Slopes, nearly constant loss, universality, and hopping rates for dispersive ionic conduction

The title topics are investigated, discussed, and new insights provided by considering isothermal frequency response data for seven different materials having quite different conductivity spans and involving different electrode polarization effects and temperatures. These data sets were fitted using several different models, including the Kohlrausch-related K0 and K1 ones derived from stretched-exponential response in the temporal domain. The quasi-universal UN model, the K1 with its shape parameter, β₁, fixed at 1/3, fitted most of the data very well, and its fits of such data were used to compare its predictions for hopping rate with those derived from fitting with the conventional 'universal dynamic response' Almond–West real-part-of-conductivity model. The K1-model theoretical hopping rate, involving the mean waiting time for a hop and derived from microscopic stochastic analysis, was roughly twice as large as the empirical Almond–West rate for most of the materials considered and should be used in place of it. Its use in a generalized Nernst–Einstein equation led to comparison of estimates of the concentration of fully dissociated mobile charge carriers in superionic PbSnF₄ with earlier estimates of Ahmad using an Almond–West hopping rate value. Agreement with an independent structure-derived value was relatively poor. Fitting results obtained using the K0 model, for Na₂SO₄ data sets for two different polycrystalline material phases, and involving severely limited conductivity variation, were far superior to those obtained using the K1 model. The estimated values of the K0 shape parameter, β₀, were close to 1/3 for both phases, strongly suggesting that the charge motion was one dimensional for each phase, even though they involved different crystalline structures.