Adsorption of hard spheres: structure and effective density according to the potential distribution theorem

TL;DR

This paper introduces a new effective density concept based on the potential distribution theorem to accurately map free energy from uniform to nonuniform hard-sphere fluids, validated through Monte Carlo simulations and a novel density functional theory.

Contribution

It proposes a pseudo-density approach derived from the potential distribution theorem and develops a new closure-based density functional theory for hard sphere adsorption.

Findings

Pseudo-densities exhibit oscillatory behavior out of phase with singlet densities.

The new density functional theory accurately reproduces Monte Carlo density profiles.

The approach effectively characterizes hard sphere adsorption at various densities.

Abstract

We propose a new type of effective densities via the potential distribution theorem. These densities are for the sake of enabling the mapping of the free energy of a uniform fluid onto that of a nonuniform fluid. The potential distribution theorem gives the work required to insert a test particle into the bath molecules under the action of the external (wall) potential. This insertion work W_ins can be obtained from Monte Carlo (MC) simulation (e.g. from Widom's test particle technique) or from an analytical theory. The pseudo-densities are constructed thusly so that when their values are substituted into a uniform-fluid equation of state (e.g. the Carnahan-Starling equation for the hard-sphere chemical potentials), the MC nonuniform insertion work is reproduced. We characterize the pseudo-density behavior for the hard spheres/hard wall system at moderate to high densities (from \rho^*= 0.5745 to 0.9135). We adopt the MC data of Groot et al. for this purpose. The pseudo-densities show oscillatory behavior out of phase (opposite) to that of the singlet densities. We also construct a new closure-based density functional theory (the star-function based density functional theory) that can give accurate description of the MC density profiles and insertion works. A viable theory is established for several cases in hard sphere adsorption.