Resolving distribution of relaxation times in Poly(propylene glycol) on the crossover region

TL;DR

This paper applies a novel numerical method combining constrained least squares and Monte Carlo techniques to analyze dielectric relaxation data of poly(propylene glycol), revealing detailed relaxation spectra and behavior in the crossover region.

Contribution

The study introduces a new approach to extract relaxation time distributions without prior assumptions, providing deeper insights into molecular relaxations in poly(propylene glycol).

Findings

Resolved alpha and beta relaxations in PPG.

Identified Arrhenius behavior post-crossover.

Showed beta relaxation continuity with different activation energy.

Abstract

In this paper, a recently developed numerical technique [{\em Tuncer E and Guba{\'n}ski S M, IEEE Trans Diel El Insul {\bf 8}(3)(2001) 310-320}] is applied to poly(propylene glycol) complex dielectric data to extract more information about the molecular relaxation processes. The method is based on a constrained-least-squares (\clsq) data fitting procedure together with the Monte Carlo (\mc) method. We preselect the number of relaxation times with no {\em a-priori} physical assumption, and use the Debye single relaxation as ``kernel'', then the obtained weighting factors at each \mc step from the \clsq method builds up a relaxation time spectrum. When the analysis is repeated for data at different temperatures a {\em relaxation-image} is created. The obtained relaxation are analyzed using the Lorentz (Cauchy) distribution, which is a special form of the L{\'e}vy statistics. In the present report the $\beta$ and $\alpha$ relaxations are resolved for the \ppg. A comparison of the relaxations to those earlier reported in the literature indicate that the presented method provides additional information compared to methods based on empirical formulas. The distribution of relaxation times analysis is especially useful to probe the crossover region where the $\alpha$- and $\beta$- relaxations merge and the results show that the relaxation after the crossover region at higher temperatures is Arrhenius-type as the $\beta$-relaxation. Moreover, this relaxation is more likely to be the continuation of the $\beta$-relaxation, but with a different activation energy.