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. For example, for $\epsilon =10$ the potential looks like

See also

• Harmonic repulsion potential

References

Related reading

• Jian Yang and Kenneth S. Schweizer "Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. I. Activated relaxation, kinetic vitrification, and fragility", Journal of Chemical Physics 134 204908 (2011)
• Jian Yang and Kenneth S. Schweizer "Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. II. Shear modulus, relaxation-elasticity connections, and rheology", Journal of Chemical Physics 134 204909 (2011)