## 4 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(r)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(r)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(r), 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(r)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 [PERSON]'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. **Supplementary Materials:** The following are available online at [[http://www.mdpi.com/2076-3417/10/4/1310/s1](http://www.mdpi.com/2076-3417/10/4/1310/s1)]([http://www.mdpi.com/2076-3417/10/4/1310/s1](http://www.mdpi.com/2076-3417/10/4/1310/s1)), Table SI-1. List of MMMs prepared. Figure S-1 EDX of Pebax(r)1657/CuNi-MOF (a) and PEEK-WC/CuNi-MOF (b) at an accelerating voltage of 15 Kv. Figure S-2 SEM images of cross section for MMMs of Pebax(r)1657/CuNi-MOF and PEEK-WC/CuNi-MOF. Table S-2 Pure gas permeability, solubility and diffusion coefficients, and respective selectivity for neat Pebax1657 and Pebax1657/CuNi MMMs. Table S-3 Pure gas permeability, solubility and diffusion coefficients, and respective selectivity for neat PEEK-WC and PEEK-WC/CuNi MMMs. Table S-4 Mixed gas permeabilities and selectivities of PEEK-WC/CuNi 23 wt % membrane using binary mixture CO2/CH4 (35/65) at pressure of 1-6 bar.