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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi\left( r \right) } is the intermolecular pair potential, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|} is the distance between site 1 and site 2, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is the hard diameter, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon } is the energy well depth ($\epsilon >0$), and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \kappa } is a parameter that controls the interaction range (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 )

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_c = 0.0228 + 0.0742 T_c}

and (Eq. 4)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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)