AC CONDUCTION IN DISORDERED SOLIDS - COMPARISON OF EFFECTIVE-MEDIUM AND DISTRIBUTED-TRANSITION-RATE-RESPONSE MODELS

Dyre has proposed that in the low-temperature limit an effective mediu m approximation, termed the Bryksin equation here (the BEM), predicts a universal frequency dependence for the normalized small-signal ac fr equency relaxation response of nonmetallic disordered solids. This res ponse has been claimed to be practically identical to that found for a n exponential distribution of transition rates (EDTR) in the particula r limiting uniform-energy-barrier-distribution case, but comparison of the two responses has been inadequate so far. Although it is shown he re that they can be well differentiated, the question of which or eith er is universal still requires further comparisons with experiment for its answer. A generalization of the limiting low-temperature BEM equa tion applicable for nonzero temperatures, the GBEM, is developed and u sed to evaluate the temperature and frequency ranges for which the BEM is still adequate. It is found that GBEM response can be well approxi mated by the important EDTR solution and leads to a frequency exponent with the same temperature dependence as the latter. An expression der ived herein for the dc conductivity predicted by the GBEM involves 1/3 of the maximum thermal activation energy (i.e., the effective percola tion energy), however, rather than the energy itself. Further, unlike the BEM, the GBEM predicts the presence of an intrinsic temperature-in dependent high-frequency-limiting conductivity whose magnitude is eval uated. The combination of conductive- and dielectricsystem response, a lways experimentally present for a conductive system, is evaluated for the GBEM, and in the frequency range where the GBEM and BEM are indis tinguishable it leads to frequency and temperature response remarkably similar to that observed for most disordered materials. Finally, it i s suggested that Dyre's macroscopic simulations of the relaxation prob lem do not seem fully relevant to physical situations of interest and thus should not be taken to confirm the universality of the BEM equati on response. Nevertheless, the present results broaden the likely rang e of applicability of both the BEM and GBEM and the EDTR and suggest t hat one or the other may indeed be particularly appropriate for descri bing the frequency and temperature response of a wide variety of disor dered materials.