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Wamsler K, Head LC, Shendruk TN. Lock-key microfluidics: simulating nematic colloid advection along wavy-walled channels. SOFT MATTER 2024; 20:3954-3970. [PMID: 38682298 PMCID: PMC11095502 DOI: 10.1039/d3sm01536j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Accepted: 04/10/2024] [Indexed: 05/01/2024]
Abstract
Liquid crystalline media mediate interactions between suspended particles and confining geometries, which not only has potential to guide patterning and bottom-up colloidal assembly, but can also control colloidal migration in microfluidic devices. However, simulating such dynamics is challenging because nemato-elasticity, diffusivity and hydrodynamic interactions must all be accounted for within complex boundaries. We model the advection of colloids dispersed in flowing and fluctuating nematic fluids confined within 2D wavy channels. A lock-key mechanism between homeotropic colloids and troughs is found to be stronger for planar anchoring on the wavy walls compared to homeotropic anchoring on the wavy walls due to the relative location of the colloid-associated defects. Sufficiently large amplitudes result in stick-slip trajectories and even permanent locking of colloids in place. These results demonstrate that wavy walls not only have potential to direct colloids to specific docking sites but also to control site-specific resting duration and intermittent elution.
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Affiliation(s)
- Karolina Wamsler
- School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Louise C Head
- School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Tyler N Shendruk
- School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
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2
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Renner J, Schmidt M, de Las Heras D. Reduced-variance orientational distribution functions from torque sampling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:235901. [PMID: 36974000 DOI: 10.1088/1361-648x/acc522] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 03/08/2023] [Indexed: 06/18/2023]
Abstract
We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium. Instead of the traditional counting of events, we reconstruct the orientational distribution function via an orientational integral of the torque acting on the particles. We test the torque sampling method in two- and three-dimensions, using both Langevin dynamics and overdamped Brownian dynamics, and with two interparticle interaction potentials. In all cases the torque sampling method produces profiles of the orientational distribution function with better accuracy than those obtained with the traditional counting method. The accuracy of the torque sampling method is independent of the bin size, and hence it is possible to resolve the orientational distribution function with arbitrarily small angular resolutions.
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Affiliation(s)
- Johannes Renner
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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3
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Monderkamp PA, Wittmann R, Te Vrugt M, Voigt A, Wittkowski R, Löwen H. Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals. Phys Chem Chem Phys 2022; 24:15691-15704. [PMID: 35552573 DOI: 10.1039/d2cp00060a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Observing and characterizing the complex ordering phenomena of liquid crystals subjected to external constraints constitutes an ongoing challenge for chemists and physicists alike. To elucidate the delicate balance appearing when the intrinsic positional order of smectic liquid crystals comes into play, we perform Monte-Carlo simulations of rod-like particles in a range of cavities with a cylindrical symmetry. Based on recent insights into the topology of smectic orientational grain boundaries in two dimensions, we analyze the emerging three-dimensional defect structures from the perspective of tetratic symmetry. Using an appropriate three-dimensional tetratic order parameter constructed from the Steinhardt order parameters, we show that those grain boundaries can be interpreted as a pair of tetratic disclination lines that are located on the edges of the nematic domain boundary. Thereby, we shed light on the fine structure of grain boundaries in three-dimensional confined smectics.
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Affiliation(s)
- Paul A Monderkamp
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
| | - Michael Te Vrugt
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Axel Voigt
- Institut für Wissenschaftliches Rechnen, Technische Universität Dresden, 01062 Dresden, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
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4
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Monderkamp PA, Wittmann R, Cortes LBG, Aarts DGAL, Smallenburg F, Löwen H. Topology of Orientational Defects in Confined Smectic Liquid Crystals. PHYSICAL REVIEW LETTERS 2021; 127:198001. [PMID: 34797147 DOI: 10.1103/physrevlett.127.198001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Revised: 06/28/2021] [Accepted: 09/22/2021] [Indexed: 06/13/2023]
Abstract
We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in pointlike units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive Monte Carlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showing how the observed defect networks can be universally reconstructed from simple building blocks. We further find that the curvature of the confining wall determines the anchoring behavior of grain boundaries, such that the number of nodes in the emerging networks and the location of their end points can be tuned by changing the number and smoothness of corners, respectively.
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Affiliation(s)
- Paul A Monderkamp
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Louis B G Cortes
- School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA
| | - Dirk G A L Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Frank Smallenburg
- Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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5
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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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6
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Affiliation(s)
- Michael P. Allen
- Department of Physics, University of Warwick, Coventry, UK
- H. H. Wills Physics Laboratory, Royal Fort, Bristol, UK
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8
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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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9
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Rahimi M, Ramezani-Dakhel H, Zhang R, Ramirez-Hernandez A, Abbott NL, de Pablo JJ. Segregation of liquid crystal mixtures in topological defects. Nat Commun 2017; 8:15064. [PMID: 28452347 PMCID: PMC5414351 DOI: 10.1038/ncomms15064] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2016] [Accepted: 02/24/2017] [Indexed: 01/29/2023] Open
Abstract
The structure and physical properties of liquid crystal (LC) mixtures are a function of composition, and small changes can have pronounced effects on observables, such as phase-transition temperatures. Traditionally, LC mixtures have been assumed to be compositionally homogenous. The results of chemically detailed simulations presented here show that this is not the case; pronounced deviations of the local order from that observed in the bulk at defects and interfaces lead to significant compositional segregation effects. More specifically, two disclination lines are stabilized in this work by introducing into a nematic liquid crystal mixture a cylindrical body that exhibits perpendicular anchoring. It is found that the local composition deviates considerably from that of the bulk at the interface with the cylinder and in the defects, thereby suggesting new assembly and synthetic strategies that may capitalize on the unusual molecular environment provided by liquid crystal mixtures. Liquid crystal mixtures are used in commercial applications and their composition affects their properties. Here Rahimi et al. use atomistic simulations to show that defects influence the molecular arrangement of the mixture components leading to a deviation of the local order from that of the bulk.
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Affiliation(s)
- Mohammad Rahimi
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Hadi Ramezani-Dakhel
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Rui Zhang
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Abelardo Ramirez-Hernandez
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA.,Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Nicholas L Abbott
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Juan J de Pablo
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA.,Argonne National Laboratory, Argonne, Illinois 60439, USA
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10
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Püschel-Schlotthauer S, Meiwes Turrión V, Hall CK, Mazza MG, Schoen M. The Impact of Colloidal Surface-Anchoring on the Smectic A Phase. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2017; 33:2222-2234. [PMID: 28165243 DOI: 10.1021/acs.langmuir.6b03941] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Liquid-crystalline phases are known for their unique properties, i.e., the combination of fluidity and long-range orientational and/or positional order. The presence of a colloidal particle gives rise to perturbations of this order locally. These perturbations are the origin of intercolloidal forces driving the colloidal self-assembly in a directed manner. Hence, the understanding of these perturbations is the first step in understanding and controlling the self-assembly process. Here, we perform Monte Carlo simulations to investigate the perturbations of orientational and positional order in a smectic A phase caused by a spherical colloid. We model the host phase via an interaction potential that reproduces characteristic features of phase behavior, structure, dynamics, and elasticity [S. Püschel-Schlotthauer et al. J. Chem. Phys. 2016, 145, 164903]. For strong homeotropic anchoring conditions, we find a Saturn ring defect and an onion structure in the smectic A phase; the latter has never been reported for colloids so far. For strong planar anchoring conditions, we find Boojum defects that become elongated at low temperature, similar to what is observed in experiments. However, for weak planar anchoring conditions, a double surface ring defect is exhibited in the smectic A phase.
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Affiliation(s)
- Sergej Püschel-Schlotthauer
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Technische Universität Berlin , Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Victor Meiwes Turrión
- Max Planck Institute for Dynamics and Self-Organization (MPIDS) , Am Faßberg 17, 37077 Göttingen, Germany
| | - Carol K Hall
- Department of Chemical and Biomolecular Engineering, North Carolina State University , Engineering Building I, Box 7905, 911 Partners Way, Raleigh, North Carolina 27695, United States
| | - Marco G Mazza
- Max Planck Institute for Dynamics and Self-Organization (MPIDS) , Am Faßberg 17, 37077 Göttingen, Germany
| | - Martin Schoen
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Technische Universität Berlin , Straße des 17. Juni 135, 10623 Berlin, Germany
- Department of Chemical and Biomolecular Engineering, North Carolina State University , Engineering Building I, Box 7905, 911 Partners Way, Raleigh, North Carolina 27695, United States
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11
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Tiribocchi A, Da Re M, Marenduzzo D, Orlandini E. Shear dynamics of an inverted nematic emulsion. SOFT MATTER 2016; 12:8195-8213. [PMID: 27714315 DOI: 10.1039/c6sm01275b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Here we study theoretically the dynamics of a 2D and a 3D isotropic droplet in a nematic liquid crystal under a shear flow. We find a large repertoire of possible nonequilibrium steady states as a function of the shear rate and of the anchoring of the nematic director field at the droplet surface. We first discuss homeotropic anchoring. For weak anchoring, we recover the typical behaviour of a sheared isotropic droplet in a binary fluid, which rotates, stretches and can be broken by the applied flow. For intermediate anchoring, new possibilities arise due to elastic effects in the nematic fluid. We find that in this regime the 2D droplet can tilt and move in the flow, or tumble incessantly at the centre of the channel. For sufficiently strong anchoring, finally, one or both of the topological defects which form close to the surface of the isotropic droplet in equilibrium detach from it and get dragged deep into the nematic state by the flow. In 3D, instead, the Saturn ring associated with the normal anchoring disclination line can be deformed and shifted downstream by the flow, but remains always localized in the proximity of the droplet, at least for the parameter range we explored. Tangential anchoring in 2D leads to a different dynamic response, as the boojum defects characteristic of this situation can unbind from the droplet under a weaker shear with respect to the normal anchoring case. Our results should stimulate further experiments with inverted liquid crystal emulsions under shear, as most of the predictions can be testable in principle by monitoring the evolution of liquid crystalline orientation patterns or by tracking the position and shape of the droplet over time.
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Affiliation(s)
- A Tiribocchi
- Dipartimento di Fisica e Astronomia and Sezione INFN di Padova, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy.
| | - M Da Re
- Dipartimento di Fisica e Astronomia and Sezione INFN di Padova, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy.
| | - D Marenduzzo
- SUPA and The School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, UK
| | - E Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN di Padova, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy.
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12
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Alama S, Bronsard L, Lamy X. Analytical description of the Saturn-ring defect in nematic colloids. Phys Rev E 2016; 93:012705. [PMID: 26871133 DOI: 10.1103/physreve.93.012705] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2015] [Indexed: 06/05/2023]
Abstract
We derive an analytical formula for the Saturn-ring configuration around a small colloidal particle suspended in nematic liquid crystal. In particular we obtain an explicit expression for the ring radius and its dependence on the anchoring energy. We work within Landau-de Gennes theory: Nematic alignment is described by a tensorial order parameter. For nematic colloids this model had previously been used exclusively to perform numerical computations. Our method demonstrates that the tensorial theory can also be used to obtain analytical results, suggesting a different approach to the understanding of nematic colloidal interactions.
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Affiliation(s)
- Stan Alama
- Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4K1
| | - Lia Bronsard
- Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4K1
| | - Xavier Lamy
- Institut Camille Jordan, Université Lyon 1, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne Cedex, France and Max-Planck Institut, Inselstrasse 22, 04103 Leipzig, Germany
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13
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Stieger T, Püschel-Schlotthauer S, Schoen M, Mazza MG. Flow-induced deformation of closed disclination lines near a spherical colloid immersed in a nematic host phase. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1096973] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Tillmann Stieger
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 115, 10623, Berlin, Germany
| | - Sergej Püschel-Schlotthauer
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 115, 10623, Berlin, Germany
| | - Martin Schoen
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 115, 10623, Berlin, Germany
- Department of Chemical and Biomolecular Engineering, North Carolina State University, 911 Partners Way, Raleigh, NC 27695, USA
| | - Marco G. Mazza
- Max-Planck-Institut für Dynamik und Selbstorganisation, Am Faßberg 17, 37077 Göttingen, Germany
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Rudyak VY, Emelyanenko AV. Orientational ordering of Janus colloids in cholesteric liquid crystals. SOFT MATTER 2015; 11:7237-7240. [PMID: 26291514 DOI: 10.1039/c5sm01784j] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this paper we show that Janus colloids, which are spherical particles with hybrid anchoring conditions, have preferable orientations in cholesteric media depending on the cholesteric wave vector. Simulations reveal that the tilt angle of a particle varies greatly with variation of the particle diameter to the cholesteric pitch ratio, which makes it possible to stabilize the appropriate particle orientation and to control it by variation of the cholesteric pitch.
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15
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Ilnytskyi JM, Trokhymchuk A, Schoen M. Topological defects around a spherical nanoparticle in nematic liquid crystal: Coarse-grained molecular dynamics simulations. J Chem Phys 2014; 141:114903. [DOI: 10.1063/1.4894438] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Affiliation(s)
- Jaroslav M. Ilnytskyi
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1, Svientsitskii Str., 79011 Lviv, Ukraine
| | - Andrij Trokhymchuk
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1, Svientsitskii Str., 79011 Lviv, Ukraine
| | - Martin Schoen
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany and Department of Chemical and Biomolecular Engineering, Engineering Building I, Box 7905, North Carolina State University, 911 Partners Way, Raleigh, North Carolina 27695, USA
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16
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Melle M, Schlotthauer S, Hall CK, Diaz-Herrera E, Schoen M. Disclination lines at homogeneous and heterogeneous colloids immersed in a chiral liquid crystal. SOFT MATTER 2014; 10:5489-5502. [PMID: 24954626 DOI: 10.1039/c4sm00959b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In the present work we perform Monte Carlo simulations in the isothermal-isobaric ensemble to study defect topologies formed in a cholesteric liquid crystal due to the presence of a spherical colloidal particle. Topological defects arise because of the competition between anchoring at the colloidal surface and the local director. We consider homogeneous colloids with either local homeotropic or planar anchoring to validate our model by comparison with earlier lattice Boltzmann studies. Furthermore, we perform simulations of a colloid in a twisted nematic cell and discuss the difference between induced and intrinsic chirality on the formation of topological defects. We present a simple geometrical argument capable of describing the complex three-dimensional topology of disclination lines evolving near the surface of the colloid. The presence of a Janus colloid in a cholesteric host fluid reveals a rich variety of defect structures. Using the Frank free energy we analyze these defects quantitatively indicating a preferred orientation of the Janus colloid relative to the cholesteric helix.
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Affiliation(s)
- Michael Melle
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany.
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17
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Greschek M, Gubbins KE, Schoen M. Imprinting substrate structures onto a nematic liquid crystal. J Chem Phys 2012; 137:144703. [DOI: 10.1063/1.4757391] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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18
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Melle M, Schlotthauer S, Mazza MG, Klapp SHL, Schoen M. Defect topologies in a nematic liquid crystal near a patchy colloid. J Chem Phys 2012; 136:194703. [PMID: 22612105 DOI: 10.1063/1.4717619] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Using isothermal-isobaric Monte Carlo simulations we investigate defect topologies due to a spherical colloidal particle immersed in a nematic liquid crystal. Defects arise because of the competition between the preferential orientation at the colloid's surface and the far-field director ̂n(0). Considering a chemically homogeneous colloid as a special case we observe the well-known surface and saturn ring defect topologies for weak and strong perpendicular anchoring, respectively; for homogeneous, strong parallel anchoring we find a boojum defect topology that has been seen experimentally [see P. Poulin and D. A. Weitz, Phys. Rev. E 57, 626 (1998)] but not in computer simulations. We also consider a heterogeneous, patchy colloid where the liquid-crystal molecules anchor either preferentially planar or perpendicular at the surface of the colloid. For a patchy colloid we observe a boojum ring defect topology in agreement with recent experimental studies [see M. Conradi, M. Ravnik, M. Bele, M. Zorko, S. Žumer, and I. Muševič, Soft Matter 5, 3905 (2009)]. We also observe two other novel defect topologies that have not been reported thus far neither experimentally nor theoretically.
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Affiliation(s)
- Michael Melle
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Technische Universität Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany
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19
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Berardi R, Lintuvuori JS, Wilson MR, Zannoni C. Phase diagram of the uniaxial and biaxial soft–core Gay–Berne model. J Chem Phys 2011; 135:134119. [DOI: 10.1063/1.3646310] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Hernández-Ortiz JP, Gettelfinger BT, Moreno-Razo J, de Pablo JJ. Modeling flows of confined nematic liquid crystals. J Chem Phys 2011; 134:134905. [DOI: 10.1063/1.3567098] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
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21
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Tojo K, Furukawa A, Araki T, Onuki A. Defect structures in nematic liquid crystals around charged particles. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2009; 30:55-64. [PMID: 19756793 DOI: 10.1140/epje/i2009-10506-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2009] [Revised: 05/27/2009] [Accepted: 08/05/2009] [Indexed: 05/28/2023]
Abstract
We numerically study the orientation deformations in nematic liquid crystals around charged particles. We set up a Ginzburg-Landau theory with inhomogeneous electric field. If the dielectric anisotropy epsilon 1 is positive, Saturn-ring defects are formed around the particles. For epsilon 1< 0 , novel "ansa" defects appear, which are disclination lines with their ends on the particle surface. We find unique defect structures around two charged particles. To lower the free energy, oppositely charged particle pairs tend to be aligned in the parallel direction for epsilon 1> 0 and in the perpendicular plane for epsilon 1< 0 with respect to the background director. For identically charged pairs the preferred directions for epsilon 1> 0 and epsilon 1< 0 are exchanged. We also examine competition between the charge-induced anchoring and the short-range anchoring. If the short-range anchoring is sufficiently strong, it can be effective in the vicinity of the surface, while the director orientation is governed by the long-range electrostatic interaction far from the surface.
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Affiliation(s)
- K Tojo
- Department of Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
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22
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Cheung DL, Allen MP. Effect of substrate geometry on liquid-crystal-mediated nanocylinder-substrate interactions. J Chem Phys 2008; 129:114706. [DOI: 10.1063/1.2977968] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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23
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Dolganov PV, Nguyen HT, Joly G, Dolganov VK, Cluzeau P. Different mechanisms of nucleation and self-organization of droplets in ferroelectric smectic membranes. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2008; 25:31-37. [PMID: 18264663 DOI: 10.1140/epje/i2007-10261-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2007] [Accepted: 12/20/2007] [Indexed: 05/25/2023]
Abstract
New mechanisms of droplet nucleation and self-organization in ferroelectric membranes are described. The droplets may be accompanied by different number of topological defects (zero, one, two) whose location may be on the droplet boundary or in the membrane. Nucleation and self-organization of droplets with total topological charge S = 0 , S = + 1 and S = - 1 were investigated. We found that an S = - 1 topological defect may be the center of both droplet nucleation and chain formation. This mechanism of chaining drastically differs from the droplet self-organization described earlier which is realized by attraction of droplet-defect pairs. Our observations demonstrate new possibilities for manipulating the inclusions and their self-organization in smectic membranes.
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Affiliation(s)
- P V Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow district, Russia.
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24
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Cheung DL, Allen MP. Liquid-crystal-mediated force between a cylindrical nanoparticle and substrate. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:041706. [PMID: 17995012 DOI: 10.1103/physreve.76.041706] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2007] [Indexed: 05/25/2023]
Abstract
Using classical density functional theory, the structure of a molecular fluid around a cylindrical nanoparticle near a solid substrate is studied. The solvent-mediated force between the nanoparticle and the substrate is calculated in both the nematic and isotropic phases of the solvent. In the nematic phase, the force is short ranged and arises due to interaction between high-density regions near the substrate and nanoparticle. In the isotropic phase, the formation of a nematic bridge between the substrate and nanoparticle gives rise to an attractive force between them. The potential between the nanoparticle and substrate as a function of separation calculated numerically is compared to that calculated from the Derjaguin approximation. In the isotropic phase these are found to be in reasonable agreement at low separations, while the agreement is poorer in the nematic phase.
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Affiliation(s)
- David L Cheung
- Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom.
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25
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26
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Nanoparticles in Liquid Crystals: Synthesis, Self-Assembly, Defect Formation and Potential Applications. J Inorg Organomet Polym Mater 2007. [DOI: 10.1007/s10904-007-9140-5] [Citation(s) in RCA: 281] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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27
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Qi H, Lepp A, Heiney PA, Hegmann T. Effects of hydrophilic and hydrophobic gold nanoclusters on the stability and ordering of bolaamphiphilic liquid crystals. ACTA ACUST UNITED AC 2007. [DOI: 10.1039/b701411b] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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28
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Völtz C, Maeda Y, Tabe Y, Yokoyama H. Director-configurational transitions around microbubbles of hydrostatically regulated size in liquid crystals. PHYSICAL REVIEW LETTERS 2006; 97:227801. [PMID: 17155844 DOI: 10.1103/physrevlett.97.227801] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2006] [Indexed: 05/12/2023]
Abstract
A high-pressure technique is introduced which allows a continuous variation of the inclusion size in liquid crystal colloids. We use a nematic liquid crystal host into which micrometer-sized gas bubbles are injected. By applying hydrostatic pressures, the diameter of these gas bubbles can be continuously decreased via compression and absorption of gas into the host liquid crystal, so that the director configurations around a single bubble can be investigated as a function of the bubble size. The theoretically predicted transition from a hyperbolic hedgehog to a Saturn-ring configuration, on reduction of the particle size below a certain threshold, is confirmed to occur at the radius of a few micrometers.
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Affiliation(s)
- C Völtz
- Liquid Crystal Nano-System Project, Japan Science and Technology Agency, 5-9-9 Tokodai, Tsukuba 300-2635, Japan.
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29
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Tasinkevych M, Andrienko D. Effective triplet interactions in nematic colloids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 21:277-82. [PMID: 17205211 DOI: 10.1140/epje/i2006-10065-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2006] [Accepted: 12/11/2006] [Indexed: 05/13/2023]
Abstract
Three-body effective interactions emerging between parallel cylindrical rods immersed in a nematic liquid crystals are calculated within the Landau-de Gennes free-energy description. Collinear, equilateral and midplane configurations of the three colloidal particles are considered. In the last two cases the effective triplet interaction is of the same magnitude and range as the pair one.
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Affiliation(s)
- M Tasinkevych
- Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, 70569, Stuttgart, Germany.
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30
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Sulaiman N, Marenduzzo D, Yeomans JM. Lattice Boltzmann algorithm to simulate isotropic-nematic emulsions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041708. [PMID: 17155079 DOI: 10.1103/physreve.74.041708] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2006] [Revised: 07/26/2006] [Indexed: 05/12/2023]
Abstract
We present lattice Boltzmann simulations of the dynamical equations of motion of a drop of isotropic fluid in a nematic liquid crystal solvent, both in the absence and in the presence of an electric field. The coupled equations we solve are the Beris-Edward equations for the dynamics of the tensor order parameter describing the nematic solvent, the Cahn-Hilliard equation for the concentration evolution, and the Navier-Stokes equations for the determination of the instantaneous velocity field. We implement the lattice Boltzmann algorithm to ensure that spurious velocities are close to zero in equilibrium. We first study the effects of the liquid crystal elastic constant, K, anchoring strength, W, and surface tension, sigma, on the shape of the droplet and on the director field texture in equilibrium. We then consider how the drop behaves as the director field is switched by an applied electric field. We also show that the algorithm allows us to follow the motion of a drop of isotropic fluid placed in a liquid crystal cell with a tilted director field at the boundaries.
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Affiliation(s)
- N Sulaiman
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, United Kingdom
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31
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Tian P, Smith GD, Glaser M. Molecular dynamics simulations studies of nanoparticles in an isotropic liquid crystal matrix: Single particle behavior and pairwise interactions. J Chem Phys 2006; 124:161101. [PMID: 16674121 DOI: 10.1063/1.2194534] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report results of molecular dynamics simulation studies of the behavior of spherical nanoparticles (NPs) in a dense isotropic nematogen matrix comprised of soft spherocylinders (SSCs). The SSCs exhibit a tendency for frustrated planar anchoring at the NP surface that results in a long-range (compared to the size of the NPs and SSCs) reduction in local orientational ordering and increased fluctuations in local orientational ordering compared to the pure isotropic phase of the SSCs. The potential of mean force between two nanoparticles exhibits a novel long-range repulsive tail separated from short-range molecular packing peaks by a shallow local minimum in free energy. The long-range repulsion is caused by NP-induced ordering fluctuations while the shallow minimum results from increased local ordering within the confinement region in between two NPs. The influence of the NPs on local orientational order in the nematogen matrix and the nematogen-induced interaction between NPs are found to depend strongly on the size of the NPs.
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Affiliation(s)
- Pu Tian
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA
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32
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Foret L, Onuki A. Charged inclusion in nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031709. [PMID: 17025656 DOI: 10.1103/physreve.74.031709] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2006] [Indexed: 05/12/2023]
Abstract
We present a general theory of liquid crystals under inhomogeneous electric field in a Ginzburg-Landau scheme. The molecular orientation can be deformed by electric field when the dielectric tensor is orientation dependent. We then investigate the influence of a charged particle on the orientation order in a nematic state. The director is aligned either along or perpendicular to the local electric field around the charge, depending on the sign of the dielectric anisotropy. The deformation becomes stronger with increasing the ratio Ze/R, where Ze is the charge and R is the radius of the particle. Numerical analysis shows the presence of defects around the particle for large Ze/R. They are nanometer-scale defects for microscopic ions. If the dielectric anisotropy is positive, a Saturn ring defect appears. If it is negative, a pair of point defects appear apart from the particle surface, each being connected to the surface by a disclination line segment.
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Affiliation(s)
- Lionel Foret
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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33
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Cheung DL, Allen MP. Structure of a liquid crystalline fluid around a macroparticle: Density functional theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:021701. [PMID: 17025446 DOI: 10.1103/physreve.74.021701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2006] [Revised: 05/17/2006] [Indexed: 05/12/2023]
Abstract
The structure of a molecular liquid, in both the nematic liquid crystalline and isotropic phases, around a cylindrical macroparticle, is studied using density functional theory. In the nematic phase the structure of the fluid is highly anisotropic with respect to the director, in agreement with results from simulation and phenomenological theories. On going into the isotropic phase the structure becomes rotationally invariant around the macroparticle with an oriented layer at the surface.
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Affiliation(s)
- David L Cheung
- Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom.
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34
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Noël CM, Bossis G, Chaze AM, Giulieri F, Lacis S. Measurement of elastic forces between iron colloidal particles in a nematic liquid crystal. PHYSICAL REVIEW LETTERS 2006; 96:217801. [PMID: 16803274 DOI: 10.1103/physrevlett.96.217801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2006] [Indexed: 05/10/2023]
Abstract
The forces that arise between two iron particles in a nematic liquid crystal with a strong homeotropic anchoring were studied. For the first time, the short range repulsive force resulting from the presence of a hedgehog defect between two particles was precisely determined thanks to application of a small magnetic field and observation of the equilibrium position resulting from the balance between the elastic and magnetic forces. Above a given threshold force, the particles stuck together whereas the hedgehog defect was expelled and transformed into a Saturn ring located between the particles. The attractive part of the interparticle force was determined with the same method on the entire range of separation distances; we found that the equilibrium distance between two particles was r = 1.19 +/- 0.05 <d> (<d> was the average diameter of the pair of particles).
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Affiliation(s)
- C M Noël
- Laboratoire de Physique de la Matière Condensée (UMR6622), Université de Nice Sophia-Antipolis, Parc Valrose 06108 Nice Cedex 2, France
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35
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Lev B, Nych A, Ognysta U, Chernyshuk SB, Nazarenko V, Skarabot M, Poberaj I, Babic D, Osterman N, Musevic I. Anisotropic laser trapping in nematic colloidal dispersion. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 20:215-9. [PMID: 16779526 DOI: 10.1140/epje/i2006-10015-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2006] [Accepted: 05/26/2006] [Indexed: 05/10/2023]
Abstract
The interaction between a colloidal particle and a focused laser beam in a nematic liquid crystal reveals an unusual anisotropic Coulomb-like character. Experiments demonstrate two opposite directions in which the particle is attracted to and repelled from the nematic region deformed by the light-induced director reorientation. In this work we present analytical analysis of such behavior and derive the energy of interaction between colloidal particle and deformed director field. The analytical solution is in good agreement with recent results obtained by computer simulation.
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Affiliation(s)
- B Lev
- Institute of Physics, 46 Nauky ave., 03039, Kyiv-39, Ukraine
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36
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Skarabot M, Ravnik M, Babic D, Osterman N, Poberaj I, Zumer S, Musevic I, Nych A, Ognysta U, Nazarenko V. Laser trapping of low refractive index colloids in a nematic liquid crystal. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:021705. [PMID: 16605354 DOI: 10.1103/physreve.73.021705] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2005] [Revised: 01/06/2006] [Indexed: 05/08/2023]
Abstract
We describe and analyze laser trapping of small colloidal particles in a nematic liquid crystal, where the index of refraction of colloids is smaller compared to the indices of the liquid crystal. Two mechanisms are identified that are responsible for this anomalous trapping: (i) below the optical Fréedericksz transition, the trapping is due to the anisotropic dielectric interaction of the polarized light with the inhomogeneous director field around the colloid, (ii) above the optical Fréedericksz transition, the optical trapping is accompanied by the elasticity-mediated interaction between the optically distorted region of a liquid crystal and the colloid. In the majority of the experiments, the trapping above the Fréedericksz transition is highly anisotropic. Qualitative agreement is found with a numerical analysis, considering the nematic director elastic distortion, dielectric director-light field coupling and optical repulsion due to low refraction index colloid in high index surroundings.
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Affiliation(s)
- M Skarabot
- J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
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37
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Qi H, Hegmann T. Formation of periodic stripe patterns in nematic liquid crystals doped with functionalized gold nanoparticles. ACTA ACUST UNITED AC 2006. [DOI: 10.1039/b611501b] [Citation(s) in RCA: 158] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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38
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Sokolovska TG, Sokolovskii RO, Patey GN. Colloid-induced structure in liquid crystal media. J Chem Phys 2005; 122:124907. [PMID: 15836424 DOI: 10.1063/1.1870912] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The structural perturbations induced by colloidal particles immersed in a model nematic subjected to an external field are calculated employing integral equation methods. Maps of the density-orientational distribution about a colloidal particle are obtained, and these provide a microscopic picture of the colloid's nematic coat. We focus on colloidal particles that favor homeotropic anchoring, but planar anchoring cases are also considered. The range and structure of the nematic coat is shown to be significantly influenced by the nature of the anchoring, the size of the colloidal particle, the range and strength of the colloid-nematogen interaction, and the external field strength. All of these factors are discussed.
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Affiliation(s)
- T G Sokolovska
- Department of Chemistry, University of British Columbia, Vancouver V6T 1Z1, British Columbia, Canada
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39
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Loudet JC. Colloidal inclusions in liquid crystals: Phase separation mechanisms and some dynamical aspects. LIQUID CRYSTALS TODAY 2005. [DOI: 10.1080/14625180500137803] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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40
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Loudet JC, Barois P, Auroy P, Keller P, Richard H, Poulin P. Colloidal structures from bulk demixing in liquid crystals. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2004; 20:11336-11347. [PMID: 15595755 DOI: 10.1021/la048737f] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
This experimental paper deals with phase separations of binary mixtures composed of a continuous liquid crystal phase and an isotropic dispersed phase. In contrast to isotropic binary mixtures, the investigated mixtures do not lead to a full phase separation but to a self-ordering of colloidal particles, as reported earlier (Loudet, J. C. et al. Nature 2000, 407, 611). We present here further aspects of such phase separations which include the kinetics of the phase separation, the origin of the formation of dislocation-like patterns, the influence of surfactants, chiral additives, and temperature on the formed colloidal structures. The present results show that (i) the dislocations in chain arrays can be seen as kinetically frozen defects, (ii) temperature can be used to control the size of the domains formed upon demixing, (iii) a slight change in surface chemistry, via the addition of surfactants, profoundly alters the formed colloidal structures, and (iv) chiral additives allow the formation of unique helical pearl chains which reflect the symmetry of the liquid crystal phase they are embedded in.
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Affiliation(s)
- J C Loudet
- Centre de Recherche Paul Pascal, CNRS, avenue A. Schweitzer 33600 Pessac, France
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41
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Kim EB, Guzman O, Grollau S, Abbott NL, de Pablo JJ. Interactions between spherical colloids mediated by a liquid crystal: A molecular simulation and mesoscale study. J Chem Phys 2004; 121:1949-61. [PMID: 15260747 DOI: 10.1063/1.1761054] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Monte Carlo simulations and dynamic field theory (DyFT) are used to study the interactions between dilute spherical particles, dispersed in nematic and isotropic phases of a liquid crystal. A recently developed simulation method (expanded ensemble density of states) was used to determine the potential of mean force (PMF) between the two spheres as a function of their separation and size. The PMF was also calculated by a dynamic field theory that describes the evolution of the local tensor order parameter. Both methods reveal an overall attraction between the colloids in the nematic phase; in the isotropic phase, the overall attraction between the colloids is much weaker, whereas the repulsion at short range is stronger. In addition, both methods predict a new topology of the disclination lines, which arises when the particles approach each other. The theory is found to describe the results of simulations remarkably well, down to length scales comparable to the size of the molecules. At separations corresponding to the width of individual molecular layers on the particles' surface, the two methods yield different defect structures. We attribute this difference to the neglect of density inhomogeneities in the DyFT. We also investigate the effects of the size of spherical colloids on their interactions.
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Affiliation(s)
- Evelina B Kim
- Department of Chemical and Biological Engineering, University of Wisconsin, Madison, Wisconsin 53706, USA
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42
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Kim EB, de Pablo JJ. Potential of mean force between a spherical particle suspended in a nematic liquid crystal and a substrate: sphere size effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061703. [PMID: 15244594 DOI: 10.1103/physreve.69.061703] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2003] [Indexed: 05/24/2023]
Abstract
The expanded ensemble density of states method (ExEDOS) is used to investigate the effective interaction of a spherical colloidal particle suspended in a confined liquid crystal (LC) with a substrate. The potential of mean force (PMF) is determined as a function of the normal distance between the particle and the substrate's surface. The presence of the substrate induces a layered structure of the LC, which in turn greatly influences the PMF. We analyze the structure of the Saturn ring defect that accompanies the colloidal sphere, and find that the ring is displaced slightly towards the surface when the sphere is within the first LC surface layer. A transition occurs from an overall attraction of the colloid to the substrate to a global repulsion when the sphere's radius is roughly twice the length of the LC molecules.
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Affiliation(s)
- Evelina B Kim
- Department of Chemical and Biological Engineering, University of Wisconsin, Madison, Wisconsin 53706, USA
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43
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Fukuda JI, Stark H, Yoneya M, Yokoyama H. Interaction between two spherical particles in a nematic liquid crystal. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:041706. [PMID: 15169032 DOI: 10.1103/physreve.69.041706] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2003] [Indexed: 05/24/2023]
Abstract
We numerically investigate the interaction between two spherical particles in a nematic liquid crystal mediated by elastic distortions in the orientational order. We pay attention to the cases where two particles with equal radii R0 impose rigid normal anchoring on their surfaces and carry a pointlike topological defect referred to as a hyperbolic hedgehog. To describe the geometry of our system, we use bispherical coordinates, which prove useful in the implementation of boundary conditions at the particle surfaces and at infinity. We adopt the Landau-de Gennes continuum theory in terms of a second-rank tensor order parameter Q(ij) for the description of the orientational order of a nematic liquid crystal. We also utilize an adaptive mesh refinement scheme that has proven to be an efficient way of dealing with topological defects whose core size is much smaller than the particle size. When the two "dipoles," composed of a particle and a hyperbolic hedgehog, are in parallel directions, the two-particle interaction potential is attractive for large interparticle distances D and proportional to D-3 as expected from the form of the dipole-dipole interaction, until the well-defined potential minimum at D approximately 2.46 R0 is reached. For the antiparallel configuration with no hedgehogs between the two particles, the interaction potential is repulsive and behaves as D-2 for D less than or approximately equal 10R0, which is stronger than the dipole-dipole repulsion (approximately D-3 ) expected theoretically as an asymptotic behavior for large D.
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Affiliation(s)
- Jun-ichi Fukuda
- Yokoyama Nano-structured Liquid Crystal Project, ERATO, Japan Science and Technology Agency, 5-9-9 Tokodai, Tsukuba 300-2635, Japan.
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44
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Al-Barwani MS, Sutcliffe GS, Allen MP. Forces between Two Colloidal Particles in a Nematic Solvent. J Phys Chem B 2004. [DOI: 10.1021/jp037650k] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Muataz S. Al-Barwani
- Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Muscat, Sultanate of Oman
| | - Gregory S. Sutcliffe
- Centre for Scientific Computing and Department of Physics, University of Warwick, CV4 7AL, Coventry, United Kingdom
| | - Michael P. Allen
- Centre for Scientific Computing and Department of Physics, University of Warwick, CV4 7AL, Coventry, United Kingdom
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45
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Fukuda JI, Yoneya M, Yokoyama H. Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2004; 13:87-98. [PMID: 15024619 DOI: 10.1140/epje/e2004-00043-2] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We investigate the orientation profile and the structure of topological defects of a nematic liquid crystal around a spherical particle using an adaptive mesh refinement scheme developed by us previously. The previous work [J. Fukuda et al., Phys. Rev. E 65, 041709 (2002)] was devoted to the investigation of the fine structure of a hyperbolic hedgehog defect that the particle accompanies and in this paper we present the equilibrium profile of the Saturn ring configuration. The radius of the Saturn ring r(d) in units of the particle radius R(0) increases weakly with the increase of Epsilon, the ratio of the nematic coherence length to R(0). Next we discuss the energetic stability of a hedgehog and a Saturn ring. The use of adaptive mesh refinement scheme together with a tensor orientational order parameter Q (alpha, beta) allows us to calculate the elastic energy of a nematic liquid crystal without any assumption of the structure and the energy of the defect core as in the previous similar studies. The reduced free energy of a nematic liquid crystal, F= F/L1RO, with L(1) being the elastic constant, is almost independent of Epsilon in the hedgehog configuration, while it shows a logarithmic dependence in the Saturn ring configuration. This result clearly indicates that the energetic stability of a hedgehog to a Saturn ring for a large particle is definitely attributed to the large defect energy of the Saturn ring with a large radius.
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Affiliation(s)
- Jun-Ichi Fukuda
- Yokoyama Nano-structured Liquid Crystal Project, ERATO, Japan Science and Technology Agency, 5-9-9 Tokodai, 300-2635, Tsukuba, Japan,
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Feng JJ, Zhou C. Orientational defects near colloidal particles in a nematic liquid crystal. J Colloid Interface Sci 2004; 269:72-8. [PMID: 14651897 DOI: 10.1016/j.jcis.2003.08.048] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
We study the interaction between a surface-anchoring colloidal particle and a liquid-crystalline host, and in particular the formation of orientational defects near the particle. A mean-field theory based on the nonlocal Marrucci-Greco nematic potential is used to represent molecular interactions in an inhomogeneous orientational field. An evolution equation for the molecular configuration tensor is solved numerically whose steady state minimizes the total free energy of the system. With strong homeotropic anchoring on the particle surface, three types of solutions may appear depending on initial conditions and particle size: Saturn rings, satellite point defects, and polar rings. The Saturn ring remains stable on micrometer-sized particles, contrary to previous calculations but consistent with experiments. A phase diagram is constructed for the three regimes. Based on the free energy, the most stable state is the Saturn ring for smaller particles and the satellite defect for larger ones.
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Affiliation(s)
- James J Feng
- The Levich Institute for Physicochemical Hydrodynamics, City College of the City University of New York, New York, NY 10031, USA.
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Guzmán O, Kim EB, Grollau S, Abbott NL, de Pablo JJ. Defect structure around two colloids in a liquid crystal. PHYSICAL REVIEW LETTERS 2003; 91:235507. [PMID: 14683198 DOI: 10.1103/physrevlett.91.235507] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2003] [Indexed: 05/24/2023]
Abstract
This Letter investigates the defect structures that arise between two colloidal spheres immersed in a nematic liquid crystal. Molecular simulations and a dynamic field theory are employed to arrive at molecular-level and mesoscopic descriptions of the systems of interest. At large separations, each sphere is surrounded by a Saturn ring defect. However, at short separations both theory and simulation predict that a third disclination ring appears in between the spheres, in a plane normal to the Saturn rings. This feature gives rise to an effective binding of the particles. The structures predicted by field theory and molecular simulations are consistent with each other.
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Affiliation(s)
- O Guzmán
- Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706-1691, USA
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Andrienko D, Tasinkevych M, Patrício P, Allen MP, Telo da Gama MM. Forces between elongated particles in a nematic colloid. ACTA ACUST UNITED AC 2003; 68:051702. [PMID: 14682806 DOI: 10.1103/physreve.68.051702] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2003] [Indexed: 11/07/2022]
Abstract
Using molecular dynamics simulations we study the interactions between elongated colloidal particles (length to breath ratio >>1) in a nematic host. The simulation results are compared to the results of a Landau-de Gennes elastic free energy. We find that depletion forces dominate for the sizes of the colloidal particles studied. The tangential component of the force, however, allows us to resolve the elastic contribution to the total interaction. We find that this contribution differs from the quadrupolar interaction predicted at large separations. The difference is due to the presence of nonlinear effects, namely, the change in the positions and structure of the defects and their annihilation at small separations.
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Affiliation(s)
- D Andrienko
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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Grollau S, Kim EB, Guzmán O, Abbott NL, de Pablo JJ. Monte Carlo simulations and dynamic field theory for suspended particles in liquid crystalline systems. J Chem Phys 2003. [DOI: 10.1063/1.1582843] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Grollau S, Abbott NL, de Pablo JJ. Dynamic interaction between suspended particles and defects in a nematic liquid crystal. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:051703. [PMID: 12786160 DOI: 10.1103/physreve.67.051703] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2002] [Indexed: 05/24/2023]
Abstract
Insertion of spherical particles into a uniform nematic liquid crystal gives rise to the formation of topological defects. In the present work, we investigate how a spherical particle accompanied by its topological defects interacts with neighboring disclination lines. We perform two- and three-dimensional dynamic simulations to analyze the effect of a particle on the annihilation process of two disclination lines. The dynamics of the liquid crystal is described by a time-dependent evolution equation on the symmetric traceless order parameter that includes some of the salient features of liquid crystalline materials: excluded volume effects, or equivalently, short-range order elasticity and long-range order elasticity. At the surface of the particle, the liquid crystal is assumed to exhibit strong homeotropic anchoring. The particle is located between two disclination lines of topological charges +1/2 and -1/2. Two-dimensional simulations indicate that the topological defects bound to the particle mediate an interaction between the two disclination lines which increases the attraction between them. This result is confirmed by three-dimensional simulations that provide a complete description of the director field and of the order parameter around the particle. These simulations indicate that a spherical particle between two disclination lines can be surrounded by a Saturn ring, and suggest that the dynamic behavior of disclination lines could be used to report the structure of a defect around the particle.
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Affiliation(s)
- S Grollau
- Department of Chemical Engineering, University of Wisconsin, 1415 Engineering Drive, Madison, Wisconsin 53706, USA
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