Comparison of the universal dynamic response power-law fitting model for conducting systems with superior alternative models

For at least 5 years there has been considerable controversy concerning the relative value of power-law and electric modulus formalism models for fitting and interpreting dispersed frequency-response data for ionically conducting glasses, melts, and other disordered solids. Conclusions of various authors have ranged from preferring one or the other to neither. Here, detailed complex-nonlinear-least-squares fitting of data for a trisilicate glass with several different dispersion models leads to the conclusion that ‘neither’ of the above is the correct conclusion for an adequate analysis of bulk-material behavior in this and other materials. The power-law model is nonphysical, and the usual modulus formalism approach is faulty in two different ways. For the near-room-temperature data set analyzed here, it was found that when electrode effects were included in a composite fitting model, they contributed significantly to high-, but not low-frequency response. Their presence may explain the increasing log–log slope of the real part of the conductivity with increasing frequency found for many materials. The corrected modulus formalism approach, involving a Kohlrausch–Williams–Watts model, the KWW1, was found to be the best of those used to represent bulk response. Contrary to common expectation, the original modulus formalism and KWW1 models do not lead to stretched-exponential response in the time domain. Best fitting required not only a model for bulk response but one for electrode response as well and necessarily also involved a separate fitting parameter to account for high-frequency-limiting dipolar dielectric effects.