Square well model

The square well model is given by

${\mathrm{\Phi }}_{12}(r)=\{\begin{array}{ccc}\mathrm{\infty }& ;& r<\sigma \\ -ϵ& ;& \sigma \le r<\lambda \sigma \\ 0& ;& r\ge \lambda \sigma \end{array}$

where ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential, $ϵ$ 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)
• 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)