Entropic origin of dielectric relaxation universalities in heterogeneous materials (polymers, glasses, aerogel catalysts)

TL;DR

This paper derives a universal dielectric relaxation function for heterogeneous materials based on entropy principles, linking relaxation behaviors to fractal and nonextensivity parameters, and validating it against experimental data.

Contribution

It introduces a new universal relaxation model derived from maximum entropy principles for nonextensive systems, applicable to diverse heterogeneous materials.

Findings

Relaxation function relates to fractal and entropy parameters.

Power law behaviors match Weron generalized dielectric function.

Model aligns with Jonscher universality principle.

Abstract

We have derived a universal relaxation function for heterogeneous materials using the maximum entropy principle for nonextensive systems. The power law exponents of the relaxation function are simply related to a global fractal parameter and for large time to the entropy nonextensivity parameter q. For intermediate times the relaxation follows a stretched exponential behavior. The asymptotic power law behaviors both in the time and the frequency domains coincide with those of the Weron generalized dielectric function derived in the stochastic theory from an extension of the Levy central limit theorem. These results are in full agreement with the Jonscher universality principle and find application in the characterization of the dielectric properties of aerogels catalytic supports as well as in the problem of the relation between morphology and dielectric properties of polymer composites.