Analytical representations for relaxation functions of glasses

TL;DR

This paper derives analytical representations of common relaxation functions in glasses using $H$-functions, facilitating experimental data fitting in both time and frequency domains.

Contribution

It introduces new $H$-function based analytical forms for non-Debye relaxation functions, enhancing modeling capabilities.

Findings

Derived $H$-function representations for Cole-Cole, Cole-Davidson, Havriliak-Negami functions

Provided $H$-function form for stretched exponential susceptibility

Facilitated improved fitting of experimental relaxation data

Abstract

Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the complex frequency dependent Cole-Cole, Cole-Davidson and Havriliak-Negami susceptibilities are also represented in terms of $H$-functions. In the frequency domain the complex frequency dependent susceptibility function corresponding to the time dependent stretched exponential relaxation function is given in terms of $H$-functions. The new representations are useful for fitting to experiment.