Introduction: Resistance to ion transport in ion exchange membranes (IEMs) is detrimental to the performance of IEM-based processes such as electrodialysis (ED) and reverse electrodialysis (RED). IEM resistance depends on solution composition. However, such understanding is currently limited and of a qualitative nature (e.g., IEM resistance decreases with salt concentration in solution, multivalent ions increase IEM resistance). Therefore, a quantitative understanding of this dependency is needed to predict ED/RED performance. Accordingly, we measured the resistance of representative IEMs in single-solute solutions and used our results to draw quantitative and mechanistic conclusions.

Methods: IEM resistance values were obtained using electrochemical impedance spectroscopy with the membrane mounted in a diffusion cell. The resistance of one representative cation (CEM) and one anion (AEM) exchange membrane was investigated in 15 single-solute solutions.

Results: In general, membrane resistance for both the CEM and AEM decreased with increasing solution concentration. Membrane resistance was on the order of tens to hundreds of ohm.cm² in dilute (<0.01M) solutions and a few to tens of ohm.cm² in concentrated (>0.1M) solutions. The primary findings include:

-Membrane resistance was sensitive to salt identity only in the case of the CEM, for which it depended on the counter-ion identity.

-Membrane resistance increased with increasing hydration free energy of the counter-ion in bulk solution, indicating that steric effects are important determinants of membrane ionic resistance.

-Membrane resistance had a strong inverse correlation with solution concentration below 0.1 M, and remained approximately constant at higher concentrations.

-The dependence of membrane resistance on salt concentration in bulk solution was fitted well by a semi-empirical expression containing a concentration-independent term and a concentration-dependent term; the latter followed a non-linear dependence on bulk solution concentration.

The non-linear dependence on bulk solution concentration suggests that the interconnectedness of the structural domains within the membrane that contribute to ionic resistance has a certain level of randomness. Future studies are required to fully understand the dependence of membrane ionic resistance on bulk solution concentration at low salt concentrations, including why membrane resistance depends on the co-ion identity only at relatively low salt concentrations (0.001-0.05 M).

Conclusions: Overall, our analysis produced a quantitative understanding of the dependence of IEM resistance on the identity and properties of single-salt solutions, and contribute necessary information towards the development of a complete theory for IEM resistance. Specifically, we found that steric effects are a primary determinant of membrane resistance and that the structural domains are arranged randomly (as opposed to in series or parallel). Thus, future work to develop a complete IEM resistance theory should include (i) understanding how the hydration free energy of ions relates to their interactions with water and the membrane, (ii) elucidating how these interactions relate to ion mobility, and (iii) developing a mathematical model describing the random interconnectedness of structural membrane domains.