A polymer nanocomposite for separating a target gas from a second gas in a gas mixture includes: (a) a matrix formed from a modified polymer, and (b) nanoparticles incorporated in the matrix, the nanoparticles being functionalized to have a stable interaction with the matrix. The modified polymer has a backbone including (i) a polymer having a selectivity for the target gas over the second gas, and (ii) functional groups covalently linked to the polymer (i) as part of the backbone. The functional groups are capable of further increasing the selectivity of the modified polymer by interacting with the target gas and/or with the second gas.