Penetrable sphere model: Difference between revisions
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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''' is given by <ref>[http://dx.doi.org/10.1051/jphys:0198900500100126700 C. Marquest and T. A. Witten "Simple cubic structure in copolymer mesophases", Journal de Physique France '''50''' pp. 1267-1277 (1989)]</ref>: | |||
The '''penetrable sphere model'''<ref>[http://dx.doi.org/10. | |||
:<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> and <math>\sigma</math> is the radius of the core. 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>. In the limit <math>\epsilon \rightarrow \infty</math> one has the [[hard sphere model]]. | |||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category : models]] | [[category: models]] | ||
Latest revision as of 12:28, 23 May 2017
The penetrable sphere model is given by [1]:
where is the intermolecular pair potential, is the hight of the repulsive core, is the distance between site 1 and site 2 and is the radius of the core. 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 . In the limit one has the hard sphere model.
