1202.4276 (L. L. Lee et al.)

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

L. L. Lee, G. Pellicane

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.

View original: http://arxiv.org/abs/1202.4276