## 3 Result and Discussion
### Adsorption Kinetics  
Figure 5 shows the kinetics of NP adsorption onto the modified MWCNTs. The obtained result shows that the equilibrium is established in 14 h (Figure 4a). In the beginning, the rate of adsorption was high probably due to a large number of free surface sites available on the MWCNTs. Afterward, the adsorption rate became slower and finally reached the equilibrium state. Thus, it could be concluded that free binding sites and affinity between the modified MWCNT and NP might be responsible for the NP adsorption, similar to the result from our previous study in which NP was adsorbed to clays and soil materials [50]. In fact, the kinetics profile from the current NP adsorption study is characterized with two linear regions; they are the liquid film diffusion layer and the intra-particle diffusion one [51]. The rate of NP adsorption in the liquid film diffusion layer is expressed as Equation (1):  
\[\frac{dq}{dt}=k_{f}S_{0}(C-C_{i}) \tag{1}\]  
where \(S_{0}\) is the particle surface area per unit particle volume, and \(k_{f}\) is the rate constant.  
The intra-particle diffusion model assumes that the adsorption density, \(q_{t}\), varies proportionally with \(t^{\frac{1}{2}}\), as shown in Equation (2),  
\[q_{t}=k_{id}\sqrt{t}+I\]  
Figure 4: Effect of (**a**) pH (MWCNT) = 0.5 mg/L) and (**b**) adsorbent (MWCNTs) dose (at pH 4) on the adsorption of NP by MWCNTs. Experimental conditions: [NP] = 2.5 mg/L, T = 25 \({}^{\circ}\)C).  
Figure 5: The kinetics of NP adsorption described by the film diffusion and the intra-particle diffusion models. Experimental conditions: [NP] = 2.5 mg/L, T = 25 \({}^{\circ}\)C, pH = 4, and [MWCNT] = 0.5 mg/L.  
where \(I\) and \(k_{id}\) is the intercept and the intra-particle diffusion rate constant, respectively. The boundary layer effect is indicated by the initial high slope, and the intra-particle diffusion or pore diffusion is demonstrated by the less steep slope (Figure 5).  
The NP adsorption capacity increases with the increase in the adsorbent surface area (\(S_{0}\)) [45]. Moreover, the increase in the surface area of the adsorbent strongly correlates with the equilibrium adsorption capacity [49]. This kind of relationship has already been described in the literature [52]. It suggests that the pore-filling mechanism is mostly responsible for the adsorption. Generally, small-size organic compounds are responsible for pore-filling [43; 53]. In addition, the octanol-water partitioning coefficient (\(\log\) K\({}_{\text{ow}}\)), an indicator of hydrophobicity of an organic compound, plays an important role in the adsorption [1]. Therefore, the compound with a high \(\log\) K\({}_{\text{ow}}\) (i.e., \(\log\) K\({}_{\text{ow}}\) > 4) should exhibit a strong adsorption affinity towards the active binding sites of the adsorbent [1]. Since the \(\log\) K\({}_{\text{ow}}\) of NP is 4.8-5.3 (Table 1), NP seems to have a strong adsorption affinity.  
Table 3 lists the kinetics models that were applied for the NP adsorption to the modified MWCNTs. The coefficients of determination for the kinetics models are in the order of Elovich (R\({}^{2}\) = 0.96) > pseudo-first order (0.93) > pseudo-second order (0.46).  
The calculated \(q_{e}\) value was not in agreement with the experimental data, indicating that the pseudo-second-order kinetic model may not explain the adsorption of NP onto the modified MWCNTs. Preferably, the experimental adsorption capacity data well fit to the [PERSON] model, which implies that the NP adsorption is governed by chemisorption processes [54].