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

${\mathrm{\Phi }}_{12}(r)=\{\begin{array}{ccc}\mathrm{\infty }& ;& r<\sigma \\ {ϵ}_1& ;& \sigma \le r<{\lambda }_1\sigma \\ -{ϵ}_2& ;& {\lambda }_1\sigma \le r<{\lambda }_2\sigma \\ 0& ;& r\ge {\lambda }_2\sigma \end{array}$

where ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential, ${ϵ}_1$ and ${ϵ}_2$ 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. 2.

Liquid-liquid transition

For certain parameter sets the square shoulder + square well model has a liquid-liquid transition.

References

1. 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)
2. 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)