Liquid crystal alignment and light propagation in nematic liquid crystal cells

This dissertation is devoted to theoretical study of liquid crystal alignment and optical properties in multidimensional nematic liquid crystal cells in which the director depends on two or three space variables.; First of all, a simplified model to describe the director and electric field configurations in multidimensional liquid crystal (LC) cells with possible wall defect structures will be introduced and developed. Two important situations are considered here: a LC cell with wall defect layers where the director lies in one plane and there is no twist deformation, and the other, more general situation of a LC cell with twist wall layers. An example of the former kind of LC cells is a two dimensional (2D) cell which combines the concept of in-plane switching (IPS) with vertical alignment (VA). An example of the latter kind of LC cells is a three dimensional (3D) cell associated a homeotropic to multidomainlike transition (HMD cell). The model provides an alternative to the traditional method of direct computer solution of the Euler-Lagrange equations for the director and electric field in analyzing the behavior of LC cells. Instead of solving the Maxwell equation for the electric displacement vector, it uses an approximate analytical expression for the electric field which is helpful in understanding some interesting features in the behavior of the electric field in the wall defect region. Another advantage of the model is that it is about 100 times faster than direct computer solution, providing about the same accuracy. The model is used to calculate the director and electric field for the cell which combines IPS and VA, and for the HMD cell. To make a comparison of this model with other methods of director calculation, the usual relaxation method for computing director and electric field has been developed and comparison between the results produced by the two methods will be shown.; An approximate but still accurate method of treating a LC cell with ±1/2 disclination lines using Landau-De Gennes theory inside the disclination core region was found. It has been shown that the deviation of the tensor order parameter from its Frank form far away from the core center decreases as 1/r 2, where r is the distance from the center, and has an azimuthal dependence. A temperature dependent estimate for the size of the defect core has been found. The free energy of a cell with disclination lines has been calculated and compared with the corresponding value for the same cell with a wall defect structure. (Abstract shortened by UMI.)...