Surface tension - Revision history

Carl McBride: Added a recent publication

2018-01-30T11:26:48Z

Added a recent publication

← Older revision		Revision as of 13:26, 30 January 2018
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	change of the surface area is performed at constant <math> V, T, </math> and <math> N </math>.		change of the surface area is performed at constant <math> V, T, </math> and <math> N </math>.
	The explicit equations can be written in terms of the diagonal components of the [[pressure]] tensor of the system.		The explicit equations can be written in terms of the diagonal components of the [[pressure]] tensor of the system.
	Mechanical arguments can also be invoked to arrive at equivalent conclusions (see Ref <ref name="Gloor"> </ref> for a detailed discussion of these issues).		Mechanical arguments can also be invoked to arrive at equivalent conclusions (see Ref <ref name="Gloor"></ref> for a detailed discussion of these issues).

	=== System-size analysis ===		=== System-size analysis ===
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	*[https://doi.org/10.1016/j.molliq.2016.11.103 A. Maslechko, K. Glavatskiy, V.L. Kulinskii "Surface tension of molecular liquids: Lattice gas approach", Journal of Molecular Liquids '''235''' pp. 119-125 (2017)]		*[https://doi.org/10.1016/j.molliq.2016.11.103 A. Maslechko, K. Glavatskiy, V.L. Kulinskii "Surface tension of molecular liquids: Lattice gas approach", Journal of Molecular Liquids '''235''' pp. 119-125 (2017)]
	*[https://doi.org/10.1016/j.molliq.2016.12.062 Stephan Werth, Martin Horsch and Hans Hasse "Molecular simulation of the surface tension of 33 multi-site models for real fluids", Journal of Molecular Liquids '''235''' pp. 126-134 (2017)]		*[https://doi.org/10.1016/j.molliq.2016.12.062 Stephan Werth, Martin Horsch and Hans Hasse "Molecular simulation of the surface tension of 33 multi-site models for real fluids", Journal of Molecular Liquids '''235''' pp. 126-134 (2017)]
			*[https://doi.org/10.1063/1.5008473 T. Dreher, C. Lemarchand, L. Soulard, E. Bourasseau, P. Malfreyt, and N. Pineau "Calculation of a solid/liquid surface tension: A methodological study", Journal of Chemical Physics '''148''' 034702 (2018)]

	==External links==		==External links==
	*[http://dx.doi.org/10.4249/scholarpedia.9218 Charles Pfister "Interface free energy", Scholarpedia, 5(2):9218 (2010)]		*[http://dx.doi.org/10.4249/scholarpedia.9218 Charles Pfister "Interface free energy", Scholarpedia, 5(2):9218 (2010)]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride: /* References */ Added recent publications

2017-05-10T10:04:22Z

References: Added recent publications

← Older revision		Revision as of 12:04, 10 May 2017
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	*[http://dx.doi.org/10.1016/0021-9991(76)90078-4 Charles H. Bennett "Efficient estimation of free energy differences from Monte Carlo data", Journal of Computational Physics '''22''' pp. 245-268 (1976)]		*[http://dx.doi.org/10.1016/0021-9991(76)90078-4 Charles H. Bennett "Efficient estimation of free energy differences from Monte Carlo data", Journal of Computational Physics '''22''' pp. 245-268 (1976)]
	*[http://dx.doi.org/10.1063/1.432627 J. Miyazaki, J. A. Barker and G. M. Pound "A new Monte Carlo method for calculating surface tension", Journal of Chemical Physics '''64''' pp. 3364-3369 (1976)]		*[http://dx.doi.org/10.1063/1.432627 J. Miyazaki, J. A. Barker and G. M. Pound "A new Monte Carlo method for calculating surface tension", Journal of Chemical Physics '''64''' pp. 3364-3369 (1976)]
			*[https://doi.org/10.1016/j.molliq.2016.11.103 A. Maslechko, K. Glavatskiy, V.L. Kulinskii "Surface tension of molecular liquids: Lattice gas approach", Journal of Molecular Liquids '''235''' pp. 119-125 (2017)]
			*[https://doi.org/10.1016/j.molliq.2016.12.062 Stephan Werth, Martin Horsch and Hans Hasse "Molecular simulation of the surface tension of 33 multi-site models for real fluids", Journal of Molecular Liquids '''235''' pp. 126-134 (2017)]

	==External links==		==External links==
	*[http://dx.doi.org/10.4249/scholarpedia.9218 Charles Pfister "Interface free energy", Scholarpedia, 5(2):9218 (2010)]		*[http://dx.doi.org/10.4249/scholarpedia.9218 Charles Pfister "Interface free energy", Scholarpedia, 5(2):9218 (2010)]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride: Added link to Scolarpedia + refereces changed to Cite format

2011-02-10T15:10:38Z

Added link to Scolarpedia + refereces changed to Cite format

← Older revision		Revision as of 17:10, 10 February 2011
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	==Computer Simulation==		==Computer Simulation==
	Different techniques may be used to compute this quantity, such as the traditional [[stress \| stress tensor]] route. More recently, several methods have been proposed which avoid the some times difficult calculation of the stress tensor, e.g., the [[test area method]] and [[wandering interface method]]. A review can be found in the paper by Gloor ''et al.'' ~~(Ref~~. 1).		Different techniques may be used to compute this quantity, such as the traditional [[stress \| stress tensor]] route. More recently, several methods have been proposed which avoid the some times difficult calculation of the stress tensor, e.g., the [[test area method]] and [[wandering interface method]]. A review can be found in the paper by Gloor ''et al.'' <ref name="Gloor">[http://dx.doi.org/10.1063/1.2038827 Guy J. Gloor, George Jackson, Felipe J. Blas and Enrique de Miguel "Test-area simulation method for the direct determination of the interfacial tension of systems with continuous or discontinuous potentials", Journal of Chemical Physics '''123''' 134703 (2005)]</ref>.

	==Liquid-Vapour Interfaces of one component systems ==		==Liquid-Vapour Interfaces of one component systems ==
	=== Binder procedure===		=== Binder procedure===
	Here, only an outline of the procedure is presented, more details can be found in ~~Reference 2~~.		Here, only an outline of the procedure is presented, more details can be found in <ref>[http://dx.doi.org/10.1103/PhysRevA.25.1699 K. Binder "Monte Carlo calculation of the surface tension for two- and three-dimensional lattice-gas models", Physical Review A '''25''' pp. 1699 - 1709 (1982)]</ref>.
	For given conditions of volume and temperature, the [[Helmholtz energy function]] is computed as a function of the number of molecules, <math> A(N;V,T)</math>. The calculation is usually carried out using [[Monte Carlo]] simulation using [[periodic boundary conditions]]		For given conditions of volume and temperature, the [[Helmholtz energy function]] is computed as a function of the number of molecules, <math> A(N;V,T)</math>. The calculation is usually carried out using [[Monte Carlo]] simulation using [[periodic boundary conditions]]
	If liquid-vapour equilibrium occurs, a plot of the [[chemical potential]], <math> \mu \equiv (\partial A/\partial N)_{V,T} </math>,		If liquid-vapour equilibrium occurs, a plot of the [[chemical potential]], <math> \mu \equiv (\partial A/\partial N)_{V,T} </math>,
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	:<math> \Omega (N) \equiv A(N) - \mu_{eq} N = - p_{eq} V + \gamma {\mathcal A}(N) </math>.		:<math> \Omega (N) \equiv A(N) - \mu_{eq} N = - p_{eq} V + \gamma {\mathcal A}(N) </math>.

	For appropriate values of <math> N </math> one can estimate the value of the surface area, <math> {\mathcal A} </math> (See MacDowell ''et al.'', ~~Ref~~. 3), and compute <math> \gamma </math> directly as:		For appropriate values of <math> N </math> one can estimate the value of the surface area, <math> {\mathcal A} </math> (See MacDowell ''et al.'' <ref>[http://dx.doi.org/10.1063/1.2218845 L. G. MacDowell, V. K. Shen, and J. R. Errington "Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systems", Journal of Chemical Physics '''125''' 034705 (2006)]</ref>), and compute <math> \gamma </math> directly as:

	:<math> \gamma = \frac{ \Omega(N) + p_{eq} V } { {\mathcal A}(N) } = \frac{ \Omega(N) - \frac{1}{2}(\Omega(N_l)+\Omega(N_v)) }{{\mathcal A}(N)} </math>		:<math> \gamma = \frac{ \Omega(N) + p_{eq} V } { {\mathcal A}(N) } = \frac{ \Omega(N) - \frac{1}{2}(\Omega(N_l)+\Omega(N_v)) }{{\mathcal A}(N)} </math>
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	change of the surface area is performed at constant <math> V, T, </math> and <math> N </math>.		change of the surface area is performed at constant <math> V, T, </math> and <math> N </math>.
	The explicit equations can be written in terms of the diagonal components of the [[pressure]] tensor of the system.		The explicit equations can be written in terms of the diagonal components of the [[pressure]] tensor of the system.
	Mechanical arguments can also be invoked to arrive at equivalent conclusions (see Ref 1 for a detailed discussion of these issues).		Mechanical arguments can also be invoked to arrive at equivalent conclusions (see Ref <ref name="Gloor"> </ref> for a detailed discussion of these issues).

	=== System-size analysis ===		=== System-size analysis ===

	The [[Finite size effects \|system-size dependence]] of the results for <math> \gamma </math> have to be taken into account in order to obtain accurate results for [[Models \|model systems]].		The [[Finite size effects \|system-size dependence]] of the results for <math> \gamma </math> have to be taken into account in order to obtain accurate results for [[Models \|model systems]].
	Spurious effects that occur due to small system sizes can appear in the ''explicit interface'' methods. (See P.Orea ''et al.'' ~~Ref~~. 4).		Spurious effects that occur due to small system sizes can appear in the ''explicit interface'' methods. (See P.Orea ''et al.'' <ref>[http://dx.doi.org/10.1063/1.2018640 Pedro Orea, Jorge López-Lemus, and José Alejandre, "Oscillatory surface tension due to finite-size effects", Journal of Chemical Physics '''123''' 114702 (6 pages) (2005)]</ref>).

	== Mixtures ==		== Mixtures ==
			Different ensembles can be used to compute the surface tension between two phases in the case of mixtures (See for example see Y. Zhang ''et al.'' <ref>[http://dx.doi.org/10.1063/1.469927 Yuhong Zhang, Scott E. Feller, Bernard R. Brooks, and Richard W. Pastor, "Computer simulation of liquid/liquid interfaces. I. Theory and application to octane/water", Journal of Chemical Physics, '''103''', pp. 10252-10266 (1995)]</ref>).
	Different ensembles can be used to compute the surface tension between two phases in the case of mixtures (See for example see Y. Zhang ''et al.'' ~~Ref 5~~).
	The simulation techniques are essentially the same as those for one-component systems, but different ensembles can be more adequate.		The simulation techniques are essentially the same as those for one-component systems, but different ensembles can be more adequate.
	For instance, for binary mixtures (with components 1 and 2), the [[isothermal-isobaric ensemble]], <math> N_1,N_2,p.T </math> is a ''more natural'' ensemble to compute		For instance, for binary mixtures (with components 1 and 2), the [[isothermal-isobaric ensemble]], <math> N_1,N_2,p.T </math> is a ''more natural'' ensemble to compute
	<math> \gamma </math> using explicit interface techniques (See Ref. 6 as an example).		<math> \gamma </math> using explicit interface techniques (See Ref. <ref>[http://dx.doi.org/10.1063/1.2751153 E. de Miguel, N. G. Almarza, and G. Jackson, "Surface tension of the Widom-Rowlinson model", Journal of Chemical Physics, '''127''', 034707 (10 pages) (2007)]</ref> as an example).
	In the case of the Binder technique		In the case of the Binder technique
	the analysis can be carried out by fixing the total number of particles: <math> N \equiv N_1 + N_2 </math>, the [[pressure]], <math> p </math>, and the [[temperature]] <math> T </math>. Then		the analysis can be carried out by fixing the total number of particles: <math> N \equiv N_1 + N_2 </math>, the [[pressure]], <math> p </math>, and the [[temperature]] <math> T </math>. Then
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	==References==		==References==
	#[http://dx.doi.org/10.1063/1.2038827 Guy J. Gloor, George Jackson, Felipe J. Blas and Enrique de Miguel "Test-area simulation method for the direct determination of the interfacial tension of systems with continuous or discontinuous potentials", Journal of Chemical Physics '''123''' 134703 (2005)]		<references/>
	#[http://dx.doi.org/10.1103/PhysRevA.25.1699 K. Binder "Monte Carlo calculation of the surface tension for two- and three-dimensional lattice-gas models", Physical Review A '''25''' pp. 1699 - 1709 (1982)]		;Related reading
	#[http://dx.doi.org/10.1063/1.2218845 L. G. MacDowell, V. K. Shen, and J. R. Errington "Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systems", Journal of Chemical Physics '''125''' 034705 (2006)]		*[http://dx.doi.org/10.1063/1.1747248 John G. Kirkwood and Frank P. Buff "The Statistical Mechanical Theory of Surface Tension", Journal of Chemical Physics '''17''' pp. 338-343 (1949)]
	#[http://dx.doi.org/10.1063/1.2018640 Pedro Orea, Jorge López-Lemus, and José Alejandre, "Oscillatory surface tension due to finite-size effects", Journal of Chemical Physics '''123''' 114702 (6 pages) (2005)]		*[http://dx.doi.org/10.1016/0021-9991(76)90078-4 Charles H. Bennett "Efficient estimation of free energy differences from Monte Carlo data", Journal of Computational Physics '''22''' pp. 245-268 (1976)]
	~~#[http:~~//dx.doi.org/10.1063/1.469927 Yuhong Zhang, Scott E. Feller, Bernard R. Brooks, and Richard W. Pastor, "Computer simulation of liquid/liquid interfaces. I. Theory and application to octane/water", Journal of Chemical Physics, '''103''', pp. 10252-10266 (1995)]		*[http://dx.doi.org/10.1063/1.432627 J. Miyazaki, J. A. Barker and G. M. Pound "A new Monte Carlo method for calculating surface tension", Journal of Chemical Physics '''64''' pp. 3364-3369 (1976)]
	#[http://dx.doi.org/10.1063/1.2751153 E. de Miguel, N. G. Almarza, and G. Jackson, "Surface tension of the Widom-Rowlinson model", Journal of Chemical Physics, '''127''', 034707 (10 pages) (2007)]		==External links==
	#[http://dx.doi.org/10.1063/1.1747248 John G. Kirkwood and Frank P. Buff "The Statistical Mechanical Theory of Surface Tension", Journal of Chemical Physics '''17''' pp. 338-343 (1949)]		*[http://dx.doi.org/10.4249/scholarpedia.9218 Charles Pfister "Interface free energy", Scholarpedia, 5(2):9218 (2010)]
	#[http://dx.doi.org/10.1016/0021-9991(76)90078-4 Charles H. Bennett "Efficient estimation of free energy differences from Monte Carlo data", Journal of Computational Physics '''22''' pp. 245-268 (1976)]
	#[http://dx.doi.org/10.1063/1.432627 J. Miyazaki, J. A. Barker and G. M. Pound "A new Monte Carlo method for calculating surface tension", Journal of Chemical Physics '''64''' pp. 3364-3369 (1976)]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Nice and Tidy: /* Explicit interfaces */

2010-02-11T14:04:35Z

Explicit interfaces

← Older revision		Revision as of 16:04, 11 February 2010
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	=== Explicit interfaces ===		=== Explicit interfaces ===
	In these methods one performs a direct simulation of the two-phase system. [[~~boundary conditions \|~~Periodic boundary conditions]] are usually employed.		In these methods one performs a direct simulation of the two-phase system. [[Periodic boundary conditions]] are usually employed.
	Simulation boxes are elongated in one direction, and the interfaces are built (and expected to stay) perpendicular to		Simulation boxes are elongated in one direction, and the interfaces are built (and expected to stay) perpendicular to
	such a direction.		such a direction.

Nice and Tidy: /* Binder procedure */

2010-02-11T14:04:05Z

Binder procedure

← Older revision		Revision as of 16:04, 11 February 2010
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	=== Binder procedure===		=== Binder procedure===
	Here, only an outline of the procedure is presented, more details can be found in Reference 2.		Here, only an outline of the procedure is presented, more details can be found in Reference 2.
	For given conditions of volume and temperature, the [[Helmholtz energy function]] is computed as a function of the number of molecules, <math> A(N;V,T)</math>. The calculation is usually carried out using [[Monte Carlo]] simulation using [[~~boundary conditions \|~~periodic boundary conditions]]		For given conditions of volume and temperature, the [[Helmholtz energy function]] is computed as a function of the number of molecules, <math> A(N;V,T)</math>. The calculation is usually carried out using [[Monte Carlo]] simulation using [[periodic boundary conditions]]
	If liquid-vapour equilibrium occurs, a plot of the [[chemical potential]], <math> \mu \equiv (\partial A/\partial N)_{V,T} </math>,		If liquid-vapour equilibrium occurs, a plot of the [[chemical potential]], <math> \mu \equiv (\partial A/\partial N)_{V,T} </math>,
	as a function of <math> N </math> shows a loop.		as a function of <math> N </math> shows a loop.

Nice and Tidy: /* Computer Simulation */ Lower case name spaces.

2009-05-11T09:15:29Z

Computer Simulation: Lower case name spaces.

← Older revision		Revision as of 11:15, 11 May 2009
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	==Computer Simulation==		==Computer Simulation==
	Different techniques may be used to compute this quantity, such as the traditional [[stress \| stress tensor]] route. More recently, several methods have been proposed which avoid the some times difficult calculation of the stress tensor, e.g., the [[~~Test Area Method~~]] and [[~~Wandering Interface Method~~]]. A review can be found in the paper by Gloor ''et al.'' (Ref. 1).		Different techniques may be used to compute this quantity, such as the traditional [[stress \| stress tensor]] route. More recently, several methods have been proposed which avoid the some times difficult calculation of the stress tensor, e.g., the [[test area method]] and [[wandering interface method]]. A review can be found in the paper by Gloor ''et al.'' (Ref. 1).

	==Liquid-Vapour Interfaces of one component systems ==		==Liquid-Vapour Interfaces of one component systems ==

Lgmac: added link to wim

2009-05-10T21:49:55Z

added link to wim

← Older revision		Revision as of 23:49, 10 May 2009
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	==Computer Simulation==		==Computer Simulation==
	Different techniques may be used to compute this quantity, such as the traditional [[stress \| stress tensor]] route or the ~~more recent~~ [[~~test area method~~]]. A review can be found in the paper by Gloor ''et al.'' (Ref. 1).		Different techniques may be used to compute this quantity, such as the traditional [[stress \| stress tensor]] route. More recently, several methods have been proposed which avoid the some times difficult calculation of the stress tensor, e.g., the [[Test Area Method]] and [[Wandering Interface Method]]. A review can be found in the paper by Gloor ''et al.'' (Ref. 1).

	==Liquid-Vapour Interfaces of one component systems ==		==Liquid-Vapour Interfaces of one component systems ==

Carl McBride: /* Liquid-Vapour Interfaces of one component systems */ Changed internal links to boundary conditions

2008-04-09T09:12:36Z

Liquid-Vapour Interfaces of one component systems: Changed internal links to boundary conditions

← Older revision		Revision as of 11:12, 9 April 2008
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	=== Binder procedure===		=== Binder procedure===
	Here, only an outline of the procedure is presented, more details can be found in Reference 2.		Here, only an outline of the procedure is presented, more details can be found in Reference 2.
	For given conditions of volume and temperature, the [[Helmholtz energy function]] is computed as a function of the number of molecules, <math> A(N;V,T)</math>. The calculation is usually carried out using [[Monte Carlo]] simulation using [[periodic boundary conditions]]		For given conditions of volume and temperature, the [[Helmholtz energy function]] is computed as a function of the number of molecules, <math> A(N;V,T)</math>. The calculation is usually carried out using [[Monte Carlo]] simulation using [[boundary conditions \|periodic boundary conditions]]
	If liquid-vapour equilibrium occurs, a plot of the [[chemical potential]], <math> \mu \equiv (\partial A/\partial N)_{V,T} </math>,		If liquid-vapour equilibrium occurs, a plot of the [[chemical potential]], <math> \mu \equiv (\partial A/\partial N)_{V,T} </math>,
	as a function of <math> N </math> shows a loop.		as a function of <math> N </math> shows a loop.
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	=== Explicit interfaces ===		=== Explicit interfaces ===
	In these methods one performs a direct simulation of the two-phase system. [[Periodic boundary conditions]] are usually employed.		In these methods one performs a direct simulation of the two-phase system. [[boundary conditions \|Periodic boundary conditions]] are usually employed.
	Simulation boxes are elongated in one direction, and the interfaces are built (and expected to stay) perpendicular to		Simulation boxes are elongated in one direction, and the interfaces are built (and expected to stay) perpendicular to
	such a direction.		such a direction.

Carl McBride: Added internal link

2008-02-15T15:03:26Z

Added internal link

← Older revision		Revision as of 17:03, 15 February 2008
Line 1:		Line 1:
	The '''surface tension''',		The '''surface tension''',
	<math> \gamma </math>, is a measure of the work required to create an [[interface]] between		<math> \gamma </math>, is a measure of the [[work]] required to create an [[interface]] between
	two bulk phases.		two bulk phases.

Carl McBride: /* Explicit interfaces */

2008-02-12T13:29:54Z

Explicit interfaces

← Older revision		Revision as of 15:29, 12 February 2008
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	Taking into account the [[canonical ensemble]] definition (see above), one computes the change in the [[Helmholtz energy function]] when a small (differential)		Taking into account the [[canonical ensemble]] definition (see above), one computes the change in the [[Helmholtz energy function]] when a small (differential)
	change of the surface area is performed at constant <math> V, T, </math> and <math> N </math>.		change of the surface area is performed at constant <math> V, T, </math> and <math> N </math>.
	The explicit equations can be written in terms of the diagonal components of the [[pressure ~~tensor~~]] of the system.		The explicit equations can be written in terms of the diagonal components of the [[pressure]] tensor of the system.
	Mechanical arguments can also be invoked to arrive at equivalent conclusions (see Ref 1 for a detailed discussion of these issues).		Mechanical arguments can also be invoked to arrive at equivalent conclusions (see Ref 1 for a detailed discussion of these issues).