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{\mu^2_1 \mu^2_2}{ | :<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> | ||
where: | where: | ||
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* <math>T</math> is the [[temperature]] | * <math>T</math> is the [[temperature]] | ||
* <math>k_B</math> is the [[Boltzmann constant]] | * <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== | ==References== | ||
#[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)] | #[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]] | [[category:models]] | ||
Revision as of 15:04, 15 July 2008
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The Keesom potential is a Boltzmann average over the dipolar section of the Stockmayer potential, resulting in
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \Phi _{12}(r)=4\epsilon \left[\left({\frac {\sigma }{r}}\right)^{12}-\left({\frac {\sigma }{r}}\right)^{6}\right]-{\frac {1}{3}}{\frac {\mu _{1}^{2}\mu _{2}^{2}}{(4\pi \epsilon _{0})^{2}k_{B}Tr_{12}^{6}}}}
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r) } is the intermolecular pair potential between two particles at a distance r;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is the diameter (length), i.e. the value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} at Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi(r)=0} ;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon } : well depth (energy)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu} is the dipole moment
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} is the temperature
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_B} is the Boltzmann constant
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon_0} 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4\pi\epsilon_0}
term.