## 1 Introduction
Numerous reports of different catalytic reactions exist in the literature where CeO\({}_{2}\) can be a part of dehydration [12] or even in CO\({}_{2}\) adsorption and catalysis. Specifically for CO\({}_{2}\), it can be found that it can be reduced to CH\({}_{3}\)OH [13] and CH\({}_{4}\)[4]. CeO\({}_{2}\) can capture CO\({}_{2}\)[5] similarly to other oxides (SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\) and ZrO\({}_{2}\)) [14], and in the case of CeO\({}_{2}\), it can also happen at room temperature, where CO\({}_{2}\) can adopt different configurations [2]. Finally, CeO\({}_{2}\) can participate in heterogeneous catalysis with alcohols or amines, showing selectivity to organic carbonates in the reaction of CO\({}_{2}\) with alcohols but without the formation of ethers by the intermolecular dehydration of alcohols [7]. Even though CeO\({}_{2}\) is a material with fascinating properties, it also has certain limitations, especially in catalysis. The CeO\({}_{2}\) particles show low surface area ratios, quick deactivation during the catalytic reactions [12], rapid recombination of electron-hole pairs and low-efficiency utilization of photons [4]. It is quite understandable that for catalytic reactions with CeO\({}_{2}\), the specific surface area must be increased. Furthermore, a material that can act as a supporting bed for the catalytic particles should be used with significant consideration. In the literature, many materials can be used in heterogeneous catalysis, and graphene is considered one of the most important. Graphene has a high surface area and can form monolithic structures via hydrothermal green techniques in a relatively straightforward manner [15,16]. Combining metallic catalysts with graphene-based materials, such as rGO, is promising and can support highly dispersed metallic catalysts [17]. These monolithic composite structures will add a high specific surface area, low pressure dropsand excellent mechanical and thermal stability compared with those of the corresponding particulate catalysts [4; 12]. There are some examples in the literature in which CeO\({}_{2}\) particles were combined with reduced graphene oxide or graphene for different applications [3; 10; 18; 19; 20; 21; 22]. Even though it can be a potential composite for CO\({}_{2}\) adsorption and a possible photocatalyst for its reuse, the synthesis of monolithic structures of rGO with CeO\({}_{2}\) is not well studied, especially in terms of functionalization and its effect on the interactions with CO\({}_{2}\). The study of monoliths with this type of particle is not present in the literature. In this work, the objective is to prepare monolithic structures of rGO with CeO\({}_{2}\) nanoparticles and polymer brushes grafted \"from\" the surface of the particles. The monolithic materials are studied in terms of porosity and structure to investigate the CO\({}_{2}\) adsorption and how the capacity is affected by the initial particles of CeO\({}_{2}\) compared with the ones with polymer brushes. The polymer brushes were synthesized from (1) poly(acrylic acid) (PAA), (2) poly(vinyl caprolactam) (PVCL), and (3) poly([2-(methoxyloxy)ethyl) trimethylammonium chloride] (PMETAC) (Scheme 1). A range of composite monoliths were synthesized--rGO monolith (G), rGO/CeO\({}_{2}\) (GCE), rGO/CeO\({}_{2}\)/PAA (GCePA), rGO/CeO\({}_{2}\)/PVCL (GcePV), and rGO/CeO\({}_{2}\)/PMETAC (GcePM)--that offered the possibility to study the effect of different functional polymers inside a monolith on the CO\({}_{2}\) adsorption. The use of polymer brushes with different responses in different environments, such as pH, can show other aggregations of the particles with the polymer brushes. Thus, it can also affect the preparation of the monolith with the addition of particles with different functionalities and responses.