Extending the simple weighted density approximation for a hard-sphere fluid to a Lennard-Jones fluid

A simple weighted density approximation (SWDA) was extended to nonuniform Lennard-Jones fluids by following the spirit of a partitioned density function theory [S. Zhou, Phys. Rev. E 68 (2003) 061201] and mapping the hard-core part onto an effective hard-sphere fluid whose higher order terms beyond the second order of the functional perturbation expansion are treated by the SWDA. The resultant DFT formalism performs well for Lennard-Jones fluids under the influence of diverse external fields. With the present DFT formalism, we investigate in detail the structure and adsorption properties of a low-density LJ gas in a spherical cavity with a wall consisting of hard-sphere or LJ particles. It was found that when the cavity wall exerts an attractive external potential on the LJ particles in the cavity, the excess adsorption decreases as the temperature increases, while when the cavity wall exerts a hard repulsive external potential on the LJ particles in the cavity, the excess adsorption increases as the temperature increases.