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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is the sphere diameter.

Equations of state

Hard sphere fluid:

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

Related systems

Hard disks in a 2-dimensional space

Hard rods in one dimension

Widom-Rowlinson model

Polydisperse hard spheres

Data

Virial coefficients of hard spheres and hard disks

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)