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Integral Equation Approach to Condensed Matter Relaxation



Jack F. Douglas


A model of relaxation in supercooled and polymer liquids is developed starting from an integral equation describing relaxation in liquids near thermal equilibrium and probabilistic modeling of the dynamic heterogeneity presumed to occur in these complex fluids. The treatment of stress relaxation considers two types of dynamic heterogeneity- temporal heterogeneity reflecting the extreme intermittency of particle motion in cooled liquids and spatial heterogeneity or particle clustering governed by Boltzmann=s law. Exact solution of the model relaxation integral equation by fractional calculus methods leads to a two parameter family of relaxation functions for which the memory indices (Β, θ) provide measures of the influence of the temporal and spatial heterogeneity on the relaxation process. The exponent Β is related to the geometrical form of the spatial heterogeneity. Relaxation function classes are identified according to the asymptotics of the Ψ(t;Β, θ) functions at long and short times and their integrability properties. The integral equation model for relaxation provides a framework for understanding the existence of universality in condensed matter relaxation under restricted circumstances.
Journal of Physics B-Atomic Molecular and Optical Physics


glass, heterogeneity, polymer, relaxation, viscoelasticity


Douglas, J. (1999), Integral Equation Approach to Condensed Matter Relaxation, Journal of Physics B-Atomic Molecular and Optical Physics, [online], (Accessed June 20, 2024)


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Created January 1, 1999, Updated June 2, 2021