Introduction

Adsorption reactions at solid-water interfaces are relevant to ion-selective capture1,2,3,4,5,6,7, chemical separations8,9,10,11, catalysis6, and environmental fate and transport12,13,14. When solid surfaces are nanoconfined (for nanoparticles or inside nanopores), their apparent reactivity starts being influenced by the surface energy terms, which become significant at the nano-scale6,15,16,17,18. Importantly, inside nanopores filled with aqueous solutions electrical double-layers (EDL) extending from the charged surfaces may overlap, causing the structures of nanoconfined solutions to differ from those observed at unconfined surfaces. Nanoconfined water has a lower dielectric response19,20,21,22,23,24, and lower density and surface tension25, defined by the H-bonding structures16,26 and slower rotational dynamics in near-interfacial regions27,28. Despite much information about nanoconfined water, the reactivities of nanoconfined surfaces, including the pathways and products of adsorption reactions, are not easily predicted15,17,18,29,30,31,32,33. This uncertainty is because adsorption in nanoconfined systems is dictated by both surface chemistry (e.g., the density of Si–OH, Al–OH, or other functional groups17,18,30,31 and charge distribution34) as well as the size of the pore/channel that determines the solute structures within the overlapping EDLs. These interdependent effects have hindered the discovery of reliable predictors for how the energetics, pathways, and products of adsorption reactions change under nanoconfinement12,13,29,30. Here we show that the hydration energy of an adsorbing ion (ΔGhydr) could be used as a meaningful predictor.

Previous studies have reported that nanoconfinement enhances inner-sphere adsorption and shifts the net adsorption heat from exo- (unconfined) to endothermic (nanoconfined) for cation adsorption onto negatively-charged silica (SiO2) surfaces and on zeolites15,29,30,32,35. Ilgen et al. concluded that the adsorption of cations with less exothermic (less negative) ΔGhydr is affected more by nanoconfinement compared to cations with more exothermic ΔGhydr and tighter hydration shells29. This trend was observed for the products and heats of adsorption for SiO2 surfaces nanoconfined within pores under 7 nm in diameter29. Therefore, the ΔGhydr of an ion could be used to anticipate the extent of nanoconfinement effects on its adsorption behavior. However, this trend has only been shown thus far for negatively-charged SiO2 surfaces29. Here we study lanthanide adsorption on positively-charged alumina (Al2O3) surfaces and present further evidence that ΔGhydr is in fact a reliable predictor of nanoconfinement effects on adsorption.

To test our hypothesis that ΔGhydr controls whether cation adsorption energetics and products are affected by nanoconfinement, we exploit the gradual change in the ΔGhydr of trivalent lanthanide cations (Ln3+) and compare their adsorption on unconfined Al2O3 (i.e., corundum) and Al2O3 surfaces nanoconfined within 4.4 nm pores. Using operando flow microcalorimetry we show that at low surface coverages, adsorption reaction is endothermic for unconfined Al2O3 and becomes exothermic when Al2O3 surfaces are nanoconfined; adsorption becomes more endothermic as surface coverage is increased. Using X-ray absorption fine structure (XAFS) spectroscopy, we show that local structures around adsorbed neodymium (Nd3+) are vastly different for corundum and nanoconfined Al2O3 surface, while they are virtually indistinguishable on both surfaces for the stronger-hydrated lutetium (Lu3+). To our knowledge, this is the first study of lanthanide adsorption on nanoconfined Al2O3 surfaces that describes interfacial structures together with adsorption energetics.

Accurate molecular-scale descriptions of nanoconfined Al2O3 surface reactivities are crucial for predictive models of contaminant mobilities, immobilization of radionuclides within heterogeneous nuclear wastes, and water purification with Al2O3 membranes36. Al2O3 is a building block of soils and rocks, therefore it can drive macroscopic chemical fluxes in the environment12,13,37. Furthermore, understanding structure-reactivity relationships for Ln3+ in nanoconfined systems can enable the separation of these critical elements using reactive nanopores38. The presented work illustrates that the energetics and products of adsorption could be predictably controlled by changing the size of a reactive nanopore.

Results and discussion

Adsorption complexes on corundum and nanoconfined Al2O3 surfaces

The local coordination environment of adsorbed Nd, Tb, and Lu on corundum and nanoconfined Al2O3 surfaces was characterized using XAFS. We found that nanoconfinement promotes inner-sphere adsorption for Nd3+ cations and causes subtle elongation of the Lu–O bonds for inner-sphere Lu complexes. There is a stark difference in the surface speciation of adsorbed Nd when compared to Lu: Lu forms inner-sphere complexes (chemisorption) on both corundum and nanoconfined Al2O3 surfaces. Nd, however, only forms outer-sphere complexes (physisorption) on corundum, and inner-sphere complexes on porous Al2O3 surfaces (Fig. 1). This conclusion is based on the Nd LIII-edge Fourier transformed XAFS spectrum for corundum Al2O3 having no detectable 2nd shell neighbor, while for Nd adsorbed onto nanoconfined Al2O3 surfaces the 2nd shell due to Nd-Al backscattering is well-resolved in the spectrum (Fig. 1). This observation supports our hypothesis that a cation’s ΔGhydr defines the extent to which nanoconfinement affects its adsorption products. In the examined set of cations, Nd3+ has the least exothermic ΔGhydr (−3336 kJ·mol−1)39, and shows the most pronounced difference in the adsorption products when unconfined Al2O3 surfaces are compared to Al2O3 nanopores. On the other hand, Lu3+, which has the most exothermic ΔGhydr (−3589 kJ·mol−1)39, produces nearly identical XAFS spectra when corundum and nanoconfined Al2O3 surfaces are compared. All shell-by-shell fitting results for Nd, Tb, and Lu XAFS data are shown in Table 1. Raw data plotted in k-space with k-weight of 3 is shown in Fig. S1 in the Supporting Information file.

Fig. 1: X-ray absorption fine structure spectroscopy data for neodymium and lutetium adsorbed onto non-porous and porous alumina.
figure 1

X-ray absorption fine structure data for Nd (a) and Lu (b) adsorbed on corundum (dashed lines) and nanoconfined Al2O3 surfaces (solid lines); Fourier transform of each spectrum is shown. The insets in each panel illustrate back-transformed spectra of the isolated 2nd shell. For Nd, the 2nd shell is observed in the spectrum for the nanoconfined Al2O3 surface and corresponds to Nd-Al backscattering due to inner-sphere complexation; No 2nd shell is present for Nd adsorbed on corundum. For Lu, both spectra for corundum and nanoconfined Al2O3 are showing evidence for inner-sphere complexation.

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Table 1 Summary of X-ray absorption fine structure (XAFS) spectroscopy shell-by-shell fitting results for Nd3+, Tb3+, and Lu3+ adsorbed onto corundum and nanoconfined Al2O3 with 4.4 nm pores.
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The 1st Nd–O shell for both corundum and nanoconfined Al2O3 surface was fit with a combination of two Nd–O theoretical backscattering paths at 2.45 ± 0.01 Å and 2.63 ± 0.01 Å (Table 1). The average Nd–O distance in these samples (2.54 Å) is similar to that reported for Nd3+ adsorbed onto SiO2 surfaces nanoconfined within 4 nm to 7 nm pores29. The 2nd shell due to Nd-Al backscattering (observed only for nanoconfined Al2O3 surface) was fit with a Nd-Al theoretical path at 3.46 ± 0.05 Å, consistent with a bi-dentate bi-nuclear complex geometry.

For Tb, XAFS data was collected only for nanoconfined Al2O3 surfaces, where Tb forms inner-sphere surface complexes. The 1st Tb–O shell was fit with a combination of two Tb–O theoretical paths at 2.33 ± 0.01 Å and 2.46 ± 0.01 Å, again showing a similar local environment to that of Tb adsorbed onto SiO2 surfaces nanoconfined within 4 nm and 7 nm SiO2 pores29. The 2nd shell fits with a Tb-Al theoretical backscattering path at 3.4 ± 0.01 Å, which indicates a bi-dentate bi-nuclear surface complex geometry. XAFS data and fits for Tb, including fitting isolated 2nd shell, is shown in the Supporting Information file, Fig. S2. Similar to our earlier reported observations for Cu(II) and Ln(III) adsorbed on nanoconfined SiO2 surfaces29,30, dimerization reactions were evident for Tb and Lu on Al2O3: there is evidence of Tb-Tb and Lu-Lu backscattering contributions to the collected XAFS spectra. The presence of Tb–Tb backscattering suggests that some (not all) adsorbed Tb forms dimers or other types of polymeric species on nanoconfined Al2O3 surfaces; the Tb–Tb distance of 3.61 ± 0.06 Å suggests that the Tb polymerization is in the form of edge-sharing moieties (e.g., as in the structure of xenotime40).

Similar to Nd and Tb, two Lu–O backscattering paths were required to fit the 1st shell of the  Lu spectra. For corundum, the Lu-O distances are 2.23 ± 0.02 Å and 2.34 ± 0.01 Å. For nanoconfined Al2O3 surfaces, the Lu-O distances are slightly longer, at 2.26 ± 0.01 Å and 2.41 ± 0.02 Å (Table 1). The elongation of the Lu-O distance under nanoconfinement may indicate that the local pH inside Al2O3 pores is lower than the controlled/measured pH of the adsorption reactor (6.0 ± 0.1). In our earlier publication, we show that for Lu adsorbed onto SiO2 surface at pH 4.0 the Lu-O distances are ~0.1 Å longer, compared to an analogous sample at pH 6.0, likely due to the lower abundance of OH− in the 1st shell around Lu at lower pH and shorter Lu-OH− distances compared to the Lu-H2O distance29. Recent studies indicate that inside SiO2 nanopores protons are concentrated, driven by the negative surface charge inside nanopore41. However, Al2O3 surfaces are expected to be positively charged42,43 at the near-neutral pH of our experiments. Therefore, Lu-O elongation may be happening due to the EDL overlap and corresponding changes to the structure (hydrogen bonding) in nanoconfined water, rather than a higher proton concentration inside nanopores. The 2nd shell for Lu adsorbed onto corundum and nanoconfined Al2O3 surfaces was fit with Lu-Al theoretical backscattering path at 3.8 ± 0.06 Å, indicating a bi-dentate bi-nuclear adsorption complex, and additional Lu-Lu backscattering contribution indicating Lu dimers or other types of polymer surface species. The Lu–Lu distance of ~3.9 Å indicates a corner-sharing arrangement for Lu polyhedra (as we discuss in the previous publication29, Lu-Lu edge-sharing would result in a shorter distance at ~3.55 Å, as in keiviite structure44). Similar to Lu adsorption on SiO2, for Al2O3 we also observe bi-dentate complexation. On iron oxides, however, Lu tends to form mono-dentate complexes at pH 8 on hematite and at pH 5 on ferrihydrite45.

Cation adsorption studies on nanoconfined Al2O3 surfaces are extremely limited and often lack spectroscopic analyses detailing surface speciation. On unconfined corundum surfaces uranium U(VI) likely adsorbs as outer-sphere complex because U(VI) adsorption was found to be both pH- and ionic-strength-dependent. However, on nanoconfined Al2O3 within ~1.3 nm pores U(VI) likely adsorbs as inner-sphere complexes since the adsorption is pH-dependent, while is independent of ionic strength42. These assumptions are also confirmed by sequential desorption experiments, where U(VI) shows irreversible adsorption onto nanoconfined Al2O3 and fully-reversible adsorption on corundum surfaces42. The most common U(VI) species at near-neutral pH is UO2CO346, for which ΔGhydr was quantified at −41.17 kcal·mol−1 (−172.3 kJ·mol−1)47. The −172.3 kJ·mol−1 ΔGhydr value for U(VI) is by far less favorable than that for Nd3+ (−3336 kJ·mol−1); therefore macroscopically-observed differences in the U(VI) adsorption onto porous vs. non-porous Al2O3 agree with our predictions and observations for lanthanides.

Heats of Ln3+ adsorption quantified with operando flow microcalorimetry

Heats of Ln3+ adsorption on corundum and nanoconfined Al2O3 surfaces were quantified using operando flow microcalorimetry. At the conditions of these experiments, for all three Ln3+, nanoconfinement reverses the enthalpic sign from an endothermic signal for the non-porous corundum to an exothermic signal on nanoconfined Al2O3 surfaces (Fig. 2). This finding is consistent with our previous investigations of Cu2+ and Ln3+ adsorption unto porous SiO2 surfaces29,30 whereby nanoconfinement resulted in a reversal of the enthalpic sign in the flow-through experiments. Additionally, operando flow microcalorimetry data can also point to the nature of surface complexes: e.g., the adsorption of Cr3+ as inner-sphere complexes is exothermic for SiO2 (quartz) and corundum, while the adsorption of Al3+ on the same surfaces as outer-sphere complexes is endothermic48.

Fig. 2: Operando microcalorimetry data for neodymium, terbium, and lutetium adsorbing onto non-porous and porous alumina.
figure 2

Calorimetric signal obtained for the complexation of (a) Nd3+, (b) Tb3+and (c) Lu3+ on corundum and Al2O3 surfaces nanoconfined within 4 nm pores. An increase in voltage resulting in a positive peak corresponds to a release of energy and hence an exothermic reaction. For porous Al2O3, the concentrations were 7.86 μM for Nd(NO3)3, 11.22 μM for Tb(NO3)3 and 8.42 μM for Lu(NO3)3. Due to the low calorimetric signal obtained for corundum at the same aqueous concentrations (d), the concentrations of the stock solutions were increased to 157.2 μM for Nd(NO3)3, 224.4 μM for Tb(NO3)3, and 168.4 μM for Lu(NO3)3. This data is not normalized to the mass of solids used nor is it obtained for the same Ln3+ concentrations. See text and Table 2 for normalized energies.

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In comparing the two Al2O3 surfaces, the adsorption of Ln3+ was significantly more energetic on nanoconfined Al2O3 surfaces than on corundum surfaces, potentially indicating enhanced inner-sphere complexation. The summary of the microcalorimetric results (Qads in mJ·m−2 and ΔHads in kJ·mol−1) and surface coverages (in mol·m−2) is shown in Table 2. The molar enthalpies, ΔHads, for Lu3+, Tb3+, and Nd3+ were calculated to be –34.8, –13.4 and –55.3 kJ·mol−1 on nanoconfined Al2O3 surfaces, and +1.77, +0.66, and +0.62 kJ.mol−1 on non-porous corundum surfaces, respectively. The largest difference between both surfaces was observed for Nd3+, which is consistent with our XAFS data and our hypothesis that the lightest lanthanides with the least exothermic ΔGhydr are affected more by nanoconfinement. It is crucial to note that no detectable calorimetric signal was detected at first for non-porous Al2O3, indicating that Qads was ~0 mJ·m−2. To achieve a detectable calorimetric signal, the microcalorimetry experiments on non-porous Al2O3 were conducted at a higher Ln3+ concentration, resulting in higher surface coverages for non-porous corundum than for porous Al2O3. It is therefore possible that the overall higher energy measured for nanoconfined Al2O3 is disproportionately influenced by the high-energy sites, which are typically occupied first and can contribute more to the overall signal at lower surface coverages.

Table 2 Summary of thermodynamic parameters calculated from batch adsorption data and measured by operando flow microcalorimetry experiments.
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Enthalpy, entropy, and Gibbs Free energy of adsorption measured in temperature-controlled batch experiments

To assess the impact of surface coverage on the adsorption energetics we measured adsorption equilibrium constants in batch samples at temperatures ranging from 25 ± 1 °C to 45 ± 1 °C (298 K to 318 K). The surface coverages for all samples are provided in Table 2. In all batch reactors, the adsorbed Ln amount increases with increasing temperature, indicating endothermic adsorption for all Ln3+ cations on porous and non-porous Al2O3. The dataset used for thermodynamic calculations is included in the Supporting Information file (Table S1). While the calculated ΔHads values were positive for both solids, ΔSads values were negative for Al2O3 nanopores, and positive for corundum surfaces (Table 2). This result indicates a higher degree of freedom for species adsorbed onto the corundum surface and increased ordering of surface complexes inside nanopores. Due to these entropic effects, the calculated ΔGads values at room temperature are negative for corundum, indicating a spontaneous reaction, and positive for Al2O3 nanopores, indicating that adsorption is non-spontaneous.

When all batch and flow samples are considered, ΔHads values show a dependency on the surface coverage up to ~0.5 mmol m−2, at which point mono-layer coverage is achieved (Table 2, Fig. 3). With increasing surface coverages ΔHads values become more endothermic. This finding is not surprising, as we noted above, since at lower surface coverages the adsorption predominantly occurs at high-energy sites; and with increasing surface coverage, lower energy sites become progressively occupied. All data from the batch and operando microcalorimetry experiments is summarized in Table 2 and plotted in Fig. 3 to illustrate this point.

Fig. 3: All measured enthalpies plotted as a function of surface coverage.
figure 3

Red symbols are Al2O3 nanopores, blue symbols are corundum. Data at <0.001 mmol m−2 coverage is from microcalorimetry measurements, and data for higher surface coverages is from batch adsorption measurements.

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Direct calorimetric measurements of adsorption enthalpies as a function of the amount adsorbed remain limited. However, using titration calorimetry, Machesky et al.49 found that for the adsorption of iodate, fluoride, phosphate, and salicylate onto goethite, adsorption enthalpies become less exothermic as surface coverage increases, while at high surface coverages (>70%) even become endothermic for phosphate and fluoride. More recently Falaise et al.50 observed variations of adsorption enthalpies with surface coverage for the sorption of Th4+, [UO2]2+, and Nd3+ in a porous metal-organic framework, although each cation exhibited a different trend depending on its adsorption process.

Interpreting data on structure and energetics together

The overall free energy of adsorption is the sum of the electrostatic and chemical free energy changes (favorable to adsorption) and the solvation free energy change (unfavorable to adsorption)51:

$$\triangle {G}_{{ads}}=\triangle {G}_{{coul}}-\triangle {G}_{{hydr}}+\triangle {G}_{{chem}}$$
(1)

Consider electrostatic interactions (ΔGcoul) first: in our experiments, the Al2O3 surfaces are positively charged as they are in solutions at pH 6.0, which is below the reported point of zero charge (pHPZC) values for various porous and non-porous Al2O3 phases. The pHPZC values are 8.7 for γ-Al2O3 with 2 nm pores43, 10.9 for porous Al2O3 with ~1.3 nm pores42, and 9.7 for corundum42. Lanthanides are Brønsted acids and can hydrolyze water; however, pKa values for the first hydrolysis product for the Ln3+ cations considered here are >752, thus in our experiments, Ln3+ cations are expected to be in the aqua-ion form [Ln·(H2O)8]3+. Therefore, the coulombic interactions at Al2O3 surfaces are unfavorable for adsorption and are likely more unfavorable for Nd3+ because of its larger solvation shell and less effective charge screening compared to Lu3+. Consider hydration energies (ΔGhydr) second: the ΔGhydr for Nd3+ is lower than that of Lu3+, which is then harder to de-solvate prior to inner-sphere adsorption. Consider chemical free energy changes (ΔGchem) third: the Lu-O bond length is shorter by ~0.2 Å compared to Nd-O bond length (Table 1); therefore, ΔGchem for Lu surface complexes at Al-OH sites is more favorable than for the analogous Nd complexes. We observed that Lu3+ undergoes chemisorption on both confined and unconfined surfaces, while Nd3+ undergoes physisorption on unconfined, and chemisorption on nanoconfined surfaces. We conclude that the ΔGchem term for Lu3+ compensates for the more unfavorable ΔGhydr contribution in both nanoconfined and unconfined systems. For Nd3+, because of its lower degree of charge screening and less favorable ΔGchem, physisorption dominates for unconfined surfaces. We interpret the switch from outer- to inner-sphere adsorption for Nd in nanopores to be due to ΔGhydr becoming less negative due to nanoconfinement, which allows Nd3+ to shed 1–2 H2O molecules prior to adsorption in nanopores. It is important to note, that all of the considered ΔG values are likely affected by nanoconfinement in different ways. Solvation free energies become less negative in nanopores, compared to the reported ΔGhydr values29, however, the exact change in the ΔGhydr value remains unresolved. Similarly, ΔGcoul likely increases in nanopores because of decreased charge screening due to ΔGhydr values becoming less negative. Future work is urgently needed to unravel all the important thermodynamic contributions in charged nanopores, that control surface reactivities in important ways presented here.

Conclusions

In summary, we show that an ion’s ΔGhydr determines whether nanoconfinement changes the products of its adsorption and associated thermodynamics, and therefore ΔGhydr can be used as a predictor. Since Nd3+ has less negative ΔGhydr compared to Lu3+, it forms different surface complexes on unconfined versus nanoconfined Al2O3 surfaces. The balance between an ion’s (de)solvation costs, coulombic interactions, and chemical free energy change dictates whether adsorption will occur through an outer- or an inner-sphere complex. Therefore, in nanoconfined systems where the average dielectric response of water is lowered19, inner-sphere complexation is promoted. This is because a decreased dielectric response makes Ln3+ ΔGhydr less negative, reducing the energetic cost of the ion’s partial desolvation prior to inner-sphere adsorption.

Methods

Al2O3 materials and temperature-controlled batch adsorption experiments

Alumina Al2O3 with a mean pore diameter of 4.4 ± 0.1 nm and surface area of 335 ± 2 m2 g−1 (herein referred to as “nanoconfined Al2O3 surfaces”) and non-porous corundum α-Al2O3 particles with a surface area of 1.5 m2 g−1 were purchased from Sigma Aldrich. Lanthanide stock solutions were made from nitrate salts Ln(NO3)3 using 18 MΩ·cm Milli-Q water.

To determine enthalpy (ΔHads), entropy (ΔSads), and Gibbs free energy (ΔGads) of Ln3+ adsorption samples were prepared by shaking 20 ± 1 mg of dry Al2O3 powders in ~19 mL of 0.01 M HEPES (N-(2-Hydroxyethyl)piperazine-N′-(2-ethanesulfonic acid)) buffer solution for 1 hour prior to adding Ln3+. To begin the adsorption experiment, ~1 mL of Ln3+ stock solution was added to each reactor to obtain a 20 mL total volume at a Ln3+ concentration of 0.03-0.34 µM. The pH was 6.5 ± 0.1 for all samples. Adsorption proceeded for 23 hours at controlled temperatures of 25 ± 1 °C, 35 ± 1 °C, and 45 ± 1 °C in a water bath. Samples were withdrawn while still submerged in the water bath and filtered using a 0.2 µm nylon membrane immediately, so no temperature changes occur during sampling. Samples were acidified with 6 N ultrapure HNO3. The concentrations of each Ln3+ remaining in the solution after adsorption took place were quantified using inductively coupled plasma mass spectrometry (ICP-MS, NexION 350D, Perkin Elmer). Calibration curves for each analyte were obtained by running certified standard solutions prior to each analytical run, with a resulting R2 value of 0.9999 or better. After equilibrium Kd values were determined from aqueous concentrations, enthalpy, and entropy values were then calculated using van't Hoff Eq. (2); and free energy was calculated using Eq. (3):

$${{{{{\rm{ln}}}}}}({K}_{d})=\varDelta S/R{{{{{\rm{\hbox{-}}}}}}}\varDelta H/{RT}$$
(2)
$$\varDelta G=\varDelta H{{{{{\rm{\hbox{-}}}}}}}T\varDelta S$$
(3)

where Kd is the equilibrium constant for a given temperature and Ln3+ concentration, T is the absolute temperature (K), and R is the universal gas constant (8.314 J·mol−1·K−1). Plotting ln(Kd) vs 1/T yielded straight lines for both Al2O3 solids and for all Ln3+, and we used the slope and intercept values to estimate ΔHads, ΔSads, and ΔGads.

X-ray absorption fine structure analysis

Samples for the XAFS analyses were prepared by shaking 400 ± 5 mg of dry Al2O3 powders in 148 mL of 0.01 M NaCl for a minimum of 48 h. To begin the adsorption experiment, ~1 mL of Ln3+ stock solution was added to each reactor to obtain a 150 mL total volume at a Ln3+ concentration of 0.1 mM. These solutions were immediately adjusted to pH 6.0 ± 0.1 with NaOH or HCl. Throughout our experiments we chose pH 6.0 or pH 6.5 because this pH range is environmentally relevant: due to the atmospheric CO2 dissolution into natural waters, pH between 6 and 6.5 is typical in natural systems. The second reason for choosing pH <7 is because it is below the first hydrolysis constant for lanthanides (>7), therefore the cations of interest were present as aqua-complexes with +3 charge in solution52. Ln3+adsorption proceeded for 48 h at ambient temperature (22 °C), at which point adsorption equilibrium was reached. Samples were then centrifuged, and the supernatant was filtered using a 0.2 µm nylon membrane filter before being acidified with 6 N ultrapure HNO3. The concentrations of each Ln3+ remaining in the solution after adsorption took place were quantified using ICP-MS, NexION 350D.

The remaining wet pastes from the bottom of the centrifuged reactors were stored in a refrigerator at 4 °C for XAFS spectroscopy analyses. Prior to data collection, these pastes were mounted on plastic sample holders with ~2 mm depth. XAFS data at the Nd, Tb, and Lu LIII-edges was collected using beamline 10-BM at the Advanced Photon Source (APS), Argonne National Laboratory. The beamline is equipped with a water-cooled Si(111) monochromator, which was detuned by 50% to reject higher harmonics and calibrated using metal reference foils. The monochromator step size was 10 eV in the pre-edge, 0.5 eV in the XANES region, and 0.05 Å−1 in the XAFS region. Fluorescent counts were collected using a Vortex Si Drift solid-state 4-element detector. The XAFS data were processed using the Athena interface and fitted using the Artemis interface53 to the IFEFFIT54 by fitting theoretical paths55, which were based on the structures of lanthanide-containing apatite56. The structure files were edited to remove partial occupancies so that FEFF calculations could be performed. The background subtraction (AUTOBK algorithm57), normalization, and conversion into k-space were conducted as described elsewhere58. The fitting was done in R-space using a Hanning window and k-weights of 1, 2, and 3. R-factor cut-off of <0.05 was used to indicate a reasonable fit. In our samples, R-factors are between 0.01 and 0.02. The amplitude reduction factor (S0) was determined by fitting XAFS spectra collected on Nd2O3, Tb2O3, and Lu2O3 standards; S0 was 0.88 for Nd, 0.67 for Tb, and 0.71 for Lu. Fitting errors at a 95% confidence level (2 sigma) are shown in parenthesis in Table 1.

Flow microcalorimetry experiments

Custom flow microcalorimeter in the Kabengi Laboratory at Georgia State University59 was used to obtain thermal signatures and subsequently, the heats of Nd3+, Tb3+, and Lu3+ ion exchange using a uniformly-packed micro-column with 20.0 ± 0.5 mg porous Al2O3 sample or 50.0 ± 0.5 mg of corundum particles. The packed microcolumn was equilibrated with a 0.01 M NaNO3 solution at a flow rate of 0.30 ± 0.03 mL min−1 until a steady baseline indicative of thermal equilibrium was observed. A known mass of Ln3+ was injected into the column with a controlled volume of Ln(NO3)3 stock solution. The calorimetric signal corresponding to the interaction of Ln3+ with the Al2O3 surfaces was obtained following Ln3+ injection. Once the thermal signal returned to the original baseline, the input solution was switched back to 0.01 M NaNO3. For porous Al2O3, the concentrations were 7.86 μM for Nd(NO3)3, 11.22 μM for Tb(NO3)3 and 8.42 μM for Lu(NO3)3. Due to the low calorimetric signal obtained for corundum, the concentrations of the stock solutions were increased to 157.2 μM for Nd(NO3)3, 224.4 μM for Tb(NO3)3, and 168.4 μM for Lu(NO3)3. Aqueous concentrations of Ln3+ in the column effluent samples were quantified using ICP-MS as described above. The mass of Ln3+ retained at (and subsequently desorbed from) the surface was determined by a mass balance calculation between the mass of the injected Ln3+ and the mass recovered in all effluents. The heats of reactions (Qads in mJ∙m−2) and molar enthalpies (ΔHads in kJ∙mol−1) were calculated by integrating the calorimetric peaks that were converted to energy units (Joules) by calibration with calorimetric peaks of known energy inputs generated from a calibrating resistor placed inside the microcolumn. The solution pH was adjusted daily to pH 6.0 ± 0.1 using dropwise addition of 0.1 M HNO3 and 0.1 M NaOH. Changes in total concentration and ionic strength resulting from pH adjustments were determined to be negligible.