## 6 Adsorption Isotherms
In general, the sorption process involves a combination of diverse types of interactions between adsorbent and sorbate including complexation, ion exchange, electrostatic interaction, and precipitation, which are the key mechanisms implicated in the sorption of dyes [35; 51]. In the present study, the adsorption capacity of Ca-rich cactus biochar for RB dye is significantly higher than that of adsorbents prepared from various feedstocks reported in previous studies [1; 31; 44]. For instance, [PERSON] et al. [1] found a maximum adsorption capacity for removing SFG CLL dye of around 49.0, 50.8, and 61.7 mg/g for biochar prepared from cow bone waste at 500, 600, and 700 \({}^{\circ}\)C, respectively. Likewise, [PERSON] et al. [47] tested Ca-rich biochars produced from the co-pyrolysis of poultry manure, date palm fronds, and waste marble powder for amoxicillin (AMX) removal. The highest AMX removal capacity was obtained for Ca-rich biochar prepared at 900 \({}^{\circ}\)C (56.2 mg/g) compared to biochars prepared at 700 \({}^{\circ}\)C (14.6 mg/g) and 800 \({}^{\circ}\)C (46.8 mg/g). The characteristics of the biochar, including its aromaticity and mineral content could be behind the difference in adsorption performance. Figure 6a compares the FTIR spectra of biochar before (CCB700) and after (CCB700-RB) adsorption tests, in order to highlight possible interactions. A remarkable difference can be noticed in the chemical features. As shown in the Supplementary Materials, the RB dye contains several functionalities: C=O, S=O, NH\({}_{2}\), and NH groups, while, as illustrated in Figure 2a, the FTIR spectrum of CCB700 reveals the existence of CaO and CaCO\({}_{3}\) at 1427, 874, and 708 cm\({}^{-1}\). After adsorption, these peaks weaken or disappear, suggesting that surface complexes can be generated between the Ca-rich biochar and the RB dye molecules via two possible mechanisms: (i) electrostatic attraction (CO\({}_{3}\)\({}^{2-}\)) and (ii) ion exchange (Ca\({}^{2+}\)) [32; 47]. On the other hand, the peak at 1613 cm\({}^{-1}\) is significantly intensified, which shows that the RB dye has been successfully adsorbed by the CCB700. A similar trend \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Sample** & \multicolumn{3}{c}{**[PERSON]**} & \multicolumn{3}{c}{**Freundlich**} \\ \hline  & **K\({}_{\rm L}\)** & **Q\({}_{\rm n}\) (mg/g)** & **R\({}_{\rm L}\)** & **R\({}^{2}\)** & **K\({}_{\rm L}\) (mg/g)** & **B\({}_{\rm r}\)** & **n** & **R\({}^{2}\)** \\ \hline CCB500 & 0.0708 & 39.3701 & 0.33 & 0.9984 & 9.0148 & 0.9852 & 1.0150 & 0.8270 \\ \hline CCB600 & 0.1174 & 51.2821 & 0.14 & 0.9896 & 9.0463 & 0.9537 & 1.0485 & 0.6106 \\ \hline CCB700 & 1.5752 & 56.1798 & 0.13 & 0.9999 & 9.6268 & 0.3732 & 2.6790 & 0.3275 \\ \hline \end{tabular}
\end{table} 
Table 3: Best-fit kinetic parameters for the Freundlich and Langmuir adsorption models and statistical indicators of the level of fit. for anionic Remazol Brilliant Blue R adsorption from aqueous solution using various crop residue waste-based biochars was reported by [PERSON] et al. [31]. The authors highlighted the importance of the biochar mineral matter content, which was among the factors behind differences in the dye adsorption performance. For example, the positive and high correlation between biochar Ca\({}^{2+}\) concentration and Q\({}_{\text{m}}\) implies the possibility of metal bonding or cation-\(\pi\) interaction. The influence of pH on adsorption efficiency may also be relevant to the mechanism between the adsorbent and the adsorbate [52]. In this study, the adsorption of the RB dye is optimal at an acidic pH2. The surface groups of the adsorbent are therefore protonated and electrostatically attracted to the negatively charged sulphonic acid group (-SO\({}_{3}\)H) of the anionic RB dye. This indicates significant electrostatic interactions between the RB dye and the CC biochar.