## 3 Results and Discussion
### Separation Performance  
The permeability coefficients of pure CO\({}_{2}\) and N\({}_{2}\) have been determined for two different feed humidity contents (75% and 95%) at 40 \({}^{\circ}\)C and 1.5 bar. The Table 5 summarized the permeation data for the pure and modified cmNFC-based membranes mixed with 20% PVAm. The gas transport properties of cmNFC were relevantly affected by the water content within the membrane matrix. The Table 5 showed that at RH = 75% the membrane presented low CO\({}_{2}\) permeability, 3 Barrer, whereas at high humidity content the permeability increased by 15 times, reaching a value of 40 Barrer. For hydrophilic materials, such as cmNFC, the presence of water \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & \multicolumn{5}{c}{**Elemental Weight Concentration**} & \multirow{2}{*}{**DS \({}^{\text{a,b}}\)**} \\ \cline{2-2} \cline{4-6}  & \%C & \%O & \%H & \%N & \%Si \\ \hline \multirow{2}{*}{cmNFC} & 44.1 & 50.0 & 5.9 & 0.0 & - \\  & (44.1) \({}^{*}\) & (49.8) \({}^{*}\) & (6.0) \({}^{*}\) & (-) \({}^{*}\) & (-) \({}^{*}\) & 0.32 \({}^{\text{a}}\) \\ \hline \multirow{2}{*}{cmNFC-PVAm} & 44.0 & 41.5 & 8.1 & 6.4 & - \\  & (46.6) \({}^{*}\) & (39.7) \({}^{*}\) & (7.1) \({}^{*}\) & (6.5) \({}^{*}\) & (-) \({}^{*}\) & 0.76 \({}^{\text{b}}\) \\ \hline \multirow{2}{*}{cmNFC-PVAm-AEAPT TMS-A} & 43.8 & 42.4 & 7.6 & 6.1 & 0.1 \\  & (43.4) \({}^{*}\) & (36.6) \({}^{*}\) & (7.6) \({}^{*}\) & (8.7) \({}^{*}\) & (3.8) \({}^{*}\) & 0.64 \({}^{\text{b}}\) \\ \hline \multirow{2}{*}{cmNFC-PVAm-AEAPT TMS-B} & 44.2 & 42.8 & 7.8 & 5.0 & 0.2 \\  & (43.4) \({}^{*}\) & (36.6) \({}^{*}\) & (7.6) \({}^{*}\) & (8.7) \({}^{*}\) & (3.8) \({}^{*}\) & 0.92 \({}^{\text{b}}\) \\ \hline \hline \end{tabular} \({}^{*}\) (theoretical values), DS \({}^{\text{a,b}}\) values relative to carboxymethyl groups \({}^{\text{a}}\) or amide groups \({}^{\text{b}}\).  
\end{table} 
Table 4: Elemental weight concentration of each element obtained by elemental analysis. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**PermCO\({}_{2}\)[Barrer]**} & \multicolumn{2}{c}{**Selectivity CO\({}_{2}\)/N\({}_{2}\)**} \\ \cline{2-4}  & [+/-5\%] & & **RH = 75\%** & **RH = 95\%** \\ \hline \multirow{2}{*}{cmNFC [64]} & 3 & 40 & 25 & 56 \\  & 10 & 50 & 20 & 71 \\  & 20 & 92 & 40 & 131 \\  & 20 & 90 & 40 & 128 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Permeation data for cmNFC, cmNFC-PVAm, cmNFC-PVAm, AEAPT TMS-A and cmNFC-PVAm-AEAPT TMS-B at 40 \({}^{\circ}\)C and 1.5 bar (Error calculated by sample repetition). induced an increase in gas permeability due to an extensive swelling and dilation of the membrane. The ideal selectivity for CO\({}_{2}\)/N\({}_{2}\) pairs increased also along with the water content in the membrane. The N\({}_{2}\) permeability seemed to be less affected by the water content due larger kinetic size and smaller solubility in water [52]. The addition of PVAm had a positive effect on the separation performance. The presence of PVAm induced an increase in CO\({}_{2}\) permeability, with a noticeable improvement at the lower humidity content. At 75% of humidity, the CO\({}_{2}\) permeability coefficient was increased by 233%, whereas at 95%, it was only by 25%. The addition of PVAm brought hydrophobicity, which induced clusters formation of water and a decrease of gas transport at high water content. The same behavior has been observed by [PERSON] et al. [52], the permeability of their MFC-Lupamine nanocomposite appeared to be less affected by the water content in the high activity range. The selectivity for CO\({}_{2}\)/N\({}_{2}\) pairs increased as well with the presence of PVAm within cmNFC but only by 27%, which could be related to higher air permeability of the cmNFC-PVAm membrane. When cmNFC was crosslinked with PVAm and aminosilanes, a clear enhancement of the separation performance was observed with respect to pure cmNFC membranes.