Condensed Matter Physics, 2011, vol. 14, No. 3, 33601: 115
DOI:10.5488/CMP.14.33601
arXiv:1202.4276
Title:
Adsorption of hard spheres: structure and effective density according to the potential distribution theorem
Author(s):

L.L. Lee
(Department of Chemical \& Materials Engineering, California State University, Pomona, California, USA )
,


G. Pellicane
(School of Physics, University of KwazuluNatal, Private Bag X01 Scottsville, 3209 Pietermaritzburg, South Africa )

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 pseudodensities are constructed thusly so that when their values are substituted into a uniformfluid equation of state (e.g. the CarnahanStarling equation for the hardsphere chemical potentials), the MC nonuniform insertion work is reproduced. We characterize the pseudodensity 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 pseudodensities show oscillatory behavior out of phase (opposite) to that of the singlet densities. We also construct a new closurebased density functional theory (the starfunction 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.
Key words:
potential distribution theorem, hard spheres, adsorption, effective density, structure, integral equation, closure
PACS:
68.43.De
