Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling

TL;DR

This paper develops and tests methods to extract the kinetics and free energy landscape of hard sphere crystallization from simulations, enabling analysis across various supersaturations without equilibrium sampling.

Contribution

It introduces two novel approaches to reconstruct free energy barriers from steady state distributions, validated through simulations and theoretical models.

Findings

Methods accurately reconstruct free energy barriers.

Results align with classical nucleation theory predictions.

Quantitative fits suggest a large effective interfacial tension.

Abstract

We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, the second on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow to probe a wide range of supersaturations, and to reconstruct the kinetics and the free energy landscape from the same simulation. Results are consistent with the scaling predicted by classical nucleation theory although a quantitative fit requires a rather large, effective interfacial tension.