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==== | |||
For the [[second virial coefficient]] of a mixture | |||
<ref>[http://dx.doi.org/10.1063/1.1724353 I. Amdur and E. A. Mason "Properties of Gases at Very High Temperatures", Physics of Fluids '''1''' pp. 370-383 (1958)]</ref> | |||
:<math>B_{ij} = \frac{\left(B_{ii}^{1/3}+B_{jj}^{1/3}\right)^3}{8}</math> | |||
====Berthelot rule==== | ====Berthelot rule==== | ||
:<math>\epsilon_{ij} = \sqrt{\epsilon_{ii} \epsilon_{jj}}</math> | :<math>\epsilon_{ij} = \sqrt{\epsilon_{ii} \epsilon_{jj}}</math> | ||
====Hudson and McCoubrey==== | |||
<ref>[http://dx.doi.org/10.1039/TF9605600761 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)]</ref> | |||
====Kong rules==== | |||
<ref>[http://dx.doi.org/10.1063/1.1680358 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)]</ref> | |||
====Lorentz rule==== | ====Lorentz rule==== | ||
:<math>\sigma_{ij} = \frac{\sigma_{ii} + \sigma_{jj}}{2}</math> | :<math>\sigma_{ij} = \frac{\sigma_{ii} + \sigma_{jj}}{2}</math> | ||
See also [[Lennard-Jones model]] | See also [[Lennard-Jones model]] | ||
==== | ====Tang and Toennies==== | ||
<ref>[http://dx.doi.org/10. | <ref>[http://dx.doi.org/10.1007/BF01384663 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)]</ref> | ||
====Waldman-Hagler rules==== | ====Waldman-Hagler rules==== | ||
<ref>[http://dx.doi.org/10.1002/jcc.540140909 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)]</ref> | <ref>[http://dx.doi.org/10.1002/jcc.540140909 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)]</ref> | ||
==References== | ==References== | ||
<references/> | <references/> | ||
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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]
Berthelot rule
Hudson and McCoubrey
Kong rules
Lorentz rule
See also Lennard-Jones model
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)
- ↑ 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)
- ↑ 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)
Related reading
- 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)
- 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)