Ordering of oblate hard particles between symmetric penetrable walls

We find the structure of a model discotic liquid crystal (DLC) confined between symmetric walls of controllable penetrability. The model consists of oblate hard Gaussian overlap (HGO) particles. Particle-substrate interactions are modelled as follows: each substrate sees a particle as a disc of zero thickness and diameter (Formula presented.) less than or equal to that of the actual particle, (Formula presented.), embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This allows us to control the anchoring properties of the substrates, from planar (edge-on) for (Formula presented.) to homeotropic (face-on) for (Formula presented.). This system is investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager’s second-virial approximation with Parsons-Lee rescaling. We find that the agreement between theory and simulation is substantially less good than for prolate HGOs; in particular, the crossover from edge-on to face-on alignment is predicted by theory to occur at (Formula presented.), but simulation finds it for (Formula presented.). These discrepancies are likely a consequence of the fact that Onsager’s theory is less accurate for discs than for rods. We quantify this by computing the bulk isotropic-nematic phase diagram of oblate HGOs.