Hard sphere model: Difference between revisions
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where <math> V\left(r \right) </math> is the potential energy between two spheres at a distance <math> r </math>, and <math> \sigma </math> is the sphere | where <math> V\left(r \right) </math> is the potential energy between two spheres at a distance <math> r </math>, and <math> \sigma </math> is the diameter of the sphere. | ||
== Equations of state == | == Equations of state == | ||
Revision as of 16:11, 21 March 2007
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 diameter of the sphere.
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 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
- 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)