Free energy of cluster formation and a new scaling relation for the nucleation rate

Abstract

Recent very large molecular dynamics simulations of homogeneous nucleation with $(1-8)\cdot 10^9$ Lennard-Jones atoms [Diemand et al. J. Chem. Phys. {\bf 139}, 074309 (2013)] allow us to accurately determine the formation free energy of clusters over a wide range of cluster sizes. This is now possible because such large simulations allow for very precise measurements of the cluster size distribution in the steady state nucleation regime. The peaks of the free energy curves give critical cluster sizes, which agree well with independent estimates based on the nucleation theorem. Using these results, we derive an analytical formula and a new scaling relation for nucleation rates: $\ln J^{\prime }/\eta$ is scaled by $\ln S/\eta$, where the supersaturation ratio is $S$, $\eta$ is the dimensionless surface energy, and $J^{\prime }$ is a dimensionless nucleation rate. This relation can be derived using the free energy of cluster formation at equilibrium which corresponds to the surface energy required to form the vapor-liquid interface. At low temperatures (below the triple point), we find that the surface energy divided by that of the classical nucleation theory does not depend on temperature, which leads to the scaling relation and implies a constant, positive Tolman length equal to half of the mean inter-particle separation in the liquid phase.

arXiv comment7 figures

References in corpus (7)

• Large Scale Molecular Dynamics Simulations of Homogeneous Nucleation
• Systematic Improvement of Classical Nucleation Theory
• Modification of the classical nucleation theory based on molecular simulation data for surface tension, critical nucleus size, and nucleation rate
• Molecular Dynamics Simulations of the Nucleation of Water: Determining the Sticking Probability and Formation Energy of a Cluster
• Shape and area fluctuation effects on nucleation theory
• Properties of Liquid Clusters in Large-scale Molecular Dynamics Nucleation Simulations
• Grand canonical steady-state simulation of nucleation

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• A Two-parameter Extension of Classical Nucleation Theory
• Canonical free-energy barrier of particle and polymer cluster formation
• Bubble Evolution and Properties in Homogeneous Nucleation Simulations
• Height of a faceted macrostep for sticky steps in a step-faceting zone
• Scaling law for crystal nucleation time in glasses
• Systematic Coarse-Graining in Nucleation Theory
• The seeding method: A test case for classical nucleation theory in small systems