On the hard sphere plus attractive mean field approximation for inhomogeneous fluids

As many theories for inhomogeneous fluids use a mean field approximation for the attractive intermolecular forces the thermodynamic consequences of this approximation are investigated for the homogeneous phases and the saturation curve of the Lennard-Jones fluid. The pressure at a given density is reasonably accurate for the gas but considerably too high for the liquid; the consequences for the density at a given chemical potential are discussed. The bubble densities are generally too low by more than 10 per cent, the dew-line is too steep, and the critical temperature is kT/ϵ = 1·412. Moreover, a coarse graining prescription introduced earlier into the Born-Green-Yvon equation is tested for hard spheres near a hard wall. The density profiles are qualitatively correct but the layering is not pronounced enough. We also prove that for hard spheres near a hard wall the sum rule n(0) = p/kT is true for a wide class of approximations to the Born-Green-Yvon equation.