微粒悬浮nematic liquid crystal细胞中位置转换快速“通道”的形成
Formation of a fast "lane" for positional transition in a microparticle-suspended nematic liquid crystal cell
摘要：
本文在利用格林函数方法对总能量进行数值计算的基础上，发现外加电场对微粒悬浮液晶盒的作用，如果达到一个临界值，结合其方向、表面锚定特性和分子介电各向异性，就有可能在微粒周围产生一个各向异性的“气泡”，并形成一条垂直的快“道”，其中微粒可以在不对称浮力的驱动下，从细胞的中平面迅速垂直移动到新的平衡位置，触发作者先前发现的位置转变。这种新的平衡位置是通过浮力和由沿着“通道”的弹性能量梯度在微粒上建立的有效力之间的竞争来决定的。外场的阈值取决于厚度$L$和Frank弹性常数$K$，并且以类似于Fréedericksz的方式但通过因子略微取决于微粒尺寸和密度。对于平面取向的双折射液晶盒，当外加电场方向（a）垂直于分子介电各向异性为正的盒的两个平板，或（b）平行于分子介电各向异性为负的盒的两个平板和锚定方向时，发现了转变的双折射平衡结构。除了垂直快速“车道”的形成外，当施加的电场平行于两个板并且垂直于锚定方向时，悬浮在双折射液晶中的微粒倾向于被捕获在中平面中，而与分子介电各向异性的符号无关。这种现象也发生在负分子介电各向异性，而外部施加垂直于两个板。
英文摘要：
In this paper, based on the numerical calculation of total energy utilizing the Green's function method, we found that the external electric field applied to a microparticle-suspended nematic liquid crystal cell, if reaching a critical value, combined with its direction, surface anchoring feature and molecular dielectric anisotropy, is possible to create an anisotropic "bubble" around the microparticle with a vertical fast "lane", in which the microparticle can, driven by the asymmetric buoyant force, vertically move swiftly from the cell's midplane to a new equilibrium position, triggering a positional transition discovered by the author previously. Such a new equilibrium position is decided via a competition between the buoyant force and the effective force built upon the microparticle by the elastic energy gradient along the "lane". The threshold value of external field, depends on thickness $L$ and Frank elastic constant $K$ and slightly on the microparticle size and density, in a Fréedericksz-like manner, but by a factor. For a nematic liquid crystal cell with planar surface alignment, a bistable equilibrium structure for the transition is found when the direction of the applied electric field is (a) perpendicular to the two plates of the cell with positive molecular dielectric anisotropy, or (b) parallel to the two plates and the anchoring direction of the cell with negative molecular dielectric anisotropy. Except for the formation of a vertical fast "lane", when the electric field applied is parallel to both the two plates and perpendicular to the anchoring direction, the microparticle suspended in the nematic liquid crystal tends to be trapped in the midplane, regardless of the sign of the molecular dielectric anisotropy. Such phenomenon also occurs for negative molecular dielectric anisotropy while the external is applied perpendicular to the two plates.
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