TY - JOUR

T1 - Free energy of cluster formation and a new scaling relation for the nucleation rate

AU - Tanaka, Kyoko K.

AU - Diemand, Jürg

AU - Angélil, Raymond

AU - Tanaka, Hidekazu

PY - 2014/5/21

Y1 - 2014/5/21

N2 - 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: lnJ′/η is scaled by lnS/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.

AB - 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: lnJ′/η is scaled by lnS/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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U2 - 10.1063/1.4875803

DO - 10.1063/1.4875803

M3 - Article

AN - SCOPUS:84901496008

SN - 0021-9606

VL - 140

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 19

M1 - 194310

ER -