Criticality in charge-asymmetric hard-sphere ionic fluids

Phase separation and criticality are analyzed in z:1 charge-asymmetric ionic fluids of equisized hard spheres by generalizing the Debye-Hückel approach combined with ionic association, cluster solvation by charged ions, and hard-core interactions, following lines developed by Fisher and Levin for the 1:1 case (i.e., the restricted primitive model). Explicit analytical calculations for 2:1 and 3:1 systems account for ionic association into dimers, trimers, and tetramers and subsequent multipolar cluster solvation. The reduced critical temperatures, T_c^* (normalized by z), decrease with charge asymmetry, while the critical densities increase rapidly with z. The results compare favorably with simulations and represent a distinct improvement over all current theories such as the mean spherical approximation, symmetric Poisson-Boltzmann theory, etc. For z≠1, the interphase Galvani (or absolute electrostatic) potential difference, Δϕ(T), between coexisting liquid and vapor phases is calculated and found to vanish as ∣T−T_c∣^β when T→T_c—with, since our approximations are classical, β=1/2. Above T_c, the compressibility maxima and so-called k-inflection loci (which aid the fast and accurate determination of the critical parameters) are found to exhibit a strong z dependence.