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Melnyk R, Trokhymchuk A, Baumketner A. Excluded volume of the system of hard-core spheres revisited: New insights from computer simulations. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120672] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Gómez de Santiago M, Gurin P, Varga S, Odriozola G. Extended law of corresponding states: square-well oblates. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:104002. [PMID: 34874295 DOI: 10.1088/1361-648x/ac3fd8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2021] [Accepted: 12/03/2021] [Indexed: 06/13/2023]
Abstract
The vapour-liquid coexistence collapse in the reduced temperature,Tr=T/Tc, reduced density,ρr=ρ/ρc, plane is known as a principle of corresponding states, and Noro and Frenkel have extended it for pair potentials of variable range. Here, we provide a theoretical basis supporting this extension, and show that it can also be applied to short-range pair potentials where both repulsive and attractive parts can be anisotropic. We observe that the binodals of oblate hard ellipsoids for a given aspect ratio (κ= 1/3) with varying short-range square-well interactions collapse into a single master curve in theΔB2*-ρrplane, whereΔB2*=(B2(T)-B2(Tc))/v0,B2is the second virial coefficient, andv0is the volume of the hard body. This finding is confirmed by both REMC simulation and second virial perturbation theory for varying square-well shells, mimicking uniform, equator, and pole attractions. Our simulation results reveal that the extended law of corresponding states is not related to the local structure of the fluid.
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Affiliation(s)
- Miguel Gómez de Santiago
- Área de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, 02200 Ciudad de México, Mexico
| | - Péter Gurin
- Physics Department, Center for Natural Sciences, Faculty of Engineering, University of Pannonia, PO Box 158, Veszprém H-8201, Hungary
| | - Szabolcs Varga
- Physics Department, Center for Natural Sciences, Faculty of Engineering, University of Pannonia, PO Box 158, Veszprém H-8201, Hungary
| | - Gerardo Odriozola
- Área de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, 02200 Ciudad de México, Mexico
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Rickayzen G, Heyes DM. Isotropic-nematic phase transition of uniaxial variable softness prolate and oblate ellipsoids. J Chem Phys 2017; 146:164505. [PMID: 28456193 DOI: 10.1063/1.4981887] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Onsager's theory of the isotropic-nematic phase separation of rod shaped particles is generalized to include particle softness and attractions in the anisotropic interparticle force field. The procedure separates a scaled radial component from the angular integral part, the latter being treated in essentially the same way as in the original Onsager formulation. Building on previous treatments of more idealised hard-core particle models, this is a step toward representing more realistic rod-like systems and also allowing temperature (and in principle specific chemical factors) to be included at a coarse grained level in the theory. The focus of the study is on the coexisting concentrations and associated coexistence properties. Prolate and oblate ellipsoids are considered in both the small and very large aspect ratio limits. Approximations to the terms in the angular integrals derived assuming the very large (prolate) and very small (oblate) aspect ratios limits are compared with the formally exact treatment. The approximation for the second virial coefficient matches the exact solution for aspect ratios above about 20 for the prolate ellipsoids and less than ca. 0.05 for the oblate ellipsoids from the numerical evaluation of the angular integrals. The temperature dependence of the coexistence density could be used to help determine the interaction potential of two molecules. The method works at temperatures above a certain threshold temperature where the second virial coefficient is positive.
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Affiliation(s)
- G Rickayzen
- School of Physical Sciences, University of Kent, Canterbury, Kent CT2 7NH, United Kingdom
| | - D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 OEX, United Kingdom
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van Westen T, Oyarzún B, Vlugt TJH, Gross J. An analytical equation of state for describing isotropic-nematic phase equilibria of Lennard-Jones chain fluids with variable degree of molecular flexibility. J Chem Phys 2015; 142:244903. [DOI: 10.1063/1.4922921] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
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Varga S, Meneses-Júarez E, Odriozola G. Empty liquid phase of colloidal ellipsoids: The role of shape and interaction anisotropy. J Chem Phys 2014; 140:134905. [DOI: 10.1063/1.4869938] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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Martínez-Richa A. Determination of molecular size of O-(2-hydroxyethyl)cellulose (HEC) and its relationship to the mechanism of enzymatic hydrolysis by cellulases. Carbohydr Polym 2012. [DOI: 10.1016/j.carbpol.2011.10.039] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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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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Analysis of the experimental pressure–temperature behavior in the isotropic–nematic phase transition for p-azoxianisol by using different Convex Peg models. J Mol Liq 2009. [DOI: 10.1016/j.molliq.2009.06.011] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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12
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Franco-Melgar M, Haslam AJ, Jackson G. A generalisation of the Onsager trial-function approach: describing nematic liquid crystals with an algebraic equation of state. Mol Phys 2008. [DOI: 10.1080/00268970801926958] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Ibarra-Avalos N, Gil-Villegas A, Martinez Richa A. Excluded volume of hard cylinders of variable aspect ratio. MOLECULAR SIMULATION 2007. [DOI: 10.1080/08927020701191349] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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García-Sánchez E, Martínez-Richa A, Villegas-Gasca JA, Mendoza-Huizar LH, Gil-Villegas A. Predicting the Phase Diagram of a Liquid Crystal Using the Convex Peg Model and the Semiempirical PM3 Method. J Phys Chem A 2002. [DOI: 10.1021/jp021453o] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Eduardo García-Sánchez
- Facultad de Química, Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., 36050, México, Instituto de Física, Universidad de Guanajuato, Lomas del Bosque 103, León, Gto., 37150, México, and Molecular Engineering Program, Instituto Mexicano del Petróleo, México
| | - Antonio Martínez-Richa
- Facultad de Química, Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., 36050, México, Instituto de Física, Universidad de Guanajuato, Lomas del Bosque 103, León, Gto., 37150, México, and Molecular Engineering Program, Instituto Mexicano del Petróleo, México
| | - José Antonio Villegas-Gasca
- Facultad de Química, Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., 36050, México, Instituto de Física, Universidad de Guanajuato, Lomas del Bosque 103, León, Gto., 37150, México, and Molecular Engineering Program, Instituto Mexicano del Petróleo, México
| | - Luis Humberto Mendoza-Huizar
- Facultad de Química, Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., 36050, México, Instituto de Física, Universidad de Guanajuato, Lomas del Bosque 103, León, Gto., 37150, México, and Molecular Engineering Program, Instituto Mexicano del Petróleo, México
| | - Alejandro Gil-Villegas
- Facultad de Química, Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., 36050, México, Instituto de Física, Universidad de Guanajuato, Lomas del Bosque 103, León, Gto., 37150, México, and Molecular Engineering Program, Instituto Mexicano del Petróleo, México
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