正弦信道上的Nematic liquid crystals：锯齿形不稳定性
Nematic liquid crystals on sinusoidal channels: the zigzag instability
摘要：
化学或形貌图案化的基板诱导各种液晶纹理。液晶对竞争表面取向的响应（典型的图案化基板）由弹性常数的各向异性和相关长度尺度（诸如相关长度和表面几何参数）的相互作用来确定。通常具有不同对称性的不同纹理之间的转变可以在广泛的条件下发生。我们使用的朗道-德Gennes自由能调查的纹理的向列相在正弦通道与平行锚定的向列相空气界面，有利于垂直（各向同性）锚定。在微米尺寸的通道5CB被观察到表现出非平凡的纹理，其特征在于在通道内的向错线，其被分成Z字形图案。我们的计算表明，当向列相的弹性各向异性不有利于扭曲变形时，缺陷是沿着通道延伸的直线向错线，当扭曲弹性常数变得足够小时，它会分解成具有特征周期的锯齿形图案。与张开和弯曲常数相比。这种转变是通过扭转不稳定性发生的，扭转不稳定性驱动缺陷线从其原始位置旋转。能量上有利的扭曲变形，诱导缺陷旋转和液晶锚定在表面之间的相互作用导致之字形图案。我们详细研究了锯齿形图案的周期性对正弦通道的几何参数的依赖关系，这与实验结果一致，被发现是非线性的。
英文摘要：
Substrates which are chemically or topographically patterned induce a variety of liquid crystal textures. The response of the liquid crystal to competing surface orientations, typical of patterned substrates, is determined by the anisotropy of the elastic constants and the interplay of the relevant lengths scales, such as the correlation length and the surface geometrical parameters. Transitions between different textures, usually with different symmetries, may occur under a wide range of conditions. We use the Landau-de Gennes free energy to investigate the texture of nematics in sinusoidal channels with parallel anchoring bounded by nematic-air interfaces that favour perpendicular (hometropic) anchoring. In micron size channels 5CB was observed to exhibit a non-trivial texture characterized by a disclination line, within the channel, which is broken into a zigzag pattern. Our calculations reveal that when the elastic anisotropy of the nematic does not favour twist distortions the defect is a straight disclination line that runs along the channel, which breaks into a zigzag pattern with a characteristic period, when the twist elastic constant becomes sufficiently small when compared to the splay and bend constants. The transition occurs through a twist instability that drives the defect line to rotate from its original position. The interplay between the energetically favourable twist distortions that induce the defect rotation and the liquid crystal anchoring at the surfaces leads to the zigzag pattern. We investigate in detail the dependence of the periodicity of the zigzag pattern on the geometrical parameters of the sinusoidal channels, which in line with the experimental results is found to be non-linear.
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