continuous jet of the reactants can be produced, and the reaction products can be spatially detected by X-ray

Analysis of Mesocrystals

239

scattering techniques or a very fast sampling technique for electron microscopy with immediate cryo-quenching of the growth process [4]. All of these techniques are experimentally demanding, but the insight into the very early stages of a nucleation process is very important analytical information, which has to be obtained, at least, for some model systems. It is also useful to look at the solution composition by means of simple pH [6] and conductivity [7,8], or ion concentration measurements, as it can indicate the formation of early aggregates or complexes and can allow for the calculation of the time-dependent supersaturation [9]. For the model case in Figure 9.1, the supersaturation drops significantly upon the nucleation burst within the first minute of the precipitation reaction [5]. The fast growth of the primary nanoparticles can also be detected by synchrotron SAXS.

9.2 Rapid Aggregation and Formation of Randomly Oriented Aggregates The rapid aggregation of the nanoparticles to disordered aggregates can be indirectly monitored by TEM cross sections of particle cores, as well as by density measurements of the crystals by helium pycnometry, revealing an internal porosity of about 14% in the discussed case. The disordered aggregate nature can be evidenced by diffraction rings in the electron diffraction pattern of a microtomed TEM sample. The initial random aggregation becomes plausible if the colloidal stability and the number of the primary nanoparticles are considered. The large number density of particles initially induces a high collision frequency and, with a relatively high ionic concentration of around 0.005 M, results in a thin electric double layer of only 3 nm and thus low colloidal stability. This leads to a random agglomeration of the particles (Figure 9.1) [5]. When the particles aggregate in a random fashion by simple contact, little change in the total system energy would be expected, as they would have an open porosity, i.e., no larger reduction of surface area per unit volume. Such aggregation processes can be monitored in a timeresolved manner using static light scattering down to the millisecond region. Even dynamic light scattering can be used, although here with a restricted time resolution of about 30 s per frame due to the measuring principle [10].

9.3 Mesocrystal Formation As particle number density and the corresponding collision frequency decrease, the particles start to aggregate to a more ordered behavior, brick-by-brick. This more ordered attachment is supported by the decrease in the overall ionic strength (decreasing supersaturation), which increases the electric double layer thickness to 5.7 nm after 30 min. This allows reorientation of an attached nanoparticle to find the global energy minimum, which corresponds to a crystallographically well-aligned orientation [5]. This leads to a mesocrystal, as shown in Figure 9.1. This mesocrystal can be evidenced by TEM cross sections yielding single crystalline diffraction patterns. Simultaneously, the polycrystalline nature of the mesocrystal can be seen if the cut has the appropriate thickness and was not damaged by the microtoming process. The polycrystalline nature of the mesocrystal can also be shown by several other techniques, including scanning electron microscopy of a fracture surface or a whole particle. If the nanoparticle building units of the mesocrystal

240


Figure 9.2 (a) Topography of a typical particle with an aging time of 2 min, measured with atomic force microscopy; (b) Three-dimensional view of a typical particle under construction. (Reprinted from [5] with permission of the American Chemical Society.)

are sufficiently small (< 100 nm), their crystallite size can be determined with the Scherrer equation via the line broadening in the WAXS diffractograms. AFM is also a very good technique to show the polycrystallinity of a mesocrystal and is able to determine the particle size of the nanoparticles building up the mesocrystal via the heights of the nanoparticle layers. It also allows for a three-dimensional inspection of the mesocrystal. This is demonstrated for the copper oxalate mesocrystal captured during its construction process and presented in Figure 9.2. AFM measurements revealed a crystallite size of 70 nm in the [110] direction and 50 nm in the [001] direction, which corresponds very well with the crystallite size of 70 nm from WAXS. In Figure 9.2 a, one can also see the primary nanocrystallites in the area around the mesocrystal.

9.4 Fusion of the Mesocrystal to a Single Crystal / Ripening and Ion-Mediated Recrystallization Towards an Outer Single Crystalline Shell Finally, the crystallographically oriented nanoparticles fuse together to single crystalline domains eliminating their common crystal faces at the contact points. This reduces the surface energy of the system, as discussed above a number of times and results in single crystalline domains around a nonoriented core. In addition, a single crystalline shell around the superstructure is observed after ripening. This could be due to nanoparticle fusion into a crystallographic register, or an ion-mediated classical recrystallization event taking place to optimize the surface structure. This core–shell–shell structure of the final particles can again be evidenced by microscopy. After partial dissolution, the disordered core becomes visible, surrounded by the ordered mesocrystal layer, partially fused to single crystalline domains, which are more difficult to dissolve than the nanoparticles, Thus the structure appears porous. The outer single crystalline shell does not dissolve easily and remains intact (see Figure 9.3). It is difficult to access these regions with different order and structure in a spatially resolved manner. TEM cross sections bear the danger that the microparticle is fractured so that it is not known a posteriori from where the fracture pieces originate.


241

Figure 9.3 SEM micrographs of partially dissolved copper oxalate cubic particles showing the core–shell structure proposed in the modified growth model. (Reprinted from [5] with permission of the American Chemical Society.)

The above example illustrates how complex mesocrystal analysis can be. Also, the transient nature of many mesocrystals becomes evident. The overall particle shape significantly develops with time, as is demonstrated by a series of HRSEM images capturing the mesocrystal formation stage, as well as the ripening process (Figure 9.4). It also indicates that classical and nonclassical crystallization can occur in the same crystallization mechanism, but at different times. Therefore multiple analytical techniques must be combined to reveal the full picture. In the present case, this was a combination of SEM, TEM, electron diffraction, AFM, SAXS, WAXS, laser diffraction, pH measurements, and density measurements.

9.5 Analytical Techniques for Mesocrystals In some cases, other or further techniques will be necessary. Therefore, the most suitable analytical techniques for the characterization of mesocrystals are listed below: (1) Microscopic techniques (a) TEM: allows the observation of the mesocrystal structure with a very high spatial resolution down to the crystal lattice planes (HRTEM) and can be combined with selected area electron diffraction (SAED). Also, the mesocrystal interior can be observed. The disadvantage is that in almost every case, cross sections of the mesocrystal have to be made, which bear the danger of mesocrystal fracture. Also, beam damage might be an issue for high magnifications and there is a danger of drying artefacts upon sample preparation. Only snapshots are possible in a timedependent process. (b) SEM: good technique to observe the polycrystalline nature of a mesocrystal in a quasi-three-dimensional view. Lower danger of beam damage compared to TEM. Disadvantages are that the particle interior cannot be observed unless the mesocrystal can be fractured, there is a danger of drying artefacts upon sample preparation, and only snapshots are possible in a time-dependent process.

242


Figure 9.4 HRSEM micrographs of copper oxalate particles as a function of precipitation time at high and low magnifications after: (a) 2 min; (b) 8 min; (c) 12 min; (d) 30 min; and (e) 2 weeks. (Reprinted from [5] with permission of the American Chemical Society.)


243

(c) ESEM; good for the observation of samples where drying artefacts might be an issue. Only snapshots are possible in a time-dependent process. (d) Light microscopy: easy technique for the observation of microcrystals in solution and can be used in a time-resolved manner. Different modes, like phase contrast, polarized light, confocal (for scanning ‘through’ a microparticle with three-dimensional image reconstruction), and fluorescence detection/labeling are possible. It can also be combined with Raman scattering and then allows selective imaging of different polymorphs or phases in hybrid particles. Disadvantages are limited optical resolution and that only microparticles can be seen, no mesocrystal substructure is available, but polarization microscopy can reveal the iso-orientation of the subunits in a mesocrystal. (e) AFM: allows the determination of the sample topography and three-dimensional image reconstruction for an investigation of the mesocrystal exterior with nm resolution. Imaging of selected properties is possible, if an appropriate tip is used (charge, magnetism etc.). It can image hard and soft regions by phase contrast and can also be applied in solution, but only if the sample is attached to a surface. There is very good resolution in sample height, but limited lateral resolution due to extension of the AFM tip, typically around 10 nm. AFM can also be applied in a time-resolved manner and directly in the crystallization medium. (2) Scattering/diffraction techniques (a) SAXS: can yield particle size and shape, and order in a mesocrystal in the range

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