## 3 Results and Discussion
### ORR Electrocatalytic Activities
This is supported by the elemental analysis results where the percentages of nitrogen obtained were 5.0%, 3.8%, and 1.8% for NrGO\({}_{325}\)-4, NrGO\({}_{100}\)-4, and NrGO\({}_{10}\)-4, respectively. Then, the ORR kinetics at different potentials were assessed with the Koutecky-Levich (K-L) plots obtained with the application of the K-L equation to the LSVs (in Figure 7) at rotation speeds in the range of 400 to 3000 rpm. The K-L plots of the graphene materials are presented in Figure S8, and those corresponding to Pt/C are shown in Figure S7c. For the graphene materials, the \(j^{-1}\) increases with increasing \(\omega^{-1/2}\), which suggests a first-order electrocatalytic oxygen reduction with respect to the concentration of oxygen dissolved. Additionally, all the K-L plots of the non-doped materials show different slopes, suggesting that \(\hat{n}_{O2}\) depends on the applied potential, while for the N-doped ones, the differences are less significant. This suggests that in this case, \(n_{\text{O2}}\) is less dependent on the potential. The ORR process in alkaline medium can proceed by two pathways: a direct one involving one step (Equation 2) or an indirect one involving two steps (Equation 3 and 4) [reference 2 in ESI]. \[\text{O}_{2}+\text{H}_{2}\text{O}+4\text{e}^{-}\rightarrow\text{HO}^{-} \tag{2}\]  
\[\text{O}_{2}+\text{H}_{2}\text{O}+2\text{e}^{-}\rightarrow\text{HO}_{2}^{-}+ \text{HO}^{-} \tag{3}\]  
\[\text{HO}_{2}{}^{-}+\text{H}_{2}\text{O}+2\text{e}^{-}\rightarrow\text{3 HO}^{-} \tag{4}\]  
The mean \(n_{O2}\) (\(\hat{n}_{\text{O2}}\)) values estimated from Equation 3 in ESI are depicted in Table 3, and Figure 8a shows the changes of \(n_{\text{O2}}\) with the applied potential. For the non-doped materials, as the potential decreases from 0.46 to 0.26 V versus RHE, there is an increase in \(n_{\text{O2}}\) values with \(\Delta\)E values of 1.0, 0.53, and 0.71 V for rGO\({}_{10}\)-3, rGO\({}_{100}\)-3, and rGO\({}_{325}\)-3, respectively. The variation for the N-doped materials is less significant with 0.40 \(\geq\Delta\)E \(\geq\) 0.22 V versus RHE. The results of mean \(n_{\text{O2}}\) values obtained suggest that rGO\({}_{100}\)-3 and rGO\({}_{325}\)-3 proceed through the indirect pathway, while rGO\({}_{10}\)-3, NrGO\({}_{10}\)-4, and NrGO\({}_{100}\)-4 seem to proceed through a mixed mechanism, similar to \(\hat{n}_{\text{O2}}\approx 3\). This behavior has already been reported for other N-doped structures [58]. On the other hand, for the NrGO\({}_{325}\)-4, a one-step \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & \(\mathbf{E_{\text{onset}}}\) **vs. RHE** & \(j_{L}\) **(mA cm\({}^{-2}\))** & \(\hat{n}_{\text{O2}}\) & **Tafel Slopes (mV dec\({}^{-1}\)) \({}^{*}\)** \\ \hline Pt/C (20 wt \%) & 0.94 & \(-\)4.70 & 4.0 & 89 \\ rGO\({}_{325}\)-3 & 0.81 & \(-\)3.40 & 2.6 & 98 \\ rGO\({}_{100}\)-3 & 0.80 & \(-\)2.92 & 2.2 & 48 \\ rGO\({}_{10}\)-3 & 0.80 & \(-\)3.46 & 3.1 & 65 \\ NrGO\({}_{325}\)-4 & 0.82 & \(-\)4.05 & 3.9 & 62 \\ NrGO\({}_{100}\)-4 & 0.80 & \(-\)3.94 & 3.3 & 99 \\ NrGO\({}_{10}\)-4 & 0.79 & \(-\)3.03 & 3.0 & 78 \\ \hline \hline \end{tabular} \({}^{*}\) normalized by the mass of catalysts  
\end{table} 
Table 3: Relevant ORR parameters for commercial Pt/C and activated carbons prepared. four-electron transfer mechanism seems to be the leading process, since \(\hat{n}_{O2}\) = 3.9. This value is equal to the one obtained for Pt/C. Additionally, this result is better than that obtained for the other N-doped carbon nanotubes and graphene [32; 59; 60]. The better ORR performances (\(j_{\mathrm{L}}\) and \(\hat{n}_{\mathrm{O2}}\)) of the N-doped materials in comparison with the non-doped may be related to the presence of nitrogen as explained before, while the differences between the three N-doped materials to the percentages and types of N species found could also be related to the particle size of the starting graphite.