# SALR potential

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 ${\displaystyle \sigma }$ , along with combination of two Yukawa potentials:

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

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

## LJ+Y

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

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