# Effect of Washing Temperature on Adsorption of Cationic Dyes by Raw Lignocellulosic Biomass
## 3 Results and Discussion
### Results of Methylene Blue and Crystal Violet Adsorption on Raw Materials
#### 3.2.3 Modeling Adsorption Kinetics  
The nonlinear plots of the pseudo-first-order (PFO) and pseudo-second-order (PSO) models for the adsorption kinetics of MB and CV on MPC and CC are shown in Figures 23 and 24. The kinetic parameters obtained from these models are presented in Table 7. The most suitable model was evaluated based on the correlation coefficient (R\({}^{2}\)) and the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Dye**} & \multirow{2}{*}{**Adsorbent**} & \(\Delta\)H\({}^{0}\) & \(\Delta\)S\({}^{0}\) & \multicolumn{4}{c}{\(\Delta\)G\({}^{0}\) (kJ mol\({}^{-1}\))} \\ \cline{3-8}  & & **(kJmol\({}^{-1}\))** & **(Jmol\({}^{-1}\) K\({}^{-1}\))** & **283K** & **293K** & **303K** & **313K** \\ \hline \multirow{4}{*}{MB} & MPC & \(-\)7.43 & 36.52 & \(-\)17.76 & \(-\)18.14 & \(-\)18.48 & \(-\)18.86 \\  & MPW & \(-\)6.44 & 37.48 & \(-\)17.02 & \(-\)17.46 & \(-\)17.80 & \(-\)18.15 \\  & MPH & \(-\)5.91 & 31.60 & \(-\)14.86 & \(-\)15.16 & \(-\)15.49 & \(-\)15.80 \\  & CC & 5.74 & 73.23 & \(-\)14.97 & \(-\)15.75 & \(-\)16.45 & \(-\)17.17 \\  & CW & 2.86 & 62.99 & \(-\)14.95 & \(-\)15.63 & \(-\)16.25 & \(-\)16.84 \\  & CH & 3.59 & 64.70 & \(-\)14.71 & \(-\)15.39 & \(-\)16.02 & \(-\)16.65 \\ \hline \multirow{4}{*}{CV} & MPC & 9.60 & 95.44 & \(-\)17.36 & \(-\)18.42 & \(-\)19.37 & \(-\)20.22 \\  & MPW & 5.21 & 77.22 & \(-\)16.64 & \(-\)17.42 & \(-\)18.18 & \(-\)18.96 \\ \cline{1-1}  & MPH & 4.76 & 71.77 & \(-\)15.56 & \(-\)16.25 & \(-\)16.95 & \(-\)17.73 \\ \cline{1-1}  & CC & 6.04 & 77.32 & \(-\)15.86 & \(-\)16.60 & \(-\)17.38 & \(-\)18.18 \\ \cline{1-1}  & CW & 7.61 & 82.55 & \(-\)15.74 & \(-\)16.59 & \(-\)17.38 & \(-\)18.23 \\ \cline{1-1}  & CH & 4.64 & 72.08 & \(-\)15.78 & \(-\)16.46 & \(-\)17.16 & \(-\)17.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Thermodynamic parameters of MB and CV adsorption on raw materials. comparison of the maximum quantity obtained from these models with the experimentally obtained values. Table 7 reveals that both adsorption kinetics models provided good fits across different concentrations, indicated by correlation coefficients (R\({}^{2}\)) close to unity and minimal differences between the experimental equilibrium adsorption quantities (Q\({}_{e,\mathrm{exp}}\)) and those calculated using both models. However, the PSO model was more suitable for determining the adsorption kinetics of MB and CV on MPC and CC across the entire range of concentrations studied, as its R\({}^{2}\) correlation coefficients were higher than those of the PFO model. The intraparticle diffusion model is commonly used to identify the mechanisms involved in adsorption. Generally, for this model to be applicable in describing adsorbate fixation phenomena, the plot of Q\({}_{\mathrm{t}}\) versus t\({}^{0.5}\) should be linear. Moreover, if this line passes through the origin, it indicates that intraparticle diffusion is solely responsible for the adsorption process, and the rate of intraparticle diffusion is the limiting step in the interaction [94]. However, in some cases, the model may exhibit a multilinear form, suggesting that the adsorption process is controlled by multiple steps [95; 96]. For the adsorption of MB and CV by MPC and CC (Figures 25 and 26, respectively), two linear sections were observed, indicating that the adsorption of these dyes by the raw biosorbents is governed by two steps: the diffusion of the dyes into the solid phase, followed by an adsorption equilibrium where the actual binding occurs. Figure 23: Nonlinear fit of the PFO and PSO models of MB and CV adsorption on MPC. Figure 24: Nonlinear fit of the PFO and PSO models of MB and CV adsorption on CC. The diffusion coefficients for the adsorption of MB and CV by the raw materials (Table 8) decreased significantly over time. This can be attributed to the fact that, in the initial phase, the high diffusion of these dyes within the adsorbent structure leads to a substantial reduction in the number of pores available for further diffusion.