Editing Stockmayer potential
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The '''Stockmayer potential''' consists of the [[Lennard-Jones model]] with an embedded point | The '''Stockmayer potential''' consists of the [[Lennard-Jones model]] with an embedded point dipole. Thus the Stockmayer potential becomes: | ||
:<math> \ | :<math> \Phi(r, \theta_1, \theta_2, \phi) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}- \left( \frac{\sigma}{r}\right)^6 \right] - \frac{\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> \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 | * <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> | * <math> \epsilon </math> : well depth (energy) | ||
* <math> \epsilon </math> | |||
* <math> \epsilon_0 </math> is the permittivity of the vacuum | * <math> \epsilon_0 </math> is the permittivity of the vacuum | ||
* <math>\mu</math> is the dipole moment | * <math>\mu</math> is the dipole moment | ||
* <math>\theta_1 | * <math>\theta_1,\theta_2 </math> is the inclination of the two dipole axes with respect to the intermolecular axis. | ||
* <math>\phi</math> is the azimuth angle between the two dipole moments | * <math>\phi</math> is the azimuth angle between the two dipole moments | ||
If one defines | If one defines the reduced dipole moment, <math>\mu^*</math> | ||
:<math>\mu^* := \sqrt{\frac{\mu^2}{4\pi\epsilon_0\epsilon \sigma^3}}</math> | :<math>\mu^* := \sqrt{\frac{\mu^2}{4\pi\epsilon_0\epsilon \sigma^3}}</math> | ||
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For this reason the potential is sometimes known as the Stockmayer 12-6-3 potential. | For this reason the potential is sometimes known as the Stockmayer 12-6-3 potential. | ||
==References== | ==References== | ||
#[http://dx.doi.org/10.1080/00268979400100294 M. E. Van Leeuwe "Deviation from corresponding-states behaviour for polar fluids", Molecular Physics '''82''' pp. 383-392 (1994)] | |||
[[category: models]] | [[category: models]] |