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Cousins JRL, Bhadwal AS, Corson LT, Duffy BR, Sage IC, Brown CV, Mottram NJ, Wilson SK. Weak-anchoring effects in a thin pinned ridge of nematic liquid crystal. Phys Rev E 2023; 107:034702. [PMID: 37073024 DOI: 10.1103/physreve.107.034702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 02/10/2023] [Indexed: 04/20/2023]
Abstract
A theoretical investigation of weak-anchoring effects in a thin two-dimensional pinned static ridge of nematic liquid crystal resting on a flat solid substrate in an atmosphere of passive gas is performed. Specifically, we solve a reduced version of the general system of governing equations recently derived by Cousins et al. [Proc. R. Soc. A 478, 20210849 (2022)10.1098/rspa.2021.0849] valid for a symmetric thin ridge under the one-constant approximation of the Frank-Oseen bulk elastic energy with pinned contact lines to determine the shape of the ridge and the behavior of the director within it. Numerical investigations covering a wide range of parameter values indicate that the energetically preferred solutions can be classified in terms of the Jenkins-Barratt-Barbero-Barberi critical thickness into five qualitatively different types of solution. In particular, the theoretical results suggest that anchoring breaking occurs close to the contact lines. The theoretical predictions are supported by the results of physical experiments for a ridge of the nematic 4^{'}-pentyl-4-biphenylcarbonitrile (5CB). In particular, these experiments show that the homeotropic anchoring at the gas-nematic interface is broken close to the contact lines by the stronger rubbed planar anchoring at the nematic-substrate interface. A comparison between the experimental values of and the theoretical predictions for the effective refractive index of the ridge gives a first estimate of the anchoring strength of an interface between air and 5CB to be (9.80±1.12)×10^{-6}Nm^{-1} at a temperature of (22±1.5)^{∘}C.
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Affiliation(s)
- Joseph R L Cousins
- Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom
- School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, United Kingdom
| | - Akhshay S Bhadwal
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, United Kingdom
| | - Lindsey T Corson
- Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom
| | - Brian R Duffy
- Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom
| | - Ian C Sage
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, United Kingdom
| | - Carl V Brown
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, United Kingdom
| | - Nigel J Mottram
- School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, United Kingdom
| | - Stephen K Wilson
- Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom
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Zidanšek A, Hölbl A, Ranjkesh A, Cordoyiannis G, Kutnjak Z, Kralj S. Impact of random-field-type disorder on nematic liquid crystalline structures. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:63. [PMID: 35876902 DOI: 10.1140/epje/s10189-022-00217-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Accepted: 07/04/2022] [Indexed: 06/15/2023]
Abstract
We study bicomponent systems where one component represents a liquid crystalline (LC) phase, and the other component randomly perturbs the LC order. Such systems can serve as a testbed to systematically analyse the impact of qualitatively different types of random-type sources of perturbation on the orientational and/or translational order. This mini-review presents typical representatives of such systems, where orientational and translational order is probed in nematic and smectic A LCs, respectively. As a source of perturbation, we consider either different porous matrices (control-pore glass, aerogels) or aerosil nanoparticles, which can form in LCs' different fractal-like network organizations. In such complex systems, LC ordering fingerprints the interplay among LC elastic forces, interfacial forces, and randomness. The resulting LC behaviour could be characterised by either long-range, quasi long-range, or short-range order. We demonstrate under which conditions random-field-like phenomena or interfacial effects dominate. However, these effects are relatively strongly entangled in most experimental systems, and individual impacts cannot be precisely identified.
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Affiliation(s)
- Aleksander Zidanšek
- Jožef Stefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia.
- Jožef Stefan International Postgraduate School, Jamova cesta 39, 1000, Ljubljana, Slovenia.
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia.
| | - Arbresha Hölbl
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia
| | - Amid Ranjkesh
- Jožef Stefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia
| | | | - Zdravko Kutnjak
- Jožef Stefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia
| | - Samo Kralj
- Jožef Stefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia
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Molecular Simulation Approaches to the Study of Thermotropic and Lyotropic Liquid Crystals. CRYSTALS 2022. [DOI: 10.3390/cryst12050685] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Over the last decade, the availability of computer time, together with new algorithms capable of exploiting parallel computer architectures, has opened up many possibilities in molecularly modelling liquid crystalline systems. This perspective article points to recent progress in modelling both thermotropic and lyotropic systems. For thermotropic nematics, the advent of improved molecular force fields can provide predictions for nematic clearing temperatures within a 10 K range. Such studies also provide valuable insights into the structure of more complex phases, where molecular organisation may be challenging to probe experimentally. Developments in coarse-grained models for thermotropics are discussed in the context of understanding the complex interplay of molecular packing, microphase separation and local interactions, and in developing methods for the calculation of material properties for thermotropics. We discuss progress towards the calculation of elastic constants, rotational viscosity coefficients, flexoelectric coefficients and helical twisting powers. The article also covers developments in modelling micelles, conventional lyotropic phases, lyotropic phase diagrams, and chromonic liquid crystals. For the latter, atomistic simulations have been particularly productive in clarifying the nature of the self-assembled aggregates in dilute solution. The development of effective coarse-grained models for chromonics is discussed in detail, including models that have demonstrated the formation of the chromonic N and M phases.
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Han Y, Harris J, Majumdar A, Zhang L. Elastic anisotropy in the reduced Landau-de Gennes model. Proc Math Phys Eng Sci 2022; 478:20210966. [PMID: 35645599 PMCID: PMC9131130 DOI: 10.1098/rspa.2021.0966] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2021] [Accepted: 04/22/2022] [Indexed: 11/25/2022] Open
Abstract
We study the effects of elastic anisotropy on Landau–de Gennes critical points, for nematic liquid crystals, on a square domain. The elastic anisotropy is captured by a parameter, L2, and the critical points are described by 3 d.f. We analytically construct a symmetric critical point for all admissible values of L2, which is necessarily globally stable for small domains, i.e. when the square edge length, λ, is small enough. We perform asymptotic analyses and numerical studies to discover at least five classes of these symmetric critical points—the WORS, Ring±, Constant and pWORS solutions, of which the WORS, Ring+ and Constant solutions can be stable. Furthermore, we demonstrate that the novel Constant solution is energetically preferable for large λ and large L2, and prove associated stability results that corroborate the stabilizing effects of L2 for reduced Landau–de Gennes critical points. We complement our analysis with numerically computed bifurcation diagrams for different values of L2, which illustrate the interplay of elastic anisotropy and geometry for nematic solution landscapes, at low temperatures.
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Affiliation(s)
- Yucen Han
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XQ, UK
| | - Joseph Harris
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XQ, UK
| | - Apala Majumdar
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XQ, UK
| | - Lei Zhang
- Beijing International Center for Mathematical Research, Center for Quantitative Biology, Peking University, Beijing 100871, People's Republic of China
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Cousins JRL, Duffy BR, Wilson SK, Mottram NJ. Young and Young-Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states. Proc Math Phys Eng Sci 2022; 478:20210849. [PMID: 35370444 PMCID: PMC8966048 DOI: 10.1098/rspa.2021.0849] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Accepted: 02/25/2022] [Indexed: 11/22/2022] Open
Abstract
Motivated by the need for greater understanding of systems that involve interfaces between a nematic liquid crystal, a solid substrate and a passive gas that include nematic–substrate–gas three-phase contact lines, we analyse a two-dimensional static ridge of nematic resting on a solid substrate in an atmosphere of passive gas. Specifically, we obtain the first complete theoretical description for this system, including nematic Young and Young–Laplace equations, and then, making the assumption that anchoring breaking occurs in regions adjacent to the contact lines, we use the nematic Young equations to determine the continuous and discontinuous transitions that occur between the equilibrium states of complete wetting, partial wetting and complete dewetting. In particular, in addition to continuous transitions analogous to those that occur in the classical case of an isotropic liquid, we find a variety of discontinuous transitions, as well as contact-angle hysteresis, and regions of parameter space in which there exist multiple partial wetting states that do not occur in the classical case.
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Affiliation(s)
- Joseph R L Cousins
- Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK.,School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, UK
| | - Brian R Duffy
- Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK
| | - Stephen K Wilson
- Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK
| | - Nigel J Mottram
- Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK.,School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, UK
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Zhang XJ, Sun YW, Li ZW, Sun ZY. Transition kinetics of defect patterns in confined two-dimensional smectic liquid crystals. Phys Rev E 2021; 104:044704. [PMID: 34781539 DOI: 10.1103/physreve.104.044704] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 10/04/2021] [Indexed: 01/21/2023]
Abstract
Topological defects in liquid crystals under confined geometries have attracted extensive research interests. Here, we perform molecular dynamics simulations to investigate the formation and transition of defect patterns in two-dimensional smectic Gay-Berne liquid crystals with a simple rectangular confinement boundary. Two typical types of defect patterns, bridge and diagonal defect patterns, are observed, which can be transformable continuously between each other over time. The transition usually starts from the line or point defect regions, and the competition between neighboring and opposite boundary effects induces the continuous realignments of the smectic layers to connect the neighboring or opposite walls. The relative stability of these two defect patterns can be controlled by changing the confinement conditions. These results deepen our understanding of transition kinetics of defect patterns in confined liquid crystals.
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Affiliation(s)
- Xiao-Jie Zhang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China and University of Science and Technology of China, Hefei 230026, China
| | - Yu-Wei Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China and University of Science and Technology of China, Hefei 230026, China
| | - Zhan-Wei Li
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China and University of Science and Technology of China, Hefei 230026, China
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China and University of Science and Technology of China, Hefei 230026, China
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Electrically Tuneable Optical Diffraction Gratings Based on a Polymer Scaffold Filled with a Nematic Liquid Crystal. Polymers (Basel) 2021; 13:polym13142292. [PMID: 34301049 PMCID: PMC8309354 DOI: 10.3390/polym13142292] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Revised: 07/10/2021] [Accepted: 07/10/2021] [Indexed: 11/28/2022] Open
Abstract
We present an experimental and theoretical investigation of the optical diffractive properties of electrically tuneable optical transmission gratings assembled as stacks of periodic slices from a conventional nematic liquid crystal (E7) and a standard photoresist polymer (SU-8). The external electric field causes a twist-type reorientation of the LC molecules toward a perpendicular direction with respect to initial orientation. The associated field-induced modification of the director field is determined numerically and analytically by minimization of the Landau–de Gennes free energy. The optical diffraction properties of the associated periodically modulated structure are calculated numerically on the basis of rigorous coupled-wave analysis (RCWA). A comparison of experimental and theoretical results suggests that polymer slices provoke planar surface anchoring of the LC molecules with the inhomogeneous surface anchoring energy varying in the range 5–20 μJ/m2. The investigated structures provide a versatile approach to fabricating LC-polymer-based electrically tuneable diffractive optical elements (DOEs).
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Han Y, Harris J, Walton J, Majumdar A. Tailored nematic and magnetization profiles on two-dimensional polygons. Phys Rev E 2021; 103:052702. [PMID: 34134325 DOI: 10.1103/physreve.103.052702] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2021] [Accepted: 04/07/2021] [Indexed: 11/07/2022]
Abstract
We study dilute suspensions of magnetic nanoparticles in a nematic host, on two-dimensional polygons. These systems are described by a nematic order parameter and a spontaneous magnetization, in the absence of any external fields. We study the stable states in terms of stable critical points of an appropriately defined free energy, with a nemato-magnetic coupling energy. We numerically study the interplay between the shape of the regular polygon, the size of the polygon, and the strength of the nemato-magnetic coupling for the multistability of this prototype system. Our notable results include (1) the coexistence of stable states with domain walls and stable interior and boundary defects, (2) the suppression of multistability for positive nemato-magnetic coupling, and (3) the enhancement of multistability for negative nemato-magnetic coupling.
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Affiliation(s)
- Yucen Han
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XQ, United Kingdom
| | - Joseph Harris
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XQ, United Kingdom
| | - Joshua Walton
- School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, United Kingdom
| | - Apala Majumdar
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XQ, United Kingdom
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9
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Al Sallo AS, Walker AJ, Boswell GP. Structure of smectic-A liquid crystals in nonuniform domains: Modeling the impact of imperfect boundaries. Phys Rev E 2020; 101:032703. [PMID: 32289914 DOI: 10.1103/physreve.101.032703] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Accepted: 02/21/2020] [Indexed: 11/07/2022]
Abstract
This paper describes the construction of equilibrium configurations for smectic-A liquid crystals subjected to nonuniform physical boundary conditions, with two-dimensional dependence on the director and layer normal, and a nonlinear layer function. Euler-Lagrange equations are constructed that describe key properties of liquid crystals confined between two boundaries exhibiting spatial imperfections. The results of the model are shown to be consistent with previous published findings in simple domains while results are obtained on how the structure of the liquid crystals changes in response to boundary perturbations. Domain sizes are considered representing those currently used in applications while predictions in smaller domains at the limit of current technologies are also made. In particular, it is shown that the curvature along a boundary impacts on the liquid crystal's structure distant from the boundary feature and therefore previously developed mathematical models, that essentially reduced the problem to a single spatial dimension, cannot be used in such circumstances. Consequences for practical applications are briefly discussed.
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Affiliation(s)
- Ayad S Al Sallo
- School of Computing and Mathematics, University of South Wales, Pontypridd CF37 1DL, United Kingdom
| | - Alan J Walker
- School of Computing, Engineering and Physical Sciences, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
| | - Graeme P Boswell
- School of Computing and Mathematics, University of South Wales, Pontypridd CF37 1DL, United Kingdom
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Bisht K, Wang Y, Banerjee V, Majumdar A. Tailored morphologies in two-dimensional ferronematic wells. Phys Rev E 2020; 101:022706. [PMID: 32168669 DOI: 10.1103/physreve.101.022706] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2019] [Accepted: 02/04/2020] [Indexed: 11/07/2022]
Abstract
We focus on a dilute uniform suspension of magnetic nanoparticles in a nematic-filled micron-sized shallow well with tangent boundary conditions as a paradigm system with two coupled order parameters. This system exhibits spontaneous magnetization without magnetic fields. We numerically obtain the stable nematic and associated magnetization morphologies, induced purely by the geometry, the boundary conditions, and the coupling between the magnetic nanoparticles and the host nematic medium. Our most striking observations pertain to domain walls in the magnetization profile, whose location can be manipulated by the coupling and material properties, and stable interior and boundary nematic defects, whose location and multiplicity can be tailored by the coupling too. These tailored morphologies are not accessible in uncoupled systems and can be used for multistable systems with singularities and stable interfaces.
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Affiliation(s)
- Konark Bisht
- Department of Physics, Indian Institute of Technology, Delhi, Hauz Khas 110016, New Delhi, India
| | - Yiwei Wang
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology, Delhi, Hauz Khas 110016, New Delhi, India
| | - Apala Majumdar
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XQ, United Kingdom.,Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
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