## 3 Results and Discussion
### Methylene Blue Adsorption Isotherms  
To comprehend the adsorption mechanism on the samples, charge distribution experiments were carried out. Figure 8 shows the charge distribution of the materials studied, according to the method reported by [PERSON] et al., 2011 [PERSON] et al. (2011). The hydroxyapatite presented a basic behavior characteristic, with a PZC of 10.91, while the rest of the materials (the AC and its respective modifications) had a more complex character and a PZC that varied depending on the oxidation degree and the CaSiO\({}_{3}\) addition. Figure 8: Charge distribution of the different materials. Figure 7: EDS analysis of carbon and HAp-modified carbon materials; (**a**) AC, (**b**) AC-HAp, (**c**) AC-1 hHAp, and (**d**) AC-2 hHAp. For the commercial material (AC), a PZC of 7.82 with a relatively basic distribution was observed, and the value was affected by its contact with the HNO\({}_{3}\), which tended to acidify the surface based on the time the material spent with the oxidizing agent due to the oxygenated functional groups formed [15; 34]. The AC-1h and AC-2h presented a PZC of 4.69 and 3.20, respectively [35]. The materials immersed in the SBF showed an increase in the PZC, with a tendency to be more basic, according to the charge distribution, due to the presence of ions from the SBF solution and hydroxyapatite deposits. The materials with only 21 days of incubation presented a basic behavior compared to the precursors (AC-1h and AC-2h), with a PZC of 7.48 and 8.28 for the AC-1h21 and AC-2h21, respectively. However, for the AC and AC-21 with PZCs of 7.89 and 7.01, a change in the PZC, determined by the insufficiency of the carboxylic sites that interact with the SBF ions, increased this value. Finally, the materials with the addition of CaSiO\({}_{3}\) during incubation showed the highest PZC values of 7.98, 8.78, and 8.98 for the AC-HAp, AC-1 hHAp, and AC-2 hHAp, respectively, and correlated to the HAp deposits on the surface, which presented a basic behavior in the aqueous solution [36]. Batch adsorption experiments were carried out, and the corresponding isotherms were performed. Figure 9 presents the adsorption isotherms of the non-oxidized materials (AC, AC-21, and AC-HAp in Figure 9a), the oxidized materials for 1h (AC-1h, AC-1h21, and AC-1 hHAp in Figure 9b), and the materials oxidized for 2h (AC-2h, AC-2h21, and AC-2 hHAp in Figure 9c) in varying initial concentrations. The materials presented very similar adsorption capacities, with an average removal percentage of 100% for the first two initial concentrations (0.5 and 1 mg\(\cdot\)L\({}^{-1}\)) and removal percentages of 96.78, 86.70, 73.24, 33.10, 16.21, and 8.22% for the concentrations of 2, 5, 10, 25, 50, and 100 mg\(\cdot\)L\({}^{-1}\), respectively. The relationship between the concentration of the methylene blue in the solution with respect to the amount removed in the equilibrium made an L-I type isotherm for the adsorption isotherms [37]: it started with a linear behavior at the beginning and gradually reduced the adsorption capacity until the surface was saturated with the adsorbate, and the equilibrium was reached. The parameters of the Langmuir and Freundlich models (Table 2) were calculated to estimate the adsorption capacity. An error (%), expressing the uncertainty of the measurements, is the ratio of the standard deviation divided by the average value of the measured constants. The average error value for the Langmuir model was 1.45%, and for the Freundlich model, it was 2.01%.