# Graphene-Based Membranes for CO2/CH4 Separation: Key Challenges and Perspectives
## Mixed-Matrix Membranes  
Among the different types of graphene-based membranes for CO\({}_{2}\)/CH\({}_{4}\) separation discussed herein, the mixed-matrix membrane design is the most functional and possesses the greatest commercial potential [52]. Mixed-matrix membranes are defined when a solid phase filler material is added into a continuous matrix of polymer phase [53]. In this context, the graphene-based materials serve as the filler materials. The rationale of doing so is to utilize the key attributes of the graphene-basedmaterials to engineer the transport properties of the polymer matrix. As already mentioned in the Introduction, the key attributes of graphene-based materials are their 2D morphologies and tunable physicochemical properties. The role of graphene-based materials in a mixed-matrix design is slightly different from the stacked laminates. At low loadings, the graphene-based materials capitalize on their well-defined interlayer spacing as low resistance nanochannels for diffusion of the smaller CO\({}_{2}\) molecules. Comparatively, the slightly larger CH\({}_{4}\) molecules are unable to gain access into the interlayer spacing and are forced to diffuse around the graphene-based fillers and through the polymer matrix with higher transport resistance (Figure 4a). For example, [PERSON] et al. prepared a polyether block amide (PEBA) mixed-matrix membrane containing 0.1 wt% GO nanosheets and reportedly observed a 100% enhancement in CO\({}_{2}\) permeability without compromising on the CO\({}_{2}\)/CH\({}_{4}\) selectivity (Table 1) [54]. At high loadings, however, the graphene-based fillers play a role that is similar to that of the stacked laminates. This was demonstrated by [PERSON] et al. who prepared a poly(amide-6-b-ethylene oxide) (Pebx)-based mixed-matrix membrane incorporated with 10 wt% polyethylene glycol- and polyethyleneimine-functionalized GO (PEG-PEI-GO) nanosheets [55]. Accordingly, the high-aspect-ratio of the GO nanosheets generated a tortuous pathway, which favored the diffusion of smaller CO\({}_{2}\) molecules at a lower transport resistance as compared to the larger CH\({}_{4}\) molecules. This result was exemplified by the higher CO\({}_{2}\)/CH\({}_{4}\) diffusivity selectivity when PEG-PEI-GO was incorporated. Another key highlight of the work by [PERSON] et al. [55] was the chemical functionalization of GO nanosheets. Chemical functionalization was used in this case to afford an intimate interfacial gap between the GO nanosheets and the Pebax matrix, making the mixed-matrix membrane defect-free. Intrinsically, pristine GO nanosheets already possess hydrophilic oxygen-containing functional groups, such as hydroxyl and carboxyl groups, that are compatible with a number of polymer matrices, including Pebax. To further strengthen their capacity to create an ideal interfacial gap for a multitude of other polymer matrices, grafting GO nanosheets with amine- and amino-based functional groups has become a widely adopted strategy [55; 56; 5]. This strategy not only improves the compatibility at the GO/polymer interface but the amine- and amino-based groups also increase the CO\({}_{2}\) affinity, leading to an enhanced CO\({}_{2}\) permeability without compromising on the CO\({}_{2}\)/CH\({}_{4}\) selectivity. Essentially, such merits are only realizable owing to the tunable physicochemical properties of the graphene-based materials. Apart from enhancing the CO\({}_{2}\)/CH\({}_{4}\) separation performances, graphene-based materials are also well-known for their good mechanical properties [57]. Critically, their use as fillers in mixed-matrix membranes can help to enhance the mechanical properties of the membranes. For example, [PERSON] et al. added 10 wt% loading of GO nanosheets in a Matrimid(r) matrix to demonstrate a \(>\)100% increment in Young's modulus of the membrane [58].