## 4 Discussion  
### Influence of Filler Content on Water Uptake  
Once the moisture is absorbed on the upstream surface of the material, it diffuses across the thickness of the protective films and penetrates the panel, accumulating in it. The use of a protective coating with nanolamellar architecture showed a significant reduction of the moisture uptake and the absorption rate. The efficacy of protection against water uptake (\(\eta\)) has been estimated according to Equation (5). \[\eta=\frac{M_{P}-M_{Ref}}{M_{Ref}} \tag{5}\]  
where \(M_{P}\) and \(M_{Ref}\) are the values of the moisture uptake in the coated panel and in the reference panel after 3 days and 41 days, respectively. The parameter \(\eta\) represents the mass uptake saved with respect to the unprotected system. The data of efficiency are reported in Table 6 for all the analysed panels. It is at maximum for panels protected with 70 wt% of GNPs and then decreases with filler content, both at 3 days and 41 days. Further, the efficacy is higher at shorter periods of time, highlighting that the protective coating not only reduces the maximum moisture uptake at saturation but slows the absorption phenomenon over time. The hydrophobic nature of GNPs, combined with the very high in-plane orientation of nanoplatelets and the low matrix content, creates an impervious path for vapour and gases [54]. For a material filled with nanoplatelets, oriented perpendicular to the diffusion direction, the diffusivity depends on the matrix diffusivity and on the path that the molecules follow when they cross the two phases [55]. The longer the distance travelled by the diffusing molecule across the film's thickness, the more tortuous the pathway. [PERSON] et al. found that the lateral size of the nanoplatelet influences the permeability of the film, and a high lateral size of nanofiller results in a low transmission rate [56]. A tortuosity factor (\(\tau\)) is defined in Equation (6) for nanocomposites reinforced with lamellar-oriented nanoplatelets, which depends on the filler aspect ratio (\(AR\)) and volume fraction (\(\
u_{f}\)) [55]. It increases with the volumetric filler fraction, reducing asymptotically to zero. \[\tau=1+\frac{AR}{2}\cdot v_{f} \tag{6}\]  
According to Equation (6), the tortuosity factor in the case of GNP films loaded with 70, 80, and 90 wt% of GNPs are computed and listed in Table 7. By increasing the nanofiller content, the nanoarchitecture of the films, composed of highly oriented nanoplatelets, should force the water molecules to move in an increasingly tortuous path, resulting in a reduction of diffusion through the protective film. \begin{table}
\begin{tabular}{c c c} \hline
**ID** & \(\boldsymbol{\eta}\) **(t = 3 Days)** & \(\boldsymbol{\eta}\) **(t = 41 Days)** \\ \hline P70 A & \(-82\pm 3\%\) & \(-35\%\pm 4\%\) \\ P70 B & \(-79\%\pm 2\%\) & \(-32\%\pm 6\%\) \\ P80 A & \(-71\%\pm 4\%\) & \(-21\%\pm 2\%\) \\ P80 B & \(-65\%\pm 3\%\) & \(-20\%\pm 2\%\) \\ P90 A & \(-61\%\pm 4\%\) & \(-14\%\pm 5\%\) \\ P90 B & \(-61\%\pm 5\%\) & \(-14\%\pm 3\%\) \\ \hline \end{tabular}
\end{table} 
Table 6: Effective protection against moisture uptake at 3 days and 41 days. On the contrary, experimental data showed that in panels coated with GNP films, the absorption depends on the coating composition and increases with an increasing nanofiller content. The lowest absorption is found in the panel protected with film @70 wt% of GNP. A rationale for this behaviour is found in the material's inner architecture. Morphological observations of previous works have revealed a maximum level of compaction in nanocomposites with 70 wt% of GNPs [57]. By increasing the filler content up to 90 wt%, the nanostructure is modified by the presence of dry spots and voids, as shown in the SEM images in Figure 7. The matrix phase at high filler contents appears to be discontinuous, partially covering the nanoplatelets' surface [46,58]. These uncovered areas may be detrimental to the barrier effect.