Hard core Yukawa potential: Difference between revisions
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The '''hard core Yukawa''' potential has two forms, the attractive Yukawa potential: | 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: | |||
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Revision as of 12:03, 23 April 2010
The hard core Yukawa potential [1] has two forms, the attractive Yukawa potential:
![{\displaystyle \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\geq \sigma \end{array}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54a0e1abaf83826da9b26ab63511f7429ad0fc77)
and the repulsive form
![{\displaystyle \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\geq \sigma \end{array}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bac4936e842e1c8959739f8910c4222cee4fc176)
where is the intermolecular pair potential, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|} is the distance between site 1 and site 2, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is the hard diameter, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon } is the energy well depth (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon > 0 } ), and is a parameter that controls the interaction range (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \kappa > 0 } ).
The repulsive form has been used to study charge-stabilised 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 [2])
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_c = 0.0228 + 0.0742 T_c}
and (Eq. 4)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_c = 0.2534 + 0.071 \frac{1}{T_c}} .
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 [3].
Virial coefficients
For the attractive form of the potential the virial coefficients have been calculated by Naresh and Singh [4].
Liquid-vapour coexistence
Phase diagram
- Main article: Phase diagram of the Yukawa potential
Two-term Yukawa potentials
Both the attractive and the repulsive form have been combined to produce the hard-sphere plus two Yukawa potential (H2Y) [6].
References
- ↑ J. S. Rowlinson "The Yukawa potential", Physica A: Statistical Mechanics and its Applications 156 pp. 15-34 (1989)
- ↑ 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)
- ↑ 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)
- ↑ Lloyd L. Lee, Michael C. Hara, Steven J. Simon, Franklin S. Ramos, Andrew J. Winkle, and Jean-Marc Bomont "Crystallization limits of the two-term Yukawa potentials based on the entropy criterion", Journal of Chemical Physics 132 074505 (2010)
Related reading
- 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)
- 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)