Dispersed electrical-relaxation response: Discrimination between conductive and dielectric relaxation processes

Relations and distinctions which are relevant to small-signal electrical-re laxation behavior are reviewed and applied to the important problem of iden tifying the physical processes leading to dispersed relaxation response. Co mplex-nonlinear-least-squares fitting of a response model to frequency-resp onse data is found not to allow one to distinguish unambiguously in most ca ses between conductive-system response of Wagner-Voigt type, which may be c haracterized by a distribution of conductive-system relaxation times [DCRT] , and dielectric- system response of Maxwell type, characterized by a distr ibution of dielectric-system relaxation times [DDRT], In general, one must include a parallel conductivity element, sigma(CP), as well as a high-frequ ency-limiting dielectric-system dielectric constant, in a conductive-system fitting model used to represent dielectric-system data with non-zero de co nductivity. Contrary to earlier predictions of Gross and Meixner, accurate numerical inversion of a set of exact frequency- response data to estimate the distribution with which it is associated shears that no discrete line n ecessarily appears in a DCRT associated with a truncated continuous DDRT. A discrete line can appear in general, however, when sigma(CP) not equal 0 a nd is unaccounted for in an inversion process. The novel result is establis hed that. a data set mathematically described in terms of a dielectric syst em with de leakage and involving a Maxwell-circuit exponential distribution of relaxation times may be well represented within usual experimental erro r by a Wagner-Voigt conductive system involving a form of the important Koh lrausch-Williams-Watts response model.