Scaling and modeling in the analysis of dispersive relaxation of ionic materials

Problems with scaling of conductive-system experimental M-dat"(omega) and s igma (")(dat)(omega) data are considered and resolved by dispersive-relaxat ion-model fitting and comparison. Scaling is attempted for both synthetic a nd experimental M"(omega) data sets. A crucial element in all experimental frequency-response data is the influence of the high-frequency-limiting dip olar-and-vibronic dielectric constant epsilon (D infinity), often designate d epsilon (infinity), and not related to ionic transport. It is shown that epsilon (D infinity) precludes scaling of M-dat"(omega) for ionic materials when the mobile-charge concentration varies. When the effects of epsilon ( D infinity) are properly removed from the data, however, such scaling is vi able. Only the sigma'(omega) and epsilon"(omega) parts of immittance respon se are uninfluenced by epsilon (D infinity). Thus, scaling is possible for experimental sigma (')(omega) data sets under concentration variation if th e shape parameter of a well-fitting model remains constant and if any parts of the response not associated with bulk ionic transport are eliminated. C omparison between the predictions of the original-modulus-formalism (OMF) r esponse model of 1972-1973 and a corrected version of it that takes proper account of epsilon (D infinity), the corrected modulus formalism (CMF), dem onstrates that the role played by epsilon (D infinity) (or epsilon (infinit y)) in the OMF is incorrect. Detailed fitting of data for three different i onic glasses using a Kohlrausch-Williams-Watts response model, the KWW1, fo r OMF and CMF analysis clearly demonstrates that the OMF leads to inconsist ent shape-parameter (beta (1)) estimates and the CMF does not. The CMF KWW1 model is shown to subsume, correct, and generalize the recent disparate sc aling/fitting approaches of Sidebottom, Leon, Roling, and Ngai. (C) 2001 Am erican Institute of Physics.