A completely analytic perturbation theory for the square-well fluid of variable well width

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Abstract
We present an analytic equation of state, without any adjustable parameters, for the square-well fluid of variable well width (1 ⩽ λ ⩽ 2) based on perturbation theory using the real expression for the radial distribution function of hard spheres that we have recently developed. This work can be regarded as the analytic counterpart of the numerical perturbation theory of Barker and Henderson. The explicit description of the square-well fluid in closed form allows us to easily assess the accuracy of perturbation theory, particularly for the critical properties and vapour-liquid equilibrium which require the integration of the equation of state. As a test of this equation of state, the real fluids neon, argon and methane are considered. A good correlation is obtained between the new equation of state and experimental pVT data, except near the critical point, and the potential parameters for these fluids obtained from the best fit of our equation of state to experimental data can be used over whole density range. We also develop an analytic expression for the contact value of radial distribution for the case of λ = 1·5 that is useful elsewhere, including the development of theory for chain fluids.