Monodispersed Particles

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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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 C^if 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 C^i, 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 r^oo distance from the center of a tetradecahedral particle to a {100} surface r^ii 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^^io» 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) ^i 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 radiatedfi^ommagnetic 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, <2„, may be proportional to n^^, so that if a^ and v^ denote the surface area of a monomer in the liquid phase and its volume in the solid, respectively, then a„ = a^n^ = (36izv\)"'ny\

(1.1.10)

Therefore, the intrinsic surface energy of the n-mer, \p„°, is given by

1. NUCLEATION

i|f^t|;V/3

(1.1.11)

regardless of the shape of the monomers. Here, the intrinsic surface energy means the surface energy of a pure surface without any adsorption of ions or foreign molecules. The intrinsic specific surface energy, or intrinsic surface energy per unit area of the spherical n-mer particle, y^, is given by

.oA.H.zH!^. ^n

^1

(1.1.12)

(36711)^^^

Polycrystal particles consisting of randomly oriented subcrystals are normally spherical. The surface energies of such particles may be formulated in the same way as that of the amorphous particles, as represented by Eq. (1.1.11) or (1.1.12). However, in the case of spherical single crystals, which are occasionally obtained in the course of dissolution or intraparticle Ostwald ripening, the theoretical treatment is more or less different, as shown in the section 1.1.4. 1.1.2. Intrinsic Surface Energy of Single-Crystal Particles Single-crystal particles normally assume their own characteristic habits. In this case, the treatment may differ from that of amorphous or polycrystalline spherical particles, since the surface monomers are regularly oriented. For the treatment of polyhedral microcrystals, we first direct our attention toward the coordination numbers of atoms in crystals. Each atom in a crystal has its own coordination number, and each molecule or monomer is bonded together through the definite bonding spots of its constituent atoms. Since the surface energy is due to the excess free energy of the bond-free open sites of the surface monomers, one may assume that the surface energy of a surface monomer is allocated to each bond-free site of the surface monomer. If we interpret the surface energy of a solid in this manner, we will be able to avoid the difficulty in specifying the originally ambiguous concepts of the microscopic surface areas of a n-mer and free monomer, since we can clearly defme the numbers of their bond-free open sites. If we consider that a crystal is constructed through the repeated addition of each neutral monomer unit onto the crystal surface, a neutral bond-free open site, or simply an "open site," of a monomer may be defined as the minimum unit of the "bond-free spots" of its constituent atoms, through

FUNDAMENTALS

Bonding of Atomic Molecules

#

Bonding of General Molecules a negative bond-free spot (S-)

a positive bond-free spot (S+)

An open site = A pair of S+ and SFig. 1.1. The concept of an open site of an atomic molecule or of an ionic molecule. which the monomer lying on a surface is connected with another monomer in the surface layer. For example, if a crystal consists of only one kind of atoms, like metal crystals, the number of the open sites of the monomer is equal to the coordination number of the atom. On the other hand, the coordination number of a Ag atom or a Br atom in the face-centered cubic crystal of AgBr is six. Hence, a Ag atom has six positive bond-free spots, while a Br atom has six negative bond-free spots. In this case, one open site of a AgBr monomer consists of a pair of each one bond-free spot of Ag and Br. Thus a AgBr free monomer in the solution phase of a suspension

1. NUCLEATION

7

of AgBr microcrystals has five open sites, since a pair of a bond-free spot of Ag and Br is already used for the bonding of the AgBr monomer of its own. Also, the surface monomers of the {100}, {110}, and {111} faces of the AgBr microcrystals have one, two, and three open sites, respectively, per a surface monomer, since the bond-free spots of Ag^ or Br" on the {100}, {110}, and {111} faces are one, two, and three, respectively (see Fig. 1.4). Generally, if a monomer is composed of cations and anions, the cations and anions have, in total, an equal number of bond-free spots, which is also equal to the number of the open sites of the monomer, regardless of the states of the monomer - such as a free monomer or surface monomer of a certain surface layer. In this treatment, we may not need to take into account the other monomeric species in the forms of dissociated ion-pairs and complexes coexisting in the solution phase, since the dissociation and complexation of a monomer are events which are independent of the formation of a free monomer from the solid. We will thus be able to deal with any kinds of crystals including ionic, covalent, and metallic ones, through this general treatment. Figure 1.1 illustrates the concept of an open site for an atomic or ionic molecule. Based on the above guidelines, let us consider the intrinsic surface energy of a polyhedral microcrystal bound by surfaces of a specific face index. Generally, the intrinsic surface energy of a surface monomer, \|)°'^, is given by ^O,o^j^0.o_|j^0^

(1.1.13)

where \i^'° is the standard chemical potential of the surface monomer, and \i^ is that of a monomer in the interior of the solid. If n / and n^ denote the numbers of the open sites of a surface monomer in the specific surface layer, and a free monomer in the liquid phase, respectively, the surface energy of an open site, e, common to both monomers, is given by e =i t ! : . l ! .

Using \|)° in Eq. (1.1.8), one obtains

(1.1.14)

FUNDAMENTALS i|;^'^ = Xt'=-AJknnX(„^,

(1.1-15)

X-^.

(1-1-16)

where

The intrinsic specific surface energy of the crystal, y^, is thus obtained as Y^ = iV>^»^ = -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 ^o.o.^o.a,_^o,„;(^o.<,_^0) Thus,

(1.1.26)

1. NUCLEATION

11

"^^kTlaal

y=K -,.0

=

(1.1.27)

y''+N°kThial,

where y" is the intrinsic specific interfacial energy without the adsorption of non-matrix components N^n:=N:

(1.1.28)

The relation of Eq. (1.1.27) can be derived directly from the fundamental equation of y as well.^ On the other hand, if the adsorbate is only species z, and if T^ and T^ denote the surface densities of species i and solvent L, respectively,

^L-^PrNl

(1.1.29)

Hence, the mole fraction of the adsorbed solvent molecules, jc/, is given by X, = I

r.-r,

(1.1.30)

iVs-(v,-i)r, If Xj° is close to unity, A / may be approximated as a / - JC/. In this case, Y is given from Eqs. (1.1.27) and (1.1.30) as (1.1.31)

y = y°+N°kTln\ 1 - -

(

Jv;-(v,-i)rj

1.1.4. Surface Energy of Silver Halide Microcrystals Silver halide particles, including silver bromide microcrystals in particular, may be among the most popular colloidal particles for their excellent monodispersity and characteristic variety in crystal habit. Furthermore, a good deal of reliable thermodynamic data on the stability

FUNDAMENTALS

12

constants of their complexes in the solutions and some experimental data on the specific surface energies are also available. They are thus likely to be among the most suitable materials for the comparison of the above theory on the surface energy of colloidal particles with the corresponding experimental results. Silver Bromide The silver bromide crystal belongs to the face-centered cubic system, as illustrated in Fig. 1.2. Also, the coordination numbers of Ag and Br atoms are both 6 and the number of the open sites of a monomer, n^, is 5, as is obvious from the scheme of the monomer shown in Fig. 1.3. On the other hand. Fig. 1.4 depicts the atomic arrays of the {100}, {110}, and {111} faces, along with the shapes of AgBr microcrystals bound by the respective crystal faces. The hypothetical regular {111} surfaces of an octahedral particle consist of four triangular planes covered with Ag atoms only and the corresponding four Br-planes, where the Ag- and Br-planes are located alternately, as shown in Fig. 1.5. Hence, if a surface is a Ag-plane, the

• Ag

O Br

Fig. 1.2. Unit cell of the facecentered cubic crystal.

Ag+

Br" Fig. 1.3. Scheme of a AgBr free monomer with n, = 5.

1. NUCLEATION

13

[001]

[100] Fig. 1.4. Atomic arrays of {100}, {110}, and {111} faces of AgBr, corresponding to the respective shaded planes. The closed and open circles represent cations and anions, respectively. The black and white arrows stand for the directions of the respective cationic and anionic bond-free spots of a surface monomer on each surface. The « / values for {100}, {110}, and {111} faces are 1, 2, and 3, respectively.

Fig. 1.5. Hypothetical regular {111} faces of an octahedral particle. The left-hand model is an octahedron, bound alternatively by positive (black) surfaces of cations and negative (white) surfaces of anions. The right-hand model is one bound only by neutral (gray) surfaces with equal numbers of unifonnly distributed cations and anions. reverse side of the octahedron is a Br-plane, and thus one may consider that one Ag-atom in a surface layer and one Br-atom in the surface layer of the reverse side constitute one AgBr surface monomer. However, the actual {111} surfaces of an octahedral particle of AgBr are supposed to be neutralized by randomly distributed ions of the opposite charge through

FUNDAMENTALS

14

occupying about a half of the adsorption sites of the regular surfaces to minimize the total surface energy. Even so, the surface monomer density, A^, and the number of open sites of a surface monomer, «/, are regarded to be the same, because the total number of open sites is unchanged by this procedure. As a consequence, n / = 1, 2, and 3 for the {100}, {110}, and {111} faces, respectively, and thus the >^ values (= AI//AZ^) of these faces are 1/5, 2/5, and 3/5, respectively. If the lattice parameter of AgBr is denoted by flo» the A^ values of the {100}, {110}, and {111} faces are given by 2la^, V2/flo^ and ima^, respectively, where a^ = 5.7748 A at 25 °C. If Pii» ^'(«)» ^ ^ ^sp denote the stability constant of monomers in aqueous solution, defined by [^]/[v4][5], the solubility of the bulk solid in terms of molarity of the monomers (not the total solubility for all monomeric species), and solubility product of a AS-type bulk crystal, c\^^ is given by <«)=Pii^^

(1.1.32)

Furthermore, the mole fraction of the monomers in equilibrium with the bulk solid is given by Eq. (1.1.19) (JC^^^ = c\^^V^, where V^ is the molar volume of the solvent (KQ = 1.807x10"^ dm^ mol'^ for water at 25 ^C). For AgBr at 25 °C, p^^ = 10^^ and K^ = 10"'^^' (see ref. 5 or 6). If we calculate the values of the intrinsic specific surface energy -f of the {100}, {110}, and {110} faces of AgBr in water using Eq. (1.1.17), we obtain Y^QQ^ = 109, Yuo° = 154, Yni' = 188 mJ m'^ at 25 X , where YIOO' : Yno" : Yin' = 1 : V2 : V3. On the other hand, cubic, regular dodecahedral, and regular octahedral microcrystals of AgBr are bound by only {100}, {110}, and {111} faces, respectively, as shown in Fig. 1.6. If we define the shape factor )3 of a particle as

Fig. 1.6. Cubic, dodecahedral, and octahedral AgBr microcrystals bound by only {100}, {110}, and {111} faces, respectively.

1. NUCLEATION

15

(1.1.33)

P=

where A and V are the surface area and volume of a polyhedron, p = 32, 16V2, and 16V3 for a cube, dodecahedron, and octahedron, respectively. Since

^27pr^>'^

27Pu,n^

(1.1.34)

where v^ is the volume of a monomer and n is the number of the monomers composing the particle, the ratio of the surface areas per unit volume of a cube, dodecahedron, and octahedron is given hyA^^ :A^^ :A^^f = 1: (1/2)^^^ : (3/4)^^^ = 1 : 0.891 : 0.953. Since the intrinsic surface energy of a n-mer, ip^''^, is given by ,0,0

0^

(1.1.35)

the ratio of the xp^^ values of these polyhedra is tp^cu^^ : '^n,dof • '^n,oct^ = 1:2^^ : (9/2)^^ = 1 : 1.26 : 1.65. The ratio is independent of the number of the constituent monomers, n. Thus, although the difference m %^ is smaller than that in y^, a cubic particle is the most stable of these regular polyhedral microcrystals. If the AgBr particle is a spherical single crystal, A/^n/ is given by (1.1.36) «o

since a hemisphere, viewed from a position perpendicular to a {100} face of a spherical f.c.c. crystal, contains open sites directed normal to the {100} face whose number is the same as that of a {100} circular plane of the same radius, and the total number of such open sites of the sphere is equal to that of six {100} circular planes of the same radius (N^nf = 6itr(llaQ)IAT(r^). (Detailed calculation gives A^ values with n / = 1, 2, and 3 as 0.603/^0^, 0.7005/flo^ and 0.332/ao^ respectively; 1 x 0.603/^0^ + 2 x 0.7005/ao^ + 3 X 0.332/^0^ = 3^0^.) Although the spherical f.c.c. single crystals of AgBr

16

FUNDAMENTALS

and AgCl were treated in the same way as amorphous spheres in ref. 3, the treatment with Eq. (1.1.36) may be, at least, theoretically more reasonable. Hence, •f of a spherical AgBr is calculated as y" = 163 mJ m'^ from Eqs.(1.1.17) and (1.1.36). Since the shape factor of a sphere is P = 16n/3, A^ :A^, = 1: 0.806 and ^^^J : %J' = 1 : 1.21. Thus, the reduction of the total surface area is quite effective in lowering the total surface energy of a particle. Also, it is expected that if the difference in y" among the facets of a polyhedron is smaller than a certain limit, the total surface energy of the polyhedron may be lowered by the reduction of the total surface area even if the overall y" is raised, as wOl be shown later. The above calculations for AgBr microcrystals in water at 25 °C are summarized as foDows: AgBr: K^ = 10"^"^ moP dm'^ p^ = lO'-^ moK^ dm^ c\^) = lO"'*^ mol dm-^ x^^^ = 2.79x10-^"; \jj° = 9.06x10-2° J; a^ = 5.7748 A; Tjj =fl„3/4= 4.8145x10-2 nm^ n, = 5 {100} face: A^ = 2/aQ^ = 5.997 ran-^, « / = 1, X = 1/5 Yioo" = 109 mJ m-2 {110} face: N° = VI/OQ^ = 4.241 nm'^, n / = 2, X = 2/5 Yuo" = 154 mJ m-2 {111} face: N° = 2/V3ao^= 3.463 nm-^, « / = 3, X = 3/5 Yui" = 188 mJ m-2 Spherical surface: N°k = 3/500^ = 1.799 nm'^ Y^" = 163 mJ m-2

iVioo" : ^110" : ^111" = 1 : W 2 : 1/V3

Aa^ • A^:A^:A^

= 1: (l/2)i'« : (3/4)^"* : (jt/6)^^ = 1 : 0.891 : 0.953 : 0.806

1. NUCLEATION

17

Yioo° : Yuo" : Yui" : Y^." = 1 : V2 : V3 : 3/2 = 1 : 1.41 : 1.73 : 1.50

^..J

•• %J

•• %J

•• %J

= 1 : 2^'' : m r

•• (9:t/16r

= 1 : 1.26 : 1.65 : 1.21 The value of v^ was obtained from the lattice parameter. Silver Chloride The AgCl crystal belongs to the same crystal system as the AgBr, facecentered cubic (f.c.c.) system, so the treatment is identical to that for AgBr. The results of the calculations for AgCl microcrystals at 25 °C are summarized below. AgCl: K^ = 10-"^ mol^ dm'*; p^ = lO^-^ mol"^ dm^ c\„^ = lO"*"^ mol dm-^ X(„) = 6.39x10-'; ^\)'' = 7.77x10"^ J; a^ = 5.5502 A; Vi = 4.2743x10-^ nm^; «, = 5 {100} face: AT = 6.493 nm'^ nf =l,k=

1/5

Yioo" = 101 mJ m"^ {110} face: iV" = 4.591 nm-^ « / = 2, X = 2/5 Yiio" = 143 mJ m-2 {111} face: AT = 3.748 nm'^, n° = 3, X = 3/5 Yni" = 175 mJ m-^ Spherical surface: N°X = 2,l5a^ = 1.948 nm"^ Y^; = 151 mJ m-^ The v•^ was obtained from the lattice parameter. Silver Iodide The wurtzite-type (p-type; hexagonal) and zinc-blende-type (Y-type; cubic) crystals are known to be stable up to 137 °C and from 137 to 146 °C,

FUNDAMENTALS

18

respectively, as shown in Fig. 1.7. However, they are usually observed as their mixture in normal precipitation around room temperature. Since each coordination number of Ag and I is 4 for both crystal types, w^ = 3 for both P- and Y-types, as shown in Fig. 1.8. If we assume that the solubility product, solubility in terms of the Agl monomer, and molecular volume are common to both types, we can calculate the Y° values of their individual faces in water. For the calculation of Y° of spherical particles, we used the molecular volume {v^ = 6.88x10"^ nm^) calculated from the specific gravity (d = 5.67) (C/. V calculated from the lattice parameters: 6.86x10"^ nm^ for the P-type; 6.80x10'^ nm^ for the Y-type). The following are the properties of Agl and calculated "f values of each face of the p - and Y-types and of the spherical surface. The calculation of Y° of spherical Agl particles is based on Eq. (1.1.12), as is different from the cases of f.c.c. crystals of AgBr and AgCl. K^ = 10-^^^^ moP dm-^ p,, = 10'' mol"^ dm^ c\^) = 10" 8.59 mol dm-^ x^^^ = 4.63x10"^^; ^ = 9.80x10-2° J; v, = 6.88x10-^ nm^ /(-type Agl: a^ = 4.59 A, CQ = 7.52 A, n, = 3

• Ag

O I

Wurtzite-type (P-type) hexagonal crystal

Ag

O I

Zinc- blende- type (y- type) face- centered cubic crystal

Fig. 1.7. Unit cells of the P-type and y-type of Agl crystals.

1. NUCLEATION

19

{0001} face: N° = l/VSoo^ = 2.80 nm-^ « / = 1*, X = 1/3 Yoooi" = 91.5 mJ m-^ (*«/ = 1 and 3 are possible, but nf = 1 was taken because of its higher stability.) {lOlO} face: A^ = 1/a^o = 2.90 nm-^ nf = 2,X = 2/3 Yioro" = 189 mJ ni-2 Y-type Agl: a^ = 6.48 A, n, = 3 {100} face: N" = lla^^ = 2.38 nm-^ n° = 2, X = 2/3 Yioo" = 156 mJ m"^ {110} face: iST = ^/2|a^ = 3.37 ^m-^ n / = 1, X = 1/3 Yiio° = 110 mJ m-^

A P-AgI

^ y-Agi

Fig. 1.8. Schemes of a monomer in P-AgI or Y-AgI (w^ = 3 for both types).

20

FUNDAMENTALS

{111} face: AT = 2/V3ao' = 2.75 nm-^ nf = 2, X = 2/3 Yni° = 180 mJ m'^ Spherical surface: a^ = {367w^y^ = 8.12x10"^ nm^ Y^,' = 121 mJ m-^ Table 1.1 shows comparison between the theoretical Y° values and the experimental ones obtained by potentiometric measurement on the basis of the Gibbs-Thomson relation.^ Normally, the comers and edges of a microcrystal are not completely sharp on the atomic scale, and this effect becomes conspicuous as the size is reduced. For example, the most stable form of a AgBr or AgCl microcrystal is cubic, but, as the size decreases, the rounded comers and edges become prominent and the final shape looks like a sphere in a size range below several hundred angstroms. This may be because the surface monomers at the comers and edges, having high chemical potentials with greater nf values than those at the flat surfaces {100}, tend to rearrange themselves, e.g., with partial interbonding among the surface monomers, to reduce their overall chemical potentials to some extent within the geometric

Table 1.1. Comparison between theoretical and experimental Y values of AgCl, AgBr, and Agl {Source: Ref. 3) Y (mJ m"^) Temp.

AgBr

AgCl

CC)

Exper.

Theor.

Exper.

10

104

102

112

20

102

101

25

102

30 40 Facets

Agl Exper

Theor.

111

128

125

107

109

120

122

101

104

109

116

121

102

101

105

108

117

119

100

100

102

107

112

116

{100}

Theor.

{100}

sphere

1. NUCLEATION

21

limitations. In this case, the total surface energy of a particle, ip„, may be reduced to some level even below % of a perfect cube having the same n, despite the increase in overaU y of the particle. For example. Fig. 3.1 in chapter 3 illustrates octahedral, intermediate tetradecahedral, and cubic AgBr microcrystals, where a tetradecahedral particle is bound by eight {111} faces and six {100} faces. If we refer to the general form of the tetradecahedra from the tetradecahedron M to the cube as "B-type," the total surface energy % and volume F of a B-type tetradecahedron are given by * . = 12[2r^oo-3(\/3rioo-rni)']Yioo

(1.1.37)

and

where r^oo and r^^^ are the distances from the center of the particle to the {100} and {111} serfaces.^ Eliminating r^oo from Eqs. (1.1.37) and (1.1.38), g^ [2-y/3(yl3-a)(y/3-pff

^

(1 1 39)

where g s ^\^„V(6V^ym)^ « = Ym/Yioo. and/7 s r,J^^, Here, g^^ is the % of a tetradecahedron, relative to that of a perfect cube of the same volume (= 6P^^yioo)- If/? is varied at constant V, Y^QQ, and a, then g or \p„ assumes the minimum at /? = a from dg/dp = 0. Hence, the minimum value of g is given by

Figure 1.9 shows g^.„ as a function of a. If a = V3, g^^ = 1 and thus \p„ = 6F^Yioo- This means that, when a = V3, the most stable form is a perfectly sharp-edged cube. However, if the chemical potentials of the monomers at the comers are reduced to some extent by their self-rearrangement as usual, a may become less than V3. In this case, g^^ in Eq. (1.1.40) is still below unity, and hence \p„ of the tetradecahedron of a less than V3 is lower than

FUNDAMENTALS

22

T

r—ll-2

Fig. 1.9. g^ and Y/Y«J, as functions of a. that of a cube of the same volume. On the other hand, the total surface area of the tetradecahedron, A, is given by A = 12[2rJoo-(3-^/3)(^/3r,oo-r,ll)2].

(l-l-^l)

Thus, the overall y at the minimum \p„ is given by 100

^

(1.1.42)

2-i3-^)0-af

Since YIOO = Yc,*.

_l_-i = _&llMlf)L ycub

(1.1.43)

2-(3-^/3)0-ccf

and thus y/y^j, > 1 for a tetradecahedron of type B (2/V3 < a < V3). Figure

1. NUCLEATION

23

1.9 shows Y/YCU^, as a function of a together with g^„. Therefore, \|)„ of the tetradecahedral particle of type B is lower than that of the cubic particle of the same volume, while the overall y of the former is significantly higher than that of the latter. In other words, if a < V3, the reduction of the total surface area per unit volume outweighs the increase of the total surface energy per unit surface area. This means that the stability of the shape of a particle should be assessed from its total surface energy, \|)„°, and not from the overall specific surface energy, y- Also, when the chemical potentials of the surface monomers at the comers and edges are somewhat lowered by the intermolecular rearrangement, ip„ is efficiently reduced by the degeneration of the sharp comers and edges. This seems to be the reason why exceedingly small particles look like spheres, although not perfect spheres whose \p„ is somewhat higher than that of a cube of the same n, owing to some contribution of the facets of much higher Y° in the spherical surface. In this context, Berry^ estimated Y° of AgBr particles to be ca. 140 mJ m"^ from the data of the size-dependent solubility using the well-known GibbsThomson relationship [y = (kTr/2v2)]n(c/c^„^); r - particle radius]. This value is much higher than the calculated y° of the cubic particles (=109 erg cm"^), but it is not an unreasonable data if one considers the shape effect of a particle on its total surface energy. AgCl particles having sizes of the order of submicrons prepared by the ordinary double-jet technique^ are almost always cubic, reflecting the lowest surface energy of the cubic particle. In the case of AgBr, however, octahedral particles are readily obtained despite the calculated high \p„° of the octahedral particles, when the excess concentration of bromide ions is simply adjusted to a level slightly above that for the preparation of the cubic particles. In addition, dodecahedral AgBr particles cannot be obtained unless some specific adsorptives are added.^ Although these particle shapes are mostly accounted for in terms of the steady growth form, they are closely related to the equilibrium form,^ so that there seems to be some special reason for the easy formation of the octahedral AgBr particles, skipping the dodecahedral particles of an intermediate Tp„°. As mentioned above, the specific surface energies of the {111} and {110} faces, corresponding to the comers and edges, respectively, of cubic microcrystals, are thought to be lowered to some extent by the self-rearrangement of the surface monomers at these sites. However, the exceptionally high probability of generation of the octahedral AgBr particles bound by the {111} faces cannot be explained by the reduction of the specific surface energy of the {111} faces caused by the self-rearrangement of the surface monomers.

24

FUNDAMENTALS

Neither can it be explained by adsorption of Br" ions, since it is consistent neither with the case of AgCl with only a cubic shape nor the impossibility of the formation of the dodecahedral AgBr particles without adsorptives. Thus, this phenomenon is a consequence of the specific nature of the {111} faces of AgBr. Presumably, it may be ascribed to some specifically allowed electronic relaxation of the Ag and Br atoms in the top layer of the {111} faces of AgBr, based on the significant covalent content of the Ag-Br bonds. Therefore, there seems to be a possibility of a considerable overestimation involved in the high theoretical values of y^^^^ (= 188 mJ m' ^) and Ygph° (= 163 mJ m"^), for which the specific nature of the {111} faces of AgBr is not taken into account. To date, the liquid-solid interfacial energies have been evaluated by experiments on the nucleation or growth rates of precipitates or sizedependent solubilities, on the basis of the Gibbs-Thomson relationship. For AgBr particles in aqueous solutions, several data for y are available; Le,, 140 mJ m"^ by Berry^ 120 mJ m"^ by Ljalikow^°, 200 mJ m"^ by Nielsen^\ etc. For AgCl, Nielsen^^ estimated y to be ca. 100 mJ m'^ from the measurement of the nucleation rate. On the other hand, Walton^^ proposed the foUowing relation by correlating the surface energy with the lattice energy of ionic crystals: y^-

'—^,

(1.1.44)

eF^mN^r^^ where y;^ is the intrinsic specific surface energy of a {hM} face, Uj is the lattice energy at temperature T, r^ is the mean ionic radius, F ^ is the structure factor depending on the crystal face {hid} and atomic arrangement (e.g., F^oo = 9 and F^^^ = 3 at 25 **C for alkali hahde crystals), and mNg is the number of ions in one mole of solid. If we pick up the approximate surface energies y for AgBr, AgCl, and Agl calculated from Eq. (1.1.44) with Fioo = 9 and listed in a table of ref. 12, in comparison with the surface tensions extrapolated from the molten salts to 25 °C in the same reference, 156 mJ m-^ (161 mJ m"^) for AgBr, 172 mJ m"^ (170 mJ m'^) for AgCl, 121 mJ m"^ for Agl, where the values in the parentheses are those of the surface tensions extrapolated from the melts. However, the good agreement of the values, calculated for the {100} faces of AgBr and AgCl on the basis of Eq. (1.1.44), with the respective surface tensions extrapolated from the melts may not necessarily mean that the theory is valid, since the surface tensions

1. NUCLEATION

25

obtained above the melting points of these salts may correspond to the specific surface energies of the randomly oriented surface molecules. Benson and his coworkers^^ performed a number of calculations for the surface energy of alkali halides, taking into account the electrostatic, dipoledipole, and dipole-quadrupole interactions and the Bom repulsive forces among the surface ions: e,g., NaCl (YIQO = 188 mJ m"^; YUO = 445 mJ m"^), KCl (Yioo = 163 mJ m"^; YHO = 352 mJ m"^), LiCl (YIOO = 209 mJ m"'; Yuo = 558 mJ m"^), LiF (YIQO = 169 mJ m"^; YUO = 832 mJ m"^), etc. These YIOO values are considerably different from those calculated from Eq. (1.1.44): Le., 169, 108, 193, and 336 mJ m"^ for NaCl, KCl, LiCl, and LiF, respectively.^^ In addition, the differences between YIOO ^ ^ Yno seem too large from the viewpoint of the present theory (YIOO°^ YIIO° = 1 • ^2). The above inconsistencies in the foregoing theoretical treatments may imply the inherent difficulty in theoretical approaches to the surface energy of solids from the the complex interactive factors of the solid surface molecules. Moreover, in the existing theoretical treatments, the interaction of the surface molecules with the solvent, which seems to be one of the decisive factors to be considered, is not taken into account. In contrast, the present theory, formulated on the basis of the equilibrium concentration of the monomers of a bulk solid in the solution phase, may be of advantage in its straightforward approach to the chemical potentials of the surface monomers exposed to the same environment. On the other hand, probably the most reliable experimental approach to the liquid-solid interfacial energy available at present may lie in the precise measurement of the size-dependent solubility of ultrafine particles, with the simple Gibbs-Thomson equation firmly based on thermodynamics. This is because the other methods represented by the analysis of the nucleation or growth processes, with the simplified classical theories of these processes, contain many assumptions and approximations. In this sense, the excellent agreement between the present theory and experimental determination of Y^ of AgBr particles, on the basis of the Gibbs-Thomson equation, may suggest the feasibility of the present theory.^ However, the possible effects of atomic and/or electronic relaxation of the surface monomers on the surface energy are disregarded in the present theory. These effects must also be taken into consideration in some cases as suggested by the specific behavior of the {111} faces of AgBr. In such cases, the calculated values of Y° are regarded as the maximum values of each crystal surface, since all relaxation processes, including atomic displacement, molecular distortion, electronic depolarization, etc., always lead to the reduction of the surface

26

FUNDAMENTALS

energy.

1.2. Equilibrium Concentrations of Three-Dimensional Nuclei For the start of nucleation of fine particles, the concentration of the solute must be sufficiently higher than the solubility of the solid. In other words, the solution must be in a supersaturated state. If we consider the free energy of formation, AG„, of a n-mer at the standard state (jc„ = 1) from n monomers in the supersaturated solution, AG„ may be given by AG„=ti:-n^ = |i:-n(n^^A:nnjc),

(1-2.1)

where |x® and [x^^ are the standard chemical potentials of a monomer and nmer at mole fractions x = 1 and jc„ = 1 in the liquid phase, respectively; and X is the mole fraction of the monomers in the supersaturated state. If we use the mole fraction of the monomers in equilibrium with the bulk solid, x^^y Eq. (1.2.1) may be rewritten as AG„= -nkThi—

+ |x^-n^x^

(1.2.2)

where \i^ is the chemical potential of a monomer in the bulk solid (n = oo). On the other hand, the surface energy of the n-mer, \|)„, is given by .0^

(1.2.3)

Thus, if a supersaturation energy parameter ^ is defined by (1.2.4)

*=

Eq. (1..2.2) can be written as = -n + i|r„.

(1.2.5)

The supersaturation energy parameter, (j), is the difference of the chemical potentials of a monomer at supersaturation and that at equilibrium with the bulk solid. In other words, it is equivalent to the work needed to transfer

1. NUCLEATION

27

a monomer from the interior of the bulk solid to the liquid phase and disperse it to the supersaturated concentration. Since xlx^^-^ is the supersaturation ratio, S, i.e.. S,

(1.2.6)

\-)

(|> 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 ^IkT (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)

^«=^<^»

and thus c„' is given by

(-AG.

c„' = Uo'exp = UQ exp [ kT )

f^n-ijrn^ kT

(1.2.17)

Hence, the equilibrium concentration of the critical nuclei, c„*, is the lowest of all kinds of the n-mers, since AG* is the maximum of AG„ for all kinds of n-mers. The potential barrier, AG*, corresponds to the activation energy for nucleation, so the nucleation is enhanced if AG* is lowered with reduction of \p by adsorption or with increase of (j) due to increasing supersaturation (see Eq. 1.2.14). For example. Fig. 1.11 shows AG„ as a function of n with variation of (|), in which AG* is inversely proportional to

Fig. 1.11. AGJkT as a function of n with variation of ^/kT, (From Ref. 14.)

30

FUNDAMENTALS

1.3. Nucleation Rate as a Function of Supersaturation If jX(^)° denotes the chemical potential of a monomer in a n-mer, it is given by 0 e e fA(n)=l^i,-JA;,-l-

(1.3.1)

Hence, it follows from Eq. (1.2.1) that dAG

n

(1.3.2)

dn On the other hand, from Eqs. (1.2.5) and (1.2.12),

9n

^ = -(j)+—1^ = -|x + |IO+_IJ^. dn dn

(1.3.3)

Comparison between Eqs. (1.2.2) and (1.2.3) yields ^»„,= , o . ^ = , o . | * n - > / 3 .

(1.3.4)

If the dissolution of this n-mer is in equilibrium with the deposition of the monomers in the solution phase, ^ ^

= ^ " - , = 0.

(1-3.5)

TTius, dAGJdn = 0 is equivalent to [i^„°= M- In this case, one obtains from Eq. (1.3.4) <|,= H - n 0 ^ 2 ^ „ - i / 3

(1.3.6)

This is identical to Eq. (1.2.13). If the mole fractions of monomers in equilibrium with a n-mer and bulk solid are represented by JC(„) and x^„y and

1. NUCLEATION

31

their number concentrations by c^^^ and c^^^, respectively, (1.3.7) SO that C(^) is given by

^^">=^->^^Hi]^)

(1.3.8)

from Eq. (1.3.6) and ^ = kT[n{X(^y/Xf^^) in Eq. (1.2.4). This equation and Eq. (1.2.13) correspond to the so-called Gibbs-Thomson equation. If the equilibrium condition between dissolution of a n-mer and deposition of monomers given from Eq. (1.3.5) as

is rewritten from a kinetic standpoint, k^a c

=k^a

(1.3.10)

where kf is the rate constant of the deposition of monomers to a unit surface area of a (n-l)-mer; kj^ is the absolute release rate of monomers from the resulting n-mer per unit surface area; a^_^ and a^ are the respective surface areas of the (n-l)-mer and n-mer. If a denotes the surface area of a monomer and if a n-mer can be assumed to be a sphere, a„ = a,n^

(1.3.11)

SO that

When the deposition of the monomers is in equilibrium with the dissolution of bulk solid (n = oo),

32

FUNDAMENTALS

k^c

^k^

(1.3.13)

where kj^ is the absolute release-rate of monomers from the bulk solid per unit area. Since c^^^ and kj are constants, kf is a constant independent of n as the number of monomers composing a n-mer. On the other hand, kj corresponds to the release rate of monomers from a bulk solid when the monomers are totally absent in the solution phase. Hence kf, given by ^Qo%(oo)» is not the collision frequency of the monomers of a unit concentration to the surface of a solid per unit area, but the rate constant of the incorporation of the monomers into the surface layer of the solid. As a consequence, it follows from Eqs. (1.3.8), (1.3.12) and (1.3.13) that rO

sOln-l .2/3

2i|f

*n = *«| — 1 exp [3kTn'f^)

(1.3.14)

Hence, k^^ is a function of n. Normally, some monomeric species other than monomers in the molecular form coexist in the form of dissociated ions and complexes coordinated by anions or cations in the solution phase of a heterogeneous system. If c^^o/, kj, and kj denote the number concentration of an arbitrary monomeric species i in equilibrium with bulk solid, its deposition rate constant, and its release rate from the bulk solid, respectively, the overall dissolution rate of the bulk solid per unit area, k„, may be written as Tlk'x' k^^EkL = Ek!,cU=-^C„=k,C^,

(1.3.15)

where x^^^' is the mole fraction of the monomeric species / in equilibrium with the bulk solid, C„ is the total number concentration of the monomeric species in equilibrium with the bulk solid, and k^ is the overaD deposition rate constant for all monomeric species defined by

1. NUCLEATION

33

^d

E ^ _

(1.3.16)

Although k^ and k^ are constants in a given system, each of them may be a function of C„ owing to the change of the activation energy for deposition of the monomers and dissolution of the solid by adsorption of anions and/or cations to the solid surface. Thus, k^ should be determined as a function of C^ by the measurement of the dissolution rate of sufficiently large particles, while k^ can be determined by k^ = kJC„. If C^^^ denotes the total concentration of the monomeric species in equilibrium with a n-mer, C^^^C^ = c^^^c^^^ so that the equation for the overaU absolute dissolution rate of a nmer per unit area, k^, corresponding to Eq. (1.3.14) is given by

K-K

( exp

2^^ I \'ikTn'^^)

(1.3.17)

where K=KC.-

(1-318)

Let us consider the following unit process consisting of a forward reaction of a monomeric species X with a (n-l)-mer, Z^_p and reverse reaction of a n-mer: X . X „ . , . X„.

(1.3.19)

If the average surface charge density of n-mers is assumed to be the same as that of the bulk solid regardless of the n value, the forward reaction rate J^_^^ and reverse reaction rate J^^_^ may be given by

and

34

FUNDAMENTALS

(1.3.21)

^«,n-l = *n^n^n'

where C and c^ are the total concentration of the supersaturated monomeric species and the concentration of the n-mers, respectively. If a quasi-steady state is assumed in the following sequential reaction, in which the concentration of each class of the clusters keeps a steady level, but slowly changes with the change of C: ^1

^2

^n-1

^n

(1.3.22)

^n*

the overall forward reaction rate, J, is given by /i-i,n

ii,/i-i

a n-i

n-l

n n n^

(1.3.23)

where J corresponding to the nucleation rate is independent of n, from the assumption of a quasi-steady sequential reaction. On the other hand, if c^ denotes the concentration of the n-mers in equilibrium with the supersaturated monomeric species, it holds that H-i

n n

(1.3.24)

^A-i from Eq. (1.3.23) with J = 0. (1.3.24), J can be written as

Eliminating it„ from Eqs. (1.3.23) and

J=K°n-f*^n-l

c , n-l _ €

\ ^«-l

c II e

(1.3.25)

^n I

Since J is independent of AZ, the value n in Eq. (1.3.25) can be replaced by w+1, so that Eq. (1.3.25) is rewritten from Eqs. (1.2.7), (1.2.17), and (1.3.18) as

1. NUCLEATION

35

ka

J=

n

( ^n \

I (|)

«xp|-g;|exp

dn

kT

(1.3.26)

e

where the vSurface area of a n-mer, a^, is given by (1.3.27) Eq. (1.3.26) can also be obtain by eliminating k^ from Eqs. (1.2.23) and (1.2.24) and using k„ in Eq. (1.3.17) with Eq. (1.2.17). Since c^/c/ must approach zero as n becomes infinite, it follows from Eq. (1.3.26) that JVn

<

(36nvl)'fXoxp(mT)

(1.3.28) 213^

xjn'^^exp

>MJ^U_ 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 ,

13<|)J

= „'^l.

(1.3.37)

This equation means that (1.3.38)

JocC n%l

in a Hmited range of C. Thus, at least theoretically, it is possible to determine n* from the plot of log J vs log C. Once n* is determined, AG* (= ^n*/2) and \|; (= 3^n*^^^/2) can be calculated. The ratio of steady concentration of n-mer to its equilibrium concentration, cjc^', is given from Eqs.(1.3.32) and (1.3.35) as (1.3.39)

If we use the error function defined by erAx) ^ - ^ f'exp(-)'2)rfy = A

fW")'')^.

(1-3.40)

it follows that

l\xv{-f)dy=^-j\xv{-f)dy=^{l-erm. Hence,

(1-3.41)

38

FUNDAMENTALS

c'n'/2

Fig. 1.12. Distributions of c„ and c/ as functions of fu

(1.3.42)

Specifically, at n = n*, x = 0 and thus cjc^"" = 1/2. Figure 1.12 illustrates c^ and c^"" as functions of n. With respect to the nucleation rate, Becher and Doring^^ derived the following formula: y=

\l/2 ' AG*' 2D In5 exp kT ) d\. \6Tin* ^

(1.3.43)

where D is the diffusion coefficient of solute, d is the diameter of a monomer, and the other notations are the same as those in this book. Afterwards, Zeldovich^* derived the same formula using a mathematically

1. NUCLEATION

39

different method. If we rewrite this equation using Eq. (1.2.13) in order to facilitate the comparison between this equation and Eq. (1.3.35), J ID /=

34)^

exp

'-LG^'

(1.3.44)

kT

One may find a considerable difference between Eq. (1.3.44) and Eq. (1.3.35). As far as the assumption of a quasi-steady state in the sequential reaction of Eq. (1.3.22) is concerned, both treatments are based on the same assumption. They represented J^_^^ and J^^.^ as Jn-,.n = K-l.nClC„.,

(1-3.45)

and

respectively, where c^ is the concentration of the monomers. Since they did not distinguish monomeric species from monomers, c^ in Eq. (1.3.45) may correspond to our C. However, the most serious problem is that the dissolution rate of a n-mer, k^„.i, was postulated to be independent of n. Since A:^^.^ corresponds to k^a^ in our formulation, neither the effect of the increasing surface area a^ nor the size dependence of k^ was taken into consideration. As it is obvious that the dissolution rate of a whole n-mer must increase proportionally with its increasing surface area, this effect cannot be ignored. Also, since ^^^.^ was assumed to be independent of the n value of the n-mer in their theory, k^_^^ was assumed to be size dependent in order to satiwsfy k^_^^c^c^_^^ = k^^_^c^\ However, this treatment basically contradicts the original basis of the Gibbs-Thomson relationship in Eq. (1.3.8), since both the size dependence of k^ Qxk^^_Ja^ in Eq. (1.3.17) and the size independence of k^ or k^,i^/a^_^ have been derived from the GibbsThomson relationship which is based on the greater dissolution rate of a nmer per unit area than that of the bulk solid, owing to the chemical potential of a monomer in the n-mer originally being higher than that in the bulk solid. In addition, k^^_^ was related with the diffusion coefficient of solute, D, and the diameter of a solute molecule, d, as

40

FUNDAMENTALS

This relationship was derived by equating ^^^.^ with the inverse of time, r\ and the root-mean square displacement, )^ with d in the Einstein diffusion equation, k^/^Zt) = D. However, the dissolution process may not be represented by the diffusion model of free monomers, since some activation process of the monomers bound in the surface layer is generally needed for their detachment from the original lattice positions. Incidentally, although the content of jc in Eq.(1.3.42) for cjc^"" is different from that in the corresponding equation of the Becher-Doring theory (x = (lnS/6n*f\n-n*) = {AG/3kT)'^(n/n*-l)), the apparent form of their equation is the same and, similarly, cjc^^ = 1/2 at JC = 0 or n = «*. Experimental measurement of the nucleation rate is often performed by turbidimetry after instantaneous mixing of the reagents,^^'^^ multichannel spectrophotometry in combination with the stopped-flow technique,^^'^ spectrophotometry of products with a streak-camera and photomultiplier synchronized with pulse-radiolysis of a medium,^^'^ etc. However, for the analysis of the nucleation rate or evaluation of the size of the critical nuclei, n*, on the basis of the nucleation theories described in this section, the condition of the quasi-steady state of the sequential reaction of the stationary nuclei must be established, since these nucleation theories are all based on this presumption. In order to realize this premise, the monomers must be furnished steadily from some reservoir involved in the system. Otherwise, what we follow is the extremely fast reaction of forming transient complexes, non-steady nucleation at the expense of the precursor complexes, and subsequent Ostwald ripening of the nuclei preformed by the non-steady nucleation, any of which the quasi-steady nucleation theory cannot be applied to. Thus it may be necessary to reassess past experimental data from this viewpoint. In addition, it must be noted that the quasisteady nucleation process is not independent of the concurrent growth of the nuclei. Rather, the nucleation rate is determined by the growth of the preformed nuclei, and is closely related to the size control of general monodisperse particles, as will also be shown in the following section.

1.4. The Nucleation Process in Closed Monodisperse Systems

1. NUCLEATION

41

In this section 1.4, the theory of the spontaneous nucleation process in closed monodisperse systems and its application to closed systems for the formation of monodisperse AgCl and AgBr particles are described.^^'^'' 1.4.1. Theory In a typical monodisperse particle system, the monomeric species are initiaUy accumulated in the system through some reaction from a reservoir of the monomeric species involved in the system. In this stage, no appreciable nucleation occurs, even if the concentration of the monomeric species exceeds the solubility level of the bulk solid (prenucleation stage). When the concentration reaches a critical level for nucleation (critical supersaturation level), the nucleation virtually starts to be observed (the start of the nucleation stage). In this stage, the nucleation rate is rather low, so the concentration of the monomeric species continues to increase, though the increasing rate is a little lowered due to their consumption for nucleation. However, as the concentration still increases, the nucleation is drastically accelerated and, finally, the concentration of the monomeric species reaches the maximum level (maximum supersaturation). At this stage, the generation of the monomeric species and their consumption by nucleation and the growth of the preformed nuclei is balanced. After that, the concentration of the monomeric species starts to be reduced, due to the increasing consumption of the monomeric species by growth of a number of the preformed nuclei. When the concentration of the monomeric species goes down to the critical supersaturation level again, the nucleation is terminated (the end of the nucleation stage). Even after the end of the nucleation, the remaining stable nuclei can continue to grow with a supersaturation below the critical level for nucleation (growth stage), because the two-dimensional nucleation on the growing particles does not need as high a supersaturation as the three-dimensional nucleation (see chapter 2). When the concentration of the monomeric species becomes close to the solubility level of the bulk solid, the particle growth finishes. The change of concentration of the monomeric species may be illustrated by Fig. 1.13, where C^^ corresponds to the critical level for nucleation. This is the so-called LaMer diagram proposed by LaMer and Dinegar^ for presenting the formation process of monodisperse particles in a simple diagram. For the preparation of monodisperse particles, the nucleation stage should be as short as possible and the renucleation in the growth stage should strictly be inhibited. The distinct separation between the nucleation and growth stages is normally the first requirement for the formation of monodisperse particles of an excellent uniformity. It

42

FUNDAMENTALS

Time Fig. 1.13. LaMer diagram. The regions I, II, III represent prenucleation stage, nucleation stage, and growth stage, respectively. (From: Ref. 23.) must be noted, however, that a clear-cut critical supersaturation level cannot be defined, because the nucleation event is basically a probability process. Thus, when the concentration of the monomeric species exceeds the solubility level of the solid, there is always some probability of nucleation. Nevertheless, the simple LaMer diagram is helpful for understanding the general rule of monodisperse particle formation. From the above insight into the nucleation stage of monodisperse particles, the duration of the nucleation period is obviously governed by the rate of consumption of the monomeric species by growth of the preformed nuclei. Hence, we have to formulate a nucleation theory in conjunction with the growth of the nuclei. The study of ref. 26 is a trial to formulate the nucleation theory from this viewpoint. The aim of this study was to establish the background for the mechanism of automatic size control of the monodisperse particles in open systems, in which the reactants, as sources of the monomers, are introduced from outside and the particles are grown by a kind of the Ostwald ripening through the dissolution of a part of the nascent nuclei instantly generated in a limited zone into which the reactants are introduced. This theory was verified in the formation process of monodisperse AgBr particles in the controlled-double-jet precipitation

1. NUCLEATION

43

system. For the extension of the theory of nucleation in open systems to general closed systems in which the particles are generated through the spontaneous nucleation, it seems necessary to modify the theory using the concept of the quasi-steady spontaneous nucleation theory described in the foregoing section. Figure 1.14 illustrates an evolution of the size distribution of the stationary nuclei with the increasing concentration of the solute continuously generated or supplied from an internal reservoir. Figures 1.14(a) and (b) correspond to the prenucleation stage up to the onset of the nucleation of stable nuclei and the nucleation stage of the stable nuclei, respectively, where / is the frequency or distribution function of the size distribution, r is the particle radius of a nucleus, r* is the particle radius of a nucleus whose solubility is equal to the current concentration of the solute, as related by the Gibbs-Thomson equation, and r^* is the minimum r* at the maximum supersaturation. If the solute concentration is denoted by C, r* decreases with increase of C and increases with the reduction of C. The stable nuclei are defined as relatively large nuclei, mostly greater than r* in

Fig. 1.14. The evolution of the size distribution of the stationary nuclei and the change of r* with time in the prenucleation and nucleation stages of the stable nuclei. The dashed curve in (a) represents the extension of the predetermined steady distribution of the stationary nuclei at the maximum supersaturation. The D.F. is the distribution front of the propagating stationary nuclei: (a) prenucleation stage; (b) nucleation stage. (From Ref. 23.)

44

FUNDAMENTALS

radius, to be grown to the final product, in contrast to the relatively smaU unstable nuclei with r around r* or mostly less than r*, to be eventually dissolved. However, this distinction between the stable and unstable nuclei is only a matter of probability. Namely, some nuclei in a size class are stable nuclei to be grown to the final product, while the other nuclei in the same size class are unstable nuclei to be finally dissolved. Nevertheless, the probability to become stable nuclei increases with the increase in size. According to the classical nucleation theory in section 1.3, the size distribution of the stationary nuclei in a quasi-steady state is in the form of a monotonously decaying curve from the monomer level to the infinite size. In a real nucleation system, however, there must be an upper size limit in the distribution, and the upper size limit or distribution front (D.F.) must continue to advance to complete the predetermined steady distribution curve proper to the supersaturation. The nucleation rate, J, is equivalent to the generation rate of the largest nuclei at the distribution front. Thus, if the particle volume of the largest nuclei is denoted by v^^^y the consumption rate of the solute for the quasi-steady propagation of the stationary nuclei is equal to Jv^JV^ in molarity. In other words, the consumption rate of solute increases with increasing v^^^, even if C and thus J are unchanged, and hence the increasing consumption rate with the increase of C is accelerated by this effect. However, since the supply rate of monomer, Q, is greater than the consumption rate, Jv^^JV^, in the prenucleation stage, the concentration of the solute, C, must increase as

dt

V^

As C rises up to the critical supersaturation level close to the maximum supersaturation, r* is lowered to be close to r^* and the nucleation may start to be observed. Due to the critical dependence of the nucleation rate on supersaturation, the nucleation is dramatically pronounced with a slight increase of C in this stage and C soon reaches its upper limit or the maximum supersaturation, corresponding to f^ in Fig. 1.1.4. At this moment, r'^'^r^* and dC/dt=0, so that ^

m

max

For maintaining the J constant at the maximum supersaturation, Q is required to increase with the increase of v^^^^. However, if Q is constant or

1. NUCLEATION

45

its increasing rate is small, J must start to be declined, since v^^^ unconditionally increases with the growth of the largest nuclei, owing to the much lower solubility of the largest nuclei with radius r^^^ than the supersaturation level (/.e., r^^^ > r*). With the declining steady nucleation rate, J, the distribution function in the relatively small size range is lowered, but the distribution front continues to advance. Hence, a considerable amount of the stationary nuclei, preformed and grown into the range greater than r*, may return to be dissolved even though r* remains close to r^*. It seems noteworthy that a considerable number of once generated nuclei of r > r* are dissolved through a kind of Ostwald ripening even in the closed system. In contrast to the ordinary Ostwald ripening, even a nucleus of r > r* has a high probability of dissolution, since the absolute value of r is sufficiently small. Finally, J becomes virtually zero at the end of the nucleation stage and the size distribution is split into two and the distance between the two distribution groups is enlarged with the progress of the growth process. The supersaturation kept near the maximum supersaturation level during the nucleation of the stable nuclei gradually declines in the growth stage with the growth of the stable nuclei. As is obvious from the description of the nucleation process, the starting point of the nucleation is not definite. However, if one considers that the stationary nuclei always exist even at a solute concentration level below the critical supersaturation and that some nuclei once generated are dissolved again, it seems rather reasonable to define the "nucleation" in general as the "generation of the stable nuclei." One may assume that the nucleation in this definition starts when C reaches the maximum supersaturation. In any case, soon after the maximum supersaturation, the relation of Q = Jv^JV^ loses its quantitative significance, since the system is not in the quasi-steady state of the stepwise propagation of the stationary nuclei anymore, on which the relation is based. Hence, we need to find a new approach to the nucleation process after the maximum supersaturation. For this purpose, one may divide the consumption of the supplied solute into two components; Le., the generation of the stable nuclei and the growth of the generated stable nuclei:

The first term in the right-hand side is the component for the generation of the stable nuclei and the second term is the component for the growth of

46

FUNDAMENTALS

the generated stable nuclei, where VQ" is the initial particle volume of the stable nuclei, equivalent to v^^^ at the moment of the maximum supersaturation, v^ is the mean volumic growth rate of the stable nuclei, n^ is their number density, and QQ is the supply rate of the solute which is assumed to be kept constant during the short nucleation period. As we set the initial conditions as n = 0 and dnjdt = J = QQVJV^^ at r = 0, the stable nuclei in this model are defined as those generated after r = 0 and thus greater than v^^ in particle volume. The increment of the particle size of the stable nuclei, relative to the initial size (= v^^ in particle volume), is thought to be sufficiently small in the nucleation stage, since the supplied solute is mainly consumed for the increase in the number of the stable nuclei. Thus, i)^ may be regarded as nearly a constant during nucleation stage, since v^ is a function of the maximum supersaturation and the mean particle volume of the stable nuclei. Hence, one may describe the behavior of n^ as a function of time by using the time-averaged i)^ in Eq. (1.4.3) as

„..«^ 1-exd

-vj

(1.4.4)

0

/J

As a consequence, the final particle density at r = <», AI^°°, is given from Eq. (1.4.4) as O V n:=-^^.

(1.4.5)

This is the fundamental equation for size control of monodisperse systems.«'^^'2^'^« As has been mentioned earlier, the nucleation rate, J(= dnjdt\ is given by J^ = Go'^m/'^max ^^ * ^ maximum supersaturation. If <2o is varied, J may adjust itself to the change of j2o by only a slight variation of the maximum supersaturation level by virtue of the critical dependence of J o n supersaturation. In other words, the difference in the maximum supersaturation level with the variation of j2o is very small. However, even if the difference is extremely small, the difference between the maximum supersaturation level and the critical or minimum supersaturation level for nucleation may be proportional to j2o- ^^ addition, if dCldt is proportional to go, the time required for reaching the maximum supersaturation from the critical supersaturation must be the same, irrespective of the Q^ value. In this case.

1. NUCLEATION

47

'^max ^^ ^he maximum supersaturation, or v^^, is a constant, irrespective of QQ, and thus the increase of the mean particle volume of the stable nuclei thereafter is independent of QQ. When both the maximum supersaturation and the mean particle volume of the stable nuclei are independent of QQ, V^ is also independent of QQ, The variation of QQ without the change of v^ may be possible by controlling the release rate of the reactants from an internal reservoir for the generation of the monomer, without changing the initial composition and temperature. On the other hand, i)^ may be varied independently of QQ by addition of some accelerators of growth such as solvents of the solid, or restrainers such as strong adsorptives to the solid surfaces. In these cases, Ai^* is expected to be proportional to QQ and inversely proportional to v^, leading to the precise control of the final particle size by changing a single factor of either go or TJ^.. On the other hand, if we vary QQ by changing the initial composition or the temperature, v^ is normally varied at the same time and hence, in this case, the hnear relationship between «^" and QQ or 1/v^ may not be observed. Nevertheless, there is no direct interdependence between QQ and v^ during the nucleation period, and Eq. (1.4.5) may always hold even if v^ and QQ are varied simultaneously by changing the initial composition or the temperature, as is obvious from the derivation procedure of Eq. (1.4.5). Eq. (1.4.5) suggests an important conclusion that the final particle density, w^°°, is determined only by QQ and i)^, irrespective of the momentary nucleation rate, dnjdt, and the size of the generated stable nuclei. This is in contrast to the conventional elucidation of the final size of colloidal particles in closed systems, in which the nucleation rate is treated as the major factor for determination of the final particle density or, at least, as an essential competitive factor on equal terms with the growth rate, and the supply rate of solute is usually not taken into account. Probably, this is because the concept of the mass balance at a constant feed rate of solute is not involved in conventional nucleation theories. The growth-limited nucleation is the key concept in the fundamental approach to the principle of size control of coUoidal particles. Figure 1.15 illustrates the change of n^ as a function of time. Here tj^ in Fig. 1.15 is a time constant given by tj^ = n^'^/(dnjdt\^ = n^"v^7Qo^m = v^^/v^. As long as QQ can be regarded to be constant throughout the nucleation and early growth periods, it holds for the time t from the start of the nucleation that

48

FUNDAMENTALS n. r1 : 1 \

'1 1 :

•^ CO

c O

'^ CO

/

1 / 1 /:

'/ •

//

if

Q.

^

Time

Fig. 1.15. Change of «+ as a function of time, where r^ is a time constant corresponding to the nucleation period. (From Ref. 23.)

QoVJ = ".^.-

(1.4.6)

where v^ is the average volume of all nuclei at time t. Thus, Eqs. (1.4.4) and (1.4.6) yield

(i) J] 0 +

(1.4.7)

0 +

1-exp

n

\

1

'* }

The change of v^ during nucleation is small, as shown in Fig. 1.16. However, the end of the nucleation is more indefinite than its start. If t until the intersection between the straight lines, vjv^^ = (vjv^^t and vjv^^ = 1, is defined as the nucleation period /^, r^ is given by

^N=—•

(1.4.8)

Since tj^ is determined only by u^° and i)^, the nucleation period as a

1. NUCLEATION

49

determinant of monodispersity is basically independent of QQ,

vjv:

D.

D.

Fig. 1.16. Change of vjv^^ as a function of time. (From Ref. 23.)

1.4.2. AgCI and AgBr Systems a) AgCl Systems The experimental system for the spontaneous nucleation of silver chloride particles is based on an idea that the spontaneous nucleation may be triggered if silver ions are gradually released from their gelatin complex by lowering the pH with hydrolysis of diethyl sulfate (DES), in the presence of chloride ions. In addition, gelatin as a powerful protective colloid is expected to prevent the coagulation of the generated AgCl particles. Moreover, it may be possible to directly follow the change of supersaturation as a function of time with a Ag/Ag2S electrode (Ag2S-coated Ag electrode).^ The reaction is started by adding DES to 400 cm^ of a transparent gelatin solution containing AgN03, KCl, and KOH at pH 10.8 in a 500-cm^ Teflon

50

FUNDAMENTALS

beaker in a water bath at a constant temperature. The solution is continuously agitated by a magnetic stirrer. The change of the silver potential is followed with a Ag/Ag2S electrode connected with a Ag/AgCl reference electrode ([KCl] = 0.010 mol dm^^) through a salt bridge of 1.5 % agar containing 2 mol dm'^ KNO3 solution. The change of pH is followed, at the same time, with a glass electrode with a double junction reference. All experiments are conducted under a red light to avoid the possible photolysis of AgCl particles. Produced particles are all uniform cubes. An inert deionized gelatin is used in all cases as a 2.0 w/v % solution. In the standard system, the concentrations of AgN03, KCl, and KOH in the gelatin solution are 2.0 x 10"^, 2.0 x 10-^ and 7.0 x 10"^ mol dm-^ respectively; the reaction temperature is 25°C; the added volume of DES is 1.0 cm^, which corresponds to 1.8 x 10"^ mol dm"^ in the final solution. In addition, potentiometry was also carried out in a system without KCl, as a control. Out of the results for the effects of the added amount of DES in the range of 0.5 to 2.0 cm"^, of the initial concentration of KCl ranging from 2.5 X 10""* to 4.0 X 10"^ mol dm"^ and of the reaction temperature varying from 25 to 40 °C,^ only the effects of the DES content, or the Q^ value, on the maximum supersaturation ratio and the final particle density, in addition to the results obtained under the standard conditions, will be described in this book. Nucleation under the Standard Conditions Figure 1.17 shows the [Ag*] and pH changing with time in the presence or absence of KCl under the standard conditions. There is almost no effect of KCl on either the pH curves throughout the experiments or [Ag^]-curves until the start of nucleation. We can clearly observe the typical changing pattern of supersaturation in the [Ag*]-curve, like the LaMer diagram illustrated in Fig. 1.13, when KCl is present. Figure 1.18 shows the changes of the supersaturation ratio, 5, and the amount of the precipitated solid, P, obtained from the analysis of the [Ag^]curve of the standard system in Fig. 1.17. The supersaturation ratio, S, is defined as S^Wmi

(1.4.9)

where [Ag^] and [CI"] are the concentrations of free Ag" ions and CI" ions.

1. NUCLEATION

51

Fig. 1.17. Time evolutions of Ag"^ concentration and pH in the standard AgCl system (solid line) and in KCl-free system (dotted line). (From Ref. 23.)

4

2.5 2.0

3

«? E 1.5

CO

2

T3

E 1.0 o

1h

H 0.5

30

60 Time (min)

90

0.0 120

Fig. 1.18. Supersaturation ratio, S, and molarity of precipitated AgCl, P, as a function of time in the standard system. (From Ref. 23.)

respectively; K^ is the solubility product of AgCl. Particularly, the maximum supersaturation, S^, corresponds to S at [Ag*]„,ax- Th^ amount of the precipitated solid, P, can be calculated from the total silver ion

52

FUNDAMENTALS

concentration and the remaining portion linked to gelatin, the latter of which is a function of pH and [Ag*], and thus can be evaluated from the changing pH and [Ag"]. On the other hand, the supply rate of the monomer in the nucleation period, QQ, is obtained from the product of the tangential slope of the curve of [Ag^] vs t at [Ag^]^3^ in Fig. 1.17 and the ratio of the total concentration of free solute to [Ag^], as a function of [CI"]. When Q^ is obtained, i)^ can be calculated from Eq. (1.4.5) with <2o ^uid AZ^" obtained from electron microscopy on the final product. Hence r^ and i;+° (= 4jt(r^^V3) can be calculated numerically from the following relationship with the data of 1)+, S^, y (specific surface energy of AgCl = 100.9 mJ m"^),^ C(«) (solubility of the bulk solid), and D (diffusivity of the solute obtained from the analysis of the growth process): ^»-«p

i'2-yV\ rlRT

(1.4.10)

n

Finally, r^* and the minimum free energy for nucleation, AG„*, are obtained from the Gibbs-Thomson relation; 2Yn, KHaS.

(1.4.11)

and

171

(1.4.12) 3(/?nn5j2

respectively, where AG„* corresponds to the energy barrier for nucleation at the maximum supersaturation. The nucleation time, /^, is obtained from Eq. (1.4.8) with v° and ti,. As a result, one obtains: j2o = 5.95 x 10'* mol dm'^ s"\ 5„ = 3.56, r„* = 1.66 nm, ^GJ = 1.16 x 10''* J, n' = 5.88 x 10^" dm"^ (d' = 552 ran), i)^ = 2.62 X 10^ nm^ s'S r° = 5.28 nm, v+° = 618 nm^ and t^ = 0.236 s in the standard system, in which the total silver ion content [Ag*]^ = 2.0 x 10"^ mol dm-^ [Cl-]o = 2.0 x 10"^ mol dm'^ [DESJo = 1.81 x lO'^ mol dm-\ [gelatin] = 2.0 w/v %, temperature 25 °C, initial pH 10.8, K^ = 1.77 x 10"^°

1. NUCLEATION

53

moP dm"^ initial C(«) = 5.04 x 10"^ mol dm•^ and i) = 1.44 x 10"^ cm^ s'K Effects of QQ Figure 1.19 shows the effect of the DES content on the time evolution

o 4 CO

2.0

1.6

1.0

0.75

0.50 cm3

3 2 1 n

30

60

1 90

1 120

Time (min) Fig. 1.19. Effect of the DES content in 400 cm^ of the gelatin solution on the time evolution of the supersaturation ratio in the AgCl system. (From Ref. 23.)

5

10

15

20

Qo(10-® mol dm-3 s-1) Fig. 1.20. Linear relationship between Qg and n^" by variation of [DES](, vmder otherwise the standard conditions in the AgCl system. (From Ref. 23.)

54

FUNDAMENTALS

of the supersaturation ratio. Obviously, the maximum supersaturation ratio is little affected by the variation of the DES content due to the critical dependence of the nucleation rate on the supersaturation. Figure 1.20 shows an excellent proportionality of n^" to QQ changed by varying the initial content of DES, [DES]o, which supports the assumption that v^ is a constant independent of QQ, b) AgBr Systems The experimental and the analytical procedures of the present AgBr systems are basically the same as the above AgCl systems, based on the gradual release of Ag^ ions from the Ag*-gelatin complex with the reduction of pH by the hydrolysis of diethyl sulfate (DES) in the presence of Br" ions. The change of the supersaturation ratio is monitored by potentiometry with a Ag/Ag2S electrode coupled with a Ag/AgBr electrode ([KBr]=0.010 mol dm~^) as a reference. Produced particles are all uniform cubes.^"* The standard conditions of the AgBr system (400 cm^) are: [AgN03]o = 2.4 X 10-^ mol dm-^ [KBr]o = 2.4 x lO"^ mol dm-^ [KOH]o = 7.0 x 10"^ mol dm-^ (initial pH 10.8), and [gelatin] = 2.0 w/v %, [DES]o = 1.0 cmV400 cm^ (1.8 X 10"^ mol dm"^), and temperature 25°C. Here, K^ = 4.88 x 10'^^ moP dm-^ initial C(„) = 2.04 x 10"^ mol dm"^ and Z) = 1.04 x 10"^ cm^ s'^ Out of the effects of the initial content of DES, initial concentration of KBr, and reaction temperature, examined in the ranges of 0.5 - 3.0 cm^, 3.0 X 10"^ - 3.6 X 10"^ mol dm-^ and 25 - 40°C, respectively,^^ only the effects of the initial content of DES, as well as the results under the standard conditions, will be described. Nucleation under the Standard Conditions The Jesuits in the AgBr standard system are as follows: QQ = 2.95 x 10"^" mol dm-^ s-\ S^ = 3.61, rj = 1.97 nm, ^GJ = 1.79 x 10"^' J, /i," = 1.66 X 10'^ dm"^ {d,^ = 92.9 nm), i), = 5.15 nm^ s\ r," = 2.12 nm, -u^" = 39.9 nm^, and ^^ = 7.74 s. The very low Q^, compared to that in the AgCl system, is due to the much lower solubility product of AgBr, which limits the total silver ion content to a much lower level. The small values of i)^ and r^ are also due to the low solubility of AgBr. However, it is noteworthy that S^ and r^* are rather close to those in the AgCl system. Ejfects ofQo Figure 1.21 shows the time evolutions of the supersaturation ratio with

1. NUCLEATION

55

CO

120

Fig. 1.21. Effect of the DES content in 400 cm^ of the gelatin solution on the time evolution of the supersaturation ratio in the AgBr system. (From Ref. 24.) different contents of DES in the range of 0.50 - 3.0 cm^ in 400 cm^ of the gelatin solution. In a similar manner to the AgCl system, the peak of S appears earlier with the increasing content of DES, due to the earlier arrival at the pH level necessary for the maximum supersaturation. However, in contrast to the AgCl systems, S^ is significantly lowered with the decreasing content of DES or with the decreasing QQ. Since the nucleation rate in general strongly depends on the supersaturation, the maximum supersaturation is almost constant for QQ above a certain minimum value. However, if the supersaturation approaches the maximum supersaturation level with a QQ smaller than the minimum value, QQ must be balanced with the nucleation rate at a supersaturation below the maximum supersaturation. Such a trend is expected in a system in which QQ is very small. In the AgBr systems, the original content of Ag^, [Ag'^Jg, is lower than in the AgCl systems by a factor of 0.12 due to the limitation of the solubility of AgBr, so that QQ values in the AgBr systems are much smaUer than in the AgCl systems. The Qo-dependent S in the AgBr system is observed for this reason. The v^^ and v^ of the stable nuclei generated under a relatively low supersaturation are somewhat larger than those obtained with a sufficiently high supersaturation. Figure 1.22 shows the linear relationship between the final particle density, n^"", and QQ, as in the AgCl systems. The slightly upward deviation of «^" with the increasing QQ is due to the relatively large i)^ in the low QQ

FUNDAMENTALS

56

5

10

15

Qo(10-''0moldm-3s-'») Fig. 1.22. Relationship between Qo and «^" by variation of [DES]o under otherwise the standard conditions in the AgBr system. (From Ref. 24.)

range, which is caused by the enlarged v^^ in the low QQ range. c) Discussion Klein et al}^ determined the critical supersaturation ratio, 5^„.^, by conductometry in a system of homogeneous precipitation of AgCl in the excess of Ag"^ ions, using the hydrolysis of alkylchloride as a source of CI" ions. They found 5,„,= 1.51, 1.73, and 1.85 at 15, 25, and 35°C, respectively, where S = ([Ag'][Cr]/iC,^)^^ by their definition. If this definition of supersaturation ratio is converted into ours {S s [Ag*][Cr]/K^^), the results correspond to 2.28, 2.99, and 3.42, respectively, in fairly good agreement with the results of the present study. However, the temperature dependence of the 5^„.^ is opposite to that of the present study. Though the cause of this contrariety is not clear, the reduction of 5,„.^ with the increase in temperature may be rather reasonable, since the nucleation rate is drastically changed with a slight change of AGJ/kT, and thus AG^*/kT, which is in proportion to r^(ln5^)-^ from Eq. (1.4.12), is deemed to be kept nearly constant with the change of temperature in a given system. Incidentally, the definition of S must be [Ag'][Cl']/K^p, since the supersaturation ratio in terms of the monomer concentration, [AgCl], is originally given by S = [AgCl]/[AgCl](„) = [Ag1[Cr]/X,^.

1. NUCLEATION

57

Tanaka and Iwasaki^^'^^ studied the nucleation process of AgCl and AgBr particles using the stopped-flow technique coupled with a multichannel spectrophotometer, which is useful for studying a rapid process of the order of msec. They found that some specific silver halide complex of AgX^^'""^^" having a rather narrow UV absorption band was formed instantly on mixing a AgC104 solution of the order of IQ-^mol dm"^ with a KX (X = CI or Br) solution of the order of 10"^ to lO'^mol dm"^ followed by its rapid decay of the order of 10 ms while forming an intermediate product having a broad UV absorption and much slower change in the spectrum of the intermediate. They interpreted the intermediate product as monodisperse nuclei, (AgX)„, consisting of n molecules, and determined n from the apparent relationship of -dCldt oc C" at r = 0, for varying initial concentrations, C, of the precursor AgXj""'^- {n = 7-10 for AgCl; n = 3-4 for AgBr). However, since the precursor, AgX^^'""^^", decays in a non-steady way, the quasisteady nucleation theory does not apply in this nucleation process, and thus the so-obtained n value does not correspond to the n* value of the critical nuclei. If the intermediate product comprises monodisperse nuclei of n formed at the expense of the monomeric complex, the relation of -dC/dt oc C may not hold unless we assume that clusters smaller than the n-mers are in the equilibrium, ^f.i/f.iC^ = Z^^^.^c., with each other in the sequential reaction of c^-*C2-*C3-^ **—*c^_^-*c„, and only the last step of c^^^-^c^ is irreversible; Le,, c^^C2^c^^'"^c^_^'^c^. In addition, the concentrations of the clusters from 2 to n-1 must be assumed to have negligibly low equilibrium concentrations. However, there seems to be no reason for justifying these assumptions. On the other hand, we tried to calculate the radii of the critical nuclei and the supersaturation ratios S at the end of the rapid process, using y = 101 mJ m'- for cubic AgCP^ and y = 109 mJ m"^ for cubic AgBr^° on the assumption that the n values thus obtained, 7-10 for AgCl^^ and 3 - 4 for AgBr^°, are equivalent to the size of the monodisperse nuclei, «*. As a result, we found I r* = 0.451 nm and S = 105 for AgCl with n* = 9; r* = 0.358 nm and 5 = 1230 for AgBr with n* = 4. Since their systems are comparable to those of Davies and Jones^° who obtained the critical supersaturation of AgCl around 1.7-2.0 at 25 °C by conductometry on direct mixing of equal volumes of dilute AgNOg and KCl aqueous solutions, the extremely high S values may not represent the actual supersaturation ratios in equilibrium with the intermediate nuclei. It seems more reasonable to attribute the intermediate product with the broad UV absorption to nuclei of a much larger mean size with a broad sizedistribution generated by a non-steady sequential reaction. The subsequent

58

FUNDAMENTALS

slow change of the intermediate nuclei seems to be due to their Ostwald ripening. In the above context, Nielsen^^ also obtained similar n* around 12, and corresponding S greater than 10^ for the nucleation of barium sulfate particles, from measurements of the turbidity as a function of supersaturation, using «* = dlogl/dlogC in the Becher-Doring theory, similar to Eq. (1.3.37) but giving (n* + 1) instead of n*. Since the solutions of barium ions and sulfate ions were directly mixed in this experiment, the fast nonsteady nucleation must have finished immediately after the mixing, and what was measured might be the rate of the slow succeeding Ostwald ripening and/or coalescence of the generated nuclei. This seems to be the reason for the unreasonably small n* value and the extremely high supersaturation. Hence we must note again that some reservoir of monomeric species which releases them in response to their consumption is always needed for the achievement of the quasi-steady nucleation in a closed system. All classical nucleation theories, including the Becher-Doring theory, implicitly presume such a condition. Hayes et al?^ studied the non-steady nucleation process of silver halides by pulse-radiolysis of water containing a methylene halide and silver ions, in which methylene halide was decomposed to release halide ions by the hydrated electrons generated by pulse radiation ranging from 4 ns to 3 [xs. The spectra of the products were recorded with a photomultiplier and streak camera, and it was found that the monomeric precursors of the silver halides were formed within a time of the order of [is, followed by a nucleation process similar to that observed by Tanaka and Iwasaki^^*^^. Their results clearly show that the nucleation process of silver halides by direct mixing of the reactants consists of two elementary steps; le,, the formation of a monomeric precursor in the order of [JLS, and a subsequent transition to nuclei in the order of 10 ms. It should be noted that the mean size of the nuclei is around 10 nm. As to the supersaturation ratios for the nucleation of AgCl particles in open systems, in which high concentrations of reactants such as AgN03 and KCl are continuously introduced into a gelatin solution throughout the precipitation. Strong and Wey'^ reported 1.029 (SOX) - 1.260 (40°C) and Leubner^^ reported 1.024 at 60°C, as estimated from the measurement of the growth rate of AgCl seed particles at the critical supersaturation. On the other hand, for open systems of AgBr particles, some estimated values of the critical supersaturation ratio, S,„.^, have been reported: S,„.^ « 1.5 at 70 °C by Wey and Strong^^ from the size-dependent maximum growth rate

1. NUCLEATION

59

determined by finding the threshold of renucleation in varied addition rates of a AgNOg solution with a KBr solution in the presence of seed particles by the double-jet technique; S^„.^ = 1.2-1.5 at 25°C by Jagannathan and Wey^"^ as the maximum supersaturation ratio determined on the basis of the Gibbs-Thomson equation with their data of the minimum average size of nuclei observed by electron microscopy during the nucleation stage of double-jet precipitation of AgBr. In the calculation of these 5^„., values, they assumed y = 140 mJ m"^. Since the nucleation in open systems corresponds to a survival process of nascent embryos generated in a local zone of an exceedingly high supersaturation near the outlets of the reactants, the critical supersaturation corresponds to the concentration of the solute in equilibrium with the embryos of the maximum size. If we employ the data of Sugimoto^^ on the maximum radius of AgBr embryos in open systems (« 8.3 nm) with the theoretical y for cubic AgBr (= 109 mJ m'^f, the critical supersaturation ratio, 5^„.p is calculated to be 1.36 at 25°C (if y is assumed to be 140 mJ m"^, then S^^.^ = 1.48). Hence, in any case, the critical supersaturations in open systems of silver halide particles are generally much lower than the maximum supersaturations (probably close to the critical supersaturations) in closed systems. This is because the mean radius of the embryos generated in a local zone of an open system is much larger than r^* in a closed system, probably due to instantaneous coalescence of the highly concentrated primary embryos in the local zone of an open system with a high local concentration of the electrolyte.

1.5. The Nucleation Process in Open Monodisperse Systems In this section we deal with the nucleation process in open systems in which reactants are continuously supplied from outside.^ In this sense, open systems can be regarded as particle-formation systems having at least one of their own reservoirs of monomeric species outside them in contrast to closed systems. The theory of nucleation in open systems and its application to the real systems of AgBr particle formation will be described in sections 1.5.1 and 1.5.2, respectively. For simplicity, we assume that the reservoirs of the reactants are both located outside them and that the reactants are introduced simultaneously into the reaction vessel containing a certain volume of well stirred liquid medium. In this case, the outlets of the two reactant solutions are set close to each other in order to confine the initial reaction to a limited local zone. We usually call this kind of

60

FUNDAMENTALS

precipitation mode "double-jet precipitation" from the characteristic way of introduction of the reactants (see section 8.1.1).^'^^'^^ 1.5J. Theory Nucleation Model The most salient characteristic of open systems is that non-steady nucleation occurs instantaneously in a domain into which the reactants are introduced due to the extremely high supersaturation, as is obvious from the discussion in the preceding section. If we call the nascent nuclei "embryos," the introduction of the reactants is equivalent to that of the embryos. The embryos are first dissolved, but as the monomeric species are accumulated by the dissolution of the embryos, some of them may start to grow, owing to the increasing supersaturation. Hence, the growth and dissolution of the embryos must proceed basically through the Ostwald ripening. Since the embryos are constantly furnished and built up as stationary nuclei, the stationary nuclei will reach a quasi-steady state of balance between generation and either dissolution or growth and a part of them will grow to become stable nuclei as the origin of the final product particles. The overall insights may lead to the following general scheme for the nucleation process in an open system. As the addition of the reactants starts, the generated embryos may simply be dissolved to saturate the bulk solution, but only a slight dissolution may be sufficient for a sparingly soluble solid to achieve the saturation. Following a certain time of accumulation of the stationary nuclei in a non-steady state of change in their size distribution function, most of them existing in the size range of the embryos must reach a quasi-steady state of the balance between generation and either dissolution or growth. The nuclei of radius less than the critical radius r* dissolve, while those of radius greater than r* grow. In this stage, the other nuclei that have grown to exceed the size range of the embryos may continue to grow and increase in number at the expense of the stationary nuclei remaining in the size range of the embryos: the former are defined as "stable nuclei," and the latter as "unstable nuclei." Accordingly, the critical radius, r*, initially infinite, must plummet to approach the mean radius of the embryos due to the unilateral dissolution of the generated nuclei, then turn to be lifted by degrees with the growth of the increasing stable nuclei, and eventually reach the maximum radius of the embryos, r^. Since the nucleation may be defined as the formation of the stable nuclei, this is the end of the nucleation stage. After this moment, r* exceeds Tp,

61

1. NUCLEATION

and the growth stage ensues at the same time, during which the growing stable nuclei {r>r^) cease to increase in number and the unstable nuclei (r^p) remain in a quasi-steady state of the balance between their generation and unilateral dissolution. The model of the nucleation process is illustrated in Fig. 1.23, where the bold arrows represent the flows of monomeric species through the solution phase and the growth of unstable nuclei into stable ones. MONOMERS

^-r To

Fig. 1.23. The model of the nucleation process in an open system. (From Ref. 26.)

The Distribution Function and Number of the Unstable Nuclei Generally, the change of the distribution function f(r,t) of the existing nuclei is given by

df

d(ff) .,

,.

(1.5.1)

where NQ is the number of the embryos generated per unit time, and g{r) is the normalized distribution function of the embryos. Since the generation of the embryos occurs in a limited local zone, A^^, is independent of the total volume of the system, and thus it is more convenient to express NQ by the

62

FUNDAMENTALS

total number of embryos rather than by the number concentration in open systems. Therefore, / has a dimension of reciprocal length. In the quasisteady state of the unstable nuclei {dfldt « 0), Eq. (1.5.1) for the unstable nuclei is reduced to diff) ^N.g(r) = 0. dr

(1.5.2)

If we assume that the growth and dissolution rates of the stationary nuclei are limited by the diffusion of the monomeric species, the diffusion-limited growth rate or dissolution rate, r, is given by DV_ r=

IDyVlC^

•(C-C^)-

r-r'

RT

(1.5.3)

r'r'

where C is the concentration of the monomeric species, and Q is the solubility of a particle of radius r, since (

(^yv.\ [rRT)

C = C.exp

2YK„^ 1+——^ r*RT)

(1.5.4)

and C.-C

1+

2Y^] rRTJ

from Eq. (1.3.8) (Gibbs-Thomson equation). (1.5.2) and (1.5.3) yields Jir,t)-

RTN,0

(1.5.5)

The combination of Eqs.

r

r-r ""^

(1.5.6)

-j;,8ir)dr. Vo

r-r

where v^ is the mean volume of the embryos (as (4jt/3)/oVg(r)rfr), given by

1. NUCLEATION

63

«o =

OK

(1.5.7)

and n^ is a dimensionless constant defined by ^ .

QRT

(1.5.8)

Q in Eqs. (1.57) and (1.58) is the feed rate of the reactants, equivalent to that of the monomeric species with dimensions of mol s"\ different from the dimensions of the supply rate of the monomeric species in closed systems, mol dm"^s'\ Here we simulate the nomialized distribution function of the embryos, g{r), by the following cosine function for 0 < r ^ ITQ. sir)

(1.5.9)

=-—cos28A

2

28A

where 2eo is the half width of g{r), and TQ is the meanradiusof the embryos (ro = 28o). For r > ITQ, g{r) = 0. Figure 1.24 illustrates the cosine distribution function. Eq. (1.5.9) can be rewritten with the maximum radius of the embryos r^ (= ITQ) as ^(r)=—sin^ nr

(1.5.10)

\'p;

If we define a dimensionless distribution function of the unstable nuclei, h{p,p*), as h(p,p*) = {rjn^{r,t) with p = rlr^ and/>* = r*/rp, one obtains from Eqs. (1.5.6) and (1.5.10)

Kp,p) = —^'^^-^ «o P-P\ for r* <. Tp and

, sin27rj?-sin2itp* 2lT

(1.5.11)

FUNDAMENTALS

64 g(r) A g(r)= A^cos^

IT mi

2eo

0

r„

Tp

Fig. 1.24. The cosine distribution function. (From Ref. 26.)

Fig. 1.25. The dimensioniess distribution function, h(p, p*), at different p* values. (From Ref. 26.)

h(j>,P ) = — ^ - ^ ^ 1-/7

sin27t/>

(1.5.12)

2TC

for r* £ r„, where u . is the maximum volume of the embryos (= (4jt/3)r ^)

65

1. NUCLEATION

and V/VQ = 5.747. The dimensionless distribution function, h(p,p*), is illustrated in Fig. 1.25 for various p* values, where p* = 0.6814 is the minimum value of/?*, as will be shown later, p * = 1 corresponds to the end of the nucleation, and /?* = oo corresponds to the ultimate stage of the growth at r* = 00. The h(pp*) at/? = 1 becomes zero when/?* = 1, which means that the distribution functions of the unstable and stable nuclei completely split from each other at the end of nucleation. The number of unstable nuclei, «., is given by n.= r7{r,t)dr-nJWp,pldp, Jo

(1-5.13)

JO

Figure 1.26 shows nJriQ as a function of/?*, which has a peak, 4.479, at/?* = 0.6814. The unstable nuclei are retained even in the growth stage (r* > r ), and their number converges to n^ as r* approaches infinity, irrespective of the form of g(r), as derived from Eqs. (1.5.6) and (1.5.13). Thus, if the ultimate n_ is denoted by «_",

u„ •'0 L JO

dr=n^.

Fig. 1.26. n./«o as a function of;;*. (From Ref. 26.)

(1.5.14)

66

FUNDAMENTALS

The Number and Mean Radius of the Stable Nuclei In the quasi-steady state of the unstable nuclei, the rate of increase in the number of the stable nuclei, /i^, is given by

K=ff\r..r=NS:sir)dr. p

(1.5.15)

J r

On the other hand, the increment in the total volume of the stable nuclei per unit time can be written as

" " 3 Jr, af

3 Jr, dr

(1.5.16)

Combination of Eqs. (1.5.3), (1.5.15), and (1.5.16) yields (1.5.17)

' : . - i ^ = xA^,

v". where r+ is the mean radius of the stable nuclei defined by

(1.5.18)

-];>• T is a time constant defined as RTv. X =

(1.5.19)

SIIDYKX and X* is a fraction of the number of the embryos whose radius is greater than r*, and is given by

x*^f:gir)dr.

(1.5.20)

1. NUCLEATION

67

Also, the following mass balance generally holds for the total volume of the precipitate consisting of both unstable and stable nuclei,

No%t- ^^fy^r^ I'^/>''''''

(^-^-^^^

where t is the time from the start of the introduction of the monomelic species, including the non-steady state of the unstable nuclei. Here, t is divided into two components, t_ and r^, as (1.5.22)

t=t.^t^.

where t =

471

(1.5.23)

and (1.5.24)

Hence, t_ and t^ are the total volumes of the unstable and stable nuclei, respectively, in a time unit. If (r-r^lr^ is much less than unity, Eq.(1.5.24) can be approximated as

\fdr 0"0 3

3N^

^["frdr-lfydr

1 . 1 < ^ fdr = ^0^0

Thus, one obtains

K

r=nj — - 2

(1.5.25)

The simultaneous equations (1.5.15), (1.5.17), and (1.5.25) forn^, r^, and t^

68

FUNDAMENTALS

lead to the following differential equation for t^ as a function of/?*:

^4K (1.5.26) 3T1P'(3/»*-2)^(P')-2(XO-X*)3

(3p'-2)[x;-(3p'-2)x'] where q(p*) = r^(r*) and (1.5.27) If t^ is set r, = 0, then n^ = 0 from Eq. (1.5.25), jc* = x^* (= v^v^) from Eq. (1.5.17), r^ = Tpfromthe definition of r^. By use of the initial condition, one obtains the solution of Eq. (1.5.26) as — =exp IKFipldp'

(1.5.28)

T

xp;G(p*)exp|-p.>(pVp* dp% 'Po

where pg* is p* at t^ = 0, 3^0

F(p*)

(1.5.29)

(3p*-2)[jCo-(3p'-2)xT

and G(j>*)^

3[p'(3p'-2)g(p')-2«-x')]

(1.5.30)

(3p*-2)[A:o*-(3/''-2)xT On the other hand, njng and rjr^ can be written as follows from Eqs. (1.5.17) and (1.5.25):

1. NUCLEATION

69

« - _ x^t^-3zp*(x^-x*) «o

(1.5.31)

Tx;i3p'-2)

and T. _ />*[V.-2T(JCO'-JC*)] '•p

(1.5.32)

XOX-3TJ7*(^O'-^')

Thus, /jy«o and r^z-p are now given as functions of p* by use of tjx from Eq. (1.5.28). Furthermore, if t^, n^, and r^ at the end of the nucleation (p* = 1) are designated by t°, n", and r°, then n" and r^" are given from Eqs. (1.5.31) and (1.5.32) withp* = 1 by

Z!l = ! l - 3

(1.5.33)

and r"

f:-2T

^P

^"-3T

(1.5.32)

If we use the cosine function of Eq. (1.5.9) for g{r), both nJriQ and rjr^ change with p* as illustrated in Fig. 1.27, where x^* = VQ/V^ = 0.1740 (i.e., PQ* = 0.6814). The njrig rises sharply with p* and then asymptotically approaches 1.567. The values of t^, n^, and r^ at the end of the nucleation (p* = 1) are given by t" = 4.567T =

4.567/?Tu„ ^,

(1.5.35)

70

FUNDAMENTALS

nr=1.567nn

1.561QRT SnOyVC

(1.5.36)

and (1.5.37)

r:=1.638r

While t^^ and r^"" are independent of Q, but dependent on the size parameters of the embryos, v^ and r^, respectively, n^" is proportional to Q, but independent of these size parameters. Here note that the n^" is the total number of the stable nuclei in a given system, while n^* in closed systems described in the foregoing section is the number concentration of the stable nuclei. Since jc* = 0 at/7* = 1, it follows that AI^" = nQ/(rJr*-l) at/?* = 1 from Eq. (1.5.17). Hence, one obtains — - 1 = 0.638.

(1.5.38)

2.0

1.638 1.567

0.6814

Fig. 1.27. n>o 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 <|)„ = i t n n - ^ ,

(2.1.14)

which corresponds to the ^ value of C(„) - see Eq. (1.2.4). If
(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^ = ^--<^^hn-^^--<^^^. on 5

(2.1.17)

from Eqs. (1.3.5), (1.2.12), and (2.1.15), one obtains

Fig. 2.2. Two-dimensional nucleus composed of n' monomers on a small particle of n monomers.

90

FUNDAMENTALS

AG^=-((l)-(j)>/.V«^^^.

(2.1.18)

Hence, the effective supersaturation energy parameter is reduced by (^^ on a small particle as compared to that on the bulk surface. The «'* value of the critical nuclei and AG'*, the maximum AG'„,, are given by *

n^* =

/

P

(2.1.19)

2(<1>-<|)J

and AG' =

*^

(2.1.20)

4(ct)-,)

As a consequence, the number-concentration of the two-dimensional n'mers, c'^f, is given by /c

-2/3

c'^/=Uo exp

i^'^y-w^

(2.1.21)

kT

This c'^f is of importance when we consider the growth of very small particles, especially the growth of the exceedingly small stable nuclei during, and immediately after, the nucleation period. As n approaches infinity, ^^ approaches zero, and thus Eq. (2.1.21) agrees with Eq. (2.1.13) for c'J on a bulk solid surface.

2.2. Nucleation Rate of Two-Dimensional Nuclei The nucleation rate, J', of two-dimensional nuclei of /i' on a small particle of n may be written in a similar manner to J for three-dimensional nuclei in Eq. (1.3.25) as

91

2. GROWTH

J' = k'a'>,Cc", d

n -I

,

<^n'-l

<^n'

(2.2.1)

n-l n-l

n'}

where a'^,_^ is the surface area of the side surface of the two-dimensional nucleus consisting of AI'-1 monomers, and C is the number concentration of all monomeric species in the solution phase. The k'^ is the deposition rate constant of the monomeric species to a unit area of the vertical side surface of the two-dimensional nucleus, so it may be much greater than k^ in Eq. (1.3.16) for the deposition to a unit area of the overall solid surface, because the steps and kinks of the side surfaces preferentially stabilize the deposited monomeric species. The deposition of the monomeric species and the dissolution of the solid may take place exclusively via such specific sites. However, since the difference between k'^ and k^ is only due to the difference in density of such sites, the equilibrium between the deposition and dissolution may be unaffected. Hence, k'^ and the corresponding k'^ may satisfy the following fundamental relationship: (2.2.2)

If we assume a quasi-steady state for the nucleation of the surface nuclei as weU, the nucleation rate J' on a n-mer is given by J'=-

"

(± exd ii'-KW-W'^

" exp

kT

kT

dn

C'n'

(2.2.3)

v<%

where a'^t = Inr'h = l^Tzh\y^n',

Since djc'j

= 0 at «' = oo,

(2.2.4)

92

FUNDAMENTALS L2li J'y>:

C'n'

c'l,

2^fnhv[k',expii^lkT)

'!>'

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

<'

J'<

c",

k'^ N "''«i(*-*»)

kT

^AG"-
kT

At «' = 1, c'„/c'„' = 1 and x' - - « , so that

(2.2.9)

2. GROWTH

93

/Jexp(-;c'^)d;«'- [\xp(-x'^)dx'=

sf^.

(2.2.10)

As a consequence,

f.^U^

-„

2/3

M

kT

exa

-AG' +<|> ifej

(2.2.11)

Also, it follows from Eqs. (2.2.9) and (2.2.11) that (2.2.12) c ,

^n

By a method similar to the derivation of Eq. (1.3.42), (2.2.13) n

At«' = n'*, jc' = 0 and thus c'Jc'^f = 1/2, which is the same as the result for three-dimensional nuclei.

23. Growth Rate by Surface Reaction In this section, a new theory on the rate of growth by surface reaction will be formulated on the basis of the above two-dimensional nucleation theory. Figure 2.3 is a scheme for the propagation of the two-dimensional surface nuclei. Let us direct our attention to a growing two-dimensional particle A on the crystal surface. A new two-dimensional particle B starts to grow on the surface particle A after an average time-lag of A^. Each statistical growth pattem of these particles starting from one molecule is assumed to be the same, as illustrated in Fig. 2.4. The growth rate of the two-dimensional particles may be small in the early stage, due to the high probability of dissolution of a small particle, but it may finally become constant when they become sufficiently large under a constant supersatura-

94

FUNDAMENTALS

Particle B

Fig. 2.3. Scheme of the propagation of two-dimensional nuclei.

tion. Also, the average time-lag, A/, for them to reach the same radius level is kept constant throughout the growth process because of the same growth pattern. If a two-dimensional nucleus of a certain size, large enough in the constant growth rate range, is regarded as a stable nucleus generated by the quasi-steady surface nucleation, and if the particle A has grown in radius by /•/ from the stage of the stable nucleus by the time the stable nucleus of the particle B is formed on the particle A, the difference r/ is equivalent to r' on the growth curve of particle A at a time ty This t^ is obtained as the intersection of the straight line extrapolated from the linear part of the growth curve of particle B with the r-axis, as shown in Fig. 2.4. If the surface area of particle A at radius /•/ is A^, one may consider that it takes A/, on average, for the origin of a new stable nucleus to be generated in a surface area A^ In this argument, the choice of the size of a stable nucleus is arbitrary, so long as it is in the constant growth-rate range, since J' is equivalent to the flux of the stationary n-mers, which is independent of the n value in the quasi-steady state for the surface nucleation. Also, r^' or A^ are independent of the choice of the size of a stable nucleus, as is obvious from the above procedure. As a consequence, the nucleation rate of the two-dimensional particles, J', is written as

2. GROWTH

95 Particle A

Particle B

>- t

Fig. 2.4. Growth patterns of two-dimensional nuclei A and B starting with a time lag, Ar, between them.

J'-

A^Lt

(2.3.1)

Since we assume a disk-like two-dimensional particle, we have A, = i r r / ^

(2.3.2)

If Tj' is sufficiently larger than the monomer radius, r„', r / = ;k,Af.

(2.3.3)

where k•^ is the constant growth rate of a sufficiently large two-dimensional particle at a given supersaturation. Hence, A/ is given by Af =

1

(J'nklfl^

(2.3.4)

96

FUNDAMENTALS

The nucleation of the two-dimensional particles may occur everywhere on the original crystal surface and on the growing two-dimensional particles, as shown in Fig. 2.3. Nevertheless, the growing front of a twodimensional particle 5 on a preformed two-dimensional particle A cannot overtake the growing front of particle A until the fringe of particle A attaches to those of other particles in the same layer, so long as the growth pattern of the particles A and B is assumed to be the same. Also, when the growing front of particle A stops, by attachment with other particles in the same layer, the spaces between the attached points will be filled by growth of the attached particles before particle B runs over the halted front of particle A, Therefore, the two-dimensional growth of the particles in the second layer is generally not limited by that in the first layer beneath the second layer. In addition, the state of the second layer, in particle number density and total surface area, is statistically the same as that achieved in the first layer at a time A^ before, since each nucleation event in the second layer happens, on average. A/ after the corresponding nucleation in the first layer. In other words, each layer is completed ist after the layer just underneath is completed. As a consequence, the growth rate perpendicular to the crystal plane, dridt, is given by ^ = A = /,(j/jk^^)i/3, dt At

(2.3.5)

where h is the thickness of the two-dimensional particles equivalent to that of each layer. If the surface area of a three-dimensional particle of radius, r, as the substrate of the two-dimensional particles, AQ, is so small as to be comparable to or less than A^ defined above. At is determined by AQ as Ar=—.

(2.3.6)

This suggests that the first layer is completed before the next nucleation on the same first layer. If At' denotes the At in Eq. (2.3.6) in distinction from the At in Eq. (2.3.1) without the restriction of AQ, then At' ^ At, and AQ ^ A^ happens when

2. GROWTH

97 / ^0^

.2^l/3

(2.3.7) //2

= ^1-

In this case, the growth rate of this three-dimensional particle is given by — = A = j'AJi = 4izr^hf. dt At' "

(2.3.8)

This growth mode may correspond to the so-called "mononuclear-layer growth",^ in which dr/dt is proportional to r. Also, one may find that dr/dt is proportional to T and independent of k^, in contrast to Eq. (2.3.5) in the case of v4o »Ay If the supersaturation is kept constant, J' is constant so that r=

(2.3.9) l-^Tihfr^t

where TQ is r at / = 0. This relationship holds for values of r limited by

r^

N

47C

f^il 2 U^^j

1/3

(2.3.10)

On the other hand, when r is sufficiently greater than (kJJ'itf^^H^ dr/dt is given by Eq. (2.3.5) in which dr/dt is independent of the size of the threedimensional particle. This growth mode may correspond to the "polynuclear-layer growth".^ It is now obvious that the mononuclear-layer and polynuclear-layer growth modes correspond to the earlier and later growth modes, respectively, of any kinds of solid. In fact, if ^^ is sufficiently small, the mononuclear-layer growth mode is finished in the early stage of the growth. However, Hk^ is close to, or smaller than, r^VA/, we must take the size of the monomeric species into consideration and Eq. (2.3.3) must be written as r ^=k Af+r ^

(2.3.11)

in which it is possible for k^ to be zero. In the extreme case of k^ = 0, the

98

FUNDAMENTALS

three-dimensional particle growth proceeds only in the polynuclear-layer growth mode from the beginning, and the nucleation theory on solid surfaces in section 2.2 becomes meaningless, because it is based on the quasi-steady growth of the two-dimensional nuclei. In this case, J' may simply be proportional to the difference between the concentration of the solute and the solubihty of the three-dimensional particle, and dridt is given as drIdt = h/At = J'AJi = J'Up where A^ is the partial molecular area of a monomer. Such a situation may typically be observed in the growth of amorphous particles. Even in the nucleation theory of the three-dimensional crystalline particles, this growth mode is presumed to be a reciprocal process of the dissolution in the quasi-steady growth of the stationary nuclei. This presumption may indeed be reasonable for the stationary nuclei close to, or smaller than, the critical nuclei, since they may not need the two-dimensional nucleation for their growth, owing to their rough surfaces. It may not apply, however, to sufficiently large crystalline particles beyond the size level of the critical nuclei, which need the surface nucleation for their growth. The quantity k^ is a function of the supersaturation, and may be given as k, = k,\iC-C^„,),

(2.3.12)

where /:/ is a constant independent of the supersaturation, v^ is the volume of a monomer, C is the number-concentration of the monomeric species, and C(^) is the number concentration of the monomeric species in equilibrium with the three-dimensional particles consisting of n monomers. Since the supersaturation for the growth of a three-dimensional particle is normally low. — ^

(^-^.] l^t^

= exi^

kT

(2.3.13) kT '

so that k^ may be written as fc/uiC(„)(<|)-4>„) kT

(2.3.14)

Inserting this relationship and Eq. (2.2.11) into Eq. (2.3.5), one finally obtains

2. GROWTH

99

-AG '%*^ 3kT

(2.3.15)

where

K=

kTk'rh-'i\'i\'i'c^,

(2.3.16)

2/9

If the three-dimensional particle is sufficiently large, C^^^ in this equation can be replaced by C^^y In Eq. (2.3.15), even if 5 = 10, (t)/AG'* « 1/10, and thus (j) in the exponent of this equation can normally be neglected. For example, even the critical supersaturation ratio for the nucleation of AgBr in open systems is less than 1.5 (see section 1.5) and, normally, S is around 1.2 or less in the growth stage. Also, if we consider the growth of AgBr particles larger than 0.1 (xm in diameter, (])„ can be regarded to be zero. If 5 = 1.2 and ([)„ = 0 with y = 142 mJ m"^ and v^ = 4.8145x10-2^ cm^ for AgBr at 25 °C, (j) = itJln 5 = 7.50x10-^2 J, ip' = 2Y(jrhi; J^^ « 2yn^'\)^^^ = 6.66x10-2° J, r'* = yu,/(l) = 9.12 nm, «'* = {^^12(S^f = 1.97xl0^ and AG'* = \p'2/4(|) = 1.48x10'^^ J. Since r/ must at least be greater than r'*, the maximum radius of a three-dimensional particle in the mononuclear-layer growth mode, TQ, is at least 4.56 nm, since Anf^ = Jc(r/)2 > jt(r'*)2. In this case, (1)/AG'* = 5.07x10"^, so that ^ in the exponent of Eq. (2.3.15) can be neglected. Thus, in most cases, Eq. (2.3.15) may be approximated by

dt

1 kT

5/6

exp

- A G /*

(2.3.17)

3itT

or, using cj) = kT\x)S and AG'* « \|)'2/4(t). ,/2

— = /i:(lnS)^^Sxp| dt

(2.3.18)

\2{kTf\nS

Hence, it is true that the supersaturation dependence of dridt is much smaller than that of the three-dimensional nucleation rate, J, because AG'*

100

FUNDAMENTALS

is proportional only to (InS)'^ with the smaUer ip'in the former - see Eq. (1.2.14) for the three-dimensional nucleation. The quantity dr/dt is often treated as being proportional to 5-1 or (S-lf, where m is a constant greater than unity. However, this approximation is allowed only in a very small range of variation in 5, except for the case of ^^ - 0 including the growth of amorphous particles, as is obvious from the form of Eq. (2.3.18).

2.4. Growth of Polyhedral Particles by Surface Reaction 2.4.1. Surface Energy of a Two-Dimensional Nucleus Although the simple disk model of two-dimensional nuclei is convenient for general discussion of the growth process by surface reaction, we need a rather more sophisticated model for understanding the formation of the specific shape of crystalline particles. Let us consider a two-dimensional nucleus on a flat plane in the form of a truncated regular pyramid, as shown in Fig. 2.5. If LQ, H, h, r, and 6 denote the circumference of the regular polygonal bottom, the height of the original pyramid, the height of the truncated pyramid, the radius of the inscribed circle of the polygonal bottom, and slope angle of inscribed circular cone, respectively, the surface area of the polygonal bottom, AQ, is given by

^

V ^ j ^ 2 2tane

(2.4.1)

and thus the total surface area of the upper and side planes of the polyhedral two-dimensional nucleus. A, is given by A=

2sine

i-|i-A]%cose(i-A

(2.4.2)

Hence, the increment in the surface area by formation of the two-dimensional nucleus, A/4 (= A-A^), is given by ^^^J^c^ sine

^ ° [

M^ll^^L^A. 2HJ sine °

If we define the shape factor of the polygonal bottom plane, P', as

(2.4.3)

2. GROWTH

101

Fig. 2.5. Two-dimensional nucleus on a flat plane in the form of a truncated regular pyramid.

(2.4.4) 4^0 Eq. (2.4.1) is rewritten as AA =

2^p'u,A(l-cose)

(2.4.5)

,/l/2

sin 6

where v^ and n' are the molecular volume of the solid (monomer volume) and number of the monomer composing the two-dimensional nucleus. If Y denotes the specific surface energy of the nucleus, the surface energy of the nucleus, \|)'^,, is given by wj= AA-v = —^

n'' .

(2.4.6)

sine Hence, the surface energy for a monomer of the nucleus is given by

102

FUNDAMENTALS

2/pV(l-cose)Y sin6

(2.4.7)

This is the general formula for \p' for a two-dimensional nucleus. For example, if the surface nucleus is a disk, P' = jr and 6 = 90°, so that \p' = 2Y(JtUih)^^, in agreement with Eq. (2.1.3). Let us evaluate the ip' values of two-dimensional nuclei bound by {100}, {110}, and {111} faces on a face-centered cubic crystal. Figure 2.6 illustrates the respective surface nuclei on cubic, dodecahedral, and octahedral microcrystals.

tS^

Fig. 2.6. Surface nuclei on cubic, dodecahedral, and octahedral microcrystals.

{100}-nucleus Since h = ao/l (UQ = lattice parameter), YIOO = (2/5ao^)vp° {^^ = surface energy of a free monomer) from Eq.(1.1.17), v^ = UQ^/A, fi' - A for a square, and e = 90°, \p\oo is given by
(2.4.8)

{110}-nucleus In this case, h = aJ2y/2, YUO = (2V2/5ao^)\p°, P' = 3V2 for a rhombus with interior angles sin-\2V2/3) and 180° - sin-^(2V2/3), and 6 = 60°, so that

2. GROWTH

103 (2.4.9)

^no=^r

{lll}-nucleus In this case, h = Ug/lVS, Ym = (2V3/5ao^y\\?°, P' = 3V3 for a regular triangle, and 6 = sin-^(2V2/3) = 70.529°, so that

^'nr-W-

(2.4.10)

Thus, i|''ioo:'»i''iio:'4''iii = 2V2 : 2 : 3. For AgBr at 25 °C, ^ = 9.06x10"^ J (see section 1.1.4), so i|)'ioo = 5.13x10-2" J, ip'no = 3.62x10-2" J, and '^\,, = 5.44x10-2° J. For AgCl at 25 "C, V = 7.77x10-2" J, so Tj^'ioo = 4.40x10-2" J, TJJ'UO = 3.11x10*2" J, and \\>\^i = 4.66x10-2" J. 2A2. Growth Rate For a general two-dimensional nucleus, the vertical component of the side surface area is given by (2.4.11)

a'„,= 2p'hM^n'

in place of Eq. (2.2.4) for a disk-like nucleus, and tp' is given by Eq. (2.4.7). Hence, J' is written analogously to Eq. (2.2.11) as

J' =

hi Vo^N

exp Tz \ kT ) \

'

(2.4.12)

kT

where AG'* is given by Eq. (2.1.20) including ip' of Eq. (2.4.7). On the other hand, A^ in Eq.(2.3.2) is generally given by

A^=^'rl

(2.4.13)

where r, is the inscribed radius of the polygonal bottom of the two-

104

FUNDAMENTALS

dimensional nuclei. Also, Af in Eq.(2.3.4) is rewritten as

As a consequence, dridt is given in the same form as Eq. (2.3.15) or the approximate Equation (2.3.17), but K^

- ^

^

^(n)

(2.4.15)

in which C(„) can be replaced by C„ when the three-dimensional particle is sufficiently large. It is of interest that the order in the magnitude of \|)' is ip^^^ > TJ;\OO » ip'iio for f.c.c. microcrystals since tj;^^^ : xp^^o • "^'loo = 3 : 2 : 2V2 as derived in the preceding section, while ^]f^J > \\)^^f > ip^^.^ since \\^„J : ^\>^^f : 'ypri,cub^ = 1.65 : 1.26 : 1.00 (see section 1.1.4). Thus, from a thermodynamic viewpoint, the most stable shape is a cube, the intermediate one is a dodecahedron, and the least stable one is an octahedron. However, from a kinetic viewpoint, the growth rate of the {110} face must be the highest because of the lowest AG'* [= ip'V4((|)-(t)J from Eq. (2.1.20)], and thus the {110} face must soon disappear, leaving the {111} or {100} faces much lower in growth rate. This deductive conclusion may explain the fact that the {110} face has never been observed in the growth of the typical f.c.c. particles of AgBr and AgCl, unless some specific adsorptives are present (see section 1.1.4). Although \\)\^^ is a little greater than \p\oo» ^ ^ ^^us the probability of the formation of the octahedral particles bound by the {111} faces is more or less higher than that of the cubic particles due to the lower growth rate of the former, the difference in \p' is rather small ('vp'm/ip'ioo = 1.06). In addition, it is quite likely that the highest specific surface energy, Yiip is apt to be reduced to some extent by adsorptives and/or electronic relaxation. In this case, a slight reduction of Ym may be enough for reversing the relationship between \\f\^^ and \p\oQ, and hence we can obtain either octahedral or cubic AgBr particles by relatively minor variation of the preparation conditions such as pBr, concentration of ammonia, etc. In the case of AgCl, we usually obtain only cubic particles. Since AgCl particles normally grow by diffusion-controlled growth mode,-'^ they are thought to

105

2. GROWTH

assume an equilibrium form determined by the ratio of Yioo/Ym and not by the surface nucleation rate/'^ as wUl be described in detail in chapter 3. Thus, as long as YVYIU = 1/^^, we obtain only cubic AgCl particles, inespective of the ip' value.

2.5. Diffusion-Controiied and Reaction-Controlled Growth Modes Particles suspended in fluid actively move around as a result of Brownian motion. In this case, one may assume some stagnant fluid layer of thickness 8 around each particle, and a bulk liquid phase outside the stagnant layer. Figure 2.7 shows the relations between the particle radius r of density d and rib for a particle moving in a fluid of density 1 g cm"^ under the influence of convection, where the left part of each curve in which rib goes down with increase in r is due to the Brownian motion, and the final sharp increase of rib is due to convection.^ One may find from this figure that the thickness of the stagnant layer of colloidal particles of radius less than a few microns is determined by the Brownian motion with almost no influence of convection. If a coUoidal particle grows in conditions of supersaturation, the solute may diffuse from the bulk liquid phase containing a uniform concentration of solute, Q , to the particle surface through a diffusion layer corresponding

/

/ / / /

/ /

i l l

i !^

1 ^

I I !

[

/ / / f

F^^~^?***'**» ~^^--^^S2;2^flB,N.„,^

|_

/ /

!

/

i 1 /

."~ 10

10'

10'

Fig. 2.7. Relationships between the particle radius, r, and rlh in aqueous dispersion at different solid densities, d, (From Ref. 6.)

106

FUNDAMENTALS

to the stagnant fluid layer with some concentration gradient, as shown in Fig. 2.8(a), where C. is the concentration of the solute at the solid/liquid interface, and C^ is the solubility of the particle. Figure 2.8(b) is a macroscopic scheme of the diffusion layer around a spherical particle of radius r, where x is the distance from the center of the particle. The total flux of solute, J, passing through a spherical plane with radius x within the diffusion layer is written by Fick's First Law as (2.5.1)

dx where D is the diffusion coefficient of the solute and C is the concentration of the solute at x. Since J is constant irrespective of x due to the steady state of the solute diffusion, integration of C(x) from (r+8) to r with respect to X gives (2.5.2) 0

As has been shown in Eq. (2.3.17), the linear growth rate of a particle by the surface reaction is not simply proportional to {S - 1). However, it may be allowed to be treated so within a limited range of {S - 1). Thus, if k denotes the rate constant of the surface reaction of solute at the particle surface, the consumption rate of the solute at the particle surface by the

a)

Diffusion Uyer

Bulk Solution

b)

a-

Fig. 2.8. Microscopic (a) and macroscopic (b) views of the diffusion model. (From Ref. 8.)

2. GROWTH

107

surface reaction, which is equal to J, is given by J=47cr2jt(C.-C,).

(2.5.3)

By eliminating Q from Eqs. (2.5.2) and (2.5.3), one obtains the general linear growth rate, dridt (= JVJATir\ as

(2.5.4)

Also, from Eqs. (2.5.2) and (2.5.3), it follows that 1 + -^ . C^,-C^ kr\ 5

(2.5.5)

If there is a great difference between D and kr, either the diffusion process or reaction process becomes the rate-determining step of the overall growth process. If D « hr, C,. - C, from Eq.(2.5.5), and thus the rate-determining step is the diffusion process of the solute, in which drIdt is given by ^^^{uL\v(r-C\.

(2.5.6)

If rlh « 1, this relation reduces to

f = :?^(C,-C,). at

(2.5.7)

r

If D » kr, then C. « Q, and thus the particle grows by the reactioncontrolled growth mode, in which drIdt is given by - = ^ySCb-Cr)dt " * '

(2.5.8)

Figure 2.9 shows the solute concentration profiles in the general growth mode, the diffusion-controlled growth mode, and the reaction-controlled

108

FUNDAMENTALS (Diffusion Layer)

(Bulk Solution)

a

Fig. 2.9. The solute-concentration profiles of diffusion-controlled and reactioncontrolled growth modes. growth mode. Since r/b is mostly kept around 0.25 for a colloidal particle of a few microns or submicrons in radius from Fig. 2.7, we may use Eq. (2.5.7) in place of Eq. (2.5.6) in the diffusion-controlled growth mode, by replacing D with an apparent diffusion coefficient equivalent to D multiplied by a factor of ca. 1.25. As a consequence, the characteristic of the diffusion-controlled growth is that the linear growth rate is inversely proportional to the particle radius, while the linear growth rate in the reaction-controlled growth mode is independent of the particle radius. Here it is noteworthy that the diffusion-controlled growth mode generally switches to the reaction-controlled growth mode with decreasing mean size, when kr becomes much smaller than D.

2.6. Criteria for the Distinction of Growth Modes 2.6.1. Magnitude of the Growth Since the diffusion-controlled reaction rate constant is so high diffusion rate of the solute to the

Rate growth is observed when the surface that the growth rate is limited by the particle, it is the growth mode with the

2. GROWTH

109

maximum conceivable growth rate in a given system. In Eq. (2.5.7), the diffusion coefficient D is nomially of the order of 10"^ cm^ s"^ at room temperature in dilute aqueous solutions. Thus, if (C-Q) or (C-C^) is known, dr/dt can be estimated roughly beforehand. If the linear growth rate is much smaller than estimated from Eq. (2.5.7), the growth mode must be the reaction-controlled one. Also, if the growth rate of a particle is lower than that of one different in crystal habit or structure under the same conditions, the growth of the former must be in a reaction-controlled growth mode, since the diffusioncontrolled growth must be the fastest of all possible growth processes under the given conditions. 2.6.2. Activation Energy of the Growth Rate The activation energy of the diffusion coefficient D is normally around 5 kcal mol"^ (= 21 kJ mol"^) in aqueous solutions,^'^ while that of the rate constant of surface reaction depends strongly on the species of the solid and is usually much higher than that of the diffusion coefficient. Hence, this general trend can be used as a subsidiary criterion for distinction between the two growth modes. 2.6.3. Size Dependence of the Growth Rate As has been stated above, the linear growth rate is inversely proportional to the particle radius in the diffusion-controlled growth mode, while it is independent of the particle radius in the reaction-controlled growth mode. These characteristics of the two growth modes can be used as the criterion. 2.6.4. Evolution of the Size Distribution Width Strictly speaki>:g, the term (C - C^) in Eqs. (2.5.7) and (2.5.8) is not independent of the particle size, inasmuch as Q is a function of the particle radius based on the Gibbs-Thomson relation: C,= Q e x p

f^vi'J

(2.6.1)

rRT )

This Gibbs-Thomson effect is significant when the particle size is very small. If 2yVJrRT « 1, Q is approximated as

no

FUNDAMENTALS

Cr=C, 1 . ^ rRT ;

(2.6.2)

c=c\

(2.6.3)

Likewise, C is written as 1+

r'RTl

where r* is the particle radius in equilibrium with the bulk solution. In the case of the diffusion-controlled growth mode, the linear growth rate is written from Eq. (2.5.7) as (2.6.4)

where

2yDiic, Ko^

(2.6.5)

RT

If the size distribution is sufficiently narrow, the change of the standard deviation, Ar, at a certain r* may be given by d(Ar) dt

Kj,Lr(

2 J_ f

(2.6.6)

r*

where r is the mean particle radius. Accordingly, d(Ar)/dt > 0 for r/r"^ < 2, while d(Ar)/dt ^ 0 for r/r* ^ 2. Thus, if the supersaturation is sufficiently high as r /r* ^ 2, the size distribution becomes narrower with the progress of growth (self-sharpening of size distribution). However, if r/r* is less than 2, Ar tends to increase; Le., the size distribution becomes rather broader under a low supersaturation even in the diffusion-controlled growth mode. Figure 2.10 illustrates the behavior of dln(Ar)/dt and dr/dt with the progress

2. GROWTH

111

of the particle growth.^ Actually, Wey and Strong^ observed the selfsharpening at a high supersaturation and the distribution broadening at a low supersaturation in a AgBr particle system in the diffusion-limited growth mode. Hence, if one wants to promote monodispersity in the diffusioncontrolled growth mode, the supersaturation should be set as high as possible below the critical supersaturation level. In the case of the reaction-controlled growth mode, dridt may be written from Eqs. (2.5.8), (2.6.2), and (2.6.3) as dr

„

(2.6.7) r*

r

where ^«=

(2.6.8) RT

Similarly, d(Ar)/dt is given by
(2.6.9)

dt Thus, d(Ar)/dt is positive for any r so that some broadening of size distribution takes place in the reaction-controlled growth mode due to the Gibbs-Thomson effect, though this effect diminishes with the increase of the mean particle radius, r. In addition, since d{Ar)/dt is independent of r*, the broadening effect cannot be avoided by lifting the supersaturation. As a consequence, in the diffusion-controlled growth mode, the GibbsThomson effect becomes negligible with the progress of the particle growth, and the self-sharpening in size distribution becomes most pronounced when r is around 3r*, as is obvious from Fig. 2.10. However, as the particles grow still more, d(Ar)/dt approaches zero, and thus the self-sharpening also becomes ineffective. In the reaction-controlled growth mode, d(^r)/dt soon becomes virtually zero due to the small Kp, and thus Ar becomes constant with the particle growth. Hence, if we observe some self-sharpening in size distribution with the particle growth, the growth mode is the diffusioncontrolled one or, at least, is very close to it. However, it should be noted

112

FUNDAMENTALS

Fig. 2.10. [dfldt\IKj) and [Jln(Ar)/rfr]/Xp as functions of r for diffusion-controlled growth with the infinite diffusion layer. (From Ref. 8.)

that, even in the diffusion-controlled growth mode, the size distribution can be broadened when the mean size is very small {r"^
2. GROWTH

113 X < r +S

Fig. 2.11. Overlapping of diffusion layers. mode. Hence, it can be used as a criterion for discriminating between the two modes. 2.6.6. Solubility Dependence of the Growth Rate If the total solubility of particles is varied by changing the pH, concentration of the anions or cations, concentration of solvents of the solid, etc. under a constant supersaturation ratio, the growth rate of the particles is virtually proportional to the change of the solubility, as long as the growth of the particles is in the diffusion-controlled growth mode, since the effect of change in the composition of the solution phase on the diffusion coefficient is rather small. However, if the change of the growth rate is far from being proportional to the solubility change, this may suggest that the particle growth is in the reaction-controlled mode, in which the growth rate constant itself is directly affected by the change of composition of the solution phase. But it should be noted that a proportional change of the growth rate with the solubility does not necessarily mean the diffusioncontrolled growth. 2.6.7. Chronomals Nielsen^ proposed the so-called "chronomal analysis" for distinction between the diffusion-controlled growth mode, polynuclear-layer reactioncontrolled growth mode, and mononuclear-layer growth mode. These growth modes may be depicted as in Fig. 2.12.^^ However, as mentioned in section 2.3, the mononuclear-layer growth mode is a special growth

114

FUNDAMENTALS DIFFUSION CONTROLLED GROWTH

REACTION CONTROLLED GROWTH Polynuclear Layer Growth

Mononuclear Layer Growth

O H^ or _ DV„(C.-C m^ b e) dt r r: particle radius D: diffusion coefficient V^: molar volume

— = k V (C.-C^)

f = ^V'(VCe)

k : reaction ^ rate constant

k : reaction rate constant

Fig. 2.12. Schemes of the three growth modes. (From Ref. 11.) mode in the very early stage of particle growth, even if it is actuaUy present. Hence, the chronomal analysis is normally limited to the distinction between the diffusion-controlled growth mode and the polynuclear-layer reactioncontrolled growth mode. First, the degree of reaction, § (the ratio between the amount of a substance, that has reacted, and the total amount able to react), is defined as

i^

(2.6.10)

where Q is the initial concentration of solute, C is the concentration of solute at time t, and C„ is the solubility of the bulk solid of the particles. Here, the particle size is assumed to be large enough for the GibbsThomson effect to be neglected. If r„ denotes the final particle radius at ^ = 1 or C = C„, the particle radius, r, at an arbitrary ^ is given by

r = rj so that

(2.6.11)

2. GROWTH

115

d^^}V_dr dt r^ dt'

(2.6.12)

In the diffusion-controlled growth mode, it follows from Eqs. (2.5.7) and (2.6.10) that "^^ =K,dt, ^^''(1-0

(2.6.13)

where Kj =

"• \ ° — : ; : .

(2.6.14)

f — ^ L _ =^.. •'oxV'(l-x) "

(2.6.15)

2

Hence,

In case of reaction-controlled (polynuclear-layer) growth, if we assume that the linear growth rate of a spherical particle can be described by ^^kVJC-CJ",

(2.6.16)

r

(2.6.17)

one obtains

where

—

= Kt,

116

FUNDAMENTALS

j^^^ 3fc^i«(<^o CJ"

^2.6.18)

If one finds a linear relationship in the plots of the left-hand-side integrals in Eq. (2.6.15), or Eq. (2.6.17) for various values of n against t, one may regard that it represents the growth mode. It should be noted that this method for the discrimination of the growth modes is applicable only to extremely simple monodisperse systems, in which the particles are precipitated from a homogeneous solution without renucleation and coagulation after the initial nucleation, and the ratedetermining step of the total reaction is the final deposition process of the solute onto the growing particles. Thus, it cannot be applied to general monodisperse systems, including the gel-sol systems containing a solid reservoir of monomelic species; or homogeneous closed systems in which the rate-determining step of the total reaction is a preceding step for the formation of the monomeric precursor, such as hydrolysis, reduction, oxidation, or thermal decomposition of the starting materials, including alkoxides in sol-gel systems, metal ions, organic or inorganic precursor compounds, etc., and slow release of a metal ion from a soluble complex; or open systems into which monomeric species is introduced continuously from outside. Therefore, the applicable monodisperse systems are quite limited. When we use this method, previous analysis on the rate-determining step is indispensable. Incidentally, if we formulate the chronomal in the mononuclear-layer growth mode, dr/dt may be given by --kVy(C-CJ.

(2.6.19)

Thus, ff»5

where

dx

^

-KJ,

(2.6.20)

2. GROWTH

117

K-^KV.rSCo-CJ".

(2-6.21)

In addition to the fact that the mononuclear-layer growth is limited only to the exceedingly early stage of particle growth, the assumption of a constant solubility of the particles during their growth may not be allowed, because of the drastic change in their mean size of the extremely small particles. As a consequence, Eq. (2.6.20) may have almost no chance to be used in practical systems.

References 1. A. E. Nielsen, "Kinetics of Precipitation." Pergamon, Oxford, 1964. 2. C. Wagner, Z. Elekrochem, 65, 581 (1961). 3. R. W. Strong and J. S. Wey, Photogr, ScL Eng. 23, 344 (1979). 4. T. Sugimoto, J. Colloid Interface ScL 91, 51 (1983). 5. T. Sugimoto, J. Colloid Interface ScL 93, 461 (1983). 6. T. Sugimoto, AIChE J. 24, 1125 (1978). 7. T. Sugimoto, Photogr. ScL Eng, 28, 137 (1984). 8. T. Sugimoto, Adv, Colloid Interface ScL 28, 65 (1987). 9. J. S. Wey and R. W. Strong, Photogr. ScL Eng. 21, 248 (1977). 10. R. Jagannathan and J. S. Wey, J. Crystal Growth 51, 601 (1981). 11. T. Sugimoto, Hyomen 29, 978 (1991).

CHAPTERS HABIT FORMATION 3.1. Surface Chemical Potential of a Crystal Face Gibbs^ suggested that a polyhedral crystal in equilibrium with the surroundings would assume a shape with the minimum surface free energy. This idea was formulated by Wulff as follows:

l i = l? = ...= Ii = ...= i?:inZ,

(3.1.1)

where Y, is the specific surface energy of the zth face of the polyhedral crystal, r^ is the central distance to the ith face, v^ is the molecular volume of the solid, P is the vapor pressure of the polyhedral crystal, and P„ is the vapor pressure of a crystal of infinite dimensions. The vapor pressures are replaced by the solubilities for a crystal in a solution. This is the concept of the "equilibrium form." Meanwhile, Curie"^ considered that a crystal growing under supersaturation might maintain the equilibrium form with its minimum surface energy. However, his hypothesis has never been verified for the growth of real polyhedral crystals of large dimensions. This is partly because there is virtually no difference in vapor pressure or solubility between a large crystal and the infinite-sized one, Le., P « Poo, so that Eq. (3.1.1) loses its significance, and partly because the shape of a crystal is determined by the difference in growth rate of the individual facets for the reaction-controlled growth ("growth form"). As a consequence, we are liable to believe that the equilibrium form is only a conceptual shape, and that it is independent of the growth form. We know, on the other hand, that as the crystal size is reduced to that of the colloidal particle level of microns or less, the small crystals are subject to Ostwald ripening due to only a slight difference in solubility among them with a small size difference. This means that the equilibrium form of

3. HABIT FORMATION

119

colloidal microcrystals may have at least some significance, even when they grow under some supersaturation. Thus it seems necessary to consider the growth form of colloidal particles in conjunction with the equilibrium form, since the growth form is essentially a kinetic shape created by the deviation from the equilibrium between the surroundings and solid phase. For this purpose, a thermodynamic quantity, the "surface chemical potential" of each crystal facet, may be useful/

[octahedron]

tetradecahedron A

[tetradecahedron M]

tetradecahedron B

[cube]

Fig. 3.1. An octahedron, tetradecahedra A, M, and B, and a cube. (From Ref. 4.) Let us consider a simple tetradecahedral microcrystal bound by six {100} faces and eight {111} faces illustrated in Fig. 3.1. The extreme shapes are the octahedron bound by eight {111} faces only and the cube bound by six {100} faces only. Tetradecahedron A is an intermediate form between the octahedron and tetradecahedron M, while tetradecahedron B corresponds to a shape between tetradecahedron M and the cube. The surface chemical potential (SCP) of a {100} face of a tetradecahedral microcrystal, ^oo' is now defined as a change of surface free energy of the microcrystal by the growth of the {100} face with one mole of the component molecules in the direction normal to the {100} face, where the central distance to the {111} faces is fixed. The SCP of a {111} face is also defined in an analogous manner. In the meantime, the surface free energy of a tetradecahedron, \|)^, is written as *n='SiooYioo^^iiiY 111'

(3.1.2)

where S^oo and S^^^ are the total surface areas of the {100} and {111} faces, respectively, of the particle, and YIOO and y^^^ are the specific surface energies of the respective faces. Thus, (x^oo and \i^^^ are given by

120

FUNDAMENTALS

1^100

(3.1.3)

and

"111

(3.1.4)

where n is the mole number of the component molecules of the particle, TJOO and r^•^^ the central distances to a {100} face and {111} face, respectively, V^ the molar volume of the solid, and v the volume of the particle. For tetradecahedron A (with 1/V3 s r^u^r^gg £ 2/V3), i|»„=12(;/3ri„-rioo)2Yj^

(3.1.5)

*12v^[ri„-(\/3ri„-''ioo)'lYin.

V = 4v/3riii - 4(V^rm - r^^^^,

(3.1.6)

and for tetradecahedron B (with 2/V3 £ '•in/''ioo ^ ^3), l|f„=12[2rfoo-3(^/3r,oo-r,l,)^]Y,oo + 12y3(v/3r,oo-riii)2Yiii,

(3.1.7)

D = 8rfoo-4V3(V3r,oo-riii)3

(3.1.8)

Inserting Eqs. (3.1.5)-(3.1.8) into Eqs. (3.1.3) and (3.1.4), moo and n ^ are obtained as summarized in Table 3.1. The chemical potential of solute in equilibrium with a {100} face, m is given by

121

3. HABIT FORMATION

Table 3.1. The surface chemical potentials of the {100} and {111} faces for tetradecahedra A and B (Source: Ref. 4) Tetradecahedra

M-ioo

M-iii

Type A (l/^/3^^„^/^,^^2/^/3) Type B

| 1 = 1*100* l^(-)^

(3.1.9)

where \i^^^ is the chemical potential of one mole of the component molecules (monomers) in the solution phase in equilibrium with a bulk solid, which s equal to the chemical potential, (x°, of monomers in a bulk solid. On the other hand, ^i and \i^^^ are related to the activities of a monomelic species or the solubility products of the dissociated ions as ^ = lx^+/^7lnx;sp100

(3.1.10)

iX(„^=ii^+/?rhijg,

(3.1.11)

and

where \i^ is the standard chemical potential of solute, iC^^°" is the solubility product of the {100} faces of the particle, and KJ^ is the solubility product of the bulk solid. Similar relationships are also obtained for a {111} face. Thus, K^^^^ and^^^^^ are expressed as functions of/^ioo ^^f^nv respectively: •111 = JCexp[^] sp ^j^TJ ; C = 0^p|RT

i.ioo_

3.2. Stable Forms

(3.1.12)

122

FUNDAMENTALS

3.2.1. Equilibrium Forms If both of the {100} and {111} faces coexist within a tetradecahedron, and are in equilibrium with common solution, (3.2.1)

1^100= ^A 111-

Applying this relationship to ^QQ and \i^^^ in Table 3.1, it follows for both types A and B that (3.2.2)

p=a.

where p = ^m/^'ioo ^nd a s Ym/Yioo- Thi^ ^^ in accord with the Wulff theorem in Eq. (3.1.1). In this case, a must be in the range of 1/V3 < a < V3 due to the geometric restriction of a tetradecahedron, Le., 1/V3 [Xjoo for any value ofp within the range 1/V3 < p < V3, as is obvious from Table 3.1. Hence, {100} faces continue to grow with the dissolution of {111} faces until the {100} faces disappear to form a perfect octahedron (p = 1/V3), since the solubility of the {100} faces is always lower than that of {111} faces - see Eq. (3.1.12). If a ^ V3, on the other hand, {111} faces continue to grow at the expense of {100} faces until

a)

0^^1//T

(a-1/2)

b)

l//T
cj

rf>yT

(o(=2)

P I

'^

I

'^

I

"^

I

"*

H

-5

Fig. 3.2. Reduced surface chemical potentials as functions of p. (From Ref. 4.)

123

3. HABIT FORMATION

Table 3.2. Reduced surface chemical potentials, /^QQ and/^u, as functions of p for tetradecahedra A and B with a constant volume (Source: Ref. 4) Tetradecahedra TypeA(l/V3^p^2/V3)

TypeB(2/V3^p^V3)

Ao ^p'-(}f3p-\?

fu ' Via- \

V3;7'-(V3p-l)'

'Vlp-l V3p - I + (V3 - 2/7)a

i-jiVz-p? V3-a

3V3p - 7 + 3(V3 - p)a

l-yCVI-p)'

2-3(V3-/>)2

'W^p

Table 3.3. Equilibrium forms and their surface chemical potentials with the ranges of Ym/Yioo values (Source: Ref. 4) Yni'Yioo value

^iir^ioo .

value

Equilibrium Form

Surface Chemical Potentials of Equilibrium Fonn M-ioo

l/\/3
l/v/3

Oct.

-00

Yiii'Vioo

Tetradec.

^YlOO'^^m/''lOO

73

Cub.

M-ioo

—00

the {111} faces disappear to form a perfect cube (p = V3), since (JL^^^ < [x^oo for 1/V3

124

FUNDAMENTALS

Cubic Range

(O'lii/O'ioo ^73)

/T

1.5 Tetradecahedral Range

(l//3"<«'iii/ffioo^ ^^)

F n i / n 00 (•
1//T 0.5

Octahedral Range

{
Fig. 3.3. p values of the equilibrium forms of AgBr microcrystals plotted as a function of pBr, which were obtained by aging monodispersed cubic particles of r^oo = 0.242 \im (n) or octahedral particles of r^^^ = 0.286 \xm (A) at 50 ^C for 30 min in the presence of 0.5 mol dm"^ NH3 plus 1.0 mol dm^^ NH4NO3 (pH 8.48). (From Ref. 4.) Since the equilibrium form of a microcrystal is determined by the ratio of the specific surface energies of the facets of the microcrystal, specific adsorption depending on the concentration of adsorptives is the predominant factor. In the case of silver bromide particle systems, the concentration of bromide ions in the solution phase [Br'], or pBr (= -log[Br"]), and coexisting solvent of silver halides, such as anmionia, are the determinants. Figure 3.3 shows the/? value (s r^^^/r^Qo) of the equilibrium form of AgBr microcrystals as a function of pBr, attained by aging cubic or octahedral AgBr particles of ca, 0.5 \xm for 30 min at a constant concentration of

3. HABIT FORMATION

125

ammonia (0.50 mol dm"^ NH3 + 1.0 mol dm"^ NH4NO3 at pH 8.48) and temperature 50°C.'^ The p values were determined by a dye adsorption method.^"^ In this system, p values of the equilibrium form of AgBr particles decreased with increase in [Br"], or decrease in pBr, within the range of 1/V3 to V3, and thus/? = a. The considerably low a values around 1.3 below V3 in the relatively high pBr range around 2.5 seem to be mainly due to the adsorption of ammonia, while the decrease of a with increasing [Br"] seems to be due to the additional adsorption of bromide ions. Since both Yioo 3nd y^^^ must be reduced by adsorption of NH3 and Br", the drop in a seems to be due to the more pronounced reduction of y^^^. The extremely small change of a in the pBr range below ca. 1.8 may be explained by the limited adsorption of negatively charged Br" ions and bromide complexes of silver ions (see section 1.1.3). 3,2,2, Steady Forms It is expected that, if particles grow under a constant supersaturation with a constant composition in the solution phase, the particles may assume a constant growth form. We may call such a constant growth form a "steady form."' a) Steady Forms in the Reaction-Controlled Growth Mode Figure 3.4(b) is a transmission electron micrograph of a carbon replica of AgBr particles aged from the octahedral particles in Fig. 3.4(a) at pBr = 1.40 under the same conditions used for attaining the equilibrium forms in Fig. 3.3. Figure 3.4(c) shows particles grown from those in Fig. 3.4(b) by subsequent simultaneous addition of AgN03 and KBr solutions under otherwise identical conditions of pBr, [NH3], [NH4NO3], pH, and temperature for the formation of the particles in Fig. 3.4(b) from those in Fig. 3.4(a). Obviously the growth form in Fig. 3.4(c) is different from the equilibrium form in Fig. 3.4(b). If a particle is in a steady state of growth, it is necessary for the/? value of the particle that p = 0.

(3.2.3)

On the other hand, the differentiation ofp with regard to time yields

126

FUNDAMENTALS

1 ^m Fig. 3.4. TEMs of replicas of AgBr particles in a reaction-controlled steady form (a, c) and in an equilibrium form (b) at the same pBr. They were all formed in a system containing 0.5 mol dm"^ NH3 and 1.0 mol dm'^ NH4NO3 at 50 °C and pBr 1.40, but (a) original octahedra grown by the CDJ method, (b) transformed ones after aging of the original octahedra for 30 min, and (c) sharp-cornered octahedra resumed after CDJ processing of the particles in (b). (From Ref. 4.)

P=-

100

'111

'100

'100/

(3.2.4)

It follows from Eqs. (3.2.3) and (3.2.4) that P=-

111

(3.2.5)

'100

Designating the steady state with an asterisk, Eq. (3.2.5) can be written as •

^iii(C

Cjii)

P =

:

(3.2.6)

^ioo(^ ^loo) unless S^oo = 0 or S^^^ = 0, where k^^^ and k^^^ are the growth rate constants of the {100} and {111} faces, respectively, on the assumption of reaction-

127

3. HABIT FORMATION

0

0.2

0.4 0.6

a)

o(^l//J-

0.8

1.0

(DCl/2)

1.2 1.4

1.6

1.8

0.6

0.8 1, 0

1.2 1.4

1.6

1.8

0.6

0.8

1.0

1.2 1.4

1.6

1.8

Fig. 3.5. The graphic method for the determination of the steady forms. The arrows indicate the directions of the driving forces. (From Ref. 4.)

controlled growth, C the solute concentration in the bulk solution, and C\^^ and C*ioo the solubilities of the {111} and {100} faces of the steady form, respectively. The solutions of Eq. (3.2.6) for/?* are given graphically by intersections of the following two functions ofp: (3.2.7)

V^lll and C-C,,, 3^2 =

C-C 100

CIC^-cjq?{n.JRT)

(3.2.8)

C/C^-ei^(fi,JRT)

where C„ is the solubility of the bulk solid - see Eq. (3.1.12). The broken lines in Fig. 3.5 are the straight lines ofy^ passing through the origins. The solid lines are the curves of ^2 calculated for the three ranges of a: a :^ 1/V3, 1/V3 < a < V3, and a ^ V3 represented by a = 1/2, 1, and 2, respectively, where we assume that C/C^ = 1.3, v = 1 \AnP, and y^oo = 1^^ mJ m'^.

128

FUNDAMENTALS

In Fig. 3.5, the intersections of P^ and P2 satisfy Eq. (3.2.3). However, the following condition is required additionally for a particle to be stable: ^<0. dp

(3.2.9)

This relationship means that if/? is slightly displaced from/^*, the particle is subject to a force of pulling back to /?*. Thus, only P^ out of P^ and P2 satisfies Eq. (3.2.9). Furthermore, P3, where/? = 1/V3 or V3, satisfies Eqs. (3.2.3) and (3.2.9) independently of Eq. (3.2.6). The F3's in Fig. 3.3 correspond to the equilibrium forms in the respective a ranges. Hence, there is only one steady form in the case of 1/V3 < a < V3, while there are two steady forms in some ranges of ^ni/^ioo ^^ ^^e cases where a ^ 1/V3 and a ^ V3, suggesting the possibility of simultaneous formation of two dif^" rent steady forms in these a ranges. The/? values of the steady forms are ^ )wn in Fig. 3.6 as functions of ^ni/^ioo ^^^ ^he respective a ranges. The approximate p* values are listed in Table 3.4 for the special cas of 2yVJrRT « 1 and 1.2 < C/C^ < 1.5. For 1/V3 < a < V3, all particles in a growth system have a single p* of P^ during their growth [see Figs. 3.5(b) and 3.6(b)], and /?* is given approximately by p =— v3

for

= 'hll ^100

^100

^— , v3

for±<^<^, v^

^•loo

^100

Figure 3.7 shows the pBr-dependence of the growth rates of the {100} and {111} faces of AgBr microcrystals, obtained from the growth rates of cubic particles 11^^^, (T^QQ = 0.462 \im) or octahedral particles 11^^^ {r^^^ = 0.376 [xm) by dissolution of a large amount of much smaller cubic particles Ub (''loo = 0.115 fim) under the conditions of [NH3] = 0.50 mol dm"\ [NH4NO3] = 1.0 mol dm•^ pH = 8.48, [gelatin] = 1 wt%, and temperature = 50 °C. It is obvious from this figure that the growth rates of the {100} and {111} faces show opposite pBr dependences in this system, and that the change of the solubility of the bulk solid with pBr is not proportional to the

3. HABIT FORMATION

129

Fig. 3.6. Steady forms as functions of A:,ii/A,oo for the three ranges of a. (From Ref. 4.) Table 3.4. Approximate p* values of the steady forms in a case of lyVJrRT « 1 and 1.2 < C/C^ < 1,5 {Source: Ref. 4) ^iiAoo scale 0

a <. l/>/5

\l>fh
^ ^


y/k\ - CJC)

i/>/5(i - c^C)

J3

iM

V3

1/^

\/S \/J3

v5

l/>/5

kiii/kioo

y/3

^Ill/^IOO 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/^ioo- 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/^ioo < V3, the/7 value (= r^^^lr^^ of the steady form, /?*, must be nearly equal to A:in/^ioo> 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//3
j

\

\

rm/rioo _\

,'^—

Equilibrium

X\\\IX\Q^

o /o/

L

/ Octahedral Range

/

(kin/kiooil/ZJ)

/

// / / L...

1

1

-fc---1--

1 . 1

1

1

1

1

1

1

L . „ . l ..J

L

pBr

Fig. 3.8. The /:n#ioo ratio, steady r^^^lr^^ ratio, and equilibrium rm/rloo ratio of AgBr particles, as functions of pBr, in the system at 50 °C containing 0.5 mol dm"^ NH3 plus 1.0 mol dm"^ NH4NO3. The particles were grown at the expense of much smaller coexisting particles for the ^ni/^ioo and steady r^^-Jr^^^ ratios, while the data for the equilibrium r^^-^lr^^^ ratio are from Fig. 3.3. (From Ref. 4.) or ^111/^100 ^ ^3, respectively, since a is in the range of 1/V3 < a < V3. The solid line in Fig. 3.8 was obtained from this theoretical prediction. The circles in this figure are data of/?* values actually determined by the dyeadsorption method for AgBr particles obtained by simultaneous introduction of 500 cm"^ of 1.2 mol dm"^ AgNOg and almost the same volume of 1.2 mol dm"^ KBr solution containing 1.0 mol NH3 and 2.0 mol dm"^ NH4NO3

132

FUNDAMENTALS

Fig. 3.9. AgBr particles prepared at pBr 1.40, 1.90, and 2.30 in the presence of 0.5 mol dm"^ NH3 plus 1.0 mol dm"^ NH4NO3 at 50 °C by the CDJ method. (From Ref. 4.)

into 1000 cm^ of an agitated aqueous solution containing 2 wt% gelatin, 0.50 mol NH3, and 1.0 mol dm'^ NH4NO3 (pH 8.48) without seed particles at 50 "^C. Thus, the concentration of ammonia and the temperature in the reaction vessel are the same as those for the growth of the AgBr particles in the closed systems for Fig. 3.7. In this experiment, the addition rate of AgN03 was kept constant, and that of the KBr solution was regulated potentiometricaUy with a silver electrode to keep the pBr of the dispersion constant. This method is referred to as "controlled double jet (CDJ) technique."^"^^ Their excellent agreement with the solid line verifies the theoretical prediction for the steady form in the case of 1/V3 < a < V3 in Fig. 3.6. The pBr dependence of the/? value of the equilibrium form in Fig. 3.3 is also shown again by the dotted line for reference. Figure 3.9 shows transmission electron micrographs of carbon replicas of octahedral, tetradecahedral, and cubic particles of AgBr prepared by the simultaneous addition of AgNOj and KBr solutions at pBr 1.40, 1.90, and 2.30 under the same conditions as for the growth of AgBr particles represented by the circles in Fig. 3.8. The shapes of these AgBr particles in Fig. 3.9 are typical steady forms in the reaction-controlled growth mode. Stranski and Kaischew^^ suggested that the activation energy for the formation of the two-dimensional nuclei on a {111} face is almost zero in the absence of adsorption, whereas it is high enough on a {100} face. Thus {100} faces are developed to form a cubic shape. However, if some molecules are adsorbed to {100} and {111} faces, the peripheral surface energy of the two-dimensional nuclei on the {100} faces is lowered by the

3. HABIT FORMATION

133

preferential adsorption of the molecules to their peripheral steps whereas that of the {111} faces is, on the contrary, raised by the lower adsorption to the peripheries of the two-dimensional nuclei than to the rest of the {111} planes.^^'^"* Thus, any adsorption to {100} faces and/or {111} faces favors the development of {111} faces to give an octahedral shape. Moisar and Klein^^ used the Stranski theory to explain the morphological change of AgBr microcrystals, from cubes to octahedra, in terms of the adsorption of bromide ions to both {100} and {111} faces on the basis of their experiments on the adsorption isotherms of bromide ions to these faces. This may be a reasonable explanation for the opposite pBr dependences of the growth rate constants of the {100] and {111} faces shown in Fig. 3.7. If only one steady form is found in a reaction-controlled growth system of polyhedral particles bound by more than one kind of faces, there may be the following general relationship from the above discussion: r,:r,:r,...:r,...:r„=k,:k,:k,...:k,...:k„,

(3.2.10)

where r. and k. are, respectively, the central distance to and the growth rate constant of the faces of the zth kind. Here it should be noted that, if two kinds of steady forms are found in a system at the same time, or if the polyhedral particles are bound by only one kind of faces, this relationship does not necessarily hold. b) Steady Forms in the Diffusion-Controlled Growth Mode If a polyhedral microcrystal grows under ideal diffusion control where both growth and dissolution at the interface are sufficiently fast compared to the diffusion of solute toward the interface, the concentration of solute at interface must be virtually in equilibrium with each face of the microcrystal. Accordingly, the steady form of a polyhedral microcrystal which grows under ideal diffusion control must be the same as the equilibrium form.^^ In other words. Curie's hypothesis, referred to earlier, is valid for a fine microcrystal which grows under the ideal diffusion control mechanism. This model for a tetradecahedral particle in 1/V3 < a < V3 is illustrated in Fig. 3.10. Even if the solubility levels of the two kinds of faces a and b, C^ and Q, are initially different, as shown in the left-hand diagram, both of them will finally become equal to the concentration level, C-, of the solute at the solid/liquid interface after recrystallization by dissolution of face a and growth of face fo, as shown in the right-hand diagram. Therefore, p * for a tetradecahedral microcrystal bound by {100} and/or {111} faces in the

134

FUNDAMENTALS

diffusion-controlled growth mode is written as: . 1 p =—

. 1 for OS — ,

= Illl for±
= v/3

V3

for

a^y/3.

Ca I

Ca. Cb

Cfe

1^

non-steady state

steady state

Fig. 3.10. Concentration levels of solute for diffusion-controlled growth of a tetradecahedral particle in a non-steady state and in the steady state for 1/V3 < a < V3. The two kinds of faces are designated by a and b. The arrows indicate the directions of mass transfer of solute. (From Ref. 15.)

Figure 3.11 shows the critical growth rates of the {100} and {111} faces as functions of pBr, obtained by the CDJ technique with simultaneous introduction of AgNOj and KBr solutions into 1000 cm^ of an agitated solution, containing 1 wt% inert gelatin (pH 5.80) and 2.35x10"^ mol dm'^ monodisperse cubic AgBr particles (T^QQ = 0.255 \im) or octahedral AgBr particles (r^^^ = 0.221 \mi), at 60 °C in the absence of ammonia. Each critical growth rate, corresponding to the maximum growth rate under the critical supersaturation for nucleation, was determined by varying the addition rate of AgNOj at each pBr, in the presence of the seed particles, to detect the threshold of renucleation with an electron microscope.^^ Since the spontaneous nucleation occurs at a certain level of the supersaturation ratio irrespective of pBr, the supersaturation ratio is common for all pBr values.

135

3. HABIT FORMATION 20 ^1

^\ \ ^ \ >- \ h \ \ \ k

1 h

-

\

\ \

10

,-, ^ c S 8 o ^

\ ^\

6

4-*

\\

± S

"^^

\

\\

/ //

/^

/

X

• •

*

N

^

\

1

A

1

\

1

/ / •

, 1.5

2.0

_

iJc

.

.

If ^

^

Cub

1

1

2.5

1

1

4.0

pBr

Fig. 3.11. Critical growth rates of the {100} and {111} faces of AgBr as functions of pBr in an open system at 60 °C containing no ammonia. (From Ref. 15.) The remarkably different pBr dependence in the growth rate of the {100} and {111} faces in Fig. 3.7 is mainly due to the absence of anraionia that reduces the growth rate constants of each face by its adsorption.^^ Figure 3.12 shows the pBr dependences of the ratio of the apparent growth rate constants, K^^^IK^^^, obtained from r^i and r^^^ in Fig. 3.11 and/?* (= steady ^iii/^ioo) obtained from the dye-adsorption method of the particles actually formed by the CDJ technique in the absence of the seed particles. Since /?* changes from 1/V3 to V3 while K^-^^IK^,^^ stays close to unity, it is obvious

FUNDAMENTALS

136

Cubic Range

(kiii>kioo>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 fr^i" 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 F^a^a)-^'^ 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

4. RECRYSTALLIZATION

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 ^in/^ioo 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

4. RECRYSTALLIZATION

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/^ioo < 1/^3. Similarly, if small octahedral particles coexist with larger cubic particles at a sufficiently high pBr to attain k^n/k^oo > ^^^ ^^^ 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 r^u/r^QQ-, the prime designates the quantities of 11^ in distinction from those of ' [Cub] Icub- (From Ref. 33.) 1

1

4. RECRYSTALLIZATION

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^y^ioo* 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

4. RECRYSTALLIZATION

149

i.
A

o| o

o •!

^y

ael uV

•

/

\i2Vf 0°

1°

2° 3° 4° 5° Excbaneint; time (hr)

6

Fig. 4.8. Effect of Aza added before filtering on the curve of the degree of ion exchange. Curve A is that of a AgCl system plotted with samples filtered without Aza, while curve B is that with Aza added immediately after every sampling. (From Ref. 24.)

at 25 °C, which was determined radiochemically, with radioactive ^^Cr ions, by following the change of the radioactivity of the ^^Cl" ions in the solid, after the addition of the radioactive ^^Cl" to a suspension of AgCl particles.^"* As defined by Kolthoff and Rosenblum,^^ the degree of the ion exchange for chloride ions between the solid and liquid phases in a suspension of AgCl particles is given by (4.5.1)

where AQ is the total radioactivity of the suspension; A^ is the radioactivity of the solution phase at time t; M^ and M^ are the mole numbers of the nonradioactive chloride ions in the solid and solution phases, respectively. The separation of the solid phase from the liquid phase is normally performed by filtration. The curve A in Fig. 4.8 was obtained by filtering each sample by suction immediately after sampling, while the curve B was obtained in a similar manner, but each sample was once mixed with a solution of 4~ hydroxy-6-methyl-l,3,3a,7-tetraazaindene (Aza) to halt the Ostwald ripening immediately after sampling and filtered 5 min later. The great discrepancy between the two curves was due to the dramatic effect of Aza, as shown by the TEM images of the replicas of AgCl particles in Fig. 4.9, in which the original cubic AgCl particles, without mixing with Aza before filtration, were subject to a drastic recrystallization into a continuous

FUNDAMENTALS

150

iJL Fig. 4.9. TEM images of the carbon replicas of AgCi particles: (a) original particles after centrifugal separation with Aza; (b) a sample on afilterafterfiltrationwithout Aza added; (c) a sample on a filter after filtration with Aza added. (From Ref. 24.) structure consisting of large flat grains on the filter (b), whilst the particles treated with Aza beforehand remained intact (a). It is evident from the rapid exchange of chloride ions between the solid and solution phases that the dramatic change of the particles in Fig, 4.9(b) is due to a fast recrystaUization via the solution phase. Since the rapid recrystallization was caused by the contact of particles, it was named ''Contact Recrystallization,'' The same phenomenon was observed whenever any kinds of silver halide particles, including AgCl, AgBr, Agl, and their mixture, were in contact by flocculation on addition of electrolyte such as KNO3, or by centrifugation. Figure 4.10 shows the instantaneous halide-ion exchange by addition of KNO3 to a suspension of AgCl or AgBr at 25 °C. Figure 4.11 demonstrates AgCl

151

4. RECRYSTALLIZATION

10 20 30 40 50 Exchanging time (min)

Fig. 4.10. Rapid halide-ion exchange on addition of KNO3 in a AgCl or a AgBr system at 25 °C, where [KNO3] = 0.2 mol dm'l (From Ref. 24).

particles after flocculation or centrifugation.^^ When a mixed suspension of AgCl and AgBr or that of AgBr and Agl was filtered by suction, they instantly formed the respective solid solutions.^"* When the halide-ion concentration is in excess of the silver-ion concentration in the solution phase of a suspension of silver halide particles, the driving force of the Ostwald ripening, in terms of the chemical potential difference between the monomers in a small particle of radius r^ and in a larger particle of radius r^, (Ajx)^^, is given from the Gibbs-Thomson equation by

(1

(4.5.2) '2)

where [Ag^J^ and [Ag*]2 are the concentrations of silver ions in equilibrium with the particles of radii r^ and r^, respectively. If two spherical particles of radius r^ are in contact and in the progress of contact recrystallization in a monodisperse system, the driving force of the contact recrystallization, (A[iXanr inay be written as

152

FUNDAMENTALS

Fig. 4.11. TEM images of carbon replicas of AgCl particles showing the evidence of the contact recrystallization by flocculation or centrifugation: (a) original particles, (b) sample after flocculation of the particles in (a) with KNO3 shown in Fig. 4.10; (a') original particles (4 h old), (b') sample after centrifugation for 30 min with the particles in (a'), started at the age of 3.5 h. (From Ref. 34.)

(ALL)

=/?7Tn——i= yV

(4.5.3)

where r2a is the longitudinal negative radius of the neck in the boundary region of the particles in contact, and r2i, is the latitudinal positive radius, as illustrated in Fig. 4.12.^ In general, the absolute value of r2a is very small, especially in the early stage of contact recrystallization. This model is reminiscent of the sintering theory of Clark and White.^^ The solute preferentially deposits onto the necks, owing to the total negativity of the term, {llr2a + V^ih)^ i^ Eq. (4.5.3), which induces the dissolution of the surfaces of the particles of radius r^ by reducing the concentration of the

153

4. RECRYSTALLIZATION

D

Fig. 4.12. Model of the contact recrystallization. (From Ref. 34.) solute. If the r^ values m Eqs. (4.5.2) and (4.5.3) are equal, the driving force of the contact recrystallization, (Api^^^ is much greater than (Ajx^^) for the normal Ostwald ripening, owing to the small negative value of r2a' This seems to be the reason why the rate of contact recrystaUization is much greater than that of Ostwald ripening. Although the typical contact recrystallization, which readily occurs even at room temperature, was first found for silver halide microcrystals, it may not be limited to silver halides. Probably, it may be common to the colloidal particles whose rate constant of the surface reaction for their growth is sufficiently high as to make the growth mode a diffusioncontrolled one, or very close to it. Moreover, even if the drastic contact recrystallization is not observed, it is not rare to find that the contact points of aggregated particles act as active sites for the preferential deposition of solute in ordinary growth systems, leading to rigid agglomerates or junctioned particles.

References 1. C. M. Flynn, Jr., Chem, Rev. 84, 31 (1984). 2. M. A. Blesa and E. Matijevic, Adv. Colloid Interface Sci. 29, 173 (1989). 3. W. Ostwald, Z Phys. Chem. 34, 495 (1900). 4. R. Liesegang, Z Phys. Chem. 70, 374 (1910).

154

FUNDAMENTALS

5. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961). 6. C. Wagner, Z Elektrochem. 65, 581 (1961). 7. L. Kampmann and M. Kahlweit, Ber. Bunsenges. Phys. Chem. 71, 78 (1967). 8. M. Kahlweit, Ber. Bunsenges. Phys. Chem. 78, 997 (1974). 9. M. Kahlweit, Adv. Colloid Interface Sci. 5, 1 (1975). 10. D. B. Dadyburior and E. Ruckenstein, J. Crystal Growth 40, 279 (1977). 11. T. Sugimoto, J. Colloid Interface Sci. 63, 16 (1978). 12. T. Sugimoto, J. Colloid Interface Sci. 63, 369 (1978). 13. J. A. Marqusee and J. Ross, J. Chem. Phys. 79, 373 (1983). 14. J. Schmelzer, Z. Phys. Chem. (Leipzig) 266, 1057 (1985). 15. C. W. Davies and G. H. NancoUas, Trans. Faraday Soc. 51, 818 (1955). 16. E. J. Meehan and W. H. Beattie, J. Phys. Chem. 65, 1522 (1961). 17. C. R. Berry and D. C. Skillman, J. Phys. Chem. 70, 1871 (1966). 18. C. R. Berry and D. C. Skillman, Photogr. Sci. Eng. 13, 69 (1969). 19. H. Mager and K. H. Lieser, Z. Phys. Chem. (N. F.) 79, 288 (1972). 20. E. Klein, E. Moisar, and E. Roche, /. Photogr. Sci. 19, 55 (1971). 21. F. H. Claes and H. Borginon, J. Photogr. Sci. 21, 155 (1973). 22. L. E. Oppenheimer, T. H. James, and A. H. Herz, in "Particle Growth in Suspensions," (A. L. Smith, Ed.), p. 159. Academic Press, New York, 1973. 23. T. G. Bogg, M. J. Harding, and D. N. Skinner, J. Photogr. Sci. 24, 81 (1976). 24. T. Sugimoto and G. Yamaguchi, J. Phys. Chem. 80, 1579 (1976). 25. T. Sugimoto and H. Yanagida, Nippon Shashin Gakkaishi 40,15 (1977). 26. J. S. Wey and M. J. Schad, J. Imaging Sci. 30, 193 (1986). 27. T. Sugimoto, J. Colloid Interface Sci. 91, 51 (1983). 28. T. Sugimoto, J. Colloid Interface Sci. 93, 461 (1983). 29. T. Sugimoto, Photogr. Sci. Eng 28, 137 (1984). 30. T. Sugimoto, J. Imaging Sci. 33, 203 (1989). 31. C .R. Berry, Photogr. Sci. Eng 20, 1 (1976). 32. T. Sugimoto, J. Colloid Interface Sci. 150, 208 (1992). 33. T. Sugimoto, J. Soc. Photogr. Sci. Technol. Jpn. 46, 306 (1983). 34. T. Sugimoto and G. Yamaguchi, J. Crystal Growth 34, 253 (1976). 35. I. M. Kolthoff and C. Rosenblum, J. Am. Chem. Soc. 56, 1658 (1934). 36. P. W. Clark and J. W. White, Trans. Brit. Ceram. Soc. 49, 305 (1950).

CHAPTER 5 SOLID-SOLUTION FORMATION Functional particles used as advanced materials are, in many cases, composite particles consisting of more than one component. Such multicomponent particles often exhibit unexpected properties entirely different from those of the individual constituents due to their complex composition and internal structures. For controlling the structures which determine their properties, some fundamental knowledge of thermodynamics and kinetics relevant to the formation process of mixed particles are required. In this chapter, the thermodynamic aspects of this process and the kinetics of the conversion process for the formation of mixed particles will be described with concrete examples of well-defined silver halide systems.

5.1. Equilibrium Compositions 5.1.1. Theory Let us consider the solid mixing of two kinds of sparingly soluble monovalent salts which differ in either the cations or anions. Since the treatment is the same for either case, we consider only the case of mixing two kinds of salts, AB^ and AB2, having identical cations A and different anions, B^ and 82^ In a system of mixed particles of A{Bi,Bo) in the form of a solid-solution, suspended in a solution of their solute, the activity of the monomers oiAB^ in the liquid phase in equilibrium with the monomers of AB^ in the mixed particles may be approximated by their mole fraction in the liquid phase, jc^, from the assumption of a sparingly soluble solid. In this case, the chemical potential, fx^, of 1 mole of monomers AB^ is given by Hi = | i i + / f n n x i ,

(5.1.1)

where m® is the standard chemical potential of 1 mole of monomers AB-^ in

156

FUNDAMENTALS

the solution phase. If the particles are pure AB^, the equilibrium chemical potential of the monomers in the liquid phase, \I^Q, is given by

where X^Q is the activity of the monomers AB^ in this case. Hence, m can be rewritten as |jii=|jii,+/?nn-^. •^1,0

(5.1.3)

On the other hand, the chemical potential, ^^^ of the monomers AB^ in the solid-solution is given by

where /^ is the activity coefficient of the monomers AB^ in the solidsolution, and x^^ is their mole fraction in the solid-solution. Since \X^Q = \i^^, and since at equilibrium it holds that \ir-\^l

(5.1.5)

one obtains, on an assumption of a constant ionic strength, that

^,,;.A.I1TW,

(5.1.6)

where \A^] and [B^~] are the concentrations of ^"^ and 5 f in the liquid phase, respectively; and Kj^^ is the solubility product of the pure solid AB^, since the ion product [^^][^r] is proportional to Xp irrespective of the composition of the solid. The corresponding relation for component 2 is

'2.0 •*'»*'

As a consequence, one obtains

-»™ sp

157

5. SOLID-SOLUTION FORMATION

(5.1.8)

If JC2VJC1* and [B2']/[B^'] are measured analytically, f^ and /2 can be determined as a fimction of jc/ or X2 from Eq. (5.1.8) and the following Gibbs-Duhem equation:

(5.1.9)

XidWi*4dhif2 = 0

If some appropriate electrode is available, it is possible to determine these activity coefficients directly from the electrochemical measurement. For example, if AB^ and AB2 are silver halides of different halide ions, the /i and /2 can be determined readily by setting up the following cell with silver electrodes, where Ag(Xi,X2) is sufficiently large particles of a mixed silver halide consisting of AgX^ and AgX2; AgX^ is sufficiently large pure AgX^ particles whose solubility product Kj^^ is much greater than that of AgX2, KJ"^^; KX^ and KX2 are the potassium sahs of the respective halide ions. The concentrations of KX^ in both half cells are set to be equal and sufficiently high. KXi

Ag

KX2 Ag(X„X2)

Ag AgX,

The concentration of silver ions in the solution of the left-hand half cell, [Ag*]xi^. and that of the right-hand half cell, [Ag*]xi, are given from Eq.(5.1.7) as [Ag*]X [ ^

and

_

aiP

m

(5.1.10)

158

FUNDAMENTALS

(5.1.11)

[^8\ =

Hence, the potential difference, E, between the left- and right-hand electrodes is given by

£= M]j,^lL}^

= ^lnf,xl.

(5112)

[Agl where E is always zero or negative. From the measurement of E, one can directly obtain the value of/p and thus/2 as well, from the Gibbs-Duhem relation in Eq. (5.1.9). The free energy of formation, AG, of one mole of a solid-solution consisting of AgX^ of mole fraction x^^ and AgX2 of mole fraction X2 from each pure substance of AgX^ and AgX2 is given as AG = xli\i\-\i\) =

+x^i\il- ji^

RT(x^f,x',^x;}nf^) (5.1.13)

= RT

= FE+x^RThi

K^m

In some cases, the crystal system of a solid-solution is different from that of one of the pure starting solids. If pure AgX2 is different in crystal system from the solid-solution of Ag(XpX2), AG consists of AG^ for the transition from the pure AgX2 to pure AgX2 of the new crystal system of the solid-solution and AG2 for mixing with AgX^ to form the solid-solution. If the pure AgXj of the new crystal system of the solid-solution is indicated by an asterisk (*), AG^ and AG2 are given by

5. SOLID-SOLUTION FORMATION

159

and AG^ = FE^j4RThii^,

(5.1.15)

respectively. After all, AG (= AG^ + AG2) agrees with Eq. (5.1.13), so that Eq. (5.1.13) holds even if the solid solution is different in crystal system from the starting crystal of AgX2. As a matter of course, the situation is the same even if AgX^ or both of AgX^ and AgX2, are transformed into a solid-solution of a different crystal system. 5.1.2. Ag(Cl,Br) Systems The equilibrium between the mixed crystals of AgCl and AgBr and their halide ions in the solution phase was first studied by Kiister\ and has been investigated by many researchers since then.^"^ Figure 5.1 shows the relationship between the mole fraction of AgBr in the solid-solution of Ag(Cl,Br) and [Br"]/[Cr] in the solution phase at equilibrium, given by Pouradier et al} by averaging the data of Chateau,^ Flood,"^ Yutzy and Kolthoff,^'^ and Eastman and Milner.^ From this figure, it is obvious that the composition of the solid-solution of Ag(Cl,Br) continuously changes from jc^gj,/ = 0 to 1 with the change in the [Br"]/[Cr] ratio in the solution phase, and the [Br-]/[Cl-] ratio at jc^^^/ = 0.5 is 2.7x10"^ at 25 °C. Flood,^ particularly, defined the following parameter Kj as

K,^^En^,

(5.1.16)

and determined Kj as a function of the mole fraction of AgBr in the sohdsolution, Jc^gfl/, and the absolute temperature, T as follows:

FUNDAMENTALS

160

0,4

0,6

0,8

1,0

Fig. 5.1. [Br-]/[Cl-] vs x^^^. (From Ref. 8.)

890+180xLa,

(5.1.17)

If we use this parameter, it is possible to calculate the relationship between [Br"]/[Cr] and x^^^ at an arbitrary temperature. For the activity coefficients /^ and / j , Flood and Bruun^ and Chateau^ gave the following relationships:

where parameter ^ is a function of temperature and is 0.239 at 25 °C. Pouradier et a/, ^determined the relation between [Br"]/[Cr] and E using a cell of Ag(Cl,Br)-AgCl system similar to the one described in the foregoing section (AgX^ = AgCl; AgX2 = AgBr). They found an excellent agreement

161

5. SOLID-SOLUTION FORMATION

with the same relationship calculated from Eq. (5.1.12) with the data of [Br ]/[Cl-] v^ jc^g/ shown in Fig. 5.1 and available f^^a- ^ ^c^' Pouradier et al} used a cell with silver electrodes coated with a thin layer of AgCl or AgBr by electrolysis, instead of Ag(Cl,Br) and AgCl particles, and found the electromotive forces identical, irrespective of the kinds of electrodes. Also, X-ray diffraction data on the overall compositions of the silver halide layer were not in accord with those expected from the electrochemical measurement. Thus, they suggested that only the top layer of the silver halide coating was in equilibrium with the halide ions in the solution phase. 5.1.3. Ag(Br,I) Systems In contrast to the Ag(Cl,Br) system, there is an upper limit to the mole fraction of Agl component in mixing with the face-centered cubic (f.c.c.) AgBr crystal, Le., practically, around 0.40 in mole fraction. When the ratio of [r]/[Br"] in the solution exceeds a level in equilibrium with this maximum mole fraction in the f.c.c. solid phase, a new solid phase of hexagonal Ag(Br,I) crystals containing only a small amount of AgBr, less than ca, 5 mol %, appears. This is because iodide ions, having larger dimensions than bromide ions, raise the lattice strain energy with their increasing content in the f.c.c. crystals of Ag(Br,I) until, finally, the enthalpy

20

40

60

80

100

Mole percent iodide Average composition of solid

Fig. 5.2. Equilibrium Agl contents in f.c.c. Ag(Br,I) phase and in P-type Ag(Br,I) phase as a function of average iodide content in solid. (From Ref. 9.)

FUNDAMENTALS

162

increase by this effect exceeds the increase of the mixing entropy term. Figure 5.2 shows the equilibrium composition in the solid phases as a function of average composition of solid.^ Such a phase separation is actually observed when a mixed solution of soluble salts of bromide and iodide is added to a solution of a soluble silver salt (reverse mixing), or simultaneously added with the silver salt solution to an inert aqueous solution (double jet mixing) (see section 8.4.1). However, there seems to be no theoretical reason for the reduction of the iodide content of the cubic Ag(Br,I) phase with the increasing average iodide content of solid above ca, 40 mol % in Fig. 5.2. Chateau et al}^ studied the equilibrium of the Ag(Br,I) system. Figure 5.3 is one of their results for the linear relationship between [r]/[Br"] and x^J at 25 °C and 70 "C ([r]/[Br-] = 6WxlO-^xJ at 25 °C, and [r]/[Br-] = 2.07xl0-^x^/ at 70 °C). Figure 5.4 is their result for £ vs x^J using Ag electrodes coated with AgBr, KBr for KX^ and Kl for KX2, but for the data at x^J = 0.52 they used some supersaturated mixed crystals prepared from a mixed melt.

0,10

0,20

0,30

X^gi

Fig. 5.3. [r]/[Br-] vs x^J at 25 °C and 70 °C. (From Ref. 10.)

163

5. SOLID-SOLUTION FORMATION

0,10

0,20

0,30

0,40

QSO XAgi

Fig. 5.4. E vs x^J. (From Ref. 10.)

The thermodynamically stable form of pure Agl below 137 °C at 1 atm is a hexagonal crystal (P-type), while the Agl component in a f.c.c. solidsolution of Ag(Br,I) is in the form of f.c.c. crystal. On the other hand, the pure f.c.c. Agl crystal (8-type) is stable only above 3020 atm (= 306 MPa). Hence, for the formation of a f.c.c. solid solution of Ag(Br,I) near the room temperature, it is reasonable to consider that the P-AgI is once transformed into 8-AgI and then incorporated into the f.c.c. solid solution.^° Thus, Eq. (5.1.8) for a f.c.c. solid solution may be written as (5.1.19)

[Br-] Kl^Y,x\ where the components 1 and 2 correspond to AgBr and Agl components, respectively; the superscript 6 indicates the parameters for the f.c.c. crystals. On the other hand, from Eq. (5.1.6),

If a hexagonal solid-solution coexists, an analogous relation holds for it as

where the superscript p indicates the parameters for the hexagonal crystals.

164

FUNDAMENTALS

Hence,

and

[n_CV«

CV

[Br-] ^^V-f

0,\^

(5.1.23)

since /2^ « 1. This is because even the maximum mole fraction of the AgBr component in the hexagonal solid-solution is only around 0.01, which is achieved when the equilibrium mole fraction of the Agl component in the coexisting f.c.c. solid-solution reaches saturation (JC2* = 0.312 at 25 °C).^^'^^ When f.c.c. and hexagonal solid-solutions coexist, the potential difference E is generally given by

E= ^ I n / i V - —In F

F

^^—^

.

(5-1-24)

i£j>^([/-]/[Br-])

When x^^ = 0.312, [rMBr] = 1.89x10"^ and thus E = -2.92 mV at 25 °C. This E value is in good agreement with -3.2 mV obtained by the electrochemical measurement for Fig. 5.4. If C2 and VQ denote the molarity of the monomers AB2 and the molar volume of the solvent, respectively, the mole fraction of AB2 in the liquid phase is generally given by x, = c,V,.

(5.1.25)

Also, if K2 denotes the stability constant of AB2, K^

Hence,

^ - .

(5.1.26)

5. SOLID-SOLUTION FORMATION

165

x^ = IC,V,[A^][B^].

(5.1.27)

From Eq. (5.1.2), 1^2= 1^2.0= \xl*RTlnx,,= vil^RTlnK^V.^RThiK^K

(5.1-28)

Thus, from Eq. (5.1.4), one obtains

If we apply this formula to the f.c.c. solid-solution of ^4(5^^2)' nf = iil^RmK,V,^RTinKS\4 •

(^'^'^O)

For the hexagonal solid-solution, fxf = ,.^/^^lnJ^,K,.i^7^n4^>V.^^ If the two solid-solutions coexist, Kj'^%%^ = Kj^^h^ so that u

=11^ =11^

from

(5.1.31) Eq. (5.1.22)

(5.1.32)

where \i^^j, [x^^/, and \i^J are the chemical potentials of the Agl monomers in the liquid phase, 8-type solid-solution, and p-type solid-solution, respectively. Similarly, for the AgBr monomers, u >^ 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/(1^AJ)) 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.)

5. SOLID-SOLUTION FORMATION

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

5. SOLID-SOLUTION FORMATION

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

5. SOLID-SOLUTION FORMATION

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-

5. SOLID-SOLUTION FORMATION

175 3rd Step

2nd Step

A g *——^^ /<^^ , c r ^X /;rAg*' Ag As \ / \ Br--sU,Ag* '•V

Br"

fln*fK^"i^iii

Br"

' i l l " ' ""^fy^ Br" An"^

w. C r - i / ^ Ag* y

Vflr" Br"

A g * _ ^ \ ^ , - « ^ ^ A g * ^ ^ - ~ Ag*

Fig. 5.14. Schematic models of the first, second, and third steps of the partial conversion of AgCl particles with KBr. (From Ref. 14.) zoles, or tetraazaindenes, are used. Figure 5.14 illustrates the schematic models of the first, second, and third steps. The first step is an instantaneous step for the surface conversion of the AgCl microcrystals, within a few seconds after the introduction of bromide ions, to establish the equilibrium between the surfaces of the AgCl particles and the solution phase containing Br" and CI" ions. The second step is a rapid process of about 1 min at 25 ""C for the nucleation and epitaxial growth of nearly pure AgBr guest crystals on every comer and partly on the edges of the cubic AgCl hosts by the reaction of bromide ions with silver ions dissolved from the {100} faces of the AgCl particles. The third step is a much slower process of about 2 h at 25 °C (5 min at 45 °C) for the two-dimensional growth of the AgBro5Clo5 solid-solution on the AgCl host surfaces from the joints of guest/host by simultaneous dissolution of the AgBr guests and the open areas of the AgCl hosts. Finally, further steps form a solid-solution of a higher chloride content by the dissolution of the foregoing one formed in the preceding step together with the remaining host surfaces. From a thermodynamic viewpoint, the first and second steps are elementary processes for the reduction in enthalpy to form AgBr from AgCl (enthalpy processes), while the third and later steps are those for the increase in entropy to form AgCl^.^Br^ solid-solution from AgCl and AgBr (entropy processes). It is now obvious that the conversion reaction of this system proceeds by way of a stepwise intra-particle recrystallization, in which the nucleation and growth of the new solid phase initially occur at the comers and/or edges of each particle with the dissolution of other parts. The preferential nucleation of the guest particles on the comers and/or edges of the host particles seems to be due to the high

176

FUNDAMENTALS

density of bond-free sites on these parts. Then the AgBr guest crystals were found to be grown epitaxially on the AgCl host crystals, as revealed by electron diffractometry focused on a host crystal and one of its guest.^"^ Hence, generally, some active parts for the nucleation and growth of a new solid phase may be needed on the surfaces of the host particles for a wellregulated intra-particle recrystallization. Incidentally, there is no possibility of direct diffusion of bromide ions into the AgCl particles, as has been shown by a tracer technique^^'^^ and by the exceedingly low mobility of halide ions in silver halide crystals below 100 °C, as has been observed by Batra and Slifkin.^^ 5.2.2. Thermodynamics As has been shown in Fig. 5.8, the silver-ion concentration sharply dropped to reach a minimum in a few seconds after the introduction of Br" ions into the AgCl system, and a temporary equilibrium between the solution phase and the AgCl surfaces was established. The thickness of the surface layer rich in bromide content must correspond to one or more atomic layers, as is readily deduced from the radiochemical analyses, which indicate a very quick halide exchange between the the solution phase and silver halide surface layer.^^*^^ In this case, the atoms in the surface layer must be compressed with each other in order to be set epitaxially on the AgCl substrate of smaller lattice parameter (5.77 A/AgBr; 5.55 A/AgCl). On the other hand, if condensed CI" ions are introduced into a suspension of AgBr crystals with little excess of Br" ions in the solution phase, the surface layer of the AgBr crystals may turn into a solid-solution of silver chlorobromide of a high chloride content. In this case, the atomic bonds in the surface layer must be stretched laterally because of the greater lattice parameter of the AgBr substrate. The conceptual schemes of these situation are illustrated in Fig. 5.15. Thus, in both cases, some surface stress energy must be built up in the surface layer, and the chemical potentials of AgBr and AgCl components will be lifted by the surface stress energy (SSE), E^. For the AgBr component, the chemical potential, jx/, in the top atomic layer is given by

H^li^.E^./mnVJ.

(5-2.1)

where jx^^*^ is the standard chemical potential of the AgBr component in the top layer, /^ its activity coefficient, and JC/ its mole fraction. Thus one obtains from Eq. (5.2.1)

177

5. SOLID-SOLUTION FORMATION

K^ =

K^%x'^xpiEJRT),

(5.2.2)

where K^^ is the solubihty product of the AgBr component in the surface layer, and Kj^-^ is the solubihty product of pure AgBr. For the AgCl component. (5.2.3)

K^^K'^y^x'cOxpiEJRT).

The quantity E^ is a function of [Br']/[Cr] or x^/x^, and it will increase as jc/ becomes higher on the AgCl substrate. If £, = 0, then i C / = K^^^f^B so that K^^ is always equal to or smaUer than Kj^"^, Hence, if X^^ is found to be hi^er than K^^^, there must be some SSE in the surface layer. If the activities of silver ions in equilibrium with the AgBr component in the surface layer and with pure AgBr under the same bromide ion concentration are denoted by a^^^ and a^g+°, respectively, the potential difference A£ between them is given as RT.^^Ag^^RT^J^sp A£:=mhi 0 F

a) AgBr Surface Layer on AgCl

(5.2.4) pOB

b) AgCl Surface Layer on AgBr

Fig. 5.15. Schemes of the lattice compression and stretching of the surface layers on different silver halide substrates. The arrows stand for the compressive and stretching forces. (From Ref. 15.)

FUNDAMENTALS

178

On the other hand, if the mole fraction of the AgBr component in the surface layer on the AgCl substrate is close to unity, Eq. (5.2.2) reduces to (5.2.5)

K^^K^JcxpiEJRT),

since )^ = 1 when jc/ = 1. Since the second step of the conversion process corresponds to this case, E^ is given by (5.2.6)

E^ = FAE.

If we set a cell, as follows, with a sufficiently high initial concentration of KBr, the electromotive force at the minimum silver potential - reached immediately after the addition of KBr in the left-hand half cell - corresponds to the AE in Eq. (5.2.6), and thus we can determine the SSE. KBr [Br-]o Ag

KBr [Br-]o

KCl 5.0xlO-^M AgCl 0.40 M

Ag AgBr 0.40 M

The initial concentrations of KBr of both half cells were varied while keeping them equal in a range above 10"^ M, which is high enough for neglecting the portion of the bromide consumed for the surface exchange. Figure 5.16 shows the A£, 21.8 ± 0.45 mV, so obtained, corresponding to E^ = 503 cal mol"^ (2.10 kJ mol"^). If the concentration of KBr in the right-hand half cell is fixed at 0.10 M, and the total concentration of KBr added in the left-hand half cell is increased as follows from a very low level below 3.0 x 10"^ M, AE will be kept almost constant as long as the added [KBr] is sufficiently small, due to the small mole fraction of AgBr absorbed into the surface layer of the AgCl particles. KBr [Brio Ag

KBr O.IOM

KCl 5.0xlO-^M AgCl 0.40M

Ag AgBr 0.40M

5. SOLID-SOLUTION FORMATION

179

I <

01

2 3 4 5 6 7 8 9 [Br-]/10-'Af

10 11

Fig. 5.16. The minimum potential difference, A£, measured between the AgCl and AgBr suspensions containing the same amount of Br' ions for each half cell. The common [Br"]o was varied above 10'^ M. (From Ref. 15.) However, it will start to decline when the added [KBr] exceeds a certain level, due to the contribution of the AgBr component in the surface layer. Hence the intersection of the extrapolated lines of the initial plateau and succeeding declining curve will give the saturated amount of bromide in the surface layer. Figure 5.17 shows the result of this experiment, where the open circles represent the potential difference when AgBr particles were used in place of the AgCl particles in the left-hand half cell in this experiment. From this experiment the amount of bromide ions necessary for the saturation of the surface layer of AgCl was found to be 1.65 x 10'^ mol dm"^, corresponding to the molarity of the AgCl molecules in the exactly one atomic surface layer. The closed triangles in Fig. 5.17 represent the plotting of AE against the actual concentrations of bromide ions in the solution phase, as obtained by subtracting 1.65 x 10"^ mol dm"^ from each added concentration of KBr. The complete agreement of this plot with the straight line extrapolated from the higher concentration range of KBr reconfirms the propriety of the procedure for the thickness of the converted surface layer. Although the surface atomic layer of a crystal in the course of dissolution and rapid exchange of chloride by bromide must always retain the SSE due

180

FUNDAMENTALS 250 \ ^ 1.65X 10-3moledm -^

>

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.

5. SOLID-SOLUTION FORMATION

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

5. SOLID-SOLUTION FORMATION

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.)

5. SOLID-SOLUTION FORMATION

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

6. GENERAL PRINCIPLES

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.

6. GENERAL PRINCIPLES

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

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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;^^ Cu^O^

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"'

6. GENERAL PRINCIPLES

195

N-alkyl polyimine

Au'°

Polyvinylalcohol

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

Hydroxypropyl cellulose

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

Polyacrylic acid

a-FeA;'" PS"

Polymaleic acid and copolymers

a-Fe^Oj^^

Polymers with sulfonic acid

a-Fe^Oj'^

Polymers with thioether and sulfonic acid groups

AgBr," AgCl"

Cyclodextrin

AgBr/« AgCl,'«

Dextran sulfate

Cr(0H)3^'

Proteins (ovalbumin, Y-globulin, lysozyme)

a-Fe^Og,^''' 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^°

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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'^i5^^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

6. GENERAL PRINCIPLES

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 ^un) 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

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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

6. GENERAL PRINCIPLES

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)

^IDV^AC'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.)

6. GENERAL PRINCIPLES

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.^'^'^^^^^'^"^"^^^

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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 follov^ed 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

7. MONODISPERSED SYSTEMS

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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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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-

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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-

7. MONODISPERSED SYSTEMS

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-CH^OH) 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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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-

7. MONODISPERSED SYSTEMS

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 - # ^ ^ V^Ai IO|im i

Qg(jy^ ^^^

^j

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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 ^un; 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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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.)

7. MONODISPERSED SYSTEMS

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 y^i^[^Y^ j^aj. 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

7. MONODISPERSED SYSTEMS

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) •2Ru^OC03-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.

7. MONODISPERSED SYSTEMS

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-

7. MONODISPERSED SYSTEMS

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 nici^el 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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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 (Jd^O^^^^'^ 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

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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.

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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

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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

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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

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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 « k^in-^)[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*]

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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

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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

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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.)

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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-

7. MONODISPERSED SYSTEMS

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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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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,^'' fyfiM^As nfc^^eaAi 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-^im 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 ^ec-butyllithium, in a non-polar solvent, such as n-hexane

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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-

7. MONODISPERSED SYSTEMS

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.

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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 fe^O^ (large sphere)

FeCOHjgnHgO

Fe^O^ (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

7. MONODISPERSED SYSTEMS

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-

7. MONODISPERSED SYSTEMS

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-

7. MONODISPERSED SYSTEMS

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.

7. MONODISPERSED SYSTEMS

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).)

7. MONODISPERSED SYSTEMS

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^^ ^^^IQI 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.

7. MONODISPERSED SYSTEMS

A-3 (B-3) I

"H

S^irn

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

7. MONODISPERSED SYSTEMS

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 ^it 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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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.

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

"' = 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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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-

7. MONODISPERSED SYSTEMS

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-^^O °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

7. MONODISPERSED SYSTEMS

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-^ec-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),'''

7. MONODISPERSED SYSTEMS

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 ^ec-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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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.)

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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.) 2^olites 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

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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-

7. MONODISPERSED SYSTEMS

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

7. MONODISPERSED SYSTEMS

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.)

7. MONODISPERSED SYSTEMS

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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tsu, Y. Shintoku, and T. Sugimoto, in "Proc. 50th Symp. Colloid Interface Chem.," (Chem. Soc. Jpn.), p. 320. Saga, Oct. 1997. 462. T. Sugimoto, H. Kawasaki, and A. Muramatsu, in "Proc. 52nd Symp. Colloid Interface Chem.," (Chem. Soc. Jpn.), p. 136. Morioka, Oct. 1999. 463. T. Sugimoto and Y. Wang, J. Colloid Interface Sci. 207, 137 (1998). 464. S. Waki, A. Muramatsu, and T. Sugimoto, in "Proc. 51st Symp. Colloid Interface Chem.," (Chem. Soc. Jpn.), p. 245. Chiba, Sept. 1998. 465. B. Breitscheidel, J. Zieder, and U. Schubert, Chem. Mater. 3, 559 (1991). 466. R. C. Fumeaux, W. R. Rigby, and A. P. Davidson, Nature 337, 147 (1989); F. Keller, M. S. Hunter, and D. L. Robinson, J. Electrochem. Soc. 100, 411 (1953); H. Akabori and T. Fukushima, J. Electron Microscopy 13, 162 (1964). 467. S. Kawai and R. Ueda, J. Electrochem. Soc. 122, 32 (1975). 468. D. AlMawlawi, N. Coombs, and M. Moskovits, J. Appl. Phys. 70, 4421 (1991). 469. C. A. Foss, Jr., G. L. Homyak, J. A. Stockert, and C. R. Martin, J. Phys. Chem. 96, 7497 (1992). 470. C. A. Foss, Jr., G. L. Homyak, J. A. Stockert, and C. R. Martin, Adv. Mater. 5, 135 (1993). 471. C. A. Foss, Jr., G. L. Homyak, J. A. Stockert, and C. R. Martin, J. Phys. Chem. 98, 2963 (1994). 472. G. L. Homyak, C. J. Patrissi, and C. R. Martin, J. Phys. Chem. B 101, 1548 (1997). 473. H. Masuda and K. Fukuda, Science 268, 1466 (1995). 474. P. Hoyer, N. Baba, and H. Masuda, Appl. Phys. lett. 66, 2700 (1995). 475. P. Hoyer, Langmuir 12, 1411 (1996). 476. B. B. Lakshmi, P. K. Dorhout, and C. R. Martin, Chem. Mater. 9, 857 (1997). 477. C. J. Bmmlik and C. R. Martin, J. Am. Chem. Soc. 113, 3174 (1991). 478. W. Liang and C. R. Martin, J. Am. Chem. Soc. 112, 9666 (1990). 479. T. Kyotani, L. Tsai, and A. Tomita, Chem. Mater. 7, 1427 (1995). 480. T. Kyotani, L. Tsai, and A. Tomita, Chem. Mater. 8, 2109 (1996). 481. R. V. Parthasarathy, K. L. N. Phani, and C. R. Martin, Adv. Mater. 7, 896 (1995). 482. G. Che, B. B. Lakshmi, C. R. Martin, E. R. Fisher, R. S. Ruoff, Chem. Mater. 10, 260 (1998). 483. L.-F. Rao, A. Fukuoka, N. Kosugi, H. Kuroda, and M. Ichikawa, J.

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Phys. Chem. 94, 5317 (1990); P. Galin, Y. B. Taarit, and C. Naccache, J. Catal. 59, 357 (1979). 484. (a) M. Ichikawa, Polyhedron 7, 2351 (1988); (b) M. Ichikawa, Adv. Catal. 38, 283 (1992); (c) M. Ichikawa, Zeoraito 10, 9 (1993). 485. K. Itabashi, in "Zeoraito no Kagaku to Ohyoh," (H. Tominaga, Ed.), pp. 79-92. Kodansha, Tokyo, 1987. 486. M. C. Connaway and B. E. Hanson, Inorg. Chem. 25, 1445 (1986). 487. G.-C. Shen, T. Shido, and M. Ichikawa, J. Phys. Chem. 100, 16947 (1996). 488. P. Gorllezat, in "Metal Clusters," (M. Moskovits, Ed.), p. 219. Wiley, New York, 1986; M. Iwamoto and S. Hasegawa, J. Phys. Chem. 90, 5244 (1986). 489. G. Bergeret, P. Gallezot, and F. Lefebvre, Stud. Surf. Sci. Catal. 28, 401 (1986); S. Kawi and B. C. Gates, J. Am. Chem. Soc. 115, 4830 (1993). 490. S. Kawi and B. C. Gates, J. Chem. Soc, Chem. Comm. 702 (1992). 491. M. Ichikawa, L.-F. Rao, T. Ito, and A. Fukuoka, Faraday Discuss. Chem. Soc. 87, 321 (1989). 492. A. Fukuoka, L.-F. Rao, and M. Ichikawa, Nippon Kagaku Kaishi 561, (1989). 493. A. De Malhnann and D. Barthomeuf, Catal. Lett. 5, 293 (1990); G. Schulz-Ekloff, R. J. Lipski, N. I. Jaeger, and P. Hiilstede, ibid. 30, 65 (1995); L. Kubelkova, L. Drozdova, L. Brabec, J. Novakova, J. Kotrla, P. Hiilstede, N. I. Jaeger, and G. Schulz-Ekloff, J. Phys. Chem. 100, 15517 (1996). 494. G.-J. Li, T. Fujimoto, A. Fukuoka, and M. Ichikawa, J. Chem. Soc, Chem. Comm. 1337 (1991); G.-J. Li, T. Fujimoto, A. Fukuoka, and M. Ichikawa, Catal. Lett. 12, 171 (1992); R.-J. Wang, T. Fujimoto, T. Shido, and M. Ichikawa, J. Chem. Soc, Chem. Comm. 962 (1992). 495. L. L. Sheu, H. Knozinger, and W. M. H. Sachtler, Catal. Lett. 2, 129 (1989); L. L. Sheu, H. Knozinger, and W. M. H. Sachtler, J. Am. Chem. Soc 111, 8125 (1989). 496. A.-M. Liu, T. Shido, and M. Ichikawa, J. Chem. Soc, Chem. Comm. 509 (1995). 497. G.-C. Shen, A.-M. Liu, T. Shido, and M. Ichikawa, Top. Catal. 2,141 (1995). 498. G.-C. Shen and M. Ichikawa, J. Phys. Chem. 100, 14265 (1996). 499. W. M. Meier and D. H. Olson, Zeolites 12, 449 (1992). 500. Y. Wang and N. Herron, J. Phys. Chem. 91, 257 (1987); N. Herron, Y.

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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, ^erow/ 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).

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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 <2o 2^d inversely proportional to TJ^.. It means that there are two ways for size control: 1) Control of the supply rate of the monomers; 2) Control of the growth rate. In open systems, the control of the supply rate of the monomers can be performed by controlling the feed rate of the monomer sources. In closed systems, the supply rate of the monomers corresponds to the formation rate of the precursor monomeric species or release rate of the monomers from a reservoir, so that the same objective is generally achieved by controlling the temperature of aging, pH, and/or initial concentration of the solute, or by choosing a monomer reservoir giving an appropriate release rate of the monomers. On the other hand, the growth-rate control is performed by regulating the apparent solubility of the solid with some solvent for the solid, or by using some adsorptives to control the growth rate constant, for both open and closed systems.

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In contrast to the general methods for size control, the seeding technique is known as an effective alternative that is independent of Eq. (8.1.1). Namely, if we add a known amount of seeds to a system at a relatively low supersaturation below the critical level for nucleation, the seeds will grow without nucleation. In this case, the final particle number can be controlled by the number of the seeds. The same puq)0se may be achieved by adding anions or cations of the final product to a system containing a small amount of counterions in excess of the monomers in a reservoir. Also, the technique of supersaturation quenching^ can be used for size control, in which the high supersaturation in the midst of nucleation is intentionally lowered by changing temperature and/or pH, or by addition of a solvent for the solid or complexing agent. More concrete examples of the controlling factors will be given below. 8.1.1. Feed Rate As has been shown earlier in Fig. 1.32 of section 1.5.2, the final particle number of monodisperse silver bromide in a controlled double-jet (CDJ) system is proportional to the addition rate of silver nitrate and potassium bromide solutions.^ Although this result was obtained under a diffusioncontrolled growth condition, the linear relationship between the feed rate of the monomer sources and the final particle number holds even in reactioncontrolled systems,^"* since v^ in Eq. (8.1.1) is independent of the feed rate irrespective of the growth mode. The linear relationship is also found in the CDJ system of AgCl.^ The CDJ system, illustrated in Fig. 1.30 in section 1.5.2, is a typical open system often used for the preparation of monodispersed silver halide particles in the photographic industry.^"^ As described in section 1.5.2, the AgNOg solution in Fig. 1.30 is added at a rate programmed beforehand, while the flow rate of the halide salt solution is regulated by monitoring pAg (= -log[Ag^]) or pBr (= -log[Br"]) with a silver electrode. Hence, this system has a merit of easy control of pAg as one of the most important factors for determining the crystal habit of the product, in addition to the precise control of the flow rate of the reactants. This method has recently been applied to the preparation of uniform particles other than silver halides; e.g., sulfates, such as strontium sulfate^ and lead suifate,^'^" barium titanate,^^'^^ zinc oxide,^^ and cupric oxide.^"* In view of the size distributions of the spherical particles of barium titanate and zinc oxide, fairly narrow but a little broader than those of typical monodisperse particles grown by deposition of the monomeric species, and the clear evidence of

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aggregation in their SEM images including somewhat deformed aggregates, these particles are thought to have been grown by aggregation of preformed fine particles. In fact, the mean size of the zinc oxide particles was rather increased with increasing flow rate of their reactants, while the size of the subcrystals of each polycrystalline particle decreased with the increase of the flow rate.^^ This fact strongly supports the aggregation mechanism. Needless to say, the above rule of the proportionality of the final particle number to the feed rate of the monomer sources does not apply to such a system. Also, when the final product is formed through a rather slow phase transformation of the solid in a CDJ system, the above rule does not hold, since for the application of this rule a steady state must be established in the precipitation of the final product with the continuous introduction of the reactants. Nevertheless, the rule can apply to any kind of monodisperse particles including amorphous or polycrystalline ones, as long as the steady state is secured without aggregation. Conversely, if this rule does not hold in a colloidal system, it may suggest a possibility of coagulation of the growing particles or a multistep process. 8.1.2. Temperature In order to control the size of the final product, we often vary the temperature of the system. In an open system in which the feed rate of the monomer sources, QQ, can be predetermined independently of the temperature of the system, the final particle number decreased or the final particle size is increased by the elevation of temperature, because i)^ in Eq. (8.1.1) increases with the elevation of temperature.^ However, in a closed system, it is not rare to find that the final size even decreases with elevation of temperature, since the activation energy for the production of the precursor species, e.g., by hydrolysis of metal ions or metal alkoxides, dissolution of solid precursors, dissociation of metal chelates, etc. is often higher than that for the particle growth. In this case, the increase in QQ with increasing temperature is greater than the increase in v^. For example, the final size of the monodisperse hematite particles in the gel-sol system can be reduced fi-om a few microns to ca, 0.3 (xm without appreciable degrading of the uniformity simply by raising the temperature from 50 to 100 °C in their nucleation period.^^ Also, the final size of the silica particles in a sol-gel system can be reduced in the same way.^^ However, this method of size control has some limitations, since the uniformity of the final product is degraded by degrees with increasing temperature, because of the promoted nucleation concurrent with the growth of the nuclei.

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8.1.3. Reservoirs In most monodisperse systems, some reservoir of the monomer is included (see section 6.3). For example, many kinds of monodisperse metal sulfide particles were prepared from the corresponding concentrated metal chelates^^ or metal oxide }^'^^ In these systems, the size of the final product can be varied by using different kinds of chelating agents, since the number of nuclei generated by the initial reaction with the dissolved metal ions, in equilibrium with a chelate or precursor solid as a reservoir of the monomers, depends strongly on the stability constant or solubility product of the reservoir and its release rate of metal ions, the latter of which corresponds to the supply rate of the monomers, QQ, Hence, the choice of reservoirs is one of the important means for controlling the size of the final product. In the gel-sol system for the formation of monodisperse anatase titania (see section 7.3.1),^'^^ the size of the final product depended strongly on the degree of gelation as a function of aging time for the gelation; /.e., the final size increased with increasing degree of gelation. This is due to the reduction of the concentration of the free metal complexes with the development of the gel, corresponding to the lowering supersaturation for nucleation in the second aging at a higher temperature. This is an example of the size control by the same monomer reservoir in different states. As has been described earlier in section 1.4 for the formation of silver chloride and silver bromide particles in a closed system, it is also possible to control the release rate of metal ions with dissociation of the metal complexes caused by the gradual hydrolysis of some foreign compound, such as diethyl sulfate, to release protons. The size of the final product can be controlled by changing the content of diethyl sulfate. 8.1.4. Solvents for Solids We have seen many examples of the important role of ammonia as a solvent for solid in promoting particle growth by increasing the apparent solubility of the solid. For example, it is weU known that the growth of silver halide particles is greatly accelerated by the presence of ammonia at the order of 10"^ - 1 mol dm"^ This is due to the formation of ammonia complexes of silver ions, such as Ag(NH3)2^, to increase the apparent solubility of silver halides. Namely, even if the supersaturation ratio is identical, the difference between the supersaturated total concentration and total solubility, as the driving force of particle growth, is much greater when such a complexing agent is present. This effect of ammonia was also used for the preparation of monodisperse metal sulfides^^"^^*^^'^ and spindle-like

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anatase titania^°'^^ in the gel-sol systems. Since v^ increases with increasing concentration of ammonia, the volume of each particle of the final product increases in proportion to i)^ from Eq. (8.1.1). In addition to ammonia, thiocyanate, thioethers, and thiourea are well known as solvents of solid. However, since these solvents of solid are a kind of complexing agents for metal ions, they are also adsorbed to the metal ions of the solid surface, so that they have the effect of inhibiting the surface reaction for particle growth in some cases. In other words, complexing agents are of a more or less dual nature for particle growth. For example, the growth of silver bromide particles in the pBr range of diffusion control is switched to reaction control by adsorption of a highly concentrated ammonia.^"* Also, the growth rate of the spindly anatase particles is rather retarded by the presence of an excessive concentration of ammonia.^ As a rule, too high a concentration of a good solvent of solid, or the use of a complexing agent of an excessively high stability constant as a solid solvent, often brings about a contrary effect. 8.1.5. Restrainers of Growth If the stability constant of a complex of metal ions is high and its solubility is low, the complexing agent may be adsorbed strongly to the surface of solid and thus act as a restrainer of particle growth. For example, nucleic acids and their components, such as DNA, RNA, adenine, and guanine,^^^ benzotriazoles^^'^^ benzimidazoles^^ mercapto compounds^^'^^ dithiocarbamates,^^'^^ 4 -hydroxy - 6-methyl -1,3,3a, 7 - tetraazaindene,^^ cyanine dyes^^ merocyanine dyes^^ etc. are well known as effective restrainers of particle growth of silver halides. These compounds may be applied to the growth control of other kinds of colloidal particles. For example, Yonezawa et aO^ reduced the size of gold particles to ca, 3 nm from ca. 20 imi by use of sodium 3-mercaptopropionate in the preparation of gold particles by reduction of Au-^^ ions with sodium citrate. Also, heavy metal ions, such as lead ion,^^'^^ and cadmium ion^^ and anions such as iodide^^ are known as strong restrainers to the growth of silver halides due to their chemical adsorption to anion and cation sites, respectively, of the solid surfaces. With respect to the restrainers of the growth of metal oxides, anions such as sulfate and phosphate are known to retard the growth of hematite ( a - F e A ) particles.^°'^^ The final particle size can be reduced by use of these restrainers, since v^ at the end of the nucleation period is lowered in Eq. (8.1.1).

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Also, as has been referred to earlier in section 7.3.4, nonionic, anionic, and cationic surfactants may retard the growth of the particles in water pools of reversed micelles. However, it should be noted that, in some cases, the final particle size rather increases with the increase in the concentration of a surfactant; e.g,, the increase of the particle size of silica particles in a sol-gel system with sodium dodecylsulfate (SDS), probably due to the coalescence of the nuclei by the effect of the anionic surfactant, as an electrolyte, during nucleation stage."*^ Hence, if one uses ionic surfactants as a protective agent in particle growth, special care is required, since their properties dramatically change with their own concentration, pH, solvent species, the surface properties of the particles, etc. 8.1.6. pH The pH is an important factor for controlling particle size, especially in the formation of metal oxides, metal hydroxides, and metal sulfides. For example, the final size of the hematite particles prepared in the gel-sol system depends strongly on the pH or excess concentration of ferric ions in the nucleation stage.''^'^ In this case, the control of pH and that of the excess concentration of ferric ions are equivalent because of the constant solubility product of the Fe(0H)3 gel. Since the solute in the solution phase is in equilibrium with the Fe(0H)3 gel in the nucleation stage of the hematite,"*^ the supersaturation for this nucleation, in terms of solubility product, is kept constant with the change of pH, and thus the enhanced nucleation with increasing pH must be explained by increase in the concentration of some specific hydroxide precursor complex of ferric ions with pH. Hence, if the pH is lowered below a certain level such as pH « 1 by the formation of p-FeOOH, the nucleation of hematite ceases. As a consequence, it is possible to control the final size of the hematite by varying pH or the excess concentration of ferric ions. Also, as readily expected from this conclusion, nanosized hematite less than 10 nm is produced by forced hydrolysis of a sufficiently dilute homogeneous solution (< 10"^ mol dm'^) of a ferric salt, such as FeCl3, Fe(C104)3, or Fe(N03)3, at a relatively high pH above 3, though the product is extremely small in amount. These trends are more or less observed in general synthetic systems of metal oxides and metal hydroxides. If we use thioacetamide as a reservoir of sulfide ions for the preparation of metal sulfides in concentrated chelate systems, the final size of the metal sulfides depends strongly on the initial pH.^ Namely, the final size decreases with increasing pH, because the concentration of sulfide ions in

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equilibrium with thioacetamide increases according to Eq. (7.2.1) in chapter 7, the effect of which overcomes the effect of the decrease in concentration of free metal ions. Even in an open system of silver halide, a pH effect on the final size is observed when some solvent for the solid, such as ammonia, is included. That is, since the proportion of the effective solvent molecules free from protonation increases with increasing pH, the concentration of its silver-ion complex increases, and thus the final size increases due to the enhanced growth rate. Such an indirect effect of pH is generally observed in a system with some solvent of solid. As one may readily infer from this fact, the final size generally decreases with increasing pH in the presence of some organic restrainer to be adsorbed to cation sites of particle surfaces. 8.1,7. Seeding Seeding is a useful technique for obtaining monodisperse particles, since size distribution broadening during the nucleation period can be avoided by adding seeds in a system at a low supersaturation below the critical level for nucleation. Also, if the release rate of monomers from their reservoir is the rate-determining step for particle growth, the supersaturation is lowered by addition of the seeds, so that the separation between nucleation and growth can be achieved readily (see chapter 6). Furthermore, if the added seeds work at maximum efficiency, the final particle number will be equal to the number of the seeds. Even if the efficiency is not 100 %, the final particle number is at least proportional to the number of the added seeds, and thus quantitative size control of a high reproducibility is readily realized. For example, the final sizes of monodisperse hematite particles in a dilute homogeneous system"*^ and in condensed gel-sol systems^^'^'*^ were controlled by using seeds of hematite of less than 10 nm in mean diameter. Figure 8.1 shows TEM images of ellipsoidal hematite particles controlled in size by seeding at a constant concentration of sulfate ions in a condensed gel-sol system.^^'"*^ Similarly, the size of the monodisperse basic aluminum sulfate particles was varied by using their seeds."*^ Also, the final size of monodisperse cadmium sulfide particles in condensed chelate systems was controlled by changing the concentration excess of cadmium ions over the concentration of EDTA used as a chelating agent, as being equivalent to a change in the amount of the seeds.^^*^ The seeding technique is widely used in emulsion polymerization and dispersion polymerization as well. However, unlike inorganic particles, the reaction proceeds through swelling of the seed particles with the monomer.

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Fig. 8.1. Size control of ellipsoidal hematite by seeding with different amount of seeds. (From Ref. 15.)

and thus it is possible to grow polymer seeds to large particles by the twostep swelling method,"*^ dynamic swelling method/^ accelerated molecular diffusion method/^ etc. (see section 7.2.3). Particularly, we can readily obtain very large monodispersed particles of even more than 100 \xm from 1-2 tun seeds by the two-step swelling method. 8.1.8. Supersaturation Quenching The size of the basic aluminum sulfate particles in the condensed gelsol system was varied by lowering the pH with acid at different times during their nucleation stage."*^ As the timing of the supersaturation quenching was delayed, the final size was reduced, due to the increase in the number of preformed nuclei, and, besides, the size distribution was narrowed, due to

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PREPARATION

the efficient prevention of the renucleation by the greater number of nuclei.

8.2. Shape Control As has been shown in chapter 3, monocrystalline particles assume a variety of crystal habits proper to the crystal system, according to the environment of their growth. The diffusion-controlled steady growth form is equivalent to, or at least close to, the equilibrium form determined by the ratio of the specific surface energy of each facet, while the reactioncontrolled steady-growth form is mainly determined by the ratio of the growth rates of each facet.^'*'^^ In both growth modes, some adsorptives are responsible for the habit control. This rule applies to even internally polycrystalline particles consisting of subcrystals of a definite crystal orientation, since their two-dimensional surface nucleation and subsequent growth occur epitaxially on the crystal lattices of the substrate. Apart from the shape control by adsorption of additives, it is also possible to initiate anisotropic particle growth by activating some parts of crystal lattices or by external magnetic or electric field. In contrast, the shape of polycrystalline particles grown through nonepitaxial surface nucleation is spherical, because of the random orientation of the subcrystals. Similarly, amorphous particles grown through deposition of the monomeric species without the reorientation for crystallization are also spherical. On the other hand, the shape control of polymer latices to form nonspherical particles, such as symmetric or asymmetric doublets, and confetto-like particles, is performed on the basis of unique controlling techniques applied to monomer-swollen polymer seeds in emulsion polymerization. In this section, examples of these shape controlling techniques are described. 8.2.1. Shape Control by Adsorption a) Inorganic Controllers Anions as a component of a particle are often found to be an effective shape controller. For example, bromide ions are well known as a shape controller of silver bromide particles (see section 3.2). As the excess concentration of bromide ions increases, the shape of a silver bromide

8. CONTROL OF PARTICLE CHARACTERISTICS

377

microcrystal changes from a cube to an octahedron via tetradecahedra. This pBr dependence of the growth form may be explained by the enhanced growth of the {100} faces and suppressed growth of the {111} faces with the progress of the adsorption of bromide ions, due to the lowered specific surface energy at the peripheries of the surface nuclei on the {100} faces below the specific surface energy of the remaining areas of the {100} faces and the peripheral surface energy of those on the {111} faces kept high relative to the surface energy of the remaining areas of the {111} faces.^'^^ However, this explanation may be limited to the case of reaction-controlled growth. The morphological change within the pBr range from 2.6 to 3.5 in which the particle growth is in the diffusion-controlled mode is due to the change in the ratio of the overall specific surface energies of the two different faces (see Figs. 3.11 and 3.13).^^ On the other hand, magnetite particles prepared by oxidation of ferrous hydroxide gel with air are not perfectly uniform as yet, but show a definite pH dependence of their shape: spheres at pH ^ 8, cubes at pH « 10, and octahedra at pH ^ 13.^^'^^ In this system, there is almost no sign of coagulation in the pH region above 10, probably due to the absence of an appreciable concentration of polyvalent ferrous hydroxide complexes in addition to the effect of the gel network. The habit modification of the monocrystalline spinel magnetite from a cube to an octahedron with increasing pH may be explained in terms of the effect of adsorbed hydroxide ions on the analogy of the morphological change of face-centered cubic silver bromide with adsorption of bromide ions in the reaction-controlled growth mode. Moreover, it was found that the {001} faces of hematite^ and basic aluminum sulfate"*^ particles were developed to yield platelet particles with increasing pH, due to the inhibited growth of these faces of the hexagonal system by adsorption of hydroxide ions. Figure 7.21(d) in chapter 7 gives SEM images of monodispersed platelet particles of hematite prepared by phase transformation from p-FeOOH in a highly alkaline solution of 7.5 mol dm"^ NaOH. Figure 8.2 shows SEM images of basic aluminum sulfate particles prepared at different [NaOH]/[Al^*] ratios with a constant [SO/"]/[Al^*] ratio of 1/4. Obviously, the shape of the basic aluminum sulfate particles changed from cube bound by only the {012} faces to disk with developed basal {001} planes, via octahedra bound by the {001} and {012} faces, with increasing initial pH. The silver bromide particles shown in Fig. 3.9 in chapter 3 were prepared at different pBr in the presence of ammonia, which is known as a shape controller as well as a solvent of silver halides to accelerate the

378

PREPARATION C4

ipm

4ym

Fig. 8.2. SEM images of basic aluminum sulfate particles systematically controlled in crystal habit at [S04^-]/[Al^^] = 1/4 by variation of the overall [NaOH]/[Al^^] ratios as indicated in the parentheses: C-1 (1.5), C-2 (1.8), C-3 (2.4), and C-4 (2.7). (From Ref. 46.)

8. CONTROL OF PARTICLE CHARACTERISTICS

379

growth of silver halide particles. When ammonia is present, the rate constant of the surface reaction for the growth of {100} faces of silver bromide is lowered by adsorption of ammonia, and thus the minimum pBr of their reaction-controlled growth range is drastically lowered, while the pBr range of the reaction-controlled growth for {111} faces is little affected. For example, while the reaction-controlled pBr range for the {100} faces is above 3.5 without ammonia in Fig. 3.11, it is above 1.5 with anmionia in Fig. 3.7. The maximum pBr for the {111} faces in the reaction control is around 2.6 in both cases. As a result, with increase in ammonia concentration, the threshold of pBr for the formation of cubic particles shifts to the lower pBr as shown in Fig. 8.3.^^ Also, the aspect ratio (ratio of length to width) of the anatase titania particles prepared by the gel-sol procedure increased with increasing concentration of ammonia by lowering the relative growth rate in the direction normal to the c-axis.^^*^^

Fig. 8.3. Effect of ammonia on the pBr range for the formation of cubic or octahedral AgBr particles. (From Ref. 55.)

Matijevic and Scheiner^^ prepared hematite particles of different shapes by forced hydrolysis of dilute solutions of iron salts with different anions in acidic media. They obtained ellipsoidal particles from Fe(N03)3, ellipsoidal and star-like particles from Fe(C104)3, and pseudocubic, spheroidal, and double-ellipsoidal particles from FeCl3. Ozaki et al^^ controlled the aspect ratio of uniform ellipsoidal particles of hematite by

380

PREPARATION

forced hydrolysis of ferric chloride in its dilute acidic solutions containing different concentrations oi phosphate ions (see section 7.2.10). Figures 7.21(a)-(c) in chapter 7 show SEM images of hematite particles

o

E c 3 o

E <

(c) thick platelets

•e o

< (d) thin platelets

—*

1x10'

2x10'^

3x10-

4x10"* -3x

Equilibrium Concentration of Sulfate (mol dm' ) Fig. 8.4. Adsorption Isotherms of sulfate ions at pH 1.0 and 100 °C after aging for 24 h with a-FcjOg particles of different shapes: ellipsoids, pseudocubes, thick platelets, and thin platelets, which are mainly bound by planes parallel to the c-axis for ellipsoids, {012} for pseudocubes, {001}+{012} for thick platelets, and {001} faces for thin platelets. (From Ref. 59.)

8. CONTROL OF PARTICLE CHARACTERISTICS

381

controlled in shape by changing the added amount of sulfate ions in a gelsol system, containing 3 mol dm"^ chloride ions from ferric chloride used as a starting iron salt.'*^'^^ The anisotropic growth is due to the lowered growth rate in the direction nomial to the c-axis of the hexagonal crystal system by adsorption of sulfate or phosphate ions. In fact, it has been found that sulfate and phosphate ions are much more strongly adsorbed to the crystal planes parallel to the c-axis of the hexagonal crystal than to the cfaces perpendicular to the c-axis.^^'^ Figure 8.4 shows adsorption isotherms of sulfate ions to ellipsoidal, pseudocubic, thick-platelet, and thin-platelet particles rich in the planes parallel to the c-axis, {012}, {001}+{012}, and {001} faces, respectively.^^ This trend has been elucidated by the better matching of the 0 - 0 distance of these anions (2.45 A for SO/"; 2.50 A for PO/") with the Fe-Fe distance of the planes parallel to the c-axis (2.29 A) than with the Fe-Fe distance of the c-plane (2.91 A).^^ For sulfate ions, in particular, FTIR analysis revealed the bidentate adsorption to the planes parallel to the c-axis, much stronger than monodentate adsorption, and the monodentate adsorption to the {001} faces, as has been expected from the geometry."^^ In particular, the peanut-like particles are formed by radial distortion of the growing elongated subcrystals on both ends of each particle due to the nucleation and growth of new subcrystals in the spaces between the preformed subcrystals. Figure 8.5 shows TEM images of an ellipsoidal particle starting to form the peanut-like shape in a relatively early stage of

aOOnai Fig. 8.5. (a) TEM of a hematite particle after aging for 4 days in the presence of 0.10 mol dm"^ SO/"; (b) its close-up view of the end part of the ellipsoidal particle. (From Ref. 40.)

382

PREPARATION

Fig. 8.6. Schematic model of the formation of peanut-type hematite particles. growth, in which we find densely growing subcrystal whiskers on both the ends. Figure 8.6 is an illustration of the schematic model for the formation of a peanut-type particle. Similar shape control can be achieved by phosphate ions as weU.^^ On the other hand, if ferric nitrate or ferric perchlorate, having rather inert anions, is used as a starting iron salt in place of ferric chloride in the gel-sol system, only polydispersed and more or less elongated particles of hematite are obtained.^^ Thus, the pseudocubic particles themselves bound by the {012} faces in Fig. 7.21(a) in chapter 7 must have been brought about by adsorption of chloride ions retarding the growth of the {012} faces. In the case of basic aluminum sulfate, chloride ions retard not only the growth of the {012} faces but also of other faces except the {001} faces, so that ellipsoidal particles slightly elongated in the direction of the c-axis are obtained in the presence of chloride ions, as shown in Fig. 8.7. The surfaces of the prolate particles are rather rough as compared to the other particles in Figs. 7.23 and 8.2, but they are thought to be single crystals, or at least very close to single crystals, from their XRD profiles which are as sharp as those of the other particles."*^ Hence, extraneous anions may not be incorporated in the basic aluminum sulfate particles in contrast to hematite. Cations of some heavy metals are strongly adsorbed to the anion sites of particle surfaces, and control the growth form of the particles. For example, dodecahedral silver chloride particles bound by the {110} faces are obtained with the aid of cadmium ions.^^

8. CONTROL OF PARTICLE CHARACTERISTICS

2 jim

383

1 )im

Fig. 8.7. SEM and its close-up view of ellipsoidal basic aluminum sulfate particles prepared by the gel-sol method in the presence of L67 mol dm"^ chloride ions. (From Ref. 46.)

Since the density of bond-free sites is high at the corners and edges of a polyhedral particle, the adsoq^tion of shape controllers tends to be concentrated on these places to reduce the total surface energy of the particle, and thus the sharpness of the comers and edges are often degenerated by their adsorption. As has been shown in Fig. 7.23 of chapter 7, basic aluminum sulfate particles (a), prepared at [SO/"]/[Al^*] = 2/3 with [NaOH]/[Al^^] = 1.8, have their comers and edges degenerated, and the shape is rather close to a spheroid, in contrast to the pseudocubic particles (b) with sharp comers and edges, prepared at [S04^"]/[A1^^] = 1/4 and [NaOH]/[Al^^] =1.8. The rounded comers and edges are thought to be caused by the adsorption of sulfate ions which inhibits the rapid growth of these parts. A similar trend is observed in the pseudocubic hematite particles grown in the presence of concentrated chloride ions. On the other hand, one may find the comers and edges of silver bromide particles, prepared in the presence of ammonia in Fig. 3.9 in chapter 3, to be also somewhat rounded, as compared to those in Fig. 3.13 obtained in the absence of ammonia. However, in this case, while there may be some contribution from a similar effect of ammonia as an adsorptive, the main cause seems to be its solvent effect which promotes the overall particle

384

PREPARATION

growth even with a lowered supersaturation, and thus the supersaturation is reduced to a level below the solubilities of the sharp corners and edges of the silver bromide particles when the feed rate of the monomer sources is comparable. b) Organic Controllers Organic adsorptives are widely used as shape controllers of monodisperse particles. For example, Claes et al^^ prepared rhombic dodecahedral silver chloride particles bound by {110} faces using 2-(carboxymethyl-mercaptoj-benzimidazole. Maskasky^ prepared four new kinds of regular polyhedral particles of silver bromide by additional growth onto cubic or octahedral AgBr cores in the presence of different kinds of organic adsorptives which inhibit growth of selective faces. He obtained trisoctahedra, two types of icositetrahedra, tetrahexahedra, and hexaoctahedra, in addition to the previously known three kinds including cubes, octahedra, and rhombic dodecahedra, by using derivatives of tetraazaindenes, rhodanines, mercaptoimidazoles, and benzimidazoles. In the icositetrahedra are included two different kinds bound by {211} and {311} faces, respectively. As a result, all of the polyhedral AgBr particles possible for the f.c.c. crystal system shown in Fig. 8.8 have been presented. Probably, the shape control was achieved by single or multiple coordination of the sulfur and/or nitrogen

Rhombic dodecohedron

(211)

Icostretrohedron

(311) IcosiieJrohedron

(2IQ TefroheKahedron

{33!} Trisocfohedron

{321) Hexoctohedron

Fig. 8.8. Schemes of all fee crystal habits. (From Ref. 64.)

8. CONTROL OF PARTICLE CHARACTERISTICS

385

atoms of these compounds to the silver ions of some specific surfaces of the face-centered-cubic crystals. Sapieszko and Matijevic^^ prepared disk-like hematite particles by heating a highly basic solution of ferric triethanolamine complexes at an elevated temperature (~ 250 °C). Since hexagonal platelet particles are usually obtained in basic media, the circular disks seem to have been produced due to the dissolution of the side comers through the intra-particle recrystallization when the total concentration of the solute became below the solubility of the side comers in the last stage of precipitation. In this case, triethanolamine may have played a role of a solvent of hematite to enhance the recrystallization at the high temperature. Hamada et al^^ prepared uniform double spheres of hematite by the forced hydrolysis of FeCl3 in a dilute acidic medium in the presence of glycine. Although the formation mechanism is unknown, it may be explained in a similar manner to the growth process of the peanut-type particles in the gel-sol system,"*^ since the shape is close to that of the peanut-type particles prepared with phosphate.^^ On the other hand, ellipsoidal hematite particles of 0.5-0.8 jmi in length and 7-15 in aspect ratio with fairly narrow size distributions were prepared by use of organic phosphonic acids.^^'^^ It is also possible to form ellipsoidal and rod-like hematite particles with oxalate^^ and citrate,^^ respectively. Moreover, it is possible to control the aspect ratio of monodispersed ellipsoidal hematite particles with dihydroxybenzenes, benzoquinones, dihydroxynaphthaleneSy NTA, EDTA, etc. in gel-sol systems with acidic media around pH 1-2 in the presence of a high concentration of chloride ions, 3.0 mol dm'\ at 100 °C.^ It is of interest that /7-dihydroxybenzene Qiydroquinone) and o-dihydroxybenzene {catechol) are effective, while mdihydroxybenzene (resorcinol) is ineffective, and that monomeric hydroquinone and catechol as well as their oxidized species, benzoquinones, are not adsorbed to hematite. Nevertheless, the effective dihydroxybenzenes are readily oxidized to benzoquinones in the presence of ferric ions and polymerized mainly on the surfaces of hematite particles to control the shape of hematite by adsorption of the polymers. Figure 8.9 shows examples of so-obtained hematite particles with organic shape controllers. Daichuan et aV^ observed morphological change of hematite from monocrystalline spheroidal shape to rhombohedral one by the presence of urea in the forced hydrolysis process of FeCl3 in an acidic range. This may be due to the specific adsorption effect of urea. On the other hand, Hamada et alJ^ prepared uniform poly crystalline spheroidal particles of hematite (0.35 |xm) by forced hydrolysis of 2,2'-bipyridine-iron(II) complex in the

386

PREPARATION

4fsem

Fig. 8.9. TEM images of hematite particles controlled in shape by organic additives: (a) no additive (control); (b) hydroquinone (1.0 x 10"^ mol dm"^); (c) 1,2dihydroxy-3,5-benzene disulfonic acid disodium salt (3.0 x 10"^ mol dm'^; (d) 1,8dihydroxy-3,6-naphthalenedisulfonic acid disodium salt (3.0 x 10"^ mol dm'^); (e) ethylenediaminetetraacetic acid (1.0 x 10"^ mol dm"^); (f) nitrilotriacetic acid (3.0 X 10"^ mol dm'^). (From Ref. 72.)

presence of KNO3 as an oxidizing agent of Fe(II) in an acidic medium. In view of the considerably narrow size distribution (a = 9 %) and the slightly deformed shape from a perfect sphere, the particles are thought to be epitaxially grown through deposition of monomeric precursor, and the internal discontinuities seem to be formed by the blocked fusion of twodimensional nuclei during the growth, owing to the adsorption of hipyridine. In this sense, the growth process may somewhat resemble that of the pseudocubic hematite particles prepared by the gel-sol method in the presence of a high concentration of chloride ions (see section 8.3), but the comers and edges of the characteristic polyhedral shape are more degenerated by strong adsorption of bipyridine. Hence it may be reasonable to

8. CONTROL OF PARTICLE CHARACTERISTICS

0.2 Mm

387

Fig. 8.10. SEM of spherical polycrystalline hematite particles, prepared by phase transformation from 0.5 mol dm"^ p-FeOOH suspension containing 3.0 x 10"^ mol dm'^ NTA-2Na, 6.0 x lO'^ mol dm'^ HCl, and a-Fe203 seeds (ca. 3 nm) at 100 °C for 48 h.

suspect that a considerable amount of bipyridine is incorporated in the particles. Also, Sugimoto and Itoh prepared virtually spherical polycrystalline hematite particles by use of NTA (nitrilotriacetic acid) through phase transformation from 0.5 mol dm"^ p-FeOOH suspension containing 3.0 X 10-2 J^QJ JJ^-3 NTA-2Na, 6.0 x 10"^ mol dm"^ HCl, and a-Fe203 seeds {ca, 3 nm) at 100 X for 48 h. Figure 8.10 shows a SEM of so obtained polycrystalline a-Fe203 spheres with rough surfaces. Since it has been confirmed in a separate experiment that the shape of hematite particles is changed from a sphere to an ellipsoid with increasing concentration of chloride ions when 3.0 x 10'^ mol dm'^ NTA is present in the gel-sol system, it is obvious that the shape difference between the ellipsoidal hematite in ref. 72 and the spherical hematite with the same concentration of NTA is caused by the much higher concentration of the coexisting chloride ions in the former than in the latter. As a consequence, when both NTA and a high concentration of chloride ions are present at the same time, ellipsoidal particles are produced, while NTA only and a high concentration of chloride only yield spheres and pseudocubes, respectively. These facts may imply that, originally, NTA is strongly adsorbed to hematite irrespective of the crystal faces and thus produces spherical particles, but yields ellipsoidal ones in synergistic action with chloride ions. More detailed

388

PREPARATION

mechanistic studies may be needed to clarify the backgrounds. Nonionic and ionic surfactants are known to work as shape controllers because of their nature as adsorptives to solids. For example, the elongated barium carbonate particles prepared in WIO microemulsions increase their aspect ratio as the H2O/NP-6 ratio decreases in NP-6/cyclohexane systems, where NP-d is poly(oxyethylene)-nonylphenylether with six oxyethylene groups on average.^^ Also, the shape of uniform germanium dioxide particles prepared in reversed micellar systems of AOT/cyclohexane changes from cubes to ellipsoids with a decreasing H2O/AOT ratio or an increasing concentration of AOT, where AOT is sodium dioctylsulfosuccinate (Aerosol OT).'^ 8.2.2. Shape Control by Anisotropic Acceleration a) Twinning Control It is also known that if the excess concentration of bromide ions exceeds 10"^^ mol dm"^ (pBr 1.5), the probability of the formation of twin crystals of AgBr during the nucleation stage increases, owing to the increasing probability of stacking faults mainly on the {111} faces by adsorption of bromide ions. Figure 8.11 illustrates double twin and single twins of silver bromide crystals.

twin planes

Fig. 8.11. Illustration of double and single twins of silver bromide crystals. (From Ref. 80.) The side troughs at the end of the twin planes become highly active for the formation of the linear surface nuclei with the progress of adsorption of bromide ions to the troughs.^^ Thus, at a high excess concentration of bromide ions, the growth of a single twin normal to the every other side face with a trough halts when these side faces reach their utmost ends, while

8. CONTROL OF PARTICLE CHARACTERISTICS

389

Fig. 8.12. TEM of a carbon replica of tabular double-twin grains of AgBr. The black spheres are standard particles of polystyrene.

the double twins with a trough on every side face can keep growing to be large tabular grains. Hence, the nuclei of the coexisting regular particles and single twins disappear by dissolution through a kind of Ostwald ripening with the growth of the tabular double twins. Figure 8.12 shows an electron micrograph of a carbon replica of tabular AgBr grains prepared at 75 °C by a stepwise process, consisting of the nucleation at pBr 1.4, the subsequent aging to eliminate the coexisting regular and single-twin nuclei by Ostwald ripening, and the final controUed-double-jet growth at pBr 1.8. It is possible to make the size distribution still narrower by nucleation with twinning at a low temperature, such as 35 °C, and the subsequent screening of regular and single-twin nuclei at a high temperature, such as 75 °C, to minimize the mean size of the double-twin nuclei, and the final growth at a somewhat higher pBr to control the reactivity of the troughs.^^ It is also known that the probability of the twinning is dramatically increased by a trace of iodide ions.^^ b) Dislocation Control Mignot et al^ prepared rectangular tabular grains of silver bromide bound only by the {100} faces through a sequential process: the first controlled-double-jet precipitation of AgBr nuclei for a short time at a

390

PREPARATION

/VY.

^

,^

^. / .

Fig. 8.13. Screw-dislocation-induced growth model proposed by Mignot et aL (From Ref. 80.) relatively low pAg, such as 6 to 7, and at a low temperature, such as 40 °C, to introduce screw or edge dislocations into the AgBr nuclei, the subsequent aging at an elevated temperature, such as 60 °C, to remove only the regular nuclei having no dislocation from the mixed nuclei with and without dislocations by Ostwald ripening, and the final growth by the CDJ procedure. Similarly, AgBr^.J^ (x = 0.005) particles were also prepared by Bogg.^^ Figure 8.13 illustrates the scheme of the screw dislocation-induced growth model proposed by Mignot and coworkers.®^ Also, tabular grains of silver chloride bound by the {100} faces have been prepared by the CDJ technique, but in the presence of iodide or bromide ions in the initial nucleation stage at ca, 40 ""C and at a pCl in the range of 1.9 to 2.3.^^ The

8. CONTROL OF PARTICLE CHARACTERISTICS

391

Fig. 8.14. SEM of {100} tabular grains of AgCl prepared by the dislocation-control technique. double-jet nucleation process is followed by a 10-min hold to allow ripening, then a double-jet growth is performed with sodium chloride while maintaining a constant excess halide level in the pCl range from 1.2 to 2.5. In the case with iodide ions, the final iodide content is 0.1 mol % or less. The lattice misfitting between a Ag(I,Cl) or Ag(Br,Cl) nucleus and the AgCl crystal grown thereon is likely to create the dislocations as active growth centers. The aspect ratio in this case increases with the decreasing excess halide level during the growth stage; e.g., increase of the aspect ratio from 2.5 to 14 with the change of pCl from 1.2 to 2.4. Figure 8.14 shows a SEM of tabular AgCl particles thus prepared. On the other hand, it is known that isometric NaCl-type crystals of PbS also have rectangular shapes with different orthogonal edge lengths whose ratios are also varied among the particles.^^'^ Since the surface planes are all equivalent {100} faces, the anisotropic growth may not be explained in terms of growth control by adsorption of solute or of impurity. Presumably, this unique growth mechanism may also be elucidated in terms of the dislocation-induced growth,^ like the rectangular {100} microcrystals of AgBr and AgCl.

c) Catalytic Control

392

PREPARATION

Figure 8.15 shows a SEM image of silver wires (3-5 [iin long, 0.1-0.5 \mi thick) prepared by reduction of silver ions in the polyol process (see section 7.2.1) in the presence of platinum nuclei {ca, 50 A). TTie long axis is collinear with the [110] direction of the f.c.c. crystal. If this process is performed in the absence of the Pt nuclei, only spheroidal Ag particles are obtained.

Fig. 8.15. SEM of silver wires, prepared by reduction of silver ions in the polyol process in the presence of platinum nuclei (ca. 50 A). (From Ref. 85.) Since metallic silver belongs to the face-centered-cubic system, there seems to be two possibilities in this growth mechanism. One is the heterogeneous nucleation of a twin crystal of Ag on the surfaces of the Pt nuclei, followed by rapid anisotropic growth with the trough of the twin crystal. The other is the growth of a regular crystal from the contact interface between Pt and Ag with continuous supply of Ag^ ions and electrons at this interface, like the growth of silver filaments from a silver halide grain during the photographic development or the growth of hair. However, if the latter is true, why do the silver wires appear to grow singly from each Pt nucleus without radial development of more wires from a Pt nucleus? and why is the thickness of a wire is much greater than the size of a Pt nucleus? Hence, if one considers in addition the definite growth direction, the former mechanism is more likely, though it must be confirmed by high-resolution electron microscopy or other means. d) Magnetic Control Figure 8.16 is a SEM image of nickel filaments formed by reduction of Ni(0H)2 in the polyol process under an external magnetic field, where only

8. CONTROL OF PARTICLE CHARACTERISTICS

393

Fig. 8.16. SEM of nickel filaments (10 ^m X 0.5 \xm) formed by reduction of Ni(0H)2 in the polyol process with ethyleneglycol at 205 °C in a magnetic field. (From Ref. 86.) spheroidal Ni particles are obtained without the magnetic field.*^ The authors elucidated the growth mechanism that tiny Ni particles, formed in the early stage of growth, are linearly attached together under the influence of the magnetic field, which are then grown to the metallic filaments while cementing the small particles in a linear array. Although the filament size and shape are not uniform as yet, this technique, perhaps applicable to other kinds of ferromagnetic materials as well, appears to be promising as a new method for the controlled anisotropic growth of magnetic particles. 8.2.3. Shape Control of Polymer Particles The shape control of nonspherical polymer colloids is mostly performed by the phase separation of guest polymer in each host polymer particle incompatible with the guest polymer, or by a kind of phase separation of the guest polymer of the same species as the host polymer, but with a highly

Fig. 8.17. SEM of pear-like polystyrene particles prepared by phase separation of the guest polymer. (From Ref. 87.)

394

PREPARATION

cross-linked host polymer. These techniques are commonly based on the seeded polymerization with host polymer particles swollen with the monomer of the guest polymer. For example, it is possible to cause the local phase separation of incompatible guest polymer in each polystyrene host sphere by polymerization of a styrene/hydrophilic acrylate comonomer or a methylmethacrylate/hydrophilic acrylate comonomer incorporated in the host polymer spheres. Figure 8.17 shows an example of so-prepared nonspherical pear-like particles.^^ The degree of anisotropy can be altered by varying the extent of the incompatibility of the host and the guest polymers

Fig. 8.18. SEM images of polystyrene latices grown from a 5.2-jim seed latex cross-linked with 0.20 % divinyibenzene and swollen by the monomer at different monomer/polymer ratios: (a) 1/1; (b) 2/1; (c) 3/1; (d) 4/1. Scale bar = 10 um. (From Ref. 90.)

8. CONTROL OF PARTICLE CHARACTERISTICS

395

or by changing the ratio of the monomer of the guest polymer to the host. One may regard this process as a kind of heterojunction of a polymer version, corresponding to the heterojunction of inorganic matters (see section 8.8). Similarly, Okubo et al}'^ prepared raspberry-like particles by seeded polymerization of styrene-swollen polyethylacrylate seeds with a water soluble initiator such as potassium persulfate. In this process, the use of water soluble initiator is a key factor for local condensation of the polystyrene phase near the surfaces of the host particles, since use of an oil soluble initiator, such as benzoyl peroxide, results in the formation of only spherical composite particles, due to the phase separation of polystyrene

Fig. 8.19. SEM images of polystyrene latices grown from 5.2-jim seed latices cross-linked with: (a) 0.06 %; (b) 0.20 %; (c) 0.60 %; (d) 1.50 % divinylbenzene (monomer/polymer = 3/1; scale bar = 10 ^m). (From Ref. 90.)

396

PREPARATION

uniformly dispersed in the polyethylacrylate matrix. On the other hand, Sheu et al}^'^ extensively studied the phase separation of polystyrene in cross-linked polystyrene particles. Figure 8.18 exhibits the effect of the monomer/polymer ratio in a styrene-swollen polystyrene system with 2,2'azobis-(2-methylbutyronitrile) as an oil-soluble initiator and a polystyrene seed latex cross-linked with 0.20 % divinylbenzene.^ Also, Fig. 8.19 shows the effect of the cross-linking degree of seed particles on the shape of the product in the same system.^ In these experiments, the swelling of the seed polymer with monomer was carried out overnight at room temperature and the seeded polymerization was performed at 70 °C for 24 h. The results in Figs. 8.18 and 8.19 may be readily understood if one considers the mechanism, consisting of the extrusion of the bulged monomer out of a cross-linked monomer-swollen spherical seed to form a guest hemisphere on heating up to 70 °C and further transfer of monomer to swell the new hemisphere in the progress of the polymerization with only a very little cross-linking agent, divinylbenzene, as well as the elastic pressure of the highly cross-linked host network to push out the monomer therein to the guest.

8.3. Internal Structure Control As has been described in sections 7.3.1 and 8.2.1, monodisperse pseudocubic, ellipsoidal, and peanut-type particles of hematite (a-Fe203) can be obtained in the gel-sol systems. Basically, the pseudocubic particles are prepared by adding 5.4 A^ NaOH to an equal volume of 2.0 M ¥tC\^ at room temperature to precipitate Fe(0H)3 gel and aging for 8 days at 100 °C in a laboratory oven (standard system). Hence, the pseudocubic particles are prepared in the presence of a high concentration of chloride ions. For the ellipsoidal and peanut-type particles, sodium sulfate (Na2S04) or sodium phosphate monobasic dihydrate (NaH2P04 -21120) is added to the Fe(0H)3 gel to control the anisotropic growth of hematite. From electron microscopy on the slices of the pseudocubic and peanut-type particles prepared in the presence of sulfate ions, they turned out to be polycrystals consisting of much smaller subcrystals developed radially from the center or the revolution axis, as has been shown in Fig. 7.22.^^""^ From the orientedparticulate-monolayer (OPML) XRD analysis^^ (see section 10.6), it was found that the pseudocubic particles were bound only by the {012} faces of the hexagonal crystal system, and that the revolution axis of a peanut-type

8. CONTROL OF PARTICLE CHARACTERISTICS

397

particle was coUinear with the c~axis. Since only the X-ray diffractions of the (012) and (024) faces are obtained from the OPML-XRD of the pseudocubic particles, it is evident that the individual subcrystals of a particle are only subunits of a pseudocubic single crystal with some discontinuity between the subunits. Hence, the growth of the pseudocubic particles must proceed basically in the same fashion as the polynuclear-layer epitaxial growth of single-crystal particles (see section 2.3). However, if the surface particles, grown from each surface nucleus shown in the scheme of Fig. 8.20, cannot fuse with each other for some reason when they come into contact after their lateral development, two-dimensional grain boundaries must finally be formed as illustrated in Fig. 8.21. As each particle grows from a small nucleus by repeating this procedure layer by layer, we will finally find radially developed subcrystals from the center of each particle with three-dimensional grain boundaries of the subcrystals, as is in accord with the section TEM in Fig. 7.22(a) in chapter 7. Since the concentration of chloride ions with a strong affinity to ferric ions is as high as 3 mol dm"^ in the standard system, the blocked fusion of the surface particles must be attributed to the adsorption of chloride ions to the side faces of the surface particles. In fact, the incorporated chloride ions in the particles was found to reach 2 mol % of

Fig. 8.20. Development of the first layer of two-dimensional nuclei.

Fig. 8.21. Two-dimensional grain boundaries of the first layer of the surface particles, as a result of the blocked fusion among them by adsorptives.

398

PREPARATION

Fe atoms of hematite as revealed by EDX analysis on the sections of the pseudocubic particles.^^ In addition, Fig. 8.22 shows SEM images of pseudocubic particles and the close-up views of a particle prepared from once washed p-FeOOH particles under different aging conditions of chloride concentration / temperature / time: a) 3.0 mol dm~^ / 100 °C / 8 days, b) 3.0 mol dm"^ / 140 °C / 3 days, and c) 0.10 mol dm"^ / 140 °C / 3 days.^^ The mean thicknesses of the {012}, {104}, and {110} planes of the subcrystals of the respective particles, obtained from XRD with the Scherrer equation, are given in Table 8.1,^^ showing the effects of chloride ions and aging temperature on the size of the suHcrystals.

Fig. 8.22. SEM images of pseudocubic particles and their close-up views of one particle prepared from washed P-FeOOH particles, under different aging conditions of chloride concentration / temperature / time: a) 3.0 mol dm"^ / 100 °C / 8 days, b) 3.0 mol dm'^ / 140 °C / 3 days, and c) 0.10 mol dm"^ /140 °C / 3 days. (From Ref. 15.)

8. CONTROL OF PARTICLE CHARACTERISTICS

399

Table 8.1. Effects of CI" and aging temperature on the mean thicknesses of the {012}, {104}, and {110} planes of the subcrystals of the hematite particles (a), (b) and (c) in Fig. 8.22, obtained from XRD with the Scherrer equation (Source: Ref. 15) Sample

[CI"]

Temp

Aging Time

(mol dm"^)

CC)

(days)

(a)

3.0

100

(b)

3.0

(c)

0.1

Thickness (nm) {012}

{104}

{110}

8

30

22

29

140

3

47

35

38

140

3

>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

8. CONTROL OF PARTICLE CHARACTERISTICS

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

8. CONTROL OF PARTICLE CHARACTERISTICS

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

8. CONTROL OF PARTICLE CHARACTERISTICS

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

8. CONTROL OF PARTICLE CHARACTERISTICS

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

8. CONTROL OF PARTICLE CHARACTERISTICS

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

8. CONTROL OF PARTICLE CHARACTERISTICS

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-^AljO^ 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) •2Ru^OC03 •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^^

8. CONTROL OF PARTICLE CHARACTERISTICS

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

«
ous addition of KBr at 25 and 45 ""C are shown in Fig. 8.33, while the changes of the mole fraction of AgCl in the generated solid-solution phase Ag(Cl, Br) and of the molar ratio of remaining pure AgCl to the initial one with the addition of KBr are illustrated in Fig. 8.34. Here, 0.4 mol dm'^ KBr was continuously added at 7.5 cm^ min"^ to 1350 cm^ of a well-stirred suspension of silver chloride containing 0.18 mol of AgCl microcrystals with 1.8 X 10-^ mol of KCl and 18 g of inert gelatin at 25 °C.

417

8. CONTROL OF PARTICLE CHARACTERISTICS

u < u <

0.5 (•^Br)3,,,,/(AgCl)^

Fig. 8.34. Mole fraction of the AgCl component of the growing solid solution Ag(Cl,Br) and (AgCl)/(AgCl)o as functions of (KBr)3ddcd/(AgCl)o changing with the continuous conversion at 25 °C (solid lines) or at 45 °C (dotted lines), where (AgCl), (AgCl)o, and (KBT)^^! are the gram molecules of the remaining pure AgCl phase, the initial pure AgCl particles, and KBr added, respectively. (From Ref. 163.)

8.5. Layered Structure Control To minimize the interaction among particles, or to stabilize the particles in a given medium, or to impart a specific function to the particles, it is often useful to modify the original particles into layered structures by coating them with different substances, or by allowing other crystals to grow epitaxially on the cores. 8.5.1. Inorganic Coating a) Coating of Inorganic Particles Kratohvil and Matijevic developed a novel technique for coating amorphous aluminum hydrous oxide on monodispersed hematite ( a Fe203), chromium hydrous oxide, and amorphous titanium oxide.^^ Aluminum hydrous oxide is deposited onto the preformed cores in an aqueous dispersion of this colloid, containing hydrated aluminum complexes.

418

PREPARATION

An aluminum sulfate solution preheated at 100 °C in the presence of urea for a proper period of time was cooled, added to the dispersion at room temperature, and then diluted with distilled water. This slightly elevated the pH, yet it was sufficient to cause the precipitation of aluminum hydrous oxide onto the cores. The coating thickness could be varied by properly adjusting the concentrations of particles and aluminum salt, as well as by the reaction time. Matijevic and coworkers also produced coated particles of hematite ( a Fe203), such as chromium hydrous oxide/a-Fe203 by forced hydrolysis of chrome alum in its dilute solution,^^^ SI02/a-Fe203 by aging a suspension of hematite in the presence of Na2Si03 at pH 5 for 3 h at 100 °C,^^" or by hydrolysis of tetraethyl orthosilicate (TEOS) at 40 °C,^^^ zirconium hydrous oxide/a-Fe203 by forced hydrolysis of zirconium sulfate in its dilute solution in the presence of formamide as a promoter of hydrolysis (by releasing ammonia) and a stabilizing agent such as polyvinylpyrrolidone or polyvinyl alcohol at 70 °C,^^^ and yttrium basic carbonate/a-Fe203 by aging for ca. 2 h at 90 °C a suspension of hematite containing YCI3 and urea.^^^ Here, it should be noted that A/B for a double-layered particle indicates shell(A)/core(B) in this book. They obtained silica-coated iron particles by reducing the silica-coated hematite with hydrogen gas,^^°'^^^ as well as yttria-coated hematite by calcination of the hematite particles covered with yttrium basic carbonate at 800 °C for 3 h.^^^ Monodispersed silica spheres coated with yttrium basic carbonate and the reverse were also produced.^^" Furthermore, silica particles coated with titanium hydrous oxide^^^ were prepared by aging a dispersion of silica particles in the presence of titanyl sulfate at 90 ""C for 1 h. On calcination of the coated powder at 800 °C for 1 h, the amorphous coating was crystallized into anatase, while the same powder calcined at 1000 °C was characteristic of both anatase and rutile. Also, zinc oxide particles coated with titanium hydrous oxide were prepared by hydrolysis of titanium butoxide in an ethanolic solution at 100 °C.^^^ On calcination above 700 ''C the shell of Ti02 reacted with the ZnO cores forming zinc titanates of various stoichiometrics (a-Zn2Ti04, Zn2Ti308, and ZnTi03). A multitude of doublestructured particles are also available: e.g., Y(OH)C03/Zr2(OH)5S04,^^^ HfO^HnJQ^,''' TiN/Si02,''' Ti02/CuO,^'' Mn203/«-Fe203,''' (MnOMn02)/a-Fe203/'' NiO/Mn203,''' Ni/Mn,^'' and Sn02/a-Fe203.^'' Figure 8.35 shows silica-coated ellipsoidal a-Fe203 particles and silica-coated Fe particles obtained by reduction of the Si62/a-Fe203 particles as examples of the inorganic coating of inorganic particles.^^^

8. CONTROL OF PARTICLE CHARACTERISTICS

419

Fig. 8.35. Silica-coated hematite particles (a) and silica-coated iron particles (b). (From Ref. 169.)

Toshima et al prepared double-structured bimetallic nanoparticles of p^/pt 180,181 pd/Au,^«2 Pt/Au,^^' and Rh/Pt^^ by reduction of metal ions in a solution containing two kinds of metal salts, out of HAUCI4, H^PtCl^, PdCl2, and RhCl3, using alcohol in the presence of poly(N-vinyl--2pyrrolidone). They found a definite order in the trend to form the core of the core-shell structure (Au > 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

8. CONTROL OF PARTICLE CHARACTERISTICS

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«^o«

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.

8. CONTROL OF PARTICLE CHARACTERISTICS

423

[Scheme 2] O II

O

o KOH

-•

---

I

'

-^^O'^

) - 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)
Radical graft polymerization of acrylamide from ultrafine silica surface was performed in a redox system consisting of eerie ions and reducing agents, such as alcoholic hydroxyl, amino, and mercapto groups, conjugated with the hydroxyl groups on the silica surface.^^ As a result, hydrophilic polyacrylamide-grafted silica was synthesized. These reducing groups, linked to the surface of silica, were introduced by reactions of surface silanol groups with 3-glycidoxypropyltrimethoxysilane (GPS), 3-aminopropyltriethoxysilane (APS), 3-mercaptopropyltrimethoxysilane (MPS), respectively. Similarly, polyacrylamide-grafted carbon black was derived.^°^ Scheme 4 represents such reactions. [Scheme 4] GPS^

O .^^^

OH

APS

/-^-^

I

•

^

/0-Si-(CH2)5-NH2

^

f

Vo-Si-^^Hi^SH

OH

8. CONTROL OF PARTICLE CHARACTERISTICS

425

R-OH 1-NH2

+

nCH2=CH CONH2

^

W^

(

V .^

}-R'-(Cm-CH);;H CONH:

R' = R-0, R-NH, R-S

l-SH

Radical polymerization initiated by adsorbed initiators Yamaguchi et al.^^ found a dramatic electrostatic effect between electrically charged solid surfaces and ionic end groups of polymer chains on the coating efficiency of colloidal particles with polymethylmethacrylate by radical polymerization in aqueous media. Namely, the coating efficiency of BaS04 and a-AljOj particles by polymerization with a cationic radical initiator, AAP (2,2'-azobis(2-amidinopropane) hydrochloride), which gives a positive end group to each polymer chain, greatly increases from less than 10 % to almost 100 % with increasing negative surface charge of the particles. Also, while the coating efficiency of positively charged a-Al203 (C-potential +40 mV) is ca. 32 % with AAP but ca, 100 % with KPS (potassium persulfate: anionic radical initiator), the coating efficiency of negatively charged Si02 particles (^-potential -47 mV) is ca. 95 %, but ca. 9 % with KPS. Scheme 5 shows the case of polymerization of methylmethacrylate on the surface of a positively charged a-Al203 particle with persulfate. [Scheme 5] (^H3

-(^^H.-C^ nCH2=C-CH3 COOCH3

While the authors explained the results in terms of the electrostatic interaction between the end group of the growing polymer chains and the solid surfaces like the adsorption and desorption of ionic surfactants, the

426

PREPARATION

polymerization itself may also start from the solid surface with an electrostatically adsorbed initiator and the polymer chains may remain anchored to the solid surfaces throughout the polymerization in the case of a highly efficient coating. Similar trend is also found for coating SiOj particles with vinyl polymers by radical polymerization with AAP as an initiator, even in non-aqueous media such as mixed solvents of Ethanol/THF. Namely, Yoshinaga et al. coated silica particles with polystyrene by radical polymerization with AAP in the presence of HFC (hydroxypropyl cellulose), as a stabilizer, in mixed media of Ethanol/THF.^^ They also introduced functional groups such as amino and carboxyl groups to the polymer shell by polymerization in the presence of thiol chain transfer agents, such as 3-mercaptopropionic acid, thiomalic acid, or 3-mercaptopropylamine.^ However, in this procedure, amino groups appeared to be occluded into the polymer layer. Thus, they also tried to introduce amino groups to the surface of the polymer layer via copolymerization of styrene and divinylbenzene with chloromethylstyrene, [Scheme 6] -iCH^-CK^ AAP, DVB + nCH2=CH

AAP, DVB COOH

HS O

o

OH

AAP, DVB HS^NHz

AAP, DVB CH2=CH

CH2CI CH2CI

8. CONTROL OF PARTICLE CHARACTERISTICS

427

oiK CH2CI

CH2NH2

conversion of the chloromethyl groups in the copolymer to methylphthalimide groups, and aminolysis of the phthalimide groups with hydrazine. As a result, they successfully obtained polystyrene-coated silica particles with surface amino groups.^^ The reactions are summarized in Scheme 6. Similarly, they prepared polystyrene-coated silica with surface hydroxyl groups 01 p-nitrobenzenesulfonate groups to be further converted to diverse functional groups with different nucleophiles.^^ For example, the pnitrobenzenesulfonate group initiates ring-opening cationic polymerization of 2-methyl-2-oxazoline.^^ It is also possible to coat sihca with polymethylmethacrylate or poly(2-hydroxyethylmethacryiate) by use of AAP?"^ As Yoshinaga et al.^^ found that PMMA and PHEMA did not coat silica particles in this polymerization when 2,2'-azobis(isobutylonitrile) (AIBN) was used instead of AAP, the specific affinity of AAP to silica has been suggested even in the non-aqueous media. (3) Copolymerization with Surface-bound Vinyl Groups Monomeric acrylic acid, irreversibly adsorbed to the surface of titanium oxide mtile particles from benzene solution, is readily copolymerized with styrene to yield polystyrene-coated titania.^^^ Similariy, poly(ethylene glycol dimethacrylate)-coated titania was prepared, using adsorbed monomeric methacrylic acid with aluminum nitrate as a binder, but in an aqueous dispersion.^^" Also, oleophilic poly(divinyibenzene)-coated oxides, such as Al(OH)3, Si02 and AI2O3, were prepared by preadsoq^tion of vinyl coupling agents, such as 4-vinylpyridine or vinylpyrrolidone, and subsequent radical copolymerization of divinylbenzene with the adsorbed 4 vinylpyridine or vinylpyrrolidone.^^^ Surface-bound methacryl groups, linked to the hydroxyl groups on the

428

PREPARATION

silica surface by the reaction with y-methacryloxypropyltrimethoxysilane (yMPS), act as a polymerizable group in the free radical polymerization of monomers, such as styrene and methylmethacrylate.^^ Similarly, poly(ethyi acrylate)-coated silica was prepared in an aqueous dispersion.^^^ Vinylphenylene groups are bonded with the pyridinium groups of poly(4vinylpyridine) or the carboxyl end group of a poly(N-vinyl-2-pyrrolidone) with chloromethylstyrene, and radical polymerization of styrene is carried out in a mixed medium of H20/EtOH/THF (5:36:4 by volume) in the presence of the hydrophilic macromers having vinyl groups and oxide or hydroxide particles such as SiOj, TiOj, SbjOj, and Al(OH)3. Probably, styrene is copolymerized with the vinyl groups of the hydrophilic intermediate macromers adsorbed to the oxide or hydroxide particles, in a fashion similar to dispersion polymerization.^^^ This type of coating may generally be represented by Scheme 7. [Scheme 7] R' (

VRCH

+ nCH2=CH

•

f

\RCH-(CH^CH-^

CH2=CHR : acrylic acid, 4-vinylpyridine, vinylpyrrolidone, y-MPS CH2=CHR'

'- styrene, ethylene glycol dimethylacrylate, divinylbenzene, methylmethacrylate, ethylmethacrylate

(4) Living Polymerization Terminated by Surface-bound Groups The anionic end groups of living polymers in anionic polymerization of styrene, 2 - or 4-vinylpyridine, etc. are allowed to react with chlorinated silica, and the polymers are chemically grafted to the silica surface via silicon-carbon-bonds,^^"* which is much more stable to hydrolysis than silicon-oxygen-carbon bonds, as illustrated in Scheme 8.^^^ (5) Coating via Intermediate Adsorption Layer Furusawa et al}^^ coated silica particles with polystyrene, via adsorption of hydroxypropyl cellulose (HPC) as an intermediate layer, by emulsion

8. CONTROL OF PARTICLE CHARACTERISTICS

429

[Scheme 8]

OH

CI

•

i

+ Li®®CH-CHf
6 6

j-C]

~^'^^»

(

)-(CH-CHf^R

^^

polymerization initiated by potassium persulfate. The coating with polystyrene was not observed in the absence of the HPC intermediate layer. (6) Polymerization Initiated by Solid Surfaces Matijevic et al. coated oxide particles such as a-FCjOj, Ce02, CuO, NiO, and Si02 with polypyrrole by polymerization of pynrole in the presence of the oxide powders suspended in a water/ethanol medium in open air without the use of a soluble oxidant.^^^ In this reaction, dissolved oxygen initiated the polymerization. For CuO and Ce02, however, the polymerization proceeded to some extent even in the absence of dissolved oxygen. In the presence of oxygen, the Cu^* and Ct^^ ions may act as an additional oxidizing agent and/or as a catalyst of the oxidation process by oxygen. Similarly, they coated CuO particles with polyaniline."^^ For coating inorganic particles with a polymer in one of these systems, the polymer molecules are required to have much greater affinity to the seed particles and to their own molecules than to the solvent. The aerosol technique lends itself to the production of solid cores coated with an organic layer. Titania spheres coated with polyurea were prepared in a continuous process in which titanium alkoxide droplets were first hydrolyzed with water vapor, followed by condensation of diisocyanate on the particles which were finally exposed to ethylenediamine.^^° (7) Direct Reaction of Polymer Coupling Agents Instead of modifying the surfaces of inorganic particles to provide them with reactivity for surface polymerization of monomers, polymers themselves are often modified to be reactive with hydroxyl groups of oxide

430

PREPARATION

surfaces. This method has an advantage over the modification of solid surfaces in simplicity. For this purpose, in most cases, a chlorosilane or a alkoxysilane group is introduced to a polymer chain as a terminal group. For example, terminal chlorosilane groups are introduced to polymer chains by termination of anionic polymerization by chlorosilane compounds, such as dichlorodimethylsilane or trichloromethylsilane, or by chain transfer with these chlorosilane compounds in radical polymerization. The terminal chlorosilane groups are readily converted to alkoxysilane groups by treatment with alcohols, which is more stable to hydrolysis reactions. Polymers with pendent silane groups are synthesized by copolymerization of a monomer with another having a pendent silane group, such as ymethacryloxypropyltrimethoxysilane.^^ Scheme 9 represents the reaction. Laible^^^ prepared polystyrene-coated oxides such as Si02, TiOj, FejOj, FeO(OH), ZnO, and CFJOJ, using polystyrene with terminal chlorosilane or methoxysilane. In addition to the polystyrene (PS), polymethylmethacrylate (PMMA) directly linked to terminal chlorosilane or alkoxysilane group is also available.^^'^^^'^^" Similar polymer coupling agents, such as aminopropyltriethoxysilane-linked polymers of PS, PMMA, PHEMA, and PEG, have also been synthesized .^^^ The reaction of these polymer coupling agents with silanol groups of silica is known to be accelerated by ammonia.^^ Moreover, alternate copolymers of maleic anhydride with styrene, methylmethacrylate, or vinyl acetate having thiopropylmethoxysilane terminal group, prepared by radical polymerization of the respective comonomers with AIBN and 3-mercaptopropyltrimethoxysilane, were coated on silica particles and cross-linked by esterification with diol to form high-density carboxyl groups at the same time on the polymer coatings.^^' Yoshinaga et al used these copolymers with carboxyl groups to bind a protein, bovine serum albumin (BSA), for immunoassay of anti-BSA antibody.^^ See also section 12.6.2 for medical or biochemical applications. [Scheme 9]

I

OH + X-Si-(CH-CHrVR

't

X: -CI, -OCH3

-HX

•

R : -CI, -OCH3, -CH3

8. CONTROL OF PARTICLE CHARACTERISTICS

431

On the other hand, oleophilic polyisobutene-grafted silica was prepared by using a modified polyisobutene with a terminal group, such as tetraethylenepentamine, to be reacted with the silanol groups on silica.^^"*'^^^ b) Coating of Organic Particles The principle of surface initiation of polymerization is also applicable to the coating of organic particles with polymer shells. For example, copper phthalocyanine pigments are coated with polystyrene by cationic polymerization of styrene initiated by acyl perchlorate groups?^^ Also, copper phthalocyanine and azo pigments were coated with polyester by anionic ring-opening copolymerization of ethylene carbonate and phthalic anhydride initiated by the surface carboxylate or sulfonate groups.^^^ The coating of polymer particles with polymer shells different in composition for the purpose of surface modification is nomially performed by seeded copolymerization on the polymer seeds with comonomers having some specific functional groups; e.g,, sulfonic acid group,^^^ chloromethyl group^^ carboxyl group^^^ hydroxyl group^^^ bromodecyl group^^^ sulfodecyl group^^^ mercapto group^^^ and phospholipids ?^^ These layerstructured polymer particles are mainly composed of polystyrene cores and copolymer shells consisting of styrene and its derivatives with functional groups. As a rule, if there is a large difference between core and shell in composition, phase separation within each particle, nonuniform coating, or independent precipitation of shell polymer may happen, and thus special precaution must be taken to avoid drastic compositional changes. Kobayashi and Uyama^^ prepared polystyrene and polymethylmethacrylate polymer latices with a relatively high surface density of poly(2-oxazoline) chains by dispersion or emulsion copolymerization of styrene or methylmethacrylate with poly(2-oxazoline) macromonomer having a styryl terminal group. Although the polymerization was performed without seeds, the ratio of poly(2-oxazoline) to polystyrene or polymethylmethacrylate at the particle surfaces was as high as ten times the total ratio or more. This fact suggests a kind of phase separation of poly(2-oxazoline) to form a double structure. The lyophilicity of the polymer colloid can be controlled readily by altering a residue of a poly(2-oxazoline) molecule. El-Aasser etal.^^ 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 K2S20g as an initiator in the polymerization of both core and shell, in which they slowly added the monomer mixture during the

432

PREPARATION

polymerization of the shell in order to keep the steady monomer concentration below the nucleation level. Okubo et al}^^ prepared polyCn-butyl methacrylate)-coated polystyrene by polymerization of n-butyl methacrylate-swoUen polystyrene particles at a relatively low temperature, such as 30 °C, with an active initiator, 2,2'-azobis(4-methoxy-2,4-dimethylvaleronitrile), contained in the swollen PS particles. In this procedure, the temperature for swelling PS particles with BMA monomer by the dynamic swelling technique was also set at a very low temperature such as 0° C to localize the BMA monomer inhomogeneously near the surface of each PS particle as well as to prevent polymerization of BMA during the swelling process. The coating appears to be more uniform than by ordinary seeded dispersion polymerization without the swelling step.^^ For further information on surface modification of polymer particles mainly used in biochemical fields, see section 12.6.2. 8.5.3. Epitaxial Multilayers The CDJ technique enables us to prepare double-structured silver halide microcrystals of exceedingly narrow size distribution consisting of a Ag(Br,I) solid-solution core with a AgBr shell or a AgBr core with a AgCl shell. In these cases, the shell crystals grow epitaxially on the cores, and the thickness of the shell can be controlled precisely by the quantity of the shell material added, relative to the total surface area of the cores in the system. The core-shell particles are often used in the photographic industry to improve photographic speed, presumably due to the charge separation of the electron-hole pairs generated on exposure to light by the difference in the valence-band level between the core and shell (see section 12.1).^^ Sugimoto and Hayakawa^^ introduced a thin internal layer of a Ag(Br,I) solid solution of a high iodide content into either AgBr microcrystals or low-iodide Ag(Br,I) microcrystals to minimize their intrinsic sensitivity to the pressure or strain exerted on the photographic film. In these cases, each resulting particle possesses an internal sublayer of a high iodide content (see section 12.1).

8.6. Hollow Structure Control The polystyrene particles coated with yttrium basic carbonate^*^ were converted into hollow particles of yttria by calcination at 800 ''C for 3 h.

433

8. CONTROL OF PARTICLE CHARACTERISTICS

shown by TEM in Fig. 8.36.^^ A relatively low heating rate is an important factor for producing the hollow particles without cracks formed by the pressure of generated CO2 and H2O gases, and a slow cooling is also needed to avoid cracks resulting from thermal shrinkage of Y2O3. The thermal transitions of the shell and core are as follows: Shell 170 ^'C

Y(OH)C03-H20

-^

630 *'C

350 T

Y(0H)C03

-*

intermediates

^

Y,0, ^2^3

Core Polystyrene

430 "C -* CO2 and H2O

Since the size control of uniform polystyrene is easy, the size of the hollow particles can readily be controlled. This method may be applied to the preparation of general hoUow particles or microcapsules of metal oxides of different sizes. Sugimoto et al}^ prepared uniform hollow particles of CuS oica. 40 nm

Fig. 8J6. Hollow yttria particles. (From Ref. 236.)

Fig. 8.37. Hollow CuS particles. (From Ref. 17.)

434

PREPARATION

in a Cu^^-trimethylenediamine chelate system in the presence of ammonia and gelatin by oxidation of S^" ions in CuS particles with air, as shown by TEM in Fig. 8.37. In this system, ammonia works as an accelerator of the reaction by removing Cu^^ produced with the oxidation of sulfide ions, and adsorbed gelatin inhibits the oxidation of the external sulfide in the surface layer of CdS particles while allowing the diffusion of oxygen into the interiors. Hollow polymer spheres are synthesized not only by the treatment of core-shell particles to extract selectively core polymers with suitable solvents,^^'^^ but also directly by polymerization. Okubo et al.^^ prepared hollow spheres of a cross-linked polymer by seeded polymerization of divinylbenzene with polystyrene seeds swollen by toluene and divinylbenzene. As they observed the homogeneous swelling of the linear (or noncrosslinked) PS seeds with DVB and toluene, one may infer as a possibility that the hollow particles were formed by a kind of intraparticle phase separation of the PDVB and the toluene-swollen linear PS into the shell and the core, respectively, in the course of the polymerization, and the subsequent deposition of the linear PS to the internal waU of each PDVB shell with the escape of toluene by drying.

8.7, Porous Structure Control Porous metal oxide particles can generally be prepared by calcination of metal carbonate, basic carbonate, basic sulfate, and amorphous hydrous oxide particles with their original shape unchanged (see section 8.4.3). The uniform rhombohedral cadmium oxide particles of porous structure^^^ prepared by calcination of uniform rhombohedral cadmium carbonate particles and porous rod-like zinc oxide^^^ prepared from basic carbonate particles of the same shape are typical examples of such particles. On the other hand, if uniform organic latices are calcined in the absence of oxygen, uniform porous carbon particles can be obtained, e.g., from polyvinylidene chloride^^^ mid poly(divinylbenzene)^^^ spheres. Porous polymer spheres are generally prepared by the seeded polymerization with linear polymer seeds swollen by the same monomer, a crosslinking agent such as divinylbenzene, a diluent, and an initiator, foUowed by extraction of the linear polymer and diluent."^^^ For example, Cheng et al}"^^ studied extensively the synthesis of porous polystyrene by seeded copolymerization of styrene and divinylbenzene with linear polymer seeds of

8. CONTROL OF PARTICLE CHARACTERISTICS

435

polystyrene swollen by the comonomer, a diluent, such as «-hexane, nheptane, 1-hexanol or toluene, and an initiator, AIBN, followed by extraction of the linear PS and diluent with methylene chloride. While Okubo et al.,^^^ as shown in the preceding section, prepared hollow polymer particles in a similar procedure, they used a much greater amount of DVB and toluene relative to PS, without styrene monomer. Also, Okubo et al}'^^ prepared porous polystyrene particles by seeded polymerization of butylmethacrylate with PS seeds swollen by varying BMA/PS(w/w) ratio at different temperatures, followed by extraction of PBMA with acetic acid. This method has an advantage of easy control of the pore density and the location of the pores in a continuous matrix of PS. On the other hand, Uyama et al}"^^ prepared uniform porous polyacrylonitrile spheres directly by dispersion polymerization in a mixed solvent of DMF/methanol(4/l) in the presence of polyvinylpyrrolidone as a stabilizer. The authors also observed that the size of the PAN particles dramatically increased from 1 to 4 pim with a rather small increase in the fraction of DMF of the mixed solvent from 70 to 85 %, but the size of the subunit of the porous structure was rather reduced with increase in the proportion of DMF. As PAN particles are not swollen by AN monomer, the authors explained the formation of the porous particles in terms of the deposition of polymer clusters preformed in the medium. However, this elucidation may involve some inconsistency with the formation of the uniform particles, since such polymer clusters, continuously formed in the medium, may always have some probability to become the nuclei of new particles, yielding poly dispersed particles (see section 7.2.11). Hence, at least, for the formation of uniform particles, the PAN particles may grow by deposition of the oligomer radicals as solute. The subsequent polymerization of the deposited oligomer radicals may proceed mainly on the particle surfaces with the monomer in the medium, in view of the low affinity of PAN with AN monomer. If it is the case, the porous structure may be created by the clustering of the polymer chains with the progress of the polymerization of the surface oligomer radicals. Also, one may explain the dramatic increase in the particle size with the increasing fraction of DMF in terms of the increase in the solubility of the oligomer radicals, leading to the increase of the i)^ term in Eq. (8.1.1). The reduction of the subunit size may be elucidated in terms of the inhibition of the extensive clustering of the surface polymer chains with increasing affinity of the solvent to the polymer chains.

436

PREPARATION

8.8. Heterojunction Heterojunction means the joining of particles of different species through epitaxial or nonepitaxial growth of one kind on the other. This technique has also been developed for attaining some superadditive functions over the functions of the respective constituents. Although it is well known that different kinds of particles are joined together through heterocoagulation, owing to the opposite signs of surface charge, it will not be dealt with in this section, but briefly referred to in section 11.5 in Part 4. 8.8.1. Epitaxial Heterojunction Many attempts of heterojunction have been made for silver halide microcrystals of different halide species in order to improve photographic speed by limiting sites for formation of latent images to the borders of guest/host junctions. For example, Maskasky^"*^ prepared hexagonal Agl particles with AgCl guest crystals epitaxially grown on only their {0001} faces by using the limited matching of the lattice parameter through the CDJ technique. Furthermore, the growth sites of AgCI guests were specified to the corners of octahedral AgBrQ94lo.o,^ host crystals by the preceding

Fig. 8.38. Octahedral Ag(Br,I) particles with AgCi guests on the six comers of each host particle.

Fig. 839. Octahedral AgBr particles with Agl guests on the six comers of each host particle. (From Ref. 248.)

8. CONTROL OF PARTICLE CHARACTERISTICS

437

adsorption of a spectral sensitizing dye as a site-director to the host surfaces, as shown in the TEM of a carbon rephca of so-prepared particles in Fig. 8.38.^^^'^^ He also prepared AgSCN/AgBr and AgSeCN/AgBr by selective deposition of AgSCN and AgSeCN on the comers of octahedral AgBr in the presence of a site director;^"*^*^"*^ AgCl/AgBr by deposition of AgCl on the comers of tabular AgBr particles in the presence of a site director;^"*^ and AgCl/AgBr by deposition of AgCl on the comers of rhombic dodecahedral AgBr particles in the presence of 2-mercaptopyridine as a growth-modifier of the rhombic dodecahedra?"*^ On the other hand, unifomi AgCl particles with AgBr guest crystals on the host comers were prepared by partial conversion of prefomied AgCl microcrystals with Br" ions at room temperature (see section 5.2).^"'^"*^ Also, it was found that Agl guest crystals were grown selectively on the comers of octahedral AgBr particles without any site-director through dissolution-recrystallization when nascent ultrafine Agl particles {ca. 15 nm) were introduced into a AgBr suspension at 65 °C, followed by aging for 15 min.^"*^ Figure 8.39 shows a TEM of a carbon replica of the obtained heterojunctioned Agl/AgBr particles. 8.8.2. Non-epitaxial Heterojunction To achieve a high catalytic activity, the technique of heterojunction between catalyst particles and their supports is essential for preparing heterogeneous catalysts. For example, Haruta et al}^^ prepared highly dispersed ultrafine gold particles {ca, 4 nm) of narrow size distribution on support oxides of the iron group, including a-Fe203, C03O4, and NiO. They obtained such composite particles by adding a base to a mixed solution of a salt of the corresponding metal and HAuCl^, and then leaching the coprecipitated solid, which was dried, and finally calcined at 400 °C in air. On the other hand, Sugimoto et al^^ selectively deposited ultrafine gold particles (ca, 1 nm) onto well-defined polycrystalline ellipsoidal particles of hematite (a-Fe203) from a dilute solution of HAUCI4 aged at 100 °C for 48 h (see section 7.3.8 and Fig. 7.44 in chapter 7). In this system, the Au^^ ions appeared to be reduced to gold particles by electron transfer from coordinated OH', or from water molecules, on the hematite particles acting as a catalyst for the electron transfer. A sign of such reduction of Au^^ on hematite was observed even at room temperature. Also, the pH around 6 was a decisive factor for the achievement of both the minimum particle size and maximum yield of the final product. Figure 8.40 shows the pH dependence of the yield of gold particles under the standard conditions after

438

PREPARATION 2.0 1.8

# metallic Au

1.6

O AuO(OH)

f"l.4 E

"o 1.2

li.o J 0.8 .^0.6 0.4 0.2

W^

o o\

0.0

6

9

Jd 10

PH Fig. 8.40. Effects of pH on the yield of gold particles on ellipsoidal hematite support by the selective deposition method at 100 °C after 48 h and adsorption of auric complexes at 25 °C after 48 h. (From Ref. 250.)

aging at 100 °C for 48 h and that of the adsorption of auric complexes at 25 °C after 48 h. Au^"^ ions are thought to be in the form of a negatively charged complex, Au(0H)3Cr, or a neutral complex, Au(0H)3, around pH 6, while the auric complex is expected to be negative in the alkaline range in the form of Au(0H)4". In a highly acidic range of pH, the auric complex is thought to be in the form of a negative complex of AUCI4" on account of the coordination number of Au^*, four, and the relatively strong affinity of chloride ions to auric ions. If we consider the point of zero charge (PZC) of hematite around pH 7.8, the adsorption of Au(0H)4' to hematite may be increasingly inhibited with increase in pH above lEP, due to the increasing electrostatic repulsive force. However, the adsorption of AUCI4" to the positively charged hematite surfaces in the acidic range may be rather reduced, since there is no specific affinity between H^ on the hematite surfaces and AUCI4", and since the probability of the adsorption of hydroxide complexes of auric ions to the hematite surfaces through hydrogen bonding is lowered with decreasing pH. The effect of pH on the yield and mean size of the gold particles may be explained in terms of the preferential adsorption of the hydroxide complexes of auric ions to the hematite support around pH 6, and the high surface density of thus generated gold nuclei.

8. CONTROL OF PARTICLE CHARACTERISTICS

439

Ishikawa and Matijevic^^° obtained junctioned particles of CojOya-FCjOj by aging a Co(CH3COO)2 solution at pH 7.0 for 3 h in the presence of spindle-type hematite particles. On the other hand, Sugimoto et al have observed selective growth of needle-like crystals of Ni(OH)2,^^ Co(OH)2,^^ and a-FeOOH^^ on monodispersed ellipsoidal particles of hematite, in the direction parallel to the c-axis of the hematite particles for Ni(OH)2 and perpendicular to the c-axis for Co(OH)2 ^ ^ a-FeOOH, as shown in TEM images of Fig. 8.41. The Ni(OH)2/a-Fe203 particles were prepared by aging at 100 ^C for 24 h a suspension of 2.0 x 10"^ mol dm'^ Ni(0H)2 (amorphous gel) in the presence of 1.0 x 10"^ mol dm'^ a-Fe203, whose initial pH was adjusted to 10.0 with NaOH. The amorphous Ni(0H)2 was transformed through dissolution-recrystallization into the needle-like crystals grown selectively on the hematite surfaces. In the absence of hematite under otherwise the same conditions, the amorphous Ni(OH)2 gel was transformed into well-developed hexagonal tabular microcrystals of ca, 0.08 Jim in mean diameter, instead of the acicular crystals. Nevertheless, even in the absence of hematite, acicular particles similar to those on hematite were also formed in the pH range higher than 10, and the proportion increased with increasing pH. On reduction of the composite powder of Ni(OH)2/a-Fe203 suspended in n-hexadecane with hydrogen at 250 °C for 4 h, the needle-like Ni(0H)2 on hematite tumed into ultrafine metallic Ni particles of ca, 10 nm, while the carrier particles of hematite were completely oxidized into magnetite (Fe304), but their original shape was retained. The deposited Ni(0H)2 and thus the Ni on the ellipsoidal polycrystalline hematite was 0.096, in molar ratio of Ni/Fe, and showed excellent catalytic activity with high stability in hydrogenation of 1-octene, as compared to the activity and stability of the composite particles with ellipsoidal monocrystalline hematite carrier of comparable shape and size, whose Ni/Fe ratio was only 0.030 under the same preparation conditions. This is mainly due to the difference between them in the specific surface area of the carrier; Le., 106 m^g for the former and 19 mVg for the latter. On the other hand, the Co(OH)2/a-Fe203 composite particles were obtained by aging at 100 °C for 72 h a solution of 5.0 x 10"^ mol dm"^ cobalt(II) citrate at an initial pH 10.0 in the presence of 1.0 x 10'^ mol dm"*^ a-Fe203. In the absence of hematite under otherwise the same conditions, only gellike Co(OH)2 precipitated. On gas-phase reduction of 1 g of the composite powder at 300 °C for 1 h in the stream of hydrogen at 50 ml min~\ the carrier hematite particles were completely reduced to magnetite, but retaining the original shape, while the needle-like Co(OH)2 was unchanged

440

PREPARATION

Fig. 8.41. TEM images of the acicuiar crystals of (a) Ni(0H)2, (b) Co(OH)2, and (c) a-FeOOH, grown on ellipsoidal hematite particles. (From Refs. 251, 252, and 59, respectively.) not only in its shape, but also in its original composition of Co(OH)2. When the composite particles were reduced at 450 °C for 2 h under otherwise the same conditions, the carrier hematite was completely decomposed into much smaller metallic Fe particles, but the needle-like Co(OH)2 remained intact. The a-FeOOH/a-FCjOj particles were prepared by aging at 100 ''C for 24 h a solution consisting of 9.0 x 10"^ mol dm"'' FeClg, 0.12 mol dm"^ Na2S04,

8. CONTROL OF PARTICLE CHARACTERISTICS

441

and 4.5 x 10"^ mol dm"^ a-Fe203. If a-Fe202 is absent in this system, only cubic particles of basic iron sulfate, Fe3(S04)2(OH)5 -21120, precipitate.

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442

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84. T. Sugimoto, S. Chen, and A. Muramatsu, Colloids Surfaces A: Physicochem. Eng. Aspects 135, 207 (1998). 85. C. Ducamp-Sanguesa, R. Herrera-Urbina, and M. Figlarz, J. Solid State Chem. 100, 272 (1992). 86. F. Fievet, J. P. Lagier, and M. Figlarz, MRS Bull. 14(12), 29 (1989). 87. A. T. Skjeltorp, J. Ugelstad, and T. Ellingsen, J. Colloid Interface Sci. 113, 577 (1986). 88. T. Matsumoto, M. Okubo, and S. Shibao, Kobunshi Ronbunshu 33, 575 (1976); M. Okubo, Y. Katsuta, and T. Matsumoto, J. Polym. Sci.: Polym. Lett. Ed 18, 481 (1980). 89. E. R. Sheu, M. S. El-Aasser, and J. W. Vanderhoff, J. Polym. Sci. A: Polym. Chem. 28, 629 (1990). 90. E. R. Sheu, M. S. El~Aasser, and J. W. Vanderhoff, J. Polym. Sci. A: Polym. Chem. 28, 653 (1990). 91. D. Shindo, S. Aita, G. Park, and T. Sugimoto, Mater. Trans., JIM 34, 1226 (1993). 92. G. Park, D. Shindo, Y. Waseda, and T. Sugimoto, J. Colloid Interface Scu 177, 198 (1996). 93. D. Shindo, G. Park, Y. Waseda, and T. Sugimoto, J. Colloid Interface Sci. 168, 478 (1994). 94. D. Shindo and T. Sugimoto, in "Current Topics in Colloid and Interface Science," Vol. 3, pp. 53-64. Research Trends, Trivadrum (India), 1999. 95. T. Sugimoto, A. Muramatsu, K. Sakata, and D. Shindo, J. Colloid Interface Sci. 158, 420 (1993). 96. D. Shindo, B. Lee, Y. Waseda, A. Muramatsu, and T. Sugimoto, Mater Trans., JIM 34, 580 (1993). 97. J. Yang, D. Shindo, G. E. Dirige, A. Muramatsu, and T. Sugimoto, J Colloid Interface Sci. 183, 295 (1996). 98. A. H. M. Andreasen, K. Skeel-Christensen, and B. Kjaer, Kolloid-Z. 104, 181 (1943). 99. J. J. Petres, Gj. De2elic, and B. Te2ak, Croat. Chem. Acta 41, 183 (1969). 100. K. Takiyama, Bull. Chem. Soc. Jpn. 31, 950 (1958). 101. J. H. L. Watson, R. R. Cardell, Jr., and W. Heller, J. Phys. Chem. 66, 1757 (1962). 102. H. Tamura and E. Matijevic, 7. Colloid Interface Sci. 90, 100 (1982). 103. A. E. Rega2Zoni and E. Matijevic, Colloids Surfaces 6, 189 (1983). 104. E. Matijevic, C. M. Simpson, N. Amin, and S. Arajs, Colloids Surfaces

446

PREPARATION

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184. M. Harada, K. Asakura, and N. Toshima, J. Phys. Chem. 98, 2653 (1994). 185. T. Yonezawa and N. Toshima, J. Chem. Soc, Faraday Trans. 91, 4111 (1995). 186. N. Kawahashi and E. Matijevic, J. Colloid Interface Sci. 138, 534 (1990). 187. J. Ugelstad, L. Soderberg, A. Berge, and J. Bergstrom, Nature 303, 95 (1983). 188. J. Lee and M. Senna, Colloid Polym. Sci. 273, 76 (1995). 189. T. Ihara, S. Ito, M. Suzuki, and M. Kiboku, Shildzai Kyokaishi 60, 603 (1987). 190. R. Laible and K. Hamann, Adv. Colloid Interface Sci. 13, 65 (1980). 191. G. P. H. L. de Silva, P. F. Luckham, and Th. F. Tadros, Colloids Surfaces 50, 251 (1990); ibid. 50, 263 (1990). 192. T. E. Mates and T. A. Ring, Colloids Surfaces 24, 299 (1987). 193. H. Thiele and H. S. von Levem, J. Colloid Sci. 20, 679 (1965). 194. T. J. Matemaghan and R. H. OttewUl, J. Photogr. Sci. 22, 279 (1974); O. B. Bangham, T. J. Matemaghan, and R. H. Ottewill, Photogr. Sci. Eng. 23, 45 (1979); T. J. Matemaghan, O. B. Bangham, and R. H. Ottewill, J. Photogr. Sci. 28, 1 (1980). 195. A. Muramatsu and T. Sugimoto, J. Colloid Interface Sci. 187, 167 (1997). 196. N. Moriyama, J. Colloid Interface Sci. 50, 80 (1975). 197. N. Fery, R. Laible, and K. Hamann, Angew. Makromol. Chem. 34, 81 (1973). 198. E. Dietz, N. Fery, and K. Hamann, Angew. Makromol. Chem. 35, 115 (1974). 199. N. Tsubokawa, A. Kogure, and Y. Sone, J. Polym. Sci. A: Polym. Chem. 28, 1923 (1990). 200. N. Tsubokawa, A. Yamada, and Y. Sone, Polym. Bull. 10, 63 (1983); N. Tsubokawa, A. Yamada, and Y. Sone, Polym. J. 16, 333 (1984). 201. N. Tsubokawa, K. Murayama, Y. Sone, and M. Shimomura, Polym. J. 21, 475 (1989). 202. N. Tsubokawa, K. Fujiki, and Y. Sone, J. Polym. Sci.: Polym. Chem. Ed 24, 191 (1986); N. Tsubokawa, K. Fujiki, and Y. Sone, J. Macromol. Sci. A: Chem. 25, 1159 (1988). 203. T. Yamaguchi, T. Ono, M. Nozawa, M. Sekine, T. Iwai, and T. Okada, Kobunshi Ronbunshu 40, 259 (1983). 204. K. Yoshinaga, T. Yokoyama, Y. Sugawa, H. Karakawa, N. Enomoto,

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H. Nishida, and M. Komatsu, Polym. Bull. 28, 663 (1992). 205. K. Yoshinaga, K. Nakanishi, K. Nagao, and T. Kito, Kobunshi Ronbunshu 50, 303 (1993). 206. K. Yoshinaga, T. Yokoyama, and H. Karakawa, Polym. Adv. Tech. 4, 522 (1993). 207. K. Yoshinaga and Y. Hidaka, Polym. J. 26, 1070 (1994). 208. K. Yoshinaga and M. Komatsu, Sen-i Gakkaishi 49, 130 (1993). 209. K. NoUen, V. Kaden, and K. Hamann, Angew. Makromol. Chem. 6, 1 (1969). 210. J. P. Lorimer, T. J. Mason, D. Kershaw, I. Livsey, and R. TempletonKnight, Colloid Polym. Sci. 269, 392 (1991). 211. H. T. Ohyama, R. Sprycha, Y. Xie, R. E. Partch, and E. Matijevic, J. Colloid Interface Sci. 160, 298 (1993). 212. Ph. Espiard, A. Revillon, A. Guyot, and J. E. Mark, ACS PMSE Reprint 64, 349 (1991). 213. K. Yoshinaga, T. Yokoyama, and T. Kito, Polym. Adv. Tech. 4, 38 (1993). 214. J. Horn, R. Hoene, and K. Hamann, Makromol. Chem., Suppl. 1, 329 (1975). 215. W. Noll, "Chemie und Technologic der Silicone," p. 203. Verlag Chemie, Weinheim, 1960. 216. K. Furasawa, Y. Kimura, and T. Taguchi, Kobunshi Ronbunshu 40, 697 (1983). 217. C. Huang and E. Matijevic, J. Mater. Res. 10, 1327 (1995); R. E. Partch, S. G. GangoUi, E. Matijevic, W. Cai, and S. Arajs, J. Colloid Interface Sci. 144, 27 (1991). 218. C. Huang, R. E. Partch, and E. Matijevic, J. Colloid Interface Sci. 170, 275 (1995). 219. R. Laible, Farbe Lack 84, 149 (1978). 220. K. P. Krenkler, R. Laible, and K. Hamann, Angew. Makromol. Chem. 53, 101 (1976). 221. K. Yoshinaga, R. Horie, F. Saigoh, T. Kito, N. Enomoto, H. Nishida, and M. Komatsu, Polym. Adv. Tech. 3, 91 (1992); K. Yoshinaga, K. Nakanishi, Y. Hidaka, and H. Karakawa, Composite Interfaces 3, 231 (1995). 222. K. Yoshinaga and K. Nakanishi, Composite Interfaces 2, 95 (1994). 223. K. Yoshinaga, K. Kondo, and A. Kondo, Polym. J. 27, 98 (1995). 224. H. de Hek and A. Vrij, J. Colloid Interface Sci. 79, 289 (1981). 225. C. Pathmamanoharan, Colloids Surfaces 34, 81 (1988/89).

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226. R. Kroker and K. Hamann, Angew. Makromol. Chem. 13, 1 (1970). 227. J. H. Kim, M. Chainey, M. S. El-Aasser and J. W. Vanderhoff, J. Polym. Sci. A: Polym. Chem. 27, 3187 (1989). 228. M. Okubo, K. Ikegami, and Y. Yamamoto, Colloid Polym. Sci. 267, 193 (1989). 229. K. Sakota and T. Okaya, J. Appl. Polym. Sci. 20, 1735 (1976); D. C. Blackley, "High Polymer Latices," pp. 294-295. Maclaren, London, 1966; T. Matsumoto and M. Shimada, Kobunshi Kagaku 22, 172 (1965); S. Muroi and K. Hosoi, ibid. 26, 424 (1969). 230. S. Tsaur and R. M. Fitch, J. Colloid Interface Sci. 115, 450 (1987). 231. S. Watanabe, S. Nakahama and K. Yamaguchi, Kobunshi Ronbunshu 50, 271 (1993). 232. S. Kobayashi and H. Uyama, Kobunshi Ronbunshu 50, 209 (1993). 233. R. Hu, V. L. Dimonie, and M. S. El-Aasser, J. Appl. Polym. Sci. 64, 1123 (1997); M. S. El-Aasser, 1. Segall, and V. L. Dimonie, Macromol. Symp. 101, 517 (1996). 234. S. Bando, Y. Shibahara, and S. Ishimaru, J. Imaging Sci. 29, 193 (1985). 235. T. Sugimoto and T. Hayakawa, U.S. Patent 4,614,711 (1986); 4,713,318 (1987). 236. N. Kawahashi and E. Matijevic, J. Colloid Interface Sci. 143, 103 (1991). 237. A. Kowalski, M. Vogel, and R. M. Blankenship, U.S. Patent 4,427,836 (1984). 238. M. Okubo, K. Ichikawa, and M. Fujimura, Colloid Polym. Sci. 269, 1257 (1991). 239. M. Okubo, H. Minami, and T. Yamashita, Macromol. Symp. 101, 509 (1996). 240. C. M. Cheng, F. J. Micale, J. W. Vanderhoff, and M. S. El-Aasser, J. Polym. Sci. A: Polym. Chem. 30, 235 (1992); C. M. Cheng, J. W. Vanderhoff, and M. S. El-Aasser, ibid. 30, 245 (1992). 241. H. Uyama, K. Takahashi, and S. Kobayashi, Kobunshi Kako 45, 492 (1996). 242. J. E. Maskasky, Photogr. Sci. Eng. 25, 96 (1981). 243. J. E. Maskasky, U.S. Patent 4,463,087 (1984). 244. J. E. Maskasky, J. Imaging Sci. 32, 160 (1988). 245. J. E. Maskasky, U.S. Patent 4,471,050 (1984). 246. J. E. Maskasky, J. Imaging Sci. 32, 95 (1988). 247. T. Sugimoto and K. Miyake, J. Colloid Interface Sci. 140, 348 (1990).

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248. T. Sugimoto, Jpn. Patent (A) 4-139440, 4-139441, 4-139439, 4-139442 (1992). 249. M. Haruta and B. Delmon, J. Chim. Phys. 83, 859 (1986); M. Hanita and H. Sano, Shokubai 26, 140 (1984). 250. T. Sugimoto, Y. Shintoku, and A. Muramatsu, in "Proc. 72nd Ann. Meet. Chem. Sec. Jpn.," Vol. 1, p. 90. Tokyo, Mar. 1997. 251. T. Sugimoto, A. Nakamura, and A. Muramatsu, in "Proc. 49th Symp. Colloid Interface Chem.," (Chem. Soc. Jpn.), p. 288. Hachiooji, Sept. 1996. 252. T. Sugimoto, Y. lida, H. Itoh, and A. Muramatsu, in "Proc. 72nd Ann. Meet. Chem. Soc. Jpn.," Vol. 1, p. 90. Tokyo, Mar. 1997.

PART 3. ANALYSES INTRODUCTION In this Part, the information obtained from different analytical techniques for the formation processes of monodisperse particles and for the characterization of the products will be described in chapters 9 and 10, respectively.

CHAPTER 9 ANALYSES OF FORMATION PROCESSES 9.1. Electron Microscopy Figure 9.1 shows TEM images of the solid phase during the aging of a solution of 2.0 x 10"^ mol dm"^ FeCl3 at 100 °C in the presence of 4.5 x 10" "^ mol dm"^ KH2P04.^ The acicular fine particles observed 8 h after the start of the aging are those ofy?-FeOOH, which are then dissolved to contribute to the growth of the ellipsoidal hematite (a-Fe203) particles, as revealed from photo b) and thereafter. In general, electron microscopy in combination with identification of the solid species by XRD, FTIR, etc. gives us primary information on particle growth. For these analyses, the growth reaction must be stopped at each time of sampling. In the case of the growth reaction in the hematite system above, prompt quenching to room temperature is enough for this purpose, as long as the succeeding pretreatment for these analyses is done within a few hours. However, if the reaction is fast even at room temperature, we must use some efficient inhibitor or inactivate the reactivity by changing the reaction conditions. For example, a merocyanine dye as follows was used for instantaneous halting of the rapid conversion reaction of AgCI particles by Br" ions at 25 °C (see section 5.2)^ and the nucleation process of AgBr particles in an open

454

ANALYSES

Fig. 9,1. TEM images showing the evolution of the solid phase during the aging of a solution of 2.0 x 10"^ mol dm"^ FeCl, at 100 °C in the presence of 4.5 x 10"^ mol dm"' KH2PO4: (a) 8 h, (b) 1 day, (c) 2 days, (d) 4 days, (e) 7 days. (From Ref. 1.)

system at different temperatures ranging from 40 to 70 °C (see section 1.5).^ This dye is instantly adsorbed to the particles and stops the reaction without damage on the surfaces.

C2H5

II CH2COOH

In the case of the rapid reaction of thioacetamide with Cd(0H)2 to yield CdS particles through a dissolution-recrystallization process in the presence of ammonia, the pH of each sample was lowered to ca. 4 with acetic acid to stop the reaction instantly."* In many cases, cooled storage of specimens

9. ANALYSES OF FORMATION PROCESSES

455

before the washing procedure is recommended. Also, instantaneous quenching with liquid nitrogen followed by freeze drying is often adopted for the same purpose if there are no remaining salts to be precipitated by the quenching or they bring no disadvantage to the final analyses. It must be noted that ordinary electron microscopy is not an in-situ observation, but involves many prior intermediate processes, such as repeated centrifugal washing including sedimentation, decantation, and redispersion, and the final drying. Hence, in most cases, electron micrographs cannot be used as direct evidence of aggregation events without other convincing support, unless the specimens keep the original state frozen in the media in a supercooled electron microscope. In addition, special precautions are needed in the observation of a sample vulnerable to the electron beam, which often destroys the original particles or creates new metallic particles on a gel network or on original individual particles during observation. In some cases, this leads to misinterpretation of the formation mechanism in the original systems. Also, in some special cases, filtration or centrifugation causes drastic contact recrystallization, as in the silver halide particle systems without any inhibitor, such as gelatin, the above merocyanine dye, l,l'-diethyl-2,2'-cyanine, 4-hydroxy-6-methyl-l,3,3a,7tetraazaindene, or mercaptotetrazole. (see section 4.5).^'^

9.2. X-ray Diffractometry Figure 9.2 shows X-ray diffraction profiles in the progress of the solid phase transformation of the hematite particles displayed in Fig. 9.1. From the XRD patterns, the acicular particles in Fig. 9.1a and the ellipsoidal particles observed with the acicular ones in Figs. 9.1b-e were identified as ^-FeOOH and a-Fe203, respectively, by reference to the JCPDS data files.^ Also, Fig. 5.13 in chapter 5 shows a stepwise increase of the AgCl content in the growing sohd solution on the AgCl host crystals at 45 °C. From the face intervals of {220} given by its diffraction peaks, the mole fraction of AgCl in each solid solution was obtained from the calibration curve of the mole fraction against the lattice constant or from approximate calculation with the Vegard law prescribing the proportional increment of lattice constant to the mole fraction of a component of a larger atom in a binary solid-solution. For exact analysis of XRD, the pretreatment of the samples for removing the extraneous salts again has a decisive influence on the final results. For

456

ANALYSES

7 day$

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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

9. ANALYSES OF FORMATION PROCESSES

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

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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.^Ishizuka 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 <

/

\

.Omin.

-

/^/\/20

-

1.5

< ^ \ \ X V .100

-

1.0

^^^-^ ^ ^ / 1 6 0

0.5 0.0

300

AOO

500

600

Wavelength / nm

700

800

Fig. 9.6. Evolution of the UV-VIS spectrum of an AuCl4"-CP"^ complex with the reduction of Au^"" ions by hydrazine at room temperature under the initial conditions: [HAuCi4] = 0.5 mmol dm'^ [CPCl] = 2.0 mmol dm"^; [N2H2] = 1.0 mmol dm'^. (From Ref. 14.)

Tanaka and Iwasaki studied the non-steady nucleation process of silver chloride^^ and silver bromide^^ using a multichannel UV spectrophotometer with a stopped flow apparatus, which enabled the measurement of a relatively rapid nucleation process of the order of several 10 msec (see c) Discussion of section 1.4.2). For example, the UV spectra in Fig. 9.7 show the formation of ultrafine particles of silver bromide of a broad absorption band at the expense of a silver bromide complex having an absorption peak at 233 nm after instantaneous mixing of a silver perchlorate solution with a potassium bromide solution.^^ Within the studied time span, the contribution of light scattering was negligible. Thus, if some species which participates directly or indirectly in precipitation has a UV or visible absorption band, and if there is no other

9. ANALYSES OF FORMATION PROCESSES

461

substance to interfere with the measurement by its own strong absorption, UV-VIS spectroscopy lends itself to the study of particle fomiation. OA 35-C cell : 2 mm 2.5xlO-^M AgClO^ + 0.2M KBr ( pBr = 1.0) \lms

'

5 ms

9 0.2 " 9 m s \ \ /

17 ms

L U T ' ^ X Vi(^

25 ms

57rns^^ ^^V^,^_57ms

2A0

Imb ^^,.,;;^^ 270 Wavelength ( nm

'—= 300

Fig. 9.7. Time-resolved UV spectra of AgBr^('"-^>-compiex and AgBr nuclei, as revealed by multichannel spectrophotometry in combination with stopped flow technique. (From Ref. 16.)

9.5, Potentiometry a) pH Measurement Probably, the most popular potentiometry may be the measurement of the pH during precipitation in aqueous solutions with a glass electrode, since the pH always changes with a progress of precipitation or dissolution of metal oxides and metal hydroxides. For example, Figure 9.8 shows the changes of the pH and the concentration of phosphate ions in the forced hydrolysis system for the preparation of ellipsoidal hematite particles from a dilute FeClg solution in the presence of phosphate, corresponding to Figs. 9.1, 9.2, and 9.3.^ The initial rapid drop in pH is simply due to the consumption of hydroxide ions furnished from water with the precipitation of p-FeOOH particles as an intermediate. On the other hand. Fig. 7.20 in section 7.3.1 shows the pH change in the condensed gel-sol system for the preparation of monodisperse hematite particles.^^ In this system, the initial drop in pH is due to the formation from Fe(0H)3 of p-FeOOH, of a lower solubility product, and the subsequent slow decrease is due to the formation from PFeOOH of a-Fe203, of a still lower solubility product, since there is no pH change in the stoichiometry of these phase transformations. Incidentally, the

462

ANALYSES

2

3

4

5

6

Time (day)

Fig. 9.8. Changes of the pH and the concentration of phosphate ions in the forced hydrolysis system for the preparation of ellipsoidal hematite particles from a dilute solution of 2.0 x 10"^ mol dm'^ FeClg in the presence of phosphate, corresponding to Figs. 9.1, 9.2, and 9.3. (From Ref. 1.) slow reduction of pH after the initial drop in Fig. 9.8 is partly due to the phase transformation of p~FeOOH to a-Fe203 and partly due to the direct precipitation of a-Fe203 from the solution phase.^ The initial pH drop with the formation of p-FeOOH in both systems is of great significance in separation of the nucleation and growth stages for the formation of monodispersed hematite particles, as has been mentioned earlier in section 7.3.1 for the gel-sol system. In the synthesis of monodisperse metallic nickel particles by reduction of Ni(OH)2 particles with sodium hypophosphite (NaH2P02), we also observed a marked pH drop (see Fig. 7.31 in section 7.3.1), which served for the formation of monodispersed particles.^^ In this case, the pH drop is due to the higher basicity of P02^" than P03^", since protons are not produced stoichiometrically with the reduction of Ni(0H)2 by NaH2P02. The pH drop in Fig. 7.28 in section 7.3.1 for the formation of CdS particles from Cd(0H)2 with thioacetamide (TAA: CH3CSNH2) is due to the protons liberated by the reaction of TAA with Cd^^ and its ammonia

9. ANALYSES OF FORMATION PROCESSES

463

complexes initiaUy dissolved in equilibrium with Cd(OH)2 ^ ^ ^he reaction with those remaining after the complete dissolution of Cd(0H)2. It is not due to the reaction of TAA with Cd(0H)2, since this reaction does not produce protons/ The pH change in Fig. 7.30 of chapter 7 for the preparation of uniform CujO particles from CuO particles by reduction with hydrazine (N2H4) through a dissolution-recrystallization process reveals the progress of the reaction; Le,, the initial rise due to the release of OH" ions by the dissolution of CuO particles, induced by the depletion of the free Cu^* ions by complexation with N2H4 for reduction of Cu^* to Cu*, the subsequent fall due to the nucleation and growth of CU2O associated with the consumption of OH', and the final increase due to the accumulation of NH3 which is a stronger base than N2H4.^^ b) Metal-Ion Potentiometry The activities or concentrations of many kinds of metal ions can be measured by potentiometry with the corresponding electrodes, as correlated by the Nemst equation. The change of Cd potential in Fig. 7.28 in section 7.3.1 for the formation of CdS particles is due to the reaction of cadmium ions in the solution phase with S^" ions released from TAA. From the changing pattem of the Cd potential detected with a Cd/CdS electrode, it is possible to specify the nucleation and growth periods, as well as the behavior of cadmium ions during the formation process of the CdS particles. That is, the initial sharp drop of Cd potential, a subsequent plateau lasting for about 1 min, and a final gradual decline are due to the sequential reaction of S^" ions, promptly furnished from TAA, with the Cd^^ ions initially present in the solution phase, subsequently released from Cd(0H)2 by dissolution, and remaining after the complete dissolution of Cd(0H)2, respectively."* Figure 9.9 shows the change of Cd potential with a stepwise addition of totally 50 cm^ of 1.0 mol dm"^ TAA to 50 cm^ of 1.0 mol dm"^ Cd(0H)2 suspension at 20 °C. On addition of 12.5 cm^ of the TAA solution, the Cd potential initially at 53 mV dropped sharply to the minimum, followed by a rapid and subsequent gradual recovery to around the initial level in about 1 h. Similar pattems were noted until the third addition of 12.5 cm^ of TAA, but the minimum of each potential-drop and its recovered level become lower with the steps of each addition. When 10 cm^ of TAA was added as the fourth addition, a slight potential retrieval was still observed. At the final addition of 2.5 cm^, the Cd potential was gradually lowered without recovery. The

464

ANALYSES 160 100

ll

-

B -100

i

/

^

^ T

_-!__ -

N 'L^

—

\

S. -200

E t — ..-. -_..

-[--

-—

I -^50 F T — o

—

f

E E

f

1

J

"r

-300

-400

FT"

-—

—f—

•

\ }

J

J 40

'

H

i

H

• •

—

30

f*

I 0)

J 1 J 20 S

X ^axn

»-••

-250

-350

/

/

0 -50

_-[— j_. - - -4-

«_

SO

"1 J so

,

--

J J

--

2

3

Time (hour)

-450

Fig. 9.9. Change of the Cd-potential with the stepwise addition of totally 50 ml of 1.0 mol dm"^ TAA to 50 ml of 1.0 mol dm"^ Cd(0H)2 suspension at 20 °C. (From Ref. 4.) sharp drop in Cd potential and its rapid recovery observed in the early additions correspond, respectively, to a prompt reaction of TAA with Cd^^ ions present in the solution phase and the fast dissolution of Cd(OH)2 induced by the depletion of Cd^* ions in the solution phase. The lowering of the minimum of each potential drop and its recovered level, as the addition of TAA is repeated, seems to be due to the increasing density of the CdS layer covering the surfaces of Cd(0H)2 particles, as a result of direct reaction of S^' ions with Cd(0H)2, which appears to occur mainly in the course of the recovery of Cd^* concentration. The unilateral slow decrease of Cd potential at the final addition of TAA is attributed to the reaction of TAA present in a stoichiometric amount with the remaining Cd(0H)2 with Cd^^ ions slowly released from the Cd(0H)2, through the surface walls of the CdS layer. The potentiometry of Cu^* ions in the preparation of CujO particles using a Cu/CuS electrode in the absence of gelatin in Fig. 7.30 in chapter 7 provides us with detailed information on the rather complex growth process when combined with pH and ICP measurements, as has been described in section 7.3.1. If we use a silver electrode in the study of nucleation of silver halide

465

9. ANALYSES OF FORMATION PROCESSES

particles or on their conversion process, the behavior of silver ions can be readily detected in-situ; e.g., Figs. 1.17 and 1.21 in chapter 1 and Figs. 5.9, 5.16, 5.17, and 5.18 in chapter 5. Conversely, the potentiometric technique can be applied to the control of particle growth of silver halide by feeding the detected potential back to the control system for the addition of the reagents, such as the controlled double-jet (CDJ) technique (see sections 1.5.2, 3.2, 7.3.1, 8.1.1, and 8.2.1). The CDJ or controlled single-jet technique may be applied for the preparation of a wide variety of monodisperse particles by using an appropriate metal electrode or a glass electrode for pH control in a pH stat.^^

9.6, Inductively Coupled Plasma Spectrometry Figure 9.10 shows the change 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"^ FeClj at 100 X in the

XV LJ

E •o o E E

r—~T

•

1

•

1

'

1

•

1

^""1

a-FeaOa

^

-X

15

to

10

o

1

»

c o c a> 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

9. ANALYSES OF FORMATION PROCESSES

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 Cu^O 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

9. ANALYSES OF FORMATION PROCESSES

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

9. ANALYSES OF FORMATION PROCESSES

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

9. ANALYSES OF FORMATION PROCESSES

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

9. ANALYSES OF FORMATION PROCESSES

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 <

OC

ri___J

n

8

o

0

y—E

I

o u. a

^

UJ Q.

(0

0) C

1

1

1

20

40

AGIN6 TIME (m in)

6

Fig. 9.23. Changes of the specific radioactivities of ^^Fe in the solution phase (<4* IA>\ in the ferrous hydroxide gel (\ and the differential radioactivity of Fe304 () as a function of aging time in the system for the formation of unifomi magnetite particles from ferrous hydroxide by partial oxidation with KNO3. (From Ref. 26.)

hydroxide compared to that of ferrous hydroxide. It is now evident that the radiochemical techniques are particularly useful for the analysis of the recrystallization process. However, it should be noted that they have some limits when the radioactive ions have a considerably high diffusivity in the solid like silver ions in silver halides.^^'^ Fortunately, the diffusion of halide ions in silver halide crystals is negligible below 100 OQ 28,29 ^}jj(»jj is tj^g gyen in nascent precipitates, as is obvious from the fact that the adsorbed Aza which freely allows the surface exchange of halide ions completely inhibits further exchange, even in the early stage of precipitation.

9.10, Seeding Analysis Figure 9.24 shows the effect of various amounts of ultrafine hematite seeds (ca. 3.2 nm) on the reaction rate for the formation of ellipsoidal hematite particles by forced hydrolysis in a dilute FeClj solution (2.0 x 10"^ mol dm-^) in the presence of 4.5 x lO"" mol dm"^ KH2PO4 at 100 °C }

478

ANALYSES AULJ

1

"T" '

r -^^r—'

1 ' -1 • '

1

O

E E^

'

1

a J

E 15 Supernatant iron species 10

o

o

jO

5 \ l Run 2

g

'"" 3

Al

0

^''^^^^w^

^^s^^^

1

1

2

3

4

5

1 . i 6

7

Time (day)

E

i E

5 2

3

4

5

Time (day)

Fig. 9.24. Changes of the iron concentrations in the supernatant solution (a) and in the solid phase consisting of a-Fe203 and p-FeOOH (b) for Runs 1, 2, and 3 with different contents of the a-Fe203 seeds: 0, 1.50 x 10'^, and 1.50 x 10"^ mol dm'^ respectively. (From Ref. 1.)

Obviously, the reaction for the formation of a-Fe203 is greatly accelerated. Correspondingly, the size of the final product was diminished with the increasing amount of seeds, as shown in TEM images of the products in Fig. 9.25. The analytical results of these systems with and without seeds are sunmiarized in Table 9.2, in which the number of generated nuclei is assumed to be equal to the particle number of the product prepared without seeds. From this table the final particle numbers are found to be nearly equal to the respective total numbers of nuclei including the seeds. If the

479

9. ANALYSES OF FORMATION PROCESSES

Fig, 9.25. TEM images of the ellipsoidal hematite particles prepared in each run in Fig. 9.24 after varying aging times: (a) Run 1 (7 days); (b) Run 2 (4 days); (c) Run 3 (2 days). (From Ref. 1.)

Table 9.2. Comparison of the systems aged in the absence or presence of the aFe203 seeds {Source: Ref. 1) Number of Nuclei

Sample

Added Seeds (dm-^)

Product Particles

(%)

Mean Length (^m)

Mean Aspect Ratio

Mean Volume (^im^)

Particle Number (dm-')

Genrtd. Nuclei (dm-')

Total (dm"^)

Yield

(a)

0

8.4x10^'

8.4x10"

77.8

0.67

6.7

2.8x10-'

8.4x10"

(b)

2.7x10'^

8.4x10"

3.5x10'^

94.2

0.46

6.5

1.0x10-'

2.9x10'"

1 (c)

2.7x10'^

8.4x10"

2.8x10'^

97.7

0.22

6.3

1.2x10-^

2.5x10^5

particles were formed mainly through aggregation of preformed primary particles, the formation reaction would not be accelerated by addition of seeds, since the supersaturation for the nucleation of primary particles is unaffected, or rather lowered, by the additional consumption of solute for the growth of the seeds. Also, it seems to be obvious that aggregation between existing primary particles and the seeds, if any, has no effect on the reaction rate for the formation of hematite. Thus there is no doubt from the seed effect that the growth of the hematite proceeds through deposition of the monomeric solute. The agreement between the particle numbers of the total nuclei and the final product supports this conclusion, since it is not expected in the aggregative growth mechanism unless the hypothetical

480

ANALYSES

primary particles aggregate exclusively to the ultrafine seeds without aggregation among the seeds or among the primary particles. Here, it should be noted that if dissolution of the preformed p-FeOOH is the ratedetermining step for the growth of hematite, the reaction is not accelerated by seeds. Thus, the observed acceleration of the reaction by the seeds also indicates that the rate-determining step is the deposition process of solute in this system, and not the dissolution process of p-FeOOH. A similar seed effect was also observed in the condensed gel-sol system of pseudocubic hematite, in which the reaction finished within 1 day in the presence of a large amount of seeds, while it usually takes about 8 days in their absence.^^ Hence, the growth mechanism of monodisperse hematite particles is basically the same, irrespective of the homogeneity of the starting system and the presence of shape controllers. As a consequence, the seeding technique is useful not only for the preparation of uniform particles and their size control, but also for the study of their growth mechanism (see also sections 6.1, 7.2.9, 7.2.10, 7.3.1, and 8.1.7). However, it should be noted that this method as a probe for distinction of a particle growth mechanism is inapplicable to systems whose rate-determining step of the particle growth is some process preceding to the deposition process of solute including its diffusion and surface reaction.

References 1. T. Sugimoto and A. Muramatsu, J. Colloid Interface Sci. 184, 626 (1996). 2. T. Sugimoto and K. Miyake, J. Colloid Interface Sci. 140, 335 (1990). 3. T. Sugimoto, J. Colloid Interface Sci, 150, 208 (1992). 4. T. Sugimoto, G. E. Dirige, and A. Muramatsu, J. Colloid Interface Sci, 176, 442 (1995). 5. T. Sugimoto and G. Yamaguchi, J, Crystal Growth 34, 253 (1976). 6. T. Sugimoto and G. Yamaguchi, J, Phys, Chem. 80, 1579 (1976). 7. Joint Committee on Powder Diffraction Standards, Diffraction Data File No. 34-1266, JCPDS International Center for Diffraction Data, Pennsylvania, 1984; ibid No. 33-664, 1983. 8. T. Sugimoto, H. Itoh, and H. Miyake, J, Colloid Interface Sci, 188, 101 (1997). 9. G. Herzberg, "Infrared and Raman Spectra of Polyatomic Molecules," Van Nostrand, New York, 1945.

9. ANALYSES OF FORMATION PROCESSES

481

10. J. A. Gadsden, "Infrared Spectra of Minerals and Related Inorganic Compounds," Butterworths, London, 1975. 11. P. T. Davey, G. M. Lukaszewski, and T. R. Scott, Aust. J. Appl. Sci. 14, 137 (1963). 12. T. Sugimoto, G. E. Dirige, and A. Muramatsu, J. Colloid Interface Sci. 182, 444 (1996). 13. T. Sugimoto, G. E. Dirige, and A. Muramatsu, J. Colloid Interface Sci. 180, 305 (1996). 14. H. Ishizuka, T. Tano, K. Torigoe, K. Esumi, and K. Meguro, Colloids Surfaces 63, 337 (1992). 15. T. Tanaka and M. Iwasaki, J. Photogr. Sci. 31, 13 (1983). 16. T. Tanaka and M. Iwasaki, J. Imaging Sci. 29, 86 (1985). 17. T. Sugimoto, K. Sakata, and A. Muramatsu, J. Colloid Interface Sci. 159, 372 (1993). 18. T. Sugimoto, H. Kikuchi, and A. Muramatsu, in "Proc. 72nd Ann. Meet. Chem. Soc. Jpn.," Vol. 1, p. 89. Tokyo, Mar. 1997. 19. A. Muramatsu and T. Sugimoto, J. Colloid Interface Sci. 189, 167 (1997). 20. D. Shindo, G. Park, Y. Waseda, and T. Sugimoto, J. Colloid Interface Sci. 168, 478 (1994). 21. T. Sugimoto, S. Chen, and A. Muramatsu, Colloids Surfaces A: Physicochem. Eng. Aspects 135, 207 (1998). 22. T. Sugimoto and H. Yanagida, Nippon Shashin Gakkaishi 40, 15 (1977). 23. E. T. Larson, F. W. H. Mueller, and H. Hoerlin, J. Phys. Chem. 57, 802 (1953). 24. C. R. Berry and D. C. Skillman, J. Phys. Chem. 70, 1871 (1966). 25. C. R. Berry and D. C. Skillman, Photogr. Sci. Eng 11, 411 (1967). 26. T. Sugimoto and E. Matijevic, J. Colloid Interface Sci. 74, 227 (1980). 27. K. Reber, Photogr. Korr. 105, 191 (1969). 28. W. D. Compton and R. J. Maurer, Phys. Chem. Solids 1, 191 (1956). 29. A. P. Batra and L. M. Slifkin, J. Phys. C 9, 947 (1976).

CHAPTER 10 CHARACTERIZATION OF PRODUCTS The characterization of products is of importance for understanding their properties as weU as their formation mechanisms. This chapter is devoted to describing typical analytical techniques for the characterization of monodispersed particles.

10.1. Transmission Electron Microscopy If the thickness of a particle is sufficiently small (below ca, 0.1 (xm), it is possible to observe the internal microstructure directly with a highresolution electron microscope, as has been shown for the lattice structure of a nearly single crystalline ellipsoidal particle of hematite (a-Fe203) and a poly crystalline spherical particle of cadmium sulfide (CdS), in section 8.3. However, if the thickness of a particle is much greater, we need to slice it, embedded in a resin matrix, with a ultramicrotome to see the internal structure. For example. Fig. 10.1 shows TEM images of a series of consecutive slices of acrylic resin (polymethyl methacrylate : polybutyl methacrylate = 3 : 7 or 2 : 3, benzoyl peroxide 1.5-1.7 %) in a gelatin capsule holding slices of pseudocubic hematite particles at a low magnification (a) and close-up views of consecutive slices of a specific particle at a certain position (b), indicated by A to E in the upper figure.^ Figure 10.2 is a schematic illustration showing the positions of the consecutive slices of a particle in Fig. 10.1b. Figure 10.3 shows a transmission electron micrograph of a section around a comer of a pseudocubic particle and a high-resolution micrograph of a part of it. From this figure, the surface of the pseudocubic polycrystal is revealed to cc)nsist o£ subcrystals whose surfaces are also only {012} faces, where (0112) and (1102) are equivalent to {012}. By using this technique, the internal structures of pseudocubic and peanut-type hematite particles and CdS particles prepared in an EDTACd chelate system were disclosed (see section 8.3).

483

10. CHARACTERIZATION OF PRODUCTS

T^.^M, ,.^--M—M ^.

Fig. 10.1. TEM images of consecutive slices of pseudocubic hematite particles embedded in resin (a) and of enlarged photos of one particle for slices A to E (b). (From Ref. 1.)

\:^^N .-••"B:*. •

-• ^

•

.

Jc

.--'

••-' •

•

'

•

.

.-••

.---'A

c:*-

n * •

'

.

J

Fig. 10.2. Schematic illustrations of the positions of the consecutive slices (a) and the asterisks (b), corresponding to those in Fig. 10.1. (From Ref. 1.)

484

ANALYSES

Fig. 10.3. (a) TEM of a section of a pseudocubic hematite particle around its comer; (b) high-resolution TEM of the area indicated by the arrow in (a) and its Fourier diffractogram in the inset. (From Ref. 1.) If a carbon replica of some particles on a substrate, such as a mica plate, is prepared by deposition of evaporated carbon in a vacuum and subsequent dissolution of the particles with a proper solvent, their stereomicrograph can be obtained. Figure 10.4 is a transmission electron micrograph of soobtained cobalto-cobaltic oxide (C03OJ particles.^ In this case, the particles were settled onto a mica chip, shadowed with chromium, cast in carbon, and then dissolved in concentrated hydrochloric acid. From the shadowing angle, the height of each particle can be calculated. Hence, the method is often used for determining thicknesses of platelet particles. Chromium, platinum, and platinum-palladium alloy are usually used for shadowing. Figure 4.9 in section 4.5 also shows TEM images of carbon replicas of silver chloride particles prepared on a mica plate (a) or on membrane filters (b,c). The silver chloride particles were dissolved in sodium thiosulfate solution, and the liberated carbon replicas were observed with an electron microscope. This method is particularly useful for direct observation of the particles on a filter without changing their state. For the determination of the Miller indices of the facets of microcrystals, carbon replicas are useful; z.e., the Miller indices of two adjacent planes can be determined by measuring the intersecting angle of the planes by rotating the sample-stage to adjust the direction of observation to that of the line of the

10. CHARACTERIZATION OF PRODUCTS

0.5 ^m

485

Fig. 10.4. TEM of a carbon replica of the uniform cubic particles of C03O4. (From Ref. 2.)

intersection. In this way, Maskasky-' determined the Miller indices of the facets of regular polyhedral microcrystals of silver bromide (see section 8.2.1). The same purpose can be achieved by a much simpler method, the OPML-XRD, to be described in section 10.6.

10.2. Scanning Electron Microscopy Scanning electron microscopy provides us with abundant information on the surface structure of particles as well as their three-dimensional shape. Surface structures more or less reflect the internal structures of the particles, as has been shown in section 8.3. However, in some cases, the size and shape of subcrystals at external surfaces of polycrystals do not necessarily represent the internal ones, as was found for cadmium sulfide particles prepared in Cd-EDTA chelate systems (see section 8.3). Since the samples are normally subject to much greater exposure to electron beams than in transmission electron microscopy, special care is needed in scanning electron microscopy on samples vulnerable to electron-beam damage.

486

ANALYSES

10.3. Electron Diffractometry Electron diffractometry is used for the identification of particle species at the same time as microscopic observation, determination of a local or total crystallographic orientation of a particle section or a thin particle, assessment of crystal imperfections, etc. For example, we have determined or assessed by electron diffractometry the orientation of elongated subcrystals of a peanut-type particle of hematite as shown in Fig. 8.23(b) of chapter 8, the Miller index of the surfaces of subcrystals at the surface of a pseudocubic hematite particle in Fig. 10.3, the internal crystal structure of ellipsoidal hematite particles prepared with sulfate or phosphate ions in Fig. 8.24 of chapter 8, etc. Figure 10.5 shows an electron diffraction image (b) of the small ellipsoidal particles in the circle in the electron micrograph (a), in which much larger hematite particles of a similar shape are also observed. This precipitate was sampled from a forced hydrolysis system of 2.0 x 10"^ mol dm"^ FeClg solution after aging for 4 days at 100 °C in the presence of 4.5 X 10"^ mol dm"^ KH2PO4 (see chapter 9)."* From the face intervals calculated from the radii of the diffraction rings in (b), the small particles

0.4 |.im

Fig. 10.5. (a) TEM of the precipitate after aging 2.0 x IQ-^ mol dm"^ FeClj for 4 days at 100 °C in the presence of 4.5 x 10"^ mol dm'^ KH2PO4; (b) electron diffraction image of the particles in the circle of photo (a). (From Ref. 4.)

10. CHARACTERIZATION OF PRODUCTS

487

Table 10.1. Face intervals calculated from the radii of the diffraction rings in Fig. 10.5(b) and the corresponding face indices of P-FeOOH (Source: Ref. 4)

d 1

Diffraction Ring

a

b

c

Face Interval (A)

7.46

5.25

3.33

2.64

Face Index

(110)

(200)

(310)

(400) J

1 1

e

i

g

h

i

J

k

2.57

2.30

2.09

1.95

1.75

1.65

1.52

1.45

(211)

(301)

(321)

(600)

J521^

(002)

(541) 1

^411)

were identified as ^-FeOOH. The face intervals and corresponding face indices of p-FeOOH are summarized in Table 10.1. Figure 10.6 shows a TEM and an electron diffraction image of a section of an ellipsoidal hematite particle sliced perpendicular to the revolution axis.

a

0.3 F^

Fig. 10.6. TEM and electron diffraction pattern of a slice perpendicular to the caxis of an ellipsoidal hematite particle controlled in shape by 3.0 x 10"^ mol dm"^ P0/~ in a gel-sol process at 140 °C for 3 days in the presence of a reduced concentration of chloride ions (0.1 mol dm'^).

488

ANALYSES

A corresponding electron diffraction pattern of a section of an ellipsoidal particle sliced parallel to the revolution axis is shown in Fig. 8.24(b) in chapter 8. The diffraction patterns of the sections parallel and perpendicular to the revolution axis reveal that the revolution axis is coUinear with the caxis of the hexagonal crystal system, in accord with the result from OPMLXRD. Figure 10.7 illustrates electron diffraction patterns of a AgCl host and a AgBr guest of a AgBr/AgCl composite particle prepared by partial conversion of AgCl particles with KBr, described in detail in section 5.2. From the agreement in crystallographic orientation between the host and guest, it is evident that the AgBr guest is grown epitaxially on the AgCl host crystal.^

Fig. 10.7. Electron diffraction pattems of a AgBr/AgCl heterojunctioned particle for its AgCl host crystal (a) and one of the AgBr guests grown on the host's comers (b). (From Ref. 5.)

10.4. Energy Dispersive X-ray Spectrometry Figure 10.8 shows EDX spectra of sections of pseudocubic and platelet-

10. CHARACTERIZATION OF PRODUCTS

489

type hematite particles prepared from Fe(OH)3 gels containing a total of 1.0 mol dm"^ iron in the presence of 3.0 mol dm"^ CI', and repeatedly washed with doubly distilled water by centrifugation.^ The pseudocubic particle has a small K^, peak of CI at 2.62 keV in addition to the strong characteristic X ray intensity of Fe, in contrast to the platelet-type particle which has no peak of CI. From EDX spectra of sections of the pseudocubic particles, the quantity of chloride ions in the interiors is around 0.02 in average atomic ratio of CI to Fe. The result reflects the presence of chloride ions condensed at the grain boundaries between the internal subcrystals of the pseudocubic particles and the absence of such subcrystals in the monocrystalline platelettype particles. The great difference between the two types of hematite

a

i

1

j

i

1 [fT

Hi- - j —

'a

\

i

1 11

1 IV- J i

l.n .

•

L_ i J

\ il

1 11

! li

3

1

-J j i 1

y;y^iy,y^WBy/rfiW II

1

I is

5

7

Energy ( kcV )

b >

MJ— 'II

^ 5 j

B

11 m

r

1

^^Si^^y^^ • Energy (kcV)

Fig. 10.8. EDX spectra for sections of pseudocubic (a) and platelettype (b) hematite particles. (From Ref. 1.)

ANALYSES

490

particles in chloride content and internal structure is caused by the difference in the pH range for the preparation of these particles. Namely, the pseudocubic particles are prepared in the pH range below 2, in which chloride ions are strongly adsorbed to the growing hematite particles, whereas the platelet-type particles are prepared in the pH range above 14, in which chloride ions are completely excluded from the growing hematite surfaces by hydroxide ions. Figure 10.9 is an EDX spectrum obtained from a section of a peanuttype hematite particle prepared from Fe(OH)3 gel containing a total of 1.0 mol dm-^ iron with 3.0 x 10"^ mol dm'^ S O / ' and 3.0 mol dm"^ CI". In distinction from the EDX spectrum of pseudocubic particles in Fig. 10.8, a K„ peak of S is observed at 2.31 keV with a much smaller peak of CI at 2.62 keV.^ This result demonstrates that a considerable amount of SO/" ions is incorporated in the peanut-type particles, and that chloride ions are mostly excluded by sulfate ions of a much greater adsorption strength. The internal sulfate ions must be condensed at the internal grain boundaries of the subcrystals.

p^ 1 i D

s

1 li

mim Vi'i^fl'i^ i^fvfflTV !4^>«*Vs«*'*f i j i i Energy (keV)

Jib

Fig. 10.9. EDX spectrum for a section of a peanut-type hematite particle controlled in shape by sulfate ions. (From Ref. 6.)

Figure 10.10 shows the so-obtained internal distribution of sulfate ions in a peanut-type hematite particle, revealing their rather uniform distribution.^ The uniform distribution of the sulfate ions is readily understood if one considers the high concentration of sulfate ions during the growth stage in the solution phase of this gel-sol system (> 3.0 x 10"^ mol dm'^),^ sufficient for the saturated adsorption of sulfate ions to growing surfaces of

10. CHARACTERIZATION OF PRODUCTS

491

3-5 o

30

ii)

?5

%

o ^ 2.0

£

1,5

-2 £ 5

0,5

<

0.0

I

r~^

I

I 1 1I n

I

I

^r^

r-^

r*~1

1I I I I

to

Fig. 10.10. Internal distribution of sulfate ions in a peanut-type hematite particle obtained from EDX spectrometry on a section sliced parallel to the revolution axis of the particle, shown by the upper right TEM. The S/Fe atomic ratios in the histogram correspond to those at the spots of ca. 0.1 jxm diameter in the upper left section scheme. (From Ref. 7.)

hematite particles (see Fig. 8.4 in chapter 8). Although we cannot expect high accuracy in the quantitative analysis of low-content impurities by EDX spectrometry, it enables us to estimate the local composition within the order of 10 nm in a section of a particle or the compositions of individual ultrafine particles in the view of the electron microscope.

10.5. Powder X-ray Diffractometry Powder XRD is one of the most fundamental means of characterization of particulate products for the identification of crystalline particles, estimation of the crystallinity, evaluation of the size of the subcrystals or the magnitude of the internal strain in individual particles, determination of the composition of mixed crystals, etc. The solid species can be identified by reference to the JCPDS data files (see section 9.2), if corresponding data have been compiled.

492

ANALYSES

The thickness of each crystal face of a subcrystal in polycrystalline particles can be estimated with the following Scherrer equation'^ L= p COS6Q'

where L is the thickness of the lattice plane, X. is the wavelength of the X ray, and p is the integral width in 26 of an intrinsic diffraction profile of a sample powder at a Bragg angle 6^ which gives the diffraction peak of a crystal face. The intrinsic diffraction profile is obtained by subtracting the contribution of an apparatus factor using a reference with single crystal units of sufficiently large dimensions, without crystal strains. The integral width is that of a hypothetical rectangular diffraction line whose peak height and area are equal to the respective quantities of the intrinsic diffraction profile of the sample. Figure 10.11 shows powder XRD (CrATJ profiles of pseudocubic hematite particles prepared from a gel-sol system in the presence of 3.0 mol dm"^ Cr and annealed at 1000 ""C for 3 h, the original pseudocubes

40

50

20/deg.(CrKa)

Fig- 10.11. Powder XRD profiles of hematite particles of annealed pseudocubes (control) (a) and asprepared powders: pseudocubes (b), platelets (c), and spindles (d). (From Ref. 9.)

10. CHARACTERIZATION OF PRODUCTS

493

Table 10.2. Mean thicknesses of the {012}, {104}, and {110} layers of the single crystal units of hematite particles for the as-preapred pseudocubes, platelets, and spindles, calculated from the XRD data shown in Fig. 10.11 {Source: Ref. 9)

Pseudocubes (e.L, 1.65 |Lim)

{012}

{104}

{110}

25.5 nm

24.6 nm

32.3 nm

Platelets (d., 1.90 fim; t.. 0.20 |Lim)

>300 nm

>300 nm

>300 nm

Spindles (1., 0.43 fxm; w., 0.13 fxm)

>300 nm

>300 nm

130 nm

Note: e.L (edge length); d (diameter); t. (thickness); I. (length); w. (width). without annealing, platelet-type hematite particles prepared in an alkaline medium by the gel-sol method, and spindle-type hematite particles prepared by forced hydrolysis from a dilute FeCIg solution in the presence of phosphate ions.^ From the integral width of the diffraction line of each face, such as {012}, {104}, or {110}, the thickness of each face of a single crystal unit of these particles was estimated as summarized in Table 10.2, where the single crystal units of the annealed sample used as a reference is assumed to be sufficiently large, beyond the limit of the size effect on the linewidth. From this table, it is found that the pseudocubes are polycrystals consisting of much smaller subcrystals, while the platelets and spindles whose mean width is ca. 130 nm are single crystals. If the thickness of the subcrystals becomes smaller than ca. 1 nm, the line width becomes too broad for accurate measurement. On the other hand, if the thickness of the crystallites exceeds ca. 300 nm, accurate determination of the dimensions of the crystallites becomes difficult, because of the very small difference in linewidth between the sample powder and the reference of virtually infinite dimensions. Hence, this method is most suitable for the measurement of the dimensions of crystallites within these limits. Figure 10.12 illustrates effects of stress on XRD (CuK^j) profiles of the (220) faces of uniform octahedral particles of AgBrI (2 mol % Agl; 1.4 [xm in diameter) coated on a polyethylene terephthalate film-base with gelatin, where the weight ratio of Ag (in AgBrl)/gelatin = 1.5, and the coated amount of AgBrI in Ag was 4 g m"^. The "dry sample" was a sample stored

494

ANALYSES

Wet Sample (39.818^) c, I *,

;': ;A I [

39.5^

Dry Sample (39.842^ Stressed Dry Sample (39.879^)

40.0'*

40.5'

29

Fig. 10.12. Stress effect on the XRD (CuK^) profiles of the (220) faces of uniform octahedral particles of AgBrl (2 mol % Agl; 1.4 (iim in diameter) coated on a polyethylene terephthalate film-base with gelatin, for wet, dry, and stressed samples. The values in the parentheses are those of 20 at the peaks. at relative humidity 40 % and temperature 25 °C, and the XRD measurement was carried out under the same conditions. The "stressed sample" was one compressed by winding a dry film around a steel stick of 2.5 mm diameter, with the coated plane inside, and rewound before the XRD measurement under the same ambient conditions as those for the dry sample. The "wet sample" was prepared by wetting the stressed sample with distilled water to swell the gelatin matrix, and the XRD measurement was conducted on the sample with its gelatin swollen with water. It was found that a wet sample, obtained directly from a dry sample without mechanical stressing, showed a diffraction peak identical in position, peak height and linewidth, with the wet sample subjected to the mechanical stress beforehand. This means that the strain created in the particles by the mechanical stress was within the limit of the elasticity, and that it was completely removed by wetting for relaxation of the gelatin matrix. In addition, since the dry sample is higher in peak position in 26 and broader in linewidth than the wet sample, it was evident that the particles in the dry sample were already subjected to a compressive stress from the gelatin matrix, through the drying process after coating. Table 10.3 shows the rates of compression (M/d) of

495

10. CHARACTERIZATION OF PRODUCTS

Table 10.3. Compressibility, (M/d), of the AgBrI particles in dry gelatin films with and without additional stress prior to XRD A(2e) (radian)

Sample

Compressibility (M/d)

Pressure (MPa)

Unstressed Sample

4.54 X 10"^

6.25 X 10-^

27.5

Stressed Sample

8.90 X 10"^

1.23 X 10"'

54.0

the AgBrI particles in the dry and stressed samples, calculated from the average peak differences of these samples from the wet one, A(26), and pressures to the particles estimated from the rates of compression with the Young modulus of AgBr (4.4 x 10^° N m'^^ According to Berry et ai,^^ the limit of elasticity of AgBr in compression or expansion, \M/d\ is ca. 2 X 10"^ Hence, even the mechanically stressed particles were within the limit of elasticity, in accord with there being no difference between the diffraction peaks of the wet samples with and without previous compression. Figures 10.13 and 10.14 show XRD profiles of precipitates on filters after filtration of mixed suspensions of AgCl and AgBr particles and those

AgCI-AgBr (200)

NoAza

With Aza

_j

W

I

I

HUr 32" CUKQ 2 6

I

i

sr

Fig. 10.13. XRD profiles of the precipitates on filters after filtration of a mixed suspension of AgCl and AgBr particles with or without Aza (AgCl/AgBr = 1 in molar ratio). (From Ref. 11.)

496

ANALYSES AeBr-AsI (200)

-J—I—I

22«

24°

w

iv ur CuKo 2 0

I

3r

I

.1

34"

Fig. 10.14. XRD profiles of the precipitates onfiltersafter filtration of a mixed suspension of AgBr and Agl particles with or without Aza (AgBriAgI = 4:1). (From Ref. 11.)

of AgBr and Agl particles, in the presence or absence of 4-hydroxy-6-methyl-l,3,3a,7-tetraazaindene (Aza).^^ In the filtration of the mixed suspension of AgCl and AgBr at a molar ratio of 1 : 1 in the absence of Aza, they formed an almost completely mixed solid solution of AgCl-AgBr (1:1) by the contact recrystallization (see section 4.5), while no solid solution was formed in the presence of Aza. In the case of the mixed suspension of AgBr and Agl at a molar ratio of 4 : 1, a solid solution of AgBr-Agl was also formed in the absence of Aza, but the recrystallization appeared to be somewhat restricted, owing to the effect of iodide ions reducing the recrystallization rate of silver halide.^^ In the presence of Aza, the contact recrystallization was almost completely inhibited in this mixed suspension as well. The compositions of the solid solutions can readily be calculated by use of the Vegard law (see section 9.2).

10.6. Oriented Particulate Monolayer X-ray Diffractometry Sugimoto, one of the authors of ref. 9,^ introduced a XRD technique, named "Oriented Particulate Monolayer X-ray Diffractometry (OPMLXRD)," for determination of the Miller indices of the facets of polyhedral microcrystals, those of the basal planes of platelet particles, and the

10. CHARACTERIZATION OF PRODUCTS

497

crystallographic direction of the revolution axis of elongated particles. For this purpose, a few drops of ca, 3 wt % gelatin solution containing ca, 1 wt % of sample-powder, well dispersed beforehand in an ultrasonic bath at about 40 ""C, were dropped onto a flat glass plate, expanded evenly with a glass stick, cooled to room temperature to convert the gelatin membrane to a jelly, and dried naturally or in blowing cool air to make an oriented particle monolayer fixed to the glass plate. In this method, the particle density per unit area should be as small as possible to minimize the overlapping of the particles, within the detectable range of XRD. By this procedure, the polyhedral or anisometric particles are all oriented with their surface planes or revolution axes parallel to the substrate, as illustrated in Fig. 10.15. Thus, we can obtain only the selective diffractions of the lattice faces parallel to the substrate. Figure 10.16 shows some examples of OPML-XRD of different-shaped hematite particles, where the pseudocubic particles were prepared by the gel-sol method,^ the platelet particles by a gel-sol method for the formation of uniform platelet-type particles,^^ and the spindle-type particles by forced hydrolysis from a dilute FeClj solution.^ Incidentally, the diffraction of the (104) face of the platelet particles observed in Fig. 8 of ref. 9 seems to be due to the stacked aggregates of the rather ill-defined platelets prepared by a conventional method.

Fig. 10.15. Section schemes of the oriented particulate monolayers (OPML) of particles different in shape: (a) pseudocubes; (b) platelets; (c) spindles. (From Ref. 9.)

498

ANALYSES

OPML-XRD —

I

—

I

—

I

—

I

—

I

—

|

—

Control (powder XRD on pseudocubes)

(104)

im

(012)

(113)

(024)

(116)

(300)

3) Pseudocubes (012)

(024)

L M J W>M*»,>..yywA^^ji.4ui, CO b) Platelets (006)

iu»i<»VKjirM^^I
^I^Q)

(300)

I

20

30

•

I

40

•

I

50

I

I

60

l _

70

2e/dcg.(CuKa) Fig. 10.16. OPML-XRD (CuKa) of hematite particles of different shapes with pseudocubes in random orientation (a) as a control: (b) pseudocubes; (c) platelets; (d) spindles. [From Ref. 9 for (a), (b), and (d); Ref. 13 for (c).]

10. CHARACTERIZATION OF PRODUCTS — 1 — 1 — 1 — 1 — 1 — j — 1 — 1 — 1 — 1 —

2 9,

1 1

1 -

499 1

•

1

'

A-1

^ o

1

•

]

1 1JL-JL_ J ^

'[

A-3 (B-3) 1

3

3,

s

n-

B-5

B-5[3]

1

1

.,— 1 — . — 1 — . — 1 — . — 1

1 . !•

20

40

60

80

100

20 (degree, CuKa)

Fig. 10.17. OPML-XRD patterns of basic aluminum sulfate particles in the forms of round-comered hexagonal oblates with well-developed basal planes (A-1), round-comered cubes [A-3(B-3)], truncate-cornered cubes (B-5), and sharpcomered cubes (B-5[3]). (From Ref. 14.) Figure 10.17 shows OPML-XRD patterns of basic aluminum sulfate particles in the forms of round-comered hexagonal oblates with welldeveloped basal planes (A-1), round-comered cubes [A-3(B-3)], truncatecomered cubes (B-5), and sharp-comered cubes (B-5[3]). The particles, A-3(B-3) and B-5[3], are the same as those in the SEMs of Fig. 7.23 in chapter 7. As is obvious from the XRD patterns, the main facet of the basic aluminum sulfate, apart from A - 1 , is {012}. The basal planes of the hexagonal oblate particles of A-1 are found to be the {001} faces, while the side planes are the {012} faces.^"*

500

ANALYSES

10.7. X-ray Photoelectron Spectroscopy X-ray photoelectron spectroscopy (XPS) is used to measure ionization energies of inner-shell electrons of atoms in molecules on solids or the surface atoms of solids by characteristic X-rays. It is a useful means for qualitative and quantitative analyses of surface atoms and studies of their electronic states. Figure 10.18 shows XPS spectra of ellipsoidal hematite particles prepared by the gel-sol method in the presence of 2.0 x 10"^ mol dm"^ hydroquinone (HQ) and of a powder prepared by grinding the original particles in a planetary ball mill. From this data and the amount of HQ incorporated as a polymeric species into the hematite particles {ca, 82 % of the added HQ), the overall C/Fe atomic ratio of HQ to a-Fe203 and the internal C/Fe atomic ratio were calculated to be 0.12 and 0.10, respectively (see section 8.2.1(b)).^^ As has been shown in Fig. 7.45 in chapter 7, XPS was used for

(a) Original

-JL (b) Ground

700

600

500

400

300

Binding energy (eV)

Fig. 10.18. XPS spectra of ellipsoidal hematite particles prepared by the gel-sol method in the presence of 2.0 x 10"^ mol dm"^ hydroquinone (a) and of a powder prepared by grinding the original particles (b). Fe 2pi/2> Fe 2^2n» ^^^ ^^ LMM are photoelectrons from the 2pi;2 ^ ^ '^Vsa orbitals of Fe and LMM Auger electrons from Fe, respectively; C Is is due to photoelectrons from the 1st orbital of C; O Is and O KLL are photoelectrons from the Is orbital of O and KLL Auger electrons from O, respectively. (From Ref. 15.)

501

10. CHARACTERIZATION OF PRODUCTS

identification of the nanosized noble metal particles in the platinum group, including Ru, Rh, Pd, Ir, and Pt, and their precursor particles on a metal oxide support, where the precursor particles were metal hydrous oxides prepared by the selective deposition method and the metal particles were produced by hydrogen reduction (250 °C) of precursor particles on monodispersed ellipsoidal polycrystalline hematite particles.^^ On the other hand, it is possible to achieve the selective deposition of gold nanoparticles simply by aging a solution of a hydroxide complex of Au^^ ions at 100 °C for 48 h without addition of any reducing agent (see section 7.3.8). Figure 10.19 shows XPS spectra of the as-prepared gold particles with some remaining Au(0H)3 gel on ellipsoidal hematite particles and of the pure gold particles on the same hematite support after treatment of the as-prepared gold particles with 0.02 mol dm"^ HCl to remove the Au(0H)3 residue. A spectrum of pure bulk gold is also shown as a reference. This result clearly demonstrates the direct deposition of gold particles from the solution phase in this particular system containing no foreign reducing agent. I

•

I '

I '

I '

1

P

t

<

•

96

I

94

.

.

.

I

92

•

•

•

»

90

•

•

.

'

•

88

•

•

'

•

86

•

•

I

84

•

«

•

«

82

80

Binding Energy (eV)

Fig. 10.19. XPS spectra of: (a) as-prepared gold particles on ellipsoidal hematite particles with a small amount of Au(OH)3 residue; (b) pure gold particles after treatment of the as-prepared gold particles on the hematite support with hydrochloric acid; (c) pure bulk gold as a reference.

502

ANALYSES

10*8. Infrared Spectroscopy The infrared optical properties of a powdered ionic solid depend on the size, shape, and aggregation state of the particles.^ ^"^^ These properties result from the polarization charge induced at the particle surfaces by an external electromagnetic field when the particle dimensions are smaller than the wavelength of the incident radiation. The phonon mode characteristic of small particles is generally referred to as the surface phonon mode. For the study of the effects of the characteristics of fine particles on the surface phonon modes, well-defined particles are needed. Sema et al^'^^ investigated the effect of the shape of hematite particles on the IR spectrum using uniform spherical and spindle-type particles as well as disk-like ones and found characteristic differences in their IR spectra. Also, Sugimoto et al}'^'^ studied comprehensively the effects of the size, shape, internal structure, and aggregation of hematite particles, using monodispersed hematite particles systematically controlled in these characteristics. They found that the absorption peak frequencies of the pseudocubic particles are located between the corresponding theoretical peak frequencies of spheres and cubes and shift to lower frequencies as particle size increases, corresponding approximately with the Mie theory. Nevertheless, the basic spectrum pattem was determined by the morphology of the particles. Observations on ellipsoids with various aspect ratios revealed some essential discrepancies in the peak frequency between experiment and the theory on the surface phonon modes in small particles, even if the particles were completely dispersed in the medium. The internal stmcture mainly affects the peak width, which increases with reducing subcrystal size. Aggregation of pseudocubic particles of 0.075 [xm in mean edge length caused peak broadening toward lower frequency, and the peaks of the 1 and II modes at 578 cm"^ and of the ± mode at 485 cm"^ slightly shifted to lower frequencies within a few cm'^ Figures 10.20 to 10.23 show the effects of particle size, subcrystal size, aspect ratio, and morphology of hematite particles, respectively, on the IR spectrum. Here, the particle size in Fig. 10.20 is represented by the mean edge length of pseudocubes; the subcrystal size in Fig. 10.21 was represented by the thickness of {012} faces, calculated with XRD data and the Scherrer equation for pseudocubic particles of the same mean particle size (-1.1 \jimm edge length), but with different subcrystal sizes; the symbols L and // in Fig. 10.22 indicate mfrared active modes polarized perpendicular and parallel to the c-axis of the hexagonal crystal system, respectively. The scale bars of the TEM and SEM images in Figs. 10.21 to 10.23 are common

10. CHARACTERIZATION OF PRODUCTS

Fig. 10.20. Size effect of pseudocubic monocrystais of hematite on FTIR spectra. (From Ref. 23.)

Fig. 10.22. Aspect-ratio effect of ellipsoidal monocrystais of hematite [1: perpendicular mode; //: parallel mode]. (From Ref. 23.)

Fig. 10.21. Subcrystal size effect of l.l-jbim pseudocubic particles of hematite. (From Ref. 23.)

Fig. 10.23. Shape effect of tabular monocrystais, pseudocubic polycrystals, and peanut-type polycrystals. (From Ref. 23.)

503

ANALYSES

504

MO

Fig. 10.24. Experimental, theoretical, and modified theoretical FTIR spectra for single-crystal hematite particles of ellipsoids {da = 2.5, c - 0.44 |jim), pseudocubes (cla 1.1, edge length = 0.15 fxm), and platelets {da = 0.3, c = 0.39 |Lim). The modified theoretical spectra were obtained using modified N^ and N^ values. (From Ref. 23.)

500

WaTcoumbcr (cm"')

to the respective figures. Figure 10.24 shows the experimental, theoretical, and modified theoretical IR spectra for single-crystalline particles of ellipsoids {da = 2.5, c = 0.44 jmi), pseudocubes {da = 1.1, edge length = 0.15 tim), and platelets {da = 0.3, c = 0.39 |xm). Here, c and a are the length in the direction of the revolution axis of the anisometric particles and that normal to the revolution axis, respectively. The modified theoretical spectra were obtained using modified N\\ and N^ values. See ref. 23 for the details of the theoretical treatment.

10.9. Ultraviolet-Visible Spectroscopy If a strong adsorptive on some particles has some specific spectrum in the UV or VIS range, the infinite reflectivity, K, measured at some wavelength under conditions where there is no transmittance and the concentration of the adsorptive, c, are related by the Kubelka-Munk function.

K S

(i-RJ'

€

IR^

S

10. CHARACTERIZATION OF PRODUCTS

505

where K and S are the absorption and scattering coefficients of the particles with the adsorptive, and e is the molar absoq^tion coefficient of the adsorptive in the adsorbed state (see also section 12.5.1).^'* Herz et al found the proportionality of K/S to c for the J-band of l,r-diethyl-2,2'-cyanine dye on octahedral AgBr particles in a dispersion up to the saturation coverage^ and significantly different reflection spectra of carhocyanine dyes on cubic and octahedral silver bromide particles.^^ If we make use of these findings, it is possible to measure the specific surface area and particle size of monodispersed silver halide particles. Furthermore, if both the adsorption strength and absorption spectrum of the adsorptive differ between different kinds of facets of a polyhedral particle, there must be some inflection points in the plot of {l-R„f/2R^ at a wavelength against c, corresponding to the saturation points of the different facets. For example. Figs. 10.25 and 10.26 show reflection spectra of different concentrations of the following Dye 1 adsorbed to a certain amount of octahedral and cubic particles of AgBrI (2.2 mol % Agl; ~ 0.5 [xm) bound by the {111} and {100} faces, respectively:^^ Dye 1 ^ ^ ^ ^ S

CH3

The reflection spectra of Dye 1 on the octahedral AgBrI particles are characterized by the typical J-band at 630 nm, while there is no specific absorption peak at this wavelength in the reflection spectra of the dye on the cubic particles. On the other hand. Figs. 10.27 and 10.28 show reflection spectra of various concentrations of Dye 1 to some cubo-octahedral AgBrI particles (2.2 mol % Agl; 0.52 \xm) and a plot of (I-R^f/IR^ at 630 nm v^ c. The first and second inflection points in Fig. 10.28 correspond to the saturation points of the {100} and {111} faces, respectively. If we use the limiting areas of dye 1 per molecule on the {111} and {100} faces of the AgBrI, 62 A^ and 69 A^, respectively, we are able to determine the area ratio of the {111} faces to the {100} faces. Once the area ratio is given, the ratio of the distance from the center of a cubo-octahedron to a {111} face to that of a {100} face, r^^^/ r^Q^, can be calculated. The r^u/r^QQ or Ym/Yioo of the AgBr microcrystals given as a function of pBr in Fig. 3.3 in chapter 3 was determined using this technique. If we use the total volume of

ANALYSES

506

"400

500

m

Toi

Wavelength (nm)

400

500

600

Wavelength (nm)

Fig. 10.25. Reflection spectra of varying amounts of dye 1 added to a gelatinous suspension of octahedral AgBrl particles (J: J band on the solid; M: M band on the solid; dashed-line arrows: M band (550 nm) and H band (510 nm) in the gelatin solution. (From Ref. 27.)

Fig. 10.26. Reflection spectra of varying amounts of dye 1 added to a gelatinous suspension of cubic AgBrl particles (D: Double-band caused by dye aggregates of a costate structure on the solid). (From Ref. 27.)

no

Wft\ °

^

D IJB

Hi/^Jll

50

0^

0

1.

400

1

500

_,600

Wavelength (nm)

u 700

Fig. 10.27. Reflection spectra of varying amounts of dye 1 added to a gelatinous suspension of cubooctahedral AgBrl. (From Ref. 27.)

10. CHARACTERIZATION OF PRODUCTS

507

1.0

g

saturation point

«i

/•

St

•*

/

1

1 0^ »ftdt J

'

J. . 2

4

Vol. (m/) of soln. added

JL

«

1

8

1

1

10

of dye 1 (0. 294^)

Fig. 10.28. Plot of (1-R„)V2R„ for the spectra of Fig. 10.27. (From Ref. 27.)

uniform cubo-octahedral AgBr particles in a given system, the absolute values of r^^^ and r^oo ^ ^ ^^^ obtained. These techniques may be applied to the determination of the particle size of general particles and the area ratio of different facets of general polyhedral particles if some appropriate adsorptive is available for this puq50se.

10.10. Photon Correlation Spectroscopy Photon correlation spectroscopy (PCS) is based on the dynamic light scattering of a laser beam of a certain wavelength by particles or macromolecules in a liquid medium.^^ The scattered and diffracted laser beam has a distribution in frequency owing to the Doppler shift by Brownian motion of the scatterers. Figure 10.29 shows the frequency distribution of the scattered beam about the frequency of the incident laser beam (f^ at a certain scattering angle, where T is the half-width at the half-height of the peak. The frequency of the incident laser beam is normally about 6 x 10^"* Hz. The frequency distribution of the scattered beam can be transformed into a power spectrum in which the amplitude is represented as a function of 2[/'-/o|, as shown in Fig. 10.30. The shape of the power spectrum is known as Lorenzian and 2 r typically ranges from a few kHz down to perhaps 20 Hz. On the other hand, if we follow the change of the total amplitude as a function of time at a certain scattering angle with a photomultiplier, we obtain a fluctuating photosignal as shown in Fig. 10.31. If we take the relative amplitudes to the average level at time t, A{t\ and A{t-^x) after a time-lag x, and calculate the autocorrelation function, C(T),

ANALYSES

508

^•^

Frequency

Fig. 10.29. Frequency distribution of the scattered beam.

2lf-fol Fig. 10.30. Power spectrum as a function of 2|f-fo|.

=0

> 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: 4^iAo . 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

10. CHARACTERIZATION OF PRODUCTS

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

10. CHARACTERIZATION OF PRODUCTS

x = n^izr^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
where a = 2Kr/X\ m = ji/Mt)? ^' is the wavelength in the medium surrounding the particles ( = X/MO)» ^ is the wavelength in vacuo, \i and \IQ are the refractive indices of the particle and surrounding medium, respectively. For larger particles, ^^ must be calculated from the Mie equations as a function of a and m?^ The specific turbidity^° for spheres is given by

1 = JZLx^, c

IX'p

(10.11.4)

a '

where p is the density of the particle and c is the concentration in g cm"^. For Rayleigh particles, the size is obtained from the relationship, T_47ia^|^m^-lf

(10.11.5)

For larger particles, fija is not a simple function, and their size is given from graphs of ^Ja vs a. If the particles have some distribution in size, T is given by T = n^nrfir)f^fi^dr,

(10.11.6)

J0

where /(r)dr is their normalized frequency in a range from r to (r + dr). The concentration c is given by

514

ANALYSES

47cn p f^^

.

(10.11.7)

Thus the specific turbidity is X

3 /o>)^^^

(10.11.8)

Jo

If the size distribution can be approximated by a type of distribution, the average size and width may be calculated from measurement of specific turbidities at two different wavelengths. For example, the log-normal distribution is defined by fir)dr =

inogr-logr^\^

1 V^loga

\/27irlna

exp

Jlogr (10.11.9)

exp

l/lnr/r^f 2

Ina8

dr.

)

where r is the geometric mean radius, and a is the geometric standard deviation: Inr =E-^lnr, ;i.e., r ^nr,"''"'

(10.11.10)

and Ino

(10.11.11)

'N

The number-average (r„), surface-average (r,), and weight-average ( r j radii are defined by:

10. CHARACTERIZATION OF PRODUCTS

515

''n=^-[>)rdr, En. Jo

(10.11.12)

r = —L-L = ^ , En.rf r7(r)rVr

(10.11.13)

Jo

and

r.= - ^

=-

•

(10.11.14)

Jo

If we use the general formula

the different averages are related to r^ and cig as = 0.5\n^o^,

(10.11.15)

ln(Vrp = 2 . 5 1 n \ .

(10.11.16)

l n ( r > p = 3.5ta^o^.

(lO-H-H)

Mrjr^)

and

Figures 10.34 and 10.35 show x/c of AgBr sols, calculated as a function of r^ for three o^ values from Eq. (10.11.8) with Eq. (10.11.9), at wavelengths 450 nm and 800 nm, respectively.^^ Figure 10.36(a) shows two curves of a^ vs r^ when the specific turbidities are fixed at those actually measured at 450 nm and 800 nm for a silver bromide sol. From the intersection, one obtains r^ = 59 nm and cig = 1.36 (r„ = 62 nm, r^^ = 82

ANALYSES

516

Fig. 1034. Specific turbidity, T/C, of AgBr as a function of geometric average radius, r^, for three og values at 450 nm. (From Ref. 31.)

Fig. 10J5. Same as Fig. 10.34, but at 800 nm. (From Ref. 31.)

O 450mp O 800mp

0.04

Dia. (^l),

0 '0

Fig. 10.36. (a) Graphical determination of Og and r^ of a AgBr sol, using the specific turbidities at 450 and 800 mji. (b) Size distribution curve of the AgBr sol, calculated with the data of a^ and r^ on the assumption of a log normal distribution, and its size distribution histogram obtained from electron microscopy. (From Ref. 31.)

10. CHARACTERIZATION OF PRODUCTS

517

nm).^^ Figure 10.36(b) is the size distribution of this silver bromide sol from electron microscopy or from calculation with the data of r^ and a^ obtained by the procedure shown in Fig. 10.36(a). For Rayleigh particles, there is the following general relationship from Eqs. (10.11.3) and (10.11.8):

rmr'dr JQ

rmr^dr

= I P A ^ I m ^ 1 t; m'-l}

(10.11.18)

c

Jo

Since the left-hand side is a function proper to the size distribution and independent of the nature of incident light, the right-hand side is constant, irrespective of the wavelength of the incident light. In other words, the relation between r^ and o^ in the log-normal distribution is unchanged with different wavelengths, and thus it is impossible to determine r^ and o^. Hence the above method for determination of r^ and a^ is useful only for particles larger than Rayleigh particles.

10.12. Coulter Principle The Coulter principle for measuring particle-size distributions is based on the detection of increasing electric resistance for a current across an orifice filled with electrolyte, in proportion to the volume displaced by a particle passing through the orifice.^^ The change of resistance is measured by converting it into an amplified voltage pulse, and the particle number in each class of particle volume is counted at the same time. The measurable size ranges from ca. 0.3 to 1200 ^un using apertures of different diameters. This method has an advantage that particle volumes can be measured with little or no effect of their shape and optical absorption. However, the apparent resistance of a conductive particle is dependent on the voltage drop over the particle when it passes the orifice. Below a critical voltage drop, all particles act as insulators, giving correct particle sizes, while above this value particles act as conductors, causing large errors.-^-^'^ Harfield^^ found that Coulter-counter response depends on the conductivity of the medium as well as of the particles. When the conductivity of particles is less than twice the medium, size-measurement errors are minimal. Horak et al}^ reported on the influence of particle porosity. Since porous

518

ANALYSES

particles are filled with electrolyte, the displaced volume is smaller than the outer dimensions of the particle. Porosity data were correlated with this effect. Figure 4.7 in chapter 4 is an example of the application of this technique to the study of the reversed Ostwald ripening of AgBr particles, in which the grown particles differ from the dissolved ones in shape and size. Probably, such a kind of study is possible only with a Coulter counter.

References 1. G. Park, D. Shindo, Y. Waseda, and T. Sugimoto, J, Colloid Interface ScL 111, 198 (1996). 2. T. Sugimoto and E. Matijevic, J. Inorg. Nucl Chem, 41, 165 (1979). 3. J. E. Maskasky, J. Imaging ScL 30, 247 (1986). 4. T. Sugimoto and A. Muramatsu, J. Colloid Interface ScL 184, 626 (1996). 5. T. Sugimoto and K. Miyake, J. Colloid Interface ScL 140, 335 (1990). 6. D. Shindo, G. Park, Y. Waseda, and T. Sugimoto, J, Colloid Interface ScL 168, 478 (1994). 7. T. Sugimoto and Y. Wang, J, Colloid Interface ScL 207, 137 (1998). 8. A. Guinier, "Theorie et Technique de la Radiocristallographie," 3rd Edn.. Dunod, Paris, 1964. 9. T. Sugimoto, A. Muramatsu, K. Sakata, and D. Shindo, J. Colloid Interface ScL 158, 420 (1993). 10. C. R. Berry, M. H. van Horn, and R. L. Griffith, Acta Cryst. 7, 135 (1954). 11. T. Sugimoto and G. Yamaguchi, J. Crystal Growth 34, 253 (1976). 12. C. R. Berry and D. C. Skillman, /. Phys, Chem, 70, 1871 (1966). 13. T. Sugimoto, S. Waki, H. Itoh, and A. Muramatsu, Colloids Surfaces A: Physicochem. Eng. Aspects 109, 155 (1996). 14. T. Sugimoto, H. Itoh, and H. Miyake, J. Colloid Interface ScL 188, 101 (1997). 15. T. Sugimoto, H. Itoh, and T. Mochida, J. Colloid Interface ScL 205, 42 (1998). 16. T. Sugimoto, H. Kawasaki, and A. Muramatsu, in "Proc. 52nd Symp. Colloid Interface Chem.," (Chem. Soc. Jpn.), p. 136. Morioka, Oct. 1999. 17. R. Ruppin and R. Englman, Rep. Prog Phys. 33, 149 (1970).

10. CHARACTERIZATION OF PRODUCTS

18. 19. 20. 21.

519

L. Genzel and T. P. Martm, Surf. Sci. 34, 33 (1973). S. Hayashi and H. Kanamori, J. Phys. C 13, 1529 (1980). C. J. Sema, M. Ocaiia, and J. E. Iglesias, J. Phys. C 20, 473 (1987). J. E. Iglesias, M. Ocaiia, and C. J. Sema, Appl. Spectrosc. 44, 418 (1990). 22. T. Sugimoto, Y. Wang, H. Itoh, and A. Muramatsu, Colloids Surfaces A: Physicochem. Eng. Aspects 134, 265 (1998). 23. Y. Wang, A. Muramatsu, and T. Sugimoto, Colloids Surfaces A: Physicochem. Eng. Aspects 134, 281 (1998). 24. P. Kubelka and F. Munk, Z. Techn. Physik 12, 513 (1931); P. Kubelka, J. Opt. Soc. Amer. 38, 448, 1067 (1948); W. Wm. Wendlandt and H. G. Hecht, "Reflectance Spectroscopy." Interscience, New York, 1966. 25. A. H. Herz and J. O. Helling, Kolloid-Z. Z. Polym. 218, 157 (1967). 26. W. L. Gardner, D. P. Wrathall, and A. H. Herz, Photogr. Sci. Eng. 21, 325 (1977). 27. T. Tani, Nippon Kagaku Kaishi 942 (1984). 28. M. Kerker, "The Scattering of Light and Other Electromagnetic Radiation," p. 666. Academic Press, New York, 1969; B. Chu, "Laser Light Scattering," p. 317, Academic Press, New York, 1974; Y. D. Yan and J. H. R. Clarke, Adv. Colloid Interface Sci. 29, 277 (1989). 29. H. C. van de Hulst, "Light Scattering by Small Particles." Wiley, New York, 1957. 30. W. Heller and W. J. Pangonis, J. Chem. Phys. 26, 498 (1957). 31. E. J. Meehan and W. H. Beattie, J. Phys. Chem. 64, 1006 (1960). 32. H. G. Barth and S.-T. Sun, Anal. Chem. 57, 151R (1985). 33. G. van der Plaats and H. Herps, Powder Technol. 36, 131 (1983). 34. G. van der Plaats, H. Herps, and L. Willens, in "Particle Size Analysis 1981," (N. Stanley-Wood and T. Allen, Eds.), p. 209. Wiley, Chichester, 1982. 35. J. G. Harfield, in "Particle Size Analysis 1981," (N. Stanley-Wood and T. Allen, Eds.), p. 165. Wiley, Chichester, 1982. 36. D. Horak, J. Peska, F. Svec, and J. Stamberg, Powder Technol. 31, 263 (1982).

PART4, APPLICATIONS INTRODUCTION In this Part, the application of monodispersed particles to fundamental studies and the possibilities of their industrial application will be described in chapters 11 and 12, respectively. Typical examples cited in this Part are chosen mainly on the basis of their fundamental importance for future development.

CHAPTER 11 APPLICATION TO FUNDAMENTAL STUDIES 11.1. Determination of the Avogadro Number All particles, including molecules in the gas phase or dissolved in a solvent and colloidal particles suspended in a liquid medium, are subject to the effect of gravity. Since gas molecules, as well as medium molecules, are in thermal motion, there is always a density or concentration gradient in a vertical direction for gas molecules and colloidal particles in a medium. Actually, we know that the atmosphere becomes rarer with increasing altitude. If m denotes the mass of a gas molecule, the density, «;,, at height h from a standard level, at which the density is /IQ, is given by

where k is the Boltzmann constant, R is the gas constant, and A^ is the Avogadro number. Colloidal particles suspended in a medium are subject to buoyancy as well as gravity, so that the apparent mass, m\ of a particle of volume, u, and

11. APPLICATION TO FUNDAMENTAL STUDIES

521

solid density, p, in a medium of density PQ is given by '«'=i)(p-po).

(11.1.2)

Hence, Nv(p-p^gh n^ = noexp

(11.1.3)

RT

or N--

-RT -InHp'P()gh HQ

(11.1.4)

Perrin^'^ determined the Avogadro number as (6.5-7.2) x 10^ mol"^ from scrupulous measurements of the density of uniform spheres of gamboge and mastic in sedimentation equilibrium, as a function of A (1908). Figure 11.1 shows the density distributions of monodisperse microspheres of gamboge and mastic in the sedimentation equilibria. The values obtained were only a little larger than the most accurate one available at present. For this experiment, Perrin and his students precipitated a latex of a broad sizedistribution by dilution with water from a methanol solution of gamboge, and took a few months to obtain a few hundred mg of monodisperse spheres from 1 kg of gamboge by repeated centrifugal separation, since monodisperse particles are indispensable for this measurement. Westgren^ observed that the number concentration of the monodispersed gold sol of Zsigmondy and Thiessen"* in a sedimentation equilibrium decreased exponentially with height, and obtained A^ = 6.05 x 10^ m o r \ which is very close to the accurate value. On the other hand, Einstein^ and Smoluchowski^ investigated the Brownian motion of colloidal particles caused by collision of the medium molecules in thermal motion, and almost simultaneously derived the following relation: <.^> = 2DA.= ^ ^ : ^ ' . 3TirAr

(11.1.5)

APPLICATIONS

522 JJ 1

-

a

•

•

•

1

• *

*•

r • "•••

[

*

•

•

1

•*• •*'••• • #• *|

• • • • • • , . • •• « , • . • . • ' •" •• • ••••• ••

. I 1

• •• L » • • : • • "* • • ••

*•' 1 • • 1 .• 11

.' • • * •'.•. . \ • *. •• • • • V •• . • . • • •• • •• •• •

L.;-'^'.•.••,•.••...•.; -*•••'•••

1

%*

•

•

•

J

:• .• -.-.r • .:•. •

1-

^

-

••

1

uy •..{-.-.••••vl •; • •!

V^

•.*^«." • ••

••

• •

•.'•*••*•

•.;• ^<->^t :.••••••••. .^ Fig. 11.1. Examples of the sedimentation equilibrium of suspensions: (a) gamboge spheres (r = 0.29 jxm) at levels, 10 pim apart; (b) mastic spheres (r = 0.52 \xm) at levels, 12 fxm apart. (From Ref. 1.)

where <x^> is the mean value of the square of the displacement, x, in a definite direction during a sufficiently large time interval, At (see Fig. 11.2), D is the diffusion coefficient of the particles, r is the radius of a particle, Ti is the viscosity of the medium, and A^ is the Avogadro number. Perrin^ and Svedberg' obtained 6.5 x 10^^ mol"' and 6.2 x 10^^ mol"' from Eq. (11.1.5) using monodisperse sols. From these facts, one may find that the thermal behavior of colloidal particles is analogous to that of molecules. The determination of the

11. APPLICATION TO FUNDAMENTAL STUDIES

523

Fig. 11.2. Brownian displacement at 30 second intervals of spherical particles (r = 0.52 jiim), suspended in water at 20 °C. The lattice interval is 3.125 |Lim. (From Ref. 2.) Avogadro number, performed at the beginning of the 20th century, may be one of the earliest applications of monodispersed particles.^

11.2. Measurement of Zeta-Potential Figure 11.3 represents the potential distribution of the electric double layer proposed by Stem,^ where jc at 8 is the boundary between the adsorption layer {Stern layer) and diffuse layer (Gouy layer). When an electric field, E, is applied parallel to the flat surface of the solid with the double layer in an electrolyte solution, movement of the liquid is observed {electroosmotic movement). In the stationary state, the flow velocity of a liquid layer of thickness ^ at jc is constant because of the force balance Stern Layer

0 6

Fig. 11.3. Stem model of the electric double layer.

524

APPLICATIONS

between the flow of the liquid layer, driven by the movement of ions owing to the field, E, and the frictional resistance of the neighboring layers. Hence, (dv Epdx=r]\—\ [dx

^u (dv -Ti — Uri^i^dtc, \dx dx2 x^dx \ "* J

(11.2.1)

where r] is the viscosity of the liquid, v is the flow rate at x, and p is the space charge density at x}" From the Poisson Equation, A,|r=—P-,

(11.2.2)

in which EQ is the vacuum permittivity and e, is the relative permittivity of the liquid, one finds - £ e „ e , ^ =r i ^ .

(11-2.3)

Assuming the slipping plane located in the diffuse layer close to 8 and using the boundary conditions: —i-=0, — = 0 dx dx

atx=oo

ij; = C, i> = 0 at the slipping plane one obtains Tl

Representing u for JC = oo as v^ and using t|j(<») = 0, one finds "£ =

^0^^^^ 11

(11.2.5)

On the other hand, if an electric field is applied to a suspension of charged colloidal particles in a closed horizontal cylindrical cell along the axis, we observe a parabolic rate profile of a return flow of the uniform electro-osmotic movement of the liquid in the opposite direction, where the

11. APPLICATION TO FUNDAMENTAL STUDIES

525

maximum velocity of the return flow is in the middle of the cross section and the total of the liquid transport is zero at the stationary state. If we observe the velocity of sufficiently large particles with a thin double layer at a position where the flow rate is zero, which is located at a/V2 from the central axis of the cylindrical cell of radius a, the mobility of a particle per unit field, u^ (= v^/E), may be given from Eq. (11.2.5) as . =io^C

(112.6)

since the relative flow-rate of the liquid to the solid in electrophoresis is equal to that in electro-osmosis. This equation, called Smoluchowski's formula,^^ is valid under the conditions that the double-layer is sufficiently thin, compared to the dimensions of the particles, and that the particles are insulators whose surface conductance is so small as to have no influence on the external field. These restrictions, under which the particles are exposed to a homogeneous field, are common to Eq. (11.2.5) for electro-osmosis. The shape of the particles is also of no importance as in electro-osmosis, in which Eq. (11.2.5) is valid for an arbitrary shape of the porous plug. On the other hand, the space-charge density, p, at potential xp(jc) is given from the Boltzmann equation as p = Ez.n^^exp

-z,.^i|r "^

(11.2.7)

kT

where z^ is the valency of ion /, n- is the number concentration of ions / in the bulk solution (x = oo), and e is the charge of a proton. Combination of Eqs. (11.2.2) and (11.2.7) yields the Poisson-Boltzmann equation in a spherical coordinate system: ^ . 2 J t _ _ L 5 :

[i!i!t]

If \zpifs\ « kT (Izjtpjl « 25.7 mV) for all ionic species,

(11-2.8)

526

APPLICATIONS

j , W ^ kT

(11.2.9)

and Eq. (11.2.8) reduces to ^ ^ m ^ ^ ^ ^ dr^ r dr

(11.2.10)

where K is the Debye-Hiickel parameter corresponding to the reciprocal thickness of the double layer or the reciprocal Debye length defined by ^'^^^

(11.2.11)

K=

The solution of Eq. (11.2.9) for ip at r from the center of a sphere of radius a IS

i|r = i|f,^exp[-K(r-fl)], r

(11.2.12)

where \p§ is the Stern potential. From this equation and the Gauss equation for a sphere of surface charge density, a, a=-e,e(^

'•mj

.

(11.2.13)

the total surface charge Q (= Aiui^o) is given by <2=4Ka8o8^(l+ica)i|f^.

(11.2.14)

When Ka « 1, the mobility u^ (= vIE) follows from tp^ « S and the Stokes equation.

11. APPLICATION TO FUNDAMENTAL STUDIES

u=

527

QE 6Tzr\a

(11.2.15)

2 ^o^C

(11.2.16)

as

H-

This relation derived first by Hiickel^^ holds when the dimensions of the particle are so small as compared to the thickness of the double layer {KU « 1) that the deformation of the field by the presence of the particle is insignificant. Taking account of the deformation of the field by the presence of the colloidal particles, Henry^^ showed that the electrophoretic mobility of a particle, M^, can be expressed in the general form:

H-

H^^

/(K^)

(11.2.17)

This equation covers the Smoluchowski and Hiickel formulae, where/(KA) is a function of Ka, and a is the radius of a spherical or cylindrical particle. For a non-conducting sphere, /(KA) = 2/3 for Ka « 1 and /(Ka) = 1 for Ka » 1. Figure 11.4 shows/(Ka) for non-conducting or conducting spheres and cylinders parallel or perpendicular to the electric field. If the surface conductance of the particle is high owing to the presence of a high concentration of ions in the double layer, we must take account of cylinder //field

cylinder Xfield 1/2

10-'

Fig. 11.4. The numerical factor /(Kfl) for a (non-conducting) sphere, conducting sphere, and cylinder parallel or perpendicular to the field. (From Ref. 13.)

528

APPLICATIONS

:^^$^ ^>yvor ^ ! ! ^ ^ / //ewy

2/3

Equation

,j^i^/

I

s.*-!^^^

10'

1

Fig. 11.5. Relaxation effect for different types of electrolytes on /(KA) of a negatively charged particle with t, = -50 mV. The dashed curve stands for the Henry equation without taking account of the relaxation effect. (From Ref. 14 (a).)

?^

\

2/3

^ /

•^>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[l^exp(-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.

11. APPLICATION TO FUNDAMENTAL STUDIES

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

11. APPLICATION TO FUNDAMENTAL STUDIES

533

Monitor

• Controller

V J

Personal computer

Photo-diode

Beam expander

Polarizing ^eaj" 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.)

11. APPLICATION TO FUNDAMENTAL STUDIES

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

11. APPLICATION TO FUNDAMENTAL STUDIES

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

11. APPLICATION TO FUNDAMENTAL STUDIES

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

11. APPLICATION TO FUNDAMENTAL STUDIES

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 ^un 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

^

' ^

^

•• ! •

-rv^I • 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.)

11. APPLICATION TO FUNDAMENTAL STUDIES

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

11. APPLICATION TO FUNDAMENTAL STUDIES

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

11. APPLICATION TO FUNDAMENTAL STUDIES

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
(11.6.2)

with the radius of the wetted periphery, r, and the angle of the meniscus against the horizontal plane, ip (see Fig. 11.28).

rp<0

unwettable sphere

^>0

wettable sphere

Fig. 11.28. Radius of the wetted periphery of a sphere and the angle of the meniscus against the horizontal plane, ip, for unwettable or wettable sphere. The name of capillary charge comes from the analogy of Eq. (11.6.1) to the two-dimensional Coulomb force between two particles with electric charges Qj and (22- Th^ capillary force is an attractive one for particles of the same sign of \p (\pii|)2 > 0), while it is a repulsive force for those of opposite signs {y\>{\\>2 < 0), as shown in Fig. 11.29. It is proportional to the

551

11. APPLICATION TO FUNDAMENTAL STUDIES

6th power of the particle radius for two equal spheres floating at the liquid surface, while it is proportional to the square of the particle radius when they are attached to a substrate plane parallel to the liquid surface, and hence more or less protruded from the liquid surface.^"^ The latter is of significance when particles form an ordered particulate monolayer or multilayer on a substrate. a) ^ , ^ 2 > 0 Attraction

Attraction

b) 0 i 0 2 < O Repulsion

Fig. 11.29. Models of interaction between two particles on a water surface for the cases of i(Ji'i|)2 > 0 and ^^{^2 < ^•

Although there are a variety of elucidations for the two-dimensional particle interactions on liquid surfaces, their origins do not appear to have been fiilly understood yet. However, in any case, there is no doubt that monodispersed particles are indispensable for the experimental studies of two-dimensional ordering of colloidal particles, like those for the threedimensional ordering.

552

APPLICATIONS

11.7. Studies of Light Scattering An isolated sphere illuminated by a parallel beam of linearly polarized light becomes polarized in the electromagnetic field because of the displacement of the electrons with respect to the nuclei. If the sphere is small compared to the wavelength and is isotropic, the secondary field induced within the sphere is uniform and parallel to the external field. If 7(6) denotes the intensity of light scattered per unit volume of suspension of particles at an angle 6 from the forward direction of an unpolarized incident beam of intensity IQ, at a distance b from the scattering volume, the Rayleigh ratio Rj^G) defined by I{d)h^/lQ is written as

Rum-Vu(^)^»u(^)^

(11.7.1)

where Vj^Q) and HJQ) are vertically and horizontally polarized components of RJff), where the horizontal plane corresponds to a plane comprising the directions of the incident and scattered beams. For non-absorbing spheres of radius r < X.y20, K^(e) and 7/^(6) are given by nX^a^ ^ m ^ - 1 ^ '

vm=- Sn^

(11.7.2)

m^+2)

and t i X /2^6/ oc m^-l

Hm=-^ 871^ [m^^2j cos^O,

(11.7.3)

where n^ is the number concentration of the particles, X' is the wavelength in the medium, a is the size parameter (= 2jtr/X.'), and m is the refractive index of the particles relative to the medium.^°^ The radius vector to the contours for ^^(6), HJfi), and R^{Q) from the scatterers at the origin in Fig. 11.30 gives the intensity of the scattered light in the direction 6, where the y-z plane corresponds to the horizontal plane, and the direction of the incident light is coUinear with the z-axis. If we use the turbidity x of Eq. (10.11.2) in chapter 10, we obtain the following relationship:

553

11. APPLICATION TO FUNDAMENTAL STUDIES

Rui&) 180

*> z 0

y

90° Fig. 11.30. Contours of the intensity vectors of scattered light, //„, F„, and R^ in the y-z plane, as a function of 6 for Rayieigh scattering of unpoiarized incident light.

/?„(e) = n o ) +/f„(e) = -i-xd+cos^e).

(11.7.4)

iDTt

If the particle size is comparable to the wavelength of the incident beam, we must consider not only the radiation from the oscillating electric dipole but also superposition of the radiation from the complete set of oscillating electric and magnetic multipoles. In this case, the Rayieigh ratios for the spheres are given by Mie^°^ as

v„ie)-

».(e)=

(11.7.5) „=in(n+l)

x\ 1v^ 2n+l

» » " "'

,

,

.

(11.7.6)

„=i n(n+l)

The functions a^ and b^ are the electric and magnetic multipole moments, respectively; jt^ and T^ give the angular distribution of the field radiated by

554

APPLICATIONS Rayleigh

180°

Scattering

Mie

^ 0°

Scattering

180°'

Fig. 11.31. Contours of intensity vectors of F^(0) in the y-z plane: (a) Rayleigh scattering; (b) Mie scattering (a = 6; w = 1.44). (From Ref. 109 for (b).)

the respective oscillating multipoles. The former functions, a^ and h^, depend only on the size parameter, a, and the relative refractive index of the particles to the medium, m. The latter functions, JT^, and T„, depend only on the angle of observation, Q}^^ Figure 11.31 depicts the contours of the radius vector of VJ^Q) in the y-z plane for Rayleigh scattering of smaU spheres of r < llllQ and Mie scattering of large spheres of a = 2jtr/X.' = 6 and m = 1.44.^°^ From the strong angular dependence of the scattered light intensity for the large spheres, a dramatic color variation of the scattered light with a white incident light, the so-called higher-order Tyndall spectrum (HOTS), is expected according to the observation angle, if we use highly monodispersed particles. Johnson and LaMer^°^ actually observed red and green colored bands in the various directions, which appeared in a continually greater number of bands during the growth of monodisperse sulfur spheres by the decomposition of Na2S203 with sulfuric acid. Figure 11.32 exhibits the angular dependence of the ratio of the red intensity (X = 629 nm) to green intensity {k = 524 nm) for a ^ = 5, \et/^green = l-2> and m = 1.44, calculated from the Mie theory. The authors referred to the bands of the reddish hue, corresponding to the peaks of (red intensity)/(green intensity), as ''red spectral scattering orders'' or simply "orders." As shown by Fig. 11.33, they found an excellent agreement, in order position as a function of particle radius, between the Mie theory and experiments on

555

11. APPLICATION TO FUNDAMENTAL STUDIES

30

^20

n

•S 10 4)

0

30

i

1 J

V^

(W

60 90 120 Angle, degrees.

150

180

Fig. 11.32. Angular dependence of the ratio of the red intensity to green intensity of scattered light by a sphere, calculated using the Mie theory: 0^^^ = 5, ^^d/^grccn = 1.2, m = 1.44. (From Ref. 109.)

0.2

0.3 0.4 Radius, microns.

0.5

0.6

Fig. 11.33. Theoretical and experimental "order" positions for sulfur sols: Q and O, experimental results; ©, theoretical, calculated using the Mie theory with m = 1.44. (From Ref. 109.)

APPLICATIONS

556

monodispersed sulfur particles. The HOTS was so sensitive to the monodispersity of particles that it was practically obliterated when two sols containing monodispersed sulfur particles of mean radius 0.467 [im and 0.476 \xm, different only by 2 %, were mixed together at ratio of 1 : 1, as demonstrated in Fig. 11.34.

130 140 Angle, degrees.

150

Fig. 11.34. Experimentally determined red-green intensity ratio for the light scattered by homogeneous sulfur sols and mixtures: Sol A, 0.467-|Lim radius; Sol B, 0.476-fim radius; O 100 % A; © 90 % A, 10 % B; e 50 % A, 50 % B; A 100 % B. (From Ref. 109.)

The specific turbidity for a monodisperse sol of arbitrary size is given by

g

8ir^prn=i

where g is the particle concentration in gram per one gram of the dispersion, p is the density of the particles, and p' is the density of the dispersion. ^^^ Figure 11.35 is a plot of this against the size parameter, a, for m = 1.10, 1.20. and 1.30 up to a = 26.^^° Obviously, there is an intermediated range of sizes where the particles have an optimum efficiency for scattering light, which is located at a much higher than the Rayleigh scattering range in a < 0.3. There is the possibility of at least two values of size parameter at the

11. APPLICATION TO FUNDAMENTAL STUDIES

557

Fig. 11.35. Specific turbidity of an aqueous sol of spheres, x/c, calculated for different m values with vacuum wavelength, 546 nm, at 25 °C. The concentration, c, refers to 0.01 volume fractions. (From Ref. 110.)

same specific turbidity for a given soh Measurement of the specific turbidity for a sol of sufficiently uniform spherical particles, with a known relative refractive index at two or more different wavelengths, allows one to decide whether the size parameters are on the ascending or descending branch of the theoretical curve of x/c vs a, and thus to specify each size parameter, leading to the mean radius of the particles. Polystyrene and polyvinyltoluene latices of a narrow size distribution are convenient for testing the usefulness of this method for particle size analysis.^^^'^^"* The polarization ratio, p„(e), defined by if^(e)

//((x)i/,(e,a)rfa

^«^^)

//(a)K„(e,a)rfa

P«(e) =

(11.7.8)

is quite sensitive to the breadth of the size-distribution function, /(a). Figure 11.36 is based on the calculation for m = 1.43 and shows the effect of varying CTQfi-om0.100 to 0.300 on p,(e) at a contant a^ for the following distribution function:

APPLICATIONS

558

/(e) =

exp[-(lna-lna^)^/2ao]

(11.7.9)

v/2tiaoa^exp(ao/2)

where a^^ is the modal value of the size parameter and o^ is the breadth parameter.^^^ For QQ = 0.100, the curve shows the typical oscillations characteristic of monodisperse systems. However, this structured character is obliterated as the distribution becomes broader. It is the characteristic structure that permits the precise determination of the size distribution from the data on polarization ratios. Hence, as the distribution becomes increasingly broader, the precision becomes increasingly poorer.

Fig. 11J6. Effect of GQ on p„(0) for a = 5.0. The insert shows the corresponding extreme distribution curves, where a = radius in nm. (From Ref. 115.)

Figure 11.37 shows the experimental results obtained with a sodium chloride aerosol of a narrow size distribution using two wavelengths: K = 436 mji and 546 m[x. The theoretical results which best fit these data are a^i = 2.5, 00 = 0.115, and a^, = 2.0, 00 = 0.130, respectively. The size distributions in the inset, obtained from the two sets of a^^ and 0o, are in excellent agreement, while the scattering curves are quite different.^^^

11. APPLICATION TO FUNDAMENTAL STUDIES

559

Fig. 11.37. A comparison of experimental p(6) curves for a NaCl aerosol measured at X 546 nm and X 436 nm. The inset shows the size distribution calculated from each set of data at X = 546 and 436 nm. (From Ref. 116.)

11.8, Studies of Optoelectronic Properties of Fine Particles. The optoelectronic properties of fine particles are quite sensitive to particle size, crystal habit, and composition. Hence, for the precise analysis of these properties, monodispersed particles are used. Murray et aO^'^ prepared uniform nanosized semiconductor particles of CdE (E = S, Se, Te) by pyrolysis of organometallic reagents in a hot coordinating solvent and measured the absorption and luminescence spectra. Figure 11.38 shows the room temperature absorption spectra of CdSe nanocrystalites of different sizes dispersed in hexane. The absorption edge shifts to shorter wavelength with reduction of the particle size due to the quantum size effect.^^^ Their uniform particles with a size distribution of less than 5 % in relative standard deviation are ideal materials for this kind of experiment. Silver halide particles are of practical importance as photographic material, and their monodispersed particles have been used for fundamental studies of the optoelectronic processes. The eariiest studies of the electronic processes in silver halide grains^^^"^^ were performed on the basis of the experiment of Haynes and Shockley^^"*, who observed the displacement of

APPLICATIONS

560

300 350 400 450 500 550 600 650 700 750 Wavelength (nm)

Fig. 11.38. Absorption spectra of CdSe nanoparticles of different sizes. (From Ref. 117.)

photolytic silver clusters on large crystals of silver chloride by synchronized light and electric field pulses. The light pulse technique allows for the displacement of electronic carriers during the microsecond pulse time, before there is significant motion of ionic carriers. Hamilton and Brady^^^ measured the lifetime of photoexcited carrier electrons with conventional photographic emulsions, and found that the lifetime was of the order of 1 |isec from the displacement of developable latent-image centers, by using a delayed "field technique developed by Webb^^^ in which the field pulse was delayed after the light exposure. In a similar experiment, delay of the light flash after the beginning of the field pulse permits the determination of the time for internal field relaxation owing to ionic conductivity. The delayed-pulse techniques revealed a striking correlation between ionic field decay times and electronic lifetimes, showing the absence of deep traps in the emulsions tested and that the electron's lifetime is determined by the following ionic event (reaction of a migrating interstitial silver ion with a trapped electron to form a silver atom), presumably at a shallow trapping center.^^^'^^'^^ Smimov and Meiklyar^^^ also confirmed the correspondence between the electron lifetime and the field-decay time with tabular grains of silver bromide, and the effects of divalent impurities, Cd^* and Zn^\ and of the silver-ion complexing l-phenyl-5-mercaptotetrazole on ionic

11. APPLICATION TO FUNDAMENTAL STUDIES

561

conductivity. Keevert^^^ used a four-capacitor bridge arrangement with a light flash and a delayed field to measure electron trapping times, and confirmed the correspondence between this and the field-decay time, as noted by Hamilton and Brady.^^'^^^ In silver chloride emulsions, the field-decay time was as much as 40 times greater than the electron trapping time. Keevert discussed the result in terms of pre-existing electron traps of at least 0.5 eV depth. The possibility that electron trapping involves the alternate ionic process, by which a silver ion is extracted from the lattice to create a vacancy, is another explanation of the difference.^^^ Microwave photoconductivity measurement for electron lifetimes in silver halide particles was developed by Baranov and Akimov^^^, and has been extended by Kellogg et al}^^'^^^ and Beutel.^^^ This technique is based on the detuning of a microwave cavity, in which a sample is placed and initially tuned to the microwave field, by the free carrier (electron) response to the microwave field upon light exposure. A summary of the data for electron lifetimes is given in Table 11.1.^^^ Table 11.1. Electron lifetime in silver halide particles {Source: Ref. 128) Composition AgBr

AgCl Ag(BrJ)

Size

Shape

Temp.

8 1 1 5 0.5 0.4-0.95 0.7 0.5 0.2 0.18 -

tabular cubic octahedral tabular cubic cubic cubic cubic cubic cubic cubic

room room room room room room room 77 K 77 K room room

Lifetime (fxsec) 3 2 1 3.3 1.7 <1 9.5 4800 1600 1.5 60

Ref. 121,122 125 125 126 131 132 127 131 131 127 127

11.9. Studies of Ionic Properties of Fine Particles The ionic and electronic properties of fine particles are strongly dependent on their size, crystal habit, and composition. Hence, for studies of these properties, it is necessary to use monodisperse and well-controlled

APPLICATIONS

562

particles in size, shape, and composition. For instance, the ionic properties of silver halide particles to be used in photographic emulsions are examined with monodispersed silver halides of different crystal habits. The ionic conductivity of silver halide microcrystals at room temperature is due to the diffusion of the interstitial silver ions. Van Biesen^^^ first applied tht Maxwell-Wagner technique to determine the effective ionic conductivity of silver halide particles imbedded in a gelatin binder. This technique is based on the principle that the peak in the loss factor of dielectric dispersion, plotted as a function of an applied microwave frequency, gives the reciprocal of the ionic decay time of the particles. He confirmed and extended many of the features of optoelectronic and ionic processes of silver halide particles determined previously by the modified Haynes-Shockley technique (see the next section 11.9). Figure 11.39 shows the dielectric loss versus frequency for cubic and octahedral silver bromide particles of the same size (0.3 Mm), indicating the low ionic conductivity and long decay time of cubic particles as compared to octahedral ones.^^^ This result suggests that the interstitial silver ions are generated mainly at the surfaces of the particles. Takada^^'^^^ studied the ionic property of silver bromide and silver chloride particles by using this technique and examined in detail the effects of particle size and doped

o Cubic Particles 0.16

A't^s

A Octahedral Particles

0.12

0.08

ao4

L^L'

Fig. 1U9. Dielectric loss versus frequency for cubic and octahedral AgBr particles (0.3 Mm size). (From Ref. 133.)

563

11. APPLICATION TO FUNDAMENTAL STUDIES

polyvalent impurities, such as Cd^^, Pb^"^, Fe^*, and Ir^*. He found that the interstitial silver ions of silver chloride particles were also generated in excess at the surface. Figure 11.40 shows the effect of particle size or surface/volume ratio on the frequency maximum (frequency at the maximum dielectric loss) for cubic silver bromide particles.^^ The increase in the frequency maximum with the increasing surface/volume ratio is consistent with the surface generation of interstitial silver ions. Takada and Tani^^^ also showed that sensitizing dyes adsorbed to negatively charged surface sites caused a conductance increase, whereas those adsorbed to positively charged sites caused a decrease. Grain Size {//)

>ao=HZ

1.0

0.5

0.3

1

1

1

1

4.0hk

/^» 2.0 f

L_ 10

20

SurfaceA'olume 6dVd' 0«n-')

Fig. 11.40. Effect of particle size or surface/volume ratio on the frequency maximum (frequency at the maximum dielectric loss) for cubic silver bromide particles. (From Ref. 134.)

Keevert^^^ used the four-capacitor bridge arrangement to measure photoconductive response from a light flash delayed after the application of a field pulse. From these data he determined the field-decay time in silver bromide, silver chloride, and silver iodobromide emulsions. A sununary of the data on ionic properties of silver halide microcrystals is given in Table 11.2. As a consequence of the preferential generation of interstitial silver ions at the surface, it is known that a space-charge layer consisting of interstitial

564

APPLICATIONS

silver ions and silver ion vacancies is formed near the surface, but extended toward the interior of a silver halide particle.^^^"^^^ Table 11.2. Room-temperature ionic properties of silver halide microcrystals {Source: Ref. 128) Composi -tion

Size (f^m)

AgBr

8 1 1 0.3 0.3 1 5 0.25 0.67 0.7

tab. cub. Oct. cub. Oct. cub. tab. cub. sph. cub.

0.4 0.2 0.7 0.18

cub. cub. cub. cub.

0.3 -

cub. cub.

1.6 2.4

*

0.23

hex.

4

*

AgCl

Ag(Br,I)

Shape

\ (usee) 0.9 5 1

10 1.7 4 7 3.4

«•

(Q-'cm"')

A£ (eV)

*. (V)

0.9x10"'

0.42 0.245

3.3x10"' 0.3x10"' 1x10"' 0.73x10"'

0.39 0.42

-0.26

0.8x10"'

0.62

-0.17

2000 180 60

Ref. 128 125 125 133 133 134 126 * * 127 135 * 127 127

127

Agl

T,: Ionic Decay Time; a,: Conductivity; A£: Activation Energy; ^;. Surface Potential. * H. A. Hoyen, Jr., unpublished results.

11.10. Studies of Magnetic Properties of Fine Particles As has been mentioned in sections 11.4 and 11.5, the interactive forces between two isolated non-magnetic particles are generally described by the DLVO theory. In this case, the total interactive energy consists of electrostatic energy, London-van der Waals energy, and short-range

11. APPLICATION TO FUNDAMENTAL STUDIES

565

repulsive energy (Bom potential). The Bom repulsion is dominant in the surface-to-surface separation range of ca. 0.5 to 1 nm. The London-van der Waals energy in aqueous solution is nomially effective within 100 nm. The electrostatic energy may range up to a few (im when the ionic strength is extremely small. For magnetic particles, we need to consider the magnetic attractive energy in addition, which can range up to several jmi, but depend strongly on the size and magnitude of the magnetic moment. The attractive magnetic energy between two particles, K^, is given by^'*^

where M is the magnetic dipole moment of a particle, m, is the magnetic peraieability of vacuum, R {-la^-h) is the center-to-center distance between the two particles of radius A at a surface-to-surface separation A, and p is a constant varying from -2 to 2 according to the orientation of the magnetic moments. The magnetic dipole moment of a single domain particle is written by M=/oi),

(11.10.2)

where /Q is the spontaneous magnetization per unit volume of the particle and V is its volume. Ozaki et al}^^ calculated the total interactive energy of cubic hematite particles in aqueous solutions of low ionic strength, V^ (= V^+Vj^), as the sum of the electrostatic repulsive energy, V^, and the magnetic attractive energy, V^, Here the London - van der Waals attractive energy and the Bom repulsive energy were neglected, because only the long-range interaction are dominant at low ionic strengths. In this calculation, they assumed p = 2, /Q = 2.3 x 10"^ Wb m'^ (0.36 emu g'^f^^, 2a = the edge length of a cubic particle, and V^ for parallel plates, given by

^

K

exp(-KA). [4kT)

(1110-3)

where S is the area of the interaction, n is the number concentration of a 11 electrolyte, h is the surface-to-surface separation between the facing parallel planes of the cubes, and \po is the surface potential.^^*^^ Figures

566

APPLICATIONS

11.41 and 11.42 show the respective effects of ionic strength and particle size on V^ as a function of the center-to-center distance.^"*^ These results suggest a considerable effect of the magnetic energy of hematite particles whose specific magnetic moment, /Q, is extremely small compared to typical magnetic particles, such as maghemite with IQ = 0.5 Wb m"^ (74 emu g'^)^'*^ Also, for the experimental study on magnetic properties of colloidal particles, monodispersed particles must be used, as is obvious from the strong size dependence in Fig. 11.42.

500

1000

DISTANCE/nm Fig. 11.41. Effect of ionic strength on the theoretical curves of V^ vs R for cubic hematite particles of 1.2 jim under the influence of electrostatic repulsion and magnetic attraction in aqueous solutions of 1-1 electrolyte, calculated on assumption of % = 30 mV. (From Ref. 141.)

500

1000

DISTANCE/nm Fig. 11.42. Effect of the size of cubic hematite particles on the theoretical curves of V^ vs R under the influence of electrostatic repulsion and magnetic attraction in an aqueous solution, calculated on assumption of ipo = ^^ ^^ and the ionic strength = 1 x 10"* mol dm-\ (From Ref. 141.)

Under the influence of an external magnetic field, H, magnetic particles of magnetic moment M are expected to be arrayed along the external field. The degree of orientation may be assessed in terms of the Langevin equation^^

11. APPLICATION TO FUNDAMENTAL STUDIES

^ = cotha-l, M a

567

(11-10.4)

where M^ is the average magnetic moment and a is a s — . kT

(11.10.5)

For a » 1 the majority of the magnetic particles will be oriented with their magnetic moments in the direction of the external field, while for a « 1 they will not be oriented, owing to the exceedingly small magnetic energy as compared to the thermal agitation. Ozaki et ^z. 141,144,145 actually observed the orientation of pseudocubic, ellipsoidal, and platelet-type particles of hematite by the very weak geomagnetic field (- 0.3 Oe) through an inversed-type metaUurgical microscope. Figure 11.43 shows the optical micrographs of the chain-like agglomerates of pseudocubic and ellipsoidal hematite particles, arrayed in the direction of the geomagneticfield.^"*^Since the magnetic moment of hematite is in the c-plane of the hexagonal crystal system^"*", the ellipsoidal particles whose revolution axis is coUinear with the c-axis are oriented with their revolution axis normal to the field direction and arrayed in the direction of the field. Similarly, platelet particles were arrayed in the direction of the geomagnetic field, with their c-planes parallel to the field, whilst, when a strong magnetic field was applied in the direction perpendicular to the bottom of the cell or to the c-planes of the platelet particles, they were disassembled and oriented into the upright position with their c-planes parallel to the applied field, as shown by the optical micrographs in Fig. 11.44.^"*^ The same workers also discussed the magnetic interaction of platelet-type hematite particles fi-om a theoretical viewpoint.^"*^ Haque et al}^^'^^^ studied the effect of the magnetic field on the adhesion of magnetic particles to substrates, such as stainless steel and glass beads loaded in a cylinder as a column bed, by flowing suspensions of magnetic particles through the column bed in a magnetic field applied transverse to the fluid flow. The magnetic energy K^, due to the interaction of a particle and a bead of magnetic moments /tp and 11^ (in CGS units), is generally given by

568

APPLICATIONS

a

^m ''•ij»«?:i

10 ^im

^ : i^ :

**IW^|^|,

^^^^SR ' **

^11 li^

l l ^ ^

101101

Fig. 11.43. Optical micrographs of the arrayed hematite particles: (a) pseudocubes; (b) ellipsoids. (From Ref. 141.)

11. APPLICATION TO FUNDAMENTAL STUDIES

569

20 fxm Fig. 11.44. Optical micrographs of the platelet-type hematite particles lying or standing upright according to the direction of the external magnetic field. (From Ref. 145.)

(11.10.6) ''"

R'

~

R'

where R is the center-to-center distance (= r,,+rp+h) and R is the vector of R. For particles and beads magnetized along the applied field, the magnetic interaction is the most attractive for an approach along the bead axis in the direction of the field. In this case, 2m^m^OyO^ VM —

(11.10.7)

where m^, and m^ are the mass of a bead and that of a particle, respectively; Qb and Op are the magnetic moments per unit mass (mass-specific magnetic moments) for beads and particles, respectively. The mass-specific magnetic moment a^, (Oe cm^ g"^) is a function of the external field H (Oe). For instance, o^ for the stainless steel beads used was measured as^"*^

570

APPLICATIONS

a^ = 0.252+0.0314/?.

(11.10.8)

On the other hand, the mass-specific magnetic moment o^ is a function of both the external field, H, and the field due to the magnetized beads, H^. In the uniaxial geometry in connection with Eq. (11.10.7), the bead field is given by 2m^^87ta,p,r,^^8^ '

R'

3R'

3

(1110 9) ''^''

where p^ is the density of the beads, and R{-r^'¥rp-\-h) « r^ due to r^ » r^+h in the column bed system of interest. For steel beads, H^, is comparable to H in order of magnitude, for all fields of interest. Hence the effective field Hgff may be defined as H^j^=H^H,.

(11.10.10)

If the particles are in the size range of a single magnetic domain, they will show the nature of superparamagnetism in solution due to the particle rotation, and thus the mass-specific magnetic moment, a^, of such particles may be written by the Langevin function (see Eq. 11.10.4), ie., kT ""p

1

kT )

(11.10.11)

^p^O^eff,

where OQ is the spontaneous magnetization per unit mass of the particles. In the case of hematite, for example, QQ is given by^^^ o^ = 0.264 +0.196xl0-^ff^.

(11.10.12)

The total energy, K,, of interaction between beads and particles is given as the sum of the magnetic attraction energy, K^, the electrostatic energy, K^, and the London-van der Waals attractive energy, t^ (F^ = ^M + ^£ + ^ ) ' where V^ and V^ are given by Eqs. (11.5.2) and (11.5.4) in section 11.5 {a^ = r^, ^2 = ^^\ the Bom repulsion can be neglected, because the particles are normally trapped at the secondary minimum of the total energy located

11. APPLICATION TO FUNDAMENTAL STUDIES

571

around 50 nm from the surfaces of collector beads. Here, the secondary mmimum is an energy minimum located at a surface-to-surface separation normally around 50 nm, which is formed at intermediate ionic strengths and is very shallow in the absence of a magnetic field. In contrast, another energy minimum, the primary minimum, is a deep minimum located at a separation less than 1 nm, in which the contribution of the Bom repulsive energy is involved (see section 11.5). Figure 11.45 shows the total interaction energy calculated as a function of surface-to-surface separation at different magnetic field strengths for the hematite particles - steel beads system in an aqueous electrolyte solution, using the parameters in the caption. This figure suggests that the depth of the secondary minimum will increases significantly with increasing external magnetic field, and that the particles will be trapped rapidly at the secondary minimum in the presence of a sufficiently strong magnetic field. In addition, if the magnetic field is cut off after the accumulation of the particles at the secondary minimum, they will be released readily to the bulk solution, in contrast to the irreversible trapping at the primary minimum without the magnetic field. Figure 11.46 shows experimental results for the effect of the magnetic field on the relative excluded area, a/rj^n, and the collision efficiency, a, under the conditions of pH = 11 and ionic strength = 2 x 10'^ mol dm'^ in a 40i HEMATITE • STEEL

20 H/Oe

w w » 0

;^

20

-40

^

KV_

-60 1

V L__

1 500

1

,

A (A)

2000

1

_ 1 1000

1

Fig. 11.45. Total interaction energy calculated as a function of h at different magnetic field strengths for hematite particles - steel beads system in an aqueous electrolyte solution using the following parameters: ionic strength = 2 x 10"^ mol dm'^; temperature = 22 °C; Hamaker constant = 7 x 10'^ J; r^ = 0.041 \im; r^ = 33.4 fim; pp = 5.24 g cm~^ pb = 8.3 g cm"^; % = -40 mV; ipb = -30 mV. (From Ref. 147.)

APPLICATIONS

572

^ o.«

0.2

2000

1000

H/Oe

5000

Fig. 11.46. Effect of the magnetic field strength on the relative excluded area, a/rp\ and the collision efficiency, a, for the hematite-steel system at 22 °C, / (ionic strength) 2 x 10'^ mol dm•^ and pH 11. (From Ref. 147.)

hematite particles - steel beads system (r^ = 0.041 [xm, particle number concentration of inlet suspension = 4.4 x 10^^ dm"^; r^ = 33.4 \im).^^^ At pH 11, the surface charges of hematite particles and steel beads were both negative, since the isoelectric points of the hematite and steel were 7.1 and 5.7, respectively. Here, the relative excluded area, a/rj^n, is defined as the ratio of the surface area of the beads occupied by one particle, a, to the projective surface area of one particle, rJ^Tc, The collision efficiency, a, is the ratio of the rate constant of attachment to that of rapid deposition by convective diffusion in the absence of a repulsive barrier. The relative excluded area becomes almost zero above 1000 Oe, suggesting multilayer adsorption, while the collision efficiency rises dramatically up to 0.5, until H reaches 1500 Oe. Figure 11.47 shows the reversible detachment of the particles, previously trapped at the secondary minimum by different magnetic field strengths of 250 Oe or higher, by rinsing with a solution of pH 11 and ionic strength 2 x 10"^ mol dm'^^"*^ The same workers also investigated the effect of magnetic field on the deposition of hematite ( a Fe203), akaganeite (p-FeOOH), and chromium hydroxide (Cr(OH)3) particles of different sizes and shapes onto steel beads,^"^^ as well as the

11. APPLICATION TO FUNDAMENTAL STUDIES

573

HEMATITE-STEEL

pHMl / = 0.002 mol dm'^l

DEPOSITION Qt H : O 0 A 250 Oe o 2000 Oe DETACHMENT ot H=0

20

40

f/min

Fig. 11.47. Fraction of released hematite particles from steel beads as a function of time by rinsing with a NaNOg solution (22 °Q pH 11, / = 2.0 X 10"' mol dm"') at a flow rate 1.9 cm' min'^ in the absence of magnetic field. The hematite particles for this experiment were previously attached on the steel beads at different magnetic field strengths, including 0, 250, and 2000 Oe, using a hematite sol (4.4 X 10^^ particles dm'') at 22 °C, pH 11 and / = 2.0 x 10"' mol dm"', flowing at the rate of 1.9 cm' min-^ for 6 h. (From Ref. 147.)

deposition of magnetite particles onto steel and glass beads.^"^^ In the latter, they found that the magnetic field drastically enhanced the deposition of magnetite particles even on glass beads, owing to the reduction of the electrostatic repulsion barrier by initially attached particles at the primary minimum.

References 1. 2. 3. 4.

J. Perrin, Ann. de Chim. et de Phys. [8" serie] 18, 5 (1909). J. Penin, "Les Atomes." Felix Alcan, Paris, 1920. A. Westgren, Z Anorg. Allgem, Chem. 93, 231 (1915). R. Zsigmondy and P. A. Thiessen, "Das KoUoide Gold." Akad. Veragsges., Leipzig, 1925. 5. A. Emstein, Ann, Physik, Ser. 4, 19, 371 (1906). 6. M. von Smoluchowski, Ann. Physik, Ser. 4, 21, 756 (1906). 7. T. Svedberg, "Colloid Chemistry," 2nd Edn. Chemical Catalog

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Company, New York, 1928. 8. J. Th. G. Overbeek, Adv. Colloid Interface Sci. 15, 251 (1982). 9. O. Stem, Z. Elektrochem. 30, 508 (1924). 10. J. Th. G. Overbeek, in "Colloid Science," (H. R. Kruyt, Ed.), Vol. 1, p. 199. Elsevier, Amsterdam, 1952. 11. M. von Smoluchowski, Phys. Z. 6, 529 (1905). 12. E. Hiickel, Phys. Z. 25, 204 (1924). 13. D. C. Henry, Proc. Roy. Soc. London A 133, 106 (1931). 14. (a) J. Th. G. Overbeek, in "Advances in Colloid Science," (H. Mark and E. J. W. Verwey, Eds.), Vol. 3, pp. 97-135. Interscience, New York, 1950; (b) J. Th. G. Overbeek, in "Colloid Science," (H. R. Kruyt, Ed.), Vol. 1, pp. 194-244. Elsevier, Amsterdam, 1952. 15. F. Booth, Trans. Faraday Soc. 44, 955 (1948); Nature 161, 83 (1948); Proc. Royal Soc. London A 203, 514 (1950). 16. D. C. Henry, Trans. Faraday Soc. 44, 1021 (1948). 17. P. H. Wiersema, A. L. Loeb, and J. Th. G. Overbeek, J. Colloid Interface Sci. 22, 78 (1966). 18. J. Th. G. Overbeek and P. H. Wiersema, in "Electrophoresis," (M. Bier, Ed.), Vol. 2, p. 1. Academic Press, New York, 1967. 19. T. Sugimoto, T. Takahashi, H. Itoh, S. Sato, and A. Muramatsu, Langmuir 13, 5228 (1997). 20. J. Visser, Adv. Colloid Interface Sci. 3, 331 (1972). 21. E. J. W. Verwey and J. Th. G. Overbeek, "Theory of the Stability of Lyophobic Colloids." Elsevier, Amsterdam, 1948. 22. H. C. Hamaker, Physica 4, 1058 (1937). 23. T. Sihite, H. Sasaki, A. Muramatsu, and S. Usui, Shigen Sozai Gakkaishi 107, 215 (1991). 24. E. Matijevic and P. Scheiner, J. Colloid Interface Sci. 63, 509 (1978). 25. W. A. Ducker, T. I. Senden, and R. M. Pashley, Nature 353, 239 (1991). 26. E. L. Binning, C. F. Quate, and C. F. Gerber, Phys. Rev. Lett. 56, 930 (1986). 27. L. Meagher, /. Colloid Interface Sci. 152, 293 (1992). 28. Y. Q. Li, N. J. Tao, J. Pan, A. A. Garcia, and S. M. Lindsay, Langmuir 9, 637 (1993). 29. A. Ashkin, J. M. Dziedzic, and J. E. Bjorkholm, Opt. Lett. 11, 288 (1986). 30. A. Ashkin, J. M. Dziedzic, and T. Yamane, Nature 330, 769 (1987). 31. S. Sato, M. Ohyumi, H. Shibata, H. Inaba, and Y. Ogawa, Opt. Lett.

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16, 282 (1991). 32. S. Sato, Y. Harada, Y. Waseda, and T. Sugimoto, Rev. Laser Eng. 24, 1193 (1996). 33. A. Simon and A. Libchaber, Phys. Rev. Lett. 68, 3375 (1992). 34. J. C. Crocker and D. G. Grier, Phys. Rev. Lett. 73, 352 (1994). 35. A. E. Larsen and D. G. Grier, Nature 385, 230 (1997). 36. B. V. Derjaguin and L. Landau, Acta Physichochim. URSS 14, 633 (1941). 37. E. Matijevic and N. P. Ryde, J. Adhesion 51, 1 (1995). 38. E. Matijevic, Ceram. Trans. 19, 155 (1991). 39. C. S. Hirtzel and R. Rajagopalan, "Colloidal Phenomena: Advanced Topics," pp. 119-159. Noyes Publications, Park Ridge (New Jersey), 1985. 40. N. KaUay, MRS Bull. 15 (1), 41 (1990). 41. N. Kallay, E. Barouch, and E. Matijevic,/4rfv. Colloid Interface Sci. 27, 1 (1987). 42. R. Kuo and E. Matijevic, /. Chem. Soc. Faraday Trans. I 75, 2014 (1979). 43. R. J. Kuo and E. Matijevic, J. Colloid Interface Sci. 78, 407 (1980). 44. N. Kallay, J. Nelligan, and E. Matijevic, J. Chem. Soc. Faraday Trans. I 79, 65 (1983). 45. G. Thompson, N. Kallay, and E. Matijevic, Chem. Eng. Sci. 38, 1901 (1983). 46. E. Matijevic and N. Kallay, Croat. Chem. Acta. 56, 649 (1983). 47. H. Sasaki, G. E. Dirige, and T. Sugimoto, Powder Technol. 78, 137 (1994). 48. V. Privman, H. L. Frisch, N. Ryde, and E. Matijevic, J. Chem. Soc. Faraday Trans. 87, 1371 (1991). 49. N. Ryde, N. KaUay, and E. Matijevic, J. Chem. Soc. Faraday Trans. 87, 1377 (1991). 50. N. Ryde, H. Kihira, and E. Matijevic, J. Colloid Interface Sci. 151, 421 (1992). 51. A. Zelenev and E. Matijevic, Colloids Surfaces A: Physicochem. Eng. Aspects 125, 171 (1997). 52. G. Pozamsky and E. Matijevic, J. Adhesion 63, 53 (1997). 53. H. D. Mendoza, H. Sasaki, I. Matsuoka, and T. Sugimoto, J. Disp. Sci. Tech. 17, 735 (1996). 54. H. D. Mendoza, H. Sasaki, I. Matsuoka, and T. Sugimoto, J. Disp. Sci. Tech. 17, 767 (1996).

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55. B. V. Deijaguin, Discuss. Faraday Soc. 18, 85 (1954). 56. R. Hogg, T. W. Healy, and D. W. Fuerstenau, Trans. Faraday Soc. 62, 1638 (1966). 57. E. Ruckenstein and D. C. Prieve, AIChE J. 22, 276 (1976). 58. E. Ruckenstein and D. C. Prieve, AIChE J. 22, 1145 (1976). 59. J. H. Schenkel and J. A. Kitchner, Trans. Faraday Soc. 56, 161 (1960). 60. Th. F. Tadros (Ed.), "Solid/Liquid Dispersion." Academic Press, London, 1987. 61. E. J. Clayfield and E. C. Lumb, Discuss. Faraday Soc. 42, 285 (1966). 62. E. J. Clayfield and A. L. Smith, Environ. Sci. Technol. 4, 413 (1970). 63. J. Th. G. Overbeek, Colloids Surfaces 51, 61 (1990). 64. H. Kihira, N. Ryde, and E. Matijevic, Colloids Surfaces 64, 317 (1992). 65. H. Kihira, N. Ryde, and E. Matijevic,/. Chem. Soc. Faraday Trans. 88, 2379 (1992). 66. H. Kihira and E. Matijevic, Langmuir 8, 2855 (1992). 67. H. Kihira and E. Matijevic, Adv. Colloid Interface Sci. 42, 1 (1992). 68. A. K. Arosa and B. V. R. Tata (Ed.), "Ordering and Phase Transitions in Charged Colloids," VCH Publishers, New York, 1996. 69. W. Luck, M. Klier, and H. Weslau, Ber. Bunsenges. Phys. Chem. 67, 75 (1963); W. Luck, M. Klier, and H. Weslau, ibid 67, 84 (1963). 70. A. Kose, M. Ozaki, K. Takano, Y. Kobayashi, and S. Hachisu, J. Colloid Interface Sci. 44, 330 (1973). 71. S. Hachisu and Y. Kobayashi, J. Colloid Interface Sci. 46, 470 (1974). 72. K. Takano and S. Hachisu, /. Chem. Phys. 67, 2604 (1977). 73. J. G. Kirkwood, J. Chem. Phys. 1, 919 (1939). 74. B. J. Alder and T. E. Wainwright, Phys. Rev. Ill, 359 (1962); B. J. Alder, W. G. Hoover, and D. A. Young, J. Chem. Phys. 49, 3688 (1968). 75. I. Sogami and N. Ise, J. Chem. Phys. 81, 6320 (1984). 76. N. Ise, Angew. Chem. Int. Ed. 25, 323 (1986). 77. S. Dosho, N. Ise, K. Ito, S. Iwai, H. Kitano, H. Matsuoka, H. Nakamura, H. Okumura, T. Ono, I. Sogami, Y. Ueno, H. Yoshida, and T. Yoshiyama, Langmuir 9, 394 (1993). 78. T. Okubo, Prog. Polym. Sci. 18, 481 (1993). 79. T. Okubo, in "Macro-ion Characterization," (K. S. Schmitz, Ed.), ACS Symp. Ser. 548, p. 364. Am. Chem. Soc, Washington D. C, 1994. 80. J. V. Sanders and M. J. Munay, Nature 275, 201 (1978). 81. J. V. Sanders, Phil. Mag. A 42, 705 (1980). 82. S. Hachisu and S. Yoshimura, Nature 283, 188 (1980).

11. APPLICATION TO FUNDAMENTAL STUDIES

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83. S. Yoshimura and S. Hachisu, Prog. Colloid Polym. Sci. 68, 59 (1983). 84. M. Hasaka, H. Nakashima, and K. Oki, Nippon Kinzoku Gakkaishi 45, 347 (1981). 85. P. Bartlet, R. H. OttewUl, and P. N. Pussy, Phys. Rev. Lett. 68, 3801 (1992). 86. D. Frenkel, Phys. World 6(24), (1993). 87. H. Xu and M. Baus, J. Phys. Condensed Matter 4, L663 (1992). 88. S. Hachisu, Phase Transitions 21, 243 (1990). 89. J. Zhu, M. Li, R. Rogers, W. Meyer, R. H. Ottewill, STS-73 Space Shuttle Crew, W. B. Russel, and P. M. Chaikin, Nature 387, 883 (1997). 90. T. Alfirey, Jr., E. B. Bradford, and J. W. Vanderhoff, J. Opt. Soc. Am. 44, 603 (1954). 91. W. Luck, M. Klier, and M. Wesslau, Naturwissenschaften 50, 485 (1963). 92. J. W. Goodwin, R. H. Ottewill, and A. Parentich, J. Phys. Chem. 84, 1580 (1980). 93. P. Pieranski, Phys. Rev. Lett. 45, 569 (1980). 94. A. J. Hurd and D. W. Schaefer, Phys. Rev. Lett. 54, 1043 (1985). 95. G. Y. Onoda, Phys. Rev. Lett. 55, 226 (1985). 96. M. M. Nicolson, Proc. Cambridge Phil. Soc. 45, 288 (1949). 97. W. A. Gifford and L. E. Scriven, Chem. Eng. Sci. 26, 287 (1971). 98. J. Migins and A. Scheludko, J. Chem. Soc. Faraday Trans. I 75, 1 (1979). 99. D. Y. C. Chan, J. D. Henry, and L. R. White, J. Colloid Interface Sci. 167, 47 (1994). 100. M. A. Forres, Can. J. Chem. 60, 2889 (1982). 101. P. A. Kralchevsky, V. N. Paunov, I. B. Ivanov, and K. Nagayama, J. Colloid Interface Sci. 151, 79 (1992). 102. V. N. Paunov, P. A. Kralchevsky, N. D. Denkov, I. B. Ivanov, and K. Nagayama, Colloids Surfaces 67, 119 (1992). 103. P. A. Kralchevsky, V. N. Paunov, N. D. Denkov, I. B. Ivanov, and K. Nagayama, J. Colloid Interface Sci. 155, 420 (1993). 104. V. N. Paunov, P. A. Kralchevsky, N. D. Denkov, 1. B. Ivanov, and K. Nagayama, J. Colloid Interface Sci. 157, 100 (1993). 105. P. A. Kralchevsky and K. Nagayama, Langmuir 10, 23 (1994). 106. Lord Rayleigh, Phil Mag., Ser. 5, 12, 81 (1881). 107. G. Mie, Ann. Physik, Ser. 4, 25, 377 (1908). 108. M. Kerker, Ind Eng. Chem. 60 (10), 30 (1968).

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109. I. Johnson and V. K. LaMer, J. Am. Chem. Soc. 69, 1184 (1947). 110. W. HeUer and H. J. McCarty, J. Chem. Phys. 29, 78 (1958). 111. R. M. Tabibian, W. HeUer, and J. N. Epel, J. Colloid Sci. 11, 195 (1956). 112. J. B. Bateman, E. J. Weneck, and D. C. Eshler, J. Colloid Sci. 14, 308 (1959). 113. Gj. De2elic and J. P. Kratohvil, J. Colloid Sci. 16, 561 (1961). 114. S. H. Maron, P. E. Pierce, and I. N. Ulevitch, J. Colloid Sci. 18, 470 (1963). 115. M. Kerker, E. Matijevic, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid Sci. 19, 213 (1964). 116. W. F. Espenscheid, E. Matijevic, and M. Kerker, J. Phys. Chem. 68, 2831 (1964). 117. C. B. Murray, D. J. Norris, and M. G. Bawendi, J. Am. Chem. Soc. 115, 8706 (1993). 118. J. H. Webb, J. Appl. Phys. 26, 1309 (1955). 119. J. F. Hamilton, L. E. Brady, and F. A. Hamm, J. Appl. Phys. 29, 800 (1958). 120. J. F. Hamilton and L. E. Brady, J. Phys. Chem. 66, 2384 (1962). 121. J. F. Hamilton and L. E. Brady, J. Appl. Phys. 30, 1902 (1959). 122. L. E. Brady and J. F. Hamilton, J. Appl. Phys. 37, 2268 (1966). 123. L. E. Brady and J. F. Hamilton, J. Appl. Phys. 35, 1565 (1964). 124. J. R. Haynes and W. Shockley, Phys. Rev. 82, 935 (1951). 125. L. E. Brady and J. F. Hamilton, J. Appl. Phys. 36, 1439 (1965). 126. J. P. Smimov and P. V. Meiklyar, Photogr. Sci. Eng. 17, 285 (1973). 127. J. E. Keevert, in "Proc. 28th Ann. Conf. Semin. on Quality Control, Denver 1975" pp. 186-187. Soc. Photogr. Sci. Eng., Denver, 1975. 128. J. F. Hamilton, in "The Theory of the Photographic Process," 4th Edn. (T. H. James, Ed.), p. 105. Macmillan, New York, 1977. 129. E. V. Baranov and I. A. Akimov, Dokl. Akad. Nauch. SSSR 154, 7 (1964). 130. L. M. Kellogg, N. B. Liebert, and T. H. James, Photogr. Sci. Eng. 16, 115 (1972). 131. L. M. Kellogg, Photogr. Sci. Eng. 18, 378 (1974). 132. J. Beutel, Photogr. Sci. Eng. 19, 95 (1975). 133. J. Van Biesen, J. Appl. Phys. 41, 1910 (1970). 134. S. Takada, Jpn. J. Appl. Phys. 12, 190 (1973). 135. S. Takada, Photogr. Sci. Eng. 18, 500 (1974). 136. T. Tani and S. Takada, Photogr. Sci. Eng. 18, 620 (1974); S. Takada

11. APPLICATION TO FUNDAMENTAL STUDIES

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and T. Tani, J. Appl. Phys. 45, 4767 (1974). 137. K. L. Kliewer and J. S. Koehler, Phys. Rev. Sect. A (2) 140, 1226, 1241 (1965). 138. K. L. Kliewer, /. Phys. Chem. Solids 27, 705, 719 (1966). 139. Y. T. Tan, Prog. Solid State Chem. 10, 193 (1975). 140. S. Chikazumi, "Physics of Magnetism." Wiley, New York, 1964. 141. M. Ozaki, T. Egami, N. Sugiyama, and E. Matijevic, J. Colloid Interface Sci. 126, 212 (1988). 142. A. Tasaki, K. Shiratori, and S. lida, J. Phys. Soc. Jpn. Suppl. B-117, 235 (1962). 143. G. Bate, in "Magnetic Oxides," (D. J. Craik, Ed.), Part 2, p. 703. WUey, New York, 1975. 144. M. Ozaki, H. Suzuki, K. Takahashi, and E. Matijevic, J. Colloid Interface Sci. 113, 76 (1986). 145. M. Ozaki, N. Ookoshi, and E. Matijevic, J. Colloid Interface Sci. 137, 546 (1990). 146. I. Okada, M. Ozaki, and E. Matijevic, J. Colloid Interface Sci. 142, 251 (1991). 147. M. F. Haque, N. Kallay, V. Privman, and E. Matijevic, J. Colloid Interface Sci. 137, 36 (1990). 148. M. F. Haque, N. Kallay, V. Privman, and E. Matijevic, J. Adhesion Sci. Technol. 4, 205 (1990). 149. V. Privman, N. Kallay, M. F. Haque, and E. Matijevic, J. Adhesion Sci. Technol. 4, 221 (1990). 150. G. J. Muench, S. Arajs, and E. Matijevic, J. Appl. Phys. 52, 2493 (1981).

CHAPTER 12 INDUSTRIAL APPLICATIONS Monodispersed particles precisely controlled in size, shape, structure, and composition are not only excellent models for fundamental research, but are also expected to be ideal particulate materials for practical use as highperformance advanced materials. However, they are not necessarily widely used yet in the industry, because of their low productivity or high cost in most cases. Nevertheless, in view of their superb potential functions and the recent remarkable development of simple and inexpensive general methods for their production in large quantities (see sections 7.2.6 and 7.3.1), there seems to be no doubt that a great part of particulate materials will be replaced by monodispersed particles in the near future. In this chapter, industrial applications of monodispersed particles, including their possibilities, will be described.

12.1. Photographic Materials Monodispersed silver halide particles are widely used in the photographic industry, which may be one of the rare examples of practical use of monodispersed particles. They are used in the forms of mixed silver halides, such as AgBrI, AgBrCl, and AgClBrI, nearly pure AgBr and AgCl, or core/shell particles consisting of a core and shell different in composition. The shapes occur in wide variety, including cubes, octahedra, cubooctahedra, spheres, and platelets. Strict control of their shape, size, and composition is essential for the control of their photographic properties, including photosensitivity, spectral sensitivity, image contrast, granularity of the developed images, covering power (= optical density / two-dimensional density of developed silver in film), etc. Indeed, the invention of the controlled double-jet method for the preparation of monodispersed silver halide particles in the 1960s (see sections 1.5.2 and 7.3.2) has made an invaluable contribution to the progress of photographic science and technology.

581

12. INDUSTRIAL APPLICATIONS

Silver halide particles to be used for photographic materials are sensitized to an optimum level of light-sensitivity by surface treatment with chemical sensitizers such as chloroauric acid (HAUCI4) plus sodium thiosulfate or other organic sulfur compounds (gold-sulfur sensitization) after preparation of the particles, but the photographic speed or light sensitivity of photographic materials depends primarily on the grain size of each silver halide particle. Here, the photographic speed is defined as the inverse number of incident photons per unit area required for making a certain fraction of the light-exposed particles developable. For understanding the importance of grain size for photographic speed, the knowledge on the concept of quantum sensitivity may be needed. The quantum sensitivity is defined as the minimum number of absorbed photons (quanta) per grain to create one developable silver cluster in a grain. Hence, the smaller the value of the quantum sensitivity is, the higher is the quantum sensitivity of the grain. The minimum number of absorbed photons per grain is normally defined by the absorbed photons per grain necessary for the development of a half of the light-exposed particles. Figure 12.1 shows the relationship between

^=0-5

A Emulsion No. I O D X

+

0 0 h .s o 0-5

o O 10

o

1-5 I- o lA

20

< o

o 20

Log,^ Grain Volume fp^j 10

Fig. 12,1. Relationship between iogio(grain volume) and Iogio(absorbed quanta/grain) required for making a half of the grains developable. (From Ref. 1.)

582

APPLICATIONS

logioCgrain volume) and log^oCabsorbed quanta/grain) for a half of each sizeclass to be developable in various photographic emulsions 1 - 6.^ This figure shows that the quantum sensitivity of a particle in each size class is almost constant in a given photographic emulsion, irrespective of the grain size in a practical size range up to ca, 1 fim^. Since a silver halide grain in a properly sensitized photographic emulsion is almost constant, regardless of the grain size up to a certain level, and since the number of absorbed photons per grain is known to be almost proportional to the grain volume, the photographic speed of an optimally sensitized photographic material of monodispersed grains is approximately proportional to the mean volume of a grain. As a consequence, strict control of the size of each grain in a system is of vital importance for designing a high-performance photographic emulsion. For this purpose, monodispersed silver halide particles are ideal materials. It is also noteworthy that ideally precise assessment of quantum sensitivity is possible only with monodispersed particles. This is the main reason why almost all fundamental studies on quantum sensitivity are performed with well-defined monodispersed particles varied in shape and mean size. As a rule, rather polydispersed particles, or uniform particles of different mean sizes coated in multilayers, are used for color or black and white negative films in order to reserve a wide light-exposure latitude with their low-contrast developed image. On the other hand, uniform particles of a narrow size distribution are used for positive photographic materials, such as color or black and white printing papers, reversal films. X-ray films, microfilms, lithographic films, instant direct-positive materials, etc., to give a high-contrast developed image. Figure 12.2 illustrates general features of optical density of developed images vs log^oClight exposure energy), or D/Log^gE curve, for negative and positive photographic materials. For example, monodispersed octahedral silver bromide particles are actually used in some high-speed instant direct-positive color materials, in which each particle is strongly sensitized at an intended internal position by a gold-sulfur sensitizer, and weakly sensitized at the particle surface as well. The internal sensitization is performed when the particles are grown to a certain size level by the controlled double-jet technique, and then further growth is continued until the sensitized position reaches a certain depth. After being spectrally sensitized to yellow, green, or red light by adsorption of a spectral sensitizing dye, the particles are finally coated in a layer of an instant color material consisting of ca. 20 layers, having specific functions. On exposure to light, one or more silver clusters are formed as internal

12. INDUSTRIAL APPLICATIONS

583

Positive u

Q

1 O

logE Fig. 12.2. General features of optical density of developed images vs log^oGight exposure intensity), or D/Log^oE curve, for negative and positive photographic materials. latent images at the internal chemically-sensitized center in each particle exposed to light, through the electronic and ionic processes (see section 11.8), while unexposed particles remain free from internal silver clusters. When they are exposed to an alkaline solution of developer, a nucleating agent (a kind of reducing agent, such as hydrazines, aldehydes, and acetylenes, ordinarily with some adsorptive group to silver halides) which has previously been coated with the silver bromide particles is activated by alkali and injects electrons into both light-exposed and unexposed particles. By this action of the nucleating agent, while the unexposed particles form silver clusters on their weakly-sensitized surfaces, the light-exposed particles form no silver clusters on their surfaces, because the injected electrons are trapped by the internal silver clusters as a much deeper electron trap than the surface sensitivity center. As a consequence, while the lightexposed particles are not developed by developing agent, the unexposed ones are developed to form a positive image. The oxidized developing agent reacts with a dye-releaser in the neighboring layer to make it release and diffuse the anchored dye to a dye-receiving layer across a reflection layer, for forming a positive dye image. Figure 12.3 depicts the action of the nucleating agent. The precise control of the position of the internal

584

APPLICATIONS

Weak Chemical Sensitization >^ Strong Chemical Sensitization \ \ Latent Image Speck Nucleating Agent hv

rJ—^

undevelopable Nucleating Agent

developable

Fig. 12.3. The action of the nucleating agent in a silver halide particle of a directpositive photographic material. sensitivity centers and the achievement of the delicate balance between the internal and surface sensitization in the sophisticated "instant" system are impossible unless monodispersed particles are used. Even for low-contrast negative films consisting of polydispersed particles, it may be desirable to design a mixed system of monodispersed particles of different mean sizes optimally sensitized in the individual monodisperse systems, since optimal conditions for chemical sensitization strongly depend on the grain size. In this sense, the multilayered assemblies composed of different monodisperse systems are in accord with this requirement. Silver halides used for photography are originally sensitive to only blue light (k - 450 nm) and ultraviolet light, so they have to be spectrally sensitized to green light (X. - 550 nm) and red light (>^ ~ 650 nm) with sensitizing dyes such as carbocyanines or merocyanines which are adsorbed to the surfaces of silver halide grains. These absorb incident photons of particular wavelength ranges, and the excited electrons in the sensitizers are transferred to silver halide grains to form latent images in the grains. Specifically, for color reproduction in color photography, not only the choice of spectral sensitizing dyes with proper absorption bands, but also the composition of the silver halide particles and their crystal habits are important determinants, since their composition and crystal habits strongly

12. INDUSTRIAL APPLICATIONS

585

affect the absorption spectra of sensitizing dyes (see section 10.9). Thus, strict control of the composition and crystal habit of silver halide particles is needed for this purpose as well. The design of the double-structured core/shell grains with different compositions in core and shell, partly described in section 8.5.3, may be one of the most effective ways for using the best functions of individual silver halides.^"^ Bando et al"^ studied the characteristics of double-structure grains (DSG), AgBro9loi(core)/AgBr(shell), which were monodispersed octahedra of 0.8 |xm in diameter and the silver contents of the core and shell were equal. Figure 12.4 shows characteristic curves of D/log^oE for pure AgBr grains (emulsion A), AgBro95loo5 grains uniform in composition (emulsion B), and DSG (emulsion D) at different development times in a typical color development process, CN-16, after white-light exposure. All the specimens for Fig. 12.4 were optimally sensitized for the grain surfaces with a gold-sulfur sensitizer, and thus latent images in the form of silver clusters were formed exclusively on the grain surfaces. The AgBr grains (emulsion A) and AgBrg 95I0.05 grains (emulsion B) were also monodispersed ones of 0.8 pun in diameter. The results clearly show that the DSG has both the merits of pure AgBr and AgBrI without their respective demerits; /.e., pure AgBr is fast in development, but low in photographic speed owing to the small intrinsic absorption of blue light, whilst AgBrI containing iodide is slow in development and low in image contrast, but high in photographic speed due to the extended absorption edge to the longer wavelength with increasing iodide content.^

3.0 • Emulsion (A)

" Emulsion (B) /

2.0

Ifr

x^V^

3 min

2.Oh

> C ^ 2 min 30

sec

^

min

^

'

2 min

^ ^ 1

*^v^^ 1 min

=>i.oh

//

'^'^^30

1 * * * ^ ° ^ ^ ^ 1 ., 3.0

1 ..

2.0 1.0 0.0 LOG EXPOSURE

1 0.0 ISi^^^i—-^^""^1 1.0 3.0 2.0 1.0 0.0 LOG EXPOSURE 4

min.

1.0 sec

j 1 -J

1,0

3.0

2.0 1,0 0.0 LOG EXPOSURE

1.0

Fig. 12.4. Characteristic curves of (A) AgBr, (B) AgBro.95Io.05, and (D) DSG. (From Ref. 4.)

Moreover, when the DSG grains were spectrally sensitized, a significant

586

APPLICATIONS

2.0

H.O

Fig. 12.5. Relative photographic speed vs amount of dye (a) added: (A) AgBr (O); (B) AgBro.95Io.05 (^); (D) DSG (G). (From Ref. 4.)

6.0

ADDED DYE (a) (10"* mol / mol silver halide)

effect of the DSG was found against dye-desensitization (= bleaching of surface latent images by dye-holes) for blue radiation, as shown in Fig. 12.5, where varying amounts of a red-sensitizing dye (dye (a)) of the following formula were added to each emulsion. C2H5

r

(CH2)3S03^ (CH2:

(CH2)3S03Na

In order to elucidate this effect, Bando and coworkers'* investigated the ESR signals resulting from the dye-holes for these samples. Table 12.1 shows the relative intensities of light-induced ESR signals of dye (a) adsorbed to the particles of emulsions A, B, and D (8.0 x 10"^ mol/mol Ag), for exposure to monochromatic light of X. = 640 nm (red) and X = 420 nm (blue). The signal intensity, I^^, is proportional to the number of positive holes staying in the dyes after injection of photoelectrons into the silver halide grains by radiation with the red light, while I^iue is proportional to the number of the positive holes trapped by the dyes, but originally generated in the grains by the blue light and transferred to the dyes. The small values of both Ijgjj and \^^^ for emulsion B, as compared to emulsion A, may be due to the hole-trapping of the iodide ions of the AgBr^95I005 grains.^ Also, the low Ibiue/^red ^^^^^ ^^ I^^G (cmulsion D) seems to be due to trapping of the

587

12. INDUSTRIAL APPLICATIONS

Table 12.1. Relative intensities of light-induced ESR signals of the dye adsorbed to (A) AgBr, (B) AgBro.95Io.05, and (D) DSG {Source: Ref. 4) Emulsion (A) AgBr (B) AgBro.95lo (C) DSG

IK,

100 50 100

100 49 54

\\uJ\ bW'rcd 100 98 54

cores after their generation by the blue positive holes in the A^XQ^\^ radiation, and to the blocking of the hole transfer from the dyes to the grain by the AgBr shell after generation of positive holes in the dyes by the red radiation. The prevention of the hole transfer from the core to the dye is thought to be the main reason for the inhibited dye-desensitization. As a consequence, they proposed the band-structure model of DSG in Fig. 12.6, by reference to the work of Berry^. The concentration of positive holes in the AgBrI core is in accord with the results of Hirsch^: this was attributed to the effect of the DSG against the dye-desensitization for blue radiation. As has been shown above with a few examples, the fundamental and practical studies on advanced processing of silver halide particles, including precise control of crystal imperfections, heavy metal doping, core/shell control, heterojunction of different silver halides, etc. (see chapter 8), are being actively continued with monodispersed silver halide particles in order to extract the ultimate functions from their inherent potentialities. CONDUCTION BAND

^

o.^ h

VALENCE BAND

Fig. 12.6. Band structure model of the double-structured grain for the efficient charge separation between photoelectrons and positive holes. (From Ref. 4.)

588

APPLICATIONS

12.2. Ceramic Materials The scaling law for the sintering model indicates that powders of 10 nm in size will sinter 10^ - 10^ faster than micron-size powders.^ Mazdiyasni et al^'^^ prepared a variety of very small high-purity metal oxide particles of less than 20 nm by thermal decomposition and hydrolysis of metal alkoxides. However, the predicted advantage on the sintering time and temperature was not necessarily realized due to the agglomeration of the smaU particles, since agglomerates are generaUy sintered so fast that they become large particles in the early stage of sintering and create large voids around them.^^"^"* In the meantime, Stober et al}^ prepared monodispersed and unagglomerated silica particles of 0.05-2 |xm by hydrolysis of silicon alkoxides in the presence of ammonia. In this procedure, as the length of the alkyl chains of alcohols, used as the solvent, and silicon esters, as the starting material, becomes larger, the final size increases owing to the slower hydrolysis and thus the lower nucleation rate. Other factors, such as the concentrations of anwnonia and water, and temperature, are also effective in determining the final size (see section 7.2.9). The concentration of silicon alkoxides is less than ca. 0.3 mol dm"^, significantly lower than used in the ordinary sol-gel processing of colloids, in order to avoid aggregation of growing silica particles. On the other hand, Rhodes^^ demonstrated that the alkoxide-derived oxide particles developed by Mazdiyasni et al^'^^ can be sintered at very low temperatures, ca. 1100 °C, as opposed to 1700 ""C for calcined and milled powders, by dispersing, eliminating the agglomerates, and centrifugally compacting the particles. For the achievement of lowtemperature sintering, a highly dense microstructure of the compact is generally required. For this purpose, monodispersed spherical particles are ideal, since they readily form a compact ordered structure of face-centered cubic array if we utilize the electrostatic repulsive forces of their charged surfaces and settling owing to the gravitational or centrifugal forces in polar liquid media (see section 11.6).^^'^^ Bowen and coworkers prepared amorphous Ti02 and Zr02 spheres of narrow size distributions and their doped particles by hydrolysis of the corresponding metal alkoxides and studied this effect extensively. Namely, Barringer and Bowen^^*^" prepared fairly uniform TiOj particles {ca. 30% in relative standard deviation) by hydrolysis of 0.1-0.2 mol dm"^ titanium tetraethoxide at 25 ""C, and investigated the effect of dense packing on the sintering temperature by gravitational or centrifugal settling at appropriate pH values above 9 or below 4, sufficiently away from the isoelectric point (I.E.P.- 5.5)^\ at ionic

12. INDUSTRIAL APPLICATIONS

589

strengths less than 0.01 mol dm'^ They found a significant reduction of sintering temperature to 1050 ''C for >99 % of the theoretical density using the dense compact (green compact) of the uniform Ti02 powder of 0.35 \xm, ca, 300 °C lower than 1300 - 1400 °C necessary for conventional Ti02 powders to sinter to 97 % of the theoretical density. Figure 12.7 shows SEM images of the so-obtained dense and uniform compact of Ti02 and the microstructure sintered to >99 % of the theoretical density in 90 min at 1050 °C.^^ They also found that the sintering temperature was further lowered to 800 °C with a dense compact of Ti02 powder of 0.08 |xm in mean diameter, prepared from titanium isopropoxide. Although some particle aggregation is observed in the TEM of this original powder, the fairly uniform and dense compact and the small particle size may favor the dramatic reduction of the sintering temperature. Similarly, ZrOj spheres of a narrow size distribution were also prepared from zirconium alkoxides.^^"^ Typical parameters were 0.1 mol dm"^ zirconium n-propoxide, 0.50 mol dm'^ H2O, and a reaction time of 2 min at 50 °C. Moon et al^'^'^ prepared monodisperse Zr02 powders with a mean diameter of ca. 0.3 \xm by hydrolysis of a relatively high concentration of zirconyl chloride (ZrOCy such as 0.2 mol dm"^ in 1-propanol or 2-propanol in the presence of water and ca. 0.1 wt % HPC (hydroxypropyl cellulose, MW « 100,000) as a dispersant. They raised the reaction temperature rapidly to the boiling point of the solution by using a microwave oven, which was effective for the formation of the monodisperse particles, probably because of the improved separation between the short nucleation period and the subsequent growth stage.

Fig. 12.7. SEM images of uniform green compact of Ti02 (A) and its sintered structure (B). (From Ref. 19.)

590

APPLICATIONS

For uniform spheres of ZrOj (d = 0.2 [im, I.E.P.= 6-7.5) and SiOj (d = 0.4 \xm, I.E.P.= 2-3), the effect of the dense microstnicture of the green compacts, prepared at pH 4 or 9-11 for Zr02 and at pH ^ 5 for Si02, on the sintering temperatures were tested, and the sintering temperatures were found to be 1160 ''C for the Zr02 compact {ca, 1700 °C for conventional milled Zr02 powders) and ca. 1100 ^C for the Si02 compact.^*^^ Doping a host powder with a small amount of different metal ions is a useful technique for the modification of the physical or chemical properties of original ceramic powders. Since TiOj ceramics doped with various combinations of cations have been studied for use as low-voltage varistors,^^ grain-boundary capacitor materials,^° oxygen sensors,^^ current-collecting electrodes in Na-S batteries,^^ etc., singly-doped Ti02 powders with either Ta205 or Nb205 and doubly-doped Ti02 with BaO, CuO, or SrO and either Ta205 or Nb205 were also prepared. The Ti02 powders singly-doped with Ta205 or Nb205 were made by co-hydrolysis of Ti(OC2H5)4 with Ta(002115)5 or Nb(OC205)5, while the doubly-doped samples were prepared by precipitating the carbonates of Ba^^, Cu^^, and Sr^^ onto the once-washed singly-doped Ti02 particles in aqueous solutions of their metal chlorides in the presence of (NH4)2C03. On heating, these carbonates are converted into oxides. For the doping with SrO, co-hydrolysis of Ti(OC2H5)4 and Sr(iso031170)2 were also performed.^^*^^ The contents of these dopants ranged from 0.1 to 1.0 wt % of Ti02. Fegley, Barringer and Bowen"^*^^ concluded, from transmission electron microscopy and X-ray diffractometry on the amorphous spheres, that the dopants, Ta and Nb, were homogeneously distributed in each singly-doped Ti02 particles. However, since the hydrolysis rates of two different alkoxides are generally not equal, and thus there is a high possibility of formation of a compositional double structure in each particle, some other means such as XPS analysis may be recommended for more precise assessment. In order to attain a uniform composition, proper choice of alkoxyl group for each alkoxide, or controlled continuous addition of an active alkoxide to a hydrolysis system of the other less active alkoxide, is required in many cases. For the stabilization of the cubic phase of Zr02 ceramics to avoid the phase transition between the monoclinic and tetragonal phases with the change of temperature and for the reduction of their sintering temperature, yttria-stabilized zirconia (YSZ) is widely used.^"*'^^*^"* Fegley et al}^ prepared Zr02 particles of a narrow size distribution with 0.2 |im mean diameter, doped with 6.3 mol % Y2O3 by co-hydrolysis of ca, 0.08 mol dm"^ Zr(n-C3H70)4 and ca. 0.01 mol dm"^ Y(iso-C3H70)3 at 50 °C. The reaction was instantaneous. The uniformly

12. INDUSTRIAL APPLICATIONS

591

packed compact sintered to >98% of the theoretical density at temperatures as low as 1160 °C, similar to the result for pure ZiQ^?^ Monodispersed SiOj powders doped with a high content of B2O3 (e.^., 1:1 in molar ratio) were also prepared by partially hydrolyzing 81(062115)4, adding B(n-C4H90)3, and then completely hydrolyzing this mixture?^'^^ The uniform compact of the B-doped Si02 (1:1) powder of 0.2 \xm could be densely sintered at temperatures approaching 700 °C, significantly lower than the sintering temperature (-1100 °C) of a uniform compact of a pure monodispersed Si02 powder (d = 0.4 [im) prepared in a similar manner. The chemical and physical properties of uniform ceramic powders prepared by Bowen et al are summarized in Table 12.2.^ In this table, there are striking differences in specific surface area between powders washed with alcohol and with water. For example, the BET specific surface areas of the water-washed Ti02 powders of 0.3-0.7 [im in mean particle diameter are as high as 170 to 200 mVg, which are equivalent to the specific surface areas of a sphere with a diameter of 88 to 75 A. Similar results were obtamed by Kondo et al as well.^ If we assume that the alkoxide remaining only on the external surfaces is hydrolyzed by washing with water to form very small titania particles on the surfaces, the upper limit of the enlarged specific surface area is calculated as only 4.63 times the original surface area, irrespective of the generated particle size, on the assumption of a closest-packed particulate monolayer. Thus, as-prepared amorphous titania particles must retain a considerable amount of unreacted alkoxide in the interiors, and become porous with hydrolysis of the internal alkoxide by permeating water used for washing. Fegley and Barringer^ also proposed the use of porous ceramics, prepared by sintering the uniform compacts of high-purity monosized powders at relatively low temperatures, for filter membranes, chromatography substrates, catalytic substrates, and sensor elements. Unlike the most alkoxide-based particles being amorphous, Heistand and Chia^^ prepared polycrystalline spheres of ZnO, having a narrow size distribution of 0.2 pim in diameter and 15 nm in crystallite size, by hydrolysis of ca. 0.2 mol dm"^ ethylzinc r-butoxide, (C2H5)Zn(r-C4H90), at room temperature, which may be used as a ZnO-based varistor material. Besides the synthesis of uniform ceramic particles by hydrolysis of alkoxides, Nishisu and Kobayashi^^ prepared monodisperse spheres of EujOa-doped Y2O3 (0.1-0.3 \xm), to be used as a red phosphor, by precipitation of the monodispersed mixed carbonate spheres from a dilute solution of mixed chloride salts of Y^^ and Eu^* (totally 1.0 x lO'^mol dm"^)

592

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g

«1

ex o

I •a

i d

" CO

a o

Sub

s

o

I

U o

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P.O

^

J'

I ps s 35.3:

^

VI

8

1

^ I rH

d

I

r-H

d

A

I

?

> ^,-^ ^ &

1a.

o c5

^

d

d

o I

d

d

I

d d

1 i"0

OS

""

"2»^

S '«

1-H

in I

£5 I

I•3

I

3

3

1t a

3

3

II ^I I

t I ri

•«

P

8

8

::l 8

I

o

en

I

I

Q.

o

C/O

APPLICATIONS

C/3

u

C/3

GO

5-

5 u

C/3

U

593

12. INDUSTRIAL APPLICATIONS

and urea (5.0 x 10"^ mol dm"^) at 97 "^C for 60 min and final calcination at temperatures above 650 °C for 60 min after repeated centrifugal washing with deionized water and propanol. The composition of the mixed carbonate can be varied from pure Eu2(C03)3 to pure Y2(C03)3 with excellent monodispersity, and the yield was always more than 99% after aging at 97 °C for 60 mm. The amorphous carbonate particles were converted into crystalline Eu-doped Y2O3 (cubic crystal) with a specific emission at 611 nm by calcination at temperatures above 650 ""C without changing their spherical shape. Figures 12.8 and 12.9 show a TEM of sample A - 1 (Eu:Y = 0.05:0.95) calcined at 850 °C for 1 h and emission spectra of Eu-doped Y2O3 powders depending on the doped content of EU2O3, respectively. In Fig. 12.9, while Y2O3 with no EU2O3 shows no emission, sample A - 1 with 5 mol% EU2O3 demonstrates the strongest emission, and the specific emission is rather lowered with an increasing content of EU2O3 over 5 mol % due to the concentration-extinction. The advantage of the monodispersed particles may be the uniform distribution

nm ^'-V

->' ^ y ^H^

^ ^ ^ ^ ^ ^ ' « ' ,. M

P^:^''

%i^>^''^ ^^

*,%„«„/;,;,;',„, ', ''"y'i

'-.i^^

mmf- ^

->^''''%'" ' ^"/H'^,'"'" /'*

570

580

590

600

610

620

630

640

Wavelength (nm)

Fig. 12.8. TEM of Eu203-doped Y2O3 particles (Eu:Y = 0.05:0.95) prepared by calcination of the corresponding carbonate particles at 850 ""C for 1 h. (From Ref. 36.)

Fig. 12.9. Emission spectra of Eudoped Y2O3 powders, depending on the doped content of EU2O3. (From Ref. 36.)

594

APPLICATIONS

of Eii203 content among particles as well as the sharp size distribution, both of which have a critical influence on the luminescent property of the final product. There is a number of merits to the above uniform particles, including the simple preparative procedures at moderate temperatures, high purity, high yields, and low sintering temperatures. However, if the concentrations of starting materials are limited to ca. 0.2 mol dm'^ and cannot be increased significantly without degrading the uniformity of the products, then the cost of scale-up to large liquid volumes, as well as the rather costly starting materials, may outweigh the advantages.^^ One of the solutions to this problem may be to ust polymeric steric stabilizers to inhibit aggregation.^^'^^ For example, Jean and Ring'*^ found hydroxypropylcellulose (HPC) to be an effective stabilizer in the growth system of TiOj particles by hydrolysis of titanium ethoxide. The unagglomerated powder with HPC formed a uniformly packed compact by sedimentation in ethanol and proved to have the excellent sinterability {e.g,, 99% of theoretical density by sintering at 1050 ''C for 90 min with Ti02 particles of 0.36 pun). Since then, HPC has been used also for the preparation of fairly uniform AI2O3 particles'*^ and ZrOj particles.^^'^^ Although it is not easy, so far, to exceed the concentration level of 0.2 mol dm"^ for achievement of satisfactory monodispersity even with HPC in these systems, the use of polymers or surfactants as stabilizers undoubtedly offers a promising way for the production of highly condensed monodisperse particles. hi addition, it is of great importance to develop new productive methods, such as the gel-sol method, or to extend conventional productive methods, such as the controlled double-jet (CDJ) method (see section 7.3). Recently, Her et al^'^'^'^ have prepared fairly uniform particles of pure and Zr- and Sr-doped BaTiOj particles for use as ceramic dielectrics. These were produced by simultaneous introduction of a mixed solution of BaClj, TiCl4, and the chloride salts of desired dopant metals and a NaOH solution into a vessel containing a NaOH solution, under stirring at 85 °C, based on the double jet method. The total concentration of the used chloride salts in the whole system was ca. 0.37 mol dm'^. Interestingly, the nearly spherical particle products have considerably narrow size distributions, despite the clear evidence of coagulation of the primary particles during the growth of the product particles. Probably, the hydroxide gel network preformed in the highly alkaline media may prevent extensive agglomeration, like the synthetic system of uniform magnetite particles.'^ The dielectric property of barium titanate so-obtained with 20 % Zr substitution and sintered at

595

12. INDUSTRIAL APPLICATIONS

Fig. 12.10. SEM of a Zr-doped BaTiOg powder (Zr/Ti = 0.25) prepared by the double-jet method. (From Ref. 43.) 1275 "^C meets the specifications of Y5V multilayer capacitors. The grain sizes ranged from 1 to 3 (im. Solids with an extremely sharp change in dielectric constant as a function of temperature, which are suitable for application as thermal IR detectors, can be obtained when both Sr and Zr are incorporated as dopants. Figure 12.10 shows a SEM of a Zr-doped BaTi03 powder. Figure 12.11 displays the relative dielectric constant (K) as a function of temperature of Zr-doped BaTiOj powders of different Zr contents; (a) 17%, (b) 20%, and (c) 23% of Ti atoms, sintered at 1275 °C. The peak shift of the maximum dielectric constant to lower temperature. 10000 8000 6000 4000 H 2000

0

50

T (X)

100

150

Fig. 12.11. Relative dielectric constant (K) as a function of temperature of Zr-doped BaTiOg powders of different Zr contents; (a) 17%, (b) 20%, and (c) 23% of Ti atoms, sintered at 1275 °C. (From Ref. 43.)

APPLICATIONS

596

with increasing content of BaZr03, corresponds to the Curie-point shift at which the crystal lattice undergoes a structure change from tetragonal to cubic and exhibits a sharp peak in the dielectric constant. Figure 12.12 is a relation of K V5 T for a BaTi03 powder doubly doped with Zr and Sr, showing a very sharp peak of dielectric constant. This sample was also sintered at 1275 °C. Both BaZr03 and SrTi03 are known as typical Curie point shifters of BaTi03 to control the temperature and the magnitude of the maximum dielectric constant of barium titanate. 40000

30000

K

20000

10000

150

Fig. 12.12. Kvs T for a BaTi03 powder doubly doped with Zr and Sr, sintered at 1275 ^C [(Ba+Sr)/ (Ti+Zr) = 0.996; Sr/Ba = 0.061; ZryTi = 0.184]. (From Ref. 43.)

12.3. Magnetic Recording Materials For understanding the importance of monodispersed particles as magnetic recording media, it seems necessary to have some knowledge on the fimdamentals of the mechanism of magnetism and the effects of particle shape and size. For this purpose, the fundamental aspects of magnetism will be surveyed first. 12.3.1. Fundamentals of Magnetism a) Magnetic Force and Its Unit Systems In the COS system of units, the magnetic force, F, between magnetic poles of respective strengths, nij and m2, separated by r in a vacuum is given by

12. INDUSTRIAL APPLICATIONS

597

F= !!lf!l

(12.3.1)

where the magnitude of pole strength, m, is defined as 1 emu, when m =mj = m2, r = 1 cm, and F = 1 dyne. On the other hand, the corresponding equation in the SI unit system is given by F= —^—^ ,

(12.3.2)

471 l l /

where Mo is a constant to yield F in newton (N), when rtij and m2 are given in weber (Wb), and r in meter (m). Since l/4jt emu cm"^ = 1 gauss = lO""* Wb m"^ or Wb = (l/4n) x 10^ emu as the definition of Wb unit, and since emu^ cm'^ = dyne = 10"^ N, F in N unit for m^ = m2 = 1 Wb and r = 1 m is given from Eq. (12.3.1) as JO^^

(12.3.3)

On the other hand, from Eq. (12.3.2) F=-^N.

(12.3.4)

Comparison between Eqs. (12.3.3) and (12.3.4) yields Mo = 471x10-1

(12.3.5)

If B and H denote the magnetic flux density and magnetic field, respectively, at magnetic pole 2 under the influence of pole 1, Eq. (12.3.2) may be rewritten as F = - ^ - — • m , = B- — • m , = i f - w , , where

(12.3.6)

598

APPLICATIONS

^=_^!L. =A

(12.3.7)

5=-^.

(12.3.8)

and

471 r^

In the SI unit system, A m'^ is used as a unit of the magnetic field, if, instead of the Wb m"^ unit used for the magnetic flux density, B, and the constant \x^ is redefined as a physical quantity with a unit, henry m'^ As a consequence, ^ = 4JI x 10"^ henry m'\ and there are the following relationships among these units: A m"^ = N Wb'"\ Wb m'^ = (henry m"^)(A m-'), and N = (Wb m-^)(m henry-')Wb = (A m-')Wb. If we place a magnetic substance in a magnetic field H (A m"^), where the dimensions of the magnetic substance in all directions perpendicular to the magnetic field are virtually infinite, the magnetic flux density, 5, in the magnetic substance is given by B=n^^+/,

(12.3.9)

where / (Wb m"^) is the magnetization, equivalent to the magnetic moment per unit volume. Magnetic flux density, B in Wb m"^, corresponds to the external magneticfield,H^^ in A m'\ as 5 = Mo^«- Magnetization, / in Wb m'^, corresponds to demagnetizing field, H^ in A m'\ a magnetic field induced by H^ in the direction opposite to H^^, related as / = \Xffld' Hence, H is the effective magnetic field in the magnetic substance, given by H = H^^ - H^, which is an alternative expression to Eq. (12.3.9). In order to characterize a magnetic substance, (x (magnetic permeability), ft (relative permeability), % (magnetic susceptibility), and x (relative susceptibility) are defined as

and

12. INDUSTRIAL APPLICATIONS

X =^ ;

599

X =^ =- ^ -

(12.3.11)

There are the following relationships between x and |i, and between x and fl: |Ji = tio"'X'

ii = l + X-

(12.3.12)

In particular, Ho is called the vacuum permeability according to the definition of magnetic permeability of a magnetic substance, \i (= B/H). Basically, SI units are used in this book unless specified otherwise, but it seems convenient to refer to the relations between the units in SI and CGS systems, in view of many available data of magnetic properties given by CGS units. For example, the equation in the CGS unit system corresponding to Eq. (12.3.9) is B = H^4nI,

(12.3.13)

where the unit of B and 4jt/ is gauss (G), and the unit of H is oersted (Oe), but the magnitudes in gauss and oersted are equal (G = Oe). If 5 = b Wb m"^ H = h A m"\ Mo = KQ henry m"^ (KQ = 4jr X 10'^), and / = z Wb m"^ in Eq. (12.3.9) in the SI system, whilst B =fc'G,H = A'Oe, and 4jt/ = 4jt/'G in Eq. (12.3.13) in the CGS system, it holds from the equality between the absolute magnitudes of the corresponding terms in Eqs. (12.3.9) and (12.3.13) that 6 Wb m-2 = b' G, (KQ henry m'')(h A m'') = h' Oe, and i Wb m"^ = 4m' G, wherefe,h, KQ, Z,fc',A', and V are the dimensionless multipliers of the respective units. Using G = Oe = 10"^ Wb m"^ and Wb = henry A, we obtain b = IQ-^fc', h = 10"^/I7KO, and / = 4jt x 10"^/', so that G = 10-^ Wb m-2 Oe = (1/47C) X 10^ Am"'

(b' = 1, fo = 10"^) (A' = 1, A = IQ-^/KQ)

G' = 4jt X 10-" Wb m-^

(/' = 1, / = 4JCX10^)

where G' represents a gauss unit for magnetization in the CGS system, which is 4jt times greater than the gauss unit G for magnetic flux density, 5, (G = 10"^ Wb m"^). It may also be noted that the emu unit for magnetic moment is equal to emu (for magnetic pole strength) x cm; z.e., emu (magnetic moment) = emu

APPLICATIONS

600

(pole strength) x cm = 4jt x 10"^° Wb m. If we use the emu unit for magnetic moment, then emu cm'^ = G' = 4jr x 10"* Wb m'^ for (volumic) magnetization, corresponding to magnetic moment per unit volume, while emu g'^ = 4jt x 10'^ Wb m kg"^ for mass magnetization, corresponding to magnetic moment per unit mass. In addition, the relative permeability in the SI unit system, pT, is equal to the magnetic permeability in the CGS unit system, while the relative susceptibility % in the SI system is 4jt times the magnetic susceptibility in the CGS system. h) Classification of Magnetisms All substances are more or less magnetized when they are in a strong magnetic field. In this sense, all materials are magnetic substances, but their magnetic properties vary widely according to the characteristics of their Table 12.3. Classification of magnetisms Magnetism Ferromagnetism (X = 10^-10^)

Subgroup Ferromagnetism

Fe, Co, Ni, Gd, Cu2MnAl, MnBi, MnSb, Cr02, CrTe, CrBrg, EuO, EuS

Ferrimagnetism

M^Fe^^'O^, Y-FeA. RgFejOj^, MO-6Fe203, FeTiOj, FeCr204

Parasitic Ferromagnetism

a-Fe203

Metamagnetism Paramagnetism (X = 10-^-10-^)

FeCl2 Paramagnetism

Sc Ti, V, Cr, Pd, Pt, Al, O2, N2O

Antiferromagnetism Diamagnetism

Example

FeO, MnO, MnF2 most other substances

(X = -io-*~io-^) Note: M"Fe2"^04 = spinel-type ferrites (M": divalent metals); R3Fe50i2 = garnettype ferrites (R: ianthanides from Sm to Lu, or Y(III)); MO'6Fe203 = magnetoplumbite-type ferrites (M: Ba, Sr, Pb).

12. INDUSTRIAL APPLICATIONS

601

atomic magnetic moments. They may be classified as in Table 12.3. Ferromagnetism The subgroups of the ferromagnetism family, such as ferromagnetism in a narrow sense,/emmagneri^m, dis\di parasitic ferromagnetism are classified according to the ways of alignment of a material's atomic magnetic moments or spins. Ferromagnetism in a narrow sense is characterized by the alignment of all spins in the same direction in the individual magnetic domains of a crystal. The relative susceptibility, x M very large - in the range of 10^ to 10^. However, % is not constant against the increase of //, but shows a saturation magnetization, /^, and a hysteresis in the magnetization, as shown in Fig. 12.13. Here, H^ is the coercive force or coercivity, which is the reverse magnetic field to return / to zero, and /^ is the residual magnetization or remanent magnetization when H is reduced to zero from a suflFiciently high positive value. The quantities H^, /^, /^, and IJI^ (squareness) are important parameters for characterizing the magnetic properties of ferromagnetics. Above the Curie temperatures they become paramagnetic. Most metals and their alloys of strong magnetism belong to this group. Typical ferromagnetic substances (Curie temperatures) are Fe (1043K), Co (1388K), Ni (627K), Gd (292K), CujMnAl (710K), CrO^ (352K), CrTe (339K), CrBr3 (37K), MnBI (630K), MnSb (587K), EuO (77K), EuS (16.5K), etc. Ferrimagnetism is characterized by the alternate antiparallel alignments of spins of magnetic atoms on different lattice points, A and B, in each r B

/. —:> c

/y

-He

JD 0

E

H

}.

•

H

Fig. 12.13. Hysteresis of magnetization of a ferromagnetic material.

602

APPLICATIONS

crystal unit cell. The strong magnetization is due to the great difference in magnitude of the magnetic moments at the points, A and B. Magnetic properties of ferrimagnetism are almost the same as those proper to the above ferromagnetism. The relative susceptibilities of ferrimagnetic materials are similarly in the range from 10^ to 10^, and they are also widely used as magnetic materials. Typical ferrimagnetic substances are ferrites, including spinel-type ferrites (M"Fe2^°04, M° = divalent metals), garnet-type ferrites (R3Fe50i2, R = lanthanides from Sm to Lu, or Y(III)) and hexagonal magnetoplumbitetype ferrites (MO'6Fe203, M = Ba, Sr, Pb), and compounds other than ferrites, such as ilmenite (FeTIOj), or chromite (FeCr204). Above all, inverse spinel-type ferrites, represented by maghemite (Y-Fe203), cobalt ferrite (CoFe204), and magnetite (Fe304) are important as magnetic recording materials or their precursors. Spinel-type ferrites in general consist of a close-packed cubic lattice of oxygen ions with interstitial cations occupying A and B sites, the former positions being surrounded tetrahedrally by four oxygen ions, the latter by six oxygen ions placed octahedrally. The number of oxygen ions in a unit cell is 32, and there are 8 A-sites and 16 B-sites in a unit cell. For the regular spinel, the 8 A sites are occupied by divalent cations and the 16 B-sites by trivalent cations such as Fe^^; e.g, ZnFe204. For the inverse spinel, the 8 A-sites are occupied by trivalent cations, and the 16 B-sites randomly by 8 divalent cations and 8 trivalent cations; e.g., CuFe204, MgFe204, CoFe204, and Fe304. Although maghemite (Y-Fe203) is a kind of inverse spinel, the 16 B-sites are occupied only by 13Vi Fe^* ions, and the remaining 2% B-sites are vacant. Parasitic ferromagnetism is a very weak magnetism due to equivalent antiparallel spins at A and B lattice sites, but with partly reversed spins at the B sites. A typical example is hematite (a-Fe203). The magnetic behavior is very close to antiferromagnetism to be referred to below. Metamagnetism, Paramagnetism^ and Diamagnetism Metamagnetism, first found in FeCl2 crystals, is characterized by the paramagnetic behavior within a low magnetic field {I ^ H) and a sharp increase in / to a relatively high saturation magnetization when H reaches a certain high level around 2 - 3 x 10^ A m"\ However, in contrast to normal ferromagnetism, no hysteresis is observed. The sharp lift of / is believed to be due to the transient spontaneous magnetization caused by a high magnetic field breaking the antiferromagnetic spin aligiunent.

12. INDUSTRIAL APPLICATIONS

603

Paramagnetism is a very weak magnetism with / in proportion to H (x = 10"^ - 10'^). In most cases, the relation of 1/x to T is a straight line passing through the origin, which suggests that the magnetic spins are randomly oriented by thermal oscillation. Transition metals^ such as So, Ti, V, Cr, Pd, and Pt, and their compounds, aluminum (Al), oxygen (O2), nitrous oxide (N2O), etc. belong to this group. Antiferromagnetism is also a weak magnetism classified into a kind of paramagnetism in a broad sense, but the weak magnetism is due to the almost completely antiparallel alignment of spins at A and B lattice sites. Above a certain transition temperature (the Neel temperature), the alignment becomes random by thermal oscillation. With elevation of temperature, 1/x is lowered and turns to increase linearly above the Neel temperature, while normal paramagnetic substances show only a linear increase of 1/x with increasing temperature from 0 K. Typical antiferromagnetic substances are FeO, MnO, and MnF2. Diamagnetism is also a very weak magnetism of negative x whose absolute value is of the order of 10'^ or less, owing to Larmor's precession of electronic orbitals of the atoms. A majority of all substances, including most gases, metals, salts, and organic compounds, belong to this category. Practically, only the ferromagnetic and ferrimagnetic substances are used as magnetic materials. According to conventional usage, we hereafter call them simply, "ferromagnetic substances," without distinction between them, unless it is required. c) Size Effects of Ferromagnetic Particles If we place a ferromagnetic solid in a magnetic field, H, the magnetization is dependent on the shape of the solid and the direction of the principal axes of the anisotropic form relative to the magnetic field. If the demagnetizing factor in the direction of the magnetic field, H, is denoted by A^, the magnetic flux density, B, is generally given by B=\i^^NI, where / is the magnetization. obtains

(12.3.14)

From H - H^^ - H^ and B = m/^^^, one

H.^N—.

(12.3.15)

If N^, Ny, and N^ denote the demagnetizing factors of the solid in the

APPLICATIONS

604

directions of the tliree principal axes nonnal to each other, it generally holds that (12.3.16)

N^^N^^N^^h

If the length in the direction of jc axis is virtually infinite as compared to the others, then A^^ = 0 because the distance between the negative and positive poles is infinitely large. Hence, if the magnetic material is a plate with its flat plane peq^endicular to the magnetic field in the direction of the x axis, then A^ = 1, corresponding to Eq. (12.3.9), because N = N^=^ 1 and Ny = N^ = 0. If the plate is set with its flat plane parallel to the direction of the magnetic field, or if a rod-like material is set with its principal axis parallel to the magnetic field, then A^ = 0 in both cases, because N =^ N^ = Ny = 0 and N^ = I in the former case, and N = N^ =^ 0 and Ny = N^ = 1/2 in the latter. Similarly, N = 1/2 when the magnetic field is perpendicular to the principal axis of a rod, and A^ = 1/3 when the solid is a sphere. If a magnetic solid is a prolate spheroid with a half length, a, and a half width 6, the demagnetizing factors along the polar axis, N^ is given by N^

1

a

a^-1

^M

ln(a+ya^-l)-l

(12.3.17a)

where a = a/b. For an oblate spheroid with a half length of the polar axis a and equatorial radius fe.

P^

-sm ^ 2 (P2.1)3/2-

(12.3.17b) p

p2.i

where p = fc/a. Since A^^ + 2Nf, = 1 in both cases, A^^, for a prolate spheroid and N^ for a oblate spheroid can be calculated as well. In the CGS unit system, each A^ value is 47C times the corresponding A^ value in the SI unit system; e.g., N^ -^ Ny -¥ N^ = 4jt, and H^ = NL In the absence of external magnetic field, a large ferromagnetic crystal with uniaxial magnetocrystalline anisotropy such as cobalt is divided into many magnetic domains separated by parallel domain walls. The spins in a magnetic domain are oriented in the same direction, but the directions in adjacent domains are opposite, to minimize the magnetostatic energy. If we

12. INDUSTRIAL APPLICATIONS

605

consider a single-domain prolate spheroid with uniaxial magnetocrystalline anisotropy along the polar axis in the absence of external magnetic field, the magnetic field, //, is only the demagnetizing field of its own, so that H=-—L,

(12.3.18)

Hence, if the volume of the single-domain particle is denoted by v, its magnetic energy is only the magnetostatic energy of the particle, U^, given by r2

(12.3.19)

U=-1HIV^!^V.

"

2 ^ 2|io

If the particle is a sphere {N = 1/3), t/=-£-u. m

(12-3.20)

6^0

If the spherical particle is changed into a double-domain particle with two magnetic domains of magnetic moments antiparallel to each other, the magnetostatic energy is reduced to a half of the original, but a domain wall energy with a specific waU energy, y, is generated (y = 1 ~ 5 mJ m'^)."*^ Hence, if the effect of the thickness of the domain wall is neglected for simplicity, the critical radius, r^, at which the magnetic energies of a single domain particle and a double domain particle are equal is given from

Ur^^'wlH as

rK ' cJ

(12.3.21)

606

APPLICATIONS

9|io

rr-^yIs

(12.3.22)

The relative weight of the domain wall energy in the total magnetic energy increases with size reduction of a magnetic particle, because the waU energy is proportional to r^, while the magnetostatic energy is proportional to r^. Hence, the particle initially consisting of many magnetic domains reduces the total area of the domain wall with decreasing particle size, and finally it is switched to a single domain particle with no domain wall at a certain critical radius, as given by Eq. (12.3.22), in order to minimize the total magnetic energy. This treatment was applied to platelet-type particles as well with uniaxial magnetocrystalline anisotropy."*^ In the case of a ferromagnetic particle of a cubic crystal with easy directions for magnetization in the principal axes of the cubic crystal such as iron, the magnetic spins may be arrayed in a squire flux closure with triangular domains or rectangular flux closure with triangular and trapezoidal domains. Although the magnetostatic energy is zero in this domain structure due to the internal flux closure, the domain wall energy and magnetocrystalline anisotropy energy are present, so that there is also a critical size for transition to a single-domain particle."*^ If the magnetocrystaUine anisotropy is small in a multidomain particle, the domain structure may be represented by ring-shaped domains in which the spins are arrayed in a circular configuration, so that there is no magnetostatic energy due to the internal flux closure without poles. However, the total of the exchange energies between adjacent spins in each ring per unit volume increases with size reduction, since the exchange energy between adjacent spins in a circular flux increases with increasing curvature of the circularflux.'^^'*'''*^Hence there is also a critical size for transition from the circular domain structure to a single domain one with parallel spin alignment."*^ However, as the single domain particle becomes still smaller to a particle volume level at which the magnetic energy is close to the thermal energy, kT, the atomic magnetic moments start to be randomly oriented. In this size range, the particles are readily magnetized to the saturation magnetization with a relatively weak magnetic field, but show no hysteresis in the magnetization curves, and thus the coercive force is zero. This characteristic magnetism is called superparamagnetism. As a consequence, the coercive

607

12. INDUSTRIAL APPLICATIONS

Multidomain

o U

Particle Volume Fig. 12.14. Coercivity as a function of the mean volume of ferromagnetic particles. force, //^, has a peak around r^ for transition to a single domain particle and it declines with size reduction until, finally, the particle becomes superparamagnetic {H^ = 0), as shown in Fig. 12.14.^° The critical diameter for transition of particles of isotropic shape from multidomain to single domain is of the order of 10 to 100 nm,"*^ while the size range of superparamagnetic particles is ca. 10 nm or less.^^ According to the theoretical calculation on the basis of the circular multidomain model, the critical particle volume of transition from a multidomain particle to a single-domain particle increases with increasing aspect ratio of elongated ellipsoidal particles (aspect ratio = ratio of length to width)."*^'"*^ Figure 12.15 shows the critical length (= 2a) between multidomain and single-domain structures, as a function of the bla ratio, for ellipsoidal particles of maghemite (Y-Fe203) and magnetite (Fe304), calculated by Morrish and Yu'*^ Here a and fe denote the half length and equatorial radius of an ellipsoid, respectively. Obviously, the critical length for ellipsoidal particles of magnetite greatly increases with increasing aspect ratio. For maghemite the critical size is somewhat larger. Moreover, the critical size increases significantly with increasing particle density, owing to the reduction of the magnetostatic energy in each particle, caused by magnetic interaction among the particles.^^ It is also known that the critical size drastically decreases as the degree of orientation of ellipsoids is

608

APPLICATIONS

Fig. 12.15. The critical singledomain length (= 2«) as a function of the bla ratio for ellipsoidal particles of maghemite (7-^6203) and magnetite (FcgO^). (From Ref. 49.)

lowered .^^" The single-domain particles of relatively large coercive force are used for magnetic recording materials, while much smaller superparamagnetic particles with no hysteresis in magnetization are mainly used for magnetic fluids, etc. d) Effects of the Magnetic Anisotropics The magnetic properties of ferromagnetic single domain particles depend strongly on their magnetic anisotropics. For example, if they have no magnetic anisotropy, they may behave like superparamagnetic particles which show neither hysteresis nor coercive force in their magnetization curves. Hence significant magnetic anisotropy is required for ferromagnetic particles used for recording media. Major magnetic anisotropics are shape anisotropy, magnetocrystalline anisotropy, and strain anisotropy."^^ Shape Anisotropy Let us consider a particularly important particle as an magnetic recording element, an ellipsoidal single-domain particle, whose aspect ratio a/b (a = half-length of polar axis, b = equatorial radius) ranges from 0 to 00. Figure 12.16 shows a prolate spheroid {a/b > 1) in a magnetic field, H, with its

12. INDUSTRIAL APPLICATIONS

609

^H

Fig. 12.16. A prolate spheroid {alh > 1) in a magnetic field, //, with its polar axis tilted by 9 from the positive direction of H. The angle between the directions of the saturation magnetization, 7^, and the polar axis of the particle and that between /^ and H are al; and (|), respectively. (From Ref. 48.)

polar axis tilted by 6 from the positive direction of H. The angle between the directions of the saturation magnetization, 7^, and the polar axis of the particle and that between 7^ and 77 are \p and cj), respectively."*^ There is the following relationship between them: <|) = e-M|f.

(12.3.23)

For a general ellipsoid, the shape-anisotropy energy per unit volume associated with the demagnetizing field is

' (N^al^N/^^N/;).

(12.3.24)

''-2H where cx^, tty, a^ are the direction cosines of 7^ with respect to the principal axes, and N^, Ny, N^ are the demagnetizing factor along the principal axes, where JV^ + A^^ + iV^ = 1 (see Eq. (12.3.16)). In addition, the energy per unit volume due to the applied field is Ejj= -ffl^coscj).

(12.3.25)

Using N^ = A^^, Ny^N^= N^, a^ = cos \|), a^ = sin \p, and a^ = 0, E^ and the variable part of the total energy £ (= JE^ + E^) may be written as (12.3.26)

and

610

APPLICATIONS

E=Ksm^-HIcos<^,

(12.3.27)

where NrN.

A:=--^—^//.

(12.3.28)

2^0

When the ellipsoid is a prolate spheroid {a > b\ N^ > N^ and K^ > 0. K^ is a magnetic anisotropy constant representing the magnitude of the shape anisotropy. Using \p = (]) - 6, and treating /^ and 6 as fixed, cj) values which give the minima, inflection points, and maxima of E^ are obtained fi-om BE - ^ = ^,sin2( = 0

a<|)

(12.3.29)

At the minima, inflection points, and maxima of E^, the following d^Eld^^ values are positive, zero, and negative, respectively: — = 2^^cos2(<|)-e)+/f/^cos(|). d(|)

(12.3.30)

As H is changed from +» to -oo via zero along the H axis at a constant 6, (|) may increase from zero to reach 6 when / / = 0, and then jump from an angle greater than 6 to an angle between 180"" and (180° + 6) when H reaches a certain negative value, as readily expected from Eq. (12.3.29). Finally, ^ may return to 180° with further increase of H in the negative direction. The jump of cj) occurs when H reaches a certain negative value at which the branch of the energy minimum is united with that of an energy maximum to form an inflexion point, and E is allowed to go down to another energy minimum branch located at ^ between 180° and 180° + 6 at the same H, Figure 12.17 shows the relations between h (= HIJ2K^) as a dimensionless magnetic field and cos (j) (=//4) as a dimensionless magnetization, at different 6 values (in degrees). In the case of an oblate spheroid (a < h) in Fig. 12.18, E is also given by Eq. (12.3.27), but ^ , < 0 since N^ < A^^. As H is changed from +« to 00 via zero along the H axis, ^ changes from zero to reach (6 - 90°) (< 0°) when / / = 0, and then the magnetization vector, /,, rotates around the polar axis on the equatorial plane to make (j) = 6 + 90° with a slight increase of

611

12. INDUSTRIAL APPLICATIONS

1

1

-L

0 .

1

.

1

I 1

[

1

1

1

^^^=^'' _

45

-

-

/ /io /io

0,10,90

1

1

^.''cos ^0 ,

1

1

L

7/ /

\

J A

AS

\ 45.JL^

-j

^y//

V

10 0

L ,,.

1 0,10.90

'

10

\cosf5o y COS (j>

1

0

_____^ f

i

l

l

1 ,1

Fig. 12.17. The relationships between a dimensionless magnetic field, h (= HIJTK^, and a dimensionless magnetization, cos (j) (^I/Qy for a prolate spheroid at different 0 values on the curves (in degrees). The dotted curves give cos ^Q and cos ct)'o, where ^Q and (|)'o are the angles made with the positive field direction by the magnetization vector at the beginning and the end of the discontinuous change at the critical value, /IQ, of the field. (From Ref. 48.)

^H

Fig. 12.18. An oblate spheroid (a/b < 1) in a magnetic field, H.

H in the negative direction, since no additional energy is required for this rotation of the /, vector. Finally, the /, vector turns toward the negative direction of H with increasing ^ to 180°. Hence, cos ^ plumnniets from a positive value to a negative value of the same absolute magnitude at / / = 0, so that the magnetization curves show no hysteresis and thus no coercive force.

APPLICATIONS

612

If we consider an assembly of similar spheroids with their polar axes oriented at random in a magnetic field, //, the mean resolved value of cos (|) in the positive field direction of the magnetization is given by X ^H r^/2 COS(|)= — = / (cossin6J6,

(12.3.31)

where I„ is the mean resolved value oil, in the field direction. Figure 12.19 shows mean values of cos (|) as a function of h (= HIJIK^) for prolate spheroids (solid lines) and oblate spheroids (broken lines) at random orientation, as obtainedfi-omthe numerical integration of Eq. (12.3.31) using (j) as a function of 0 in Eqs. (12.3.29) and (12.3.30) at each h. As has been predicted for a single oblate spheroid, the mean value of cos ^ for an assembly of randomly oriented oblate spheroids falls from a positive value to a negative value of the same absolute magnitude at A = 0 and thus the coercive force H^ = 0.

cos ^

Fig. 12.19. Mean values of cos (j) as a function of h (= HIJIK^) for prolate spheroids (solid lines) and oblate spheroids (broken lines) at random orientation. (From Ref. 48.)

For an assembly of prolate spheroids at random orientation,"*^

12. INDUSTRIAL APPLICATIONS

613

Coercive force:

H = 0.479 — ^ — ^ 1^0

Initial susceptibility:

2V.0

[dHL

Residual magnetiz0ion:

3(N,-N)

/^= —/^

Magnetocrystalline Anisotropy Magnetocrystalline anisotropy energy is an excess magnetic energy due to orientation of the magnetization vector away from the easy crystal axes for magnetization. The magnetocrystalline anisotropy energy, E^, for uniaxial anisotropy, apart from constant terms, is given by E^ = K^,sm^^ -^ JS:^sin>,

(12.3.32)

where xj) is the angle between the direction of magnetization and the primary axis of symmetry of the anisometric crystal .^^ If K^^ + K^2 > 0, E^ is minimum at ip = 0°. If X„^ ^K^2<^^ ^c is minimum at ij) = 90°. \fK^iK^2 < 0 and (-KJ2K^2y^ < 1, £, is minimum at \p between 0° and 90° or between 90° and 180°. As a typical ferromagnetic material of uniaxial anisotropy, the hexagonal crystal of cobalt has K^j = 4.3 x 10^ J m'^ and K^2 = 1.2 X 10^ J m'^.^^ As an example of magnetic materials with K^^j + ^2^ < 0 having easy magnetization directions in a plane of \|)= 90°, the so-called ferroxplana such as Ba3Co2Fe2404i is known.^^ Also, some ferroxplanas are known to have easy magnetization directions in a conical plane of \p ?« 0°, 90°. The magnetocrystalline anisotropy energy for cubic crystals with isometric principal axes x, y, and z is given, apart from constant terms, by £, = ^ i ( a ' a ^ a ' a ^ a^a^)+^2«^a;a',

(12.3.33)

where ot^, a^, a^ are direction cosines of /^ with respect to the cubic axes.^^ For the <100> directions of a-iron (body-centered cubic crystal), Kj = 4.2 X 10"* J m"^ and K2 = 1.5 x 10"* J m'"'.^^ In this case, the easiest direction

614

APPLICATIONS

for magnetization are the <100> axes, including [100], [010], and [001]. The most difficult magnetization directions are <111>, and the intermediate ones are <110>. For the <100> directions of nickel (face-centered cubic crystal), K^ = -5.1 x 10^ J m"^ and iC^ " 0 J ^'^^^ Hence, for nickel, the [100], [010], and [001] axes are the difficult magnetization directions, while the <111> axes are the easiest directions. On the other hand, representative magnetic oxides, maghemite (Y-Fe203) and magnetite (FejOJ, of inverse spinel stmcture in the cubic crystal group have negative magnetocrystalline anisotropy constants such as K^ = -4.64 X 10^ J m-^ for Y-FePs and K^ = -1.10 x 10^ J m"^ for YtfiJ^'' and thus their easiest magnetization directions are collinear with the body diagonals or <111> axes. If the magnetocrystalline energy of uniaxial anisotropy in Eq. (12.3.32) is approximated by £^ = A:„sin^i|;,

(12.3.34)

the variable part of the total energy of a spherical single-domain particle with magnetocrystalline anisotropy in a magnetic field, //, is written in a manner similar to Eq. (12.3.27) as E^K^sm^

'HIfos^,

(12.3.35)

where (j) is the angle between the directions of H and 7^. Hence, E in Eq. (12.3.35) for magnetocrystalline anisotropy can be related in the same way as that in Eq. (12.3.27) for shape anisotropy. If an ellipsoidal particle has a uniaxial magnetocrystalline anisotropy as well, with easy directions of magnetization along the polar axis or on the equatorial plane, the variable part of the total energy may be written as £:=^sin^i|r-^/^cos<j),

(12.3.36)

K^K^^K^.

(12.3.37)

where

Strain Anisotropy For a single-domain spherical particle of negligible magnetocrystalline

12. INDUSTRIAL APPLICATIONS

615

anisotropy, and isotropic in respect of the saturation magnetization coefficient, X, subject to uniform tension, a, the dependence of the magneto-strain energy on the angle, \|), between 4 2uid a is given apart from constant terms by^^ E =A:sin^i|r,

(12.3.38)

where K^lxa. ^ 2

(12.3.39)

If K^ is substituted for K^ in Eq. (12.3.27), then £ = i:^sin^t|f-ff/^cos
(12.3.40)

and thus the result obtained for shape anisotropy can be applied to strain anisotropy. If "k and a are of the same sign (e.g., nickel under compression and iron under tension), the magnetic characteristics are similar to those of a single domain prolate spheroid. If X. and a are of opposite sign, the magnetic characteristics are similar to those of an oblate spheroid. 12.3.2. Relations between the Magnetic Anisotropies and Coercive Force a) Shape Anisotropy If we neglect the contribution of the magnetocrystalline anisotropy for randomly oriented prolate spheroids with aspect ratio a/b « », then A^^ - N^ = 1/2 and thus, if we assume the Stoner-Wohlfarth modeU^^ the coercive force H^ for various magnetic materials can be calculated from H^ = 0A79(N^'N,)IJ[iQ = 1.906 x 10' /, (A m'^). For example, Fe: /, = 2.154 Wb m"^ (1714 emu cm"^); H, « 4.1 x 10' A m"' (-- 5200 Co: 4 = 1.787 Wb m'^ (1422 emu cm"^); //, - 3.4 x 10' A m"' {^ 4300 Ni: /, = 0.608 Wb m'^ ( 484 emu cm''); H, « 1.2 x 10' A m'^ (-- 1500 Y-FejOj: /, = 0.52 Wb m-\414 emu cm"^); //, « 1.0 x 10' A m-X^1200

Oe) Oe) Oe) Oe)

If these acicular particles are uniformly oriented in the direction of the magnetic field, H, is given by H^ = IJ2\i^ = 3.98 x 10' /^ (A m"^), which is greater than H^ at random orientation by a factor of 2.09 (= 1/0.479).

616

APPLICATIONS

Moreover, even if we assume a much smaller aspect ratio such as 10 or 5, the reduction of (iV^ - N^) is rather small; e,g., N^ - N^ = 0.470 for a/b = 10; and N^, - N, = 0.416 for a/b = 5. b) Magnetocrystalline Anisotropy The coercive force of an assembly of randomly oriented single domain spheres with uniaxial magnetocrystalline anisotropy may be calculated from A=///y2/^=0.479;i.e., fl^ =

0.958^, -^

For example, if we assume spherical single-domain particles of hexagonal cobalt and barium ferrite (BaO •6Fe203), their H^ values at random orientation may be calculated as Co:

4 = 1.787 Wb m'^ (1422 emu cm"^) i „ = 4.3 X 10^ J m~^ (4.3 x 10^ erg cm'^) H^ « 2.3 X 10^ A m"' (^ 2900 Oe)

BaO-6Fe203:

/, = 0.45 Wb m'^ (358 emu cm"^) K^ = 3.3 X 10' Jm"' (3.3 x 10' erg cm"^) 7/, « 7.0 X 10' A m-' (^ 8800 Oe)

If thin platelet-type particles of barium sulfate are coated parallel to the substrate film, the coercive force due to the crystalline anisotropy in the direction perpendicular to the flat basal planes may be estimated as H^ « 1.5 X 10' A m"^ (- 18000 Oe) from /i = 1 and thus from //, = IKJI^, In this case, the contribution of shape anisotropy to the coercive force is about H^ = -3.6 X 10' A m-^ (~ - 4500 Oe) from H^ = (N^-N,)IJ\IQ with iV^, = 0 and A^, « 1. Hence, totally, H, - 1.1 x 10' A m"^ (- 14000 Oe). For the treatment of cubic crystals, we must use Eq. (12.3.33), in place of Eq. (12.3.32) for uniaxial crystalline anisotropy, and the coercive force, i/^, is equal to oKJI^ with a depending on the direction, but having a maximum value of 2.^^ This allows us to estimate the maximum coercive forces of cubic crystals due to crystalline anisotropy. For example,

12. INDUSTRIAL APPLICATIONS

617

Fe(^c)max = 2x4.2x10^/2.15 « 3.9 x 10' A m"' (~ 490 Oe) Ni: (^c)max = 2x5.1x10^/0.61 « 1.7 x 10' A m"^ (^ 210 Oe) Y-Fe^Gj: (i/J^,, = 2x4.6x10^/0.52 « 1.8 x 10' A m"^ (~ 220 Oe) The coercive forces, due to crystalline anisotropy, for randomly oriented particles would be considerably less. c) Strain Anisotropy If we assume a high pressure, 2 x 10^ kg m"^ (= 1.96 x 10^ J m"^), to estimate the maximum coercive forces due to strain anisotropy from h = 2KJHJ^ = 3ka/HJ, = 1, they may be calculated as'^ Fe: Ni: Co:

X = 1.8 X 10-^ /, = 2.15 Wb m'^ //, = 4.9 x 10' A m"' (- 620 Oe) X = -3.3 X 10-^ /, = 0.61 Wb m'^ if, = 3.2 x 10" A m"' (- 4000 Oe) X = -0.4 -- -2.0 x 10^^ depending on direction, /, = 1.8 Wb m"^; H^ = 1.3 ~ 6.5 X 10' A m-^ (160 ~ 820 Oe) depending on the direction.

d) Some Reductive Factors for Coercive Force The observed coercive forces of acicular particles of Fe, Co, and yFe203, mainly due to shape anisotropy, are nomGially in the following ranges. Fe: H, « 3.2 x 10' ~ 1.4 x 10^ A m"' (400 - 1800 Oe) Co: H, « 3.2 X 10' ~ 8.0 x 10' A m"' (400 - 1000 Oe) Y-Fe^Gj: H, « 1.6 x 10' ~ 3.6 x 10' A m"' (200 ~ 450 Oe) Obviously, the experimental coercive forces are much smaller than the theoretical ones, particularly for those based on shape anisotropy. This is mainly because the above Stoner-Wohlfarth model is based on the assumption of only coherent rotation of atomic magnetic moments in the reversal of magnetization, and because the effect of the magnetic interaction among particles is disregarded in the theory. Also, the significant size dependence of the coercive force is inexplicable by this model. Hence, in addition to the coherent rotation, another uniform reversal mode of spins, fanning (chain-of-spheres asymmetric fanning), and non-uniform reversal modes, such as curling and buckling, have been proposed.^'"^^ In the latter two non-uniform reversal modes, H^ is dependent on particle radius, as proportional to r'^ for curling, and to r"~^ for buckling, when crystalline anisotropy can be ignored. The dominant reversal mode out of these is

618

APPLICATIONS

different according to size ranges. Although the reversal modes other than coherent rotation are useful to some extent for explaining the low coercive forces and their size dependence, the actual coercive forces are still lower. One of the other major reasons for the rather small coercive forces may be the magnetic interaction in an assembly of magnetic particles, mainly observed in the coercivity due to shape anisotropy. As pointed out by Neel,^^ a linear reduction in the coercive force, H^, with increasing powder density, d, is usually observed for single domain particles whose coercive force is governed by shape anisotropy. This is a characteristic of the coercive force due to shape anisotropy, in contrast to the coercivity by magnetocrystalline anisotropy, showing almost no dependence on particle density."^^"^^ Figure 12.20 displays some examples of H^, depending on d/dg (d = powder density in binder; d^ = density of the bulk material), for acicular y-Fe203 and FCjO^ (1 jmi in mean length; 7 ~ 8 in aspect ratio) and cuboidal Fe304 (1.5 ^mi in mean diameter), where the acicular Y-Fe203 and Fe304 are thought to be single domain particles, while the cuboidal Fe304 particles are likely to be multidomain ones from the theoretical calculation of Morrish and Yu,"*^ shown in Fig. 12.15. The intercepts at 1 d/dg = 0 in Fig. 12.20 may correspond to H^ values due only to crystalline anisotropy.

9^\J y \

^ ' .—. 240 CO o

^/

a O hi

/A

••>* -^^

y

/

tan

/

y

/

,

/

o Ui

>

A

/

-^-3-1

bi O

"

80

0 0

.2

.6

.8

(l-i)

LO

Fig. 12.20. Dependence of H^ on dldg (d = powder density in binder; dg = density of the bulk material), for acicular y-F^Os and ¥^^0^ (1 \xm in mean length; 7 ~ 8 in aspect ratio) and cuboidal Fe304 (1.5 \im in mean diameter). (From Ref. 49.)

12. INDUSTRIAL APPLICATIONS

619

12.3.3. Magnetic Particles Used for Recording Media It is now obvious that the size and shape are decisive factors for the fundamental properties of a given ferromagnetic particulate material used for recording media. Hence narrow distributions in size and shape are strongly desired for these materials. In addition, a properly high coercivity, large saturation magnetization, high dispersibility, high chemical stability, sufficient mechanical strength, etc. are also required.^^ As magnetic materials used for recording media in audio and video systems, computer memory systems, magnetic cards, etc., maghemite (Y-Fe203), cobaltmodified maghemite, iron, chromium dioxide, and barium ferrite are well known. Except for barium ferrite, almost all of them are used in the form of acicular particles in order to achieve a high coercive force by shape anisotropy, because of their relatively low magnetocrystalline anisotropy. Barium ferrite, as a hexagonal crystal, having a strong uniaxial crystalline anisotropy in the direction perpendicular to the c-faces is used in the form of small platelets of ca. 0.08 \Jim in diameter with flat basal planes of cfaces. a) Maghemite Elongated maghemite (Y-Fe203) articles 0.2-0.5 \im in length and ca, 10 in aspect ratio are manufactured mainly from acicular goethite (a-FeOOH) particles without changing the original shape of a-FeOOH in a sequential process of hydration from a-FeOOH to a-Fe203 at ca. 300 °C, reduction from a-Fe203 to Fe304 with hydrogen gas at 300 - 400 °C, and oxidation from Fe304 to Y-Fe203 at ca, 250 °C.^'^^ For the precipitation of a-FeOOH precisely controlled in size and aspect ratio, ferrous hydroxide precipitated from a solution of ferrous salt, such as ferrous sulfate or ferrous chloride, with alkali is oxidatively converted into a-FeOOH seeds with air, which are then grown further to a desired size and aspect ratio. In order to keep the original shape of a-FeOOH, the surfaces of a-FeOOH are treated with silica^^ or phosphate^^ prior to the thermal treatment. It is also possible to produce elongated Y-Fe203 by reduction-reoxidation of ellipsoidal a-Fe203 prepared from Fe(0H)3 ^" *he presence of organic phosphonates^"* or forced hydrolysis of ferric ions in a dilute ferric chloride solution (- 0.02 mol dm" ^) in the presence of inorganic phosphates.^^ The Y--Fe203 thus-obtained has an advantage of being pore-free over Y-Fe203 particles prepared from a FeOOH, since it is difficult to completely remove pores generated during the dehydration process of a-FeOOH. Amdt^^ prepared tin-doped Y-Fe203 particles from ellipsoidal a-Fe203, obtained by thermal transformation from

620

APPLICATIONS

Fe(0H)3, to improve the magnetic properties of Y-Fe203. b) Cobalt-Modified Maghemite Cobalt ferrite of inverse spinel structure, which can form solid solutions with y"Fe203 and Fe304 in the same crystal system, has a magnetocrystalline anisotropy constant X^ = 2 x 10^ J m"^, much higher than K^ = -4.64 x 10^ J m"^ for Y-Fe203 and K^ = -1.10 x 10^ J m"^ for Fe304, by a factor of 10 or more in absolute value. However, Co-doped Y~F^203 of a high coercivity prepared on the basis of this nature of cobalt ferrite^^ was not stable enough in magnetic properties such as magnetization and coercive force, against the change of temperature and pressure.^^**^^ This problem has been resolved by depositing CoO and FeO solely onto the surfaces of acicular Y-Fe203 particles, through adsorption of Co^^ and Fe^^ ions followed by addition of an alkaline solution^^*^*"^° or by growing CoFe204 on the surfaces of Y-Fe203 particles.^^*^^ These procedures for surface modification yielded magnetic particles of a high coercive force of ca. 4.5 x 10"* A m'^ (- 570 Oe), with a high thermal stability and small demagnetization with repeated playback, comparable to stable pure Y-Fe203, whose maximum coercive force achieved by now is, however, practically ca, 3.6 x 10"* A m"^ ir- 450 Oe). c) Iron Pure a-Fe has a saturation magnetization as high as 2.74 x 10"^ Wb m kg'^ (= 218 emu g"^) at room temperature, so it is an ideal material for high density recording systems and is actually widely used. Iron powder is normally manufactured from acicular particles of goethite (a-FeOOH) by dehydration and subsequent gas-phase reduction with hydrogen without extensive change of the original shape.^*^"* In order to prevent the sintering of the iron powder during the thermal treatments, the starting material, a FeOOH, is pretreated with silicone oil, silver or cobalt compounds, silica, or alumina.^^'^^ Also, for preventing corrosion of the iron powder, the surfaces are carefully oxidized to form a thin but dense oxide layer.^^'^^ Although the saturation magnetization of thus-prepared iron powders is reduced to ca. 60 - 70 % of that of pure iron, a high coercive force such as 1.2 X 10^ A m'^ (- 1500 Oe) or more can readily be attained. One of the key aspects of this technology may be the achievement of a high resistivity to oxidative corrosion. d) Chromium Dioxide

12. INDUSTRIAL APPLICATIONS

621

Cr02 is an artificial compound of strong ferromagnetism developed by the Du Pont Company in 1961. The acicular single-crystal particles of Cr02 (tetragonal crystals) is prepared by a dissolution-reciystaUization process from CrOg at a high pressure and high temperature in the presence of Sb203 or RUO2 as a catalyst, and a small amount of water.^^ Since it is easy to achieve a high coercivity, such as 4.0 ~ 6.4 x 10"* A m"^ (500 - 800 Oe) with Cr02 particles, they were widely used as high-quality magnetic material.^^ However, as magnetic media with cobalt-modified Y-Fe203 have prevailed, Cr02 appears to be less used, probably because of some disadvantages such as somewhat low thermal stability in coercivity and in residual magnetization, due to the relatively low Curie temperature around 386 K, high production cost, etc. e) Barium Ferrite Barium ferrite (BaO*6Fe203) belongs to the hexagonal magnetoplumbite-type ferrites with the easy direction for magnetization coUinear with the c-axis perpendicular to the flat basal plane. It has widely been used for permanent magnets because of its high coercive force such as 3.2 - 4.8 X 10^ A m"^ (4000 ~ 6000 Oe) due to the high magnetocrystalline anisotropy. Although the coercive force was too high for ordinary recording materials, it attracted special attention because of its potentiality as a highdensity recording material proper to a perpendicular recording system with the platelet-type particles coated parallel to substrate films.^^ Since it is possible to reduce the coercive force of barium ferrite to a proper level by partly substituting the Fe^^ ions with Co'^ and Ti'^^^^'^^ Kubo et al}^^^ prepared platelet-type barium ferrite particles of mean diameter 80 nm and thickness 20 nm with H^ = 7.2 x 10"* A m"^ (~ 900 Oe) and saturation magnetization a^ = 6.9 x 10'^ Wb m kg'^ (~ 55 emu g"^), using a newly developed glass crystallization method, in which the constituents of barium ferrite were heated to above 1300 °C to be dissolved in a melt of a glass forming substance such as B2O3, quenched to be fixed in the glass matrix, and reheated above 700 °C to form crystals of barium ferrite. Finally, the solid matrix was removed with weak acid. Ba-ferrite-coated tapes demonstrated a recording density higher than a tape of Co-modified maghemite and even higher than a Fe-coated tape in a wavelength range shorter than 1 \xm}^ Platelet-type particles of barium ferrite can also be prepared by coprecipitation followed by calcination above 850 °c,^^'^^ hydrothermal synthesis,^^'^^ the sol-gel process followed by calcination,^" coprecipitation

622

APPLICATIONS

in W/0 microemulsions followed by calcination,^^ the stearic acid gel method,^ etc. As it is difficult to coat the magnetic platelets so as to be oriented completely parallel to the film base like acicular particles, it has been proposed to prepare acicular polycrystalline barium ferrite particles, each of which consists of small barium ferrite subcrystals arrayed along its long axis, with each c-axis of the subcrystals perpendicular to the long axis.^^*^ The polycrystalline acicular barium ferrite particles were obtained by adding NaHC03 to a BaCl2 solution containing acicular a-FeOOH particles to deposit BaCOj onto the a-FeOOH particles, and subsequent calcination at 780 - 840 °C with a small amount of either B2O3, P2O3, or 31363 after washing the precipitate with water and drying. During the thermal treatment, Ba^^ ions diffused into the acicular a-FeOOH particles to convert them into the polycrystalline acicular barium ferrite particles of the unique structure.^^ Although the saturation magnetization turned out to be ca, 4.0 X 10'^ Wb m kg"^ (~ 32 emu g"^), corresponding to ca. 60 % of the saturation magnetization of ordinary platelet-type barium ferrite, it is noteworthy as a new approach of interest. The magnetic properties of the main ferromagnetic particles are summarized in Table 12.4.^^'^^'^^ Besides the above materials, iron nitride (mainly Fe4N), prepared by reducing dehydrated goethite particles in the presence of ammonia,^^ is known for its high saturation magnetization and high coercivity, comparable to iron. However, it does not appear to be used practically as a recording medium, at present, because of some problems in magnetic stability. Acicular magnetic particles are dispersed in a polymer solution and coated on a film base. The wet coating is then passed through an oriented magnetic field to align the coated particles with their polar axis in the running direction of the film base, dried, and calendered to smooth the surface. 12.3.4. Monodispersed Particles for Magnetic Recording Media Strict control of the size and shape of a given magnetic material is of vital importance for recording media, since its magnetic properties are mostly determined by the size and shape of the individual particles. Hence, monodispersed particles with a sharp distribution in size and shape are the ideal materials. In this case, there may be two different roles for monodispersed magnetic particles.

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The first is their role as ideal models for fundamental studies on definite relations between the moq)hological, dimensional, and structural characteristics and the magnetic properties. These data may be compared directly to the theoretical predictions. For example, Ozaki and Matijevic^^ obtained uniform ellipsoidal particles of y-FCjOj through a reduction-reoxidation process of uniform a-Fe203 of the same shape prepared by forced hydrolysis of dilute FeCl3 solutions in the presence of phosphate ions. The coercive force increases with reducing particle size and increasing aspect ratio in this size range, as expected from theories.'*^''*^'^^ While one may need more systematic data for concluding the optimum size and shape of maghemite particles as a recording material, the highest coercive forces are observed when the particle length is less than ca, 0.4 |xm with the aspect ratio of 5 - 6, and thus the upper size limit of single-domain particles is somewhat smaller than the theoretical prediction, ~ 0.9 |xm at the aspect ratio of 5, suggested by Morrish and Yu."*^ Also, while studies on the mechanisms of the reversal of magnetization of individual particles, in comparison with the theoretical models, are in progress,^^"^^^ monodispersed particles are expected to be useful for such experiments. For example, isolated uniform ellipsoidal particles of y-FcjOj converted directly from a Fe203 of the same shape were found by Lorenz microscopy to have a much higher coercive force of about 9.5 x 10"* A m"^ (~ 1200 Oe) for Y-Fe203 than in their close assembly.^°° The other role of monodispersed magnetic particles is, of course, to be actually used as the most advanced magnetic materials in the future. In fact, though we cannot produce uniform particles in condensed systems by using the conventional forced hydrolysis of metal salts, it is possible to produce monodisperse a-Fe203 particles systematicaUy controlled in size, shape, and internal structure, in large quantities, by use of the recently developed gelsol technique }^^ Studies on the systematic control of monodispersed yFcjOj particles and relevant magnetic particles, converted from precisely controlled a-Fe203 prepared by the gel-sol method, are now in progress, as partly presented earlier.^^^"^^ Such a systematic approach may lead us to the final conclusion on the ideal shape, size, and internal structure of the magnetic recording materials. Figure 12.21 shows some typical TEM images of uniform ellipsoidal maghemite of different sizes at a constant aspect ratio, converted from the corresponding hematite particles prepared by the gel-sol method from a solid precursor, p-FeOOH, containing phosphate ions in the interior of each particle.^^^ Figure 12.22 shows the relationships between the volume of a maghemite particle with different

12. INDUSTRIAL APPLICATIONS

625

0.2|im

Fig. 12.21. TEMs of monodispersed ellipsoids of maghemite (Y-Fe203) systematically controlled in size and shape. (From Ref. 104.)

aspect ratios and the coercive force. This result suggests that the maximum coercive force is located at a particle volume in the range of 7 x 10"^ - 1 X 10"^ ptm^, irrespective of the aspect ratio, and that the upper limit of the aspect ratio that gives the maximum coercive force is close to seven. If the aspect ratio is 5, the length of the principal axis giving the maximum coercive force is ca, 0.36 [im, which is close to a result of Ozaki and Matijevic,^ who found a maximum coercivity with ellipsoidal particles of ca. 0.4 \xm long with aspect ratios 5 - 6 . Meanwhile, the particle volume giving the peak of coercivity corresponds to the critical particle volume between the single-domain and multi-domain particles, which is expected to increase significantly with increasing aspect ratio according to the

APPLICATIONS

626 450 Aspect ratio = 7

400

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350

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100 50 h

1x10"^

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Particle volume (^m^) Fig. 12.22. Relationships between the volume of amaghemite particle with different aspect ratios and coercivity (powder density in the gelatin binder = 2.26 g cm"^). (From Ref. 104.)

theoretical calculation based on the circular multidomain model (see Fig. 12.15).'^^ However, the above experimental results may imply that the actual dependence of the critical particle volume on the aspect ratio is, at least, much smaller than the theoretical prediction, while it is true that the critical size is a rather complex function not only of the aspect ratio, but also of the particle density and particle orientation. On the other hand, maghemite particles converted from nearly monocrystalline hematite particles are superior to those from polyorystalline hematite in coercivity. This fact may imply that the original crystal imperfections are retained in the final product, although XRD analysis revealed that the final particles, even if originated from monocrystalline hematite particles, became polycrystalline maghemite without changing their external shape during the reduction-reoxidation

12. INDUSTRIAL APPLICATIONS

627

Table 12.5. Magnetic properties of monodispersed y-FejOj particles controlled systematically in mean particle volume and aspect ratio Particle Length (^m)

Particle ^ Volume (^m )

1.0 1.0 1.0 1.0 1.0 1.0

0.03 0.05 0.08 0.11 0.14 0.20

2.70X10-^ 1.25X10"^ 5.12X10-^ 1.33X10"^ 2.74X10-^ 8.00X10-^

126 133 143 140 134 126

0.35 0.36 0.34 0.36 0.38 0.36

2.5 2.4 2.4 2.0 2.1 2.0

0.04 0.09 0.16 0.20 0.24 0.32

7.46X10-^ 5.56X10-^ 3.12X10'* 8.95X10-* 1.40X10-^ 3.67X10-^

195 225 256 204 174 131

0.39 0.47 0.54 0.51 0.50 0.49

2.7 2.9 2.7 2.6

0.10 0.18 0.22 0.29

6.71X10*^ 3.10X10-* 6.35X10r* 1.61X10"^

255 285 301 232

0.58 0.61 0.62 0.61

3.9 3.9 3.8 3.9 4.0

0.16 0.20 0.29 0.36 0.52

1.11X10-* 2.18X10"* 6.81X10* 1.32X10-^ 3.63X10*^

285 301 338 308 230

0.61 0.64 0.71 0.68 0.69

5.2 4.9 5.1 5.0 5.1 5.3 5.2

0.11 0.20 0.23 0.36 0.43 0.54 0.62

2.08X10'^ 1.41X10-* 1.98X10-* 7.91X10^ 1.29Xia^ 2.37X10-^ 3.73X10-^

275 305 325 379 322 236 236

0.58 0.65 0.68 0.71 0.69 0.67 0.68

5.8 5.9 6.0 5.8

0.15 0.26 0.36 0.46

4.24X10-^ 2.13X10-* 5.47X1 a* 1.22X10-^

290 347 392 312

0.62 0.69 0.72 0.69

6.7 6.9 6.8 6.8 6.8

0.24 0.36 0.42 0.52 0.68

1.30X10-* 4.13X10-* 6.75X10-* 1.28X10-^ 2.87X10-^

355 412 344 276 239

0.67 0.73 0.71 0.69 0.70

Aspect Ratio

Coercivity (Oe)

Squareness

628

APPLICATIONS

process. Main magnetic properties of these maghemite particles are summarized in Table 12.5. In response to the growing potential demand for much higher recording density and signal/noise ratio, the finer particles of excellent inherent properties, with sharp distributions in size and dimensional ratio, are required.

12A Catalysts One of the most important applications of ultrafine metal particles may be their use as catalysts, indispensable for selective and efficient production of intermediates or final products in the chemical industry. The properties of metal catalysts depend strongly on their particle size. There seems to be three main reasons for this: (1) Effect of specific surface area With increase m specific surface area (surface area per unit weight), the catalytic activity per unit weight generally increases. The increase in catalytic activity with size reduction down to ca, 10 nm or less is mainly due to this effect. (2) Effect of active sites With a reduction of particle size the relative proportion of active sites, such as comers and edges, per unit area of the metal particles increases, so that much higher catalytic activity or a highly selective reactions may be expected, particularly in a size range below 10 nm. (3) Quantum size effect As the particle size becomes less than 5 nm, the continuous electronic band structure of a metal starts to be separated into discrete energy levels of the molecular orbitals of a cluster consisting of a finite number of metal atoms (the quantum size effect).^°^ In this size range, the original properties of the bulk metal are lost, and it is not rare to find some new functions as the metal clusters become significant. Metal catalysts are used in the form of well dispersed particles in liquids or on some supports, and thus they may be classified into two categories. One is the dispersed catalysts in liquids, and the other is the supported catalysts on solids or solvated polymers.

12. INDUSTRIAL APPLICATIONS

629

12.4.1. Preparation and Uses of Metal Catalysts a) Dispersed Catalysts Condensation in Gas Phases When a metal is evaporated by heating with an electric resistance heater, plasma heater, high-frequency inductive heater, electronic beam heater, or arc heater in inert gases such as He, Ar, or Xe at pressures of 0.01 to a few hundred Torr, the evaporated metal atoms are condensed as ultrafine metal particles in the gas phase by collision with the inert gas molecules. They are collected in organic solvents or trapped in a frozen organic medium. For example, ultrafine metal particles of Be, Mg, Al, V, Cr, Mn, Fe, Co, Ni, Fe-Ni, Fe-Co, Cu, Zn, Ga, Se, Ag, Cd, In, Sn, Te, Au, Pb, Bi, etc. have been prepared by this method.^°^ In pure inert gases, they are mostly single-crystal particles with characteristic shapes. The mean size depends strongly on the kind of inert gas and the gas pressure. Figure 12.23 shows the relationships between the mean diameter of Al or Cu particles generated by condensation in gas phases and the pressure of an inert gas, such as He, Ar, or Xe.^°^ Obviously, the mean diameter diminishes in the order Xe, Ar, and He, and is proportional to the cube-root of the gas pressure, irrespective of the kind of the inert gases. In order to obtain particles with a relatively narrow size distribution, the temperature of the molten metal for evaporation

200

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20

50

100

200

PRESSURE [torr]

Fig. 12.23. Relationships between the mean diameter of Al or Cu particles generated by condensation in gas phases and the pressure of an inert gas, such as He, Ar, or Xe. (From Ref. 107.)

630

APPLICATIONS

must be kept constant. The mean diameter ranges from 10 to 200 nm. Similarly, it is possible to deposit metal atoms or clusters in a frozen trap of organic solvent from a gas phase, and obtain metal particles suspended in the solvent matrix by melting the frozen solvent. The mean size of the particles, ranging from a few nm to 1500 nm, depends on the kind of solvent and the degree of dilution.^°^ Thus-obtained Ni particles showed highly selective activity in the hydrogenation of 1,3-cyclooctadiene to cyclooctene^^^ and in the dehydrogenation of 2-propanol to acetone^^^ Ultrafine composite particles, consisting of Cu hosts of 15 to 45 nm with still smaller ZnO guests of 2 to 3 nm on each Cu host, were obtained by mild oxidation of bimetallic particles of Cu-Zn deposited from an inert gas phase, and showed almost the same activity and selectivity in the synthesis of methanol from CO and H2 as catalysts prepared by the conventional coprecipitation method.^^^ Precipitation in Liquid Phases A wide variety of metal catalysts are prepared in liquid phases, because it is rather easy to realize conditions for the preparation and stabilization of fairly uniform nanoparticles in liquid media. For example, metal particles of ca. 15 imi or less can be obtained readily by heating metal salts in an organic solvent such as tetrahydrofiiran with metallic potassium as a reducing agent.^^^ However, metal particles are normally lyophobic, and thus it is often necessary to use some protective colloid to stabilize them in liquid media. In aqueous solutions, hydrophilic polymers, such as poly(N-vinyl-2pyrrolidone) (PVP), polyvinyl alcohol (PVA), polyacrylamide, or polyacrylic acid, are used widely as protective colloids in the forms of their homopolymers or copolymers. Cationic surfactants such as dodecyltrimethylammonium chloride (DTAC), or tetradecylpyridinium bromide, anionic surfactants such as sodium dodecylsulfate (SDS), or sodium dodecylsulfonate, amphoteric surfactants such as N-dodecyl-N,N-dimethylbetaine, or N tetradecyl-2-aminopropionic acid, and nonionic surfactants such as hexaoxyethylene dodecyl ether orpolyoxyethylene(20) sorbitan monolaurate, are also used as anticoagulants. Metal ions are normally reduced in the presence of one of these protective agents. For reduction of metal ions, hydrogen gas, sodium borohydride (NaBHJ, citric acid, or alcohol, are used. In particular, when alcohol is used as a mild reducing agent in the presence of PVP or PVA, small and fairly uniform noble metal particles, such as Pd,

12. INDUSTRIAL APPLICATIONS

631

Rh, Pt, Ir, or Os, of mean diameter ranging from 1 to 6 nm, can be obtained.^^^ Also, irradiation with visible light plus ultraviolet rays^^"^ for Pt^*, with ultraviolet rays^^^'^^^ for Ag% Au^, or Rh^*, or with y-rays^^'^^'^^^ for Ir^* or Pt"** is useful for reduction of these metal ions to produce the corresponding still smaller particles. SpecificaUy, y-rays can be used for the preparation of base metal particles as well, such as Co, Ni, Zn, Pb, or Cu-Pb alloys.^^^ It is known that y-rays can generate solvated electrons as a reducing agent of metal ions through ionization of solvent molecules. If we apply NaBH^ to iron, cobalt, or nickel ions, the respective ultrafine metal boride particles are obtained.^^ Platinum particles of ca. 2 nm prepared in a solution of DTAC by irradiation with UV-VIS light from a super-high-pressure mercury lamp showed a much higher activity than those prepared by reduction with alcohol or hydrogen gas in hydrogenation of vinyl acetate, ^^"^ Dispersed Rh particles have specially high activity for the hydrogenation of olefins, so they selectively hydrogenate only the double bond of olefins when other kinds of double bonds, such as aromatic, carbonyl or nitro groups, or C-C triple bonds coexist with an aliphatic double bond in a compound.^^^ This is in contrast to Rh metal particles supported by active carbon which hydrogenate not only olefins but also a large proportion of other kinds of double bonds.^^ Dispersed Rh particles of very small size, such as 1 nm or less, are particularly effective in the hydrogenation of inner aliphatic double bonds rather than terminal ones, while this is normally difficult for supported Rh particles or large dispersed particles, owing to the steric hindrance.^^ NijB particles dispersed in liquid are also active in the hydrogenation of olefins, but are particularly effective in the hydrogenation of terminal methylenes.^^ For example, D-limonene and a-methylstyrene are hydrogenated only at their isopropenyl group by NiB catalyst. Pd particles of mean diameter 2.5 nm, prepared by reduction of palladium chloride with alcohol in a solution of polyvinylpyrrolidone (PVP), hydrogenate only one C-C double bond of the two double bonds of cyclopentadiene, 1,3-cyclooctadiene, or 1,5-cyclooctadiene, while commercially available Pd/active carbon catalysts catalyze the total hydrogenation of these dienes at the same time.^^ Bimetallic nanoparticles of Pd-Pt and Pd-Au, prepared in a similar manner, showed higher catalytic activity than pure Pd particles in the selective hydrogenation of cyclic dienes.^^'^^^ The selective hydrogenation of cyclic dienes can be achieved also with Ni particles prepared by deposition from inert gas phases.^^^ Pd

632

APPLICATIONS

particles dispersed in PVP solution are also active in selective hydrogenation of one double bond of two in a linoleic acid molecule,^^ and those suspended in PVA or gum Arabic solution were found to be active in the hydrogenation of the nitro group, with no effect on aromatic and carbonyl double bonds and carbon-halogen bonds, in nitrobenzene, halogenated nitrobenzene, and nitroacetophenone.^^^ Ir particles suspended in PVA or gum Arabic solution have a similar selective activity in the hydrogenation of nitro groups.^^^ Cu particles of ca, 10 nm suspended in PVP, PVA, or dextrin solution can be used as a catalyst to hydogenate only the cyano group of unsaturated nitriles, such as acrylonitrile and methacrylonitiile, without forming ethylene cyanohydrin.^^° b) Supported Catalysts Although the uniformly dispersed catalysts have the general advantages of high efficiency in catalytic reactions owing to the free diffusion of the catalyst particles and the prompt dispersion of the reaction heat and products, there are some difficulties in handling for repeated use and in the complete prevention of coagulation during reaction and recovery of catalysts. Also, they are unsuitable as catalysts for gas-phase reactions. Hence, many catalysts are used practically with some appropriate supports or carriers. In some cases, the carriers play a decisive role in the catalytic reaction in consort with the metallic parts. A great variety of methods are known for fixing metal particles on solid supports, such as silica, alumina, silica/alumina, hematite, titania, zirconia, active carbon, or zeolite. For instance, metal atoms or clusters deposited in a frozen solvent at 77 K from a gas phase can be transferred uniformly onto oxide supports.^^^'^^^ Also, metal ions are fixed on the extemal and/or internal surfaces of solids, by soaking the solids in solutions of the metal salts, and then reduced by some reducing agents.^^^ In this case, if organometallic compounds are in contact with solid supports from gas or liquid phases and fixed on the supports by heat treatment for reduction or oxidation, we often obtain fairly uniform metal or metal oxide nanoparticles for catalysts.^^ It is also possible to fix highly dispersed metal particles on an oxide support by coprecipitation of hydroxides of different metal ions for catalyst and support in an alkaline range, followed by dehydration and heat treatment with hydrogen gas for reduction of the metal ions. However, in the preparation of gold catalysts supported on oxides such as a-FejOj (hematite), C03O4, or NiO, Au particles of less than 10 nm

12. INDUSTRIAL APPLICATIONS

633

of fairly narrow size distribution can be obtained only by heating a dried mixed precipitate of auric and ferric hydroxides at ca, 400 °C in air.^^^ Ueno et al prepared highly dispersed ultrafine Ni on Si02^^^*^"^'^^ and Co on TiOj^^^^^^ by hydrolyzing Si- or Ti-alkoxides with Ni(N03)2 or Co(N03)2 in ethylene glycol at 80 °C, followed by calcination in air and then in hydrogen atmosphere. The formation processes were probed through EXAFS spectroscopy.^^^^^^'^^^ In the preparation of photocatalysts such as Pt/TiOj, ultrafine Pt particles can be deposited on TiOj particles by UVirradiation to a Ti02 sol containing H2PtCl6, in which Pt(IV) ions are reduced by photoelectrons to Pt nanoparticles on the surfaces of Ti02 particles.^^^ In place of these inorganic solids, one may use polymer gels^^^ or ion-exchange resins^^^*^'*^ as supports. Instead of direct support of metal particles by polymer matrices, one may indirectly fix metal particles to support polymers by forming complexes or chemical bondings between support polymers and protective polymers holding metal particles.^"*^"^"*^ Rh-Fe,'^^'^ Rh by pyrolysis of Rh carbonyl clusters,'^^^ Rh-Zr,'^^" RhZr-Mn^'*^'' catalysts supported on SiOj, ZrOj, TiOj, etc. are used for production of C2H5OH from CO and H2 in the gas phase. Similarly, we use Rh-Mn,^"'^ Rh-Mn-Na,'"'" Rh-Mn-Mg,^"'^ and Rh-V-Li^'^' on Si02 for production of CH3CHO, and Rh-MgClj^^^ on SiOj for production of CH3COOH fi:om CO and H2. Rhodium on oxide supports is used as a catalyst for reduction of NO^ in the exhausts of automobiles.^^^ On the other hand, Rh particles fixed on hydrophilic polyacrylamide gel showed relatively high activity in the hydrogenation of olefins with hydrophilic groups. Particularly, the activity of the resin-supported Rh catalyst was much higher than dispersed Rh catalysts for hydrogenation of olefins with carboxyl groups, such as acrylic acid and 3-butenoic acid, having a strong affinity to the amino groups of the polymer gel.^"*^ The catalytic activity was kept almost constant even after repeated use and recovery. Resin-supported Pd catalyst particles of 1 - 6 nm in diameter showed a high activity in the selective hydrogenation of cyclooctadiene to cyclooctene, like dispersed Pd particles.^^ RU/AI2O3 catalyst shows an especially high activity in the FischerTropsch synthesis for formation of CH4 from CO and H2, while most transition metals have more or less activity in this reaction.^^^ In addition, Fe, Ni, and Co on AljGj,^^^ and Ni on T\0^^^ and on c-FejN^^^ are wellknown catalysts for the same purpose. Also, Ni/SiOj catalyst prepared from nickel ethylene glycoxide and tetraethyl silicate by the sol-gel procedure showed a highly selective activity

634

APPLICATIONS

in the hydrogenation of propionaldehyde to l-propanol with drastically lowered probability of decarbonylation, when the mean diameter was less than 5 nm.^^^(^)'^^^ Cii/oxide is used as a catalyst for the formation of H2 from CH3OH and Ag/oxide is used for the oxidation and dehydrogenation of CH3OH to produce HCHO when methanol is in excess, while MoOj-FCjOj/oxide catalyst is used when oxygen is in excess.^^^ Au nanoparticles of less than 10 nm on oxides such as a-FCjOj were found to be specifically active in the oxidation of CO.^^^ The specific activity of Au/a-Fe203 catalyst for oxidation of CO was explained in terms of the acceleration of the oxidation of CO on a-Fe203, whose rate-limiting step is the adsorption process of CO, by the Au parts acting as adsorption sites for CO. Co/SiOj catalyst, prepared by deposition of Co clusters with solvent vapor and subsequent contact with Si02 supports, is used as a catalyst for the hydrogenation of 1-butene. The activity was found to be raised about 100 times by the addition of a small amount of Mn, probably due to the zero-valent cobalt clusters highly dispersed by the presence of Mn, as revealed by EXAFS analysis.^^^^^'^"> Pt catalysts supported on nylon were found to be powerful in the hydrogenation of benzene solely to cyclohexane.^^^ Pt catalysts supported on polymers through covalent bondings with protective colloids were proved to have a few tens-of-times higher activity than conventional Pt catalysts supported on active carbon in the hydrogenation of olefins, such as cyclohexene and ethyl vinyl ether.^"*^ Pt/AljOs catalysts are also used for the oxidation of CO and paraffins. The composition of the exhausts of automobiles is normally controlled to be nearly in stoichiometric balance between gases to be oxidized (hydrocarbons, CO, and H^ and oxidizing gases (O2 and NO^^), so that we can minimize hydrocarbons, CO and NO,^ using some catalysts to promote the reactions between the reactive gases, such as a triple catalyst consisting of Pt, Pd, and a small amount of Rh on AI2O3. Both Pd and Pt particles are useful for oxidation of hydrocarbons and CO, but Pd is particularly effective in the oxidation of CO, olefins, and methane, while Pt oxidizes more efficiently paraffins of C3 or higher. There is almost no difference between Pd and Pt in activity for the oxidation of aromatic hydrocarbons.^^^'^^^ A smaU amount of Rh is indispensable for reducing NO^.^"*^ Pt/TiOjCa)^^ and Pt/RuGj/TiOjCa)^^^ are known as typical catalysts for

635

12. INDUSTRIAL APPLICATIONS

the photolysis of water, where (a) indicates anatase-type Ti02 particles. The Pt parts of the composite particles of Pt/Ti02 may play the role of active sites for electron transfer from the conduction bands of the Ti02 particles to protons. A high quantum yield such as 30 % has been reported for a system of Pt/Ru02/Ti02(a) in a HCl solution of pH 1.5.^^^ The photocatalysts are also useful for the photolysis of water and alcohols, such as CH3OH, C2H5OH, n-C^HjOH, /-C3H7OH, and AZ-QH^OH, to produce H2 and CO2, where the reactivities of these alcohols are in this order.^^^ In the photolysis of alcohol with H2O, it is not difficult to attain a quantum yield of 40 % or higher.'^^ 12.4.2. Size Effects According to the definition of the turnover frequency (TOP) as the number of reacted molecules per unit number of surface metal atoms and unit time, metal catalysts may be classified into the following four groups: (1) stmcture-insensitive catalysts of a TOP constant with change of particle size; (2) structure-sensitive catalysts of TOP decreasing with increasing particle size; (3) those of TOP increasing with increasing particle size; (4) those of a maximum TOP at some particle size, as illustrated in Pig. 1224}^ Even if the TOP is constant with the change of the size of metal

\ \

\

\

/

/

^^ / \

\

y

/ \

(JU.

0 H

/

/

\ 4 \

\

\

\

"1 / y 1 / / /

\

-3 *»«-* •v^

-1 - 2

Size

Fig. 12.24. Typical four patterns in TOP changing as a function of particle size. (Prom Ref. 164 (c).)

636

APPLICATIONS

particles, the specific surface area of the metal particles, or the surface area per unit weight, is inversely proportional to the mean particle diameter, so that the activity of a catalyst per unit weight is always more or less dependent upon the particle size. Also, it is not rare to find size-dependent selectivity in catalytic reactions. In this sense, the strict control of a mean size and a sharp size distribution are strongly desired for a given catalytic material. a) Size Control of Metal Particles Although the size distributions of most nanoparticles of metal catalysts are not sharp enough to clear the criterion of monodisperse particles - that the coefficient of variation of the size distribution must be 10 % at the most - strenuous efforts have continued to approach the utmost level. As referred to eariier, rather mild reduction conditions are adequate for producing fairiy uniform metal nanoparticles with mean diameters of 6 nm or less; e.g,, reduction of metal ions by alcohols^^^ or still milder reduction by irradiation with UV-rays^^^'^^^ or y-rays^^"^'^^^, in the presence of protective colloids such as PVP, PVA, or DTAC. The mild conditions and the use of protective colloids are in accord with the general requirements for the formation of uniform particles; z.e., (1) complete separation between the nucleation and growth stages, and (2) the inhibition of coagulation during the growth stage. Occlusion of metal ions in a rather rigid gel-matrix of silicon hydroxide by the sol-gel procedure and subsequent reduction with hydrogen in the dried gel,^^^ or uniform dispersion of metal particles on the surface of a metal oxide support at a relatively low temperature on melting a frozen organic solvent such as «-hexane containing metal clusters previously trapped from a gas phase at 77 K,^^^'^^^ are also known as methods giving well dispersed and relatively uniform catalyst particles. Coagulative growth is minimized in both cases. It is also possible to control particle size using the interaction of metal ions or complexes with the surface of the support. For example, it is hardly necessary to say that the mean size of metal particles on a support generaUy becomes smaller with increasing specific surface area of the support when the metal particles are formed by gas-phase reduction of metal ions impregnated in a dry support powder.^^ Moreover, if the surface charge of a support is negative over a wide range of pH, as with silica, one may be able to deposit a positive complex of metal ions more uniformly than a negative one, and thus minimize the agglomeration of metal ions during calcination in air prior to the reduction with hydrogen. For example,

12. INDUSTRIAL APPLICATIONS

637

Dorling et al}^^ obtained significantly smaller Pt particles on silica gel, when they used Pt(NH3)/^ complex in place of PtCl/", to be adsorbed to the silica gel support in the first process. On the other hand, if we use porous supports of different but definite pore sizes, such as many kinds of zeolite, we will be able to control the size of metal particles formed in the pores according to the pore size and the total surface area of the support, including the interiors. For instance, if we use Y-type zeolite as a template for the formation of Pt particles, then Pt agglomerates of less than 1 nm are formed in the supercages, owing to the limitation of the size of the supercages, while Pt crystallites of 1.5 to 2.0 nm are formed on the external surfaces of the zeolite.^^^ b) Size Effects on the Electronic States of Metal Particles As the size of a metal particle is reduced, the ionization potential, electron affinity, Fermi level, polarizability, magnetic susceptibility, etc. are changed, reflecting the change of the electronic structure from the bulk metal. From the extended Hiickel- and CNDO molecular orbital calculations for Agn clusters, it has been shown that the energy levels of the LUMO (lowest unoccupied molecular orbital) and HOMO (highest occupied molecular orbital) vary in a zigzag manner with cluster size, indicating that clusters with even numbers of atoms have greater ionization potentials than those with odd numbers of atoms, as illustrated in Fig. 12.25a.^^^ The sawtooth behavior, or the odd-even effect, can actually be observed in the experiment of Kr^ sputtering on Ag metal.^^^ The calculated energy gap between the HOMO and LUMO of Ag clusters decreases gradually with increasing cluster size, as shown in Fig. 12.25b.^^^ The odd-even effect is due to the presence of two electrons in the HOMO for Ag clusters with even numbers of atoms and an unpaired electron in the HOMO for clusters of odd numbers of atoms. Hence, the odd-even effect is observed for Na^ clusters as well,^^° but not for Pd clusters consisting of atoms with two valence electrons. If photoelectrons are ejected from inner shells, the positive holes generated are screened by neighboring electrons in a large metal particle. However, this extra-atomic effect is not fully effective in a small metal cluster owing to the discrete molecular orbitals, and thus the binding energy of the inner-sheU electrons of the latter is greater than that of a bulk metal.^^^ For example. Table 12.6 shows the effect of particle size on the binding energy of the 4fj^ level of Au particles on amorphous carbon.

638

APPLICATIONS

a

s

d

Stoles

Stotes

Number of otoms

Fig. 12.25. (a) HOMO and LUMO of Ag as a function of cluster size; (b) Energy gap between HOMO and LUMO of Ag as a function of cluster size. (From Ref. 168.) relative to that of the bulk metal, from X-ray photoelectron spectroscopy (XPS).^^^ The kinetic energy of the conesponding Auger electrons is hence reduced with reducing particle size.^"^ If electron transfer from metal particles to the support occurs, the binding energy of the valence electrons of the metal particles is also expected to increase. Figure 12.26 shows X-ray photoelectron spectra of the 4f-

639

12. INDUSTRIAL APPLICATIONS

Table 12.6. Effect of particle size on the binding energy of the XPS Ai-^,^ level of Au particles on amorphous carbon relative to that of the bulk metal {Source: Ref. 172) Sample

Coverage (10*' atoms/cm^)

Average Area Diameter

Width of Area Distribution

(A)

(A)

0

4f7^ Level Shift (eV)

A

0.45

15

8

+ 0.7

B

1.1

25

15

+ 0.2

C

3.5

60

30

+ 0.2

D

5.1

100

45

+ 0.12

(o)

^^-"

•••w

••~.^_^__^ j "

(b)

*-.

[.....„>•.• '

'

-

-

:

'

-

•

•

'^^^^•'•'-^•--—A-1

4-

1

1

75

73

71

Binding energy (eV)

Fig. 12.26. XPS of the 4f-electrons of Pt foil (a) and Pt/Si02 (b). (From Ref. 173.) electrons of Pt foil and Pt nanoparticles (1.2 - 2.0 nm) on SiOj.'^^ The 1.5 eV higher binding energy of Pt on Si02 than of Pt foil was elucidated in terms of the electron transfer from Pt to Si02. Figure 12.27 shows ultraviolet photoelectron spectra (UPS) of Pd nanoparticles of various sizes on Si02.^^'* We can detect the spectrum proper to discrete Pd atoms at ca. 2.9 eV below the Fermi level, when the surface density of Pd atoms reaches the level of 0.3 x 10^^ cm"^ (b). The characteristic spectrum of Pd metal around 2 to 3 eV becomes detectable from ca, 2.0 X 10^^ cm"^ {ca, 2 - 3 nm) (d), and becomes almost the same as that of the bulk metal at 14.0 x 10^^ cm"^ (h). This figure may suggest that the metallic properties of paUadium become significant as the size exceeds ca, 2 - 3 nm.

640

APPLICATIONS

- 1 — I — I — I — r

5 ^ 3 2 1 Ep Energy below Ep (eV)

Fig. 12.27. UPS of Pd nanoparticles of various sizes on Si02 in terms of the number of Pd atoms per cm': (a) 0, (b) 0.3, (c) 0.7, (d) 2.0, (e) 3.3, (f) 6.8, (g) 9.8, (h) 14.0 X 10^^ (From Ref. 174.)

Greegor and Lytle^^^ inferred the shapes and sizes of metal particles of less than 2 nm on different oxide supports from EXAFS data on the average coordination numbers of the metal atoms, around 7 - 10 - considerably smaller than the value 12 for closely packed atoms, as shown in Table 12.7. The low coordination number, corresponding to a large number of unsaturated surface atoms, is directly relevant to the catalytic activity of these particles. As has been described above, there are two types of Pt particles on the Y-type zeolite; Le,, agglomerates of less than 1 nm and crystallites of 1.5 - 2 nm. It is known that the IR stretching absorption of NO molecules adsorbed to the Pt agglomerates is at 1828 cm~\ while that adsorbed to Pt crystallites is at 1825 cm'\ suggesting a cationic nature of the small agglomerates owing to electron transfer from the agglomerates to the zeolite support. When electron transfer from the small Pt agglomerates to the Jtorbitals of NO is reduced due to the lowered electron density in the agglomerates, the frequency of the IR stretching absorption of NO generally becomes higher.^^^ The increasing frequency of IR absorption with

641

12. INDUSTRIAL APPLICATIONS

Table 12.7. Shapes and sizes of metal particles on Si02 or AI2O3 supports, estimated from EXAFS data on their coordination numbers and mean diameters (Source: Ref. 175) Catalyst

Average radius of Metal Particles (A) Disks (minihedra)

Os on Si02 Ru on Si02 Cu on Si02 Pt on Si02^ Pt on Al203^ IT on Si02 IT on AI2O3

Cubes (minihedra)

Spheres (maxhedra)

7 ± 2 (6)"

7±3 5±2

6±2 5±2

14 ± 7 (18)" 19 ± 5 5±2 4±3 6±2 6±3

T h e values in parentheses indicate weighted average sizes taken from electron microscopy. ^ The Shape trend is uncertain and may indicate distribution of shapes.

2 3 Diameter (nm) Fig. 12.28. IR spectra of NO molecules adsorbed to Pt particles on alumina. (From Ref. 167.)

642

APPLICATIONS

decreasing particle size is also observed in NO molecules adsorbed to Pt particles on AljOa,^^^ as shown in Fig. 12.28. These results may suggest that NO molecules can be used as a probe of the electronic state of metal catalysts. c) Size Effects on Activity and Selectivity

TERRACE MONATOMIC STEP STEP-ADATOM

TERRACE VACANCY

Fig. 12.29. Schematic model of a heterogeneous solid surface. (From Ref. 176.) Somoqai^^^'^^^ showed, using single crystals of Pt with surfaces of different lattice indices, that the activity of Pt for hydrogenation of hydrocarbons associated with the scission of C-C bonds was proportional to the number of kinks, or steps, of crystal surfaces of Pt (see Fig. 12.29), while the activity for dehydrogenation associated only with scission of C~H bonds was independent of the number of kinks or steps. Since the kinks and steps may correspond to the comers and edges of small particles, hydrogenation with scission of C-C bonds or dehydrogenation with cyclization is expected to be enhanced with decreasing size of metal catalysts, owing to the dramatic increase in the fractions of comer atoms and edge atoms on the surfaces, as illustrated in Fig. 12.30,^^^ while dehydrogenation or hydrogenation without scission or formation of C-C bonds is independent of particle size in many cases. On the other hand, since sufficiently large metal particles consisting of an ample number of metal atoms are required for dissociation of some adsorbed molecules such as C=0 and N=N, the activity of catalysts in terms of TOF (tumover frequency) is generally lowered with reducing particle size in the hydrogenolysis of these triple bonds for ammonia and FischerTropsch syntheses with Ni or Fe catalysts.^^^^ Catalytic activity is often reduced, when the particle size is so small that the metaUic properties are

12. INDUSTRIAL APPLICATIONS

643

i ;

20

25

Fig. 12.30. The numbers of comer atoms (€4^'^°), edge atoms (Cj^, and plane atoms (Cg^) of an octahedral metal cluster, relative to the total surface atoms, as a function of the dimensionless cluster diameter, d^^i (= diameter of a sphere of the same volume relative to the atomic volume). (From Ref. 178.)

lost by electron transfer to the support, or when the space for a dynamic process of large molecules on a metal cluster is too small. Typical examples of the four groups of catalytic reactions in Fig. 12.24 are as follows. (1) Reactions of a Constant TOP with Size Change Oxidation of Hj to H p with Ft/Si02'^^'^ Hydrogenation of ethylene to ethane with Pt/Al203^^^ Hydrogenation of benzene to cyclohexane with Pt/Al20

179

Dehydrogenation of cyclohexane to benzene with Pt/Al20

180

Hydrogenation of methylcyclopentane to n-hexane with Pt/Al203^^^ (2) Reactions of an Increasing TOF with Size Reduction Hydrogenation of ethane to methane with Ni/Si02-Al203^^^

644

APPLICATIONS Hydrogenation of pentane to CH4, €2^^ and CjHg with Rh/Al203^^^ Dehydrocyclization of n-heptane to toluene with Pt/Al203^^ Hydrogenation of propionaldehyde to 1-propanol with Ni/Si02^^ 185 Isomerization of2-methylpentane to 3-methylpentane withPt/Al20 L2v^3

(3) Reactions of a Decreasing TOF with Size Reduction Oxidation of CO with Pt/Si02^^^ Synthesis of CH4 from CO and H2 with Ni/Si02^^^ Synthesis of C^H^ from CO and H2 with Ru/Al203^^^ or Co/Al203^^^ Synthesis of C2H5OH from CO and H2 with Rh/Si02^^° Synthesis of NH3 from N2 and H2 with Fe/MgO^^^ (4) Reactions of a Maximum TOF with Size Change Isotope exchange between H2 and D2 with Pd/C, Pd/Si02 (1.3 nm)^^Hydrogenation of benzene to cyclohexane with Rh/Si02 (1.8 nm)^^^ Hydrogenation of benzene to cyclohexane with Ni/Si02 (1.2 nm)^^"* Here, the figures in parentheses for the reactions in group (4) indicate the sizes at the respective maximum activities. The size-dependent catalytic activity leads to a size-dependent catalytic selectivity. For example, the decarbonylation of propionaldehyde with the Ni/SiOj catalyst is dramatically suppressed, and 1-propanol is produced selectively when the size of the Ni becomes less than 5.0 nm.^^ This has been explained by the high activity of Ni atoms at the comers and edges for hydrogenation of aldehydes. Further, it is known that cyclization and structural isomerization become. predominant in the hydrogenolysis of whexane with an ultrathin membrane Pt catalyst, when the size of the Pt

12. INDUSTRIAL APPLICATIONS

645

crystallites becomes less than 2 nm. This is also believed to be a consequence of the specific action of the comer atoms and edge atoms of Pt crystallites.^^"^ 12.4.3. The Roles of the Support Supports for ultrafine metal catalysts may have been employed originally to permit the use of unstable and elusive nanoparticles repeatedly in a well dispersed state. However, the roles of supports for heterogeneous catalysts are not limited only to these basic aspects, but they also play decisive roles in the dramatic expansion of the versatile functions of catalysts. For example, they act as controllers of mean size and size distribution of metal crystallites in their preparation, stabilizers of the metal particles, adsorption media in catalytic reaction, electronic-state controllers, cooperating catalysts, etc. a) Controller of the Mean Size and Size Distribution of Metal Particles The factors of supports, responsible for controlling the mean size and size distribution of metal particles, may be summarized as follows. (1) Effect of the Specific Surface Area Inorganic solids and organic polymers or resins, used as supports for metal catalysts, normally have large specific surface areas (surface areas per unit weight) to load as many highly dispersed metal crystallites as possible. The final size of the metal particle is generally reduced as the specific surface area of the support increases, as long as the preparation conditions are otherwise the same and the nucleation of the metal particles occurs on the surface of the support, because of the enlarged surface area for nucleation of a fixed amount of metal. If the metal particles are formed in a liquid in the presence of a support, this characteristic may be used as evidence of heterogeneous nucleation of metal particles on the surface of the support, since, otherwise, the particle size must be independent of the surface area of the support. If precursor metal ions impregnated in a dry support powder are reduced by hydrogen gas, the size of the metal particles must reduce with increasing specific surface area of the support, since the nucleation of metal particles undoubtedly occurs on the surface of the support. Figure 12.31 shows an example of the effect of the specific surface area of a silica support on the mean particle size of Pt particles prepared on the support by reduction of Pt ions impregnated in silica powders of different specific surface areas.^^^

APPLICATIONS

646

200

400 SILICA. AREA (fn2/q)

bOO

Fig. 12.31. Effect of the specific surface area of a silica support on the mean crystallite size of Pt prepared by reduction of Pt ions impregnated in silica powders of different specific surface areas: sizes from CO chemisorption (A), X-ray data (v), and average of both measurements (o). (From Ref. 166,)

(2) Effect of the Surface Roughness The effect of the surface roughness of a support may be difficult to distinguish from the effect of the specific surface area when the individual particles of a support powder are partly sintered to form a porous agglomerate. However, unevenness of the order of the size of metal particles may have a substantial effect on the stability of the metal particles, since concave parts of a rough surface may hold and greatly stabilize the particles. For example, the gold and platinum particles prepared on platelet-type hematite particles with smooth surfaces in Figs. 7.44 and Fig. 12.42 are particularly large as compared to those on the other supports with rough surfaces. Similar result was also obtained with nickel particles on different hematite supports.^^^ Fig. 12.32 shows the effect of the surface roughness of hematite supports on the catalytic activity of Ni particles for hydrogenation of 1octene. Here the nickel particles were prepared by reducing nickel acetylacetonate with NaBH4 in the presence of spindle-type, pseudocubic, or platelet-type hematite particles (Ni/hematite molar ratio = 1/20) in 2 propanol at its boiling temperature, 355 K, for 10 min. The mean diameter of the Ni particles on the spindle-type or pseudocubic hematite particles with rough surfaces was ca, 4 nm, while it was ca, 20 nm for Ni particles on the platelet-type particles with smooth surfaces proper to their single crystal structure. The nickel particles on smooth-surface platelet-type hematite are not only originally low in catalytic activity, because of their large particle size, but also lose their catalytic activity during the hydrogenation reaction, because of their further growth. (3) Effect of the Pore Size

647

12. INDUSTRIAL APPLICATIONS 20

T—I—I—I—I—\—I—I—I—r O

:Spindle

A

'.Pseudocube

•

:Platelet

J

0

20

40

60

80

100

Time on Stream (min.)

i

L

120

Fig. 12J2. Effect of the surface roughness of hematite supports on the catalytic activity of Ni particles for hydrogenation of 1-octene in 60 cm^ of 2-propanol. Reaction conditions: 5.0 x 10'^ mol of Ni; molar ratio of [Ni]/[a-Fe203] = 1/20; 3.2 X 10"^ mol of 1-octene; flow rate of H2 = S.OxlO"^ mol h'\ temperature = 82 ®C. (From Ref. 195.)

If Rh^^ ions are incorporated in the supercages of NaY zeolite (internal diameter = 1.3 nm; entrance diameter = 0.7 nm) by ion exchange, and reductively carbonylated with CO and H2, a Rh-carbonyl cluster, Rh6(COX6, of ca. 1 nm in diameter can be formed in the supercages ("ship-in-bottle synthesis" - see section 7.3.10).^^^ One can obtain corresponding Rh^ nanoparticles in the supercages by oxidizing the Rh carbonyl clusters with O2 to remove the coordinated CO, followed by reduction with Hj.^^^ If Pt ions are introduced into a NaY zeolite and treated with CO plus H2O, one can obtain a cluster, [Pt3(CO)6]/- (n = 3, 4), corresponding to the pore size of the NaY zeolite.^^ Also, if we use FSM-16 (folded-sheet mesoporous material - 16), having a honeycomb structure with pores of 2.7 and 4.7 nm, in place of NaY zeolite, carbonyl clusters, [Pti5(CO)3o]^', are formed in the pores.^^^ These Pt carbonyl clusters can be reduced to the corresponding Pt nanoparticles with hydrogen.^^^ When the Pt ions incorporated in FSM--16 were irradiated with light or y-rays in the presence of 2-propanol and water, Pt nanowires were found to grow along the channels of the cylindrical pores.^° These Pt nanoparticles and nanowires are particularly active catalysts in the gas shift reaction of CO + H2O -* CO2 + H2. Figure 12.33 shows a scheme for the formation of the nanowires and nanoparticles of platinum in FSM-16.^°°^> If we use these kinds of templates of a definite pore size, we will be able to obtain ideally uniform nanoparticles of a predetermined size. In these systems, however, the size of the internal catalyst particles is invariably determined by the pore size of a given support. Hence, if we can control

648

APPLICATIONS

evacuated at 473K -CO

Nano Particles

Fig. 12.33. Scheme of the formation of the nanowires and nanoparticles of platinum in FSM-16. (From Ref. 200 (b).)

the relative size of the internal metal particles, independently of the pore size to some extent, for example, by changing the size of the ligands of the cluster complexes in the pores, we could use this technique for the preparation of a tailor-made catalyst with an optimum particle size and reaction space suitable for each specific reaction. (4) Effect of the Affinity to Metal Particles Cusumano et al}^ investigated the relationship between the catalytic activity of Pt catalysts for the dehydrogenation of cyclohexane and the degree of dispersion of the Pt particles on the support, using Pt/AljOj and Pt/SiOj AIjOj catalysts. They found that Pt particles on aluminum were dispersed to a much greater extent than on silica-alumina, from the measurement of chemisorption of hydrogen. The mean sizes of these Pt particles were calculated to be ca, 1 nm or less and 8.5 nm, respectively, on the assumption of a cubic shape. However, from the comparison of the degree of dispersion with the catalytic activity for these catalysts, they concluded that the TOP was essentially unaffected by differences in the supports used. They prepared the Pt catalysts by impregnation of alumina of specific surface area 295 mVg or silica-alumina (13% AI2O3, 87% Si02) of s. s. a. 450 m^/g with aqueous chloroplatinic acid solution, followed by drying and subsequent calcination in air for 1 h at 540 °C. As the specific

12. INDUSTRIAL APPLICATIONS

649

surface area of the former is rather smaUer than the latter, the higher dispersion of Pt particles on alumina may be attributed to the greater affinity of Pt to the alumina than to the silica-alumina. (5) Effect of the Affinity to Metal Complexes Figure 12.34 shows the relationships between their content (wt %), F, and the specific surface area, 5, for Pt particles on a silica gel support prepared by reducing Pt ions with hydrogen in gas phase after deposition of Pt ions by ion exchange with [PtCNHj)^^* or by impregnation with PtCl^^".^^^ As mentioned earlier (section 12.4.2), the positively charged [Pt(NH3)4]^* complex is adsorbed uniformly to the negatively charged silica gel surface. Hence, the great difference between the two cases in the behavior of the total surface area of Pt particles changing with Pt content may reflect the great difference in the state of deposited Pt ions before reduction with hydrogen. That is, in the case of ion exchange with [Pt(NH3)4]^^, the apparently linear relationship between S and V may suggest that the Pt particles were formed from uniformly dispersed Pt ions adsorbed on the negative sites of the support. On the other hand, in the case of impregnation of PtClg^", the downward deviation from linearity of S vs V may suggest direct deposition of aggregated clusters of the metal salt formed in the course of condensation of the covering solution with drying, because the metal ions are not adsorbed to the support beforehand. As a rule, the random coagulation of clusters in a liquid phase, which is dramatically enhanced by condensation, results in large agglomerates with a broad size distribution.

4

6

PLATINUM CONTENT (wt «/o)

Fig. 1234. Surface area of R particles per unit weight of catalyst, 5, against Pt content (wt %), K, for the ion-exchange and impregnation methods. (From Ref. 166.)

650

APPLICATIONS

If the final number of metal particles per unit area of support is proportional to the surface density of metal ions, the mean particle volume is kept constant with the change of the surface density of metal ions. In this case, the surface area of the metal particles per unit weight of catalyst, 5, is proportional to the total metal content, V. Thus the linear relationship for ion exchange in Fig. 12.34 indicates that the number density of the Pt particles was proportional to that of Pt ions. Hence, the downward deviation of 5 vs F for impregnation means that the number density of Pt particles was lower than expected from the proportionality. If one considers the state of Pt ions in the case of impregnation, one may readily understand the result in Fig. 12.34 for this case. However, the surface density of Pt particles, proportional to the loaded Pt ions in the case of the ion exchange, may need some theoretical elucidation. As we cannot find this in the original literature, some theoretical approach to this aspect has been attempted for this book in particular, in the Appendix entitled Growth of metal particles on supports by stepwise coalescence (see the last part of section 12.4). From this theoretical approach, if the vapor pressure of the bulk metal at the given temperature is sufficiently low in a reducing atmosphere, one may ascribe the linear relationship in Fig. 12.34 to particle growth by a stepwise coalescence process of the smallest mobile metal clusters with clusters of the same class or with higher immobile clusters. In this growth model, the difftisivity of the smallest clusters at an arbitrary stage is assumed to be much higher than those of the other higher classes, so that the latter are regarded to be virtually immobile during the coalescence process of the smaUest clusters in each step. Another important conclusion of the theoretical approach is that for obtaining the highly dispersed metal particles, the reduction of metal ions should be done as quickly as possible, for example, with a high pressure of hydrogen at a relatively low temperature, in order to achieve a migration-controlled particle growth by the mobile metal clusters, rather than a reduction-controlled growth by a low concentration of hydrogen. In the theoretical approach, it is presumed that the maximum mobile cluster size is determined as a fimction of temperature. This assumption may be supported by experiment as shown in Fig. 12.35, where the particle size in terms of dispersity (H/Pt) by adsorption of H2 becomes constant after a certain time of aging in the presence of hydrogen at a level proper to each temperature, regardless of the content of Pt.^°^ As referred to in the Appendix, the final mean particle size being determined only by temperature, irrespective of the initial density of metal ions, is equivalent to the final particle density being in proportion to the initial

12. INDUSTRIAL APPLICATIONS

651

H/Pt ATOMIC RATIO (FRACTION OF METAL ATOMS EXPOSED)

o

Pi, Wt% CATALYST

ae

0.4 04 0.8 2.0

E 0 A B C

Fig. 12.35. H/Pt values changing with aging in hydrogen at different temperatures for Pt particles on Pt/Ai203 catalysts different in Pt content. (From Ref. 201.) density of the metal ions at a given temperature. However, it should be noted that the proportionality of the final particle density to the initial ion density holds only when the starting metal ions are uniformly distributed without agglomeration. Hence, this condition will not be attained with an excessively high initial surface density of metal ions, even if the metal complex has a strong affinity to the support.

IMPREGNATION 300

d 200

200

300

400

FIRING TEMPERArURE(°C)

500

Fig. 12.36. Effect of the pretreatment temperature in air prior to hydrogen reduction on the final particle size of Pt (2.5 wt% Pt) on silica gel (Davison 70) for the ionexchange method with [Pt(NH3)4] CI2 and for the impregnation method with H2PtCl6. (From Ref. 166.)

652

APPLICATIONS

Figure 12.36 shows that the highly dispersed Pt particles on Si02 by ion exchange of the cationic complex are stable in heat treatment in air before reduction with hydrogen, as compared to those from impregnation of anionic complex.^^^ This result may again be readily accounted for in terms of the affinity of the metal complexes to the support. As would be expected, the uniformity in size distribution of the Pt particles on Si02 prepared by the ion exchange method is superior to that from the impregnation method. Figure 12.37 shows the size distributions of Pt particles prepared by these two different methods at varying temperatures for the heat treatment in air prior to the reduction in hydrogen.^^

-

^

30 -

1 ES-i soo'c

1

T'

I

1

\

\

ES-iv 770°C

IS-i -

j ^ _ ^ ^

soo'c

rj-'

IS-ii

1

-- 600°C 1

—^-^—,

1 1 8

1

_a~l~~^ 1 12 16 20

*"•—«—,__^ 1 24

CRYSTAL DIMENSION. A

1

1

Fig. 12.37. Effect of the pretreatment temperature in air prior to the hydrogen reduction on the size distribution of the Pt particles prepared by the ion-exchange method (ES) or the impregnation method (IS). (From Ref. 202 (a).)

b) Stabilizer Ultrafine metal particles for catalysts are liable to coagulate, so one of the most important roles of their supports is as stabilizers against coagulation during catalytic reaction. Most of the above-mentioned features of supports for controlling the mean size and size-distribution of metal particles in their preparation can also be applied to the stabilization of metal particles on supports. For example, we should choose for the support a material which is characterized by a large specific surface area, a high

12. INDUSTRIAL APPLICATIONS

653

surface roughness of the order of the size of the metal particles, a strong affinity to the metal particles, and a strong affinity to the metal complexes or ions, in order to obtain a thermally stable catalyst. The change of the specific surface area of metal particles on a support, S, is generally given by dS ^-KSP, dt where X is a constant and the exponent p depends strongly on the atmosphere in some case; e.g., p ranges from ca, 2 to 16 for Pt on y-AIjOj.^"^ For example, /? = 2 in air,^^^^^'^^ while /? = 6 ~ 15 in hydrogen, increasing with temperature.^°^ In addition, oxygen drastically accelerates the particle growth of Pt, as shown in Fig. 12.38.^°^ 240 220 | 200 180

~r

T

1

1

r

700»C

A Air atmosphere, Wynblatt a Gjostein • 2 % O 2 1 N 2 atmosphere, Wynblatt a Gjostein •Oxidizing atmosphere (unspecified), Somorjoi

-160 |Q= 140

10

20

30 t(h)

40

.50

60

70

Fig. 12.38. Effect of oxygen on the growth of Pt particles on y-AloOg at 700 °C. (From Ref. 206.)

Ruckenstein et al.'^^ attributed the growth of Pt particles to coalescence of the metal clusters on the support, and explained the acceleration of the growth of Pt caused by oxygen in terms of increased diffusion coefficients of the metal clusters by adsorption of oxygen affecting the interfacial energies of Pt/gas and Al203/gas interfaces, tadeed, the bondmg strength between Pt and AI2O3 may be lowered with decreasing contact area between them, since the surface areas of Pt/gas and Al203/gas interfaces may be increased due to the reduction of the Pt/gas and Al203/gas interfacial

654

APPLICATIONS

energies by adsorption of oxygen. Hence, they accounted for the effect of oxygen on p by the shift of the rate-determining step in the whole coalescence process from the surface migration step of the clusters to the inter-fusion step of the clusters in collision. In the meantime, Wanke et aL^'^ proposed an atomic migration model in which metal particles are assumed to grow by a kind of Ostwald ripening. Hence, in their model, atomic monomers are intermediates in the process, instead of the direct migration of clusters. It is possible to assume two growth modes in this model as well; i,e., diffusion-controlled Ostwald ripening and reaction-controlled Ostwald ripening (see section 4.2), corresponding to the migration-controlled coalescence and the fusioncontrolled coalescence, respectively, in the above coalescence model. The two different growth mechanisms may be distinguished on the basis of the difference in the shape or skewness of the resulting size distributions. If a regular size scale is taken as the abscissa, the modal diameter is expected to shift leftward from the distribution center in the coalescence process, as often represented by the log-normal distribution, while being shifted rightward from the distribution center in the Ostwald ripening process.^°^ Figure 12.39 represents typical size distributions of Pt particles prepared by reducing Pt ions on an AI2O3 support with hydrogen at different temperatures:^^^ the changes in surface area with time have been shown in Fig. 12.35. This figure suggests that Pt particles on AI2O3 in a reducing

NUMBER OF PARTICLES

o

©

1.0

2.0

3.0

4.0

1.0

2.0

3.0

4.0

1.0

U 2.0

I 3.0

I 4.0

10

i I 1 2.0 3.0 4.0 PARTICLE SIZE, nm

Fig. 12.39. Effect of temperature in hydrogen reduction of Pt ions on the size distribution of the resulting Pt particles [Pt(0.8 wt%)/Al203 system]: (I) 500 "*€, 110 h; (II) 550 ^C, 60 h; (III) 600 °C, 60 h; (IV) 675 °C, 10 h. (From Ref. 201.)

12. INDUSTRIAL APPLICATIONS

655

atmosphere with hydrogen are grown by the coalescence process. However, if we consider the exceedingly slow migration of metal clusters^°^ as compared to the very fast interfusion of clusters in contact^^° (e.g,, 3300 A in 5 h for migration of a Pt cluster of 25 A on AI2O3 at 600 ''C; 1.3 msec for complete fusion of Pt clusters of 25 A in contact on AI2O3 at 600 °C), the fusion-controlled growth in the coalescence model seems unlikely even if the migration of the clusters is accelerated to a great extent by oxygen. Moreover, there may be no special reason for attributing the reduction of the Pt/gas and Al203/gas interfacial energies only to the adsorption of oxygen, since hydrogen is also a very strong adsorbate for platinum. Hence, the significant role of oxygen may be ascribed to some other reasons, such as the formation of volatile Pt02 which may intermediate the Ostwald ripening of the metal particles through diffusion via the gas phase (and the surface of the support).^^^^^'^^^^^' ^^' ^^^^^ In this case, the contribution of the surface diffusion of Pt02 may not be negligible if its surface density, in equilibrium with the vapor, and the diffusivity on the support are sufficiently high. If this Ostwald ripening process becomes predominant in the growth of a metal catalyst, it is hard to completely exclude this process only from the design of the support. c) Adsorption Medium Supports for metal catalysts, such as active carbon, silica gel, and zeolites, may work as adsorption media to concentrate reactants near the metal sites. As stated eariier, a Rh catalyst supported by polyacrylamide resin with amino groups showed a definite selectivity in hydrogenation of olefins according to their degree of hydrophilicity.^"*^ For example, when the activity of the resin-supported catalyst was assessed in terms of activity relative to that of a comparable dispersed Rh catalyst, the resin-supported catalyst displayed much higher relative activity for the hydrogenation of hydrophiUc olefins, such as ethyl vinyl ether and allyl alcohol, than for the hydrogenation of hydrophobic olefins, such as cyclohexene and 1-pentene. The result was explained by the difference in effective density of reactants near the metal particles. In particular, the relative activity of the resinsupported catalyst was especially high for olefins bearing carboxyl groups. This effect may be accounted for in terms of the condensation of these olefins around the Rh particles by the electrostatic attractive force between their negatively charged carboxyl groups and the positively charged amine groups of the support.

656

APPLICATIONS

d) Controller of the Electron Density of Metal Particles Figure 12.40 shows a relationship between the electronegativity of oxide supports, or additives to a AI2O3 support, of Ru/support catalysts and TOF (turnover frequency) for synthesis of ammonia from N2 and H2. The figure suggests that the catalytic activity for the synthesis of ammonia is reduced with increasing electronegativity of the support or increasing electron transfer from metal to the support.^^^'^^^

Fig. 12.40. Relationship between the electronegativity of oxide supports, or additives to a Ai203 support, of Ru/support catalysts and TOF (turnoverfrequency)for synthesis of ammonia from N2 and H2. (From Ref. 211.)

Taylor et al}^^ found that the specific activity of Ni on SiOj, in terms of TOF for hydrogenolysis of ethane to methane, was particularly high relative to Ni on AI2O3 or on SiOj-AlzOa (Si02:Al203 = 87:13). It may imply some electronic interaction between Ni and the supports. Similarly, Vannice and Garten^^^ found a Ni/TiOj catalyst to have a specially high specific activity for the hydrogenation of CO to produce methane and higher molecularweight hydrocarbons, as compared to the conventional Ni/Si02, Ni/Ti-Al203, and Ni/a-Al203 catalysts for the selective production of methane in the same reaction. Resasco and Haller^^"* reported that the specific activity of a Rh/Ti02 catalyst prepared by reduction at a high temperature such as 773 K was drastically lowered by three orders of magnitude for the hydrogenolysis of ethane, relative to the same catalyst prepared by reduction at a lower temperature such as 523 K, while the specific activity for the dehydrogena-

12. INDUSTRIAL APPLICATIONS

657

tion of cyclohexane was unaffected by the reduction temperature. They attributed these effects partly to migration of reduced species of TiOj onto Rh metal particles during the reduction at the higher temperature, and partly to the localized electron-transfer from Ti02 to Rh at the higher temperature, in contrast to the delocalized electron-transfer from Rh to Ti02 at the lower temperature. e) Synergistic Catalyst Pt nanoparticles supported on styrene-divinylbenzene copolymer beads with sulfonic acid groups can produce acetone from a equimolar mixture of propylene and water.^^^ In this system, propylene is first converted to 2 propanol by the hydrated sulfo groups as a catalyst, and then the generated 2-propanol is converted into acetone by the Pt particles as a catalyst for dehydrogenation. Thus the support works as a first-step catalyst in this two-step process. The a-Fe203 support of the aforementioned Au/a-FcjOj catalyst for the oxidation of CO in section 12.4.1 is believed to work as a main catalyst assisted by Au particles as adsorption sites for CO in the reaction of CO with O2 adsorbed on the a-Fe203 surfaces.^^^ The supports of photocatalysts such as Pt/TiOjCa), Pt/RuGj/TiOjCa), Pt/TiOjCr), and Pt/SrTiOj are also rather main catalysts for the photolysis of water into H2 and O2 gases: (a) and (r) indicate anatase and rutile, respectively. The catalytic activity is in the order, Ti02(a) > Ti02(r) > SrTiOj.^^^ The activity of anatase being higher than that of rutile in the generation of hydrogen is due to the negatively higher conduction band level of the former, coming from the greater band gap by 0.2 eV. Although the conduction band level of the single crystal of SrTi03 is close to that of anatase-type Ti02 and the catalytic activity of the single crystal is rather higher than that of rutile-type Ti02,^^^ the catalytic activity of SrTiOj powder is even lower than that of rutile-type Ti02, because of the cryst^d imperfections of SrTi03 powder as electron traps and the dissolution of Sr^^ during catalysis.^^^ The photocatalytic activity is generally enhanced with size reduction of the semiconductor support.^^^ This size effect may be explained in terms of the electropotential floating effect?^'^^ Namely, when generated positive holes react with H2O or organic compounds, the energy levels of the semiconductor particles including the conduction-band level are lifted in the negative direction, so that the activity of the photoexcited electrons for the reduction of H2O is elevated. This effect of potential floating is pronounced

658

APPLICATIONS

as the particle size becomes smaller owing to the decreasing electric capacitance.^^^ In addition, the activity of the positive holes for the photooxidation of H2O is also raised with the size reduction. This effect may further enhance the potential floating effect. 12AA. Application of Monodispersed Particles to Catalysts As has been seen in the preceding sections, the particle size of metal catalysts is a decisive factor for catalytic activity and selectivity (see section 12.4.2). Also, as would be expected from the specific roles of the individual surface sites of Pt crystals in selective reactions of hydrocarbons,^^^'^^^ the crystal habit of metal particles may be another important factor to be controlled. For supports of heterogeneous catalysts, the external size, pore size, surface roughness, composition, etc. are the main factors to be controlled in order to attain the utmost functions in a composite catalyst system (see section 12.4.3). In this sense, monodispersed particles, well controlled in mean size, crystal habit, and internal structure, are the ideal particulate materials for both the catalysts themselves and their supports. However, for enjoying the numerous benefits of monodispersed particles as catalyst materials for practical use, we have to clear many barriers in the technology for the preparation of monodispersed nano- and micro-particles, fully controlled in mean size, crystal habit, and external and internal structures, and in large quantities, to achieve a low cost. The general principles for the preparation of monodispersed particles, i.e., the complete separation between nucleation and growth periods and the complete inhibition of coagulation during the growth period are valid even for the synthesis of monodispersed nanoparticles as well. However, the achievement of these conditions becomes harder with decreasing particle size, particularly in the range of nanometers, because the extensive nucleation needed for the synthesis of ultrafine particles make it difficult to separate the nucleation stage from the growth stage, and because the high particle density is liable to lead to drastic coagulation due to both kinetic and energetic requirements. Hence, even the use of powerful protective colloids such as polyvinylpyrrolidone, polyvinyl alcohol, and various surfactants is normally unsatisfactory for the synthesis of homogeneous dispersions of monodispersed nanoparticles of less than 10 % in the coefficient of variation of the size distribution. One of the most promising methods known for the preparation of monodispersed nanoparticles in dispersion may be the synthesis in W/0 microemulsions, as represented by the early work of Boutonnet et al for the

12. INDUSTRIAL APPLICATIONS

659

preparation of monodispersed nanoparticles (d = 3 - 5 nm; standard deviation « 10 %) of metals in the platinum group, including Pt, Rh, Pd, and Ir (see section 7.3.4).^^ Figure 12.41 shows a size distribution of Rh particles thus prepared. This method was further developed by Nagy and coworkers for the preparation of uniform nanoparticles (d = 2 - 7 nm) of FeB as a catalyst, in particular, for anmionia and Fischer-Tropsch syntheses,^^ NijB for selective hydrogenation of the C=C double bond,^^"*-^^ and COjB having activity for the hydrogenation of C=0 and C=0 bonds.^^ The secret of success in the achievement of monodispersity of nanoparticles seems to lie in the strict limitation in final size to be reached, by the strong adsorption of exceedingly high concentrations of surfactants in the microemulsions, in addition to the effect of suppressed coagulation by the condensed surfactants. Probably, the condensed surfactants play a key role in the formation of the uniform particles in this system. The major issue for this method in future may be the systematic control of the mean size and crystal habit without degrading the uniformity.

67»/.

20»/.

2.5

Fig. 12.41. A size distribution of Rh particles prepared in a microemuision. (From Ref. 222.)

In the control of the size and stability of heterogeneous metal catalysts with solid supports, such as metal oxides, silica, or active carbon, the supports play a key role, as described in the above section. Except for some special cases, such as tht photo-plating of Pt particles onto TiOj particles.

660

APPLICATIONS

metal catalysts are nonnally prepared on their supports by reduction of the ions previously deposited on the supports by impregnation or ion exchange. However, even if the metal ions are uniformly distributed over the support surfaces by the ion-exchange method, broadening of the size distribution is inevitable during the reduction of metal ions by hydrogen, since the growth of the metal particles proceeds basically through coalescence or Ostwald ripening, as referred to in the above section. The situation is unchanged even if the deposition of metal particles is performed by direct deposition of vaporized metal atoms onto a support from the gas phase. Hence, if possible, the deposition of metal particles should be carried out in a liquid phase, in which the mechanism of a definite two-step process of nucleation and subsequent growth is in effect. Recently, a new method, selective deposition method, has been developed for the preparation of fairly uniform and densely dispersed nanoparticles of noble metal catalysts (Au, Ru, Rh, Pd, Ir, and Pt) on metal oxide supports (see section 7.3.8).^^^ As the supports, monodispersed metal oxide particles controlled in size, shape, and surface structure were used. The selective deposition method is based on a very simple procedure of aging a solution of a hydroxide precursor complex of metal ions to be selectively deposited onto coexisting support particles at 100 °C. In the case of Au particles, the deposited hydroxide precursor is catalytically reduced on the supports without addition of reducing agents.^^^*^'^^ But, for metals in the platinum group, such as Ru, Rh, Pd, Ir, and Pt, hydrogen reduction was needed for the selectively deposited hydroxide particles on supports.^^^^""^ This method for the preparation of the metal catalysts in the platinum group differs from the ion-exchange method, described in section 12.4.3(a) in principle, since the former is based upon the selective deposition of hydroxide complex associated with the hydrolysis of metal ions at a high temperature such as 100 ^^C, resulting in an extremely high loading of metal particles on supports

Fig. 12.42. High-resolution TEM images of some representative nanoparticles of noble metals prepared by the selective deposition method on metal oxide supports, different in composition and surface roughness: (a) Rh/a-Fe203(E); (b) Ir/a-FczOj (E); (c) Pt/a-Fe203(E); (d) Pt/a-Fe203(P); (e) Pt/ZrOj; (f) PtmOj. Here, a Fe203(E) is poiycrystalline ellipsoidal hematite with a rough surface; a-Fe203(P) is monocrystailine platelet-type hematite with a smooth surface; Zr02 is monocrystalline spherical zirconia with a microscopically rough surface; TiOj is monocrystailine ellipsoidal titania with a microscopically rough surface.

661

12. INDUSTRIAL APPLICATIONS (a) Rh/a-FcjOsCE)

(c) Pt/a-FejOjCE)

(b) Ir/a-Fe203(E)

(d) Pt/a-Fe^OjCP)

10 nm

662

APPLICATIONS

(« 20 wt %) in a high dispersity comparable to or even better than those by the ion-exchange method (< 5 wt %). Figure 12.42 shows some representative TEM images of so-prepared nanoparticles of noble metals deposited on metal oxide supports, different in composition and surface roughness. Above all, Pt/TiOjCa) catalyst showed an excellent performance as a catalyst for hydrogenation of l-octene.^^^""^ Fortunately, monodispersed well-defined metal oxide particles, such as hematite, titania, and zirconia, precisely controlled in size and surface structure are becoming available in large quantities (see section 7.3.1), and thus we may say that we are ready to develop practical heterogeneous catalysts with metal nanoparticles of a sharp size-distribution, on monodispersed support particles strictly controlled in size and surface structure. Zeolite is a kind of composite oxide mainly of Si, Al, Na, and Ca. Its natural minerals or synthetic products are widely used as inorganic molecular sieves in many fields, because of its unique structures with regular micro- or meso-pores of different sizes. In the field of catalysis, it is used as elementary catalysts or as supports or templates of catalysts, because of its excellent performance as an adsorbent and the well-defined pore structures. In general, synthetic zeolite is prepared by a hydrothermal treatment of reactive alkaline aluminosilicate gels at relatively low temperature (100 °C) and pressure, as introduced by Milton in the late 1940s.^^^'^^ Addition of cationic surfactants to the systems for the synthesis of zeolite results in a marked reduction of crystal size to submicrometer order.^^^ Meanwhile, Ueda et al^^ synthesized several types of zeolite from homogeneous solution systems. Nowadays a wide variety of zeolite particles of submicrons or less are synthesized and their size distributions are controlled in a fairly narrow range. For detailed information on this field, the extensive studies of Schoeman et al on the synthesis of zeolite particles and their growth mechanisms are available.^^'^^ There seems to be no doubt that the advancement in the field of zeolite synthesis, including the perfect control of the size distribution, mean size, and crystal habits, as well as the pore size, would make a great contribution to the development of the science and technology of catalysts. In this book, the text on catalysts has mostly been limited to metal catalysts, because precise control of the size and size-distribution directly governs the activity, selectivity, and stability of a catalyst. However, even if the topics are limited only to heterogeneous catalysts, non-metallic heterogeneous catalysts are widely used in various chemical industries. They may cover a great part of heterogeneous catalysis, comparable to - or

12. INDUSTRIAL APPLICATIONS

663

even greater than - the territory of metal catalysts. However, from a scientific viewpoint, they do not look easy to approach, and little is known of their essential natures as catalysts, probably because of their ill-defined characteristics and the complex mechanisms in catalysis. In this sense, the field of non-metallic catalysts appears to be full of fascinatmg scientific subjects to be explored. The use of monodispersed particles, including metal oxides, metal sulfides, and metal phosphates, for practical nonmetallic catalysts may be a future issue. However, there seems no doubt that if a wide variety of general and practical methods of low cost for the preparation of monodisperse particles become available, many non-metallic catalysts will be replaced by monodispersed catalysts ideally controlled in size, shape, external and internal structures, and chemical composition, since the importance of weU-defined particles is unchanged for non-metallic catalysts as well. Such attempts are already in progress, as represented by the early work of Hamta et al on the preparation of monodispersed spheres of molybdenum sulfide and cobalt sulfide as catalysts for hydrodesulfurization.^^

Appendix: Growth of Metal Particles on Supports by Stepwise Coalescence This appendix concerns the theoretical approach to the mechanism of formation of metal particles from the metal ions uniformly dispersed on a support, as represented by Pt/Si02 prepared by ion exchange of cation complexes such as Pt(NH3)4^^ followed by drying and reduction with hydrogen. Prior to the derivation of the theory, we make the following assumptions. (1) Small clusters of metal can move on a support, but the mobility of clusters of each size class, defined by the number of the constituent metal atoms, is so discrete that the coalescence of mobile clusters of the nth size class with clusters of the same or higher size classes virtually starts after the exhaustion of all clusters of the n-7th class. This assumption of stepwise coalescence is based on the idea that the diffusion coefficient of a cluster may be inversely proportional to the number of its atoms in contact with the support. (2) The maximum size of mobile metal clusters is determined by the temperature of the growth process on the support in the gas phase. This assumption is supported by some experimental studies.^^ (3) Dissociation of each metal cluster does not occur. In this case, the

664

APPLICATIONS

coalescence is governed only by the probability of collision of mobile clusters with mobile or immobile clusters, in which the clusters in collision are assumed to fuse together with a certain probability up to unity. This assumption is reasonable when the surface density of the metal monomers, in equilibrium with the vapor pressure of the bulk metal at the given temperature, is extremely low as compared to their actual surface density in all stages of the growth process. From assumption (3), the change of the surface density of the nth clusters consisting of n atoms, c^, is given by

where k^^ denotes the rate constant of coalescence between a monomer and an nth cluster. If one totals the left- and right-hand sides for n greater than unity, one obtains: ^

= k c"

(2)

where AZ2 is the total surface density of the dimers and still higher clusters,

From the mass balance of generation of metal monomers by reduction of metal ions and consumption for the formation of clusters larger than the monomer, the change of density of the monomers may be written as

where a is the surface density of metal ions during the reduction by hydrogen and Jto is the rate constant. Here the term, -Tk^^^c^^, on the righthand side corresponds to the consumption rate of monomers for forming dimers whose formation rate is k^^c^^. Since the rate of generation of the metal monomers is equal to the decay rate of the ions, it holds that

12. INDUSTRIAL APPLICATIONS

665

da

,

Hence, if the initial value of a is denoted by GQ, then a is given by a = aoexp(-V).

W

The rate constants, k^^, may increase with increasing n because of the increasing positive factors, such as the capture cross-section of mobile clusters, van der Waals attraction, and stability in terms of surface energy. But, for the present, one may assume '^l,!

'^l^

'^1,3

^ '^V

for simplicity, since the essential feature seems unaffected by this assumption. Hence, Eq. (3) may be rewritten as —- = k^ - Ik^c^ - k^c^n^. dt

(^)

Here, we consider two cases. One is that the migration of the metal monomers is the rate-determining step for the growth of metal particles (^0^0 » Ik^a^ or k^ » Tk^a^, The other is that the reduction of metal ions is the rate-determining step (Jc^ « ^^a^. Case 1. Migration-controlled growth (^Q » 2k^aQ) In this case, all metal ions are promptly reduced to metal monomers, and then the metal monomers migrate to coalesce with each other and with cumulatively generated higher clusters. When all the monomers are depleted in this first step for growth, the much slower coalescence of dimers with themselves and still higher clusters will follow as the second step. In this way, further steps for the growth of metal particles will follow at the expense of the smallest clusters at each step, until finally the minimum size of the remaining clusters exceeds the maximum mobile size proper to the temperature.

666

APPLICATIONS

1st step A s ^0^ = 0 in Eq. (5), it reduces to

(6)

Eliminating t from Eqs. (2) and (6),

dcj

(7)

2ci+n2

Now let us consider the behavior of monomers {n = 1) and still higher clusters (n ^ 2) in the first step. For n = i If we use, instead of n^, the total surface density of all clusters including the smallest clusters (monomers in this case), 2, given by

we obtain from Eq. (7) that

"At

.(0)

= z(°)exp|

,(0)

^K^\

(8)

where the symbol (0) indicates the initial values of the first step, and thus 2<°> = c/°^ = AQ, KS^^ = a^e'^. If c^ is written as a function of 2, JJ<0) Cj = - z l n

(9)

The total surface density of all clusters at the end of the first step, z^^\ is given from Eq. (8) with c^ = 0 as

667

12. INDUSTRIAL APPLICATIONS

zW = z<»)exp|

^1 (0)

K^^'^^a^e-K

(10)

\ z

For n > 2 From Eqs. (1) and (2), dc

c ^'C n-1

n _

n

(11)

If one uses z and c^ in Eq. (9), this is transformed as ^n-l

dz

(12)

z

Moreover, if one defines A^ and y in place of c„ and z, respectively, as c

r(0)

Eq. (12) reduces to

dy

= A.n-l

(13)

Since A^ is given as a function of y from Eq. (9) and the definitions of A^ and y by = -y, A = -L = -In z z

(14)

and since the y values at the start and end of the first step are -1 and 0, respectively, A^ at the end of the 1st step, A}^\ for n ^ 2 is given by the following multiple integration repeated n-l times as

668

APPLICATIONS

c'''

""'-^s-nv-i^)*-**-

<^=>

For example,

4^>=1, ^

A1^>=I, A1^>=1,

2

^

3

^

8

^<^>=J-,^

(16)

30

Although we have assumed that y is virtually zero at the end of the first step, this must be much higher than the level expected from the vapor pressure of the bulk metal.

2nd step For w = 2 Equations corresponding to Eqs. (2), (6), and (7) for the behavior of the surface density of the clusters of the minimum size, c„, and the total surface density of clusters higher than the smallest clusters, n^^p hold not only for the first step, but also for the second and further steps. Namely, for the mth step when the number of atoms of a minimum cluster is m, the following equations hold.

dt

^

= -2Vm-*»V«.l .

and

If 2 in the mth step is defined as

^^^>

12. INDUSTRIAL APPLICATIONS

669

^^^^n^^m.l

in a similar manner, the relationship between 2 and c^ during the mth step is given by "C

(m-l)\

zexp -^l = z<'"-^>exp| V^ \ ^

s j^m-1)

(20)

/

Hence, 2 at the end of the mth step, z^'^\ is given from Eq. (20) with c^ Oas

= z^-^>exp(-^l^-^>).

2(m) = ^(m-l)^^p| \

.T(»»-1)

(21)

I

At the end of the second step, r' is given by W^ = = ao« ..-3/2 z^^J = zWexp(-xn

(22)

For « = 3 Since coupled dimers jump directly into tetramers, the change of c-^ is given by (23)

Hence, using Eq. (18), (24) If we use Cj = -zln^^V^, ^3 = c-Jz, and y = IniKP'Vz), this equation reduces to

670

APPLICATIONS (25)

—^ = 0. dy Since A^ is constant during the second step, A _ ^ ( 2 ) _ .(1)_

1

(26)

For n = 4 The change of c^ is given by (27) and hence dc^ c^-c^ dn^

(28)

Cj

Similarly Eq. (28) reduces to dA^ dy

(29)

A,= -[\ydy^A'^'=-^y'^^

(30)

^f=i.

(31)

Thus

and

4 For n = 5 A^ during the 2nd step and A^^'^^ are given by

12. INDUSTRIAL APPLICATIONS

671

^5 = / . i ^ ' f y ^ ^ 5 ' ' 4 3 ' + ^ ^3 ' ' 3' 5

(32)

and

f>=l.

(33)

^' " 5 For n ^ 4, in general, /I _

n-2

n

(34)

and dA ''=.4 , . 'dy

(35)

Therefore, for n = 2r (n = even number; r ^ 2)

^S^ = /-l/'i •••/.V-)')'^-^'^"^2^ 2 "2

(36a)

For n = 2r+l (« = odd number; r ^ 2)

^-'=/.i/.V"/.i3^-'^^^^-'2 2

(36b)

2

3rd step z(3) = z(2)exp(-4'^) = V-"/«.

(37)

672

APPLICATIONS

AfKAfKl;

^f) = A f = l . 5

(38)

z<^) = z % x p ( - A f ) = aoC-25/12.

(39)

Af = 4^> = A f = l

(40)

4

4th step

5th step z<5> = z^%xpi-Af)

= a,e''''f''.

(^l)

Generally, the total number of clusters at the end of the mth step, z^°'\ is given from Eq. (21) as zW = aoexp(-Exf-'V

(42)

1=1

where ^(1-1) ^ f i _ ^0-1) • For example,

(43)

12. INDUSTRIAL APPLICATIONS j(0)_i

Al

jU). 1

673 A2)_ 1

- l, A2 ~ T ' -^3 " T '

2 4(3)_ 1 ^W- 1 . . .

3

(44)

and

j,(4)=

-25/12^^(5)^

-137/«

...

As a consequence, the total surface density of the metal particles at the end of an arbitrary step is proportional to the initial surface density of the metal ions, ^0, at least under the condition of an equal rate constant for coalescence of mobile minimum clusters with different clusters of the same or higher classes in a given step, Lc, k„ = k„^^ = k^^,, = k^^^,^ -• With the progress of the stepwise coalescence, the initial number fraction of the minimum clusters for each step, Af'^^ is lowered, and the difference in diffusivity between the minimum clusters and those of neighboring classes becomes small, so that these small clusters of several classes will proceed to move at the same time in a group. Nevertheless, the proportionality of the final particle density to the initial ion density at a given temperature will be retained, since the situation is unchanged as long as the smallest group behaves in the same way as the smallest discrete class. General features of Case 1 If we assume size-dependent rate constants of coalescence between the minimum clusters and the other clusters of different sizes at a given step, the treatment for the change of total particle density at each step may be much more complex. However, even if we assume size-dependent rate constants in the first step, it follows from Eqs. (1), (2), and (3) with a = 0 that

(Kn^ ^^"2 [ * U j <^1 1*1.1 J and

674

APPLICATIONS

dCy

-2-

ik \ k

f3_ <^1

••• .

<^1

Since it is evident that the change of nJaQ can be described as a function only of cja^ from these equations with the initial conditions of nja^ = 0 and CJQQ = 1, HJUQ at the end of the first step {cja^ = 0) is a dimensionless constant without a^. In other words, n^ at the end of the first step is proportional to a^. It can be shown likewise that the decrease in ^2 ^it the end of the second step is also proportional to ^2 at the end of the first step. Consequently, n^ at the end of the second step is proportional to a^. In this manner, the total surface density of the metal particles at the end of an arbitrary step is shown to be proportional to a^. If the rate constant of coalescence of the mobile minimum clusters with the higher clusters increases with increasing size of the latter, the decay rate of the minimum clusters is more accelerated with the generation of the higher clusters than in the case of an equal rate constant. In this case, the increase of n^^^ in this step becomes the smaller due to the more rapid reduction of c^, and thus the increase in mean particle size in this step is the greater. These are obvious if one considers the decay rate of monomers and the increasing rate of AI2 in the first step in Eqs. (2) and (3) with a = 0. For further insight into this effect, it seems useful to simulate Eq. (3) at a = 0 with the following much simpler equation for the change of c^ during the first step: a 2-a

(46)

where a is a dimensionless parameter. This equation always agrees with Eq. (3) with A = 0 at the start of the 1st step (c^ = a^), regardless of a. Using Eq. (2), one obtains (47)

Since ^2 = 0 at c^ = a^, n^^\ corresponding to «2 ^^ the end of the first step (c^ = 0), is given by

12. INDUSTRIAL APPLICATIONS

/,W. "2

675

^0 . 2(o + l)

(48)

If *ii = )fci2 = ^13 = ••% then «2<^Vao = e'^ - 1/2.72 so that a = e/2 - 1 0.36. If ifc,, < ^1,2 "^^ ^1,3 '^ ***» ^'^^^ ^ TDLVL^X be a > 0.36. If the decay rate of c^ is simulated with a relatively large a, such as 2, until c^ is close to zero, then n^^^^la^ = 1/6, corresponding to the increase of mean particle volume by a factor of 6 in the first step. As the factor of increase in particle volume for each step is progressively lowered, the factor of 6 may be close to the upper limit for the proportion of the volume increase in one step. It is now evident that the normalized size distribution of the metal particles after the same number of times of repetition of this procedure is identical regardless of the initial surface density of metal ions, and that the particle number is proportional to the initial surface density of the metal ions. Since the maximum size of mobile clusters is assumed to be determined by the temperature, the number of times for the repetition of this procedure at a given temperature is fixed, and thus the final particle number at a given temperature is proportional to the initial surface density of the metal ions. In other words, the final particle size is determined only by temperature, irrespective of the initial concentration of the metal ions. In this case, a linear relationship is obtained for S vs V. Case 2. Reduction-controlled

growth (ICQ « ^k^a^)

In this case, the metal monomers are in a quasi-steady state of the generation fi:om the metal ions and the consumption for the growth of the metal particles, so one may obtain the following relationship for the first step from Eq. (5) with dc^/dt « 0:

Eliminating c^ from Eqs. (2) and (49), one obtains

676

APPLICATIONS

dx __ / f c i a a y ^ ^ 4 ^ e x p ( - y ) - y ^ x "idt' 2

(50)

where x = HJUQ, Although dxidt is independent of a^ as dxidt = ^oexp(-V) in the early stage of the first step, it becomes inversely proportional to a^ with time. Hence, n^^^ as n^ at the end of the first step must be lower than expected from the initial proportionality to a^, so that the plot of 5 as a function of V at the end of the first step will deviate downward from a linear increase. Therefore, a linear relationship between S and V cannot be expected in Case 2, even at a later stage of the stepwise procedure.

12.5. Pigments Pigments are particulate color materials relatively insoluble in solvents and used in paints, varnishes, cosmetics, etc. mainly for coloring something, but also for coating to protect the substrates from harmful irradiation, corrosion, or contamination, or to hide original colors of the substrates, or to impart to the coated materials some specific functions such as magnetism or electrical conductivity. Since they are used in the form of dispersions in liquid media, they are distinguished from dyes, which are used similarly as coloring materials, but normally in the form of molecules dissolved in solvents. Although pigments are generally classified into inorganic and organic groups, we will mainly deal with the former in this book, because the studies on the effects of the size and shape of individual particles upon the optical properties of colored pigments have been performed mainly for inorganic pigments using monodispersed particles. Nonetheless, the general theory of the optical natures of colloidal particles, based on light scattering and absorption, is common to both groups. As examples of inorganic pigments according to their colors, the most typical ones may be as follows. White: Black: Yellow: Orange: Red: Blue:

TiO^, ZnO, ZnS Ytp^, C PbCr04-PhSO^, PbCrO^, a-FeOOH, TiO,-NiO-Sb^, CdS 25PbCr04 •4PbMo04 •PbS04, PbCr04-PbO a-ftp^, Cd(S,Se) Na^,Si,2.A4-NayS,, KFe[Fe(CN)J, CoG-wAlA

12. INDUSTRIAL APPLICATIONS

Green: Violet:

677

CT2O2, CoO-nZnO Co3(P04)2

In addition to the above pigments, colorless powders of CaC03, BaSO^, AI2O3 •nH20, Al2Si205(OH)4, etc. of relatively low refractive indices, around 1.5-1.7, are used as extender pigments (diluents of colored pigments) or white pigments. Although the color of a pigment is primarily determined by the substance or its chemical composition, the size and shape of the particles have significant effects on the color. Hence, if these colored pigments are prepared as monodispersed particles precisely controlled in mean size and shape, we will be able to obtain, ideally, pure-colored pigments which are not yet achieved, but may be used as pure single pigments or, if necessary, as elementary components of mixed pigments. 12.5.1. Relationship between Particle Size and Color The optical properties of spherical particles can be fully quantified if their refractive index and diameter are known.""^ For experimental studies on the optical properties of uniform colloidal particles, extinction spectra in visible and UV ranges of non-absorbing polymer latices,^^^*^^^ of highly absorbing metal particles such as gold and silver,~^^ and of moderately absorbing dielectric particles such as hematite^^"^"*^ have been measured and compared with calculations based on the Lorenz-Mie theory?'^^ For calculation of extinction spectra of light-absorbing particles, the most fundamental parameter is the complex refractive index, m, defined by m = n(l-id),

(12.5.1)

where n is the real part of the refractive index given by the ordinary vacuum refractive index divided by the refractive index of the medium, and K is the absorption index. For the determination of the absorption index, K, studies on slightly absorbing particles of atmospheric aerosols,^"*^ highly absorbing metals,^"^ and pigments^^'^"^^ are known. In particular, Kerker et alr'^ determined the absorption index, K, of hematite (a-Fe203) as a function of wavelength, using Rayleigh scatterers {rfk < 0.05) which require no information on the particle size. Namely, the extinction cross-section of a single particle, C^^, is written as the sum of the cross-sections for scattering, Q^^, and absorption, C^^,:

678

APPLICATIONS

c^=c at

+c.. sea

(12.5.2)

abs

The corresponding relationship for a colloidal dispersion is !^fir)C^{r)dr = [^mC^a(r)dr^f^Ar)C^mr,

(12-5.3)

where/(r)rfr is the number of particles per unit volume between radius r and r+dr. This relation may be expressed alternatively as (12.5.4)

€=T+A,

where the extinction e, turbidity x, and absorption A represent the total power attenuated, scattered, and absorbed per unit volume of dispersion for unit incident irradiation. If the particle sizes are sufficiently small for the Rayleigh approximation to be applied, T and A are given by T =

12871- m^-l

3k'

(12.5.5)

w^+2 Jo

and A=

Im X

m^-\

|/;/(r)r'*.

(12.5.6)

{m^-^2

where Im denotes the imaginary part of the complex number. On the other hand, the Rayleigh ratio RJJd), representing the radiance per unit volume of the dispersion per unit solid angle scattered into direction 6 for unit unpolarized incident irradiation, is related to the turbidity, T, for Rayleigh scatterers as 3(l^W0)^_ 16n

(12.5.7)

As a consequence, dividing through Eq. (12.5.4) by the particle concentra-

679

12. INDUSTRIAL APPLICATIONS tion in g/cIn^ c, given by _ 4K p

llmPdr,

(12.5.8)

one obtains

c

16K

^«(6)

6K

3(l+cos^0)

c

Xp

Im

m^-1

(12.5.9)

ym^-^l)

where p is the sohd density of the particles. This equation is used to evaluate K from the measurement of the specific extinction, T/C, and the specific Rayleigh ratio, Rj[&)/c, at dilutions sufficiently high to avoid multiple scattering, along with data of the real refractive index, n, obtained by separate experiments of ellipsometry^"*^ or an immersion technique.^'*^'^'*^ Figures 12.43 and 12.44 show the thus-obtained, K, and the real refractive index, respectively, as functions of wavelength - the latter of which Kerker et al obtained using compiled data of other reports.^^ The numerical values

0.05

Q02

0.005

0.002

0.001

400

500

X . (nm)

600

700

Fig. 12.43. Absorption index, K, of hematite as a function of vacuum wavelength. (From Ref. 238.)

APPLICATIONS

680

nsCC

75o~ X^ (nm)

Fig. 12.44. Real part of the refractive index, w, of hematite as a function of vacuum wavelength. (From Ref. 238,)

Table 12.8. Complex refractive indices, m = n{l-Ki\ of hematite particles at various wavelengths at 25 °C (Source: Ref. 239) ^(nm) 350 375 398 420 436 455 479

1 500

n

K

\)(nm)

n

1.53 1.85 2.02 2.12 2.18 2.25 2.30 2.32

0.68 0.52 0.41 0.33 0.27 0.21 0.17 0.144

525 546 560 579 600 625 650

2.34 2.34 2.33 2.31 2.30 2.27 2.24

K

0.104 0.072 0.051 0.029 0.017 0.010 0.006

of K and n are summarized in Table 12.8.^^ Once K and n are given as functions of wavelength, the extinction spectra and thus the chromaticities of monodispersed spherical particles of a given mean radius can be calculated for single scattering at an arbitrary scattering angle by the Lorenz-Mie theory.^'^^'^^ For concentrated suspensions, the

12. INDUSTRIAL APPLICATIONS

681

reflection spectra can be calculated from the Kubelka-Munk multiple scattering theory^^^r:^ -R=l

K

+ --

ik .+. \s^ s

(K^

,1/2

(12.5.10)

with

iS^

(12.5.11)

and

^^9C,,(l-)^

(12.5.12)

where the symmetry factor is cosd weighted by the scattering irradiance.^'^'*^'^^ Figures 12.45 and 12.46 show calculated chromaticities of monodispersed hematite particles for single scattering at 90"" to the incident irradiation of white light and for reflection based on the KubelkaMunk theory, as a function of the particle diameter from 20 to 3000 nm, respectively.^^ The curves within the horseshoe-shaped spectrum diagrams are the loci of the chromaticity coordinates with varying particle diameters from 20 to 3000 nm as indicated. One may recall that the intercept on the spectrum diagram of the line drawn from the source point, S, through the chromaticity coordinates gives the dominant wavelength. Also, the length of the segment from the source point to the chromaticity coordinates, relative to the total line length, gives the purity of the color. A chromaticity coordinate position lying within the triangle ASAB, formed by the lines from S to the coordinate positions of spectrum stimuli 380 nm. A, and 770 nm, B, and their joint connecting straight-line AB, has a complementary wavelength given by the intercept on the spectrum diagram of the line passing through the chromaticity coordinate position and source point, S. The purity of the complementary color is given by the length of S to the chromaticity position, relative to the full length extended to the joint connecting line between 380 and 770 nm. In Fig. 12.45 the color of 20 nm-diameter particles is blue (k = 475 nm) of about 50 % purity. As the colors swing around the spectrum with increasing size, they become nearly

APPLICATIONS

682 1.0 r 52(

1^

^ 54 0

' piO ^60

\^ Y

J-aoc

J .58 1

1

2oa _

0.4 r\\

0.2r

f\ L

isop V

/

\^ \ \

^0

\

^^1

s

ir

V

^^

r 620

7 1&

-T" ^

^6

p^7<5

21

^

1^ 02

^ 99 0.4

0.6

0.8

Fig. 12.45. Calculated chromaticities of monodispersed hematite particles for single scattering at 90° to the incident irradiation of white light as a function of the particle diameter from 20 to 3000 nm. (From Ref. 238.)

Fig. 12.46. Calculated chromaticities of monodispersed hematite particles for reflection based on the Kubelka-Munk theory, as a function of the particle diameter from 20 to 3000 nm. (From Ref. 238.)

683

12. INDUSTRIAL APPLICATIONS

achromatic in a narrow size range round 150 nm, and then range through almost pure yellows to reds from about 200 to 1000 nm diameter. At still larger sizes the colors become increasingly achromatic and shift toward the violet. In Fig. 12.46 for the locus of the chromaticity coordinates on the Kubelka-Munk multiple scattering model, the chromaticity is yellowish to reddish for all sizes from 20 to about 1000 nm diameter. The scattering light becomes progressively achromatic for sizes larger than 1000 nm diameter. These calculated chromaticities are quite consistent with the observed ones. Experimental and calculated Mie extinction efficiencies, corresponding to the extinction cross-sections, for nearly spherical hematite particles of various diameters are shown as a function of the wavelength of incident light in Fig. 12.47.^^^ The concentrations of the dispersions used in this measurement were less than 10"^ g/g to avoid multiple scattering. As the size increases from 0.10 to 0.16 |xm, the color of the dilute dispersions gradually changes from yellowish orange to reddish, owing to the expansion of the absorption spectmm region from near-violet to blue-green. It is noteworthy that a very small variation in particle size, even a difference of

4 _

, , . , EXPERIMENTAL ^ ^ . . ^ T ^ X

a

3

. ^ T O o > z

IL. kl

z o H o z X liJ

^*V ' \ \ "-..

\

D(M»nM

\

\0.i6

2 V

••

1

V

N

Ui

o u.

*'•. N

lU

4 •

.

^

1

1—^,,_^

1

2

*•. \

^N

1 1

1

\

*'^'

S

1

1-1

\

'5=*Itf^"\. \ \ N

• 0.13 H •.

' ^ ' ^ ^ ' • • . . 0 12

" o'o.l

CALCULATED ^-"^ 3

•.. N

HEMATITE

\

*. \

\

'. \

\ \

1 \

1

Fig. 12.47. Experimental and calculated Mie extinction efficiencies for nearly spherical hematite parti^ ^ • • • : > . 0.13 ^-.^" 0.12 1 J • " Q.IQi cles of various diameters (D) as a 400 500 600 70( "^^0 function of the wavelength of inciWAVELENGTH (nm) dent light. (From Ref. 239.) "^N^v V\ \ \

' - .-X D(/im) - ^ 0.16

APPLICATIONS

684

the order of 0.01 [jim, causes a dramatic change in the extinction spectram. The measured peaks are shifted somewhat toward the longer wavelengths, as compared to the calculated values, which may be due to the lessweighted contribution to the extinction of a small number of larger particles as well as to a small deviation from the exact values of the complex refractive indices.^^ It is of interest to compare the spectra of colloidal hematite as a representative of dielectric particles with those of colloidal gold as a representative of metal particles. Figure 12.48 shows the calculated absorption efficiencies of hematite and gold sols at various wavelengths as a function of particle diameter.^^ For the calculation of the spectra of gold sols, previously reported refractive index values^^^^*^^^ were used. For hematite particles, the absorption shifts toward the longer wavelengths with increasing particle size, corresponding to the observed color change from yellow to orange, red, and dark red. The sharp resonances in the absorption efficiency, as typically observed with dielectric particles especially at high wavelengths with small values of K, are likely to be due to surface waves,^^ as suggested in ref. 239. Generally, the resonances are observed for

»

J

398 ntn ^

/'436

:'/

1 "I 1 1 1 HEMATITE-CALCULATED

_ /

1

\

/54€ 625

o

__i _

1 0.2

1

0.4

i

l

l

0.8

0.6

-I 1 i 1 rGOLD SOL - CALCULATED

liJ

Z

o CL

Q:

o

2h ; ;.'43Vs*.

CO

m <

ifi / • ,V

\5^«

'

-....r.r:...

*

0.1

*

0.2

0.3

DIAMETER (/im)

Fig. 12.48. Calculated absorption efficiencies of hematite and gold sols at various wavelengths as a a4 function of particle diameter. (From Ref. 239.)

12. INDUSTRIAL APPLICATIONS

685

dielectric particles with a positive dielectric constant and with a high real refractive index, n, and a low absorption index, K « 1. On the other hand, the color of colloidal gold dispersions changes from ruby red through purple and violet to pale blue as the particle size increases. The great difference in color change from that of hematite sols is mainly due to the strong absorption by surface plasmons^^*^"* with a maximum at X^ = 510 nm (Frolich mode) for 0.05 |im < D < 0.1 \xm, which occurs for metal particles when the real part of the dielectric constant is negative. As a rule, metal sols give strong surface-plasmon absorption in the visible/near-UV region, whereas the phonon vibrations, corresponding to the virtual modes^^ of the dielectric particles, shift to the IR region.^^'^^ 12.5.2. Shape Effect on Optical Properties Figure 12.49 shows the calculated scattering and absorption crosssections of ellipsoidal hematite particles of: (a) / = 335 nm, w = 220 nm; (b) / = 467 nm, w = 216 nm; (c) Z = 556 nm, w = 180 nm.^^^ The calculated

0.5

Scattering and absorption cross sections EUlpsoldal particles

0.0 400

500

600

700

X/nin Fig. 12.49. Calculated scattering and absorption cross-sections of ellipsoidal hematite particles of: (A) / = 335 nm, w = 220 nm; (B) / = 467 nm, w = 216 nm; (C) / = 556 nm, w = 180 nm. (From Ref. 241.)

686

APPLICATIONS

spectra were in good agreement with the experimental ones. 12.5.3. Hiding Power Hiding power is one of the most important characteristics of pigments used for hiding the colors of the substrates or for shielding the substrates from harmful irradiation such as UV rays. It is a function of the relative refractive index of the pigment particles, the absorption index, volume fraction, and particle size. If we consider a white pigment of a relative refractive index, m {m = n = fi/Mt)j K = 0, where \i and \x^ are the refractive indices of the pigment particles and the medium in vacuum, respectively.), the hiding power increases with (/n^-l)/(/n^+2), as would be expected from Eq. (12.5.5) for the turbidity of Rayleigh scatterers. Hence, whiteners must have high refractive indices; e.g,, Ti02 (\i « 2.7 for rutile; \i « 2.5 for anatase); ZnO (\i « 2.0); ZnS + BaSO^ (\i « 1.7-2.2). The refractive indices of media such as linseed oil, castor oil, or resins are normally in the range of 1.45 - 1.60. When the particle diameter, d, is much smaller than the wavelength (d « X), the scattering efficiency is proportional to d^fk"^ (see Eq. 12.5.5), but when d » X, it is proportional to l/d. Thus, there is a maximum in the scattering efficiency and thus hiding power at a certain particle size. With respect to the subject of optimum particle sizes for hiding power, many studies are known.^^*^^ For example, Mitton^^^ calculated the optimum diameters of various white pigments in linseed oil for blue, green, and red light as summarized in Table 12.9, using the following equation, and reported that the calculated values were in good agreement with the diameters actually measured. rf=

^ ^^"^ . 1.414|ioTr m^'l

(12.5.13)

The hiding power of white pigments is due to the reflection by light scattering, whereas not only the scattering but also light absorption contributes to the hiding power of colored pigments. Thus, color pigments are normally higher in hiding power, and the optimum sizes to give maximum hiding powers are considerably smaller than those of white pigments. This principle also applies to white pigments with UV absorption. For example, ultrafine powders of rutile titania of ca. 30 nm diameter, having a strong absorption band in the UV range, are particularly useful for the foundations of cosmetics to screen harmful UV radiation.^^ Here, the UV absorbance of a coating of the above titania of ca. 30 nm diameter per

12. INDUSTRIAL APPLICATIONS

687

Table 12.9. Calculated optimum diameters of white pigments in linseed oil for blue, green, or red light (Source: Ref. 259) Pigment

Blue Light

Green Light

Red Light

Rutile Titania

0.140 ^m

0.192 fim

0.205 iLim

Anatase Titania

0.158

0.215

0.230

Zinc Flower

0.275

0.389

0.416

Barium Sulfate

0.070

1.30

1.36

Calcium Carbonate

1.44

1.74

1.84

unit surface density was about three times higher than that of rutile titania powder of ca. 300 nm diameter usually used as a whitener. In any case, monodispersed particles precisely controlled in size and shape are ideal for controlling the hiding powers of both white and color pigments. 12.5.4. Composite Pigments and Tlieir Optical Properties Since the color of particles is quite sensitive to even a small change of particle size, it is essential to make the colored matter as uniform as possible and to control strictly the mean size. Since most pigments cannot be prepared as weU-defined dispersions at present, it may be convenient to combine dyes with uniform spheres which can be prepared by conventional techniques. An organic dye, 3 Mordant Blue, was incorporated into uniform amorphous spheres of aluminum hydroxide by heating dilute solutions of aluminum sulfate in the presence of the chelating dye.^^^ The resulting colored aluminum hydroxide spheres were 0.23 to 0.73 \xm in diameter, and the maximum content of the dye was as high as 30 mol % of Al in the solid phase. However, with increasing incorporation of the dye, the size distribution was considerably broadened as 0.46 in coefficient of variation at a molar ratio of dye/Al = 0.29. Similarly, uniform silica spheres are used as a matrix for incorporated dyes or as a core of hybrid particles covered with a dye layer.^^^*^^ For this purpose, colloidal silica is particularly useful because of its sphericity, uniformity, and low refractive index. For example, Hsu et al^^ incorporated Methylene Blue or Azure A in silica particles by coprecipitation, and coated Ethyl Violet or Thioflavine T by adsorption on the silica surface.

APPLICATIONS

688

Figure 12.50 shows reflectance spectra of powders consisting of aminomodified silica particles coupled with different dyes, such as Flavazin L, C. 1. Acid Red 183, Violamin R, and C. 1. Acid Blue 45.^^

Fig. 12.50. Reflectance spectra of powders consisting of amino-modified silica particles (a) and those coupled with different dyes: (b) Flavazin L, (c) C. 1. Acid Red 183, (d) Violamin R, (e and f) C. 1. Acid Blue 45. (From Ref. 263.)

On the other hand, as the optics of particles consisting of concentric spheres is fuUy understood,^ it is possible to design dispersions for specific use, such as whiteners. Figures 12.51 - 12.53 show a model of a coreshell particle of Ti02/Si02, the calculated scattering efficiency, Q^^^, of silica cores covered with different thicknesses of titania, as a function of the optical size, 2jrr/X, (r = particle radius; X = wavelength of the light), in a cellulose matrix, and the reflectance spectra of the core-shell particles.

CELLULOSE, n„ = 1.45

Fig. 12.51. Model of a core-shell particle of Ti02/Si02 in a cellulose matrix. (From Ref. 264.)

12. INDUSTRIAL APPLICATIONS

689

TITANIA COATED SILICA

A *^^^

0.20

1

^v^^_

TiOj 1

o.norfri \

yyy

< 1

/

>^.06 ^

^

-''"S^

0 2

4

.

6

8

OPTICAL SIZE(2TTr/x)

100

a

=!P^

80 Al f

AO

m o z <

20 0

o UJ

100

-J

80

1.0 u m

ft 1 c* 1 fc'/^RLP2 fir / /

60

Si02

wt.V. Cooting 50 AO 30 20

1

1

-b ^*m^

mma^mmMASmmid

1

UJ 60 AO

- —

!tlh RIP 2 20 0

Fig. 12.52. Calculated scattering efficiencies, Q^ca, as a function of the optical size, 2jcr/X, for titania (heavy line) and core-shell particles, consisting of silica cores covered with different thicknesses . 1 of titania, in a cellulose matrix. (From Ref. 264.)

i

3 00

• AOO

500

AO w t . %

600

1.3 1.0 0.8 0.5

Cooting

700

WAVELENGTH (nm)

8a

Fig. 12.53. The reflectance spectra of the core-shell particles, consisting of the same silica particles of 1 fxm diameter coated with different amounts of titania (a) and of silica particles of different sizes coated with the same percent amount (40%) of titania (b). The heavy solid lines are for a commercial titania sample (RLP2), (From Ref. 264.)

consisting of the same silica particles of 1 |iin diameter coated with different amounts of titania (a) and of silica particles of different sizes coated with the same percent amount (40 %) of titania (b), respectively.^^ 12.5.5. Other Properties Required for Pigments When pigments are used in paints, coatings, cosmetics, fillers, etc., the properties required are not limited only to color, whiteness, and hiding power. For cosmetics, for example, appropriate gloss, brightness, agreeable

690

APPLICATIONS

touch, smooth spreading, and affinity to the human skin are important properties, which are closely related to the crystal structure, particle shape, mean size, and size distribution of pigments used including colored and extender pigments. Extender pigments are uncolored powders mixed with general colored pigments or whiteners to control their final properties. For this purpose, they are required to have no absorption band in the visible range and a low refractive index around 1.5 - 1.7, close to those of the medium called the vehicle such as vegetable oils and resins, so that they become transparent when dispersed in the vehicles. Thus, materials widely used as extender pigments are clay minerals (pi = 1.5-1.6), such as kaolinite (Al2Si205(OH)4), halloysite (Al2Si205(OH)4 •2H2O), and talc (Mg3Si40io(OH)2), common mica (KAl2(AlSi3)Oio <0H)2; pi = 1.55-1.59), CaCOj (pi = 1.5-1.66), SiO^ (pi - 1.45), SiO^fiH^O ((x - 1.45), AXfi^nH2O (|x = 1.7-1.8), and BaS04 (pi - 1.64). For example, talc has been used as an extender pigment to improve the spread of cosmetics over the human skin, because of its softness by virtue of the very weak bonding between he crystal layers. The kinetic friction coefficient of talc is lowered from 0.46 to 0.24 with particle diameter increasing from 2.3 to 9.2 pun,^^ showing that the spreading property is improved with increasing size. However, as the particle size exceeds a few tens of microns, it becomes to feel rough, and thus there is some optimum size. Recently, however, monodispersed spheres of nylon, polymethyl methacrylate, polystyrene, etc. of a few microns to a few tens of microns in diameter have also become popular as extenders in cosmetics, because of their smooth spread over the skin. This is a consequence of their low kinetic friction coefficient, probably caused by rolling of these elastic spheres (see Table 12.10). As an application of spherical latices, some hybrid pigments such as nylon spheres covered with ultrafine titania particles, prepared by milling a mixture of the components, are in practical use as face masks or foundations of cosmetics.^^ Such hybrid pigments have several advantages in whiteness, UV screening, and smooth spreading, at the same time. The affinity of cosmetics to the human skin nomially increases as the size of the extender such as talc is reduced. This is one of the important factors of cosmetics to be considered. The gloss is also an important property. Since it is caused by regular reflection of light by flat particles, mica particles are often used as foundations for giving a proper gloss to the skin. The gloss of mica particles is known to increase with decreasing diameter in the range of 2 to 10 pmi.^° As the gloss also depends strongly upon the aspect ratio of

12. INDUSTRIAL APPLICATIONS

691

Table 12.10. Kinetic friction coefficients of various powders (Source: Ref. 260) Powder Species

Mean Diameter (^ni)

Talc Mica Kaoline Titania Titania (ultrafine) Zinc Flower Silica spheres Alumina spheres Nylon spheres Polystyrene spheres Polymethylmethacrylate spheres

3-10 3^-5 3-5 0.2-0.3 0.02-0.03 0.4-0.6 4-10 5-10 3-5 5-10 5-10

Kinetic Friction Coefficient 0.27-0.33 0.42-0.47 0.54-0.59 0.49 0.80 0.60 0.28-0.32 0.29 0.33 0.26-0.30 0.29

platelet particles and the smoothness of their surfaces, the shape and structure control of cosmetic powders is also strongly desired, in addition to the precise size control. To increase the brightness of color pigments, ultrafine barium sulfate powder of ca. 50 nm diameter is used widely as an extender pigment for cosmetics. It dramatically improves the affinity to the skin as well, owing to its small particle size. Ultrafine barium sulfate powders are also used as extender pigments for coating automobiles to give a gloss and improve the smoothness and anticorrosion properties. Rheological properties are also of importance for the practical use of paints, printing inks, cosmetics, etc. In order to increase the viscosity of aqueous and nonaqueous dispersions, ultrafine silica powders of the order of 10 to 20 nm in diameter are used as extenders. In this case, the size control of silica powder is decisive for providing functions mentioned in the above applications of barium sulfate particles.

12.6. Biological and Medical Uses Diverse functional particles called "microspheres" are widely utilized in biology and medicine for mechanistic studies of endocytosis of phagocytes, cell separation, diagnostic assays, remedial uses as represented by drugdelivery systems, etc.

692

APPLICATIONS

Except for the studies of some non-specific endocytosis of phagocytes, the biological and medical uses of microspheres are mostly based on the specific reactions between microspheres and some specific cells, such as antigen-antibody, saccharide-lectin, and enzyme-substrate reactions. For this purpose, microspheres are functionalized by conjugation with some functional groups such as antibodies, lectins, or enzymes to be reacted with antigens, saccharides, substrates, etc. on specific viruses or cells such as bacteria, or malignant tumor cells. In addition to the discriminative function for specific cells and other organisms, the microspheres are provided simultaneously with many devices for a variety of functions, such as labeling of the bound cells with markers, collection of the bound cells with loaded ultrafine magnets, or timed release of drugs to the bound tumor cells. In this section, we shall survey the biological and medical uses of functional microspheres, including their application to cytology and diagnostic examination in vivo, applications to cell separation and diagnostic assays, and remedial uses. Finally, the roles of monodispersed particles in this field are referred to. 12.6.1. Applications to Cytology and Diagnostic Examinations in Vivo a) Specific Staining of Proteins in Cells As an application of ultrafine particles, ultrafine gold particles ranging from 4 to 40 nm in mean diameter have been used to visualize specific target proteins in cells for light microscopy and electron microscopy, based on the immunological reactions between an antigen protein and an antibody linked to a gold particle. The procedure called the IGS (Immuno Gold Staining) method was introduced by Faulk and Taylor^^ in 1971, and have been developed extensively by De May et al'^^''^^ The characteristics of this method are as follows. 1) Clear transmission- and scanning-electron-microscope images of antigens by virtue of the high electron density of gold and the strong radiation of the secondary electrons. 2) Easy double staining for different antigens in each cell, using two kinds of gold particles of different sizes carrying different antibodies corresponding to the respective antigens. 3) High detection sensitivity, greatly enhanced by the deposition of metaUic silver onto the gold particles in a development process called the IGSS {Immuno Gold-Silver Staining) method.

12. INDUSTRIAL APPLICATIONS

693

4) The inert electrostatic adsorption of gold to bulky protein molecules such as antibody molecules, exerting no influence on the activity of the protein. 5) The long-term preservability of the stained samples. The advantages of gold particles are: 1) The easy preparation of fairly uniform particles with different mean sizes. 2) The high electron density necessary for clear electron microscope images. 3) A strong affinity to proteins. As is obvious from the purpose of this method, the size distribution of the gold particles must be as narrow as possible. Commercially available gold particles are prepared by reduction of HAUCI4 in dilute homogeneous solutions normally with a diethyl ether solution saturated with yeUow phosphorus for those of 3 to 5 nm, and with sodium borohydride or salts of ascorbic acid or citric acid under different conditions for larger ones varying in mean diameter up to 40 nm. Although there are two methods, the direct and indirect methods, for the IGS procedure, we employ more frequently the indirect method in which a secondary antibody, previously combined with a gold particle, is linked with a specific antigen through the intermediacy of a primary antibody bound directly with the antigen. As a rule, the indirect method is characterized by its high sensitivity and broad applicability to almost all antigens using a limited number of typical secondary antibodies combined with gold particles. Figure 12.54 shows the principle of the indirect immuno gold staining method. Protein A, which is a kind of protein of molecular weight 42,000 as a cell wall component of staphylococcus aureus, is often used in Gold Particle

Secondary Antibody

Primary Antibody Antigen

Fig. 12.54. The principle of the indirect IGS (immuno gold staining) method.

694

APPLICATIONS

Fig. 12.55. (a) Electron micrograph of a cell (PTK2 cell) stained with antitubulin and 5-nm gold particles linked to antibody, goat anti-rabbit/IgG, clearly illustrating labeled microtubules and mitochondria, (b) Light micrograph of PTK2-cell stained with antitubulin and 20-nm gold particles linked to goat antirabbit/IgG. The microtubules are stamed in red. In the anaphase cell, the interzonal fibers and remaining microtubules are clearly resolved. (From Ref. 268.) place of the secondary antibodies, because of its nature to link with the Fc part of immuno-globulins (IgG), as primary antibodies reacted previously

695

12. INDUSTRIAL APPLICATIONS

with specific antigens, and to physically adsorb gold particles. Some examples of IGS of a cell is shown in Fig. 12.55.^^^ The IGS and IGSS methods are also applied to the detection of extremely small amounts of specific proteins separated in a striped pattem on a cellulose membrane, prepared by transferring the same pattem of the polyacrylamide-gel electrophoresis through blotting (blotting method)?^^ Non-specific staining with simple gold particles for all proteins separated in a striped pattem on a cellulose membrane is often combined with the specific-staining blotting method for the accurate identification of each protein. Figure 12.56 is an example of non-specific staining of polypeptide bands of a protein blot on a nitrocellulose sheet with 15-nm gold particles, showing the effect of pH during the incubation for staining the blot with the gold sol on the staining intensity.^^^

k I

pk

'-

r

M

H

I !'

I

feB

C

D

E

Q

H

Fig. 12.56. Effect of pH during the mcubation for staining of a blot of a HMW protein standard, consisting of known amounts of proteins, with a 15-nm gold sol overnight: A, 3.15; B, 4.06; C, 5.10; D, 6.18; E, 7.07; F, 7.81; G, 8.45; H, 10.06. Maximal staining was obtained at pHs 3.15 and 4.06. The original color of the gold stain is purple. (From Ref. 272.)

b) Magnetopneumography The lung has a function of clearing dusts settled in itself, through endocytosis of some cells, called macrophages, in the puhnonary alveoli and their migration to the trachea at the end of their lives. The diagnostic examination of this dust-clearance function of the lung is conducted by inhaling ca, 1 mg of magnetite particles {- 2.8 (im) into the lungs, followed

696

APPLICATIONS

by checking every month the magnetic moment of the remaining magnetite particles with a highly sensitive magnetic flux meter, the so-called SQUID (Superconducting Quantum Interference Device), inmiediately after application of a magnetic field to the lungs to cause the magnetic orientation of the remaining magnetite particles.^^^ For this purpose, strict control of the mean size with a sufficiently narrow size ditribution is desired for the magnetite particles, since the retention time in the lungs is strongly dependent on the particle size; Le., the smaller the particle, the longer is the retention time.^^"* Cohen et al}'^^ reported that the amount of magnetic particles remaining after one year for non-smokers was found to reduce to ca. 10 % of the initial value on average in a first-order decay, while the corresponding value for smokers remained as high as 50 %. In the SQUID measurement, the relaxation of the residual magnetic moment is so fast - of the order of seconds due to the active microscopic motion of alveolar macrophages^^^ - that the measurement must be done at a fixed time immediately after magnetization. In other words, if we measure the relaxation of the residual magnetic moment as a function of time within a few minutes, it is possible to quantify the activity of the macrophages.^^^ Nowadays, this technique is known to be applicable to the measurement of the activity of general cells having some affinity and endocytic nature to foreign bodies. c) Mechanistic Studies of Endocytosis Although a wide variety of cells have some non-specific endocytic nature, as shown above, it is possible to provide cells with specificity in their endocytic activity by modifying the surfaces of solid particles with socalled biological ligands to be coupled with some specific receptors on the cells.^^^ For example, Sato et al}''^ modified the surfaces of ultrafine ferrite particles (10-20 nm) by coating bovine serum albumin (BSA) and subsequently conjugating the BSA with biological ligands, asialoglycopeptide (ASGP), having an ability to form complexes with specific receptors on Kupffer and parenchymal cells in the rat liver. Both for coating ferrite particles with BSA and for conjugating the BSA-coated ferrite particles with ASGP, glutaraldehyde was used as a cross-linking agent and a conjugating agent, respectively. The magnetic microspheres having the biological ligands were introduced into rat livers by perfusion or by injection in vivo through the tail vein. The magnetic particles were enclosed as a number of vesicles through endocytosis into each Kupffer cell and parenchymal cell, as observed by transmission and scanning electron microscopy on ultrathin

12. INDUSTRIAL APPLICATIONS

697

sections stained with uranyl acetate and lead nitrate. Meanwhile, the endocytic vesicles (endosomes) and lysosomes fused with endosomes, bound by the magnetic microspheres, were isolated using the HGMS (HighGradient Magnetic Separation) technique^ from rat liver homogenates. This technique may be applied to mechanistic studies of many processes associated with the endocytic activity of cells, including ligand-receptor complexation, the invagination of foreign bodies as vesicles, subsequent splitting of the vesicles, transport and fusion of the endosomes with lysosomes, recycling of the receptors, etc.^^ 12.6.2. Applications to Cell Separation and Diagnostic Assay As has been referred to in the introduction to this section 12.6, specific discrimination of cells or other organisms is required, in the first place, for their separation or labeling.^^^ For this purpose, we utilize various specific reactions, such as antigen-antibody,^^^'^^^ saccharide-lectin,^^^ and different reactions of receptors on cells with Fc part of antibodies, complements, saccharides, etc.^^^ If we fix an antibody or lectin to some support such as an agarose gel and use it as a column for cell affinity chromatography, particular cells with a specific kind of antigens, receptors, or saccharides on their surfaces can be captured and isolated selectively by the affinity chromatography. In the meantime, colloidal particles - polymer microspheres in particular - are also used widely in place of the fixed support for the labeling or separation of cells and for diagnostic assays. This is because of the high efficiency in separation, and thus high detective sensitivity, owing to the active motion of fine particles, and the fitness for small scale separation, as compared to affinity chromatography.^^^ In the cell separation with particles, however, an additional procedure is normally needed for the separation of cells bound by reactive particles from free cells, by natural or centrifugal settlement, electrophoresis,^°° magnetic separation,^° etc., on the basis of differences in specific gravity, electric charge, magnetic moment, etc.^^ If needed, the condensed cells bound by the reactive particles are isolated and purified by recovering the cells from the particles binding them. Figures 12.57 and 12.58 schematically illustrate the principle of the cell separation using reactive particles and a high-gradient separator.^^ When the magnetism of reactive microspheres is utilized for the separation of cells, the magnetic particles incorporated singly or multiply in each polymer microsphere are normally of ferromagnetic materials, but in a size range of superparamagnetism to avoid self-agglomeration among the

APPLICATIONS

698

cells

oo ooo

magnetic labeled antibody

I Oo

Ooo

magnetic separation

oo

ooo

Fig. 12.57. The principle of the cell separation by the use of inmiunoreaction between magnetic labeled antibody and antigen on cells with a high-gradient magnetic separator.

Suspension of Cells Labeled with Magnetic Micro^heres

Rinse

\ \ / /

Fig. 12.58. Scheme of a magnetic cell-separation apparatus.

microspheres; e.g., 10-50 mn for magnetite. The detection or quantitative evaluation of condensed or labeled cells is performed by light microscopy, electron microscopy,^^^^^^ turbidimetry, cohrimetry,^'^'''fluorometry,''' radiometry^''^''^''''^^''^'^ luminometry,'''-''^ etc.

12. INDUSTRIAL APPLICATIONS

699

For light and electron microscopy, surface-modified reactive ultrafine inorganic particles of a high electron density are usually used as visual markers of specific cells. In this case, separation of the cells is not necessarily needed for observation, as long as the concentration of the target cells is sufficiently high. On the other hand, since reactive particles normally have more than one reactive site each, when they are introduced into a suspension of mixed cells, the particles and target cells may be coagulated and precipitated by the bridging action of each other. But, if we choose appropriate conditions, it is possible to keep the aggregates metastable for a while and to quantify the content of the specific cells by tuibidimetry. If we use inmiunoreactive particles conjugated with chromophores, luminescent groups, fluorescent groups, or ligands containing radioactive elements such as ^H, ^^I, or ^^Co, we can evaluate the quantity of the bound, labeled, and isolated cells by colorimetry, luminometry, fluorometry, or radiometry with high sensitivity. In this case, if the optical groups can be liberated from the particles in the cell-particle aggregates by reaction with some added enzyme or by some alternative reactions after the immunoreaction, we will be able to measure the optical groups without the influence of the light scattering. Moreover, if we use inmiunoreactive particles conjugated with an enzyme in place of the optically active groups and add, after the inmiunoreaction, a substrate of the enzyme having groups which become luminescent on reaction with the enzyme, we can also avoid the influence of the light scattering of the cell-particle aggregates by measuring the luminescence of only the luminescent groups released from the substrate by the enzyme-substrate reaction and separated from the cell-particle aggregates. The advantages of using reactive particles for cell separation and immunoassay may be sununarized as follows. 1) High sensitivity owing to the active motion of fine particles. 2) Efficient separation and collection of specific cells or other organisms by the use of immunoreactive particles with a magnetic moment, electric charge, or high specific gravity. 3) There are numerous possibilities in labeling specific cells, leading to accurate measurement with high sensitivity. Above all, the potential ability of functional particles for the rapid separation and efficient condensation of specific target cells may be most

700

APPLICATIONS

highly appreciated. In particular, magnetic immunoparticles containing magnetite or ferrites are widely used because of the easy procedure of cell separation using a magnet. The original particles, prior to the surface modification with functional groups, consist of magnetic particles and some inorganic or organic polymers as a substrate for surface modification. These are as follows. a) Latices of synthetic polymers, such as polystyrene, poly(methyl methacryiate), polyacrylamide, polyacrylic acid, poIy(2-hydroxyethyI methacrylate), poIy(4-vinylpyridine), and copolymers thereof containing magnetic particles dispersed or as a single core in each polymer particle,^^^"^^^'^^^'^^^"^^^ or being coated with ultrafine magnetic oxide particles.^^^ b) Biopolymer particles such as albumin,^^"*'^^^*^^^"^^^ dextran,^^^ and gelatin,^^^ containing magnetic particles dispersed or as a single core in each polymer particle. c) Magnetic oxide particles covered with a silicon oxide layer having functional groups such as amino, carboxy, or isocyano groups.^^ d) Inorganic particles, such as porous glass or other ceramics, containing dispersed ultrafine magnetic particles.^^^ The composite particles consisting of small magnetic particles and organic or inorganic polymers are called magnetic microspheres. The mean size of magnetic microspheres ranges from tens of nm to tens of \xm according to the objectives. The incorporation of dispersed magnetic particles in each synthetic particle can be achieved by emulsion polymerization or radiation polymerization of monomers in the presence of magnetic oxide particles.^^^" 293,301,313314,316 j ^ ^ incorporation of a magnetic particle as a core in each polymer particle is performed by precipitation of magnetic particles in a solution of hydrophilic polymer such as dextran^°^ which can be adsorbed to the generated magnetic particles, or by polymerization of hydrophilic monomers with persulfates as a initiator in the presence of magnetite particles.^^^ The coating of magnetic particles over the surfaces of polymer particles is carried out by precipitation of magnetic particles in the presence of polymer particles. A silica layer having functional groups can be coated over the surfaces of magnetic oxide particles or general oxide particles containing magnetic particles by treating the oxide particles with silane coupling agents ?^'^^'^ This technique is important for providing oxide particles with reactive radicals on their surfaces, which are necessary for further linkage with additional functional groups. For this purpose, a multitude of silane

12. INDUSTRIAL APPLICATIONS

701

coupling agents can be used preferably, as represented by the general formula, (YR')j^SiR4_n, wherein Y is a member selected from the group consisting of amino, aminophenyl, carbonyl, carboxy, isocyano, diazo, isothiocyano, nitroso, epoxy, and halocarbonyl; R' is a member selected from the group consisting of lower alkyl, lower phenyl, and alkylphenyl; R is a member selected from the group consisting of lower alkoxy, phenoxy, and halo; and « is an integer having a value of 1-3.^^^* The group R, typically a methoxy or ethoxy group, is readily converted into the hydroxy group as a result of hydrolysis by water in an acidic organic solvent such as methanol and ethanol. The silane couplers are then polymerized and at the same time conjugated to the hydroxy groups of metal oxide particles, by condensation with the release of water molecules, as illustrated below.^^^^

Y R'

RO-Si-OR I OR

Y +H2O

R'

•HO-Si-OH OH

-H2O

OH OH

The methods for coupling functional proteins, such as antibodies, lectins, protein A as a connector of antibodies, etc., with magnetic microspheres may be classified into physical methods and chemical methods. The physical methods are based on the physical adsorption through hydrophobic bonding between functional proteins and the hydrophobic surfaces of monodispersed latices such as polystyrene spheres.^^ They have some merits over chemical methods in being a simple procedure with little effect on the activity of the functional proteins. In addition, the dispersive stability of the magnetic microsphere, basically low due to the high hydrophobicity, can be improved with little effect on the hydrophobic bonding by partial copolymerization of hydrophilic monomers such as acrylamide or styrene sulfonate, or by limited coating of hydrophilic matters such as albumin or polyethylene glycol.-'^ However, further studies may be required to clear the essential problems proper to the physical methods, such as the low specificity in hydrophobic bonding and the low bonding stability. The chemical methods are based on chemical bonding between the functional groups of proteins and the particle surfaces,^^^'^^ so they are superior to physical bonding, at least, in specificity and stability. For this

702

APPLICATIONS

Table 12.11. Chemical methods for conjugation between microspheres and functional proteins Carbodiimide Method [Al-C-OH + Ri-N=C=N-R2 + H+

•

[Al-C-O-C

H2N-[B] •

[A]-C-NH-[B]

/NHRi ,

/NHRi + 0=C,

+ H*

Cyanogen Bromide Method

[A]

+ BiCN — • [A]^ /C = NH OH O , . x , ™, r^ 0-C-NH-[B] H2N-[B] /O^ / II ^ ^ ! - ? - • [A]^ /C=N-[B] [A] NH ^O ^oH

0-C-NH-[B] ,^/ II [A]^ O ^OH

Glutaraldehyde Method [AJ-NH2 +H-C-(CH2>-C-H+ HJS[-[B] O

•

[A]-N=C-(CH2>-C=N-[B]

O

H

H

Maleimido- Hinge Method

[A]-NH2 +

r-
"

+

HS-[B]

x

o'^ -•

[A]-NH-C-k^^N II

o

^ ^

o

S-[B]

12. INDUSTRIAL APPLICATIONS

703

purpose, hydrophilic polymers with carboxy, amino, and hydroxy radicals, such as polymethacrylic acid, polyacrylamide, poly(2-hydroxyethyl methacrylate), and biopolymers, are used for microspheres. Typical reaction systems are those between carboxyl and amino groups mediated by carbodiimides {Carbodiimide method)^^ between hydroxy and amino groups mediated by cyanogen bromide {Cyanogen bromide method),^^^ between two amino groups mediated by glutaraldehyde {Glutaraldehyde method),^^^'^^^ and between amino and thiol groups mediated by N-(Y-maleimidobutyryloxy)succinimide {Maleimido-hinge method),^^^ as shown in Table 12.11. Here, one of [A] and [B] is a microsphere and the other is a protein. It is, of course, possible to connect [A] and [B] in a way such as linking diamines (H2N-R-NH2) to [A] first by one of the carbodiimide, cyanogen bromide, and maleimido-hinge methods, and then to [B] having amino groups by the glutaraldehyde method. Similarly, diols and dicarboxylates may be usable as a spacer, like the diamines. We shall now review a few examples of magnetic microspheres used for cell separation and diagnostic assays. a) Use of Magnetic Microspheres for Cell Separation Heden^^^ suggested in 1972 the utility of magnetic particles with surfaces modified and conjugated with enzymes, antibodies, and antigens, for the separation of biologically active proteins. Hersh and Yaverbaum^^ also used an immunoadsorbent of anti-digoxin antibodies coupled through an intermediate silane to magnetic iron oxide particles for determining the concentration of digoxin in human plasma by radioimmunoassay with ^^^I on the basis of magnetic separation. The magnetic particles used were ca, 2.5 [im in modal diameter with a size distribution ranging from 1.5 to 10 |im. Nye et al}^^ reported polymer-coated finely divided magnetic iron oxide particles conjugated to antibodies for the immunoradioassay of thyroxine, human placental lactogen, and digoxin, in which they used polymerized m-diaminobenzene as the polymer matrix. After that, Guesdon and Avrameas ^^^ developed polyacrylamide agarose-magnetite microspheres for enzyme-immunoassay for antibodies such as rabbit anti-bovine serum albumin antibodies, sheep anti-rabbit immunoglobulin antibodies, and human immunoglobulins including IgA, IgM, IgG, and IgE. They prepared the polyacrylamide agarose-magnetite beads by radical polymerization of acrylamide monomers in the presence of melted agarose, a cross-linking agent, ammonium persulfate as an initiator, and suspended Fe304 particles. The size distribution of the magnetic beads and the distribution of the

704

APPLICATIONS

magnetic oxide content were both rather broad, so they removed the ironfree beads by magnetic separation and excessively large beads by passing them through a sieve of 250 \im mesh to obtain beads of a size distribution approximately from 50 to 100 [xm in diameter. Furthermore, Molday et al}^^ and Rembaum et al?^^ prepared a wide variety of magnetic immunomicrospheres of mean diameter from 10 nm to 8 jmi, containing ultrafine magnetite particles, for cell separation, by radiation polymerization (y-ray) or emulsion polymerization of mixed or pure monomers such as methylmethacrylate (MMA), 2-hydroxyethyl methacrylate (HEMA), methacrylic acid (MAA), acrylamide (AA), and 4-vinylpyridine (VP), together with a cross-linking agent such as ethylene glycol dimethacrylate (EGDMA) and bisacrylamide (BAM), in the presence of ultrafine Fe304 particles for magnetic fluids. Then they conjugated antibodies or lectins to the magnetic microspheres through the reaction of the carboxy and/or hydroxy groups on the microspheres with amino groups of the antibodies and lectins using the carbodiimide, cyanogen bromide, or glutaraldehyde methods. According to the report of Molday, Yan, and Rembaum^^'', the magnetic microspheres were prepared by the Co-y irradiation of mixed monomers of 1.6 g MMA, 0.9 g HEMA, 0.3 g MAA, and 0.2 g EGDMA with 1 g of ultrafine FCjO^ particles and 1 g of Triton X-405 (0.2 Mrad at 0 °C for 60 min). Since it is difficult to achieve a uniform distribution of the iron content of each microsphere in this method, they classified the prepared microspheres by density-gradient centrifugation into some classes according to the iron content, and used one of these. The resulting copolymer microspheres containing Fe304 particles were 40 mn in average diameter. As the magnetic microspheres have hydroxyl and carboxyl groups, their hydroxyl groups were derivatized with a spacer, diaminoheptane, by the cyanogen bromide method, andfluoresceinisothiocyanate was tagged to the terminal amino groups for fluorescent labeling, whilst the carboxyl groups were coupled with diaminoheptane by the carbodiimide method, each of whose terminal amino group was then linked with an antibody, such as goat anti-rabbit Ig and goat anti-mouse Ig (Ig = immunoglobulin), by the glutaraldehyde method. For example, they conjugated goat anti-mouse Ig to the fluorescent magnetic microspheres and then mixed them with mouse spleen lymphocytes to separate only B cells having Ig receptors from T cells having no Ig receptors, using a horseshoe magnet, where ca, 97-99 % of the labeled B cells were retained by the magnet. The labeled cells were easily distinguished from unlabeled ones under a fluorescence microscope. Finally, applications of magnetic microspheres as visual markers of SEM

12. INDUSTRIAL APPLICATIONS

705

and TEM and as diagnostic and/or therapeutic agents were also suggested. b) Separation of Cancerous Cells Kronick et al?^^ coated magnetite particles of diameter ca. 50 nm with a copolymer of 2-hydroxyethyl methacrylate and methacrylic acid along with a cross-linking agent, N,N'-methylene-bisacrylamide, by a redox polymerization in which coexisting ammonium persulfate is reduced by a trace of Fe^^ ions dissolved from the magnetite particles and initiates the polymerization by transferring its electrons to the monomers for forming free radicals. Thus, the magnetite particles are efficiently covered with the hydrophilic copolymer to yield magnetic microspheres containing a single magnetite particle in each sphere. The mean diameter of the magnetic microspheres is controllable in a range from tens of nm to tens of ^m. The magnetic microspheres are then conjugated with choleragen (cholera enterotoxin) using the diaminoheptane spacer by the carbodiimide and glutaraldehyde methods. By utilizing the nature of choleragen to link specifically to a glycolipid, ganglioside G^p on neuroblastoma cells (tumor cells of a cancer mainly of children), they isolated the Gj^^-containing neuroblastoma cells, corresponding to 10-20 % of the total neuroblastoma cells, with a purity of over 99 %. As will be shown in the next section 12.6.3, this technique was developed to therapeutic application in the efficient extracorporeal removal of neuroblastoma cells from bone marrow by the use of monoclonal antibodies conjugated to magnetic microspheres,^^^ where the monoclonal antibody is a uniform clone antibody produced from antibody-forming cells by a reaction with a specific antigen. c) Diagnosis of Virus Diseases Mizutani et a/.^°^'^^ developed a high-sensitivity diagnostic method for virus diseases based on an immunospecific reaction of an excessive amount of large non-magnetic immunomicrospheres with viruses, a subsequent reaction of an excessive amount of much smaller magnetic immunomicrospheres with the viruses previously bound by the large non-magnetic microspheres, centrifugal sedimentation of the vimses sandwiched between magnetic and non-magnetic microspheres, and quantitative measurement of the captured viruses by an optical device equipped with a magnet, as illustrated in Fig. 12.59. In this optical measurement they counted the number of interference fringes projected onto a screen by a laser beam incident upon and reflected from a meniscus created by the attractive force of a magnetic pole set slightly above the surface of the sample liquid to lift

706

APPLICATIONS

virus o oo

magnetic labeled antibody centrifugation X.J.XX

micro beads

~i^

antibody

magnetic pole laser beam

interference fringe

electromagnet

Fig. 12.59. Procedure for the quantitative measurement of captured viruses by an optical device equipped with a magnet. (From Ref. 303 (b).)

part of the fluid underneath containing concentrated magnetic microspheres holding the viruses together with the non-magnetic large microspheres. Figure 12.60 shows an example of the laser interference fringes for influenza virus EB3. The mean sizes of the EB viruses, the small magnetic microspheres, and the large non-magnetic microspheres were ca, 90, 35, and 1000 nm, respectively. To the large non-magnetic microspheres (-1 \im) and the small magnetic microspheres (-35 nm), purified rabbit IgG antibody was conjugated. Though they used a commercially available latex suitable for the conjugation of the IgG antibody for the large non-magnetic microspheres, the small magnetic microspheres were prepared according to the method of Molday and Mackenzie,^°^ in which an ammoniacal solution was added dropwise to the mixture of ferrous and ferric chloride in a dextran solution up to pH 1 0 -

12. INDUSTRIAL APPLICATIONS

707

Fig. 12.60. An example of the laser interference fringes for influenza virus EB3. (From Ref. 303 (b).)

11, while stirring and heating to 60-65 °C for 15 min. The resulting dextran-coated magnetite particles in a size range of 30-40 nm with a magnetite core of ca. 15 nm after purification by gelfiltrationchromatography were quite stable against homocoagulation as well as non-specific heterocoagulation with cells in the physiological buffer. The ferromagnetic dextran microspheres were then oxidized with NaI04 by a modified procedure of Dutton et al?'^^ and covalently coupled with protein A extracted from staphylococcus aureus. The IgG antibody was linked to the protein A - ferromagnetic dextran conjugate through the protein A sites (see example (a) in section 12.6.1). In addition to the simplicity of the procedure, the detection sensitivity for virus EBB was about 4 times higher than the conventional fluoroimmunoassay. Moreover, since the viruses could be condensed up to 100 times the original concentration, it was possible to identify their viruses directly by electron microscopy and thus to make a diagnosis in the early stage of infection. This highly sensitive method may be applied to general immunoassays of dilute cells including many kinds of bacteria, as well as early diagnosis of virus diseases in general including AIDS. But, in the case of cells much larger than viruses, the large non-magnetic particles used as a baUast are not needed, since centrifugal separation of bound and unbound magnetic particles is possible without ballasting particles. d) Chemiluminescent Enzyme-Immunoassay for Tumor Markers Some proteins or carbohydrates in serum, such as carcinoembryonic antigen (CEA), a-fetoprotein (AFP), and tumor-related antigens including CA19-9 and CA125, are well known as markers of malignant tumors such

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as colorectal carcinoma, hepatoma, and pancreatic and ovarian cancers.'^^^ The clinical assays of these antigens as tumor markers are of vital importance for diagnosis of the corresponding tumors, and thus they have been studied extensively. Above all, chemiluminescent enzyme immunoassay may be one of the most sensitive methods for this purpose. Nishizono et al?^'^ successfully conducted highly sensitive enzyme immunoassays for the above tumor markers using a unique chemiluminescent compound, AMPPD, first introduced by Bronstein et al?^^~'^^^ as an ultrasensitive substrate for an enzyme, alkaline phosphatase (ALP). AMPPD is a derivative of 1,2dioxetane phosphate, described as 3-(2'-spiroadamantane)-4-methoxy-4(3"-phosphoryloxy)phenyl-l,2-dioxetane disodium salt, having a 1,2dioxetane moiety to generate the energy for chemiluminescent emission and a phenol phosphate group as a trigger of luminescence by ALV?^^ Enzymatic cleavage of the phosphate group destabilizes and decomposes the AMPPD molecule to produce a light emission at 470 nm. Prior to the immunoassay, monoclonal antibodies to the marker antigens and Fg^. fragments of the antibodies are conjugated to albumin-coated magnetic microspheres and to the enzyme ALP, respectively. Then, both the antibody-magnetic microsphere conjugate and F^^. fragment-ALP conjugate are mixed with a sample containing a marker antigen to form a sandwich complex of A-M-A', where/I is an antibody on a magnetic microsphere, A' is di Fjb' fragment of antibody A linked to ALP, and M is a marker antigen. After collecting the sandwich complexes by high-gradient magnetic separation, AMPPD is added to react with the ALP of the collected complexes, followed by luminometry. Nishizono et al?^^ used a monodispersed polystyrene/polyacrylate copolymer latex coated with 50 wt % ultrafine magnetite particles of overall diameter 0.3 tmi, prepared by partial oxidation of FeCl2 with NaN03 in the presence of the latex particles suspended in a buffer solution. The magnetite-coated particles were further coated with antibodies and then with bovine serum albumin by adsorption. For the conjugation of V^, fragments of antibodies, prepared by pepsin digestion of antibodies, to the ALP of calf intestine, they applied the maleimido-hinge method by using N-(Y-maleimidobutyryloxy)succinimide for modification of ALP,^^^ in which the thiol groups in the hinge region of the Fj^b- fragments of the antibodies are linked to the maleimido groups of the modified ALP. 12.6.3. Remedial Uses The medical application of microspheres is not limited to diagnostic

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assays. They are extensively used as carriers in drug delivery systems^ bioreactors, biocleaners, heat sources in thermotherapy such as hyperthermia, etc. for treatment of a multitude of intractable diseases such as malignant tumors. Strenuous efforts are being continued to explore new therapeutic systems. The sizes of the microspheres are in a very wide range from ca. 10 nm to even a few millimeters if we include large beads as artificial organs ?^^ a) Drug Delivery Systems Drug delivery systems (DDS) applied through intravascular administration or direct infusion into the affected part are particularly useful means for attacking malignant tumors intensively with minimized side effects.^^^ The materials of the microspheres used for drug delivery are mostly chosen from those which are biocompatible and readily subject to biodegradation, such as albumin, fibrinogen, gelatin, starch, polylactides, polyglycolides, and dextran. However, in some cases, materials which are not decomposed in vivo, such as ethylceliulose, are used. Microspheres containing medicines, such as anticancer agents, for DDS are prepared by several methods, such as solvent evaporation, thermal modification, or cross-linking, in the presence of the medicines. For designing microspheres, their size, porosity, drug-content distribution, and the hydrophobicity of the drug and its matrix are important factors to be controlled, since they have a decisive influence on the drug release rate. Thus, the microspheres should be monodisperse, or intentionally poly dispersed under strict control of the size distribution. The size of the microspheres is responsible for their distribution in vital tissues. For example, when microspheres of 0.1 - 3 tmi in mean diameter are infused through an artery or a vein, they may be removed rapidly from blood through endocytosis by the Kupffer cells in the liver or by the spleen tissue. Intravenous administration of microspheres larger than 7 [im may cause embolism of the capillary vessels in the lung, so they may be captured there. If the size exceeds 12 \xm, microspheres injected through an artery are shortly trapped in the tissues downstream. Hence the size of the microspheres is chosen according to the target organs. In this sense, albumin microspheres are particularly convenient, since their size can be changed in a wide range from 0.3 to 500 ^un by controlling some factors in the preparation of the emulsion.^^^"^^^ Since cancerous cells are more active in metabolism than normal cells for their rapid proliferation, their proliferation is suppressed by clogging the

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arteries which supply routes for oxygen and nutrition: z.e., embolization therapy ?^^ If an effective therapeutic drug is enclosed in the microspheres, the remedial effect is still more pronounced, by virtue of the long-term retention of a high local concentration of the drug in addition to the embolization effect {chemical embolization therapy)?^^ Magnetic microspheres are also used in DDS for more selective targeting. Widder et al}^ prepared albumin microspheres (0.2 - 2 pun) including both an anticancer drug (doxorubicin) and magnetite particles ( 1 0 - 2 0 nm) by heat solidification and administered them through an artery to Yoshidasarcoma-bearing rats on each tail. They observed a total remission rate as high as 75 % for rats having a magnet fixed on the tail, owing to the concentration of the magnetic microspheres in the tumor on the tail, while the remission rate was zero for those without a magnet on the tail. Similar concentration of magnetic microspheres or magnetic emulsion has also been observed for other organs of rats, such as the lung, bladder, and kidney, in the same procedure.^^^ The immunospecific magnetic microspheres, widely used in diagnostic assays, are expected to constitute the most efficient drug delivery systems. For establishing such systems in clinical treatment, we must compile a great deal of data on safety assessments, in addition to the ultimate refinement of the methods including the rapid clearance of the magnetic metal or metal oxide particles, while evading the endocytosis in the liver and spleen, after completion of their missions. b) Bioreactors L-asparaginase has been used extensively for the treatment of acute lymphoblastic leukemia on the assumption that the circulating L-asparagine is essential for leukemic cells which appear to lack the abUity of producing L-asparagine. However, the use of L-asparaginase involves several problems, such as hypersensitivity, antibody formation, rebound phenomenon due to the rapid induction of liver L-asparagine synthetase. To overcome these problems, the enzyme was immobilized in solid drug carriers, such as microspheres and liposomes, giving a higher stability against denaturation and reduced immunogenicity. Also, it was reported that L-glutaminase used together with L-asparaginase reduced the rebound phenomenon. Edman et alr'^^ injected L-asparaginase-L-glutaminaseloaded polyacrylamide microspheres (~1 jmi) directly into the abdominal cavity of a rat, and found that L-glutamine and L-asparagine were both decreased, and kept much lower than the ordinary level for five days, while

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the level of L-asparagine was expected to be restored within 24 h if Lglutaminase was not used together. Moreover, they installed such microspheres into outer compartment of a commercial hollow fiber dialyzer and completed an efficient extracorporeal reactor for decomposing circulating Lasparagine and L-glutamine. Hence it has been suggested that the use of such bioreactors may have an potential applicability for the treatment of acute lymphoblastic leukemia. c) Biocleaners Treleaven et al?^^ proposed a therapeutic application of magnetic microspheres in the treatment of the childhood cancer, neuroblastoma, through extracorporeal clearance of the neuroblastoma cells by magnetic separation from harvested bone marrow destined for autologous transplantation. In this system, they prepared monodisperse magnetic polystyrene beads of 3 |xm diameter containing 19.4 wt % of ultrafine magnetite by polymerization of styrene in the presence of divinylbenzene as a cross-linking agent and ultrafine magnetite particles, and subsequent modification to render them hydrophilic. Then sheep anti-mouse Ig was mixed with the magnetic beads to be physically adsorbed thereon. In the meantime, they admixed a mouse anti-neuroblastoma monoclonal antibody with bone marrow harvested from a patient to label selectively the tumor cells of neuroblastoma therein with the monoclonal antibody. Finally, they mixed the magnetic immunospecific microspheres with the so-treated bone marrow and collected selectively only the tumor cells combined with the magnetic microspheres through the immunological reaction between the Ig antibody on the magnetic beads and the monoclonal antibody on the tumor cells using Sm-Co permanent magnets arrayed along a flow tube. They removed more than 99.9 % of the tumor cells by this method. This method may be suitable for the efficient treatment of a small amount of biofluid without loss. Inununomicrospheres are used also as a blood cleaner. For example. Savin et al?^^ obtained a good result in the treatment of adverse digitalis effects by hemoperfusion through a colunm of the antidigoxin antibody fixed to agarose polyacrolein microspheres. d) Hyperthermia Hyperthermia is a modality for cancer therapy. This is a kind of thermotherapy of cancer, in which the whole body, affected part, or blood is wanned up by use of hot water, microwaves, radiofrequency, ultrasound,

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or some other energy sources, since cancerous cells are mostly more vulnerable to heat than are nomial cells. However, it is difficult to limit the heating only to the tumorous region deep in the body. In this respect, the method of Luderer et al?^^ is noteworthy. These workers used a fenimagnetic glass-ceramic of mean dimensions 1.5 (im, nominally consisting of Li ferrite (--72 wt %), P2O5 (23.7 wt %), SiO^ (3.4 wt %), and AI2O3 (0.4 wt %). The powder was prepared by milling a glass of the above composition, containing ferrimagnetic Li ferrite, crystallized from the melt. They injected mice with the magnetic powder, suspended in a physiological saline solution, into the region of a subcutaneously transplanted mammary carcinoma in the left thigh, and attained a high total regression (-50 %) and a total cure (-12 %) by applying an alternating magnetic field (10 kHz, 500 Oe) for intensive heating up to 43.5 °C only on the tumorous part, based on the energy of the magnetic hysteresis loss. This method is outstanding in its highly efficient local heating of a target deep in the body. Probably because of the large particle size around 1.5 [im, the particles remained virtually inunobile at the site of injection for at least 8 days post-injection. The next development of this method may be inmiunospecific targeting and appropriate mobility, both for targeting and for smooth post-mission excretion. 12.6A. Roles of Monodispersed Particles As is obvious from the survey on the biological and medical use of microspheres, their size control is of primary importance for realizing their ultimate functions, and thus the size distribution must also be strictly controlled to be as sharp as possible or of some designed distribution. Now that some synthetic polymers are available as almost perfectly monodispersed latices with mean sizes over a wide range, at least, the technology in size control of functional microspheres of these non-biopolymers may be close to the ultimate goal. However, once we consider the application of multiftmctional microspheres to remedial purposes by way of administration, they must not only be pathologically powerful against diseases, but also in perfect conformity with all physiological conditions. This seems to be the main reason for the still modest use of fully functional microspheres for clinical treatments, as compared to their remarkably positive use for diagnostic examinations in vitro. Thus it is requisite for their use in vivo to add another function to the microspheres used in vitro; i.e., the readiness for rapid excretion or biodegradation after completion of their missions. For this purpose, it would be desirable to advance the development of new

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technologies for the preparation of monodispersed particles of biopolymers, or fully biocompatible synthetic polymers, perfectly controlled in mean size. It is also important to provide the magnetic particles with some evasive nature from the endocytic processes in the liver and/or the spleen, and to make the mechanistic studies on the clearance of foreign bodies such as artificial polymer latices, magnetic metal oxides, etc. remaining in the human body. The ultrafine magnetic oxide particles used for the functional microspheres are usually magnetite (FejOJ particles with a mean size mostly in a range of 10-50 nm, corresponding to the range of transition from ferromagnetism to superparamagnetism (see section 12.3.1), in order to keep their stability against coagulation due to their magnetic attraction. For the preparation of ideal microspheres of high stability and uniform performance, the distribution in the magnetic oxide content among microspheres must be minimized. This is not necessarily achieved yet even in systems with almost perfectly monodispersed polymer latices prepared by emulsion polymerization in the presence of magnetic oxide particles. For this purpose, we must realize a homogeneous dispersion of the magnetic oxide particles and their uniform incorporation into all latex particles during their growth. An alternative solution of this problem may be the specific deposition of magnetic particles onto the surfaces of monodispersed latex particles, if necessary, followed by additional growth of the latex particles to incorporate the magnetic oxide layer, or selective growth of a polymer shell over a monodispersed magnetic oxide core. If each microsphere consists of a single magnetic oxide core and a polymer shell layer, the use of monodispersed magnetic oxide particles precisely controlled in their mean size is highly desirable, since the magnetic response of each particle to the external magnetic field is quite sensitive to its size, particularly in the transition range of the magnetism. However, the magnetic oxide particles available so far in such a size range, including magnetite particles in the range of 10 - 50 nm, is far from satisfactory in uniformity, even for those obtained in reversed micellar systems (see section 7.3.4). The development of a new technology for the synthesis of monodispersed magnetic oxide particles strictly controlled in mean size within this size range is important for the future. Also important is the shape control to form ellipsoidal magnetic particles of a definite aspect ratio, affecting their movement in blood vessels, their retention time in a target region, and their magnetic performance based on their shape anisotropy (see section 12.3.1).

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In the near future, multifunctional microspheres including magnetic inmiunomicrospheres will be used widely as a powerful measure for clinical treatment including gene therapy. In particularly, it will be necessary to design multifunctional microspheres characterized by a navigation system for accurate targeting, immunospecific affinity to target cells of malignant tumors, intensive release of medicines at a predetermined rate, biodegradation of the matrix polymer following the achievement of the mission, and rapid excretion of the remainders, such as magnetic navigator particles, decomposed fragments of the matrix polymer, etc. The treatment will be performed in combination with embolization therapy and some magnetic recovery system with empty satellite magnetomicrospheres for absorbing the surplus or remaining medicines which are harmful to normal tissues, and/or for capturing the post-mission major microspheres. For realizing these strategies with multifunctional microsphere systems, it is indispensable to continue the comprehensive studies from the total viewpoints of colloid science, including areas such as particle formation, particle interaction, and surface modification, as well as bioscience including genetics, immunology, biochemistry, pharmacy, cytology, bacteriology, physiology, and pathology. This is undoubtedly one of the most fascinating fields in the application of monodispersed particles at present and for the future.

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(1983); I. Pastan and M. C. Willingham, "Endocytosis." Plenum, New York, 1985. 279. (a) S. B. Sato, Y. Sako, S. Yamashita, and S. Ohnishi, J. Biochem. 100, 1481(1986); (b) S. Sato and S. Ohnishi, Kagaku to Seibutsu 26(3), 144 (1988). 280. R. R. Oder, IEEE Trans. Magn. 12, 428 (1976). 281. R. S. Molday, "CeU Separation: Method and Selected Application," Vol. 3, pp. 237-263. Academic Press, New York, 1984. 282. H. Wigzell and O. Makela, J. Exp. Med. 132, 110 (1970). 283. G. Edelman, U. Rutishauser, and F. Millette, Proc. Natl. Acad. Sci. U.SA. 68, 2153 (1971). 284. L. Chess, R. P. MacDermott, and S. F. Schlossman, J. Immunol. 113, 1113 (1974). 285. J. A. Steinkamp, M. J. Fulwyler, J. R. Coulter, R. Hiebert, J. Homey, and P. MuUaney, Rev. Sci. Instrum. 44, 1301 (1973). 286. D. R. Parks, V. Bryan, V. Oi, and L. Herzenberg, Proc. Natl. Acad. Sci. U.SA. 76, 1962 (1979). 287. T. M. Jovin and D. J. Amdt-Jovin, Ann. Rev. Biophy. Bioeng. 7, 527 (1978). 288. G. Kohler and C. MUstein, Nature 256, 495 (1975). 289. C. G. Heden, Biotechnol. Bioeng. Symp. 3, 173 (1972). 290. L. S. Hersh and S. Yaverbaum, Clin. Chim. Acta 63, 69 (1975); U.S. Patent 3,933,997 (1976). 291. L. Nye, G. C. Forrest, H. Greenwood, J. S. Gardner, R. Jay, J. R. Roberts, and J. Landon, Clin. Chim. Acta 69, 387 (1976). 292. J. L. Guesdon and S. Avrameas, Immunochemistry 14, 443 (1977). 293. R. S. Molday, S. P. S. Yen, and A. Rembaum, Nature 268, 437 (1977). 294. D. S. Ithakissios, D. O. Kubiatowicz, D. C. Windorski, and J. H. Wicks, Clin. Chim. Acta 84, 69 (1978). 295. D. S. Ithakissios and D. O. Kubiatowicz, Clin. Chem. 23, 2072 (1977). 296. G. R. Mansfield, K. L. Travis, and W. P. Vann, U.S. Patent 4,297,337 (1981). 297. (a) J. J. Killion and G. M. Kollmorgen, Nature 259, 674 (1976); (b) T. Kitao and K. Hattori, Nature 265, 81 (1977); (c) T. Nakano, Y. Imai, M. Naiki, and T. Osawa, J. Immunol. 125, 1928 (1980); (d) T. Osawa and R. Mori, "Lectin." Kodansha, Tokyo, 1976. 298. H. Miyamoto, in "Chobiryushi Handbook," (S. Saito, Ed.), pp. 860 -864. Fuji Technosystem, Tokyo, 1990. 299. M. Yamazaki, S. Ishii, and K. Iwai (Eds.), "Affinity Chromatography,"

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Kodansha, Tokyo, 1975. 300. A. J. K. Smolka, S. Margel, B. H. Nerren, and A. Rembaum, Biochim. Biophys. Acta 588, 246 (1979). 301. R. S. Molday, W. J. Dreyer, A. Rembaum, and S. P. S. Yen, J. Cell Biol. 64, 75 (1975). 302. R. S. Molday and D. Mackenzie, J. Immunol. Methods 52, 353 (1982). 303. (a) H. Mizutani, H. Mizutani, K. Nozaki, and K. Fujiwara, Microbiol. Immunol. 33, 593 (1989); (b) H. Mizutani and H. Mizutani, in "Chobiryushi Handbook," (S. Saito, Ed.), pp. 852-855. Fuji Technosystem, Tokyo, 1990. 304. F. Bucheggev, J. Immunol. Methods 49, 129 (1982). 305. R. D. Nargessi, J. Ackland, M. Hanssen, G. C. Forrest, D. S. Smitli, and J. Landon, Clin. Chem. 26, 1701 (1980); M. E. JeUey, C. J. Wang, S. J. Ekenberg, M. S. Zuelke, and D. M. Kelso, J. Immunol. Methods 67, 21 (1984). 306. R. S. Yalow and S. A. Berson, J. Clin. Invest. 39, 1157 (1960); D. M. P. TTiompson, J. Krupey, S. O. Freedman, and P. Gold, Proc. Natl. Acad. Set U.SA. 64, 161 (1969); B. C. Del Villano, S. Brennan, P. Brock, et al, Clin. Chem. 29, 549 (1983); R. C. Bast, Jr., T. L. Klug, E. John, et al. New Engl. J. Med 309, 883 (1983). 307. G. H. G. Thorpe and L. J. Kricka, Methods Enzymol. 133, 331 (1986). 308. I. Weeks, I. Beheshti, F. McCapra, A. K. Campbell, and J. S. Woodhead, Clin. Chem. 29, 1474 (1983). 309. I. Bronstein, B. Edwards, and J. C. Voyta, J. Biolumin. Chemilumin. 4, 99 (1989). 310. I. Bronstein, J. C. Voyta, G. H. G. Thorpe, L. J. Kricka, and G. Annstrong, Clin. Chem. 35, 1441 (1989). 311. I. Bronstein, J. C. Voyta, and B. Edwards, Anal. Biochem. 180, 95 (1989). 312. I. Nishizono, S. lida, N. Suzuki, H. Kawada, H. Murakami, Y. Ashihara, and M. Okada, Clin. Chem. 37, 1639 (1991). 313. J. G. Treleaven, F. M. Gibson, J. Ugelstad, A. Rembaum, T. Philips, G. D. Gaine, and J. T. Kemshead, Lancet No. 8368, 70 (1984). 314. G. Gaudermack, T. Leivestad, J. Ugelstad, and E. Thorsby, J. Immunol. Methods 90, 179 (1986). 315. P. L. Kronick, G. L. Campbell, and K. Joseph, Science 200, 1074 (1978). 316. A. Rembaum, S. P. S. Yen, and W. Volksen, CHEMTECH 8 (March), 182 (1978).

730

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317. (a) G. E. Davies and J. Janata, U.S. Patent 4,177,253 (1979); (b) R. A. Whitehead, M. S. Chagnon, E. V. Groman, and L. Josephson, U.S. Patent 4,554,088 (1985). 318. K. J. Widder, A. E. Senyei, and D. G. Scarpelli, Proc. Soc. Exp. Biol. Med. 158, 141 (1978). 319. K. J. Widder, G. Flouret, and A. E. Senyei, J. Pharm. Set 68, 79 (1979). 320. K. J. Widder, A. E. Senyei, and D. F. Ranney, in "Advances in Pharmacology and Chemotherapy," (S. Garottini et al., Eds.), Vol. 16, p. 213. Academic Press, New York, 1979. 321. K. J. Widder, R. M. Morris, G. Poore, D. P. Howard, Jr., and A. E. Senyei, Proc. Natl. Acad. Sci. USA. 78, 579 (1981). 322. K. C. Lee, I. B. Koh, and I. J. Oh, Arch. Pharmacal Res. 9, 145 (1986). 323. (a) J. M. Singler and C. M. Plotz, Am. J. Med 21, 888 (1956); (b) B. D. Fair and A. M. Jamieson, J. Colloid Interface Sci. 11, 525 (1980). 324. M. Miyamoto and S. Sasagawa, in "Chobiryushi Handbook," (S. Saito, Ed.), pp. 840-846. Fuji Technosystem, Tokyo, 1990. 325. T. Goodfriend, L. Levine, and G. Passman, Science 144, 1344 (1964). 326. R. Axen, J. Porath, and S. Emback, Nature 214, 1302 (1967); P. Cuatrecasas, J. Biol. Chem. 245, 3059 (1970). 327. T. Kitagawa and T. Aikawa, J. Biochem. 79, 233 (1976); E. Ishikawa, S. Yoshitake, M. Imagawa, and A. Sumiyoshi, Ann. N. Y. Acad. Sci. 420, 74 (1983). 328. H. Mizutani, H. Mizutani, and K. Fujisawa, in "Intern. Symp. Basic and Clinical Approaches to Virus Chemotherapy," Final Programme, p. 35. Helsinki, 1988; K. Fujiwara, H. Mizutani, and H. Mizutani, ibid. p. 37. 1988. 329. A. H. Dutton, K. T. Tokuyasu, and S. J. Singer, Proc. Natl. Acad. Sci. USA. 76, 3392 (1979). 330. H. Kitano, in "Chobiryushi Handbook," (S. Saito, Ed.), pp. 856-859. Fuji Technosystem, Tokyo, 1990. 331. M. Nakano, Y. Morimoto, and K. Sugibayashi, "Drug Delivery Systems." Nanzando, Tokyo, 1986. 332. J. E. Dion, R. N. Rankin, F. Vinnela, A. J. Fox, A. C. Wallace, and M. Mervart, Radiology 160, 717 (1986). 333. T. Kato, R. Nemoto, H. Mori, and I. Kumagai, Cancer 46, 14 (1980). 334. P. Edman, P. Artursson, E. Bjoerk, and B. Davidsson, Int. J. Pharm. 34, 225 (1987).

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731

335. H. Savin, L. Marcus, S. Margel, M. Ofarim, and M. Ravid, Am. Heart J. 113, 1078 (1987). 336. A. A. Luderer, N. F. Borrelli, J. N. Panzarino, G. R. Mansfield, D. M. Hess, J. L. Brown, E. H. Bamett, and E. W. Hahn, Radiation Res. 94, 190 (1983).

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NAME INDEX Abe, A 629 Acher, O. 270 Ackland, J. 698 Acquista, C. 337 Adachi, M. 336 Adair, J. H. 311 Adler, S, F. 653 Aharoni, A 617, 624 Ahn, T.-M. 654 Ahrenkiel, R. K. 585 Aika, K. 656 Aikawa, T. 703, 708 Aikawa, Y. 657, 658 Aiken, B. 238, 240, 336, 407, 414, 418 Aiken, J. D., m 196, 217 Aita, S. 270, 275, 277, 394, 395, 396 Akaboii, H. 330 Akhtar, K. 240, 418 Akimov, L A 561 Akinc, M. 238, 413 Aldag, A 643 Alder, B. J. 546 Alessi, M. 240, 407, 414 Alfrey, T., Jr. 292, 293, 394, 295, 304, 548 Alivisatos, A. P. 310 AUen, S. J. 412 Allen, T. 517 AlMawlawi, D. 330 Almog, Y. 194, 259, 260 Amemiya, H. 620 Amemiya, M. 620 Amiel, O. 336 Amin, N. 407 Anderson, J. R. 644, 645, 656 Anderson, R. B. 633 Andreasen, A H. M. 218, 221, 234, 235, 406

Andres, M. 254 Andres-Verges, M. 230, 255 Anthon, D. W. 242 Antl, L. 260 Antoniades, M. G. 291, 390 Antonietti, M. 291 Arai, H. 635, 652 Arai, K. 336 Arai, S. F. 696 Arai, Y. 622 Arajs, S. 407, 429, 570 Arakawa, H. 644 Araki, T. 300 Armstrong, G. 698, 708 Amdt, V. 619 Amdt-Jovin, D. J. 697 Arnold, S. 413 Arosa, A K. 545 Arriagada, F. J. 310 Arther, P., Jr. 621 Artursson, P. 710 Asada, S. 620 Asakura, K. 194, 216, 419, 631 Asano, M. 261 Asano, Y. 310, 311 Asher, S. A 311, 314 Ashihara, Y. 698, 708 Ashkin, A 532, 684 Atik, S. S. 311 Auser, W. 336 Avrameas, S. 697, 698, 700, 703 Awan, M. A 260, 263, 264, 265 Axen, R. 703 Ayyub, P. 314

Baba, N. 330 Baetzold, R. C.

637, 638

734 Bailey, J. K. 245, 252 BaiUy, R. 679 Baker, M. 677 Balboa, A. 336, 338, 407, 410 Bales, S. E. 630 Bando, K. 253 Bando, S. 432, 585, 586, 587 Bangham, O. B. 421 Baranov, E. V. 561 Bard, A. J. 633, 657 Barkalov, V. S. 372 Barnes, M. D. 233 Barnett, E. H. 712 Barnickel, P. 309 Baron, K. 634 Barouch, E. 535, 537 Barrer, R. M. 662 Barret, K. E. J. 258, 259, 260, 261 Barringer, E. A. 245, 411, 588, 589, 590, 591, 592 Barth, H. G. 517 Bartholomew, C. H. 644 Barthomeuf, D. 332, 647 Bartlet, P. 548 Bartley, W. J. 633 Bassett, D. R. 294 Bast, R. C, Jr. 698 Bate, G. 566, 619 Bateman, J. B. 557 Batra, A P. 176, 477 Battaglia, C. J. 372 Baum, T. H. 336 Baus, M. 548 Bawendi, M. G. 242, 559, 560 Bean, C P. 617 Beattie, W. H. 140, 515, 516, 517 Beaudoin, B. 196, 270 Beaupere, D. 214 Becher, R. 38, 615 Beck, J. S. 333 Beddow, J. K. 607, 624 Behal, S. 194, 217 Beheshti, I. 698 Bein, T. 332, 334 Bell, A. 252, 256, 257 Belloni, J. 217, 631, 636

NAME INDEX Benson, G. C. 25 Benson, J. E. 643 Berendsen, R. 83, 289 Berge, A 294, 296, 297, 300, 375, 420, 434 Bergeret, G. 332 Bergna, H. E. 245, 246, 247 Bergstrom, J. 300, 420 Berman, H. 679 Berner, A 337 Berriraan, R. W. 80, 83 Berry, C R. 23, 24, 77, 80, 83, 132, 140, 141, 161, 162, 289, 369, 372, 407, 474, 495, 496, 585, 587 Berson, S. A 698 Beutel, J. 561 Bianchi, C L. 240, 407, 414 Bickford, L. R. 620 Bier, M. 529 Binning, E. L. 531 Biswas, P. 336 Bjoerk, E. 710 Bjorkholm, J. E. 532 Bjorling, M. 309 Black, D. L. 291, 390 Blackley, D. C. 300, 431 Blankenship, R. M. 434 Blesa, M. A 139, 240, 253, 270, 407, 414 Blin, B. 196, 214, 270 Bllue, C. 336 Boardman, A D. 685 Bobalek, E. G. 300 Bockris, J. O'M. 202, 252 Bodart-Ravet, I. 310 Bogg, T. G. 140, 390 Bogush, G. H. 245, 246, 247, 248 Bohn, E. 243, 244, 411, 588 Bohren, C. R 677, 685 Bond, G. C 635, 637, 640, 641, 642 Boolchand, P. 336 Booth, F. 528 Bordeaux, J. J. 236 Borgarello, E. 634, 635 Borginon, H. 140, 194 Bonelli, N. F. 712 Bosboora, M. 252

NAME INDEX Bothe, J. V. 242 Boudart, M. 635, 642, 643, 644, 656 Boulanger, L. 310 Boutonnet, M. 309, 659 Bowen, H. K. 245, 319, 411, 588, 589, 590, 591, 592 Brabec, L. 332 Brace, R. 252, 256, 257 Bradford, E. B. 292, 293, 294, 295, 304, 548 Bradley, J. S. 194, 216, 217 Bradshaw, A. M. 639, 640 Brady, L. E. 559, 560, 561, 564 Brain, J. D. 696 Breck, D. W. 662 Breitscheidel, B. 329, 330 Brennan, J. F. 634 Brennan, S. 698 Breuer, N. 196, 217 Bridget, K. 255, 266, 414 Brinker, C. J. 245, 252, 590, 591, 592 Britz, T. J. 242 Brock, P. 698 Bronstein, I. 698, 708 Brown, B. D. 370 Brown, J. L. 712 Brown, P. W. 242 Brown, W. R, Jr. 617 Browning, R. S. 677 Brownlow, J. M. 620 Brumlik, C. J. 330 Brunelle, J. P. 644 Brus, L. E. 310 Brust, T. B. 291, 390 Bruun, B. 159, 160 Bryan, V. 697 Bucheggev, F. 698 Budnik, M. 252 Budz, J. A. 291, 390 Buhrman, R. A 629, 654 Buining, P. A 252 Bulatov, A V. 634 Burwell, R. L., Jr. 644 Buss, D. H. 253, 256 Butler, E. A 231 Butler, J. L. 644

735 Butt, J. B. 644 Buttet, J. 638, 639 Byers, C. H. 245

Cabane, B. 313 Cai, W. 429 Cairati, P. 240, 407, 414 Calabrese, J. C. 333 Calvert, P. D. 245, 589 Campbell, A K. 698 Campbell, G. L. 700, 705 Candal, R. J. 240, 407, 414 Candau, F. 311 Candau, S. 311 Cardell, R. R., Jr. 252, 406 Cardon, F. 412 Carroll, B. H. 412 Carter, J. L. 643 Castellano, M. 239, 241, 414, 434 Catinat, M. 388, 389, 390 Catone, D. L. 252, 254, 256 Cayey, N. W. 252, 256 Cazeau, P. 336 CegUe, A- 312 Ceresa, E. M, 619 Chagnon, M. S. 700, 701 Chaikin, P. M. 548 Chaiko, D. J. 311 Chainey, M. 300, 431 Charabellan, A. 644 Chan, D. Y. C. 550 Chang, C. 310 Chang, M. 340, 341 Chang, S. 311, 314 Chang, Y. C. 291, 390 Chanter, J. B. 581, 582 Charlson, R. J. 677 Chateau, H. 159, 160, 162, 163, 164, 166 Chaudret, B. 194, 216 Chawanya, H. 631, 632 Che, G. 330, 331 Chen, H. Y. 621 Chen, S. 194, 225, 228, 247, 371, 374, 391, 421, 433, 469, 470, 473, 474 Chen, Y. 286

736 Cheng, C M. 298, 434 Chess, L. 697 Chevalier, J. P. 217, 631, 636 Chia, Y.-H. 245, 591 Chibante, P. 260 Chien, C L. 255, 414 Chikazumi, S. 565, 566, 567 Chin, G.-Y. 588 Chini, P. 333 Chittofrati, A. 195, 230 Chiu, G. 219, 224 Cho, H. M. 621 Chohno, M. 634 Choi, G. N. 260 Chon, M. C 369, 411, 594, 595, 596 Chou, K.-S. 232, 411 Chu, B. 507 Chu, C. T. 333 Chubachi, R. 620 Chung, S. K. 340, 341 Chylek, P. 684 Cizeron, J. 311 Qaerbout, A. 310, 314 Qaes, F. 83, 289 Qaes, F. H. 140, 384 Qark, D. E. 590, 591, 592 Qark, P. W. 152 Qarke, J. H. R. 507 Qaxton, T. A 25 Qayfield, E. J. 540 Cohen, A 677 Cohen, D. 696 Cohen, G. L. 233 Cohen, J. B. 644 Colfen, H 291 Collins, L. F. 684 Colvin, M. 340, 341 Combes, J. R. 260 Compton, W. D. 477 Connaway, M. C. 332 Cooke, D. D. 336, 337, 677, 679, 680, 681, 682 Coombs, N. 330 Coquard, M. 159, 160, 161 Corolleur, C 644 Corolleur, S. 644

NAME INDEX Corradi, A R. 619 Corti, M. 312 Coulter, J. R. 697 Couprie, S. 162, 163, 166 Courbon, H. 635 Cox, D. E. 332 Cox, N. L. 621 Cox, R. J. 194 Craik, D. J. 566, 619, 606 Crocker, J. C 532 Croucher, M. D. 260 Cuatrecasas, P. 703 Cupp, R. E. 677 Curie, P. 118 Cusumano, J. A. 643, 648

da Vila, L. D. 238, 411 Dadyburjor, D. B. 140, 653 Dahl, L. F. 333 Daichuan, D. 239, 385 Daneels, G. 692, 695 Daniels, E. S. 294 Danielsson, I. 309 Dankliker, W. B. 292 Dartigues, J. M. 644 Das, K. P. 312 Datka, J. 637, 640, 641, 642 Dauchot, J. 213 Dautzenberg, F. M. 650, 651, 654, 663 Davey, P. T. 459 David, L. D. 254 Davidson, A. P. 330 Davidsson, B. 710 Davies, C. W. 57, 140 Davies, G. E. 700, 701 Davis, E. J. 337 Davis, R. F. 588 Davis, S. C. 632, 634, 636 Davolos, M. R. 238, 411 Davy, E. 233 Dawkins, J. V. 260 Day, K. L. 685 De, T. K. 311 De Bittetto, D. J. 621 De Brabander, M. 692, 694, 695

NAME INDEX De Brabandere, L 194 de Cugnac, A. 159, 160, 161, 162, 163, 166 de Hek, H. 431 De Mallmann, A 332, 647 De Mey, J. 692, 694, 695 de Silva, G. P. H. L. 421 de Vore, J. R. 686 Dean, J. A. 261 DeBaun, R. M. 653 Degiorgio, V. 312 DeGroot, K. 242 Del Villano, B. C. 698 Delannay, F. 233, 663 Delcouit, M. O. 217, 631, 636 Delmon, B. 202, 233, 437, 633, 634, 657, 663 DeLuisi, J. J. 677 Dembinski, G. W. 643, 648 Demchak, R. 252, 253, 256 Denkov, N. D. 550 Denny, P. J. 662 Derjaguin, B. V. 533, 535, 536, 545, 546, 565 Derouane, E. G. 310, 659 Derr, V. E. 677 DeSimone, J. M. 260 De2elic, Gj. 196, 222, 235, 406, 557 Dietz, E. 422 Dimonie, V. L. 260, 263, 264, 265, 300, 431 Dinegar, R. H. 41, 199, 219 Ding, W. 621 Dion, J. E. 710 Dirige, G. E. 194, 196, 225, 226, 227, 228, 231, 232, 247, 282, 283, 371, 373, 374, 405, 406, 421, 454, 459, 460, 463, 464, 465, 466, 535, 541, 542, 543, 544 Dirksen, J. A 245 Disdier, J. 635 Dislich, H. 244 Dixon, J. G. 242 Doremus, R. H. 677, 684 Dorhout, P. K. 330 Doring, W. 38, 615 Dorling, T. A 636, 637, 643, 645, 646,

737 649, 651, 652 Dosho, S. 546 Dougharty, N. A 643 Douglass, D. C 310 Dreyer, W. J. 698, 700, 701, 703 Driessen, A A. 242 Drozdova, L. 332 Du, Y. 621 Dube, G. 270 Duboudin, F. 336 Ducamp-Sanguesa, C. 194, 214, 215, 392 Ducker, W. A 531 Dumesic, J. A 644 Dumont, B. 194, 270 Duncan, T. M. 310 Dunn, W. W. 657 Dunworth, W. P. 632 Duonghong, D. 634, 635 Duteil, A 194, 216 Dutton, A H. 707 Duvauchelle, N. 215 Dziedzic, J. M. 532

Eastman, E. D. 159 Eddy, M. M. 332 Edelman, G. 697 Edelson, L. H. 245, 247 Edman, P. 710 Edwards, B. 698, 708 Efner, H. F. 630 Egami, T. 565, 566, 567, 568 Eicke, H.-F. 309 Einstein, A 521 Ekenberg, S. J. 698 El-Aasser, M. S. 194, 259, 260, 261, 263, 264, 265, 292, 294, 298, 299, 300, 396, 431, 434 EUingsen, T. 294, 296, 297, 298, 375, 434, 393, 394 Ellis, A B. 657 Engler, E. M. 336 Englman, R. 502 Enomoto, N. 426, 430 Epel, J. N. 557 Epstein, N. 370

738 Ernback, S. 703 Eshler, D. C. 557 Espenscheid, W. F. 233, 558, 559 Espiard, Ph. 428 Esumi, K. 195, 196, 211, 212, 213, 460 Evva, F. 372 Ewart, R. H. 292, 294, 304

Faerman, G. P. 372 Fair, B. D. 701 Fan, X. 407 Farnell, G. C 581, 582 Farone, W. A. 233, 558 Fassman, G. 703 Faulk, W. P. 692 Feeney, P. J. 295 Fegley, B., Jr. 245, 411, 588, 590, 591, 592 Feitknecht, W. 266 Feltin, N. 311 Fery, N. 422, 423 Fiedorow, R. M. J. 654, 655 Fievet, F. 194, 196, 202, 214, 270, 393 Fievet-Vincent, F. 194, 196, 270 Figlarz, M. 194, 196, 202, 214, 215, 270, 392, 393 Figliolia, N. E. 253 Fink, A. 243, 244, 411, 588 Finke, R. G. 196, 217 Fischer, C. 270 Fischer, I. 252, 257 Fischer, W. R. 385 Fisher, E. R. 330, 331 Fitch, R. M. 300, 311, 431 Hood, H. 159, 160 Flouret, G. 700, 709 Flynn, C. M., Jr. 139 Flynn, P. C. 654 Fogler, H. S. 310 Forres, M. A. 550 Forrest, G. C. 697, 698, 700, 703 Forsterling, C. 679 Foss, C. A , Jr. 330 Fournet, G. 313 Fox, A. J. 710

NAME INDEX Francois, E. 388, 389, 390 Franta, E 311 Frechet, J. M. J. 300 Fredrikson, K. C. 253, 254 Freedman, A P. 696 Freedman, S. O. 698 Frei, E. H. 617 Frenkel, D. 548 Freyhardt, H. C 619 Friberg, S. E. 202, 312, 314, 315, 316 Frisch, H. L. 535, 536 Fuchs, R. 685 Fuerstenau, D. W. 536, 545 Fujiki, K. 424 Fujimoto, K. 261, 264 Fujimoto, T. 332, 333, 647 Fujimura, M. 434 Fujino, A 310 Fujisawa, K. 705 Fujisawa, Y. 242 Fujishige, S. 631 Fujishiro, Y. 229 Fujita, T. 621 Fujiwara, K. 698, 705 Fukai, K. 385, 619 Fukuda, K. 330 Fukui, H. 253 Fukui, T. 245 Fukuoka, A. 332, 333, 334, 647, 648 Fukushima, T. 330 Fukushima, Y. 333, 334, 647 Fulwyler, M. J. 697 Fumeaux, R. C. 330 Furusawa, K. 428

Gadsden, J. A. 458 Gaine, G. D. 700, 705, 711 Galembeck, F. 219 Galin, P. 332 Gallezot, P. 332, 637, 640, 641, 642 Gangolli, S. 336, 415, 429, 434 Garcia, A A 531 Gardner, J. S. 697, 698, 700, 703 Gardner, W. L. 125, 505 Garg, A. 418

NAME INDEX Garottini, S. 700, 709, 710 Garten, R. L. 633, 656 Garton, G. 677 Gates, B. C 332, 657 Gatteschi, D. 240, 407, 414 Gaudermack, G. 700 Gault, F. G. 644 Gehlen, K. V. 679 Genzel, L. 502 Gerber, C F. 531 Gestblom, B. 312 Geuens, G. 692, 694, 695 Gherardi, P. 235, 407 Gibbons, E. F. 590 Gibbs, J. W. 118 Gibson, F. M. 700, 705, 711 Gibson, J. M. 310 Giesche, H. 413, 418, 687, 688 Gifford, W. A 550 Gilbert, R. G. 295 Gillespie, W. G. 642, 658 Ginell, A. M. 222 Ginell, R. 222 Girvin, C. H. 643 Gjostein, N. A 653, 655 Glaeser, A M. 245, 247 Glatter, O. 313 Glemser, O. 253, 256 Gobe, M. 310 Gobet, J. 233 Goia, D. V. 270 Gold, P. 698 Goldstein, M. S. 653 Gonzalez-Carreiio, T. 252, 255 Goodfriend, T. 703 Goodwin, J. W. 260, 294, 549 Gordon, L. 56 Gordon, S. 40 Gorllezat, P. 332 Gourgue, A 310, 659 Gowda, G. 319 Granqvist, C. G. 629, 654, 677 Gratzel, M. 634, 635 Graydon, W. F. 644 Greegor, R. B. 640, 641 Green, F. H. Y. 696

739 Greenwood, H. 697, 698, 700, 703 Grier, D. G. 532 Griffith, R. L. 495 Groman, E. V. 700, 701 Gruber, E. E. 655 Gniber, H. L. 653 Grunze, M. 639, 640 Gu, J. 692 Guesdon, J. 697, 698, 700, 703 Guinier, A 313, 492 Gulik-Krzywicki, T. 309, 313 Gunesin, B. Z. 260 Gustafson, R. J. 260 Guyot, A 428

Hachenberg, H. 633 Hachisu, S. 545, 546, 548 Hada, H. 217, 631, 636 Hahn, E. W. 712 Hair, M. L. 195, 259, 300, 415, 434 Hall, W. K. 652 Haller, G. L. 656 Hamada, S. 202, 213, 218, 219, 220, 223, 229, 235, 252, 253, 254, 269, 385, 414 Hamaker, H. C. 530 Hamann, K. 420, 422, 423, 424, 427, 428, 430, 431 Hamashima, M. 294 Hamielec, A E. 294 Hamilton, J. F. 559, 560, 561, 564 Hamm, F. A. 559 Hanami, T. 252 Hansen, F. K. 297, 375 Hanson, B. E. 332 Hanssen, M. 698 Haq, I. 239, 240, 418 Haque, M. F. 567, 569, 571, 572, 573 Harada, M. 194, 216, 419, 631 Harada, Y, 532 Harding, M. J. 77, 140 Hardy, A B. 319 Harfield, J. G. 517 Harkins, W. D. 292, 294, 295, 296 Harris, M. T. 245 Harris, T. D. 310

740 Harrison, D. P. 632, 634 Hartog, F. 642, 643 Hartsell, D. L. 291, 390 Haruta, M. 202, 233, 437, 633, 634, 657, 663 Hasaka, M. 548 Hasegawa, S. 229, 332 Hashimoto, K. 657 Hattori, H. 656 Hattori, K. 196, 697 Hattori, M. 260 Haugh, E. F. 194 Hautecler, M. 213 Havey, K. 311 Hayakawa, S. 690 Hayakawa, T. 432 Hayama, F. 620 Hayashi, C. 630 Hayashi, S. 502 Hayashi, T. 630, 631 Hayes, D. 40, 58 Haynes, J. R. 559 Healy, T. W. 536, 545 Hearn, J. 294 Heatley, F. 311 Hecht, H. G. 505 Heden, C. G. 697, 703 Hegedus, L. L. 634 Heintz, J. M. 336 Heistand, R. H., II 245, 591 Helbig, W. 196, 217 Helenius, A. 696 Heller, A. 270 Heller, W. 252, 406, 513, 556, 557 Helling, J. O. 125, 412, 505 Hench, L. L. 245, 411, 588, 590, 591 Henry, D. C. 527, 528 Henry, J. D. 550 Henry, M. 245 Her, Y.-S. 238, 244, 257, 282, 369, 411, 594, 595, 596 Herak, M. J. 222 Herak, M. M. 222 Hermann, B. M. 677 Herps, H. 517 Herrera-Urbina, R. 194, 214, 215, 392

NAME INDEX Herring, C. 588 Herrmann, A. 637 Herrmann, J. M. 635 Herrmann, R. A. 653 Herron, N. 332 Hersh, L. S. 697, 698, 700, 703 Herz, A. H. 125, 140, 505 Herz, P. K. 642, 658 Herzberg, G. 458 Herzenberg, L. 697 Heseltine, D. W. 372 Hess, D. M. 712 Hesselink, F. Th. 193 Hibst, H. 622 Hidaka, Y. 427, 430 Hidehira, Y. 621 Hiebert, R. 697 Higashimoto, N. 334, 647 Higgins, J. B. 333 Hill, E. W. 194, 216, 217 Hill, R. D. 260 Hillenbrand, C. 337 Hiller, D. M. 621 Hillier, J. 212 Hines, L. 633 Hirai, H. 194, 195, 216, 217, 270, 419, 631, 632, 633, 634, 636, 655 Hirai, T. 310 Hirasawa, I. 291, 369 Hirashima, H. 245 Hirata, A. 83, 410 Hirata, J. 620 Hirsch, H. 167, 587 Hirtzel, C. S. 535 Ho, C. C. 294 Hochepied, J. F. 311 Hodgson, A. W. 336 Hoekstra, J. 634 Hoene, R. 428 Hoerlin, H. 474 Hofiman, D. 254 Hofmann, A. W. 231 Hogg, R. 536, 545 Hohnishi, S. 83 Hoilister, K. H. 195 Holm, L. 297, 375

NAME INDEX Honda, H. 690 Hoover, W. G. 546 Horak, D. 517 Horie, R. 430 Horn, J. 428 Homey, J. 697 Homyak, G. L. 330 Hortig, G. 637 Hoshino, F. 260, 294 Hosoda, S. 287, 288 Hosoe, M. 194, 216 Hosoi, K. 300, 431 Hosotani, T. 195, 260, 261, 299, 411, 432, 435 Hosoya, K. 300 Hou, M. J. 314 House, G. L. 291, 390 Houston, R. J. 653 Howard, D. P., Jr. 700, 709 Hoyen, H. A., Jr. 564 Hoyer, P. 330 Hsia, Y. 286 Hsu, W. P. 194, 223, 237, 238, 239, 240, 253, 255, 257, 270, 407, 411, 412, 413, 414, 418, 677, 680, 683, 684, 687, 688, 689 Hu, R. 260, 300, 431 Hu, Z. 286 Huang, C. 240, 429 Hubbard, A. 696 Huber, C. 334 Huckel, E. 527 Hudson, J. E. 621 Huffman, D. R. 677, 685 Hughes, S. 336 Hughes, T. R. 653 Hughes, W. 686 Hulstede, P. 332 Hunderi, O. 677 Hunter, M. S. 330 Hurd, A. J. 549 Hyson, M. T. 340, 341

Ichikawa, K. 434 Ichikawa, M. 332, 333, 334, 633, 647, 648

741 Ichikawa, S. 213, 646, 647 Ida, T. 633, 636 Ido, T. 621 Iglesias, J. E. 502 Iguchi, M. 195, 320, 321 Diara, T. 420 lida, S. 565, 698, 708 lida, Y. 439, 440 lijima, H. 633 lijima, S. 633, 634, 657 Ikeda, M. 321 Ikegami, K. 195, 259, 260, 300, 431 Ikemoto, T. 245, 411, 589, 590 Imagawa, M. 703, 708 Imai, Y. 697 Imaoka, Y. 620 Imelik, B. 637, 640, 641, 642 Imizu, Y. 632, 634, 636 Inaba, H. 532 Inagaki, M. 239, 414 Inagaki, S. 333, 334, 647, 648 Ingebrethsen, B. J. 336, 338, 407, 410 Ingert, D. 311 Ingrahara, J. N. 621 Inn, E. C. Y. 336 Inoue, T. 381 Isaacs, P. K. 300, 414 Ise, N. 546 Ishida, A. 620 Ishigami, Y. 294 Ishii, S. 697 Ishijima, H. 245 Ishikawa, E. 703, 708 Ishikawa, T. 195, 196, 241, 252, 255, 413, 414, 418, 439 Ishimaru, S. 432, 585, 586, 587 Ishimizu, E. 310, 311 Ishiyama, I. 213, 218, 229 Ishizaka, T. 291, 390, 690 Ishizuka, H. 196, 211, 460 Ishizuka, M. 195 Itabashi, K. 332 Ithakissios, D. S. 697, 698, 700 Ito, H. 229 Ito, K. 546 Ito, S. 420

742 Ito, T. 297, 332, 375 Itoh, H. 41, 42, 43, 48, 49, 51, 53, 194, 231, 243, 270, 273, 274, 275, 276, 277, 278, 279, 280, 324, 370, 371, 372, 374, 375, 377, 378, 379, 381, 382, 383, 385, 386, 387, 398, 399, 401, 402, 404, 406, 439, 440, 457, 458, 469, 497, 498, 499, 500, 502, 529, 532, 533, 534, 624, 625, 626 Ivanov, I. B. 550 Iwai, K. 697 Iwai, S. 546 Iwai, T. 425 Iwamoto, M. 332 Iwasaki, M. 40, 57, 58, 318, 460, 461 Iwasaki, S. 621 Iwasaki, Y. 260 Iwasawa, Y. 632 Izumi, J. 195, 260, 261, 299, 411, 432, 435

Jablonski, J. 252, 256 Jacobs, I. S. 617 Jacowitz, R. 336 Jaeger, N. I. 332 Jaenicke, W. 686 Jafelicci, M., Jr. 219 Jagannathan, R. 59, 80, 112, 369 Jain, T. K. 311 Jakusch, H. 622 James, T. H. 14, 77, 140, 372, 561, 564, 585 Jamieson, A, M. 701 Janata, J. 700, 701 Janekovic, A. 235, 237, 413, 434 Jansen, J. B. H. 252 Jay, R. 697, 698, 700, 703 Jean, J. H. 195, 245, 594 Jelley, M. E. 698 Jiang, Y. 621 Jimbo, G. 690 Joekes, I. 219 John, E. 698 Johnson, I. 233, 554, 555, 556 Johnson, J. E. 195

NAME INDEX Johnson, O. W. 590 Jones, A. L. 57 Jones, M. E. 252, 256 Jorgedal, A. 297, 375 Jorgensen, C V. 231 Joseph, K. 700, 705 Josephson, L. 700, 701 Jovin, T. M. 697 Jubb, N. 411, 588, 590, 591 Judd, D. B. 680, 681 Junkers, G. 412

Kaden, V. 427 Kaeriyama, K. 633 Kaetsu, I. 261 Kaggerud, K. H. 294, 296, 297, 375, 434 Kahlweit, M. 140 Kaischew, R. 132 Kallay, N. 252, 257, 535, 536, 537, 567, 569, 571, 572, 573 Kamel, A A. 292 Karapmann, L. 140 Kanai, H. 632, 636 Kanamori, H. 502 Kandori, K. 195, 196, 241, 252, 255, 310, 311 Kaneko, H. 245, 607 Kaneko, S. 253 Kano, H. 223 Karakawa, H. 426, 427, 430 Karasawa, S. 195 Kasai, T. 245 Kashiwabara, M. 261, 264 Kasper, G. 337 Kataoka, S. 260, 264 Katayama, Y. 260 Katila, T. 696 Kato, H. 260 Kato, M. 245, 411, 589, 590 Kato, T. 710 Katsanis, E. P. 222 Katsuta, Y. 299, 395 Katzer, J. R. 657 Kawada, H. 698, 708 Kawaguchi, H. 260, 261, 264, 294

NAME INDEX Kawahara, M. 260 Kawahashi, N. 419, 432, 433 Kawai, S. 330 Kawai, T. 310, 311, 635, 657 Kawasaki, H. 323, 326, 327, 328, 329, 501, 660, 662 Kawashima, Y. 252, 255 Kawi, S. 332 Keevert, J. E. 412, 561, 563, 564 Keffer, K. D. 245 Keghouche, N. 217, 631, 636 Keller, F. 330 Kellogg, L. M. 561 Kelly, T. M. 412 Kelso, D. M. 698 Kemshead, J. T. 700, 705, 711 Kennedy, L. A. 634 Kerker, M. 233, 292, 336, 337, 507, 554, 556, 558, 559, 677, 679, 680, 681, 682, 688 Kershaw, D. 427 Ketellapper, L. 194 Khan, M. M. 270, 274, 276, 277, 372, 381, 382, 385 Khidekel, M. L. 634 Kiboku, M. 420 Kido, T. 311 Kiehl, J. T. 684 Kihira, H. 535, 536, 545 Kikuchi, H. 287, 288, 462 Killion, J. J. 697 Kim, C. H. 195, 253, 254, 589, 594 Kim, D. K. 195, 253, 254, 589, 594 Kim, J. H. 300, 431 Kim, M. J. 224, 230, 235, 407 Kimata, K. 300 Kimoto, T. 620 Kimura, H. 317, 318, 319 Kimura, Y. 428 King, D. L. 644 Kinoshita, K. 639 Kirkwood, J. G. 546 Kirschner, J. 637 Kishimoto, M. 620 Kiss, I. 195 Kitaev, G. A. 233

743 Kitagawa, T. 703, 708 Kitahara, A. 195, 242, 310, 311, 388 Kitajima, S. 239 Kitamoto, T. 613, 622, 623 Kitamura, K. 239, 414 Kitani, S. 336, 558 Kitano, H. 546, 709 BCitao, T. 697 Kitchner, J. A. 537 Kito, T. 427, 428, 430 Kittel, C. 605, 606, 607, 624 Kiuchi, H. 197 Kiwi, J. 634, 635 Kizling, J. 309, 312, 659 Kjaer, B. 218, 221, 234, 235, 406 Klabunde, K. J. 630, 632, 634, 636 Kleder, J. 336 Klein, C. 194, 216, 217 Klein, C. P. A. T. 242 Klein, D. H. 56 Klein, E. 132, 133, 140, 289, 369, 377, 412, 585 KHer, M. 545, 549 Kliewer, K. L. 564, 685 Klimisch, R. L. 633, 634 Klomp, C. J. 620 Klug, T. L. 698 Knacke, O. 133, 377 Knowels, I. E. 624 Knozinger, H. 332 Ko, M. K. W. 684 Kobayashi, C 197 Kobayashi, H. 339, 634 Kobayashi, M. 238, 407, 411, 414, 591, 593 Kobayashi, S. 194, 260, 300, 431, 435 Kobayashi, T. 229, 633, 634, 657 Kobayashi, Y. 545, 546 Kodas, T. T. 336, 337 Koehler, J. S. 564 Koga, F. 634, 644 Koga, J. 338, 339 Koga, T. 619 Kogure, A. 422 Koh, I. B. 700 Kohler, G. 697

744 Koide, M. 310, 388 Koide, Y. 621 Koishi, M. 690 Koiwai, A. 333 Koizumi, M. 662 Koka, T. 385 Kolar, D. 245 Koliadima, A. 224 Kollmorgen, G. M. 697 Kolthoff, I. M. 149, 159 Koma, Y. 377 Koraasawa, I. 310 Komatsu, M. 426, 427, 430 Komatsuzaki, S. 633 Koraiyama, M. 632, 633, 634, 655 Kon-no, K. 310, 311, 388 Kondo, A 297, 375, 430 Kondo, K. 430 Kondo, M 591 Kondo, T. 194, 195, 196 Konnb, M. 245 Koopal, L. K. 677 Kortan, R. 310 Kose, A 545, 546 Kosec, M. 245 Kosugi, N. 332, 647 Kotera, Y. 633, 634, 636, 644 Kotria, J. 332 Kousaka, Y. 336 Kowalski, A 434 Kraeutler, B. 633 Kralchevsky, P. A 550, 551 Kratky, O. 313 Kratohvil, J. P. 222, 233, 412, 557, 677, 679, 680, 681, 682, 687 Kratohvil, S. 194, 237, 239, 252, 253, 256, 257, 269, 379, 407, 414, 417 Krenkler, K P. 430 Kresge, C. T. 333 Kricka, L. J. 698, 708 Krieger, I. M. 260 Kroker, R. 431 Kronick, P. L. 700, 705 Kruyt, H. R. 524, 528, 529 Krupey, J. 698 Kubelka, P. 505

NAME INDEX Kubelkova, L. 332 Kubiatowicz, D. O. 697, 698, 700 Kubo, O. 621 Kubo, R. 628 Kubo, T. 690 Kubota, Y. 620 Kuczynski, G. C 654 Kudo, Y. 213, 218, 219, 220, 223, 229, 235, 252, 253, 254, 385, 414 Kumagai, I. 710 Kuraagai, S. 686, 690, 691 Kumar, P. 314 Kumazawa, H. 621 Kunitake, T. 372 Kuo, R. J. 535 Kuroda, H. 197, 332, 647 Kuroda, K 333 Kurster, F. W. 159 Kusahara, T. 644 Kushihashi, K 194, 216, 419, 631 Kyotani, T. 330, 331, 332

Lagier, J. P. 194, 196, 202, 214, 270, 393 Laible, R. 420, 422, 423, 424, 428, 430 Lajoie, G. 260 Lakshmi, B. B. 330, 331 Lamaitre, J. 233, 663 Lambert, R. M. 334, 647 LaMer, V. K 41, 199, 219, 233, 336, 554, 555, 556 Landau, L. 533, 535, 546, 565 Landolt, D. 638, 639 Landon, J. 697, 698, 700, 703 Langan, M. D. 644 Langangar, G. 692, 695 Lanza, P. 77 Larsen, A E. 532 Larson, E, S. 679 Larson, E. T. 474 Larson, J. G. 633, 634 Larson, R. L 252, 256 Lategan, P. M. 242 Le Blanc, J. T. 412 Le Page, J. F. 644 Lecky, J. 633

NAME INDEX Leclere, C. 217, 631 Lee, B. 270, 277, 404 Lee, B. I. 619, 620 Lee, J. 195, 300, 420 Lee, K. C. 700 Lee, S.-H. 244, 257, 282, 369 Lee, S.-K. 321 Lee, S. Y. 588 Lee, V. Y. 336 Lefebvre, F. 332 Lehn, J. M. 657 Leivestad, T. 700 Lekkerkerker, H. N. W. 252 Leong, Y. S. 311 Leonm, R. 334 Leonowicz, M. E. 333 Lester, G. R. 634 Leubner, L H. 58, 80, 369 Leupold, E. I. 633 Levern, H. S. see von Levem, H. S. Levine, L. 703 Levoy, N. 588 Levy, L. 311 Levy, M. 194, 259, 260 Lewis, J. D. 290 Lewis, K. E. 195 Li, D. 622 Li, G.-J. 332, 333, 647 U, K. 260 U, M. 548 Li, T. 311 Li, Y. Q. 531 Liang, W. 330 Lianos, P. 311 Libchaber, A. 532 Libeer, J. 384 Lide, D. R. 622, 623 Liebert, N. B. 561 Liesegang, R. 140 Lieser, K. H. 140 Ufshitz, L M. 140, 141 Lijalikow, K. S. 24 Lin, C. L 677 Un, Y. 196, 217 Lindberg, R. 314 Lindman, B. 309, 312

745 Lindsay, S. M. 531 Lindsey, A. D. 252, 256 Liou, S. H. 255, 414 Lipski, R. J. 332 Lisiecki, L 309, 313 Uu, A - M . 332 Liu, C T. 413 Uu, L. 311, 314 Liu, Y. 622 Livage, J. 245 Livsey, I. 427 Lixon, P. 309, 310 Loeb, A. L. 529 Lohmer, G. 196, 217 Lok, K. P. 195, 259, 260 Lok, R. 291, 390 Londergan, M. C. 686 Longoni, G. 333 Look, J.-L. 195, 245, 246, 247 Lorimer, J. P. 427 Lu, L. 622 Lu, M. 286 Lu, P. 194, 270 Lu, Y. Y. 194, 259, 261, 264, 265 Luborsky, F. E. 618 Luck, W. 545, 549 Luckham, P. F. 421 Luderer, A. A. 712 Ludwig, M. H. 311 Lufimpadio, N. 310, 659 Lukas, R. 260 Lukaszewski, G. M. 459 Lumb, E. C. 540 Luymes, W. 259 Lynch, B. W. J. 637, 646, 649, 651, 652 Lynch, C T. 588 Lytle, E. W. 640, 641

Maat, H. J. 644, 653, 655 MacDermott, R. P. 697 MacDonald, R. J. 644, 645 Mackay, R. A. 337 Mackenzie, D. 698, 700, 701, 703, 706 Mackenzie, J. D. 247, 319 Maeda, U. 195, 320

746 Maeda, Y. 621 Maenhout-Van der Vorst, W. 412 Mager, H. 140 Maire, G. 309, 659 Maitra, A. 311 Majima, H. 377 Makela, O. 697 Malinkowski, S. 241 Mangels, J. A. 245, 589 Mansfield, G. R. 697, 700, 712 Marcus, L. 711 Margel, S. 697, 711 Margolese, D. 334 Maiic, B. 245 Marignier, J. L. 217, 631, 636 Marino, S. J. 132, 289, 369, 407 Mark, H. 528, 529 Mark, J. E. 428 Markocki, W. 379 Maron, S. H. 557 Maroto, A. J. G. 253 Marqusee, J. A. 140 Martin, C. R. 330, 331 Martin, T. P. 502 Martinengo, S. J. 333 Martinez, M. 254 Maruyama, H. 259 Masaki, K. 607, 614, 620, 622, 623, 624 Maskasky, J. E. 77, 384, 413, 436, 437, 485 Mason, T. J. 427 Massardier, J. 637, 640, 641, 642 Masuda, H. 330 Masuda, Y. 242 Masuzawa, K. 254 Matemaghan, T. J. 421 Mates, T. E. 195, 421 Mathieu, H. J. 638, 639 Matijevic, E. 139, 193, 194, 195, 196, 197, 202, 213, 218, 219, 222, 223, 224, 230, 231, 232, 233, 235, 237, 238, 239, 240, 241, 244, 252, 253, 254, 255, 256, 257, 258, 261, 266, 267, 269, 270, 282, 286, 336, 337, 338, 369, 370, 379, 385, 391, 407, 410, 411, 412, 413, 414, 415, 417, 418, 419, 427, 429, 432, 433, 434,

NAME INDEX 439, 476, 477, 484, 485, 530, 535, 536, 537, 545, 558, 559, 565, 566, 567, 568, 569, 570, 571, 572, 573, 594, 595, 596, 619, 624, 625, 677, 680, 683, 684, 685, 687, 688, 689 Matsuda, E. 195, 196, 241 Matsuda, H. 229 Matsuda, M. 286 Matsuda, Y. 644 Matsuhira, N. 633 Matsui, Y. 334 Matsumoto, S. 338, 339, 385, 619 Matsumoto, T. 219, 299, 300, 385, 395, 431 Matsumoto, Y. 194, 260 Matsuo, K. 632, 636 Matsuoka, H. 546 Matsuoka, I. 535, 536, 537, 538, 539, 540, 541 Matsushita, N. 195, 320, 594 Matsuzaki, T. 644 Maurer, R. J. 477 Maury, E. E. 260 Mayville, F. C. 336 Mazdiyasni, K. S. 588 Mazzei, I. 77 McCapra, F. 698 McCarty, H. J. 556, 557 McQain, J. B. 260 McCullen, S. B. 333 McFadyen, I. 624 McFadyen, P. 218, 286 McGown, G. N. L. 195 Mclntyre, D. A 606 Mcmahon, T. J. 319 McMurray, H. N. 218 McNice, G. T. 677 McNulty, J. 259 Meagher, L. 531 Mecartney, M. L. 245, 252 Mecholsky, J. 311 Meehan, E. J. 140, 219, 224, 515, 516, 517 Meguro, K. 194, 195, 196, 211, 212, 213, 460 Meier, W. M. 332

NAME INDEX Meiklyar, P. V, 560, 561, 564 Meisel, D. 40, 58 Meites, L. 252 Mellraan, I. 696 MelviUe, J. B. 252, 253, 256 Menceloglu, Y. Z. 260 Mendoza, H. D. 535, 536, 537, 538, 539, 540, 541 Menigan, J. A. 412 Mervart, M. 710 Meschmeyei, T. 334 Messing, G. L. 245, 589 Meyer, W. 548 Mfutakamba, H. R. 297, 375 Micale, F. J. 298, 434 Mie, G. 553, 677, 680 Mifsud, A. 230, 255 Migins, J. 550 Mignot, A. 388, 389, 390 Milic, N. B. 253 Miller, G. R. 590 Miller, M. 637 Millette, F. 697 Milner, R. T. 159 Milstein, C. 697 Minagawa, K. 253 Minarai, H. 259, 434, 435 Minami, T. 244, 245, 336, 373 Mita, Y. 633 Mitarai, Y. 245 Mittal, K. L. 310, 314 Mitton, P. B. 686, 687 Miya, S. 620 Miyake, H. 270, 278, 279, 374, 375, 377, 378, 382, 383, 457, 458, 469, 499 Miyake, K. 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 179, 180, 181, 182, 184, 194, 415, 416, 417, 437, 453, 488 Miyake, M. 194, 216 Miyamori, S. 194, 260, 263, 264, 265 Miyamoto, H. 697 Miyamoto, M. 701 Miyazaki, H. 259 Mizutani, Hiroko 698, 705, 706, 707 Mizutani, Hiromichi 698, 705, 706, 707

747 Mizutani, N. 245, 320, 321, 411, 589, 590, 591 Mochida, T. 270, 275, 385, 386, 387, 406, 500 Moeremans, M. 692, 694, 695 Moffat, J. B. 241 Moffatt, W. C. 245 Mohri, M. 334 Moisar, E. 132, 133, 140, 289, 369, 377, 412, 585 Molday, R. S. 697, 698, 700, 701, 703, 704, 706 MoUer, K. 332, 334 Moncet, M. C. 164 Monot, R. 638, 639 Moon, J. 311 Moon, Y. T. 195, 253, 254, 589, 594 Morales, M. P. 252, 255 Mori, H. 710 Mori, R. 697 Morimoto, Y. 709, 710 Morita, H. 620 Morita, Y. 260, 261, 264 Moriyama, N. 194, 195, 196, 422 M0rk, P. C. 294, 296, 297, 375, 434 Morris, R. M. 700, 709 Morriss, R. H. 684 Morrish, A. H. 606, 607, 608, 618, 619, 624, 626 Monone, A. 311 Mosai, F. 585 Moscou, L. 644, 653, 655 Moseley, M. E. 312 Moskovits, M. 330, 332 Moss, R. L. 636, 637, 643, 645, 646, 649, 651, 652 Motte, L. 309, 310 Movilliat, P. 336 Mozzanega, M. N. 635 Mueller, F. W. H. 474 Muench, G. J. 570 Mulac, W. A. 40 Mullaney, P. 697 MuUer, A. J. 310 Mumaw, C. T. 194 Munk, F. 505

748 Murakami, H. 698, 708 Muramatsu, A. 194, 196, 225, 226, 227, 228, 231, 232, 247, 252, 255, 258, 269, 270, 271, 273, 274, 275, 276, 277, 278, 281, 282, 283, 284, 285, 287, 288, 323, 324, 325, 326, 327, 328, 329, 370, 371, 372, 373, 374, 375, 377, 381, 382, 385, 391, 396, 397, 398, 399, 401, 402, 403, 404, 405, 406, 421, 433, 437, 438, 439, 440, 453, 454, 456, 457, 459, 460, 461, 462, 463, 464, 465, 466, 467, 469, 470, 473, 474, 477, 478, 479, 480, 486, 487, 492, 493, 496, 497, 498, 501, 502, 503, 504, 529, 530, 531, 532, 533, 534, 624, 646, 647, 660, 662, 685 Muraoka, K. 291, 369 Murayama, K. 424 Murdock, T. O. 630 Muroi, S. 300, 431 Murray, C. B. 242, 559, 560 Munay, J. G. 260 Murray, M. J. 547 Muto, H. 318

Naccache, C. 332 Nagai, N. 621 Nagai, T. 197 Nagao, K. 427 Nagata, N. 195, 320, 321 Nagayama, K. 550, 551 Nagayama, T. 630, 631 Nagy, J. B. 310, 314, 659 Naiki, M. 697 Naka, Y. 261 Nakagawa, M. 245 Nakagawa, T. 259 Nakahama, S. 300, 431 Nakajiraa, H. 195, 320, 594 Nakajo, T. 633 Nakamura, A. 377, 439, 440 Nakamura, H. 546 Nakamura, K. 336, 337, 338, 407, 410 Nakamura, M. 294 Nakamura, Y. 633 Nakanishi, K. 245, 427, 430

NAME INDEX Nakano, M. 709, 710 Nakano, T. 697 Nakao, Y. 195, 216, 631, 633, 636 Nakashima, H. 241, 548 Nakatani, S. 385, 619 Nakayama, Y. 631 Nancollas, G. H. 140 Napper, D. H. 295 Nargessi, R. D. 698 Ned, L. 606, 618 NelHgan, J. 535 Nemoto, I. 696 Nemoto, R. 710 Nerren, B. H. 697 Nichols, R A 655 Nicolaon, G. 336, 337 Nicolson, M. M. 550 Nielsen, A E. 24, 40, 58, 97, 113, 199 Niizeki, S. 229, 385 Ninham, B. 309 Nishi, M. 621 Nishida, H. 426, 430 Nishida, M. 318 Nishikawa, S. 252, 254 Nishimori, H. 244, 245, 373 Nishimura, H. 253 Nishisu, Y. 238, 407, 411, 414, 591, 593 Nishizono, I. 698, 708 Noda, M. 630 Noeth, C. 242 Noll, W. 428 Nollen, K. 427 Nord, F. F. 632 Nonis, D. J. 242, 559, 560 Novakova, J. 332 Novich, B. 245 Nozaki, K. 698, 705 Nozawa, M. 425 Nustad, K. 297, 375 Nuydens, R. 692, 694, 695 Nye, L. 697, 698, 700, 703

O'DriscoU, K. F. 633 Ober, C. K. 195, 259, 260 Oberli, L. 638, 639

NAME INDEX Ocaiia, M. 247, 252, 254, 255, 336, 418, 502 Ochiai, T. 318 Oda, M. 242 Oder, R. R. 697 Ofarim, M. 711 Ogata, N. 195, 320, 321, 322, 594 Ogawa, K. 195, 320, 321 Ogawa, Y. 532 Ogihara, T. 195, 245, 320, 321, 322, 411, 589, 590, 594 Oguri, Y. 245 Oh, I. J. 700 Oh, J. H. 621 Ohara, T. 633, 634 Ohmori, M. 418, 419 Ohnishi, S. 696 Ohno, M. 217, 631, 636 Ohshima, S. 656 Ohta, K. 608, 613, 614, 622, 623 Ohtaki, M. 217, 631, 633, 634, 636, 655 Ohtsuka, Y. 260, 264, 294 Ohya, A 656 Ohyama, H. T. 427 Ohyumi, M. 532 Oi, V. 697 Oka, K. 377 Okada, I. 567 Okada, J. 223 Okada, K. 371, 372, 379 Okada, M. 270, 278, 279, 280, 324, 698, 708 Okada, T. 425 Okai, T. 242 Okamura, H. 245 Okaya, T. 259, 300, 431 Oki, K. 548 Okubo, M. 195, 259, 260, 261, 297, 299, 300, 375, 395, 411, 431, 432, 434, 435 Okubo, T. 547, 548 Okumura, H. 546 Okumura, Y. 242 Okuwaki, A. 229 Okuyama, K. 336 Okuyama, M. 245 Olson, D. H. 332, 333

749 Omote, Y. 620 Onishi, E. 245 Ono, T. 425, 546 Ono, Y. 195 Onoda, G. Y. 549 Onoe, S. 299 Onofusa, M. 195 Ooki, R. 591 Ookoshi, N. 567, 569 Ootsuka, K. 286 Oppegard, A. L. 621 Oppenheimer, L. E. 140 Osada, M. 334, 647, 648 Osawa, T. 697 Oshida, I. 608, 613, 614, 622, 623 Osseo-Asare, K. 310 Oster, C. F, Jr. 132, 289, 369 Ostrovskaya, I. K. 233 Ostwald, W. 140 Otero-Schipper, P. H. 644 Otterstedt, J.-E. 662 Ottewill, R. H. 233, 243, 260, 294, 421, 548, 549, 588 Otto, K. 644 Overbeek, J. Th. G. 193, 202, 246, 523, 524, 528, 529, 530, 533, 535, 545, 546, 565, 588 Owen, S. M. 260 Oyaraa, S. T. 418 Oyamada, T. 291, 390 Ozaki, A, 656 Ozaki, M. 202, 252, 253, 255, 257, 269, 379, 413, 545, 546, 565, 566, 567, 568, 569, 619, 620, 624, 625 Ozaki, Y. 245 Ozeki, K. 389 Ozeki, T. 291, 390 Ozin, G. A 334 Ozkar, S. 334

Pacchioni, G. 334, 647 Pailliotet, A 77 Paine, A. J. 259 Palmour, H., Ill 588 Pan, J. 531

750 Pangonis, W. J. 513 Pannel, R. B. 644 Panzarino, J. N. 712 Papavassiliou, G. C. 677 Papendorf, H. 385 Papworth, S. 260 Parentich, A. 549 Parfitt, G. D. 195 Parish, M. V. 588 Park, G. 270, 275, 277, 394, 395, 396, 398, 399, 400, 467, 468, 482, 483, 484, 489, 490 Park, H. K. 253, 254, 589, 594 Park, J. 197 Parkin, S. S. P. 336 Parks, D. R. 697 Partch, R. E. 240, 336, 337, 338, 407, 410, 415, 418, 427, 429, 434 Parthasarathy, R. V. 330, 331 Pashley, R. M. 531 Passaggio, S. I. 253 Pastan, I. 696 Patel, R. C. 256, 257, 266 Pathmamanoharan, C. 252, 431 Patrissi, C. J. 330 Paunov, V. N. 550 Pelizzetti, E. 202, 310, 374, 388, 634, 635 Pelton, R. H. 260, 294 Pendleton, P. 300, 415, 434 Peng, Y. B. 412 Penners, N. H. G. 677 Penoyei, R. F. 620 Perez-Maqueda, L. A. 224 Perrin, J. 521, 522, 523 Park, H. K. 195 Persson, A. E. 662 Peska, J. 517 Peter, D. G. 231 Peterson, E. E. 642, 658 Petit, C. 309, 310 Petres, J. J. 196, 222, 235, 406 Petroff, P. M. 334 Phani, K. L. N. 330, 331 Philips, T. 700, 705, 711 Pichat, P. 635 Pier, T. J. 242

NAME INDEX Pieranski, P. 549 Pierce, P. E. 557 Pileni, M. P. 309, 310, 311, 312, 313, 314 Pillai, V. 314 Piller, H. 679 Pinjie, H. 239, 385 Plotz, C. M. 701 Pober, R. L. 245, 411, 588, 589, 590, 591 Polak, J. M. 692 Pontius, R. B. 372 Poore, G. 700, 709 Pope, E. J. A. 619, 620 Porath, J. 703 Porstendoerfer, J. 337 Porta, F. 237, 240, 407, 414 Porter, R. L. 588 Pouradier, J. 77, 159, 160, 161, 162, 163, 164, 166 Pouyet, G. 311 Pozamsky, G. 535, 536 Prasad, R. 634 Pratsinis, S. E. 337 Prieve, D. C. 536, 537 Primet, M. 637, 640, 641, 642 Privman, V. 197, 535, 536, 567, 569, 571, 572, 573 Puckett, S. A. 291, 390 Pulvermacher, B. 653 Pussy, P. N. 548

Qi, L. 291 Quaiser, S. A 196, 217 Quate, C F. 531 Quiben, J. 195, 241, 407

Rajagopalan, R. 535 Ramsey, J. M. 413 Rand, D. A. J. 202, 252 Rankin, R. N. 710 Ranney, D. F. 700, 709, 710 Rao, C. N. R. 194, 215 Rao, L.-F. 332, 647 Rapaport, E. 337 Rase, H. F. 632, 634

NAME INDEX Ravet, I. 659 Ravid, M. 711 Rawlinson, D. A. 622 Rayleigh, Lord 552 Reber, K. 477 Reetz, M. T. 196, 217 Reeve, K. D. 588 Regazzoni, A. E. 240, 269, 407, 414 Reich, S. 194, 259, 260 Rembaum, A. 697, 698, 700, 701, 703, 704, 705, 711 Rempel, G. L. 633 Rendon, J. L. 685 Resasco, D. E. 656 Ressl, M. G. 242 Reuel, R. C. 644 Revillon, A. 428 Rey, F. 334 Rhim, W. K. 340, 341 Rhine, W. E. 319 Rhodes, W. H. 588, 590 Rhodes, W. W. 590 Ribot, F. 407, 414 Rieke, R. D. 630 Riess, G. 311 Rigby, W. R. 330 Rigotti, G. 253 Riman, R. E. 319 Ring, T. A. 195, 202, 245, 421, 594 Roberts, J. R. 697, 698, 700, 703 Robinson, D. L. 330 Robinson, S. E. 696 Roche, E. 140 Roche, K. 336 Rodriguez-Qemente, R. 247, 255 Rogers, R. 548 Romack, T. J. 260 Ronnquist, L. 253, 255 Ropple, R. 630 Rosenblum, C. 149 Rosenthal, O. 231 Ross, J. 140 Ross, P. N. 639 Ross, W. D. 681 Roth, W. J. 333 Roy, I. 311

751 Ruch, R. 594 Ruckenstein, E. 140, 536, 537, 634, 653 Rudin, A 260 Rudolf, P. 622 Ruoff, R. S. 330, 331 Ruppin, R. 502, 685 Russel, G. 77 Russel, W. B. 548 Rutishauser, U. 697 Ryde, N. P. 535, 536, 545, 677, 685

Sachtler, W. M. H. 332 Sacks, M. D. 588 Sada, E. 621 Sadler, M. S. 621 Sager, W. 309 Saigoh, F. 430 Saito, K. 317, 318 Saito, S. 607, 614, 620, 622, 623, 686, 690, 691, 697, 698, 701, 705, 709 Saito, Y. 630 Saitoh, S. 620 Saitou, M. 290, 291, 389, 390 Sakamoto, Y. 195 Sakata, K. 270, 271, 272, 273, 274, 275, 277, 278, 373, 374, 396, 397, 403, 404, 461, 480, 492, 493, 496, 497, 498 Sakata, T. 635, 657 Sako, Y. 696 Sakota, K. 300, 431 Sakurai, C. 245 Sailing, C. 624 Salmon, R. 336 Sanchez, C 245 Sanders, J. V. 547 Sankar, G. 334 Sano, H. 437, 633, 634, 657 Sano, K. 633 Sano, Y. 586 Santos, H. S. 219 Sapieszko, R. S. 213, 252, 253, 256, 257, 385 Sasagawa, S. 701 Sasaki, Hiroshi 530, 531, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544

752 Sasaki, Hitoshi 197 Sasaki, M. 334, 647, 648 Sato, H. 310 Sato, S. 529, 532, 533, 534, 657, 696 Sato, S. B. 696 Sato, T. 217, 229, 245, 259, 594, 631, 634, 636, 644 Satoh, M. 621 Sauvage, J. P. 657 Savin, H. 711 Sawabe, Y. 334 Sawada, E. 300 ScarpeUi, D. G. 700, 709 Schad, M. J. 140 Schaefer, D. W. 549 Schaumberg, G. 253, 256 Scheiner, P. 252, 257, 258, 269, 379, 530, 677, 679, 680, 681, 682 Scheludko, A. 550 Schenkel, J. H. 537 Scherer, G. W. 245 Schlatter, J. C. 633, 634 Schlenker, J. L. 333 Schlossman, S. F. 697 Schraelzer, J. 140 Schmid, R. 297, 375 Schmidt, H. J. 633 Schmidt, ¥L H. 40, 58 Schmitt, K. D. 333 Schmitz, K. S. 547, 548 Schoeman, B. J. 662 Schubert, U. 329, 330 Schuerman, D. W. 684 Schultz, J. F. 633 Schultz, M. 223 Schultz, S. 624 Schulz-Ekloff, G. 332 Schumacher, E. 637 Schwab, F. C. 260 Schwertmann, U. 385 Scott, T. R. 459 Scott, W. B. 252, 253, 256 Scriven, L. E. 550 Segal, D. 594 Segall, I. 300, 431 Sekiguchi, T. 41, 42, 43, 48, 49, 51, 53,

NAME INDEX 194, 231, 243 Sekine, M. 425 Seligraan, B. 633 Senden, T. I. 531 Senna, M. 195, 300, 420 Senyei, A. E. 700, 709, 710 Serafini, T. T. 300 Sermon, P. A. 622 Serna, C. J. 230, 247, 252, 254, 255, 502, 685 Seshadri, R. 194, 215 Sessoli, R. 240, 407, 414 Shah, D. O. 310, 314 Shaw, J. N. 294 Shaw, L. 633 Shaw, W. H. R. 236 Shen, G.-C. 332 Shen, J. 286 Sheppard, E. W. 333 Sheu, E. R. 396 Sheu, H. R. 299 Sheu, L. L. 332 Shiba, F. 2, 8, 20, 25, 41, 42, 43, 48, 49, 51, 52, 53, 54, 55, 56, 78, 83, 194, 231, 243 Shibahara, Y. 432, 585, 586, 587 Shibao, S. 299, 395 Shibata, H. 532 Shibata, S. 413 Shido, T. 332, 333, 334, 647 Shiga, D. 245 Shimada, M. 300, 431 Shimazaki, K. 656 Shimizu, C. 318 Shimizu, T. 297, 375 Shimohira, T. 245 Shimomura, M. 424 Shimoyama, Y. 644, 645 Shinata, Y. 286 Shindo, D. 228, 247, 270, 274, 275, 277, 394, 395, 396, 398, 399, 400, 403, 404, 405, 406, 467, 468, 482, 483, 484, 489, 490, 492, 493, 496, 497, 498 Shindo, Y. 242 Shinoda, K. 196 Shinoda, S. 630

NAME INDEX Shinozaki, K. 245, 321, 591 Shintoku, Y. 323, 324, 325, 329, 437, 438, 660 Shiozaki, M. 259, 260, 297, 375 Shiraga, N. 334 Shiratori, K. 565 Shirota, K. 656 Shizuka, N. 310 Shockley, W. 559 Shtrikman, S. 617 Shushan, D. 239, 385 Sieg, R. P. 653 Sihite, T. 530, 531 SUlen, L. G. 14, 21 Silvert, P.-Y. 194, 215 Simon, A. 532 Simpson, C. M. 407 Sinclair, D. 336 Sinfelt, J. H. 643, 648, 656 Singer, S. J. 707 Singh, S. S. 257 Singler, J. M. 701 Sipek, M. 291, 369 Sjoblom, J. 312, 314 Skeel-Christensen, K. 218, 221, 234, 235, 406 Skillman, D. C. 80, 132, 140, 289, 369, 372, 474, 496 Skinner, D. N. 140 Skjeltorp, A. T. 298, 393, 394 Slifkin, L. M. 176, 477 Slyozov, V. V. 140, 141 SmaU, J. V. 692 Smimov, J. P. 560, 561, 564 Smith, A- L. 140, 540 Smith, D. S. 698 Smith, J. S. 588 Smith, W. P. 412 Smith, W. V. 292, 293, 294, 304 Smolka, A J. K. 697 Smoluchowski, M. see von Smoluchowski, M. Soderberg, L. 300, 420 Sogami, I. 546 Sokolova, T. P. 233 Somoijai, G. A. 642, 653, 655, 657, 658

753 Sone, Y. 422, 424 Sonnenberg, W. 261 Sood, A 337 Sordelet, D. 238, 413 Spoerri, P. E. 222 Springsteen, L. L. 195, 241 Sprycha, R. 252, 256, 427 Stadler, H. L. 590 Stamberg, J. 517 Stanley-Wood, N. 517 Stavek, J. 291, 369 Steams, E. J. 686 Steigerwald, M. L. 310 Steinkamp, J. A 697 Stenius, P. 309, 312, 659 Stem, O. 523 Sterte, J. 662 Stevenson, P. C 212, 677 Steyer, T. R. 685 Stilbs, P. 312 Still, E. 372 Stimming, U. 196, 217 Stober, W. 243, 244, 411, 588 Stockert, J. A 330 Stonehart, P. 639 Stoner, E. C 606, 608, 609, 611, 612, 615, 616, 617 Stover, H. D. H. 260 Stranski, I. N. 132, 133, 377 Stroink, G. 696 Strong, R. W. 58, 77, 83, 104, 109, 111, 134, 199, 290 Stucchi, E. B. 238, 411 Stucky, G. 332, 334 Stumier, D. M. 372 Sudol, E. D. 260, 294 Sueyoshi, T. 620 Sugawa, Y. 426 Sugi, Y. 294, 644 Sugibayashi, K. 709, 710 Sugier, A 644 Sugimoto, M. 622 Sugimoto, N. 334, 647, 648 Sugimoto, T. 2, 8, 11, 20, 23, 25, 28, 29, 41, 42, 43, 46, 48, 49, 51, 52, 53, 54, 55, 56, 59, 60, 61, 64, 65, 70, 71, 72, 73, 74,

754 75, 76, 77, 78, 79, 80, 81, 82, 83, 105, 108, 109, 111, 112, 113, 114, 119, 121, 122, 123, 124, 125, 126, 127, 129, 130, 131, 132, 133, 134, 135, 136, 137, 140, 141, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 179, 180, 181, 182, 184, 187, 188, 191, 192, 193, 194, 196, 197, 199, 200, 201, 202, 219, 225, 226, 227, 228, 231, 232, 243, 246, 247, 252, 255, 258, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 287, 288, 289, 290, 293, 310, 320, 321, 323, 324, 325, 326, 327, 328, 329, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 391, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 415, 416, 417, 421, 432, 433, 436, 437, 438, 439, 440, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 529, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 594, 624, 625, 626, 646, 647, 660, 662, 685 Sugimura, T. 242 Sugiyama, N. 565, 566, 567, 568 Sugiyaraa, T. 220, 235 Suito, E. 690 Sukigara, M. 657, 658 Sullivan, J. C. 40 Suraiyoshi, A. 703, 708 Summers, J. C. 634 Sun, S.-T. 517 Sundberg, D. C. 261 Suresh, M. 337 Sutoh, M. 372 Sutton, R. C. 195 Suzuki, A. 377 Suzuki, H. 253, 567, 634, 644 Suzuki, M. 195, 211, 212, 420

NAME INDEX Suzuki, N. 333, 698, 708 Suzuki, S. 620 Suzuki, T. 297, 375, 621 Suzuki, Y. 633, 634, 636, 644 Svec, F. 517 Svedberg, T. 522 Swift, E. H. 231 Swoboda, T. J. 621 Szucs, M. 194, 195, 372

Taarit, Y. B. 332 Tabibian, R. M. 557 Tachibana, J. 333 Tadros, M. 255, 414 Tadros, Th. R 421, 537, 594 Tagawa, K. 622 Taguchi, T. 428 Takada, S. 412, 562, 563, 564 Takagi, A. 318, 319 Takahashi, A 657, 658 Takahashi, H. 690 Takahashi, K. 194, 260, 263, 264, 265, 435, 567 Takahashi, Tadahito 217, 270, 631, 636 Takahashi, Takashi 317 Takahashi, Tetsuya 529, 532, 533, 534 Takamiya, Y. 245 Takamoii, T. 254 Takano, K. 545, 546 Takasaki, S. 634, 644 Takashima, Y. 338, 339 Takasu, Y. 639, 640, 644 Takeshita, K. 338, 339 Takeuchi, K. 644 Takezawa, K. 634 Takezawa, N. 634 Takiyama, K. 212, 234, 406 Talham, D. R. 311 Tamagawa, N. 620 Tamai, H. 299 Tamaru, K, 633, 636 Tamura, H. 269, 407 Tan, B. J. 632, 636 Tan, C G. 370 Tan, Y. T. 564

NAME INDEX Tan, Z. C. H. 372 Tanabe, S. 633, 636 Tanaka, M. 686, 690, 691 Tanaka, N. 300 Tanaka, T. 40, 57, 58, 460, 461, 622, 632, 636 Tani, T. 125, 505, 506, 563, 586 Taniguchi, T. 413 Tano, T. 195, 196, 211, 212, 213, 460 Tanori, J. 309, 312, 313 Tao, N. J. 531 Tarkowski, H. L. 295 Tasaki, A. 565, 630 Tata, B. V. R. 545 Tatsumisago, M. 244, 245, 336, 373 Taylor, G. 260 Taylor, G. M. 692 Taylor, K. C. 633, 634 Taylor, T. I. 231 Taylor, W. F. 656 Tazaki, A. 622 Tekaia-Elhsissen, K. 194, 215 Templeton-Knight, R. 427 Tentorio, A. 412, 687 Terada, K. 259 Teranishi, T. 194, 216 Teshe, B. 639, 640 Tezak, B. 196, 222, 235, 406 Thayer, A M . 310 Thiele, H. 193, 194, 195, 211, 421 Thiessen, P. A 521 Thomas, J. K. 311 Thomas, J. M. 334 Thompson, D. M. P. 698 Thompson, G. 535 Thompson, M. 40 Thomson, B. 260 Thorpe, G. H. G. 698, 708 Thorsby, E. 700 Tibbitt, J. M. 657 Tien, T. Y. 590 Tkacheva, L. M. 372 Todo, N. 634, 644 Tohge, N. 336 Tohji, K. 633, 636 Toida, H. 690

755 Tojo, T. 218, 414 Tokunaga, H. 377 Tokuoka, Y. 620 Tokuyasu, K. T. 707 Tomanova, D. 644 Tominaga, H. 332 Tomita, A 330, 331, 332 Tomkins, F. C. 637, 640, 641, 642 Toneguzzo, P. 270 Tops0e, H. 644 Torigoe, K. 195, 196, 211, 212, 460 Tormey, E. S. 245, 589 Toshima, N. 194, 195, 216, 217, 270, 419, 631, 632, 633, 634, 636, 655 Touroude, R. 309 Towata, S. 245 Toyokura, K. 291, 369 Toyoshima, I. 644 Toyotama, H. 696 Travis, K. L. 697, 700 Treleaven, J. G. 700, 705, 711 Treves, D. 617 Trofimow, A 300, 414 Tsai, L. 330, 331, 332 Tsaur, A K. 291, 390 Tsaur, S. 300, 431 Tseng, C. M. 194, 259, 261, 264, 265 Tseng, T.-Y. 588 Tsubokawa, N. 422, 424 Tsuchida, T. 239, 414 Tsujihiro, M. 259, 260, 297, 375 Tsukuda, Y. 259, 260, 297, 375 Tsushima, R. 297, 375 Tsuwano, Y. 410 Tulyupa, F. M. 372 Turkevich, J. 212, 677 Tyblewski, M. 241

Uchida, Y. 334 Uchiyama, K. 245, 411, 589, 590 Udagawa, Y. 633, 636 Ueda, R. 330 Ueda, S. 662 Uematsu, K. 245 Ueno, A 633, 634, 636, 644

756 Ueno, Y. 546 Ugelstad, J. 294, 296, 297, 298, 300, 375, 434, 393, 394, 420, 700, 705, 711 Ulevitch, I. N. 557 Ulrich, D. R. 245, 247, 319, 411, 588, 590, 591, 592 Umeki, S. 620 Unwin, R. 639, 640 Urabe, S. 389 Usatenko, Yu. I. 372 Usui, S. 530, 531 Uyama, H. 194, 260, 300, 431, 435 Uyeda, R. 630

Van Biesen, J. 562, 564 van Blaaderen, A. 245, 246 van de Hulst, H. C 513 van den Hooff, A. 242 van der Giessen, A. A. 620 van der Plaats, G. 517 Van Dijck, A. 692, 695 van Geest, J. 245, 246 van Grunderbeeck, F. 213 van Haldeveld, R. 642, 643 van Horn, M. H. 495 van Zeggeren, F. 25 Vanassche, W. 384 Vanderhoff, J. W. 194, 259, 261, 264, 265, 292, 293, 294, 295, 298, 299, 300, 304, 396, 431, 434, 548 Vann, W. P. 697, 700 Vannice, M. A. 633, 656 Vartuli, J. C 333 Vartuli, W. J. 333 Vekeman, G. 412 Velikanov, A. A. 233 Verwey, E. J. W. 528, 529, 530, 533, 535, 546, 565 Viau, G. 196, 270 Vibert, P. 194, 215 Vijayakrishnan, V. 194, 215 Vincent, B. 300, 415, 434 Vincenzini, P. 235 Vinnela, F. 710 Visca, M. 336, 634, 635

NAME INDEX Visser, J. 529 Vitkuske, J. F. 293, 294, 295, 304 Vogel, M. 434 Vogel, R. 196, 217 Volksen, W. 700, 704 Volz, H. G. 677 von Levem, H. S. 193, 194, 195, 211, 421 von Smoluchowski, M. 521, 525 Vought, R. C. 372 Voyta, J. C. 698, 708 Vrij, A. 193, 245, 246, 431

Wachter, W. A. 644 Wada, K. 320 Wagner, C. 83, 104, 140, 141, 143 Wagner, F. T. 657 Wainwright, T. E. 546 Waki, S. 270, 275, 276, 324, 326, 377, 404, 497, 498 Walker, D. G. 236 WaU, D. 696 Wallace, A. C. 710 Walnut, T. H. 56 Walton, A. G. 24, 25 Wang, C. J. 698 Wang, G. 194, 238, 407, 414 Wang, J. F. 314 Wang, L. 311 Wang, R. J. 332, 333 Wang, Xiaohui 622 Wang, Xin 622 Wang, Ying 332 Wang, Yinsheng 270, 273, 274, 277, 324, 370, 374, 375, 380, 381, 398, 399, 400, 401, 402, 404, 439, 440, 490, 491, 502, 503, 504, 624, 685 Wang, Yuan 194, 270 Wanke, S. E. 654, 655 Ward, A. J. I. 202, 314, 315, 316 Waseda, Y. 270, 275, 277, 396, 398, 399, 400, 404, 467, 468, 482, 483, 484, 489, 490, 532 Watanabe, H. 242, 334 Watanabe, S. 300, 431 Watillon, A. 213

NAME INDEX Watson, J. H. L. 252, 406 Watts, J. 255, 414 Watzky, M. A. 196, 217 Webb, J. H. 559, 560 Wedlock, D. J. 202, 252 Weeks, I. 698 Weinberg, H. 696 Weinstock, S. E. 337 Welch, B. J. 202, 252 Weldock, D. J. 270 WeUs, P. B. 637, 640, 641, 642 Wendlandt, W. Wm. 505 Weneck, E. J. 557 Weslau, H. 545 Wesslau, M. 549 Westenbroek, C. J. A 621 Westgren, A. 521 Wey, J. S. 58, 59, 77, 80, 83, 104, 109, 111, 112, 134, 140, 199, 290, 369 White, J. W. 152 White, L. R. 550 White, P. 245, 411, 588, 590, 592 Whitehead, R. A 700, 701 Whiten, W. B. 413 Wicks, J. H. 697, 698, 700 Widder, K. J. 700, 709, 710 Wierseraa, P. H. 529 Wigzell, H. 697 Wilcox, W. R. 83, 238, 257 Wilhelray, D. M. 231, 232, 391, 407 Wilhelmy, R. B. 222 Willens, L. 517 Williamson, B. 260 Willingham, M. C. 696 Willis, E. 195 Wilson, G. R. 652 Wilson, I. B. 336 Wilson, T. P. 633 Winchell, A N. 679 Winchell, H. 679 Windorski, D. C. 697, 698, 700 Winnik, F. M. 259 Winnik, M. A 260 Winzor, C. L. 261 Wohlfarth, E. P. 606, 608, 609, 611, 612, 615, 616, 617

757 Wojtowicz, W. 252 Wokaun, A 309 Wolczanski, P. T. 657 Wolfe, K. J. 336, 337, 338, 407, 410 Wolter, H. B. M. 650, 651, 654, 663 Woodbridge, R. F. 233, 243 Woodhead, J. S. 698 Woste, L. 637 Wrathall, D. P. 125, 505 Wrighton, M. S. 657 Wrischer, M. 222 Wu, T.-H. 232, 411 Wulff, G. 118 Wunder, F. 633 Wynblatt, P. 653, 654, 655 Wyrsch, D. 382

Xiao, G. 255, 414 Xie, Y. 418, 427 Xu, H. 548

Yabuuchi, M. 195, 320 Yaguchi, N. 260 Yalow, R. S. 698 Yamada, A. 422 Yaraada, H. 195 Yamada, N. 633, 634, 657 Yamada, Y. 260, 264 Yamaguchi, G. 140, 148, 149, 150, 151, 152, 153, 176, 192, 455, 470, 471, 472, 495, 496 Yamaguchi, K. 300, 431, 657 Yamaguchi, T. 425 Yamamoto, I. 194, 260 Yamamoto, T. 242, 333, 334, 634, 647 Yamamoto, Y. 195, 245, 259, 260, 261, 300, 431 Yamane, M. 413 Yamane, T. 532 Yamashita, S. 291, 390, 696 Yamashita, T. 195, 259, 260, 261, 297, 299, 375, 411, 432, 434, 435 Yamazaki, M. 697 Yamazaki, S. 294

758 Yamazaki, T. 194, 216, 419 Yamazaki, Y. 621 Yan, M. 588, 590 Yan, Q. 621 Yan, Y. D. 507 Yanagawa, T. 195, 320, 321, 322, 594 Yanagi, M. 310, 311 Yanagida, H. 140, 148, 176, 192, 474, 475, 476 Yanagisawa, M. 294 Yang, J. 228, 247, 405, 406 Yano, T. 413 Yao, H. C. 644 Yao, Y.-F. Yu 644 Yasuda, H. 299 Yasukawa, A. 195, 196, 241 Yasumori, A. 413 Yates, D. J. C 656 Yaverbaum, S. 697, 698, 700, 703 Yen, S. P. S. 697, 698, 700, 701, 703, 704 Yokoyama, H. 621 Yokoyama, T. 426, 427, 428 Yonezawa, T. 194, 216, 372, 419, 631 Yonezawa, Y. 217, 631, 636 Yoshida, H. 546 Yoshida, I. 620 Yoshida, K. 195, 320, 321, 322, 594 Yoshida, M. 261 Yoshida, S. 377, 632, 636 Yoshida, T. 320 Yoshihara, M. 259 Yoshikawa, K. 195 Yoshimatsu, A. 297, 375 Yoshimura, S. 548 Yoshinaga, K. 426, 427, 428, 430 Yoshitake, S. 703, 708 Yoshiyama, T. 546 Young, D. A. 546 Young, W. S. 336 Yu, R. 194, 238, 239, 270, 412, 414, 418, 687, 688, 689 Yu, S. P. 606, 607, 608, 618, 624, 626 Yura, K. 253, 254, 418 Yutzy, H. C 159 Yuze, E. 286

NAME INDEX Zacmanidis, P. J. 590 Zaleski, A 379 Zana, R. 313 Zekhnini, Z. 311 Zeldovich, Ya. B. 38 Zelenev, A 261, 535, 536 Zhang, J. 621 Zhang, L. 622 Zhang, N. 621 Zhaong, W. 621 Zhong, Q. 197, 222, 223, 336, 337, 338, 369, 370 Zhow, D. 336 Zhu, J. 548 Zieder, J. 329, 330 Ziessel, R. 657 Zitkovsty, I. 336 Zsigmondy, R. 191, 212, 521 Zuelke, M. S. 698 Zukoski, C. F. 195, 245, 246, 247, 248

SUBJECT INDEX AAO, see Anodic aluminum oxide film Acetonitrile (CH3CN) dielectric constant, 211 for electrochemical reduction, 217 for nonaqueous emulsions, 319-320 product of thioacetamide, 227 Acetylacetone, see Chelating agents Adatom, 642 Adhesion, 535-545 effects of magnetic field, 567-573 adhesion to glass, 573 adhesion to steel, 567-573 a-FcjOj/glass system, 541-545 pH effect, 541-543 size classification, 541-544 SiOj/a-FejOg/glass system, 537-541 attachment, 538-540 bridging effect, 540 detachment, 540-541 tumbling method, 537-538 Aerosol MA, see Sodium dihexylsulfosuccinate Aerosol OT, see Sodium dioctylsulfosuccinate Aerosol systems, 336-338 falling liquid film technique, 337 preparation in, 336-338 composites, 336-338, 430-431 metal oxides, 336-338 polymer particles, 336-338 seeding, 337 Sinclair-LaMer method, 337 AFM, see Atomic force microscope Aggregative growth model, 196-198, 235, 245, 247-248, 255-256, 266-269, 277-278, 369-370, 477-480 particle species barium sulfate, 235

barium titanate/CDJ method, 369-370 ceria, 255 copper(II) oxide, 282 gold, 197 hematite, 255, 277-278, 477-480 magnetite, 196, 266-269 silica, 245-248 silver, 197 tin(IV) oxide, 255 titania, 245, 247 zinc oxide, 255 zinc oxide/CDJ method, 197, 369-370 primary particles, 196, 247, 266, 277 controlled aggregation, 266-269 diffusion hole, 197, 223 seeding analysis, 247, 255, 277, 282, 477 Akaganeite (P-FeOOH) particles FTIR, 456-457 gel-sol process, 190-191 hydrolysis of Fe^* ions, 252 shape and structure, 406 magnetic adhesion, 572 phase transformation, 139 support of metals, 324 Albumin drug delivery systems, 709, 710 magnetic microspheres, 700, 703, 710 Alloys Ag-Pd, 215 Au-Pd, 216, 631 Au-Pt, 216 Co-Ni, 270, 330 Cu-Pb, 631 Cu-Pd, 270 Cu-Pt, 270 Cu-Zn, 630 Fe-Co-Ni, 270 Ni-Co-B, 310

760 Ni-P, 289 Pd-Cu, 216 Pd-Ni, 270 Pd-Pt, 216, 631 Pt-Rh, 216 Rh4Fe2(CO)i5, 332 Rh,.X(CO),„ 332 Alumina (AI2O3) particles calcination of hydrous oxide a-alumina, 239, 414 Y-alumina, 320 Ti-alumina, 239, 414 ceramic materials, 592, 594 coating with polymer, 425 composites, see Composites dye-doped pigment, 687 extender pigment, 677, 690 preparation aerosol process, 336 firing of solid precursors a-alumina, 334-336 forced hydrolysis, 252, 254 of Al(acac)3, 229 of butoxide, 252, 254 of sulfate salts, 252, 256-257 with urea, 239 nonaqueous emulsion process, 320 composite formation, 320 protective agents, 195 shapes and structures, 229, 335 support of metals, 632-634 Aluminum hydrous oxide, see Alumina particles Aluminum hydroxide, see Alumina particles Aluminum phosphate particles direct reaction of ions, 222 crystalline spheres, 222 Aluminum sulfate, see Basic aluminum sulfate particles Ammonia, see Growth promoters, Complexing agents, and Shape controllers Anodic aluminum oxide (AAO) film, 330 Anticoagulants, see Protective agents Antigen-antibody reaction, see Magnetic microspheres AOT (Aerosol OT), see Sodium dioctyl-

SUBJECT INDEX sulfosuccinate Arrested growth mechanism, 202 Artificial organs, 709 Atomic force microscope (AFM), 531 Autocorrelation function, 507-509 Avogadro number determination of, 520-523

Barium carbonate particles microemulsion process, 310, 388 shape control, 388 Barium fenite (BaO-6Fe203) particles magnetic properties, 602, 616, 621 Barium sulfate particles coating with polymer, 425 composites, see Composites extender pigment, 677, 687, 690, 691 internal structure, 406 preparation CDJ method, 291 decomposition of EDTA-Ba, 234 direct reaction of ions, 221 oxidation of SjOj^', 234 protective agents, 196, 235 shapes, 222, 234, 291 controllers, see Shape controllers size control, 221 turbidimetry, 58 Barium titanate particles amorphous spheres, 235, 245, 320 calcination, 245, 320 composites, see Composites preparation decomposition of EDTA-Ba, 235 hydrolysis of Ti-alkoxides, 245 in nonaqueous emulsions, 320, 321 protective agents, 195 Zr- or Sr-doped, 594-596 dielectric constants, 594-596 Basic aluminum sulfate particles FTIR, 457-459 gel-sol method, 278-279 OPML-XRD, 499 shape control, 278, 377-378, 382-383 size control, 374, 375

SUBJECT INDEX XRD, 382 Basic cerium (IE) carbonate, see also Cerium oxydicarbonate particles Ce^*-Y^* basic carbonate, 407 amorphous spheres, 407 hydrolysis with urea, 407 Basic cobalt carbonate particles hydrolysis with urea, 241, 414 needle-type, 242, 414 Basic cobalt cyanatocarbonate particles hydrolysis with urea, 241, 414 spherical, 241, 414 Basic copper(II) nitrate particles liquid-crystal process, 316 rectangular, 316 Basic copper(n) carbonate particles amorphous spheres (Cu2(OH)2C03), 239 forced hydrolysis with urea, 239 composites, see Composites Basic copper(II) sulfate particles composites, see Composites preparation forced hydrolysis of chelates, 229 liquid-crystal process, 315-316 shape and structure, 229, 315-316 Basic europium carbonate, see Basic lanthanide carbonate particles Basic gadolinium carbonate, see Basic lanthanide carbonate particles Basic iron(III) sulfate particles forced hydrolysis, 252 shapes and structures, 252, 253 Basic lanthanide carbonate particles composites, 240, 407 hydrolysis with urea, 229, 238 shapes and structures, 229, 238 Basic lanthanum carbonate, see Basic lanthanide carbonate particles Basic nickel carbonate particles forced hydrolysis with urea, 241 spheres (Ni2(OH)2C03 ^20), 241 Basic nickel phosphate particles amorphous spheres (Ni2(OH)P04), 241 catalyst, 241 hydrolysis with urea and NaHjPO^, 241 porous structure, 241

761 protective agents, 195 Basic samarium carbonate, see Basic lanthanide carbonate particles Basic terbium carbonate, see Basic lanthanide carbonate particles Basic thorium sulfate particles amorphous or polycrystalline spheres, 253 forced hydrolysis, 253 Basic yttrium carbonate particles amorphous spheres, 238 composites, see Composites dye-doped, 238, 412 forced hydrolysis with urea, 238 Basic zinc carbonate particles forced hydrolysis with urea, 239 shape control by anions, 239 Basic zirconiiun carbonate particles dye-doped, 412 oxy-basic zirconium carbonate, 240 protective agents, 194 Zr-Y basic carbonate, 407 Basic zirconium sulfate particles from Zr(S04)2 with urea, 240 protective agents, 240 spheres (Zr2(OH)6S04 •2H2O), 240 Becher-Doring theory, see Nucleation rate Benzimidazoles, see Growth restrainers and Shape controllers Benzoquinones, see Shape controllers Biocleaners, 711 Biocompatible polymers, 700, 709, 710 Biological use, 691, see also Medical use Bioreactors, 710-711 Boehmite (a-AlOOH) particles crystalline clusters, 252, 253 forced hydrolysis, 252 Bond-free open site, 5 Bond-free spot, 5 Bom potential, 536-537, 564-565

Cadmium carbonate particles reaction with hydrolyzed urea, 235 rhombohedral, 235 Cadmium chalcogenide particles CdS, CdSe, CdTe, 242

762 nanoparticles, 242 pyrolysis of organometallics, 242 Cadmium oxide particles calcination of CaCOg, 237 porous structure, 237 rhombohedral, 237 Cadmium phosphate particles amorphous spheres, 241 cadmiimi-nickel basic phosphate, 407 cadmium-nickel phosphate, 241 dye-doped, 412 protective agents, 195 reaction of NaH2P04 with urea, 241 Cadmium selenide particles preparation microemulsion process, 310 pyrolyis of organometallics, 242 selenourea process, 233 zeolite process, 332 quantum size effect, 559-560 spherical poly crystals, 233 Cadmium sulfide particles Cd-potentiometry, 282-284, 463-464 composites, see Composites pigment, 676 preparation from organometallic reagents, 242 from TAA and Cd chelates, 225-229 chelating agents, 225 gel-sol method, 225 growth mechanism, 225-229 role of ammonia, 225-229 role of gelatin, 225 from TAA and Cd(0H)2, 282-284 gel-sol method, 282 growth mechanism, 282-284 role of gelatin, 282 from TAA and free Cd^*, 231 CdS-ZnS, CdS-PbS, 231 in anodic aluminum oxide, 330-334 nanotubes and nanofibers, 330 in microemulsions, 310-311 CdS/SiOj composites, 311 Cd,Mni.,S, 311 Cd,Zni_,S, 311 in zeolite, 332

SUBJECT INDEX (CdS)4 clusters, 332 quantum size effect, 559 shape and structure, 226, 227-228, 282, 330, 405-406 size control, 371, 373, 374 TEM for sections, 405 Cadmium telluride particles pyrolysis of organometallics, 242 quantum size effect, 559 Calcium carbonate particles extender pigment, 677, 690 microemulsion process, 310 Calcium titanate particles calcination of peroxo-hydroxide, 230 composite spheres (CaTiOj-TiOj), 230 Calcium titanium peroxo-hydroxide (CaTijOgCOH)^ particles amorphous spheres, 230 chelating agents, 230 reaction of Ca^* and peroxotitaniumNTA complex, 230 Capillary charge, 550 Capillary force, 549-550 Carbodiimide method, 701-703 Carbon particles pigment, 676 preparation AAO process, 330-334 nanotubes, nanofibers, 330-334 from polymer latices, 300, 336, 415 protective agents, 195, 196 surface modification, 422, 424 Carbonyl compounds, see Metal carbonyl clusters Catalysts, 628, see also Metal catalysts growth on supports, theory, 663-676 metal catalysts, 629-662 non-metallic catalysts, 662-663 quantum size effect, 628 Catalytic shape control, 391-392 CDJ, see Controlled double jet Cell separation, see also Medical use cell affinity chromatography, 697 miaosphere methods, 697 Ceramic materials, 588-596 composites, see Composites

SUBJECT INDEX doped powders, 590-594 green compact, 589, 590 particle species alumina, 592, 594 barium titanate; Zr-, Sr-doped, 594 silica, 588, 591, 592 titania, 588, 589, 590, 592, 594 yttria, Eu-doped, 591-594 zinc oxide, polycrystalline, 591 zirconia, 589, 590, 592, 594 yttria-stabilized, 590-591 porous ceramics, 591 properties; chemical, physical, 592 sintering behavior, 588-590 agglomeration, 588 compact structure, 588 monodispersity, 588 particle shape, 588 size effect, 588 sol-gel processing, 588 Ceria (CeOj) particles calcination of oxycarbonate, 238, 413 ellipsoidal, 238, 413 YjOj-CeOj composite, 238, 407 forced hydrolysis, 253 seeding analysis, 255 polycrystalline spheres, 253 Cerium(IV) oxide, see Ceria particles Cerium(III) oxydicarbonate particles ellipsoids (Ce20(C03)2 'Hfi), 238 forced hydrolysis with urea, 238 Cerium(III) phosphate, see Lanthanide phosphate particles Cesium tungstophosphate particles crystalline spheres or octahedra, 224 reaction of protonated PWi204o^', 224 Cetyltrimethylammonium bromide (CTAB), 310, see also Protective agents Cetyltrimethylammonium chloride (CTAC), see Protective agents Chelates, 224-231 Al(acac)3, 229 2,2-bipyridineiron(II), 219 bis(dibenzylidene acetone)palladium, 217 bis(ethylenediamine)silver(I), 214 copper(II) tartrate, 218

763 Cu(DETA)22^ 228 Cu(TMD)2'\ 228 EDTA-Ba, 234 EDTA-Cd, 224-228 EDTA-Cu, 228 EDTA-lanthanides, 229-230 EDTA-Nb(OH)3^EDTA-Ni, 213 EDTA-Pb, 228 EDTA-Zn, 228 ethylenediaminocopper(II), 218 glycinatoiron(ni), 229 Ni(acac)2, 646 NTA-Nb(0H)4*, 235 NTA-hJb03'-, 230 NTA-Pb", 230, 235 Pd(acac)2, 213, 330 Pt(acac)2, 330 tris(oxalato)-germanium(IV), 235 Chelating agents, 224-231 acetylacetone, 210, 213, 229, 330, 646 aspartic acid, 225 2,2'-bipyridine, 219 citric acid, 198, 222 dibenzylidene acetone, 217 diethylenetriamine (DETA), 225 N,N-dimethylethylenediamine, 225 ethylenediamine, 210, 214, 218, 229, 230 ethylenediamine-N,N,N',N'-tetraacetic acid (EDTA), 198, 213, 225, 230, 234 glycine, 229, 385 hexamethylenetetramine, 230 nitrilotriacetic acid (NTA), 198, 225,226, 230, 235 oxalic acid, 235 tartaric acid, 218 triethanolamine, 230, 280, 385 triethylenetetramine, 225 trimethylenediamine (TMD), 225 tris{2-aminoethyl)amine, 225 Chemical embolization therapy, 710 Chini-type clusters, 333 Chromium(III) hydroxide particles alumina-coated, 417 amorphous spheres, 252, 253

764 forced hydrolysis, 252 magnetic adhesion, 572 protective agents, 195 Citric acid chelating agent, 198, 222 protective agent, 212 reducing agent, 210, 212, 630 shape controller, 222, 385 Qosed systems, 40-59 silver bromide, 54-59 silver chloride, 49-54, 56-59 spontaneous nucleation theory, 41-49 Coagulation, see also Colloidal stability inhibition of, 192-198 electric double layer, 192-193 gel network, 192-193 protective colloid, 192-196, see also Protective agents Coating, see Layered-structure control Cobalt, see Cobalt particles Cobalt basic salts, see individual Basic cobalt salts Cobalt boride (COjB) particles composites, see Alloys hydrogenation catalyst, 310, 631, 659 microemulsion process, 309 Cobalt carbonates, see Basic cobalt carbonate particles and Basic cobalt cyanatocarbonate particles Cobalt ferrite (CoFe204) particles magnetic properties, 602, 619, 623 oxidation of Co,Fei_,(OH)2 gel, 269 Co,NiyFe(II),_,.yFeA, 269 Cobalt hydroxide particles whisker from hematite, 439-440 forced hydrolysis of Co-citrate, 439 Cobalt particles alloys, see Alloys EXAFS, 633, 634 magnetic properties, 600, 601, 613, 615, 616, 617, 623 preparation Y-radiolysis, 217, 631 AAO process, 330-334 nanotubes and nanowires, 330-334 Hj reduction in silica gel, 330

SUBJECT INDEX Hj reduction of CO3O4, 241, 414 polyol process with Co{OH)2, 270 protective agents, 196 supported catalyst, 633, 634 Cobalt phosphate particles pigment (violet), 677 protective agents, 195, 196, 241 reaction with urea, 241 Cobalt sulfide particles desulfurization catalyst, 663 reaction with TAA, 663 Cobalto-cobaltic oxide (CO3O4) particles preparation calcination of carbonates, 241, 414 calcination of basic sulfate, 414 oxidation of Co(OH)2 gel, 266 precursor, CoCCHjCOO)*, 266 shape and structure, 241, 266, 414, Coercivity, see Magnetic recording materials and Magnetism Colloidal crystals, see Colloidal ordering Colloidal ordering, 545-551 capillary charge, 550 capillary force, 549-550 colloidal superlattice structure, 547 effect of gravity, 548 face-centered cubic structure, 545 order-disorder transition, 546 two-dimensional ordering, 549-551 Colloidal stability, 210-213 coagulation, 192-198 DLVO theory, 533, 546, 564 interparticle forces, 531-535 organic solvents, 211-212 dielectric constants, 211-212 effect of Aerosol OT, 211-212 stabilizers, see Protective agents Complexing agents, see also Chelating agents acetate, 210, 266 ammonia, 215, 225-230, 284, 333, 371, 637, 649-652 bromide, 243 carbonate, 223-224 chloride, 215, 216, 223, 323, 326, 335-336, 637, 649-652

SUBJECT INDEX gelatin, 49, 54, 243 hydrazine, 284 hydroxide, 256, 257 iodide, 243 sulfate, 256, 257 Composites, see also Alloys doped composites (host: dopant) AgBr:Ag°, 412 AgBr:Ag,S, 412 AgBriAu, 412 AgBr:B, C, O, P, S, Cd, Xe, Te, Pb, or Bi, 412 AgBr:dye, 413 AgBnlr, 412 Al(OH)3:dye, 412 BaTi03:(Zr,Sr), 594-596 BaTiOjiSr, 594-596 BaTiOj-.Zr, 594-596 Cd3(P04)2:dye, 412 Y-Fe203:CoO, 620, 623 Y-Fe203:Sn02, 619 PSrdye, 413 SiOjidye, 412-413, 687-691 TiOjiBaO, 411, 590, 592 Ti02:CuO, 411, 590, 592 TiOjidye, 412 TiOj-.NbA, 245, 411, 590, 592 Ti02:SrO, 254, 411, 590, 592 Ti02:Ta205, 245, 411, 590, 592 Y(0H)C03:dye, 412 Y203:Eu, 238, 591-594 Y202S:Eu, 238, 411 Y3Al50i2:Tb, 254 ZnSiAgjS, 232, 412 Zr(OH)2C03:dye, 412 Zr02:Y203, 245, 411, 590-592 heterojunctions (guest/host) Ag/Si02, 330 AgBr/Aga, 167-174, 437 Aga/Ag(Br,I), 436 AgCVAgBr, 437 AgCl/AgI, 436 Agl/AgBr, 437 AgSCN/AgBr, 437 AgSeCN/AgBr, 437 Au/a-Fe203, 323-326, 437-438

765 Au/a-FeOOH, 324-326 Au/p-FeOOH, 324-326 AU/CO3O4, 437 Au/NiO, 437 Au/Si02, 326 Au/ri02, 324-326 Au/Zr20, 324-326 CdS/SiOj, 311 Co/Si02, 330 Co(OH)2/a-Fe203, 439-440 C03O4/a-Fe2O3, 439 Cu/Si02, 330 a-FeOOH/a-Fe203, 439-441 Ir/a-Fe203, 326-329 Ni/Si02, 330 Ni(OH)2/a-Fe203, 439-440 PA/PS, 394 Pd/a-FejO,, 326-329 Pd/SiOj, 329-330 Pt/a-Fe203, 326-329 Pt/SiOj, 330 Pt/TiOj, 326-329 Pt/Zr02, 326-329 Rh/a-Fe203, 326-329 Ru/a-Fe203, 326-329 ZnO/Cu, 630 layered composites (shell/core) AgBr/Ag(Br,I), 432 AgBr/Ag(Br,I)/AgBr, 432 AgCl/AgBr, 432 Al(OH)3/a-Fe203, 417 Al(OH)3/Cr(OH)3, 417 Al(0HX/ri02, 417 CdS/SiOj, 311 CoFe20VY-Fe203, 620, 623 (CoO-FeO)/Y-Fe203, 620, 623 Cr(OH)3/a-Fe203, 418 Cu-phthalocyanine/PS, 420 Fe30/PS, 300, 420 functional groups/PS, 300, 431 Hf02/In203, 418 Mn203/a-Fe203, 418 (MnO-Mn02)/a-Fe203, 418 Ni/Mn, 241, 418 NiO/Mn203, 241, 418 noble metals (Pd/Au, Pd/Pt, Pt/Au,

SUBJECT INDEX

766 Rh/Pt), 216, 419 PBMA/PS, 260, 432 polymer/BaS04, 425 polymer/carbon, 422, 424 polymer/organic pigment, 431 polymer/oxide, 422-431 poly(2-oxazoline)/PMMA, 431 poly(2-oxazoline)/PS, 431 protective agent/particle, 421-422 PS/PMMA, 260 SiOj/Ag, 311 Si02/CdS, 311 SiOj/enzyme, 311 SiOj/Fe, 418, 419 SiOj/a-FejOj, 418, 419 Si02/Y-Fe203, 619 Si02/Pu02, 311 Si02/Y(OH)C03, 418 Sn02/a-Fe203, 418 TiN/Si02, 418 Ti02/Al203, 338, 407, 410 TiOj/CuO, 240, 418 TiOj/SiOj, 338, 407, 410, 418 Ti02/ZnO, 418 Y(OH)C03/a-Fe203, 418 Y(OH)C03/PS, 419 Y(OH)C03/Si02, 418 Y(OH)C03/Zr3(OH)6S04, 418 Y203/a-Fe203, 418 Zr02/a-Fe203, 418 mixed compounds AgBr-AgI, 161-167, 407-410 AgQ-AgBr, 159-161, 167-185, 407-408, 415-416 AI2O3 in poly urea, 336 Al203-Si02, 252, 320 (Cd-Ni) basic phosphate, 241, 407 Cd3(P04)2-Ni3(P04)2, 241

CdS-MnS, 311 CdS-PbS, 231, 407 CdS-ZnS, 231, 311, 407 (Ce-Y) basic carbonate, 238, 407 Co,NiyFe(II)i_,_yFe204, 269, 407 Cu basic salts, 239, 407 (Cu-lanthanide) basic carbonates, 240, 407

(Cu-Y) basic carbonate, 407 Pb(ZrJij.JOj (PZT), 245 PBMA in PS, 411 Pt02-Re02, 310 Si02-B203, 411, 591, 592 TiOj in polyurea, 336 titanates, 235, 245, 319-321, 407 (Y-Eu) basic carbonate, 407 (Y-Zr) basic carbonate, 407 Y2O3-AI2O3, 320 Y203-Ce02, 407 Zr02-Al203, 320 Zr02-Y203, 240 Composition control, 406-417 mixing, 407-411 doping, 411-413 conversion, 413-417 Compositional mixing, 407-411, see also Composites and Solid-solution formation Contact recrystallization, 148, 192, 495 causes, 149-152 centrifugation, 151-152 coagulation, 192 mtration, 149-150 flocculation, 150-152 halide-ion exchange, 149-152 inhibitors, 148-150 model, 152-153 radiochemical analysis, 149, 151 silver halide, 148-152, 495-496 Continuous procedures aerosol systems, 337 liquid systems alumina, 257 basic lanthanide carbonates, 238, 257 basic yttrium carbonate, 238, 257 hematite, 257 silica, 257 silicone, 318 Controlled double jet, 60-61, 74-75, 289-291, 369-370 apparatus, 75 embryos, 60, 289, 367 non-steady nucleation, 60 nucleation model, 61

SUBJECT INDEX nucleation zone, 289 Ostwald ripening, 60 particles prepared by barium sulfate, 291, 369 barium titanate, 369, 594 copper(II) oxide, 282, 369 lead sulfate, 291, 369 palladium sulfide, 223 silver bromide, 58-59, 74-83, 131-132, 134-137, 289, 369 silver chloride, 58, 289, 369 strontium sulfate, 291, 369 zinc oxide, 197, 369 photographic materials, 580 stable nuclei, 60 unstable nuclei, 60 Controls, 368-441 composition, 406-417 heterojunction, 436-441 hollow stucture, 432-434 internal structure, 396-406 layered structure, 417-432 porous structure, 434-435 shape, 376-396 size, 368-376 Conversion, 413-417 from alkoxides to oxides, 336-338 from carbonates to oxides, 413-414 from hematite to maghemite, 619, 624 from monomer droplets to polymer particles, 336-341 from oxides to metals, 414 from polymer particles to carbon, 414-415 from silver chloride to silver bromide, 167-181, 415-416 shape control through, 414 Cooling precipitation, see Homogeneous synthesis Copper, see Copper particles Copper(II) basic salts, see individual Basic copper(II) salts Copper(II) carbonate, see Basic copper(II) carbonate particles Copper(I) oxide particles preparation

767 from Cu(II) chelates with sugars, 218 from CuO with N2H4, 284-286 gel-sol process, 284-286 protective agents, 194 reducing agents, 218, 284 shape and structure, 218, 284-286 Copper(II) oxide particles composites polyaniline-coated, 240, 430 TiOj-coated, 240, 418 preparation calcination of basic carbonate, 413 shape control by, 413 gel-sol process from Cu(OH)2, 281 shapes and structures, 281, 414 Copper particles alloys, see Alloys catalyst, 632, 634 EXAFS, 641 preparation H2 reduction in silica gel, 330 H2 reduction of CUjO, 218 H2 reduction of Cu2(OH)2C03, 239,414 microemulsion process, 309, 312-314 NH2OH reduction of Cu2(OH)2C03, 270 polyol process from Cu(II)0, 270 protective agents, 194 Copper sulfide (CuS) particles from EDTA-Cu with H2S, 224 from Cu-chelates with TAA, 225-229 chelating agents, 225 effect of air, 228, 433-434 gel-sol method, 225 growth mechanism, 225-229 growth promoter, ammonia, 225-229 hollow structure, 228, 433-434 protective agent, gelatin, 194, 225 shape and structure, 224, 227, 433 Cordierite-type oxide particles prepared in aerosol systems, 336 Core-shell composites, see Composites Coulter principle, 517-518 Critical micelle concentration (CMC), 190, 292, 295-296 Critical nuclei, 28

768

SUBJECT INDEX

Critical particle radius, 57, 60 Critical supersaturation, 41 Cross-linking agents, 396, 426, 704, 705 Crystal habit catalytic activity, 642, 658 formation of, 118-137 growth forms, 118 ionic properties, 562 stable forms equilibrium form, 122-125 steady form, 125-137 Stranski theory, 132-133 surface chemical potential, 118-121 CTAB, see Cetyltrimethylammonium bromide CTAC, see Cetyltrimethylammonium chloride Cupric, see Copper(II) Cuprous, see Copper(I) Curie temperature, see Magnetism Curie's hypothesis, see Equilibrium forms Cyanogen bromide method, 701-703 Cytology, see Medical use

solvents, 258 steric stabilizers, 194-196, 258-260 surface modification, 260 Dispersion stability, see Colloidal stability Dissociative reactions, see Homogeneous synthesis Dissolution-controlled grov^h, 139-140 Divinylbenzene, see Polydivinylbenzene particles Dodecyltrimethyl ammonium chloride (DTAC), see Protective agents DLVO theory, 533, 535, 546, 549, 564 Doped composites, 411-413, 563, 590-596, see also Composites Doppler shift, 507 Drug delivery systems, 709-710 biocompatible microspheres, 709, 710 DTAC, see Dodecyltrimethyl ammonium chloride Dye adsorption method evaluation of crystal habits, 125, 504-507 Dynamic light scattering, see Photon correlation spectroscopy

Debye length, 193 Deposition-controlled growth, 139-140 Dextran drug delivery systems, 709 magnetic microspheres, 700, 703 Diagnostic assay, see Medical use Diethyl sulfate, see pH controllers Diffusion-controlled growth, 105-115 concentration profile, 108 size dependence, 107 size distribution, 110-111 Diffusion hole, see Aggregative growth model Diffusion layer, 105-108 Dislocation shape-control, 389-391 Dispersion polymerization, 189-190, 258 anionic polymerization, 259, 263-265 chain-transfer agents, 265 initiators, 259, 261, 265 nucleation and growth mechanisms, 261 seeded polymerization, 259

EDTA, see Ethylenediamine-N,N,N',N'tetraacetic acid EDX, see Energy dispersive X-ray spectrometry Einstein's diffusion equation, 40 Electric double layer, 192-193 Electro-osmosis, see Zeta-potential Electrodes Ag/AgjS, 49-50, 54 Ag/AgBr, 54 Ag/AgQ, 50 Cd/CdS, 282 Cu/CuS, 464 glass electrode, 50 Electron diffractometry (ED), 486-488 AgBr/AgQ epitaxy, 488 akaganeite, 486 hematite, sliced, 400, 401, 487 Electron microscopy, 453-455, 482-485 carbon replicas, 484-485 conversion of AgCl by Br", 168, 171

SUBJECT INDEX formation of CdS, 282-284, 454-455 formation of a-FejOg, 453-454 sliced hematite, 482-484 Electrophoresis, see Zeta-potential Electropotential floating effect, 657 Electrostatic energy, 550, 564, 570 Embryos, 60-61, 80-83 Emulsion polymerization, 190, 291-309 chain-transfer agents, 297 effect of agitation, 296-297 leveling-out effect, 296-297 emulsifier-free, 189, 294 Harkins theory, 292-294 inhibitors, 298 initiators, 292, 297, 299 seeded polymerization, 294-295, 297-300 swelling methods, 297-298 Smith-Evert theory, 292-294 theory on growth rate, 300-309 surface modification, 300 Endocytosis, see Medical use Energy dispersive X-ray spectrometry, 488-491 internal atoms (Fe, Q, S) hematite slices, 398-400, 488-491 Epitaxial multilayers, 432 CDJ technique, 432 double-structured silver halide, 432 interlayered silver halide, 432 Equilibrium compositions Ag(Br,I) systems, 161-167 Ag(a,Br) systems, 159-161 Equilibrium concentrations monomers, 4, 30-31 /2-mers, 26-30, 38 two-dimensional nuclei, 86-90 Equilibrium forms, 122-125 Curie's hypothesis, 118, 133 definition, 118, 122 diffusion-controlled growth, 133-137 silver bromide, 124, 134-137, 144-145 Wulffs theorem, 118, 122, 123, 137 1,2-Ethanediamine, see Ethylenediamine Ethylenediamine, see Chelates, Chelating agents. Protective agents, and Shape

769 controllers Ethylenediamine-N,N,N',N'-tetraacetic acid (EDTA), see Chelates, Chelating agents, and Shape controllers Europium(ni) carbonate, see Basic lanthanide carbonate particles Europium(III) oxide, see Lanthanide oxide particles Europium(III) phosphate, see Lanthanide phosphate particles EXAFS, see Extended X-ray absorption fine structure Extended X-ray absorption fine structure Co clusters on SiOj, 634 Co clusters on TiOj, 633 Cu, Ir, Os, Pt, Ru on oxides, 641 Ni clusters on SiOj, 633

Falling liquid film technique, see Aerosol systems Faraday's gold sol, 212 Fehling's solution, 218 Ferric, see Iron(III) Ferrites, 269, 407, 602 garnet-type, 602 magnetoplumbite-type, 602 spinel-type, 602 inverse spinels, 602 regular spinels, 602 Ferrous, see Iron(II) Ferroxplana, 613 Final particle density, 46, 70, 75-79 Firing of solid precursors, 334-336 preparation of a-AljOj, 334-336 Fischer-Tropsch synthesis, 642 Forced hydrolysis, 191, 252-258 rate-determining step, 255 roles of anions, 256-257 Foreign nuclei, see Heterogeneous nuclei Free energy of formation free molecule from solid, 3 w-mer from n monomers, 26-30 Freeze-fracture electron microscopy microemulsion, 311, 313

770 FTIR, see Infrared spectroscopy

Gadolinium carbonate, see Basic lanthanide carboante particles Gadolinium oxide, see Lanthanide oxide particles Gallium hydrous oxide particles forced hydrolysis, 253 shape and structure, 253 Gamboge, 521-522 Gas chromatography, 466-467 reaction product of hydrazine, 466 reaction product of thoacetamide, 466 Gauss equation, 526 Gel network, 192-193, 266-268, 270-273 Gel-sol process, 193, 225, 270-289, 624 principle, 270-271 Gelatin adsorption layer, 421, 511-512 complexing agent, see Complexing agents drug delivery systems, 709 magnetic microspheres, 700, 703 protective agent, see Protective agents removal, proteolytic enzyme, 195, 512 Germanium(IV) oxide particles preparation cooling method, 220 decomposition of chelate, 235 microemulsion process, 310 shape control, 388 shapes, 220, 388 Gibbs-Thomson equation, 31, 62 Glutaraldehyde method, 701-703 Glycine, see Shape controllers Goethite (a-FeOOH) preparation growth on hematite, 440-441 phase transformation, 139 support of metals, 324 Gold particles absorption index, 677 alloys, see Alloys colloidal superlattice, 548 determination of Avogadro number, 521 heterojunction to oxides, 323-326

SUBJECT INDEX preparation AAO process, 330-334 nanotubes and nanowires, 330-334 microemulsion process, 309 polyol process, 215 reduction in solutions, 197, 211, 212 selective deposition method, 323-326 reduction by water, 323-324 UV-photolysis, 217, 631 protective agents, 193-196, 211-213 reducing agents, 212, 215, 309, 323-324 specific cell staining, 692-695 stability on supports, 646 supported catalyst, 632, 634, 660 UV-Vis spectroscopy, 460 XPS, 501, 637-639 Growth forms, 118 Growth methanisms aggregative growth, 196-198, 266-269 coalescence on supports, 663-676 dispersion polymerization, 261-265 emulsion polymerization, 291-297, 300-309 monomeric deposition, 86-105 Growth modes choice of, 199-202 deposition-control, 139-140 diffusion-control, 105-115 dissolution-control, 139-140 distinction of, 108-117 effects on size distribution, 109-112 feed patterns based on, 199-202 Nielsen's chronomal analysis, 113-117, 232, 246, 255 reaction-control, 105-117 seeding analysis, 247-248, 255-256, 477-480 Growth promoters metal sulfide particles ammonia, 225-227, 371 silver halide particles ammonia, 124, 144, 289, 371 thiocyanate, 372 thioethers, 372 thiourea, 372 titania particles

SUBJECT INDEX ammonia, 371-372 Growth rate, 93-100, 103-108 coalescence on supports, 663-676 emulsion polymerization, 300-309 general growth activation energy, 109 concentration dependence, 188 rate-detennining steps, 105-117 size dependence, 107, 109 Growth restrainers, 372-373 gold particles sodium 3-mercaptopropionate, 372 metal oxide particles phosphate ion, 372 sulfate ion, 372 silver halide particles adenine, 372 benzimidazoles, 372 benzotriazoles, 372 cyanine dyes, 148, 174, 372, 455 dithiocarbamates, 372 guanine, 372 iodide ion, 372 lead ion, 474 mercapro compounds, 174, 372, 455 merocyanine dyes, 174, 372, 454, 455 nucleic acids, 372 tetraazaindenes, 148-150, 175, 372, 455

Hafnium hydroxysulfate particles hydrolysis of HfOQ^ with SO/', 254 amorphous spheres, 254 Hafnium oxide particles calcination of hydroxysulfate, 254 polycrystalline spheres, 254 force hydrolysis of HfCl4, 254 monoclinic ellipsoids, 254 Hamaker constant, 529-531, 536 determination of, 529-531 flocculation methods, 529 hematite, 530-531 overall Hamaker constant, 536 Hematite (a-Fe203) particles adhesion, 537-545, 571-573

771 characterization ED, 400, 401, 486, 487 EDX of sections, 398-400, 488-491 FHR, 381, 456-457, 502-504 OPML-XRD, 275, 396-397, 496-498 section-TEM, 400, 401, 404, 483-484 XRD, 399, 455-456, 492-493 coating inorganic coating, 417-419 polymer coating, 429-430 composites, see Composites controls heterojunction, 323-329, 437-441 internal structure control, 275, 277, 396-406, 624-628 shape control, 229, 239, 252, 257, 274-276, 377,379-382, 385-388, 619, 624-628 size control, 273-274, 370, 373, 374, 624-628 Hamaker constant, 530-531 magnetic adhesion, 571-573 magnetic array, 565-569 phase transformation, 139 pigment, 676, 677, 679-686 absorption index, 679 refractive index, 680 shape effect, 685 size effect, 681-685 preparation calcination of amorphous FejOj, 320 forced hydrolysis of Fe'\ 239, 252 forced hydrolysis of chelates, 229 gel-sol method, 271-278, 624-628 pH effect, 272-273 oxidation of Fe^* chelate, 219 protective agents, 195, 196, 421 seeding analysis, 277-278, 477-480 self-recrystallization, 385 support of metals, 324, 327, 632-634 zeta-potential, 543 Henry's formula, 527 Heterogeneous nuclei AgQ or NaCl nuclei in aerosols, 337 Au nuclei for Se particles, 213 Pt nuclei for Ag wires, 392

772 Heterogeneous synthesis, 265-341 aerosol-droplet conversion, 336-338 emulsion polymerization, 291-309 inhomogeneous hydrolysis, 316-319 liquid-crystal process, 314-316 microemulsion process, 309-314 non-aqueous emulsion process, 319-322 oscillatory nozzle jet, 338-341 Ostwald ripening, 289-291 phase transformation, 265-289 condensed systems, 270-289 dilute systems, 265-270 solid-matrix process, 329-330 solid-precursor firing, 334-336 solid-surface process, 322-329 solid-template process, 330-334 Heterojunction, 322-329, 436-441, see also Composites epitaxial heterojunction, 436-437 non-epitaxial heterojunction, 437-441 Hexadecyltrimetylammonium chloride, see Cetyltrimethylammonium chloride High gradient magnetic separation, 697 High-order Tyndall spectrum, 554, 556 Hiding power, see Pigments Hollow-structure control copper sulfide, 228, 433-434 polymers, 259, 434 yttria, 432-433 Holmium phosphate, see Lanthanide phosphate particles Homogeneous synthesis, 208-265 alkoxide hydrolysis, 243-252 cooling precipitation, 220-221 decompositional reaction, 233-243 dispersion polymerization, 258-265 dissociative reaction inorganic complexes, 223-224 organic complexes, 224-231 organic compounds, 231-233 forced hydrolysis, 252-258 homogeneous redox reaction, 210-219 oxidation, 219 partial reduction, 218-219 reduction, 210-218 ionic direct reaction, 221-223

SUBJECT INDEX poor-solvent precipitation, 219-220 HOTS, see Light scattering HPC, see Hydroxypropyl cellulose Hiickel's formula, 527 Hybrids, see Composites Hydrolysis alkoxides, in aerosol systems, 336 in homogeneous systems, 189, 243 growth mechanism, 245-252 in inhomogeneous systems, 316-319 silicone, 316-319 in nonaqueous emulsions, 319-322 metal ions, 252-258 thioacetamide, 231 urea, 236-237 4-Hydroxy-6-methyl-l,3,3a,7-tetraazaindene, 148-150, 372, 455 Hydroxypropyl cellulose (HPC) anticoagulant, see Protective agents surface polymerization medium, 428-429 Hyperthermia, see Medical use

Immunoglobulin, 703, 704, 706 Immunoreaction, 698 Impregnation method, see Metal catalysts Indium hydroxide (In(OH)3) particles forced hydrolysis of chelate, 229 forced hydrolysis of In^*, 253 shapes and structures, 229, 253 Indium(III) oxide particles calcination of In(OH)3, 229, 254 HfOj-coated, 418 shapes and structures, 229, 254 Inductively coupled plasma spectrometry (ICP), 465-466 copper(I) oxide formation, 466 hematite formation, 465-466 Industrial applications, 581-714 catalysts, 628-676 ceramic materials, 588-596 magnetic recording materials, 596-628 medical use, 691-714 photographic materials, 580-587 pigments, 676-691

SUBJECT INDEX Infrared spectroscopy, 456-459, 502-504 akaganeite, 456-457 basic aluminum sulfate, 457 CO on Pd particles, 217 hematite, 456-457, 502-504 shape and dimensions, 502-504 NO on Pt/(zeolite or AI2O3), 640-641 s o / ' on hematite, 381 Inhomogeneous hydrolysis, 316-319 Inorganic complexes, 223-224 Interfacial energy, see Surface energy Internal structure akaganeite (P-FeOOH), 406 bariimi sulfate, 406 copper(I) oxide, 286 hematite, 396-406 metal sulfides, 227-228 cadmium sulfide, 406 Internal-structure control, see Controls Internal-structure controllers barium sulfate citrate ion, 406 EDTA, 406 copper(I) oxide hydrazine, 286 hematite chloride ion, 396-399 organic controllers, 405-406 phosphate ion, 396, 401-404 sulfate ion, 396, 399-402 Interparticle force measurement atomic force microscope (AFM), 531 optical trapping technique, 532-535 Interstitial ions, 562 Intraparticle recrystallization AgQ by Br' ions, 167-185 introduced imperfections, 414 self-recrystallization silver bromide, 144, 145 hematite, 385 Ion chromatography, 467-470 oxidation products of CuS, 469-470 sulfate ions, 467-468 Ion-exchange method, see Metal catalysts Ion implantation, 412 Ionic conductivity, 562

773 Ionic properties, 561-564 silver halide, 561-564 Ionic strength, 193 Iridium particles alloys, see Alloys catalyst, 632, 660-662 EXAFS, 641 preparation y-radiolysis, 217, 631 alcohol reduction, 216, 631 microemulsion process, 309, 659 selective deposition, 323-329, 660 protective agents, 195, 196, 216 reducing agents, 216, 631 XPS, 328 Iron, see Iron particles Iron basic sulfate, see Basic iron sulfate particles Iron boride particles hydrogenation catalyst, 631, 659 microemulsion process, 310 Iron hydroxide (Fe(0H)3) particles H2O2 oxidation of Fe(C0)5, 219 Iron oxide (Fe203) particles, see also Hematite particles nonaqueous emulsion process, 320 amorphous spheres, 320 protective agents, 195 Iron particles alloys, see Alloys magnetic adhesion, 567, 571, 572 magnetic properties, 600, 601, 613, 615, 617, 619, 620, 623 preparation AAO process, 330-334 nanotubes, nanowires, 330-334 H2 reduction from a-Fe203, 414 polyol process from Fe(0H)2, 270 protective agents, 196 shape control, 413, 414 Iron phosphate (FeP04) particles direct ionic reaction, 222 spherical, 222 Isoelectric point, 193, 194, 268, 269

774 Kink, 642 Kirkwood-Alder transition, 546 Kubelka-Munk function, 504-505,681-682

LaMer diagram, 42 LaMer mechanism, 41-42, 189-190, 197, 245-246 Langevin equation, 566-567 Lanthanide carbonates, see Basic lanthanide carbonate particles Lanthanide hydroxycarbonate, see Basic lanthanide carbonate particles Lanthanide oxide particles, see also Composites calcination of basic carbonates, 229, 238, 240, 407, 413 lanthanide-Cu(n) composites La, Gd, Dy, Ho, Er, 240, 407 lanthanide oxides La, Ce, Gd, Eu, Tb, Sm, 229, 238 Lanthanide phosphate particles lanthanides La, Ce, Nd, Sm, Eu, Ho, Tb, 229 reaction of EDTA complexes with NaH2P04, 229-230 shapes, 229 Lanthanum carbonate, see Basic lanthanum carbonate particles Lanthanum iodate (La(I03)3) particles ionic direct reaction, 222 Lanthanum oxide, see Lantanide oxide particles Lanthanum phosphate, see Lanthanide phosphate particles Larmor's procession, 603 Laser trapping technique, see Interparticle force measurement Layered composites, see Composites Layered-structure control, 417-432 epitaxial multilayers, 432 inorganic coating for inorganic partilcles , 417-419 for organic partilcles , 419-420 organic coating for inorganic partilcles , 420-431

SUBJECT INDEX for organic partilcles , 431-432 Lead, see Lead particles Lead iodate (Pb(I03)2) particles direct ionic reaction, 222 Lead niobate particles calcination of a precursor, 230, 235 polycrystalline spheres, 230, 235 Lead niobium peroxo-hydroxide particles amorphous spheres, 230, 235 preparation Nb03-NTA'- and Pb-NTA", 230, 235 Nb(0H)3-EDTA'- and Pb^* 230 Lead particles preparation by yradiolysis, 217, 631 Lead selenide particles dissociation of selenourea, 233 polycrystalline spheres, 233 Lead sulfate particles double jet technique, 291, 369 Lead sulfide particles cubic or rectangular, 231, 391 mixed particles, CdS-PbS, 231 preparation from HjS and EDTA complex, 224 from TAA and free W\ 231 from TAA and Pb chelates, 225 chelating agents, 225 gel-sol method, 225 growth mechanism, 225-229 protective agent, gelatin, 225 role of ammonia, 225-229 size control, 371-372, 373 Lead titanate particles amorphous spheres, 235, 320 calcination of, 320 preparation decomposition of NTA-Pb, 235 in nonaqueous emulsion, 320 protective agent, 195 Lead zirconate-titanate (PZT) particles amorphous spheres/Pb(Zr,,Tii.J03, 245 calcination of, 245 hydrolysis of alkoxides, 245 Lennard-Jones potential, 537 Light scattering, 552-559 high-order Tyndall spectrum (HOTS),

SUBJECT INDEX 554, 556 Mie scattering, 553-554, 677 polarization ratio, 557-559 size distribution, 557-559 Rayleigh scattering, 553-554, 678-679 red spectral scattering orders, 554 specific turbidity, 556-557 Linear growth rate, 107 Liquid-crystal system, 314-316 basic copper nitrate, 316 basic copper sulfate, 315-316 Tween 80, 314-315 Lithium tantalate (LiTaOj) particles aerosol process, 336 amorphous spheres, 336 Living polymer, 260, 428 London-van der Waals force, 536, 564 Lorenz-Mie theory, 677, 680 LSW theory, see Ostwald ripening

Maghemite (y-FejOj) particles cobalt-doped, 620, 623 controls: size, shape, structure, 624-628 conversion from a-FCjOj, 413, 624 gel-sol method, 624 magnetic properties, see Magnetic recording materials XRD, 626 Magnesium fluoride particles ionic direct reaction, 223 spherical, 223 Magnetic anisotropies, see Magnetism Magnetic domain, see Magnetism Magnetic energy, 565, 567-570 Magnetic microsphers, 696, 700, see also Medical use assay techniques, 698-699 fabrication of magnetic body, 700 ferromagnetic particles for, 697-698 functionalization of, 692, 701-703 chemical methods, 701-703 carbodiimide method, 701-703 cyanogen bromide method, 701-703 glutaraldehyde method, 701-703

775 maleimido-hinge method, 701-703 physical methods, 701 polymers for, 700, 701, 703, 708, 710 sensitization, 699 silica coating, 700-701 specific reactions of antigen-antibody reaction, 692 enzyme-substrate reaction, 692 saccharide-lectin reaction, 692 types, 700 Magnetic recording materials, 600-603, 607-608, 613-628 barium ferrite (BaO •6Fe203), 600, 602, 616, 619, 621-623 chromium dioxide (CrOj), 600, 601, 619, 620-621, 623 cobalt, 600, 601, 613, 615, 616, 617, 623 cobalt fenite (CoFep^), 600, 602, 619, 623 iron, 600, 601, 613, 615, 617, 619, 620, 623 iron nitride (Fe4N), 622 maghemite (y-FejOa), 600,602,607-608, 614, 615, 617, 618, 619-620, 623, 624-628 aspect ratio, 624-627 cobalt-modified, 619, 620, 623 coercivity, 624-627 controls size, shape, structure, 624-628 from goethite, 619 from hematite, 619, 624-628 gel-sol technique, 624 monodipersed, 624-628 silica-coated, 619 squareness, 627 tin-doped, 619 magnetite {]^^fi^\ 607, 614, 618, 623 nickel, 600, 601, 614, 615, 617, 623 Magnetic shape control, 392-393 Magnetism, 596-618 classification of, 600-603 antiferromagnetism, 600, 603 diamagnetism, 600, 603 ferrimagnetism, 600, 602 ferromagnetism, 600-602

776 metamagnetism, 600, 602 paramagnetism, 600, 603 parasitic fenomagnetism, 600, 602 coercivity, 615-618 magnetic anisotropics, 615-617 magnetic interaction, 618 reversal modes of spin, 617-618 Stoner-Wohlfarth model, 615, 617 Curie temperature, 601 demagnetizing factor, 603-605 magnetic anisotropics, 608-618 magnetocrystalline, 613-614, 616 shape, 608-613, 615-616 strain, 614-615, 617 magnetic domain, 604-608 magnetic force, 596-600 Neel temperature, 603 size effect, 603-608 Stoner-Wohlfarth model, 608-615, 617 superparamagnetism, 606-607 unit systems; SI-, CGS-, 596-600 Magnetite (Fe304) particles magnetic properties, 607, 614, 618, 623 polystyrene coated by, 300, 420 preparation oxidation of Fe(OH)2 gel, 266-269 aggregative growth, 196, 266-269 growth mechanism, 266-269 oxidizing agent, NO3", 266 role of gel network, 266-269 microemulsion process, 310 protective agents, 195 shape control, 377 magnetic adhesion, 573 radiochemical analysis, 476-477 pigment, 676 magnetopneumography, 695-696 magnetic microspheres, 698, 703, 704, 705, 708, 710, 713 Maleimido-hinge method, 701-703 Manganese, see Manganese particles Manganese(II) carbonate particles preparation dissociation of HCO3", 223 reaction with urea, 240-241 shape control, 223-224, 240-241

SUBJECT INDEX Manganese(II) niobate particles amorphous spheres (MnNbjOg), 224 dissociation of Nb complex, 224 Manganese oxide particles composites, see Composites MnO, from MnCOj in Nj, 241 MnjOj, from MnC03 in air, 241 S-MnOj, by forced hydrolysis, 253 Y-MnOj, from MnCOj in Oj, 224 shapes and structures, 223, 241 Manganese particles H2 reduction of Mn203, 241 Ni-coated, 241, 418 Manganese(II) phosphate particles amorphous spheres (Mn3(P04)2), 241 from Mn^* and P04^" with urea, 241 protective agents, 195 Manganese(II) sulfide particles Cd^Mn^.^S in microemulsion, 311 Mastic, 521-522 Maximum supersaturation, 41 Medical use, 691-714 cell separation, 697-708 cell affinity chromatography, 697 enzyme-immunoassay, 707-708 for cancerous cells, 705 for viruses, 705 magnetic microspheres for, 703-705 cytology, 692-697 endocytosis, 696-697 magnetopneumography, 695-696 specific cell staining, 692-695 diagnostic assay, 705-708 monodispersed particles for, 712-714 remedial use, 708-712 biocleaners, 711 bioreactors, 710-711 drug delivery systems, 709-710 hyperthermia, 711-712 Mercapto compounds, see Growth restrainers and Shape controllers Mercury(n) iodide particles reduction of IO3" with S03^", 234 Mesoporous molecular sieves, see also Solid templates FSM-16, MCM^l, 333-334, 647-648

SUBJECT INDEX Metal carbonyl clusters Co-, Fe-, Ir-, Pt-, Rh-, Ru-, 332 preparation in zeolites, 332-333, 647 in mesoporous molecular sieves, 333-334, 647-648 Metal catalysts, 629-676 catalyses, 630-635, 658-659, 662 effects of crystal habit, 642, 658 effects of size, 635-645 monodispersed particles for, 658-663 preparation in gas phases, 629-630 in liquid phases, 630-631 on supports, 632-662 impregnation method, 649-652 ion-exchange method, 649-652 photo-plating, 659-660 selective deposition, 660-662 protective agents, 630, 632 roles of supports, 645-658 size control, 636-637 supports, 632, 633 2D-coalescence, theory, 663-676 Microemulsion systems, 309-314 catalysts prepared in, 658-659 characterization of, 310-312 dielectric spectroscopy, 312 dynamic light scattering, 312 freeze-fracture EM, 311, 313 NMR; "C, '^, 'H, 310-312 SAXS, 311, 313 UV-VIS spectroscopy, 311 formation mechanism in, 312 self-assembly model, 312-314 water-core size, 310 Microspheres, 691, see also Magnetic microspheres Mie scattering, 553-554 Miller index, 496 Mixed compounds, see Composites and Compositional mixing Molybdenum sulfide particles desulfurization catalyst, 663 reaction with TAA, 233 spherical, 233

777 Monoclonal antibody, 705 Monodispersed particles definition, 1 formation principles, 188-202 Monodispersed systems, 208-341 classification, 208-210 heterogeneous systems, 265-341 homogeneous systems, 210-265 Monomer definition, 2 Monomeric precursor model oligomer precursor mechanism, 252 siloxane oligomers, 249-252 sol-gel process, 249-252 Mononuclear-layer growth, 116-117 Morphology, see Shape and Crystal habit Mullite (3AI2O3-25102) calcination of amorphous precursor, 321 Multichannel spectrophotometry, 57

Nano-tubes, -wires, -fibers, 330-332 preparation in anodic aluminum oxide (AAO) Au, C, CdS, Co, Co-Ni, Fe, Pt, polyacetylene, TiOj, WO3, ZnO, 330-334 in mesoporous molecular sieves Pt, 647-648 Neel temperature, see Magnetism Neodymium phosphate, see Lanthanide phosphate particles Nickel, see Nickel particles Nickel boride (NijB) particles composites, see Alloys hydrogenation catalyst, 310, 631, 659 microemulsion process, 310 Nickel fenite (NiFe204) particles oxidation of Ni(OH)2-Fe(OH)2 gel, 269 Co,NiyFe(II)i.,_yFe204 ferrite, 269 Nickel hydroxide particles whisker grown on hematite, 439-440 Nickel oxide particles calcination of carbonates, 241 spherical, 241 Nickel particles

778 catalyst, 633, 642-644, 656 EXAFS, 633 magnetic properties, 600, 601, 614, 615, 617, 623 magnetic shape control, 392-393 metallic composites, see Alloys Ni-P alloy amorphous spheres, 286 NaHjPOj reduction of Ni(0H)2, 286-289 preparation AAO process, 330-334 nanotubes and nanowires, 330-334 electrochemical reduction, 217 Y-radiolysis, 217, 631 Hj reduction in silica gel, 330 Hj reduction of NiO, 241 H2O2 reduction of EDTA-Ni, 213 polyol process from Ni(OH)2, 270 spheroids or filaments, 392-393 protective agents, 195, 196 reducing agents, 213 stability on supports, 646-647 Nickel carbonate, see Basic nickel carbonate particles Nickel phosphate particles amorphous spheres, 241 cadmium-nickel phosphate, 241 urea process with PO/', 241 Nielsen's chronomals, 113, 232, 246, 255 Niobium pentoxide particles amorphous spheres, 320 nonaqueous emulsion process, 320 Nitrilotriacetic acid (NTA), see Chelates and Chelating agents «-mer definition, 2 equilibrium concentration of, 26-30, 38 steady concentration of, 33-38

NMR CK '% ^H) microemulsions, 310-312 Nonaqueous emulsion systems, 319-322 acetonitrile, 319-320 formation mechanism, 321-322 hydrolysis in, 319-322 protective agents, 321

SUBJECT INDEX Non-steady nucleation, 40, 57, 58, 60 NP-6, see Polyoxyethylene(6)-nonylphenyl ether NTA, see Nitrilotriacetic acid Nucleation-controUed precursor model, 189-190 Nucleation period, 47-49, 72, 79-80 Nucleation process, 30-83 for silver bromide, 54-56, 74-83 for silver chloride, 49-54 in closed systems, 40-59 in open systems, 59-83 theories basic theory, 30-40 for closed systems, 40-49 for open systems, 59-74 Nucleation rate Becher-Doring theory, 38-40, 58 concentration dependence, 188 in closed systems, 44 in open systems, 66 measurements, 40 stopped flow technique, 57 streak camera, 58 turbidimetry, 58 supersaturation ratio, 30-40 two-dimensional, 90-93 Zeldovich method, 39 Nylon particles, TiOj-coated, 690

Odd-even effect, metal clusters, 637 Oligomer radicals, see Oligomers Oligomers anionic oligomers, 190 living oligomers, 190 oligomer precursor mechanism, 252 oligomer radicals, 189, 190 Open site, see Bond-free open site Open systems, 59-83 nucleation model, 60-61 nucleation zone, 289 optimum feed patterns, 199-202 silver bromide, 74-83 silver chloride, 58 OPML-XRD, see Oriented particulate

SUBJECT INDEX monolayer X-ray diffractometry Optical trapping technique, see Interparticle force measurement Optoelectronic properties, 559-561 cadmium chalcogenides, 559-560 dopant effects, 560 photoelectron lifetime, 560 silver halides, 560-561 Organic complexes, see also Chelates dissociative reaction of, 224-231 Oriented particulate monolayer X-ray diffractometry (OPML-XRD), 496 basic aluminum sulfate, 499 hematite, 275, 396-397, 496-498 Oscillatory nozzle-jet technique preparation of polymer beads, 338-341 Osmium particles alcohol reduction, 216, 631 EXAFS, 641 protective agents, 195, 216 Ostwald ripening, 58, 75-76, 140-148 diffusion-controlled, 141-142 in open systems, 289-291 LSW theory, 141-144 reaction-controlled, 142-144 reversed, 144-148 Oxidation, 219, 266 Oxidizing agents hydrogen peroxide, 219 oxygen, 266, 433 potassium nitrate, 219, 266 Oxy-basic zirconium carbonate particles reaction with urea, 240 spheres (Zr202(OH)2C03), 240

PAA, see Polyacrylic acid Palladium particles catalyst, 631, 633, 634, 644, 660-662 composites, see Alloys and Composites FHR of adsorbed CO, 217 heterojunction to oxides, 326-329 metal composites, see Alloys preparation alcohol reduction, 216, 631 CO reduction of chelate, 217

779 electrochmical reduction, 217 H2 reduction in silica gel, 329-330 H2 reduction of chelate, 217 microemulsion process, 309 polyol process, 215 pyrolytic reduction of Pd(acac)2, 213 selective deposition method, 323-329 protective agents, 194-196, 211-212, 216, 217, 237, 631 reducing agents, 215-217 stability, organic solevents, 211-212 UPS, 639-640 XPS, 328 Palladium sulfide particles double jet method, 223 protective agent, CTAB, 223 PAN, see Polyacrylonitrile particles PCS, see Photon correlation spectroscopy pH control, see Size control pH controllers diethyl sulfate, 49, 53, 55, 231, 243 urea, 236-237, 239 pH Stat, 465 Phase transformation, 139-140, 265-289 deposition-controlled growth, 139-140 dissolution-controlled growth, 139-140 Phosphonic acids, see Shape controllers Photocatalysts, 657-658 Photochemical hole burning, 413 Photoelectrons, 560-561 Photographic materials, 580-587 controlled double-jet method, 580 silver halide, 580-587 direct positive, 582-584 double structure grains, 585-587 dye desensitization, 586-587 image contrast, 582-583 internal sensitization, 582 quantum sensitivity, 581-582 spectral sensitization, 584-587 Photon correlation spectroscopy, 507-512 silver bromide adsorbed gelatin layer, 511-512 size distribution, 510-512 Photoplating, see Metal catalysts Pigments, 676-691

780 absoprption efficiency, 684 dielectrics and metals, 684 hematite, gold, 684 absorption index, 677, 679 affinity to skin, 690 brightness, 691 chromaticities, 682 colored pigments, 676-677 composite pigments, 687-687, 690 cosmetics, 689-691 extender pigments, 677, 690 extinction efficiency, 683 gloss, 690 hiding power, 686-687 kinetic friction coeffficients,691 Kubelka-Munk theory, 681-682 Lorenz-Mie theory, 677, 680 particles BaSO^, 677, 686-687, 690, 691 dye-doped A1(0H)3, 412, 687 dye-doped PS, 413 dye-doped Si02, 413, 687-688 dye-doped Y(0H)C03, 413, 238 hematite, 676, 677, 679-686 silica, 687-691 TiOj-coated SiOj, 688-689 titania, 676, 686-691 zinc oxide, 676, 686-687 zinc sulfide, 676, 686 Rayleigh scatterers, 677, 678 refractive index, 677-680 hematite, 677, 679-680 aerosols, metals, pigments, 677 Theological properties, 691 shape effect, 685-686 size effect, 677-685 vehicles, 690 Platinum, see Platinum particles Platinum carbonyl particles Chini-type clusters, 333 preparation, 332-334, 647-648 in mesoporous molecular sieves Pti5(CO)3o^', 333-334, 647-648 in zeolites YX,{CO\,^-, Pti2(CO)24^ 332-333, 647-648

SUBJECT INDEX Platinum particles catalyst, 631, 632-635, 637, 642-644, 657, 659, 660-662 composites, see Alloys and Composites EXAFS, 641 FDR for NO on Pt, 641 preparation alcohol reduction, 216, 631 Y-radiolysis, 217, 631 Hj reduction in silica gel, 330 in anodic AljOj films nano-tubes, -wires, 330-334 in mesoporous molecular sieves nano-particles, -wires, 647-648 in microemulsions, 309 in zeolites, 332-333, 647-648 selective deposition, 323-329 UV-photolysis, 217, 631 protective agents, 194, 216 reducing agents, 216, 309, 326, 332 stability on supports, 645-646, 648-655 XPS, 328, 639 PMMA, see Polymethylmethacrylate particles Poisson equation, 524 Poisson-Boltzmann equation, 525 Polyacetylene particles AAO process, 330-334 nanotubes and nanofibers, 330-334 Polyacrylamide particles copolymers, 260 magnetic microspheres, 700, 703, 704 preparation dispersion polymerization, 260 copolymers, 260-261 N-substituted, 260 stabilizer-free, 260 W/O microemulsion process, 310 Polyacrylic acid, see Protective agents Polyacrylonitrile (PAN) particles dispersion polymerization, 260, 435 porous spheres, 260, 435 protective agent, PVP, 194 Polyalkylmethacrylate particles dispersion polymerization, 260 copolymers, 260

SUBJECT INDEX core-shell particles, 260 Poly(ciiethyleneglycol diraethacrylate) particles y-ray dispersion polymerization, 261 Polydivinylbenzene (PDVB) particles copolymers, 260, 298, 336, 338, 434 CTOSS-Iinking agent, 260, 394-396, 434 hollow particles, 434 porous particles, 434 preparartion aerosol process, 336 dispersion polymerization, 260 emulsion polymerization, 298 oscillatory nozzle jet, 338-339 Polyethylacrylate particles copolymers with styrene, 299, 395 emulsion polymerization, 299, 395 shape control, 395 Poly(glycerol monomethacrylate) particles Oscillatory nozzle-jet technique, 340 Poly(2-hydroxyethylmethacrylate) particles copolymers, 700, 704, 705 magnetic microspheres, 700, 703, 704 preparation dispersion polymerization, 260 Oscillatory nozzle jet, 340 Polymethylmethacrylate particles composites, see Composites dispersion polymerization, 260 copolymers, 260 core-shell particles, 260 solvents, 260 steric stabilizers, 260 emulsion polymerization, 294 copolymers, 294 shape modification, 298-299 extender pigment, 690 magnetic microspheres, 700, 704 protective agents, 194 size control, 374-375 Polynuclear-layer growth, 113-116 Polyol process, 214-215, 270 heterogeous systems, 270 homogeneous systems, 214-215 mechanism, 214 Polyols

781 as protective agents, 196, 270 as reducing agents, 214-215 Polyorganosilsesquioxane particles factors for uniformity, 319 hydrophobicity/hydrophilicity, 318 inhomogenous hydrolysis, 316-318 Polyoxyethylene(lO) isooctylphenyl ether (Triton X-100), see Protective agents and Shape controllers Polyoxyethylene(40) isooctylphenyl ether (Triton X-405), see Protective agents Polyoxyethylene(6) nonylphenyl ether (NP-6), see Shape controllers Polyoxyethylene sorbitan monooleate (Tween 80), see Liquid crystal systems Polypyrrole particles dispersion polymerization, 260 Polystyrene (PS) particles colloidal ordering, 545, 547 two-dimensional ordering, 548-549 composites, see Composites dye-doped pigment, 413 extender pigment, 690 inorganic coating, 300, 419-420 interparticle force, 532-535 light scattering, 557 magnetic microspheres, 700, 701 preparation dispersion polymerization, 259 holllow particles, 259 anionic polymerization, 259-260 copolymers, 260 core-shell particles, 260 living polymer, 258 seeded polymerization, 259 steric stabilizers, 259 emulsion polymerization, 292-300 anionic polystyrene, 294 cationic polystyrene, 294 copolymers, 294, 298-300 core-shell elastomer, 300 emulsifier-free, 294 inhibitors, 298 porous particles, 298 seeded polymerization, 294, 297-300

782 shape control, 298-299, 393-396 size control, 374-375 in aerosol systems, 336 in O/W miCToemulsions, 311 protective agents, 194, 195 surface modification, 260, 300, 431 Polyurea particles aerosol process, 336 AljOj-dispersed polyurea, 336 TiOj-dispersed polyurea, 336 Polyvinylalcohol, see Protective agents Poly(N-vinylformamide) particles dispersion polymerization, 260 Polyvinylidene chloride particles emulsion polymerization, 300 conversion to carbon particles, 300 Polyvinylpyrrolidone (PVP), see Protective agents Polyvinyltoluene particles light scattering, 557 Poor-solvent precipitation, 219-220 Porous structure control, 434-435 inorganic particles, 237, 241, 434, 591 polymer particles, 434-435 Potassium niobate (KNbOj) particles amorphous spheres, 224 reaction of Nb complex, 224 Potentiometries, 461-465 Ag-potentiometry for silver halides conversion process, 170, 181-185 nucleation process, 49-51, 53-55 solid-solution composition, 155-170 surface stress energy, 176-181 Cd-potentiometry CdS formation, 228, 282-284, 463 Cu-potentiometry C u p formation, 284-286, 464 pH measurement CdS formation, 283, 462 CU2O formation, 285, 462 a-FCjO, formation, 461-462 Ni-P formation, 287, 462 Precipitation polymerization, 258 Precursor, 189, 190, 193 Prenucleation stage, 41-42 Primary particles, 196, 197, 266-269,

SUBJECT INDEX 277-278 Protective agents, 192-196, 210-211, 421-422 acetic acid, 213 N-alkyl polyimine, 195 amphipathic block copolymers poly(terr-butylstyrene)-6-poly(2vinylpyridine), 421 polystyrene-Z7-polybutadiene, 258,260 polystyrene-b-polydimethylsiloxane, 260 polystyrene-^-polyvinylacetate, 258, 259 AVANEL S-150, 224 cetyltrimethylammonium chloride (CTAC), 196, 211, 241 cetyltrimethylammonium bromide (CTAB), 223 cyclodextrin, 195 dextran sulfate, 195 N-dodecyl-N,N-dimethylbetaine, 210, 630 dodecylpyridinium bromide, 196 dodecyltrimethyl ammonium chloride (DTAC), 210, 630, 631, 636 ethylenediamine, 214 gelatin, 193,194, 225, 282, 284, 290, 421 Y-globulin, 195 hexadecylpyridinium chloride, 196 hexaoxyethylene dodecyl ether, 211, 630 hydroxypropyl cellulose (HPC), 195,254, 258, 259, 321, 421, 426, 589 lysozyme, 195 ovalbumin, 195 perfluoro polyether carboxylate, 195 poly aery lamide, 210, 260 polyacryUc acid (PAA), 195, 210, 258, 259, 421 polyacrylic acid hydrazide, 193,194, 421 poly(2-ethyl-2-oxazoline), 194, 260 polyethylene glycol (PEG), 286, 421 polyethyleneimine, 194, 260 polymaleic acid, 195, 421 polymethacrylic acid (PMAA), 260 polyol, 196, 270 polyoxoanion P2Wi5Nb3062'", 196

SUBJECT INDEX polyoxyethylene alkylphenol ether, 196 polyoxyethylene dodecylalcohol ether, 196 polyoxyethylene(lO) isooctylphenyl ether (Triton X-100), 196, 235 polyoxyethylene(40) isooctylphenyl ether (Triton X-405), 238 polyoxyethylene solbitan monolaurate, 211, 630 polyphosphate, 196 polyvinylalcohol (PVA), 195, 210, 421, 630, 632, 636 poly(N-vinyl~5-methoxa2olidone), 193, 194, 421 polyvinylpyrrolidone (PVP), 194, 210, 214-216, 238, 240, 258-260, 270, 419, 421, 630, 632, 636 Rhodasurf TB970, 261 sodium alkylbenzene sulfonate, 195 sodium citrate, 212 sodium dihexylsulfosuccinate (Aerosol MA), 222 sodium dioctylsulfosuccinate (Aerosol OT), 195, 210, 211-212 sodium dodecylsulfate (SDS), 195, 210, 241, 421, 630 sodium oleate, 195, 420 tetraalkylammonium, 196, 217-218 N-tetradecyl-2-aminopropionic acid, 210-211, 630 tetradecylpyridinium bromide (TDPB), 210, 630 Triton X-305, 235 Protective colloids, see Protective agents Protective value, 193 PS, see Polystyrene particles Pulse radiolysis nucleation of silver halide, 58 PVA, see Polyvinylalcohol PVP, see Polyvinylpyrrolidone PZT, see Lead zirconate-titanate particles

Quantum size effect nanosized semiconductors, 559-560 metals, 628, 637-642

783 Quasi-steady nucleation, 40

Radiochemical analysis, 470-477 magnetite system, ^^e^*, 476-477 silver halide systems coalescence, ^Br", 474 contact recrystallization ^^ar, ^^Br", 148-153 experimental errors, 475-476 Ostwald ripening ^CC, *^Br", 471-475 surface-ion exchange, ^^Q", 469-470 Rayleigh scattering, 553-554 Reaction-controlled growth, 105-117 concentration profile, 108 size dependence, 107 size distribution, 111-112 Recrystallization, 139-153 contact recrystallization, 148-153 intraparticle recrystallization, 167-185 Ostwald ripening, 140-144 diffusion-controlled, 141-142 reaction-controlled, 142-144 reversed, 144-148 phase transformation, 139-140 self-recrystallization, 144 Redox systems heterogeneous, 266-270, 284-289, 322-334 homogeneous, 210-219 Reducing agents alcohols, 216, 630, 631, 636 ascorbic acid, 197 carbon monoxide, 210, 217 citric acid, 210, 630 formaldehyde, 212 glucose, 218 hydrazine, 210, 211, 213, 309 hydrogen, 217, 309, 630 hydrogen peroxide, 213 hydroxylamine, 210, 213, 270 polyols, 214-215 sodium borohydride, 210, 310, 630, 631, 646 sodium hypophosphite, 286

784 sodium nitrite, 219 sugars, 218 sulfite, 234 water, 323-324 Reduction, 210-219 electrochemical, 217 partial, 218-219 photolytic, 210, 217, 631, 636 pyrolytic, 213, 217, 218 radiolytic, 210, 217, 631, 636 Reservoirs, 139, 191, 198-199, 371 Reversed Ostwald ripening, 144-148 narrowing of size distribution, 148 silver bromide, 147-148 surface chemical potential, 146-147 Rhenium oxide (ReOj) particles microemulsion process, 310 PtOj-ReOj composite, 310 Rhodanines, see Shape controllers Rhodium particles catalyst, 631, 633, 644, 655, 656, 660 composites, see Alloys and Composites preparation alcohol reduction, 216, 631 microemulsion process, 309 selective deposition, 323-329 UV-photolysis, 217, 631 zeolite process, 332-333 protective agents, 196, 216 reducing agents, 216 XPS, 328 Ruthenium, see Ruthenium particles Ruthenium double-salt particles amorphous spheres, 237 reaction of RuQj with urea, 237 Ruthenium(IV) oxide particles autocatalytic reduction of RuO^, 218 calcination of Ru double salt, 237 Ruthenium particles catalyst, 633, 644, 656, 660-662 EXAFS, 641 preparation Hj reduction of RuOj, 237, 414 selective deposition, 323-329 XPS, 328

SUBJECT INDEX Samarium (III) carbonate, see Basic samarium(III) carbonate particles Samarium(in) phosphate, see Lanthanide phosphate particles Samarium(in) oxide particles calcination of basic carbonate, 413 spherical, 413 SAXS, see Small angle X-ray scatttering Scandium oxyhydroxide (y-ScOOH) particles crystalline disks, 254 forced hydrolysis, 254 Schener equation, 492 SDS, see Sodium dodecylsulfate Seeded dispersion polymerization, see Dispersion polymerization Seeded emulsion polymerization, see Emulsion polymerization Seeding, 374-375 basic aluminum sulfate, 374 cadmium sulfide, 374 gold, 191 hematite, 274, 374 polystyrene, 259, 294, 297-300 ruthenium dioxide, 218 titania, 280 Seeding analysis, 255-256, 477-480 ceria, 255 copper(II) oxide, 282 hematite, 277-278, 477-480 silica, 247-248 titania, 280-281 Selective deposition method, 322-329, 660-662, see also Metal catalysts Selenium particles gold nuclei, 213 reducing agents, 213 reduction of selenous acid, 213 Selenourea selenide formation, 233 Self-assembly systems, 312-314 Self-recrystallization, 144 hematite, 385 silver bromide, 144, 145 surface chemical potential, 144 Shape control, 376-396, 413-414

SUBJECT INDEX adsorption of controllers, 376-388 anisotiotic acceleration, 388-393 catalytic control, 391-392 dislocation control, 389-391 magnetic control, 392-393 twinning control, 388-389 for polymer particles, 393-396 of precursor particles, 413-414 Shape controllers, 256-257, 376-388 barium carbonate particles NP-6, 388 barium sulfate particles Aerosol MA, 222 citrate, 222 EDTA, 222 PEG-6-PMAA, 291 (PEG-^-PMAA)-aspartic acid, 291 PMAA (polymethacrylic acid), 291 Triton X-100, 222 basic aluminum sulfate particles chloride ion, 278, 382 hydroxide ion, 278, 377 sulfate ion, 278, 383 copper(I) oxide particles ethylenediamine, 286 glucose, 218 hexamethylenetetramine, 218 hydrazine, 286 tartaric acid, 218 germanium dioxide particles Aerosol OT, 388 hematite particles benzoquinones, 385 bipyridine, 385 chloride ion, 257, 275 citrate, 385 dihydroxybenzenes, 274, 385 dihydroxynaphthalenes, 274, 385 EDTA, 275, 385 glycine, 229, 385 hydroxide ion, 275, 377 NTA, 275, 385, 387 organic phosphonic acids, 385, 619 oxalate, 385 phosphate ion, 257, 275, 380, 381, 619, 624

785 sulfate ion, 257, 275, 380-382 triethanolamine, 385 urea, 385 magnetite paticles hydroxide ion, 377 manganese carbonate particles sulfate ion, 223-224 silver bromide particles ammonia, 377, 379, 383 benzimidazoles, 384 bromide ion, 124, 132-133, 376-377 mercaptoimidazoles, 384 rhodanines, 384 tetraazaindenes, 384 silver chloride particles cadmium ion, 382 mercaptobenzimidazole, 384 zinc oxide particles ammonia, 230 ethylenediamine, 230 hexamethylenetetramine, 230 triethanolamine, 230 Shape effects catalyts, 642, 658 ceramics, 588 cosmetics, 690-691 electrophoresis, 527 ionic properties of solids, 562 magnetic properties, 608-613, 615-616, 624-627 optoelectronic properties, 561 photographic properties, 580, 584-585 pigments, 685-686 spectra of adsorbed dyes, 505-507 Ship-in-bottle synthesis, 332-333, 647 Silan coupling agents, 420, 429-430 alkoxysilane, 420, 429-430 aminopropyltriethoxysilane, 429 chlorosilane, 420, 429-430 thiopropylmethoxysilane, 430 Silica gel matrix, 329-330 Hj reduction in, 330 metal nanoparticles, 330 Silica particles adhesion, 537-541 ceramic materials, 588, 591, 592

786 colloidal ordering, 545, 547-549 composites, see Composites dye-doped, 412-413, 687-688 inorganic coating, 311, 410, 418, 688 interparticle forces, AFM, 531 pigments, 687-691 composites, 687-691 extender, 690, 691 preparation (alkoxide hydrolysis) aerosol process, 336 homogenous process, 243-245 continuous method, 244 growth mechanism, 245-252 microemulsion process, 310, 311 composites, 311 nonaqueous emulsion process, 320 protective agents, 421 silicon alkoxides, 189 size control SDS, 244, 373 temperature, 370 supports of metals, 326, 329-330, 632-634 surface modification, 422-431 surface structure, 248 zeta-potential, 543 Silicone, see Polyorganosilsesquioxane particles Silver, see Silver particles Silver bomide particles adsorbed gelatin layer, 421, 510-512 bond-free spots, 6-11 chemical sensitization, 581 composites, see Composites controls heterojunction, 436-437 layered structure, 432 shape, 118-137, 384-385, 388-391 size, 55-56, 76-77, 369, 371, 372 crystal habit, 13-14, 124, 128-137 equilibrium forms, 124, 137, 144 steady forms, 128-137 diffusion-controlled range, 290 dislocation-controlled growth, 389 double-structured grains, 432, 585 dye-doped, 413

SUBJECT INDEX electron diffractometry AgBr/AgQ junction, 488 growth controllers, see Growth promoters or Growth restrainers heterojunction, 167-174, 436-437 ion implantation, 412 iridium-doped, 412 nucleation process in closed systems, 54-59 in open systems, 74-83 pulse radiolysis, 58 stopped-flow analysis, 57-58 UV-VIS spectroscopy, 460-461 Ostwald ripening in CDJ process, 289-290 in closed systems, 289, 472-474 of tabular double-twin, 289 reversed, 147-148 photographic materials, 580-587 preparation CDJ method, 59, 74, 132, 134, 389 conversion from AgQ, 415-417 decomposition of AgBr^^""^^', 243 dissociation of Ag*-gelatin, 54-59 hydrolysis of diethylsulfate, 54 reduction of BxO{, 233 seeded Ostwald ripening, 289 properties ionic, 561-564 optoelectronic, 559-560 protective agents, 54, 194, 195, 421 radiochemical analysis contact recrystallization, 150-151 Ostwald ripening, 472-474 recrystallization contact-, 151, 495, 496 intraparticle-, 144, 167-185, 415 self-, 144-145 reflection spectra {111}/{100} ratio, 505-507 adsorbed dyes, 505, 506 roles of ammonia, 289, 377, 379, 474 size distribution Coulter counter, 148 dynamic light scattering, 510-512 turbidimetry, 515-517

SUBJECT INDEX solid solutions Ag(Br,I), 161-167, 496 Ag(a, Br), 159-161, 172-175, 495 stress effect, XRD 493-495 supersaturation ratio, 55, 58-59, 83 surface energy, 6-17, 20 tabular grains, 289, 388-390 Silver chloride particles composites, see Composites controls heterojunction, 167-174, 436-437 multilayered structure, 432 shape, 23, 50, 382, 390-391 size, 369, 371 conversion AgQ by Br" ions, 167-176, 415-417 kinetics, 181-185 thermodynamics, 176-181 diffusion-controlled growth, 290 dislocation-controlled growth, 391 electron diffractometry AgBr/AgQ heterojunction, 488 growth controllers, see Growth promoters or Growth restrainers heterojunction, 167-174, 436-437 nucleation process, 49-54 in closed systems, 49-54, 56-58 in open systems, 58 pulse radiolysis, 58 stopped flow analysis, 57-58 UV-VIS spectroscopy, 460 Ostwald ripening in CDJ process, 289-290 of tabular particles, 289 photographic materials, 580-587 preparation CDJ method, 58, 390-391, 432 dissociation of Ag*-gelatin, 49-54 hydrolysis of diethyl sulfate, 49 hydrolysis of alkylchloride, 56 microemulsion process, 310, 311 reaction in 95 % ethanol, 222 properties ionic properties, 561-564 optoelectronic properties, 559-560 protective agents, 49, 194, 195, 421

787 radiochemical analysis, 148, 470 contact recrystallization, 148, 470 Ostwald ripening, 471-472 surface-ion exchange, 470-471 recrystallization contact-, 148-153, 470-472, 495 intraparticle-, 167-185 solid solution, Ag(a, Br), 159, 173 supersaturation ratio, 50-51, 58 surface energy, 17, 20 Silver iodide particles composites, see Composites contact recrystallization, 150, 496 heterojunction, 436, 437 ionic properties, 561-564 photographic materials, 580-587 preparation CDJ method, 74-75 decomposition of Agl„^°^^^~, 243 protective agents, 421 solid solution, Ag(Br,I), 161, 496 surface energy, 17-20 wurtzite-type, 18 zinc-blende-type, 18 Silver particles absorption index, 677 anisotropic growth, 392 composite, see Alloys and Composites MO levels, size effect, 637-638 preparation Hj reduction in silica gel, 330 hydroquinone reduction, 197 microemulsion process, 309 silica-coated, 311 polyol process from AgjCOj, 270 homogenous reduction, 214-215 with Pt; microwires, 392 reduction of chelate, 214 UV-photolysis, 217, 631 protective agents, 194, 214 supported catalyst, 634 Sinclair-LaMer method, 337 Sintering, see Ceramic materials Size control in gas phases, 629

788 in liquid phases, 47, 368-376 by seeding, 374-375 by supersaturation quenching, 375 factors for size control feed rate, 369-370 growth restrainer, 372-373 pH, 373-374 reservoir, 371 solvent of solid, 371 temperature, 370 in templates, 332-334, 647-648 on solid surfaces factors for size control affinity to complexes, 649-652 affinity to particles, 648-649 pore size, 646-648 specific surface area, 645-646 surface roughness, 646 growth theory, 663-676 Size distributions growth diffusion control, 110-111 reaction control, 111-112 Ostwald ripening diffusion control, 142-143 reaction control, 142-143 reversed ripening, 144-148 stationary nuclei, 43 unstable nuclei, 64 Size effects catalysts, 635-645 ceramics, 588 drug delivery microspheres, 709-710 ionic properties, 563 light scattering, 552-559 magnetic properties, 566, 607, 624-627 photosensitivity, 581 pigments 677-685 quantum size effect, 559, 628, 637-642 Small angle X-ray scattering (SAXS) microemulsion systems, 311,313 Smoluchowski's formula, 525 Sodium chloride particles light scattering, 558-559 Sodium dihexylsulfosuccinate (Aerosol MA), see Protective agents

SUBJECT INDEX and Shape controllers Sodium dioctylsulfosuccinate (Aerosol OT), 310, 312, see also Protective agents and Shape controllers Sodium dodecylsulfate (SDS), see Protective agents Sodium magnesium fluoride particles cubes (NaMgF3), 223 direct ionic reaction, 223 Sol-gel process, 189, 243-252 ceramic powders, 588 mechanisms, 245-252 monomeric precursor model, 249-252 Solid matrix particle formation in, 329-330 porous silica, 329-330 Solid-solution formation, 155-185 conversion for AgQ by Br" ions, 167-176 kinetics, 181-185 thermodynamics, 176-181 equilibrium compositions, 155-167 Ag(Br,I) systems, 161-167 Ag(a,Br) systems, 159-161 theory, 155-159 XRD, 174, 455, 495 Solid surfaces particle formation on, 322-329 selective deposition method, 329, 660 supported catalysts, 632-662 roles of supports, 645-658 Solid templates anodic aluminum oxide, 330-332 nanotubes and nanowires, 330-332 mesoporous molecular sieves, 333, 647 metal carbonyls, 333-334, 647-648 metallic nanoparticles, 333, 647 nanowires, 647-648 zeolites, 332-333, 637, 640-641, 647 metal carbonyls, 332-333, 647 metallic nanoparticles, 332, 647 Solvents (for solids), 371-372 Spinel, see Ferrite Spontaneous nucleation, 41-59, 191 silver bromide, 54-56 silver chloride, 49-54

SUBJECT INDEX theory, 41-49 Squareness, 627 SQUID, 696 Stabilizers, see Protective agents or Growth restrainers Stable forms, 121-137 equilibrium forms, 122-125 steady forms, 125-137 Stable nuclei, 45-49, 60, 66-71 Staining, see Medical use Stationary nuclei distribution front, 43-44 size distribution, 43 Steady forms definition, 125 reaction-controlled, 125-133 diffusion-controlled, 133-137 silver bromide, 128-137 Stranski's theory, 132-133 Steric stabilizers, see Protective agents Stokes equation, 526-527 Stoner-Wohlfarth model, see Magnetism Stopped flow technique, 57 Stranski's theory, 132-133 Stress effects silver bromide particles, 493-495 XRD measurement, 493-495 surface stress energy, 176-178 potentiometry, 176-181 Strontium carbonate particles microemulsion process, 310 Strontium sulfate particles controlled double-jet method, 291 Strontium titanate particles amorphous spheres, 320 nonaqueous emulsion process, 319, 320 perovskite-type crystals from, 321 protective agents, 195 Subcrystals randomly oriented, 197-198 regularly oriented, 275-277 Sulfur particles diffusion-controlled growth, 219, 220 preparation decomposition of Na2S203, 233 for light scattering, 554-556

789 oxidation of HjS, 219 poor-solvent precipitation, 219-220 Superconducting oxide particles aerosol process, 336 Superparamagnetism, 606-607 Supersaturation quenching, 191, 243, 375 Supersaturation ratio energy parameter, (j), 26 nucleation rate, 30-40 silver halides, 50-51, 55-59, 83 Surface chemical potential definition, 120 reversed Ostwald ripening, 144-148 self-recrystallization, 144 solubility of each crystal face, 121 theory of habit formation, 118-129 Surface energy, 1-26 effect of adsorption, 8-11 intrinsic surface energy, 5 of a molecule, 3, 27 of a /z-mer, 26 of a polyhedral particle, 5-8 of a spherical particle, 15-16 amorphous, 5 polycrystal, 5 single-crystal, 15-16 of a two-dimensional nucleus, 100-103 silver halide microaystals, 11-20 Surface imperfections, 642 Surface modification, 417-432 Surface stress energy, 176-178 AgQ covered by AgBr, 178-181 potentiometry, 176-181 Synergistic catalysts, 657-658

TAA, see Thioacetamide Tantalum(V) oxide particles amorphous spheres, 320 preparation in aerosol systems, 336 in alkoxide solutions, 245 in nonaqueous emulsions, 320 Templates, see Solid templates Terbium carbonate, see Basic terbium carbonate particles

790 Terbium(III) phosphate, see Lanthanide phosphate particles Terbium(III) oxide particles calcination of basic carbonate, 413 spherical, 413 Tetraazaindenes, see Growth restrainers and Shape controllers Thallium(I) iodide particles reduction of \0{, 234 Thioacetamide (TAA) hydrolysis, 231 reversible dissociation, 227, 231 gas chromatography, 466 pH effect, 373-374 UV-VIS spectroscopy, 459 sulfide formation, 231-233, 282-284 Thorium sulfate, see Basic thorium sulfate particles Thorium tungstophosphate particles amorphous spheres, 224 from protonated Vy^yP^^', 224 Thorium tungstosilicate particles amorphous spheres, 224 from protonated SiWi204o^", 224 Tin(IV) oxide particles amorphous spheres, 245, 336 from aerosols, 336 from alkoxide solutions, 245 crystalline spheres or rods, 254 forced hydrolysis, 254 Titania (TiOj) particles ceramic materials, 588, 589, 590, 592, 594 coating, 417, 418, 421, 427-431 composites (doped, layered, mixed; heterojunctions), see Composites compositional mixing, 245, 407, 410 doping (Ba, Cu, Nb, Sr, Ta), 245, 411, 590 dye-doped, 412 pigment, 676, 686-691 hiding power, 686-687 TiOj/SiOj, Ti02/nylon, 688-690 UV absorbance, 686-689, 690 preparation AAO process, 330-334

SUBJECT INDEX nanotubes, nanofibers, 330-334 aerosol process, 336 polyurea-coated TiOj, 336-337 TiOj-dispersed polyurea, 336 alkoxide hydrolysis, 245 growth mechanism, 245-252 forced hydrolysis, 252 anatase cubes, 253 rutile spheres, 252 gel-sol method, 278-281 role of gel network, 280-281 nonaqueous emulsion process, 320 protective agents, 195, 421 size control, 371, 372 supports of metals, 324, 327, 632-634 surface modification, 245, 422, 427-431 Titanium dioxide, 5ee Titania particles Tracer, see Radiochemical analysis Triethanolamine shape controller, 230, 385 stabilizer of alkoxides, 280 Triton X-100, see Polyoxyethylene(lO) isooctylphenyl ether Triton X-405, see Polyoxyethylene(40) isooctylphenyl ether Tungsten(VI) oxide particles AAO process, 330-334 nanotubes, nanofibers, 330-334 Tungstic acid (H2WO4) particles ellipsoidal thin platelets, 252 from supersaturated solutions, 252 Turbidimetry, 512-517, 556-557 nucleation, BaSO^, 58 size distribution, AgBr, 515-517 Turnover frequency, 635, 643-645 Tween 80, see Polyoxyethylene sorbitan monooleate Twinning shape control, 388-389 Two-dimensional nuclei, 86-104 equilibrium concentrations, 86-90 models, 86, 89 nucleation rate, 90-93 polyhedral particles, 100-105 propagation of, 93-100 surface energy of, 100-103

SUBJECT INDEX Ultraviolet photoelectron spectroscopy Pd on silica, 636-640 Ultraviolet-visible spectroscopy Au particles, growth, 460 CdSe, quantum size effect, 559-560 dyes on Ag(Br,I), 505-507 {111}/{100} ratio, 505-507 Kubelka-Munk function, 504-505 nucleation; AgBr, AgQ, 460-461 thioacetamide, reaction 459 Unstable nuclei, 60-65 size ditribution of, 64 UPS, see Ultraviolet photoelectron spectroscopy Urea carbonate formation, 235-241, 413-414 hydrolysis of, 235-237 oxide formation, 239 pH controller, 236-237, 239, 241-242 phosphate formation, 241-242 shape controller, 239, 385

van der Waals force, 536, 550, 564, 570 Vegard law, 455, 496

Wulffs theorem, see Equilibrium forms

XPS, see X-ray photoelectron spectroscopy X-ray diffractometry, 455-456, see also OPML-XRD composition Ag(Br,I), 174, 455, 496 Ag(a,Br), 174, 455, 495 crystallinity, Ni-P, 289 crystallite size hematite, 399, 492-493 dopant distribution, TiOj, 590 identification akaganeite, 455-456 hematite, 455-456 internal structure basic aluminum sulfate, 382 maghemite, 626

791 stress, AgBro.98lo.o2, 493-495 X-ray photoelectron spectroscopy, 500 Au on amorphous carbon, 639 Au on a-Fe203, 501 C distribution in a-Fe203, 500 Pt on SiOj, 639 Pt-group metal oxides on a-Fe203, 328 Pt-group metals on a-Fe203, 328 surface composition, mixed oxide, 410 XRD, see X-ray diffractometry

YAG, see Yttrium aluminum garnet Yttria (Y2O3) particles calcination of Y(0H)C03, 238, 413 Y203-Ce02, Y203:Eu, 238

composites, see Composites YAG, 238, 254, 320 Yttrium aluminum garnet (YAG) particles calcination of basic carbonates, 238 forced hydrolysis, 254 Tb-doped, 254 nonaqueous emulsion process, 320 calcination of product, 320 shapes and structures, 238, 254, 320 Yttrium carbonate, see Basic yttrium carbonate particles Yttrium oxide, see Yttria particles Yttrium oxysulfide (Y2O2S) particles from S-treated basic carbonates, 238 Eu-doped, 238 spherical, 238

Zeldovich method, see Nucleation rate Zeolite, see also Solid templates NaX, NaY, ALPO-5, ZSM-5, 332-333 particle synthesis in, 332-334, 647 ship-in-bottle synthesis, 333, 647 preparation of zeolite particles, 662 Zeta-potential, 193, 523-529 coagulation, 193 electro-osmosis, 523, 525 electrophoresis, 525-529 relaxation effect, 528 shape effect, 527

792 Zinc, see Zinc particles Zinc carbonate, see Basic zinc carbonate particles, 239 Zinc oxide particles chelating agents, 230 complexing agent, ammonia, 230 pigment, 676, 686-687 preparation AAO process, 330-334 nanotubes, nanofibers, 330-334 alkoxide hydrolysis, 245 calcination of Zn2(OH)2C03, 239 shape control by, 239, 414 double jet method, 197, 222 aggregative growth, 222 forced hydrolysis of chelates, 230 protective agents, 195 shapes and structures, 222, 230, 239 TiOj-coated, 418 varistor, 591 Zinc phosphate particles amorphous spheres, 241 reaction with urea, 241 Zinc sulfide particles chelating agents, 224, 225 internal structure, 227-228 pigment, 676, 686 preparation from HjS and EDTA chelate, 224 from TAA and free Zn^*, 231 Ag-doped, 232 Cd,Zni_,S composite, 231, from TAA and Zn chelates, 225 gel-sol process, 225 growth mechanism, 225-229 role of gelatin, 225, 421 role of ammonia, 225-229 in microemulsions, 310 Cd^Zni_,S composite, 311 shape and structure, 224, 225, 231 size control, 371, 373 Zinc particles Y-radiolysis, 217, 631 Zincite, 245, see Zinc oxide particles Zirconia (ZrOj) particles ceramic materials, 589, 590, 594

SUBJECT INDEX composites, see Composites preparation alkoxide hydrolysis, 245 growth mechanism, 245-252 calcination of precursors, 240 decomposition of Zr-soap, 242 forced hydrolysis, 253, 254 gel-sol method, 325-326 microemulsion process, 310 nonaqueous emulsion process, 320 protective agents, 195, 254 supports of metals, 324, 327, 632 yttria-doped zirconia, 245, 411, 590-592 Zirconium basic salts, see individual Basic zirconium salts Zirconium carbonate, see Basic zirconium carbonate particles Zirconium dioxide, see Zirconia particles 21irconium tungstosilicate particles amorphous spheres, 224 from protonated SiWi^O^o"*", 224