## 3 Results and Discussion
### Adsorption Kinetics and Adsorption Isotherms
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Kinetic Model** & **Parameter** & **SW** & **CM** & **AC1** & **AC2** & **CAC** \\ \hline \multirow{6}{*}{[PERSON]} & \(Q_{e}\) theoretical & \multirow{2}{*}{39.65} & \multirow{2}{*}{20.04} & \multirow{2}{*}{50.95} & \multirow{2}{*}{38.23} & \multirow{2}{*}{51.45} \\  & (mg/g) & & & & & \\  & (mg/g) & & & & & \\  & \(K\) (min\({}^{-1}\)) & 0.038 & 0.028 & 0.027 & 0.034 & 0.025 \\  & n & 0.25 & 0.11 & 0.22 & 0.20 & 0.304 \\  & r\({}^{2}\) & 1.0000 & 1.0000 & 0.9989 & 0.9943 & 0.9984 \\ \hline \multirow{2}{*}{[PERSON]} & \(K\) (g) & 18.62 & 13.60 & 24.11 & 20.39 & 17.95 \\  & \(\alpha\) & 0.19 & 0.094 & 0.18 & 0.16 & 0.25 \\  & r\({}^{2}\) & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 \\ \hline \multirow{2}{*}{Esquivel} & \(Q_{e}\) (mg/g) & 36.63 & 18.44 & 45.16 & 34.86 & 45.27 \\  & \(K\) (min) & 1.649 & 0.484 & 1.42 & 1.11 & 2.898 \\  & r\({}^{2}\) & 0.9572 & 0.9588 & 0.9604 & 0.9593 & 1.0000 \\ \hline \multirow{2}{*}{Pseudo 3 rd Order} & \(Q_{e}\) (mg/g) & 41.27 & 19.81 & 50.67 & 38.70 & 52.07 \\  & \(K_{3}\) (mg/g*min) & 0.73 & 3.38 & 0.86 & 1.16 & 0.38 \\  & r\({}^{2}\) & 0.9763 & 0.9714 & 0.9806 & 0.9785 & 0.9741 \\ \hline \multirow{2}{*}{Pseudo 2 nd Order} & \(Q_{e}\) (mg/g) & 36.63 & 18.44 & 45.16 & 34.86 & 45.27 \\  & \(K_{2}\) (mg/g*min) & 0.61 & 2.07 & 0.70 & 0.90 & 0.35 \\  & r\({}^{2}\) & 0.9572 & 0.9588 & 0.9604 & 0.9593 & 0.9547 \\ \hline \multirow{2}{*}{Pseudo 1 st Order} & \(Q_{e}\) (mg/g) & 33.22 & 17.47 & 41.05 & 32.03 & 40.27 \\  & \(K_{1}\) (min\({}^{-1}\)) & 0.44 & 1.26 & 0.52 & 0.65 & 0.25 \\  & r\({}^{2}\) & 0.8852 & 0.9188 & 0.8910 & 0.8930 & 0.8847 \\ \hline \multirow{2}{*}{Weber-Morris} & \(K_{il}\) (mg/g * min\({}^{0.5}\)) & 4.33 & 1.81 & 5.30 & 3.92 & 5.65 \\  & \(C\) (mg/g) & 12.19 & 9.36 & 15.9 & 13.7 & 10.9 \\  & r\({}^{2}\) & 0.7724 & 0.5337 & 0.7633 & 0.7068 & 0.8724 \\ \hline \hline \end{tabular}  
* \(Q_{e}\), amount of CV removed at equilibrium; \(K_{1}\), pseudo-first order constant; \(K_{2}\), pseudo-second order constant; \(k_{il}\) Weber-Morris constant; CV concentration, \(3\times 10^{-5}\) M; adsorbent load, 10 mg; and temperature, 25 *C. The pH employed was 7.5, 7.2, 6.5, 7.0, and 7.2 for SW, CM, AC1, AC2, and CAC, respectively.  
\end{table} 
Table 4: Adsorption kinetic parameters of CV. The Freundlich model for AC2, CM, and CAC predicts a maximum adsorption capacity of 207.8 mg g\({}^{-1}\), 3.9 mg g\({}^{-1}\), and 5 \(\times\) 10\({}^{7}\), respectively, whereas the same model predicts an adsorption capacity of ~17 and 9.6 mg g\({}^{-1}\) for AC1, and SW, respectively. Further, CAC showed the largest value mainly explained by its large S\({}_{\text{BET}}\). Interestingly, the adsorption capacity of AC2 was higher than those reported using modified rice husk (24.5 mg g\({}^{-1}\)) [46], chitosan nanow whiskers (59.5 mg g\({}^{-1}\)) [23], corn cob complexes (59.5 mg g\({}^{-1}\)) [10], and other adsorbents listed in Table 1.  
\(E_{a}\) was calculated from of the Avrami \(k\) constant. It is defined as the minimum energy needed for adsorption to take place. It is accepted that when this value is lower than 17.6 kJ/mol the process is designated as physisorption, whereas higher values are characteristic of chemisorption [47]. Further, adsorbents showed a decrease in the rate constant (\(K\)) as the temperature increased hindering the interaction forces between the surface functional groups of these adsorbents and CV. Further, the increase in temperature increased the number of collisions, resulting in desorption rather than adsorption mostly favoring the diffusion rate of the adsorbate across the external boundary layer. Further, a low \(E_{a}\) was associated with a low PZC and a large ionization degree allowing for a rapid and spontaneous physisorption process, especially in AC1 and AC2. Interestingly, CM presented the highest \(E_{a}\) suggesting a chemisorption process although further thermodynamics studies need to be conducted in order to corroborate this finding.