**1 - 5**of

**5**| Next »

## Surface-Layer Phase-Transitions in Nematic Liquid-Crystals04/15/1994Surface-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 transition (T(NI)). The coupled Euler-Lagrange nonlinear differential equations obtained from the Landau-de Gennes free energy were solved exactly by numerical integration. This problem had been studied previously employing various limits and approximations with several differences in the phase diagram reported. The exact results allow one to determine which 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 uniaxially ordered surface layer at sufficiently high temperatures. For weak surface coupling, no surface phase transition occurs and the uniaxial layer remains the stable state until T(NI) is reached. When the surface coupling is increased, there is a single first-order (prewetting) transition from uniaxial to biaxial surface ordering as the temperature is reduced towards T(NI). This transition boundary becomes second order (by way of a tricritical point) when the surface coupling is further 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 increasing surface coupling strength) uniaxial-biaxial phase boundary terminating on the bulk transition line rather than becoming asymptotic to it. |

## Phase-Transitions in Finite-Thickness Nematic Liquid-Crystal Films - Planar Anchoring10/15/1995Phase transitions in finite-thickness nematogenic materials bounded by two planar surfaces and characterized by identical surface interactions linearly proportional to the order parameter have been studied theoretically by solving the coupled nonlinear Euler-Lagrange equations. The surface interaction was assumed to favor molecular orientation in the surface plane with no rubbed or preferred direction. The related problem of a semi-infinite film having a single surface has been studied previously at temperatures above the bulk nematic-isotropic phase transition point T-NI. For that geometry and physically relevant elastic constants, it was shown that, in addition to the bulk transition, there is a second transition at higher temperatures between biaxial and uniaxial ordering of the surface layer when the strength of the surface coupling is not too weak. It is shown here that this double phase transition reduces to a single one for sufficiently thin layers. |

## Surface Phase Transitions in Nematic Liquid Crystals With Planar Anchoring04/15/1997We 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 stale 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. |

## Theory of a Symmetry-Breaking Phase-Transition in a Surface-Layer of Nematic Liquid-Crystal08/15/1993For a surface interaction linear in the order parameter and favoring an orientation in which liquid-crystalline molecules lie parallel to the surface (but which is independent of whether the orientation is uniaxial or isotropic in the bounding plane), a symmetry-breaking phase transition in a surface layer is possible at temperatures above that of the bulk isotropic to nematic transition. At the surface transition, the high-temperature in-plane isotropic state becomes unstable with respect 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 transition boundary is calculated explicitly and the results are compared with earlier theoretical studies on systems with linear or quadratic surface interaction potentials. Numerical estimates indicate that systems having the required linear surface potentials can be prepared and possible techniques for observing a BKT-type phase transition are discussed. |