Deducing low-frequency scaling of transport properties in an inhomogeneous medium from thermodynamics and geometry

Abstract

It is shown that it is possible to generate some known results for size-dependent scaling of cluster relaxation properties using simple thermodynamic and geometrical arguments. Decomposition of inhomogeneous media, for which transport may be mapped on to random impedance networks, into clusters of impedances, makes it possible for these results to be adapted to low frequency (large clusters) scaling properties of transport. The critical (scaling) frequency must be determined by other means (i.e. standard ‘critical path’ analysis of percolation theory). Applications are made to low temperature screening effects and to non-ohmic transport in a somewhat simplified description of cluster topology. Suggestions for application to more realistic cluster representations are given.