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N-6 Lennard-Jones potential

2022-05-04T13:59:10Z

MohammadSB: /* References */

{{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>

where
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>
* <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> \epsilon </math> is the well depth (energy)
==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>. 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/>
;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]]

Gibbs ensemble Monte Carlo

2017-04-25T21:58:59Z

MohammadSB: Fixing the GitHub link

Phase separation is one of the topics to which [[Computer simulation techniques |simulation techniques]] are increasingly applied. Different procedures are available for this purpose. For the particular case of chain systems, one can employ simulations in the [[Semi-grand ensembles | semi-grand canonical ensemble]], [[histogram reweighting]], or characterization of the [[spinodal curve]] from the study of computed [[collective scattering function]].
The Gibbs ensemble Monte Carlo method has been specifically designed to characterize [[phase transitions]]. It was mainly developed by Panagiotopoulos <ref>[http://dx.doi.org/10.1080/00268978700101491 Athanassios Panagiotopoulos "Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble", Molecular Physics '''61''' pp. 813-826 (1987)]</ref>
<ref>[http://dx.doi.org/10.1080/00268978800100361 A. Z. Panagiotopoulos, N. Quirke, M. Stapleton and D. J. Tildesley "Phase equilibria by simulation in the Gibbs ensemble: Alternative derivation, generalization and application to mixture and membrane equilibria", Molecular Physics '''61''' pp. 527-545 (1988)]</ref> to avoid the problem of finite size interfacial effects. In this method, an [[Canonical ensemble |NVT]] (or [[Isothermal-isobaric ensemble |NpT]]) ensemble containing two (or more) species is divided into two (or more) boxes. In addition to the usual particle moves in each one of the boxes, the algorithm includes moves steps to change the volume and composition of the boxes at mechanical and chemical equilibrium. Transferring a chain molecule from a box to the other requires the use of an efficient method to insert chains. The [[Configurational bias Monte Carlo | configurational bias method]] is specially recommended for this purpose.
==See also==
*[[Gibbs ensemble]]
==References==
<references/>
;Related reading
*[http://dx.doi.org/10.1063/1.4930848 Mohammadhasan Dinpajooh, Peng Bai, Douglas A. Allan and J. Ilja Siepmann "Accurate and precise determination of critical properties from Gibbs ensemble Monte Carlo simulations", Journal of Chemical Physics '''143''' 114113 (2015)]
==External links==
*[http://kea.princeton.edu/jerring/gibbs/ Gibbs ensemble Monte Carlo code] on the [http://www.princeton.edu/che/people/faculty/panagiotopoulos/group/ Panagiotopoulos Group Homepage]
*[http://gomc.eng.wayne.edu GPU Optimized Monte Carlo] on the [https://github.com/GOMC-WSU GOMC GitHub Page]
[[category: Monte Carlo]]
[[category: Computer simulation techniques]]

Gibbs ensemble Monte Carlo

2017-04-25T21:55:52Z

MohammadSB: Added an external link to GOMC project website and GitHub page.

Phase separation is one of the topics to which [[Computer simulation techniques |simulation techniques]] are increasingly applied. Different procedures are available for this purpose. For the particular case of chain systems, one can employ simulations in the [[Semi-grand ensembles | semi-grand canonical ensemble]], [[histogram reweighting]], or characterization of the [[spinodal curve]] from the study of computed [[collective scattering function]].
The Gibbs ensemble Monte Carlo method has been specifically designed to characterize [[phase transitions]]. It was mainly developed by Panagiotopoulos <ref>[http://dx.doi.org/10.1080/00268978700101491 Athanassios Panagiotopoulos "Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble", Molecular Physics '''61''' pp. 813-826 (1987)]</ref>
<ref>[http://dx.doi.org/10.1080/00268978800100361 A. Z. Panagiotopoulos, N. Quirke, M. Stapleton and D. J. Tildesley "Phase equilibria by simulation in the Gibbs ensemble: Alternative derivation, generalization and application to mixture and membrane equilibria", Molecular Physics '''61''' pp. 527-545 (1988)]</ref> to avoid the problem of finite size interfacial effects. In this method, an [[Canonical ensemble |NVT]] (or [[Isothermal-isobaric ensemble |NpT]]) ensemble containing two (or more) species is divided into two (or more) boxes. In addition to the usual particle moves in each one of the boxes, the algorithm includes moves steps to change the volume and composition of the boxes at mechanical and chemical equilibrium. Transferring a chain molecule from a box to the other requires the use of an efficient method to insert chains. The [[Configurational bias Monte Carlo | configurational bias method]] is specially recommended for this purpose.
==See also==
*[[Gibbs ensemble]]
==References==
<references/>
;Related reading
*[http://dx.doi.org/10.1063/1.4930848 Mohammadhasan Dinpajooh, Peng Bai, Douglas A. Allan and J. Ilja Siepmann "Accurate and precise determination of critical properties from Gibbs ensemble Monte Carlo simulations", Journal of Chemical Physics '''143''' 114113 (2015)]
==External links==
*[http://kea.princeton.edu/jerring/gibbs/ Gibbs ensemble Monte Carlo code] on the [http://www.princeton.edu/che/people/faculty/panagiotopoulos/group/ Panagiotopoulos Group Homepage]
*[http://gomc.eng.wayne.edu GPU Optimized Monte Carlo] on the [https://github.com/GOMC-WSU/GOMC GOMC GitHub Page]
[[category: Monte Carlo]]
[[category: Computer simulation techniques]]