Insight into the relationship between molecular morphology and water/ion diffusion in cation exchange membranes: Case of partially sulfonated polyether sulfone

The molecular design of cation exchange membranes (CEM) is of prime importance due to their significant role in many applications. It has been shown that water and ion transport through CEM depends on the membrane morphology which itself is a function of polymer structure and hydration level. There has been a great deal of experimental research devoted to correlating the polymer structure to water/ion diffusion, with speculations about the relationship between molecular interactions, morphology formation, and water/ion diffusion. In our simulation studies, first, we calculated the water anomalous diffusion coefficients (Da) in sulfonated poly(ether sulfone) (sPES) membranes and compared them with the experimentally ones, confirming an excellent consistency between the results in various conditions. Then we introduced quantitative measures of membrane morphology, namely the pore limiting diameter (PLD), largest cavity diameter (LCD), and pore size distribution (PSD), that strongly correlate with the water/ion anomalous diffusion coefficients. Thus, we show how polymer structure and membrane hydration level change the membrane morphology and that there is a direct correlation between PLD and water/ion anomalous diffusion coefficients. We find a critical PLD value, precisely equal to the size of the diffusing ion (Na+, K+), below which the ion's mobility is extremely limited and above which the ion's anomalous diffusion coefficient increases linearly with PLD. Above the critical PLD, the slope of the D-PLD relation strongly correlates with the ion's residence time near the sulfonate group. Also, our simulations show that a larger hydration level results in a more interconnected and uniform water network, faster water/ion diffusion, less water/ion residence time close to the sulfonate ion and a closer-to-normal water/ion diffusion behavior.