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

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.

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Cited by in corpus (13)

• Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation
• Colloidal Hard Spheres: Triumphs, Challenges and Mysteries
• Studying Rare Events using Forward-Flux Sampling: Recent Breakthroughs and Future Outlook
• Interfacial free energy and Tolman length of curved liquid-solid interfaces from equilibrium studies
• Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension
• Classical Nucleation Theory for the Crystallization Kinetics in Sheared Liquids
• Thermodynamic stability of hard sphere crystals in dimensions 3 through 10
• Statistical mechanics of crystal nuclei of hard spheres
• A robust and memory-efficient transition state search method for complex energy landscapes
• Evidence and quantification of memory effects in competitive first passage events
• Calculation of Critical Nucleation Rates by the Persistent Embryo Method: Application to Quasi Hard Sphere Models
• The Impact of Hydration Shell Inclusion and Chain Exclusion in the Efficacy of Reaction Coordinates for Homogeneous and Heterogeneous Ice Nucleation
• Theory of Nonequilibrium Crystallization and the Phase Diagram of Active Brownian Spheres