Isotropic-nematic transition of hard ellipses

The orientational freezing of a system of hard ellipses, as a first approximation for a nematogen adsorbed on a smooth substrate, is studied with the aid of an approximate density-functional theory used previously for the study of hard ellipsoids. The isotropic-nematic transition, which was first order for the ellipsoids, is shown to proceed via a continuous transition in the case of the ellipses. We also show that when reducing the dimensionality of the angular space of ellipsoids, the width of the transition shrinks continuously and reaches zero only for a strictly two-dimensional angular space.