Density profile of hard spheres interacting with a hard wall

On the virial expansion of model adsorptive systems

We investigate the thermodynamic properties of various super-critical model adsorptive systems with different fluid-solid attractive strengths using the confined-density virial expansion, with coefficients calculated using the Mayer-sampling Monte Carlo method up to fifth order. We find that the virial expansion converges for adsorptive systems over a density range corresponding approximately to the film-formation regime. Beyond this regime, higher order effects become increasingly important. The virial expansion of the density profile is also investigated. It is determined that this expansion gives insight into the structure associated with adsorption. We also find that weakly attractive systems have a more negative second virial coefficient than strongly attractive systems. This runs counter to the usual interpretation of bulk fluid virial coefficients. This is due to the infinite-dilution limit being very different for adsorbed fluids compared to bulk fluids.

Pair correlation function in a fluid with density inhomogeneities: parametrization for hard spheres near a hard wall

The pair correlation function, g( z 1 , z 2 , r 12 ), of a system of hard spheres near a hard wall is approximated by a simple function that interpolates in a reasonable manner between the Percus shielding approximation for the case when the line of centres of the spheres is normal to the surface of the wall and the bulk pair correlation function, with a semi-empirical modification, for the case when the spheres are equidistant from the wall. This modification is chosen so that the surface tension, calculated from the pair correlation function, is given correctly. The resulting pair correlation function is in good agreement with computer simulations and satisfies a sum rule for the slope of the density profile fairly well.