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Square well model

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The square well model is given by [1]

\Phi _{{12}}\left(r\right)=\left\{{\begin{array}{ccc}\infty &;&r<\sigma \\-\epsilon &;&\sigma \leq r<\lambda \sigma \\0&;&r\geq \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]


Critical point[edit]

[3] [4] [5]

Direct correlation function[edit]

Direct correlation function [6].

See also[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)

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