受限胆甾相液晶中的毛细管和缠绕相变
Capillary and winding transitions in a confined cholesteric liquid crystal
摘要：
本文考虑了一个平面胞腔（狭缝孔）中手性粒子的Lebwohl-Lasher模型，在不同的边界条件下，用平均场论求解。研究了该体系的相行为随温度和孔宽的变化规律。观察到两种现象：（i）各向同性-弯曲过渡，其表现出相对于孔宽度的振荡结构，和（ii）由弯曲节距和孔宽度之间的弯曲效应引起的无限组的弯曲过渡。后者的过渡已被预测和分析的其他作者胆固醇局限在一个固定的孔和受外部场促进单轴相变;在这里，我们诱导绕组过渡仅从几何形状通过改变孔的宽度在零外部场（最近在原子力显微镜实验探索的设置）。与以往的研究结果相比，我们得到了温度-孔宽平面上的相图，包括各向同性相变、弯曲相变以及它们之间的复杂关系。特别地，缠绕过渡的结构通过三相点终止于毛细管各向同性-胆甾相过渡，其中受限的各向同性相与具有不同螺旋指数的两种胆甾相共存。对于对称和非对称单稳态平板锚定，相图定性相似。
英文摘要：
We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature and pore width is studied. Two phenomena are observed: (i) an isotropic-cholesteric transition which exhibits an oscillatory structure with respect to pore width, and (ii) an infinite set of winding transitions caused by commensuration effects between cholesteric pitch and pore width. The latter transitions have been predicted and analysed by other authors for cholesterics confined in a fixed pore and subject to an external field promoting the uniaxial nematic phase; here we induce winding transitions solely from geometry by changing the pore width at zero external field (a setup recently explored in Atomic-Force Microscopy experiments). In contrast with previous studies, we obtain the phase diagrams in the temperature vs pore width plane, including the isotropic-cholesteric transition, the winding transitions and their complex relationship. In particular, the structure of winding transitions terminates at the capillary isotropic-cholesteric transition via triple points where the confined isotropic phase coexists with two cholesterics with different helix indices. For symmetric and asymmetric monostable plate anchorings the phase diagram are qualitatively similar.
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