Phase separation in the size-asymmetric primitive model

For the class of size-asymmetric primitive models (SAPM) of binary electrolyte solutions (models comprising equal numbers of positively and negatively charged hard-spheres of different diameter) we examine the dependence of the liquid-liquid coexistence line as the degree of size-asymmetry between cations and anions is varied. The asymmetry is measured by the ratio ω of the diameters of the cationic and anionic species. The phase diagram for liquid-liquid equilibria is calculated under a modified Bjerrum theory, in which the electrolyte solution is represented as a mixture of free ions and (cation-anion) ion-pairs. More specifically, we have extended to the SAPM model the theory of Ebeling and Grigo originally formulated for the restricted primitive model (RPM). Several schemes for estimating the association constant for ion-pair formation are considered. We find that the features of the coexistence line are very sensitive with respect to ω, with the critical temperature, the critical density, and the width of the coexistence line increasing as the asymmetry of the SAPM model increases. We also report results for the critical parameters of the RPM calculated under the associative-mean spherical approximation; these values serve to gauge the limitations of the simpler Ebeling-Grigo theory.