  The confining effect of a spherical substrate inducing anchoring (normal to
the surface) of rod-like liquid crystal molecules contained in a thin film
spread over it has been investigated with regard to possible changes in the
nature of the isotropic-to-nematic phase transition as the sample is cooled.
The focus of these Monte Carlo simulations is to study the competing effects of
the homeotropic anchoring due to the surface inducing orientational ordering in
the radial direction and the inherent uniaxial order promoted by the
intermolecular interactions. By adopting entropic sampling procedure, we could
investigate this transition with a high temperature precision, and we studied
the effect of the surface anchoring strength on the phase diagram for a
specifically chosen geometry. We find that there is a threshold anchoring
strength of the surface below which uniaxial nematic phase results, and above
which the isotropic fluid cools to a radially ordered nematic phase, besides of
course expected changes in the phase transition temperature with the anchoring
strength. In the vicinity of the threshold anchoring strength we observe a
bistable region between these two structures, clearly brought out by the
characteristics of the corresponding microstates constituting the entropic
ensemble.
