Mie potential

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]

{\displaystyle \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:

$r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$ {\displaystyle r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|}
$\Phi _{12}(r)$ {\displaystyle \Phi _{12}(r)} is the intermolecular pair potential between two particles at a distance r;
$\sigma$ {\displaystyle \sigma } is the value of $r$ {\displaystyle r} at $\Phi (r)=0$ {\displaystyle \Phi (r)=0} ;
$\epsilon$ {\displaystyle \epsilon } : well depth (energy)

Note that when $n=12$ {\displaystyle n=12} and $m=6$ {\displaystyle 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)}

{\displaystyle r_{min}=\left({\frac {n}{m}}\sigma ^{n-m}\right)^{1/(n-m)}}

(14,7) model[edit ]

^[2] ^[3]

Second virial coefficient[edit ]

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

References[edit ]

Mie potential

(14,7) model[edit ]

Second virial coefficient[edit ]

References[edit ]

Navigation menu

Search