Sutherland potential - Revision history

Carl McBride: Added a correct but broken (Taylor & Francis!) DOI.

2010-04-06T13:32:16Z

Added a correct but broken (Taylor & Francis!) DOI.

← Older revision		Revision as of 15:32, 6 April 2010
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	The '''Sutherland potential''' <ref>W. Sutherland, Philosophical Magazine '''36''' pp. 507- (1893) </ref><ref>[http://dx.doi.org/10.1103/RevModPhys.36.1025 H. W. Graben and R. D. Present "Third Virial Coefficient for the Sutherland (∞, ν) Potential", Reviews of Modern Physics '''36''' pp. 1025-1033 (1964)]</ref> is given by		The '''Sutherland potential''' <ref>[http://dx.doi.org/10.1080/14786449308620508 William Sutherland "The viscosity of gases and molecular force", Philosophical Magazine '''36''' pp. 507-531 (1893)]</ref><ref>[http://dx.doi.org/10.1103/RevModPhys.36.1025 H. W. Graben and R. D. Present "Third Virial Coefficient for the Sutherland (∞, ν) Potential", Reviews of Modern Physics '''36''' pp. 1025-1033 (1964)]</ref> is given by

	:<math>		:<math>

Carl McBride: Changed diameter for radius

2010-04-06T12:37:51Z

Changed diameter for radius

← Older revision		Revision as of 14:37, 6 April 2010
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	where <math> \Phi_{12}\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math> is the distance between site 1 and site 2,		where <math> \Phi_{12}\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math> is the distance between site 1 and site 2,
	<math> \sigma </math> is the hard ~~diameter~~, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and		<math> \sigma </math> is the radius of the central hard core, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and
	<math> \gamma </math> is a parameter that controls the interaction range. For example, for <math>\gamma=6</math> the potential look like		<math> \gamma </math> is a parameter that controls the interaction range. For example, for <math>\gamma=6</math> the potential look like

Carl McBride: Moved image.

2010-04-06T11:54:37Z

Moved image.

← Older revision		Revision as of 13:54, 6 April 2010
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	~~[[Image:Sutherland.png\|thumb\|right]]~~
	The '''Sutherland potential''' <ref>W. Sutherland, Philosophical Magazine '''36''' pp. 507- (1893) </ref><ref>[http://dx.doi.org/10.1103/RevModPhys.36.1025 H. W. Graben and R. D. Present "Third Virial Coefficient for the Sutherland (∞, ν) Potential", Reviews of Modern Physics '''36''' pp. 1025-1033 (1964)]</ref> is given by		The '''Sutherland potential''' <ref>W. Sutherland, Philosophical Magazine '''36''' pp. 507- (1893) </ref><ref>[http://dx.doi.org/10.1103/RevModPhys.36.1025 H. W. Graben and R. D. Present "Third Virial Coefficient for the Sutherland (∞, ν) Potential", Reviews of Modern Physics '''36''' pp. 1025-1033 (1964)]</ref> is given by

Line 12:		Line 11:
	where <math> \Phi_{12}\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math> is the distance between site 1 and site 2,		where <math> \Phi_{12}\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math> is the distance between site 1 and site 2,
	<math> \sigma </math> is the hard diameter, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and		<math> \sigma </math> is the hard diameter, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and
	<math> \gamma </math> is a parameter that controls the interaction range.		<math> \gamma </math> is a parameter that controls the interaction range. For example, for <math>\gamma=6</math> the potential look like

			:[[Image:Sutherland.png\|500px]]
	==References==		==References==
	<references/>		<references/>

Carl McBride: Added plot of potential

2010-04-06T11:49:02Z

Added plot of potential

← Older revision		Revision as of 13:49, 6 April 2010
Line 1:		Line 1:
	The '''Sutherland potential''' <ref>W. Sutherland, Philosophical Magazine '''36''' pp. 507- (1893) </ref> is given by		[[Image:Sutherland.png\|thumb\|right]]
			The '''Sutherland potential''' <ref>W. Sutherland, Philosophical Magazine '''36''' pp. 507- (1893) </ref><ref>[http://dx.doi.org/10.1103/RevModPhys.36.1025 H. W. Graben and R. D. Present "Third Virial Coefficient for the Sutherland (∞, ν) Potential", Reviews of Modern Physics '''36''' pp. 1025-1033 (1964)]</ref> is given by

	:<math>		:<math>
Line 16:		Line 17:
	<references/>		<references/>
	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1103/RevModPhys.36.1025 H. W. Graben and R. D. Present "Third Virial Coefficient for the Sutherland (∞, ν) Potential", Reviews of Modern Physics '''36''' pp. 1025-1033 (1964)]
	*[http://dx.doi.org/10.1063/1.431141 D. Levi and M. de Llano "Closed form of second virial coefficient for Sutherland potential", Journal of Chemical Physics '''63''' pp. 4561-4562 (1975)]		*[http://dx.doi.org/10.1063/1.431141 D. Levi and M. de Llano "Closed form of second virial coefficient for Sutherland potential", Journal of Chemical Physics '''63''' pp. 4561-4562 (1975)]
	*[http://dx.doi.org/10.1142/S0217979204025142 Jianxiang Tian and Yuanxing Gui "Liquid-gas phase transition to first order of an argon-like fluid modeled by the hard-core similar Sutherland potential", International Journal of Modern Physics B '''18''' pp. 2057-2069 (2004)]		*[http://dx.doi.org/10.1142/S0217979204025142 Jianxiang Tian and Yuanxing Gui "Liquid-gas phase transition to first order of an argon-like fluid modeled by the hard-core similar Sutherland potential", International Journal of Modern Physics B '''18''' pp. 2057-2069 (2004)]

Carl McBride: Added some more publications

2010-04-06T08:59:58Z

Added some more publications

← Older revision		Revision as of 10:59, 6 April 2010
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	The '''Sutherland potential''' is given by		The '''Sutherland potential''' <ref>W. Sutherland, Philosophical Magazine '''36''' pp. 507- (1893) </ref> is given by

	:<math>		:<math>
Line 14:		Line 14:

	==References==		==References==
			<references/>
	'''Related reading'''		'''Related reading'''
			*[http://dx.doi.org/10.1103/RevModPhys.36.1025 H. W. Graben and R. D. Present "Third Virial Coefficient for the Sutherland (∞, ν) Potential", Reviews of Modern Physics '''36''' pp. 1025-1033 (1964)]
	*[http://dx.doi.org/10.1063/1.431141 D. Levi and M. de Llano "Closed form of second virial coefficient for Sutherland potential", Journal of Chemical Physics '''63''' pp. 4561-4562 (1975)]		*[http://dx.doi.org/10.1063/1.431141 D. Levi and M. de Llano "Closed form of second virial coefficient for Sutherland potential", Journal of Chemical Physics '''63''' pp. 4561-4562 (1975)]
			*[http://dx.doi.org/10.1142/S0217979204025142 Jianxiang Tian and Yuanxing Gui "Liquid-gas phase transition to first order of an argon-like fluid modeled by the hard-core similar Sutherland potential", International Journal of Modern Physics B '''18''' pp. 2057-2069 (2004)]
	*[http://dx.doi.org/10.1016/j.fluid.2007.01.011 A. Díez, J. Largo and J. R. Solana "Structure and thermodynamic properties of Sutherland fluids from computer simulation and the Tang–Lu integral equation theory", Fluid Phase Equilibria '''253''' pp. 67-73 (2007)]		*[http://dx.doi.org/10.1016/j.fluid.2007.01.011 A. Díez, J. Largo and J. R. Solana "Structure and thermodynamic properties of Sutherland fluids from computer simulation and the Tang–Lu integral equation theory", Fluid Phase Equilibria '''253''' pp. 67-73 (2007)]
	*[http://dx.doi.org/10.1063/1.2828720 Jianguo Mi, Yiping Tang, and Chongli Zhong "Theoretical study of Sutherland fluids with long-range, short-range, and highly short-range potential parameters", Journal of Chemical Physics '''128''' 054503 (2008)]		*[http://dx.doi.org/10.1063/1.2828720 Jianguo Mi, Yiping Tang, and Chongli Zhong "Theoretical study of Sutherland fluids with long-range, short-range, and highly short-range potential parameters", Journal of Chemical Physics '''128''' 054503 (2008)]
	*[http://dx.doi.org/10.1063/1.3371710 Roman Melnyk, Pedro Orea, Ivo Nezbeda, and Andrij Trokhymchuk "Liquid/vapor coexistence and surface tension of the Sutherland fluid with a variable range of interaction: Computer simulation and perturbation theory studies", Journal of Chemical Physics '''132''' 134504 (2010)]		*[http://dx.doi.org/10.1063/1.3371710 Roman Melnyk, Pedro Orea, Ivo Nezbeda, and Andrij Trokhymchuk "Liquid/vapor coexistence and surface tension of the Sutherland fluid with a variable range of interaction: Computer simulation and perturbation theory studies", Journal of Chemical Physics '''132''' 134504 (2010)]
			*[http://dx.doi.org/10.1016/j.fluid.2009.10.027 F. Paragand, F. Feyzi and B. Behzadi "Application of the SAFT-VR equation of state to vapor–liquid equilibrium calculations for pure components and binary mixtures using the Sutherland potential", Fluid Phase Equilibria '''290''' pp. 181-194 (2010)]

	[[Category: Models]]		[[Category: Models]]

Carl McBride: Added a recent publication

2010-04-05T08:46:38Z

Added a recent publication

← Older revision		Revision as of 10:46, 5 April 2010
Line 14:		Line 14:

	==References==		==References==
	#[http://dx.doi.org/10.1063/1.431141 D. Levi and M. de Llano "Closed form of second virial coefficient for Sutherland potential", Journal of Chemical Physics '''63''' pp. 4561-4562 (1975)]		'''Related reading'''
	#[http://dx.doi.org/10.1016/j.fluid.2007.01.011 A. Díez, J. Largo and J. R. Solana "Structure and thermodynamic properties of Sutherland fluids from computer simulation and the Tang–Lu integral equation theory", Fluid Phase Equilibria '''253''' pp. 67-73 (2007)]		*[http://dx.doi.org/10.1063/1.431141 D. Levi and M. de Llano "Closed form of second virial coefficient for Sutherland potential", Journal of Chemical Physics '''63''' pp. 4561-4562 (1975)]
	#[http://dx.doi.org/10.1063/1.2828720 Jianguo Mi, Yiping Tang, and Chongli Zhong "Theoretical study of Sutherland fluids with long-range, short-range, and highly short-range potential parameters", Journal of Chemical Physics '''128''' 054503 (2008)]		*[http://dx.doi.org/10.1016/j.fluid.2007.01.011 A. Díez, J. Largo and J. R. Solana "Structure and thermodynamic properties of Sutherland fluids from computer simulation and the Tang–Lu integral equation theory", Fluid Phase Equilibria '''253''' pp. 67-73 (2007)]
			*[http://dx.doi.org/10.1063/1.2828720 Jianguo Mi, Yiping Tang, and Chongli Zhong "Theoretical study of Sutherland fluids with long-range, short-range, and highly short-range potential parameters", Journal of Chemical Physics '''128''' 054503 (2008)]
			*[http://dx.doi.org/10.1063/1.3371710 Roman Melnyk, Pedro Orea, Ivo Nezbeda, and Andrij Trokhymchuk "Liquid/vapor coexistence and surface tension of the Sutherland fluid with a variable range of interaction: Computer simulation and perturbation theory studies", Journal of Chemical Physics '''132''' 134504 (2010)]


	[[Category: Models]]		[[Category: Models]]

Nice and Tidy: Better defined r

2008-07-17T13:54:12Z

Better defined r

← Older revision		Revision as of 15:54, 17 July 2008
Line 2:		Line 2:

	:<math>		:<math>
	\~~Phi~~\left( r \right) =		\Phi_{12}\left( r \right) =
	\left\{ \begin{array}{lll}		\left\{ \begin{array}{lll}
	\infty & ; & r \leq \sigma \\		\infty & ; & r \leq \sigma \\
Line 9:		Line 9:
	</math>		</math>

	where <math> \~~Phi~~\left( r \right) </math> is the [[intermolecular pair potential]], <math> r </math> is the distance,		where <math> \Phi_{12}\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math> is the distance between site 1 and site 2,
	<math> \sigma </math> is the hard diameter, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and		<math> \sigma </math> is the hard diameter, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and
	<math> \gamma </math> is a parameter that controls the interaction range.		<math> \gamma </math> is a parameter that controls the interaction range.

Carl McBride at 10:22, 8 February 2008

2008-02-08T10:22:16Z

← Older revision		Revision as of 12:22, 8 February 2008
Line 5:		Line 5:
	\left\{ \begin{array}{lll}		\left\{ \begin{array}{lll}
	\infty & ; & r \leq \sigma \\		\infty & ; & r \leq \sigma \\
	- \left( \frac{ ~~\epsilon~~ \sigma }{r}\right)^{\gamma} & ; & r > \sigma		- \epsilon\left( \frac{ \sigma }{r}\right)^{\gamma} & ; & r > \sigma
	\end{array} \right.		\end{array} \right.
	</math>		</math>

Carl McBride: New page: The '''Sutherland potential''' is given by : $\Phi\left( r \right) = \left\{ \begin{array}{lll} \infty & ; & r \leq \sigma \\ - \left( \frac{ \epsilon \sigma }{r}\right)^{\gamma} & ...$

2008-02-08T10:20:18Z

New page: The '''Sutherland potential''' is given by :<math> \Phi\left( r \right) = \left\{ \begin{array}{lll} \infty & ; & r \leq \sigma \\ - \left( \frac{ \epsilon \sigma }{r}\right)^{\gamma} & ...

New page

The '''Sutherland potential''' is given by

:<math>
\Phi\left( r \right) =
\left\{ \begin{array}{lll}
\infty & ; & r \leq \sigma \\
- \left( \frac{ \epsilon \sigma }{r}\right)^{\gamma} & ; & r > \sigma
\end{array} \right.
</math>

where <math> \Phi\left( r \right) </math> is the [[intermolecular pair potential]], <math> r </math> is the distance,
<math> \sigma </math> is the hard diameter, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and
<math> \gamma </math> is a parameter that controls the interaction range.

==References==
#[http://dx.doi.org/10.1063/1.431141 D. Levi and M. de Llano "Closed form of second virial coefficient for Sutherland potential", Journal of Chemical Physics '''63''' pp. 4561-4562 (1975)]
#[http://dx.doi.org/10.1016/j.fluid.2007.01.011 A. Díez, J. Largo and J. R. Solana "Structure and thermodynamic properties of Sutherland fluids from computer simulation and the Tang–Lu integral equation theory", Fluid Phase Equilibria '''253''' pp. 67-73 (2007)]
#[http://dx.doi.org/10.1063/1.2828720 Jianguo Mi, Yiping Tang, and Chongli Zhong "Theoretical study of Sutherland fluids with long-range, short-range, and highly short-range potential parameters", Journal of Chemical Physics '''128''' 054503 (2008)]
[[Category: Models]]