Electrostatic origins of mixed salt partitioning phenomena in uncharged poly(ethylene oxide)-based membranes

There is significant interest in using membranes to recover valuable resources (e.g., lithium) from naturally occurring and human-made sources, such as geothermal brine or produced water from fracking. One fundamental question which stymies the use of membranes in such applications is the limited understanding of how complex electrolyte mixtures equilibrate across the membrane-solution interface. To elucidate the physics of mixed electrolyte partitioning into membranes, we experimentally probed the partitioning of binary salt mixtures into a model PEO-based material as a function of solution composition and total solution ionic strength. We observe substantial systematic differences between single salt and mixed salt partition coefficients for a variety of salt mixtures. We performed atomistic molecular dynamics simulations to probe the thermodynamics of ion partitioning from aqueous solution and observe drastically different transfer free energies for cations and anions. We then derive a classical thermodynamic model and show that the observed mixed salt partitioning trends arise from the large differences between cation and anion transfer free energies and the constraint of electrical neutrality in each phase. By employing a Debye-Huckel limiting law expression for the membrane phase activity coefficients, we extend our model to accurately predict mixed salt partitioning into our PEO-based membranes without invoking any adjustable parameters.