## 3 Results and Discussion
### 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 \({}^{\circ}\)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(r)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(r)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(r)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  
Figure 4: DSC thermograms for the membrane of (**a**) neat PeBax1657 and (**b**) neat PEEK-WC and MMMs with different concentration of CuNi-MOF during the second eating. 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. Figure 5: (**a**) Permeability, (**b**) diffusivity, and (**c**) solubility coefficients, and their respective selectivity towards N\({}_{2}\) (**d**,**e**,**f**) for each gas as functions of the weight percentage of CuNi-MOF in Pebax®1657. In contrast to the effect in Pebax(r)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. Figure 6: (**a**) Permeability, (**b**) diffusivity, (**c**) solubility coefficients, and respective N\({}_{2}\) selectivity (**d**,**e**,**f**) for each gas as functions of weight percentage of MOF loaded in PEEK-WC.