## 1 Introduction  
Over the last few decades, one of the major environmental challenges has been reducing emissions of greenhouse gases to the atmosphere--especially carbon dioxide (CO\({}_{2}\))--and minimizing the carbon footprint due to anthropogenic activities [1]. In the foreseeable future, industries will need to comply with increasingly strict regulations on CO\({}_{2}\) emissions. Thus, carbon capture, utilization, and storage (CCUS) technologies appear to be a viable industrial low-cost alternative to prevent its dispersion in the environment towards a zero-emission pathway for energy production [2; 3]. Several technologies have been proposed to capture CO\({}_{2}\) from power plant emissions, including absorption, adsorption, cryogenic distillation, and membrane separation [2]. Traditionally, for post-combustion processes, packed columns have been used for absorption but this technique is energy consuming and suffers from various problems including flooding, foaming, and/or solvent degradation [4]. Membrane separation presents many advantages, like compactness, and easy integration in already installed facilities [2; 3; 4; 5; 6; 7; 8; 9]. In the current commercial gas separation membranes, mainly based on dense polymer, the transport can be described by a solution-diffusion mechanism, depending on the kinetic diameter and condensability of the gas molecules [10]. This mechanism, however, tends to suffer from an inherent trade-off between permeability and selectivity, which limits the separation performance of the materials [11; 12]. A number of strategies has been developed over the years to overcome this limitation, using, for example, mixed matrix membranes [13; 14; 15] or polymer and block copolymers with high CO\({}_{2}\) affinity [16; 17; 18; 19]. As an alternative to conventional polymeric membranes, facilitated transport membranes (FTMs) have attracted attention because of the potential to achieve both high permeability and high selectivity [20; 21]. FTMs selectively permeate CO\({}_{2}\) by adding to the transport of free CO\({}_{2}\) molecules an additional mechanism of facilitated diffusion through complexation with an agent incorporated in the membrane, named carrier [22; 23; 24; 25], whereas gases such as H\({}_{2}\), N\({}_{2}\), and CH\({}_{4}\) will permeate exclusively by a solution-diffusion mechanism. For CO\({}_{2}\) separation, amine moieties represent a quite reasonable choice as carriers which was exploited in several works [26; 27; 28; 29; 30]. The mechanism, which regulates the interaction between aminated molecules and CO\({}_{2}\), is not yet completely understood, even though two main reactions are commonly considered to occur within the matrix [31; 30; 32]. When unhindered amines are present, carbon dioxide tends to form a carbamate ion through a zwitterion mechanism, a pathway originally described by [PERSON] [33] and presented in Figure 1a. If a hindered amine is present, a second mechanism is preferred, due to the carbamate ion instability, related to its large steric hindrance as presented in Figure 1b [30]. In both schemes, the reaction starts at the upstream side of the film, which represents the complexing of CO\({}_{2}\) to the carrier molecule once the gas is dissolved. The opposite reaction will take place at the downstream side, leading to the decomplexation of the carbon dioxide and allowing the molecule to pass once again into the gaseous phase. Historically, the earliest examples of FTMs were supported liquid membranes (SLM), introduced by [PERSON] and [PERSON] [23]; they impregnated the pores of a microporous support with a carrier solution enabling the CO\({}_{2}\) molecules to bond with functional group capable of permeating through the film and  
Figure 1: Preferential pathways and mechanisms of CO\({}_{2}\) molecules through unhindered (**a**) or hindered (**b**) amines groups across the membranes. releasing them on the downstream side. With this system, they managed to achieve excellent separation performances.