不同初始分布向列相液晶电容特性的相场法研究

液晶盒内的液晶分子在不同的外加电场作用下重新排布,其极化指向发生改变,从而影响液晶盒整体的电学特性。本文考虑液晶材料的挠曲电效应,分析液晶盒的整体自由能表达式,包含弹性形变自由能密度、介电自由能密度和挠曲电自由能密度。基于液晶弹性理论和相场方法,构建描述液晶核指向矢分布及演化的相场方程,并运用离散方法推导出液晶盒约化电容的表达式。讨论边界强锚定的混合液晶盒(HAN)和平行液晶盒(PAN)表面电荷密度对液晶核指向矢偏转角的影响。进一步分析了挠曲电系数、表面电荷密度以及液晶盒厚度对两种不同初始指向分布液晶盒电容性能的影响。数值分析结果表明,表面电荷密度越大、挠曲电系数越小,液晶核指向矢偏角越大。在混合液晶盒中,约化电容随着表面电荷或液晶厚度的增加而增加,最终趋于饱和;而在平行液晶盒中,当表面电荷密度或液晶盒厚度达到某个临界值时,液晶核的指向矢才发生改变,液晶的约化电容才有明显的变化。随着表面电荷密度增加,液晶核指向矢发生偏转的临界厚度减小。

Phase field method in capacitance characteristics of nematic liquid crystals with different initial alignments

Subjected to different electric fields, liquid crystal molecules would rearrange and the polarization directors would change, which could affect the capacitance characteristics of liquid crystal cells. Based on the free energy of liquid crystals due to the flexoelectric effect, the expressions of the elastic, dielectric and flexoelectric free energy density are obtained. Applying the elastic theory and the phase filed methods of liquid crystals, the phase field equations describing the distribution and switching of liquid crystal director are obtained, and the expression of the capacitance of the liquid crystal cell is derived by discrete methods. The influences of the surface charge density on the liquid crystal directors are discussed in the strong anchoring hybrid alignment nematic (HAN) and the parallel alignment nematic (PAN) liquid crystal cells. Furthermore, the effects of flexoelectricity, surface charge density and the thickness of the liquid crystal cell on the capacitance performance of two different initial alignments are analyzed in detail. The results of numerical analysis show that the larger surface charge density and the smaller flexoelectric coefficients would induce the larger angle of the director. In the HAN liquid crystal cell, the capacitance increases with increasing surface charge or liquid crystal thickness, and finally becomes saturated. In the PAN liquid crystal cell, the liquid crystal directors switch only upon the surface charge density or the thickness of the liquid crystal cell reaching a certain critical value, and the capacitance of the liquid crystal changes significantly. With increasing surface charge density, the critical thickness of the liquid crystal cell decreases.