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 medium approximation, termed the Bryksin equation here (the BEM), predicts a universal frequency dependence for the normalized small-signal ac frequency relaxation response of nonmetallic disordered solids. This response has been claimed to be practically identical to that found for an exponential distribution of transition rates (EDTR) in the particular limiting uniform-energy-barrier-distribution case, but comparison of the two responses has been inadequate so far. Although it is shown here that they can be well differentiated, the question of which or either is universal still requires further comparisons with experiment for its answer. A generalization of the limiting low-temperature BEM equation applicable for nonzero temperatures, the GBEM, is developed and used to evaluate the temperature and frequency ranges for which the BEM is still adequate. It is found that GBEM response can be well approximated by the important EDTR solution and leads to a frequency exponent with the same temperature dependence as the latter. An expression derived herein for the dc conductivity predicted by the GBEM involves 1/3 of the maximum thermal activation energy (i.e., the effective percolation energy), however, rather than the energy itself. Further, unlike the BEM, the GBEM predicts the presence of an intrinsic temperature-independent high-frequency-limiting conductivity whose magnitude is evaluated. The combination of conductive- and dielectricsystem response, always experimentally present for a conductive system, is evaluated for the GBEM, and in the frequency range where the GBEM and BEM are indistinguishable it leads to frequency and temperature response remarkably similar to that observed for most disordered materials. Finally, it is suggested that Dyre's macroscopic simulations of the relaxation problem do not seem fully relevant to physical situations of interest and thus should not be taken to confirm the universality of the BEM equation response. Nevertheless, the present results broaden the likely range of applicability of both the BEM and GBEM and the EDTR and suggest that one or the other may indeed be particularly appropriate for describing the frequency and temperature response of a wide variety of disordered materials.