Double square well model

The double square well model can be seen as a variant (or vice versa) of the square shoulder + square well model. In other words

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

where ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential, ${ϵ}_1$ and ${ϵ}_2$ are the well depths (${ϵ}_1,{ϵ}_2>0$), $r$ is the distance between site 1 and site 2 where $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$, σ is the hard core diameter and ${\lambda }_1,{\lambda }_2>1$

References

1. M. Reza Sadr-Lahijany, Antonio Scala, Sergey V. Buldyrev, and H. Eugene Stanley "Liquid-State Anomalies and the Stell-Hemmer Core-Softened Potential", Physical Review Letters 81 pp. 4895-4898 (1998)
2. J. R. Solana "Thermodynamic properties of double square-well fluids: Computer simulations and theory", Journal of Chemical Physics 129 244502 (2008)