## 3 Results and Discussion
### Methylene Blue Adsorption Isotherms
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**adsorbent**} & \multicolumn{4}{c}{**Langmuir Model**} & \multicolumn{4}{c}{**Freundlich Model**} \\ \cline{2-9}  & \(\begin{array}{c}\textit{q}_{max}\\ \textbf{(mg\cdot g}^{-1}\end{array}\)) & \(\begin{array}{c}\textit{k}_{\textbf{L}}\\ \textbf{(L\cdot mg}^{-1}\end{array}\)) & \(\textbf{R}^{2}\) & \(\begin{array}{c}\textbf{Error}\\ \textbf{(\%)}\end{array}\) & \(\begin{array}{c}\textit{n}\\ \textbf{(mg\cdot g}^{-1}\textbf{)}\textbf{(g\cdot m}^{-1}\textbf{)}\end{array}\) & \(\textbf{R}^{2}\) & **Error (\%)** \\ \hline AC & 7.336 & 4.618 & 0.910 & 1.325 & 0.075 & 5.577 & 0.867 & 1.942 \\ \hline AC-21 & 8.399 & 1.394 & 0.971 & 0.753 & 0.150 & 4.674 & 0.782 & 2.326 \\ \hline AC-HAp & 6.446 & 2.106 & 0.891 & 2.024 & 0.107 & 4.315 & 0.875 & 1.622 \\ \hline AC-1h & 7.752 & 5.018 & 0.960 & 0.993 & 0.117 & 5.061 & 0.743 & 2.427 \\ \hline AC-1h21 & 8.846 & 1.598 & 0.920 & 1.521 & 0.096 & 5.710 & 0.658 & 2.095 \\ \hline AC-1 hHAp & 7.202 & 1.732 & 0.915 & 1.224 & 0.120 & 4.548 & 0.831 & 1.931 \\ \hline AC-2h & 9.144 & 1.436 & 0.932 & 0.937 & 0.111 & 5.846 & 0.735 & 2.120 \\ \hline AC-2h21 & 9.818 & 2.123 & 0.730 & 2.486 & 0.061 & 7.664 & 0.883 & 1.321 \\ \hline AC-2 hHAp & 7.959 & 1.148 & 0.985 & 0.846 & 0.160 & 4.223 & 0.793 & 2.285 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the adsorption models. For the MB adsorption, most of the adsorbents fitted the Langmuir model, where a formation of a monolayer of the adsorbed molecules existed in this adsorption process [38]. All the superficial sites had the same possibility of being occupied but only by one molecule  
Figure 9: Adsorption isotherms of methylene blue on various carbon-based materials: (**a**) AC, AC-21, and AC-HAp; (**b**) AC-1h, AC-1h21, and AC-1 hHAp; (**c**) AC-2h, AC-2h21, and AC-2 hHAp, at 36 \({}^{\circ}\)C, pH 7, and initial dose of 0.1 mg of each adsorbent. of the adsorbate at the same time, and, in addition, an interaction between the adsorbed molecules was not observed [39]. The AC-2h21 was adjusted for the Freundlich model, but its R\({}^{2}\) value in the Langmuir was very close to this one; for this reason, the Langmuir model was used to describe the MB adsorption phenomena for all the adsorbent materials. The Langmuir estimated the maximum adsorption capacity (q\({}_{\text{max}}\)) of the adsorbents, and an average value, as compared with other similar adsorbents, was observed [40; 41; 42; 43; 44], which increased with the HNO\({}_{3}\) treatment and the immersion of the SBF without CaSiO\({}_{3}\). Due to oxidation, the AC-1h and AC-2h showed a higher pore diameter, so a better interaction of the adsorbate molecule with the surface of the material was observed, with an increase from 7.33 mg\(\cdot\)g\({}^{-1}\) to 7.75 mg\(\cdot\)g\({}^{-1}\) and 9.14 mg g\({}^{-1}\). For the 21-day-incubated samples, the increase in the adsorption capacity occurred because of the PZC, AC-21 with a q\({}_{\text{max}}\) of 8.40 mg\(\cdot\)g\({}^{-1}\), AC-1h21 with a q\({}_{\text{max}}\) of 8.45 mg\(\cdot\)g\({}^{-1}\), and AC-2h21 with a q\({}_{\text{max}}\) value of 9.81 mg\(\cdot\)g\({}^{-1}\). For the adsorbents with HAp deposits in the pores, a decrease in the maximum adsorption capacity for the MB was observed (6.44, 7.20, and 7.95 mg\(\cdot\)g\({}^{-1}\), respectively, for the AC-HAp, AC-1 hHAp, and AC-2 hHAp). Many mechanisms have been attributed to adsorbent materials, such as electrostatic attraction, ion exchange, the formation of hydrogen bonds, pore-filling, and \(\pi\)-\(\pi\) interactions [45; 46; 47; 48]. Some of the mechanisms reported were excluded due to the monolayer formation of the adsorbate molecules on the surface of the adsorbent and the micropores in the AC [49]. Therefore, the mechanism by which MB was adsorbed onto the materials is due to the \(\pi\)-\(\pi\) interactions between the electron-\(\pi\) of the carbonaceous adsorbents and the electron-\(\pi\) of the aromatic ring of the adsorbate, according to the report by [PERSON] et al.