SALR potential: Difference between revisions
Carl McBride (talk | contribs) (Inserted figure) |
Carl McBride (talk | contribs) (Added a publication) |
||
| Line 1: | Line 1: | ||
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 | |||
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> | ||
| Line 20: | Line 24: | ||
==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]] | ||
Revision as of 17:43, 14 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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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\geq \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].
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)
- Related reading