## 1 Introduction
In this work, the gas transport properties for MMMs prepared by embedding the same oxamate-based MOF in two different polymers, Pebax(r)1657 rubbery polymer and PEEK-WC glassy polymer, will therefore be investigated. The oxamate-based MOF, previously reported [20], with formula NiII\({}_{2}\)[NiII\({}_{4}\)[CuII\({}_{2}\)(Me\({}_{3}\)mpba)\({}_{2}\)]\({}_{3}\)]\(\cdot\)54H\({}_{2}\)O (where Me\({}_{3}\)mpba is the N\({}_{2}\),N\({}^{*}\)-2,4,6-trimethyl-1,3-phenylenebis (oxamate) ligand), has already shown interesting gas separation properties [21]. Single-crystal X-ray diffraction measurements unveil the crystal structure of CuNi-MOF. The anionic NiII\({}_{6}\)CuII\({}_{6}\) open-framework structure exhibits a pillared square/octagonal layer architecture, where nickel(II) and copper(II) ions are located on the vertices and midpoints of the edges, respectively, featuring three types of pores, different in size and shape, propagating along the c axis and enfolding up to 60% of the total lattice volume. Free nickel(II) cations are further accommodated within pores of the MOF. It consists of regularly spaced, small, almost square-sized pores (with a virtual diameter of ca 0.4 nm) and two kinds of hydrophobic and hydrophilic octagonal pores (Figure 1) resulting from the different disposition of the trimethyl-substituted phenylene spacers, pointing inwards or outwards from the voids, which accounts for their virtual diameters of ca. 1.5 and 2.2 nm, respectively (Figure 1). PEEK-WC is a glassy poly(ether-ether-ketone) with a cardo group in the polymer backbone,which makes it soluble in various common organic solvents. It has been used extensively in membrane preparation and characterization under the names PEEK-WC, PEEKWC or PEK-C [22]. Membranes have been prepared in the form of hollow fibres for liquid filtration [23] and as flat films for liquid filtrations [24] or for gas separation [25; 26; 27] and numerous other applications [22]. In this work, we take advantage of its good solubility in chloroform for the preparation of mixed matrix membranes by the solvent evaporation method. PEEK-WC presents a high selectivity but a too low permeability to be interesting as a material for industrial application. For this reason, different researchers have tried to improve its permeability without loss in selectivity by means of nanoparticle addition. An extensive protocol to obtain MMMs based on PEEK-WC, embedding NaA (LTA) zeolite, was developed in order to improve gas separation parameters [28]. However, no one procedure has enhanced gas transport properties of the neat polymer, and a decrease in selectivity was observed probably due to a presence of defects at interface between polymer and zeolite. Some methods have been developed in order to further improve the adhesion of PEEK-WC for 3D-mesoporous nanoparticles. For example, the MIL-101 was functionalized with a sulfonic acid group to further increase the affinity for the polymer matrix. The resulting membranes have shown an improved CO\({}_{2}\) permeability and CO\({}_{2}\)/gas selectivity. The increased selectivity was mainly attributed to the increased polar interaction between CO\({}_{2}\) and sulfonic acid groups, as well as the good filler-polymer interface compatibility [29]. Pebax(r)1657 is a thermoplastic elastomer multiblock-copolymer containing linear chains of rigid polyamide segments interspaced with flexible polyether segments. The hard polyamide (PA) blocks supply mechanical strength and the presence of the polar ethylene oxide (PEO) group, increases the affinity for CO\({}_{2}\), allowing for a good CO\({}_{2}\)/non-polar (H\({}_{2}\), N\({}_{2}\), and CH\({}_{4}\)) species separation and permselectivity. Several membranes have been prepared in the form of composite hollow fibre membranes [30; 31; 32], hybrid and mixed matrix membranes for gas separation [33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43].