Editing Hard core Yukawa potential

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

:<math>
\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.
</math>

and the repulsive form

:<math>
\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.
</math>

where <math> \Phi\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> is the distance between site 1 and site 2, 
<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>).

The repulsive form has been used to study charge-stabilised [[Colloids |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 <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>

and (Eq. 4)

:<math>\rho_c = 0.2534 + 0.071 \frac{1}{T_c}</math>.
The repulsive form of the potential has no critical point. 
==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==
:''Main article: [[Phase diagram of the Yukawa potential]]''
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1063/1.3281416 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)]
[[Category: Models]]
@@ Line 1: / Line 1: @@
-The '''hard core Yukawa''' potential <ref>[http://dx.doi.org/10.1016/0378-4371(89)90108-8 J. S. Rowlinson "The Yukawa potential", Physica A: Statistical Mechanics and its Applications '''156''' pp. 15-34 (1989)]</ref>
+The '''hard core Yukawa''' potential has two forms, the attractive Yukawa potential:
-has two forms, the attractive Yukawa potential:
 :<math>
@@ Line 32: / Line 31: @@
 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 points | critical point]].
+The repulsive form of the potential has no critical point.
 ==Triple points==
 The [[triple point |triple points]] for this model have been studied by Azhar and co-workers
@@ Line 40: / Line 38: @@
 ==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>.
-==Liquid-vapour coexistence==
-<ref>[http://dx.doi.org/10.1063/1.3385894  E. B. El Mendoub, J.-F. Wax, and N. Jakse "Evolution of the liquid-vapor coexistence of the hard-core Yukawa fluid as a function of the interaction range", Journal of Chemical Physics '''132''' 164503 (2010)]</ref>
-==Surface tension==
-[[Surface tension]] <ref>[http://dx.doi.org/10.1063/1.3578637 G. Odriozola, M. Bárcenas, and P. Orea "Vapor–liquid surface tension of strong short-range Yukawa fluid", Journal of Chemical Physics '''134''' 154702 (2011)]</ref>.
-==Radial distribution function==
-[[Radial distribution function]]<ref>[http://dx.doi.org/10.1080/00268976.2010.505586 Douglas Henderson and Dezső Boda "Mean spherical approximation for the Yukawa fluid radial distribution function", Molecular Physics '''109''' pp. 1009-1013 (2011)]</ref>
 ==Phase diagram==
-[[Phase diagrams | Phase diagram]]
+:''Main article: [[Phase diagram of the Yukawa potential]]''
-<ref>[http://dx.doi.org/10.1063/1.466781 Enrique Lomba and Noé G. Almarza "Role of the interaction range in the shaping of phase diagrams in simple fluids. The hard sphere Yukawa fluid as a case study", Journal of Chemical Physics '''100''' pp. 8367-8372 (1994)]</ref>
-<ref>[http://dx.doi.org/10.1063/1.467526     M. H. J. Hagen and D. Frenkel  "Determination of phase diagrams for the hard-core attractive Yukawa system", Journal of Chemical Physics '''101''' pp. 4093-4097  (1994)]</ref>
-<ref>[http://dx.doi.org/10.1063/1.2743623      Yurko Duda, Ascención Romero-Martínez, and Pedro Orea "Phase diagram and surface tension of the hard-core attractive Yukawa model of variable range: Monte Carlo simulations", Journal of Chemical Physics '''126''' 224510 (2007)]</ref>
-<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>
-==Density-functional theory==
-[[Density-functional theory]] <ref>[http://dx.doi.org/10.1063/1.4742154  Marius M. Hatlo, Priyanka Banerjee, Jan Forsman, and Leo Lue "Density functional theory for Yukawa fluids", Journal of Chemical Physics '''137''' 064115 (2012)]</ref>.
-==See also==
-*[[SALR potential]]
-*[[Soft sphere attractive Yukawa model]]
 ==References==
 <references/>
 '''Related reading'''
 *[http://dx.doi.org/10.1063/1.3281416 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)]
-*[http://dx.doi.org/10.1063/1.3357352 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)]
-*[http://dx.doi.org/10.1063/1.3610400 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)]
 [[Category: Models]]