## 2 Cu-Based Catalyst-Activated PMS Processes
### Magnetic Copper Ferrite
Numerous investigations have reported the performances of \(CuFe_{2}O_{4}\) spinel and supported \(CuFe_{2}O_{4}\) catalysts synthesized through coprecipitation and sol-gel methods for activating PMS [41,92,94]. \(CuFe_{2}O_{4}\) is catalytically more stable than \(CuFeO_{2}\), which has additionally been employed to produce \(SO_{4}^{\bullet}\) from PMS in a recent investigation [95]. The choice of an appropriate synthesis technique is crucial for the efficient preparation of the catalyst. For instance, solvothermally prepared \(CuFe_{2}O_{4}\), (with organic solvent and surfactant) shows decreased catalytic activity and organic compound release compared to the catalyst fabricated without employing any organic ingredients [96]. In relation to the PMS activation, \(CuFe_{2}O_{4}\) as a Cu-Fe mixed-metal catalyst imparts synergistic redox reactions to the surface for \(Cu^{3+}/Cu^{2+}\), \(Cu^{2+}/Cu^{+}\), and \(Fe^{3+}/Fe^{2+}\) in a tetrahedral and/or octahedral structure to optimally produce \(SO_{4}^{\bullet}\) radicals from PMS via the following mechanism (Equations (3)-(7)):  
\[Cu^{2+}+HSO_{5}^{-}\rightarrow\text{Cu}^{+}+SO_{5}^{\bullet-}+H^{+} \tag{3}\]  
\[Cu^{+}+HSO_{5}^{-}\rightarrow\text{Cu}^{2+}+SO_{4}^{\bullet-}+OH^{-} \tag{4}\]  
\[Cu^{+}+Fe^{3+}\rightarrow\text{Cu}^{2+}+Fe^{2+} \tag{5}\]  
\[Fe^{3+}+HSO_{5}^{-}\to Fe^{2+}+SO_{5}^{\bullet-}+H^{+} \tag{6}\]  
\[Fe^{2+}+HSO_{5}^{-}\to Fe^{3+}+SO_{4}^{\bullet-}+OH^{-} \tag{7}\]  
X-ray photoelectron spectroscopy provides evidence of the transformation in the Cu oxidation state transitioning from \(Cu^{2+}\) to a blend of \(Cu^{2+}/Cu^{+}\) in \(CuFe_{2}O_{4}\) pre-reaction and post-reaction [97]. The synergistic effect between cupric cations and ferric cations is clearly apparent. Since the generated \(Cu^{+}\) (Equation (3)) could undergo disproportionation readily (e.g., with molecular oxygen), electron transfer from \(Cu^{+}\) to \(Fe^{3+}\) (Equation (5))  
Figure 2: Proposed activation mechanism of the \(CuFe_{2}O_{4}\)/PMS system. produces \(Fe^{2+}\), which shows greater thermodynamic stability against disproportionation. Therefore, this process enhances the generation of \(SO_{4}^{\bullet-}\) from PMS [98]. \[4 Cu^{+}+O_{2}+4H^{+}\to 4 Cu^{2+}+2H_{2}O \tag{8}\]  
\[4 Fe^{2+}+O_{2}+4H^{+}\to 4 Fe^{3+}+2H_{2}O \tag{9}\]  
It is noteworthy that the one-electron transition of PMS to \(Cu^{2+}\) to generate \(SO_{5}^{\bullet-}\) is unfavorable under standard conditions given the standard reduction potentials of \(Cu^{2+}/Cu^{+}\) (\(E^{\circ}=+0.17\) V vs. NHE), \(SO_{5}^{\bullet-}/HSO_{5}^{-}\) (\(E^{\circ}=+1.1\) V vs. NHE), and \(SO_{5}^{\bullet-}/SO_{5}^{2-}\) (\(E^{\circ}=+0.81\) V vs. NHE) [98]. For the redox reaction to take place, PMS forms a surface complex on the catalyst's surface, potentially by displacing the surface hydroxyl groups. The increased rate of interfacial electron transfer due to the formation of a PMS-metal oxide complex [99] and the relatively low concentration of \(SO_{5}^{\bullet-}\) in the reaction environment lead to lower actual reduction potential values for \(SO_{5}^{\bullet-}/HSO_{5}^{\circ-}\) and \(SO_{5}^{\bullet-}/SO_{5}^{2-}\) in real aqueous systems. This thermodynamic condition makes the reaction (Equation (3)) feasible [92]. Observations of PMS complexes on metal oxide surfaces have been detected through IR and Raman spectroscopy [41]. Additionally, it is plausible that PMS is activated by \(CuFe_{2}O_{4}\) via the \(Cu^{2+}-Cu^{3+}-Cu^{2+}\)(\(Cu^{3+}/Cu^{2+}\), \(E^{\circ}=2.40\) V vs. NHE) redox transition [71]. \(Cu^{3+}/Cu^{2+}\) possesses a comparatively elevated standard reduction potential (\(E^{\circ}\) of \(Cu^{3+}/Cu^{2+}\) in solution and solid phases are +1.57 vs. NHE and +2.30 V vs. NHE, respectively) [100]. The discrepancies in \(E^{\circ}\) values between the dissolved and solid \(Cu^{2+}\) phases provide additional insight into the inferior performance of dissolved \(Cu^{2+}\) ions in contrast to heterogeneous \(Cu^{2+}\) catalysts.