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Rajendra D, Mandal J, Hatwalne Y, Maiti PK. Packing and emergence of the ordering of rods in a spherical monolayer. SOFT MATTER 2022; 19:137-146. [PMID: 36477473 DOI: 10.1039/d2sm00799a] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Spatially ordered systems confined to surfaces such as spheres exhibit interesting topological structures because of curvature induced frustration in orientational and translational order. The study of these structures is important for investigating the interplay between the geometry, topology, and elasticity, and for their potential applications in materials science, such as engineering directionally binding particles. In this work, we numerically simulate a spherical monolayer of soft repulsive spherocylinders (SRSs) and study the packing of rods and their ordering transition as a function of the packing fraction. In the model that we study, the centers of mass of the spherocylinders (situated at their geometric centers) are constrained to move on a spherical surface. The spherocylinders are free to rotate about any axis that passes through their respective centers of mass. We show that, up to moderate packing fractions, a two dimensional liquid crystalline phase is formed whose orientational ordering increases continuously with increasing density. This monolayer of orientationally ordered SRS particles at medium densities resembles a hedgehog-long axes of the SRS particles are aligned along the local normal to the sphere. At higher packing fractions, the system undergoes a transition to the solid phase, which is riddled with topological point defects (disclinations) and grain boundaries that divide the whole surface into several domains.
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Affiliation(s)
- Dharanish Rajendra
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bengaluru 560012, India.
| | - Jaydeep Mandal
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bengaluru 560012, India.
| | | | - Prabal K Maiti
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bengaluru 560012, India.
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Mirzad Rafael E, Corbett D, Cuetos A, Patti A. Self-assembly of freely-rotating polydisperse cuboids: unveiling the boundaries of the biaxial nematic phase. SOFT MATTER 2020; 16:5565-5570. [PMID: 32539067 DOI: 10.1039/d0sm00484g] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Colloidal cuboids have the potential to self-assemble into biaxial liquid crystal phases, which exhibit two independent optical axes. Over the last few decades, several theoretical works have predicted the existence of a wide region of the phase diagram where the biaxial nematic phase would be stable, but imposed rather strong constraints on the particle rotational degrees of freedom. In this work, we use molecular simulation to investigate the impact of size dispersity on the phase behaviour of freely-rotating hard cuboids, here modelled as self-dual-shaped nanoboards. This peculiar anisotropy, exactly in between the oblate and prolate geometry, has been proposed as the most appropriate to promote phase biaxiality. We observe that size dispersity radically changes the phase behaviour of monodisperse systems and leads to the formation of an elusive biaxial nematic phase, being found in a large region of the packing fraction vs. polydispersity phase diagram. Although our results confirm the tendencies reported in past experimental observations on colloidal dispersions of slightly prolate goethite particles, they cannot reproduce the direct isotropic-to-biaxial nematic phase transition observed in these experiments.
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Affiliation(s)
- Effran Mirzad Rafael
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL, UK.
| | - Daniel Corbett
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL, UK.
| | - Alejandro Cuetos
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Sevilla, Spain
| | - Alessandro Patti
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL, UK.
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Pappu LM, Martin-Palma R, Martín-Adrados B, Abdulhalim I. Voltage controlled scattering from porous silicon Mie-particles in liquid crystals. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2019.02.085] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Klopotek M, Hansen-Goos H, Dixit M, Schilling T, Schreiber F, Oettel M. Monolayers of hard rods on planar substrates. II. Growth. J Chem Phys 2017; 146:084903. [DOI: 10.1063/1.4976308] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- M. Klopotek
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, D–72076 Tübingen, Germany
| | - H. Hansen-Goos
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, D–72076 Tübingen, Germany
| | - M. Dixit
- Theory of Soft Condensed Matter, Physics and Materials Sciences Research Unit, Université du Luxembourg L-1511 Luxembourg, Luxembourg
| | - T. Schilling
- Theory of Soft Condensed Matter, Physics and Materials Sciences Research Unit, Université du Luxembourg L-1511 Luxembourg, Luxembourg
| | - F. Schreiber
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, D–72076 Tübingen, Germany
| | - M. Oettel
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, D–72076 Tübingen, Germany
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Martínez-Ratón Y, González-Pinto M, Velasco E. Biaxial nematic phase stability and demixing behaviour in monolayers of rod-plate mixtures. Phys Chem Chem Phys 2016; 18:24569-81. [PMID: 27539250 DOI: 10.1039/c6cp05022k] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We theoretically study the phase behaviour of monolayers of hard rod-plate mixtures using a fundamental-measure density functional in the restricted-orientation (Zwanzig) approximation. Particles can rotate in 3D but their centres of mass are constrained to be on a flat surface. In addition, we consider both species to be subject to an attractive potential proportional to the particle contact area on the surface and with adsorption strengths that depend on the species type. Particles have board-like shape, with sizes chosen using a symmetry criterion: same volume and same aspect ratio κ. Phase diagrams were calculated for κ = 10, 20 and 40 and different values of adsorption strengths. For small adsorption strengths the mixtures exhibit a second-order uniaxial nematic-biaxial nematic transition for molar fraction of rods 0 ≤x≲ 0.9. In the uniaxial nematic phase the particle axes of rods and plates are aligned perpendicular and parallel to the monolayer, respectively. At the transition, the orientational symmetry of the plate axes is broken, and they orient parallel to a director lying on the surface. For large and equal adsorption strengths the mixture demixes at low pressures into a uniaxial nematic phase, rich in plates, and a biaxial nematic phase, rich in rods. The demixing transition is located between two tricritical points. Also, at higher pressures and in the plate-rich part of the phase diagram, the system exhibits a strong first-order uniaxial nematic-biaxial nematic phase transition with a large density coexistence gap. When rod adsorption is considerably large while that of plates is small, the transition to the biaxial nematic phase is always of second order, and its region of stability in the phase diagram considerably widens. At very high pressures the mixture can effectively be identified as a two-dimensional mixture of squares and rectangles which again demixes above a certain critical point. We also studied the relative stability of uniform phases with respect to density modulations of smectic, columnar and crystalline symmetry.
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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.
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Oettel M, Klopotek M, Dixit M, Empting E, Schilling T, Hansen–Goos H. Monolayers of hard rods on planar substrates. I. Equilibrium. J Chem Phys 2016; 145:074902. [DOI: 10.1063/1.4960618] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- M. Oettel
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, D–72076 Tübingen, Germany
| | - M. Klopotek
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, D–72076 Tübingen, Germany
| | - M. Dixit
- Theory of Soft Condensed Matter, Physics and Materials Sciences Research Unit, Université du Luxembourg, L-1511 Luxembourg, Luxembourg
| | - E. Empting
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, D–72076 Tübingen, Germany
| | - T. Schilling
- Theory of Soft Condensed Matter, Physics and Materials Sciences Research Unit, Université du Luxembourg, L-1511 Luxembourg, Luxembourg
| | - H. Hansen–Goos
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, D–72076 Tübingen, Germany
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Varga S, Martínez-Ratón Y, Velasco E, Bautista-Carbajal G, Odriozola G. Effect of orientational restriction on monolayers of hard ellipsoids. Phys Chem Chem Phys 2016; 18:4547-56. [PMID: 26796794 DOI: 10.1039/c5cp05702g] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The effect of out-of-plane orientational freedom on the orientational ordering properties of a monolayer of hard ellipsoids is studied using the Parsons-Lee scaling approach and replica exchange Monte Carlo computer simulation. Prolate and oblate ellipsoids exhibit very different ordering properties, namely, the axes of revolution of prolate particles tend to lean out, while those of oblate ones prefer to lean into the confining plane. The driving mechanism of this is that the particles try to maximize the available free area on the confining surface, which can be achieved by minimizing the cross section areas of the particles with the plane. In the lack of out-of-plane orientational freedom the monolayer of prolate particles is identical to a two-dimensional hard ellipse system, which undergoes an isotropic-nematic ordering transition with increasing density. With gradually switching on the out-of-plane orientational freedom the prolate particles lean out from the confining plane and destabilisation of the in-plane isotropic-nematic phase transition is observed. The system of oblate particles behaves oppositely to that of prolates. It corresponds to a two-dimensional system of hard disks in the lack of out-of-plane freedom, while it behaves similar to that of hard ellipses in the freely rotating case. Solid phases can be realised by lower surface coverage due to the out-of-plane orientation freedom for both oblate and prolate shapes.
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Affiliation(s)
- Szabolcs Varga
- Institute of Physics and Mechatronics, University of Pannonia, PO Box 158, Veszprém, H-8201 Hungary
| | - 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 and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Gustavo Bautista-Carbajal
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México, Distrito Federal, Mexico and Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, 07160, México, D. F., Mexico
| | - Gerardo Odriozola
- Area de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, 02200 México, D. F., Mexico.
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González-Pinto M, Martínez-Ratón Y, Velasco E, Varga S. Effect of shape biaxiality on the phase behavior of colloidal liquid-crystal monolayers. Phys Chem Chem Phys 2015; 17:6389-400. [PMID: 25655742 DOI: 10.1039/c4cp04812a] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We extend our previous work on monolayers of uniaxial particles [J. Chem. Phys., 2014, 140, 204906] to study the effect of particle biaxiality on the phase behavior of liquid-crystal monolayers. Particles are modelled as board-like hard bodies with three different edge lengths σ1 ≥ σ2 ≥ σ3, and the restricted-orientation approximation (Zwanzig model) is used. A density-functional formalism based on the fundamental-measure theory is used to calculate phase diagrams for a wide range of values with the largest aspect ratio κ1 = σ1/σ3 ∈ [1,100]. We find that particle biaxiality in general destabilizes the biaxial nematic phase already present in monolayers of uniaxial particles. While plate-like particles exhibit strong biaxial ordering, rod-like ones with κ1 > 21.34 exhibit reentrant uniaxial and biaxial phases. As particle geometry is changed from uniaxial- to increasingly biaxial-rod-like, the region of biaxiality is reduced, eventually ending in a critical-end point. For κ1 > 60, a density gap opens up in which the biaxial nematic phase is stable for any particle biaxiality. Regions of the phase diagram, where packing-fraction inversion occurs (i.e. packing fraction is a decreasing function of density), are found. Our results are compared with the recent experimental studies on nematic phases of magnetic nanorods.
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Affiliation(s)
- Miguel González-Pinto
- Departamento de Física Teórica de la Materia Condensada, Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
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Mederos L, Velasco E, Martínez-Ratón Y. Hard-body models of bulk liquid crystals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:463101. [PMID: 25335432 DOI: 10.1088/0953-8984/26/46/463101] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Hard models of anisotropic particles give rise to complex phase diagrams, including uniaxial and biaxial nematic phases, discotic phases and spatially ordered phases such as smectic, columnar or crystal. Also, their mixtures exhibit additional interesting behaviours where demixing competes with orientational order. Here we review the different models of hard particles used in the theory of bulk anisotropic liquids, leaving aside interfacial properties and discuss the associated theoretical approaches and computer simulations, focusing on applications in equilibrium situations. The latter include one-component bulk fluids, mixtures and polydisperse fluids, both in two and three dimensions, and emphasis is put on liquid-crystal phase transitions and complex phase behaviour in general.
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Affiliation(s)
- Luis Mederos
- Instituto de Ciencia de Materiales de Madrid, CSIC, Sor Juana Inés de la Cruz, 3, E-28049 Madrid, Spain
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