Square well model: Difference between revisions
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==Direct correlation function== | ==Direct correlation function== | ||
[[Direct correlation function]] <ref>[http://dx.doi.org/10.1063/1.3154583 S. Hlushak, A. Trokhymchuk, and S. Sokolowski "Direct correlation function of the square-well fluid with attractive well width up to two particle diameters", Journal of Chemical Physics '''130''' 234511 (2009)]</ref>. | [[Direct correlation function]] <ref>[http://dx.doi.org/10.1063/1.3154583 S. Hlushak, A. Trokhymchuk, and S. Sokolowski "Direct correlation function of the square-well fluid with attractive well width up to two particle diameters", Journal of Chemical Physics '''130''' 234511 (2009)]</ref>. | ||
==Helmholtz energy function== | |||
[[Helmholtz energy function]] <ref>[https://doi.org/10.1080/00268976.2017.1392051 Francisco Sastre, Elizabeth Moreno-Hilario, Maria Guadalupe Sotelo-Serna and Alejandro Gil-Villegas "Microcanonical-ensemble computer simulation of the high-temperature expansion coefficients of the Helmholtz free energy of a square-well fluid", Molecular Physics '''116''' pp. 351-360 (2018)]</ref>. | |||
==See also== | ==See also== | ||
*[[2-dimensional square well model]] | *[[2-dimensional square well model]] | ||
Revision as of 12:09, 9 January 2018
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
Direct correlation function
Direct correlation function [6].
Helmholtz energy function
Helmholtz energy function [7].
See also
References
- ↑ A. Rotenberg "Monte Carlo Equation of State for Hard Spheres in an Attractive Square Well", Journal of Chemical Physics 43 pp. 1198-1201 (1965)
- ↑ Achille Giacometti, Giorgio Pastore and Fred Lado "Liquid-vapor coexistence in square-well fluids: an RHNC study", Molecular Physics 107 pp. 555-562 (2009)
- ↑ 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)
- ↑ Lourdes Vega, Enrique de Miguel, Luis F. Rull, George Jackson, and Ian A. McLure "Phase equilibria and critical behavior of square‐well fluids of variable width by Gibbs ensemble Monte Carlo simulation", Journal of Chemical Physics 96 pp. 2296-2305 (1992)
- ↑ 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)
- ↑ S. Hlushak, A. Trokhymchuk, and S. Sokolowski "Direct correlation function of the square-well fluid with attractive well width up to two particle diameters", Journal of Chemical Physics 130 234511 (2009)
- ↑ Francisco Sastre, Elizabeth Moreno-Hilario, Maria Guadalupe Sotelo-Serna and Alejandro Gil-Villegas "Microcanonical-ensemble computer simulation of the high-temperature expansion coefficients of the Helmholtz free energy of a square-well fluid", Molecular Physics 116 pp. 351-360 (2018)
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)
- Yuri Reyes , César A. Flores-Sandoval and Pedro Orea "Common behavior of the critical properties of the 2D and 3D square-well fluids", Journal of Chemical Physics 139 164505 (2013)
- J. Richard Elliott, Andrew J. Schultz and David A. Kofke "Combined temperature and density series for fluid-phase properties. I. Square-well spheres", Journal of Chemical Physics 143 114110 (2015)
- L. A. Padilla and A. L. Benavides "The constant force continuous molecular dynamics for potentials with multiple discontinuities", Journal of Chemical Physics 147 034502 (2017)