Cover
Preface
About the Companion Website
1 Nucleation
1. 1.1 Thermodynamics of Interfaces
2. 1.2 Homogeneous Nucleation
3. 1.3 Non‐Homogeneous Nucleation
4. 1.4 Exercises
5. Bibliography
2 Growth
1. 2.1 Traditional Crystal Growth Models
2. 2.2 Face Growth Theories
3. 2.3 Measurement of Particle Size and Shape
4. 2.4 Exercises
5. Bibliography
3 Inter‐Particle Forces
1. 3.1 Inter‐Molecular Forces
2. 3.2 Inter‐Particle Forces
3. 3.3 Measurement of Inter‐Molecular Forces
4. 3.4 Measurement of Forces between Surfaces
5. 3.5 Exercises
6. Bibliography
4 Stability
1. Charged Interface
2. 4.1 Electrostatic Potential Near a Charged Surface
3. 4.2 Solution of the Poisson–Boltzmann Equation
4. 4.3 Repulsive Force between Two Surfaces
5. 4.4 Steric Stabilization
6. 4.5 Kinetics of Stability
7. 4.6 Measurement of Surface Potential
8. 4.7 Exercises
9. Bibliography
5 Elementary Concepts of Number Balance
1. 5.1 State of a Particle
2. 5.2 State of a Population of Particles
3. 5.3 Number Balance for a Seeded Batch Crystallizer
4. 5.4 Number Balance for Open Systems
5. 5.5 Exercises
6. Bibliography
6 Breakage and Aggregation
1. 6.1 Breakage Functions
2. 6.2 Number Balance for Breakage
3. 6.3 The Process of Aggregation
4. 6.4 Exercises
5. Bibliography
7 Solution of the Population Balance Equation
1. 7.1 Operations Involving Moments of the PBE
2. 7.2 Analytical Solutions of the PBE
3. 7.3 Numerical Solution of the PBE
4. 7.4 Exercises
5. Bibliography
8 Kinetic Monte Carlo Simulation
1. 8.1 Random Variables
2. 8.2 Algorithm for KMC Simulation
3. 8.3 Exercises
4. Bibliography
Appendix A: Mathematical Topics
1. A.1 Geometry of a Heterogeneous Drop
2. A.2 Young's Equation
3. A.3 Chord Theorem
4. A.4 Jacobian of Variable Transformation in a Multiple Integral [1]
5. A.5 Method of Characteristics [2]
6. Bibliography
Appendix B: Solution of Selected Problems
1. B.1 General Problem Solving Strategy
2. B.2 Solutions of Selected Problems
3. Bibliography
Appendix C: Codes
1. C.1 Distance‐Dependant Potential
2. C.2 Solution of Breakage PBE
3. C.3 Solution of Aggregation PBE
4. C.4 Sampling of a Discrete Distribution
5. C.5 Sampling of a Continuous Distribution
6. C.6 Simulation of Breakage Using KMC
7. C.7 Simulation of Brainvita Game
Appendix D: Experimental Demonstration
1. Bibliography
Index
End User License Agreement

List of Illustrations

Chapter 1
1. Figure 1.1 Distance‐dependant interaction potential. The negative sign indicat...
2. Figure 1.2 Difference in coordination number between surface and bulk atoms. I...
3. Figure 1.3 The geometry of a curved interface: derivation of the Young–Laplace...
4. Figure 1.4 Surface of zero net curvature.
5. Figure 1.5 The contact angle and curved interface in a capillary tube: the rea...
6. Figure 1.6 Vapour–liquid equilibrium in an isothermal system.
7. Figure 1.7 Formation of a liquid nucleus in a supersaturated vapour.
8. Figure 1.8 as a function of for and .
9. Figure 1.9 Embryos crossing the activation barrier to become nuclei.
10. Figure 1.10 Significant portion of the integrand in eqn 1.14.
11. Figure 1.11 Experimental determination of the critical supersaturation of homo...
12. Figure 1.12 Left: homogeneous vs heterogeneous drops. Right: drop volume as a ...
13. Figure 1.13 Slow formation of a bubble on the tip (Exercise 1.2).
14. Figure 1.14 A complex cavity (Exercise 1.6).
Chapter 2
1. Figure 2.1 Build up and exhaustion of supersaturation during the nucleation gr...
2. Figure 2.2 Transport, adsorption, and integration of the growth unit to the gr...
3. Figure 2.3 Mass balance in a spherical shell around the growing spherical part...
4. Figure 2.4 Formation of surface nuclei.
5. Figure 2.5 Micrographs of two‐dimensional nucleation: polynuclear growth [3].
6. Figure 2.6 Growth of semiconductor nanocrystals (data for Example 2.1).
7. Figure 2.7 Screw dislocation.
8. Figure 2.8 Micrograph of growth spirals [3].
9. Figure 2.9 Schematic of spiral growth.
10. Figure 2.10 Faceted crystal.
11. Figure 2.11 A two‐dimensional faceted crystal. This crystal is defined by the ...
12. Figure 2.12 Kinetic shape of a crystal. Top: the crystal continues to grow in ...
13. Figure 2.13 Different lattice planes, their interplaner distances, and their g...
14. Figure 2.14 Flat, stepped, and kinked crystal faces.
15. Figure 2.15 The top surface has two periodic bond chains. It grows epitaxially...
16. Figure 2.16 The periodic bond chain (PBC) for the lattice shown in Figure 2.15...
17. Figure 2.17 Scattering of light from a particle.
18. Figure 2.18 Rayleigh scattering.
Chapter 3
1. Figure 3.1 Charge–dipole interaction.
2. Figure 3.2 Dipole–dipole interaction.
3. Figure 3.3 Hamaker's pairwise additivity approach.
4. Figure 3.4 Hamaker's pairwise additivity approach.
5. Figure 3.5 Molecule–semi‐infinite body interaction.
6. Figure 3.6 Sphere–semi‐infinite body interaction.
7. Figure 3.7 Tracing the force displacement curve using a spring.
8. Figure 3.8 Surface force apparatus (figure taken from Ref. [2]).
Chapter 4
1. Figure 4.1 Dissociation of ions at the water–solid interface to form a charged...
2. Figure 4.2 An elementary volume near a charged surface.
3. Figure 4.3 Surface pressure.
4. Figure 4.4 Counter‐ions arranged in a single layer at a distance from the su...
5. Figure 4.5 Various possible landscapes for the net potential.
6. Figure 4.6 Diffusion of particles with radius towards a particle with radius...
7. Figure 4.7 potential: the case when . The surface charge is negative. The v...
8. Figure 4.8 potential: the case when . The surface charge is negative. The v...
9. Figure 4.9 The situation in the EDL when . The surface charge is negative.
10. Figure 4.10 Interaction between two spheres.
Chapter 5
1. Figure 5.1 An MSMPR and a batch crystallizer. In both cases, the vessel is wel...
2. Figure 5.2 SEM micrograph of copper sulphate pentahydrate crystal.
3. Figure 5.3 TEM micrograph of copper nanoparticles.
4. Figure 5.4 Representation of a population of particles using sieve analysis an...
5. Figure 5.5 Particle size distribution of the same sample obtained with three d...
6. Figure 5.6 Number densities obtained by dividing the bin population by the bin...
7. Figure 5.7 Number density function at an instant in a batch crystallizer. The ...
8. Figure 5.8 Number balance for a pure growth process. The number of particles t...
9. Figure 5.9 Number balance for a pure growth process. The evolved number densit...
10. Figure 5.10 An MSMPR crystallizer.
Chapter 6
1. Figure 6.1 Beta probability density function.
2. Figure 6.2 Birth and death due to breakage processes.
3. Figure 6.3 Liquid–liquid dispersion.
4. Figure 6.4 Birth and death of particles due to pure aggregation.
5. Figure 6.5 Extensional degradation of polymers.
6. Figure 6.6 Cell cycle.
7. Figure 6.7 Making ‘Granola Grin’.
8. Figure 6.8 A controlled environment chamber.
Chapter 7
1. Figure 7.1 Change of limit for moment operation. Gray indicates the original o...
2. Figure 7.2 Division of the domain into one finite and one infinite domain, and...
3. Figure 7.3 Discretization of space using a geometric grid. The bin boundaries ...
Chapter 8
1. Figure 8.1 Selection of events for a discrete probability distribution.
2. Figure 8.2 Selection of IQ: sampling from a continuous distribution.
3. Figure 8.3 Daughter distribution functions: (a) probability density and (b) cu...
4. Figure 8.4 Progress of a peg solitaire game.

This edition first published 2019
© 2019 John Wiley & Sons Ltd

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Jayanta Chakraborty to be identified as the author of this work has been asserted in accordance with law.

Registered Offices
John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA
John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

Editorial Office
The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of Warranty
In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging-in-Publication Data

Names: Chakraborty, Jayanta, 1976- author.
Title: Engineering of submicron particles : fundamental concepts and models / Jayanta Chakraborty, Department of Chemical Engineering, Indian Institute of Technology Kharagpur, India.
Description: Hoboken, NJ, USA : John Wiley & Sons, Inc., [2019] | Includes bibliographical references and index. |
Identifiers: LCCN 2019015637 (print) | LCCN 2019018492 (ebook) | ISBN 9781119296454 (Adobe PDF) | ISBN 9781119296782 (ePub) | ISBN 9781119296461 (hardcover)
Subjects: LCSH: Nanoparticles.
Classification: LCC TA418.78 (ebook) | LCC TA418.78 .C475 2019 (print) | DDC 620.1/15–dc23
LC record available at https://lccn.loc.gov/2019015637

Cover Design: Wiley
Cover Image: Courtesy of Jayanta Chakraborty

Preface

In the process industry, many products and intermediates exist in the form of fine particles. Many next‐generation processes, such as colloidal heat transfer fluids for electronic cooling, also involve small particles. However, the ability of the process industry to deal with particulate processes in a quantitative way is limited. The process industry must enhance its capability in the engineering of fine particles.

Many research laboratories also produce and handle submicron particles. In a broader sense, such particulate systems include powders, polymers, colloids or even human populations. While many engineering textbooks and reference books deal with particles of micron scale and above, submicron particles are discussed mostly under very specialized subtopics and a reference book discussing the fundamental concepts of such systems is missing.

Everyday activities in an industrial or academic research laboratory where particulate systems are involved require application of a number of quantitative relations called models. Even experimental facilities use models to relate the raw data with the quantity of interest and often the user is not aware that the outputs are actually from a model. Most models are not straightforward and no single resource is available to provide understanding of frequently used techniques and concepts. New researchers often find themselves at a loss and tend to trust data blindly. This book attempts to resolve this problem by discussing the fundamental theories behind many frequently encountered particulate processes. A large number of diagrams, software, examples, brief experimental demonstrations, and exercises with answers are included and have been carefully planned to provide good learning.

Particulate systems are used by physicists, chemists, mathematicians, and engineers. It is difficult to provide fundamental knowledge to the degree demanded by all. This book is mainly aimed at senior undergraduate or graduate chemical engineering students but provides enough background material in the appendices to be also useful to students from other branches of science and engineering.

Models are used at various levels in particle technology. A set of basic models describe the fundamental process of nucleation, growth, and aggregation of particles. In these models, the rate of nucleation of particles from a medium of given supersaturation, the rate of increase of size of a particle of given size under a set of environmental conditions, and the rate of aggregation of given pairs are provided.

Classical nucleation theory is discussed at length in this text. Other nucleation mechanisms, e.g. the organizer mechanism, are also introduced. For growth, the classical growth models such as diffusion controlled and surface nucleation controlled growth are discussed, along with newer models like connected net analysis. Aggregation models and inter‐particle potentials are discussed with a brief but useful prelude on inter‐molecular and surface forces.

The basic models alone cannot describe the dynamics of an engineering system containing a large number of particles of varying attributes. For this a number balance equation (population balance) is needed. In this book the emphasis is on formulating the number balance equation (the population balance model) for a given system. Analytical and numerical solutions of population balance models are also discussed briefly. Software with open code is provided for the solution of a population balance model through discretization.

To my knowledge no book serves such a diverse yet unified purpose. This book has been in my mind throughout my career over the past decade, during which I made my journey from an experimental laboratory to two theoretical laboratories and then back to experiments. This book contains useful insights which I acquired over time.

This book is heavily indebted to several books and monographs which helped me in assimilating the content. I kept close to the flow of ideas and concepts of the parent books whenever I felt that was best for the reader. I acknowledge major contributions from the following books and monographs:

Foundations of Colloid Science by R. J. Hunter and Kinetics of Precipitation by A. E. Nielsen for the nucleation and growth chapters.
The chapter on inter‐molecular and inter‐particle force has ideas and contents from Intermolecular and Surface Forces by Jacob Israelachvili.
The stability chapter is heavily indebted to Paul C. Hiementz (Principles of Colloid and Surface Chemistry).
The particulate system modelling section is indebted to Population Balances by D. Ramkrishna and Theory of Particulate Processes by A. D. Randolph and M. A. Larson.
Much of the book is also influenced by the lecture notes circulated during my graduate course on modelling at the Indian Institute of Science, Bangalore by Prof. K. S. Gandhi and Prof. Sanjeev Kumar.

Apart from these major resources there are many other books and monographs that helped me to understand, assimilate, and express the ideas. I also acknowledge help from students at IIT Kharagpur who took this course (Fundamentals of Particle Technology, CH60026), asked critical questions, and helped me write this book. I hope this book will be useful to the others. Of course there are multiple errors and omissions which I'm eager to hear from the readers and correct in a future edition.

Jayanta Chakraborty
IIT Kharagpur
Autumn 2018

Engineering of Submicron Particles

Fundamental Concepts and Models

Preface

About the Companion Website