Mie potential: Difference between revisions
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The '''Mie potential''' was proposed by Gustav Mie in 1903. It is given by | The '''Mie potential''' was proposed by Gustav Mie in 1903. It is given by | ||
:<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> | ||
where: | where: | ||
* <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> \sigma </math> is the diameter (length), i.e. the value of <math>r</math> at <math> \Phi(r)=0</math> ; | * <math> \sigma </math> is the diameter (length), i.e. the value of <math>r</math> at <math> \Phi(r)=0</math> ; | ||
* <math> \epsilon </math> : well depth (energy) | * <math> \epsilon </math> : well depth (energy) | ||
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#[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)] | #[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)] | ||
#[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)] | #[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)] | ||
==References== | ==References== | ||
#[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) | #[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) | ||
[[Category: Models]] | [[Category: Models]] | ||
Revision as of 15:08, 17 July 2008
The Mie potential was proposed by Gustav Mie in 1903. 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 diameter (length), i.e. 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 \Phi(r)=0} ;
- : 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.
(14,7) model
- 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)