## 3 Results and Discussion
### Adsorption Kinetics  
The experimental kinetic data at different temperatures and the theoretical curves of the two models are shown in Figure 11; the parameters associated with these models are reported in Table 4. Visually, the PSO model is the most adequate to describe the experimental adsorption data of the two studied pollutants. This is confirmed by the high R\({}^{2}\) values and the low \(\chi^{2}\) compared with those of the PSO model. Moreover, the theoretical q\({}_{\rm e.cal}\) values of the two adsorbates are very close to the experimental q\({}_{\rm e.exp}\) values. The works of [PERSON] et al. [84] and [PERSON] et al. [85] support these results. They studied, respectively, the adsorption of CV and Cr (VI) on activated carbons synthesised from lignocellulosic waste. These authors found that the PSO model describes the adsorption process well.  
Figure 10: Effect of time and temperature on the adsorption of CV and Cr (VI) on ACSCGs.  
In order to obtain information on the different stages of the diffusion mechanism of the two adsorbates from the solution to the active sites of the activated carbon, the intraparticle diffusion model, described by the Weber and Morris equation (Equation (6)), was applied to analyse the experimental data. Figure 12 shows the curves of the intraparticle model for the two pollutants. Table 5 shows the values of the intraparticle rate constant \(\mathrm{k_{di}}\), the boundary layer thickness \(\mathrm{C_{i}}\), and \(\mathrm{R^{2}}\) for the four temperatures. Figure 12 shows that the intraparticle model curves for both pollutants are composed of three segments whatever the temperature studied, indicating the intervention of three steps in the adsorption process.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **Parameters** & \multicolumn{3}{c}{**CV**} & \multicolumn{3}{c}{**Cr (VI)**} \\ \cline{2-10}  & **T (K)** & **298** & **303** & **313** & **323** & **298** & **303** & **313** & **323** \\ \hline \multirow{4}{*}{PFO} & \(\mathrm{q_{e,cap}}\) (mg/g) & 96.2 & 94.5 & 92.9 & 91 & 63.4 & 60.2 & 59.3 & 57.8 \\  & \(\mathrm{q_{e,cal}}\) & 98.7 & 97.7 & 95.9 & 94.5 & 66.2 & 62.98 & 62.3 & 61.0 \\  & \(\mathrm{k_{1}}\) (min\({}^{-1}\)) & 0.146 & 0.148 & 0.150 & 0.152 & 0.209 & 0.227 & 0.242 & 0.257 \\  & \(\mathrm{R^{2}}\) & 0.981 & 0.991 & 0.992 & 0.993 & 0.980 & 0.979 & 0.975 & 0.970 \\  & \(\mathrm{\chi^{2}}\) & 6.61 & 6.46 & 5.67 & 4.45 & 7.08 & 7.32 & 8.40 & 9.26 \\ \hline \multirow{4}{*}{PSO} & \(\mathrm{q_{e,cal}}\) (mg/g) & 95.5 & 94.5 & 92.6 & 91.1 & 62.3 & 59.3 & 58.7 & 57.5 \\  & \(\mathrm{k_{2}}\) (g/mg\(\cdot\)min) & 0.0039 & 0.0040 & 0.0043 & 0.0044 & 0.0052 & 0.0058 & 0.0060 & 0.0063 \\ \cline{1-1}  & \(\mathrm{R^{2}}\) & 0.998 & 0.999 & 0.999 & 0.999 & 0.999 & 0.999 & 0.999 & 0.999 \\ \cline{1-1}  & \(\mathrm{\chi^{2}}\) & 4.62 & 4.57 & 4.53 & 3.49 & 1.25 & 1.02 & 0.62 & 0.38 \\ \hline \end{tabular}
\end{table}
Table 4: Adsorption rate constants of PFO and PSO.  
Figure 11: Plots of the PPO and PSO models at different temperatures.  
The linear segments do not pass through the origin, indicating that intraparticle diffusion is not the only rate-controlling step during the diffusion of CV and Cr (VI) from the solution to the pores of the activated carbon [86]. The first stage, the fastest, represents the adsorption of CV and Cr (VI) on the external surface of the carbon. The second stage corresponds to the progressive adsorption of the two adsorbates, where intraparticle diffusion limits the adsorption phenomenon. The third stage indicates the final equilibrium state, where intraparticle diffusion starts to slow down due to low residual adsorbate concentrations in the solutions.