Mie potential page on SklogWiki - a wiki for statistical mechanics and thermodynamics

The Mie potential was proposed by Gustav Mie in 1903 ^[1]. 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)}

(14,7) model

The second virial coefficient ^[4] and the Vliegenthart–Lekkerkerker relation ^[5].

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