LIMITING ELECTRICAL RESPONSE OF CONDUCTIVE AND DIELECTRIC SYSTEMS, STRETCHED-EXPONENTIAL BEHAVIOR, AND DISCRIMINATION BETWEEN FITTING MODELS

Given a fitting model, such as the Kohlrausch-Williams-Watts (KWW)/str etched-exponential response, three plausible approaches to fitting sma ll-signal frequency or time-response data are described and compared. Fitting can be carried out with either of two conductive-system formal isms or with a dielectric-system one. Methods are discussed and illust rated for deciding which of the three approaches is most pertinent for a given data set. Limiting low-and high-frequency log-log slopes for each of the four immittance levels are presented for several common mo dels; cutoff effects are considered; and an anomaly in the approach to a single-relaxation-time Debye response for one of the conductive-sys tem approaches is identified and explained. It is found that the tempo ral response function for the most appropriate conductive-system dispe rsion (CSD) approach, designated the CSD1, one long used in approximat e form for frequency-response data analysis, does not lead to stretche d-exponential transient behavior when a KWW response model is consider ed. Frequency-domain fitting methods and approaches are illustrated an d discriminated using 321 and 380 K Na2O-3SiO(2) data sets. The CSD1 a pproach using a KWW model is found to be most appropriate for fitting these data exceedingly closely with a complex nonlinear least-squares procedure available in the free computer program LEVM. Detailed examin ation and simulation of the approximate, long-used CSD1 modulus fittin g formalism shows the unfortunate results of its failure to include se parately the effects of the always present high-frequency-limiting die lectric constant, epsilon(D infinity). The stretched-exponential expon ent, beta, associated with this fitting approach has always been misid entified in the past, and even after its reinterpretation, the result is likely to be sufficiently approximate that most physical conclusion s derived from such fitting will need reevaluation. (C) 1997 American Institute of Physics.