Based on dynamic theory of liquid crystal and finite-difference iterative method, dynamic response of strong anchoring hybrid aligned nematic (HAN) liquid crystal cell as removing applied voltage was studied. Flexoelectricity of liquid crystal material was considered. Time-dependences of transmittance through a HAN cell were obtained. It indicates that response time decreases with increasing of absolute value of the sum of splay and bend flexoelectric coefficient |e₁₁+e₃₃|. Especially, at |e₁₁+e₃₃|=50 pC·m^-1 response time is half shortened relative to the case with no flexoelectric effect.

Nematic droplets are studied with Monte Carlo simulations with a modified Gruhn-Hess pair potential. The potential is spatially anisotropic and potential parameters are related to elastic constants K₁₁ ,K₂₂ ,K₃₃ and surface-like elastic constant K₁₃. It is assumed that nematic droplet surface is a free surface. Second order parameters and introrse intensity, which describes quantitatively intrinsic anchoring induced by surface at low temperatures, are calculated with a modified Gruhn-Hess pair potential and are compared with those in Gruhn-Hess model I. It is shown that the modified model with K₁₃ induces intrinsic anchoring near droplet surface, orientation and intrinsic anchoring strength depend strongly on K₁₃, and introrse intensity is related to K₃₃/K₁₁. Order degree of nematic droplet is lower from inner shell to outer shell due to incomplete anisotropic nematic-nematic interactions.

Flexoelectric effect on electro-optical characteristics of a nematic liquid crystal cell is investigated.Differential equations and boundary conditions for director of liquid crystal are obtained with variation theory.Distributions of director of nematic liquid crystal (NLC) cells with strong anchoring and weak anchoring are calculated by a finite-difference iterative method.With Jones matrix method,transmittance-voltage characteristics of liquid crystal cells are obtained.Surface flexoelectric effect and bulk flexoelectric effect are considered.

With an equivalent anchoring energy formula for grating surface and elastic theory, a hybrid aligned nematic (HAN) liquid crystal cell proposed by Bryan-Brown et al is studied. Equations and boundary conditions for tilt angle and twist angle of director are obtained with variation theory. Tilt angle and twist angle of director with applied voltage at certain δ/λ are calculated with finite-difference iterative method. Electro-optical effect of liquid crystal cells is investigated with Jones matrix method. It depends on geometrical parameters of the grating surface, pitch λ and amplitude δ.

With elastic theory of liquid crystal,we investigate bulk flexoelectric effect in a nematic liquid crystal(NLC) cell with applied voltage.The differential equation of director tilt angle θ is obtained by the variation theory. The distributions of director in a strong anchoring planar aligned cell and in a hybrid aligned nematic(HAN) cell are calculated. The transmittance characteristic of these liquid crystal cells is obtained with Jones matrix method.Influence of bulk flexoelectric effect on the distribution of director and characteristic transmittance of liquid crystal cells are analyzed.