Distribution of relaxation times in $\alpha$-phase polyvinylidene fluoride

TL;DR

This paper applies a novel non-parametric numerical method to analyze the distribution of relaxation times in the dielectric response of $eta$-phase PVDF, avoiding empirical formulas and providing a detailed relaxation map.

Contribution

It introduces a non-parametric numerical approach combining Monte Carlo and constrained least-squares methods for dielectric data analysis of PVDF.

Findings

The relaxation map of $eta$-phase PVDF was successfully constructed.

The method provides results comparable to traditional empirical formulas.

It offers a more flexible analysis without relying on empirical assumptions.

Abstract

In this paper, a recently developed numerical method to analyze dielectric-spectroscopy data is applied to $\alpha$-phase polyvinylidene fluoride (PVDF). The numerical procedure is non-parametric and does not contain any of the extensively used empirical formulas mentioned in the literature. The method basically recovers the unknown distribution of relaxation times of the generalized dielectric function representation by simultaneous application of the Monte Carlo integration method and of the constrained least-squares optimization. The relaxation map constructed after the numerical analysis is compared to $\alpha$-phase PVDF data presented in the literature and results of the parametric analysis with a well-known empirical formula.