Square well model

The square well model is given by

\[ \Phi_{12}\left( r \right) = \left\{ \begin{array}{ccc} \infty & ; & r < \sigma \\ - \epsilon & ; &\sigma \le r < \lambda \sigma \\ 0 & ; & r \ge \lambda \sigma \end{array} \right. \]

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

Main article: Equations of state for the square well model

Virial coefficients

Main article: Square well potential: virial coefficients

Liquid-vapour coexistence

• Achille Giacometti, Giorgio Pastore and Fred Lado "Liquid-vapor coexistence in square-well fluids: an RHNC study", Molecular Physics 107 pp. 555-562 (2009)

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)
• 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)

Direct correlation function

For the direct correlation function see:

• 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)

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)