SALR potential: Difference between revisions
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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== | ||
Revision as of 13:37, 15 March 2018
The SALR ( short-range attractive - long-range repulsive) potential. This potential has a variety of functional forms.
HCDY
The SALR potential is often expressed as a hard core of diameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } , along with combination of two Yukawa potentials:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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. }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi\left( r \right) }
is the intermolecular pair potential, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|}
is the distance between site 1 and site 2.
The Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon }
control is the energy of the repulsive and attractive parts, whilst the
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \kappa }
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 [2][3][4].
LJ+Y
Another SALR model consists of a generalised Lennard-Jones model in conjunction with a long-range repulsive Yukawa term [5] [6] [7]
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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}}
References
- ↑ 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)
- ↑ 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)
- ↑ 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)
- ↑ 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)
- ↑ 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)
- ↑ 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)
- ↑ 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)
- Related reading