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Li Z, Raab A, Kolmangadi MA, Busch M, Grunwald M, Demel F, Bertram F, Kityk AV, Schönhals A, Laschat S, Huber P. Self-Assembly of Ionic Superdiscs in Nanopores. ACS NANO 2024; 18:14414-14426. [PMID: 38760015 PMCID: PMC11155240 DOI: 10.1021/acsnano.4c01062] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2024] [Revised: 04/23/2024] [Accepted: 05/01/2024] [Indexed: 05/19/2024]
Abstract
Discotic ionic liquid crystals (DILCs) consist of self-assembled superdiscs of cations and anions that spontaneously stack in linear columns with high one-dimensional ionic and electronic charge mobility, making them prominent model systems for functional soft matter. Compared to classical nonionic discotic liquid crystals, many liquid crystalline structures with a combination of electronic and ionic conductivity have been reported, which are of interest for separation membranes, artificial ion/proton conducting membranes, and optoelectronics. Unfortunately, a homogeneous alignment of the DILCs on the macroscale is often not achievable, which significantly limits the applicability of DILCs. Infiltration into nanoporous solid scaffolds can, in principle, overcome this drawback. However, due to the experimental challenges to scrutinize liquid crystalline order in extreme spatial confinement, little is known about the structures of DILCs in nanopores. Here, we present temperature-dependent high-resolution optical birefringence measurement and 3D reciprocal space mapping based on synchrotron X-ray scattering to investigate the thermotropic phase behavior of dopamine-based ionic liquid crystals confined in cylindrical channels of 180 nm diameter in macroscopic anodic aluminum oxide membranes. As a function of the membranes' hydrophilicity and thus the molecular anchoring to the pore walls (edge-on or face-on) and the variation of the hydrophilic-hydrophobic balance between the aromatic cores and the alkyl side chain motifs of the superdiscs by tailored chemical synthesis, we find a particularly rich phase behavior, which is not present in the bulk state. It is governed by a complex interplay of liquid crystalline elastic energies (bending and splay deformations), polar interactions, and pure geometric confinement and includes textural transitions between radial and axial alignment of the columns with respect to the long nanochannel axis. Furthermore, confinement-induced continuous order formation is observed in contrast to discontinuous first-order phase transitions, which can be quantitatively described by Landau-de Gennes free energy models for liquid crystalline order transitions in confinement. Our observations suggest that the infiltration of DILCs into nanoporous solids allows tailoring their nanoscale texture and ion channel formation and thus their electrical and optical functionalities over an even wider range than in the bulk state in a homogeneous manner on the centimeter scale as controlled by the monolithic nanoporous scaffolds.
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Affiliation(s)
- Zhuoqing Li
- Institute
for Materials and X-ray Physics, Hamburg
University of Technology, Denickestr. 15, 21073 Hamburg, Germany
- Centre
for X-ray and Nano Science CXNS, Deutsches
Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
| | - Aileen Raab
- Institut
für Organische Chemie, Universität
Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Mohamed Aejaz Kolmangadi
- Bundesanstalt
für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12205 Berlin, Germany
| | - Mark Busch
- Institute
for Materials and X-ray Physics, Hamburg
University of Technology, Denickestr. 15, 21073 Hamburg, Germany
- Centre
for X-ray and Nano Science CXNS, Deutsches
Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
| | - Marco Grunwald
- Institut
für Organische Chemie, Universität
Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Felix Demel
- Institut
für Organische Chemie, Universität
Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Florian Bertram
- Deutsches
Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
| | - Andriy V. Kityk
- Faculty of
Electrical Engineering, Czestochowa University
of Technology, Al. Armii
Krajowej 17, 42-200 Czestochowa, Poland
| | - Andreas Schönhals
- Bundesanstalt
für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12205 Berlin, Germany
- Institut
für Chemie, Technische Universität
Berlin, Straße des
17. Juni 135, 10623 Berlin, Germany
| | - Sabine Laschat
- Institut
für Organische Chemie, Universität
Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Patrick Huber
- Institute
for Materials and X-ray Physics, Hamburg
University of Technology, Denickestr. 15, 21073 Hamburg, Germany
- Centre
for X-ray and Nano Science CXNS, Deutsches
Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
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2
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Langeslay B, Fahy W, Juarez G. Stress and alignment response to curved obstacles in growing bacterial monolayers. Phys Rev E 2024; 109:054608. [PMID: 38907398 DOI: 10.1103/physreve.109.054608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Accepted: 05/09/2024] [Indexed: 06/24/2024]
Abstract
Monolayers of growing bacteria, confined within channel geometries, exhibit self-organization into a highly aligned laminar state along the axis of the channel. Although this phenomenon has been observed in experiments and simulations under various boundary conditions, the underlying physical mechanism driving this alignment remains unclear. In this study, we conduct simulations of growing bacteria in two-dimensional channel geometries perturbed by fixed obstacles, either circular or arc shaped, placed at the channel's center. Our findings reveal that even sizable obstacles cause only short-ranged disruptions to the baseline laminar state. These disruptions arise from a competition between local planar anchoring and bulk laminar alignment. At smaller obstacle sizes, bulk alignment fully dominates, while at larger sizes planar anchoring induces increasing local disruptions. Furthermore, our analysis indicates that the resulting configurations of the bacterial system display a striking resemblance to the arrangement of hard-rod smectic liquid crystals around circular obstacles. This suggests that modeling hard-rod bacterial monolayers as smectic, rather than nematic, liquid crystals may yield successful outcomes. The insights gained from our study contribute to the expanding body of research on bacterial growth in channels. Our work provides perspectives on the stability of the laminar state and extends our understanding to encompass more intricate confinement schemes.
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Chaâbani W, Lyu J, Marcone J, Goldmann C, Ten Veen EJM, Dumesnil C, Bizien T, Smallenburg F, Impéror-Clerc M, Constantin D, Hamon C. Prismatic Confinement Induces Tunable Orientation in Plasmonic Supercrystals. ACS NANO 2024; 18:9566-9575. [PMID: 38507585 DOI: 10.1021/acsnano.3c12799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/22/2024]
Abstract
Throughout history scientists have looked to Nature for inspiration and attempted to replicate intricate complex structures formed by self-assembly. In the context of synthetic supercrystals, achieving such complexity remains a challenge due to the highly symmetric nature of most nanoparticles (NPs). Previous works have shown intricate coupling between the self-assembly of NPs and confinement in templates, such as emulsion droplets (spherical confinement) or tubes (cylindrical confinement). This study focuses on the interplay between anisotropic NP shape and tunable "prismatic confinement" leading to the self-assembly of supercrystals in cavities featuring polygonal cross sections. A multiscale characterization strategy is employed to investigate the orientation and structure of the supercrystals locally and at the ensemble level. Our findings highlight the role of the mold interface in guiding the growth of distinct crystal domains: each side of the mold directs the formation of a monodomain that extends until it encounters another, leading to the creation of grain boundaries. Computer simulations in smaller prismatic cavities were conducted to predict the effect of an increased confinement. Comparison between prismatic and cylindrical confinements shows that flat interfaces are key to orienting the growth of supercrystals. This work shows a method of inducing orientation in plasmonic supercrystals and controlling their textural defects, thus offering insight into the design of functional metasurfaces and hierarchically structured devices.
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Affiliation(s)
- Wajdi Chaâbani
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Jieli Lyu
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Jules Marcone
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Claire Goldmann
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Eleonora J M Ten Veen
- Soft Condensed Matter, Debye Institute of Nanomaterials Science, Utrecht University, 3584 CC Utrecht, Netherlands
| | - Clément Dumesnil
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Thomas Bizien
- SWING Beamline, SOLEIL Synchrotron, 91190 Gif-sur-Yvette, France
| | - Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | | | - Doru Constantin
- Institut Charles Sadron, CNRS and Université de Strasbourg, 67034 Strasbourg, France
| | - Cyrille Hamon
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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4
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Wensink HH, Grelet E. Elastic response of colloidal smectic liquid crystals: Insights from microscopic theory. Phys Rev E 2023; 107:054604. [PMID: 37329078 DOI: 10.1103/physreve.107.054604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 05/05/2023] [Indexed: 06/18/2023]
Abstract
Elongated colloidal rods at sufficient packing conditions are known to form stable lamellar or smectic phases. Using a simplified volume-exclusion model, we propose a generic equation of state for hard-rod smectics that is robust against simulation results and is independent of the rod aspect ratio. We then extend our theory by exploring the elastic properties of a hard-rod smectic, including the layer compressibility (B) and bending modulus (K_{1}). By introducing weak backbone flexibility we are able to compare our predictions with experimental results on smectics of filamentous virus rods (fd) and find quantitative agreement between the smectic layer spacing, the out-of-plane fluctuation strength, as well as the smectic penetration length λ=sqrt[K_{1}/B]. We demonstrate that the layer bending modulus is dominated by director splay and depends sensitively on lamellar out-of-plane fluctuations that we account for on the single-rod level. We find that the ratio between the smectic penetration length and the lamellar spacing is about two orders of magnitude smaller than typical values reported for thermotropic smectics. We attribute this to the fact that colloidal smectics are considerably softer in terms of layer compression than their thermotropic counterparts while the cost of layer bending is of comparable magnitude.
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Affiliation(s)
- H H Wensink
- Laboratoire de Physique des Solides-UMR 8502, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - E Grelet
- Centre de Recherche Paul Pascal-UMR 5031, CNRS, Université de Bordeaux, 33600 Pessac, France
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Renner J, Schmidt M, de Las Heras D. Reduced-variance orientational distribution functions from torque sampling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:235901. [PMID: 36974000 DOI: 10.1088/1361-648x/acc522] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 03/08/2023] [Indexed: 06/18/2023]
Abstract
We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium. Instead of the traditional counting of events, we reconstruct the orientational distribution function via an orientational integral of the torque acting on the particles. We test the torque sampling method in two- and three-dimensions, using both Langevin dynamics and overdamped Brownian dynamics, and with two interparticle interaction potentials. In all cases the torque sampling method produces profiles of the orientational distribution function with better accuracy than those obtained with the traditional counting method. The accuracy of the torque sampling method is independent of the bin size, and hence it is possible to resolve the orientational distribution function with arbitrarily small angular resolutions.
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Affiliation(s)
- Johannes Renner
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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6
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Chen ZQ, Sun YW, Zhang XJ, Zhu YL, Li ZW, Sun ZY. External field induced defect transformation in circular confined Gay-Berne liquid crystals. J Chem Phys 2023; 158:104902. [PMID: 36922133 DOI: 10.1063/5.0135483] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2023] Open
Abstract
Normally, defects in two-dimensional, circular, confined liquid crystals can be classified into four types based on the position of singularities formed by liquid crystal molecules, i.e., the singularities located inside the circle, at the boundary, outside the circle, and outside the circle at infinity. However, it is considered difficult for small aspect ratio liquid crystals to generate all these four types of defects. In this study, we use molecular dynamics simulation to investigate the defect formed in Gay-Berne, ellipsoidal liquid crystals, with small aspect ratios confined in a circular cavity. As expected, we only find two types of defects (inside the circle and at the boundary) in circular, confined, Gay-Berne ellipsoids under static conditions at various densities, aspect ratios, and interactions between the wall and liquid crystals. However, when introducing an external field to the system, four types of defects can be observed. With increasing the strength of the external field, the singularities in the circular, confined system change from the inside to the boundary and the outside, and the farthest position that the singularities can reach depends on the strength of the external field. We further introduce an alternating, triangular wave, external field to the system to check if we can observe the transformation of different defects within an oscillating period. We find that the position of the singularities greatly depends on the oscillating intensity and oscillating period. By changing the oscillating intensity and oscillating period of the external field, the defect types can be adjusted, and the transformation between different defects can be easily observed. This provides a feasible way to modulate liquid crystal defects and investigate the transformation between different defects.
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Affiliation(s)
- Zi-Qin Chen
- 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
| | - 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
| | - You-Liang Zhu
- College of Chemistry, Jilin University, Changchun 130012, China
| | - Zhan-Wei Li
- College of Chemistry and Green Catalysis Center, Zhengzhou University, Zhengzhou 450001, People's Republic of 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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7
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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.
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8
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Te Vrugt M, Wittkowski R. Perspective: New directions in dynamical density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:041501. [PMID: 35917827 DOI: 10.1088/1361-648x/ac8633] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2022] [Accepted: 08/01/2022] [Indexed: 06/15/2023]
Abstract
Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.
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Affiliation(s)
- Michael Te Vrugt
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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9
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Martínez-Ratón Y, Velasco E. Effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids. Phys Rev E 2022; 106:034602. [PMID: 36266879 DOI: 10.1103/physreve.106.034602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Accepted: 08/17/2022] [Indexed: 06/16/2023]
Abstract
We introduce a model for a fluid of polydisperse rounded hard rectangles where the length and width of the rectangular core are fixed, while the roundness is taken into account by the convex envelope of a disk displaced along the perimeter of the core. The diameter of the disk has a continuous polydispersity described by a Schulz distribution function. We implemented the scaled particle theory for this model with the aim of studying: (i) the effect of roundness on the phase behavior of the one-component hard-rectangle fluid and (ii) how polydispersity affects phase transitions between isotropic, nematic, and tetratic phases. We found that roundness greatly affects the tetratic phase, whose region of stability in the phase diagram strongly decreases as the roundness parameter is increased. Also, the interval of aspect ratios where the tetratic-nematic and isotropic-nematic phase transitions are of first order considerably reduces with roundness, both transitions becoming weaker. Polydispersity induces strong fractionation between the coexisting phases, with the nematic phase enriched in particles of lower roundness. Finally, for high enough polydispersity and certain mean aspect ratios, the isotropic-to-nematic transition can change from second (for the one-component fluid) to first order. We also found a packing-fraction inversion phenomenon for large polydispersities: the coexisting isotropic phase has a higher packing fraction than the nematic.
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Affiliation(s)
- Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911, Leganés, Madrid, Spain
| | - Enrique Velasco
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC) and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049, Madrid, Spain
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10
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Monderkamp PA, Wittmann R, Te Vrugt M, Voigt A, Wittkowski R, Löwen H. Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals. Phys Chem Chem Phys 2022; 24:15691-15704. [PMID: 35552573 DOI: 10.1039/d2cp00060a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Observing and characterizing the complex ordering phenomena of liquid crystals subjected to external constraints constitutes an ongoing challenge for chemists and physicists alike. To elucidate the delicate balance appearing when the intrinsic positional order of smectic liquid crystals comes into play, we perform Monte-Carlo simulations of rod-like particles in a range of cavities with a cylindrical symmetry. Based on recent insights into the topology of smectic orientational grain boundaries in two dimensions, we analyze the emerging three-dimensional defect structures from the perspective of tetratic symmetry. Using an appropriate three-dimensional tetratic order parameter constructed from the Steinhardt order parameters, we show that those grain boundaries can be interpreted as a pair of tetratic disclination lines that are located on the edges of the nematic domain boundary. Thereby, we shed light on the fine structure of grain boundaries in three-dimensional confined smectics.
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Affiliation(s)
- Paul A Monderkamp
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
| | - Michael Te Vrugt
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Axel Voigt
- Institut für Wissenschaftliches Rechnen, Technische Universität Dresden, 01062 Dresden, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
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11
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Salgado-Blanco D, Llanas-García AH, Díaz-Herrera E, Martínez-González JA, Mendoza CI. Structural properties and ring defect formation in discotic liquid crystal nanodroplets. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:254001. [PMID: 35358952 DOI: 10.1088/1361-648x/ac630b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 03/31/2022] [Indexed: 06/14/2023]
Abstract
In this work, we performedNpTMonte Carlo simulations of a Gay-Berne discotic liquid crystal confined in a spherical droplet under face-on anchoring and fixed pressure. We find that, in contrast to the unbounded system, a plot of the order parameter as function of temperature does not show a clear evidence of a first-order isotropic-nematic transition. We also find that the impossibility of simultaneously satisfy the uniform director field requirement of a nematic phase with the radial boundary conditions, results in the appearance of a ring disclination line as a stress release mechanism in the interior of the droplet. Under further cooling, a columnar phase appears at the center of the droplet.
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Affiliation(s)
- Daniel Salgado-Blanco
- Cátedras CONACyT-Centro Nacional de Supercómputo, Instituto Potosino de Investigación Científica y Tecnológica, Camino a la Presa San José 2055, 78216, San Luis Potosí, México
- División de Materiales Avanzados, IPICYT, Camino a la Presa San José 2055, Col. Lomas 4a Sección, San Luis Potosí, S. L. P., 78216, México
| | - Andrea H Llanas-García
- División de Materiales Avanzados, IPICYT, Camino a la Presa San José 2055, Col. Lomas 4a Sección, San Luis Potosí, S. L. P., 78216, México
| | - Enrique Díaz-Herrera
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Ave. San Rafael Atlixco 186, Col. Vicentina, 09340 México, Ciudad de México, Mexico
| | - José A Martínez-González
- Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Av. Parque Chapultepec 1570, San Luis Potosí 78210 SLP, Mexico
| | - Carlos I Mendoza
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apdo. Postal 70-360, 04510 México, Ciudad de México, Mexico
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12
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Yao X, Zhang L, Chen JZY. Defect patterns of two-dimensional nematic liquid crystals in confinement. Phys Rev E 2022; 105:044704. [PMID: 35590543 DOI: 10.1103/physreve.105.044704] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 03/23/2022] [Indexed: 06/15/2023]
Abstract
A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface-confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form a deformed texture that may display defect points or defect lines, for which winding numbers can be clearly defined. Here, a particular attention is paid to the case when the liquid crystal molecules prefer to form a boundary nematic texture in parallel to the wall surface (i.e., following the homogeneous boundary condition). A general theory, based on geometric argument, is presented for the relationship between the sum of all winding numbers in the system (the total winding number) and the type of confinement angles and curved segments. The conclusion is validated by comparing the theoretical defect rule with existing nematic textures observed experimentally and theoretically in recent years.
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Affiliation(s)
- Xiaomei Yao
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Lei Zhang
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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