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Schimming CD, Viñals J. Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines. SOFT MATTER 2022; 18:2234-2244. [PMID: 35234228 DOI: 10.1039/d1sm01584b] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We introduce a characterization of disclination lines in three dimensional nematic liquid crystals as a tensor quantity related to the so called rotation vector around the line. This quantity is expressed in terms of the nematic tensor order parameter Q, and shown to decompose as a dyad involving the tangent vector to the disclination line and the rotation vector. Further, we derive a kinematic law for the velocity of disclination lines by connecting this tensor to a topological charge density as in the Halperin-Mazenko description of defects in vector models. Using this framework, analytical predictions for the velocity of interacting line disclinations and of self-annihilating disclination loops are given and confirmed through numerical computation.
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Affiliation(s)
- Cody D Schimming
- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA.
| | - Jorge Viñals
- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA.
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2
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Aya S, Kougo J, Araoka F, Haba O, Yonetake K. Nontrivial topological defects of micro-rods immersed in nematics and their phototuning. Phys Chem Chem Phys 2022; 24:3338-3347. [PMID: 35060569 DOI: 10.1039/d1cp03363h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Combinations of different geometries and surface anchoring conditions give rise to the diversity of topological structures in nematic colloid systems. Tuning these parameters in a single system offers possibilities for observing the evolution of the topological transformation and for manipulating colloids through topological forces. Here we investigate the nontrivial topological properties of micro-rods dispersed in nematic liquid crystals through experimental observation and computer simulation. The topological variation is driven by photodynamically changing the surface anchoring using azobenzene-based surface-commander molecules, the majority of which are localized on both the substrates and the surface of micro-rods. By comparing experimental and simulation results, we show previously unidentified topological properties of the two-body LC-rod-colloid system. Moreover, unlike the traditional photoresponsive liquid crystal systems, the localization of azobenzene molecules on the surfaces makes it possible to change only the direction of the surface orientation, not disordering of the bulk structures. The results assist in the development of photo-driven micro-robotics in fluids.
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Affiliation(s)
- Satoshi Aya
- South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Molecular Science and Engineering, South China University of Technology, Guangzhou 510640, China. .,Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou 510640, China
| | - Junichi Kougo
- South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Molecular Science and Engineering, South China University of Technology, Guangzhou 510640, China. .,Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou 510640, China
| | - Fumito Araoka
- RIKEN Center for Emergent Matter Science (CEMS), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Osamu Haba
- Graduate School of Organic Materials Science, Yamagata University, Yonezawa 992-8510, Yamagata, Japan
| | - Koichiro Yonetake
- Graduate School of Organic Materials Science, Yamagata University, Yonezawa 992-8510, Yamagata, Japan
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3
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Qiu M, Feng JJ, Loudet JC. Phase-field model for elastocapillary flows of liquid crystals. Phys Rev E 2021; 103:022706. [PMID: 33736098 DOI: 10.1103/physreve.103.022706] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 01/19/2021] [Indexed: 11/07/2022]
Abstract
We propose a phase-field model to study interfacial flows of nematic liquid crystals that couple the capillary forces on the interface with the elastic stresses in the nematic phase. The theoretical model has two key ingredients: A tensor order parameter that provides a consistent description of the molecular and distortional elasticity, and a phase-field formalism that accurately represents the interfacial tension and the nematic anchoring stress by approximating a sharp-interface limit. Using this model, we carry out finite-element simulations of drop retraction in a surrounding fluid, with either component being nematic. The results are summarized by eight representative steady-state solutions in planar and axisymmetric geometries, each featuring a distinct configuration for the drop and the defects. The dynamics is dominated by the competition between the interfacial tension and the distortional elasticity in the nematic phase, mediated by the anchoring condition on the drop surface. As consequences of this competition, the steady-state drop deformation and the clearance between the defects and the drop surface both depend linearly on the elastocapillary number.
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Affiliation(s)
- Mingfeng Qiu
- Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
| | - James J Feng
- Department of Mathematics and Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
| | - Jean-Christophe Loudet
- Université de Bordeaux, CNRS, Centre de Recherche Paul Pascal (UMR 5031), F-33600 Pessac, France
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4
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Denniston C. Theory and simulation of objects in liquid crystals. ADVANCES IN PHYSICS: X 2020. [DOI: 10.1080/23746149.2020.1806728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022] Open
Affiliation(s)
- Colin Denniston
- Department of Applied Mathematics and Department of Physics and Astronomy, The University of Western Ontario, London, ON, Canada
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5
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Conklin C, Tovkach OM, Viñals J, Calderer MC, Golovaty D, Lavrentovich OD, Walkington NJ. Electrokinetic effects in nematic suspensions: Single-particle electro-osmosis and interparticle interactions. Phys Rev E 2018; 98:022703. [PMID: 30253587 DOI: 10.1103/physreve.98.022703] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2017] [Indexed: 11/07/2022]
Abstract
Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.
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Affiliation(s)
- Christopher Conklin
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - O M Tovkach
- Department of Mathematics, The University of Akron, Akron, Ohio 44325, USA.,Bogolyubov Institute for Theoretical Physics, NAS of Ukraine, Metrologichna 14-b, Kyiv 03680, Ukraine
| | - Jorge Viñals
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - M Carme Calderer
- School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Dmitry Golovaty
- Department of Mathematics, The University of Akron, Akron, Ohio 44325, USA
| | - Oleg D Lavrentovich
- Liquid Crystal Institute, Department of Physics and Chemical Physics Interdisciplinary Program, Kent State University, Kent, Ohio 44242, USA
| | - Noel J Walkington
- Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
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6
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Wang Y, Zhang P, Chen JZY. Topological defects in an unconfined nematic fluid induced by single and double spherical colloidal particles. Phys Rev E 2017; 96:042702. [PMID: 29347619 DOI: 10.1103/physreve.96.042702] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2017] [Indexed: 06/07/2023]
Abstract
We present numerical solutions to the Landau-de Gennes free-energy model under the one-constant approximation for systems of single and double spherical colloidal particles immersed in an otherwise uniformly aligned nematic liquid crystal. A perfect homeotropic surface anchoring of liquid-crystal molecules on the spherical surface is considered. A large parameter space is carefully examined, including those in the free-energy model and those describing the dimer configurations and the background liquid-crystal orientation. The stability of the resulting liquid-crystal defects appearing in the neighborhood of the colloidal dimer pair is analyzed in light of the numerical results for their free energies. A number of scenarios are considered: a free dimer pair in a nematic fluid where the free-energy ground states are described in terms of a phase diagram, and a constrained dimer pair where the interparticle distance and the relative orientation of the distance vector to the nematic director can be manipulated. We pay particular attention to the nonsymmetric solutions, which yield several metastable defect states that can be observed in real systems. The high-precision numerical calculations are based on a spectral method, which is an enabling factor that allows us to compare the subtle difference in the free energies of different defect structures.
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Affiliation(s)
- Yiwei Wang
- LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China
| | - Pingwen Zhang
- LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada
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7
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Chu G, Vilensky R, Vasilyev G, Deng S, Qu D, Xu Y, Zussman E. Structural Transition in Liquid Crystal Bubbles Generated from Fluidic Nanocellulose Colloids. Angew Chem Int Ed Engl 2017. [DOI: 10.1002/ange.201703869] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Guang Chu
- Faculty of Mechanical Engineering; Technion-Israel Institute of Technology; Haifa 32000 Israel
| | - Rita Vilensky
- Faculty of Mechanical Engineering; Technion-Israel Institute of Technology; Haifa 32000 Israel
| | - Gleb Vasilyev
- Faculty of Mechanical Engineering; Technion-Israel Institute of Technology; Haifa 32000 Israel
| | - Shengwei Deng
- Faculty of Mechanical Engineering; Technion-Israel Institute of Technology; Haifa 32000 Israel
| | - Dan Qu
- State Key Laboratory of Inorganic Synthesis and Preparative Chemistry; Jilin University; 2699 Qianjin Street Changchun 130012 China
| | - Yan Xu
- State Key Laboratory of Inorganic Synthesis and Preparative Chemistry; Jilin University; 2699 Qianjin Street Changchun 130012 China
| | - Eyal Zussman
- Faculty of Mechanical Engineering; Technion-Israel Institute of Technology; Haifa 32000 Israel
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8
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Chu G, Vilensky R, Vasilyev G, Deng S, Qu D, Xu Y, Zussman E. Structural Transition in Liquid Crystal Bubbles Generated from Fluidic Nanocellulose Colloids. Angew Chem Int Ed Engl 2017; 56:8751-8755. [PMID: 28570772 DOI: 10.1002/anie.201703869] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2017] [Indexed: 11/05/2022]
Abstract
The structural transition in micrometer-sized liquid crystal bubbles (LCBs) derived from rod-like cellulose nanocrystals (CNCs) was studied. The CNC-based LCBs were suspended in nematic or chiral nematic liquid-crystalline CNCs, which generated topological defects and distinct birefringent textures around them. The ordering and structure of the LCBs shifted from a nematic to chiral nematic arrangement as water evaporation progressed. These packed LCBs exhibited a specific photonic cross-communication property that is due to a combination of Bragg reflection and bubble curvature and size.
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Affiliation(s)
- Guang Chu
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, 32000, Israel
| | - Rita Vilensky
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, 32000, Israel
| | - Gleb Vasilyev
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, 32000, Israel
| | - Shengwei Deng
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, 32000, Israel
| | - Dan Qu
- State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, Jilin University, 2699 Qianjin Street, Changchun, 130012, China
| | - Yan Xu
- State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, Jilin University, 2699 Qianjin Street, Changchun, 130012, China
| | - Eyal Zussman
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, 32000, Israel
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