On two incompatible models for dispersion in ionic conductors

Abstract

The two models considered are the widely used 1973 original modulus formalism (OMF) of Moynihan and associates, and the later corrected modulus formalism (CMF). Both approaches involve a dispersive frequency-response model derived from Kohlrausch stretched-exponential temporal response, the KWW1 model, also termed the K1. A brief summary of the derivation of this model is followed by consideration of the small but crucial differences between OMF and CMF analysis approaches and the reasons why the OMF and an inferred physical basis for its behavior, variable correlation between mobile ions, are inappropriate. After discussions of some prior criticisms of the OMF approach, results of accurate least-squares fitting of experimental frequency-response data to OMF and CMF models for a variety of ionic materials illustrate these differences and demonstrate a crucial inconsistency of the OMF, one that critically falsifies it.