Lennard-Jones equation of state

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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.


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.


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).


  1. 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)
  2. Simon Stephan, Ulrich K. Deiters "Characteristic Curves of the Lennard‑Jones Fluid" International Journal of Thermophysics 41 147 pp. 112772 (2020)
  3. J. Karl Johnson, John A. Zollweg and Keith E. Gubbins "The Lennard-Jones equation of state revisited", Molecular Physics 78 pp. 591-618 (1993)
  4. 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)
  5. Francis H. Ree "Analytic representation of thermodynamic data for the Lennard‐Jones fluid", Journal of Chemical Physics 73 pp. 5401-5403 (1980)
  6. Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A 2 pp. 221-230 (1970)
  7. G. Sh. Boltachev and V. G. Baidakov "Equation of State for Lennard-Jones Fluid", High Temperature 41 pp. 270-272 (2003)
  8. 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)
  9. 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)
  10. 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)

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