MICROSCOPIC THEORIES OF CURVED LIQUID SURFACES

In this review we discuss the different expressions which have appeare d in the literature for the Tolman length (closely related to the spon taneous curvature), the rigidity constant of bending and the rigidity constant associated with Gaussian curvature of simple liquid surfaces. These three quantities appear as coefficients in an expansion of the surface free energy to second order in the curvature, where the zeroth order term (no curvature) is the surface tension of the planar interf ace. For the surface tension of the planar interface, sigma, four impo rtant types of expression are known: the mechanical expression which r elates the surface tension to the excess tangential pressure; the mean -field (van der Waals) expression, which expresses sigma in terms of t he density profile through the interface; the Triezenberg-Zwanzig form ula where sigma is given in terms of the direct correlation function, and the Kirkwood-Buff formula relating sigma to the pair density and t he interaction potential. Although the picture is still incomplete, al most all these different types of expression have been derived for the Tolman length and rigidity constants. We briefly discuss critiques re garding the expandability of the surface free energy in the curvature.