Soft sphere potential - Revision history

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

2016-04-05T13:49:20Z

References: Added a recent publication

← Older revision		Revision as of 15:49, 5 April 2016
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	==References==		==References==
	<references/>		<references/>
			;Related reading
			*[http://dx.doi.org/10.1063/1.4944824 Sergey A. Khrapak "Note: Sound velocity of a soft sphere model near the fluid-solid phase transition", Journal of Chemical Physics '''144''' 126101 (2016)]

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

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

2012-11-27T10:47:21Z

Equation of state: Added a recent publication

← Older revision		Revision as of 12:47, 27 November 2012
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	where <math> \Phi_{12}\left(r \right) </math> is the [[intermolecular pair potential]] between two soft spheres separated by a distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\epsilon </math> is the interaction strength and <math> \sigma </math> is the diameter of the sphere. Frequently the value of <math>n</math> is taken to be 12, thus the model effectively becomes the high temperature limit of the [[Lennard-Jones model]] <ref>[http://dx.doi.org/10.1103/PhysRevA.2.221 Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A '''2''' pp. 221-230 (1970)]</ref>. If <math>n\rightarrow \infty</math> one has the [[hard sphere model]]. For <math>n \le 3</math> no thermodynamically stable phases are found.		where <math> \Phi_{12}\left(r \right) </math> is the [[intermolecular pair potential]] between two soft spheres separated by a distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\epsilon </math> is the interaction strength and <math> \sigma </math> is the diameter of the sphere. Frequently the value of <math>n</math> is taken to be 12, thus the model effectively becomes the high temperature limit of the [[Lennard-Jones model]] <ref>[http://dx.doi.org/10.1103/PhysRevA.2.221 Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A '''2''' pp. 221-230 (1970)]</ref>. If <math>n\rightarrow \infty</math> one has the [[hard sphere model]]. For <math>n \le 3</math> no thermodynamically stable phases are found.
	==Equation of state==		==Equation of state==
	The soft-sphere [[Equations of state \| equation of state]]<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref> has recently been studied by Tan, Schultz and Kofke<ref name="Tan">[http://dx.doi.org/10.1080/00268976.2010.520041 Tai Boon Tan, Andrew J. Schultz and David A. Kofke "Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model", Molecular Physics '''109''' pp. 123-132 (2011)]</ref> and expressed in terms of [[Padé approximants]]. For <math>k_BT/\epsilon=1.0</math> and <math>n=6</math> one has (Eq. 8):		The soft-sphere [[Equations of state \| equation of state]]<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref> has recently been studied by Tan, Schultz and Kofke<ref name="Tan">[http://dx.doi.org/10.1080/00268976.2010.520041 Tai Boon Tan, Andrew J. Schultz and David A. Kofke "Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model", Molecular Physics '''109''' pp. 123-132 (2011)]</ref>
			<ref>[http://dx.doi.org/10.1063/1.4767065 N. S. Barlow, A. J. Schultz, S. J. Weinstein, and D. A. Kofke "An asymptotically consistent approximant method with application to soft- and hard-sphere fluids", Journal of Chemical Physics '''137''' 204102 (2012)]</ref>
			and expressed in terms of [[Padé approximants]]. For <math>k_BT/\epsilon=1.0</math> and <math>n=6</math> one has (Eq. 8):


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	:<math>Z_{n=9} = \frac{1 + 3.098829 \rho + 5.188915 \rho^2 + 5.019851 \rho^3 + 2.673385 \rho^4 + 0.601529 \rho^5}{1+ 0.262771 \rho + 0.168052 \rho^2 - 0.010554 \rho^3}</math>		:<math>Z_{n=9} = \frac{1 + 3.098829 \rho + 5.188915 \rho^2 + 5.019851 \rho^3 + 2.673385 \rho^4 + 0.601529 \rho^5}{1+ 0.262771 \rho + 0.168052 \rho^2 - 0.010554 \rho^3}</math>

	==Virial coefficients==		==Virial coefficients==
	Tan, Schultz and Kofke<ref name="Tan"> </ref> have calculated the [[Virial equation of state \| virial coefficients]] at <math>k_BT/\epsilon=1.0</math> (Table 1):		Tan, Schultz and Kofke<ref name="Tan"> </ref> have calculated the [[Virial equation of state \| virial coefficients]] at <math>k_BT/\epsilon=1.0</math> (Table 1):

Carl McBride: /* Glass transition */ Added a recent publication

2011-03-01T09:06:31Z

Glass transition: Added a recent publication

← Older revision		Revision as of 11:06, 1 March 2011
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	\|}		\|}
	==Glass transition==		==Glass transition==
	<ref>[http://dx.doi.org/10.1063/1.3266845 D. M. Heyes, S. M. Clarke, and A. C. Brańka "Soft-sphere soft glasses", Journal of Chemical Physics '''131''' 204506 (2009)]</ref>		<ref>[http://dx.doi.org/10.1063/1.3266845 D. M. Heyes, S. M. Clarke, and A. C. Brańka "Soft-sphere soft glasses", Journal of Chemical Physics '''131''' 204506 (2009)]</ref><ref>[http://dx.doi.org/10.1063/1.3554378 Junko Habasaki and Akira Ueda "Several routes to the glassy states in the one component soft core system: Revisited by molecular dynamics", Journal of Chemical Physics '''134''' 084505 (2011)]</ref>

	==Transport coefficients==		==Transport coefficients==
	<ref>[http://dx.doi.org/10.1080/00268970802712563 D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics '''107''' pp. 309-319 (2009)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970802712563 D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics '''107''' pp. 309-319 (2009)]</ref>

Carl McBride: Added a recent publication

2011-02-14T09:35:24Z

Added a recent publication

← Older revision		Revision as of 11:35, 14 February 2011
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	==Transport coefficients==		==Transport coefficients==
	<ref>[http://dx.doi.org/10.1080/00268970802712563 D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics '''107''' pp. 309-319 (2009)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970802712563 D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics '''107''' pp. 309-319 (2009)]</ref>
			==Radial distribution function==
			<ref>[http://dx.doi.org/10.1063/1.3554363 A. C. Brańka and D. M. Heyes "Pair correlation function of soft-sphere fluids", Journal of Chemical Physics '''134''' 064115 (2011)]</ref>
	==References==		==References==
	<references/>		<references/>
	{{numeric}}		{{numeric}}
	[[category: models]]		[[category: models]]

Carl McBride: Added values for the melting point

2011-01-19T11:12:32Z

Added values for the melting point

@@ Line 20: / Line 20: @@
 :<math>Z_{n=9} = \frac{1 + 3.098829 \rho + 5.188915 \rho^2 + 5.019851 \rho^3 + 2.673385 \rho^4 + 0.601529 \rho^5}{1+ 0.262771 \rho + 0.168052 \rho^2 - 0.010554 \rho^3}</math>
 ==Virial coefficients==
-Tan, Schultz and Kofke<ref name="Tan">[ </ref> have calculated the [[Virial equation of state | virial coefficients]] at <math>k_BT/\epsilon=1.0</math> (Table 1):
+Tan, Schultz and Kofke<ref name="Tan"> </ref> have calculated the [[Virial equation of state | virial coefficients]] at <math>k_BT/\epsilon=1.0</math> (Table 1):
 :{| border="1"
@@ Line 38: / Line 38: @@
 | <math>B_8</math>  || -0.074(2)  || 0.071(4) || 0.44(2)
 |}
-==Solid phase==
+==Melting point==
-<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>
+For <math>n=12</math>
 ==Glass transition==
 <ref>[http://dx.doi.org/10.1063/1.3266845 D. M. Heyes, S. M. Clarke, and A. C. Brańka "Soft-sphere soft glasses", Journal of Chemical Physics '''131''' 204506 (2009)]</ref>

Carl McBride: Added table of virial coefficients

2011-01-17T16:08:39Z

Added table of virial coefficients

← Older revision		Revision as of 18:08, 17 January 2011
Line 9:		Line 9:
	where <math> \Phi_{12}\left(r \right) </math> is the [[intermolecular pair potential]] between two soft spheres separated by a distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\epsilon </math> is the interaction strength and <math> \sigma </math> is the diameter of the sphere. Frequently the value of <math>n</math> is taken to be 12, thus the model effectively becomes the high temperature limit of the [[Lennard-Jones model]] <ref>[http://dx.doi.org/10.1103/PhysRevA.2.221 Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A '''2''' pp. 221-230 (1970)]</ref>. If <math>n\rightarrow \infty</math> one has the [[hard sphere model]]. For <math>n \le 3</math> no thermodynamically stable phases are found.		where <math> \Phi_{12}\left(r \right) </math> is the [[intermolecular pair potential]] between two soft spheres separated by a distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\epsilon </math> is the interaction strength and <math> \sigma </math> is the diameter of the sphere. Frequently the value of <math>n</math> is taken to be 12, thus the model effectively becomes the high temperature limit of the [[Lennard-Jones model]] <ref>[http://dx.doi.org/10.1103/PhysRevA.2.221 Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A '''2''' pp. 221-230 (1970)]</ref>. If <math>n\rightarrow \infty</math> one has the [[hard sphere model]]. For <math>n \le 3</math> no thermodynamically stable phases are found.
	==Equation of state==		==Equation of state==
	The soft-sphere [[Equations of state \| equation of state]]<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref> has recently been studied by Tan, Schultz and Kofke<ref name="Tan">[http://dx.doi.org/10.1080/00268976.2010.520041 Tai Boon Tan, Andrew J. Schultz and David A. Kofke "Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model", Molecular Physics '''109''' pp. 123-132 (2011)]</ref> and ~~experssed~~ in terms of [[Padé approximants]]. For <math>n=6</math> one has (Eq. 8):		The soft-sphere [[Equations of state \| equation of state]]<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref> has recently been studied by Tan, Schultz and Kofke<ref name="Tan">[http://dx.doi.org/10.1080/00268976.2010.520041 Tai Boon Tan, Andrew J. Schultz and David A. Kofke "Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model", Molecular Physics '''109''' pp. 123-132 (2011)]</ref> and expressed in terms of [[Padé approximants]]. For <math>k_BT/\epsilon=1.0</math> and <math>n=6</math> one has (Eq. 8):


Line 20:		Line 20:
	:<math>Z_{n=9} = \frac{1 + 3.098829 \rho + 5.188915 \rho^2 + 5.019851 \rho^3 + 2.673385 \rho^4 + 0.601529 \rho^5}{1+ 0.262771 \rho + 0.168052 \rho^2 - 0.010554 \rho^3}</math>		:<math>Z_{n=9} = \frac{1 + 3.098829 \rho + 5.188915 \rho^2 + 5.019851 \rho^3 + 2.673385 \rho^4 + 0.601529 \rho^5}{1+ 0.262771 \rho + 0.168052 \rho^2 - 0.010554 \rho^3}</math>
	==Virial coefficients==		==Virial coefficients==
	<ref name="Tan">[ </ref>		Tan, Schultz and Kofke<ref name="Tan">[ </ref> have calculated the [[Virial equation of state \| virial coefficients]] at <math>k_BT/\epsilon=1.0</math> (Table 1):

			:{\| border="1"
			\|-
			\| \|\| n=12 \|\| n=9 \|\| n=6
			\|-
			\| <math>B_3</math> \|\| 3.79106644 \|\| 4.27563423 \|\| 5.55199919
			\|-
			\| <math>B_4</math> \|\| 3.52761(6) \|\| 3.43029(7) \|\| 1.44261(4)
			\|-
			\| <math>B_5</math> \|\| 2.1149(2) \|\| 1.08341(7) \|\| -1.68834(9)
			\|-
			\| <math>B_6</math> \|\| 0.7695(2) \|\| -0.21449(11) \|\| 1.8935(5)
			\|-
			\| <math>B_7</math> \|\| 0.0908(5) \|\| -0.0895(7) \|\| -1.700(3)
			\|-
			\| <math>B_8</math> \|\| -0.074(2) \|\| 0.071(4) \|\| 0.44(2)
			\|}
	==Solid phase==		==Solid phase==
	<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>
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	==References==		==References==
	<references/>		<references/>
			{{numeric}}
	[[category: models]]		[[category: models]]

Carl McBride: Added two EOS (for n=6 and 9)

2011-01-17T15:57:03Z

Added two EOS (for n=6 and 9)

← Older revision		Revision as of 17:57, 17 January 2011
Line 9:		Line 9:
	where <math> \Phi_{12}\left(r \right) </math> is the [[intermolecular pair potential]] between two soft spheres separated by a distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\epsilon </math> is the interaction strength and <math> \sigma </math> is the diameter of the sphere. Frequently the value of <math>n</math> is taken to be 12, thus the model effectively becomes the high temperature limit of the [[Lennard-Jones model]] <ref>[http://dx.doi.org/10.1103/PhysRevA.2.221 Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A '''2''' pp. 221-230 (1970)]</ref>. If <math>n\rightarrow \infty</math> one has the [[hard sphere model]]. For <math>n \le 3</math> no thermodynamically stable phases are found.		where <math> \Phi_{12}\left(r \right) </math> is the [[intermolecular pair potential]] between two soft spheres separated by a distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\epsilon </math> is the interaction strength and <math> \sigma </math> is the diameter of the sphere. Frequently the value of <math>n</math> is taken to be 12, thus the model effectively becomes the high temperature limit of the [[Lennard-Jones model]] <ref>[http://dx.doi.org/10.1103/PhysRevA.2.221 Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A '''2''' pp. 221-230 (1970)]</ref>. If <math>n\rightarrow \infty</math> one has the [[hard sphere model]]. For <math>n \le 3</math> no thermodynamically stable phases are found.
	==Equation of state==		==Equation of state==
	<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref>		The soft-sphere [[Equations of state \| equation of state]]<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref> has recently been studied by Tan, Schultz and Kofke<ref name="Tan">[http://dx.doi.org/10.1080/00268976.2010.520041 Tai Boon Tan, Andrew J. Schultz and David A. Kofke "Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model", Molecular Physics '''109''' pp. 123-132 (2011)]</ref> and experssed in terms of [[Padé approximants]]. For <math>n=6</math> one has (Eq. 8):


			:<math>Z_{n=6} = \frac{1 + 7.432255 \rho + 23.854807 \rho^2 + 40.330195 \rho^3 + 34.393896 \rho^4 + 10.723480 \rho^5}{1+ 3.720037 \rho + 4.493218 \rho^2 + 1.554135 \rho^3}</math>


			and for <math>n=9</math> one has (Eq. 9):


			:<math>Z_{n=9} = \frac{1 + 3.098829 \rho + 5.188915 \rho^2 + 5.019851 \rho^3 + 2.673385 \rho^4 + 0.601529 \rho^5}{1+ 0.262771 \rho + 0.168052 \rho^2 - 0.010554 \rho^3}</math>
	==Virial coefficients==		==Virial coefficients==
	<ref>[http://dx.doi.org/10.1080/00268976.2010.520041 Tai Boon Tan, Andrew J. Schultz and David A. Kofke "Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model", Molecular Physics '''109''' pp. 123-132 (2011)]</ref>		<ref name="Tan">[ </ref>
	==Solid phase==		==Solid phase==
	<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>

Carl McBride: Added a publication

2011-01-17T15:23:24Z

Added a publication

← Older revision		Revision as of 17:23, 17 January 2011
Line 10:		Line 10:
	==Equation of state==		==Equation of state==
	<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref>		<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref>
			==Virial coefficients==
			<ref>[http://dx.doi.org/10.1080/00268976.2010.520041 Tai Boon Tan, Andrew J. Schultz and David A. Kofke "Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model", Molecular Physics '''109''' pp. 123-132 (2011)]</ref>
	==Solid phase==		==Solid phase==
	<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>

Nice and Tidy: Added a new reference.

2009-12-01T10:10:43Z

Added a new reference.

← Older revision		Revision as of 12:10, 1 December 2009
Line 7:		Line 7:
	</math>		</math>

	where <math> \Phi_{12}\left(r \right) </math> is the [[intermolecular pair potential]] between two soft spheres separated by a distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\epsilon </math> is the interaction strength and <math> \sigma </math> is the diameter of the sphere. Frequently the value of <math>n</math> is taken to be 12, thus the model effectively becomes the high temperature limit of the [[Lennard-Jones model]] <ref>[http://dx.doi.org/10.1103/PhysRevA.2.221 Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A '''2''' pp. 221-230 (1970)]</ref>.		where <math> \Phi_{12}\left(r \right) </math> is the [[intermolecular pair potential]] between two soft spheres separated by a distance <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>\epsilon </math> is the interaction strength and <math> \sigma </math> is the diameter of the sphere. Frequently the value of <math>n</math> is taken to be 12, thus the model effectively becomes the high temperature limit of the [[Lennard-Jones model]] <ref>[http://dx.doi.org/10.1103/PhysRevA.2.221 Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A '''2''' pp. 221-230 (1970)]</ref>. If <math>n\rightarrow \infty</math> one has the [[hard sphere model]]. For <math>n \le 3</math> no thermodynamically stable phases are found.
	==Equation of state==		==Equation of state==
	<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref>		<ref>[http://dx.doi.org/10.1063/1.1672728 William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics '''52''' pp. 4931-4941 (1970)]</ref>
	==Solid phase==		==Solid phase==
	<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>
			==Glass transition==
			<ref>[http://dx.doi.org/10.1063/1.3266845 D. M. Heyes, S. M. Clarke, and A. C. Brańka "Soft-sphere soft glasses", Journal of Chemical Physics '''131''' 204506 (2009)]</ref>
	==Transport coefficients==		==Transport coefficients==
	<ref>[http://dx.doi.org/10.1080/00268970802712563 D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics '''107''' pp. 309-319 (2009)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970802712563 D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics '''107''' pp. 309-319 (2009)]</ref>

Nice and Tidy: Added a new reference.

2009-05-21T12:27:07Z

Added a new reference.

← Older revision		Revision as of 14:27, 21 May 2009
Line 12:		Line 12:
	==Solid phase==		==Solid phase==
	<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>		<ref>[http://dx.doi.org/10.1080/00268970802603507 Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics '''107''' pp. 295-299 (2009)]</ref>
			==Transport coefficients==
			<ref>[http://dx.doi.org/10.1080/00268970802712563 D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics '''107''' pp. 309-319 (2009)]</ref>
	==References==		==References==
	<references/>		<references/>
	[[category: models]]		[[category: models]]