Lennard-Jones equation of state

Johnson, Zollweg and Gubbins equation of state

Johnson et al ^[1] proposed an equation of state based on 33 parameters within a modified Benedict, Webb and Rubin equation of state, which accurately reproduces the vapor liquid equilibrium curve.

The Kolafa and Nezbeda equation of state ^[2] provides us with the Helmholtz energy function: (Eq. 30):

A=A_{\mathrm {HS} }+\exp(-\gamma \rho ^{2})\rho T\Delta B_{2,{\mathrm {hBH} }}+\sum _{ij}C_{ij}T^{i/2}\rho ^{j}

z\equiv {\frac {P}{\rho T}}=z_{\mathrm {HS} }+\rho (1-2\gamma \rho ^{2})\exp(-\gamma \rho ^{2})\Delta B_{2,{\mathrm {hBH} }}+\sum _{ij}jC_{ij}T^{i/2-1}\rho ^{j}

and the internal energy (Eq. 32)

U={3(z_{\rm {HS}}-1) \over d_{\rm {hBH}}}\,{\partial d_{\rm {hBH}} \over \partial (1/T)}+\rho \exp(-\gamma \rho ^{2})\,{\partial \Delta B_{\rm {2,hBH}} \over \partial (1/T)}-\sum _{ij}\left({i \over 2}-1\right)C_{ij}\,T^{i/2}\rho ^{j}

The solid and liquid densities along the melting line are given by the equations of Mastny and de Pablo (Ref ^[3] 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

\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]

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