document: The Statistical Associating Fluid Theory (SAFT) is a well-developed perturbation theory used to describe quantitatively the volumetric properties of fluids. The reader is referred to several reviews on the topic which describe the various stages of its development and the multiple versions available [50–53]. The fundamental difference between the versions is in the underlying intermolecular potential employed to describe the unbounded constituent particles. Hard spheres, square well fluids, LJ fluids, argon, alkanes have all been employed as reference fluids in the different incarnations of SAFT. For the purpose of this work we will center on a particular version of the SAFT EoS, i.e. the SAFT-VR Mie recently proposed by Laffitte et al. [54] and expanded into a group contribution approach, SAFT-γ, by Papaioannou et al. [55]. This particular version of SAFT provides a closed form EoS that describes the macroscopical properties of the Mie potential [56], also known as the (m,n) potential; a generalized form of the LJ potential (albeit predating it by decades). The Mie potential has the form(1)ϕ(r)=Cεσrλr−σrλawhere C is an analytical function of the repulsive and attractive exponents, λa and λr, respectively, σ is a parameter that defines the length scale and is loosely related to the average diameter of a Mie bead; ɛ defines the energy scale and corresponds to the minimum potential energy between two isolated beads; expressed here as a ratio to the Boltzmann constant, kB. The Mie function, as written above, deceivingly suggests that four parameters are needed to characterize the behaviour of an isotropic molecule, however the exponents λa and λr are intimately related, and for fluid phase equilibria, one needs not consider them as independent parameters [57]. Accordingly, we choose herein to fix the attractive exponent to λa=6 which would be expected to be representative of the dispersion scaling of most simple fluids and refer from here on to the repulsive parameter as λ=λr. The potential simplifies to(2)ϕ(r)=λλ−6λ66/(λ−6)εσrλ−σr6
extractive_keyphrases: alkanes argon bead beads closed form eos fluid fluids group contribution approach hard spheres intermolecular potential isotropic molecule lj potential mie potential perturbation theory saft unbounded constituent particles
abstractive_keyphrases: lj fluids (m,n) potential reference fluids saft eos saft-vr mie saft-γ simple fluids square well fluids statistical associating fluid theory