Hertzian sphere model

The Hertzian sphere model is given by (Eq. 1):

${\mathrm{\Phi }}_{12}(r)=\{\begin{array}{ccc}ϵ(1-r/\sigma {)}^{5/2}& ;& r<\sigma \\ 0& ;& r\ge \sigma \end{array}$

where ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential, $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$ is the distance between site 1 and site 2. $\sigma$ represents a length scale and $ϵ$ an energy. In the limit $k_{B}T/ϵ\to 0$ this potential becomes the hard sphere model.