Frequency and Temperature Scaling in the Conductivity and Its Structural Consequences

We have studied the temperature (T) and frequency (ω/2π) dependence of the complex conductivity σ(ω, T) of several systems where hopping conduction is dominant: conducting carbon-black/polymer composites as a function of carbon-black (CB) concentration, aggregates of molecular cluster compounds as a function of the size and of the distance between the metal cores and polymers as a function of degree of doping. For all compounds the conductivity as a function of ω and T can be scaled onto single curves. Using an extension of the anomalous diffusion model the specific details of these curves for the CB composites are shown to be characteristic of the underlying fractal structure. The main features of the scaled dependence of σ(ω, T) of the randomly packed cluster compounds are well described by effective medium theories, except at low frequencies where percolation effects become important. Similar features are seen in polythiophene derivatives at doping levels above the percolation threshold.