Soft sphere potential: Difference between revisions
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==Solid phase== | ==Solid phase== | ||
<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref> | <ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref> | ||
==Transport coefficients== | |||
<ref>[http://dx.doi.org/10.1080/00268970802712563 D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics '''107''' pp. 309-319 (2009)]</ref> | |||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: models]] | [[category: models]] | ||
Revision as of 13:27, 21 May 2009
The soft sphere potential is defined as
- 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 \Phi_{12}\left( r \right) = \left\{ \begin{array}{lll} \epsilon \left( \frac{\sigma}{r}\right) ^n & ; & r \le \sigma \\ 0 & ; & r > \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 \Phi_{12}\left(r \right) } is the intermolecular pair potential between two soft spheres separated by 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 := |\mathbf{r}_1 - \mathbf{r}_2|} , 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 \epsilon } is the interaction strength 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. Frequently the value of 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 n} is taken to be 12, thus the model effectively becomes the high temperature limit of the Lennard-Jones model [1].
Equation of state
Solid phase
Transport coefficients
References
- ↑ Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A 2 pp. 221-230 (1970)
- ↑ William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics 52 pp. 4931-4941 (1970)
- ↑ Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics 107 pp. 295-299 (2009)
- ↑ D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics 107 pp. 309-319 (2009)