Hard core Yukawa potential

The hard core Yukawa potential has two forms, the attractive Yukawa 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 \Phi\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 \ge \sigma \end{array} \right. }

and the repulsive form

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) = \left\{ \begin{array}{lll} \infty & ; & r < \sigma \\ \left( \frac{ \epsilon \sigma }{r}\right) \exp \left[- \kappa \left( \frac{r}{\sigma} - 1 \right) \right] & ; & r \ge \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 } is the distance, 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 (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)

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 (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)