Lennard-Jones equation of state: Difference between revisions
Jump to navigation
Jump to search
Carl McBride (talk | contribs) No edit summary |
Carl McBride (talk | contribs) |
||
| Line 2: | Line 2: | ||
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> | ||
| Line 8: | Line 8: | ||
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 14:24, 17 September 2007
|
This page contains numerical values and/or equations. If you intend to use ANY of the numbers or equations found in SklogWiki in any way, you MUST take them from the original published article or book, and cite the relevant source accordingly. |
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)