Phase Field Method In Capacitance Characteristics Of Nematic Liquid Crystals With Different Electrical Boundary Conditions

With the rapid development of semiconductor and capacitor industries,the capacitance characteristics of liquid crystal cells have attracted the wide attention.In this paper,considering the flexoelectric effect of liquid crystal materials,a mathematical model of the microcosmic structure of liquid crystal cell was established,and the orientation distribution of liquid crystal molecules was analyzed by the phase field method.The capacitance characteristics of liquid crystal cell with different electric boundary conditions were discussed in detail.liquid crystal molecules would rearrange and the polarization directors would change under different applied electric fields,which affects the overall electrical characteristics of liquid crystal cell.In this paper,considering the flexoelectric effect of liquid crystal material,the expressions of the elastic,dielectric and flexoelectric free energy density are obtained.Based on the elastic theory of liquid crystal and the Ginzburg-Landau equation,the distribution and evolution of the liquid crystal director under two different electrical boundary conditions(surface charge density and voltage)were constructed.The phase field equation was solved by the finite difference method and the fourth order Runge-Kutta method,the expression of the reduced capacitance of liquid crystal cell was deduced by discrete method.The effects of the bending elastic constants,flexoelectric coefficients,and the thickness of liquid crystal cell on the reduced capacitance performance of two different initial directional distribution liquid crystal cells,Hybrid aligned nematic(HAN)and Parallel aligned nematic(PAN),were discussed numerically with the applied surface charge density and applied voltage.The numerical results show that under the surface charge density condition,the liquid crystal director of the hybrid liquid crystal cell changed continuously from 0 to ?/2 in the thickness direction.The large the surface charge density,the small flexoelectric coefficient and the small bending elastic constant would cause the large director,which finally would stabilize along the direction of electric loading.The reduced capacitance increases with the surface charge and liquid crystal thickness and tended to a constant value.In parallel liquid crystal cells,the liquid crystal director presents symmetrical distribution along the thickness direction.There are critical surface charge density and thickness of the liquid crystal cell.When the surface charge density exceeds the critical value,liquid crystal director will change,and the reduced capacitance of the liquid crystal will change obviously.Flexoelectric coefficient has little effect on these critical values,but the large bending elastic constant would cause the large critical surface charge density.With increasing surface charge density,the critical thickness of the liquid crystal cell will decrease rapidly.While the reduced capacitance of large thickness liquid crystal cell was independent on the surface charge density.Under the applied voltage boundary condition,for the hybrid liquid crystal cell,the big applied voltage and dielectric anisotropy,the small flexoelectric coefficient and the bending elastic constant would cause the large liquid crystal director,which finally would tend to a stable value.The reduced capacitance would increase with the increase of applied voltage and eventually tends to a constant value.In parallel liquid crystal cell,the flexoelectric effect would cause the nonuniform electric field distribution in the liquid crystal cell,hence the liquid crystal director shows an asymmetric distribution in the thickness direction.When the applied voltage increases and exceeds the critical value,the director of the liquid crystal will change significantly,and the reduced capacitance increases sharply.The critical applied voltage value is also affected by the bending elastic constant and dielectric anisotropy.The large bending elastic constant and the small dielectric anisotropy would cause the great critical applied voltage value,while the flexoelectric coefficient and the thickness of the liquid crystal cell have no effect on the critical applied voltage value.In this paper,the capacitance characteristics of HAN and PAN liquid crystal cells under the applied charge density and applied voltage are systematically studied,which is helpful to guide the design of the capacitance of liquid crystal devices.