Mobile ion partitioning in ion exchange membranes immersed in saline solutions

Ion exchange membranes (IEMs) are extensively used in separation and energy storage systems. Prior studies have suggested that rigorous thermodynamic modeling is essential to describe mobile ion partitioning in IEMs, especially weakly charged ionic membranes, immersed in aqueous salt solutions. Based on a recently developed polyelectrolyte nonrandom two-liquid (NRTL) activity coefficient model, this work presents a thermodynamic analysis for the mobile ion partitioning between external salt solutions with ionic strength from 0.01 to 1 molal and membranes of poly (ethylene glycol diacrylate) (PEGDA) copolymerized with 2-acrylamido-2-methylpropanesulfonic acid (AMPS). We show that mobile ion partitioning in the uncharged membranes and the weakly charged membranes immersed in saline solutions is controlled by the long-range "point-to-point" electrostatic interactions and the short-range van der Waals interactions in the membrane phase. For the strongly charged membrane samples, the long-range "point-to-line" electrostatic interactions also play a role, the mobile ion mean ionic activity coefficients are close to unity, and the ion sorption data may be qualitatively interpreted with either the ideal Donnan equilibrium model or Manning's limiting law.