Outer-Sphere Water Clusters Tune the Lanthanide Selectivity of Diglycolamides.

Fundamental understanding of the selective recognition and separation of f-block metal ions by chelating agents is of crucial importance for advancing sustainable energy systems. Current investigations in this area are mostly focused on the study of inner-sphere interactions between metal ions and donor groups of ligands, while the effects on the selectivity resulting from molecular interactions in the outer-sphere region have been largely overlooked. Herein, we explore the fundamental origins of the selectivity of the solvating extractant N,N,N',N'-tetraoctyl diglycolamide (TODGA) for adjacent lanthanides in a liquid-liquid extraction system, which is of relevance to nuclear fuel reprocessing and rare-earth refining technologies. Complementary investigations integrating distribution studies, quantum mechanical calculations, and classical molecular dynamics simulations establish a relationship between coextracted water and lanthanide extraction by TODGA across the series, pointing to the importance of the hydrogen-bonding interactions between outer-sphere nitrate ions and water clusters in a nonpolar environment. Our findings have significant implications for the design of novel efficient separation systems and processes, emphasizing the importance of tuning both inner- and outer-sphere interactions to obtain total control over selectivity in the biphasic extraction of lanthanides.

Introduction

Over the past 25 years climate change has become an area of considerable international interest. Nuclear power, with an energy unit cost similar to conventional forms of energy production[1] and carbon emissions on par with renewable energy sources,[2] is an attractive high-density alternative power source. However, concerns about the ultimate disposal of nuclear waste have stalled its expansion. These concerns can be addressed by processing used nuclear fuel to reduce the volume of high-level radioactive waste that must be stored in geological waste repositories, and fully separating fission products for further use or transmutation in a nuclear reactor. Recovery of high-value fission products such as precious metals and lanthanides from the complex mixture of transition metals and f-block elements making up used nuclear fuel is an increasingly attractive proposition as their use in electronics and other high-technology consumer goods increases.[3] Meanwhile, transmutation of hazardous long-lived radionuclides will reduce the amount of time needed for the activity of nuclear waste to reach background by several orders of magnitude, from tens of thousands of years to only hundreds of years.[4] These goals can be met through the development of new extractants and separations processes, the improvement of existing processes, or some combination thereof.

The trivalent f-block elements are challenging to separate from one another due to their similar charge densities and near-identical chemistries. Amide extractants were originally considered for use in the separation of f-block elements after being described by Siddall in 1960.[5] Neutral diglycolamide extractants were first explored as alternatives to bidentate malonamide ligands in the early 2000s.[6,7] Both classes of extractant are fully incinerable, making them attractive for applications in the management of high-level radioactive waste.[7] However, the additional ether oxygen in tridentate diglycolamide extractants greatly increases their affinity for trivalent lanthanides and actinides over bidentate malonamide ligands. While the extraction capabilities of numerous different diglycolamides have been explored in the literature, most work has focused on N,N,N′,N′-tetraoctyl diglycolamide (TODGA) due to its low solubility in water, high solubility in organic diluents, and high affinity for trivalent f-block elements.[7] Work with these extractants has focused on the utility of diglycolamides in the separation of trivalent actinides from lanthanides. However, the high affinity of diglycolamide extractants for trivalent lanthanides suggests that they may also have applications in the separation of adjacent lanthanides.

Traditional approaches to the solution-phase separation of adjacent lanthanides have focused on the effect of the contraction of trivalent lanthanides’ ionic radii on their inner-sphere coordination environment.[8] The trivalent lanthanides are hard acids with very similar chemical and physical properties,[9] making this small decrease in size across the series, shown in Figure , the primary difference that can be leveraged to accomplish mutual separations in lanthanide mixtures. The primary effect of this contraction is the increased strength of ion–dipole interactions between the lanthanides and extractant molecules with increasing atomic number. In a solvent extraction system, this corresponds to slightly better extraction of the heavier lanthanides. However, this simplistic understanding of the extraction chemistry of the lanthanides fails to include the possible effects of interactions occurring beyond the first coordination sphere. Determining the nature of these interactions, which are most effectively probed at high metal concentrations, may be essential to designing efficient lanthanide separation processes.

Figure 1

Ionic radii of the lanthanides decrease steadily across the series.[9] Extraction of the lanthanides by 0.1 M TODGA increases from the light to mid-lanthanides, after which it levels off.[7]

The affinity of TODGA for the trivalent lanthanides does not follow a linearly increasing trend across the lanthanide series as would be expected if the strengths of the electrostatic interactions between the lanthanide and extractant were the only property impacting extraction. Instead, distribution data show a steady increase in extraction across the light lanthanides and a break in this trend at Gd beyond which metal distribution is effectively constant (Figure ).[7] In a previously reported study, this trend was attributed to a similar but much less pronounced break in the energy difference between an aqueous-solvated lanthanide ion and a diglycolamide-solvated lanthanide ion, measured relative to the energy of lanthanum solvation.[10] This difference is referred to as the aqueous-phase selectivity, and takes into account only the energetics of inner-sphere coordination. However, the less pronounced agreement between the experimental distribution data and aqueous-phase selectivities suggests that there are additional factors affecting the observed selectivity trend that have not yet been identified.

Prior work looking at the structure of diglycolamide–lanthanide complexes has determined that the extractant amide and ether groups are directly coordinated to the central metal cation in a tridentate fashion, while charge-neutralizing anions are located in the outer-sphere of the complex. This structure has been determined in the solid state for lanthanide and actinide nitrates,[11,12] and verified for solution-phase species in solvent extraction samples.[10,13] The calculation of aqueous-phase selectivities does not take these outer-sphere anions into account. However, the behavior of outer-sphere species may provide an additional basis for the observed selectivity.

More recently, the importance of anion placement in the outer coordination sphere of extracted complexes to the selectivity of TODGA for the lanthanides was established using extraction studies, X-ray absorption spectroscopy, density functional theory (DFT) calculations, and classical molecular dynamics (MD) simulations.[14] These complementary techniques validated the 1:3 lanthanide to TODGA stoichiometry, and provided detailed insight into the molecular structure of TODGA clusters in the organic phase. The configuration of TODGA and charge-neutralizing anions (either Cl– or NO3–) around the central metal cation was found to contribute to the stabilities of these complexes, resulting in a high affinity of TODGA for the lanthanides. However, the impact of outer-sphere coordination on lanthanide selectivity across the series was not addressed.

The purpose of this work is to achieve a fundamental understanding of the impact of outer-sphere coordination on the lanthanide selectivity of diglycolamides in a liquid–liquid extraction system, which is of relevance to nuclear fuel reprocessing and rare-earth refining technologies. We establish for the first time the correlation between lanthanide extraction and the amount of water coextracted in the organic phase, indicating the importance of molecular interactions extending beyond the inner coordination shell. DFT calculations show that unlike the first coordination shell bond lengths, which decrease linearly in the series, the outer-sphere distances increase from La to Gd and then remain constant across the heavy lanthanides, following a trend that closely correlates with the extraction data for lanthanides and water coextraction by TODGA. This suggests that the mechanism underlying water uptake is related to the surface area of the nitrate counterions available to interact with coextracted water. MD simulations further elucidate that outer-sphere nitrate ions form hydrogen bonds with water molecules, which are dynamic in nature and can move easily from one nitrate to another, occasionally forming peculiar snakelike cluster chains around the lanthanide complex in a nonpolar environment. In a broader perspective, our results have significant implications for the design of novel efficient separation systems and processes for trivalent f-block metal ions, emphasizing the importance of tuning both inner- and outer-sphere interactions to obtain total control over selectivity in the biphasic extraction of lanthanides.

Results and Discussion

Experimental Samples

The investigated solvent extraction system consisted of an organic phase with 0.25 M TODGA dissolved in an n-dodecane diluent contacted with a 0.001 M HNO3 aqueous phase containing macroscopic amounts of NaNO3 and lanthanides from across the series. The organic-phase TODGA concentration was chosen to be high enough that it could reasonably be considered for use in an industrial-scale operation, where a high saturation of the organic phase by metal is desired. The aqueous-phase composition was chosen to minimize the impact of competitive extraction on the system. A salting out agent in the aqueous phase is required for approximately 50% extraction of the light lanthanides by a 0.25 M TODGA organic phase. Nitric acid, a salting out agent used in applied separations, competes with metals for extractant, adding an additional experimental parameter that must be considered. In these experiments, a background electrolyte consisting of approximately 0.5 M NaNO3 was used to improve the extraction of the lanthanides without Na+ being extracted. The absence of significant Na+ extraction was demonstrated in 22Na radiotracer experiments, which are described in the Supporting Information. A small amount of nitric acid was added to the aqueous phase to prevent hydrolysis of the metals, for a final acid concentration of 0.001 M HNO3.

Limiting Organic Concentrations

According to solvent extraction[15] and EXAFS studies,[10] trivalent lanthanides are likely extracted as a 1:3 metal to TODGA species according to the following equilibrium relationship:

This equation suggests a theoretical value for the maximum concentration of metal that can be extracted into a 0.25 M TODGA organic phase. A fully saturated organic phase would have a 0.083 M metal concentration, corresponding to all TODGA molecules being a part of a trimeric extracted metal species. However, like other neutral solvating extractants, TODGA is known to form a third phase before this saturation concentration can be reached.[16] Third-phase formation in a solvent extraction system occurs when the organic phase splits into an upper, diluent-rich organic phase, and a heavy, extractant- and metal-rich organic phase in equilibrium with the aqueous phase. Third-phase formation is correlated with high metal concentrations in the organic phase.

The limiting organic concentration (LOC) is defined as the greatest concentration of metal that can be extracted into an organic phase before a third phase is formed. The LOCs of six metals from across the light, middle, and heavy lanthanides (La, Pr, Sm, Gd, Dy, and Tm) were found by incrementally changing the initial aqueous-phase concentrations of each metal. The result is an “S”-shaped curve, shown in Figure a, in which the LOC starts at a high concentration and decreases slowly across the light lanthanides, rapidly across the early-middle lanthanides, then levels off beginning at the late-middle lanthanides. The point of inflection of this curve roughly corresponds to Nd, and the complete leveling-off of the LOCs takes place at Gd. The leveling-off of the LOC takes place at the same point in the series at which metal extraction is also observed to level off. However, the “S”-shape does not correspond to other important reported physical or chemical attributes of the lanthanide ions in solution, including ionic radii, softness, enthalpy and entropy of hydration, conductivity, and others.[9] This suggests that the observed trend is not the result of a direct interaction between the metal ion and extractant. Rather, it may be the result of outer-sphere coordination effects.

Figure 2

(a) Lanthanide LOCs in a TODGA solvent extraction system (0.25 M TODGA) form an “S”-shaped curve when plotted against atomic number. (b) The distribution ratios of the lanthanides in this system (0.25 M TODGA) are inversely proportional to concentration and ionic radii.

Lanthanum comes the closest to the theoretical limit of saturation of the organic phase before forming a third phase at an organic concentration of 0.077 M, followed by Pr at 0.070 M. The remaining lanthanides reach the LOC at concentrations much less than the theoretical saturation point of the organic phase. The proximity of the LOC to the saturation concentration of the organic phase further validates the formation of the 1:3 metal to TODGA species for La and Pr established in prior work.[10,14]

Distribution Data

The distribution ratio, D, is a measure of metal extraction, and is calculated as shown in eq , where the organic-phase concentration of a metal, [M]org, is divided by the aqueous-phase concentration, [M]aq.

In the absence of confounding factors like competitive extraction, distribution ratios are expected to decrease with increasing metal concentration as saturation of the organic phase is approached. This trend is observed in the distribution ratio values shown in Figure b. The distribution ratios of La, Pr, Sm, and Gd decrease exponentially with increasing metal concentration in the system until the LOC is reached. The heavy lanthanides Dy and Tm are sufficiently well-extracted that their aqueous-phase concentrations were undetectable by ICP-OES, preventing the calculation of distribution ratios for these metals. Because of the high recovery of the heavy lanthanides, the leveling-off of the distribution ratio from Gd onward that has been observed in dilute extraction experiments could not be verified for concentrated systems. However, the distribution data collected for La, Pr, Sm, and Gd under concentrated conditions follow the same trend as that observed in dilute systems. For a given equilibrium organic-phase concentration of metal, the distribution ratio increases with increasing atomic number.

Trends in Water Coextraction

The amount of water extracted with each lanthanide is shown in Figure a. The point at zero lanthanide concentration in the organic phase corresponds to the equilibrium composition of a 0.25 M TODGA phase contacted with 0.5 M NaNO3. As expected, the amount of Na extracted into the organic phase in representative samples was extremely low, resulting in final organic-phase concentrations of approximately 50 μM in 22Na radiotracer experiments performed both with and without lanthanides. The specifics of these experiments are given in the Supporting Information. The water concentration in the equilibrium organic phase increases with increasing metal concentration at different rates depending on the identity of the extracted metal. The equilibrium organic-phase water concentration increases at the slowest rate with increasing La concentration, followed by Pr, Sm, and Gd. At Gd the amount of extracted water stops increasing, such that the increase in water concentration with metal concentration is the same for Gd, Dy, and Tm.

Figure 3

(a) The amount of water extracted with each lanthanide (0.25 M TODGA) increases with increasing metal concentration. Error bars have been omitted for clarity. Lines are included to guide the eye and do not represent a model fit. (b) The expected amount of coextracted water in an organic phase (0.25 M TODGA) with a 0.014 M lanthanide concentration increases for the light lanthanides and levels off for the heavy lanthanides. This trend in water coextraction appears to closely follow the trend in lanthanide extraction by 0.1 M TODGA.[7] Data can be found in Table S4 of the Supporting Information.

For a constant organic-phase lanthanide concentration, the observed trend in water coextraction follows the distribution ratio trend across the lanthanides. The number of water molecules coextracted with each nitrate ion in the organic phase increases steadily to Gd, beyond which it remains approximately constant. Figure b shows the increase in water coextraction for a constant lanthanide concentration of 0.014 M. These values were determined from linear interpolation of the data shown in Figure a, and transformation of these values to waters per nitrate as described in the Supporting Information. This trend compares favorably with the trend in distribution ratios across the lanthanide series, also shown in Figure b. The close agreement between these data suggests a relationship between the water coextracted with a metal and how well that metal is extracted by TODGA. However, the exact nature of this relationship is unclear.

Water is not a part of the inner coordination sphere of TODGA-extracted trivalent lanthanides. A time-resolved laser-induced fluorescence spectroscopy (TRLFS) study on the complexation of Eu by TODGA demonstrated that water is not coordinated to the metal.[17] This finding was validated by solution-phase EXAFS studies of TODGA-extracted Pr, Nd, Eu, Yb, and Lu, which showed the inner coordination sphere of these ions saturated by the ligand.[10] These findings, as well as the low concentration of water in the organic phase without metals, mean that this water is likely being coextracted in the outer coordination sphere of the lanthanides, suggesting a link between the outer-sphere coordination chemistry of the lanthanides and their extraction by TODGA. Such outer-sphere effects have been considered as an explanation for the extraction chemistry of a malonamide extractant, although the explicit molecular origins of these effects were not identified.[18]

Computational Insights

The observed impact of the interactions beyond the inner coordination shell on the lanthanide selectivity warrants understanding of this phenomenon at the molecular level. In this regard, quantum chemical and classical molecular dynamics (MD) simulations can provide detailed molecular insights into the outer-sphere region, where conventional experimental structural methods of analysis are limited. Previous DFT studies[10] of the diglycolamide aqueous complexation in the lanthanide(III) series established a steady but nonlinear increase in selectivity with decreasing size of the metal ion, showing a larger slope for the early lanthanides (Figure ). This trend, which is only partially consistent with liquid–liquid extraction experiments (Figure ), was attributed exclusively to an interplay between the ligand steric strain and coordination energies, since no counterions were included in the DFT calculations of the lanthanide complexes.[10] To account for the effects of outer-sphere counterions on the binding properties of DGA ligands, we computationally assessed the Gibbs free energy change, ΔΔ(La/Ln), for the following reaction of competitive complexation of La(III) over Ln(III):

Figure 4

Plots of predicted aqueous-phase selectivities, ΔΔ(La/Ln) in kcal/mol (Ln = La, Pr, Sm, Gd, Dy, Tm, Yb), for the DGA complexes with and without inclusion of nitrate counterions in the second coordination sphere.

The results in Figure show that the inclusion of NO3– anions in the DFT calculations only slightly improves the agreement between experimental and predicted selectivities, indicating a sharper leveling-off from Tm to Yb compared to the calculations that neglect the presence of counterions in the second coordination shell of the lanthanide complexes.[10] Additional calculations, considering implicit solvation of Ln(TEDGA)3(NO3)3 in an aqueous medium, show almost exactly the same trend in selectivity as observed in the low-dielectric-constant organic phase (see Figure S1 of the Supporting Information).

As thermodynamic calculations using implicit solvation models are not sufficient to fully explain a break in the linearly increasing extraction trend at Gd (Figure ), we investigated structural changes in the lanthanide complexes upon outer-sphere nitrate coordination. As seen in Figure , the first coordination shell of the optimized Ln(TEDGA)3(NO3)3 clusters consists of nine donor oxygen atoms of TEDGA, while nitrate anions are located in hydrophobic clefts between the TEDGA ligands in agreement with a recent EXAFS study, suggesting the formation of structurally similar trefoil-shaped outer-sphere Ln(DGA)3(Cl)3 (Ln = Nd/Pr) complexes in a liquid–liquid extraction system.[14] As expected, the inner-sphere Ln–Oinner bond lengths linearly decrease across the considered light (La, Pr), middle (Sm, Gd, Dy), and heavy (Tm, Yb) lanthanides, which is consistent with the contraction of the lanthanide ionic radii that leads to increasing of Ln3+ charge density, promoting stronger electrostatic interactions between the oxygen donor atoms of TEDGA and heavier lanthanide ions. However, in striking contrast to the first coordination shell, the outer-sphere Ln–O(nitrate) (denoted as Ln–Oouter in Figure ) and Ln–N(nitrate) (Figure S2 of the Supporting Information) distances increase from La to Gd and remain constant later in the series, following a trend that closely correlates with extraction data for lanthanides and water coextraction by TODGA (Figure b). This behavior of NO3– anions in the second coordination shell can be attributed to the increase in steric crowding at the metal center as the metal ion radii contract across the series, pushing the nitrate anions farther away from the lanthanide ion. This suggests that the polar surfaces of nitrates are more exposed to interact with water molecules, rationalizing the increased amount of water associated with the extraction complexes of Gd and heavier lanthanides.

Figure 5

Structures of the representative DFT-optimized Ln(TEDGA)3(NO3)3 complexes along with the inner-sphere (Ln–Oinner) and outer-sphere (Ln–Oouter) average distances (Å) plotted against atomic number. Color scheme: La, orange; Gd, purple; Yb, gray; O, red; N, blue; C, teal; H, white.

While it is not currently possible to run DFT calculations using a full representation of the ligand in the explicit solvent environment with adequate sampling of intermolecular interactions, we next turn our attention to the atomistic classical MD simulations. In addition to providing time-averaged coordination metrics for counterions, MD simulations were employed to better understand how water molecules interact with metal extraction complexes in a low-dielectric-constant medium. Since recent EXAFS measurements[14] have corroborated X-ray diffraction experiments[12] indicating that homoleptic Ln(DGA)3Cl3/Ln(DGA)3(NO3)3 complexes prevail in organic extractive solutions and have shown very minor differences in the inner-sphere bond lengths in the presence of different counterions, we can freeze the inner-sphere coordination during the MD simulations at the DFT-optimized geometry and focus on the structural changes in the outer coordination shell. This will allow us to utilize conventional force fields without the need to develop force field parameters for lanthanide ions. A single Ln(TODGA)3(NO3)3 (Ln = La, Gd, and Yb) complex with 160 dodecane solvent molecules was equilibrated at T = 298 K for 8–10 ns. A total of nine systems with three metal ions representing early, middle, and late lanthanides, each containing 0, 6, and 12 water molecules were considered. In agreement with present DFT calculations and previously reported results for the inner-sphere Ln complex with Cl– anions,[14] NO3– anions on average are symmetrically positioned in the clefts between the three coordinating DGA ligands, forming complexes with charge-neutralizing anions positioned in the outer-sphere that are favored by low-dielectric-constant solvents. A snapshot of the representative solution structure of Gd(TODGA)3(NO3)3 with 12 water molecules forming snakelike chains around nitrate anions is illustrated in Figure .

Figure 6

Snapshot of the Gd(TODGA)3(NO3)3 complex with 12 water molecules in dodecane from classical MD simulations. Gd, nitrate anions, and water molecules are shown using van der Waals spheres. Solvent molecules are not visualized for clarity.

To probe structural correlations in the outer coordination shells, we first analyzed the radial distribution functions (RDFs), g(r), between nitrate N and Ln atoms. The corresponding Ln–N(nitrate) distances in Figure indicate that nitrate anions are closely confined in the clefts of the complexes by strong electrostatic forces. The results fully support DFT findings that as the metal ion radius becomes smaller, and the steric crowding becomes more severe, the nitrate anions are pushed away from the metal center until a point around Gd, where the structural differences for outer-sphere nitrate coordination between Gd and heavier lanthanides are minimal (Figure ). It is worth noting, however, that our simulation results cannot be corroborated by EXAFS,[14] because unlike chlorides that backscatter X-rays with greater intensity, there is no measurable backscattering from the lighter N and O atoms of nitrates.

Figure 7

Radial distribution functions (g(r)) of N atoms of nitrate anions around Ln3+ (Ln = La, Gd, and Yb) in dodecane (left panel) and dodecane with 12 water molecules (right panel).

As expected, water molecules are attracted by nitrate anions, producing a notable impact on the RDFs peaks (Figure , right panel) that slightly broaden and shift to longer distances without changing relative positions for different metal ions. The orientation of nitrate anions with respect to the metal center is also affected by the presence of water. This is evident from the Gd–O(nitrate) RDFs in Figure a, showing a progression from mostly a bidentate orientation of nitrates in the absence of water to an admixture of a monodentate orientation increasing in weight with increasing water content. Interestingly, the position of the first RDF peak hardly changes with the addition of water despite some decrease in the peak intensity. This suggests that the observed increase in the Ln–N(nitrate) distance with increasing water content is mostly due to a change in nitrate orientation.

Figure 8

(a) Radial distribution functions (g(r); solid curves, left axis) of O atoms of nitrate anions around Gd3+ and their integration (coordination number, CN; dashed curves, right axis) for Gd(TODGA)3(NO3)3 with 0, 6, and 12 water molecules. (b) Radial distribution functions (g(r); solid curves, left axis) of O atoms of water around N atoms of nitrate anions and their integration (coordination number, CN; dashed curves, right axis) for Ln(TODGA)3(NO3)3 (Ln = La, Gd, and Yb) with 12 water molecules.

To further examine the interaction between nitrate and water molecules for the lanthanide complexes, in Figure b we plotted the RDFs of water around nitrates. The N(nitrate)–O(water) RDFs exhibit a major peak at ≈3.6 Å corresponding to strongly bound water molecules in the first shell, followed by weak correlations at ≈4.6 and 7.0 Å. The absence of well-defined features after the first peak is an indication that water molecules in the outer shells have significant freedom to move from one nitrate anion to another, occasionally forming interconnected chains, as illustrated in Figure . From integration of the area under the main peak of the RDF, we are able to calculate the number of water molecules in the primary solvation shell around nitrates. Here, the average number of strongly bound water molecules per nitrate is ≈2.5, which can be compared to the range 1.1–1.7 of coextracted water molecules at low lanthanide concentration across the series (Figure b). This indicates that water molecules coextracted with lanthanide cations are expected to be strongly bound to nitrate counterions residing in the outer coordination shell. However, the MD simulations are unable to show a slightly higher water uptake for middle and late lanthanides compared to early lanthanides, because the RDFs and, thus, the potentials of mean force between nitrate and water for La, Gd, and Yb complexes are all very similar. This problem most probably is due to the deficiency of the nonpolarizable force field that does not take into account polarization and charge transfer effects that could effect a slightly different charge distribution in nitrates depending on the distance to the metal ion. Notwithstanding recent progress,[19] it has proven difficult to explicitly include both polarization and charge transfer for trivalent lanthanides in a broadly applicable classical force field.[20] Nevertheless, based on the complementary results from DFT and MD, it is reasonable to suggest that, compared to the Gd, and Yb complexes, more tightly bound nitrate anions in the La extraction complex would be more strongly polarized toward the metal center diminishing the strength of hydrogen-bonding interactions with water molecules.

Taking together the results of liquid–liquid extraction, water coextraction, and theoretical calculations, we can develop a hypothesis as to why TODGA shows a characteristic nonlinear trend in selectivity and has a diminished ability to discriminate the late members of the lanthanide series. In the simplest example of solvent extraction from aqueous solutions containing nitrate anions with no aggregation and interaggregate interaction, the equilibrium constant for the extraction reactionis given bywhich can be expressed as a product of the aqueous stability constant, βcomplex, and distribution ratios for a complex, Dcomplex, and a free ligand, Dligand, as

Only the first two fundamental constants, βcomplex and Dcomplex, are metal ion dependent and thus can impact lanthanide selectivity. The aqueous stability constant quantifies the strength of the metal–ligand interactions in the primary coordination shell. DFT calculations taking into account solvent effects are expected to provide a good measure of such interactions. For DGA ligands, DFT results demonstrate higher separation ability for early lanthanides than for late lanthanides, but as was mentioned, the extent of nonlinearity in the selectivity for late lanthanides is significantly underestimated compared to the selectivity in extraction experiments.

The remaining discrepancies between the DFT-predicted and experimental selectivities are likely due to phenomena that manifest beyond the first coordination sphere, which are included in the distribution ratio for the complex, Dcomplex. Unlike in an aqueous environment, counterions in the nonpolar solvents core are stabilized in the second solvation shell due to strong electrostatic attraction with the metal ion. As counterions constitute an integral part of a lanthanide extraction complex, it is essential to include counterions in the DFT calculations and test their impact on inner-sphere geometry and selectivity. Although their inclusion appears to have a modest effect on the calculated selectivity trend for DGA ligands, the results now are more consistent with extraction data showing higher separation factors for early and lower separation factors for late lanthanides compared to the case with no counterions. The coextraction of water with middle and heavy lanthanides could influence selectivity in opposite ways. Outer-sphere water could be increasing the thermodynamic stability of Ln–TODGA complexes for middle and late over early lanthanides in the organic phase by solvating the nitrate counterions, which become increasingly exposed as the lanthanide ionic radius decreases. However, additional water molecules increase the polar character of the extracted complexes, decreasing their solubility. As a result, the effects of counterions and water located outside the primary coordination sphere could combine to produce a substantial impact on the trend in lanthanide extraction selectivity. Experimentally, the reduction in solubility appears to outcompete any increased stabilization by water of outer-sphere nitrate counterions.

Beyond the simplest picture of complexation, the formation of extractant aggregates can also influence the separation factors.[18,21,22] The low concentration of nitric acid used in this work helps to minimize aggregation and micellization,[23,24] as evident by relatively modest water coextraction under tested conditions (Figure a). Also, the magnitude of weak interactions between complexes or larger aggregates that drive phase transitions can vary depending on the identity of the metal and impact selectivity slightly differently at low and high metal ion loading near the LOC. The results in Figure suggest that as the LOC values drop for middle-late lanthanides, the weak attractive interparticle potential must increase to drive mesoscale solution ordering.

In a broader perspective, this study emphasizes the significance of inner- and outer-sphere interactions, both playing an important role in determining selectivity for the biphasic extraction of lanthanides. The effects beyond the coordination sphere could not only modulate selectivity, but also sometimes reverse the trend, as is often observed by replacing organic solvent with ionic liquid.[25] The importance of secondary interactions is evident from the high sensitivity of extraction selectivity to the presence of certain ions, acids, phase modifiers, the type and length of hydrophobic chains, chosen hydrophobic diluent, concentration variations, etc.[26] Due to computational limitations, DFT calculations currently can address only some aspects of the outer-sphere interactions using truncated models of extractants and making certain assumptions about the stoichiometry and structure of the extraction complexes. Force-field-based methods are, perhaps, more suited to describe second and outer-sphere effects, provided that empirical potentials are well-calibrated against high-level calculations and experiment. Despite recent progress, this is a particularly challenging task for trivalent lanthanides[19] where strong polarization and induced charge transfer by multivalent ions must be included in the models in order to reproduce structural features and energetics of ion dehydration and coordination. Therefore, current computational models at best can only reproduce the trends in the extraction across the lanthanide series. This still represents a big step forward to providing a theoretical framework for computer-aided ligand design and screening for process development compared to mostly empirical approaches used in the past.

Conclusions

The trivalent lanthanides are difficult to separate from each other because of similarities in their physical and chemical properties. Most mutual separation processes take advantage of the small decrease in ionic radius that occurs across the lanthanide series, which would be expected to result in steadily increasing extraction across the series. However, this trend is not observed with TODGA, for which lanthanide extraction is observed to increase across the light to middle lanthanides, then remain constant across the heavy lanthanides. A combination of experimental extraction studies, and thermodynamic and structural calculations, suggest that the two TODGA extraction regimes defined across the lanthanide series result from differences in the placement of the charge-neutralizing nitrate counterions. Experimentally, this phenomenon is suggested by the trend in coextracted water, which closely follows TODGA distribution ratio data. DFT-optimized geometries of Ln(TEDGA)3(NO3)3 complexes show that the distances between the central Ln ions and inner-sphere TEDGA donor atoms decrease steadily across the series, while the distance between the lanthanides and outer-sphere nitrate anions is consistent with lanthanide and water extraction trends. Classical MD simulations corroborate changes in the location of nitrate anions in the outer-sphere of TODGA complexes and elucidate hydrogen-bonding interactions between nitrates and water molecules in the organic phase. The results of our studies demonstrate the combined importance of inner- and outer-sphere effects to the selectivity of solvent extraction ligands, and provide essential insight into the molecular basis for extraction trends in DGA and similar systems.