Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension

TL;DR

This paper integrates multiple numerical methods to comprehensively analyze the crystallization process of hard spheres, accurately calculating nucleation work, surface tension, and pressure differences across various regimes.

Contribution

It introduces a combined approach using three numerical methods to accurately determine nucleation work and interfacial tension in hard sphere crystallization.

Findings

Methods agree in overlapping regimes

Nucleation work spans three orders of magnitude

Bulk quantities are inaccurate for nucleation rate

Abstract

Combining three numerical methods (forward flux sampling, seeding of droplets, and finite size droplets), we probe the crystallization of hard spheres over the full range from close to coexistence to the spinodal regime. We show that all three methods allow to sample different regimes and agree perfectly in the ranges where they overlap. By combining the nucleation work calculated from forward flux sampling of small droplets and the nucleation theorem, we show how to compute the nucleation work spanning three orders of magnitude. Using a variation of the nucleation theorem, we show how to extract the pressure difference between the solid droplet and ambient liquid. Moreover, combining the nucleation work with the pressure difference allows us to calculate the interfacial tension of small droplets. Our results demonstrate that employing bulk quantities yields inaccurate results for the nucleation rate.