Luo Chong, Majumdar Apala, Erban Radek
Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061702. doi: 10.1103/PhysRevE.85.061702. Epub 2012 Jun 8.
A planar bistable liquid crystal device, reported in Tsakonas et al. [Appl. Phys. Lett. 90, 111913 (2007)], is modeled within the Landau-de Gennes theory for nematic liquid crystals. This planar device consists of an array of square micrometer-sized wells. We obtain six different classes of equilibrium profiles and these profiles are classified as diagonal or rotated solutions. In the strong anchoring case, we propose a Dirichlet boundary condition that mimics the experimentally imposed tangent boundary conditions. In the weak anchoring case, we present a suitable surface energy and study the multiplicity of solutions as a function of the anchoring strength. We find that diagonal solutions exist for all values of the anchoring strength W ≥ 0, while rotated solutions only exist for W ≥ W_{c}>0, where W_{c} is a critical anchoring strength that has been computed numerically. We propose a dynamic model for the switching mechanisms based on only dielectric effects. For sufficiently strong external electric fields, we numerically demonstrate diagonal-to-rotated and rotated-to-diagonal switching by allowing for variable anchoring strength across the domain boundary.
察科纳斯等人[《应用物理快报》90, 111913 (2007)]报道的一种平面双稳态液晶器件，在向列型液晶的朗道 - 德热纳理论框架内进行建模。这种平面器件由一系列微米级的方形阱组成。我们得到了六类不同的平衡分布，这些分布被分类为对角或旋转解。在强锚定情况下，我们提出一种狄利克雷边界条件，它模拟了实验施加的切向边界条件。在弱锚定情况下，我们给出了合适的表面能，并研究解的多重性作为锚定强度的函数。我们发现，对于所有锚定强度(W\geq0)的值，对角解都存在，而旋转解仅在(W\geq W_{c}>0)时存在，其中(W_{c})是通过数值计算得到的临界锚定强度。我们提出了一种仅基于介电效应的切换机制的动态模型。对于足够强的外部电场，通过允许在域边界上有可变的锚定强度，我们在数值上证明了对角到旋转以及旋转到对角的切换。
