Hydroxide-exchange membranes are developed for facilitated transport CO2 in post-combustion flue-gas feed. First, a correlation between the basicity of fixed-site functional groups and CO2-separation performance is discovered. This relationship is used to identify phosphonium as a promising candidate to achieve high CO2-separation performance. Consequently, quaternary phosphonium-based hydroxide-exchange membranes are demonstrated to have a separation performance that is above the Robeson upper bound. Specifically, a CO2 permeability as high as 1090 Barrer and a CO2/N2 selectivity as high as 275 is achieved. The high performance observed in the membranes can be attributed to the quaternary phosphonium moiety.