Generalized van der Waals theories for surface tension and interfacial width

Abstract

An exact relation between surface tension and the direct correlation function (DCF) for the inhomogeneous region is developed which may be viewed as an exact formulation of the van der Waals density gradient theory for inhomogeneous fluids. A reasonable approximation to the DCF is employed to obtain characteristic features of the interfacial density gradient over an extended temperature range. This theory predicts that the interfacial width increases as ${\text{(1−T/T}}_c{)}^{\text{−0.65}}$ at the ``low'' temperatures considered, and these results are in good agreement with the corresponding predictions of our earlier capillary wave treatment of interfaces. Comparison is also made with the predictions of an alternate, exact van der Waals‐like formulation which is obtained from the expression for surface tension in terms of the pair number density and the intermolecular force. A combination of the DCF formulation and the capillary wave theory provides the possibility of predicting both interfacial thicknesses and surface tension, a route also available from pair capillary wave theory. Numerical examples corresponding to argon at 90°K are given.