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| The '''triangular well model''', proposed by Takeo Nagayima in one dimension <ref>[https://www.jstage.jst.go.jp/article/ppmsj1919/22/8-9/22_8-9_705/_article Takeo Nagayima "Statistical Mechanics of One-dimensional Substances I", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 705-720 (1940)]</ref><ref>[https://www.jstage.jst.go.jp/article/ppmsj1919/22/12/22_12_1034/_article Takeo Nagayima "Statistical Mechanics of One-dimensional Substances. II", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 1034-1047 (1940)]</ref>, is given by | | {{stub-general}} |
| | The '''triangular well model''' is given by |
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| :<math> | | :<math> |
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| where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth | | where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth |
| and λ > 1. | | and λ > 1. |
| ==2 dimensions==
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| <ref>[http://dx.doi.org/10.1063/1.4967254 Yuri Reyes, Mariana Bárcenas, Gerardo Odriozola and Pedro Orea "Thermodynamic properties of triangle-well fluids in two dimensions: MC and MD simulations", Journal of Chemical Physics '''145''' 174505 (2016)]</ref>
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| ==Equation of state== | | ==Equation of state== |
| <ref>[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]</ref>
| | :''Main article: [[Equations of state for the triangular well model]]'' |
| <ref>[http://dx.doi.org/10.1080/00268976.2010.538738 Mustafa Koyuncu "Equation of state of a long-range triangular-well fluid", Molecular Physics '''109''' pp. 565-573 (2011)]</ref>
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| <ref>[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]</ref>
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| <ref>[http://dx.doi.org/10.1016/j.molliq.2012.03.014 Hervé Guérin "Improved analytical thermodynamic properties of the triangular-well fluid from perturbation theory", Journal of Molecular Liquids '''170''' pp. 37-40 (2012)]</ref>
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| <ref>[http://dx.doi.org/10.1080/00268976.2012.655338 L.D. Rivera, M. Robles and M. López de Haro "Equation of state and liquid–vapour equilibrium in a triangle-well fluid", Molecular Physics '''110''' pp. 1317-1323 (2012)]</ref>
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| ==Virial coefficients==
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| <math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref>
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| <ref>[http://dx.doi.org/10.1063/1.1696837 R. H. Fowler, H. W. Graben, Andrew G. De Rocco and M. J. Feinberg "Some Additional Results for the Triangle-Well Potential Model", Journal of Chemical Physics '''43''' pp. 1083-1084 (1965)]</ref>
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| and <math>B_4</math> <ref>[http://dx.doi.org/10.1063/1.1675133 W. C. Farrar and Andrew G. De Rocco "Perturbation Theory for a High-Temperature Triangle-Well Fluid", Journal of Chemical Physics '''54''' pp. 2024-2025 (1971)]</ref>
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| ==Critical point== | | ==Critical point== |
| ==Solid phase== | | ==Solid phase== |
| <ref>[http://dx.doi.org/10.1080/00268970110120300 Jhumpa Adhikari and David A. Kofke "Monte Carlo and cell model calculations for the solid-fluid phase behaviour of the triangle-well model", Molecular Physics '''100''' pp. 1543-1550 (2002)]</ref>
| | #[http://dx.doi.org/10.1080/00268970110120300 Jhumpa Adhikari and David A. Kofke "Monte Carlo and cell model calculations for the solid-fluid phase behaviour of the triangle-well model", Molecular Physics '''100''' pp. 1543-1550 (2002)] |
| ==References== | | ==References== |
| <references/>
| | #T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 855- (1940) |
| ;Related reading
| | #[http://dx.doi.org/10.1063/1.1675133 W. C. Farrar and Andrew G. De Rocco "Perturbation Theory for a High-Temperature Triangle-Well Fluid", Journal of Chemical Physics '''54''' pp. 2024- (1971)] |
| *[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)]
| | #[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)] |
| *[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)]
| | #[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)] |
| *[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)]
| | #[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)] |
| *[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)]
| | #[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)] |
| *[http://dx.doi.org/10.1080/00268976.2014.887801 M. Bárcenas, G. Odriozola and P. Orea "Coexistence and interfacial properties of triangle-well fluids", Molecular Physics '''112''' pp. 2114-2121 (2014)]
| | #[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)] |
| | | #[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)] |
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| [[category: models]] | | [[category: models]] |