Editing SALR potential

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>]]

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>
\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>.
==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>
<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>

==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]]