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 ${ϵ}_r=0.5$, ${\kappa }_r=0.5$, ${ϵ}_a=2$, ${\kappa }_a=1$, 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:

${\mathrm{\Phi }}_{12}(r)=\{\begin{array}{ccc}\mathrm{\infty }& ;& r<\sigma \\ {ϵ}_r(\frac{\sigma }{r})\exp [-{\kappa }_r(\frac{r}{\sigma }-1)]-{ϵ}_a(\frac{\sigma }{r})\exp [-{\kappa }_a(\frac{r}{\sigma }-1)]& ;& r\ge \sigma \end{array}$

where $\mathrm{\Phi }(r)$ is the intermolecular pair potential, $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$ is the distance between site 1 and site 2. The $ϵ$ 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

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

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)