## 3 Results and Discussion  
### Membrane Preparation  
In this report, we combined cmNFC raw material and an amine-based polymer to improve the compatibility between the nanofillers and the PVAm matrix by crosslinking with the use of amine-based fixed carriers to enhance the CO\({}_{2}\) permeability performance. Indeed, carboxylic acid functions of the cmNFC nanofillers can react with primary amine functions of the PVAm matrix to create a new covalent bond between the filler and the matrix by amidation [77]. AEAPTMS were also grafted onto cmNFC surface to enhance the compatibility between the filler and the matrix and to add new potential site for CO\({}_{2}\) capture. Such membranes were elaborated according the following strategy (Figure 3). The elaboration of the membranes was performed either in a one-step process (process A) or in a two-step process (process B). In process A, all components were mixed together in one pot, whereas in process B, the crosslinking between the nanofillers and the matrix was first carried out and then the grafting of the aminosilane was performed by dipping the crosslinked membranes inside the aminosilane solution. Process A could provide different type of crosslinking reactions. Indeed, the aminosilanes can react either with their amine end-chain groups (towards -COOH groups) or their siloxanes (towards -OH groups) inducing a second network but reducing the amount of potential free -NH\({}_{2}\) site for CO\({}_{2}\) capture. Process B was more controlled; all the carboxylic acid functions of the cmNFC nanofiller should first react with the pendant amine functions of the PVAm matrix and then the aminosilanes should only be grafting onto -OH groups by dipping for 5 min and curing for 2 h at 100 \({}^{\circ}\)C [81]. The approach of crosslinking chosen consisted in first creating ionic bonds between deprotonated -COO- groups of the cmNFC and the protonated NH\({}_{3}\)\({}^{+}\) at pH 4 and then forming the covalent bond by a heat-induced step at 100 \({}^{\circ}\)C for 2 h [81].  
The chemical modification of cmNFC with AEAPTMS was optimized by following the hydrolysis-condensation kinetics of the aminosilane in acidic D\({}_{2}\)O/EtOH (20/80) medium followed by \({}^{29}\)Si NMR (Figure 4) [78; 82; 83]. Different species were observed in the reaction medium: silanes (T0R), silanols (T0H), dimers (only T1), linear oligomeric chains (T1 and T2), and 3D-chains (T1, T2, and T3). In order to simplify the evaluation of the reactivity of the aminosilane solution over time, the active silanol reactivity (Active-SiO) of the solution was proposed as a measurement parameter. This simple parameter reflected the probability of number of SiO-sites that could be grafted onto the cmNFC surface. This parameter was adapted from an empirical expression proposed by [PERSON] et al. [84]  
\[Active-SiO=\frac{(3\times\%T0)+(2\times\%T1)+(1\times\%T2)}{3}, \tag{6}\]  
Figure 3: Strategies of elaboration of amine-functionalized cmNFC-PVAm crosslinked membranes.  
We opted for the chemical hydrolysis-condensation reactions occurring for 1.5 h in order to obtain mostly linear oligomers (presence of T1 and T2 species) with a probability of grafting superior to 50% and avoiding the presence of three-dimensional T3 species.