Tempered relaxation with clustering patterns

TL;DR

This paper introduces a new frequency-domain relaxation function that models dielectric susceptibility data with distinct low- and high-frequency exponents, accounting for clustering and stochastic processes in relaxation phenomena.

Contribution

It presents a novel framework deriving a relaxation function that captures the entire two-power-law dielectric spectrum with independent exponents, explaining the underlying physical processes.

Findings

The model fits the full range of dielectric spectroscopy data.

Different physical mechanisms explain high- and low-frequency behaviors.

Clustering influences low-frequency relaxation patterns.

Abstract

This work is motivated by the relaxation data for materials which exhibit a change of the relationship between the fractional power-law exponents when different relaxation peaks in their dielectric susceptibility are observed. Within the proposed framework we derive a frequency-domain relaxation function fitting the whole range of the two-power-law dielectric spectroscopy data with independent low- and high-frequency fractional exponents \gamma\ and -\alpha, respectively. We show that this effect results from a contribution of different processes. For high frequencies it is determined by random stops and movement of relaxing components, and the low-frequency slope is caused by clustering in their temporal changes.