Mie potential: Difference between revisions

Revision as of 16:38, 4 August 2015

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)}

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

Related reading

@@ Line 8: / Line 8: @@
 * <math> \epsilon </math> : well depth (energy)
 Note that when <math>n=12</math> and <math>m=6</math> this becomes the [[Lennard-Jones model]].
+The location of the potential minimum is given by
+:<math> r_{min} = \left( \frac{n}{m} \sigma^{n-m} \right) ^ {1/(n-m)} </math>
 ==(14,7) model==
 <ref>[http://dx.doi.org/10.1063/1.2901164 Afshin Eskandari Nasrabad "Monte Carlo simulations of thermodynamic and structural properties of Mie(14,7) fluids", Journal of Chemical Physics '''128''' 154514 (2008)]</ref>