Conductivity of disordered solids: Resolution of discrepancies between micro- and macro-response models

The widely used 1972 macroscopic electric-modulus formalism for conductive-system frequency-response data analysis is corrected to render it properly consistent with purely mobile-charge situations. The corrected model is found to be fully consistent with a 1973 microscopic stochastic-response approach based on continuous-time random-walk hopping when the effect of a limiting high-frequency dielectric constant associated only with charge motion is added to the latter model. When stretched-exponential temporal response with a temperature-dependent {β} exponent is used to generate the modulus-formalism response model, its temporal dependence is not of stretched-exponential character, and ac conductivity may show non-Arrhenius behavior and an approach to saturation at high temperatures.