Critical examination of the mismatch-and-relaxation frequency-response model for dispersive materials

Accurate calculations of the frequency and time responses of the hew dynami c-mismatch conductive-system frequency-response model of Funke, designated by CMR, indicate that its predictions are inconsistent with some of the phy sically based assumptions used in deriving the model. Although it does not lead to good quantitative agreement with real-part conductivity data for 0. 4Ca(NO3)(2).0.6KNO(3) [CKN] for several temperatures, it may be useful for fitting other disordered or crystalline materials showing frequency dispers ion. Calculation of the full complex-conductivity frequency response, not w ell fitted by the KWW response model, and of its unique underlying distribu tion of relaxation times, leads to specification of the conditions necessar y for the appearance of two peaks in the frequency response of the imaginar y part of the complex modulus. Important conclusions about modulus plotting and the modulus formalism fitting approach are presented, and the normaliz ation expression used in the CMR is corrected. The appropriate expression f ound for the tau(0), normalization quantity, which is relevant for scaling, cannot be fully evaluated independently of experimental results. It involv es a conductive-system-effective dielectric constant whose zero-frequency v alues, epsilon(C0) were found from the CKN fitting to be of the order of 10 and showed small temperature dependence. On the other hand, based on limit ed data, tau(0), itself showed approximate Arrhenius behavior. CMR macrosco pic transient response is shown to be fitted exceptionally well by the comb ination of an ordinary exponential and a stretched exponential, both applyi ng over the full time range, a type of parallel response quite different fr om the serial responses of the Ngai coupling model and of the closely relat ed but more plausible distribution-of-relaxation-times cutoff model. (C) 19 99 Elsevier Science B.V. All rights reserved.