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Campos-Villalobos G, Dijkstra M, Patti A. Nonconventional Phases of Colloidal Nanorods with a Soft Corona. PHYSICAL REVIEW LETTERS 2021; 126:158001. [PMID: 33929217 DOI: 10.1103/physrevlett.126.158001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Accepted: 03/11/2021] [Indexed: 06/12/2023]
Abstract
Using computer simulations, we investigate the phase behavior of hard-core spherocylinders with a length-to-diameter ratio L/σ=5 and coated by a soft deformable corona of length λ/σ=1.35. When quasi-two-dimensional layers are formed in smectic and solid phases at low temperatures, the competition between the two intrinsic length scales of the parallel aligned particles leads to the stabilization of different in-plane lattices of nonconventional symmetry, including low-density hexagonal, square, and high-density hexagonal crystals, as well as an intriguing dodecagonal quasicrystal. Our Letter opens up the opportunity to control the assembly of anisotropic nanoparticles into structures with preengineered symmetry-dependent physical properties.
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Affiliation(s)
- Gerardo Campos-Villalobos
- Department of Chemical Engineering and Analytical Science, University of Manchester, Sackville Street, Manchester M13 9PL, United Kingdom
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Department of Physics, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Department of Physics, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Alessandro Patti
- Department of Chemical Engineering and Analytical Science, University of Manchester, Sackville Street, Manchester M13 9PL, United Kingdom
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2
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Sastre F, Sotelo-Serna MG, Moreno-Hilario E, Benavides AL. Helmholtz free-energy high-temperature perturbation expansion for square-well and square-shoulder potentials. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1887527] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Francisco Sastre
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León de la Universidad de Guanajuato, León, Guanajuato, Mexico
| | | | | | - Ana Laura Benavides
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León de la Universidad de Guanajuato, León, Guanajuato, Mexico
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3
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Gámez F, Rodríguez-Almeida LF, Trejos VM. Thermodynamics of two-dimensional molecular fluids: Discrete perturbation theory and Monte Carlo simulations. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2019.112293] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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4
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Lopes JT, M. Franco LF. New Thermodynamic Approach for Nonspherical Molecules Based on a Perturbation Theory for Ellipsoids. Ind Eng Chem Res 2019. [DOI: 10.1021/acs.iecr.9b00766] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Joyce T. Lopes
- School of Chemical Engineering, University of Campinas, Av. Albert Einstein 500, 13083-852 Campinas, Brazil
| | - Luís F. M. Franco
- School of Chemical Engineering, University of Campinas, Av. Albert Einstein 500, 13083-852 Campinas, Brazil
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Sastre F, Moreno-Hilario E, Sotelo-Serna MG, Gil-Villegas A. Microcanonical-ensemble computer simulation of the high-temperature expansion coefficients of the Helmholtz free energy of a square-well fluid. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1392051] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Francisco Sastre
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León de la Universidad de Guanajuato, AP E-143, 37150, Leon, Mexico
| | - Elizabeth Moreno-Hilario
- División de Ciencias e Ingenierías, Campus León de la Universidad de Guanajuato, AP E-143, 37150, Leon, Mexico
| | | | - Alejandro Gil-Villegas
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León de la Universidad de Guanajuato, AP E-143, 37150, Leon, Mexico
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6
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7
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Oyarzún Rivera B, van Westen T, Vlugt TJH. Liquid-crystal phase equilibria of Lennard-Jones chains. Mol Phys 2016. [DOI: 10.1080/00268976.2015.1134824] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
| | - Thijs van Westen
- Process and Energy Laboratory, Delft University of Technology, Delft, The Netherlands
| | - Thijs J. H. Vlugt
- Process and Energy Laboratory, Delft University of Technology, Delft, The Netherlands
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8
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Wu L, Müller EA, Jackson G. Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF. Macromolecules 2014. [DOI: 10.1021/ma401230x] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Liang Wu
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Erich A. Müller
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - George Jackson
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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Wu L, Jackson G, Müller EA. Liquid crystal phase behaviour of attractive disc-like particles. Int J Mol Sci 2013; 14:16414-42. [PMID: 23965962 PMCID: PMC3759919 DOI: 10.3390/ijms140816414] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2013] [Revised: 07/24/2013] [Accepted: 07/25/2013] [Indexed: 11/17/2022] Open
Abstract
We employ a generalized van der Waals-Onsager perturbation theory to construct a free energy functional capable of describing the thermodynamic properties and orientational order of the isotropic and nematic phases of attractive disc particles. The model mesogen is a hard (purely repulsive) cylindrical disc particle decorated with an anisotropic square-well attractive potential placed at the centre of mass. Even for isotropic attractive interactions, the resulting overall inter-particle potential is anisotropic, due to the orientation-dependent excluded volume of the underlying hard core. An algebraic equation of state for attractive disc particles is developed by adopting the Onsager trial function to characterize the orientational order in the nematic phase. The theory is then used to represent the fluid-phase behaviour (vapour-liquid, isotropic-nematic, and nematic-nematic) of the oblate attractive particles for varying values of the molecular aspect ratio and parameters of the attractive potential. When compared to the phase diagram of their athermal analogues, it is seen that the addition of an attractive interaction facilitates the formation of orientationally-ordered phases. Most interestingly, for certain aspect ratios, a coexistence between two anisotropic nematic phases is exhibited by the attractive disc-like fluids.
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Affiliation(s)
- Liang Wu
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK; E-Mails: (L.W.); (G.J.)
| | - George Jackson
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK; E-Mails: (L.W.); (G.J.)
| | - Erich A. Müller
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK; E-Mails: (L.W.); (G.J.)
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Chapela GA, Díaz-Herrera E, Armas-Pérez JC, Quintana-H J. Effect of flexibility on liquid-vapor coexistence and surface properties of tangent linear vibrating square well chains in two and three dimensions. J Chem Phys 2013; 138:224509. [DOI: 10.1063/1.4807322] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Gámez F, Benavides AL. Perturbation theory for non-spherical fluids based on discretization of the interactions. J Chem Phys 2013; 138:124901. [DOI: 10.1063/1.4794783] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
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12
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Jiménez-Serratos G, Vega C, Gil-Villegas A. Evaluation of the pressure tensor and surface tension for molecular fluids with discontinuous potentials using the volume perturbation method. J Chem Phys 2012. [DOI: 10.1063/1.4767375] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Zheng YX, Yu YX, Li YF. An Equation of State for the Isotropic–Nematic Phase Transition of Semiflexible Polymers. Ind Eng Chem Res 2011. [DOI: 10.1021/ie102379h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Yuan-Xiang Zheng
- Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
| | - Yang-Xin Yu
- Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
| | - Ying-Feng Li
- Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
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Franco-Melgar M, Haslam AJ, Jackson G. Advances in generalised van der Waals approaches for the isotropic–nematic fluid phase equilibria of thermotropic liquid crystals–an algebraic equation of state for attractive anisotropic particles with the Onsager trial function. Mol Phys 2009. [DOI: 10.1080/00268970903352335] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Green MJ, Parra-Vasquez ANG, Behabtu N, Pasquali M. Modeling the phase behavior of polydisperse rigid rods with attractive interactions with applications to single-walled carbon nanotubes in superacids. J Chem Phys 2009; 131:084901. [DOI: 10.1063/1.3204024] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Varga S, Vesely FJ. A new generic model potential for mesogenic systems: Square well line potential of variable range. J Chem Phys 2009; 131:194506. [DOI: 10.1063/1.3264109] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Murat M, Kantor Y. Elasticity of a system with noncentral potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031124. [PMID: 17025611 DOI: 10.1103/physreve.74.031124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2006] [Indexed: 05/12/2023]
Abstract
We derive expressions for determination of the stress and the elastic constants in systems composed of particles interacting via noncentral two-body potentials as thermal averages of products of first and second partial derivatives of the interparticle potentials and components of the interparticle separation vectors. These results are adapted to hard potentials, where the stress and the elastic constants are expressed as thermal averages of the components of normals to contact surfaces between the particles and components of vectors separating their centers. The averages require knowledge of the simultaneous contact probabilities of two pairs of particles. We apply the expressions to particles for which a contact function can be defined, and demonstrate the feasibility of the method by computing the stress and the elastic constants of a two-dimensional system of hard ellipses using Monte Carlo simulations.
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Affiliation(s)
- Michael Murat
- School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
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del Río EM, de Miguel E. Smectic phase in a system of hard ellipsoids with isotropic attractive interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:051710. [PMID: 16089554 DOI: 10.1103/physreve.71.051710] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2005] [Indexed: 05/03/2023]
Abstract
The smectic phase is studied for a thermotropic fluid model consisting of aligned hard ellipsoids with superimposed square-well attractive interactions of variable range. The system is analyzed using a density functional theory in which the hard-core contributions to the free-energy functional are treated within a nonlocal weighted density approximation and the attractive contributions are considered at a mean-field level. In the absence of attractions the model reduces, under appropriate scaling, to a fluid of hard spheres and therefore does not exhibit smectic ordering. It is shown that above a certain value of the square-well range, smectic ordering is stable relative to the nematic state at densities well inside the fluid region. The nematic-smectic-A transition is found to be continuous at high temperatures and first order at low temperatures, these two regimes being separated by a tricritical point at an intermediate temperature. These predictions have been confirmed by computer simulation of the model fluid. The results highlight that smectic ordering can be stabilized by coupling anisotropic short-range repulsions with the isotropic contribution of the soft attractive interactions. By increasing the pressure, the range of stability of the smectic phase is seen to decrease. At sufficiently high pressure, the smectic phase is suppressed, and the solid phase dominates. Our calculations show that smectic ordering is no longer stable if the range of the attractions is made too long ranged.
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Affiliation(s)
- Elvira Martín del Río
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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20
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Martínez-Haya B, Cuetos A, Lago S. Solution of the Percus-Yevick equation for square well spherocylinders. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:051201. [PMID: 12786138 DOI: 10.1103/physreve.67.051201] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2002] [Revised: 01/13/2003] [Indexed: 05/24/2023]
Abstract
The Percus-Yevick equation for square-well spherocylinders has been numerically solved for some selected orientations following a methodology proposed previously for different fluids of elongated molecules. The equation is solved for particles of aspect ratios ranging from L/sigma=0.3 up to L/sigma=5.0, attractive range lambda/sigma=1.5, and packing fractions within eta=0.1-0.3. The resulting pair correlation functions are checked against isothermal-isobaric Monte Carlo simulations and good agreement is found for the short-range structure, at intermolecular distances within one molecular diameter sigma to contact for each of the selected orientations. At larger distances, the integral equation tends to overestimate the pair correlations. The results confirm the prediction of reference-system average Mayer-function perturbation theory for short aspect ratios, reaching the Onsager limit for the greater aspect ratios. Some instabilities of the solution for the longest models and higher densities are tentatively discussed in terms of their possible relation to frustration phenomena found in some polymer and complex systems.
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Affiliation(s)
- B Martínez-Haya
- Departamento de Ciencias Ambientales, Facultad de Ciencias Experimentales, Universidad Pablo de Olavide, Ctra. de Utrera Km 1, 41013 Seville, Spain.
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21
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McBride C, Vega C. A Monte Carlo study of the influence of molecular flexibility on the phase diagram of a fused hard sphere model. J Chem Phys 2002. [DOI: 10.1063/1.1517604] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Cuetos A, Martı́nez-Haya B, Rull LF, Lago S. Monte Carlo study of liquid crystal phases of hard and soft spherocylinders. J Chem Phys 2002. [DOI: 10.1063/1.1491872] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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MARTÍNEZ-HAYA B, RULL LF, CUETOS A, LAGO S. Gibbs ensemble simulation of the vapour-liquid equilibrium of square well spherocylinders. Mol Phys 2001. [DOI: 10.1080/00268970010018675] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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24
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GARCIA EDUARDO, WILLIAMSON DAVEC, MARTINEZ-RICHA ANTONIO. Effects of molecular geometry on liquid crystalline phase behaviour: isotropic-nematic transition. Mol Phys 2000. [DOI: 10.1080/00268970009483281] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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25
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Casey A, Harrowell P. Liquid crystal phase transitions in clusters of spherocylinders. J Chem Phys 2000. [DOI: 10.1063/1.480593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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26
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Williamson DC, Guevara Y. Deviation from Corresponding States for a Fluid of Square Well Spherocylinders. J Phys Chem B 1999. [DOI: 10.1021/jp990353o] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Dave C. Williamson
- Instituto de Física, Universidad de Guanajuato, Apdo Postal E-143, León, Guanajuato, 37150 México
| | - Yolanda Guevara
- Instituto de Física, Universidad de Guanajuato, Apdo Postal E-143, León, Guanajuato, 37150 México
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