Jump Relaxation: Simple Equations, Relevant Functions, and Kohlrausch-Williams-Watts Behavior

Abstract

AbstractSolid electrolytes with structural disorder generally exhibit characteristic deviations from standard-theory spectra. The effect is known as “universal” dynamic response. In the jump-relaxation model, the phenomena are consistently explained in terms of the non-random hopping resulting from the repulsive Coulomb interaction among the mobile ions. In previous stages of the development of the model, the treatment required either crude approximations or extensive numerical calculations. Now. however, we are able to present, for the first time. simple analytic expressions for the relevant time correlation functions, derived from the rate equations of the model. In particular, the dependence of the ionic conductivity on frequency and temperature is now expressed by a simple equation. Furthermore, we recover the Kohlrausch-Williams- Watts behavior and find the KWW exponent. β. and the mismatch parameter of our model, α. to be identical. The validity of the KWW law is shown to be limited to the dispersive regime on the frequency and time scales.