## 3 Results and Discussion
### Adsorption Thermodynamics  
To analyze the energy variations associated with the adsorption of MB onto ZOG10 nanosheets, thermodynamic parameters such as the standard Gibbs free energy change (\(\Delta\text{G}^{0}\)), enthalpy change (\(\Delta\text{H}^{0}\)), and entropy change (\(\Delta\text{S}^{0}\)) were calculated using Equation (14) and the van't Hoff Equation (15), which expresses the changes of the equilibrium constant with the temperature [61]  
\[\Delta\text{G}^{0}=-\text{RTlnK}_{\text{e}} \tag{14}\]  
\[\frac{\text{dlnK}_{\text{e}}}{\text{dT}}=\frac{\Delta\text{H}^{0}}{\text{RT}^ {2}} \tag{15}\]  
For proper application of the van't Hoff equation, the equilibrium constant, Ke, must be dimensionless. Since Ke represents the thermodynamic equilibrium constant, it is derived from the distribution coefficient Kd of MB, related to MB distribution between the adsorbent and the aqueous phase (Figure S3). Using the linear portion of the adsorption isotherm data at four different temperatures, Kd (L mg\({}^{-1}\)) is determined by fitting the data to Equation (16) [62]  
\[\text{q}_{\text{e}}=\text{K}_{\text{d}}\text{C}_{\text{e}} \tag{16}\]  
To obtain a dimensionless equilibrium constant suitable for the van't Hoff equation, the following conversion (Equation (17)) was employed:  
\[\text{K}_{\text{e}}=\frac{\text{K}_{\text{d}}\text{M}_{\text{a}}\,*\,1000}{ \gamma_{\text{e}}} \tag{17}\]  
where Ma represents the molar weight of MB (319.85 g mol\({}^{-1}\)), and ye is the activity coefficient (dimensionless) of MB in solution [63], which, in the infinite dilution scale, approaches unity (ye = 1) [64]. Thus, the entropy (\(\Delta\text{S}^{0}\)) and enthalpy (\(\Delta\text{H}^{0}\)) parameters can be determined from Equation (17), which is a combination of Equations (14) and (15) [63, 65], by fitting the data of lnK\({}_{\text{e}}\) vs. T\({}^{-1}\) and assuming that the standard enthalpy change is independent of T in the small temperature interval considered (Figure 11):  
\[\text{ln}\frac{\text{K}_{\text{e}}}{\gamma_{\text{e}}}=\frac{\Delta\text{S}^{ 0}}{\text{R}}-\frac{\Delta\text{H}^{0}}{\text{RT}}\cong\text{l}_{\text{n}} \text{K}_{\text{e}} \tag{18}\]  
Figure 11: van’t Hoff regression for determining the thermodynamic parameters of MB adsorption onto ZOG10.  
The adsorption process is classified as physisorption when the \(\Delta\)G\({}^{\circ}\) values range from 0 to \(-\)20 kJmol\({}^{-1}\), while \(\Delta\)G\({}^{\circ}\) values between \(-\)80 and \(-\)400 kJmol\({}^{-1}\) indicate a chemisorption process. However, the distinction between these two categories is not entirely precise [5]. The calculated \(\Delta\)G\({}^{\circ}\) values, ranging from \(-\)29.1 to \(-\)35.5 kJmol\({}^{-1}\), indicated that the adsorption of MB onto ZGO10 occurred through a hybrid mechanism involving both physisorption and chemisorption. The spontaneity of this process at different temperatures, evidenced by the negative \(\Delta\)G\({}^{\circ}\) values, suggested a strong interaction between the MB ions and the ZGO10 surface, which was driven by the relatively high entropy change associated to the adsorption process (Table 5). This could be due to an ion exchange mechanism between MB and the cations contained in the composite material.  
On the other hand, the determined value of \(\Delta\)H\({}^{\circ}\) provided insights into the adsorption mechanism. Enthalpy values between 2.1 and 20.9 kJmol\({}^{-1}\) are characteristic of physical adsorption, dominated by low-energy interactions such as van der Waals forces, whereas values in the range of 80 to 200 kJ mol\({}^{-1}\) are typical of chemisorption processes, involving stronger chemical bonds. Therefore, a \(\Delta\)H\({}^{\circ}\) of 40 kJmol\({}^{-1}\) suggested that the predominant mechanism was a physico-chemical adsorption process, where physical and weak chemical interactions coexist, in line with the previously discussed Gibbs free energy values [61; 66].