Monovalent Cation Selectivity in Ion Exchange Membranes Near the Percolation Threshold

Structure-property relationships in ion-exchange membranes (IEMs) have been developed to understand the trade-off between membrane conductivity and selectivity toward the counter-ion (e.g. Na⁺ in cation IEMs). Engineering membranes with high-selectivity toward counter-ions of the same valence, however, remains an open challenge in the field. In this work, we leverage differences in the hydrated radii and hydration free energies of monovalent cations (Li⁺, Na⁺, K⁺) to engineer cation exchange membranes with tunable selectivity. We control the sulfonation level (SL) of polystyrene-r-sulfonated polystyrene (PS-r-SPS) copolymers and neutralize these random copolymers with Li⁺, Na⁺, and K⁺ cations. Using a combination of wide-angle x-ray scattering (WAXS), ion-exchange capacity (IEC), swelling degree (SD), and conductivity measurements, we find a critical ion cluster percolation threshold below which membranes are unable to exchange ions with the external electrolyte. In turn, this percolation threshold determines the minimum required water volume fraction in the hydrated membrane. Mixed-salt permeation experiments conducted for membranes just above the required show favorable transport to K⁺ relative to Li⁺. We attribute the favorability for transport at this lower limit of membrane hydration to the difference in hydration free energy between the two ions. Thus, we demonstrate that a fundamental, intrinsic property of CEMs (i.e. hydration) can be manipulated to achieve novel separations and that membrane topology (i.e. percolation threshold) limits the exploitation of the difference in hydration free energy.