Exp-6 potential - Revision history

Carl McBride: Added {{lowercase title}} template tag

2015-05-14T09:04:43Z

Added {{lowercase title}} template tag

← Older revision		Revision as of 11:04, 14 May 2015
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			{{lowercase title}}
	The '''exp-6 potential''' (or '''Exp-Six''' potential) is a modified form of the [[Buckingham potential]] and is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):		The '''exp-6 potential''' (or '''Exp-Six''' potential) is a modified form of the [[Buckingham potential]] and is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):

Carl McBride: Corrected functional form: r_min NOT sigma

2014-02-25T17:35:18Z

Corrected functional form: r_min NOT sigma

← Older revision		Revision as of 19:35, 25 February 2014
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	The '''exp-6 potential''' is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):		The '''exp-6 potential''' (or '''Exp-Six''' potential) is a modified form of the [[Buckingham potential]] and is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):

	:<math> \Phi_{12}(r) = \frac{\epsilon}{1-6/\alpha} \left[ \left( \frac{6}{\alpha} \right)		:<math> \Phi_{12}(r) = \frac{\epsilon}{1-6/\alpha} \left[ \left( \frac{6}{\alpha} \right)
	\exp \left[ \alpha \left( 1-\frac{r}{~~\sigma~~} \right) \right] - \left( \frac{~~\sigma~~}{r}\right)^6 \right] </math>		\exp \left[ \alpha \left( 1-\frac{r}{r_{min}} \right) \right] - \left( \frac{r_{min}}{r}\right)^6 \right] </math>

	where		where
	* <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>		* <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>
	* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites''		* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites''
	* <math> ~~\sigma~~ </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math>		* <math> r_{min} </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)</math> is a minimum.
	* <math> \epsilon </math> is the well depth (energy)		* <math> \epsilon </math> is the well depth (energy)
	* <math>\alpha</math> is the "steepness" of the repulsive energy		* <math>\alpha</math> is the "steepness" of the repulsive energy

Carl McBride: /* References */ Added a publication

2014-02-17T10:56:37Z

References: Added a publication

← Older revision		Revision as of 12:56, 17 February 2014
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	*[http://dx.doi.org/10.1063/1.1840523 Marvin Ross and Berni Alder "Shock Compression of Argon. II. Nonadditive Repulsive Potential", Journal of Chemical Physics '''46''' pp. 4203-4210 (1967)]		*[http://dx.doi.org/10.1063/1.1840523 Marvin Ross and Berni Alder "Shock Compression of Argon. II. Nonadditive Repulsive Potential", Journal of Chemical Physics '''46''' pp. 4203-4210 (1967)]
	*[http://dx.doi.org/10.1063/1.440106 Marvin Ross and F. H. Ree "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]		*[http://dx.doi.org/10.1063/1.440106 Marvin Ross and F. H. Ree "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]
			*[http://dx.doi.org/10.1023/A:1024798909685 Teik-Cheng Lim "Scaling Function Between the Exponential-6 and the Generalized Lennard-Jones Potential Functions", Journal of Mathematical Chemistry '''33''' pp. 279-285 (2003)]


	[[category: models]]		[[category: models]]

Carl McBride: /* Melting point */ Corrected typo

2012-01-23T12:01:58Z

Melting point: Corrected typo

← Older revision		Revision as of 14:01, 23 January 2012
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	* <math>\alpha</math> is the "steepness" of the repulsive energy		* <math>\alpha</math> is the "steepness" of the repulsive energy
	==Melting point==		==Melting point==
	An approximate method to locate the melting point is given in <ref>[http://dx.doi.org/10.1063/1.3552948 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics '''134''' 054120 (2011)]</ref>. See also <ref>[http://dx.doi.org/ 10.1080/00268976.2011.616544 Sergey A. Khrapak and Franz Saija "Application of phenomenological freezing and melting indicators to the exp-6 and Gaussian core potentials", Molecular Physics '''109''' pp. 2417-2421 (2011)]</ref>.		An approximate method to locate the melting point is given in <ref>[http://dx.doi.org/10.1063/1.3552948 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics '''134''' 054120 (2011)]</ref>. See also <ref>[http://dx.doi.org/10.1080/00268976.2011.616544 Sergey A. Khrapak and Franz Saija "Application of phenomenological freezing and melting indicators to the exp-6 and Gaussian core potentials", Molecular Physics '''109''' pp. 2417-2421 (2011)]</ref>.

	==See also==		==See also==

Carl McBride: /* Melting point */ Added a recent publication

2012-01-23T12:01:38Z

Melting point: Added a recent publication

← Older revision		Revision as of 14:01, 23 January 2012
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	* <math>\alpha</math> is the "steepness" of the repulsive energy		* <math>\alpha</math> is the "steepness" of the repulsive energy
	==Melting point==		==Melting point==
	An approximate method to locate the melting point is given in <ref>[http://dx.doi.org/10.1063/1.3552948 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics '''134''' 054120 (2011)]</ref>.		An approximate method to locate the melting point is given in <ref>[http://dx.doi.org/10.1063/1.3552948 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics '''134''' 054120 (2011)]</ref>. See also <ref>[http://dx.doi.org/ 10.1080/00268976.2011.616544 Sergey A. Khrapak and Franz Saija "Application of phenomenological freezing and melting indicators to the exp-6 and Gaussian core potentials", Molecular Physics '''109''' pp. 2417-2421 (2011)]</ref>.

	==See also==		==See also==
	*[[Buckingham potential]]		*[[Buckingham potential]]

158.195.19.140 at 15:31, 13 April 2011

2011-04-13T15:31:24Z

← Older revision		Revision as of 17:31, 13 April 2011
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	:<math> \Phi_{12}(r) = \frac{\epsilon}{1-6/\alpha} \left[ \left( \frac{6}{\alpha} \right)		:<math> \Phi_{12}(r) = \frac{\epsilon}{1-6/\alpha} \left[ \left( \frac{6}{\alpha} \right)
	\exp \left[ \alpha \frac{1-r}{\sigma} \right] - \left( \frac{\sigma}{r}\right)^6 \right] </math>		\exp \left[ \alpha \left( 1-\frac{r}{\sigma} \right) \right] - \left( \frac{\sigma}{r}\right)^6 \right] </math>

	where		where

Carl McBride: Added a recent publication

2011-02-08T10:50:16Z

Added a recent publication

← Older revision		Revision as of 12:50, 8 February 2011
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	* <math> \sigma </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math>		* <math> \sigma </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math>
	* <math> \epsilon </math> is the well depth (energy)		* <math> \epsilon </math> is the well depth (energy)
	* <math>\alpha</math> is the "steepness" of the repulsive energy		* <math>\alpha</math> is the "steepness" of the repulsive energy
			==Melting point==
			An approximate method to locate the melting point is given in <ref>[http://dx.doi.org/10.1063/1.3552948 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics '''134''' 054120 (2011)]</ref>.
	==See also==		==See also==
	*[[Buckingham potential]]		*[[Buckingham potential]]

Carl McBride: /* References */ Added a paper

2010-09-06T14:54:58Z

References: Added a paper

← Older revision		Revision as of 16:54, 6 September 2010
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	<references/>		<references/>
	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1063/1.440106 M. Ross and F. H. Ree "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]		*[http://dx.doi.org/10.1063/1.1840523 Marvin Ross and Berni Alder "Shock Compression of Argon. II. Nonadditive Repulsive Potential", Journal of Chemical Physics '''46''' pp. 4203-4210 (1967)]
			*[http://dx.doi.org/10.1063/1.440106 Marvin Ross and F. H. Ree "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]
	[[category: models]]		[[category: models]]

Carl McBride: Created page with "The '''exp-6 potential''' is given by (Eq. 1 in [http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six)..."

2010-09-06T14:43:45Z

Created page with "The '''exp-6 potential''' is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six)..."

New page

The '''exp-6 potential''' is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):

:<math> \Phi_{12}(r) = \frac{\epsilon}{1-6/\alpha} \left[ \left( \frac{6}{\alpha} \right)
\exp \left[ \alpha \frac{1-r}{\sigma} \right] - \left( \frac{\sigma}{r}\right)^6 \right] </math>

where
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>
* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites''
* <math> \sigma </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math>
* <math> \epsilon </math> is the well depth (energy)
* <math>\alpha</math> is the "steepness" of the repulsive energy
==See also==
*[[Buckingham potential]]
*[[Lennard-Jones model]]
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1063/1.440106 M. Ross and F. H. Ree "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]
[[category: models]]