SALR potential

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

HCDY

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.

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

$\Phi _{12}\left(r\right)=\left\{{\begin{array}{lll}\infty &;&r<\sigma \\\epsilon _{r}\left({\frac {\sigma }{r}}\right)\exp \left[-\kappa _{r}\left({\frac {r}{\sigma }}-1\right)\right]-\epsilon _{a}\left({\frac {\sigma }{r}}\right)\exp \left[-\kappa _{a}\left({\frac {r}{\sigma }}-1\right)\right]&;&r\geq \sigma \end{array}}\right.$

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 .

LJ+Y

Another SALR model consists of a generalised Lennard-Jones model in conjunction with a long-range repulsive Yukawa term

$\Phi _{12}(r)=4\epsilon \left[\left({\frac {\sigma }{r}}\right)^{2a}-\left({\frac {\sigma }{r}}\right)^{a}\right]+A{\frac {e^{-r/\xi }}{r/\xi }}$

References

Related reading

• Andrew J. Archer and Nigel B. Wilding "Phase behavior of a fluid with competing attractive and repulsive interactions", Physical Review E 76 031501 (2007)