Editing Square shoulder + square well model

The '''Square shoulder + square well''' model consists, as its name suggests, of a combination of the [[square shoulder model]] and the [[square well model]]. The model is given by

:<math>
\Phi_{12}\left( r \right) = 
\left\{ \begin{array}{ccc}
\infty & ; & r < \sigma \\
 \epsilon_1 & ; &\sigma \le r < \lambda_1 \sigma \\
- \epsilon_2 & ; &\lambda_1\sigma \le r < \lambda_2 \sigma \\
0         & ; & r \ge \lambda_2 \sigma \end{array} \right.
</math>

where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>\epsilon_1</math> and <math>\epsilon_2</math> are the well ''depths'', <math>r</math> is the distance between site 1 and site 2  where <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, &sigma; is the hard core diameter
and <math>\lambda_1,\lambda_2>1</math>
==Critical points and liquid-liquid transition==
For certain parameter sets the square shoulder + square well model has a  [[Polyamorphic systems | liquid-liquid transition]] along with a corresponding liquid-liquid [[Critical points | critical point]]
<ref>[http://dx.doi.org/10.1088/0953-8984/11/50/308 Andreas Lang, Gerhard Kahl, Christos N Likos, Hartmut Löwen and Martin Watzlawek "Structure and thermodynamics of square-well and square-shoulder fluids", Journal of Physics: Condensed Matter '''11''' pp. 10143-10161  (1999)]</ref>
<ref>[http://dx.doi.org/10.1038/35055514 Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley "Generic mechanism for generating a liquid-liquid phase transition", Nature '''409''' pp. 692-695 (2001)]</ref>
<ref>[http://dx.doi.org/10.1103/PhysRevE.66.051206 Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Metstable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly", Physical Review E '''66''' 051206 (2002)]</ref>
<ref>[http://dx.doi.org/10.1103/PhysRevE.69.061206 Anna Skibinsky, Sergey V. Buldyrev, Giancarlo Franzese, Gianpietro Malescio, and H. Eugene  Stanley,  "Liquid-liquid phase transitions for soft-core attractive potentials", Physical Review E '''69''' 061206 (2004)]</ref>
<ref>[http://dx.doi.org/10.1103/PhysRevE.71.061504 Gianpietro Malescio, Giancarlo Franzese, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range", Physical Review E '''71''' 061504 (2005)]</ref>.
==See also==
*[[Double square well model]]
==References==
<references/>
;Related reading
*[http://dx.doi.org/10.1063/1.2970884 W. Rzysko, O. Pizio, A. Patrykiejew, and S. Sokolowski "Phase diagram of a square-shoulder, square-well fluid revisited", Journal of Chemical Physics '''129''' 124502 (2008)]
*[http://dx.doi.org/10.1063/1.2982162 Shiqi Zhou, A. Lajovic, and A. Jamnik "Local structures of fluid with discrete spherical potential: Theory and grand canonical ensemble Monte Carlo simulation",  Journal of Chemical Physics '''129''' 124503 (2008)]
[[Category: Models]]
[[category: Polyamorphic systems]]