Analysis of ac conduction in disordered solids

Abstract

Dyre [J. Appl. Phys. 64, 2456 (1988)] has recently stated that the random free-energy barrier model of ac conduction in disordered solids, solved in the continuous time random-walk approximation with the effects of the maximum jump frequency eliminated, is quantitatively satisfactory in describing hopping conduction for a large number of solids. Here, predictions of this model, equivalent to the long-used box model, which posits a distribution of equally probable activation energies, are examined in depth, both without and with an upper cutoff. It is first demonstrated that the type of log-log plot on which Dyre appears to base his conclusion of quantitative adequacy does not allow adequate discrimination to be made between box-model predictions and those of other models, such as the Kohlrausch–Williams–Watts model, even when exact data are used. The results of numerous complex nonlinear least-squares fits of exact box-model data, and of such data containing substantial proportionally added random errors, to the box model, the WW model, the constant-phase-element model, and the Davidson–Cole [J. Chem. Phys. 19, 1484 (1951)] response model make it clear that when using this fitting technique, one can identify the correct model, discriminate against incorrect ones, and obtain good parameter value estimates for the correct model. Further, when the highest frequency of the data exceeds the maximum jump frequency, its value can be accurately estimated. It is concluded that the case for the quantitative adequacy of the box model remains unproven. Future data fitting using complex nonlinear least squares should, however, allow a best-fit model to be selected unambiguously from those compared.