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'''Argon''' (Ar) has long been a popular choice for [[Computer simulation techniques |computer simulations]] of simple liquids. Some of the first computer simulations of liquid argon were those of Wood and Parker in 1957 <ref>[http://dx.doi.org/10.1063/1.1743822 W. W. Wood and F. R. Parker "Monte Carlo Equation of State of Molecules Interacting with the Lennard‐Jones Potential. I. A Supercritical Isotherm at about Twice the Critical Temperature", Journal of Chemical Physics '''27''' pp. 720- (1957)]</ref>  and of Rahman in 1964 <ref name="Rahman">[http://dx.doi.org/10.1103/PhysRev.136.A405 A. Rahman "Correlations in the Motion of Atoms in Liquid Argon", Physical Review '''136''' pp. A405–A411 (1964)]</ref>. Sadus and Prausnitz have shown that three-body repulsion makes a significant contribution to [[Idealised models#Three-body potentials|three-body interactions]] in the liquid phase
[[Image:Lennard-Jones.png|thumb| The Lennard-Jones model for argon.]]
'''Argon''' (Ar) has a mass of 39.948 [[atomic mass units | umas]]. Sadus and Prausnitz have shown that three-body repulsion makes a significant contribution to [[Idealised models#Three-body potentials|three-body interactions]] in the liquid phase
<ref>[http://dx.doi.org/10.1063/1.471172 Richard J. Sadus and J. M. Prausnitz "Three-body interactions in fluids from molecular simulation: Vapor–liquid phase coexistence of argon", Journal of Chemical Physics '''104''' pp. 4784-4787 (1996)]</ref>
<ref>[http://dx.doi.org/10.1063/1.471172 Richard J. Sadus and J. M. Prausnitz "Three-body interactions in fluids from molecular simulation: Vapor–liquid phase coexistence of argon", Journal of Chemical Physics '''104''' pp. 4784-4787 (1996)]</ref>
(for use of the [[Axilrod-Teller interaction]] see  
(for use of the [[Axilrod-Teller interaction]] see  
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However, the generic [[Lennard-Jones model]] has been frequently used due to its simplicity; some parameters are quoted in the next section. A specific interatomic potential for Ar has been proposed by Aziz  
However, the generic [[Lennard-Jones model]] has been frequently used due to its simplicity; some parameters are quoted in the next section. A specific interatomic potential for Ar has been proposed by Aziz  
<ref>[http://dx.doi.org/10.1063/1.466051  Ronald A. Aziz "A highly accurate interatomic potential for argon", Journal of Chemical Physics '''99''' p. 4518 (1993)]</ref>.
<ref>[http://dx.doi.org/10.1063/1.466051  Ronald A. Aziz "A highly accurate interatomic potential for argon", Journal of Chemical Physics '''99''' p. 4518 (1993)]</ref>.
 
==Lennard-Jones parameters==
==Thermophysical properties (experimental) ==
The [[Lennard-Jones model |Lennard-Jones]] parameters for liquid argon are listed in the following table:
 
{| border="1"
{| border="1"
|-  
|-  
| Property  <ref>[http://www.webelements.com/argon/physics.html Physical properties of Argon on webelements]  </ref> || Temperature || Pressure
| Authors || <math>\epsilon/k_B</math> (K) || <math>\sigma</math>  (nm)|| Reference
|-
| Triple point || 83.8058 K  || 69 kPa
|-
| Critical point || 150.87 K || 4.898 MPa
|-
| Melting point || 83.80 K ||
|-
| Boiling point ||87.30 K ||
|}
==Models==
====Lennard-Jones parameters====
[[Image:Lennard-Jones.png|thumb| The Lennard-Jones  model for argon (Rowley, Nicholson and Parsonage parameters).]]
A selection of parameters for the [[Lennard-Jones model]] for liquid argon are listed in the following table:
{| border="1"
|-
| Authors || <math>\epsilon/k_B</math> (K) || <math>\sigma</math>  (nm)|| Reference (year)
|-
| Rahman || 120  || 0.34  || <ref name="Rahman"></ref> (1964)
|-  
|-  
|Barker, Fisher and Watts  ||142.095   || 0.33605 || <ref>[http://dx.doi.org/10.1080/00268977100101821 J. A. Barker, R. A. Fisher and R. O. Watts "Liquid argon: Monte carlo and molecular dynamics calculations", Molecular Physics '''21''' pp. 657-673 (1971)]</ref> (1971)
| Rowley, Nicholson and Parsonage || 119.8   || 0.3405 || <ref>[http://dx.doi.org/10.1016/0021-9991(75)90042-X  L. A. Rowley, D. Nicholson and N. G. Parsonage "Monte Carlo grand canonical ensemble calculation in a gas-liquid transition region for 12-6 Argon", Journal of Computational Physics '''17''' pp. 401-414 (1975)]</ref>
|-  
|-  
| Rowley, Nicholson and Parsonage || 119.8   || 0.3405 || <ref>[http://dx.doi.org/10.1016/0021-9991(75)90042-X  L. A. Rowley, D. Nicholson and N. G. Parsonage "Monte Carlo grand canonical ensemble calculation in a gas-liquid transition region for 12-6 Argon", Journal of Computational Physics '''17''' pp. 401-414 (1975)]</ref> (1975)
|Barker, Fisher and Watts  ||142.095   || 0.33605 || <ref>[http://dx.doi.org/10.1080/00268977100101821 J. A. Barker, R. A. Fisher and R. O. Watts "Liquid argon: Monte carlo and molecular dynamics calculations", Molecular Physics '''21''' pp. 657-673 (1971)]</ref>
|-  
|-  
| White  || 125.7  ||  0.3345    || <ref>[http://dx.doi.org/10.1063/1.479848 John A. White "Lennard-Jones as a model for argon and test of extended renormalization group calculations", Journal of Chemical Physics '''111''' pp. 9352-9356 (1999)]</ref> parameter set #4 (1999)
| White  || 125.7  ||  0.3345    || <ref>[http://dx.doi.org/10.1063/1.479848 John A. White "Lennard-Jones as a model for argon and test of extended renormalization group calculations", Journal of Chemical Physics '''111''' pp. 9352-9356 (1999)]</ref> parameter set #4
|}
|}
====Buckingham potential====
The [[Buckingham potential]] for argon is given by (Eq. 27 <ref>[http://dx.doi.org/10.1098/rspa.1938.0173 R. A. Buckingham "The Classical Equation of State of Gaseous Helium, Neon and Argon", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''168''' pp. 264-283 (1938)]</ref>):
:<math>E(r) = 1.69 \times 10^{-8} e^{-r/0.273} -102 \times 10^{-12} r^{-6} </math>
where <math>E</math> is in ergs ( 10<sup>−7</sup> J) and <math>r</math> in &#8491;.
====BBMS potential====
The Bobetic-Barker-Maitland-Smith potential <ref>[http://dx.doi.org/10.1103/PhysRevB.2.4169 M. V. Bobetic and J. A. Barker "Lattice Dynamics with Three-Body Forces: Argon", Physical Review B '''2''' 4169-4175 (1970)]</ref> <ref>[http://dx.doi.org/10.1080/00268977100103181 G. C. Maitland and E. B. Smith "The intermolecular pair potential of argon", Molecular Physics '''22''' pp. 861-868 (1971)]</ref>.
====Dymond-Alder pair potential====
<ref>[http://dx.doi.org/10.1063/1.1671724 J. H. Dymond and B. J. Alder "Pair Potential for Argon", Journal of Chemical Physics '''51''' pp.  309-320 (1969)]</ref>
==Radial distribution function==
==Radial distribution function==
[[Radial distribution function]] <ref>[http://dx.doi.org/10.1103/PhysRevA.7.2130 J. L. Yarnell, M. J. Katz, R. G. Wenzel and S. H. Koenig "Structure Factor and Radial Distribution Function for Liquid Argon at 85°K", Physical Review A '''7''' pp. 2130-2144 (1973)]</ref>
[[Radial distribution function]]
==Nucleation==
*[http://dx.doi.org/10.1103/PhysRevA.7.2130 J. L. Yarnell, M. J. Katz, R. G. Wenzel and S. H. Koenig "Structure Factor and Radial Distribution Function for Liquid Argon at 85°K", Physical Review A '''7''' pp. 2130-2144 (1973)]
[[Supercooling and nucleation | Nucleation]]<ref>[http://dx.doi.org/10.1063/1.3474945  Matthew J. McGrath, Julius N. Ghogomu, Narcisse T. Tsona, J. Ilja Siepmann, Bin Chen, Ismo Napari1, and Hanna Vehkamäki "Vapor-liquid nucleation of argon: Exploration of various intermolecular potentials", Journal of Chemical Physics '''133''' 084106 (2010)]</ref>
==Quantum simulations==
==Quantum simulations==
<ref>[http://dx.doi.org/10.1080/00268978900100811 J. R. Melrose and K. Singer "An investigation of supercooled Lennard-Jones argon by quantum mechanical and classical Monte Carlo simulation", Molecular Physics '''66''' 1203-1214 (1989)]</ref>
*[http://dx.doi.org/10.1080/00268978900100811 J. R. Melrose and K. Singer "An investigation of supercooled Lennard-Jones argon by quantum mechanical and classical Monte Carlo simulation", Molecular Physics '''66''' 1203-1214 (1989)]
==Virial equation of state==
[[Virial equation of state]] <ref>[http://dx.doi.org/10.1063/1.3627151 Benjamin Jäger, Robert Hellmann, Eckard Bich, and Eckhard Vogel "Ab initio virial equation of state for argon using a new nonadditive three-body potential", Journal of Chemical Physics '''135''' 084308 (2011)]</ref>
==Viscosity==
[[Viscosity]] <ref>[http://dx.doi.org/10.1063/1.4704930  S. V. Lishchuk "Role of three-body interactions in formation of bulk viscosity in liquid argon", Journal of Chemical Physics '''136''' 164501 (2012)]</ref>.
==Heat capacity==
[[Heat capacity]] <ref>[http://dx.doi.org/10.1080/00268976.2012.655795 Ali Morsali, S. Ali Beyramabadi, S. Hooman Vahidi & Maryam Ghorbani "A molecular dynamics study on the role of attractive and repulsive forces in excess heat capacity at constant volume of dense fluids", Molecular Physics '''110''' pp. 483-490 (2012)]</ref>.
==Surface tension==
[[Surface tension]] <ref>[http://dx.doi.org/10.1063/1.4885351  Florent Goujon, Patrice Malfreyt and Dominic J. Tildesley "The gas-liquid surface tension of argon: A reconciliation between experiment and simulation", Journal of Chemical Physics '''140''' 244710 (2014)]</ref>.
==Liquid-vapour coexistence==
<ref>[https://doi.org/10.1063/1.5025726 Himanshu Goel, Sanliang Ling, Breanna Nicole Ellis, Anna Taconi, Ben Slater, and Neeraj Rai "Predicting vapor liquid equilibria using density functional theory: A case study of argon", Journal of Chemical Physics 148, 224501 (2018)]</ref>.
==References==
==References==
<references/>
<references/>
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*[http://dx.doi.org/10.1080/00268976800100721 D. Henderson and J. A. Barker "On the solidification of argon", Molecular Physics '''14''' pp. 587-589 (1968)]
*[http://dx.doi.org/10.1080/00268976800100721 D. Henderson and J. A. Barker "On the solidification of argon", Molecular Physics '''14''' pp. 587-589 (1968)]
*[http://dx.doi.org/10.1103/PhysRevA.5.2238  F. Lado "Numerical Calculation of the Density Autocorrelation Function for Liquid Argon", Physical Review A '''5''' pp. 2238-2244 (1972)]
*[http://dx.doi.org/10.1103/PhysRevA.5.2238  F. Lado "Numerical Calculation of the Density Autocorrelation Function for Liquid Argon", Physical Review A '''5''' pp. 2238-2244 (1972)]
*[http://dx.doi.org/10.1016/j.molliq.2009.09.009  Ali Asghar Davoodi and Farzaneh Feyzi "A new approach for long range corrections in molecular dynamics simulation with application to calculation of argon properties", Journal of Molecular Liquids '''150''' pp. 33-38 (2009)]
*[http://dx.doi.org/10.1063/1.4740465  Jonas Wiebke, Elke Pahl, and Peter Schwerdtfeger "Sensitivity of the thermal and acoustic virial coefficients of argon to the argon interaction potential", Journal of Chemical Physics '''137''' 064702 (2012)]
*[http://dx.doi.org/10.1080/00268976.2013.798696 C. Fan, D.D. Do, D. Nicholson and E. Ustinov "Chemical potential, Helmholtz free energy and entropy of argon with kinetic Monte Carlo simulation", Molecular Physics '''112''' pp. 60-73 (2014)]
*[https://doi.org/10.1016/j.molliq.2017.01.079 Nikolay P. Malomuzh, and Konstantin S. Shakun "Specific properties of argon-like liquids near their spinodals", Journal of Molecular Liquids '''235''' 155-162 (2017)]
*[http://dx.doi.org/10.1080/00268976.2016.1246760 Gábor Rutkai, Monika Thol, Roland Span and Jadran Vrabec "How well does the Lennard-Jones potential represent the thermodynamic properties of noble gases?", Molecular Physics '''115''' pp. 1104-1121 (2017)]
*[http://dx.doi.org/10.1063/1.4991012 Maryna Vlasiuk and Richard J. Sadus "Ab initio interatomic potentials and the thermodynamic properties of fluids", Journal of Chemical Physics '''147''' 024505 (2017)]


[[category: models]]
[[category: models]]
{{Numeric}}
{{Numeric}}
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