## 3 Result and Discussion
### Thermodynamic Aspects  
Temperature affects the adsorption capacity of an adsorbent. It was observed that the amount of NP adsorbed increased as temperature increased, indicating an endothermic process. To evaluate the spontaneity of the adsorption process, the thermodynamic parameters, i.e., changes in the Gibb's free energy (\(\Delta\text{G}^{\circ}\), kJ/mol), the enthalpy (\(\Delta\text{H}^{\circ}\), kJ/mol), and the entropy (\(\Delta\text{S}^{\circ}\), kJ/mol/K) of the process were calculated by Equations (3)-(5):  
\[\Delta\text{G}=-\text{R}\;\text{T}\;\ln\;K_{\text{L}} \tag{3}\]  
\[\Delta\text{G}^{\circ}=\Delta\text{H}^{\circ}-\text{T}\;\Delta\text{S}^{\circ}, \tag{4}\]  
\[\ln K_{\text{L}}=\frac{\Delta\text{S}^{\circ}}{R}-\frac{\Delta H^{\circ}}{RT} \tag{5}\]  
where R is the universal gas constant (8.314 \(\times\)\(10^{-3}\) kJ/mol\(\cdot\)K), and T is the absolute temperature (K). The \(K_{\text{L}}\) (L/g), equilibrium constant, is calculated from the Langmuir constant, \(q_{m}\)[55]. The value of \(\Delta\text{G}^{\circ}\) was calculated from Equation (3), while \(\Delta\text{H}^{\circ}\) and \(\Delta\text{S}^{\circ}\) were estimated from the slop and intercept of the graph (straight line) of ((1/T) vs. In K) (Figure S2). The values of various thermodynamic parameters for the NP adsorption onto the modified MWCNTs are presented in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Isotherm model** & **Parameter** & **Value** & **R2** & **Reference** \\ \hline Langmuir & \(q_{e}=\frac{k_{\text{L}}\times q_{m}\times\text{C}_{e}}{1+k_{\text{L}}C_{e}}\) & \(q_{\text{m}}\) (mg/g) & \(1.11\times 10^{4}\) & 0.9763 & [55] \\ \cline{3-5}  & \(K_{\text{L}}\) (L/mg) & 1.5 & & \\ \hline [PERSON] & \(q_{e}=K_{f}\text{C}e^{\frac{1}{g_{f}}}\) & \(\begin{array}{c}K_{\text{f}}\text{ (mg/g)}\\ \text{(mg/L)}^{1/n}\end{array}\) & 33.20 & & \\ \cline{3-5}  & \(n_{\text{f}}\) & 0.89 & & \\ \hline Temkin & \(q_{e}=\) & \(C_{\text{e}}\) (g/mg) & 6.03 \(\times\)\(10^{4}\) & 0.9986 & [57; 59] \\ \cline{3-5}  & \(BlnA_{T}+BlnC_{e}\) & \(A_{\text{T}}\) (L/mg) & 0.60 & & \\ \hline [PERSON] & \(q_{e}=K_{E}q_{m}\text{C}_{e}e^{\frac{\alpha_{e}}{\text{cm}}}\) & \(q_{\text{m}}\) (mg/g) & \(2.5\times 10^{4}\) & 0.9996 & [53] \\ \cline{3-5}  & \(K_{\text{E}}\) (L/mg) & 0.38 & & \\ \hline [PERSON] & \(q_{e}=q_{m}\big{(}1-e^{K_{\text{L}}C_{e}}\big{)}\) & \(K_{\text{j}}\) (L/mg) & 0.22 & & \\ \cline{3-5}  & \(q_{m}\) (g/mg) & 47.37 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of NP adsorption based on various models. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Temp. (\({}^{\circ}\)C)** & **K (L/mol)** & \(\Delta\text{G}^{\circ}\) **(k/mol)** & \(\Delta\text{H}^{\circ}\) **(k/mol)** & \(\Delta\text{S}^{\circ}\) **(J/K mol)** \\ \hline
15 & 1.47 & \(-\)0.93 & 11.18 & 42.02 \\
25 & 1.72 & \(-\)1.35 & & \\
35 & 2.00 & \(-\)1.77 & & \\
45 & 2.29 & \(-\)2.19 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Values of various thermodynamic parameters for adsorption of NP to MWCNTs. The negative \(\Delta\)G\({}^{\circ}\) values suggest that the adsorption of NP onto the MWCNTs is spontaneous. The \(\Delta\)G\({}^{\circ}\) value negatively increases as the temperature increases. This indicates that the adsorption is more favorable at a higher temperature from the thermodynamics point of view (values of K\({}_{\text{L}}\) increased from 1.47 to 2.29). Additionally, the \(\Delta\)H\({}^{\circ}\) and \(\Delta\)S\({}^{\circ}\) values are all positive, indicating the NP adsorption onto the modified MWCNTs is endothermic at the temperature range of 288-318 K.  
From the adsorption and kinetics data, the following three important factors governing the adsorption of NP onto the modified MWCNTs can be drawn; they are (1) physical properties of the adsorbent, i.e., size, shape, surface area, impurities, functional group, and pore size; (2) environmental condition, i.e., pH; (3) \(\pi\)-\(\pi\) interaction between the MWCNTs and NP.