Dielectric relaxation: an overview

The classical theory of dielectric relaxation of an assembly of polar molecules is briefly reviewed as a prelude to the derivation of the fractional diffusion equation, which is used to extend the Debye-Frohlich model of relaxation over a potential barrier to anomalous diffusion governed by the Cole-Cole equation. A detailed derivation of the fractional diffusion analogue of the classical Smoluchowski equation for the evolution of the distribution function in configuration space excluding inertial effects is given by considering the continuum limit of the discrete orientation or site model of dielectric relaxation with the waiting times at the sites given by a Levy distribution. (C) 2004 Elsevier B.V. All rights reserved.