Electrolyte solutions that unmix. Hydrophobic ions in water

Simple models for the solvent-averaged ion-ion pair potentials for aqueous solutions of tetraalkylammonium halides were previously treated under the HNC (hypernetted chain) approximation to find the parameters needed to fit osmotic coefficient data of the corresponding real solutions. Here the model Pr₄NI is modified by changing the A_+– Gurney parameter to give the Pr₄NX model which exhibits the unmixing (separation into two solution phases of different concentrations) that has been reported for several real aqueous tetraalkylammonim salt solutions. The models used here are established at the McMillan-Mayer (MM) or solvent-averaged level, so careful attention is given to the choice of the thermodynamic potential from which we may derive the condition of material stability (stability with respect to separation into two phases of slightly different composition), and calculate the required thermodynamic coefficients from the MM pair correlation functions. The emphasis is on the study of the hydrophobic unmixing in terms of thermodynamic coefficients derived from the pair correlation functions calculated for the Pr₄NX model under HNC. In the temperature-concentration (T-c_S) plane we can locate the solvability line (which separates states for which the HNC equation can be solved from the rest) and portions of the coexistence line. To locate the coexistence line in regimes in which the double tangent method is not effective we use a method based on the osmotic pressure and the solute chemical potential isotherms. Our results suggest that for the Pr₄NX model in the T-c_S plane the spinodal line lies within the solvability line which, in turn, lies within the coexistence line for the states where the latter could be determined. The role of the thermodynamic inconsistency implicit in the HNC correlation functions is given special attention, as is the remarkable role of the 1/r⁴ cavity term in the model pair potential. Single-ion activity coefficients and DEL functions are calculated for some of the states studied.