Editing Triangular well model

The '''triangular well model''', proposed by T. Nagayimain one dimension <ref>[http://www.journalarchive.jst.go.jp/english//jnlabstract_en.php?cdjournal=ppmsj1919&cdvol=22&noissue=8-9&startpage=705 T. Nagayima "Statistical Mechanics of One-dimensional Substances I", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp.  705-720 (1940)]</ref><ref>[http://www.journalarchive.jst.go.jp/english//jnlabstract_en.php?cdjournal=ppmsj1919&cdvol=22&noissue=12&startpage=1034 T. 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

:<math>
\Phi_{12}\left( r \right) = 
\left\{ \begin{array}{ccc}
\infty & ; & r \leq \sigma \\
 \frac{\epsilon (r/\sigma - \lambda)}{(\lambda -1)}  & ; &\sigma < r \leq \lambda \sigma \\
0         & ; & r > \lambda \sigma \end{array} \right.
</math>

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 &lambda; &gt; 1.
==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>
<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>
<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>
<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>
<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>

==Virial coefficients==
<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>
<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>
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>
==Critical point==
==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>
==References==
<references/>
;Related reading
*[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/10.1080/00268970701832397 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)]
*[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)]



[[category: models]]