## 3 Results and Discussion
### Tensile Properties
The B parameter of the Einstein model for the SCB-PE/GNPs no BM nanocomposites equals 35.3, and the corresponding value for the ball-milled samples is 51.5, indicating that the interfacial adhesion between the filler particles and the matrix is better in the case of the SCB-PE/GNPs w BM nanocomposites. The fitting of the Ji model on the experimental elastic modulus of the nanocomposites is presented in \[V_{f}^{dis}=\Big{(}1-f\Big{(}V_{f}\Big{)}\Big{)}\,V_{f}, \tag{12}\]7 As seen, the Ji model results in \(E_{c}\) values close to the elastic modulus values of SCB-PE/GNPs no BM nanocomposite, while in the case of the ball-milled samples, this model presents large deviations from the experimental data. The derived values of the interfacial modulus \(E_{i}(0)\) and the interphase's thickness \(\tau\) for both cases of the nanocomposites are presented in \[V_{f}^{dis}=\Big{(}1-f\Big{(}V_{f}\Big{)}\Big{)}\,V_{f}, \tag{12}\]8 The \(E_{i}(0)\) of the SCB-PE/GNPs no BM is 74.54, while the corresponding value for the ball-milled nanocomposites is 98.67; These results indicate a more extensive reinforcement of the interfacial modulus of the SCB-PE/GNPs w BM samples, possibly induced by the ball-milling process, which causes stronger interfacial adherence between the filler particles and the polymer matrix. Likewise, the derived \(\tau\) values for the SCB-PE/GNPs no BM and w BM nanocomposites are 29.45 and 43.9 nm, respectively, suggesting that the ball-milling step assists in the formation of a thicker interfacial layer around the platelet particle. \[V_{f}^{dis}=\Big{(}1-f\Big{(}V_{f}\Big{)}\Big{)}\,V_{f}, \tag{12}\]9 Theoretical modeling of elastic modulus for the SCB-PE/GNPs no BM and SCB-PE/GNPs w BM nanocomposites’ experimental data as a function of filler volume fraction, using the Ji and modified Halpin-Tsai models. The predicted \(E_{c}\) by the modified Halpin-Tsai equation is also presented in Figure 2, along with the prepared materials' experimental elastic modulus; the extracted results are shown in \[E_{agg}=E_{f}\Big{(}V_{f}-V_{c}\Big{)}^{c}, \tag{13}\]0 As observed, the elastic modulus behavior of SCB-PE/GNPs w BM nanocomposites is better described by the modified Halpin-Tsai model compared to the Ji fitting on the experimental data. For the solely melt-mixed samples, the predicted \(E_{c}\) values, while close to the experimental data, present larger deviations than the ones of the Ji fitting. The \(f_{W}\) parameter of the ball-milled samples presents a higher value compared to the solely melt-mixed samples, considering that the ball milling process causes a high curvature of the graphene nanoplatelets. The \(\alpha\) parameter from Equation (26) holds a similar value in both cases of the prepared materials. On the other hand, the \(\beta\) parameter's value of the SCB-PE/GNPs w BM is lower than that of the SCB-PE/GNPs no BM nanocomposites. Since this parameter is related to the degree of the filler's agglomeration, it can be suggested that the ball-milled nanocomposites present better GNPs dispersion compared to the solely melt-mixed counterpart, thus resulting in higher values of elastic modulus.