ABSTRACT A striking feature of lyotropic chromonic liquid crystals confined in cylinder model exhibit double-twist director configurations. Evidence suggests that saddle-splay deformation is among the most important factors for the distortions of director. Previous researches limit the director to distort at a fixed plane (r-ϕ plane) by using specific boundary conditions such as degenerate planar anchoring condition. In this work, we consider lyotropic chromonic liquid crystals confined between two coaxial cylinders with free-surface boundary conditions and Rapini-Papoular-type anchoring conditions. By using finite-difference iterative method to solve the numerical solution of Euler equation, we find that saddle-splay deformation leads to double-twist director configurations under free-surface boundary conditions, which consist of the result under degenerate planar anchoring conditions. Furthermore, at Rapini-Papoular-type anchoring conditions, saddle-splay deformation has a great influence on the director in the radial direction (r direction) and the director distorts in three-dimensional space. Remarkably, our method provides a more accurate theory basis for the measured values of saddle-splay elastic constant K24。 Graphical abstract

中文翻译：

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马鞍形变形对限制在两个同轴圆柱之间的溶致发色液晶的影响

摘要 限制在圆柱模型中的溶致发色液晶的一个显着特征表现出双扭曲导向器配置。有证据表明，马鞍形变形是导致导向器失真的最重要因素之一。以前的研究通过使用特定的边界条件（例如退化平面锚定条件）来限制导向器在固定平面（r-φ 平面）处发生扭曲。在这项工作中，我们考虑了限制在具有自由表面边界条件和 Rapini-Papoular 型锚定条件的两个同轴圆柱之间的溶致发色液晶。通过使用有限差分迭代法求解欧拉方程的数值解，我们发现在自由表面边界条件下，鞍形变形导致双扭曲导向器构型，由退化平面锚定条件下的结果组成。此外，在Rapini-Papoular型锚定条件下，马鞍形变形对径向（r方向）的导向器有很大影响，导向器在三维空间发生扭曲。值得注意的是，我们的方法为鞍展弹性常数K24的测量值提供了更准确的理论基础。