Mie potential: Difference between revisions

Revision as of 11:51, 16 September 2016

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 ^[4] and the Vliegenthart–Lekkerkerker relation ^[5].

Related reading

@@ Line 15: / Line 15: @@
 <ref>[http://dx.doi.org/10.1063/1.2953331 Afshin Eskandari Nasrabad, Nader Mansoori Oghaz, and Behzad Haghighi "Transport properties of Mie(14,7) fluids: Molecular dynamics simulation and theory", Journal of Chemical Physics '''129''' 024507 (2008)]</ref>
 ==Second virial coefficient==
-The [[second virial coefficient]] and the Vliegenthart–Lekkerkerker relation <ref>[http://dx.doi.org/10.1063/1.3578469 V. L. Kulinskii "The Vliegenthart–Lekkerkerker relation: The case of the Mie-fluids", Journal of Chemical Physics '''134''' 144111 (2011)]</ref>.
+The [[second virial coefficient]] <ref>[http://dx.doi.org/10.1063/1.4961653  D. M. Heyes, G. Rickayzen, S. Pieprzyk and A. C. Brańka "The second virial coefficient and critical point behavior of the Mie Potential", Journal of Chemical Physics '''145''' 084505 (2016)]</ref> and the Vliegenthart–Lekkerkerker relation <ref>[http://dx.doi.org/10.1063/1.3578469 V. L. Kulinskii "The Vliegenthart–Lekkerkerker relation: The case of the Mie-fluids", Journal of Chemical Physics '''134''' 144111 (2011)]</ref>.
 ==References==
 <references/>