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 .

Surface tension

Surface tension .

Radial distribution function

Radial distribution function

Phase diagram

Phase diagram

Density-functional theory

Density-functional theory .

See also

• SALR potential
• Soft sphere attractive Yukawa model

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)
• Pedro Orea, Carlos Tapia-Medina, Davide Pini, and Albert Reiner "Thermodynamic properties of short-range attractive Yukawa fluid: Simulation and theory", Journal of Chemical Physics 132 114108 (2010)
• Eun-Young Kim, Soon-Chul Kim, and Baek-Seok Seong "Structure and thermodynamics of hard-core Yukawa fluids: Thermodynamic perturbation approaches", Journal of Chemical Physics 135 034505 (2011)