# Square well model

The **square well model** is given by ^{[1]}

where is the intermolecular pair potential, is the well depth, is the distance between site 1 and site 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]

- ↑ 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) - ↑ 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**

- 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)