The fractal nature of the cluster model dielectric response functions

Abstract

Calculable fractal circuit models are used to show that the cluster model response functions result from the combination of two types of self-similarity. The analysis is extended to the molecular scale where the cluster model is seen to be based on sequential relaxation processes. An outline is given of the physical origin for such behavior, and the self-similar processes are identified with the basic concepts of (i) an efficient (compact) exploration of a fractal lattice and (ii) self-similarity in the contacts between internally connected regions (clusters). The relationship of the cluster model parameters n and m to system dimensionalities are derived for a number of cases.