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

Φ_{12} (r) = (\frac{n}{n - m}) {(\frac{n}{m})}^{m / (n - m)} ϵ [{(\frac{σ}{r})}^{n} - {(\frac{σ}{r})}^{m}]

where:

$r : = | r_{1} - r_{2} |$
$Φ_{12} (r)$ is the intermolecular pair potential between two particles at a distance r;
$σ$ is the value of $r$ at $Φ (r) = 0$ ;
$ϵ$ : 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_{m i n} = {(\frac{n}{m} σ^{n - m})}^{1 / (n - m)}

(14,7) model

The second virial coefficient ^[4] ^[5] ^[6] and the Vliegenthart–Lekkerkerker relation ^[7].

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