Criticality in Charge-asymmetric Hard-sphere Ionic Fluids

TL;DR

This paper extends the Debye-Hückel theory to analyze phase separation and criticality in charge-asymmetric ionic fluids, accounting for ionic association and cluster solvation, and compares favorably with simulations.

Contribution

It provides explicit analytical calculations for 2:1 and 3:1 ionic systems, improving upon existing theories by including multipolar cluster effects and electrostatic potential differences.

Findings

Critical temperature decreases with charge asymmetry

Critical density increases rapidly with charge asymmetry

Results agree well with simulations and outperform previous models

Abstract

Phase separation and criticality are analyzed in $z$:1 charge-asymmetric ionic fluids of equisized hard spheres by generalizing the Debye-H\"{u}ckel 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, $T_c^*$ (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, $\Delta \phi(T)$, 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.