Multi-anchored state equations applied to square-well fluids with differing well-widths

Abstract

Abstract In the continuing effort to relate material properties to molecular structure, it has proven helpful to obtain a synoptic equation of state (EOS) even for simplistic model fluids having idealized yet specified intermolecular forces. This paper extends such methods to square-well fluid (SWF) of arbitrary well-depth (ϵ) and well-width [ω = λ − 1], with λ, the dimensionless attractive range. Because SWF second and third virial coefficients are known exactly for all ranges, while high-density, high-temperature properties are known to substantial accuracy, all available MC/MD results can be consolidated and multiply-anchored to particular isotherms and isochores using reduced densities [y = π(σ 3 N/V)/6] and inverse temperature scales [x = (γ 3 − 1)(exp(ϵ/kT) − 1)]. Thus y is the packing fraction and the second virial coefficient is linear in x, with x = 1 corresponding to the Boyle temperature. Using this particular scaling, SWF's of arbitrary width and depth will all have a similar EOS, in the form of a compressibility factor Z = zhs - axy, with ZHS(y) that for a hard-sphere fluid and with an effective van der Waals attraction coefficient (a) varying about the value 4. Even the limited MC/MD data currently available then yields a useful EOS family based upon Lagrange interpolation between three anchoring isotherms at infinite, Boyle, and critical temperatures.