Asymmetric Framework for Predicting Liquid-Liquid Equilibrium of Ionic Liquid-Mixed-Solvent Systems. 1. Theory, Phase Stability Analysis, and Parameter Estimation

A new approach for modeling liquid-liquid equilibrium in electrolyte/mixed-solvent systems is presented, with particular focus on systems involving a dilute aqueous solution of an ionic liquid (IL). This new approach involves an asymmetric framework in which different phases have different degrees of electrolyte dissociation, and are thus represented by different Gibbs free energy models. As a first case, we consider the situation in which the electrolyte is either completely dissociated or completely paired (molecular), with its state depending on the dielectric constant of the mixed solvent and on the concentration of the salt in the phase in question. The theory underlying this asymmetric framework is developed, and a rigorous approach for phase stability analysis is presented. It is explained how to formulate and solve the parameter estimation problem for determining model parameters from binary data, and this process is demonstrated using examples. An immediate goal is to use this approach to predict liquid-liquid equilibrium for ternary IL/solvent/water systems, using parameters obtained from binary and pure component data only.