Abstract
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.
Highlights
Interfaces are omnipresent in real materials and understanding how systems behave at boundaries is key to technological control and manipulation at the smallest scales
We examine the interfacial properties of vapour-liquid interfaces by molecular dynamics simulation and examine the effect of different surface geometries on the vapour-liquid interfacial tension and related thermodynamic properties such as the energy and entropy associated with these interfaces
The change in energy ∆U(r) of a molecular configuration under a shift in the metric can be written as a Taylor expansion in a dimensionless parameter ε that characterizes the extent of the distortion
Summary
Interfaces are omnipresent in real materials and understanding how systems behave at boundaries is key to technological control and manipulation at the smallest scales. For a planar vapour-liquid interface, the change in free energy associated with a deformation in the interfacial area was shown to be fully characterized by the average of the change in configurational energy; this leadingorder contribution to the surface tension is found to be equivalent to that obtained with the mechanical relation (cf Eq (1)). Following an alternative thermodynamic approach, Joswiak et al. employed the mitosis method to evaluate the free energy associated with separating a liquid drop into a pair of smaller drops, providing an estimate of the vapour-liquid interfacial tension of drops of water for the TIP4P/2005 potential model These authors found that the vapour-liquid interfacial tension at ambient conditions (300 K) increased continuously from the planar limit of γ∞ = 65.5 mN m−1 (for the TIP4P/2005 model not including long-range corrections25) to γ ∼ 77 mN m−1 on decreasing the size of the nanodrop to a radius of R ∼ 6 Å.
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