Some remarks on ac conduction in disordered solids

Abstract

Alternating current conduction in disordered solids is discussed, from a general point of view. As regards experiment, it is argued that the observed power-law behavior of the frequency-dependent conductivity, σ(ω), is probably not fundamental, that the Ngai relation between dc and ac conductivity activation energies follows from independent experimental facts, that the shape of the modulus peak has no fundamental significance, and that there are interesting mechanical analogies to the observed ac electrical behavior. As regards hopping models for ac conduction, it is shown that three commonly used arguments against the existence of a distribution of activation energies are all incorrect. Also, it is shown that σ( ω) ≠ σ(0) only if there are correlations in the directions of different charge carrier jumps; in particular this result implies σ( ω) = σ(0) for all frequencies in the continuous time random walk (CTRW) model. In the final section a number of open problems are listed, and suggestions are made for future work.