Statistical mechanical theory for nonuniform fluids: Properties of the hard-sphere system and a perturbation theory for nonuniform simple fluids

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Abstract
We present a formal theory for the statistical mechanics of a nonuniform classical fluid and apply it to the hard‐sphere fluid using the Wertheim–Thiele solution for the direct correlation function in the Percus–Yevick approximation. With a knowledge of the nonuniform hard‐sphere fluid results, we develop a perturbation theory of nonuniform simple fluids motivated by the Weeks, Chandler, Andersen perturbation theory of uniform fluids. Using our perturbation theory, the properties of a Lennard‐Jones liquid–vapor interface are calculated and compared with recent numerical experiments near the triple point. We find excellent agreement. Comparisons with other formulations are made, and the agreement is not so good.