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

Abstract

Problems with scaling of conductive-system experimental M dat ″ (ω) and σ dat ′ (ω) data are considered and resolved by dispersive-relaxation-model fitting and comparison. Scaling is attempted for both synthetic and experimental M ″ (ω) data sets. A crucial element in all experimental frequency-response data is the influence of the high-frequency-limiting dipolar-and-vibronic dielectric constant ε D∞ , often designated ε ∞ , and not related to ionic transport. It is shown that ε D∞ precludes scaling of M dat ″ (ω) for ionic materials when the mobile-charge concentration varies. When the effects of ε D∞ are properly removed from the data, however, such scaling is viable. Only the σ ′ (ω) and ε ″ (ω) parts of immittance response are uninfluenced by ε D∞ . Thus, scaling is possible for experimental σ ′ (ω) data sets under concentration variation if the shape parameter of a well-fitting model remains constant and if any parts of the response not associated with bulk ionic transport are eliminated. Comparison between the predictions of the original-modulus-formalism (OMF) response model of 1972–1973 and a corrected version of it that takes proper account of ε D∞ , the corrected modulus formalism (CMF), demonstrates that the role played by ε D∞ (or ε ∞ ) in the OMF is incorrect. Detailed fitting of data for three different ionic glasses using a Kohlrausch–Williams–Watts response model, the KWW 1 , for OMF and CMF analysis clearly demonstrates that the OMF leads to inconsistent shape-parameter (β 1 ) estimates and the CMF does not. The CMF KWW 1 model is shown to subsume, correct, and generalize the recent disparate scaling/fitting approaches of Sidebottom, León, Roling, and Ngai

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