Modeling of activity coefficients of aqueous solutions of quaternary ammonium salts with the electrolyte-NRTL equation

Ionic liquids (ILs) have been studied recently as potential "green" solvents because of their negligible vapor pressure. Modeling the phase behavior of such liquids with water and organic solvents and their partitioning between aqueous and organic phases is vital for an evaluation of their many potential uses. Unfortunately, phase behavior data for the popular imidazolium and pyridinium salts are still somewhat limited. However, a wealth of data exists for aqueous solutions of quaternary ammonium salts, a class of compounds that includes potentially interesting ILs. Therefore, as a first step toward modeling the phase behavior of IL solutions, we show how a conventional electrolyte model, the electrolyte nonrandom two-liquid (NRTL) model proposed by Chen et al. (AIChE J. 1982, 28, 588), can be applied to model activity coefficients of quaternary ammonium salts in water. This model requires two parameters per salt that must be fit to the experimental data. Particular attention is paid to computing these binary parameters using a reliable parameter estimation technique, which is based on interval analysis. Indeed, this technique allows us to find deterministically the global minimum and, if desired, all local minima in the parameter estimation problem within a given interval. Results indicate that this model is able to capture the nonideal phase behavior of these salts in aqueous solutions up to relatively high concentrations. Limitations of this simple model appear at higher concentrations and for highly branched compounds, most likely due to effects of incomplete dissociation and micelle formation that are not taken into account in the model.