Supplementary Material
a. DFT calculations and simulation of FTIR spectra
In order to help in interpreting IR spectra, the structures of malonamide with water or acid were
optimized through DFT calculations and the vibration frequencies and IR intensities were
calculated. In a previous study,1 it has been shown that the IR spectra of tetraethylmalonamide in
octane could be reproduced very well by such calculations. N,N’-dimethyl-N,N’-diethyl
methylethoxymalonamide (labelled as DMDEMEMA) was used as a simplified model of
DMDOHEMA.
In the presence of water and nitric acid, starting structures were built where H2O and HNO3 were
hydrogen bonded to the carbonyl functions. With HCl, two starting structures were optimized: in
the first, HCl was directly hydrogen bonded to one carbonyl function while in the second, HCl
was bound to a water molecule which is itself hydrogen bonded to the carbonyl. In the molecular
structures, the chloride ion was solvated with three water molecules, to take into account the
significant amount of co-extracted water. In both optimized structures, HCl dissociates and the
proton is transferred to one carbonyl group.
In the experimental spectra, the most interesting IR regions after acid addition lie between 16001700 cm-1 (C=O stretching band), between 1400-1420 cm-1 (displacement and decrease of the
absorption band) and around 1515 cm-1 (appearance of a peak after acid extraction). The
calculated frequencies and intensities corresponding to these regions are given in Table a1.
Table a1. Calculated frequencies and IR intensities in the C=O region and for selected C-N, CH3,
and CH2 vibrations in DMDEMEMA with and without water or acid.
DMDEMEMA
DMDEMEMA.H2O
DMEMEMA.HNO3
DMEMEMA.3H2O.HCl
DMEMEMA.HCl.3H2O
ν C=O
I
ν1a
I
ν2 a
I
(cm-1)
(km/mol
(cm-1)
(km/mol)
(cm-1)
(km/mol)
1672
1655
1639
1630
1664b
1656
1630
1662
521
307
237
802
804b
160
502
444
1500
1495
1503
1496
1504
1500
58
39
74
42
43
59
1406
1411
1410
1418
1414
1418
88
126
82
121
22
95
1646
483
1508
1492
1507
1487
40
41
77
31
1637
1419
1624
1421
235
125
495
120
a
C-N stretching and bending frequencies of CH3 and CH2 groups directly attached to the amide nitrogen
atom; b HNO3 asymmetric stretching frequency.
According to the calculation, the bands in the 1515 and 1400-1420 cm-1 region correspond to the
C-N stretching coupled with the bending frequencies of CH3 and CH2 groups directly attached to
the amide nitrogen atom.
The spectrum of DMDOHEMA without water or acid was measured in octane in a previous
study.1 The values measured for the C=O stretching region (1657 and 1670 cm-1) are in close
agreement with those calculated for DMDEMEMA (1655 and 1672 cm-1). A good agreement
was also found for the C-N stretching and CH3, CH2 bending frequencies measured at 1488 and
1402 cm-1 and calculated at 1495-1500 cm-1 (v1) and at 1406-1411 (v2) cm-1.
When one carbonyl function is involved in a hydrogen bond with either water or nitric acid, the
corresponding carbonyl stretching frequency decreases by 15 to 30 cm-1, whereas  and 
increase by a few wavenumbers. The intensity of  is approximately halved. In the presence of
HNO3, a high intensity IR frequency corresponding to nitric acid was calculated in the C=O
region at 1664 cm-1. When there is a proton transfer towards one carbonyl function, as occurs in
the presence of HCl, a high intensity band appears at shorter wavenumbers (around 1620-1630
cm-1). This corresponds to the C-N stretching frequency of the protonated amide moiety, which
appears in the ~ 1410 cm-1 region for the unprotonated amide. Moreover this band at around
1620-1630 cm-1 is broad, which means that there could be overlapping of different signals
coming from C=O (1650 cm-1), protonated C-N (1620 cm-1), and an additional broadening due to
the presence of water or hydrated proton.2
To summarize, calculations show that HNO3 forms a hydrogen bond with the carbonyl function,
whereas in the presence of hydrated HCl one proton can be transferred to one of the carbonyl
functions. Both structures present similar IR signatures: the broadening and the displacement of
the band in the carbonyl stretching region at lower wavenumbers by several tens of cm-1, the
displacement of the  and 2 bands appearing around 1500 and 1410 cm-1 at longer
wavenumbers by a few cm-1, and the decrease of the intensity of the 2 band.
b. SANS data modelling
Deuterated n-heptane was chosen as the diluent in order to minimize the hydrogen incoherent
scattering background and to exploit the neutron contrast between the deuterium atoms of the
diluent and the hydrogen atoms of the extractant molecule.
In the oil phase as measured here and modelled on absolute scale by SAXS and SANS,3 two
types of non- homogeneities in the solvent have to be considered: "monomers" of DMDOHEMA
as well as ‘reverse micelles’ or aggregates containing less than 10 molecules. It has been shown
in previous work4 that typically, half of the extractant molecules are present as monomers and the
other half as N-mer aggregates, with N smaller than 10. Therefore, the standard classical
factorisation in structure and form factors as introduced by Hayter and Penfold5 is not a valid
approximation. Advantage can be taken of the fact that near the 2 phase - 3 phase boundary,
repulsive "steric" terms compensate with attractive interactions at first order. Structure factors
can therefore be ignored, and the scattering amplitude decomposed in two terms. The intensity
observed is then the square of the amplitude scattered by monomers and micelles, i.e. the form
factors associated, but also a crossed term, coming from the product of the scattering amplitude
of monomers and micelles. Experimentally, this is taken into account as a crossed term which is
explicitly calculated from molecular volumes and contrasts. This crossed term coexists with
incoherent background coming from protons as well as the background produced by the
compressibility of the solvent:
I (q) exp  I (q) mono  I (q) agg  I (q) dil  I (q) incoherent  I (q) crossed
(1)
The solvent scattering is determined with high precision by making the correction for volume
fraction and separately measuring pure solvent at the same temperature on absolute scale.6
I(q) dil   vol,dil .I(q) pure,dil
(2)
Since the incoherent background comes from proton concentration, the background can be
deduced from the known amount of protons scattering incoherently in the sample:
I(q ) incoherent  mol ,diamide .I(q ) pure,diamide
(3)
Once these two "backgrounds" have been subtracted, only scattering coming from micelles,
monomers and the crossed-term remain. All these three terms can be calculated with only
aggregation numbers and the monomer concentration as parameters. It should be noted that since
aggregation numbers are low, the transition is not sharp and the existence of micelles "before" the
critical aggregation concentration (CAC) as well as monomers "beyond" the CAC have to be
considered explicitly.7
I(q) normed  I(q) mono  I(q) agg  I(q) crossed
(4)
Finally, the scattering intensity produced by the monomers in solution can be verified by
measuring DMDOHEMA in n-heptane (≈ 0,05 mol/L) in an aqueous phase containing LiNO3
(2.93 mol/L). In this situation, only monomers are present and produce all the heterogeneities in
the solvent. The form factor which can be approximated to the intensity by ignoring
compressibility effects P(q)mono is therefore determined experimentally and is not a parameter in
the fitting procedure.
The crossed term is treated as incoherent, i.e. by ignoring the correlation between positions of
monomers and reverse aggregates:
P(q)  (f mono (q, R1 )  f mono (q, R 2 )  f agg (q, R1 )  f agg (q, R 2 )) 2
Therefore:
(5)
P(q)  P(q) mono  P(q) agg  2.(f mono (q, R 1 )  (f mono (q, R 2 )).( f agg (q, R 1 )  f agg (q, R 2 ))
(6)
with : - P(q)mono = (fmono(q,R1)+ fmono(q,R2))2 : monomer form factor;
- P(q)mono = (fagg(q,R1)+ fagg(q,R2))2 : aggregate form factor;
- 2.(fmono(q,R1)+ fmono(q,R2)).(fagg(q,R1)+ fagg(q,R2)) : crossed term.
If the concentration of monomers is known, scattering produced by monomers as well as the
crossed term is evaluated in each loop of the fitting, along the self-consistent method introduced
by Hayter8 and taking into account molecular volumes. Curves are fitted on absolute scale, and
scale factor is not an adjustable parameter.9 Figure a1 shows the relative importance of the
different terms in scattering on a logarithmic scale. Fitting in absolute scale and therefore
determination of aggregation numbers is not possible without carefully taking into account the
effect of monomers in this way. Whenever an attractive potential is needed, the structure factor is
affecting only the form factor of micelles, in a classical way.10
Figure a1: Experimental SANS signal with the relative importance of the different terms in
scattering intensity I(q)exp for DMDOHEMA solution (0.483 mol/L) in deuterated n-heptane in
thermodynamic equilibrium with LiNO3 solution (2.93 mol/L) at 24 °C.
Components shown : I(q)mono () scattered by free monomers at 0.21 mol/L, I(q)agg ()
scattering by reverse aggregates, I(q)dil () background from deuterated heptane and due to its
isothermal compressibility, I(q)incoherent () incoherent scattering, and I(q)crossed () the
aggregate-monomer cross-term.
Using this procedure requires a definition of the "polar" and "apolar" parts of the complexing
molecule. The polar part belongs to the core and the apolar part is mixed with the solvent when
calculating scattering length densities. It is important to understand that this partition can be
arbitrarily decided on: the final fit in aggregation number and attraction potentials is independent
of this choice.11 Exact values of the polar core radius in tables depend on the choice and a
definition of "polar" and "apolar" part related to the structure of the molecule was taken, see
Figure a2.
Figure a2. Self-consistent definition of “polar” and “apolar” parts of the extractant molecules
involved (DMDOHEMA). The scattering lengths of nuclei of the two parts of the molecule as
well as partial molar volumes were taken into account in modeling the scattering.
Since all molecular volumes were known, as well as the volume of co-extracted water, the only
parameters required were the aggregation number, the concentration of monomers and the depth
(in units of kBT) of the sticky hard sphere potential, assumed to be active in a range taken as
R/10, where R is the radius of the micelle polar core.
Figure a3 gives SANS data for organic solution of DMDOHEMA in n-heptane after contact with
3 mol/L LiNO3 (non extracted salt), 3 mol/L HNO3 and 2.5 mol/L HClO4 on an absolute intensity
scale (water activity was kept constant). The intensity of the signal I(Q) was corrected for the
contribution of the diluent and for the incoherent scattering signal due to the DMDOHEMA
hydrogen atoms.
Figure a3. Experimental SANS signal I(q) for 0.483 M DMDOHEMA solution in deuterated nheptane after contact with: 3 mol/L LiNO3 (only water is extracted in organic solution), 3 mol/L
HNO3 , 2.7 mol/L HCl, and 2.5 mol/L HClO4 at 24 °C.
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