## 3 Results and Discussion
### Characterization of Solid Adsorbent  
The proprieties of GAC as an adsorbent solid were determined and evaluated, as these parameters are essential for obtaining an efficient adsorption process. Figure 10 illustrates the N\({}_{2}\) adsorption and desorption isotherm for GAC; the results show a behavior of type I isotherm, according to the International Union of Pure and Applied Chemistry (IUPAC) classification. This classification is characteristic of microporous solids with high selectivity. It was noticed that after adsorption and the combined processes, the solid maintained the isotherm with the same behavior; however, the volume of N\({}_{2}\) adsorbed at the relative pressures was slightly different from the volume obtained for natural GAC. This difference in N\({}_{2}\) volumes indicates that the specific values of textural characteristics changed throughout the three stages evaluated, as shown in Table 10.  
After adsorption, the surface area of commercial GAC (534.415 m\({}^{2}\)/g) decreases to 483.715 m\({}^{2}\)/g. This suggests that the available active sites of GAC were filled by the caffeine molecules [62]. The GAC used has a pore size larger than the CAF size of 0.78 \(\times\) 0.61 \(\times\) 0.21 nm [64], which guaranteed the adsorption process. Studies on the removal of organic compounds have also reported high efficii \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stage** & **A\({}_{\text{BET}}\) (m\({}^{2}\)/g)** & **V\({}_{\text{pore}}\) (cm\({}^{3}\)/g)** & **D\({}_{\text{pore}}\) (Å)** \\ \hline GAC & 534.415 & 0.120 & 4.818 \\ GAC-A & 483.715 & 0.105 & 4.816 \\ GAC-2 CP & 531.059 & 0.108 & 4.837 \\ GAC-4 CP & 576.459 & 0.139 & 4.836 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: BET/BH results for GAC textural characteristics, where -A is after adsorption, -2 CP is after second combined process, and -4 CP is after fourth combined process. Figure 10: N\({}_{2}\) adsorption and desorption isotherm for GAC. the adsorption operation, with similar values for surface area [20; 38; 45; 62; 66; 65] and for average pore diameter [20; 62; 66]. After the second cycle of the CP, the surface area increased to 531.059 m\({}^{2}\) g\({}^{-1}\), and after the fourth cycle, it reached 576.459 m\({}^{2}\) g\({}^{-1}\). These results highlight the role of the Fenton reaction as a regenerating agent for GAC, since in the second cycle, the surface area neared the one observed in natural GAC, and in the fourth cycle, it surpassed the initial surface area, indicating that the surface of activated carbon was oxidized by the Fenton reagent. Furthermore, the total pore volume of GAC after the second cycle of the combined process was 0.108 cm\({}^{3}\) g\({}^{-1}\), increasing to 0.139 cm\({}^{3}\) g\({}^{-1}\) after the fourth cycle. The average pore diameter was maintained in the microporosity range (less than 200 A) in both cases, indicating that the GAC remains microporous. Figure 11 shows the XRD patterns corresponding to the solid samples analyzed. The pattern obtained for activated carbon before and after adsorption reflects the characteristic structure of activated carbons, with main reflections at approximately 25\({}^{\circ}\) and 45\({}^{\circ}\)[17; 67; 68]. The peak at 25\({}^{\circ}\) is typical of the structure of disordered aromatic carbons, while the peak at 45\({}^{\circ}\) is associated with the planes of the hexagonal structure of the graphite phase, evidencing the characteristic behavior of non-crystalline amorphous solids [63; 67; 68; 69]. After adsorption and combined processes, the diffraction pattern of the GAC did not change significantly, but there were slight changes in the intensity of some signals, which can be attributed to the interaction between GAC and caffeine and between GAC and Fenton reagents. The absence of shifts in the basal spacings between the peaks indicates that the predominant interaction between caffeine and activated carbon occurred on the surface of the material [35; 45; 70].