Synergy in Extraction System Chemistry: Combining Configurational

Article pubs.acs.org/Langmuir

Synergy in Extraction System Chemistry: Combining Configurational Entropy, Film Bending, and Perturbation of Complexation J. Rey,† S. Dourdain,*,† L. Berthon,‡ J. Jestin,§ S. Pellet-Rostaing,† and T. Zemb† †

ICSM/LTSM, CEA/CNRS/UM2/ENSCM UMR5257, Site de Marcoule, Bat. 426, 30207 Bagnols sur Cèze, France CEA, Nuclear Energy Division, RadioChemistry & Processes Department, 30207 Bagnols sur Cèze, France § Laboratoire Léon Brillouin CEA/CNRS, CEA Saclay, 91191 Gif-sur-Yvette, France ‡

S Supporting Information *

ABSTRACT: Iron-uranium selectivity in liquid−liquid extraction depends not only on the mole fraction of extractants, but also on the nature of the diluent used, even if the diluent has no complexation interaction with the extracted ions. Modeling strong nonlinearity is difficult to parametrize without a large number of parameters, interpreted as “apparent constants”. We determine in this paper the synergy curve versus mole fraction of HDEHPTOPO (di(2-ethylexyl) phosphoric acid/tri-n-octyl phosphine oxide) and compare the free energy of aggregation to the free energy of extraction in various diluents. There is always a concomitant maximum of the two quantities, but with a gradual influence on intensity. The diluent is wetting the chains of the reverse aggregates responsible of the extraction. We show here that the intensity of the unexplained synergy peak is strongly dependent on the “penetrating” or “nonpenetrating” nature of the diluent. This experimental determination allows us to attribute the synergy to a combination of entropic effects favoring extraction, opposed to perturbation of the first coordination sphere by penetration as well as surfactant film bending energy.

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INTRODUCTION In separation chemistry, solvent extraction is the most widely method used in very different applications from pharmaceutical industry,1−3 production of precious metals,4,5 recycling of rare earth elements from electronic wastes,6 to chemical treatment of used nuclear fuel.7,8 In these various applications, solvent extraction efficiency is known to be optimized in so-called synergetic formulations. Synergistic properties can be extremely large: a hundred times more is extracted for a large domain of composition. This means exaltation of the order of 3kT or 5 kJ/ mol (extracted ion pair) at the ideal mole ratio used in formulation. Synergism has been described with various couples of extractants9 like N,N′-dimethyl-N,N′-dioctylhexylethoxymalonamide (DMDOHEMA) with di(2-ethylexyl) phosphoric acid (HDEHP),9 tri-n-butyl phosphate (TBP) with di-n-butyl phosphate (HDBP),10 and HDEHP with tri-n-octyl phosphine oxide (TOPO)11 for extraction of various elements as actinides/lanthanides, precious metals or essential oils. While synergy is known since a long time and commonly applied, the mechanisms at its origin is not yet understood. As an example, a classification and rationalization of effect of the diluent, temperature, pH, and noncomplexing species on the free energy of extraction observed, required 16 different types of liquid−liquid extraction “types” as distinct categories.12 When looking at the chelation properties, competition or adduct addition mechanisms are sometimes proposed. Since the pioneering suggestion of Osseo-Asare,13 and the subsequent © 2015 American Chemical Society

identification of the thermodynamic driving force of charged species between coexisting fluids,14 the approach combining supramolecular direct complexation with the first neighbor with self-assembly in the solvent15−17 is only rarely quantitatively considered in industrially used solvent extraction systems,14,18 and even less exploited for synergism understanding. Ellis et al. studied HDBP and TBP synergistic system on dysprosium extraction.10 Looking at aggregation with and without metal in aqueous phase, small-angle X-ray scattering (SAXS) data allowed them to observe a significant reordering in the mixed system with largest aggregate at the maximum of dysprosium extraction. In these examples, the aggregation effect of the extractant mixture appears to be an interesting feature to take into account to explain higher metal extraction. However, it was also shown that aggregate size alone cannot explain the nonmonotonic variation of the synergy (expressed as double difference in free energy of extraction) observed when pH/ temperature or any other physicochemical parameters are varied. Concerning the mixed system HDEHP-TOPO, an equilibrium was proposed by Bunus et al. and Blake et al. to explain synergistic extraction of uranium in kerosene diluent.19,20 Hiding the self-assembled aggregates in the form of an equivalent “complex”, and ignoring coextracted species in the Received: April 23, 2015 Revised: June 4, 2015 Published: June 8, 2015 7006

DOI: 10.1021/acs.langmuir.5b01478 Langmuir 2015, 31, 7006−7015

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Langmuir

values of extraction free energy and aggregate formation free energy? This question seems initially paradoxical: in the historical approach used since the 1970s, one considers the extractions as the result of well-defined competing complexes, where the balance reactions used do consider ligand activity in the diluent, but one does not consider the activities of diluent. The influence of the Hildebrandt parameter, that is, the relative variation of the diluent cohesion enthalpy between water and solvent phase, should also come into play. To our best knowledge, this influence has never been clearly evidenced. However, as a second order term, it will not be considered here. Different diluents have been tested to evaluate the influence of aggregation in synergistic uranium extraction mechanisms. For this, the solvent extraction system containing extractants, di-(2-ethylhexyl)phosphoric acid (HDEHP) and trioctyl phosphine oxide (TOPO), in various ratios was investigated in aliphatic diluents with different chain lengths, from heptane to hexadecane. The two molecules considered are sketched in Figure 1 together with a scheme of a typical reverse water-in-oil (w/o) aggregate expected to be formed with such molecules.

explicit notation of some complex assumed to be dominant, it was proposed that TOPO can increase any complex solubility by saturating the first coordination sphere: UO2 A 2(HA)2 + mTOPO ↔ UO2 A 2(HA)2 (TOPO)m

More recently, Beltrami and co-workers published in 2014 a study, using time-resolved laser-induced fluorescence spectroscopy combined with DFT calculation, confirming the presence of TOPO in first coordination sphere and of a water molecule in second coordination sphere;21 therefore, a dominant complex could be written as: UO2 A 2 (HA)2 (TOPO) ·H 2O

Looking at the aggregation properties of HDEHP and TOPO, we have established in a recent study the quantative relation between11 (a) the free energy of extraction selectivity between iron and uranium, which is a well-defined double difference of energy of transfer (ΔΔGtransfer) of uranium and iron in the presence of phosphates, and (b) the enhanced free energy associated with w/o aggregate formation, ΔΔGagg. We have shown that these two quantities are close to each other for synergic as well as for nonsynergic extraction, and that there is some cooperativity, that is (a) > (b). Two main other important facts came out of this first quantitative comparison of aggregate formation and extraction selectivity: (i) When mole fraction of extraction is varied, keeping everything else constant, the maximum of synergy is observed at the same mole fraction than the minimum amount of free “extractant” in monomer form in the diluent, showing that synergy of extraction is concomitant with a favored aggregation. (ii) The double difference ΔΔGtransfer is larger than ΔΔGagg for any selected sample; this is called “cooperativity” in oil extraction using surfactant/cosurfactant systems,22 as well as cofactors are used in enzymology. This study showed also from the estimation of free energies of transfer and aggregation that aggregation alone cannot describe quantitatively the extraction. Some other mechanisms at colloid scale need to be taken into account. Among the motors of extraction, chelation is always proposed, but less commonly identified terms as noncomplexing terms are also involved.23 Among the terms quenching the transfer of ionic species from water to oil, it was shown that free energy cost of reverse micelle formation, image charge effects at the dielectric interface, extractant film bending and stretching energy associated with extraction, and concomitant water and acid coextraction are the most important ones.24 In the present paper, our aim is to investigate the physical origin of the “diluent effect” on synergy and selectivity, by studying several diluents and their mixtures as diluents. As diluents are traditionally expected to modify aggregation without perturbing chelation mechanisms, this study should help evaluating the importance of aggregation in the synergistic extraction mechanisms. It is known by practice in systematic tests of formulations that choice of linear, branched diluent, aromatic diluents give rise to different values of the extraction efficiency.25−27 Moreover, the nature of the diluent, either penetrating the film of extractant or nonpenetrating, has a strong influence on the location of the three-phase boundary line in the phase diagram.28,29 Penetrating diluents decrease the spontaneous packing parameter, while nonpenetrating diluents enhance depletion effects between aggregates. Hence, our driving question is this: How do diluents affect the relative

Figure 1. HDEHP and TOPO extractant molecules and scheme of a core−shell aggregate made by four HDEHP molecules and one TOPO molecule. Complexation heads of extractant molecules are forming the polar part of the reverse aggregate (blue circle), and alkyl chains are considered as the shell.

It is known that these nonelectrolyte core−shell aggregates exist as weak aggregates or as more organized entities that are reminiscent of bigger reverse micelles.30 The shell is usually considered to be composed of the apolar tails of the extractants while the core contains the polar heads plus the water, acid and cations extracted. This couple of extractant agents is mainly known for synergistic extraction of uranium from phosphoric ores, as exploited in the URanium and PHOSphoric (URPHOS) process. In this context, the mixture exhibits an enhancement of uranium extraction of 1500% for a specific combination of the two molecules in dodecane: 1 TOPO for 4 HDEHP compared to uranium extraction by pure HDEHP or pure TOPO. Different diluents have been used here, and all other parameters were kept constant, to evaluate their influence on synergistic mechanisms. At first look, the chelation properties coming from first neighbor interactions and the selectivity curve as shown in Figure 2 should not be sensitive to the nature of the diluent. If extraction proceeds not only from some organometallic complexes with known and fixed stoichiometry, then the quantitative study of selectivity variation can be linked to other transfer free energy terms, such as those proposed by Dufrêche and Zemb.24 7007


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Figure 2. Distribution coefficients for uranium (a) and iron (b) at constant total extractant concentration (0.5 mol/L) in hexadecane (blue), in dodecane (red), and in heptane (black) after contact with 5 M H3PO4, uranium 1 mmol/L, and iron 45 mmol/L. The selectivity factor is shown in (c).

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(calibration value on superficial tension of dodecane γdodecane/air = 25.4 mN/m). Drops of diluent containing same quantities of extractant, but with variable mole fraction of TOPO are formed on the tip of a curved needle immersed in the aqueous phase. To avoid any further ion exchange between the aqueous and organic phase, the organic drop was measured in the same acidic solution with which it was previously contacted and equilibrated for the extraction. The surface tension γ is derived from the shape of the drop using the following equation and neglecting correction due to nonspherical droplet:

MATERIALS AND METHODS

Alkyl chains with increased chain lengths from heptane (C7) to hexadecane (C16) have been tested as diluent, as well as mixtures of long and short chain alkane diluent, respectively, hexadecane and heptane. The experiment with mixed diluent is crucial, for reasons that will be explained below. To characterize the effect of the diluent on the synergy of extraction, for each diluent tested, five organics solutions, containing total extractant concentration (HDEHP + TOPO) of 0.5 M, were contacted to 5 M phosphoric acid aqueous solution with uranium and iron at concentrations of 1 and 45 mmol to be in the similar conditions as in the URPHOS process. To look over conditions in and out of synergism, molar fractions of the extractant molecules were varied from [TOPO]:[HDEHP + TOPO]) = 0, 0.1, 0.2, 0.3, 0.4, to 0.5, since TOPO is no longer soluble at 0.6. Extracted solutes were analyzed by inductively coupled plasma (ICP) spectroscopy and by coulometric analysis. Aggregation was characterized by small angle scattering techniques (SAS: SAXS/ SANS), and the critical aggregation concentrations (cac) were determined with tensiometry, using drop shape analysis.11 To study extraction efficiency of the system in the various diluents, TOPO ratio was increased by steps up to 50% molar ratio (i.e., means the mole fraction of TOPO in the extractant mix) with a total concentration of [HDEHP + TOPO] kept constant at 0.5 M. For the determination of cac, ranges of [HDEHP + TOPO] concentrations were prepared from 5 × 10−3 to 0.5 M for each TOPO ratio. Extractions were performed in test tubes by contacting and mixing 1/1 volumes of aqueous and organic phases during 1 h. Extraction Analysis. The extraction of uranium and iron (initially, respectively, 1 and 45 mmol), which is diluted 30 times, was analyzed by inductively coupled plasma atomic emission spectrophotometry (ICP-OES, Spectro Arcos) using calibrators from 0 to 15 mg/L of uranium and iron. The concentration in aqueous solution was measured before and after the extraction step. Water extraction was characterized by coulometric titration of the organic phases, while phosphoric acid extraction was determined on back extracted aqueous phases by P analysis using ICP-OES. All extraction values are given in the Supporting Information (Table S1) as the water and acid extraction plotted as a function of the TOPO molar ratio (Figure S1 in the Supporting Information). Tensiometry. Interfacial tensions of HDEHP/TOPO/dodecane phases were measured using the drop shape method using a Krüss tensiometer apparatus with an accuracy of 2% on the measurement

γ=

ΔρVg 2πrF

(1)

where Δρ is the density difference between the two phases, V and r are the volume and the radius of the detached drop, respectively, g is the gravity, and F is the Harkins and Brown empirical correction factor, tabulated as a function of (r/V)1/3. The densities of the organic and the aqueous phases were measured with an ultrahigh precision thermostated density analyzer Anton-Paar DSA5000 based on an oscillatory fork. When thermostat is stable, 5 digits in precision and reproducibility are obtained. Neutron. Small-angle neutron scattering (SANS) measurements were performed at the French neutron facility Laboratoire Léon Brillouin/Orphée (LLB/Orphée) on the PACE spectrometer using two configurations with two sample-to-detector distances equal to 800 and 5130 mm, one value of wavelength λ equal to 4.5 Å (Δλ/λ ∼ 10%), and a standard two diaphragm collimation geometry (7 mm/20 mm, collimation distance of 2500 mm). By shifting the position of the detector relative to the neutron beam center, we can both increase the accessible Q max and the overlap between the two configuration which permits to cover a total q-range from 0.01 to 0.4 Å−1. All measurements were done under atmospheric pressure and room temperature. Measurements were performed in quartz Hellma cells of optical path of 2 mm. Standard corrections for sample volume, neutron beam transmission, empty cell signal subtraction, inelastic scattering, and detector efficiency were applied to obtain the scattered intensities. The absolute scale (cm−1) was calculated by normalization with the incident neutron beam. The data reduction has been done using “PASINET” software. 7008


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Figure 3. Interfacial surface tension determined in synergism at TOPO ratio 0.2, and out of synergism at 0 and 0.5, in heptane and hexadecane diluents. (Aq ph.: 5 M H3PO4, 1 mM uranium, and 45 mmol iron).

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RESULTS Functional Study. To determine the antagonist or synergistic nature of an extractant mixture, in a first step, the distribution ratios of metals are plotted versus the TOPO molar ratio. The distribution coefficients for U and Fe, DU and DFe, and the selectivity of the U extraction toward Fe, SU/Fe, are defined as follows: DU =

DFe =

[U]org, f [U]aq, f [Fe]org, f [Fe]aq, f

=

=

ΔXX == x0ΔGagg = NkT ln

(2)

[Fe]aq, i − [Fe]aq, f [Fe]aq, f

(3)

and

SU/Fe =

DU DFe

(4)

To define the synergistic properties of the system, the molar ratio of TOPO/HDEHP was varied from 0 to 0.5, keeping constant the total extractant concentration (at 0.5 M). The variation of relative efficiency can be directly related to the free energy of transfer ΔΔΔGtransfer:11 U 20 Δorg aq ΔFe Δ0 Gtransfer

⎧ ⎪ = kT ⎨ln ⎪ ⎩

DU50% DFe DU0% DFe

(6)

where X is the TOPO ratio. (2) Higher uranium extraction for longer chains lengths of diluent should be examined in this sense too. (3) The decrease after 20% can be either due to (a) extractant film bending energy or alternatively due to (b) a perturbation of the first coordination sphere of the metallic center. We will check this point considering the “penetrating power” of mixed diluents, as investigated in w/o systems by Chen, Evans, and Ninham nearly 30 years ago.31 This point will be examined in detail in the following. Considering that extraction free energy is the difference between positive terms which are the supramolecular complexation energy and the entropy of configuration in large aggregates,23 and negative terms favoring desextraction that are the free energy of aggregation, image charge, polarization, and film bending energy, we first test the point related to aggregation. It must be stressed that considering the conditions used with typical aqueous phases (1 mM uranium and 50 mM iron in 5 M phosphoric acid), only one aggregate out of 100 contains “filled” reverse micelles. We rely therefore on the measurement of the free energy of aggregation with very few extracted ions in the cores, and use a method similar to the one used for studying extraction of acids only.32,33 To estimate free energy of aggregation, we determine the critical aggregation concentrations (cac’s) for each TOPO ratio determined from surface tension measurements. Interfacial tensions of the mixed system HDEHP/TOPO were therefore measured and plotted as a function of the logarithm of the total concentration of [HDEHP + TOPO] for different TOPO molar ratios 0, 0.2, and 0.5. Figure 3 shows the interfacial surface tension as a function of the total concentration of ligand at 0, 0.2, and 0.5 TOPO molar ratio in hexadecane, dodecane, and heptane. In each graph, the inflection point in the curve, where the second derivative is maximum, is significant of the activity of extractant that is high enough to drive formation of micelles in bulk instead of a linear increase of surface.34 The cac’s derived from surface tension measurements are gathered in Figure 4. They are plotted as a function of the TOPO ratio in heptane, dodecane, and hexadecane. These experiments show that, whatever the diluent, the cac is minimized at 20% TOPO molar ratio, which confirms that synergistic extraction of uranium is concomitant with a synergistic spontaneous aggregation of HDEHP/TOPO couple. Free energy of aggregation is therefore a good measure of the best mole fraction of HDEHP/TOPO for which

[U]aq, i − [U]aq, f [U]aq, f

cac(X = x) cac(X = 0)

⎫ aq ⎪ [Fe]aq 50% [U]0% ⎬ − ln aq [U]aq 50% [Fe]0% ⎪ ⎭ (5)

In Figure 2, distribution coefficient for U and Fe, and the selectivity factor U/Fe are plotted as a function of the molar ratio of TOPO in three different aliphatic diluents from hexadecane to heptane. For all the diluents, a nonlinear trend is observed for uranium extraction, with a synergistic peak centered on 20−30% of TOPO. Figure 2 shows also that uranium extraction is more efficient for the heaviest diluents. Distribution coefficients reach 7 (87.5% extraction) in heptane, to 17 (94.5% extraction) in hexadecane. Selectivity curve shows the same shape as uranium extraction curve due to the linear extraction of iron which is not very dependent on the TOPO molar ratio. Without any theoretical consideration, three hypotheses can be drawn first: (1) The increase uranium extraction and uranium selectivity versus iron could be attributed to higher increased aggregation numbers or to favored aggregation and therefore to lower cac, as demonstrated in our previous study11 from the equation of free energy of aggregation: 7009


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signals with a plateau at small angles and a decrease at larger angles which are consistent with the presence of globular aggregates in the organic phases.9−11,28,35 It can be observed that the scattering intensity at low Q increases linearly with the increase of TOPO, and with the chain length of the diluent. Considering that the extractant molecules self-assemble to form reverse-micelle-like aggregates, as it is often modeled for these systems,36 it can be shown that SANS intensities being sensitive to the contrast between the deuterated (the organic diluent) and the nondeuterated part of the samples are characteristic of the whole volume of the aggregates. Therefore, the increase of scattered intensity observed with the TOPO ratio is consistent with the increase of TOPO content in the organic phase that has a higher molecular volume than HDEHP, by considering a core−shell model and the proportional relationship of the scattered intensity at low Q with the aggregate volume. It is also consistent with the increase of the volume of extracted solutes in the aggregates. As shown in Table 1, the volumic fractions of extracted polar

Figure 4. Critical aggregation concentration (cac) plotted as a function of the TOPO ratio at constant total extractant concentration (0.5 mol/ L) in heptane (bleue), in dodecane (red), and in hexadecane (black).

aggregation is easier, even with very low amount of extracted ions, and hence aggregation quenches less the main driving force, which is complexation. The selectivity curves always show the same shape, but the value of the maximum changes gradually with the diluents chain length. This shows an unexpected influence of the nature of the diluent on the extraction selectivity measured at the maximum of selectivity. Indeed, while maximum of synergism is always concomitant with lower ΔΔGagg, the diluent effect on the uranium extraction cannot be attributed to a favored aggregation. The cac’s are globally increasing with the chain length of the diluent, which shows that the uranium extraction increase with the chain length is not related to a lower energy of aggregation. This paradox opens two essential questions in this study: What are the reasons for lower cac in diluents having shorter chain length? What are the reasons for higher uranium extraction in longer alkyl chains? Structural Study. To better understand these behaviors and specifically the diluent effect on aggregation properties, SANS measurements were performed, as they provide a direct characterization of the aggregates in the solution. Measurements were collected for all solutions using different diluents after contact with the model aqueous phase containing 5 M H3PO4, uranium, and iron. Here again, it has to be restated that, in the conditions used (1 mM of uranium and 50 mM of iron), only one aggregate out of 100 contains “filled” reverse micelles. Figure 5 shows the log−log plot of the absolute scattered intensity, expressed in cm−1, as a function of the wave vector Q, for various molar ratios of HDEHP/TOPO in diluent heptane, dodecane, and hexadecane. For all diluents, SANS data show

Table 1. Volume fraction of the Polar Solutes Extracted (Considering Extracted Water, Acid, and Metals) In the Organic Phase for [HDEHP + TOPO]tot = 0.5 M TOPO molar ratio heptane dodecane hexadecane

0

0.1

0.2

0.3

0.4

0.5

0.17 0.16 0.14

0.24 0.2 0.19

0.35 0.33 0.3

0.51 0.48 0.45

0.65 0.61 0.6

0.79 0.76 0.73

solutes which are estimated from the measurement of the molar concentrations of water, acid, uranium and Iron in the organic phases, also increases with the TOPO ratio. Now looking at the evolution of this intensity with the chain length of the diluent, which increases for fattier diluent, it is more difficult to conclude with a simple qualitative analysis. As the scattering length density contrasts, the extracted solute as well as the cac values, play also important role in the evolution of scattering intensity, a complete quantitative estimation of the main parameters is necessary to fully interpret and understand the data. Fit of SANS Data. Ignoring the crossed-term scattering between monomers and aggregates,37,33 equations of scattering for a spherical core−shell model was therefore expressed at first order approximation as detailed in the Supporting Information. In this model, a polar core containing the extracted solute and

Figure 5. Log−log plot of the SANS data for the HDEHP:TOPO mixtures at total extractant concentration of 0.5 M after contact with 5 M H3PO4, uranium 1 mmol/L, and iron 45 mmol/L at different TOPO ratios 0, 0.2, and 0.5, and in three different diluents heptane, hexadecane, and dodecane, and the calculated curve from the core−shell model. 7010


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Langmuir Table 2. Parameters Obtained from the Fit of SANS Spectraa diluent heptane

dodecane

hexadecane

TOPO molar ratio

0

Δρ2 (×1021 cm−2) N core radius (nm) aggregate radius (nm) x Δρ2 (×1021 cm−2) N core radius (nm) aggregate radius (nm) x Δρ2 (×1021 cm−2) N core radius (nm) aggregate radius (nm) x

1.64 3.1 0.37 0.85 1.3 3.28 4.4 0.41 0.84 0.3 3.57 4.3 0.40 0.81 0.2

±Δe 0.31 0.037 0.085 0.26 0.44 0.041 0.084 0.06 0.43 0.04 0.081 0.04

0.2 1.87 3.6 0.37 0.88 1.2 2.47 4.9 0.42 0.96 0.6 2.44 4.9 0.42 0.98 0.5

±Δe 0.036 0.037 0.088 0.24 0.49 0.042 0.096 0.12 0.49 0.042 0.01 0.1

0.5 1.75 4.2 0.39 1.00 1.5 2.66 4.9 0.4 0.98 0.6 3.36 4.6 0.39 0.93 0.3

±Δe 0.42 0.039 0.1 0.3 0.49 0.04 0.098 0.12 0.46 0.039 0.093 0.06

a Δρ, scattering length density contrast between aggregates and the diluent; N, average aggregation number; deduced core; total aggregate radii; and x, penetration rate of diluent molecules in the outer shell of reverse aggregates as a function of the TOPO ratio 0, 0.1, 0.2, 0.3, 0.4, and 0.5 for [HDEHP + TOPO]tot = 0.5 M.

the core−shell model with a modulated penetration of the diluent in the aggregates (typically values of x are determined with a 20% precision). Fit of SANS spectra show that aggregate size increases with the TOPO ratio and slightly with the chain length of the diluent. The other important result concerns the penetration of the diluents in the apolar shell of the aggregates, characterized by the parameter x. Considering the error bar, it appears to be quasi constant with the TOPO ratio, but decreases significantly with the diluent chain length. Direct mechanism of wetting protruding chains is favored by entropy in short or branched diluent, as already noticed when studying third-phase formation.40 This will be exploited and discussed in the following to understand how the diluent, and its influence on aggregation, affects the synergistic extraction of uranium.

the polar heads of the extractant molecules is distinguished from the apolar shell made up with the alkyl chains of the extractant molecules, and all the aggregates are assumed to be composed of a mixture of TOPO and HDEHP following the proportions introduced in the solution. This assumption has been verified by ESI-MS and IR, and UV measurements and is described elsewhere.38 The concentrations of water, acid, uranium, and iron have been determined experimentally (results in the Supporting Information) and used to estimate the scattering length densities of the core and of the shell of the aggregates as well as the theoretical volume and therefore radius of the cores and of the global aggregates for each aggregation number. A discrete polydispersity on the aggregation number has been introduced in the calculation into which the proportions of n-mers, from n = 2 to 7, were adjusted. The quantity of monomers (n = 1) was fixed to the value of the cac determined experimentally. The signal of the diluent has been considered as constant over the q range of interest. After being pondered by its volume fraction, it was added to the calculated intensity of the aggregates. To obtain acceptable fit of the data, an additional parameter had to be introduced: the penetration of the diluent molecule in the shell of the aggregates made by the flexible chain. It was noted x and defined by the number of molecules of diluent per extractant molecules that penetrate in the shell of the aggregates, hence increasing the partial molar volume V of the surfactant layer in the evaluation of the packing parameter p.39 For direct micelles in water, this parameter is known as the hydration rate of the surfactant molecules. In this study, it has been introduced in the calculation of the volume and of the scattering length density of the shell. Finally the structural quantities derived from the fit are the average aggregation number, N, and the chain length of the diluent penetrating in the shell of aggregates, x. They are reported in Table 2 for all the diluent and TOPO ratio tested, together with the deduced averaged radii of the aggregates and of the cores. The calculated scattering intensities are plotted in red lines in Figure 5 for the three molar ratios of HDEHP and TOPO, and in three aliphatic diluents C7, C12, and C16. They are in excellent agreement with the experimental data, which validates

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DISCUSSION

While in a specific diluent, maximum of synergy is always concomitant with lower ΔΔGagggregation, when changing the diluent, higher uranium extraction is not associated with a favored aggregation. This paradoxical behavior opens questions on the diluent effect on aggregation state of the organic phase of solvent extraction, and on its effect on extraction efficiency. Diluent Effect on Aggregation and Extraction Efficiency. In the present study, changing the diluent does not affect the peak shape of the synergistic curve, but it strongly affects the global level of extraction. Characterizing aggregation in details shows that aggregation numbers of the mixed species HDEHP-TOPO are increasing for longer chain lengths of the diluent. This phenomenon was also reported by Tadros41 while studying C14G1 surfactant in various n-alkane diluent by SAXS. Changing oil from heptane to hexadecane favors micellar growth. It was reported that surfactants as C14G1 have the ability to adopt different structure depending of the chain length of alkanes without any external addition of water. In the same manner, higher uranium extraction in hexadecane could here be associated with formation of bigger aggregates able to extract more metals in the organic phase. These results are also in agreement with those obtained from Ellis et al. looking at aggregation states of HDBP and TBP synergistic system on dysprosium extraction.10 With and without metal in aqueous 7011


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Langmuir phase, SAXS data showed a significant reordering in the mixed system with largest aggregate at the maximum of dysprosium extraction, showing the influence of configurational entropy in complexation when adducts are present. Fit of SANS data required also to consider an “x” term related to the penetration power of the diluent. Comparing x values in Table 2 shows that shorter diluents penetrate more the apolar shell of the aggregates, than longer ones. Similar behaviors were observed by Berthon et al. when looking at the effect of diluent and extractant chain length on third phase formation.40 As for HDEHP-TOPO, they showed that malonamide extractants self-assemble in reverse micelles with different apparent sizes depending on the diluent used. They conclude that the stability of the organic phase is governed by the concept of steric stabilization due to short chain penetration. The effect of diluent on apparent size of aggregates and on diluent penetration can therefore be linked to the curvature energy through the decrease of the spontaneous packing parameter associated with mixed film. Indeed, as cosurfactants, diluents having chain length comparable to the extractant molecules chain lengths, can penetrate and swell the apolar volume of the aggregates. This has the consequence to raise the effective packing parameter to a state of minimum flexibility, and therefore to decrease the curvature of the film of extractant. This has already been described on DDAB aggregates. When adding shorter alcohols, interfacial curvature is modified, leading to an increase of the aggregates curvature and a higher oil uptake.42 Diluents affect aggregation mainly by penetration, implying effect on curvature energy and on the size of aggregates. These phenomena can be taken as main responsible of the effect of diluents on extraction efficiency. Identifying the Origins of Synergy. This implies quantifying the effect of the nature of the diluent on the synergistic peak. First, whatever the diluent used, origin of the increase of selectivity appears to be both due to higher amount of aggregates for the synergistic ratio, characterized by lower cac, and to bigger aggregates characterized by bigger aggregation numbers. First effect of the diluent is to induce an increase of aggregation number for U-occupied micelles of Nagg = 3 at TOPO 0%, toward N = 3.5 at the maximum of synergy in the case of heptane and toward Nagg = 5 in the case of hexadecane. This increase of aggregation number is directly related to the penetration power of the diluent: entropy favors penetration of shorter and branched chains.40 This is the order of magnitude expected, but cannot be demonstrated directly, since the aggregation number is an average over the whole sample, and only one aggregate out of 100 contains an uranium atom. Since the increase of the average aggregation number is of the order of 1, and the scattering goes like square of the volume, it can be estimated that the aggregates containing uranium include more than 10 extractant molecules, and may even belong to the class of bicontinuous structures predicted by theory. By using simple approximations, we can compare the variation of entropy with the variation of free energy of transfer by considering configuration entropy inside an aggregate43 (more information, see the Supporting Information):

Fe 20 Δaq org ΔU Δ0 S

⎧⎡ ⎤20% ⎡ ⎤0%⎫ Nagg! Nagg! ⎪ ⎪ ⎥ ⎥ ⎬ = kT ⎨⎢ln − ⎢ln ⎢ Nc! (Nagg − Nc)! ⎥⎦ ⎪ ⎪⎢⎣ Nc! (Nagg − Nc)! ⎥⎦ ⎣ ⎩ ⎭ ⎧⎡ ⎤20% ⎡ ⎤0%⎫ Nagg! Nagg! ⎪ ⎪ ⎥ ⎥ ⎬ − ⎨⎢ln − ⎢ln ⎪⎢⎣ Nc! (Nagg − Nc)! ⎥⎦ ⎣⎢ Nc! (Nagg − Nc)! ⎥⎦ ⎪ ⎩ ⎭

Fe

U

(7)

The value obtained for the configuration entropy is 0.7 ± 0.2kT/extractant, which is in the order of magnitude but lower than the energy of transfer (ΔΔΔGtransfer) estimated to 4kT/ uranyl between TOPO ratios 0 and 20% (eq 4). This result concerns the diluent heptane by taking into account a complexation number Nc = 2 for uranyl cation44−46 and Nagg = 3 and 4, respectively, for 0% and 20% TOPO molar ratio. As mentioned before, approximately one over 100 reverse aggregate contains a uranyl ion. Assuming that ΔΔΔS and ΔΔΔGtransfer are mainly due to difference of Nagg between “full” and “empty” reverse aggregates, a value of Nagg in the order of ∼10 at a mole fraction of 20% of TOPO is needed to induce a ΔΔΔS = ΔΔΔGtransfer = 4kT and to explain that transfer is mostly due to configurational entropy. As indicated previously, this number cannot be measured since one measures only an average, but it appears fully realistic for aggregates containing uranyl.47 Now, to evaluate the mechanistic origin of the sharp decrease transfer energy, estimated to 4kT when TOPO molar ratio increases from 20 to 50%. We consider the contribution of the extractant film bending energy. Using the harmonic approximation for extractant film bending, the drop in selectivity for the mixed system HDEHP/TOPO therefore states has to be compared with:48 20 Δ50 G bending =

1 K *{(p − p0 )20% 2 − (p − p0 )50% 2 } 2

(8)

where p is the effective packing parameter, p0 is the spontaneous packing parameter, and K* is the bending constant. Since the reverse phase does not take up more than one water molecule in the absence of salt and acid, the spontaneous packing parameter is approximated to 3, the value for a cone. Besides, considering that the bending constant of a linear chain C12 is typically in the order of magnitude of 1kT, and that it scales with the cube of the chain length and with the number of chains (typically 3 in case of extractants), the bending constant K* of the present system, can be estimated to 0.88kT from the following equation:49 ⎛ 8 ⎞3 * ⎜ ⎟ × 3 K * = KlinearC 12 ⎝ 12 ⎠

(9)

Effective packing parameters of 3 and 3.4 were obtained by considering internal and total radius of aggregate determine by SANS,29 leading to a bending energy applied between TOPO ratios 20 and 50% of 1.5kT/molecule. Elastic bending energy cost appears to be far too low to explain alone the drop of 4kT observed in transfer energy, whatever the value of p0 and K* taken, respectively, between 2 and 4, and 0.2 and 10. What other general mechanism could be responsible for the major part of the drop in selectivity when mole ratio is beyond 0.2? Beyond cost in bending, there may be a perturbation of the first or second neighbor shell of the ion extracted. Methyl end 7012


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the two mechanisms (a) and (b) intervene together, we suppose at this stage that they are additive: (a) When short chain (or branched) diluents penetrate, the probability of the presence of an end methylene group in the first or second coordination sphere of anion or cation extracted increases, thus reducing the uranium extraction and then the absolute selectivity without changing the location of the maximum. (b) When diluent penetration increases, the effective packing parameter increases, as assumed before from 3.5 to 4+. Thus, even if the effective packing parameter is modified by diluent penetration, it is impossible to reach the value of ΔΔΔGtransfer of 4kT by only considering this phenomenon. Penetration power of the diluent has been shown by Berthon and co-workers40 to be the dominant mechanism in quenching the third-phase boundary condition limit: when the diluent shortens, it penetrates more, so the chains of the extractant protrude, enhancing the steric repulsion between adjacent reverse micelles along the mechanism established by Erlinger et al.53 The effect of perturbation of the complexation is shown on the same scale as the entropy and film bending in Figure 7.

groups are strongly repelled from soft cations, so perturbation by the second coordination sphere can be considered.50,51 To try to attribute relative importance of film bending versus perturbation of the coordination, we designed an experiment to test if the “penetrating power” of the diluent is involved, following the path on classical studies performed since long time on “penetrating power” of diluent mixtures in surfactant microemulsions.31,42,52 In the case of double chain cationic synthetic lipid able to extract (i.e., solubilize) large amounts of water, it was found that long chains did not penetrate into the extractant film, hence allowing large curvature radius (spontaneous curvature p = 1). Inversely, short or branched alkanes can adapt their conformation, so they mix easily with the ethyl-hexyl branched chains. The result is that the branched diluents “wet” more easily the polar cores of the micelles. This is routine in the formulation of oil-soluble lubricants. The crucial point (and experimental proof of the mechanism) of diluent penetration is the nonlinearity effect when mole fractions of long and short chain alkanes are used. Suppose that penetration of diluents, that is, mixing of alkane and ethyl-methyl chain, occurs: if one uses even 25% of short chain alkane mixed with 75% of long chain, the effect of the 25% of short chain will be nonlinear, since there is preferential penetration and some partition in chain wetting. If mean field approach for diluent effect applies, then the curve of selectivity should follow the dashed line with mixed diluents, using a linear interpolation according to the constituents of diluent mixture. If, on the other hand, diluent penetration in the outer shell is the dominant mechanism, then some of the molecules only penetrate in the outer shell. There are always enough molecules available for this at low entropic cost, with shorter or branched chains. As Figure 6 shows, strong nonlinearity in the direction

Figure 7. Main results plotted on the selectivity curve U/Fe and ΔGtransfer, as a function of the TOPO molar ratio.

■

CONCLUSION Finally, the main results can be all plotted in Figure 7, containing the mechanisms contributing to the diluent effects on U/Fe selectivity: (i) Any maximum of uranium extraction and selectivity versus mole fraction of extractants always correspond to a favored free energy of aggregation. (ii) The increase until the maximum of synergy can be explained by an increase of aggregation numbers for U-occupied micelles of Nagg = 3 without TOPO added toward Nagg = 3.5 at the maximum synergy in the case of heptane to Nagg = 5 in the case of hexadecane. This is the order of magnitude expected, but cannot be demonstrated directly, since a scattering experiment is not easy for samples containing 10−50 times less uranium than extractant molecules. Configurationally, entropy between aggregation numbers and complexation numbers explains the increase of synergy always observed for initial addition of TOPO. The decrease after 20% TOPO ratio involves the two hypotheses proposed in the beginning: (a) extractant film bending energy and (b) perturbation of the first coordination

Figure 6. Evidence of the nonlinearity of extraction by modifying the diluent as a function of the molar TOPO ratio. Pure heptane (black), pure hexadecane (blue), experimental mixed diluent 25% heptane/ 75% hexadecane (red), and expected effect diluent 25% heptane/75% hexadecane (red dashed line).

expected for diluent penetration occurs above the maximum of selectivity for TOPO mole fraction 20%, but not below. Therefore, the free energy cost of bending associated with diluent penetration mechanism occurs to participate in the quenching of selectivity above the maximum of the selectivity curve. In a systemic chemistry approach, this nonlinearity effect of mixed diluent (as “input”) on the selectivity (as “output”) is a direct proof that diluent penetration, with short chain alkanes, participates to the quenching of the efficiency of uranium extraction when the TOPO molar ratio is beyond 0.2. Since, 7013


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(4) Shen, Y.; Xue, W.; Niu, W. Recovery of Co(II) and Ni(II) from Hydrochloric Acid Solution of Alloy Scrap. Trans. Nonferrous Met. Soc. China 2008, 18, 1262−1268. (5) Zhang, P.; Yokoyama, T.; Itabashi, O.; Suzuki, T. M.; Inoue, K. Hydrometallurgical Process for Recovery of Metal Values from Spent Lithium-Ion Secondary Batteries. Hydrometallurgy 1998, 47, 259−271. (6) Wong, C. P.; Urasaki, N. Separation of Low Molecular Siloxanes for Electronic Application by Liquid-Liquid Extraction. IEEE Trans. Electron. Packag. Manuf. 1999, 22, 295−298). (7) Mishra, S.; Chakravortty, V.; Rao, P. R. V. Synergistic Extraction of uranium(VI) and americium(III) with Binary Mixtures of Aliquat 336 and PC 88A-TOPO from Nitric-Sulfuric Acid Medium. J. Radioanal. Nucl. Chem. 1995, 201, 325−331. (8) Pai, S. A.; Lohithakshan, K. V.; Mithapara, P. D.; Aggarwal, S. K. Solvent Extraction of Uranium(VI), Plutonium(VI) and Americium(III) with HTTA/HPMBP Using Mono- and Bi-Functional Neutral Donors: Synergism and Thermodynamics. J. Radioanal. Nucl. Chem. 2000, 245, 623−628. (9) Muller, J. Spéciation Dans Les Phases Organiques Des Systèmes D’extraction Liquide-Liquide Contenant Un Malonamide et Un Acide Dialkylphosphorique; Thèse de l’Université de Paris XI, 2012. (10) Ellis, R. J.; Anderson, T. L.; Antonio, M. R.; Braatz, A.; Nilsson, M. A SAXS Study of Aggregation in the Synergistic TBP−HDBP Solvent Extraction System. J. Phys. Chem. B 2013, 117, 5916−5924. (11) Dourdain, S.; Hofmeister, I.; Pecheur, O.; Dufrêche, J.-F.; Turgis, R.; Leydier, A.; Jestin, J.; Testard, F.; Pellet-Rostaing, S.; Zemb, T. Synergism by Coassembly at the Origin of Ion Selectivity in Liquid−Liquid Extraction. Langmuir 2012, 28, 11319−11328. (12) Rydberg, J.; Musikas, C.; Choppin, G. R. Principles and Practices of Solvent Extraction; M. Dekker: New York, 1992. (13) Osseo-Asare, K. Aggregation, Reversed Micelles, and Microemulsions in Liquid-Liquid Extraction: The Tri-N-Butyl Phosphatediluent-Water-Electrolyte System. Adv. Colloid Interface Sci. 1991, 37, 123−173. (14) Zemb, T.; Bauer, C.; Bauduin, P.; Belloni, L.; Déjugnat, C.; Diat, O.; Dubois, V.; Dufrêche, J.-F.; Dourdain, S.; Duvail, M.; Larpent, C.; Testard, F.; Pellet-Rostaing, S. Recycling Metals by Controlled Transfer of Ionic Species between Complex Fluids: En Route to “ienaics”. Colloid Polym. Sci. 2014, 1−22. (15) Wilson, A. M.; Bailey, P. J.; Tasker, P. A.; Turkington, J. R.; Grant, R. A.; Love, J. B. Solvent Extraction: The Coordination Chemistry behind Extractive Metallurgy. Chem. Soc. Rev. 2014, 43, 123−134. (16) Ross, J.; Ellis, Y. M. Periodic Behavior of Lanthanide Coordination within Reverse Micelles. Chem.Eur. J. 2013, 19, 2663−2675. (17) Ross, J.; Ellis, Y. M. Complexation-Induced Supramolecular Assembly Drives Metal-Ion Extraction. Chem. - Eur. J. 2014, 20, 12796−12807. (18) Gannaz, B. Spéciation Moléculaire et Supramoléculaire de Systèmes D’extraction Liquide-Liquide À Base de Malonamide Et/ou D’acides Dialkylphosphoriques Pour La Séparation An(III)/Ln(III); Thèse de l’Université de Paris XI, 2007. (19) Baes, C.; Blake, C. A.; Brown, K. B. Solvent Extraction with Alkyl Phosphoric Compounds. Ind. Eng. Chem. 1958, 50, 1763−1767. (20) Bunus, F. T.; Domocoş, V. C.; Dumitrescu, P. Synergic Extraction of Uranium from Phosphate Solutions with Di-(2 Ethylhexyl) Phosphotic Acid and Tri-N-octylphosphine Oxide. J. Inorg. Nucl. Chem. 1978, 40, 117−121. (21) Beltrami, D.; Mercier-Bion, F.; Cote, G.; Mokhtari, H.; Courtaud, B.; Simoni, E.; Chagnes, A. Investigation of the Speciation of uranium(VI) in Concentrated Phosphoric Acid and in Synergistic Extraction Systems by Time-Resolved Laser-Induced Fluorescence Spectroscopy (TRLFS). J. Mol. Liq. 2014, 190, 42−49. (22) Wennerstrom, H.; Lindman, B. Micelles - Physical-Chemistry of Surfactant Association. Phys. Rep. 1979, 52, 1−86. (23) Zemb, T.; Duvail, M.; Dufreche, J.-F. Reverse Aggregates as Adaptive Self-Assembled Systems for Selective Liquid-Liquid Cation Extraction. Isr. J. Chem. 2013, 53, 108−112.

sphere. A loss of extraction/coordination energy when diluent penetrates in the first/second coordination sphere can indeed not be excluded. The full curve (including the nonlinearity beyond x = 0.3), instead of being strange counterintuitive values that cannot be adjusted without a dozen parameters within the multiple equilibrium models, could be qualitatively rationalized based on first-principles only by considering: (i) Curvature free energy frustration associated with the volume of coextracted species shows that spontaneous curvature is larger than the real curvature, once extracted species is in the core but appears to be a minor term. (ii) Diluent penetration near the first coordination sphere may degrade further the efficiency of supramolecular complexation within the aggregate that is mixed with diluent. Since the scattering cannot be done in conditions where all (or most) reverse aggregates are occupied, direct determination of the quantitative relative influences of this four mechanism cannot be performed at the moment. However, temperature variation as well as measuring the synergy while exchanging the proton of HDEHP to sodium may allow one to measure the predictive power of the first, to our knowledge, nonparametric explanation of synergetic extraction as proposed in this paper. In this work, the role of the chain length of aliphatic diluents on solvent extraction mechanisms was studied, in particular the case of a synergistic mixture of extractant HDEHP:TOPO. As changing the diluent is expected to play on the aggregation and not on chelation properties of the extractant molecules, this strategy aimed at estimating the importance of these extraction motors in the extraction mechanisms. We proposed here the interplay between configurational entropy, film bending entropy cost, and perturbation of the complexation shell as the combined origins for the selectivity observed, that varies strongly with nature of diluent.

■

ASSOCIATED CONTENT

S Supporting Information *

Molecular concentrations of extracted solutes; water content and acid extraction for contacted samples; model to fit SANS data; configurational entropy calculation. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b01478.

■ ■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the European ERC REE_CYCLE project and the France Labex Chemisyst ANR_LABEX_05_01, NEEDS Resources, ITU; discussion with J. Causse and P. Bauduin is acknowledged.

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REFERENCES

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