Configurational entropy of polydisperse supercooled liquids

TL;DR

This paper introduces a computational method to accurately measure the configurational entropy in polydisperse glass-formers, addressing issues caused by continuous size distributions and improving upon existing free energy techniques.

Contribution

A novel method extending the Frenkel-Ladd approach to include particle diameter permutations, resolving divergence issues in mixing entropy for polydisperse systems.

Findings

Successfully measures configurational entropy in polydisperse systems

Automatically accounts for mixing entropy without divergence

Simplifies the computation compared to previous methods

Abstract

We propose a computational method to measure the configurational entropy in generic polydisperse glass-formers. In particular, our method resolves issues related to the diverging mixing entropy term due to a continuous polydispersity. The configurational entropy is measured as the difference between the well-defined fluid entropy and a more problematic glass entropy. We show that the glass entropy can be computed by a simple generalisation of the Frenkel-Ladd thermodynamic integration method, which includes permutations of the particle diameters. This approach automatically provides a physically meaningful mixing entropy, and includes contributions that are not purely vibrational. The proposed configurational entropy is thus devoid of conceptual and technical difficulties due to continuous polydispersity, while being conceptually closer and technically simpler than alternative free energy approaches.