Disclination elastica model of loop collision and growth in confined nematic liquid crystals (original) (raw)
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Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
The combination of low elasticity modulus, anisotropy, and responsiveness to external fields drives the rich variety of experimentally observed pattern formation in nematic liquid crystals under capillary confinement. External fields of interest in technology and fundamental physics are flow fields, electromagnetic fields, and surface fields due to confinement. In this paper we present theoretical and simulation studies of the pattern formation of nematic liquid crystal disclination loops under capillary confinement including branching processes from a m=+1 disclination line to two m=+1/2 disclination curves that describe the postnucleation and growth regime of the textural transformation from radial to planar polar textures. The early postnucleation and growth of emerging disclination loops in cylindrical capillaries are characterized using analytical and computational methods based on the nematic elastica that takes into account line tension and line bending stiffness. Using subdi...
Disclination loops, standing alone and around solid particles, in nematic liquid crystals
Physical Review E, 1995
A suspended particle with specific director anchoring on its surface introduces a complex distortion Geld in a nematic liquid crystal matrix. Topological defectsdisclination loops, boojums, and hedgehogs, are needed to match the director near the particle surface with that at the far distance, which is determined by boundary conditions on the sample. This paper analyzes the elastic energy and stability of a singular loop of wedge disclination and the first-order transition of the radial hedgehog into a wide singular loop, driven by an external magnetic Geld. The far field of distortions, created by a "Saturn ring" of disclination around the spherical radial particle, allows one to calculate the potential of interaction between such particles and with the surface of the liquid crystal. Particles are repelled from each other and from the rigidly anchored surface with the potential U 1/r. If the sample surface has soft anchoring, the particle is attracted to it at close distances and is repelled, if beyond the anchoring coherence length (. Several experiments to test these conclusions are suggested.
Shape control of surface-stabilized disclination loops in nematic liquid crystals
Physical review. E, 2018
Recent studies on topological defects in conventional and active nematic liquid crystals have revealed their potential as sources of advanced functionality whereby the collective behavior of the constituent molecules or cells is controlled. On the other hand, the fact that they have high energies and are metastable makes their shape control a nontrivial issue. Here, we demonstrate stabilization of arbitrary-shaped closed disclination loops with 1/2 strength floating in the bulk by designing the twist angle distribution in a liquid crystal cell. Continuous variation of the twist angle from below to above |π/2| allows us to unambiguously position reverse twist disclinations at will. We also analyze the elastic free energy and uncover the relationship between the twist angle pattern and shrink rate of the surface-stabilized disclination loop.
The Journal of Chemical Physics, 2008
We study the annihilation of hedgehog-antihedgehog defects in confined nematic liquid crystals using Brownian molecular dynamics simulations. After the collision, merging of defects, and building a loop disclination structure, system can experience a structural transition into another nematic structure, triggered by a nucleation of loop disclination structure. In our rough theoretical approach we calculate the size of the emerged loop structure as the function of the typical size of the confining cavity. Attention is paid also to the dynamics of the loop structure after collision.
Periodic deformations in nematic liquid crystals
Physical Review E, 2002
We reconsider the possibility of periodic deformations in nematic liquid crystal samples, and present a simple method to analyze their stability near the threshold. Our method consists in finding the matrix characterizing the total energy in terms of the integration constants of the linearized solutions of the variational problem. In the undeformed state all the integration constants are identically zero. Hence the analysis of the stability of the undeformed state reduces to the analysis of the sign of the determinants of the principal minors of the matrix of the quadratic form representing the total energy of the nematic sample. We discuss the role of the saddle-splay elastic constant and of the anchoring energy strength in the stability of the modulated structure. The role of the thickness of the sample, as well as of the polar and azimuthal anchoring energies, in the phenomenon is also considered.
Expulsion of disclinations in nematic liquid crystals
European Journal of Applied Mathematics, 2003
We study the interactions between a nematic liquid crystal disclination and the surface of the half-space which bounds it. When strong anchoring conditions are applied on the boundary, we show how the biaxial core of the disclination affects the repulsive force that tends to drive the disclination away from the surface. If we replace the strong boundary conditions with an anchoring potential, the surface-disclination interaction depends on the surface extrapolation length. In particular, we show that the nematic may expel the disclination if the anchoring strength is below a critical value.
Coarsening dynamics of biaxial nematic liquid crystals
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
We study the coarsening dynamics of two- and three-dimensional biaxial nematic liquid crystals, using Langevin dynamics. Unlike previous work, we use a model with no a priori relationship among the three elastic constants associated with director deformations. Biaxial nematics possess four topologically distinct classes of defects, three of which have half-integer charge, while the fourth, which plays a minor role in coarsening, is of integer charge. We find a rich variety of coarsening behavior, including the presence of one, two, or three of the half-integer classes at late times, depending on the relative values of the elastic constants and the resulting energetics of the decay channels of the defects. The morphology of the defect tangle in three dimensions when all three classes are present is particularly interesting. Rather than forming independent defect loops (as occurs when only one or two of the classes are present), the defect lines meet at junction points which are distr...
A Model of Capillary Rise of Nematic Liquid Crystals
Langmuir, 2003
A general model for the capillary rise for uniaxial nematic liquid crystals has been derived using fundamental principles and classical liquid crystal physics and partially validated using existing experimental data. A rigorous formulation of the contributions of surface and bulk nematic elasticity was implemented. The surface contribution is a function of the surface anchoring strength at the liquid crystalcapillary wall. The exact bulk elasticity contribution is a function of the director field in the meniscus. The specific form of the capillary rise equation for four typical nematic textures was developed and analyzed. It is found that capillary rise depends on the presence of bulk disclinations and on the orientation field close to the contact line. It is found that orientation gradients at the contact line are the most significant nematic contribution to capillary rise. The model explains unusual features in experimental capillary rise measurements, including why parallel nematic orientation at the capillary wall exhibits a higher capillary rise than orthogonal orientation.
A Numerical Investigation on Configurational Distortions in Nematic Liquid Crystals
Journal of Nonlinear Science, 2011
When subjected to magnetic or electric fields, nematic liquid crystals confined between two parallel glass plates and initially uniformly oriented may undergo homogeneous one-dimensional spatial distortions (Fréedericksz and Zolina, Trans. Faraday Soc. 29:919, 1933) or periodic distortions (Lonberg and Meyer, Phys. Rev. Lett. 55 : 718-721, 1985; and Srajer et al., Phys. Rev. Lett. 67(9):1102-1105. According to the experimental observations, periodic phases are stable configurations at intermediate intensity of the acting field, while homogeneous phases are stable at higher strengths.
Planar Anchoring of Achiral Nematic Liquid Crystals in Capillaries---with a Twist
In the common three-term Frank free energy of a nematic liquid crystal, the ground state configuration will have no deformations and all nematic directors will be parallel. However, certain confining geometries can impose significant deformations on the ground state, even if a zero-deformation configuration can be drawn that satisfies all boundary conditions. By solving the Euler-Lagrange problem of the Frank free energy equation, including the saddle-splay term, with cylindrical confinement and degenerate planar anchoring, we find conditions for a highly deformed ground state configuration that has a double twist like structure. We explore these effects experimentally with both thermotropic and lyotropic liquid crystal materials, finding good agreement with the theoretically predicted configuration. We also observe a rich phenomenology of defect structures in the liquid crystal samples.