The power law dependence of the a.c. conductivity on frequency in amorphous solids

The a.c. conductivity sigma(ac) of polyaniline prepared with a.c. plasma polymerization was studied recently at low angular frequencies (omega less than or equal to 1 MHz) (Mathai J et al 2002 J. Phys. D: Appl. Phys. 35 240). The data were analysed considering a power dependence of the a.c. conductivity on frequency sigma(ac) proportional to omega(n), n less than or equal to 1. It was found that the index n varies between 0.4 and 1. In this work, we show that these values conflict with the bounds of the n parameter predictions of the Austin and Mott model, which assumes a single mode of charge hopping in amorphous media. We suggest that multiple a.c. conductivity mechanisms of the Austin and Mott type may contribute to the measured a.c. conductivity. A numerical calculation for a couple of mechanisms showed that the resulting a.c. conductivity curve exhibits effective n values which can explain the wide distribution of the indexes evaluated in polyaniline.