## 2 Materials and Methods  
The membranes used for the present study are commercial Nafion 117 (DuPontTM, Wilmington, DE, USA) cation-exchange membranes. These membranes are perfluorosulfonic films with a fixed charge density of 0.9 meq/g and a thickness of 183 \(\upmu\)m. A lab scale setup formed by a 3-compartment electrodialysis cell was utilized for conducting chronopotentiometric experiments. The three compartments were filled with the same electrolyte and concentration to avoid concentration gradients other than those arising due to the application of a current density. The membrane under study was placed separating the central and cathodic compartment, while an auxiliary anion-exchange membrane was used to separate the anodic and cathodic compartment and minimize the effect of the anode reaction on the ionic transport taking place through the membrane under study. Two Ag/AgCl reference electrodes immersed in Luggin capillaries were used to measure the voltage drop across the membrane, U\({}_{\text{m}}\), and a potentiostat/galvanostat Autolab PGSTAT 20 was used as power source. More details and a schematic view of the experimental setup can be found in our previous work [17]. Different metallic sulfate solutions were used as electrolyte with the aim of comparing the transport of ions with different charge and which give rise to a variety of complex species. Na\({}_{2}\)SO\({}_{4}\), NiSO\({}_{4}\), Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) and Cr\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) purchased from Panreac (Castellar del Valles, Spain) were used to prepare solutions with distilled water.  
Among available techniques for the characterization of ion transport through ion-exchange membranes, chronopotentiometry allows for the obtaining of information on the transients of ion transport at different current regimes. Additionally, the steady state values of U\({}_{\text{m}}\) obtained from each current pulse were used to plot the current-voltage curves of the different membrane/electrolyte systems investigated. Figure 1 shows the principle of the chronopotentiometric experiments. The chronopotentiograms evolve differently depending on the level of current density applied. At current densities i \(<\) i\({}_{\text{lim}}\), concentration profiles at the depleting side of the membrane are not fully developed, so that the ionic resistance of the membrane phase is still the predominant one. Consequently, the response of U\({}_{\text{m}}\) is almost plane. When the i\({}_{\text{lim}}\) is approached, the selective transport of counterions through the membrane implies a depletion of ions at the diluted side of the membrane, the concentration of ions approaches zero near the membrane and a sharp increase in resistance is registered. This increased resistance can be tracked by a jump in U\({}_{\text{m}}\) in the chronopotentiograms. If the current density is further increased, the depletion layer near the membrane can increase in thickness. The jump in U\({}_{\text{m}}\) takes place faster and the final membrane resistance increases further. In the present work, the current was applied during 300 s and the relaxation of the membrane potential after switching the current off was further monitored for 150 s.  
Figure 1: Correlation between the shape of the input applied current density, the profiles of concentration through the membrane system and the corresponding response of U\({}_{\text{m}}\).