THEORY OF A SYMMETRY-BREAKING PHASE-TRANSITION IN A SURFACE-LAYER OF NEMATIC LIQUID-CRYSTAL

For a surface interaction linear in the order parameter and favoring a n orientation in which liquid-crystalline molecules lie parallel to th e surface (but which is independent of whether the orientation is unia xial or isotropic in the bounding plane), a symmetry-breaking phase tr ansition in a surface layer is possible at temperatures above that of the bulk isotropic to nematic transition. At the surface transition, t he high-temperature in-plane isotropic state becomes unstable with res pect to a biaxial phase, the transition being continuous and therefore of-the Berezinskii-Kosterlitz-Thouless (BKT) type, It is expected to occur for intermediate surface couplings but not at very weak or very strong couplings. The bulk phase always remains disordered. The BKT tr ansition boundary is calculated explicitly and the results are compare d with earlier theoretical studies on systems with linear or quadratic surface interaction potentials. Numerical estimates indicate that sys tems having the required linear surface potentials can be prepared and possible techniques for observing a BKT-type phase transition are dis cussed.