Glassy PEEK-WC vs. Rubbery Pebax ® 1657 Polymers: E ﬀ ect on the Gas Transport in CuNi-MOF Based Mixed Matrix Membranes

: Mixed matrix membranes (MMMs) are seen as promising candidates to overcome the fundamental limit of polymeric membranes, known as the so-called Robeson upper bound, which deﬁnes the best compromise between permeability and selectivity of neat polymeric membranes. To overcome this limit, the permeability of the ﬁller particles in the MMM must be carefully matched with that of the polymer matrix. The present work shows that it is not su ﬃ cient to match only the permeability of the polymer and the dispersed phase, but that one should consider also the individual contributions of the di ﬀ usivity and the solubility of the gas in both components. Here we compare the gas transport performance of two di ﬀ erent MMMs, containing the metal–organic framework CuNi-MOF in the rubbery Pebax ® 1657 and in the glassy poly(ether-ether-ketone) with cardo moiety, PEEK-WC. The chemical and structural properties of MMMs were investigated by means of FT-IR spectroscopy, scanning electron microscopy and EDX analysis. The inﬂuence of MOF on the mechanical and thermal properties of both polymers was investigated by tensile tests and di ﬀ erential scanning calorimetry, respectively. The MOF loading in Pebax ® 1657 increased the ideal H 2 / N 2 selectivity from 6 to 8 thanks to an increased H 2 permeability. In general, the MOF had little e ﬀ ect on the Pebax ® 165 membranes because an increase in gas solubility was neutralized by an equivalent decrease in e ﬀ ective di ﬀ usivity. Instead, the addition of MOF to PEEK-WC increases the ideal CO 2 / CH 4 selectivity from 30 to ~48 thanks to an increased CO 2 permeability (from 6 to 48 Barrer). The increase in CO 2 permeability and CO 2 / CH 4 selectivity is maintained under mixed gas conditions. to a di ﬀ erent size-selectivity for small and large gas species due to the highly-interconnected free volume. These results suggest that the CuNi-MOF particles, with their internal void structure, have a similar e ﬀ ect on the gas di ﬀ usion of Pebax ® 1657 and PEEK-WC, introducing preferential di ﬀ usion pathways into the system which change the main transport mechanism, especially for the small molecules. As described above, the remarkably lower e ﬀ ective di ﬀ usion in Pebax ® 1657 is due


Introduction
The research field on materials for gas separation membranes is constantly expanding due to the pressing industrial request for more performing materials to employ in gas treatment, such as hydrogen recovery (H 2 /CO 2 ) [1], oxygen-enriched air production (O 2 /N 2 ) [2,3], biogas up-grading [4,5] and 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].
Appl. Sci. 2020, 10,1310 3 of 20 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 CO2 permeability and CO2/gas selectivity. The increased selectivity was mainly attributed to the increased polar interaction between CO2 and sulfonic acid groups, as well as the good filler-polymer interface compatibility [29]. Pebax ® 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 CO2, allowing for a good CO2/non-polar (H2, N2, and CH4) 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]. Mixed matrix membranes based on amine-functionalized and pristine MIL-53(Al) in Pebax1657 have shown an increased CO2 separation and the higher permeability (PCO2 100 Barrer and αCO2/CH4 = 17; CO2/N2 = 50), was attributed to high porosity introduced by the presence of the MOF, as well as the selective adsorption of CO2 inside the MOF [41]. Liu   Pebax ® 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]. Mixed matrix membranes based on amine-functionalized and pristine MIL-53(Al) in Pebax1657 have shown an increased CO 2 separation and the higher permeability (PCO 2 100 Barrer and αCO 2 /CH 4 = 17; CO 2 /N 2 = 50), was attributed to high porosity introduced by the presence of the MOF, as well as the selective adsorption of CO 2 inside the MOF [41]. Liu et al. designed nanosheet-enhanced Pebax-MoS2 Appl. Sci. 2020, 10, 1310 4 of 20 mixed matrix membranes for CO 2 capture, increasing CO 2 /N 2 selectivity until 90 [44]. Composite hollow fibre membranes with a selective layer of Pebax ® 1657 and different functionalized Uio-66 MOF have demonstrated a simultaneous improvement in gas permeance and selectivity. The enhanced selectivity was attributed to an increased rigidity of the polymer matrix due to a formation of a hydrogen bond between the MOF and Pebax ® 1657 polymer chains [45]. Pebax ® 1657 containing Cu 3 BTC 2 -MOF have shown an increased CO 2 /CH 4 ideal selectivity about 15% compared to the neat Pebax ® 1657 [46]. The improvement in selectivity was attributed to the improvement in the CO 2 solubility, which, having a strong quadrupole moment, presents a higher affinity with unsaturated Cu sites than CH 4 , leading to a higher CO 2 permeability. In this work, the CuNi-MOF was dispersed in the Pebax ® 1657 rubbery polymer and in the PEEK-WC glassy polymer, which, presenting a Cu site and well-defined cages (1.5 nm and 2.2 nm), is expected to influence at the same time the solubility and diffusion coefficient. The aim is to understand the main factors that determine the behaviour when a MOF is dispersed within a glassy or rubbery polymeric matrix. FT-IR, EDX, DSC and SEM analyses investigate the potential chemical interaction between CuNi-MOF and polymers. Besides, pure gas permeability tests with six different gases were carried out to obtain a general understanding of the MMM performance, while permeation tests were also carried out with binary CO 2 /N 2 and CH 4 /CO 2 gas mixtures to evaluate its potential performance in a real separation process. These two gas pairs simulate flue gas in view of the potential use of the membranes in CO 2 capture, and biogas in view of the potential exploitation of renewable energy in a strongly emerging market.
PEEK-WC was provided as a powder by the Institute of Applied Chemistry, Changchun, China, and was used as received, without further purification. The

Membranes Preparation
Mixed matrix membranes were prepared by loading different concentrations of CuNi-MOF (9 wt %, 17 wt %, 23 wt %) in Pebax ® 1657 and in PEEK-WC. The Pebax ® 1657 solution at 10 wt % was prepared by swelling polymer pellets in a mixture of distilled water and ethanol (ratio 30:70 wt/wt) at room temperature overnight, in agreement with previously-reported procedure [30]. Then a homogeneous dope solution was obtained by heating to 80 • C under magnetic stirring for at least 10 min. The CuNi-MOFs were dispersed and sonicated in water-ethanol mixture for 30 min and subsequently added to the Pebax ® 1657 solution under magnetic stirring. While, homogenous solution at 5 wt % of PEEK-WC was obtained by dissolving the polymer powder in chloroform at room temperature for 24 h. Concurrently, the CuNi-MOFs were separately dispersed in chloroform and sonicated in an ultrasonic bath for 30 min before filtering the PEEK-WC solution through glass wool into the suspension. One hour of mechanical stirring and 30 min of sonication made each solution homogeneous. The resulting solutions were cast into levelled flat Teflon petri-dish and left to evaporate over 2-3 days. The MMMs produced were dried in the oven at 70 • C under vacuum conditions for 24 h.

Structural Characterization
Chemical and morphological analysis of membranes were performed by scanning electron microscopy (Phenom Pro X desktop SEM, Phenom-World). The samples for cross-section SEM characterization were prepared by freeze-fracturing in liquid nitrogen. Samples were analyzed without sputter-coating with gold. Elemental analysis was performed with the Phenom-Pro X desktop SEM, which is equipped with an energy dispersive X-ray spectroscopy detector (EDX). Infrared spectroscopy (FT-IR) analyses were performed by means of Spectrum Spotlight Chemical Imaging Instrument (PerkinElmer) in ATR mode.

Thermal and Mechanical Characterization
DSC analysis was carried out using a Pyris Diamond Differential Scanning Calorimeter (Perkin Elmer, Shelton, CT, USA) equipped with an intracooler refrigeration system. Samples of 15-20 mg were used. Unless specified otherwise, three cycles were performed. The PEEK-WC samples were first heated from −60 • C to 300 • C, kept at this temperature for 1 min, and cooled down to 0 • C, where they were kept for 5 min. In the second run, the samples were heated up again to 300 • C. The DSC runs were performed at a scan rate of 15 • C min −1 . Before the measurements, the samples were kept at 50 • C under vacuum for one night in order to remove possibly adsorbed water. The Pebax ® 1657-based samples were tested using an identical method in the range from −40 • Tensile tests were carried out at room temperature on a single column Universal Testing Machine, Zwick/Roell model Z2.5, equipped with a 50 N load cell and pneumatic clamps. The surface of one flat clamp was covered with adhesive rubber to avoid slipping or damaging of the samples, while the second clamp had a convex surface to increase the local pressure and to avoid the extraction of the sample. The average value and the standard deviation of the Young's modulus, the tensile strength and the maximum deformation were determined on a series of at least four samples. The sample width was 5 mm, and the grip-to-grip distances 40 and 30 mm for Pebax ® 16 and PEEK-WC, respectively.

Single Gas Permeation Method
Single gas permeation tests were carried out at 25 • C and at a feed pressure of 1 bar, using a fixed-volume pressure increase instrument (ESSR), described elsewhere [48]. Permeability coefficients, P, and diffusion coefficients, D, were determined by the time-lag method [49]. The permeability coefficient, P, is calculated from the permeation curve in the steady state described by: The last term in (Equation (1)) represents the so-called permeation time lag, Θ, which is inversely proportional to the diffusion coefficient of the gas: The approximate gas solubility coefficient, S, was obtained indirectly as the ratio of the permeability to the diffusion coefficient by assuming the solution-diffusion transport mechanism: Permeabilities are reported in Barrer [1 Barrer = 10 −10 cm 3 (STP) cm cm −2 s −1 cm Hg −1 ].

Mixed Gas Permeation Measurement
Mixed gas permeation tests were carried out using a custom made constant pressure/variable volume instrument, described in detail elsewhere [50], equipped with a quadrupole mass filter (HPR-20 QIC Benchtop residual gas analysis system, Hiden Analytical, Warrington, UK). Measurements were performed from 1 to 6 bar(a) with two binary gas mixtures of CO 2 /N 2 (15:85 vol %) and CO 2 /CH 4 (35:65 vol %), simulating flue gas and biogas, respectively. Argon was used as a sweeping gas and as the internal standard for the calculation of the permeate gas composition.

Chemical and Morphological Characterization
The MOF loading in polymer matrix was evidenced by the distinctive color of obtained membranes, and it was accurately confirmed by the EDX analysis, which revealed the attendance of Cu and Ni metals in both Pebax ® 1657 and PEEK-WC polymers (See SI, Figure S1a,b, respectively). The chemical characterization of neat membranes and MMMs, as well as the interaction between polymer chains and nanoparticles were investigated by FTIR-ATR. Figure 2b

Chemical and Morphological Characterization
The MOF loading in polymer matrix was evidenced by the distinctive color of obtained membranes, and it was accurately confirmed by the EDX analysis, which revealed the attendance of Cu and Ni metals in both Pebax ® 1657 and PEEK-WC polymers (See SI, Figure S1a,b, respectively). The chemical characterization of neat membranes and MMMs, as well as the interaction between polymer chains and nanoparticles were investigated by FTIR-ATR. Figure 2b In the spectrum of Pebax ® 1657/CuNi-MOF, characteristic peaks appear at 1578 cm −1 due to C-C aromatic band of MOF's phenylene, at 1608 cm −1 of stretching of oxamate ligand of MOF and a peak at 1330 cm −1 , which could be considered diagnostic of the presence of bridging oxamate between Cu and Ni [51]. Finally, the characteristic peaks between 2900 cm −1 and 2800 cm −1 due to the symmetric and asymmetric C-H stretching are slightly shifted to lower wavelengths, confirming the interaction of hydrogen bonds at the interface between MOF and Pebax ® 1657, as it was also seen by Khosravi et al. for Pebax1657/CuBTC mixed matrix membranes [52]. Figure 2d offers a comparison of PEEK-WC membrane and PEEK-WC/CuNi spectrum. The functional groups of PEEK-WC give In the spectrum of Pebax ® 1657/CuNi-MOF, characteristic peaks appear at 1578 cm −1 due to C-C aromatic band of MOF's phenylene, at 1608 cm −1 of stretching of oxamate ligand of MOF and a peak at 1330 cm −1 , which could be considered diagnostic of the presence of bridging oxamate between Cu and Ni [51]. Finally, the characteristic peaks between 2900 cm −1 and 2800 cm −1 due to the symmetric and asymmetric C-H stretching are slightly shifted to lower wavelengths, confirming the interaction of hydrogen bonds at the interface between MOF and Pebax ® 1657, as it was also seen by Khosravi et al. for Pebax1657/CuBTC mixed matrix membranes [52]. Figure 2d offers a comparison of PEEK-WC membrane and PEEK-WC/CuNi spectrum. The functional groups of PEEK-WC give characteristic peaks at 3052 cm −1 and 3075 cm −1 for aromatic C-H stretch, at 1767 cm −1 for ketonic and esteric C=O stretching, and at 1589 cm −1 for the C-C aromatic band [53]. In PEEK-WC/CuNi, the peak for the C-C aromatic band is shifted on the lower wavelengths, probably due to the π· · · π stacking interaction between the benzene rings of polymers and MOF. In fact, when the ring is very conjugated, a weak band can be observed at around 1580 cm −1 , such as the one is visible from the PEEK-WC/CuNi spectrum. The peaks due to the stretch of the aromatic C-H appear to be totally fused with the water peak (3370 cm −1 ) that reveals the relatively hydroscopic nature of the MOFs. The interaction between the Pebax ® 1657 and CuNi-MOF was also confirmed by SEM analysis, and in the enlarged particular of Figure 2a, it is possible to see that polymer phase of Pebax ® 1657creates a sort of circular compressed polymer region around the MOF, which Koros defined as "Case I matrix rigidification" [37]. On the other hand, the distribution of MOF in the PEEK-WC polymer produces a defined and regular network structure ( Figure 2c) with a homogenous dispersion of nanoparticles without significant sedimentation across the membranes (See SI Figure S-2). Instead, the addition of MOFs in Pebax ® 1657 shows no significant agglomeration at the lowest 9 wt % that becomes more significant at highest 29 wt % concentration.

Mechanical and Thermal Properties
All membranes are dense mixed matrix membranes with good mechanical resistance for handling. The results of the tensile tests, performed on the nanocomposite films obtained on the series with different concentrations of CuNi-MOFs in Pebax ® 1657 and in PEEK-WC, are shown in Figure 3. The PEEK-WC presents a Young's module about 1.14 GPa [54] and Pebax ® 1657 has a Young's module about 0.10 GPa [55]. In both polymers, the loading of CuNi-MOF increases the Young's modulus. The increase of the Young's modulus indicates an increase of stiffness for both polymers, increasing the MOF concentrations. The glassy PEEK-WC presents a higher modulus compared to the rubbery Pebax ® 1657, as expected, and it remains higher even when the MOF concentration was increased. On the other hand, the maximum deformation is higher in the more flexible MMMs based on the rubbery Pebax ® 1657 compared to the MMMs based on the rigid glassy PEEK-WC.
Appl. Sci. 2020, 10, 1310 7 of 20 characteristic peaks at 3052 cm −1 and 3075 cm −1 for aromatic C-H stretch, at 1767 cm −1 for ketonic and esteric C=O stretching, and at 1589 cm −1 for the C-C aromatic band [53]. In PEEK-WC/CuNi, the peak for the C-C aromatic band is shifted on the lower wavelengths, probably due to the π⋯π stacking interaction between the benzene rings of polymers and MOF. In fact, when the ring is very conjugated, a weak band can be observed at around 1580 cm −1 , such as the one is visible from the PEEK-WC/CuNi spectrum. The peaks due to the stretch of the aromatic C-H appear to be totally fused with the water peak (3370 cm −1 ) that reveals the relatively hydroscopic nature of the MOFs. The interaction between the Pebax ® 1657 and CuNi-MOF was also confirmed by SEM analysis, and in the enlarged particular of Figure 2a, it is possible to see that polymer phase of Pebax ® 1657creates a sort of circular compressed polymer region around the MOF, which Koros defined as "Case I matrix rigidification" [37]. On the other hand, the distribution of MOF in the PEEK-WC polymer produces a defined and regular network structure ( Figure 2c) with a homogenous dispersion of nanoparticles without significant sedimentation across the membranes (See SI Figure S-2). Instead, the addition of MOFs in Pebax ® 1657 shows no significant agglomeration at the lowest 9 wt % that becomes more significant at highest 29 wt % concentration.

Mechanical and Thermal Properties
All membranes are dense mixed matrix membranes with good mechanical resistance for handling. The results of the tensile tests, performed on the nanocomposite films obtained on the series with different concentrations of CuNi-MOFs in Pebax ® 1657 and in PEEK-WC, are shown in Figure 3. The PEEK-WC presents a Young's module about 1.14 GPa [54] and Pebax ® 1657 has a Young's module about 0.10 GPa [55]. In both polymers, the loading of CuNi-MOF increases the Young's modulus. The increase of the Young's modulus indicates an increase of stiffness for both polymers, increasing the MOF concentrations. The glassy PEEK-WC presents a higher modulus compared to the rubbery Pebax ® 1657, as expected, and it remains higher even when the MOF concentration was increased. On the other hand, the maximum deformation is higher in the more flexible MMMs based on the rubbery Pebax ® 1657 compared to the MMMs based on the rigid glassy PEEK-WC. The break strength decreases for Pebax ® 1657/CuNi membranes, indicating that the membranes become weaker compared to the neat polymer. On the contrary, the break strength increases for PEEK-WC/CuNi membranes, suggesting a good adhesion between MOF and polymer that makes the MMMs stronger than the neat PEEK-WC membrane. The thermal properties of the membranes were studied using DSC analysis, and the results are displayed in Figure 4. For neat Pebax ® 1657, the two dominant endothermal peaks at 19 °C and 200 °C are attributed to the fusion of the crystalline fraction of the soft poly(ethylene oxide) (PEO) blocks and the hard polyamide (PA) blocks, respectively. In the presence of MOF, the melting enthalpy of both PEO and PA decreases. However, the peak maximum shifts to a higher temperature, indicating that the MOF stabilizes the crystalline PEO and that it mainly interacts with this phase. On the other hand, no significant changes occur in the glass transition temperature of PEEK-WC at 230 °C as a function of the MOF concentration. The break strength decreases for Pebax ® 1657/CuNi membranes, indicating that the membranes become weaker compared to the neat polymer. On the contrary, the break strength increases for PEEK-WC/CuNi membranes, suggesting a good adhesion between MOF and polymer that makes the MMMs stronger than the neat PEEK-WC membrane. The thermal properties of the membranes were studied using DSC analysis, and the results are displayed in Figure 4. For neat Pebax ® 1657, the two dominant endothermal peaks at 19 • C and 200 • C are attributed to the fusion of the crystalline fraction of the soft poly(ethylene oxide) (PEO) blocks and the hard polyamide (PA) blocks, respectively. In the presence of MOF, the melting enthalpy of both PEO and PA decreases. However, the peak maximum shifts to a higher temperature, indicating that the MOF stabilizes the crystalline PEO and that it mainly interacts with this phase. On the other hand, no significant changes occur in the glass transition temperature of PEEK-WC at 230 • C as a function of the MOF concentration. The break strength decreases for Pebax ® 1657/CuNi membranes, indicating that the membranes become weaker compared to the neat polymer. On the contrary, the break strength increases for PEEK-WC/CuNi membranes, suggesting a good adhesion between MOF and polymer that makes the MMMs stronger than the neat PEEK-WC membrane. The thermal properties of the membranes were studied using DSC analysis, and the results are displayed in Figure 4. For neat Pebax ® 1657, the two dominant endothermal peaks at 19 °C and 200 °C are attributed to the fusion of the crystalline fraction of the soft poly(ethylene oxide) (PEO) blocks and the hard polyamide (PA) blocks, respectively. In the presence of MOF, the melting enthalpy of both PEO and PA decreases. However, the peak maximum shifts to a higher temperature, indicating that the MOF stabilizes the crystalline PEO and that it mainly interacts with this phase. On the other hand, no significant changes occur in the glass transition temperature of PEEK-WC at 230 °C as a function of the MOF concentration.

Pure Gas Transport Properties
Single gas permeation experiments were carried out in the order H2, O2, N2, CH4 and CO2 at 25 °C, but repeated experiments with N2 and O2 at the end of the cycle were identical and revealed no structural changes in the material. An overview of the results of the Pebax ® 1657-based MMMs and PEEK-WC based MMMs with different filler loadings is given in Figures 5 and 6, respectively. All permeability, diffusivity and solubility data, and their respective selectivities, are given in the supporting information (See SI Tables 2 and 3). The dispersion of CuNi-MOF does not produce a substantial change in the permeability of the rubbery Pebax ® 1657. The most permeable species is CO2, confirming a solubility controlled transport (CO2 > H2 > CH4 > O2 > N2), typical for the rubbers ( Figure  5a). A remarkably strong decrease in the effective diffusion coefficients of all gases as a function of the MOF loading (Figure 5b) is balanced by a proportional increase in their solubility coefficients (Figure 5c). This results in a similar permeability and selectivity (Figure 5d) for MMMs as in the neat Pebax ® 1657, with the only exception of the H2/CH4 gas pair, which suggests a favourable effect of the MOF on the size-selectivity. This is confirmed by the slight increase in the diffusion selectivities (Figure 5e), apparently because the MOF's provide preferential diffusion paths for smaller gases.
While the gas solubility upon addition of the MOF to Pebax increases as expected, given the generally high sorption capacity of MOFs for gases, it was not expected that this increase was more or less similar for all gases, and it was even less expected that the porous fillers would effectively lead to a decrease in the diffusion coefficient. The explanation is that the filler does not effectively decrease the diffusion coefficient in the membrane, but the highly-sorbing MOF transforms the permeation experiment in a sort of breakthrough experiment. The reason for the apparently slower diffusion is the accumulation of the gas inside the pores of the filler, similar to the phenomenon of immobilizing adsorption [56,57], but in this case it has a virtually negligible net effect on the permeability.

Pure Gas Transport Properties
Single gas permeation experiments were carried out in the order H 2 , O 2 , N 2 , CH 4 and CO 2 at 25 • C, but repeated experiments with N 2 and O 2 at the end of the cycle were identical and revealed no structural changes in the material. An overview of the results of the Pebax ® 1657-based MMMs and PEEK-WC based MMMs with different filler loadings is given in Figures 5 and 6, respectively. All permeability, diffusivity and solubility data, and their respective selectivities, are given in the supporting information (See SI Tables S2 and S3). The dispersion of CuNi-MOF does not produce a substantial change in the permeability of the rubbery Pebax ® 1657. The most permeable species is CO 2 , confirming a solubility controlled transport (CO 2 > H 2 > CH 4 > O 2 > N 2 ), typical for the rubbers (Figure 5a). A remarkably strong decrease in the effective diffusion coefficients of all gases as a function of the MOF loading (Figure 5b) is balanced by a proportional increase in their solubility coefficients (Figure 5c). This results in a similar permeability and selectivity (Figure 5d) for MMMs as in the neat Pebax ® 1657, with the only exception of the H 2 /CH 4 gas pair, which suggests a favourable effect of the MOF on the size-selectivity. This is confirmed by the slight increase in the diffusion selectivities (Figure 5e), apparently because the MOF's provide preferential diffusion paths for smaller gases.
While the gas solubility upon addition of the MOF to Pebax increases as expected, given the generally high sorption capacity of MOFs for gases, it was not expected that this increase was more or less similar for all gases, and it was even less expected that the porous fillers would effectively lead to a decrease in the diffusion coefficient. The explanation is that the filler does not effectively decrease the diffusion coefficient in the membrane, but the highly-sorbing MOF transforms the permeation experiment in a sort of breakthrough experiment. The reason for the apparently slower diffusion is the accumulation of the gas inside the pores of the filler, similar to the phenomenon of immobilizing adsorption [56,57], but in this case it has a virtually negligible net effect on the permeability.
In contrast to the effect in Pebax ® 1657, CuNi-MOF causes a drastic increase in the gas permeability for all gases as function of MOFs loading in the glassy PEEK-WC, and the order of permeation obeys that of the diffusion-controlled gas transport mechanism with H 2 > CO 2 > O 2 > N 2 > CH 4 , typical for glassy polymers (Figure 6a). The increase in permeability is a direct consequence of an increase in diffusion coefficient (Figure 6b), whereas there is no substantial change in solubility coefficient (Figure 6c). The enhanced diffusion clearly indicates transport within the pore structure of CuNi-MOFs, which increases the total free volume of MMMs promoting the gas diffusion for all gases. The presence of MOF with chemical groups having a high affinity for CO 2 increases its solubility, its CO 2 /CH 4 and CO 2 /N 2 solubility selectivity (Figure 6f), and ideal selectivity for these two gas pairs (Figure 6d). Instead, the diffusion selectivity is not strongly affected by CuNi-MOF. In contrast to the effect in Pebax ® 1657, CuNi-MOF causes a drastic increase in the gas permeability for all gases as function of MOFs loading in the glassy PEEK-WC, and the order of permeation obeys that of the diffusion-controlled gas transport mechanism with H2 > CO2 > O2 > N2 > CH4, typical for glassy polymers (Figure 6a). The increase in permeability is a direct consequence of an increase in diffusion coefficient (Figure 6b), whereas there is no substantial change in solubility coefficient (Figure 6c). The enhanced diffusion clearly indicates transport within the pore structure of CuNi-MOFs, which increases the total free volume of MMMs promoting the gas diffusion for all gases. The presence of MOF with chemical groups having a high affinity for CO2 increases its solubility, its CO2/CH4 and CO2/N2 solubility selectivity (Figure 6f), and ideal selectivity for these two gas pairs (Figure 6d). Instead, the diffusion selectivity is not strongly affected by CuNi-MOF. For a better understanding of the transport phenomena of gas separation membranes, the diffusion and solubility coefficients are often correlated with the molecular properties of gases [58]. For a better understanding of the transport phenomena of gas separation membranes, the diffusion and solubility coefficients are often correlated with the molecular properties of gases [58]. Both neat polymers show a linear dependency of the diffusivity (D) on the squared gas diameter (d 2 eff ) (Figure 7a,b), suggesting that the gas transport in neat polymers follows the diffusion solution model. In the presence of the MOF, both polymers show non-linearity of the D vs. d 2 eff correlation (Figure 7), which becomes more evident at higher MOF loading. A similar trend was recently observed for PIMs [59], where it was attributed to a different size-selectivity for small and large gas species due to the highly-interconnected free volume. These results suggest that the CuNi-MOF particles, with their internal void structure, have a similar effect on the gas diffusion of Pebax ® 1657 and PEEK-WC, introducing preferential diffusion pathways into the system which change the main transport mechanism, especially for the small molecules. As described above, the remarkably lower effective diffusion in Pebax ® 1657 is due to the much higher sorption capacity of the MOFs than of the neat Pebax ® 1657 [43]. Only for the CO 2 /N 2 gas pair, there is a remarkable inversion from preferential N 2 diffusion in the neat Pebax ® 1657 to preferential CO 2 diffusion for the sample with the highest MOF concentration. Instead, in the glassy PEEK-WC, with much lower intrinsic diffusion coefficients in the neat polymer, the MOF has a strong positive effect on the total permeability of the mixed matrix membrane due to the far more rapid diffusion through the cages of the MOFs. In PEEK-WC, after an initial decrease, compared to the neat polymer, the solubility of all gases increases with the CuNi-MOF concentration. This is similar to what was observed in Pebax ® 1657, but only in PEEK-WC leads to an increasing permeability due to the positive effect on the diffusivity as well.
( Figure 7a,b), suggesting that the gas transport in neat polymers follows the diffusion solution model. In the presence of the MOF, both polymers show non-linearity of the D vs. d 2 eff correlation (Figure 7), which becomes more evident at higher MOF loading. A similar trend was recently observed for PIMs [59], where it was attributed to a different size-selectivity for small and large gas species due to the highly-interconnected free volume. These results suggest that the CuNi-MOF particles, with their internal void structure, have a similar effect on the gas diffusion of Pebax ® 1657 and PEEK-WC, introducing preferential diffusion pathways into the system which change the main transport mechanism, especially for the small molecules. As described above, the remarkably lower effective diffusion in Pebax ® 1657 is due to the much higher sorption capacity of the MOFs than of the neat Pebax ® 1657 [43]. Only for the CO2/N2 gas pair, there is a remarkable inversion from preferential N2 diffusion in the neat Pebax ® 1657 to preferential CO2 diffusion for the sample with the highest MOF concentration. Instead, in the glassy PEEK-WC, with much lower intrinsic diffusion coefficients in the neat polymer, the MOF has a strong positive effect on the total permeability of the mixed matrix membrane due to the far more rapid diffusion through the cages of the MOFs. In PEEK-WC, after an initial decrease, compared to the neat polymer, the solubility of all gases increases with the CuNi-MOF concentration. This is similar to what was observed in Pebax ® 1657, but only in PEEK-WC leads to an increasing permeability due to the positive effect on the diffusivity as well.

Mixed Gas Transport Properties
Mixed gas permeation measurements were carried out on the representative membranes with the highest MOF concentration in each polymer in view of two relevant industrial gas separations, namely biogas upgrading and CO 2 capture from flue gas, involving CO 2 separation from CH 4 and N 2 , respectively ( Figure 8) (See Table SI [4][5]. For this purpose, measurements were performed from 1 to 6 bar(a) with simulated flue gas (CO 2 /N 2, 15/85 vol %) and simulated biogas (CO 2 /CH 4 , 35/65 vol %). The glassy PEEK-WC MMM exhibits typical dual-mode behavior with the CO 2 /CH 4 mixture, showing a decrease of CO 2 permeability as a function of the increased feed pressure, which causes a simultaneous and slightly smaller decrease of CO 2 /CH 4 selectivity. This indicates that the free volume in the PEEK-WC phase and in the MOFs' pores is gradually becoming occupied by CO 2 , and as a result, the CH 4 permeability slightly decreases as a function of pressure. Moreover, some hysteresis of CO 2 and CH 4 permeability is observed when reducing the pressure after the initial pressure increase steps. This is ascribed to a slight CO 2 -induced dilation of the polymer, leaving a higher free volume when the pressure is decreased, and thus a higher CH 4 permeability and a slightly lower selectivity. In the separation of the CO 2 /N 2 mixture, no further hysteresis takes place because of the lower CO 2 partial pressure, and for the same reason the CO 2 permeability is slightly higher than in the biogas mixture.
Contrary to the glassy PEEK-WC, the rubbery Pebax ® 1657/CuNi-MOF (23 wt %) membrane shows essentially pressure-independent permeability and selectivity (Figure 8a), after only a slight increase in permeability with pressure in the first run, apparently due to a certain conditioning of the sample. The transport properties of the Pebax-based membrane are dominated by the rubbery phase, and the dispersed MOFs only provide a higher gas sorption capacity in the membrane but do not significantly affect the overall performance.

Mixed Gas Transport Properties
Mixed gas permeation measurements were carried out on the representative membranes with the highest MOF concentration in each polymer in view of two relevant industrial gas separations, namely biogas upgrading and CO2 capture from flue gas, involving CO2 separation from CH4 and N2, respectively (Figure 8) (See Table SI [4][5]. For this purpose, measurements were performed from 1 to 6 bar(a) with simulated flue gas (CO2/N2, 15/85 vol %) and simulated biogas (CO2/CH4, 35/65 vol %). The glassy PEEK-WC MMM exhibits typical dual-mode behavior with the CO2/CH4 mixture, showing a decrease of CO2 permeability as a function of the increased feed pressure, which causes a simultaneous and slightly smaller decrease of CO2/CH4 selectivity. This indicates that the free volume in the PEEK-WC phase and in the MOFs' pores is gradually becoming occupied by CO2, and as a result, the CH4 permeability slightly decreases as a function of pressure. Moreover, some hysteresis of CO2 and CH4 permeability is observed when reducing the pressure after the initial pressure increase steps. This is ascribed to a slight CO2-induced dilation of the polymer, leaving a higher free volume when the pressure is decreased, and thus a higher CH4 permeability and a slightly lower selectivity. In the separation of the CO2/N2 mixture, no further hysteresis takes place because of the lower CO2 partial pressure, and for the same reason the CO2 permeability is slightly higher than in the biogas mixture.
Contrary to the glassy PEEK-WC, the rubbery Pebax ® 1657/CuNi-MOF (23 wt %) membrane shows essentially pressure-independent permeability and selectivity (Figure 8a), after only a slight increase in permeability with pressure in the first run, apparently due to a certain conditioning of the sample. The transport properties of the Pebax-based membrane are dominated by the rubbery phase, and the dispersed MOFs only provide a higher gas sorption capacity in the membrane but do not significantly affect the overall performance.

Robeson's Plots and Performance Overview
The gas transport properties for all membranes are summarized in the Robeson diagrams in Figure 9 for four gas pairs representing industrially important separations: CO2/N2, CO2/CH4, O2/N2 and H2/N2.

Robeson's Plots and Performance Overview
The gas transport properties for all membranes are summarized in the Robeson diagrams in Figure 10 for four gas pairs representing industrially important separations: CO 2 /N 2 , CO 2 /CH 4 , O 2 /N 2 and H 2 /N 2 .

Robeson's Plots and Performance Overview
The gas transport properties for all membranes are summarized in the Robeson diagrams in Figure 9 for four gas pairs representing industrially important separations: CO2/N2, CO2/CH4, O2/N2 and H2/N2. upper bound [8,9]; yellow line 2015 [60]; purple line 2019 upper bound [61]. The arrows qualitatively indicate the direction of increasing MOF loading. The clouds of blue "X" and red "X" symbols represent the mixed gas data in the pressure range of 1-6 bar for Pebax1657/CuNi-MOF at 29 wt % and PEEK-WC/CuNi-MOF at 23 wt % of MOF loading. Please refer to the electronic version for colour figures.
For all gases except H2, the neat rubbery Pebax ® 1657 is more permeable than the neat glassy PEEK-WC. On the other hand, PEEK-WC is more selective than Pebax ® 1657 for all gas pairs, except for the CO2/N2 separation (Figure 9a). For the CO2/N2 gas pair, with the nearly identical diameters of the molecules, the selectivity is almost entirely due to solubility selectivity, which is higher in Pebax then in PEEK-WC. However, whereas CuNi-MOF in Pebax ® 1657 has a marginal effect, CuNi-MOF in the glassy PEEK-WC increases drastically not only the CO2/N2 selectivity (from 25 to 37), but also the CO2 permeability (from 6 to ~50 Barrer), near the CO2 permeability of the rubbery Pebax ® 1657 (PCO2 ~69 Barrer) (Figure 9a).
For CO2/CH4 separation, the PEEK-WC-based MMMs show far superior properties than the Pebax ® -based membranes, which hardly change with the MOF concentration. A strong contribution of size selectivity between CO2 and the much bulkier CH4 molecules ( Figure 7b) and a further increase of both solubility and diffusivity with increasing MOF concentration leads to enhanced selectivity (from 30 to ~50, above that of Pebax) and CO2 permeability (from 6 to ~50 Barrer), exceeding the 1991 Robeson upper bound. For both mixtures, the performance is very similar to the ideal selectivity and pure gas permeability, indicating the absence of a significant coupling effect (Figure 9b).
The O2/N2 separation (Figure 9c) is mainly due to diffusion selectivity. Neither the permeability nor the selectivity changes much in Pebax ® 1657 upon the addition of CuNi-MOF, but in PEEK-WC the permeability of both gases increases 5-fold in the presence of 23 wt % CuNi-MOF, maintaining an almost constant O2/N2 selectivity.
Finally, the trend for H2/N2 separation is similar to that of O2/N2, but in this case, for both polymers, the MOFs also have a slightly higher H2/N2 selectivity than the neat polymers, as a result of increased diffusion selectivity. The H2 permeability in Pebax ® 1657 slightly increases from 8 to 11 Barrer, and the H2/N2 selectivity and permeability in the PEEK-WC/CuNi-MOF MMMs both strongly increase, surpassing the 1991 upper bound.  [8,9]; yellow line 2015 [60]; purple line 2019 upper bound [61]. The arrows qualitatively indicate the direction of increasing MOF loading. The clouds of blue "X" and red "X" symbols represent the mixed gas data in the pressure range of 1-6 bar for Pebax1657/CuNi-MOF at 29 wt % and PEEK-WC/CuNi-MOF at 23 wt % of MOF loading. Please refer to the electronic version for colour figures.
For all gases except H 2, the neat rubbery Pebax ® 1657 is more permeable than the neat glassy PEEK-WC. On the other hand, PEEK-WC is more selective than Pebax ® 1657 for all gas pairs, except for the CO 2 /N 2 separation (Figure 10a). For the CO 2 /N 2 gas pair, with the nearly identical diameters of the molecules, the selectivity is almost entirely due to solubility selectivity, which is higher in Pebax then in PEEK-WC. However, whereas CuNi-MOF in Pebax ® 1657 has a marginal effect, CuNi-MOF in the glassy PEEK-WC increases drastically not only the CO 2 /N 2 selectivity (from 25 to 37), but also the CO 2 permeability (from 6 to~50 Barrer), near the CO 2 permeability of the rubbery Pebax ® 1657 (PCO 2 69 Barrer) (Figure 10a).
For CO 2 /CH 4 separation, the PEEK-WC-based MMMs show far superior properties than the Pebax ® -based membranes, which hardly change with the MOF concentration. A strong contribution of size selectivity between CO 2 and the much bulkier CH 4 molecules ( Figure 7b) and a further increase of both solubility and diffusivity with increasing MOF concentration leads to enhanced selectivity (from 30 to~50, above that of Pebax) and CO 2 permeability (from 6 to~50 Barrer), exceeding the 1991 Robeson upper bound. For both mixtures, the performance is very similar to the ideal selectivity and pure gas permeability, indicating the absence of a significant coupling effect (Figure 10b).
The O 2 /N 2 separation (Figure 10c) is mainly due to diffusion selectivity. Neither the permeability nor the selectivity changes much in Pebax ® 1657 upon the addition of CuNi-MOF, but in PEEK-WC the permeability of both gases increases 5-fold in the presence of 23 wt % CuNi-MOF, maintaining an almost constant O 2 /N 2 selectivity.
Finally, the trend for H 2 /N 2 separation is similar to that of O 2 /N 2 , but in this case, for both polymers, the MOFs also have a slightly higher H 2 /N 2 selectivity than the neat polymers, as a result of increased diffusion selectivity. The H 2 permeability in Pebax ® 1657 slightly increases from 8 to 11 Barrer, and the H 2 /N 2 selectivity and permeability in the PEEK-WC/CuNi-MOF MMMs both strongly increase, surpassing the 1991 upper bound.

Conclusions
The development of novel, well-performing gas separation membranes requires a good understanding of their transport properties. This is even more important for complex systems such as mixed matrix membranes in which a porous filler is dispersed in the polymer matrix. Therefore, this work describes the comparison of the performance of two sets of membranes, glassy PEEK-WC membranes and rubbery Pebax ® 1657 membranes, with different concentrations of an oxamate-based CuNi-MOF. An increase of the Young's modulus for both membrane sets confirms that the MOF increases the stiffness of the polymer. In the case of the Pebax ® 1657 membrane, this is also accompanied by a slight shift of the melting peak of the PEO phase to higher temperatures, which suggests a good interaction of the MOF with the PEO phase. On the other hand, the presence of the MOF reduces the melting enthalpy and thus the overall crystallinity of both the PEO phase and the PA phase of Pebax ® , whereas it does not affect the glass transition temperature of PEEK-WC. Only for PEEK-WC, along with the Young's modulus, the tensile strength also increases, but for both polymers, the maximum deformation decreases with the addition of the MOF.
In terms of transport properties, the permeability of PEEK-WC strongly increases with increasing MOF content, mostly due to an increase in the effective diffusion coefficient, whereas unexpectedly, the effective diffusion coefficient in Pebax ® 1657 drastically decreases upon addition of the MOF. This is almost completely compensated by an increase in solubility so that the permeability remains nearly constant. The increase in diffusivity favors especially the smaller gas species, and as a result, the PEEK-WC MMMs show a simultaneous increase in CO 2 permeability and CO 2 /CH 4 selectivity, and the membranes with the highest MOF loading approach Robeson's 2008 upper bounds for these gas pairs. In the range of 1-6 bar(a), the mixed gas permeation tests with CO 2 /N 2 15/85 vol % and CO 2 /CH 4 35/65 vol % mixtures show only a weak pressure-dependence for the CO 2 /CH 4 mixture in PEEK-WC with 30% MOF, typical for materials with dual-mode sorption behaviour, but not for the CO 2 /N 2 mixture in PEEK-WC and for both mixtures in the Pebax-based MMMs.
In summary, the detailed analysis of the gas transport properties of the two series of MMMs highlights the enormous impact of the polymer matrix on the effectiveness of the same MOF when it is embedded in a rubbery or a glassy polymer. Even if the MOF improves significantly the gas solubility, this may not have a positive effect on the permeability if the diffusivity is not increased simultaneously. The successful development of better-performing MMMs can therefore not rely on studies of only the overall permeability but necessitates knowledge of the individual solubility and diffusion coefficient. For both parameters, the values of the polymer and the porous filler should be carefully matched to yield optimum performance.