## 3 Results and Discussion
### Adsorption Isotherm  
Figure 4a,b depict the adsorption isotherms of Nd(III), Ce(III), Er(III), Y(III), and Fe(III) at room temperature to TK221. REE adsorption increased with the target ion concentration of the feed solution, resulting in higher adsorption capacities, consistent with previous experiments that used DGA [20]. The equilibrium adsorption data were fitted and analyzed using Langmuir and Freundlich isotherms, and the results are illustrated in Table 5. The Langmuir isotherm exhibited a higher correlation coefficient than the Freundlich isotherm, indicating that the recovery of Nd(III), Ce(III), Er(III), Y(III), and Fe(III) mainly occurred via homogenous monolayer adsorption. The saturated adsorption capacities (q\({}_{\text{max}}\)) were found to be 45.2 mg Nd/g, 43.1 mg Ce/g, 35.1 mg Er/g, 15.6 mg Y/g, and 12.3 mg Fe/g. Values of the Langmuir coefficient (K\({}_{\text{L}}\)) are related to the relative affinity of the functional groups towards the target ions [46; 47; 48]. This means that when the five elements coexist in solution, the TK221 resin will preferentially extract the target elements in the following order: Er > Y > Fe > Nd > Ce (Table 5).  
These results also align with hard and soft acid-base (HSAB) theory, where both amide and phosphine oxide functional groups are considered \"soft\" bases [49; 50], so they have a higher affinity towards \"soft acids\". In this study, the use of 3 M HCl, while not strong enough to alter the charge states of the ions, allowed us to consider their relative charge densities as a primary factor in determining their behavior. Based on this analysis, we can establish an order of increasing charge density among the studied elements: Ce > Nd > Er  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Element**} & \multicolumn{2}{c}{**Adsorption (mg/g)**} & \multicolumn{2}{c}{**\%Recovery**} \\ \cline{2-5}  & **360 min** & **1440 min** & **360 min** & **1440 min** \\ \hline Fe & 11.1 & 10 & 23 & 21 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Fe adsorption and recovery at 360 and 1440 min.  
Figure 4: (**a**) Freundlich Isotherm fitting Nd, Ce, Er, Y, and Fe and (**b**) Langmuir Isotherm fitting Nd, Ce, Er, Y, and Fe.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Element**} & \multicolumn{2}{c}{**Pseudo-First-Order**} & \multicolumn{3}{c}{**Pseudo-Second-Order**} \\ \cline{2-7}  & **k1** & **Qe** & **R\({}^{2}\)** & **k2** & **Qe** & **R\({}^{2}\)** \\ \hline Nd & 0.539 & 7.18 & 0.949 & 0.220 & 7.65 & 1.00 \\ Ce & 0.661 & 9.27 & 0.945 & 0.189 & 9.90 & 1.00 \\ Er & 0.403 & 10.48 & 0.903 & 0.021 & 12.4 & 1.00 \\ Y & 0.440 & 8.75 & 0.964 & 0.409 & 8.99 & 1.00 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Kinetic rate law fitting parameters for Nd, Ce, Er, and Y on TK221.  
\(>\) Y \(>\) Fe. This ordering implies that REEs possess a higher degree of softness compared to Fe, which is a significant finding in understanding their chemical behavior.  
The ability of TK221 resin to selectively extract REEs from aqueous solutions suggests that it is a promising alternative to solvent extraction, but pretreatment steps to concentrate REEs or remove interfering ions like Fe may be necessary for improved performance and selectivity. Moreover, the use of TK221 as an adsorbent for REE removal may offer several advantages over other methods, such as its low cost, ease of regeneration, and potential for scalability. Overall, as shown in Table 6, these findings highlight the potential of TK221 as a highly effective and practical adsorbent for the removal of REEs from aqueous solutions and may contribute to the development of efficient and sustainable methods for REE recovery.