Mie potential: Difference between revisions

Revision as of 13:48, 6 April 2010

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.

Related reading

@@ Line 5: / Line 5: @@
 * <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>
 * <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles at a distance r;
-* <math> \sigma </math> is the  diameter (length), i.e. the value of <math>r</math> at <math> \Phi(r)=0</math> ;
+* <math> \sigma </math> is the value of <math>r</math> at <math> \Phi(r)=0</math> ;
 * <math> \epsilon </math> : well depth (energy)
 Note that when <math>n=12</math> and <math>m=6</math> this becomes the [[Lennard-Jones model]].