J. Phys. Chem. 1992,96, 11079-11085
11079
Kinetics of "Extraction" of Copper( I I ) by Micelle-Solubilized Complexlng Agents of Varying Hydrophilic Lipophilic Balance. 2. Interfacial versus Bulk Aqueous-Phase Mechanisms Christian Tondre* and Marc Harant Luboratoire #Etude des SystPmes Organigues et Colloidaux (LESOC), Unite Associee au CNRS 406, Faculte des Sciences, Universite de Nancy I , B.P. 239, 54506 Vandoeuvre-IPs- Nancy Cedex, France (Received: April 8, 1992; In Final Form: July 28, 1992) This paper follows part 1 (preceding paper in this issue) in which the complexation of copper(I1) with a series of complexing agents (6-(alkylamino)methyI-2-(hydroxymethyl)pyridines (C,NHMePy) with alkyl chains varying from methyl to hexadecyl) was studied by stopped-flow kinetics in different micellar media. The micellar pseudophases have been used here to mimic the part played by the organic phase in a classical solvent extraction process in order to get some insight into the mechanisms involved. The data are interpreted with two different mechanisms, bulk aqueous phase reaction and interfacial reaction, through computer modeling. The parameters needed for the calculations have been either experimentally determined (partition coefficients) or deduced from the best least-squares fitting. The results obtained tend to demonstrate that (in the pH conditions used) a bulk mechanism prevails in the case of CTAB micelles, whereas the role of the interface cannot be neglected in the case of CI2EO6.Conversely the extraction of copper ions in the micellar pseudophase appears to be much more effective in the latter case. The influence of ionic strength on the type of mechanism involved is finally discussed, in relation with previously reported data.
Introduction In the preceding paper (part l'), we have reported a number of results relative to the kinetics of copper(I1) complexation by a series of extractant molecules solubilized in different types of micelles. If we consider that the micellar pseudophase plays a part analogous to that played by the organic phase in a classical solvent extraction process, we can speak of "extraction" kinetics. From this viewpoint one of our objectives is to push a little bit further the analogy and see what can be drawn from these model systems in terms of extraction mechanisms and particularly concerning the role of the interface. In fact the subject of extraction mechanisms has caused much ink to flow, and, according to a recent paper? a good model of extraction processes would certainly be welcomed by industrial chemical engineers. It would also help in designing new extractant molecules. In the present state of our knowledge, we do not know really if the reaction of complex formation between a lipophilic extractant and a metal ion is taking place in the bulk aqueous phase, at the organic/aqueous interface, or in a small reaction volume close to the interface, on the aqueous side.3 There have been supporters of the different possibilities (see refs 3-8 and also references cited therein). There were also authors who denied any significant role to the interface, claiming that the rate determining step occurs in the bulk aqueous phase only, and who were led later on, after technical improvements of their experimental device, to consider reaction pathways involving the interface as well? Osseo-Asare recently brought to our attention the difficulty of drawing clearcut conclusions from correlation pl0t.9.~ One of us contributed to several papers related to this problem, using micellar model system^.^*^^ In one of the last contributions, NMR spectroscopy was used in combination with UV-visible spectroscopy to demonstrate that in some instances metal ion complexation and interaction of the complex formed with the interface are taking place ~imultaneously.~~ Critical examination of the data showed nevertheless that the interpretation of this observation is not unique. Another related problem concerns the effect of the system dimensionality (surface or volume) on the rate of chemical reactions. H m again we find contradictory papers in the literature. For instance Schelly and co-workers demonstrated both theoretically" and e~perimentally'~ that the rate constants for a bimolecular proctss in heterogeneous systems are extremely reduced compared to those in homogeneous solutions because of the reduction of dimensionality at interfaces. This appears to be in line with the observations made on the rate of complexation of metal ions in micellar systems when the hydrophobic character of the
extractantlJOis varied. On the other hand, Grfitzel and cow o r k e r ~ ~came ~ J ' to a completely different conclusion after examining different reactions taking place in micellar systems. According to these works, reduction of dimensionality dramatically increases the probability of reaction. This would be in agreement with observations independently reported'*J9 and tending to demonstrate that the rate constant for the interfacial reaction is larger than that for the bulk reaction. The main problem behind this conflicting situation arises from the need of having a clear definition of the rate constant considered: apparent or overall rate constants or true mechanistic rate. Micellar model systems can certainly help in improving our knowledge of these complicated kinetic processes and mechanisms, but they bring with them specific problems which cannot be overlooked. The fmt one is related to the defdtion of the reaction volume in the micellar pseudophase. This is a common problem in the field of micellar catalysisa20 The choice of the reaction volume is a crucial one, particularly for bimolecular reactions, as it turns out that the rate constant in the micellar pseudophase is always appearing in the equations in the form of its product with the reaction volume involved. So, from the moment there is an uncertainty concerning the assumed reaction volume, it is difficult to believe in the absolute correctness of a micellar rate constant deduced this way. A second problem comes from the lifetime of micelles. The dynamic nature of micelles is well established,*' and one of the consequences of this property is that micelles have a certain lifetime.22Surprisingly this usually does not need to be taken into consideration in the kinetic treatment of chemical reactions in micellar media, probably because the average situation prevails. It has to be taken in mind anyway when discussing what is really the micellar reaction volume. Imagine a micelle, containing a lipophilic extractant, which enters in a complete deaggregation process. If reaction takes place during this time, the reaction volume may be seen as the space just occupied by the micelle. These points being precised, this paper is intended to add our modest contribution to the elucidation of the mechanisms involved in biphasic extraction of metal ions. It was made possible owing to a fruitful collaboration with P. Scrimin and P. Tecilla from the University of Pad0va,2~*~~ which has led to the numerous results described in part 1.'
Experimental Part Details concerning the experimental procedures as well as the origin of the chemicals used to obtain the data which constitute
0022-3654/92/2096-11079$03.00/00 1992 American Chemical Society
11080 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
the basis of this theoretical study can be found in part 1.' Fortran programs, which were previously available for nonlinear least-squares curves fitting procedures, were adapted to the problem considered here. They are based on the Marquardt which was also used for the analysis of the relaxation kinetic data.26 When the convergence criterion could not be met this way, a simple curve drawing procedure was considered to search for an estimation of the parameters best fitting the experimental data. The Fortran programs were run on a NM 4/30 Computer Automation (Yrel, France) interfaced with a Regent 40 display terminal, a Centronic 702 line printer, and a Tektronix 4662 digital plotter. When the preceding procedure definitely did not go to convergence or converge to values having no physical meaning, we had recourse in the solver function of Excel (Microsoft). This software allows one to impose a positive values to the best fit parameters. The experimental determinations of the partition coefficients of the extractants between the micellar pseudophases and the bulk aqueous phase (or the binding constants to the micelles, which are equivalent) by a microdialysis method have been described in full detail in a previous p~blication.~'
Data Analysis Several kinetic models have been developed in the literature to interpret the results of reaction kinetics in micellar or microemulsion systems.'0*20*28-31 The micelles can be considered simply as solubilized macromolecular entities or as a separate pseudophase. The interfacial region can be treated as a twedimensional interface or as an interfacial volume. In the former case we are faced with the problem of evaluating surface concentrations expressed in moles per surface unit. Some authors have made use of a Langmuir adsorption isotherm3 or the Gibbs equation32for this purpose. A recent work performed by Schomticker et al.29 tends to demonstrate that there is no difference in treating the interface two-dimensionally or as interfacial volume since the equations obtained in both cases are equivalent. For the purpose of the present work we have considered two different mechanisms. In mechanism I the reaction of complex formation is assumed to take place only in the bulk water phase and the micellar pseudophase acts as a reservoir for the unreacted extractant species and as the extracting phase for the metal complex. This model corresponds to Scheme I. In mechanism I1 an interfacial contribution was considered, so that complex formation can m u r as well in the bulk aqueous phase as in the micellar pseudophases (see Scheme 11). In both models the subscripts m and w refer to the micellar phase and to the water phase, respectively. The last line of equilibria in Scheme I remains valid if one takes into consideration the partitioning of the protons and consequently the protonation constant in the micellar pseudophase KQl,,,= [L,][HG]/[LHG]. It is recalled that kf and kd stand for the overall rate constants corresponding to the coupled equilibria: k
k
k-2
k-3
LH+ + Cu2+& LHCu3+2 LCu2+
Tondre and Hgbrant
L H ~
L,
LCUZ
L H ~
where L, LH+,and LCu2+represent respectively the neutral extractant, its monoprotonated form, and its complex with copper(I1).
SCHEME II: Interfacial Contribution L,
+ CUE
L,
+ cup
kl,
e LC"% ..I
LCU? k-1
in comparison with the extractant concentration; (iv) in Scheme I the concentration of copper ions is assumed not to be affected by the presence of micelles, which is of course not applicable to the case of anionic micelles (SDSin the present work). The definitions of the equilibrium constants neccssary in the calculations are the following:
(3)
+ H+ (4)
The application of the steady-stateapproximation to LHCu3+leads to kf =
k2k3 k-2 + k3
kd =
k-2 + k3
k-2k-3
The kinetic equations have been derived for both models, with the following assumptions: (i) the partitioning equilibria (which have been treated as association constants to the micellized surfactant with units M-l) are considered to be always established, which means that the corresponding reactions are fast compared to complex formation;30(ii) the species LH22+was considered unreactivez4and completely solubilized in the aqueous phase; (iii) the metal ion concentration was considered always in large excess
The mass balance equation for the extractant is given by [LIo
[Lwl + [LmI + [LH:I + [LH;I + [LH:;] + [LCu$+] + [LCui']
(7)
In these equations the subscript zero refers to the analytical concentration. All the concentrations between brackets are concentrations reported to the total volume of the solution (the local concentrations in the pseudophases will be equal to these
The Journal of Physical Chemistry, Vol. 96, No.26, 1992 11081
Kinetics of YExtraction”of Cu(I1) concentrations divided by the volume fraction of the pseudophase considered). Cis the concentration of micellized surfactant equal to Cto,.- cmc (cmc = critical micelle concentration). The rate equations and the relaxation times for the two mechanisms considered can be easily e~tablished:~’ For Scheme I: d [LCu2+] = kl [Cu2+][L,] + kr[Cu2+][LH;] - k-,[LCui+] dt
Mechanism I can thus be theoretically tested by using eqs 13,21, and 22 in a computer program. For scheme Jk the volume fractions of the micellar and aqueous peudophases (& and 4w,respectively) need to be introduced into the rate equation which takes the following form (the rate of appearance of LCu2+is equal to the sum of the individual rates in the pseudophases weighed by the volume fractions of each pseudophaseZ0): [LCUi+] d [LCu2+] [LWI [Cui+] +wkl-- 4wk-ldt 4 w 4w 4W [ L H 3 [Cui+] [LCUi+l [H,+I + 4wh- 4wkd- 4 w 4 w 4w 4w
+
-
Equation 8 can be rearranged after introducing relations 1-6 d[LCu2+] dt This equation can be rearranged similarly to the former case with introduction of the mass balance equation in the form and from the mass balance equation [LH:I
[ L H 3 = ([LI,
([LIo - [LCu2+1)/am
(1 1)
- [LCuZ+I)/aint
(24)
with
with Ka I -(1 [H+l
[H+l + KLC) + 1 + KLHC + Ka2
(12)
integration of eq 10 in pseudo-first-order conditions leads to an exponential increase of the concentration of LCu2+with a time constant 7 7-1 = kfPP[CU2+], k p (13)
(the subscript int is used here to indicate that an interfacial contribution has been considered). Integration of eq 23 is again consistent with an exponential increase of LCu2+ with a time constant of the same form as eq 13 with
+
A preliminary in~estigation~~ had given the following expressions for the same quantities obtained in pure water (subscript w for the rate constants):
Note that the quantitia 4w/[H]: and &,/ [H;] are related to the inverse of the local pHs. Considering that 4wis very close to 1, the same reasoning as for am(see eq 20) leads to
+
cohpidering the pK values in water (pKaI = 9.01 and pKa2= 1.35) and the pH conditions chosen in this work (pH = 3.5 i 0.2), a, can be taken q u a l to unity with an error of less than 1% a, = 1
kffp =
(19)
Similarly, a close examination of the terms involved in amshows that CY, EJ 1 + KLHC (20) with again an error of less than 1% considering the values of the partition constants obtained from dialysis experiment^.^' With these observations, eqs 14 and 15 can be replaced by eqs 21 and 22:
elp kt,tp/(l
+ KLHC)
(21)
&PP
+ KLCUC)
(22)
= k.dpWp/(l
aintEJ 1 KLHC (28) In addition, eqs 26 and 27 can be rearranged by use of eqs 16 and 19
[
k‘,
4W
1 + -@$KLHCKC~C 4m
I/
(1 + Kc,C)(1 + KLHC) (29)
= [kapwp + kwLCUc1/( 1 + KLCUC)
(30)
where
are the expressions analogous to (16) and (1 7) for the reaction in the micellar pseudophase.
11082 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
Tondre and H&brant
TABLE I: DirMbutiaa Pa~nmetersin M i c e k at 25 O C for the Protonated (LH) and Neutral (L) Extractantsa CTAB (no added salt)
n 8 10 12 14 16
KLHW ' ) 0.45 4.0 3 1.6* 510* 1732*
KL W ' ) 708* 7943* 4.0 x 104 3.2 x 105 2.5 X lo6
C12E06 (no added salt)
KLH(M-l) 13.2* 80.0* 620* 5.0 x 103 3.5 x 104
KL
w-9
299* 6310* 2.2 x 104 1.6 X los 1.1 x 106
CTAB (NaCI, 0.015 M)
cI 2EO6 (NaCI, 0.015 M)
K'LH W )
K'LHOf-')
18** 243** 1985**
102**
9585*
aValues obtained from microdialysis experiments (see ref 27, indicated with a single asterisk) and present work (indicated with two asterisks). The values with no asterisk have been obtained from the extrapolation of the straight lines giving log Ki versus n.
The validity of mechanism I1 can thus be tested by introducing eqs 13, 29, and 30 in a computer program.
Results and Discussion The equations to be fitted with the experimental data contained a large number of unknown quantities. KLH and KLh for the first mechanism and, in addition for the second mechanism, Kcu, &,,
15
Li
4
A h.
I
F!!, k"d:-
The values of KLH (as well as those for KL, although they do not enter in the theoretical expressions considered) have been obtained from microdialysis experiment^.^' We have collected in Table I, the values previously obtained either from direct experimental determinations or from extrapolations when n is varied, when this was not possible. It has appeared that the partitioning of the extractant is considerably affected by the ionic strength in the case of CTAB micelles. The values K'LH in Table I have been obtained from dialysis experiments in the presence of 0.015 M NaCl, which is equivalent to the ionic strength brought by a M in CuC12 (i.e. the concentration used concentration 5 X in the kinetic experiments that we want to take into account theoretically). Owing to the large differences between KLH and K'LHfor CTAB (see Table I), it is clear that only the second value is relevant for a quantitative fitting of the data. NaCl was chosen instead of NaBr to adjust the ionic strength, because copper chloride had to be replaced. The drawback of this choice lies in the fact that Br-/Cl- ion exchanges can take place on the surfactant polar heads, with possible changes of cmc, micellar shape, and surface potential. These effects can be safely neglected in the present case since we checked that changing CTAB against CTACl has almost no influence on the kinetic data. The values of KLcu and Kcu could not be independently determined. In the case of Kcu the eventual differences of concentration in the two compartments of a dialysis cell were within the experimental error. The nonionic surfactant should not affect the copper ion concentration, but we expect it to be considerably reduced in the vicinity of CTAB micelles. For what amcem Km, the problem comes from the fact that, due to possible dissociation, the complex cannot be considered as a simple entity. Kcu and KLcuwere thus used as free adjustable parameters in least-squares fitting procedures. In the case of mechanism I, it is interesting to note that the values of KLHand KLcucould in principle be obtained from the variations of 1/7 versus the metal ion concentration, as indicated by eqs 13, 21, and 22: (33)
(34)
where & j P and &ff are respectively the slopes and intercepts of the straight lines 1/7 =f([Cu2+l0) (see part 1). The volume fraction of the micellar pseudophase &, where the reaction is supposed to take place in mechanism I1 was arbitrarily taken equal to the volume occupied by the micellized surfactant, as is frequently done.20 = vc (35)
-0
2
4
6
0
102xCcTm (md dm3)
Figure 1. T-' versus CTAB concentration for a series of C,NHMePy: n = 10 (m); n = 12 (0); n = 14 (A); n = 16 (+);dashed line, experimental; full line, theoretical, according to mechanism I.
Pbeing the molar volume of the micellized surfactant. We would like to emphasize that this assumption does not imply that the reaction occurs in the hydrophobic core of the micelles (this point was already approached in the Introduction). It just means that we associate to each micellized surfactant a reaction volume that we are unable to define more precisely. For spherical micelles, assuming that the proper volume of the micelle is excluded for the reaction, #, would be represented by a shell around the micelles, whose thickness would be 26%of the micelle radius (Le. about 13 A for a micelle radius of 50 A). The last quantities which are needed for the calculations are k;: and 4 .;: We have assumed that their values can be taken equal to those measured for the more hydrophobic extractant C16NHMePy(seepart l l ) . Indeed, the fact that 7-I is practically independent of the surfactant concentration provided it is larger M for CTAB and than 2 X M for C12E06,strongly suggests that this extractant is totally associated with the micelles in the conditions used to measure the apparent rate constants (2.5 X M CTAB or 2 X M ClzEO6). The results given in part 1 demonstrated that when the alkyl chain length of the extractant is short enough, the reciprocal relaxation time is almost insensitive to the surfactant concentration. For this reason we will not consider here the results obtained in CTAB with n < 10 and those obtained in C12E06with n < 8. Test of Mechanism I. We have considered three different ways of fitting the data with mechanism I. They correspond to the letters A, B, and C in Tables I1 and 111. In method A, K L H and KLcuwere free adjustable parameters in a least-squares procedure and the values given in the tables are those corresponding to the best fits. In method B, only KLcuwas a free adjustableparameter and KLH was given the value obtained from dialysis experiments. Finally in method C, KLH and KLCu were calculated from eqs 34 and 35 applied to the data reported in part 1. Of these three possible methods, we have only selected some of the best fits obtained to be represented in Figum 1 and 2. It can be deduced from these results that mechanism I is in excellent agreement with the data obtained with CTAB (Figure l), except for the more hydrophobic term of the series, whereas in CI2EO6(Figure 2) large discrepancies exist between the experimental results and the theoretical prediction. The difference between the two sets of results is all the more significant since the theoretical curves
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 11083
Kinetics of "Extraction" of Cu(I1)
TABLE 11: Distribution Parameters in C,,EO. for the Three Ways of Fitting the Data with Mechnism I' A_ B . n
KLH
8 10 12 14 16
8.0 30.9 83.6 1640 8820
KLCU
KLH
8.0 717 8119 11.5 X 5410
13.2 80 620 5.0 x 103 3.5 x 104
C-
KLCU
KLH
KLCU
5.6 142 963 1130 1200
3.81 69.3 342
27.9 120 153
Method A: KLH and KLCu as free adjustable parameters. Method B: KLH from dialysis, KLcu as free adjustable parameter. Method C: KLH and KLcu from the kinetic curves. bThe lack of physical meaning of this value (result of least-squares fitting) is discussed in the text. TABLE III: Distribution Parameters in CTAB for the Tbree Ways of Fitting the Data with Mecbanism I" A B n
KLH
KLCU
KLH
KLCU
10 12 14 16
25.0 169 1007 2307
24.9 169 850 1723
18 243 1985 9585
36.2 110 615
C
KLH 28.6 287 589
KLCU
14.4 98 470
575
'Method A: KLH and KLCu as free adjustable parameters. Method B: KLH from dialysis (in the presence of NaCl, 0.015 M), KLC,,as free adjustable parameter. Method C: KLH and K L C from ~ the kinetic curves. TABLE IV Distribution and Kinetic Parameters in C,,E06 for the Best Fits of tbe Data with Mechanism 11' kinetic rate constants in as free adjustable F-,.. micelles llUlll parameters dialysis with n = 16
TABLE V Distribution and Kinetic Parameters in CTAB for tbe Best Fits of tbe Data witb M e c M s m IP kinetic rate constants in as free adjustable L , . . . . micelles '1U111 parameters dialy& with = 16
n
Kcu
KLCU
KLH
e!!
4%
n
Kcu
KLCU
KLH
e!!
: 4
8
0.213 0.33 0.500 0.243 0.291
5.4 737 1593 11.5 X 8.6 X lolob
13.2 80 620 5.0 X 10' 3.5 X lo4
280 280 280 280 280
1.5 1.5 1.5 1.5 1.5
10 12 14 16
-0 -0 -0 0.221
36.7 125 398 1640
18 243 1985 9585
130 130 130 130
0.25 0.25 0.25 0.25
10
12 14 16
was taken equal to ?C with ? = 0.450 Lmol-I. bThe lack of physical meaning of these values (results of least-squares fitting) is discussed in the text. a&,
"4, was taken equal to VC with ? = 0.365 L-mol-'. ence of NaC1,0.015 M.
the pres-
r-l(a-5 20
15
10
5
-0 0
2
4
6 l02xCq9&md
Figure 2.
2
4
6
8
102xCCTAB(mol dm4)
0
7-l
8
an")
Figure 3. CTAB. Same conditions as in Figure 1, except mechanism 11.
versus CI2EO6concentration for a series of C,NHMePy:
n = 8 (M); n = 10 (A);n = 12 (0)n;= 14 (+); n = 16 ( 0 ) ;dashed line,
experimental; full line, theoretical, according to mechanism I.
represented in the figures were obtained with method A (two adjustable parameters) in the case of CI2EO6and with method B (KLHfrom dialysis) in the case of CTAB. Note that method C can reasonably be used only if the surfactant concentrations introduced in eqs 34 and 35 are smaller ~ longer varies (with n = 12 in C12E06 than those for which 1 / no and n = 14 in CTAB we were close to this limit, so that the values obtained must be considered with reservations). Test of MechrnlPm IL The values introduced in the calculations when an interfacial contribution was considered have been collected in Tables IV and V. Only the values of Kcu and KLcuwere left free to vary in a least-squares fitting procedure; all the other values needed were known from dialysis or kinetic experiments. The best fits obtained have been represented in Figures 3 and 4
0
2
4
6
0
l 0 5 1 C C , ~ e ( m dan-3)
Figure 4. CI2EO6.Same conditions as in Figure 2,except mechanism 11.
11084 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
for CTAB and C12E06,respectively. The results demonstrate that the theoretical prediction from mechanism I1 is in much better agreement with the experimental data for CI2EO6than the prediction from mechanism I. For the case of CTAB, either scheme can explain the kinetic behavior (at least when n < 16) since both mechanisms seem to give a good repmentation of the experimental data. Nevertheless we would like to emphasize that there is no real need of an interfacial contribution to explain the variation of 1/r with the surfactant concentration, except for C16NHMePy. In fact the equation describing the interfacial mechanism becomes identical to that of the bulk mechanism from the moment that both Kcu and &$ are close to zero. The reaction is thus likely to take place mainly in the bulk water phase. This is consistent with the fact that the approach of the interface by copper ions is made difficult, due to electrostatic repulsions. Such an interpretation leads one to admit that the eventual contribution of anionic copper species33 such as [CUBr4l2-is very unlikely, even though several times molar concentration of bromide ions exist in the vicinity of CTAB micelles.34 The values found for KLH and KLcu (see Tables I11 and V) are both increasing, as expected, with the hydrophobicity of the extractant, but, for a defined value of n, they have similar orders of magnitude. This is not really surprising, since the loss of hydrophilicity upon complexation (which is the basis of solvent extraction) is expected to more or less compensate for the rise of the repulsive electrostatic term. This means that the complex with copper is not more extracted in the micellar pseudophase than the free extractant itself. On the other hand, only the interfacial model gives a good description of the data obtained with C12E06.So in this case the reaction is likely to proceed simultaneously in the bulk water phase and at the interface. An examination of the values of KLH and KLcUin Table IV shows that the complex is more extracted than the free extractant as soon as n > 8 and the difference becomes more and more pronounced when n increases. It should also be stressed that the values found for Kcu are consistent with a total absence of interaction between the metal ion and the nonionic micelles. Returning to the definition of Kcu (eq 4) and remembering that the absence of interaction signifies that the partition coefficient Qu = 1, it is easily demonstrated that, this being true, one should have
Kcu = P
(36)
Taking P- 0.450dm3*mol-lfor CI2EO6and remembering the number of parameters involved in the calculations, one can consider the values in Table IV to be in line with this prediction. It is also noteworthy that the values of KcYobtained when the interfacial model is applied to CTAB are close to zero (with again an exception for the more hydrophobic extractant), which tends to further reject this model in that case. On the other hand the large values of KLcuwhich came out of the calculations performed with n 2 14 in CI2EO6(see Tables I1 and IV) call for some comments. They indicate that the association of the copper complex to the micelles is even stronger than the association of a surfactant monomer to the same micelles, which is somewhat disturbing. Indeed the association constant of a surfactant molecule can be estimated as almost equal to the reciprocal of the cmc, which gives a value of about 1.5 X lo4 M (note that for nonionic for cI2Eo6 surfactants the cmc is expected to be devided about 10 times for each addition of two CH2 groups). Consequently, care must be taken regarding the actual meaning of the large values reported for KLC,, (the same comment holds for any type of association constant to micelles). We believe that these values are strongly overestimated, and we have verified that they can be considerably reduced without any visible change in the quality of the fits, although the sum of squared deviations increases continuously but very slightly. For this reason, we have no objective criteria for selecting a particular value, except that we would expect a linear dependence of log KLcu with n, as for the uncomplexed ligands?' For C12E06,for instance, replacing the values 11.5 X lo6 and 8.6 X 1O1O(Table IV) by 3.2 X lo4 and 5.6 X lo5 would satisfy this requirement. These
Tondre and Htbrant
10
0 ' " ' ' ' " " " " " ' ~ 0 2 4
8
8
1c2xccrm(mol dm-3)
Figure 5. Effect of ionic strength on the variation of 7-' versus CTAB concentration for C,*NHMem: full line, no salt added (0);dashed line, 0.1 M NaBr added (@).
problems of fitting procedures do not question the reliability of the model. So far the values of the micellar rate constants entered in the calculations were apparent rate constants in the sense that (i) they refer to both the neutral and cationic extractant species and (ii) they were obtained from a plot of l/r versus the copper concentration, where the latter was the analytical concentration and not the concentration in the micellar pseudophase. The above discussion tends to prove that these two concentrations can be considered almost identical in the case of C12E06. On the other hand, one cannot exclude that the proportion of neutral and cationic extractant species in the neighborhood of the micelles changes with n. This could induce dramatic changes of the global rate constant since, in water, the rate of reaction of the neutral species has been shown24to be 5.6 X lo5times larger than that for the cationic species, at least when n = 4. Unfortunately we would rather expect a larger contribution of the fastest = -1.7 reacting species owing to the fact that pKa,,,, according to an estimation made on the basii of a thermodynamic approa~h.~'The results are going in the reverse direction. In the present state of our knowledge we can hardly say more about the values of the rate constants in the micellar domains, except that small fluctuations with the variation of n are very likely, as in purely aqueous medium. A close examination of the equations corresponding to the two different mechanisms provides a further substantiation of the models postulated for CTAB and CI2EO6.The bulk mechanism predicts that l/r tends toward zero at large surfactant concentration, in quite good agreement with the behavior experimentally observed for CTAB. On the contrary, the interfacial mechanism leads to an equation of 1/7 which tends toward a finite value at large surfactant concentration, in perfect agreement with the data relative to CI2EO6.This finite value is in any case larger than 1.5 s-l (contribution of the 4%term). The part contributed by the 6% term is more difficult to evaluate precisely. The occurrence of this nonzero asymptote is also shown in Figure 5 , where we have studied how the curve relative to CIzNHMePy in CTAB is modified when an ionic strength 0.1 M NaBr is added. It is clear that not only the salt induces an increase of KLH,which makes the curve steeper at low surfactant concentration, but also the asymptotic behavior is completely changed. By salting the system, there is a shielding of the electrostatic interactions so that the CTAB micelles behave almost exactly as the nonionic ones, with very likely a correlative change of mechanism. The attribution of a bulk-phase mechanism for copper complexation in CTAB micelles may seem iflconsistent with previous publications of this laboratory concerned with the complexation (Cl,-HQ) with of 744 ethyl-l-methyloctyl)-8-hydroxyquinoline nickel ions.12 In fact we would like to emphasize that there is no contradiction with the present situation. Indeed, Kim and Tondre12 postulated a bulk aqueous phase mechanism for 8hydroxyquinoline (HQ) and deduced a partition coefficient of 378. This value was incorrectly criticized by Freiser et because
Kinetics of "Extraction" of Cu(I1) these authors have compared values which were not comparable: the partition coefficient was without dimension, and it should be multiplied by the molar volume of CTAB (0.365dm3.mol-') to get an association constant in M-I. The value obtained this way is 138 M-I, which is in remarkable agreement with the value found by the above mentioned authors for CTAN (132 f 10 M-1).35 The bulk mechanism postulated in this case is confirmed by the discussion of the present paper. For what mncems the case of CI,-HQ, the situation was totally different because the partition coefficient, which could not be measured, was probably larger by orders of magnitude. In addition, the extractant was in a neutral form (pH was equal to 8.0) whereas those examined in the present work are in a protonated form. Finally a 0.1 M buffer concentration was used, which is equivalent to adding a certain ionic strength. For all these reasons, and from consideration of the comments associated with Figure 5 , the previous interpretation is not necessarily inconsistent with the present work. Our aim in this work was to use micellar pseudophases as extracting phases for metal ions. The results obtained are very encouraging both from a fundamental and from an applied point of view. They demonstrate that such systems are very useful for mechanistic studies since they have permitted us to determine precisely in which conditions bulk or interfacial reactions prevail. They have also provided information concerning the distribution parameters of the metal complexes in micelles. Practical application for removal of metal ion traces from aqueous streams using ultrafiltration techniques36is now in progress. Acknowledgment. We are indebted to Profs. P. Scrimin and P. Tecilla (University of Padova) for the synthesis of the extractant molecules and to Mr. S.-G. Son (LESOC, University of Nancy I) for kinetic measurements. We acknowledge the help of Mr. E. Dumortier (LESOC) for suggesting efficient computer procedures.
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