A new family of bridge functions for electrolyte solutions

We present a new set of closures for restricted models of electrolyte solutions at the McMillan-Mayer level that improve upon the Hypernetted Chain prediction for the ion-ion pair correlation functions. The improvement is accomplished by proposing simple functional forms for the bridge functions and the specification of certain adjusting parameters according to several criteria. Under the new closures, and unlike the HNC case, the “sum” direct correlation function, which is crucial for determining the stability of the solution with respect to phase separation, remains finite at thermodynamic states along the spinodal and at the critical point.Для спрощених моделей розчинів електролітів ми представляємо новий набір замикань на рівні МакМіллана–Маєра, який покращує передбачення для парних кореляційних функцій іон-іон, отриманих у гіперланцюговому наближенні. Покращення здійснюється введенням простих функціональних форм для місткових функцій і деяких підгоночних параметрів, які відповідають різним критеріям. При нових умовах замикання, на противагу до гіперланцюгового наближення, пряма кореляційна функція “сума”, що є важливою для визначення стійкості розв’язку по відношенню до фазового розділення, залишається скінченою при термодинамічних станах уздовж спінодалі і в критичній точці

Dipolar origin of the gas-liquid coexistence of the hard-core 1:1 electrolyte model

We present a systematic study of the effect of the ion pairing on the gas-liquid phase transition of hard-core 1:1 electrolyte models. We study a class of dipolar dimer models that depend on a parameter R_c, the maximum separation between the ions that compose the dimer. This parameter can vary from sigma_{+/-} that corresponds to the tightly tethered dipolar dimer model, to R_c --> infinity, that corresponds to the Stillinger-Lovett description of the free ion system. The coexistence curve and critical point parameters are obtained as a function of R_c by grand canonical Monte Carlo techniques. Our results show that this dependence is smooth but non-monotonic and converges asymptotically towards the free ion case for relatively small values of R_c. This fact allows us to describe the gas-liquid transition in the free ion model as a transition between two dimerized fluid phases. The role of the unpaired ions can be considered as a perturbation of this picture.Comment: 16 pages, 13 figures, submitted to Physical Review

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