Hard core Yukawa potential: Difference between revisions

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


:<math>
:<math>
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\infty & ; & r < \sigma \\
\infty & ; & r < \sigma \\
- \left( \frac{ \epsilon \sigma }{r}\right)  \exp \left[- \kappa \left( \frac{r}{\sigma} -  1 \right) \right] & ; & r \ge \sigma  
- \left( \frac{ \epsilon \sigma }{r}\right)  \exp \left[- \kappa \left( \frac{r}{\sigma} -  1 \right) \right] & ; & r \ge \sigma  
\end{array} \right.
</math>
and the repulsive form
:<math>
\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.
\end{array} \right.
</math>
</math>
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<math> \sigma </math> is the hard diameter, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and
<math> \sigma </math> is the hard diameter, <math> \epsilon </math> is the energy well depth (<math> \epsilon > 0 </math>), and
<math> \kappa </math> is a parameter that controls the interaction range (<math> \kappa > 0 </math>).
<math> \kappa </math> is a parameter that controls the interaction range (<math> \kappa > 0 </math>).
The repulsive form has been used to study charge-stabilised [[Colloids |colloid-colloid]] interactions.
==Critical point==
==Critical point==
The repulsive form of the potential has no critical point.
==Triple points==
#[http://dx.doi.org/10.1063/1.481068 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==
==Phase diagram==
:''Main article: [[Phase diagram of the Yukawa potential]]''
:''Main article: [[Phase diagram of the Yukawa potential]]''
==References==
==References==
[[Category: Models]]
[[Category: Models]]

Revision as of 12:24, 6 March 2008

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

and the repulsive form

where is the intermolecular pair potential, is the distance, is the hard diameter, is the energy well depth (), and is a parameter that controls the interaction range ().

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

References