# Theory for Glassy Behavior of Supercooled Liquid Mixtures

## TL;DR

This paper develops a dynamical facilitation-based model to predict the relaxation behavior and glass transition temperatures of supercooled liquid mixtures, moving beyond empirical interpolation methods.

## Contribution

It introduces a multi-component kinetically constrained model that captures mixture dynamics and predicts relaxation times using a single effective energy scale.

## Key findings

- Experimental relaxation times collapse onto the parabolic law.
- Model accurately predicts glass transition temperatures of mixtures.
- Provides a physical basis for mixture behavior beyond empirical models.

## Abstract

We present a model for glassy dynamics in supercooled liquid mixtures. Given the relaxation behavior of individual supercooled liquids, the model predicts the relaxation times of their mixtures as temperature is decreased. The model is based on dynamical facilitation theory for glassy dynamics, which provides a physical basis for relaxation and vitrification of a supercooled liquid. This is in contrast to empirical linear interpolations such as the Gordon-Taylor equation typically used to predict glass transition temperatures of liquid mixtures. To understand the behavior of supercooled liquid mixtures we consider a multi-component variant of the kinetically constrained East model in which components have a different energy scale and can also diffuse when locally mobile regions, i.e., excitations, are present. Using a variational approach we determine an effective single component model with a single effective energy scale that best approximates a mixture. When scaled by this single effective energy, we show that experimental relaxation times of many liquid mixtures all collapse onto the 'parabolic law' predicted by dynamical facilitation theory. The model can be used to predict transport properties and glass transition temperatures of mixtures of glassy materials, with implications in atmospheric chemistry, biology, and pharmaceuticals.