Methods for examining phase equilibria

Springer Series in Chemical Physics

Volumn 86, Issue , 2007, Pages 353-387

  Shell, M Scott ^a   Panagiotopoulos, Athanassios ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 62849116253     PISSN: 01726218     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-38448-9_10     Document Type: Review

References (117)

1. Frenkel, D.; Smit, B., Understanding Molecular Simulation, (2nd edition) Academic: San Diego, 2002
2. Binder, K., Applications of Monte Carlo methods to statistical physics, Rep. Prog. Phys. 1997, 60, 487-559
3. Deem, M. W., Recent contributions of statistical mechanics in chemical engineering, AIChE J. 1998, 44, 2569-2596
4. Siepmann, J. I., Monte Carlo methods for simulating phase equilibria of complex fluids, Monte Carlo Methods Chem. Phys. 1999, 105, 443-460
5. de Pablo, J. J.; Yan, Q.; Escobedo, F. A., Simulation of phase transitions in fluids, Ann. Rev. Phys. Chem. 1999, 50, 377-412
6. Panagiotopoulos, A. Z., Monte Carlo methods for phase equilibria of fluids, J. Phys.: Condens. Matt. 2000, 12, R25-R52
7. Widom, B., Some topics in the theory of fluids, J. Chem. Phys. 1963, 39, 2808-2817
8. Möller, D.; Fischer, J., Vapour liquid equilibrium of a pure fluid from test particle method in combination with npt molecular dynamics simulations, Mol. Phys. 1990, 69, 463-473
9. Lotfi, A.; Vrabec, J.; Fischer, J., Vapour liquid equilibria of the Lennard-Jones fluid from the NPT plus test particle method, Mol. Phys. 1992, 76, 1319-1333
10. Kofke, D. A; Cummings, P. T., Quantitative comparison and optimization of methods for evaluating the chemical potential by molecular simulation, Mol. Phys. 1997, 92, 973-996
11. Boda, D.; Liszi, J.; Szalai, I., An extension of the NPT plus test particle method for the determination of the vapour-liquid equilibria of pure fluids, Chem. Phys. Lett. 1995, 235, 140-145
12. Vrabec, J.; Fischer, J., Vapour liquid equilibria of mixtures from the NPT plus test particle method, Mol. Phys. 1995, 85, 781-792
13. Vrabec, J.; Lotfi, A.; Fischer, J., Vapour liquid equilibria of Lennard-Jones model mixtures from the NPT plus test particle method, Fluid Phase Equil. 1995, 112, 173-197
14. Spyriouni, T.; Economou, I. G.; Theodorou, D. N., Vapour liquid equilibria of Lennard-Jones model mixtures from the NPT plus test particle method, Phys. Rev. Lett. 1998, 80, 4466
15. Spyriouni, T.; Economou, I. G.; Theodorou, D. N., Phase equilibria of mixtures containing chain molecules predicted through a novel simulation scheme, Macromolecules 1998, 31, 1430-1431
16. Kumar, S. K.; Szleifer, I.; Panagiotopoulos, A. Z., Molecular simulation of the pure n-hexadecane vapor-liquid equilibria at elevated temperature, Phys. Rev. Lett. 1991, 66, 2935
17. Panagiotopoulos, A. Z., Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble, Mol. Phys. 1987, 61, 813-826
18. Panagiotopoulos, A. Z.; Quirke, N.; Stapleton, M.; Tildesley, D. J., Phase equilibria by simulation in the Gibbs ensemble: alternative derivation, generalization and application to mixture and membrane equilibria, Mol. Phys. 1988, 63, 527-545
19. Smit, B.; Smedt, P. De; Frenkel, D., Computer simulations in the Gibbs ensemble, Mol. Phys. 1989, 68, 931-950
20. Smit, B.; Frenkel, D., Calculation of the chemical potential in the Gibbs ensemble, Mol. Phys. 1989, 68, 951-958
21. Lopes, J. N. C.; Tildesley, D. J., Multiphase equilibria using the Gibbs ensemble Monte Carlo method, Mol. Phys. 1997, 92, 187-196
22. Kristof, T.; Liszi, J., Application of a new Gibbs ensemble Monte Carlo method to site-site interaction model fluids, Mol. Phys. 1997, 90, 1031-1034
23. Kristof, T.; Liszi, J., Application of a new Gibbs ensemble Monte Carlo method to site-site interaction model fluids, Mol. Phys. 1998, 94, 519
24. Baranyai, A.; Cummings, P. T., On the molecular dynamics algorithm for Gibbs ensemble simulation, Mol. Simul. 1996, 17, 21-25
25. Kotelyanskii, M. J.; Hentschke, R., Gibbs-ensemble molecular dynamics: liquid-gas equlibria for Lennard-Jones spheres and n-hexane, Mol. Simul. 1996, 17, 95-112
26. Hentschke, R.; Bast, T.; Aydt, E.; Kotelyanskii, M., Gibbs-ensemble molecular dynamics: a new method for simulations involving particle exchange, J. Mol. Model. 1996, 2, 319-326
27. Bruce, A. D., Finite-size critical behavior in the Gibbs ensemble, Phys. Rev. E 1997, 55, 2315-2320
28. Mon, K. K.; Binder, K., Finite size effects for the simulation of phase coexistence in the Gibbs ensemble near the critical point, J. Chem. Phys. 1992, 96, 6989-6995
29. Panagiotopoulos, A. Z., Exact calculations of fluid-phase equilibria by Monte Carlo simulation in a new statistical ensemble, Int. J. Thermophys. 1989, 10, 447-457
30. Laso, M.; de Pablo, J. J.; Suter, U. W., Simulation of phase equilibria for chain molecules, J. Chem. Phys. 1992, 97, 2817-2819
31. Mooij, G. C. A. M.; Frenkel, D.; Smit, B., Direct simulation of phase equilibria of chain molecules, J. Phys.: Condens. Matter 1992, 4, L255-L259
32. Kofke, D. A., Gibbs-Duhem integration: a new method for direct evaluation of phase coexistence by molecular simulation, Mol. Phys. 1993, 78, 1331-1336
33. Kofke, D. A., Direct evaluation of phase coexistence by molecular simulation via integration along the saturation line, J. Chem. Phys. 1993, 98, 4149-4162
34. Mehta, M.; Kofke, D. A., Coexistence diagrams of mixtures by molecular simulation, Chem. Eng. Sci. 1994, 49, 2633-2645
35. Agrawal, R.; Mehta, M.; Kofke, D. A., Efficient evaluation of three-phase coexistence lines, Int. J. Thermophys. 1994, 15, 1073-1083
36. Kofke, D. A., Semigrand canonical Monte Carlo simulation; integration along coexistence lines, Adv. Chem. Phys. 1999, 105, 405-442
37. Escobedo, F. A.; de Pablo, J. J., Monte Carlo simulation of athermal mesogenic chains: pure systems, mixtures, and constrained environments, J. Chem. Phys. 1997, 106, 9858-9868
38. Escobedo, F. A.; de Pablo, J. J., Pseudo-ensemble simulations and Gibbs-Duhem integrations for polymers, J. Chem. Phys. 1997, 106, 2911-2923
39. Escobedo, F. A.; de Pablo, J. J., Gibbs-Duhem integrations in lattice systems, Europhys. Lett. 1997, 40, 111-116
40. Agrawal, R.; Kofke, D. A., Solid-fluid coexistence for inverse-power potentials, Phys. Rev. Lett. 1995, 74, 122-125
41. Bolhuis, P.; Frenkel, D., Tracing the phase-boundaries of hard spherocylinders, J. Chem. Phys. 1997, 106, 666-687
42. Meijer, E. J.; Azhar, F. El, Novel procedure to determine coexistence lines by computer simulation. application to hard-core Yukawa model for charge-stabilized colloids, J. Chem. Phys. 1997, 106, 4678-4683
43. Mehta, M.; Kofke, D. A., Molecular simulation in a pseudo grand-canonical ensemble, Mol. Phys. 1995, 86, 139-147
44. Camp, P. J.; Allen, M. P., Phase coexistence in a pseudo-Gibbs ensemble, Mol. Phys. 1996, 88, 1459-1469
45. Escobedo, F. A., Novel pseudoensembles for simulation of multicomponent phase equilibria, J. Chem. Phys. 1998, 108, 8761-8772
46. Escobedo, F. A., Tracing coexistence lines in multicomponent fluid mixtures by molecular simulation, J. Chem. Phys. 1999, 110, 11999-12010
47. Ferrenberg, A. M.; Swendsen, R. H., Optimized Monte Carlo data analysis, Phys. Rev. Lett. 1989, 63, 1195-1198
48. Panagiotopoulos, A. Z.; Wong, V.; Floriano, M. A., Phase equilibria of lattice polymers from histogram reweighting Monte Carlo simulations, Macromolecules 1998, 31, 912-918
49. Torrie, G. M.; Valleau, J. P., Nonphysical sampling distributions in Monte Carlo free-energy estimation - umbrella sampling, J. Comp. Phys. 1977, 23, 187-199
50. Berg, B. A.; Neuhaus, T., Multicanonical ensemble: a new approach to simulate first-order phase transitions, Phys. Rev. Lett. 1992, 68, 9-12
51. Wilding, N. B., Critical-point and coexistence-curve properties of the Lennard-Jones fluid: a finite-size scaling study, Phys. Rev. E 1995, 52, 602-611
52. Wilding, N. B., Critical end point behavior in a binary fluid mixture, Phys. Rev. E 1997, 55, 6624-6631
53. Wilding, N. B.; Schmid, F.; Nielaba, P., Liquid-vapor phase behavior of a symmetrical binary fluid mixture, Phys. Rev. E 1998, 58, 2201-2212
54. Potoff, J. J.; Panagiotopoulos, A. Z., Critical point and phase behavior of the pure fluid and a Lennard-Jones mixture, J. Chem. Phys. 1998, 109, 10914-10920
55. Wilding, N. B., Simulation studies of fluid critical behaviour, J. Phys.: Condens. Matter 1997, 9, 585-612
56. Ferdinand, A. E.; Fisher, M. E., Bounded and inhomogeneous Ising models: I. specific-heat anomaly of a finite lattice, Phys. Rev. 1969, 185, 832-846
57. Fisher, M. E.; Barber, M. N., Scaling theory for finite-size effects in the critical region, Phys. Rev. Lett. 1972, 28, 1516-1519
58. Privman, V., (Ed.), Finite Size Scaling and Numerical Simulation of Statistical Mechanical Systems, World Scientific, Singapore, 1990
59. Bruce, A. D.; Wilding, N. B., Scaling fields and universality of the liquid-gas critical point, Phys. Rev. Lett. 1992, 68, 193-196
60. Wilding, N. B.; Bruce, A. D., Density fluctuations and field mixing in the critical fluid, J. Phys.: Condens. Matter 1992, 4, 3087-3108
61. Orkoulas, G.; Panagiotopoulos, A. Z., Phase behavior of the restricted primitive model and square-well fluids from Monte Carlo simulations in the grand canonical ensemble, J. Chem. Phys. 1999, 110, 1581-1590
62. Sengers, J. V.; Levelt-Sengers, J. N. H., Thermodynamic behavior of fluids near the critical point, Ann. Rev. Phys. Chem. 1986, 37, 187-222
63. Liu, A. J.; Fisher, M. E., The three-dimensional ising model revisited numerically, A. Physica 1989, 156, 35-76
64. Valleau, J. P., Thermodynamic scaling methods in Monte Carlo and their application to phase equilibria, Monte Carlo Methods Chem. Phys. 1999, 105, 369-404
65. Kiyohara, K.; Spyriouni, T.; Gubbins, K. E.; Panagiotopoulos, A. Z., Thermodynamic scaling Gibbs ensemble Monte Carlo: a new method for determination of phase coexistence properties of fluid, Mol. Phys. 1996, 89, 965-974.
66. Errington, J. R.; Panagiotopoulos, A. Z., Phase equilibria of the modified Buckingham exponential-6 potential from Hamiltonian scaling grand canonical Monte Carlo, J. Chem. Phys. 1998, 109, 1093-1100
67. Berg, B. A.; Celik, T., New approach to spin-glass simulations, Phys. Rev. Lett. 1992, 69, 2292-2295
68. Lee, J., New Monte Carlo algorithm: entropic sampling, Phys. Rev. Lett. 1993, 71, 211-214
69. Smith, G. R.; Bruce, A. D., A study of the multicanonical Monte Carlo method, J. Phys. A 1995, 28, 6623-6643
70. Fitzgerald, M.; Picard, R. R.; Silver, R. N., Monte Carlo transition dynamics and variance reduction, J. Stat. Phys. 1999, 98, 321-345
71. Wang, F.; Landau, D. P., Efficient, multiple-range random walk algorithm to calculate the density of states, Phys. Rev. Lett. 2001, 86, 2050-2053
72. Wang, F.; Landau, D. P., Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram, Phys. Rev. E 2001, 64, 056101
73. Wang, J. S.; Swendsen, R. H., Transition matrix Monte Carlo method, J. Stat. Phys. 2001, 106, 245-285
74. Yan, Q.; Faller, R.; de Pablo, J. J., Density-of-states Monte Carlo method for simulation of fluids, J. Chem. Phys. 2002, 116, 8745-8749
75. Shell, M. S.; Debenedetti, P. G.; Panagiotopoulos, A. Z., Generalization of the Wang-Landau method for off-lattice simulations, Phys. Rev. E 2002, 90, 056703
76. Lotfi, A.; Vrabec, J.; Fischer, J., Vapour liquid equilibria of the Lennard-Jones fluid from the NPT plus test particle method, Mol. Phys. 1992, 76, 1319-1333
77. Errington, J. R., Prewetting transitions for a model argon on solid carbon dioxide system, Langmuir 2004, 20, 3798-3804
78. Ebner, C.; Saam, W. F., New phase-transition phenomena in thin argon films, Phys. Rev. Lett 1977, 38, 1486-1489
79. Calvo, F., Sampling along reaction coordinates with the Wang-Landau method, Mol. Phys. 2002, 100, 3421-3427
80. Wilding, N. B., Critical-point and coexistence-curve properties of the Lennard-Jones fluid: a finite-size scaling study, Phys. Rev. E 1995, 52, 602-611
81. Wilding, N. B., Computer simulation of fluid phase transitions, Am. J. Phys 2001, 69, 1147-1155
82. Gelb, L. D.; Gubbins, K. E., Studies of binary liquid mixtures in cylindrical pores: phase separation, wetting and finite-size effects from Monte Carlo simulations, Physica A 1997, 244, 112-123
83. Noguchi, H.; Yoshikawa, K., First-order phase transition in a stiff polymer chain, Chem. Phys. Lett. 1997, 278, 184-188
84. Noguchi, H.; Yoshikawa, K., Morphological variation in a collapsed single homopolymer chain, J. Chem. Phys. 1998, 109, 5070-5077
85. Liang, H. J.; Chen, H. N., First-order transition of a homopolymer chain with Lennard-Jones potential, J. Chem. Phys. 2000, 113, 4469-4471
86. Wang, Y. U.; Chen, H. N.; Liang, H. J., Monte Carlo simulation on thermodynamic properties of a heteropolymer chain, J. Chem. Phys. 2001, 115, 3951-3956
87. Huang, L.; He, X. H.; Wang, Y. Y.; Chen, H. N.; Liang, H. J., Phase transitions of short chains at ultralow temperature, J. Chem. Phys. 2003, 119, 2432-2438
88. Bhattacharya, K. K.; Sethna, J. P., Multicanonical methods, molecular dynamics, and Monte Carlo methods: comparison for Lennard-Jones glasses, Phys. Rev. E 1998, 57, 2553-2562
89. Bandyopadhyay, P.; Ten-No, S.; Iwata, S., Ab initio Monte Carlo simulation using multicanonical algorithm: temperature dependence of the average structure of water dimer, Mol. Phys. 1999, 96, 349-358
90. Mau, S. C.; Huse, D. A., Stacking entropy of hard-sphere crystals, Phys. Rev. E 1999, 59, 4396-4401
91. Faller, R.; Yan, Q. L.; de Pablo, J. J., Multicanonical parallel tempering, J. Chem. Phys. 2002, 116, 5419-5423
92. Hansmann, U. H. E.; Okamoto, Y., New Monte Carlo algorithms for protein folding, Curr. Opin. Struct. Biol. 1999, 9, 177-183
93. Hansmann, U. H. E., Computer simulation of biological macromolecules in generalized ensembles, Int. J. Mod. Phys. C 1999, 10, 1521-1530
94. Mitsutake, A.; Sugita, Y.; Okamoto, Y., Generalized-ensemble algorithms for molecular simulations of biopolymers, Biopolymers 2001, 60, 96-123
95. Dinner, A. R.; Lazaridis, T.; Karplus, M., Understanding beta-hairpin formation, Proc. Natl Acad. Sci. USA 1999, 96, 9068-9073
96. Higo, J.; Nakajima, N.; Shirai, H.; Kidera, A.; Nakamura, H., Two-component multicanonical Monte Carlo method for effective conformation sampling, J. Comput. Chem. 1997, 18, 2086-2092
97. Sayano, K.; Kono, H.; Gromiha, M. M.; Sarai, A., Multicanonical Monte Carlo calculation of the free-energy map of the base-amino acid interaction, J. Comput. Chem. 2000, 21, 954-962
98. Sugita, Y.; Kitao, A.; Okamoto, Y., Multidimensional replica-exchange method for free-energy calculations, J. Chem. Phys. 2000, 113, 6042-6051
99. Mitsutake, A.; Okamoto, Y., Replica-exchange simulated tempering method for simulations of frustrated systems, Chem. Phys. Lett. 2000, 332, 131-138
100. Vorontsov-Velyaminov, P. N.; Yolkov, N. A.; Yurchenko, A. A., Entropic sampling of simple polymer models within Wang-Landau algorithm, J. Phys. A 2004, 37, 1573-1588
101. Vlugt, T. J. H., Measurement of chemical potentials of systems with strong excluded volume interactions by computing the density of states, Mol. Phys. 2002, 100, 2763-2771
102. Kim, E. B.; Faller, R.; Yan, Q.; Abbot, N. L.; de Pablo, J. J., Potential of mean force between a spherical particle suspended in a nematic liquid crystal and a substrate, J. Chem. Phys. 2002, 117, 7781-7787
103. Faller, R.; de Pablo, J. J., Density of states of a binary Lennard-Jones glass, J. Chem. Phys. 2003, 119, 4405-4408
104. Jain, T. S.; de Pablo, J. J., Calculation of interfacial tension from density of states, J. Chem. Phys. 2003, 118, 4226-4229
105. MacDowell, L. G.; Virnau, P.; Müller, M.; Binder, K., The evaporation/condensation transition of liquid droplets, J. Chem. Phys. 2004, 120, 5293-5308
106. de Menezes, M. A.; Lima, A. R., Using entropy-based methods to study general constrained parameter optimization problems, Physica A 2003, 323, 428-434
107. Rathore, N.; IV, T. A. Knotts; de Pablo, J. J., Density of states simulations of proteins, J. Chem. Phys. 2002, 118, 4285-4290
108. Rathore, N.; IV, T. A. Knotts; de Pablo, J. J., Configurational temperature density of states simulations of proteins, Biophys. J. 2003, 85, 3963
109. Rathore, N.; Yan, Q.; de Pablo, J. J., Molecular simulation of the reversible mechanical unfolding of proteins, J. Chem. Phys. 2004, 120, 5781-5788
110. Liang, F., Annealing contour Monte Carlo algorithm for structure optimization in an off-lattice protein model, J. Chem. Phys. 2004, 120, 6756-6763
111. Smith, G. R.; Bruce, A. D., Multicanonical Monte Carlo study of a structural phase transition, Europhys. Lett. 1996, 34, 91-96
112. Smith, G. R.; Bruce, A. D., Multicanonical Monte Carlo study of solid-solid phase coexistence in a model colloid, Phys. Rev. E 1996, 53, 6530-6543
113. Errington, J. R., Direct calculation of liquid-vapor phase equilibria from transition matrix Monte Carlo simulation, J. Chem. Phys. 2003, 118, 9915-9925
114. Singh, J. K.; Kofke, D. A.; Errington, J. R., Surface tension and vapor-liquid phase coexistence of the square-well fluid, J. Chem. Phys. 2003, 119, 3405-3412
115. Errington, J. R., Solid-liquid phase coexistence of the Lennard-Jones system through phase-switch Monte Carlo simulation, J. Chem. Phys. 2004, 120, 3130-3141
116. Errington, J. R., Evaluating surface tension using grand-canonical transition-matrix Monte Carlo simulation and finite-size scaling, Phys. Rev. E 2003, 67, 012102
117. Bruce, A. D.; Jackson, A. N.; Ackland, G. J.; Wilding, N. B., Lattice-switch Monte Carlo method, Phys. Rev. E 2000, 61, 906-919