## 3 Results and Discussion
### Effect of Electrode Configuration
The anode potentials were +0.7 V and +1.2 V, respectively, implying that as the anode potential of Group 2 increased continuously to +1.2 V, the scope of the cathode potential broadened (\(-\)3.5 V in Figure 3a). That is, the graphite anode-titanium cathode electrode configuration facilitated the extension of the cathode potential under the same conditions. This behavior may be attributed to the different reducibilities and oxidizabilities of the different electrode materials. In Groups 2, 3, 4, and 5, the reducibility values of the cathode materials increased in the order of G \(<\) Cu \(<\) Pb \(<\) Ti, and the desorption efficiencies at the cathode decreased in the order of Ti \(>\) Cu \(>\) Pb \(>\) G. Clearly, the reducibility declined, resulting in a desorption efficiency decrease, although deviations appeared at the Cu and Pb cathodes. This discrepancy might be related to the formation of an oxidation film on the surface of the lead electrode in air. Supporting this idea, the researcher [PERSON] stated that lead is easily and rapidly oxidized to lead oxide over a wide temperature range [52]. Anode oxidizability also significantly affects the desorption efficiency. The higher oxidizability of the graphite anode than that of titanium likely explains the lower desorption efficiency of Group 1 than of Group 2. Therefore, the cathode potential might be extended by increasing the oxidizability and reducibility discrepancies between the anode and cathode. This conclusion provides a direction for optimizing the design of CDI devices, especially reactors that undergo chemisorption during the electrosorption process. The electrodesorption process was also described based on theoretical electrochemistry. The desorption reaction for adsorbed Cl\({}^{-}\) from the GAC surface can be described by the following simple chemical equation  
\[\mathrm{Cl^{-}_{ads}}\mathrm{\rightarrow}\mathrm{Cl^{-}_{aq}}+\mathrm{GAC} \tag{2}\]  
where ads and aq denote the adsorbed phase and solution phase, respectively. The electrochemical potential of Cl\({}^{-}\) adsorbed on GAC and that in the solution can be expressed as:  
\[\overline{\mu}_{\mathrm{aq}}=\mu_{\mathrm{aq}}^{\emptyset}+RT\ln\left[\mathrm{ Cl_{aq}^{-}}\right]-\psi_{0}F \tag{3}\]  
\[\overline{\mu}_{\mathrm{ads}}=\mu_{\mathrm{ads}}^{\emptyset}+RT\ln\left[ \mathrm{Cl_{ads}^{-}}\right]-\psi F \tag{4}\]  
where \(\mu_{\mathrm{aq}}^{\emptyset}\) and \(\mu_{\mathrm{ads}}^{\emptyset}\) are the standard state chemical potentials of Cl\({}^{-}\) in the liquid phase and in the solid phase, respectively, R (8.314 J mol\({}^{-1}\) K\({}^{-1}\)) is the universal gas constant, T (K) is the absolute temperature, F (96485 C mol\({}^{-1}\)) is the Faraday constant, \(\psi_{0}\) (V) is the potential of the solution, and \(\psi\) is the diffuse layer potential (where the value is relative to the potential of the solution (\(\psi_{0}\))). When the desorption of adsorbed Cl\({}^{-}\) occurs, the Gibbs free energy change (\(\Delta_{\mathrm{r}}G_{\mathrm{m}}\)) is given by:  
\[\Delta_{\mathrm{r}}G_{\mathrm{m}}\mathrm{=}\ \mu_{\mathrm{aq}}^{\emptyset}+RT\ln \left[\mathrm{Cl_{aq}^{-}}\right]-\ \psi_{0}F\ -\ (\mu_{\mathrm{ads}}^{ \emptyset}+RT\ln\left[\mathrm{Cl_{ads}^{-}}\right]-\ \psi F) \tag{5}\]  
where \(\mu_{\mathrm{aq}}^{\emptyset}\) and \(\mu_{\mathrm{ads}}^{\emptyset}\) are the standard-state chemical potentials of Cl\({}^{-}\) in the liquid phase and in the solid phase, respectively; \(\psi\) is the diffuse layer potential (where the value is \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Electrode** & **Reference** & **Desorption Efficiency/\%** & **Time/min** & **Potential/V** \\ \hline GAC & This study & 100 & 300 & \(-\)1.7 \\ Fe\({}_{2}\)O\({}_{3}\)/NORIT & [50] & 64 & 480 & \(-\)3.0 \\ Fe\({}_{2}\)O\({}_{3}\)/G5 & [50] & 80 & 480 & \(-\)3.0 \\ LiMn\({}_{2}\)O\({}_{4}\) & [51] & \textless{}45 & 500 & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The comparison of desorption efficiency.