The Effect Of Grooved Surface On The Alignment Of Biaxial Nematic Liquid Crystal

Surface anchoring of a liquid crystal has been among the most important subjects of liquid crystal research. In most practical applications including displays, Achievement of proper anchoring is of crucial importance in accomplishing desirable performance of liquid crystal devices. Because of the thickness of the liquid crystal layer in the liquid crystal cell is only the microns order of magnitude, so the anchoring action of the substrate will show an deep influence on the liquid crystal inside the liquid crystal cell. As early as in 1972, Berreman proposed a simple model attributing the surface anchoring to the elastic distortion of the liquid crystal induced by the grooves of a surface. Berreman showed that the surface anchoring energy is proportional to sin 2? , with ? being the angle between the director at infinity and the direction of the surface grooves. Jun-ichi Fukuda argued that Berreman's assumption of negligibly small azimuthal distortion of the nematic is not valid. Proper treatment of the azimuthal distortion reveals that the Berreman's model should yield a surface anchoring energy proportional to sin 4? .In nematic liquid crystal, theoretical analysis pointed out that for non-cylindrical symmetric molecules, the system can enter into a biaxial state due to molecular interactions. In basic research, elastic theory of biaxial nematic is an important area. Saupe used a similar method of solid theory and derived a elastic energy density formula of biaxial nematic liquid crystal. The formula contains 12 independent elastic coefficients, the value of which is decided by the experimental measurements. In 1984, E. Govers and G. Vertogen also obtained 12 rotational invariants related to director distortion.In this paper, under the approximation of Berreman, any grooved surface with arbitrary shape can be described in terms of Fourier series. Based on the theory of Fukuda et al, the expression of anchoring energy with an additional term was obtained, taken into the surface like elastic term in biaxial nematic liquid crystal. The figures of reduced anchoring energies versus the angle between the direction of the grooves and main director were simulated under the different values of surface like elastic constant in certain cases and the effect of biaxial elastic constant on easy axes was discussed.