Lau Gabriel V, Ford Ian J, Hunt Patricia A, Müller Erich A, Jackson George
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.
Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, Gower Street, London WC1E 6BT, United Kingdom.
J Chem Phys. 2015 Mar 21;142(11):114701. doi: 10.1063/1.4913371.
The test-area (TA) perturbation approach has been gaining popularity as a methodology for the direct computation of the interfacial tension in molecular simulation. Though originally implemented for planar interfaces, the TA approach has also been used to analyze the interfacial properties of curved liquid interfaces. Here, we provide an interpretation of the TA method taking the view that it corresponds to the change in free energy under a transformation of the spatial metric for an affine distortion. By expressing the change in configurational energy of a molecular configuration as a Taylor expansion in the distortion parameter, compact relations are derived for the interfacial tension and its energetic and entropic components for three different geometries: planar, cylindrical, and spherical fluid interfaces. While the tensions of the planar and cylindrical geometries are characterized by first-order changes in the energy, that of the spherical interface depends on second-order contributions. We show that a greater statistical uncertainty is to be expected when calculating the thermodynamic properties of a spherical interface than for the planar and cylindrical cases, and the evaluation of the separate entropic and energetic contributions poses a greater computational challenge than the tension itself. The methodology is employed to determine the vapour-liquid interfacial tension of TIP4P/2005 water at 293 K by molecular dynamics simulation for planar, cylindrical, and spherical geometries. A weak peak in the curvature dependence of the tension is observed in the case of cylindrical threads of condensed liquid at a radius of about 8 Å, below which the tension is found to decrease again. In the case of spherical drops, a marked decrease in the tension from the planar limit is found for radii below ∼ 15 Å; there is no indication of a maximum in the tension with increasing curvature. The vapour-liquid interfacial tension tends towards the planar limit for large system sizes for both the cylindrical and spherical cases. Estimates of the entropic and energetic contributions are also evaluated for the planar and cylindrical geometries and their magnitudes are in line with the expectations of our simple analysis.
测试区域（TA）微扰方法作为一种在分子模拟中直接计算界面张力的方法，越来越受到关注。尽管最初是针对平面界面实现的，但TA方法也已用于分析弯曲液体界面的界面性质。在这里，我们对TA方法进行一种解释，认为它对应于仿射畸变下空间度量变换时自由能的变化。通过将分子构型的构型能量变化表示为畸变参数的泰勒展开式，我们推导出了三种不同几何形状（平面、圆柱和球形流体界面）的界面张力及其能量和熵分量的紧凑关系式。虽然平面和圆柱几何形状的张力由能量的一阶变化表征，但球形界面的张力取决于二阶贡献。我们表明，计算球形界面的热力学性质时，预计比平面和圆柱情况具有更大的统计不确定性，并且评估单独的熵和能量贡献比张力本身带来更大的计算挑战。该方法用于通过分子动力学模拟确定293K时TIP4P/2005水在平面、圆柱和球形几何形状下的气液界面张力。在半径约为8 Å的凝聚液圆柱线的情况下，观察到张力的曲率依赖性存在一个弱峰，在此半径以下，张力再次下降。在球形液滴的情况下，对于半径小于约15 Å的情况，发现张力从平面极限明显下降；没有迹象表明张力随曲率增加而出现最大值。对于圆柱和球形情况，气液界面张力在大系统尺寸时趋向于平面极限。还对平面和圆柱几何形状的熵和能量贡献进行了估计，其大小与我们简单分析的预期一致。
