We present a study of the effects of nano-confinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring while the other favours either weakly homeotropic or planar anchoring. These systems are 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. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. Theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

A theoretical analysis is presented of a nematic liquid crystal confined between substrates patterned with squares that promote vertical and planar alignment. Two approaches are used to elucidate the behavior across a wide range of length scales: Monte Carlo simulation of hard particles and Frank-Oseen continuum theory. Both approaches predict bistable degenerate azimuthal alignment in the bulk along the edges of the squares; the continuum calculation additionally reveals the possibility of an anchoring transition to diagonal alignment if the polar anchoring energy associated with the pattern is sufficiently weak. Unlike the striped systems previously analyzed, the Monte Carlo simulations suggest that there is no "bridging" transition for sufficiently thin cells. The extent to which these geometrically patterned systems resemble topographically patterned substrates, such as square wells, is also discussed.

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 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 allows us to control the anchoring properties of the substrates, from planar (edge-on) for D ∼ 0 to homeotropic (face-on) for D ∼ σ 0 . This system is investigated using both Monte Carlo simulation and densityfunctional 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 D ∼ 0.65σ 0 , but simulation finds it for D ∼ 0.55σ 0 . 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.

Here, we use molecular simulation to consider the behaviour of a thin nematic film confined between two identical nano-patterned substrates. Using patterns involving alternating stripes of homeotropic-favouring and homogeneous-favouring substrate, we investigate the influence of the relative stripe width and the film thickness. From this, we show that the polar anchoring angle can be varied continuously from planar to homeotropic by appropriate tuning of these parameters. For very thin films with equal stripe widths, we observe orientational bridging, the surface patterning being written in domains which traverse the nematic film. This dual-bridging-domain arrangement breaks down with increase in film thickness, however, being replaced by a single tilted monodomain. Strong azimutahl anchoring in the plane of the stripe boundaries is observed for all systems.

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are non-uniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a non-linear, integral Euler-Lagrange equation, or (ii) perform a direct multi-dimensional free energy minimisation. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the Multi-Layer Perceptron (MLP) artificial neural network for minimising the free energy of a fluid of hard non-spherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible and refinable. Furthermore, it can be readily generalised to the richer experimental patterned-substrate geometries that are now experimentally realisable but very problematic to conventional theoretical treatments.