Penetrable sphere model: Difference between revisions
Carl McBride (talk | contribs) (New page: {{stub-general}} The '''penetrable sphere model'''<ref>[http://dx.doi.org/10.1063/1.1673203 B. Widom and J. S. Rowlinson "New Model for the Study of Liquid–Vapor Phase Transitions", Jour...) |
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The '''penetrable sphere model'''<ref>[http://dx.doi.org/10. | The '''penetrable sphere model''' is given by <ref>[http://dx.doi.org/10.1051/jphys:0198900500100126700 C. Marquest et T.A. Witten "Simple cubic structure in copolymer mesophases", Journal de Physique France '''50''' pp. 1267-1277 (1989)]</ref>: | ||
:<math> | |||
\Phi_{12}\left( r \right) = | |||
\left\{ \begin{array}{ccc} | |||
\epsilon & ; & r < \sigma \\ | |||
0 & ; & r \ge \sigma \end{array} \right. | |||
</math> | |||
where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>\epsilon</math> is the hight of the repulsive core <math>r</math> is the distance between site 1 and site 2 <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>. Note: an earlier, different, penetrable sphere model was proposed, but is now known as the [[Widom-Rowlinson model]]. This model can be seen as the limiting case of the | |||
[[Gaussian overlap model]] where <math>n \rightarrow \infty</math>. | |||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: models]] | |||
[[category : models]] | |||
Revision as of 14:39, 1 October 2009
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The penetrable sphere model is given by [1]:
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \Phi _{12}\left(r\right)=\left\{{\begin{array}{ccc}\epsilon &;&r<\sigma \\0&;&r\geq \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}(r)} is the intermolecular pair potential, 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 hight of the repulsive core 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} is the distance between site 1 and site 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 r := |\mathbf{r}_1 - \mathbf{r}_2|} . Note: an earlier, different, penetrable sphere model was proposed, but is now known as the Widom-Rowlinson model. This model can be seen as the limiting case of the Gaussian overlap model where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle n\rightarrow \infty } .