表面弹性自由能k_(13)项与楔形液晶盒中阈值厚度附近的指向矢分布

k_(13) Surfacelike Elastic Term and Distribution of Director on the Wedged Liquid Crystal Cell Nearby Critical Thickness

考虑楔形液晶盒,液晶指向矢倾角θ是两个空间变量x,z的函数,即θ=θ(x,z)。导出了液晶盒的吉布斯自由能,其中包括表面弹性自由能k13 项。由拉格朗日 欧拉方程得到了θ(x,z)满足的微分方程。在k11 k33近似下,方程变为二维拉普拉斯方程。在阈值厚度 hc 附近θ很小,方程的解可近似为θ=cz(qx-1)。代入自由能表达式中,求极值可确定 c和q 的值。计算和讨论了k13项对液晶指向矢分布的影响。

The wedged liquid crystal cell and the director of liquid crystal as the function of two special variable measurement x and z are considered, namely θ=θ(x,z). The Gibbs free energy of the liquid crystal cell is derived, which includes surface elastic free energy term k_(13). The differential equation that is satisfied by θ(x,z) is got by Euler-Lagrange equation. According to the assumption k_(11)k_(33), the equation will convert two dimensional Laplace equation. θ is very small in the vicinity of critical thickness, the equation resolution can be described to θ=cz(qx-1). Substituting it into the expression of free energy, c and q can be determined by minimizing it. The influence of the term k_(13) on the director of liquid crystal is calculated and discussed.