Lennard-Jones equation of state: Difference between revisions

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The equation of state of the [[Lennard-Jones model]].
The [[equations of state |equation of state]] of the [[Lennard-Jones model]].
==Johnson, Zollweg and Gubbins==
Johnson, Zollweg and Gubbins <ref>[http://dx.doi.org/10.1080/00268979300100411 J. Karl Johnson, John A. Zollweg and Keith E. Gubbins "The Lennard-Jones equation of state revisited", Molecular Physics '''78''' pp. 591-618 (1993)]</ref> proposed an equation of state based on 33 parameters within a modified [[Benedict, Webb and Rubin equation of state]], which accurately reproduces the [[Density-temperature | vapour-liquid equilibrium]] curve.


==Kolafa and Nezbeda==
The Kolafa and Nezbeda equation of state <ref>[http://dx.doi.org/10.1016/0378-3812(94)80001-4  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)]</ref>
provides us with the [[Helmholtz energy function]]: (Eq. 30):
:<math>A=A_{\mathrm{HS}} + \exp (-\gamma \rho^2) \rho T \Delta B_{2,{\mathrm{hBH}}} + \sum_{ij} C_{ij} T^{i/2} \rho^j</math>
the [[compressibility factor]] (Eq. 31)
:<math>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</math>
and the [[internal energy]] (Eq. 32)
:<math>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
</math>
On the following page is the [[FORTRAN code for the Kolafa and Nezbeda equation of state]].
==Ree==
The Ree equation of state <ref>[http://dx.doi.org/10.1063/1.439940 Francis H. Ree "Analytic representation of thermodynamic data for the Lennard‐Jones fluid", Journal of Chemical Physics '''73''' pp. 5401-5403 (1980)]</ref> is an extension of the earlier work of Hansen <ref>[http://dx.doi.org/10.1103/PhysRevA.2.221 Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A '''2''' pp. 221-230 (1970)]</ref> in the high temperature region.
==Boltachev and Baidakov==
Boltachev and Baidakov have paid particular attention to including data from the metastable region <ref>[http://dx.doi.org/10.1023/A:1023394122000 G. Sh. Boltachev and V. G. Baidakov "Equation of State for Lennard-Jones Fluid", High Temperature '''41''' pp. 270-272 (2003)]</ref>.
==Pieprzyk-Brańka-Maćkowiak and Heyes==
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]].
==PeTS==
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==
#[http://dx.doi.org/10.1080/00268979300100411 J. Karl Johnson, John A. Zollweg and Keith E. Gubbins "The Lennard-Jones equation of state revisited", Molecular Physics '''78''' pp. 591-618 (1993)]
<references/>
#[http://dx.doi.org/10.1063/1.1823371    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)]
'''Related reading'''
#[http://dx.doi.org/10.1021/ie0495628 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)]
*[http://dx.doi.org/10.1080/00268977900101051 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)]
#[http://dx.doi.org/10.1063/1.2753149     Ethan A. Mastny and Juan J. de Pablo "Melting line of the Lennard-Jones system, infinite size, and full potential", Journal of Chemical Physics '''127''' 104504 (2007)]
*[http://dx.doi.org/10.1016/0378-3812(93)87002-I  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)]
*[http://dx.doi.org/10.1021/ie0495628 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)]
*[http://dx.doi.org/10.1063/1.1823371     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)]
*[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)]
 
 
{{Numeric}}
[[category: equations of state]]
[[category: equations of state]]

Revision as of 13:01, 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):

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

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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