The Lennard-Jones 9:3 adsorptive system I: The Percus–Yevick and hypernetted chain theories and their modifications

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Abstract
The growing adsorbent molecule model is solved for the Lennard‐Jones 9:3 wall/Lennard‐Jones 12:6 fluid system using the Percus–Yevick and hypernetted chain closures. Both low density (ρ*=0.06707) and high density (ρ*=0.65) cases are examined. Comparison with Monte Carlo simulations of Rowley et al. and Abraham et al. is made. Due to the Henderson–Abraham–Baker formulation, it is possible to obtain the direct correlation function, C′12 (z), inside the wall. Its behavior is exhibited. At low densities, HNC and PY results are close to each other at high temperatures, but differences appear at low temperatures where HNC density profile exhibits more pronounced structure. Surface properties for the argon–graphite adsorptive system, such as the surface energy, excess number, and surface pressure, are calculated. The PY results seem to be more accurate in comparison with the Monte Carlo values. At higher densities, two modified PY and HNC theories are presented, called the ’’enhanced’’ PY theory (EPY) and the enhanced HNC theory (EHNC). The EHNC theory gives better description of the wall density profile than the EPY theory. They are recognized as the lowest (zeroth) order terms in an inhomogeneous system perturbation theory.

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