## 3 Results and Discussion
### Adsorption Isotherm  
To describe the adsorption process in the composite materials at four different temperatures (298, 318, 323, and 333 K), the experimental data were fitted to the Langmuir, Freundlich, Temkin II and Dubinin-Radushkevich models. The Langmuir model assumes that adsorption occurs in a single molecular layer on a uniform surface, where the adsorption sites are energetically equivalent, and the adsorbed molecules do not interact with each other. The maximum adsorption capacity, representing the maximum amount of adsorbate that can be retained by the adsorbent per unit mass, is determined through the Langmuir equation [38; 51]. \[\mathrm{q_{e}}=\frac{\mathrm{q_{m}K_{L}C_{e}}}{1+\mathrm{K_{L}C_{e}}} \tag{10}\] \begin{table}
\begin{tabular}{l c c c c} \hline
**Adsorbents** & **Kp (mg g\({}^{-1}\) min\({}^{-1/2}\))** & **C (mg g\({}^{-1}\))** & **Ri** & **R\({}^{2}\)** \\ \hline ZGO2.5 & 29 \(\pm\) 3 & 1.2 \(\pm\) 0.6 & 0.98 & 0.9287 \\ ZGO5.0 & 17 \(\pm\) 1 & 6.2 \(\pm\) 1.3 & 0.93 & 0.9888 \\ ZGO10 & 22 \(\pm\) 2 & 5.5 \(\pm\) 1.5 & 0.92 & 0.9006 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the intraparticle diffusion (IPD) model for MB adsorption on ZGO2.5, ZGO5, and ZGO10. Figure 8: Intraparticle diffusion plot showing three regions of linearity (C\({}_{0}\) = 100 mg L\({}^{-1}\), T = 298 K). where qm (mg g\({}^{-1}\)) represents the maximum adsorption capacity, and K\({}_{\rm L}\) (L mg\({}^{-1}\)) is the Langmuir constant, which is related to the adsorption free energy. The Freundlich model assumes that adsorption occurs on a surface with a heterogeneous distribution of energy at the active sites. This implies that the adsorption capacity varies across different regions of the surface. This model is described by equation [5]  
\[\rm{log}q_{e}=K_{F}C_{e}{}^{1/n} \tag{11}\]  
where K\({}_{\rm F}\) is the adsorption capacity (mg L\({}^{-1}\)), and n is the surface heterogeneity and intensity of adsorption. The Temkin II model studies the linear decrease in the heat of adsorption as the surface coverage increases in an adsorption process, considering the interactions between the adsorbed molecules; this model is represented by the following equation [52; 53]:  
\[q_{e}=q_{T}\,ln(1+K_{T}C_{e}) \tag{12}\]  
where qT = qm/f, with f being a dimensionless constant given by the sum of the exponential factors of the adsorption and desorption first-order rate equations, and K\({}_{\rm T}\) their ratio [53; 54]. The Dubinin-Radushkevich (D-R) model, a temperature-dependent model, is used to describe the adsorption mechanism, whether chemisorption or physisorption, on heterogeneous surfaces. It is based on the assumption of a Gaussian energy distribution [55]. The Dubinin-Radushkevich isotherm is represented by Equation (13) [54]  
\[q_{e}=q_{m}e^{-\beta[RTIn(\frac{\zeta_{h}}{\zeta_{e}})]^{2}} \tag{13}\]  
where \(\beta\) is a constant related to the mean free energy of adsorption E = 1/\(\sqrt{2\beta}\), Cs is the solute solubility, R is the universal gas constant (8.314 J mol\({}^{-1}\cdot\)  
The Temkin model also fitted the experimental data well and supported the idea of a non-uniform surface. This model assumes a distribution of adsorption energies on the adsorbent and considers that the adsorbed molecules interact with one another, affecting the adsorption energy of subsequent molecules [54; 55]. The Dubinin-Radushkevich (D-R) model provided additional insights into the adsorption mechanism. This model showed an adequate fit (R\({}^{2}\)) at temperatures above 298 K, suggesting that the adsorption process occurred in pores and was dominated by energy heterogeneity and diffusion. This behavior was supported by the intraparticle diffusion analysis of Weber-Morris, where the final stage corresponded to diffusion within the pores. The maximum adsorption capacity (qm) estimated by the D-R model ranged from 84 to 119 mg g\({}^{-1}\), exceeding the values determined by the Langmuir model.