Coupling Consequences Of Flexoelectricity On Director Distribution And Local Mass Density In Nematic Liquid Crystals

With the wide application of liquid crystal,how to improve the display effect of liquid crystals has always been a very important research field.The quality of liquid crystal display depends on the distribution of liquid crystal molecules in liquid crystal,and the flexoelectric effect in liquid crystal has an important influence on the distribution of liquid crystal molecules.In this paper,a parallel aligned nematic liquid crystal cell is used to research.Under the electrical boundary conditions of the surface free charge density and the applied voltage,the coupled phase-field method is used to analyze the coupling consequences of flexoelectricity on director distribution and local mass density fluctuation.First,the total free energy of liquid crystal system including the total elastic energy density,director-density coupling free energy density,flexoelectric energy density and dielectric energy density is constructed using the director-density coupling theory.Then the Ginzburg-Landau phase field equation of the liquid crystal director evolution and Cahn-Hilliard equation of the local mass density change are established to couple the evolution process and final distribution of liquid crystal director and local mass density by finite difference method and fourth-order Runge-Kutta method.Analysis and discussion about the coupling consequences of flexoelectricity on director distribution and local mass density in liquid crystals are presented.The numerical results show that:under the surface free charge density condition,as the surface free charge density and dielectric anisotropy increase or the absolute value of the flexoelectric coefficients sum and the bend elastic constant decrease,the deflection angle of liquid crystal molecules,the diffusion of liquid crystal molecules from the center to the two substrates,the polarization intensity and change of internal electric field increase.With the coupling constant u1 of the director-density coupling theory increasing,the deflection angle,the polarization,and change of internal electric field decrease,and the diffusion of liquid crystal molecules from the central to the two substrates becomes larger.When u1 increases a large value,the diffusion of liquid crystal molecules will gradually stabilize.Under the applied voltage condition,changes of the deflection angle of the liquid crystal director,the mass density fluctuation,the polarization and internal electric field are basically the same as the results of the applied surface free charge density condition.However,the existence of the flexoelectric effect makes the deflection angle and local density of the liquid crystal molecules lose symmetry along the thickness direction,and the degree of symmetry loss increases with the increase of the flexoelectric coefficient.In addition,when the sum of flexoelectric coefficients is positive,the peak deflection angle and the peak local mass density are closer to the low potential substrate,and when the sum of flexoelectric coefficients is negative,the peak deflection angle and the peak local mass density are closer to the high potential substrate.In this paper,the coupling phase field method is used to systematically discuss the effects of different physical parameters on liquid crystal directors,local mass density,polarization and internal electric field under different electrical boundary conditions.It is also possible to grasp the distribution of liquid crystal molecules in the liquid crystal cell.It also provides a theoretical help for improving the liquid crystal display.