Distribution of Relaxation Time Analysis for Non-ideal Immittance Spectrum: Discussion and Progress

The problem regarding the distribution of relaxation times (DRT) is revisited and discussed from the view point of mathematics and computing algorithms. Although the algorithm in conventional DRT analysis software involves an implicit hypothesis that the DRT is a continuous real function with a continuous relaxation time, this hypothesis is not a principle of nature but a requirement of a mathematical equation used for analysis. Note that the DRT calculated using the conventional algorithm is a continuous distribution of relaxation times (CDRT). As per the CDRT hypothesis, the DRT is a set of discrete values. On the other hand, there is a model that involves the discrete distribution of relaxation times (DDRT). Thus, the fundamental difference between the CDRT and DDRT models originates from their basic hypothesis. Using modern computers, the DDRT can be beneficial for analyzing non-Debye-type spectra.