Models of Agglomeration and Glass Transition

by Kerner, Richard

• ISBN13: 9781860947568
• ISBN10: 1860947565
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-12-01
• Publisher: IMPERIAL COLLEGE PRESS

Summary

This book is for any physicist interested in new vistas in the domain of non-crystalline condensed matter, aperiodic and quasi-crystalline networks and especially glass physics and chemistry. Students with an elementary background in thermodynamics and statistical physics will find the book accessible. The physics of glasses is extensively covered, focusing on their thermal and mechanical properties, as well as various models leading to the formation of the glassy states of matter from overcooled liquids. The models of agglomeration and growth are also applied to describe the formation of quasicrystals, fullerenes and, in biology, to describe virus assembly pathways.

Table of Contents

Preface	p. vii
Introduction	p. 1
Self-Similarity	p. 7
Self-Similarity in Lattices and Networks	p. 7
The concept of self-similarity: a few examples	p. 7
Self-similarity and scale	p. 10
Mathematical Description of Self-Similar Growth	p. 13
One-Sided Growth by Agglomeration	p. 19
Probabilistic description of agglomeration process	p. 19
Energy barriers and Boltzmann factors	p. 23
Topological and Statistical Properties of Networks	p. 29
General Considerations	p. 29
Topology and Geometry of Tilings and Networks	p. 30
Statistical Properties of Networks, Configurational Entropy and Local Order	p. 42
Topological Defects and Curvature	p. 46
Bonds and Interactions in Networks	p. 51
Preamble: A Historical Reminder	p. 51
Properties of Chemical Bonds	p. 53
Generalities	p. 53
The four types of bonds	p. 54
Dendritic and Ring-Forming Tendencies in Covalent Networks	p. 59
A Lagrangean Approach to Network Interactions	p. 63
A model in two dimensions	p. 64
Generalization to three dimensions	p. 75
Stochastic Agglomeration Model	p. 85
General Considerations	p. 85
A Two-Component Model in One Dimension	p. 86
Dendritic Agglomeration of Star-Like Entities	p. 90
Agglomeration of Rings in Two Dimensions	p. 94
Second agglomeration step: chains and cells	p. 102
Markov Chains and Random Walks	p. 110
Basic definitions	p. 110
Detailed balancing	p. 112
The Stochastic Matrix Method	p. 113
Bond saturation	p. 114
Rim saturation	p. 119
Model of Quasi-Crystalline Growth	p. 121
Preamble: Aperiodic Structures and Quasicrystals	p. 121
The discovery of quasicrystals	p. 121
A few generalities on aperiodic structures	p. 123
Mathematical Properties of Penrose Tilings	p. 126
Agglomeration Model for a 2-dimensional Quasicrystal	p. 131
The first agglomeration step: creating the doublets	p. 133
The second step: creating chains and cells	p. 136
Other Models of Quasi-Crystalline growth	p. 142
Nucleation and Growth of Fullerenes	p. 149
Preamble: A Short History of Fullerenes' Discovery	p. 149
Other carbon nanostructures	p. 151
Dynamical Model of Fullerene Growth	p. 153
Statistical model based on self-similarity	p. 153
Kinetic and energetic considerations	p. 161
Geometry of Onion Fullerenes	p. 163
Icosahedral Virus Capsid Growth	p. 169
Preamble: Capsid Viruses	p. 169
Probabilistic Analysis of Capsid Agglomeration	p. 172
Combinatorics of Icosahedral Capsid Growth	p. 176
Regular capsids	p. 176
Agglomeration rules for the MS2 phage	p. 185
Hindering capsid agglomeration	p. 189
Glasses and their Properties	p. 191
Preamble: A Concise History of Glass Making	p. 191
Definition and Classification of Glasses	p. 195
Glass Transition and its Characteristic Features	p. 201
The Entropy in Glasses	p. 204
Residual entropy and Kauzmann's paradox	p. 204
Entropy and Viscosity	p. 210
Microscopic model of viscosity	p. 210
Viscosity and configurational entropy	p. 213
Kinetics of Crystallization in Liquids	p. 217
Agglomeration Velocity	p. 217
Nucleation velocity	p. 218
Kinetic factors	p. 220
Crystallization Velocity	p. 225
The Kolmogorov-Avrami Equation and the TTT Diagram	p. 230
Immiscibility. Spinodal and Binodal Curves	p. 233
Stochastic Agglomeration Model of Glass Transition	p. 239
General Setting	p. 239
Preliminary considerations	p. 239
The phase space landscape	p. 242
A Simple Model: Agglomeration of Covalent Atoms	p. 244
Evolution of probabilities during agglomeration	p. 244
Physical interpretation	p. 248
Stochastic Matrix Model of Glass Transition	p. 257
Structural model of pure B[subscript 2]O[subscript 3] glass	p. 265
A random walk model of pure glass B[subscript 2]O[subscript 3]	p. 273
Ternary and Multicomponent Glasses. Immiscibility	p. 277
Ternary Glass Model	p. 277
Low modifier concentration	p. 277
General case: inclusion of B - B and C - C links	p. 283
Comparison with experimental data	p. 285
The Finite Volume Effect and Immiscibility	p. 286
The fixed point and its stability	p. 291
Immiscibility dome of the (SiO)[subscript 1-x](Na[subscript 2]O)[subscript x] glass	p. 293
Glass Transition and the Cooling Rate	p. 297
Models of Rapid Cooling	p. 297
Critical cooling rate from crystallization kinetics	p. 298
Structural relaxation model	p. 299
Time-dependent stochastic agglomeration	p. 303
Rapid Cooling within the Stochastic Matrix Model	p. 310
Rigidity, Connectivity and Homogeneity in Glasses	p. 315
General Principles	p. 315
Rigidity, Vibrational Modes and Thermodynamics	p. 319
Connectivity, rigidity and local structure in glasses	p. 323
Connectivity in pure dendritic networks	p. 323
Connectivity conservation in alkali-borate glasses	p. 325
Self-Organization in Glasses	p. 329
The intermediary isostatic phase	p. 329
Stochastic versus correlated regimes	p. 331
The Composition of Window Glass	p. 333
A Mathematical Complement	p. 341
Stochastic matrices and their properties	p. 341
General properties	p. 341
Projectors and asymptotics	p. 344
Asymptotic form of M[superscript infinity]	p. 346
Non-linear Differential Equations	p. 347
Bibliography	p. 353
Index	p. 361
Table of Contents provided by Ingram. All Rights Reserved.