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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>: | | {{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", Journal of Chemical Physics '''52''' pp. 1670-1684 (1970)]</ref> was designed to study [[Gas-liquid phase transitions | vapour-liquid equilibrium]] |
| :<math>
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| \Phi_{12}\left( r \right) =
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| \left\{ \begin{array}{ccc}
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| \epsilon & ; & r < \sigma \\
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| 0 & ; & r \ge \sigma \end{array} \right.
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| </math>
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| 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]].
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| ==References== | | ==References== |
| <references/> | | <references/> |
| | | '''Related reading''' |
| | | *[http://dx.doi.org/10.1080/00268977200101921 T. W. Melnyk, J. S. Rowlinson and B. L. Sawford "The penetrable sphere and related models of liquid—vapour equilibrium" Molecular Physics '''24''' pp. 809-831 (1972)] |
| [[category: models]] | | [[category : models]] |