## 3 Results
### Characterization of Bare and Grafted CeO\({}_{2}\) Particles
#### 3.1.3 Molecular-Thermal Characterization  
In this part, characterization of the size and z-potential of the samples with DLS and the z-potential was conducted. Moreover, the grafting density of the polymer brushes was investigated with TGA. GPC was used in order to study the molecular weight of the polymer brushes from the surface. In Figure 6, the TGA results can be found, and in Table 1, the results obtained from the techniques mentioned earlier can be seen. Figure 6: TGA results of the CeO\({}_{2}\) and CeO\({}_{2}\)@polymers. From Figure 6, the grafting density of the polymer brushes was calculated, and it is presented in Table 1. It can be seen that the initial particles were pretty stable during the whole range of TGA until 800 \({}^{\circ}\)C, and they lost less than 0.15% of their initial mass. The samples with polymer brushes had similar behavior but were distinct from the initial particles. It can be seen that they lost between 0.6 and 1% of their mass until 100 \({}^{\circ}\)C (that is, the water molecules that were absorbed out of the hydrophilic polymers). At 800 \({}^{\circ}\)C, after removing the percentage that originated from the humidity, the grafting density of the polymer brushes could be calculated via TGA. It was found that PAA was grafted in 5.83%, PNVCL was grafted in 6.09%, and PMETAC was grafted in 6.08%. From the DLS and z potential, interesting results could be found for the sizes of the particles in different pH levels. Moreover, the changes of the z potential could be seen when the particles were modified with polymer brushes. In Figure S3, the size distributions for the different samples can be seen. From Table 1 and Figure S3, the alteration of the sizes by changing the pH can be seen, as well as the z potential of these samples. For the sizes, it can be seen that the samples with polymer brushes had a wider size distribution compared with the initial particles. Moreover, by changing the pH, the aggregation of the particles was different, showing different agglomeration. As expected, CeO2@PAA's average size decreased when increasing the pH. The particles' size was 50% lower. This can easily be explained because of the conformation of the PAA chains as they adopted a globular conformation at a low pH and tended to aggregate. In a basic pH, the conformation was extended, and the particles tended to not aggregate due to electrostatic repulsion. Thus, smaller populations were observed (Figure S3 for CeO2@PAA). The opposite effect was observed for the particles of CeO2@PMETAC, where at an acidic pH, the chains were extended and showed smaller populations (Table 2 and Figure S3). The particles of CeO2@PNVCL also showed changes in size when measured at different pH levels. These changes were attributed to further aggregation of the particles. From the TGA (Figure 6), a grafting of around 6% for all polymer brushes could be seen, and that means that the CeO2 particles would affect the aggregation and the z potential, since the coverage was not entirely on the surface. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Samples**} & **Grafting Density** & \multirow{2}{*}{**M\({}_{\mathbf{w}}\)b**} & **Z\(-\)Potential c** \\  & **(\%)a  & \multirow{2}{*}{**(\%)**} \\  & & & \\ \hline CeO2 & – & – & \(-\)25.4 \\ \hline CeO2@PAA & 5.83 & \begin{tabular}{c} 36,500 \\ 44,500 \\ \end{tabular} & \(-\)21.3 \\ \hline CeO2@PNVCL & 6.09 & \
\begin{tabular}{c} 27,000 \\ 46,500 \\ \end{tabular} & \(-\)6.99 \\ \hline CeO2@PMETAC & 6.08 &
\begin{tabular}{c} 26,000 \\ 43,500 \\ \end{tabular} & \(-\)0.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results for the z-potential, GPC, and TGA for the initial particles and the ones with the polymer brushes.