Combining rules: Difference between revisions
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The '''combining rules''' (also known as ''mixing rules'') for binary [[mixtures]] are variously given by: | |||
The '''combining rules''' (also known as ''mixing rules'') for binary [[mixtures]] are variously given by | |||
==Admur and Mason== | ==Admur and Mason== | ||
For the [[second virial coefficient]] of a mixture | For the [[second virial coefficient]] of a mixture |
Revision as of 16:50, 7 July 2011
The combining rules (also known as mixing rules) for binary mixtures are variously given by:
Admur and Mason
For the second virial coefficient of a mixture [1]
Böhm-Ahlrichs
Diaz Peña-Pando-Renuncio
Fender-Halsey
The Fender-Halsey combining rule for the Lennard-Jones model is given by [5]
Gilbert-Smith
The Gilbert-Smith rules for the Born-Huggins-Meyer potential[6][7][8].
Good-Hope rule
The Good-Hope rule for Mie–Lennard‐Jones or Buckingham potentials [9] is given by (Eq. 2):
Hudson and McCoubrey
Kong rules
Lorentz-Berthelot rules
The Lorentz rule is given by [12]
which is only really valid for the hard sphere model.
The Berthelot rule is given by [13]
These rules are simple and widely used, but are not without their failings [14] [15] [16].
Mason-Rice rule
The Mason-Rice rule for the Exp-6 potential [17].
Sikora rules
The Sikora rules for the Lennard-Jones model [18].
Tang and Toennies
Waldman-Hagler rules
References
- ↑ I. Amdur and E. A. Mason "Properties of Gases at Very High Temperatures", Physics of Fluids 1 pp. 370-383 (1958)
- ↑ Hans‐Joachim Böhm and Reinhart Ahlrichs "A study of short‐range repulsions", Journal of Chemical Physics 77 pp. 2028- (1982)
- ↑ M. Diaz Peña, C. Pando, and J. A. R. Renuncio "Combination rules for intermolecular potential parameters. I. Rules based on approximations for the long-range dispersion energy", Journal of Chemical Physics 76 pp. 325- (1982)
- ↑ M. Diaz Peña, C. Pando, and J. A. R. Renuncio "Combination rules for intermolecular potential parameters. II. Rules based on approximations for the long-range dispersion energy and an atomic distortion model for the repulsive interactions", Journal of Chemical Physics 76 pp. 333- (1982)
- ↑ B. E. F. Fender and G. D. Halsey, Jr. "Second Virial Coefficients of Argon, Krypton, and Argon-Krypton Mixtures at Low Temperatures", Journal of Chemical Physics 36 pp. 1881-1888 (1962)
- ↑ T. L. Gilbert "Soft‐Sphere Model for Closed‐Shell Atoms and Ions", Journal of Chemical Physics 49 pp. 2640- (1968)
- ↑ T. L. Gilbert, O. C. Simpson, and M. A. Williamson "Relation between charge and force parameters of closed‐shell atoms and ions", Journal of Chemical Physics 63 pp. 4061- (1975)
- ↑ Felix T. Smith "Atomic Distortion and the Combining Rule for Repulsive Potentials", Physical Review A 5 pp. 1708-1713 (1972)
- ↑ Robert J. Good and Christopher J. Hope "New Combining Rule for Intermolecular Distances in Intermolecular Potential Functions", Journal of Chemical Physics 53 pp. 540- (1970)
- ↑ G. H. Hudson and J. C. McCoubrey "Intermolecular forces between unlike molecules. A more complete form of the combining rules", Transactions of the Faraday Society 56 pp. 761-766 (1960)
- ↑ Chang Lyoul Kong "Combining rules for intermolecular potential parameters. II. Rules for the Lennard-Jones (12–6) potential and the Morse potential", Journal of Chemical Physics 59 pp. 2464-2467 (1973)
- ↑ H. A. Lorentz "Ueber die Anwendung des Satzes vom Virial in der kinetischen Theorie der Gase", Annalen der Physik 12 pp. 127-136 (1881)
- ↑ D. Berthelot "Sur le mélange des gaz", Comptes rendus hebdomadaires des séances de l’Académie des Sciences, 126 pp. 1703-1857 (1898)
- ↑ Jérôme Delhommelle; Philippe Millié "Inadequacy of the Lorentz-Berthelot combining rules for accurate predictions of equilibrium properties by molecular simulation", Molecular Physics 99 pp. 619-625 (2001)
- ↑ Dezso Boda and Douglas Henderson "The effects of deviations from Lorentz-Berthelot rules on the properties of a simple mixture", Molecular Physics 106 pp. 2367-2370 (2008)
- ↑ W. Song, P. J. Rossky, and M. Maroncelli "Modeling alkane+perfluoroalkane interactions using all-atom potentials: Failure of the usual combining rules", Journal of Chemical Physics 119 pp. 9145- (2003)
- ↑ Edward A. Mason and William E. Rice "The Intermolecular Potentials of Helium and Hydrogen", Journal of Chemical Physics 22 pp. 522- (1954)
- ↑ P. T. Sikora "Combining rules for spherically symmetric intermolecular potentials", Journal of Physics B: Atomic and Molecular Physics 3 pp. 1475- (1970)
- ↑ K. T. Tang and J. Peter Toennies "New combining rules for well parameters and shapes of the van der Waals potential of mixed rare gas systems", Zeitschrift für Physik D Atoms, Molecules and Clusters 1 pp. 91-101 (1986)
- ↑ M. Waldman and A. T. Hagler "New combining rules for rare-gas Van der-Waals parameters", Journal of Computational Chemistry 14 pp. 1077-1084 (1993)
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