Equilibrium director structures in two thin hybrid planar films of biaxial nematics are investigated through Markov chain Monte Carlo simulations based on a lattice Hamiltonian model within the London dispersion approximation. While the substrates of the two films induce similar anchoring influences on the long axes of the liquid crystal molecules (viz. planar orientation at one end and perpendicular, or homeotropic, orientations at the other), they differ in their coupling with the minor axes of the molecules. In Type-A film the substrates do not interact with the minor axes at all (which is experimentally relatively more amenable), while in Type-B, the orientations of the molecular axes at the surface layer are influenced as well by their biaxial coupling with the surface. Both films exhibit expected bending of the director associated with ordering of the molecular long axes due to surface anchoring. Simulation results indicate that the Type-A film hosts stable and noise free director structures in the biaxial nematic phase of the LC medium, resulting from dominant ordering of one of the minor axes in the plane of the substrates. High degree of this stable order thus developed could be of practical interest for in-plane switching applications with an external field. Type-B film, on the other hand, experiences competing interactions among the minor axes, due to incompatible anchoring influences at the bounding substrates, apparently leading to frustration, and hence to noisy equilibrium director structures.
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