Mie potential: Difference between revisions

Revision as of 18:38, 4 August 2015

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)}

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>