Square well model: Difference between revisions
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where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>\epsilon</math> is the well depth, <math>r</math> is the distance between site 1 and site 2 <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, σ is the hard diameter | where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>\epsilon</math> is the well depth, <math>r</math> is the distance between site 1 and site 2 <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, σ is the hard diameter | ||
and λ > 1. | and λ > 1. For an infinitesimally narrow well one has the [[sticky hard sphere model]] proposed by Baxter. | ||
==Equation of state== | ==Equation of state== | ||
:''Main article: [[Equations of state for the square well model]]'' | :''Main article: [[Equations of state for the square well model]]'' | ||
Revision as of 10:56, 25 March 2011
The square well model is given by [1]
- 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 \Phi_{12}\left( r \right) = \left\{ \begin{array}{ccc} \infty & ; & r < \sigma \\ - \epsilon & ; &\sigma \le r < \lambda \sigma \\ 0 & ; & r \ge \lambda \sigma \end{array} \right. }
where 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 \Phi_{12}(r)} 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 \epsilon} is the 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 r} 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 r := |\mathbf{r}_1 - \mathbf{r}_2|} , σ is the hard diameter and λ > 1. For an infinitesimally narrow well one has the sticky hard sphere model proposed by Baxter.
Equation of state
- Main article: Equations of state for the square well model
Virial coefficients
- Main article: Square well potential: virial coefficients
Liquid-vapour coexistence
Critical point
- John J. Kozak, I. B. Schrodt and K. D. Luks "Square-Well Potential. II. Some Comments on Critical Point Behavior and Scaling Laws", Journal of Chemical Physics 57 pp. 206- (1972)
- Marianela Martiacuten-Betancourt, José Manuel Romero-Enrique and Luis F. Rull "Finite-size scaling study of the liquid-vapour critical point of dipolar square-well fluids", Molecular Physics 107 pp. 563-570 (2009)
Direct correlation function
For the direct correlation function see:
References
Related reading
- J. A. Barker and D. Henderson "Perturbation Theory and Equation of State for Fluids: The Square-Well Potential", Journal of Chemical Physics 47 pp. 2856-2861 (1967)
- Kraemer D. Luks and John J. Kozak "The Statistical Mechanics of Square-Well Fluids", Advances in Chemical Physics 37 chapter 4 pp. 139-201 (1978)
- Elisabeth Schöll-Paschinger, Ana Laura Benavides and Ramon Castañeda-Priego "Vapor-liquid equilibrium and critical behavior of the square-well fluid of variable range: A theoretical study", Journal of Chemical Physics 123 234513 (2005)
- R. López-Rendón, Y. Reyes and P. Orea "Thermodynamic properties of short-range square well fluid", Journal of Chemical Physics 125 084508 (2006)