1
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Chen H, Jiang M, Guo Y, Chaganava I, Wei QH. Nematic-isotropic phase transitions in thin slabs of liquid crystals with topological defect arrays. SOFT MATTER 2023; 19:8863-8870. [PMID: 37955055 DOI: 10.1039/d3sm01156a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/14/2023]
Abstract
We study the nematic-to-isotropic phase transitions in thin slabs of nematic liquid crystals with photopatterned director fields of topological defect arrays at constant heating rates and show that the transition kinetics is significantly impacted by both the heating rate and the topological strengths of these defects. Specifically, with ±1/2 defect arrays, the isotropic domains emerge from the defect cores when the heating rate is high, while from random places when the heating rate is low. With ±1 defect arrays, the isotropic domains always emerge from the defect cores regardless of the heating rate. Furthermore, the isotropic domains show significant movements at slow heating rates, and the total area of the isotropic domains grows with the temperature T following a simple power law (T - T')γ, where the exponent γ is approximately 1 in most cases and is 2/3 for the ±1 defect arrays at low heating rates when the isotropic domains are pinned on the defect cores. We attribute this phenomenon to an interplay between the surface tension and bulk free energy.
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Affiliation(s)
- Hao Chen
- Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
| | - Miao Jiang
- Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
| | - Yubing Guo
- School of Medical Technology, Beijing Institute of Technology, Beijing 100081, China
| | - Irakli Chaganava
- Institute of Cybernetics, Georgian Technical University, 5 Sandro Euli Str., 0186 Tbilisi, Georgia
| | - Qi-Huo Wei
- Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
- Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen, China
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2
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Guo X, Zhou L, Roul B, Wu Y, Huang Y, Das S, Hong Z. Theoretical Understanding of Polar Topological Phase Transitions in Functional Oxide Heterostructures: A Review. SMALL METHODS 2022; 6:e2200486. [PMID: 35900067 DOI: 10.1002/smtd.202200486] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Revised: 06/15/2022] [Indexed: 06/15/2023]
Abstract
The exotic topological phase is attracting considerable attention in condensed matter physics and materials science over the past few decades due to intriguing physical insights. As a combination of "topology" and "ferroelectricity," the ferroelectric (polar) topological structures are a fertile playground for emergent phenomena and functionalities with various potential applications. Herein, the review starts with the universal concept of the polar topological phase and goes on to briefly discuss the important role of computational tools such as phase-field simulations in designing polar topological phases in oxide heterostructures. In particular, the history of the development of phase-field simulations for ferroelectric oxide heterostructures is highlighted. Then, the current research progress of polar topological phases and their emergent phenomena in ferroelectric functional oxide heterostructures is reviewed from a theoretical perspective, including the topological polar structures, the establishment of phase diagrams, their switching kinetics and interconnections, phonon dynamics, and various macroscopic properties. Finally, this review offers a perspective on the future directions for the discovery of novel topological phases in other ferroelectric systems and device design for next-generation electronic device applications.
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Affiliation(s)
- Xiangwei Guo
- School of Materials Science and Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, China
- Institute of Advanced Semiconductors and Zhejiang Provincial Key Laboratory of Power Semiconductor Materials and Devices, Hangzhou Innovation Center, Zhejiang University, Hangzhou, Zhejiang, 311200, China
- Cyrus Tang Center for Sensor Materials and Applications, State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou, Zhejiang, 310027, China
| | - Linming Zhou
- School of Materials Science and Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, China
| | - Basanta Roul
- Materials Research Centre, Indian Institute of Science, Bangalore, 560012, India
- Central Research Laboratory, Bharat Electronics Limited, Bangalore, 560013, India
| | - Yongjun Wu
- School of Materials Science and Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, China
- Cyrus Tang Center for Sensor Materials and Applications, State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou, Zhejiang, 310027, China
| | - Yuhui Huang
- School of Materials Science and Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, China
| | - Sujit Das
- Materials Research Centre, Indian Institute of Science, Bangalore, 560012, India
| | - Zijian Hong
- School of Materials Science and Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, China
- Cyrus Tang Center for Sensor Materials and Applications, State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou, Zhejiang, 310027, China
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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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Yao X, Zhang L, Chen JZY. Defect patterns of two-dimensional nematic liquid crystals in confinement. Phys Rev E 2022; 105:044704. [PMID: 35590543 DOI: 10.1103/physreve.105.044704] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 03/23/2022] [Indexed: 06/15/2023]
Abstract
A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface-confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form a deformed texture that may display defect points or defect lines, for which winding numbers can be clearly defined. Here, a particular attention is paid to the case when the liquid crystal molecules prefer to form a boundary nematic texture in parallel to the wall surface (i.e., following the homogeneous boundary condition). A general theory, based on geometric argument, is presented for the relationship between the sum of all winding numbers in the system (the total winding number) and the type of confinement angles and curved segments. The conclusion is validated by comparing the theoretical defect rule with existing nematic textures observed experimentally and theoretically in recent years.
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Affiliation(s)
- Xiaomei Yao
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Lei Zhang
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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5
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Lebovka NI, Tatochenko MO, Vygornitskii NV, Tarasevich YY. Confinement effects on the random sequential adsorption packings of elongated particles in a slit. Phys Rev E 2021; 104:054104. [PMID: 34942691 DOI: 10.1103/physreve.104.054104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 10/22/2021] [Indexed: 11/07/2022]
Abstract
The behavior of a system of two-dimensional elongated particles (discorectangles) packed in a slit between the two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption model with continuous positional and orientational degrees of freedom. The aspect ratio (length-to-width ratio, ɛ=l/d) of the particles was varied within the range ɛ∈[1;32] while the distance between the walls was varied within the range h/d∈[1;80]. The properties of deposits in jammed state [the coverage, the order parameter, and the long-range (percolation) connectivity between particles] were studied numerically. The values of ɛ and h significantly affected the structure of the packings and the percolation connectivity. Particularly, the observed nontrivial dependencies of the jamming coverage φ(ɛ) or φ(h) were explained by the interplay of the different geometrical factors related to confinement, particle orientation degrees of freedom and excluded volume effects.
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Affiliation(s)
- Nikolai I Lebovka
- Laboratory of Physical Chemistry of Disperse Minerals, F. D. Ovcharenko Institute of Biocolloidal Chemistry, NAS of Ukraine, Kyiv 03142, Ukraine
| | - Mykhailo O Tatochenko
- Laboratory of Physical Chemistry of Disperse Minerals, F. D. Ovcharenko Institute of Biocolloidal Chemistry, NAS of Ukraine, Kyiv 03142, Ukraine
| | - Nikolai V Vygornitskii
- Laboratory of Physical Chemistry of Disperse Minerals, F. D. Ovcharenko Institute of Biocolloidal Chemistry, NAS of Ukraine, Kyiv 03142, Ukraine
| | - Yuri Yu Tarasevich
- Laboratory of Mathematical Modeling, Astrakhan State University, Astrakhan 414056, Russia
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6
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Wittmann R, Cortes LBG, Löwen H, Aarts DGAL. Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement. Nat Commun 2021; 12:623. [PMID: 33504780 PMCID: PMC7840983 DOI: 10.1038/s41467-020-20842-5] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Accepted: 12/14/2020] [Indexed: 12/24/2022] Open
Abstract
Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic colloidal layers dictated by the interplay between entropy and an imposed external topology. Considering an annular confinement as a basic example, a plethora of competing states is found with nontrivial defect structures ranging from laminar states to multiple smectic domains and arrays of edge dislocations, which we refer to as Shubnikov states in formal analogy to the characteristic of type-II superconductors. Our particle-resolved results, gained by a combination of real-space microscopy of thermal colloidal rods and fundamental-measure-based density functional theory of hard anisotropic bodies, agree on a quantitative level.
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Affiliation(s)
- René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany.
| | - Louis B G Cortes
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY, 14853, USA
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany.
| | - Dirk G A L Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK.
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7
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Yao X, Chen JZY. Rodlike molecules in extreme confinement. Phys Rev E 2020; 101:062706. [PMID: 32688519 DOI: 10.1103/physreve.101.062706] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 06/15/2020] [Indexed: 11/07/2022]
Abstract
A unique feature of colloid particles and biopolymers is the molecule's intrinsic rigidity characterized by a molecular-level length scale. Under extreme confinement conditions at cellular scales or in nanodevices, these molecules can display orientational ordering accompanied by severe density depletion. Conventional liquid-crystal theories, such as the Oseen-Frank or Landau-de Gennes theories, cannot capture the essential molecular-level properties: the boundary effects, which extend to a distance of the rigidity length scale, and the drastic variations of the inhomogeneous molecular density. Here we show, based on a simple interpretation of the Onsager model, that rodlike molecules in extreme annular confinement produce unusual liquid-crystal defect structures that are independent phases from the patterns usually seen in a weaker confinement environment.
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Affiliation(s)
- Xiaomei Yao
- School of Chemistry, Beihang University, Beijing 100191, People's Republic of China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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8
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Martínez-Ratón Y, Velasco E. Highly confined mixtures of parallel hard squares: A density-functional-theory study. Phys Rev E 2020; 100:062604. [PMID: 31962445 DOI: 10.1103/physreve.100.062604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Indexed: 11/06/2022]
Abstract
Using the fundamental-measure density-functional theory, we study theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting of two consecutive big squares, or three small squares, in the transverse direction, perpendicular to the walls, are forbidden. We analyze two different mixtures with edge lengths of species selected so as to allow or forbid one big plus one small square to fit into the channel. For the first mixture we obtain first-order transitions between symmetric and asymmetric packings of particles: Small and big squares are preferentially adsorbed at different walls. Asymmetric configurations are shown to lead to more efficient packing at finite pressures. We argue that the stability region of the asymmetric phase in the pressure-composition plane is bounded so that the symmetric phase is stable at low and very high pressure. For the second mixture, we observe strong demixing between phases which are rich in different species. Demixing occurs in the lateral direction, i.e., the dividing interface is perpendicular to the walls, and phases exhibit symmetric density profiles. The possible experimental realization of this behavior (which in practical terms is precluded by jamming) in strictly two-dimensional systems is discussed. Finally, the phase behavior of a mixture with periodic boundary conditions is analyzed and the differences and similarities between the latter and the confined system are discussed. We claim that, although exact calculations exclude the existence of true phase transitions in (1+ε)-dimensional systems, density-functional theory is still successful in describing packing properties of large clusters of particles.
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Affiliation(s)
- Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
| | - Enrique Velasco
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, 28049, Madrid, Spain
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9
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Yao X, Zhang H, Chen JZY. Topological defects in two-dimensional liquid crystals confined by a box. Phys Rev E 2018; 97:052707. [PMID: 29906923 DOI: 10.1103/physreve.97.052707] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2018] [Indexed: 06/08/2023]
Abstract
When a spatially uniform system that displays a liquid-crystal ordering on a two-dimensional surface is confined inside a rectangular box, the liquid crystal direction field develops inhomogeneous textures accompanied by topological defects because of the geometric frustrations. We show that the rich variety of nematic textures and defect patterns found in recent experimental and theoretical studies can be classified by the solutions of the rather fundamental, extended Onsager model. This is critically examined based on the determined free energies of different defect states, as functions of a few relevant, dimensionless geometric parameters.
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Affiliation(s)
- Xiaomei Yao
- School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of China
- School of Chemistry, Beihang University, Beijing 100191, People's Republic of China
| | - Hui Zhang
- School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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10
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Wittmann R, Sitta CE, Smallenburg F, Löwen H. Phase diagram of two-dimensional hard rods from fundamental mixed measure density functional theory. J Chem Phys 2017; 147:134908. [DOI: 10.1063/1.4996131] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- René Wittmann
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - Christoph E. Sitta
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Frank Smallenburg
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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11
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Gârlea IC, Mulder P, Alvarado J, Dammone O, Aarts DGAL, Lettinga MP, Koenderink GH, Mulder BM. Finite particle size drives defect-mediated domain structures in strongly confined colloidal liquid crystals. Nat Commun 2016; 7:12112. [PMID: 27353002 PMCID: PMC4931596 DOI: 10.1038/ncomms12112] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2015] [Accepted: 05/31/2016] [Indexed: 11/25/2022] Open
Abstract
When liquid crystals are confined to finite volumes, the competition between the surface anchoring imposed by the boundaries and the intrinsic orientational symmetry-breaking of these materials gives rise to a host of intriguing phenomena involving topological defect structures. For synthetic molecular mesogens, like the ones used in liquid-crystal displays, these defect structures are independent of the size of the molecules and well described by continuum theories. In contrast, colloidal systems such as carbon nanotubes and biopolymers have micron-sized lengths, so continuum descriptions are expected to break down under strong confinement conditions. Here, we show, by a combination of computer simulations and experiments with virus particles in tailor-made disk- and annulus-shaped microchambers, that strong confinement of colloidal liquid crystals leads to novel defect-stabilized symmetrical domain structures. These finite-size effects point to a potential for designing optically active microstructures, exploiting the as yet unexplored regime of highly confined liquid crystals. Liquid crystals confined to micrometre-sized geometries can be well described by a continuum theory, where the size effect of constituent mesogens is negligible. Here, the authors show how the continuum theory breaks down in colloidal liquid crystal, leading to the formation of defect-mediated domains.
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Affiliation(s)
- Ioana C Gârlea
- Department of Systems Biophysics, FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands
| | - Pieter Mulder
- Department of Systems Biophysics, FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands
| | - José Alvarado
- Department of Systems Biophysics, FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands
| | - Oliver Dammone
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
| | - Dirk G A L Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
| | - M Pavlik Lettinga
- Institute of Complex Systems (ICS-3), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Gijsje H Koenderink
- Department of Systems Biophysics, FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands
| | - Bela M Mulder
- Department of Systems Biophysics, FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands
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12
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Ye S, Zhang P, Chen JZY. Nematic ordering of semiflexible polymers confined on a toroidal surface. SOFT MATTER 2016; 12:5438-5449. [PMID: 27248049 DOI: 10.1039/c6sm01098a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We study the isotropic-like and nematic states of wormlike liquid-crystal polymers embedded on the surface of a torus. The role played by surface curvature, which couples to the molecular rigidity, is reported as the main reason that causes the weak nematic ordering in an otherwise ordinary isotropic phase. The same coupling has a profound effect on the nematic states as well, which are stabilized by the Onsager excluded-volume interaction; the latter has been frequently used to study lyotropic liquid crystal polymers and is used here as an example of the physical mechanisms that drive the system to make orientational ordering. We identify important parameters in the system which are used as axes of the four-dimensional phase diagram. The numerical study demonstrates a strong correlation between the liquid-crystal defect-free and defect structures and the geometry of the liquid-crystal embedded surface.
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Affiliation(s)
- Shiwei Ye
- LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, People's Republic of China.
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13
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14
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Müller T, de las Heras D, Rehberg I, Huang K. Ordering in granular-rod monolayers driven far from thermodynamic equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062207. [PMID: 26172705 DOI: 10.1103/physreve.91.062207] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2014] [Indexed: 06/04/2023]
Abstract
The orientational order in vertically agitated granular-rod monolayers is investigated experimentally and compared quantitatively with equilibrium Monte Carlo simulations and density functional theory. At sufficiently high number density, short rods form a tetratic state and long rods form a uniaxial nematic state. The length-to-width ratio at which the order changes from tetratic to uniaxial is around 7.3 in both experiments and simulations. This agreement illustrates the universal aspects of the ordering of rod-shaped particles across equilibrium and nonequilibrium systems. Moreover, the assembly of granular rods into ordered states is found to be independent of the agitation frequency and strength, suggesting that the detailed nature of energy injection into such a nonequilibrium system does not play a crucial role.
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Affiliation(s)
- Thomas Müller
- Experimentalphysik V, Universität Bayreuth, D-95440 Bayreuth, Germany
| | | | - Ingo Rehberg
- Experimentalphysik V, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Kai Huang
- Experimentalphysik V, Universität Bayreuth, D-95440 Bayreuth, Germany
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15
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Geigenfeind T, Rosenzweig S, Schmidt M, de las Heras D. Confinement of two-dimensional rods in slit pores and square cavities. J Chem Phys 2015; 142:174701. [DOI: 10.1063/1.4919307] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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16
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Gârlea IC, Mulder BM. Defect structures mediate the isotropic-nematic transition in strongly confined liquid crystals. SOFT MATTER 2015; 11:608-614. [PMID: 25435377 DOI: 10.1039/c4sm02087a] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Using Monte Carlo simulations, we study rod-like lyotropic liquid crystals confined to a square slab-like geometry with lateral dimensions comparable to the length of the particles. We observe that this system develops linear defect structures upon entering the planar nematic phase. These defect structures flank a lens-shaped nematic region oriented along a diagonal of the square box. We interpret these structures as a compromise between the 2-fold order of the bulk nematic phase and the 4-fold order imposed by the lateral boundaries. A simple Onsager-type theory that effectively implements these competing tendencies is used to model the phase behavior in the center of the box and shows that the free-energy cost of forming the defect structures strongly offsets the transition-inducing effects of both the transverse and lateral confinement.
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Affiliation(s)
- Ioana C Gârlea
- FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands.
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17
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de Las Heras D, Velasco E. Domain walls in two-dimensional nematics confined in a small circular cavity. SOFT MATTER 2014; 10:1758-1766. [PMID: 24652373 DOI: 10.1039/c3sm52650j] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Using Monte Carlo simulation, we study a fluid of two-dimensional hard rods inside a small circular cavity bounded by a hard wall, from the dilute regime to the high-density, layering regime. Both planar and homeotropic anchoring of the nematic director can be induced at the walls through a free-energy penalty. The circular geometry creates frustration in the nematic phase and a polar-symmetry configuration with a distorted director field plus two +1/2 disclinations is created. At higher densities, a quasi-uniform structure is observed with a (minimal) director distortion which is relaxed via the formation of orientational domain walls. This novel structure is not predicted by elasticity theory and is similar to the step-like structures observed in three-dimensional hybrid slit pores. We speculate that the formation of domain walls is a general mechanism to relax elastic stresses under the conditions of strong surface anchoring and severe spatial confinement.
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Affiliation(s)
- Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
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18
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González-Pinto M, Martínez-Ratón Y, Velasco E. Liquid-crystal patterns of rectangular particles in a square nanocavity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032506. [PMID: 24125284 DOI: 10.1103/physreve.88.032506] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2013] [Indexed: 06/02/2023]
Abstract
Using density-functional theory in the restricted-orientation approximation, we analyze the liquid-crystal patterns and phase behavior of a fluid of hard rectangular particles confined in a two-dimensional square nanocavity of side length H composed of hard inner walls. Patterning in the cavity is governed by surface-induced order as well as capillary and frustration effects and depends on the relative values of the particle aspect ratio κ≡L/σ, with L the length and σ the width of the rectangles (L≥σ), and cavity size H. Ordering may be very different from bulk (H→∞) behavior when H is a few times the particle length L (nanocavity). Bulk and confinement properties are obtained for the cases κ=1, 3, and 6. In bulk the isotropic phase is always stable at low packing fractions η=Lσρ_{0} (with ρ_{0} the average density) and nematic, smectic, columnar, and crystal phases can be stabilized at higher η depending on κ: For increasing η the sequence of isotropic to columnar is obtained for κ=1 and 3, whereas for κ=6 we obtain isotropic to nematic to smectic (the crystal being unstable in all three cases for the density range explored). In the confined fluid surface-induced frustration leads to fourfold symmetry breaking in all phases (which become twofold symmetric). Since no director distortion can arise in our model by construction, frustration in the director orientation is relaxed by the creation of domain walls (where the director changes by 90^{∘}); this configuration is necessary to stabilize periodic phases. For κ=1 the crystal becomes stable with commensurate transitions taking place as H is varied. These transitions involve structures with different number of peaks in the local density. In the case κ=3 the commensurate transitions involve columnar phases with different number of columns. In the case κ=6 the high-density region of the phase diagram is dominated by commensurate transitions between smectic structures; at lower densities there is a symmetry-breaking isotropic to nematic transition exhibiting nonmonotonic behavior with cavity size. Apart from the present application in a confinement setup, our model could be used to explore the bulk region near close packing in order to elucidate the possible existence of disordered phases at close packing.
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Affiliation(s)
- Miguel González-Pinto
- Departamento de Física Teórica de la Materia Condensada, Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
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de las Heras D, Martínez-Ratón Y, Mederos L, Velasco E. Two-dimensional nematics in bulk and confined geometries. J Mol Liq 2013. [DOI: 10.1016/j.molliq.2012.08.014] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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van Bijnen RMW, Otten RHJ, van der Schoot P. Texture and shape of two-dimensional domains of nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:051703. [PMID: 23214801 DOI: 10.1103/physreve.86.051703] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2012] [Revised: 08/07/2012] [Indexed: 06/01/2023]
Abstract
We present a generalized approach to compute the shape and internal structure of two-dimensional nematic domains. By using conformal mappings, we are able to compute the director field for a given domain shape that we choose from a rich class, which includes drops with large and small aspect ratios and sharp domain tips as well as smooth ones. Results are assembled in a phase diagram that for given domain size, surface tension, anchoring strength, and elastic constant shows the transitions from a homogeneous to a bipolar director field, from circular to elongated droplets, and from sharp to smooth domain tips. We find a previously unaccounted for regime, where the drop is nearly circular, the director field bipolar, and the tip rounded. We also find that bicircular director fields, with foci that lie outside the domain, provide a remarkably accurate description of the optimal director field for a large range of values of the various shape parameters.
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Affiliation(s)
- R M W van Bijnen
- Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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Woodhouse FG, Goldstein RE. Spontaneous circulation of confined active suspensions. PHYSICAL REVIEW LETTERS 2012; 109:168105. [PMID: 23215137 DOI: 10.1103/physrevlett.109.168105] [Citation(s) in RCA: 79] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2012] [Indexed: 06/01/2023]
Abstract
Many active fluid systems encountered in biology are set in total geometric confinement. Cytoplasmic streaming in plant cells is a prominent and ubiquitous example, in which cargo-carrying molecular motors move along polymer filaments and generate coherent cell-scale flow. When filaments are not fixed to the cell periphery, a situation found both in vivo and in vitro, we observe that the basic dynamics of streaming are closely related to those of a nonmotile stresslet suspension. Under this model, it is demonstrated that confinement makes possible a stable circulating state; a linear stability analysis reveals an activity threshold for spontaneous autocirculation. Numerical analysis of the longtime behavior reveals a phenomenon akin to defect separation in nematic liquid crystals and a high-activity bifurcation to an oscillatory regime.
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Affiliation(s)
- Francis G Woodhouse
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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Galanis J, Nossal R, Losert W, Harries D. Nematic order in small systems: measuring the elastic and wall-anchoring constants in vibrofluidized granular rods. PHYSICAL REVIEW LETTERS 2010; 105:168001. [PMID: 21231016 PMCID: PMC6528800 DOI: 10.1103/physrevlett.105.168001] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2010] [Revised: 08/22/2010] [Indexed: 05/30/2023]
Abstract
We investigate nematic order in vibrated granular rods confined to a small quasi-2D container less than 10 rod lengths in diameter. As rod density ρ increases, patterning shifts from bipolar to uniform alignment. We find that a continuum liquid crystal free energy functional captures key patterning features down to almost the particle size. By fitting theory to experiments, we estimate the relative values of bend and splay elastic constants and wall anchoring. We find that splay is softer than bend for all ρ and rod lengths tested, while the ratio of the average elastic constant to wall anchoring increases with ρ.
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Affiliation(s)
- Jennifer Galanis
- Institute of Chemistry and The Fritz Haber Center, The Hebrew University, Jerusalem, 91904, Israel
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de Oliveira BF, Avelino PP, Moraes F, Oliveira JCRE. Nematic liquid crystal dynamics under applied electric fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041707. [PMID: 21230295 DOI: 10.1103/physreve.82.041707] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2010] [Revised: 08/13/2010] [Indexed: 05/30/2023]
Abstract
In this paper we investigate the coarsening dynamics of liquid crystal textures in a two-dimensional nematic under applied electric fields, using numerical simulations performed using a publicly available liquid crystal algorithm developed by the authors. We consider both positive and negative dielectric anisotropies and two different possibilities for the orientation of the electric field (parallel and perpendicular to the two-dimensional lattice). We determine the effect of an applied electric field pulse on the evolution of the characteristic length scale and other properties of the liquid crystal texture network. In particular, we show that different types of defects are produced after the electric field is switched on, depending on the orientation of the electric field and the sign of the dielectric anisotropy.
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Affiliation(s)
- B F de Oliveira
- Centro de Física do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
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