## 3 Results and Discussion
### CDI Performance of the Electrodes
When the Cs\({}^{+}\) ion concentration in the influent water was 50 mg L\({}^{-1}\) and 100 mg L\({}^{-1}\), the maximum adsorption capacity decreased according to an increase in the flow rate, whereas the maximum adsorption capacity increased according to an increase in the flow rate in the influent water of 200 mg L\({}^{-1}\) Cs\({}^{+}\). The enhanced adsorption capacity of 200 mg L\({}^{-1}\) Cs\({}^{+}\) influent water is attributed to fast ion transport [35]. Figure 6: (**a**) Effluent conductivity of CsNO\({}_{3}\) according to the cell potentials during the adsorption process and (**b**) specific adsorption capacity of Cs\({}^{+}\) ions and charge efficiency (Experimental conditions: Influent of 200 mg L\({}^{-1}\) Cs\({}^{+}\) ions at pH 3 solution was fed with a flow rate of 20 mL min\({}^{-1}\) for 10 min adsorption/desorption, respectively). The fast flow rate, especially at high concentrations of influent, demonstrates excellent rate capability along with a high ion adsorption capacity. The radioactive wastewater containing Cs\({}^{+}\) generated in nuclear facilities is stored in a highly acidic solution, and the pH value is an important indicator. We measured the effect of pH to further investigate the electrosorption performance for the AC-CPL. Figure 8a shows the concentration of Cs\({}^{+}\) in the effluent water during the electrosorption process. The concentration of Cs\({}^{+}\) in the effluent decreased rapidly at the initial stage and gradually increased to the initial concentration. In particular, the amount of adsorbed Cs\({}^{+}\) decreased after the electrode reached saturation at pH 3, which was presumably due to the co-ions release from the EDL near the pores and neutral salt discharge from the electrode [12]. We monitored the pH variation of the influent solution during the electrosorption process, and the results are shown in Figure 8b. In contrast to the concentration curves of Cs\({}^{+}\) ions in the effluent, the water pH variation showed the opposite trend, indicating that H\({}^{+}\) ions were competitively electrosorbed at the electrode surface. This result was definitively observed at pH 2 (Figure S1). It shows that the concentration of the effluent reached 31.92 \(\mathrm{m}\mathrm{e}\mathrm{L}^{-1}\) in the first 45 \(\mathrm{s}\) and increased rapidly to the initial influent concentration. The maximum adsorption capacity was 0.75 \(\mathrm{m}\mathrm{g}\mathrm{g}^{-1}\), and it can be seen that the adsorption of H\({}^{+}\) dominated through the results of the pH profile. Generally, the pH of the influent water directly affects the zeta potentials by adsorbing H\({}^{+}\) or OH\({}^{-}\) ions on the surface of electrodes [36]. In acidic conditions, the zeta potential was shielded due to the adsorption of more H\({}^{+}\), and consequently, the electrosorption performance decreased significantly [13]. Ragome plots of SAR vs. SAC in the CDI system visually show the electrosorption performance of the electrode. As presented in Figure 9, the SAC increased, and the SAR decreased during the electrosorption process. The surface area adsorbed on the electrode reduced in size as the electrosorption proceeded. When the concentration of Cs\({}^{+}\) in the influent water increased, the Ragone plot shifted to the upper and righter area. The SAR and SAC show similar initial values, but as the adsorption time elapsed, most of the SAR values showed a decreasing curve, and the SAC value at pH 4 reached a constant value. At pH 3, the SAC value decreased as the adsorption time increased, which was largely due to the adsorption of H\({}^{+}\) competing ions, as mentioned in Figure 8.  
Figure 7: Maximum adsorption capacity of Cs\({}^{+}\) ions as a function of flow rate and influent concentration. Adsorption was conducted until the cell potential reached 1.2 V (Experimental conditions: Influent of pH 3 was fed for 60 min adsorption).