Keesom potential - Revision history

Nice and Tidy: Better defined r

2008-07-17T14:09:12Z

Better defined r

← Older revision		Revision as of 16:09, 17 July 2008
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	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> ;

Carl McBride: Removed r subscript.

2008-07-16T14:13:52Z

Removed r subscript.

← Older revision		Revision as of 16:13, 16 July 2008
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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:

Carl McBride: Defined r better

2008-07-16T08:53:22Z

Defined r better

← Older revision		Revision as of 10:53, 16 July 2008
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	~~{{Stub-general}}~~
	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

Line 5:		Line 4:

	where:		where:
			* <math>r = \|\mathbf{r}_{12}\|</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> ;

Carl McBride: /* References */ Added classic reference.

2008-07-16T08:29:11Z

References: Added classic reference.

← Older revision		Revision as of 10:29, 16 July 2008
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	For dipoles dissolved 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.		For dipoles dissolved 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==
			# 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)]		#[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]]

Nice and Tidy: Spelling correction

2008-07-15T17:12:52Z

Spelling correction

← Older revision		Revision as of 19:12, 15 July 2008
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	* <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.		* <math>\epsilon_0</math> 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 <math>4\pi\epsilon_0</math> term.

	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]]

Lgmac at 14:04, 15 July 2008

2008-07-15T14:04:29Z

← Older revision		Revision as of 16:04, 15 July 2008
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	The '''Keesom potential''' is a [[Boltzmann average]] over the dipolar section of the [[Stockmayer potential]], resulting in		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}{~~3k_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_{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]]

Carl McBride at 13:35, 15 July 2008

2008-07-15T13:35:48Z

@@ Line 1: / Line 1: @@
 {{Stub-general}}
 ==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)]
 [[category:models]]

Carl McBride: New page: {{Stub-general}} ==References== #[http://dx.doi.org/10.1080/00268979600100661 Richard J. Sadus "Molecular simulation of the vapour-liquid equilibria of pure fluids and binary mixtures cont...

2008-07-15T13:24:39Z

New page: {{Stub-general}} ==References== #[http://dx.doi.org/10.1080/00268979600100661 Richard J. Sadus "Molecular simulation of the vapour-liquid equilibria of pure fluids and binary mixtures cont...

New page

{{Stub-general}}
==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)]
[[category:models]]