Ultraconfined oblate hard particles between hybrid penetrable walls

We have investigated, by Monte Carlo simulation, the orientational structure of very thin films of a discotic liquid crystal (DLC) confined between hybrid walls of controllable penetrability, as a function of wall separation L_{z}. Our purpose was to clarify whether, as predicted by continuum theory, the preferred orientation of the DLC is uniform, changes linearly, or changes discontinuously, when L_{z} and the anchoring strengths at either wall are changed. The model consists of oblate hard Gaussian overlap (HGO) particles: each wall sees a particle as a disk of zero thickness and diameter D less than or equal to that of the actual particle σ_{0}, embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This provides a particle-level mechanism to control the anchoring properties of the walls, from planar (edge-on) for D∼0 to homeotropic (face-on) for D∼σ_{0}, which can be done independently at either wall. As in our earlier work [C. Anquetil-Deck et al., J. Phys. Chem. B 124, 7709 (2020)1520-610610.1021/acs.jpcb.0c05027], which was restricted to L_{z}=6σ_{0}, depending on the values of D_{s}≡D/σ_{0} at the top (D_{s}^{t}) and bottom (D_{s}^{b}) walls, we find domains in (D_{s}^{b},D_{s}^{t}) space in which particle alignment is uniform planar (UP), uniform homeotropic (UH), or varies linearly from planar at one wall to homeotropic at the other (L), but no bistable or tristable regions are identified between these domains. Most importantly, there appears never to occur an abrupt change of the LC orientation when the walls strongly favor different anchorings, in general agreement with the scenario proposed by Velasco and co-workers [D. de las Heras et al., Phys. Rev. E 79, 011712 (2009)1539-375510.1103/PhysRevE.79.011712], but in contrast to the behavior of equivalent calamitic systems [F. Barmes et al., Phys. Rev. E 69, 061705 (2004)1539-375510.1103/PhysRevE.69.061705; Phys. Rev. E, 71, 021705 (2005)1539-375510.1103/PhysRevE.71.021705; C. Anquetil-Deck et al., Phys. Rev. E 86, 041707 (2012)1539-375510.1103/PhysRevE.86.041707]. However, for the thinnest films investigated (L_{z}=2σ_{0}), the system is unable to accommodate a rotation of the preferred particle orientation from one wall to the other and adopts instead a tilted configuration, similar to that reported earlier for Gay-Berne films in symmetric confinement [T. Gruhn et al., Thin Solid Films 330, 46 (1998)0040-609010.1016/S0040-6090(98)00799-8; Mol. Phys. 93, 681 (1998)10.1080/002689798169014] but which, as far as we know, has been missed in most earlier work.