## 3 Results and Discussion  
### Adsorption Experiment  
Figure 1 compares the experimental results of single La(III) and Eu(III) by using L1 or L2 at pH 4. The rapid increase of the adsorption capacity in the initial stage might be associated with the abundant reactive sites. As time increases further, the accessibility of the REEs ions to unoccupied active sites on the adsorbent surface gradually decreases, and these sites ultimately become saturated when the process reaches its equilibrium. L2 adsorbs more than L1 does, which agrees with the adsorption and desorption rate calculation results, shown in Section 3.4, later. Figure 1 shows that Eu(III) has a larger adsorption ability under identical conditions. The same tendency was found under the presence of other REEs ions (i.e., in multiple solution; refer to Figure S2). This may be attributed to the fact that the stability constant of La-EDTA is smaller than that of Eu-EDTA, which are 15.5 and 17.4, respectively [34; 35]. The data of adsorption isotherms, kinetic models and the thermodynamic study were shown in Supplementary Information as Figures S3-S10 and Tables S1-S6. For many adsorption studies, adsorption performance is generally assessed and expressed by the adsorption capacity. However, the judgement based only on the adsorption capacity is not objective, because the maximum adsorption capacity is sensitively affected by the initial concentration of target ions. If sorbent is exposed to a higher concentration of target ions, it is usually exhibiting a higher adsorption capacity [36; 37]. Hence, instead of using adsorption capacity alone, the concept of the partition coefficient (PC) was also used to explain the performance of the adsorbent. In general, PC evaluation permits the conclusion that higher PC refers to a good adsorption affinity. Therefore, the detailed experimental data of adsorption process under different effect factors were provided in Table 2. Both of the effects of contact time and initial concentration were compared to confirm the adsorption performance. From Table 2, as long as the initial concentration is the same (120 \(\mathrm{\SIUnitSymbolMicro g\cdot L^{-1}}\)), the PC of L2 is higher than that of L1 even under different contact time. This indicates that the adsorption affinity of L2 is better than L1 no matter whether the concept of adsorption capacity or that of the PC was used. Unlike the effect of contact time, a lower PC was obtained at higher adsorption capacity. This means that the better adsorption capacity is not necessarily equivalent to an outstanding adsorption affinity. The comparison of the data obtained at different initial concentrations suggests that the adsorbent performance should be compared after adjusting these effects. Essentially, the partition coefficient for a solid-liquid adsorption system represents the ratio of analyte concentration in and on the solid adsorbent phase to its concentration in the liquid phase at equilibrium [38]. It may be presumed that the interaction strength between the absorbate and the adsorbent is dominated by the surface charge of the adsorbent. To verify this assumption, the zeta potentials of the sample (L1 and L2) dispersed in aqueous solution were measured. As shown in Table 3, the zeta potentials of L1 and L2 at pH 4 are 35.3 mV and 20.2 mV, respectively. Both the zeta potentials of L1 and L2 are positive, which implies that the host layers may be positively charged. It is important to note that the zeta potential of L1 is larger than that of L2. On the other hand, the adsorption ability is larger for L2 than for L1, as mentioned before. Moreover, with the increase of pH, the zeta potential decreases (as shown in Figure 2) and the adsorption ability of REEs ions increases. In other words, it is suggested that the sample having high adsorption capacity has a low zeta potential. Therefore, the complexation of EDTA (i.e., LDH-EDTA) leads to a lower zeta potential, which leads to the adsorption ability of REEs ions (i.e., cation, having positive charge) larger than LDH.