## 3 Results and Discussion
### Adsorption Isotherm  
An adsorption isotherm describes the relationship between the equilibrium concentration of a solution and the corresponding equilibrium adsorption capacity, which is attained when the adsorption process reaches equilibrium at a given temperature. To model this equilibrium, two widely used isotherm equations, the [PERSON] (1958) and [PERSON] (1958) models, are often employed to fit experimental data. The mathematical expressions for these models are as follows:  
\[q_{e}=\frac{K_{L}q_{max}C_{e}}{1+K_{L}C_{e}}, \tag{3}\]  
\[q_{e}=K_{F}C_{e}^{\frac{1}{2}}, \tag{4}\]  
where \(q_{e}\) is the adsorption capacity of the unit adsorbent to BPA at the adsorption equilibrium (mg/g); \(C_{e}\) is the concentration of BPA in solution at equilibrium (mmol/L); \(q_{max}\) is the theoretical maximum adsorption capacity (mg/g); and \(K_{L}\), \(K_{F}\), and \(n\) are all model constants. The value of \(n\) serves as an indicator of the ease or difficulty associated with the adsorption process. Adsorption is more likely to occur when the value of \(n\) is within the range of 1 to 10.  
The data on the adsorption of BPA by the SWCNTs/Fe\({}_{x}\)O\({}_{y}\) were also analyzed using the Dubinin-Radushkevich (D-R) adsorption isotherm model. The mathematical expressions for the model are as follows:  
\[q_{e}=q_{max}exp\left[-\beta\left\{RTln\left(1+\frac{1}{C_{e}}\right)\right\}^ {2}\right], \tag{5}\]  
\[\varepsilon=RTln\left(1+\frac{1}{C_{e}}\right), \tag{6}\]  
\[E_{a}=\frac{1}{\sqrt{2\beta}}, \tag{7}\]  
where \(q_{max}\) is the maximum adsorption capacity calculated according to the D-R model, mg\(\cdot\)g\({}^{-1}\); \(\beta\) is a constant related to the adsorption energy \(E_{a}\) (k\(\cdot\)mol\({}^{-1}\)), mol\({}^{2}\cdot\)k\({}^{-2}\); \(\varepsilon\) is the Polanyi adsorption potential. When the \(E_{a}\) value is in the range of 1-8 kJ\(\cdot\)mol\({}^{-1}\), it indicates physical adsorption. When the \(E_{a}\) value exceeds 8 kJ\(\cdot\)mol\({}^{-1}\), chemisorption is predominant.  
Figure 10 illustrates the Langmuir, Freundlich, and D-R adsorption isotherms associated with the removal of BPA from solution using SWCNTs/Fe\({}_{x}\)O\({}_{y}\). The corresponding fitting parameters were presented in Table 2. The data demonstrate a better fit with the Langmuir and D-R isotherm models, as indicated by the correlation fitting coefficient (R\({}^{2}\)) values of 0.903 and 0.913, respectively, compared to the R\({}^{2}\) value of 0.874 for the Freundlich model. This implies that the BPA molecules are likely adsorbed onto the SWCNTs/Fe\({}_{x}\)O\({}_{y}\) in a uniform monolayer. The maximum adsorption capacity as determined by the Langmuir model is 78.89 mg/g. The BPA adsorption energy calculated using the D-R model is 1.543 kJ/mol, indicating that the adsorption process is predominantly physical adsorption. As indicated in the table, the value of n is 5.559, suggesting that the adsorption process occurs easily.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **[PERSON]** & & & **[PERSON]** & & & **Dubinin–Radushkevich (D-R)** & \\ \hline \(q_{max}\) & \(K_{L}\) & \(R^{2}\) & \(K_{F}\) & \(n\) & \(R^{2}\) & \(q_{max}\) & \(\beta\) & \(E_{a}\) & \\ (mg\(\cdot\)g\({}^{-1}\)) & (L\(\cdot\)mg\({}^{-1}\)) & \(R^{2}\) & \(K_{F}\) & \(n\) & \(R^{2}\) & (mg\(\cdot\)g\({}^{-1}\)) & (mol\({}^{2}\cdot\)k\({}^{-2}\)) & (k\(\cdot\)mol\({}^{-1}\)) & \\ 78.89 & 4.714 & 0.903 & 52.68 & 5.559 & 0.874 & 76.22 & 0.20989 & 1.543 & 0.913 \\ \hline \end{tabular}
\end{table}
Table 2: Fitting parameters of isothermal adsorption models.