Compensation rule between the parameters of 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 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 and the fractional exponent in many cases. In the present work, the observed compensation is interpreted in terms of two fundamental characteristics of disordered matter: Universality and scaling. For this, Ghosh and Pan’s Scaling Rule (SR), which links the direct current (DC) conductivity to the AC one, and the Jonscher Universal Dielectric Response merge into 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.