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:

• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle V(r)}  : potential energy of interaction between two particles at a distance r;

• $\sigma$ : diameter (length);

• $\epsilon$ : well depth (energy)

Reduced units:

• Density, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T } is the absolute temperature and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_B } is the Boltzmann constant

References

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