Limited ion-ion selectivity of salt-rejecting membranes due to enthalpy-entropy compensation

Water and ion transport in salt-rejecting membranes, such as nanofiltration (NF) and reverse osmosis (RO), are exposed to different hindrance effects that result in selectivity between species. In this study, we explored systematically the hindrance effects that govern water-salt and ion-ion selectivity in NF and RO membranes. More specifically, we measured the permeability of different species at varying temperatures and applied an Eyring-type equation to quantify the enthalpic and entropic barriers for their transport in three types of salt-rejecting membranes. We found that water-salt selectivity is entropically driven, where water molecules gain entropy in the membrane, while the salt ions face a substantial entropic barrier due to their larger size that reduces their possible configurations in the membrane. As the enthalpic barriers of the water and salt did not show a prominent difference (with minor effect on the water-salt selectivity), most ion-ion separations were restricted by an enthalpy-entropy compensation (EEC) effect; that is, an ion with a higher entropic barrier experienced a lower enthalpic barrier compared to the competing ion, resulting in minor variations in the free-energy barriers between ions that limit the ion-ion selectivity. We conclude by proposing possible mechanisms that promote EEC during ion transport in salt-rejecting membranes.