Hard core Yukawa potential: Difference between revisions

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(New page: Hard Core Yukawa Potential (Attractive): <math> V\left( r \right) = \left\{ \begin{array}{ccc} \infty & ; & r < \sigma \\ - \left( \frac{ \epsilon \sigma }{r}\right) \exp \left[- \kappa...)
 
m (Replaced mention of a model with a See also section)
 
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Hard Core Yukawa Potential (Attractive):
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>
has two forms, the attractive Yukawa potential:


<math>
:<math>
V\left( r \right) =  
\Phi_{12}\left( r \right) =  
\left\{ \begin{array}{ccc}
\left\{ \begin{array}{lll}
\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  
Line 9: Line 10:
</math>
</math>


where <math> V\left( r \right) </math> is the potential energy of interaction between pairs of particles, <math> r </math> is the distance,  
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> \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==
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==
<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]]

Latest revision as of 15:00, 14 March 2018

The hard core Yukawa potential [1] has two forms, the attractive Yukawa potential:

Φ12(r)={∞;r<σ−(ϵσr)exp[−κ(rσ−1)];r≥σ

and the repulsive form

Φ12(r)={∞;r<σ(ϵσr)exp[−κ(rσ−1)];r≥σ

where Φ(r) is the intermolecular pair potential, r:=|r1−r2| 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.

Critical point[edit]

For the attractive form of the potential, from a study of the law of corresponding states, one has (Eq. 3 in [2])

Pc=0.0228+0.0742Tc

and (Eq. 4)

ρc=0.2534+0.0711Tc

The repulsive form of the potential has no critical point.

Triple points[edit]

The triple points for this model have been studied by Azhar and co-workers [3].

Virial coefficients[edit]

For the attractive form of the potential the virial coefficients have been calculated by Naresh and Singh [4].

Liquid-vapour coexistence[edit]

[5]

Surface tension[edit]

Surface tension [6].

Radial distribution function[edit]

Radial distribution function[7]

Phase diagram[edit]

Phase diagram [8] [9] [10] [11]

Density-functional theory[edit]

Density-functional theory [12].

See also[edit]

References[edit]

  1. ↑ J. S. Rowlinson "The Yukawa potential", Physica A: Statistical Mechanics and its Applications 156 pp. 15-34 (1989)
  2. ↑ Pedro Orea and Yurko Duda "On the corresponding states law of the Yukawa fluid", Journal of Chemical Physics 128 134508 (2008)
  3. ↑ 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)
  4. ↑ D.J. Naresh and Jayant K. Singh "Virial coefficients of hard-core attractive Yukawa fluids", Fluid Phase Equilibria 285 pp. 36-43 (2009)
  5. ↑ 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)
  6. ↑ G. Odriozola, M. Bárcenas, and P. Orea "Vapor–liquid surface tension of strong short-range Yukawa fluid", Journal of Chemical Physics 134 154702 (2011)
  7. ↑ Douglas Henderson and Dezső Boda "Mean spherical approximation for the Yukawa fluid radial distribution function", Molecular Physics 109 pp. 1009-1013 (2011)
  8. ↑ 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)
  9. ↑ 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)
  10. ↑ 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)
  11. ↑ Pedro Orea and Yurko Duda "On the corresponding states law of the Yukawa fluid", Journal of Chemical Physics 128 134508 (2008)
  12. ↑ Marius M. Hatlo, Priyanka Banerjee, Jan Forsman, and Leo Lue "Density functional theory for Yukawa fluids", Journal of Chemical Physics 137 064115 (2012)

Related reading

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