Interaction free energy between planar walls in dense fluids: An Ornstein-Zernike approach with results for hard-sphere, Lennard-Jones, and dipolar systems

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Abstract
The interaction free energy per unit area between planar walls is given as a convolution of wall-solvent pair-correlation functions. This result, derived from the large radius limit of the macrosphere-solvent Ornstein-Zernike equations, and from the hypernetted-chain closure, provides a statistical-mechanical basis for the Derjaguin approximation, and is both generally applicable and computationally tractable. It is found that the interaction between hard walls in a hard-sphere fluid is oscillatory, and in good agreement with simulations. The van der Waals attraction emerges from asymptotic analyses of Lennard-Jones and dipolar fluids, and the full expression allows calculation of this quantity down to molecular separations. This is demonstrated by numerical results for dipolar fluids.