Complex dynamics of glass-forming liquids : a mode-coupling theory / Wolfgang Gotze.

Format:

Book

Author/Creator:

Götze, Wolfgang, 1937-

Series:

International series of monographs on physics (Oxford, England) ; 143.

International series of monographs on physics ; 143

Language:

English

Subjects (All):

Viscosity.

Mode-coupling theory.

Equations of motion.

Complex fluids.

Molecular dynamics.

Physical Description:

xi, 641 p. : ill.

Edition:

1st ed.

Place of Publication:

Oxford ; New York : Oxford University Press, 2009.

Summary:

Amorphous condensed matter can exhibit complex motions on time scales which extend up to those relevant for the functioning of biomaterials. The book presents the derivation of a microscopic theory for amorphous matter, which exhibits the evolution of such complex motions as a new paradigm of strongly interacting particle systems.

Contents:

Intro

Contents

Preface

1 Glassy dynamics of liquids-facets of the phenomenon

1.1 Stretching of the dynamics

1.2 Power-law relaxation

1.3 Superposition principles

1.4 Two-step relaxation through a plateau

1.5 The cage effect

1.6 Crossover phenomena

1.7 Hard-sphere systems: the paradigms

1.8 Hard-sphere systems with short-range attraction

2 Correlation functions

2.1 The evolution of dynamical variables

2.2 Correlation-function description of the dynamics

2.3 Spectral representations

2.4 Memory-kernel descriptions of correlators

2.4.1 Zwanzig-Mori equations

2.4.2 Models for correlation functions

2.5 Linear-response theory

2.6 The arrested parts of correlation functions

3 Elements of liquid dynamics

3.1 Preliminaries

3.1.1 Homogeneous isotropic systems without chirality

3.1.2 Densities and density fluctuations

3.2 Tagged-particle dynamics

3.2.1 Basic concepts and general equations

3.2.2 Tagged-particle diffusion

3.2.3 The friction coefficient

3.2.4 The cage effect and glassy-dynamics precursors of the velocity correlations

3.3 Densities and currents in simple liquids

3.3.1 Definitions and general equations

3.3.2 Transverse-current diffusion

3.3.3 The generalized-hydrodynamics description of transverse-current correlations

3.3.4 Visco-elastic features and glassy-dynamics precursors of the transverse-current correlators

3.3.5 Representations of the density correlators in terms of relaxation kernels

3.3.6 Sound waves and heat diffusion

3.3.7 Visco-elastic features and glassy-dynamics precursors of the density-fluctuation correlators

4 Foundations of the mode-coupling theory for the evolution of glassy dynamics in liquids

4.1 Self-consistent-current-relaxation approaches

4.1.1 The factorization ansatz.

4.1.2 Self-consistency equations for density correlators

4.2 A mode-coupling theory

4.2.1 Equations of motion and fixed-point equations

4.2.2 Mode-coupling-theory models

4.2.3 The basic version of microscopic mode-coupling theories

4.2.4 An elementary mode-coupling-theory model

4.3 Glass-transition singularities

4.3.1 Regular and critical states

4.3.2 Examples for bifurcation diagrams

4.3.3 Classification of the critical states

4.3.4 Correlation arrest near A[sub(2)] singularities

4.3.5 Density-fluctuation arrest in hard-sphere-like systems

4.3.6 Arrest in systems with short-ranged-attraction

4.4 Dynamics near glass-transition singularities

4.4.1 Relaxation through plateaus

4.4.2 Below-plateau relaxation

4.4.3 Structure and structure relaxation

4.4.4 Descriptions of some glassy-dynamics data

5 Extensions of the mode-coupling theory for the evolution of glassy dynamics of liquids

5.1 Extensions of the MCT for simple systems

5.1.1 MCT equations for the glassy shear dynamics

5.1.2 Glassy-relaxation features of shear correlations

5.1.3 MCT equations for the tagged-particle dynamics

5.1.4 Idealized transitions from diffusion to localization

5.1.5 Glassy-dynamics features of tagged-particle motions

5.2 A mode-coupling theory for mixtures of spherical particles

5.2.1 The equations of motion

5.2.2 Density-fluctuation arrest

5.2.3 Hard-sphere mixtures

5.2.4 Sodium-disilicate melts

5.3 A mode-coupling theory for molecular liquids

5.3.1 A theory for interaction-site-density correlators

5.3.2 Systems of symmetric dumbbells

5.3.3 Glassy Rouse dynamics

5.4 Some addenda

6 Asymptotic relaxation laws

6.1 Dynamics of the first-scaling-law regime

6.1.1 Reformulation of the MCT equations of motion

6.1.2 The critical dynamics.

6.1.3 Asymptotic description of the A[sub(2)]-bifurcation dynamics

6.1.4 The scaling-limit description of the generic liquid-glass-transition dynamics

6.1.5 Extended scaling-limit description of the generic A[sub(2)]-bifurcation dynamics

6.2 Dynamics of the second-scaling-law regime

6.2.1 Equations of motion for the second-scaling-law regime

6.2.2 The second-scaling-law description of the liquid dynamics

6.2.3 Asymptotic corrections for the second scaling limit

6.3 Relaxation near higher-order singularities

6.3.1 Correlation arrest near higher-order singularities

6.3.2 Logarithmic relaxation

A: Mathematical miscellanies

A.1 Laplace transforms

A.2 Fourier transforms

A.3 Positive-definite and positive-analytic functions

A.4 Harmonic-oscillator correlators

A.5 Matrix correlators

A.6 Product correlators

A.7 Power-law variations

A.8 Logarithmic variations

B: Symmetries of fluctuation correlators

C: Smoothened correlators

D: Theorems on MCT equations

D.1 Convergence of the approximant sequences

D.2 Completely monotonic approximants

D.3 The maximum-eigenvalue inequality

D.4 Further properties of stability matrices

Bibliography

Index

A

B

C

D

E

F

G

H

I

K

L

M

N

O

P

Q

R

S

T

U

V

W

Y

Z.

Notes:

Includes bibliographical references (p. [621]-633) and index.

Description based on publisher supplied metadata and other sources.

ISBN:

0191553042

9780191553042

OCLC:

476240713