Criticality in Charge-asymmetric Hard-sphere Ionic Fluids

Abstract

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 (1993, 1996) 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, $T_c^{\ast }$ (normalized by $z$), \textit{decrease} with charge asymmetry, while the critical densities \textit{increase} rapidly with $z$. The results compare favorably with simulations and represent a distinct improvement over all current theories such as the MSA, SPB, etc. For $z$$\ne$1, the interphase Galvani (or absolute electrostatic) potential difference, $\Delta \varphi (T)$, between coexisting liquid and vapor phases is calculated and found to vanish as $|T-T_c{|}^{\beta }$ when $T\to T_c-$ with, since our approximations are classical, $\beta =1/2$. 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.

25 pages, 14 figures; last update with typos corrected and some added references

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