## 4 Conclusions  
The preparation of different polymeric brushes from CeO\({}_{2}\) particles was investigated as the first aim of this work. In particular, brushes of PAA, PNVCL, and PMETAC were grafted from CeO\({}_{2}\). Different characterization methods showed the successful synthesis of the polymers (FTIR, GPC, Z potential, and TGA).  
The materials mentioned above were used to prepare rGO monoliths for studying their adsorption capacities compared with monoliths with only CeO\({}_{2}\) particles. The initial differences in the morphology of the SEM images revealed a different structure by changing the type of particles used. The adsorption-desorption with N\({}_{2}\) showed that these materials had different microporosities, SSAs, and total pore volumes only by changing the introduced particle type. The differences in the average pore diameter and the other parametersrelated to pores showed that these particles aggregated differently during the preparation of the monoliths. This can also affect their porosity and subsequently the adsorption. The hysteresis type revealed an H3 hysteresis loop typical for slit-shaped pores for almost all materials, except the GCePA monolith. In the latter case, the hysteresis loop was similar to H4, typical for narrow, slit-shaped pores.  
Finally, the adsorption of CO\({}_{2}\) revealed that the monoliths with superior SSAs and total pore volumes did not show better adsorption. Instead, the samples with different functionalities (different chemical groups) could also significantly influence adsorption. The GCePN monolith showed higher adsorption, having a lower SSA than the monolith with the initial CeO\({}_{2}\). Moreover, the GCePA monolith also showed similar results to GCe, with an SSA and total pore volume far lower than those for GCe. The acidity of the CO\({}_{2}\) also played a role in the final adsorption, since it could probably affect the conformation of the particles covered with polymers that could have structural changes inside the acidic pH of the gas.  
The following are available online at [[https://www.mdpi.com/article/10.3390/app112311154/s1](https://www.mdpi.com/article/10.3390/app112311154/s1)]([https://www.mdpi.com/article/10.3390/app112311154/s1](https://www.mdpi.com/article/10.3390/app112311154/s1)). Figure S1: TEM images of the initial CeO\({}_{2}\) nanoparticles and with the different polymer brushes; Figure S2: FTIR of all spectra from top to bottom for (a) CeO\({}_{2}\), (b) CeO\({}_{2}\)@PAA, (c) CeO\({}_{2}\)@PNVCL and (d) CeO\({}_{2}\)@PMETAC; Figure S3: DLS size distribution by intensity for all samples and in all three pHs (4, 7 and 10).  
Conceptualization, N.P.; methodology, N.P.; formal analysis, N.P., L.S.C., J.A.C. and R.T.; investigation, N.P., L.S.C., J.A.C. and I.B.; resources, R.T., L.S.C. and J.A.C.; data curation, N.P., L.S.C. and J.A.C.; writing--original draft preparation, N.P.; writing--review and editing, N.P., L.S.C., J.A.C. and R.T.; project administration, N.P. and R.T.; funding acquisition, R.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Basque government, grant number GV IT999-16.  
Not applicable.  
Data availability Statement: Data are contained within the article or Supplementary Material.  
The authors declare no conflict of interest.