Finite size effects on liquid-solid phase coexistence and the estimation of crystal nucleation barriers

TL;DR

This paper investigates how finite system sizes influence the coexistence of liquid and solid phases and provides a method to estimate crystal nucleation barriers without detailed interface analysis, validated on a colloid-polymer mixture model.

Contribution

It introduces a novel approach to estimate nucleation barriers in finite systems without precise interface location or interfacial tension calculations.

Findings

Nucleation barriers are consistent with classical nucleation theory.

Method applicable to nuclei of arbitrary shape, assuming spherical symmetry.

Analysis validated on a colloid-polymer mixture model.

Abstract

A fluid in equilibrium in a finite volume $V$ with particle number $N$ at a density $\rho = N/V$ exceeding the onset density $\rho_f $ of freezing may exhibit phase coexistence between a crystalline nucleus and surrounding fluid. Using a method suitable for the estimation of the chemical potential of dense fluids we obtain the excess free energy due to the surface of the crystalline nucleus. There is neither a need to precisely locate the interface nor to compute the (anisotropic) interfacial tension. As a test case, a soft version of the Asakura-Oosawa model for colloid polymer-mixtures is treated. While our analysis is appropriate for crystal nuclei of arbitrary shape, we find the nucleation barrier to be compatible with a spherical shape, and consistent with classical nucleation theory.