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

The a.c. conductivity σ ac of polyaniline prepared with a.c. plasma polymerization was studied recently at low angular frequencies (ω⩽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 σ ac ∝ω n , n ⩽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.