Nematic Liquid Crystal Locking Menisci

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. 1. Introduction The field of liquid crystals, since its discovery in late 19th century, developed into a highly interdisciplinary research field [1]. The most known application of liquid crystals is LC displays. In recent times there are many other technologies and applications ready to be placed on the market, such as organic light emitting diodes, organic field effect transistors, and photovoltaic devices [2–6]. The liquid crystal structures are important also in biology, predominantly for the membranes of living cells, but also for some unusual applications as spider silks, which are spun from a lyotropic nematic liquid crystal precursor [7]. The emergence of this intermediate phase is due to the high concentration of rodlike molecules or aggregates in the watery dope solution. Nematic liquid crystals build intermediate phase combining liquid-like fluidity and solid-like orientational order. These phases are formed by a wide variety of materials comprised of rigid rodlike molecules. The orientational order of liquid crystals (LC) results from the spontaneous alignment of their molecules along a common preferred direction called director and described by a unit vector , where is the position vector. The states and are equivalent because the LC molecules are nonpolar. Director therefore can be thought of as a headless vector. Because many physical properties (e.g., optical, rheological, and mechanical) can be tailored by adjusting their geometric, external, and interfacial constraints (i.e., shape of the container, molecular orientation imposed by the surface, etc.), the nematic LCs can be very useful in various research fields [8]. As indicated before, the orientational order of LC molecules in principle varies with the position; therefore is valid only locally. For this reason complex orientational textures are formed [8–12]. Textures often contain defects, which usually correspond to regions (points or lines) where the director field cannot be uniquely defined [12, 13]. In order to distinguish between line and point defects one introduces the winding number , also called the Frank index [14,