Negative liquid crystal MBBA that aligns along the normal to the plates in liquid crystal cell will arise the flexoelectric effect when a external electric field is applied in the plane of slab.Based on the elastic theory of liquid crystal and variation theory, the effect is studied, and the differential equation and boundary condition about the director of liquid crystal have heen obtained.Finite-difference iterative method is used for numerical solution. Under the approximation of small angle, analytical solution of the distribution of the director has been also obtained, and compared with the numerical solution and the result of book.

The two-particle cluster theory of nematic liquid crystals is generalized to study a two-dimensional model of cholesteric phase. The chiral molecules are placed at the sites of a three-dimensional simple cubic lattice with molecular orientations confined to two dimensions. The theoretical result shows that the helical wave-vector for equilibrium state depends on temperature and the cholesteric-isotropic phase transition exists. The two-particle cluster theory, taking into accout short-range correlations between molecules, yields numerical results which are closer to those of the Monte Carlo simulation than the mean field theory.

The molecular field theory is used to invesigate the behaviour of the nematic alignment transition within nematic liquid crystal (NLC) films confined by two rubbed substrates. The molecular centres of mass are located at the sites of a simple cubic lattice. The NLC consists of polar molecules and the molecules of the first layer of the NLC adjacent to the soild bounding surface are affected by both surface dispersion and polar forces. From self-consistent numerical calculations, three types of phase diagram are obtained, which exhibit a transition from a high temperature homogeneous alignment to a low temperature homeotropic alignment. The parameter ranges of two surface interaction which leads to the homogeneous-to-homeotropic alignment transition is obtained. The results show that the surface dispersion action, not the surface polar one, can be changed by the grating of the substrate and the surface polar interaction can give rise to the homogeneous-to-homeotropic alignment transition.

Based on Ericksen-Leslie's elastic theory and dynamic theory, the responsive time parameter of the in-plane switching liquid crystal displays is analyzed, the chiral-planar alignment is introduced into this mode, and the dynamic equation of the director is given. The relation of the responding time and the twist angle is obtained by calculating the instantaneous distribution of the director in this mode. The computational result demonstrates that there is a short responding time in IPS-Chiral-Planar liquid crystal cell with a certain twist angle.

A new surface potential form is proposed to describe the action of the rubbed substrate to the liquid crystal molecules. By means of the molecular field theory, thin liquid crystal films confined by two rubbed substrates which lead to a homogeneous planar alignment of the liquid crystal molecules are studied. Adopting the Lebwohl-Lasher model,the molecular centers of mass are located at the sites of a simple cubic lattice. Numerical calculations are made for a liquid crystal film composed of 20 molecular layers. Three states with the different preferred directions of the molecular orientations exist and the one oriented along the rubbed direction has the lowest free energy. In addition, the symmetry of the biaxiality induced by the surface action is considered.

In the supertwisted nematic-liquid crystal display (STN-LCD), the director of liquid crystal is determined by the tilt angle θ and the twist angle φ. The ordinary differential equations and the boundary conditions satisfied by θ,φ and the electric potential U are obtained, based upon the continuum theory of liquid crystals. Solving two-point boundary problem of the ordinary differential equations by means of the relaxation method, dependence of the optical threshold voltage on the anchoring strength is calculated.