Monodispersed Particles

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Monodispersed Particles

Monodispersed Particles

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Monodispersed Particles Tadao Sugimoto Institute for Advanced Materials Processing Tohoku University Katahira 2-1-1, Aobaku Sendai 980-8577, Japan

2001

ELSEVIER Amsterdam - London - New York - Oxford - Paris - Shannon - Tokyo

ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

© 2001 Elsevier Science B.V. All rights reserved. This work is protected under copyright by Elsevier Science, and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier Science Global Rights Department. PO Box 800. Oxford 0X5 IDX. UK: phone: (+44) 1865 843830. fax: (+44) 1865 853333. e-mail: permissions(0'elsevier.co.uk. You may also contact Global Rights directly through Elseviers home page (http://www.elsevier.nl). by selecting "Obtaining Permissions". In the USA. users may clear permissions and make payments through the Copyright Clearance Center. Inc.. 222 Rosewood Drive. Danvers. MA 01923. USA: phone: (+1) (978) 7508400. fax: ( + 1) (978) 7504744. and m the UK through the Copyright Licensmg Agency Rapid Clearance Service (CLARCS). 90 Tottenham Court Road. London WIP OLR UK: phone: (-(-44) 207 631 5555: fax: (-t~44) 207 631 5500. Other countries may have a local reprographic rights agency for payments. Derivative Works Tables of contents may be reproduced for internal circulation, but permission of Elsevier Science is required for external resale or distribution of such material. Permission of the Publisher is required for all other derivative works, including compilations and translations. Electronic Storage or Usage Permission of the Publisher is required to store or use electronically any material contained in this work, including any chapter or pan of a chapter Except as outlined above, no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the Publisher Address permissions requests to: Elsevier Global Rights Department, at the mail, fax and e-mail addresses noted above. Notice No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made.

First edition 2001 Library of Congress Cataloging in Publication Data A catalog record from the Library of Congress has been applied for. ISBN: 0 444 89569 8 Transferred to digital printing 2005 Printed and bound by Antony Rowe Ltd, Eastbourne

Preface The term "monodispersed particles" as the antonym of "polydispersed particles" means a group of particles made highly uniform in size and shape. If they are defined in terms of size distribution, one may expect the coefficient of variation (= standard deviation / mean size) to be within 10 %. The major significance of monodispersed particles is attributed to the uniformity in physico-chemical properties of individual particles in a dispersion system, which allows us to directly correlate the properties of a whole system with those of each particle and facilitates theoretical approaches. Their practical importance seems to be due to the potential capability for precise control of their own properties. Thus, they are of obvious importance not only in the fields of physical chemistry, dealing with the dynamic behavior and stability of particulate systems, but also in the industries including catalysts, ceramics, electromagnetic materials, photographic emulsions, pigments, medicines, etc. Complying with so many scientific and practical demands, great efforts have been devoted to the preparation of well-defined colloidal particles for a long time. One may be able to trace the history back to the beginning of the twentieth century. For example, uniform gold particles were prepared by Zsigmondy as early as in the 1900s using a seeding technique; monodispersed barium sulfate particles of different shapes by Andreasen et al (1943); spherical sulfur particles by LaMer and Barnes (1946); polystyrene latex by Bradford and Vanderhoff (1955); cubic and octahedral silver bromide particles by Berry et aim the early 1960s; spindle-like akaganeite (P-FeOOH) by Watson et al (1962); spherical silica particles by Stober et al (1968); spherical chromium hydroxide particles by Demchak and Matijevic (1969); platinum nanoparticles in microemulsions by Boutonnet et al (1982); synthesis of hematite particles of different shapes in the gel-sol system (1992). However, the substantial progress in this field, including theory and practice, is rather recent and particularly remarkable for the last two decades. While the fundamental and practical importance is generally accepted, it may not seem easy to attain monodisperse systems exactly serving individual purposes, because many factors have decisive influences on the monodispersity and other relevant characteristics. In fact, a large iiuiiiber of monodisperse particles have been prepared only by trial and error or by

vi

PREFACE

optimization of preparation conditions, and it appears rather rare to find studies which genuinely shed light on the fundamental formation mechanisms, leading to general principles, or design synthetic systems on the basis of reasonable guidelines. Nevertheless, it is also true that steady efforts have been continued to investigate the underlying mechanisms of the formation of monodispersed particles, so that the formation processes are gradually being clarified. Such efforts will finally lead us to reasonable and more precise control of monodispersed systems. Moreover, in response to the persistent demand for the industrial use of monodispersed particles of enormous potential benefits, highly condensed monodisperse systems, socalled the "gel-sol systems," was invented in 1992 to resolve the essential problem, the extremely low productivity, in existing dilute monodisperse systems. The new method is based on an idea of using highly condensed precursor gels as a matrix of growing final particles for preventing their coagulation, which is eventually transformed into a condensed sol of the final particles through a dissolution-recrystallization process. This idea was first realized for the synthesis of monodisperse hematite particles, as referred to above. Since a monodispersed sol is formed from a gel, in contrast to the sol-gel process, the method has been named "gel-sol method." This invention is a kind of challenge to the conventional physical chemistry for colloidal systems, on which existing monodispersed systems have been fabricated. Since the backgrounds of the colloid chemistry in condensed systems essentially differ in a sense from those in dilute systems, establishment of the new colloid chemistry is an urgent issue. In view of these situations, it seems timely to publish a comprehensive book on the preparation, characterization, and application of monodispersed particles, which will be useful for systematic understanding of the underlying principles of general monodispersed systems and mechanisms of individual practical cases and for creating novel systems. This book covers diverse aspects of monodispersed particles, consisting of four parts: Le,, Fundamentals, Preparation, Analyses, and Applications. In Part 1 (Fundamentals), I will introduce the fundamental concepts of nucleation, growth, habit formation, recrystallization, and solid-solution formation in its individual chapters, in each of which theories and the corresponding experimental results will be given. In Part 2 (Preparation), the general principles for the formation of monodispersed particles will be summarized in the first place, and then all examples of monodispersed or fairly uniform systems will be classified into homogeneous or heterogeneous systems, being reviewed systematically according to the characteristics of the individual reactions. In particular, considering the convenience for readers.

PREFACE

vii

I tried to compile as many examples as possible from available literature for uniform inorganic and organic particles, with sizes ranging from a few nanometers to several hundreds of micrometers. As a result, even such particles as fairly unifoim but not so complete as to be called "monodispersed particles" are also covered in this part, in accord with the comprehensive nature of this book. Also, the techniques and underlying principles for the control of particle characteristics, such as mean size, shape, internal homogeneous structure, composition, layered structure, hollow structure, porous structure, and heterojunction, will be described in detail. In Part 3 (Analyses), methods for the analysis of the formation processes of monodisperse particles and for the characterization of the products will be explained comprehensively. In Part 4 (Applications), applications of monodispersed particles as models of colloidal systems to fundamental studies and as advanced particulate materials for practical use will be delineated. For the practical use of monodispersed particles, special emphasis is placed on their potentialities and infinite possibilities in future rather than the current applications, since it is only the latest event that we have found some general clue to their manufacture for practical purposes. I hope that this book, probably the first comprehensive book dealing with general aspects of monodispersed particles, will serve as a guide to the fascinating field of uniform colloidal systems for students of senior and graduate-level courses up to advanced specialists in both academic and industrial centers. Perhaps, the readers will find that this book is not an ordinary textbook, but a unique one which involves numerous new ideas of the author in every chapter, and may notice his implicit intention to lead the readers naturally to the essential principles ruling the wonderland of monodispersed particles. Particularly, I have developed a number of new theories for this book, whenever 1 felt it necessary. A book such as this could not have appeared without the sustained help of many people. I am especially indebted to Prof. E. Matijevic of Clarkson University in the United States for his inspiring encouragements and kind offer of his latest publications. Special thanks are also due to Drs. A. Muramatsu and H. Itoh in my laboratory for their help in searching for the literature and in the preparation of many electron micrographs and the name index. Tadao Sugimoto Sendaiy Japan September, 2000


Contents PART 1. FUNDAMENTALS 1. Nucleation 1.1. Surface Energy 1 1.1.1. Intrinsic Surface Energy of Amorphous or Poly crystalline Spherical Particles 2 1.1.2. Intrinsic Surface Energy of Single Crystal Particles 5 1.1.3. Surface Energy under the Influence of Adsorption 8 1.1.4. Surface Energy of Silver Halide Microcrystals 11 Silver bromide^ Silver chloride^ Silver iodide 1.2. Equilibrium Concentrations of Three-Dimensional Nuclei 26 1.3. Nucleation Rate 30 1.4. The Nucleation Process in Closed Monodisperse Systems 40 1.4.1. Theory 41 1.4.2. AgCl and AgBr Systems 49 a) AgCl Systems 49 Nucleation under the standard conditions, Effects of QQ b) AgBr Systems 54 Nucleation under the standard conditions, Effects of Qo c) Discussion 56 1.5. The Nucleation Process in Open Monodisperse Systems 59 1.5.1. Theory 60 Nucleation model, The distribution function and number of the unstable nuclei. The number and mean radius of the stable nuclei, Nucleation period, Discussion 1.5.2. AgBr Systems 74 Final particle number, Nucleation period. Size of the embryos References 83

X

CONTENTS

2. Growth 86 2.1. Equilibrium Concentrations of Two-Dimensional Nuclei 86 2.1.1. On a Bulk-Solid Surface 86 2.1.2. On a Particle Surface 88 2.2. Nucleation Rate of Two-Dimensional Nuclei 90 2.3. Growth Rate by Surface Reaction 93 2.4. Growth of Polyhedral Particles by Surface Reaction 100 2.4.1. Surface Energy of a Two-Dimensional Nucleus 100 2.4.2. Growth Rate 103 2.5. Diffusion-Controlled and Reaction-Controlled Growth Modes 105 2.6. Criteria for the Distinction of Growth Modes 108 2.6.1. Magnitude of the Growth Rate 108 2.6.2. Activation Energy of the Growth Rate 109 2.6.3. Size Dependence of the Growth Rate 109 2.6.4. Evolution of the Size Distribution Width 109 2.6.5. Effect of the Particle Number Concentration 112 2.6.6. Solubility Dependence of the Growth Rate 113 2.6.7. Chronomals 113 References 117 3. Habit Formation 3.1. Surface Chemical Potential of a Crystal Face 118 3.2. Stable Forms 121 3.2.1. Equilibrium Forms 122 3.2.2. Steady Forms 125 a) Steady Forms in the Reaction-Controlled Growth Mode 125 b) Steady Forms in the Diffusion-Controlled Growth Mode 133 References 138

118

4. Recrystallization 4.1. Phase Transformation 139 4.2. Ostwald Ripening 140 4.2.1. Diffusion-Controlled Ostwald Ripening 141 4.2.2. Reaction-Controlled Ostwald Ripening 142 4.3. Self-Recrystallization 144 4.4. Reversed Ostwald Ripening 144 4.5. Contact RecrystaUization 148 References 153

139

CONTENTS

5. Solid-Solution Formation 5.1. Equilibrium Compositions 155 5.1.1. Theory 155 5.1.2. Ag(Cl,Br) Systems 159 5.1.3. Ag(Br,I) Systems 161 5.2. Conversion by Intra-Particle Recrystallization 5.2.1. Conversion of AgCl Particles by Br' Ions 5.2.2. Thermodynamics 176 5.2.3. Kinetics 181 References 185

xi

155

167 167

PART 2. PREPARATION 6. General Principles for the Formation of Monodispersed Particles 6.1. Separation of the Nucleation and Growth Stages 6.2. Inhibition of Random Coagulation 192 a) Use of Electric Double Layers 193 b) Use of Gel Networks 193 c) Use of Protective Agents 193 6.3. Reserve of Monomers 198 6.4. Choice of Growth Modes 199 6.5. Introduction of Alternative Mechanisms 202 References 202

187 188

7. Monodispersed Systems 7.1. Classification of Monodispersed Systems 208 7.2. Homogeneous Systems 210 7.2.1. Homogeneous Redox Reaction 210 a) Reduction 210 b) Partial Reduction 218 c) Oxidation 219 7.2.2. Precipitation by Poor Solvents 219 7.2.3. Precipitation by Cooling 220 7.2.4. Direct Reaction of Ions 221 7.2.5. Dissociative Reaction of Inorganic Complexes 223 7.2.6. Dissociative Reaction of Organic Complexes 224 7.2.7. Dissociative Reaction of Organic Compounds 231

208

xii

CONTENTS

7.2.8. Decompositional Reaction of Compounds 233 7.2.9. Hydrolysis of Alkoxides 243 7.2.10. Forced Hydrolysis of Metal Ions 252 7.2.11. Dispersion Polymerization 258 7.3. Heterogeneous Systems 265 7.3.1. Phase Transformation of Solids 265 a) Dilute Systems 266 b) Condensed Systems 270 7.3.2. Ostwald Ripening 289 7.3.3. Emulsion Polymerization 291 Growth Mechanism in Emulsion Polymerization 7.3.4. Reaction in Microemulsions 309 7.3.5. Precipitation from Liquid Crystals 314 7.3.6. Inhomogeneous Hydrolysis 316 7.3.7. Hydrolysis in Nonaqueous Emulsions 319 7.3.8. Reaction on Solid Surfaces 322 7.3.9. Reaction in Solid Matrices 329 7.3.10. Reaction in Solid Templates 330 7.3.11. Firing of Solid Precursors 334 7.3.12. Conversion of Aerosol Droplets 336 7.3.13. Oscillatory Nozzle-Jet Techniques 338 References 341 8. Control of Particle Characteristics 8.1. Size Control 368 8.1.1. Feed Rate 369 8.1.2. Temperature 370 8.1.3. Reservoirs 371 8.1.4. Solvents for Solids 371 8.1.5. Restrainers of Growth 372 8.1.6. pH 373 8.1.7. Seeding 374 8.1.8. Supersaturation Quenching 375 8.2. Shape Control 376 8.2.1. Shape Control by Adsorption 376 a) Inorganic Controllers 376 b) Organic Controllers 384 8.2.2. Shape Control by Anisotropic Acceleration a) Twinning Control 388 b) Dislocation Control 389

300

368

388

CONTENTS

xiii

c) Catalytic Control 391 d) Magnetic Control 392 8.2.3. Shape Control of Polymer Particles 393 8.3. Internal Structure Control 396 8.4. Composition Control 406 8.4.1. Mixing 407 8.4.2. Doping 411 8.4.3. Conversion 413 8.5. Layered Structure Control 417 8.5.1. Inorganic Coating 417 a) Coating of Inorganic Particles 417 b) Coating of Organic Particles 419 8.5.2. Organic Coating 420 a) Coating of Inorganic Particles 420 (1) Adsorption 420 (2) Initiation of Polymerization from Solid Surfaces 422 Anionic polymerization initiated by surface-bound groups] Radical polymerization initiated by surfacebound groups. Radical polymerization initiated by adsorbed initiators (3) Copolymerization with Surface-bound Vinyl Groups 427 (4) Living Polymerization Terminated by Surface-bound Groups 428 (5) Coating via Intermediate Adsorption Layer 428 (6) Polymerization Induced by Solid Surfaces 429 (7) Direct Reaction of Polymer Coupling Agents 429 b) Coating of Organic Particles 431 8.5.3. Epitaxial Multilayers 432 8.6. Hollow Structure Control 432 8.7. Porous Structure Control 434 8.8. Heterojunction 436 8.8.1. Epitaxial Heterojunction 436 8.8.2. Non-epitaxial Heterojunction 437 References 441

PARTS. ANALYSES

xiv

9. Analyses of Formation Processes 9.1. Electron Microscopy 453 9.2. X~ray Diffractometry 455 9.3. Infrared Spectroscopy 456 9.4. Ultraviolet-Visible Spectroscopy 459 9.5. Potentiometry 461 a) pH Measurement 461 b) Metal-Ion Potentiometry 463 9.6. Inductively Coupled Plasma Spectrometry 9.7. Gas Chromatography 466 9.8. Ion Chromatography 467 9.9. Radiochemical Analysis 470 9.10. Seeding Analysis 477 References 480

CONTENTS

453

465

10. Characterization of Products 10.1. Transmission Electron Microscopy 482 10.2. Scanning Electron Microscopy 485 10.3. Electron Diffractometry 486 10.4. Energy Dispersive X-ray Spectrometry 488 10.5. Powder X-ray Diffractometry 491 10.6. Oriented Particulate Monolayer X-ray Diffractometry 10.7. X-ray Photoelectron Spectroscopy 500 10.8. Infrared Spectroscopy 502 10.9. Ultraviolet-Visible Spectroscopy 504 10.10. Photon Correlation Spectroscopy 507 10.11. Turbidimetry 512 10.12. Coulter Principle 517 References 518

482

496

PART 4. APPLICATIONS 11. Application to Fundamental Studies 11.1. Determination of the Avogadro Number 520 11.2. Measurement of Zeta-Potential 523 11.3. Determination of Hamaker Constants 529 11.4. Measurement of Interparticle Forces 531 11.5. Studies of Particle Adhesion 535

520

CONTENTS

XV

11.6. Studies of Colloidal Ordering 545 11.7. Studies of Light Scattering 552 11.8. Studies of Optoelectronic Properties of Fine Particles 559 11.9. Studies of Ionic Properties of Fine Particles 561 11.10. Studies of Magnetic Properties of Fine Particles 564 References 573 12. Industrial Applications 12.1. Photographic Materials 580 12.2. Ceramic Materials 588 12.3. Magnetic Recording Materials 596 12.3.1. Fundamentals of Magnetism 596 a) Magnetic Force and Its Unit Systems 596 b) Classification of Magnetisms 600 Ferromagnetism, Ferrimagnetism, Parasitic ferromagnetism, Metamagnetism, Paramagnetism, Antiferromagnetism, Diamagnetism c) Size Effects of Fenomagnetic Particles 603 d) Effects of the Magnetic Anisotropics 608 Shape Anisotropy, Magnetocrystalline Anisotropy, Strain Anisotropy 12.3.2. Relations between the Magnetic Anisotropics and Coercive Force 615 a) Shape Anisotropy 615 b) Magnetocrystalline Anisotropy 616 c) Strain Anisotropy 617 d) Some Reductive Factors for Coercive Force 617 12.3.3. Magnetic Particles Used for Recording Media 619 a) Maghemite 619 b) Cobalt-Modified Maghemite 620 c) Iron 620 d) Chromium Dioxide 620 e) Barium Ferrite 621 12.3.4. Monodispersed Particles for Magnetic Recording Media 622 12.4. Catalysts 628 12.4.1. Preparation and Uses of Metal Catalysts 629 a) Dispersed Catalysts 629 Condensation in gas phases 629

580

xvi

CONTENTS

Precipitation in liquid phases 630 b) Supported Catalysts 632 12.4.2. Size Effects 635 a) Size Control of Metal Particles 636 b) Size Effects on the Electronic States of Metal Particles 637 c) Size Effects on Activity and Selectivity 642 (1) Reactions of a Constant TOP with Size Change 643 (2) Reactions of an Increasing TOP with Size Reduction 643 (3) Reactions of a Decreasing TOP with Size Reduction 644 (4) Reactions of a Maximum TOP with Size Change 644 12.4.3. The Roles of the Support 645 a) Controller of the Mean Size and Size Distribution of Metal Particles 645 (1) Effect of the Specific Surface Area 645 (2) Effect of the Surface Roughness 646 (3) Effect of the Pore Size 646 (4) Effect of the Affinity to Metal Particles 648 (5) Effect of the Affinity to Metal Complexes 649 b) Stabilizer 652 c) Adsorption Medium 655 d) Controller of Electron Density of Metal Particles 656 e) Synergistic Catalyst 657 12.4.4. Application of Monodispersed Particles to Catalysts 658 Appendix: Growth of Metal Particles on Supports by Stepwise Coalescence 663 12.5. Pigments 676 12.5.1. Relationship between Particle Size and Color 677 12.5.2. Shape Effect on Optical Properties 685 12.5.3. Hiding Power 686 12.5.4. Composite Pigments and Their Optical Properties 687 12.5.5. Other Properties Required for Pigments 689 12.6. Biological and Medical Uses 691 12.6.1. Applications to Cytology and

CONTENTS

xvii

Diagnostic Examinations in Vivo 692 a) Specific Staining of Proteins in Cells 692 b) Magnetopneumography 695 c) Mechanistic Studies of Endocytosis 696 12.6.2. Applications to Cell Separation and Diagnostic Assay 697 a) Use of Microspheres for Cell Separation 703 b) Separation of Cancerous Cells 705 c) Diagnosis of Virus Diseases 705 d) Chemiluminescent Enzyme-hnmunoassay for Tumor Markers 707 12.6.3. Remedial Uses 708 a) Drug Delivery Systems 709 b) Bioreactors 710 c) Biocleaners 711 d) Hyperthermia 711 12.6.4. Roles of Monodispersed Particles 712 References 714 Name Index

733

Subject Index

759


LIST OF SYMBOLS A A(t) a

surface area, Hamaker constant, or light absoq)tion relative amplitude to the average level in dynamic light scattering particle radius, or solid surface area divided b y the number o f the adsorbed particles UQ lattice parameter of fl-axis a^ surface area o f a m o n o m e r a„ surface area of a cluster consisting of n monomers ( n - m e r ) , or electric multipole moment B magnetic flux density b„ magnetic multipole m o m e n t C total concentration o f all monomeric species CQ initial C Cfj C in the bulk in the liquid phase o f a particle growth system Cîf C at the critical supersaturation C at the solid/liquid interface in a particle growth system Cj C in equilibrium with a particle of radius r Cj. C„ C in equilibrium with a bulk solid C(„) C in equilibrium with a n - m e r Cjv C in equilibrium with the stable nuclei at the end of nucleation C close to Cî, but slightly below C^^ C* A C * C*'C^ C ( T ) autocorrelation function in dynamic light scattering C^ extinction cross-section of a particle Q^j absorption cross-section o f a particle C^c^ scattering cross-section of a particle c concentration of monomers, or weight concentration of particles CQ lattice parameter of c - a x i s C(oo) concentration o f m o n o m e r s in equilibrium with a bulk solid C(„) concentration of monomers in equilibrium with a n - m e r c„ number concentration o f n - m e r s c„^ c„ in equilibrium with supersaturated monomers c^ number concentration of radicals in m o n o m e r - s w o l l e n polymer particles per unswoUen unit volume c* number concentration of precursor radicals in the aqueous phase of an

XX

LIST OF SYMBOLS

emulsion polymerization system diffusion coefficient of solute molecules or particles transverse diffusivity of particles diameter of a monomer or a particle electric field, or energy magnetic energy of crystalline anisotropy magnetic energy of external magnetic field magnetic energy of shape anisotropy magnetic energy of strain anisotropy electric charge of an electron Faraday constant, or force size distribution function, frequency of a laser beam, or activity coefficient G(T) distribution function of T in photon correlation spectroscopy g normalized size distribution function of embryos, or particle concentration in gram per one gram of the dispersion H external magnetic field, or peak height of a pyramid extrapolated from a two-dimensional nucleus in the form of a truncated pyramid HQ separation between the Stem layers of two particles H^ coercive force HJ^Q) horizontal component of a Rayleigh ratio, RJ^Q) h dimensionless size distribution function, dimensionless magnetic field, surface-to-surface interparticle distance, or height in general / magnetization, intensity of transmitted light, or initiator of polymerization /• initiator radical /Q spontaneous magnetization per unit volume of a particle, or intensity of incident light Ij. residual magnetization /j saturation magnetization J nucleation rate K absorption coefficient of a particle KQ stability constant of initiator radicals Kj) rate constant in the diffusion-controlled growth mode K^ constant in Nielsen's chronomal of diffusion-controlled growth K^ constant in Nielsen's chronomal of mononuclear-layer growth Kj^ rate constant in the reaction-controlled growth mode Kj, constant in Nielsen's chronomal of (polynuclear-layer) reactioncontrolled growth K^ magnetic shape-anisotropy constant

D Dj d E E^ Efj E^ E^ e F /

LIST OF SYMBOLS

K^ K^ K^ k k^ k„ kj k^ kf k^ k^ k^

k„ kj^ k^ k^ L LQ / M m N NQ

Np N^ n

n* n^ HQ n^

xxi

solubility product uniaxial magnetocrystalline anisotropy constant magnetic strain-anisotropy constant Boltzmann constant, or growth rate constant (= k^) reaction rate constant of initiator radicals with monomer k^ of a bulk solid (n = oo) kj" of a bulk solid (n = oo) overall deposition rate constant of all monomeric species per unit area deposition rate constant of monomers per unit area number of radicals entering a polymer particle per unit time averaged k^ for all polymer particles in a system number of monomers polymerized by a radical per unit time in monomer-swollen polymer particles, or reaction rate constant of mononuclear-layer particle growth absolute dissolution rate of a n-mer per unit area absolute release rate of monomers from a n-mer per unit area in the absence of complexing agents recombination rate constant of radicals in monomer-swollen polymer particles rate constant of the surface process for the entry of radicals into a monomer-swollen polymer particle per unit area ligand circumference of a two-dimensional nucleus in the form of a truncated pyramid length magnetic dipole moment of a particle or monomer for polymerization refractive index of a particle relative to that of the medium, magnetic pole strength, or mass of a particle Avogadro number, or demagnetization factor number of embryos generated per unit time (= QVJVQ) number concentration of polymer particles surface density of monomers number of monomeric subunits of a n-mer, real part of the relative refractive index, m, of a particle, or number concentration of cations or anions of 1-1 electrolytes number of monomeric subunits of a critical nucleus n* at the maximum supersaturation QRT/SnDyV^C^, or number concentration of particles in a sol at the ground level under the influence of gravity number or number concentration of stable nuclei in a system

xxii

LIST OF SYMBOLS

«^" final number or final number concentration of stable nuclei in a system after the nucleation period n_ number of unstable nuclei in a system n_* final number of unstable nuclei in a system n^ number concentration of particles n^ number concentration of particles at a height h n^ number concentration of ion / n,^ « of a nucleus at the front of a quasi-steady size distribution n^ average number of radicals in a polymer particle n^ number of bond-fi:ee open sites of a free monomer n/ number of bond-free open sites of a surface monomer P molarity of precipitate P ''lu/^'ioo' or r/rp Q

generation rate of monomeric species in a unit volume, feed rate of monomeric species, total electric surface charge of a particle, or capillary charge of a particle. QQ generation rate or feed rate of monomeric species, assumed to be constant during the nucleation stage q magnitude of a scattering vector in dynamic light scattering R gas constant, or center-to-center interparticle distance R^ infinite reflectivity Rj^ recombination rate of radicals in a polymer particle 7?^(e) Rayleigh ratio for unpolarized incident light r particle radius, circle radius, distance from a particle center, or degree of ion exchange r* radius of a particle in equilibrium with the monomeric species in a solution phase ^min* ''* ^^ ^he maximum supersaturation f mean particle radius TQ mean radius of embryos or initial degree of ion exchange rôo distance from the center of a tetradecahedral particle to a {100} surface rîi distance from the center of a tetradecahedral particle to a {111} surface r+ mean linear growth rate of a stable nucleus Too ultimate particle radius at the end of the growth Tg geometric mean radius Tp maximum radius of an embryo, or unswoUen radius of a polymer particle swollen with the monomers

LIST OF SYMBOLS

xxiii

r^v r„ r^ r^ S

mean radius of stable nuclei at the end of a nucleation stage number-average radius surface-average radius weight-average radius supersaturation ratio (= c|c^^^ = CIC^, surface area, or scattering coefficient of a particle S^^ maximum supersaturation ratio T absolute temperature t time tj^ nucleation period U^ magnetostatic energy of a particle u^ electric mobility of a particle V volume of a particle FQ molar volume of solvent molecules V^ London - van der Waals attractive energy Vg B o m repulsive energy V^ Electric repulsive energy V^ magnetic energy V^ molar volume of a solid Vj total potential energy Vj[Q) vertical component of a Rayleigh ratio, Rj(Q) v^ volume of a monomer unit of a linear polymer chain Vp unswollen volume of a polymer particle swollen with the monomer X monomer in a liquid phase X^ species / [ZJ molarity of species i X^ cluster consisting of n monomers (n-mer) X° monomer in a surface molecular layer X mole fraction of monomers in a liquid phase, or distance in general jc* fraction of the number of the embryos whose radius is greater than r* Xo*

X* at r, = 0 (=

VQ/V^)

x^ x^ JC(„) JC(«) z^

mole fraction o f monomeric species i in a liquid phase mole fraction o f n - m e r s in a liquid phase m o l e fraction of monomers in equilibrium with n - m e r s mole fraction of monomers in equilibrium with a bulk solid (n = oo) valency of ion /

Greek letters YIU/YIOO r^îo» aspect ratio of a prolate particle (= l/w), optical size a parameter (= 2jrr/X.'), magnetic energy parameter (= MH/kT), direction

xxiv

LIST OF SYMBOLS

cosine of saturation magnetization, or collision efficiency of particles to a solid in a magnetic field P shape factor of a particle defined by 44^271^, the ratio of the swollen volume of a polymer particle to its unswollen volume, or ratio of the equatorial radius to a half length of the revolution axis of an oblate particle P„ stability constant of complex ML^ (= {ML^]l{M\[Lf) P^ ratio of the scattering cross section of a particle to its geometric cross section r half-width at the half-height of an amplitude peak as a function of frequency at a certain scattering angle in dynamic light scattering Y specific surface energy, or specific wall energy of a magnetic domain 6 thickness of a Stem layer, or thickness of a diffusion layer e optical extinction t surface energy of a bond-free site, or molar optical absorption coefficient eg vacuum permittivity, or width parameter of a size distribution of embryos e^ relative permittivity ^ zeta potential ri viscosity 6 scattering angle, diffraction angle, slope angle of the inscribed circular cone of a two-dimensional nuclei, or angle between magnetic field and primary axis of an anisometric particle K Debye-Hiickel parameter, or light absorption index of a particle X Wj7«j, or wavelength in vacuum X' wavelength in a medium (= \l\x^\ m, = refractive index of the medium) î chemical potential of a monomer in liquid phase, refractive index of particles in vacuum, or magnetic permeability II magnetic moment vector of a particle [I relative permeability (= \kj\k^, \x^ = vacuum magnetic permeability) ti® standard chemical potential of a monomer in a liquid phase \j^ refractive index of a medium in vacuum, or vacuum magnetic permeability moo surface chemical potential of the {100} face of a polyhedral particle jiiii surface chemical potential of the {111} face of a polyhedral particle tJL° chemical potential of a monomer in the interior of a pure bulk solid \k^^^ chemical potential of a monomer in a n-mer (X(^) chemical potential of a monomer in a liquid phase in equilibrium with a monomer in a n-mer

LIST OF SYMBOLS

pi(„)

xxv

chemical potential of a monomer in a liquid phase in equilibrium with a monomer in a bulk solid (n = oo) \ii chemical potential of species /, or surface chemical potential of the ith face of a polyhedral particle \i^ chemical potential of a n-mer in a liquid phase |x„° chemical potential of a n-mer in the interior of a bulk solid |i^® standard chemical potential of a n-mer in a liquid phase \f chemical potential of a monomer in a surface molecular layer H^" '^ standard chemical potential of a monomer in a surface molecular layer Vj. number of adsorption sites occupied by an adsorbate molecule / ^ degree of reaction in Nielsen's chronomals jt„ angular distribution of afieldradiatedfrom electric multipoles in light scattering p space charge density, or density of a solid p' overall density of a particle dispersion Po density of a medium p„(e) polarization ratio (= Hj[Q)/V^{Q)) o surface charge density, mass specific magnetic moment, standard deviation of a size distribution, or collision parameter OQ mass-specific spontaneous magnetization, or breadth parameter of a particle size distribution Gg geometric standard deviation of a size distribution o^ modal value of the optical size parameter a Qp mass-specific magnetic moment RTVp/SiiDyV^C^ (a time constant), time constant in autocorrelation X function, or turbidity T^ angular distribution of the field radiatedfiômmagnetic multipoles in light scattering V volume, or velocity VQ molecular volume of a solvent, or mean volume of embryos v^ volume of a monomer v^ mean volume of stable nuclei i;/ initial v^, equivalent to the v^^ at the maximum supersaturation TJ^ mean volumic growth rate of stable nuclei '^max volume of a nucleus at the front of a quasi-steady size distribution v^ volume of a n-mer Vp maximum volume of an embryo (j) work for transferring a monomer from a bulk solid (n = «>) into a liquid phase and dispersing it to a mole-fraction level (= kTinS), or angle between the directions of magnetization and a magnetic field

xxvi

([)„

LIST OF SYMBOLS

supersaturation energy parameter of the solubility of a n-mer against that of the bulk solid (= mn(C(„/C(«))) X magnetic susceptibility X relative magnetic susceptibility (= X/MO) \p \p„ per n^^ for a n-mer (= ^l^^n^^), or angle between the direction of magnetization and the primary axis of an anisometric particle \po potential difference between the bulk solid and the solution phase in an inhomogeneous system \|)° surface energy of a free monomer \|)„° intrinsic surface energy of a n-mer \p„ surface energy of a n-mer \p§ Stem potential \p°''' intrinsic surface energy of a surface monomer \p^ surface energy of a surface monomer

PART 1. FUNDAMENTALS INTRODUCTION The so-called "monodispersed particles" are generally defined as particles which are uniform in size, shape and internal structure. Their size distribution is exceedingly narrow - say, less than 10% in coefficient of variation (= standard deviation / mean size). Because of these characteristics, they are not only used widely as ideal models for fundamental studies in colloid science, but are also expected to possess infinite potentialities as the most ideal particulate materials in industry for ceramics, electromagnetic devices, catalysts, photographic materials, pigments, medicines, etc. For these applications, it is necessary to establish general principles for the synthesis of monodispersed particles perfectly controlled in their mean size, shape, and internal structure. As an introduction to this final goal, the backgrounds of the fundamental unit processes including nucleation, growth, habit modification, recrystallization, and solid-solution formation will be described in Part 1. Although the arguments in Part 1 are focused on the particle formation in liquid systems, they may mostly be applied to gaseous systems as well.

CHAPTER 1 NUCLEATION 1.1. Surface Energy Probably, the surface energy, or more rigorously the interfacial energy, is one of the most fundamental quantities in the elementary processes of particle formation, including the nucleation event, particle growth, Ostwald ripening, coagulation, etc. In this sense, it seems quite reasonable to deal

2

FUNDAMENTALS

with this quantity first of all m this book. However, despite its crucial importance, this essential quantity in coUoid and interface science and all other sciences dealing with phenomena in inhomogeneous systems had never been defined quantitatively or formulated as a function of more elementary quantities, such as chemical potentials, in thermodynamics of inhomogeneous systems since its advent in the late 19th century. This was the very reason why the author started to consider, presumably, the greatest fundamental problem of modem thermodynamics left unsolved, hi the course of the reconsideration on the background of the interfacial energy, the author became aware of serious inconsistencies involved in the two principal theorems of modem thermodynamics for inhomogeneous systems, which seemed to have inhibited the sound development of thermodynamics of their own; ie,, (1) the chemical potential of each component is equal throughout an inhomogeneous system including its interfacial chemical potential when the system is in equilibrium; (2) the interfacial energy is an excess energy of an interface independent of the chemical potentials of the interfacial components. Hence, what the author had to do first was to disprove logically these conventional theorems.^ After that, on the basis of the deductive conclusion that the origin of the interfacial energy is the difference in the chemical potential of each component between the interface and bulk phases, a new theoretical approach to the interfacial energy has been proposed.^"^ The formulation of the surface energy of solid in liquids, or solid-liquid interfacial energy, to be described in this book is based on this general theory. I J . l . Intrinsic Surface Energy of Amorphous or Polycrystaiiine Spherical Particles Let us call the minimum subunit of a particle a "monomer," corresponding to the molecular formula of the solid, Afip such as AgBr, Si02, FCjOj, CU2O, etc., and a cluster consisting of n monomers a "n-mer." In the solution phase, some of the monomers may exist in different forms such as complexes or dissociated ions. All of them including the monomer in the original molecular form of Afij will generally be referred to as "monomeric species" in this book. The term "monomer" will also normally indicate a monomeric species in the molecular form of A^Bj without dissociation or complexation. First, let us direct our attention to the monomers in the molecular form ofAJSj in the solution phase, at equilibrium with the bulk solid (n = 00). If the monomers in the bulks of the solid phase, a, and liquid phase, p, are

1. NUCLEATION

3

represented by IC and Z, respectively, the formation of a free monomer X in the liquid phase from the solid phase a and solvent molecule, L, in the liquid phase may be written as

where XL^ is the monomer X coordinated or solvated by the molecules L in the liquid phase. The standard free energy of formation of XL^ per single molecule, \p°, is given by

where fx^Ln® is the standard chemical potential of JSLL^ per single molecule m the liquid phase, (i^"'" is that of Z" in the solid phase a, and ]x^ is that of L in the liquid phase p. The superscript e of (x^Ln® indicates [x^Ln ^^ "^^le fraction x-^^^ 1 obtained by extrapolation from x^^« 1, while the superscript 0 of [ix°'" or ^ means the chemical potential of each pure substance at %°= 1 or jc^ = 1. The op" is equivalent to the interfacial energy of the monomer X or, conventionally, the surface energy of the monomer X If the system is in equilibrium between phases a and p, it follows from Eq. (1.1.1) that li°'« = ^ ^ ^ - « ^ , .

(1.1.3)

If the p-phase is a dilute solution, the mole fraction of U ^L> ^^^ ^^ approximated as x^ « 1, and thus \x^ « ^^, Hence, it holds that ^«>« = ^ ^ - „ H ° .

(1.1.4)

If we redefine V-xii^-ny^.^ and V^xurn\k^ as the standard chemical potential, [i®, and chemical potential, ji, of the monomer in the solution phase, respectively: le.,

Eq. (1.1.4) is rewritten as

4

FUNDAMENTALS

^0,a^^

(1.1.6)

In this treatment, the solvent is regarded as only a medium, and the formation energy of the coordinated n solvent molecules from the free molecules is incorporated into the standard chemical potential of the monomer X. Such a treatment is allowed only for dilute solution phases, such as we deal with in this book. On the other hand, if the mole fraction of Z in phase P in equilibrium with the sparingly soluble solid phase a is denoted by x^^y \i can be written as \x=\i-^kThix^^y

(1.1.7)

Hence, the surface energy of a free monomer is given by ^^=^^-/=-i{:7Tnjc^^,

(11.8)

where [x® and [x° are abbreviations for jx®*^ and pi°'°, respectively. Strictly speaking, the surface energy of a free monomer, ip^, should be referred to as the "liquid-solid interfacial energy" of a free monomer. However, we will use the term "surface energy" hereafter in this book, according to the convention. If c^^^ and VQ denote the solubility of the bulk solid in number concentration of the monomers and the molecular volume of the solvent, respectively, x^^^ is given by

Hence, \p° in Eq. (1.1.8) can be calculated readily using this relationship. On the other hand, if the monomers composing an amorphous n-mer of a sufficiently large n are randomly oriented in the n-mer, the n-mer may assume a spherical shape, owing to its amorphous structure, and the surface area of such a n-mer, ^»^ = -N'^kkTlnx^^y

(1.1.17)

where A^ is the surface number density of the surface monomers.^ The A^ and n / depend on the surface structure of a given crystal, while the n^ depends on the internal crystal structure, as will be discussed in section 1.1.4. 1.1.3. Surface Energy under the Influence of Adsorption While the effect of adsorption on interfacial energy, y, is already involved in the formula of y in the fundamental theory,^ it can be derived also from a concept of the surface complex, in a manner similar to the derivation of the absolute value of solid-liquid interfacial energy in the preceding sections 1.1.1 and 1.1.2. In this book the latter approach is adopted to show that the same result as that of the fundamental theory is obtained in a different way of derivation."* If the monomeric species and/or dissociated ions of the solid or foreign molecules are adsorbed to the solid surfaces, the surface energy will be reduced. In this case, the adsorption sites of an adsorbate are assumed to be limited to either of the cationic or anionic bond-free spots, and not both. Thus the number of the adsorption sites of a surface monomer is equal to the number of the open sites of a surface monomer, «/. In addition, we further assume that an arbitrary adsorbate molecule Y) can be adsorbed to v^. cationic adsorption sites (v,. ^1), but a solvent molecule can be adsorbed to only one adsorption site (v^ = 1). In this case, the free energy of formation of one surface complex Y^"^, %"",fromv^. sites of a monomer in the bulk solid and an adsorbate molecule of Y^ in the bulk liquid may be written as

1. NUCLEATION

i|;r=tir-^ti°-^,,

(1.1.18)

where m"", \i^, and ^ are the chemical potentials of a surface complex l^"^, a monomer Z in the bulk solid phase, and a free molecule of Y^ in the liquid phase, respectively; « / is the number of the cationic adsorption sites of a surface monomer. It should be noted that ^ 7 ^ / corresponds to the chemical potential of a site of a bulk solid monomer to be reacted with a solvent molecule or Y^ if the bulk monomer is assumed to be located at the solid surface. Since the ip^"^ corresponds to the interfacial energy of a surface complex Y^^, the specific interfacial energy y is given by

where 2 means the sununation for all surface complexes including the surface complex of the solvent, A^^"" is the maximum surface density of Y^"" and y^^ is the coverage of Y-^ over the cationic adsorption sites. At equilibrium of adsorption, dy equals 0 for the changes of any y^"^. Since Idy;" = 0 from ly,"" = 1, JY = S A f > W

(1120)

where the ip^^ is the interfacial energy of a surface complex of a solvent molecule with an adsorption site (z=l), and I! means the summation for all surface complexes with the adsorption sites except the surface complex of a solvent molecule. Since Eq. (1.1.20) must be satisfied for independent changes of all y."^ for i^2 at equilibrium, it must holds for any kinds of X^" with i^2 that

where Nf is the surface number density of the cationic adsorption sites. Hence, y at equilibrium is given by

FUNDAMENTALS

10

Y=w:*i.

(1.1.22)

The tpi" is given by ,0

V^"

M"

(1.1.23)

where \f and pi^ are the chemical potentials of a solvated surface monomer but free from adsorption of Y^ and a solvent molecule in the liquid phase, respectively. If [x^'"^"^ and [i^^ denote the standard chemical potential of a part of a surface monomer in the solid-side surface layer a^ and the chemical potential of a coordinated solvent molecule to the surface monomer, respectively, (1.1.24) = 1^

-^n^V^L ^n^kTbiaL,

where [ij^'"^ is the standard chemical potential of the coordinated solvent molecule, and a / is the activity of the coordinated solvent molecules at the surface. Since jx^-Mi" for Mz, ^ Eq. (1.1.23) where tx/ is the chemical potential of a solvent molecule of the pure solvent, one obtains from Eqs. (1.1.23) and (1.1.24) that i|r^ = :!!LL+jt7Tna^,

(1.1.25)

o

where xp^'"^ is the standard free energy for the formation of a surface monomer of the clean solid surface without the adsorption of non-matrix components, given by ô.o.ô.a,_ô,„;(ô. may be written, (1.2.7)

^ = kT]nS. Since the surface area of a n-mer, a„, is given by Eq. (1.1.34), 27Pui 1'n = V«n = Y

I 4

\l/3 ,2/3

(1.2.8)

j

If we define xp as f27PUi * =Y

\l/3

(1.2.9)

\p„ is written as (1.2.10)

i|;^=i|;n 2/3

Although \p defined by Eq. (1.2.9) corresponds to \|J„ extrapolated to n = 1, it is generally not equal to the surface energy of a monomer, ij)°, but is a function of the shape and crystal structure of the n-mer (see section 1.1.2). Nevertheless, if the n-mer can be regarded as an amorphous sphere particle, and free from adsorption of its own ions or any other foreign molecules, \p is equal to ip° [see Eq. (1.1.8)]. In this special case. i|r = i|rO = -JkTTnx

H'

(1.2.11)

as can be confirmed if one inserts P = 16jr/3 and y" of Eq. (1.1.12) into Eq. (1.2.9). For fee single-crystal particles, ip/ij)" = 0.952 (cube), 1.20 (dodecahedron), 1.57 (octahedron), 1.15 (sphere), from ip/xp^ = {3/4)aQY^\

FUNDAMENTALS

28

Nf\, As a consequence, AG^ can generally be written as AG = -(t)n + \|rn^^

(1.2.12)

If AG„ consisting of the components, -^n and \|)n^^^, is illustrated as a function of n at a given c|), one may find a peak as shown in Fig. 1.10.^"^ Normally, the n-mer which gives the peak of AG„ is referred to as a "critical nucleus." If the number of monomers composing the critical nucleus is denoted by n*, n* is given from d^GJdn = 0 by

-(f

(1.2.13)

If the maximum AG„ is denoted by AG*, AG* is given by (1.2.14)

On the other hand, when n-mers are dispersed, so as to be equilibrated

J

60r ;

2

/ Jt!lL

50

I kT

4G'

kT 2

30

kT

kT

n

\ 3 « \

'^ 1 20

10

'

0

-10

-20 •

-30

-40

•

.• 10

\ \ .'.

20

kT

•

\

Fig. 1.10. AG„/A:T and its components as functions of « at a given ÎkT (From Ref. 14.)

29

1. NUCLEATION

with the supersaturated monomers, \i'n\i = AG+it7Tnx = 0,

(1.2.15)

where [t^ is the chemical potential of a n-mer and x„ is the mole fraction of the n-mers. If c„" and VQ denote the number-concentration of the n-mers in equilibrium with the supersaturated monomers and the molecular volume of the solvent, respectively, x„ is given by (1.2.16)

^«=^MJÛ_ kT

J n

If we use n* in Eq. (1.2.13) and AG* in Eq. (1.2.14), AG„ in Eq. (1.2.28) may be transformed as ( \ / \2/3 Ag„ _ -(|)n+i|rw^/3 _ AG* n + 3' n ' -2 kT kT kT Kn') \n )

(1.3.29)

If we take the first three terms of the Taylor expansion of Eq. (1.3.29) for (nln*)'-'^ at {jiln*)"-" = 1, \2

where

AG„

AG-

kT

kT

1-3

-^-1

INn' ) \

AG* 2 ^ . kT

(1.3.30)

36

FUNDAMENTALS

x=.

3AG' N kT

N

-^-1

dx =

i|r

dn

(1.3.31)

the latter of which is obtained by using AG* = Mf{n*)^l3 in Eq. (1.2.14). As a consequence, Eq. (1.3.28) is transformed as ^n

-^"o i

3

\l/3

{kT\l^ kT

(1.3.32)

3AG' N kT

(1.3.33)

\Anv\] xfexpi-y^ydy. At /I = 1,

3AG" N kT

X = ,

i\/^ J

Let us estimate the magnitude of jc at n = 1. For example, tj> - \|>P" =9.06x10-2" J and S = 2 for AgBr at 25 °C, (|) = 2.85x10-^1 J and AG* = 1.36x10-1' J, so that AG*/A:r = 3.30xlO^ Even if 5 = 10, (|) = 9.48x10-^^ J and AG* = 1.23xl0-i* J, so that AG*/itr = 2.98x10". Thus, J: at n = 1 is normally of a sufficiently large negative value, so that j""exp(-/)rfy - J"exp(-y-)rfy = /ir.

(1.3.34)

In addition, c^/c^' = 1 at /i = 1, so that one finally obtains from Eq. (1.3.32)

4u N kT^^^l oV3^/^j

(1.3.35) kT

If we use AG* = 4\pV27(|)2 in Eq. (1.2.14), (t> = kT[T\S in Eq. (1.2.7), and \|) - V = -^71n(C(„)Vo) in Eq. (1.1.8) when the effect of adsorption on \|> can be ignored, J may be written more concretely as

1. NUCLEATION

k

37

(A

2 \ 1/3

j = — ^0

4[ln(C(.)Uo)]' +lnS 27(ln5)2

^-ln(C(.)Uo) exp

(1.3.36)

From Eq. (1.3.35) with Eqs. (1.2.13) and (1.2.14) it follows that dlogJ _ dhiJ _ d dlogC dhiS ~ 7^ [ 274,^

(2±]\i ,

13o and rjr^ as functions of p*. (From Ref. 26.)

71

1. NUCLEATION

As long as Q remains constant, the ratio of rjr* (=1.638) is maintained throughout the growth stage, due to the constant n^", despite the change in the individual variables of r^ and r*. Nucleation Period In general, tjx is given from Eqs. (1.5.6) and (1.5.23) by

t. ^ H r^f p y C qfp^dpldp = php^dp,

(1-5.39)

where q(p) = r^gir). If the cosine function of Eq. (1.5.9) is assumed for g(r), tJx is determined as a function oip*, as shown in Fig. 1.28 together with tJx from Eq. (1.5.28) and tlx (= tJx + tJx). The t. at p* = 1, C, is given by f." = 0.530T,

(1.5.40)

0.530

0.6814

Fig. 1.28. tJx, uh, and t/x- (= tJx + tJx) as functions of p*. (From Ref. 26.)

72

FUNDAMENTALS

Therefore, the nucleation period tf^ is obtained from Eqs. (1.5.35) and (1.5.40) as ?A,= f - + r :

= 5.097T =

5.097/Jru„ ^

(1.5.41)

Hence, t^ is independent of Q, but proportional to v^. Therefore, the knowledge of v^ is required for determining r^. Conversely, if r^ can be determined by some means, the values of i^p, r^, and r^ are obtained by using Eq. (1.5.41). The sum of nJriQ and nJtiQ changes with/?* as demonstrated in Fig. 1.29 and takes 3.858 atp* = 1. If n_ atp* = 1 is represented by nj" (= 2.291no), the ratio of (n_" + AZ^*) to «^* is given by

n.^n, _ 3.858 -2.5 1.567

(1.5.42)

5 U

4 \-

3.858

y

no

1.567

V"

0

T 1 0.6814

2

3 P*

5

Fig. 1.29. nJriQ, njn^^, and HJHQ + HJUQ as functions of p*. (From Ref. 26.)

1. NUCLEATION

73

Thus, it is possible to determine t^ from experimental data on log(«_+n^) vs t and on n^", since tj^ can be specified by the time when \og{nj-n^ = logw^*" + log 2.5. Discussion Since the unstable nuclei must be in a quasi-steady state of generation and dissolution in the growth stage of the stable nuclei, the quasi-steady state must be established at the latest by the end of nucleation. On the other hand, if one sets r^ = 0 or n^ = 0, r* and jc* take the minimum, TQ*, and the maximum, XQ*, respectively, so that n^ assumes its maximum, as is obvious from Eq. (1.5.15). However, since r* has already been below r^ before n^ reaches its maximum, some stable nuclei must have been produced, and thus n^ ^Q prior to the establishment of the quasi-steady state of the unstable nuclei. In other words, there must be some non-steady state of the unstable nuclei beforehand for the production of the stable nuclei, so that t^ is already greater than zero when the quasi-steady state starts. As a result, r* does not actually reach TQ* = 0.6814rp and, when r* reaches its actual minimum, more or less higher than TQ*, the unstable nuclei may enter the quasi-steady state. However, once the unstable nuclei attain the quasi-steady state, the individual values of t^, n^, and r^ are specified by r* which satisfies the initial condition r* = TQ* corresponding to t^ = 0. Consequently, n^", r / , r/, and t^ take the same individual values, regardless of the starting point of the quasi-steady state. Although n^" is independent of r^, it depends on the form of g(r). For example, the effect of the relative distribution width EQ/KQ of the cosine ftinction of Eq. (1.5.9) on n^7wo is shown in Table 1.2, where Tp = TQ + 2EQ. Also shown is w+7«o in the case of g{r) of the normal (Gauss) distribution with the coefficient of variation of EQ/K^ = 1/3 and r^ = 2ro, where EQ is the standard deviation. In general, though AZ^" increases with reduction of EQ/KQ, Table 1.2. Effects of Co/rg on W+^/WQ for cosine and normal distributions (Source: Ref. 26) Normal"

Cosine Co/ro

0.1

0.2

0.3

0.4

0.5

1/3

n"/no

2.40

1.90

1.71

1.63

1.57

1.67

' For the normal distribution, BQ is the standard deviation.

74

FUNDAMENTALS

the effect is rather insignificant unless zjr^ is extremely small. On the other hand, the size distribution of the embryos is expected to be broad, ranging from the dimensions of a monomeric species (r « 0) to r^, due to the instantaneous nonsteady formation process of the embryos, which may involve some coalescence. Thus it seems reasonable to postulate the maximum ^Jr^ for the cosine function, viz., Ejr^ = 0.5. In the meantime, if we simulate g(r) with the nomial distribution of a large standard deviation, g(0) cannot be zero and, besides, r^ is indefinite. These are the main reasons for the choice of the cosine function with ZJTQ = 0.5 to represent the normalized size distribution of the embryos. However, fortunately, the effect of the form of g{r) on «^" is also rather minor as long as the distribution is broad enough. If {r^-r^lr^ « 1, the approximation of Eq. (1.5.24) to Eq.(1.5.25) is unconditionally allowed. In this sense, the {r^-r^lr^ equal to 0.638 appears a little higher than the criterion. However, as is obvious from Fig. 1.27, the increment of n^ is negligibly small after p* exceeds about 0.85, at which nJriQ « 1.50 and (r^-r^lr^ is as low as 0.35, where the approximation is still good enough. Therefore, the final value of n^, /i^" (= 1.567/io), is nearly free from the error due to the approximation, whereas there may be some allowances for r^" and r^" due to it. 1.5.2. AgBr Systems To confirm the theoretical predictions by experiment, open systems of monodisperse AgBr particles were chosen, because of the availability of the well-established controlled double-jet technique,^*^^'^^ in which two solutions of silver nitrate and potassium bromide are introduced simultaneously into a well-stirred aqueous solution of gelatin, while controlling automatically the flow rate of the potassium bromide solution to keep the activity of silver ions or bromide ions precisely at a certain level through detecting the silverion potential with a silver electrode. Figure 1.30 vShows a scheme of the controlled double-jet apparatus.^ The gelatin works as a protective colloid to protect the existing particles against coagulation and secondary nucleation.^^ In this experimental study, 1 mol dm"^ AgNOg coupled with 1.002 mol dm"^ KBr was employed as a source of the monomeric species, and the feed rate of AgN03 was kept constant in each run. The two reactant solutions were introduced into 1000 cm^ of 2 wt % inert gelatin solution of pH 5.0, containing 10"^ mol of KBr, through separate tubes directed toward and ending at the most efficient mixing zone of the impeller. The pBr (= log[Br']) was always set at 3.0 in the middle of the diffusion-controlled

1. NUCLEATION

75

Fig. 1.30. Controlled double-jet apparatus for the preparation of monodispersed silver halide particles. (From Ref. 8.) range for growth,^^ while the diffusion-controlled dissolution is secured irrespective of pBr.9^'^^ Final Particle Number According to the theory, if the addition rate of monomelic species Q is kept constant, the mean sizes of the unstable and stable nuclei as functions of time must be independent of the Q value, since n_ and n^ are both proportional to HQ, and thus to Q, from Eqs. (1.5.13) and (1.5.31). Figure 1.31 for the mean radius of the observed particles plotted against time, for a variety of addition rates of the monomeric species at 70 °C, substantiates the theoretical prediction. The result proves as well that n^^ is proportional to Q as predicted from Eq. (1.5.36), and shown in Fig. 1.32, in which each data-point at ^ = 10 min was used. Here it must be noted that the unstable nuclei are normally not observed together with the particles grown from the stable nuclei by transmission electron microscopy on an aliquot withdrawn from the mother dispersion in the later stage of the growth period due to their prompt dissolution, despite the use of an efficient restrainer which can halt instantaneously the growth and dissolution of AgBr particles. This seems to be due to the fast Ostwald ripening caused by the great difference in solubility between the exceedingly

76

FUNDAMENTALS

Fig. 1.31. The mean particle radius changing with time at different flow rates of 1 A^ AgN03 at 70 °C and pBr 3.0: (o) 10 cm^ min'\ (A) 20 cm^ min'^ (^) 30 cm^ min"\ (n) 40 cm^ min'\ and (•) 60 cm^ min"\ (From Ref. 26.)

fine unstable nuclei and the fully grown particles from the stable nuclei. Thus, the observed particle number apparently goes down to n^ in the growth period, though the unstable nuclei are sufficiently stable to be observed with the stable ones until the end of nucleation and in the very early stage of the growth period, owing to their small difference in solubility. Hence, the measurement of «^* should be done after the apparent particle number becomes constant in the growth stage. If the right-hand side of Eq. (1.5.36) is divided into two terms as n, =

1.567

QRT

(1.5.43)

the Y may be obtained from the slope of the plot of nj" against {QRTI 8jtDK^C„) changing with temperature, since the temperature dependence of Y over a relatively small temperature range, e.g,, from 40 to 70 °C, may be regarded as almost constant compared to the drastic change of w^" and

1. NUCLEATION

77

0.5

1.0

1.5

2.0

Q [mmol-s'^]

Fig. 1.32. Relationship between Q and /z^" at 70 ""C and pBr 3.0. The closed circles stand for the results of repeated experiments. (From Ref. 26.)

{QRmixDVJO^), in view of Eq. (1.1.12) for f. For the temperature dependence of Z), one may use the data of Strong and Wey^^ from 0.88 x 10"^ m^ s-^ at 35 °C to 2.34 x 10"^ m^s'^ at 80 X (activation energy = 4.70 kcal mol'^). V^ is 29.0 cm^ mol'^ for AgBr. For calculation of the total solubility, C^, as a function of pBr and temperature in the presence of 2 wt % gelatin, the data in refs. 37-41 were used. The result is illustrated in Fig. 1.33. On the other hand, Fig. 1.34 shows the changes of the observed particle number with time at 40, 50, 60, and 70 °C, where Q and pBr were fixed at g = 10"^ mol s"^ and pBr 3.0. The values of D, C«„ and n^" at 40, 50, 60, and 70 °C are summarized in Table 1.3. Figure 1.35 shows the plot of n / against QRT/8TCDV^C^, whose slope gives y = 177 mJ m ' l The theoretical n^* values in Table 1.3 correspond to those calculated from Eq.(1.5.36) with y = 177 mJ m"^. For the y value of AgBr there are many proposals ranging from 100 to 200 mJ m'l The rather wide range of the scattered data may be due to the characteristic shape effect of AgBr (see section 1.1.2), the uncertainty of the diffusivity of solute, and the difference

78

FUNDAMENTALS

in growth mode. In any case, there are some limitations in the determination of Y from nucleation processes.^

10"

10-

10"

S

10-

\^

10-

„.

7(n:

•

>

^

A^^/J

.—-":1.

'"^y^

Fig. 1.33. C„ as a function of pBr and temperature in the absence (solid lines) and m the presence (dashed lines) of 2 wt% gelatin at pH 5.0, (From Ref. 26.)

,.^--'

10"

10-

pBr

10 1 8 40''C

50**C

10 1 7 60*'C -no < ^

A *sF

10 1 6

A. -

0

—o— 70°C

0

1

1

1

2

-o • •

t [min]

"^^

1

-Ky

J

Fig. 134. The observed particle numbers changing with time at different temperatures {Q = 10"^ mol s-\ pBr 3.0). (From Ref. 26.)

79

1. NUCLEATION

Table 13. Values of D, C„, and n," at 40, 50, 60, and 70 °C {Source: Ref. 26) ^ "

«+

Temperature CC)

D

40 50 60 70

9.94x10-'° 1.26x10-' 1.56x10-' 1.92x10-'

(mol dm-^)

Theory

Experiment

1.01x10-' 2.14x10"' 4.34x10-' 8.42x10-'

3.15x10" 1.22x10'' 4.97x10'^ 2.14x10'^

3.20x10" 1.25x10" 4.60x10'^ 2.20x10'^

Q = 10"' mol s-\ pBr 3.0, m.s. IN AgNO3/1.002Ar KBr

1

2

3

4

ORT/STcDVrr^Coo [mJ m - 2 ]

Fig. 1.35. Relationship between QRm7d)V„C„ and n," from the data at 40 °C (A), 50 ^C (V), 60 °C (o), and 70 °C (o), yielding the y value. (From Ref. 26.)

Nucleation Period As anticipated from the theoretical curve of nJnQ-^nJriQ in Fig. 1.29, a peak in the particle number is observed for every curve in Fig. 1.34. This is direct evidence of the nucleation process proceeding through Ostwald ripening since, otherwise, the particle number must simply increase up to a certain constant level. According to the method in the theory, the nucleation period r^ is given

80

FUNDAMENTALS

by t at the intersection of the curve of the logarithm of the observed particle number against t with the straight line parallel to the ^-axis above log n^"" by log 2.5, as shown in Fig. 1.36. The nucleation periods at 40, 50, 60, and 70 °C were found to be 82, 38, 12, and 8 s, respectively, by applying the above procedure to the curves in Fig. 1.34. It is noteworthy that the nucleation periods at relatively high temperatures are much shorter than generally believed before, say, 1-2 min^"*^. This is because the nucleation period had been regarded as the time for the observed particle number to reach the limiting value of w^","*^*"*^ which is theoretically inappropriate since the number of the stable nuclei is fixed much earlier. From Eq. (1.5.41), tj^ is independent of Q i£v^ is independent of Q, and vice versa. Since the changing pattern of r with time is independent of Q from Fig. 1.32, it is obvious that t^ is actually independent of Q, Hence v^ is also independent of Q,

log nT

Fig. 1.36. The procedure for the determination of nucleation time tj^ value with log w+" changing with time. (From Ref. 26.)

Size of the Embryos Combmation of Eqs. (1.5.36) and (1.5.41) yields

1. NUCLEATION

81

5.097i)„ t = E ^ 1.567

(1.5.44)

If the plot of tf^, obtained with change in temperature against the corresponding values of n^'^/QV^, results in a straight line passing through the origin, v^ must be kept constant for the change of temperature, and the concrete value will be given from the slope of the straight line. The respective values of r^ and n^^lQV^ at 40, 50, 60, and 70 °C are listed in Table 1.4, and /^ is plotted as a function of n^^lQV^ in Fig. 1.37, which clearly displays ^^ in proportion to n^^lQV^, and v^ independent of temperature. From the slope of the straight line in Fig. 1.37, v^ = 2.43 x 10"^^ cm^ so that r^ = 83.4 A and TQ = 41.7 A. On the other hand, the mean radius of the nuclei, including both unstable and stable nuclei obtained by extrapolation to r = 0 from those observed in the early stage of precipitation, was found to be about 60 A, regardless of temperature from 40 to 70 °C. Figure 1.38 shows the case at 50 °C, as an example. The definite initial radius reveals the instantaneous formation of the embryos. The observed mean radius of the embryos somewhat larger than determined with Eq. (1.5.44) seems to be a result of the fast dissolution of the extremely small embryos by Ostwald ripening, within a few seconds immediately after sampling until quenching, since the particles less than about 20 A in radius were undetectable even by electron microscopy on samples immediately quenched on microgrids in liquid nitrogen, followed

Table 1.4. Dependence of r^ and n^lQV^ on temperature {Source: Ref. 26) Temperature CC)

r^ (s)

n^^lQV^ (s cm-^)

40

82

1.10 X 10'^

50

38

4.31 X 10''

60

12

1.58 X 10''

70

8

7.59 X 10''

Note: Q = 10"^ mol s'\ pBr 3.0, m.s. liV AgNO3/1.002N KBr

FUNDAMENTALS

82

Fig- 1.37. Nucleation period, tf^ as a function of n,'IQV„: (A) 40 °C, (V) 50 °C, (o) 60 °C, and (o) 70 °C. (From Ref. 26.)

tf?/QV« [lO^'s-cm^]

3

Fig. 1.38. Mean radius of nuclei as a function of time at 50 °C. (From Ref. 26.)

1. NUCLEATION

83

by freeze drying. In addition, the apparent mean radius of the nuclei at the end of the nucleation period was about 100 A, irrespective of temperature. It corresponds to r^, because r^ agrees with r* at the end of nucleation, which is always equal to the mean radius of all nuclei in a system of diffusion control."*^ Hence, the apparent mean radius of the embryos is about 50 A. Since the contribution of the particles less than about 20 A in radius is likewise excluded, the actual TQ must be somewhat smaller than 50 A, and thus the deduced value of about 40 A seems reasonable. From the extrapolation to / = 0 in the open systems for the preparation of AgBr particles, Berry"*^, Claes and Berendsen'*^ and Wey"^^ estimated the mean diameter of the embryos to be 275, 200-600, and 140 A, respectively. From these mean diameters, Berriman"^, Hirata and Hohnishi"^^, and Wey and Strong^^ estimated the supersaturation ratio in equilibrium with the embryos as 1.15-1.3, 1.3-1.4, and 1.44-1.54, respectively. Here, it should be noted that these supersaturation ratios are not the critical supersaturation ratios for the formation of the stable nuclei, since the latter correspond to the supersaturation ratio when r* is at r^ and not at TQ. If we use r^ = 41.7 A in our systems, the mean diameter of the embryos is 83.4 A. If y is assumed to be 106 mJ m"^ at 50 °C,^ the corresponding supersaturation ratio [= &xp(2yVJrQRT)] at 50 °C is 1.73 and the critical supersaturation ratio at r* = r^ is 1.32. The r* value which gives the maximum supersaturation ratio is located between 56.8 (= 83.4x0.6814) and 83.4 A. In any case, the mean radius of the embryos is much greater than the r^* of AgBr particles, ca. 20 A, in a closed system as described in section 1.4.2, considerable coalescence among the generated embryos must be involved in the localized reaction zone in the practical open systems as a result of the use of the highly concentrated reactant salts. Hence, the size of the embryos must be affected to a great extent by the agitation strength and positions of the outlets of the reactants. This may be the cause of the rather scattered data reported on the size of the embryos in the literature.

References 1. T. Sugimoto, J. Colloid Interface ScL 181, 259 (1996); ibid. 183, 299 (1996). 2. T. Sugimoto, J. Phys. Chem. B 103, 3593 (1999). 3. T. Sugimoto and F. Shiba, J. Phys. Chem. B 103, 3607 (1999). 4. T. Sugimoto and F. Shiba, J. Phys. Chem. B 103, 3616 (1999).

84

FUNDAMENTALS

5. T. H. James (Ed.), "The Theory of the Photographic Process," 4th Edn., p. 9. Macmillan, New York, 1977. 6. L. G. Sillen, "Stability Constants of Metal-Ion Complexes, Section I," Special Publication No. 17. The Chemical Society, London, 1964. 7. C. R. Berry, Photogr. Sci. Eng. 20, 1 (1976). 8. T. Sugimoto, MRS Bull. 14 (12), 23 (1989). 9 T. Sugimoto, J. Colloid Interface Sci. 91, 51 (1983). 10. K. S. Lijalikow, Wiss. Phot. Photophys. Photochem. 50, 151 (1955). 11. A. E. Nielsen, " Kinetics of Precipitation, " p. 64. Pergamon, New York, 1964. 12. A. G. Walton, "The Formation and Properties of Precipitates," p. 122. Interscience, New York, 1967; A. G. Walton, J. Am. Ceram. Soc. 48, 151 (1965). 13. F. van Zeggeren and G. C. Benson, J. Chem. Phys. 26, 1077 (1957); G. C. Benson and T. A. Claxton, Can. J. Phys. 41, 1287 (1963). 14. T. Sugimoto, in "Koroido Kagaku (Colloid Science)," (Chem. Soc. Jpn., Ed.), Vol. 1, pp. 135-152. Tokyo Kagaku Dojin, Tokyo, 1995. 15. R. Becher and W. Doring, Ann. Physik, Ser. 5, 24, 719 (1935). 16. Ya. B. Zeldovich, J. Exp. Theor. Phys. 12, 525 (1942). 17. A. E. Nielsen, Acta Chem. Scand. 11, 1512 (1957). 18. A. E. Nielsen, Acta Chem. Scand. 15, 441 (1961). 19. T. Tanaka and M. Iwasaki, J. Photogr. Sci. 31, 13 (1983). 20. T. Tanaka and M. Iwasaki, J. Imaging Sci. 29, 86 (1985). 21. K. H. Schmidt and S. Gordon, Rev. Sci. Instrum. 50, 1656 (1979); K. H. Schmidt, S. Gordon, M. Thompson, J. C. Sullivan, and W. A. Mulac, Radiat Phys. Chem. 21, 321 (1983). 22. D. Hayes, K. H. Schmidt, and D. Meisel, J. Phys. Chem. 93, 6100 (1989). 23. T. Sugimoto, F. Shiba, T. Sekiguchi, and H. Itoh, Colloids Surfaces A: Physicochem. Eng. Aspects 164, 183 (2000). 24. T. Sugimoto and F. Shiba, Colloids Surfaces A: Physicochem. Eng. Aspects 164, 205 (2000). 25. V. K. LaMer and R. H. Dinegar, J. Am. Chem. Soc. 72, 4847 (1950). 26. T. Sugimoto, J. Colloid Interface Sci. 150, 208 (1992). 27. T. Sugimoto, Hyomen 29, 978 (1991). 28. T. Sugimoto, Gendai Kagaku 263, 42 (1993). 29. D. H. Klein, L. Gordon, and T. H. Walnut, Talanta 3, 177 (1959). 30. C. W. Davies and A. L. Jones, Dicuss. Faraday Soc. 5, 103 (1949). 31. R. W. Strong and J. S. Wey, Photogr. Sci. Eng. 23, 344 (1979).

1. NUCLEATION

32. 33. 34. 35. 36. 37.

38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.

85

I. H. Leubner, J. Imaging Sci. 29, 219 (1985). J. S. Wey and R. W. Strong, Photogr. Sci. Eng. 21, 14 (1977). R. Jagannathan and J. S. Wey, J. Crystal Growth 73, 226 (1985). T. Sugimoto, Adv. Colloid Interface Sci. 28, 65 (1987). T. Sugimoto, J. Colloid Interface Sci. 93, 461 (1983). J. Pouradier, A. Pailliotet, and C. R. Berry, in "The Theory of the Photographic Process," 4th Edn.,(T. H. James, Ed.), p. 1. Macmillan, New York, 1977. M. J. Harding, J. Photogr. Sci. 27, 1 (1979). J. E. Maskasky, J. Imaging Sci. 33, 10 (1989). G. Russel, J. Photogr. Sci. 15, 151 (1967). P. Lanza and I. Mazzei, J. Electroanal. Chem. 12, 320 (1966). I. H. Leubner, R. Jagannathan, and J. S. Wey, Photogr. Sci. Eng. 24, 268 (1980). C. R. Berry and D. C. Skillman, J. Phys. Chem. 68, 1138 (1964). R. W. Berriman, J. Photogr. Sci. 12, 121 (1964). C. Wagner, Z Elektrochem. 65, 581 (1961). C. R. Berry, PSA Tech. Quarterly, Nov., 149 (1955). F. Claes and R. Berendsen, Photogr. Korresp. 101, 37 (1965). J. S. Wey in "Preparation and Properties of Solid State Materials," (W. R. Wilcox Ed.), Vol. 6. M. Dekker, New York, 1981. A. Hirata and S. Hohnishi, Nippon Shashin Gakkaishi 16, 1 (1966).

CHAPTER 2 GROWTH 2.1. Equilibrium Concentrations of Two-Dimensional Nuclei 2.1.1. On a Bulk-Solid Surface Based on analogy with three-dimensional nuclei, disk-like twodimensional nuclei may be appropriate for the formulation of the theory of nucleation on a solid surface. The free energy of formation of a disk-like two-dimensional nucleus (n'-mer) on a bulk solid surface, shown in Fig. 2.1, from n' monomers in a supersaturated solution, AG'„,, is given by AG;,= -(j)n^-Ht|r;„

(2.1.1)

where (j) (= kJlriS) is common to the supersaturation parameter for the three-dimensional nucleation, and \|)'„. is the surface energy of a twodimensional n*-mer. The new surface for the two-dimensional nucleus on the bulk solid is only its side surface, so that i|f^^, = Inr^-i = 2y^nhv^n\

1 r 1

,

-*

1

Fig. 2.1. Model of a two-dimensional nucleus.

(2.1.2)

2. GROWTH

87

where r' and h are the radius and height of the two-dimensional nucleus, respectively, and v^ is the volume of a monomer. Since the surface energy of a monomer on the solid surface, \j)', is given by V=2Yy^7rADp

(2.1.3)

i|r'„/ = i|;'n'*'^.

(2.1.4)

\|)'„. can be written by

and hence AG'/=-
(2.1.5)

The number of monomers composing a two-dimensional critical nucleus, n'*, is given from dAG'Jdn' = 0 as n'* =

(2.1.6) \2^}

and AG'*, the maximum of AG'„, is given by AG'* = ^ = ^ ^ 4* 2

= 4>n'*.

(2.1.7)

If we rewrite n'* in terms of the critical radius, r'*, ./•

(2.1.8)

r'* = .

This relationship holds, irrespective of h. Also, AG'* can be rewritten as ,2

AG

(2.1.9)

4)

88

FUNDAMENTALS

On the other hand, r* and AG* for a three-dimensional spherical nucleus are given from Eqs. (1.2.13) and (1.2.14) as

r* =

3«*Uj

2YUI

4%

*

\

(2.1.10)

and AG' =

167CViY^

(2.1.11)

3e

Hence, both r'* and r* are inversely proportional to ^, and there is the following relationship between them: J*.

r_ 2

(2.1.12)

Also, note that AG'* and AG* are inversely proportional to ^ and ^^, respectively. This means that the three-dimensional nucleation rate drops sharply as ^ decreases, while the (l)-dependence of the two-dimensional nucleation rate is much smaUer. The equilibrium number-concentration of the two-dimensional n'-mers per unit area, c'J, is given in a similar manner to Eq. (1.2.17) for threedimensional n-mers as /e

(-AGO

-2/3

(2.1.13)

i kT =

WQ

exp

kT

where Vg is the volume of a solvent molecule and tij,^ corresponds to its partial molecular area on the solid surface, on the assumption that the solvent molecules are randomly oriented on the solid surface. 2.12. On a Particle Surface Let us define a supersaturation energy parameter, (|)„, of the concentration

2. GROWTH

89

of monomers in equilibrium with a three-dimensional n-mer, C(„), against that with the bulk solid, C(„), as (2.1.15)

The free energy of formation of a two-dimensional nucleus consisting of n' monomers from a supersaturated solution on a small particle composed of n monomers, as shown in Fig. 2.2, is given by

where |X(^ ° is the chemical potential of a monomer in the small particle consisting of n monomers and \i is the chemical potential of a monomer in the supersaturated solution phase - see Eq. (1.3.5). Since f^'!nrf^ = ^--,Cc", d

n -I

,

'

1/2.

'exp

(2.2.5)

-i^-^y^^n'"' dn'. kT

In this equation, AGV

/j.,i,/«/l/2 -(4>->'+iJr'n

kT

kT

(2.2.6)

AG"'

kT

/2 AG^* 71

\n y

= -jc' +

.

kT

where 1

;c'=,

\

(2.2.7)

AG"

kT

and AG'* dn' dx'=^ 2 ^ n'*kT ^'

1 A

4>-„ an dn

kT

(2.2.8)

^/

Thus, Eq. (2.2.5) becomes /,.2/3

fh /5

kiii/kioo

y/3

Îll/ÎOO y/3

1

^ ^

changes of the growth rates of both faces. This means that the growth of these faces is in the reaction-controlled mode (see section 2.6.6). Since r^^Q

130

FUNDAMENTALS —q 10

p

\

h

\

4 ^

p

J

a

F^

n

H -|

[r

\(100)

H H

• « - / ' " "

P

H

y

r r

J

J /

1

> -J

/

4n

1 ^'^

10

1

1

1

Solubility

Li.. 1 1 1 1 1 i 1

1 1.5

2.0 PBr

2.5

Fig. 3.7. The pBr dependence of the growth rates of the {100} and {111} faces of AgBr microcTystals in the presence of 0.5 mol dm"^ NH3 plus 1.0 mol dm"^ NH4NO3 at 50 °C, where the particles were grown at the expense of much smaller coexisting particles. (From Ref. 4.)

and f^^^ were obtained from the growth rates of the sufficiently large cubic and octahedral particles, respectively, the solubilities of these {100} and {111} faces are approximately equal to the solubility of the bulk solid, and thus one may consider that rin/^'ioo * ^m/îoo- Hence, the broken line of ^111/^100 i^ Fig. 3.8 was obtained from the ratio of r^^^ to T^QQ ^^ ^ function of pBr in Fig. 3.7. On the other hand, within the range of 1/V3 < ^m/îoo < V3, the/7 value (= r^^^lr^^ of the steady form, /?*, must be nearly equal to A:in/îoo> while p* must be almost equal to 1/V3 or V3 for k^x\l^ws ^ 1/^^

3. HABIT FORMATION

131

Cubic Range

'

(kiii/kiooi»^)

i^^--

kin/kioo

vj

1.5 h

1.0

0.5

Tetradecahedral Range

/ ^ Steady

(l//3kioo>v'3')

/T

^ ic

L—steady

rui/rioo

/ / 0/ //

*

/ /

0.5

/

/

/ •''

1

^ 1/T

/

/ /

/ /

1

1 Octahedral Range

I

1

1

(KUI/KIOO ^ 1 / ^ )

1

1

1

Fig. 3.12. ^111/^100 ^"^ ''in/^'ioo ratios as functions of pBr for AgBr particles prepared in the absence of ammonia at 60 °C. (From Ref. 15.) that the steady form is not a consequence of the reaction-controlled growth. Particularly, in the pBr range from 2.6 to 3.5 in which Kxw^^m = 1' ^^'^ of the {100} and {111} faces are in the diffusion-controlled growth mode. Hence, the morphological change from octahedron to cube is due to the change of Ym/Yioo frî" 1/^3 to V3 with increasing pBr. The growth rate constant of the surface reaction of the {100} face must increase with decreasing pBr, so that the critical growth rate of the {100} face in the pBr range below 2.6 in Fig. 3.11 must be the diffusion-controlled growth rate. At the same time, the critical growth rate of the {111} face in this pBr range gradually deviated downwards with reducing pBr, due to the increasing

137

3. HABIT FORMATION

Fig. 3.13. AgBr particles prepared by the CDJ method at pBr 2.0, 2.8, and 4.0 in the absence of ammonia at 75 ^C. (From Ref. 17.)

contribution of the reaction-controlled mode. Similarly, the critical growth rate of the {111} face in the pBr range above 3.5 corresponds to the diffusion-controlled growth rate, while that of the {100} face deviates downwards with increasing pBr by the increasing contribution of the reaction-controlled mode. Figure 3.13 shows transmission electron micrographs of carbon replicas of AgBr particles prepared by the CDJ technique, in the absence of anunonia at 75 °C at different pBr's.^^ Although the octahedral particles prepared at pBr 2.0 and the cubic particles at pBr 4.0 involve some contribution of the reaction-controlled mode in the growth of their respective {111} and {100} faces, the tetradecahedral particles prepared at pBr 2.8 are of a typical diffusion-controlled steady form equivalent to the equilibrium form. The steady form of a general polyhedral particle bound by more than one kind of faces after a typical diffusion-controlled growth can be written as r,:r^:r^...:r..

^ = Yi:Y2-Y3-*Yr-*Vn'

(3.2.11)

where r. and y^. are, respectively, the central distance to and the specific surface energy of the faces of the zth kind. This relationship agrees with the Wulff theorem in Eq. (3.1.1) for the equilibrium form. Here, it should be noted that if the particle is bound by only one kind of faces this relationship does not necessarily hold.

138

FUNDAMENTALS

References 1. J. W. Gibbs, "Collected Works." Longmans, New York, 1928. 2. G. Wulff, Z. Krist. 34, 449, (1901). 3. P. Curie, Bull. Soc. Fr. Mineral. 8, 4 (1885). 4. T. Sugimoto, J. Colloid Interface Sci. 91, 51 (1983). 5. A. H. Herz and J. O. Helling, Kolloid-Z. Z. Polym. 218, 157 (1967). 6. W. L. Gardner, D. P. Wrathall, and A. H. Herz, Photogr. Sci. Eng. 21, 325 (1977). 7. T. Tani, "181st ACS Nat. Meet., Atlanta 1981." Am. Chem. Soc, 1981. 8. C. R. Berry, J. Opt. Soc. Am. 52, 888 (1962). 9. C. R. Berry, S. J. Marino, and C. F. Oster, Jr., Photogr. Sci. Eng. 5, 332 (1961). 10. C. R. Berry and D. C. Skillman, Photogr. Sci. Eng. 6, 159 (1962). 11. E. Moisar and E. Klein, Ber. Bunseges. Phys. Chem. 67, 949 (1963). 12. I. N. Stranski and R. Kaischew, Phys. Z. 36, 393 (1935). 13. O. Knacke and I. N. Stranski, Z. Elektrochem. 60, 816 (1956). 14. I. N. Stranski, VDI-Berichte 20, 5 (1957). 15. T. Sugimoto, J. Colloid Interface Sci. 93, 461 (1983). 16. J. S. Wey and R. W. Strong, Photogr. Sci. Eng. 21, 14 (1977). 17. T. Sugimoto, MRS Bull. 14(12), 23 (1989).

CHAPTER 4 RECRYSTALLIZATION 4.1. Phase Transformation Let us consider a solid species suspended in a liquid. If a more stable species is known, it is at least thermodynamically possible for the less stable species to be transformed into the more stable one. The stability of a solid species in a liquid may be measured by its solubility, Le., the higher solubility corresponds to the lower stability. For example, amorphous ferric hydroxide has a higher solubility than goethite (a-FeOOH) and akaganeite O^-FeOOH), and the latter have higher solubilities than hematite ( a Fââ)-^'^ In this case, ferric hydroxide is the least stable and hematite is the most stable among them. The stability also depends on the composition of the solution phase and on the temperature as well. In any case, when two different solid species of different solubilities coexist in a liquid system, the species of higher solubility will be dissolved and the other one of lower solubility will grow by deposition of the solute released from the former. In general, the concentration level of the solute in the solution phase is located somewhere between the two solubilities. If the dissolution rate constant of the higher-solubility species is much greater than the growth rate constant of the other of lower solubility, the steady concentration level is close to the higher solubility level. In this case, the rate of the total recrystallization process is limited by the deposition process (depositioncontrolled growth). In contrast, if the growth rate constant is much greater than the dissolution rate constant, the concentration level is close to the lower solubility level, and thus the rate-determining step is the dissolution process (dissolution-controlled growth). These relations are illustrated in Fig. 4.1. The phase transformation through this kind of recrystallization is of great importance for the formation of monodisperse particles in which some unstable vsolid species is used as a reservoir of the monomers of the final stable product, as will be described in detail in Part 2. Also, the

FUNDAMENTALS

140

distinction between deposition control and dissolution control is essential for the regulation of the supersaturation during the growth of monodisperse particles.

Dissolving Solid

Solution Phase

Growing Solid

Fig. 4.1. The concentration levels of solute in the deposition-controlled and dissolution-controlled growth modes.

4.2. Ostwald Ripening The Ostwald ripening is nonnally known as a growth process of particles by the dissolution of coexisting smaller particles, as illustrated in Fig. 4.2. The phenomenon was first described by Ostwald,^ and afterwards named "Ostwald ripening" by Liesegang."* This process is caused by the solubility difference between large particles and the smaller particles of a higher solubility due to the Gibbs-Thomson relation in Eq. (2.6.1). Since it is important not only for the fundamental study of particle growth but also for industrial applications, there are a number of theoretical^"^"^ and experimental^^"^^ studies. Practically, it can be used for the preparation of uniform

4. RECRYSTALLIZATION

141

Fig. 4.2. Concept of the Ostwald ripening.

particles in a closed system in which relatively large seed particles grow at the expense of a great amount of small particles. In fact, the supersaturation during the particle growth can be kept constant without renucleation in this simple closed system, and the supersaturation level can be controlled by changing the size of the smaller particles. These advantages were fully used for fundamental studies of habit formation of polyhedral microcrystals^^'^^ and the growth mechanism of tabular grains of silver bromide.^^"^^ In addition, the preparation of silver halide particles in open systems, widely used in the photographic industry, is essentially based on the Ostwald ripening process, in which exceedingly fine embryos - instantly generated by continuous introduction of silver and halide ions - act as a source of silver and halide ions, through dissolution, for the growth of the stable nuclei."^^'-^^ The fundamental theory of Ostwald ripening in closed systems was established by Lifshitz and Slyozov^ and by Wagner^. It is often referred to as "LSW theory." In this section, only the essence of this theory will be described from Wagner's paper.^ 4.2.1. Diniision-Controlled Ostwald Ripening For simplicity, both the dissolution and growth are assumed to be controlled by the diffusion of the solute. In this case, the size distribution function in the steady state of dissolution and growth is given by

142

FUNDAMENTALS /

/(r,0 = const {Utlz'j,)'^

3 yi/3

2

,7/3

13 +p

3

:;:"P

U J

(

exp -P 3 r"P

\

(4.2.1)

U i

where p s rlr"*", r is the particle radius, r* the particle radius in equilibrium with the solute, t the time, and T'p a time constant given by / ^ 9ro*'/?r

(4.2.2)

8Y/)C.^^^

where r^* is r* at r = 0. This equation holds for p ^ 3/2, while /(r,0 = 0 for p ^ 3/2. If the arithmetic mean radius of the particle system is denoted by r, it is given by (4.2.3)

r^r . Also, r*{t) is given by r\t) = Tl{Utlx'j,yi' 1/3

\l/3

^yDcjj

(4.2.4)

9RT

Hence r* or r is proportional to the cube root of t. 4.2.2. Reaction-Controlled Ostwald Ripening On the assumption of the first-order reaction control with an identical reaction constant, the size distribution function for p ^ 2 was derived as

fint)

where

const (1^^/t^/

(l^Hl^t).

,4.2.5)

143


Reaction Control

Diffusion Control

Fig. 4.3. The steady forms of the size-distribution functions of diffusion-controlled and reaction-controlled Ostwald ripening. (From Ref 6.)

/ _

'•o'^^

"= R =

(4.2.6)

ykcX

and k is the growth rate constant in dr/dt = kVJC-CJ. 0. The relationship between f and r* is given by - 8 . r=—r . 9

For p a 2, f(r,t)

(4.2.7)

Also, r*(t) is given as a function of time by: r-(r) = ro(l+r/x'^)i/2 \l/2

v^'.;

- vi^ ykcj^^t

(4.2.8)

RT

so that r* or (9/8)f is proportional to the square root of t. Figure 4.3

144

FUNDAMENTALS

illustrates the size distribution functions of the diffusion-controlled and reaction-controlled Ostwald ripening. Although the LSW theory has been formulated on the simple assumption that both the dissolution and growth of particles are either diffusioncontrolled or reaction-controlled in a first-order reaction with the same reaction constants, the Ostwald ripening processes in real systems are not necessarily so simple. For example, one of the dissolution and growth processes is diffusion controlled and the other is reaction controlled in a higher-order reaction mode. Some theoretical studies^^'^^ deal with such cases.

4.3. Self-Recrystallization As has been discussed in chapter 3, if the surface chemical potential, or the solubility, of one kind of faces of a polyhedral particle bound by two kinds of faces is higher than the other kind in a closed system, the former will be dissolved and the latter will be grown by the deposition of the solute released from the former, in order to approach the equilibrium form of the particle. The particles in Fig. 3.4(b) were thus formed from those in Fig. 3.4(a). This intra-particle recrystallization may specifically be called the ''Self-Recrystallization,'' Figure 4.4 shows the equilibrium forms reached from cubic AgBr particles at pBr 1.40 (a) and from octahedral ones at pBr 2.48 (b), by self-recrystallization for 30 min at 50 °C in the presence of 0.5 mol dm'^ NH3 plus 1.0 mol dm'^ NH4NO3, similar to the transformation of the octahedra in Fig. 3.4(a) to the particles in 3.4(b).^^ If the size distribution is broad, the Ostwald ripening, a kind of inter-particle recrystallization, will occur at the same time. In this case, a perfect equilibrium form will not be attained in a reaction-controlled growth system.

4.4. Reversed Ostwald Ripening If monodispersed small cubic AgBr particles (I^J ^ ^ present with monodispersed larger octahedral particles (11^^^) in a closed reactioncontrolled system, in which 1/V3 < Ym/Yioo < ^^ and the pBr is sufficiently low for în/îoo to be less than 1/V3, the smaller cubic particles I^^^ will grow at expense of the larger octahedral ones 11^^, since the surface chemical potential of the {100} faces at the comers of the octahedral

145


30 min later * ^

1 |i m Fig. 4.4. TEM images of replicas of the equilibrium fomis reached from cubic AgBr particles at pBr 1.40 (a) and from octahedral ones at pBr 2.48 (b), by selfrecrystallization for 30 min at 50 °C in the presence of 0.5 mol dm'^ NH3 plus 1.0 mol dm-^ NH4NO3. (From Ref. 27.)

FUNDAMENTALS

146

particles is higher than that of the {100} faces of the cubic particles (case 1).^^ In this case, while the cubic particles 1^^^, will be subject to the selfrecrystallization owing to the high surface chemical potential of the {111} faces at their own corners, it will not contribute to the increase in their particle volume. Also, the growth of the {111} faces of the octahedral particles 11^,^^ will be negligible due to ^m/îoo < 1/^3. Similarly, if small octahedral particles coexist with larger cubic particles at a sufficiently high pBr to attain k^n/kôo > ^^^ ^^^ smaller octahedral particles will grow at the expense of the larger cubic particles (case 2). Since smaller particles are grown at the expense of the larger ones in these systems, one may call this inter-particle recrystallization the ''Reversed Ostwald Ripening.'' If the size difference between the two kinds of particles is sufficiently small in these systems, the final shape of all particles at the end of the

so b)

B

40

^'

*

30 •

20

-

10

.

I

i 1

[0.6

[Oct]

0 .8

1

1

1.0

1

1

1.2

[M]

1

r

1

1.4

p " p'

1

1.6

Fig. 4.5. (a) Diagram for the change of the / values of 1(100), 1(111), 11(100), and 11(111) with the progress of the reversed Ostwald ripening in case 1; (b) Diagram for the corresponding change of each particle volume of I and II. Here, 1(100), 1(111), 11(100), and 11(111) indicate the respective face indices, {100} and {HI}, for I^^ and Iloct,- p is equal to rû/r^QQ-, the prime designates the quantities of 11^ in distinction from those of ' [Cub] Icub- (From Ref. 33.) 1

1


147

reversed Ostwald ripening will be close to the equilibrium form, proper to the given system. Since the driving force for the growth of the smaller particles will disappear at this moment, the normal reaction-controlled Ostwald ripening for the growth of the larger particles will follow at the expense of the smaller particles. Figure 4.5 illustrates the change of the reduced surface chemical potential (f) and that of the particle volumes of 1^^^ and IIQ^ in case 1 for the reversed Ostwald ripening and succeeding normal Ostwald ripening processes, where the reduced surface chemical potential / for I^.yb or IIQ^^ is a surface chemical potential of a facet of I^^^, or II^^^ divided by the initial surface chemical potential of the {100} faces of a cubic particle at the start of the reversed Ostwald ripening (see Fig. 3.2). The initial surface chemical potential, ([iioo)o' ^^ ^^^ {100} faces of the cubic particles is given by (|iioo)o = ^Yioo^yîoo* where YIOO is the specific surface energy of the {100} faces, V^ is the molar volume of the solid, and U^QQ is the radius of the inscribed sphere of the cube. ^..^

I fim

^

Fig. 4.6. TEM images of carbon replicas showing the evidence of the reversed Ostwald ripening in case 1: (a) original mixture; (b) resulting particles after aging at 50 °C for 60 min in the presence of 0.5 mol dm"^ NH3 plus 1.0 mol dm"^ NH4NO3 and 1 wt % gelatin. (From Ref. 33.)

148

FUNDAMENTALS

50

-

40

,

g 30 u L. 0)

o.

(

E 20 3

> 10 0

^ 0.2

,

^

—1

0.4 0.6 0.8 1.0 2.0 diameter of the equivalent sphere [pin]

i—

4.0

Fig. 4.7. Histograms of the size distributions of the particles in Fig. 4.6(a) and (b), corresponding to the broken and solid lines, respectively, obtained with a Coulter counter, where the equivalent sphere is a sphere having the same volume as a nonspherical particle. (From Ref. 33.)

The TEM images of carbon replicas of the AgBr particles in Fig. 4.6 show an example of the reversed Ostwald ripening in case 1. The corresponding histograms of the size distributions, obtained with a Coulter counter are shown in Fig. 4.7. One may find there considerable narrowing of the size distribution by the reversed Ostwald ripening. More detailed theoretical treatment is given in ref. 33.

4.5. Contact Recrystallization When silver halide particles are in contact with each other in an aqueous solution by coagulation, centrifugation, or filtration, they are found to undergo an extremely rapid recrystallization, which is completed within a few seconds at room temperature.^"**^'^ This recrystallization, as well as the normal or reversed Ostwald ripening, can be inhibited by some additives, such as 4-hydroxy-6-methyl-l,3,3a,7-tetraazaindene or l,l'-diethyl-2,2'cyanine. For example. Fig. 4.8 shows the degrees of the exchange of chloride ions between AgCl particles and the solution phase, r, changing with the progress of the Ostwald ripening in a suspension of AgCl particles


149

i.^ AgBr

=11^ =11^ y^ AgBr

(5.1.33)

V'AgBr'

^

The free energy of formation of 1 mole of a single f.c.c.-type solidsolution is given from Eq. (5.1.13) as AG = F£+Jc^^/?nn

{KT^' -sp j^sl^ sp

[/-]!

(5.1.34)

[5r-]

If the solid-solution of the same composition is formed from 1 mole of pure AgBr, the free energy of formation, AG', is given by

FUNDAMENTALS

166

AG

y "pJB

^S

Q5O

OJO

Q3O

Fig. 5.5. AG and AG' (= AG/(1ÂJ)) as a function of x^^J, (From Ref. 10.)

X '

AG/ =

AG

(5.1.35)

\-x Azi The AG' corresponds to the change of free energy when 1 mole of AgBr is mixed with varied amounts of Agl, and hence as long as it is lowered with the increasing amount of Agl, the mixing is promoted. However, if it reaches a minimum and starts to increase with further incorporation of Agl, the system will rather stay near the minimum AG' by retaining the excess pure P-AgI unchanged. Figure 5.5 shows the changes of AG and AG' for the formation of the f.c.c. solid-solution of Ag(Br,I) at 25 °C as a function of x^^f}^ The minimum AG' gives the mole fraction of Agl in the solidsolution thermodynamically saturated with Agl (JC^^/ = 0.312). In other words, while the curve of AG in Fig. 5.5 corresponds to the free energy of formation of 1 mole of f.c.c. Ag(Br,I) from pure AgBr and P-AgI, as a function of the mole fraction of Agl, it is equivalent to the minimum free energy of formation at each overall mole fraction of Agl in the system up

5. SOLID-SOLUTION FORMATION

167

to 0.312. However, when the overall mole fraction of Agl exceeds 0.312, the total free energy of formation at each overall mole fraction of Agl is rather lowered below AG by increasing the proportion of unreacted pure p Agl at the expense of the f.c.c. Ag(Br,I) with a Agl mole fraction kept close to 0.312. The uniformly mixed particles of f.c.c. Ag(Br,I) can be prepared by the controlled double jet (CDJ) technique (see section 1.5.2) using a AgNOg solution and a mixed solution of KI and KBr with a mole fraction of KI equal to or less than 0.312. However, even if the mole fraction of BCI in the mixed solution of alkali halides exceeds 0.312 to some extent, we can obtain mixed particles of uniform f.c.c. solid-solution, because the increase of AG' with the increasing JC^^/ above 0.312 is rather small, and because some supersaturation in the liquid phase is needed for the nucleation and growth of P-AgI particles. The smaU reduction in the iodide content in the f.c.c. mixed crystals after the peak with the increasing total iodide m Fig. 5.2 may reflect the lower supersaturation for the growth of P-Agi than is needed for its nucleation. Normally, the maximum mole fraction of mixed Ag(Br,I) particles of f.c.c. solid-solution prepared by the CDJ technique is around 0.345 at 25 ""C, and the mole percent of the maximum Agl content increases with increasing temperature in degrees centigrade as^^ xlgjimol%) = 34.5 +0.165(f-25).

(5.1.36)

5.2. Conversion by Intra-Particle Recrystallization The conversion technique for transforming monodisperse particles into others, different in composition and/or structure, is one of the most important procedures for producing new kinds of particulate materials. In particular, conversion processes by intra-particle recrystallization (recrystallization within each particle) are of interest not only from a thermodynamic viewpoint but also have great practical significance for the production of hetero-junctioned particles, new types of particles containing a high density of crystal defects, etc. This section will be devoted to describing the fundamental aspects of this process, focusing on a well-defined conversion process of silver chloride particles by bromide ions.^"*'^^ 5.2.1. Conversion of AgCI Particles by Br" ions

168

FUNDAMENTALS

Fig. 5.6. Morphological change of the AgCl particles with time at 25 °C after introduction of a solution of KBr corresponding to 10 mol % of the AgCl: (a) 3, (b) 10, (c) 20, and (d) 50 s. Initial composition: [AgCl]o = 10"' M, [KCl]o = 10'^ M, [KBrJo = 10-2 ^^ ^^^ [gelatin] = 1 wt %. (From Ref. 14.)


169

AgCI{220}

50" 20" 10"

39*

40'

4r

42'

DIFFRACTION ANGLE (20)

Fig. 5.7. Change of the corresponding XRD pattern. (From Ref. 14.)

If a different kind of soluble anions or cations is added to a suspension of sparingly soluble particles, and if the added anions or cations can form a more stable solid with the cations or anions of the suspended particles, the latter may be converted, partly or totally, into the more stable particles by recrystallization via the solution phase. Figure 5.6 shows transmission electron micrographs of carbon replicas of cubic AgCl particles of mean edge length 0.41 ^mi in the progress of a partial conversion at 25 °C after instantaneous addition of a KBr solution containing 10 mol % of KBr to AgCl (initial composition immediately after the addition of KBr: [AgCl]o = 10"^ M, [KCl]o = 10"^ M, [KBr]o = 10"" M, and [gelatin] = 1 wt %)}'^ The conversion reaction was stopped instantly by mixing each sample with a merocyanine dye for the electron microscopy. Figure 5.7 shows the corresponding XRD patterns. Figures 5.8 and 5.9 exhibit the change of the silver-ion concentration from potentiometry with a silver electrode, and the change of [Br'] calculated from the potentiometry for the silver-ion concentration (solid line) and from XRD on annealed solid samples (closed circles), respectively. The particles sampled at the end of

FUNDAMENTALS

170

0

10

20

30 40 t/sec

50

60

70

Fig. 5.8. Change of the corresponding silver-ion concentration. (From Ref. 14.)

b

Fig. 5.9. Change of the corresponding bromide-ion concentration. (From Ref. 14.) the initial sharp drop of [Ag^] revealed no appreciable change in morphology (Fig. 5.6(a)) or composition (Fig. 5.7). Thus, in this first step, the reaction was limited to the consumption of silver ions originally equilibrated with AgCl along with a surface conversion of AgCl particles by ionic exchange with bromide ions. The temporary stability in [Ag"^] at the end of the initial drop implies the establishment of the surface equilibrium. Soon after the first step very small verrucae were found to emerge on the comers and edges of the cubic AgCl particles (Fig. 5.6(b)) and then the ones on the comers grew, while the others on the edges appeared to be dissolved together with the open areas of each AgCl particle. The new solid parts consisted of nearly pure AgBr microcrystals, as demonstrated by XRD in Fig. 5.7. Figure 5.9, for the change of [Br"], clearly shows that almost all

171


b) ;^: •*?;.•

''^'€^:Ps^ ^

"7- $ .

%K

-Q y%m

'1^ ' ^ I Pffil '"ftm^nr

•iiiiujrij,!.

Fig. 5.10. Electron micrographs of the composite particles with different [KBr]o/[AgCl]o molar ratios after aging at 25 °C for 50 s from the addition of KBr. [KBr]o/[AgCl]o: (a) 0.1, (b) 0.2, (c) 0.4, and (d) 1.0. (From Ref. 14.)

172

FUNDAMENTALS AgBr{220}

AgCI{220}

CKBr]^/[AgCI]o 1.0

3sr 4or 4r 42" DIFFRACTION ANGLE (26)

Fig. 5.11. XRD patterns corresponding to the particles in Fig. 5.10. (From Ref. 14.)

bromide ions were used up in 60 s for the formation of the AgBr particles joined to the comers of the AgCl particles. This period is defined as the second step. Figures 5.10 and 5.11 show electron micrographs and the corresponding XRD pattems for the particles after conversion for 50 s at 25 °C with a variety of initial molar ratios of [KBr]o/[AgCl]o. In any case, the AgBr parts finished forming in 60 s regardless of the initial molar ratio. Since the dissolution of the AgCl particles can readily follow the great increase in [KBrjg and finish the reaction at the same time, it is suggested that the the rate-determining step of the total reaction is not the dissolution process of the AgCl particles but the growth process of the AgBr particles in the second step. Interestingly, the original AgCl particles were almost totally decomposed into the nearly eight-fold number of AgBr particles when [KBr]o/[AgCl]o = 1 (Fig. 5.10(d)). After the end of the second step, [Ag^] still kept rising as shown in Fig. 5.8, when [KBr]o/[AgCl]o < 1. This implies the possibility of the third step, which appears, however, to be much slower than the earlier steps. In order to accelerate this slow process, the temperature was raised to 45 °C under the otherwise standard conditions. Figures 5.12 and 5.13 show electron micrographs and the corresponding XRD pattems of the particles in the course of conversion at 45 °C. Obviously, the particles at 1 and 3 min in


173

Fig. 5.12 were already in a stage later than the second step, since they formed a new solid-solution of AgClo5Bro5 according to Fig. 5.13. The solid-solution must have grown from the borders of the guest/host joints and

Fig. 5.12. Morphological change of the composite particles of AgClo.9Bro.i with aging time at 45 °C: (a) 0.5, (b) 1.0, (c) 3.0, and (d) 10 min. (From Ref. 14.)

174

FUNDAMENTALS AgCI{220}

0.5' 39"

40'

4r

42^

DIFFRACTION ANGLE {2$)

Fig. 5.13. XRD corresponding to the particles in Fig. 5.12. (From Ref. 14.)

developed two-dimensionally toward the inside of the host surfaces, as clearly observed in Fig. 5.12(c). Here, it is noteworthy that the composition of AgClo 5610 5 was not altered, as long as the AgBr guests were present until 5 min as shown in Fig. 5.13. This stage, when the solid-solution of AgClo 5610 5 is grown by the simultaneous dissolution of the AgBr guests and AgCl hosts, is defined as the third step. The third step lasted for about 2 h at 25 °C. The third step is followed by still further steps to form a solid-solution having a higher chloride content, as shown by the XRD profile at 10 min in Fig. 5.13(d), corresponding to the irregularly shaped particles in Fig. 5.12(d). The solid-solution must have grown at the expense of the AgClo5Bro5 and the AgCl hosts. In this stage, however, there was no evidence of the definite stepwise progress. The reaction rate became slower by degrees as the chloride content of the solid-solution increased. When the initial molar ratio of [KBr]o/[AgCl]o was as low as 0.1, the reaction virtually stopped midway to yield double-structured particles consisting of a Ag(Cl,Br) shell and AgCl shell. For stabilizing the hetero-junctioned particles with eight AgBr guest particles at all comers of each AgCl host, some stabilizers, such as merocyanine dyes, cyanine dyes, mercaptotetra-


175 3rd Step

2nd Step

A g *——^^ /

200

< H

150

100

50

10^

[Br-]/M

Fig. 5.17. Minimum silver potential E„ for the AgCi suspension (A) and silver potential E for the AgBr suspension (o) as a function of [Br'Jo. A AgBr suspension containing 0.1 M KBi was used as the reference for the potentiometry. The symbol (^) represents the plotting as a function of the actual bromide concentration in the solution phase, obtained by subtracting the bromide quantity consumed for the surface conversion from that added. (From Ref. 15.) to the direct joint with the substrate different in lattice parameter, the surfaces of the growing parts may be free from the SSE, owing to the absence of the lattice misfitting between the top layer and its underneath. This relationship creates the driving force for the growth of the AgBr particles from their own nuclei on the comers of the host particles of AgCl during the second step of the conversion, since the solubility of the AgBr surface layer is higher than that of the three-dimensional AgBr particles on the comers of the hosts, because of the SSE of the dissolving surface layer. The supersaturation ratio for the growth of the guest AgBr particles is calculated to be 1.34 from Eq. (5.2.2) w i t h / ^ / « 1 and £, = 2.10 kJ mol"\ At the end of the second step, [Br"] sharply drops, because the dissolved bromide ions are almost used up in the rapid second step. When the [Br"] /[Cr] ratio reaches the level of Kj^/Kj^, the mole fractions of AgBr and AgCl components in the surface layer of the host particles become equal to 1/2, as is obvious from Eqs. (5.1.8) and (5.1.18). At the same time, the mole fi:actions of these two components in the surface layer of the guest particles of AgBr also become equal, since their growth stops at this stage. The surface stress energies of both surface layers may also be equivalent.


181

since each lattice misfitting seems to be almost equal, though the surface layer of the hosts is subject to compression, while that of the guests is subject to stretching. If the [Br"]/[Cr] ratio shifts from this balance, it will soon be retrieved by enhanced dissolution of either surface layer of a higher SSE. Hence, the molar ratio of the two components in the new solid phase formed during the third step must be kept constant at 1 : 1. Also, the third step must be much slower than the second step, due to the much lower supersaturation for the growth of the new solid phase, as a result of the lowered SSE and increased entropy in the surface layer of each host particle with its compositional transition from AgBr to Ag(Clo5Bro5). These theoretical conclusions are in accord with the aforementioned experimental results. 5.2.3. Kinetics In order to find the rate-determining step of the recrystallization in the second step, some experiments were planned. Either the number of AgCl particles or their total surface area was altered using AgCl particles different in mean edge length (0.649 ^mi and 0.344 \xm\ and then the change of [Br"] was followed at 25 °C, as shown in Fig. 5.18. The molarities of the AgCl particles for runs (a), (b), and (c) were 2.0 x 10"^ M (0.649 \xm), 2.98 x 10"^ M (0.344 [im), and 1.06 x 10"^ M (0.344 [im), under the same conditions of

CO

70

80

Fig. 5.18. Effects of the particle number and the total surface area of AgCl microcrystals on the conversion rates in runs (a), (b), and (c) in Table 5.1. (From Ref. 15.)

182

FUNDAMENTALS

[Br-]o = 1.0 X 10-21^^ jQ-j ^ 5 Q ^ jQ-3 j^^ gjjjj JQj^jj, strength = 0.1. The particle numbers and the surface areas for these rans are summarized in Table 5.1.

Table 5.1. The specific values of the AgCl particles for runs a, b, and c {Source: Ref. 15) Runs

Particle numbers (dm-')

Surface areas (m' dm-')

a

1.89 X 10"

47.6

b

1.89 X 10"

13.4

c

6.71 X 10"

47.6

If the dissolution process of the AgCl is the rate-determining step, the overall reaction rate is determined only by the total surface area of the system. In this case, the reduction rate of [Br'] for runs (a) and (c) must be equal and much higher than in run (b), because the total surface area for runs (a) and (c) is equal and much greater than in run (b). On the other hand, if the growth process of the guest particles of AgBr is the rate-determining step, the overall reaction rate is determined only by the number of growth sites of the AgBr guest particles. In this case, the reduction rate of [Br~] for runs (a) and (b) must be equal and much lower than in run (c), because the number of growth sites for runs (a) and (b) is equal and much smaller than in run (c). From the result of Fig. 5.18, it is now evident that the rate-determining step of the recrystallization in the second step is the growth process of the AgBr particles, as is expected from the experiment on the effect of the initial concentration of bromide ions in Figs. 5.10 and 5.11. Although the actual shape of the guest crystals of AgBr is close to an octahedron and 7/8 of the surface area is exposed to the solution phase, it seems rather convenient to assume it to be a sphere of radius r, for simplicity. In this case, the changing rate of [Br"] in the second step, J[Br"]M is given by


183

d[Br-] _ 2Si:Nr^ dr dt dt

(5.2.7)

where N is the number of the host particles of AgCl in a unit volume, V^ is the molar volume of AgBr, and r^ is given by

i^y-T ([Bri-iBnf".

r2 =

(5.2.8)

(iSnN)

Combination of Eqs. (5.2.7) and (5.2.8) yields

— I 'iBrl^

'252KA^V'^^

dt\ [Br-],

1-

[Br]^

'

\Br-\

dr\

(5.2.9)

[Br-],"" dtj

This is a general equation which holds, regardless of the growth mechanism. On the other hand, when [Br~]/[Br']o was plotted as a function of time in a series of experiments for the effect of variation of [Br"]^ under the otherwise standard conditions ([AgCl]o = 10"^ M, edge length 0.41 [im, [Crjo = 10"^ M, [gelatin] = 1 wt %, temp. = 25 °C), all points traced a single curve regardless of [Br"]o, as shown in Fig. 5.19. In other words, rf([Br"]/[Br"]o)/dt is independent of [Br"]o. In addition, dr/dt depends on the current bromide concentration and not on the initial concentration. From Eq. (5.2.9), the requirement for bothrf([Br"]/[Br']o)/rfrand dr/dt to be independent of [Br"]o is fulfilled only when dr/dt can be written as dr = M^^-]l/^ dt

(5.2.10)

where X^ is a constant independent of [Br J^, [Br"] and /. Substituting Eq. (5.2.10) into Eq.(5.2.9), one obtains

(z

dz

d'z')'^ where

_(28nNY\ ^ 3K„

(5.2.11)

FUNDAMENTALS

184

t/sec Fig. 5.19. [Br"]/[Br"]o as a function of time in a variety of [Br"]o: (o) 5.0 x 10•^ (•) 1.0 X 10-^ (n) 2.0 X 10-^ and (A) 3.0 x 10"^ M. (From Ref. 15.)

Fig. 5.20. Relationship between t and 7^, calculated from the data of Fig. 5.19. The symbols are the same as in Fig. 5.19. (From Ref. 15.)


185

Z-{l-[Br-y[Bn,y'\

(5.2.12)

The integral on the left-hand side of Eq. (5.2.11), 4, is given by 7^= lln[(l-z^)V3^^]-±LctaD[^^^"^'^'^'"^]

\/3[

{

(5.2.13)

yf3z

Here, it must be noted that Eq. (5.2.11) has been derived onlyfromthe premise that both dr/dt and rf([Br"]/[Br"]o)M are independent of [Br"]o, and that there is no guarantee that Eq. (5.2.9) with dr/dt in the form of Eq. (5.2.10) represents the experimental curve of Fig. 5.19. However, Eq. (5.2.11) suggests that, if Eq. (5.2.10) for dr/dt is correct, the plot of 4 against t with the use of the data of Fig. 5.19 must give a straight line passing through the origin. Conversely, if we obtain such a linear relationship between t and 4, the general Equation (5.2.9) with dr/dt in Eq. (5.2.10) gives the experimental curve of Fig. 5.19, supporting the validity of Eq. (5.2.10). Hence, Fig. 5.20 which shows the linear relationship between t and 4 in the second step validates Eq. (5.2.10) for dr/dt. From the slope of this straight line, one obtains ^ = 6.62 x 10'^ cm^ mol"^^ s"\ The form of dr/dt in Eq. (5.2.10) suggests a reaction-controlled growth by some complexes adsorbed onto the surfaces of the guest crystals and not the diffusion-controlled growth.

References 1. 2. 3. 4. 5. 6. 7. 8.

F. W. Kiirster, Z. Anorg, Chem. 19, 81 (1899). E. D. Eastman and R. T. Milner, J, Chem. Phys. 1, 444 (1933). H. Flood and B. Bruun, Z. Anorg. Allgem. Chem. 229, 85 (1936). H. Flood, Kgt. Norske Videnskab., Selskabs. Skrifter, No. 2, 23 (1941). [Chem. Abstr. 40, 6322 (1946).] H. C. Yutzy and I. M. Kolthoff, J. Am. Chem. Soc. 59, 916 (1937). I. M. Kolthoff and H. C. Yutzy, J. Am. Chem. Soc. 59, 1634 (1937). H. Chateau, C. R. Acad Sci. 248, 1950 (1959). J. Pouradier, M. Coquard, and A. de Cugnac, J. Chim. Phys. 64, 843 (1967).

186

FUNDAMENTALS

9. C. R. Berry, PSA Tech. Quarterly, Nov., 149 (1955). 10. H. Chateau, S. Couprie, A. Cugnac-Pailliotet, and J. Pouradier, J. Chim. Phys. 66, 757 (1969). 11. H. Chateau and J. Pouradier, C. R. Acad. Set 234, 623 (1952). 12. H. Chateau, M. C. Moncet, and J. Pouradier, in "Proc. Intern. Conf. Photogr. Sci. - Koln 1956," p. 20. Koln, 1956. 13. H. Hirsch, J. Photogr. Sci. 10, 129 (1962). 14. T. Sugimoto and K. Miyake, J. Colloid Interface Sci. 140, 335 (1990). 15. T. Sugimoto and K. Miyake, J. Colloid Interface Sci. 140, 348 (1990). 16. T. Sugimoto and G. Yamaguchi, J. Phys. Chetn. 80, 1579 (1976). 17. T. Sugimoto and H. Yanagida, Nippon Shashin Gakkaishi 40, 15 (1977). 18. A. P. Batra and L. M. Slifkin, J. Phys. C 9, 947 (1976).

PART 2. PREPARATION INTRODUCTION Part 2 consists of chapters 6, 7, and 8. Based on the fundamentals in Part 1, the general principles for the preparation of monodisperse particles will be described first in chapter 6. In chapter 7, the synthetic systems of monodispersed particles are classified into two categories, homogeneous and heterogenous systems, each of which consists of subdivisions of different reaction modes, and the characteristics of the classified individual systems will be delineated from fundamental viewpoints on the basis of the general principles. Then, the techniques for controlling the characteristics of monodispersed particles, including mean size, shape, structures, etc., will be described in chapter 8.

CHAPTER 6 GENERAL PRINCIPLES FOR THE FORMATION OF MONODISPERSED PARTICLES For the preparation of monodisperse particles, there are several essential requirements. They are: (1) the separation of nucleation and growth stages; (2) the inhibition of random coagulation of growing particles; (3) the reserve of monomers.^'^ Almost all genuinely monodispersed systems, for example, with ca. 5 % or less in the relative standard deviation of the size distribution, fulfill these requirements. In addition, if it is possible to choose the growth mode - either the diffusion-control mode or reaction-control mode - in a given particle system, we can make the absolute size distribution still narrower by choosing the diffusion-control mode with a supersaturation kept sufficiently high (see section 2.5). In this chapter, we will consider these

PREPARATION

188

factors leading to highly uniform particles and finally suggest a possibility of some new mechanism particularly useful for the synthesis of nanosized uniform particles.

6.1. Separation of the Nucleation and Growth Stages If nucleation occurs continuously with the growth of the particles, or if renucleation occurs in the growth stage after the initial nucleation, we cannot expect to achieve a monodisperse system. Thus, the first requirement for the formation of monodisperse particles is the strict separation between the nucleation and growth stages. If such separation can be achieved automatically, as shown in the LaMer diagram of Fig. 1.13 in chapter 1, at least the one necessary condition is cleared. Figure 6.1 shows general concentration dependences of nucleation and growth rates.^ As has been discussed in chapters 1 and 2, the nucleation rate is much more strongly dependent on supersaturation than the growth rate. That is, the nucleation rate is negligibly smaU when the supersaturation level is low, but soars abruptly when the supersaturation exceeds some critical level, whereas the growth

Cmin

Cmax

CONCENTRATION

Fig. 6.1. Concentration dependences of nucleation and growth rates. Here, V is the total volume of the precipitate. (From Ref. 2.)

6. GENERAL PRINCIPLES

189

rate increases gradually with increasing supersaturation, due to the low energy barrier for the formation of two-dimensional surface nuclei. The LaMer model is based on these properties of the nucleation and growth processes. In fact, for achievement of the automatic separation in general particle systems, the supply rate of monomers must be limited so that the generated nuclei can efficiently reduce the supersaturation below the critical level for nucleation by consuming the monomers for their own growth. For this purpose, we usually control the supply rate of monomers by regulating the addition rate of their sources in open systems, or the release rate of monomers from a selected reservoir, or the formation rate of precursory monomeric species by pH control, etc. It is also useful to promote the growth of nuclei by addition of some solvent for the solid, such as coordinating agents of metal ions, or by temperature control. In the original LaMer model, the supersaturation is described in terms of the overall supersaturation of solute, in which the solute consists of a single species or each component of a multicomponent solute is presumed to be in equilibrium with each other. However, this is not always true in general monodisperse systems, and instead only a specific species, a precursor, is often responsible for supersaturation. In an extreme case, the behavior of the whole solute is entirely independent of the precursor's, while the precursor may follow the LaMer mechanism, as proposed in section 7.2.9 for the formation of monodispersed particles in sol-gel systems. For example, in a silica system, siloxane oligomers of a low solubility, produced from a hydrolysis product of a silicon alkoxide through a polycondensation process, are the most likely precursor, which may nucleate when their concentration exceeds a supersaturation level. In this system, the concentration evolution of the hydrolysis product is independent of the behavior of the precursor. One may assume a similar mechanism for the separation between nucleation and growth stages in the formation of monodispersed polymer latices by radical dispersion polymerization or emulsifier-free emulsion polymerization (see sections 7.2.11 and 7.3.3). The precursor in the polymer systems is deemed to be oligomer radicals with a low solubility in the given medium. In such cases, the LaMer model may need some modification. Nevertheless, the concentration of the precursor is commonly lowered by the presence of nuclei in these typical monodisperse systems. Hence, the automatic control of supersaturation by generated nuclei in the original LaMer model and its modifications may be one of the most typical general rules for the automatic separation between nucleation and growth stages. For the nucleation-controlled precursor model as a modification of

190

PREPARATION

the LaMer model, more detailed discussion will be given in sections 7.2.9, 7.2.11, and 7.3.3 of chapter 7. In emulsion polymerization with emulsifier, generated oligomer radicals are absorbed by coexisting emulsifier micelles swollen by monomers to form polymer nuclei from the beginning, and the remaining oligomer-free emulsifier micelles left unreacted are finally decomposed all at once, when the total surface area of the polymer nuclei becomes sufficiently large to reduce the concentration of the free emulsifier to the level below the CMC (critical micelle concentration) by adsorption. The duration of this stage is regarded as the nucleation period of this system, unlike the ordinary spontaneous nucleation via a critical supersaturation. In a sense, this system may rather resemble seeded monodisperse systems and thus the final particle size strongly depends on the number concentration of the emulsifier micelles. Since the initial number concentration of the emulsifier micelles is normally designed to be sufficient for the generated nuclei to suppress the steady concentration of the oligomer radicals below the critical level for their spontaneous nucleation, renucleation after the "nucleation period" is prevented. Hence, although the separation of the nucleation and growth stages is not directly controlled by the generated nuclei like the emulsifierfree system, the mechanism for the formation of the monodispersed particles may also be regarded to be based on the nucleation-controUed precursor model. In an anionic dispersion polymerization system, on the other hand, an organometallic initiator may react almost instantly with the monomers to start the polymerization, and then the growing anionic oligomers may nucleate almost simultaneously at a concentration corresponding to their critical supersaturation, followed by the growth stage in which the nuclei consisting of the living oligomers may grow by further polymerization with monomers absorbed jfrom the solution phase. In this system, renucleation may not occur, because there are no living oligomers left in the solution phase in the growth stage. Hence, the mechanism of this automatic separation between nucleation and growth stages essentially differs from the LaMer mechanism. In some other systems, the automatic separation of nucleation and growth stages occurs independently of the nucleation. For example, monodisperse hematite (a-Fe203) particles are produced in the gel-sol process (see section 7.3.1 in chapter 7), owing to the precipitation of p-FeOOH particles as an intermediate from Fe(0H)3 gel to a~Fe203, because the phase transformation from Fe(0H)3 to p-FeOOH significantly reduces the


191

concentration of the precursor complex of hematite by the associated reduction of both pH and the solubility product of Fe^^ and OH" ions in the solution phase, which contributes to the reduction of the supersaturation for the nucleation of a-Fe203 to a level sufficiently below the critical supersaturation. Thus a-Fe203 nuclei initially generated with the precipitation of P-FeOOH can grow without renucleation. Hence, the mechanism of this automatic separation between nucleation and growth stages is also clearly distinguished from the LaMer mechanism, since the effective reduction of supersaturation is brought about by the formation of p-FeOOH, and not by the nucleation of a-Fe203. However, the automatic separation of nucleation and growth is not always possible in every system. If it is difficult to achieve the automatic separation, we must intentionally separate the two stages by lowering the supersaturation immediately after some time for nucleation. For this purpose, reduction of pH in the forced hydrolysis of metal ions, dilution with the solvent, addition of some growth accelerator, a quick change of temperature, etc. are often effective. We may call such techniques, ^^supersaturation quenching}^' One of the extreme measures to separate growth from nucleation may be the ^'seeding,^' as first used by Zsigmondy for gold colloids,^ where seed crystals are introduced into a monomer solution under a relatively low supersaturation below the critical level for nucleation. Thus, in this procedure, the nucleation process is performed in a completely separate system. However, the seeding seems to have more profound meanings. Namely, if the growth rate of the seeds is limited by the release rate of the monomer from the reservoir whose equilibrium monomer concentration is higher than the critical supersaturation level for the nucleation of the product particles, the seeds may positively reduce the supersaturation to prevent the spontaneous nucleation itself. In contrast, if the growth rate of the seeds is limited not by the release rate of the monomer from the reservoir, but by the deposition of monomer onto the seeds, the supersaturation is not lowered by the presence of seeds, and thus the spontaneous nucleation during the growth stage may not be prevented. However, even in such a case, a large number of seeds may achieve a monodisperse system by nullifying the contribution of a small number of the spontaneous nuclei to the final product. Hence, this seed effect is not based on the separation between nucleation and growth stages, but a kind of masking effect of seeds. As a consequence, seeding is a useful technique for the synthesis of monodispersed particles even in originally polydisperse systems.

192

PREPARATION

62. Inhibition of Random Coagulation If particles are in contact with each other during their growth, the contact points become active sites for the deposition of solute, as has been shown for the contact recrystallization of silver halide particles in section 4.5.'*'^ This trend may be more or less common to many kinds of colloidal particles, even though the drastic recrystallization is not observed. Also, once the solute deposits preferentially to the contact points, the particles in contact are cemented together irreversibly. In such a case, it is almost impossible to obtain monodispersed particles. For the inhibition of coagulation, some measures are known, such as the use of the repulsive force of the electric double layers, the use of gel network, and use of protective agents. Figure 6.2 illustrates these schematic models. Electric Double Layer

Protective Colloid

Gel Network Particles Gel Network

Fig. 6.2. Three methods for inhibition of coagulation.


193

a) Use of Electric Double Layers As a typical measure against coagulation, it is well known that the electric double layers of charged particles exert repulsive forces against each other, as a function of the zeta potential and Debye length. The repulsive force becomes more effective as the electrolyte concentration is lowered. Accordingly, precipitation from a homogeneous solution is normally carried out in a range away from the isoelectric point and at a low ionic strength. b) Use of Gel Networks If a gel-like precursory solid precipitates in the beginning and the nucleation of the final product occurs on the gel network, all particles growing from the nuclei are expected to be pinned down on the substrate so that random coagulation of the growing particles will be minimized. This effect is involved in the formation of uniform cubic particles of €0304,^ uniform spherical particles of magnetite (FCgOJ,^ etc. on the substrates of corresponding precursory hydroxides. This finding has led to the invention of a new general method named the "gel-sol method" for the synthesis of monodisperse particles in large quantities, as will be described in detail in chapter 7. c) Use of Protective Agents One of the most effective ways to stabilize lyophobic colloidal particles may be the use of protective agents or protective colloids, including lyophilic polymers, surfactants and complexing agents, as adsorptives to particles. The particle stabilization is mainly based on the Coulombic repulsion, osmotic pressure, and/or steric hindrance at the overlapped regions of the adsorbed layers of individual particles.^ Thiele and Van Levem^° evaluated the ability of many kinds of protective agents for stabilization of colloidal gold, and defined the "protective value." They found polyacrylic acid hydrazide, gelatin, and poly-N-vinyl-5methoxazolidone to be the most powerful protective agents for Au particles. When we use these protective agents, it must be noted that they often act not only as protective colloids, but also as growth inhibitors and/or shape controllers. When we use a surfactant as a protective agent, we must note that the adsorption of surfactants is strongly affected by the surface charge of the particles and that the stability of the sol is not a simple function of the added amount of a surfactant. For example, an anionic surfactant is efficiently adsorbed to positively charged surfaces of metal oxide particles

194

PREPARATION

in a pH range below the isoelectric point. However, if the added amount of the surfactant is equal to or less than that required for the saturation adsorption, the sol is subjected to coagulation, since the particles are covered by a shell of the hydrophobic moiety of the surfactant molecules. Hence, in order to restabilize the sol, one must add sufficient amount of the anionic surfactant to exceed the saturated monolayer and form a double layer of the surfactant molecules with the hydrophilic polar moiety of the outermost surfactant layer directed outward.^^ When a sol is coagulated by an insufficient amount of an anionic surfactant, additional introduction of cationic or nonionic surfactant is also useful for redispersion, since they can direct their hydrophilic moieties to the water phase by linking their hydrophobic moieties to the hydrophobic moiety of the outermost anionic surfactant layer. However, if the added amount of an ionic surfactant exceeds a still higher concentration level, it causes coagulation again by its electrolytic effect to shield the electric double layer of the particles.^^ Typical protective agents or stabilizers and examples of particles stabilized by them are listed in Table 6.1.

Table 6.1. Protective agents and examples of their use Polymers Polyacrylic acid hydrazide

Au^°

Gelatin

Au;>° AgBr,""'^ AgCl;"'"-" CdS,'*"^^ ZnS.^"'^^ PbS,^ CuS;^^ CuÔ^

Poly-N-vinyl-5-methoxazolidone

Au'"

Polyvinylpyrrolidone

Au,'"''' Cu," Ag,^ Pd,""^ Pt,^' ^ _ P J J 28,32 pd-Ni,2=' Cu-Pt,^ Pd-Pt,'^

Poly-2-ethyl-2-oxazoline

Au-Pd/* Pd-Cu," Au-Pt,'* Pt-Rh;^' Zr(OH)2C03 * Y(OH)C03/Al(OH)3;'" PS « PMMA,"' PAN"" PMMA"'

Poly-ethylenimine

PMMA"'


195

N-alkyl polyimine

Au'°

Polyvinylalcohol

?d;' Rh/"^ Pt,^" h,'' Os;^^ PS^''^"

Hydroxypropyl cellulose

TiOj,"' ZrOj/" AI2O3," FeÔj," BaTiOj,^' SrTiOj/^ PbTiOj,^' AljOj/SiOj;'" P S "

Polyacrylic acid

a-FeA;'" PS"

Polymaleic acid and copolymers

a-FeÔj^^

Polymers with sulfonic acid

a-FeÔj'^

Polymers with thioether and sulfonic acid groups

AgBr," AgCl"

Cyclodextrin

AgBr/« AgCl,'«

Dextran sulfate

Cr(0H)3^'

Proteins (ovalbumin, Y-globulin, lysozyme)

a-FeÔg,^''' Cr(0H)3^^

Anionic surfactants Sodium dodecylsuifate (SDS)

a-Fe,03,^^'^^^^ Cd3(P04)2,^^ Ni2(OH)P04,'' Mn3(P04)2,'' CosCPOV''"' (Cd,Ni,.,f(PO,),^^

Sodium alkylbenzene sulfonate

a-Fe203''

Sodium dioctyisulfosuccinate (Aerosol-OT)

Pd,^' C (in n-heptane),^^ Ti02 (in xylene)^^

Sodium oleate Perfluoro polyether carboxyiate Cationic surfactants

ZnO^°

196

PREPARATION

Cetyltrimethylammonium chloride

Co3(P04)2,^^ Au''^

Hexadecylpyridinium chloride

Au^^

Tetraalkylammonium bromide

PdJ^ Ni^^

Dodecylpyridinium bromide (with SDS)

a-Fe203

Nonionic surfactants Polyoxyethylene(lO) isooctylphenyl BaSO^^ ether (Triton X-100) Polyoxyethylene dodecylalcohol ether (with SDS) Polyoxyethylene alkylphenol ether

C (in water)^^

Others Polyol (ethylene glycol, diethylene glycol, etc.)

Co,^^ Ni,^^ Fe^*^

Polyphosphate

a-FeA''

Polyoxoanion

^2'î5^^3^62'

Ir^

Gelatin, in particular, has an advantage over other protective agents that, if necessary, adsorbed gelatin can readily be removed afterward with a trace of proteolytic enzyme.^^ In some special cases, however, fairly uniform particles can be obtained even by an aggregative growth mechanism. For example, fairly uniform spherical magnetite particles were obtained by this mechanism, in which very small primary particles of magnetite preformed on the precursory solid, green rust, were aggregated to form some secondary nuclei, and then the secondary nuclei were grown by gathering the surrounding primary particles by the strong magnetic attraction of the relatively large secondary nuclei.^ Nevertheless, the coagulation of the secondary particles themselves was inhibited by the support of the solid substrate on which they were separated


197

from one another by some spacing. Also, we can show other examples of colloidal particles, with a relatively narrow size distribution, probably formed by aggregative growth process; e.g,, silver particles (d = 0.88 |xm; a = 31 %) by simple mixing ammoniacal silver nitrate with hydroquinone,^^ gold particles (d « 2.0 ûn) by mixing HAuCl^ with ascorbic acid,^^ and zinc oxide particles (d = 1.50 \xm; a = 20 %) by a double jet mixing of zinc nitrate and triethanolamine.^° In these cases, the primary particles seem to be instantly generated on mixing the reactants, followed by clustering thereof and growth of the clusters by diffusion of the primary particles. If we regard the clustering and subsequent growth by the convergent diffusion of primary particles as nucleation at the critical supersaturation and subsequent diffusion-controlled particle growth, the formation process is analogous to that of the ordinary monodisperse particles grown by diffusion of monomeric species in accordance with the LaMer model.^ The selective aggregation of the primary particles to the growing clusters seems to be ascribed to a stationary concentration slope, for the diffusion of primary particles around each growing cluster, formed by the rapid absorption of the nearest primary particles due to the strong van der Waals force of a large cluster, leading to the convergent diffusion of primary particles toward each secondary particle. In other words, each secondary particle grows by gathering even considerably distant primary particles falling into the dijfusion hole. On the other hand, the probability of coagulation of the large secondary particles may be rather small due to their low number concentration and inactive Brownian motion. The characteristic of this growth mode is that not only the formation of the primary particles but also the subsequent aggregation of primary particles to the neighboring secondary particles is so fast as to realize the diffusion-controlled growth of the secondary particles by diffusion of the primary particles. For example, the total reaction time for the formation of the micrometer-size spherical silver particles in the above example is only a few seconds or less. Similarly, the gold particles are formed within 3-20 s. In the case of the zinc oxide particles prepared by the double jet method, the aggregation also appears to be so fast as to be instantly finished with addition of the reactants. Resulting secondary particles in these examples are all spheres consisting of much smaller subcrystals. Their size distributions are relatively broad as compared to typical monodisperse particles, because of some probabilities of coagulation between the growing secondary particles and between primary particles, even if the aggregation conditions are carefully chosen. However, it must be noted here that the growth mechanism cannot be

198

PREPARATION

concluded only from the particle shape and structure, since it is not rare to find that even polycrystal-structured spherical particles consisting of randomly oriented subcrystals have been grown by ordinary deposition of monomelic species. For identification of a growth mechanism, scrupulous analysis of the growth process is generally needed. More detailed discussions in this respect are given in chapters 7 and 9 (section 9. 10).

6.3. Reserve of Monomers In order to reconcile the two conflicting demands of a moderate supersaturation and an ample concentration of monomers for particle growth, some monomer reservoir must be built in for the preparation of monodisperse particles. For example, complexing agents such as ethylenediamineN,N,N',N'-tetraacetic acid (EDTA), nitrilotriacetic acid (NTA) and citric acid shield a large amount of multivalent metallic cations, and thus drastically reduce the supersaturation of free metal ions. In addition, these complexing agents contribute to the inhibition of coagulation of growing particles by reducing the ionic strength of individual systems. Hence these effects of complexing agents serve to prevent concurrent nucleation as well as coagulation during the growth stage of monodisperse particles, without reducing the product yield through constant release of metal ions. In a similar manner, thioacetamide works as a reservoir of sulfur for the preparation of metal sulfides; monomer droplets release the monomers into the aqueous medium in emulsion polymerization systems; and water solvent serves as a reservoir of hydroxide ions for hydrolysis of metal ions in an aqueous solution at low pH. If the hydrolysis has to be performed in the neutral pH range because of the high solubility product of the solid, some pH buffer system may be required to keep the hydroxide concentration at an adequate level. In this case, the buffer system is a reservoir of hydroxide. Furthermore, a solid precursor acts as a reservoir of the solute in heterogeneous systems, where the solid precursor is transformed into the final product through recrystallization (see section 7.3.1). As a consequence, some reservoir of monomers is indispensable for almost all monodisperse systems. The criteria for the choice of reservoirs are the concentration of monomers in equilibrium with a reservoir and the release rate of monomers from the reservoir. If the equilibrium monomer concentration of a reservoir is higher than the critical supersaturation level of the final product, it is impossible to avoid the concurrent nucleation in


199

the growth stage unless the release rate of the monomers is low enough to keep the steady concentration below the critical supersaturation level of the growing particles. Hence, the reservoirs are required to have a low equilibrium monomer concentration below the critical supersaturation level of the final product, or a sufficiently low release rate of monomers. In the former case, the release rate of the monomers should be high enough to maintain a reasonable growth rate of the product particles. In the latter case, the growth rate constant of the product particles must be high enough to maintain the steady concentration of the monomers below the critical supersaturation level of the product particles.

6.4. Choice of Growth Modes As has been described in section 2.6, if we can choose the diffusioncontrolled growth mode in a given system, we can expect a self-sharpening of the size distribution as long as the supersaturation is sufficiently high. For example, regular silver bromide particles grow by diffusion-limited kinetics in the pBr range of 2.6 to 3.5 (see Fig. 3.11), so this effect can be expected in this pBr range. The diffusion-controlled growth mode is also found in the growth of regular silver chloride particles in most pCl range,^^ sulfur particles,^^'^^ etc. However, the diffusion-controlled growth systems are rather rare in the known monodisperse systems, and the majority of them, including most metal oxides and metal sulfides, grow in the reaction-controlled growth mode. In the latter, the self-sharpening of size distribution does not occur, and only the relative width of the size distribution against the mean size is narrowed by the increase of the mean size with a nearly constant absolute distribution width initially determined in the nucleation stage. Here, it should be noted that even some reduction in the mean size, or use of a solvent for the solid, e.g., anunonia, thioether, or thiourea, for silver halides, could alter an originally diffusion-controlled system to a reaction-controlled one (see sections 2.6 and 3.2). In an open system such as the controlled double-jet (CDJ) system in which the solute is continuously introduced from outside, the addition rate of solute can be readily regulated as a function of time. In such a system, it is possible to perform the formation of uniform particles at the maximum efficiency in accordance with the growth mode.^'^^ Namely, if the growth of particles on some preformed nuclei is conducted while maintaining the

200

PREPARATION

supersaturation as high as a level slightly below the critical supersaturation for nucleation, the mean particle radius as a function of time in the diffusion-controlled mode is given from Eq. (2.5.7) as (6.4.1)

ÎDVÂC't,

where AC* is the difference between a supersaturated concentration of the solute close to the critical supersaturation and the solubility of the solid. Here, the Gibbs-Thomson effect of the growing particles is neglected, and the initial particle radius is approximated by zero. If n denotes the number of the stable nuclei, the consumption rate of solute, -dC/dt, is given by dC dt

Aizr^n dr = 4v/27u/iKf (Z)AC*)^^f^^. V^ ~dt

(6.4.2)

I

DIFFUSION CONTROL -dC/dtcc v T

o

\

H

C/3

o u

*- t TIME

Fig. 6.3. -dCldt vs t for reaction-controlled growth and diffusion-controlled growth. (From Ref. 83.)


201

For a first-order reaction control, r is given by (6.4.3)

r=kV\C*t, SO that

(6.4.4) dt Hence, the consumption rate of solute is proportional to the square root of time in the case of diffusion control, while it is proportional to the square of time in the case of reaction control. Figure 6.3 shows the relations of -dC/dt vs t for reaction-controlled and diffusion-controlled growth modes.^"*'^ This relationship for reaction control generaUy holds, irrespective of the form of the kinetic equation of the surface reaction. These characteristics can be used for distinguishing between the two growth modes. For example, if the feed rate of solute, Q (= -dC/dt), is regulated as being

Q A

Change of Q { Q oc t )

Diffusion- Control Pattem {Q^

ft )

Fig. 6.4. Renucieation occurs at r = r^ and thereafter, when Q increases in proportion to r in a diffusion-controlled growth mode.

202

PREPARATION

proportional to the square of time in a diffusion-controlled system, drastic renucleation will occur within a short time, no matter how the feed rate is reduced. As a rule, the n value in Q ^ f should be set n ^ 1/2 for diffusion-controlled growth, whereas « < 2 for reaction-controlled growth, in order to avoid renucleation during the growth stage. For example, if Q cc t {n = 1), the renucleation cannot be avoided in the case of diffusioncontrolled growth, as shown in Fig. 6.4. Nevertheless, if the feed mode fits the growth mode, one will be able to grow monodisperse particles at the maximum supersaturation, AC*, free from renucleation.

6.5. Introduction of Alternative Mechanisms As suggested in ref. 1, there is some possibility of automatic cessation of growth at a certain size level by adsorption of concentrated surfactants in microemulsion systems or by depletion of primary particles around each secondary particle fixed in a gel network, as observed in the gel-sol system for the formation of magnetite particles (see also section 7.3.1).^'^ This mechanism - maybe referred to as Arrested Growth Mechanism - is independent of the LaMer mechanism, so that the two mechanisms can be combined or only the arrested growth mechanism may function even in a system in which the LaMer mechanism does not work. In a system for the formation of uniform nanosized particles in particular, the arrested growth mechanism is expected to be of great use, since the LaMer mechanism may not fully function in such a system because of the excessive weight of the nucleation stage compared to the growth process. For this purpose, it may be required to select or design some specific adsorptives out of polymers, surfactants, complexing agents, adsorptive ions, solvents, etc., which are able to completely halt the growth of each particle within a certain time-lag after nucleation. The general principles given above may also be of some help for readers to approach the underlying backgrounds of numerous systems for the formation of monodisperse particles in review articles.^'^'^^^^^'^"^"^^^

References L T. Sugimoto, Adv, Colloid Interface Sci 28, 65 (1987).


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2. T. Sugimoto, Hyomen 22, 177 (1984). 3. R. Zsigmondy, Z Anorg. Allgem, Chem. 99, 105 (1917). 4. T. Sugimoto and G. Yamaguchi, J. Phys, Chem, 80, 1579 (1976). 5. T. Sugimoto and G. Yamaguchi, J. Crystal Growth 34, 253 (1976). 6. T. Sugimoto and H. Yanagida, Nippon Shashin Gakkaishi 40,15 (1977). 7. T. Sugimoto and E. Matijevic, J. Inorg. Nucl Chem. 41, 165 (1979). 8. T. Sugimoto and E. Matijevic, J. Colloid Interface Sci. 74, 227 (1980). 9. F. Th. Hesselink, A. Vrij, and J. Th. G. Overbeek, J. Phys, Chem. 75, 2094 (1971). 10. H. Thiele and H. S. von Levem, J. Colloid Sci. 20, 679 (1965). 11. K. Meguro and T. Kondo, Nippon Kagaku Zasshi 76, 642 (1955); K. Meguro, Kogyo Kagaku Zasshi 58, 905 (1955). 12. N. Moriyama, J. Colloid Interface Sci. 50, 80 (1975). 13. C. T. Mumaw and E. F. Haugh, J. Imaging Sci. 30, 198 (1987); M. Sziics, J. Signalaufz.- Mater. 11, 259 (1983); L. De Brabandere, L. Ketellapper, and H. Borginon, in "Photographic Gelatine II," (R. J. Cox, Ed.), pp. 335-348. Academic Press, London, 1976. 14. T. Sugimoto, J. Colloid Interface Sci. 91, 51 (1983); T. Sugimoto, ibid. 93, 461 (1983). 15. T. Sugimoto, J. Colloid Interface Sci. 150, 208 (1992); T. Sugimoto and F. Shiba, Colloids Surfaces A: Physicochem. Eng. Aspects 164, 205 (2000). 16. T. Sugimoto and K. Miyake, J. Colloid Interface Sci. 140, 335 (1990); T. Sugimoto and K. Miyake, ibid. 140, 348 (1990). 17. T. Sugimoto, F. Shiba, T. Sekiguchi, and H. Itoh, Colloids Surfaces A: Physicochem. Eng. Aspects 164, 183 (2000). 18. T. Sugimoto, G. E. Dirige, and A. Muramatsu, J. Colloid Interface Sci. 173, 257 (1995). 19. T. Sugimoto, G. E. Dirige, and A. Muramatsu, J. Colloid Interface Sci. 176, 442 (1995). 20. T. Sugimoto, G. E. Dirige, and A. Muramatsu, J. Colloid Interface Sci. 180, 305 (1996). 21. T. Sugimoto, G. E. Dirige, and A. Muramatsu, J. Colloid Interface Sci. 182, 444 (1996). 22. T. Sugimoto, S. Chen, and A. Muramatsu, Colloids Surfaces A: Physicochem. Eng. Aspects 135, 207 (1998). 23. A. Muramatsu and T. Sugimoto, J. Colloid Interface Sci. 189, 167 (1997). 24. R. Seshadri and C. N. R. Rao, Mater. Res. Bull. 29, 795 (1994); P-Y.

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46. H. Hirai, Y. Nakao, and N. Toshima, J. Macromol. Sci. A: Chem. 13, 727 (1979). 47. M. Okubo, T. Hosotani, T. Yamashita, and J. Izumi, Colloid Polym. Sci. 275, 888 (1997). 48. J. Lee and M. Senna, Colloid Polym. Sci. 273, 76 (1995). 49. J. H. Jean and T. A. Ring, Am. Ceram. Soc. Bull. 65, 1574 (1986); T. E. Mates and T. A. Ring, Colloids Surfaces 24, 299 (1987); J. H. Jean and T. A. Ring, ibid. 29, 273 (1988); J.-L. Look and C. F. Zukoski, Ceram. Tram. 26, 1 (1992). 50. Y. T. Moon, D. K. Kim, and C. H. Kim, J. Am. Ceram. Soc. 78, 1103 (1995); Y. T. Moon, H. K. Park, D. K. Kim, and C. H. Kim, ibid. 78, 2690 (1995). 51. T. Ogihara, H. Nakajima, T. Yanagawa, N. Ogata, K. Yoshida, and N. Matsushita, J. Am. Ceram. Soc. 74, 2263 (1991). 52. T. Ogihara, M. Yabuuchi, T. Yanagawa, N. Ogata, K. Yoshida, N. Nagata, K. Ogawa, and U. Maeda, Funtai Kogaku Kaishi 31, 620 (1994). 53. T. Ogihara, T. Yanagawa, N. Ogata, K. Yoshida, M. Iguchi, N. Nagata, and K. Ogawa, Funtai Kogaku Kaishi 31, 795 (1994). 54. T. Ogihara, T. Yanagawa, N. Ogata, K. Yoshida, M. Iguchi, N. Nagata, and K. Ogawa, J. Ceram. Soc. Jpn. 102, 778 (1994). 55. C. K. Ober, K. P. Lok, and M. L. Hair, J. Polym. Sci.: Polym. Lett. Ed 23, 103 (1985). 56. K. P. Lok and C. K. Ober, Can. J. Chem. 63, 209 (1985); M. Okubo, K. Ikegami, and Y. Yamamoto, Colloid Polym. Sci. 267, 193 (1989). 57. K. H. Hoihster and R. C. Sutton, J. Imaging Sci. 31, 148 (1987). 58. M. Szucs and I. Kiss, J. Inform. Rec. Mater. 16, 439 (1988). 59. M. Onofusa and E. Matijevic, J. Colloid Interface Sci. 74, 451 (1980). 60. J. E. Johnson and E. Matijevic, Colloid Polym. Sci. llî, 353 (1992). 61. J. E. Johnson and E. Matijevic, Colloid Polym. Sci. 270, 364 (1992). 62. K. Esumi, Y. Sakamoto, K. Yoshikawa, and K. Meguro, Bull. Chem. Soc. Jpn. 61, 1475 (1988); K. Esumi, Y. Ono, M. Ishizuka, and K. Meguro, Colloids Surfaces 32, 139 (1988). 63. L. L. Springsteen and E. Matijevic, Colloid Polym. Sci. 161, 1007 (1989). 64. T. Ishikawa and E. Matijevic, J. Colloid Interface Sci. 123, 122 (1988). 65. K. Kandori, E. Matsuda, A. Yasukawa, and T. Ishikawa, J. Jpn. Soc. Colour Mater. 68, 75 (1995). 66. J. Quiben and E. Matijevic, Colloids Surfaces A: Physicochem. Eng.

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Aspects 82, 237 (1994). 67. K. Esumi, M. Suzuki, T. Tano, K. Torigoe, and K. Meguro, Colloids Surfaces 55, 9 (1991); K. Esumi, T. Tano, and K. Meguro, Langmuir 5, 268 (1989); T. Tano, K. Esumi, and K. Meguro, J. Colloid Interface Sci. 133, 530 (1989); A. Kitahara, S. Karasawa, and H. Yamada, J. Colloid Interface Sci. 25, 490 (1967). 68. K. E. Lewis and G. D. Parfitt, Trans. Faraday Soc. 62, 1652 (1966). 69. G. N. L. McGown, G. D. Parfitt, and E. WUlis, J. Colloid ScL 20, 650 (1965). 70. A. Chittofrati and E. Matijevic, Colloids Surfaces 48, 65 (1990). 71. H. Ishizuka, T. Tano, K. Torigoe, K. Esumi, and K. Meguro, Colloids Surfaces 63, 337 (1992). 72. M. T. Reetz and W. Helbig, J. Am. Chem. Soc. 116, 7401 (1994); M. T. Reetz, W. Helbig, S. A. Quaiser, U. Stimming, N. Breuer, and R. Vogel, Science 267, 367 (1995); M. T. Reetz and G. Lohmer, Chem. Comm. 1921 (1996). 73. J. J. Petres, Gj. Dezelic, and B. Teiak, Croat. Chem. Acta 38, 277 (1966); ibid. 40, 213 (1968). 74. N. Moriyama, K. Hattori, and K. Shinoda, Nippon Kagaku Zasshi 90, 35 (1969). 75. (a) F. Fievet, J. P. Lagier, and M. Figlarz, MRS Bull. 14(12), 29 (1989); (b) F. Fievet, J. P. Lagier, B. Blin, B. Beaudoin, and M. Figlarz, Solid State Ionics 32/33, 198 (1989); (c) G. Viau, F. Fievet-Vincent, and F. Fievet, Solid State Ionics 84, 259 (1996). 76. G. Viau, F. Fievet-Vincent, and F. Fievet, J. Mater. Chem. 6, 1047 (1996). 77. M. A. Watzky and R. G. Finke, J. Am. Chem. Soc. 119, 10382 (1997); Y. Lin and R. G. Finke, Inorg Chem. 33, 4891 (1994); J. D. Aiken III, Y. Lin, and R. G. Finke, J. Mol. Catal. A: Chemical 114, 29 (1996). 78. H. Sasaki, H. Kiuchi, C. Kobayashi, H. Kuroda, and T. Nagai, Shigen to Sozai 110, 1121 (1994). 79. V. Privman, D. V. Goia, J. Park, and E. Matijevic, J. Colloid Interface Sci. 213, 36 (1999). 80. Q. Zhong and E. Matijevic, J. Mater. Chem. 6, 443 (1996). 81. R. W. Strong and J. S. Wey, Photogr. Sci. Eng 23, 344 (1979). 82. V. K. LaMer and R. H. Dinegar, J. Am. Chem. Soc. 72, 4847 (1950). 83. A. E. Nielsen, "Kinetics of Precipitation," Pergamon, Oxford, 1964. 84. T. Sugimoto, Gendai Kagaku 263, 42 (1993). 85. T. Sugimoto, in "Koroido Kagaku (Colloid Science)," (Chem. Soc. Jpn.,


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Ed.), Vol 1, pp. 135-152. Tokyo Kagaku Dohjin, Tokyo, 1995. 86. E. Matijevic, in "Trends in Electrochemistry," (J. O'M. Bockris, D. A. J. Rand, and B. J. Welch, Eds.), p. 177. Plenum, New York, 1977. 87. E. Matijevic, Pure Appl Chem. 50, 1193 (1978). 88. E. Matijevic, Corrosion 35, 264 (1979). 89. E. Matijevic, Pure Appl. Chem. 52, 1179 (1980). 90. E. Matijevic, Ann. Rev. Mater. Set 15, 483 (1985). 91. E. Matijevic, Langmuir 2, 12 (1986). 92. E. Matijevic, Chem. Mater. 5, 412 (1993). 93. E. Matijevic, in "Controlled Particle, Droplet and Bubble Formation," (D. J. Wedlock, Ed.) p. 39. Butterworth-Heinemann, London, 1994. 94. E. Matijevic, Langmuir 10, 8 (1994). 95. E. Matijevic, Prog. Colloid Polym. Sci. 101, 38 (1996). 96. E. Matijevic, J. Europ. Ceram. Soc. 18, 1357 (1998). 97. J. Th. G. Overbeek, Adv. Colloid Interface Sci. 15, 251 (1982). 98. M. Hanita and B. Delmon, J. Chim. Phys. 83, 859 (1986). 99. S. Hamada, Hyomen 25, 143 (1987). 100. M. Ozaki, MRS Bull. 14(12), 35 (1989). 101. A. J. 1. Ward and S. E. Friberg, MRS Bull. 14(12), 41 (1989). 102. T. A. Ring, MRS Bull. 15(1), 34 (1990). 103. T. Sugimoto, MRS Bull. 14(12), 23 (1989). 104. T. Sugimoto, Nippon Kinzoku Gakkai Kaiho 26, 272 (1987). 105. T. Sugimoto, Bunri Gijutsu 18, 135 (1988). 106. T. Sugimoto, Shigen Shorigijutsu 38(2), 18 (1991). 107. T. Sugimoto, Boundary 7(11), 22 (1991). 108. T. Sugimoto, Hyomen 29, 978 (1991). 109. T. Sugimoto, in "Ceramic Data Book," p. 67. Kogyo-Seihin Gijutsu Kyokai, Tokyo, 1991. 110. T. Sugimoto, Nippon Kessho Gakkaishi 34, 244 (1992). 111. T. Sugimoto, Funtai Kogaku Kaishi 29, 912 (1992). 112. T. Sugimoto, Zairyo 42, 1251 (1993). 113. T. Sugimoto, Kagaku Kogaku 59, 158 (1995). 114. T. Sugimoto, Materia Japan (Nippon Kinzokugakkai Kaiho) 35, 1012 (1996). 115. T. Sugimoto, Kogyo Zairyo 44(13), 110, 1996. 116. T. Sugimoto, in "Fine Particles Science and Technology," (E. Pelizzetti, Ed.), pp. 61-70. Kluwer, Dordrecht, 1996.

CHAPTER 7 MONODISPERSED SYSTEMS 7.1. Classification of Monodispersed Systems Monodispersed particle systems are classified into homogeneous systems or heterogeneous systems according to the number of phases in a system prior to the precipitation of the final product. A homogeneous system initially consists of one phase, where the monomer reservoir is normally built in, in the form of solute. Precipitation of the final product takes place directly from the homogenous solution. A large number of monodisperse particles have been prepared in homogeneous systems through: 1) Homogeneous Redox Reaction^ 2) Precipitation by Poor Solvents, 3) Precipitation by Cooling, 4) Direct Reaction of Ions, 5) Dissociative Reaction of Inorganic Complexes, 6) Dissociative Reaction of Organic Complexes, 7) Dissociative Reaction of Organic Compounds, 8) Reaction by Decomposition of Compounds, 9) Hydrolysis of Alkoxides, 10) Forced Hydrolysis of Metal Ions and 11) Dispersion Polymerization, A heterogeneous system initially consists of more than one phase (mostly two) prior to the precipitation of the final product. The monomers are reserved in one or each of the phases, whereas the precipitation of the final product takes place in one of them. Various characteristic systems belong to this category, in which monodisperse particles have been synthesized through: 1) Phase Transformation of Solids, 2) Ostwald Ripening, 3) Emulsion Polymerization, 4) Reaction in Microemulsions, 5) Precipitation from Liquid Crystals, 6) Inhomogeneous Hydrolysis, 7) Hydrolysis in Nonaqueous Emulsions, 8) Reaction on Solid Surfaces, 9) Reaction in Solid Matrices, 10) Reaction in Solid Templates, 11) Firing of Solid Precursors, 12) Conversion of Aerosol Droplets, and 13) Oscillatory Nozzle-Jet Techniques, These systems are summarized in Table 7.1. In this classification of reaction systems, some system may belong to more than one group at the same time. In such a case, it is put into a group which seems to represent the system most distinctly. For example:

7. MONODISPERSED SYSTEMS

209

Table 7,1. Synthetic systems of monodispersed particles Homogeneous Systems 1) Homogeneous Redox Reaction a) Reduction, b) Partial Reduction, c) Oxidation 2) Precipitation by Poor Solvents 3) Precipitation by Cooling 4) Direct Reaction of Ions 5) Dissociative Reaction of Inorganic Complexes 6) Dissociative Reaction of Organic Complexes 7) Dissociative Reaction of Organic Compounds 8) Reaction by Decomposition of Compounds 9) Hydrolysis of Alkoxides 10) Forced Hydrolysis of Metal Ions 11) Dispersion Polymerization Heterogeneous Systems 1) Phase Transformation of Solids a) Dilute Systems, b) Condensed Systems 2) Ostwald Ripening 3) Emulsion Polymerization 4) Reaction in Microemulsions 5) Precipitation from Liquid Crystals 6) Inhomogeneous Hydrolysis 7) Hydrolysis in Non-aqueous Emulsions 8) Reaction on Solid Surfaces 9) Reaction in Solid Matrices 10) Reaction in Solid Templates 11) Firing of Solid Precursors 12) Conversion of Aerosol Droplets 13) Oscillatory Nozzle-Jet Techniques

{a) Homogeneous redox reactions of metal ions are all classified into the group of the Homogeneous Redox Reaction, even if the reactions are accompanied by dissociation of complexes, pyrolysis, and/or forced hydrolysis; (b) Dissociation of chelates follovêd by forced hydrolysis is classified into the Dissociative Reaction of Organic Complexes; (c) Both dissociation of chelates and dissociation of an organic compound are used at the same time, the system is classified into the Dissociative Reaction of Organic Complexes; (d) Irreversible decomposition of chelates is classified into the Reaction by Decomposition of Compounds; (e) Decomposition of

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a starting material by redox reaction to produce precursor ions is classified into the Reaction by Decomposition of Compounds; (/) Even if some solid is partly precipitated as an intermediate during aging a homogeneous solution, such a system is classified into the Homogeneous Systems; (g) Redox reactions by way of phase transformation in heterogeneous systems are classified into the Phase Transformation of Solid; Qi) If final products are prepared by dry conversion processes, such as calcination and gas-phase reduction, from the precursor particles, they are classified into the original systems for preparation of the precursors. Also, note that the particles cited in this chapter are not necessarily limited to only perfectly monodispersed ones in a rigorous sense, because of the comprehensive nature of this book to cover a wide variety of fairly uniform particles. As another characteristic of this chapter, a special stress is placed upon the description of the underlying mechanisms of individual systems, and thus relatively large spaces are spared for the introduction of mechanistic studies.

7.2. Homogeneous Systems 7.2.1. Homogeneous Redox Reaction a) Reduction For the reduction of metal ions or metal complexes, not only typical reducing agents, such as hydrogen gas, sodium borohydride (NaBHJ, hydrazine, hydroxylamine, carbon monoxide, and citric acid, but also much milder reducing agents, such as many kinds of alcohols and organic complexing agents including acetic acid, acetylacetone, 1,2-ethanediamine, etc., are used. In some cases, irradiation of solutions of metal salts with visible lights, ultraviolet rays, y-rays, etc. are useful for inducing the reduction of noble metal ions. On the other hand, as metal particles are normally unstable in solvents, they are mostly prepared in the presence of some protective agents, including lyophilic polymers such as polyvinyl pyrrolidone (PVP), polyvinyl alcohol (PVA), polyaerylamide (PAAM), polyacrylic acid (PAA), and their copolymers; cationic surfactants such as dodecyltrimethyl ammonium chloride (DTAC), tetradecylpyridinium bromide (TDPB), etc.; anionic surfactant such as sodium dodecylsulfate (SDS), sodium bis(2-ethylhexyl)sulfosuccinate (Aerosol OT), etc.; amphoteric surfactants such as N-dodecyl-N^N-dimethylbetaine, N-tetradecyl-2-

211


aminopropionic acid, etc.; nonionic surfactants such as hexaoxyethylene dodecyl ether, polyoxyethylene solbitan monolaurate, etc. For the choice of protective agents, the extensive work of Thiele and Van Levem^ on stabilization of gold particles with a wide variety of protective agents is useful as a reference for their selection (see also Table 6.1 in section 6.2). Ishizuka et al? also tested the effects of different kinds of cationic surfactants on the mean size of spherical gold (Au) particles in the range of 10 to 50 nm, prepared by reduction of 0.5 mmol dm"^ AUCI4" complex with 1.0 mmol dm"^ hydrazine in aqueous solutions at room temperature.^ They tested three kinds of surfactants, Le. hexadecylpyridinium chloride (CPCl), dodecylpyridinium chloride (DPCl), and hexadecyltrimethylammonium chloride (CTAC), and found that the power of the reduction of the particle size was in the order CPCl > CTAC » DPCl, suggesting the salient effect of hydrocarbon chain length and the less effect of the head group species. In this context, Esumi et al? tested the effects of organic solvents and an anionic surfactant, sodium bis(2-ethylhexyl)sulfosuccinate (Aerosol OT), on the stability of fairly uniform spherical palladium (Pd) particles of mean

r«s

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20

30

Dielectric constant of solvent

40

Fig. 7.1. Correlations of the zetapotentiai and colloidal stability of Pd particles, in terms of the absorbance of their suspensions at X = 500 nm, with the dielectric constants of solvents: (1) n~hexane, (2) toluene, (3) o-xylene, (4) 1,4dioxane, (5) chloroform, (6) ethyl acetate, (7) methylisobutylketone, (8) 1-butanol, (9) acetone, (10) ethanol, and (11) acetonitrile. (From Ref. 3.)

PREPARATION

212

(a) i 10

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Concn. of Aerosol OT/mmoldm"'

Fig. 7.2. Effects of the concentration of Aerosol OT on the zetapotential of the Pd particles and their colloidal stability in terms of the absorbance of their suspensions at X = 500 nm. (From Ref. 3.)

diameter 260 nm. Figure 7.1 shows effects of the dielectric constants of tested organic solvents on the zeta-potential and colloidal stability of the Pd particles in terms of absorbance of the suspensions at X = 500 nm. Figure 7.2 exhibits the effects of the concentration of Aerosol OT on the zeta potential of the Pd particles in n-hexane and their colloidal stability in terms of the absorbance, where Aerosol OT ions are believed to be adsorbed to the particles with their hydrocarbon chain toward the hydrophobic metal surfaces. Obviously, the choice of solvents as weD as protective agents is essential for the preparation of uniform metal particles. Zsigmondy"^ obtains monodisperse gold (Au) sols by reducing chloroauric acid with formaldehyde. He also found that monodisperse gold colloids were readily produced by using Faraday's gold sols (ca. 3 nm in mean diameter) as seed crystals with high reproducibility.^ Takiyama^ and Turkevich et alJ improved Zsigmondy's method by reducing chloroauric acid with sodium citrate and obtained highly uniform spherical gold particles of 20 nm in mean diameter. The citrate appears to work as a protective agent against coagulation by adsorption to gold particles. Also, the extensive experimentation for proper conditions of temperature and concent-


213

Fig. 7.3. Uniform particles obtained by redox reactions: (a) Se particles (From Ref. 8); (b) Star-like CU2O particles (From Ref. 42).

ration of the reactants seems to be basically an endeavor to avoid concurrent nucleation during the growth. Watillon et al^^ obtained highly uniform selenium (Se) particles (40 500 nm) by reducing selenious acid with hydrazine^ or hydroxylamine^ in the presence of foreign nuclei of gold. Figure 7.3(a) shows a TEM of the selenium particles. Sapieszko and Matijevic^° prepared spherical nickel (Ni) particles of a narrow size distribution by reducing a EDTA-Ni complex with hydrogen peroxide in highly basic media at 250 °C. Similar nickel particles were also obtained with hydrazine in place of hydrogen peroxide. In these systems, decomposition of EDTA and reduction of Ni^^ ions took place at the same time. Esumi et al}^ also prepared spherical palladium (Fd) particles (fee crystals) of a narrow size distribution with mean diameter in a range from 10 to 260 nm by pyrolytic reduction of 0.3 - 2.0 mmol dm"^ palladium(II) acetylacetonate or palladium(Il) acetate in methyl isobutyl ketone refluxed near the boiling point (117-118 °C) for 5 - 9 0 min. In this experiment they found addition of Pd(acac)2 solution to preheated methyl isobutyl ketone at its boiling point was essential for narrowing the size distribution. This result may be explained by the shortened nucleation period at a high temperature. Probably, oxidation product of the acetylacetonate, such as acetic acid, may also have served as a stabilizer of the Pd particles. Hamada et al}^ prepared quasi-spherical silver (Ag) particles of ca. 0.5 fxm with a relative standard deviation ca, 10 % by pyrolytic reduction of 1.0

214

PREPARATION

mmol dm"^ bis(l,2-ethanediamine)silver(I) complex in the aqueous solution in the presence of 1.0 mol dm'^ 1,2-ethanediamine at 100 ""C and pH 10.8 for 40 min. In this system, the high concentration of 1,2-ethanediamine may also function as a stabilizer of generated Ag particles. Fievet et al}^ developed a new method for the preparation of many kinds of metal particles (e.g., Co, Ni, Cu, Pb, Pt, and Ag) of the order of microns or submicrons with a narrow size distribution by reduction of metal ions in liquid polyols, such as diethylene glycol (DEG), ethylene glycol (EG) and their mixture, normally at a relatively high temperature up to the boiling points of these polyols around 200 °C, in which these polyols act as both reductant and solvent (polyol process). Since the main reaction product of ethylene glycol (CHpH-CHÔH) was diacetyl (CH3COCOCH3), metal ions are believed to be reduced by acetaldehyde, as an intermediate generated by degrees through dehydration of ethylene glycol, to be duplicatively oxidized to diacetyl.^"* If this reaction scheme is the case, the dehydration reaction of ethylene glycol must be a reversible one whose rate is affected by the succeeding reaction of acetaldehyde with metal ions, since the reduction rate of metal ions strongly depends on the metal-ion species in the polyol process. However, if the dehydration reaction is not in effect, or if it is virtually an irreversible one, one must take into account a possibility of the direct reduction of metal ions by polyols. For the preparation of metal particles by the polyol process, starting materials may be solids such as hydroxides and oxides, or soluble salts such as nitrates and acetates. In this section, we deal with only the cases in which soluble salts are used as a starting material (see section 7.3.1 for the polyol process with solid precursors). Ducamp-Sanguesa et al}^ prepared silver (Ag) particles of a narrow size distribution from a homogeneous EG solution of AgN03 by polyol process in the presence of PVP, in which the Ag/EG molar ratio was 0.025, equivalent to ca. 0.45 mol dm"^ AgNOj. Interestingly, quasi-equiaxial submicrometer particles were obtained by homogeneous nucleation, whilst rod-like particles, with typical dimensions: 3 \mi long and 0.5 jmi thick, were obtained by heterogeneous nucleation on platmum nanosized nuclei and the aspect ratio of the rod-like particles whose side planes were the {110} faces was found to increase with the increasing content of PVP. They found the final size of the silver particles to be increased with increasing temperature, in contrast to most polyol systems in which the final size is reduced with increasing temperature. Since the final particle size of monodispersed particles is determined by the ratio of the supply rate of precursor monomers to the volumic growth rate


215

of the particles at the end of the nucleation period (see sections 1.4 and 8.1.1), the increase in the volumic growth rate with increasing temperature may surpass the increase of the reduction rate of silver ions in the case of silver particles fonnation. It was also found that there was a suitable PVP/Ag ratio for stabilization of Ag particles, which increases with increasing temperature. Hence, the reduction in the stability of the Ag particles with increasing temperature may make some contribution to the increase in the growth rate of the Ag particles with increasing temperature. Also, too high or too low a content of PVP caused aggregation of the product particles. An excessive amount of PVP may increase the probability of bridging adsorption of a polymer chain to multiple particles. Similarly, Silvert et al}^ obtained Ag particles with a narrow size distribution by the polyol process. Seshadri and Rao^^ prepared quasi-spherical gold (Au) particles of a mean diameter 0.48 ^mi with a relative standard deviation 12.5 % by adding EG solution of HAUCI4 to the same volume of refluxing DEG in the presence of 0.4 w/v % PVP at pH 4.5 followed by refluxing for 3 4 h. Similarly, Silvert et al}^ prepared Au particles of comparable diameters by the polyol process, in which they added a small volume of an EG solution of HAUCI4 (5 cm^) to a large volume of a hot EG solution of PVP (70 cm^), which may serve the distinct separation of nucleation and growth stages, as mentioned above. They also found that a higher concentration of PVP was needed for inhibition of coagulation in accordance with increasing temperature. Sanguesa et al}^ and Silvert^^ prepared fairly uniform spherical palladium (Pd) particles of mean diameters in the submicrometer range from palladium (II) tetramine, such as Pd(NH3)4"*, by the polyol process in EG, DEG, or TEG at relatively low temperatures even below 0 °C or around room temperature with the aid of an auxiliary reductant, such as hydrazine, where the system was not agitated during the aging for 1 h. Moreover, Silvert et al^^^^ prepared nanosized alloy particles of Ag-Pd, such as Ag7oPd3o, with a relatively narrow size distribution by the polyol process starting from nitrates of the corresponding metal ions in the presence of PVP in EG. In this case, they dissolved these salts in an EG solution of PVP at room temperature and gradually raised the temperature up to 120 °C, followed by aging at this temperature (the total reaction time = 4 h). Since nanosized metal particles are of special interest as catalysts for a wide variety of reactions (see section 12.4), extensive studies for the preparation of well-defined stable nanoparticles of noble metals have been performed. As a rule, for the preparation of fairly uniform metal nanoparticles, rather mild reduction of metal salts with alcohols or by photolytic

216

PREPARATION

reduction is often chosen, because it is relatively easy to realize the homogeneous nucleation and the separation between the nucleation and succeeding growth stages. For example, Hirai et al.^ prepared palladium (Pd), rhodium (Rh), platinum (Pt), iridium (Ir), and osmium (Os) particles of mean diameters ranging from 1 to 6 nm by reduction with alcohols such as methanol and ethanol in the presence of PVA. Similarly, Toshima et al prepared bimetallic nanoparticles of diameters from 1 to 2 nm, such as PdPt,^'24 Au-Pd,^ Au-Pt,^ and Pt-Rh,^^ by reduction of mixed salts, chosen out of HAUCI4, H2PtCl6, PdCl2, and RhClg, with alcohols in the presence PVP. They were found to form a core/shell structure with a clear order of preference for forming the core: Au > Pt > Pd > Rh. Presumably this order seems to be determined by the concentration of free metal ions dissolved in equilibrium with each mixed complex coordinated by chloride ions and pyrrolidone residue, in addition to the electronic trends of the individual metal ions characterized by the ionization series. Hence, the order of the preference for core formation may depend on the species of the used complexes. Teranishi et alP^ prepared platinum (Pt) particles of mean diameters from 2 to 4 nm with relative standard deviations (coefficients of variation) around 10 %, by refluxing 0.6 mmol dm"^ H2PtClg in an alcohol/water (9/1, v/v) mixed solvent with 0.067 wt % PVP (M^ = 40,000) for 3 h at 100 °C, where the alcohols used as a reducing agent were methanol, ethanol, and 1-propanol. They found that the final mean size of the product was reduced as the species of the alcohol was changed from methanol through ethanol to 1-propanol, which was in accord with the order of the reducing rate of platinum ions, increasing from methanol through ethanol to 1-propanol, corresponding to the order of the nucleation rate. Also, the final particle size was found to decrease with the increasing proportion of alcohol in the mixed media in all cases, as readily understood in terms of the increasing reducibility. They prepared monolayers of these Pt particles by electrophoretic deposition on electrodes. Bradley et al}^ prepared fairly uniform Pd-Cu alloy particles of mean diameters in the range of 3-5 nm with a relative standard deviation, ca. 10 %, by heating mixtures of palladium acetate and copper acetate in 2-ethoxyethanol in the presence of PVP. In a typical preparation process of a Pdo5Cuo5 colloid, 30 cm^ of 2-ethoxyethanol containing 75 mmol each of Pd(0Ac)2 and Cu(0Ac)2 and 1.66 g of PVP (M^ = 40,000) was refluxed for 2 h (135 °C). They showed the presence of both metal atoms at the surfaces of these alloy particles by IR spectroscopy on the characteristic absorption bands of adsorbed carbon monoxide. Typical examples of the preparation of metallic


217

nanoparticles, mostly in a size range of 2-3 nm, by photolytic reduction of metal salts or metal complexes are: platinum (Pt) particles^° by visibleultraviolet irradiation; gold (Au) and silver (Ag) particles,^^ and rhodium (Rh) particles^^ by UV-ray irradiation; iridium (Ir) particles^^, platinum (Pt) particles^^ cobalt (Co), nickel (Ni), zinc (Zn), lead (Pb), and Cu-Pb particles^^ by y-ray irradiation. However, if one carefully chooses optimum conditions required for the formation of monodispersed particles in the presence of some powerful protective agents, one will be able to obtain fairly uniform nanoparticles of metals, comparable to those produced with alcohols or by photolytic reduction, even with much stronger reducing agents or by local reduction techniques. For example, Bradley etal^^ obtained fairly uniform palladium (Pd) particles of 2.0-2.5 nm in mean diameter by reducing a Pd complex, bis(dibenzylidene acetone)palladium, with H2 or CO gas as a reducing agent in dichloroethane in the presence of PVP at 25 "^C. It is noteworthy that they suggested a possibility of amorphous structure of Pd particles of mean diameter 2.0 nm prepared in a few seconds with CO gas, while those of mean diameter 2.5 nm prepared in 1 h with H2 gas were found to be fee crystals, as revealed by electron diffraction. Also, their results of the effect of H2 pressure on the final particle size may suggest that an excessively high concentration of reductant and a too long aging give a chance of significant coagulation. They found a clear difference in the IR spectrum of CO adsorbed to Pd particles of different sizes, suggesting an increasing contribution of edges and vertices of the crystallites with decreasing particle size. Moreover, they found no significant effects of the molar ratio of PVP in monomer unit to metal, ranging from 10 to 30, and the molecular weight of PVP, from 10,000 to 90,000, on the mean particle size and size distribution. Finke et al?^ prepared fairly uniform iridium (Ir) particles of ca. 2.5 nm in mean diameter by reducing a [Bu4N]5Na3[(l,5-COD)Ir(P2Wi5Nb3062)] complex with H2 gas in a mixed solvent, cyclohexene-acetone, at 22 °C, in which the polyanion, P2W^5Nb3062^' ^ ^ ^he cation, BU4N*, worked as a stabilizer of the produced Ir particles. They studies the formation mechanisms of nanoparticles of noble metals using the new system. On the other hand, Reetz et al?^ developed a new system for the preparation of nanosized transition metal clusters, such as palladium (Pd) and nickel (Ni), based on electrochemical reduction of metal ions, furnished from the sacrificial anode of the bulk metal, at the interface of a platinum cathode in a dry oxygenfree mixed medium, acetonitrile/tetrahydrofuran (4:1), in the presence of tetraalkylammonium stabilizers, such as ^N(n-C4H9)4, *N(n-C8Hi7)4, and

218

PREPARATION

*N(n-Ci8H37)4, which served as a supporting electrolyte as well. Though a very sharp size distribution cannot be expected in this system because of the lack of the condition for separation between nucleation and growth stages, the system has many advantages, such as the easy control of the mean particle size by variation of the current density, the high productivity, and the absence of undesired by-products. In general, it is not an easy task to prepare so ideally uniform nanoparticles as to be called monodispersed particles, because the relative standard deviation of the size distribution of monodispersed particles is reduced through the growth process of the stable nuclei, having a large relative standard deviation as a result of the concurrent growth with their continuous generation during the nucleation period. In other words, the formation of nanoparticles is characterized by the great proportion of the nucleation stage against the weight of their growth stage. In this case, it seems necessary to introduce an additional mechanism for the improvement of the uniformity of nanoparticles; e.g., automatic cessation of growth at a certain size level by adsorption of a designed stabilizer which needs some time-lag for complete suppression of the particle growth after nucleation, as suggested in chapter 6 (section 6.5). Such a mechanism, however, may have partly been functioning unintentionally even in existing homogeneous systems. b) Partial Reduction Andreasen etaL^^ prepared monodispersed cubic copper(I) oxide (CU2O) particles of diameter about 2 jmi by reducing cupric tartrate in Fehling's solution with sugars such as glucose, lactose, and dextrin at temperatures above 60 °C. A hydrolysis reaction proceeds simultaneously in this process. Similarly, McFadyen and Matijevic"^ prepared monodisperse polyhedral CU2O particles of 0.3 - 1.6 tim by reducing a cupric tartrate complex with glucose. CU2O particles thus prepared were reduced to spherical copper (Cu) particles of mean diameters 0.46, 0.62, and 1.26 \xm with hydrogen gas at temperatures in 69 - 111 °C and flow rate of hydrogen 400 cm^ min"^^^ Also, Hamada et al^^ prepared octahedral and star-like CU2O particles from l,2-ethanediaminocopper(II) complex by partial degradation of 1,2ethanediamine to aldehyde in the absence and presence of hexamethylenetetramine, respectively, at pH 11 and 100 °C for 30 min. Figure 7.3b shows a SEM of thus prepared star-like CU2O particles. McMurray''^ prepared monodispersed spherical ruthenium dioxide hydrate (Ru02tx:H20) particles in a range of the mean diameter from 50 to 160 nm by autocatalytic reduction of 7.52 x 10"^ mol dm'^ aqueous ruthe-


219

nium tetroxide (RUO4) by solvent water at pH 5.5-6.5 from their seeds of a mean diameter 40 nm, which were prepared by homogeneous nucleation with NaN02 stoichiometrically equivalent to 3 % for reduction of total Ru^"*^ to Ru"*"^. The reaction was performed at 20 °C for 20-60 h without agitation except for the moments of the admixing of the reducing agent and seeds. Since no appreciable reduction of RUO4 is observed in the absence of both NaN02 and RuOj !x:H20 seeds, the nucleation and growth stages are ideally separated in this system. c) Oxidation Chiu and Meehan"^ precipitated uniform sulfur (S) particles by oxidizing hydrogen sulfide in aqueous solutions with air. The growth kinetics was found to be a diffusion-controlled one, so the size divStribution seems to have been narrowed as the sulfur particles grew. Joekes et al^^ obtained monodisperse ferric hydroxide (Fe(0H)3) particles from iron pentacarbonyl oxidized by hydrogen peroxide in ethanol solutions. Hamada et al^^ prepared spheroidal monodispersed hematite (a-Fe203) particles of 0.35 tim in mean diameter with a relative standard deviation 9 % from 2,2'-bipyridineiron(II) complex by oxidation of Fe(II) ions with potassium nitrate and subsequent hydrolysis of Fe(III) at pH 2.2-2.4 and 100 °C for 24 h, where [FeCl3] = 1.0 x 10"' mol dmr\ [bpy] = 3.0 x 10"^ mol dm-^ [HCl] = 6.0 x 10"^ mol dm-\ and [KNO3] = 5.0 x 10"^ mol dm'^ Since magnetite (Fe304) particles are formed from Fe(II), in equilibrium with ferrous hydroxide, by oxidation with KNO3 in neutral or alkaline media,"^^ the preferential formation of a-Fe203 in their study seems to be due to the low pH around 2.3 and the exceedingly low concentration of free Fe^^ in equilibrium with 2,2'-bipyridineiron(II) complex, where the concentrations of OH" and Fe^"^ may remain below the levels for the solubility product of Fe304, though sufficient for the formation of a-Fe203 ([Fe^*][OH']^ < Kp{K,^'f where X / = [Fe^1[Fe^1^[OH1« for Fe304; ^ = [Fe^1[OH-f for a-Fe203). The rate-determining step of the total reaction is supposed to be the oxidation process of the low concentration of free F^* ions to Fe^^, as these authors speculated. The spherical shape may result from the shape control by adsorbed 2,2'-bipyridine, liberated with the formation of hematite. 7.2.2. Precipitation by Poor Solvents LaMer and Dinegar"*^ prepared monodisperse sulfur (S) particles from

220

PREPARATION

ethanol solutions of sulfur slowly diluted up to the critical supersaturation with water. However, this system is not ideally homogeneous, since the locally high supersaturation in the feed zone of water causes precipitation of sulfur, and thus uniform dilution is unattainable by this method. In fact, the concentration of sulfur in the ethanol and the addition rate of water were found to have a crucial influence upon the uniformity of the final product, showing that rapid nucleation and growth associated with coagulation of the generated particles happened in the local zone. As a rule, in such a quasihomogeneous system, vigorous agitation as well as strict control of the addition rate of the poorer solvent is needed for quick dissipation of the local high density of particles which leads to their coagulation. If these factors are properly controlled, the nucleation stage in the local zone during the addition of a poor solvent and the subsequent growth stage under a relatively low supersaturation in the uniform solution after the addition of the poor solvent will be separated, and thus uniform particles will be produced. Also, the self-sharpening of size distribution is expected in the sulfur particle system owing to the diffusion-controlled growth kinetics. 7.2.3. Precipitation by Cooling Hamada et al^^ prepared uniform polyhedral gennanium(IV) dioxide {GtO^ particles of ca, 2.0 (im in mean diameter by reducing temperature of an ethanolic solution (30 vol %), contaming 8.4 x 10"^ mol dm"^ Ge(IV) and 1.7 mol dm"^ HCl, from 50 °C to 10 °C and succeeding aging for 3 h. Figure 7.4 shows a SEM of so-prepared Ge02 particles."*^ It seems that in this system they previously prepared precursor complex of Ge02 at 50 °C by hydrolysis of Ga(IV) ions and made the system supersaturated with the precursor through reducing temperature to 10 °C. This method may be

MS"^ ^ Fig. 7.4. SEM of Ge02 particles prepared by cooling an ethanolic solution (30 vol %), containing 8.4 X 10-2 J^QJ ^^-3 - # ^ ^ VÂi IO|im i

Qg(jy^ ^^^

^j

mol dm"^ HCl, from 50 ""C to 10 ^'C and succeeding aging for 3 h. (From Ref. 49.)


221

useful for synthesis of uniform particles of a relatively high solubility. 7.2.4. Direct Reaction of Ions If it is possible to separate the nucleation and growth stages using the supersaturation difference between the feed zone of reactants and the uniform solution after the nucleation, we may expect the formation of monodisperse particles, even by direct addition of reactants. Andreasen et al.^^ prepared monodispersed spherical particles of barium sulfate (BaS04) of 2-3 |xm in mean diameter by mixing BaCl2 solution containing HCl with an equal volume of H2SO4 solution containing HCl through quickly pouring the two solutions into the third beaker at the same time at 20 °C, where typical compositions of these solutions were 1/18 mol dm"^ BaCl2 + 10/3 mol dm"^ HCl (30 cm^) and 1/18 mol dm"^ H2SO4 + 10/3 mol dm"^ HCl (30 cm^), respectively. Figure 7.5 shows a TEM of BaS04 particles thus prepared. This unique way of mixing served to a great extent in producing the uniform particles. The hydrochloric acid was added for increasing the solubility of barium sulfate in order to increase the final particle size. This is in accord with the rule of size control of monodispersed particles, since the increase in solubility leads to the increase in the volumic growth rate, TJ^, at the end of the nucleation (see section 1.4). They also found that the final size of barium sulfate particles was dramatically reduced by replacing the water increasingly with propylalcohol(Le., fi-om 3 \Jim to ca. 0.3 pun with increasing proportion of alcohol from 0 to 60 vol %). This seems to be due to the decrease in i)^ by the decrease in solubility

Fig. 7.5. Monodispersed spherical BaS04 particles prepared by mixing a BaCl2 solution with an equal volume of a H2SO4 solution through pouring the two solutions simultaneously into the third beaker at 20 °C. (From Ref. 39.)

222

PREPARATION

of barium sulfate. Petres et al^^ studied the effect of adsorptives, such as nonionic surfactant Triton X-100 (alkyl aryl polyether alcohol), anionic surfactant Aerosol MA (dihexyl sodium sulfosuccinate), and complexing agents (citrate and EDTA), on the morphology of BaS04 particles prepared on the basis of this method of Andreasen et aL, and found that both Triton X-100 and EDTA yielded uniform ellipsoidal particles with sizes decreasing with increasing content of these additives, -whilt Aerosol MA gave rectangular particles with jagged surfaces and citrate produced spherical particles under suitable conditions. Ginell et al^^ prepared monodisperse silver chloride (AgCl) particles by mixing anunonium chloride and silver nitrate in 95 % ethanol. The particles were stabilized by the negative charges of the adsorbed chloride ions in an excess of chloride. Herak et al^^ precipitated monodisperse lead iodate (Pb(I03)2) particles of about 100 imi by slow addition of a dilute potassium iodate solution to a dilute lead nitrate solution. They also obtained monodisperse particles of lanthanum iodate (La(I03)3) in the same way.^^ Wilhelmy and Matijevic^'^^ obtained monodisperse spherical particles of ferric phosphate (FeP04) by mixing a ferric perchlorate solution (8.0 x 10"^ mol dm'^) and a phosphoric acid solution (3.0 x 10"^ mol dm"^), followed by aging at 40 "^C for 24 h. Uniform spherical crystalline particles of aluminum phosphate (Al(OH)2H2P04) were also obtained by mixing acidic solutions of A1(N03)3 and Na2HP04, foUowed by aging at 98 °C.^^ In these two cases for the formation of phosphate particles, some hydrolysis process of the metal ions must be involved, as is obvious from the compositions of the intermediate complexes^"* and the final product.^^ Zhong and Matijevic^^ prepared spherical zinc oxide (ZnO) particles of mean diameters from 0.2 to 1.5 jim with a relatively narrow size distribution (a « 20 %) by continuous double jet addition of 100 cm^ each of 2.0 x 10"^ mol dm'^ ZnN03 and 1.6 mol dm"^ triethanolamine (base) at a flow rate in 14-600 cm^ min"^ to 100 cm^ of water at 90 °C under stirring. They found that the spherical particles were polycrystals consisting of much smaUer subcrystals ranging from 25 to 63 nm. Since the subcrystal size decreased, but the particle size increased, with increasing addition rate of the reactants, there is no doubt that the particles were grown by aggregation of the continuously generated primary particles with mixing the reactants. The preferential aggregation of the primary particles to the growing particles may be elucidated by the slope for the diffusion of the primary particles formed around each growing particle (see section 6.2 in chapter 6). In order to


223

minimize the coagulation between primary particles and between growing particles, the conditions of ionic strength, reactant concentration, and temperature were carefully chosen. Hsu et al^^ prepared monodispersed spherical magnesium fluoride (MgF2) and cubic sodium magnesium fluoride (NaMgF3) particles of about 1 [im in diameter by aging a mixed solution of NaF and MgCl2 in a concentration range from 0.01 to 0.3 mol dm"^ for each at 80 °C for 3 h. The MgF2 particles were obtained at a low concentration of fluoride ions, while the NaMgFg particles precipitated at a stoichiometrically sufficient concentration of fluoride ions. Since only a small amount of solid precipitated on mixing both reactants at room temperature despite the much higher concentrations of these reactants than usual homogeneous monodisperse systems, there seems to be a significant contribution of fluoride complexes of Mg^^ ions for the formation of these monodispersed particles. However, as the detailed formation mechanism thereof is unknown, this system has been classified tentatively into the group of the direct reaction of ions. Schultz an Matijevic^^ prepared nanoparticles of palladium sulfide (PdS) by continuous double jet mixing of PdCl2 or Na2(PdCl4) and Na2S. They found that the particle size was 20-30 nm in mean diameter obtained in acidic media (pH = 2-3), but 2-5 nm in alkaline media, probably due to the high equilibrium concentration of sulfide ions S^' by dissociation of H2S and HS" in the alkaline media (pH = 10-12). Cationic surfactant, cetyl trimethyl ammonium bromide (CTAB), was found to be useful for stabilizing the small particles prepared in the alkaline media. In all of the quasi-homogeneous systems, including the direct reaction of ions and the precipitation by poor solvents, the strict control of the concentrations of reactants, the addition rate of reactants, and the agitation rate is essential for the formation of uniform particle with high reproducibihty. 7.2.5. Dissociative Reaction of Inorganic Complexes Hamada et al^ prepared spherical particles {ca. 5 pmi) and monocliniclike particles {ca. 28 |im) of manganese(II) carbonate (MnC03) with a relatively narrow size distribution by mixing dilute solutions of MnS04 and NH4HCO3 at 50 °C for both the particles, but in the presence of a relatively high concentration of sulfate ions, ca. 1 mol dm'\ for the latter. In this system, carbonate ions may be reserved in the complex anions HCO3', but the reaction was almost instantaneous in the absence of the high concentra-

224

PREPARATION

tion of sulfate ions whereas it took about 7 h for initiating the precipitation of MnCOg in the presence of 1 mol dm~^ (NH4)2S04. Obviously, sulfate ions have a strong effect on the formation of the characteristic crystal habit. They converted these particles into Y-manganese(IV) oxide (Mn02) with the same shapes as the original carbonate particles by heating with oxygen at relative humidity 50 % at 400 °C for 6 h. Kim and Matijevic^^ prepared submicrometer-size amorphous manganese niobate (MnNb206) and potassium niobate (KNb03) spheres with narrow size distributions by the reaction of the corresponding cations with niobium oxo-hydroxide complexes in aqueous solutions at pH 8-9 over the temperature range of 25-70 °C, and crystallized the so-obtained powders by calcination at 800-850 °C for 30 min. Perez-Maqueda and Matijevic^^ prepared crystalline spherical and octahedral particles of cesium tungstophosphate (CS3PW12O40) of a mean diameter 0.9 ^m and amorphous spheres of thorium tungstophosphate of a mean diameter 0.5-0.6 [xm with a relatively narrow size distribution by a direct reaction of 8 x 10"^ mol dm"^ tungstophosphoric acid with 2 x 10"^ mol dm"^ CsCl or with 2.5 x 10"^ mol dm"^ Th(N03)4 at 90 °C for 1 h (final pH = 3.5 for the former and 2.4 for the latter), immediately after mixing the corresponding reactants at room temperature. The octahedral Cs3PW^204o particles were obtained in the presence of anionic surfactant AVANEL S150 (0.2 g dm"^; PPG Ind.). Although these reactions appear to be direct reactions between the corresponding cations and tungstophosphate anion, the actual concentration of the latter in equilibrium with protonated complexes may be extremely small and released gradually from the complexes at 90 °C, in view of the slow reaction at room temperature. Similarly, Koliadima et al^^ prepared submicrometer-size amorphous spheres of zirconium tungstosilicate (ZrSiWi2O40-26ZrO2 5cH2O) and thorium tungstosilicate (ThSiWi204o aH20) by reaction of ZrCl4 or Th(N03)4 with heteropolytungstosilicic acid (H4SiWi204o)7.2.6. Dissociative Reaction of Organic Complexes Chiu prepared monodisperse crystalline particles of metal sulfides, such as lead sulfide (PbS; cubes; ca. 100 A),^ cupric sulfide (CuS; hexagonal bipyramids; ca. 200 A),^ and zinc sulfide (ZnS; multifaceted spheres; 0.1 0.4 (xm),^^ by introducing hydrogen sulfide gas into dilute acidic solutions of the EDTA complexes of the corresponding metal ions (10""* - 10""^ mol dm"^) for several minutes at room temperature. EDTA appears to prevent both nucleation and coagulation during the


225

particle growth by shielding the metal ions. Meanwhile, the EDTA complexes liberate metal ions, by degrees, with the progress of particle growth. The use of chelating agents is one of the most promising techniques for producing uniform particles, since it is relatively easy to meet all the requirements for monodisperse particle formation described in chapter 6. However, even if we use chelating agents, it is generally impossible to produce uniform particles in highly concentrated solutions of chelates such as those of the order of 10"^ mol dm~^ or more, due to the tremendous coagulation. Nevertheless, this difficult issue has been cleared by applying a new synthetic method named the "Gel-Sol method" originally developed for the preparation of monodisperse hematite (a-Fe203) particles (see section 7.3.1). Namely, gelatin tumed out to be a powerful anticoagulant acting as a protective colloid or gel-network former in the synthesis of monodisperse metal sulfide particles in condensed chelate systems, including cadmium sulfide (CdS),''"'^ zinc sulfide (ZnS),^''' lead sulfide (PbS),'' and cupric sulfide (CuS).^^ Figure 7.6 shows a SEM of so-obtained CdS particles and their close-up view. One of the advantages of gelatin over other anticoagulants is that it can be removed readily by the use of a very small amount of proteinase, if needed. In these condensed chelate systems, many kinds of chelating agents were used, such as ethylenediamine-N,N,N\N'-tetraacetic acid (EDTA), nitrilotriacetic acid (NTA), L-aspartic acid (AA), trimethylenediamine (TMD)y NjN-dimethylethylenediamine (DMED), diethylenetriamine (DETA), triethylenetetramine (TETA), and tris(2-aminoethyl)amine (TAEA).^^ The criteria for the choice of chelating agents were the stability constant of each chelate and the release rate of metal ions. If the stability constant is too low, as less than 10^°, the separation of the nucleation and growth stages is generally difficult, due to the excessively high supersaturation. On the other hand, if the stability constant is as high as 10^^, the reaction rate is practically too low except for the CuS systems. For the chelating agents giving intermediate stability constants, the release rate of metal ions should be so low as to be able to achieve a low steady concentration of free metal ions below the critical supersaturation level during the growth of the metal sulfides. Since chelates having lower stability constants give the higher supersaturation in the nucleation stage, they normally yield the smaller particles. This can be used for size control of the products. Another important aspect of these systems is the role of the highly concentrated ammonia included in all of them as an accelerator of the

226

PREPARATION

0.5 urn Fig. 7.6. SEM of the uniform CdS particles (a) and its close-up view (b), prepared by aging a condensed EDTA-Cd system at 60 °C for 8 h [0.24 mol dm"^ TAA, 0.2400 mol dm"^ Cd(0H)2, 0.2424 mol dm"^ EDTA- 2Na, 1.6 mol dm"^ CH3COONH4, 0.48 mol dm"^ NH3, 1 wt% gelatin]. (From Ref. 67.)

growth of the metal sulfides. As has been described in section 3.2, ammonia has a strong effect in increasing the growth rate of silver bromide by increasing the apparent solubility of AgBr. On this analogy, the significant promotion of the growth of the metal sulfides may be mainly due to the increase of their apparent solubility. Since the stability constants of ammonia complexes are generally much lower than typical chelates of EDTA, NTA, etc., they can promptly release metal ions with the consumption of free metal ions for particle growth. Hence, ammonia complexes of metal ions play an important role of the accelerator of particle growth as an intermediary of metal ions between a chelate of a high stability constant and the growing particles, without increasing the supersaturation ratio. In the absence of ammonia in the EDTA-Cd system, on the other hand, the final product was polydispersed particles with a yield of only ca. 2 % after aging at 60 °C for 8 h, in contrast to the highly monodispersed product with the yield of more than 90 % in the presence of ammonia. The production

227


Without Ammonia

With Ammonia

Cd-EDTA

Dissociation

Renucleation

Cd(NH3)„^* Cd-EDTA

Dissociation

Nucleation

9.!l!^9i!fl§MP!!!j?^^^^ Growth

t Growth

Fig. 7.7. Role of the ammonia complexes for the formation of monodisperse particles of CdS in a EDTA-Cd system. (From Ref. 68.) of the polydisperse particles in the absence of ammonia is a result of the high supersaturation ratio of free Cd^* ions above the critical level, caused by the exceedingly low growth rate of CdS particles. In this case, the ratedetermining step for the formation of CdS is the deposition process of the solute, in contrast to the case with ammonia in which the release of Cd^^ from the EDTA-Cd complex is the rate-determining step. Figure 7.7 shows the role of the ammonia complexes for the formation of monodisperse particles of CdS in the EDTA-Cd system.^^ In all of these systems, thioacetamide (TAA) was commonly used as a source of sulfide ions, which was found to be in the following chemical equilibrium with a very low concentration of sulfide ions:^° CH3CSNH2

CH3CN + 2H" + S^

(7.2.1)

When the S^" ions were consumed by the reaction with Cd^^ ions, TAA was found to release S^" ions so fast that the rate-determining step of the total reaction was the release process of Cd^* ions from the EDTA-Cd chelate. Hence, the formation rate of the CdS particles was completely determined by the first-order release rate of Cd^^ ions from the EDTA-Cd chelate. All of these metal sulfide particles except lead sulfide are polycrystalline

228

PREPARATION

spherical particles consisting of much smaller randomly oriented subcrystals, while lead sulfide particles are of a rectangular monocrystalline form. Hence, the polycrystalline particles are grown through a repeated nonepitaxial nucleation of the surface nuclei followed by their limited growth. In this case, the surfaces of the spherical secondary particles serve only as triggers for the surface nucleation, like heterogeneous nucleation. For the CdS particles, the size of the subcrystals of each secondary particle increased with the progress of their growth, as revealed by high-resolution electron microscopy on the ultrathin sections of the secondary particles prepared with a microtome.^^ This fact suggests that the nucleation rate on the surfaces of the secondary particles goes down more rapidly with the lowering supersaturation than does the growth rate of the subcrystals from these surface nuclei. In other words, the size of the subcrystals is determined by their relative growth rate against the surface nucleation rate. In the cupric sulfide systems, a high stability constant of a chelate does not necessarily mean a slow release of metal ions, due to the extremely high rates of both association and dissociation of the chelate. For example, the reactions of chelates, Cu(TMD)2^* and Cu(DETA)2^*, with TAA finish within 2 min at 25 °C to yield rather small CuS particles of ca, 40 to 50 nm, despite the respective high stability constants, 10^^^ and 10^^-^, which are comparable to, or even much higher than, the stability constants of EDTA chelates of the other kinds of metal ions, such as Cd'^, Zn"^, and Pb^*, which are much slower in releasing these metal ions. Interestingly, the internal sulfide ions of the produced CuS particles covered with an adsorption layer of gelatin are preferentially oxidized by oxygen with the aid of ammonia and dissolved into the solution phase with Cu^^ ions, yielding monodisperse hollow particles of CuS.^^ From the dramatic effect of ammonia on the growth rate of metal sulfides, one may readily notice that the growth of the polycrystalline spheres of metal sulfide in the metal chelate systems proceeds with deposition of solute and not with aggregation of primary particles, since there is no reason for accelerated formation of primary particles by ammonia. This conclusion can be confirmed from the distinct separation between the nucleation and growth stages, as clearly shown by Cdpotentiometry combined with electron microscopy, and from the fact that new nuclei generated during the growth stage always become additional growth centers leading to a polydispersed product.^^ Incidentally, the wSeeding analysis as a probe for distinction of the growth mechanism does not work in this system, because the rate-determining step of the particle


229

growth is the release of metal ions from metal chelates and not the deposition process of the solute including its diffusion and surface reaction (see section 9.10 in chapter 9). Hamada et al prepared a number of uniform metal (hydrous) oxide particles from metal chelates in dilute aqueous solutions by forced hydrolysis of metal ions, gradually released from the chelates, at a high temperature such as 80 to 100 ""C;^^ e.g., double spheres of hematite ( a Fe203) of ca. 4.2 |xm in length from glycinatoiron(III) complex,^^ amorphous aluminum hydrous oxide (A1(0H)3) spheres (d = 0.45 ûn; a = 9 %) from acetylacetonato-aluminum complex,^"* rod-like monoclinic cupric hydroxysulfate (Cu4(OH)6S04) via polydispersed platelets of monoclinic cupric hydroxide sulfate hydrate (Cu4(OH)6S04-1120) from 1,2-ethanediaminocopper(II) complex at pH 6 in the presence of sulfate ions,"*^ spheroidal poly crystalline indium hydroxide (In(0H)3) particles (d = 0.31 jmi; a = 12 %) from indium 2-aminobutyrato complex,^^ and crystalline lanthanum(ni) hydroxycarbonate spheres (La(C03)0H) (d = 2.8 [xm; a = 12 %) from 1,2-ethanediamine-lanthanum complex.^^ The metastable platelets of Cu4(OH)5S04 -1120 are precipitated prior to the precipitation of the rod-like Cu4(OH)5S04 and are recrystallized to the latter with aging. It seems that the initial supersaturation is kept so high as above the critical level of the nucleation for the preceding platelet particles that they are polydispersed, while the supersaturation for the rod-like particles, determined by the solubility of the platelet particles, is kept sufficiently below the critical level for the nucleation so that the rod-like particles are nearly monodispersed. Thus, it seems reasonable to consider that the nucleation of the rod-like particles has been finished by the end of the precipitation of the platelets of Cu4(OH)6S04 ^ 2 0 . On the other hand, in the system of La(C03)0H, the carbonate ions are furnished by partial degradation of 1,2-ethanediamine via formation of aldehyde by virtue of a mild oxidant, nitrate ions, present as a counter ion of lanthanum. The In(0H)3 and La(C03)0H particles were converted to the corresponding oxides, indium oxide (^263) and lanthanum oxide (La203), without deforming the original shapes. Fujishiro et alJ^ prepared submicrometer or micrometer lanthanide(III) phosphate particles of a relatively narrow size distribution (spheroidal ones for La, Ce, Nd, Sm, Eu, Ho, and Tb; elhpsoidal ones for La, Ce, Nd, Sm, and Eu; rod-like ones for Ho and Tb), by thermal dissociation of 8 x 10"-^ mol dm'^ EDTA complexes of these metals in the presence of NaH2P04 at temperatures from 100 to 200 °C, but mainly at 150 °C, for 2 h in nearly neutral or acidic media. In this reaction system the reduction of the stability

230

PREPARATION

constants of the EDTA complexes with increasing temperature is utilized, and thus temperature control is deemed to be a key factor for the formation of uniform particles. Chittofrati and Matijevic^^ prepared uniform crystalline zinc oxide (ZnO; zincite) of different shapes, such as ellipsoids, spherulitic intertwins of ellipsoids, and spheroids, by forced hydrolysis in the presence of ammonia, ethylenediamine, or triethanolamine, while needles or spherulitic intertwins of needles in the presence of KOH or NaOH instead of the above bases. Andres-Verges et aV^ also obtained zinc oxide particles of different morphologies such as needles, their spherulitic intertwins, and prisms by forced hydrolysis of zinc ions in the presence of hexamethylenetetramine. There may be several interpretations for the formation of the spherulitic intertwins of needles. It may be possible to elucidate that they are formed as a result of random aggregation of nuclei and subsequent radial growth in the directions of the c-axes of the individual crystallites of the initial aggregates. This elucidation is not only congruent with the principle of monodispersed particle formation, but also implies a possibility of controlled aggregation of the nuclei by intentional regulation of ionic strength to produce uniform spherulites. Since both metal ions and hydroxide ions are reserved in chelates and water, respectively, in these systems, one can make the total content of the metal ions higher than in ordinary forced hydrolysis processes in which only hydroxide ions in water are reserved. Kim and Matijevic^ prepared uniform submicrometer amorphous spheres of calcium titanium peroxo-hydroxide (CaTi308(OH)4) and lead niobium peroxo-hydroxides (Pb3(H02)3Nb40io(OH)3 •9H2O; Pb5>fb60i7(OH)i4) by replacing peroxotitanium in a peroxotitanium-NTA chelate with a Ca^^ ion slowly added at 25 or 50 °C for the former, and by replacing hydroxoniobium (Nb(OH)3^0 in a Nb(0H)3-EDTA^" complex with Pb^^ ions or by replacing Pb^^ and Nb03' ions in a mixed chelates of Pb-NTA' and Nb03-NTA^" with Ca^^ ions at 25 °C for the latter. Although the transition metal ions are shielded by chelating agents, there may be some possibility of continuous nucleation near the outlet of the slowly introduced solution of metal ions, followed by dissolution of the transient nuclei as in the controlled double-jet system of silver halides (see sections 1.5 and 7.3.2). The so-obtained amorphous particles were converted on calcination to composite crystalline oxides such as calcium titanate (CaTi03) + titania (Ti02) and lead niobates (Pb3Nb40i3; Pb3Nb208). Uniform particles of silver cliloride (AgCl) and silver bromide (AgBr) were formed by the reaction of existing halide ions with silver ions


231

gradually released from the gelatin reservoir with lowering pH, based on the hydrolysis of diethylsulfate (see section 1.4.2).^^ 1.2J. Dissociative Reaction of Organic Compounds Matijevid and Wilhelmy^^ prepared uniform spherical polycrystalline particles of cadmium sulfide (CdS) by reaction of Cd^^ ions with thioacetamide (TAA) in a dilute acidic media (pH < 2). The reaction finished within 1 h at 26 °C. They used seed crystals of CdS to promote the uniformity of the final product, and analyzed the growth kinetics using Nielsen's chronomal. They also prepared zinc sulfide (ZnS; polycrystalline spheres),^ lead sulfide (PbS; monocrystalline tetragonal galena),^"^ cadmium zinc sulfide (CdS-ZnS; amorphous and crystalline spheres),^ and cadmium lead sulfide (CdS-PbS; crystalline polyhedra),^ in a similar manner. Figure 7.8 shows a SEM of so-prepared PbS particles. The authors assumed that the precipitation of these metal sulfides was controlled by the hydrolysis reaction of TAA promoted by protons in the acidic conditions. However, the hydrolysis of TAA observed in acidic and alkaline ranges is a much slower process than observed in the precipitation of these metal sulfides,^^'^^" ^^ and it may not be accelerated by consumption of S^" ions because of its irreversible nature. In addition, the reaction virtually finished with a great part of the starting metal ions and TAA left unreacted, suggesting an established equilibrium of the entire system. Also, it has already been verified that the probability of direct reaction of TAA with metal ions is zero, or at least negligible, from its strong dependence of pH in reactivity.^° Thus, there seems to be another possibility that the main path is the release

Fig. 7.8. PbS particles prepared by the reaction of Pb^* ions with TAA in a dilute acidic medium (pH < 2). (From Ref. 84.)

232

PREPARATION

of S^~ ions from TAA according to the aforementioned reaction scheme with the production of acetonitrile in Eq. (7.2.1), which halts when TAA reaches equilibrium with the remaining metal ions. Since the release rate of S^" in the reversible process of Eq. (7.2.1) in a low pH range is low/" it can be the rate-determining step for the formation of metal sulfides in place of the hydrolysis of TAA. In fact, this hypothetical conclusion seems to be consistent with another experimental result of the same authors;^^ Le., the significant reduction of both the growth rate and the final mean size of the CdS particles on addition of TAA to the seed suspension, revealing some instantaneous renucleation. Also, it seems obvious that the deposition process of the solute, including its diffusion and surface reaction, is not the rate-determining step of the entire process from their additional experimental fact that the consumption rate of the remaining Cd^^ ions in the seed suspension is virtually unaffected by the increase in the added amount of TAA, despite the significant increase of the effective nuclei, where the added amounts of TAA were small enough as compared to the large amount of the remaining TAA in the seed suspension. In any case, it is of importance, in general, to clarify the rate-determining step prior to Nielsen's chronomal analysis, since if the precipitation is controlled by the generation of monomer source, preceding to the diffusion of the monomer source to the particle surfaces and its reaction on the growing particle surfaces, the application of Nielsen's chronomal analysis is meaningless (see section 2.6.7). Submicrometer uniform crystalline spheres of silver-doped zinc sulfide (ZnS:Ag) were prepared by aging 0.04 mol dm"^ Zn(N03)2 and 2.80 x 10"^ - 1.68 X 10"^ mol dm"^ AgN03 with 0.4 mol dm^^ TAA for up to 100 min at initial pH 1.52 and 73 °C.^ The authors found that the final number concentration of the particles decreased with increasing content of silver ions, whereas the total reaction rate was virtually unaffected by the significant difference in the total surface area of the particles. In fact, the final particle diameter increased fi-om 0.3 to 1.1 [im with increase in the content of silver ions fi-om 5.6 x 10"^ to 1.68 x 10'^ mol dm'^ Since [Ag*]/[Zn2"]^^ » ( A ; / ^ ^ X P ^ ' ^ - {lO-'^'llO-^f^ = W-'^' at 25 °C where A,^ is the solubility product, Ag2S is deemed to precipitate first even at 73 °C. These facts may suggest a possibility that the Ag2S nuclei reduce the number of the ZnS particles by heterocoagulation with the ZnS nuclei in the nucleation stage of the latter, instead of working as centers for heterogeneous nucleation of ZnS. It is also suggested the total reaction is governed only by the dissociation rate of TAA at the low pH. Hence, Nielsen's


233

chronomal analysis is inapplicable to such systems. Incidentally, the resulting composite particles in the ZnS:Ag system are expected to have a core-shell structure with a core rich in Ag2S content. Haruta et al^^ prepared spherical particles of molybdenum sulfide and cobalt sulfide with a narrow size distribution by reaction of dilute ammonium orthomolybdate or cobalt(II) acetate with sulfide ions liberated from thioacetamide, as a reservoir of S^" ions, in weakly acidic media. These particles had no distinct crystal structure, as shown by X-ray diffractometry. These materials are useful as hydrodesulfurization catalysts. In these systems, TAA was assumed to release sulfide ions by hydrolysis accelerated by hydrazine. Since the concentration of S^" in equilibrium with TAA is extremely low despite the exceedingly high release rate constant of S^~ in the reversible reaction of Eq. (7.2.1), this assumption is reasonable if the concentrations of the free metal ions are too low for the nucleation of the metal sulfides. However, if the role of hydrazine is other than an accelerator of the hydrolysis of TAA, and if the deposition rate of the metal sulfide monomers or the release rate of metal ions from the metal ion complexes, such as orthomolybdate or cobalt acetate, is the rate-determining step of the precipitation, there is a possibility of the path of Eq. (7.2.1) for the release of S^" ions. One method to differentiate these reactions of TAA may be the analysis of the by-product of TAA, since CH3COOH is the main by-product of the hydrolysis, while CH3CN is produced in the reversible reaction of Eq. (7.2.1). Gobet and Matijevic^ produced monodisperse particles of cadmium selenide (CdSe) and lead selenide (PbSe) by dissociation of selenourea in solutions of the corresponding metal salts. As with the corresponding metal sulfides, the cadmium selenide particles were spherical polycrystals and the lead selenide particles were of a cubic symmetry. The dissociation equilibrium is written as^^'^ (NH2)2CSe ^ NH2CN + IW + Se--

(7.2.2)

7.2.8. Decompositional Reaction of Compounds LaMer and Bames^^ obtained monodisperse sulfur (S) particles by decomposition of thiosulfate with acid. The particles were so exceedingly uniform that they were used as a material to test the light scattering theory.^^-^^ Ottewill and Woodbridge^^ obtained monodisperse silver bromide (AgBr) particles by reducing BTO{ with nitrous acid at pH 3 in the presence

234

PREPARATION

of silver ions. Andreasen et al?^ prepared monodisperse tetragonal mercury(II) iodide (Hgy crystals of ca. 10 tmi in mean diameter by reducing sodium iodate (NaI03) with sodium sulfite (Na2S03) to release I" ions slowly (IO3" + 3S03^- -* r + 3S0/-) in the presence of HgCl2 at pH 6.4. Similarly, they obtained monodisperse thallium(l) iodide (Til) particles of much smaller size than the corresponding mercury iodide particles. Andreasen etal?^ prepared monodispersed ellipsoidal particles of barium suifate(BaS04; rhombic crystal) of 3-4 [xm in mean diameter by oxidation of sodium thiosulfate (Na2S203) with hydrogen peroxide (H2O2) to release SO/- ions gradually (2S203^- + 4H2O2 -* SO/" + S3O/- + 4H2O), in the presence of Ba^^ ions. When a citrate salt was present in such a system, the particle size was reduced with increasing content of citrate probably due to the strong adsorption of citrate ions. According to a transmission electron micrograph of small ellipsoidal particles {ca. 0.14 |xm) in their paper, the particles appear to have a porous structure. Takiyama^°° prepared monodisperse spindle-type particles of BaS04 by decomposing tht EDTA-Ba complex with hydrogen peroxide, as shown by their TEM in Fig. 7.9. In this reaction, the initial concentration of the

l/zm —if

1

Fig. 7.9. Monodispersed spindletype BaS04 particles by decomposing the EDTA-Ba complex with hydrogen peroxide at 80 °C for 40 min, where the initial pH was adjusted to 10 by a NH3NH4CI pH buffer at room temperature. Initial composition: 4.4 x 10"^ mol dm"^ EDTA-Ba, 4.4 x 10"^ "^^^ ^^'^ (NH4)2S04, and 6 % H2O2. (From Ref. 100.)


235

EDTA-Ba complex is a decisive factor in the separation of the nucleation and growth stages. Petres et al}^^ found nonionic surfactants such as Triton X-100 (alkyl aryl polyether alcohol) and Triton X-SOS were useful for stabilization of BaS04 particles prepared by the method of Takiyama. They also observed the internal structure of the so-prepared BaS04 particles by electron microscopy on their ultrathin sections of 30-50 nm thick, sliced with an ultramicrotome, and found the intemal structure porous with a mean pore size ca, 3 nm}^ The same porous structure is also observed in a direct TEM of small ellipsoidal particles of BaS04 {ca. 0.14 tmi) prepared by oxidation of thiosulfate with hydrogen peroxide in the presence of citrate by Andreasen et al,^^ Although Petres et fl/.^°'^°^ elucidated the growth mechanism in terms of aggregation of preformed primary particles from their electron microscopy, more detailed analysis may probably be needed. Kim and Matijevic^"-^ prepared uniform submicrometer amorphous spheres of lead niobium peroxo-hydroxide of different compositions by decomposition of NTA complexes of Pb^^ and Nb(0H)4'^ with H2O2 at elevated temperatures (50-90 °C) for ca. 4 h or less. The particles were converted on calcination (720 °C, 30 min) into lead niobate particles consisting of mixed phases, such as Pb3Nb20g, Pb5Nb40i5, Pb2Nb207' ^ ^ Pb3Nb40i3.

Gherardi and Matijevic^^ prepared submicrometer-size uniform amorphous spheres of barium titanate (BaTi03 aH20) by decomposition of EDTA complex of Ba^* ions with H2O2 in the presence of stabilized Ti(IV) alkoxide and ammonia at pH 9-10 and temperatures 40-60 °C, where each concentration of Ba^^ and Ti"** was in the range from 5 x 10"^ to 1 X 10"^ mol dm"^ Similarly, submicrometer-size uniform amorphous spheres of lead titanate (PbTi03 •XH2O) were prepared using NTA as a chelating agent.^°^ These as-prepared amorphous particles contained considerable amount of peroxidic oxygen (6 - 8 wt %). Hamada et al."^^'^^^ prepared uniform cubic germanium(IV) dioxide (Ge02) particles of a mean diameter 3.4 ^mi by decomposition of tris(oxalato)germanium(IV) with hydrogen peroxide at 100 °C for 15 h, leading to germanium(lV) hydroxocomplexes. Janekovic and Matijevic^^^ produced uniform rhombohedral cadmium carbonate (CdC03) particles by mking a urea solution {ca. 10 mol dm"^), preheated at 80 °C for 24 h and cooled to room temperature, with an equal volume of a dilute solution of cadmium salt (2 x 10'^ mol dm"^) at room temperature. Figure 7.10(a) shows a SEM of so prepared cadmium

236

PREPARATION

carbonate particles using CdCl2. They found no appreciable influence of different anion species of cadmium salts, such as acetate, chloride, nitrate, and sulfate. In this system, the urea is slowly decomposed into ammonium isocyanate and then rapidly hydrolyzed into ammonium carbonate at an elevated temperature. The carbonate ions which had been built up by preheating the urea solution brought about a single burst of nucleation on mixing with the solution of cadmium salt and gradual growth ensued. Thus, although the start of precipitation is rather inhomogeneous, no further nucleation occurs after the initial one, due to the low supersaturation of carbonate ions in the growth stage. It was also found that the morphology of the cadmium carbonate particles was totally different from the rhombohedron when they were produced from cadmium acetate with an extremely low concentration of urea such as 2.0 x 10"^ mol dm"^ while only rhombohedral particles were obtained, regardless of the anions of the starting cadmium salts including cadmium acetate, when the concentration of urea was as high as 2 mol dm"^ or more. Hence, urea may work as a habit modifier and stabilizer of the product by adsorption as well as a reservoir of carbonate ions. This method is based on the slow decomposition reaction of urea via ammonium cyanate (NH4NCO) at relatively high temperatures above 70 OQ 108,109 yî^[^Y^ jâj. widely been used from of old for homogeneous precipitation of metal carbonate and/or hydroxide particles. The ratedetermining step of the net reaction, consisting of thermal isomerization from urea to ammonium cyanate ((NH2)2CO - • NH4NCO) and subsequent hydrolysis of cyanate ions to ammonium and carbonate (NCO" + 2H2O - • NH/ + COj^"), is the first isomerization process. The isomerization is a first-order reaction with respect to urea over a wide concentration range. In other words, urea is thermally decomposed virtually in an irreversible process. The rate constants of the first-order reaction are 3.3 x 10'^ and 1.1 X 10"^ s"^ at 80 and 90 °C, respectively. ^^^ Hence, only about 4 % of urea is decomposed in 1 h at 90 °C. This is a main reason why the molar ratio of urea to metal ions is set exceedingly high in most cases. The net reaction scheme is as follows: 2(NH2)2CO + 5H2O -* 4NH/ + OH" + HCO3- + 003^-

(7.2.3)

As is obvious from this formula, carbonate ions, 063^", are released and pH is raised up to ca. 9 at maximum. Thus this reaction can be used not only for preparation of metal carbonates but also for processes promoted by


1|U.m

237

1iUm

Fig. 7.10. Rhombohedral CdCOg particles prepared by mixing 40 cm^ of 10 mol dm"^ urea (preheated at 80 °C for 24 h and cooled to room temperature) with the same volume of 2 x 10~^ mol dm"^ CdCl2 at room temperature (a), and CdO particles obtained by calcination of the CdCOg particles for ca, 3 h at 300 °C and a constant pressure of argon (20 Torr) (b). (From Ref. 107.)

increase of pH, such as precipitation of metal hydroxides, metal oxides, and metal phosphates, wherein the formation of metal phosphates is pronounced by the increase of the proportions of deprotonated phosphate ions, such as PO/- and HPO/", from H2P04" and H3PO4. It seems that when the affinity of the coexisting anions or hydroxide ions to the metal ions is stronger than that of carbonate ions, the latter are not included in the product. The same workers also prepared uniform and highly porous cadmium oxide (CdO) by calcination of the uniform cadmium carbonate particles, as shown in Fig. 7.10(b).^°^ After this heat treatment, the CdO particles still retained the original shape of CdCOj but were given a high porosity (BET specific surface area: 1.8 mVg for CdCOj; 22 mVg for CdO). Porta et al}^^ prepared uniform submicrometer amorphous spheres of a ruthenium double salt ((NH3)2Ru'°0(NO) •2RuÔC03-SHp) by aging solutions of ruthenium chloride (RUCI3) containing K2SO4 and urea at 85 °C for 1 h in acidic media (pH 2-3). The powder was readily converted to ruthenium oxide (RUO2) by calcination at 400 °C, or to metallic ruthenium (Ru) by heating at 250-300 °C in a stream of H^. To preserve particle morphology the original powder was coated with silica before calcination. Kratohvil and Matijevic^^^ prepared uniform submicrometer amorphous

238

PREPARATION

spheres by aging an aqueous solution of PdCl2 at 75-90 ""C for 100-40 min in the presence of urea and nonionic surfactant Triton X-405 (1 x 10"^ to 8 X 10"^ %) as a useful anticoagulant. The typical composition for the formation of particles of 0.29 \im was 4.0 x 10'^ mol dm"^ PdCl2, 0.5 mol dm"^ urea, 4.0 x 10"^ % Triton X-405, and 5.0 x 10"^ mol dm"^ HCl; temp = 90 °C; time = 45 min. The composition of the amorphous particles was indefinite, but Pd = 56.2-59.7 %, C = 4.1-6.9 %, CI = 5.8-7 %, N = 12.3-12.9 %, and H = 2.4-2.9 %. The precursor particles were reduced to uniform spherical metallic palladium (Pd) particles of a little smaller diameter by 5.0 x 10'^-5.0 x 10"^ mol dm~^ hydrazine at room temperature or 1 % ascorbic acid at 90 °C for more than 20 min. They also found that PVP (0.1-0.5 %) was effective as an anticoagulant in the reduction process. Uniform micrometer-size crystalline ellipsoidal particles of cerium(III) oxydicarbonate (Ce20(C03)2-1120) and submicrometer-size amorphous basic carbonate spheres of lanthanides such as gadolinium (Gd), europium (Eu), terbium (Tb), and samarium (Sm),^^^ and of yttrium (vy^^'^^"* were prepared by aging solutions of corresponding salts at elevated temperatures in the presence of urea. These particles were also prepared by continuous procedures.^^^'^^^ Corresponding uniform crystalline oxide particles were readily obtained without morphological change by calcination of these precursor particles at ca. 600-700 °C, where cerium(III) oxydicarbonate was converted to face-centered cubic Ce(IV)02. Her et al}^^ further studied the sintering behavior of uniform spheres of Y2O3 converted from Y(0H)C03 particles prepared by the continuous procedure. Aiken et al}^"^ also prepared uniform composite spheres of yttria-ceria in the same way by calcination of corresponding precursor particles prepared from corresponding mixed salts, suggesting a continuous mixing of f.c.c. Ce02 and b.c.c. Y2O3. Similarly, submicrometer-size spheres of yttrium aluminum garnet (YAG: Y3AI5O12) were also prepared by calcination of corresponding mixed basic carbonate particles at 950 °C.^^^ Nishisu and Kobayashi^^^ prepared uniform spheres of Eu-doped yttria, as an important red phosphor of CRT, in a similar manner. Vila et al}^^ farther converted so-obtained undoped and doped yttrium basic carbonates to submicrometer-size uniform spheres of Y2O2S and Y202S:Eu using a solid-gas reaction of these precursors with elemental sulfur vapor under an argon atmosphere. They are also important materials as red phosphors. Hsu et al}^^ prepared uniform amorphous spheres of Y(0H)C03 in a similar manner in the presence of anionic organic dyes and obtained good Y(0H)C03 pigments containing the anionic dyes in the interiors.


239

Rod-like,^^ prismatic,^^^ and spindle-like^^^ uniform particles of zinc oxide (ZnO) of several micrometers in length were obtained from basic zinc carbonate particles of the same shapes prepared by aging zinc salts at ca. 90 °C in the presence of urea. The shape of the precursor particles was changed with variation of anion species of the zinc salts and concentrations of the salts and urea. Tsuchida et al}^^ also prepared amorphous spheres of hydrated alumina (Al203-nH20) by aging 10"^ mol dm"^ Al2(S04)3 in the presence of 1.5x10 mol dm"^ urea at 90 °C for 2 h and calcined to ri-Al203 at 900 ""C for 30 min. Transition to a-Al203 was observed at 1100 °C. The mean diameter could be varied from 0.2 to 1.0 |xm by increasing the concentration of aluminum sulfate from 0.5 x 10"^ to 2.0 x 10"^ mol dm"^. In the asprepared hydrated alumina, carbonate ions were not included. Daichuan et al}^^ prepared uniform submicrometer-size spherical and tetragonal hematite (a-Fe203) particles by hydrolysis of ferric ions through the increase of pH with decomposition of urea induced by microwave radiation. In this procedure, the effect of the pH increase associated with the decomposition of urea and the rapid and uniform elevation of temperature by microwave radiation are utilized. The rapid increase of temperature and pH minimizes the nucleation time, as is in conformity with the principle of formation of uniform particles (see chapter 6). The definite crystal habit of the hematite particles in a tetragonal form, when the concentration of urea is high, may reveal that urea is strongly adsorbed to the surfaces of the hematite particles and regulates the growth of the facets. In a similar manner, uniform amorphous spheres of basic copper(II) carbonate (malachite: Cu2(OH)2C03) of ca. 2 [mi m mean diameter were obtained by aging Cu(N03)2 solutions in the presence of urea at 85 °C and reduced the powders to metallic copper (Cu) of the same shape with hydrogen gas at 150 - 200 ""CP^ It was also found that the composition and morphology of the precursor particles strongly depended on the anion species of the starting copper salts: bipyramidal particles of atacamite (CuCl2-3Cu(OH)2) from CUCI2, needle-like brochantite (CUSO4 •3Cu(OH)2) or platelets of posnjakite (CUSO4 •3Cu(OH)2) from CUSO4, as well as spherical amorphous malachite from Cu(N03)2.^^'^ Obviously, C03^" ions are replaced by CI" or 804^" which are thought to be more strongly coordinated to copper ions than NO3" and C03^". Interestingly, however, when CO2 in the system for preparation of Cu2(OH)2C03 particles was purged by bubbling with argon during the precipitation, crystalline platelets of Cu2(OH)3N03 were obtained instead of amorphous spheres of Cu2(OH)2C03.^^ All of

240

PREPARATION

these basic copper particles were converted to highly porous copper(II) oxide but with the same shapes on calcination at 700 - 800 °C. Also, uniform amoqjhous spheres of copper(II)-gadoliniuin basic carbonate^^^ and copper(II)-lanthanide(ni) basic carbonates (L = Gd, Dy, Ho, Er)^^^ were prepared in a similar manner and converted to the corresponding composite oxide particles by calcination. Furthermore, titania-coated basic copper carbonate and titania-coated copper(II) oxide particles were prepared by hydrolysis of Ti(IV) butoxide in the presence of basic copper carbonate spheres and, in the latter case, subsequent calcination.^^ Also, polyaniline-coated copper(II) oxide particles were synthesized by polymerization of aniline in the presence of copper oxide particles prepared from basic copper carbonate particles, where CuO acted as an oxidant to initiate the polymerization of aniline.^^^ Uniform submicrometer-size spheres of basic zirconium sulfate (Zr2(OH)6S04 -21120) and oxy-basic zirconium carbonate (Zr202(OH)2C03 •2H2O) were prepared by aging a solution, consisting of 5 x 10"^ mol dm"^ Zr(S04)2, 5 X 10"^ mol dm"^ HNO3, 1.8 mol dm"^ urea, and 3 wt % PVP, for 5 h at 50 °C, and by aging the same solution at 80 °C, respectively. Since the decomposition of urea below 70 °C is extremely slow and the pH of the solution at 50 °C for the formation of the basic zirconium sulfate remained actually unchanged within the reaction time for 5 h, the role of urea in the formation of the basic zirconium sulfate is believed to promote the formation of a hydrated complex of zirconium ions such as Zr(OH)(H20)^^, as a precursor to the basic zirconium sulfate. Here, PVP was particularly useful as an anticoagulant. On calcination, both precursor particles were crystallized to tetragonal zirconia (Zr02) at ca, 600-700 °C with their original spherical shape retained. Composite particles of ZrYo.803.2 of a mixed cubic-tetragonal structure were also obtained by calcination (800 °C) of precursor particles of ZrYo.8(OH)3.8(C03)i.3, prepared by aging a mixed solution of 5.0 x 10"^ mol dm"^ in Zr(S04)2, 4.0 x 10"^ mol dm"^ in Y(N03)3, 5.0 x lO'^ mol dm'^ in HNO3, 3.0 wt % in PVP and 1.8 mol dm""' in urea at 80 °C for 5 h. However, a similar attempt to prepare precursor particles of a mixed composition containing sulfate in place of carbonate by aging at 50 °C was unsuccessful. But, instead, it was possible to coat basic zirconium sulfate particles with Y(0H)C03 by aging a solution of 1.0 x 10"^ to 4.0 x 10"^ mol dm'^ in YNO3 and 0.6 mol dm'^ in urea in the presence of 0.15 to 0.60 g dm"^ of Zr2(OH)6S04 -21120 powder at 90 °C for 2 h.'^' Haq et al}^^ prepared uniform cubic manganese carbonate (rhodochro-


241

site: MnC03) particles and nearly spherical particles of basic nickel carbonate (NiCOj •Ni(0H)2-1120) ^Y heating solutions of the respective metal sulfates in the presence of urea at 80-85 °C. These precursor particles were then converted into manganese oxides (Mn203 in air; MnO in N2) and niciêl oxide (NiO) by calcination at 700 °C, the latter of which was further reduced to metallic nickel (Ni) with H2 at 350 °C, with their shape retained. They also coated manganese carbonate particles with basic nickel carbonate and converted the core and shell into Mn203 and NiO by calcination at 700 °C in air, which on further heating at 350 °C in H2 were reduced to Mn and Ni, respectively. Ishikawa and Matijevic^^^ prepared nearly spherical micrometer-size basic cobalt(II) cyanato carbonate particles from solutions of cobalt salts with urea at 80 ''C in systems open to air and calcined to cobalto-cobaltic oxide (C03O4) spheres at 300 °C, which were then reduced to metallic cobalt (Co) spheres with H2 at 300 ^'C. In similar systems but closed to air, needle-type basic cobalt(II) carbonate particles were obtained. Seemingly, the escape of CO2 may favor the coordination of cyanate ions to Co(II) and thus the formation of spherical basic cobalt cyanato carbonate particles. They also prepared uniform submicrometer-size amorphous spheres of cobalt phosphate (Co3(P04)2 •XH2O; x = 3.4-3.7) by heating a solution containing 5 x 10"^ mol dm"^ CoSO^, 5 x 10"^ mol dm"^ NaH2P04, 1 mol dm"^ urea, and 10"^ mol dm"^ sodium dodecyl sulfate (SDS) at 80 °C for 3 h.^^^ The particles released water at 300 °C and were crystallized at ca, 600 °C. In this system, the suitable concentration range of SDS is very narrow, i.e,, 5 X 10"^ to 1 X 10"^ mol dm"^. Lower or higher concentrations than this range caused aggregation of the precipitate. A cationic surfactant, cetyltrimethylammonium chloride (CTAC), was also found effective as an anticoagulant and as a size controller, whilst a nonionic surfactant, polyoxyethylene(20) nonylphenyl ether (NP-20), had little effect.^^^ Castellano and Matijevic^^^ prepared micrometer-size uniform amorphous spheres of hydrated zinc phosphate particles by aging solutions containing 10"^ mol dm'^ zinc salts and 3 x lO"* mol dm"^ NaH2P04 with ca. 10'^ mol dm"^ urea at 90 °C for 3 h in a closed tube. Similarly, amorphous spheres of cadmium phosphate (Cd3(P04)2 •3.5H20),^^'* basic nickel phosphate (Ni2(OH)P04 •3.5H20),'^' manganese phosphate (Mn3(P04)2 •3.2H20),'^^ and composite phosphate, cadmium-nickel phosphate ((Cd,Ni)3(P04)2 tx:H20),^^^ have been prepared. Basic nickel phosphate in particular is known for its high porosity^"''^'^''^ and catalytic activity for dehydration and dehydrogenation of alcohols.^^^'^^^ Also, metal phosphates in general are useful for anticorro-

242

PREPARATION

sive pigments/^^ blue light lasers,^"^^ ceramics,^"^^ bioceramics,^"^^ water purification agents,^"*^ etc. Sugimura etal}^ prepared amorphous spheres of zirconia (ZrOj) of 0.20.8 |xm in mean diameter with a relative standard deviation of ca. 20 % at the minimum by decomposing zirconium soaps {ca. 5 wt %), such as (CnH2n.iCOO)4Zr (n = 11, 13, 15, 17), dispersed in higher alcohols, such as C„H2„.iOH (n = 8, 10, 12, 14), at temperatures 140-200 °C for ca, 25 h. In this system, the particle size significantly decreased from 0.7 to 0.2 |xm with increasing chain length of zirconium soap from n = 11 to n = 17, while the chain length of the alcohol medium and the temperature had little effect. The zirconium soaps were prepared by the use of the reaction of sodium salts of fatty acids with zirconium chloride in aqueous solutions. ^"^^ While random coagulation among large particles may be inhibited to a considerable extent in this system by virtue of their low diffusivity in the viscous media, the constant nucleation and the inevitable coagulation among smaller particles may be responsible for the rather broad size distributions. In such a system, the size distribution is expected to be more or less narrowed by prolonging the reaction time because of uptake of smaller particles by large ones, as actually observed in this system. Murray et aO^^ prepared uniform nanoparticles of cadmium chalcogenides including CdS, CdSe, and CdTe over a diameter range of 1.2-11.5 nm with narrow size distributions (a < 5 %) by airless pyrolysis of organometallic reagents, injected into a hot coordinating solvent, over a period of a few hours of steady growth, while modulating the growth temperature in response to the change in size distribution as estimated from the absorption spectroscopy on samples removed at regular intervals. They used dimethylcadmium as a cadmium source; bis(trimethylsilyl)sulfide, bis(trimethylsilyl)selenium, bis(/err-butyldimethylsilyl)tellurium, trioctylphosphine selenide, and trioctylphosphine telluride as chalcogen sources; tri-«-octylphosphine (TOP) and tri-n-octylphosphine oxide (TOPO) as organic coordinating solvents. A mixed solution of Me2Cd and an organochalcogenide in TOP is injected into a hot TOPO, for example, at 300 °C. The temperature was controlled between 100 and 300 °C according to the species of chalcogen sources and desired particles sizes. Particles of different sizes from 1.2 to 11.5 nm were obtained by sampling at different aging times in the course of particle growth. A characteristic of this method is that the renucleation during growth is minimized by modulating the growth temperature to regulate the pyrolysis rate of the organometallic reagents, based on the m situ spectrometry of the evolving size distribution. It seems that such


243

evaluation of size distribution by spectrometry is generally possible in nanosized semiconductor particle systems in which the threshold of the absorption band strongly depends upon the particle size (quantum size effect). Once the best temperature pattem has been established after repeated tests in each system, one can completely prevent renucleation and achieve excellent uniformity simply by following the temperature program. In addition, it is likely that the high temperature at the moment of injection of reagents and the following rapid drop of temperature corresponds to the "supersaturation quenching" for separation between the nucleation and growth stages (see chapter 6), and that the coordinating solvents work as powerful anticoagulants. Thus, this system seems to fulfill all requirements for the formation of monodispersed particles. Ottewill and Woodbridge^"*^ decomposed silver halide complexes in aqueous solutions by dilution with water and obtained monodisperse silver bromide (AgBr) and silver iodide (Agl) particles. These systems are not rigorously homogeneous, since homogeneous dilution was not achieved by this method. Hence, they are basically quasi-homogeneous systems, so that the mean size and size distribution were strongly affected by the dilution and agitation rates. The shape of the particles was different, depending on pAg (= -log[Ag^]). In a high pAg range, the shape of AgBr was octahedral, whereas in a low pAg range it was cubic. For the morphological change of AgBr due to the adsorption of bromide ions, a detailed discussion is given in chapter 3. As has been described in sections 1.4.2 and 7.2.6, uniform silver chloride (AgCl) and silver bromide (AgBr) particles were prepared by dissociation of a silver-ion complex of gelatin. The dissociation of the silver-gelatin complex was caused by protons released slowly with decomposition, or hydrolysis, of diethyl sulfate. In this system, homogeneous nucleation was realized, and the growth was completely controlled by the hydrolysis of diethyl sulfate.^^ 7.2.9, Hydrolysis of Alkoxides Stober et al}^^ prepared exceedingly uniform spherical particles of silica (Si02) by hydrolysis of tetraalkyl silicates and subsequent condensation of silicic acid in alcoholic solutions containing water and anunonia at low temperatures around room temperature. Figure 7.11 is an example of thusprepared silica particles.^"*^ The basic reaction scheme is as follows: Si(OC2H5)4 + 4H2O -^ Si(0H)4 + 4C2H5OH

(7.2.4)

244

PREPARATION

9 Fig. 7.11. Monodispersed silica particles prepared by hydrolysis of tetraethyl orthosilicate (0.28 mol dm"^) at 22 ""C in ethanol containing water and ammonia. (From Ref. 148.)

Si(0H)4 -* Si02 + 2H2O

(7.2.5)

Ammonia acted as a catalyst to enhance the hydrolysis reaction. The mean size ranged from 0.05 to 2 jmi and any mean size could be chosen from this size range by controlling the compositions of water and/or ammonia and the kind of alcohols. This technique is an application of the sol-gel process for the production of glass at low temperatures, in which hydrolysis of silicon alkoxides to form silica sol and aggregation of the sol to yield silica gel are involved.^"*^ Nishimori et al ^^^ found that the size of silica particles increased from 0.09 to 1.2 Jim in the hydrolysis of tetraethyl orthosilicate in the presence of an anionic surfactant, sodium docecyl sulfate (SDS), increasing in concentration up to 0.25 wt %. The effect of SDS was explained in terms of initial aggregation of the nuclei enhanced by SDS from observation that probability of double spheres increased with increasing concentration of SDS associated with the increase in electrolyte concentration. Her et al}^^ studied a continuous process for the synthesis of silica. Because of the high monodispersity, spherical shape, amorphous structure, transparency, chemical


245

inertness, abundance of Si in nature, etc., a multitude of modifications of the uniform silica have been attempted, such as doping and coating with inorganic or organic matters (see sections 8.4 and 8.5). The first procedure for sol formation in the sol-gel method is now widely applied to the preparation of monodisperse particles of different metal oxides.^^^'^^^ For example, uniform particles of titania (Ti02),^^'*'^^^ barium titanate (BaTiOj),^^^ titania doped with TvLfi^, NbjOg, or SrO, and their surface modification with BaO, CuO, or SrO,^^° zinc oxide (ZnO), '^^'^'^ zirconia {ZxO^,^^^^^'^'^'' yttria-doped zirconia (Y-doped Zr02),''^''^' tantalum(V) oxide (JdÔ^^^^'^ tinOV) oxide (SnO,),''' and lead zirconate-titanate (PZT; Pb(Zr^,Tii_J03),^^° have been prepared by hydrolysis of the corresponding metal alkoxides in alcohol solutions. Asprepared metal oxide particles by this technique are normally hydrated amorphous spheres, whereas they are crystallized by calcination with the release of H2O. However, in some exceptional cases, the product is crystalline. For example, Heistand and Chia^^^ prepared uniform polycrystalline zincite (ZnO) of ca. 0.2 \ym diameter consisting of 15 nm crystallites by hydrolysis of 0.2 mol dm"^ ethylzinc-rerr-butoxide in a mixed solution of toluene/ethanol (30/67, by volume) in the presence of 3.2 mol dm"^ H2O at room temperature for 3 h. Some advantages of this method for preparation of uniform particles may be: 1) simple and rapid reactions around room temperature; 2) relatively pure products free from inorganic anions; 3) a relatively high productivity owing to the allowance for the upper limit of the starting material concentration for the production of uniform particles {ca, 10"^ mol dm'^). Nucleation and Growth Mechanisms There is a controversy on the growth mechanism of the sol-gel process: i,e,, diffusion-controlled deposition of monomeric species for Si02,^^^'^^^ Ti02,^^^'^^'* and Zr02^^^; reaction-controlled deposition of monomeric species for Si02^^°'^^^ and Zr02^^^ aggregative deposition of preformed primary particles onto the growing particles for Si02^^^'^^^ and Ti02^^^'^^^'^^° Although the diffusion-controlled and the reaction-controlled growth models differ from each other in the interpretation of the rate-determining step in the deposition process of monomeric species, they are commonly in the group of the monomeric growth model and thus based on the LaMer mechanism for the formation of monodisperse particles (see chapter 6). The monomeric growth model has an advantage that it clearly explains the reason for the achievement of the excellent monodispersity on the basis of

246

PREPARATION

the LaMer principle. However, most of these assertions are not based on clear evidence of the LaMer process in these particular systems, and only the rate-determining step for the particle growth is discussed from Nielsen's chronomal analysis or from the evolution of the size distribution, on the presumption of the LaMer process. In addition, Nielsen's chronomal analysis is of no use in these systems, since the hydrolysis of the alkoxides is the rate-determining step of the overall process and thus the chronomal analysis gives no information on the growth mechanism (see section 2.6.7). From the complete agreement between the volumic growth rate of oxide particles and the first-order hydrolysis reaction of the conesponding alkoxides,^^^*^^^'^^^ there is no doubt that the rate-determining step for the overall particle growth is the hydrolysis process. On the other hand, if the hydrolysis is not the rate-determining step, the hydrolysis must finish earlier than the oxide formation, and the hydrolysis product, neutral or dissociated hydroxides, may form a gel structure through hydrogen bondings. Even in such a case, the chronomal analysis is still meaningless, since the concentration of soluble hydroxocomplexes, virtually in equilibrium with the gel, is kept almost constant throughout the growth process. Moreover, there is some confusion in interpretation of the evolution of size distribution. It is true that the evolution of size distribution reflects the growth mode, but its behavior is not simple, as described in section 2.6.4. Nevertheless, in any case, the absolute standard deviation should be used as the criterion of the growth mechanism, rather than the relative standard deviation to the mean particle size, since the former is normally kept almost constant in the (polynuclear-layer) reaction-controlled growth mode, but is decreased in the diffusion-controlled growth mode, while the latter only decreases in both cases.^^^'^^^ If we reconsider the growth mode from this standpoint on the assumption of the monomeric growth mechanism, the particle growth in solgel systems seems to be generally in a polynuclear-layer reaction-controlled growth mode from the available data for the evolution of the absolute standard deviation of size distribution in the above literature. Here, the reaction-controlled growth mode in this context indicates only the ratedetermining step for the solute deposition process onto the growing particles, and not for the entire process for the particle growth. As mentioned above, the rate-determining step for the entire process is the preceding hydrolysis step. Also, unlike conventional monomeric growth models, the monomeric species directly involved in the particle growth may not be the whole soluble hydrolysis product, but only some specific precursor produced from the hydrolysis product, as described below.


247

In the meantime, Zukoski et al}''^'^'^^ proposed an aggregative growth mechanism, in which some primary particles are assumed to be continuously generated throughout the particle formation process and aggregate selectively onto the growing particles. On the assumption of such primary particles being present, their sizes have been supposed to be of the order of ca. 3 nm for Si02^^^'^^ and of ca. 10 nm for Ti02.^^^ The proposal of Zukoski et al is based on their finding from conductivity measurement that the concentration of the soluble hydrolysis product of alkoxides initially increases to a high level and declines steadily with the growth of the particles, but it remains considerably high as probably sufficient for the nucleation of the oxide particles even in the later stage of the growth. In addition, the evolution of the concentration of the soluble hydrolysis product is unaffected by the presence of seeds of the oxide whose content is sufficient for preventing the generation of new particles. They thought that if the soluble hydrolysis product directly deposits onto growing particles, the steady concentration of the hydrolysis product must be lowered significantly by the presence of the seeds. The sizes of the primary particles were estimated mainly from the microscopic surface roughness of the resulting particles, as observed by scanning electron microscopy. In fact, the surfaces of spherical silica prepared by a sol-gel process in our laboratory appear to suggest that the particles are grown by aggregation of small primary particles, as shown by a SEM image in Fig. 7.12. Although rough surfaces and amorphous or polycrystalline structures are not necessarily indicative of aggregative growth, as obvious from the examples of metal sulfide particles^^"^^ and many other particles to be introduced in section 7.3, their proposal is quite fascinating. Obviously, they implicitly assume that the soluble hydrolysis product directly serves as the solute for the formation of primary particles; e.g., poly condensation of silicic acids, as a polymerization process with the formation of siloxane bondings and release of water, for the nucleation of primary particles. However, if it is the case, the concentration of the soluble hydrolysis product must be kept almost constant at a critical level for the nucleation of the primary particles in the balance of the production of the solute and its consumption for nucleation, since the nucleation rate in general critically depends on the supersaturation of solute. Hence, the actually observed drastic up-and-down of the concentration of the hydrolysis product appears to be adverse to their argument. Moreover, one may wonder why the direct deposition of solute onto the growing particles is not allowed, despite the presumption that the primary particles are formed by the ordinary monomeric process. Also, even if we assume that primary

248

PREPARATION

Fig. 7.12. Close-up SEM of silica particles prepared by the sol-gel process. particles of silica are formed through a polycondensation process of the hydrolysis product without a distinct nucleation step, it seems difficult to find the reason for the definite limitation of their growth to a certain size level assumed for primary particles in the aggregative growth model. If we explain this in terms of quick aggregation of the nascent particles to the growing secondary particles before the former are grown up to a large size, we may encounter the same difficulty again in finding the reason for the absence of the particle growth by direct deposition of the hydrolysis product through the polycondensation process. Apart from these essential problems of the aggregative growth model, the weakest point of this proposal may be the difficulty in the explanation of the excellent monodispersity of the silica particles, since we have to assume an exclusive aggregation of primary particles to growing secondary particles with neither the coagulation among the primary particles nor among the growing particles. Although Bogush and Zukoski^^^^ tried to explain the selective aggregation using the Smoluchowski aggregation equation, it does not appear to be successful in the reproduction of the sharp characteristic distribution profile of the monodispersed silica particles with no appreciable tailing. On the other hand, if we consider that a monomeric precursor to silica particles is produced "irreversibly" from the hydrolysis product, any change


249

in the concentration of the precursor may have no influence on the concentration change of the preceding hydrolysis product, because there is no reverse reaction from the precursor to the hydrolysis product. Hence, if the steady concentration of the precursor is sufficiently low, the evolution of the total concentration of the ionic hydrolysis product monitored by electric conductometry must be unaffected by the presence of the seed particles. The low concentration of the precursor may be achieved, if only the reaction rate of the precursor to form silica particles is sufficiently high. Also, if the rate constant for the formation of the precursor from the hydrolysis product is relatively small, the total concentration of the hydrolysis product must remain high to maintain the sequential steady process. Therefore, if we only assume a monomeric precursor which does not nucleate, but can deposit onto coexisting particles, below the critical supersaturation of its own, we need not postulate primary particles anymore which have never actually been observed. Instead, the excellent monodispersity can be explained readily by this monomeric precursor model, in terms of the automatic control of the supersaturation of the precursor on the basis of the LaMer mechanism, in perfect conformity with experimental aspects so far known in the sol-gel systems. While it may not necessarily be required to identify the species of the monomeric precursor for understanding the fundamental growth mechanism, the specification of the precursor species is of interest for the complete understanding of the entire features of the formation process of oxide particles in the sol-gel system. As an example, let us consider the characteristics of the precursor species to silica particles. In a silica system, the hydrolysis product may generally be represented by (R0)4_^Si(0H)^, but probably most typically by ortho-silicic acid (m = 4), Si(0H)4, which may partly be linked together through hydrogen bondings and include its deprotonated species in an alkaline medium. Here, it seems reasonable to assume that the irreversible process to produce the precursor from the hydrolysis product is the condensation process to form low-molecularweight condensates in the form of soluble siloxane oligomers retaining some silanol groups. On the other hand, since it is obvious from the seeding analysis that the hydrolysis product, mainly consisting of ortho-silicic acids having silanol groups, does not chemically react with the surface silanol groups of silica particles through the condensation process, condensation reaction of the precursor with the surface silanol groups may not appreciably occur either. In this sense, siloxane oligomers in a suitable solubility range may be able to grow silica particles by their deposition (not by the

250

PREPARATION

condensation reaction) and may also act as solute which does not nucleate unless it exceeds its own critical supersaturation, but can deposit onto the growing particles with a supersaturation below the critical level. The nucleation of silica particles may start, when the siloxane oligomers reach their critical supersaturation, partly due to the reduction of solubility with the progress of their polycondensation and partly due to the increase in concentration. The nucleation may cease, when the steady concentration of the oligomers is lowered to a level below their critical supersaturation, owing to the total consumption of the constantly produced oligomers by the generated nuclei for their own growth. Then, monodispersed particles are produced through the succeeding growth process without renucleation. Condensation reaction among the deposited oligomers retaining silanol groups may proceed on the surfaces of the growing particles at the same time. Since the siloxane oligomers in a limited solubility range must be more or less soluble species having their own critical supersaturation levels for the nucleation of silica particles, they may be treated as a kind of monomeric species in clear distinction from particulate matters which have already surmounted the free energy barrier for nucleation. If A, B, C*, and P denote an alkoxide, the hydrolysis product, and the monomeric precursor (siloxane oligomer), and the product particles, respectively, the entire process may be represented by the following irreversible sequential steps in the steady state (/:i[/4][0H']'" = k2{n'-l)[Bf = A:3S(n-l)[C*]; n = the number of the monomer units in a precursor oligomer molecule; S = total surface area of the product particles in a unit volume): K-%

A + mOH" -^

'va

ICn

B

^

C*

-^

P

where it may hold that \A] » [B] » [C*] from k,[OliT « kîn-^)[B] « ^ 3 % - ! ) with k,[A][OUT = k,(n-l)[Bf = k,S{n-l)[C*] in the steady state; 1 :s m ^ 4; n ^ 2. Figure 7.13 shows a general scheme for the evolution of \Al [B] and [C*] in an early stage of hydrolysis of an alkoxide in a sol-gel system in the absence or presence of seeds. The concentration of alkoxide, [^], is located at a level much higher above [B], and decays with time by a first-order reaction of hydrolysis. The behavior of \A] is unaffected by the movement of [B] and [C*] or the density of seeds, [seed], and the change of [B] is unaffected by [C*] and [seed], while the evolution of [C*]


251

o

o G

6

[C*]

Time Fig. 7.13. Concentration evolution of alkoxide. Ay the hydrolysis product, B, and the monomeric precursor, C*, in a sol-gel system in the absence (•) or presence (O) of seeds. strongly depends on [seed]. If the density of seeds is sufficiently high, [C*] does not reach the critical level for nucleation as shown in Fig. 7.13, and hence the seeds grow without renucleation. If the oxide particles are grown by deposition of a monomeric precursor, the surface roughness must be created by two-dimensional clustering of the monomeric species loosely fixed or adsorbed on the growing surfaces. This

252

PREPARATION

proposal, however, does not negate some probabilities of renucleation and coagulation among the growing particles, depending on the number concentration of the particles and the ionic strength. Particularly in the nucleation period, the number concentration of nascent nuclei is expected to be reduced via coagulation to a level predetermined by the ionic strength, resulting in the increase in the final particle size. However, such events during the growth stage always result in some broadening of the size distribution. Although the oligomer precursor mechanism, as a kind of the monomeric precursor mechanism, deduced from the insights into the nature of particle growth in some sol-gel systems has to be rigorously verified in individual systems, it may be allowed to consider that the formation mechanisms of monodisperse particles in the most of sol-gel systems are basically the same as in the silica system. 7.2.10. Forced Hydrolysis of Metal Ions Watson et al observed the growth of uniform ellipsoidal thin platelets of tungstic acid (H2WO4) of 0.2-0.3 \Jim in length at room temperature^^^ Also, they obtained uniform acicular particles of akaganeite (P-FeOOH) by hydrolysis of Fe^^ ions in dilute FeCl3 solutions (20-60 mmol dm'^) for several months at room temperature, and disclosed by electron microscopy on their ultrathin sections that each particle consists of a bunch of lengthy subcrystals.^^^ Although the synthesis of these uniform particles was performed at room temperature, these findings are of great significance as predecessors to the synthesis of uniform metal hydrous oxide particles by forced hydrolysis of metal ions at high temperatures close to 100 ""C. Demchak and Matijevic^^^ prepared highly uniform spherical particles of chromium hydroxide (Cr(0H)3) ^y forced hydrolysis of chromium ions in acidic media around 80 °C. This method for the preparation of uniform metal (hydrous) oxide particles has been developed extensively by Matijevic and coworkers since then, as summarized in Matijevic's review articles.^^^'^^^ Besides the chromium hydroxide sol,^^^'^^^"^°^ a number of uniform particles of metal (hydrous) oxides were produced in homogeneous systems by Matijevic's group and others.; e.g., aluminum hydrous oxide (AI2O3 •A1H2O; amorphous spheres),^^"^^^ alumina-silica composite (Al203-Si02; amorphous spheres),^^ boehmite (a-AlOOH; crystalline clusters),^°^'^^ hematite (a-Fe203; crystalline ellipsoids, cubes, and spheres),^^"^^^ basic iron sulfate (Fe3(S04)2(OH)5 -21^20; crystalline (hexagonal) truncated cubes and oblate spheroids),^^^ titania (Ti02; crystalline (rutile) spheres^^^ and


253

polycrystalline (anatase) cubes^^°), basic thorium sulfate (Th(OH)2S04 • H2O; amorphous or polycrystalhne spheres),^^^ gallium hydrous oxide (amorphous spheres and crystalhne rods),^^^'^^ manganese dioxide (8Mn02),^^ zirconia (Zr02; amorphous spheres),^^^'^^ cerium(IV) oxide (Ce02; polycrystalhne spheres),^^'' indium hydroxide(In(OH)3;crystalline cubes, prisms, ellipsoids, spheres, octahedra, and hexagonal platelets),^^^'^^^

Fig. 7.14. Monodispersed particles prepared by forced hydrolysis of metal ions: (a) Cr(0H)3, (b) a-AlOOH, (c) a-Fe203, and (d) basic iron sulfate. (From Refs. 187, 205, 211, and 218, respectively.)

254

PREPARATION

indium oxide (111203) by calcination of In(0H)3,^^^ hafnium hydroxysulfate (Hf(OH)314(804)043 •JCH2O; amorphous spheres by hydrolysis of HfOCl2 in a solution at room temperature),^^^ hafnium oxide (Hf02; polycrystalline monoclinic spheres by calcination of hafnium hydroxysulfate,^^ or polycrystalline monoclinic ellipsoids^^ directly by forced hydrolysis of HfCl4 in a solution at 100 °C), scandiumail) oxyhydroxide (y-ScOOH; crystalline disks and elliptical disks),^^ and tin(IV) oxide (Sn02(cassiterite); fuzzy polycrystalline spheres and monocrystalline rods),^^'^^ and Tb-doped YAG (Y3Al50i2:Tb; crystalline polyhedra).^^ Figure 7.14 shows a TEM, SEM, TEM, and carbon replica TEM of uniform particles of chromium hydroxide, boehmite, hematite, and basic iron sulfate, respectively, prepared by forced hydrolysis of metal ions. Most of the original particles were prepared by heating dilute solutions of metal sahs (lO-^-lO"^ mol dm"^) over 50 to 150 °C at low pH (1.0-4.0) for several hours or days. In some cases, however, much higher concentrations, or much lower or higher temperatures are employed. For example, Moon et al}'^^ prepared submicrometer-size amorphous spheres of Zr02 from 0.2 mol dm"^ ZrOCl2 in a mixed solution of water/2-propanol (1/5, by volume) containing 0.1 wt % hydroxypropyl cellulose (HPC), as an anticoagulant, by microwave heating up to the boiling point of the mixed medium (80.3 °C). Ocaiia et al.^^ prepared uniform submicrometer-size amorphous spheres of hafnium hydroxysulfate by hydrolysis of hafnium oxychloride in acidic solution in the presence of sulfate ions at room temperature for 2 h. Takamori et aL^^ prepared uniform polyhedral particles of Tb-doped YAG (Tb-Y3Al50i2) ^f ^ mean diameter ca. 8 trni by hydrothermal process for a mixed solution of the constituent chloride or citrate salts at 500 °C (100 MPa), wherein the number concentration of the nuclei was controlled by raising the initial temperature to a somewhat higher temperature than for the growth, e,g., 590 °C. Also, Catone and Matijevic^ used dilute aluminum s-^c-butoxide (2 x 10"^ mol dm"^ in Al^^) as a starting material for the preparation of uniform amorphous spheres of aluminum hydrous oxide in acidic aqueous solutions at 99 °C in the presence of sulfate ions. Since this is a typical forced hydrolysis procedure, it has been treated as a forced hydrolysis process rather than the hydrolysis of alkoxides performed in organic media under mild conditions. For the same reason, the formation of alumina-silica composite particles^^^ has been classified into this section, in which a mixed alkoxide, aluminum tert-butoxide/tetraethyl orthosilicate, is first hydrolyzed at room temperature for ca, 1 h, and then the final sol is formed in the presence of sulfate ions by forced hydrolysis for polycon-


255

densation at 98 °C for 24 h at initial pH 2.3. As an application of this method, uniform particles of maghemite (yFe203; crystalline ellipsoids) were prepared by conversion from hematite of the same shape through a sequence of reduction-reoxidation processes.^^^ Uniform iron (Fe) particles are also obtained by reducing the well-defined hematite particles with hydrogen.^^^'^^ The coagulation is prevented mainly by the repulsive force of the electric double layer exerted from the positively charged surface of each particle in the low pH range, which is effective at a low ionic strength. In most cases, the precipitation of a product is sufficiently slow so that the diffusion process of the precursor complexes cannot be the ratedetermining step of the particle growth. Hence, there are two possibilities for the rate-determining step of the particle growth; /.e., the hydrolysis of the metal ions for the formation of precursor complexes or the surface reaction of the precursor complexes on the growing particles. If the hydrolysis process is the rate-determining step, Nielsen's chronomal analysis is meaningless in such a system (see section 2.6.7). If the surface reaction process is the rate-determining step, the chronomal analysis may be useful for the determination of the apparent reaction order. The two possibilities can be distinguished by using seed particles as a probe of the growth mechanism. Namely, the precipitation rate is unaffected by the presence of seeds in the case of the hydrolysis-controlled growth, whilst the precipitation rate is significantly accelerated by the presence of seeds in the case of the reaction-controlled growth. Based on this criterion, the growth of hematite particles in a dilute solution of ferric chloride was concluded to be controlled by the surface reaction of the precursor complexes."^^ An aggregative growth mechanism has been proposed not only for the particle growth in sol-gel systems, but also for the growth of some uniform particles prepared in homogeneous forced-hydrolysis systems; e.g., a Fe203,2^^-^^^ CeO^,^^^ SnO^,^^^'^ and ZnO,^^ as summarized in the review article by Ocaiia et al}^ However, as has been demonstrated by the seeding technique, the hematite (a-Fe203) particles obtained by forced hydrolysis of ferric ions in dilute acidic solutions of FeClj are grown undoubtedly via direct deposition of monomeric species, regardless of the surface roughness, morphology, and internal structure (see section 9.10).^^^ The same result was also obtained for the ceria (Ce02) system as well, and the extremely small particles assumed earlier to be the primary particles of ceria in the literature could not be observed under the conditions for the formation of the spherical monodisperse particles.^^^ These facts may imply that the seeding

256

PREPARATION

analysis, described in section 9.10 of chapter 9, is useful not only for finding the rate-determining step, but also for distinction between the 2iggregative and monomeric growth mechanisms, when the precursor species to the final product is in equilibrium with the whole solute. Again, it is noteworthy that the surface roughness, polycrystalline porous structure, casual coexistence of extremely small particles, presence of some particles revealing the clear evidence of aggregation, etc. are often observed in ordinary systems as well in which the particles are grown essentially by deposition of monomeric species. The low pH used in these systems is particularly important for maintaining the supersaturation with hydroxide complexes in the growth stage at a relatively low level to prevent renucleation. In addition, the pH is generally still lowered with the progress of hydrolysis. This also favors the reduction of the supersaturation of hydroxide complexes, though it is the main cause of the relatively low yield in the forced hydrolysis systems. Relatively high temperatures are normally employed in the forced hydrolysis systems mainly for acceleration of the surface reaction or hydrolysis of metal ions. But it is not rare to find some specific complexes generated as precursors of precipitates at elevated temperature. It is therefore not surprising that different products precipitate, at times, merely because of a difference in temperature in otherwise identical systems.^^^'^'^ The counterions to metal ions are known to play a definite role through the formation of their precursor complexes. For example, monodisperse amorphous chromium hydroxide particles are generated from chromium salts of sulfate and phosphate, while no precipitation occurs if chloride, nitrate or perchlorate is used instead under the same conditions.^^^*^^^"^^ Sulfate and phosphate form many kinds of mixed complexes with chromium and hydroxide ions. With respect to sulfate, [Cr2(OH)2S04]^^ and Cr(0H)S04 are believed to be units of the precursor complexes.^^"* The nucleation of chromium hydroxide particles occurs as a result of the higher polymerization or the condensation of these precursor complexes with release of sulfate ions. The bulky mixed complexes may not be suitable for forming a crystal structure due to the steric hindrance and/or the low activity. This seems to be the reason why the uniform spherical particles of chromium hydroxide are amorphous. Similarly, unless either sulfate or phosphate ions are used as counterions to aluminum ions, the product is not spherical aluminum hydroxide but hydrous oxide in the form of rods, needles or unique clusters.^^"^^^ Thus, anions are highly responsible for the structure and morphology of the final


257

product. As for the aluminum complexes, Al4(OH)ioS04 is known as one of the fundamental units.^"*^ The reaction mode is similar to that of chromium hydroxide, so the resulting particles are also amoq)hous, but an appreciable amount of sulfate is incorporated in the as-grown aluminum hydroxide particles, in contrast to chromium hydroxide which is free of sulfate ions.^'^'^«^ In the case of basic iron sulfate (Fe3(S04)2(OH)5 -21120), the complexes such as Fe(OH)^^, Fe2(OH)2'*^ and FeS04^ were supposed to be responsible for the particle formation.^'^^ Since these complexes initiate nucleation in the form of monomers or dimers, they appear to have a high degree of freedom and activity for the formation of a crystal structure. In fact, they are known to be of a hexagonal crystal symmetry, and sulfate ions are built in as a component of the crystal lattice. Counterions to ferric ions, other than sulfate and phosphate, used in the hydrolysis of ferric ions at low pH normally give hematite (a-Fe203). However, the shape of the hematite varies with the anion species; e.g,, nitrate and perchlorate give ellipsoids, whereas chloride yields cubes, spheres, ellipsoids, or double ellipsoids. However, rod-like akaganeite (PFeOOH) is also produced in a relatively higher concentration range of Fe"^* on aging of acidic ferric chloride solutions.^"^ After all, the choice of counterions is of great importance for the hydrolysis of metal ions, because some of them give no precipitation, while others decisively dominate the composition and morphology of the final products. It is also noteworthy that a small amount of adsorptives causes, at times, anisotropic particle growth; e.g., phosphate yields spindle-like hematite."^^ All the above procedures are based on batch systems. However, a method is also available for the continuous preparation of uniform metal (hydrous) oxide particles by forced hydrolysis; e.g,, Si02,^^^ AI2O3 •nH20,^^^ and a-Fe203.^^'' Although the conditions for uniform particle formation in the continuous system are essentially the same as those in the batch technique, the former seems to be of more practical significance when the reaction is fast enough without degradation of uniformity. The same continuous process was also successfully applied to the preparation of basic carbonates of lanthanides (Ga, Eu, Tb, and Sm)^^^ and yttrium^^^ (see section 7.2.8). Finally, it should be noted that there is some probability of involvement of phase transformation or recrystallization in the formation of some metal oxides apparently precipitated from homogeneous solutions. For example, it was found that rod-like p-FeOOH particles prevailed on short aging of

258

PREPARATION

ferric chloride in acidic media, but that on prolonged heating, a-Fe203 was produced as the main product under some conditions.^^^ In this example, about a half of the Fe^^ ions are precipitated first in the form of p-FeOOH as an intermediate to a-Fe203, but the other half remaining in the solution phase are used directly for the formation of a-Fe203, when 2.0 x 10"^ mol dm"^ FeCl3 is employed as a starting solution ?^^ 7.2.11. Dispersion Polymerization Polymerization process for the formation of polymer as a precipitate from a homogeneous solution of the monomer is generally referred to as "precipitation polymerization," in which the precipitate is normally obtained as agglomerated floe. On the other hand, dispersion polymerization is usually defined as a polymerization process for production of dispersed polymer particles from a homogeneous solution of monomer in the presence of some steric stabilizer (see also section 7.3.3 for emulsion polymerization)?^^ However, in some systems, the product is obtained in the form of dispersed particles in the absence of foreign stabilizers. In this case, the polymer particles are stabilized by their own partial lyophilicity with lyophilic segments of a comonomer or with some remaining lyophilic nature of the homopolymer itself. Thus one may regard such a particular case of precipitation polymerization as a dispersion polymerization in its broad sense, because the particle growth proceeds in the form of a dispersion. If we redefine the dispersion polymerization in the broad sense, it is a general polymerization process for the formation of dispersed polymer particles from a homogeneous monomer solution, based on the difference in solubility between the monomer and the polymer in a given medium and on the colloidal stability of the polymer particles as a dispersion. This is particularly useful for the preparation of monodispersed polymer latices in a size range from submicrons to ca. 10 ^m. As the solvents of dispersion polymerization, polar solvents, such as ethanol, methanol, and their mixtures with water, and non-polar solvents, such as n-hexane, cyclohexane, nheptane, and w-dodecane, are widely used for radical polymerization, while the non-polar solvents are also used for anionic polymerization. The solvents are mainly chosen on the criterion of the solubilities as the monomer and as the polymer of a given polymer material and from a viewpoint of size control. As the steric stabilizers, polyvinylpyrrolidone (PVP), hydroxypropyl cellulose (HPC), polyacrylic acid (PAA), amphipathic block copolymers such as polystyrene-fo/oc^-polyvinylacetate, polystyreneWoc/:-polybutadiene, etc. are well known. The key point of dispersion


259

polymerization is the good choice of suitable solvents and, if needed, stabilizers, according to the polymer species. For the preparation of monodispersed spheres of polystyrene by radical dispersion polymerization with an initiator, such as benzoyl peroxide (BPO) or 2,2'-azobis(isobutyronitrile) (AIBN), typical solvents are alcohols, such as ethanol, methyl cellosolve, and their mixtures with water, while popular stabilizers are graft copolymers,^"*^ polymeric stabilizers plus quatemary ammonium salts,^'' fyfiMÂs nfc^êaAi pAA,2^« ?S-b-?WAc,^'' etc. For example, 7.5 g of HPC (M^ = 100,000) is dissolved in a mixed solvent of 175 cm^ of ethanol and 250 cm^ of methyl cellosolve (2methoxyethanol) under a nitrogen atmosphere with mechanical stirring over 30 min at 65 °C, followed by addition of 3 g of benzoyl peroxide (BPO) dissolved in 75 cm^ of styrene monomer. One observes the homogeneous mixture become cloudy after 5 min. After 2 h, the temperature was raised to 75 °C and the reaction was allowed to proceed for 24 h, followed by cooling, centrifugal washing with water, and freeze drying. The produced PS particles are monodispersed 10-îm spheres, as shown in Fig. 7.15.^"*^

Fig. 7.15. Polystyrene particles prepared by dispersion polymerization using polyvinylpyrrolidone as a stabilizer. (From Ref. 245 (b).)

Okubo et al prepared monodisperse PS particles {ca, 1 \xm) by polymerization of seed particles swollen with styrene monomer (original size ca. 2 pim).^^ They also obtained hollow particles by polymerization of seed particles swollen with toluene and divinylbenzene^^ or by extracting with toluene the cores of core/shell particles composed of a linear polymer core and a cross-linked polymer shell.^^ Monodispersed polystyrene spheres are also prepared by anionic dispersion polymerization with an organometallic catalyst, such as dibutylmagnesium or êc-butyllithium, in a non-polar solvent, such as n-hexane

260

PREPARATION

or cyclohexane, in the presence of a steric stabilizer such as PS-fo-PBu.^^'^"^ Like ordinary anionic polymerization, the reaction of an organometallic catalyst with monomer is so fast that all initiated monomer anions, styryl anions, start the polymerization almost at the same time, and thus the resulting molecular weight distribution of the linear polymer chains is very narrow. The active terminal of each polymer chain keeps its activity for a long time, so it is called the "living polymer," in contrast to radical polymerization with a high probability of termination by recombination of the radicals. Since living polymer anions are mostly incorporated in each uniform particle, thus it is possible to achieve a high solid content by repeated addition of monomer without degrading the uniformity .^^^'^"^ Monodispersed spheres of polymethylmethacrylate^^^^'*^'^^^'^^^ and other polymethacrylate esters (ethyl, n-butyl, iso-hutyl, tert-butyl, benzyl)^^° are also prepared by radical dispersion polymerization in non-polar solvents, such as Az-hexane and n-heptane,^"*^^^^"^^ polar solvents, such as methanQJ243, 259,260 ^ j mixtures (e.g,, methanol/water, methanol/ethyleneglycol(EG), and DMF/EG),^° or supercritical carbon dioxide.^^^ Typical stabilizers are polystyrene-fc/ocit-polydimethylsiloxane in hexane;^^'^^^ poly(2-ethyl-2oxazoline),^^ branched polyethyleneimine,^^ and PVP^° in methanol. Besides, uniform spheres of poly(N-vinylformamide),^^^ poly(2hydroxyethylmethacrylate,^^ porous polyacrylonitrile,^^'* styrene/ butylacrylate copolymer,^^ styrene/butadiene copolymer,^^^ cross-linked polydivinylbenzene and styrene/divinylbenzene copolymer,^^^"^^^ styrene/butylmethacrylate copolymer,^^^ double-structured (shell/core) polybutylmethacrylate/polystyrene^^^ and polystyrene/polymethylmethacrylate,^^^ etc. have been prepared by dispersion polymerization. Surface modification of polymer spheres for introduction of functional groups has also been performed. For example, Okubo et al. introduced chloromethyl groups^"*^ or vinyl groups^^^'^^^ to the surfaces of polystyrene seed particles by dispersion copolymerization of styrene with chloromethylstyrene or divinylbenzene in the presence of the seeds. Pelton and Chibante^^"* and Kawaguchi etaL^^^'^^^ prepared monodispersed hydrogel microspheres of N-substituted polyacrylamides by stabilizer-free dispersion polymerization in ethanol in the presence of a comonomer such as methacrylic acid. For the synthesis of monodispersed microspheres of acrylamide/methylenebisacrylamide/methacrylic acid copolymer with AIBN in ethanol, methacrylic acid was found to play a key role as a stabilizer of the microspheres through its copolymerization.^^^ Similarly, monodispersed hydrogel microspheres of p-nitrophenyl aery-


261

late/acrylamide/methylenebisacrylamide/methacrylic acid copolymer were also obtained.^^^ Yoshida et al?'^^ prepared monodispersed microspheres of polydiethyleneglycol dimethacrylate in ethylacetate by y-ray radiation without stabilizers. It was found that no particles were obtained when the proportion of monofunctional monomer as a substitute of the bifunctional one was increased, suggesting the necessity of a cross-linking reaction for the nucleation.^^^ This result may also imply that the polymer retains a relatively high lyophilicity, leading to the self-stabilization of the particles. Zelenev et al.^^ prepared monodisperse polypyrrole particles ranging from 17 to 59 nm in diameter in an aqueous solution by oxidation of pyrrole with sodium persulfate in the presence of a nonionic polymer stabilizer, Rhodasurf TB970, and 4-ethyl benzenesulfonic acid as a dopant. The detail of the formation mechanism is so far unknown, but in view of the solubility of pyrrole in water, ca. 8 g per 100 g water at 25 °C,^^^ sufficiently high for total dissolution of the used pyrrole, and the highly uniform product, the polypyrrole particles seem to be formed by a kind of dispersion polymerization. Nucleation and Growth Mechanisms To date, the mechanism of the formation of monodispersed particles by radical dispersion polymerization appears to be explained as foUows.^'*^'^'^'* In the course of polymerization, when the oligomer radicals reach a certain critical chain length, they start to coalesce and precipitate due to the loss of the solubility. The nuclei thus generated are then self-stabilized or stabilized by adsorption of a coexisting stabilizer, followed by their growth through the polymerization of the monomer absorbed by the polymer particles for their swelling. During this growth stage, oligomer radicals are believed to be constantly generated, but captured by the growing particles before they reach the critical length for nucleation. In ordinary dispersion polymerization systems, the monomer concentration in the homogeneous vSolution phase during the growth stage remains high even if a considerable amount of the monomer is absorbed by the growing polymer particles for their swelling. This is obvious from an experimental result of Okubo et al}^^ that core-shell particles consisting of PS shell and PMMA core were obtained by dispersion polymerization of styrene in the presence of PMMA seeds without previous swelling with styrene monomer, under the conditions in which core-shell particles of PMMA shell and PS core are expected to be formed if the PMMA seeds are completely swollen by styrene monomer in advance.^^^ Perhaps, the

262

PREPARATION

concentration of the initiator in the solution phase of an ordinary dispersion polymerization system may be also sufficiently high even in the growth stage. In other words, it seems certain that monodisperse particles can be obtained even with constant generation of the oligomer radicals during the growth stage. However, if oligomer radicals are constantly produced in the solution phase and if some of those exceeding the critical chain length are assumed to nucleate invariably, it does not seem possible to achieve a monodisperse system by preventing all oligomer radicals from exceeding the critical length for nucleation. In view of such inconsistency, there seems to be some essential concept lacking in the conventional elucidation. Namely, we may need to introduce the concept of the "critical supersaturation" of oligomer radicals for the nucleation of polymer particles as well, as a function not only of the chain length but also of the concentration of the oligomer radicals, instead of the "critical chain length." In other words, even if the chain length of each oligomer radical is relatively large, their nucleation may be prevented as long as their concentration is lower than the critical supersaturation level proper to the chain length. Also, at a supersaturation below the critical level, while the oligomer radicals do not nucleate, they can deposit onto coexisting polymer particles. As a consequence, the concept of the critical supersaturation of oligomer radicals as a kind of solute or a monomeric precursor, like the analogous sol-gel systems of inorganic colloids (see section 7.2.9), seems to lead us to the complete understanding of the mechanism for the formation of monodisperse particles in radical dispersion polymerization systems. The incorporated oligomer radicals may continue their polymerization with the monomer constantly supplied from the solution phase or already involved in the polymer particles swollen by the monomer absorbed from the solution phase. To this polymerization process in the polymer particles, the initiator, initiator radicals, and monomer radicals, absorbed independently from the solution phase, may also make some contribution. Hence, it seems that there are two parallel processes for the growth of the polymer particles in radical dispersion polymerization systems; Le,, the continuous deposition of oligomer radicals formed in the solution phase and the polymerization of the incorporated oligomer radicals with the monomer in the polymer particles swollen by the monomer continuously absorbed from the solution phase. The final particle number is determined during the nucleation stage by the balance among the formation rate of the oligomer radicals, the coagulation rate of the generated nuclei, the adsorption rate of the stabilizer to them, and the growth rate of the stabilized nuclei.


263

In the case of anionic dispersion polymerization, in which monomer anions are almost instantly formed on introduction of an organometallic initiator, the nucleation of oligomer anions may occur when they reach the critical supersaturation with a critical concentration of oligomer anions of a certain chain length. As the number concentration of the oligomer anions is almost kept constant from the start of the polymerization, the increase of the supersaturation ratio is based mostly on the reduction of the solubility of the oligomer anions with the progress of the polymerization. Since the molecular weights of the oligomer anions are expected to be quite uniform at the moment of the nucleation, the nucleation period must be very short and almost all oligomer anions are deemed to be incorporated into the nuclei at this moment. Nevertheless, there must be some molecular-weight distribution for the oligomer anions even in such a system, and thus the nucleation may be terminated when a sufficient amount of nuclei has been generated for absorbing the remaining oligomer anions in the progress of polymerization, in a manner similar to radical dispersion polymerization. The number of the oligomer anions in each nucleus is in a range of about 10^ - 10^ in some polystyrene systems, as revealed from the number of the linear polymer chains composing a final polymer particle.^"** In anionic dispersion polymerization systems, the number of oligomer anions in a nucleus is equivalent in the meaning to the final particle number, which may be determined by a mechanism basically similar to radical dispersion polymerization. The nuclei and their aggregates may be stabilized by steric stabilizer during the short nucleation period and grow by the reaction of the incorporated oligomer anions with the monomer within each particle swollen by the monomer continuously absorbed from the solution phase. In view of the very large number of polymer chains in a particle as compared to the number of monomer units of a chain on the order of several hundreds, the head groups of the anionic polymer chains must be distributed uniformly in a particle, and thus the polymerization may proceed uniformly in the interior of each particle. The uniform molecular-weight distribution of the linear polymer chains^^^ may also supports this idea. In such a system, renucleation may not occur, since there are virtually no oligomer anions left in the homogeneous liquid phase in the growth stage. It is known that the final particle number normally decreases, and thus the final particle size increases, with increasing affinity of the solvent (solvency) to the polymer particles in radical dispersion polymerization systems.^^ Also, the increase of monomer concentration, leading to the increase in the solvency of the medium, mostly results in the reduction of

264

PREPARATION

the final particle number?"^'^^ These are cx)nventionally explained in terms of the retarded aggregation of the oligomer as a result of the increased critical chain length for aggregation on account of the increased solvency 244^77 However, if we interpret these phenomena in this manner, we have to assume that the aggregation of the oligomer of a somewhat higher molecular weight is rather enhanced in the medium of a higher solvency to achieve the more reduced particle number. Since a higher solvency generally leads to a higher stability of polymer particles as a result of the reduced surface energy, this explanation seems to involve a self-contradiction in itself. In fact, it is not rare to find opposite examples; e.g., increase in particle number with increasing monomer concentration in anionic polymerization,^^^ or with increasing lyophilicity of a polymer by copolymerization of lyophilic monomer units in a radical dispersion polymerization system.^^^ Generally, when solvency is increased, the volumic growth rate of a nucleus, v^, in Eq. (1.4.5) for the final particle number, /i^.°°, may greatly increase to reduce w^*" due to the increase in the soluble concentration of the oligomer in the nucleation stage, and the coagulation of the generated nuclei may be arrested due to the increased stability of the nuclei. Normally, the former of these reciprocal effects seems to be stronger than the latter, leading to the reduction of the final particle number or the increase of the final particle size. However, the former effect may not work in anionic dispersion polymerization, because the number concentration of oligomer anions does not increase with increase in the monomer concentration, unless the concentration of the initiator is increased. On the other hand, the increase in particle number in the copolymerization system may suggest a pronounced self-stabilization of the generated nuclei by the copolymerized lyophilic segments. Nevertheless, if solvency increases excessively, particles may become "sticky" so that coagulation of generated nuclei may turn to be enhanced. Such a sign appears to be observed in a result for the effect of monomer concentration in anionic dispersion polymerization by Awan et al.^^^ Needless to say, the final molecular weight of linear polymer in anionic dispersion polymerization is basically determined only by the molar ratio of monomer to initiator, independently of the particle size, as is obvious from the living nature.^"* In contrast, the molecular weight of linear polymer in radical dispersion polymerization is generally decreased with increasing particle size by increasing solvency, even if the molar ratio of monomer to initiator is the vsame.^^° Perhaps this may be due to a higher probability of the recombination of the polymer radicals in a larger particle containing a


265

greater number of radicals. The final particle number usually decreases with increasing initiator content in both radical and anionic dispersion polymerization systems.^'*^'^'*''^^^ Takahashi et al.^^ also observed in radical dispersion polymerization of methyl methacrylate in a mixed methanol/water solvent (MMA 20 g, MeOH 48 g, water 32 g, PVP 2 g, AIBN 0.4 g; 65 °C, 8 h) that increase of added mercaptoacetic acid, as a chain-transfer agent, up to 1.5 g results in the reduction of the final particle number or the increase of the final particle size from about 2 to 5 \xm, as well as reduction of the molecular weight (M^) of the linear polymer from about 4 x 10^ to 2 x lO"*. In these systems with a high concentration of initiator or with a chain transfer agent, the critical supersaturation for the nucleation of the polymer particles may be reached with a high concentration of oligomer of a relatively low molecular weight, and thus the volumic growth rate of the nuclei, i;^, in Eq. (1.4.5) in the nucleation stage is expected to be large, owing to the high concentration of the oligomer with high diffusivity, resulting in a small final particle number. In this case, the effect of the relatively high QQ in Eq. (1.4.5), as an increasing factor for «^", may be minimized by the rapid coagulation of the generated nuclei before their stabilization by the stabilizer.

7.3. Heterogeneous Systems 7.3.1. Phase Transformation of Solids In this system, a solid precursor different in composition from the final product is dissolved to yield the more stable and uniform final particles. There are some varieties in this precipitation mode: 1) direct fonnation of final product by dissolution of a solid precursor previously precipitated; 2) multi-step phase transformation of more than one solid precursor through sequential dissolution; 3) phase transformation of a solid precursor prepared in a separate system and pretreated before use. The most typical system in this category may be the "gel-sol system" recently developed for the preparation of general monodisperse particles in large quantities, in which highly viscous condensed gels are used as a solid precursor. If a solid precursor itself does not form a gel structure, some substances such as lyophilic polymers or surfactants are used as a subsidiary additive to form a gel structure. In a broad sense, even the highly condensed chelate systems with gelatin, described in section 7.2.4, may also

266

PREPARATION

be included in the gel-sol system. The examples of this system with a solid precursor and their more detailed explanation will be given in the later part of this section {Condensed Systems). a) Dilute Systems Sugimoto and Matijevic^"' prepared monodisperse cubic particles of cobalto-cobaltic oxide (C03O4; 0.1 - 0.2 ptm) with a spinel structure by hydrolysis of cobalt(II) with partial oxidation of Co^^ ions above 90 to 100 °C for several hours, starting from an aqueous solution of ca, 10"^ mol dm"^ Co(II) acetate at pH 7.3. A green cobalt hydroxide gel precipitated at first and then the final particles formed thereon. The oxidation of Co^"^ ions was caused by oxygen dissolved in the solution and thus it was greatly pronounced by bubbling oxygen or air. The counter-ions (acetate) worked as a pH buffer and also as a component of the precursor complexes to the C03O4 particles.^^ Too high a pH over 8 gave no precipitation of C03O4 on the Co(OH)2 gel, so a specific complex such as CoAc^ may be responsible for the precipitation of the C03O4 solid. The Co(OH)2 gel served as a gel network to hold each C03O4 particle to prevent coagulation. This observation led to the idea of the gel-sol method later on. Sugimoto and Matijevic"*^ also prepared uniform spherical particles of magnetite (Fe304) by partial oxidation of ferrous hydroxide gel with nitrate. The uniform magnetite particles were obtained at a slight excess of Fe^^, and the mean size depended critically on the excess concentration of Fe^"" or the pH. Figure 7.16 shows SEM images of Fe304 particles prepared at different excess concentrations of FeS04. The preparation conditions are: the initial [FeS04] = 2.5 X 10"^ mol dm'^ [KNO3] = 0.2 mol dm'^ temperature = 90 °C; aging time = 4 h. First, the Fe(0H)2 gel precipitated on mixing ferrous sulfate with potassium hydroxide. Then the ferrous hydroxide gel shortly turned into irregular platelets, holding extremely small magnetite particles (< 0.1 \kxa) thereon, by partial oxidation on introduction of potassium nitrate as a mild oxidizing agent for ferrous ions at 90 °C. The platelets of a dark green color are thought to be a partly oxidized Fe(0H)2 called green rust.^^^ The phase transformation from the pure Fe(0H)2 to the green rust finished within 15 min at 90 ""C, as revealed by radiochemical analysis."*^ In this early stage, the fine magnetite particles increased in number, whereas no appreciable growth took place without coagulation among them, owing to the gel-like substrate of the partly oxidized ferrous hydroxide. In the course of dissolution of the substrate with an accumulation of the primary particles


267 I. u * I u

EXCESS LFeSO^J = 3 . 0 X 1 0 'M

r-i

5 pm I

1

Fig. 7.16. Fe304 particles prepared at different excess concentrations of FeS04 over [OH'] from a dilute Fe(0H)2 gel with oxidizing agent, KNO3, at 90 °C. Excess [FeSO^] = 3 X 10-\ 1.0 x 10•^ 5.0 x 10•^ and 1.0 x 10'^ mol dm'\ (From Ref. 47.)

of magnetite, they suddenly started to coagulate to form clusters as the nuclei of the secondary particles consisting of a limited number of primary particles. The secondary nuclei promptly gathered the neighboring primary

268

PREPARATION feÔ^ (large sphere)

FeCOHjgnHgO

FeÔ^ (fine cube)

Fig. 7.17. Scheme of the growth of the uniform magnetite spheres from a Fe(0H)2 gd network. (From Ref. 181.)

particles within the individual attraction fields, presumably by magnetic attraction in addition to van der Waals forces at a pH close to the isoelectric point. The residual gel substrate might prevent random coagulation among the isolated secondary particles, to yield uniform spherical magnetite particles. Figure 7.17 presents the growth model.^^^ The coagulation of the primary particles appears to be against the general rules for the formation of monodisperse particles. However, if the clustering of the primary particles is regarded as the nucleation of the secondary particles, this system is still in compliance with the rules. In this case, the selective growth of the secondary particles seems to be due to their own increasing attractive forces of magnetism and van der Waals potential with their growth. As a consequence, the role of the remaining gel network is essential for separation of the growing secondary particles, with a proper inter-particle distance being necessary for keeping them out of each potential field of attraction. The mean size of the magnetite particles was strongly dependent on the excess concentration of the ferrous ions or the pH, ranging from 0.03 to 1.1 jxm. The maximum particle size was found at pH - 6.7, and the size was dramatically lowered to either side of this pH. Since the specific pH is


269

close to the isoelectric point of magnetite, the strong pH-dependence of the particle size seems to be due to the drastic change in the repulsive force of the electric double layer about the isoelectric point between the growing secondary particles and the neighboring primary particles. It is not surprising that the particles are spherical but crystalline, if one considers the formation mechanism. The rather smooth surface of the spherical magnetite may be a consequence of the rapid contact recrystallization of the constituent primary particles, forming the rigid polycrystalline structure (see section 4.5). However, it must be noted that polycrystalline spheres are also prepared by normal deposition of monomeric solute, as has been shown in the formation of the uniform spherical polycrystalline particles of metal sulfides in section 7.2.6. We have ample examples similar to this case, as will be shown later. Thus, we may be able to predict the final particle shape and structure from the formation mechanism, but it is quite risky to draw conclusions about the formation mechanism conversely from only characterization of the product. In a similar manner, uniform spherical particles of nickel ferrite (NiFe204),^^^ cobalt ferrite (CoFepj,^^^ cobalt-nickel ferrite (Co^NiyFe"i_^_yFe"^204)»^^ ^^^^ prepared. Precipitation of ferric hydroxide gel was also observed in the preparation of spindle-like hematite particles in a dilute ferric chloride solution in the presence of phosphate.^^^ In this case, however, the positive role of the gel was not definite since similar uniform hematite particles were also obtained in homogeneous systems in the presence of the same anions.^^^ Also, Hamada and Matijevic^^ prepared uniform particles of pseudocubic hematite by hydrolysis of ferric chloride in aqueous solutions of alcohol (10-50 %) at 100 °C for several days. In this reaction, it was observed that acicular crystals of P-FeOOH precipitated first and then dissolved with formation of the pseudocubic particles of hematite. The intermediate p-FeOOH appears to work as a reservoir of the solute to maintain an ideal supersaturation for the nucleation and growth of the hematite. Since the p-FeOOH as an intermediate and the pseudocubic shape of the hematite particles are not peculiar to the alcohol/water medium,^°^ alcohol may favor the formation of the uniform particles, as a poorer solvent for )8-FeOOH, by reducing the supersaturation for hematite after its nucleation. In fact, the concentration of ferric ions in the supernatant solution was as low as ca. 5 % of the initial concentration of ferric chloride (1.9 x 10"^ mol dm"^) after the precipitation of p-FeOOH, while it was ca. 50 % in an alcohol-free aqueous solution of ferric chloride with a comparable initial concentration (2.0 x 10"^ mol dm" ^)?^^ Since this system starts from a dilute homogeneous solution, it has

270

PREPARATION

been treated as a homogeneous system. However, it involves also a characteristic of a heterogeneous system in itself, since this system has a by-path to hematite via j8-FeOOH precipitated in advance. For the phase transformation of iron oxides, oxyhydroxides, and hydrous oxides in aqueous media, a comprehensive review article^^^ is available. The polyol process for the preparation of metal particles by redox reaction in homogeneous systems^^ is also useful for the formation of metal particles by phase transformation of solids in heterogeneous systems. For example, submicrometer-size silver (Ag) from silver carbonate;^^^ cobalt (Co), nickel (Ni), and cobalt-nickel (Co-Ni) alloy from the corresponding metal hydroxides;^'^^^'^^^ iron (Fe) from Fe(II)(OH)2;2^^ iron-cobalt-nickel (Fe-Co-Ni) alloy from the mixed metal hydroxides of Fe(0H)2, Co(OH)2, and Ni(OH)2;''''''' copper (Cu) from Cu(II)0.2^295 j^^ ^j^^^^ p^jy^j systems, typical concentration of the metals is relatively high as about 0.2 mol dm~^. In the cases of Co, Ni, and Fe, polyol works as a protective agent as well, while some steric stabilizers such as PVP are needed for the preparation of Cu and noble metal particles. Also, nanosized copper-platinum (Cu-Pt) alloy,^^^ copper-palladium (Cu-Pd) alloy,^^^ and palladium-nickel (PdNi) alloy^^^ are prepared from the corresponding mixed metal hydroxides at pH - 10. For the synthesis of these bimetallic nanoparticles useful as a highly active hydrogenation catalyst, the metal concentration is of the order of mmol dm"^ and PVP is mdispensable for their stabilization. Cubic copper particles of a mean edge length ca, 2 [im were prepared by phase transformation from basic copper(II) carbonate with hydroxylamine hydrochloride in an aqueous solution.^^^'^^^ b) Condensed Systems The total concentration of solute in most of the monodispersed particle systems remains in the range from 10"^ to 10"^ mol dm"-' for the essential reason of the tremendous coagulation. The low productivity may be the most difficult problem for general monodispersed particles to be used as industrial products despite their ideally controlled properties. In order to resolve this problem, the new general process named the "gel-sol method" has been invented.^^^'^^^"^^^ This method is based on an idea that if we make use of an extremely condensed precursor gel as a matrix for the subsequently generated product particles, as well as a reservoir of the metal (and hydroxide) ions, it may be possible to prevent the coagulation of the particles by fixing them in the gel matrix, even at a high concentration of electrolyte, and keep them growing without renuclea-


271

tion at a moderate supersaturation by constant release of metal (and hydroxide) ions. Finally, the gel as a reservoir of metal ions is expected to disappear at the end of the total process. Hence, the gel-sol process is reverse in concept to the original sol-gel process in which a gel is formed from a sol (see section 7.2.9), though the former may cover more general areas than the latter which is essentially based only on the hydrolysis of alkoxides. On the basis of the above expectation, the synthesis of monodisperse hematite (a-Fe203) particles, as one of the most popular metal oxides, was attempted first, and its exceedingly uniform pseudocubic particles were successfully obtained from a highly condensed ferric hydroxide gel.^^^'"^°^ To

t#.

Fig. 7.18. TEM images showing the evolution of the solid phase for the formation of monodisperse pseudocubic hematite particles in the gel-sol process with [Fe^"^] = 0.1 mol dm-^ and [Fe(0H)3] = 0.9 moi dm"^ at 100 °C: (a) 0 h, (b) 6 h, (c) 1 day, (d) 2 days, (e) 4 days, and (f) 8 days. (From Ref. 300.)

272

PREPARATION

2um

Fig. 7,19. TEM images showing the effect of the nominal excess concentration of ferric ions or initial pH (measured at room temperature) on the final product species and final particle sizes of the products, after aging Fe(0H)3 gels of x mol dm~^ plus (l-x) mol dm"^ Fe(0H)3 for 8 days at 100 °C: x = (a) 1.0 (pH 0.87), (b) 0.10 (pH 1.9), (c) 0.05 (pH 3.9), and (d) 0.00 (pH 7.7), where the particle species are: (a) p FeOOH and (b)-(d) a-FeA- (From Ref. 299.)

be specific, 5.4 mol dm~^ NaOH was added to the same volume of 2.0 mol dm"^ FeClj in 10 min at room temperature under agitation, and the resulting highly viscous Fe(0H)3 gel (pH - 2.0) was aged in an oven preheated at 100 ± 0 . 1 ^'C for 8 days. Through this simple procedure, monodisperse pseudocubic hematite particles, ca, 1.6 Jim in edge length, were produced with yield nearly 100 %. As shown by the transmission electron micro-


273

graphs in Fig. 7.18, the initial Fe(0H)3 g^l (^) turned into very fine needlelike p-FeOOH crystals in a few hours at 100 °C (b). After 1 day, very small but uniform pseudocubic particles were observed with the slightly grown p-FeOOH (c). They are a-Fe203 particles in their early stage of growth. With the progress of aging, the a-Fe203 particles continued to grow at the expense of the p-FeOOH particles until finally the p-FeOOH particles totally disappeared after 8 days. Hence, the a-Fe203 particles were formed through a two-step phase transformation of Fe(OH)3 -^ p-FeOOH - • a-Fe203 by a dissolution-recrystallization process. In this phase transformation process, the acicular p-FeOOH also formed a viscous network, preventing the coagulation of a-Fe203 particles. On the other hand, it was found that the initial pH or an excessive concentration of Fe^^ ions had a strong effect on the final size of the product, as shown in Fig. 7.19.^^^ The drastic enhancement of nucleation of the hematite with increasing initial pH or decreasing excess concentration of ferric ions suggests a dramatic increase of some specific ferric hydroxide complex as a precursor for the formation of hematite particles with increasing pH, since the supersaturation for the formation of hematite in terms of solubility product is identical for all pH due to the presence of Fe(0H)3 gel. Also, Fig. 7.20 shows the evolution of the supernatant iron species, composition of the solid phase, and pH, measured at room temperature. The sharp drop of pH fi-om 2.0 to 1.0 with the transformation of Fe(0H)3 to p-FeOOH served to cease the nucleation of hematite, since it efficiently lowered the supersaturation of the precursor complex. The nucleation stage was found to be limited within a time range from the start of the mixing of NaOH with the FeCl3 solution to the end of the formation of p-FeOOH after ca. 3 h of aging at 100 ''C. Hence, the system fulfills all the requirements for monodisperse particles formation; z.e., inhibition of random coagulation, separation between nucleation and growth stages, and reserve of monomers (see chapter 6). Size control of the hematite particles must be performed during the nucleation period by controlling the temperature or pH, or by adding very fine seeds of a-Fe203. For example, the mean size can be reduced continuously from a few microns to ca. 0.3 \xm without degrading the uniformity, by changing the temperature from below room temperature to 100 °C during the addition of 5.4 mol dm"^ NaOH to 2.0 mol dm"^ FeCl3.^°^ The same purpose can be achieved to some extent by raising the pH through reducing the excess concentration of ferric ions, but in this case some size-distribution broadening occurs, due to an enhanced growth with

274

PREPARATION I n

O.lp a I

U

\

C-H

I

AGING TIME [ d a y s ]

Fig. 7.20. The evolutions of the supernatant iron species, composition of the solid phase, and pH in a gel-sol system for hematite, aged under the same conditions as those in Fig. 7.18, where these values are those measured at room temperature after quenching. (From Ref. 300.)

the nucleation. Probably, the best way to control the particle size is the addition of ultrafine seeds to the Fe(OH)3 gel under otherwise standard conditions, because the simultaneous progress of nucleation and growth can be avoided in this procedure. If we use very fine seeds of ca. 3 nm in this method, it is possible to extend the lower limit of the final size to 0.03 \xm or less without degrading the monodispersity (see section 8.1.7).^^ The shape of the hematite particles is dramatically changed fi'om the pseudocube to an ellipsoid or peanut-like shape by addition of sulfate or phosphate ions to the Fe(0H)3 gel.^^^"^^ Similarly, ellipsoidal particles are also obtained by addition of dihydroxybenzenes, dihydroxynaphthalenes.


275

EDTA, and NTA.^°^ In contrast to these anisometric uniform particles prepared in acidic conditions (pH < 2), monodisperse platelet-type a-Fe203 particles were obtained by aging highly condensed p-FeOOH particles suspended in a strong alkaline medium with 7.5 mol dm"^ NaOH at 70 ""C for 8 days.^°^ If we simply age Fe(0H)3 gel in ordinary alkaline conditions, we have to raise the aging temperature up to 150 °C or higher to convert fairly stable a-FeOOH (goethite) particles generated as an intermediate into a-Fe203. In this case, only polydispersed tabular hematite particles are produced, since the high temperature raises the probability of renucleation of a-Fe203 during their growth. Scanning electron micrographs of the pseudocubic particles prepared under the standard conditions, ellipsoidal particles with 10"^ mol dm'^ SO/", peanut-type particles with 3 x 10"^ mol dm"^ SO/", and platelet particles in the strong alkaline conditions are shown in Fig. 7.21. The surface planes of the pseudocubic particles were the {012} faces, the long axis of the ellipsoids and peanuts coincided with the c-axis of the hexagonal system, and the basal and side planes of the platelets were the {001} and {012} faces, respectively, as identified by the OPML-XRD.^^ The anisotropic growth of these characteristic particles was explained by the specific adsorption of the anions or the organic additives to some particular faces, inhibiting the growth of these faces: i.e., CY to the {012} faces; SO/", PO/", and the organic additives to the faces parallel to the c-axis, and OH" to the {001} and {012} faces. Thus, these characteristic forms are reaction-controlled steady forms (see section 3.2). The anions such as CI", SO/", PO/", and OH" have a strong effect not only on the shape, but also on the internal structure. Figure 7.22 shows transmission electron micrographs of ultrathin sections of pseudocubic and peanut-type particles of hematite prepared with an ultramicrotome.^"^"^^ Obviously, the pseudocubic and peanut-type particles are polycrystals consisting of much smaller subcrystals of a definite orientation. From the overall definite particle shape and the regular orientation of the subcrystals, it seems reasonable to consider that the overall growth mode of these polycrystalline particles is basically identical to ordinary monocrystalline particles in which two-dimensional surface nuclei are repeatedly generated epitaxially on the growing surfaces and laterally developed, reflecting the lattice structure of the substrate crystal planes, but there must be some specific reason for the formation of the internal discontinuity. The cause of the internal discontinuity has been explained in terms of the blocked fusion among the developing two-dimensional surface grains by the strong adsorption of CI" and/or S04^" ions to the side faces of the surface grains.

276

PREPARATION

Fig. 7.21. SEM images of hematite particles of different shapes prepared by the gel-sol method: (a) pseudocubes, (b) ellipsoids, (c) peanuts, and (d) platelets. The respective shape controllers: (a) 3.0 mol dm"^ CI", (b) 1.0 x 10"^ mol dm"^ S O / ' , (c) 3.0 X 10"^ mol dm"^ S O / ' , and (d) 7.5 mol dm'^ OH'. (From Ref. 302 for (a)(c); Ref. 306 for (d).)


277

Fig. 7.22. TEM images of thin sections of pseudocubic and peanut-type hematite particles prepared by the gel-sol method in the presence of 3.0 mol dm"^ CI" and 3.0 X 10"^ mol dm"^ S04^~ (in addition to 3.0 mol dm"^ CI"), respectively. (From Ref. 307.)

leading to the internal discontinuity of a particle by repetition of this process during its three-dimensional growth (see section 83)300.303304 Q^^ ^J^^ ^^ÎQI hand, the platelet particles were found to be single crystals from the close observation of their ultrathin sections.-^^° In addition, there were significant differences between the species of anions including Cr, SO/", and PO/" in their effect on the internal structure, and considerable amounts of the added anions were found to be incorporated in the hematite particles.-^^^'^^ More detailed discussion on the effects of adsorptives on the relationship between the particle shape and internal structure will be given in chapter 8 (sections 8.2 and 8.3). Incidentally, in some cases uniform particles are grown by aggregation of preformed primary particles, as has been shown earlier in the growth of the spherical magnetite particles, in which the gel network inhibited the random coagulation of the growing particles. However, such a case seems rather exceptional. If some particles grow by such a mechanism, there must be some special reason, as in the case of the magnetite particles. One of the most useful methods to distinguish between the normal growth by deposition of monomeric solute and the aggregative growth with primary particles may be the observation of the effect of seed particles on the overall reaction rate

278

PREPARATION

(see section 9.10).^^^'^° If the growth of particles proceed through aggregation of primary particles, the overall reaction will not be accelerated by addition of seeds, since seed particles may not enhance the formation of primary particles m the solution phase. On the other hand, if the particles are grown by the deposition of monomeric species, the overall reaction will be accelerated as long as the supersaturation is kept nearly constant, due to the increase of the deposition area. Hence, if the overall reaction is accelerated by addition of seeds, the growth of the particles is controlled by the deposition of the monomeric species, and the preceding process, if any, for the release of monomers from their reservoir, such as hydrolysis of metal alkoxides or metal ions, dissociation of metal complexes, or dissolution of solid precursors, is not the rate-determining step of the total reaction. This method can be applied to any kind of particulate systems including dilute homogeneous systems. By using this procedure, it was found that the ratedetermining step for the formation of the monodisperse particles of hematite in the gel-sol process was the surface-reaction step for the deposition of the monomeric species and not the dissolution step of the p-FeOOH. Here, it should be noted that if the overall reaction rate is limited by the release rate of the monomers from their reservoir, the addition of seeds has no effect on the overall reaction rate, regardless of the growth mechanism. In other words, even if addition of seeds has no influence on the overall reaction rate, it does not necessarily imply the aggregative growth mechanism. The scanning electron micrographs in Fig. 7.23 are those of monodispersed basic aluminum sulfate (Al3(S04)2(OH)5 •2H2O; hexagonal crystal system) particles prepared by aging highly condensed aluminum hydroxide gels containing sulfate ions at 100 °C for several days with different total concentrations of SO/".^^^ The morphological difference between those in A-3[B-3] and B-5[3] is due to the adsorption of sulfate ions. Namely, the cuboidal particles, A-3[B-3], with rounded comers and edges by the adsorption of sulfate ions become sharp-cornered cubic particles bound by only the {012} faces, B-5[3], with the reduction of the total concentration of sulfate ions, [SO/"]. The shape of the basic aluminum sulfate particles is also dramatically changed by adsorption of hydroxide and chloride ions, as will be shown in section 8.2.1 (see Figures 8.2 and 8.7). Figure 7.24 shows a scanning electron micrograph of spindle-like uniform particles of titania (Ti02; anatase) prepared by the gel-sol method.^^^'^^^ Triethanolamine and titanium tetraisopropoxide were mixed in nitrogen atmosphere at a molar ratio 2 : 1 , and then doubly distilled water was added to make a stock solution containing 0.50 mol dm"^ titanium ions.


A-3 (B-3) I

"H

Sîrn

279

B-5P3

2|im

Fig. 7.23. Basic aluminum sulfate particles in a round-comered cuboidal shape (A~ 3[B-3]) and in a sharp-comered cube (B-5[3]), prepared by the gel-sol method at [S04^-]/[Al^"] = 2/3 and 1/4, respectively, where [S042-]/[Al^*] is the ratio of sulfate to aluminum ions in total concentration. (From Ref. 311.)

Fig. 7.24. SEM image of the uniform ellipsoidal titania prepared by the gel-sol method, based on the hydrolysis of a complex of titanium ions converted from titanium isopropoxide with triethanolamine. (From Ref. 312.)

PREPARATION

280

IxlO'

0

10 20

30 40 50 60 70 Aging time (h)

80

90 100

Fig. 7.25. Evolution of the concentration of the supernatant titanium ions under the standard conditions in the gel-sol process. (From Ref. 313.)

To the stock solution an equal volume of 2.0 mol dm"^ NH3 was added at room temperature, and aged at 100 °C for 24 h in a Pyrex culture tube (1st aging), followed by aging in an autoclave at 140 ''C for 3 days (2nd aging). The triethanolamine was used as a stabilizer for titanium tetraisopropoxide to prevent hydrolysis at room temperature. The first aging was for the gel formation of titanium hydroxide, and the possibility of nucleation of titania during the first aging was negligibly small because the final size and shape of the product were virtually unaffected by the change of the duration of the first aging, ranging from 8 to 24 h after the rigid gel had been formed. The nucleation of the Ti02 seemed to be limited within the early stage of the second aging, including the time for the elevation of temperature to 140 °C, when the concentration of titanium ions in the supernatant solution of the gel was drastically lowered at the same time due to the enhanced hydrolysis of the remaining titanium alkoxide complex of triethanolamine and incorporation of the resulting titanium hydroxide into the gel network (see Fig. 7.25). After the rapid drop of the supernatant concentration of titanium ions, the slope of its reduction became very small, conesponding to the steady state in the growth stage of the titania with the dissolution of the titanium hydroxide gel. When seed particles of titania were introduced into the gel-sol system before the start of the first aging, the reaction completed


281

in only 1 day, in contrast to 3 days in the standard system without seeds. This result clearly demonstrates that the rate-detennining step of the total growth reaction is not the dissolution process of the hydroxide gel, and that the titania particles are grown by the deposition of the solute and not by aggregation of preformed primary particles. Also, when the first aging for gelation was skipped, a drastic aggregation of the product was observed, showing the important role of the gel network as an anticoagulant. Leaflet-like uniform cupric oxide (CuO) particles were obtained by adding 100 cm^ of 0.80 mol dm~^ NaOH to the same volume of 0.40 mol dm"^ Cu(N03)2 with stirring and aged at 40 °C for 6 h under agitation. The

lOmin

Fig. 7.26. Evolution of the solid phase for the formation of the leaflet-type CuO particles by dissolution of Cu(0H)2 8^1 ît 40 °C after the mixing of 100 cm^ ot 0.0572 mol dm'^ NaOH with an equal volume of 0.0286 mol dm"^ Cu(N03)2. (From Ref. 239.)

282

PREPARATION

CuO particles were grown by deposition of the monomeric solute furnished through dissolution of a condensed cupric hydroxide gel, as has been verified by the seeding method.^^ The composition and vShape of the copper oxide particles are identical to those prepared earlier by Lee et al in a dilute controlled double-jet system in which cupric nitrate and sodium hydroxide solutions were introduced simultaneously into a large volume of water, followed by aging of the precipitate.^^"^ Similar uniform CuO particles were also obtained simply by replacing the 0.80 mol dm"^ NaOH and 0.40 mol dm"^ Cu(N03)2 with 0.0572 mol dm"^ NaOH and 0.0286 mol dm"^ Cu(N03)2 in the above procedure of adding a NaOH solution to a Cu(N03)2 solution, followed by aging at 40 °C for 1 h, as shown in the TEMs of Fig. 7.26 for the evolution of the solid phase. In this dilute heterogeneous system, the final concentration of CuO is equal to that in the controlled double-jet system. Although Lee et al suggested an aggregative growth mechanism of preformed CuO primary particles for the growth of the uniform leafletlike CuO particles, it seems more reasonable to consider that the process proceeds through the dissolution-recrystallization of Cu(0H)2 gel in all these cases, regardless of the mixing mode and the final concentration of CuO. If a precursor solid does not form a gel structure, it is necessary to use subsidiary substances, such as gelatin, polyethylene glycol, etc., which form a gel-like structure or acting as a protective colloid. For example, uniform particles of cadmium sulfide (CdS; polycrystalline spheres; 40 nm in mean diameter) consisting of randomly oriented subcrystals of 8.6 nm were prepared from a suspension of 0.5 mol dm"^ Cd(0H)2 crystals with 0.55 mol dm"^ thioacetamide and 1.0 mol dm"^ NH4NO3 in the presence of 1 wt % gelatin at 20 °C and pH 8.5 adjusted with NH3, as shown by SEM images in Fig. 7.27.^°'^^^ The reaction was so fast as to finish within ca, 1 min. The nucleation stage corresponded to the instantaneous reaction of the Cd^^ ions initially in equilibrium with the Cd(0H)2 with S^" promptly liberated from TAA after the introduction of TAA. The rate-determining step of the growth process was the dissolution of the Cd(0H)2 particles, so that the supersaturation was sufficiently lowered in the growth stage, as has been detected by potentiometry with a Cd/CdS electrode (Fig. 7.28). The plateau of the Cd-potential after the sharp drop corresponds to the steady state of the dissolution of Cd(0H)2 and the deposition of the solute onto the CdS particles in their growth stage. The initial pH drop shown in the lower part of Fig. 7.28 is mainly due to the reaction of TAA with Cd^* and its ammonia complex, initially dissolved in the solution phase, which induces the dissolution of Cd(0H)2. The seeding method for distinction between the


400 nm Fig. 7.27. SEM images of the Cd(0H)2 powder as a starting material (a) and CdS particles as the product (b). (From Ref. 70.)

5

10

Time (min)

j Fig. 7.28. The Cd-potential and ] pH changing with time in the system for the synthesis of monodisperse CdS particles from Cd(0H)2. (From Ref. 70.)

284

PREPARATION

growth mode by deposition of the monomeric solute and that by aggregation of preformed primary particles cannot be applied to this system, because the rate-determining step is the dissolution of the Cd(0H)2. Nevertheless, the growth of the CdS particles was found to proceed through the direct deposition of the solute from the effect of the addition mode of TAA on the size distribution of the product. Namely, when TAA was introduced by a two-step addition of a half of the total amount for each step at a time interval of 15 min, the final size distribution became bimodal. When it was introduced continuously for 20 min at a constant rate, the resulting size distribution of the product was found to be very broad. These facts cleariy demonstrated that the new nuclei generated during the growth stage of the preformed particles simply acted as centers for the growth of new particles without aggregation to the preformed particles. In the meantime, the gelatin played several decisive roles in the formation of uniform particles by preventing the direct attack of S^" ions on the Cd(0H)2 solid and the coagulation of the growing particles, in addition to the role as a powerful pH buffer. Ammonia served as a pH buffer as well as a promoter of the particle growth by forming Cd(NH3)/^ complexes. Uniform spherical particles of cuprous oxide (CU2O; polycrystals; 0.27 \im in mean diameter) were prepared by aging a 0.5 mol dm"*' CuO suspension containing 0.5 mol dm"^ N2H4 (hydrazine) and 3 wt % deionized gelatin for 3 h at 30 °C under constant agitation.^^^ The initial pH was adjusted to 9.3 ±0.1 at 30 °C. Figure 7.29 shows SEM images of the starting material CuO and the product CU2O. Use of amorphous Cu(0H)2 as a reservoir of copper ions in place of the crystalline CuO yielded polydispersed particles, due to the too high solubility of Cu(OH)2, causing renucleation of CU2O during its growth. Thus, the choice of solid reservoirs, in terms of solubility and dissolution rate, is generally important for controlling the supersaturation in the formation of uniform particles by the gel-sol method, like the choice of chelating agents in the formation of uniform metal sulfide particles in chelate systems (see section 7.2.6). The role of the gelatin is the same as those in the above CdS system. On the other hand. Fig. 7.30 shows the changes of the concentration of Cu^^ ions, pH, and total concentration of soluble Cu species in the solution phase in a standard system but without gelatin. The initial increase in pH after the introduction of hydrazine is due to the dissolution of the CuO solid caused by the sharp drop of [Cu^^] with complexation of N2H4 with Cu^^ in the solution phase initially in equilibrium with CuO. The subsequent drop of pH after a peak corresponds to the reduction of Cu^"^ to Cu*, probably


285

0.5 ^m Fig. 7.29. SEM images of the CuO powder as a precursor solid (a) and the uniform CU2O spheres as the product (b). (From Ref. 316.)

I I ' I II » I 1 I ' I I II II I I I IM II

0 0

0. 0) 3

0

2

E "o

0

E

n3

0

1

0 U)

30

60

Time (min)

Fig. 7.30. [Cu^*], pH, and total Cu^"" changing with time in the system for the formation of the uniform CU2O particles from the CuO powder. (From Ref. 316.)

286

PREPARATION

through electron transfer from the coordinated N2H4 ligands, leading to the nucleation and growth of the CU2O particles, as revealed by the corresponding drop of the concentration of the soluble Cu species. The final reincrease of pH is due to the formation of anmionia with the oxidation of N2H4 of a basicity lower than NH3. It was found from the quantitative analysis of the product that 38 % of N2H4 was consumed by the following first reaction and 15 % by the second. N2H4 + CuO -^ I/2CU2O + I/2N2 + NH3 + I/2H2O N2H4 + 4CuO - • 2CU2O + N2 + 2H2O In this system, strict control of the initial pH is essential for forming the uniform CU2O particles. When the initial pH was below 9.0, the ratedetermining step for the growth of CU2O shifted from the dissolution process of CuO to the deposition process of CU2O monomers, due to the lowered reducing activity of hydrazine, so that the size distribution of the product became broad, as a result of the lifted supersaturation above the critical level for renucleation. Since it is unlikely that the slight pH difference strongly affects the selectivity in aggregation of primary particles to the growing secondary particles, and since there was no characteristic particle group to be regarded as primary particles, there seems to be no possibility of the aggregative growth mechanism. In contrast to the formation of the monocrystalline CU2O particles of different crystal habits such as cubes, cubo-octahedra, and octahedra produced by reduction of copper(II) tartrate with glucose,"*^ the non-epitaxial growth of the spherical polycrystalline CU2O particles may be brought about by the N2H4 adsorbed on the surface of the CU2O particles, blocking the rearrangement of the CU2O molecules for the epitaxial nucleation on the surfaces. Hu et al?^"^ and Yuze et al}^^ prepared amorphous nickel-phosphorus (Ni-P) alloy spheres of 0.1 to 2 ^m in diameter by phase transformation from nickel hydroxide with sodium hypophosphite, as a reducing agent. In the preparation of amorphous Ni particles, problems were their aggregation and rather broad size distribution. In the meantime, uniform spherical particles of metallic nickel (Ni; amorphous) were prepared by adding 8 mol dm"^ NaH2P02 (sodium hypophosphite) as a reducing agent preheated at 50 °C to an equal volume of a suspension of 0.2 mol dm~^ crystalline Ni(OH)2 particles containing 10 wt % polyethylene glycol (average molecular weight = 1000) as an anticoagulant at 50 °C, and aging for 12 h at the same


287

temperature under constant agitation.^^^ Ion chromatography on the ionic reaction products has revealed that the overall chemical equation is as follows: NaH2P02 + Ni(0H)2 "* NaH2P03 + Ni + HP The pH value of the Ni(0H)2 suspension with NaH2P02, initiaUy at ca, 13 at 50 °C, was raised to ca. 10.2 by addition of a small amount of a concentrated NaOH solution 1 min after the addition of NaH2P02. The pH started to decline soon after the adjustment of pH to 10.2, showing the start of the formation of the Ni particles. The drop of pH, due to the generation of VO^' higher than P02^" in acidity, was initiaUy fast, but became slower with the progress of the particle growth. The Ni particles are formed by deposition of Ni monomers generated through the reduction of the Ni^^ ions furnished from Ni(0H)2 by dissolution. On the other hand, it was found that a considerable amount of Ni(OH)2 remained unreacted when the concentration of the reducing agent was lowered to a half of the standard one, and that the reaction did not start even after 12 h when the concentra-

12 10 8 h

X

Standard Standard + NHs

10

12

Aging Time (h) Fig. 7.31. Evolution of pH in the standard system for the formation of amorphous Ni particles and in the same system but with ammonia (0.7 mol dm"^ in NH3). (From Ref. 319.)

PREPARATION

Fig. 7J2. TEM images of Ni particles prepared in the systems of Fig. 7.31: (a) Standard; (b) Standard + NH3. (From Ref. 319.)

tion of NaH2P02 was reduced to one eighth of the standard one. Since the standard concentration ratio of the NaH2P02 to Ni(0H)2 is originally 40 times higher than the stoichiometric ratio, the concentration of NaH2P02 is still as high as 5 times the stoichiometry even if it is reduced to one eighth of the standard ratio. The strong dependence of the reaction rate on the concentration of the reducing agent in its extremely excess range clearly demonstrates that the rate-determining step for the growth of the Ni particles is the reduction of Ni^^, and not the dissolution process of Ni(OH)2. As a consequence, it seems that the uniform Ni particles are produced by the rapid drop of pH after the addition of the NaH2P02 solution, since the reducing activity of hypophosphite is drastically lowered with decreasing pH. In fact, when the initial pH was adjusted to 10.2 with ammonia (0.7 mol dm"^) instead of NaOH, only polydispersed particles were obtained, due to the very slow pH drop by the buffer action of ammonia. The pH change and the resulting particles after aging for 12 h in these two cases are shown in Figs. 7.31 and 7.32. It was also found that polyethylene glycol played a significant role in inhibiting the coagulation of the growing particles. The Ni particles thus obtained are amorphous with their high phosphorus content


289

around 26 mol % in elemental P, as confinned by XRD and elemental analysis. 7.3,2. Ostwald Ripening Fairly uniform tabular double-twin particles of silver bromide (AgBr) were grown by dissolution of a great amount of very fine particles of silver bromide through Ostwald ripening.^^'^^^ This method is based on the high activity of the troughs of the side planes of the tabular particles for the onedimensional surface nucleation and the high solubility of the coexisting fine particles. The activity of the side troughs for the lateral growth of the tabular particles was found to increase dramatically with increasing concentration of the excess bromide ions or decreasing pBr (= -log[Br"]). As a result, the coefficient of variation or the relative standard deviation of the size distribution was kept almost constant during their growth at a low pBr, while it was reduced at a high pBr due to the diminishing activity of the side troughs, as explained by a spherical diffusion model. Since threedimensional nucleation does not occur in this system, the broadening of the size distribution due to nucleation does not take place. This method can be applied to the growth of nomial monodispersed single-crystal particles of silver halides without degrading the uniformity of the original particles. In this case, anunonia is useful as an accelerator of the Ostwald ripening.^^^ Berry and coworkers,^^"^^^ Moisar and Klein,^^^ Claes and Berendsen^^^ developed the so-called the controlled double-jet (CDJ) method, and obtained monodisperse particles of silver bromide (AgBr) and silver chloride (AgCl) by the simultaneous introduction of silver nitrate and the corresponding halide solutions into a gelatin solution at precisely controlled rates (see section 1.5.2). In this process, very fine primary nuclei, embryos, are generated in a domain of the gelatin solution where these reactant solutions are injected. In the meantime, the embryos are dispersed into the bulk solution region where relatively large stable nuclei grow at the expense of the smaller unstable nuclei by Ostwald ripening.^^^ Thus, in this open system, a nucleation zone and a bulk zone for particle growth coexist in the same solution throughout the precipitation process, as shown in Fig. 7.33. In the early stage, the number of stable nuclei increases with the growing supersaturation by the dissolution of the unstable nuclei, and when a sufficient number of stable nuclei somewhat grown have been built up in the bulk phase, they become able to absorb the whole solute provided by the constant dissolution of the stationary primary nuclei. From this moment, the growing particles cease to increase in number, whereas the primary nuclei

290

PREPARATION AgNOj + KBr AgNO,

• AgBr + KNO3

z

Fig. 7.33. The jiuclealion zone and Ostwald ripening zone in a double jet system for the preparation of silver halide particles. generated in the nucleation zone begin to act simply as a monomer source. In other words, two distinct stages of the nucleation {i.e., accumulation of stable nuclei) and growth are observed in this system, as with usual homogeneous monodisperse systems. This is the reason for the formation of monodisperse particles in this system. In this system, gelatin plays a definite role as a protective colloid to prevent coagulation among the primary nuclei as well as the growing particles at a high ionic strength. In addition, silver bromide particles obey the diffusion-controlled growth mechanism within the range of pBr 2.6-3.5 (pBr = -log[Br"]),-'^^ where we can take advantage of the reduction of the absolute size distribution width (see section 2.6.4). This self-sharpening effect is almost always expected for AgCl particles, because of its diffusion-controlled growth in most of the pCl range.''' If the bulk concentration of solute is kept just below the critical supersaturation for nucleation throughout the precipitation by raising the addition rate of the reactants with the particle growth, the broadening of the size distribution by the Gibbs-Thomson effect is expected to be minimized in diffusion-controlled growth (see section 2.6.4). In fact, the use of such an effect has been proposed in patents for the manufacture of silver halide emulsions in the photographic industry.''^'''^ Recently, tabular silver chloride (AgCl) particles of a high aspect ratio


291

have been prepared by the double jet precipitation technique with silver nitrate and sodium chloride solutions in the presence of iodide or bromide ions in the early stage of the precipitation and a low methionine gelatin, to induce and promote the anisotropic growth.^^^ The large-sized iodide or bromide ions are believed to introduce dislocations into each AgCl grain owing to the lattice misfitting between a Ag(I,Cl) or Ag(Br,Cl) nucleus and the AgCl crystal grown thereon, leading to the anisotropic growth of the twin plane-free tabular grains bound only by the {100} faces (see section 8.2.2). Such particles have essential advantages of efficient photon capturing and rapid development, when used as a photographic material. The well-established double-jet technique was also applied to the preparation of uniform particles of metal sulfates, such as strontium sulfate (SrSOJ,^^' lead sulfate (PbSO^),^'"'''' and barium sulfate (BaSOJ.^^^ Interestingly, Qi et al?^^ prepared rectangular, rod-like, peanut-like, and peach-like BaS04 particles, in the absence or presence of poly(methacrylic acid), poly(ethyleneglycol)-block-poly(methacrylic acid), and this block copolymer with side chains of aspartic acid, respectively. It seems reasonable to consider that these particles were also grown by the Ostwald ripening process of the primary nuclei. The formation of monodisperse particles by Ostwald ripening in an open system is possible only when the primary nuclei can be dissolved quickly even with a subtle undersaturation. 7,3,3. Emulsion Polymerization Emulsion polymerization is a representative method for the synthesis of monodisperse polymer particles in a heterogeneous system, in contrast to the dispersion polymerization for the same purpose in a homogeneous system (see section 7.2.11). In the former the monomer is reserved as an emulsion dispersed normally in water with a water-soluble initiator and the polymer particles is stabilized by some foreign emulsifier or by the ionic end groups of their own polymer chains, while in the latter the monomer is dissolved in an organic medium with an oil-soluble initiator and some polymeric stabilizer. In both cases, polymers are insoluble in the respective media. As will be discussed later in detail, the mechanism of the automatic separation between nucleation and growth stages necessary for the formation of monodispersed particles in emulsion polymerization systems seems to be different between the processes with and without emulsifier. Namely, the emulsion polymerization with an emulsifier, strongly affected by the number concentration of the emulsifier micelles, resembles seeded monodisperse

292

PREPARATION

systems, while the emulsifier-free emulsion polymerization may be explained by the nucleation-controlled precursor model (see section 6.1), similar to the mechanism proposed in section 7.2.11 for radical dispersion polymerization, in which oligomer radicals are thought to play a key role as a precursor in the automatic separation between the nucleation and growth stages. Nevertheless, the growth process after the nucleation stage is common to these emulsion polymerization systems, regardless of the presence or absence of emulsifier. In a manner similar to dispersion polymerization, the growth of polymer particles in any emulsion polymerization systems may proceed through two parallel processes: (1) deposition of oligomer radicals produced by a polymerization process in the continuous liquid phase; (2) polymerization of the deposited oligomer radicals with monomer in each polymer particle swollen with the monomer absorbed from the continuous liquid phase. To the polymerization process of the monomer in the polymer particles, any supersaturated oligomer radicals with different chain lengths may make some contribution by depositing onto and/or entering through the particle surfaces. Polystyrene latices produced by emulsion polymerization may belong to a group of the most typically monodispersed colloids. They have been used widely as internal standards for electron microscopy,-'^^'^''^ materials for the study of light scattering,''^^'^'*^ specimens for the studies of interactions of colloidal particles,^"*^'^^ functional microspheres for medical use (see section 12.6), etc., because of their excellent uniformity. According to Harkins^"*^ and Smith and Ewart''*^, radical polymerization of monomer slightly dissolved in the water phase of an 0/W emulsion with emulsifier is started by an initiator such as potassium persulfate in the aqueous phase, and then the oligomer radicals are absorbed into the micelles of the emulsifier swollen with monomer due to the hydrophobic aliphatic hydrocarbon chains of the oligomer, followed by polymerization of the monomer in the micelles. This stage has been regarded as the nucleation period of the emulsion polymerization with emulsifier. The polymer nuclei continue to grow with the monomer supplied from the monomer droplets stabilized by the emulsifier, through the water phase of the emulsion. During this growth stage, the micelles of the emulsifier are decomposed to form an adsorbed surfactant layer on the polymer particles, which serves for stabilization of the polymer particles. The decomposition of oligomer-free micelles is believed to take place all at once, when the concentration of the free emulsifier is reduced to the CMC (critical micelle concentration). This is thought to be a key to producing uniform particles owing to the absence of


293

MONOMER DROPLET

WATER PHASE

Fig. 7.34. Scheme of emulsion polymerization with emulsifier. (From Ref. 181.)

nucleation sites in the growth stage. Hence, in this particular system, the nucleation mode significantly differs from the spontaneous nucleation via a critical supersaturation in ordinary monodisperse systems. The final particle size, thus, strongly depends on the number of the emulsifier micelles in a system. However, strictly speaking, the nucleation by this definition must continue as long as the oligomer-free emulsifier micelles remain, and thus the nucleation period lasts until the extinction of all oligomer-free micelles. Also, even in this system with emulsifier, the renucleation of the oligomer radicals in the growth stage is prevented by the presence of the growing particles which continue to absorb the generated oligomer radicals. Figure 7.34 shows a scheme of the emulsion polymerization with emulsifier.^^^ Vanderhoff and his coworkers^^ found that the volume of the individual particles of a polystyrene latex grew at a rate proportional to the mean particle radius to ca, the 2.5 power from the evolution of the size difference between two kinds of monodisperse latices different in mean particle size. This leads to narrowing of the relative width of the size distribution during growth. However, it may not always be the case, since Smith^"*^ suggested from his experimental results that the exponent is zero rather than 2.5 for

294

PREPARATION

polystyrene. Similarly, Ugelstad et al^^ and Sudol et a/.^^ also obtained the linear increase of polymer yield with time, as is in favor of the volumic growth rate being independent of particle size. On the other hand, the increase of volumic growth rate with particle size is also observed, especially when the contents of emulsifiers are reduced.^"*^'^* Since the reduction of the content of an emulsifier results in the decrease in particle number or the increase in final particle size, the size dependence of volumic growth rate may be found in a relatively large size range, such as above 3 Jim, used by Vanderhoff and coworkers. In fact, Vanderhoff et al^^ also suggested reduction of the exponent from experiments in much smaller size ranges. If this is true, the linear growth rate of a particle, dridt, is inversely proportional to the square of the particle radius, so that significant selfsharpening of the size distribution can be expected, at least, in a relatively small size range such as below 1 [im. The size-independent volumic growth rate as a characteristic growth mode in emulsion polymerization was explained on assumption that the number of radicals in a growing particle is 0.5 on average by Smith and Ewart.^"*^ More detailed discussion on the growth mechanism and the size effect on the volumic growth rate will be given in the last part of this section for emulsion polymerization. On the other hand, some monodisperse latices, such as anionic polystyrene,^"*^"^^^ cationic polystyrene,^^^ polymethylmethacrylate,^^^ and styrene-acrylamide copolymers,^^"*' ^^^ have been synthesized in the absence of emulsifiers. In these cases, the ionic oligomer radicals may nucleate to form their own micellar nuclei when their concentration reaches their critical supersaturation level, followed by the growth of the nuclei through the continuous deposition of oligomer radicals along with the polymerization of the incorporated oligomer radicals with the monomer in the nuclei, swollen by the monomer furnished from the monomer droplets via the aqueous medium. Hence this is a typical system in which the automatic separation between the nucleation and growth stages is described in terms of the nucleation-controlled precursor model. Accordingly, the final particle size or the number of polymer particles is controlled mainly by regulating the generation rate of the monomer radicals leading to the oligomer radicals. The ionic groups of the surfaces of individual particles stabilize the particles against coagulation during their growth stage. Figure 7.35 shows a TEM of polystyrene particles prepared by emulsifier-free emulsion polymerization. The seeding technique is recommended for emulsion polymerization as well to achieve a high uniformity of the product. However, too high a concentration of emulsifier added to stabilize the seed particles results in

1, MONODISPERSED SYSTEMS

295

Fig. 7.35. Polystyrene particles prepared by emulsifier-free emulsion polymerization (relative standard deviation = 2.8 %). rather polydisperse particles, since it provides the system with free micelles as nucleation centers.^"*^'^^^ This fact clearly teUs us that the micelles containing monomer are efficient centers of nucleation. This may be used for size control by variation of the contents of emulsifiers in usual systems without seeds. In this context, it is of interest whether or not the remaining unreacted micelles, which must mostly contain considerable monomer molecules, are disintegrated simply by the reduction of the concentration of the emulsifier in the aqueous phase below the CMC with the generation of nuclei, as suggested by Harkins.^^ It is quite likely that the micelles strongly associated with monomer molecules may persist even with a concentration of the emulsifier below the CMC of its own. For example, if the affinity of an emulsifier to monomer droplets is comparable to that to the polymer particles, the micelles with monomer may persist until finally all of them have reacted with the monomer radicals. In this case, the number of the generated nuclei is equal to that of the micelles and thus the final particle number is a function of the initial number of the micelles, though the final number of the stable nuclei may be reduced considerably by coagulation of the generated nuclei as suggested by Feeney et al?^^ In any case, not only the generation rate of oligomer radicals and the absorption rate of the oligomer radicals by the generated nuclei, but also the number of micelles is an important determinant of final particle number in

296

PREPARATION

the presence of emulsifier above the CMC in the aqueous phase, in contrast to the emulsifier-free emulsion polymerization. One of the most salient features of emulsion polymerization is that the size and size distribution often depend on the agitation strength. If an emulsifier-free system is not agitated or the agitation is very weak, the monomer and the aqueous solution may be separated into two uniform phases and thus the dissolution rate of the monomer into the aqueous phase may be the rate-determining step for the whole process because of the extremely small interfacial area. However, according to a report of Harkins,^-' the absolute dissolution rate of a styrene-monomer droplet is about 2.6 (xm min"^ at a diameter of 1.4 mm and 4.4 ^m min'^ at a diameter of 0.25 mm at 40 °C. Thus, the dissolution rate of monomer droplets is sufficiently fast to keep the monomer concentration in the aqueous phase close to the solubility of monomer in the aqueous phase if the system is agitated properly. In the presence of an emulsifier of a concentration much higher than the CMC, the dissolution process of the monomer droplets may not be the rate-determining step, even without agitation. Also, the swelling of growing polymer particles with the monomer in the emulsion polymerization of styrene is likely to be sufficiently fast to keep the degree of the swelling of the growing polymer particles almost constant during the polymerization, since, according to Harkins,^^ all styrene monomer has been absorbed into the polymer particles when about 50 to 60 % of the monomer is converted to polymer. Hence, the effect of agitation may be mainly attributed to the change of the interfacial area for adsorption of emulsifier, affecting the concentration of emulsifier in the aqueous phase. Particularly, when the concentration of emulsifier is close to the CMC, the strength of agitation has decisive effects on the number of micelles and the stability of the generated nuclei, affecting the final mean size of the particles and their size distribution.^"*^ A more dramatic effect of agitation may be the formation of uniform particles by direct polymerization of monomer in monomer droplets, suggested by Ugelstad et al^'^ Namely, when the homogenization pressure is raised to bring the size of the monomer droplets to a level of 0.1 to 0.3 tmi in the presence of stabilizers, the direct polymerization in the monomer droplets becomes predominant due to the sufficiently large interfacial area and thus the absence of micelles as nucleation centers. Since the volumic growth rate of a polymer particle of a submicrometer diameter or less is constant regardless of the particle size, and since the mole fraction of monomer in each polymer particle must become equal due to the thermodynamic requirement to equalize the chemical potentials of


297

monomer in different particles by monomer exchange via the aqueous phase, the particle size tends to be equalized while growing. This effect, referred to as "leveling-out effect" by Ugelstad et al., may be a typical characteristic of emulsion polymerization for further promotion of monodispersity, in addition to the size-independent volumic growth rate. Ugelstad et al have produced large (0.5-100 fim) monodisperse polymer spheres of polystyrene and its copolymers^^'^^^*^^^ by emulsion polymerization of monodispersed polymer seeds swollen with the monomers. This method is based on a two-step swelling process of seed polymer particles before the final polymerization: the 1st swelling with a relatively low molecular-weight compound, oil-soluble but less soluble in water than monomer, such as dioctyladipate, chlorododecane, hexadecane, and octadecanol; the 2nd swelling with monomer. An oil-soluble initiator, such as BPO, AIBN, or di-lauroylperoxide, may be absorbed into the seed particles at the same time in the first or second swelling. The first step may be replaced by swelling with monomer and a chain transfer agent, such as carbon tetrabromide, carbon tetrachloride, mercaptanes, or toluene, followed by polymerization to form a large amount of oligomer in the polymer particles. In this case, the oligomer serves as a highly water-insoluble compound. The driving force of the absorption of monomer into the preswoUen polymer particles is the large difference in chemical potential between the pure monomer molecules in the monomer droplets and in the polymer particles containing a highly water-insoluble compound, because the mole fraction of the monomer molecules in a polymer particle is drastically reduced by the presence of the water-insoluble compound with a relatively low molecular weight. The reason for the use of a highly water-insoluble compound is to prevent the reverse diffusion of the diluent from the polymer particles to the monomer droplets. By this two-step swelling method, it is not difficult to swell seed particles several thousand times by volume, in contrast to only 0.5 to 5 times by a simple one-step swelling of polystyrene with its monomer. As an alternative to the two-step swelling method, Okubo etal.^^'^^ proposed 2i single-step dynamic swelling method, in which seed particles are swollen up to 30 to 40 times by volume with monomer together with oil-soluble initiator in a mixed medium of ethanol/water by slowly reducing the solubility of the monomer through adding water or salt, or through cooling. Since this method is based on the use of monomer initially dissolved in the medium, it may be regarded as an application of dispersion polymerization rather than of emulsion polymerization. Also, Yoshimatsu et al?^^ proposed another single-step swelling

298

PREPARATION

procedure, accelerated molecular dijfusion method, in which polystyrene seeds are swollen up to 300 times by volume with divinyl benzene (DVB) monomer by use of an emulsion of DVB monomer droplets containing 5 wt % iso-amyl acetate, which is more soluble in water than the monomer. This method is totally different from the two-step swelling method in principle, since the single-step method does not use the enhanced chemical potential difference between the monomer molecules in the monomer droplets and in the polymer particles. This is obvious from the fact that they found no acceleration of swelling in a combination of polymer particles, previously swollen with iso-amyl acetate, and pure DVB droplets. The authors attempted to elucidate this phenomenon in terms of the GibbsThomson effect based on the reduced droplet size with the reduction of interfacial energy. However, since the solubility change by this effect is at most ca, 10"^ of the original solubility and, besides, the change does not necessarily lead to a positive contribution, this explanation may not be quite likely. As a remaining possibility, one may ascribe the dramatically enhanced swelling to some significant increase of the apparent solubility of DVB in water by its complexation with iso-amyl acetate. The polymerization of polymer particles thus swollen is initiated by raising temperature up to 60-80 °C normally with an oil-soluble initiator previously incorporated in the monomer-swollen polymer particles to minimize the renucleation in the aqueous phase, since an appreciable concentration of monomer is dissolved in the aqueous phase in equilibrium with the monomer in the swollen polymer particles. In order to boost the suppression of the polymerization in the aqueous phase, a small amount of some water-soluble inhibitor, such as hydroquinone, sodium nitrite (NaN02), or copper(Il) chloride (CuCy, is often used. If seeded emulsion polymerization is performed with polymer seeds consisting of a linear polymer, swollen with the monomer, a cross-linking agent, a solvent of the polymer (diluent) and an initiator, and then the linear polymer and diluent are extracted from the cross-linked polymer particles with a solvent such as methylene chloride, porous polymer particles are obtained, as found in the study of Cheng et al?^^ They showed that the pore size of polystyrene latices can be controlled by varying the molecular weight of the linear polymer or by changing the degree of crosslinking of the seed particles. Skjeltorp et al?^^ prepared pear-shaped composite particles of polystyrene-hydrophilic polyacrylate and polymethylmethacrylate-hydrophilic polyacrylate by swelling polystyrene seed particles with a mixture of


299

styrene/hydrophilic acrylate or of methyl methacrylate/hydrophilic acrylate and subsequent polymerization (see Fig. 8.17). The anisotropic shaped has been elucidated in terms of the phase separation of a new polymer phase from the host polymer phase. Sheu et al}^ prepared nonspherical polystyrene latices of different shapes, such as ellipsoids, egg-like singlets, symmetric or asymmetric doublets, and ice-cream cone-like or popcornlike multiplets, by emulsion polymerization of monomer-swollen crosslinked seeds (see Figs. 8.18 and 8.19). The different shapes are attained by variation of the monomer/polymer ratio, the degree of crosslinking of the seed particles or the new polymer phase, the size of the seeds, the shape of the seed particles, the polymerization temperature, etc. (see section 8.2). Tamai and Yasuda^^^ prepared star-like copolymer particles of polystyrenepoly(N-vinylimidazole) containing copper ions by treatment of PS-PVI copolymer spheres, prepared by soap-free emulsion polymerization, in an aqueous solution of CUCI2 for absorption of copper ions and subsequent swelling in an emulsifier-free emulsion of an organic solvent, such as toluene, benzene, and MMA. They speculated that the star-like shape was formed through the swelling of the copolymer particles whose surface layers are internally cross-linked by intermolecular complexation of imidazole groups with copper ions. Also, Okubo et al prepared raspberry-shaped composite particles of polystyrene/polyalkyi acrylate (alkyl = methyl, ethyl, butyl; PS/PAA = 1 by molar ratio of the monomers) by seeded emulsion polymerization of styrene with polyalkylacrylate seeds and a water soluble initiator such as potassium persulfate or hydrogen peroxide, in which the small spherical particles of polystyrene are formed heterogeneously in the surface layers of the polyalkylacrylate seeds. When this seeded polymerization was carried out with an oil-soluble initiator such as benzoyl peroxide, the external shape remained spherical.^^^ On the other hand, when they performed seeded emulsion polymerization with polystyrene seeds swollen with butyl methacrylate monomer and an oil-soluble azo-type initiator, they obtained spherical composite particles of polybutyl methacrylate-polystyrene, in which polybutyl methacrylate deposited as small clusters in the spherical PS matrix.-'^^ Thus, it has been concluded that the raspberry-shaped composites are formed by phase separation of new polymer subparticles condensed in the surface layer of each matrix particle, due to the polymerization near the surfaces of the matrix particles with the water soluble initiator."^^^ In order to provide monodispersed polymer particles (mainly polystyrene) with a multitude of functions, different functional groups are introduced to

300

PREPARATION

the surfaces of seed particles by emulsion copolymerization with comonomers having some specific functional groups; e.g., sulfonic acid group,^^^ carboxyl group,^^^'^^° hydroxyl group,^^^ bromodecyl group,^^^ sulfodecyl group,^^^ mercapto group,^^^ phospholipids,^^ and poIy(2oxazoline) chain.^^^ Hosoya et aO'^'^ bound poly(N-isopropylacrylamide) as a graft to the internal or external surfaces of porous polystyrene spheres. Also, the seeded emulsion polymerization technique is used for coating polymer seeds with inorganic functional nanoparticles as well; e.g., magnetite/polystyrene.^^^ Pendleton et al?^^ obtained monodisperse carbon particles of ca. 0.1 [im by heat treatment or chemical dehydrochlorination of a uniform polyvinylidene chloride latex prepared by emulsion polymerization.^^^ Specifically, the carbon particles obtained by heating at 700 °C in a nitrogen atmosphere were highly porous and uniform, though subjected to considerable shrinkage. It is known that monodisperse latex particles of poly(butadiene-styrene) copolymer (40/60 by weight) up to 560 nm can be obtained by emulsion polymerization, using lithium stearate as a emulsifier and potassium persulfate as an initiator.^^^ El-Aasser et aO^^ prepared monodispersed core-shell particles consisting of rubbery core of poly(butadiene-styrene) (90/10 by weight) and glassy shell of poly(styrene-acrylonitrile) (72/28 by weight) by seeded emulsion polymerization using K2S2O8 as initiator in polymerization of both core and shell, in which they slowly added the monomer mixture during the polymerization of the shell in order to keep the steady monomer concentration below the nucleation level. The polymerization under the monomer-starved conditions may be applicable as a useful technique for inhibiting the renucleation in general emulsion polymerization. The rubbery core - glassy shell particles are used for toughening thermoplastic matrix such as polycarbonate. The authors studied the effects of various parameters in toughening polycarbonate with the well-defined core-shell latex.

Growth Mechanism in Emulsion Polymerization Let us consider some aspects of the growth mechanism in emulsion polymerization. Size effects on the voluniic growth rate of a polymer particle If the recombination rate constant, k^, of radicals in a polymer particle of


301

unswoUen volume v^ is defined as the frequency of recombination for two radicals per unit particle volume, the recombination rate, R^, in a particle containing n, radicals may be given by

yn^-l\

R=k-' ' 2 vV

P

)

since the number of the combination of the radicals for recombination per unit particle volume is (l/2)(nyv^)[(n^-l)/v^]. Here, it should be noted that kj^ is a function of the degree of swelling of the polymer particle. First, let us consider two cases, in which the average number of radicals, Ai^, in a polymer particle during growth is sufficiently larger or less than 1.5. Case 1. n^ » 1.5 Since two radicals are lost by one recombination, the extinction rate of radicals by recombination is twice as much as the recombination rate, and thus the changing rate of the number of the radicals in a particle, dnjdt, may be given by n-\ "p' P

(7.3.1)

/

where k^ is the number of radicals entering the particle per unit time. Since dnjdt = 0 in the steady state, one obtains

'

1 1 K _ 2 ^^ + _ v 4 k ^

(7.3.2)

From the assumption of n^ » 1.5, one may approximate n^ « n^-1 in Eq. (7.3.1), and hence

w.

y\K

If k^ and v^ denote the polymerization rate of a radical in terms of the

302

PREPARATION

number of monomer units and the volume of a monomer unit of the polymer, respectively, the volumic growth rate of a polymer particle is given by

t^-

(7.3.3)

If the entry of precursor radicals is in the diffusion-controlled mode, it^ = 47rDc*Pr

(7.3.4)

where r^ is the unswollen radius of the polymer particle, D is the diffusion coefficient of the precursor radical, c* is the number concentration of the precursor radicals in the bulk aqueous phase, and p is the ratio of the radius of the swollen particle to that of its unswollen state. One may assume p to be independent of the particle size. Since v^ = 4jrr^^/3, Z?c*p

—- = 47iA; v^ dt "" '"^

2

(7.3.5)

Thus, the volumic growth rate is proportional to r^ in the diffusioncontrolled entry under a given concentration of precursor radicals in the aqueous phase. If the entry of the precursor radicals is in the reaction-controlled mode,

k^ =

(7.3.6)

Ai:kf\^r/

where k^ is the rate constant of the surface process. In this case, it follows from Eq. (7.3.3) that K^

2.5

(73.7)

Thus, the volumic growth rate is proportional to r^^^ at a given c* in the reaction-controlled entry.


303

Hence, if we use two kinds of monodispersed latices in a system as seeds different in mean particle size, whose mean radii are r^ and r^ at an arbitrary time and the corresponding mean particle volumes are v^ and v^,, respectively, it always holds that

idvjdt) (dvjdt)

(7.3.8)

where a = 2 for the diffusion-controlled entry and a = 2.5 for the reactioncontrolled entry. Case 2. AX, < 1.5 In this case, the recombination rate is so fast that a radical which enters a polymer particle already containing one radical recombines with the latter before the next entry of an additional radical. Hence, the number of the radicals in a particle does not exceed two, and thus the treatment differs from that in Case 1. Figure 7.36 illustrates such a case, in which radicals enter a polymer particle n times in a unit time; radicals captured when the particle contains

Unit Time 1st

Ai O

2nd

3rd

4th

nXh

A2Otr

Fig. 7.36. The life scheme of the radicals in a particle in the case that two radicals are always recombined before the entry of the third one. A and B are the radicals captured in the absence and the presence of a living radical in a polymer particle, respectively. The radicals are assumed to enter a polymer particle n times per unit time. Also, t^ indicates the mean time interval between the entry of a radical B and its recombination with an existing radical A and the length of an arrow of a radical corresponds to the life time of the radical in the particle.

304

PREPARATION

no radical are denoted by Aj, A2, A^, —•, and those captured when a radical A is present are denoted by Bj, B2,fi^,-—;the length of an arrow of a radical corresponds to the life time of the radical in the particle; t^ is the mean interval between the entry of a radical B and its recombination with an existing radical A. Here we assume t^ < 1/n, The mean life time of radical A is 1/n + t^ and the entry frequency is n/2, while they are t^ and n/2, respectively, for radical B, Hence the average number of radicals in such a particle is given by

'

n (^L.tVUt^l^nt^ 2[n ') 2' 2 '

(7.3.9)

The life time of radical B, t^, may be written in terms of v^ and k^ as r^=^,

(7.3.10)

since t^ = l/R^ = 2v^[k/iXn,-l)] with n, = 2. Thus, from Eq. (7.3.9) with k^

n =1 +^ . 2 k^ Figure 7.37 shows n^ as a function the straight line of Eq. (7.3.11) to K^f/K beyond unity. Particularly, corresponding to the Smith-Ewart

(7.3.11)

of k^v^/k^, indicating that n^ transfers from the curve of Eq. (7.3.2) with increasing if nt^ « 1/2 or k^Vp/k^ « 1, then n^ « 1/2, case 2?"^ In this extreme case.

±P=kvn=^kv. n in r dt

r\ ni

M

(7-3.12)

Hence, dVp/dt is constant independently of k^ and r^, as long as k^ as a function of the degree of swelling is kept constant. Figure 7.37 clearly demonstrates that, as v^ increases, n^ increases from 1/2 to much larger numbers. Accordingly, dv/dt initially independent of r^ becomes proportional to rj^ or to r^. This theoretical derivation may lead to reasonable explanation of the aforementioned apparent inconsistency between the findings of Smith^"*^ and Vanderhoff et al^^ In view of dvjdt being proportional to r^^ in the large size range, as found by Vanderhoff et

305


"' = i^V^¥ 1 . K^p

Fig. 7.37. The number of the radicals in a particle, w^, as a function of k^VjJk^. a/., the radical entry may be controlled by the surface reaction process and not by the diffusion process. Time evolution of v^ and polymer yield Next, let us consider the time evolution of v^ and that of the polymer yield for the cases of n^ » 1.5 and rij. = 1/2. The number concentration of the polymer particles is assumed to be fixed. Case 1. rij. » 1.5 It seems reasonable to consider that there is an equilibrium between the dissociation of an initiator and association of the initiator radicals during the emulsion polymerization process and thus the formation of initiator radicals is not an irreversible decomposition process of initiator, since initiators are normally stable enough in the absence of monomer to be reacted with. If we assume an initiator to be split into two initiator radicals, the equilibrium may be written as

306

PREPARATION

/^2/-,

(7.3.13)

where / and /• denote the initiator and the initiator radical, respectively. The equilibrium concentration of/-is usuaUy extremely small as compared to that of /, and thus the stability constant of /•, K^, in the following equilibrium formula must be exceedingly small. |2

K,= ^ , "-0

(7.3.14)

m

Nevertheless, the initiator radicals are deemed to be promptly furnished from the initiator when consumed for polymerization. Here, we assume that the direct attack of the hydrophilic initiator radicals to the monomer in the polymer particles is negligible. Hence, if some monomer is dissolved in the aqueous phase of the emulsion polymerization system, the initiator radicals may react to form the monomer radicals, M-, foDowed by the polymerization. In this case, if the recombination among the radicals, including the initiator radicals, monomer radicals, and the higher oligomer radicals, is dominant in the aqueous phase, the steady deposition of such a recombination product onto polymer particles may yield final particles composed of extremely low-molecular-weight linear polymer. Thus, one may assume, for simplicity, that the generated monomer radicals are used simply for the production of oligomer radicals to be absorbed into polymer particles as the precursor radicals through a sequential polymerization process in a steady state. In this steady state, it is not necessary to specify the molecular weight of the oligomer radicals to be absorbed by the polymer particles, but one may consider that any class of the oligomer radicals including the monomer radicals has some probability of deposition onto polymer particles. Since all generated radicals are assumed to be finally absorbed by the coexisting polymer particles, the following relationship generally holds.

where k^ is the rate constant for the formation of the monomer radicals, k^ is the overaged k, for all the coexisting polymer particles, and N^ is the number concentration of the coexisting polymer particles. Here, it is noteworthy that the averaged /:„ k^, is independent of the mean particle


307

volume and of the entry mode of the radicals, such as the diffusioncontrolled or the reaction-controlled mode, in contrast to the k^ of each particle depending on its particle volume (see Eqs. (7.3.4) and (7.3.6)). Since the concentration of the monomer in the aqueous phase, [M], is virtually kept constant until the reserved monomer is almost used up in an emulsion polymerization system, one obtains from Eq. (7.3.14) and a relation in Eq. (7.3.15), -2d[I]ldt = kQ[I'][M], that J ^ =l~-

(7.3.16)

- ^ = fl--^f,

(7.3.17)

and

mo I W where the subscript 0 indicates the initial values and x is a time constant given by

^^_VEiL.

(7.3.18)

Also, using the other relation in Eq. (7.3.15), k^ll ][M] = kjsf^, Eqs. (7.3.14), and (7.3.16), one obtains -_fc,^/Jq7r,[M]/

t]

(7.3.19)

Using the k^ instead of k^ in Eq. (7.3.3), one reaches '"'n

r—

t

—^^KJiTAl-- 1--, dt ^ "'i X and thus

(7.3.20)

308

PREPARATION

fM

"p^

^-fH-f]

(7.3.21)

where /C is a constant given by (7.3.22)

If V » (yX then

^P =

16*^v^[/]f 9k^X'^[M]N

,3/2

1--

(7.3.23)

T

Hence, in this case, v^ is inversely proportional to N^, and the total unswoUen volume of the polymer particles, V^ (= v^Np), is independent of Np. This is because the total polymerization rate is predetermined by the first reaction of the initiator radicals with the monomer in the aqueous phase, inespective of the number concentration of the polymer particles, owing to the irreversibility of the first reaction and the assumption of a steady recombination process of the radicals in polymer particles. Case 2. n, = 1/2 From Eq. (7.3.12), p

^

(7.3.24)

m tn

and thus P P

r\ m m

p

(7.3.25)

In contrast to Case 1, v^ is independent of the number concentration of the polymer particles, Np, and thus the slope of V^ against t is proportional to A^^ in Case 2. This is because n^ is always 1/2 in Case 2, irrespective of the


309

entry frequency of the radicals generated in the aqueous phase, owing to the assumption of instantaneous recombination of the radicals in polymer particles. In this case, one may expect a specifically marked selfsharpening in the particle size distribution with growth, owing to the linear growth rate inversely proportional to the square of the particle radius. This effect may be significant in a relatively small size range such as submicron orders. The theoretical treatment for the growth mechanism in emulsion polymerization may apply to radical dispersion polymerization as well. 7.3.4* Reaction in Microemulsions Macroscopically, a microemulsion may be defined as a single phase composed of at least three components, water, oil, and surfactant, optically isotropic, and thermodynamically stable.^^ However, microscopically, a nanosized water or oil core is included in a surfactant shell of each reversed or normal micelle dispersed in a continuous oil or aqueous medium, though the water or oil cores are deemed to be repeatedly exchanged through the rapid association and dissociation of the micelles. Since reactants are confined in the cores of micelles and the reaction occurs at the interfaces or in the cores, the microemulsion is treated as a heterogeneous system in this book. Boutonnet et al?^^ obtained ultrafine monodisperse metal particles of the platinum group, including platinum (Pt), rhodium (Rh), palladium (Pd), and iridium (Ir) by reducing the corresponding salts the in water pools of W/0 microemulsions with hydrazine or hydrogen gas. Rapid reduction of the metal ions was required to obtain the monodispersed particles. The mean particle size ranged from 3 to 5 nm with a narrow size distribution within 10 % in relative standard deviation. They have a high potential for industrial application as catalysts. For example, they applied this technique to the preparation of nanosized Pt catalysts for hydrogenation of 1-butene and its isomerization to trans 2-butene or cis 2-butene.^^^ The most stable suspensions were formed in microemulsions consisting of pentaethyleneglycol dodecylether/water/n-hexane or n-hexadecane. Furthermore, the so-prepared Pt particles in an microemulsion were transferred to a support of an alumina powder, and their catalytic activity and selectivity in isomerization of 2-methylpentane and in hydrogenolysis of methylcyclopentane to 3-methylpentane or n-hexane were studied.^^^ Similarly, this method is applied to the synthesis of other nanoparticles, such as gold (Au),^^ silver (Ag),^^"''' and copper (Cu).'''-''^

310

PREPARATION

Nagy et al?^'^^^ prepared, as highly active catalysts for hydrogenation, uniform and very fine nickel boride and iron boride particles in W/0 microemulsions of the CTAB/water/n-hexanol system by reducing the corresponding metal ions with sodium borohydride. They discussed the structure of the microemulsions, the mechanism of the particle formation in microemulsions, and the catalytic activity and selectivity of so-obtained metal borides, such as NijB, C02B, and Ni-Co-B.^^ For example, ^^CNMR and UV-VIS absorption spectroscopy revealed that Ni(II) and Co(II) ions were solubilized in the inner water cores of the reversed micelles in the corresponding W/0 microemulsions of a CTAB/water/hexanol system and that the hexanol molecules participated in the first coordination shell of both Ni(II) and Co(II) ions. Also, the mean radius of the water cores, ranging from 9 to 17 A, was found to increase with increase in the water content and in the metal ion concentration, through ^^F-NMR based on the distribution of 6-fluorohexanol as a probe between the interface and the hexanol medium. They also found that the size of the metal boride particles increased with the increase of the water content, but took a minimum value with the change of the concentration of the metal salts, as was explained in terms of the critical supersaturation for nucleation of the metal borides at the beginning of the reduction of the metal ions. They tested the catalytic properties of thus-obtained Ni2B and C02B particles for liquid-phase hydrogenation of crotonaldehyde at room temperature, and found that the C=C double bond was preferentially hydrogenated on Ni2B particles, in contrast to C02B particles on which the hydrogenation of C=0 was not negligible. Their works for the preparation of NijB, C02B, Ni-Co-B, Pt, ReOj and Pt-Re-Gj in microemulsion systems, including CTAB/water/nhexanol and pentaethyleneglycol dodecylether/water/hexane, are summarized in a review article.^^^ Also, Petit and Pileni^^^ studied the effect of the water content on the size of C02B particles prepared by reduction of cobalt bis(2ethylhexyl) sulfosuccinate, Co(AOT)2, with sodium borohydride, and examined their magnetic properties. Gobe et al}^^ performed hydrolysis of mixed solutions of ferrous and ferric ions with ammonia in W/0 microemulsions to obtain magnetite (FcjOJ particles of a narrow size distribution. Similarly, ultrafine uniform particles of barium carbonate (BaC03),^^^ calcium carbonate (CaC03),'''''°° strontium carbonate (SrC03),^' silica (Si02),'''-''' and silver chloride (AgCl),^' germanium oxide {GtO^,"^^ zirconia {ZxO^,'''' cadmium sulfide (CdS),^'^-^'^ zinc sulfide (ZnS),^'^ and cadmium selenide (CdSe/^"* have been produced by using a variety of chemical reactions in


311

Fig. 7.38. TEM of silica particles (a) and a SEM of AgCl particles (b), prepared in W/0 microemulsions. (Courtesy of Prof. K. Kon-no.) W/0 microemulsions. Figure 7.38 shows a TEM of silica particles'*^^ and a SEM of silver chloride particles prepared in a W/0 microemulsion.'^^^ Microemulsion systems are also used for the synthesis of composite nanoparticles; e.g., enzyme-encapsulated siiica,"*^^ PuOj-encapsulated silica,'^' CdS/Si02 composites,'^''^« silica-coated silver/'^ Cd^Zn^.^S,"'' and CdxMni.xS."*^ The enzyme-encapsulated silica particles are to be used as nanosized carrier for drug delivery of [^^l]tyraminylinulin, FlTC-dextran, and horse radish peroxidase. The encapsulation of a hazardous polymeric nuclear waste of Pu(IV) extracted in a microemulsion system was performed by acid-catalyzed hydrolytic polycondensation of tetraethoxysilane within the aqueous microdroplets, to recover the polymeric Fu(IV) at a high efficiency. The sulfide composites were studied mainly from the interest in the performance as semiconductors for nonlinear optics. In the meantime, ultrafine particles of polystyrene (20 - 40 nm) were prepared by polymerization in 0/W microemulsions,"*^^'"*^^ whereas those of polyacrylamide (< 50 nm) and its copolymers in W/0 microemulsions.'*^^"'^' For characterization of microemulsions, a wide variety of means are utilized in addition to the above ^^F NMR, UV-VIS spectroscopy, SAXS, and freeze-fracture electron microscopy; e,g., Fourier transform pulsed-

312

PREPARATION

gradient spin-echo ^H and ^^C NMR for the measurement of self-diffusivity of each component to provide the information on the dimensions of the hydrophilic and hydrophobic regions;"*^ dynamic light scattering to measure the size of micellar aggregates;"^^^ dielectric spectroscopy for the information on the relaxation behavior of the components of a micelle, such as the bound water, surfactants, and cosurfactants in reversed micelles."*^^ In general, the monodisperse particles prepared in microemulsions have the characteristics of very small mean size, narrow size distribution, and high stability in the systems. Since the mass of each particle obtained by this method is normally much greater than the quantity of the monomeric species dissolved in individual water pools of a W/0 emulsion, each water pool is not isolated but repeats rapid association and dissociation with the others. In addition, it is also evident that there are numerous vacant water pools containing no particles and thus acting simply as a monomer reservoir to furnish monomeric species to water pools containing one or more particles. Thus, there is no doubt that the monomeric species are exchanged among water pools. However, in distinction from homogeneous systems, the growth rate of each particle may be greatly lowered by adsorption of the highly concentrated surfactant and a more or less limited transfer of the monomeric species from vacant water pools. In this case, the number of the generated nuclei must be increased by the rather slow reduction in supersaturation because of the slow consumption of the solute by their growth. When the supersaturation becomes below the critical level of nucleation by promoted nucleation, the nucleation will halt and the growth stage will ensue. The coagulation of the growing particles may be inhibited by the adsorption of the surfactant. These seem to be the reasons for the formation of the uniform and ultrafine particles in microemulsion systems. Hence, the temperature, content of surfactant, and ratio of water to oil are important factors for achieving the above conditions for the formation of uniform particles. Since highly concentrated surfactants are used in these systems, they often affect the morphology of the products by adsorption. Incidentally, Tanori and Pileni^^ prepared spherical copper particles of narrow size distribution (d = 7 - 10 nm; a = 11 - 25 %) by reduction of Cu(II) with hydrazine in a Cu(AOT)2/water/isooctane system with [Cu(A0T)2] = 5 X 10"^ mol dm'\ where CuCAOT)^ is copper(II) bis(2ethylhexyl)sulfosuccinate. They also found cylindrical particles of ca, 20 nm in length with an aspect ratio of 2 - 3, mixed with the spherical ones, in which the proportion of the cylindrical particles varied from a few % to ca, 40 % in number according to the drastic structural change of the


313

micellar system with variation of water content, such as spherical reverse micelles, cylindrical reverse micelles, interconnected cylindrical reverse micelles, and a birefringent mixed lameUar phase consisting of planar lamellae and sphenilites.^^^ They used a special technique for direct observation of the state of the micelles, "freeze-fracture electron microscopy," in which a thin layer of a sample, 20 to 30 (xm thick, on a thin copper holder, quenched in liquid propane, was fractured with a liquid-nitrogencooled knife in vacuum, and then its platinum-shadowed carbon replica was observed through an electron microscope.^^^ The mean size and shape of micelles and the structures of their assemblies were characterized by small angle X-ray scattering (SAXS)."*^^ The proportion of the cylindrical particles was the highest in the region of the interconnected cylindrical reverse micelles. It is of particular interest that the authors explained the formation of the cylindrical particles in terms of a template effect of the interconnected cylindrical micelles,fromthe correlation between the micellar structure and the proportion of the cylindrical particles in the mixed products of spheres and cylinders. However, as they suggested, the cylindrical particles are deemed to be twin crystals grown in the direction parallel to the {111} faces of the fee crystal system.^^° Since the anisotropic growth of rod-like twin crystals is routinely observed in ordinary homogeneous solutions, there may be an alternative possibility that the cylindrical shape is not due to the shape of the micelles as a template, but due simply to the characteristic growth of the twin crystal. In this case, one must take into account the causes of the twinning event, which could be strongly affected by variation of the water content; e.g., the concentrations of dissociated Cu(II) ions and hydrazine in the water pools, the degree of adsorption of Cu(II) and/or AOT to the growing Cu particles, and the state of the water in the reverse micelles. In addition, cylindrical particles are virtually not observed with w (=[H20]/[A0T]) from 1 to 20 when the overall concentration of Cu(II) ions is 10"^ mol dm"^ in an analogous system,^^^ while high contents of cylindrical particles are found within the same range of w in the present systems with 5 x 10"^ mol dm""' in the overall concentration of Cu(II) ions. Hence, it may be also reasonable to consider that the high overall concentration of Cu(A0T)2, 5 x 10"^ mol dm"^, is the main cause of the high probability of the stacking fault leading to twin crystals. In fact, even in a region of spherical reverse micelles (w ^ 35), ca, 14 % of all particles in a sample were found to be cylindrical. Moreover, one must consider some other aspects as well: e.g., the percentage of the cylindrical particles is not necessarily high (e.g., 9 % at iv = 26) in a region

314

PREPARATION

of w, 20 < w < 30, rich in interconnected cylindrical micelles, while it is the highest, 42 %, at w = 34 close to the spherical reverse micelle region; the dimensions of the cylindrical Cu particles are much greater than those of the cylindrical micelles; even if the shape of the micelles is cylindrical on average, the shape of each micelle is not statically fixed and the contents of the reverse micelles are rapidly exchanged among them, as is obvious from the product particles much larger than the reverse micelles in dimensions; the size and shape of the cylindrical Cu particles are rather similar, despite the drastic change in the micellar structure. Hence, for concluding the mechanism of the morphological change in this particular system, more detailed analyses may be needed. Nevertheless, there seems to be no doubt that the use of relatively rigid self-assembly systems as templates is one of the promising techniques for the shape control or size control of colloidal particles. For reviewing microemulsion systems, several review articles are now available.^^^'^^^'^^2-435 7.3.5. Precipitation from Liquid Crystals A nonionic surfactant, Tween 80 (polyoxyethylene sorbitan monooleate: see Fig. 7.39), is known to form normal micelles, hexagonal liquid crystals, and reversed micelles with its increasing content in water. Figure 7.40 shows the phase diagram of the water-Tween 80 binary system at 25 "C."*^^' K copper sulfate is precipitated in a solution of Tween 80 in the normal micelle range at room temperature, large rod-like crystals of copper sulfate pentahydrate (ca, 100 \im in length) precipitate in its concentration range of

HO(C2H40X^

,(OC2H4)xOH

CH(OC2H4)YOH

Q

CH2(OC2H4)2-0-C(CH2)7CH=CH(CH2)7CH3 i

I

j-—hydrophiRc head group I

-J-

I

hydrophobic tail — - ;

I

w+xi-y+z = 20 Molecular Weight = 1.308 g/mol

Fig. 7.39. Chemical fomiula of Tween 80. (From Ref. 436.)

7. MONODISPERSED SYSTEMS 100wt% H p 0

69 31

I Solution Normal Micelles

315 49 51 I

38 28 0 62 72 100wt% Tween 80 1 h1

Hexagonal Liquid Crystal

Solution Inverse Micelles

Fig. 7.40. Phase diagram of the water-Tween 80 binary system at 25 °C rprom Ref. 436.)

1.0-1.3 mol dm"^, similar to the precipitation from an ordinary aqueous solution at 1.6 mol dm"^. In the liquid crystal range, on the other hand, the precipitation of copper salts occurs at a much lower concentration, and the particle composition and shape depend strongly on the copper sulfate concentration. For example, the precipitate in the concentration range of 0.012-0.020 mol dm"^ consists of rather uniform ellipsoidal basic copper sulfate (Cu4(OH)6S04) particles of ca. 1.8 jmi in length (relative standard deviation « 20 % in the size distribution) and ca. 0.8 [xm in width, as shown in Fig. 7.41(a). The precipitation of basic copper sulfate is observed even at a pH as low as 2.6. In the range of 0.02-0.05 mol dm"^, relatively large flower-like aggregates (Cu4(OH)6S04 'H2O) are mixed with ellipsoidal particles. In the range of 0.05-0.10 mol dm"\ only the flower-like aggregates are formed. In the concentration range above 0.10 mol dm"^, only irregular aggregates are obtained. In the reversed micellar solutions or in a 47.6 wt% polyethyleneglycol solution, basic copper sulfate also precipitates, but the size and shape are irregular, suggesting some contribution of ethylene oxide group to the precipitation of the basic salt. Although the reason was not explained in the literature, the result may imply a dramatic reduction of the solubility of the basic sulfate complexes of copper ions in the aqueous media mixed with an extremely high concentration of hydrophilic ethylene oxide groups. Similarly, the drastic size reduction and

316

PREPARATION

Fig. 7.41. Basic copper sulfate particles (a) and basic copper nitrate particles (b) precipitated from lyotropic liquid crystals. (From Ref. 436.)

the lowered precipitation concentration may also be explained by the reduction of the solubihty of the basic sulfate complexes. Adsorption of the surfactant to the growing basic copper sulfate particles may be an additional cause of the size reduction, as weU as a cause of the characteristic shape. The cause of the relatively narrow size distribution was reasonably attributed to the inhibition of the random aggregation among the growing particles in the highly viscous lyotropic liquid crystal, in accord with the concept of the gel-sol method which may be traced back to the systems for the formation of monodispersed C03O4 and Fe304 particles on the respective precursor gel networks (see section 7.3.1). Figure 7.41(b) also shows a SEM of basic copper nitrate particles with a relatively narrow size distribution, similarly precipitated from the lyotropic liquid crystal, but at a very high concentration, 3 mol dm"^. Again the aggregation of the particles appears to be inhibited by the matrix of the liquid crystal. To improve the sharpness of the size distribution in this system to the level of monodisperse particles, some additional measures for supersaturation control to separate the growth stage from the nucleation stage may be needed. 7.3.6. Inhomogeneous Hydrolysis Uniform spherical silicone particles (polyorganosilsesquioxane particles) with a narrow size distribution close to the level of monodisperse particles have been prepared by hydrolysis and polycondensation of organotrialkoxy-


317

silanes in an inhomogeneous system.'*^^"'^ Here, silicone is a kind of siloxane polymer with organic groups, such as alkyl, allyl, and aryl groups, bonded with the silicon atoms, and it is characterized by its hydrophobicity, heat-resistivity, lubricity, etc. The silicone particles are used as fillers of rubbers, plastics, papers, pigments, paints, etc. to improve the lubricity, water repellency, heat resistivity, brightness, toughness, chemical resistivity, etc.; as controllers of surface electric charges and fluidity of toners; as dispersants of ceramic powders; as additives of cosmetics to improve the smoothness and UV absorptivity. Typically, methyltrimethoxysilane, synthesized frommethyltrichlorosilane and methanol, is hydrolyzed and polymerized by a polycondensation process in an inhomogeneous system consisting of an upper oil phase and a lower aqueous phase containing anmionia, with gentle swirling at 20 r.p.m. for ca. 3 h in a four-necked flask equipped with a reflux condenser, until the upper oil phase disappears. The temperature is then raised up to SO-^Ô °C, at which the prepolymer suspended in the aqueous phase is further polymerized for additional 3 h while stirring. When 400 g of ammoniacal solution, containing 5 g of 28 wt % ammonia, and 60 g of methyltrimethoxysilane, containing 3.3 ppm of methyltrichlorosilane, were used in this experiment, the mean diameter of the spherical product was 1.9 |im, with a size distribution ranging from 1.7 to 2.1 [xm, and the contact electric charge density was -1000 jxC/g. The key factor in this experiment is the way of agitation. If the agitation is so strong as to mix the oil and aqueous phases together, the particles stick together to form large aggregates and hence result in a broad size distribution. However, if the agitation is too weak, all particles deposit to the bottom of the flask and form a bulky agglomerate. As an improved method for the preparation of very fine silicone particles of a mean diameter ranging from 0.01 to 1 |im, a new procedure was proposed."*"*^ In this method, organotrialkoxysilane is first hydrolyzed into organosilanetriol in an aqueous solution of organic acid such as acetic acid, and then the silanol solution is admixed with an ammoniacal solution for polycondensation. The advantage of this method is that it is possible to produce uniform silicone particles with different refractive indices, lubricities, and capabilities for surface modification, by using different organic groups for R in organotrialkoxysilane, RSi(0R')3, such as alkyl groups with 2 to 6 carbons, cycloalkyl groups, aralkyl groups, aryl groups, alkenyl groups, or substituted hydrocarbon groups, since it is difficult to fabricate uniform particles by the preceding method with organotrialkoxysilanes having organic groups other than methyl group. For example, 68 g of

318

PREPARATION

methyltrimethoxysilane and 99 g of phenyltrimethoxysilane were added to 108 g of an aqueous solution, containing 0.02 g of acetic acid, while stirring at 30 ""C. The temperature rose up to 60 °C in 10 min with the progress of hydrolysis. The transparent silanol solution thus obtained was further aged with stirring for additional 4 h, and finally the reaction mixture was filtered. After the first step, 27.5 g of the silanol solution was added dropwise to an ammoniacal solution, consisting of 200 g of water and 10 g of 28 wt % ammonia, at 25 °C for ca. 180 min while stirring, followed by additional stirring for 24 h for polycondensation to yield a white milky dispersion of silicone particles. The mean diameter of the product was 0.1 \xm with a size distribution from 0.05 to 0.2 \mi. In this method, it was also found that the final particles size could be enlarged up to 3-10 \im by drastic increase in the ratio of silanol to anunonia and quiescent aging in the polycondensation process at relatively low temperatures, such as 20-10 °C, after the initial stirring just for mixing ammonia with the silanol solution."*^^ Also, a more efficient continuous method has been proposed for the fabrication of the spherical silicone particles.'*'*^ Namely, methyltrialkoxysilane is passed through the membrane of a porous pipe filter of 0.1-1.5 |im in mean pore size from outside to be mixed with water flowing through the internal pipe for forming an 0/W emulsion and then admixed with an ammoniacal catalyst solution for hydrolysis and polycondensation. By this continuous method, fairly uniform silicone spheres with a mean diameter of 0.5 to 5.5 |im can be prepared. A variety of surface modifications are proposed for the silicone particles. For example, to control the surface electric charge from the extremely negative charge of the original particles to less negative or even positive charges by treatment with an organotrialkoxysilane having a hydrocarbon group partly substituted with amino groups such as H2N(CH2)2NH(CH2)3Si(OCH3)3, ^^ alkoxides of transition metals such as titanium alkoxides or aluminum alkoxides."*^ To increase the hydrophobicity or water repellency, the surface treatment is performed with compounds having, at least, a trialkyl silicon group such as hexamethyldisiloxane, and trimethylchlorosilane,"*"*^ or with compounds having, at least, a perfluoroalkyl group."*^^ To increase the hydrophilicity, the particle surfaces are treated with a block- or graft-copolymer comprising polyoxyalkylene segments and polysiloxane segments."*^^ To provide the particles with UV absorptivity, they are treated with titanium alkoxides"*^^ or with p-diketones and organic silicon compounds with amino group."^^ The silicone particles can readily be converted to silica particles without changing the original shape by pyrolysis at a


319

temperature in the range from 500 to 1300 °C.^^° While the hydrolysis of organotrialkoxysilane to organosilanetriol occurs at the oil-water interface, the polycondensation of organosilanetriol takes place in the ammoniacal solution. Hence the second half of the total process is the same as the formation of silica particles from silicon tetraalkoxides. However, the colloidal instability of the growing particles due to their less hydrophilic surfaces may make the achievement of a high monodispersity a little more difficult. For the improvement of their monodispersity, important factors may be the control of the hydrolysis rate of the organotrialkoxysilane and the feed rate of the hydrolyzed silanol and the uniform distribution of the silanol in the ammoniacal phase, to inhibit the renucleation of the silicone particles during their growth. Figure 7.42 shows a SEM of fairly uniform polymethylsilsesquioxane particles prepared under ideally controlled conditions.

Fig. 7.42. SEM of silicone particles prepared under ideally controlled conditions.

7.3.7. Hydrolysis Hardy et al^^^ titanate (SrTi03) mixed alkoxides acetonitrile (AN)

in Nonaqueous Emulsions prepared fairly uniform spherical particles of strontium by hydrolysis and polycondensation of corresponding in a mixed solvent of butanol containing 25 vol % and 8 equiv. of water. This method is based on the

320

PREPARATION

decrease of the solubility of the mixed metal oxide polymer by the presence of AN, as is obvious from the fact that the oxide sol is not formed at all without AN. Nevertheless, the mechanism seems to be basically the same as for the formation of uniform oxide spheres by hydrolysis of alkoxides in homogeneous systems, but for the control of the hydrolysis rate and solubility of the product by addition of AN. On the other hand, the same authors prepared rather polydispersed but unagglomerated spheres of aluminum hydrous oxide, zirconia {ZTO2), and titania (Ti02) by hydrolysis of the aluminum tri-êc-butoxide, zirconium-n-propoxide, and titanium butoxide, respectively, in an emulsion of alkoxide droplets dispersed in the continuous medium, AN, containing some water as a reactant. They used the nature of pure AN virtually immiscible with metal alkoxide, unless a certain amount of alcohol is mixed with. They suggested that this emulsion technique is particularly useful when the hydrolysis reaction of an alkoxide is too fast to yield well-defined particles by ordinary homogeneous hydrolysis. In this system, it has been postulated that the alkoxide droplets are directly converted to the corresponding oxide particles by hydrolysis and condensation with water permeating through the interfaces of the droplet/medium, like the hydrolysis of alkoxide aerosol by water vapor for the formation of oxide particles (see section 7.3.12). Hence, if it is true, the mechanism of particle formation is totally different from that for the formation of SrTiOj in the above homogeneous system with the mixed solvent of AN/butanol. However, it should be noted that the direct conversion mechanism in the AN medium has never actually been verified. In any case, it seems to be of interest to see the effect of AN increasing in the mixed medium of AN/alcohol on the particle formation in the alkoxide system. When the ratio of AN to alcohol exceeds a certain level, metal alkoxide starts to precipitate and thus form an emulsion. Actually, Ogihara et al prepared many kinds of amorphous spheres of narrow size distribution by varying the fraction of AN in combination with different kinds of alcohol;^^2.453 ^^^ alumina (Al203),^^'^^^ zirconia (ZrO^),^'^ titania (Ti02),^^^ niobium pentoxide (Nb205),^^^ tantalum pentoxide (J^2^s\'^^^ iron oxide (Fe203),'^^^ zirconia-alumina (Zr02-Al203),^^^ yttria-alumina (Y203-Al203),^^' alumina-silica (Al203-Si02),''' barium titanate (BaTi03),'^^ strontium titanate (SrTi03)?^^ and lead titanate (PbTi03).'^^ These amorphous particles can be crystallized on calcination at high temperatures without changing the original spherical shape. For example, they obtained y-alumina (Y-AI2O3) (1000 °C),^^^ hematite (a-Fe,03) (500 ""Cy yttrium aluminum garnet (YAG: Y3Al2(A104)3) (lOOb °C),'''


321

mullite (3Al203-2Si02) (1000 °C)/^^ and perovskite-type crystals (600 OQ459 g.Qj^ barium, strontium, and lead titanates. They confimied that this method is particularly useful when the hydrolysis and polycondensation of a metal alkoxide is too fast. Similarly, Ikeda et al,^^ prepared barium titanate (BaTi03) spheres. They found the combination of acetonitrile (AN) and octanol was the best as the mixed medium for the most of the tested metal alkoxides in the preparation of uniform particles, particularly with ca, 40 vol % of AN in the mixed medium, since 40 vol % of AN is the minimum fraction of AN for emulsification of metal alkoxides, and thus the emulsion is the most stable,"*^^ probably due to the minimum specific interfacial energy. They employed hydroxypropylcellulose (HPC), as a stabilizer, which is one of the most popular stabilizers of oxide particles in sol-gel systems. Typically, to 50 cm^ of octanol solution containing 1.23 g of aluminum êc-butoxide and 0.04 g of HPC, 50 cm^ of acetonitrile solution containing 0.09 g of water and 10 cm^ of ethanol is added and mixed for 1 min at 40 °C. The soobtained emulsion is transferred to a water bath, set at 25 °C, and aged quiescently at this temperature for 60 min, yielding ca, 0.5 g of amorphous alumina particles of ca. 0.3 ^m in mean diameter."*^' They have explained the particle formation in terms of the direct conversion of the alkoxide droplets, and have related the particle uniformity to the stability of the emulsion."*^^"*^^ Their argument is likely to be based on their optical in-situ observation of the evolution of the overall size distribution of the alkoxide droplets and generated oxide particles, from the initial one of the large alkoxide droplets to the final one of only the oxide particles via a bimodal distribution of the coexisting alkoxide droplets and oxide particles. However, this may not necessarily mean that the oxide particles are formed inside the alkoxide droplets. Moreover, if the oxide particles are actually formed based on this mechanism, there must be an essential limit in uniformity of the product in this technique, since it depends totally upon the size distribution of the emulsion droplets which is not specifically controlled and thus, seemingly, considerably broad even if the best fraction of AN is chosen. Nonetheless, if the preparation conditions are carefully optimized, the final size distribution becomes comparable or, at least, very close to the level of monodispersed particles obtained from homogeneous hydrolysis systems. For example, Fig. 7.43 shows SEM images of zirconia particles prepared by variation of the volume percent of AN in a the mixed medium of AN/octanol."^^^ In addition, except for the case of the alumina particles, the final size of the particles, including Zr02-

322

PREPARATION

Fig. 7.43. SEM images of Zr02 particles prepared by varying the volume percent of acetonitrile in a mixed medium of acetonitrile/octanol (scale bar = 1 jiim). (From Ref. 455.)

AI2O3, Al203-Si02, and MTi03 (M = Ba, Sr, Pb), rather decreases with the increase in AN fraction above 0.4. This appears incongruent with the aforementioned mechanism, since the size of the alkoxide droplets nomially increases with the increasing volume fraction of AN above 0.4. Moreover, in most cases, comparably uniform particles can be obtained even at 20 vol % of AN as well, at which metal alkoxides are usually dissolved in the mixed medium. Hence, there seems to be no reason to negate a possibility of an alternative mechanism that the nucleation and growth of the oxide particles with hydrolysis and polycondensation occur outside the alkoxide droplets, in the continuous mixed medium, with alkoxide molecules steadily fumiwShed from their droplets as a reservoir, like the emulsion polymerization of polymer latices in section 7.3.3. If one considers the hydrophilic nature of the oxide surfaces, this mechanism may appear even more reasonable, since AN is a highly hydrophilic liquid. Since the direct mixing of alkoxide with water is obviated in this manner and since the concentration of alkoxide is controlled to a suitable level in the mixed medium, it may be possible to separate the nucleation and growth stages as a prerequisite for the formation of monodispersed particles, even if the reactivity of the alkoxide with water is high. In any case, prior to the final conclusion of the formation mechanism, more detailed analyses may be needed. 7.3.8. Reaction on Solid Surfaces Solid surfaces work, in some cases, as a trigger of heterogeneous nucleation of fine particles and/or a useful matrix for their stabilization


323

during their growth. Hence, one may be able to use such solid surfaces as a field for the formation of uniform particles. Probably, heterogeneous catalyst particles on solid supports may be the most suitable systems for this purpose. In particular, it is of interest to review the synthesis of uniform nanoparticles of noble metal catalysts on well-defined support powders. Conventionally, noble metal catalysts on supports have been synthesized, for example, by impregnation of a solution of a noble metal salt into an ordinary support powder, or by coprecipitation of a noble metal ion with a large amount of a base metal ion as a mixed hydroxide with a strong alkali, and subsequent reductive calcination. However, the final mean size of thus obtained noble metal particles is mostly about 4 nm or more with a broad size distribution, even if the loaded amount of a noble metal on a support is a few weight % or less. Hence, of special interest are the recent findings for deposition of fairly uniform noble particles of ca. 2 nm or less in mean size, including gold (Au), platinum (Pt), palladium (Pd), iridium (Ir), rhodium (Rh), and ruthenium (Ru), even at ca, 20 load weight % on well-defined supports,"^^^*"^^^ Metallic gold particles of ca. 1 nm in mean size are selectively deposited onto monodispersed polycrycrystalline ellipsoidal hematite (a-Fe203) particles without addition of any specific reducing agent in total darkness."*^^ The deposition of the Au particles is performed simply by aging quiescently a solution of 2.0 x 10"^ mol dm"^ HAuCl^ with 8.0 x 10"^ mol dm"^ NaOH at room temperature for 24 h, and further quiescent aging at 100 °C for 48 h with 1.6 g dm"^ (1.0 x 10"^ mol dm'^) hematite particles added at the start of this second aging. The chloride complex, AuCl^", is transformed to hydroxide complex, Au(0H)3 or Au(0H)3Cr, by the first aging at room temperature for 24 h, during which the color of the solution changes from yellow to transparent, while pH shifts from 10.8 to 6.0. During the second aging at 100 °C, precipitation of the polymerized hydroxide occurs and the Au^^ ions are reduced to metallic Au" probably through electron transfer from the coordinated OH" ions on the surfaces of hematite particles as a catalyst of the electron transfer. The reduction of Au^* ions is not observed in the absence of hematite. Therefore, the essential reducing agent is water in this case. The precipitation of Au hydroxide, which is observed even in the absence of hematite as well, is enhanced in the presence of hematite. With the reduction of 1 mol of Au(0H)3 to Au", 1.5 mol of O (oxygen atoms) must be released if this mechanism is correct (2Au(OH)3 - • 2Au" + 30 + 3H2O). In fact, the released oxygen was observed in the form of CIO", CIO3", CIO4", and O^, whose total molarity in O was found to be 1.45

324

PREPARATION

times the reduced molarity of Au^^, very close to 1.5 times. As is obvious from the above mechanism, pH is also an important factor for obtaining the highest yield of Au°, and the optimum pH has been found to be around 6, at which Au(0H)3 or Au(OH)3Cr is dominant. In this process, the chemical composition and surface structure of the solid support are the dominant factors for the mean size, stability, and uniformity of the noble metal particles. Table 7.2 summarizes the yields of Au hydroxide precipitated but left unconverted to Au^, Au°, and the mean sizes of the Au^ on different supports, including polycrystalline ellipsoidal hematite (A),^°^ monocrystalline ellipsoidal hematite (B),^°^ monocrystalline pseudocubic hematite,^^^ monocrystalline thin-platelet hematite,"*^ goethite (a-FeOOH),"*^^ akaganeite (P-FeOOH),^°^ rough-surface spherical tetragonal zirconia (A),"*^ smooth-surface spherical tetragonal zirconia (B),"*^ and ellipsoidal anatase titania.-^^^'^^"^ In this experiment, the amount of the each solid supports was fixed at 1.6 g dm"^. Each amount of the remaining Au(0H)3 precipitate and the product, gold, was determined from ICP measurement of the amounts of gold ions remaining in the supernatant solution before and after treatment

Table 7.2. Yields and sizes of gold particles on different supports Gold Particles

Support Particles Species

Shape

Structure

Size

SSA^

Yield (%)

Size (nm)

(|im)

a-Fe203

ellip.^ ellip. p. cub.'' plat.''

p. c.^ s. c.^ s. c. s. c.

0.20x0.038 0.46x0.10 0.090 13.3x1.5

136 21.8 15.9 0.70

75.1 60.6 74.7 8.50

1.5 3.5 4.0 10.5

a-FeOOH

needle

s. c.

0.50x0.020

41.0

67.6

10.5

P-FeOOH

needle

b. c'

0.25x0.012

112

62.7

15.0

ZrO^

r. s. s.^ s. s. s.^

s. c. s. c.

0.015 0.015

153 118

99.0 95.1

0.50 1.8

TiO/

ellip.

s. c.

0.35x0.045

37.5

54.8

3.5

''anatase titania; êllipsoid, '^pseudocube, ''platelet, ''rough-surface sphere ^smooth-surface sphere; ^ polycrystal, * single crystal, 'bunched cTystal; ^specific surface area


325

lOnm Fig. 7.44. Nanoparticles of gold on different supports: (a) ellipsoidal hematite, (b) pseudocubic hematite, (c) platelet-type hematite, and (d) spherical zirconia. (From Ref. 461.)

with 0.02 N HCl, by which only Au(0H)3 precipitate was dissolved. To confirm the identification of metallic gold and gold hydroxide, XPS was also used. The rough-surface tetragonal zirconia particles of 15 nm in mean size, used as a support, were synthesized by a gel-sol procedure at 200 °C for 60 min. The smooth-surface zirconia was prepared by an intraparticle Ostwald ripening of the rough-surface zirconia at 200 ""C for 3 days and the

326

PREPARATION

mean size of the smooth-surface zirconia was nearly the same as the roughsurface one/^"^ Figure 7.44 shows some typical TEM images of Au particles on different supports. In view of the rather small difference in the yield of Au^ among the hematite supports, including polycrystalline ellipsoids (A), monocrystalline ellipsoids (B), and monocrystalline pseudocubes, the specific surface area (S.S.A.) may have little effect on the yield of Au°, unless the S.S.A. is extremely small like the platelet hematite. In contrast, the S.S.A. appears to have a strong effect on the final particle size of Au°, as obvious from the comparison among the different hematite supports. The effect of the S.S.A. on the final particle size is due to the difference in available surface area for heterogeneous nucleation of Au° particles. In this S.S.A. effect, the effect of surface roughness to stabilize the gold particles thereon may also be involved. On the other hand, apart from the S.S.A. effect, there is an order of catalytic activity in the different support species for the reduction of Au^"^ to Au", as represented by the yield of Au°: Zr02 » a-Fe203 > a-FeOOH > Ti02 > p-FeOOH. The final size of the Au° particles also strongly depends on the support species. This may reflect the difference in affinity of gold to the supports. One may be able to enumerate the support species in the order of the size reduction effect: Zr02 > a-Fe203 > Ti02 » a FeOOH > p-FeOOH. It is also noteworthy that we owe a great part to the unique reducing method in the achievement of the exceedingly small and fairly uniform gold particles on the Zr02 and a-Fe203 supports. Incidentally, when monodispersed amorphous SiOj particles prepared by hydrolysis of tetraethyl orthosilicate was used as a support, neither the adsorption of A1(0H)3 nor the reduction of Au^^ of Au(0H)3 was observed. This fact may suggest a possibility that Au(0H)3 exists in the form of Au(OH)3Cr, which will not be adsorbed to the negatively charged Si02 surfaces at pH around 6. On the other hand, if we use RUCI3, RhCl3, PdCl2, H2lrCl5, or H2PtCl6 in place of HAUCI4 in the same process, metal hydrous oxides of these noble metals selectively deposit onto the solid supports, but the reduction of the noble metal ions does not take place, unlike the case of gold ions. Nevertheless, we can obtain very fine and well-dispersed nanoparticles of these noble metal particles on the solid supports by reducing the metal hydrous oxides on the supports with flowing hydrogen gas at 250 ^^C for a few hours depending on the metal species (1 h for Ru, Pd, Ir; 2 h for Pt; 4 h for Rh)."*^^ Tables 7.3 and 7.4 show the sizes of the precursor metal hydrous oxide particles and the final metal particles for Pt on different


327

supports and for different metals on the polycrystalline ellipsoidal hematite (A), respectively. It is of interest that the S.S.A. and species of the solid Table 7.3. Yields and sizes of Pt02*«H20 precursor particles and sizes of Pt particles on different supports Support Particles

Pt02 •WH2O

Pt

Species^

Shape

Structure

SSA

Yield (%)

Size (nm)

Size (nm)

a-Fe203

ellip. ellip.* p. cub. plat.

p. c. s. c. s. c. s. c.

136 12.9 15.9 0.70

88.8 68.5 50.0 46.1

1.3 1.3 1.5 1.5(25)^

2.0 2.5 2.0 5.5

Zr02

r. s. s. s. s. s.

s. c. s. c.

153 118

84.1 72.4

1.5 1.6

2.2 2.4

Ti02

ellip.

s. c.

37.5

76.2

1.5

1.3

36.6

35.0

None

''All support particles, but ellipsoidal a-Fe203 indicated by an asterisk (*), are the same as those in Table 7.2 for gold particles. ^ The value in the parentheses, 25 nm, is the mean size of Pt02*«H20 particles precipitated apart from the support.

Table 7.4. Mean sizes of the metal hydrous oxide precursor particles to different noble metals on the ellipsoidal polycrystalline a-Fe203 support (SSA = 136 m^ g"^) and those of metal particles reduced from the precursors Metal Element

Precursor Particles (nm)

Metal Particles (nm)

Ru

0.4 ± 0.2

1.5 ± 1.0

Rh

0.7 ± 0.5

1.8 ± 0.7

Pd

3.0 ± 1.0

4.0 ± 2.0

h

0.6 ± 0.3

1.1 ± 0.5

Pt

1.5 ± 0.5

2.0 ± 0.5

PREPARATION

328

' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I • ' ' I ' '•

b) Rh species

296

294

292

290 288 286 284 282 B i n d i n g E n e r g y (eV)

280

278

276

322

320

318

316 314 312 310 Binding E n e r g y (eV)

308

306

304

' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I '

d) Ir species

350

348

346

344 342 340 338 B i n d i n g E n e r g y (eV)

336

334

332

76

74

72

70 68 66 64 Binding E n e r g y (eV)

62

60

58

Fig. 7.45. XPS spectra of the noble metal species, on ellipsoidal polycrystalline hematite particles, asprecipitated and those after reduction with H2, along with those of the corresponding bulk metals. (From Ref. 462.) 88

86

84

82 80 78 76 74 B i n d i n g Energy (eV)

72

70

68

supports have little effect on the size of the precursor particles of Pt, while the precursor particle size strongly depends on the species of the noble metal ions. Except for the Pt/Ti02, the mean size of the metal particles more or less increases from that of the corresponding precursor particles in the


329

reducing process, suggesting some aggregative process during the reduction of the precursors. In the case of the Pt/Ti02, the size of the metallic Pt rather decreases from the precursor particles, probably due to the strong affinity of Pt to Ti02 which inhibits the extensive migration of Pt atoms and/or Pt clusters on the Ti02 surfaces. Figure 7.45 exhibits XPS spectra of the as-precipitated precursor particles of the noble metals of the platinum group on ellipsoidal hematite (A), after the reduction of the precursor particles, and the corresponding bulk metals. Examples of TEM images of the noble metals on different supports and catalytic activities of so-obtained Pt particles are shown in section 12.4.4. Since the new method for the synthesis of metal catalysts with welldispersed and highly condensed nanoparticles of noble metals, such as Au and Pt-group metals, on oxide supports is characterized by the selective deposition of the precursor particles onto supports, one may call it the ''selective deposition method.''"^^^'"^^^ 7.3.9. Reaction in Solid Matrices Porous solid matrix is also a useful medium for the preparation of fairiy uniform nanoparticles of metals through reduction of metal ions occluded in the porous matrix with hydrogen gas. For example, Breitscheidel et al^^^

Fig. 7.46. Scanning transition electron micrograph of Pd particles of 3.8 nm in mean diameter in a silica matrix prepared by the three-step process. (From Ref. 465.)

330

PREPARATION

prepared nanoparticles of silver (Ag), cobalt (Co), nickel (Ni), copper (Cu), palladium (Pd), and platinum (Pt) in an amorphous silica matrix through a three-step process: (1) Homogeneous hydrolysis and polycondensation of an alkoxysilane of X(CH2)3Si(OEt)3 type (X = NH2, NHCH2CH2NH2, CN) with a metal salt (AgN03, AgOAc, Cd(N03)2, Co(OAc)2, Cu(0Ac)2, Ni(0Ac)2, Pd(acac)2, or Pt(acac)2) and, optionally, Si(0R)4 (1st step); (2) Calcination of the polycondensates to form metal oxide/Si02 composites (2nd step); (3) Reduction with hydrogen gas to form metal/Si02 composites (3rd step). In the 1st step, the ethoxy group is totally replaced by oxygen, but the metal ions are linked to the resulting silica through the bifunctional moiety X of the remaining X(CH2)3-group on silica. Thus-prepared metal particles were in a size range 2-60 nm, and they achieved extremely small size such as 2-4 nm for Cu, Pd, and Pt particles. Figure 7.46 shows a scanning transition electron micrograph of Pd particles of 3.8 nm in mean diameter with a narrow size distribution ranging over 2.8-5.2 nm."*^^ 7.3.10. Reaction in Solid Templates When an aluminum plate is anodically oxidized in an acidic electrolyte, a porous oxide layer is formed on one side of the plate, consisting of an array of parallel and straight channels of a uniform diameter. The pore size (10-250 nm) and its density (10^^-10^^ m"^) can be controlled by changing the anodizing voltage, while the thickness of the oxide film (more than a few 10 \Jim) by varying the anodic oxidization period.'*^^ After the electrooxidation, the anodic oxide fihn is separated from the aluminum substrate by reversing the polarity of the cell, and the impervious back layer of the separated film is etched by immersing the film in 20 wt % sulfuric acid for Ih. The anodic aluminum oxide (AAO) film has widely been used as a template of nanotubes and nanowires or a host material of microdevices: e.g., magnetic recording media (Co and Co-Ni alloy,"*^^ Fe,"*^^); optical devices (Au);"*^^'"^^^ nanohole arrays (Au and Pt,"*^^ CdS"*^"*); nanotubes or nanofibers of metal oxides (TiO^,''''''' WO3,''' ZnO,"''), metals (Au"''), and polymers (polyacetylene"*^^). As an application of the anodic aluminum oxide film, Kyotani et al,^^^'^^ Parthasarathy et al,^^^ and Che et al^^'^ prepared monodispersed carbon nanotubes. For example, Kyotani et al^^^ impregnated furfuryl alcohol in the internal walls of the microchannels of an aluminum oxide film. The impregnated furfuryl alcohol is then polymerized and carbonized in the channels by heating the film under N2 flow up to 900 °C at a rate of 5 °C


331

min"^ and holding for 3 h. Finally, the aluminum oxide film template was removed by treating the film with 46 % HF solution at room temperature. On the other hand, Parthasarathy et al^^^ polymerized acrylonitrile on the internal walls of the microchannels and carbonized by heating the polyacrylonitrile tubes at 600 °C under Ar flow for 30 min. In this case, the oxide template was removed by treatment with 1 mol dm"^ NaOH. The thickness of the carbon nanotubes can be controlled by varying the polymerization time. Kyotani et a/."*^^'"*^ also attempted to form carbon nanotubes by pyrolytic carbon deposition on the intemal walls of the microchannels with 2.5 % propylene gas diluted in N2 gas passing through the reactor at 800 °C. The thickness of the carbon tubes were controlled by varying the deposition time; z.e., 3-5 nm for 1 h, 40-45 nm for 6 h, 60-80 nm for 12 h in microchannels of 230 nm diameter. Figures 7.47 and 7.48 show a schematic illustration of the procedure for the preparation of carbon nanotubes by this method and SEM images of thus-prepared carbon nanotubes after different deposition times, respectively. Che et al^^^ found ethylene and pyrene to be also useful for the pyrolytic carbon deposition. They showed that it was possible to prepare carbon nanowires without definite hollow by extending the deposition time. Moreover, they prepared highly crystallized carbon nanofibers at a low temperature around 500 °C by using a template film with microchannels coated with a Ni catalyst.

Anodic aluminum oxide film

Carbon tubes

Fig. 7.47. Schematic illustration of the procedure for the preparation of carbon nanotubes. (From Ref. 480.)

332

PREPARATION

200 nm Fig. 7.48. SEM images of carbon nanotubes prepared by pyrolytic carbon deposition on the internal walls of the microchannels of an anodic alumina film after different deposition times: (a) 1 h, (b) 6 h, (c) 12 h. (From Ref. 480.) 2ôlites are aluminosilicate crystals consisting of uniform cavities and channels of molecular dimensions (0.6-1.3 nm) with small windows. Such micropores may be used as a template for the synthesis of uniform nanoclusters or nanoparticles of metal carbonyls, chalcogenides, and pure metals. For example, Rao et al^^^ synthesized Rh5(CO)i5 clusters of ca. 1 nm diameter in the supercages of NaY zeolite (internal diameter = 1.3 nm; entrance diameter = 0.7 nm) by ion exchange with Rh^^ and reductive carbonylation with CO and H2, which were then converted to Rh^ metal clusters. Since this method is characterized by the synthesis of a cluster inside a supercage with inlets smaller than the cluster by previous introduction of still smaller components of the cluster, such as metal ions and CO molecules, through the inlets, it has been named "ship-in-bottle synthesis'"*^"* (see section 12.4.3). Similarly, many carbonyl and chalcogenide clusters have been synthesized in the supercages of NaY or NaX zeolite (faujasite: the dimensions of the supercages of NaX and NaY zeolites are almost the same, but molar ratio Si02/Al203 = 2-3 for NaX and 3-6 for NaY'*^^; ^-g-^ C04(CO)i„^«^ Co,(CO)i„^«^ HFe3(CO)ir,^«« Ir,(CO),„^«^ Ir,(CO)i/-,^^ Rh,. ^T,{CO\,r ^,^t,{CO\t''^ [Pt3(CO)J„^- (/I =3,4),^^^'^^ Pdi3(CO)„^^^ HRu,(CO)i5-,''' Ru,(CO)i5'/'' HCoRu3(CO)i3'/'' HRuCo3(CO)i2/'' €11484,^^ and Cd4Se4.^°^ Figure 7.49 shows schematics of the ship-in-bottle synthesis of Rh6.,Ir,(CO)i6 in NaY zeolite.^^' If ALPO-5 zeolite, having smaller supercages (0.7 nm) than those of


CRh6-iIrx]/NaY

333

[Rh6-iIri(C0)i6]/NaY (x«0,2,3,4,6)

Fig. 7.49. Schematics of the ship-in-bottle synthesis of Rh6_xIrx(CO)i6 in NaY zeolite. (From Ref. 484 (c).) NaY (1.3 nm), is used in the reductive carbonylation of Rh2(CO)4Cl2, only Rh4(COX2 is obtained, instead of Rh6(C0Xg as produced from NaY zeolite, owing to the limitation in the space of a supercage."*^"^'^"^ Here, it is noteworthy that the size of the final product depends, in some cases, on the species of the guest molecules, even if the same zeolite is used as a template. For example, in the ship-in-bottle synthesis of the Chini-type Pt carbonyl clusters, [Pt3(CO)6]/',^°^ using a NaY zeolite, Pti2(CO)24^" is obtained from Pt^^ ion, while ?tg(CO\^^' (0.8 nm x 0.8 nm) from Pt(NH3)4^^ complex."*^ This has been explained in terms of the increase in basicity with coordination of anmionia,^°^ since the reduction of n of the Chini-type clusters with increasing basicity was observed in their synthesis by reductive carbonylation of H2PtCl6 in a methanol solution .^^ In any case, it is impossible to synthesize still larger Chini-type clusters with n ^ 5 using NaY zeolite, as is obvious from the size limit of a supercage. For this purpose, we need other templates having much larger pore sizes. On the other hand, it is now possible to synthesize mesoporous molecular sieves, such as MCM-41 (Mesoporous Crystal Material - 4lf^^ and FSM16 (Folded Sheet Mesoporous Material - 16),^^^ using different micelle surfactant templates. These materials consist of mesoporous channels of 2 10 nm in diameter, much larger than those of conventional zeolites, such as ZSM-5, ALPO-5, and NaY. They are potentially useful as hosts or

334

PREPARATION

templates for the synthesis of more bulky organometallic complexes,^°^ metal particles, chalcogenides,^°^'^°^ etc. For example, Yamamoto et ai^ prepared a trigonal prismatic cluster anion Pti5(CO)3o^" (AZ = 5 in [PtsCCO)^]^^") in FSM--16 , having a honeycomb structure with uniform hexagonal channels of 2.75 nm in diameter. On thermal evacuation at 473 K, the carbonyl clusters were converted to uniform platinum (Pt) nanoparticles of ca. 1.5 nm diameter consisting of 55 ± 5 atoms.^^° Figure 7.50 is a proposed scheme of cluster transformation of a [Pt3(CO)3]5^" to a Pt nanoparticle in FSM-16 by the thermal evacuation.^^°' FSM-16 H2PtCl6/Et4NCl/FSM.16

900 m^/g 630 m^/g

^^50-60 particle size = 15A • :C0

at363K CN = 7.3

at473K C.N = 7.8 650 m^/g

Fig. 7.50. Scheme of cluster transfomiation of a [Pt3(CO)3]5^~ to a Pt nanoparticle in FSM-16 by thermal evacuation at 473 K, as deduced from data of EXAFS, FTIR, and TEM. (From Ref. 510 (a).)

7.3.11. Firing of Solid Precursors Mohri et al^^^'^^^ prepared fairly uniform monocrystalline particles of a alumina (a-Al203) in a size range of micrometer order directly by firing transition alumina, such as y-alumina, 8-alumina, S-alumina, etc., or


335

Fig. 7^1, SEM of an a-AljOg powder prepared by firing a transition alumina precursor in hydrochloric atmosphere. (Courtesy of Messrs. Y. Uchida and M. Mohri, Sumitomo Chemical Co., Ltd.)

aluminum hydroxide in hydrochloric atmosphere {ca. 30 vol% HCl or 35 vol% CI2 + 5 vol% H2O in N2 at 1 atm) at a temperature around 1100 °C for about 30 min. Figure 7.51 shows an example of thus-obtained a-Al203. The a-alumina particles are likely to be crystallized by nucleation and growth on the surface of the solid precursor, as a starting material, via aluminum chloride complexes produced by the reaction of the solid precursor and HCl, since the product is exclusively formed on the solid precursor without depositing onto the neighboring wall. Presumably, the uniformity of the product may have been achieved by inhibiting their coagulation through fixing the growing particles on the solid surface of the starting material. The intermediate, aluminum chloride complexes, may diffuse through the gas phase and/or migrate on the surface of ihe solid precursor. There is no doubt that a-alumina particles have been formed by a kind of recrystallization via chloride complexes from the solid precursor by the aid of HCl as a catalyst of this reaction, and not by direct conversion from the solid precursor, as is obvious from the fact that the mean size of the starting material with a very broad size distribution is normally much larger than that of the product. The separation between nucleation and growth stages is deemed to have been achieved by the preformed nuclei of

336

PREPARATION

a~alumina which reduce the supersaturation of the aluminum chloride complexes with their growth. 7.3.12. Conversion of Aerosol Droplets Aerosol technique can be applied to the hydrolysis of metal alkoxide droplets with water vapor to produce monodisperse metal oxides in carrier gases such as helium. In fact, the technique has been employed in the preparation of monodisperse spheres of silica (Si02/^^ titania (Ti02),^^'* alumina (Al203),^^^ tantalum oxide (T2i20s),^^^ tin oxide (Sn02),^^^ titania/ alumina (Ti02/Al203) composite,^^^ and lithium tantalate (LiTa03/^^ by hydrolysis of corresponding alkoxides. Also, titania/siiica (Ti02/Si02) composite particles were obtained by hydrolysis of mixed droplets of titanium ethoxide and silicon tetrachloride,^^^ or tetraethyl orthosilicate, with water vapor.^^^ Some attempts to synthesize mixed oxide powders of more than two components by the aerosol technique are also known; e.g., cordierite-type oxides^^^ and superconducting oxides.^^^ The same technique was used for preparation of uniform particles of polystyrene and its derivatives^^"* and divinylbenzene-ethylvinylbenzene copolymers^^^ by polymerization of the corresponding monomer droplets in helium carrier as with a vaporized initiator (e.g., trifluoromethanesulfonic acid). The divinylbenzene/ethylvinylbenzene copolymer particles were further converted to highly porous carbon (C) spheres of 3-5 \xm in diameter (BET specific surface area = 650 m^ g'^) by thermal degradation in an inert atmosphere at 500 °C.^^^ Partch et al^^^ also produced monodisperse polyurea and mixed metal oxide-polyurea particles such as titania-polyurea and alumina-polyurea. The polyurea particles were obtained by direct reaction of liquid droplets of toluene 2,4-diisocyanate or hexamethylene with ethylenediamine vapor in the absence of any other additives. The particles obtained were further treated with metal alkoxide vapor, which on subsequent hydrolysis in a water vapor atmosphere resulted in mixed metal oxide/polyurea particles. The metal oxides of the mixed particles were incorporated in the polyurea beads rather than forming a surface layer. Figure 7.52 shows a SEM of spherical polyurea particles containing titania (metal content 3.1 %) prepared by the aerosol technique.^"^ Moreover, Mayville et al.^^^ prepared polyurea-coated titania (polyurea/Ti02) particles by a stepwise continuous process, consisting of hydrolysis of titanium ethoxide droplets with water vapor to yield Ti02 aerosol, condensation of hexamethylene diisocyanate or toluene 2,4-


337

Fig. 7.52. SEM of polyurea particles containing titania (metal content 3.1 %) prepared by the aerosol technique. (From Ref. 527.) diisocyanate on the Ti02 aerosol particles, and exposure to ethylenediamine vapor. The size distribution and the mean size of the solid particles are basically determined by those of the liquid droplets of the starting materials in aerosol systems. Thus, specific devices are concentrated on the generation of uniform liquid droplets, including the design of nebulizers,^^^ heterogeneous seeding of AgCl or NaCl (Sinclair-LaMer method^^^'^^^), falling liquid film technique,^^^'^^^ reevaporation-recondensation technique,^^^"^^^ etc.^^^'^^^ In other words, the formation of solid particles is simply a sort of conversion from the liquid droplets. The coagulation among liquid droplets is minimized by the spatial separation from each other and the quick solidification in the laminar flow of carrier gas. In fact, Kodas et al^^^ found a significant advantage of the laminar flow of inert gas over the turbulent flow for the uniformity in size distribution of alumina particles prepared by the aerosol technique. Here, the reaction of an aerosol droplet is thought to be completed in less than 1 sec.^^^ It is of interest that Kodas et al^^^ also found a dramatic additional effect of seeds, such as AgCl and NaCl, for inhibition of deposition of the liquid droplets onto the wall of the reaction chamber; le., the wall deposition as high as 90 % in the absence of seeds was reduced to ca, 10 % with seeds. Figure 7.53 illustrates a typical aerosol system.^^^ The aerosol process is a versatile technique for the preparation of fairly uniform particles of organic and inorganic compounds and their composites. In addition, it is suitable for continuous processing and for the production of highly pure powders. On the other hand, the internal composition of a

338

PREPARATION

Fig. 7.53. Schematic presentation of the aerosol generator: (a) He gas tank, (b) drying column containing silica gel and molecular sieve, (c) Millipore membrane of 0.1-^m pore size, (d) flow meter, (e) nuclei generator containing silver chloride, (f) boiler of monomer liquids, (g) and (n) chambers for vapor condensation, (h) reheater, (i) chamber for recondensing droplets, (j) container with ethylenediamine (EDA), (k) EDA vapor injection chamber, (1) and (q) reaction chambers, (m) boiler of metal alkoxides, (o) container with water, (p) water vapor injection chamber, (r) thermopositor. (From Ref. 527.)

multicomposite is normally inhomogeneous owing to the different reaction rate of each component; e.g., the above composite particles of Ti02/Si02^^'^^^ and Ti02/Al203^^^ are both enriched in titania in their surface layers, suggesting the fast hydrolysis of titanium ethoxide relative to the used silicon and aluminum alkoxides. It may be basically difficult to avoid such an internal inhomogeneity in the aerosol process unless the reactivity of each starting material is designed equal, while there are many means to avoid a similar inhomogeneity in solution systems; e,g., control of the pH, solubility of each starting component with a variety of solvents, or feed rate of each component. Also, it is not easy to realize a very high monodispersity, because there seems to be so far some limit in production of perfectly uniform liquid droplets. For this problem, development of a more precisely controlled nebulizer system is desired; e.g., application of the oscillatory nozzle~jet methods (see the next section). 7.3.13. Oscillatory Nozzle-Jet Techniques Matsumoto et al^^^ prepared monodispersed styrene/divinylbenzene copolymer beads in a mean size range from hundreds of microns to several millimeters by passing the corresponding comonomer with an initiator (such as 0.6 wt % benzoyl peroxide) and a solution of a shell-forming material


339

(such as 0.8 wt % sodium alginate) through a coaxial double nozzle vibrated at a constant frequency by an amplified oscillator, solidifying the shell of the uniform encapsulated comonomer droplets falling into a hardener solution (such as 20 wt % CaCOj), polymerization of the encapsulated comonomer at an elevated temperature (such as 75 °C) for 7 h, and removing the solid shell with a reagent solution (such as 10 wt % sodium polyphosphonate). The size of the polymer beads is controlled by regulating the flow rate of the monomer and frequency of the osciUator. The relatively large but quite uniform polymer spheres (relative standard deviation 2S 2 %) are particularly useful as ion exchange resins or column bed beads in liquid chromatography. Figures 7.54 and 7.55 show the schematic diagram of the generator of uniform encapsulated monomer droplets^^^*^ and a SEM of 2.3 mm copolymer beads thus produced, respectively.^*'^

11

10

@

13 3 «

lA

D

n

7 ^12

e

3

{!5-*^ ^

«8

15 Fig. 7.54. Schematic diagram of the generator of the unifomi encapsulated monomer droplets: 1. N^ cylinder, 2. buffer tank, 3. monomer tank, 4. shell material tank, 5. rotameter, 6. orifice flow meter, 7. dual axial nozzle, 8. hardening agent, 9. speaker, 10. amplifier, 11. oscillator, 12. lamp, 13. photo sensor, 14. digital counter, 15. oscilloscope. (From Ref. 539.)

Fig. 7.55. SEM of 2.3-mm styrene /divinylbenzene copolymer beads prepared using the generator of uniform encapsulated monomer droplets in Fig. 7.54. (From Ref. 539.)

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PREPARATION

Colvin et al^^ produced monosized beads of poly(2-hydroxyethyl methacrylate) and poly(glycerol monomethacrylate) in a size range of 50400 \xxa by passing the monomers under a pressure through a nozzle coupled to an energized piezoelectric crystal vibrating at a constant frequency, instantaneous freezing of the uniform monomer droplets falling into liquid nitrogen, irradiation of the vitrified monomer droplets with a ^Co gamma source, and intradroplet polymerization with thawing. Figures 7.56 and 7.57 demonstrate a scheme of the monosized droplets generator and an optical micrograph of so-prepared 155 |xm poly(2-hydroxyethyl methacrylate) beads, respectively. While the oscillatory nozzle-jet method is now mostly hmited to the preparation of relatively large polymer particles, it may be applied to inorganic particles starting from metal alkoxides or inorganic salts in aqueous solutions, and the utility will greatly expand if multiple nozzles with a much smaller diameter of the order of micrometers or less become available.

-STROBE LIGHT

CHAflBING BLECTflOOE COVER

COLLEaiON PAN

INSULATION

Fig. 7.56. Schematic presentation of the generator of monosized monomer droplets. (From Ref. 541.)


341

Fig. 7.57. Optical micrograph of 155-(im poiy(2-hydroxyethyl methacrylate) beads prepared using the generator of uniform monomer droplets in Fig. 7.56. (From Ref. 541.)

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Wang, M. M. Eddy, G. D. Stucky, D. E. Cox,, K. Moller, and T. Bein, J. Am. Chem. Soc. I l l , 530 (1989). 501. K. Moller, M. M. Eddy, G. D. Stucky, N. Herron, and T. Bein, J. Am. Chem. Soc. I l l , 2564 (1989). 502. J. Tachibana and M. Ichikawa, Hyomen 35, 256 (1997). 503. J. C. Calabrese, L. F. Dahl, P. Chini, G. Lx)ngoni, and S. J. Martinengo, J. Am. Chem. Soc. 96, 2614 (1974). 504. T. Yamamoto, T. Shido, S. Inagaki, Y. Fukushima, and M. Ichikawa, J. Am. Chem. Soc. 118, 5810 (1996). 505. C. T. Kresge, M. E. Leonowicz, W. J. Vartuli, and J. S. Beck, Nature 359, 710 (1992); J. S. Beck, J. C. Vartuli, W. J. Roth, M. E. Leonowicz, C. T. Kresge, K. D. Schmitt, C. T. Chu, D. H. Olson, E. W. Sheppard, S. B. McCullen, J. B. Higgins, and J. L. Schlenker, J. Am. Chem. Soc. 114, 10834 (1992). 506. S. Inagaki, Y. Fukushima, and K. Kuroda, J. Chem. Soc, Chem. Comm. 680 (1993); S. Inagaki, A. Koiwai, N. Suzuki, Y. Fukushima, and K. Kuroda, Bull. Chem. Soc. Jpn. 69, 1449 (1996). 507. C. Huber, K. Moller, and T. Bein, J. Chem. Soc, Chem. Comm. 2619 (1994). 508. T. Meschmeyer, F. Rey, G. Sankar, and J. M. Thomas, Nature 378, 159 (1995); G. A. Ozin and S. Ozkar, Chem. Mater. 4, 511 (1992). 509. R. Leonm, D. Margolese, G. Stucky, and P. M. Petroff, Phys. Rev. B 52, 2285 (1995). 510. (a) T. Yamamoto, T. Shido, S. Inagaki, Y. Fukushima, and M. Ichikawa, J. Phys. Chem. B 102, 3866 (1998); (b) M. Ichikawa, in "Chemisorption and Reactivity on Supported Clusters and Thin Films," (R. M. Lambert and G. Pacchioni, Eds.), pp. 153-192. Kluwer, Dordrecht, 1997; (c) M. Sasaki, M. Osada, N. Sugimoto, S. Inagaki, Y. Fukushima, A. Fukuoka, and M. Ichikawa, Microporous Mesoporous Mater. 21, 597 (1998); (d) M. Sasaki, M. Osada, N. Higashimoto, T. Yamamoto, A. Fukuoka, and M. Ichikawa, J. Mol. Catal. A: Chemical 141, 223 (1999). 511. M. Mohri, Y. Uchida, Y. Sawabe, and H. Watanabe, Jpn. Patent (A) 6-191833, 6-191835, 6-191836 (1994). 512. Y. Uchida, Y. Sawabe, M. Mohri, N. Shiraga, and Y. Matsui, Ceram. Trans. 54, 159 (1995). 513. P. Movilhat, Ann. Occup. Hyg. 4, 275 (1962). 514. M. Visca and E. Matijevic, J. Colloid Interface Sci. 68, 308 (1979). 515. B. J. Ingebrethsen and E. Matijevic, J. Aerosol Sci. 11, 271 (1980).

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516. O. Amiel, J. M. Heintz, F. Duboudin, and R. Salmon, J. Aerosol Sci. 21, 799 (1990); J. M. Heintz, O. Amiel, and R. Salmon, J. Mater. Sci. Lett. 9, 403 (1990). 517. M. Ocana and E. Matijevic, J. Aerosol Sci. 21, 811 (1990). 518. B. J. Ingebrethsen, E. Matijevic, and R. E. Partch, J. Colloid Interface Sci. 95, 228 (1983). 519. O. Amiel, P. Cazeau, and R. Salmon, J. Mater. Sci. 30, 3674 (1995). 520. A. Balboa, R. E. Partch, and E. Matijevic, Colloids Surfaces 27, 123 (1987). 521. E. Matijevic, Q. Zhong, and R. E. Partch, êrow/ Sci. Technol. 22,162 (1995). 522. R. Salman and E. Matijevic, Ceram. Intern. 16, 157 (1990). 523. P. Biswas, D. Zhow, I. Zitkovsty, C. Bllue, and P. Boolchand, Mater. Lett. 8, 233 (1989); T. T. Kodas, E. M. Engler, V. Y. Lee, R. Jacowitz, T. H. Baum, K. Roche, S. S. P. Parkin, W. S. Young, S. Hughes, J. Kleder, and W. Auser, Appl. Phys. Lett. 52, 1622 (1988); K. Okuyama, M. Adachi, K. Arai, Y. Kousaka, N. Tohge, M. Tatsumisago, and T. Minami, Fmtai Kogaku Kaishi 26, 146 (1989). 524. R. E. Partch, E. Matijevic, A. W. Hodgson, and B. F. Aiken, J. Polym. Sci.: Polym. Chem. Ed. 21, 961 (1983). 525. K. Nakamura, R. E. Partch, and E. Matijevic, J. Colloid Interface Sci. 99, 118 (1984). 526. S. GangoUi, R. E. Partch, and E. Matijevic, Colloids Surfaces 41, 339 (1989). 527. R. E. Partch, K. Nakamura, K. J. Wolfe, and E. Matijevic, J. Colloid Interface Sci. 105, 560 (1985). 528. F. C. Mayville, R. E. Partch, and E. Matijevic, /. Colloid Interface Sci. 120, 135 (1987). 529. D. Sinclair and V. K. LaMer, Chem. Rev. 44, 245 (1949). 530. V. K. LaMer, E. C. Y. hin, and I. B. Wilson, J. Colloid Sci. 5, 471 (1950). 531. E. Matijevic, S. Kitani, and M. Kerker, J. Colloid Sci. 19, 223 (1964). 532. G. Nicolaon, D. D. Cooke, M. Kerker, and E. Matijevic, J. Colloid Interface Sci. 34, 534 (1970). 533. G. Nicolaon, D. D. Cooke, E. J. Davis, M. Kerker, and E. Matijevic, J. Colloid Interface Sci. 35, 490 (1971). 534. E. Rapaport and S. E. Weinstock, Experiencia 11, 363 (1955). 535. M. Suresh, R. A. Mackay, and C. Acquista, Aerosol Sci. Technol. 1, 441 (1982).


367

536. G. Kasper and A. Bemer, Staub-Reinhalt Luft 38, 183 (1978). 537. C. Hillenbrand and J. Porstendoerfer, Staub-Reinhalt. Luft 38, 52 (1978). 538. T. T. Kodas, A. Sood, and S. E. Pratsinis, Powder Technol. 50, 47 (1987). 539. S. Matsumoto, K. Takeshita, J. Koga, and Y. Takashima, J. Chem. Eng. Jpn. 22, 691 (1989). 540. S. Matsumoto and H. Kobayashi, in "Proc. 2nd Intern. Conf. Liquid Atomization and Spray Systems," p. 63, 1982; S. Matsumoto, H. Kobayashi, and Y. Takashima, J. Microencapsulation 3, 25 (1986). 541. M. Colvin, S. K. Chung, M. T. Hyson, M. Chang, and W. K. Rhim, J. Polym. Set A: Polym. Chem, 28, 2085 (1990).

CHAPTER 8 CONTROL OF PARTICLE CHARACTERISTICS 8.1, Size Control For the preparation of monodisperse particles in general, renucleation or concurrent nucleation with particle growth must be strictly prevented, so that the final particle number is determined during the nucleation stage preceding the growth stage. Hence size control of monodisperse particles must be done during the nucleation stage, since the volume of each particle is inversely proportional to the final particle number as long as the total volume of the solid is fixed. If the final particle number, supply rate of the monomers at the end of nucleation, molar volume of the solid, and volumic growth rate of a particle at the end of nucleation are denoted by n^"", QQ, V^, and i)^, respectively, n^" is given by O V

(see sections 1.4 and 1.5). Thus, the final particle number is proportional to 300

>300

>300

On the other hand, each peanut-type particle has a rough surface and the long axis of each subcrystal developed radially from the revolution axis of the particle is collinear with the c-axis of the hexagonal system, as displayed in the SEM image and electron diffractometry on a section in Figs. 8.23(a) and (b), respectively.^^ The mean length and width of a subcrystal of the peanut-type particles are 70 nm and 5-10 nm, respectively. These facts verify the prediction for the growth mechanism of the peanuttype particles, represented by the schematic model in Fig. 8.6. Although ellipsoidal hematite particles of a comparable aspect ratio can be obtained with either sulfate or phosphate ions, their effects on the internal structure of the product are quite different.^^ Figure 8.24 shows SEM images, TEM images of the sections, and electron diffraction patterns of ellipsoidal particles prepared with sulfate and phosphate at 140 °C from p FeOOH in the presence of a minimized concentration of chloride ions, 0.10 mol dm'-'. Effects of the anionic species, sulfate and phosphate, on the mean sizes of the subcrystals are summarized in Table 8.2. Obviously, the ellipsoidal particles prepared with sulfate are polycrystals with subcrystals developed radially from the revolution axis, while the ones prepared with phosphate are nearly single crystals. The difference in effect on the internal structure of hematite may be due to the difference in the absolute amounts of incorporated sulfate and phosphate, since about 90 % of the used sulfate (3.0 X 10-^ mol dm"^) or 70 % of phosphate (3.0 x 10"^ mol dm"^) in the standard systems were apparently incorporated into the hematite particles."*^'^^ The sulfate ions were found to be uniformly distributed in a peanut-type particle, as revealed by local EDX analysis on a section of a particle (see

400

PREPARATION

Fig. 8.23 (a) Close-up SEM of a peanut-type hematite; (b) TEM of the thin section of a peanut-type hematite and the electron diffraction pattems of its parts indicated by circles, showing the directions of the c-axis of the subcrystals in these parts. (From Ref. 93.)

Fig. 10.10 in chapter 10).^^ The observed different effects of chloride, sulfate, and phosphate are directly observed by electron microscopy on much smaUer particles prepared with these anions. Figure 8.25 shows TEM images of a) pseudocubes prepared in a gel-sol system at 1.5 mol dm" CI"

8. CONTROL OF PARTICLE CHARACTERISTICS

401

Fig. 8.24. SEM images, close-up SEMs, TEMs of the sections, and electron diffraction patterns of ellipsoidal particles prepared with (a) sulfate (3.0 x 10'^ mol dm'^) and (b) phosphate (3.0 x 10"^ mol dm"^) at 140 °C from p-FeOOH in the presence of a minimized concentration of chloride ions, 0.10 mol dm"^. The scale bars are common for (a) and (b), but for the section TEMs. (From Ref. 15.)

PREPARATION

402

Table 8.2. Effects of anions on the mean size of the subcrystals of hematite particles (a) and (b) in Fig. 8.24, aged at 140 °C for 3 days {Source: Ref. 15) Sample

Anions (mol dm"^) [C1-]

[SO/-]

1 (a)

0.1

3.0x10""

1 (b)

0.1

-

[PO/-]

3.0x10'^

Thickness (nm) {012}

{104}

{110}

106

79

63

>300

>300

>300

Fig. 8.25. TEM images of a) pseudocubes prepared in a gel-sol system at 1.5 mol dm"^ Cr by aging for 3 days at 100 °C with ultrafine seeds of hematite of mean diameter 8.3 nm, b) ellipsoids prepared in the same way as a), but with 3.0 x 10"" mol dm'^ Na2S04, c) pseudocubes prepared by aging a dilute homogeneous solution of FeCl3 (2.0 X 10'" mol dm"^) at 100 °C for 3 days, and d) ellipsoids prepared in the same way as c), but with 4.5 x lO""* mol dm"^ KH2PO4 by aging for 7 days. (From Ref. 15.) by aging for 3 days at 100 °C with ultrafine seeds of hematite of mean diameter 8.3 nm, b) ellipsoids prepared in the same way as a), but with 3.0 X 10'^ mol dm"^ Na2S04, c) pseudocubes prepared by aging a 2.0 x 10'^ mol


403

Fig. 8.26. High-resolution TEM of ellipsoidal hematite showing the lattice structure. (From Ref. 95.)

404

PREPARATION

Fig. 8.27. Section TEM of a platelet-type hematite particle. (From Ref. 96.)

dm"^ FeClj at 100 °C for 3 days, and d) ellipsoids prepared in the same way as c), but with 4.5 x lO"* mol dm"^ KH2PO4 by aging for 7 days.^^ Obviously, the particles in a) and b) are have porous structures, whereas those in c) and d) are nearly single crystals. The clear structural difference between the particles prepared by the gel-sol method in a) and b) and those by aging dilute FeCl3 solutions in c) and d) is basically due to the great difference in chloride concentration; i.e,, [CI"] = 1.5 mol dm'^ in a) and b), while [Cr] = 0.06 mol dm'^ in c) and d). However, in the porous structure of the ellipsoids in b), an additional contribution of sulfate ions is involved. The ellipsoids in d) are virtually single crystals, as revealed from the perfectly continuous lattice structure by high-resolution electron microscopy on an ellipsoid prepared in almost the same way as d), as shown in Fig. 8.26.^^ Hence, phosphate ions themselves have little effect on the internal structure of hematite unlike sulfate ions. The internal structure of the uniform platelet particles of hematite prepared in a highly basic medium^ must be single crystals, as observed in the TEM images of a section of a platelet particle prepared in a basic medium in Fig. 8.27.^^ In this case, even a high concentration of coexisting chloride ions has no effect on the internal structure, probably because of the exclusive adsorption of hydroxide ions in the alkaline range. Ellipsoidal


405

Fig. 8.28. Section TEMs of CdS particles prepared from the Cd-EDTA complex system: (a) total image of a section of a CdS particle; (b) high-resolution image of a central part (C in (a)); (c) high-resolution image of a surface part (S in (a)). (From Ref. 97.)

hematite particles are also prepared with organic shape controllers, as stated in section 8.2.1. In particular, hydroquinone was found to be uniformly

406

PREPARATION

incorporated in the particles in the form of a polymer and make their internal structure polycrystallineJ^ On the other hand, the internal structure of the spherical particles of cadmium sulfide, prepared from the EDTA-Cd system in Fig. 7.6 in chapter 7, is polycrystal consisting of randomly oriented small subcrystals, as shown in the TEM images of a section in Fig. 8.28.^^ From these TEM photos, the well developed subcrystals near the surface are found to be much larger than those in the core. This seems to be a result of the decreasing nucleation rate of the two-dimensional nuclei for the particle growth with the declining supersaturation as the TAA and cadmium ions are consumed. The random orientation of the subcrystals is a consequence of the nonepitaxial surface nucleation. Andreasen et aV^ prepared small ellipsoidal barium sulfate particles (0.14 jrni) in the presence of citric acid. Their transmission electron micrograph reveals undoubtedly that the BaS04 particles are porous polycrystals. Presumably, adsorption of citrate is responsible for the external shape and the internal structure, since they also presented a significant effect of citrate on the reduction of the final size of the BaS04 particles, suggesting the strong adsorption of citrate. Petres et aL^^ also demonstrated the porous structure of monodispersed spindle-like BaS04 particles, prepared by decomposition of the EDTA-Ba complex after Takiyama,^°° with a TEM of their ultrathin sections sliced with an ultramicrotome. EDTA may have contributed to the formation of the ellipsoidal shape and porous structure. It seems reasonable to consider that the organic compounds, such as citric acid and EDTA, may be incorporated into the particles. The transmission microscopy on particle sections was also applied in the study of the internal structure of spmdle-type akaganeite (p-FeOOH) particles by Watson et al.,^^^ and the particles were found to be composed of a bundle of much thinner subcrystals.

8.4. Composition Control Composition control is an important technique for modifying the properties of original particles, since multicomponent particles often exhibit unexpected properties entirely different from those of the individual constituents, due to their complex composition and internal structure. Uniform mixing of different components, doping by a trace of different species, and conversion of original particles to other particles of a different


407

composition may be included in this technique. 8.4.1. Mixing For modifying the properties of single-component particles, one of the most useful procedures is the internal admixing of one or more components. Many composite colloids of narrow size distribution have been produced: for example; ferrites of Co/Fe,^°^ Co/Ni/Fe,'^^ Cr/Fe,^^ Ba/Fe,^°^ and Sr/Fe,^°' by oxidation of the corresponding mixed hydroxide gels (Note: there is a possibility that these ferrites of Ba/Fe and Sr/Fe are magnetite^^); spherical amorphous particles of BaTiOj^^^ and PbTiOj^"^ by decomposition of complex peroxidic species of titanium in the presence of Ba or Pb chelates in alkaline media; Ce'VY'"-,'°''^^° Cn^'/Y^W'' Cu^'fLsi^W Cu'VGd'*basic carbonate,^^^ Cu^*/L^*-basic carbonates (L = Gd, Dy, Ho, Er),^^^ Y'VZr'*,^^' and Y'"/Eu^*-basic carbonate,^^^ Y'^-basic carbonate/aluminum hydroxide,^^^ and Cd^*/Ni^* basic phosphate^^^ from homogeneous solutions of corresponding mixed salts in the presence of urea. Copper compounds, different in composition and particle shape, were prepared by homogeneous precipitation from solutions of copper salts in the presence of urea: ie., amorphous spheres of malachite composition, Cu2(OH)2C03, from Cu(N03)2; bipyramidal particles of atacamite, 3 Cu(OH)2 • CUCI2, from CUCI2; acicular particles of brochantite, 3Cu(OH)2 • CUSO4, or platelets of posnjakite, 3Cu(OH)2 • CuSO^ • H2O, from CuSO^.'^^ CdS/ZnS and CdS/PbS were prepared from acidic solutions of corresponding mixed salts in the presence of thioacetamide;^^*^^^ AgCI/AgBr and AgI/AgBr'2° by the CDJ technique; and Ti02/Al203,^'' Ti02/Si02/'' Ti02/polyurea,^^^ and Al203/poIyurea^^ in aerosol systems. The mixed basic carbonates^^^"^^^ are amorphous spheres to be converted into the corresponding functional mixed oxides by calcination. Here it should be noted that the internal composition of these basic carbonates and conesponding oxides is not necessarily uniform. For example, Cu^'^/Y^*and Cu^*/La^* basic carbonate particles have a compositional gradient in the interiors, ie., richer in copper content in the cores, because of the faster precipitation of copper basic carbonate.^^^ Although the spherical particles of CdS and ZnS are normally crystalline, the mixed CdS/ZnS particles are amorphous if grown at low temperature while crystalline at high temperature. The morphology, crystallinity, and internal structure of CdS/PbS depend strongly on the molar ratio of the starting materials and on the aging temperature.^'' The solid solution of Ag(Ci,Br) can take arbitrary compositions, whereas

408

PREPARATION

AgNOa-^

Single Jet

KX--,

AgN03-i

Reverse Mixing

r-KX

Double Jet

Fig. 8.29. Three addition modes of reactants, including silver nitrate and alkali halides, for the preparation of silver halide particles.

the mole fraction of Agl in face-centered cubic Ag(Br,I) is limited to about 0.4 as a maximum, and that of AgBr in hexagonal Ag(Br,I) is limited to about 0.05. For the precipitation of silver halides in open systems, there are three typical addition modes of monomer sources; ie., the single-jet mode in which a silver nitrate solution is gradually added to a solution of soluble halides, the reverse mixing mode in which a solution of soluble halides is added to a silver nitrate solution, and the double-jet mode in which the two solutions at a nearly stoichiometric ratio are added simultaneously to an extremely dilute solution of halide or silver ions, as shown in Fig. 8.29. Here, it should be noted that the composition of the precipitate depends on the addition mode. Figures 8.30 and 8.31 illustrate the evolution of the equilibrium compositions of the solid phases for the three mixing modes in the precipitations of silver chlorobromide, whose overaU composition is Ag(Clo5Bro5), and silver bromoiodide, whose overall composition is Ag(Bro9loi), respectively. Here, the equilibrium compositions are assumed to be uniform in each solid phase. The great difference in the composition of the face-centered cubic crystals between the addition modes is due to the equilibrium mole-fractions of bromide in Ag(Cl,Br) solid and of iodide in Ag(Br,I) solid, much higher than the corresponding mole fractions of bromide and iodide in the respective solution phases (see chapter 5). However, since recrystallization processes are involved in the later part of an actual single-jet precipitation, there are normally three peaks in the composition of the face-centered cubic crystals in the later stage of precipitation. Namely, in an Ag(Cl,Br) system, we usually have three solid phases of a high bromide content remaining from the early stage but in the


409 1

i

1—

—

•]

Single Jet o

Single Jet 0.5

"1 •

_

"Double Jet ^***N^^^^^

or Reverse Mixmg"*"*-.*.,....,^ j 1

0

0.5 Fraction of AgNOs

1

Fig. 8.30. Equilibrium compositions of Ag(Cl,Br) with addition of AgNOj and/or (KCl + KBr) in the three addition modes with a total halide concentration ratio of [Cr]/[Br"] = 1/1.

0

1

1

0.5 Fraction of AgNOa

1

Fig. 8.31. Equilibrium compositions of Ag(Br,I) with addition of AgNOg and /or (KBr + KI) in the three addition modes with a total halide concentration ratio of [r]/[Br-] = 1/9.

course of dissolution, an intermediate bromide-content as a result of recrystallization from the old and new precipitate, and a low bromidecontent as a new precipitate. There must be a gradient of bromide fraction, decreasing from the core to the surface, in each particle of the intermediate solid phase. For single-jet precipitation in a Ag(Br,I) system, nearly pure hexagonal Agl precipitates first, and then precipitation of nearly pure AgBr follows with recrystallization of the AgBr and the preformed Agl to form a f.c.c. AgBrI phase with a high iodide content ca, 40 mole %. When Agl has totally been dissolved, a new AgBrI phase with an intermediate iodide content around 20 mole % starts to precipitate by recrystallization of the AgBro 5I0.4 of a high iodide content and the nearly pure AgBr phases. The overall iodide content of the AgBrI phase with an intermediate iodide content is lowered with the progress of AgN03 addition, owing to the formation of a low-iodide surface layer covering the AgBrI particles of a high iodide content in the course of their dissolution with the preferential release of iodide in exchange for deposition of bromide ions. In addition, the compositional evolution depends on the temperature and the addition rate of AgNOj. As is readily anticipated, the size distribution of the particles obtained by the single jet method is very broad. Figure 8.32 shows an example of the compositional evolution in a real Ag(Br,I) system of single

410

PREPARATION

(a) Iodide Contents of Ag(Br,I) Phases

(b) Mole % of Ag(Br,l) Phases 100

40 /—N

(3)

..^^

i

^ 'o

30

c oc

20

o

J \

(4) \

10 i

0 1

(2)

i B ^

^

1 •1

AgN03 (mole %)

100

0 AgN03 (mole %)

Fig. 8.32. Typical compositional changes of the solid phases in the single-jet addition of AgNOg solution to a gelatin solution containing a stoichiometric amount of mixed salts of KBr and KI with 10 mole % KI: (1) nearly pure Agl; (2) nearly pure AgBr; (3) Ag(Br,I) with a high iodide content close to 40 mole %; (4) Ag(Br,I) of an intermediate iodide content decreasing from ca. 20 mole %. (From Ref. 124.)

jet addition of AgNOj to a mixed stoichiometric solution of KBr and KI with 10 mole % Kl}^"^ Here, (1) is the nearly pure Agl, (2) is the nearly pure AgBr, (3) is the AgBrI of a high iodide content, and (4) is the AgBrl of an intermediate iodide content. XPS measurement on TiOj/AljOj^^^ and TiOj/SiOz^^^ particles obtained by the aerosol technique indicated an enhanced surface-concentration of titanium over the bulk value. This may be explained by the hydrolysis rate of titanium alkoxide by water vapor being higher than those of aluminum and silicon alkoxides in the respective mixed droplets in the given aerosol systems, since the hydrolysis in the aerosol systems proceeds from the droplet-vapor interfaces. However, rather than forming a surface layer, Ti02 or AI2O3 mixed with polyurea was incorporated in the beads of poly urea. ^^ This result may suggest that the rates of hydrolysis of the metal alkoxides are lower than that of absorption of water vapor by the polyurea beads. It seems that the aerosol technique in which particles are formed in each isolated droplet is particularly useful for forming mixed particles when it is difficult to obtain mixed particles from a corresponding mixed solution


411

because of the phase separation of soHds. It is possible to control the internal distribution of small phase domains of a polymer in a matrix particle of incompatible polymer species. For example, Okubo et al}^^ found that small spots of poly(n-butyl methacrylate) phase were distributed inside polystyrene particles by seeded polymerization of n-butyl methacrylate-swollen PS latex, whereas the PS particles were coated with PBMA to form a core-shell structure when the seeded polymerization was started with unswoUen PS seeds and BMA monomer dissolved in the medium. They also found that the distribution of the PBMA spots became more uniform from a localized distribution near the surface of a PS particle with increase in the ratio of BMA to PS, or with elevation of the temperature, in the seeded polymerization of BMA-swoUen PS seeds.^2^ In any case, thermodynamic and kinetic analyses on a given system are necessary for precise control of the overall composition of a particle and/or the compositional gradient in a particle in the system. 8.4.2. Doping Synthesis procedures for doped powders of Si02 and Ti02 were derived from those developed for pure Si02^^^ and Ti02^"^ The monodisperse spherical powders were generated through controlled hydrolysis of dilute alcoholic solutions of metal alkoxides. The dopants, such as B in Si02^^^ and Ta, Nb, Ba, Sr, and Cu in TiOj/^" were selectively placed either within the particles during the hydrolysis and growth reactions, or on the surfaces after particle formation. With the aid of these dopants, uniform, finegrained, and dense microstructures were produced for the sintered ceramics of Si02 and Ti02 at substantially lower temperatures (- 1100 °C). For stabilizing the meta-stable tetragonal phase of zirconia, uniform Ydoped Zr02 spheres have been prepared by hydrolysis of corresponding mixed metal alkoxides.^^^*^^^ Her and Matijevic prepared Zr- and Sr-doped BaTiOj particles, to be used as multilayer capacitors or thermal IR detectors, by a double-jet technique.^2'^^^ Vila etal}^"^ prepared uniform YjOjS and Eu-doped YjOjS particles, as excellent electroluminescent materials or red phosphors in color TV, by heating uniform undoped and Eu-doped yttrium basic carbonate precursor powders under a sulfur atmosphere at 770 °C. The precursor particles were prepared by homogeneous precipitation from solutions of the respective chloride salts in the presence of urea.^^^'^^^

412

PREPARATION

Chou and Wu^^^ prepared uniform Ag-doped ZnS spheres, to be used as a blue-emitting phosphor, by homogeneous precipitation from mixed solutions of Zn(N03)2 and AgNOg with thioacetamide in acidic media. In the photographic industry, doping of transition metal ions, chalcogenides, etc. in silver halide particles is a requisite technique for controlling the photographic properties. Monodispersed silver halide particles are indispensable for fundamental studies of the effect of these dopants. Junkers et al}^^ studied the topogiaphy of latent image and doping centers such as silver clusters, gold clusters, silver sulfide, and gold/silver sulfide using monodispersed cubic particles of silver bromide. For this purpose, they doped these centers at different depths of each silver bromide microcrystal in the course of precipitation of the silver bromide particles by the CDJ technique. Keevert et al}^^ doped monodispersed cubic particles of silver bromide and silver chlorobromide coated in a monolayer on polymer films with different elements such as B, C, O, P, S, Cd, Xe, Te, Pb, or Bi by ion implantation, and studied the effects of the doping on the surface and internal photographic speeds. On the other hand, iridium ions are well known for their dual function as a photoelectron trap and hole trap, and used practically as a dopant for reducing both high-intensity and low-intensity reciprocity-law failures and for internal sensitization of direct positive emulsions.^^^ The doped molar ratio to silver atoms in silver halides normally ranges from 10"^ to 10"^. By reason of their practical importance, the chemical and physical properties of photographic emulsions doped with iridium have been studied in detail. For example, Takada^"*^ studied the effect of the internally doped positions in monodispersed silver bromide particles on the ionic conductivity; Le Blanc et al}"^^ studied the correlation between the internal positions of doped Ir ions and generated latent images by light exposure; Vekeman et al}"^^ studied the effect of the concentration of internally doped Ir ions at a certain depth in tetradecahedral silver bromide particles on the transient photoconductivity. Some attempts have been made to incorporate organic substances into inorganic colloidal particles. For example, Tentorio et al}^^ prepared colloidal spheres of amorphous aluminum hydroxide containing a chelating dye (3 Mordant Blue) up to about 20 mol % by forced hydrolysis of aluminum sulfate solutions in the presence of the dye. Such dispersions can serve as model systems for pigments. Hsu et aO^ systematically synthesized uniform spherical particles of Y(0H)C03, Al(OH)3, Zr(OH)2C03, TiOj, Cd3(P04)2, and Si02 doped with a wide variety of organic dyes by coprecipitation of inorganic salts or silicon alkoxide (TEOS) with organic


413

dyes, and studied the optical properties of dye-doped Y(0H)C03 and Si02 pigments extensively. The dye retention by the carrier particles was tested by leaching the pigments with acetone or ethanol. Also, Giesche and Matijevic^"*^ studied monodispersed silica - acid dye systems. Shibata et al}"^^ tested the doping efficiency of dyes into SiOj particles with various dyes and found that the hydrophilicity is a key factor; i.e., water-soluble porphyrins « phthalocyanine > nile blue > rhodamine 6G « nile red > qunizarin « DCM. For porphyrin-doped silica particles they studied the photochemical hole burning (PHB) property at 5 K and the fluorescence life time. In this context, Arnold et al}^^ observed PHB of dye-doped polystyrene spheres at room temperature. Also, Maskasky^"^^ incorporated spectral sensitizing dyes up to ca. 0.1 mol % into AgBr microcrystals of the order of 100 (im by aging AgBr„^""^^~ complexes in the matrix of a silica gel or hardened gelatin in the presence of the dyes. Although the particles may be too large to be defined as colloidal particles, this is a new attempt to expand the utilization of spectral sensitizers, which had been limited to the surfaces of silver halide particles. 8.4.3. Conversion When it is too difficult, or impossible, to obtain a final product of specific properties directly, some indirect procedures such as total conversion of the composition of the original uniform particles may be applied. For example, monodispersed spindle-type Y-Fe203 particles were prepared through a sequence of reduction-reoxidation processes from a-Fe203 of the same morphology.^"*^ Similarly, colloidal a-iron of nearly the same shape was also prepared by reducing uniform hematite powder by hydrogen above 400 °C.^^° Janekovic and Matijevic^^^ produced uniform rhombohedral cadmium carbonate (CaC03) particles by mixmg a urea solution (~ 10 mol dm"^), preheated at 80 °C for 24 h, with an equal volume of a dilute solution (2 x lO"-^ mol dm"^) of cadmium salt at room temperature. The CdC03 particles were calcinated to CdO which retained the original morphology but became highly porous. Similarly, crystalline ¥203^^^ and lanthanide oxides^^^ including GdjOj, EU2O3, Tb203, Sm203, and Ce203 were obtained by thermal degradation at about 600 °C of the corresponding basic metal carbonate particles preformed by precipitation m the presence of urea. Here, it is noteworthy that, except for the ellipsoidal crystalline particles of cerium oxycarbonate, the other rare earth basic carbonate precursors are all amorphous spheres. As has been described in section 8.4.1, mixed oxides

414

PREPARATION

of the transition metals can be obtained as well in a similar manner from the corresponding mixed basic metal carbonate particles.^^^"^^^ If we make use of the unique effects of anions or some other factors in the synthesis of precursor particles to metal oxides by the urea method, we are able to expand the variety of the shape of the final oxide particles. For example, rod-like porous ZnO and fuzzy spheroidal ZnO particles can be obtained on calcination of the rod-like basic zinc carbonate and gel-like amorphous spherulites of the same composition, respectively.^^"^ Moreover, we can obtain different-shape CuO particles, such as spheres, bipyramids, needles, and platelets, on calcination of precursor particles of different copper compounds prepared by homogeneous precipitation from solutions of copper salts of different anions in the presence of urea (see section 8.4.1).^^^ On the other hand, needle-type basic cobalt carbonate particles are generated from a C0SO4 solution containing urea in its closed system, whereas spherical basic cobalt cyanatocarbonate in its system open to air. Spherical C03O4 particles are obtained on calcination of the latter at 300 "C.^^"* Also, uniform spheres of aluminum hydrous oxide are produced from a solution of aluminum sulfate in the presence of urea. Calcination of the amorphous spheres yields nearly perfect ri-AljOa spheres at 900 °C and slightly deformed a-ÂljO^ spheres at 1100 °C.^^^ Metallic Co spheres can be prepared by reduction of the above spherical C03O4 particles with hydrogen at 300 'C.^^'* Uniform Ru spheres are obtained by reduction of spherical RUO2 powder with hydrogen at 250-300 °C, where the RUO2 is prepared by calcination of ruthenium double salt, (NH3)2Ru°'0(NO) •2RuÔC03 •5H2O, at 400 °C, as a product of homogeneous precipitation from a ruthenium chloride solution containing K2SO4 and urea at an elevated temperature. To preserve the particle integrity the original powder was coated with nanosized silica (ca. 10 nm) before calcination.^^^ Similarly, Cu spheres have been obtained by calcination of basic copper(II) carbonate spheres at 300 °C, as a product of the urea process, and subsequent reduction of the so-obtained CuO particles with hydrogen at 150-200 ''C. Again, nanosized silica was used to prevent the sintering of the particles during calcination.^^^ Similar Cu spheres have also been prepared by hydrogen reduction of nearly spherical uniform copper(I) oxide particles synthesized by reducing Cu(II) in Fehling's solution with glucose.^^^ Uniform Fe cubes^^^ and Fe spindles^^^ are prepared by reduction of uncoated or silica-coated cubic and spindly hematite particles, respectively, with hydrogen at 300-500 °C. Polyvinylidene chloride particles prepared by emulsion polymerization^^


415

were converted into carbon particles by heating at 700 ""C in a nitrogen atmosphere.^^^ Uniform amorphous carbon spheres are obtained by thermal degradation of uniform poly(divinylbenzene) spheres as well. The latter are prepared by the aerosol technique (see section 7.3.12), in an oxygen-free nitrogen atmosphere at 500 **C.^^^ Incidentally, the aerosol technique itself for the preparation of monodispersed colloids is also based on a kind of the conversion process. It should be noted that the products of the direct conversion process by the controlled calcination with preserved morphological integrity are mostly porous in the internal structure with rough surfaces, as readily understood from the process associated with the compositional change with limited movement of the solid atoms and the release of gaseous species from the interiors of the precursor solids. If a KBr solution is added instantaneously to an equal or smaller mole number of AgCl suspension at 25 °C, the cubic AgCl particles are totally decomposed into an eight-fold number of AgBr in ca, 1 min (see section 5.2).^^"' However, if the KBr solution is added continuously at a constant rate for 60 min, the decomposition of the original particles is almost completed when about half of the KBr has been added, since a considerable amount of CI" is incorporated in the newly precipitated solid phase in the case of the continuous addition, in which the concentration of Br" ions in the solution phase is kept much lower than in the case of instantaneous addition. In the case of the continuous addition of equimolar KBr to AgCl, the original particles are decomposed into 9 parts (i.e., one AgCl plus eight Ag(Cl,Br) particles) when about a half of the KBr has been added, in contrast to the case of instantaneous addition of equimolar KBr in which the original particles are decomposed into eight parts of nearly pure AgBr. In the later stage, the remaining pure AgCl particles continue to dissolve for the growth of the separated solid-solution particles of Ag(Cl,Br) in collaboration with the continuously introduced KBr. There is a compositional gradient in the solid-solution particles with chloride ions rich in each core. However, if the continuous addition is performed at a higher temperature, such as 45 °C, no decomposition is observed, because of the promoted intra-particle recrystallization to fill up the reentrants at the hostguest joints, concurrently with the fundamental three-step conversion process illustrated in Fig. 5.14 in chapter 5. Presumably, a high concentration of imperfections is introduced into the apparently homogeneous AgBr microcrystals in the final stage by the intra-particle recrystallization. TEM images of carbon replicas of the particles at different stages in the continu-

PREPARATION

% -'i$*h% '•- 'i f V. ='*^-5l

« Pt > Pd > Rh), and accounted for the formation of the core-shell structure in terms of the coordination strength of the metal ions and their redox potential (see section 7.2.1).^^^ b) Coating of Organic Particles It is of interest that even polystyrene spheres were covered with yttrium basic carbonate under certain proper conditions in the presence of urea and polyvinylpyrrolidone (PVP), for example, by aging at 90 °C for 2 h a dispersion consisting of 100 mg dm"^ cationic polystyrene latex, 5 x 10"-^ mol dm-^ Y(N03)3, 1.8 mol dm"^ urea, and 1.2 wt % PVP.^^^ In this case, the type of polystyrene latex, pH, concentrations of Y(N03)3 and urea, and temperature were the determinants of the uniform coating. In particular, no coating could be deposited on an anionic PS latex and, even with cationic

420

PREPARATION

PS, selective deposition of Y(0H)C03 was not attained when the pH was lower than the isoelectric point of Y(0H)C03 at around pH 7.6. Thus they suggested a possibility of some contribution of heterocoagulation of preformed fine particles of Y(0H)C03 ^^ PS particles in the coating process. Fe304-coated polystyrene particles were prepared by seeded emulsion polymerization of styrene in the presence of ultrafine magnetite particles (ca, 10 nm) with polystyrene seeds.^^^'^^^ For this puq)ose, Lee and Senna^^^ used surface-modified magnetite particles with adsorbed sodium oleate to increase the stability of the magnetite particles in the aqueous medium and the affinity of the magnetite particles to polystyrene. Ihara etal}^^ prepared Cu-phthalocyanine-coated polystyrene pigment by physical vapor deposition technique. 8.5.2. Organic Coating a) Coating of Inorganic Particles Probably, the simplest organic coating of inorganic particles may be the "adsorption" of organic matters to the surfaces of inorganic particles. However, if the organic matters themselves do not have sufficient affinity to the inorganic solids and thus they cannot directly be adsorbed to the solid surfaces, it is usually required to modify the particle surfaces, chemically or physically, prior to the coating. For chemical modification of oxide particles, the hydroxyl groups on their surfaces can be utilized as a joint of chemical bonds in the creation of new reactive groups, such as surface initiating groups for radical or anionic polymerization, surface-bound monomers with a vinyl group to be used as anchor segments in polymerization for coating, and surface terminators of living polymers. For physical modification, vSome intermediates, having specific affinity to the solid as well as to polymers to be coated thereon, are physically adsorbed to the solid beforehand. On the other hand, an alternative principle for organic coating is the introduction of an reactive moiety, capable of reacting with the surface hydroxyl groups of oxide particles, into polymer molecules as a terminal or a pendent group of the polymer. The most typical ones may be the socalled silane coupling agents which include alkoxysilane or chlorosilane groups }^^ Some other methods based on somewhat different principles are also known: e,g., seeded polymerization with inorganic heterogeneous seeds in a liquid or a gas phase. (1) Adsorption


421

De Silva et al}^^ prepared block copolymers of poIy-2-vinyl pyridine/ poly-tert-butylstyrene (P2VP/PBS) as a stabilizer of silica particles in non-aqueous media such as dioxane. In this case, P2VP chains are strongly adsorbed to silica as anchors whilst long PBS chains are strongly solvated by the medium to stabilize the silica particles. Here, it should be noted that the homopolymer of P2VP itself can be adsorbed strongly to silica but does not stabilize the particles, while the homopolymer of PBS has a strong affinity to non-aqueous media but cannot be adsorbed to silica. Thus, the stabilization of colloidal silica has been achieved by the combination of the respective advantages. This idea may be applied to the synthesis of new types of stabilizers to be used in aqueous and non-aqueous media. Mates and Ring^^ searched for polymer surfactants appropriate for stabilizing titania particles suspended in ethanol on several criteria: 1) high solubility in ethanol, 2) high protective power against aggregation, 3) reversible adsorption, and 4) high stability to particle aggregation during the precipitation in the sol-gel systems of titanium alkoxides in ethanol. Out of the tested surfactants, including hydroxypropylcellulose (HPC), polyvinylpyrrolidone (PVP), polyvinyibutyral (PVB), polypropylene glycol/carboxylic acid graft (PPG graft), polyethylene glycol (PEG), polypropylene glycol (PPG), PPG/PEG block copolymer, ethylcellulose, PEG stearate, PEG cetyl ether, PEG stearyl ether, and polyvinyl alcohol (PVA), they first eliminated ethylcellulose, PEG stearate, PEG ethers, and PVA, because of their low solubility in ethanol. Then, PEG, PPG, and PPG/PEG block copolymer were eliminated, because of their low protective power. The PPG graft was eliminated, because of their irreversible adsorption. Finally, PVP and PVB were eliminated because of the low stability to aggregation during the precipitation. As a consequence, only HPC was found to clear all requirements, while the growth rate is somewhat reduced. The minimum coverage of HPC for protecting TiOj particles fi-om coagulation was ca. 10 %. As powerful protective agents of gold particles in aqueous media, polyacrylic acid hydrazide, gelatin, and poly-N-vinyl-5-methoxazolidone are known.^^"^ Particularly, gelatin is also effective for the protection of silver halides, by forming an adsorption layer of ca. 300 A in aqueous media,^^ metal sulfides,^^"^^'^^'^ cuprous oxide,^^^ etc. On the other hand, anionic surfactants such as sodium dodecyl sulfate, sodium dodecanoate, sodium alkyl(C^2)''^^2^^^sulfonate, sodium alky^C^naphthalenesulfonate, polyacrylic acid, polymaleic acid, copolymers of maleic acid, and the formalin condensate of p-naphthalenesulfonic acid, are known as good

PREPARATION

422 stabilizers of hematite particles in aqueous media.^^^ See also Table 6.1 in chapter 6. (2) Initiation of Polymerization from Solid Surfaces

Anionic polymerization initiated by surface-bound groups Aminophenyl groups can be bound to the silica surface from the surface hydroxyl or silanol groups, through a series of processes: chlorination with thionyl chloride, phenylation of the bound chloride with phenyllithium, nitration of the phenyl groups with acetyl nitrate, and reduction of the nitrophenyl groups with hydrazinium hydrate to aminophenyl groups.^^^ Acting as a basic compound, the aminophenyl groups are capable of initiating the ring-opening anionic polymerization of N-carboxy-a-amino acid anhydride on the silica surface in dioxane, yielding polyamide-grafted silica/^^ Scheme 1 shows the series of the reactions. [Scheme 1]

O

SOCb

OH

CH3C00NO2

Q ^ N H .

•

a«ô«

Q ^ N O . !1:!1:^ Q)^.NH, R + n 0=C - C H I I O NH

(

Y(^>-NH-eCO-CH-NH>n H

Potassium carboxylate groups (-COOK), introduced by the reaction of 4-trimethoxysilyltetrahydrophthalic anhydride with the hydroxyl groups on the surfaces of silica, titania, and nickel zinc ferrite particles, were found to initiate the anionic ring-opening copolymerization of epoxides with cyclic acid anhydrides, yielding oleophilic polyester-grafted oxide particles.^^^ Similariy, polyester-grafted carbon black is also obtained.^^ Scheme 2 shows the series of the reactions.


423

[Scheme 2] O II

O

o KOH

-•

---

I

'

-^Ô'^

) - 0 - S i - l ^COK II

o

n H2C — CH O

+ n 0=C^ ^€=0 O

0-Si k^cCKCH2CH-0-C-R'-C-0)^K I II I II li ^" O R O O

Radical polymerization initiated by surface-bound groups By diazotization of the aminophenyl groups with sodium nitrite and subsequent coupling of the diazonium groups with mercaptans such as naphthalene-thiol-(2), phenyl-diazo group are generated on the silica surface, which are decomposed on heating at elevated temperatures, such as 60 °C, to form phenyl radicals chemically bound to silica surface and unbound thio radicals, both of which are able to initiate the free radical polymerization of vinyl monomers.^^'' Scheme 3 represents such reactions. Various polymers are grafted to silica surfaces by this radical polymerization; e.g., polystyrene (in toluene or bulk), poly(methylmethacrylate) (in toluene or bulk), polyacrylamide (in water), polyacrylonitrile (in DMF), polyacrylic acid (in water), and poly(4-vinylpyridine) (in ethanol or bulk). The silica-bound phenyl-diazo groups were also used for coupling reactions

424

PREPARATION

with single-stranded DNA, and the product was expected to be useful for DNA hybridization reactions.^^ [Scheme 3]

O ^ N H . i!5^!2^ Q ^ N T c f NaSR' •

Q_yQ^-

+ nCH2=CH

•

(^J)iLsX..>JuL...w»A.AAJ

(0

c

hJL^—-J' LX^.,JLJIA-JUL--.AXJ

20

40

60

26(degree, CuKa)

80

Fig. 9.2. X-ray diffraction profiles of solid phases in Fig. 9.1. (From Ref. 1.)

example, if the centrifugation rate is too low in washing the precipitates with distilled water in the hematite system, the fine p-FeOOH particles readily escape on subsequent decantation, especially in the later stage of washing when most of the extraneous electrolyte has been removed. In this stage, even 18,000 q5m for 30 min is not enough for complete settlement, and thus distilled water mixed with a less polar solvent such as methanol, ethanol, or acetone may be useful as a washing medium in the later stage. For the XRD analysis on solid solutions of silver halide particles, the contact recrystallization in the washing procedure can be prevented by the adsorption layer of gelatin, even in the absence of the merocyanine dye.

9.3. Infrared Spectroscopy Figure 9.3 shows Fourier-transform infrared (FT-IR) spectra in the absorbance mode for the solid phases consisting of )5-FeOOH and a-FejOj, corresponding to the TEM images in Fig. 9.1 and XRD pattems in Fig. 9.2. The content of a mixed solid in the KBr matrix of an IR specimen is 0.25 wt %. From the IR spectra one can determine the molar ratio of a-Fe203 to p-FeOOH from overall absorbances at 845, 580, 538, and 430 cm"^ using the molar absorptivities of pure p-FeOOH and pure a-Fe203 at these wave numbers, obtained from the respective calibration curves of absorbance

9. ANALYSES OF FORMATION PROCESSES

1000

800

600

Wavenumber (cm'^)

457

Fig. 9.3. FTIR corresponding to Fig. 9.2. (From Ref. 1.)

against content in KBr for p-FeOOH powder taken after aging for 8 h and a-Fe203 powder separated from a mixed solid sample after aging for 7 days by centrifugal solid-solid separation. The absolute quantities of the respective solid components at each time of aging are determined from the molar ratio and total amount of each mixed precipitate. The shapes of pure a-Fe203 and pure p-FeOOH used for the preparation of the calibration curves must be similar to those in the mixed samples, since the IR spectrum of hematite particles depends strongly on their shape, as will be shown in chapter 10. This trend may not be limited to hematite. Figure 9.4 shows the evolution of the FT-IR spectrum of the solid phase in a gel-sol system of basic aluminum sulfate at 100 °C, in which the overall composition is :[A1'"] = 1.0 mol dm"', [S04--]/[Al^"] = 2/3, and [NaOH]/[Al^*] = 1.8 (see section 8.2).^ The solid samples were washed repeatedly with doubly distilled water and freeze-dried before the measurement. The solid phase, initially an amorphous gel, was rapidly transformed into crystalline particles of basic aluminum sulfate, Al3(S04)2(OH)5-2H20, in times between 2 and 4 h through a dissolution-recrystaUization process, followed by a slow transformation completed after 3 days, as revealed from electron micrography and X-ray diffractometry. The spectrum of an nonaged sample in Fig. 9.4 is appreciably different from that of A1(0H)3 prepared by mixing a A1(N03)3 solution with a NaOH solution. The characteristic peaks at 1120 and 610 cm"^ of the non-aged sample are

ANALYSES

458

3000

2000

Wavenumber (cm'^)

Fig. 9.4. Evolution of the FT-IR spectrum of the solid phase in a gel-sol system for the formation of uniform basic aluminum sulfate particles at 100 °C. (From Ref. 8.)

assigned to the vibrational modes of V3 and v^ of SO/", respectively.^ This result indicates that sulfate ions were incorporated in the initial hydroxide gel and that a considerable part of them was retained even after repeated washing with doubly distilled water. With the formation of basic aluminum sulfate, the broad absorption around 900 cm"\ as well as the peaks of the sulfate ions in the aluminum hydroxide gel at 1120 and 610 cm~\ were gradually replaced by the split sharp peaks characteristic of sulfate ions in basic aluminum sulfate. Since the splitting of the absorption bands of the V4 modes is attributed to the distortion of the tetrahedron of SO/",^^ the split bands may reflect the change of the environment for SO/" ions from a relatively flexible amorphous hydroxide gel to a rigid crystal of basic aluminum sulfate. The strong diffuse absorption peak around 3500 cm'\ observed with all samples, is ascribed to the v^ and V3 vibrational modes of the water molecule, as well as the stretching of 0 - H groups. The small peak at 1650 cm"^ is attributed to the v^ vibrational mode of the coordinated water of the initial hydroxide gel. The sharpening absorption around 3500 cm"^ and the decreasing peak at 1650 cm'^ with aging time may correspond to the loss of the coordinated water with the formation of the crystal structure. In addition, the absorption at 1230 cm"' of the final product is


459

known to be characteristic of basic aluminum sulfate, ascribed to the bending vibration of the hydroxyl groups in the lattice.^^ Nevertheless, the similarity in the fundamental spectrum of the initial amoq)hous precipitate to the final crystalline product, basic aluminum sulfate, implies that the amorphous gel assumes a structure more or less disordered by hydration, but essentially similar to that of basic aluminum sulfate. As a consequence, IR spectroscopy is useful for identification of solid species and the specification of their changes in composition and in the state of each component, even when the sample is amorphous and thus X-ray analysis provides us with no further information.

9.4. Ultraviolet-Visible Spectroscopy Figure 9.5 shows the reduction of UV absorption of thioacetamide (TAA) with its consumption in the solution phase of a condensed Cd-EDTA chelate system for the precipitation of CdS particles, in the absence of gelatin as an anticoagulant.^^ Despite the tremendous coagulation of the growing CdS particles due to the absence of gelatin,^^ the consumption rate of TAA coincides with the formation rate of monodispersed CdS particles in the presence of gelatin under otherwise the same conditions, indicating that either the presence of gelatin or the reduction of the specific surface

1

1

1

1—1—r— 1

1

1

1

0 min 1 5 min 1 30 min H

1/ ''\

L

1 — 1 — r — I

1^

60 min

o o c

j

(0

o

Ih

120 min J

(0

< 0.5 h

1 .

,

1 . 250

.

. S s 1 1 1 1 L—. 300

Wavelength (nm)

350

Fig. 9.5. UV absorption of thioacetamide decreasing with its consumption in a condensed CdEDTA chelate system for the precipitation of CdS particles under the standard conditions at 60 °C, but in the absence of gelatin. (From Ref. 12.)

ANALYSES

460

area of the growing particles by coagulation has no effect on the formation rate of the CdS particles. Thus, this result suggests that neither the diffusion of the solute nor the surface reaction is the rate-determining step of the growth process. It is in accord with the fact that the rate-determining step is the dissociation process of the Cd-EDTA complexes.Îshizuka et al}^ followed the formation process of gold particles with the reduction of AuCl4"-cationic surfactant complexes. Figure 9.6 illustrates the evolution of UV-VIS spectrum with the reduction of AuCl4'-CP^ by hydrazine at room temperature, where CP"^ is hexadecylpyridinium ion. This clearly demonstrates the increasing plasmon resonance absorption of gold around 530 nm at the expense of the AuCl4"-CP* complex with an absorption band at 340 nm.

2.5 h

2.0

c o n k_ o n
o c o

.

^^^X 5

/

^

Supernatant iron species

~

4

/

\

p-heOOH M

C)

1

1 2

.

1 3

Y .

1 4

.

1 5

.

1 6

.

1 7

Time (day)

Fig. 9.10. Change of the concentrations of iron species in the solution- and solidphases of the system for the formation of uniform ellipsoidal hematite particles by forced hydrolysis of 2.0 x 10"^ mol dm"^ FeCij at 100 ''C in the presence of potassium dihydrogen phosphate. (From Ref. 1.)

466

ANALYSES

presence of potassium dihydrogen phosphate.^ This figure was obtained by successive measurement of the iron content in the supernatant liquid of each sample by inductively coupled plasma (ICP) spectrometry in combination with FT-IR spectroscopy on the precipitate. The change in concentration of phosphate ions in the solution phase in Fig. 9.8 was also obtained by ICP measurement of the phosphorus content. The change of the concentration of the soluble copper species in the solution phase in the system for the preparation of CujO particles from CuO in Fig. 7.30 in chapter 7 was obtained by ICP spectrometry on the copper element. The rapid increase in soluble Cu species on addition of hydrazine is due to the dissolution of CuO with the fast depletion of Cu^^ ions in the solution phase, as is obvious from the corresponding sharp drop in Cu^^ concentration and lift of pH. The subsequent decrease corresponds to the precipitation of CU2O. This spectrometry can also be applied to the analysis of the solid content in a suspension, or the composition in a solid, by dissolving the solid with a proper solvent. Thus, ICP spectrometry is one of the most fundamental measures for the study of the process of particle formation.

9.7. Gas Chromatography It was found that the product from thioacetamide in the preparation of CdS particles by its reaction with Cd(OH)2 was acetonitrile (CH3CN) (see section 7.3)."* First, the by-product was identified as either acetonitrile or methyl isocyanide (CH3NC) by gas-chromatography-mass spectrometry, as shown in Fig. 9.11. From gas chromatography, the final concentration of the CH3CN or CH3NC was found to reach 98.0 ± 1.0 % of the stoichiometric concentration. Finally, it was determined to be CH3CN from the FT-IR spectrum of the product obtained by distillation under reduced pressure at 30 °C of the supernatant liquid of the system. This finding led to the elucidation of the prompt release of S^~ ions from thioacetamide in the systems for the formation of general monodispersed metal sulfide particles by use of thioacetamide. In order to study the mechanism of the formation of uniform CujO spheres from a CuO powder by reduction with hydrazine (NjH^), the products from N2H4 were assayed.^^ Table 9.1 shows the products from N2H4 after aging at 30 °C for 4 h a suspension of 0.50 mol dm"^ CuO containing 0.50 mol dm'^ N2H4 in the absence of gelatin, where Nj and H2


467

B

C

21

II

Fig. 9.11. Gas chromatograph mass spectra of the supernatant solution of the system for the precipitation of CdSfromCd(0H)2 and thioacetamide (in the absence of gelatin) (a), acetonitrile (CH3CN) (b), and methyl isocyanide (CH3NC) (c).

41

Mass numbers

gases were collected in a gas bag and analyzed by gas chromatography. From this result, it was concluded that 38 % of the N2H4 was consumed by the reaction: N2H4 + CuO -^ 1/2 CU2O + 1/2 N2 + NH3 + 1/2 H2O and 15 % by N2H4 + 4CuO -* 2CU2O + N2 + 2H2O. Table 9.1. Products from 0.50 mol dm'^ N2H4 after aging for 4h in the system for the formation of CuÔ spheres from 0.50 mol dm"^ CuO {Source : Ref. 19) NH3 (mol dm"^)

Nj (mol dm"^)

H2 (mol dm"^)

0.19

0.17

1.6 X 10-^

9.8. Ion Chromatography Figure 9.12 shows the change of the concentration of SO/" with aging time in the gel-sol system for the formation of peanut-type hematite particles from condensed Fe(0H)3 gel (see section 7.3.1).^ The data were

ANALYSES

468 B

•o o B B^ CO

C

o

*t.5

4 3.5< 1

3 2.5

3

CO

o c o

2 1.5

1

g o c o U

0.5

0 ' C

1

2

3

5

5 Tinie(D ay)

6

7

8

Fig. 9.12. Change of [SO^^'] in the solution phase of the gel-sol system for the formation of the unifomi peanut-type hematite particles, ^rom Ref. 20.)

obtained by ion chromatography on the supernatant solutions of the system. Since the initial concentration of sulfate ions in equilibrium with Fe(0H)3 gel is 3.5 mmol dm•^ about 88 % of the total sulfate (30 nmiol dm"^) is adsorbed to the Fe(0H)3 gel. The initial drop of [SO/'] seems to be due to the strong adsorption of sulfate to the fine particles of p-FeOOH precipitated as an intermediate, which surpasses the release with the dissolution of Fe(OH)3. The following gradual rise is due to the release of sulfate ions with the dissolution of p-FeOOH for the formation of relatively large a Fe203 particles. The final lowering is due to the adsorption and incorporation of the S04^" ions into the growing a-Fe203 particles, exceeding the release from p-FeOOH in the final stage. Figure 9.13 illustrates the changes in concentrations of Al^^ and S O / ' in the solution phase of a system for the formation of basic aluminum sulfate (Al3(S04)2(OH)5 • 2H2O) particles, corresponding to the FT-IR spectra in Fig. 9.4.^ In this figure, the concentration of SO/" ions was determined by ion chromatography, and that of Al^* by ICP spectrometry. The concentrations of both reactants decrease rapidly for ca, 30 min, but then keep increasing for 1.5 h, followed by an initially rapid but afterwards very slow decline. This result indicates that the development of the gel network of the amorphous hydroxide is promoted up to ca. 30 min with an increasing internal temperature, but turns to be partly dissolved when the internal temperature approaches the external temperature, 100 °C, owing to the increased solubility. The drop in Al^^ concentration after ca, 2 h is due to the growth of the stable basic aluminum sulfate through dissolution of the


469

Fig. 9.13. Changes of [Ai^] and [S04^~] in the gel-sol system for the formation of uniforai basic aluminum sulfate particles. (From Ref. 8.) hydroxide gel of a higher solubility. The final slow decline results from a quasi-steady state in the balance of the dissolution of the remaining amorphous gel and growth of the basic aluminum sulfate particles. The rather rapid drop of the SO/" concentration from ca, 2 to 10 h is attributed to the incorporation of SO/" ions into the growing basic aluminum sulfate particles from the solution phase and to the adsorption to their surfaces. Since the SO/"/Al^^ molar ratio in the liquid phase after 10 h is much lower than 2/3, the adsorption of SO/" onto the basic aluminum sulfate is decidedly strong. As has been described in section 7.2.6, the CuS particles prepared in a Cu-trimethylenediamine (TMD) chelate system in the presence of ammonia start to dissolve, owing to oxidation by naturally dissolved oxygen.^^ Figure 9.14 shows changing concentrations in S atoms of the sulfur species produced by the oxidation under the same conditions, but in the absence of gelatin, as determined by ion chromatography. The assignment of these species was made by comparing the retention times of the detected peaks of each sample with those of the pure possible species in this reaction, while the absolute concentration of each species was determined with a calibration curve prepared with the pure species. The so-obtained total sulfur content in the supernatant liquid of a sample at each time was in excellent agreement with the concentration of Cu^* of the same sample determined by ICP spectrometry. From this figure, it is suggested that the S^' ions of CuS solid are first oxidized to 8203^" ions, which are then further oxidized to SOj^", SO/", and S2O/". Since the amount of elemental S is kept almost

470

ANALYSES 0.15 w E 0.10 "o C

o 2 0.05 h c

8 C

o O

0

2

4

6

8

Time (h) Fig. 9.14. Concentrations of different sulfur species and Cu^* ions, changing with the oxidation of CuS particles by air, in the solution phase of a system for the synthesis of CuS particles after the formation of the CuS particles from trimethylenediamine-Cu chelate with thioacetamide. (From Ref. 21.) constant after the early increase, it seems to be produced by disproportionation of 8203^" and not by direct oxidation of S^". While the quantitative analysis of sulfate ions in the hematite and basic aluminum sulfate systems can be made by ICP spectrometry as well, the ion chromatography cannot replaced for assignment and determination of the quantities of the different sulfur species in the copper sulfide.

9.9. Radiochemical Analysis Radioactive isotopes are useful for studying the exchange of ions between the solution and solid phases in a colloidal suspension during the progress of the particle growth. Thus, in some systems, they provide us with direct information on the growth mechanism. As has been shown in Fig. 4.8 in chapter 4 for experiments on ionexchange of chloride ions in a suspension of AgCi microcrystals by use of radioisotope ^Ci", even if we use an efficient stopper of recrystallization such as Aza, the initial degree of exchange, r, defined by Eq. (4.5.1) is not equal to zero because of instantaneous ion-exchange between the solution phase and the solid surfaces.^ The initial degree of exchange, denoted by


471

TQ, is proportional to the specific surface area (surface area per unit weight), S, as shown in Fig. 9.15, from whose slope the thickness of the surface layer subjected to the rapid ion-exchange was found to be 4.69 ± 1.13 A, equivalent to 1.69 ± 0.41 atomic layers.

Fig. 9.15. Relationship between KQ and S in the AgCi system. (From Ref. 6.) On the other hand. Fig. 9.16 shows the growth of AgCl particles in the mean particle volume, v, by Ostwald ripening after the addition of 200 cm^ of 20 mmol dm"^ AgN03 to the same volume of 30 mmol dm""^ KCl over a period of 200 s at 25 °C, in the absence or presence of 2.0 mmol dm"^ NH3 added 2 min after the addition of AgN03. Obviously, the Ostwald ripening was accelerated by ammonia.

1

2'

10' 100' Time af tir tki Mtf of WH^ iMitioii (nil)

1000'

Fig. 9.16. Relations of v vs time in the AgCi system with and without ammonia (2.0 mmol dm"^) at 25 ^C. (From Ref. 6.)

ANALYSES

472

r

2' 10' 100' 200' Time after the end of AgNOa addition (niin)

Fig. 9.17. Relations of r vs time in the AgCl system. (From Ref. 6.)

1.01

«/°°

a4 02 1

1

I

»19

5

10

I

I

IS

»[fw?m

)

20

2

Fig. 9.18. Relations oirvsv in the AgCl system. (From Ref. 6.)

Figure 9.17 shows the corresponding changes in the degree of exchange, r, where RI solutions were added 1 min after the addition of AgN03. When r was plotted as a function of v for these two cases with and without ammonia, both curves coincided, as shown in Fig. 9.18, suggesting that the ion exchange in both cases was due only to Ostwald ripening, without coalescence or direct diffusion of the radioactive chloride ions into the solid. Hence, the change of r is due to the instantaneous ion-exchange with surface layer and the slow Ostwald ripening. However, if some coalescence is associated with Ostwald ripening, the curve of r vs V will deviate from that in a system without coalescence. Figures 9.19, 9.20, and 9.21 show vvs t,r vs U and r vs v, respectively, for a AgBr particle system after addition of 25 cm^ of 20 mmol dm"^ AgNOj to an equal volume of 30 mmol dm"^ KBr over 30 s at 25 ^'C, in the absence or presence of 10 mmol dm"^ NH3 or 0.20 mmol dm'^ Pb(N03)2, added 2

473


0

10

20

30

40

50

60

Aging time [mini Fig. 9.19. Relations of ij vs time at 25 "C in the AgBr system with Pb^* (0.20 mmoi dm"') or ammonia (10 mmol dm'') and for the control without them. (From Ref. 21.)

10

20

30

40

50

60

Aging time i m Fig. 9.20. Relations of r vs time in the AgBr system. (From Ref. 21.)

474

ANALYSES

0

10

20

30

40

Fig. 9.21. Relations of r vs v in the AgBr system. (From Ref. 21.) min after the addition of AgN03.^^ The radioactive solution of ^^Br" (0.02 cm"^) w a s added to each suspension 1 min after the addition of A g N 0 3 , and thus 1 min before the addition of NH3 or Pb^*. Since it is well known that Pb^^ ions strongly inhibit particle growth of silver halide by adsorption as long as their coalescence is prevented by the presence of gelatin,^"^ the rapid particle growth with Pb^^, even faster than with anmionia as a typical accelerator, as shown in Fig. 9.19, must be due to the coalescence caused by the adsorption of Pb^^, canceling the negative charge of the A g B r surface, in the absence of gelatin. A s a result, the rate of bromide-ion exchange in the suspension with Pb^^ ions is lower than with ammonia, and the m a x i m u m level is also lower, as shown in Fig. 9.20. However, in view of the much higher exchange rate, as compared to the control, the contact recrystallization caused by the coalescence must be involved in the ion exchange. Figure 9.21 shows still more clearly the growth process of the system with Pb^"^; i.e., initial coalescence with little i o n - e x c h a n g e , subsequent contact recrystallization with a rapid ion exchange, and ending with a considerable amount of pure A g B r remaining intact in each core of aggregates. Incidentally, in the AgBr systems as well, Aza was always added to each sample before filtration (0.04 cm^ of 0.1 mol dm"^ Aza per 2.0 cm^ of a sample) to halt all kinds of recrystallization, and the radioactivity (y-ray) of each filtrate was measured with a scintillation counter, in contrast to the A g C l systems in which the radioactivity of ^^Cl (P-ray) was measured for each solid remaining on a filter with a Geiger-Mueller counter. Also, it is


475

not surprising to find that r often exceeds unity during the recrystallization, since a high concentration of radioactive ions is initiaUy incorporated into the solid phase by deposition from the solution phase in exchange for dissolution of different parts of the solid containing no radioactive ions. In the determination of r, one must choose the best way to minimize the errors of measurement according to the given system. liMJM^ is represented by m in Eq. (4.5.1), A^ must be measured directly when m « 1, while the radioactivity of solid, A^, must be measured mstead of A^ when m » 1, because A^ obtained indirectly from AQ ~ A^ with a measured A^ includes a great relative error in the former case, in which A^ becomes close to AQ in the very early stage, while A^ indirectly obtained from AQ - A^ with a measured A^ includes a great relative error in the latter case, in which ^4, always stays close to AQ. However, even if we follow this general procedure and prolong the counting time to reduce the statistical errors, it is not easy to measure the weak radioactivity of a sample with high precision without contamination of the other phase of high radioactivity. Hence, m should be set as close as possible to unity. On the other hand, the following definition of the degree of exchange, r', is also often used in place of r in Eq. (4.5.1):

Fig. 9.22. Relationship between r' vs r at different m. (From Ref. 22.)

476

ANALYSES

r'=lJ.—*±^.

(9.9.1)

There is the following relationship between r' and r: ^/^r(l_^ r+m

(9.9.2)

However, as shown by the several curves of r' vs r at different m values in Fig. 9.22, r' cannot be used as a criterion of the degree of exchange when m « 1, since it is so misleading as to be apparently close to unity even when the recrystallization is only in the very early stage and r is still close to zero.^^ As m increases, r' approaches r, and becomes virtually equal to r when m » 1. As a consequence, r may be better as a general criterion of the degree of ion exchange. Figure 9.23 shows the changes of the relative radioactivities of ^^Fe (gamma emitter) of different phases in a system at 90 ''C for the formation of uniform magnetite (FcjOJ particles from 2.5 x 10"^ mol dm'^ Fe(OH)2 gel by partial oxidation of the ferrous ions by 0.20 mol dm"^ KNO3 in the presence of excess Fe^"^ in the solution phase.^ The tracer ^^Fe^"^ was added after aging the Fe(0H)2 gel with the excess ferrous ions for 1 h, followed by addition of KNO3 immediately after the addition of RI. The aging time in this figure is taken after the addition of RI and KNO3. The quantities, y4*, JB*, and rfC* are the radioactivities of the solution phase, Fe(0H)2 gel, and the increment of the radioactivity of Fe304 at each sampling time, respectively: A, B, and dC are the molarities of Fe species and the increment of the molarity in the respective phases. The radioactivities in brackets ( ) are their relative quantities in (yl*+5*+C*)/(/4+5+C) units. The figure shows a rapid ion-exchange between the solution and gel, and that the iron constituting magnetite crystals is mainly generated directly from the ferrous hydroxide gel. Although a part of the iron of the magnetite is supplied indirectly via the solution phase by the dissolution of Fe(0H)2 and concurrent oxidation of ferrous ions in the solution phase, as revealed from a rapid pH drop observed after the most of the ferrous hydroxide has been dissolved, the weight of this route seems to be very small. This may be readily understood if one considers the extremely low concentration of ferric ions, much lower than of ferrous ions, dissolved in the solution phase in the neutral pH range, owing to the exceedingly low solubility product of ferric

9. ANALYSES OF FORMATION PROCESSES (0

H

1

1

1

^

477

1

z3 a •

03

< ^ *^ ^•f «CD < Z

>H

1

1

J1

I1\

J

1- \

A V

>

P

V

^

1 '0 N o V*^ o
M*»,>..yywA^^ji.4ui, CO b) Platelets (006)

iu»i t

Fig. 10.31. Fluctuant photosignal as a function of time.

as a time-average of A{t)A{t-¥x) for t. C(T) = U(OM(t)) = limi; rAm(t^^)dt, Tr-*» TJo I Jo

(10.10.1)

we obtain a curve simply declining toward zero with x, as shown in Fig. 10.32. The autocorrelation function of x is equivalent to the power spectrum as a function of the spreading of frequency: one is the Fourier transform of the other. Both functions contain the same information on the mean particle size or molecular weight, shape, and size distribution.

10. CHARACTERIZATION OF PRODUCTS

0

509

X

Fig. 10.32. Autocorrelation function as a function of T. If the particles are monodisperse, C(x) is given as C(T) = C(0)exp(-2rT),

(10.10.2)

where C(0) = C4^(0)), T is the half-width at the half-height in the amplitude spectrum in Fig. 10.29, given by (10.10.3)

T = D^\

Here, q is the magnitude of the scattering vector determined by factors independent of the nature of the particles, including the wavelength of the incident beam, X^, refractive index of the medium, \IQ, and scattering angle, 6: 4îAo . e

q=

sin—

K

(10.10.4)

2

Dj is the transverse diffusivity of a particle related to the hydrodynamic diameter (Stokes diameter), d, and the viscosity of the medium, r\, by the Stokes-Einstein equation:

510

ANALYSES

D ^ - ^ .

(10.10.5)

If we define a function of x, g{x) as g(T) = exp(-rT),

(10.10.6)

^(T) can be obtained from Fig. 10.32 for Eq. (10.10.2), where g(x) = [C(T)/C(0)]^^, and thus d can be calculated from T given as the slope of the straight line of log [^(T)] V^ T with Eqs. (10.10.3), (10.10.4) and (10.10.5). For polydisperse particles, the size-distribution function corresponds to the distribution function of F, G(r), so that g{x) in this case is given by

g(T) = f "G(r)exp(-rT) j r .

(10.10.7)

•'0

In a cumulant method, the exponential part in Eq. (10.10.7) is approximated by a series expansion of x, and the coefficients of the series giving mean values of F, F^, F^, — are determined by curve-fitting to the autocorrelation function. In a histogram method, the distribution of F is represented by a histogram for F divided by a finite number of intervals of F of a certain width AF, and each G(F,.) in n

g(x) = EG(r.)exp(-r.T)Ar

(10.10.8)

i=l

is determined by curve fitting to the autocorrelation function using a nonlinear least-squares method, the modified Maquardt method. Although this histogram method has a great advantage that the form of the size-distribution function is not previously assumed, there may be some risk of errors in calculation of the size-distribution function, modal diameter, and standard deviation at the same time from the small deviation from the exponential decay of the autocorrelation function. Thus, in some cases, only the modal diameter and standard deviation are calculated on the previous assumption of the distribution form, such as a normal distribution, log-normal distribution, etc. The size range measurable by PCS is over a few nm to ca, 3 \xm. Figure 10.33 shows a TEM image of cubic AgBr particles of a rather

511


broad size distribution with an adsorption layer of gelatin around each particle and their size distributions with and without the gelatin layer by photon correlation spectroscopy (histogram method) with no previous assumption of the distribution function. The thickness of the dried gelatin

%

•

•

•

lOOmn 2'^ \i

—

- c •

].:r

>? 12 h

•Ud

]Q7

iilliiUL

149 i", 2GT 2^^ c Diameter (nm)

J00

Li

;

^

I

—

'

—

•

•

•

. ,

1.

•

,.

-J

J 1

'1

•

1 ••-j

•

7] 90 n5 uii. i^Ji. 2?6 m Diameter (nm)

Fig. 10.33. TEM of cubic AgBr particles of a rather broad size distribution with an adsorption layer of gelatin around each particle and their size distributions with and without the gelatin layer by PCS (histogram method) with no previous assumption of the distribution function.

512

ANALYSES

Table 10.4. Comparison between TEM and PCS for the measurement of mean particle size of a sample of cubic AgBr particles Method TEM

Mean Diameter (nm) 90.0

PCS (Cumulant Mode)

90.3 (174)''

PCS (Histogram Mode)

78.0 (169)"

Standard Deviation (nm) 13.2

8.6 (20.7)"

° The figures in the parentheses are those with the adsorbed gelatin layer. layer is ca. 8 nm from the electron microscopy. The sample without a gelatin layer was prepared by pretreatment with a solution of 0.01 % proteolytic enzyme (Actinase E). The mean diameter and standard deviation of equivalent spheres with the same volume as each cube from TEM and those from the cumulant and histogram methods of PCS are summarized in Table 10.4, where the figures in parentheses are those of the sample with the gelatin layer. From the results of PCS on samples with and without the adsorbed gelatin layer, the thickness of the wet gelatin layer swollen with water is estimated to be ca, 44 nm. One of the merits of PCS is that it provides us with information on the state of the adsorption layer of polymers on particles in a fluid. It should be noted that even a small amount of dust has a significant effect on the results of PCS normally performed with highly dilute suspensions.

lO.ll, Turbidimetry When light passes through a thickness, /, of non-absorbing scatterers, the turbidity x is given by T =lln^, / /

(lOll-l)

where /Q and / are the incident and transmitted intensities, respectively. For monodisperse spheres of radius r


x = nîzr^fi^,

513

(10.11.2)

where n^ is the number concentration of the particles and P^ is the ratio of scattering cross section to geometric cross section. For Rayleigh particles (r = 0 at the slipping plane one obtains Tl

Representing u for JC = oo as v^ and using t|j(v

I

10-*

10-

Fig. 11.6. Effect of ^-potential on f(Ka, I) for 1-1 electrolyte. The figures, 0, 1, 2, and 4 are et/kT values, corresponding to t, about 0, 25, 50, and 100 mV, respectively. (From Ref. 14 (a).)

a relaxation effect, Le., the displacement of th charge of the double layer in a direction opposite to the applied field (counter electromotive force), which depresses the electric velocity on account of the reverse field.^"^'^^ It is readily expected that an unsymmetrical electrolyte such as 4-1 electrolyte may strongly enhance this effect on negatively charged particles, since the cation charge density in the double layer is much higher than with a 1-1 electrolyte due to n^.(8) = n.{oo)txp{-zfiy\)^kT). On the other hand, this effect with the 1-4 electrolyte may be much weaker than with 1-1 electrolyte, because of the deficient charge density of anions with 1-4 electrolyte. However, according to Overbeek,^"* the total effect of the deformation of the field by the relaxation effect with 1-1 electrolyte and by the presence of the particles on the electrophoretic velocity is rather close to Henry's correction of the field deformation only by the presence of the particle, and the electrophoretic velocity with 1-4 electrolyte under both effects is expected

11. APPLICATION TO FUNDAMENTAL STUDIES

529

to be rather increased. Figure 11.5 shows his theoretical derivation for the relaxation effect of different types of electrolyte on f(Ka) of negatively charged particles with ^ = -50 mV. He also considered the effect of the magnitude of the ^-potential onf{Ka, Xd for a 1-1 electrolyte, u,= ^^fiKa,0.

(11-2.18)

as demonstrated in Fig. 11.6.^"* More detailed analysis on the relaxation effect is found in refs. 17 and 18. From the above theoretical predictions, one may find that the particle size in terms of Ka has a considerable effect on the electrophoretic mobility. Thus, the use of monodispersed particles is desirable for the measurement of ^-potential. However, it must be kept in mind that even monodispersed particles in size and shape are not necessarily uniform in ^-potential. For example, some commercially available monodispersed polystyrene latex showed a very broad distribution of electrophoretic mobility or of ^ potential - as much as 22 % in relative standard deviation.^^ For monodispersed silica particles prepared by hydrolysis of tetraethyl orthosilicate, it is not rare to find similar results. Hence, even when we use these typical monodispersed particles, one is recommended to check the distribution of electrophoretic mobility before use, especially for precise experiments related to particle interaction, electrokinetics, etc.

11.3. Determination of Hamaker Constants The Hamaker constant is an important parameter of the London-van der Waals forces in describing particle interactions including coagulation, flotation, dispersion, and ordering. For many materials, Hamaker constants have now been compiled.^ For calculation of Hamaker constants, many methods are proposed: e.g., colloid chemical methods based on flocculation of particles, interaction of two crossed metal wires, and equilibrium or dynamic fibn thickness measurements; determination from surface tension measurements; rheological method; and measurements of solid-solid interactions between macroscopic bodies at long distances.^" In this section, one of the flocculation methods with monodispersed particles will be introduced. The repulsive potential energy between two particles of the same radius

530

APPLICATIONS

a for Ka » 1 is given by F^ = 27ieo8/^ln[lêxp(-Kffo)],

(H-^.l)

where t, is the zeta-potential of th particles, K is the Debye-Hiickel parameter, and HQ is the separation between the Stem planes of the two particles.^^ The attractive potential energy of the London-Van der Waals force, F^, is given by Hamaker^^ as

^

( 1 +— 2 +jn , s^-A^ 6 1^5^-4 5^ S2

(11.3.2)

where A is the Hamaker constant and s is the ratio of the central distance between the two particles, i?, to their radius a {s ^ Rid). Thus, if the thickness of the Stem layer is denoted by 6, ^^2«^V26

(11.3.3)

If the electrolyte concentration is below a certain level, there may be a maximum in the total energy, V^, of V^ + K^, as a function of //Q. At the critical coagulation concentration (the minimum concentration of an electrolyte for the coagulation of the particles, or "c.c.c"), the maximum of V^ must be zero. Hence it is possible to determine the Hamaker constant experimentally by finding A which satisfies this criterion with the zetapotential, thickness of the Stem layer 8, and c.c.c. value substituted in Eqs. (11.3.1) and (11.3.2).^ Figure 11.7 shows HQ - V^ curves of monodispersed nearly spherical hematite particles of mean diameter 0.13 |im in a variety of A values at temperature 25 °C, pH 10.4, c.c.c. 3.2 x 10"^ mol dm"^ with KNO3, and zeta-potential -21.2 mV. The hematite particles were prepared by the forced hydrolysis of ferric ions in a dilute ferric chloride solution.^"^ The critical concentration of coagulation (c.c.c.) of KNO3 was determined by finding the minimum concentration of KNO3 for the coagulation of the hematite particles from the apparent mean diameter of (coagulated) particles as a function of the electrolyte concentration. For accurate determination of Hamaker constants by this method, the particles are required to be monodisperse.


50 100 ^ Particle separation (Ho), A

150

531

Fig. 11.7. HQ - V, curves of monodispersed nearly spherical hematite particles of mean diameter 0.13 |Lim in a variety of the Hamaker constant at 25 °C (pH 10.4; c.c.c. = 3.2 X 10"^ mol dm"^; zeta-potential = -21.2 mV). (From Ref. 23.)

11.4. Measurement of Interparticle Forces Ducker et al?^ measured the interparticle forces between spherical silica particles of 3.5 \ym by setting them on a stage and fixing one to a tip of a cantilever in an atomic force microscope^\AVH\ as illustrated in Fig. 11.8. In a similar manner, Meagher^^ measured the interactive forces between a silica particle and silica plate, and Li et al?^ measured the interparticle forces between polystyrene particles of 2 [xm.

Cantilever

Stage

Fig. 11.8. Interparticle force measurement with AFM. (From Ref. 25.)

532

APPLICATIONS

On the other hand, the optical trapping technique with a focused laser beam, developed by Ashkin et ai,^^ has become an important tool for the precise manipulation of micrometer-size particles such as biological cells,^ polystyrene latex particles,^^ anisometric iron oxide particles,^^ etc. In addition, the double-laser-beam technique was also developed,^^ and has been applied to particle or cell manipulation or to estimation of the interparticle forces as a function of the separation of two colloidal particles.^"**^^ However, it seemed difficult to measure precise interparticle forces and separation at the same time within the range of a micron or less by this optical technique. In the meantime, a new method was introduced into the optical trapping technique, and precise measurement of the interparticle forces and surface-to-surface separation has become possible. Namely, Sugimoto et al}^ trapped two polystyrene latex particles of mean diameter 2.13 Jim, with two laser beams of wavelength 1.064 jmi set at different separations. They then gradually attenuated one of the beams at each interparticle separation, while trapping the other particle with a beam at the fall power, and determined the critical trapping force at each separation by detecting a moment when the particle trapped with the attenuating beam started to shift from its beam center owing to interparticle repulsion or attraction. The critical trapping force is equal to the repulsive or attractive force at a given interparticle separation. Figure 11.9 shows a block diagram of the apparatus, where the interbeam distance of the two beams was regulated by changing the direction of the path of one beam with the rotatable mirror B, whose angle was changeable with a micrometer, while the power of the other beam reflected by the fixed mirror C was continuously changed by the ND filter. The relationship between the horizontal trapping force and the beam power was predetermined, with the aid of the Stokes equation, from the critical beam power at the moment of the start of the displacement of a particle trapped by a gradually attenuating beam against the frictional force of the medium used in horizontal motion with a sample cell on a moving stage driven by a linear motor at various constant rates,^^ as shown in Fig. 11.10. The surface-to-surface separation between the two particles was accurately determined from the difference between the central distances obtained from the VTR images of the two particles at the trapped positions and in the state where they were attached together by addition of a concentrated electrolyte after one series of measurements, at various separations of a particular particle pair, performed without releasing a counterpart. Figure 11.11 shows interparticle forces as a function of interparticle separation at different electrolyte concentrations with KNO3 at


533

Monitor

• Controller

V J

Personal computer

Photo-diode

Beam expander

Polarizing êaj" splitter

)J2 waveplate

Nd:YAG Laser

Fig. 11.9. Block diagram of the optical trapping apparatus. (From Ref. 19.)

Fig. 11.10. Determination of the correlation between the horizontal trapping force and the beam power. 25 °C, where the symbols such as cubes, triangles, and circles are the experimental results by the optical method, and the solid curves are those calculated from the DLVO theory?^^^^ For the calculation of the theoretical

534

APPLICATIONS

curves, the following equations were used. _

64itamRT, ,21 exp(-icA), [4RT)

(11.4.1)

-32Afl*

(11.4.2)

3h\2a^h)\4a*Kf

100

200

Separation (nm) Fig. 11.11. Interparticie forces as a function of interparticle separation at different electrolyte concentrations: (a) 1.15 x lO"^, (b) 1.00 x 10"^ (c) 5.00 x 10"' mol dm'l Experimental results are shown by symbols (n, A, o), while the solid curves are calculated ones from the DLVO theory. (From Ref. 19.)


535

and

F^F^^Fj,.

(11.4.3)

where F^, F^, and F are the repulsive force for Ka » 1, the attractive force, and the total force, respectively, K is the Debye-Hiickel parameter, a is the radius of a particle, h is the surface-to-surface separation, m is the molarity of the symmetric electrolyte of the z-z type, 2 = 1, F is the Faraday constant, % is the Stem potential, and A is the Hamaker constant. There is an excellent agreement between the experiment and theory, including a weak attraction range located around 50 nm in interparticle separation at 5.00 x 10"^ mol dm"^ KNO3. This technique has the merit of being able to measure intrinsic interparticle forces without any influence from neighboring particles or supporting bodies such as a cantilever and stage. In any case, monodispersed particles must be used for these measurements, because size difference has a decisive effect on the measurements. For the optical trapping procedure, monodispersed polystyrene particles of mean diameter 2.13 [mi with a coefficient of variation (= standard deviation / mean diameter) 0.028 were specifically synthesized by soap-free emulsion polymerization, as shown in the TEM of Fig. 7.35. In this experiment, the distribution of electrophoretic mobility or zeta-potential of each particle must also be as sharp as possible. While the coefficient of variation of the electrophoretic mobility distribution of the polystyrene particles used was 0.033, it was found to be as large as 0.22 for a commercially available monodispersed polystyrene latex. This fact suggests that we must check the distribution of zeta-potential before conducting this kind of experiment, even if we use particles with a high monodispersity in size.

11.5. Studies of Particle Adhesion There are numerous studies of particle adhesion phenomena, including particle deposition onto solid surfaces from liquid and detachment from substrates into liquid, as summarized in review articles.^^"^^ This is because of their practical significance, as well as fundamental importance for studies of solid-solid interactions as described by the DLVO theory?^'^^ The adhesion can be treated theoretically as heterocoagulation of unlike particles'*^"^'* with a large difference in their size. The usual multilayer

536

APPLICATIONS

deposition may be interpreted in terms of heterocoagulation for the particlecollector interaction and homocoagulation for the particle-particle interaction."*^"^^ However, in some cases, the multilayer deposition must be interpreted in terms of heterocoagulation for both the particle-collector and particle-particle interactions.^^'^ The energetic background of particle adhesion may be described by the total energy (V^) of London-van der Waals attractive energy (F^), electrostatic repulsive or attractive energy (V^), and short-range Bom repulsive energy (V^) for two dissimilar spheres: V,= V^^V^^V^.

(11.5.1)

The London-van der Waals potential for two dissimilar particles of radius Uj and ^2 is

(11.5.2) '*

6

h

h(h+2a) J

where A is the overall Hamaker constant between particle 1 and particle 2 in liquid 3, a = aja2l{ai-M^, and h is the surface-to-surface separation between particles 1 and 2.^^ If one of the dissimilar particles is replaced by a flat plane or a large bead, its radius can be regarded to be infinite. The overall Hamaker constant A is given by ^ =(^-^)(^-/4;),

(11-5.3)

where A^, A2, and A^ are the individual Hamaker constants of particle 1, particle 2, and the medium in vacuo, respectively. The electrostatic interactive energy in the constant surface potential model is given by » ' £ = ^ M r « [ ( * i ^ * 2 ) V l + e - ^ + (i|ri-i|;/ln(l-e-'^)](11.5^^^ where EQ is the vacuum permittivity, e^ is the relative permittivity of the medium, K is the Debye-Hiickel parameter, and '[\)^ and \})2 are the surface potentials of particles 1 and 2, respectively .^^'^^ This equation does not apply to an interaction energy at very small separations. The Bom repulsion involves molecular interaction owing to their electron-orbital overlapping, which acts at very short separations and affects the potential well. Ruckenstein and Prieve^^'^® introduced the following expression for the Bom


537

repulsive energy on the basis of the Lennard-Jones potential:

r„ =

&a+h 7560 (2a ^Kf

6a-h h^

(11.5.5)

where a is the collision parameter having the dimension of length proper to the solids. For hematite-silica and hematite-glass interactions, a = 6 A was arbitrarily chosen."*^'^"^'^^ Figure 11.12 depicts a typical energy profile of V^ as a function of A. The potential barriers for the particle attachment and detachment correspond to the energy differences from zero to the maximum (AK^) and from the bottom of the potential well to the maximum (AK2), respectively. A criterion of the energy barrier for the occurrence of particle attachment or detachment is believed to be around 25 kT (« 10"^^ j)59.60

secondary minimum

7 ^ primary mmimum -^h

Fig. 11.12. Typical energy profile of V^ as a function of h.

Figure 11.13 shows an apparatus which used the tumbling method for efficiently collecting hematite and silica particles in their mixed suspension with large glass beads in a tumbling Pyrex tube.^^ For this experiment, monodispersed spheroidal hematite particles of mean diameter 0.10 (xm,

538

APPLICATIONS Front

Side

m h4

2 ( hrts

m Fig. 11.13. Apparatus of tumbling. (From Ref. 53.)

0)

s: o (0

c o o (0

u.

8

12

Time

16

24

( min )

Fig. 11.14. Fractions of hematite and silica particles attached to the glass beads as a function of tumbling time at pH 5 for a mixed sol of hematite and silica (1.35 x 10^^ particles per dm^ for each). The electrolyte concentration was 10"^ mol dm"^ with KNO3. (From Ref. 53.)

monodispersed spheres of silica of mean diameter 0.12 \im, and spherical glass beads of mean diameter 80 (im were used. Fractions of hematite and silica particles attached to the glass beads at room temperature and pH 5 are

539


shown as a function of tumbling time in Fig. 11.14, where the isoelectric points of hematite, silica, and the glass beads were pH 7.8, 2.9, and 2, respectively; the total number concentration of silica and hematite particles at a mixing ratio 1:1 was 1.35 x 10^° per cm^; and the volume of the suspension containing 5 g of glass beads and 1 x 10"^ mol dm"^ KNO3 in addition to the mixed particles was 30 cm^ It is of interest that silica particles can be collected by glass beads of a very close isoelectric point by the presence of hematite particles. Silica particles are of course not attached to glass beads in the absence of hematite at pH 5, since silica and glass beads are both negatively charged. The experiment was performed inunediately after mixing the individual suspensions of hematite and silica. It was found that the curve for hematite was identical to that when the same experiment was conducted with a single suspension of hematite without silica, and that there was some time lag for the coUection of silica by the glass beads. Since it took about 12 h for the hetero-coagulation between

0*10|im Fig. 11.15. SEM of hematite and silica particles attached to a glass bead. (From Ref. 53.)

540

APPLICATIONS

hematite and silica under these conditions without glass beads, the result of Fig. 11.14 may suggest that the hematite particles adhered first to the glass beads and then the silica particles attached to the hematite particles on the surfaces of he glass beads under these conditions. This means that the hematite particles acted as bridges between the glass beads and silica particles, as is clearly demonstrated by a scanning electron micrograph of the hematite and silica particles attached to a glass bead in Fig. 11.15. When the glass beads attached by hematite with silica were rinsed with 120 cm^ of 1 X 10"^ mol dm"^ KNO3 solution at a flow rate of 2 cm^ min'^ at 25 °C, using the colunm-bed technique developed by Clayfield et al,^^'^^ the detachment of silica was greatly enhanced with increasing pH of the solution, while the detachment of hematite was much smaller and showed virtually the same pH dependence as its single detachment without silica, as shown in Fig. 11.16.^"* —

1

—

r

^ • — 1 — ' — r — T — J

L 1 Double Detachment | 1 0 Silica 0.8 r D Hematite L 1 Single Detachment | o (0 1 • Hematite #^ 4)

•",••••,"

i

j / t)

0.6k

-^

Q

c o 0.4h o

//

(0

u. 0.2 h 1^

/ ^flf—rz^j^r^jff7.....-"djl^'—' 1 10 P H

11

1

12

13

Fig. 11.16. Fractions of the silica and hematite particles detached from the glass beads by rinsing the bed of the glass beads, doubly attached by hematite and silica, with 120 cm^ of 1 X IQ-^ KNO3 different in pH at a flow rate 2 cm^ min"^ (double detachment). A result for the single detachment of the hematite particles is also shown. (From Ref. 54.)

These results were explained by the calculated energy profiles for glass beads - hematite and hematite - silica systems in Figs. 11.17 and 11.18, respectively. In these figures, one may find that while AK2 for hematite is greater than 80 x lO'^^ J even at pH 11.5, AK^ is below 10 x 10"^ J at pH

541


10 or higher. 90

I I" I

IT-

jGlass Beads-Hematite Interactton]

90

I ' ' I • ' ' ' I • ' • ' I ' • ', {Hematite-Silica Interaction!

, i

^pH 11.5

150

Fig. 11.17. Total potential energy curves for glass beads - hematite interaction as a function of separation, h, at different pH conditions. A = 1.87 x 10-^ J. (From Ref. 54.)

200

Fig. 11.18. Total potential energy curves for hematite - silica interaction as a function of separation, h, at different pH conditions. A = 1.12 x 10'^ J. (From Ref. 54.)

On the other hand, Fig. 11.19 shows a schematic diagram of a column bed apparatus of glass beads for an experiment of coUecting hematite particles suspended in aqueous solutions flowing through the column bed."*^ For this experiment, a sol of polydisperse spheroidal hematite particles of diameters ranging from 0.1 to 0.6 (xm with a median diameter 0.20 \Jim and glass beads of mean diameter ca, 50 ûn were used. The zeta-potentials of the hematite particles and glass beads are shown as functions of pH in Fig. 11.20. The isoelectric points of the hematite and glass beads were 7.8 and 2.4, respectively. Figure 11.21 shows the recovery (collected fraction) of the hematite particles as a function of pH at room temperature with a flow rate of 2 cm^ min'"\ where the concentration of hematite in the feed solution, whose ionic strength was kept at 10'^ with KNO3, was 100 ppm, and the amount of glass beads used for one run was 6 g, whose height in the column bed was ca. 1.5 cm. Near the isoelectric point of hematite, the

542

APPLICATIONS

^ -a ia •

• •

Column reservoir

•

•

U Column, 1.8 cm i.d.

• Effluent collector

•

• •

B

• .

^

Fig. 11.19. Schematic diagram of a column bed apparatus. (From Ref. 47.) recovery collected on the glass beads dropped sharply to approximately 50 % at pH 8, and eventually reached close to 10 % at pH 9. In the pH range above 10, virtually no adhesion of hematite was observed, owing to its strong negative charge having the same sign as the charge on the glass beads. This result was unchanged with the tested flow rates ranging from 2 to 29 cm^ min"\ Figure 11.22 shows the recovery of hematite particles for each size class at pH 8, suggesting a strong size-dependence in the attachment of hematite to glass beads at pH slightly higher than the isoelectric point of hematite. This characteristic phenomenon was explained by the calculated profiles of total interactive energy, V^, for different particle sizes of hematite, as shown in Fig. 11.23, in which the Bom potential is omitted. At pH 8, slightly above the isoelectric point, the potential barrier of adhesion is low enough for the small particles to- surmount within a certain time, but too high for the larger particles.

543

11. APPLICATION TO FUNDAMENTAL STUDIES -80

Glass Beads -60

-40 h

-20

> E

0

20 h

Hematite

40 h

60

J

80

I

I

'

I

.

I

.

I

1 10

I 12

14

pH Fig. 11.20. Zeta-potentials of hematite particles and glass beads. (From Ref. 47.)

1

^

' ^

^

•• ! •

-rvÎ • n

T

\

1

1

j

80

^ ^ ^

—

60

>> u

>

S ^0 4>

» \ \

-j

\

^

20

0

l--_J

L.- J

L

L__j

L

1

T'^'^sai A 10 12

1 14

pH Fig. 11.21. Recovery of the hematite particles as a function of pH. (From Ref. 47.)

APPLICATIONS

544 100

I

••

^

80h

I

^

^

1

'

\

'

•X

L

J

\*

60 h-

I

J

u

> ©

40

20 1-

I

1

L— 0.2

I

N^

1 0.4

D

^

i 0.6

«uJ

I 0.8

(piin)

Fig. 11.22. Recovery of hematite particles for each size class at pH 8. (From Ref. 47.)

100

b

-100

-200 200

Fig. 11.23. Calculated profiles of total interactive energy K, at pH 8 for different particle sizes of hematite. (From Ref. 47.)


545

As is shown explicitly by the last example, the attachment and detachment of colloidal particles depend considerably on their particle size, especially in attachment near the isoelectric point. Accordingly, at least for comparison with theory, monodispersed particles are generaUy used in the experiments on adhesion. Incidentally, if one considers the hetero- or homo-coagulation from a kinetic viewpoint, there are significant discrepancies between conventional theories^^'^^'^ and experiments in stability coefficient (a degree of stability) as a function of the ionic strength; Le,, the colloidal stability is much less than the theoretical predictions in a low ionic-strength range. Kihira et al.^~^^ explained the discrepancy in terms of the discrete distribution of surface charges. For the final conclusion to this problem, it seems necessary to compile ample precise data of interparticle forces by direct and noncontact measurement, particularly between particles very closely separated.

11.6. Studies of Colloidal Ordering Charged coUoidal suspensions form an ordered structure, called ''colloidal crystals,'' when the extraneous electrolytes are removed by ion-exchange resins. If the volume fraction of the colloidal particles becomes high, or the electrolyte concentration is at an intermediate level, we can observe a phase separation of ordered and disordered phases, or crystal and liquid or gas phases. For the study of these interesting phenomena, monodispersed polystyrene spheres prepared by the soap-free emulsion polymerization and silica spheres prepared by hydrolysis of silicon alkoxides (see chapter 7) are widely used,^* because it is relatively easy to obtain well-defined monodisperse spherical particles with a variety of sizes and surface charges. As the concentration of electrolyte in a monodispersed polystyrene suspension is lowered, the color of the suspension changes from turbid white to translucent blue and green, and the hue varies with the change of the direction of the incident light, suggesting that the iridescence is due to the Bragg reflection from an ordered structure of the polystyrene latex. From spectroscopic study on a monodispersed polystyrene suspension, Luck et al}^ demonstrated that the polystyrene spheres formed a face-centered cubic structure. Also, Kose et aV^ actually observed the {111} face of the f.c.c. crystal structure as a result of the hexagonal closest packing of polystyrene or styrene-butadiene copolymer particles developed from the bottom of the container through metallurgical microscopy, as shown in Fig. 11.24.^"

546

APPLICATIONS

Fig. 11.24. Metallurgical micrograph of the {111} face of a face-centered cubic colloidal crystal of astyrene-butadiene copolymer latex [0.28 |iim diameter; particle density 1 vol %]. (From Ref. 70.)

Hachisu and coworkers^^'^^ explained the phase transition from a disordered structure to an ordered structure in terms of the Kirkwood-Alder transition/^'^"* in which particles at a high concentration are expected to form an ordered structure to minimize the total free energy by reducing the excessive internal pressure of the disordered structure at the expense of the lowered entropy. This phase transition is expected to happen in the absence of an attractive force element. However, if one chooses some electrolyte concentrations or particle concentrations, extensive voids - corresponding to dilute gas phases - are observed in ordered crystalline phases and/or disordered liquid phases. This appears to suggest vSome attractive force among particles. On the other hand, Ise et aV^~^^ explained the phase transition in terms of a long-distance energy minimum caused by an interparticle attractive force arising from the intervening counterions between two particles. However, at least from the DLVO theory dealing with the interactive forces between two particles,"^'^^ in which the effect of intervening counterions is already taken into account, the long-distance attractive force cannot be expected. It seems that compilation of more detailed experimental data and further theoretical studies, including multibody


547

treatments, may be needed for complete explanation of this intriguing phenomenon. It is possible to grow well-developed colloidal single crystals in a suspension of monodispersed polystyrene or silica spheres, if one chooses appropriate conditions of particle concentration and electrolyte concentration.^^'^^ Figure 11.25 shows the strong dependence of average colloidal crystal size, consisting of polystyrene particles of 109 nm in mean diameter, on its particle concentration in volume fraction in a highly desalted suspension/^ The colloidal crystals grow to great dimensions of several mm when the particle concentration is lowered below a critical concentration ((t)c), due to the limited nucleation of the colloidal crystals, in a manner similar to ordinary crystallization of molecules or atoms.

e 4

_

o

g.

1 C/D

^ 3

u ^ 13 3 *o

:=3

6 2-

o

o

MH

O (D

o

.a C/D 00

§ 1 u

s 0

1

0.010c

o

V

0.1

_Q

1 2 100(t)

1

5

Fig. 11.25. Relationship between the final size of the colloidal crystals and the volume fraction, cj), of polystyrene of 109 nm diameter in a highly desalted system. Here, ^^ (= 1.6 X lO"^) is the cTitical volume fraction of the polymer particles for the nucleation of colloidal crystals. (From Ref. 78.)

Figure 11.26 is a phase diagram as a function of NaCl concentration and particle concentration for a suspension of monodisperse silica spheres, where the largest circles represent colloidal crystals of more than 3 mm in average size and the smallest ones correspond to those of less than 0.2 mm.^^ Sanders and Murray^'^^ found that the iridescence of opal was due to an alloyed stmcture (superlattice) of silica particles of two different sizes. Since then, many kinds of colloidal superlattice structures have been

548

APPLICATIONS

attained by using monodispersed latex particles of different sizes.^^"^^ Also, Hachisu^^ showed that a mixture of a monodispersed silica sol with particle diameter 530 nm and a gold sol with average particle size of 80 nm formed NaCl-type colloidal crystals. For the formation of these superlattices or some particular crystal structures, monodispersed particles strictly controlled in size are required. IQ-i L

solid phase

§

liquid phase

I 10-3

10-4

10-

uuL.

LIXLL

I I I I I III

10-« 10-5 [NaCl] (moldm-^)

10-4

Fig. 11.26. Phase diagram of colloidal crystals of silica as a function of NaCl concentration and particle density. The size of the circles corresponds to the size of the colloidal crystals; Le., the largest and the smallest circles correspond to colloidal crystals equal to or larger than 3 mm and equal to or smaller than 0.2 mm, respectively. (From Ref. 79.) Zhu et al}^ reported the effects of microgravity on colloidal crystallization performed in the Space Shuttle Columbia; le,, formation of only random stacking of hexagonally close-packed planes (r.h.c.p.) in microgravity, in contrast to the mixture of r.h.c.p. and f.c.c. in normal gravity; observation of dendritic growth instabilities that are not evident in the normal gravity; rapid crystallization of a glassy sample in less than two weeks in microgravity, in contrast to the much slower transition for more than a year in the normal gravity. Obviously, gravity is one of the decisive factors governing the colloidal crystallization. On the other hand, Alfrey et al^ prepared a two-dimensionally ordered


549

colloidal membrane of a hexagonal closest-packed colloidal crystal by slowly drying a dilute dispersion of monodispersed polystyrene spheres on a smooth substrate. Luck et al^^ attributed the opal-like iridescence of this membrane to the two-dimensional Bragg reflection. In a similar manner, Goodwin et al^ also prepared two-dimensional colloidal crystals of polystyrene particles. Pieranski^^ observed ordering of polystyrene latex particles of mean diameter 0.245 (im trapped at the water/air interface of desalted water, where the interparticle separation of the ordered particles was more than 10 times the particle diameter (Fig. 11.27a). As the inteq)article separation becomes larger, the the arrays of the particles become disordered as in Fig. 11.27b, while the interparticle distances are almost uniform, even when the mean interparticle separation becomes about 10 (xm or more. This suggests that the interparticle force at a low particle density is mainly due to the electrostatic repulsive force among the surface particles. Hurd and Schaefer^ studied the clustering of silica particles of ca. 0.3 |im at the water/air interface with water at a high ionic strength. Onoda^^ observed the ordering process of polystyrene particles of different sizes at the water/air interface, and found no clustering with particles of less than 1 [xm, reversible clustering with particles of 2 |xm, and irreversibly stable clusters for particles of 5 |im or more in diameter under his experimental conditions. The size effect was explained in terms of the DLVO theory, but the increasing contribution of the attractive capillary force with increasing cluster size was

Fig. 11.27. Ordering of polystyrene particles at the water/air interface: (a) crystalline structure; (b) disordered structure. (From Ref. 93.)

550

APPLICATIONS

also suggested. Generally, it is believed that particles floating at a liquid/gas interface are subject to a long-distance force, capillary force, in addition to London-van der Waals and electrostatic forces.^^"^^^ If the central distance, R, between two particles floating at a liquid surface is much smaller than the reciprocal capillary constant (2.7 nun for water) and if the radii of their wetted peripheries, r^ and r2y are sufficiently smaUer than R, the lateral capillary force between them is given by F=2ny^,

(11-6.1)

where y is the surface tension of the liquid; Qj and Q2 are the capillary charges of particles 1 and 2.^^'^°^'^°^ The capillary charge is defined by

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