Criticality in Gaussian-molecule mixtures

Abstract

A continuum binary fluid model consisting of Gaussian molecules with interactions specified by the Mayer f-functions f _ab(r) = −exp(-r ²/r ² ₀), f _aa = f _bb = 0, exhibits phase separation and criticality in dimensions d > 1. While critical behaviour of Ising (or lattice gas) character is to be expected, previous analyses of the virial expansions to 13th order have led to results leaving this surmise open to serious question. We report the 14th-order terms and study, in particular, expansions in fugacity and pressure for d = 2, 3, 4 and 5 using modern series analysis techniques to estimate the critical exponents α, γ and γ₄ (= γ + 2Δ), and a universal amplitude ratio involving the sixth-order susceptibility. Except for the poor behaviour of the series estimates for α, good evidence is obtained for consistency with Ising-type behaviour. However, the d = 2 expansions show the significant influence of intrinsic corrections to leading power laws associated with the exponent θ = 4/3. The virial series are demonstrated to be misleading because of induced corrections that seriously distort the pure power laws.