## 3 Results and Discussion
### Adsorption Kinetics Studies  
The experimental data were fitted to the pseudo-first-order, pseudo-second-order, and Elovich kinetic models to describe the adsorption kinetics of the materials. The pseudo-first-order kinetic model assumes that the rate of adsorption is directly proportional to the number of active adsorption sites on the adsorbent surface. This model can be mathematically expressed as follows [38]:  
\[\frac{\mathrm{d}\mathrm{q}_{\mathrm{t}}}{\mathrm{d}t}=\mathrm{k}_{1}(\mathrm{ q}_{\mathrm{e}}-\mathrm{q}_{\mathrm{t}}) \tag{3}\]  
\[\log\left(\mathrm{q}_{\mathrm{e}}-\mathrm{q}_{\mathrm{t}}\right)=\log\mathrm{ q}_{\mathrm{e}}-\frac{\mathrm{k}_{1}}{2.303}\mathrm{t} \tag{4}\]  
where \(\mathrm{k}_{1}\) is the rate constant of the pseudo-first-order sorption process (min\({}^{-1}\)), \(\mathrm{q}\mathrm{t}\) is the adsorption capacity at a specific time (t), and \(\mathrm{q}\mathrm{e}\) represents the equilibrium adsorption capacity (mg g\({}^{-1}\)). The pseudo-second-order kinetic model assumes that the rate of adsorption is proportional to the square of the number of unoccupied active sites. This model is described by the Ho equation [47]:  
\[\frac{\mathrm{d}\mathrm{q}_{\mathrm{t}}}{\mathrm{d}t}=\mathrm{k}_{2}\big{(} \mathrm{q}_{\mathrm{e}}-\mathrm{q}_{\mathrm{t}}\big{)}^{2} \tag{5}\]  
\[\frac{\mathrm{t}}{\mathrm{q}\mathrm{t}}=\frac{1}{\mathrm{k}_{2}\mathrm{q}_{ \mathrm{e}}^{2}}+\frac{1}{\mathrm{q}_{\mathrm{e}}}\mathrm{t} \tag{6}\]  
where \(\mathrm{q}\mathrm{e}\) and \(\mathrm{q}\mathrm{t}\) are the concentrations of MB per unit mass at equilibrium and time (t), respectively. The Elovich model describes the heterogeneous adsorption of an analyte by chemisorption, assuming no interactions between the adsorbed species. It is expressed by the following equation [48]:  
\[\mathrm{q}_{\mathrm{t}}=\left(\frac{1}{\beta}\right)\ln(\alpha\beta\mathrm{t} +1) \tag{7}\]  
where \(\alpha\) is the initial adsorption rate (mg.g\({}^{-1}\cdot\)min\({}^{-1}\)), and \(\beta\) is a constant (mg g\({}^{-1}\)) depending on the number of sites available for adsorption and desorption, related to surface coverage and activation energy. The kinetic analysis presented in the Figure 7 illustrates the fit of the pseudo-first-order and pseudo-second-order models, both achieving a coefficient of determination (R\({}^{2}\)) greater than 0.9, indicating their potential suitability. However, the pseudo-first-order model required longer contact times to reach equilibrium (plateau) compared to the pseudo-second-order model. Consequently, the pseudo-second-order model exhibited a better fit and aligned more closely with the data. In contrast, the [PERSON] model demonstrated a significantly poorer fit, as indicated by its low R\({}^{2}\) value, and was therefore excluded from further consideration. A comparison of the pseudo-first-order and pseudo-second-order models, based on the sum of squared errors (SSE) criterion, revealed that the pseudo-second-order model provided a more precise representation of the data. Graphene oxide, due to its large surface area, significantly enhanced the adsorption capacity of zeolite for methylene blue ions. This effect was attributed to \(\pi\)-\(\pi\) interactions between the aromatic ring of the dye and the graphene oxide structure [49], as well as to hydrogen bonding between the ammonium groups of methylene blue and the carboxylic  
Figure 7: Adsorption kinetics of MB on ZGO2.5, ZGO5, and ZGO10 as a function of contact time (up to 120 min). (**a**) Pseudo-first- and -second order models; (**b**) Elovich model. groups present in graphene oxide. This synergy greatly enhanced the adsorption capacity of the composite material. As shown in Table 1, the theoretical (qtcal) and experimental (qtexp) values of the maximum adsorption capacity aligned closely. However, increasing the proportion of graphene oxide did not lead to a proportional enhancement in the composite material's adsorption capacity.