Structure and Free Energy of the Interface between Fluid Phases in Equilibrium near the Critical Point

Abstract

The theory of van der Waals and of Cahn and Hilliard, which yields the density or concentration profile through an interface and the associated interfacial tension, is generalized by replacing the equation of state assumed originally by one that reproduces more accurately the known thermodynamic singularities at the critical point. Though the correct equation of state is not known, its presumed homogeneity of form is alone sufficient to allow most features of the interface to be determined explicitly. In particular, the maximum density gradient in the interface, the asymptotic behavior of the interface profile at large distances from the position of its maximum gradient, and the surface tension, are each obtained up to a dimensionless, and presumably universal, proportionality constant that reflects only the functional form of the equation of state. Numerical evaluation of the surface tension requires a knowledge of the limits approached by the correlation length and compressibility in the homogeneous fluid as the phase transition point is approached. These are only imperfectly known, so the surface tension calculated from the theory is subject to some uncertainty, but within its limits of uncertainty it is in agreement with experiment.