Adsorption of Hard Spheres: Development of a Re-Summed Bridge Function Theory for the Structures and Work of Insertion At Moderate to High Densities (ρ0 = 0. 5745 ~ 0.9135)

We propose a star-function bases density functional theory* for accurate determination of the density profiles in the hard sphere/hard wall adsorptive system.  We transform the Euler-Lagrange equation into an equivalent bridge-function based equation. The bridge function is analyzed in terms of a functional Taylor expansion and the terms in the infinite expansion are re-summed into a closed expression** for calculation. This new closure is tested on the simple system of hard spheres.  Results for bulk densities varying from ρ₀ = 0. 5745 ~ 0.9135 are compared with Monte Carlo data and very close agreement is obtained.  The exact sum rule of wall density is incorporated into the closure.  We also characterize the insertion work function W(z) (work required to insert a test particle into the fluid at position z away from the wall) as the density varies.  Comparison is made with other theories on the hard sphere fluids.

*..            Lee L. L.,  J. Chem. Eng. Data, 2010, 55, 1897.

**..         Lee L. L.,   Pellicane G., Chapman W.G., J. Supercritical Fluids 2010,  55, 524.