Generalized Distribution Function of Relaxation Times with the Davidson-Cole Model as a Kernel

TL;DR

This paper introduces a generalized distribution function of relaxation times using the Davidson-Cole model as a kernel, providing analytical expressions for various impedance models to better understand complex relaxation phenomena.

Contribution

It proposes a new generalized DFRT based on the Davidson-Cole model and derives explicit analytical formulas for several well-known impedance models.

Findings

Derived analytical expressions for generalized DFRTs.

Unified framework for multiple impedance models.

Enhanced understanding of relaxation time distributions.

Abstract

In this paper we propose a generalized distribution function of relaxation times (DFRT) considering the Davidson-Cole model as an elementary process instead of the standard Debye model. The distribution function is retrieved from the inverse of the generalized Stieltjes transform expressed in terms of iterated Laplace transforms. We derive computable analytical expressions of the generalized DFRT for some of the most known normalized impedance (or admittance) models including the constant phase element, the Davidson-Cole, Havriliak-Negami and the Kohlrausch-Williams-Watts models.