A Numerical Investigation on Configurational Distortions in Nematic Liquid Crystals
A Numerical Investigation on Configurational Distortions in Nematic Liquid Crystals
复制标题
向列液晶构型畸变的数值研究
作者：
A. Pandolfi;G. Napoli
当受到磁场或电场的作用时，限制在两个平行玻璃板之间且初始取向均匀的向列相液晶可能经历均匀的一维空间变形(Fréedericksz和Zolina，Trans)。Faraday Soc.29：919,1933)或周期性扭曲(Lonberg和Meyer，Phys.莱特牧师。55(7)：718-721,1985；以及Srajer等人，Phys。莱特牧师。67(9)：1102-1105,1991年)。根据实验观察，在中场强作用下，周期相是稳定的构型，而在较高场强下，均相是稳定的，提出了一种完全非线性的有限元方法，能够描述具有强平面锚定边界条件的受限向列相液晶盒中的均匀构型和周期构型。通过将系统离散化总能量的第一个变量设置为零，得到了稳定的组态。通过评估解在小的数值扰动下的行为来识别不稳定的构型。数值计算能够描述作为外加电场的函数的位形畸变的演化，并且能够捕捉均匀相和周期相之间的临界点。新提出的方法已被证明是预测不稳定或亚稳态扭曲存在的极好工具，其特征是较高的能级。
When subjected to magnetic or electric fields, nematic liquid crystals confined between two parallel glass plates and initially uniformly oriented may undergo homogeneous one-dimensional spatial distortions (Fréedericksz and Zolina, Trans. Faraday Soc. 29:919, 1933) or periodic distortions (Lonberg and Meyer, Phys. Rev. Lett. 55(7):718–721, 1985; and Srajer et al., Phys. Rev. Lett. 67(9):1102–1105, 1991). According to the experimental observations, periodic phases are stable configurations at intermediate intensity of the acting field, while homogeneous phases are stable at higher strengths.We present a fully nonlinear finite element approach able to describe homogeneous and periodic configurational phases in a cell of confined nematic liquid crystal with strong planar anchoring boundary conditions. Stationary configurations are obtained by setting to zero the first variation of the discretized total energy of the system. Unstable configurations are identified by evaluating the behavior of the solution under small numerical perturbations. Numerical calculations are able to describe the evolution of the configurational distortions as a function of the applied field and are able to capture the critical points between homogeneous and periodic phases. The proposed approach has been proved to be an excellent tool to predict the existence of unstable or metastable distortions, characterized by higher energy levels.