## 3 Results and Discussion
### Adsorption Isotherm
Considering the nature of the process, the \(\beta\) parameter from the D-R model allowed for the calculation of the mean free energy (E = \(1/\sqrt{2\beta}\)), with values in the range of 9.4 to 13.0 kJ mol\({}^{-1}\). These results suggested a chemisorption mechanism [56]. As the temperature increased, the adsorbate molecules acquired greater kinetic energy, increasing their mobility, which facilitated their dispersion into the pores and enhanced their fixation at the active sites of the adsorbent. Figure 9: Fitting of the experimental isotherm data at different temperatures using the isotherm models of (**a**) [PERSON]; (**b**) [PERSON]; (**c**) [PERSON]; (**d**) Dubinin–Radushkevich. The adsorption mechanism of methylene blue (MB) onto ZGO can be explained through a synergistic process involving the following components: (1) electrostatic interactions; (2) \(\pi\)-\(\pi\) interactions; (3) hydrogen bonding; (4) cation exchange; (5) diffusion within the microporous structure (Figure 10). MB\({}^{+}\) is electrostatically attracted to the negatively charged sites of zeolite and the functional groups of GO. Simultaneously, \(\pi\)-\(\pi\) stacking interactions occur between the aromatic rings of MB and the graphenic regions of GO, stabilizing the adsorption. Additionally, the hydroxyl (-OH) and carboxyl (-COO\({}^{-}\)) groups of GO form hydrogen bonds with MB, facilitating its immobilization. The ion exchange capacity of zeolite, involving the exchange of cations (e.g., Na\({}^{+}\), K\({}^{+}\), Ca\({}^{2+}\)) with MB\({}^{+}\) from the solution, further enhances adsorption. Finally, MB can diffuse into the micropores of zeolite, where it becomes trapped through physical and chemical interactions, increasing the stability of the adsorption process. This combination of mechanisms grants ZGO a high capacity for removing cationic dyes from aqueous solutions. The mechanism can be represented as follows:  
\begin{tabular}{l c c c c} \hline
**Isotherm** & \multicolumn{4}{c}{**Temperatures**} \\
**Parameters** & **298 K** & **318 K** & **323 K** & **333 K** \\ \hline Langmuir model & & & & \\ KL (L mg\({}^{-1}\)) & 0.0085 \(\pm\) 0.001 & 0.023 \(\pm\) 0.005 & 0.020 \(\pm\) 0.005 & 0.023 \(\pm\) 0.005 \\ qm (mg g\({}^{-1}\)) & 58 \(\pm\) 6 & 65 \(\pm\) 4 & 81 \(\pm\) 5 & 83 \(\pm\) 5 \\ R\({}^{2}\) & 0.92371 & 0.9433 & 0.9401 & 0.9487 \\ SSE & 149 & 143 & 233 & 215 \\ Freundlich model & & & & \\ K\({}_{\rm F}\) (mg\({}^{(1-n)}\)g\({}^{-1}\) & 4.3 \(\pm\) 1.9 & 11.3 \(\pm\) 1.4 & 13.5 \(\pm\) 2.3 & 15.1 \(\pm\) 2.2 \\ L\({}^{1/n}\)) & 0.37 \(\pm\) 0.07 & 0.27 \(\pm\) 0.02 & 0.26 \(\pm\) 0.02 & 0.25 \(\pm\) 0.03 \\ R\({}^{2}\) & 0.8310 & 0.9686 & 0.9545 & 0.9620 \\ SSE & 329 & 79 & 177 & 159 \\ Temkin II model & & & & \\ q\({}_{\rm T}\) (mg g\({}^{-1}\)) & 14 \(\pm\) 3 & 12 \(\pm\) 1 & 15 \(\pm\) 2 & 14 \(\pm\) 1 \\ K\({}_{\rm T}\) (L mg\({}^{-1}\)) & 0.053 \(\pm\) 0.03 & 0.35 \(\pm\) 0.11 & 0.28 \(\pm\) 0.12 & 0.35 \(\pm\) 0.14 \\ R\({}^{2}\) & 0.9077 & 0.9828 & 0.9 Mn\({}^{+}\) is an exchangeable cation present in zeolite (Na\({}^{+}\), K\({}^{+}\), Ca\({}^{2+}\)). It is important to highlight the significant increase in methylene blue (MB) adsorption when incorporating graphene oxide into the zeolite structure. The contact time analysis showed that pristine zeolite had an adsorption capacity of qt = 37 mg g\({}^{-1}\) to 120 min, which increased with the addition of graphene oxide (Figure 6). This composite material achieved a maximum adsorption capacity (qm) of 119 mg g\({}^{-1}\), which is a competitive value compared to those of other adsorbents used in industrial applications (Table 4). Moreover, this performance underscored the feasibility of using zeolite, a low-cost material, as a base for developing advanced adsorbents. The combination with graphene oxide may not only enhance its efficiency but also expand its potential applications in various industrial processes, reinforcing its promise as an effective and economical adsorbent.