1
|
Radka BP, Lee T, Smalyukh II, White TJ. The association of structural chirality and liquid crystal anchoring in polymer stabilized cholesteric liquid crystals. SOFT MATTER 2024; 20:1815-1823. [PMID: 38305433 DOI: 10.1039/d3sm01558k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/03/2024]
Abstract
Polymer stabilized cholesteric liquid crystals (PSCLCs) are electrically reconfigurable reflective elements. Prior studies have hypothesized and indirectly confirmed that the electro-optic response of these composites is associated with the electrically mediated distortion of the stabilizing polymer network. The proposed mechanism is based on the retention of structural chirality in the polymer stabilizing network, which upon deformation is spatially distorted, which accordingly affects the pitch of the surrounding low molar-mass liquid crystal host. Here, we utilize fluorescent confocal polarized microscopy to directly assess the electro-optic response of PSCLCs. By utilizing dual fluorescent probes, sequential imaging experiments confirm that the periodicity of the polymer stabilizing network matches that of the low molar-mass liquid crystal host. Further, we isolate distinct ion-polymer interactions that manifest in certain photopolymerization conditions.
Collapse
Affiliation(s)
- Brian P Radka
- Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA.
| | - Taewoo Lee
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Ivan I Smalyukh
- Materials Science and Engineering Program, University of Colorado, Boulder, CO 80309, USA
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
- Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Colorado, Boulder, CO 80309, USA
| | - Timothy J White
- Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA.
- Materials Science and Engineering Program, University of Colorado, Boulder, CO 80309, USA
| |
Collapse
|
2
|
Optical Imaging and Analytical Design of Localized Topological Structures in Chiral Liquid Crystals. Symmetry (Basel) 2022. [DOI: 10.3390/sym14122476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022] Open
Abstract
We combine numerical modeling and analytical design techniques to study several of the most common localized topological structures in frustrated chiral nematic liquid crystal cells. An energy minimization procedure is applied to the lattice model to simulate the director field distributions. These distributions are also approximated using the suitably designed analytical ansatz. We present both simulated and approximated results for optical polarizing microscopy textures and different visualizations of director field structure such as distributions of the azimuthal director angle and isolines for the normal component of the director in coordinate planes. The ansatz correctly mimicked the geometry and optical properties of the solitonic structures under consideration.
Collapse
|
3
|
Chan MC, Liao TH, Hsieh CS, Jeng SC, Zhuo GY. Imaging of nanoscale birefringence using polarization-resolved chromatic confocal microscopy. OPTICS EXPRESS 2021; 29:3965-3975. [PMID: 33770985 DOI: 10.1364/oe.414511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Accepted: 01/14/2021] [Indexed: 06/12/2023]
Abstract
We demonstrate a homebuilt confocal microscope with ∼60 nm axial resolution to visualize the optical path length (OPL) of liquid crystals (LCs) inside a 2-domain alignment LC cell. Since the microscope is sensitive to light polarization, it is capable of determining LC orientation by accounting for the OPL variation, ΔOPL. The resolution of birefringence depends on the measured ΔOPL from two cross-polarized channel detections, of which the concept is different from other polarization-resolved optical imaging techniques, but is relatively simple in optical layout and analysis. The different orientations of LCs and the voltage-dependent LC rotation properties in the 2-domain LC cell are monitored and analyzed. Additionally, the complicated LC orientation distribution at the junction of the two domains with different alignments can be clearly observed. It shows great possibilities of examining tissue birefringence related to disease progression and tiny birefringence variation of electro-optical materials under an external field, which are hardly resolved by conventional optical imaging techniques.
Collapse
|
4
|
Smalyukh II. Review: knots and other new topological effects in liquid crystals and colloids. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 83:106601. [PMID: 32721944 DOI: 10.1088/1361-6633/abaa39] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.
Collapse
Affiliation(s)
- Ivan I Smalyukh
- Department of Physics, Department of Electrical, Computer and Energy Engineering, Materials Science and Engineering Program and Soft Materials Research Center, University of Colorado, Boulder, CO 80309, United States of America
- Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, CO 80309, United States of America
| |
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
Durey G, Sohn HRO, Ackerman PJ, Brasselet E, Smalyukh II, Lopez-Leon T. Topological solitons, cholesteric fingers and singular defect lines in Janus liquid crystal shells. SOFT MATTER 2020; 16:2669-2682. [PMID: 31898713 DOI: 10.1039/c9sm02033k] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Topological solitons are non-singular but topologically nontrivial structures in fields, which have fundamental significance across various areas of physics, similar to singular defects. Production and observation of singular and solitonic topological structures remain a complex undertaking in most branches of science - but in soft matter physics, they can be realized within the director field of a liquid crystal. Additionally, it has been shown that confining liquid crystals to spherical shells using microfluidics resulted in a versatile experimental platform for the dynamical study of topological transformations between director configurations. In this work, we demonstrate the triggered formation of topological solitons, cholesteric fingers, singular defect lines and related structures in liquid crystal shells. We show that to accommodate these objects, shells must possess a Janus nature, featuring both twisted and untwisted domains. We report the formation of linear and axisymmetric objects, which we identify as cholesteric fingers and skyrmions or elementary torons, respectively. We then take advantage of the sensitivity of shells to numerous external stimuli to induce dynamical transitions between various types of structures, allowing for a richer phenomenology than traditional liquid crystal cells with solid flat walls. Using gradually more refined experimental techniques, we induce the targeted transformation of cholesteric twist walls and fingers into skyrmions and elementary torons. We capture the different stages of these director transformations using numerical simulations. Finally, we uncover an experimental mechanism to nucleate arrays of axisymmetric structures on shells, thereby creating a system of potential interest for tackling crystallography studies on curved spaces.
Collapse
Affiliation(s)
- Guillaume Durey
- Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, Université PSL, 10 rue Vauquelin, 75005 Paris, France.
| | | | | | | | | | | |
Collapse
|
7
|
Senyuk B, Aplinc J, Ravnik M, Smalyukh II. High-order elastic multipoles as colloidal atoms. Nat Commun 2019; 10:1825. [PMID: 31015420 PMCID: PMC6478862 DOI: 10.1038/s41467-019-09777-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2018] [Accepted: 03/28/2019] [Indexed: 11/09/2022] Open
Abstract
Achieving and exceeding diversity of colloidal analogs of chemical elements and molecules as building blocks of matter has been the central goal and challenge of colloidal science ever since Einstein introduced the colloidal atom paradigm. Recent advances in colloids assembly have been achieved by exploiting the machinery of DNA hybridization but robust physical means of defining colloidal elements remain limited. Here we introduce physical design principles allowing us to define high-order elastic multipoles emerging when colloids with controlled shapes and surface alignment are introduced into a nematic host fluid. Combination of experiments and numerical modeling of equilibrium field configurations using a spherical harmonic expansion allow us to probe elastic multipole moments, bringing analogies with electromagnetism and a structure of atomic orbitals. We show that, at least in view of the symmetry of the "director wiggle wave functions," diversity of elastic colloidal atoms can far exceed that of known chemical elements.
Collapse
Affiliation(s)
- Bohdan Senyuk
- Department of Physics and Soft Materials Research Center, University of Colorado, Boulder, CO, 80309, USA
| | - Jure Aplinc
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia
| | - Miha Ravnik
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.,J. Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
| | - Ivan I Smalyukh
- Department of Physics and Soft Materials Research Center, University of Colorado, Boulder, CO, 80309, USA. .,Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, CO, 80309, USA. .,Renewable and Sustainable Energy Institute, University of Colorado, Boulder, CO, 80309, USA.
| |
Collapse
|
8
|
Peng H, Jiang W, Liu Q, Chen G, Ni M, Liang F, Liao Y, Xie X, Smalyukh II. Liquid Crystals under Confinement in Submicrometer Capsules. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:10955-10963. [PMID: 30130404 DOI: 10.1021/acs.langmuir.8b01056] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Liquid crystal (LC) ordering and phase transition behavior under confined conditions have attracted extensive attention and enabled many applications. However, the ordering and phase transition behavior of LCs in submicrometer capsules have seldom been studied, primarily due to the lack of proper capsulizing and visualization approaches to such small LC microcapsules. Herein, we achieve submicrometer LC capsules with the sizes down to 100 nm by using emulsion-based interfacial sol-gel reaction. The behavior of LCs under the submicrometer confinement conditions is investigated while the sizes and chemical composition of the microcapsule shell surface are tuned in a controllable way. The phase transition temperatures of LCs in the submicrometer capsules shift from those of bulk LCs due to the surface-induced ordering of LCs under the strong confinement conditions, which causes formation of topological defects and alters the order parameter. Using nonlinear optical imaging technology, we explore the structures of director field of LCs that arise as a result of the competition between the surface boundary conditions and LC elasticity. The results show that the nanoscale encapsulation can significantly influence the structural configurations of the director and phase transitions of LCs under various confinement conditions.
Collapse
Affiliation(s)
- Haiyan Peng
- Key Lab for Material Chemistry of Energy Conversion and Storage, Ministry of Education, and Hubei Key Lab of Material Chemistry and Service Failure, School of Chemistry and Chemical Engineering , Huazhong University of Science and Technology (HUST) , Wuhan 430074 , P. R. China
- Sino-U.S. Joint Research Center on Liquid Crystal Chemistry and Physics , HUST and CUB
| | - Wenhong Jiang
- Key Lab for Material Chemistry of Energy Conversion and Storage, Ministry of Education, and Hubei Key Lab of Material Chemistry and Service Failure, School of Chemistry and Chemical Engineering , Huazhong University of Science and Technology (HUST) , Wuhan 430074 , P. R. China
- State Key Lab of Polymer Physics and Chemistry , Institute of Chemistry, Chinese Academy of Sciences , Beijing 100190 , P. R. China
| | - Qingkun Liu
- Department of Physics and Materials Science and Engineering Program , University of Colorado at Boulder (CUB) , Boulder , Colorado 80309 , United States
| | - Guannan Chen
- Key Lab for Material Chemistry of Energy Conversion and Storage, Ministry of Education, and Hubei Key Lab of Material Chemistry and Service Failure, School of Chemistry and Chemical Engineering , Huazhong University of Science and Technology (HUST) , Wuhan 430074 , P. R. China
| | - Mingli Ni
- Key Lab for Material Chemistry of Energy Conversion and Storage, Ministry of Education, and Hubei Key Lab of Material Chemistry and Service Failure, School of Chemistry and Chemical Engineering , Huazhong University of Science and Technology (HUST) , Wuhan 430074 , P. R. China
| | - Fuxin Liang
- State Key Lab of Polymer Physics and Chemistry , Institute of Chemistry, Chinese Academy of Sciences , Beijing 100190 , P. R. China
| | - Yonggui Liao
- Key Lab for Material Chemistry of Energy Conversion and Storage, Ministry of Education, and Hubei Key Lab of Material Chemistry and Service Failure, School of Chemistry and Chemical Engineering , Huazhong University of Science and Technology (HUST) , Wuhan 430074 , P. R. China
- Sino-U.S. Joint Research Center on Liquid Crystal Chemistry and Physics , HUST and CUB
| | - Xiaolin Xie
- Key Lab for Material Chemistry of Energy Conversion and Storage, Ministry of Education, and Hubei Key Lab of Material Chemistry and Service Failure, School of Chemistry and Chemical Engineering , Huazhong University of Science and Technology (HUST) , Wuhan 430074 , P. R. China
- Sino-U.S. Joint Research Center on Liquid Crystal Chemistry and Physics , HUST and CUB
| | - Ivan I Smalyukh
- Department of Physics and Materials Science and Engineering Program , University of Colorado at Boulder (CUB) , Boulder , Colorado 80309 , United States
- Sino-U.S. Joint Research Center on Liquid Crystal Chemistry and Physics , HUST and CUB
| |
Collapse
|
9
|
Lee SH. Optimal integration of wide field illumination and holographic optical tweezers for multimodal microscopy with ultimate flexibility and versatility. OPTICS EXPRESS 2018; 26:8049-8058. [PMID: 29715778 DOI: 10.1364/oe.26.008049] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Accepted: 03/04/2018] [Indexed: 05/29/2023]
Abstract
We introduce one-of-a-kind optical microscope that we have developed through optimized integration of wide-field and focused-light microscopies. This new instrument has accomplished operation of the same laser for both wide field illumination and holographic focused beam illumination interchangeably or simultaneously in a way scalable to multiple lasers. We have demonstrated its powerful capability by simultaneously carrying out Epi-fluorescence, total internal reflection fluorescence microscopy, selective plane illumination microscopy, and holographic optical tweezers with five lasers. Our instrument and the optical design will provide researchers across diverse fields, cell-biology and biophysics in particular, with a practical guidance to build an all-around multimodal microscope that will further inspire the development of novel hybrid microscopy experiments.
Collapse
|
10
|
Trivedi RP, Tasinkevych M, Smalyukh II. Nonsingular defects and self-assembly of colloidal particles in cholesteric liquid crystals. Phys Rev E 2016; 94:062703. [PMID: 28085464 DOI: 10.1103/physreve.94.062703] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2016] [Indexed: 11/07/2022]
Abstract
Cholesteric liquid crystals can potentially provide a means for tunable self-organization of colloidal particles. However, the structures of particle-induced defects and the ensuing elasticity-mediated colloidal interactions in these media remain much less explored and understood as compared to their nematic liquid crystal counterparts. Here we demonstrate how colloidal microspheres of varying diameter relative to the helicoidal pitch can induce dipolelike director field configurations in cholesteric liquid crystals, where these particles are accompanied by point defects and a diverse variety of nonsingular line defects forming closed loops. Using laser tweezers and nonlinear optical microscopy, we characterize the ensuing medium-mediated elastic interactions and three-dimensional colloidal assemblies. Experimental findings show a good agreement with numerical modeling based on minimization of the Landau-de Gennes free energy and promise both practical applications in the realization of colloidal composite materials and a means of controlling nonsingular topological defects that attract a great deal of fundamental interest.
Collapse
Affiliation(s)
- Rahul P Trivedi
- Department of Physics and Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - Mykola Tasinkevych
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstrasse 3, D-70569 Stuttgart, Germany.,IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Ivan I Smalyukh
- Department of Physics and Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA.,Soft Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA.,Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
11
|
Varney MCM, Zhang Q, Senyuk B, Smalyukh II. Self-assembly of colloidal particles in deformation landscapes of electrically driven layer undulations in cholesteric liquid crystals. Phys Rev E 2016; 94:042709. [PMID: 27841645 DOI: 10.1103/physreve.94.042709] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2016] [Indexed: 04/26/2023]
Abstract
We study elastic interactions between colloidal particles and deformation landscapes of undulations in a cholesteric liquid crystal under an electric field applied normal to cholesteric layers. The onset of undulation instability is influenced by the presence of colloidal inclusions and, in turn, layers' undulations mediate the spatial patterning of particle locations. We find that the bending of cholesteric layers around a colloidal particle surface prompts the local nucleation of an undulations lattice at electric fields below the well-defined threshold known for liquid crystals without inclusions, and that the onset of the resulting lattice is locally influenced, both dimensionally and orientationally, by the initial arrangements of colloids defined using laser tweezers. Spherical particles tend to spatially localize in the regions of strong distortions of the cholesteric layers, while colloidal nanowires exhibit an additional preference for multistable alignment offset along various vectors of the undulations lattice. Magnetic rotation of superparamagnetic colloidal particles couples with the locally distorted helical axis and undulating cholesteric layers in a manner that allows for a controlled three-dimensional translation of these particles. These interaction modes lend insight into the physics of liquid crystal structure-colloid elastic interactions, as well as point the way towards guided self-assembly of reconfigurable colloidal composites with potential applications in diffraction optics and photonics.
Collapse
Affiliation(s)
- Michael C M Varney
- Department of Physics and Soft Materials Research Center, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Qiaoxuan Zhang
- Department of Physics and Soft Materials Research Center, University of Colorado at Boulder, Boulder, Colorado 80309, USA
- Materials Science and Engineering Program, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Bohdan Senyuk
- Department of Physics and Soft Materials Research Center, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Ivan I Smalyukh
- Department of Physics and Soft Materials Research Center, University of Colorado at Boulder, Boulder, Colorado 80309, USA
- Materials Science and Engineering Program, University of Colorado at Boulder, Boulder, Colorado 80309, USA
- Department of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA
- Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado at Boulder, Boulder, Colorado 80309, USA
| |
Collapse
|
12
|
Senyuk B, Liu Q, Yuan Y, Smalyukh II. Edge pinning and transformation of defect lines induced by faceted colloidal rings in nematic liquid crystals. Phys Rev E 2016; 93:062704. [PMID: 27415331 DOI: 10.1103/physreve.93.062704] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2016] [Indexed: 06/06/2023]
Abstract
Nematic colloids exhibit a large diversity of topological defects and structures induced by colloidal particles in the orientationally ordered liquid crystal host fluids. These defects and field configurations define elastic interactions and medium-mediated self-assembly, as well as serve as model systems in exploiting the richness of interactions between topologies and geometries of colloidal surfaces, nematic fields, and topological singularities induced by particles in the nematic bulk and at nematic-colloidal interfaces. Here we demonstrate formation of quarter-strength surface-pinned disclinations, as well as a large variety of director field configurations with splitting and reconnections of singular defect lines, prompted by colloidal particles with sharp edges and size large enough to define strong boundary conditions. Using examples of faceted ring-shaped particles of genus g=1, we explore transformation of defect lines as they migrate between locations in the bulk of the nematic host to edge-pinned locations at the surfaces of particles and vice versa, showing that this behavior is compliant with topological constraints defined by mathematical theorems. We discuss how transformation of bulk and surface defect lines induced by faceted colloids can enrich the diversity of elasticity-mediated colloidal interactions and how these findings may impinge on prospects of their controlled reconfigurable self-assembly in nematic hosts.
Collapse
Affiliation(s)
- Bohdan Senyuk
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Qingkun Liu
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Ye Yuan
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
- Soft Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA
- Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
13
|
Points, skyrmions and torons in chiral nematic droplets. Sci Rep 2016; 6:26361. [PMID: 27198649 PMCID: PMC4873801 DOI: 10.1038/srep26361] [Citation(s) in RCA: 58] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2016] [Accepted: 04/27/2016] [Indexed: 01/12/2023] Open
Abstract
Chiral nematic droplets with perpendicular surface alignment of liquid crystalline molecules frustrate the helical structure into convoluted 3D textures with complex topology. We observe the droplets with fluorescent confocal polarising microscopy (FCPM), and reconstruct and analyse for the first time the topology of the 3D director field using a novel method of director reconstruction from raw data. We always find an odd number of topological defects, which preserve the total topological charge of the droplet of +1 regardless of chirality. At higher chirality, we observe up to 5 point hedgehog defects, which are elastically stabilized with convoluted twisted structures, reminiscent of 2D skyrmions and toron-like structure, nested into a sphere.
Collapse
|
14
|
Ackerman PJ, Smalyukh II. Reversal of helicoidal twist handedness near point defects of confined chiral liquid crystals. Phys Rev E 2016; 93:052702. [PMID: 27300955 DOI: 10.1103/physreve.93.052702] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2016] [Indexed: 06/06/2023]
Abstract
Handedness of the director twist in cholesteric liquid crystals is commonly assumed to be the same throughout the medium, determined solely by the chirality of constituent molecules or chiral additives, albeit distortions of the ground-state helicoidal configuration often arise due to the effects of confinement and external fields. We directly probe the twist directionality of liquid crystal director structures through experimental three-dimensional imaging and numerical minimization of the elastic free energy and show that spatially localized regions of handedness opposite to that of the chiral liquid crystal ground state can arise in the proximity of twisted-soliton-bound topological point defects. In chiral nematic liquid crystal confined to a film that has a thickness less than the cholesteric pitch and perpendicular surface boundary conditions, twisted solitonic structures embedded in a uniform unwound far-field background with chirality-matched handedness locally relieve confinement-imposed frustration and tend to be accompanied by point defects and smaller geometry-required, energetically costly regions of opposite twist handedness. We also describe a spatially localized structure, dubbed a "twistion," in which a twisted solitonic three-dimensional director configuration is accompanied by four point defects. We discuss how our findings may impinge on the stability of localized particlelike director field configurations in chiral and nonchiral liquid crystals.
Collapse
Affiliation(s)
- Paul J Ackerman
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
- Soft Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA
- Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
15
|
Senyuk B, Pandey MB, Liu Q, Tasinkevych M, Smalyukh II. Colloidal spirals in nematic liquid crystals. SOFT MATTER 2015; 11:8758-8767. [PMID: 26358649 DOI: 10.1039/c5sm01539a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
One of the central experimental efforts in nematic colloids research aims to explore how the interplay between the geometry of particles along with the accompanying nematic director deformations and defects around them can provide a means of guiding particle self-assembly and controlling the structure of particle-induced defects. In this work, we design, fabricate, and disperse low-symmetry colloidal particles with shapes of spirals, double spirals, and triple spirals in a nematic fluid. These spiral-shaped particles, which are controlled by varying their surface functionalization to provide tangential or perpendicular boundary conditions of the nematic molecular alignment, are found inducing director distortions and defect configurations with non-chiral or chiral symmetry. Colloidal particles also exhibit both stable and metastable multiple orientational states in the nematic host, with a large number of director configurations featuring both singular and solitonic nonsingular topological defects accompanying them, which can result in unusual forms of colloidal self-assembly. Our findings directly demonstrate how the symmetry of particle-generated director configurations can be further lowered, or not, as compared to the low point group symmetry of solid micro-inclusions, depending on the nature of induced defects while satisfying topological constraints. We show that achiral colloidal particles can cause chiral symmetry breaking of elastic distortions, which is driven by complex three-dimensional winding of induced topological line defects and solitons.
Collapse
Affiliation(s)
- Bohdan Senyuk
- Department of Physics, University of Colorado, Boulder, CO 80309, USA.
| | - Manoj B Pandey
- Department of Physics, University of Colorado, Boulder, CO 80309, USA.
| | - Qingkun Liu
- Department of Physics, University of Colorado, Boulder, CO 80309, USA.
| | - Mykola Tasinkevych
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, CO 80309, USA. and Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 80309, USA
| |
Collapse
|
16
|
Redding B, Schwab M, Pan YL. Raman Spectroscopy of Optically Trapped Single Biological Micro-Particles. SENSORS 2015; 15:19021-46. [PMID: 26247952 PMCID: PMC4570358 DOI: 10.3390/s150819021] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/30/2015] [Revised: 06/30/2015] [Accepted: 07/27/2015] [Indexed: 12/20/2022]
Abstract
The combination of optical trapping with Raman spectroscopy provides a powerful method for the study, characterization, and identification of biological micro-particles. In essence, optical trapping helps to overcome the limitation imposed by the relative inefficiency of the Raman scattering process. This allows Raman spectroscopy to be applied to individual biological particles in air and in liquid, providing the potential for particle identification with high specificity, longitudinal studies of changes in particle composition, and characterization of the heterogeneity of individual particles in a population. In this review, we introduce the techniques used to integrate Raman spectroscopy with optical trapping in order to study individual biological particles in liquid and air. We then provide an overview of some of the most promising applications of this technique, highlighting the unique types of measurements enabled by the combination of Raman spectroscopy with optical trapping. Finally, we present a brief discussion of future research directions in the field.
Collapse
Affiliation(s)
- Brandon Redding
- U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783, USA.
| | - Mark Schwab
- U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783, USA.
| | - Yong-le Pan
- U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783, USA.
| |
Collapse
|
17
|
Orlova T, Aßhoff SJ, Yamaguchi T, Katsonis N, Brasselet E. Creation and manipulation of topological states in chiral nematic microspheres. Nat Commun 2015; 6:7603. [PMID: 26145716 PMCID: PMC4506501 DOI: 10.1038/ncomms8603] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2015] [Accepted: 05/25/2015] [Indexed: 12/26/2022] Open
Abstract
Topology is a universal concept that is encountered in daily life and is known to determine many static and dynamical properties of matter. Taming and controlling the topology of materials therefore constitutes a contemporary interdisciplinary challenge. Building on the controllable spatial properties of soft matter appears as a relevant strategy to address the challenge, in particular, because it may lead to paradigmatic model systems that allow checking theories experimentally. Here we report experimentally on a wealth of complex free-standing metastable topological architectures at the micron scale, in frustrated chiral nematic droplets. These results support recent works predicting the formation of free-standing knotted and linked disclination structures in confined chiral nematic fluids. We also demonstrate that various kinds of external fields (thermal, electrical and optical) can be used to achieve topological remote control. All this may foster the development of new devices based on topologically structured soft media.
Collapse
Affiliation(s)
- Tetiana Orlova
- Laboratoire Ondes et Matière d'Aquitaine, University of Bordeaux, CNRS, 351 cours de la Libération, Talence F-33400, France
| | - Sarah Jane Aßhoff
- Laboratory for Biomolecular Nanotechnology, MESA+ Institute for Nanotechnology, University of Twente, PO Box 207, Enschede 7500AE, The Netherlands
| | - Tadatsugu Yamaguchi
- Laboratory for Biomolecular Nanotechnology, MESA+ Institute for Nanotechnology, University of Twente, PO Box 207, Enschede 7500AE, The Netherlands
| | - Nathalie Katsonis
- Laboratory for Biomolecular Nanotechnology, MESA+ Institute for Nanotechnology, University of Twente, PO Box 207, Enschede 7500AE, The Netherlands
| | - Etienne Brasselet
- Laboratoire Ondes et Matière d'Aquitaine, University of Bordeaux, CNRS, 351 cours de la Libération, Talence F-33400, France
| |
Collapse
|
18
|
Senyuk B, Liu Q, Bililign E, Nystrom PD, Smalyukh II. Geometry-guided colloidal interactions and self-tiling of elastic dipoles formed by truncated pyramid particles in liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:040501. [PMID: 25974426 DOI: 10.1103/physreve.91.040501] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2015] [Indexed: 06/04/2023]
Abstract
The progress of realizing colloidal structures mimicking natural forms of organization in condensed matter is inherently limited by the availability of suitable colloidal building blocks. To enable new forms of crystalline and quasicrystalline self-organization of colloids, we develop truncated pyramidal particles that form nematic elastic dipoles with long-range electrostaticlike and geometry-guided low-symmetry short-range interactions. Using a combination of nonlinear optical imaging, laser tweezers, and video microscopy, we characterize colloidal pair interactions and demonstrate unusual forms of self-tiling of these particles into crystalline, quasicrystalline, and other arrays. Our findings are explained using an electrostatics analogy along with liquid crystal elasticity and symmetry breaking considerations, potentially expanding photonic and electro-optic applications of colloids.
Collapse
Affiliation(s)
- Bohdan Senyuk
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Qingkun Liu
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Ephraim Bililign
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Philip D Nystrom
- Department of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
- Department of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA
- Liquid Crystals Materials Research Center and Materials Science and Engineering Program, University of Colorado at Boulder, Boulder, Colorado 80309, USA
- Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado at Boulder, Boulder, Colorado 80309, USA
| |
Collapse
|
19
|
Abstract
Geometric shape and topology of constituent particles can alter many colloidal properties such as Brownian motion, self-assembly, and phase behavior. Thus far, only single-component building blocks of colloids with connected surfaces have been studied, although topological colloids, with constituent particles shaped as freestanding knots and handlebodies of different genus, have been recently introduced. Here we develop a topological class of colloids shaped as multicomponent links. Using two-photon photopolymerization, we fabricate colloidal microparticle analogs of the classic examples of links studied in the field of topology, the Hopf and Solomon links, which we disperse in nematic fluids that possess orientational ordering of anisotropic rod-like molecules. The surfaces of these particles are treated to impose tangential or perpendicular boundary conditions for the alignment of liquid crystal molecules, so that they generate a host of topologically nontrivial field and defect structures in the dispersing nematic medium, resulting in an elastic coupling between the linked constituents. The interplay between the topologies of surfaces of linked colloids and the molecular alignment field of the nematic host reveals that linking of particle rings with perpendicular boundary conditions is commonly accompanied by linking of closed singular defect loops, laying the foundations for fabricating complex composite materials with interlinking-based structural organization.
Collapse
|
20
|
Ackerman PJ, van de Lagemaat J, Smalyukh II. Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals. Nat Commun 2015; 6:6012. [PMID: 25607778 PMCID: PMC4354077 DOI: 10.1038/ncomms7012] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2014] [Accepted: 12/01/2014] [Indexed: 12/22/2022] Open
Abstract
Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains that exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields. Topological defects can be spontaneously generated to thermodynamically stabilize a variety of peculiar condensed matter phases for technological applications. Here, Ackerman et al. show electrically controllable self-assembly of knotted defects into periodic arrays in chiral liquid crystals.
Collapse
Affiliation(s)
- Paul J Ackerman
- 1] Department of Physics, University of Colorado, Boulder, Colorado 80309, USA [2] Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - Jao van de Lagemaat
- 1] Department of Physics, University of Colorado, Boulder, Colorado 80309, USA [2] National Renewable Energy Laboratory, Golden, Colorado 80401, USA [3] Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| | - Ivan I Smalyukh
- 1] Department of Physics, University of Colorado, Boulder, Colorado 80309, USA [2] Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA [3] Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA [4] Liquid Crystal Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
21
|
Pandey MB, Ackerman PJ, Burkart A, Porenta T, Žumer S, Smalyukh II. Topology and self-assembly of defect-colloidal superstructure in confined chiral nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012501. [PMID: 25679632 DOI: 10.1103/physreve.91.012501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2014] [Indexed: 06/04/2023]
Abstract
We describe formation of defect-colloidal superstructures induced by microspheres with normal surface anchoring dispersed in chiral nematic liquid crystals in confinement-unwound homeotropic cells. Using three-dimensional nonlinear optical imaging of the director field, we demonstrate that some of the induced defects have nonsingular solitonic nature while others are singular point and line topological defects. The common director structures induced by individual microspheres have dipolar symmetry. These topological dipoles are formed by the particle and a hyperbolic point defect (or small disclination loop) of elementary hedgehog charge opposite to that of a sphere with perpendicular boundary conditions, which in cells with thickness over equilibrium cholesteric pitch ratio approaching unity are additionally interspaced by a looped double-twist cylinder of continuous director deformations. The long-range elastic interactions are probed by holographic optical tweezers and videomicroscopy, providing insights to the physical underpinnings behind self-assembled colloidal structures entangled by twisted solitons. Computer-simulated field and defect configurations induced by the colloidal particles and their assemblies, which are obtained by numerically minimizing the Landau-de Gennes free energy, are in agreement with the experimental findings.
Collapse
Affiliation(s)
- M B Pandey
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - P J Ackerman
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - A Burkart
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - T Porenta
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - S Žumer
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia and J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA and Liquid Crystal Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA and Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
22
|
Porenta T, Copar S, Ackerman PJ, Pandey MB, Varney MCM, Smalyukh II, Žumer S. Topological switching and orbiting dynamics of colloidal spheres dressed with chiral nematic solitons. Sci Rep 2014; 4:7337. [PMID: 25477195 PMCID: PMC4256655 DOI: 10.1038/srep07337] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2014] [Accepted: 11/13/2014] [Indexed: 12/29/2022] Open
Abstract
Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that “dress” the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed.
Collapse
Affiliation(s)
- T Porenta
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - S Copar
- 1] Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia [2] J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia [3] Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA
| | - P J Ackerman
- 1] Department of Physics, University of Colorado, Boulder, CO 80309, USA [2] Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 80309, USA
| | - M B Pandey
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - M C M Varney
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - I I Smalyukh
- 1] Department of Physics, University of Colorado, Boulder, CO 80309, USA [2] Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 80309, USA [3] Liquid Crystal Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, CO 80309, USA [4] Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, CO 80309, USA
| | - S Žumer
- 1] Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia [2] J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
| |
Collapse
|
23
|
Tasinkevych M, Campbell MG, Smalyukh II. Splitting, linking, knotting, and solitonic escape of topological defects in nematic drops with handles. Proc Natl Acad Sci U S A 2014; 111:16268-73. [PMID: 25369931 PMCID: PMC4246280 DOI: 10.1073/pnas.1405928111] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Topologically nontrivial field excitations, including solitonic, linked, and knotted structures, play important roles in physical systems ranging from classical fluids and liquid crystals, to electromagnetism, classic, and quantum field theories. These excitations can appear spontaneously during symmetry-breaking phase transitions. For example, in cosmological theories, cosmic strings may have formed knotted configurations influencing the Early Universe development, whereas in liquid crystals transient tangled defect lines were observed during isotropic-nematic transitions, eventually relaxing to defect-free states. Knotted and solitonic fields and defects were also obtained using optical manipulation, complex-shaped colloids, and frustrated cholesterics. Here we use confinement of nematic liquid crystal by closed surfaces with varied genus and perpendicular boundary conditions for a robust control of appearance and stability of such field excitations. Theoretical modeling and experiments reveal structure of defect lines as a function of the surface topology and material and geometric parameters, establishing a robust means of controlling solitonic, knotted, linked, and other field excitations.
Collapse
Affiliation(s)
- Mykola Tasinkevych
- Max-Planck-Institut für Intelligente Systeme, D-70569 Stuttgart, Germany; Institut für Theoretische Physik IV, Universität Stuttgart, D-70569 Stuttgart, Germany;
| | - Michael G Campbell
- Department of Physics, University of Colorado, Boulder, CO 80309; Liquid Crystal Materials Research Center, University of Colorado, Boulder, CO 80309
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, CO 80309; Liquid Crystal Materials Research Center, University of Colorado, Boulder, CO 80309; Department of Electrical, Computer, and Energy Engineering and Materials Science and Engineering Program, University of Colorado, Boulder, CO 80309; and Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, CO 80309
| |
Collapse
|
24
|
Petit-Garrido N, Trivedi RP, Sagués F, Ignés-Mullol J, Smalyukh II. Topological defects in cholesteric liquid crystals induced by monolayer domains with orientational chirality. SOFT MATTER 2014; 10:8163-8170. [PMID: 25113825 DOI: 10.1039/c4sm00872c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Unless stabilized by colloids or confinement with well-defined boundary conditions, defects in liquid crystals remain elusive short-lived objects that tend to disappear with time to minimize the medium's free energy. In this work we use multimodal three-dimensional imaging to visualize cholesteric director structures to show that self-assembled chiral molecular monolayer domains can stabilize topologically constrained defect configurations when in contact with a cholesteric liquid crystal. The cholesteric liquid crystal, having features of both coarse-grained lamellar and nematic liquid crystal with chiral symmetry breaking, allows us to explore the interplay of chirality and implications of layering on the formed defects and director configurations.
Collapse
Affiliation(s)
- Núria Petit-Garrido
- Departament de Química Física and Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain.
| | | | | | | | | |
Collapse
|
25
|
Senyuk B, Varney MCM, Lopez JA, Wang S, Wu N, Smalyukh II. Magnetically responsive gourd-shaped colloidal particles in cholesteric liquid crystals. SOFT MATTER 2014; 10:6014-6023. [PMID: 24994521 DOI: 10.1039/c4sm00878b] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Particle shape and medium chirality are two key features recently used to control anisotropic colloidal self-assembly and dynamics in liquid crystals. Here, we study magnetically responsive gourd-shaped colloidal particles dispersed in cholesteric liquid crystals with periodicity comparable or smaller than the particle's dimensions. Using magnetic manipulation and optical tweezers, which allow one to position colloids near the confining walls, we measured the elastic repulsive interactions of these particles with confining surfaces and found that separation-dependent particle-wall interaction force is a non-monotonic function of separation and shows oscillatory behavior. We show that gourd-shaped particles in cholesterics reside not on a single sedimentation level, but on multiple long-lived metastable levels separated by a distance comparable to cholesteric periodicity. Finally, we demonstrate three-dimensional laser tweezers assisted assembly of gourd-shaped particles taking advantage of both orientational order and twist periodicity of cholesterics, potentially allowing new forms of orientationally and positionally ordered colloidal organization in these media.
Collapse
Affiliation(s)
- Bohdan Senyuk
- Department of Physics, University of Colorado, Boulder, CO 80309, USA.
| | | | | | | | | | | |
Collapse
|
26
|
Ackerman PJ, Trivedi RP, Senyuk B, van de Lagemaat J, Smalyukh II. Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012505. [PMID: 25122322 DOI: 10.1103/physreve.90.012505] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2014] [Indexed: 06/03/2023]
Abstract
We explore spatially localized solitonic configurations of a director field, generated using optical realignment and laser-induced heating, in frustrated chiral nematic liquid crystals confined between substrates with perpendicular surface anchoring. We demonstrate that, in addition to recently studied torons and Hopf-fibration solitonic structures (hopfions), one can generate a host of other axially symmetric stable and metastable director field configurations where local twist is matched to the surface boundary conditions through introduction of point defects and loops of singular and nonsingular disclinations. The experimentally demonstrated structures include the so-called "baby-skyrmions" in the form of double twist cylinders oriented perpendicular to the confining substrates where their double twist field configuration is matched to the perpendicular boundary conditions by loops of twist disclinations. We also generate complex textures with arbitrarily large skyrmion numbers. A simple back-of-the-envelope theoretical analysis based on free energy considerations and the nonpolar nature of chiral nematics provides insights into the long-term stability and diversity of these inter-related solitonic field configurations, including different types of torons, cholestric-finger loops, two-dimensional skyrmions, and more complex structures comprised of torons, hopfions, and various disclination loops that are experimentally observed in a confinement-frustrated chiral nematic system.
Collapse
Affiliation(s)
- Paul J Ackerman
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - Rahul P Trivedi
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - Bohdan Senyuk
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Jao van de Lagemaat
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and National Renewable Energy Laboratory, Golden, Colorado 80401, USA and Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA and Liquid Crystal Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA and Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
27
|
Silvestre NM, Liu Q, Senyuk B, Smalyukh II, Tasinkevych M. Towards template-assisted assembly of nematic colloids. PHYSICAL REVIEW LETTERS 2014; 112:225501. [PMID: 24949776 DOI: 10.1103/physrevlett.112.225501] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2014] [Indexed: 06/03/2023]
Abstract
Colloidal crystals belong to a new class of materials with unusual properties in which the big challenge is to grow large-scale structures of a given symmetry in a well-controlled and inexpensive way. Recently, template-assisted crystallization was successfully exploited experimentally in the case of colloidal particles dispersed in isotropic fluids. In liquid crystal (LC) colloids, particles are subjected to long-range anisotropic elastic forces originating from the anisotropic deformation of the underlying order parameter. These effective interactions are easily tunable by external electric or magnetic fields, light, temperature, or confinement and, thus, provide additional handles for better control of colloidal assembly. Here we use the coupling between microsculptured bounding surfaces and LC elasticity in order to guide the self-assembly of large-scale colloidal structures. We present explicit numerical calculations of the free energy landscape of colloidal particles in the presence of convex protrusions modeled as squared pyramids comparable to the size of the particles. We show the existence of strong trapping potentials that are able to efficiently localize the colloidal particles and withstand thermal fluctuations. Three-dimensional optical imaging experiments support the theoretical predictions.
Collapse
Affiliation(s)
- Nuno M Silvestre
- Departamento de Física da Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa, Portugal and Centro de Física Teórica e Computacional, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa, Portugal
| | - Qingkun Liu
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Bohdan Senyuk
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer, and Energy Engineering and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA and Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| | - Mykola Tasinkevych
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstrasse 3, D-70569 Stuttgart, Germany and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| |
Collapse
|
28
|
Pandey MB, Porenta T, Brewer J, Burkart A, Copar S, Zumer S, Smalyukh II. Self-assembly of skyrmion-dressed chiral nematic colloids with tangential anchoring. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:060502. [PMID: 25019708 DOI: 10.1103/physreve.89.060502] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2014] [Indexed: 06/03/2023]
Abstract
We describe dipolar nematic colloids comprising mutually bound solid microspheres, three-dimensional skyrmions, and point defects in a molecular alignment field of chiral nematic liquid crystals. Nonlinear optical imaging and numerical modeling based on minimization of Landau-de Gennes free energy reveal that the particle-induced skyrmions resemble torons and hopfions, while matching surface boundary conditions at the interfaces of liquid crystal and colloidal spheres. Laser tweezers and videomicroscopy reveal that the skyrmion-colloidal hybrids exhibit purely repulsive elastic pair interactions in the case of parallel dipoles and an unexpected reversal of interaction forces from repulsive to attractive as the center-to-center distance decreases for antiparallel dipoles. The ensuing elastic self-assembly gives rise to colloidal chains of antiparallel dipoles with particles entangled by skyrmions.
Collapse
Affiliation(s)
- M B Pandey
- Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA and Department of Physics, VSSD College, Kanpur 208 002, India
| | - T Porenta
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - J Brewer
- Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA
| | - A Burkart
- Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA
| | - S Copar
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia and Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
| | - S Zumer
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia and Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
| | - Ivan I Smalyukh
- Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer, and Energy Engineering and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA and Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
29
|
Campbell MG, Tasinkevych M, Smalyukh II. Topological polymer dispersed liquid crystals with bulk nematic defect lines pinned to handlebody surfaces. PHYSICAL REVIEW LETTERS 2014; 112:197801. [PMID: 24877965 DOI: 10.1103/physrevlett.112.197801] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2013] [Indexed: 06/03/2023]
Abstract
Polymer dispersed liquid crystals are a useful model system for studying the relationship between surface topology and defect structures. They are comprised of a polymer matrix with suspended spherical nematic drops and are topologically constrained to host defects of an elementary hedgehog charge per droplet, such as bulk or surface point defects or closed disclination loops. We control the genus of the closed surfaces confining such micrometer-sized nematic drops with tangential boundary conditions for molecular alignment imposed by the polymer matrix, allowing us to avoid defects or, on the contrary, to generate them in a controlled way. We show, both experimentally and through numerical modeling, that topological constraints in nematic microdrops can be satisfied by hosting topologically stable half-integer bulk defect lines anchored to opposite sides of handlebody surfaces. This enriches the interplay of topologies of closed surfaces and fields with nonpolar symmetry, yielding new unexpected configurations that cannot be realized in vector fields, having potential implications for topologically similar defects in cosmology and other fields.
Collapse
Affiliation(s)
- Michael G Campbell
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA
| | - Mykola Tasinkevych
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer, and Energy Engineering and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA and Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
30
|
Martinez A, Ravnik M, Lucero B, Visvanathan R, Zumer S, Smalyukh II. Mutually tangled colloidal knots and induced defect loops in nematic fields. NATURE MATERIALS 2014; 13:258-263. [PMID: 24390381 DOI: 10.1038/nmat3840] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2013] [Accepted: 11/18/2013] [Indexed: 06/03/2023]
Abstract
Colloidal dispersions in liquid crystals can serve as a soft-matter toolkit for the self-assembly of composite materials with pre-engineered properties and structures that are highly dependent on particle-induced topological defects. Here, we demonstrate that bulk and surface defects in nematic fluids can be patterned by tuning the topology of colloidal particles dispersed in them. In particular, by taking advantage of two-photon photopolymerization techniques to make knot-shaped microparticles, we show that the interplay of the topologies of the knotted particles, the nematic field and the induced defects leads to knotted, linked and other topologically non-trivial field configurations. These structures match theoretical predictions made on the basis of the minimization of the elastic free energy and satisfy topological constraints. Our approach may find uses in self-assembled topological superstructures of knotted particles linked by nematic fields, in topological scaffolds supporting the decoration of defect networks with nanoparticles, and in modelling other physical systems exhibiting topologically analogous phenomena.
Collapse
Affiliation(s)
- Angel Martinez
- 1] Department of Physics, University of Colorado, Boulder, Colorado 80309, USA [2] Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA
| | - Miha Ravnik
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia
| | - Brice Lucero
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | | | - Slobodan Zumer
- 1] Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia [2] Jozef Stefan Institute, Jamova 39, Ljubljana 1000, Slovenia
| | - Ivan I Smalyukh
- 1] Department of Physics, University of Colorado, Boulder, Colorado 80309, USA [2] Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA [3] Department of Electrical, Computer, and Energy Engineering and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA [4] Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
31
|
Varney MCM, Jenness NJ, Smalyukh II. Geometrically unrestricted, topologically constrained control of liquid crystal defects using simultaneous holonomic magnetic and holographic optical manipulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022505. [PMID: 25353487 DOI: 10.1103/physreve.89.022505] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2013] [Indexed: 06/04/2023]
Abstract
Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as "handles" to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.
Collapse
Affiliation(s)
- Michael C M Varney
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Nathan J Jenness
- Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627, USA
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309, USA and Department of Electrical, Computer, and Energy Engineering, Materials Science and Engineering Program, Liquid Crystals Materials Research Center, University of Colorado at Boulder, Boulder, Colorado 80309, USA and Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado at Boulder, Boulder, Colorado 80309, USA
| |
Collapse
|
32
|
Chen BGG, Ackerman PJ, Alexander GP, Kamien RD, Smalyukh II. Generating the Hopf fibration experimentally in nematic liquid crystals. PHYSICAL REVIEW LETTERS 2013; 110:237801. [PMID: 25167530 DOI: 10.1103/physrevlett.110.237801] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2012] [Indexed: 06/03/2023]
Abstract
The Hopf fibration is an example of a texture: a topologically stable, smooth, global configuration of a field. Here we demonstrate the controlled sculpting of the Hopf fibration in nematic liquid crystals through the control of point defects. We demonstrate how these are related to torons by use of a topological visualization technique derived from the Pontryagin-Thom construction.
Collapse
Affiliation(s)
- Bryan Gin-ge Chen
- Instituut-Lorentz, Universiteit Leiden, Postbus 9506, 2300 RA Leiden, Netherlands and Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Paul J Ackerman
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Gareth P Alexander
- Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Randall D Kamien
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
33
|
Lee T, Mundoor H, Gann DG, Callahan TJ, Smalyukh II. Imaging of director fields in liquid crystals using stimulated Raman scattering microscopy. OPTICS EXPRESS 2013; 21:12129-12134. [PMID: 23736433 DOI: 10.1364/oe.21.012129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We demonstrate an approach for background-free three-dimensional imaging of director fields in liquid crystals using stimulated Raman scattering microscopy. This imaging technique is implemented using a single femtosecond pulsed laser and a photonic crystal fiber, providing Stokes and pump frequencies needed to access Raman shifts of different chemical bonds of molecules and allowing for chemically selective and broadband imaging of both pristine liquid crystals and composite materials. Using examples of model three-dimensional structures of director fields, we show that the described technique is a powerful tool for mapping of long-range molecular orientation patterns in soft matter via polarized chemical-selective imaging.
Collapse
Affiliation(s)
- Taewoo Lee
- Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA
| | | | | | | | | |
Collapse
|
34
|
Abstract
Topological defects that form on surfaces of ordered media, dubbed boojums, are ubiquitous in superfluids, liquid crystals (LCs), Langmuir monolayers, and Bose-Einstein condensates. They determine supercurrents in superfluids, impinge on electrooptical switching in polymer-dispersed LCs, and mediate chemical response at nematic-isotropic fluid interfaces, but the role of surface topology in the appearance, stability, and core structure of these defects remains poorly understood. Here, we demonstrate robust generation of boojums by controlling surface topology of colloidal particles that impose tangential boundary conditions for the alignment of LC molecules. To do this, we design handlebody-shaped polymer particles with different genus g. When introduced into a nematic LC, these particles distort the nematic molecular alignment field while obeying topological constraints and induce at least 2g - 2 boojums that allow for topological charge conservation. We characterize 3D textures of boojums using polarized nonlinear optical imaging of molecular alignment and explain our findings by invoking symmetry considerations and numerical modeling of experiment-matching director fields, order parameter variations, and nontrivial handle-shaped core structure of defects. Finally, we discuss how this interplay between the topologies of colloidal surfaces and boojums may lead to controlled self-assembly of colloidal particles in nematic and paranematic hosts, which, in turn, may enable reconfigurable topological composites.
Collapse
|
35
|
Evans JS, Sun Y, Senyuk B, Keller P, Pergamenshchik VM, Lee T, Smalyukh II. Active shape-morphing elastomeric colloids in short-pitch cholesteric liquid crystals. PHYSICAL REVIEW LETTERS 2013; 110:187802. [PMID: 23683245 DOI: 10.1103/physrevlett.110.187802] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2012] [Indexed: 06/02/2023]
Abstract
Active elastomeric liquid crystal particles with initial cylindrical shapes are obtained by means of soft lithography and polymerization in a strong magnetic field. Gold nanocrystals infiltrated into these particles mediate energy transfer from laser light to heat, so that the inherent coupling between the temperature-dependent order and shape allows for dynamic morphing of these particles and well-controlled stable shapes. Continuous changes of particle shapes are followed by their spontaneous realignment and transformations of director structures in the surrounding cholesteric host, as well as locomotion in the case of a nonreciprocal shape morphing. These findings bridge the fields of liquid crystal solids and active colloids, may enable shape-controlled self-assembly of adaptive composites and light-driven micromachines, and can be understood by employing simple symmetry considerations along with electrostatic analogies.
Collapse
Affiliation(s)
- Julian S Evans
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | | | | | | | | | | | | |
Collapse
|
36
|
Senyuk B, Behabtu N, Pacheco BG, Lee T, Ceriotti G, Tour JM, Pasquali M, Smalyukh II. Nonlinear photoluminescence imaging of isotropic and liquid crystalline dispersions of graphene oxide. ACS NANO 2012; 6:8060-6. [PMID: 22881340 DOI: 10.1021/nn302644r] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
We report a visible-range nonlinear photoluminescence (PL) from graphene oxide (GO) flakes excited by near-infrared femtosecond laser light. PL intensity has nonlinear dependence on the laser power, implying a multiphoton excitation process, and also strongly depends on a linear polarization orientation of excitation light, being at maximum when it is parallel to flakes. We show that PL can be used for a fully three-dimensional label-free imaging of isotropic, nematic, and lamellar liquid crystalline dispersions of GO flakes in water. This nonlinear PL is of interest for applications in direct label-free imaging of composite materials and study of orientational ordering in mesomorphic phases formed by these flakes, as well as in biomedical and sensing applications utilizing GO.
Collapse
Affiliation(s)
- Bohdan Senyuk
- Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, United States
| | | | | | | | | | | | | | | |
Collapse
|
37
|
Liu Q, Senyuk B, Tang J, Lee T, Qian J, He S, Smalyukh II. Plasmonic complex fluids of nematiclike and helicoidal self-assemblies of gold nanorods with a negative order parameter. PHYSICAL REVIEW LETTERS 2012; 109:088301. [PMID: 23002777 DOI: 10.1103/physrevlett.109.088301] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2012] [Indexed: 05/23/2023]
Abstract
We describe a soft matter system of self-organized oblate micelles and plasmonic gold nanorods that exhibit a negative orientational order parameter. Because of anisotropic surface anchoring interactions, colloidal gold nanorods tend to align perpendicular to the director describing the average orientation of normals to the discoidal micelles. Helicoidal structures of highly concentrated nanorods with a negative order parameter are realized by adding a chiral additive and are further controlled by means of confinement and mechanical stress. Polarization-sensitive absorption, scattering, and two-photon luminescence are used to characterize orientations and spatial distributions of nanorods. Self-alignment and effective-medium optical properties of these hybrid inorganic-organic complex fluids match predictions of a simple model based on anisotropic surface anchoring interactions of nanorods with the structured host medium.
Collapse
Affiliation(s)
- Qingkun Liu
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | | | | | | | | | | | | |
Collapse
|
38
|
Lopez-Leon T, Fernandez-Nieves A, Nobili M, Blanc C. Smectic shells. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:284122. [PMID: 22738871 DOI: 10.1088/0953-8984/24/28/284122] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Confining a smectic liquid crystal between two spherical surfaces results in the formation of a complex defect structure characterized by a set of curvature walls that divide the sphere into crescent domains, causing the undulation of the smectic layers. In this paper, we examine in detail these smectic textures and discuss the various possible origins of the observed patterns.
Collapse
Affiliation(s)
- Teresa Lopez-Leon
- Université Montpellier 2, Laboratoire Charles Coulomb UMR5221, F-34095, Montpellier, France
| | | | | | | |
Collapse
|
39
|
Kim Y, Jeong J, Jang J, Kim MW, Park Y. Polarization holographic microscopy for extracting spatio-temporally resolved Jones matrix. OPTICS EXPRESS 2012; 20:9948-55. [PMID: 22535087 DOI: 10.1364/oe.20.009948] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
We present a high-speed holographic microscopic technique for quantitative measurement of polarization light-field, referred to as polarization holographic microscopy (PHM). Employing the principle of common-path interferometry, PHM quantitatively measures the spatially resolved Jones matrix components of anisotropic samples with only two consecutive measurements of spatially modulated holograms. We demonstrate the features of PHM with imaging the dynamics of liquid crystal droplets at a video-rate.
Collapse
Affiliation(s)
- Youngchan Kim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea
| | | | | | | | | |
Collapse
|
40
|
Smalyukh II, Kaputa D, Kachynski AV, Kuzmin AN, Ackerman PJ, Twombly CW, Lee T, Trivedi RP, Prasad PN. Optically generated reconfigurable photonic structures of elastic quasiparticles in frustrated cholesteric liquid crystals. OPTICS EXPRESS 2012; 20:6870-6880. [PMID: 22453364 DOI: 10.1364/oe.20.006870] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We describe laser-induced two-dimensional periodic photonic structures formed by localized particle-like excitations in an untwisted confined cholesteric liquid crystal. The individual particle-like excitations (dubbed "Torons") contain three-dimensional twist of the liquid crystal director matched to the uniform background director field by topological point defects. Using both single-beam-steering and holographic pattern generation approaches, the periodic crystal lattices are tailored by tuning their periodicity, reorienting their crystallographic axes, and introducing defects. Moreover, these lattices can be dynamically reconfigurable: generated, modified, erased and then recreated, depending on the needs of a particular photonic application. This robust control is performed by tightly focused laser beams of power 10-100 mW and by low-frequency electric fields at voltages ~10 V applied to the transparent electrodes.
Collapse
Affiliation(s)
- Ivan I Smalyukh
- Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA.
| | | | | | | | | | | | | | | | | |
Collapse
|
41
|
Reconfigurable interactions and three-dimensional patterning of colloidal particles and defects in lamellar soft media. Proc Natl Acad Sci U S A 2012; 109:4744-9. [PMID: 22411822 DOI: 10.1073/pnas.1119118109] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Colloidal systems find important applications ranging from fabrication of photonic crystals to direct probing of phenomena typically encountered in atomic crystals and glasses. New applications--such as nanoantennas, plasmonic sensors, and nanocircuits--pose a challenge of achieving sparse colloidal assemblies with tunable interparticle separations that can be controlled at will. We demonstrate reconfigurable multiscale interactions and assembly of colloids mediated by defects in cholesteric liquid crystals that are probed by means of laser manipulation and three-dimensional imaging. We find that colloids attract via distance-independent elastic interactions when pinned to the ends of cholesteric oily streaks, line defects at which one or more layers are interrupted. However, dislocations and oily streaks can also be optically manipulated to induce kinks, allowing one to lock them into the desired configurations that are stabilized by elastic energy barriers for structural transformation of the particle-connecting defects. Under the influence of elastic energy landscape due to these defects, sublamellar-sized colloids self-assemble into structures mimicking the cores of dislocations and oily streaks. Interactions between these defect-embedded colloids can be varied from attractive to repulsive by optically introducing dislocation kinks. The reconfigurable nature of defect-particle interactions allows for patterning of defects by manipulation of colloids and, in turn, patterning of particles by these defects, thus achieving desired colloidal configurations on scales ranging from the size of defect core to the sample size. This defect-colloidal sculpturing may be extended to other lamellar media, providing the means for optically guided self-assembly of mesoscopic composites with predesigned properties.
Collapse
|
42
|
Liu Q, Asavei T, Lee T, Rubinsztein-Dunlop H, He S, Smalyukh II. Measurement of viscosity of lyotropic liquid crystals by means of rotating laser-trapped microparticles. OPTICS EXPRESS 2011; 19:25134-25143. [PMID: 22273904 DOI: 10.1364/oe.19.025134] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We describe a simple microrheology method to measure the viscosity coefficients of lyotropic liquid crystals. This approach is based on the use of a rotating laser-trapped optically anisotropic microsphere. In aligned liquid crystals that have negligible effect on trapping beam's polarization, the optical torque is transferred from circularly polarized laser trapping beam to the optically anisotropic microparticle and creates the shear flow in the liquid crystalline fluid. The balance of optical and viscous torques yields the local effective viscosity coefficients of the studied lyotropic systems in cholesteric and lamellar phases. This simple yet powerful method is capable of probing viscosity of complex anisotropic fluids for small amounts of sample and even in the presence of defects that obstruct the use of conventional rheology techniques.
Collapse
Affiliation(s)
- Qingkun Liu
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | | | | | | | | | | |
Collapse
|
43
|
Petit-Garrido N, Trivedi RP, Ignés-Mullol J, Claret J, Lapointe C, Sagués F, Smalyukh II. Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers. PHYSICAL REVIEW LETTERS 2011; 107:177801. [PMID: 22107584 DOI: 10.1103/physrevlett.107.177801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2011] [Indexed: 05/31/2023]
Abstract
We use Langmuir-Blodgett molecular monolayers and nematic liquid crystals as model two- and three-dimensional orientationally ordered systems to study the stability and healing of topological defects at their contact interfaces. Integer-strength defects at the monolayer induce disclinations of similar strength in the nematic that, however, do not propagate deep into the bulk, but rather form single- or double-split arch-shaped loops pinned to the interface. This behavior is qualitatively independent of the far-field director orientation and involves either half-integer singular or twist-escaped unity-strength nonsingular nematic disclinations. These two defect configurations can be selected by varying sample preparation given their comparable free energy, consistently with direct probing by use of laser tweezers.
Collapse
Affiliation(s)
- Núria Petit-Garrido
- SOC&SAM group, IN2UB, and Departament de Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain
| | | | | | | | | | | | | |
Collapse
|
44
|
Portable magnetic tweezers device enables visualization of the three-dimensional microscale deformation of soft biological materials. Biotechniques 2011; 51:29-34. [DOI: 10.2144/000113701] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2011] [Accepted: 05/16/2011] [Indexed: 11/23/2022] Open
Abstract
We have designed and built a magnetic tweezers device that enables the application of calibrated stresses to soft materials while simultaneously measuring their microscale deformation using confocal microscopy. Unlike previous magnetic tweezers designs, our device is entirely portable, allowing easy use on microscopes in core imaging facilities or in collaborators' laboratories. The imaging capabilities of the microscope are unimpaired, enabling the 3-D structures of fluorescently labeled materials to be precisely determined under applied load. With this device, we can apply a large range of forces (∼1–1200 pN) over micron-scale contact areas to beads that are either embedded within 3-D matrices or attached to the surface of thin slab gels. To demonstrate the usefulness of this instrument, we have studied two important and biologically relevant materials: polyacrylamide-based hydrogel films typical of those used in cell traction force microscopy, and reconstituted networks of microtubules, essential cytoskeletal filaments.
Collapse
|
45
|
Liu Q, Beier C, Evans J, Lee T, He S, Smalyukh II. Self-alignment of dye molecules in micelles and lamellae for three-dimensional imaging of lyotropic liquid crystals. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2011; 27:7446-7452. [PMID: 21598933 DOI: 10.1021/la200842z] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We report alignment of anisotropic amphiphilic dye molecules within oblate and prolate anisotropic micelles and lamellae, the basic building blocks of surfactant-based lyotropic liquid crystals. Absorption and fluorescence transition dipole moments of these dye molecules orient either parallel or orthogonal to the liquid crystal director. This alignment enables three-dimensional visualization of director structures and defects in different lyotropic mesophases by means of fluorescence confocal polarizing microscopy and two-photon excitation fluorescence polarizing microscopy. The studied structures include nematic tactoids, Schlieren texture with disclinations in the calamitic nematic phase, oily streaks in the lamellar phase, developable domains in the columnar hexagonal phase, and various types of line defects in the discotic cholesteric phase. Orientational three-dimensional imaging of structures in the lyotropic cholesterics reveals large Burgers vector dislocations in cholesteric layering with singular disclinations in the dislocation cores that are not common for their thermotropic counterparts.
Collapse
Affiliation(s)
- Qingkun Liu
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | | | | | | | | | | |
Collapse
|
46
|
Choudhury TD, Rao NVS, Tenent R, Blackburn J, Gregg B, Smalyukh II. Homeotropic Alignment and Director Structures in Thin Films of Triphenylamine-Based Discotic Liquid Crystals Controlled by Supporting Nanostructured Substrates and Surface Confinement. J Phys Chem B 2011; 115:609-17. [DOI: 10.1021/jp106344f] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Trirup Dutta Choudhury
- Department of Chemistry, Assam University, Silchar-788011, Assam, India; Department of Physics, University of Colorado, Boulder, Colorado 80309, United States; National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado 80401, United States; Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado, 80309, United States; and Renewable and Sustainable Energy Institute, University of Colorado, Boulder, Colorado 80309, United States
| | - Nandiraju V. S. Rao
- Department of Chemistry, Assam University, Silchar-788011, Assam, India; Department of Physics, University of Colorado, Boulder, Colorado 80309, United States; National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado 80401, United States; Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado, 80309, United States; and Renewable and Sustainable Energy Institute, University of Colorado, Boulder, Colorado 80309, United States
| | - Robert Tenent
- Department of Chemistry, Assam University, Silchar-788011, Assam, India; Department of Physics, University of Colorado, Boulder, Colorado 80309, United States; National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado 80401, United States; Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado, 80309, United States; and Renewable and Sustainable Energy Institute, University of Colorado, Boulder, Colorado 80309, United States
| | - Jeffrey Blackburn
- Department of Chemistry, Assam University, Silchar-788011, Assam, India; Department of Physics, University of Colorado, Boulder, Colorado 80309, United States; National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado 80401, United States; Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado, 80309, United States; and Renewable and Sustainable Energy Institute, University of Colorado, Boulder, Colorado 80309, United States
| | - Brian Gregg
- Department of Chemistry, Assam University, Silchar-788011, Assam, India; Department of Physics, University of Colorado, Boulder, Colorado 80309, United States; National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado 80401, United States; Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado, 80309, United States; and Renewable and Sustainable Energy Institute, University of Colorado, Boulder, Colorado 80309, United States
| | - Ivan I. Smalyukh
- Department of Chemistry, Assam University, Silchar-788011, Assam, India; Department of Physics, University of Colorado, Boulder, Colorado 80309, United States; National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado 80401, United States; Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado, 80309, United States; and Renewable and Sustainable Energy Institute, University of Colorado, Boulder, Colorado 80309, United States
| |
Collapse
|