Bevilacqua Giuseppe, Napoli Gaetano
CNISM and Dipartimento di Fisica, Università di Siena, via Roma 56, 53100 Siena, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Mar;81(3 Pt 1):031707. doi: 10.1103/PhysRevE.81.031707. Epub 2010 Mar 22.
This paper derives theoretical results for the periodic splay-twist Fréedericksz transition in nematic liquid crystals confined between two infinite concentric cylinders. The calculation of Lonberg and Meyer [Phys. Rev. Lett. 55, 718 (1985)], for nematics sandwiched between two infinite planes, is extended to annular domains. The phase transition is triggered by an applied voltage between the outer and the inner delimiting walls. The critical threshold behavior is analyzed via the linearized Euler-Lagrange equations related to the Frank's free energy. It is found that, the threshold depends on both the ratio between the twist and the splay elastic constants, and the sample radii ratio. Results for planar samples are recovered in the thin cell limit. With respect to the planar geometry, our analysis predicts that for annular geometries the periodic Fréedericksz transition is also allowed for elastic anisotropies K2/K1>0.303.
本文推导了限制在两个无限长同轴圆柱之间的向列型液晶中周期性展曲 - 扭曲弗雷德里克斯转变的理论结果。朗伯格和迈耶[《物理评论快报》55, 718 (1985)]对夹在两个无限大平面之间的向列相的计算被扩展到环形区域。相变由施加在外壁和内壁之间的电压触发。通过与弗兰克自由能相关的线性化欧拉 - 拉格朗日方程分析临界阈值行为。结果发现，阈值既取决于扭曲弹性常数与展曲弹性常数之比，也取决于样品半径比。在薄单元极限情况下可恢复平面样品的结果。相对于平面几何形状，我们的分析预测，对于环形几何形状，当弹性各向异性K2/K1>0.303时，周期性弗雷德里克斯转变也是允许的。
