Compensation between the parameters of the Jonschers's Universal Relaxation Law in disordered materials

TL;DR

This paper explores the relationships and compensation rules among parameters in Jonscher's Universal Relaxation Law, supported by extensive experimental data, and merges it with the Ghosh-Pan Scaling Rule to deepen understanding of dielectric properties.

Contribution

It introduces a new compensation rule linking the parameters of Jonscher's Law using a partial differentiation approach and integrates it with the Ghosh-Pan Scaling Rule, supported by experimental validation.

Findings

Parameters of the Universal Dielectric Response Law are interrelated through a compensation rule.

The study confirms proportionality between the logarithm of the pre-exponential factor and the fractional exponent.

The theoretical framework aligns well with extensive experimental data across various materials.

Abstract

Experimental results for a huge number of different materials published during the past fifty years confirm the validity of the Jonscher's Universal Dielectric Response Law. Accordingly,the ac conductivity is a fractional power of frequency. AC conductivity spectra recorded at different temperatures evidence for a proportionality between the logarithm of the pre-exponential factor to the fractional exponent, as well. The dc conductivity, pre-exponential factor and fractional exponent of the ac conductivity are three state variables, which describe the electric and dielectric properties. These constitute a unique relation by merging the Jonscher's Dielectric Response Law and the Ghosh - Pan Scaling Rule, respectively. A partial differentiation chain theorem combined with the temperature dependencies of the dc conductivity, pre-exponential factor and fractional exponent of the ac response, establishes a compensation rule between the parameters of the Universal Dielectric Response Law. The compatibility of the present theorynwth published experimental results is discussed.