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

Abstract

Relations and distinctions which are relevant to small-signal electrical-relaxation behavior are reviewed and applied to the important problem of identifying the physical processes leading to dispersed relaxation response. Complex-nonlinear-least-squares fitting of a response model to frequency-response data is found not to allow one to distinguish unambiguously in most cases between conductive-system response of Wagner-Voigt type, which may be characterized by a distribution of conductive-system relaxation times [DCRT], and dielectric- system response of Maxwell type, characterized by a distribution of dielectric-system relaxation times [DDRT]. In general, one must include a parallel conductivity element, σCP, as well as a high-frequency-limiting dielectric-system dielectric constant, in a conductive-system fitting model used to represent dielectric-system data with non-zero dc conductivity. 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 shows that no discrete line necessarily appears in a DCRT associated with a truncated continuous DDRT. A discrete line can appear in general, however, when σCP ≠ 0 and is unaccounted for in an inversion process. The novel result is established that a data set mathematically described in terms of a dielectric system with dc leakage and involving a Maxwell-circuit exponential distribution of relaxation times may be well represented within usual experimental error by a Wagner-Voigt conductive system involving a form of the important Kohlrausch-Williams-Watts response model.