# Adsorption Separation of Various Polar Dyes in Water by Oil Sludge-Based Porous Carbon
## 4 Discussion  
### The Adsorption Models and Mechanisms of OSC  
Figure 8 displays the adsorption kinetic curves and thermodynamic curves for OSC700 adsorption of MG, MB, and CV, fitted to different models. The results show that the Langmuir isothermal adsorption model has a higher fitting correlation coefficient compared to the Freundlich isothermal adsorption model, indicating a better fit to the data (Table 4). This indicates that the adsorption of MG, MB, and CV molecules by OSC700 follows the Langmuir isothermal adsorption model, indicating a monolayer adsorption mechanism on the outer surface of OSC700. As mentioned earlier, OS particles are primarily composed of quartz (57.03%), which is characterized by its high density and strength. The internal light and heavy organic matters are decomposed and deposited at high temperatures, leaving only a C network structure on the surface of the sludge particles. According to calculations, the theoretical saturation adsorption capacities (q\({}_{\text{m}}\)) of OSC700 for MG, MB, and CV are 33.41 mg/g, 16.41 mg/g, and 13.56 mg/g, respectively. These values are in good agreement with the actual experimental results obtained in the adsorbent dosage gradient adsorption experiments. The Pseudo-second-order model (PSO) fitting correlation coefficients for the adsorption process of the three dyes are 0.99999, 0.99806, and 0.99669, respectively, which are all extremely close to 1 and higher than those of the Pseudo-first-order model (PFO) (Figure 8c,d and Table 5). Furthermore, the equilibrium adsorption capacity (qe) calculated by the PSO kinetic model is in closer agreement with the experimental value, indicating that the PSO kinetic model is more suitable for describing the adsorption process of OSC700 on the three dyes. The main reason is that the adsorption of OSC700 to the three dyes involves a combination of both chemical and physical adsorption mechanisms. The surface of OSC700 is rich in functional groups, including hydroxyl and carboxyl groups, which can interact with dye molecules, facilitating chemical adsorption. In the study of adsorption kinetics, the PFO and PSO models have limitations in fully explaining the diffusion mechanism involved in the adsorption process. Therefore, the intraparticle diffusion model is applied to further investigate the adsorption mechanism, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**[PERSON]**} & \multicolumn{3}{c}{**[PERSON]**} \\ \cline{2-7}  & **q\({}_{\text{m}}\) (mg/g)** & **K\({}_{\text{L}}\) (L/mg)** & **R\({}^{2}\)** & **K\({}_{\text{F}}\) (mg/g)** & **n** & **R\({}^{2}\)** \\ \hline MG & 33.41129 & 0.16215 & 0.98824 & 65.61603 & 1.83793 & 0.9801 \\ MB & 16.40958 & 0.02874 & 0.98351 & 3.52866 & 2.28707 & 0.98101 \\ CV & 13.56116 & 0.32721 & 0.9909 & 215.04037 & 1.99561 & 0.53733 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The model parameters of adsorption isotherm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**PFO**} & \multicolumn{3}{c}{**PSO**} \\ \cline{2-7}  & **q\({}_{\text{e}}\) (mg/g)** & **K\({}_{\text{1}}\)** & **R\({}^{2}\)** & **q\({}_{\text{e}}\) (mg/g)** & **K\({}_{\text{1}}\)** & **R\({}^{2}\)** \\ \hline MG & 0.0475 & 0.01544 & 0.90162 & 9.7267 & \(-\)0.04305 & 0.9999 \\ MB & 1.1593 & 0.0642 & 0.8155 & 5.3578 & 0.0724 & 0.9981 \\ CV & 1.1525 & 0.0616 & 0.9203 & 8.6311 & 0.4595 & 0.9967 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Kinetic constants for the adsorption of MG, MB, and CV. as shown by the fitting curves in Figure 8e. The adsorption results of OSC700 on three dyes revealed a linear relationship between qt and t0.5, with intercepts of 9.43 mg/g, 3.8115 mg/g, and 6.2624 mg/g, respectively. The fact that these intercepts do not pass through the origin suggests that diffusion is not the sole factor controlling the adsorption rate.