Exploring the universality of the alternating conductivity of disordered materials using the Gaussian distribution of activation energies.

Abstract

This paper presents a newapproach for the analysis of ACconductivity, s*(w)= s¢(w)+is(w), in disordered solids which brings together the quasi-universal frequency-dependent conductivity and the idea of a Gaussian distributions of probable activation energy barriers for hopping carriers. An explicit expression forAC conductivity was obtained using a complex dielectric response function and a continuous time random walk treatment applied to a lattice obeying the Kubo’s fluctuationdissipation theorem. This expression provides an insight into the universality of the form s¢(w) μ ws (0  s  1) and s(w) μ kw (k is the dielectric constant), aswell into the effect of the Gaussian disorder on exponent s.We discuss the similarities and differences with the Random Free Energy Barrier model equivalent to the long-used box model, and it brings support to an extending expression proposed by JCDyre and one of the authors. The applicability of the model to experimental observations on poly[(2-methoxy-5-hexyloxy)-p-phenylenevinylene] reveals the dielectric constant, mean energy and variance of the Gaussian distribution for hopping carriers in this disordered conjugated polymer.