SALR potential

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The SALR ( short-range attractive - long-range repulsive) potential. This potential has a variety of functional forms.


Plot of a region of the HCDY potential for the parameters \epsilon_r=0.5, \kappa_r=0.5, \epsilon_a=2, \kappa_a=1, as used in the work of Sweatman et. al. [1]

The SALR potential is often expressed as a hard core of diameter  \sigma , along with combination of two Yukawa potentials:

\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  \Phi\left( r \right) is the intermolecular pair potential, r := |\mathbf{r}_1 - \mathbf{r}_2| is the distance between site 1 and site 2. The  \epsilon control is the energy of the repulsive and attractive parts, whilst the  \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] [5].


Another SALR model consists of a generalised Lennard-Jones model in conjunction with a long-range repulsive Yukawa term [6] [7] [8] [9] [10]

 \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}


  1. 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)
  2. 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)
  3. 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)
  4. 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)
  5. Andrew J. Archer and Nigel B. Wilding "Phase behavior of a fluid with competing attractive and repulsive interactions", Physical Review E 76 031501 (2007)
  6. 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)
  7. 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)
  8. 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)
  9. 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)
  10. Jakub Pȩkalski, Andrew P. Santos, Athanassios Z. Panagiotopoulos "From Compact to Open Clusters in Systems with Competing Interactions", arXiv 1703.01213 (2017)
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