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 $z\ne 1$, the interphase Galvani (or absolute electrostatic) potential difference, $\Delta \varphi \left(T\right)$, between coexisting liquid and vapor phases is calculated and found to vanish as ${\mid T-T_c\mid }^{\beta }$ when $T\to T_c$—with, since our approximations are classical, $\beta =\frac{1}{2}$. 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.

• Received 30 June 2005

DOI:https://doi.org/10.1103/PhysRevE.72.041501