N-6 Lennard-Jones potential: Difference between revisions
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The '''n-6 Lennard-Jones potential''' is a variant the more well known [[Lennard-Jones model]] (or from a different point of view, a particular case of the [[Mie potential]]) | {{lowercase title}} | ||
The '''n-6 Lennard-Jones potential''' is a variant the more well known [[Lennard-Jones model]] (or from a different point of view, a particular case of the [[Mie potential]]). The potential is given by <ref>[http://dx.doi.org/10.1063/1.3253686 Alauddin Ahmed and Richard J. Sadus "Solid-liquid equilibria and triple points of n-6 Lennard-Jones fluids", Journal of Chemical Physics '''131''' 174504 (2009)]</ref>: | |||
:<math> \Phi_{12}(r) = \epsilon \left( \frac{n}{n-6} \right)\left( \frac{n}{6} \right)^{\frac{6}{n-6}} \left[ \left(\frac{\sigma}{r} \right)^{n}- \left( \frac{\sigma}{r}\right)^6 \right] </math> | :<math> \Phi_{12}(r) = \epsilon \left( \frac{n}{n-6} \right)\left( \frac{n}{6} \right)^{\frac{6}{n-6}} \left[ \left(\frac{\sigma}{r} \right)^{n}- \left( \frac{\sigma}{r}\right)^6 \right] </math> | ||
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where | where | ||
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | * <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | ||
* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles | * <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles, "1" and "2". | ||
* <math> \sigma </math> is the diameter (length), ''i.e.'' the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math> | * <math> \sigma </math> is the diameter (length), ''i.e.'' the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math> | ||
* <math> \epsilon </math> is the well depth (energy) | * <math> \epsilon </math> is the well depth (energy) | ||
==Melting point== | ==Melting point== | ||
An approximate method to locate the melting point is given in <ref>[http://dx.doi.org/10.1063/1.3552948 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics '''134''' 054120 (2011)]</ref>. | An approximate method to locate the melting point is given in <ref>[http://dx.doi.org/10.1063/1.3552948 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics '''134''' 054120 (2011)]</ref>. See also <ref>[http://dx.doi.org/10.1063/1.4707746 J. M. G. Sousa, A. L. Ferreira, and M. A. Barroso "Determination of the solid-fluid coexistence of the n − 6 Lennard-Jones system from free energy calculations", Journal of Chemical Physics '''136''' 174502 (2012)]</ref>. | ||
==Shear viscosity== | |||
<ref>[http://dx.doi.org/10.1063/1.4919296 Stephanie Delage-Santacreu, Guillaume Galliero, Hai Hoang, Jean-Patrick Bazile, Christian Boned and Josefa Fernandez "Thermodynamic scaling of the shear viscosity of Mie n-6 fluids and their binary mixtures", Journal of Chemical Physics '''142''' 174501 (2015)]</ref> | |||
==References== | ==References== | ||
<references/> | <references/> | ||
;Related reading | |||
*[http://dx.doi.org/10.1063/1.3627148 Zane Shi, Pablo G. Debenedetti, Frank H. Stillinger, and Paul Ginart "Structure, dynamics, and thermodynamics of a family of potentials with tunable softness", Journal of Chemical Physics '''135''' 084513 (2011)] | |||
*[http://dx.doi.org/10.1063/1.4930138 Jason R. Mick, Mohammad Soroush Barhaghi, Brock Jackman, Kamel Rushaidat, Loren Schwiebert and Jeffrey J. Potoff "Optimized Mie potentials for phase equilibria: Application to noble gases and their mixtures with n-alkanes", Journal of Chemical Physics '''143''' 114504 (2015)] | |||
*[https://doi.org/10.1021/acs.jced.6b01036 Jason R. Mick, Mohammad Soroush Barhaghi, Brock Jackman, Loren Schwiebert, and Jeffrey J. Potoff "Optimized Mie Potentials for Phase Equilibria: Application to Branched Alkanes", Journal of Chemical Engineering Data '''62''' 1806–1818 (2017)] | |||
*[https://doi.org/10.1080/00268976.2017.1297862 Mohammad Soroush Barhaghi, Jason R. Mick, and Jeffrey J. Potoff "Optimised Mie potentials for phase equilibria: application to alkynes", Journal of Molecular Physics '''115''' 1378-1388 (2017)] | |||
*[https://doi.org/10.1063/1.5039504 Richard A. Messerly, Michael R. Shirts, and Andrei F. Kazakov "Uncertainty quantification confirms unreliable extrapolation toward high pressures for united-atom Mie λ-6 force field", Journal of Chemical Physics '''149''' 114109 (2018)] | |||
[[category: models]] | [[category: models]] | ||
Latest revision as of 14:59, 4 May 2022
The n-6 Lennard-Jones potential is a variant the more well known Lennard-Jones model (or from a different point of view, a particular case of the Mie potential). The potential is given by [1]:
![{\displaystyle \Phi _{12}(r)=\epsilon \left({\frac {n}{n-6}}\right)\left({\frac {n}{6}}\right)^{\frac {6}{n-6}}\left[\left({\frac {\sigma }{r}}\right)^{n}-\left({\frac {\sigma }{r}}\right)^{6}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f27dcbb376b2716bf1ca362c9d484c709b691f7)
where
- is the intermolecular pair potential between two particles, "1" and "2".
- is the diameter (length), i.e. the value of at which
- is the well depth (energy)
Melting point[edit]
An approximate method to locate the melting point is given in [2]. See also [3].
Shear viscosity[edit]
References[edit]
- ↑ Alauddin Ahmed and Richard J. Sadus "Solid-liquid equilibria and triple points of n-6 Lennard-Jones fluids", Journal of Chemical Physics 131 174504 (2009)
- ↑ Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics 134 054120 (2011)
- ↑ J. M. G. Sousa, A. L. Ferreira, and M. A. Barroso "Determination of the solid-fluid coexistence of the n − 6 Lennard-Jones system from free energy calculations", Journal of Chemical Physics 136 174502 (2012)
- ↑ Stephanie Delage-Santacreu, Guillaume Galliero, Hai Hoang, Jean-Patrick Bazile, Christian Boned and Josefa Fernandez "Thermodynamic scaling of the shear viscosity of Mie n-6 fluids and their binary mixtures", Journal of Chemical Physics 142 174501 (2015)
- Related reading
- Zane Shi, Pablo G. Debenedetti, Frank H. Stillinger, and Paul Ginart "Structure, dynamics, and thermodynamics of a family of potentials with tunable softness", Journal of Chemical Physics 135 084513 (2011)
- Jason R. Mick, Mohammad Soroush Barhaghi, Brock Jackman, Kamel Rushaidat, Loren Schwiebert and Jeffrey J. Potoff "Optimized Mie potentials for phase equilibria: Application to noble gases and their mixtures with n-alkanes", Journal of Chemical Physics 143 114504 (2015)
- Jason R. Mick, Mohammad Soroush Barhaghi, Brock Jackman, Loren Schwiebert, and Jeffrey J. Potoff "Optimized Mie Potentials for Phase Equilibria: Application to Branched Alkanes", Journal of Chemical Engineering Data 62 1806–1818 (2017)
- Mohammad Soroush Barhaghi, Jason R. Mick, and Jeffrey J. Potoff "Optimised Mie potentials for phase equilibria: application to alkynes", Journal of Molecular Physics 115 1378-1388 (2017)
- Richard A. Messerly, Michael R. Shirts, and Andrei F. Kazakov "Uncertainty quantification confirms unreliable extrapolation toward high pressures for united-atom Mie λ-6 force field", Journal of Chemical Physics 149 114109 (2018)