Extension of scaled particle theory to inhomogeneous hard particle fluids. I. Cavity growth at a hard wall

The methods of traditional scaled particle theory (SPT) are used to develop an extended scaled particle theory that is now applicable to hard particle fluids confined by hard walls. The new theory, labeled inhomogeneous SPT (I-SPT), introduces the function (G) over bar that describes the average value of the anisotropic density of hard particle centers contacting a cavity placed at or behind a hard wall. We present an exact relation describing (G) over bar for certain cavity sizes and, similar to the original SPT, an accurate interpolation scheme for larger cavity radii. Given (G) over bar, the reversible work of inserting a cavity centered at or behind the hard wall can be estimated. The work predictions at low to moderate packing fractions are extremely accurate, though small deviations from simulation results become apparent at packing fractions close to the bulk hard sphere freezing transition. I-SPT also reveals the importance of the line tension in determining the free energy of cavity formation for cavities intersecting a hard wall, a term which has been previously neglected. Furthermore, this paper provides the initial groundwork needed to develop a more complete SPT-based theory that can accurately predict the depletion force between a hard particle and a hard structureless wall.