Mie potential: Difference between revisions
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The '''Mie potential''' was proposed by Gustav Mie in 1903 <ref>[http://dx.doi.org/10.1002/andp.19033160802 Gustav Mie "Zur kinetischen Theorie der einatomigen Körper", Annalen der Physik '''11''' pp. 657-697 (1903)] (check this reference)</ref>. It is given by | The '''Mie potential''' was proposed by Gustav Mie in 1903 <ref>[http://dx.doi.org/10.1002/andp.19033160802 Gustav Mie "Zur kinetischen Theorie der einatomigen Körper", Annalen der Physik '''11''' pp. 657-697 (1903)] (Note: check the content of this reference)</ref>. It is given by | ||
:<math> \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] </math> | :<math> \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] </math> | ||
| Line 5: | Line 5: | ||
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | * <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | ||
* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles at a distance r; | * <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles at a distance r; | ||
* <math> \sigma </math> is | * <math> \sigma </math> is the value of <math>r</math> at <math> \Phi(r)=0</math> ; | ||
* <math> \epsilon </math> : well depth (energy) | * <math> \epsilon </math> : well depth (energy) | ||
Note that when <math>n=12</math> and <math>m=6</math> this becomes the [[Lennard-Jones model]]. | Note that when <math>n=12</math> and <math>m=6</math> this becomes the [[Lennard-Jones model]]. | ||
The location of the potential minimum is given by | |||
:<math> r_{min} = \left( \frac{n}{m} \sigma^{n-m} \right) ^ {1/(n-m)} </math> | |||
==(14,7) model== | ==(14,7) model== | ||
<ref>[http://dx.doi.org/10.1063/1.2901164 Afshin Eskandari Nasrabad "Monte Carlo simulations of thermodynamic and structural properties of Mie(14,7) fluids", Journal of Chemical Physics '''128''' 154514 (2008)]</ref> | |||
<ref>[http://dx.doi.org/10.1063/1.2953331 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)]</ref> | |||
==Second virial coefficient== | |||
The [[second virial coefficient]] | |||
<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/10.1063/1.5030679 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>. | |||
==References== | ==References== | ||
<references/> | <references/> | ||
'''Related reading''' | '''Related reading''' | ||
*[http://dx.doi.org/10.1016/j.physleta.2008.10.047 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)] | *[http://dx.doi.org/10.1016/j.physleta.2008.10.047 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)] | ||
*[http://dx.doi.org/10.1080/00268976.2015.1025112 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)] | |||
*[http://dx.doi.org/10.1016/j.molliq.2016.12.026 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)] | |||
*[http://dx.doi.org/10.1080/00268976.2016.1206218 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)] | |||
*[https://doi.org/10.1063/1.5041320 Richard J. Sadus "Second virial coefficient properties of the n-m Lennard-Jones/Mie potential", Journal of Chemical Physics 149, 074504 (2018)] | |||
[[Category: Models]] | [[Category: Models]] | ||
Latest revision as of 14:11, 12 September 2018
The Mie potential was proposed by Gustav Mie in 1903 [1]. It is given by
![{\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]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a560ce2bd238cf1a42ca7c69fe05109929428913)
where:
- is the intermolecular pair potential between two particles at a distance r;
- is the value of at ;
- : well depth (energy)
Note that when and this becomes the Lennard-Jones model.
The location of the potential minimum is given by
(14,7) model[edit]
Second virial coefficient[edit]
The second virial coefficient [4] [5] [6] and the Vliegenthart–Lekkerkerker relation [7].
References[edit]
- ↑ 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)
- Richard J. Sadus "Second virial coefficient properties of the n-m Lennard-Jones/Mie potential", Journal of Chemical Physics 149, 074504 (2018)