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

Recent very large molecular dynamics simulations of homogeneous nucleation with (1 − 8) × 10{sup 9} Lennard-Jones atoms [J. Diemand, R. Angélil, K. K. Tanaka, and H. Tanaka, J. Chem. Phys. 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{sup ′}/η is scaled by ln S/η, where the supersaturation ratio is S, η is the dimensionless surface energy, and J{sup ′} 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 amore » constant, positive Tolman length equal to half of the mean inter-particle separation in the liquid phase.« less

Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819 (Japan)

Institute for Computational Science, University of Zürich, 8057 Zürich (Switzerland)

Publication Date:

OSTI Identifier:

22254853

Resource Type:

Journal Article

Resource Relation:

Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 19; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)