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Mehri S, Dyre JC, Ingebrigtsen TS. Hidden scale invariance in the Gay-Berne model. Phys Rev E 2022; 105:064703. [PMID: 35854604 DOI: 10.1103/physreve.105.064703] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 06/01/2022] [Indexed: 06/15/2023]
Abstract
This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity, where we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the mean-square displacement and the reduced-unit time-autocorrelation functions of the velocity, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph-invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the molecules and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation, in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.
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Affiliation(s)
- Saeed Mehri
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Trond S Ingebrigtsen
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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Kaur J, Deb D. Pressure-tensor method evaluation of the interfacial tension between Gay-Berne isotropic fluid and a smooth repulsive wall. SOFT MATTER 2021; 17:10566-10579. [PMID: 34779475 DOI: 10.1039/d1sm01293b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The interfacial properties of a confined thermotropic liquid crystalline material are investigated using a molecular dynamics simulation technique. The pairwise interaction among the soft ellipsoidal particles is modeled by the Gay-Berne (GB) potential. The GB ellipsoids are confined by two soft, smooth, repulsive walls defined by the Weeks-Chandler-Andersen (WCA) potential. The aperiodic confinement due to walls makes the system mechanically anisotropic. Hence using the pressure-tensor method, the interfacial tension of an interface between the bulk isotropic (I) phase and WCA wall at various number densities (ρ) is calculated. From the pressure tensor and orientational order profiles, the arrangement of ellipsoids in the bulk and the vicinity of the wall is determined. The effect of system size and the wall-particle interaction strength (εW) on is also analyzed by varying the system size and εW.
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Affiliation(s)
- Jagroop Kaur
- School of Physics and Materials Science, Thapar Institute of Engineering and Technology, Bhadson Road, Patiala, Punjab - 147004, India.
| | - Debabrata Deb
- School of Physics and Materials Science, Thapar Institute of Engineering and Technology, Bhadson Road, Patiala, Punjab - 147004, India.
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Lopes JT, Franco LF. A possible way to explicitly account for different molecular geometries with an equation of state. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.115676] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Velasco E, Mederos L. Anisotropic line tension of domains in lipid monolayers. Phys Rev E 2019; 100:032413. [PMID: 31639977 DOI: 10.1103/physreve.100.032413] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2019] [Indexed: 06/10/2023]
Abstract
We formulate a simple effective model to describe molecular interactions in a lipid monolayer and calculate the line tension between coexisting domains. The model represents lipid molecules in terms of two-dimensional anisotropic particles on the plane of the monolayer. These particles interact through forces that are believed to be relevant for the understanding of fundamental properties of the monolayer: van der Waals interactions originating from lipid chains and dipolar forces between dipole groups in the molecular heads. The model stresses the liquid-crystalline nature of the ordered phase in lipid monolayers and explains coexistence properties between ordered and disordered phases in terms of molecular parameters. Thermodynamic and interfacial properties of the model are analyzed using density-functional theory. In particular, the line tension at the interface between ordered and disordered phases turns out to be highly anisotropic with respect to the angle between the nematic director and the interface separating the coexisting phases. This important feature mainly results from the tilt angle of lipid chains and, to a lesser extent, from dipolar interactions perpendicular to the monolayer. The role of the two dipolar components, parallel and perpendicular to the monolayer, is assessed by comparing with computer simulation results for lipid monolayers.
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Affiliation(s)
- E Velasco
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC) and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - L Mederos
- Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, C/Sor Juana Inés de la Cruz, 3, E-28049 Madrid, Spain
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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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Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals. Polymers (Basel) 2013. [DOI: 10.3390/polym5020328] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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8
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Avazpour A, Avazpour L. Density functional theory of liquid crystals and surface anchoring: hard Gaussian overlap-sphere and hard Gaussian overlap-surface potentials. J Chem Phys 2010; 133:244701. [PMID: 21198002 DOI: 10.1063/1.3520148] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.
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Affiliation(s)
- A Avazpour
- Department of Physics, College of Science, Yasouj University, Yasouj 75919, Iran.
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Gurin P, Varga S. Orientational ordering of hard zigzag needles in one dimension. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041713. [PMID: 21230301 DOI: 10.1103/physreve.82.041713] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2010] [Indexed: 05/30/2023]
Abstract
The orientational ordering and the tilt angle behavior of a one-dimensional fluid of hard zigzag needles are examined by means of transfer matrix method and Onsager theory. The centers of mass of the particles are restricted to a line, while the orientational unit vectors are allowed to rotate freely in two dimensions. It is shown that zigzag needles do not undergo an isotropic-nematic phase transition, but the system is always in an orientationally ordered phase where the order parameter increases with the density. For hard needles and any other kinds of particles with an axis of symmetry the orientational distribution function is symmetric around its maximum value and the nematic director is perpendicular to the layer. For zigzag needles, which have nonconvex shape without an axis of symmetry, the orientational order is anisotropic around its maximum value and the nematic director is density dependent even at very high densities, i.e., the structure of one-dimensional fluid is always tilted. It is found that the density dependence of the tilted structure depends strongly on the shape of the zigzags. Surprisingly, the Onsager theory produces quite accurate results for the order parameters and tilt angles even in very dense systems.
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Affiliation(s)
- Péter Gurin
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém H-8201, Hungary
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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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11
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Houssa M, Rull LF, Romero-Enrique JM. Bilayered smectic phase polymorphism in the dipolar Gay–Berne liquid crystal model. J Chem Phys 2009; 130:154504. [DOI: 10.1063/1.3111953] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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12
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Teixeira PIC, Barmes F, Anquetil-Deck C, Cleaver DJ. Simulation and theory of hybrid aligned liquid crystal films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:011709. [PMID: 19257054 DOI: 10.1103/physreve.79.011709] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2008] [Indexed: 05/27/2023]
Abstract
We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.
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Affiliation(s)
- P I C Teixeira
- Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, P-1950-062 Lisbon, Portugal
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13
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Malijevský A, Jackson G, Varga S. Many-fluid Onsager density functional theories for orientational ordering in mixtures of anisotropic hard-body fluids. J Chem Phys 2008; 129:144504. [DOI: 10.1063/1.2982501] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
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14
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Tarazona P, Cuesta J, Martínez-Ratón Y. Density Functional Theories of Hard Particle Systems. THEORY AND SIMULATION OF HARD-SPHERE FLUIDS AND RELATED SYSTEMS 2008. [DOI: 10.1007/978-3-540-78767-9_7] [Citation(s) in RCA: 75] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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15
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De Miguel E, Blas FJ, Del Río EM. Molecular simulation of model liquid crystals in a strong aligning field. Mol Phys 2006. [DOI: 10.1080/00268970600893045] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Moradi M, Wheatley RJ, Avazpour A. Density functional theory of liquid crystals and surface anchoring. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:061706. [PMID: 16485963 DOI: 10.1103/physreve.72.061706] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2005] [Revised: 10/21/2005] [Indexed: 05/06/2023]
Abstract
This paper applies the density functional theory to confined liquid crystals comprising ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The restricted orientation model proposed by Rickayzen [Mol. Phys. 95, 393 (1998)] is extended to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the Percus-Yevick DCF for hard spheres; the anisotropy is introduced by means of the closest approach parameter. The average number density and orientational order parameter profiles of a HGO fluid confined in between planar walls are obtained using a hard needle-wall potential to represent the particle-wall interactions. For short and long needle lengths, the homeotropic and planar anchoring are observed, respectively. For the bulk isotropic phase the calculated density and order parameter profiles are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 69, 61705 (2004)]. However, for the bulk nematic phase the theory gives the correct density profile between the walls. The correct order parameters are obtained close to the walls whereas for the region in the middle of the walls, the agreement is less satisfactory.
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Affiliation(s)
- M Moradi
- Department of Physics, College of Science, Shiraz University, Shiraz 71454, Iran.
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17
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Mishra P, Ram J. Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2005; 17:345-51. [PMID: 16007371 DOI: 10.1140/epje/i2005-10014-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2005] [Accepted: 04/22/2005] [Indexed: 05/03/2023]
Abstract
We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 < or = x(0) < or = 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x(0) considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x(0). The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.
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Affiliation(s)
- Pankaj Mishra
- Department of Physics, Banaras Hindu University, Varanasi, India.
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18
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de Miguel E, Martín del Río E, Blas FJ. Stability of smectic phases in the Gay–Berne model. J Chem Phys 2004; 121:11183-94. [PMID: 15634073 DOI: 10.1063/1.1810472] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a detailed computer simulation study of the phase behavior of the Gay-Berne liquid crystal model with molecular anisotropy parameter kappa=4.4. According to previous investigations: (i) this model exhibits isotropic (I), smectic-A (Sm-A), and smectic-B (Sm-B) phases at low pressures, with an additional nematic (N) phase between the I and Sm-A phases at sufficiently high pressures; (ii) the range of stability of the Sm-A phase turns out to be essentially constant when varying the pressure, whereas other investigations seem to suggest a pressure-dependent Sm-A range; and (iii) the range of stability of the Sm-B phase remains unknown, as its stability with respect to the crystal phase has not been previously considered. The results reported here do show that the Sm-A phase is stable over a limited pressure range, and so it does not extend to arbitrarily low or high pressures. This is in keeping with previous investigations of the effect of molecular elongation on the phase behavior of Gay-Berne models. A detailed study of the melting transition at various pressures shows that the low-temperature crystalline phase melts into an isotropic liquid at very low pressures, and into a nematic liquid at very high pressures. At intermediate pressures, the crystal melts into a Sm-A liquid and no intermediate Sm-B phase is observed. On the basis of this and previous investigations, the reported Sm-B phase for Gay-Berne models appears to be a molecular solid rather than a smectic liquid phase.
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Affiliation(s)
- Enrique de Miguel
- Departamento de Física Aplicada, Facultad de Ciencias Experimentales, Universidad de Huelva, 21071 Huelva, Spain
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19
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Paci I, Dunford J, Cann NM. Role of achiral interactions on discrimination in racemates. J Chem Phys 2003. [DOI: 10.1063/1.1562609] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Tian P, Smith GD. A molecular-dynamics simulation study of the influence of attractive dispersion interactions on the phase behavior of rigid bead-necklace molecules. J Chem Phys 2002. [DOI: 10.1063/1.1475760] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Varga S, Szalai I, Liszi J, Jackson G. A study of orientational ordering in a fluid of dipolar Gay–Berne molecules using density-functional theory. J Chem Phys 2002. [DOI: 10.1063/1.1469607] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Coussaert T, Baus M. Density-functional theory of the columnar phase of discotic Gay–Berne molecules. J Chem Phys 2002. [DOI: 10.1063/1.1467340] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Tian P, Bedrov D, Smith GD, Glaser M. A molecular dynamics simulation study of the phase behavior of an ensemble of rigid bead-necklace molecules. J Chem Phys 2001. [DOI: 10.1063/1.1410380] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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TEIXEIRA PIC, CHRZANOWSKA A, WALL GD, CLEAVER DJ. Density functional theory of a Gay—Berne film between aligning walls. Mol Phys 2001. [DOI: 10.1080/00268970010017027] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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27
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Ginzburg VV, Singh C, Balazs AC. Theoretical Phase Diagrams of Polymer/Clay Composites: The Role of Grafted Organic Modifiers. Macromolecules 2000. [DOI: 10.1021/ma991324e] [Citation(s) in RCA: 164] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Valeriy V. Ginzburg
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh Pennsylvania 15261
| | - Chandralekha Singh
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh Pennsylvania 15261
| | - Anna C. Balazs
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh Pennsylvania 15261
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28
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Analytical solution of the Ornstein-Zernike equation with the mean spherical closure for a nematic phase. J Mol Liq 1999. [DOI: 10.1016/s0167-7322(99)00098-7] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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29
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Ginzburg VV, Balazs AC. Calculating Phase Diagrams of Polymer−Platelet Mixtures Using Density Functional Theory: Implications for Polymer/Clay Composites. Macromolecules 1999. [DOI: 10.1021/ma990135t] [Citation(s) in RCA: 107] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Valeriy V. Ginzburg
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
| | - Anna C. Balazs
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
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30
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TEIXEIRA PIC. A thermotropic nematic of slightly non-spherical molecules: generalized van der Waals theory. Mol Phys 1999. [DOI: 10.1080/00268979909483017] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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31
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Velasco E, Mederos L. A theory for the liquid-crystalline phase behavior of the Gay–Berne model. J Chem Phys 1998. [DOI: 10.1063/1.476804] [Citation(s) in RCA: 49] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Padilla P, Velasco E. The isotropic–nematic transition for the hard Gaussian overlap fluid: Testing the decoupling approximation. J Chem Phys 1997. [DOI: 10.1063/1.474075] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ginzburg VV, Glaser MA, Clark NA. A new potential for the description of intermolecular interactions for rigid biaxial molecules. Chem Phys 1997. [DOI: 10.1016/s0301-0104(96)00314-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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34
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de Miguel E, Martín del Rio E, Brown JT, Allen MP. Effect of the attractive interactions on the phase behavior of the Gay–Berne liquid crystal model. J Chem Phys 1996. [DOI: 10.1063/1.472292] [Citation(s) in RCA: 122] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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