Lennard-Jones equation of state: Difference between revisions

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==Boltachev and Baidakov==
==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>.
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>.
==Melting line==
The solid and liquid densities along the [[Melting curve |melting line]] are given by the following equations
====van der Hoef====
van der Hoef (Ref. <ref>[http://dx.doi.org/10.1063/1.1314342 Martin A. van der Hoef "Free energy of the Lennard-Jones solid", Journal of Chemical Physics '''113''' pp. 8142-8148 (2000)]</ref> Eqs. 25 and 26):
:<math>\rho_{\mathrm {solid}} = \beta^{-1/4} \left[ 0.92302 - 0.09218 \beta + 0.62381 \beta^2 -0.82672 \beta^3 + 0.49124  \beta^4 -0.10847 \beta^5\right]</math>
and
:<math>\rho_{\mathrm {liquid}} = \beta^{-1/4} \left[ 0.91070 - 0.25124 \beta + 0.85861 \beta^2 -1.08918 \beta^3 + 0.63932 \beta^4 -0.14433 \beta^5\right]</math>
====Mastny and  de Pablo====
Mastny and  de Pablo (Ref <ref>[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)]</ref> Eqs. 20 and 21):
:<math>\rho_{\mathrm {solid}} = \beta^{-1/4} \left[ 0.908629 - 0.041510 \beta + 0.514632 \beta^2 -0.708590\beta^3 + 0.428351 \beta^4 -0.095229 \beta^5\right]</math>
and
:<math>\rho_{\mathrm {liquid}} = \beta^{-1/4} \left[ 0.90735 - 0.27120 \beta + 0.91784 \beta^2 -1.16270\beta^3 + 0.68012 \beta^4 -0.15284 \beta^5\right]</math>


==References==
==References==

Revision as of 15:38, 22 December 2015

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):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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_{\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].

References

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

Related reading


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