Stretched-exponential decay functions from a self-consistent model of dielectric relaxation

TL;DR

This paper proposes a self-consistent model using fractional calculus to explain the physical origin of the stretched exponential dielectric relaxation function, providing a statistical-mechanical foundation for the KWW behavior.

Contribution

It introduces a kinetic model based on time-fractional derivatives that naturally results in the stretched exponential decay observed in dielectric materials.

Findings

The model reproduces the KWW relaxation function.

It links charge transport mechanisms to fractional dynamics.

Provides a theoretical basis for dielectric relaxation phenomena.

Abstract

There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter of debate in the literature. In this paper we suggest a model of dielectric relaxation, which naturally leads to a stretched exponential decay function. Some essential characteristics of the underlying charge conduction mechanisms are considered. A kinetic description of the relaxation and charge transport processes is proposed in terms of equations with time-fractional derivatives.