# 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 ^{[1]}^{[2]}. The one of Kolafa and Nezbeda was therein found to be the most robust and accurate Lennard-Jones EOS. Ref. ^{[1]} 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[edit]

Johnson, Zollweg and Gubbins ^{[3]} 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[edit]

The Kolafa and Nezbeda equation of state ^{[4]}
provides us with the Helmholtz energy function: (Eq. 30):

the compressibility factor (Eq. 31)

and the internal energy (Eq. 32)

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

## Ree[edit]

The Ree equation of state ^{[5]} is an extension of the earlier work of Hansen ^{[6]} in the high temperature region.

## Boltachev and Baidakov[edit]

Boltachev and Baidakov have paid particular attention to including data from the metastable region ^{[7]}.

## Pieprzyk-Brańka-Maćkowiak and Heyes[edit]

The Pieprzyk-Brańka-Maćkowiak and Heyes equation of state ^{[8]}
consists of a parameterisation of the modified Benedict, Webb and Rubin equation of state.

## PeTS[edit]

The PeTS (perturbed truncated and shifted) equation of state for pure components ^{[9]} and mixtures ^{[10]} (only for the Lennard-Jones truncated and shifted fluid).

## References[edit]

- ↑
^{1.0}^{1.1}Simon Stephan, Jens Staubach, Hans Hasse "Review and comparison of equations of state for the Lennard-Jones fluid", Fluid Phase Equilibria**523**pp. 112772 (2020) - ↑ Simon Stephan, Ulrich K. Deiters "Characteristic Curves of the Lennard‑Jones Fluid" International Journal of Thermophysics
**41**147 pp. 112772 (2020) - ↑ J. Karl Johnson, John A. Zollweg and Keith E. Gubbins "The Lennard-Jones equation of state revisited", Molecular Physics
**78**pp. 591-618 (1993) - ↑ Jirí Kolafa, Ivo Nezbeda "The Lennard-Jones fluid: an accurate analytic and theoretically-based equation of state", Fluid Phase Equilibria
**100**pp. 1-34 (1994) - ↑ Francis H. Ree "Analytic representation of thermodynamic data for the Lennard‐Jones fluid", Journal of Chemical Physics
**73**pp. 5401-5403 (1980) - ↑ Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A
**2**pp. 221-230 (1970) - ↑ G. Sh. Boltachev and V. G. Baidakov "Equation of State for Lennard-Jones Fluid", High Temperature
**41**pp. 270-272 (2003) - ↑ S. Pieprzyk, A. C. Brańka, Sz. Maćkowiak and D. M. Heyes "Comprehensive representation of the Lennard-Jones equation of state based on molecular dynamics simulation data", Journal of Chemical Physics
**148**114505 (2018) - ↑ Michaela Heier, Simon Stephan, Jinlu Liu, Walter G. Chapman, Hans Hasse and Kai Langenbach "Equation of state for the Lennard-Jones truncated and shifted fluid with a cut-off radius of 2.5σ based on perturbation theory and its applications to interfacial thermodynamics", Molecular Physics
**116**pp. 2083-2094 (2018) - ↑ Simon Stephan, Kai Langenbach, Hans Hasse "interfacial properties of binary Lennard-Jones mixtures by molecular simulation and density gradient theory", Journal of Chemical Physics
**150**pp. 174704 (2019)

**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)