Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan.
Institute for Computational Science, University of Zürich, 8057 Zürich, Switzerland.
J Chem Phys. 2014 May 21;140(19):194310. doi: 10.1063/1.4875803.
Recent very large molecular dynamics simulations of homogeneous nucleation with (1 - 8) × 10(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'/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.
最近，通过（1-8）×10(9)个 Lennard-Jones 原子进行的均相成核的非常大的分子动力学模拟[J. Diemand, R. Angélil, K. K. Tanaka 和 H. Tanaka, J. Chem. Phys. 139, 074309 (2013)]使我们能够准确地确定在广泛的团簇尺寸范围内的团簇形成自由能。现在之所以能够实现，是因为这样的大规模模拟允许非常精确地测量在稳态成核区域中的团簇尺寸分布。自由能曲线的峰值给出了临界团簇尺寸，这与基于成核定理的独立估计很好地吻合。利用这些结果，我们推导出了成核率的分析公式和新的标度关系：ln J'/η 按 ln S/η 进行标度，其中过饱和度比为 S，η 是无维表面能，J(')是无维成核率。该关系可以使用平衡时的团簇形成自由能来推导，这对应于形成气液界面所需的表面能。在低温（低于三相点）下，我们发现表面能除以经典成核理论的表面能不依赖于温度，这导致了标度关系，并意味着常数，正 Tolman 长度等于液相中粒子间平均距离的一半。
