Hard sphere model

Interaction Potential

The hard sphere interaction potential is given by

$V\left(r\right)=\left\{{\begin{array}{lll}\infty &;&r<\sigma \\0&;&r\geq \sigma \end{array}}\right.$

where $V\left(r\right)$ is the potential energy between two spheres at a distance $r$, and $\sigma$ is the diameter of the sphere.

Equations of state

Hard sphere fluid:

1. See Carnahan-Starling (three dimensions)
2. See Ref.1

Hard sphere solid:

1. See Ref. 2

Related systems

Hard disks in a 2-dimensional space

Hard rods in one dimension

Widom-Rowlinson model

Polydisperse hard spheres

Quantum hard spheres

Data

Virial coefficients of hard spheres and hard disks are to be found in the table.

Experimental results

For results obtained from the Colloidal Disorder - Order Transition (CDOT) experiments performed on-board the Space Shuttles Columbia and Discovery see Ref. 3.

References

1. Robin J. Speedy "Pressure of the metastable hard-sphere fluid", Journal of Physics: Condensed Matter 9 pp. 8591-8599 (1997)
2. Robin J. Speedy "Pressure and entropy of hard-sphere crystals", Journal of Physics: Condensed Matter 10 pp. 4387-4391 (1998)
3. Z. Chenga, P. M. Chaikina, W. B. Russelb, W. V. Meyerc, J. Zhub, R. B. Rogersc and R. H. Ottewilld, "Phase diagram of hard spheres", Materials & Design 22 pp. 529-534 (2001)