We investigate numerically the lattice orientation of cholesteric blue phases in contact with surfaces enforcing unidirectional planar anchoring. Our study is based on the Landau-de Gennes continuum theory in which the orientational order of the liquid crystal is described by a second-rank tensor. We particularly focus on blue phase I (BP I) with its (110) plane parallel to the surfaces, and blue phase II (BP II) with its (100) plane parallel to the surfaces. In the former case, the angle between the direction of unidirectional anchoring and the $\left[1\overline{1}0\right]$ axis of the BP I lattice is $\simeq 38.5^{\circ }$, insensitive to the anchoring strength, and consistent with the experimental finding for a cooling process [Takahashi et al., J. Phys. D 51, 104003 (2018)]. In the latter case, the [100] axis of the BP II lattice makes an angle of $45.0^{\circ }$ with the direction of unidirectional anchoring. Unidirectional anchoring of strength on the order of $1\times {10}^{-5}{\mathrm{J}\mathrm{m}}^{-2}$ is sufficient enough to lock the orientation of the blue phase lattice.

中文翻译：

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胆甾醇蓝相的晶格取向与表面接触，迫使表面单向锚固

我们在数值上研究与单向平面锚固表面接触的胆甾蓝相的晶格取向。我们的研究基于Landau-de Gennes连续体理论，其中液晶的取向顺序由二等张量描述。我们特别关注其（110）平面平行于表面的蓝相I（BP I），以及（100）平面平行于表面的蓝相II（BP II）。在前一种情况下，单向锚固方向与$\left[\mathrm{1个}\overline{\mathrm{1个}}0\right]$ BP I晶格的轴是 $\simeq 38。5^{\circ }$，对锚固强度不敏感，并且与冷却过程的实验结果一致[Takahashi等。，J。Phys。d 51，104003（2018）]。在后一种情况下，BP II晶格的[100]轴成$45。0^{\circ }$单向锚固的方向。单向锚固强度约为$\mathrm{1个}\times {10}^{-5}{\mathrm{Ĵ}\mathrm{米}}^{-2}$ 足以锁定蓝相晶格的方向。