Lennard-Jones model: Difference between revisions
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* <math> | * <math> \Phi(\sigma) = 0 </math> | ||
* Minimum value of <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:
- is the intermolecular pair potential 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
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
- 1-dimensional case: Lennard-Jones rods.
- 2-dimensional case: Lennard-Jones disks.