Editing Keesom potential

The '''Keesom potential''' is a [[Boltzmann average]] over the dipolar section of the [[Stockmayer potential]], resulting in

:<math> \Phi_{12}(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}-  \left( \frac{\sigma}{r}\right)^6 \right] - \frac{1}{3}\frac{\mu^2_1 \mu^2_2}{(4\pi\epsilon_0)^2 k_BT  r^6}</math>

where:
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>
* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles at a distance r; 
* <math> \sigma </math> is the  diameter (length), i.e. the value of <math>r</math> at <math> \Phi(r)=0</math> ;
* <math> \epsilon </math> : well depth (energy)
* <math>\mu</math> is the [[dipole moment]]
* <math>T</math> is the [[temperature]]
* <math>k_B</math> is the [[Boltzmann constant]]
* <math>\epsilon_0</math> is the permitiviy of free space.


For dipoles disolved in a dielectric medium, this equation may be generalized by including the dielectric constant of the medium within the <math>4\pi\epsilon_0</math> term.
==References==
# W. H. Keesom "On the Deduction from Boltzmann’s Entropy Principle of the Second Virial-coefficient for Material Particles (in the Limit Rigid Spheres of Central Symmetry) which Exert Central Forces Upon Each Other and For Rigid Spheres of Central Symmetry Containing an Electric Doublet at Their Centers", Communications Physical Laboratory University of Leiden Supplement, Ed. By H. Kamerlingh Onnes, Eduard Ijdo Printer, Leiden, Supplement 24b to No. 121-132 pp. 23-41, (1912)
#[http://dx.doi.org/10.1080/00268979600100661 Richard J. Sadus "Molecular simulation of the vapour-liquid equilibria of pure fluids and binary mixtures containing dipolar components: the effect of Keesom interactions", Molecular Physics '''97''' pp. 979-990 (1996)]
[[category:models]]