Revisiting actinide–DTPA complexes in aqueous solution by CE-ICPMS and ab initio molecular dynamics

Abstract

Although thermodynamics of An^IVDTPA⁻ (DTPA = diethylenetriaminepentaacetic acid) complexation have been reported for 50 years, reliable data at low ionic strength is still missing. Owing to the use of capillary electrophoresis coupled with an inductively coupled plasma mass spectrometer, it is possible to simultaneously detect at ultra-trace level all An^IVDTPA⁻ species in various conditions (concentration of ligand, pH) and to determine the formation constants. New values were obtained for tetravalent actinides with DTPA as well as with nitrilotriacetate (NTA) used as a competitor. Besides, the formation constants of hydrolyzed An(OH)DTPA²⁻ species (An = Np, Pu) were also obtained for the first time using the variation of electrophoretic mobility as a function of pH at a constant DTPA concentration. The use of these data in radiotoxicology indicates that two stable species, namely PuDTPA⁻ and Pu(OH)DTPA²⁻ are present at approximately the same concentration in blood. From ab initio molecular dynamic (AIMD), the metal–oxygen distances d_An–O were calculated, and a linear relation was shown between d_An–O and the formation constants. The interpolation of data allowed determination of K values along the tetravalent actinide series, e.g. K_NpDTPA⁻, K_PaDTPA⁻ and K_{U(OH)DTPA²⁻}.

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A. Introduction

Diethylenetriaminepentaacetic acid (DTPA) is a versatile polyaminocarboxylic acid used in medicine as an actinide chelating agent and in the nuclear industry as a component of a synergistic mixture with lactic acid for lanthanide/actinide separation (TALSPEAK process).^1,2 Despite widespread applications in various fields (medicine, nuclear industry and separation sciences), the available stability constants related to actinides and in particular, the tetravalent actinides are rather scarce and scattered. Reported data for the formation of tetravalent actinide DTPA complexes An^IVDTPA⁻ consist of a set of values obtained at only three ionic strengths (I = 0.1, 0.5 and 1 M) and two temperatures (T = 20 and 25 °C). The formation of other species such as An^IV(H)DTPA in acidic medium and An^IV(OH)DTPA²⁻ in basic medium are reported only for the lighter actinides Th and U.

At low ionic strength (I = 0.1 M), a critical evaluation related to the complexation of metals by DTPA showed that for tetravalent actinides only data related to the formation constants of ThDTPA⁻, Th(H)DTPA and Th(OH)DTPA²⁻ complexes are available and these are still considered as provisional values by the IUPAC.³ Other values are also reported for the formation of ThDTPA⁻ but are quite different compared to those recommended by the IUPAC.^4,5 An indirect estimated value is also proposed for UDTPA⁻ based on data from Th^IV,⁶ and the relative stability for U^IV and Th^IV complexes.⁷ However, no values are reported for Np^IV and Pu^IV in the literature.

At I = 0.5 M, a series of studies using the same technique by the same authors is available which provided the stability constants for Th^IV, U^IV, Np^IV and Pu^IV.^7–10 All these values were obtained in the 1970s and no other estimation has since been carried out.

At I = 1 M, several studies are reported which cover all tetravalent actinides using several techniques. The number of publications is more important because the industrial processes (TALSPEAK, SANEX-TODGA) requires reliable data. They have been carried out because of inconsistencies observed between data.^11–14 As an example, a recent study shows a difference up to three orders of magnitude between old and recent data for Th, U, and above four orders of magnitude for Pu.¹³

The data related to either An^IV(H)DTPA or An^IV(OH)DTPA²⁻ species are surprisingly scarce despite a strong need of reliable data for biological or environmental studies. This lack of reliable data is due to the sensitivity of tetravalent actinide towards hydrolysis. However, despite only two papers being published in the 1950s and 1960s, respectively, a fair agreement can be observed for the formation of Th(OH)DTPA²⁻.^6,15 A unique study was carried out at the same period for U(OH)DTPA²⁻,¹⁶ and up now no data have been proposed for transuranic elements.

In radiotoxicology, the ligand usually recommended for removing actinide from the human body is DTPA but despite a common use for decorporating plutonium, we have not found the stability constants related to the species Pu^IVDTPA⁻, including the potential hydrolyzed form at I = 0.1 M and basic pH, conditions that approximately correspond to those encountered in human blood. The aim of this study is to obtain new consistent data for tetravalent actinides at low ionic strength, for which extrapolation down to zero can be done without adjustable parameters. Particular attention will be brought to hydrolyzed species since the pH in blood is sufficiently high for assuming their potential presence. To achieve this goal, the use of ab initio molecular dynamics (AIMD) will be used in conjunction with experiments to propose new reliable values of chemical systems which cannot be experimentally studied, such as for instance Pa^IVDTPA⁻ or U^IVDTPA⁻. Indeed, despite an expected high stability constant, the operating conditions of separation do not permit stabilization of these oxidation states. In addition, in biological medium, the matrix contains numerous ligands at pH incompatible with the stability of actinide aquo ions. Since AIMD has been successfully tested,¹⁷ its use with experimental values of other actinides will allow to evaluate them as well as the hydrolyzed forms without performing the corresponding experiment.

A unique technique able to simultaneously compare all tetravalent actinides under the same experimental conditions will be used: capillary electrophoresis coupled with an inductively coupled plasma mass spectrometry (CE-ICPMS). Besides the capability to simultaneously detect all metal ions, CE-ICPMS presents other advantages such as a very high sensitivity enabling to work at ultra-trace level for radioactive elements (down to 10⁻¹⁰ M) and the capability to separate species without altering the initial speciation due to the physical mechanism of separation (electric field). The separation by capillary electrophoresis is based on the difference of ion velocity when an electric field is applied at the extremities of the capillary. The speciation is not altered providing that the concentration of the ligand is constant at any time and any place in the capillary.

B. Materials and methods

1. Chemicals

Background electrolyte (BGE).
NaNO₃ medium. Millipore deionised water (18.2 MΩ cm) is acidified by 40.3 × 10⁻³ mole of freshly prepared 0.1 M HNO₃ solution (Ampoule Titrisol® for 1 L, [HNO₃] = 0.1 mol L⁻¹ (±0.5%), Merck). The desired amount of DTPA (diethylenetriaminepentaacetic acid, Sigma 99%) or NTA (nitrilotriacetic acid, minimum 98%, Sigma) is dissolved in the solution, then the ionic strength is adjusted to 0.1 M by an appropriate weighed amount of NaNO₃ (>99.5%, Fisher Scientific). As a result, the concentration added in NaNO₃ was 0.0597 M.
BGE at various pH. MES for 6 < pH < 8 (low moisture content, Sigma 99%) or HEPES for 8 < pH < 9.5 (minimum titration 99.5%, Sigma) were added to a variable volume of TMAOH (tetramethylammonium hydroxide solution 10%, Merck) to the desired pH and to obtain a final ionic strength of about 0.1 M (including the contribution of DTPA). The ionic strength was calculated for each BGE and varied from 0.096 to 0.143 M (lowest to highest). The effect upon the stability constant (variation of ±0.030 in log unit for the reaction AnDTPA⁻ + OH⁻ ⇌ An(OH)DTPA²⁻) is largely within the overall uncertainties and will be ignored. The pH of each BGE was measured before and after the separation using a “high-precision 780 pH meter” (Metrohm) and a “combined metrosensor glass electrode” denoted “biotrode” (Metrohm). The pH variations were less than 0.3 pH unit resulting in a negligible variation of ligand concentration during the separation. The calibration of the electrode was carried out daily using commercial solutions (pH 4.01, 6.87, and 9.18 Schott Instruments).

Sample preparation. The Th^IV stock solution was prepared by dissolving thorium nitrate (Th(NO₃)₄·5H₂O) in nitric acid solution. The U^IV solution (1.1 M HNO₃, 0.15 M N₂H₅⁺) was prepared by catalytic reduction of U^VI, and then was stabilized by hydrazinium nitrate solution. This solution is diluted to obtain a 4.8 × 10⁻² M U^IV stock solution in 0.5 M HNO₃. The Np^IV solution was prepared by reducing 5 × 10⁻² M Np^V in 0.5 M HCl with 0.5 M hydroxylamine chloride at 70 °C during a few days. The resulting stock solution is stable over several months. The Pu^IV solution was prepared by the purification in an anionic ion exchanger (Dowex, AGMP1). The eluate is diluted to get a final concentration of 3.15 × 10⁻⁶ M in 0.95 M HNO₃ solution. All samples were prepared by diluting the appropriate volume of Th^IV, U^IV, Np^IV and Pu^IV stock solutions into the BGE. Dimethylformamide (DMF) was added (0.2 μL) in the samples before the analysis in order to determine the magnitude of the electroosmotic flow (eof). The concentrations were 10⁻⁸ M for all tetravalent actinides.

2. Apparatus

A Beckman Coulter P/ACE MDQ commercial Capillary Electrophoresis (CE) system equipped with a UV detector (Fullerton, USA) was used for all the measurements. The measurements were carried out using conventional fused silica capillaries, 75 μm internal diameter, 60 cm total length, 10.1 cm optical window (Beckman Coulter, Fullerton, USA). The capillaries were preconditioned by rinsing (1) with deionised water, (2) with a 0.1 mol L⁻¹ NaOH solution, (3) with a 0.1 mol L⁻¹ HCl solution, (4) with deionized water again and finally (5) with the appropriate BGE before use (at 5 psi during 5 min for each solution). The CE system was provided with a tailor-made capillary cartridge support designed for the adaptation of an external detector, i.e. an Axiom (VG Elemental, Winsford, Cheshire, UK) inductively coupled plasma sector field mass spectrometer (ICP-SF-MS). Both apparatus are hyphenated by a commercial interface using a parallel path micro-nebulizer (Mira Mist CE, Burgener, Mississauga, Canada) especially designed for capillary electrophoresis. A makeup liquid (HNO₃ 2% and ethyl alcohol absolute 10%) is introduced via a syringe pump (11 Pico Plus, Harvard Apparatus, Holliston, MA) at a nominal flow rate of 6 μL min⁻¹, (i) to improve the signal stability by decreasing the surface tension of the water droplets and the size of the droplets and (ii) to provide a nominal flow rate for the nebulizer. Samples were injected at the capillary inlet for 4 s at a constant pressure of 2 psi. Separations were performed at +10 kV, 25 °C and a constant pressure of 0.5 psi (to avoid capillary clogging). The voltage value was chosen with respect to Ohm’s law and to avoid for any experiment with a temperature rise of greater than 1 °C. It is noted that the temperature never decreased below 25 °C but could rise up to 26 °C by Joule heating for the highest electrolyte conductivity. The buffer vial was changed every run to avoid the effects of electrolysis.

3. Ab initio molecular dynamics (AIMD)

In heavy actinide systems, the presence of correlated 5f electrons leads to an improper description of the electronic and the structural properties by density functional theory (DFT-LDA). The best method to overcome this fact is to go beyond the Local Density Approximation using the so-called LDA + U or GGA + U. Except for thorium (no 5f electron in Th^IV), Hubbard U and Hund’s J parameters are introduced for the onsite interaction strength (U = 4 eV, J = 0.2 eV).¹⁸ Apart from Th^IV (5f⁰), in order to avoid metastable states, the electron–electron interaction potential was fixed in the Hamiltonian according to a given occupancy matrix n_ij^σ, for the 5f correlated states during the first eight steps of the energy minimization procedure. The simulations are run in the isokinetic ensemble at 298 K until equilibration is achieved, i.e. until the variations in pressure stabilize to an oscillatory pattern, without any long-term trend. The size of the simulation cell (45 Bohr) is chosen in order to minimize electrostatic interactions between ions and to obtain a pressure close to zero. Following equilibration, the pressure and energy are calculated by averaging over the next 4000 time steps of 0.48 fs each. All calculations have been performed with the ABINIT package at the Γ point,¹⁹ the center of the Brillouin zone. For each element a PAW data (Projector Augmented Wave) set have been fixed and a pseudo-potential built.²⁰ The data were generated for the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional with relativistic corrections to the wave function.²¹ We have chosen a standard actinide basis set with 7s, 6p, 6d, 5f in the valence band and 6s and 6p as the semicore orbitals.

C. Theoretical

The interaction between tetravalent actinides and DTPA as An^IVDTPA⁻ and An^IV(H)DTPA complexes has been studied by two methods: (1) the direct complexation between An^IV (aquo cation or hydroxo complex) and DTPA, and (2) the complexation between the An^IV cation stabilized with a polyaminocarboxylic acid as ligand competitor, nitrilotriacetic acid (NTA) and DTPA. In addition, depending on the pH, the formation of either protonated or hydroxo DTPA–An species has been studied.

The general equilibrium reaction is (charge omitted):

An(L₁)_n + L₂ + H_i ⇌ An(H_i)L₂ + nL₁, (1)

where in case of competition L₁ and L₂ stand for NTA (n = 1 or 2) and DTPA respectively; and in case of direct complexation n = 0 and L₂ = DTPA (no hydrolysis) or n = 1, L₁ = DTPA and no L₂ (with hydrolysis). For the protonated or hydrolyzed species we adopted the following convention: i = 1 (H₁ = H⁺) or i = −1 (H₋₁ = OH⁻).

The formation constant is:

In the case of fast formation/dissociation kinetics, the variation of overall electrophoretic mobility μ is a simple linear combination of all species present in the migration band. As example, in acidic medium with the protonated species taken into account μ is written:

μ = α_An⁴⁺μ_An⁴⁺ + α_AnDTPA⁻μ_AnDTPA⁻ + α_An(H)DTPAμ_An(H)DTPA + α_AnNTA⁺μ_AnNTA⁺ + α_{An(NTA)2²⁻}μ_{An(NTA)2²⁻}, (3)

with

The Levenberg–Marquardt algorithm is used to minimize the function.

In the case of slow dissociation kinetics and/or the formation of strong complexes, the data treatment becomes easier because one peak per species is observed,²² resulting in the determination of the corresponding peak area instead of the overall electrophoretic mobility. It is easily demonstrated the variation of the molar fraction as a function of the ligand concentration follows a sigmoidal curve of general equation:

with A_1,2 = 0 or 1 (depending on the studied molar fraction), p = 1 and [DTPA]₀ the concentration of DTPA at the inflexion point, i.e. for the condition where [AnL₂] = [AnL₁].

The overall uncertainty is calculated from standard deviations calculated by the fitting procedure and Monte-Carlo simulation of 100 000 trials. In particular, a mutual dependence is present for the couple (log K, log K_H) requiring a linear constraint to be applied. In practice, the formation constant of the protonated species K_H cannot be smaller than K.

D. Results

Two methodologies have been applied at a constant proton molar concentration and various concentrations of ligand, and at a constant concentration of ligand and various pHs. The first method is used to evaluate the formation constants of An^IVDTPA⁻ and whenever possible that of An^IV(H)DTPA. The experiments were carried out either with no other complexing ligand when hydrolysis does not compete (e.g. Th) or by adding a competitor, namely NTA, when hydrolysis must be prevented (e.g. Pu).

The second method allows determining the formation constants of An^IV(OH)DTPA²⁻ species.

1. Study as function of ligand concentration at a constant p_cH

The experiments by CE-ICPMS were carried out in acidic medium, at the free proton molar concentration p_cH = 1.395 in 0.1 M (Na,H)NO₃ media for Th⁴⁺ and Pu⁴⁺. The overall concentration of DTPA varied from 10⁻¹⁰ to 10⁻² M. The point at C_DTPA = 10⁻¹⁰ M corresponds to the experiment free of DTPA and was arbitrarily set at this concentration. It allows fixing the initial electrophoretic mobility free from ligand during the fitting procedure. Neither U⁴⁺ nor Np⁴⁺ was studied due to chemical instability for the former (U⁴⁺ was almost completely oxidized to hexavalent state in acidic medium)¹⁷ and to a lack of solution for Np⁴⁺. Literature data suggests the existence of the protonated species Th(H)DTPA (log β ≈ 2.1)^6,11 which has been critically evaluated by IUPAC.³ The log K(ML + H) = 2.16 ± 0.05 at 20 °C was proposed as a provisional value. Since the experiments by CE-ICPMS were carried out in acidic medium (p_cH = 1.395), the presence of the protonated species could not be ignored.

Th. Thorium is the single element among the tetravalent actinides for which the stability constants are available for all species of DTPA complexes in aqueous solution: ThDTPA⁻, Th(H)DTPA and Th(OH)DTPA²⁻. Therefore, it was interesting to compare our results with those obtained by other techniques.

The variation of the electrophoretic mobility as a function of the DTPA concentration was fitted by using eqn (3). The first approach consisted in measuring the overall electrophoretic mobility as function of DTPA without the presence of a competing ligand. As a result, eqn (3a) and (3b) are not considered here whereas, as discussed in the Ancillary data section, based on OECD recommended stability constants for Th hydrolyzed species,²⁴ the hydrolyzed species Th(OH)³⁺ is not taken into account because of its very low relative concentration (1.6%). Indeed, the correction factor to be applied to the stability constant would be +0.008 (see Discussion section). This contribution will be ignored. The interaction between Th⁴⁺ and nitrate ions leads to a correction which is described in the Discussion section.

Eqn (3) contains numerous parameters. They must be carefully evaluated and whenever possible reduced to improve the quality of the fit. First, μ_Th(H)DTPA = 0 because the electrophoretic mobility of neutral species is zero. Second, under our experimental conditions, 10⁻¹⁰ M < C_DTPA < 10⁻² M, and at a constant p_cH = 1.395, the molar fractions of ThDTPA and Th(H)DTPA are constant. This results in a substantial reduction of the number of free parameters, in particular eqn (3a) and (3b) are not considered for the direct formation of ThDTPA⁻. The presence of Th(H)DTPA in our experiments has been indirectly confirmed by noticing that the overall electrophoretic mobility value for C_DTPA = 10⁻² M, μ_pcH=1.395 = −0.94 × 10⁻⁴ cm² V⁻¹ s⁻¹, was not equal to that obtained at pH 6 (see ESI data†), μ_pH=6.045 = −1.56 × 10⁻⁴ cm² V⁻¹ s⁻¹ (i.e. for a pH where the ThDTPA⁻ species is the only species present in the solution). By solving the equation α_ThDTPA⁻μ_ThDTPA⁻ + α_Th(H)DTPAμ_Th(H)DTPA = −0.94 × 10⁻⁴, with μ_ThDTPA⁻ = −1.56 × 10⁻⁴ cm² V⁻¹ s⁻¹, μ_Th(H)DTPA = 0, and α_ThDTPA⁻ + α_Th(H)DTPA = 1, the following molar fraction is obtained: α_ThDTPA⁻ = 0.60. According to the proposed provisional IUPAC value, α_ThDTPA⁻ should be equal to about 0.2 under our conditions. However if such value was correct, we should have observed an overall electrophoretic mobility of −0.3 × 10⁻⁴ cm² V⁻¹ s⁻¹. This evaluation is far from the experimental electrophoretic mobility. Further, this value is not in agreement with the conclusion given by Brown and co-workers who found a very small contribution of Th(H)DTPA at 1 M by potentiometry. Although unambiguously present, the protonated species is not the major species under our experimental conditions. Nevertheless, its concentration is sufficient enough to be included in the fitting procedure. Finally, the following stability constants were found:

Th⁴⁺ + DTPA⁵⁻ + H⁺ ⇌ Th(H)DTPA, log K_H = 29.8 ± 0.7 (5a)

Th⁴⁺ + DTPA⁵⁻ ⇌ ThDTPA⁻, log K = 28.67 ± 0.46 (5b)

The stability constant for the stepwise reaction ThDTPA⁻ + H⁺ ⇌ Th(H)DTPA is found to be 1.1 ± 1.3.

In order to confirm this result, another approach based on ligand competition was applied here. The method consists in displacing the chemical equilibrium from an initial and “well” known complex AnL₁ toward another one AnL₂. In this study, the ligand L₁ is NTA (see Ancillary data) whereas the ligand L₂ is DTPA. Although ternary complexes have been reported with NTA and several ligands such as EDTA, IDA, etc.,²⁵ no data is available for the system An^IV/DTPA/NTA probably because the binding of NTA via three donor groups (the three carboxylates) is in competition with the complexation by the three nitrogen and the five carboxylates of DTPA.²⁶ Eight coordination sites are occupied by DTPA leaving for instance for Pu⁴⁺ no remaining sites to complete the inner coordination sphere by water or a secondary ligand. Since NTA binds only via its three carboxylate groups, it is likely to suppose that ternary complexes are not favored.

The method of ligand exchange, inducing a higher complexity for the fitting procedure in eqn (3), can lead to numerical instabilities. In order to reduce the number of free parameters and to prevent numerical problems, several parameters in eqn (3) have been fixed: β₁ = 10^16.67, β₂ = 10^30.26 (see Ancillary data for the determination of these constants), C_NTA = 2 × 10⁻⁴ M, [H⁺] = 4 × 10⁻² M, μ_Th(H)DTPA = 0, eqn (3c) is not considered because α_Th⁴⁺ = 0 (the relative concentration of Th⁴⁺ is 0.07%), μ_ThNTA⁺ = 2.56 × 10⁻⁴ cm² V⁻¹ s⁻¹ and μ_{Th(NTA)2²⁻} = −2.67 × 10⁻⁴ cm² V⁻¹ s⁻¹ (see Fig. 7 in the Ancillary data).

The mobility value for the species ThDTPA⁻ is found to be −1.62 × 10⁻⁴ cm² V⁻¹ s⁻¹ in good agreement with the value obtained at pH = 6.045 (−1.56 × 10⁻⁴ cm² V⁻¹ s⁻¹, see ESI data†). The following stability constants (in log units) are obtained: 28.96 ± 0.14 for the formation of ThDTPA⁻ and 30.20 ± 0.10 for the protonated species.

Pu. The complex PuDTPA⁻ is a very unusual one. In contrast to other An^IVDTPA⁻ compounds where a continuous variation of the electrophoretic mobilities was observed with increasing pH or with increasing ligand concentration, one peak per species is observed for the experiments at various pH and those by competition with NTA. This behavior corresponds to the limiting case described by Sonker and collaborators of strong complexation or a slow kinetics of dissociation.²²

The formation constant of PuDTPA⁻ was determined by studying its competition with NTA. The direct determination failed because the log K value was too high. Indeed, down to C_DTPA = 10⁻⁹ M, the electrophoretic mobility remains negative and constant (μ_PuDTPA⁻ = −1.22 × 10⁻⁴ cm² V⁻¹ s⁻¹) which corresponds to the unique species PuDTPA⁻. Below C_DTPA = 10⁻⁹ M, the electrophoretic mobility switches abruptly to a positive value which impedes the possibility to accurately fit data. No protonated species was evidenced because the electrophoretic mobility does not vary from p_cH = 1.395 to pH = 5. The stepwise reaction of protonation must be certainly smaller than that observed for Th.

As a result, the second method was applied with NTA as competitor at the concentration of 0.2 mM. Two peaks were detected which were attributed to Pu(NTA)₂²⁻ and PuDTPA⁻. According to the data in the Ancillary data, Pu(NTA)₂²⁻ is the major species in solution (98.2%) at p_cH = 1.395 and C_NTA = 0.2 mM. Therefore, eqn (4) applies and only the equilibrium below is considered:

Pu(NTA)₂²⁻ + DTPA⁵⁻ ⇌ PuDTPA⁻ + 2NTA³⁻, (8)

with

At the inflexion point [DTPA]₀ determined by eqn (4), the concentration of both species is equal. Therefore, we get:

with log α_NTA = 10.08 ± 0.09, log α_DTPA = 21.43 ± 0.14, [DTPA]₀ the concentration of DTPA for [PuDTPA⁻] = [Pu(NTA)₂²⁻].

The inflexion point is found at [DTPA]₀ = (2.61 ± 0.89) × 10⁻⁵ M (see Fig. 1). The calculated stability constant is therefore log K_exc = −1.54 ± 0.28.

Fig. 1 Variation of relative areas as function of the total DTPA concentration; conditions I = 0.1 M NaNO₃, p_cH = 1.395, T = 25 °C, C_NTA = 0.2 mM. At the intersection of the two fitted curves, C_DTPA = (2.61 ± 0.89) × 10⁻⁵ M.

The stability constant related to the equilibrium Pu⁴⁺ + DTPA⁵⁻ ⇌ PuDTPA⁻ can be calculated from the equilibria Pu⁴⁺ + 2NTA³⁻ ⇌ Pu(NTA)₂²⁻ and Pu(NTA)₂²⁻ + DTPA⁵⁻ ⇌ PuDTPA⁻ + 2NTA³⁻ and subsequent rearrangement of the associated mass balance equations:

log K = log K_exc + log K_Pu(NTA)2. (10)

Since log K_Pu(NTA)2 = 37.90 ± 0.23, we find log K_PuDTPA⁻ = 36.36 ± 0.36. It is worth noting K_exc in eqn (9) does not involve taking into account the hydrolysis reaction. However, in eqn (10) the log K_Pu(NTA)2 must also corresponding to a value free from hydrolysis. Therefore we used values in Table 5 (see Ancillary data section) where hydrolysis was taken into account during the fitting procedure. As a result, log K_PuDTPA⁻ in Table 1 is calculated in the absence of hydrolysis reactions.

Table 1 log K stability constants for tetravalent actinides and DTPA at various ionic strengths and 25 °C (unless otherwise noted). The free molar proton concentration p_cH = −log[H⁺] or the pH is reported if available as footnote. The stability constants have been obtained either by CE-ICPMS (direct and competition), and from literature, or evaluated by interpolation by combining CE-ICPMS experiments (log K_AnDTPA) and ab initio molecular dynamic (d_An–O). These values are not corrected from medium effects (see Discussion)

Equilibrium/comments	I = 0.1 M	I = 0.5 M (20 °C)	I = 1.0 M
a pcH = 0.2–1.8 (HCl).b pcH = 0.2 (HCl).c pcH = 0 (HNO3).d pcH = 0 (HClO4).e pcH = 0.05 (HCl).f pH = 1.290–1.760.g pH = 0.587–1.057.h pH = 0.550–0.522.i pH = 0.549–0.556.j pH = 2, t = 20 °C.k This work, pcH = 1.395 (HNO3).l This work, recalculated from the equilibrium An(OH)DTPA^2− + H^+ ⇌ AnDTPA^− + H2O and by using pKw = 13.775 in 0.1 M NaCl, 25 °C as the same water ionic product in 0.1 M TMAX (X = MES or HEPES).^23
Th^4+ + DTPA^5− ⇌ ThDTPA^−	28.78 ± 0.10 (ref. 6)^j	26.64 ± 0.03 (ref. 8)^f	29.6 ± 1.0 (ref. 13)^a
	30.34 ± 0.04 (ref. 5)^j		26.6 (ref. 11)
Direct method	28.67 ± 0.46^k
By competition with NTA	28.96 ± 0.14^k
ThDTPA^− + H^+ ⇌ Th(H)DTPA	2.16 ± 0.05 (ref. 6)^j		0.2 ± 1.4 (ref. 13)^a
	2.0 (ref. 11)
Direct method	1.1 ± 1.3^k
By competition with NTA	1.24 ± 0.12^k
ThDTPA^− + OH^− ⇌ Th(OH)DTPA^2−	4.9 ± 0.2 (ref. 3, 6)
	≈4.9 (ref. 15)^l
[DTPA] = 10^−2 M	5.24 ± 0.07^l
[DTPA] = 10^−4 M	5.32 ± 0.12^l
Pa^4+ + DTPA^5− ⇌ PaDTPA^−; evaluation from log KAnDTPA = f(dAn–O)	32.0 ± 1.0
U^4+ + DTPA^5− ⇌ UDTPA^−	30.9 (ref. 6, 7) (20 °C)	28.76 ± 0.09 (ref. 7)^g	31.8 ± 0.1 (ref. 13)^b
			28.8 (ref. 11)
			29.9 (ref. 14)^c
UDTPA^− + OH^− ⇌ U(OH)DTPA^2−	6.1 ± 0.1 (ref. 3, 16)^l
	6.08 ± 0.02 (ref. 16)^l
Evaluation from log KAn(OH)DTPA = f(KAnOH)	5.84 ± 0.23^l
Np^4+ + DTPA^5− ⇌ NpDTPA^−		29.29 ± 0.02 (ref. 9)^h	32.3 ± 0.1 (ref. 13)^b
			30.3 (ref. 11)
			30.5 (ref. 14)^c
			30.33 ± 0.12 (ref. 12)^d
Evaluation from log KAnDTPA = f(dAn–O)	34.8 ± 2.4 (this work)
NpDTPA^− + OH^− ⇌ Np(OH)DTPA^2−
[DTPA] = 10^−2 M	5.97 ± 0.26^l
[DTPA] = 10^−4 M	5.89 ± 0.10^l
Pu^4+ + DTPA^5− ⇌ PuDTPA^−		29.49 ± 0.10 (ref. 10)^i	33.67 ± 0.02 (ref. 13)^e
			29.5 (ref. 11)
			31.4 (ref. 14)^c
Direct method	– (Hydrolysis)
By competition with NTA	36.36 ± 0.36^k
PuDTPA^− + OH^− ⇌ Pu(OH)DTPA^2−
[DTPA] = 10^−2 M	6.44 ± 0.31^l
[DTPA] = 10^−4 M	6.28 ± 0.15^l
Am^4+ + DTPA^5− ⇌ AmDTPA^−; evaluation from log KAnDTPA = f(dAn–O)	36.4 ± 2.0
Bk^4+ + DTPA^5− ⇌ BkDTPA^−; evaluation from log KAnDTPA = f(dAn–O)	35.2 ± 1.6

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2. Study as function of pH at a constant concentration of ligand

Experiments were performed by CE-ICPMS from pH 6 to 9.5 at two concentrations of DTPA of 10⁻⁴ and 10⁻² M. Both concentrations have been chosen is such a way that An^IV ions are solely present as the species An^IVDTPA⁻ at pH 6. The medium was 0.1 M TMAX (X = MES or HEPES) and the temperature was set to 25 °C. Among the four actinides studied, U^IV was never detected in this medium due to oxidation to U^VI. Since UO₂²⁺ is not complexed by DTPA, it was not detected in the anionic separation mode of CE-ICPMS.¹⁷

Th. The existence of Th(OH)DTPA²⁻ is reported in the literature with a stability constant in log unit of ≈5 for the equilibrium ThDTPA⁻ + OH⁻ ⇌ Th(OH)DTPA²⁻. The electrophoretic mobility (see ESI data†) varied from −1.56 × 10⁻⁴ cm² V⁻¹ s⁻¹ at pH 6 to −2.69 × 10⁻⁴ cm² V⁻¹ s⁻¹ at pH 9.5 suggesting a variation of charge and the presence of a more negatively charged species at the highest pH. In absence of other ligands, this electrophoretic mobility suggests the presence of Th(OH)DTPA²⁻. It is noticed that the decrease is not strictly twice the electrophoretic mobility at pH 6 as might be expected for an ion of the same size and twice the elementary charge. We, however, also note that μ_{Th(OH)DTPA²⁻} = 0.58μ_ThDTPA⁻ obeys “Chandler’s rule” which was noticed by Chandler based on experimental observation that the equivalent conductivity of a negative ion of a dibasic acid is 0.6 the equivalent conductivity of its fully ionized species.²⁷ We obtained for the equilibrium Th(OH)DTPA²⁻ + H⁺ ⇌ ThDTPA⁻ + H₂O the following values: 8.53 ± 0.07 for C_DTPA = 10⁻² M and 8.45 ± 0.12 for C_DTPA = 10⁻⁴ M. To be consistent with literature data, both values were recalculated for the equilibrium ThDTPA⁻ + OH⁻ ⇌ Th(OH)DTPA²⁻ (see Table 1). Our results are in fair agreement and not incompatible with the tentative value proposed by IUPAC.

Np. The electrophoretic mobility of neptunium varied from −1.58 × 10⁻⁴ cm² V⁻¹ s⁻¹ at pH 6 to −2.48 × 10⁻⁴ cm² V⁻¹ s⁻¹ at pH 9.6. As for Th, the mobility ratio between NpDTPA⁻ and Np(OH)DTPA²⁻ obeys Chandler’s rule with μ_{Np(OH)DTPA²⁻} = 0.64μ_NpDTPA⁻. The values log K = 7.88 ± 0.10 and 7.80 ± 0.26 were found for the equilibrium Np(OH)DTPA²⁻ + H⁺ ⇌ NpDTPA⁻ + H₂O.

Pu. As previously mentioned, Pu behaves very differently. Instead of observing a continuous variation of μ as for Th and Np, the experiments at increasing pH showed two peaks which have been attributed to PuDTPA⁻ and Pu(OH)DTPA²⁻ compounds (see Fig. 2). In order to explain this behavior, ab initio molecular dynamics simulations were performed with one hydroxyl anion and twenty water molecules as a solvation sphere in Th and Pu DTPA complexes. According to the actinide the effect is rather different. PuDTPA⁻ retains the hydroxyl ion OH⁻ at a distance d_Pu–O(OH) = 2.153 Å (298 K) and the general effect is an opening of the complex with a slight increase of all the bond lengths (d_Pu–O = 2.354 Å, d_Pu–N = 2.988 Å). The distance Pu–O(OH) is shorter than the shortest Pu–O bond in the system. Opposite to the plutonium case we observed in Th(OH)DTPA²⁻ a departure of OH⁻ from Th after about 1.1 ps of simulation. This ion recombines to form a water molecule. Such behavior is also known for Np, which does not show irreversibility for hydrolysis reactions, contrary to the adjacent element Pu. These results may be correlated to formation constant of hydrolysed An^IVDTPA species (Fig. 3).

Fig. 2 Examples of electropherograms of Pu^IVDTPA⁻ compounds as a function of the pH; C_DTPA = 10⁻² M, I = 0.1 M TMAX (X = MES or HEPES), 25 °C.

Fig. 3 Relative area variation of Pu(OH)DTPA²⁻ and PuDTPA⁻ for C_DTPA = 10⁻⁴ M. At the inflexion point . The stability constant for the equilibrium Pu(OH)DTPA²⁻ + H⁺ ⇌ PuDTPA⁻ + H₂O is found to be 7.49 ± 0.15.

Under these conditions, data treatment becomes easier since no parameterization is mandatory. The results of the two experiments are gathered in Table 1. At the intersection of the S-shape curve (see Fig. 3) the concentrations are equal and are inversely proportional to the concentration of the free ligand. To our knowledge, no other study detected and quantified the formation of a Pu^IV–hydroxo DTPA complex.

E. Discussion

The two methods give similar values for the ThDTPA⁻ complex, 28.67 and 28.96, in a very good agreement with the tentative value (28.78). Both determinations match for two reasons: (1) the hydrolysis in the direct method is negligible (the correction factor represents 1.7% of the overall uncertainty); (2) the ligand exchange reaction is insensitive towards hydrolysis. The IUPAC tentative value was determined in 1967 by potentiometry in 0.1 M and pH 2 based on pK_as almost identical for pK_a1–pK_a5 as those adopted in this paper. However, since our experiments were performed in very acidic medium (p_cH = 1.395), we have included pK_a6 and pK_a7 values which were unknown in Bottari’s study. Despite differences of the two set of pK_as values, the α_DTPA calculated at pH 2 are almost identical (α_DTPA = 10^18.25 (ref. 28) and 10^18.26 (present work)). As a result, no error is evidenced which could be due to different sets of pK_as. Moreover, despite the fact that the temperature is not the same in both studies (20 °C instead of 25 °C in our experiments), the effect on temperature does not induce significant changes in the stability constant. Kinard and co-workers determined enthalpy and entropy of the reaction for the two complexes ThDTPA⁻ and Th(H)DTPA.²⁹ They found the same enthalpy (−12.3 ± 0.3 kJ mol⁻¹) and a strong entropy effect (510 ± 2 and 550 ± 2 J mol K⁻¹, respectively). The recalculation of Bottari’s data at 25 °C by means of the van’t Hoff equation leads to a slight correction of −0.04 to the initial value (28.78).

Regarding Th(H)DTPA, there is a discrepancy between old data^6,11 and recent values (ref. 13 and our results). Brown proposed a value of 0.2 ± 1.4 at I = 1 M NaCl¹³ whereas we determined a stability constant of 1.24 ± 0.12 at I = 0.1 M NaNO₃. Although it is not possible to compare both values without a complete set of parameters for the Specific Interaction Theory (SIT), we can roughly compare them according to the following procedure:

The log K variation as a function of the ionic strength I_m (in molal unit) is described by:

log K_H = log K⁰_H + Δz²D − ΔεI_m, (6)

with , Δz² = −2 for the reaction ThDTPA⁻ + H⁺ ⇌ Th(H)DTPA, and Δε_{NaCl medium} = ε_Th(H)DTPA − ε_H⁺,Cl⁻ − ε_{ThDTPA⁻,Na⁺}, with ε_Th(H)DTPA = 0, and ε_H⁺,Cl⁻ = 0.12.

By extrapolating our value at I = 0 by the Davies equation, and by assuming I_m (m) ≈ I (M), the following extrapolation is obtained at I = 1 M NaCl:

log K_H^{I=1 M} = 1.33 − 0.29 + ε_{ThDTPA⁻,Na⁺}. (7)

ε_{ThDTPA⁻,Na⁺} is unknown but it is noted that most of the ε_X⁻,Na⁺ values reported in the literature are near zero or negative.³⁰ As example, the value 0.01 ± 0.16 is reported for similar compounds AmEDTA⁻ and PuEDTA⁻.³¹ The estimated log K value is probably <1, in agreement with the Brown’s value (0.2 ± 1.4), whereas the application of this method to the Bottari’s value leads to an incompatible result. At the present time it is not possible to state whether the tentative IUPAC value is reliable or if the two recent determinations by potentiometry and CE-ICPMS failed for unknown reasons.

All the results given in Table 1 were calculated with no medium correction. This is justified because all other data from the literature were also not corrected for a medium effect. If such a correction is invalid for ligands such as IDA or MIDA, it cannot be accepted for EDTA or DTPA.^3,31 According to Anderegg, the correction factor needed to take into account the formation of NaDTPA⁴⁻ in 0.1 M NaNO₃ is 1 + [Na⁺]K_NaDTPA. Up to 2005, the stability constant of NaDTPA⁴⁻ was not yet published. Recently, Bretti and collaborators provided not only the stability constants of Na–NTA, –EDTA, –DTPA and –TTHA complexes but also the SIT and Pitzer interaction parameters.³² The value proposed by the authors for NaDTPA⁴⁻ have been adopted despite a disagreement for the formation of the analog NaEDTA³⁻ with log K_NaEDTA = 1.80 which is about one log unit below the one recommended by the NEA–TDB (log K_NaEDTA = 2.8 ± 0.3).³¹

We have adopted for the formation of NaNTA²⁻ data published by Daniele and collaborators³³ because they provided, with the same methodology the value for NaEDTA³⁻, in excellent agreement with the one recommended by NEA–TDB.³¹ On the contrary, the one proposed by Bretti³² will not be adopted here because of a deviation of about 0.8 log unit smaller than that of proposed by Daniele.

Additional correction is required because the interaction between An^IV and NO₃⁻, even if weak, must be also taken into account.

Finally, the following corrections terms must be applied:³¹

log K_corr = log K + log(1 + K_NaL[Na⁺]) + log(1 + K_AnNO3³⁺[NO₃⁻]). (11)

with L = DTPA or NTA.

Rigorously, the contribution of hydrolysis should be also taken into account for the direct method. In practice, there is only one experiment available (with Th). The term log(1 + K_ThOH³⁺[OH⁻]) at 0.1 M NaNO₃ and [H⁺] = 0.040 M, and log K_ThOH³⁺ = 10.63 (ref. 24) is 0.008. This value is very minor and does not change the result.

Based on Ancillary data, corrections were applied for An^IVNTA and An^IVDTPA compounds (Table 2). The correction is unnecessary for protonated and hydrolyzed AnDTPA complexes. For NaNTA²⁻ and NaDTPA⁴⁻ the corrections log K_corr are +0.37 and +0.40, respectively.

Table 2 Stability constants at I = 0.1 M NaNO₃ medium, 25 °C, corrected by the formation of NaL (L = NTA, DTPA) and AnNO₃³⁺. Values for Pu compounds have been corrected for hydrolysis (see Ancillary data) whereas the correction is negligible for Th

Reaction	log Kcorr
Th^4+ + DTPA^5− ⇌ ThDTPA^−	29.17 ± 0.48
	29.46 ± 0.21
Average	29.41 ± 0.19
Th^4+ + NTA^3− ⇌ ThNTA^+	17.14 ± 0.53
Th^4+ + 2NTA^3− ⇌ Th(NTA)2^2−	30.73 ± 0.22
Pu^4+ + DTPA^5− ⇌ PuDTPA^−	37.11 ± 0.42
Pu^4+ + NTA^3− ⇌ PuNTA^+	23.10 ± 0.28
Pu^4+ + 2NTA^3− ⇌ Pu(NTA)2^2−	38.37 ± 0.23

---

1. Evaluation of unknown systems from the relationship log K = f(z_eff/d_An–O) at a constant p_cH

Ab Initio Molecular Dynamics (AIMD) was used to evaluate the distances An–O and An–N in AnDTPA⁻ complexes. Instead of testing several geometries at 0 K, AIMD provides realistic distances without assumptions. AIMD was successfully tested on actinide DTPA complexes by comparison with EXAFS experiments in a previous paper.¹⁷ Results are given in Table 3. Th remains at the edge of the cup-shape DTPA structure whereas the other actinides enter deeper in the structure. From U to Am, the distances An–O and An–N are constant. This suggests the covalent bonds with nitrogen are of the same magnitude and the differences observed for the stability constants can be assigned to the hard character of the actinide. Since the same An compounds are studied, it is relevant to extrapolate unknown stability constants based on an ionic model of chemical bonding³⁴ with the covalent bond with nitrogen remaining an additional and constant term along the An series. Fig. 4 shows a linear relation between log K values (data from literature and by this study) and z_eff/d_An–O.

Table 3 Distances An–O and An–N in AnDTPA⁻ compounds obtained by AIMD at 298 K

An^IV	dAn–O/Å	dAn–N/Å
Th	2.354 ± 0.05	2.830 ± 0.05
Pa	2.275 ± 0.05	2.751 ± 0.05
U	2.248 ± 0.05	2.724 ± 0.05
Np	2.248 ± 0.05	2.724 ± 0.05
Pu	2.248 ± 0.05	2.671 ± 0.05
Am	2.248 ± 0.05	2.724 ± 0.05
Bk	2.278 ± 0.05	2.645 ± 0.05

---

Fig. 4 Variation of log K_AnDTPA⁻ as a function of the metal–oxygen ligand distance calculated by ab initio molecular dynamic (AIMD).¹⁷ (○) data obtained by CE-ICPMS (Th, Pu), (◇) data from literature (Th, U). Interpolated values give for Pa^IV and Np^IV: d_Np–O = 2.26 Å, log K_NpDTPA⁻ = 34.8; d_Pa–O = 2.275 Å and z_eff = 3.85, log K_PaDTPA⁻ = 32.0.

Pa, Np, Bk. The formation constant of PaDTPA⁻ can be determined if both the effective charge and the distance Pa–O in PaDTPA⁻ are known. The distance Pa–O is calculated by AIMD based on calibration realized in a previous paper.¹⁷ The effective charge of Pa⁴⁺ is actually unknown but by assuming a regular variation from Th⁴⁺ (z_eff = +3.82) to Pu⁴⁺ (z_eff = +3.97)³⁵ z_eff can roughly be evaluated to +3.85. As a result, the formation constant associated with the equilibrium Pa⁴⁺ + DTPA⁵⁻ ⇌ PaDTPA⁻ can be evaluated from the linear relation depicted in Fig. 4. We found log K = 32.0 ± 1.0. It is noticed that U and Pa have similar z/d distances and therefore similar K values. It is worth noting that by applying the same methodology with a constant charge of +4 instead of the effective charge for all actinides, the formation constant of PaDTPA⁻ would be 33.5 ± 1.5. This other estimate is not significantly different from the previous one. Similarly, the formation constants of NpDTPA⁻, AmDTPA⁻ and BkDTPA⁻ are obtained: log K_NpDTPA⁻ = 34.8 ± 2.4, log K_AmDTPA⁻ = 36.4 ± 2.0, and log K_BkDTPA⁻ = 35.2 ± 1.6. The complexes AmDTPA⁻ and BkDTPA⁻ do not exist in solution due to their high potential of M(IV)/M(III). However, such prediction is of relevance in other solvents such as ionic liquids, because this oxidation state is known to be stabilized in these solvents.

2. Evaluation of unknown systems from the relationship log K_{An(OH)DTPA²⁻} = f(log K_AnOH³⁺) at a constant concentration of ligand

Due to the electrostatic nature of the bonding, a linear trend between the first hydrolysis stability constant and the dAn–O(OH) distance is expected. The simulation performed by AIMD at 0 K shows a correlation between the distance and the stability constants. The following values were calculated: dTh–O(OH) = 2.230 Å, dNp–O(OH) = 2.135 Å, and dPu–O(OH) = 2.137 Å. The decrease of this distance along the actinide series is necessarily linked to the bond strength as only one site remains to complete the nine-coordination mode of the tetravalent actinide. As a result, a relation is expected between the stability constant of the AnDTPA− complex and the hydrolysis constant. As depicted in Fig. 5, a linear relation is observed and in particular the similar distances calculated for Np and Pu match with their almost identical first hydrolysis formation constants, log KAnOH3+I=0.1 M = −1.21 and −1.26 at I = 0.1 M, respectively.

Fig. 5 Variation of the formation constant of hydrolysed AnDTPA species as a function of the first hydrolysis of An^IV recalculated at 0.1 M TMAX (X = MES or HEPES) with the Davies equation at 25 °C; (○) data obtained by CE-ICPMS, (◆) data from literature (not considered for the linear regression).

U. Unfortunately, we were not able to stabilize U^IVDTPA⁻ species during the separation by capillary electrophoresis. Nevertheless, the stability constant related to the formation of U(OH)DTPA²⁻ can be evaluated from data obtained for Th, Np and Pu (see Table 1). Based on the first hydrolysis of each actinide, it is possible to correlate log K_AnOH³⁺ with log K_{An(OH)DTPA²⁻}. A linear relation is observed (Fig. 5) allowing us to evaluate the formation constant of U(OH)DTPA²⁻. To be consistent, only data obtained by CE-ICPMS were used here since all actinides except U were present in the same sample under the same conditions of separation. Beside, literature data for Th and U agree well with the linear relationship depicted in Fig. 5.

Application. The application of the brand new set of values for the chemical system PuDTPA allows to build a new speciation diagram as a function of pH. The domains of existence of the species PuDTPA⁻, and Pu(OH)DTPA²⁻ at trace levels are depicted in Fig. 6. Two chemically species are observed to exist in blood, PuDTPA⁻ (53% rel.) and Pu(OH)DTPA²⁻ (47%). Both species are stable and therefore could present different chemical behaviours in terms of complexation, metabolism or fixation. These values should now be taken in consideration for further decorporation studies.

Fig. 6 Speciation diagram of PuDTPA species as function of pH. Conditions: [Pu⁴⁺] = 10⁻⁸ M, C_DTPA = 10⁻⁴ M, I = 0.1 M, 25 °C.

F. Conclusions

Capillary electrophoresis coupled with inductively plasma mass spectrometry was used to determine the stability constants of several An^IVDTPA⁻ compounds (An = Th, U, Np, Pu) including protonated and hydrolysed species. Plutonium compounds behave differently with the kinetics of dissociation being slower than for the rest of the tetravalent actinide series, resulting in the simultaneous presence of stable PuDTPA⁻ and Pu(OH)DTPA²⁻ complexes at blood physiological pH. Relations between parameters and theoretical calculation by ab initio molecular dynamic along the actinide series were evidenced which allowed us to assess the formation constants of U(OH)DTPA²⁻, NpDTPA⁻, and even PaDTPA⁻.

G. Ancillary data

The competition between NTA and DTPA is through:

ThNTA⁺ + DTPA⁵⁻ ⇌ ThDTPA⁻ + NTA³⁻ (12)

and

Th(NTA)₂²⁻ + DTPA⁵⁻ ⇌ ThDTPA⁻ + 2NTA³⁻ (13)

To determine the stability constant related to only the interaction between DTPA and An, the knowledge of the stability constants of the following reactions are necessary:

The calculation of the stability constant β_i from that β^*_i obtained by CE-ICPMS experiments is obtained thanks to the relation:

β_i = α_NTAβ^*_i, (16)

where α_NTA is defined as

1. Nitrilotriacetic acid pK_as

A recent critical evaluation has been carried out by Leguay concerning the protonation constants of nitrilotriacetic acid.³⁶ Based on the results recently published by Thakur et al.³⁷ at several ionic strengths (0.3–6.6 m) and a recalculation of the protonation constants using the Specific Interaction Theory within the validity range of this theory (0–3 m), Leguay extrapolated the three pK_as to zero ionic strength and proposed new interaction parameters Δε_i. We recalculate these values at I = 0.1 M using the Davies equation. However, it is noticed that the recalculation using either Davies equation or the SIT theory gave exactly the same values. In addition, use of just one source does not warrant the validity of the data. Therefore, we used other data and we averaged them (see Table 4). Finally, the coefficient α_NTA is calculated to be 10^{(10.08±0.09)} at p_cH = 1.395.

Table 4 Ancillary data: NTA and DTPA acidity constants and other data, I = 0.1 M (NaNO₃), T = 25 °C

Reaction	Formation constant		Ref./comments
H4NTA^+ ⇌ H3NTA + H^+	log Ka4	1.0	38
Average		1.0 ± 0.1	The uncertainty is arbitrarily set to 0.1
H3NTA ⇌ H2NTA^− + H^+	log Ka3	1.92 ± 0.01	36, 37
		1.80	39
		1.72	28
		1.90	40
		1.84	41
		1.74
Average		1.82 ± 0.10
H2NTA^− ⇌ HNTA^2− + H^+	log Ka2	2.90 ± 0.02	36, 37, the Dixon test for outlier data fails
		2.51	38
		2.52	39
		2.5	28
		2.48	40
		2.46	41
Average		2.49 ± 0.03
HNTA^2− ⇌ NTA^3− + H^+	log Ka1	9.69 ± 0.05	36, 37
		9.67	38
		9.70	39
		9.73	28
		9.65	40
		9.66	41
Average		9.68 ± 0.04
H7DTPA^2+ ⇌ H6DTPA^+ + H^+	log Ka7	1.45 ± 0.15	42
H6DTPA^+ ⇌ H5DTPA + H^+	log Ka6	1.60 ± 0.15
H5DTPA ⇌ H4DTPA^− + H^+	log Ka5	1.80 ± 0.05
H4DTPA^− ⇌ H3DTPA^2− + H^+	log Ka4	2.55 ± 0.05
H3DTPA^2− ⇌ H2DTPA^3− + H^+	log Ka3	4.31 ± 0.02
H2DTPA^3− ⇌ HDTPA^4− + H^+	log Ka2	8.54 ± 0.02
HDTPA^4− ⇌ DTPA^5− + H^+	log Ka1	10.51 ± 0.01
Na^+ + NTA^3− ⇌ NaNTA^2+	log K	1.35 ± 0.05	33, no medium specified
Na^+ + DTPA^5− ⇌ NaDTPA^4+	log K	1.4 ± 0.2	32, recalculated at I = 0.1 M by Davies equation
Th^4+ + NO3^− ⇌ ThNO3^3+	log K	0.4 ± 0.2	24, recalculated at I = 0.1 M by Davies equation in absence of SIT parameters for NaNO3 medium
Th^4+ + 2NO3^− ⇌ Th(NO3)2^2+	log K	0.8 ± 0.4
Pu^4+ + NO3^− ⇌ PuNO3^3+	log K	1.09 ± 0.15	30, recalculated at I = 0.1 M by Davies equation in absence of SIT parameters for NaNO3 medium

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2. Determination of the formation constants for the system Th–NTA

The hydrolysis of tetravalent actinides occurs even in acidic medium. We use the OECD–TDB recommended data extrapolated at zero ionic strength and recalculated at I = 0.1 M NaNO₃ using the specific interaction coefficients.²⁴ At p_cH = 1.395 and [Th⁴⁺] = 10⁻⁷ M, only one minor hydrolysed species is present, Th(OH)³⁺, at a relative concentration of 1.6%. Therefore, this species will not be considered during the fitting procedure using eqn (3) because the magnitude upon the overall electrophoretic mobility falls within the uncertainty (0.4%).

The experimental variation of the mobility of thorium in presence of increasing concentration of NTA in both sample conditions and BGE is reported in Fig. 7. For the following reactions, the apparent stability constants calculated by eqn (3) are:

Th⁴⁺ + NTA³⁻ ⇌ ThNTA⁺, log β₁ = 16.67 ± 0.53

Th⁴⁺ + 2NTA³⁻ ⇌ Th(NTA)₂²⁻, log β₂ = 30.26 ± 0.22

Fig. 7 Variation of μ_Th as function of the total concentration of nitrilotriacetic acid (NTA) at I = 0.1 M (NaNO₃), T = 25 °C and [H⁺] = 0.040 M. The results of the fitting process give log β^*₁ = 6.59 ± 0.52 for the formation of ThNTA⁺ and log β^*₂ = 10.10 ± 0.13 for the formation of Th(NTA)₂²⁻.

The value related to the first equilibrium is in excellent agreement with the tentative IUPAC recommendation (log β₁ = 16.9).³ No value is available in the literature for the formation of Th(NTA)₂²⁻. To our knowledge, it is the first time that such a value is proposed.

3. Determination of the formation constants for the system Pu–NTA

The same procedure as that applied for Th has been used with a special attention paid to the hydrolysis which is more pronounced for Pu. The OECD recommended data were taken except for the polymeric species because of the ultra-trace level and only monomeric species are considered.

Under our experimental conditions ([Pu⁴⁺] = 10⁻⁸ M, p_cH = 1.395), two hydroxo species are present: Pu(OH)³⁺ (14.5%) and Pu(OH)₂²⁺ (83.5%), the others are about 2% (Pu⁴⁺ and Pu(OH)₃⁺) and will be neglected. The hydrolysis constants³⁰ has been recalculated at 0.1 M NaNO₃ by the Davies equation since no Pu⁴⁺ SIT parameter is available in this medium. The stability constants obtained are corrected with hydrolysis taken into account, considering only the 1 : 2 hydroxo complex as the major species (90% relative) under our experimental conditions. The formation of Pu(H)NTA²⁺ is not considered here because under our conditions this species if present, is very minor. Only one preliminary study is available in the literature which states the presence of the protonated complex at pH 1.10.⁴³ Despite huge discrepancy with our data of ten orders of magnitude (log β₁₀₁ = 12.86 ± 0.03, log β₁₁₁ = 13.83 ± 0.04, I = 0.1 M), the stability constant related to the protonation of the complex log K_H = log β₁₁₁ − log β₁₀₁ = 0.97 leads in our conditions (p_cH = 1.395) to neglect this species because the calculation of the speciation diagram gives either no protonated species (data from ref. 43) or only 0.6% relative concentration (data in Table 5 + log K_H).

Table 5 Stability constants of An^IVNTA systems at I = 0.1 M NaNO₃ and 25 °C, 95% confidence level. These data are not corrected for complexation of NTA³⁻ with Na⁺, and of An⁴⁺ with NO₃⁻ (see Discussion section)

Reaction	log K
a Corrected for Pu^4+ hydrolysis.
Th^4+ + NTA^3− ⇌ ThNTA^+	16.67 ± 0.53
Th^4+ + 2NTA^3− ⇌ Th(NTA)2^2−	30.26 ± 0.22
Pu^4+ + NTA^3− ⇌ PuNTA^+	22.38 ± 0.28^a
Pu^4+ + 2NTA^3− ⇌ Pu(NTA)2^2−	37.90 ± 0.23^a

---

It is difficult to find the reason for such deviation but it seems that a conditional constant was determined in the ref. 43 rather than a measured constant. Indeed, by applying eqn (14), we found an apparent stability constant of about 23.8 in fair agreement with our results. In addition, a previous determination in 0.5 M HNO₃ by the same technique (spectrophotometry) was obtained: log K = 17.4 ± 0.2.⁴⁴ The extrapolation to 0.1 M by the Specific Interaction Theory leads to an apparent stability constant of about 22,⁴⁴ which also agrees with our determination (see Table 5).

Finally, the following equilibria are studied:

Pu(OH)₂²⁺ + xNTA³⁻ + 2H⁺ ⇌ Pu(NTA)_x^2−3x + 2H₂O (18)

withand

The results are gathered in Table 5. To our knowledge, no older determination is available in the literature.

4. Diethylenetriaminepentaacetic acid pK_as

In this work, we used the acidity constants K_a1–K_a5 from Moeller and Thompson’s work performed at 20 °C and I = 0.1 M (K,H)NO₃,⁴⁵ and recalculated at 25 °C by Leguay and co-workers,⁴² using the available enthalpy variation for K_a1–K_a3. Leguay and co-workers have carried out a critical evaluation of data and proposed acidity constants at 25 °C and 0.1 M. These values and their associated uncertainties have been adopted in this paper (see Table 4). Finally, the coefficient α_DTPA is calculated to be 10^{(21.43±0.14)} at p_cH = 1.395.

Acknowledgements

This work was funded under project name DACFAM by the French transverse program “Toxicologie Nucléaire”.

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Footnotes

† Electronic supplementary information (ESI) available: Experimental details on electrophoretic mobilities. See DOI: 10.1039/c6ra08121e

‡ In memoriam 1981–2015.

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