Determination of ionic diffusion coefficients in ion-exchange membranes: strong electrolytes and sulfates with dissociation equilibria

Ionic diffusion coefficients in the membrane are needed for the modelling of ion transport in ion-exchange membranes (IEMs) with the Nernst-Planck equation. We have determined the ionic diffusion coefficients of Na⁺, OH^-, H⁺, Cl^-, SO₄^2-, NaSO₄^-, and HSO₄^- from the diffusion experiments of dilute NaCl, NaOH, HCl, Na₂SO₄, and H₂SO₄ solutions through IEMs and the membrane conductivity measured in these solutions, using electrochemical impedance spectroscopy. The order of diffusion fluxes across the anion-exchange membrane is found to be as H₂SO₄>HCl>NaCl>Na₂SO₄>NaOH, whereas for the cation-exchange membrane it was NaOH>NaCl>Na₂SO₄≥H₂SO₄. Special attention is given to sulfates because of the partial dissociation of bisulfate and NaSO₄^-, which makes the use of the Nernst-Hartley equation, that is, splitting the electrolyte diffusion coefficient into its ionic contributions, impossible. The expression of the diffusion coefficient of sulfates taking into account the dissociation equilibrium has been derived and the corresponding Fick equation has been integrated. In addition, for sulfates, finite element simulations with COMSOL Multiphysics, applying a homogeneous membrane model, were done to give estimates of their ionic diffusion coefficients. This work offers a convenient approach to finding diffusion coefficients of various ions inside IEMs.