Abstract
We study meniscus driven locking of point defects of nematic liquid crystals confined within a cylindrical tube with free ends. Curvilinear coordinate system is introduced in order to focus on the phenomena of both (convex and concave) types of menisci. Frank's description in terms of the nematic director field is used. The resulting Euler-Lagrange differential equation is solved numerically. We determine conditions for the defects to be trapped by the meniscus.
Highlights
The field of liquid crystals, since its discovery in late 19th century, developed into a highly interdisciplinary research field [1]
In this paper we presented theoretical and numerical study of locking the defects by meniscus in capillaries filled with nematic liquid crystal molecules having homeotropic anchoring at the capillary walls
Addition quantitative changes are expected if nematic order parameter spatial variations would be taken into account [33]
Summary
The field of liquid crystals, since its discovery in late 19th century, developed into a highly interdisciplinary research field [1]. In the problem of interest we study the impact of menisci curvature on position of defects deep in the nematic’s phase In this case key features are dominated by Frank elasticity. Convex and concave menisci for ξ = H, there is a typical finite radius of curvature ρ(H) = a which depends on the structure (geometrical and chemical) of the liquid crystal molecules and on the boundary conditions of the system. In terms of the parameterization introduced, we calculate the free energy density (concave and convex menisci give the same result):. Appropriate equation, regarding concave and convex cases, was used to numerically test the behavior of the defects enclosed by the cylinder and exposed to the predicted boundary conditions.
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