Hard core Yukawa potential

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The hard core Yukawa potential [1] 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.

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.

where  \Phi\left( r \right) is the intermolecular pair potential, r := |\mathbf{r}_1 - \mathbf{r}_2| is the distance between site 1 and site 2,  \sigma is the hard diameter,  \epsilon is the energy well depth ( \epsilon > 0 ), and  \kappa is a parameter that controls the interaction range ( \kappa > 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])

P_c = 0.0228 + 0.0742 T_c

and (Eq. 4)

\rho_c = 0.2534 + 0.071 \frac{1}{T_c}

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)

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