Study On Director Orientation Of Nematic Liquid Crystals Confined In Cylindrical System

The alignment of liquid crystal molecules is one of the hot spots in liquid crystal physics research,and it is also a critical issue in the production of liquid crystal display devices.Liquid crystals have been made outstanding progress in the application of planar structures.The application in complex geometry,such as capillaries,topological channels,etc.,needs further research.The stable arrangement of liquid crystal molecules can be affected significantly by system symmetry,anchoring effect,thickness of cell,electric effect,elastic anisotropy,flexoelectric effect,saddle-splay deformation and so on.In this paper,the director distributions of nematic liquid crystals confined in a coaxial cylinder are studied by liquid crystals’continuum elasticity theory and the finite difference iteration method.Firstlly,the coaxial cylindrical shell is filled with nematic liquid crystals and boundary conditions of strong anchoring or weak anchoring are imposed on the inner and outer surfaces causing hybrid aligned nematic director structures.We derive the equations for the bulk and boundary conditions of the cylinder.By computer simulation,the flexoelectric effect on the director distributions under different flexoelectric coefficients and the dependence of the shift voltage on the applied voltage are obtained.The flexoelectric coefficients e₁₁+e₃₃ and e₁₁ can affect the director distributions.And a novel method to determine the flexoelectric coefficients by measuring the shift voltage is put forward.Secondly,the directors are confined at a fixed plane（φ-z plane）because saddle-splay free energy is the function ofβ.A theoretical study of saddle-splay term on nematic liquid crystal confined in coaxial cylindrical shell elucidates director configurations initially.We investigate the spontaneous deformation by saddle-splay term K₂₄ in the axial director structures.And we compare the effect of the twist elastic constant K₂₂ on director distortion to the influence of saddle-splay term K₂₄ in the twist director structures.Then,we calculate the critical radius ratio and the critical twist elastic constant in the director structures,in which the spontaneous deformation occurs.Finally,we consider director distortion in three-dimensional space（including two independent variablesαandβ）and investigate the influence of saddle-splay term on director distributions deeply.We consider lyotropic liquid crystals SSY confined in two coaxial cylinders with free-surface boundary conditions and R-P anchoring conditions.The effect of saddle-splay term on director distributions is studied.We find that saddle-splay deformation leads to double-twist director configurations under free-surface boundary conditions,which consists of the result under degenerate planar anchoring conditions.Furthermore,under the R-P anchoring conditions,saddle-splay deformation has a great influence on the director in the radial direction and the director distorts in three-dimensional space.This paper will provide theoretical guidance for the study of the flexoelectric coefficients and the elastic constants of the saddle-splay deformation in different liquid crystals,and provide new ideas for the study of the elastic behavior of nematic liquid crystals in cylindrical microcavity.