Compensation between the parameters of the Jonschers's Universal Dielectric Response Law in disordered 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.