On the Ionic Conductivity of Cation Exchange Membranes in Mixed Sulfates Using the Two-Phase Model

The concentration dependence of the conductivity of ion exchange membranes (IEMs), as well as other transport properties, has been well explained by the contemporary two-phase model (Zabolotsky et al., 1993) considering a gel phase and an inter-gel phase filled with electroneutral solution. Here, this two-phase model has been adopted and first applied in electrolytes containing mixed counter-ions to investigate the correlation between the membrane ionic conductivity and its microstructure. For three representative commercial cation exchange membranes (CEMs), the total membrane conductivity (κT) when in equilibrium with mixed MgSO₄ + Na₂SO₄ and H₂SO₄ + Na₂SO₄ electrolytes could be well predicted with the experimental composition of counter-ions in the gel and inter-gel phase, as well as the counter-ion mobility in the gel phase when the membrane is in a single electrolyte. It is found that the volume fraction of the inter-gel phase (f2) has little impact on the predicted results. The accuracy of the model can be largely improved by calculating the inter-gel phase conductivity (κin) with the ionic mobility being the same as that in the external solution (obtained via simulation in the OLI Studio), rather than simply as equivalent to the conductivity of the external solution (κs). Moreover, a nonlinear correlation between the CEMs' conductivities and the counter-ion composition in the gel phase is observed in the mixed MgSO₄ + Na₂SO₄ solution, as well as for the Nafion117 membrane in the presence of sulfuric acid. For CEMs in mixed MgSO₄ + Na₂SO₄ electrolytes, the calculated conductivity values considering the interaction parameter σ, similar to the Kohlrausch's law, are closer to the experimental ones. Overall, this work provides new insights into membrane conductivity with mixed counter-ions and testifies to the applicability of the contemporary two-phase model.