Barrett Jonathan C
Nuclear Department, DCEME, HMS Sultan, Military Road, Gosport PO12 3BY, United Kingdom.
J Chem Phys. 2006 Apr 14;124(14):144705. doi: 10.1063/1.2179425.
Density functional theory is used to calculate the surface tension of planar and slightly curved surfaces, which can be written as gamma(R)=gamma(infinity)(1-2delta(infinity)R), where R is the radius of curvature of the surface. Calculations are performed for a Lennard-Jones fluid, split into a hard-sphere repulsive potential and an attractive part. The repulsive part is treated using the local density approximation. The attractive part is treated using a high temperature approximation (HTA) in which the pair correlation function is approximated by the Percus-Yevick pair correlation function of a uniform hard-sphere fluid evaluated at a position-dependent average density. An expression relating the Tolman length delta(infinity) to the density profile of the planar surface is derived. Numerical results are presented for the planar surface tension gamma(infinity) and for delta(infinity) and are compared with those using mean field theory (MFT) and with those using the square-gradient approximation. Values for gamma(infinity) using the HTA are 30%-40% higher than those using MFT. Values for delta(infinity) using the HTA are around -0.1 (in units of the Lennard-Jones parameter sigma) and only weakly dependent on temperature. These values are less negative than the values from MFT. The square-gradient approximation gives reasonable estimates of the more accurate nonlocal results for both the MFT and the HTA.
密度泛函理论用于计算平面和微曲面的表面张力，其可写为γ(R)=γ(∞)(1 - 2δ(∞)/R)，其中R为曲面的曲率半径。对 Lennard-Jones 流体进行了计算，该流体分为硬球排斥势和吸引部分。排斥部分采用局域密度近似处理。吸引部分采用高温近似(HTA)处理，其中对关联函数由均匀硬球流体在位置相关的平均密度下评估的 Percus-Yevick 对关联函数近似。推导了 Tolman 长度δ(∞)与平面密度分布的关系式。给出了平面表面张力γ(∞)和δ(∞)的数值结果，并与使用平均场理论(MFT)和平方梯度近似得到的结果进行了比较。使用 HTA 得到的γ(∞)值比使用 MFT 得到的值高 30%-40%。使用 HTA 得到的δ(∞)值约为-0.1（以 Lennard-Jones 参数σ为单位），且仅微弱依赖于温度。这些值比 MFT 得到的值负性小。平方梯度近似对 MFT 和 HTA 更精确的非局部结果给出了合理估计。
