Hertzian sphere model

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

$\Phi _{12}\left(r\right)=\left\{{\begin{array}{lll}\epsilon (1-r/\sigma )^{5/2}&;&r<\sigma \\0&;&r\geq \sigma \end{array}}\right.$

where $\Phi _{12}\left(r\right)$ 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 $\epsilon$ an energy. In the limit $k_{B}T/\epsilon \rightarrow 0$ this potential becomes the hard sphere model.