Editing Lennard-Jones equation of state
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The [[equations of state |equation of state]] | The [[equations of state |equation of state]] of the [[Lennard-Jones model]]. | ||
==Johnson, Zollweg and Gubbins== | ==Johnson, Zollweg and Gubbins== | ||
Johnson | Johnson et al <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 | vapor liquid equilibrium]] curve. | ||
==Kolafa and Nezbeda== | ==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> | 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> | ||
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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 | The solid and liquid densities along the 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== | ||
<references/> | <references/> | ||
'''Related reading''' | '''Related reading''' | ||
*[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/10.1016/0378-3812(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/10.1023/A:1023394122000 G. Sh. Boltachev and V. G. Baidakov "Equation of State for Lennard-Jones Fluid", High Temperature '''41''' pp. 270-272 (2003)] | |||
*[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/10.1021/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/10.1063/1.1823371 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)] | ||
{{Numeric}} | {{Numeric}} | ||
[[category: equations of state]] | [[category: equations of state]] |