## 2 Materials and Methods
### Hydrometallurgical-Electrodialytic Experiments  
The combined hydrometallurgical-electrodialytic experiments were carried out in duplicate, using cells electrically connected in series, i.e., the cathode of one of the ED cells was connected to the anode of the other one, assuring that both cells were submitted to the same electrical current. The experiments were performed at constant current of 50 mA by means of a DC power supply unit (Genesys RDK Lambda GEN 600-2.6), which corresponded to a current density of 1 mA cm\({}^{-2}\) referred to the internal diameter of the ED cell. The experimental system is schematically presented in Figure 1.  
Each ED cylindrical cell was built using three methacrylate compartments (4 cm length and 8 cm internal diameter). The central compartment of the electrodialytic cell was connected with an external vessel and a separatory funnel of 100 mL capacity. A volume of 350 mL of the suspension with the LiCoO\({}_{2}\) particles in 0.1 M HCl (\(L\):\(S\) = 200) was initially placed in the magnetically and well stirred vessel. The suspension was continuously pumped from the vessel to the central compartment, passing through the separatory funnel using a four-channel Watson Marlow 302S peristaltic pump. The conical shape of the separatory funnel helps the solid particles to not follow the liquid phase containing the extracted metals and therefore prevents the particles from reaching the central compartment of the ED cell. A fiberglass filter was added at the upper end of the separatory funnel to assure that no solid particles were dragged by the aqueous flow. The liquid phase continuously flowed back to the vessel from the central compartment. The flow rate was 0.2 mL s\({}^{-1}\), optimized to assure the retention of the undissolved particles in the separatory funnel.  
The central compartment was separated from both electrode compartments by means of CEMs (Neosepta CMX-fg standard grade; electrical resistance 1.8 \(\Omega\) cm\({}^{-2}\), thickness 0.16 mm, stability pH 0-14). The commercial anode consisted of the base titanium material covered with mixed oxides, mainly Ir, to prevent their oxidation (Metakem GmbH), and the cathode was stainless steel. The catholyte was 0.1 M HCl, similar to the extracting solution. In turn, the anolyte was 0.1 M HNO\({}_{3}\) solution, as it could not be further oxidized at the anode. The use of CEMs to separate the anode and the central compartments hindered the passing of Cl\({}^{-}\) towards the anode and the corresponding oxidation to chlorine gas. This configuration allows the regeneration and reuse of the extracting solution, which is an advantage of this technique due to the continual addition of extracting agent solution not being necessary.  
Liquid samples of 10 mL from the catholyte and the central compartments were withdrawn twice a day during the experimental time (6 days). With the aim of keeping the liquid volume constant, 10 mL of 0.1 M HCl solution was added to the central compartment after sampling. The metal concentration of all liquid samples was determined by an AAS Varian SpectrAA-110.  
At the end of the experiment, the cells were disassembled and the cathodes were soaked in 1:1 HNO\({}_{3}\) solution for 24 h to determine the metal electrodeposited on them. Similarly, the CEMs were soaked in 1 M HNO\({}_{3}\) solution for 24 h to determine the amount of metal accumulated. The membranes used in these experiments are stable in strong acids, which allows low pH regeneration. With the aim of complete global mass balance, the fiberglass was also soaked in concentrated acid to extract the metals accumulated. Particles attached to the fiberglass used in the separator funnel were considered as part of the central compartment solution.