SURFACE PHASE-TRANSITIONS IN NEMATIC LIQUID-CRYSTALS WITH PLANAR ANCHORING

We calculate the thermodynamic phase diagram of a semi-infinite nemati c liquid crystal system above its bulk ordering temperature for the ca se of planar boundary conditions. The latter are assumed to favor a un iaxially ordered surface state, characterized by a negative orientatio nal order parameter, at sufficiently high temperatures. All symmetry-a llowed terms either linearly or quadratically proportional to the tens or order parameter characterizing the transition to a biaxially ordere d surface stale are included in the analysis. The Euler-Lagrange equat ions obtained by minimizing the Landau-de Gennes free energy expressio n are solved exactly by numerical methods, we find that both first- an d second-order transitions are possible; they occur in different secti ons of the thermodynamic phase boundary separated by a line of tricrit ical points. In the second-order region, we evaluate the effect of flu ctuations on this quasi-two-dimensional system by introducing the Bere zinskii-Kosterlitz-Thouless mechanism, and calculating its effect on t he phase boundary and nature of the transition. Possible ways of obser ving this phase transition experimentally are considered and some pote ntially useful techniques noted.