Generalized van der Waals theory of hard sphere oscillatory structure

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Abstract
The recently developed generalized van der Waals (GvdW) theory, a free energy density functional theory based on cell theory and van der Waals approximations, is here applied to the prediction of hard sphere oscillatory structures at a hard wall, between two hard walls, and around a hard sphere. Three different functional forms of the crucial free volume factor are compared. The results confirm that the fine-grained GvdW theory containing a nonlocal entropy functional yields structures reproducing packing oscillations not only qualitatively but to quantitative accuracy. The error depends on the choice of free volume factor and can be made small except at high density where the range and magnitude of oscillations are overestimated. Evidence of early onset of a hard sphere freezing transition is seen.