SALR potential - Revision history

Carl McBride: Slight tidy

2018-03-15T13:17:08Z

Slight tidy

← Older revision		Revision as of 15:17, 15 March 2018
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	This potential also goes by the names of the ''hard-sphere plus two Yukawa'' (H2Y) or ''hard-core double-Yukawa'' (HCDY) potential		This potential also goes by the names of the ''hard-sphere plus two Yukawa'' (H2Y) or ''hard-core double-Yukawa'' (HCDY) potential
	<ref>[http://dx.doi.org/10.1063/1.1518687 Yang-Zheng Lin, Yi-Gui Li, Jiu-Fang Lu and Wei Wu "Monte Carlo simulation for the hard-core two-Yukawa fluids and test of the two-Yukawa equation of state", Journal of Chemical Physics '''117''' 10165 (2002)]</ref><ref>[http://dx.doi.org/10.1063/1.3308648 Lloyd L. Lee, Michael C. Hara, Steven J. Simon, Franklin S. Ramos, Andrew J. Winkle, and Jean-Marc Bomont "Crystallization limits of the two-term Yukawa potentials based on the entropy criterion", Journal of Chemical Physics '''132''' 074505 (2010)]</ref><ref>[http://dx.doi.org/10.1063/1.4942199 J. Montes, M. Robles and M. López de Haro "Equation of state and critical point behavior of hard-core double-Yukawa fluids", Journal of Chemical Physics '''144''' 084503 (2016)]</ref>.		<ref>[http://dx.doi.org/10.1063/1.1518687 Yang-Zheng Lin, Yi-Gui Li, Jiu-Fang Lu and Wei Wu "Monte Carlo simulation for the hard-core two-Yukawa fluids and test of the two-Yukawa equation of state", Journal of Chemical Physics '''117''' 10165 (2002)]</ref><ref>[http://dx.doi.org/10.1063/1.3308648 Lloyd L. Lee, Michael C. Hara, Steven J. Simon, Franklin S. Ramos, Andrew J. Winkle, and Jean-Marc Bomont "Crystallization limits of the two-term Yukawa potentials based on the entropy criterion", Journal of Chemical Physics '''132''' 074505 (2010)]</ref><ref>[http://dx.doi.org/10.1063/1.4942199 J. Montes, M. Robles and M. López de Haro "Equation of state and critical point behavior of hard-core double-Yukawa fluids", Journal of Chemical Physics '''144''' 084503 (2016)]</ref>
			<ref>[http://dx.doi.org/10.1103/PhysRevE.76.031501 Andrew J. Archer and Nigel B. Wilding "Phase behavior of a fluid with competing attractive and repulsive interactions", Physical Review E '''76''' 031501 (2007)]</ref>.
	==LJ+Y==		==LJ+Y==
	Another SALR model consists of a generalised [[Lennard-Jones model]] in conjunction with a long-range repulsive Yukawa term		Another SALR model consists of a generalised [[Lennard-Jones model]] in conjunction with a long-range repulsive Yukawa term
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	<references/>		<references/>
	;Related reading		;Related reading
	*[http://dx.doi.org/10.1103/PhysRevE.76.031501 Andrew J. Archer and Nigel B. Wilding "Phase behavior of a fluid with competing attractive and repulsive interactions", Physical Review E '''76''' 031501 (2007)]
	[[Category: Models]]		[[Category: Models]]

Carl McBride: Added some links to publications

2018-03-15T13:14:23Z

Added some links to publications

← Older revision		Revision as of 15:14, 15 March 2018
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	<ref>[http://dx.doi.org/10.1039/C3SM53058B Ethayaraja Mani, Wolfgang Lechner, Willem K. Kegel and Peter G. Bolhuis "Equilibrium and non-equilibrium cluster phases in colloids with competing interactions", '''10''' pp. 4479-4486 (2014)]</ref>		<ref>[http://dx.doi.org/10.1039/C3SM53058B Ethayaraja Mani, Wolfgang Lechner, Willem K. Kegel and Peter G. Bolhuis "Equilibrium and non-equilibrium cluster phases in colloids with competing interactions", '''10''' pp. 4479-4486 (2014)]</ref>
	<ref>[http://dx.doi.org/10.1021/ct501067t Štěpán Růžička and Michael P. Allen "Monodisperse Clusters in Charged Attractive Colloids: Linear Renormalization of Repulsion", Journal of Chemical Theory and Computation '''11''' pp. 3811-3817 (2015)]</ref>		<ref>[http://dx.doi.org/10.1021/ct501067t Štěpán Růžička and Michael P. Allen "Monodisperse Clusters in Charged Attractive Colloids: Linear Renormalization of Repulsion", Journal of Chemical Theory and Computation '''11''' pp. 3811-3817 (2015)]</ref>
			<ref>[http://dx.doi.org/10.1039/C7SM01721A Andrew P. Santos Jakub Pȩkalski and Athanassios Z. Panagiotopoulos "Thermodynamic signatures and cluster properties of self-assembly in systems with competing interactions", Soft Matter '''13''' pp. 8055-8063 (2017)]</ref>
			<ref>[https://arxiv.org/abs/1703.01213 Jakub Pȩkalski, Andrew P. Santos, Athanassios Z. Panagiotopoulos "From Compact to Open Clusters in Systems with Competing Interactions", arXiv 1703.01213 (2017)]</ref>

	:<math> \Phi_{12}(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{2a}- \left( \frac{\sigma}{r}\right)^a \right] + A \frac{e^{-r/\xi}}{r/\xi}</math>		:<math> \Phi_{12}(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{2a}- \left( \frac{\sigma}{r}\right)^a \right] + A \frac{e^{-r/\xi}}{r/\xi}</math>

Carl McBride: Added another model

2018-03-15T12:37:44Z

Added another model

← Older revision		Revision as of 14:37, 15 March 2018
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	This potential also goes by the names of the ''hard-sphere plus two Yukawa'' (H2Y) or ''hard-core double-Yukawa'' (HCDY) potential		This potential also goes by the names of the ''hard-sphere plus two Yukawa'' (H2Y) or ''hard-core double-Yukawa'' (HCDY) potential
	<ref>[http://dx.doi.org/10.1063/1.1518687 Yang-Zheng Lin, Yi-Gui Li, Jiu-Fang Lu and Wei Wu "Monte Carlo simulation for the hard-core two-Yukawa fluids and test of the two-Yukawa equation of state", Journal of Chemical Physics '''117''' 10165 (2002)]</ref><ref>[http://dx.doi.org/10.1063/1.3308648 Lloyd L. Lee, Michael C. Hara, Steven J. Simon, Franklin S. Ramos, Andrew J. Winkle, and Jean-Marc Bomont "Crystallization limits of the two-term Yukawa potentials based on the entropy criterion", Journal of Chemical Physics '''132''' 074505 (2010)]</ref><ref>[http://dx.doi.org/10.1063/1.4942199 J. Montes, M. Robles and M. López de Haro "Equation of state and critical point behavior of hard-core double-Yukawa fluids", Journal of Chemical Physics '''144''' 084503 (2016)]</ref>.		<ref>[http://dx.doi.org/10.1063/1.1518687 Yang-Zheng Lin, Yi-Gui Li, Jiu-Fang Lu and Wei Wu "Monte Carlo simulation for the hard-core two-Yukawa fluids and test of the two-Yukawa equation of state", Journal of Chemical Physics '''117''' 10165 (2002)]</ref><ref>[http://dx.doi.org/10.1063/1.3308648 Lloyd L. Lee, Michael C. Hara, Steven J. Simon, Franklin S. Ramos, Andrew J. Winkle, and Jean-Marc Bomont "Crystallization limits of the two-term Yukawa potentials based on the entropy criterion", Journal of Chemical Physics '''132''' 074505 (2010)]</ref><ref>[http://dx.doi.org/10.1063/1.4942199 J. Montes, M. Robles and M. López de Haro "Equation of state and critical point behavior of hard-core double-Yukawa fluids", Journal of Chemical Physics '''144''' 084503 (2016)]</ref>.
			==LJ+Y==
			Another SALR model consists of a generalised [[Lennard-Jones model]] in conjunction with a long-range repulsive Yukawa term
			<ref>[http://dx.doi.org/10.1103/PhysRevLett.93.055701 Francesco Sciortino, Stefano Mossa, Emanuela Zaccarelli, and Piero Tartaglia "Equilibrium Cluster Phases and Low-Density Arrested Disordered States: The Role of Short-Range Attraction and Long-Range Repulsion", Physical Review Letters '''93''' 055701 (2004)]</ref>
			<ref>[http://dx.doi.org/10.1039/C3SM53058B Ethayaraja Mani, Wolfgang Lechner, Willem K. Kegel and Peter G. Bolhuis "Equilibrium and non-equilibrium cluster phases in colloids with competing interactions", '''10''' pp. 4479-4486 (2014)]</ref>
			<ref>[http://dx.doi.org/10.1021/ct501067t Štěpán Růžička and Michael P. Allen "Monodisperse Clusters in Charged Attractive Colloids: Linear Renormalization of Repulsion", Journal of Chemical Theory and Computation '''11''' pp. 3811-3817 (2015)]</ref>

			:<math> \Phi_{12}(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{2a}- \left( \frac{\sigma}{r}\right)^a \right] + A \frac{e^{-r/\xi}}{r/\xi}</math>

	==References==		==References==

Carl McBride: Added a publication

2018-03-14T15:43:58Z

Added a publication

← Older revision		Revision as of 17:43, 14 March 2018
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			The '''SALR''' ( short-range attractive - long-range repulsive) potential. This potential has a variety of functional forms.

			==HCDY==
	[[Image:SALR.png\|thumb\|right\|Plot of a region of the HCDY potential for the parameters <math>\epsilon_r=0.5</math>, <math>\kappa_r=0.5</math>, <math>\epsilon_a=2</math>, <math>\kappa_a=1</math>, as used in the work of Sweatman ''et. al.'' <ref>[https://doi.org/10.1063/1.4869109 Martin B. Sweatman, Rui Fartaria, and Leo Lue "Cluster formation in fluids with competing short-range and long-range interactions", nal of Chemical Physics '''140''' 124508 (2014)]</ref>]]		[[Image:SALR.png\|thumb\|right\|Plot of a region of the HCDY potential for the parameters <math>\epsilon_r=0.5</math>, <math>\kappa_r=0.5</math>, <math>\epsilon_a=2</math>, <math>\kappa_a=1</math>, as used in the work of Sweatman ''et. al.'' <ref>[https://doi.org/10.1063/1.4869109 Martin B. Sweatman, Rui Fartaria, and Leo Lue "Cluster formation in fluids with competing short-range and long-range interactions", nal of Chemical Physics '''140''' 124508 (2014)]</ref>]]
	The ~~'''~~SALR~~''' ( short-range attractive - long-range repulsive)~~ potential is often expressed as a hard core of diameter <math> \sigma </math> , along with combination of two [[Hard core Yukawa potential \| Yukawa potentials]]:
			The SALR potential is often expressed as a hard core of diameter <math> \sigma </math> , along with combination of two [[Hard core Yukawa potential \| Yukawa potentials]]:

	:<math>		:<math>
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	==References==		==References==
	<references/>		<references/>
			;Related reading
			*[http://dx.doi.org/10.1103/PhysRevE.76.031501 Andrew J. Archer and Nigel B. Wilding "Phase behavior of a fluid with competing attractive and repulsive interactions", Physical Review E '''76''' 031501 (2007)]
	[[Category: Models]]		[[Category: Models]]

Carl McBride: Inserted figure

2018-03-14T14:53:27Z

Inserted figure

← Older revision		Revision as of 16:53, 14 March 2018
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			[[Image:SALR.png\|thumb\|right\|Plot of a region of the HCDY potential for the parameters <math>\epsilon_r=0.5</math>, <math>\kappa_r=0.5</math>, <math>\epsilon_a=2</math>, <math>\kappa_a=1</math>, as used in the work of Sweatman ''et. al.'' <ref>[https://doi.org/10.1063/1.4869109 Martin B. Sweatman, Rui Fartaria, and Leo Lue "Cluster formation in fluids with competing short-range and long-range interactions", nal of Chemical Physics '''140''' 124508 (2014)]</ref>]]
	The '''SALR''' ( short-range attractive - long-range repulsive) potential is often expressed as a hard core of diameter <math> \sigma </math> , along with combination of two [[Hard core Yukawa potential \| Yukawa potentials]]:		The '''SALR''' ( short-range attractive - long-range repulsive) potential is often expressed as a hard core of diameter <math> \sigma </math> , along with combination of two [[Hard core Yukawa potential \| Yukawa potentials]]:

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	This potential also goes by the names of the ''hard-sphere plus two Yukawa'' (H2Y) or ''hard-core double-Yukawa'' (HCDY) potential		This potential also goes by the names of the ''hard-sphere plus two Yukawa'' (H2Y) or ''hard-core double-Yukawa'' (HCDY) potential
	<ref>[http://dx.doi.org/10.1063/1.1518687 Yang-Zheng Lin, Yi-Gui Li, Jiu-Fang Lu and Wei Wu "Monte Carlo simulation for the hard-core two-Yukawa fluids and test of the two-Yukawa equation of state", Journal of Chemical Physics '''117''' 10165 (2002)]</ref><ref>[http://dx.doi.org/10.1063/1.3308648 Lloyd L. Lee, Michael C. Hara, Steven J. Simon, Franklin S. Ramos, Andrew J. Winkle, and Jean-Marc Bomont "Crystallization limits of the two-term Yukawa potentials based on the entropy criterion", Journal of Chemical Physics '''132''' 074505 (2010)]</ref><ref>[http://dx.doi.org/10.1063/1.4942199 J. Montes, M. Robles and M. López de Haro "Equation of state and critical point behavior of hard-core double-Yukawa fluids", Journal of Chemical Physics '''144''' 084503 (2016)]</ref>.		<ref>[http://dx.doi.org/10.1063/1.1518687 Yang-Zheng Lin, Yi-Gui Li, Jiu-Fang Lu and Wei Wu "Monte Carlo simulation for the hard-core two-Yukawa fluids and test of the two-Yukawa equation of state", Journal of Chemical Physics '''117''' 10165 (2002)]</ref><ref>[http://dx.doi.org/10.1063/1.3308648 Lloyd L. Lee, Michael C. Hara, Steven J. Simon, Franklin S. Ramos, Andrew J. Winkle, and Jean-Marc Bomont "Crystallization limits of the two-term Yukawa potentials based on the entropy criterion", Journal of Chemical Physics '''132''' 074505 (2010)]</ref><ref>[http://dx.doi.org/10.1063/1.4942199 J. Montes, M. Robles and M. López de Haro "Equation of state and critical point behavior of hard-core double-Yukawa fluids", Journal of Chemical Physics '''144''' 084503 (2016)]</ref>.

	==References==		==References==
	<references/>		<references/>

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

Carl McBride: Created page with "The '''SALR''' ( short-range attractive - long-range repulsive) potential is often expressed as a hard core of diameter $\sigma$ , along with combination of two..."

2018-03-14T12:55:17Z

Created page with "The '''SALR''' ( short-range attractive - long-range repulsive) potential is often expressed as a hard core of diameter <math> \sigma </math> , along with combination of two..."

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The '''SALR''' ( short-range attractive - long-range repulsive) potential is often expressed as a hard core of diameter <math> \sigma </math> , along with combination of two [[Hard core Yukawa potential | Yukawa potentials]]:

:<math>
\Phi_{12}\left( r \right) =
\left\{ \begin{array}{lll}
\infty & ; & r < \sigma \\
\epsilon_r \left(\frac{ \sigma }{r}\right) \exp \left[- \kappa_r \left( \frac{r}{\sigma} - 1 \right) \right] - \epsilon_a \left( \frac{ \sigma }{r}\right) \exp \left[- \kappa_a \left( \frac{r}{\sigma} - 1 \right) \right] & ; & r \ge \sigma
\end{array} \right.
</math>

where <math> \Phi\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.
The <math> \epsilon </math> control is the energy of the repulsive and attractive parts, whilst the
<math> \kappa </math> controls the interaction range.

This potential also goes by the names of the ''hard-sphere plus two Yukawa'' (H2Y) or ''hard-core double-Yukawa'' (HCDY) potential
<ref>[http://dx.doi.org/10.1063/1.1518687 Yang-Zheng Lin, Yi-Gui Li, Jiu-Fang Lu and Wei Wu "Monte Carlo simulation for the hard-core two-Yukawa fluids and test of the two-Yukawa equation of state", Journal of Chemical Physics '''117''' 10165 (2002)]</ref><ref>[http://dx.doi.org/10.1063/1.3308648 Lloyd L. Lee, Michael C. Hara, Steven J. Simon, Franklin S. Ramos, Andrew J. Winkle, and Jean-Marc Bomont "Crystallization limits of the two-term Yukawa potentials based on the entropy criterion", Journal of Chemical Physics '''132''' 074505 (2010)]</ref><ref>[http://dx.doi.org/10.1063/1.4942199 J. Montes, M. Robles and M. López de Haro "Equation of state and critical point behavior of hard-core double-Yukawa fluids", Journal of Chemical Physics '''144''' 084503 (2016)]</ref>.
==References==
<references/>

[[Category: Models]]