MacDowell Luis G
Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense, Madrid 28040, Spain.
Phys Rev E. 2017 Aug;96(2-1):022801. doi: 10.1103/PhysRevE.96.022801. Epub 2017 Aug 15.
In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of the capillary wave spectrum obtained recently in computer simulations, and the predicted translation mode of surface fluctuations reproduces to linear order in field strength an exact solution of the density correlation function for the Landau-Ginzburg-Wilson Hamiltonian in an external field.
在本文中，我们试图在密度沿垂直于界面的线给定的假设下，详细推导微观理论对毛细波的影响。在这种近似下（从对称性论证角度看可能是合理的），密度分布的菲斯克 - 威多姆标度适用于界面轮廓的冻结实现。对毛细波涨落进行热平均后，所得密度分布产生的结果与单圈近似下的重整化群计算结果一致。毛细波的热平均可以用一种修正的卷积近似来表示，其中界面的法线呈高斯分布。在没有外场的情况下，我们表明应用于无平方梯度自由能泛函的唯象密度分布能精确恢复毛细波哈密顿量。我们将该理论扩展到吸附在基底上的液膜情况。对于具有短程力的系统，我们得到一个有效界面哈密顿量，其表面张力与膜高有关，这源于基底对液 - 气界面的扭曲，与费希尔 - 金的短程润湿理论一致。在存在长程相互作用的情况下，表面张力明确依赖于外场，并恢复了纳皮奥科夫斯基和迪特里希观察到的与波矢有关的对数贡献。使用本征密度分布的误差函数，我们得到了表面张力和界面宽度的封闭表达式。我们表明表面张力的外场贡献可以用膜的排斥压力来表示。从哈梅克常数的文献值发现，流体 - 基底力可能使纳米范围内薄膜的表面张力加倍。这里描述的表面张力对膜高的依赖性与最近计算机模拟中得到的毛细波谱结果完全一致，并且预测的表面涨落平移模式在场强的线性阶上再现了朗道 - 金兹堡 - 威尔逊哈密顿量在外部场中密度相关函数的精确解。
