## 3 Results and Discussion
### Kinetic Study of Adsorption  
The progression of time reveals the nature of adsorption capability through adsorption kinetics. It is of utmost importance to determine the specific type of adsorption mechanism within a given system [52]. Table 1 provides a summary of the kinetic studies conducted on the adsorption of MB by NGC. Figure 10a illustrates kinetic plots for the pseudo-first-order adsorption of MB on NGC at constant temperatures and initial MB concentrations. The correlation coefficient \(R^{2}\) value, which is 0.8951 as presented in Table 1, indicates a moderate fit. However, the calculated equilibrium sorption capacity \(q_{e}\) of 1.4949 does not align with the experimental data of 4.6838, as shown in Table 1. This discrepancy suggests that a pseudo-first-order model is not suitable for accurately predicting MB adsorption kinetics on NGC [53; 54]. On the other hand, Figure 10b displays kinetic plots for the pseudo-second-order sorption kinetics of MB onto NGC. The calculated \(R^{2}\) value of 0.9996 indicates an excellent fit, and the computed value of the equilibrium adsorption capacity, \(q_{e}\), aligns well  
Figure 8: The impact of varying dosages on the adsorption of MB onto NGC. Figure 9: The impact of contact duration on the adsorption of MB onto NGC. with the experimental data. Therefore, the results strongly suggest that the adsorption of MB onto NGC follows a pseudo-second-order equation [55]. The Elovich Equation, which is commonly used to describe adsorption capacity, is presented in Table 1. A graphical representation in Figure 10c showcases the relationship between \(q_{t}\) and \(\ln\) (\(t\)). The Elovich constants, \(\alpha\) and \(\beta\), were determined by analyzing the intercept and slope, respectively, and their values are documented in Table 1. The correlation coefficient value of 0.9252 indicates the suitability of the Elovich model [56]. Figure 10d illustrates the kinetics of MB intraparticle diffusion. From the plot of \(q_{t}\) against \(t^{\alpha_{g}}\), the values of \(K_{diff}\) and \(R^{2}\) were determined as 0.0752 and 0.8912, respectively. The linearity observed in the plots (Figure 10d) suggests that intraparticle diffusion significantly contributes to the uptake of MB by NGC. This further confirms that the adsorption of MB onto NGC involves a multi-step process within its interior [57]. Furthermore, this interdependent relationship also suggests that the adsorption of MB on NGC occurred through a complex series of steps. When these steps are clearly distinguishable, the graph typically exhibits multiple intersecting lines. The initial line represents adsorption on the surface, while the subsequent lines illustrate intraparticle diffusion. Conversely, the absence of such distinct features in the graph indicates that the steps are not easily discernible, implying that intraparticle diffusion has been the predominant process right from the beginning of the interaction between MB and NGC. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline  & \multicolumn{2}{c}{**Pseudo-First-Order**} & \multicolumn{4}{c}{**Pseudo-Second-Order**} & \multicolumn{4}{c}{**Elovich**} & \multicolumn{4}{c}{**Intraparticle Diffusion**} \\ \hline \hline \(K_{1}\) & \(\{q_{t}\}_{t=t_{\text{exp.}}}\) & \(\{q_{t}\}_{t=t_{\text{calc.}}}\) & \(R^{2}\) & \(\{q_{t}\}_{t=t_{\text{exp.}}}\) & \(\{q_{t}\}_{t=t_{\text{calc.}}}\) & \(R^{2}\) & \(\{\alpha\}\) & \(\beta\) & \(R^{2}\) & \(B_{L}\) & \(K_{diff}\) & \(R^{2}\) \\ \hline
0.0078 & 4.6838 & 1.4949 & 0.8951 & 0.1893 & 4.6838 & 4.3840 & 0.9996 & \(1.964\times 10^{12}\) & 8.0775 & 0.9525 & 3.7679 & 0.0752 & 0.8912 \\ \hline \end{tabular}
\end{table} 
Table 1: The kinetic parameters related to the adsorption of MB onto NGC. Figure 10: Pseudo-first-order (**a**), pseudo-second-order (**b**), Elovich (**c**), and intraparticle diffusion (**d**) kinetics of the adsorption of MB on NGC. However, this information alone does not provide sufficient details to determine which of these two phases serves as the rate-limiting step [58].