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An insight into third-phase formation during the extraction of thorium nitrate: evidence for aggregate formation from small-angle neutron scattering and validation by computational studies

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,
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  An Insight into Third-Phase Formation during the Extraction of Thorium Nitrate: Evidence for Aggregate Formation from Small-Angle 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 comparethe aggregation behavior of 1.1 M solutions of tributyl phosphate (TBP) and  N,N  -dihexyloctanamide (DHOA) dissolved in di ff  erent 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 phaseformed 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 importantrole 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 benzeneduring the extraction of Th(IV) from nitric acid medium. Theoretical calculations werealso performed to gain insights into the binding of thorium nitrate with TBP and DHOA models. These calculations suggest thattwo to three molecules of both DHOA and TBP strongly coordinate to Th(NO 3 ) 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 throughnoncovalent interactions. 1. INTRODUCTION Third-phase formation during liquid − liquid extraction of metalspecies from acidic solutions often takes place when theconcentration of the tetravalent metal ions such as Th(IV),Zr(IV), and Pu(IV) or that of the mineral acid exceeds thesolubility limit in the organic phase and the organic phase splitsinto two layers. 1 − 3 This phenomenon has signi fi cant con-sequences in hydrometallurgical operations and is of particularconcern 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 systemhas been extensively evaluated for third-phase formationstudies. In addition to TBP, several other organophosphorusextractants have been evaluated for third-phase formation behavior under di ff  erent experimental conditions. 4 − 10 Reprocessing experiences have led to the identi fi cation of certain problems associated with the use of TBP such as highaqueous solubility, interference of degradation products duringstripping of Pu/U, poor decontamination factor (DF) values of Pu/U with respect to  fi ssion products, and the generation of large volumes of secondary (phosphate) wastes. Theseproblems 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 onidentifying alternative extractants of TBP to alleviate at leastsome of these problems. In this context,  N,N  -dialkyl amideshave been identi fi ed as promising alternatives of TBP for spentfuel reprocessing. 13 − 16 Based on extensive studies, straightchain  N,N  -dihexyl octanamide (DHOA) was identi fi ed as analternative of TBP for selective recovery of U and Pu fromthree-component (U, Pu, and Th) Advanced Heavy WaterReactor (AHWR) spent fuel dissolver solutions. 17,18 Inaddition, studies were also carried out to optimize theconditions for the recovery of   ∼ 100 g/L (0.431 M) Th(IV)from AHWR ra ffi nate solutions. 19 During Th recovery, third-phase formation studies are of interest in view of the largeconcentrations of Th(IV) in the ra ffi nate solutions.In third-phase-formation studies, generally e ff  orts have beenfocused on understanding the composition of the speciespresent in the heavy organic phases (HOP) and diluent-richlight organic phases (LOP) and relatively little information isavailable on structural aspects for di ff  erent 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 modi fi ers dissolves the HOP and thethird-phase formation can be prevented. Attempts have also been made to explain the third-phase-formation tendency insolvent extraction systems by invoking the similarities betweenextractant and surfactant molecules as both possess hydrophilicand hydrophobic ends. The functional groups in extractantmolecules are responsible for hydrophilic nature as it binds withthe metal ions while the long-chain alkyl substituents make theother 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 © 2013 American Chemical Society  9821  |  J. Phys. Chem. B  2013, 117, 9821 − 9828  properties which help in the transfer of the metal ions from theaqueous phase to the organic phase. 20 − 33 These studies haveused advanced spectroscopic techniques such as visible/IR spectroscopy, small-angle neutron scattering (SANS), andextended X-ray absorption  fi ne structure (EXAFS) to explainthe phenomenon of third-phase formation. Based on thesestudies, two models have been put forward to explain thephenomenon of third-phase formation: (i) particle growthmodel, due to the extensive aggregation or polymerization of the metal − extractant complexes leading to the growth of largesize aggregates, i.e., large micellar aggregation number (  N  ), 31 and (ii) Baxter sticky spheres model due to increasingly long-ranged spatial correlations between small micelles due toattractive intermicellar interactions. 20 − 30  Whereas high metalloadings in the organic phases can promote polymerization by  bridging functional groups of di ff  erent extractant molecules, thesurface 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 tocompare the third-phase formation/aggregation behavior of 1.1M DHOA vis-a    ̀ -vis 1.1 M TBP dissolved in di ff  erent diluentssuch as  n -dodecane, chloroform, and benzene during theextraction of Th(IV) from nitric acid medium. 2. EXPERIMENTAL SECTION 2.1. Materials.  DHOA used in this work was synthesized inour laboratory by following a reported method. 16 Deuterateddodecane (dodecane- d  26  , 98 atom % D, Aldrich), benzene(C 6 D 6  99.8%, Merck), and chloroform (CDCl 3  99.9%, Merck) were used as received. Sample solutions (1.1 M TBP/DHOA) were prepared by dissolving their required quantities indeuterated diluents. These diluents were used to get a bettercontrast for the aggregates formed in this study. Stock solutionsof Th(IV) (0.215 and 0.862 M) at 4 M HNO 3  were prepared by dissolving the required weight of Th(NO 3 ) 4 · 5H 2 O in asuitable nitric acid medium and adjusting to the desired acidity.Thorium and nitric acid concentrations were determined by EDTA (ethylenediaminetetraacetic acid) complexometric andalkalimetric titrations, respectively. The organic phases wereequilibrated with Th(IV) solutions (0.215 and/or 0.862 M at 4M HNO 3 ), centrifuged, and separated from aqueous phases.Table 1 provides the details of the organic samples used forSANS studies. 2.2. SANS Measurements.  These measurements werecarried out using a SANS di ff  ractometer facility at Dhruvareactor, BARC, Trombay. 34 The mean wavelength of theincident neutron beam is 5.2 Å, which has a wavelengthresolution of   ∼ 15%. The scattering wave vector ( Q  ) range of the di ff  ractometer is 0.017 − 0.35 Å  − 1 . SANS technique deals with the scattering of a monochromatic beam of neutrons fromthe sample, and the scattered neutron intensity is measured as afunction of the scattering angle. Generally, one measures thedi ff  erential scattering cross section per unit volume (d Σ /d Ω ) asa function of   Q  . The sample is taken in the form of a plate tomaintain a uniform thickness for the beam area as a function of scattering vector. The measured intensity,  I  ( Q  ), is normalizedto the di ff  erential scattering cross section d Σ /d Ω ( Q  ) using astandard procedure. 35 This technique has been found useful forstudying the material structure of sizes in the range of 10 − 200 Å. The following two models were employed to analyze thechanges in scattering intensities of organic samples underdi ff  erent experimental conditions: (1) growth of noninteractingparticles (spherical/ellipsoidal model); (2) interaction betweensmall particles (Baxter model).For a miceller system dispersed in a medium, d Σ /d Ω ( Q  ) can be expressed as  ρ ρ ΣΩ= − Q n V P Q S Q  dd( ) ( ) ( ) ( ) p s2 2 (1)  where  n  is the number density of the particles,  ρ p  and  ρ s  arerespectively the scattering length densities of the particle andthe solvent, and  V   is the volume of the particle.  P  ( Q  ) is theintraparticle structure factor and is decided by the shape andsize of the particle.  S ( Q  ) is the interparticle structure factor, which depends on the spatial arrangement of particles and isthereby sensitive to interparticle interactions. In the case of dilute solutions, interparticle interference e ff  ects are negligible( S ( Q  )  ∼  1), and, therefore, eq 1 takes the following form:  ρ ρ ΣΩ= − Q n V P Q  dd( ) ( ) ( ) p s2 2 (2)  P  ( Q  ) for a spherical particle of radius  R   is given by  = − ⎡⎣⎢⎤⎦⎥  P Q  QR QR QR QR  ( ) 3{sin( ) cos( )}( ) 32 For prolate ellipsoidal,  P  ( Q  ) is given by  ∫   μ μ =  P Q F Q  ( ) [ ( , ) d ] 012 (3)  μ  = − F Q  x x xx ( , ) 3(sin cos ) 3 (4)  μ μ = + − x Q a b [ (1 )]1/2 2 2 2 2 (5)  where  a  and  b  are the semimajor and semiminor axes of theellipsoidal 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-wellpotential of depth  U  0  ( < 0) and width  Δ . The basic results of the model are derived as the lowest order solution of theOrnstein − Zernike equation and Percus −  Yevick closurerelation. The expression for the structure factor is generally given by  = + − S Q A Q B Q  ( ) ( ) ( ) 1 2 2 (6) 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. details [Th] org  , M1 TBP: diluent rich b 0.0302 DHOA: diluent rich b 0.0173 TBP: third phase b 0.7334 DHOA: third phase b 0.2505 TBP: no third phase a 0.1386 DHOA: no third phase a 0.0737 1.1 M TBP/ n -dodecane  − 8 1.1 M DHOA/ n -dodecane  − a Prepared by contacting with 0.215 M Th(IV) solution at 4 M HNO 3 . b Prepared by contacting with 0.862 M Th(IV) solution at 4 M HNO 3 . The Journal of Physical Chemistry B  Article  |  J. Phys. Chem. B  2013, 117, 9821 − 9828 9822  η α β  λ = + −+ −− ⎛⎝⎜⎞⎠⎟  A Q  s k kc kkc kks kk ( ) 1 12 ( ) ( ) 1 ( )12( ) 3 2 (7) η α β  λ = − + −+ − − − ⎛⎝⎜⎡⎣⎢⎤⎦⎥⎡⎣⎢⎤⎦⎥⎞⎠⎟  B Q ks kkc kkks kkc kk ( ) 12 12( ) 1 ( )1 ( )121 ( ) 2 32 (8)  where  s ( k  )  ≡  sin( k  ),  c ( k  )  ≡  cos( k  ),  k   ≡  Q  ( σ   +  Δ ), and α η μη β  η μη μ λ η η = + − ′−− + ′− ′ = ′ − 1 2(1 ) , 3(1 ) , (1 ) 2 2  ληδ δ δ τ  ηην η ηη ′ = − − = +−= +− v 6[ ( ) ],1 ,1 /23(1 ) 2 1/22 The parameter  η  =  π  n ( σ   +  Δ ) 3  /6   is the e ff  ective  “  volumefraction ”  which includes the potential width  Δ . The stickinessparameter ( τ  ) is related to the potential parameters ( u 0  ,  Δ  ,  σ  )and temperature,  T   , as τ  σ  = + ΔΔ U k T  12exp( / ) 0 B  where  k  B  is Boltzmann ’ s constant. For the particle interactionmodel calculations, the parameters used were diameter of themicelles ( σ  ), width of the square-well attraction potential ( Δ ),depth of square-well potential ( U  0 ), and stickiness parameter( τ  ). When the distance between two particles is larger than  σ   but smaller than  σ   +  Δ  , the particles experience attraction. Animportant advantage of the Baxter model approximation is thatanalytical expressions have been derived for the structure factor S ( Q  ). 2.3. Computational Details.  In conjunction to theexperimental work, electronic structure calculations were alsoperformed to understand the binding of Th(NO 3 ) 4  with TBPand DHOA extractants. Density functional theory (DFT) basedcalculations using dispersion corrected BP86 functional (D3correction) with def2-SV(P) basis set is used for geometry optimizations and energy evaluations using ORCA 2.9 quantumchemical package. 36 − 39 During this calculation, e ff  ective corepotential 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 understandingof role of diluents during the third-phase formation for thechosen extractants with particular reference to the thorium fuelcycle being pursued in India. 3. RESULTS AND DISCUSSION 3.1. Studies with  n -Dodecane as the Diluent.  TheSANS studies were carried out using 1.1 M TBP and 1.1 MDHOA solutions prepared in deuterated  n -dodecane (dielectricconstant,  ε  = 2.0 at 20  ° C) medium. Our previous studiesunder identical experimental conditions have shown that the volume of the third phase formed in the case of 1.1 M TBP/ n -dodecane is relatively lower than that of the 1.1 M DHOA/ n -dodecane system. 33 Typically, the volume of the third phase inthe case of DHOA was  ∼ 2.2 times of that of TBP. This isclearly observed in terms of Th(IV) concentration in third-phase samples in the current study. Figures 1 and 2 show the variation in the di ff  erential scattering cross section per unit volume (d Σ /d Ω ) as a function of scattering vector,  Q   , for thetwo solvents (i.e., 1.1 M TBP and 1.1 M DHOA solutions in  n -dodecane) under di ff  erent experimental conditions, viz., (a)fresh solvent (without equilibration with Th(IV) solutions in 4M HNO 3 ), (b) diluent-rich phase and the third phase(obtained after contact with 0.862 M Th at 4 M HNO 3 ), and(c) extract with no third phase (obtained after contact with0.215 M Th at 4 M HNO 3 ). It is evident that even though thetwo solvents have been treated with thorium solutions underidentical conditions, the two solvents di ff  er in theircompositions. The following observations indicate that thetwo solvents display distinctly di ff  erent features in their SANSmeasurements. 3.1.1. TBP/n-Dodecane System.  The d Σ /d Ω  values for freshsolvent and third phase (containing 0.733 M Th) arecomparable, suggesting that there is no swelling of the micellesdue to interparticle attraction. The diluent molecules areexpected to be expelled from the vicinity of the extractedspecies in the presence of large concentrations of Th. However,the d Σ /d Ω  values for loaded organic phase, containing 0.138 MTh(IV) and without third phase, are signi fi cantly higher due tointermiceller interaction leading to swelling in the size of theTh 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-richorganic phase showed no such strong interaction leading to Figure 1.  SANS data for 1.1 M TBP solution in deuterated  n -dodecane. Figure 2.  SANS data for 1.1 M DHOA solution in deuterated  n -dodecane. The Journal of Physical Chemistry B  Article  |  J. Phys. Chem. B  2013, 117, 9821 − 9828 9823  smaller values of di ff  erential scattering cross section per unit volume. 3.1.2. DHOA/n-Dodecane System.  The d Σ /d Ω  values forthe third phase (containing 0.250 M Th) are maximum due toattractive micellar interaction and indicating the presence of some diluent molecules in the vicinity of the extracted species.This is re fl ected in the relative volumes of the third phases forthe two solvent systems. The scattering cross sections of theorganic phases with 0.017 M Th (diluent-rich phase) and 0.073M 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 HNO 3 /Th, will not formreverse micelles and hence there will be no aggregation. Table 2shows that when data treatment is done considering only theparticle growth model and neglecting the interactions amongthe reversed micelles, the aggregation number (  N  ) issigni fi cantly large. It is hard to visualize the growth of theparticles with such large values of   n  even in the samples havingthird phases due to high metal loadings. This suggests that thesimple aggregation model does not provide a valid explanationof the third-phase formation. The scattering data, therefore, wasinterpreted using the Baxter sticky spheres model whichinvolves surface adhesion. Table 3 lists the aggregation number(  N  ) of extractant molecules calculated after treating thescattering data using the Baxter model. The aggregationnumbers of all the samples were much lesser than thatprovided by the ellipsoidal model. It is evident that this modelprovides better data treatment, and the decrease in theaggregation number (  N  ) in third-phase samples is attributedto the presence of   n -dodecane molecules in di ff  erent pockets.By contrast, the particle growth model does not di ff  erentiate between the extractant and the diluent molecules. There is asigni fi cant enhancement in  τ  − 1  values for thorium-loadedorganic phases (diluent rich, without/with third phase) ascompared to the corresponding fresh solvents. This indicates anincrease in the short-range attractive forces between the polarcore of the reverse micelles due to dipole − dipole interactions.Therefore, the critical  τ  − 1  value under the conditions of thisstudy 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-richphases have  τ  − 1  values of 10.5, and 11.6, respectively. The  τ   values of di ff  erent samples were used to calculate the attractivepotential energy ( U  0 ) in  k  B T   units. It is evident that theattractive potential energies are substantially higher comparedto the fresh solvents. The reverse micelles are subjected to twoopposing physical forces: (a) the thermal energy ( k  B T  ) keepsthe micelles dispersed in the diluents; (b) the intermicellarattraction energy compels the micelles to stick together. Theorganic phase will be stable as long as these two opposingforces are balanced, else aggregation takes place. This study,however, shows an interesting  fi nding for TBP and DHOA systems. The attractive potential energy ( k  B T  ) values for eitherTBP or DHOA system for the diluent-rich phase and for thirdphase are comparable, i.e.,  − 1.31,  − 1.36 (for TBP), and  − 2.17, − 2.13 (for DHOA). However, the  k  B T   values are higher forDHOA compared to TBP. On the other hand, the Th-loadedphases (without third phase, samples no. 5 and 6) havecomparable ( k  B T  ) values. 3.2. Studies in Aromatic and Chlorinated Diluents. Third-phase formation is mainly observed in aliphatic diluentsand 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 signi fi cantly and contribute to an increased solubility in organic phase. 1,40,41 Even though the dielectric constant values for benzene andchloroform are not very much di ff  erent from that of   n -dodecane, no third phase was observed during the extraction of thorium using these diluents under the conditions of thepresent study. Therefore, SANS measurements were alsoperformed on 1.1 M TBP and 1.1 M DHOA solutionsprepared in CDCl 3  (dielectric constant = 4.8 at 20  ° C) andC 6 D 6  (dielectric constant = 2.3 at 20  ° C) diluents tounderstand the in fl uence of the polarity of diluents on third-phase formation during Th(IV) extraction from 4 M HNO 3 medium. Table 4 provides the sample details along with the Table 2. Aggregation Number (  N  ) Calculation on Di ff  erentSamples Using Particle Growth Model: Organic Phase(s),1.1 M TBP/1.1 M DHOA Solutions in  n -Dodecane;  T   = 25 ° C sampleno. geometry dimension(s) volume, Å  3  N  1 spherical  R   = 12.73 Å 8640 192 ellipsoidal  a  = 77.11 Å,  b  =  c  =10.41 Å 34996 583 spherical  R   = 12.44 Å 8063 184 ellipsoidal  a  = 52.77 Å,  b  =  c  =9.37 Å 19403 335 ellipsoidal  a  = 65.68 Å,  b  =  c  =9.98 Å 27397 606 ellipsoidal  a  = 35.42 Å,  b  =  c  = 6.45 Å 6171 107 spherical  R   = 11.94 Å 7129 168 spherical  R   = 9.27 Å 3336 6 Table 3. Aggregation Number (  N  ) Calculation on Di ff  erentSamples Using Baxter  ’ s Sticky Spheres Model: OrganicPhase(s), 1.1 M TBP/1.1 M DHOA Solutions in  n -Dodecane;  T   = 25 ° C sampleno. radius, Å   N  stickiness parameters,1/ τ  potential energy,  U  0  / k  B T  1 8.4 5 10.5  − 1.312 12.2 13 11.6  − 2.173 6.9 3 8.3  − 1.364 10.3 8 12.8  − 2.135 11.1 13 12.2  − 2.196 9.5 6 12.7  − 2.017 7.9 4 4.8  − 0.918 7.2 3 3.5  − 0.50 Table 4. Aggregation Number (  N  ) Calculation on Di ff  erentSamples Using Baxter  ’ s Sticky Spheres Model: OrganicPhase(s), 1.1 M TBP/1.1 M DHOA Solutions inChlorinated/Aromatic Diluents (CDCl 3  and C 6 D 6 );  T   =25 ° C sampleno. sample details [Th] org  , M radius, Å   N  1 1.1 M TBP/CDCl 3  −  10.5 112 Th-loaded 1.1 M TBP/CDCl 3  0.167 13.4 223 1.1 M TBP/C 6 D 6  −  7.6 44 Th loaded 1.1 M TBP/C 6 D 6  0.245 4.8 15 1.1 M DHOA/CDCl 3  −  12.0 126 Th-loaded 1.1 M DHOA/CDCl 3  0.079 11.9 127 1.1 M DHOA/C 6 D 6  −  8.5 48 Th-loaded 1.1 M DHOA/C 6 D 6  0.118 5.3 1 The Journal of Physical Chemistry B  Article  |  J. Phys. Chem. B  2013, 117, 9821 − 9828 9824  aggregation number (  N  ) of the extractant molecules havingdi ff  erent Th(IV) concentrations. It is obvious that the twoextractants vary signi fi cantly with respect to Th(IV) concen-tration in CDCl 3  and C 6 D 6  diluents. It is important to mentionthat no third phase was noticed during the extraction of Th(IV)from 4 M HNO 3  medium using these chlorinated/aromaticdiluents. Figures 3 and 4 show the variation in the di ff  erentialscattering cross section per unit volume (d Σ /d Ω ) as a functionof scattering vector,  Q   , for the samples prepared under theconditions of this experiment. Similar to the  n -dodecanesystem, the scattering data was interpreted using the Baxtersticky spheres model based on the attractive interaction of theextracted species. It is interesting to note that the aggregationnumber (  N  ) is higher for both extractants in the case of CDCl 3 as compared to that of C 6 D 6 . This suggests that the diluentmolecules are playing a role in holding the extracted speciesand are being expelled from the vicinity of the two neighboringspecies. 1,40,41 This study demonstrates that diluents with smalldi ff  erence in dielectric constants values behave di ff  erently withrespect to their third-phase formation behavior. Even thoughthere is no third-phase formation in CDCl 3  medium, theaggregation number (  N  ) is signi fi cantly higher as compared tothose of C 6 D 6  and deuterated dodecane. The absence of thirdphase in the case of C 6 D 6  suggests that it is e ff  ectively solublizing the extracted species but unable to act as bridge between di ff  erent extracted species. As discussed earlier, twoopposing physical forces, viz., the thermal energy ( k  B T)  and theenergy of intermicellar attraction, are responsible for holdingthe extracted species (micelles) in the diluent phase. Whereasthe thermal energy helps in the dispersion of micelles in themedium, the attractive forces are responsible for sticking themtogether. It appears that both CDCl 3  and C 6 D 6  prevent theswollen reverse micelles from reaching the level of intermicellarattraction energy required for third-phase formation. Theorganic 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(NO 3 ) 4 ] 0 (Figure 5) is conforming to thereported EXAFS measurements. 42 Thorium is bound by nitrategroups in  D 4 h  symmetry with eight occupied coordination sites.However, the coordination number of Th(IV) can extend up to12 − 14 and therefore it can further accommodate additionalligands. In this context, the structures and relative bindinga ffi nities of TBP and DHOA molecules to Th(NO 3 ) 4  were Figure 3.  SANS data for 1.1 M TBP solution in C 6 D 6  and CDCl 3 diluents without/with equilibration with 0.862 M Th at 4 M HNO 3 . Figure 4.  SANS data for 1.1 M DHOA solution in C 6 D 6  and CDCl 3 diluents without/with equilibration with 0.862 M Th at 4 M HNO 3 . Figure 5.  Optimized structures (Å) of TMP and DMAA to Th(NO 3 ) 4 at BP86/def2-SV(P) level. The Journal of Physical Chemistry B  Article  |  J. Phys. Chem. B  2013, 117, 9821 − 9828 9825
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