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de Araújo CB, de Oliveira EJL, Lyra ML, Mirantsev LV, de Oliveira IN. Formation of topological defects in nematic shells with a dumbbell-like shape. SOFT MATTER 2022; 18:4189-4196. [PMID: 35605981 DOI: 10.1039/d2sm00378c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The present study investigates dumbbell-shaped nematic liquid crystal shells. Using molecular dynamics (MD) simulations, we consider the effects of an external electric field on nematic ordering by computing the average molecular alignment's time evolution and equilibrium configuration. We show that the number and location of topological defects are strongly affected by the external field, with the orientational ordering's equilibrium configuration depending on field direction about the shell's long axis. For a transverse external field, it is verified that the defect rearrangement presents a non-linear dynamics, with a field independent characteristic time scale delimiting the short and long time regimes. Effects associated with varying the shell's Gaussian curvature are also analyzed.
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Affiliation(s)
- C B de Araújo
- Instituto de Física, Universidade Federal de Alagoas, Maceió, AL, Brazil.
| | - E J L de Oliveira
- Instituto de Física, Universidade Federal de Alagoas, Maceió, AL, Brazil.
| | - M L Lyra
- Instituto de Física, Universidade Federal de Alagoas, Maceió, AL, Brazil.
| | - L V Mirantsev
- Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
| | - I N de Oliveira
- Instituto de Física, Universidade Federal de Alagoas, Maceió, AL, Brazil.
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2
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Yao X, Chen JZY. Rodlike molecules in extreme confinement. Phys Rev E 2020; 101:062706. [PMID: 32688519 DOI: 10.1103/physreve.101.062706] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 06/15/2020] [Indexed: 11/07/2022]
Abstract
A unique feature of colloid particles and biopolymers is the molecule's intrinsic rigidity characterized by a molecular-level length scale. Under extreme confinement conditions at cellular scales or in nanodevices, these molecules can display orientational ordering accompanied by severe density depletion. Conventional liquid-crystal theories, such as the Oseen-Frank or Landau-de Gennes theories, cannot capture the essential molecular-level properties: the boundary effects, which extend to a distance of the rigidity length scale, and the drastic variations of the inhomogeneous molecular density. Here we show, based on a simple interpretation of the Onsager model, that rodlike molecules in extreme annular confinement produce unusual liquid-crystal defect structures that are independent phases from the patterns usually seen in a weaker confinement environment.
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Affiliation(s)
- Xiaomei Yao
- School of Chemistry, Beihang University, Beijing 100191, People's Republic of China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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Mesarec L, Góźdź W, Iglič A, Kralj-Iglič V, Virga EG, Kralj S. Normal red blood cells' shape stabilized by membrane's in-plane ordering. Sci Rep 2019; 9:19742. [PMID: 31875042 PMCID: PMC6930264 DOI: 10.1038/s41598-019-56128-0] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Accepted: 12/04/2019] [Indexed: 11/19/2022] Open
Abstract
Red blood cells (RBCs) are present in almost all vertebrates and their main function is to transport oxygen to the body tissues. RBCs' shape plays a significant role in their functionality. In almost all mammals in normal conditions, RBCs adopt a disk-like (discocyte) shape, which optimizes their flow properties in vessels and capillaries. Experimentally measured values of the reduced volume (v) of stable discocyte shapes range in a relatively broad window between v ~ 0.58 and 0.8. However, these observations are not supported by existing theoretical membrane-shape models, which predict that discocytic RBC shape is stable only in a very narrow interval of v values, ranging between v ~ 0.59 and 0.65. In this study, we demonstrate that this interval is broadened if a membrane's in-plane ordering is taken into account. We model RBC structures by using a hybrid Helfrich-Landau mesoscopic approach. We show that an extrinsic (deviatoric) curvature free energy term stabilizes the RBC discocyte shapes. In particular, we show on symmetry grounds that the role of extrinsic curvature is anomalously increased just below the nematic in-plane order-disorder phase transition temperature.
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Affiliation(s)
- L Mesarec
- Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, 1000, Ljubljana, Slovenia
| | - W Góźdź
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224, Warsaw, Poland
| | - A Iglič
- Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, 1000, Ljubljana, Slovenia
- Laboratory of Mass Spectrometry and Proteomics, Institute of Biosciences and BioResources, National Research Council of Italy, Napoli, 80132, Italy
| | - V Kralj-Iglič
- Laboratory of Mass Spectrometry and Proteomics, Institute of Biosciences and BioResources, National Research Council of Italy, Napoli, 80132, Italy
- Laboratory of Clinical Biophysics, Faculty of Health Sciences, University of Ljubljana, 1000, Ljubljana, Slovenia
- Laboratory of Clinical Biophysics, Faculty of Medicine, University of Ljubljana, 1000, Ljubljana, Slovenia
| | - E G Virga
- Department of Mathematics, University of Pavia, Via Ferrata 5, 27100, Pavia, Italy
| | - S Kralj
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, 2000, Maribor, Slovenia.
- Condensed Matter Physics Department, Jožef Stefan Institute, 1000, Ljubljana, Slovenia.
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Santiago JA, Chacón-Acosta G, Monroy F. Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints. Phys Rev E 2019; 100:012704. [PMID: 31499809 DOI: 10.1103/physreve.100.012704] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2019] [Indexed: 11/07/2022]
Abstract
An elastic membrane with embedded nematic molecules is considered as a model of anisotropic fluid membrane with internal ordering. By considering the geometric coupling between director field and membrane curvature, the nematic texture is shown to induce anisotropic stresses additional to Canham-Helfrich elasticity. Building upon differential geometry, analytical expressions are found for the membrane stress and torque induced by splaying, twisting, and bending of the nematic director as described by the Frank energy of liquid crystals. The forces induced by prototypical nematic textures are visualized on the sphere and on cylindrical surfaces.
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Affiliation(s)
- J A Santiago
- Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Cuajimalpa, Vasco de Quiroga 4871, 05348 Ciudad de México, Mexico.,Departamento de Química Física, Universidad Complutense de Madrid, Av. Complutense s/n, 28040, Madrid, Spain
| | - G Chacón-Acosta
- Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Cuajimalpa, Vasco de Quiroga 4871, 05348 Ciudad de México, Mexico
| | - F Monroy
- Departamento de Química Física, Universidad Complutense de Madrid, Av. Complutense s/n, 28040, Madrid, Spain.,Institute for Biomedical Research, Hospital Doce de Octubre (imas12), Av. Andalucía s/n 28041, Madrid, Spain
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Mirantsev LV, Sonnet AM, Virga EG. Lifting ordered surfaces: Ellipsoidal nematic shells. Phys Rev E 2018; 98:012701. [PMID: 30110838 DOI: 10.1103/physreve.98.012701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2018] [Indexed: 11/07/2022]
Abstract
When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeler faces an alternative. Either the order is described on the curved, physical surface where it belongs, or it is described on a flat surface that is unrolled as preimage of the physical surface under a suitable height function. This paper applies a general method that pursues the latter avenue by lifting whatever order tensor is deemed appropriate from a flat to a curved surface. We specialize this method to nematic shells, for which it also provides a simple but perhaps convincing interpretation of the outcomes of some molecular dynamics experiments on ellipsoidal shells.
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Affiliation(s)
- Leonid V Mirantsev
- Institute of the Problems of Mechanical Engineering, Academy of Sciences of Russia, St. Petersburg 199178, Russia
| | - André M Sonnet
- Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, Scotland, United Kingdom
| | - Epifanio G Virga
- Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy
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Napoli G, Vergori L. Influence of the extrinsic curvature on two-dimensional nematic films. Phys Rev E 2018; 97:052705. [PMID: 29906963 DOI: 10.1103/physreve.97.052705] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Indexed: 06/08/2023]
Abstract
Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.
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Affiliation(s)
- Gaetano Napoli
- Dipartimento di Matematica e Fisica "E. De Giorgi", Università del Salento, 73100 Lecce, Italy
| | - Luigi Vergori
- Dipartimento di Ingegneria, Università degli Studi di Perugia, 06125 Perugia, Italy
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