Aggregation and Protonation Phenomena in Third Phase

J. Phys. Chem. B 2001, 105, 2551-2564

2551

Aggregation and Protonation Phenomena in Third Phase Formation: An NMR Study of the Quaternary Malonamide/Dodecane/Nitric Acid/Water System Lydie Lefranç ois, Jean-Jacques Delpuech,* Marc He´ brant, Jacques Chrisment, and Christian Tondre Laboratoire de Chimie Physique Organique et Colloı¨dale, Unite´ Mixte de Recherche CNRS-UHP (UMR 7565), UniVersite´ Henri Poincare´ -Nancy I, B.P. 239, 54506 Nancy-VandoeuVre Cedex, France ReceiVed: July 10, 2000; In Final Form: December 7, 2000

The phase behavior of the liquid-liquid solvent extraction system DMDBTDMA (see the text) in n-dodecane/ aqueous HNO3 has been studied by NMR spectroscopy. Increasing HNO3 concentration in the aqueous phase beyond a critical value of 3.2 mol dm-3 results in the splitting of the organic phase into two layers, the so-called third phase formation. NMR investigations used three indications: (i) the variations of the chemical shifts of carbonyl groups (δco) in DMDBTDMA and of (ii) attached water molecules (δAC), induced by protonation of DMDBTDMA, and (iii) the Z,E isomerism of amide units in DMDBTDMA, characterized by the molar ratio (1-Fh ) (or Fh ) of Z (or E) units. The analytical HNO3 to DMDBTDMA ratio proved to be appropriate to represent the variations of the above NMR parameters characterizing the organic phase(s) throughout biphasic and triphasic domains, without discontinuity. Considering the organic phase(s) to contain mixtures of species AMi , resulting from the association of one DMDBTDMA (A) with i HNO3 molecules (M), allowed us to calculate the intrinsic values δico, δiAC and Fi of NMR parameters relative to each species AMi. The main results from this analysis are (i) the presence of only one associated species, AM throughout the biphasic domain, and of a mixture of all associated species AMi (i ) 1 to 3) in triphasic systems; (ii) the progressive protonation of DMDBTDMA molecules on increasing the number of associated HNO3 molecules, approaching completion when i ) 2; (iii) a stepwise behavior of the conformational fraction Fi, decreasing from 0.35 (i ) 0 and 1) to 0.22 (i ) 2 and 3). The above information suggests a phenomenon other than amide protonation to accompany third phase formation, namely a structural change in DMDBTDMA aggregates, tentatively described as the passage from a reversed micelle-like closed structure to an open “bicontinuous” structure, in analogy with the pseudophases mentioned in ternary water/surfactant/oil systems.

Introduction One important problem in designing a liquid-liquid extraction system is third phase formation, that is the splitting of the organic phase into two layers when the aqueous phase is highly concentrated in solutes.1 This problem has been especially encountered in nuclear wastes reprocessing where the separation of radioelements from used nuclear fuels is an essential step. Very schematically, nitric aqueous solutions of radioelements are submitted to liquid-liquid extraction, using an organic immiscible solvent and an extracting reagent. To improve the efficiency of these processes, studies at the CEA,2-4 in collaboration with European laboratories,5 have used new extracting reagents of the diamide type, having some required properties in the so-called DIAMEX6 (DIAMide EXtraction) process. N,N′dimethyl-N,N′-dibutyl-2-tetradecylmalonamide (DMDBTDMA) proved to be one of the best-suited diamides to extract trivalent actinides from nitric acid solutions into aliphatic diluents. Third phase formation then consists of the separation of the aliphatic solvent into an “intermediate” solute-rich (“third”) phase and an upper solute-depleted phase. Third-phase formation may then result in critically hazardous concentrations of radioelements in the solute-rich phase, and this explains why this phenomenon has been actively described and delineated in practice.2-4,7 More fundamental studies are aimed at establishing thermodynamic and structural properties of these systems in an effort to improve their efficiency and to theoretically predict third

phase formation.8-9 Some information on the structure of organic phases encountered in the DMDBTDMA/dodedane/ nitric acid/water system has already been obtained through IR spectroscopy7,10 and small-angle X-ray scattering1 (SAXS). In this prospect, this work reports NMR investigations on conformational changes suffered by DMDBTDMA molecules and on the protonation of their carbonyl groups when a dodecane solution of the diamide is put in contact with an aqueous nitric acid solution of variable concentration. In a previous publication,11 we examined a specific NMR feature of DMDBTDMA molecules in a single pure solvent (CDCl3), namely the Z,E stereoisomerism on each amide moiety. This results in the presence of four stereoisomers in the diamide, namely the ZZ, ZE, EZ, and EE conformers, where ZE and EZ are in fact an NMR-indiscernible enantiomeric pair (Scheme 1). Under favorable conditions, up to four resonances are observed by NMR spectroscopy, at the rate of one resonance per ZZ or EE conformer and two resonances for the Z and E ends of the enantiomeric pair; these resonances will be referred to as ZZ, EE, ZE, and EZ, respectively, in the following. Changes in the chemical shifts and intensities of these signals were observed when introducing nitric acid into neutral dodecane solutions of DMDBTDMA. These changes were tentatively assigned to associations AMi (i ) 0 to 3) between DMDBTDMA and HNO3 molecules (symbolized by the letters A and M, respectively, in the above formula), characterized by

10.1021/jp002465h CCC: $20.00 © 2001 American Chemical Society Published on Web 03/10/2001

2552 J. Phys. Chem. B, Vol. 105, No. 13, 2001

Lefranç ois et al.

SCHEME 1: Structure of the Four Stereoisomers ZZ, ZE, EZ, and EE of DMDBTDMA Together with cis (c) or trans (t) Positions of N-Me and N-Bu Substituents

a set of adjustable parameters. Consideration of the set of adjusted parameters allowed us in turn to shed some light on structural changes induced by third phase formation. Experimental Section Materials. N,N′-dimethyl-N,N′-dibutyl-2-tetradecylmalonamide (DMDBTDMA) was obtained from PANCHIM (France) and was purified before use by chromatography on alumina B (ICN) with pentane (Fluka) as eluent. Solutions were prepared with deuterated chloroform (euriso-top) or with dodecane (Fluka purum). Aqueous solutions were prepared with HNO3 65% (Fluka) and water purified using an Elix 3 device (Millipore). Methods. DMDBTDMA concentrations were determined in the organic phases using an HPLC protocol as described previously.1 In some instances, the NO3- concentrations in the organic phases were determined simultaneously using the first peak on the same chromatograms. H+ concentrations in the aqueous phases were determined by titration with NaOH using a Methrom 716 DMS titrino apparatus. The acidity in the organic phase was measured after back extraction of H+ with a given volume of aqueous NaOH and titration of excess NaOH by HCl. Water contents were measured using the classical Karl Fischer method (Methrom E 547). NMR Spectroscopy. 1H and {1H}13C spectra were recorded at 400 and 100.1 MHz on a Bruker DRX 400 spectrometer at 25 °C. Capillaries filled with either tetramethylsilane (TMS) in CDCl3 or 2,2-dimethyl-2-silapentane-5-sodium sulfonate (DSS) in D2O were used as external references for 13C or 1H resonances, respectively. The water content [H2O]o in the organic phases was obtained by comparing the intensity IHa of total time-averaged acidic protons (from both HNO3 and H2O) to the intensity ICH3 of the two N-methyl groups in DMDBTDMA. The concentration of water can then be deduced from the intensity ratio IHa/ICH3 by the formula

IHa/ICH3 ) (2[H2O]o + [HNO3]o)/(6[DMDBTDMA]o) provided that HNO3 and DMDBTDMA concentrations have been determined previously (see above). The results obtained by NMR are in full accord with the above measurements by Karl Fischer titrations. Results Operating Conditions. All experiments were carried out at a constant temperature of 25 °C. The phase behavior of the quaternary system dodecane/DMDBTDMA/water/HNO3 has been described in previous publications1,8-9 and can be summarized as follows. The two immiscible solvents, dodecane and

Figure 1. Plot of [DMDBTDMA]i vs [HNO3]aq showing biphasic and triphasic domains in the quaternary DMDBTDMA/dodecane//HNO3/ H2O system at 25 °C, and explored paths A, B, C in NMR investigations.

water, have opposite solubilizing properties toward the two other members of this quaternary system. On one hand, DMDBTDMA is totally soluble in dodecane and undetectable (< 10-4 mol dm-3) in aqueous phase due to strong hydrophobic properties. On the other hand, nitric acid is totally soluble in water and detected at a concentration of ca. 3 × 10-3 mol dm-3 in a dodecane phase set in equilibrium with concentrated (65% per weight) nitric acid. In the presence of a dodecane solution of DMDBTDMA with initial concentration [DMDBTDMA]i , aqueous nitric acid (concentration: [HNO3]i) is partially extracted from the aqueous to the organic phase, with partitioning concentrations [HNO3]aq and [HNO3]0, respectively. As soon as [HNO3]aq exceeds a critical limit [HNO3]lim ≈3.2 mol dm-3 when [DMDBTDMA]i ≈ 0.5 mol dm-3, the splitting of the organic phase takes place with partitioning of DMDBTDMA: the extractant concentration in the middle phase is increasing up to a limit close to 1.2 mol dm-3, while the upper dodecane phase is almost depleted as the HNO3 content is increased in the aqueous phase. According to Gibb’s phase rule,12 quaternary systems maintained at constant temperature (25 °C) and pressure (1 atm) are monovariant in triphasic domains, i.e., the concentrations of any species in any phase are determined as a function of one of these only, arbitrarily chosen as the unique variable governing the phase behavior of the system: HNO3 concentration [HNO3]aq in the aqueous phase after equilibration in the present case. Variations of [HNO3]aq then determine (i) the biphasic or triphasic nature of the system, depending on whether [HNO3]aq is smaller or larger, respectively, than a critical value [HNO3 ]c, which happens to be very close to the limiting value [HNO3 ]lim described above due to the choice of [DMDBTDMA]i ) 0.5 mol dm-3; (ii) DMDBTDMA concentrations in both intermediate and upper organic phases of triphasic systems, a′ and a′′, respectively. A plot of [DMDBTDMA] Vs [HNO3]aq then constitutes the border between biphasic and triphasic domains in the phase diagram thus obtained (Figure 1). Concentrations a′ and a′′ are obtained at the intersections M′ and M′′ of this curve with a vertical conjugation line drawn at the running concentration [HNO3]aq. Starting along a horizontal line (A in Figure 1) from the biphasic domain where the extractant is fully contained in the organic layer in the

Aggregation and Protonation Phenomena concentration [DMDBTDMA]i ) a such that a′′ < a < a′, phase splitting occurs on progressive addition of HNO3 until [HNO3]aq > [HNO3 ]lim. Concentrations a′ and a′′ are independent of the initial DMDBTDMA concentration and should obey the lever rule: V′ (a′ - a) ) V′′ (a - a′′), where V′ and V′′ are the volumes of the intermediate and upper organic phases. The boundary curve in Figure 1 is reminiscent of a consolution curve as observed in thermal phase diagrams of many surfactant/water binary systems.13 The analogy becomes clear if we imagine to turn the diagram of Figure 1 by 90° and formally replace the variable [HNO3]aq along the vertical coordinate axis thus obtained by temperature. In this view, the abovementioned critical concentration [HNO3]c is equivalent to a lower critical temperature. The existence of a consolution curve is assigned to a competition between internal energy factors, which favor phase separation, and entropy effects, which favor miscibility.14 In the present case, solute-solute (DMDBTDMA), solventsolvent (n-dodecane), and solute-solvent interactions are essentially due to hydrophobic effects between C12, C14, and alkyl chains, presumably of similar magnitude for all three, so that internal energy considerations are not likely to account for demixtion. Under these conditions, obtaining phase separation with a lower consolute point requires the magnitude of unfavorable entropy effects to clearly decrease on addition of HNO3. This may be tentatively assigned to (i) aggregation phenomena accompanying third phase formation, which decrease the configurational entropy of mixing and (ii) the existence of internally mobile structures in triphasic systems. These two phenomena would result in a less negative and a positive contribution, respectively, to the entropy change accompanying the transition from biphasic to triphasic systems, thus permitting phase separation on addition of HNO3 beyond a critical value [HNO3]c. These predictions are in line with the microscopic models proposed in the following on the basis of the present NMR investigations. Similar considerations can be made for HNO3 partitioning itself where the corresponding concentrations in the initial biphasic and in the triphasic system after demixtion are consistently denoted as N, N′, and N′′. Due to the fact that the volume of the third phase (V′) is clearly smaller than that of the parent organic phase before demixtion (V′ + V′′), there is a sudden increase of both N and a values at demixtion: N′ > N and a′ > a. However, as the DMDBTDMA and accompanying HNO3 molecules are nearly completely extracted from the parent organic layer into the third phase formed at demixtion, the ratios N/a and N′/a′, before and after demixtion respectively, are approximately equal, their variations are in perfect continuity, and they will therefore be denoted under the single denomination N/a in the following. Moreover, for a given acidity in the aqueous phase, this ratio should be constant whatever the initial DMDBTDMA concentration. This was clearly demonstrated by plotting the overall N/a molar ratio, N/a ) [extracted HNO3]/ [DMDBTDMA]i (measured over either the single organic phase of biphasic systems, or both middle and upper phases of triphasic systems) as a function of [HNO3]aq. Six series of experiments were carried out in this way, using for each one a constant initial concentration of diamide chosen among a set of values ranging from 0.12 to 1.05 mol dm-3. As expected, all of the points from all six series together are nicely arranged along the same smooth curve (Figure 2). NMR measurements were performed using the unique organic phase in biphasic systems and the middle phase of triphasic systems. A concentration [DMDBTDMA]i ) 0.46 mol dm-3 was chosen for these experiments so as to cover the entire

J. Phys. Chem. B, Vol. 105, No. 13, 2001 2553

Figure 2. Plot of the overall molar ratio N/a ) [extracted HNO3]/ [DMDBTDMA]i as a function of HNO3 concentration in the aqueous phase, using a set of six values of [DMDBTDMA]i as shown on the graph.

TABLE 1: Operating Conditions and Conformational Ratios R along Path A in the Phase Diagram (Figure 1) at 25°C and Constant Initial Concentration of DMDBTDMA of 0.46 Mol dm-3 [HNO3]ia [HNO3]aqb [HNO3]oc [H2O]oc [DMDBTDMA]oc N/ad 0.00 1.80 2.70 3.45 4.05 5.00 6.25 7.30 8.50 10.30

0.00 1.70 2.50 3.15 3.66 4.47 5.53 6.43 7.52 9.20

0.00 0.10 0.20 0.30 0.72 1.26 1.88 2.35 2.78 3.20

0.00 0.16 0.25 0.33 0.70 1.27 1.43 1.50 1.50 1.50

0.46 0.46 0.46 0.46 0.80 1.05 1.15 1.19 1.19 1.19

0.000 0.217 0.405 0.652 0.900 1.200 1.634 1.974 2.336 2.689

Re 1.82 1.82 1.82 1.82 1.88 2.16 2.54 2.95 3.27 3.35

a Initial HNO concentration in the aqueous phase. b HNO concen3 3 tration in the equilibrated aqueous phase. c Final HNO3 (N), H2O and DMDBTDMA (a) concentrations in the equilibrated organic phase (middle phase in triphasic systems). d Molar ratio [DMDBTDMA]o: [HNO3]o. e R ) ZT/ET.

triphasic domain ([HNO3 ]lim ≈ [HNO3 ]c) of the phase diagram (path A, Figure 1). Ten points were selected along this line with abscissa [HNO3]aq running from 0 to 9.2 mol dm-3. In each of these experiments, the phases in the presence were analyzed first, focusing attention on the organic phase(s) after decantation from the aqueous layer. NMR results were displayed in the following as a function of the molar ratio N/a measured in the relevant organic phase, whatever the nature of the system and the phase under examination. In this view, the switch from biphasic to triphasic systems occurs when this ratio is increased beyond ca. 0.7. Along this coordinate, third phase formation does not result into any discontinuity in representative NMR curves described further, as it is the case for the abovementioned extraction curve shown in Figure 2. The 10 samples studied in the following thus correspond to N/a molar ratios increasing from 0 to 2.69 as the HNO3 concentration in the aqueous phase after equilibration is increased from 0 to 9.2 mol dm-3 (Table 1). Individual values of N and a are also reported in Table 1, as well as the initial HNO3 concentrations required to obtain the final [HNO3]aq values after partial extraction into organic phase(s) of an equal volume to that of the aqueous phase. Other measurements, to be reported later, of a more qualitative nature, were carried out along other paths in the phase diagram so as to ascertain the generality of the results from the exploration along path A, presently described. Neutral Solutions of DMDBTDMA in Dodecane. Line splitting due to Z,E stereoisomerism and assignment of multiplet



Figure 3. Carbonyl 13C NMR spectrum of DMDBTDMA in pure n-dodecane at 100.1 MHz and 5 °C: lines 1 and 2 assigned to resonances ZZ and ZE (in ZZ and ZE conformers, respectively); lines 3 and 4 to resonances EZ and EE (in ZE and EE conformers).

components to each of the ZZ, ZE, and EE conformers have been reported in a previous publication.11 A quartet of lines, numbered 1 to 4, is expected for each single resonance of nuclei in each amide moiety. This quartet consists of a low-field doublet for Z-type resonances (i.e., ZZ and ZE, lines 1 and 2) and a high-field doublet for E-type resonances (i.e., EZ and EE, lines 3 and 4), as shown for the 13C carbonyl resonances observed at 169 ppm and 5 °C (Figure 3). The normalized line intensities pi (i ) 1 to 4) are thus related to relative populations pXY (X, Y ) Z, E) of conformers through equations

pZZ ) p1 pZE ) 2p2 ) 2p3 pEE ) p4

(1)

In the present case, p1 ) 0.415; p2 ) p3 ) 0.23; p4 ) 0.125, and consequently pZZ ) 0.415; pZE ) 0.46, and pEE ) 0.125. The overall fractions: F h ) p3 + p4 and 1 - F h ) p1 + p2 of E and Z amide units, respectively, are represented by the global relative intensities of the high-field and low-field doublets. The ratio of these intensities is equal to the ratio R of total numbers ZT and ET of amide units in Z and E conformations:

R ) ZT/ET ) (1 - F h )/F h

(2)

with R ) 1.82 in the present case. R is found to be larger than unity, as it is the case in monoamides where the R′-C(O) substituent is larger than hydrogen, as a consequence of the size of the relevant group decreasing along the sequence R′ > CH3 > O > H.15-16 This ratio is nearly temperature independent (revealing enthalpies in Z,E-equilibria close to zero) but is highly solvent-dependent, e.g., R ) 1.56 in CDCl3 and 0.43 in benzene solutions.11 Again, these variations may be accounted for qualitatively by steric considerations. Thus, CDCl3 hydrogen bonding to carbonyl groups of DMDBTDMA hinders the cis position occupied by Z bulky N-butyl substituents, thus decreasing the predominance of the Z isomer (as compared to an alkane solvent such as dodecane). Similarly, in benzene solutions, DMDBTDMA is specifically associated to nuclei of the aromatic solvent through interactions between the π electrons of benzene and the amide partial double bond.17-18 The nearby benzene ring displayed parallel to the amide plane presumably becomes the structural factor governing steric hindrance of the amide

Figure 4. (a) N-Methyl (1H, 400 MHz) and (b) carbonyl (13C, 100.1 MHz) Z(*) and E(**) lines of DMDBTDMA in pure n-dodecane at 25 °C.

moiety with the alkyl R-substituent. The cis or trans position of N-substituents in the amide plane then is mainly determined by steric interactions with the vicinal carbonyl group, in line with the observed predominance of E conformers. As in the case of CDCl3 solutions,11 it may be observed that

p1/p2 ) p3/p4 ) R

(3)

This was assigned to a random distribution of Z and E units two-by-two among DMDBTDMA stereoisomers according to probability laws:

h )2; pZE ) 2F h (1 - F h ); pEE ) F h2 pZZ ) (1 - F

(4)

The measurement of R is thus sufficient to estimate the conformational fraction F h ) (1 + R)-1 and, consequently, all the above fractional populations pi and pXY. We took advantage of this property both to improve accuracy in measuring line integrals (over couples of lines rather than over less intense singlets) and to compute conformational fractions even in the case where partial coalescence results in the presence of two lines only, each of the two Z and E doublets being transformed into two broad singlets. This is the case when neutral dodecane solutions of DMDBTDMA are observed at 25 °C. Two singlets, instead of the expected quartet, are thus observed for the 1H N-methyl lines, permitting easy measurement of R as the ratio of the two corresponding integral line elevations (Figure 4a). If we come back to 13C carbonyl lines, we observe a still more complex coalescence pattern (Figure 4b) where the two singlets themselves have partially merged into each other, thus making any quantitative measurement impossible. This dynamic behavior has been studied in a previous publication11 and has been assigned to consecutive hindered rotations about partial double bonds in each amide moiety according to the kinetic scheme k1

k2

-1

-2

} ZE{\ } EE ZZ{\ k k

(5)

Aggregation and Protonation Phenomena


TABLE 2: Rate Constants and Activation Parameters at 25 °C for the Forward Reaction in Conformational Equilibria (5): ZZ a ZE and EE a ZE k1a s-1 ∆G1q kJ mol-1 ∆H1q kJ mol-1 ∆S1q J K-1 mol-1 CDCl3 n-C12H25

2.5 10.0

70.8 65.7

68.2 74.0

-8.0 28.0

k2 s-1 ∆G2q kJ mol-1 ∆H2q kJ mol-1 ∆S2q J K-1 mol-1 CDCl3 n-C12H25

6.2 35.0

68.6 63.9

73.4 71.5

16.0 25.5

a Expected errors are (2 s-1 on rate constants, (0.5, (5 kJ mol-1, and (15 J K-1 mol-1 on ∆Giq, ∆Hiq and ∆Siq (i ) 1, 2) values, respectively.

The barriers to rotation are clearly lower in dodecane than in CDCl3 solutions (in which case quartets are still observed at room temperature). A variable-temperature study (0° to 55 °C), performed along the same lines as in CDCl3 solution, yielded the kinetic parameters, k1, k2, and the related activation free energies, enthalpies and entropies, ∆Gqi , ∆Hqi , ∆Sqi (i ) 1, 2) displayed in Table 2, together with previous values from CDCl3 solutions for the sake of comparison. The ∆Gqi rotational barriers are then seen to be lowered by ca. 5 kJ mol-1 when dodecane is used in the place of CDCl3 as a solvent. This difference may be tentatively assigned to the slightly acidic properties of CDCl3 molecules that reinforce the amide double bond character through hydrogen bonding to the negatively charged carbonyl oxygen atom. This observation is in line with the presence of sharp ZZ, ZE, EZ, and EE quartets in acidified dodecane solutions of DMDBTDMA as described below. NMR Spectroscopy in the Quaternary DMDBTDMA/ Dodecane/HNO3/Water System. Introducing nitric acid into dodecane solutions does not bring about new resonances in DMDBTDMA spectra, it simply modifies chemical shifts and line intensities. This is due to fast chemical exchange of HNO3 units (in the form of either un-ionized neutral molecules or ion pairs) among the amide molecules to which they are attached during a short time of residence. Because of the very low solubility of nitric acid in dodecane, it is best to say that transient associations AMi (i ) 0, 1, 2...) of nitric acid (M) to DMDBTDMA (A) quickly exchange their assembling units M and A, as it is usually observed in acid-base equilibria. Each time-averaged resonance observed in acidic dodecane then results from a weighted mean over the whole set of species A, AM, AM2, ... This is true not only for resonances belonging to various functional groups in DMDBTDMA molecules, but also for line-splittings induced by Z,E stereoisomerism. However, NMR patterns observed in neutral dodecane are deeply altered on addition of nitric acid as the result of modifications of the NMR time scale for cis-trans isomerizations in associated species AMi (compared to free amide molecules). This second type of chemical exchange, to be sharply distinguished from the above A,M intermolecular exchange, already slow in neutral dodecane, gets still slower under progressive acidification of DMDBTDMA solutions. This is due to both large chemical shift variations that extend the NMR time scale toward shorter residence times and to strengthening of the partial double bond through hydrogen bonding which reduces the rate of cis-trans interconversion. Thus, the 13C ill-resolved carbonyl multiplet observed in neutral dodecane appears as a sharp quartet from the fourth sample (N/a ) 0.65) examined along path A in the phase diagram. All lines are in fact shifted down field, but not at the same extent. This explains why quartet components are seen to be farther from each other as the molar ratio is increased up to ca. 1.5. For higher N/a ratios, the movement of Z lines

toward lower fields becomes slower and the quartet components again get nearer to each other, however, with neither line superposition nor coalescence (Figure 5). Observations are still more spectacular with 1H N-methylic lines. Starting from a Z,E doublet in neutral dodecane, progressive introduction of nitric acid first results in a sharp ZZ, ZE, EZ, EE quartet, finally again reduced to a Z,E doublet at the end of path A (Figure 5). It may be observed on the same spectra that 1H N-CH2 multiplets are themselves separated into two Z and E doublets of multiplets in the same region when N/a is between ca. 0.5 to 1.5. The same is true for the methine proton borne by the central carbon connecting the two amide moieties, which gives rise to three separate broadened triplets on acidification: one triplet for each conformer ZZ and EE, and one triplet only for the enantiomeric pair ZE, EZ, with intensities of p1, p4, and 2p3, respectively (triplets instead of singlets are obtained in this case due to spinspin coupling with the adjacent methylenic protons in the attached C14 alkyl chain). Carbonyl lines were selected for quantitative shift measurements because of the amplitude of chemical shift variations and of line sharpness all along path A. Measured chemical shifts δ h XY (X, Y ) Z, E) of carbonyl ZZ, ZE, EZ, and EE resonances are reported in a graph as a function of the molar ratio N/a (Figure 6). Another important point in these spectra is the increase of the intensities of Z lines at the expense of E lines on acidification; this brings the conformational ratio R ) ZT/ET from 1.82 to 3.35 when the molar ratio N/a goes from 0 to 2.69 (Table 1). This may be observed as well with 13C carbonyl as with 1H N-methylic lines. The latter were, however, selectively chosen for quantitative measurements of R (Figure 7) because of the difficulty in obtaining accurate line intensities for carbonyl quaternary carbons in the absence of relaxation reagents. To ascertain whether the behavior of the observables δ h XY and R actually only depends on the molar ratio N/a, or else on the acidity level [HNO3]aq in the aqueous phase, other paths in the phase diagram were succinctly explored, on simply measuring [HNO3]aq and R (or else, in an equivalent manner, the Z and E conformational fractions (1 - F h ) and F h ). It was first checked (path B in Figure 1) that, in biphasic systems, overall conformational fractions F and (1 - F h ) are constant for a given acidity level [HNO3]aq ) 3.14 mol dm-3 (very close to the limit for demixtion, [HNO3]lim ) 3.20 mol dm-3) when the concentration of diamide is raised from ca. 0.1 to 1.0 mol dm-3 (Figure 8a). The interior of the triphasic domain was explored along a vertical line [HNO3]aq ) 4.56 mol dm-3 limited between the boundary values [DMDBTDMA]i ) 0.055 and 1.10 mol dm-3 (path C; Figure 1). As expected from properties of phase diagrams, the diamide concentrations in the middle (third) and upper phases were found to be independent of the initial diamide concentration and approximately equal to the above boundary values; the relative volumes of the two phases approximately obey the lever rule. We checked that conformational Z and E fractions remain constant in each phase along path C (Figure 8b). Another information from 1H NMR spectroscopy was brought by the low-field singlet representing all the acidic protons in solution, namely those from water (and hydroxonium ions), nitric acid, and protonated (or hydrogen-bonded) diamide. The signals from all of these sites are indeed time-averaged into a unique line due to fast exchange phenomena. The conservation of matter indicates that these protons are in a total concentration of [HNO3]0 + 2[H2O]0. The intensity of the singlet may thus yield the water concentration in the organic phase examined, if



Figure 5. Evolution of the NMR spectra of carbonyl carbons (a) and of NCH3 (*), NCH2 (**), and CH (***) protons (b) of DMDBTDMA on increasing the molar ratio N/a from 0.21 to 1.63 and 2.69 (from top to bottom).

[HNO3]0 is known from acidimetric titration (see Experimental part). The position of this singlet δAC varies between 8.50 and 12.39 ppm along path A (Figure 9). Again, no discontinuity is observed in the plot of δAC vs N/a. Downfield shifts of this magnitude are classically assigned to an increased acidity of the solution, in line with the increasing values of the molar ratio N/a. Working out a Model for HNO3/DMDBTDMA Association. HNO3 extraction from the aqueous phase involves strong

association to the diamide present in the organic phase(s). Even restricted to organic phase(s), the information brought by NMR spectroscopy is thus highly relevant in this connection. However, some modelization is necessary to extract useful information from the above NMR results, summarized in two graphs representing the conformational ratio R (Figure 7) on one hand and the four carbonyl chemical shifts δ h XY on the other hand (Figure 6), all of them expressed as a function of the molar ratio N/a. These models should be devised so as to account best



Figure 6. Graphs showing the chemical shifts of carbonyl resonances ZZ, ZE, EZ, EE measured as a function of N/a, in either biphasic (N/a < ∼0.7) or triphasic (N/a > 0.7) systems; smooth curves result from optimization procedures applied to the equilibrated associations model (see the text) with association constants: ke1 ) 108; ke2 ) 107; ke3 ) 103 mol-1 dm3 and conformational factors Fi ) 0.354; 0.347; 0.232; 0.226 (i ) 0 to 3).

Figure 8. Fractions (1-F h ) and F h of Z and E units in DMDBTDMA molecules along either (a) path B in the biphasic domain or (b) path C in both the biphasic and triphasic domains of the phase diagram (see Figure 1).

Figure 7. Graph showing the conformational ratio R as a function of N/a in the same conditions as in Figure 6 (the solid line represents the optimized curve).

for the following: (a) Graphs do not exhibit any break point; this suggests that the structure of solutions primarily depends on the molar ratio N/a. (b) The strong deshielding of carbonyl lines, by ca. 5 ppm, on increasing N/a, cannot proceed solely from van der Waals interactions in amide aggregates, but rather from hydrogen bonding to or protonation by nitric acid. (c) δ h ZE and δ h EZ graphs lie approximately midway from δ h ZZ and δ h EE graphs (Figure 6); this suggests that protonation of (or hydrogen bonding to) DMDBTDMA involves both carbonyls simultaneously and that a single equilibrium constant for both ends of the diamide is required to describe association with nitric acid. (d) There is a lack of parallelism between R and δ h XY variations: on increasing N/a from 0 to ca.0.7, R remains approximately constant, while δ h XY curves are rapidly ascending; this suggests that another phenomenon, e.g., aggregation, may be the cause for E to Z conversion, even if protonation remains the reason for chemical shift variations, and presumably the driving force for aggregation phenomena. The Protonation Model. In the absence of pH scales, the molar ratio N/a is the only way to characterize the acidity level around DMDBTDMA molecules. The last condition (d) in the above section may then be fulfilled by assuming protonation to be the cause for R variations, this would result from a preferential protonation of Z units, shifting the E a Z equilibrium toward Z conformer formation as shown in Scheme 2 where KZ should be taken larger than KE. Pseudo equilibrium

Figure 9. Graph showing the chemical shifts δAC of HNO3/H2O acidic protons at 25 °C in the same conditions as in Figure 6 (the solid line represents the optimized curve).

SCHEME 2: The Protonation Model

constants KE, KZ in fact include the free nitric acid concentration [M] ) m, so that they should be recast in full as:

K Z ) kZ m

and KE ) kE m

(6)


2558 J. Phys. Chem. B, Vol. 105, No. 13, 2001 With these notations, R can be expressed by eq 7

R ) KA(1 + KZ)/(1 + KE)

(7)

where m and R can be computed as a function of N/a, after introducing three adjustable parameters KA, kZ, kE (KA is in fact already known from its value in neutral dodecane, if we directly assume that equilibrium constants are not altered all along path A in the phase diagram). As expected, adjusting these parameters by curve-fitting procedures proved to be impossible, the calculated graph having no inflection point as required by the sigmoid line connecting experimental points (Figure 7). Moreover, free nitric acid concentrations m have calculated values reaching 1 mol dm-3 or more, in sharp contrast to the low solubility of nitric acid in amide-free dodecane. This failure shows the impossibility to describe such solutions as containing only the free base A and its conjugate acid AM. This is the more necessary as the molar ratio N/a may exceed unity, going up to 2.69 along path A in the phase diagram. We then assume the existence of several amide species resulting from the association of DMDBTDMA to variable numbers of nitric acid molecules: A, AM, AM2...AMn, where n has a value of at least 3. Let us denote these species as AMi, where i ) 0 to n and AM0 is identical to free amide A. The overall fraction F h of amide units with E conformation is obtained as a weighted mean over the corresponding individual values Fi in each species AMi:

F h)

∑ xiFi

(8)

where xi values are the diamide fractions used to form species AMi. These fractions depend on the model of association actually used (see below). For a given model, calculated values R(j) calc of the conformational ratio R according to eqs 2 and 8 for the 10 points along path A (j ) 1 to 10) and the corresponding experimental data R(j) exp allow us to adjust the unknown Fi parameters by minimizing the sum of squared residues:

Res.R )

(j) 2 (R(j) ∑ exp - Rcalc) j)1,10

(9)

On the same grounds, each of the four chemical shifts δ h XY can be calculated by considering their values δiXY in each individual species AMi as adjustable parameters. The whole set of δiXY values can be arranged for convenience in a 4x(n + 1) matrix array, at the rate of one line per XY resonance (namely: ZZ, ZE, EZ, and EE) and of one column per associated species AMi (i ) 0 to n). Calculation of δ h XY also requires the fractions piXY of conformers XY in each species AMi. These fractions can be safely assumed to follow the probability laws shown in eq 4 extended to associated species:

piZZ ) (1 - Fi)2; piZE ) piEZ ) Fi(1 - Fi); piEE ) F2i

(10)

The averaged chemical shifts δ h XY can then be expressed as

δ h cal XY ) (

∑ xipiXYδiXY)/(i)0,n ∑ xipiXY)

(11)

i)0,n

Parameters δiXY are adjusted line after line of the δiXY matrix (this corresponds to curve-fittings successively on each of the four graphs representing δZZ, δZE, δEZ, and δEE in Figure 6) by minimizing the sum of squared residues.

Res.δXY )

∑

j)1,10

2 (δ h cal(j) h exp(j) XY - δ XY )

(12)

Two further stages of optimization were performed for all models: (i) optimization of the sum of squared residues over all δ h XY values simultaneously,

Res.δ )

∑ Res.δXY

(13)

X, Y

and (ii) optimization of the total sum of squared residues over R and δ h XY values,

Res.total ) Res.R + Res.δ

(14)

The Poisson Distribution Model. The most simple way to compute molar fractions xi of species AMi is to assume equal probabilities of formation whatever the number i of associated molecules M. This amounts to considering a random distribution of items M in number N.NA (where NA is the Avogado number) into boxes A in number a.NA, whatever the number of items in each box, and ignoring conformational effects. This model conforms a well-known statistical law derived from the binomial law, the law of Poisson, which yields molar fractions xi required in eqs 8 and 11 as

x0 ) e-N/a; x1 ) (N/a)e-N/a; ...; xi )

1 (N/a)ie-N/a; ... (15) i!

An infinite series of associated species is generated in this way, the fraction of each species decreasing to zero when the association number i grows larger. For N/a values presently used, up to six species should be considered to gather 95 to 99% of the diamide content. The first stage of optimization (eq 9) then gave a sum of squared residues Res.R ) 0.031, i.e., an estimated average error of (0.055 over individual R values. This uncertainty margin is larger than expected from the repeatability ((0.035) of experimental measurements. The unsatisfactory quality of the fit arises from too many species being present simultaneously in solution. This results in very progressive variations of R values calculated as weighted means over many terms, which cannot stick tightly to the sudden elevation of the sigmoid experimental curve, even at the price of highly incoherent series of adjusted parameters Fi. The initial assumption responsible for this matter of fact consists of assigning equal probabilities to the formation of species AMi. Switching to the opposite point of view, we assume in the following that species AMi are consecutively found one after another, or else, that the distribution of a second item in boxes A can begin only after boxes A have all been filled once, and so on. This will be called the total successive associations model. Total Successive Associations Model. In this model, dodecane solutions are assumed to contain exclusively mixtures of species A and AM, or AM and AM2, or AM2 and AM3, when the molar ratio N/a is comprised between 0 and 1, or 1 and 2, or 2 and 3, respectively. This means that, among the set of four molar fractions xi (i ) 0 to 3), two of them only have nonzero values: x0 ) 1 - N/a and x1 ) N/a; or x1 ) 2 - N/a and x2 ) N/a - 1; or x2 ) 3 - N/a and x3 ) N/a - 2, depending on the above intervals for N/a variations considered in the same sequence as above. This model, as well as the above statistical Poisson’s law, is consistent with the expectation that the composition of the solution depends only on the analytical molar ratio N/a. The first stage of optimization shows improved curve fitting of conformational ratios R; the sum of squared residues Res.R ) 0.02 is decreased by one-third with respect to Poisson’s



SCHEME 3: The Equilibrated Associations Model

model, the expected error on each individual R value falls down to 0.045, just above the experimental repeatability margin of 0.035-0.040. The second stage of optimization uses the four δ h XY representative curves. One difficulty concerned the first three points on the graphs, where the ZZ, ZE, EZ, EE quartet is reduced to a Z,E doublet due to coalescence phenomena (see above). This problem was overcome as follows. The first point in these graphs (N/a ) 0) is in fact relative to neutral dodecane solution of DMDBTDMA; the relevant δ h XY values were taken from the low temperature (5 °C) spectrum studied above; they were also used as adjustable parameters δ0XY to start the optimization procedure. For the next two points, a last step of computation was carried out to transform the calculated quartet into two fully coalesced doublets by performing the appropriate weighted means; the corresponding residues were taken between experimental and theoretical coalesced lines. The trial values of adjustable parameters δiXY used to start the optimization procedure were taken as δ h XY ordinates on the experimental representative curves for integer values N/a ) 0, 1, 2, and 3. The total sum of residues Res.δ over all chemical shifts amounts to 0.42, this gives an estimated deviation on each individual δ h XY value of 0.2 ppm, approximately in line with uncertainty ranges in 13C chemical shift measurements. A last stage of optimization gave an unchanged total sum of residues Res.total ) 0.44. Despite its simplicity, this model will be hardly improved by more sophisticated treatment on the basis of equilibria between species AMi (see below). It avoids the approximations made to overcome the problem of unknown activity coefficients in writing equilibria. It requires a minimum number of adjustable parameters, and this may hopefully give reliable trends to be used as a guide to restrict the field of optimization procedures in the last model (see below), namely: (i) The conformational fractions Fi are equal two by two according to the sequence F0 ≈ F1 ≈ 0.35 (A and AM); F2 ≈ F3 ≈ 0.20 (AM2 and AM3); and (ii) The carbonyl resonances are continuously shifted downfield whenever the number of associated HNO3 molecules is increased by one, in line with a progressive protonation of the amide carbonyls as the acidity in the vicinity of DMDBTDMA molecules is increased. Equilibrated Associations Model. A last step of improvement and also of complexity in setting up a model of solution accounting for NMR results is to introduce equilibria between associated species AMi. This was achieved by drawing an extension of Scheme 2, where we distinguish E and Z amide units in species A (E and Z), AM (EM and ZM), AM2 (EM2 and ZM2), AM3 (EM3 and ZM3). In Scheme 3, these units are displayed in a 2 × 4 matrix arrangement where the sum of elements in each line represent the total numbers ZT or ET of either Z or E units, and in each column the concentration of each species AMi. Contrary to the above model of total successive associations,

the number of associated HNO3 units may be increased above 3. In fact, computations showed that even the next species in the series, AM4, is formed by less than 5% at the upper end of the range of N/a values used in our experiments. A maximum number i ) 3 was therefore considered in the following. Scheme 3 contains two kinds of equilibrium constants: (i) Those appearing along vertical arrows (KAMi), which refer to conformational equilibria and are simply related to conformational factors Fi by the expression

Fi ) (1 + KAMi)-1

(16)

and (ii) Those appearing along horizontal arrows (KZi, KEi), which refer to association equilibria and are in fact the product of genuine equilibrium constants kzi, kei by the concentration of free HNO3

KZi ) kzim and KEi ) keim

(17)

Only seven of these equilibrium constants can be considered as independent parameters describing this system because, for example, the association constants KZi in the first line can be deduced from constants KEi in the second line through eq 18:

KZi/KEi ) KAMi/KAMi-1 (i ) 1 to 3)

(18)

One may wonder why the above modelization is not extended to individual conformers ZZi, ZEi, EEi themselves of each species AMi. This proved to be a useless complication (see Appendix A and Scheme 7 as supplementary web material), because statistical laws 10 allow us to compute individual molar fractions of conformers from overall conformational fractions Fi. The set of equilibrium constants shown in Scheme 3 allows us to express the concentrations of the eight types of amide units EMi and EZi as a function of one of these, e.g. [E] (see Appendix B as supplementary web material). Activity coefficients are assumed to be the same for all species AMi and close to unity for dilute nitric acid (m e 0.003 mol dm-3), so that apparent equilibrium constants kei, kzi, KAMi are taken as actually constant all along path A in the phase diagram. The two remaining unknown concentrations, [E] and m, are obtained from laws of conservation of either the diamide or nitric acid

a)

∑ [AMi] ) [E]f(m)

(19)

i)0,3

N-m)

∑ i[AMi] ) [E]m‚g(m)

(20)

i)1,3

where f(m) and g(m) are two polynomials in m of degrees 3


2560 J. Phys. Chem. B, Vol. 105, No. 13, 2001 and 2, respectively, containing the whole set of seven independent parameters KAMi and kei described above

TABLE 3: Optimized Set of Conformational Fractions F and of Carbonyl Chemical Shifts δZZ, δZE, δEZ, and δEE in the Series of Species A, AM, AM2, AM3

f(m) ) (1 + KA) + ke1(1 + KAM)m + ke1ke2(1 + KAM2)m2 + ke1ke2ke3(1 + KAM3)m3 g(m) ) ke1(1 + KAM) + 2ke1ke2(1 + KAM2)m + 3ke1ke2ke3(1 + KAM3)m2 Taking the ratio of expressions 19 and 20 yields m as the solution of eq 21

m)

(N -a m) φ(m) where φ(m) ) f(m)/g(m)

(21)

Free nitric acid in DMDBTDMA solutions may be assumed to exist at a concentration close to HNO3 solubility in pure dodecane (see above). This means that m can be neglected with respect to N in eq 21 (m/N e 10-3), then recast under the simplified form

m ) (N/a)φ(m)

(22)

Although this simplification is by no means required to perform calculations, it has the advantage to confirm that m, and consequently all the derived quantities xi, R, and δ h XY, depend only on the analytical molar ratio (N/a) and not on the individual concentrations of DMDBTDMA and HNO3. This again justifies the choice of (N/a) as the x-variable used in plots of the conformational ratio R or of the carbonyl chemical shifts δ h XY. Introducing the solution of eqs 21 or 22 into eq 19 yields the parent concentration [E], and in turn the whole set of concentrations [EMi] and [ZMi] in Scheme 3, and finally the concentrations (and molar fractions) of associated species AMi:

[AMi] ) [EMi] + [ZMi] (and xi ) [AMi]/a) piXY

(23)

are obtained from eqs 10 and 16. Fractions of conformers Molar fractions R, xi, piXY are available from this point on and allow us to start the cycle of optimization procedures already described. The seven independent equilibrium constants KAMi (i ) 0 to 3) and kei (i ) 1 to 3) were first adjusted using as initial KAMi values those derived from the total successive associations model and trying a large set of ke1, ke2, ke3 values. Best curve-fittings (Figure 7) are characterized by a sum of squared residues Res.R reduced to 0.01. This corresponds to average estimated deviations of only 0.03 on individual R values, in line with the precision of experimental measurements. The set of sixteen chemical shifts δiXY were then adjusted (Figure 6), again with the total successive associations model as starting point. In this case, the quality of fits was only a little better than that from the previous model: 0.38 vs 0.42, which corresponds to estimated errors of 0.19 ppm on individual measurements, again in line with experimental precision. The whole set of KAMi (or Fi) and δiXY parameters remains very close to that obtained in the above total successive associations model (Table 3). As far as association constants are concerned, the whole optimization procedure (see Table 4 in this work and Appendix C as supplementary web material) proved to be only weakly sensitive to exact values of parameters kei;. This means that optimized kei; values are in fact in each case nearly identical to trial kei values used to initiate calculations. It was therefore necessary to explore an extended tridimensional range of ke1, ke2, ke3 values,

F δZZ δZE δEZ δEE

A

AM

AM2

AM3

0.35 168.99 169.04 168.80 168.84

0.34 171.88 171.15 170.81 170.47

0.23 174.72 174.19 173.86 173.18

0.22 174.70 174.68 174.40 174.16

TABLE 4: Optimized Sums of Squared Residues on Conformational Ratios R and of Carbonyl Chemical Shifts δXY, and their Total for a Set of Association Constants, ke1 ) 10n1; ke2 ) 10n2; ke3 ) 10n3, n1 ) 3 to 9; n2 ) 4; n3 ) 3 n1

3

4

5

6

7

8

9

Res.R 0.0385 0.0155 0.0062 0.0091 0.0115 0.0120 0.0120 Res.δXY 0.0190 0.4395 0.3894 0.3763 0.3718 0.3710 0.3708 Res.total 0.5758 0.4551 0.4017 0.3855 0.3834 0.3830 0.3829

observing in each trial the whole set of optimized parameters and the quality of curve fittings. Variations by an order of magnitude were finally adopted for each successive step in this exploration, i.e., parameters ke1, ke2, ke3 were written as 10n1, 10n2, 10n3, respectively, where n1, n2, n3 are three integers possibly comprised between 1 and 9 characterizing each trial. This exploration allowed us to conclude that optimized kei; parameters span a large domain of nearly equiprobable values defined by inequalities given in eq 24:

n1 g 6; 4 e n2 e n1 - 2; 3 e n3 e n2 - 1

(24)

Here, one of the best suited sets of n1, n2, n3 exponents is n1, 4, 3, where n1 g 8, e.g., the set of kei; values ke1, ke2, ke3 ) 108; 104; 103 mol dm-3 used for further discussion. This conclusion again points to the near perfection of the total association model. Discussion Whatever the exact value of association constants, the above modelization points to the total formation of species AM as long as N/a e 0.9. In this domain of the phase diagram, the conformational ratio R does not vary due to the fact that the two species A and AM have nearly the same conformational fraction F. This is also quite clear from the speciation curves showing the fraction of diamide in each species AMi as a function of the molar ratio N/a (Figure 10a). On the contrary, triphasic systems show the simultaneous presence of AM, AM2, and AM3, e.g., when N/a ) 2, the middle phase is composed of ca. 20% AM, 60% AM2, and 20% AM3. Even at the end of the explored path A in the phase diagram (N/a ) 2.69), the middle phase still contains both AM2 and AM3 species at the rate of ca. 35 and 65%. A more detailed speciation curve (Figure 10b) represents the fractions of E and Z units in species AMi, this illustrates the increased proportions of Z conformations (ZM2, ZM3) in species AM2, AM3. A clear conclusion from this analysis is that the conformational fraction Fi does not decrease continuously along the series of species AMi, but is constant with a single step change when i passes from 1 to 2 (see the histogram, Figure 11a). This is in sharp contrast (Figure 11b) with the chemical shift variations of carbonyl carbons, which are large on going from species A to AM, and then from AM to AM2, and are small on going from species AM2 to AM3. This is in line with an expected progressive protonation of DMDBTDMA approaching completion in species AM2. The deshielding measured between species A and AM2, AM3 reaches ca. 5 ppm, of the same order of magnitude as observed for strong internal hydrogen bonding,


J. Phys. Chem. B, Vol. 105, No. 13, 2001 2561 SCHEME 4: Closed Micelle-like Structure of DMDBTDMA Aggregates Assumed to Exist in Biphasic Systems

Figure 10. Speciation curves of associated species AMi (a) and of their Z and E conformers (b) at 25 °C as a function of the molar ratio N/a.

Figure 11. Histograms showing the distribution of (a) the fractions Fi of conformation E, and of (b) the intrinsic chemical shifts of each carbonyl resonance ZZ, ZE, EZ, EE, along the series of free and associated DMDBTDMA molecules A, AM, AM2, AM3.

e.g., in salicylic aldehyde (as compared to benzaldehyde).19 A similar behavior had been observed by IR spectroscopy:7 valence vibration frequency νco is lowered by less or more than 100 cm-1 in species AM and AM2, AM3, respectively. This was assigned to hydrogen bonding to HNO3 (in AM) or to protonation (in AM2, AM3), respectively. We are rather inclined to

consider less clear-cut distinctions. In these aprotic apolar media, DMDBTDMA and HNO3 are likely to associate immediately by strong hydrogen bonding, the acidic proton being transferred progressively from HNO3 to DMDBTDMA on increasing the level of acidity N/a. However, in the ignorance of bond lengths, it seems difficult to assign definite structures to each species, even if we use the term of “protonation” in the following for the sake of brevity. The fact that carbonyl shifts reach a ceiling value as soon as the second added HNO3 molecule (in AM2) indeed suggests a full protonation in species AM2, AM3 and uncomplete hydrogen donation in species AM. The degree of protonation seems to increase less sharply along the series of species AMi (Figure 10b) for the EE than for the ZZ conformer, suggesting a slightly higher basicity of Z units toward HNO3. There is a striking lack of parallelism between the series of conformational fractions Fi and of the carbonyl chemical shifts (Figure 11). This strongly suggests another phenomenon other than protonation to be the cause for conformational changes in DMDBTDMA molecules, namely a change in DMDBTDMA aggregation induced by the addition of HNO3. Before demixtion, small-angle X-ray scattering (SAXS) has shown the presence of small DMDBTDMA aggregates in a continuum of dodecane,1,8 in which four to five DMDBTDMA molecules have in common an inner polar core as in reverse micelles (Scheme 4). This inner space would be able to absorb up to 1 mole HNO3 per mole DMDBTDMA without significant structural changes in the aggregates, hence the constant conformation ratio R as long as the molar ratio N/a is smaller than unity. Let us recall at this point that amides may suffer protonation on either carbonylic oxygen or on nitrogen atom. After a long period of controversy in the past, it is now recognized that O-protonation is much more effective than N-protonation.20 Furthermore, O-protonation requires strongly acidic solutions due to the weak basicity of carbonyl groups, e.g., pK ) -0.3 in N-methylacetamide.21-22 N-protonation also does occur, but comparatively to a negligible extent, if we consider the corresponding pK values, e.g. -7.4 or -7.0 in N-acetylmorpholine23 or N-methylacetamide.22 We therefore consider protonation to occur exclusively on carbonyl groups of DMDBTDMA in the following. There are in fact two carbonyl units per DMDBTDMA molecule; however, the second protonation of a dibasic neutral molecule is much less effective than the first protonation on electrostatic grounds, e.g., for piperazine pK1 ) 9.8 and pK2 ) 5.7.24


2562 J. Phys. Chem. B, Vol. 105, No. 13, 2001 SCHEME 5: Bicontinuous Structure Suggested to Represent Third Phase Formation

Coming back to the protonation of DMDBTDMA, this explains why we consider that, when N/a ) 1, each bicarbonyl unit is hydrogen bonded to one nitric acid molecule, each pair of bound DMDBTDMA and HNO3 molecules within the aggregates picturing the above species “AM”. Introducing more nitric acid in these swollen aggregates would result in a switch from a closed structure to an open structure similar to a bicontinuous micellar pseudophase (Scheme 5), with large domains of DMDBTDMA still in contact by their bicarbonyl polar heads with a sheath of hydrogen-bonded HNO3 molecules, themselves containing a pool of the HNO3 molecules added in excess (with respect to the number of bicarbonyl units). The phenomenon of linear aggregation of small-size micelles has been described already in the case of aqueous solutions of bile salt.25 This picture seems the more probable as similar conclusions have been drawn from SAXS analyses of the middle phase, where aggregates of expelled dodecane have been detected among a continuum of DMDBTDMA and HNO3 components.1 In this view, the distinction between species AM2 and AM3 would be made purely on stoichiometric grounds and would explain why structural factors Fi and carbonyl shifts δiXY (i ) 2 and 3) are so close to each other. The progressive protonation of DMDBTDMA on addition of HNO3 results in an enlargment of the polar surface in aggregates on electrostatic grounds, this increases the mean area per polar head and thus accounts for the direction of the structural changes observed, namely from reverse micelles to bicontinuous open stuctures.26-28 This is similar to analogous observations in ternary water/surfactant/oil systems where phase inversion phenomena (from direct to reverse micelles through bicontinuous pseudophases) can be monitored by changes in the size of polar heads under the influence of various factors: temperature, hydration, salinity... or by structural variations in

the hydrophobic chains of surfactants.27,29This phenomenon would also involve serious differences in the packing of aliphatic chains, resulting here in an increase of Z conformations at the expense of E conformations. The present NMR investigations bring support to the thermodynamic treatment used to predict third phase formation.9The Flory Huggins theory30 used in this treatment considered a solution of polymeric AM units in dodecane, in line with our finding of one predominant species AM in the vicinity of demixtion. Moreover, the Hildebrand solubility parameter δ used to define the interaction parameter χ in the frame of this theory was predicted to increase when HNO3 is added in excess. This is in accord with the microscopic model where all excess HNO3 molecules are totally absorbed by the aggregates. The role of water molecules in third phase formation could be pictured along these views as follows. It can be observed that across the middle phase domain (N/a > 0.7) the molar ratio [H2O]0/[DMDBTDMA]0 remains close to unity (in fact between 1.0 and 1.2), and consequently the ratio [H2O]0/[HNO3]0 decreases continuously (Figure 12). In fact, the ratio of water molecules per mole of bound HNO3 remains approximately equal to unity since, in our view, there are as many DMDBTDMA as HNO3 molecules bound together. The fact that one water molecule accompanies one pair of bound HNO3DMDBTDMA molecules, whatever the associated species AM, AM2, AM3, strongly suggests that H2O molecules themselves participate in hydrogen donation through the formation of the ion pair H3O+‚‚‚NO3-. Hydroxonium ion H3O+ could then be stabilized by hydrogen bonding to both the nitrate ion (keeping the ion pair structure) and the bicarbonyl unit of the bound DMDBTDMA molecule (Scheme 6). Additional HNO3, in excess with respect to DMDBTDMA (N/a > 1), may then exist as an inner pool of un-ionized molecules hydrogen bonded to


J. Phys. Chem. B, Vol. 105, No. 13, 2001 2563 pair H3O+‚‚‚NO3- (δ1AC) and un-ionized water molecules (δ0AC), the time-averaged values δAC being thus comprised between these two limits (δ0AC e δAC e δ1AC). Finally, one may wonder where these water molecules are located in solution. As water is nearly insoluble in neutral dodecane solutions of DMDBTDMA, the excess H2O molecules should accompany nitric acid molecules within the polar core of micelle-like DMDBTDMA aggregates. Conclusions

Figure 12. Graphs showing the evolution at 25 °C of (a) H2O to DMDBTDMA and of (b) H2O to HNO3 molar ratios in the organic phase of biphasic systems or in the middle phase of triphasic systems as a function of the level of acidity N/a.

SCHEME 6: The Possible Role of Hydroxonium Ions from H3O+‚‚‚NO3- Ion Pairs in the Protonation of Bicarbonyl Units of DMDBTDMA

each other and to the shell of bound H3O+‚‚‚NO3- ion pairs. On the whole, the acidity level of this assembly of HNO3/H3O+ particles would tend to an asymptotic limit on successive additions of excess nitric acid. This is actually reflected by the strong downward curvature of the graph representing δAC vs N/a (Figure 9) when N/a is running from 1 to 2.69. This portion of the curve can be simulated, again on the basis of a weighted mean over species AM, AM2 and AM3 (taken along the above speciation curves), each one with its own chemical shift δiAC; the optimization procedure then yields a set of values δiAC ) 11.2, 12.2, and 12.5 ppm (i ) 1 to 3, respectively), clearly converging to a common limit close to 12.5 ppm. In sharp contrast, the early portion of the curve, relative to the organic phase in biphasic systems (N/a < 1), is rapidly ascending in nearly linear fashion from a virtual intercept δ0AC ∼ 7.9 ppm (N/a ) 0) to δ1AC ) 11.2 ppm (N/a ) 1). This is due to the presence of water in excess with respect to nitric acid, as long as N/a < 1 (Figure 12a). The observed shift then results from a weighted mean over hydroxonium ion in the ion

NMR investigations of the quaternary system DMDBTDMA/ n-C12H25/HNO3/H2O have been possible due to the existence of two indicators: (i) a classical one, namely, the chemical shift variations of carbonyl units in DMDBTDMA and of water molecules induced by protonation, and (ii) a more specific one, namely, the Z a E conversion of amide units in DMDBTDMA molecules. Considering these solutions as containing mixtures of associated species AMi (i ) 0 to 3), analysis of carbonyl chemical shifts δ h XY allowed us to draw the corresponding speciation curves and to calculate the intrinsic chemical shifts δiXY of bicarbonyl units in each species AMi. The primary results from this analysis are (i) the presence of only one associated species AM throughout the biphasic domain and of a mixture of all associated species AMi (i ) 1 to 3) in triphasic systems, and (ii) the progressive protonation of DMDBTDMA molecules on increasing the number i of attached HNO3 molecules, approaching completion when i ) 2. On the contrary, the conformational fraction Fi of E units in DMDBTDMA molecules remains constant on the first addition of one HNO3 molecule, then is suddenly decreased by ca. 40% on addition of a second HNO3 molecule, and then remains constant again. The lack of parallelism between the information from the two indicators mentioned above suggests a phenomenon other than amide protonation to accompany third phase formation, namely, a structural change in DMDBTDMA aggregates, tentatively described as the passage from a closed micelle-like structure to an open bicontinuous structure, in analogy with structures observed in ternary water/surfactant/oil systems. The analysis of chemical shifts of acidic protons from both HNO3 and H2O molecules suggests the presence of ion pairs H3O+‚‚‚NO3- in all species AMi covering the interface between DMDBTDMA and HNO3 domains through hydrogen bonding of H3O+ to bicarbonyl units of DMDBTDMA and of NO3- and H3O+ to the inner HNO3 molecules in excess. NMR investigations have also emphasized the fact that organic phase(s) before and after demixtion may be characterized by the same unifying parameter, the analytical HNO3 to DMDBTDMA molar ratio N/a. Third phase formation occurs when this ratio is larger than a critical value, itself corresponding to a given critical concentration of nitric acid in the aqueous phase. In the quaternary system studied presently, these critical values are approximately equal to 0.7 and 3.20 mol dm-3, respectively. These values are in fact not specific to the demixtion phenomenon, because they are highly dependent on the solvent in the organic phase(s) and the nature of the acid in the aqueous phase.31 Similar structural investigations on a series of related quaternary systems would be necessary in this view to hopefully be able to establish predictive laws, in parallel with those already obtained from thermodynamic considerations.9 Acknowledgment. The authors thank GDR (Groupement de Recherche) PRACTIS, which was at the origin of this work. They are especially indebted to Dr. Charles Madic (CEA, Saclay), one of the directors of PRACTIS, who brought the

2564 J. Phys. Chem. B, Vol. 105, No. 13, 2001 problem to them and who contributed to this manuscript by his critical reading. They have also benefited from fruitful discussions with Didier Noe¨l and Fre´de´ric Belnet (EDF, Centre de Recherche des Renardie`res). M. C. Charbonnel and C. Nicol (CEA/SEMP, Marcoule) are gratefully acknowledged for the gift of DMDBTDMA. The help of E. Dumortier for computer work and E. Eppiger (Service Commun de RMN, UHP-Nancy) for the acquisition of NMR experimental data is greatly acknowledged. Thanks are also due to P. Bazard and J. L. Fringant for their valuable contribution in preparing the manuscript. L.L. is indebted to EDF for the financial support to her thesis. Supporting Information Available: The material contained in appendices A (Equilibria of Individual Conformers), B (Derivation of Equation 21) and C (Optimization of Association Constants) is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Erlinger, E.; Gazeau, D.; Zemb, T.; Madic, C.; Lefranç ois, L.; He´brant, M.; Tondre, C. SolVent Extr. Ion Exch. 1998, 16, 707. (2) Nigond, L.; Condamines, N.; Cordier, P. Y.; Livet, J.; Madic, C.; Cuillerdier, C.; Musikas, C.; Hudson, M. J. Sep. Sci. Technol. 1995, 30, 2075. (3) Nigond, L.; Musikas, C.; Cuillerdier, C. SolVent Extr. Ion Exch. 1994, 12, 261. (4) Nigond, L.; Musikas, C.; Cuillerdier, C. SolVent Extr. Ion Exch. 1994, 12, 297. (5) Madic, C.; Hudson, M. J.; Liljenzin, J. O.; Glatz, J. P.; Nannicini, R.; Facchini, A.; Kolarik, Z.; Odot, R. Proceedings of the 5th International Information Exchange Meeting on Actinide and Fission Product Partitioning and Transmutation, Mol, Belgium, 1998; published by OECD. (6) Madic, C.; Blanc, P.; Condamines, N.; Baron, N. Proceedings of the International Conference on Nuclear and Fuel Reprocessing and Waste Management, RECOD’ 94, London, 1994, vol. 3. (7) Nigond, L. Thesis; University of Clermont-Ferrand II, CEA-R-5610, 1992. (8) Erlinger, C.; Belloni, L.; Zemb, T.; Madic, C. Langmuir 1999, 15, 2290.

Lefranç ois et al. (9) Lefranç ois, L.; Belnet, F.; Noe¨l, D.; Tondre, C. Sep. Sci. Technol. 1999, 34, 755. (10) Musikas, C.; Hubert, H. SolVent Extr. Ion Exch. 1987, 5, 151. (11) Lefranç ois, L.; He´brant, M.; Tondre, C.; Delpuech, J.-J.; Berthon, C.; Madic, C. J. Chem. Soc., Perkin Trans. 2 1999, 1149. (12) Laughlin, R. G. In Surfactants; Tadros, Th. F., Ed.; Academic Press: London, 1984; pp 53-81. (13) Degiorgio, V. In Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Degiorgio, V., Corti, M., Eds.; North-Holland: Amsterdam, 1985; pp 303-335. (14) Lang, J. C. In Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Degiorgio, V., Corti, M., Eds.; North-Holland: Amsterdam, 1985; pp 336-375. (15) Stewart, W. E.; Siddall, T. H., III. Chem. ReV. 1970, 70, 517. (16) Laplanche, L. A.; Rogers, M. T. J. Am. Chem. Soc. 1963, 85, 3728. (17) Hatton, J. V.; Richards, R. E. Mol. Phys. 1962, 5, 139. (18) Laszlo, P. Prog. Nucl. Magn. Reson. Spectrosc. 1967, 3, 321. (19) Stothers, J. B. Carbon-13 NMR Spectroscopy; Academic Press: New York, 1972; p 287, 587. (20) Perrin, C. L. J. Am. Chem. Soc. 1974, 96, 5628. (21) Goldfarb, A. R.; Mele, A.; Gutsein, N. J. Am. Chem. Soc. 1955, 77, 6194. (22) Christment, J.; Delpuech, J.-J.; Rajerison, W. J. Chim. Phys. 1983, 80, 747. (23) Fehrst, A. R. J. Am. Chem. Soc. 1971, 93, 5504. (24) Perrin, D. D. Dissociation Constants of Organic Bases in Aqueous Solution; Butterworth: London, 1965; p 199. (25) Mazer, N. A.; Schurtenberger, P. In Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Degiorgio, V.; Corti, M. Eds.; NorthHolland: Amsterdam, 1985; pp 587-606. (26) Kahlweit, M.; Strey, R. Angew. Chem., Int. Ed. Engl. 1985, 24, 654. (27) Israelachivili, J. N. In Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Degiorgio, V., Corti, M. Eds.; North-Holland: Amsterdam, 1985; pp 24-58. (28) Kellay, H.; Meunier, J. J. Phys. Chem.: Condens. Matter 1996, 8, A49-A64. (29) Lindman, B. In Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Degiorgio, V., Corti, M. Eds.; North-Holland: Amsterdam, 1985; pp 7-23. (30) Hill, T. L. An introduction to statistical thermodynamics; AddisonWesley: Reading, MA, 1960; Chapter 21. (31) Lefranç ois, L. Thesis, University of Nancy I, 1999.

Aggregation and Protonation Phenomena in Third Phase

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