N-6 Lennard-Jones potential: Difference between revisions
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The '''n-6 Lennard-Jones potential''' is a variant the more well known [[Lennard-Jones model]] (or from a different point of view, a particular case of the [[Mie potential]]).. The potential is given by <ref>[http://dx.doi.org/10.1063/1.3253686 Alauddin Ahmed and Richard J. Sadus "Solid-liquid equilibria and triple points of n-6 Lennard-Jones fluids", Journal of Chemical Physics '''131''' 174504 (2009)]</ref>: | The '''n-6 Lennard-Jones potential''' is a variant the more well known [[Lennard-Jones model]] (or from a different point of view, a particular case of the [[Mie potential]]).. The potential is given by <ref>[http://dx.doi.org/10.1063/1.3253686 Alauddin Ahmed and Richard J. Sadus "Solid-liquid equilibria and triple points of n-6 Lennard-Jones fluids", Journal of Chemical Physics '''131''' 174504 (2009)]</ref>: | ||
:<math> \Phi_{ | :<math> \Phi_{n}(r) = \epsilon \left( \frac{n}{n-6} \right)\left( \frac{n}{6} \right)^{\frac{6}{n-6}} \left[ \left(\frac{\sigma}{r} \right)^{n}- \left( \frac{\sigma}{r}\right)^6 \right] </math> | ||
where | where | ||
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | * <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | ||
* <math> \Phi_{ | * <math> \Phi_{n}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites'' | ||
* <math> \sigma </math> is the diameter (length), ''i.e.'' the value of <math>r</math> at which <math> \Phi_{ | * <math> \sigma </math> is the diameter (length), ''i.e.'' the value of <math>r</math> at which <math> \Phi_{n}(r)=0</math> | ||
* <math> \epsilon </math> is the well depth (energy) | * <math> \epsilon </math> is the well depth (energy) | ||
==Melting point== | ==Melting point== | ||
Revision as of 16:00, 12 October 2011
The n-6 Lennard-Jones potential is a variant the more well known Lennard-Jones model (or from a different point of view, a particular case of the Mie potential).. The potential is given by [1]:
![{\displaystyle \Phi _{n}(r)=\epsilon \left({\frac {n}{n-6}}\right)\left({\frac {n}{6}}\right)^{\frac {6}{n-6}}\left[\left({\frac {\sigma }{r}}\right)^{n}-\left({\frac {\sigma }{r}}\right)^{6}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5c46babe1f3dad8af768415bdae81049ab31e18)
where
- is the intermolecular pair potential between two particles or sites
- is the diameter (length), i.e. the value of at which
- is the well depth (energy)
Melting point
An approximate method to locate the melting point is given in [2].
References
- ↑ Alauddin Ahmed and Richard J. Sadus "Solid-liquid equilibria and triple points of n-6 Lennard-Jones fluids", Journal of Chemical Physics 131 174504 (2009)
- ↑ Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics 134 054120 (2011)
- Related reading