Compensation rule between the parameters of the Jonscher's Universal Dielectric Response in disordered materials

Experimental results for a huge number of different types of disordered materials published during the past fifty years confirm the validity of the Jonscher's Universal Dielectric Response law. Accordingly, the alternating current (AC) conductivity is a fractional power of frequency. The analysis of AC conductivity spectra recorded evidence for a proportionality between the logarithm of the pre-exponential factor to the fractional exponent in many cases. In the present work, the observed compensation is interpreted based on the two fundamental characteristics of disordered matter: universality and scaling. For this Ghosh and Pan Scaling Rule which links the direct current (DC) conductivity to the AC one, and the Jonscher Universal Dielectric Response merge to a single function of three quantities: DC conductivity, pre-factor and power exponent. Applying the partial differentiation chain theorem and taking the temperature dependencies of these quantities for Arrhenius systems, the compensation rule is derived.