Hard core Yukawa potential

The hard core Yukawa potential has two forms, the attractive Yukawa potential:

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

and the repulsive form

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

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, $\sigma$ is the hard diameter, $\epsilon$ is the energy well depth ($\epsilon >0$), and $\kappa$ is a parameter that controls the interaction range ($\kappa >0$).

The repulsive form has been used to study charge-stabilised colloid-colloid interactions.

Critical point

For the attractive form of the potential, from a study of the law of corresponding states, one has (Eq. 3 in )

$P_{c}=0.0228+0.0742T_{c}$

and (Eq. 4)

$\rho _{c}=0.2534+0.071{\frac {1}{T_{c}}}$.

The repulsive form of the potential has no critical point.

Triple points

The triple points for this model have been studied by Azhar and co-workers .

Virial coefficients

For the attractive form of the potential the virial coefficients have been calculated by Naresh and Singh .

Phase diagram

Main article: Phase diagram of the Yukawa potential