Difference between revisions of "Square well model"

From SklogWiki
Jump to: navigation, search
m (References: Added a recent publication)
m (Moved location of reference)
 
Line 24: Line 24:
 
[[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==
[[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>.
+
[[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>
 +
<ref>[https://doi.org/10.1080/00268976.2018.1461943 Fernando del Río, Orlando Guzmán & Félix Ordoñez Martínez "Global square-well free-energy model via singular value decomposition", Molecular Physics '''116''' pp. 2070-2082 (2018)]</ref>.
 
==See also==
 
==See also==
 
*[[2-dimensional square well model]]
 
*[[2-dimensional square well model]]
Line 37: Line 38:
 
*[http://dx.doi.org/10.1063/1.4930268  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)]
 
*[http://dx.doi.org/10.1063/1.4930268  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)]
 
*[http://dx.doi.org/10.1063/1.4993436 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)]
 
*[http://dx.doi.org/10.1063/1.4993436 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)]
*[https://doi.org/10.1080/00268976.2018.1461943 Fernando del Río, Orlando Guzmán & Félix Ordoñez Martínez "Global square-well free-energy model via singular value decomposition", Molecular Physics '''116''' pp. 2070-2082 (2018)]
 
  
 
[[Category: Models]]
 
[[Category: Models]]

Latest revision as of 11:00, 9 July 2018

The square well model is given by [1]


\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 \Phi_{12}(r) is the intermolecular pair potential, \epsilon is the well depth, r is the distance between site 1 and site 2 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[edit]

Main article: Equations of state for the square well model

Virial coefficients[edit]

Main article: Square well potential: virial coefficients

Liquid-vapour coexistence[edit]

[2]

Critical point[edit]

[3] [4] [5]

Direct correlation function[edit]

Direct correlation function [6].

Helmholtz energy function[edit]

Helmholtz energy function [7] [8].

See also[edit]

References[edit]

  1. A. Rotenberg "Monte Carlo Equation of State for Hard Spheres in an Attractive Square Well", Journal of Chemical Physics 43 pp. 1198-1201 (1965)
  2. Achille Giacometti, Giorgio Pastore and Fred Lado "Liquid-vapor coexistence in square-well fluids: an RHNC study", Molecular Physics 107 pp. 555-562 (2009)
  3. 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)
  4. 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)
  5. 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)
  6. 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)
  7. 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)
  8. Fernando del Río, Orlando Guzmán & Félix Ordoñez Martínez "Global square-well free-energy model via singular value decomposition", Molecular Physics 116 pp. 2070-2082 (2018)

Related reading