## 1 Introduction  
Fixed carrier membranes containing the CO\({}_{2}\) facilitated carriers (_i.e._, amino and carboxyl groups) have both high selectivity and high permeability compared with conventional polymeric membranes, which is very attractive [1; 2; 3]. The facilitated transport in which carbon dioxide reversibly reacts with a carrier is a solution for conventional membranes that considerably enhances the CO\({}_{2}\) permeability. Recently, much effort has gone into the development of the membrane separation technique and it is mainly manifested in two aspects: new membrane materials selection [4; 5; 6; 7; 8] and preparation of the membrane materials [9; 10; 11; 12]. For gas permeation, the formation of crystals in polymer membranes due to the strong intermolecular interaction is generally deleterious since they act as impermeable obstacles to gas molecular transport [13]. It has been found that the polyvinylamine membrane showed lower CO\({}_{2}\)/CH\({}_{4}\) permselectivity in higher carrier content due to high crystallinity of polyvinylamine reducing effective permeating areas and effective carriers. Dendrimer might be a solution to the problem [14]. Starburst dendrimer has a large amount of terminal groups, high branched structure, and non crystallinity, which make it a potential material for gas separation membrane. [PERSON] firstly reported CO\({}_{2}\) separation membrane using a dendrimer as membrane material, the membrane exhibited excellent separation performance [15]. [PERSON] developed a composite membrane of polyamidoamine dendrimer with a chitosan modified substract [16]. Recenly, [PERSON] fabricated a composite membrane using pentaerythriyl tetraethylenediamine dendrimer as membrane material [8]. The star polymer is similar to a dendrimer, it consists of multiple linear chains linked together at one end of each chain by junction points, and has attracted considerable attention in recent years due to smaller hydrodynamic dimensions, higher degree of functionalities, lower degree of crystallinities and viscosities compared with the linear counterparts of the same molecular weight [17; 18; 19]. So those polymers have a potential application on membrane separation technique [20; 21]. [PERSON] _et al._[22] have successfully synthesized novel porous membranes by blending amphiphilic hyperbranched-star polymers (HPE-g-MPEG) with PVDF via the phase inversion process. The blend membranes with longer arm HPE-g-MPEGs show lower static protein adsorption, higher protein solution fluxes, and better protein solution flux recovery than the pure PVDF membrane. [PERSON] [23] reported the application of some star-shaped polymers (SSP) for transport and separation of metal cations in a liquid membrane system. [PERSON] _et al._[24] prepared sulfonated star-hyperbranched polyimide membranes and measured their proton conductivities. The results show that a good proton-transport pathway in the core-shell structure was formed when star-hyperbranched polyimide membranes with high molecular weight and this proton exchange membrane might have potential applications in fuel cells. But to our knowledge, there are few reports on application of star polymers on facilitated transport membranes for selectively removing CO\({}_{2}\) from gas mixtures. Star PDMAEMA contains tertiary amine groups, which might act as carriers for CO\({}_{2}\) facilitated transport. One of the major challenges in well-defined star polymer synthesis is the control of molecular weight with narrow polydispersity index (PDI) [25], although preparation of star polymers has been documented as early as 1948 by [PERSON] and [PERSON] [26]. Well-defined star polymers are mainly prepared by living anionic polymerization [27, 28], cationic polymerization [29], and \"living\"/controlled radical polymerization [30, 31]. In 1956, [PERSON] and his coworkers [32] were able to take advantage of the living anionic polymerization to synthesize well-defined four-armed polystyrenes for the first time by neutralizing living poly (styryllithium) with tetrachlorosilane.