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An Insight into Third-Phase Formation during the Extraction of Thorium Nitrate: Evidence for Aggregate Formation from SmallAngle Neutron Scattering and Validation by Computational Studies P. K. Verma,† P. N. Pathak,*,† P. K. Mohapatra,† V. K. Aswal,‡ B. Sadhu,§ and M. Sundararajan¶ †

Radiochemistry Division, ‡Solid State Physics Division, §Radiation Safety Systems Division, and ¶Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India ABSTRACT: Small-angle neutron scattering (SANS) studies were carried out to compare the aggregation behavior of 1.1 M solutions of tributyl phosphate (TBP) and N,N-dihexyl octanamide (DHOA) dissolved in different deuterated diluents, viz., n-dodecane, chloroform, and benzene, during the extraction of Th(IV) from nitric acid medium. The scattering data was treated using the Baxter sticky spheres model. The third phase formed in the case of DHOA displayed higher aggregation tendency compared to that of TBP. These studies have demonstrated that the nature of the diluents plays an important role in the aggregation behavior of the extracted species (reverse micelles). No third phase was observed in the case of chlorinated and aromatic diluents like chloroform and benzene during the extraction of Th(IV) from nitric acid medium. Theoretical calculations were also performed to gain insights into the binding of thorium nitrate with TBP and DHOA models. These calculations suggest that two to three molecules of both DHOA and TBP strongly coordinate to Th(NO3)4. It is noted that the highly charged Th(IV) cations are screened by nitrates and extractants which enables the interaction of second unit of such complex through noncovalent interactions.

1. INTRODUCTION Third-phase formation during liquid−liquid extraction of metal species from acidic solutions often takes place when the concentration of the tetravalent metal ions such as Th(IV), Zr(IV), and Pu(IV) or that of the mineral acid exceeds the solubility limit in the organic phase and the organic phase splits into two layers.1−3 This phenomenon has significant consequences in hydrometallurgical operations and is of particular concern in nuclear industry due to associated criticality hazards. In view of its extensive use in hydrometallurgical applications, tri-n-butyl phosphate (TBP) dissolved in n-dodecane system has been extensively evaluated for third-phase formation studies. In addition to TBP, several other organophosphorus extractants have been evaluated for third-phase formation behavior under different experimental conditions.4−10 Reprocessing experiences have led to the identification of certain problems associated with the use of TBP such as high aqueous solubility, interference of degradation products during stripping of Pu/U, poor decontamination factor (DF) values of Pu/U with respect to fission products, and the generation of large volumes of secondary (phosphate) wastes. These problems are of particular concern for the reprocessing of short-cooled fast reactor and thorium-based spent fuels.11,12 In view of these limitations, studies have been carried out on identifying alternative extractants of TBP to alleviate at least some of these problems. In this context, N,N-dialkyl amides have been identified as promising alternatives of TBP for spent fuel reprocessing.13−16 Based on extensive studies, straight chain N,N-dihexyl octanamide (DHOA) was identified as an alternative of TBP for selective recovery of U and Pu from © 2013 American Chemical Society

three-component (U, Pu, and Th) Advanced Heavy Water Reactor (AHWR) spent fuel dissolver solutions.17,18 In addition, studies were also carried out to optimize the conditions for the recovery of ∼100 g/L (0.431 M) Th(IV) from AHWR raffinate solutions.19 During Th recovery, thirdphase formation studies are of interest in view of the large concentrations of Th(IV) in the raffinate solutions. In third-phase-formation studies, generally efforts have been focused on understanding the composition of the species present in the heavy organic phases (HOP) and diluent-rich light organic phases (LOP) and relatively little information is available on structural aspects for different extractant systems. The formation of HOP at the interface has been conventionally attributed to the limited solubility of the extracted metal− ligand complexes in nonpolar diluents. However, the use of polar diluents or phase modifiers dissolves the HOP and the third-phase formation can be prevented. Attempts have also been made to explain the third-phase-formation tendency in solvent extraction systems by invoking the similarities between extractant and surfactant molecules as both possess hydrophilic and hydrophobic ends. The functional groups in extractant molecules are responsible for hydrophilic nature as it binds with the metal ions while the long-chain alkyl substituents make the other end hydrophobic in nature and it takes the metal complex from aqueous−organic interface to the bulk of organic diluents. It suggests that the extractant molecules possess surface-active Received: June 27, 2013 Revised: July 26, 2013 Published: July 29, 2013 9821

dx.doi.org/10.1021/jp4063548 | J. Phys. Chem. B 2013, 117, 9821−9828

The Journal of Physical Chemistry B

Article

incident neutron beam is 5.2 Å, which has a wavelength resolution of ∼15%. The scattering wave vector (Q) range of the diffractometer is 0.017−0.35 Å−1. SANS technique deals with the scattering of a monochromatic beam of neutrons from the sample, and the scattered neutron intensity is measured as a function of the scattering angle. Generally, one measures the differential scattering cross section per unit volume (dΣ/dΩ) as a function of Q. The sample is taken in the form of a plate to maintain a uniform thickness for the beam area as a function of scattering vector. The measured intensity, I(Q), is normalized to the differential scattering cross section dΣ/dΩ(Q) using a standard procedure.35 This technique has been found useful for studying the material structure of sizes in the range of 10−200 Å. The following two models were employed to analyze the changes in scattering intensities of organic samples under different experimental conditions: (1) growth of noninteracting particles (spherical/ellipsoidal model); (2) interaction between small particles (Baxter model). For a miceller system dispersed in a medium, dΣ/dΩ(Q) can be expressed as

properties which help in the transfer of the metal ions from the aqueous phase to the organic phase.20−33 These studies have used advanced spectroscopic techniques such as visible/IR spectroscopy, small-angle neutron scattering (SANS), and extended X-ray absorption fine structure (EXAFS) to explain the phenomenon of third-phase formation. Based on these studies, two models have been put forward to explain the phenomenon of third-phase formation: (i) particle growth model, due to the extensive aggregation or polymerization of the metal−extractant complexes leading to the growth of large size aggregates, i.e., large micellar aggregation number (N),31 and (ii) Baxter sticky spheres model due to increasingly longranged spatial correlations between small micelles due to attractive intermicellar interactions.20−30 Whereas high metal loadings in the organic phases can promote polymerization by bridging functional groups of different extractant molecules, the surface adhesion of hard spheres was attributed to the van der Waals forces between the polar cores of the reverse micelles. In this paper, SANS experiments have been carried out to compare the third-phase formation/aggregation behavior of 1.1 M DHOA vis-à-vis 1.1 M TBP dissolved in different diluents such as n-dodecane, chloroform, and benzene during the extraction of Th(IV) from nitric acid medium.

dΣ (Q ) = n(ρp − ρs )2 V 2P(Q )S(Q ) dΩ

where n is the number density of the particles, ρp and ρs are respectively the scattering length densities of the particle and the solvent, and V is the volume of the particle. P(Q) is the intraparticle structure factor and is decided by the shape and size of the particle. S(Q) is the interparticle structure factor, which depends on the spatial arrangement of particles and is thereby sensitive to interparticle interactions. In the case of dilute solutions, interparticle interference effects are negligible (S(Q) ∼ 1), and, therefore, eq 1 takes the following form:

2. EXPERIMENTAL SECTION 2.1. Materials. DHOA used in this work was synthesized in our laboratory by following a reported method.16 Deuterated dodecane (dodecane-d26, 98 atom % D, Aldrich), benzene (C6D6 99.8%, Merck), and chloroform (CDCl3 99.9%, Merck) were used as received. Sample solutions (1.1 M TBP/DHOA) were prepared by dissolving their required quantities in deuterated diluents. These diluents were used to get a better contrast for the aggregates formed in this study. Stock solutions of Th(IV) (0.215 and 0.862 M) at 4 M HNO3 were prepared by dissolving the required weight of Th(NO3)4·5H2O in a suitable nitric acid medium and adjusting to the desired acidity. Thorium and nitric acid concentrations were determined by EDTA (ethylenediaminetetraacetic acid) complexometric and alkalimetric titrations, respectively. The organic phases were equilibrated with Th(IV) solutions (0.215 and/or 0.862 M at 4 M HNO3), centrifuged, and separated from aqueous phases. Table 1 provides the details of the organic samples used for SANS studies. 2.2. SANS Measurements. These measurements were carried out using a SANS diffractometer facility at Dhruva reactor, BARC, Trombay.34 The mean wavelength of the

dΣ (Q ) = n(ρp − ρs )2 V 2P(Q ) dΩ

a b

details

[Th]org, M

1 2 3 4 5 6 7 8

TBP: diluent richb DHOA: diluent richb TBP: third phaseb DHOA: third phaseb TBP: no third phasea DHOA: no third phasea 1.1 M TBP/n-dodecane 1.1 M DHOA/n-dodecane

0.030 0.017 0.733 0.250 0.138 0.073 − −

(2)

P(Q) for a spherical particle of radius R is given by ⎡ 3{sin(QR ) − QR cos(QR )} ⎤2 P(Q ) = ⎢ ⎥ ⎦ ⎣ (QR )3

For prolate ellipsoidal, P(Q) is given by P(Q ) =

∫0

F(Q , μ) =

Table 1. Details of the Samples Used for the SANS Measurements: Organic Phase(s), 1.1 M TBP/1.1 M DHOA Solutions in n-Dodecane; T = 25 °C sample no.

(1)

1

[F(Q , μ)2 dμ]

3(sin x − x cos x) x3

x = Q [a 2μ2 + b2(1 − μ2 )]1/2

(3)

(4) (5)

where a and b are the semimajor and semiminor axes of the ellipsoidal micelle, respectively, and μ is the cosine of the angle between the directions of a and the wave vector transfer, Q. The value of S(Q) is calculated assuming attractive interaction between the particles using Baxter’s sticky hard-sphere model. In this model, particles interact via a thin attractive square-well potential of depth U0 ( < 0) and width Δ. The basic results of the model are derived as the lowest order solution of the Ornstein−Zernike equation and Percus−Yevick closure relation. The expression for the structure factor is generally given by

Prepared by contacting with 0.215 M Th(IV) solution at 4 M HNO3. Prepared by contacting with 0.862 M Th(IV) solution at 4 M HNO3.

S −1(Q ) = A2 (Q ) + B2 (Q ) 9822

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⎛ s(k) − kc(k) 1 − c(k) A(Q ) = 1 + 12η⎜α +β ⎝ k3 k2 λ s (k ) ⎞ − ⎟ 12 k ⎠

(7)

⎛ ⎡1 s (k ) 1 − c(k) ⎤ B(Q ) = 12η⎜α⎢ − 2 + ⎥ ⎝ ⎣ 2k k k3 ⎦ ⎡1 s (k ) ⎤ λ 1 − c(k) ⎞ + β⎢ − 2 ⎥ − ⎟ ⎣k k ⎠ k ⎦ 12

(8)

clearly observed in terms of Th(IV) concentration in thirdphase samples in the current study. Figures 1 and 2 show the

where s(k) ≡ sin(k), c(k) ≡ cos(k), k ≡ Q(σ + Δ), and α=

1 + 2η − μ′ , (1 − η)2

β

−3η + μ′ , (1 − η)2

6 [δ − (δ 2 − v)1/2 ], η 1 + η /2 ν=η 3(1 − η)2

λ′ =

δ=τ+

μ′ = λ′η(1 − η) Figure 1. SANS data for 1.1 M TBP solution in deuterated ndodecane.

η , 1−η

The parameter η = πn(σ + Δ)3/6 is the effective “volume fraction” which includes the potential width Δ. The stickiness parameter (τ) is related to the potential parameters (u0, Δ, σ) and temperature, T, as τ=

σ+Δ exp(U0/kBT ) 12Δ

where kB is Boltzmann’s constant. For the particle interaction model calculations, the parameters used were diameter of the micelles (σ), width of the square-well attraction potential (Δ), depth of square-well potential (U0), and stickiness parameter (τ). When the distance between two particles is larger than σ but smaller than σ + Δ, the particles experience attraction. An important advantage of the Baxter model approximation is that analytical expressions have been derived for the structure factor S(Q). 2.3. Computational Details. In conjunction to the experimental work, electronic structure calculations were also performed to understand the binding of Th(NO3)4 with TBP and DHOA extractants. Density functional theory (DFT) based calculations using dispersion corrected BP86 functional (D3 correction) with def2-SV(P) basis set is used for geometry optimizations and energy evaluations using ORCA 2.9 quantum chemical package.36−39 During this calculation, effective core potential with 60 core electrons was used for Th, while the valence electrons are described by the def2-SV(P) basis set. This work may provide a better insight into the understanding of role of diluents during the third-phase formation for the chosen extractants with particular reference to the thorium fuel cycle being pursued in India.

Figure 2. SANS data for 1.1 M DHOA solution in deuterated ndodecane.

variation in the differential scattering cross section per unit volume (dΣ/dΩ) as a function of scattering vector, Q, for the two solvents (i.e., 1.1 M TBP and 1.1 M DHOA solutions in ndodecane) under different experimental conditions, viz., (a) fresh solvent (without equilibration with Th(IV) solutions in 4 M HNO3), (b) diluent-rich phase and the third phase (obtained after contact with 0.862 M Th at 4 M HNO3), and (c) extract with no third phase (obtained after contact with 0.215 M Th at 4 M HNO3). It is evident that even though the two solvents have been treated with thorium solutions under identical conditions, the two solvents differ in their compositions. The following observations indicate that the two solvents display distinctly different features in their SANS measurements. 3.1.1. TBP/n-Dodecane System. The dΣ/dΩ values for fresh solvent and third phase (containing 0.733 M Th) are comparable, suggesting that there is no swelling of the micelles due to interparticle attraction. The diluent molecules are expected to be expelled from the vicinity of the extracted species in the presence of large concentrations of Th. However, the dΣ/dΩ values for loaded organic phase, containing 0.138 M Th(IV) and without third phase, are significantly higher due to intermiceller interaction leading to swelling in the size of the Th solvated species in n-dodecane. This self-assembly of extracted species results in the formation of large (spherical/ ellipsoidal) aggregates. On the other hand, the diluent-rich organic phase showed no such strong interaction leading to

3. RESULTS AND DISCUSSION 3.1. Studies with n-Dodecane as the Diluent. The SANS studies were carried out using 1.1 M TBP and 1.1 M DHOA solutions prepared in deuterated n-dodecane (dielectric constant, ε = 2.0 at 20 °C) medium. Our previous studies under identical experimental conditions have shown that the volume of the third phase formed in the case of 1.1 M TBP/ndodecane is relatively lower than that of the 1.1 M DHOA/ndodecane system.33 Typically, the volume of the third phase in the case of DHOA was ∼2.2 times of that of TBP. This is 9823



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By contrast, the particle growth model does not differentiate between the extractant and the diluent molecules. There is a significant enhancement in τ−1 values for thorium-loaded organic phases (diluent rich, without/with third phase) as compared to the corresponding fresh solvents. This indicates an increase in the short-range attractive forces between the polar core of the reverse micelles due to dipole−dipole interactions. Therefore, the critical τ−1 value under the conditions of this study can be ∼5. The third phases exhibit τ−1 values of 8.3 (sample no. 3, Th−TBP system), and of 12.8 (sample no. 4, Th−DHOA system), while the corresponding diluent-rich phases have τ−1 values of 10.5, and 11.6, respectively. The τ values of different samples were used to calculate the attractive potential energy (U0) in kBT units. It is evident that the attractive potential energies are substantially higher compared to the fresh solvents. The reverse micelles are subjected to two opposing physical forces: (a) the thermal energy (kBT) keeps the micelles dispersed in the diluents; (b) the intermicellar attraction energy compels the micelles to stick together. The organic phase will be stable as long as these two opposing forces are balanced, else aggregation takes place. This study, however, shows an interesting finding for TBP and DHOA systems. The attractive potential energy (kBT) values for either TBP or DHOA system for the diluent-rich phase and for third phase are comparable, i.e., −1.31, −1.36 (for TBP), and −2.17, −2.13 (for DHOA). However, the kBT values are higher for DHOA compared to TBP. On the other hand, the Th-loaded phases (without third phase, samples no. 5 and 6) have comparable (kBT) values. 3.2. Studies in Aromatic and Chlorinated Diluents. Third-phase formation is mainly observed in aliphatic diluents and has not been reported for aromatic diluents like benzene. This behavior has been attributed to their easy polarizability and they can interact with the metal−ligand solvate significantly and contribute to an increased solubility in organic phase.1,40,41 Even though the dielectric constant values for benzene and chloroform are not very much different from that of ndodecane, no third phase was observed during the extraction of thorium using these diluents under the conditions of the present study. Therefore, SANS measurements were also performed on 1.1 M TBP and 1.1 M DHOA solutions prepared in CDCl3 (dielectric constant = 4.8 at 20 °C) and C6D6 (dielectric constant = 2.3 at 20 °C) diluents to understand the influence of the polarity of diluents on thirdphase formation during Th(IV) extraction from 4 M HNO3 medium. Table 4 provides the sample details along with the

smaller values of differential scattering cross section per unit volume. 3.1.2. DHOA/n-Dodecane System. The dΣ/dΩ values for the third phase (containing 0.250 M Th) are maximum due to attractive micellar interaction and indicating the presence of some diluent molecules in the vicinity of the extracted species. This is reflected in the relative volumes of the third phases for the two solvent systems. The scattering cross sections of the organic phases with 0.017 M Th (diluent-rich phase) and 0.073 M Th (extract with no third phase) are comparable and display relatively less swelling as compared to that of the third phase. Fresh solvent, in the absence of HNO3/Th, will not form reverse micelles and hence there will be no aggregation. Table 2 Table 2. Aggregation Number (N) Calculation on Different Samples Using Particle Growth Model: Organic Phase(s), 1.1 M TBP/1.1 M DHOA Solutions in n-Dodecane; T = 25 °C sample no.

geometry

1 2 3 4 5 6 7 8

spherical ellipsoidal spherical ellipsoidal ellipsoidal ellipsoidal spherical spherical

dimension(s) R = 12.73 Å a = 77.11 Å, R = 12.44 Å a = 52.77 Å, a = 65.68 Å, a = 35.42 Å, R = 11.94 Å R = 9.27 Å

b = c =10.41 Å b = c =9.37 Å b = c =9.98 Å b = c = 6.45 Å

volume, Å3

N

8640 34996 8063 19403 27397 6171 7129 3336

19 58 18 33 60 10 16 6

shows that when data treatment is done considering only the particle growth model and neglecting the interactions among the reversed micelles, the aggregation number (N) is significantly large. It is hard to visualize the growth of the particles with such large values of n even in the samples having third phases due to high metal loadings. This suggests that the simple aggregation model does not provide a valid explanation of the third-phase formation. The scattering data, therefore, was interpreted using the Baxter sticky spheres model which involves surface adhesion. Table 3 lists the aggregation number Table 3. Aggregation Number (N) Calculation on Different Samples Using Baxter’s Sticky Spheres Model: Organic Phase(s), 1.1 M TBP/1.1 M DHOA Solutions in nDodecane; T = 25°C sample no.

radius, Å

N

stickiness parameters, 1/τ

potential energy, U0/ kBT

1 2 3 4 5 6 7 8

8.4 12.2 6.9 10.3 11.1 9.5 7.9 7.2

5 13 3 8 13 6 4 3

10.5 11.6 8.3 12.8 12.2 12.7 4.8 3.5

−1.31 −2.17 −1.36 −2.13 −2.19 −2.01 −0.91 −0.50

Table 4. Aggregation Number (N) Calculation on Different Samples Using Baxter’s Sticky Spheres Model: Organic Phase(s), 1.1 M TBP/1.1 M DHOA Solutions in Chlorinated/Aromatic Diluents (CDCl3 and C6D6); T = 25°C

(N) of extractant molecules calculated after treating the scattering data using the Baxter model. The aggregation numbers of all the samples were much lesser than that provided by the ellipsoidal model. It is evident that this model provides better data treatment, and the decrease in the aggregation number (N) in third-phase samples is attributed to the presence of n-dodecane molecules in different pockets. 9824

sample no.

sample details

1 2 3 4 5 6 7 8

1.1 M TBP/CDCl3 Th-loaded 1.1 M TBP/CDCl3 1.1 M TBP/C6D6 Th loaded 1.1 M TBP/C6D6 1.1 M DHOA/CDCl3 Th-loaded 1.1 M DHOA/CDCl3 1.1 M DHOA/C6D6 Th-loaded 1.1 M DHOA/C6D6

[Th]org, M radius, Å − 0.167 − 0.245 − 0.079 − 0.118

10.5 13.4 7.6 4.8 12.0 11.9 8.5 5.3

N 11 22 4 1 12 12 4 1



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medium, the attractive forces are responsible for sticking them together. It appears that both CDCl3 and C6D6 prevent the swollen reverse micelles from reaching the level of intermicellar attraction energy required for third-phase formation. The organic phase will be stable when the two opposing forces are balancing each other, else third-phase formation takes place when the attractive forces become stronger. 3.3. Computational Studies. The optimized structure of thorium nitrate [Th(NO3)4]0 (Figure 5) is conforming to the

aggregation number (N) of the extractant molecules having different Th(IV) concentrations. It is obvious that the two extractants vary significantly with respect to Th(IV) concentration in CDCl3 and C6D6 diluents. It is important to mention that no third phase was noticed during the extraction of Th(IV) from 4 M HNO3 medium using these chlorinated/aromatic diluents. Figures 3 and 4 show the variation in the differential

Figure 3. SANS data for 1.1 M TBP solution in C6D6 and CDCl3 diluents without/with equilibration with 0.862 M Th at 4 M HNO3.

Figure 4. SANS data for 1.1 M DHOA solution in C6D6 and CDCl3 diluents without/with equilibration with 0.862 M Th at 4 M HNO3.

scattering cross section per unit volume (dΣ/dΩ) as a function of scattering vector, Q, for the samples prepared under the conditions of this experiment. Similar to the n-dodecane system, the scattering data was interpreted using the Baxter sticky spheres model based on the attractive interaction of the extracted species. It is interesting to note that the aggregation number (N) is higher for both extractants in the case of CDCl3 as compared to that of C6D6. This suggests that the diluent molecules are playing a role in holding the extracted species and are being expelled from the vicinity of the two neighboring species.1,40,41 This study demonstrates that diluents with small difference in dielectric constants values behave differently with respect to their third-phase formation behavior. Even though there is no third-phase formation in CDCl3 medium, the aggregation number (N) is significantly higher as compared to those of C6D6 and deuterated dodecane. The absence of third phase in the case of C6D6 suggests that it is effectively solublizing the extracted species but unable to act as bridge between different extracted species. As discussed earlier, two opposing physical forces, viz., the thermal energy (kBT) and the energy of intermicellar attraction, are responsible for holding the extracted species (micelles) in the diluent phase. Whereas the thermal energy helps in the dispersion of micelles in the

Figure 5. Optimized structures (Å) of TMP and DMAA to Th(NO3)4 at BP86/def2-SV(P) level.

reported EXAFS measurements.42 Thorium is bound by nitrate groups in D4h symmetry with eight occupied coordination sites. However, the coordination number of Th(IV) can extend up to 12−14 and therefore it can further accommodate additional ligands. In this context, the structures and relative binding affinities of TBP and DHOA molecules to Th(NO3)4 were 9825



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some insights into the third-phase formation behavior of these ligands during the extraction of Th(IV) from nitric acid medium. The computation of the interaction energies was carried out using both truncated and full-sized models (TBP and DHOA) in the presence of long-chain hydrophobic residues. Whereas the full-sized model showed that dimer formations are strongly favorable for both DHOA (−21.70 kcal mol−1) and TBP (−22.24 kcal mol−1) ligands, the corresponding energies using the truncated models were −8.11 kcal mol−1 (TMP) and −1.57 kcal mol−1 (DMAA), respectively. Further, we have tested the chain size for one molecule addition of long chain DHOA and TBP to Th(NO3)4. We find that the overall binding energy is larger (by 15 kcal mol−1) as compared to truncated models (Figure 6). In addition, we have computed the interaction energy of Th(NO3)4·TBP with another TBP. Interestingly, we find that such interactions are very strong (∼14 kcal mol−1 for TBP and ∼10 kcal mol−1 for DHOA). Thus, the full-sized model clearly shows that strong interaction present between the complexed species may be responsible for third-phase formation. These studies suggest that both extractants strongly coordinate with Th(NO3)4 and thereafter the highly charged Th(IV) cation is screened by nitrates and extractants molecules (Figure 6). It is noted that a second molecule of such a complex can interact very strongly through noncovalent interactions which is responsible for the thirdphase formation.

calculated using dispersion-corrected DF. Due to the larger size of the extractants, both TBP and DHOA molecules are truncated as trimethyl phosphate (TMP) and dimethyl acetamide (DMAA) to ease the computational cost. Table 5 Table 5. Calculated Binding Affinity (kcal mol−1) of TMP and DMAA Extractants with the Th(NO3)4 Complex reaction with TMA/DMAA [Th(NO3)4] + TMA → [Th(NO3)4.TMA] [Th(NO3)4·TMA] + TMA → [Th(NO3)4.(TMA)2] [Th(NO3)4·(TMA)2] + TMA → [Th(NO3)4·(TMA)3] [Th(NO3)4·(TMA)3] + TMA → [Th(NO3)4.(TMA)4] [Th(NO3)4] + DMAA → [Th(NO3)4·DMAA] [Th(NO3)4·DMAA] + DMAA → [Th(NO3)4·(DMAA)2] [Th(NO3)4·(DMAA)2] + DMAA → [Th(NO3)4· (DMAA)3] [Th(NO3)4.(DMAA)3] + DMAA → [Th(NO3)4· (DMAA)4]

binding energies −42.1 −89.9 −120.9 −138.7 −42.1 −82.6 −106.8 −115.3

compares the relative binding energies of TMP and DMAA molecules with Th(NO3)4 complex. It is evident that sequential binding of TMP molecules with Th(NO3)4 complex is energetically favorable and phosphoryl oxygen of TBP interacts strongly with Th (2.3−2.4 Å). However, gradual addition of TMP molecules relatively weakens the bond and the addition of the fourth TMP molecule to Th further extends the bond distance (Figure 5). Nevertheless, the binding affinity increases with the addition of four TMP molecules to Th(NO3)4 complex. Similar calculations were carried out for the binding of DMAA to Th(NO3)4 complex using the truncated model (Figure 6). The binding energy and bond lengths of one

4. CONCLUSIONS SANS studies on TBP and DHOA solutions in different diluents suggest that the two extractants behave differently with respect to the interactions of their reverse micelles, leading to different scattering cross sections and aggregation numbers. The third-phase formation is essentially guided by the solubility of the extracted complex species formed between Th(IV)/ HNO3 molecules and the extractant molecules TBP or DHOA (in the present work). The SANS experiments suggested that third-phase formation takes place due to aggregation of the reversed micelles formed in the diluent phase. There will be a progressive increase in the aggregate size till the third-phase formation is achieved. The SANS data analysis using particle growth model for third-phase formation during the extraction of Th(IV) by 1.1 M TBP or 1.1 M DHOA solutions in ndodecane led to unexpectedly high aggregation numbers. On the other hand, the consideration of particle interaction using the Baxter sticky spheres model provided more consistent results. These observations have been further supported by electronic structure calculations. Our theoretical predictions of relative binding energies of TBP and DHOA molecules with Th(NO3)4 complex suggest that their sequential binding is energetically favorable and two to three molecules can be easily accommodated around the metal ion. The interaction energies for dimer formation between the complexed species indicate existence of noncovalent interactions which may be responsible for third-phase formation.

Figure 6. Optimized structures of TBP and DHOA to Th(NO3)4.

DMAA molecule with Th(NO3)4 complex are comparable to that of TBP (Figure 5, Table 5). An incremental addition of DMAA to Th increases the overall binding affinity up to four DMAA molecules. However, the addition of the fourth DMAA molecule is somewhat loosely bound to Th (>4 Å), although the overall binding affinity of the complex increases (Table 5). A similar effect is also observed for the TBP−Th system. It should be noted that both the extractants are large and therefore it puts a limitation for the study of full system as it grows exponentially. However, attempts were made to gain

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: (+91) 22 25505151. Notes

The authors declare no competing financial interest. 9826



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ACKNOWLEDGMENTS The authors thank Dr. A. Goswami, Head, Radiochemistry Division, Bhabha Atomic Research Centre, Mumbai, India, for his keen interest in this work. M.S. and B.S. thank the computer division for providing computational facilities. B.S. thanks Dr. K. S. Pradeepkumar and Dr. D. N. Sharma for their support.

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