Editing Hard core Yukawa potential

Hard Core Attractive Yukawa Potential:

<math>
V\left( r \right) = 
\left\{ \begin{array}{ccc}
\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> V\left( r \right) </math> is the potential energy of interaction between pairs of particles, <math> r </math> is the distance, 
<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>).




==References==
@@ 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>
+Hard Core Attractive Yukawa Potential:
-has two forms, the attractive Yukawa potential:
-:<math>
+<math>
-\Phi_{12}\left( r \right) =
+V\left( r \right) =
-\left\{ \begin{array}{lll}
+\left\{ \begin{array}{ccc}
 \infty & ; & r < \sigma \\
 - \left( \frac{ \epsilon \sigma }{r}\right)  \exp \left[- \kappa \left( \frac{r}{\sigma} -  1 \right) \right] & ; & r \ge \sigma
@@ Line 10: / Line 9: @@
 </math>
-and the repulsive form
+where <math> V\left( r \right) </math> is the potential energy of interaction between pairs of particles, <math> r </math> is the distance,
-:<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 points | 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>.
-==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]]
-<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]]