Kinetics, Transport, and Structure in Hard and Soft Materials

by Green; Peter F.

• ISBN13: 9781574447682
• ISBN10: 1574447688
• Format: Hardcover
• Copyright: 2005-04-20
• Publisher: CRC Press

Summary

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.

Table of Contents

Part I Tools: Elements of Diffusional Transport	1	(76)
Elements of Transport in Systems of Noninteracting Particles and the Phenomenology of Diffusion
Introduction	3	(2)
Transport of Noninteracting Particles	5	(15)
Average Thermodynamic Properties	5	(5)
Maxwell-Boltzmann Velocity Distributions	10	(1)
Distribution of Component Velocities	11	(3)
Distribution of Speeds	14	(1)
Diffusional Transport of Noninteracting Particles	15	(1)
Flux of Maxwellian Particles	16	(1)
The Diffusion Coefficient and Fick's 1st Law	17	(1)
Collision Probabilities and the Mean Free Path	18	(2)
The Diffusion Equations: Fick's Laws	20	(5)
Fick's 1st Law: Additional Comments	20	(2)
Fick's 1st Law in Cylindrical Coordinates	22	(1)
Fick's 1st Law in Spherical Coordinates	22	(1)
Fick's 2nd Law	22	(2)
Fick's 2nd Law in Cylindrical Coordinates	24	(1)
Fick's 2nd Law in Spherical Coordinates	25	(1)
Simple Problems Involving Steady State Flow	25	(3)
Flow through a Planar Layer	25	(1)
Steady State Flow through Nonplanar Surfaces: Cylinder	26	(1)
Steady State Flow through a Spherical Interface	27	(1)
Diffusion of Particles from a Point Source in One-Dimension	28	(8)
Solution to Fick's 2nd Law Using Fourier Integral Transforms	28	(3)
Solution to Fick's 2nd Law in Three Dimensions Using Laplace Transforms	31	(5)
Concentration Profile Due to a Spatially Extended Initial Source, f(x')	36	(5)
Diffusion from a Semi-Infinite Source	36	(1)
Diffusion from a Finite Source of Thickness 2h	37	(1)
Desporption/Absorption of a Species from a Sample of Finite Dimensions	38	(1)
Permeation Experiments	39	(1)
Time-Dependent Fluxes: Weight Gain Experiments	40	(1)
Concluding Remarks	41	(1)
Problems	42	(6)
References	48	(1)
Appendices	48	(3)
Integrals	48	(1)
Fourier Integral Transforms of Derivatives	48	(3)
Brownian Motion
Introduction	51	(1)
The Random Walk Problem	52	(4)
Binomial Distribution Function	52	(2)
One-Dimensional Random Walk: Diffusion	54	(1)
The Gaussian Distribution Function	54	(2)
Poisson Distribution Function	56	(1)
Correlation Functions	56	(7)
Pair Correlation Functions and the Static Structure Factor	59	(1)
Single Particle Density Distribution Function	60	(1)
Pair Distribution Function	60	(3)
Langevin Analysis	63	(4)
Velocity Autocorrelation Function	64	(1)
Mean Square Velocity	64	(1)
Mean Square Displacement	65	(1)
Stokes-Einstein Equation	66	(1)
Nernst-Einstein Equation	66	(1)
Light Scattering: Measurement of Diffusion	67	(5)
The Scattered Field	68	(1)
Scattering from a Dilute Collection of Molecules	69	(1)
Measurement of Diffusion	70	(2)
Problems for Chapter 2	72	(3)
Appendix: The Diffusion Coefficient	75	(1)
References	75	(2)
Part II Diffusion in Crystalline Materials	77	(72)
Structure, Defects and Atomic Diffusion in Crystalline Metals
Introduction	79	(2)
Crystal Structure and Point Defects	81	(8)
Bravais Lattices	81	(1)
Unit Cells, Crystal Directions, and Crystal Planes	82	(4)
Atomic Defects in Crystals	86	(3)
Tracer and Self-Diffusion in Crystals	89	(6)
Random Walk in 3-D	89	(2)
The Jump Frequency, Γ	91	(2)
Debye Frequency	93	(1)
An Expression for the Tracer Diffusion Coefficient	94	(1)
Atomic Transport in Crystals via a Single Vacancy Mechanism	95	(3)
Self-Diffusion and Tracer Diffusion via a Vacancy Mechanism	96	(2)
The Equilibrium Vacancy Concentration	98	(5)
Vacancy Concentration in Crystals: Experiment versus Theory	99	(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)
Further Reading	347	(2)
Index	349