Lennard-Jones equation of state: Difference between revisions
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The equation of state of the [[Lennard-Jones model]]. | The equation of state of the [[Lennard-Jones model]]. | ||
== | ==Johnson, Zollweg and Gubbins equation of state== | ||
Johnson et al [ | 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, which accurately reproduces the [[Density-temperature | vapor liquid equilibrium]] curve. | ||
==Kolafa and Nezbeda equation of state== | |||
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> | |||
==Melting line== | ==Melting line== | ||
The solid and liquid densities along the melting line are given by the equations of Mastny and de Pablo (Ref. | 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): | ||
:<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> | :<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> | ||
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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/> | |||
'''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/10.1023/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)] | ||
# | # | ||
[[category: equations of state]] | [[category: equations of state]] | ||
Revision as of 10:30, 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]
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):
![{\displaystyle \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]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d42739dd208f4ac0bb02525ea454ca8598593fd)
and
![{\displaystyle \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]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f25d53a5319a238d2c5b4ace3f32f59054dea660)
References
- ↑ J. Karl Johnson, John A. Zollweg and Keith E. Gubbins "The Lennard-Jones equation of state revisited", Molecular Physics 78 pp. 591-618 (1993)
- ↑ 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)
- ↑ 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)
Related reading
- 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)
- G. Sh. Boltachev and V. G. Baidakov "Equation of State for Lennard-Jones Fluid", High Temperature 41 pp. 270-272 (2003)
- 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)
- 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)