Free-energy theory of inhomogeneous fluids

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Abstract
Two different free-energy theories of inhomogeneous fluids have been developed recently. One, the modified Van der Waals theory, requires as input the pair potential and the Helmholtz free-energy density and pair-correlation function of the homogeneous fluid. The other, the approximate density-functional theory, requires the Helmholtz free-energy density and direct-correlation function of the homogeneous fluid. Although formally different, it is shown in this paper that for a liquid-vapor interface in a 6-12 Lennard-Jones fluid they predict similar surface tensions (within 12% of one another) and density profiles. The gradient approximations are a little wider and the tensions about 15% higher than those of the corresponding integral theories. The integral versions are solved variationally with a trial function shown to be accurate by comparison of the exact solutions of the gradient approximations to the variational solutions of the same.

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