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Complex Dynamics of Glass-Forming Liquids
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eBook
Complex Dynamics of Glass-Forming Liquids
2008,2009
Overview
The book presents a self-contained exposition of the mode-coupling theory for the evolution of glassy dynamics in liquids. This theory is based on polynomial expressions for the correlations of force fluctuations in terms of those of density fluctua-tions. These mode-coupling polynomials are motivated as descriptions of the cage-effect-induced transient localization of particles in condensed matter. It is proven that the implied regular mode-coupling equations of motion determine uniquely models for a correlation-function description of the dynamics. This holds for all choices of the polynomial coefficients, which serve as coupling constants. The arrested parts of the correlations are solutions of fixed-point equations. They exhibit spontaneous singularities, which are equivalent to the bifurcation singularities of the real roots of real polynomials. They deal with idealized liquid-glass and glass-glass transitions. Driving the coupling constants towards their critical values, the correlation functions exhibit the evolution of complex dynamics. Its subtleties are due to the interplay of nonlinearities and divergent retardation effects. The book discusses that the relaxation features are similar to those observed in experimental and molecular-dynamics-simulation studies of con-ventional liquids and colloids. Asymptotic expansions are derived for the mode-coupling-theory functions for small frequencies and small separations of the coupling constants from the transition values. The leading-order asymptotic contributions provide an understanding of the essential facets of the scenarios. The leading-asymptotic corrections are deduced and applied to quantify the evolution of the leading-order description.
Publisher
Oxford University Press,Oxford University Press, Incorporated
Subject
ISBN
9780199235346, 0199235341
