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arXiv 1503.05514cond-mat.softcond-mat.mtrl-sciphysics.comp-ph
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多稳态液晶器件的自由能途径

Free energy pathways of a Multistable Liquid Crystal Device

Halim Kusumaatmaja, Apala Majumdar

摘要:

已知平面双折射器件[Tsakonas \textit{et al., Appl. Phys. Lett.},2007,{ \textbf{90} },111913]具有两类不同的稳定平衡:对角和旋转解。我们在二维Landau-de Gennes理论中对该器件进行建模,具有表面势,没有任何外部场。我们系统地计算一类特殊的过渡途径,称为最小能量途径,稳定的平衡,提供新的信息,如何平衡连接在朗道-德热内自由能景观之间。这些过渡途径表现出一个中间过渡态,这是一个鞍点的Landau-de Gennes自由能。我们数值计算的结构细节的过渡态,最佳的过渡路径和平衡之间的自由能垒,作为表面锚定强度的函数。对于强锚定,过渡路径是由缺陷介导的,而我们得到的缺陷的过渡路径为中度和弱锚定。在弱锚定极限,我们恢复了尖点突变的情况下,旋转状态作为一个过渡态连接两个不同的对角状态。

英文摘要:

The planar bistable device [Tsakonas \textit{et al., Appl. Phys. Lett.}, 2007, {\textbf{90}}, 111913] is known to have two distinct classes of stable equilibria: the diagonal and rotated solutions. We model this device within the two-dimensional Landau-de Gennes theory, with a surface potential and without any external fields. We systematically compute a special class of transition pathways, referred to as minimum energy pathways, between the stable equilibria that provide new information about how the equilibria are connected in the Landau-de Gennes free energy landscape. These transition pathways exhibit an intermediate transition state, which is a saddle point of the Landau-de Gennes free energy. We numerically compute the structural details of the transition states, the optimal transition pathways and the free energy barriers between the equilibria, as a function of the surface anchoring strength. For strong anchoring, the transition pathways are mediated by defects whereas we get defect-free transition pathways for moderate and weak anchoring. In the weak anchoring limit, we recover a cusp catastrophe situation for which the rotated state acts as a transition state connecting two different diagonal states.

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