Difference between revisions of "Lennard-Jones equation of state"

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The Pieprzyk-Brańka-Maćkowiak and Heyes equation of state <ref>[https://doi.org/10.1063/1.5021560 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)]</ref>
 
The Pieprzyk-Brańka-Maćkowiak and Heyes equation of state <ref>[https://doi.org/10.1063/1.5021560 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)]</ref>
 
consists of a parameterisation of the  modified [[Benedict, Webb and Rubin equation of state]].
 
consists of a parameterisation of the  modified [[Benedict, Webb and Rubin equation of state]].
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==PeTS==
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The PeTS (perturbed truncated and shifted) equation of state <ref>[https://doi.org/10.1080/00268976.2018.1447153 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)]</ref>.
 
==References==
 
==References==
 
<references/>
 
<references/>
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*[http://dx.doi.org/10.1063/1.3561698 Sergey A. Khrapak and Gregor E. Morfill "Accurate freezing and melting equations for the Lennard-Jones system", Journal of Chemical Physics '''134''' 094108 (2011)]
 
*[http://dx.doi.org/10.1063/1.3561698 Sergey A. Khrapak and Gregor E. Morfill "Accurate freezing and melting equations for the Lennard-Jones system", Journal of Chemical Physics '''134''' 094108 (2011)]
 
*[https://doi.org/10.1063/1.4945000 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)]
 
*[https://doi.org/10.1063/1.4945000 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)]
*[https://doi.org/10.1080/00268976.2018.1447153 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)]
 
  
  
 
{{Numeric}}
 
{{Numeric}}
 
[[category: equations of state]]
 
[[category: equations of state]]

Revision as of 14:01, 12 September 2018

The equation of state of the Lennard-Jones model.

Johnson, Zollweg and Gubbins

Johnson, Zollweg and Gubbins [1] 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 [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

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_{\rm2,hBH}\over\partial (1/T)}
 - \sum_{ij} \left({i\over2}-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 [3] is an extension of the earlier work of Hansen [4] in the high temperature region.

Boltachev and Baidakov

Boltachev and Baidakov have paid particular attention to including data from the metastable region [5].

Pieprzyk-Brańka-Maćkowiak and Heyes

The Pieprzyk-Brańka-Maćkowiak and Heyes equation of state [6] consists of a parameterisation of the modified Benedict, Webb and Rubin equation of state.

PeTS

The PeTS (perturbed truncated and shifted) equation of state [7].

References

Related reading


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