Ion Transport Modeling in Ion Exchange Membranes: A Novel 4-State Model Incorporating Ion-Pairing Effects under Different Hydration Levels

Ion exchange membranes are pivotal for selectively separating ions. These systems consist of charged polymers water and ions with the same charge as the polymer (co-ions) and the opposite charge (counterions). Conventional transport models neglect counterion/co-ion interactions known as ion-pairing. To address this, we introduce a novel 4-state model to decompose interactions among counterions, co-ions, and charged polymer regions. Molecular dynamic (MD) simulations on hydrated Nafion polymer with NaCl, Na₂SO₄, MgCl₂, MgSO₄, LiCl, and Li₂SO₄ salts are performed to calculate the mean square displacement for each state. Counterion diffusivity is attributed to free or paired ion state. Probabilities of counterions in different states, , are higher for sulfates rather than chlorides. The coordination of counterion/co-ions in paired states suggests cluster formation.

For increasing hydration free counterion probabilities increase, but results show different trends for chloride and sulphate counterion co-ion paired states. Differences between the two anions is due to the preference of the co-ion/counterion adsorption for the sulfate to the polymer. As the hydration increases more clusters are in water rather than adsorbed to the polymer. Diffusivity contributions, , for paired states in water increase as the hydration rises due to more water, while it is nearly zero for Na₂SO₄. To evaluate the model, overall diffusivity is compared to MD diffusivities showing good agreement.