Comparison of methods for estimating continuous distributions of relaxation times

The nonparametric estimation of the distribution of relaxation-time 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 paper, we apply two quite different numerical inversion methods to estimate the distribution of relaxation times for glassy Li0.5La0.5TiO3 dielectric frequency-response data at 225K. 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 function equations given in the literature.