The Lennard-Jones 9:3 adsorptive system. II. Prediction of the liquid density profiles by perturbation theory

Abstract

To predict the density profiles of liquids adsorbed onto the Lennard-Jones 9:3 (LJ 9:3) wall, we derive here two new perturbation equations (called PYP and PYP1 equations) taking a simpler adsorptive system as reference. The derivation is based on the functional derivative formalism of Lebowitz and Percus for inhomogeneous systems. The generating functional is of Percus–Yevick (PY) type. The resulting expressions are first order theories. Previous known perturbation formulas, such as the blip function equation and the enhanced PY equation, are identified as special cases (zeroth order theories) of the present equations. Connections can also be made to the Ebner–Saam–Stroud density functional equation. Numerical calculations were carried out for liquid state adsorption of Lennard-Jones 12:6 molecules and hard spheres. Two types of perturbation are examined: (i) perturbation of the density profile from the hard spheres near a Weeks–Chandler–Andersen type repulsive wall to hard spheres near a Lennard-Jones 9:3 attractive wall, and (ii) perturbation of the density profile from hard spheres near a LJ 9:3 wall to Lennard-Jones 12:6 molecules near the LJ 9:3 wall. Comparison with Monte Carlo results shows that the PYP1 approach is the most satisfactory theory among all equations tested. The blip function results are inadequate for the attractive wall, while the PYP theory gives peculiar density profiles at intermediate distances despite good agreements at shorter and longer ranges.