Integral equation theory of a one dimensional hard-ellipse fluid between hard walls

Density functional theory is used to study the structure of a one dimensional fluid model of hard-ellipse molecules with their axes freely rotating in a plane, confined between hard walls. A simple Hypernetted chain (HNC) approximation is used for the density functional of the fluid and the integral equation for the density is obtained from the grand potential. The only required input is the direct correlation function of the one dimensional hard-ellipse fluid. For this model, the pressure, sum rule and the density at the walls are obtained. The Percus Yevick (PY), for lower density, and HNC, for higher density, integral equations are also solved to obtain the direct correlation function of hard-ellipse model introduced here. We obtain the average density at the wall as well as the radial density profile. We compare these with Monte Carlo simulations of the same model and find reasonable agreement.