Simple integral equation and density functional study of a hard sphere fluid in a pore formed by two hard walls

The structure of a hard sphere fluid in a pore formed by two parallel hard walls is studied as a function of the separation of the walls using the singlet theory of Henderson et al, and Lozada-Cassou with the Percus-Yevick (PY) and hypernetted chain (HNC) closures, which were studied previously, and a modified version of the Verlet (MV) closure. In addition, the density functional formalism of Tarazona et al. (TME) is employed. As noted earlier, the singlet theory yields poor results when the PY and HNC closures are used but yields quite good results when the MV closure is used. The TME approach also yields good results. The MV and singlet theory results are comparable in accuracy with those obtained from the second-order PY (PY2) theory but are much less demanding computationally.