Hard sphere model
Interaction Potential
The hard sphere interaction potential is given by
- 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 V \left( r \right) = \left\{ \begin{array}{lll} \infty & ; & r < \sigma \\ 0 & ; & r \ge \sigma \end{array} \right. }
where 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 V\left(r \right) } is the potential energy between two spheres at a distance 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 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:
- See Carnahan-Starling (three dimensions)
- See Ref.1
Hard sphere solid:
- See Ref. 2
Related systems
Hard disks in a 2-dimensional space
Hard rods in one dimension
Data
Virial coefficients of hard spheres and hard disks
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
- Robin J. Speedy "Pressure of the metastable hard-sphere fluid", Journal of Physics: Condensed Matter 9 pp. 8591-8599 (1997)
- Robin J. Speedy "Pressure and entropy of hard-sphere crystals", Journal of Physics: Condensed Matter 10 pp. 4387-4391 (1998)
- 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)