1
|
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.
Collapse
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.
| |
Collapse
|
2
|
Monderkamp PA, Wittmann R, Cortes LBG, Aarts DGAL, Smallenburg F, Löwen H. Topology of Orientational Defects in Confined Smectic Liquid Crystals. PHYSICAL REVIEW LETTERS 2021; 127:198001. [PMID: 34797147 DOI: 10.1103/physrevlett.127.198001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Revised: 06/28/2021] [Accepted: 09/22/2021] [Indexed: 06/13/2023]
Abstract
We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in pointlike units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive Monte Carlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showing how the observed defect networks can be universally reconstructed from simple building blocks. We further find that the curvature of the confining wall determines the anchoring behavior of grain boundaries, such that the number of nodes in the emerging networks and the location of their end points can be tuned by changing the number and smoothness of corners, respectively.
Collapse
Affiliation(s)
- Paul A Monderkamp
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Louis B G Cortes
- School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA
| | - Dirk G A L Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Frank Smallenburg
- Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| |
Collapse
|
3
|
Martínez-Ratón Y, Velasco E. Highly confined mixtures of parallel hard squares: A density-functional-theory study. Phys Rev E 2020; 100:062604. [PMID: 31962445 DOI: 10.1103/physreve.100.062604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Indexed: 11/06/2022]
Abstract
Using the fundamental-measure density-functional theory, we study theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting of two consecutive big squares, or three small squares, in the transverse direction, perpendicular to the walls, are forbidden. We analyze two different mixtures with edge lengths of species selected so as to allow or forbid one big plus one small square to fit into the channel. For the first mixture we obtain first-order transitions between symmetric and asymmetric packings of particles: Small and big squares are preferentially adsorbed at different walls. Asymmetric configurations are shown to lead to more efficient packing at finite pressures. We argue that the stability region of the asymmetric phase in the pressure-composition plane is bounded so that the symmetric phase is stable at low and very high pressure. For the second mixture, we observe strong demixing between phases which are rich in different species. Demixing occurs in the lateral direction, i.e., the dividing interface is perpendicular to the walls, and phases exhibit symmetric density profiles. The possible experimental realization of this behavior (which in practical terms is precluded by jamming) in strictly two-dimensional systems is discussed. Finally, the phase behavior of a mixture with periodic boundary conditions is analyzed and the differences and similarities between the latter and the confined system are discussed. We claim that, although exact calculations exclude the existence of true phase transitions in (1+ε)-dimensional systems, density-functional theory is still successful in describing packing properties of large clusters of particles.
Collapse
Affiliation(s)
- Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
| | - Enrique Velasco
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, 28049, Madrid, Spain
| |
Collapse
|
4
|
Gârlea IC, Dammone O, Alvarado J, Notenboom V, Jia Y, Koenderink GH, Aarts DGAL, Lettinga MP, Mulder BM. Colloidal Liquid Crystals Confined to Synthetic Tactoids. Sci Rep 2019; 9:20391. [PMID: 31892707 PMCID: PMC6938498 DOI: 10.1038/s41598-019-56729-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2019] [Accepted: 11/22/2019] [Indexed: 11/24/2022] Open
Abstract
When a liquid crystal forming particles are confined to a spatial volume with dimensions comparable to that of their own size, they face a complex trade-off between their global tendency to align and the local constraints imposed by the boundary conditions. This interplay may lead to a non-trivial orientational patterns that strongly depend on the geometry of the confining volume. This novel regime of liquid crystalline behavior can be probed with colloidal particles that are macro-aggregates of biomolecules. Here we study director fields of filamentous fd-viruses in quasi-2D lens-shaped chambers that mimic the shape of tactoids, the nematic droplets that form during isotropic-nematic phase separation. By varying the size and aspect ratio of the chambers we force these particles into confinements that vary from circular to extremely spindle-like shapes and observe the director field using fluorescence microscopy. In the resulting phase diagram, next to configurations predicted earlier for 3D tactoids, we find a number of novel configurations. Using Monte Carlo Simulations, we show that these novel states are metastable, yet long-lived. Their multiplicity can be explained by the co-existence of multiple dynamic relaxation pathways leading to the final stable states.
Collapse
Affiliation(s)
- Ioana C Gârlea
- AMOLF, Department of Living Matter, Amsterdam, 1098XG, The Netherlands. .,University of Vienna, Faculty of Physics, Vienna, A-1090, Austria.
| | - Oliver Dammone
- University of Oxford, Department of Chemistry, Oxford, OX1 3QZ, UK
| | - José Alvarado
- AMOLF, Department of Living Matter, Amsterdam, 1098XG, The Netherlands
| | - Valerie Notenboom
- AMOLF, Department of Living Matter, Amsterdam, 1098XG, The Netherlands
| | - Yunfei Jia
- Forschungszentrum Jülich, Institute of Complex Systems (ICS-3), Jülich, 52425, Germany
| | - Gijsje H Koenderink
- AMOLF, Department of Living Matter, Amsterdam, 1098XG, The Netherlands.,Kavli Institute of Nanoscience, Delft University of Technology, Department of Bionanoscience, Delft, 2629HZ, The Netherlands
| | - Dirk G A L Aarts
- University of Oxford, Department of Chemistry, Oxford, OX1 3QZ, UK
| | - M Paul Lettinga
- Forschungszentrum Jülich, Institute of Complex Systems (ICS-3), Jülich, 52425, Germany. .,KU Leuven, Laboratory for Soft Matter and Biophysics, Leuven, B-300, Belgium.
| | - Bela M Mulder
- AMOLF, Department of Living Matter, Amsterdam, 1098XG, The Netherlands
| |
Collapse
|
5
|
Gomes OA, Yednak CAR, da Silva BVHV, Teixeira-Souza RT. Nematic liquid crystal in a cylindrical sample: Theoretical analysis of the electrical response. Phys Rev E 2018; 97:022703. [PMID: 29548116 DOI: 10.1103/physreve.97.022703] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2017] [Indexed: 11/07/2022]
Abstract
The electrical responses of a nematic liquid crystal sample confined between two cylindrical surfaces are investigated in the framework of elastic continuum theory. The responses are the result of the molecular reorientation induced by both the applied electric field and the cylindrical geometry of the sample. The nematic medium is considered as a parallel RC circuit since the capacitance and the resistance are under the same difference of potential. The electrical properties, including the total electric current, are determined from the molecular reorientation of the director. The elastic anisotropy has been shown to influence substantially the profile of the electrical current, capacitance, and resistance characterizing the equivalent circuit for the medium.
Collapse
Affiliation(s)
- O A Gomes
- Universidade Tecnológica Federal do Paraná, Via do Conhecimento Km 1, 85503-390, Câmpus Pato Branco, Paraná, Brazil
| | - C A R Yednak
- Departamento de Física, Universidade Tecnológica Federal do Paraná, Via do Conhecimento Km 1, 85503-390, Câmpus Pato Branco, Paraná, Brazil
| | - B V H V da Silva
- Departamento de Física, Universidade Estadual de Ponta Grossa, Avenida Carlos Cavalcanti 4748, 84030-900 Ponta Grossa, Paraná, Brazil
| | - R T Teixeira-Souza
- Universidade Tecnológica Federal do Paraná, Câmpus Apucarana, Rua Marcílio Dias 635, 86812-460 Apucarana, Paraná, Brazil
| |
Collapse
|
6
|
Leoni M, Manyuhina OV, Bowick MJ, Marchetti MC. Defect driven shapes in nematic droplets: analogies with cell division. SOFT MATTER 2017; 13:1257-1266. [PMID: 28102411 DOI: 10.1039/c6sm02584f] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Building on the striking similarity between the structure of the spindle during mitosis in living cells and nematic textures in confined liquid crystals, we use a continuum model of two-dimensional nematic liquid crystal droplets to examine the physical aspects of cell division. The model investigates the interplay between bulk elasticity of the microtubule assembly, described as a nematic liquid crystal, and surface elasticity of the cell cortex, modeled as a bounding flexible membrane, in controlling cell shape and division. The centrosomes at the spindle poles correspond to the cores of the topological defects required to accommodate nematic order in a closed geometry. We map out the progression of both healthy bipolar and faulty multi-polar division as a function of an effective parameter that incorporates active processes and controls centrosome separation. A robust prediction, independent of energetic considerations, is that the transition from a single cell to daughters cells occurs at critical value of this parameter. Our model additionally suggests that microtubule anchoring at the cell cortex may play an important role for successful bipolar division. This can be tested experimentally by regulating microtubule anchoring.
Collapse
Affiliation(s)
- Marco Leoni
- Physics Department and Soft Matter Program, Syracuse University, Syracuse, NY 13244, USA. and Institut Curie, PSL Research University, CNRS, UMR 168, 26 rue d'Ulm, F-75005, Paris, France
| | - Oksana V Manyuhina
- Physics Department and Soft Matter Program, Syracuse University, Syracuse, NY 13244, USA.
| | - Mark J Bowick
- Physics Department and Soft Matter Program, Syracuse University, Syracuse, NY 13244, USA. and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106- 4030, USA
| | - M Cristina Marchetti
- Physics Department and Soft Matter Program, Syracuse University, Syracuse, NY 13244, USA.
| |
Collapse
|
7
|
DeBenedictis A, Atherton TJ, Anquetil-Deck C, Cleaver DJ, Emerson DB, Wolak M, Adler JH. Competition of lattice and basis for alignment of nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042501. [PMID: 26565259 DOI: 10.1103/physreve.92.042501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2015] [Indexed: 06/05/2023]
Abstract
Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here we consider how such alignment can be achieved using a periodic square lattice of circular or elliptical motifs. In particular, we examine ways in which the lattice and motif can combine to favor differing orientations. Using Monte Carlo simulation and continuum elasticity we find, for circular motifs, that the coverage fraction controls both the polar anchoring angle and a transition in the azimuthal orientation. If the circles are generalized to ellipses, arbitrary control of the effective easy axis and effective anchoring potential becomes achievable by appropriate tuning of the ellipse motif relative to the periodic lattice patterning. This has possible applications in both monostable and bistable liquid crystal device contexts.
Collapse
Affiliation(s)
- Andrew DeBenedictis
- Department of Physics and Astronomy, Tufts University, 574 Boston Avenue, Medford, Massachusetts 02155, USA
| | - Timothy J Atherton
- Department of Physics and Astronomy, Tufts University, 574 Boston Avenue, Medford, Massachusetts 02155, USA
| | - Candy Anquetil-Deck
- Materials and Engineering Research Institute, Sheffield Hallam University, City Campus, Howard Street, Sheffield S1 1WB, United Kingdom
| | - Douglas J Cleaver
- Materials and Engineering Research Institute, Sheffield Hallam University, City Campus, Howard Street, Sheffield S1 1WB, United Kingdom
| | - David B Emerson
- Department of Mathematics, Tufts University, 503 Boston Avenue, Medford, Massachusetts 02155, USA
| | - Mathew Wolak
- Department of Mathematics, Tufts University, 503 Boston Avenue, Medford, Massachusetts 02155, USA
| | - James H Adler
- Department of Mathematics, Tufts University, 503 Boston Avenue, Medford, Massachusetts 02155, USA
| |
Collapse
|