Adsorption and Desorption Mechanisms of Rare Earth Elements (REEs) by Layered Double Hydroxide (LDH) Modiﬁed with Chelating Agents

: In order to obtain the adsorption mechanism and adsorption structures of Rare Earth Elements (REEs) ions adsorbed onto layered double hydroxides (LDH), the adsorption performance of LDH and ethylenediaminetetraacetic acid (EDTA) intercalated LDH for REEs was investigated by batch experiments and regeneration studies. In addition to adsorption capacity, the partition coe ﬃ cient (PC) was also evaluated to assess their true performance metrics. The adsorption capacity of LDH increases from 24.9 µ g · g − 1 to 145 µ g · g − 1 for Eu, and from 20.8 µ g · g − 1 to 124 µ g · g − 1 for La by intercalating EDTA in this work; and PC increases from 45.5 µ g · g − 1 · uM − 1 to 834 µ g · g − 1 · uM − 1 for Eu, and from 33.6 µ g · g − 1 · µ M − 1 to 405 µ g · g − 1 · µ M − 1 for La. Comparison of the data indicates that the adsorption a ﬃ nity of EDTA-intercalated LDH is better than that of precursor LDH no matter whether the concept of adsorption capacity or that of the PC was used. The prepared adsorbent was characterized by XRD, SEM-EDS and FT-IR techniques. Moreover, quantum chemistry calculations were also performed using the GAUSSIAN09 program package. In this calculation, the molecular locally stable state structures were optimized by density functional theory (DFT). Both the quantum chemistry calculations and the experimental data showed that REEs ions adsorbed by EDTA-intercalated LDH are more stable than those adsorbed by precursor LDH. Furthermore, the calculation results of adsorption and desorption rates show that adsorption rates are larger for Eu(III) than for La(III), which agrees with the experimental result that Eu(III) has a higher adsorption ability under the same conditions. The LDHs synthesized in this work have a high a ﬃ nity for removing REEs ions. the of the complex compared with REEs without complexation. They also showed that the species in the of is more stable than that in its absence and that the intercalation of EDTA does indeed the stability of the adsorbed species. Finally, from our numerical results of adsorption and


Introduction
Rare Earth Elements (REEs) are the collection of 17 special elements which are usually divided into heavy rare earth elements (HREE) and light rare earth elements (LREE). REEs could be widely ·mH 2 O, where cationic M II and M III are divalent and trivalent metals, and occupy the center of octahedral in the brucite-like layer. A n− is the interlayer anion of charge n that leads to the electric neutrality of the LDH, and the coefficient x is the molar ratio of M II /(M II + M III ). The structure of LDH suggests that these materials can be intercalated easily with other anions. Various types of anions can be intercalated in its interlayer space. It has been extensively reported by both inorganic [11,12] and organic [13,14] chemistry researchers. The ability of LDH to intercalate anions makes them useful as catalysts, anion exchangers, and adsorbents. We note that several physicochemical models were proposed to rationalize the anion-exchange constants [15]. Some formalisms were derived by relating the activity of an anion to the anion-exchange constant [16], while geometric features of atoms, such as charge radii of the anions were taken into account to investigate the anion-exchange ability of halide anions on LDH [17].
Moreover, LDHs modified with hybrids have also been studied as potential adsorbents of heavy metals from aqueous solution [18][19][20]. Chelation is a type of bonding of ions or molecules to metallic ions. It involves the formation of coordinate bonds between a single central atom and ligand within multiple separate binding sites. Therefore, it can be expected that chelating agents modified LDH have higher adsorption capacity and better selectivity compared with other adsorbents for metallic ions. In our previous work [21], we synthesized and characterized LDH intercalated with the chelating agent ethylenediaminetetraacetic acid (EDTA) or N,N -1,2-ethanediylbis-1-aspartic acid (EDDS) and studied the uptake of Cd(II), Cu(II), and Pb(II) by these hybrid compounds. It turned out that the LDHs synthesized in that work were very effective for removing heavy metal ions from aqueous solutions. In fact, in our another previous work [22], to theoretically clarify the adsorption mechanism and adsorption structures of LDH, we have performed quantum chemistry calculations of reactants, locally stable states, transition states, and products among phosphorous anion, water and hydrotalcite in a variety of pH ranges.
As mentioned above, a number of works have been devoted to researches on the adsorption phenomena of lanthanide [4][5][6][23][24][25][26]. These works were mainly focused on the potential application of materials for removal of lanthanides from wastewater. On the other hand, the objectives of our present work are to experimentally investigate the efficiency of LDHs for adsorbing REEs from aqueous solution, as well as to unveil the adsorption mechanism and adsorption structures of lanthanide adsorbed onto LDH using quantum chemistry calculations. We carried out the uptake experiments for the adsorption of REEs (lanthanum, europium) from aqueous solutions by LDH modified with EDTA. In addition, we performed quantum chemistry calculations, including locally stable states of LDH-EDTA and optimized structures of the chemical systems. Particular emphasis is put on the elucidation of the effect of EDTA on structural stability. In the calculations, we used molecular cluster models for hydrotalcite lamellae, whose chemical structure is described by Mg 12 Al 7 (OH) 36 9+ [22,27].
Finally, to get a deeper insight into the uptake mechanism, we calculated the desorption rates of the adsorbates.

Materials and Methods
Chemical reagents, including Zn(NO 3

Synthesis of the Adsorbent
In this section, we present the synthesis processes of L1 and L2. The synthesis of LDHs intercalated with EDTA includes two steps: The preparation of the precursor NO 3 -LDH (L1), and the ion-exchange reaction between NO 3 -LDH and Ethylenediaminetetraacetic acid disodium salt.

Synthesis of Precursor L1
L1 was prepared by dropping addition of 100 mL aqueous solution of 0.02 mol Zn(NO 3 ) 2 ·6H 2 O and 0.01 mol Al(NO 3 ) 3 ·9H 2 O to 100 mL NaOH/NaNO 3 solution (pH 10, molar ratio 1:1). Then, the solutions were agitated at 70 • C for 8 h by maintaining the pH, separated by centrifugation, and washed until they became neutral.

Synthesis of L2
L2 was synthesized as follows. Under an N 2 atmosphere, 0.015 mol of EDTA was added to the 150 mL of the suspended solution of L1. Then, the mixing solutions were agitated at 70 • C for 8 h under a certain pH degree, separated by centrifugation, washed until they became neutral, and then dried at 60 • C overnight.
The above synthesis processes were conducted with N 2 purging to avoid CO 2 uptake from the atmosphere. The preparation and purification of the adsorbent, and the characterization of the samples were reported in detail in our previous paper [21].

Characterization of the Adsorbent
Infrared spectra were obtained using the KBr disc method, with wavenumbers from 400 to 4000 cm −1 on an FT-IR (JASCO, Tokyo, Japan: FTIR-4200). The XRD pattern of LDHs samples was carried out on a RINT2500HR-PC (RIGAKU Corporation, Tokyo, Japan) using Cu Kα radiation in the scanning range of 2-80 • . A Nova Nano SEM450 scanning electron microscope (FEI Co., Ltd., New York, NY, USA) was performed to examine the surface morphology and element distribution of L1 and L2 after the adsorption of lanthanide. The zeta-potentials of LDHs samples were measured by electrophoretic light scattering method (Otsuka, Tokyo, Japan: ELSZ-2000ZS).

Adsorption Experiments Using L1 and L2 as Adsorbents
Twenty milligrams of L1 or L2 were put into contact with 30 mL of an aqueous solution containing La(III) or Eu(III) ion with known initial concentration. Batch adsorption experiments were conducted in the pH range of 4-6 (optimum pH), contact time from 10 min to 8 h, temperature 25 • C, and adsorbent dosage 20 mg. The pH of each solution was adjusted using 0.1 mol·L −1 NH 4 OH and 0.1 mol·L −1 HNO 3 . Following the adsorption experiment, the suspension was filtered (0.45 µm, Mixed Cellulose Ester 47 mm, Advantec MFS, Inc., Dublin, CA, USA). In order to discuss the target ions before and after the adsorption, we have dissolved the sample and measured the concentration of Ln ions by an Inductively Coupled Plasma-Mass Spectrometry (Agilent HP4500, Santa Clara, CA, USA). The operating conditions of Inductively Coupled Plasma-Mass Spectrometry (ICP-MS) are shown in Table 1.

Desorption and Regeneration Experiments
After the adsorption experiment, the exhausted adsorbent was washed and dried overnight. Then it was shaken in a 100 mL flask which contained 30 mL HCl or HNO 3 solution with different concentrations. After the system reached equilibrium, the suspension was filtered, and finally, Eu(III) and La(III) content in the filtrate was determined. Subsequently, the adsorbent was neutralized by ultrapure water for several times and reconditioned for adsorption in succeeding cycles. The second adsorption experiments were carried out by using regeneration adsorbent under the optimum condition. The adsorption-desorption processes were repeated five times in this work.

Quantum Chemistry Calculation
All of the present quantum chemistry calculations were performed using the GAUSSIAN09 program package [28]. The molecular locally stable state structures were optimized by density functional theory (DFT) at the theoretical level of B3LYP. The basis sets were SDD (Stuttgart-Dresden) for Europium atoms and 6-311G (d, p) for other atoms. To take into account the effect of a water environment on our target systems, polarizable continuum medium (PCM method) with an appropriate dielectric constant for the solvent (water) was used [29]. To model the adsorbent, molecular cluster models for hydrotalcite lamellae whose chemical structure is described by Mg 12 Al 7 (OH) 36 9+ were used [27,30]. The interlayer distance was kept 9.3 Å to imitate the experimentally observed one [31].

Calculation of Adsorption and Desorption Rates
The following equation was derived in Reference [32]: Appl. Sci. 2019, 9, 4805 5 of 16 Here, C Ln is the metal ion concentration at a given time t in the aqueous solution in mmol L −1 and C Ln,0 is its initial concentration in mmol L −1 . In Equation (1), we defined In Equations (2) and (3), B, D, and M/(AV) are the constants determined by adsorption constant k ad , desorption constant k d , and the volume of the solution in liters V. By fitting the experimental data on the metal ion concentration, C Ln , versus time, t, by Equation (1), we obtain the constants, α, β, and D because C Ln , C Ln,0 , and t are determined experimentally. Using the constants, α, β, and D, obtained in this way, we can get B, D, and M/(AV) from Equations (2) and (3), In Equation (2), we have where K is the adsorption equilibrium constant of the solute, From Equation (4), we immediately find Because we have obtained M/(AV) above and K is known from the experiment, we can obtain k d from Equation (6). Then, from Equation (5), k ad is expressed as Above, k d and k ad are the required adsorption and desorption rates, respectively. To fit the aqueous concentration of adsorbates versus time by Equation (1) and to obtain k d and k ad , we have used a genetic algorithm [33]. The remarkable difference between our work and Ref. [32] is that k DES,Ln was determined by iterating Equation (1) until the best fit was obtained to the experimental results in the latter case, while the genetic algorithm makes it unnecessary to do such computationally demanding iterations in order to obtain k d and k ad in the former case. 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.

Adsorption Experiment
Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci 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 Figure S3-S10 and Table 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 μg·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]. 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 µg·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.

Characterization of L1 and L2
The Zn:Al ratio and the amount of Ln absorbed are shown in Table 4. The component analysis result, shown in Table 4, indicates that the molar ratio of Zn/Al is approximately equal to that in the preparing solution, which shows that the dosage of reagents is reasonable. L1 and L2 were dissolved by HNO3 after adsorption of Ln ions. The amounts of Ln ions in the LDH phase, which were obtained by an ICP-MS are also shown in Table 4. The adsorption ability of REEs ions can be evaluated from these results.

Characterization of L1 and L2
The Zn:Al ratio and the amount of Ln absorbed are shown in Table 4. The component analysis result, shown in Table 4, indicates that the molar ratio of Zn/Al is approximately equal to that in the preparing solution, which shows that the dosage of reagents is reasonable. L1 and L2 were dissolved Appl. Sci. 2019, 9,4805 8 of 16 by HNO 3 after adsorption of Ln ions. The amounts of Ln ions in the LDH phase, which were obtained by an ICP-MS are also shown in Table 4. The adsorption ability of REEs ions can be evaluated from these results. The SEM images of (a   Figure 4 shows the (003), (006) and (110) peaks, which indicate that the layered structures are observed for all the L1, L2, and L2-Eu. After the intercalation by EDTA and the adsorption process, the (110) peak is still visible, as shown in Figure 4b,c. These figures show that the layer structure was destroyed by the intercalating process neither for EDTA nor for EDTA-Ln(III). However, the layer structure may be destroyed by repeated desorption process, which results in the decrease of the removal efficiency after the cycle adsorption. Based on the angle of peak (003) corresponding to the basal spacing, the basal spacing values of L1, L2 and L2-Eu were estimated to be 0.89 nm, 1.47 nm and 1.47 nm, respectively. These values were calculated by the Bragg equation. The interlayer distance was obtained by subtracting from the basal spacing to the layer width (0.48 nm) [39]. The interlayer distance of L2 and L2-Eu indicates that EDTA coexists and that EDTA is intercalated into L1 successfully. The adsorption process also increases the interlayer distance because it is close to the dimensions of EDTA complexes (0.9-1 nm) generally found for by single-crystal XRD of M-EDTA (M: Metallic ions)  Figure 4 shows the (003), (006) and (110) peaks, which indicate that the layered structures are observed for all the L1, L2, and L2-Eu. After the intercalation by EDTA and the adsorption process, the (110) peak is still visible, as shown in Figure 4b,c. These figures show that the layer structure was destroyed by the intercalating process neither for EDTA nor for EDTA-Ln(III). However, the layer structure may be destroyed by repeated desorption process, which results in the decrease of the removal efficiency after the cycle adsorption. Based on the angle of peak (003) corresponding to the basal spacing, the basal spacing values of L1, L2 and L2-Eu were estimated to be 0.89 nm, 1.47 nm and 1.47 nm, respectively. These values were calculated by the Bragg equation. The interlayer distance was obtained by subtracting from the basal spacing to the layer width (0.48 nm) [39]. The interlayer distance of L2 and L2-Eu indicates that EDTA coexists and that EDTA is intercalated into L1 successfully. The adsorption process also increases the interlayer distance because it is close to the dimensions of EDTA complexes (0.9-1 nm) generally found for by single-crystal XRD of M-EDTA (M: Metallic ions) compound [40]. The very sharp peak at 1380 cm −1 in Figure 5a can be attributed to the NO3 -stretching vibration, while the corresponding peak is absent in Figure 5b

Regeneration Studies
From industrial and technological points of view, it is desirable to recover and reuse the adsorbed material. The effective reuse of adsorbent materials directly affects the cost factor, so its practicability in continuous batch adsorption process is important [43,44]. In this work, the regeneration of the used EDTA-LDH adsorbent was investigated. The desorption efficiency of the exhausted adsorbent is shown in Figure 6, and the removal efficiency of the regenerated L2 adsorbent The very sharp peak at 1380 cm −1 in Figure 5a can be attributed to the NO3 -stretching vibration, while the corresponding peak is absent in Figure 5b

Regeneration Studies
From industrial and technological points of view, it is desirable to recover and reuse the adsorbed material. The effective reuse of adsorbent materials directly affects the cost factor, so its practicability in continuous batch adsorption process is important [43,44]. In this work, the regeneration of the used EDTA-LDH adsorbent was investigated. The desorption efficiency of the exhausted adsorbent is shown in Figure 6, and the removal efficiency of the regenerated L2 adsorbent is shown in Figure 7. From Figure 6, the desorption by HNO3 shows good desorption efficiency for

Regeneration Studies
From industrial and technological points of view, it is desirable to recover and reuse the adsorbed material. The effective reuse of adsorbent materials directly affects the cost factor, so its practicability in continuous batch adsorption process is important [43,44]. In this work, the regeneration of the used EDTA-LDH adsorbent was investigated. The desorption efficiency of the exhausted adsorbent is shown in Figure 6, and the removal efficiency of the regenerated L2 adsorbent is shown in Figure 7. From Figure 6, the desorption by HNO 3 shows good desorption efficiency for both La(III) and Eu(III).  The optimum concentration was 200 mmol·L −1 . The desorption efficiency of La(III) was found to be 95.67%, whereas that of Eu(III) was slightly lower; this may be due to the fact that the stability constant of Eu-EDTA (17.4) is higher than that of La-EDTA (15.5). Figure 7 shows the better reuse performance of L2 after three cycles. The hydrogen ions may destroy the structure during the desorption process, which results in the decrease of the removal efficiency after the fourth or fifth cycle.

Numerical Results of Adsorption and Desorption Rates
The temporal evolutions of the ion concentrations of Eu(III) and La(III) in the aqueous solution are shown in Figure 8 ((a) Eu(III), (b) La(III)). In general, the ion concentrations in aqueous solution decrease unilaterally with time, which is consistent with Equation (1). In addition, it can be found that the genetic algorithm actually fits the experimental time evolutions of the ion concentrations very well.  The optimum concentration was 200 mmol·L −1 . The desorption efficiency of La(III) was found to be 95.67%, whereas that of Eu(III) was slightly lower; this may be due to the fact that the stability constant of Eu-EDTA (17.4) is higher than that of La-EDTA (15.5). Figure 7 shows the better reuse performance of L2 after three cycles. The hydrogen ions may destroy the structure during the desorption process, which results in the decrease of the removal efficiency after the fourth or fifth cycle.

Numerical Results of Adsorption and Desorption Rates
The temporal evolutions of the ion concentrations of Eu(III) and La(III) in the aqueous solution are shown in Figure 8 ((a) Eu(III), (b) La(III)). In general, the ion concentrations in aqueous solution decrease unilaterally with time, which is consistent with Equation (1). In addition, it can be found that the genetic algorithm actually fits the experimental time evolutions of the ion concentrations very well. The optimum concentration was 200 mmol·L −1 . The desorption efficiency of La(III) was found to be 95.67%, whereas that of Eu(III) was slightly lower; this may be due to the fact that the stability constant of Eu-EDTA (17.4) is higher than that of La-EDTA (15.5). Figure 7 shows the better reuse performance of L2 after three cycles. The hydrogen ions may destroy the structure during the desorption process, which results in the decrease of the removal efficiency after the fourth or fifth cycle.

Numerical Results of Adsorption and Desorption Rates
The temporal evolutions of the ion concentrations of Eu(III) and La(III) in the aqueous solution are shown in Figure 8 ((a) Eu(III), (b) La(III)). In general, the ion concentrations in aqueous solution decrease unilaterally with time, which is consistent with Equation (1). In addition, it can be found that the genetic algorithm actually fits the experimental time evolutions of the ion concentrations very well. The adsorption and desorption rates calculated from the fittings in Figure 8 are shown in Table 5. We can see that the adsorption rate is larger for Eu(III) than for La(III), which agrees with the experimental result that Eu(III) has a higher adsorption ability under the identical conditions, as shown in Section 3.3. In addition, Table 5 suggests that Eu(III) desorbs more easily than La(III). As shown in Figure 7 experimentally, the recovery efficiency of La(III) is smaller than that of Eu(III). This means that the rate of desorption is low if the recovery efficiency is small. Therefore, our numerical results reasonably suggest that recovery efficiency is large if the rate of desorption is large.

Quantum Chemistry Calculation
The structures of the complexes themselves are shown in Supplementary Information (Figure S11 and Tables S7-S10). Figure 9 shows the energies of (a) [Eu(H2O)8] 3+ adsorbed on precursor LDHs and (b) Eu 3+ adsorbed on EDTA-intercalated LDH relative to the dissociation limit. It can be seen that Eu 3+ adsorbed on EDTA-intercalated LDH is more stable than the dissociation limit (panel (b)), whereas [Eu(H2O)8] 3+ adsorbed on precursor LDH is more unstable than the dissociation limit (panel (a)). This The adsorption and desorption rates calculated from the fittings in Figure 8 are shown in Table 5. We can see that the adsorption rate is larger for Eu(III) than for La(III), which agrees with the experimental result that Eu(III) has a higher adsorption ability under the identical conditions, as shown in Section 3.3. In addition, Table 5 suggests that Eu(III) desorbs more easily than La(III). As shown in Figure 7 experimentally, the recovery efficiency of La(III) is smaller than that of Eu(III). This means that the rate of desorption is low if the recovery efficiency is small. Therefore, our numerical results reasonably suggest that recovery efficiency is large if the rate of desorption is large.

Quantum Chemistry Calculation
The structures of the complexes themselves are shown in Supplementary Information ( Figure  S11 and Tables S7-S10). Figure 9 shows the energies of (a) [Eu(H 2 O) 8 ] 3+ adsorbed on precursor LDHs and (b) Eu 3+ adsorbed on EDTA-intercalated LDH relative to the dissociation limit. It can be seen that Eu 3+ adsorbed on EDTA-intercalated LDH is more stable than the dissociation limit (panel (b)), whereas [Eu(H 2 O) 8 ] 3+ adsorbed on precursor LDH is more unstable than the dissociation limit (panel (a)). This implies that the adsorption of Eu 3+ on EDTA-intercalated LDH is energetically more probable than that on precursor LDH. Actually, the strongly intercalated structure between EDTA and LDH, shown in panel (b), indicates a more stable configuration than the weakly bonded structure between coordination H 2 O and LDH, shown in panel (a). This is reasonable because the Coulomb repulsion between precursor LDHs (charge = +14) and . This is a result consistent with the experimental finding that the complexation of EDTA improves the adsorption capacity of LDH. We note that the experimental results were shown for different adsorption efficiencies of phosphate anions on [Mg-Al]-LDH and [Zn-Al]-LDH [15]. The work concluded that the adsorption efficiency of the latter is larger than that of the former. This is basically due to the fact that the different ionic radii lead to different crystalline structures. Because of this, [Mg-Al]-LDH does not change its crystalline structure upon the adsorption of phosphate, while [Zn-Al]-LDH dramatically changes it, in order to ease the adsorption of phosphate. If this is the case, the replacement of Mg cations by Zn cations may lead to different adsorption efficiencies, shown in the present work, which originates from their different crystalline structures. We note that the experimental results were shown for different adsorption efficiencies of phosphate anions on [Mg-Al]-LDH and [Zn-Al]-LDH [15]. The work concluded that the adsorption efficiency of the latter is larger than that of the former. This is basically due to the fact that the different ionic radii lead to different crystalline structures. Because of this, [Mg-Al]-LDH does not change its crystalline structure upon the adsorption of phosphate, while [Zn-Al]-LDH dramatically changes it, in order to ease the adsorption of phosphate. If this is the case, the replacement of Mg cations by Zn cations may lead to different adsorption efficiencies, shown in the present work, which originates from their different crystalline structures.

Comparison with Other Adsorbents
In general, although the adsorption affinity is usually compared based on the adsorption capacity, it is difficult to evaluate each adsorbent on a parallel basis by using adsorption capacity alone. Adsorption experiments of each material are usually conducted under various initial concentrations or volumes of solution. From Table 2, although the adsorption capacity obtained at high initial concentration is larger than that at lower initial concentration, the PC at high initial concentration shows a reverse tendency. Hence, the concept of PC was also used here to compare the adsorption affinity with other reported adsorbents. The comparison of the adsorption properties of other previous adsorbents was shown in Table 6.  Table 6, EDTA modified LDH which synthesized in this work has relatively high adsorption capacity (145 µg·g −1 for L2-Eu, 124 µg·g −1 for L2-La) relative to only LDH. It means the chelating agents improve the adsorption affinity of LDH. However, comparing with some adsorbents which were exposed to a higher concentration of target ions measured under their adsorption experiments, it shows a lower adsorption capacity. It is difficult to compare each other under different conditions (even thousand times difference among them). This is a result of adsorption capacity sensitively to the initial concentration of target ions. Therefore, introducing the concept of PC is also important to reduce this difference. The PC of both L2-Eu and L2-La are larger in comparison with others, which can indicate that LDH intercalated by EDTA has superior adsorption performance.

Conclusions
In conclusion, we performed XRD, SEM-EDS, and FT-IR experiments to characterize layered double hydroxides (LDHs) modified with EDTA and to identify the prepared LDH-NO 3 (L1) and LDH-EDTA (L2). In addition, based on these experimental results, the adsorption capabilities and mechanisms of REEs ions on L1 and L2 were experimentally accessed. It was shown that both La(III) and Eu(III) could rapidly be adsorbed, and that the adsorption capacity of L2 was larger than that of L1 no matter whether the concept of adsorption capacity or that of the PC was used. In addition, comparing with other adsorbents, the PC of both L2-Eu and L2-La are relatively larger. It indicates that LDH intercalated by EDTA has superior adsorption performance. The complexation of REEs ions with EDTA (i.e., L2) brought about a lower zeta potential, which indicates that the former plays the role more dominant than the latter and that the latter is just a secondary result stemming from the former. In accord with this, quantum chemistry calculations showed that the complexation actually leads to the negatively charged species being adsorbed on LDHs, which promotes the adsorption of the complex compared with REEs without complexation. They also showed that the species in the presence of EDTA is more stable than that in its absence and that the intercalation of EDTA does indeed improve the stability of the adsorbed species. Finally, from our numerical results of adsorption and desorption rates, it was suggested that the recovery efficiency is large if the rate of desorption is large. Both the quantum chemistry calculation results and the adsorption and desorption rate results are consistent with the experimental ones. The LDH-EDTA synthesized in this work have a high affinity for removing REEs ions.
Supplementary Materials: The following are available online at http://www.mdpi.com/2076-3417/9/22/4805/s1, Figure S1: Effect of common ions (Ca 2+ , Mg 2+ , Na + and K + ) on the removal efficiency of lanthanides using ground original sample, Figure S2: Adsorption capacity of (a) La(III) and (b) Eu(III) both in single and multiple solution by using L1 or L2, Figure S3: Langmuir isotherm for La(III) adsorption onto L2, Figure S4: Freundlich isotherm for La(III) adsorption onto L2, Figure S5: Langmuir isotherm fitting for Eu(II) adsorption onto L2, Figure S6: Freundlich isotherm fitting for Eu(III) adsorption onto L2, Figure S7: The kinetic models for La(III) adsorption onto L2, Figure S8: The kinetic models for Eu(III) adsorption onto L2, Figure S9: Plots of lnK d vs. 1/T for the estimation of thermodynamic parameters obtained for the adsorption of (a) La(III) and (b) Eu(III) on L2, Figure S10 Table S1: Coefficients of Langmuir and Freundlich isotherms for La(III) adsorption onto L2, Table S2: Coefficients of Langmuir and Freundlich isotherms for Eu(III) adsorption onto L2, Table S3: Kinetic parameters of Pseudo-first order and Pseudo-second order, Table S4: Kinetic parameters of Elovich model and Intraparticle diffusion, Table S5: Thermodynamic parameters for the adsorption of La(III) on L2, Table S6: Thermodynamic parameters for the adsorption of Eu(III) on L2,  3+ shown in Panel (a) of Figure S3, Table S8