Hemmer and Stell model

The Hemmer and Stell model intermolecular pair potential, ${\mathrm{\Phi }}_{12}(r)$, is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3):

${\mathrm{\Phi }}_{12}(r)={\mathrm{\Phi }}_{12}(r{)}_{\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{s}\mathrm{i}\mathrm{v}\mathrm{e}}+{\mathrm{\Phi }}_{12}(r{)}_{\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}}$

where a short range piece-wise potential

${\mathrm{\Phi }}_{12}(r{)}_{\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{s}\mathrm{i}\mathrm{v}\mathrm{e}}=\{\begin{array}{cc}\mathrm{\infty }& r<d\\ V_0(\frac{1-(r-d)}{\lambda d})& d<r<d(1+\lambda )\\ 0& d(1+\lambda )<r\end{array}$

where $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$, $d$ is the hard core radius, along with a long-range attractive potential;

${\mathrm{\Phi }}_{12}(r{)}_{\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}}=-a\gamma \exp (-\gamma r)$

where $a$ is a positive constant.

References

1. P. C. Hemmer and G. Stell "Fluids with Several Phase Transitions", Physical Review Letters 24 pp. 1284 - 1287 (1970)
2. G. Stell and P. C. Hemmer, "Phase Transitions Due to Softness of the Potential Core", Journal of Chemical Physics' 56, pp. 4274-4286 (1972)