Kinetics, Transport, and Structure in Hard and Soft Materials

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ISBN: 9781574447682 | 1574447688
Cover: Hardcover
Copyright: 4/20/2005

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Emphasizing the interdisciplinary nature of transport in materials, Kinetics, Transport, and Structure in Hard and Soft Materials discusses the connection between the mechanisms of transport of atomic or molecular entities that occur in a diverse range of materials and how these transport processes are connected to a wide range of innovative materials applications across several industries. It presents its material in a user-friendly format for readers from any discipline with a foundation in elementary differential equations and thermodynamics or physical chemistry. Topics include diffusional transport, mechanisms of transport in crystalline/structurally disordered materials, and various types of instabilities leading to morphological evolution.

Part I Tools: Elements of Diffusional Transport

(76)

Elements of Transport in Systems of Noninteracting Particles and the Phenomenology of Diffusion

Introduction

(2)

Transport of Noninteracting Particles

(15)

Average Thermodynamic Properties

(5)

Maxwell-Boltzmann Velocity Distributions

(1)

Distribution of Component Velocities

(3)

Distribution of Speeds

(1)

Diffusional Transport of Noninteracting Particles

(1)

Flux of Maxwellian Particles

(1)

The Diffusion Coefficient and Fick's 1st Law

(1)

Collision Probabilities and the Mean Free Path

(2)

The Diffusion Equations: Fick's Laws

(5)

Fick's 1st Law: Additional Comments

(2)

Fick's 1st Law in Cylindrical Coordinates

(1)

Fick's 1st Law in Spherical Coordinates

(1)

Fick's 2nd Law

(2)

Fick's 2nd Law in Cylindrical Coordinates

(1)

Fick's 2nd Law in Spherical Coordinates

(1)

Simple Problems Involving Steady State Flow

(3)

Flow through a Planar Layer

(1)

Steady State Flow through Nonplanar Surfaces: Cylinder

(1)

Steady State Flow through a Spherical Interface

(1)

Diffusion of Particles from a Point Source in One-Dimension

(8)

Solution to Fick's 2nd Law Using Fourier Integral Transforms

(3)

Solution to Fick's 2nd Law in Three Dimensions Using Laplace Transforms

(5)

Concentration Profile Due to a Spatially Extended Initial Source, f(x')

(5)

Diffusion from a Semi-Infinite Source

(1)

Diffusion from a Finite Source of Thickness 2h

(1)

Desporption/Absorption of a Species from a Sample of Finite Dimensions

(1)

Permeation Experiments

(1)

Time-Dependent Fluxes: Weight Gain Experiments

(1)

Concluding Remarks

(1)

Problems

(6)

References

(1)

Appendices

(3)

Integrals

(1)

Fourier Integral Transforms of Derivatives

(3)

Brownian Motion

Introduction

(1)

The Random Walk Problem

(4)

Binomial Distribution Function

(2)

One-Dimensional Random Walk: Diffusion

(1)

The Gaussian Distribution Function

(2)

Poisson Distribution Function

(1)

Correlation Functions

(7)

Pair Correlation Functions and the Static Structure Factor

(1)

Single Particle Density Distribution Function

(1)

Pair Distribution Function

(3)

Langevin Analysis

(4)

Velocity Autocorrelation Function

(1)

Mean Square Velocity

(1)

Mean Square Displacement

(1)

Stokes-Einstein Equation

(1)

Nernst-Einstein Equation

(1)

Light Scattering: Measurement of Diffusion

(5)

The Scattered Field

(1)

Scattering from a Dilute Collection of Molecules

(1)

Measurement of Diffusion

(2)

Problems for Chapter 2

(3)

Appendix: The Diffusion Coefficient

(1)

References

(2)

Part II Diffusion in Crystalline Materials

(72)

Structure, Defects and Atomic Diffusion in Crystalline Metals

Introduction

(2)

Crystal Structure and Point Defects

(8)

Bravais Lattices

(1)

Unit Cells, Crystal Directions, and Crystal Planes

(4)

Atomic Defects in Crystals

(3)

Tracer and Self-Diffusion in Crystals

(6)

Random Walk in 3-D

(2)

The Jump Frequency, Γ

(2)

Debye Frequency

(1)

An Expression for the Tracer Diffusion Coefficient

(1)

Atomic Transport in Crystals via a Single Vacancy Mechanism

(3)

Self-Diffusion and Tracer Diffusion via a Vacancy Mechanism

(2)

The Equilibrium Vacancy Concentration

(5)

Vacancy Concentration in Crystals: Experiment versus Theory

(4)

Divacancies and Their Effect on Diffusion

103

(3)

Diffusion of Interstitials in Crystals

106

(1)

Ring Mechanism of Atomic Diffusion

107

(1)

The Interstitialcy Mechanism of Atomic Diffusion

108

(1)

Diffusion in the Presence of Impurities

108

(6)

``Kick-Out'' and Dissociative Mechanisms

109

(1)

Diffusion of Vacancy-Substitutional Impurity Pairs

109

(1)

Concentration of Vacancies and Impurities in a Dilute Alloy

109

(2)

Substitutional Impurity-Vacancy Pair Diffusion

111

(3)

Isotope Effects

114

(1)

Effects of Pressure on Diffusion

114

(1)

Diffusion Near Dislocations and Grain Boundaries

115

(2)

Final Remarks

117

(1)

Problems for Chapter 3

117

(4)

References and Additional Reading

121

(2)

Diffusion in Ionic Crystals: Alkali Halides

Introduction

123

(1)

Defects in Ionic Crystals

124

(1)

Frenkel Defect Concentration

125

(1)

Schottky Defect Concentration

126

(1)

Diffusional Transport of Cationic and Ionic Defects

127

(2)

Diffusivity of Frenkel Defects

129

(1)

Diffusion of Schottky Defects

130

(1)

The Effect of Multivalent Impurities on Conductivity

131

(2)

Comments on Transport in Alkali Halide Crystals: Transport Coefficients

133

(2)

Problems for Chapter 4

135

(2)

References and Additional Reading

137

(2)

Diffusion in Semiconductors

Introduction

139

(1)

Structure and Point Defects in Silicon

140

(1)

Self-Diffusion in Silicon and Germanium

140

(3)

Diffusion of Dopants

143

(3)

Mechanisms of Atomic Transport

144

(1)

Examples

145

(1)

Concluding Remarks

146

(1)

Problems for Chapter 5

147

(1)

References

147

(2)

Part III Diffusional Transport in Systems That Lack Long-Range Structural Order

149

(116)

Transport and Viscoelasticity of Large Macromolecules

Introduction and Context

151

(2)

Classification of Polymers

153

(2)

Properties of a Single Polymer Chain

155

(7)

Freely Jointed Chain Model

155

(1)

Freely Rotating Chain Model

156

(2)

Hindered Rotation Chain Model

158

(1)

Persistence Length

159

(1)

Single Chain Statistics: Excluded Volume Effects

160

(2)

Single Chain Statistics Continued: Gaussian Statistics

162

(1)

Phenomenology of the Viscoelastic Behavior of Polymers

162

(17)

Maxwell and Voigt Phenomenological Models

164

(4)

The Viscosity: Experimental Observations

168

(1)

Temperature Dependence of the Viscosity

169

(2)

Time-Temperature-Superposition and Shift Factors

171

(2)

Oscillatory Shear Measurements

173

(2)

Connections between G (t) and Frequency Domain Experiments

175

(4)

Microscopic Model for Diffusion and Viscoelasticity in Polymer Melts

179

(24)

Rouse Model: Unentangled Chains

180

(2)

Reptation: Dynamics of Entangled Chains

182

(5)

The Stress Relaxation Modulus, the Viscosity, and the Steady State Compliance

187

(3)

Summary of Chain Segmental Dynamics

190

(1)

The Entanglement, the Molecular Weight, and the Critical Molecular Weight

190

(2)

The Viscosity of Polymers

192

(1)

The Diffusion Coefficient of Entangled Chains

193

(3)

Temperature Dependence of Diffusion

196

(2)

Tube Length Fluctuations

198

(1)

Constraint Release Mechanism

199

(3)

Dynamic Moduli G'(ω) and G''(ω)

202

(1)

Concluding Remarks

203

(1)

Problems for Chapter 6

204

(4)

References

208

(3)

Transport Processes in Inorganic Network Glasses

Introduction

211

(2)

The Structure of Inorganic Network Glass Formers: An Introduction

213

(3)

Bulk Transport Processes Inorganic Network Glass Formers

216

(6)

Temperature Dependence of the Viscosity: The VTF Equation

217

(1)

Comments Regarding the Glass Transition

218

(2)

Temperature Dependence of the Viscosity: Adam-Gibbs Model

220

(2)

Connection between Kinetic and Thermodynamic Fragility

222

(1)

``Strong'' versus ``Fragile'' Network Glass Melts, a Structural Connection

223

(5)

Influence of Alkali Content on Heat Capacity and Activation Energy for Flow

224

(2)

The Viscosity of Mixed Alkali Glass Melts

226

(1)

Effect of Alkali Composition on Tg

227

(1)

The Energy ``Landscape'' Approach

228

(1)

Relaxation Functions

228

(2)

Mechanical Relaxations

230

(5)

Primary Relaxations

230

(2)

Secondary Mechanical Relaxations (T < Tg)

232

(3)

Phenomenology of Secondary Relaxations: Ionic Conductivity

235

(1)

Ionic Conductivity and Diffusion

235

(6)

Case I

237

(1)

Case II

237

(1)

Comments Regarding Ionic Conductivity in Network Glasses

237

(3)

The Electrical Modulus Representation

240

(1)

Secondary Relaxations in ECR and MR Experiments

241

(2)

Mechanism of Cation Transport in Ionic Glasses

243

(3)

Single Alkali Glasses

243

(1)

Option I

243

(1)

Option II

244

(1)

Mixed Alkali Glasses

245

(1)

Final Remarks

246

(1)

Problems for Chapter 7

246

(3)

References

249

(3)

Appendix

252

(3)

Comments on Heterogeneous Dynamics in the Disordered State

Introduction

255

(1)

Temperature Dependencies of Relaxations

256

(4)

Dispersive Dynamics Associated with Disorder

257

(3)

Comments on Dynamics in the Supercooled State

260

(1)

Comments on the Stokes-Einstein Relationship

261

(1)

Final Comments

262

(1)

References

262

(3)

Part IV Instabilities and Pattern Formation in Materials

265

(84)

Phase Separation in Binary Mixtures: Spinodal Decomposition and Nucleation

Introduction

267

(2)

Free Energy of Mixing of a Binary Polymer-Polymer Mixture

269

(4)

Phase Diagram of a Simple Binary Mixture

271

(2)

Spinodal Decomposition

273

(5)

Linearized Theory for the Early Stages of Spinodal Decomposition

273

(5)

Structure Factor

278

(1)

An Example Involving a Polymer-Polymer Mixture

278

(2)

Remarks Regarding Spinodal Decomposition

280

(1)

Nucleation

281

(5)

Nucleation in the A/B Mixture

282

(1)

Elements of the Classical Theory of Nucleation

282

(2)

Steady State Growth Rate

284

(2)

Heterogeneous Nucleation

286

(1)

Concluding Remarks on Nucleation and Growth

287

(1)

Problems for Chapter 9

287

(2)

References for Spinodal Decomposition

289

(1)

References for Nucleation and Growth

290

(3)

Interdiffusion: Diffusion in Chemical Potential Gradients

Introduction

293

(3)

Transport in Diffusion Couples

296

(5)

Onsager Analysis

296

(2)

The Darken Equation

298

(2)

Marker Velocity

300

(1)

The Hartley-Crank Equation

301

(1)

Interdiffusion in Polymers

302

(3)

Measurements of Interdiffusion

305

(4)

Marker Experiments

306

(3)

Concluding Remarks

309

(1)

Problems for Chapter 10

309

(1)

References

310

(3)

Growth: Moving Interfaces and Instabilities in Bulk Materials

Introduction

313

(2)

Effect of Curvature on the Properties of Small Particles

315

(5)

Elementary Concepts of Classical Capillarity

315

(3)

Effect of Curvature on the Properties of Small Systems

318

(2)

Moving Front in a Supercooled Melt

320

(8)

Stationary Solutions (planar interface, k= 0)

324

(1)

Linear Stability Analysis

325

(3)

Instabilities at an Interface in a Supersaturated Environment

328

(2)

Brief Comments on Microstructure

330

(1)

Problems for Chapter 11

331

(3)

References and Further Reading

334

(3)

Comments on Instabilities and Pattern Formation in Condensed Matter

Introduction

337

(1)

Instabilities That Arise in Driven Liquid Films

338

(2)

Instabilities in Macroscopically Thick Films

338

(2)

Instabilities in Films of Nanoscale Thickness

340

(3)

Pattern Formation in Nanometer-Thick Films

340

(2)

Fingering in Ultrathin Films

342

(1)

Instabilities Involving Macroscopic or Bulk Flows

343

(3)

Rayleigh-Benard Instability

344

(1)

Rayleigh Instability

345

(1)

Final Comments

346

(1)

References

346

(1)

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Kinetics, Transport, and Structure in Hard and Soft Materials

Summary

Table of Contents

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Kinetics, Transport, and Structure in Hard and Soft Materials

Summary

Table of Contents

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