## 3 Results and Discussion
### Adsorption Kinetics  
In this study, the adsorption rate and mechanism of SWCNTs/Fe\({}_{\text{x}}\)O\({}_{\text{y}}\) adsorbing BPA were examined by fitting the data to pseudo first-order and pseudo second-order kinetic models. The equations for these two adsorption kinetic models are as follows [35]:  
\[q_{t}=q_{e}\Big{(}1-e^{-k_{1}t}\Big{)}, \tag{8}\]  
\[\frac{t}{q_{t}}=\frac{1}{k_{2}q_{e}{}^{2}}+\frac{1}{q_{e}}t, \tag{9}\]  
where \(q_{t}\) is the adsorption capacity of the unit adsorbent to the BPA at time \(t\) (mg/g); \(q_{e}\) is the adsorption capacity of the unit adsorbent to BPA at adsorption equilibrium (mg/g); \(k_{1}\) and \(k_{2}\) are both adsorption rate constants.  
Figure 11a,b illustrate the kinetic fittings of the SWCNTs/Fe\({}_{\text{x}}\)O\({}_{\text{y}}\) for the BPA solutions with varying initial concentrations. The corresponding kinetic fitting parameters are listed in Table 3. The data demonstrate that the second-order kinetics model fits the experimental data of BPA better than the first-order kinetic model, with the correlation coefficients (R\({}^{2}\)) exceeding 0.99 in both cases. The equilibrium adsorption capacity, as calculated from the pseudo second-order kinetic curves, is closer to the experimental values, suggesting that chemisorption was the primary mechanism driving the adsorption process. The adsorption mechanism was likely influenced by various forces, such as \(\pi\)-\(\pi\) electron donor-acceptor interactions, hydrogen bonding, etc.  
Figure 11: Kinetic fitting curves: (**a**) pseudo first-order kinetics; (**b**) pseudo second-order kinetic (T = 25 \({}^{\circ}\)C, pH = 6, adsorbent dosage = 0.2 g/L).  
Figure 10: Langmuir, Freundlich, and D-R adsorption isotherms (T = 25 \({}^{\circ}\)C, pH = 6, adsorbent dosage = 0.2 g/L).  
To further elucidate the principal mechanism governing the adsorption process, the Weber-Morris model [36] was employed to fit the data depicted in Figure 12.  
\[q_{t}=k_{int}t^{1/2}+I, \tag{10}\]  
where \(k_{int}\) is the intraparticle diffusion rate constant. The value \(I\) represents the boundary layer thickness, i.e., the larger the intercept, the greater the boundary layer effect will be [37]. According to this model, if the fitting line of \(q_{t}\) and \(t^{1/2}\) passes through the origin, then the internal diffusion of the particle determines the adsorption rate.  
The relationship between \(q_{t}\) and \(t^{1/2}\) was observed to be nonlinear, indicating a multi-line relationship. The adsorption process can be divided into two stages: Firstly, there is the rapid adsorption stage, which is considered to be the swift diffusion of the adsorbate to the surface of the adsorbent; the SWCNTs/Fe\({}_{\times}\)O\({}_{y}\) contain abundant \(\pi\) electrons, which form \(\pi\)-\(\pi\) conjugations [38] with \(\pi\) electrons in the benzene ring in the structure of BPA. In the early stages of adsorption, the SWCNTs/Fe\({}_{\times}\)O\({}_{y}\) had a larger specific surface area and numerous available adsorption sites, allowing for more \(\pi\) electrons to be exposed for binding with BPA. Consequently, the rate of adsorption of BPA increased rapidly with the adsorption time. The second stage was a slower adsorption phase, where the BPA molecules diffused into the mesopore and macropore of the SWCNTs/Fe\({}_{\times}\)O\({}_{y}\). As the BPA concentration decreased, the number of effective adsorption sites on the SWCNTs/Fe\({}_{\times}\)O\({}_{y}\) also diminished, and the quantity of BPA molecules within the adsorbent gradually increased. Adsorption was influenced by the concentration and molecular size of the adsorbate. As adsorption approached equilibrium, the diffusion resistance rose. The fact that \(I\
eq 0\) under the test conditions suggested that intra-particle diffusion was not the sole rate-limiting step, and that several other controlling factors significantly influenced the adsorption of BPA by the CNTs.