# 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

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

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

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

the compressibility factor (Eq. 31)

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

and the internal energy (Eq. 32)

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

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

## Ree

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

## Boltachev and Baidakov

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

## Pieprzyk-Brańka-Maćkowiak and Heyes

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

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).