Quantitative Theory of a Time-Correlation Function in a One-Component Glass-Forming Liquid with Anisotropic Potential

TL;DR

This paper develops a quantitative theory for the decay of time-correlation functions in a glass-forming liquid with anisotropic interactions, highlighting the separate roles of rotational and translational processes and their temperature dependencies.

Contribution

It introduces a detailed physical analysis separating rotational and translational decay channels, providing a quantitative match with simulations across temperatures.

Findings

Correlation functions exhibit stretched exponential decay with temperature-dependent beta.

Separate decay processes are temperature independent, but combined effects depend on temperature.

The theory underscores the importance of physical process analysis in understanding glassy relaxation.

Abstract

The Shintani-Tanaka model is a glass-forming system whose constituents interact via anisotropic potential depending on the angle of a unit vector carried by each particle. The decay of time-correlation functions of the unit vectors exhibits the characteristics of generic relaxation functions during glass transitions. In particular it exhibits a 'stretched exponential' form, with the stretching index beta depending strongly on the temperature. We construct a quantitative theory of this correlation function by analyzing all the physical processes that contribute to it, separating a rotational from a translational decay channel. Interestingly, the separate decay function of each of these processes is temperature independent. Taken together with temperature-dependent weights determined a-priori by statistical mechanics one generates the observed correlation function in quantitative agreement with simulations at different temperatures. This underlines the danger of concluding anything about glassy relaxation functions without detailed physical scrutiny.