Complexation thermodynamics of tetraalkyl diglycolamides with trivalent f-elements in ionic liquids: spectroscopic, microcalorimetric and computational studies

Abstract

The thermodynamics of lanthanide complexation with a series of diglycolamides (DGAs) containing varying alkyl chain lengths (methyl, ethyl, n-butyl and n-hexyl) was studied in [C₄mim][Tf₂N], a room temperature ionic liquid. The stability constants, enthalpies and entropies of complexation were determined by spectrophotometry and calorimetry. All the DGA ligands formed a 1 : 3 (Nd³⁺/DGA) complex as the limiting species, and their stability constants increased linearly with increasing alkyl chain length. The stability constants of the Nd³⁺/DGA complexes are orders of magnitude higher in [C₄mim][Tf₂N] as compared to those observed in aqueous medium. For all the complexes, the enthalpy of complexation was negative with a positive entropy change, indicating that the complexation was driven by both enthalpy and entropy. The enthalpy changes observed in [C₄mim][Tf₂N] medium were more exothermic than those in the aqueous medium. Fluorescence lifetime data indicated that the complexation proceeded via the replacement of water molecules from the primary coordination sphere of the metal ion. DFT calculations were performed on the structures of the different Nd³⁺/tetramethyl DGA (TMDGA) complexes, and the corresponding free energies in both gas and solution phases were calculated. Insights into the structural features by DFT studies confirmed that the nature of Ln³⁺/DGA complexes formed in [C₄mim][Tf₂N], n-dodecane, and aqueous medium and that in the crystalline state is identical.

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1. Introduction

During the last decade and half, a new class of diamide extractants, namely diglycolamides (DGAs), containing an ether linkage between two amide groups (Fig. 1), has received particular attention from separation scientists engaged in the field of actinide partitioning.^1–5 Extensive studies have been carried out with DGA ligands pertaining to the selective complexation and separation of lanthanides (Lns) and actinides (Ans) from various aqueous streams. The basic studies include aqueous complexation with water-soluble DGA ligands for selective stripping of Ans,^6–8 spectroscopy, synthesis of solid complexes^9–13 and theoretical calculations with these ligands.^14–17 The applied studies extensively focused on the evaluation of DGA extractants for actinide partitioning from nuclear waste solutions.^1,2 Amongst the various DGA ligands, the most efficient actinide partitioning studies have been accomplished using TODGA (N,N,N′,N′-tetra-n-octyl diglycolamide)^18–22 and T2EHDGA (N,N,N′,N′-tetra-2-ethylhexyl diglycolamide).^23,24 TODGA has been extensively studied in different laboratories, and hot runs have been demonstrated at the European Union program on actinide recycling by separation and transmutation (ACSEPT) at ITU, Karlsruhe.^19,25

Fig. 1 Molecular structures of tetraalkyl diglycolamides (TRDGA) and the cationic and anionic components of [C₄mim][Tf₂N].

Apart from applied research, the fascinating chemistry of DGAs has caught the imagination of researchers, as is evident from a large number of publications in basic chemistry studies.^10,15,26,27 The complexation of DGA ligands with metal ions is intriguing as these ligands display a high affinity for trivalent actinide ions as compared to the hexavalent actinide ions. The distribution ratios of Ans in solvent extraction with the TODGA/n-dodecane system generally decrease in the order: An³⁺/Ln³⁺ > An⁴⁺ ≫ AnO₂²⁺ > AnO₂⁺, which is quite different from those of other known neutral extractants, such as CMPO (octyl(phenyl)-N,N-diisobutylcarbamoylmethyl phosphine oxide), TRPO (trialkylphosphine oxide), DMDBTDMA (N,N′-dimethyl-N,N′-dibutyltetradecyl malonamide), etc.²⁸ The extraction ability of the latter neutral extractants usually decreases in the order: An⁴⁺ ≅ AnO₂²⁺ > An³⁺/Ln³⁺ > AnO₂⁺, which is explained on the basis of the effective charges on these metal ions. Moreover, an analysis based on solvent extraction experiments showed some inconsistencies in the extracted complexes of An³⁺, wherein a varying number of 2–4 TODGA molecules were observed in the extracted complexes.^5,29 On the other hand, aqueous complexation of Ln³⁺/Am³⁺ with TMDGA (N,N,N′,N’-tetramethyl diglycolamide) and their crystal structures have confirmed the coordination of three DGA ligands in tridentate mode.^9–11 A similar observation has been made in the solution phase of the Eu³⁺/TODGA extracted complex in n-dodecane by EXAFS measurements.²⁶ Another report involved studies on M³⁺/TODGA complexes (M = Eu and Cm) in ethanol by time-resolved laser fluorescence measurements and the suggested analogous species.¹³

It is important to note that all the studies pertaining to DGA complexation have been made in a molecular solvent, either in aqueous medium or in solvents such as methanol, ethanol or acetonitrile.^9–11,13,30 In contrast to this, a study on the complexation of DGAs with Ln³⁺ or An³⁺ in room temperature ionic liquids (RTILs) has been unknown until recently,³¹ though extensive solvent extraction-based separation studies have been performed in RTILs with these ligands.³² One of the major advantages of a RTIL-based solvent is the unusually high extraction of metal ions as compared to that observed with molecular diluents.^33–35 This has been explained on the basis of a cation-exchange mechanism prevailing in the case of RTILs as the diluents as compared to a solvation mechanism operative in the case of the conventional molecular diluents.^36–38 Interestingly, however, there are reports in which an analogous extraction behavior of metal ions has been reported both in RTILs and in molecular solvents.³⁹

Despite numerous studies conducted on the use of RTILs for metal ion separations, fundamental studies on the thermodynamics of the interactions of metal ions with ligands in RTILs are rare. A few studies have been devoted to the fundamental understanding of the energetics of the Ln/An complexation in RTILs with simple ligands such as nitrates, chlorides, etc.^40–45 To the best of our knowledge, only limited studies on the complexation of Lns with organic ligands in RTILs have been reported.^45,46 The only study on DGA/Ln³⁺ complexation in a RTIL deals with relatively long alkyl chain derivatives of DGA (>C-5) in [C₈mim][Tf₂N] (3-octyl-1-methylimidazolium bis(trifluoromethanesulfonyl)imide).³¹ In the reported study, a RTIL having a larger alkyl chain length ([C₈mim]) was used due to limited solubility of the higher alkyl chain DGA ligands in [C₄mim][Tf₂N].

The present study deals with the DGA ligands having smaller substituents such as methyl, ethyl, n-butyl and n-hexyl so that the ligand substituent effect can be better understood. [C₄mim][Tf₂N] (1-butyl-3-methyl imidazolium bis(trifluoromethanesulfonyl)imide) was chosen as the RTIL for this study because it has physico-chemical properties (such as water immiscibility and viscosity) favourable to applications in separation processes and has been widely studied as a solvent in biphasic separations.^33–35 Furthermore, [C₄mim][Tf₂N] shows good solubility of lower alkyl chain DGA, e.g., tetramethyl to tetrahexyl DGA, and metal/ligand complexes. To gain insights into the nature of the Ln³⁺/DGA complexes formed in the RTIL, systematic studies were performed to obtain thermodynamic parameters, viz. the equilibrium constant, the enthalpy and entropy of complexation, structural factors, etc. The stability constants of Ln³⁺/DGA complexes were determined by spectrophotometric titration, whereas microcalorimetric titrations were performed to estimate the complexation heat. To understand the nature of the complexes, fluorescence spectroscopy and DFT calculations were also performed. The present fundamental study is of utmost importance to understand the extraction behaviour of metal ions in RTILs and paraffinic solvents (which have been well reported).

2. Result and discussion

2.1. Stability constants of Nd³⁺/DGA complexes: absorption spectroscopy

Fig. 2 shows the representative spectrophotometric titration data of Nd³⁺ with TMDGA, TEDGA and TBDGA. A similar spectrophotometric titration of Nd³⁺ with THDGA was also performed (Fig. S1 in the ESI†). The initial solution contained ∼10 mmol L⁻¹Nd(Tf₂N)₃. As the aliquots of DGA were added stepwise, the intensity of the absorption band at 575 nm, corresponding to the hypersensitive ⁴I_9/2 → ⁴G_5/2 and ²G_7/2 transitions of Nd³⁺, changed significantly.⁴⁷ The changes consist of three stages. In the first stage, as the quantity of the ligand increased, the absorption band at 575 nm shifted to around 580 nm, indicating the formation of an ML complex. In the second stage, the intensity of the 580 nm absorption band decreased with a simultaneous red-shift in the absorption band. In the third step, the absorption band at 583 nm splits into a triplet upon addition of the ligand. No further spectral change was observed after this point even in the presence of excess ligand (C_L/C_Nd = 10), suggesting the formation of a limiting complex. A factor analysis of the absorption spectra indicated the presence of four absorbing species, i.e., the free Nd³⁺ and three successive Nd³⁺/L complexes. The de-convoluted spectra of all the absorbing species are shown in the bottom part of Fig. 2. The spectra were fitted with the model described by eqn (2), and the calculated stability constants of the NdL³⁺, NdL₂³⁺ and NdL₃³⁺ complexes are listed in Table 1.

Fig. 2 Representative spectrophotometric titrations of Nd³⁺ with TMDGA, TEDGA and TBDGA in [C₄mim][Tf₂N] (top), and the deconvoluted spectra of the Nd³⁺, Nd(L)³⁺, Nd(L)₂³⁺ and Nd(L)₃³⁺ species (Bottom). Cuvette: 25 μmole Nd(Tf₂N)₃ (2 mL); titrant: 100 μmole mL⁻¹ ligand in [C₄mim][Tf₂N]; temperature: 25 °C.

Table 1 Stability constant data for DGA/Ln³⁺/An³⁺ at 25 °C

M^3+/DGA	Complex^a^,^b	Medium	log β	Ref.^c
a L denotes the respective DGA ligand. b The equilibrium reactions are given in the ESI. c p.w. means present work.
Nd^3+/TMDGA	NdL^3+	[C4mim][Tf2N]	4.40 ± 0.07	p.w.
	NdL2^3+		7.99 ± 0.14
	NdL3^3+		10.5 ± 0.13
Nd^3+/TMDGA	NdL^3+	1 M NaNO3	3.53 ± 0.10	9
	NdL2^3+		5.84 ± 0.19
	NdL3^3+		6.80 ± 0.19
Eu^3+/TMDGA	EuL^3+	1 M NaNO3	3.43 ± 0.08	10
	EuL2^3+		5.59 ± 0.06
	EuL3^3+		6.48 ± 0.10
Am^3+/TMDGA	AmL^3+	1 M NaNO3	3.71 ± 0.01	11
	AmL2^3+		5.95 ± 0.06
	AmL3^3+		6.93 ± 0.03
Nd^3+/TEDGA	NdL^3+	[C4mim][Tf2N]	5.28 ± 0.15	p.w.
	NdL2^3+		9.13 ± 0.11
	NdL3^3+		11.4 ± 0.19
Am^3+/TEDGA	AmL^3+	1 M NaNO3	2.9	48
	AmL2^3+		6.07
	AmL3^3+		8.33
Nd^3+/TBDGA	NdL^3+	[C4mim][Tf2N]	7.16 ± 0.16	p.w.
	NdL2^3+		10.8 ± 0.17
	NdL3^3+		12.7 ± 0.14
Nd^3+/THDGA	NdL^3+	[C4mim][Tf2N]	8.41 ± 0.32	p.w.
	NdL2^3+		12.5 ± 0.29
	NdL3^3+		14.3 ± 0.34
Nd^3+/THDGA	NdL^3+	[C8mim][Tf2N]	7.83 ± 0.05	31
	NdL2^3+		14.4 ± 0.11
	NdL3^3+		19.3 ± 0.11

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It is worth mentioning that, to the best of our knowledge, this is the first report on the determination of stability constants of a lanthanide with TMDGA, TEDGA and TBDGA in any type of RTIL. However, complexation studies have been performed earlier with TMDGA in aqueous medium, where stability constants and crystal structures of Nd³⁺/TMDGA, Eu³⁺/TMDGA and Am³⁺/TMDGA have been reported (Table 1). Apart from this, the aqueous complexation of TEDGA with Am³⁺ has also been studied with respect to the selective aqueous stripping of Am³⁺ from the loaded organic phase over lanthanides.⁴⁸ As summarized in Table 1, the log β values of Nd³⁺, Eu³⁺ and Am³⁺ with TMDGA (in aqueous medium) are in close proximity. This information gives rise to a logical conclusion that the complexation constants obtained for Nd³⁺ in the present work may be extended to Am³⁺, which is an important actinide ion from the actinide partitioning point of view.^1,2 The log β values of Nd³⁺/TMDGA complexes in [C₄mim][Tf₂N] are several orders of magnitude higher than those in aqueous nitrate medium. This observation is in line with Nd³⁺/nitrate complexation in [C₄mim][Tf₂N], where stability of the Nd³⁺/NO₃⁻ complexes in RTIL are many orders of magnitude stronger than those observed in aqueous medium.⁴⁰ A probable explanation for this unusual complexation was given based on the competition between nitrate ions and water molecules present in the primary hydration sphere of the metal ions. It is easier for the ligands to replace the water molecules from the primary coordination sphere when the metal ions are present in a hydrophobic medium such as an RTIL than when present in an aqueous medium (vide infra). When we compare the stability constants of Nd³⁺/DGA in [C₄mim][Tf₂N], the log β value increased linearly with increasing alkyl chain length of the DGA, i.e., log β_TMDGA < log β_TEDGA < log β_TBDGA < log β_THDGA (Fig. 3). This behaviour may be ascribed to the increasing +I effect on the ligand upon increasing alkyl chain length. Table 1 also includes the log β values for THDGA in [C₈mim][Tf₂N].³¹ It is intriguing to note that while the log β₁ value is lower in [C₈mim][Tf₂N] as compared to that obtained in [C₄mim][Tf₂N], the log β₂ and log β₃ values show the opposite trend. This feature might have arisen due to the different solvation power of the metal ion and the ligands in the two RTILs.

Fig. 3 Stability constants of the Nd³⁺/DGA complexes in [C₄mim][Tf₂N] at 25 °C.

2.2. Enthalpy of complexation: microcalorimetry

Fig. 4 shows the overall heat of reaction, obtained from the microcalorimetric titrations, and the speciation of Nd³⁺/DGA complexes as a function of volume of the ligand added to the metal ion solution. The measured heat, in conjunction with the equilibrium constants determined by spectrophotometry (vide supra), was used to calculate the enthalpy of complexation using the Hyperquad program.⁴⁹ As summarized in Table 2, the enthalpies of complexation for all the three complexes (with the four TRDGA ligands), viz. Nd(L)³⁺, Nd(L)₂³⁺ and Nd(L)₃³⁺, are exothermic and are in line with the enthalpy changes observed for Nd³⁺/TMDGA complexes in aqueous medium.⁹ However, the enthalpy change observed in [C₄mim][Tf₂N] medium was more exothermic than that in the aqueous medium, indicating a more favourable complexation reaction in the RTIL. This enthalpy trend in the two complexing media viz., aqueous and RTIL, may arise due to the differences in the degree of hydration/solvation of the ligand in these media. In the case of TMDGA, being more hydrated in aqueous medium, more energy is required to dehydrate the ligand before complexation, resulting in a lower exothermic enthalpy. The entropies of complexation, calculated from the enthalpies (obtained in calorimetry) and Gibbs free energies (calculated from the stability constant values), are all positive, indicating that the complexation processes are both enthalpy and entropy driven. The large positive entropies of complexation probably result from the release of the water molecules from the primary coordination sphere of Nd³⁺ upon complexation with the ligand. An important observation from Table 2 is that the stepwise enthalpy of complexation remains unchanged with values of ΔH₁ = 9.5 ± 0.6 kJ mol⁻¹, ΔH₂ = 5.9 ± 0.9 kJ mol⁻¹ and ΔH₃ = 3.7 ± 0.7 kJ mol⁻¹ (where, ΔH₁, ΔH₂ and ΔH₃ represent the enthalpy changes for the stepwise complex formation reactions) DGA ligands. This is an indication that the complexation reactions are more entropy driven, and a higher positive entropy is obtained with increasing chain length of DGA. It looks like the shorter alkyl chain DGAs form more organized complexes, whereas the longer alkyl chain DGAs bring more disruption in the system while re-organizing their chain around the metal ion resulting in a higher entropy.

Fig. 4 Calorimetric titrations of Nd³⁺/DGA in [C₄mim][Tf₂N]. The left y-axis: speciation of Nd³⁺(solid lines) as a function of titrant volume. The right y-axis: cumulative heat (○ – experimental, - - - fitted data) as a function of titrant volume. Cup solution: 8.6 μmole Nd(Tf₂N)₃ (2.7 mL); titrant: 0.1 mol L⁻¹ DGA; Temperature: 25 °C.

Table 2 Thermodynamics data for Nd³⁺/DGA complexation at 25 °C

DGA/Medium	Complex^a	ΔG (kJ mol^−1)	ΔH (kJ mol^−1)	ΔS (J mol^−1 K^−1)	Ref.^b
a L denotes the respective DGA ligand. b p.w. = present work.
TMDGA/	NdL^3+	−25.1	−10.1	50.4
[C4mim][Tf2N]	NdL2^3+	−45.6	−17.3	94.9	p.w.
	NdL3^3+	−59.9	−21.9	128
TMDGA/	NdL^3+	−20.1	−10.9	31.0
1 M NaNO3	NdL2^3+	−33.3	−15.6	59.5	9
	NdL3^3+	−38.8	−19.3	65.4
TEDGA/	NdL^3+	−30.1	−8.86	71.4
[C4mim][Tf2N]	NdL2^3+	−52.1	−14.1	127	p.w.
	NdL3^3+	−65.0	−17.2	161
TBDGA/	NdL^3+	−40.9	−9.34	106
[C4mim][Tf2N]	NdL2^3+	−61.6	−15.3	155	p.w.
	NdL3^3+	−72.5	−18.7	180
THDGA/	NdL^3+	−48.0	−9.71	128
[C4mim][Tf2N]	NdL2^3+	−71.3	−14.8	190	p.w.
	NdL3^3+	−81.6	−18.6	211

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2.3. Structural features of Ln³⁺/DGA complexes

After confirming the formation of Nd·L₃³⁺ species with all the four DGA ligands, an attempt was made to understand the nature of the complexes and the mode of complexation. Extensive complexation studies on shorter alkyl chain DGAs (TMDGAs) and the crystal structures of the Nd³⁺/TMDGA complex,⁹ the Eu³⁺/TMDGA complex¹⁰ and the Am³⁺/TMDGA complex¹¹ confirmed the formation of the 1 : 3 M/L species, where three DGA ligands are bonded with the metal via two amidic ‘O’ atoms and one etheric ‘O’ atom, without any H₂O or nitrate ions in the primary hydration sphere. Similarly, the structural features of Ln³⁺/TEDGA complexes confirmed the absence of H₂O or nitrate in the primary coordination sphere.⁴⁸ Additionally, structural studies performed on a longer alkyl chain DGA (TODGA) gave similar results.²⁶ Structural features obtained with EXAFS measurements confirmed the formation of a Eu³⁺/TODGA complex in the solution phase identical to that in the crystalline state of Eu³⁺/TMDGA.²⁶ In the present work, we assumed a similar coordination mode in [C₄mim][Tf₂N] and focused on the detailed structural investigation with the help of fluorescence spectroscopy. As will be seen from the DFT studies (vide infra), the structural features do not change with the solvent.

In order to obtain insight into the structure of the complexes, the presence of water molecules or Tf₂N⁻ ions in the primary hydration sphere of the metal centre was probed with the help of Eu³⁺ lifetime data. The lifetime of Eu(NO₃)₃ in water and Eu(Tf₂N)₃ in [C₄mim][Tf₂N] were found to be around 114 μs and 116 μs, respectively, indicating that in both cases the Eu³⁺ species are identical, i.e., Eu(H₂O)_(8-9)³⁺. The number of water molecules (N_H2O) in the primary coordination sphere of Eu³⁺ was calculated using the equation⁵⁰

N_H2O = (1.05/τ) − 0.7 (1)

where τ is the lifetime in ms. The fluorescence decay curve of the limiting EuL₃³⁺ species in [C₄mim][Tf₂N] (with all the DGAs) is shown in Fig. 5. The decay curves were fitted using mono- and bi-exponential decay equations, which predominantly predicted the presence of single species. It is worth mentioning that only single species were observed in the decay curve as the measurements were performed at the Eu³⁺/DGA ratio of 10, where the (Eu·L₃)³⁺ species is predominant. The lifetime of Eu³⁺ in the complex was in the range of a few ms (2.2 to 2.4 ms), confirming the absence of water molecules in all the Eu³⁺/DGA complexes (Table 3). In the absence of water in the primary hydration sphere of Eu³⁺, it is easier to conclude that all the available coordination sites in Eu³⁺ will have to be occupied by three tridentate DGA moieties saturating the metal coordination sites. This means that the coordination mode of a DGA in the M/L complex in [C₄mim][Tf₂N] medium is identical to that in the crystalline state^6–8 and in n-dodecane (as indicated by EXAFS measurements²²), where three DGA ligands are bonded with the metal via two carbonyl ‘O’ atoms and one etheric ‘O’ atom, satisfying the coordination number of the metal ion. The identical species and the coordination mode in the Eu³⁺/TODGA complex were also confirmed by fluorescence spectroscopy in ethanol medium.¹³

Fig. 5 Emission decay curve for Eu³⁺ using different DGAs.

Table 3 Calculated number of water molecules (nH₂O) associated with Eu³⁺/DGA complexes in different systems

System^a	Asymmetry factor (I612/I592)^b	Lifetime (ms)	N H2O
a RTIL = [C4mim][Tf2N]. b Data obtained from Fig. S2 (ESI).
Eu(NO3)3/H2O	0.45	0.114	8.51
Eu(Tf2N)3/RTIL	0.44	0.116	8.35
Eu^3+/TMDGA	1.32	2.41	−0.26
Eu^3+/TEDHA	1.28	2.35	−0.25
Eu^3+/TBDGA	2.25	2.34	−0.25
Eu^3+/THDGA	1.32	2.24	10.23

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2.4. DFT studies

2.4.1. Optimization of structures of ligand/complexes. The optimized minimum energy structures of free TMDGA and its complexes with Nd³⁺ ions in various stoichiometries in the gas phase are displayed in Fig. 6. From the optimized structure of free TMDGA (Fig. 6a), it can be seen that all three donor O atoms (2 of carbonyl O and 1 of ether O) are lying in the same plane and act as a tridentate chelating ligand. Though the structure of the ML₃ complex has been obtained by DFT calculations and reported by many authors, including us,^27,51 the structures for the stepwise complex formation have not been reported. In the case of the 1 : 1 complex (Fig. 6b) with Nd³⁺ ions, the metal ion is coordinated to three O atoms where the two carbonyl O atoms show a shorter metal–oxygen (M–O) bond distance of 2.15 Å than that with the lone ether O atom being 2.43 Å. The structure of the 1 : 2 complex (Fig. 6c) shows that the two TMDGA units are coordinating to the central metal ion in a perpendicular manner leading to a hexa-coordinated environment, which results in a slight elongation of the M–O (O of carbonyl) bond to 2.30 Å and the etheric M–O bonds to 2.55 Å. This is due to the accommodation of six O atoms within the first coordination sphere of the Nd³⁺ ion, which causes steric repulsion among the ligands. The optimized structure of the 1 : 3 metal–ligand complex is displayed in Fig. 6d, where nine O donors from three TMDGA units participate in the coordination leading to a nona-coordinated complex resulting in even longer M–O bonds with the carbonyl (2.44 Å) and etheric (2.65 Å) O atoms.

Fig. 6 Optimized structures of TMDGA and its complexes: (a) free TMDGA, (b) Nd³⁺/TMDGA, (c) Nd³⁺/(TMDGA)₂, and (d) Nd³⁺/(TMDGA)₃ phase at the B3LYP/SVP level of theory.

2.4.2. Free energy of complexation in gas and solution phases. The metal ion–ligand complexation reaction in both gas and solution phases was modeled as

M_(p) + nTMDGA_(p) = M(TMDGA)_n·(p), (2)

where M is Nd³⁺ and n ranges from 1 to 3 for the 1 : 1, 1 : 2 and 1 : 3 stoichiometric complexes, and the subscript p represents gas/n-dodecane/ionic liquid/water. The free energy (ΔG) of complexation is a crucial parameter for understanding the complexation stability with the metal ions and can be evaluated using eqn (2) as

ΔG = ΔE − ΔnRT − TΔS (3)

where T is the temperature, R is the gas constant, Δn = the number of product species–reactant species, ΔS is the entropy change and ΔE is described by:

ΔE = E_{M(TMDGA)n·(p)} − (E_M(p) + nE_TMDGA(p)) (4)

Here, E is the total electronic energy of the respective chemical species. The value of ΔS is computed using our earlier reported procedure.⁵¹ The calculated values of free energy (ΔG) in gas and solution phases are tabulated in Table S1 (ESI†). The free energy was found to be the highest for the Nd³⁺ ion in the gas phase and the lowest in water for all the 1 : 1, 1 : 2 and 1 : 3 complexes with TMDGA. The solution phase free energy was found to be reduced drastically due to dielectric screening of the solvents. The free energy of complexation for all the 1 : 1, 1 : 2 and 1 : 3 complexes with TMDGA follows the decreasing trend: gas phase > n-dodecane > ionic liquid > water. This is expected as with increasing dielectric constant of the solvent, the dielectric screening is also increased, which in turn reduces the interaction and hence the free energy. It is worth noting that the free energy of complexation is increased with an increase in the number of ligands for all the solvents and in the gas phase. It is the highest with a 1 : 3 metal/ligand stoichiometry for the Nd³⁺ ion and the lowest with a 1 : 1 metal/ligand stoichiometry and in between for the 1 : 2 metal/ligand complex. However, the values appear to be much larger than those reported above from the calorimetric studies due to the approximations in the DFT methods, which include, amongst other things, the hydration of the metal ions, which occurs in the ionic liquid case (as seen from the luminescence spectroscopic study). Similar overestimations in the case of DFT calculations are reported in the literature.⁵² It may be prudent to add here that the successive free energy difference from 1 : 1 to 1 : 2 and 1 : 2 to 1 : 3 for all the solvents and in the gas phase is reduced due to steric crowding with increasing number of molecules in the first coordination sphere of the metal ion. Thus, density functional theoretical studies not only offer insights at the molecular level, but also help in understanding the correct metal ion stability towards a ligand by incorporating the appropriate metal–ligand stoichiometry, which otherwise is not possible through experimental means alone.

2.4.3. Bonding analysis. Natural population analysis (NPA) was performed to get an insight into the nature of bonding in the complexes of TMDGA with the Nd³⁺ ion. The residual charge and atomic orbital population on the metal atom in the metal ion complexes were estimated using NPA.^53,54 The calculated values are listed in Table S1 (ESI†). There is a considerable charge transfer to the TMDGA molecule, as evident from the residual charge on the metal atom, which in turn leads to a high interaction and free energy. Furthermore, the transfer of charge is more for the 1 : 3 metal–ligand complex compared to the 1 : 2 and 1 : 1 metal–ligand complexes. There is an amplification of the electronic population in the s, d and f orbitals of the metal atom after complexation, demonstrating the covalent nature of bonding. Furthermore, the amplification in the s and d orbitals is increased with an increase in the participation of a larger number of ligands. Another interesting point is that as we move from the gas phase to n-dodecane to ionic liquid to water, the transfer of charge is reduced due to the increased dielectric screening of the solvents, which in turn reduces the interaction and hence the free energy, thus causing a reduced stability.

3. Conclusions

An effort has been made to look into the complexation thermodynamics of lanthanides with a series of diglycolamides (DGAs) containing varying alkyl chain lengths (methyl, ethyl, n-butyl and n-hexyl) in [C₄mim][Tf₂N]. Though the cation exchange mechanism predicts the species of the type ML_n³⁺ (where n can be 2 or 3), all the DGA ligands formed a 1 : 3 (Ln³⁺/DGA) complex, which is similar to the observations made during the previously reported aqueous phase complexation studies.^6–8 Poor stripping possibility due to high extraction of the metal ions can be avoided by the use of complexing agents.⁵⁵ Their stability constants in [C₄mim][Tf₂N] are orders of magnitude higher than those in the aqueous medium. In a manner similar to that reported previously in the case of the aqueous medium, the complexation reaction in [C₄mim][Tf₂N] was driven by both enthalpy and entropy. The enthalpy change observed in the [C₄mim][Tf₂N] medium was more exothermic than that in the aqueous medium. Spectroscopic data and DFT calculations confirmed the formation of 1 : 3 M/L species where three DGA ligands are bonded with the metal via two amidic ‘O’ atoms and one etheric ‘O’ atom, without any water or Tf₂N⁻ ions in the primary coordination sphere. This study reveals that the nature of Ln³⁺/DGA complexes formed in [C₄mim][Tf₂N] and n-dodecane or in the crystalline state is identical. It may be mentioned here that different stoichiometries of the extracted complex reported previously⁵ are a consequence of the diluent nature and ionic liquid medium do not take into consideration factors such as the variation in the nature of the complexed species.

4. Experimental

4.1. Materials

A series of tetraalkyl diglycolamides (Fig. 1) was synthesized by reacting diglycolyl chloride with the respective dialkyl amines as reported earlier.¹ The products were characterized by ¹H-NMR, FT-IR and mass spectrometry. The ionic liquid, [C₄mim][Tf₂N] (Fig. 1), in 99% purity was procured from Iolitec, Germany. Nd(Tf₂N)₃ and Eu(Tf₂N)₃ salts were prepared by a metathesis reaction of Nd₂O₃ or Eu₂O₃ with trifluoromethane sulfonimide (HTf₂N) procured from Sigma Aldrich. Stoichiometric amounts of Eu₂O₃ or Nd₂O₃ solids were dissolved in HTf₂N solution (0.5 g of HTf₂N/10 mL of Milli-Q water) by stirring for an hour at room temperature. The solution was filtered with a 0.2 μm syringe filter, evaporated to dryness, and finally vacuum dried to get a pink powder of Nd(Tf₂N)₃ and a white powder of Eu(Tf₂N)₃. Stock solutions of Nd(Tf₂N)₃ and Eu(Tf₂N)₃ were prepared by dissolving appropriate amounts of their salts in [C₄mim][Tf₂N], and their concentrations were confirmed by volumetric titrations with a standard EDTA solution using bromothymol blue as the indicator.

4.2. Spectrophotometry

Spectrophotometric titrations were performed by following the absorption spectra of Nd³⁺ in [C₄mim][Tf₂N] in the wavelength region of 560–610 nm, where Nd³⁺ shows well-defined hypersensitive absorption bands at around 575 nm originating from the ⁴I_9/2 → ⁴G_5/2 and ²G_7/2 transitions.⁴⁷ The spectra were recorded on a double-beam Jasco V-530 spectrophotometer using 10 mm path length quartz cells. The initial concentration of Nd(Tf₂N)₃ in the cell was ∼10 mmol L⁻¹. In each titration, appropriate aliquots of the titrant (DGA solution in [C₄mim][Tf₂N]) were added into the cell and mixed thoroughly for about 5 minutes before recording the spectrum. Usually a set of 20–25 spectra was recorded in each titration, and the stability constants of the Nd³⁺/L complexes were calculated by nonlinear least-squares regression analysis using the HypSpec® program⁴⁹ based on the following equations:

Nd³⁺ + iL = NdL⁽³⁻ⁱ⁾_i⁺ (5)

where β_i is the stability constant of ith complex and L is the DGA ligand.

4.3. Microcalorimetry

Microcalorimetric titrations at 25 °C were performed on an isothermal titration calorimeter (Nanocalorimeter TAM-III, Thermometric AB, Sweden). It is a twin thermopile heat conduction type calorimeter where the measured differential power signal is dynamically corrected for the thermal inertia of the system.⁵⁶ Both chemical and electrical calibrations were performed to validate the performance of the instrument. The chemical calibration was carried out by measuring the complexation heat of 18-crown-6 and BaCl₂. The obtained ΔH value (31.71 ± 0.04 kJ mol⁻¹) is in good agreement with the literature data.⁵⁷ The reaction vessel contained 2.7 mL of the solutions of Nd(Tf₂N)₃ in [C₄mim][Tf₂N] stirred using a mixing rotor maintained at 100 rpm. The ligand solution in [C₄mim][Tf₂N] was added into the reaction vessel through a Hamilton 500 μL syringe stepwise (10 μL per addition). About 50 injections were made in each set of titrations. The reaction heats, after correcting the dilution heats that were measured separately in a blank titration, were used in conjunction with the equilibrium constants obtained by spectrophotometry to calculate the enthalpy of complexation using the Hyperquad program.⁵⁸

4.4. Fluorescence measurements

Luminescence emission spectra were recorded and the lifetime of Eu³⁺ was determined using a fluorometer (PTI QuantaMaster 400) adapted for time-resolved measurements. The luminescence emission spectra were obtained in the wavelength region of 570–710 nm (0.5 nm per step) by excitation at 395 nm. The signals were acquired and analyzed using PTI FelixGX software from the PTI QuantaMaster. The emission lifetime data were recorded in the time-resolved mode after a delay time of 100 μs to avoid the background contribution from scattered radiation (if any). The emission lifetime data were fitted in the following decay equation by the PTI FelixGX software to get the decay constant.where τ_i is the lifetime of the ith complex.

4.5. Computational protocol

The minimum energy structures of free TMDGA and its complexes were calculated with the B3LYP hybrid density functional using the split-valence plus polarization (SVP) basis set as available in the TURBOMOLE electronic structure code.^59–62 The scalar relativistic effective core potentials (ECPs) were considered for Nd³⁺ where 28 electrons were kept in its core.^63–66 The quintet spin state was used for the Nd complexes during the optimization of structures and energy calculations. The free energy was computed at 298.15 K. The hybrid B3LYP functional was shown to be quite successful in predicting the thermodynamic properties of actinides.⁶⁷ The water, n-dodecane and ionic liquid ([C₄mim][Tf₂N]) phases were taken care of by the use of a conductor like screening model for real systems (COSMO-RS).^68–72 Dielectric constants of 80, 2.0 and 9.4 were used for water, n-dodecane and the ionic liquid, respectively. The free energy of complexation, ΔG, for the complexation reaction (eqn (2)) was evaluated using standard thermodynamic methods.^73–76 As mentioned above, the corresponding values for the water, n-dodecane and ionic liquid phases were mimicked using the equilibrated gas phase geometry by employing the COSMO-RS solvation model.^68–72 COSMO-RS incorporates the structure of the solvents by incorporating the surface charge densities through the well-defined sigma potential. The calculation has been performed using D-COSMO-RS^74,75 module of Turbomole. The required sigma potential for water has been taken from the Turbomole library, whereas for n-dodecane and [C₄mim][Tf₂N], the sigma potential was borrowed from COSMO logic.

Conflicts of interest

There are no conflicts of interest.

Acknowledgements

The authors thank Dr P. K. Pujari, Head of the Radiochemistry Division, for his constant encouragement. They are also thankful to Dr R. B. Gujar for his help during the experiments.

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Footnote

† Electronic supplementary information (ESI) available: UV-Vis spectrophotometry, luminescence spectroscopy and DFT data. See DOI: 10.1039/c7nj03925e

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