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.

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)