Triangular well model - Revision history

Carl McBride: Added recent publication. Updated broken links

2016-11-10T11:22:27Z

Added recent publication. Updated broken links

← Older revision		Revision as of 13:22, 10 November 2016
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	The '''triangular well model''', proposed by ~~T. Nagayimain~~ one dimension <ref>[~~http~~://www.~~journalarchive~~.jst.go.jp/~~english~~//~~jnlabstract_en.php?cdjournal=ppmsj1919&cdvol=~~22~~&noissue=~~8-9~~&startpage=705 T.~~ Nagayima "Statistical Mechanics of One-dimensional Substances I", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 705-720 (1940)]</ref><ref>[~~http~~://www.~~journalarchive~~.jst.go.jp/~~english~~//~~jnlabstract_en.php?cdjournal=ppmsj1919&cdvol=~~22~~&noissue=~~12~~&startpage=1034 T.~~ Nagayima "Statistical Mechanics of One-dimensional Substances. II", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 1034-1047 (1940)]</ref>, is given by		The '''triangular well model''', proposed by Takeo Nagayima in one dimension <ref>[https://www.jstage.jst.go.jp/article/ppmsj1919/22/8-9/22_8-9_705/_article Takeo Nagayima "Statistical Mechanics of One-dimensional Substances I", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 705-720 (1940)]</ref><ref>[https://www.jstage.jst.go.jp/article/ppmsj1919/22/12/22_12_1034/_article Takeo Nagayima "Statistical Mechanics of One-dimensional Substances. II", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 1034-1047 (1940)]</ref>, is given by

	:<math>		:<math>
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	where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth		where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth
	and λ > 1.		and λ > 1.
			==2 dimensions==
			<ref>[http://dx.doi.org/10.1063/1.4967254 Yuri Reyes, Mariana Bárcenas, Gerardo Odriozola and Pedro Orea "Thermodynamic properties of triangle-well fluids in two dimensions: MC and MD simulations", Journal of Chemical Physics '''145''' 174505 (2016)]</ref>
	==Equation of state==		==Equation of state==
	<ref>[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]</ref>		<ref>[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]</ref>

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

2014-09-24T10:39:20Z

References: Added a recent publication

← Older revision		Revision as of 12:39, 24 September 2014
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	*[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)]		*[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)]
	*[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)]		*[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)]
			*[http://dx.doi.org/10.1080/00268976.2014.887801 M. Bárcenas, G. Odriozola and P. Orea "Coexistence and interfacial properties of triangle-well fluids", Molecular Physics '''112''' pp. 2114-2121 (2014)]



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

Carl McBride: /* Equation of state */ Added a recent publication

2012-06-19T09:39:04Z

Equation of state: Added a recent publication

← Older revision		Revision as of 11:39, 19 June 2012
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	<ref>[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]</ref>
	<ref>[http://dx.doi.org/10.1016/j.molliq.2012.03.014 Hervé Guérin "Improved analytical thermodynamic properties of the triangular-well fluid from perturbation theory", Journal of Molecular Liquids '''170''' pp. 37-40 (2012)]</ref>		<ref>[http://dx.doi.org/10.1016/j.molliq.2012.03.014 Hervé Guérin "Improved analytical thermodynamic properties of the triangular-well fluid from perturbation theory", Journal of Molecular Liquids '''170''' pp. 37-40 (2012)]</ref>
			<ref>[http://dx.doi.org/10.1080/00268976.2012.655338 L.D. Rivera, M. Robles and M. López de Haro "Equation of state and liquid–vapour equilibrium in a triangle-well fluid", Molecular Physics '''110''' pp. 1317-1323 (2012)]</ref>

	==Virial coefficients==		==Virial coefficients==

Carl McBride: /* Equation of state */ Correcte "typo"

2012-05-21T10:53:18Z

Equation of state: Correcte "typo"

← Older revision		Revision as of 12:53, 21 May 2012
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	<ref>[http://dx.doi.org/10.1080/00268976.2010.538738 Mustafa Koyuncu "Equation of state of a long-range triangular-well fluid", Molecular Physics '''109''' pp. 565-573 (2011)]</ref>		<ref>[http://dx.doi.org/10.1080/00268976.2010.538738 Mustafa Koyuncu "Equation of state of a long-range triangular-well fluid", Molecular Physics '''109''' pp. 565-573 (2011)]</ref>
	<ref>[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]</ref>
	<ref>[http://dx.doi.org/10.1016/j.molliq.2012.03.014 Hervé Guérin "~~Improvedanalyticalthermodynamicproperties~~ of the triangular-~~wellfluid~~ from ~~perturbationtheory~~", Journal of Molecular Liquids '''170''' pp. 37-40 (2012)]</ref>		<ref>[http://dx.doi.org/10.1016/j.molliq.2012.03.014 Hervé Guérin "Improved analytical thermodynamic properties of the triangular-well fluid from perturbation theory", Journal of Molecular Liquids '''170''' pp. 37-40 (2012)]</ref>

	==Virial coefficients==		==Virial coefficients==
	<math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref>		<math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref>

Carl McBride: Added a recent publication

2012-05-21T10:52:26Z

Added a recent publication

← Older revision		Revision as of 12:52, 21 May 2012
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	<ref>[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]</ref>		<ref>[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]</ref>
	<ref>[http://dx.doi.org/10.1080/00268976.2010.538738 Mustafa Koyuncu "Equation of state of a long-range triangular-well fluid", Molecular Physics '''109''' pp. 565-573 (2011)]</ref>		<ref>[http://dx.doi.org/10.1080/00268976.2010.538738 Mustafa Koyuncu "Equation of state of a long-range triangular-well fluid", Molecular Physics '''109''' pp. 565-573 (2011)]</ref>
			<ref>[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]</ref>
			<ref>[http://dx.doi.org/10.1016/j.molliq.2012.03.014 Hervé Guérin "Improvedanalyticalthermodynamicproperties of the triangular-wellfluid from perturbationtheory", Journal of Molecular Liquids '''170''' pp. 37-40 (2012)]</ref>
	==Virial coefficients==		==Virial coefficients==
	<math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref>		<math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref>
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	*[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)]		*[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)]
	*[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)]		*[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)]
	*[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]
	*[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)]		*[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)]
	*[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)]		*[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)]
	[[category: models]]		[[category: models]]

Carl McBride: /* References */ Removed duplicated entry

2011-02-19T15:08:05Z

References: Removed duplicated entry

← Older revision		Revision as of 17:08, 19 February 2011
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	*[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)]		*[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)]
	*[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)]		*[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)]
	*[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]
	*[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]		*[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]
	*[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)]		*[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)]
	*[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)]		*[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)]
	[[category: models]]		[[category: models]]

Carl McBride: included content from "old" EOS page

2011-02-19T15:05:02Z

included content from "old" EOS page

← Older revision		Revision as of 17:05, 19 February 2011
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	and λ > 1.		and λ > 1.
	==Equation of state==		==Equation of state==
	:''~~Main article~~: ~~[[Equations~~ of state ~~for the~~ triangular well ~~model]]~~''		<ref>[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]</ref>
			<ref>[http://dx.doi.org/10.1080/00268976.2010.538738 Mustafa Koyuncu "Equation of state of a long-range triangular-well fluid", Molecular Physics '''109''' pp. 565-573 (2011)]</ref>
	==Virial coefficients==		==Virial coefficients==
	<math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref>		<math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref>

Carl McBride: References now in Cite format

2011-02-17T11:27:31Z

References now in Cite format

← Older revision		Revision as of 13:27, 17 February 2011
Line 1:		Line 1:
	~~{{stub-general}}~~		The '''triangular well model''', proposed by T. Nagayimain one dimension <ref>[http://www.journalarchive.jst.go.jp/english//jnlabstract_en.php?cdjournal=ppmsj1919&cdvol=22&noissue=8-9&startpage=705 T. Nagayima "Statistical Mechanics of One-dimensional Substances I", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 705-720 (1940)]</ref><ref>[http://www.journalarchive.jst.go.jp/english//jnlabstract_en.php?cdjournal=ppmsj1919&cdvol=22&noissue=12&startpage=1034 T. Nagayima "Statistical Mechanics of One-dimensional Substances. II", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 1034-1047 (1940)]</ref>, is given by
	The '''triangular well model''' is given by

	:<math>		:<math>
Line 12:		Line 11:
	where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth		where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth
	and λ > 1.		and λ > 1.
	~~This model was first proposed by T. Nagayima in 1940 (Refs. 1-3) in one dimension.~~
	==Equation of state==		==Equation of state==
	:''Main article: [[Equations of state for the triangular well model]]''		:''Main article: [[Equations of state for the triangular well model]]''
	==Virial coefficients==		==Virial coefficients==
	<math>B_2</math> ~~and~~ <math>B_3</math>:		<math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref>
	*[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]		<ref>[http://dx.doi.org/10.1063/1.1696837 R. H. Fowler, H. W. Graben, Andrew G. De Rocco and M. J. Feinberg "Some Additional Results for the Triangle-Well Potential Model", Journal of Chemical Physics '''43''' pp. 1083-1084 (1965)]</ref>
	*[http://dx.doi.org/10.1063/1.1696837 R. H. Fowler, H. W. Graben, Andrew G. De Rocco and M. J. Feinberg "Some Additional Results for the Triangle-Well Potential Model", Journal of Chemical Physics '''43''' pp. 1083-1084 (1965)]		and <math>B_4</math> <ref>[http://dx.doi.org/10.1063/1.1675133 W. C. Farrar and Andrew G. De Rocco "Perturbation Theory for a High-Temperature Triangle-Well Fluid", Journal of Chemical Physics '''54''' pp. 2024-2025 (1971)]</ref>
	<math>B_4</math>:
	*[http://dx.doi.org/10.1063/1.1675133 W. C. Farrar and Andrew G. De Rocco "Perturbation Theory for a High-Temperature Triangle-Well Fluid", Journal of Chemical Physics '''54''' pp. 2024-2025 (1971)]
	==Critical point==		==Critical point==
	==Solid phase==		==Solid phase==
	#[http://dx.doi.org/10.1080/00268970110120300 Jhumpa Adhikari and David A. Kofke "Monte Carlo and cell model calculations for the solid-fluid phase behaviour of the triangle-well model", Molecular Physics '''100''' pp. 1543-1550 (2002)]		<ref>[http://dx.doi.org/10.1080/00268970110120300 Jhumpa Adhikari and David A. Kofke "Monte Carlo and cell model calculations for the solid-fluid phase behaviour of the triangle-well model", Molecular Physics '''100''' pp. 1543-1550 (2002)]</ref>
	==References==		==References==
	~~(Note: the following three Nagayima~~ references ~~have not yet been checked. Numbers 1 and 3 were found in the [http:/~~/~~dx.doi.org/10.1063/1.1725746 Feinberg and De Rocco] paper, and Ref 2 in the [http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou] paper).~~		<references/>
	~~#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 705- (1940)~~		;Related reading
	~~#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 855- (1940)~~		*[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)]
	~~#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 1034- (1940)~~		*[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)]
	#[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)]		*[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]
	#[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)]		*[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]
	#[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]		*[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)]
	#[http://dx.doi.org/10.1080/00268970701725013 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics '''105''' pp. 2987-2998 (2007)]		*[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)]
	#[http://dx.doi.org/10.1080/00268970701832397 F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics '''106''' pp. 113-126 (2008)]
	#[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)]
	[[category: models]]		[[category: models]]

Carl McBride: Corrected spelling.

2009-01-07T14:54:02Z

Corrected spelling.

← Older revision		Revision as of 16:54, 7 January 2009
Line 12:		Line 12:
	where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth		where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth
	and λ > 1.		and λ > 1.
	This model was ~~firts~~ proposed by T. Nagayima in 1940 (Refs. 1-3).		This model was first proposed by T. Nagayima in 1940 (Refs. 1-3) in one dimension.
	==Equation of state==		==Equation of state==
	:''Main article: [[Equations of state for the triangular well model]]''		:''Main article: [[Equations of state for the triangular well model]]''

Carl McBride: Added more references.

2009-01-07T14:42:48Z

Added more references.

← Older revision		Revision as of 16:42, 7 January 2009
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	where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth		where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth
	and λ > 1.		and λ > 1.
			This model was firts proposed by T. Nagayima in 1940 (Refs. 1-3).
	==Equation of state==		==Equation of state==
	:''Main article: [[Equations of state for the triangular well model]]''		:''Main article: [[Equations of state for the triangular well model]]''
			==Virial coefficients==
			<math>B_2</math> and <math>B_3</math>:
			*[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]
			*[http://dx.doi.org/10.1063/1.1696837 R. H. Fowler, H. W. Graben, Andrew G. De Rocco and M. J. Feinberg "Some Additional Results for the Triangle-Well Potential Model", Journal of Chemical Physics '''43''' pp. 1083-1084 (1965)]
			<math>B_4</math>:
			*[http://dx.doi.org/10.1063/1.1675133 W. C. Farrar and Andrew G. De Rocco "Perturbation Theory for a High-Temperature Triangle-Well Fluid", Journal of Chemical Physics '''54''' pp. 2024-2025 (1971)]
	==Critical point==		==Critical point==
	==Solid phase==		==Solid phase==
	#[http://dx.doi.org/10.1080/00268970110120300 Jhumpa Adhikari and David A. Kofke "Monte Carlo and cell model calculations for the solid-fluid phase behaviour of the triangle-well model", Molecular Physics '''100''' pp. 1543-1550 (2002)]		#[http://dx.doi.org/10.1080/00268970110120300 Jhumpa Adhikari and David A. Kofke "Monte Carlo and cell model calculations for the solid-fluid phase behaviour of the triangle-well model", Molecular Physics '''100''' pp. 1543-1550 (2002)]
	==References==		==References==
			(Note: the following three Nagayima references have not yet been checked. Numbers 1 and 3 were found in the [http://dx.doi.org/10.1063/1.1725746 Feinberg and De Rocco] paper, and Ref 2 in the [http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou] paper).
			#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 705- (1940)
	#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 855- (1940)		#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 855- (1940)
	#~~[http://dx~~.~~doi.org/10.1063/1.1675133 W. C. Farrar and Andrew G. De Rocco~~ "~~Perturbation Theory for a High-Temperature Triangle-Well Fluid~~", ~~Journal~~ of ~~Chemical Physics~~ '''54''' pp. ~~2024~~- (~~1971~~)]		#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 1034- (1940)
	#[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)]		#[http://dx.doi.org/10.1139/p72-195 Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics '''50''' pp. 1419–1426 (1972)]
	#[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)]		#[http://dx.doi.org/10.1139/p74-010 Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics '''52''' pp. 80-88 (1974)]