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


Tanaka, Kyoko K; Diemand, Jürg; Angélil, Raymond; Tanaka, Hidekazu (2014). Free energy of cluster formation and a new scaling relation for the nucleation rate. Journal of Chemical Physics, 140(19):194310.

Abstract

Recent very large molecular dynamics simulations of homogeneous nucleation with (1 - 8) × 109 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'/η is scaled by ln S/η, where the supersaturation ratio is S, η is the dimensionless surface energy, and J' 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.

Abstract

Recent very large molecular dynamics simulations of homogeneous nucleation with (1 - 8) × 109 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'/η is scaled by ln S/η, where the supersaturation ratio is S, η is the dimensionless surface energy, and J' 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.

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Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute for Computational Science
Dewey Decimal Classification:530 Physics
Language:English
Date:May 2014
Deposited On:30 Sep 2014 12:46
Last Modified:08 Dec 2017 07:11
Publisher:American Institute of Physics
ISSN:0021-9606
Additional Information:Copyright 2014 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Free energy of cluster formation and a new scaling relation for the nucleation rate and may be found at http://scitation.aip.org/content/aip/journal/jcp/140/19/10.1063/1.4875803
Publisher DOI:https://doi.org/10.1063/1.4875803

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