Lennard-Jones model: Difference between revisions
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where: | where: | ||
* <math> V(r) </math> : | * <math> V(r) </math> : potential energy of interaction between two particles at a distance r; | ||
* <math> \sigma </math> : diameter (length); | * <math> \sigma </math> : diameter (length); | ||
| Line 13: | Line 13: | ||
Reduced units: | Reduced units: | ||
* Density, <math> \rho^* \equiv \rho \sigma^3 </math>, where <math> \rho = N/V </math> ( | * Density, <math> \rho^* \equiv \rho \sigma^3 </math>, where <math> \rho = N/V </math> (number of particles <math> N </math> divided by the volume <math> V </math>.) | ||
* Temperature; <math> T^* \equiv k_B T/\epsilon </math>, where <math> T </math> is the absolute temperature and <math> k_B </math> is the [[Boltzmann constant]] | * Temperature; <math> T^* \equiv k_B T/\epsilon </math>, where <math> T </math> is the absolute temperature and <math> k_B </math> is the [[Boltzmann constant]] | ||
Revision as of 13:10, 27 February 2007
The Lennard-Jones potential is given by
![{\displaystyle V(r)=4\epsilon \left[\left({\frac {\sigma }{r}}\right)^{12}-\left({\frac {\sigma }{r}}\right)^{6}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5256ed833acfbaa9f624a55f4be3f9fcb3c27e1a)
where:
- : potential energy of interaction between two particles at a distance r;
- : diameter (length);
- : well depth (energy)
Reduced units:
- Density, , where (number of particles divided by the volume .)
- Temperature; , where is the absolute temperature and is the Boltzmann constant
References
- J. E. Lennard-Jones "Cohesion", Proc. Phys. Soc. Lond. 43 pp. 461- (1931)