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

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 ρ * = 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.

The test-particle induced inhomogeneous direct correlation functions and extensions of Widom's theorem: Impacts on the incremental chemical potentials and high-order correlation functions

“…It has been shown that the ZSEP theory gives accurate structures and properties of hard spheres 23 that are dependable and with accuracies ascertained by simulation data from low to high densities (up to ρ * = 0.90). 17 In summary, for the triplet ln y (3) bca (ω) of contacting hard spheres, we use the MC data from Mueller and Gubbins (Option (a) above). For the pair ln y (2) ca (d)) at contact, we use the Carnahan-Starling equation, Eq.…”