(178aa) An Asymptotically Consistent Approximant Method with Application to Soft and Hard-Sphere fluids

A modified Padé approximant is used to construct an equation of state which has the same large density asymptotic (ρ →∞) behavior as the model fluid being described, while still retaining the low density behavior of the virial equation of state (VEOS). Within this framework, all choices of rational functions converge to the same behavior, eliminating the ambiguity of choosing the correct form of Padé approximant. The method is applied to fluids composed of “soft” spherical particles with separation distance r interacting through pair potentials, φ=ε(σ/r)ⁿ, where ε and σ are model parameters and n is the “hardness” of the spheres. For n < 9 and n ≥ 24, the approximants provide a significant improvement over the 8-term VEOS, when compared against molecular simulation data. For other n values, both the approximants and the VEOS give a relatively accurate description of the fluid behavior. When taking the limit as n →∞, an accurate and concise equation of state for hard spheres is obtained, which is closer to simulation data than the 10-term VEOS for hard spheres and is comparable to other recent equations of state. By applying a least square fit to the approximants, we obtain a general and accurate soft sphere equation of state as a function of ρ and n, valid over the full range of values.