【作者】 陈贵锋；

【导师】 杨国琛；

【作者基本信息】 河北工业大学 ， 理论物理， 2004， 硕士

【摘要】 用解析方法研究了不对称液晶盒中挠曲电效应。给出了电压作用下系统的吉布斯自由能，它包含Frank弹性自由能，介电自由能，挠曲电自由能和界面自由能，其中锚定能采用修正后的RP公式，用变分方法导出了指向矢倾角θ满足的微分方程和边界条件。证明挠曲电效应导致一项新的表面能，这项自由能对上、下基板符号相反。这是挠曲电效应的直接结果。 根据θ满足的微分方程和边界条件，研究了液晶盒的基本性质，包括阈值电压和饱和电压。不对称液晶盒的基本性质，是指向矢分布对盒中央平面不再对称。引入参量Δ反映对称性破缺，研究了阈值点和饱和点的对称性破缺参量Δ_th、Δ_sat。以上这些物理量都与上、下基板的锚定能公式出现的参量以及挠曲电系数e₁+e₃有关。给出了它们之间的关系，并用数值计算方法作了详细研究。挠曲电效应对阈值电压、饱和电压和对称性破缺参量有重要影响。 作为本项研究结果的一个应用，本文提出采用不对称液晶盒可以用来测定液晶的挠曲电系数。具体方案为：采用劈形盒，施加三个不同电压U₁、U₂、U₃，测定相应的阈值厚度l₁、l₂、l₃；或用锚定强度A₁、A₂，完全相同的上、下基板，构造厚度分别为l₁、l₂、l₃的不对称液晶盒，分别测定阈值电压U₁、U₂、U₃。不论用何种方法，都将得到三组实验数据（l₁，U₁）、（l₂，U₂）、（l₃、U₃），从而可进一步得到相应的三个与A₁、A₂以及（e₁+e₃）的方程。解此方程组，可解得e₁+e₃。本文给出了计算挠曲电系数的具体方案，这是采用常规方法测定e₁+e₃的新方案。更多还原

【Abstract】 We study the flexoelectric effect of the non-symmetric liquid crystal cell with the analytical method. We get rigorously Gibbs free energy of the system under electrical field, which involve the Frank free energy, the dielectric free energy, the flexoelectric free energy and the anchoring free energy, where the anchoring free energy is based on the modified formula of Rapini-Papoular. The differential equation and boundary condition of the director tilt angle θ are obtained by applying the proper mathematical method. We have proved that the flexoelectric effect is to produce a new term of surface anchoring energy, which has opposite at upper and lower substrates. The conclusion is the direct result of the flexoelectric effect.Applying the differential equation and boundary condition of the director tilt angle θ, the essential characters are discussed, which include the threshold voltage and the saturation voltage. The essential character of the non-symmetric liquid crystal cell is that the director distribution at the middle layer of the cell is not symmetric, So a new parameter A is introduced to reflect the breaking of symmetry. We also study the symmetry breaking parameter △th at the threshold point and the symmetry breaking parameter △sat at the saturation point. All above physical parameter establish the relation with the parameters in formula of the anchoring energy and the flexoelectric coefficiente1 +e3. The influence of the flexoelectric effect on thethreshold voltage, the saturation voltage and the symmetry breaking parameter is discussed and calculated carefully.With the result of this investigate, a new experimental plan for measurement of the flexoelectric coefficient the non-symmetric liquid crystal cell is proposed. Now we consider a wedge liquid crystal cell.When different voltages U1 U2 U3 are applied to the cell, the value of thickness l1, l2 l3 may be obtained by measurement. We also assume three non-symmetric liquid crystal cells with the same anchoring substrates. But the value of thickness of the three cells are l1 l2 l3, respectively, we can also obtain thethreshold voltage U1 U2 U3 of corresponding to thickness. Using two methods, we can obtain three values group (l1,U1) (l2,U2) (l3,U3), so we get three equations about anchoring substrates A1 A2and flexoelectric coefficient (e1 + e3). The value of e1 + e3 can be determined by resolving the equation group.A new experimental plan for measurement of e is proposed. This plan is a useful innovation in this paper.更多还原