SURFACE-LAYER PHASE-TRANSITIONS IN NEMATIC LIQUID-CRYSTALS

Surface-layer transitions in nematogenic materials characterized by a preferential planar surface interaction linear in the order parameter have been studied theoretically at temperatures above the bulk transit ion (T(NI)). The coupled Euler-Lagrange nonlinear differential equatio ns obtained from the Landau-de Gennes free energy were solved exactly by numerical integration. This problem had been studied previously emp loying various limits and approximations with several differences in t he phase diagram reported. The exact results allow one to determine wh ich of these differences are artifacts of the approximations used and which are dependent upon the ratio of elastic constants. It is found, for physically relevant elastic constants, that there is always a unia xially ordered surface layer at sufficiently high temperatures. For we ak surface coupling, no surface phase transition occurs and the uniaxi al layer remains the stable state until T(NI) is reached. When the sur face coupling is increased, there is a single first-order (prewetting) transition from uniaxial to biaxial surface ordering as the temperatu re is reduced towards T(NI). This transition boundary becomes second o rder (by way of a tricritical point) when the surface coupling is furt her increased. We also find that the mean-field boundary is suppressed due to Berezinskii-Kosterlitz-Thouless (BKT)-type phase fluctuations. Also, these fluctuations can result in the re-entrant (with increasin g surface coupling strength) uniaxial-biaxial phase boundary terminati ng on the bulk transition line rather than becoming asymptotic to it.