## 3 Results
### Moisture Diffusion in Sandwich Plates  
The sorption curves of the Kevlar/epoxy sandwich with and without the protection are shown in Figure 5, where moisture uptake is plotted against the square root of time. The moisture uptake, \(M\), is evaluated according to Equation (3) [47]:  
\[M(t)=\frac{W(t)-W_{0}}{W_{0}}\% \tag{3}\]  
where \(W_{0}\) is the panel weight at time \(t\) = 0, before starting the test, and \(W(t)\) is the weight of the panel at each weighing step of Table 2.  
Results show that the GNP layer improves the resistance to moisture uptake, both in terms of maximum absorbance and diffusion rate. A reduction of 30% of the maximum moisture absorption has been observed in protected samples with respect to the reference Kevlar/epoxy sandwich (Table 5). The GNP layer also modifies the absorption curve. In the uncoated panel, the absorption rate is higher and the saturation is reached earlier compared to coated panels. The presence of the GNP films lowers the absorption rate, thanks to the tortuous path created by the well-oriented nanoparticles. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Filler** & **Resistance,** & **Width,** & **Length,** & **Thickness,** & **Resistivity,** \\
**Content** & **\(R\)** & **\(w\)** & **\(L\)** & **\(t\)** & **\(\rho\)** \\
**[wt\%]** & **[\(\Omega\)]** & **[mm]** & **[mm]** & **[\(\mu\)m]** & **[\(\Omega\)m]** \\ \hline
80 & 4.70 & \(10\) & \(55\) & \(72\) & \(8.54\times 10^{-5}\) \\
85 & 3.49 & \(11\) & \(57\) & \(71\) & \(6.75\times 10^{-5}\) \\
90 & 1.82 & \(16\) & \(40\) & \(73\) & \(4.96\times 10^{-5}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Values of electrical resistivity of GNP films. Figure 5: Moisture uptake with time of uncoated and coated panels. Furthermore, the material's diffusivity (\(D\)) has been calculated from the results of the moisture uptake test as a function of time, according to [PERSON]'s second law. It describes the time-dependent absorption of a gas or liquid into a sheet by accounting for accumulation into the material. If a gas or liquid is absorbed in a homogeneous and infinitely long sheet, an increase in mass (\(\Delta M\)) occurs as a function of time (\(t\)) until saturation (\(\Delta M_{\text{max}}\)). At short times (\(Dt\)/\(h^{2}\) < 0.06, or equivalently \(\Delta M/\Delta M_{\text{max}}\) < 0.55), [PERSON]'s second law can be approximated to a linear relationship between the relative mass gain and the square root of time (Equation (4)) [52]. \[ \begin{array}{c}\frac{\Delta M}{\Delta M_{\text{max}}}=\frac{4}{\sqrt{\pi}} \cdot\sqrt{\frac{Dt}{h^{2}}}\\ \\ D=\frac{\pi}{16}\cdot\frac{h^{2}}{t}\cdot\left(\frac{\Delta M}{\Delta M_{\text {max}}}\right)^{2}\end{array}  \tag{4}\]  
where \(\Delta M/\Delta M_{\text{max}}\) is the relative change in mass, and \(t\) and \(h\) are the time and the thickness of the sample, respectively. A sensible reduction of the water diffusivity is found for protected panels, as shown in Figure 6. In the case of the unprotected panel, the diffusivity is 3.8 \(\times\) 10\({}^{-12}\) m\({}^{2}\)/s, consistent with data reported in the literature [53]. When a GNP coating is applied, the diffusivity reduces by an order of magnitude, as shown in Figure 6. This reduction depends on the GNP content: a minimum value is observed in the case of P70 with a \(-\)90% reduction compared to P REF. By increasing the GNP content, the efficiency of protection of the coating reduces; the diffusivity in P90 reduces by \(-\)80% compared to the reference.