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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 63, 1988 - Issue 4
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Original Articles

Phase equilibria by simulation in the Gibbs ensemble

Alternative derivation, generalization and application to mixture and membrane equilibria

, , &
Pages 527-545 | Received 09 Oct 1987, Accepted 29 Oct 1987, Published online: 26 Oct 2007

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Qu Chen, Mahinder Ramdin & Thijs J. H. Vlugt. (2023) Solubilities of CO2, CH4, C2H6, CO, H2, N2, N2O, and H2S in commercial physical solvents from Monte Carlo simulations. Molecular Simulation 49:13-14, pages 1341-1349.
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Niklas Mayr, Michael Haring & Thomas Wallek. (2023) Auto-calibration strategy for the equilibration phase of Gibbs ensemble Monte Carlo simulations. Molecular Simulation 49:11, pages 1143-1156.
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Tanawut Ploymeerusmee, Wolfhard Janke, Tawun Remsungnen, Supot Hannongbua & Tatiya Chokbunpiam. (2022) Porous material adsorbents ZIF-8, ZIF-67, Co/Zn-ZIF and MIL-127(Fe) for separation of H2S from a H2S/CH4 mixture. Molecular Simulation 48:5, pages 417-426.
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A. Rahbari, R. Hens, M. Ramdin, O. A. Moultos, D. Dubbeldam & T. J. H. Vlugt. (2021) Recent advances in the continuous fractional component Monte Carlo methodology. Molecular Simulation 47:10-11, pages 804-823.
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Matthew W. Thompson, Justin B. Gilmer, Ray A. Matsumoto, Co D. Quach, Parashara Shamaprasad, Alexander H. Yang, Christopher R. Iacovella, Clare McCabe & Peter T. Cummings. (2020) Towards molecular simulations that are transparent, reproducible, usable by others, and extensible (TRUE). Molecular Physics 118:9-10.
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Bina Kumari, Pradipta Bandyopadhyay & Subir K. Sarkar. (2020) Optimising the parameters of the Gibbs Ensemble Monte Carlo simulation of phase separation: the role of multiple relaxation times. Molecular Simulation 46:8, pages 616-626.
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Tyler R. Josephson, Ramanish Singh, Mona S. Minkara, Evgenii O. Fetisov & J. Ilja Siepmann. (2019) Partial molar properties from molecular simulation using multiple linear regression. Molecular Physics 117:23-24, pages 3589-3602.
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M. Ramdin, S. H. Jamali, T. M. Becker & T. J. H. Vlugt. (2018) Gibbs ensemble Monte Carlo simulations of multicomponent natural gas mixtures. Molecular Simulation 44:5, pages 377-383.
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Ali Poursaeidesfahani, Ahmadreza Rahbari, Ariana Torres-Knoop, David Dubbeldam & Thijs J. H. Vlugt. (2017) Computation of thermodynamic properties in the continuous fractional component Monte Carlo Gibbs ensemble. Molecular Simulation 43:3, pages 189-195.
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Van T. Nguyen, S. Johnathan Tan, D.D. Do & D. Nicholson. (2016) Application of kinetic Monte Carlo method to the vapour–liquid equilibria of associating fluids and their mixtures. Molecular Simulation 42:8, pages 642-654.
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Ahmad Kadoura, Amgad Salama & Shuyu Sun. (2016) Speeding up Monte Carlo molecular simulation by a non-conservative early rejection scheme. Molecular Simulation 42:3, pages 229-241.
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Ahmad Kadoura, Amgad Salama & Shuyu Sun. (2014) A conservative and a hybrid early rejection schemes for accelerating Monte Carlo molecular simulation. Molecular Physics 112:19, pages 2575-2586.
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Angel D. Cortés Morales, Ioannis G. Economou, Cornelis J. Peters & J. Ilja Siepmann. (2013) Influence of simulation protocols on the efficiency of Gibbs ensemble Monte Carlo simulations. Molecular Simulation 39:14-15, pages 1135-1142.
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David Dubbeldam, Ariana Torres-Knoop & Krista S. Walton. (2013) On the inner workings of Monte Carlo codes. Molecular Simulation 39:14-15, pages 1253-1292.
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Suren Moodley, Erik Johansson, Kim Bolton & Deresh Ramjugernath. (2010) Gibbs ensemble Monte Carlo simulations of binary vapour–liquid–liquid equilibrium: application to n-hexane–water and ethane–ethanol systems. Molecular Simulation 36:10, pages 758-762.
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Bernhard Eckl, Jadran Vrabec & Hans Hasse. (2008) An optimised molecular model for ammonia. Molecular Physics 106:8, pages 1039-1046.
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A. Hannemann , J.C. Schön & M. Jansen. (2008) Thermodynamic stability of solid and fluid phases in the Si3B3N7 system. Philosophical Magazine 88:7, pages 1037-1057.
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Ali Kh. Al-Matar, Ahmed H. Tobgy & Ibrahim A. Suleiman. (2008) The phase diagram of the Lennard-Jones fluid using temperature dependent interaction parameters. Molecular Simulation 34:3, pages 289-294.
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C. Heath Turner, John K. Brennan, Martin Lísal, William R. Smith, J. Karl Johnson & Keith E. Gubbins. (2008) Simulation of chemical reaction equilibria by the reaction ensemble Monte Carlo method: a review†. Molecular Simulation 34:2, pages 119-146.
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Y. Houndonougbo, K. Kuczera, B. Subramaniam & B.B. Laird. (2007) Prediction of phase equilibria and transport properties in carbon-dioxide expanded solvents by molecular simulation. Molecular Simulation 33:9-10, pages 861-869.
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R. R. Kotdawala, A. Ozgur Yazaydin, N. Kazantzis & R. W. Thompson. (2007) A molecular simulation approach to the study of adsorption of hydrogen cyanide and methyl ethyl ketone in silicalite, mordenite and zeolite beta structures. Molecular Simulation 33:9-10, pages 843-850.
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Shihai Yan, Sang Joo Lee, Sunwoo Kang & Jin Yong Lee. (2007) Computational Approaches in Molecular Recognition, Self-assembly, Electron Transport, and Surface Chemistry. Supramolecular Chemistry 19:4-5, pages 229-241.
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M. J. McGrath, J. I. Siepmann, I.-F. W. Kuo & C. J. Mundy. (2007) Spatial correlation of dipole fluctuations in liquid water. Molecular Physics 105:10, pages 1411-1417.
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M. J. McGrath, J. I. Siepmann, I.-F. W. Kuo & C. J. Mundy. (2006) Vapor–liquid equilibria of water from first principles: comparison of density functionals and basis sets. Molecular Physics 104:22-24, pages 3619-3626.
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G. R. Birkett & D. D. Do. (2006) Simulation study of methanol and ethanol adsorption on graphitized carbon black. Molecular Simulation 32:10-11, pages 887-899.
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Marcus G. Martin & Amalie L. Frischknecht. (2006) Using arbitrary trial distributions to improve intramolecular sampling in configurational-bias Monte Carlo. Molecular Physics 104:15, pages 2439-2456.
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A. O. Yazaydin & R. W. Thompson. (2006) Simulating the vapour–liquid equilibria of 1,4-dioxane. Molecular Simulation 32:8, pages 657-662.
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M.B. Sweatman, N. Quirke, W. Zhu & F. Kapteijn. (2006) Analysis of gas adsorption in Kureha active carbon based on the slit–pore model and Monte-Carlo simulations. Molecular Simulation 32:7, pages 513-522.
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J. K. Brennan*. (2005) Cavity-bias sampling in reaction ensemble Monte Carlo simulations. Molecular Physics 103:19, pages 2647-2654.
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M. B. Sweatman & N. Quirke. (2005) Modelling gas mixture adsorption in active carbons. Molecular Simulation 31:9, pages 667-681.
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Jun-Seok Lee, Collin D. Wick, John M. Stubbs & J. Ilja Siepmann . (2005) Simulating the vapour–liquid equilibria of large cyclic alkanes. Molecular Physics 103:1, pages 99-104.
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Tatsuhiko Miyata*Akira Endo, Takuji Yamamoto, Takao Ohmori, Takaji Akiya & Masaru Nakaiwa. (2004) Gibbs Ensemble Monte Carlo Simulation of LJ Fluid in Cylindrical Pore with Energetically Heterogeneous Surface. Molecular Simulation 30:6, pages 353-359.
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M.B. Sweatman & N. Quirke. (2004) Simulating Fluid–Solid Equilibrium with the Gibbs Ensemble. Molecular Simulation 30:1, pages 23-28.
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TAMÁS KRISTÓF, DEZSŐ BODA, JÁNOS LISZI, DOUGLAS HENDERSON & ERIC CARLSON. (2003) Vapour-liquid equilibrium of the charged Yukawa fluid from Gibbs ensemble Monte Carlo simulations and the mean spherical approximation. Molecular Physics 101:11, pages 1611-1616.
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Javier Carrero-Mantilla & Mario Llano-Restrepo. (2003) Boolean Scheme for Programming Trial Moves That Involve Molecule Insertion and Removal in Monte Carlo Simulation. Molecular Simulation 29:1, pages 23-28.
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TAMÁS KRISTÓF, JÁNOS LISZI & DEZSŐ BODA. (2002) The extrapolation of phase equilibrium curves of mixtures in the isobaric—isothermal Gibbs ensemble. Molecular Physics 100:21, pages 3429-3441.
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K. LEONHARD & U.K. DEITERS. (2002) Monte Carlo simulations of nitrogen using an ab initio potential. Molecular Physics 100:15, pages 2571-2585.
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DEZSŐ BODA, TAMÁS KRISTÓF, JÁNOS LISZI & ISTVÁN SZALAI. (2002) The extrapolation of the vapour—liquid equilibrium curves of pure fluids in the isothermal Gibbs ensemble. Molecular Physics 100:12, pages 1989-2000.
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DEZSÖ BODA, TAMÁS KRISTÓF, JÁNOS LISZI & ISTVÁN SZALAI. (2001) A new simulation method for the determination of phase equilibria in mixtures in the grand canonical ensemble. Molecular Physics 99:24, pages 2011-2022.
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M.B. Sweatman & N. Quirke. (2001) Modelling Gas Adsorption in Slit-Pores Using Monte Carlo Simulation. Molecular Simulation 27:5-6, pages 295-321.
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PAWEŁ BRYK, ANDRZEJ PATRYKIEJEW & STEFAN SOKOŁOWSKI. (2001) Polydisperse fluid in contact with a semipermeable membrane. Molecular Physics 99:20, pages 1709-1717.
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JÉRÔME DELHOMMELLE, PHILIPPE MILLIÉ & ALAINH. FUCHS. (2000) On the role of the definition of potential models in Gibbs ensemble phase equilibria simulations of the H2S-pentane mixture. Molecular Physics 98:22, pages 1895-1905.
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K. Oder & S. Murad. (2000) Molecular Simulations of Membrane Based Separations of Supercritical Electrolyte Solutions. Molecular Simulation 25:3-4, pages 229-238.
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T. KRISTÓF, J. VORHOLZ, J. LISZI, B. RUMPF & G. MAURER. (1999) A simple effective pair potential for the molecular simulation of the thermodynamic properties of ammonia. Molecular Physics 97:10, pages 1129-1137.
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J.J. POTOFF, J.R. ERRINGTON & A.Z. PANAGIOTOPOULOS. (1999) Molecular simulation of phase equilibria for mixtures of polar and non-polar components. Molecular Physics 97:10, pages 1073-1083.
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ERICM. YEZDIMER & PETERT. CUMMINGS. (1999) Calculation of the vapour-liquid coexistence curve for a fluctuating point charge water model. Molecular Physics 97:8, pages 993-996.
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SIMONC. MCGROTHER & KEITHE. GUBBINS. (1999) Constant pressure Gibbs ensemble Monte Carlo simulations of adsorption into narrow pores. Molecular Physics 97:8, pages 955-965.
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B. NEUBAUER, A. BOUTIN, B. TAVITIAN & A.H. FUCHS. (1999) Gibbs ensemble simulations of vapour—liquid phase equilibria of cyclic alkanes. Molecular Physics 97:6, pages 769-776.
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A. MULERO, C.A. FAÚNDEZ & F. CUADROS. (1999) Chemical potential for simple fluids from equations of state. Molecular Physics 97:3, pages 453-462.
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Jérôme Delhommelle, Anne Boutin & AlainH. Fuchs. (1999) Molecular Simulation of Vapour-Liquid Coexistence Curves for Hydrogen Sulfide-Alkane and Carbon Dioxide-Alkane Mixtures. Molecular Simulation 22:6, pages 351-368.
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J.N.CANONGIA LOPES. (1999) Phase equilibra in binary Lennard-Jones mixtures: phase diagram simulation. Molecular Physics 96:11, pages 1649-1658.
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JÉRÔME DELHOMMELLE, ANNE BOUTIN, BERNARD TAVITIAN, ALLAND. MACKIE & ALAINH. FUCHS. (1999) Vapour-liquid coexistence curves of the united-atom and anisotropic united-atom force fields for alkane mixtures. Molecular Physics 96:10, pages 1517-1524.
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A. AMADEI, M. E. F. APOL, G. CHILLEMI, H. J. C. BERENDSEN & A. DI NOLA. (1999) Derivation of a general fluid equation of state based on the quasi-Gaussian entropy theory: application to the Lennard-Jones fluid. Molecular Physics 96:10, pages 1469-1490.
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GEORGIOSC. BOULOUGOURIS, IOANNISG. ECONOMOU & DOROSN. THEODOROU. (1999) On the calculation of the chemical potential using the particle deletion scheme. Molecular Physics 96:6, pages 905-913.
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TAMAS KRISTOF JANOS LISZI. (1998) Alternative Gibbs ensemble Monte Carlo implementations: application in mixtures. Molecular Physics 94:3, pages 519-525.
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F. Cuadros, W. Okrasinski & M. Sànchez-Sànchez. (1998) Modelling of 3D Radial Distribution Functions with the Program Mathematica. Molecular Simulation 20:4, pages 223-237.
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AMPARO GALINDO LOWRI A. DAVIES ALEJANDRO GIL-VILLEGAS GEORGE JACKSON. (1998) The thermodynamics of mixtures and the corresponding mixing rules in the SAFT-VR approach for potentials of variable range. Molecular Physics 93:2, pages 241-252.
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PAWEL BRYK WIESLAWA CYRANKIEWICZ & MALGORZATA BOROWKO STEFAN SOKOLOWSKI. (1998) A fluid in contact with a semipermeable membrane: density functional approach. Molecular Physics 93:1, pages 111-116.
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S. C. Potter, D. J. Tildesley, A.N. Burgess & S. C. Rogers. (1997) A transferable potential model for the liquid-vapour equilibria of fluoromethanes. Molecular Physics 92:5, pages 825-834.
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By DEZSO BODA, KWONG-YU CHAN & ISTVAN SZALAI. (1997) Determination of vapour-liquid equilibrium using cavity-biased grand canonical Monte Carlo method. Molecular Physics 92:6, pages 1067-1072.
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By SEIJI HIGASHI and AKIRA TAKADA. (1997) Molecular dynamics study of liquid CH2 F2 (HFC-32). Molecular Physics 92:4, pages 641-650.
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J. N. CANONGIA LOPES & D. J. TILDESLEY. (1997) Multiphase equilibria using the Gibbs ensemble Monte Carlo method. Molecular Physics 92:2, pages 187-196.
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Francisco Cuadros, Wojciech Okrasinski & Waldo Ahumada. (1997) Fits of the Thermodynamic Phase Plane. Molecular Simulation 19:2, pages 131-137.
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By S. MURAD & R. MADHUSUDAN and J. G. POWLES. (1997) A molecular simulation to investigate the possibility of electro-osmosis in non-ionic solutions with uniform electric fields. Molecular Physics 90:4, pages 671-674.
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By J. G. POWLES, B. HOLTZ & W. A. B. EVANS. (1997) Can osmotic pressure be negative?. Molecular Physics 90:4, pages 665-670.
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ANPING LIU. (1996) Calculation of chemical potentials of mixtures from computer simulations. Molecular Physics 89:6, pages 1651-1658.
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PETER BEREOLOS, JULIAN TALBOT & KWANG-CHU CHAO. (1996) Simulation of free energy without particle insertion in the NPT ensemble. Molecular Physics 89:6, pages 1621-1631.
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Y. C. KONG. (1996) Monte Carlo simulations of a polyoxyethylene C12E2 lamellar bilayer in water. Molecular Physics 89:3, pages 835-865.
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Martin Lísal & Václav Vacek. (1996) Direct Evaluation of Vapour-Liquid Equilibria of Mixtures by Molecular Dynamics Using Gibbs-Duhem Integration. Molecular Simulation 18:1-2, pages 75-99.
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PHILIPJ. CAMP & MICHAELP. ALLEN. (1996) Phase coexistence in a pseudo Gibbs ensemble. Molecular Physics 88:6, pages 1459-1469.
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F. Cuadros, W. Okrasinski, W. Ahumada & A. Mulero. (1996) Accurate vapour-liquid equilibrium calculations of simple fluids. Phase Transitions 57:4, pages 183-198.
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FredericoW. Tavares & StanleyI. Sandler. (1996) Vapour-liquid equilibria of exponential-six fluids. Molecular Physics 87:6, pages 1471-1476.
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András Baranyai & PeterT. Cummings. (1996) On the Molecular Dynamics Algorithm for Gibbs Ensemble Simulation. Molecular Simulation 17:1, pages 21-25.
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Dezső Boda, Jochen Winkelmann, János Liszi & István Szalai. (1996) Vapour-liquid equilibrium of Stockmayer fluids in applied field. Molecular Physics 87:3, pages 601-624.
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N. Quirke. (1996) Some Recent Developments in Computational Chemistry. Molecular Simulation 16:1-3, pages 193-208.
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S. Murad, J.G. Powles & B. Holtz. (1995) Osmosis and reverse osmosis in solutions: Monte Carlo simulations and van der Waals one-fluid theory. Molecular Physics 86:6, pages 1473-1483.
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Shaoyi Jiang & KeithE. Gubbins. (1995) Vapour-liquid equilibria in two-dimensional Lennard-Jones fluids: unperturbed and substrate-mediated films. Molecular Physics 86:4, pages 599-612.
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L.D.J.C. Loyens, B. Smit & K. Esselink. (1995) Parallel Gibbs-ensemble simulations. Molecular Physics 86:2, pages 171-183.
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F. Cuadros, A. Mulero, J. Cachadiña & W. Ahumada. (1995) A new procedure for determining Lennard-Jones interaction parameters. International Reviews in Physical Chemistry 14:2, pages 205-213.
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LuisF. Rull, George Jackson & Berend Smit. (1995) The condition of microscopic reversibility in Gibbs ensemble Monte Carlo simulations of phase equilibria. Molecular Physics 85:3, pages 435-447.
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Dezsö Boda, János Liszi & István Szalai. (1995) Dielectric constant of a Stockmayer fluid along the vapour-liquid coexistence curve. Molecular Physics 85:3, pages 429-434.
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Rupal Agrawal & DavidA. Kofke. (1995) Thermodynamic and structural properties of model systems at solid-fluid coexistence. Molecular Physics 85:1, pages 43-59.
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W.T. Góźdź, K.E. Gubbins & A.Z. Panagiotopoulos. (1995) Liquid-liquid phase transitions in pores. Molecular Physics 84:5, pages 825-834.
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Anping Liu & Rakesh Govind. (1994) Molecular dynamics simulation of the chemical potentials of mixtures. Molecular Physics 83:4, pages 779-787.
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RichardL. Rowley, TimothyD. Shupe & MatthewW. Schuck. (1994) A direct method for determination of chemical potential with molecular dynamics simulations. Molecular Physics 82:5, pages 841-855.
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V. Paul Gregory & JohnC. Schug. (1994) NPT Monte Carlo calculation of isotherms for the Lennard-Jones fluid. Molecular Physics 82:4, pages 677-688.
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G. Galassi & D.J. Tildesley. (1994) Phase Diagrams of Diatomic Molecules Using the Gibbs Ensemble Monte Carlo Method. Molecular Simulation 13:1, pages 11-24.
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J. Karl Johnson, AthanassiosZ. Panagiotopoulos & KeithE. Gubbins. (1994) Reactive canonical Monte Carlo. Molecular Physics 81:3, pages 717-733.
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H.W. Graben & JohnR. Ray. (1993) Eight physical systems of thermodynamics, statistical mechanics, and computer simulations. Molecular Physics 80:5, pages 1183-1193.
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Mihaly Mezei. (1993) The Effect of the Combined Volume on the Efficiency of Gibbs Ensemble Simulations. Molecular Simulation 11:6, pages 395-397.
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GirijaS. Dubey, SeamusF. O'Shea & PeterA. Monson. (1993) Vapour-liquid equilibria for two centre Lennard-Jones diatomics and dipolar diatomics. Molecular Physics 80:4, pages 997-1007.
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J.R. Recht & A.Z. Panagiotopoulos. (1993) Finite-size effects and approach to criticality in Gibbs ensemble simulations. Molecular Physics 80:4, pages 843-852.
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Manoj Mehta & DavidA. Kofke. (1993) Implementation of the Gibbs ensemble using a thermodynamic model for one of the coexisting phases. Molecular Physics 79:1, pages 39-52.
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J. Karl Johnson, JohnA. Zollweg & KeithE. Gubbins. (1993) The Lennard-Jones equation of state revisited. Molecular Physics 78:3, pages 591-618.
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V. Paul Gregory & JohnC. Schug. (1993) Clustering of lennard-jones particles below the critical temperature. Molecular Physics 78:2, pages 407-420.
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M.E. Van Leeuwen, B. Smit & E.M. Hendriks. (1993) Vapour-liquid equilibria of stockmayer fluids. Molecular Physics 78:2, pages 271-283.
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J. Karl Johnson & KeithE. Gubbins. (1992) Phase equilibria for associating Lennard-Jones fluids from theory and simulation. Molecular Physics 77:6, pages 1033-1053.
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B. Smith, T. Hauschild & J.M. Prausnitz. (1992) Effect of a density-dependent potential on the phase behaviour of fluids. Molecular Physics 77:6, pages 1021-1031.
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Amal Lotfi, Jadran Vrabec & Johann Fischer. (1992) Vapour liquid equilibria of the Lennard-Jones fluid from the NpT plus test particle method. Molecular Physics 76:6, pages 1319-1333.
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AthanassiosZ. Panagiotopoulos. (1992) Direct Determination of Fluid Phase Equilibria by Simulation in the Gibbs Ensemble: A Review. Molecular Simulation 9:1, pages 1-23.
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D.M. Tsangaris & P.D. McMahon. (1992) Gibbs Ensemble Calculations with an Equation of State: An Application to Vapor-Liquid Equilibria. Molecular Simulation 9:3, pages 223-238.
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Toru Nishimura & Koichiro Nakanishi. (1992) Calculation of Vapour-Liquid Equilibria of Lennard-Jones Binary Systems by the Gibbs Ensemble Monte Carlo Simulation. Molecular Simulation 8:3-5, pages 297-304.
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Fokion Karavias & AlanL. Myers. (1991) Monte Carlo Simulation of Binary Gas Adsorption in Zeolite Cavities. Molecular Simulation 8:1-2, pages 51-72.
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B. Smit & D. Frenkel. (1991) Vapour-liquid equilibria of the hard core Yukawa fluid. Molecular Physics 74:1, pages 35-39.
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D.M. Tsangaris & P.D. McMahon. (1991) A Modified Gibbs Ensemble Method for Calculating Fluid Phase Equilibria. Molecular Simulation 7:1-2, pages 97-103.
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Enrique de Miguel, LuisF. Rull, ManojK. Chalam & KeithE. Gubbins. (1990) Liquid-vapour coexistence of the Gay-Berne fluid by Gibbs-ensemble simulation. Molecular Physics 71:6, pages 1223-1231.
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B. Smit & D. Frenkel. (1989) Calculation of the chemical potential in the Gibbs ensemble. Molecular Physics 68:4, pages 951-958.
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B. Smit, Ph. De Smedt & D. Frenkel. (1989) Computer simulations in the Gibbs ensemble. Molecular Physics 68:4, pages 931-950.
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B. Smit, C.P. Williams, E.M. Hendriks & S.W.De Leeuw. (1989) Vapour-liquid equilibria for Stockmayer fluids. Molecular Physics 68:3, pages 765-769.
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GrantS. Heffelfinger, Ziming Tan, KeithE. Gubbins, Umberto Marini Bettolo Marconi & Frank Van Swol. (1989) Lennard-Jones Mixtures in a Cylindrical Pore. A Comparison of Simulation and Density Functional Theory. Molecular Simulation 2:4-6, pages 393-411.
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KeithE. Gubbins. (1989) The Role of Computer Simulation in Studying Fluid Phase Equilibria. Molecular Simulation 2:4-6, pages 223-252.
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M.R. Stapleton, D.J. Tildesley, Z. Panagiotopoulos & N. Quirke. (1989) Phase Equilibria of Quadrupolar Fluids by Simulation in the Gibbs Ensemble. Molecular Simulation 2:3, pages 147-162.
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