Correlations between vibrational entropy and dynamics in super-cooled liquids

TL;DR

This paper explores the relationship between vibrational entropy and particle dynamics in super-cooled liquids, highlighting the role of the Boson Peak and its temperature-dependent changes in understanding glass transition phenomena.

Contribution

It derives a relation linking vibrational entropy and mean square displacement, incorporating Boson Peak effects, and connects these to fragility and the Kauzmann temperature.

Findings

Vibrational entropy correlates with mean square displacement in super-cooled liquids.

The Boson Peak's evolution influences the dynamical arrest and fragility.

Small vibrational entropy jumps in strong liquids increase with fragility.

Abstract

A relation between vibrational entropy and particles mean square displacement is derived in super-cooled liquids, assuming that the main effect of temperature changes is to rescale the vibrational spectrum. Deviations from this relation, in particular due to the presence of a Boson Peak whose shape and frequency changes with temperature, are estimated. Using observations of the short-time dynamics in liquids of various fragility, it is argued that (i) if the crystal entropy is significantly smaller than the liquid entropy at $T_g$, the extrapolation of the vibrational entropy leads to the correlation $T_K\approx T_0$, where $T_K$ is the Kauzmann temperature and $T_0$ is the temperature extracted from the Vogel-Fulcher fit of the viscosity. (ii) The jump in specific heat associated with vibrational entropy is very small for strong liquids, and increases with fragility. The analysis suggests that these correlations stem from the stiffening of the Boson Peak under cooling, underlying the importance of this phenomenon on the dynamical arrest.