Mie potential

2015-08-04T16:38:45Z

129.59.37.35: Give an expression for the location of the potential minimum.

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>

where:
* <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 value of <math>r</math> at <math> \Phi(r)=0</math> ;
* <math> \epsilon </math> : well depth (energy)
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==
<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]] 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/>
'''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/10.1080/00268976.2015.1025112 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)]

[[Category: Models]]

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Mie potential