Orientational Ordering in a Monolayer of Hard Oblate Spheroids

The Onsager theory of orientational ordering is applied to a monolayer of hard oblate spheroids. The spheroids are free to rotate, but their centers are confined to a plane. Order parameters and configurational free energy are calculated, within the Onsager theory. It is found that orientational ordering occurs in two steps, as density is increased from zero. First the spheroids' symmetry axes gradually tip into the plane. Then, in a second-order transition to a nematic phase, the spheroids' major axes align. The second transition shifts to lower density as spheroid eccentricity increases.