Macroscopic disorder and the metal-insulator transition in conducting polymers

We describe a simple model for treating the frequency-dependent conductivity sigma(e)(omega) and dielectric function Re epsilon(e)(omega) of a quasi-one-dimensional conducting polymer. The polymer is modelled as a composite medium consisting of spherical regions of ordered polymer, randomly distributed in a much more disordered polymer host. within each spherical region, the polymer chains are highly oriented, but the axis of orientation varies randomly from sphere to sphere. The disordered host is assumed to be isotropic, but with a conductivity which depends on the connectivity of the polymer chains in the host. sigma(e)(omega) and Re epsilon(omega), as calculated from this model using a suitable effective medium approximation, reproduce all the main experimental features associated with the metal-insulator transition in these polymers.