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.