Tröster Andreas, Schmitz Fabian, Virnau Peter, Binder Kurt
Institute of Materials Chemistry , Vienna University of Technology , Getreidemarkt 9 , A-1060 Wien , Austria.
Institut für Physik , Johannes Gutenberg-Universität Mainz , Staudinger Weg 9 , D-55099 Mainz , Germany.
J Phys Chem B. 2018 Apr 5;122(13):3407-3417. doi: 10.1021/acs.jpcb.7b10392. Epub 2018 Jan 10.
In a theoretical description of homogeneous nucleation one frequently assumes an "equilibrium" coexistence of a liquid droplet with surrounding vapor of a density exceeding that of a saturated vapor at bulk vapor-liquid two-phase coexistence. Thereby one ignores the caveat that in the thermodynamic limit, for which the vapor would be called supersaturated, such states will at best be metastable with finite lifetime, and thus not be well-defined within equilibrium statistical mechanics. In contrast, in a system of finite volume stable equilibrium coexistence of droplet and supersaturated vapor at constant total density is perfectly possible, and numerical analysis of equilibrium free energies of finite systems allows to obtain physically relevant results. In particular, such an analysis can be used to derive the dependence of the droplet surface tension γ( R) on the droplet radius R by computer simulations. Unfortunately, however, the precision of the results produced by this approach turns out to be seriously affected by a hitherto unexplained spurious dependence of γ( R) on the total volume V of the simulation box. These finite size effects are studied here for the standard Ising/lattice gas model in d = 2 dimensions and an Ising model on the face-centered cubic lattice with 3-spin interaction, lacking symmetry between vapor and liquid phases. There also the analogous case of bubbles surrounded by undersaturated liquid is treated. It is argued that (at least a large part of) the finite size effects result from the translation entropy of the droplet or bubble in the system. This effect has been shown earlier to occur also for planar interfaces for simulations in the slab geometry. Consequences for the estimation of the Tolman length are briefly discussed. In particular, we find clear evidence that in d = 2 the leading correction of the curvature-dependent interface tension is a logarithmic term, compatible with theoretical expectations, and we show that then the standard Tolman-style analysis is inapplicable.
在对均匀成核的理论描述中，人们常常假定液滴与周围蒸汽“平衡”共存，其蒸汽密度超过在体相气 - 液两相共存时饱和蒸汽的密度。由此，人们忽略了这样一个警告：在热力学极限下，此时蒸汽被称为过饱和蒸汽，这样的状态至多是具有有限寿命的亚稳态，因此在平衡统计力学中并非明确界定的状态。相反，在有限体积的系统中，液滴与过饱和蒸汽在恒定总密度下的稳定平衡共存是完全可能的，对有限系统平衡自由能的数值分析能够得出物理上相关的结果。特别地，这样的分析可用于通过计算机模拟得出液滴表面张力γ(R)对液滴半径R的依赖关系。然而，不幸的是，这种方法所产生结果的精度受到γ(R)对模拟盒总体积V的一种迄今未得到解释的虚假依赖的严重影响。本文针对二维d = 2的标准伊辛/晶格气体模型以及具有3自旋相互作用、气液两相缺乏对称性的面心立方晶格上的伊辛模型，研究了这些有限尺寸效应。这里还处理了被不饱和液体包围的气泡的类似情况。有人认为（至少很大一部分）有限尺寸效应源于系统中液滴或气泡的平移熵。这种效应先前已表明在平板几何结构的模拟中对于平面界面也会出现。简要讨论了对托尔曼长度估计的影响。特别地，我们发现明确的证据表明，在d = 2时，曲率相关界面张力的主导修正项是一个对数项，这与理论预期相符，并且我们表明此时标准的托尔曼式分析并不适用。
