Disclination Shape Analysis for Nematic Liquid Crystals under Micron-range Capillary Confinement
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Disclination Shape Analysis for Nematic Liquid Crystals under Micron-range Capillary Confinement Alireza Shams1, Xuxia Yao2, Jung Ok Park2, 3, Mohan Srinivasarao2, 3, 4 and Alejandro D. Rey1 1 Department of Chemical Engineering, McGill University, Montreal, Quebec H3A 2B2, Canada 2 School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA 3 Center for Advanced Research on Optical Microscopy, Georgia Institute of Technology, Atlanta, GA 30332, USA 4 School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA 30332, USA ABSTRACT Nematic liquid crystals (NLCs) under micron-range confinement exhibit a rich defect phenomenology that can be used to extract elastic (Frank moduli) material parameters of critical importance for next generation electro-optical devices. In this work we develop a model to predict defect-driven textural transformations that arise when a NLC is confined to a circular capillary. In the initial transformation stage an unstable disclination defect of strength +1 nucleates in the axis of the capillary and quickly branches into two stable +1/2 disclination defects. The model includes: (1) the Kirchhoff branch balance equation which predicts the splitting of a +1 into two +1/2 wedge disclinations; (2) the curvature of the +1/2 disclination lines as a function of elastic properties. This model shows that by increasing the ratio of tension strength to bending stiffness, the branch point angle increases, but the final defect distance decreases; and (3) the aperture branching angle of the +1/2 lines as a function of the elastic properties and the magnitude of the curvature at the branch point. These three predictions form the basis for the evaluation of the Frank elastic moduli on NLCs. The key advantage of the implemented methodology is to use time-dependent textural transformations under micron-range capillary confinement to extract elastic parametric data needed to further develop NLCs in functional and structural application. INTRODUCTION Topological defects in liquid crystals are of crucial importance in devices and material characterization and are easily observable with polarized optical microscopy.1,2. Liquid crystals under confinement 3,4 provides a controlled nucleation and coarsening environment based on frustration emanating from fixed orientation at curved bounding surfaces5,6. A disclination is defined as a 1D line defect in which rotational symmetry is violated7. To study disclinations in liquid crystals, we need to specify the molecular order and average orientation. Based on the continuum theory of liquid crystals, the local mean orientation is defined by a director field n1. For NLCs one can use a traceless tensor order parameter Q=Λ(nn-I/3)+P(mm-ll) , where (Λ, P) are the uniaxial and biaxial order parameters and (n, m, l) are the orthonormal directors1. The ∇Λ ≠ 0, ∇P ≠ 0 ) result in the core energy per defect-associated order parameter heterogeneities ( unit volume. When the disclination line is curved, additional distor
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