Comparison and evaluation of several models for fitting the frequency response of dispersive systems

摘要

Using both simulated and experimental data, detailed comparisons are made between the different physical interpretations and responses of several important models commonly employed for fitting and analyzing conductive-system data sets, such as those for ionic glasses. Those considered are one following directly from stretched-exponential temporal response, designated the Kohlrausch K0; several ones indirectly associated with such stretched-exponential response: the original modulus formalism (OMF) model and corrected modulus formalism (CMF) ones: and the ZC model, one whose real-part conductivity expression has been termed "universal dynamic response." In addition, several models involving dielectric dispersion, rather than resistive dispersion, are found to be less appropriate for the present data than are the CMF ones. Of the four main conductive-system models the CMF approach fits data for a wide variety of materials much better than do the others. The OMF is shown to be both experimentally and theoretically defective and leads to poor and inconsistent fitting results. The simple ZC model involves nonphysical low-frequency-limiting real-part conductivity response and is usually less appropriate even than the K0. High- and low-frequency expressions and fit results for the various dielectric elements are presented, along with discussion of characteristic, peak, and mean relaxation times for the various models, failing to confirm some proposed relations between these quantities suggested earlier.