## 3 Results and Discussion  
### Phenomena Related to Shifts in Chemical Equilibria during Electrodialysis of Multivalent Ions  
#### 3.1.1 Chronopotentiometric Features  
As explained above, chronopotentiometry provides information about different events happening in electrodialysis cells under the influence of an electric field, especially at the diluted diffusion boundary layer. Changes occurring as a consequence of the depletion of ions are manifested in the chronopotentiograms as an increase in the voltage drop of the membrane system [18]. Solutions with multivalent ions which form weak electrolytes give rise to additional events that can be tracked by changes in the ionic resistance of the membrane system. These can be concomitant to the decrease in ionic concentration in the diffusion boundary layer but they can be also caused by shifts in pH or chemical equilibrium. In the following, different chronopotentiograms gained from experiments conducted with metal sulfate solutions are discussed. Figure 2 shows an overview of different types of peculiar responses obtained from chronopotentiometric measurements using solutions of multivalent cations. These curves differ from those typically obtained with salts of monovalent metals, like the ones schematically shown in Figure 1. Figure 2a shows chronopotentiograms obtained with Cr\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) solutions at different current densities. The curve obtained at the lowest current density shows an inflexion point, which indicates that depletion of counter-ions at the membrane surface already occurred at this polarization level. However, as the current is further increased, a second inflection point is observed in the curves. After the first jump, U\({}_{\text{m}}\) levels off for an instant before the registration of a second jump in U\({}_{\text{m}}\). This response can be explained by a redistribution of species across the DBL and in the membrane phase, which involves formation of new ions and an intermediate increase in membrane conductivity. This intermediate step restrains a continuous and uninterrupted increase in resistance and leads to a multi-step development of concentration polarization. At sufficiently high current densities and long times, a secondary stage of concentration polarization is achieved and U\({}_{\text{m}}\) attains a steady value; from here on the voltage response resembles that achieved with single salt solutions. Figure 2b shows a different type of evolution of the membrane voltage obtained with solutions containing trivalent iron, Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\). In this case, after an initial increase in U\({}_{\text{m}}\), a maximum is reached and the membrane resistance decreases over time until an almost steady state value is registered at the end of the current pulse. This case can be also explained by a shift in the chemical equilibrium during the development of concentration polarization. However, in this case, the new species formed have higher ionic conductivities than the original ones present in the system and predominate over a wider range of currents. Moreover, the changes tracked during the registration of the curves take place slowly and at currents significantly below the i\({}_{\text{lim}}\). In this case, the subsequent increase in U\({}_{\text{m}}\) only occurs at much higher current densities (not shown in the figure). Finally, the curves presented in Figure 2c,d correspond to two different phases of the same experiments: the response registered during the application of the current pulse and during the relaxation of the membrane potential once the current is switched off. These curves were obtained with NiSO\({}_{4}\) solutions. The curve obtained at the lowest current density in Figure 2c displays an inflexion point, with a shape analogous to that typically obtained for NaCl solutions (see Figure 1), where after the jump in U\({}_{\text{m}}\), a steady state value is reached. At higher current densities, a second increase in U\({}_{\text{m}}\) is obtained in the curves.