  The effect of out-of-plane orientational freedom on the orientational
ordering properties of a monolayer of hard ellipsoids is studied using
Parsons-Lee scaling approach and replica exchange Monte Carlo computer
simulation. Prolate and oblate ellipsoids exhibit very different ordering
properties, namely, the axes of revolution of prolate particles tend to lean
out, while those of oblate ones prefer to lean into the confining plane. The
driving mechanism of this is that the particles try to maximize the available
free area on the confining surface, which can be achieved by minimizing the
cross section areas of the particles with the plane. In the lack out-of-plane
orientational freedom the monolayer of prolate particles is identical to a
two-dimensional hard ellipse system, which undergoes an isotropic-nematic
ordering transition with increasing density. With gradually switching on the
out-of-plane orientational freedom the prolate particles lean out from the
confining plane and a destabilisation of the in-plane isotropic-nematic phase
transition is observed. The system of oblate particles behaves oppositely to
that of prolates. It corresponds to a two-dimensional system of hard disks in
the lack of out-of-plane freedom, while it behaves similar to that of hard
ellipses in the freely rotating case.
