## 3 Results and Discussion
### Kinetic Modeling  
The fitting results are illustrated in Figure 3 and Table 8 for the CS-TiO\({}_{2}\)-GLA, and CS-GO-TiO\({}_{2}\)-GLA systems, respectively. The equilibrium times for dye adsorption are reflected in Table S1, and these were 540 min and 240 min for the CS-TiO\({}_{2}\)-GLA and CS-GO-TiO\({}_{2}\)-GLA systems, respectively. The pseudo-first-order (PPO) and pseudo-second-order (PSO) models were fitted to the experimental kinetics data to obtain more information about the dye adsorption mechanism and the limiting step in the process. Generally, the PPO model explains the adsorption processes by physisorption, while the PSO model explains it by chemisorption [42]. On the other hand, the PSO model can explain the adsorption mechanism by electrostatic interactions between the positively charged active sites on the adsorbent and the negatively charged molecules of the dye. Thus, electrostatic attraction plays an essential role in the adsorption of FD&C Red 40 dye by the two systems [42]. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Pseudo First Order**} \\ \hline  & q\({}_{\text{e}}\)(mg.g\({}^{-1}\)) & k\({}_{1}\)(min\({}^{-1}\)) & **R\({}^{2}\)** \\ \hline CS-TiO\({}_{2}\)-GLA & 2.05 & 0.003 & 0.7823 \\ CS-GO-TiO\({}_{2}\)-GLA & 4.96 & 0.021 & 0.8979 \\ \hline  & \multicolumn{3}{c}{**Pseudo Second Order**} \\ \hline  & q\({}_{\text{e}}\)(mg.g\({}^{-1}\)) & k\({}_{1}\)(min\({}^{-1}\)) & **R\({}^{2}\)** \\ \hline CS-TiO\({}_{2}\)-GLA & 9.39 & 0.0001 & 0.6844 \\ CS-GO-TiO\({}_{2}\)-GLA & 5.88 & 0.0013 & 0.9888 \\ \hline  & \multicolumn{3}{c}{**Elovich**} \\ \hline  & \(\beta\)(mg.g\({}^{-1}\)) & \(\alpha\)(mg.g\({}^{-1}\)-min\({}^{-1}\)) & **R\({}^{2}\)** \\ \hline CS-TiO\({}_{2}\)-GLA & 1.22 & 0.0533 & 0.8225 \\ CS-GO-TiO\({}_{2}\)-GLA & 1.01 & 0.1408 & 0.9504 \\ \hline  & \multicolumn{3}{c}{**Intraparticular Diffusion**} \\ \hline  & **C** & **K\({}_{1}\)(mg.g\({}^{-1}\)-min\({}^{1/2}\))** & **R\({}^{2}\)** \\ \hline CS-TiO\({}_{2}\)-GLA & \(-0.57\) & 0.1721 & 0.9661 \\ CS-GO-TiO\({}_{2}\)-GLA & \(-0.23\) & 0.2709 & 0.9828 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Calculated parameters of the different kinetic models for the adsorption of FD&C Red 40 dye on the two adsorbent systems. The diffusion mechanism was investigated by fitting the intraparticle diffusion model by [PERSON] [43]. Considering the R\({}^{2}\) values reflected in Table 8, it is possible to state that this model better explains the adsorbents' adsorption processes, which occur in different stages. The first stage is the transport of FD&C Red 40 dye molecules from within the solution to the external surface of the material, followed by diffusion within the pores of the adsorbents (intraparticle diffusion) and adsorption of the dye on the surface of the material through electrostatic, n-\(\pi\) stagnation, hydrogen bonding, and \(\pi\)- \(\pi\) stagnation interactions (for the system with GO) [36]. On the other hand, K\({}_{i}\) constants increase with the addition of GO to the system of CS-TiO\({}_{2}\)-GLA. That means the diffusion rate of the dye increased towards their surface [15; 44]. Additionally, the values of the C constants of this model provide information about the thickness of the boundary layer, being equal for the three systems. Since C \(\
eq\) 0, intraparticle diffusion is not the only step controlling the rate of dye adsorption [28]. The Elovich equation is one of the most effective kinetic models to explain the chemisorption of adsorption processes and finds practical application when the adsorbent surface presents heterogeneous adsorption sites [45]. The constant \(\alpha\) (mg g\({}^{-1}\) min\({}^{-1}\)) of the model is related to the initial adsorption rate and the constant \(\beta\) (g mg\({}^{-1}\)) to the degree of adsorbent surface coverage and the activation energy of the chemisorption process [46].