Theoretical considerations on single and mixed solvent electrolyte solutions

In this paper, theoretical considerations on electrolyte thermodynamic models are discussed for single and mixed solvent solutions. A literature review has revealed that for many fundamental issues there is no consensus amongst researchers in this field. Specific questions have been formulated to enable the clarification of these issues, and then answered. Electrolyte terms are considered to belong to a different framework (McMillan-Mayer) than the physical terms of the thermodynamic models (Lewis-Randall). The electrolyte terms should be converted to the framework of the physical model, prior to the combination of the physical and electrolyte terms. If the relative static permiitivity (RSP) of the solution (mixed or single) does not depend on the ionic concentration, then the two frameworks are equivalent for equations of state (EoS). For activity coefficient models (GE models), a pressure correction term is needed to consistently combine the electrolyte and the physical model. These corrections are more important for higher concentrations. However, many electrolyte models adopt ion-concentration dependent RSP, which violates the aforementioned conversion between the different frameworks; in other words, it breaks the link between electrostatic theories and thermodynamic models. This weakens the physical background of the thermodynamic models but does not make them thermodynamically inconsistent. Last but not least, we confirm the importance of the Born term for liquid-liquid equilibrium (LLE) calculations. The Born (or an equivalent) term is required in all models (EoS and GE) to consistently convert the reference state used by the models (ideal gas and ideal solution) to the real system. The functionality of the Born term is highly related to the RSP and the Born term is only consistent when the compositional derivatives of the RSP are used. If either of these conditions are not met, the model will not be able to accurately calculate mixed solvent LLE.