Hard core Yukawa
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The repulsive form has been used to study charge-stabilised [[Colloids |colloid-colloid]] interactions. | The repulsive form has been used to study charge-stabilised [[Colloids |colloid-colloid]] interactions. | ||
==Critical point== | ==Critical point== | ||
| - | For the attractive form of the potential, from a study of the [[law of corresponding states]], one has ( | + | For the attractive form of the potential, from a study of the [[law of corresponding states]], one has (Eq. 3 in <ref>[http://dx.doi.org/10.1063/1.2883694 Pedro Orea and Yurko Duda "On the corresponding states law of the Yukawa fluid", Journal of Chemical Physics '''128''' 134508 (2008)]</ref>) |
:<math>P_c = 0.0228 + 0.0742 T_c</math> | :<math>P_c = 0.0228 + 0.0742 T_c</math> | ||
| - | and ( | + | and (Eq. 4) |
:<math>\rho_c = 0.2534 + 0.071 \frac{1}{T_c}</math>. | :<math>\rho_c = 0.2534 + 0.071 \frac{1}{T_c}</math>. | ||
The repulsive form of the potential has no critical point. | The repulsive form of the potential has no critical point. | ||
==Triple points== | ==Triple points== | ||
| - | + | The [[triple point |triple points]] for this model have been studied by Azhar and co-workers | |
| + | <ref>[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)]</ref>. | ||
| + | ==Virial coefficients== | ||
| + | For the attractive form of the potential the [[Virial equation of state |virial coefficients]] have been calculated by Naresh and Singh <ref>[http://dx.doi.org/10.1016/j.fluid.2009.06.019 D.J. Naresh and Jayant K. Singh "Virial coefficients of hard-core attractive Yukawa fluids", Fluid Phase Equilibria '''285''' pp. 36-43 (2009)]</ref>. | ||
==Phase diagram== | ==Phase diagram== | ||
:''Main article: [[Phase diagram of the Yukawa potential]]'' | :''Main article: [[Phase diagram of the Yukawa potential]]'' | ||
==References== | ==References== | ||
| - | + | <references/> | |
[[Category: Models]] | [[Category: Models]] | ||
Revision as of 16:14, 25 November 2009
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 \ge \sigma
\end{array} \right.](/SklogWiki/images/math/6/a/e/6ae5fc88c4d80149130624a02cd20774.png)
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 \ge \sigma
\end{array} \right.](/SklogWiki/images/math/d/7/1/d71afb7ff068359d44255adcfc9ac450.png)
where 
is the intermolecular pair potential, 
is the distance between site 1 and site 2,
σ is the hard diameter, ε is the energy well depth (ε > 0), and
κ is a parameter that controls the interaction range (κ > 0).
The repulsive form has been used to study charge-stabilised colloid-colloid interactions.
Contents |
Critical point
For the attractive form of the potential, from a study of the law of corresponding states, one has (Eq. 3 in [1])
- Pc = 0.0228 + 0.0742Tc
and (Eq. 4)
.
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 [2].
Virial coefficients
For the attractive form of the potential the virial coefficients have been calculated by Naresh and Singh [3].
Phase diagram
- Main article: Phase diagram of the Yukawa potential
References
- ↑ Pedro Orea and Yurko Duda "On the corresponding states law of the Yukawa fluid", Journal of Chemical Physics 128 134508 (2008)
- ↑ 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)
- ↑ D.J. Naresh and Jayant K. Singh "Virial coefficients of hard-core attractive Yukawa fluids", Fluid Phase Equilibria 285 pp. 36-43 (2009)
