Mie potential: Difference between revisions
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<ref>[http://dx.doi.org/10.1063/1.4961653 D. M. Heyes, G. Rickayzen, S. Pieprzyk and A. C. Brańka "The second virial coefficient and critical point behavior of the Mie Potential", Journal of Chemical Physics '''145''' 084505 (2016)]</ref> | <ref>[http://dx.doi.org/10.1063/1.4961653 D. M. Heyes, G. Rickayzen, S. Pieprzyk and A. C. Brańka "The second virial coefficient and critical point behavior of the Mie Potential", Journal of Chemical Physics '''145''' 084505 (2016)]</ref> | ||
<ref>[https://doi.org/10.1063/1.5006035 D. M. Heyes and T. Pereira de Vasconcelos "The second virial coefficient of bounded Mie potentials", Journal of Chemical Physics '''147''' 214504 (2017)]</ref> | <ref>[https://doi.org/10.1063/1.5006035 D. M. Heyes and T. Pereira de Vasconcelos "The second virial coefficient of bounded Mie potentials", Journal of Chemical Physics '''147''' 214504 (2017)]</ref> | ||
<ref>[https://doi.org/10.1063/1.5030679 D. M. Heyes and  T. Pereira de Vasconcelos "Erratum: “The second virial coefficient of bounded Mie potentials” <nowiki>[</nowiki>J. Chem. Phys. 147, 214504 (2017)<nowiki>]</nowiki>", Journal of Chemical Physics '''148''' 169903 (2018)]</ref> | |||
and the Vliegenthart–Lekkerkerker relation <ref>[http://dx.doi.org/10.1063/1.3578469 V. L. Kulinskii "The Vliegenthart–Lekkerkerker relation: The case of the Mie-fluids", Journal of Chemical Physics '''134''' 144111 (2011)]</ref>. | and the Vliegenthart–Lekkerkerker relation <ref>[http://dx.doi.org/10.1063/1.3578469 V. L. Kulinskii "The Vliegenthart–Lekkerkerker relation: The case of the Mie-fluids", Journal of Chemical Physics '''134''' 144111 (2011)]</ref>. | ||
Revision as of 10:37, 3 May 2018
The Mie potential was proposed by Gustav Mie in 1903 [1]. It is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r) = \left( \frac{n}{n-m}\right) \left( \frac{n}{m}\right)^{m/(n-m)} \epsilon \left[ \left(\frac{\sigma}{r} \right)^{n}- \left( \frac{\sigma}{r}\right)^m \right] }
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|}
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r) } is the intermolecular pair potential between two particles at a distance r;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is the value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} at ;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon } : well depth (energy)
Note that when Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n=12} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m=6} this becomes the Lennard-Jones model.
The location of the potential minimum is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_{min} = \left( \frac{n}{m} \sigma^{n-m} \right) ^ {1/(n-m)} }
(14,7) model
Second virial coefficient
The second virial coefficient [4] [5] [6] and the Vliegenthart–Lekkerkerker relation [7].
References
- ↑ Gustav Mie "Zur kinetischen Theorie der einatomigen Körper", Annalen der Physik 11 pp. 657-697 (1903) (Note: check the content of this reference)
- ↑ Afshin Eskandari Nasrabad "Monte Carlo simulations of thermodynamic and structural properties of Mie(14,7) fluids", Journal of Chemical Physics 128 154514 (2008)
- ↑ Afshin Eskandari Nasrabad, Nader Mansoori Oghaz, and Behzad Haghighi "Transport properties of Mie(14,7) fluids: Molecular dynamics simulation and theory", Journal of Chemical Physics 129 024507 (2008)
- ↑ D. M. Heyes, G. Rickayzen, S. Pieprzyk and A. C. Brańka "The second virial coefficient and critical point behavior of the Mie Potential", Journal of Chemical Physics 145 084505 (2016)
- ↑ D. M. Heyes and T. Pereira de Vasconcelos "The second virial coefficient of bounded Mie potentials", Journal of Chemical Physics 147 214504 (2017)
- ↑ D. M. Heyes and  T. Pereira de Vasconcelos "Erratum: “The second virial coefficient of bounded Mie potentials” [J. Chem. Phys. 147, 214504 (2017)]", Journal of Chemical Physics 148 169903 (2018)
- ↑ V. L. Kulinskii "The Vliegenthart–Lekkerkerker relation: The case of the Mie-fluids", Journal of Chemical Physics 134 144111 (2011)
Related reading
- Pedro Orea, Yuri Reyes-Mercado, Yurko Duda "Some universal trends of the Mie(n,m) fluid thermodynamics", Physics Letters A 372 pp. 7024-7027 (2008)
- N.S. Ramrattan, C. Avendaño, E.A. Müller and A. Galindo "A corresponding-states framework for the description of the Mie family of intermolecular potentials", Molecular Physics 113 pp. 932-947 (2015)
- I.M. Zerón, L.A. Padilla, F. Gámez, J. Torres-Arenas, A.L. Benavides "Discrete perturbation theory for Mie potentials", Journal of Molecular Liquids 229 pp. 125-136 (2017)
- Stephan Werth, Katrin Stöbener, Martin Horsch and Hans Hasse "Simultaneous description of bulk and interfacial properties of fluids by the Mie potential", Molecular Physics 115 pp. 1017-1030 (2017)