Study On The Chiral Structures Of Nematic Liquid Crystal Under Capillary Confinement By Landau-de Gennes Theory

The boundary function of the curved surface in confined system can directly affect the director configuration of the stable state.The elastic anisotropy can cause various changes in the system.The elastic energy characteristics in the nematic liquid crystal are very important for liquid crystal display applications.Based on Landau-de Gennes theory,this paper explores the influence of the surface elasticity K₂₄(L₂₄)term and the radius curvature on the chiral structure in the system by using the relaxed iterative method.The simulation results show that the elastic anisotropy can induce the chiral structural transformation in the system,and there are defect configurations between the opposite chiral domains.Different initial directors are set to find several new structural states.The infinitely long cylindrical model is selected.The initial directors are arranged along the axial direction.Under a single constant approximation,when the elastic anisotropy is sufficiently strong(K₂₄ is sufficiently large),a double-twist structure occurs spontaneously in the system.The twist angle gradually increases from the central axis of the cylinder to the boundary,and the twist angle increases as the radius decreases（the curvature increases）.Two fine structures of domain wall and point defects are formed between opposite chiral domains in a cylinder.When the initial directors are arranged in a radial direction,the elastic anisotropy induces two new states:an ordered reconstruction state and a vortex state.As the radius of curvature increases,the critical K_24c/K(L_24c/L₁)value of the energy transition of the double-twisted state and the ordered reconstruction state increases.In different radius ranges,the interaction of elastic anisotropy and radius curvature produces different results for the structure in the system.When the initial directors are arranged at radial and linearly radialαangles respectively,the equilibrium state in the system are all ordered reconstruction states within a small radius range（R≤3000ξ₀）;and the equilibrium states in the system are respectively radial state and vortex state within a large radius range（R>3000ξ₀）.Through the energy comparison of various structures appearing in different radius scale ranges,the stability of several structures in the system is analyzed.The effects of elastic anisotropy and curvature will induce a rich structural transformation in the cylinder.The surface elasticity K₂₄ will act on the boundary of the curved surface.Combined with the boundary effect,the internal structure of the cylinder will change,and the stability of the structural state in the system will also change.