Lennard-Jones equation of state

The equation of state of the Lennard-Jones model.

Melting line

The solid and liquid densities along the melting line are given by the equations of Mastny and de Pablo (Ref. 4 Eqs. 20 and 21):

$\rho _{\mathrm {solid} }=\beta ^{-1/4}\left[0.908629-0.041510\beta +0.514632\beta ^{2}-0.708590\beta ^{3}+0.428351\beta ^{4}-0.095229\beta ^{5}\right]$

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 \rho_{\mathrm {liquid}} = \beta^{-1/4} \left[ 0.90735 - 0.27120 \beta + 0.91784 \beta^2 -1.16270\beta^3 + 0.68012 \beta^4 -0.15284 \beta^5\right]}

References

1. J. Karl Johnson, John A. Zollweg and Keith E. Gubbins "The Lennard-Jones equation of state revisited", Molecular Physics 78 pp. 591-618 (1993)
2. David M. Eike, Joan F. Brennecke, and Edward J. Maginn "Toward a robust and general molecular simulation method for computing solid-liquid coexistence", Journal of Chemical Physics 122 014115 (2005)
3. Hertanto Adidharma and Maciej Radosz "The LJ-Solid Equation of State Extended to Thermal Properties, Chain Molecules, and Mixtures", Industrial and Engineering Chemistry Research 43 pp. 6890 - 6897 (2004)
4. Ethan A. Mastny and Juan J. de Pablo "Melting line of the Lennard-Jones system, infinite size, and full potential", Journal of Chemical Physics 127 104504 (2007)