## 2 Morphology Design of Graphene-Based Composites  
### The Composites of Graphene with Faceted Particles  
Since the successful preparation of faceted anatase titania and demonstration of its exceptional photocatalytic properties [16,17], the attention on the particles with exposed high reactive facets and their role in the mechanism of photocatalysis is constantly growing [18, 19, 20]. To date, many research papers on this topic have been published. Most of them concern faceted TiO\({}_{2}\)[21, 22, 23, 24, 25, 26], but the scientific reports about other types of photocatalysts with faceted morphology, such as Cu\({}_{2}\)O [27, 28], BiVO\({}_{4}\)[29, 30], ZnO [31], AgNbO\({}_{3}\)[32], Ag\({}_{2}\)MoO\({}_{4}\)[33] and BiOCl [34, 35], are also available in the literature. For example, the morphology of anatase titania can be recognized as decahedron, octahedron, rod, belt and sheet structures. Some of these morphologies are enclosed with exposed facets such as (001), (101) and (010). The mentioned facets differ in the values of surface energy determiningthe resultant character of activity (0.90 J m\({}^{-2}\) for (001), 0.44 J m\({}^{-2}\) for (101) and 0.53 J m\({}^{-2}\) for (010)) [36]. The proper tuning of the ratio of different facets might influence the overall photocatalytic activity. In this relation, there is a still important challenge to prepare faceted particles with design ratio between facets. The intrinsic property of graphene, i.e., high electron conductivity, influences the photocatalytic activity of semiconductor particles through interaction between graphene and semiconductor at the interfaces. Taking into consideration the photocatalysts in the form of faceted particles and their composites with graphene, one can expect the synergistic effect of high reactive facets and an enhancement of electron transfer process to improve photocatalytic activity. [PERSON] et al. started the research on TiO\({}_{2}\)/G composites consisting of graphene and anatase with exposed (001) facets [37]. It has been proposed that the superior photocatalytic activity of prepared composites results from high charge separation rate because of an efficient electron transfer in the frame of semiconductor-graphene interface. Similarly, excellent activity has been reported by [PERSON] et al. on a novel core-shell-structure (G-wrapped Pt/TiO\({}_{2}\), Figure 1), in which anatase nanocrystals with co-exposed (001) and (101) facets improve the separation of photogenerated charges, and thus enhance the photocatalytic efficiency [38]. The wrapped rGO sheets as an efficient electron acceptor and transporter is not only one positive of graphene, but also the surface hydroxyl groups and extended \(\pi\) bonds are beneficial to enhance the adsorption and activation of reagents, e.g., CO\({}_{2}\). It has been proposed that rGO(shell)-Pt-TiO\({}_{2}\)(core) ternary composites might promote the vectorial electron transfer (TiO\({}_{2}\)\(\rightarrow\)Pt\(\rightarrow\)rGO), enhancing the separation of charge carriers [38]. Another promising interaction including additional presence of structural titania defects has been observed by [PERSON] et al. [39]. The rGO-wrapped titania nanocrystals (TiO\({}_{2}\) NCs@RGO) with oxygen vacancies (Vo) and Ti\({}^{3+}\) defects have been synthesized by electrostatically wrapping GO around TiO\({}_{2}\) NCs, following by thermal annealing at 400 \({}^{\circ}\)C (Figure 2). It has been found that the photocatalytic activity of TiO\({}_{2}\) NCs@RGO is 2.4 times higher than that of TiO\({}_{2}\) NCs for degradation of methyl orange. It has been proposed that  
Figure 1: Preparation procedure and photographs of (Pt/TiO\({}_{2}\))@rGO photocatalysts: (**a**) the schematic graph for the two-step synthesis of supported Pt NPs and wrapping rGO shells on the surface of TiO\({}_{2}\) nanocrystals; (**b**) the digital photograph and (**c**) SEM images of TiO\({}_{2}\), Pt/TiO\({}_{2}\) and (Pt/TiO\({}_{2}\))@rGO. Reprinted with permission from [38] after slight modification. Copyright 2018 Elsevier.