Stockmayer potential: Difference between revisions

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The '''Stockmayer potential''' consists of the [[Lennard-Jones model]] with an embedded point dipole. Thus the Stockmayer potential becomes:
The '''Stockmayer potential''' consists of the [[Lennard-Jones model]] with an embedded point dipole. Thus the Stockmayer potential becomes:


:<math> \Phi_{12}(r, \theta_1, \theta_2, \phi) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}-  \left( \frac{\sigma}{r}\right)^6 \right] - \frac{\mu_1 \mu_2}{4\pi \epsilon_0 r_{12}^3} \left(2 \cos \theta_1 \cos \theta_2 - \sin \theta_1 \sin \theta_2 \cos \phi\right) </math>
:<math> \Phi_{12}(r, \theta_1, \theta_2, \phi) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}-  \left( \frac{\sigma}{r}\right)^6 \right] - \frac{\mu_1 \mu_2}{4\pi \epsilon_0 r^3} \left(2 \cos \theta_1 \cos \theta_2 - \sin \theta_1 \sin \theta_2 \cos \phi\right) </math>


where:
where:
* <math>r = |\mathbf{r}_{12}|</math>
* <math> \Phi(r) </math> is the [[intermolecular pair potential]] between two particles at a distance r;  
* <math> \Phi(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> ;

Revision as of 15:32, 16 July 2008

The Stockmayer potential consists of the Lennard-Jones model with an embedded point dipole. Thus the Stockmayer potential becomes:

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 permittivity of the vacuum
  • is the dipole moment
  • is the inclination of the two dipole axes with respect to the intermolecular axis.
  • is the azimuth angle between the two dipole moments

If one defines the reduced dipole moment,

one can rewrite the expression as

For this reason the potential is sometimes known as the Stockmayer 12-6-3 potential.

Critical properties

In the range (Ref. 1)

References

  1. M. E. Van Leeuwe "Deviation from corresponding-states behaviour for polar fluids", Molecular Physics 82 pp. 383-392 (1994)
  2. Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E 75 011506 (2007)
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