## 3 Results and Discussion
### Adsorption Isotherms  
The adsorption isotherms in non-linear form were evaluated by fitting the data to both of the two-parameter isotherm models (Langmuir and Freundlich) and the three-parameter isotherm model (Koble-Corrigan), as shown in Figure S3. In order to affect the bias of transforming non-linear to linear forms, non-linear regression analysis was done [36]. For the Langmuir isotherm, as shown in Equation (4), this model expressed monolayer adsorption on the homogeneous surface of the adsorbent. Each active site has the same affinities for each adsorbate molecule [16; 37]. \[\mathrm{q_{e}}=\mathrm{q_{0}K_{L}C_{e}/(1+K_{L}C_{e})}, \tag{4}\]  
where \(\mathrm{q_{e}}\) is the amount of dye adsorbed per gram of MCC at equilibrium (mg g\({}^{-1}\)), \(\mathrm{q_{0}}\) is the maximum monolayer adsorption capacity of the MCC (mg g\({}^{-1}\)), \(K_{L}\) is the Langmuir constant related to the affinity of dye and the MCC (L mg\({}^{-1}\)), \(C_{e}\) is the equilibrium concentration of dye remaining after adsorption (mg L\({}^{-1}\)), and the separation factor (R\({}_{L}\)) is defined as R\({}_{L}\) = 1/(1 + K\({}_{L}\)C\({}_{e}\)). For the Freundlich model shown in Equation (5), it is based on multilayer adsorption on a heterogeneous adsorbent surface with a non-uniform distribution of adsorption energy [16; 37]. The stronger binding sites are occupied by the adsorbate first. A decrease in the binding strength is found during this increase in site occupation. \[\mathrm{q_{e}}=K_{F}C_{e}\mathrm{{}^{1/n}}, \tag{5}\]  
where \(K_{F}\) is the Freundlich constant [(mg g\({}^{-1}\))(L mg\({}^{-1}\))(1/n)] related to the binding energy and 1/n is a measure of intensity of adsorption (L g\({}^{-1}\)), which indicates how favorable the adsorption process is. A value of 1/n between 0.1 and 1.0 corresponds to a favorable adsorption. All other symbols are the same as shown in the Langmuir model. For the Koble-Corrigan isotherm shown in Equation (6), there is cooperation between the Langmuir and Freundlich isotherm models [15; 38; 39]. The adsorbate molecules occupy the various active sites on the heterogeneous surface of the adsorbent. \[\mathrm{q_{e}}=(A_{KC}C_{e}\mathrm{{}^{n}})/(1+B_{KC}C_{e}\mathrm{{}^{n}}), \tag{6}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\Delta H^{\circ}\) & \(\Delta S^{\circ}\) & & \(\Delta G^{\circ}\) (**kJ mol\({}^{-1}\)**)** & \\ \hline
**(kJ mol\({}^{-1}\))** & **(kJ mol\({}^{-1}\) K\({}^{-1}\))** & **30 \({}^{\circ}\)C** & **40 \({}^{\circ}\)C** & **50 \({}^{\circ}\)C** & **60 \({}^{\circ}\)C** \\ \hline
8.2471 & 0.0301 & \(-\)0.87 & \(-\)1.19 & \(-\)1.45 & \(-\)1.79 \\ \hline \end{tabular}
\end{table} 
Table 2: Thermodynamic parameters for the adsorption of RR120 on the MCC. where \(A_{\rm KC}\) is the Koble-Corrigan isotherm constant (mg g\({}^{-1}\))(L mg\({}^{-1}\))\({}^{n}\), \(B_{\rm KC}\) is the Koble-Corrigan isotherm constant (L mg\({}^{-1}\))\({}^{n}\), and n is the adsorption intensity. All other symbols have the same definition as the one shown in the Langmuir model. To validate the adsorption model, the normalized standard deviation was performed. Two tools of quality (coefficient of determination, R\({}^{2}\); and an error function, ERR (%)) were used, as shown in Equations (7) and (8) below. \[R^{2}=\sum\left(q_{t,\rm{cal}}-\overline{q_{t,\rm{exp}}}\right)^{2}/\sum\left( q_{t,\rm{exp}}-\overline{q_{t,\rm{exp}}}\right)^{2}, \tag{7}\]  
\[\rm{ERR}\ (\%)=\left[\sum\{[(q_{t,\rm{exp}}-q_{t,\rm{cal}})/q_{t,\rm{exp}}]^{2} /(N-1)]\}\right]^{0.5}\times 100, \tag{8}\]  
where \(q_{t,\rm{exp}}\) and \(q_{t,\rm{cal}}\) are the experimental adsorption capacity at time t (min) and the calculated adsorption capacity at time t from the model, \(\overline{q_{t,\rm{exp}}}\) is the average experimental adsorption capacity at time t, and N is the number of experimental data.