1
|
Palacio-Betancur V, Armas-Pérez JC, Hernández-Ortiz JP, de Pablo JJ. Curvature and confinement effects on chiral liquid crystal morphologies. SOFT MATTER 2023; 19:6066-6073. [PMID: 37318304 DOI: 10.1039/d3sm00437f] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Chiral liquid crystals (ChLCs) exhibit an inherent twist that originates at the molecular scale and can extend over multiple length scales when unconstrained. Under confinement, the twist is thwarted, leading to formation of defects in the molecular order that offer distinct optical responses and opportunities for colloidal driven assembly. Past studies have explored spheroidal confinement down to the nanoscopic regime, where curved boundaries produce surface defects to accommodate topological constraints and restrict the propagation of cuboidal defect networks. Similarly, strict confinement in channels and shells has been shown to give rise to escaped configurations and skyrmions. However, little is known about the role of extrinsic curvature in the development of cholesteric textures and Blue Phases (BP). In this paper, we examine the palette of morphologies that arises when ChLCs are confined in toroidal and cylindrical cavities. The equilibrium morphologies are obtained following an annealing strategy of a Landau-de Gennes free energy functional. Three dimensionless groups are identified to build phase diagrams: the natural twist, the ratio of elastic energies, and the circumscription of a BP cell. Curvature is shown to introduce helical features that are first observed as a Double Twist, and progress to Chiral Ribbons and, ultimately, Helical BP and BP. Chiral ribbons are examined as useful candidates for driven assembly given their tunability and robustness.
Collapse
Affiliation(s)
| | - Julio C Armas-Pérez
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, León (Gto.) 37150, Mexico
| | - Juan P Hernández-Ortiz
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA.
- Departamento de Materiales y Minerales, Universidad Nacional de Colombia-Sede Medellín, Medellín, Colombia.
- Colombia/Wisconsin One-Health Consortium, Universidad Nacional de Colombia Sede Medellín, Medellín, Colombia
| | - Juan J de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA.
- Materials Science Division, Argonne National Laboratory, Lemont, IL 60439, USA
| |
Collapse
|
2
|
Abstract
Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials - they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.
Collapse
|
3
|
Recent Progresses on Experimental Investigations of Topological and Dissipative Solitons in Liquid Crystals. CRYSTALS 2022. [DOI: 10.3390/cryst12010094] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Solitons in liquid crystals have received increasing attention due to their importance in fundamental physical science and potential applications in various fields. The study of solitons in liquid crystals has been carried out for over five decades with various kinds of solitons being reported. Recently, a number of new types of solitons have been observed, among which, many of them exhibit intriguing dynamic behaviors. In this paper, we briefly review the recent progresses on experimental investigations of solitons in liquid crystals.
Collapse
|
4
|
Eun J, Pollard J, Kim SJ, Machon T, Jeong J. Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement. Proc Natl Acad Sci U S A 2021; 118:e2102926118. [PMID: 34373332 PMCID: PMC8379955 DOI: 10.1073/pnas.2102926118] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Our study of cholesteric lyotropic chromonic liquid crystals in cylindrical confinement reveals the topological aspects of cholesteric liquid crystals. The double-twist configurations we observe exhibit discontinuous layering transitions, domain formation, metastability, and chiral point defects as the concentration of chiral dopant is varied. We demonstrate that these distinct layer states can be distinguished by chiral topological invariants. We show that changes in the layer structure give rise to a chiral soliton similar to a toron, comprising a metastable pair of chiral point defects. Through the applicability of the invariants we describe to general systems, our work has broad relevance to the study of chiral materials.
Collapse
Affiliation(s)
- Jonghee Eun
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Joseph Pollard
- Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - Sung-Jo Kim
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, Republic of Korea
| | - Thomas Machon
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Joonwoo Jeong
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea;
| |
Collapse
|
5
|
Electrically turning periodic structures in cholesteric layer with conical-planar boundary conditions. Sci Rep 2021; 11:8409. [PMID: 33863990 PMCID: PMC8052423 DOI: 10.1038/s41598-021-87854-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Accepted: 04/05/2021] [Indexed: 11/22/2022] Open
Abstract
Electro-optical cell based on the cholesteric liquid crystal is studied with unique combination of the boundary conditions: conical anchoring on the one substrate and planar anchoring on another one. Periodic structures in cholesteric layer and their transformation under applied electric field are considered by polarizing optical microscopy, the experimental findings are supported by the data of the calculations performed using the extended Frank elastic continuum approach. Such structures are the set of alternating over- and under-twisted defect lines whose azimuthal director angles differ by \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$180^\circ$$\end{document}180∘. The \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$U^+$$\end{document}U+ and \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$U^-$$\end{document}U--defects of periodicity, which are the smooth transition between the defect lines, are observed at the edge of electrode area. The growth direction of defect lines forming a diffraction grating can be controlled by applying a voltage in the range of \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$0\le \, V \le 1.3$$\end{document}0≤V≤1.3 V during the process. Resulting orientation and distance between the lines don’t change under voltage. However, at \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$V>1.3$$\end{document}V>1.3 V \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$U^+$$\end{document}U+-defects move along the defect lines away from the electrode edges, and, finally, the grating lines collapse at the cell’s center. These results open a way for the use of such cholesteric material in applications with periodic defect structures where a periodicity, orientation, and configuration of defects should be adjusted.
Collapse
|
6
|
Duzgun A, Nisoli C. Skyrmion Spin Ice in Liquid Crystals. PHYSICAL REVIEW LETTERS 2021; 126:047801. [PMID: 33576672 DOI: 10.1103/physrevlett.126.047801] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Revised: 10/17/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
We propose the first skyrmion spin ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic liquid crystal behave as quasiparticles that can be dynamically confined, bound, and created or annihilated individually with ease and precision. We show that these quasiparticles can be employed to realize binary variables that interact to form ice-rule states. Because of their unique versatility, liquid crystal skyrmions can open entirely novel avenues in the field of frustrated systems. More broadly, our findings also demonstrate the viability of liquid crystal skyrmions as elementary degrees of freedom in the design of collective complex behaviors.
Collapse
Affiliation(s)
- Ayhan Duzgun
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
7
|
Shvetsov SA, Rudyak VY, Gruzdenko AA, Emelyanenko AV. Axisymmetric skyrmion-like structures in spherical-cap droplets of chiral nematic liquid crystal. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.114149] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
8
|
Role of Stimuli on Liquid Crystalline Defects: From Defect Engineering to Switchable Functional Materials. MATERIALS 2020; 13:ma13235466. [PMID: 33266312 PMCID: PMC7729749 DOI: 10.3390/ma13235466] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Revised: 11/27/2020] [Accepted: 11/27/2020] [Indexed: 11/17/2022]
Abstract
Achieving tunable physical properties is currently one of the most exciting research topics. In order to realize this goal, a medium that is responsive to external stimuli and can undergo a change in its physical property is required. Liquid crystal (LC) is a prominent candidate, as its physical and optical properties can be easily manipulated with various stimuli, such as surface anchoring, rubbing, geometric confinement, and external fields. Having broken away from the past devotion to obtaining a uniform domain of LCs, people are now putting significant efforts toward forming and manipulating ordered and oriented defect structures with a unique arrangement within. The complicated molecular order with tunability would benefit the interdisciplinary research fields of optics, physics, photonics, and materials science. In this review, the recent progress toward defect engineering in the nematic and smectic phases by controlling the surface environment and electric field and their combinational methods is introduced. We close the review with a discussion of the possible applications enabled using LC defect structures as switchable materials.
Collapse
|
9
|
Hare SM, Lunsford-Poe B, Kim M, Serra F. Chiral Liquid Crystal Lenses Confined in Microchannels. MATERIALS 2020; 13:ma13173761. [PMID: 32858819 PMCID: PMC7503803 DOI: 10.3390/ma13173761] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/26/2020] [Revised: 08/17/2020] [Accepted: 08/19/2020] [Indexed: 11/16/2022]
Abstract
It is known that the liquid crystalline smectic-A phase has geometric defects, called focal conic domains, which can be used as gradient-index microlenses. Cholesteric (chiral nematic) phases also have topological defects with a central symmetry and a singularity at their center. We explore a weakly chiral system in which both types of defects can be present in the same material at different temperatures, and with this strategy we create lenses whose focal length is tunable with temperature. We measure the focal length of the tunable lenses, and we investigate the behavior of the defects near the phase transition. We identify the experimental conditions that make the simultaneous presence of the smectic focal conic domains and the circular cholesteric domains possible, such as the concentration of chiral dopant and the rate of heating and cooling. The transformation of focal conic domains into circular cholesteric domains is a new example of memory at the phase transition between smectic-A and nematic liquid crystals.
Collapse
|
10
|
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: 13] [Impact Index Per Article: 3.3] [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
|
11
|
Thermo-Optical Generation of Particle-Like Structures in Frustrated Chiral Nematic Film. CRYSTALS 2019. [DOI: 10.3390/cryst9110574] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
The creation of metastable particle-like structures in frustrated (unwound) chiral nematic film containing light-absorbing additive is studied. It is shown that such localized structures can be generated by the thermo-optical action of a focused laser beam or arise spontaneously at a phase transition from an isotropic to a liquid crystal state. Observed axisymmetric patterns resemble cholesteric spherulites with toroidal double-twisted director-field configuration.
Collapse
|
12
|
Shin MJ, Gim MJ, Yoon DK. Directed Self-Assembly of Topological Defects of Liquid Crystals. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:2551-2556. [PMID: 29368930 DOI: 10.1021/acs.langmuir.7b04216] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
One of the alluring aspects of liquid crystals (LCs) is their readily controllable self-assembly behavior, leading to comprehension of complex topological structures and practical patterning applications. Here, we report on manipulating various kinds of topological defects by adopting an imprinted polymer-based soft microchannel that simultaneously imposes adjustable surface anchoring, confinement, and uniaxial alignment. Distinctive molecular orientation could be achieved by varying the surface anchoring conditions at the sidewall polymer and the rubbing directions on the bottom layer. On this pioneering platform, a common LC material, 8CB (4'-n-octyl-4-cyano-biphenyl), was placed where various topological defect domains were generated in a periodic arrangement. The experimental results showed that our platform can change the packing behavior and even the shape of topological defects by varying the rubbing condition. We believe that this facile tool to modulate surface boundary conditions combined with topographic confinement can open a way to use LC materials in potential optical and patterning applications.
Collapse
Affiliation(s)
- Min Jeong Shin
- Graduate School of Nanoscience and Technology and KINC and ‡Department of Chemistry, KAIST , Daejeon 34141, Korea
| | - Min-Jun Gim
- Graduate School of Nanoscience and Technology and KINC and ‡Department of Chemistry, KAIST , Daejeon 34141, Korea
| | - Dong Ki Yoon
- Graduate School of Nanoscience and Technology and KINC and ‡Department of Chemistry, KAIST , Daejeon 34141, Korea
| |
Collapse
|
13
|
Topology-commanded optical properties of bistable electric-field-induced torons in cholesteric bubble domains. Sci Rep 2017; 7:16149. [PMID: 29170409 PMCID: PMC5701030 DOI: 10.1038/s41598-017-16241-4] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Accepted: 10/20/2017] [Indexed: 11/24/2022] Open
Abstract
Nowadays, complicated topological defects enable many experimental manipulations and configurational simulations of active soft matter for optical and photonic applications. Investigation of topological defects in soft anisotropic materials enables one to better understand three-dimensional orientation fields in cholesteric liquid crystals. Here, we describe optical properties of bistable bubble domain (BD) texture torons in a thin layer of cholesteric liquid crystal (CLC), frustrated by homeotropic anchoring conditions, and reliably switchable by a random process. The control of macroscopic optical density and diffraction efficiency of the BD texture is demonstrated by a selection of a confinement ratio of the CLC. Experimentally reconstructed CLC director profile reveals the topology of BD torons allowing consideration of naturally occurring BD texture for applications in optical and photonic devices, which are bistably switchable between active and transparent optical states.
Collapse
|
14
|
Afghah S, Selinger JV. Theory of helicoids and skyrmions in confined cholesteric liquid crystals. Phys Rev E 2017; 96:012708. [PMID: 29347177 DOI: 10.1103/physreve.96.012708] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2017] [Indexed: 06/07/2023]
Abstract
Cholesteric liquid crystals experience geometric frustration when they are confined between surfaces with anchoring conditions that are incompatible with the cholesteric twist. Because of this frustration, they develop complex topological defect structures, which may be helicoids or skyrmions. We develop a theory for these structures, which extends previous theoretical research by deriving exact solutions for helicoids with the assumption of constant azimuth, calculating numerical solutions for helicoids and skyrmions with varying azimuth, and interpreting the results in terms of competition between terms in the free energy.
Collapse
Affiliation(s)
- Sajedeh Afghah
- Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
| | | |
Collapse
|
15
|
Cha YJ, Yoon DK. Control of Periodic Zigzag Structures of DNA by a Simple Shearing Method. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2017; 29:1604247. [PMID: 27862385 DOI: 10.1002/adma.201604247] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2016] [Revised: 09/19/2016] [Indexed: 06/06/2023]
Abstract
A periodic zigzag structure of DNA material is successfully fabricated by a simple shearing method. The periodicity of the pattern can be finely controlled by combining the mechanical shearing method with topographic patterns of microchannels. The resultant zigzag patterns can be used as a template to control the alignment of rod-like liquid crystals due to its highly regular periodicity.
Collapse
Affiliation(s)
- Yun Jeong Cha
- Graduate School of Nanoscience and Technology and KINC, KAIST, Daejeon, 305-701, Republic of Korea
| | - Dong Ki Yoon
- Graduate School of Nanoscience and Technology and KINC, KAIST, Daejeon, 305-701, Republic of Korea
| |
Collapse
|
16
|
Guo Y, Afghah S, Xiang J, Lavrentovich OD, Selinger RLB, Wei QH. Cholesteric liquid crystals in rectangular microchannels: skyrmions and stripes. SOFT MATTER 2016; 12:6312-6320. [PMID: 27396898 DOI: 10.1039/c6sm01190j] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this paper, we present experimental and numerical studies on the microstructures of a cholesteric liquid crystal (CLC) confined in rectangular micron-channels. By using a sequence of microfabrication techniques we fabricated the micro-sized channels with accurately controlled size, aspect ratio and homeotropic surface anchoring. Through optical microscopic studies we established a phase diagram for the liquid crystal defect textures as a function of the channel depth and width. For the channel width larger than ∼2 times the cholesteric pitch p, the LC molecules are oriented primarily vertical to the channel when the channel depth is below 0.75p, form bubble domain defects when the channel depth is around 0.75p, and form stripe textures when the cell depth is above the cholesteric pitch p. In addition, the bubble domain size and the stripe texture periodicity are found to grow with the increase of the channel width. For the channel width smaller than ∼2p and the channel depth between 0.6p to 1.1p, no textures can be observed in the channels. Numerical simulations based on a director tensor relaxation approach yield detailed molecular director fields, and show that the bubble domain defects are baby-skyrmions and that the stripes are the first type of cholesteric fingerprints. A comparison with previous experiments and numerical simulations indicates that the size of the microchannels also influences what type of soliton-like topological textures form in the CLCs confined in the channels.
Collapse
Affiliation(s)
- Yubing Guo
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Sajedeh Afghah
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Jie Xiang
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | | | | | - Qi-Huo Wei
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| |
Collapse
|