## 2 Materials and Methods  
The epoxy matrix was based on a monomer denominated Araldite LY556, cured with an aromatic amine Araldite XB3473. Both components were provided by Antala Group, Cataluha, Spain. The curing was carried out at 140 \({}^{\circ}\)C for 8 h, reaching a glass transition temperature (T\({}_{\text{g}}\)) of 162-165 \({}^{\circ}\)C, measured by dynamic mechanical thermal analysis (DMTA).  
In this work, different graphene nanoplatelets have been used as nanofiller, the commercial denominations are AO1, AO2, AO3 and AO4, named in this work as GNP1, GNP2, GNP3 and GNP4, respectively. All of them were supplied by Graphene Laboratories Inc, Calverton, NY, USA with a purity close to 99%. Their main geometric characteristics are collected in Table 1. Dimensions were supplied by the manufacturer and corroborated by transmission electron microscopy (TEM).  
The manufacture of GNP/epoxy composites has been optimized in previous works [13; 14]. The procedure consists in GNPs dispersion, in all the proposed cases in a weight content of 0.5%, into the neat epoxy monomer using a high-speed mixer (Dispermat; Lumaquin, S.A, Barcelona, Spain) at 6000 rpm for 15 min to obtain the optimum doughnut effect. In order to remove the trapped air, once dispersion was completed, the mixture was degassed under vacuum at 80 \({}^{\circ}\)C for 15 min. Then, the stoichiometric ratio of the amine curing agent was added at 80 \({}^{\circ}\)C and the curing treatment was applied in an oven.  
The morphological study of pristine graphene nanoparticles and epoxy composites reinforced with different GNPs was carried out by Transmission Electron Microscopy (TEM, Phillips Tecnai 20 of 200 kV, FEI Company, Hillsboro, OR, USA) and Field-Emission Gun Scanning Electron Microscopy (FEG-SEM, Nova NanoSEM FEI 230, FEI Company). For electron microscopy (TEM and FEG-SEM), epoxy samples were cut by cryomicrotomy. In addition, the film was coated with a thin layer (5-10 nm) of Au for FEG-SEM observation. The experimental conditions of the sputtering were 30 mA for 120 s (Bal-tec, SCD-005 sputter).  
Bar-shape samples were cut with different dimensions: 35 \(\times\) 12 \(\times\) 1.5 mm\({}^{3}\) for DMTA (dynamic thermomechanical analysis) measurements and 60 \(\times\) 12.5 \(\times\) 2 mm\({}^{3}\) for flexural test. In order to carry out the study, samples were introduced in a hydrothermal chamber with a relative humidity of  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Graphene Type** & **Purity (\%)** & \begin{tabular}{c} **Specific Surface** \\ **Area (m/g\({}^{2}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Average Flake** \\ **Thickness (nm)** \\ \end{tabular} &
\begin{tabular}{c} **Average Particle Lateral** \\ **Dimension (\(\mu\)m)** \\ \end{tabular} \\ \hline
**AO1 (GNP1)** & 98.0 & 510 & 1.6 & \(\sim\)10 \\  & & & (less than 3 layers) & \\
**AO2 (GNP2)** & 99.9 & 100 & 8 & 0.55 (0.15-3) \\  & & & (20–30 layers) & \\
**AO3 (GNP3)** & 99.2 & 80 & 12 & 4.5 (1.5–10) \\  & & & (30–50 layers) & \\
**AO4 (GNP4)** & 98.5 & \(<\)15 & 60 & 3–7 \\  & & & (\(\sim\)180 layers) & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main geometric characterizes of graphene nanoplatelets.  
85% and a temperature of 40 \({}^{\circ}\)C. The moisture absorption was determined by gravimetric method. The samples were periodically removed and weighted with an accuracy of 0.01 mg. At selected times, some samples were tested by DMTA and flexural test.  
The mechanical characterization of composites was carried out by flexural test (ZwickLine Z2.5, Zwick-Roell, Ulm, Germany), following the ASTM D-790 (procedure A and B). DMTA was performed following the standard D5418-01, using the single cantilever bending mode in a DMTA Q800 V7.1 from TA Instruments, New Castle, DE, USA. All the experiments were carried out at 1 Hz frequency, by bending deformation, and scanning from 20 to 250 \({}^{\circ}\)C with a heating rate of 2 \({}^{\circ}\)C/min.