Analysis of dispersed frequency response for ionic glasses: influence of electrode and nearly constant loss effects

Analysis by D L Sidebottom of the dispersive frequency response of the real-part of the conductivity, sigma'(omega), for many alkali phosphate and metaphosphate glasses, using a fitting model involving a 'universal dynamic response' power law with an exponent n and a constant-loss term, led to anomalous n behaviour that he explained as arising from variable constriction of the local cation conduction space. In order to obtain adequate fits, he eliminated from the data all low-frequency decreases of sigma'(omega) below the dc plateau, ones actually associated with electrode effects. Such a cut-off does not, however, eliminate electrode effects possibly present in the high-frequency part of the data range. The results of the present detailed analysis and fitting of both synthetic data and several of his experimental data sets show unequivocally that his anomalous n behaviour arose from neglecting electrode effects. Their inclusion, with or without data cut-off in the fitting model, leads to the expected high-frequency slope value of n = 2/3 associated with bulk conduction, as required by recently published topological effective-dimension considerations for dielectric relaxation in conductive systems. Further, the effects of the inclusion in a full fitting model of series and possibly parallel complex constant-phaseelement contributions, representing electrode and nearly constant loss effects, respectively, have been investigated in detail. Such composite models usually lead to best fitting of either the full or cut-off complex data when they include the semi-universal, topologically based K1 bulk model, one indirectly derived from the assumption of stretched-exponential temporal behaviour.