Surface phase transitions in nematic liquid crystals with planar anchoring

Abstract

We calculate the thermodynamic phase diagram of a semi-infinite nematic liquid crystal system above its bulk ordering temperature for the case of planar boundary conditions. The latter are assumed to favor a uniaxially ordered surface state, characterized by a negative orientational order parameter, at sufficiently high temperatures. All symmetry-allowed terms either linearly or quadratically proportional to the tensor order parameter characterizing the transition to a biaxially ordered surface state are included in the analysis. The Euler-Lagrange equations obtained by minimizing the Landau--de Gennes free energy expression are solved exactly by numerical methods. We find that both first- and second-order transitions are possible; they occur in different sections of the thermodynamic phase boundary separated by a line of tricritical points. In the second-order region, we evaluate the effect of fluctuations on this quasi-two-dimensional system by introducing the Berezinskii-Kosterlitz-Thouless mechanism, and calculating its effect on the phase boundary and nature of the transition. Possible ways of observing this phase transition experimentally are considered and some potentially useful techniques noted.