Generalized van der Waals theory. VII. Interface profiles and surface tension

Abstract

An equilibrium theory of fluids based on a simple free-energy density functional developed and tested in several preceding articles is here applied to estimate the shape and surface tension of a gas/liquid interface in a simple LJ(12-6) fluid. The calculation is carried out at several different levels of approximation. In the simplest case when a step function profile is assumed the surface tension is obtained analytically. It is too high by about 50%. By using a moment expansion of the nonlocal free energy functional, the surface tension can be reduced to a simple one-dimensional integral. The result is now only slightly high. Finally, a variational calculation assuming a tanh form for the profile has been carried out. The effect of nonlocal entropy is examined and found to cause a drop in the surface tension by 5-10%. The results for the surface tension and width of the profile are in good agreement with experiment and simulation (deviation c. 0%) when plotted against T/T_c.