Materials

Sichuan University synthesized TODGA (≥98%); its purity was confirmed by FT-MS (ESI⁺) and ¹H NMR (Fig.S1–S2). Moreover, Eu(NO₃)₃·6H₂O (99.99%) was obtained from MREDA Technology Co. Ltd. Formic acid, liquid chromatography-mass spectrometry (LC-MS) grade, was purchased from Thermo Fisher Scientific. Methanol (LC-MS grade) was purchased from Honeywell Trading (Shanghai) Co., Ltd. The aqueous dilution was performed using ultrapure water (18.2 MΩ·cm). All other chemicals were of analytical grade, and the chemicals were not further purified.

Gamma irradiation

TODGA and TODGA/nDD solutions equilibrated with and without HNO₃ (3.0 mol/L) before γ-radiation were irradiated in the air at room temperature (25 ± 5 °C) using a ⁶⁰Co source (Department of Applied Chemistry in the College of Chemistry, Peking University, China) with an absorbed dose rate of 6.6 kGy/h, as determined by a Fricke dosimeter.

Quantitative analysis of TODGA after irradiation

An HPLC method with UV detection (SPD-16, Shimadzu, Japan) was used to quantitatively analyze the TODGA concentration in the irradiated samples. Additionally, HPLC was carried out at 25 ± 5 °C using an Agilent HC-C18 liquid chromatography column (5 μm, 4.6 mm × 150 mm) to achieve chromatographic separation with a UV wavelength fixed at 210 nm. The aqueous component was ultrapure water with formic acid (1‰ v/v) (A₁); the organic component was methanol (B₁). The elution program in our liquid chromatography was listed hereafter: 0–10 min, 30–100% B₁; 10–20 min, 100% B₁; 20–22 min, 100–30% B₁. The error values in the quantitative analysis experiments were within 5%. The flow rate was 1.0 mL/min, and the injection volume was 20 µL.

Identification and semi-quantification of radiolytic products

Ultra-high pressure liquid chromatography (UPLC) (ACQUITY I-Class, Waters, USA) was carried out using an Agilent HC-C18 liquid chromatography column (5 μm, 4.6 mm × 150 mm) at 40 °C to achieve chromatographic separation. The aqueous component was ultrapure water with formic acid (1‰ v/v) (A₂), and the organic component was methanol with formic acid (1‰ v/v) (B₂). The liquid chromatography elution program was listed hereafter: 0–4 min: 30–100% B₂; 4–13 min: 100% B₂; 13–13.1 min: 100–30% B₂; 13.1–15 min: 30% B. The flow rate was 0.8 mL/min with a 1 µL injection volume. The mass-spectrometer conditions of the quadrupole time-of-flight mass spectrometry (QTOF-MS) (Vion IMS QToF, Waters, USA) are listed here: desolvation temperature: 300 °C; source temperature: 120 °C; desolvation gas flow: 800 L/h; capillary voltage: 2.8 kV; cone gas flow: 50 L/h; positive mode. The data were acquired and processed using a Waters UNIFI Scientific Information System with a mass target match tolerance of less than 5 ppm.

Extraction experiment

The TODGA was dissolved with nDD to obtain a 0.7 ml organic phase with a concentration of 0.2 mol/L. The Eu(NO₃)_3·6H₂O was dissolved in 3.0 mol/L HNO₃ to obtain a 0.7 ml aqueous phase with a concentration of 1000 mg/L. Pre-equilibration of the organic extraction phase with 3.0 mol/L HNO₃ was performed before extraction. A vortex mixer at a speed of 2500 rpm (LPD2500, Leopard Scientific Instrument Co., Ltd, Beijing) was used to perform the extraction experiments at 298 ± 1 K. To achieve complete separation between the two phases, the mixtures were centrifuged for 1 min at 5000 rpm in a centrifuge (TGL-16M, Cence, Hunan). After dilution with ultrapure water, the aqueous phase was detected using an ICP-MS (ELEMENT XR, Thermo Scientific, USA) to estimate the concentration of Eu(III).

The distribution ratio of Eu(III) (D_Eu) was calculated using Eq. (1). The phase ratio equals 1:1 in the extraction experiment. $D_{\text{Eu}}=\left(C_{\text{i}}-C_{\text{f}}\right)/C_{\text{f}},$ (1) where $C_{\text{f}}$ and $C_{\text{i}}$ represent the final and initial Eu (III) concentrations in the diluted aqueous phase, respectively. The extraction had an error rate of less than 5%.

Fluorescence spectra titration

The fluorescence emission spectra of the titration experiments were investigated at 298 ± 1 K in a cuvette cell with a 1 cm path length using a fluorescence spectrophotometer (F7000, Hitachi, Japan). The concentration of TODGA was 0.1 mol/L in acetonitrile and the initial concentration of Eu(III) was 0.001 mol/L in 2.0 mL acetonitrile. Next, 4 µL of TODGA solution was added at a time. The solution was mixed using a vortexer (VORTEX 3, IKA, Germany) for 5 min after the addition of each ligand. The titration experiments used an excitation wavelength of 395 nm; the bandwidth of the excitation and emission was 2.5 nm. The interval was 1 nm and the spectra were recorded between 550 and 700 nm. Single-component spectra of the metal–ligand complexes and metal solvent species were obtained using the HyperSpec program.

Theoretical calculations

DFT calculations incorporating electron correlation effects were performed at the level of B3LYP using the Gaussian 09 package [33-35]. The relativistic effects of Eu atoms were investigated using the quasi-relativistic effective core potentials (RECPs) and associated valence basis sets, which were improved by the Stuttgart and Dresden groups [36-40]. The large-core RECPs used in the structural optimization of Eu(III) contained 52 electrons [39, 40]. All other C, N, O, and H atoms utilized the 6-31G (d) basis set. Geometrical optimization and the electronic calculations of all structures were first performed at the level of B3LYP/6-31G(d)/RECP under the gas phase conditions. The Gibbs free energy (G_g), entropy (S_g), and enthalpy (H_g) were obtained under the gas phase conditions at 298.15 K using the same theory level. To obtain the Gibbs free energy (G_aq), entropy (S_aq), and enthalpy (H_aq) of the species in the nDD phase at 298.15 K, all species were optimized at the B3LYP/6-31 G (d)/RECP level in nDD to better predict their solvation energy[41]. This theory is based on the SMD universal continuum solvation model[42].

Quantitative analysis of TODGA under different conditions after γ-ray irradiation

TODGA/nDD, HNO₃-TODGA/nDD, and neat TODGA were subjected to γ-irradiation with absorbed doses ranging from 20 to 500 kGy. The irradiated samples were measured quantitatively using HPLC-UV and their radiolytic stability was analyzed. Figure 1 shows that the TODGA concentration decreased exponentially with increasing absorbed doses, suggesting pseudo-first-order degradation kinetics for TODGA/nDD, HNO₃-TODGA/nDD, and neat TODGA. By comparing TODGA/nDD and HNO₃-TODGA/nDD, it was found that HNO₃ had little influence on the radiolysis of TODGA. Moreover, in the nDD solution, the radiolysis rate of TODGA was higher than that of the neat TODGA. A dodecane-induced "sensitization effect" is responsible for the sensitization of TODGA to radiolysis [43] due to the fact that the radiolysis of TODGA is accelerated by nDD solvents because of the efficiency of nDD in transferring positive charges [44-46].

Fig. 1Full-screen View

(Color online) $C_{\text{TODGA}}/C_{\text{TODGA}}^0$ of irradiated TODGA/nDD, HNO₃-TODGA/nDD, and neat TODGA as a function of the absorbed dose (R) (y: $C_{\text{TODGA}}/C_{\text{TODGA}}^0$, x: R)

Because the radiolysis behavior of TODGA depends on its concentration in pseudo-first-order kinetics, the rate of radiolysis causes an exponential drop in the TODGA concentration. The radiolysis rate equation is defined by Eq. (2): $-\frac{\text{d}{C}_{\text{TODGA}}}{\text{d}R}=C_{\text{TODGA}}\cdot k.$ (2)

The solution to the rate equation is presented as Eq. (3): $\frac{C_{\text{TODGA}}}{C_{\text{TODGA}}^0}=e^{-kR},$ (3) where $C_{\text{TODGA}}$ (mol/L) is the concentration of TODGA, $C_{\text{TODGA}}^0$ (mol/L) is the original concentration of TODGA before γ-radiation, R (kGy) is the absorbed dose, and the dose constant $k$ (kGy^-1) is the coefficient obtained by fitting the exponential curve.

The dose constant $k$ can be used to scale the absorbed dose when exponential behavior occurs [47]. Using all the information acquired during the irradiation experiment provides more accurate results, and standard statistical methods can be used to assess the accuracy of the results. The application of $k$ to characterize an exponential curve in terms of the absorbed dose is very similar to that of traditional time-dependent kinetics. As expressed by exponential Eq. (3), the reciprocal absorbed dose is governed by the first-order rate law instead of the reciprocal time.

If the dose constants k of different systems can be obtained, Equation (4) can be used to calculate the $G$ value (µmol/J), which is known as the radiation chemical yield: $G={10}^3{C}_{\text{TODGA}}^{0}k{\rho }^{-1}$ (4) where $\rho$ is the solution density (kg/L) (${\rho }_{\text{TODGA}}$= 0.91 and ${\rho }_{0.2 \text{mol}/\text{L TODGA}/n\text{DD}}$ = 0.77 (25 °C). The measurement results are shown in Table S1.

Table 1 shows the dose constants $k$ and radiation chemical yields $G$ of irradiated TODGA/nDD, HNO₃-TODGA/nDD, and neat TODGA. The dose constant $k$ of TODGA in nDD is higher than that of neat TODGA because of the “sensitization effect”, while the radiation chemical yields $G$ of TODGA/nDD and HNO₃- TODGA/nDD are lower than that of neat TODGA because of the different initial concentrations of irradiated TODGA. These results agree with the literature in which Sugo et al. reported that the $k$ value of 0.2 mol/L TODGA/nDD was 2.2×10^-3 kGy^-1[43, 48]. By using the $k$ value, we can predict that the absorbed doses for the half-loss of TODGA concentration (R_0.5) in irradiated TODGA/nDD, HNO₃-TODGA/nDD, and neat TODGA will be approximately 330, 315, and 1060 kGy, respectively.

Identification and semi-quantitative analysis of radiolytic products

Ultra-high-performance liquid chromatography with quadrupole time-of-flight mass spectrometry (UPLC-QTOF-MS) can be used to identify and quantify complex mixtures of unknown compounds owing to its high resolution and mass accuracy.

The major radiolytic products of TODGA were identified using QTOF-MS; these are presented in Table 2, and their UPLC-QTOF-MS spectra are shown in Figures S3–9. Seven mass signals were identified and attributed to the possible radiolytic products of TODGA (P₁ – P₇, Table 2). These radiolytic products were formed by the rupture of the C – N, C – O, and C – C bonds of TODGA. Four radiolysis routes after irradiation are shown in Scheme 1.

Table 2Full-screen View

Radiolytic products of TODGA determined by the QTOF-MS

Radiolytic products	Chemical formula	Theoretical neutral mass	Observed neutral mass	Structure
P1	C28H56N2O3	468.4291	468.4274
P2	C20H39NO4	357.2879	357.2892
P3	C18H37NO2	299.2824	299.2825
P4	C18H37NO	283.2875	283.2867
P5	C17H35NO	269.2719	269.2719
P6	C16H35N	241.2770	241.2772
P7	C19H39NO2	313.2981	313.2994

Show more

Scheme 1Full-screen View

Radiolysis routes of TODGA after γ-irradiation

Figure 2 shows the semi-quantitative analysis of the radiolytic products P₁ – P₇ in the irradiated HNO₃-TODGA/nDD and neat TODGA. The absorbed doses ranged from 20 to 500 kGy. Seven radiolytic products were found to exist in the two systems. The detector counts of the radiolytic products P₁ – P₇ roughly increased with increasing absorbed dose. However, some radiolytic products, such as P₁ in irradiated neat TODGA, showed a decrease in detector counts with absorbed doses from 400 kGy to 500 kGy. This is probably because the contents of the radiolytic products during irradiation increased from the radiolysis of the TODGA and decreased by self-radiolysis. The concentration's rate of increase was less than the rate of decrease with absorbed doses from 400 to 500 kGy for P₁ in irradiated neat TODGA. The detector counts of all radiolytic products in irradiated TODGA/nDD were higher than those in neat TODGA (Figure S10), indicating the “sensitization effect” of nDD. This agreed well with the above result of the radiolysis kinetics of the TODGA with or without nDD. However, the relative detector counts of some radiolytic products differed between the two irradiation systems. For example, the detector count of P₆ was less than that of P₄ in irradiated neat TODGA; however, the converse was true for irradiated HNO₃-TODGA/nDD. This can be attributed to the different reaction mechanisms, wherein irradiated neat TODGA produces radical cations by direct ionization reaction. Conversely, in irradiated TODGA/nDD, nDD radical cations may transfer their charge to TODGA molecules, leading to radiolysis of TODGA[43, 49].

Fig. 2Full-screen View

(Color online) Semi-quantitative analysis of radiolytic products P₁ – P₇ in: (a) irradiated neat TODGA, and (b) HNO₃-TODGA/nDD with absorbed doses ranging from 20 to 500 kGy

Influence of γ-ray irradiation on the extraction of TODGA system toward Eu(III)

HNO₃-TODGA/nDD and neat TODGA were subjected to γ-ray irradiation at absorbed doses ranging from 50 to 500 kGy. The irradiated neat TODGA was diluted with nDD to 0.2 mol/L. These organic phases were used to extract Eu(III) from the 3.0 mol/L HNO₃ aqueous phase to evaluate the extraction performance.

As shown in Fig. 3, $D_{\text{Eu}}$ decreased as the absorbed dose increased, but it was slower for irradiated TODGA than for irradiated HNO₃-TODGA/nDD, indicating that γ-ray irradiation of the ligand significantly affected the extraction of Eu(III). This further proves that the presence of nDD increased the radiolysis of TODGA. However, the HNO₃-TODGA/nDD system after γ-ray irradiation still possesses a high $D_{\text{Eu}}$ (2.2×10³), even at 500 kGy.

Fig. 3Full-screen View

(Color online) D_eu of irradiated neat TODGA and HNO₃-TODGA/nDD for extraction of Eu(III) versus the absorbed dose.

The loss of extractants was the main cause of the decline in extractability after irradiation. Owing to the presence of TODGA and its liquid radiolysis products in the irradiated organic extraction phase, the complexation of radiolytic products on Eu(III) was studied using DFT calculations. This determined the effect if any of the radiolytic products of TODGA on the extraction behavior of the irradiated extraction system.

Slope analysis and fluorescence titration

Before DFT calculations were conducted to investigate the complexation of TODGA and its radiolytic products with Eu(III), we assessed the stoichiometry of Eu ions and TODGA ligands in the extraction reaction, which could be obtained by the slope analysis in the curve of logD_M-log[L]_(org).

The extraction reaction of Eu(III) by TODGA is expressed by Eq. (5): ${\text{Eu}}_{\left(\text{aq}.\right)}^{3+}+3{\text{NO}}_{3_{\left(\text{aq}.\right)}}^{-}+n{\text{TODGA}}_{\left(\text{org}.\right)}\rightleftharpoons \text{Eu}{\left({\text{NO}}_3\right)}_3{\text{TODGA}}_n{}_{\left(\text{org}.\right)}$ (5)

The extraction equilibrium concentration constant, $K_{\text{ex}}$, is described as Eq. (6): $K_{\text{ex}}=\frac{{[\text{Eu}{\left({\text{NO}}_3\right)}_3{\text{TODGA}}_n]}_{\left(\text{org}.\right)}}{{[{\text{Eu}}^{3+}]}_{\left(\text{aq},\right)}{[{\text{NO}}_3^{-}]}_{\left(\text{aq}.\right)}^3{\left[\text{TODGA}\right]}_{\left(\text{org}.\right)}^n}$ (6)

The distribution ratio, $D_{\text{Eu}}$, is defined as Eq. (7): $D_{\text{Eu}}=\frac{{[\text{Eu}{\left({\text{NO}}_3\right)}_3{\text{TODGA}}_n]}_{\left(\text{org}.\right)}}{{[{\text{Eu}}^{3+}]}_{\left(\text{aq}.\right)}}$ (7)

Equation (7) was substituted into Eq. (6), and Eq. (6) was then transformed into a logarithmic form to obtain Eq. (8). $\log D_{\text{Eu}}=\log K_{\text{ex}}+\text{nlog}{\left[\text{TODGA}\right]}_{\left(\text{org}.\right)}+3\log {\left[{\text{NO}}_3^{-}\right]}_{\left(\text{aq}.\right)}$ (8)

The n value can be calculated from Eq. (8), which represents the average number of TODGA coordinated to one metal ion. The plot in Fig. 4 of $\log D_{\text{Eu}}$ – $\log {\left[\text{TODGA}\right]}_{\left(\text{org}.\right)}$ at a constant aqueous solution of 3.0 mol/L HNO₃ shows that the slope is 3.10 ± 0.11, which indicates that Eu(III) would form complexes with three TODGA molecules.

Fig. 4Full-screen View

(Color online) Plot of $\log D_{\text{Eu}}$ versus $\log {\left[\text{TODGA}\right]}_{\left(\text{org}.\right)}$ at a constant aqueous 3.0 mol/L HNO₃ solution (x: $\log {\left[\text{TODGA}\right]}_{\left(\text{org}.\right)}$, y: $\log D_{\text{Eu}}$)

Complexation studies were also performed with TODGA and Eu(III) using fluorescence titration. Figure 5 displays the normalized fluorescence emission spectra with different ratios of Eu(III) and TODGA resulting from the transitions of 5D₀→7F₁ and 5D₀→7F₂. The transition of 5D₀→7F₁ at 593 nm, owing to the magnetic-dipole transition, was considered independent of the ligand field. The transition of 5D₀→7F₂ at 617 nm owing to the electric–dipole transition is considered to be hypersensitive to the ligand field, and its intensity depends on the coordination symmetry around the metal ions [50]. With the addition of the TODGA ligand, the change in the ligand field led to a gradual transformation of the single peak at 617 nm into a double peak, which was finally formed at M: L = 1:3. This indicated that the inner coordination sphere of Eu(III) was gradually occupied by TODGA with the addition of the ligand, which is similar to some results from the literature [51, 52].

Fig. 5Full-screen View

(Color online) Normalized Eu(III) emission spectra as a result of the transitions of 5D₀→7F₁ and 5D₀→7F₂ for the complexation of Eu(III) with increasing TODGA in acetonitrile

The spectra of each component were obtained from the fluorescence emission spectra (Fig. 6). The [Eu(TODGA)_n]³⁺ (n = 1 – 3) complexes and Eu(III) solvent species were also discovered. No complexes with TODGA values greater than or equal to 4 were found in the fluorescence emission spectra, proving that the ratio of Eu(III) to TODGA equals 1:3.

Fig. 6Full-screen View

(Color online) Single-component spectra of the [Eu(TODGA)_n]³⁺ complexes (n = 1 – 3) and Eu(III) solvent species

The slope value was disputable, although many studies showed that the Ln(III): DGA structures are 1:3 complexes. Antonio et al. elucidated the inner coordination sphere of Eu(III) and TODGA using X-ray absorption spectroscopy (XAS)[53]. One ether O atom and two carbonyl O atoms of a TODGA molecule make up each ligand's tridentate to Eu(III). The coordination number is nine, with twelve distant carbon neighbors, six closest ones from carbonyl carbon atoms, and six slightly farther ones from the ether carbon atoms. Turanov et al.[54] found that the calculated slope value of Eu(III) extracted by TODGA in n-decane containing 0.002 mol/L dinonylnaphtalene sulfonic acid (HDNNS) was 3.28 ± 0.04. This was estimated by the plot of logD_Eu – log[TODGA] and the existence of EuL_n(NO₃)₃ species by the slope of logD_Eu – log[HNO₃], which was equal to 2.86 ± 0.08. Pathak et al.[55] investigated the influence of solvent type, acidity of extraction, and concentration of TODGA on luminescence lifetime and found that various ratios of TODGA to Eu ions resulted in the formation of Eu(TODGA)₃³⁺ species when Eu(III) was complexed with TODGA. According to the findings of Sasaki et al.[56], extracted Eu(III) complexes require three or four TODGA molecules and three nitrate ions to maintain stability in non-polar diluents by slope analysis. Zhu et al.[57] performed a slope analysis of TODGA to extract some Lns(III) and found that the slope was 3.9 for Eu(III), suggesting that the M(TODGA)₄(NO₃)₃ species finally formed. However, in this work, a 1:3 complexation ratio for TODGA with Eu(III) was determined.

The theoretical $D_{\text{Eu}}$ values at different concentrations of TODGA can also be obtained using Eq. (8). Equation (9) is obtained by linear fitting, as shown in Fig. 4. $\text{log}{D}_{\text{Eu}}=3.10\text{ log}{\left[\text{TODGA}\right]}_{\left(\text{org}.\right)}+6.75$ (9)

Equation (10) can be obtained from Fig. 1 for irradiated HNO₃-TODGA/nDD. It is an exponential radiolysis equation for the concentration of TODGA and the absorbed dose. $\frac{C_{\text{TODGA}}}{C_{\text{TODGA}}^0}=e^{-2.20\times {10}^{-3}R}$ (10)

We can obtain Equation (11) for $D_{\text{Eu}}$ and the absorbed dose by substituting Eq. (10) into Eq. (9). This empirical equation enables us to construct a mathematical relationship between the $D_{\text{Eu}}$ and absorbed dose in this system. $\log D_{\text{Eu}}=-2.965\times {10}^{-3}R+4.583$ (11)

The theoretical $D_{\text{Eu}}$ with absorbed doses ranging from 50 to 500 kGy was obtained using Eq. (11). As shown in Fig. 7, the experimental $D_{\text{Eu}}$ was higher than the theoretical $D_{\text{Eu}}$ after irradiation, particularly at a high absorbed dose above 300 kGy for the HNO₃-TODGA/nDD system. The experimental $D_{\text{Eu}}$ is close to the theoretical $D_{\text{Eu}}$ below 300 kGy, indicating that the decrease in $D_{\text{Eu}}$ is mainly related to the loss of TODGA concentration, with a slight influence from radiolytic products.

Fig. 7Full-screen View

Experimental $\log D_{\text{Eu}}$ and theoretical $\log D_{\text{Eu}}$ after irradiation for HNO₃-TODGA/nDD

Because some radiolytic products remained in coordination structures similar to those of TODGA, such as P₁ and P₂, which were identified by UPLC-QTOF, the complexation of radiolytic products on Eu(III) was investigated further using DFT calculations.

Theoretical calculations of complexation of TODGA and radiolytic products with Eu(III)

According to the slope and fluorescence titration analyses, the Eu(III): TODGA stoichiometry was 1:3. In addition, Kimberlin et al.[58] reported that several radiolytic products with the TODGA skeleton are involved in heteroleptic complexes with TODGA with a stoichiometry of 1:3 from the ESI-MS spectra. The time-resolved laser fluorescence results showed no change in the peak shape of the fluorescence spectra before and after irradiation (Fig. S11). However, the fluorescence lifetime gradually decreased with increasing absorbed dose (Fig. S12), indicating that γ radiation did not change the M: L ratio of 1:3 but caused a slight partial change in the original fluorescent species.

DFT calculations were employed to investigate the coordination abilities of TODGA and its radiolytic products with TODGA skeletons (P₁ and P₂). Figure 8 shows the optimized structures of the complexes formed by Eu(III) and the ligands. Theoretical calculations were performed for the [Eu(TODGA)₂(P_n)]³⁺ (n = 1 – 2) species and [Eu(TODGA)₃]³⁺ complexes. It is realistic that one TODGA molecule in the initial complex is replaced by one radiolytic product to form mixed Ln-radiolytic product-TODGA complexes during γ irradiation, which was already found in the ESI-MS spectra by Kimberlin et al. [58]. In addition, we investigated the optimized structures and coordination abilities of [Eu(Pn)₃]³⁺ (n = 1 – 2), which were formed using three radiolytic products to represent a more extreme coordination environment of Eu(III) after γ irradiation.

Fig. 8Full-screen View

(Color online) Optimized structures of the ligands (TODGA, P₁ and P₂) and complexes formed by Eu(III); the ligands (light pink, blue, green, red, and white spheres represent Eu(III), N, C, O, and H, respectively).

The changes in the Gibbs free energy, entropy, and enthalpy for the complexes formed by the ligands (TODGA, P₁ and P₂) and Eu(III) are shown in Table 3. It can be seen that the formation of [Eu(TODGA)₃]³⁺ complex has more negative ΔG in the gas phase (–2527.3 kJ/mol) and in the nDD phase (–1115.0 kJ/mol) than that of the [Eu(TODGA)₂(P_n)]³⁺ and [Eu(P_n)₃]³⁺ (n = 1– 2) complexes in the two phases. Moreover, the coordination abilities of the radiolytic products of TODGA decreased, as reflected by the changes in the Eu–O bond length (Table 4). The average Eu – O bond length of the complexes changed from 2.4911 Å ([Eu(TODGA)₃]³⁺) to 2.5000 Å ([Eu(P₂)₃]³⁺), indicating a decline in the coordination ability of the complex. These results indicate that TODGA shows better coordination ability than the radiolytic products of TODGA; the complexation order is TODGA > P₁ > P₂. However, the formation of the [Eu(TODGA)₂(P_n)]³⁺ and [Eu(P_n)₃]³⁺ complexes (n = 1 – 2) had a high negative ΔG in the two phases. Theoretical calculations also indicated that the radiolytic products of TODGA, such as P₁ and P₂, still maintain a good coordination ability with Eu atoms, proving that the radiolytic products retain partial complexation for Eu(III). Consequently, the experimental $D_{\text{Eu}}$ of TODGA was higher than the theoretical $D_{Eu}$ from the loss of TODGA with the increase in radiolytic products at a high absorbed dose. Furthermore, if the contents of P₁ and P₂ are determined exactly, by combining the TODGA contents, we can predict the $D_{\text{Eu}}$ of the irradiated TODGA/nDD system more precisely. This study will be conducted in future works. In our previous experiments, we found that the radiolytic products P₁ and P₂ were difficult to synthesize, and the radiolytic product P₁ was not sufficiently stable. Therefore, we used DFT calculations to evaluate the coordination abilities of these radiolytic products, thereby justifying the experimental result that the experimental $D_{\text{Eu}}$ was higher than the theoretical $D_{\text{Eu}}$ due to the high dose TODGA losses in this study.

In conclusion, by combining the exponential equation for the radiolysis kinetics of TODGA in nDD and the equation for slope analysis of the concentration of TODGA and D_Eu, we can derive a mathematical equation that includes the absorbed dose and D_Eu, which could be used to predict the extraction performance at low absorbed doses. This method can be used to study other extractant systems. This work provides in-depth insights into the effect of γ irradiation on the extraction behavior of the TODGA/nDD system and provides useful information on the use of nuclear fuel reprocessing.