Abstract
A model of relaxation in supercooled and entangled polymer liquids is developed starting from an integral equation describing relaxation in liquids near thermal equilibrium and probabilistic modelling 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 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 provide measures of the influence of the temporal and spatial heterogeneity on the relaxation process. The exponent is related to the geometrical form of the spatial heterogeneity. Relaxation function classes are identified according to the asymptotics of the 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.
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