Polyethylene oxide (PEO)-containing multi-block copolymers are good candidates for CO2 membrane separations because of their strong affinity for CO2 but PEO crystallization and weak mechanical properties are two limitations to be overcome at high PEO content. In this work, PEO block incorporation within new linear multi-block copolymers avoided PEO crystallization. The copolymers consisted in Jeffamine soft blocks (SB) and particularly stiff urea-imide hard blocks for improved physical cross-linking and excellent film-forming ability. Varying the SB content from 41 to 70 wt% led to different copolymer physical properties, morphology and CO2 permeation properties. The copolymer with the lowest SB content was a rigid glassy material with very weak phase separation. Its soft and hard blocks formed large interpenetrated domains, resulting in low CO2 permeability (2 Barrer) but extreme selectivity (alpha(CO2/N2) = 207) for CO2/N-2 separation at 2 bar and 35 degrees C. CO2 permeability greatly improved with the SB content due to strong phase separation. The copolymer with the highest SB content was a thermoplastic elastomer with soft blocks forming well-separated highly permeable percolating nano-domains. Its CO2 permeability (57 Barrer) and high selectivity (alpha(CO2/N2) = 50) are among the best properties reported for PEO-containing multi-block copolymers for CO2 capture. (C) 2017 Elsevier Ltd. All rights reserved.