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]]. | ||
==Melting line== | ==Melting line== | ||
The solid and liquid densities along the melting line are given by the equations of Mastny and de Pablo (Ref. 4): | The solid and liquid densities along the melting line are given by the equations of Mastny and de Pablo (Ref. 4 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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and | 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> | :<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 13:24, 17 September 2007
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The equation of state of the Lennard-Jones model.
Melting line
The solid and liquid densities along the melting line are given by the equations of Mastny and de Pablo (Ref. 4 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)
- 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)
- 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)
- 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)