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Subert R, Campos-Villalobos G, Dijkstra M. Achiral hard bananas assemble double-twist skyrmions and blue phases. Nat Commun 2024; 15:6780. [PMID: 39117620 PMCID: PMC11310516 DOI: 10.1038/s41467-024-50935-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2024] [Accepted: 07/23/2024] [Indexed: 08/10/2024] Open
Abstract
Skyrmions are topologically protected, vortex-like structures found in various condensed-matter systems including helical ferromagnets and liquid crystals, typically arising from chiral interactions. Using extensive particle-based simulations, we demonstrate that non-chiral hard banana-shaped particles, governed solely by excluded-volume interactions, spontaneously stabilize skyrmion structures through the bend-flexoelectric effect. Under thin confinement, we observe the formation of quasi-2D layers of isolated skyrmions or dense skyrmion lattices. These structures, comprising a racemic mixture of left- and right-handed skyrmions, show resilience against thermal fluctuations while remaining responsive to external fields, offering intriguing possibilities for manipulation. We also find that the size of these skyrmions can be adjusted by the dimensions and curvature of the banana-shaped particles. In the absence of geometric frustration due to confinement, a blue phase III may emerge, characterized by a 3D network of chiral skyrmion filaments of the nematic director field within an isotropic background. Our findings provide valuable insights into stabilizing skyrmion lattices and blue phases, showcasing non-Gaussian fluid-like dynamics in systems of achiral hard particles. Furthermore, they highlight the remarkable capacity of these complex fluids in designing advanced functional materials with diverse applications in photonics and memory devices.
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Affiliation(s)
- Rodolfo Subert
- Soft Condensed Matter & Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands
| | - Gerardo Campos-Villalobos
- Soft Condensed Matter & Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter & Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands.
- International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, 1-3-1 Kagamiyama, 739-8526, Higashi-Hiroshima, Hiroshima, Japan.
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2
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Teixeira AW, Tasinkevych M, Dias CS. Particle-based model of liquid crystal skyrmion dynamics. SOFT MATTER 2024; 20:2088-2099. [PMID: 38348527 DOI: 10.1039/d3sm01422c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/29/2024]
Abstract
Motivated by recent experimental results that reveal rich collective dynamics of thousands-to-millions of active liquid crystal skyrmions, we have developed a coarse-grained, particle-based model of the dynamics of skyrmions in a dilute regime. The basic physical mechanism of skyrmion motion is related to squirming undulations of domains with high director twist within the skyrmion cores when the electric field is turned on and off. The motion is not related to mass flow and is caused only by the reorientation dynamics of the director field. Based on the results of the "fine-grained" Frank-Oseen continuum model, we have mapped these squirming director distortions onto an effective force that acts asymmetrically upon switching the electrical field on or off. The resulting model correctly reproduces the skyrmion dynamics, including velocity reversal as a function of the frequency of a pulse width modulated driving voltage. We have also obtained approximate analytical expressions for the phenomenological model parameters encoding their dependence upon the cholesteric pitch and the strength of the electric field. This has been achieved by fitting coarse-grained skyrmion trajectories to those determined in the framework of the Frank-Oseen model.
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Affiliation(s)
- A W Teixeira
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - M Tasinkevych
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, UK
- International Institute for Sustainability with Knotted Chiral Meta Matter, Hiroshima University, Higashihiroshima 739-8511, Japan
| | - C S Dias
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
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3
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Negro G, Carenza LN, Gonnella G, Marenduzzo D, Orlandini E. Topological phases and curvature-driven pattern formation in cholesteric shells. SOFT MATTER 2023; 19:1987-2000. [PMID: 36847796 DOI: 10.1039/d2sm01347a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We study the phase behaviour of cholesteric liquid crystal shells with different geometries. We compare the cases of tangential anchoring and no anchoring at the surface, focussing on the former case, which leads to a competition between the intrinsic tendency of the cholesteric to twist and the anchoring free energy which suppresses it. We then characterise the topological phases arising close to the isotropic-cholesteric transition. These typically consist of quasi-crystalline or amorphous tessellations of the surface by half-skyrmions, which are stable at lower and larger shell sizes, respectively. For ellipsoidal shells, defects in the tessellation couple to a local curvature, and according to the shell size, they either migrate to the poles or distribute uniformly on the surface. For toroidal shells, the variations in the local curvature of the surface stabilise heterogeneous phases where cholesteric or isotropic patterns coexist with hexagonal lattices of half-skyrmions.
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Affiliation(s)
- G Negro
- Dipartimento di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari, I-70126, Italy
| | - L N Carenza
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
| | - G Gonnella
- Dipartimento di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari, I-70126, Italy
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK
| | - E Orlandini
- Dipartimento di Fisica e Astronomia, Università di Padova, 35131 Padova, Italy
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4
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Long C, Selinger JV. Explicit demonstration of geometric frustration in chiral liquid crystals. SOFT MATTER 2023; 19:519-529. [PMID: 36541414 DOI: 10.1039/d2sm01420c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Many solid materials and liquid crystals exhibit geometric frustration, meaning that they have an ideal local structure that cannot fill up space. For that reason, the global phase must be a compromise between the ideal local structure and geometric constraints. As an explicit example of geometric frustration, we consider a chiral liquid crystal confined in a long cylinder with free boundaries. When the radius of the tube is sufficiently small, the director field forms a double-twist configuration, which is the ideal local structure. However, when the radius becomes larger (compared with the natural twist of the liquid crystal), the double-twist structure cannot fill space, and hence the director field must transform into some other chiral structure that can fill space. This space-filling structure may be either (1) a cholesteric phase with single twist, or (2) a set of double-twist regions separated by a disclination, which can be regarded as the beginning of a blue phase. We investigate these structures using theory and simulations, and show how the relative free energies depend on the system size, the natural twist, and the disclination energy. As another example, we also study a cholesteric liquid crystal confined between two infinite parallel plates with free boundaries.
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Affiliation(s)
- Cheng Long
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Jonathan V Selinger
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
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5
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Hölbl A, Mesarec L, Polanšek J, Iglič A, Kralj S. Stable Assemblies of Topological Defects in Nematic Orientational Order. ACS OMEGA 2023; 8:169-179. [PMID: 36643572 PMCID: PMC9835183 DOI: 10.1021/acsomega.2c07174] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Accepted: 12/07/2022] [Indexed: 06/17/2023]
Abstract
We considered general mechanisms enabling the stabilization of localized assemblies of topological defects (TDs). There is growing evidence that physical fields represent fundamental natural entities, and therefore these features are of interest to all branches of physics. In general, cores of TDs are energetically costly, and consequently, assemblies of TDs are unfavorable. Owing to the richness of universalities in the physics of TDs, it is of interest to identify systems where they are easily experimentally accessible, enabling detailed and well-controlled analysis of their universal behavior, and cross-fertilizing knowledge in different areas of physics. In this respect, thermotropic nematic liquid crystals (NLCs) represent an ideal experiment testbed for such studies. In addition, TDs in NLCs could be exploited in several applications. We present examples that emphasize the importance of curvature imposed on the phase component of the relevant order parameter field. In NLCs, it is represented by the nematic tensor order parameter. Using a simple Landau-type approach, we show how the coupling between chirality and saddle splay elasticity, which can be expressed as a Gaussian curvature contribution, can stabilize Meron TDs. The latter have numerous analogs in other branches of physics. TDs in 2D curved manifolds reveal that the Gaussian curvature dominantly impacts the assembling and stabilization of TDs. Furthermore, a strong enough curvature that serves as an attractor for TDs is a respective field that could be imposed in a fast enough phase transition. Assemblies of created TDs created in such a disordered environment could be stabilized by appropriate impurities.
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Affiliation(s)
- Arbresha Hölbl
- Faculty of Natural
Sciences and Mathematics, University of
Maribor, Koroška
160, 2000 Maribor, Slovenia
| | - Luka Mesarec
- Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia
| | - Juš Polanšek
- Faculty of Natural
Sciences and Mathematics, University of
Maribor, Koroška
160, 2000 Maribor, Slovenia
| | - Aleš Iglič
- Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia
| | - Samo Kralj
- Faculty of Natural
Sciences and Mathematics, University of
Maribor, Koroška
160, 2000 Maribor, Slovenia
- Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
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6
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Carenza LN, Gonnella G, Marenduzzo D, Negro G, Orlandini E. Cholesteric Shells: Two-Dimensional Blue Fog and Finite Quasicrystals. PHYSICAL REVIEW LETTERS 2022; 128:027801. [PMID: 35089738 DOI: 10.1103/physrevlett.128.027801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2021] [Revised: 09/22/2021] [Accepted: 12/08/2021] [Indexed: 06/14/2023]
Abstract
We study the phase behavior of a quasi-two-dimensional cholesteric liquid crystal shell. We characterize the topological phases arising close to the isotropic-cholesteric transition and show that they differ in a fundamental way from those observed on a flat geometry. For spherical shells, we discover two types of quasi-two-dimensional topological phases: finite quasicrystals and amorphous structures, both made up of mixtures of polygonal tessellations of half-skyrmions. These structures generically emerge instead of regular double twist lattices because of geometric frustration, which disallows a regular hexagonal tiling of curved space. For toroidal shells, the variations in the local curvature of the surface stabilizes heterogeneous phases where cholesteric patterns coexist with hexagonal lattices of half-skyrmions. Quasicrystals and amorphous and heterogeneous structures could be sought experimentally by self-assembling cholesteric shells on the surface of emulsion droplets.
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Affiliation(s)
- L N Carenza
- Dipartimento di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands
| | - G Gonnella
- Dipartimento di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - G Negro
- Dipartimento di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - E Orlandini
- Dipartimento di Fisica e Astronomia, Università di Padova and INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
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7
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Long C, Selinger JV. Coarse-grained theory for motion of solitons and skyrmions in liquid crystals. SOFT MATTER 2021; 17:10437-10446. [PMID: 34761790 DOI: 10.1039/d1sm01335a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Recent experiments have found that applied electric fields can induce motion of skyrmions in chiral nematic liquid crystals. To understand the magnitude and direction of the induced motion, we develop a coarse-grained approach to describe dynamics of skyrmions, similar to our group's previous work on the dynamics of disclinations. In this approach, we represent a localized excitation in terms of a few macroscopic degrees of freedom, including the position of the excitation and the orientation of the background director. We then derive the Rayleigh dissipation function, and hence the equations of motion, in terms of these macroscopic variables. We demonstrate this theoretical approach for 1D motion of a sine-Gordon soliton, and then extend it to 2D motion of a skyrmion. Our results show that skyrmions move in a direction perpendicular to the induced tilt of the background director. When the applied field is removed, skyrmions move in the opposite direction but not with equal magnitude, and hence the overall motion may be rectified.
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Affiliation(s)
- Cheng Long
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA.
| | - Jonathan V Selinger
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA.
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8
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Napoli G, Pylypovskyi OV, Sheka DD, Vergori L. Nematic shells: new insights in topology- and curvature-induced effects. SOFT MATTER 2021; 17:10322-10333. [PMID: 34734955 DOI: 10.1039/d1sm00719j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Within the framework of continuum theory, we draw a parallel between ferromagnetic materials and nematic liquid crystals confined on curved surfaces, which are both characterized by local interaction and anchoring potentials. We show that the extrinsic curvature of the shell combined with the out-of-plane component of the director field gives rise to chirality effects. This interplay produces an effective energy term reminiscent of the chiral term in cholesteric liquid crystals, with the curvature tensor acting as a sort of anisotropic helicity. We discuss also how the different nature of the order parameter, a vector in ferromagnets and a tensor in nematics, yields different textures on surfaces with the same topology as the sphere. In particular, we show that the extrinsic curvature governs the ground state configuration on a nematic spherical shell, favouring two antipodal disclinations of charge +1 on small particles and four +1/2 disclinations of charge located at the vertices of a square inscribed in a great circle on larger particles.
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Affiliation(s)
- Gaetano Napoli
- Dipartimento di Matematica e Fisica "E. De Giorgi", Università del Salento, Lecce, Italy.
| | - Oleksandr V Pylypovskyi
- Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, 01328 Dresden, Germany
| | - Denis D Sheka
- Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine
| | - Luigi Vergori
- Dipartimento di Ingegneria, Università di Perugia, Perugia, Italy
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9
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Leonov AO. Surface anchoring as a control parameter for shaping skyrmion or toron properties in thin layers of chiral nematic liquid crystals and noncentrosymmetric magnets. Phys Rev E 2021; 104:044701. [PMID: 34781482 DOI: 10.1103/physreve.104.044701] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Accepted: 10/01/2021] [Indexed: 11/07/2022]
Abstract
Existence of topological localized states (skyrmions and torons) and the mechanism of their condensation into modulated states are the ruling principles of condensed matter systems, such as chiral nematic liquid crystals (CLCs) and chiral magnets (ChM). In bulk helimagnets, skyrmions are rendered into thermodynamically stable hexagonal skyrmion lattice due to the combined effect of a magnetic field and, e.g., small anisotropic contributions. In thin glass cells of CLCs, skyrmions are formed in response to the geometrical frustration and field coupling effects. By numerical modeling, I undertake a systematic study of skyrmion or toron properties in thin layers of CLCs and ChMs with competing surface-induced and bulk anisotropies. The conical phase with a variable polar angle serves as a suitable background, which shapes skyrmion internal structure, guides the nucleation processes, and substantializes the skyrmion-skyrmion interaction. I show that the hexagonal lattice of torons can be stabilized in a vast region of the constructed phase diagram for both easy-axis bulk and surface anisotropies. A topologically trivial droplet is shown to form as a domain boundary between two cone states with different rotational fashion, which underpins its stability. The findings provide a recipe for controllably creating skyrmions and torons, possessing the features on demand for potential applications.
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Affiliation(s)
- Andrey O Leonov
- Chirality Research Center, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan; Department of Chemistry, Faculty of Science, Hiroshima University Kagamiyama, Higashi Hiroshima, Hiroshima 739-8526, Japan; and IFW Dresden, Postfach 270016, D-01171 Dresden, Germany
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10
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Oyeka EE, Winiarski MJ, Sorolla Ii M, Taddei KM, Scheie A, Tran TT. Spin and Orbital Effects on Asymmetric Exchange Interaction in Polar Magnets: M(IO 3) 2 (M = Cu and Mn). Inorg Chem 2021; 60:16544-16557. [PMID: 34637293 DOI: 10.1021/acs.inorgchem.1c02432] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Magnetic polar materials feature an astonishing range of physical properties, such as magnetoelectric coupling, chiral spin textures, and related new spin topology physics. This is primarily attributable to their lack of space inversion symmetry in conjunction with unpaired electrons, potentially facilitating an asymmetric Dzyaloshinskii-Moriya (DM) exchange interaction supported by spin-orbital and electron-lattice coupling. However, engineering the appropriate ensemble of coupled degrees of freedom necessary for enhanced DM exchange has remained elusive for polar magnets. Here, we study how spin and orbital components influence the capability of promoting the magnetic interaction by studying two magnetic polar materials, α-Cu(IO3)2 (2D) and Mn(IO3)2 (6S), and connecting their electronic and magnetic properties with their structures. The chemically controlled low-temperature synthesis of these complexes resulted in pure polycrystalline samples, providing a viable pathway to prepare bulk forms of transition-metal iodates. Rietveld refinements of the powder synchrotron X-ray diffraction data reveal that these materials exhibit different crystal structures but crystallize in the same polar and chiral P21 space group, giving rise to an electric polarization along the b-axis direction. The presence and absence of an evident phase transition to a possible topologically distinct state observed in α-Cu(IO3)2 and Mn(IO3)2, respectively, imply the important role of spin-orbit coupling. Neutron diffraction experiments reveal helpful insights into the magnetic ground state of these materials. While the long-wavelength incommensurability of α-Cu(IO3)2 is in harmony with sizable asymmetric DM interaction and low dimensionality of the electronic structure, the commensurate stripe AFM ground state of Mn(IO3)2 is attributed to negligible DM exchange and isotropic orbital overlapping. The work demonstrates connections between combined spin and orbital effects, magnetic coupling dimensionality, and DM exchange, providing a worthwhile approach for tuning asymmetric interaction, which promotes evolution of topologically distinct spin phases.
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Affiliation(s)
- Ebube E Oyeka
- Department of Chemistry, Clemson University, Clemson, South Carolina 29634, United States
| | - Michał J Winiarski
- Faculty of Applied Physics and Mathematics and Advanced Materials Center, Gdansk University of Technology, ul. Narutowicza 11/12, 80-233 Gdansk, Poland
| | - Maurice Sorolla Ii
- Department of Chemical Engineering, University of the Philippines Diliman, Quezon City 1101, Philippines
| | - Keith M Taddei
- Neutron Scattering Division, Oak Ridge National Laboratory, 9500 Spallation Dr, Oak Ridge, Tennessee 37830, United States
| | - Allen Scheie
- Neutron Scattering Division, Oak Ridge National Laboratory, 9500 Spallation Dr, Oak Ridge, Tennessee 37830, United States
| | - Thao T Tran
- Department of Chemistry, Clemson University, Clemson, South Carolina 29634, United States
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11
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Ding L, Pelcovits RA, Powers TR. Deformation and orientational order of chiral membranes with free edges. SOFT MATTER 2021; 17:6580-6588. [PMID: 34160539 DOI: 10.1039/d1sm00629k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Motivated by experiments on colloidal membranes composed of chiral rod-like viruses, we use Monte Carlo methods to simulate these systems and determine the phase diagram for the liquid crystalline order of the rods and the membrane shape. We generalize the Lebwohl-Lasher model for a nematic with a chiral coupling to a curved surface with edge tension and a resistance to bending, and include an energy cost for tilting of the rods relative to the local membrane normal. The membrane is represented by a triangular mesh of hard beads joined by bonds, where each bead is decorated by a director. The beads can move, the bonds can reconnect and the directors can rotate at each Monte Carlo step. When the cost of tilt is small, the membrane tends to be flat, with the rods only twisting near the edge for low chiral coupling, and remaining parallel to the normal in the interior of the membrane. At high chiral coupling, the rods twist everywhere, forming a cholesteric state. When the cost of tilt is large, the emergence of the cholesteric state at high values of the chiral coupling is accompanied by the bending of the membrane into a saddle shape. Increasing the edge tension tends to flatten the membrane. These results illustrate the geometric frustration arising from the inability of a surface normal to have twist.
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Affiliation(s)
- Lijie Ding
- Department of Physics, Brown University, Providence, RI 02912, USA.
| | - Robert A Pelcovits
- Department of Physics, Brown University, Providence, RI 02912, USA. and Brown Theoretical Physics Center, Brown University, Providence, RI 02912, USA
| | - Thomas R Powers
- Department of Physics, Brown University, Providence, RI 02912, USA. and Brown Theoretical Physics Center, Brown University, Providence, RI 02912, USA and School of Engineering, Brown University, Providence, RI 02912, USA and Center for Fluid Mechanics, Brown University, Providence, RI 02912, USA
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12
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Lavrentovich OD. Design of nematic liquid crystals to control microscale dynamics. LIQUID CRYSTALS REVIEWS 2021; 8:59-129. [PMID: 34956738 PMCID: PMC8698256 DOI: 10.1080/21680396.2021.1919576] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Accepted: 04/11/2021] [Indexed: 05/25/2023]
Abstract
The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.
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Affiliation(s)
- Oleg D Lavrentovich
- Advanced Materials and Liquid Crystal Institute, Department of Physics, Materials Science Graduate Program, Kent State University, Kent, OH 44242, USA
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13
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Duzgun A, Nisoli C. Skyrmion Spin Ice in Liquid Crystals. PHYSICAL REVIEW LETTERS 2021; 126:047801. [PMID: 33576672 DOI: 10.1103/physrevlett.126.047801] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Revised: 10/17/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
We propose the first skyrmion spin ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic liquid crystal behave as quasiparticles that can be dynamically confined, bound, and created or annihilated individually with ease and precision. We show that these quasiparticles can be employed to realize binary variables that interact to form ice-rule states. Because of their unique versatility, liquid crystal skyrmions can open entirely novel avenues in the field of frustrated systems. More broadly, our findings also demonstrate the viability of liquid crystal skyrmions as elementary degrees of freedom in the design of collective complex behaviors.
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Affiliation(s)
- Ayhan Duzgun
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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14
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Palma CA. Topological Dynamic Matter. J Phys Chem Lett 2021; 12:454-462. [PMID: 33369418 DOI: 10.1021/acs.jpclett.0c03114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The principles of topology in condensed matter physics have expanded to areas such as photonics, acoustics, electronics, and mechanics. Their extension to dynamic (soft) matter could enable the control and design of topological thermodynamic (micro)states and nonreciprocal dynamics, potentially leading to paradigmatic applications in molecular and thermal waveguiding, logics, and energy management. This Perspective explores distinct topological concepts for dynamic matter and prospective function. Topological tools are exemplified and discussed for the study of nonlocal order parameters or invariants in dynamic molecular matter, toward the engineering of assemblies, reactions, and system chemistry with unconventional global properties-a scope which has the potential to push the frontiers of physical chemistry and transform chemical topology from form to function.
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Affiliation(s)
- Carlos-Andres Palma
- Institute of Physics, Chinese Academy of Sciences, 100190 Beijing, P.R. China
- Department of Physics & IRIS Adlershof, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
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15
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Binysh J, Pollard J, Alexander GP. Geometry of Bend: Singular Lines and Defects in Twist-Bend Nematics. PHYSICAL REVIEW LETTERS 2020; 125:047801. [PMID: 32794804 DOI: 10.1103/physrevlett.125.047801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Revised: 05/25/2020] [Accepted: 06/15/2020] [Indexed: 06/11/2023]
Abstract
We describe the geometry of bend distortions in liquid crystals and their fundamental degeneracies, which we call β lines; these represent a new class of linelike topological defect in twist-bend nematics. We present constructions for smecticlike textures containing screw and edge dislocations and also for vortexlike structures of double twist and Skyrmions. We analyze their local geometry and global structure, showing that their intersection with any surface is twice the Skyrmion number. Finally, we demonstrate how arbitrary knots and links can be created and describe them in terms of merons, giving a geometric perspective on the fractionalization of Skyrmions.
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Affiliation(s)
- Jack Binysh
- Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
| | - Joseph Pollard
- Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Gareth P Alexander
- Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
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16
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Tai JSB, Smalyukh II. Surface anchoring as a control parameter for stabilizing torons, skyrmions, twisted walls, fingers, and their hybrids in chiral nematics. Phys Rev E 2020; 101:042702. [PMID: 32422774 DOI: 10.1103/physreve.101.042702] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2019] [Accepted: 03/25/2020] [Indexed: 06/11/2023]
Abstract
Chiral condensed matter systems, such as liquid crystals and magnets, exhibit a host of spatially localized topological structures that emerge from the medium's tendency to twist and its competition with confinement and field coupling effects. We show that the strength of perpendicular surface boundary conditions can be used to control the structure and topology of solitonic and other localized field configurations. By combining numerical modeling and three-dimensional imaging of the director field, we reveal structural stability diagrams and intertransformation of twisted walls and fingers, torons, and skyrmions and their crystalline organizations upon changing boundary conditions. Our findings provide a recipe for controllably realizing skyrmions, torons, and hybrid solitonic structures possessing features of both of them, which will aid in fundamental explorations and technological uses of such topological solitons. Moreover, we discuss how other material parameters can be used to determine soliton stability and how similar principles can be systematically applied to other liquid crystal solitons and solitons in other material systems.
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Affiliation(s)
- Jung-Shen B Tai
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Materials Science and Engineering Program, Soft Materials Research Center and Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
- Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
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17
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Duzgun A, Nisoli C, Reichhardt CJO, Reichhardt C. Commensurate states and pattern switching via liquid crystal skyrmions trapped in a square lattice. SOFT MATTER 2020; 16:3338-3343. [PMID: 32196037 DOI: 10.1039/c9sm02312g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Using continuum based simulations we show that a rich variety of skyrmion liquid crystal states can be realized in the presence of a periodic obstacle array. As a function of the number of skyrmions per obstacle we find hexagonal, square, dimer, trimer and quadrimer ordering, where the n-mer structures are a realization of a molecular crystal state of skyrmions. As a function of external field and obstacle radius we show that there are transitions between the different crystalline states as well as mixed and disordered structures. We discuss how these states are related to commensurate effects seen in other systems, such as vortices in type-II superconductors and colloids interacting with two dimensional substrates.
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Affiliation(s)
- A Duzgun
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
| | - C Nisoli
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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18
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Topnani NB, Posnjak G, Nagaraja P, Neogi A, Musevic I, Ramarao P. Self-assembled toron-like structures in inverse nematic gels. SOFT MATTER 2020; 16:2933-2940. [PMID: 32095804 DOI: 10.1039/c9sm02547b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
A novel form of nematic gel (N-gel) wherein bright flower-like domains (BFDs) rich in gelator fibres are embedded in a matrix of liquid crystal (LC) molecules has been reported. These gels which we denote as inverse N-gels are unlike typical N-gels in which the LC is encapsulated within an aggregated network of gelator molecules. The self-organization of the helical gelator fibres within the BFDs leads to the creation of localized toron-like structures that are topologically protected due to their skyrmion director profile. Optical and confocal microscopy have been used to deduce the LC director configuration, in order to understand possible intermolecular interactions that can lead to the formation of the twisted structures and the inverse N-gels.
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Affiliation(s)
- Neha B Topnani
- Soft Condensed Matter Lab, Raman Research Institute, Bangalore 560080, India.
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19
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Chaturvedi N, Kamien RD. Gnomonious projections for bend-free textures: thoughts on the splay-twist phase. Proc Math Phys Eng Sci 2020; 476:20190824. [PMID: 32201482 PMCID: PMC7069486 DOI: 10.1098/rspa.2019.0824] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2019] [Accepted: 01/14/2020] [Indexed: 11/12/2022] Open
Abstract
The Hopf fibration has inspired any number of geometric structures in physical systems, in particular, in chiral liquid crystalline materials. Because the Hopf fibration lives on the three sphere,S 3 , some method of projection or distortion must be employed to realize textures in flat space. Here, we explore the geodesic-preserving gnomonic projection of the Hopf fibration, and show that this could be the basis for a new liquid crystalline texture with only splay and twist. We outline the structure and show that it is defined by the tangent vectors along the straight line rulings on a series of hyperboloids. The phase is defined by a lack of bend deformations in the texture, and is reminiscent of the splay-bend and twist-bend nematic phases. We show that domains of this phase may be stabilized through anchoring and saddle-splay.
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Affiliation(s)
| | - Randall D. Kamien
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6396, USA
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20
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Metselaar L, Doostmohammadi A, Yeomans JM. Topological states in chiral active matter: Dynamic blue phases and active half-skyrmions. J Chem Phys 2019; 150:064909. [DOI: 10.1063/1.5085282] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Luuk Metselaar
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Julia M. Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
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21
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Affiliation(s)
- Luuk Metselaar
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford, UK
| | - Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford, UK
| | - Julia M. Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford, UK
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