Director Distribution Of Nematic Liquid Crystals In Concentric Cylinder

The study on the director distribution of liquid crystal molecules in the cylinder has a wide range of applications in the field of liquid crystals.Liquid crystal elastic effect,the surface anchoring effect,the electric field effect will affect the distribution of liquid crystal under certain deformation(splay and bend deformation).Based on the Frank elastic free energy,the Rapini-Papoular approximation of the surface energy,the coupled dielectric free energy and the flexoelectric free energy induced by the electric field,the director distribution of nematic liquid crystals in three concentric cylinder models is investigated.The first liquid crystal cylinder is a cylindrical thin layer of mixed arrangement.Based on the Frank elastic theory and the Euler equation,the equilibrium equation and the boundary conditions about the director of liquid crystal are obtained.The numerical solution is numerically solved by the finite-difference iterative method,and then the distribution of the director is simulated by the computer.Under the condition of no electric field,the anchoring strength,the elastic anisotropy,the columnar symmetry and the layer thickness all affect the director distribution in the cylinder.When the cylinder is filled positive liquid crystal 5CB and applies a radial non-uniform electric field,a mixed arrangement liquid crystal cylinder or a radial arrangement liquid crystal cylinder will be formed.The second liquid crystal cylinder is the cylinder filled negative liquid crystal MBBA that aligns along the cylindrical radius and applies a non-uniform electric field in the radial direction.The same theoretical method is used to obtain the numerical solution of the director distribution.Under the approximation of a small angle,the maximum value of the liquid crystal director deformation and the analytic solution of the critical voltage are calculated and the director distributions are simulated.Under the condition of strong anchoring boundary,the critical exponent of Fréedericskz transformation of nematic liquid crystal in the cylinder is ? =1/2 regardless of considering the flexoelectric effect or ignoring the flexoelectric effect and the flexoelectric effect reduces the threshold voltage at which Fréedericskz transition occurs.Under the weak anchoring boundary conditions,the liquid crystal director produces a new deformation due to the electric field effect.The third liquid crystal cylinder is the cylinder filled positive liquid crystal 5CB that aligns along the cylindrical axis and applies a non-uniform electric field in the radial direction.The same theoretical method is used to simulate the director distribution.The director distribution is different from the second radial arrangement model.Under the condition of strong anchoring boundary,the flexoelectric effect increases the threshold voltage of the liquid crystal Fréedericskz transition.Under the condition of weak anchoring boundary,the liquid crystal director has a different deformation due to the effect of the electric field.Through the study of the above three kinds of liquid crystal cylinder model,the distribution of director in the cylinder is very different due to the influence of the columnar symmetry,the anchoring strength,the layer thickness,the elastic anisotropy,the electric field effect and the flexoelectric effect.