## 3 Results and Discussion
### 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.  
Figure 8: Pressure dependence of CO2 and CH4 permeabilities and CO2/CH4 selectivity using the binary mixture of CO2/CH4 (35:65 vol %) for Pebax®1657_23 wt % CuNi-MOF (**a**) and PEEK-WC_23% CuNi-MOF (**b**). Pressure dependence of CO2 and N2 permeabilities and CO2/N2 selectivity in binary mixture conditions for CO2/N2 (15:85 vol %) of Pebax®1657_23 wt % CuNi (**c**) and PEEK-WC_23% CuNi (**d**). Closed symbols for stepwise increase of the pressure and open symbols for the subsequent stepwise decrease of the pressure. Trend lines are plotted as a guide to the eye.  
For all gases except H2, the neat rubbery Pebax(r)1657 is more permeable than the neat glassy PEEK-WC. On the other hand, PEEK-WC is more selective than Pebax(r)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(r)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  
Figure 9: [PERSON]’s plots for CO2/N2 (**a**) CO2/CH4 (**b**) O2/N2 (**c**) H2/N2 (**d**) showing the data of Pebax1657/CuNi (blue) and PEEK-WC/CuNi at different MOF loadings of 0 wt % (= neat polymers, \(\bullet\),\(\bullet\)), 9 wt % (\(\blacktriangle\),\(\blacktriangle\)), 17 wt % (\(\blacktriangledown\),\(\blacktriangledown\)) and 23 wt % (\(\blacklozenge\),\(\blacklozenge\)). Blue line 1991 upper bound, red line 2008 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 “\(\times\)” and red “\(\times\)” 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.  
CO\({}_{2}\) permeability (from 6 to \(\sim\)50 Barrer), near the CO\({}_{2}\) permeability of the rubbery Pebax(r)1657 (PCO\({}_{2}\) \(\sim\)69 Barrer) (Figure 9a).  
For CO\({}_{2}\)/CH\({}_{4}\) separation, the PEEK-WC-based MMMs show far superior properties than the Pebax(r)-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 \(\sim\)50, above that of Pebax) and CO\({}_{2}\) permeability (from 6 to \(\sim\)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 O\({}_{2}\)/N\({}_{2}\) separation (Figure 9c) is mainly due to diffusion selectivity. Neither the permeability nor the selectivity changes much in Pebax(r)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(r)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.