Lennard-Jones model: Difference between revisions

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The '''Lennard-Jones''' potential, developed by [[ Sir John Edward Lennard-Jones KBE, FRS | Sir John Edward Lennard-Jones]], is given by
The '''Lennard-Jones''' potential, developed by [[ Sir John Edward Lennard-Jones KBE, FRS | Sir John Edward Lennard-Jones]], is given by


:<math> V(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}-  \left( \frac{\sigma}{r}\right)^6 \right] </math>
:<math> \Phi(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}-  \left( \frac{\sigma}{r}\right)^6 \right] </math>


where:
where:


* <math> V(r) </math> : potential energy of interaction between two particles at a distance r;  
* <math> \Phi(r) </math> is the [[intermolecular pair potential]] between two particles at a distance r;  


* <math> \sigma </math> : diameter (length);
* <math> \sigma </math> : diameter (length);

Revision as of 14:00, 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)