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Copper-based metal–organic frameworks (MOFs) with different oxidation states and near-uniform particle sizes have been successfully synthesized. Mixed-matrix polyimide membranes incorporating 0.1–7 wt% of Cu(II) benzene-1,2,5-tricarboxylic acid (Cu(II)BTC), Cu(I/II)BTC and Cu(I) 1,2-ethanedisulfonic acid (EDS) (Cu(I)EDS) MOFs were fabricated via non-solvent-induced phase inversion process. These membranes are found to be solvent resistant and mechanically stable. Liquid phase nanofiltration experiments were performed to separate toluene from n-heptane at room temperature. These membranes demonstrate preferential adsorption and permeation of the aromatic toluene over aliphatic n-heptane. The amount of MOF particles incorporated, the oxidation state of the Cu ion and membrane, and barrier layer thickness have a significant impact on the separation factor. Toluene/heptane separation factor at 1.47, 1.67 and 1.79 can be obtained for membranes incorporating 7 wt% Cu(II)BTC, Cu(I/II)BTC and Cu(I)EDS respectively at room temperature.