Mie potential

The Mie potential was proposed by Gustav Mie in 1903 . It is given by

$\Phi _{12}(r)=\left({\frac {n}{n-m}}\right)\left({\frac {n}{m}}\right)^{m/(n-m)}\epsilon \left[\left({\frac {\sigma }{r}}\right)^{n}-\left({\frac {\sigma }{r}}\right)^{m}\right]$

where:

• $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$
• $\Phi _{12}(r)$ is the intermolecular pair potential between two particles at a distance r;
• $\sigma$ is the value of $r$ at $\Phi (r)=0$ ;
• $\epsilon$ : well depth (energy)

Note that when $n=12$ and $m=6$ this becomes the Lennard-Jones model.

The location of the potential minimum is given by

$r_{min}=\left({\frac {n}{m}}\sigma ^{n-m}\right)^{1/(n-m)}$

Second virial coefficient

The second virial coefficient and the Vliegenthart–Lekkerkerker relation .

References

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)