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 Gausssian Overlap (HGO) 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 the asssumed particles in 3D are forced to exhibit planar alignment. In the nematic as well as in the smectic regime particles situated apart from the walls attain homeotropic arrangement. This unusual bistable rearrangement is named as the eigenvalue exchange problem of the order parameter tensor. At the same time a bistable arrangement is not observed in the two-dimensional case of the same system. Comparison of the DFT theory and MC simulation results has been given. Whereas comparison of the orientational properties obtained from MC simulations and DFT theory is reasonable for a large range of densities, it does not concern the density profiles. In denser systems differences become larger. It occurred, however, that by manipulating degree of penetrability of the particles at the walls one can influence the surfacial density which improves comparison. A discussion upon the problem what factors promote simultaneous existence of planar and homeotropic arrangement in a confinement has been provided.