Lennard-Jones model

The Lennard-Jones potential is given by

$V(r)=4\epsilon \left[\left({\frac {\sigma }{r}}\right)^{12}-\left({\frac {\sigma }{r}}\right)^{6}\right]$

where:

• $V(r)$ : potential energy of interaction between two particles at a distance r;

• $\sigma$ : diameter (length);

• $\epsilon$ : well depth (energy)

Reduced units:

• Density, $\rho ^{*}\equiv \rho \sigma ^{3}$, where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \rho =N/V} (number of particles $N$ divided by the volume $V$.)

• Temperature; Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle T^{*}\equiv k_{B}T/\epsilon } , where $T$ is the absolute temperature and $k_{B}$ is the Boltzmann constant

Argon

The Lennard-Jones parameters for argon are Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \epsilon /k_{B}\approx } 120 K and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \sigma \approx } 0.34 nm.

This figure was produced using gnuplot with the command:

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

References

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