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The phenomenon of ionic liquid (IL) nanoconfinement within a copolymer/IL membrane reportedly enhances membrane selectivity, solubility, and transport in gas separations. Also, the copolymer/IL membrane morphology has been found to affect IL stability at high transmembrane pressures. In this work, a combined mesoscopic dynamics simulation and hybrid grand canonical Monte Carlo/molecular dynamics (GCMC-MD) simulations were carried out to investigate the morphologies, as well as CO2/CH4 gas diffusivities, solubilities, and selectivities of polystyrene-b-poly(ethylene oxide) (PS-b-PEO)/1-Ethyl-3-methylimidazolium thiocyanate ([EMIM][SCN]) and PS-b-PEO/1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIM][Tf2N]) membranes. The latter simulations focused on nanoconfined ILs in the copolymer/IL phase boundaries at 2.5 and 5 nm confinement lengths. The investigated systems were four nanoconfined ILs, i.e., PS/[EMIM][SCN]/PEO (the IL forming a separate microphase, denoted IL-Micro), PS/[EMIM][Tf2N]/PEO, PS/[EMIM][SCN]-PEO/PS (the IL distributed in the PEO phase, denoted IL-PEO), and PS/[EMIM][Tf2N]-PEO/PS, and five control systems, i.e., PS/PEO/PS, bulk PS, bulk PEO, bulk [EMIM][SCN], and bulk [EMIM][Tf2N]. Based on the mesoscopic dynamics simulation results, the dominant membrane morphologies at IL loadings of <50 vol % were lamellar or cylindrical (favorable for both IL stability at high transmembrane pressures if the bedding planes are horizontal, i.e. at 90° to the nominal direction of the transmembrane pressure gradient) with the IL-PEO or IL-Micro phases. Also, there was an overall 50% match between the observed PS-b-PEO/[EMIM][SCN] and PS-b-PEO/[EMIM][Tf2N] membrane morphologies. Based on the MD simulation results, both CO2 and CH4 diffusivities were the smallest in the bulk PS (control) and highest in the PS/[EMIM][Tf2N]/PEO system (IL-Micro between the PS and PEO phases) at both confinement lengths. The CO2 diffusivities were, on average, larger when the confinement length increased to 5 nm. The GCMC-MD results indicated that the CO2 solubility in the IL-Micro phases was higher than in the corresponding bulk ILs at both confinement lengths, with the PS/[EMIM][Tf2N]/PEO system exhibiting the highest CO2 solubility, followed by the PS/[EMIM][SCN]/PEO system. Additionally, the permselectivities of the nanoconfined IL systems were, on average, 40–50% larger than those of the bulk systems, with the highest permselectivity observed for PS/[EMIM][Tf2N]/PEO at the confinement length of 5 nm. Overall, the IL nanoconfinement between the PS and PEO phases (IL-Micro) leads to significant improvements in the CO2/CH4 permselectivities, suggesting that strategies to create nanoconfined IL morphologies in the copolymer/IL membranes are very promising for optimizing the membrane gas separation performance.