Pore-size impacts on ionic conductivity within ion-exchange membranes

Ion-exchange membranes (IEMs) are critical components to various electromembrane processes (e.g., electrodialysis, hydrogen generation, and mineral recovery) due to their capability to selectively transport ionic species. While recent polymer advancements have emphasized improving permselectivity and material longevity, there lacks a first-principles framework that connects how the structural changes in the porous polymer network affect ion transport through the IEM. Moreover, commonly used one-dimensional transport equations cannot capture these geometric effects. In response, this work presents a steady-state, reduced-order model for a single pore of arbitrary size that acts as a bridge between two electrolyte reservoirs.

The Poisson-Nernst-Planck (PNP) equations are solved by applying regular perturbation theory and scaling analysis. The pore size is related to different conductivity mechanisms, i.e. electromigration and electroosmosis, which yield fundamental insights into how IEM conductivity can be optimized.