On the parallel-perpendicular transition for a nematic phase at a wall

We use an Onsager-level density functional theory to investigate the behaviour of the nematic phase in contact with a solid wall. The nematic consists of hard rigid rods having perfect uniform alignment and uniform spatial density. In the absence of any particle-wall interactions besides excluded-volume forces, we predict a director orientation parallel to the wall. We show that this preference for parallel alignment is due to the entropy associated with the larger volume available to the particles in their parallel orientation. An adsorption energy favouring normal alignment gives rise to a transition from a high temperature parallel orientation to a low temperature normal orientation. We derive expressions for the temperature of this transition, relating it explicitly to the wall adsorption energy, particle axial ratio, and nematic density. Effects such as layering near the wall and imperfect nematic order are argued not to be necessary for the existence of this transition.