Lennard-Jones equation of state

The equation of state (EOS) of the Lennard-Jones model. Lennard-Jones EOS are widely used – especially in soft matter physics. Lennard-Jones EOS are also often used as a point of departure for the development of models of complex fluids. A large number of Lennard-Jones EOS have been developed in the past. Several popular Lennard-Jones EOS for the fluid phases were systematically compared and evaluated to simulation data . The one of Kolafa and Nezbeda was therein found to be the most robust and accurate Lennard-Jones EOS. Ref. gives a comprehensive review of EOS of the Lennard-Jones fluid. Overall, it was found that none of the presently available EOS gives a satisfactory description of the Lennard-Jones fluid, which makes the development of LJ EOS still an active field.

Johnson, Zollweg and Gubbins

Johnson, Zollweg and Gubbins proposed an equation of state based on 33 parameters within a modified Benedict, Webb and Rubin equation of state, which accurately reproduces the vapour-liquid equilibrium curve.

Kolafa and Nezbeda

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

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

the compressibility factor (Eq. 31)

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

and the internal energy (Eq. 32)

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

On the following page is the FORTRAN code for the Kolafa and Nezbeda equation of state.

Ree

The Ree equation of state is an extension of the earlier work of Hansen in the high temperature region.

Boltachev and Baidakov

Boltachev and Baidakov have paid particular attention to including data from the metastable region .

Pieprzyk-Brańka-Maćkowiak and Heyes

The Pieprzyk-Brańka-Maćkowiak and Heyes equation of state consists of a parameterisation of the modified Benedict, Webb and Rubin equation of state.

PeTS

The PeTS (perturbed truncated and shifted) equation of state for pure components and mixtures (only for the Lennard-Jones truncated and shifted fluid).

References

Related reading

• J. J. Nicolas, K. E. Gubbins, W. B. Streett and D. J. Tildesley "Equation of state for the Lennard-Jones fluid", Molecular Physics 37 pp. 1429-1454 (1979)
• Karel Aim, Jirí Kolafa, Ivo Nezbeda and Horst L. Vörtler "The Lennard-Jones fluid revisited: new thermodynamic data and new equation of state", Fluid Phase Equilibria 83 pp. 15-22 (1993)
• 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)
• 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)
• Sergey A. Khrapak and Gregor E. Morfill "Accurate freezing and melting equations for the Lennard-Jones system", Journal of Chemical Physics 134 094108 (2011)
• Monika Thol, Gabor Rutkai, Andreas Köster, Rolf Lustig, Roland Span, and Jadran Vrabec "Equation of State for the Lennard-Jones Fluid", Journal of Physical and Chemical Reference Data 45 023101 (2016)