Lennard-Jones equation of state: Difference between revisions

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and the [[internal energy]] (Eq. 32)
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]].
==Melting line==
==Melting line==
The solid and liquid densities along the melting line are given by the equations of 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):
The solid and liquid densities along the melting line are given by the equations of 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):
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:<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>
:<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==
<references/>
<references/>

Revision as of 10:45, 26 June 2009

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The equation of state of the Lennard-Jones model.

Johnson, Zollweg and Gubbins equation of state

Johnson et al [1] proposed an equation of state based on 33 parameters, which accurately reproduces the vapor liquid equilibrium curve.

Kolafa and Nezbeda equation of state

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.

Melting line

The solid and liquid densities along the melting line are given by the equations of Mastny and de Pablo (Ref [3] Eqs. 20 and 21):

and


References

Related reading

  1. 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)
  2. G. Sh. Boltachev and V. G. Baidakov "Equation of State for Lennard-Jones Fluid", High Temperature 41 pp. 270-272 (2003)
  3. 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)
  4. 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)