Susceptibility functions for slow relaxation processes in supercooled liquids and the search for universal relaxation patterns

TL;DR

This paper introduces susceptibility functions and distribution models to describe slow relaxation in supercooled liquids, revealing universal patterns and the emergence of excess wings and beta-processes at specific correlation times.

Contribution

It develops the generalized gamma extension (GGE) distribution to accurately model dielectric spectra and identifies universal features in relaxation behaviors of glass formers.

Findings

Universal evolution of excess wing with cooling

Breakdown of high temperature mode coupling theory

Correlation times for beta-process emergence

Abstract

In order to describe the slow response of a glass former we discuss some distribution of correlation times, e.g., the generalized gamma distribution (GG) and an extension thereof (GGE), the latter allowing to reproduce a simple peak susceptibility such as of Cole-Davidson type as well as a susceptibility exhibiting an additional high frequency power law contribution (excess wing). Applying the GGE distribution to the dielectric spectra of glass formers exhibiting no beta-process peak (glycerol, propylene carbonate and picoline) we are able to reproduce the salient features of the slow response (1e-6 Hz - 1e9 Hz). A line shape analysis is carried out either in the time or frequency domain and in both cases an excess wing can be identified. The latter evolves in a universal way while cooling and shows up for correlation times tau_alpha > 1e-8 s. It appears that its first emergence marks the break down of the high temperature scenario of mode coupling theory. - In order to describe a glass former exhibiting a beta-process peak we have introduced a distribution function which is compatible with assuming a thermally activated process in contrast to some commonly used fit functions. Together with the GGE distribution this function allows in the frame of the Williams-Watts approach to completely interpolate the spectra, e.g. of fluoro aniline (1e-6 Hz - 1e9 Hz). The parameters obtained indicate an emergence of both the excess wing and the beta-process again at tau_alpha > 1e-8s.