Comparison of methods for estimating continuous distributions of relaxation times

Abstract

The nonparametric estimation of the distribution of relaxation times approach is not as frequently used in the analysis of dispersed response of dielectric or conductive materials as are other immittance data analysis methods based on parametric curve fitting techniques. Nevertheless, such distributions can yield important information about the physical processes present in measured material. In this letter, we apply two quite different numerical inversion methods to estimate the distribution of relaxation times for glassy \lila\ dielectric frequency-response data at $225 \kelvin$. Both methods yield unique distributions that agree very closely with the actual exact one accurately calculated from the corrected bulk-dispersion Kohlrausch model established independently by means of parametric data fit using the corrected modulus formalism method. The obtained distributions are also greatly superior to those estimated using approximate functions equations given in the literature.

arXiv comment4 pages and 4 figures

References in corpus (4)

• Universality, the Barton, Namikawa, and Nakajima relation, and scaling for dispersive ionic materials
• Distribution of relaxation times in $\alpha$-phase polyvinylidene fluoride
• Resolving distribution of relaxation times in Poly(propylene glycol) on the crossover region
• Origin of temperature dependent conductivity of $\alpha$-polyvinylidene fluoride

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• Distribution of relaxation times in $\alpha$-phase polyvinylidene fluoride
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• Fractional Equations of Curie-von Schweidler and Gauss Laws
• Electrical properties of polyetherimide thin films: Nonparametric dielectric reponse analysis with distribution of relaxation times