A novel model for the ionic conducting polymers with non-Arrhenius temperature dependence

A novel model is proposed to describe the ionic conduction process of polymer electrolytes with non-Arrhenius temperature dependence expressed by the empirical Vogel-Tamman-Fulcher (VTF) equation, exp(Q/(T-T0)). Following the previous numerical simulation work and the series hopping calculation scheme, a microscopic model was constructed assuming random hopping energy distribution. Using the Arrhenius form for thermal activation and order statistics, the overall resistivity was found to be related to the sum of exp(E/kT+cE12 /-E/D) where E is the hopping energy barrier, exp(-cE12 /) the WKB term, and D, an energy-related constant. Calculated from the steepest descent method, the model is able to reproduce the VTF type of temperature dependence analytically.