Lennard-Jones model: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
Line 30: Line 30:
Special points:
Special points:


* <math> V(\sigma) = 0 </math>
* <math> \Phi(\sigma) = 0 </math>


* Minimum value of <math> V(r) </math> at <math> r = r_{min} </math>;   
* Minimum value of <math> \Phi(r) </math> at <math> r = r_{min} </math>;   


: <math> \frac{r_{min}}{\sigma} = 2^{1/6} \simeq  1.12246 ...  </math>
: <math> \frac{r_{min}}{\sigma} = 2^{1/6} \simeq  1.12246 ...  </math>

Revision as of 14:01, 21 June 2007

Lennard-Jones potential

The Lennard-Jones potential, developed by Sir John Edward Lennard-Jones, is given by

where:

  •  : 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

Argon

The Lennard-Jones parameters for argon are 119.8 K and 0.3405 nm. (Ref. ?)

This figure was produced using gnuplot with the command:

plot (4*120*((0.34/x)**12-(0.34/x)**6))

Features

Special points:

  • Minimum value of at ;

Approximations in simulation: truncation and shifting

Related potential models

It is relatively common the use of potential functions given by:

with and being positive integer numbers and , and is chosen to get the minumum value of being

These forms are usually refered to as m-n Lennard-Jones Potential.

The 9-3 Lennard-Jones interaction potential is often use to model the interaction between the atoms/molecules of a fluid and a continuous solid wall. In (9-3 Lennard-Jones potential) a justification of this use is presented.

Other dimensions

References

  1. J. E. Lennard-Jones, "Cohesion", Proceedings of the Physical Society, 43 pp. 461-482 (1931)