## 3 Results
### Characterization of Bare and Grafted CeO\({}_{2}\) Particles
#### 3.1.2 Spectroscopic Characterization  
Here, the characterization via FTIR and UV will be presented to recognize specific chemical groups and evaluate the polymer shell from the particles. In Figure 4, the highlighted areas of all materials in comparison with the bare particles of CeO\({}_{2}\) are presented. Moreover, the complete spectra can be found in Figure S2. Figure 3: EDX mapping results for the initial CeO\({}_{2}\) nanoparticles and the ones with the different polymer brushes (C, N, Cl, and S: black; Ce: red; and O: blue). The FTIR results clearly demonstrate the successful synthesis of the polymer brushes. First, in the area of 3800-2800 cm\({}^{-1}\) (Figure 4a), the stretching vibration of the OH groups can be seen (3400-3300 cm\({}^{-1}\)) (Figure 4a) [25; 26; 27]. In addition, the peak centered at 2985 cm\({}^{-1}\) (Figure 4a) was assigned to C-N\({}^{+}\) stretching vibration. In the same area, C-H symmetric and asymmetric stretching was found at 2950-2900 cm\({}^{-1}\) (Figure 4a) [28; 29; 30]. The presence of C-H moieties in the composites, while they were absent in the bare CeO\({}_{2}\), is the first indication of the presence of polymer brushes in the composite particles. The second highlighted area is 2000-1000 cm\({}^{-1}\) (Figure 4b), where most of the peaks can be found. The characteristic C=O of the polymers can be seen in the area of 1600-1650 cm\({}^{-1}\) (Figure 4b), which is slightly different compared with other works [28; 29; 30; 31]. At the area 1500-1600 cm\({}^{-1}\) (Figure 4b), the bands found for the composite particles origi  
Figure 4: FTIR zooms of all samples in 3 different areas: (**a**) top, 3800–2800 cm\({}^{-1}\); (**b**) middle, 2000–1000 cm\({}^{-1}\); and (e) bottom, 1000–600 cm\({}^{-1}\). nated from the CTA grafted on the surface of the nanoparticles, since N-H (1570 cm\({}^{-1}\)), C(O)-NH (1580 cm\({}^{-1}\)), and C=O (1620 cm\({}^{-1}\)) were present in the structure (Figure 4b). For CeO\({}_{2}\), some low-intensity peaks were also present in the area of 1700-1300 cm\({}^{-1}\) (Figure 4b). Based on what can be seen in the literature, these bands were related to OH group (1630 cm\({}^{-1}\)) (Figure 4b) stretching vibrations, which were associated with the residual water molecules or physically adsorbed OH groups on the surfaces of the CeO\({}_{2}\)[32]. Another explanation is that these bands (1295, 1386, 1471, and 1587 cm\({}^{-1}\)) were attributed to the surface adsorbed carbonates [33], arising out of the synthetic procedure of the particles. It can also be seen that these peaks did not have the same maximum as the ones in the same area for the composite samples with the polymers. In the same area, at 1464 cm\({}^{-1}\) (Figure 4b), the -CH\({}_{2}\)- scissoring vibration for the sample with PAA was found [31], as well as the bending C-H (1470 cm\({}^{-1}\)) for the sample with PNVCL and the -CH\({}_{2}\)- (1476 cm\({}^{-1}\)) for the case of PMETAC (Figure 4b). In addition, an essential point for the presence of polymers was a broad band centered at 1390-1290 cm\({}^{-1}\) (Figure 4b), since this band is absent in the spectra of bare particles. Furthermore, in the spectra of the composite particles, there was the presence of bands that were absent in the bare particles in the area of 1200-1100 cm\({}^{-1}\), which was related to Si-O-Si (1180 cm\({}^{-1}\), the APTES anchored to the surface of the particles), C-O (1169 cm\({}^{-1}\), PMETAC), and C-N (1180 cm\({}^{-1}\), PNVCL) (Figure 4b). The CeO\({}_{2}\) had a characteristic peak found lower at around 1060 cm\({}^{-1}\) (Figure 4b) for the Ce-O-Ce that was also present in the polymer samples [25; 26; 27]. Finally, in the last area highlighted (1000-600 cm\({}^{-1}\)) (Figure 4c), two crucial bands appear, with the first at 950-900 cm\({}^{-1}\) only for composite particles with C-H bending vibrations (absent for the CeO\({}_{2}\)), whereas the peak centered at 700-680 cm\({}^{-1}\), characteristic for Ce-O, was present in all samples.