Dispersed electrical-relaxation response: discrimination between conductive and dielectric relaxation processes

Abstract

Relations and distinctions which are relevant to small-signal electrical-relaxation behavior are reviewed and applied to the important problem of identifying the physical processes leading to dispersed relaxation response. Complex-nonlinear-least-squares tting of a response model to frequency-response data is found not to allow one to distinguish unambiguously in most cases between conductive-system response of Wagner-Voigt type, which m a y b e c haracterized by a distribution of conductive-system relaxation times DCRT , and dielectric-system response of Maxwell type, characterized by a d istribution of dielectric-system relaxation times DDRT . In general, one must include a parallel conductivity element, CP, a s w ell as a high-frequencylimiting dielectric-system dielectric constant, in a conductive-system tting model used to represent dielectric-system data with non-zero dc conductivity. Contrary to earlier predictions of Gross and Meixner, accurate numerical inversion of a set of exact frequency-response data to estimate the distribution with which it is associated shows that no discrete line necessarily appears in a DCRT associated with a truncated continuous DDRT. A discrete line can appear in general, however, when CP 6 = 0 and is unaccounted for in an inversion process. The novel result is established that a data set mathematically described in terms of a dielectric system with dc leakage and involving a Maxwell-circuit exponential distribution of relaxation times may b e w ell represented within usual experimental error by a W agner-Voigt conductive system involving a form of the important Kohlrausch-Williams-Watts response model.

Concentration dependence of ionic relaxation in lithium doped polymer electrolytes

“…that it is virtually impossible to distinguish between dielectric and conductive responses by data fitting alone [16]. This is also our experience; the quality of fits is similar for the two circuits in figure 4.…”

“…The objective is not to present detailed equivalent circuit fits to the data, but rather to distinguish between dielectric and conductive models for the impedance response [15,16] associated with the ionic charge carriers. To this end we carry out a thorough analysis of a dielectric loss peak at frequencies slightly above the onset of the ionic conductivity response.…”

Deconvolution of immittance data: Some old and new methods

“…[4] it was shown, however, that there is a crucial difference between the inversion of data involving a continuous distribution of relaxation times and one involving a discrete distribution. Although in the numerical analysis both situations are approximated by a discrete set of Debye relaxations, these two types of response can be distinguished [4,[18][19][20], and it turns out that inversion of data associated with a discrete set of time constants is not ill-posed, in contrast to the continuous DRT situation. Extensive PNLLS DRT estimation and Kronig-Kramers analysis carried out in Refs.…”

Comparison of Parametric and Nonparametric Methods for the Analysis and Inversion of Immittance Data: Critique of Earlier Work

“…Although it has been shown that if a given data set may be well represented by a dielectricsystem DRT, it can also usually be well represented by a conducting-system one instead [9]; we shall follow the work of [11][12][13] here and consider only dielectric dispersion, consistent with Fig. 1.…”