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

Direct correlation function

Direct correlation function .

Helmholtz energy function

Helmholtz energy function .

See also

• 2-dimensional square well model

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)
• 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)
• 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)