Thermodynamic Description of Synergy in Solvent Extraction: II

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Thermodynamic Description of Synergistic Extraction: II – Thermodynamic Balance of Motors Implied In Synergistic Extraction Julien Rey, Michael Bley, Jean-Francois Dufrêche, Simon Gourdin, Stéphane Pellet-Rostaing, Thomas N Zemb, and Sandrine Dourdain Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02068 • Publication Date (Web): 23 Oct 2017 Downloaded from http://pubs.acs.org on November 4, 2017

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Thermodynamic Description

of

Synergistic Extraction:

II

–

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Thermodynamic Balance of Driving Forces Implied in Synergistic

3

Extraction J. Rey1, M. Bley1, J-F. Dufrêche1, Simon Gourdin,1 S. Pellet-Rostaing1, T. Zemb1 and S. Dourdain1

4 5 6

1

ICSM/LTSM, CEA/CNRS/UM2/ENSCM UMR5257, Site de Marcoule, Bat. 426, 30207 Bagnols sur Cèze, France

7 8

ABSTRACT - In the second part of this study, we analyze the free energy of transfer in the case of

9

synergistic solvent extraction. This free energy of the transfer of an ion in dynamic equilibrium

10

between two coexisting phases is decomposed into four driving forces combining long-range

11

interactions with classical complexation free energy associated with the nearest neighbors. We

12

demonstrate how the organo-metallic complexation is counter-balanced by the cost in free energy

13

related to structural change at colloidal scale in the solvent phase. These molecular forces of

14

synergistic extraction are not only driven by the entropic term associated with the tight packing of

15

electrolytes in the solvent and by the free energy cost of co-extracting water toward the hydrophilic

16

core of the reverse aggregates present but also by the entropic costs for the formation of the reverse

17

aggregate and by the interfacial bending energy of the extractant molecules packed around the

18

extracted species. Considering the sum of the terms, we can rationalize the synergy observed, which

19

cannot be explained in classical extraction modeling. We show an industrial synergistic mixture

20

combining an amide and a phosphate complexing site, where the most efficient/selective mixture is

21

observed for a minimal bending energy and maximal complexation energy.

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INTRODUCTION - A thermodynamic rationalization taking into account not only supramolecular

24

complexation with nearest neighbors but also molecular forces1 and bending energies2 was proposed

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for the first time in 2015.1 In this multi-scale framework, strong organo-metallic complexation with

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the nearest neighbors combines with long-range interactions as well as entropic effects to favor

2

cation transfer from the water phase to the organic phase.3 As has been increasingly proposed in the

3

literature,4 this supramolecular study based on complexation and the colloidal approach considering

4

weak molecular mechanisms5-6 confirmed that the reverse micellization of extractant molecules plays

5

a major role in solvent extraction mechanisms.3, 7 Considering a typical solvent extraction system with

6

distribution coefficients of approximately 10, it was noted that the chelation energy, which is

7

commonly estimated to be on the order of -30 kT, cannot alone explain the corresponding cation

8

transfer energy of -2 kT. To solve this discrepancy, Dufreche et al. demonstrated quantitatively that

9

the thermodynamic driving forces resulting from the extractant reverse micellization effect and from

10

the consequent effects of packing water and cations into the so-called microemulsion are the driving

11

forces towards the thermodynamic equilibrium state for solvent extraction. A thermodynamic

12

interpretation of the aggregation processes taking place in the organic phase in solvent extraction

13

systems provides crucial information about the aggregate properties and the extraction efficiency.3

14 15

Herein, we introduce a quantitative estimation of the thermodynamic contributions in the specific

16

case of synergistic liquid-liquid extraction systems. Synergy allows for increasing the efficiency of a

17

given volume of a liquid-liquid exchange column by four orders of magnitude, adding one or more

18

components to the “main” extractant. The first complete public expression of this highly classified

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industrial problem was due to HR Irving, leading the UK effort in actinide extraction at ISEC 1966.8

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The main points that were clear fifty years ago were that the observed effects were highly non-linear

21

in mixing and that some molecules seem to participate in the extracting aggregate and not with the

22

molecules engaged in complexation with a metal cation as the first neighbor. The molecules

23

participating in a water-poor reverse aggregate in the solvent but not participating in the

24

complexation chemical equilibria were called adduct. As these molecules do not participate in the

25

complexation, they do not appear in the apparent constants used for the modeling processes, and it

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has been noted since the sixties that nonlinear extraction could not be calculated unless a very large


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number of different complexes with assumed different specific free energies of transfer were

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considered.8 Precise data are necessary but are very rarely published as these are the core processes.

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Synergistic extraction was only recently correlated to the synergistic micellization of the extractant

4

molecules, which may also be named in aggregate when the reverse micelles are quite small.9-14 In

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the case of the HDEHP-TOPO (Di-(2-ethylhexyl)phosphoric acid - tri-n-octylphosphine oxide)

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synergistic system, the estimation of free energies of transfer was shown to be concomitantly

7

minimized with the free energy of aggregation/micellization15. However, in the absence of chelated

8

cations in the cores of the aggregates, synergistic aggregation could no longer be observed.15-16

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Synergistic aggregation effects are therefore not intrinsic but rather depend implicitly on the

10

chelation process as they represent a nucleation effect.17 Penetration of the hydrophobic shell of

11

reverse aggregates by the solvent is known to be dependent on the solvent configuration entropy,18-

12

20

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very important contributions to the thermodynamic balance.18-20 A first general success of taking into

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account solvent penetration was a quantitative prediction of the critical point in the Liquid/liquid

15

phase separation.3

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To rationalize all experimental evidence of the aggregation effects of synergistic extraction, the

17

present study proposes an extensive thermodynamic description of synergistic extraction at

18

equilibrium conditions. We use as an example in this work a couple of amine and phosphonate

19

extractants for which all equilibrium constants have been re-determined, and the methods of

20

characterization used are described in part I. The language has evolved since the first studies of

21

synergistic systems in the pioneering work of Irving. Currently, complexants and adducts are two

22

types of oil-soluble surface-active agents – i.e., surfactants – with an active head. The aggregation

23

number N of a given aggregate is the sum of the complexation number as determined by the titration

24

“slope” method and the number of adducts per aggregate as determined by physico-chemical

25

methods.

and it was shown that the curvature of the aggregates and the entropy of configuration represent


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In the first part of this study, it was shown that the transfer of acid and water extracted by the

4

synergistic mixed system HDEHP (bis(2-ethylhexyl) phosphoric acid)-DMDOHEMA (N,N’-dimethyl-

5

N,N’-dioctylhexylethoxymalonamide) can be quantitatively explained by considering the entropy of

6

mixing for only the two extractants. 21 We confirmed this result with a step-by-step recomposing

7

approach combining regular solution theory (RSL) and Bergström and Ericksons’ approach in which

8

aggregation phenomena are among the preponderant braking forces leading to low transfer energy

9

for an electrolyte from an aqueous to an organic phase. Bergström and Ericksons considered any

10

aggregate as a curved 2-D film with different homo and hetero in-plane interactions.22 It was found

11

that nitric acid is the critical ingredient to initiate synergistic aggregation. The corresponding

12

minimization of aggregation energy was consequently attributed to the attractive interactions

13

between the two extractants. Generally, this study included an estimation of the interactions

14

responsible for synergistic aggregation and showed that it is necessary to take into account the

15

dependencies between the enthalpy of extractant mixing, aggregation of free energy, and chelation

16

process to explain the origins of synergism.

17 18

Hence, the present and second part of this study contain a quantitative estimation of the main

19

competing thermodynamic contributions in the specific case of the synergistic extraction of

20

europium salts.

21

In Figure 1, a decomposition of the free complexation energy ΔGcomplexation is illustrated. Similar to the

22

work of Dufreche and Zemb,3 the free complexation energy ΔGcomplexation is decomposed as a sum of

23

the curvature energy of the aggregates, the bulk energy (which represents the Gibbs free energy of

24

the electrolyte solution confined in the polar core), and the complexation energy (Figure 1). The

25

approach of our paper focuses on the determination of the influence of those contributions in the

26

solvent extraction process.


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Figure 1. Schematic description of the free energy term acting as a “driving force” or a “brake” on

3

the transfer energy from the aqueous to the oil phase. The orange double arrow represents the

4

apparent transfer energy related to the difference between the standard chemical potential in the

5

aqueous and the organic phase before extraction.

6 7

This paper consists of three parts: first, the amount of extracted europium has been determined by

8

Inductively Coupled Plasma Atomic Emissions Spectroscopy (ICP-AES), and the Critical Aggregation

9

Concentration (CAC) has been determined by surface tensiometry, at several molar fractions of the

10

two extractant molecules. The aggregation number and the shape of the aggregates have been

11

characterized by Small-angle X-ray Scattering (SAXS) and Small-angle Neutron Scattering (SANS). In

12

the second part, the experimental results were interpreted with a newly developed thermodynamic

13

model for synergistic extractant systems to understand the role of the different energetic terms. In

14

the third part, the influence of the individual energetic contributions on the efficiency of the

15

extraction systems is analyzed.

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MATERIALS & METHODS - Organic phases were prepared with a well-defined quantity of

3

DMDOHEMA/HDEHP (reported in table SI 1) and analytical grade dodecane solvent.

4

Organic phases containing different mole fractions of DMDOHEMA either in contact with aqueous

5

solutions of varying composition, or the pure organic phase itself were investigated. The first

6

aqueous solution contained a 1 mol.L-1 nitric acid solution, and the second solution was composed of

7

50 mmol.L-1 europium nitrate in 1 mol.L-1 nitric acid. To obtain such a solution, the salt Eu(NO3)3·6H2O

8

was used.

9

To study the system in and out of synergism, the DMDOHEMA to HDEHP ratio was varied from

10

xDMDOHEMA=0 to xDMDOHEMA=1 with a constant total extractant concentration of 0.6 mol.L-1. For the

11

determination of the critical aggregation concentration (CAC), the concentration profiles for some

12

HDEHP to DMDOHEMA ratios were measured within a range of 5.10−3 to 0.6 mol.L-1. Extractions were

13

performed in test tubes by contacting and mixing 1/1 volumes of aqueous and organic phases for 1 h

14

at room temperature to reach phase transfer equilibrium.

15

- Extraction Analysis: The extraction of europium was analyzed by ICP-AES (Spectro Arcos). The

16

aqueous solution was measured before and after the extraction step. Water extraction was

17

characterized by coulometric measurements where the nitric acid was titrated with a 0.1 mol.L-1

18

NaOH solution.

19

- SAXS: SAXS measurements were performed on a home-built SAXS camera at ICSM in Marcoule. The

20

setup involves a Molybdenum source delivering a 1-mm-large circular beam of 17.4 keV. A

21

monochromatic beam is obtained by a Fox-2D® multi-shell mirror, and collimation of the beam is

22

achieved using 2 sets of “scatterless” slits, which turns out to be crucial for the quantification of weak

23

scattering near the beam-stop, together with precise monitoring of the transmission of the sample

24

and solvents used as the reference. The diffraction patterns were recorded with a MAR345 two-


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dimensional imaging plate with a typical duration of 1 hour. The measurements were performed with

2

transmission geometry using 3-mm glass capillaries.

3

- SANS: SANS measurements were performed at the French neutron facility Laboratoire Léon

4

Brillouin/Orphée (LLB/Orphée) with a PACE spectrometer using two configurations with two samples

5

at detector distances of 800 mm and 5130 mm, respectively. The wavelength λ was set to be equal

6

to 4.5 Å (∆λ/λ∼10%), and a standard two-diaphragm collimation geometry (7 mm/20 mm,

7

collimation distance of 2500 mm) was used for those measurements. By shifting the position of the

8

detector relative to the sample position, both the accessible Q max and the overlap between the two

9

configurations were increased, which allowed the covering of a total q-range from 0.01 Å-1 to 0.4 Å-1.

10

All measurements were taken under atmospheric pressure and room temperature. Measurements

11

were performed in quartz Hellma cells with an optical path of 2 mm. Standard corrections for the

12

sample volume, the neutron beam transmission, the empty cell signal subtraction, the inelastic

13

scattering, and the detector efficiency were applied to obtain the scattered intensities. The absolute

14

scale (cm-1) was calculated by normalizing the incident neutron beam. The data reduction was

15

performed with the “PASINET” software.

16

- Tensiometry: The interfacial tensions of the HDEHP/DMDOHEMA/dodecane phases were measured

17

using the drop shape method using a KrüssTM tensiometer apparatus. Drops of solvent containing

18

identical total concentrations of extractant, but with a variable mole fraction of DMDOHEMA, are

19

formed on the tip of a curved needle immersed in the aqueous phase. To avoid any further ion

20

exchange between the aqueous and organic phase, the organic drop was measured in the same

21

acidic solution with which it was contacted and previously equilibrated for the extraction. The

22

surface tension γ is derived from the shape of the drop using the following equation:

γ =

∆ ρVg 2πrF


Eq. 1

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1 2

where ∆ρ is the density difference between the two phases, V is the volume of the detached drop, r

3

is the radius of the tip from which the drop hangs, g is the gravitational acceleration, and F is the

4

Harkins and Brown empirical correction factor. The densities of the organic and the aqueous phases

5

were measured with an ultra-high precision thermostated density analyzer (Anton-Paar) based on an

6

oscillatory fork.

7 8

PART I - EXPERIMENTAL INVESTIGATION OF EXTRACTION AND AGGREGATION OF THE SYNERGISTIC

9

COUPLE HDEHP/DMDOHEMA.

10 11

Extraction results

12

The organic phase content was characterized after its contact with an acidic aqueous phase

13

containing 0.05 mol.L-1 of europium nitrate and 1 mol.L-1 of nitric acid for DMDOHEMA molar ratios:

14

xDMDOHEMA = [DMDOHEMA]/ ([HDEHP]+ [DMDOHEMA]) = 0, 0.25, 0.5, 0.75 and 1. [Water]org

[HNO3]org

[Eu3+] org

(mol.L-1)

(mol.L-1)

(mol.L-1)

0

0.082

0.001

0.018

0.25

0.150

0.034

0.021

0.50

0.210

0.065

0.019

0.75

0.268

0.100

0.015

1

0.282

0.119

0.006

xDMDOHEMA

15

Table 1. Extracted species in mol.L-1 for various DMDOHEMA molar ratios xDMDOHEMA for extraction system

16

contacted to 1 mol.L of nitric acid and 0.05 mol.L of europium nitrate.

17

Synergistic extraction of an extractant mixture is characterized by a non-linear extraction behavior

18

when one of the two extractant molecules is linearly increased in the mixture. The results from Table

-1

-1


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1

1 indicate that water is extracted synergistically, with a maximum of approximately x=0.75. Acid

2

extraction appears to be linear to slightly synergistic at xDMDOHEMA=0.75.

3

The distribution ratios of extracted Europium ( ) are plotted versus the DMDOHEMA molar ratio x

4

in Figure 2. These ratios are deﬁned as follows:

=

5 6

[] [] , − [] = [] []

Eq. 2

where [] / is the concentration of Eu in the organic/aqueous phase after the extraction

process, and [] , is its concentration before extraction. Distribution coefficient (Eu(III))

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0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0

20

40

60

80 100

Molar ratio of DMDOHEMA

7 8 9

Figure 2. Europium extraction by the organic phase (HDEHP-DMDOHEMA 0.6 M in dodecane) plotted as a function of the

10

A nonlinear trend is observed for europium extraction, with the maximum centered at 30% of the

11

DMDOHEMA molar ratio. The origin of this peculiar feature is discussed in the following by

12

calculating the Gibbs free energy of transfer and by relating it to an estimation of its thermodynamic

13

contributions. Additional thermodynamic parameters such as CAC and aggregation numbers were

14

thus characterized experimentally.

DMDOHEMA molar ratio xDMDOHEMA for extraction system contacted to 1 M of nitric acid and 0.05 M of europium nitrate.

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1

Derivation of CAC by drop shape tensiometry – To estimate thermodynamic contributions as free

2

energy of aggregation or curvature energy, CACs were determined by drop shape tensiometry, and

3

the corresponding aggregation numbers were derived from the fit of the SAXS/SANS data.

4

Figure 3 shows the surface tension plotted as a function of the DMDOHEMA ratio. In each graph, the

5

inflexion points, where the second derivative reaches its maximum, occurs when the activity of

6

extractants is high enough to drive the formation of micelles in bulk.23 The derived CAC values are

7

presented in FFigure 3f.

Figure 3. Surface tension plotted as a function of the total concentration logarithm determined via synergism (xDMDOHEMA=0 and xDMDOHEMA=1 (a and e)), and in synergistic conditions (xDMDOHEMA=0.25 to 0.75 (resp. b, c, d). Critical aggregation concentrations are plotted as a function of DMDOHEMA molar ratio (f)

8


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These experiments show that the CAC is minimized around xDMDOHEMA=0.25, which confirms that the

2

synergistic extraction of Europium is concomitant with a synergistic aggregation of the

3

HDEHP/DMDOHEMA couple.

4 5

Structural study - SANS and SAXS measurements were performed, as they provide a direct

6

characterization of the aggregates in the solution. Measurements were collected for all solutions

7

using different molar ratios of DMDOHEMA after contact with the model aqueous phase containing 1

8

mol.L-1 HNO3 and 50 mmol.L-1 of europium nitrate. Europium is used in sufficient quantities to

9

assume that all aggregates are filled with one metal ion.

Figure 4. Log-log plot of the SANS and SAXS data for the HDEHP/DMDOHEMA mixtures at different DMDOHEMA ratios 0, 0.2, 0.4, 0.6, 0.8 and 1 in dodecane and corresponding calculated curves from the core shell model (red line). Each data set is multiplied by 5n where n runs from -2 to 3 starting from the lowermost spectrum.

10 11

Figure 4 shows the log-log plot of the absolute scattered intensity, expressed in cm-1, as a function of

12

the wave vector Q, for various molar ratios of HDEHP/DMDOHEMA in diluent dodecane. For all molar


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1

ratios, SANS and SAXS data exhibit signals with a plateau at small angles and a decrease at larger

2

angles, which is consistent with the presence of globular aggregates in the organic phases.10, 15, 24-25

3

We assume that the extractant molecules self-assemble to form spherical reverse-micelles-like

4

aggregates, as it is often assumed for these systems.21 On the one hand, as neutron scattering is

5

sensitive to the contrast between the deuterated (organic diluent) and the non-deuterated part of

6

the samples (extractant molecules), SANS intensities are characteristic of the whole volume of the

7

aggregates. On the other hand, as X-ray scattering is sensitive to the difference of electronic contrast,

8

SAXS intensities are more sensitive to the cores of the aggregates, which are richer in electrons.

9

Therefore, the increase of the scattering intensity observed with the DMDOHEMA molar ratio is

10

consistent with the increase of the DMDOHEMA content in the organic phase, which has a higher

11

molecular volume than HDEHP. The increase of the scattering intensity is also consistent with the

12

increase in the volume of extracted solutes in the aggregates. However, a proper fit of the data is

13

necessary to derive reliable conclusions.

14 15

Fit of SAXS and SANS data - Ignoring the crossed-term scattering between monomers and

16

aggregate,26 equations of scattering for an ellipsoidal core shell model were therefore expressed at

17

first order approximation as described in detail in the supplementary materials section. In this model,

18

a polar core containing the extracted solutes and the polar heads of the extractant molecules are

19

distinguished from the apolar shell made up of the alkyl chains of the extractant molecules, and all

20

the aggregates are assumed to be composed of a mixture of DMDOHEMA and HDEHP following the

21

proportions introduced in the solution. This assumption has been verified by ESI–MS and IR

22

measurements. The concentrations of water, acid, and europium have been determined

23

experimentally and used to estimate the scattering length densities of the core of the aggregates as

24

well as the theoretical volume and therefore the radius of the cores and of the global aggregates for

25

each aggregation number (results in supplementary information). A Gaussian polydispersity on the

26

aggregation number has been introduced in the calculation from which the mean aggregation


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number was adjusted. The quantity of monomers was fixed to the value of the CAC determined

2

experimentally. The signal of the diluent has been considered to be constant over the q range of

3

interest. After being considered according to its volume fraction, it was added to the calculated

4

intensity of the aggregates.

5 6

To obtain the optimal fit of the data, the penetration of the diluent molecule in the shell of the

7

aggregates had to be taken into account. It was noted and defined by the number of molecules of

8

diluent per extractant molecules that penetrate the shell of the aggregates, hence increasing the

9

partial molar volume V of the extractant layer in the evaluation of the packing parameter p. A non-

10

sticky hard sphere model was chosen to take into account interactions between aggregates. Finally,

11

the structural quantities derived from the fit are the mean aggregation number , the ratio

12

between the semi-axis of the ellipsoid (n) and the penetration of the diluent molecule in shell y, are

13

reported in Table 2 together with the deduced averaged radii of the aggregates and of the cores.

xDMDOHEMA

0

0.2

0.4

0.6

0.8

1

2.78

1.19

3.99

6.30

16,76

66,40

26.37

12.62

10.67

5.24

3,40

3,89

1.17

1.82

2.77

4.24

6,77

13,54

S/D x1017

26.72

0.75

1.21

3.31

4,61

8,40

4,50

5,15

5.20

5.25

5.49

5.50

n

1

3

4

5

7

9

y

0.5

1

3

4

5

7

Rcore (Å)

4,44

4,58

4.49

4.34

4.22

3.86

Ragg (Å)

8,48

11,37

12.2

14.15

15.97

16.08

C/S x1020 SANS ∆ρ2

S/D x1020

(cm-2)

C/S x1022 SAXS

14


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1

Table 2. Parameters obtained from the fit of SAXS and SANS spectra: ∆ρ, scattering length density contrast

2

between shell and diluent (S/D) and between cores and shell (C/S); , average aggregation number, deduced

3

core and total aggregate radii; y, penetration rate of diluent molecules in the outer shell of reverse aggregates;

4

and n, ratio of the two semi-axes of the ellipsoid, as a function of the DMDOHEMA ratio 0, 0.2, 0.4, 0.6, 0.8, and

5

1 for [HDEHP+DMDOHEMA]tot = 0.6 mol.L .

6

The first observations derived from the fit show an elongation of the ellipsoids when the

7

DMDOHEMA molar ratio is increased. This result is consistent with the literature as HDEHP tends to

8

form a spherical core-shell structure, and DMDOHEMA forms large elongated core-shell ellipsoids.27

9

On the other hand, it appears that the mean aggregation number increases quasi-linearly by

10

increasing the DMDOHEMA molar ratio with no particular inflexion at the synergistic ratio. This result

11

is in agreement with one of our previous studies on HDEHP/TOPO extraction systems, where

12

synergistic extraction was described as a sum of several thermodynamic parameters.28 Regarding the

13

penetration of the diluent in the shell of the aggregates, it appears that it also increases with the

14

DMDOHEMA molar ratio. This result is unexpected considering the very elongated structure of the

15

aggregates and the spacing between the apolar chains imposed by geometrical concerns.

16

Surprisingly, adding DMDOHEMA causes a decrease of the radius of the polar core, whereas the

17

extraction of polar solutes increases (cf. Table 1). This difference is mainly due to the smaller polar

18

head of DMDOHEMA compared to HDEHP. As the molecular packing parameter is defined as the

19

ratio of the apolar and polar volumes, this behavior may cause an increase of the effective packing

20

parameter to a state of minimum flexibility contributing to a decrease in the curvature of the film of

21

extractants at the same time. This situation has already been described on DDAB aggregates: when

22

adding shorter alcohols, the interfacial curvature is modified, leading to an increase of the aggregates

23

curvature and a higher oil uptake.20

-1

24 25

In conclusion, it appears that the molar ratio of DMDOHEMA affects the aggregation behavior mainly

26

by an increased penetration power of the diluent and by a structure modification, indicating an effect

27

on the curvature energy and on the size of aggregates.


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Langmuir

1 2

PART II - Thermodynamic balance of Synergistic Extraction: estimation of the different terms

3

affecting transfer energy

4

Transfer energy

5

In our case, where Eu is considered, we define the apparent Gibbs free energy of transfer denoted

6

∆Gtransfer as follows: ∆ ) = ln

[] ! []"#

Eq. 3

7

where kT is the thermal energy, [Eu]org is the total concentration of Europium in the organic phase,

8

and [Eu]aq is the total concentration of Europium in the aqueous phase.

9

The metal concentration refers to the whole solution and not to the polar part of the micelles as

10

initially considered.3, 7

11

The Europium free Gibbs energy of transfer is plotted in Figure 5 as a function of the DMDOHEMA

12

molar ratio 0, 0.2, 0.4, 0.6, 0.8 and 1.

13 14

Figure 5 Europium free energy of transfer as a function of DMDOHEMA molar ratio. Organic phase: HDEHP-

15

DMDOHEMA 0.6 mol.L-1 in dodecane; aqueous phase: 1 mol.L-1 of nitric acid and 0.05 mol.L-1 of europium

16

nitrate.


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Page 16 of 32

1

In Figure 5, a nonlinear trend is observed concerning the europium free energy of transfer with a

2

synergistic peak centered at xDMDOHEMA=0.25-0.4 DMDOHEMA molar ratio.

3

Overview of the different terms of the free energy of transfer

4

J.F. Dufrêche and T. Zemb decomposed in reference 3 different thermodynamic terms related to the

5

free energy of transfer, taking into account bulk, polarization and chain reorganization terms, which

6

decrease extraction. They showed that the polarization term is negligible. In this article, we add a

7

term for the entropy of monomeric extractant in the organic phase, -N.kT ln CAC, which hinders

8

micelle formation. Dufrêche and Zemb did not include this term, because they studied the filling of

9

preexisting micelles with metal (pseudophase model) and not the creation of new micelles. The bulk

10

term, denoted ∆Gbulk, is the entropic energy associated with the packing of electrolytes inside the

11

polar core of micelles. The chain reorganization term, denoted ∆Gchain, corresponds to the

12

modification of the packing parameter of the extractant. It may be seen as the cost to bend the

13

interface near the polar head. The main driving force for extraction is the complexation, which is the

14

sum of the interactions creating micelles, without the specific interaction of the metal with the polar

15

head of the extractant, and of the specific interaction of the metal with the polar head of the

16

extractant (complexation in the common meaning). It is denoted ∆Gcomplexation. The free energy of

17

transfer can therefore be decomposed as in the following equation:

18

∆Gtransfer = ∆Gcomplexation+∆ ∆Gbulk+∆ ∆Gchain- N.kT ln CAC

Eq. 4

19 20

Bulk term - As the bulk term is the energy cost to pack metallic ions, salts, electrolytes and the

21

extractant polar heads into the polar cores of the aggregates, the following chemical equilibrium

22

describing their transfer and confinement can be defined as follows:

23

%& & $ ) + − ()) ) + *+,%, ) + (). ) + /)0 ,) 2334 (.- ) + *+,%, )+

24

& %& ) ) + $ ) + /)0 , )


Page 17 of 32

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Langmuir

1

where i, j, k, l, and w stand for the stoichiometric coefficients of the different species in the

2

aggregates. The mean value of these coefficients is considered on all type of micelles formed

3

according to the following relation: (, *, , $, / =

. [ABC;(CA] [789:;8:?>

Eq. 5

4

The calculated results are presented in Table SI 2-5 considering that HDEHP is fully deprotonated

5

when complexing a cation from low acidic media. For the mixed system in contact with europium

6

nitrate and nitric acid, considering that the osmotic coefficient originates from deviation from ideality

7

in the solvents used, one can derive the following: ∆D=E ;:8(F. BL 7[ ) − B7[ ))²

where κ* is a generalized bending constant2,

32-34

Eq. 8

, and is the mean amount of extractant

10

molecules per aggregate. The generalized bending constant κ* considered here differs from the

11

concept of Helfrich35 (detailed explanation in SI). This generalized bending constant takes into

12

account the energetic contributions per molecule, but not per surface area. For the determination of

13

the curvature energy of the interface, it is necessary to determine the shape and the related packing

14

parameter of an aggregate of a certain composition. This parameter is determined by the

15

composition of the core and geometrical properties of the involved extractants. The effective packing

16

parameter of an aggregate pmolecule is derived from the general expression for a single extractant

17

molecule. This parameter is an intensive variable that is characteristic of the effective packing in a

18

given sample and can be evaluated as B_ =Y= =

`YZ $YZ ∙ :N b c

Eq. 9

19 20

where Vchain is the volume of the non-polar hydrocarbon chains, lchain is the corresponding length, and

21

aHeadgroup is the effective head-group area of the polar parts.36 If the size and shape of the investigated

22

aggregates are known, then it is possible to transfer the concept of the packing parameter to the


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Page 20 of 32

1

considered reverse aggregates. Experimental SAXS and SANS studies showed for the investigated

2

systems that the reverse micellar aggregates are either spherical or ellipsoidal. Investigations of

3

ellipsoidal structures with two constant radii a=b and a varying length of the third geometrical

4

7[ ) = parameter c indicated a behavior of ∆YZ

5

that of a spherical shape of the same volume, up to a c/a-ratio of 10 (detailed demonstration in SI).

6

Assuming that all aggregates investigated in this case and their corresponding hydrophilic cores can

7

be described by a spherical geometry, then the radius Rcore(x1) of the hydrophobic core for a certain

8

extractant ratio can be written as dY 7[ ) = e J

κ∗ 0

. < + >. BL 7[ ) − B7[ ))², very similar to

3 . 7 + ` + 1 − 7[ )+= ,0 `Z b,0 ) 4h [ = ,[ Z b,[

Eq. 10

9

where Vhead,1 and Vhead,2 are the headgroup volumes of extractants 1 and 2, respectively. The volumes

10

of the headgroups are given by the difference between the total volume of a single extractant

11

molecule Vtotal and the volume of the hydrophobic parts. The geometric properties of the

12

hydrophobic parts are calculated using Tanford’s equations36, and the total volume of a single

13

extractant molecule is derived from its density. The largest aggregation number Nlarge for the two

14

different extractant species37 can be estimated by += =

% 4h ∙ $YZ 3 ∙ ` =

Eq. 11

15

where lchain is the length of the hydrocarbon chains, and Vtotal is the total molecular volume of the

16

extractant molecule. Therefore, a sphere with a radius lchain contains a maximum of Nlarge extractant

17

molecules of a single species. For extractant mixtures, the length of the hydrocarbon chains lchain

18

varies with the mole fraction x1: $YZ 7[ ) = 7[ ∙ $YZ ,[ + 1 − 7[ ) ∙ $YZ ,0


Eq. 12

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Langmuir

1

When all geometric parameters for reverse spherical micelles are determined, the spontaneous

2

packing parameter of an aggregate for a certain system composition po(x1)20,

3

expressed from topologic constraints as follows: BL 7[ ) = 1 +

33, 37

can always be

$YZ 7[ ) 1 $YZ 7[ ) 0 + .i j dY 7[ ) 3 dY 7[ )

Eq. 13

4

The spontaneous packing parameter of an aggregate is here determined by considering the densest

5

packing of two extractant species 1 and 2 in a sphere of radius lchain + Rcore. Therefore, the

6

spontaneous packing parameter is the densest packing of an average extractant geometry

7

dependent on the mole fraction x1. This theoretical value for an ideal aggregate geometry is

8

compared with the effective packing parameter obtained by fitting SAXS and SANS data, and it

9

provides the effective hydrocarbon chain length (x1) - Rcore(x1) for a certain composition x1

10

of the following extractant molecules: B7[ ) = 1 +

0 < d > 7[ ) − dY 7[ ) 1 < d > 7[ ) − dY 7[ ) + .k l dY 7[ ) 3 dY 7[ )

Eq. 14

11

where (x1) is the average aggregate radius derived from scattering measurements.

12

Equation 8 subsequently allows for calculation of the bending energy of the hydrophobic chains. The

13

resulting curve for the difference between ideal and effective packing (po(x1)-p(x1))2 as a function of

14

the mole fraction of DMDOHEMA is plotted in Figure 6.


Langmuir

40

∆Gchain/κ* (kT/aggregate)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

∆Gchain / κ*

20

0

0.0 0.2 0.4 0.6 0.8 1.0

DMDOHEMA Molar ratio

1 2

Figure 7. Free energy related to the bending of the interfacial film based on the difference of the

3

ideal and the effective packing parameter (po(x1)-p(x1))2 plotted as a function of the DMDOHEMA

4

molar ratio 0, 0.25, 0.5, 0.75 and 1.

5

Figure 7 The Bending free energy, normalized by the bending constant κ ∗, shows a minimum for a

6

DMDOHEMA molar ratio located between xDMDOHEMA=0.25 and xDMDOHEMA=0.5. At this minimum, the

7

spontaneous curvature of the interfacial film almost matches the effective curvature determined

8

experimentally. This minimum, which indicates a favored curvature for mixed HDEHP/DMDOHEMA

9

aggregates, appears concomitant with the maximum of the europium extraction and with the

10

minimum of the aggregation energy.

11 12

Estimation of the bending constant, κ ∗ - To our knowledge, κ ∗ has never been determined in the

13

case of micelles of extractant molecules that are rather small and highly curved compared to the

14

reverse micelles of classical surfactants. κ ∗ was estimated in the range of 3-10 kT per molecule in the

15

case of micelles of cationic lipids.32, 38 Considering that the bending constant of a linear chain with 12

16

carbon atoms κ*linear C12 is typically on the order of 1 kT, and considering that it scales with the cube of

17

the chain length and with the number of chains (typically 3 in the case of DMDOHEMA), a value of

18

0.89 kT per molecule can be estimated:39


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Langmuir

∗ κ∗ = κ= m[0

8 % ) o3 12

Eq. 15

1

A more accurate estimation has been obtained from eq. 4, applied to the case where the system

2

contains nitric acid and no Eu. For this case, we assume that the complexation energy of nitric acid is

3

linear with the DMDOHEMA molar ratio (there is indeed no inflexion point for nitric acid extraction)

4

and that it can be written as a linear equation, as in Eq 16.

5

The results for an aqueous phase containing only water and nitric acid but no Europium salts in

6

organic phases having different molar fractions of the two extractant species have been fitted by

7

combining Equations 4 and 16: ∆ :;(W) − ∆D=E :;(W) + + ln >?> = >. BL 7[ ) − B7[ ))² + :7 + p

κ∗ 2

.< +

Eq. 16

8

where only the two fitting parameters a and b and the generalized bending constant are unknown.

9

It is also considered that the bending constant κ* remains constant for all DMDOHEMA molar ratios.

10

As shown in Figure 8, a value of κ∗ = 0.3 q 0.1 /GF$C;$C correlates best between the linear fit

11

of the complexation energy and the experimental data. The bulk free energy and chain free energy

12

are taken from calculations presented in Figure 6a and Figure 7.

13


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Page 24 of 32

1

Figure 8. Fitting the complexation energy with Eq. 16 for κ∗ = 0.1 (blue dashed line), 0.5 (black

2

dashed line) and 0.3 (red full line)

3

Figure 8 also shows that the complexation energy decreases linearly from -6 kT for pure HDEHP to -

4

16 kT for pure DMDOHEMA, which is on the order of magnitude of what is typically found in the

5

literature for apolar mixed systems of extractant.7

6

Estimation of κ∗ allows derivation of the complexation energy of the mixed HDEHP/DMDOHEMA

7

system for europium extraction.

8 9

Complexation

energy

-

The

complexation

energy

of

extractant

molecules

towards

10

lanthanides/actinides in apolar diluents is difficult to determine using classical approaches as it is

11

commonly performed in a polar diluent with, for example, UV/Vis measurements. In this work, an

12

estimation is obtained by considering that it is the main remaining contribution to the transfer. The

13

complexation energy of europium is deduced from eq. 4 thanks to the previous estimation of the

14

bulk and chain free energies: ∆ ) − ∆D=E − ∆YZ + + ln >?> = ∆Y _c=r

Eq. 17

15

A bending constant κ∗ equal to 0.3 /GF$C;$C that is constant with the molar fraction of the two

16

extractants and with the addition of 0.05 mol.L-1 of Eu is considered.

17


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Langmuir

1 2

Figure 9. Complexation energy as a function of the DMDOHEMA molar ratio when the mixed system

3

is contacted to nitric acid and europium nitrate.

4

The complexation energy of europium plotted in Figure 9 exhibits values of -23 to -19 kT, which are

5

on an order of magnitude that is consistent with the values found in the literature.7 The

6

complexation energy of Lanthanum nitrate estimated theoretically for pure DMDOHEMA in an apolar

7

diluent and in the absence of nitric acid was found to be equal to ∆Y _c=r = −30 /

8 9

:ss9Cs:8C.1 The complexation energy of Europium nitrate exhibits a nonlinear shape

∆Y _c=r = −20.5 /:ss9Cs:8C to value

in

the

range

of

∆Y _c=r = −18.5 /:ss9Cs:8C,

xDMDOHEMA=0.25

to

xDMDOHEMA=0.5

with

10

minimum

11

at ∆Y _c=r = −22.4 /:ss9Cs:8C. The non-linear shape of the curve illustrates a net

12

synergistic effect of the complexation for the transfer of europium. The curve quantitatively shows

13

that the synergistic extraction is initiated by a synergistic association of the two extractants, which

14

are thus able to form new and more efficient aggregate structures compared to the single extractant

15

species. This is the first time to our knowledge that a complexation energy has been derived for a

16

synergistic system. We show that in this particular system that the remaining contribution attributed


DMDOHEMA

a

ratio

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

here to the chelation can be synergistic in itself, even though it is not the only driving force

2

responsible for synergy of transfer.

3

This paper aimed to provide a detailed description of some of the thermodynamic contributions

4

involved in the synergistic transfer of an ion. To rationalize the main origins of synergy, the values of

5

these contributions are discussed and compared in the next part, in terms of thermodynamic driving

6

forces and barriers for metal extraction.

7 8

PART III - Origin of synergism - Currently, exploiting the enhanced efficiency of synergism in solvent

9

extraction comes mainly from empiric considerations based on systematic attempts, which appear to

10

be very difficult and time consuming considering phase diagrams containing 6 to 7 different

11

compounds. In our model system, a distribution coefficient D = 0.8 is obtained at the maximum of

12

the synergy for HDEHP-DMDOHEMA (Figure 10 orange full line). In addition to this engineering

13

approach, there is also a scientific need to convert this distribution coefficient into well-understood

14

components for the comprehension of the mechanisms related to synergistic processes. As a general

15

consensus, the transfer of an ion from an aqueous to an organic phase is primarily driven by

16

molecular affinity, which means that the interactions between the ion and the extractant in a

17

complex fluid need to be investigated in terms of enthalpy.

18

This work showed that the free energy associated with the transfer of charged compounds is a

19

balance between the following:

20

-

A very strong term favoring transfer towards the solvent phase, which can be called the

21

complexation energy. This term is represented as an upward arrow in Figure 10, and it is

22

mainly of an enthalpic nature.

23 24

-

There are three different terms, which can be combined and which were found to act as counter balances against the complexation energy: the bulk term energy (Figure 10 green


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Langmuir

1

part), the chain term (Figure 10 gray part) and the micelle formation term (Figure 10 blue

2

part).

3

Among the 4 contributions, 3 were experimentally determined, and the final one was deduced from

4

the others, which then allowed us to quantify the effect of all of these terms on the transfer energy.

5

The sum of these contributions is depicted in Figure 10.

6 7

Figure 10. Plot of the free energy of transfer as a function of the DMDOHEMA molar ratio. The main

8

contributions are summed to illustrate their influence on the transfer energy.

9

Taking into account all the terms proposed in eq. 4 shows that the synergistic transfer of europium

10 11

results from a strong impulsive synergistic complexation energy, and for the three inhibitors: -

The free energy of the bulk ∆Gbulk is almost constant over the whole range of the DMDOHEMA

12

molar ratio with 5-9 kT per aggregate. This term does not show any inflexion point at the

13

particular ratio of optimal ion transfer, but it is responsible for almost 40% of the transfer

14

energy loss.

15

-

The micelle formation term –N.kT ln CAC is the preponderant inhibitor. For a DMDOHEMA

16

mole fraction between xDMDOHEMA=0 and xDMDOHEMA=0.4, it increases linearly up to a maximum

17

value of 14 kT at the synergistic ratio and then decreases until a minimum value is reached for

18

pure DMDOHEMA.


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

-

The chain term ∆Gchain is related to the interfacial curvature. The values of this inhibitor are

2

always positive, but they decrease by a factor of 30 at the synergistic ratio compared to the

3

pure DMDOHEMA case. This minimum corresponds to a favored curvature of mixed HDEHP

4

DMDOHEMA aggregates near the maximum of europium extraction and the minimum in

5

aggregation energy.

6

-

There is a partial compensation between the chain term and the micelle formation term. If

7

the chain term is lowered, then the formation of the micelle is eased, and so the CAC is

8

decreased and the cost of bringing monomeric extractant from the bulk at a CAC to the

9

micelle is increased. As all energy costs are per micelle, the compensation is good. This result

10

is a confirmation of the validity of the procedure used to estimate the chain term.

11 12

Conclusion - In this work, we show that it is operative to distinguish between the driving forces for

13

complexation and other mechanisms, such as weak interactions beyond the nearest neighbor, to

14

rationalize the peaks in synergy observed for mixed extractant formulation. To understand

15

mechanisms in synergistic extraction, this general approach takes into account the presence of two

16

extractants, co-extracted water and co-extracted acid. We calculated, for the first time in the case of

17

synergy, the main entropic terms and long-range interactions, and we derived an estimation of the

18

competing free energy of complexation, which is the driving force for an effective liquid-liquid

19

extraction.3

20

Synergism appears in these systems for a combination of favored complexation energy of the cation

21

with favored curvature energy of the aggregate at a particular ratio, which enhances the transfer. This

22

simple hypothesis occurring at a particular ratio explains the qualitative effects of the synergistic

23

system.

24

To our knowledge, this is the first thermodynamic modeling of observed synergistic self-assembly

25

based on the first principles of colloidal self-assembly. Data versus temperature, using at least one of


Page 28 of 32

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Langmuir

1

the five classes of solvents, would consolidate the model, as would calorimetry, for which some

2

measurements are in progress in single component extraction.40 However, the transfer of an

3

electrolyte from the aqueous phase to the solvent phase is concomitant to water co-extraction as well

4

as solvent activity variation due to the “wetting” of extractant by solvents. Quantifying the role of

5

entropy-enthalpy in complex fluids cannot be done as in ideal solution by the vant’Hoff method, as all

6

sources of entropy are mixed together. Experimental determination of the entropy/enthalpy requires

7

the measurement of KD for a few ions “competing” in the same solution for a limited amount of

8

extractant, varying the temperature by 10%, i.e., 30°C, as well as following the relative humidity and

9

solvent vapor pressure simultaneously. A special milli-fluidic device located in a high-quality

10

thermostated chamber and associated with solvent vapor pressure on-line measurement is currently

11

under construction within the ERC project “REE-CYCLE” to disentangle the entropic contributions of

12

the water, the solvent and the electrolyte transfer process itself.

13

Published data are indeed scarce due to industrial confidentiality: the best data points and initial

14

discussion about the failure of complexation chemistry considered alone and used in engineering text

15

books are due to Irving and are from as early as 1966. Knowledge in this domain is able to rationalize

16

observations without adjustable parameters, but prediction of the best formulation and its resilience

17

versus T, pH and solvent branching will still take ten years. However, investigation of the origins of

18

synergy has led to the concept of intramolecular synergy, when the two complexing groups are

19

separated with a linker controlling the entropy, which is realized using designed amido-phosphonates

20

in optimized solvent by Stephane Pellet-Rostaing and coworkers.41

21 22

Acknowledgements - The research leading to these results has received funding from the European

23

Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC

24

Grant Agreement n. [320915] “REE-CYCLE”: Rare Earth Element reCYCling with Low harmful

25

Emissions. This work was also supported by the France Labex Chemisyst ANR_LABEX_05_01, NEEDS


Langmuir

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1

Resources and ITU. We thank Bernard Boullis from the French CEA “Direction de l’Energie Nucléaire”

2

for bringing to our attention (since November 2003, in a prospective report for Haut commissaire à

3

l’Energie Atomique) the importance of the mysterious and strong non-linear “synergy” effects that

4

are sometimes observed. We thank Gilles Bordier, adj. Director of CEA Marcoule, for constant

5

encouragement and support in this work.41

6 7

Reference:

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Thermodynamic Description of Synergy in Solvent Extraction: II

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