Hydrated solid ionic channels for rare earth element separation and recovery

Abstract

Methods of separating rare earth elements, such as lanthanides, from an aqueous solution that includes two or more different types of rare earth elements are provided. The methods use confined solid ionic channels in layered, mixed metal oxides to separate different rare earth ions based on hydration shell size, dehydration energy, binding affinity, and / or hydration phase transformations.

Description

Atty. Dkt. No.05400-0070-PCT HYDRATED SOLID IONIC CHANNELS FOR RARE EARTH ELEMENT SEPARATION AND RECOVERY CROSS REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority to U.S. provisional patent application number 63 / 599,049 that was filed November 15, 2023, the entire contents of which are incorporated herein by reference. REFERENCE TO GOVERNMENT RIGHTS

[0002] This invention was made with government support under DE-FOA-0002563 awarded by the DOE. The government has certain rights in the invention. BACKGROUND

[0003] Rare earth elements (REEs) encompassing seventeen elements including the lanthanides, yttrium (Y), and scandium (Sc), hold immense importance for a wide range of modern technologies such as solar cells, wind turbines, electric vehicles, light-emitting diodes, optical fibers, and medical imaging. The application of REEs necessitates the attainment of high purity for each individual element; however, the challenge of effective separation among REEs has persisted since their discovery. Currently, industrial production of REEs predominantly relies on solvent extraction due to its scalability. However, refining 1 ton of REE oxide generates 40–110 tons of carbon dioxide (equivalent), produces 1.4 tons of radioactive waste, and 200 m3of acid-containing sewage water. Thus, there is an urgent need to develop sustainable methods for REEs separation to secure the supply chain. (Lee, J. et al., J. Ind. Ecol.21, 1277-1290, (2017); Navarro, J. et al., Front. Energy Res.2, (2014); Leal Filho, W. An Analysis of the Environmental Impacts of the Exploitation of Rare Earth Metals.269-277, (2016); and Hurst, C. China’s Rare Earth Elements Industry: What Can the West Learn? , (Institute for the Analysis of Global Security (IAGS), 2010).)

[0004] The separation among REEs primarily relies on two key differences in properties. The first is their ionic radius, which contracts in the lanthanides with a difference of 17.1 pm across the 15 elements. (Cheisson, T. et al., Science 363, 489-493 (2019).) The smallest difference, 0.7 pm, exists between the neighboring pair Yb3+and Lu3+. The second difference lies in their Lewis acidity, leading to varying binding affinities to ligands. These differences have paved the way for many methods of rare earth separation, including precipitationAtty. Dkt. No.05400-0070-PCT (crystallization), chromatographic separation, solvent extraction, membrane separation, and bio-separation. Particularly, methods that combine both size sieving and binding affinity exhibit high selectivity among REEs. The size effect in ligand binding, supramolecular assembly, or crystallization is usually across several binding sites within single-digit nanometers in its correlation with length. Rigid solid ionic channels, with confinement dimensions at the Angstrom scale and material dimensions at tens to hundreds of nanometers could induce coupling among incorporated species. (Ruiz Pestana, L. et al., Environ Sci Technol 51, 393-400, (2017); Pestana, L. et al., Chem Sci 9, 1640-1646, (2018); Whittakera, M. L. et al., Ion exchange selectivity in clay is controlled by nanoscale chemical–mechanical coupling. PNAS (2019).) However, such long-range confinement is largely unexplored for separation. SUMMARY

[0005] Methods of separating rare earth ions from an aqueous solution that includes different types of rare earth ions are provided.

[0006] One embodiment of a method of separating rare earth ions from an aqueous solution comprising a mixture of rare earth ions includes the steps of: providing a layered, mixed metal oxide comprising a hydration phase comprising stacked layers of a transition metal oxide and hydrated metal cations intercalated in channels between the stacked layers, wherein the channels have a pinned interlayer spacing; exposing the layered, mixed metal oxide to an aqueous solution comprising a mixture of at least two different types of rare earth ions, wherein at least some of the rare earth ions in the mixture have a lower dehydration energy barrier than other rare earth ions in the mixture; and introducing rare earth ions into the channels via electrochemical intercalation, whereby the rare earth ions having the lower dehydration energy barrier are preferentially introduced into the channels

[0007] One embodiment of a method of separating rare earth ions from an aqueous solution comprising a mixture of rare earth ions includes the steps of: providing a layered, mixed metal oxide comprising a hydration phase comprising stacked layers of a transition metal oxide and hydrated metal cations intercalated in channels between the stacked layers; exposing the layered, mixed metal oxide to an aqueous solution comprising a mixture of at least two different types of rare earth ions, wherein an ion exchange between the hydrated metal cations and at least one type of the at least two different types of rare earth ions induces a hydration phase transformation that increases a channel spacing in the layered, mixed metalAtty. Dkt. No.05400-0070-PCT oxide, and an ion exchange between the hydrated metal cations and at least one other type of the at least two different types of rare earth ions does not induce a hydration phase transformation that increases the channel spacing in the layered, mixed metal oxide; and allowing the hydrated metal cations in the channel to undergo ion exchange with the rare earth ions, whereby the rare earth ions that do not induce the hydration phase transformation are preferentially introduced into the channels

[0008] The two embodiments described above can be combined to carry out a rare earth ion separation on an aqueous solution comprising a mixture of rare earth ions, whereby the separation based on the hydration phase transformations is carried out on the aqueous solution first, followed by an additional separation using electrochemical intercalation. The layered, mixed metal oxide used in the two separations can be the same or different and / or the rare earth ions intercalated into the layered, mixed metal oxide during the first separation can be removed prior to carrying out the second separation. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Illustrative embodiments of the invention will hereafter be described with reference to the accompanying drawings, wherein like numerals denote like elements.

[0010] FIGS.1A-1D show different structural responses induced by Group I and Group II lanthanides and the pinning strategy to control the ion exchange pathway. FIG.1A shows a Group of Lanthanides. FIGS.1B, 1C are schematics showing ion exchange from Mg-buserite structure. Group I lanthanides (La3+to Nd3+) will expand the interlayer spacing to 11.1 Å (FIG.1B). Group II lanthanides (Eu3+to Yb3+) will maintain the buserite phase with interlayer spacing of 9.7 Å (FIG.1C). Sm3+is at the border of Group I and II. FIG.1D is a schematic showing La3+and Nd3+intercalation into structure with pre-seeded co-ion Mg2+. The interlayer spacing is fixed at 9.6 Å.

[0011] FIGS.2A-2F show Group structural behaviors of hydrated LnxMnO2. FIG.2A shows geometries of hydrated Dy3+(center ball, left panel) and La3+(center ball, right panel) representing heavy and light REEs, respectively. Water molecules are represented with grey and white colors for O and H atoms, respectively. Heavy REEs cations with coordination number (CN) 8 have the configuration of square antiprism (SAP), while light REEs cations with CN 9 form tricapped trigonal prism (TTP) shape. FIG.2B shows a comparison of the free spacings of three different layered MnO2 phases and the calculated first hydration shellAtty. Dkt. No.05400-0070-PCT diameters of REEs. FIGS.2C and 2D show synchrotron XRD showing the (001) peaks of Ln0.11MnO2by ion exchange starting from Mg-buserite (FIG.2C) and Na-birnessite (FIG. 2D). La3+, Pr3+, and Nd3+show the (001) peak at far-left positions while the remaining Ln have one peak from Mg-buserite but two peaks from Na-birnessite. FIGS.2E, 2F show interlayer spacing values of Ln0.11MnO2 exchanged from Mg-buserite (FIG.2E) and Na- birnessite (FIG.2F).

[0012] FIGS.3A-3B show elemental composition of the hydrated MnO2structure exchanged from Mg- buserite and Na-birnessite measured by ICP-MS. Na+and Mg2+residuals are negligible. Charge is the summation of the positive charge in the interlayers including REEs cations, Na+and Mg2+with a theoretical value of 0.32. In FIG.3A, the first bar indicates all Mg residue, bars 2-4 and 7 indicate all RE residue, and the remaining bars indicate, starting from the base of the bars, Na residue, Mg residue, and RE (bars 6, 9, 10, 12), Mg residue and RE (bar 7) and Na residue and RE (bars 11 and 13). In FIG.3B, the first bar indicates all Na residue, bars 3-6, 8 and 13 indicate all RE, and the remaining bars indicate, starting from the base of the bars, Na residue and RE.

[0013] FIG.4 shows XRD Spectra of La-water rich phase during drying process.

[0014] FIGS.5A-5K show selectivity and coordination under confinement. FIG.5A shows an enrichment factor for neighboring pairs from ion exchange using the Mg-buserite structure. Ln1and Ln2refer to elements with lower and higher atomic number, respectively. FIGS.5B and 5C show measured and accumulated enrichment factor for four same-group pairs (FIG.5B) and four cross-group pairs (FIG.5C). FIG.5D shows a STEM image and its corresponding EDS elemental mapping (Mn, Nd, and Dy) of the LnxMnO2 particle exchanged with Nd-Dy pair. Scale bar is 1 μm. FIG.5E shows an atomic ratio of Mn, Nd, and Dy to the sum of all atoms (including O, C, and Mg) for three particles imaged by STEM. Error bars representing the standard deviation of three replicate measurements. FIG. 5F shows synchrotron XRD spectra showing the (001) peaks for LnxMnO2 exchanged with REE mixtures representing the same-group and cross-group pairs. FIG.5G shows a K-edge Fourier-transformed R-space EXAFS spectra for 0.25 M nitrate solution and LnxMnO2 with single REE inside by ion exchange from Mg-buserite. The CN for each case is labeled next to the spectrum. FIG.5H shows a comparison of Fourier transform of the EXAFS in R space for Nd3+in aqueous solution and in LnxMnO2 for La-Nd pair, single element, and for Nd-Dy pair (shades from dark to light along with decreased peak intensity). FIGS.5I-5K OptimizedAtty. Dkt. No.05400-0070-PCT structures of the most stable configuration for each La3+, Nd3+, and Dy3+inside channels with the illustration showing two repeating unit cells along x-axis: fully hydrated structure of La0.125MnO2^2.125H2O with CN of 8 (FIG.5I), fully hydrated structure of Nd0.125MnO2^2H2O with CN of 8 (FIG.5J), and fully hydrated structure of Dy0.125MnO2^1.5H2O with CN of 8 (FIG.5K). Interlayer spacing values are shown with arrows.

[0015] FIGS.6A-6B show a STEM image (FIG.6A) and its corresponding EDS elemental mapping (FIG.6B) for two LnxMnO2 particles from 1:1 Nd-Dy pair ion exchange. Scale bar is 1µm.

[0016] FIG.7 shows an overlay of Fourier-transformed R-space EXAFS spectra original data for 0.25M nitrate solution and LnxMnO2 with single REE inside by ion exchange from Mg-buserite.

[0017] FIG.8 shows synchrotron XRD spectra of LnxMnO2 starting from La0.11MnO2 water rich phase.

[0018] FIG.9 shows synchrotron XRD spectra of mixed LnxMnO2starting from La0.11MnO2 water rich phase and Na-birnessite phase.

[0019] FIGS.10A-10C show optimized structures of La0.125MnO2^2.125H2O showing the repeating unit cells. To explore various hydration states and La-O coordination configurations, partially hydrated structures with coordination numbers of 9 (FIG.10A) and 8 (FIG.10B), and fully hydrated structures with coordination numbers of 9 (FIG.10C) for La- O were considered, respectively.

[0020] FIGS.11A-11C show optimized structures of Nd0.125MnO2^2H2O showing the repeating unit cells. To explore various hydration states and Nd-O coordination configurations, partially hydrated structures with coordination numbers of 9 (FIG.11A) and 8 (FIG.11B), and fully hydrated structures with coordination numbers of 9 (c) for Nd-O were considered, respectively.

[0021] FIG.12 shows optimized structures of Dy0.125MnO2^1.5H2O showing the repeating unit cells. Partially hydrated structure with coordination numbers of 8 is shown.

[0022] FIGS.13A-13C show a comparison of synchrotron (001) XRD peaks between experimental and simulated crystal structure. Simulated peaks are from optimized structures of La0.125MnO2^2.125H2O (FIG.13A), Nd0.125MnO2^2H2O (FIG.13B), andAtty. Dkt. No.05400-0070-PCT Dy0.125MnO2^1.5H2O (FIG.13C). Dashed line shows the position of the experimental XRD peak. Partial hydration and full hydration are denoted as ‘p’ and ‘f’, while coordination numbers of 9 and 8 with Ln-O are denoted as ‘CN-9’ and ‘CN-8’, respectively. FWHM for broadening of simulated crystal structures was normalized to a value of 0.05 Å-1.

[0023] FIG.14 shows total binding energy of Ln0.125^nH2O and MnO2with partial hydration and CN of 9. (Left bars are La (Group I) and right bars are Nd (Group I).)

[0024] FIG.15 shows total binding energy of Ln0.125^nH2O and MnO2with partial hydration and CN of 8. (Left bars are La (Group I), center bars are Nd (Group I), and right bars are Dy (Group II).)

[0025] FIG.16 shows total binding energy of Ln0.125^nH2O and MnO2with full hydration and CN of 9 in water-rich phase. (Left bars are La (Group I) and right bars are Nd (Group I).)

[0026] FIG.17 shows total binding energy of Ln0.125^nH2O and MnO2 with full hydration and CN of 8.. (Left bars are La (Group I), center bars are Nd (Group I), and right bars are Dy (Group II).)

[0027] FIGS.18A-18D show optimized structures of Nd0.125MnO2^2.125H2O showing the repeating unit cells. To explore various hydration states and Nd-O coordination configurations, partially hydrated structures with coordination numbers of 9 (FIG.18A) and 8 (FIG.18B), and fully hydrated structures with coordination numbers of 9 (FIG.18C) and 8 (FIG.18D) for Nd-O were considered, respectively.

[0028] FIGS.19A-19B show optimized structures of Dy0.125MnO2^2.125H2O showing the repeating unit cells. To explore various hydration states and Dy-O coordination configurations, partially hydrated structures with coordination numbers of 8 (FIG.19A), and fully hydrated structures with coordination numbers of 8 (FIG.19B) for Dy-O were considered, respectively.

[0029] FIGS.20A-20C show optimized structures of La0.125MnO2^1.5H2O showing the repeating unit cells. To explore various hydration states and La-O coordination configurations, partially hydrated structures with coordination numbers of 9 (FIG.20A) and 8 (FIG.20B), and fully hydrated structures with coordination numbers of 8 (FIG.20C) for La- O were considered, respectively.

[0030] FIGS.21A-21C show optimized structures of Nd0.125MnO2^2.125H2O showing the repeating unit cells. To explore various hydration states and Nd-O coordinationAtty. Dkt. No.05400-0070-PCT configurations, partially hydrated structures with coordination numbers of 9 (FIG.21A) and 8 (FIG.21B), and fully hydrated structures with coordination numbers of 8 (FIG.21C) for Nd- O were considered, respectively.

[0031] FIGS.22A-22D show structural response and selectivity under pinning. FIG.22A shows an in situ synchrotron XRD showing the MnO2structural change under Mg2+pinning (starting state: Mg-buserite) during electrochemical intercalation. Current, C / 4. FIG.22B shows in situ synchrotron XRD showing the MnO2structural change during electrochemical intercalation using the La-Nd pair exchanged LnxMnO2 as starting material. Current, C / 4. FIG.22C shows a comparison of enrichment factors among ion exchange, electrochemical intercalation using pair exchanged LnxMnO2 as starting material, and electrochemical intercalation under Mg2+pinning for La-Nd, La-Pr and Nd-Sm pairs. FIG.22D shows enrichment factors of Nd-Dy and La-Nd pairs after one-time and two-time of separation using ion exchange and Mg2+pinning method, respectively. Error bars representing the standard deviation of three replicate measurements.

[0032] FIG.23 shows ex-situ synchrotron XRD of the LnxMnO2 after electrochemical intercalation for the La-Pr and Nd-Sm pairs. Both (001) peaks were fixed at Mg-Buserite 9.6 Å position.

[0033] FIG.24 shows synchrotron XRD spectra of C / 4 intercalation of 0.1 M each NdSm nitrate solution into after NdSm ion exchange structure for 200min.

[0034] FIGS.25A-25D show electrochemical intercalation curves. FIG.25A shows La- Nd intercalation starting from La- Nd seed structure and Mg pinning structure. FIG.25B shows La-Pr intercalation starting from La-Pr seed structure and Mg pinning structure. FIG. 25C shows Nd-Sm intercalation starting from Nd-Sm seed structure and Mg pinning structure. FIG.25D shows La-Nd intercalation starting from Mg pinning structure with 1:1 ratio and 1:5.4 ratio mixture solution.

[0035] FIGS.26A-26E show optimized structures of hydrated Ln3+ ion, H2O, and layered MnO2. Hydrated Ln3+ ions exhibit a tricapped trigonal prism (TTP) with La (FIG. 26A) and Nd (FIG.26B), and a square antiprism (SAP) with Dy (FIG.26C), respectively. Same number of H2O molecules with FIGS.26A-26C are considered in FIG.26D. The layered MnO2 (FIG.26E) structure was optimized after removing the cation and H2O molecules from the buserite structure.Atty. Dkt. No.05400-0070-PCT DETAILED DESCRIPTION

[0036] Methods of separating rare earth ions, such as lanthanides, from an aqueous solution that includes two or more different types of rare earth ions are provided. The methods use confined solid ionic channels in layered, mixed metal oxides to separate different rare earth ions based on hydration shell size, dehydration energy, and / or binding affinity. The methods can be carried out without the use of ligands, acids, or toxic chemicals.

[0037] The methods can be used to separate different types of rare earth ions from sources that include a mixture of said ions, such as natural ores and wastes generated in the fabrication or recycling of batteries or magnets.

[0038] A variety of layered, mixed metal oxides can be used in the methods. In some embodiments the layered, mixed metal oxides are transition metal oxides in which the layers comprise sheets of edge-sharing MO6 octahedra, where M is a transition metal, such as Mn, and charge-balancing cations are located within the interlayer spaces. Terminating oxygens of the layers impart a hard base nature which provides a strong affinity to rare earth elements. One specific example of a layered, transition metal oxide that can be used is magnesium manganese oxide.

[0039] In some embodiments of the methods, the driving force for the separation of rare earth ions is based on a phase transformation in a layered, mixed metal oxide having an initial hydration phase characterized by a layer spacing. When rare earth ions having different hydration shell diameters undergo ion-exchange with metal cations intercalated in the layered, mixed metal oxide, rare earth ions having a first hydration shell diameter that is comparable to or smaller than the interlayer free spacing of the layered, mixed metal oxide can enter the channels and become confined within the initial hydration phase, while larger rare earth ions entering the channels induce a hydration phase transformation to form a more water-rich phase with a higher interlayer spacing. As a result, the introduction and confinement of the smaller rare earth ions in the narrow channels raises the dehydration energy barrier for the larger rare earth ions, relative to that of the smaller rare earth elements, and disfavors the coordination for the larger rare earth ions entering the channels.

[0040] In addition, since the water coordination number for the non-phase-transforming (smaller) rare earth ions is smaller than the water coordination number for the phase transforming (larger) ions, the smaller rare earth ions have a higher Lewis acidity, which enhances their binding to the channels, which are formed from the hydrated metal oxideAtty. Dkt. No.05400-0070-PCT layers. Therefore, both dehydration and coordination (binding) can provide driving forces for rare earth element separation based on phase transformations.

[0041] Based on the hydration phase transformation principle, when a layered, mixed metal oxide is exposed to (e.g., immersed in) an aqueous solution comprising a mixture of rare earth ions, the rare earth ions having a first hydration shell diameter that is comparable to, equal to, or smaller than the free spacing of the layered, mixed metal oxide, preferentially undergo ion exchange and confinement in the channels of the layered, mixed metal oxide, relative to rare earth ions that induce a hydration phase transformation in the layered, mixed metal oxide. (Note: Free spacing = interlayer spacing – thickness of the metal oxide layer – oxygen diameter.) After the ion exchange-based separation, the aqueous solution is enriched in the hydration-phase-transforming rare earth ions and the layered, mixed metal oxide is enriched in the smaller, non-phase-transforming ions, where enrichment is evaluated based on the initial concentrations (or ratios) of the rare earth ions in the aqueous solution.

[0042] Methods of separating rare earth elements based on hydration phase transformations in a layered magnesium manganese oxide with a buserite phase are illustrated in the Example. The Example describes the separation of smaller (heavier) lanthanides (Eu3+to Yb3+), which maintain the buserite phase after ion-exchange with the Mg, from larger (lighter) lanthanides (La3+to Nd3+), which expand the buserite phase to a new water-rich phase upon ion-exchange. The buserite phase is well-suited for this separation because the first hydration shell diameters of the lanthanides (6.6 Å to 7.1 Å) span the free spacing of the buserite (6.8 Å). Therefore, the buserite can induce different dehydration behaviors for different members of the lanthanides.

[0043] Methods for separating rare earth elements are also provided for elements that are not differentiated by their hydration phase transformation behaviors – that is, elements that induce the same or similar hydration phase transformation in the layered mixed metal oxide. In these methods, the structure of the hydration phase is fixed (“pinned”), owing to the presence of the initial cations in the interlayer spaces, which stabilize the hydration phase structure, including the layer spacing, and suppress the hydration phase transformation that would otherwise occur upon ion exchange with the rare earth ions. When the narrower confinement of the initial hydration phase is pinned, both dehydration energies and binding affinities to the metal oxide channels favor smaller (heavier) rare earth ions within a group of rare earth ions having the same hydration phase transforming properties. Therefore, theAtty. Dkt. No.05400-0070-PCT pinning strategy can be used to achieve selective separation within a mixture of such rare earth ions via electrochemical intercalation of the rare earth ions into the channels of the layered, mixed metal oxide. The pinning of the layer spacing can be achieved by pre-seeding the layered, mixed metal oxides with pinning cations in the interlayer spaces. Provided that the rate of electrochemical intercalation is higher than the rate of ion exchange (which occurs in parallel with electrochemical intercalation), some of the pinning cation initially present in the channels can be maintained in the channels throughout the separation, such that the interlayer spacing remains pinned throughout the separation.

[0044] Based on the pinning strategy, when an electrochemical intercalation is carried out on a pinned, layered, mixed metal oxide in an aqueous solution comprising a mixture of rare earth ions having the same hydration phase transforming behavior, rare earth ions having a smaller first hydration shell diameter undergo preferential electrochemical intercalation and confinement in the channels of the layered, mixed metal oxide, relative to rare earth ions with larger first hydration shell diameters. After the electrochemical intercalation-based separation, the aqueous solution is enriched in the larger rare earth ions and the layered, mixed metal oxide is enriched in the smaller rare earth ions, where enrichment is evaluated based on the initial concentrations (or ratios) of the rare earth ions in the aqueous solution. The pinning strategy for separation is particularly useful for mixtures of two or more rare earth ions having first hydration shells with diameters that are greater than the free spacing of the pinned, layered, mixed metal oxide.

[0045] Methods of separating rare earth elements based on electrochemical intercalation into a layered, magnesium manganese oxide having its buserite phase pinned by interlayer Mg2+cations are illustrated in the Example. The Example describes the enrichment of the smaller (heavier) lanthanide in an electrode comprising the layered, magnesium manganese oxide for each of the following lanthanide ion pairs: La-Pr; La-Nd; and Nd-Sm.

[0046] Generally, an electrochemical intercalation can be carried out in an electrochemical cell having a working electrode comprising the layered, mixed metal oxide, a counter electrode, and, optionally, a reference electrode. The electrodes are immersed in the aqueous solution containing the rare earth ions and a bias voltage is applied across the working and counter electrodes to induce rare earth ions from the solution to intercalate into the layered, mixed metal oxide.Atty. Dkt. No.05400-0070-PCT

[0047] The layered, mixed metal oxides may be used in a variety of forms, including as a free powder or supported on a substrate. For the electrochemical intercalation methods, the substrate may be an electrically conducting substrate to provide an electrode structure.

[0048] The separation methods may be carried out in multiple stages to improve the separation. In one embodiment of a multiple stage separation, an aqueous solution comprising rare earth ions having different hydration phase transformation properties undergoes a separation based on those different phase transformation properties, as described above, whereby rare earth elements that do not induce a hydration phase transformation upon ion exchange are preferentially removed from the aqueous solution. The aqueous solution, which is now enriched in the hydration phase transformation-inducing rare earth ions, then undergoes another separation using a pinned layered, mixed metal oxide, as described above.

[0049] Once the separation is complete, the separated rare earth elements can be recovered from the layered, mixed metal oxide, the aqueous solution, or both, by separating the rare earth elements from channels in the layered, mixed metal oxide and / or separating the rare earth elements from the aqueous solution.

[0050] The methods described here can achieve the enrichment of a smaller (heavier) lanthanide in a layered, mixed metal oxides with enrichment factors of at least 1.5, at least 3, at least 5, or at least 10, relative to a larger (lighter) lanthanide. By way of illustration, a smaller lanthanide can be enriched in a layered, mixed metal oxides with an enrichment factor in the range from 1.5 to 50, relative to a larger lanthanide.

[0051] Additional details regarding the methods disclosed herein, including procedures for determining interlayer spacings, hydration shell diameters, and enrichment factors are provided in the Example below. EXAMPLE

[0052] This Example illustrates methods to achieve separation among REEs in aqueous systems without ligands using extremely confined manganese oxide (MnO2) solid ionic channels with optimal initial layer spacing.

[0053] This Example shows that hydrated layered MnO2can provide the optimal confinement dimension (free spacing of ~6.8 Å from the interlayer lattice spacing of ~9.6 Å), which is comparable to or smaller than the first hydration shell diameter of rare earth ions, while the hard base nature of the channel chemistry from the terminating oxygen can provideAtty. Dkt. No.05400-0070-PCT strong affinity to REEs. REEs can induce different hydrated structures in MnO2 with distinct interlayer lattice spacings and, therefore, can be divided into two groups. Group I (La3+to Nd3+) expands the buserite phase to a new water-rich phase with an interlayer spacing of ~11.1 Å, while Group II (Eu3+to Yb3+) maintains the buserite phase with an interlayer spacing of ~9.7 Å, and Sm is on the border with an interlayer spacing of ~10.0 Å (FIGS.1A- 1C). These results are in quantitative agreement with the results of density functional theory calculations for the buserite and water-rich phases, with the calculations providing detailed structural information about lanthanide coordination in channels where the ions prefer to interact with water rather than the MnO2 layers. The significantly different structural responses promote separation across Group I and Group II lanthanides, preferring Group II elements due to the enlarged dehydration energy barriers and unfavorable coordination for Group I REEs entering and residing in a narrower channel occupied by Group II REEs. Moreover, to induce structural features to enhance the separation among Group I lanthanides, a pinning strategy was designed to use Mg2+co-ions to fix MnO2at the buserite phase with narrower interlayer spacing during the entire ion transport pathway of REEs via electrochemical intercalation (FIG.1D). Boosted enrichment factors of 5.4 ± 0.1 and 4.2 ± 0.1 were achieved for La-Nd and La-Pr pairs, compared to 1.6 ± 0.1, and 1.5 ± 0.1 without pinning from a 1: 1 mixture. Using the confined solid ionic channels, 92.3% and 97.0 % purity of Dy and Nd can be obtained with a two-stage separation from 1:1 Nd-Dy and La-Nd pairs, respectively. Synchrotron X-ray absorption and diffraction both showed critical evidence supporting the effect of pinning to control dehydration and coordination in confinement to achieve high selectivity among lanthanides.

[0054] Results

[0055] Group structural behaviors in hydrated LnxMnO2solid ionic channels

[0056] REEs have two different hydration configurations. Light REEs have nine water molecules in their first hydration shell with a tricapped trigonal prism (TTP) configuration, and heavy REEs have eight water molecules in their first hydration shell with a square antiprism (SAP) configuration because of the smaller ionic radius and stronger binding with water molecules (FIG.2A). (Zhang, J. et al., Inorg. Chem.53, 7700-7708, (2014).) The interlayer spacing of Mg-buserite (Mg0.16MnO2) is 9.6 Å, with a free spacing of 6.8 Å. Such free spacing dimension is ideal since it is within the range of the first hydration shell diameter of lanthanides (6.6 – 7.1 Å, shown in FIG.2B) and, therefore, could induce differentAtty. Dkt. No.05400-0070-PCT dehydration behaviors. See Supplementary Note 1 for details about the calculation of free spacings and the estimation of first hydration shell diameters. The crystal structure of Na- birnessite (Na0.32MnO2) was also selected for comparison since it gives a narrower interlayer spacing of 7.2 Å with a free spacing of 4.4 Å as the starting confinement dimension, which could lead to larger dehydration barriers. Ion exchange was used to introduce the lanthanide ions into the confined solid ionic channels of hydrated MnO2(see Methods for details). Twelve lanthanides from La to Yb were selected except for Ce and Pm since Ce is easily oxidized and Pm is radioactive. The ion exchange kinetics are fast such that more than 88 % of ion exchange is completed within 1 hour, as confirmed by inductively coupled plasma mass spectrometry (ICP-MS) (Table 1).

[0057] Table 1. Ion exchange kinetics. ~8 mg Mg-Buserite (Mg0.16MnO2) powder was added into 2 mL 0.01 M single element solution (2 times higher excess of REEs cations). Mg% is defined as the ratio of Mg2+ unexchanged compared with the starting amount. Sum is calculated by adding up all the positive charge together and should have a theoretical value of 0.32. More than ~88% ion exchange was finished within 1 h. Sample Time Mg / Mn Ln / Mn Mg / % Sum 10 min 0.05 0.08 31.3 0.32 La 0.01M 2ml 30 min 0.04 0.08 25.0 0.32 h 0.02 0.10 12.1 0.33 min 0.04 0.08 25.0 0.32min 0.03 0.08 19.4 0.31 0.01 0.09 6.5 0.31min 0.04 0.08 25.8 0.31 min 0.03 0.08 19.4 0.31 0.01 0.09 6.7 0.30

[0058] The structures of hydrated LnxMnO2 were characterized by synchrotron X-ray diffraction (XRD). As shown in FIG.2C and FIG.2E, starting from the Mg-buserite structure, a new phase formed by ion exchange with La3+, Pr3+, and Nd3+(defined as Group I lanthanides), where (001) peaks shifted to the left of the initial buserite peak with interlayer spacing of 11.1 Å, 10.9 Å, and 10.9 Å, respectively. A negligible amount of Mg2+was detected, indicating a complete ion exchange of Mg2+by Ln3+(FIGS.3A-3B). To distinguish from the existing buserite and birnessite phases, this phase is referred to as the water-rich phase. The water-rich phase loses water irreversibly and easily (within 10 mins) if exposed to air (FIG.4). This water-rich phase is rarely observed and has been reported once forAtty. Dkt. No.05400-0070-PCT La0.11MnO2 synthesis. (Luo, J. et al., Inorg. Chem. (1999).) Pr0.11MnO2 and Nd0.11MnO2 still have residue peaks around the buserite (001) position which indicates they can reside in both water-rich and buserite phases while La3+resides mostly in the water-rich phase. XRD peak deconvolutions of La0.11MnO2, Pr0.11MnO2, and Nd0.11MnO2are shown in Table 2. The other eight lanthanides, from Eu3+to Yb3+(defined as Group II lanthanides) maintained the buserite phase with interlayer spacing of ~ 9.7 Å, and with a slight right shift of the (001) peak with increasing atomic number (FIGS.2C, 2E). Sm3+is at the border of Group I and Group II such that it also expands the interlayer spacing, but to a narrower dimension of 10.0 Å compared with the water-rich phase. In contrast, starting from the Na-birnessite structure, La3+, Pr3+, and Nd3+(defined as Group I’ lanthanides) can still completely expand the interlayer spacing to ~11.3 Å regardless of a narrower starting position of 7.2 Å. The rest of the nine lanthanides, from Sm3+to Yb3+(defined as Group II’ lanthanides) showed different behavior compared to Mg-buserite. Two distinct interlayer spacings exist after ion exchange, with one of ~9.7 Å, similar to that in the Mg-buserite case, and the other one of ~7.3 Å, near the starting Na-birnessite (001) position but slightly expanded (FIGS.2D and 2F). Disappearance of the birnessite peak for Tb3+was noticed, but Tb3+was still categorized in Group II’ since it has a prominent buserite phase as shown in FIG.2D. Negligible amount of Na+residues were detected according to the ICP-MS results (FIGS.3A-3B), thus both peaks were attributed to lanthanide ions, which means that for Group II lanthanides, they can reside in both buserite and birnessite phases. Therefore, three distinct structural responses were observed with lanthanides residing in the confinement of the hydrated MnO2layers. Both the lanthanides’ characteristics and the starting confinement dimension determine the final states of Ln0.11MnO2.

[0059] Table 2. Deconvolution results of XRD (001) peaks for elements Mg, La, Pr, Nd, and Sm. Xc is peak center. A is area. w is Full width at half maximum (FWHM). ParametersPeakArea FWHM start(Å-1) end(Å-1)for drawingCenter(Å-1)peak xcA w x-range x-range Mg Gaussian 0.6443 1166.62 0.04571 0.54 0.84 Lorentzian 0.6539 2512.61 0.01316 0.54 0.84 La Lorentzian 0.567 4814.1 0.02303 0.46 0.72 Gaussian 0.6022 5024.03 0.07853 0.46 0.72 Pr Gaussian 0.577 2284.12 0.03554 0.46 0.72 Gaussian 0.6254 3770.44 0.05545 0.46 0.72 Nd Gaussian 0.5756 1656.51 0.02815 0.46 0.72 Gaussian 0.6124 3538.88 0.06132 0.46 0.72Atty. Dkt. No.05400-0070-PCT Sm Lorentzian 0.6287 3118 0.03273 0.46 0.84

[0060] Structural behavior dependent dehydration and coordination for lanthanide separation

[0061] The existence of different structural responses among lanthanides poses an important question concerning whether such a difference can induce distinct dehydration and coordination for the separation among lanthanides. The selectivity of the ion exchange process for the twelve lanthanides was evaluated using Mg-buserite. First, neighboring pair selectivity was measured. Mixture solutions with equal molar concentration (0.1 M each) of lanthanide pairs were used and the interlayer lanthanide compositions were measured using ICP-MS (See Methods for details). Most neighboring pairs showed enrichment factors close to 1.1 in the hydrated MnO2channels, with the heavier lanthanides slightly favored (FIG. 5A). Three pairs showed enrichment factors over 1.5, including La-Pr of 1.5 ± 0.1, Nd-Sm of 1.6 ± 0.1, and Gd-Tb of 1.6 ± 0.1. The selectivity between neighboring pairs is comparable with the REE extraction using 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (HEHEHP) with an average separation factor of 1.5. (SATO, T., Hydrometallurgy 22, 121- 140 (1989).) The similar preference for neighboring lanthanides within the same Group indicates similar dehydration and coordination behaviors such that the energy differences in the ion exchange process are not significant. Moreover, within the same Group, the enrichment factor of any non-neighboring pairs can be predicted from the accumulated enrichment factors of neighboring pairs (FIG.5B), which is attributed to the continuous change of Lewis acidity. Three pairs within the same groups, La-Nd, Eu-Dy, and Eu-Yb, were tested. La-Nd separation is especially important since they co-exist in the same ores and also in the recycling process of NiMH batteries. (Gasser, M. S. et al., Int. J. Miner. Process. 121, 31-38, (2013).) The measured enrichment factor of La-Nd (1.6 ± 0.1) is close to the product of the enrichment factor of La-Pr (1.5 ± 0.1) and Pr-Nd (1.0 ± 0.1) of 1.5.

[0062] Next, whether different structural behaviors could induce different dehydration and coordination to promote separation was investigated. Cross-group pairs were evaluated. Four cross-group pairs were selected, including La-Dy, Pr-Dy, Nd-Dy, and Nd-Eu, with Nd- Dy having practical importance in the recycling of NdFeB permanent magnets. (Ding, A. et al., Environ. Sci. Technol.56, 4404-4412, (2022); Kitagawa, J. et al., Sci. Rep.7, 8039, (2017); Liu, Q. et al., J. Rare Earths, (2020).) The measured enrichment factors are 7.8 ± 0.1, 5.7 ± 0.1, 4.5 ± 0.1, and 2.6 ± 0.1 for La-Dy, Pr-Dy, Nd-Dy, and Nd-Eu, respectively. TheAtty. Dkt. No.05400-0070-PCT measured selectivity showed enhancement compared to accumulated enrichment factors of 5.4 ± 0.6, 3.5 ± 0.4, 3.5 ± 0.4, and 2.0 ± 0.1 calculated from the neighboring pair enrichment factors (FIG.5C). Scanning transmission electron microscopy (STEM) with energy- dispersive X-ray spectroscopy (EDS) was used to map the elemental distribution and confirmed that the selectivity occurs at the single particle level. For the Nd-Dy pair (FIG. 5D), both elements showed uniform signals without segregation. The atomic ratio of Dy / Nd ratio was 7.07 ± 0.47 (FIG.5E) based on the EDS spectra of three particles, which is close to the ICP-MS results (average of all particles). The mapping of more particles is shown in FIGS.6A-6B.

[0063] To reveal the mechanism of enhanced cross-group selectivity, synchrotron XRD and X-ray absorption spectroscopy (XAS) were used to characterize the channel structure and the coordination of lanthanides. XRD data (FIG.5F) shows that when the pairs are from the same group of lanthanides, they induce a similar structural response to the hydrated MnO2. For example, La3+and Nd3+can both expand the buserite phase to a water-rich phase. When they are present together, the final structure still has a water-rich phase with an interlayer spacing of 11.1 Å, therefore the transport pathway is not changed significantly. However, for cross-group pairs, the final hydrated structure is fixed by the Group II lanthanides at the buserite phase with interlayer spacing of 9.7 Å owing to the presence of the initial residing Mg2+and the later exchanged Group II lanthanides. The narrower confinement of the buserite phase could induce a larger dehydration energy barrier for the Group I lanthanides which makes their entrance to the ionic channel less favorable. More evidence was provided by extended X-ray absorption fine structure (EXAFS) to unveil the origin of selectivity. (Wang, M. et al., Curr. Opin. Electrochem.30, 100803, (2021); Wang, M. et al. Electrochim. Acta 466, 143034, (2023).) The K-edge of the lanthanides was probed. The coordination environment of lanthanides in the hydrated MnO2 channel was determined from EXAFS in both single-element and pair cases. The lanthanides’ coordination number (CN) under confinement was compared to that in bulk aqueous solutions where all the cations are fully hydrated as shown in FIG.5G. For La and Nd, the peak for LnxMnO2had an obvious decrease in intensity compared to that in aqueous solutions, indicating a smaller CN, while for Dy the two peaks almost overlapped with each other, indicating a similar coordination environment (FIG.7). In the single element case in bulk aqueous solutions, La3+and Nd3+had CNs of 9.0 ± 0.8 and 9.0 ± 1.6 while Dy3+had a CN of 8.0 ± 0.6. After ion exchange, in the confinement of hydrated MnO2, La3+had a CN of 7.0 ± 0.8, showing significantAtty. Dkt. No.05400-0070-PCT dehydration from the first shell. Meanwhile, Nd3+and Dy3+had CNs of 8.4 ± 0.7 and 7.5 ± 0.6, indicating smaller degrees of dehydration owing to the smaller size of their first hydration shell. This shows that the selection of the Mg-buserite structure for the confined ionic channel is ideal in that it can induce a different dehydration process for certain lanthanides to squeeze in the structure. Furthermore, to connect with the selectivity data, the CN of Nd3+in both the same group pair (La-Nd) and the cross-group pair (Nd-Dy) has been determined (FIG.5H). When coexisting with La3+, Nd3+resides in the water-rich phase and had a CN of 8.9 ± 0.7. This is similar to the CN in bulk solution and also larger than in the single Nd3+element case. This could be due to the presence of La3+, which expanded the interlayer more completely and introduced more water molecules into the channel to coordinate with Nd3+. Therefore, although Nd3+had a lower dehydration barrier than La3+, it also had a larger CN with more water in the first shell to shield interaction with the framework. This resulted in compromised coordination strength and only a slight preference over La3+. In the case of cross-group pairs, Nd3+showed a decreased CN of 8.2 ± 0.9 in the presence of Dy3+in the buserite phase. The narrow confinement of the buserite phase indeed induced a larger dehydration barrier for Nd3+compared to the water-rich phase, which resulted in a reduced CN of Nd3+and a stronger binding strength with framework oxygen. Meanwhile, the presence of Nd3+did not affect the CN of Dy3+and the CN was still 7.5 ± 0.6. Since the CN of Dy3+was smaller than that of Nd3+, with higher Lewis acidity, Dy3+will have stronger binding to the hydrated MnO2. Therefore, both dehydration and coordination favored Dy3+and promoted the Dy to Nd selectivity. The XRD and EXAFS results prove the effectiveness of dialing the structural behavior of lanthanides for their separation and the importance of optimizing channel structure to tune energy differences in dehydration and coordination during the ion exchange process.

[0064] The water-rich and Na-buserite phases were also investigated as the starting states for lanthanide separation based on ion exchange. However, the water-rich phase can only be partially maintained by Eu3+and Gd3+from Group II with La3+residue left in the interlayers while the rest of the Group II lanthanides will convert the structure back to the buserite phase (FIGS.8-9 and Table 3). The water-rich phase induces both a smaller dehydration barrier and different coordination to lanthanides such that the selectivity of the Sm-Eu pair flipped from favoring Eu3+with an enrichment factor of 1.2 ± 0.1 to favoring Sm3+with an enrichment factor of 1.2 ± 0.1. Also, the selectivity of the Eu-Gd pair flipped from favoring Gd with an enrichment factor of 1.1 ± 0.1 to favoring Eu with an enrichment factor of 1.3 ± 0.1 (Table 4).Atty. Dkt. No.05400-0070-PCT The Na-birnessite phase, on the other hand, induces a larger dehydration barrier and also different coordination such that the energy difference is hard to differentiate even for cross- group lanthanides; therefore, the Nd-Dy selectivity was decreased to 2.5 ± 0.1 compared with that of 4.5 ± 0.1 from Mg-buserite ion exchange (Table 4). Therefore, the confinement of Mg-buserite is at the optimal state for dehydration and coordination to promote selectivity among lanthanides.

[0065] Table 3. Elemental composition of the hydrated MnO2structure exchanged from La- water rich phase measured by ICP-MS. Na+and Mg2+residuals are negligible but La3+remained unexchanged for Pr3+, Nd3+and Eu3+. Ln (La) means ion exchange with Ln3+0.1 M solution for three days starting from La0.11MnO2 water rich phase. Na / Mn is the measured Na to Mn atomic ratio. Mg / Mn is the measured Mg to Mn atomic ratio. La / Mn is the measured La to Mn atomic ratio. La / % is the calculated percentage of unexchanged residue La3+in the interlayers. RE / Mn is the summation of REEs cations to Mn atomic ratio with a theoretical value of 0.11. Sum is the summation of the positive charge in the interlayers including REEs cations, Na+and Mg2+with a theoretical value of 0.32. Larger than 0.32 value is possibly from cation absorption on particle surface. Sample Na / Mn Mg / Mn La / Mn La / % RE / Mn Sum Pr (La) 0.00 0.01 0.06 44.6 0.13 0.39 Nd (La) 0.00 0.01 0.06 46.2 0.13 0.39 Eu (La) 0.00 0.00 0.04 37.5 0.10 0.32 Gd (La) 0.00 0.00 0.02 19.4 0.10 0.31 Tb (La) 0.00 0.00 0.01 10.3 0.09 0.29

[0066] Table 4. Elemental composition of the hydrated MnO2exchanged from La- water rich phase and Na-Birnessite measured by ICP-MS. Ln1Ln2 (La) means ion exchange with Ln13+Ln23+0.1 M each mixture solution for three days starting from La0.11MnO2 water rich phase. Ln1 and Ln2 refer to elements with lower and higher atomic number, respectively. Na / Mn is the measured Na to Mn atomic ratio. Mg / Mn is the measured Mg to Mn atomic ratio. La / Mn is the measured La to Mn atomic ratio. La / % is the calculated percentage of unexchanged residue La3+in the interlayers. Ln2 / Ln1 is the measured Ln2 to Ln1 atomic ratio. RE / Mn is the summation of REEs cations to Mn atomic ratio with a theoretical value of 0.11. Sum is the summation of the positive charge in the interlayers including REEs cations, Na+and Mg2+with a theoretical value of 0.32. Larger than 0.32 value is possibly from cation absorption on particle surface.Atty. Dkt. No.05400-0070-PCT Sample Na / Mn Mg / Mn La / % Ln2 / Ln1 RE / Mn Sum SmEu (La) 0.00 0.01 40.0 0.86 0.12 0.38 EuGd (La) 0.00 0.00 38.6 0.75 0.10 0.32 GdTb (La) 0.00 0.00 18.7 1.30 0.09 0.29 LaPr (Na) 0.00 \ \ 1.53 0.10 0.31 LaNd (Na) 0.00 \ \ 1.51 0.10 0.32 NdDy (Na) 0.01 \ \ 2.47 0.11 0.34

[0067] DFT calculations

[0068] To elucidate the molecular and electronic structure where each hydrated REE is confined within the MnO2interlayer, DFT calculations were conducted. La and Nd were chosen to represent Group I lanthanides and Dy was chosen as a Group II lanthanide. For each, three water concentrations (i.e., 1.5, 2, and 2.125 water molecules per unit cell) were considered in conjunction with Ln0.125MnO2 to study the buserite and water-rich phases. A Ln to Mn ratio of 0.125 was used to represent the experimental case of Ln0.11MnO2due to the finite size of the model. Two forms of the hydrated lanthanide cation in layered MnO2 were examined: one involves direct interaction between the lanthanide and oxygens that are coordinated to Mn in combination with partial hydration (denoted “partial hydration”), and the other involves a complete first coordination shell of water (denoted “full hydration”) that typically has a smaller coordination number than in bulk water (FIGS.5A-5K and FIGS.10- 12). For all calculations, the layer spacing, coordination numbers, and overall structures have been energy minimized to represent at T=0 K structures. The optimized structures of Dy0.125MnO2^1.5H2O revealed the presence of two layers of water molecules between the MnO2 layers, whereas Nd0.125MnO2^2H2O and La0.125MnO2^2.125H2O exhibited three layers of water molecules. Then, XRD data and the lattice parameters from the simulated structures and the experimental results obtained from powder soaking were compared (FIGS.13A-13C and Table 5). Note that there were small differences in the structures depending on which hydrated configuration of Ln3+was used. However, the structures of La0.125MnO2^2.125H2O correspond closely to the experimental structure for La, that of Nd0.125MnO2^2H2O align with the structure for Nd, and that of Dy0.125MnO2^1.5H2O match with Dy, as evidenced by the XRD peak comparison in the range of 0.5~0.7 Å-1(FIGS.13A-13C). The comparisons of the interlayer spacing values in Table 5 with experimental data in FIGS.1A-1D also indicate that the structures La0.125MnO2^2H2O and Nd0.125MnO2^2.125H2O were within the range of the water-rich phase, while the structure of Dy0.125MnO2^1.5H2O was within the buserite phase.Atty. Dkt. No.05400-0070-PCT

[0069] Table 5. Unit cell parameters in optimized structure of hydrated lanthanide intercalated in MnO2by DFT calculations. Lattice parameters, interlayer spacing, and average bond length of Ln-O are included. Average (Å) c (Å) α (°) β (°) γ (°) Inter bond a (Å) b layer spacing length (Å) of Ln-O (Å) Partial hydration (CN-9) 9.87 5.77 11.3090.2983.3790.71 11.22 2.58 Partial hydration 9.92 5.70 11.2887.3184.8789.93 11.22 2.54 La0.125MnO2^2.125H2O (CN-8) Full Hydration (CN-9) 9.87 5.73 11.3191.2091.4389.62 11.31 2.57 Full Hydration(CN-8) 9.87 5.75 11.2488.5895.6289.91 11.18 2.51 Partial hydration(CN-9) 9.84 5.76 2.54 PartialNd0.125MnO2^2H2O (CN-8) 9.84 5.72 11.1588.9582.8989.77 11.06 2.47 Full(CN-9) 9.84 5.72 11.0389.9190.7589.83 11.02 2.50 Full Hydration (CN-8) 9.81 5.72 11.1887.3597.8390.14 11.06 2.46 Partial hydration Dy0.125MnO2^1.5H2O (CN-8) 9.79 5.69 9.78 88.5888.0689.79 9.77 2.38 Full Hydration (CN-8) 9.83 5.67 9.65 82.2884.7290.05 9.52 2.39

[0070] Next, the binding energies between hydrated lanthanide and MnO2 were compared to explain the underlying rationale for the selectivity exhibited by each REE cation (see Computational Details in Methods and FIGS.14-17). Although a water rich phase of Group II lanthanide was not observed in the Mg or Na-based structures, it was thought that it could become a possibility if the intercalation started from the La-based structure, as illustrated byAtty. Dkt. No.05400-0070-PCT the example of Eu-Gd for FIG.9. Thus, for those comparisons, optimized structures with a fixed molar ratio of Ln0.125MnO2^2.125H2O and Ln0.125MnO2^1.5H2O (including Dy) were considered for representing each water-rich and buserite phase, and for most structures we considered CN 8 and 9 (FIGS.18-21 and Table 6). Note that a CN of 9 for Ln-O bonds in the fully hydrated form was found to be too high in energy to be important, even when considering La and Nd in the buserite phase, due to the small interlayer spacing. Another small difference between experiments and calculations is that the experiments show a coordination number close to 7 for La3+, while the DFT results are more consistent with 8.

[0071] Table 6. Unit cell parameters in optimized structure of hydrated lanthanide intercalated in MnO2with the molar ratio of Ln0.125MnO2^2.125H2O and Ln0.125MnO2^1.5H2O by DFT calculations for binding energy calculations. Lattice parameters, interlayer spacing, and average bond length of Ln-O are included. Average bond a (Å) b (Å) c (Å) α (°) β (°) γ (°) Interlayer spacing length of (Å) Ln-O (Å) Partial hydration (CN-9) 9.85 5.7611.2690.35 83.49 90.70 11.19 2.53 Partial hydration (CN-8) 9.96 5.7011.1987.21 85.10 90.06 11.13 2.48(CN-9) 9.88 5.7211.2591.45 90.51 89.64 11.24 2.51 Full Hydration (CN-8) 9.84 5.7411.2088.63 95.84 89.93 11.24 2.46 Partial hydration 9.92 5.7011.1187.51 85.82 89.96 11.07 2.39(CN-8) 9.86 5.7411.0888.74 95.98 89.71 11.01 2.36 Partial hydration 9.81 5.71 9.90 94.04 89.25 90.37 9.88 2.59 La0.125MnO2^1.5H2O(CN-8) 9.84 5.69 9.93 87.16 86.79 89.87 9.90 2.54Atty. Dkt. No.05400-0070-PCT Full Hydration (CN-8) 9.82 5.70 9.84 83.13 85.35 90.09 9.73 2.53 Partial hydration (CN-9) 9.81 5.73 9.80 93.63 89.27 90.48 9.78 2.54 Partial Nd0.125MnO2^1.5H2O hydration (CN-8) 9.82 5.67 9.87 87.43 87.17 89.89 9.85 2.48 Full Hydration (CN-8) 9.81 5.73 9.80 93.63 89.27 90.48 9.78 2.48

[0072] In buserite, it was found (FIG.17) that the strongest binding (-9.47 eV) occurred for Dy with full hydration and a CN of 8, and then La and Nd also had large binding energies (and almost the same) (-9.25, -9.24 eV) compared to other configurations of hydration and CN (FIGS.14-16). It was therefore expected that these fully hydrated structures dominated over the partially hydrated structures. The fully hydrated structures for CN 8 were also the lowest energy structures for the water-rich phase for all three lanthanides, so again these results can be focused on rather than the partially hydrated or higher coordination number results. FIG.17 shows that for Dy, there should be a stable water-rich phase; it was assumed that this was kinetically not accessible in the experiments. The other important trend in FIG. 17 is that the binding energy increased in magnitude with increasing atomic number for the water rich phase in going from La to Nd, and it also increased for the buserite phase in going from Nd to Dy. These trends were consistent with the observed separation properties in FIG. 5A.

[0073] Pinning strategy for selectivity boost among Group I lanthanides

[0074] For Group I REEs, the larger interlayer spacing of the water-rich phase led to higher CN of REE in the channels based on the XAS results, and the binding energy differences between REE elements were reduced. To enhance the preference for REEs with a higher atomic number, a tighter confinement was required to reduce the CN. If narrower confinement of the buserite phase can be maintained for Group I pairs, both dehydration and binding could favor the heavier lanthanides to improve selectivity. Therefore, a pinning strategy was designed to use co-ion Mg2+to fix the interlayer spacing and force the Group I elements to reside in the buserite phase. The REEs were introduced into the channels via electrochemical intercalation instead of direct ion exchange. When the electrochemicalAtty. Dkt. No.05400-0070-PCT intercalation rate is faster than ion exchange, Mg2+can be maintained in the interlayers and the interlayer spacing can be pinned at the buserite phase. Eventually, the Mg2+will be replaced by REEs via ion exchange which means a larger capacity can be used to store REEs in the hydrated MnO2. Three pairs, La-Pr, La-Nd, and Nd-Sm were tested, with Nd-Sm including the border element Sm. Starting from Mg-buserite (Mg0.16MnO2), lanthanides were intercalated under C / 10 current to a final state where the charge capacity was doubled (see Methods for details). The structure evolution during electrochemical intercalation was monitored by in situ synchrotron XRD using the La-Nd pair under the rate of C / 4 for time efficiency (FIG.22A). During the entire electrochemical intercalation process, the buserite phase was maintained and the interlayer spacing was kept at ~ 9.6 Å. The pinning of La-Pr and Nd-Sm pairs was also successful, based on ex-situ synchrotron XRD of the ending states of the electrochemical intercalation (FIG.23). Based on the ICP-MS results, ion exchange was confirmed to occur in parallel with the electrochemical intercalation wherein lanthanides replaced the original Mg2+(Table 7). The pinning strategy was successful since Group I lanthanides can reside in the buserite phase as evidenced from the XRD spectra of the Pr3+and Nd3+single element ion exchange as well as in the Group I and II mixture ion exchange. Additionally, as more lanthanides were introduced, the repulsion from neighboring MnO2 layers was reduced, and this provided a driving force for the interlayer spacing to shrink rather than expand. This is proven by using the lanthanides’ exchanged structures (Lnmix0.11MnO2) as the starting materials for electrochemical intercalation. As shown in FIG. 22B, for the La-Nd pair, during electrochemical intercalation, the water-rich phase disappeared midway with only the buserite phase left (with interlayer spacing of 9.6 Å). Nd- Sm pair also showed right shifting of the (001) peak indicating narrowing of the interlayer spacing with the addition of interlayer REEs (FIG.24).

[0075] Table 7. Elemental composition of the dissolved electrochemical intercalation electrodes measured by ICP-MS. Ln1and Ln2refer to elements with lower and higher atomic number, respectively. Mg / Mn is the measured Mg to Mn atomic ratio. Ln2 / Ln1 is the measured Ln2to Ln1atomic ratio. RE / Mn is the summation of REEs cations to Mn atomic ratio with a theoretical value of 0.22. Smaller than 0.22 value could be due to possible proton insertion along the intercalation process. Sum is the summation of the positive charge in the interlayers including REEs cations, Na+and Mg2+with a theoretical value of 0.66. Smaller than 0.66 value could be due to possible proton insertion. Test Mg / Mn Ln2 / Ln1 RE / Mn Mn% SumAtty. Dkt. No.05400-0070-PCT La-Nd Ion Ex 0.02 1.58 0.05 106 0.21 La-Nd Seed La-Nd Inter 0.02 3.10 0.13 102 0.44 Mg Seed La-Nd Inter 0.04 5.37 0.12 131 0.49 La-Pr Ion Ex 0.02 1.84 0.09 113 0.33 La-Pr Seed La-Pr Inter 0.02 3.23 0.18 114 0.59 Mg Seed La-Pr Inter 0.07 4.22 0.16 126 0.62 Nd-Sm Seed Nd-Sm Inter 0.05 2.89 0.17 147 0.67 Mg Seed Nd-Sm Inter 0.01 2.72 0.19 87 0.61

[0076] The pair selectivity was evaluated after electrochemical intercalation. As shown in FIG.22C, with pinning, the enrichment factors for La-Nd, La-Pr, and Nd-Sm were boosted from 1.6 ± 0.1, 1.5 ± 0.1, and 1.6 ± 0.1 to 5.4 ± 0.1, 4.2 ± 0.1, and 2.9 ± 0.1, respectively, proving the effectiveness of the pinning strategy. Compared to electrochemical intercalation from the lanthanides’ exchanged structures (Lnmix0.11MnO2), pinning still showed enhanced enrichment factors which indicates that keeping the entire ion transport pathway under confinement is more effective in distinguishing the Group I lanthanides; therefore, dehydration and coordination can always be maintained at the optimized energy states. The confined solid ionic channel by itself was effective in the separation of cross-group REEs, and with the addition of the pinning strategy, Group I REEs can also be effectively separated. To demonstrate high purity of REEs from separation, the La-Nd and Nd-Dy pairs were tested owing to their practical importance. The ion exchange or electrochemical intercalation with Mg2+pinning was conducted twice (with a repeat cycle), and ~97.0% and ~92.3% purity of Nd and Dy can be obtained (FIG.22D, see Methods for experiment details).

[0077] Methods

[0078] Synthesis of Layered Manganese oxide nanosheet and pretreatment

[0079] To synthesize pristine layered Na0.32MnO2nanosheets, a co-precipitation method was used with slight modification from the literature. (Goff, P. L. et al., J. Mater. Chem.4, 875-881 (1994).) 40 ml of 0.5 mol / L MnCl2 solution was pre-bubbled with oxygen through a bubble stone to saturate the solution with oxygen to create an oxidative environment. An ice bath was used to increase the solubility of oxygen.11 g of NaOH in 50 ml deionized (DI) water were added to the MnCl2solution to form brownish Mn(OH)2suspension. The suspension was stirred for 5 h and the ice bath was removed after the first hour. At the end of this time, the black precipitate obtained was washed several times with DI water and thenAtty. Dkt. No.05400-0070-PCT freeze-dried. A Na-buserite phase was obtained which has the formula of Na0.32MnO2 0.72H2O.

[0080] Preparation of electrodes

[0081] All Na0.32MnO2 electrodes were prepared by casting a slurry of Na0.32MnO2, Super P carbon black (MTI Corporation; Item Number: Lib-SP; average particle size ~40 nm; purity ≥99.5%), and polyvinylidene fluoride (MTI Corporation; Item Number: Lib-PVDF; purity ≥99.5%) with a mass ratio of 80:10:10, in N-methyl-2-pyrrolidone. The electrode slurry was drop-cast on a 0.5 × 1 cm2geometrical surface of a porous carbon cloth (ELAT-H, FuelCellEtc, 406 μm in thickness, 80% porosity) current collector of 5 × 1 cm2and dried on a hotplate at 120 °C overnight.

[0082] Ion Exchange

[0083] As synthesized Na0.32MnO2 either in a form of powder or electrode depending on the experiments to be conducted was soaked in 1 M MgCl2solution overnight to form a Mg- buserite phase. (Johnson, E. A. et al., Am. Mineral.91, 609-618, (2006).) The powder or electrodes are washed several times with DI water to remove the surface adsorbed Mg2+cations for further use. The same operation with 1 M La(NO3)3 solution was adopted to form La0.11MnO2water-rich phase starting from the Mg-buserite phase. To introduce REEs (mixture) into the structure, 8 mg powder was soaked in 0.1 M (each) solution for three days. All separation tests used REE ion ratios of 1: 1 except for the second repeat cycle for Nd-Dy in the two-stage process which inherits the enrichment factor ratio from the first cycle.

[0084] Electrochemical intercalation

[0085] All electrochemical operations were performed on a Bio-Logic VMP3 workstation using a three-neck round-bottomed flask at room temperature (20~25 °C). Ag|AgCl|KCl (4.0M) was used as the reference electrode. During the co-intercalation process, all the working electrodes, paired with carbon rods as counter electrodes, would undergo intercalation in a 10 mL mixture solution composed of 0.1 M each REEs until the cutoff voltage of –0.1 V was reached using intercalation rate of 0.1C. The calculations of applied current were based on the theoretical capacity of 284 mAh / g. For instance, 0.1C for the selectivity test will be 28.4 mA / g. All separation tests used REE ion ratios of 1:1 except for the second repeat cycle for La-Nd in the two-stage process which inherits the enrichment factor ratio from the first cycle. See FIGS.25A-25D for all the electrochemical intercalation curves involved.Atty. Dkt. No.05400-0070-PCT

[0086] Synchrotron XRD characterization

[0087] All ex situ powder samples were tested in 1.5 mm quartz or 1.0 mm Kapton capillary tubes. A powder suspension together with the ion exchange solution was added to capillary tubes to make sure the powder will not dry out. Data were collected at beamline 13- BM-C, 17-BM-B and 33-BM-C of the Advanced Photon Source at Argonne National Laboratory using high-resolution powder XRD with a monochromatic X-ray incident beam with the wavelength of 0.4335 Å or 0.6199 Å. All powder sample intensities were scaled to the same range. In situ synchrotron XRD integrated with electrochemical control was done at beamline 13-BM-C of the Advanced Photon Source at Argonne National Laboratory. In these experiments, a monochromatic X-ray incident beam with a wavelength of λ = 0.4335 Å was introduced to a custom-designed electrochemical sample cell adopted for in situ measurements. The sample cell frame and all components were made of strong corrosion- resistant polymer Kel-F. A carbon cloth electrode was placed within the central position of the cell between two sealed Kapton windows. A groove can hold roughly 5 mL solution around the center to make sure the electrode is in contact with solution all the time. The background from capillary tubes and REEs solution, or from carbon cloth together with Kapton films is fit using a 5th order polynomial and extracted to make the baseline flat. In house XRD was carried out on Rigaku MiniFlex 600 diffractometer, using Cu Kα radiation (Kα 1: 1.54059 Å; Kα 2: 1.54441 Å; Kα 12 ratio: 0.4970). The tube voltage and the current used were 40 kV and 15mA. Diffractograms were recorded with a 0.01° step width and a 10° / min speed. For powder samples, 40 μL δ-MnO2 powder suspension (~8 mg in 3 mL 0.1 M REEs nitrate aqueous solution) was drop-cast onto a PTFE membrane and vacuum filtration was used to remove access amount of solution. The powder on PTFE membrane was carefully preserved to keep wet before XRD measurement. Electrode samples were put into a self-assembled Kapton pocket and play-doh was used for z-height alignment.

[0088] ICP-MS characterization

[0089] The powder samples after ion-exchange were first washed with 30 mL DI water for four times followed by ethanol for two times using a centrifuge. Precipitated powder was oven dried overnight at 60 °C, then digested with aqua regia solution for three days to ensure complete dissolution. Electrodes after intercalation were rinsed in three different 200 mL DI water for 30 min with continuous N2 bubbling to remove excess adsorbed cations and digested with aqua regia solution (6 mL concentrated HCl + 2 mL concentrated HNO3).3%Atty. Dkt. No.05400-0070-PCT HNO3 (aq) was used as the diluting matrix for later ICP-MS measurement. All the measurements used either Thermo iCAP Q ICP-MS or Thermo iCAP RQ ICP-MS. For all the powder and electrodes selectivity tests, each condition was repeated three times to generate an error bar. The enrichment factor is calculated by the measured amount of the heavier REE divided by the measured amount of the lighter REE. For example, the enrichment factor of Ln2over Ln1is calculated as, ^^^^^^^^^^మ^ ^^^^ ^^^^^^^^^^ℎ^^^^^^^^ ^^^^^^^^^^^^^^^^ଶ^^మwhere the ^^^^^^^^ is^^^^ is the atomic weight of element in ^^ / ^^^^^^. All separation tests used REE ion ratios of 1:1 except for the second repeat cycle in the two-stage process which inherits the enrichment factor ratio from the first cycle.

[0090] EXAFS characterization

[0091] XAS data were collected at 5-BM-D of Advanced Photon Source at Argonne National Lab. Standards were measured using 0.25 M nitrate solution contained in 2 mL plastic centrifuge tubes. Powder samples were first washed five times using DI water to remove surface adsorbed cations, then added to 2 mL centrifuge tubes together with DI water. The suspension was placed statically for a long enough time until all the powder was settled down. Samples were measured in the fluorescence mode by a Vortex ME4 detector and standards were measured in transmission mode by ion-chamber at room temperature. All La, Nd, and Dy were measured at K-edge to avoid overlap of Mn K-edge. Edge energy was calibrated by using the corresponding standard nitrate solution. All collected data were analyzed by using Athena to extract normalized XAS data. Fourier Transform of EXAFS were performed by Using the Hanning window function with k-weight of 2 and k-range from 3 to 9.5 Å-1. For model-based EXAFS analysis, all of the scattering paths were generated by the FEFF calculation function in Artemis based on the crystal structure of La(H2O)9, Nd(H2O)9, and Dy(H2O)8in 0.25 M aqueous solution. The generated scattering paths were then calibrated by performing the FEFFIT of the EXAFS data of the standard nitrate solutions sample, mainly to obtain the amplitude reduction factor (S02) values. With S02 known, all EXAFS data for the samples were fitted with such generated amplitudes to get the coordination number and scattering path length.Atty. Dkt. No.05400-0070-PCT

[0092] STEM-EDS characterization

[0093] Particles were removed from the electrodes and were drop-cast onto lacey carbon membrane-coated gold grids for top-view imaging. The imaging was conducted by using the aberration-corrected scanning transmission electron microscope (STEM) JEOL ARM200CF at the University of Illinois at Chicago. EDS spectra imaging was acquired using an Oxford X-Max 100TLE windowless SDD detector.

[0094] Molecular modeling and DFT calculations

[0095] Initial crystal structures were derived from a previous study of birnessite and a 2×1×1 supercell was created with a structure similar to Y0.125MnO2^xH2O. (Lucht, K. P. et al., J Phys Chem C 119, 22838-22846, (2015).) Then Y was replaced by La, Nd, and Dy and additional water molecules were added to the structures. DFT calculations were conducted with the Vienna ab initio simulation package (VASP) code. (Kresse, G. et al., Comp Mater Sci 6, 15-50, (1996); Kresse, G. et al., Phys Rev B 54, 11169-11186, (1996).) Spin-polarized calculations with the projector augmented-wave (PAW) method were implemented. A 600- eV kinetic energy cutoff for the plane-wave-basis set was used for all calculations. The electronic energy convergence parameter was set to 10−7eV, and force convergence for ionic relaxation was set to 10−2eV / Å. The k-point set was chosen to be 5×9×5 with the Monkhorst Pack scheme. A GGA functional with optB86b-vdW was used, and the nonlocal vdW-DF was used as the exchange-correlation functional was implemented to describe accurate dispersion interactions. (Perdew, J. P. et al., Phys Rev Lett 77, 3865-3868, (1996); Klimes, J. et al., Phys Rev B 83, 195131, (2011).) This exchange correlation functional has been shown in several computational studies to provide good agreement of the lattice parameters of lanthanum monazite crystal structures compared with values measured in experiments. (Gibson, L. D. et al. J Phys Chem C, (2022).) In addition, the lattice parameters of the Ln2O3 (Ln = La, Nd, and Dy) crystal structures matched very closely with experimental values (Table 8). (Bommer, H., Z Anorg Allg Chem 241, 273-280, (1939).) Adjustments to the Hubbard U parameters had minimal impact on the observed trends in the binding energies of Ln-O (Table 9), so the Hubbard U parameters were ignored in the DFT calculations. The covalent bond for the Ln-O pair was determined using a bond length that is taken to be the sum of the covalent radii of each Ln and O, as reported in Pyykkö et al. (Pyykkö, P. et al., Chem-Eur J 15, 186-197, (2009).) And 1.2 times the covalent bond (i.e., 2.92, 2.84, and 2.76Atty. Dkt. No.05400-0070-PCT Å for each La-O, Nd-O and Dy-O bond, respectively) was considered the maximum bond length in this study.

[0096] Table 8. Comparison of lattice parameters in cubic Ln2O3. La, Nd, and Dy are considered as Ln and the experimental values and simulated values using GGA with optB86b-vdW of nonlocal vdW-DF are compared. a (Å) b (Å) c (Å) α (°) β (°) γ (°) Volume

[0097] Table 9. Comparison of binding energies depending on the application of various Hubbard U parameters. The values are calculated between Ln0.125^2.125H2O (where Ln = La, Nd, and Dy) and MnO2in Ln0.125MnO2^2.125H2O structure under full hydration and CN of 8 with Ln-O bonds (unit : eV). La Nd Dywithout Hubbard U parameters -9.16 -9.25 -9.60 U = 3.9 eV (Mn) -8.63 -8.65 -9.01 U = 3.9 eV (Mn) -8.61 -8.62 -8.97Atty. Dkt. No.05400-0070-PCT

[0098] Binding Energy Calculation

[0099] Binding energy between the hydrated Ln3+and MnO2structure was calculated by following equation,^^^ா ൌ ^^^^^^^^.^ଶହ^^^^^^ଶ ^ ^^^^ଶ^^^ െ ^^^^^^^^.^ଶହ ^ ^^^^ଶ^^^ െ ^^^^^^^^^ଶ^ ^ ^^^^^^ െ ^^^^^ଶ^^^ (1)where ^^^^^^^^.^ଶହ^^^^^^ଶ ^ ^^^^ଶ^^^, ^^^^^^^^.^ଶହ ^ ^^^^ଶ^^^, ^^^^^^^^^ଶ^, and ^^^^^^ െ ^^^^^ଶ^^^ denotethe total electronic energy of hydrated Ln3+in MnO2, hydrated Ln3+, layered MnO2, and (m- n) numbers of H2O. The value of n varies for each structure in different phases, while m is fixed at 5 in this example. This equation supposes that Ln3+is intercalated with n number of H2O molecules into an empty layered MnO2 structure, so it includes both interactions of Ln3+and MnO2, and also H2O and MnO2. In this example, the total binding energy of the whole structure for each configuration was compared.1 Ln3+ion and 40 H2O molecules are considered in each hydrated Ln3+structure to describe explicit solvation up to the 2nd hydration shell, and the geometry of TTP was considered for hydrated La and Nd, and that of SAP was considered for hydrated Dy, respectively. The same number of H2O molecules compared to hydrated Ln3+models was considered, and the total energy was normalized to calculate the energy term of H2O. Layered MnO2 was optimized after removing the cation and H2O molecules in the buserite structure (FIGS.26A-26E and Table 10). Consistent grid densities of the k-point set and identical calculation settings with hydrated Ln3+in MnO2 were used for each structure.

[0100] Table 10. Lattice parameters of hydrated Ln3+ of La, Nd, and Dy and layered MnO2. a (Å) b (Å) c (Å) α (°) β (°) γ (°) La·40H2O 9.70 9.79 10.83 88.86 93.14 87.84 (TTP) Nd·40H2O 9.67 9.75 10.82 88.63 93.20 87.84 (TTP) Dy·40H2O 10.36 9.84 10.02 87.50 96.39 91.87 (SAP) 40H2O 10.61 90.00Layered MnO2 9.91 5.72 6.67 49.71 111.7 89.99 7Atty. Dkt. No.05400-0070-PCT

[0101] Supplementary Note 1

[0102] Free spacing calculation for three phases of MnO2: Free spacing = Interlayer spacing - Thickness of manganese oxide layer - Oxygen atom diameter Birnessite phase: 7.2 - 2.05 - 0.73 = 4.42 Å Buserite phase: 9.7 - 2.05 - 0.73 = 6.92 Å Water rich phase: 11.2 - 2.05 - 0.73 = 8.42 Å

[0103] REEs cations hydrated diameter estimation: Hydrated diameter = Averaged Ln-O bond length × 2 + H-O bond length × 2 For light REEs: (Ln-O(9C) × 6 + Ln-O(9P) × 3) / 9 × 2 + H-O bond length × 2 For heavy REEs: 2 × Ln-O(8) + H-O bond length × 2

[0104] The word "illustrative" is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as "illustrative" is not necessarily to be construed as preferred or advantageous over other aspects or designs.

[0105] The foregoing description of illustrative embodiments of the invention has been presented for purposes of illustration and of description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the invention. The embodiments were chosen and described in order to explain the principles of the invention and as practical applications of the invention to enable one skilled in the art to utilize the invention in various embodiments and with various modifications as suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto and their equivalents.

Claims

Atty. Dkt. No.05400-0070-PCT WHAT IS CLAIMED IS:

1. A method of separating rare earth ions from an aqueous solution comprising a mixture of rare earth ions, the method comprising: providing a layered, mixed metal oxide comprising a hydration phase comprising stacked layers of a transition metal oxide and hydrated metal cations intercalated in channels between the stacked layers, wherein the channels have a pinned interlayer spacing; exposing the layered, mixed metal oxide to an aqueous solution comprising a mixture of at least two different types of rare earth ions, wherein at least some of the rare earth ions in the mixture have a lower dehydration energy barrier than other rare earth ions in the mixture; and introducing rare earth ions into the channels via electrochemical intercalation, whereby the rare earth ions having the lower dehydration energy barrier are preferentially introduced into the channels.

2. The method of claim 1, wherein the rare earth ions have a first hydration shell diameter that is equal to or larger than a free spacing of the channels.

3. The method of claim 1, wherein the rare earth ions are lanthanide ions.

4. The method of claim 2, wherein the rare earth ions are lanthanide ions.

5. The method of claim 1, wherein the transition metal oxide is a manganese oxide.

6. The method of claim 2, wherein the transition metal oxide is a manganese oxide.

7. The method of claim 3, wherein the transition metal oxide is a manganese oxide.

8. The method of claim 5, wherein the layered, mixed metal oxide is a magnesium manganese oxide and the hydration phase is a buserite phase.Atty. Dkt. No.05400-0070-PCT 9. The method of claim 8, wherein the rare earth ions are lanthanide ions selected from lanthanum ions, cerium ions, praseodymium ions, neodymium ions, promethium ions, and samarium ions.

10. The method of claim 1, further comprising recovering the rare earth ions introduced into the channels, recovering the rare earth ions remaining in the aqueous solution, or both.

11. A method of separating rare earth ions from an aqueous solution comprising a mixture of rare earth ions, the method comprising: providing a layered, mixed metal oxide comprising a hydration phase comprising stacked layers of a transition metal oxide and hydrated metal cations intercalated in channels between the stacked layers; exposing the layered, mixed metal oxide to an aqueous solution comprising a mixture of at least two different types of rare earth ions, wherein an ion exchange between the hydrated metal cations and at least one type of the at least two different types of rare earth ions induces a hydration phase transformation that increases a channel spacing in the layered, mixed metal oxide, and an ion exchange between the hydrated metal cations and at least one other type of the at least two different types of rare earth ions does not induce a hydration phase transformation that increases the channel spacing in the layered, mixed metal oxide; and allowing the hydrated metal cations in the channel to undergo ion exchange with the rare earth ions, whereby the rare earth ions that do not induce the hydration phase transformation are preferentially introduced into the channels.

12. The method of claim 11, wherein the rare earth ions that induce the hydration phase transformation have a hydration shell diameter that is equal to or larger than a free spacing of the channels and the rare earth ions that do not induce the hydration phase transformation have a hydration shell diameter that is equal to or smaller than the free spacing of the channels.

13. The method of claim 11, wherein the rare earth ions are lanthanide ions.

14. The method of claim 12, wherein the rare earth ions are lanthanide ions.Atty. Dkt. No.05400-0070-PCT 15. The method of claim 11, wherein the transition metal oxide is a manganese oxide.

16. The method of claim 12, wherein the transition metal oxide is a manganese oxide.

17. The method of claim 13, wherein the transition metal oxide is a manganese oxide.

18. The method of claim 14, wherein the transition metal oxide is a manganese oxide.

19. The method of claim 15, wherein the layered, mixed metal oxide is a magnesium manganese oxide and the hydration phase is a buserite phase.

20. The method of claim 19, wherein the rare earth ions that induce a hydration phase transformation are lanthanide ions selected from lanthanum ions, cerium ions, praseodymium ions, neodymium ions, promethium ions, and samarium ions, and the rare earth ions that do not induce the hydration phase transformation are lanthanide ions selected from samarium ions, europium ions, gadolinium ions, terbium ions, dysprosium ions, holmium ions, erbium ions, thulium ions, ytterbium ions, and lutetium ions.

21. The method of claim 11, further comprising recovering the rare earth ions introduced into the channels, recovering the rare earth ions remaining in the aqueous solution, or both.

22. A two-stage method of separating rare earth ions from an aqueous solution comprising a mixture of rare earth ions, the method comprising: providing a layered, mixed metal oxide comprising a hydration phase comprising stacked layers of a transition metal oxide and hydrated metal cations intercalated in channels between the stacked layers; exposing the layered, mixed metal oxide to an aqueous solution comprising a mixture of at least three different types of rare earth ions, wherein an ion exchange between the hydrated metal cations and at least one type of the at least three different types of rare earth ions induces a hydration phase transformation that increases a channel spacing in the layered,Atty. Dkt. No.05400-0070-PCT mixed metal oxide, and an ion exchange between the hydrated metal cations and at least one other type of the at least three different types of rare earth ions does not induce a hydration phase transformation that increases the channel spacing in the layered, mixed metal oxide; allowing the hydrated metal cations in the channel to undergo ion exchange with the rare earth ions, whereby the rare earth ions that do not induce the hydration phase transformation are preferentially introduced into the channels; providing a pinned, layered, mixed metal oxide comprising a hydration phase comprising stacked layers of a transition metal oxide and hydrated metal cations intercalated in channels between the stacked layers, wherein the channels have a pinned interlayer spacing; exposing the pinned, layered, mixed metal oxide to the aqueous solution comprising the mixture of at least three different types of rare earth ions, wherein at least some of the rare earth ions in the mixture have a lower dehydration energy barrier than other rare earth ions in the mixture; and introducing rare earth ions into the channels via electrochemical intercalation, whereby the rare earth ions having the lower dehydration energy barrier are preferentially introduced into the channels.

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