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

$\Phi _{12}\left(r\right)=\left\{{\begin{array}{ccc}\infty &;&r<\sigma \\\epsilon _{1}&;&\sigma \leq r<\lambda _{1}\sigma \\-\epsilon _{2}&;&\lambda _{1}\sigma \leq r<\lambda _{2}\sigma \\0&;&r\geq \lambda _{2}\sigma \end{array}}\right.$

where $\Phi _{12}(r)$ is the intermolecular pair potential, $\epsilon _{1}$ and $\epsilon _{2}$ are the well depths, $r$ is the distance between site 1 and site 2 where $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$, σ is the hard core diameter and $\lambda _{1},\lambda _{2}>1$

Critical points

See Ref.s 1-5.

Liquid-liquid transition

For certain parameter sets the square shoulder + square well model has a liquid-liquid transition. See Ref.s 1-4.

References

1. 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)
2. 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)
3. 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)
4. 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)
5. 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)
6. 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)