Equation of state of the square-well fluid

The Percus-Yevick equation is solved for the square-well (SW) potential with λ = 1.5 and λ = 1.85, where λ is the ratio of the diameter of the attractive well to the diameter of the hard core. The results for the equation of state and the Gibbs free energy are calculated using a method proposed by Chen, Henderson, and Barker. The results for the equation of state are in good agreement with the simulation results for the SW fluid with λ = 1.5 over a wide range of temperatures and densities. The result for the radial distribution function is in satisfactory agreement with the simulation result for the SW fluid with λ = 1.85 in the liquid state. A first order gas-liquid phase transition occurs in the form of a typical van der Waals type in the region where the Percus-Yevick equation has solutions. The effect of the width of the SW potential on the radial distribution function and the thermodynamic properties is examined. It is shown that, for the SW fluid, the same approach to obtain the equation of state may be used with the Yvon-Born-Green theory.