## 3 Results
### Adsorption Isotherms  
To carry out a more detailed study of the adsorption mechanism, the adsorption isotherms were adjusted to the Langmuir, Freundlich and Temkin models. The constants obtained from the equations of these three models are summarized in Table 4. The results show that the Temkin model is the one that best simulates this process because of the higher correlation coefficient (R\({}^{2}\) > 0.970), and a lower mean relative error (ARE = 9.804%). Similar results were observed in the study of adsorption of MC via maize silk powder [25]. For the Langmuir model, the value of the separation factor R\({}_{\rm L}\) describes the feasibility of the adsorption process. In our study, R\({}_{\rm L}\) values vary between 0.071 and 0.652 indicating favorability of adsorption [42]. The latter also allowed us to determine the maximum uptake of MC on SSS, q\({}_{\rm m}\) = 63.29 mg/g at equilibrium time te\({}_{\rm equ}\) = 90 min. As a comparison, [PERSON] [39] determined a maximum uptake of q\({}_{\rm m}\) = 0.0365 mg/g for the adsorption of MC onto SSS treated with sodium hydroxide (0.05 M NaOH) at te\({}_{\rm equ}\) = 120 min, and [PERSON] [43] determined a maximum uptake of q\({}_{\rm m}\) = 39.4 mg/g for the adsorption of MC onto activated carbon prepared by chemical activation of SSS uses phosphoric acid (H\({}_{3}\)PO\({}_{4}\)) at te\({}_{\rm equ}\) = 150 min.  
The Freundlich isotherm model allowed us to determine the parameter n\({}_{\rm F}\), which determines the adsorption effectiveness. According to the results, the calculated value of the Freundlich isotherm model constant, n\({}_{\rm f}\) is greater than 1 (n\({}_{\rm F}\) = 1.879), which confirms that the adsorption phenomenon is favorable [42].  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Initial Concentration of MC (mg/L)** & **20** & **30** & **60** & **90** & **120** & **150** \\ \hline q\({}_{\rm e}\) (exp.) (mg/g) & 9.029 & 13.927 & 25.893 & 37.389 & 48.51 & 51.522 \\ \hline \multicolumn{8}{c}{Pseudo-first order model} \\ \hline q\({}_{1}\) (mg/g) & 0.457 & 1.528 & 7.649 & 12.222 & 12.958 & 15.979 \\ \hline k\({}_{1}\) (1/min) & 0.0358 & 0.0646 & 0.0744 & 0.0472 & 0.0371 & 0.038 \\ \hline R\({}^{2}\) & 0.87 & 0.944 & 0.969 & 0.965 & 0.989 & 0.972 \\ \hline ARE (\%) & 97.191 & 92.531 & 79.186 & 78.708 & 84.380 & 82.813 \\ \hline \multicolumn{8}{c}{Pseudo-second order model} \\ \hline q\({}_{2}\) (mg/g) & 9.047 & 12.453 & 26.247 & 38.759 & 44.444 & 54.054 \\ \hline k\({}_{2}\) (g/mg min) & 0.243 & 0.016 & 0.027 & 0.009 & 0.003 & 0.005 \\ \hline R\({}^{2}\) & 1 & 0.994 & 0.999 & 0.999 & 0.991 & 0.999 \\ \hline ARE (\%) & 1.455 & 28.099 & 2.424 & 3.064 & 26.584 & 7.421 \\ \hline \multicolumn{8}{c}{Intra-particle diffusion model} \\ \hline K\({}_{\rm d1}\) (mg/g \(\sqrt{\rm min}\)) & 0.338 & 1.137 & 1.167 & 2.62 & 2.26 & 2.62 \\ \hline C\({}_{1}\) (mg/g) & 7.863 & 9.858 & 13.433 & 20.461 & 31.975 & 23.101 \\ \hline R\({}^{2}\) & 1 & 0.993 & 0.874 & 0.914 & 0.972 & 0.978 \\ \hline K\({}_{\rm d2}\)(mg/g \(\sqrt{\rm min}\)) & 0.048 & 0.071 & 0.08 & 0.369 & 0.848 & 0.963 \\ \hline C\({}_{2}\) (mg/g) & 8.58 & 13.273 & 25.121 & 33.85 & 40.324 & 42.743 \\ \hline R\({}^{2}\) & 0.875 & 0.889 & 0.741 & 0.977 & 0.998 & 0.806 \\ \hline ARE (\%) & 3.743 & 8.439 & 15.498 & 19.304 & 3.286 & 17.329 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Kinetic parameters of the adsorption of MC on the SSS following different kinetic models.