# 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
#### 3.2.4 Modeling the Adsorption Isotherms  
The parameters obtained from isotherm modeling provide valuable insights into adsorption mechanisms, surface properties, and adsorbent-adsorbate affinities. The two most commonly used two-parameter models are the Langmuir and Freundlich models. However, for a more in-depth understanding of adsorption mechanisms, three-parameter models can also be implemented. Among these, the Sips model (Langmuir-Freundlich) and the Redlich-Peterson model are particularly notable. The applicability of these models can be evaluated based on the value of the R\({}^{2}\) correlation coefficient. The graphical representation of each isotherm (Figures 27 and 28) and Table 9, which summarizes the correlation factors and constants for each model, show that all four models adequately represent the adsorption isotherms of MB and CV on MPC and CC, with \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Dye**} & \multirow{2}{*}{
\begin{tabular}{c} **C\({}_{0}\)** \\ **(mg L\({}^{-1}\))** \\ \end{tabular} } & \multicolumn{4}{c}{**Step 1**} & \multicolumn{4}{c}{**Step 2**} \\ \cline{3-8}  & & & \(\mathbf{K_{1}}\) & **C** & \(\mathbf{K_{2}}\) & **C** & \(\mathbf{K^{2}}\) \\  & & & \(\mathbf{(mg\ g^{-1}\min^{-0.5})}\) & **(mg g\({}^{-1}\))** & **(mg g\({}^{-1}\))** & **(mg g\({}^{-1}\))** & **(mg g\({}^{-1}\))** & **(mg g\({}^{-1}\))** & **(R\({}^{2}\))** \\ \hline \multirow{8}{*}{MPC} & \multirow{4}{*}{MB} & 25 & 3.555 & 5.498 & 0.928 & 0.146 & 20.458 & 0.806 \\  & & 50 & 5.653 & 14.375 & 0.942 & 0.630 & 37.424 & 0.708 \\  & & 100 & 7.721 & 29.675 & 0.986 & 0.048 & 79.806 & 0.760 \\  & & 150 & 13.191 & 34.679 & 0.969 & 0.665 & 101.472 & 0.785 \\  & & 200 & 11.008 & 64.737 & 0.993 & 0.224 & 124.440 & 0.796 \\ \cline{2-8}  & & 25 & 2.410 & 6.929 & 0.967 & 0.058 & 22.345 & 0.758 \\  & & 50 & 3.148 & 22.544 & 0.887 & 0.233 & 41.236 & 0.789 \\  & CV & 100 & 7.226 & 20.046 & 0.998 & 0.760 & 72.296 & 0.726 \\  & & 150 & 11.042 & \(-\)13.304 & 0.982 & 1.597 & 85.738 & 0.770 \\  & & 200 & 12.282 & \(-\)8.082 & 0.960 & 1.882 & 97.591 & 0.783 \\ \hline \multirow{8}{*}{CC} & \multirow{4}{*}{MB} & 25 & 1.537 & 12.586 & 0.943 & 0.068 & 23.230 & 0.873 \\  & & 50 & 3.106 & 19.169 & 0.966 & 0.322 & 39.929 & 0.939 \\ \cline{1-1}  & & 100 & 6.706 & 18.965 & 0.958 & 0.824 & 57.204 & 0.953 \\ \cline{1-1}  & & 150 & 9.726 & \(-\)2.987 & 0.964 & 1.578 & 51.992 & 0.877 \\ \cline{1-1}  & & 200 & 8.000 & 6.171 & 0.950 & 1.305 & 55.848 & 0.950 \\ \cline{1-1} \cline{2-8}  & & 25 & 1.395 & 11.208 & 0.920 & 0.213 & 20.397 & 0.782 \\ \cline{1-1}  & & 50 & 2.221 & 25.544 & 0.972 & 0.203 & 43.793 & 0.848 \\ \cline{1-1}  & CV & 100 & 3.960 & 34.510 & 0.964 & 0.768 & 67.434 & 0.806 \\ \cline{1-1}  & & 150 & 7.035 & 32.812 & 0.928 & 0.610 & 80.357 & 0.882 \\ \cline{1-1}  & & 200 & 4.751 & 55.871 & 0.865 & 0.551 & 85.354 & 0.959 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameters of the intraparticle diffusion models of MB and CV adsorption on MPC and CC. Figure 26: Intraparticle diffusion models for the adsorption of MB and CV on CC. R\({}^{2}\) > 0.9. However, the Sips and Redlich-Peterson models, overall, provide the most accurate description of our experimental results across the entire studied temperature range. Figure 27: Non-linear modeling of the MB and CV isotherms on MPC. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & \multirow{2}{*}{**Type**} & \multirow{2}{*}{\ \begin{tabular}{c} **Temperature** \\ **(C)** \\ \end{tabular}  } & \multirow{2}{*}{
\begin{tabular}{c} **Q-exp** \\ **(mg g g g g g g  
Table 10 shows the maximum adsorption capacities of MB and CV on some raw biosorbents, including our MPC and CC samples. The comparison demonstrates that our biomaterials have a higher adsorption capacity for MB and CV than several other reported adsorbents. Thus, the selected materials are excellent adsorbents for the removal of cationic dyes.