## 3 Results and Discussion
### Characterization of Catalysts
This deviation from the ideal crystalline morphology may be due to the inhomogeneity of the local alkali concentration during the synthesis process, possibly due to insufficient reaction time or  
Figure 1: (**a**) XRD patterns of different catalysts; (**b**) FTIR spectra of different materials (different ratios of iron to cobalt). unsatisfactory stirring, resulting in localized corrosion of the otherwise well-dispersed hexagonal nanosheets. Combined with XRD and FT-IR analyses, these observations confirm the successful synthesis of the LDH structures, thus validating their applicability for subsequent catalytic or physicochemical applications. X-ray photoelectron spectroscopy (XPS) analysis was used to determine the elemental composition and chemical state of the catalyst surface. As shown in Figure 3a, FeCo-LDH (1:3) samples were successfully incorporated with iron and cobalt elements. In the Fe 2p spectra (Figure 3b), the peaks at 711.0 eV and 722.7 eV demonstrate the presence of Fe\({}^{2+}\), while the peaks at 712.9 eV and 726.2 eV indicate the presence of Fe\({}^{3+}\)[35; 36]. In the Co 2p spectra (Figure 3c), the main peaks at 781.8 eV corresponding to Co 2p3/2 and at 798.4 eV for Co 2p1/2, as well as the satellite bands at 787.4 eV and 803.7 eV, are in accordance with the reported values of Co(OH)\({}_{2}\). The peaks at 799.8 and 784.0 eV correspond to Co(II), while the peaks at 797.8 and 803.7 eV correspond to Co(III), which confirms the coexistence of Co\({}^{2+}\) and Co\({}^{3+}\) states [37]. The C1s spectrum (Figure 3d) shows peaks at 284.7, 286.7, and 289.4 eV corresponding to C-C, C-O, and C=O bonds. It was shown in [38] that the C=O group contributes to the decomposition of PMS to generate single linear oxygen, which was further confirmed in subsequent experiments. These results indicate that the metallic elements Fe and Co are already present in the obtained material. Electrochemical tests were conducted to evaluate electron transfer efficiency. Cyclic voltammetry (CV) curves (Figure 4a) show that FeCo-LDH (1:3) exhibited the highest peak current density, indicating superior reversibility and ionization potential compared to other samples. The charge transfer resistance is obtained from the Nyquist plot (real part 'Z' vs. imaginary part \"Z\") in electrochemical impedance spectroscopy (EIS),  
Figure 2: (**a–d**) TEM image of the material at different magnifications. which is characterized as a semicircle in the plot. Usually, the diameter of the semicircle corresponds to the charge transfer resistance. The real part of the impedance in the high frequency region, Z2\({}^{\prime}\), is usually the first data point or the region that is initially close to horizontal. The impedance real part Z1\({}^{\prime}\) in the low frequency region is the horizontal inflection value at the end of the semicircle. The charge transfer resistance is calculated as \(\text{Rct}=\text{Z2}^{\prime}-\text{Z1}^{\prime}\)[39; 40]. The electrochemical impedance spectroscopy (EIS) results further support the CV analysis by providing insight into the interfacial charge transfer kinetics. As shown in Figure 4b, the charge transfer resistance (Rct), approximated from the diameter of the Nyquist semicircles, decreased significantly with increasing Co content. The Rct values for FeCo-LDH (1:1), (1:2), and (1:3) were estimated to be \(\sim\)3950, \(\sim\)1860, and \(\sim\)870 \(\Omega\), respectively, indicating that FeCo-LDH (1:3) facilitates the most efficient electron transport among the three compositions. These findings suggest that an optimized Fe/Co ratio enhances the catalytic activity by improving electron mobility and reducing interfacial resistance [41; 42]. Figure 3: (a) XPS patterns of different catalysts; (b) High-resolution Fe 2p spectra of catalyst; (c) High-resolution Co 2p spectra of catalyst; (d) High-resolution C 1s spectra of catalyst.