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, 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 (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 > 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 (Ref. 1 Eq. 3)

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

and (Ref. 1 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

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

References

1. Pedro Orea and Yurko Duda "On the corresponding states law of the Yukawa fluid", Journal of Chemical Physics 128 134508 (2008)