## 2 Materials and Methods
### Water Absorption Studies  
The water absorption was evaluated by monitoring the gravimetric change due to the amount of penetrant retained as a function of time, as adopted from the standard EN-ISO62:2008 [66]. In this study, immersion temperatures of 8, 23, 58, and 70 \({}^{\circ}\)C were selected to simulate the conditions of feasible applications of these materials. First, 8 \({}^{\circ}\)C was chosen as a typical temperature in a refrigerator for the storage of food packaging. Then, 23 \({}^{\circ}\)C represents standard room temperature, which is predominantly used for storing packaging materials and is referred to in the standards EN-ISO 62 [66] and ASTM D570-98 [67]. Next, 58 \({}^{\circ}\)C was selected as the usual temperature used for biodegradation studies of PLA [38,68], as described in the standards ASTM D6400-04 [69], ASTM D6868-03 [70], ASTM D5338-11 [71], ASTM D7081-05 [72], DIN EN 13432:2000-12 [73], or ISO 14855-2 [74]. Finally, 70 \({}^{\circ}\)C may simulate applications where higher temperatures can occur, such as in automobiles or electronic parts. It also allows seeing the water uptake behavior over the glass transition of PLA in the rubbery state. The immersion at 8 \({}^{\circ}\)C was carried out in a refrigerator from Aspes Type 4 FAC4858 (Mondragon, Spain), while the temperatures of 23, 58, and 70 \({}^{\circ}\)C were achieved in an oven from Heraeus Instruments Type B 12 (Hanau, Germany). The water absorption studies were performed in duplicates, considering two specimens per sample/condition, and averages and deviations were considered as representatives. To measure the mass change, the mass of the dry samples (\(m_{0}\)) was first obtained in a Mettler Toledo AB135-S scale (Columbus, OH, USA). Then, they were placed in glass vials, assuring complete immersion in distilled water at the given temperature. After certain periods, the samples were weighed once the traces of water on the surface (\(m_{1}\)) were removed. The percentage of absorbed water (\(M_{t}\)) was calculated according to Equation (3). With many measurements of \(M_{t}\), the water absorption profiles were obtained and used to determine the time needed to reach half-saturation (\(t_{1/2}\)). With this value, the diffusion coefficient (\(D\)) in the early stages of immersion was calculated according to Equation (4), where \(l\) is the thickness of the film [75]. Furthermore, the solubility coefficient (5) was calculated according to Equation (5), where \(m_{p}\) is the weight of the PLA matrix in the composite, \(m_{s}\) is the weight of the specimen at the equilibrium or peak of water absorption, and \(m_{0}\) is the initial weight of the specimen before immersion. Finally, the permeability coefficient (\(P\)) was obtained according to Equation (6) as a function of solubility and diffusion.  
The obtained results were evaluated using main effects plots (MEP) that help determine the isolated impact of the inputs of this study (temperature and composition) on the mentioned outputs (\(M_{s}\), \(D\), \(S\), and \(P\)). By calculating the arithmetic means by adding the numeric values for the respective levels, the influence of a single input can be analyzed, while the influences of the other inputs are cancelled.  
\[M_{t}(\%)=\frac{(m_{1}-m_{0})}{m_{0}}\times 100 \tag{3}\]  
\[D=\frac{0.01227l^{2}}{\texttt{t}_{1/2}} \tag{4}\]  
\[S=\frac{(m_{s}-m_{0})}{m_{p}} \tag{5}\]  
\[P=D\times S \tag{6}\]