Comparison of methods for estimating continuous distributions of relaxation times

TL;DR

This paper compares two numerical inversion methods for estimating relaxation time distributions from dielectric data, demonstrating their accuracy and superiority over existing approximate functions, with implications for physical process analysis.

Contribution

It introduces and compares two distinct numerical inversion techniques for nonparametric relaxation time distribution estimation from dielectric data.

Findings

Both methods produce distributions closely matching the exact model.

Estimated distributions outperform existing approximate functions.

Methods provide insights into physical processes in dielectric materials.

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.