Keesom potential: Difference between revisions

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The '''Keesom potential''' is a [[Boltzmann average]] over the dipolar section of the [[Stockmayer potential]], resulting in
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_{12}^6}</math>
:<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:
where:
* <math>r = |\mathbf{r}_{12}|</math>
* <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> \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> \sigma </math> is the  diameter (length), i.e. the value of <math>r</math> at <math> \Phi(r)=0</math> ;

Latest revision as of 15:09, 17 July 2008

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

where:

  • is the intermolecular pair potential between two particles at a distance r;
  • is the diameter (length), i.e. the value of at  ;
  •  : well depth (energy)
  • is the dipole moment
  • is the temperature
  • is the Boltzmann constant
  • is the permitiviy of free space.

For dipoles dissolved in a dielectric medium, this equation may be generalized by including the dielectric constant of the medium within the term.

References[edit]

  1. 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)
  2. 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)