Classical Density Functional Theory of Lennard-Jones Fluids: The Weighted-Density Approximation Revisited

Within the classical density functional theory of fluids, the weighted-density approximation for the excess functional is applied in its full original version. The simultaneous presence of repulsion and attraction in the solvent-solvent potential requires the generation of two sets of weights instead of one. In the first step, the density-dependent weight functions are derived from the direct pair correlation functions c in the pure solvent, covering the whole density range from dilute gas to dense liquid, extracted with numerical simulation data and integral equation techniques. At subcritical temperature, the a priori forbidden two-phase region is analyzed with a special treatment, which consists to first stabilize the fluid against phase separation with a small, long-range additional repulsion and then to recover the desired function c through the random phase approximation, valid in this situation. In the second step, various solutes are immersed in the solvent, and the solvent profiles are obtained by minimizing the full functional or equating to zero its gradient. The theory is illustrated here with Lennard-Jones atomic solvents around soft and hard spheres of various sizes, both in supercritical and subcritical conditions. When one approaches the coexistence line from the liquid region, the observed dewetting solvent profiles against cavities match almost perfectly the reference simulation profiles, numerically requiring only a few tens of seconds versus hours.