Recovery of Neodymium (III) from Aqueous Phase by Chitosan-Manganese-Ferrite Magnetic Beads

Neodymium is a key rare-earth element applied to modern devices. The purpose of this study is the development of a hybrid biomaterial based on chitosan (CS) and manganese ferrite (MF) for the recovery of Nd(III) ions from the aqueous phase. The preparation of the beads was performed in two stages; first, MF particles were obtained by the assessment of three temperatures during the co-precipitation synthesis, and the best nano-MF crystallites were incorporated into CS to obtain the hybrid composite material (CS-MF). The materials were characterized by FTIR, XRD, magnetization measurements, and SEM-EDX. The adsorption experiments included pH study, equilibrium study, kinetics study, and sorption–desorption reusability tests. The results showed that for MF synthesis, 60 °C is an appropriate temperature to obtain MF crystals of ~30 nm with suitable magnetic properties. The final magnetic CS-MF beads perform maximum adsorption at pH 4 with a maximum adsorption capacity of 44.29 mg/g. Moreover, the material can be used for up to four adsorption–desorption cycles. The incorporation of MF improves the sorption capacity of the neat chitosan. Additionally, the magnetic properties enable its easy separation from aqueous solutions for further use. The material obtained represents an enhanced magnetic hybrid adsorbent that can be applied to recover Nd(III) from aqueous solutions.


Introduction
Rare-earth elements (REEs) are gaining attention in technological areas because of their properties and applications [1]. Among REEs, neodymium is a key element in the technological industry, which is mainly applied in magnets and electric motors [2], and it is considered to be a critical element due to its possible scarcity in the future. Moreover, some recent studies reveal the introduction of Nd(III) in water streams [3]. Thus, the development of technologies toward the recovery or removal of Nd(III) is highly relevant.
The recovery of Nd(III) from the aqueous phase is possible through the use of several technologies such as fractional precipitation, ion-exchange, or solvent extraction after leaching the solids (i.e., from primary sources or end-of-life products). However, these processes present some disadvantages. For instance, ion-exchange is used mainly in low-scale processes and is mostly used for heavy REEs [4], varied at 60, 70, and 80 • C, and the resultant materials were labeled as MF-60, MF-70, and MF-80, corresponding to 60, 70, and 80 • C, respectively. To prepare the material, two solutions of FeCl 3 ·6H 2 O 0.1 M and MnSO 4 ·H 2 O 0.05 M were mixed in the stoichiometric relationship Fe:Mn of 2:1; then, 9 mL of NaOH 2M was swiftly added to reach the exact pH of 10.5. The solutions had been previously heated at the corresponding experimental temperature (60, 70, or 80 • C) and agitation was kept at 500 rpm for 120 min. Lastly, the obtained particles were washed several times with deionized water and totally dried in an air convection oven (Barnstead Thermolyne-Cimarec) for 48 h at 80 • C.

Synthesis of Chitosan-Manganese Ferrite Magnetic Beads
Chitosan without prior pre-treatment was dissolved in 40 mL of acetic acid 0.5 M (2.5% w/v), and was blended at 500 rpm for 60 min at 30 • C. This solution was added with 0.5 g of MF-60 and 20 mL of acetic acid 0.5 M, and newly agitated at 1200 rpm for 120 min at 30 • C. The final mass relationship of CS:MF-60 was 2:1.
For the bead formation, the previously prepared suspension was pumped with a peristaltic pump (Pharmacia LkB Pump) at 3 mL/min and added drop by drop in a NaOH 4 M solution. The coagulation process was kept for 48 h at 10 • C. Prior to the application in adsorption studies, the beads were washed with deionized water to remove the excess of NaOH and dried in an air convection oven for 12 h at 40 • C. The resultant beads were labeled as CS-MF.

Characterization
Infrared spectra were collected from 450 to 4000 cm −1 in a FTIR-ATR Thermo Scientific Nicolet 6700 (Madison, WI, USA). Magnetization hysteresis curves of the magnetic materials were obtained at 300 K in a superconducting quantum interference device (SQUID, Quantum Design magnetometer, Darmstadt, Germany). XRD spectra patterns under Cu Kα radiation from 4 to 100 • 2θ, and an exploratory velocity of 0.02 • /s, were obtained with a Bruker D8 Advance (Bruker AXS GmBH, Karlsruhe, Germany). The pH of zero charge potential (pH pzc ) was evaluated according to previously published work of [21]. The surface morphology and elemental distribution before and after the sorption experiments of the resultant beads were determined in a scanning electron microscope with an energy-dispersive X-ray probe (SEM-EDX-Phenom XL, Rotterdam, The Netherlands). Particle size distribution measurements were performed in a Zetasizer Nano Z (Malvern Panalytical Ltd., Malvern, UK).

pH Study
The effect of pH in the adsorption uptake of Nd(III) was evaluated in both MF particles and the CS-MF beads. The pH was varied at 2.0, 4.0, and 6.0. Solutions of 25 mL of 50 mg/L of Nd(III) concentration were added with 25 mg of the sorbent material (i.e., sorbent dosage (SD) of 1 g/L). The pH of the solutions was carefully adjusted by the adding of NaOH or HNO 3 . The initial (pH i ) and final pH (pH e ) were recorded. Agitation speed (AS) and contact time (CT) were fixed at 150 rpm and 24 h respectively. The Nd(III) analysis was measured in an ICP-OES (Perkin Elmer Optima 7300). Equation (1) was applied to calculate the sorption uptake or sorption capacity of the materials.
Sorption uptake equation: where q e is the adsorption capacity in (mg/g), C i and C e are the initial and equilibrium concentrations, respectively, V is the volume in L, and w is the mass of sorbent added expressed in grams.
The experiments were carried out in triplicate.

Equilibrium Study
Solutions of 25 mL of C i from 5 to 200 mg/L of Nd(III) were added with 25 mg of sorbent materials (SD: 1 g/L) and agitated during 24 h at 150 rpm in a laboratory orbital shaker. The pH of the solution was adjusted to 4.0, which was set as the optimum pH.
Langmuir equation: q e = q max bC e 1 + bC e (2) Freundlich equation: Sips equation: where q e is the adsorption capacity calculated by Equation (1) (mg/g), C e is the equilibrium concentration (mg/L), q max is the Langmuir or Sips maximum capacity in the monolayer expressed in (mg/g), b is the Langmuir constant in (L/g), K F is the Freundlich constant, n is the sorption intensity, K s is the Sips equilibrium constant in (L/mg), and ms is the Sips model exponent. The experiments were carried out in triplicate.

Kinetics
In 1 L of Nd(III) solution of Ci 50 mg/L and pH 4.0, 100 mg of CS-MF (SD: 1 g/L) was added, and several samples were then taken through time to measure the remaining Nd(III) concentration. Pseudo-first-order (PFORE), pseudo-second-order (PSORE), Elovich, and Weber and Morris models were assessed to fit the experimental data and obtain the kinetics parameter according to Equations (5)- (8): Pseudo-first-order equation (PFORE): Pseudo-second-order equation (PSORE): Elovich equation: Weber and Morris equation: where q e is the equilibrium sorption capacity (mg/g), q t is the sorption capacity (mg/g) at any time t (h), k 1 is the PFORE rate constant (1/min), k 2 is the PSORE rate constant (g/mg min), α is the initial adsorption rate (mg/g min), β is a desorption constant related to the extent of surface coverage and activation energy for chemisorption, k int is the intraparticle diffusion rate constant in mg/g * min 1/2 , and C is the initial adsorption (mg/g).

Desorption Cycles
Sorption-desorption cycles were carried out in two stages; first, to choose a proper eluent, one sorption-desorption cycle using HCl (pH 3.5), EDTA (0.05 M), ethanol (96% v/v), and methanol (98%) was used to desorb the REEs. Secondly, the best eluent, in terms of the recovery percentage desorbed, was applied in several sorption-desorption experiments.
Nanomaterials 2020, 10, 1204 where C D and V D are the concentration (mg/L) of REEs and the volume (L) in the eluted solution experiments (desorbed), respectively, C i and C e are the initial and equilibrium concentration (mg/L), respectively and V A is the volume (L) used for adsorption experiments. The experiments were carried out in triplicate.

Characterization
The formation of MnFe 2 O 4 was confirmed by XRD analysis (Figure 1a), and the three materials presented a majority phase at (34.96) [24]. However, MF-60 matches by 70% with

Characterization
The formation of MnFe2O4 was confirmed by XRD analysis (Figure 1a), and the three materials presented a majority phase at (34.96) [24]. However, MF-60 matches by 70% with MnFe2O4, according to the crystallography open database (COD): 96-230-0586. The peaks at (42.43), (56.14), and (61.74) are characteristics of a spinel structure. MF-70 and MF-80 present similarity between them, with the appearance of a peak at (61.89) in MF-80. The crystallite size was determined with the Scherrer equation, which corresponds to 30.3, 36.5, and 40.8 nm.
The magnetic properties in the three spinel-ferrites were determined; the magnetic hysteresis loops are depicted in Figure 1b. The typical behavior of ferromagnetic materials is observed. MF-60 particles have the most significant saturation magnetization (Ms), reaching 49.6 emu/g, while MF-70 and MF-80 reach 17.2 and 11.3 emu/g, respectively. The high Ms of MF-60 confirms the largest formation of MnFe2O4, which is in concordance with the XRD patterns and lower crystallite size, while lower magnetizations in MF-70 and MF-80 confirm the partial formation of MnFe2O4.
Thus, using this synthesis procedure, 60 °C is a suitable temperature to form the chemical spinel structure with a saturation magnetization and crystallite size suitable for the adsorption purposes. Other authors such as [8], using the same co-precipitation method at 80 °C, obtained MF with Ms of around 20 emu/g. Besides, [24] reported a slightly better Ms of 66 emu/g for MF synthetized by the one-step microwave hydrothermal method at 120 °C.

pH Dependence
pH is one of the most important factors that influence the adsorption process [20]. In Figure 2a, the influence of pH in the recovery of Nd(III) by MF particles is depicted. The effect of the pH was The magnetic properties in the three spinel-ferrites were determined; the magnetic hysteresis loops are depicted in Figure 1b. The typical behavior of ferromagnetic materials is observed. MF-60 particles have the most significant saturation magnetization (Ms), reaching 49.6 emu/g, while MF-70 and MF-80 reach 17.2 and 11.3 emu/g, respectively. The high Ms of MF-60 confirms the largest formation of MnFe 2 O 4 , which is in concordance with the XRD patterns and lower crystallite size, while lower magnetizations in MF-70 and MF-80 confirm the partial formation of MnFe 2 O 4 .
Thus, using this synthesis procedure, 60 • C is a suitable temperature to form the chemical spinel structure with a saturation magnetization and crystallite size suitable for the adsorption purposes. Other authors such as [8], using the same co-precipitation method at 80 • C, obtained MF with Ms of around 20 emu/g. Besides, [24] reported a slightly better Ms of 66 emu/g for MF synthetized by the one-step microwave hydrothermal method at 120 • C.

pH Dependence
pH is one of the most important factors that influence the adsorption process [20]. In Figure 2a, the influence of pH in the recovery of Nd(III) by MF particles is depicted. The effect of the pH was studied at pHs between 2 to 6, particularly because at pH > 6, the precipitation of Nd(III) in its insoluble hydroxide form (Supplementary Figure S1) is produced.
The uptake capacity (q e ) was higher as the pH was increased. It is notable that MF-60 achieves the highest performance in contrast to MF-70 and MF-80. Overall, for the three MFs, acid conditions (i.e., pH 2) did not favor the adsorption process, due to the fact that high proton concentration affects the metal-sorbent interactions, reducing the capability of Nd(III) ions for binding active sites, while, as long as the pH is increased, the adsorption is favored, reaching the maximum adsorption capacity at pH 6 (q e = 37.87 for MF-60), representing the 75.75% of efficiency.
active sites, as well as cations, can compete for the same active sites, and as the pH reaches the pHpzc, the interactions between the Nd(III) and active surface sites are major, because there are less available protons.
On the other hand, the differences in the performance at the same pH are very notable ( Figure  2a). MF-60 particles uptake 22% more Nd(III) than MF-70 and 3 times more than MF-80 at pH 4. Similarly, at pH 6, MF-60 particles adsorb 14% and 42% more than MF-70 and MF-80, respectively. This behavior is attributed to the crystallite size and purity of the particles, which were higher for MF-60 > MF-70 > MF > 80, in line with the adsorption behavior. These material features provide high particle size, surface area, and a larger number of active surface sites (corners, edges, steps), as well as hydroxyl groups, to facilitate and improve the metal adsorption [29,30]. Many magnetic particles based on MFs have been tested for Nd(III) and heavy metal removal from aqueous solutions. Table 1 shows various results with their related pH and experimental uptake capacity (qe). It is noted that MF-60 particles present a competitive performance for Nd(III) recovery against magnetite particles. Besides, MFs applied to the removal of Pb and Cr showed capacities under the reported MF uptake.  The trend in the differences of adsorption efficiency could be explained by the role of the pH pzc , which is defined as the value in which the total charge (external and internal) of the material is neutral [25], and this property is used for determining the affinity of an adsorbent for a specific sorbate [26]. The pH pzc (Figure 2b) of MFs shows that the materials present a positive surface at the experimental conditions (pH < pH pzc ) [27]. The MF particles pH pzc were determined at 6.9, 7.2, and 6.2 for MF-60, MF-70, and MF-80, respectively. According to [28], at pHs under pH pzc , it is possible a protonation of active sites, as well as cations, can compete for the same active sites, and as the pH reaches the pH pzc , the interactions between the Nd(III) and active surface sites are major, because there are less available protons.
On the other hand, the differences in the performance at the same pH are very notable (Figure 2a). MF-60 particles uptake 22% more Nd(III) than MF-70 and 3 times more than MF-80 at pH 4. Similarly, at pH 6, MF-60 particles adsorb 14% and 42% more than MF-70 and MF-80, respectively. This behavior is attributed to the crystallite size and purity of the particles, which were higher for MF-60 > MF-70 > MF > 80, in line with the adsorption behavior. These material features provide high particle size, surface area, and a larger number of active surface sites (corners, edges, steps), as well as hydroxyl groups, to facilitate and improve the metal adsorption [29,30].
Many magnetic particles based on MFs have been tested for Nd(III) and heavy metal removal from aqueous solutions. Table 1 shows various results with their related pH and experimental uptake capacity (q e ). It is noted that MF-60 particles present a competitive performance for Nd(III) recovery against magnetite particles. Besides, MFs applied to the removal of Pb and Cr showed capacities under the reported MF uptake.

CS-MF Beads
After the evaluation of the MFs particles, MF-60 was selected to be incorporated into the CS. The CS-MF material was manufactured in the form of beads as this spherical form could be suitable for use in batch or column adsorption systems. Moreover, in this format, the MF microparticles can be fixed into the chitosan for the enhancement of its adsorption capabilities and preventing the presence of microparticles in the final aqueous phase.

Morphology and Elemental Characterization
The morphology observations and the elemental distribution of the beads after Nd(III) uptake are shown in Figure 3. On the external bead surface (Figure 3a), roughness and cracked features are observed, which helps the beads enter into the aqueous phase and, consequently, the transport of Nd(III) ions into the CS-MF material. The axial view of the beads (Figure 3b) presents a high roughness and macro porosity of about 80-300 µm, which are more pronounced than in the external surface.

CS-MF Beads
After the evaluation of the MFs particles, MF-60 was selected to be incorporated into the CS. The CS-MF material was manufactured in the form of beads as this spherical form could be suitable for use in batch or column adsorption systems. Moreover, in this format, the MF microparticles can be fixed into the chitosan for the enhancement of its adsorption capabilities and preventing the presence of microparticles in the final aqueous phase.

Morphology and Elemental Characterization
The morphology observations and the elemental distribution of the beads after Nd(III) uptake are shown in Figure 3. On the external bead surface (Figure 3a), roughness and cracked features are observed, which helps the beads enter into the aqueous phase and, consequently, the transport of Nd(III) ions into the CS-MF material. The axial view of the beads (Figure 3b) presents a high roughness and macro porosity of about 80-300 µm, which are more pronounced than in the external surface.
The EDX analysis reveals the presence of C, O, N, Fe, Mn, and Nd on the surface of the bead after Nd(III) adsorption (Figure 3c). The C, O, and N are related to the CS matrix, while Fe and Mn are related to the incorporated MF, which were homogeneously distributed along the CS ( Figure  3d,e). Furthermore, in Figure 3f, the homogeneous Nd distribution after adsorption is observed.

FTIR, XRD, and Magnetic Evaluation
The FTIR spectra (Figure 4a) show the functional groups present on the material surfaces of CS-MF, MF-60, and neat CS. The spectra of MF-60 clearly indicate the peak at 552 cm −1 related to the Fe-O vibration, which is indicative of the spinel manganese-ferrite structure [34]. CS and MF-60 FTIR spectra before the adsorption showed some common signals, i.e., a peak at 3281 cm −1 , attributed to  (Figure 3d,e). Furthermore, in Figure 3f, the homogeneous Nd distribution after adsorption is observed.

FTIR, XRD, and Magnetic Evaluation
The FTIR spectra (Figure 4a) show the functional groups present on the material surfaces of CS-MF, MF-60, and neat CS. The spectra of MF-60 clearly indicate the peak at 552 cm −1 related to the Fe-O vibration, which is indicative of the spinel manganese-ferrite structure [34]. CS and MF-60 FTIR spectra before the adsorption showed some common signals, i.e., a peak at 3281 cm −1 , attributed to the hydroxyl-related groups (stretching of C-OH and Fe-OH) and the stretching vibration of the primary amine of the N-H group of CS [35], and a band at 2885 cm −1 , which is related to the symmetric groups of -CH 2 [36]. In addition, the signal at 1640 cm −1 is attributed to the C=O stretching vibration related to the carboxylates present in polysaccharides [35], and the peaks at 1374 and 1027 cm −1 are attributed to the C-O-C and C-O of CS, respectively [16]. Despite the similitudes between CS-MF and CS, a marked difference was identified in CS-MF at 552 cm −1 , which is attributed to the incorporation of MnFe 2 O 4 into CS-MF. The incorporation of Nd(III) after the adsorption was observed by the identification of two shifts in the IR spectra, one from 1554 to 1514 cm −1 related to the C=O stretching in secondary amide [37], and a second from 1418 to 1429 cm −1 related to the amide II groups of chitosan [38].
in secondary amide [37], and a second from 1418 to 1429 cm −1 related to the amide II groups of chitosan [38].
The XRD pattern of CS-MF (Figure 4b) confirms the incorporation of MF into CS; although the XRD pattern is mostly similar to the MF (Figure 1a), there are some differences. For instance, the peak at 61.74 disappears in CS-MF, probably due to the CS interaction with MF; besides, a low decrease between the atomic planes (A) was observed. Again, the database (COD: 96-230-0586) agrees by 57% with MF, and this is due to the presence of CS in the CS-MF beads.
The magnetic hysteresis loop of CS-MF (Figure 4c) indicates an Ms of 21.4 emu/g, which is less than that of its MF-60 neat particles, but higher than those of the MF-70 and MF-80 neat particles (Figure 1b). The drop in the Ms is expected, because of the presence of CS; however, this value is enough to be considered feasible to be separated by magnetic methods.

pH Dependence
The study of pH influence on the qe of Nd(III) was carried out at various pHs of 4, 5, and 6 ( Figure 5a). The experiment was executed at these conditions because at pH < 3.5, the beads are dissolved, due to the natural hydrolysis of the CS [39]. The adsorption of Nd(III) by CS-MF beads showed that at pH 4, the major qe was produced, the qe decreased as the pH was increased, and the drop in qe at pH 6 was around 50% compared to that at pH 4. The XRD pattern of CS-MF (Figure 4b) confirms the incorporation of MF into CS; although the XRD pattern is mostly similar to the MF (Figure 1a), there are some differences. For instance, the peak at 61.74 disappears in CS-MF, probably due to the CS interaction with MF; besides, a low decrease between the atomic planes (A) was observed. Again, the database (COD: 96-230-0586) agrees by 57% with MF, and this is due to the presence of CS in the CS-MF beads.
The magnetic hysteresis loop of CS-MF (Figure 4c) indicates an Ms of 21.4 emu/g, which is less than that of its MF-60 neat particles, but higher than those of the MF-70 and MF-80 neat particles (Figure 1b). The drop in the Ms is expected, because of the presence of CS; however, this value is enough to be considered feasible to be separated by magnetic methods.

pH Dependence
The study of pH influence on the q e of Nd(III) was carried out at various pHs of 4, 5, and 6 ( Figure 5a). The experiment was executed at these conditions because at pH < 3.5, the beads are dissolved, due to the natural hydrolysis of the CS [39]. The adsorption of Nd(III) by CS-MF beads showed that at pH 4, the major q e was produced, the q e decreased as the pH was increased, and the drop in q e at pH 6 was around 50% compared to that at pH 4. Figure 5b shows ∆pH (pH e − pH i = ∆pH) in solutions without Nd(III) ions (blank solutions) at different initial pHs. Thus, the ∆pH accounts for the interactions between the CS-MF surface and H + ions, in which a positive ∆pH indicates a binding of H + ions on the CS-MF. The ∆pH shows the largest difference at lower than at higher pHs; therefore, there were more electrostatic attractions at lower pHs, and these decreased as the pH approached the pH pzc (pH pzc = 8.05). In addition, the protonation of amine groups of chitosan under its pK~6 is a well-established phenomenon [40], which provides the conditions for the Nd(III) adsorption. Similarly, comparing the ∆pH produced during Nd(III) adsorption (∆pH of 1.86 at pH 4) depicted in the inner subfigure in Figure 5a, with the ∆pH at the same pH 4 in Figure 5b (∆pH of 2.8), it is noted that when Nd(III) ions are present in the solution, they compete with H + ions, and take part of the active surface sites on CS-MF. Various studies presented similar results, which indicates that under pH pzc , cation binding takes place [22,24].
On the other hand, it is noticed that the adsorption behavior of MFs and CS-MF along the pH follows an opposite trend, which means that for MFs, higher pHi conditions result in better adsorption capacity (Figure 2a), and for CS-MF, higher pHi represents lower performance ( Figure  5a). The better adsorption capacity of the CS-MF composite at lower pH responds to a greater extent to the presence of chitosan, rather than MF-60. We attributed this phenomena to the CS-MS beads composition, which are 66.66% chitosan and 33.33% MF-60-CS:MF in a ratio of 2:1, which, in turn, can be corroborated by the following: (i) the FTIR analysis after Nd(III) adsorption suggests that amino groups of chitosan were the main groups involved in the adsorption ( Figure 4a); (ii) at pHi = 4, the CS-MF beads drive stronger electrostatic interactions than MF-60, while the better adsorption performance of MF-60 at pH = 6 is mainly attributed to the physical features (crystallite nanometric size) than to electrostatic interactions (Figure 5b vs. Figure 2b); and (iii) the CS could block some of the active surface sites of MF-60, which can be assumed by the high amorphous pattern presented in the XRD profile of the CS-MF (Figure 4b). .

Equilibrium Isotherms
The effect of the initial concentration on the adsorption uptake capacity (equilibrium isotherms) is necessary to describe the retention, release, or mobility of a substance from an aqueous system to an adsorbent at constant temperature and pH [41]. Figure 6 shows the impact of the Nd(III) initial concentration in the adsorption process. Isotherm curves of CS-MF, MF-60, and neat CS (raw form) particles were developed to compare the effect of the incorporation of MF-60 in CS.
The Nd(III) adsorption capacity of CS-MF was slightly higher than those of MF-60 and neat CS (CS-MF > MF-60 > CS) at initial Nd concentrations. At Ce over 200 mg/L of Nd(III), the CS-MF adsorption capacity was around 5 times higher than that of CS particles (37.28 mg/g for CS-MF vs. 8.20 mg/g for CS), and also showed better adsorption capacity of the MF-60 particles (~34 mg/g). On the other hand, it is noticed that the adsorption behavior of MFs and CS-MF along the pH follows an opposite trend, which means that for MFs, higher pHi conditions result in better adsorption capacity (Figure 2a), and for CS-MF, higher pHi represents lower performance (Figure 5a). The better adsorption capacity of the CS-MF composite at lower pH responds to a greater extent to the presence of chitosan, rather than MF-60. We attributed this phenomena to the CS-MS beads composition, which are 66.66% chitosan and 33.33% MF-60-CS:MF in a ratio of 2:1, which, in turn, can be corroborated by the following: (i) the FTIR analysis after Nd(III) adsorption suggests that amino groups of chitosan were the main groups involved in the adsorption ( Figure 4a); (ii) at pHi = 4, the CS-MF beads drive stronger electrostatic interactions than MF-60, while the better adsorption performance of MF-60 at pH = 6 is mainly attributed to the physical features (crystallite nanometric size) than to electrostatic interactions (Figure 5b vs. Figure 2b); and (iii) the CS could block some of the active surface sites of MF-60, which can be assumed by the high amorphous pattern presented in the XRD profile of the CS-MF (Figure 4b).

Equilibrium Isotherms
The effect of the initial concentration on the adsorption uptake capacity (equilibrium isotherms) is necessary to describe the retention, release, or mobility of a substance from an aqueous system to an adsorbent at constant temperature and pH [41]. Figure 6 shows the impact of the Nd(III) initial concentration in the adsorption process. Isotherm curves of CS-MF, MF-60, and neat CS (raw form) particles were developed to compare the effect of the incorporation of MF-60 in CS.
The Nd(III) adsorption capacity of CS-MF was slightly higher than those of MF-60 and neat CS (CS-MF > MF-60 > CS) at initial Nd concentrations. At C e over 200 mg/L of Nd(III), the CS-MF adsorption capacity was around 5 times higher than that of CS particles (37.28 mg/g for CS-MF vs. 8.20 mg/g for CS), and also showed better adsorption capacity of the MF-60 particles (~34 mg/g).
The experimental data were adjusted to the Langmuir, Freundlich, and Sips models ( Table 2). This adjustment is crucial to describe the distribution of the adsorbate between the liquid-solid phases in equilibrium. CS and CF-60 data were adjusted to the Langmuir model with a correlation coefficient (r 2 ) of 0.97 and 0.96, respectively, while CS-MF was better adjusted by the Sips model (r 2 = 0.98). According to the Langmuir theory, adsorption was produced mostly in the monolayer and could be attributed to more homogeneous surfaces, while the Sips theory is related to the more heterogeneous systems [42]. Thus, the incorporation of MF particles into the CS produces a more heterogeneous structure, which is corroborated by SEM observations (Figure 3a,b). The experimental data were adjusted to the Langmuir, Freundlich, and Sips models ( Table 2). This adjustment is crucial to describe the distribution of the adsorbate between the liquid-solid phases in equilibrium. CS and CF-60 data were adjusted to the Langmuir model with a correlation coefficient (r 2 ) of 0.97 and 0.96, respectively, while CS-MF was better adjusted by the Sips model (r 2 = 0.98). According to the Langmuir theory, adsorption was produced mostly in the monolayer and could be attributed to more homogeneous surfaces, while the Sips theory is related to the more heterogeneous systems [42]. Thus, the incorporation of MF particles into the CS produces a more heterogeneous structure, which is corroborated by SEM observations (Figure 3a,b).
With regard to the sorbate-sorbent affinity, which is related to the "b" Langmuir parameter, it was superior for MF-60 followed by neat CS and CS-MF (Table 2). MF-60 and CS showed a progressive increase in qe until the saturation plateau was reached at Ce concentrations close to 30 mg/L; then, the adsorption was limited. For CS-MF, a strict plateau was not observed. The lower affinity of CS-MF was produced by the blocking of Nd(III) ions for the MF particles' surface; however, as long as the concentration was increased, a higher adsorption capacity was reached, even surpassing the MF-60 qe. Thus, the incorporation of MF-60 into CS enhances the adsorption capacity of CS toward Nd(III) ions adsorption, and even improves the qe of the MF-60 particles.  Table 3 presents similar materials with their related sorption capacity. Remarkably, CS-MF was obtained by one of the simplest existing methods. In particular, MF particles were not subjected to the annealing process at high temperatures [9], which, consequently, eliminates the need for large amounts of energy necessary to obtain nano-MF. This study demonstrates that the use of MF particles fixed in CS in the form of beads is suitable for Nd(III) recovery. Additionally, CS-MF beads present some advantages over similar magnetic and non-magnetic materials based on chitosan (Table 3). In terms of qmax, CS-MF beads are only comparable to the chitosan nano-particles functionalized with diethylenetriamine,  With regard to the sorbate-sorbent affinity, which is related to the "b" Langmuir parameter, it was superior for MF-60 followed by neat CS and CS-MF (Table 2). MF-60 and CS showed a progressive increase in q e until the saturation plateau was reached at C e concentrations close to 30 mg/L; then, the adsorption was limited. For CS-MF, a strict plateau was not observed. The lower affinity of CS-MF was produced by the blocking of Nd(III) ions for the MF particles' surface; however, as long as the concentration was increased, a higher adsorption capacity was reached, even surpassing the MF-60 q e . Thus, the incorporation of MF-60 into CS enhances the adsorption capacity of CS toward Nd(III) ions adsorption, and even improves the q e of the MF-60 particles.
CS-MF beads show competitive performance for Nd(III) recovery. Table 3 presents similar materials with their related sorption capacity. Remarkably, CS-MF was obtained by one of the simplest existing methods. In particular, MF particles were not subjected to the annealing process at high temperatures [9], which, consequently, eliminates the need for large amounts of energy necessary to obtain nano-MF. This study demonstrates that the use of MF particles fixed in CS in the form of beads is suitable for Nd(III) recovery. Additionally, CS-MF beads present some advantages over similar magnetic and non-magnetic materials based on chitosan (Table 3). In terms of q max , CS-MF beads are only comparable to the chitosan nano-particles functionalized with diethylenetriamine, authored by [15]. However, the present material is manufactured in the form of beads, which represent an advantage for their industrial application; moreover, the non-chemical modification of CS-MF implies a reduced cost in its obtention.

Kinetics
Kinetic studies are used to determine the contact time required for adsorption between the adsorbate-sorbent, as well as to gain an insight into the accumulation processes [43]. Commonly, PFORE and PSORE are used as simplified models to describe adsorption dynamics, while the Weber and Morris equation is used to evaluate the contribution of the limited film intraparticle diffusion [44]. Figure 7 shows the kinetic profile of Nd(III) onto CS-MF, in which three progressive pseudo-steps are observed: An initial step takes around 20 min until reaching a q e of 24.2 mg/g and is attributed to the external diffusion film; a second step, which takes around 75 min, reaches a q e of 32.3 mg/g, related to a mass transfer by pore diffusion throughout the liquid film into the macropores; and a third step, which takes around 180 min, with a q e of 36.5 mg/g corresponding to a surface reaction.  On the other hand, the simplified equation brought forward by Weber and Morris evaluated the contribution of the intraparticle diffusion-limited process [44]. The representation of the Weber and Morris equation (Supplementary Figure S2) results in two linear regions, which indicates that the adsorption process is conditioned by two stages. Stage 1 indicates that Nd(III) ions were diffused onto the active sites, and that adsorption was produced at a fast velocity diffusion (Kp1) of 5.04 mg/g.min 1/2 . After this, the adsorbate starts the transportation to the inner surface sites and the film diffusion resistance increases. Consequently, the Kp2 decreases to 3.04 g/mg*min 1/2 , which also The kinetic data are better adjusted to the FSORE rather than the PFORE model (Table 4). Thus, the occupation rate of Nd(III) ions is of second order regarding the available surface sites [45]. Moreover, PSORE and Elovich suggest chemisorption as the main adsorption mechanism. On the other hand, the simplified equation brought forward by Weber and Morris evaluated the contribution of the intraparticle diffusion-limited process [44]. The representation of the Weber and Morris equation (Supplementary Figure S2) results in two linear regions, which indicates that the adsorption process is conditioned by two stages. Stage 1 indicates that Nd(III) ions were diffused onto the active sites, and that adsorption was produced at a fast velocity diffusion (Kp 1 ) of 5.04 mg/g.min 1/2 . After this, the adsorbate starts the transportation to the inner surface sites and the film diffusion resistance increases. Consequently, the Kp 2 decreases to 3.04 g/mg*min 1/2 , which also indicates that Nd(III) ions cannot be easily incorporated in this stage.

Reusability
The adsorption-desorption cycles evaluate the reusability of adsorbent materials. In this study, two phases were carried out. Firstly, in one sorption-desorption cycle, with four eluents including HCl and EDTA at pH 10, MeOH and EtOH were tested in order to ascertain the most efficient desorbing solution (Figure 8a). From this first stage, MeOH and EDTA showed better desorption efficiency than the other eluents with up to 80% of desorption, while EtOH and HCl performed 55% and 50%, respectively (Figure 8a). EDTA is considered to be a metal-complexing with high affinity for rare-earth elements, which, in turn, serves as an explanation for its optimal desorption performance, while MeOH has been tested as an excellent desorbing agent of metals from the chitosan matrix. Nanomaterials 2020, 10, x FOR PEER REVIEW 13 of 15 efficiency than the other eluents with up to 80% of desorption, while EtOH and HCl performed 55% and 50%, respectively ( Figure 8a). EDTA is considered to be a metal-complexing with high affinity for rare-earth elements, which, in turn, serves as an explanation for its optimal desorption performance, while MeOH has been tested as an excellent desorbing agent of metals from the chitosan matrix. MeOH was the desorbing agent selected for testing the reusability of the CS-MF, and the material performs up to four adsorption/desorption cycles with efficiencies over 55% (Figure 8b), from which the first three cycles achieve around 80% of recovery; however, in the fourth cycle, both adsorption and desorption efficiency drop to 55%.

Conclusions
The adsorbent magnetic beads of chitosan-manganese ferrite were developed by the use of a simple procedure, in which the temperature of coprecipitation synthesis of MF was optimized. The hybrid material was successfully applied to Nd(III) recovery from aqueous solutions. The material developed shows acceptable adsorption capacity and equilibrium reaction time; additionally, the material can be reused up to four times and can be removed by the use of a magnetic field.  MeOH was the desorbing agent selected for testing the reusability of the CS-MF, and the material performs up to four adsorption/desorption cycles with efficiencies over 55% (Figure 8b), from which the first three cycles achieve around 80% of recovery; however, in the fourth cycle, both adsorption and desorption efficiency drop to 55%.

Conclusions
The adsorbent magnetic beads of chitosan-manganese ferrite were developed by the use of a simple procedure, in which the temperature of coprecipitation synthesis of MF was optimized. The hybrid material was successfully applied to Nd(III) recovery from aqueous solutions. The material developed shows acceptable adsorption capacity and equilibrium reaction time; additionally, the material can be reused up to four times and can be removed by the use of a magnetic field.

Conflicts of Interest:
The authors declare no conflict of interest.