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# Criticality in Charge-asymmetric Hard-sphere Ionic Fluids

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### 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.

### Author and article information

###### Journal
27 October 2004
2005-07-04
cond-mat/0410692 10.1103/PhysRevE.72.041501