Adsorption of Lennard−Jones Molecules on a Hard Wall: A Case Study in the Star-Function Based Density Functional Theory

Abstract

For conventional density functional theories (DFTs), the mean-field perturbation theory was commonly invoked to evaluate the excess free energy due to attractions in the bulk fluid of an inhomogeneous system. This simplification caused inaccuracies in the predictions. We develop here a version of the DFT based on the functional Taylor expansions of the intrinsic free energy functional F[ρ] and the singlet density ρ(1)(r) to arrive at closed-form expressions for these quantities without truncations. This is made possible by incorporating the bridge functional and a “star function” proposed earlier in J. Chem. Phys. 1992, 97, 8606. The results are generally applicable to both repulsive and attractive potentials. The new formulation is applied to the Lennard−Jones molecules adsorbed on a planar hard wall. It is demonstrated that without using the mean-field approximation, we can obtain accurate density profiles for this system. A “two-way street” formulation between the uniform fluids and the nonuniform fluids is established via Percus’s concept of the “source particle” (or the test particle) approach that enables the transference of successful homogeneous liquid-theory quantities and procedures to the nonuniform systems, such as the zero-separation closure for the bridge functions. The proposed DFT is formally exact (without approximations), general (applicable to repulsive as well as attractive pair potentials), and complete (without truncations). A pair of mutually consistent equations for the free energy F[ρ] and the singlet density ρ(1)(r) result from this marriage. Prospects of application to Yukawa potentials in colloidal chemistry and Coulomb potentials in electrical double layers of electrochemistry are envisioned.