  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.
