Hard core Yukawa potential

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

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

and the repulsive form

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

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, $\sigma$ is the hard diameter, $ϵ$ is the energy well depth ($ϵ>0$), 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

References

Related reading

• J. Torres-Arenas, L. A. Cervantes, A. L. Benavides, G. A. Chapela, and F. del Río "Discrete perturbation theory for the hard-core attractive and repulsive Yukawa potentials", Journal of Chemical Physics 132 034501 (2010)