Vienna University of Technology, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, Austria.
J Chem Phys. 2012 Feb 14;136(6):064709. doi: 10.1063/1.3685221.
A recently proposed method to obtain the surface free energy σ(R) of spherical droplets and bubbles of fluids, using a thermodynamic analysis of two-phase coexistence in finite boxes at fixed total density, is reconsidered and extended. Building on a comprehensive review of the basic thermodynamic theory, it is shown that from this analysis one can extract both the equimolar radius R(e) as well as the radius R(s) of the surface of tension. Hence the free energy barrier that needs to be overcome in nucleation events where critical droplets and bubbles are formed can be reliably estimated for the range of radii that is of physical interest. It is found that the conventional theory of nucleation, where the interface tension of planar liquid-vapor interfaces is used to predict nucleation barriers, leads to a significant overestimation, and this failure is particularly large for bubbles. Furthermore, different routes to estimate the effective radius-dependent Tolman length δ(R(s)) from simulations in the canonical ensemble are discussed. Thus we obtain an instructive exemplification of the basic quantities and relations of the thermodynamic theory of metastable droplets/bubbles using simulations. However, the simulation results for δ(R(s)) employing a truncated Lennard-Jones system suffer to some extent from unexplained finite size effects, while no such finite size effects are found in corresponding density functional calculations. The numerical results are compatible with the expectation that δ(R(s) → ∞) is slightly negative and of the order of one tenth of a Lennard-Jones diameter, but much larger systems need to be simulated to allow more precise estimates of δ(R(s) → ∞).
最近提出了一种方法，通过在固定总密度的有限盒子中进行两相共存的热力学分析，来获得球形液滴和气泡的表面自由能σ(R)。本文重新考虑并扩展了这一方法。在对基本热力学理论进行全面回顾的基础上，结果表明，从这种分析中可以提取出等摩尔半径 R(e)以及张力表面的半径 R(s)。因此，可以可靠地估计在形成临界液滴和气泡的成核事件中需要克服的自由能势垒，对于物理上感兴趣的半径范围。结果发现，传统的成核理论，其中使用了平面液-气界面的界面张力来预测成核势垒，会导致显著的高估，而对于气泡，这种失败尤其大。此外，还讨论了从正则系综模拟中估计有效半径依赖的托马长度δ(R(s))的不同途径。因此，我们使用模拟对亚稳液滴/气泡的热力学理论的基本量和关系进行了有益的说明。然而，在截断的 Lennard-Jones 系统中使用模拟得到的δ(R(s))结果在某种程度上受到未解释的有限尺寸效应的影响，而在相应的密度泛函计算中则没有发现这种有限尺寸效应。数值结果与预期的结果一致，即δ(R(s)→∞)略为负，约为 Lennard-Jones 直径的十分之一，但需要模拟更大的系统才能允许对δ(R(s)→∞)进行更精确的估计。
