## 3 Results and Discussion
### Adsorption Isotherm Models  
The modelling of the adsorption equilibrium data is useful in describing and comparing the interaction between the adsorbate and adsorbent during the adsorption experiments, and is also essential for the design of the adsorption process systems. The adsorption models that are most frequently studied are the Langmuir or Freundlich adsorption isotherms, which have been adopted in this study to describe the adsorption characteristics of chelating adsorbents (WPET-SiAMPy nanofibres). In addition, the Jovanovic-Freundlich adsorption isotherm was also reviewed in this study for the close proximation of adsorption data. All the equilibrium adsorption isotherms were used to draw relationships between the Cu\({}^{2+}\) concentration in the aqueous solution and the quantity adsorbed onto the WPET-SiAMPy nanofibres. In the adsorption process, the adsorbate is adsorbed on the adsorbent until the adsorbent reaches equilibrium. The WPET-SiAMPy nanofibres' adsorption isotherms were determined using the initial concentration experimental data outcomes to predict the best fitting isotherm. The effect of the Cu\({}^{2+}\) aqueous solution initial concentration plot followed the Type II of the five types of adsorption isotherms [32]. Type II adsorption isotherms occur when there is more than one type of adsorption active site on the adsorbent surface [33]. Then, the adsorption of the adsorbate molecules to the macroporous adsorbents takes place when multilayer adsorbed molecules are formed after the coverage of the adsorbent surface with a monolayer of adsorbed molecules [34]. The active adsorption sites initiate rapid initial adsorption and these sites saturate when the first site is filled [35]. Then, adsorption rises for the second time when the second active adsorption site is filled. The second site could be a second monolayer, or in porous materials it can also be a second type of pore [36]. Type II adsorption isotherms do not display any saturation point [37], as seen in Figure 7. The plots of Langmuir (1/qe vs. 1/C\({}_{\text{e}}\)), Freundlich (logqe vs. logC\({}_{\text{e}}\)) and Jovanovic-Freundlich (lnqe vs. C\({}_{\text{e}}\)) are illustrated in Figures 9-11, which were used for the calculation of isotherm parameters in the adsorption of Cu\({}^{2+}\) ions using WPET-SiAMPy nanofibres as adsorbents. The obtained values of these parameters are summarized in Table 2.  
Figure 9: Langmuir model isotherm of Cu\({}^{2+}\) ions on WPET-SiAMPy nanofibres. Figure 11: Jovanovic–Freundlich model isotherm of Cu\({}^{2+}\) ion on WPET-SiAMPy nanofibres. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Isotherm Models** & **Constants** & **WPET-SiAMPy** \\ \hline \multirow{3}{*}{**[PERSON]**} & \(q_{m}\) (mg/g) & 0.0117 \\  & \(K_{L}\) (L/g) & 13.9145 \\  & \(\text{R}^{2}\) & 0.9905 \\  & \(\text{X}^{2}\) & 1.0602 \\ \hline \multirow{3}{*}{**[PERSON]**} & \(q_{F}\) (mg/g) & 1.2912 \\  & \(K_{F}\) (L/mg) & 0.1803 \\  & \(n\) & 0.9572 \\  & \(\text{R}^{2}\) & 0.9952 \\  & \(\text{X}^{2}\) & 0.0398 \\ \hline \multirow{3}{*}{**Jovanovic–Freundlich**} & \(q_{IF}\) (mg/g) & 1.7702 \\  & \(K_{JF}\) (L/g) & 0.5289 \\ \cline{1-1}  & \(n_{JF}\) & 0.4747 \\ \cline{1-1}  & \(\text{R}^{2}\) & 0.8445 \\ \cline{1-1}  & \(\text{X}^{2}\) & 0.4353 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters obtained from the plot of Langmuir, Freundlich isotherms, and Jovanovic–Freundlich for Cu\({}^{2+}\) adsorption using modified chelating adsorbents WPET-SiAMPy nanofibres. Figure 10: Freundlich model isotherm of Cu\({}^{2+}\) ion on WPET-SiAMPy nanofibres. In order to choose the best fit between the isotherm model parameters and the experimental outcomes, the statistical function was examined and in each case a set of isotherm parameters were determined by minimizing the respective error function across the concentration range studied [38]. The quality of the isotherm model fit was achieved by the reduced chi-square statistics [39].