A Benchmark Database for Mixed-Solvent Electrolyte Solutions: Consistency Analysis Using E-NRTL

Multi-component ion equilibria and transport in ion-exchange membranes

At the interface between an ion-exchange membrane and a multi-electrolyte solution, charged species redistribute themselves to minimize the free energy of the system. In this paper, we explore the Donnan equilibrium of membranes with quaternary electrolyte (Na+/Mg2+/K+/Ca2+/Cl-) solutions, experimentally. The data was used to calculate the ion activity coefficients for six commercial cation-exchange membranes (CEMs). After setting one of the activity coefficients to an arbitrary value, we used the remaining (N-1) activity coefficients as fitting parameters to describe the equilibrium concentrations of (N) ionic species with a mean relative error of 3 %. At increasing solution ionic strengths, the equivalent ion fractions of monovalent counter-ions inside the membrane increased at the expense of the multivalent ones in alignment with the Donnan equilibrium theory. The fitted activity coefficients were employed in a transport model that simulated a Donnan dialysis experiment involving all four cations simultaneously. The arbitrary value assigned to one activity coefficient affects the calculated Donnan potential at the membrane interface. Nevertheless, this arbitrary value does not affect the prediction of the ion concentrations inside the membrane and consequently does not affect the modeled ion fluxes.

Mixed Solvent Electrolyte Solutions: A Review and Calculations with the eSAFT-VR Mie Equation of State

In this work, mixed-solvent mean ionic activity coefficients (MIAC), vapor-liquid equilibrium (VLE), and liquid-liquid equilibrium (LLE) of electrolyte solutions have been addressed. An extended literature review of existing electrolyte activity coefficient models (eGE) and electrolyte equations of state (eEoS) for modeling mixed solvent electrolyte systems is first presented, focusing on the details of the models in terms of physical and electrolyte terms, relative static permittivity, and parameterization. The analysis of this literature reveals that the property predictions can be ranked, from the easiest to the most difficult, in the following order: VLE, MIAC, and LLE. We have then used our previously developed eSAFT-VR Mie model to predict MIAC, VLE, and LLE in mixed solvents without fitting any new adjustable parameters. The model was parameterized on MIAC of aqueous electrolyte solutions and successfully extended to nonaqueous, single solvent electrolyte solutions without any new adjustable parameters by using a salt-dependent expression for the relative static permittivity. Our approach yields excellent results for MIAC and VLE of mixed solvent electrolyte solutions, while being fully predictive. LLE is significantly more challenging, and an accurate model for the salt-free solution is crucial for accurate calculations. When the compositions of the two phases in the binary salt-free system are accurately captured, then the electrolyte extension of our model shows a lot of potential and is currently among the best eEoS for LLE prediction in the literature.