Hard core Yukawa potential

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

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

and the repulsive form

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

where $\mathrm{\Phi }(r)$ is the intermolecular pair potential, $r$ is the distance, $\sigma$ 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

The repulsive form of the potential has no critical point.

Triple points

1. Fouad El Azhar, Marc Baus, Jean-Paul Ryckaert and Evert Jan Meijer "Line of triple points for the hard-core Yukawa model: A computer simulation study", Journal of Chemical Physics 112 pp. 5121- (2000)

Phase diagram

Main article: Phase diagram of the Yukawa potential