Phase behaviour of polydisperse spheres: simulation strategies and an application to the freezing transition

TL;DR

This paper investigates the phase behavior of polydisperse spheres, using advanced simulation and theoretical methods to accurately analyze the fluid-solid transition and particle fractionation effects.

Contribution

It introduces specialized Monte Carlo and moment free energy techniques that precisely handle fractionation in polydisperse systems, improving upon previous methods.

Findings

The coexistence region shifts to higher densities with increased polydispersity.

The coexistence region does not sharply narrow as predicted by some theories.

The properties of shadow phases are characterized across different polydispersity levels.

Abstract

The statistical mechanics of phase transitions in dense systems of polydisperse particles presents distinctive challenges to computer simulation and analytical theory alike. The core difficulty, namely dealing correctly with particle size fractionation between coexisting phases, is set out in the context of a critique of previous simulation work on such systems. Specialized Monte Carlo simulation techniques and moment free energy method calculations, capable of treating fractionation exactly, are then described and deployed to study the fluid-solid transition of an assembly of repulsive spherical particles described by a top-hat "parent" distribution of particle sizes. The cloud curve delineating the solid-fluid coexistence region is mapped as a function of the degree of polydispersity $\delta$, and the properties of the incipient "shadow" phases are presented. The coexistence region is found to shift to higher densities as $\delta$ increases, but does not exhibit the sharp narrowing predicted by many theories and some simulations.