## 1 Introduction
To isolate NFC from fibers, an enzymatic or chemical pretreatment is performed in order to weaken cellulosic fibers interactions, as well as to reduce the energy consumption of the production process during the mechanical step [67; 68; 69; 70]. The fibers have diameters within the nanometric scale and lengths in the order of few micrometers [58; 59], thus resulting in a very high aspect ratio, and can show an individual tensile modulus up to 100 GPa [71]. In several works, this material has been successfully employed as a reinforcing agent for polymeric structures [71; 72], especially due to its ability to achieve the percolation threshold already at few percent of loading, when opportunely dispersed in a matrix [59; 72]. As already mentioned, a previous work [52] investigated the gas transport properties of different type of NFC pure and in a 50/50 wt % blend with PVAm, showing that the resulting film has very interesting separation performances (CO\({}_{2}\)/N\({}_{2}\) larger than 400 and CO\({}_{2}\)/CH\({}_{4}\) larger than 350) at an intermediate relative humidity. At higher humidity, though, the material showed a strong decrement of the separation performances, most likely due to excessive water sorption, which caused a severe loss of mechanical integrity. To tackle this issue, one of the solutions is to functionalize the cellulosic fibers with a carboxymethylation process [73; 74]. This modification was already reported in numerous papers with specific properties attributed to carboxymethylated NFC, i.e., highly charged surface (which can lead to ionic interactions with other molecules), and more acid groups at the surface (for post-modification purpose) in comparison to neat NFC [75; 76]. Thanks to their many carboxylic functions on the surface, cmNFC fibers are able to be easily crosslinked with several amino compounds. For instance, at high temperatures they can be crosslinked with the amine functions of PVAm forming amide bonds [77], which improves the mechanical strength of the swollen PVAm membrane at high humidity, and thus, should enhance the gas transport properties of CO\({}_{2}\) through the swollen membranes with increasing water content present in the gas stream. To further improve the compatibility between PVAm and cmNFC, aminosilanes can be used [78; 79], such as 3-(2-Aminoethylamino) propyltrimethoxysilane (AEAPTMS). In this work, this aminosilane will be grafted on the cellulosic material by the reaction between the remaining hydroxyl moieties of cmNFC and the alkoxysilanes groups through silylation after hydrolysis/condensation reactions [78]. Beside, AEAPTMS bears two amine groups, one hindered and one unhindered, which can participate in the two pathway mechanisms presented in Figure 1, and thus, can enhance the CO\({}_{2}\) selectivity and permeability through the membrane in addition. In the current report, new bio based materials for CO\({}_{2}\) separation have been developed, based on cmNFC-PVAm crosslinked membranes with the presence of an aminosilane as a second fixed carrier to enhance the CO\({}_{2}\) permeability compared to the use of neat NFC [52; 65; 79], amino acids [64] or other type of aminosilane [79] in literature. The grafting of aminosilane has been optimized by following the hydrolysis/condensation reactions by \({}^{29}\)Si NMR analyses. Different strategies have been employed to produce performant and water-swellable crosslinked membranes. While Fourier-Transform InfraRed (FTIR) spectroscopy was used in order to observe the covalent bonds between amine and carboxylic functions, Differential Scanning Calorimetry (DSC) analyses were carried out to confirm the crosslinking and determine the thermal characteristics of the membranes. Mechanical tests were also performed to assess the mechanical strength of the membranes and then, water uptake were investigated to identify their swelling properties in presence of liquid water. Air permeability and surface hydrophilicity were also studied.