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Birdi N, Wilding NB, Puri S, Banerjee V. Coarsening in bent-core liquid crystals: a molecular dynamics study. SOFT MATTER 2025. [PMID: 40364771 DOI: 10.1039/d4sm01460j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2025]
Abstract
We use molecular dynamics simulations to study coarsening dynamics in achiral banana-shaped bent-core liquid crystals following a quench from the high concentration polar smectic (SmX) phase to lower concentrations that favor the exotic twist-bend (TB) phase. Our novel result is the identification of an intermediate splay-bend state emerging prior to the eventual TB phase. The latter coarsens via the annihilation of beta lines which are analogous to string defects in nematic liquid crystals. Our findings are relevant for a large class of chiral systems assembled from achiral entities.
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Affiliation(s)
- Nishant Birdi
- School of Interdisciplinary Research, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India.
| | - Nigel B Wilding
- H.H. Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol BS8 1TL, UK.
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
| | - Varsha Banerjee
- School of Interdisciplinary Research, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India.
- Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India.
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2
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Yu H, Welch C, Mehl GH. Mapping the local ambidextrous chirality in thin films of N TB phase by circular dichroism spectra. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2025; 330:125682. [PMID: 39740582 DOI: 10.1016/j.saa.2024.125682] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2024] [Revised: 12/24/2024] [Accepted: 12/26/2024] [Indexed: 01/02/2025]
Abstract
Circular dichroism mapping (CDM) method was introduced by utilizing the highly collimated light beam of synchrotron radiation (SR) available at Diamond Light Source B23 beamline for scanning the thin films of the NTB phase. We apply SR-CDM to two achiral dimeric materials exhibiting the NTB phase: symmetric DTC5C9 and dissymmetric DTC5C9CB. The SR-CDM measurements directly capture the chiral information in the local NTB domains, providing the ultimate complement to the theoretical predictions of the helical structures: the spontaneous symmetry breaking in NTB phase is ambidextrous. The macroscopic chirality of the NTB phase is determined by the combination of doubly degenerate locally chiral domains in the illuminated area. Additionally, we investigate the temperature dependence, as well as the dynamic nature of the local chirality in the NTB phase by in-situ SR-CDM, confirming a chiral conversion influenced by the state of enantiomeric aggregation and a progressive unwinding of the helical structure in left-handed domains as the crystallization temperature is approached.
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Affiliation(s)
- Huanan Yu
- School of Materials and Chemistry, China Jiliang University, Hangzhou 310018, China.
| | - Chris Welch
- Department of Chemistry, University of Hull, Hull HU6 7RX, UK
| | - Georg H Mehl
- Department of Chemistry, University of Hull, Hull HU6 7RX, UK.
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3
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Vanakaras AG, Samulski ET, Photinos DJ. Entropy stabilized form chirality in curved rod nematics: structure and symmetries. SOFT MATTER 2025; 21:1341-1352. [PMID: 39847047 DOI: 10.1039/d4sm01229a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/24/2025]
Abstract
Monte Carlo molecular simulations of curve-shaped rods show the propensity of such shapes to polymorphism revealing both smectic and polar nematic phases. The nematic exhibits a nanoscale modulated local structure characterized by a unique, polar, C2-symmetry axis that tightly spirals generating a mirror-symmetry-breaking organization of the achiral rods-form chirality. A comprehensive characterization of the polarity and its symmetries in the nematic phase confirms that the nanoscale modulation is distinct from the elastic deformations of a uniaxial nematic director in the twist-bend nematic phase. Instead it is shown that, analogous to the isotropic-to-nematic transition, entropy stabilizes the roto-translating polar director in the polar-twisted nematic phase. The conflation of macroscale form chirality in ferroelectric nematics with that in the twist-bend nematic stems from the misattribution of the nanoscale modulation in the lower temperature nematic "NX phase" found in CB7CB dimers.
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Affiliation(s)
| | - Edward T Samulski
- Department of Chemistry and Applied Physical Sciences, University of North Carolina, Chapel Hill, NC 27599-3201, USA.
| | - Demetri J Photinos
- Department of Materials Science, University of Patras, 26504 Patras, Greece
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Fernández-Rico C, Dullens RPA. Liquid crystals from curved colloidal rods: waves, twists and more. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:094601. [PMID: 38996410 DOI: 10.1088/1361-6633/ad627b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Accepted: 07/12/2024] [Indexed: 07/14/2024]
Abstract
The curvature of elongated microscopic building blocks plays a crucial role on their self-assembly into orientationally ordered phases. While rod-like molecules form a handful of liquid crystal (LC) phases, curved or banana-shaped molecules show more than fifty phases, with fascinating physical properties, such as chirality or polarity. Despite the fundamental and technological importance of these so-called 'banana-shaped liquid crystals', little is known about their microscopic details at the single-molecule level. Curved colloidal liquid crystals-liquid crystals formed by curved colloidal rods-are excellent model systems to optically resolve the structure and dynamics of curved building blocks within these condensed phases. Recent advances in the synthesis of curved rod-like particles have unlocked the potential for studying-at the single-particle level-the intimate relationship between shape and phase symmetry, and even confirmed the stability of elusive LC phases. Further developments in this nascent field promise exciting findings, such as the first observation of the colloidal twist-bend nematic phase or the fabrication of functional materials with curvature-dependent properties. In this Report on Progress, we will highlight recent advances in the synthesis and assembly of curved colloidal liquid crystals and discuss the upcoming challenges and opportunities of this field.
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Affiliation(s)
| | - Roel P A Dullens
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
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Subert R, Campos-Villalobos G, Dijkstra M. Achiral hard bananas assemble double-twist skyrmions and blue phases. Nat Commun 2024; 15:6780. [PMID: 39117620 PMCID: PMC11310516 DOI: 10.1038/s41467-024-50935-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2024] [Accepted: 07/23/2024] [Indexed: 08/10/2024] Open
Abstract
Skyrmions are topologically protected, vortex-like structures found in various condensed-matter systems including helical ferromagnets and liquid crystals, typically arising from chiral interactions. Using extensive particle-based simulations, we demonstrate that non-chiral hard banana-shaped particles, governed solely by excluded-volume interactions, spontaneously stabilize skyrmion structures through the bend-flexoelectric effect. Under thin confinement, we observe the formation of quasi-2D layers of isolated skyrmions or dense skyrmion lattices. These structures, comprising a racemic mixture of left- and right-handed skyrmions, show resilience against thermal fluctuations while remaining responsive to external fields, offering intriguing possibilities for manipulation. We also find that the size of these skyrmions can be adjusted by the dimensions and curvature of the banana-shaped particles. In the absence of geometric frustration due to confinement, a blue phase III may emerge, characterized by a 3D network of chiral skyrmion filaments of the nematic director field within an isotropic background. Our findings provide valuable insights into stabilizing skyrmion lattices and blue phases, showcasing non-Gaussian fluid-like dynamics in systems of achiral hard particles. Furthermore, they highlight the remarkable capacity of these complex fluids in designing advanced functional materials with diverse applications in photonics and memory devices.
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Affiliation(s)
- Rodolfo Subert
- Soft Condensed Matter & Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands
| | - Gerardo Campos-Villalobos
- Soft Condensed Matter & Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter & Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands.
- International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, 1-3-1 Kagamiyama, 739-8526, Higashi-Hiroshima, Hiroshima, Japan.
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Kubala P, Cieśla M, Longa L. Splay-induced order in systems of hard tapers. Phys Rev E 2023; 108:054701. [PMID: 38115523 DOI: 10.1103/physreve.108.054701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2023] [Accepted: 10/12/2023] [Indexed: 12/21/2023]
Abstract
The main objective of this work is to clarify the role that taper-shaped elongated molecules, i.e., molecules with one end wider than the other, can play in stabilizing orientational order. The focus is exclusively on entropy-driven self-organization induced by purely excluded volume interactions. Drawing an analogy to RM734 (4-[(4-nitrophenoxy)carbonyl]phenyl-2,4-dimethoxybenzoate), which is known to stabilize ferroelectric nematic (N_{F}) and nematic splay (N_{S}) phases, and assuming that molecular biaxiality is of secondary importance, we consider monodisperse systems composed of hard molecules. Each molecule is modeled using six collinear tangent spheres with linearly decreasing diameters. Through hard-particle, constant-pressure Monte Carlo simulations, we study the emergent phases as functions of the ratio between the smallest and largest diameters of the spheres (denoted as d) and the packing fraction (η). To analyze global and local molecular orderings, we examine molecular configurations in terms of nematic, smectic, and hexatic order parameters. Additionally, we investigate the radial pair distribution function, polarization correlation function, and the histogram of angles between molecular axes. The last characteristic is utilized to quantify local splay. The findings reveal that splay-induced deformations drive unusual long-range orientational order at relatively high packing fractions (η>0.5), corresponding to crystalline phases. When η<0.5, only short-range order is affected, and in addition to the isotropic liquid, only the standard nematic and smectic-A liquid crystalline phases are stabilized. However, for η>0.5, apart from the ordinary nonpolar hexagonal crystal, three additional frustrated crystalline polar blue phases with long-range splay modulation are observed: antiferroelectric splay crystal (Cr_{S}P_{A}), antiferroelectric double-splay crystal (Cr_{DS}P_{A}), and ferroelectric double-splay crystal (Cr_{DS}P_{F}). Finally, we employ Onsager-Parsons-Lee local density functional theory to investigate whether any sterically induced (anti)ferroelectric nematic or smectic-A type of ordering is possible for our system, at least in a metastable regime.
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Affiliation(s)
- Piotr Kubala
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Michał Cieśla
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Lech Longa
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Łojasiewicza 11, 30-348 Kraków, Poland
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Kubala P, Cieśla M. Splay and polar order in a system of hard pear-like molecules: confrontation of Monte Carlo numerical simulations with density functional theory calculations. SOFT MATTER 2023; 19:7836-7845. [PMID: 37800190 DOI: 10.1039/d3sm01021j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/07/2023]
Abstract
Recent experimental discoveries of novel nematic types with polar order, including ferroelectric nematic and splay nematic, have brought the resurgence of the interest in polar and modulated phases. One of the most important factors that is widely believed to be crucial for the formation of new phases is the pear-like shape of mesogenic molecules. Such molecules were treated using second-virial density functional theory in [De Gregorio, P et al., Soft Matter, 2016, 12(23), 5188-5198], where the authors showed that the K11 splay elastic constant can become negative due to solely entropic reasons leading to long-range splay and polar correlations. To verify whether the predictions are correct, we performed Monte Carlo simulations of the same hard-core molecules used in the DFT study. As our results suggest, no polar or modulated liquid crystalline phases emerge; polar and splay correlations are either at most short-range or completely absent. On the other hand, a polar ferroelectric splay crystal was observed.
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Affiliation(s)
- Piotr Kubala
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Łojasiewicza 11, 30-348 Kraków, Poland.
| | - Michał Cieśla
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Łojasiewicza 11, 30-348 Kraków, Poland.
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8
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Kotni R, Grau-Carbonell A, Chiappini M, Dijkstra M, van Blaaderen A. Splay-bend nematic phases of bent colloidal silica rods induced by polydispersity. Nat Commun 2022; 13:7264. [DOI: 10.1038/s41467-022-34658-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 11/01/2022] [Indexed: 12/02/2022] Open
Abstract
AbstractLiquid crystal (LC) phases are in between solids and liquids with properties of both. Nematic LCs composed of rod-like molecules or particles exhibit long-range orientational order, yielding characteristic birefringence, but they lack positional order, allowing them to flow like a liquid. This combination of properties as well as their sensitivity to external fields make nematic LCs fundamental for optical applications e.g. liquid crystal displays (LCDs). When rod-like particles become bent, spontaneous bend deformations arise in the LC, leading to geometric frustration which can be resolved by complementary twist or splay deformations forming intriguing twist-bend (NTB) and splay-bend (NSB) nematic phases. Here, we show experimentally that the elusive NSB phases can be stabilized in systems of polydisperse micron-sized bent silica rods. Our results open avenues for the realization of NTB and NSB phases of colloidal and molecular LCs.
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Kubala P, Tomczyk W, Cieśla M. In silico study of liquid crystalline phases formed by bent-shaped molecules with excluded volume type interactions. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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10
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Yu G, Wilson MR. All-atom simulations of bent liquid crystal dimers: the twist-bend nematic phase and insights into conformational chirality. SOFT MATTER 2022; 18:3087-3096. [PMID: 35377382 DOI: 10.1039/d2sm00291d] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The liquid crystal dimer 1,7-bis-4-(4'-cyanobiphenyl)heptane (CB7CB) is known to exhibit a nematic-nematic phase transition, with the lower temperature phase identified as the twist-bend nematic (NTB) phase. Despite the achiral nature of the mesogen, the NTB phase demonstrates emergent chirality through the spontaneous formation of a helical structure. We present extensive molecular dynamics simulations of CB7CB using an all-atom force field. The NTB phase is observed in this model and, upon heating, shows phase transitions into the nematic (N) and isotropic phases. The simulated NTB phase returns a pitch of 8.35 nm and a conical tilt angle of 29°. Analysis of the bend angle between the mesogenic units reveals an average angle of 127°, which is invariant to the simulated phase. We have calculated distributions of the chirality order parameter, χ, for the ensemble of conformers in the NTB and N phases. These distributions elucidate that CB7CB is statistically achiral but can adopt chiral conformers with no preference for a specific handedness. Furthermore, there is no change in the extent of conformational chirality between the NTB and N phases. Using single-molecule stochastic dynamics simulations in the gas phase, we study the dimer series CBnCB (where n = 6, 7, 8 or 9) and CBX(CH2)5YCB (where X/Y = CH2, O or S) in terms of the bend angle and conformational chirality. We confirm that the bent molecular shape determines the ability of a dimer to exhibit the NTB phase rather than its potential to assume chiral conformers; as |χ|max increases with the spacer length, but the even-membered dimers have a linear shape in contrast to the bent nature of dimers with spacers of odd parity. For CBX(CH2)5YCB, it is found that |χ|max increases as the bend angle of the dimer decreases, while the flexibility of the dimers remains unchanged through the series.
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Affiliation(s)
- Gary Yu
- Department of Chemistry, Durham University, Lower Mountjoy, Stockton Road, Durham, UK.
| | - Mark Richard Wilson
- Department of Chemistry, Durham University, Lower Mountjoy, Stockton Road, Durham, UK.
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Anzivino C, van Roij R, Dijkstra M. Coupling between splay deformations and density modulations in splay-bend phases of bent colloidal rods. Phys Rev E 2022; 105:L022701. [PMID: 35291166 DOI: 10.1103/physreve.105.l022701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 02/01/2022] [Indexed: 06/14/2023]
Abstract
Using a grand-canonical Landau-de Gennes theory for colloidal suspensions of bent (banana-shaped) rods, we investigate how spatial deformations in the nematic director field affect the local density of twist-bend and splay-bend nematic phases. The grand-canonical character of the theory naturally relates the local density to the local nematic order parameter S. In the splay-bend phase, we find S and hence the local density to modulate periodically along one spatial direction. As a consequence the splay-bend phase has the key symmetries of a smectic rather than a nematic phase. By contrast we find that S and hence the local density do not vary in space in the twist-bend phase, which is therefore a proper nematic phase. The theoretically predicted one-dimensional density modulations in splay-bend phases are in agreement with recent simulations.
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Affiliation(s)
- Carmine Anzivino
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - René van Roij
- Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
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All Structures Great and Small: Nanoscale Modulations in Nematic Liquid Crystals. NANOMATERIALS 2021; 12:nano12010093. [PMID: 35010040 PMCID: PMC8746648 DOI: 10.3390/nano12010093] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Revised: 12/25/2021] [Accepted: 12/27/2021] [Indexed: 02/06/2023]
Abstract
The nature of the nanoscale structural organization in modulated nematic phases formed by molecules having a nonlinear molecular architecture is a central issue in contemporary liquid crystal research. Nevertheless, the elucidation of the molecular organization is incomplete and poorly understood. One attempt to explain nanoscale phenomena merely “shrinks down” established macroscopic continuum elasticity modeling. That explanation initially (and mistakenly) identified the low temperature nematic phase (NX), first observed in symmetric mesogenic dimers of the CB-n-CB series with an odd number of methylene spacers (n), as a twist–bend nematic (NTB). We show that the NX is unrelated to any of the elastic deformations (bend, splay, twist) stipulated by the continuum elasticity theory of nematics. Results from molecular theory and computer simulations are used to illuminate the local symmetry and physical origins of the nanoscale modulations in the NX phase, a spontaneously chiral and locally polar nematic. We emphasize and contrast the differences between the NX and theoretically conceivable nematics exhibiting spontaneous modulations of the elastic modes by presenting a coherent formulation of one-dimensionally modulated nematics based on the Frank–Oseen elasticity theory. The conditions for the appearance of nematic phases presenting true elastic modulations of the twist–bend, splay–bend, etc., combinations are discussed and shown to clearly exclude identifications with the nanoscale-modulated nematics observed experimentally, e.g., the NX phase. The latter modulation derives from packing constraints associated with nonlinear molecules—a chiral, locally-polar structural organization indicative of a new type of nematic phase.
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Ramírez González JP, Cinacchi G. Phase behavior of hard circular arcs. Phys Rev E 2021; 104:054604. [PMID: 34942798 DOI: 10.1103/physreve.104.054604] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Accepted: 10/12/2021] [Indexed: 01/26/2023]
Abstract
By using Monte Carlo numerical simulation, this work investigates the phase behavior of systems of hard infinitesimally thin circular arcs, from an aperture angle θ→0 to an aperture angle θ→2π, in the two-dimensional Euclidean space. Except in the isotropic phase at lower density and in the (quasi)nematic phase, in the other phases that form, including the isotropic phase at higher density, hard infinitesimally thin circular arcs autoassemble to form clusters. These clusters are either filamentous, for smaller values of θ, or roundish, for larger values of θ. Provided the density is sufficiently high, the filaments lengthen, merge, and straighten to finally produce a filamentary phase while the roundels compact and dispose themselves with their centers of mass at the sites of a triangular lattice to finally produce a cluster hexagonal phase.
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Affiliation(s)
- Juan Pedro Ramírez González
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain
| | - Giorgio Cinacchi
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC), Instituto de Ciencias de Materiales "Nicolás Cabrera", Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain
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