Mie potential: Difference between revisions

Revision as of 12:48, 6 April 2010

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.

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]].