Mie potential

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

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

where:

• $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$
• ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential between two particles at a distance r;
• $\sigma$ is the value of $r$ at $\mathrm{\Phi }(r)=0$ ;
• $ϵ$ : 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

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

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)