Nematicliquid crystal order reconstruction in ultraconfinement, from density-functional theory

I use the Onsager approximation of density-functional theory with a simple Parsons-Lee re-scaling to study a hybrid-aligned liquid crystal under very strong confinement. The system is modelled as a film of hard Gaussian overlap particles in a slit geometry, where anchoring is planar at one wall and homeotropic at the other. As the film density is increased from the isotropic phase, a planar-disordered layer grows from the planar-anchoring wall, and a homeotropic layer from the homeotropic-anchoring wall. For film thicknesses between 2 and 7 particle lengths, the degree of overall nematic order as measured by the spatial average of TrQ(2) (where Q is the nematic order parameter tensor) is a continuously increasing function of the density, with a pronounced rise around the bulk isotropic-nematic transition. This rise is steeper the thicker the film, and is preceded by a large amount of biaxiality growing from the planar-anchoring wall. Deeper into the nematic phase, most of the film is either planar or homeotropic, but some biaxiality persists in a region of otherwise reduced overall nematic order whose position varies with film thickness.