Stockmayer potential - Revision history

Carl McBride: /* References */ Added a recent publication

2013-11-06T15:39:06Z

References: Added a recent publication

← Older revision		Revision as of 17:39, 6 November 2013
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	*[http://dx.doi.org/10.1016/j.fluid.2007.02.009 Osvaldo H. Scalise "On the phase equilibrium Stockmayer fluids", Fluid Phase Equilibria '''253''' pp. 171–175 (2007)]		*[http://dx.doi.org/10.1016/j.fluid.2007.02.009 Osvaldo H. Scalise "On the phase equilibrium Stockmayer fluids", Fluid Phase Equilibria '''253''' pp. 171–175 (2007)]
	*[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)]		*[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)]
			*[http://dx.doi.org/10.1063/1.4821455 Jun Wang , Pankaj A. Apte , James R. Morris and Xiao Cheng Zeng "Freezing point and solid-liquid interfacial free energy of Stockmayer dipolar fluids: A molecular dynamics simulation study", Journal of Chemical Physics '''139''' 114705 (2013)]

	{{numeric}}		{{numeric}}
	[[category: models]]		[[category: models]]

Sergius: /* References */

2013-02-16T00:10:56Z

References

← Older revision		Revision as of 02:10, 16 February 2013
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	<references/>		<references/>
	'''Related reading'''		'''Related reading'''
			*[http://www.nrcresearchpress.com/doi/abs/10.1139/v77-418 Frank M. Mourits, Frans H. A. Rummens "A critical evaluation of Lennard–Jones and Stockmayer potential parameters and of some correlation methods", Canadian Journal of Chemistry '''55''' pp. 3007-3020 (1977)]
	*[http://dx.doi.org/10.1016/0378-3812(94)80018-9 M. E. van Leeuwen "Derivation of Stockmayer potential parameters for polar fluids", Fluid Phase Equilibria '''99''' pp. 1-18 (1994)]		*[http://dx.doi.org/10.1016/0378-3812(94)80018-9 M. E. van Leeuwen "Derivation of Stockmayer potential parameters for polar fluids", Fluid Phase Equilibria '''99''' pp. 1-18 (1994)]
	*[http://dx.doi.org/10.1016/j.fluid.2007.02.009 Osvaldo H. Scalise "On the phase equilibrium Stockmayer fluids", Fluid Phase Equilibria '''253''' pp. 171–175 (2007)]		*[http://dx.doi.org/10.1016/j.fluid.2007.02.009 Osvaldo H. Scalise "On the phase equilibrium Stockmayer fluids", Fluid Phase Equilibria '''253''' pp. 171–175 (2007)]

Sergius at 23:48, 15 February 2013

2013-02-15T23:48:14Z

← Older revision		Revision as of 01:48, 16 February 2013
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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.
	==Critical properties==		==Critical properties==
	In the range <math>0 \leq \mu^* \leq 2.45</math> <ref>[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)]</ref>:		In the range <math>0 \leq \mu^* \leq 2.45</math> <ref>[http://dx.doi.org/10.1080/00268979400100294 M.E. Van Leeuwen "Deviation from corresponding-states behaviour for polar fluids", Molecular Physics '''82''' pp. 383-392 (1994)]</ref>:
	:<math>T_c^* = 1.313 + 0.2999\mu^{2} -0.2837 \ln(\mu^{2} +1)</math>		:<math>T_c^* = 1.313 + 0.2999\mu^{2} -0.2837 \ln(\mu^{2} +1)</math>
	:<math>\rho_c^* = 0.3009 - 0.00785\mu^{2} - 0.00198\mu^{4}</math>		:<math>\rho_c^* = 0.3009 - 0.00785\mu^{2} - 0.00198\mu^{4}</math>

Sergius: /* References */

2013-02-15T23:34:39Z

References

← Older revision		Revision as of 01:34, 16 February 2013
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	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1016/0378-3812(94)80018-9 M. E. van Leeuwen "Derivation of Stockmayer potential parameters for polar fluids", Fluid Phase Equilibria '''99''' pp. 1-18 (1994)]		*[http://dx.doi.org/10.1016/0378-3812(94)80018-9 M. E. van Leeuwen "Derivation of Stockmayer potential parameters for polar fluids", Fluid Phase Equilibria '''99''' pp. 1-18 (1994)]
			*[http://dx.doi.org/10.1016/j.fluid.2007.02.009 Osvaldo H. Scalise "On the phase equilibrium Stockmayer fluids", Fluid Phase Equilibria '''253''' pp. 171–175 (2007)]
	*[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)]		*[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)]
	{{numeric}}		{{numeric}}
	[[category: models]]		[[category: models]]

Carl McBride: Added a recent publication

2012-04-19T10:39:29Z

Added a recent publication

← Older revision		Revision as of 12:39, 19 April 2012
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	:<math>\rho_c^* = 0.3009 - 0.00785\mu^{2} - 0.00198\mu^{4}</math>		:<math>\rho_c^* = 0.3009 - 0.00785\mu^{2} - 0.00198\mu^{4}</math>
	:<math>P_c^* = 0.127 + 0.0023\mu^{*2}</math>		:<math>P_c^* = 0.127 + 0.0023\mu^{*2}</math>
			==Bridge function==
			A [[bridge function]] for use in [[integral equations]] has been calculated by Puibasset and Belloni <ref>[http://dx.doi.org/10.1063/1.4703899 Joël Puibasset and Luc Belloni "Bridge function for the dipolar fluid from simulation", Journal of Chemical Physics '''136''' 154503 (2012)]</ref>.
	==References==		==References==
	<references/>		<references/>

Carl McBride: Slight tidy

2010-12-03T11:44:35Z

Slight tidy

← Older revision		Revision as of 13:44, 3 December 2010
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	where:		where:
	* <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>		* <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</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 <math>r</math>
	* <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> represents the well depth (energy)
	* <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,\theta_2 </math> is the inclination of the two dipole axes with respect to the intermolecular axis.		* <math>\theta_1</math> and <math>\theta_2 </math> are the angles associated with 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 a reduced dipole moment, <math>\mu^*</math>, such that:		If one defines a reduced dipole moment, <math>\mu^*</math>, such that:

Carl McBride at 11:42, 3 December 2010

2010-12-03T11:42:30Z

← Older revision		Revision as of 13:42, 3 December 2010
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	* <math>\theta_1,\theta_2 </math> is the inclination of the two dipole axes with respect to the intermolecular axis.		* <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 ~~the~~ reduced dipole moment, <math>\mu^*</math>		If one defines a reduced dipole moment, <math>\mu^*</math>, such that:

	:<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>

Carl McBride: Added original reference

2010-12-03T11:21:12Z

Added original reference

← Older revision		Revision as of 13:21, 3 December 2010
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	The '''Stockmayer potential''' consists of the [[Lennard-Jones model]] with an embedded point [[Dipole moment \|dipole]]. Thus the Stockmayer potential becomes:		The '''Stockmayer potential''' consists of the [[Lennard-Jones model]] with an embedded point [[Dipole moment \|dipole]]. Thus the Stockmayer potential becomes (Eq. 1 <ref>[http://dx.doi.org/10.1063/1.1750922 W. H. Stockmayer "Second Virial Coefficients of Polar Gases", Journal of Chemical Physics '''9''' pp. 398-402 (1941)]</ref>):

	:<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>		:<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>

Carl McBride: /* References */ Added a reference

2010-12-03T10:46:28Z

References: Added a reference

← Older revision		Revision as of 12:46, 3 December 2010
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	<references/>		<references/>
	'''Related reading'''		'''Related reading'''
			*[http://dx.doi.org/10.1016/0378-3812(94)80018-9 M. E. van Leeuwen "Derivation of Stockmayer potential parameters for polar fluids", Fluid Phase Equilibria '''99''' pp. 1-18 (1994)]
	*[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)]		*[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)]
	{{numeric}}		{{numeric}}
	[[category: models]]		[[category: models]]

Carl McBride: Added an internal link + changed references to Cite format

2010-12-03T10:39:44Z

Added an internal link + changed references to Cite format

← Older revision		Revision as of 12:39, 3 December 2010
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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 moment \|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^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>
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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.
	==Critical properties==		==Critical properties==
	In the range <math>0 \leq \mu^* \leq 2.45</math> (~~Ref. 1~~)		In the range <math>0 \leq \mu^* \leq 2.45</math> <ref>[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)]</ref>:
	:<math>T_c^* = 1.313 + 0.2999\mu^{2} -0.2837 \ln(\mu^{2} +1)</math>		:<math>T_c^* = 1.313 + 0.2999\mu^{2} -0.2837 \ln(\mu^{2} +1)</math>
	:<math>\rho_c^* = 0.3009 - 0.00785\mu^{2} - 0.00198\mu^{4}</math>		:<math>\rho_c^* = 0.3009 - 0.00785\mu^{2} - 0.00198\mu^{4}</math>
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	==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)]~~		<references/>
	#[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)]		'''Related reading'''
			*[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)]
	{{numeric}}		{{numeric}}
	[[category: models]]		[[category: models]]