Orientational properties of the HGO system in a slit geometry in two-dimensional and three-dimensional case from Monte-Carlo simulations and Onsager theory revisited

A problem of the orientational and density structure properties of a confined three-dimensional (3D) and two-dimensional (2D) hard Gaussian overlap ellipsoids has been revisited using the Onsager-type second virial approximation of density functional theory (DFT) and constant-pressure Monte-Carlo (MC) simulations. At the walls, particles are forced to exhibit planar alignment. We focus on the solution, where, at the same time, the particles situated apart from the walls attain perpendicular to the wall arrangement. This effect is known as the eigenvalue exchange effect (EEE) of the order parameter tensor and is not observed in 2D case of the same system. The comparison of the DFT theory and MC simulation results has been given. Whereas it is reasonable for the middle parts of the samples, at the surficial regimes, one observes differences in the density and orientational profiles. It occurs that by manipulating the penetrability of the particles at the walls in the DFT theory, one can influence the surficial density in such a way that the DFT outcome becomes very close to the MC results. The DFT analysis provides an argument on the stability of the presented EEE solution in comparison to the particles arrangement parallel to the walls.