Generalized van der Waals theory. III. The prediction of hard sphere structure

This article is devoted to further development of the generalized van der Waals theory and its application to non-uniform hard sphere fluids. A coarse-graining assumption included in the original derivation is replaced by a weaker assumption recognizing the non-zero range of hard core interactions. The new fine-grained theory thus contains a non-local entropy functional and allows fluid structure on a length scale shorter than the hard core diameter to be resolved. Moreover, it contains a simplified representation of the mechanism leading to hard sphere structure due essentially to geometrical packing constraints. This is shown by application of the theory to hard sphere adsorption profiles in the case of a hard wall and to radial distribution functions of a hard sphere fluid. The amount of structure is underestimated partly due to the use of a density-independent excluded volume. It is shown that this flaw can be remedied by use of a hard- sphere entropy functional which successfully interpolates between the original high density estimate and the known behaviour in the low density limit.