## 2 Materials and Methods
### Electrodialysis Cells  
ED experiments were carried out using a small glass Hittorf cell composed of two or four compartments as presented in Figure 1. For the two-compartment cell, the anode and cathode compartments were separated by the LCM and filled, respectively, by the feed and the receiver solution. This cell has the advantage of being simple to implement and allows a low global electrical resistance. In this particular case, the operation is more similar to electrolysis than to electrodialysis. However, for simplicity of presentation, we will keep the name two-compartment electrodialysis to contrast with the four-compartment electrodialysis.  
In the four-compartment cell, in addition to the feed and the receiver compartments, we added anodic and cathodic compartments, which played the role of protector compartments containing Na\({}_{2}\)SO\({}_{4}\) (0.1 M) solution. Two anion-exchange membranes AMX were added in order to protect the LCM membrane from electrodes reactions. In both cases, the feed and receiver contained LiCl + NaCl mixtures at different compositions and a 0.1 M HCl solution, respectively. The volume of each compartment (anode, feeding, receiver and cathode) in both ED cells (two-compartment and four-compartment cell) was 50 mL.  
These two solutions were stirred using a pumping system (3 L-min\({}^{-1}\)) in order to ensure their homogeneity and minimize diffusion boundary layers effects. An Agilent E3634A DC Power Supply was used as the power source. Two platinized titanium electrodes of 5 cm\({}^{2}\) surface were placed at the cell extremities to provide the current injection. The sealing of these compartments as well as the positioning of the membranes were ensured by a system of two half-flanges made of phenoplast with high thermal and mechanical performances. The effective surface of the membrane was 4.15 cm\({}^{2}\).  
For membrane performance determination, we measured the recovered cations concentrations in the receiver compartment. Selectivity coefficients towards Li\({}^{+}\) over Na  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **LCM** & **AMX** \\ \hline Membrane thickness: 1 (\(\upmu\)m) & 130 & 153 \\ \hline Membrane conductivity & 0.75 & 12.6 \\ (mS-cm\({}^{-1}\)) & in 0.1 M LiCl solution & in 0.1 M NaCl solution \\ \hline Water content: W\({}_{\text{c}}\) (\%) * & 11.3 & 24.8 \\ \hline Contact angle: \(\theta\) (\({}^{\circ}\)) & 61.3 & 63.0 \\ \hline \hline \end{tabular}  
*: W\({}_{\text{c}}=\frac{(W_{\text{w}}-W_{\text{d}})}{W_{\text{d}}}\times 100\), where W\({}_{\text{w}}\) and W\({}_{\text{d}}\) are the weights of the wet and the dry membrane, respectively.  
\end{table}
Table 1: Main static characteristics of the used LCM [47] and the AMX.  
Figure 1: Schematic illustration of the ED cells with (**A**) two and (**B**) four compartments.  
S(Li/Na) were calculated using Equation (1), where [Li+]R, [Li+]F, [Na+]R and [Na+]F are molar concentrations of Li+ and Na+ in the receiver and feeding compartment, respectively.  
\[\mathrm{S(Li/Na)}=\frac{\frac{\left[\mathrm{Li}^{+}\right]_{R}}{\left[\mathrm{Li}^ {+}\right]_{F}}}{\left[\mathrm{Na}^{+}\right]_{F}}=\frac{\left[\mathrm{Li}^{+} \right]_{R}\times\left[\mathrm{Na}^{+}\right]_{F}}{\left[\mathrm{Li}^{+} \right]_{F}\times\left[\mathrm{Na}^{+}\right]_{R}} \tag{1}\]  
The recovery rate RR was determined according to Equation (2), where [M+]R and [M+]F are the molar concentrations of M+ (Li+ or Na+) in the receiver and the feeding compartment, respectively.  
\[\mathrm{RR}\big{(}\mathrm{M}^{+}\big{)}=\frac{\left[\mathrm{M}^{+}\right]_{R} }{\left[\mathrm{M}^{+}\right]_{F}}\times 100 \tag{2}\]