J . Phys. Chem. 1989, 93, 1502-1 505
1502
TABLE 111: Critical Micelle Concentrations'
c1alkyl
Me Et n-Pr n-Bu
cmc,b mM 1.36 1.20 0.65 0.52
Br-
mM 1 .30d 1.20 0.66
cmc,b mM 0.79 0.53 0.27
cmc: mM 0.89d 0.8 1
0.56 0.24
'In water at 25 OC. bConductimetricvalues. cSurface tension values.
dReference 14.
The effect of N-alkyl groups on solubility and micelle shape parallels their contribution to the stability of the micelles. By "folding-back" the groups Et to n-Bu fill the space between headgroups at the micellar surface and therefore increase the stability of micelles. Critical Micelle Concentrations. Values of the cmc in absence of added electrolyte were determined conductimetrically at 25 OC or determined by variations in surface tension. There were no minima in plots of surface tension against log concentration, and our values of cmc agreed with literature values where available14 (Table 11). The cmc decreases with increasing size of the N-alkyl
groups and is larger for the chlorides than bromides. These differences are consistent with differences in anion binding. Fractional Ionization. Values of (Y were determined conductimetrically from the ratio of slopes of plots of specific conductance against surfactant, concentration below and above the cmc,ll or by use of Evans equation16 (Table 111). Kinetics. Reactions were followed spectrophotometrically at 326 nm. MeONs was added in 20 pL of MeCN to 3 mL of reaction solution at 25 OC, so that [MeONs] = lo4 M. The first-order rate constants, k , (s-I), the reaction in CTACl and CTABr with no added salt agree with earlier values.8b,c Rate constants k$ are corrected for the contribution of the spontaneous reaction with HzO. Note Added in ProoJ The value of the cmc of CTPeABr has been confirmed by surface tension. Acknowledgment. Support by the National Science Foundation (Organic Chemical Dynamics Program) is gratefully acknowledged. The award of a NATO grant for F.O. is gratefully acknowledged. Registry No. CTACI, 112-02-7; CTEACI, 13287-79-1; CTPACI, 110214-22-7;CTBACI, 6439-71-0; CTABr, 57-09-0;CTEABr, 1331670-6; CTPABr, 25268-61-5; CTBABr, 117942-60-6;MeONs, 5 138-53-4; Cl-, 16887-00-6;Br-, 24959-67-9.
Origin of the Apparent Breakdown of the Pseudophase Ion-Exchange Model for Micellar Catalysis with Reactive Counterion Surfactants Maria de Fiitima Santana Neves, Din0 Zanette, Frank Quina,* M6ricles Tadeu Moretti, and Faruk Nome* Departamento de Quimica, Universidade Federal de Santa Catarina, 88049 Florian6polis. SC, Brazil (Received: May 2, 1988)
One of the more important failures of the pseudophase ion-exchange (PPIE) model for micellar catalysis has been its inability to reproduce kinetic data for reactions in surfactants with highly hydrophilic counterions such as hexadecyltrimethylammonium hydroxide ((CTA)OH) and fluoride ((CTA)F). In the present work, it is shown that this apparent failure is due not to fundamental flaws in the model itself but to the inadequacy of the commonly employed assumption that the degree of micellar dissociation (a)is constant under all conditions. Thus, kinetic data in both (CTA)OH and (CTA)F are quantitatively simulated by PPIE when the appropriate surfactant concentration dependent values of a,determined by conductivity, are employed for these two detergents.
Introduction Over the last several decades, there has been a steady increase in the number of studies dealing with the effects of micelles, synthetic and natural vesicles, monolayers, microemulsions, and polyelectrolytes on a wide variety of ground- and excited-state reactions and equilibria.'S2 These experimental studies have, in turn, stimulated parallel attempts to develop semiquantitative models or formalisms capable of describing and, eventually, predicting the observed effects. For ionic micellar solutions, the best model currently available is the pseudophase ion-exchange (PPIE) formalism, which is capable of describing and predicting most ionic micellar effects on reaction rates and equilibria over a wide range of experimental conditions (pH, detergent and added salt concentrations, etc.) from a single set of parameter^.^-^ Advances in our understanding of
the various modes of substrate binding to ionic micelles have permitted application of this model to a broad spectrum of quite diverse types of bimolecular reactions in both cationic and anionic micellar solutions. For virtually all of these reactions, the dominant factor responsible for the observed micellar effects on the reaction rate is the substantial change in the local concentrations of the reactive species that results from the binding of these to the micelle surface. The fact that the PPIE model judiciously ignores all details of micelle structure, treating the micelles as if they were a bulklike pseudophase, has permitted application and extension of the basic concepts of PPIE to various other types of aqueous ionic interfaces, including synthetic vesicle^,^,' reversed micelles,* and microemuIsion~.~J~ (5) Bunton, C. A. Catal. Reu.-Sci. Eng. 1919. 20, I . (6) Fendler, J. H.; Hinze, W. L. J . Am. Chem. SOC.1981, 103, 5439. (7) Cuccovia, I. M.; Quina, F. H.; Chaimovich, H. Tetrahedron 1982, 38,
( I ) Fendler, J. H.; Fendler, E. J. Caralysis in Micellar and Macromolecular Sysrems; Academic: New York, 1975. (2) Fendler, J. H. Membrane Mimeric Chemisrry; Wiley: New York,
917.
(3) Romsted, L. S. Ph.D. Thesis, Indiana University, Bloomington, IN, 1975. (4) Quina, F. H.; Chaimovich, H. J . Phys. Chem. 1979, 83, 1844.
(8) El Seoud, 0. A,; Chinelatto, A. M. J . Colloid Inrerface Sci. 1983, 95, 163. (9) Mackay, R. A. J . Phys. Chem. 1982, 86, 4756. (IO) Silva, I. S.;Zanette, D.; Nome, F. Arual. Fis.-Quim. Org. 1985, 123.
1982.
0022-3654/89/2093-1502$01 S O / O
0 1989 American Chemical Society
PPIE Model for Micellar Catalysis
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1503
As is the case with any model that makes a deliberate comof counterions. More recently, several g r o ~ p s ~ ~have - ~ Oused promise between conceptual simplicity and theoretical rigor in spherical cell models analogous to those previously employed to calculate micellar p r ~ p e r t i e s ~to l - simulate ~~ micellar effects on order to retain experimental testability, PPIE is not without its shortcomings. The fundamental assumption of the PPIE approach, kinetics and equilibria. In this approach, local counterion coni.e., that all species are in thermodynamic equilibrium prior to centrations at the surface of spherical micelles are calculated on reaction, restricts its applicability to reactions that are slow relative the basis of numerical solutions of the nonlinear Poisson-Boltzto substrate partitioning. Specific interactions not explicitly mann equations, modified in various manners to accommodate contemplated by the general PPIE approach, such as ion pairing counterion selectivity. Even with this more sophisticated approach, with free monomer or substrate-induced premicellization, can give however, results in the presence of hydroxide ion could only be rise to problems in simulating kinetic data near the critical micelle fitted by treating the size of the (CTA)OH micelles as an adconcentration (cmc). Although systematic deviations from the justable ~ a r a m e t e r . ~ ~ . ~ ~ Although elegant in its own right, use of the Poisson-Boltzmann behavior predicted by PPIE have also been reported for systems cell model approach to treat micellar effects on rates and equilibria containing mixtures of monovalent and divalent counterions, these is not a particularly attractive alternative for resolving the problem can be largely eliminated by formulating the counterion exchange of the breakdown of PPIE. While this approach does offer some selectivity coefficient correctly (in terms of local concentrations real advantages in treating reactions or equilibria involving miof the micelle-associatedcounterions), including activity corrections celle-excluded co-ions, solving the modified nonlinear Poissonfor the aqueous counterions, and taking into account the marked Boltzmann equation requires a series of quite explicit assumptions depression of the cmc by the added divalent counterion. with respect to the geometry, size, and properties of the aggregates The most serious breakdown of conventional PPIE was first and relatively elaborate computations, both of which seriously evidenced by studies with "reactive counterion" compromise the generality of this type of approach. In addition, In these studies, a bimolecular reaction between an organic substrate and a counterion is carried out under conditions in which the differences in the PPIE and Poisson-Boltzmann approaches only one type of counterion, that of the ionic surfactant itself, is are frequently more a matter of style than of essence. Thus, in present. Given the assumption of a constant net degree of the case of reactive counterion surfactants the analytical expression counterion association with the micelle surface, PPIE unambigfor the observed rate constant of a bimolecular reaction, deduced uously predicts that, at detergent concentrations high enough to in rigorous fashion from the cell model (by taking into account incorporate all of the organic substrate into the micelles, the the radial distribution of substrates, counterions, and co-ions, observed rate of such a reaction should reach a constant limiting integrating the local rate of reaction from the micelle center out value independent of the concentrations of surfactant and added to the cell boundary or midpoint between micelles, and summing common counterion salt. In cationic micellar solutions, this over all cells, is identical with the form predicated by PPIE. The present results demonstrate that the apparent breakdown predicted behavior is indeed observed with counterions such as of PPIE in the case of (CTA)OH and (CTA)F is due not to bromide or cyanide. With highly hydrophilic counterions, such as hydroxide or fluoride, however, the rate continues to rise even fundamental defects of the model but to the inadequacy of the after complete substrate incorporation."*16 Analogously, for conventional assumption of a constant, salt and detergent conhydronium ion catalyzed reactions in anionic micellar solutions, centration independent, degree of micellar dissociation (a). Thus, the behavior predicted by PPIE is observed when the surfactant good agreement is observed between experiment and the PPIE model when correct values of a (determined directly from head group is sulfonateI7 but not when it is sulfate.'* Another straightforward conductivity measurements) are employed for the indication of the breakdown of PPIE is the rather poor agreement simulation of kinetic data for reactions in the presence of these between values of selectivity coefficients for exchange of highly two detergents. hydrophilic counterions determined by different method^.'^-^^ Several attempts were initially made to rationalize this Experimental Section breakdown of PPIE in the reactive counterion case by recourse Hexadecyltrimethylammonium bromide ((CTA)Br), chloride to ad hoc assumptions, such as an additional rate contribution from reaction across the micelle-water b o ~ n d a r y . ' ~ * 'Sub~ - ' ~ ~ ~ ~((CTA)Cl), fluoride ((CTA)F), and hydroxide ((CTA)OH) were purified by previously described p r o ~ e d u r e s . ~ J ~ J ~ sequently, Bunton et al.23showed that observed rate constants and The conductance measurements were carried out at 25.0 OC shifts in indicator equilibria for reactive counterion surfactants in a flow dilution cell under N2 atmosphere, with a Wiss-Techcould be simulated within the context of PPIE by making the nologischen Werkstatten Model D-812 bridge-type conductivity assumption that counterion binding obeyed a micelle surface meter. potential-independent mass action law, an expediency that was extended by Vera and Rodenas24-26to systems containing mixtures
Results and Discussion
(1 1) Bunton, C. A,; Romsted, L. S. In Solution Behauior of Surfactants: Theoretical and Applied Aspects; Mittal, K. L., Fendler, E. J., a s . ; Plenum: New York, 1982; p 975. (12) Nome, F.; Rubira, A. F.; Franco, C.; Ionescu, L. G. J . Phys. Chem. 1982,86, 1881. (13) Chaimovich, H.; Cuccovia, I. M.; Bunton, C. A.; Moffatt, J. R. J . Phys. Chem. 1983, 87, 3854. (14) Ionescu, L. G.; Nome, F. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 1107. (15) Stadler, E.; Zanette, D.;Rezende, M. C.; Nome, F. J . Phys. Chem. 1984,88, 1892. (16) Romsted, L. S.In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 1015. (17) Bunton, C. A.; Romsted, L. S.; Savelli, G.J. Am. Chem. SOC.1979, 101, 1253. (18) Gonsalves, M.; Probst, S.; Rezende, M. C.; Nome, F.; Zucco, C.; Zanette, D. J . Phys. Chem. 1985, 89, 1127. (19) Broxton, T. J. Aust. J . Chem. 1981, 34, 2313. (20) Broxton, T. J.; Sango, D. E. Aust. J . Chem. 1983, 36, 711. (21) Abuin, E. B.; Lissi, E.; Arajo, P. S.; Aleixo, R.M. V.; Chaimovich, H.; Bianchi, N.; Miola, L.; Quina, F. H. J. Colloid Interface Sci. 1983, 96, 193. (22) Nascimento, M. G.; Miranda, S. A. F.; Nome, F. J . Phys. Chem. 1986, 90, 3366. (23) Bunton, C . A,; Gan, L. H.; Moffatt, J. R.; Romsted, L. S.; Savelli, G. J . Phys. Chem. 1981, 85, 1148.
For a bimolecular reaction between a neutral organic substrate and a counterion X, the general PPIE expression for the observed pseudo-first-order rate constant is
where k2, and khuare the second-order rate constants for reaction in the micellar and aqueous phases and X , and X , are the analytical corresponding concentrations of the reactive counterion in each phase. For an organic substrate totally incorporated into (24) Vera, S . ; Rodenas, E. Tetrahedron 1986, 12, 143. (25) Vera, S.; Rodenas, E. J . Phys. Chem. 1986, 90, 3414. (26) Rodenas, E.; Vera, S. J . Phys. Chem. 1985,89, 513. (27) Frahm, J.; Diekmann, S . In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984. (28) Bunton, C. A,; Moffatt, J. R. J . Phys. Chem. 1985, 89, 4166. (29) Bunton, C. A,; Moffatt, J. R. J . Phys. Chem. 1986, 90, 538. (30) Ortega, F.; Rodenas, E. J . Phys. Chem. 1987, 91, 837. (31) Bell, C. M.; Dunning, A. Trans. Faraday SOC.1970, 66, 500. (32) Mille, M.; Vanderkooi, G.J . Co//oid Znterface Sci. 1977, 59, 21 1. (33) Gunnarsson, G.;Jonsson, B.; Wennerstrom, H. J . Phys. Chem. 1980, 84, 31 14.
1504 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989
Neves et al.
0 0
30
20
I
k
I
10 01 0
20
40
6.0
80
I
100
I03[CTAX] M
Figure 2. Apparent degrees of micellar dissociation (a)as a function of 0 0
20
40
6.0
8.0
detergent concentration for aqueous solutions of (CTA)Br (O), (CTA)CI (m), (CTA)OH ( O ) , and (CTA)F ( O ) ,determined from the conductivity data of Figure 1 (see text).
10.0
IO3 [ C T A X ] M
Figure 1. Specific conductance versus concentration for aqueous solutions of (CTA)Br ( O ) , (CTA)CI (B), (CTA)OH ( O ) , and (CTA)F (0).
the micellar pseudophase, Le., it has a very large incorporation coefficient K,, eq 1 simplifies to the form
6
*.
where Ox is the fractional coverage of the micelle surface by the reactive counterion X. In a reactive counterion type surfactant, where X is the only counterion present, ex = 1 - a, where (Y is the apparent degree of micellar dissociation, such that
- a) P
*E
Y
n
0
kzm(l k,m
=
(3)
Consequently, if a is constant and independent of the concentration of detergent and added common counterion salt, as is usually assumed in most applications of the PPIE formalism, k+,,, should be constant for a substrate totally incorporated into a reactive counterion surfactant. As mentioned above, this is not the behavior observed experimentally in surfactants such a (CTA)OH or (CTA)F. Indeed, several lines of evidence suggest that the PPIE assumption of a constant net degree of counterion binding, independent of the nature and concentration of the counterions present, is not strictly true, especially for highly hydrophilic counterions such as OHand F. These include studies of the properties of micelles and vesicles of hydroxide salts, of cationic ~ u r f a c t a n t s , ~and ~ - ~of~ specific counterion effects on (a) the micellar aggregation numb e r ~ , ~ ~(b) " *the cmc of ionic detergents,39*@ (c) the incorporation of pseudomonomers into ionic micelles,39(d) the micellar surface p ~ t e n t i a l , ~(e)' ~the ~ ~ rates ~ ~ ~of dye penetration into cationic micelles,43 (f) the enthalpies of m i c e l l i ~ a t i o n ,(g) ~ ~ the photoionization (h) the surface potential and surface pressure (34) Lianos, P.; Zana, R. J. Phys. Chem. 1983, 87, 1289. (35) Athanassakis, V.; Moffatt, J. R.; Bunton, C. A.; Dorshow, R. B.; Savelli, G.; Nicoli, D. F. Chem. Phys. Lett. 1985, 115, 467. (36) Brady, J. E.; Evans, D. F.; Warr, G. G.; Grieser, F.; Ninham, B. W. J . Phys. Chem. 1986, 90, 1853. (37) Anacker, E. W.; Ghose, H. M. J . Am. Chem. SOC.1968, 90, 3161. (38) Almgren, M.; Swarup, S. J . Phys. Chem. 1983, 87,876. (39) Miola, L.; Abakerli, R. B.; Ginani, M. F.; Berci Filho, P.; Toscano, V. G.;Quina, F. H. J . Phys. Chem. 1983, 87,4417. (40) Dorion, F.; Charbit, G.; Gaboriaud, R. J. Colloid Interface Sci. 1984, 101, 27. (41) Fernandez, M. S.; Fromherz, P. J. Phys. Chem. 1977, 81, 2755. (42) Chaimovich, H.; Aleixo, R. M. V.; Cuccovia, I. M.; Zanette, D.;
Quina, F. H. In Solution Behavior of Surfactants: Theoretical and Applied Aspects, Mittal, K. L., Fendler, E. J., Eds.; Plenum: New York, 1982; Vol. 2, p 949. (43) Miyashila, Y.; Hayano, S. J. Colloid Interface Sci. 1982, 86,344. (44) Paredes, S.; Tribout, M.; Supiilveda, L. J. Phys. Chem. 1984, 88, 1871.
IO3 [CTAOH] M Figure 3. PPIE simulatiQn of kinetic datals for the dehydrochlorination and DDD (0)in aqueous (CTA)OH. The curve was calof DDT (0) culated from eq 3, the a values of Figure 2, and values for k2,,,/Pof 9.73 X and 1.22 X for DDT and DDD, respectively.
of ionized monolayers adsorbed at the air-water and oil-water interfaces,46a9 (i) the electrostatic repulsion between surfactant bilayers36,@6 ) the surface excesses in detergent foams,50(k) the properties and structures of microemulsions,51 and (1) the conformation of amphiphilic ionene polyelectrolyte^.^^ In the present work, specific conductivity data were employed to determine the apparent degrees of dissociation ( a ) of (CTA)OH, (CTA)F, (CTA)CI, and (CTA)Br over the concentration range from 0 to 10 X IO" M. Figure 1 shows the experimental specific conductivity data for these four surfactants in aqueous solution. While (CTA)Br and (CTA)Cl show normal behavior, Le., straight lines of distinct slope. below and above the cmc with a sharp break at the cmc, quite different behavior is observed for (CTA)F and (CTA)OH. Indeed, for the latter two surfactants, the initial linear variation of the specific conductivity at submicellar detergent concentrations gives way to a smooth nonlinear change of the conductivity at detergent concentrations above the cmc. With these experimental data, apparent degrees of micellar dissociation were calculated (Figure 2) from the sim(45) Hautecloque, S.; Grand, D.; Bernas, A. J. Phys. Chem. 1985, 89, 2705. (46) Gcddard, E. A,; Matteson, G. H.; Totten, G. E. J . Colloid Interface Sci. 1982, 85, 19. (47) Plaisance, M.; Ter-Minassian-Saraga, L. J. Colloid Interface Sci. 1977, 59, 113. (48) Marra, J. J . Phys. Chem. 1986, 90, 2145. (49) Pal, R. P.; Chattoraj, D. K. J. Colloid Interface Sci. 1975, 52, 56. (50) Weil, I. J . Phys. Chem. 1966, 70, 133. (51) Chen, V.; Evans, D. F.; Ninham, B. W. J. Phys. Chem. 1987, 91, 1823. (52) Soldi, V.; Erismann, N. M.; Quina, F. H. Atual. Fis.-Quim. Org. 1985, 208.
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1505
PPIE Model for Micellar Catalysis 0
I
0
4
7
e
16
1
I
24
I02[CTAF] M
Figure 4. PPIE simulation of kinetic data2) for the fluoride ion catalyzed hydrolysis of p-nitrophenyl diphenyl phosphate in aqueous (CTA)F. The curve was calculated from eq 3, the CY values of Figure 2, and a value for k2J P of 0.3 1.
plified Evans' equation, a = &/SI,where SIand Szcorrespond, respectively, to the slopes of the specific conductivity vs surfactant concentration curves below and above the cmc. For (CTA)Br and (CTA)Cl, S2and SIwere determined directly from the linear portions of the conductivity vs detergent concentration profiles above and below the cmc, except in the transition region around the cmc where the values of Sz were determined from the first derivative of polynomial fits (third degree in the detergent concentration) of the conductivity data. For both (CTA)Br and (CTA)Cl, the resultant values of a above the cmc (0.25 and 0.33, respectively) are in reasonable agreement with other literature estimates of a for these two surfactants. In the case of (CTA)OH and (CTA)F, the values of S2 were determined exclusively from the first derivative of third-degree polynomial fits of the specific conductivity profiles. For both surfactants, the a values are relatively high and decrease gradually with increasing detergent concentrations (Figure 2). The behavior of a,determined from the present conductivity data, is consistent with that inferred qualitatively by other workers. Within the present context, the central question is whether these experimental values of a,when employed in the PPIE expression for the observed rate constant (eq 3), adequately reproduce experimental kinetic profiles for reactions conducted in micelles of
(CTA)OH and (CTA)F. Indeed, when the values of Figure 2 are used in the PPIE expression, excellent fits of kinetic data are obtained for both the dehydrochlorination of DDT and DDD in (CTA)OH (Figure 3) and the fluoride ion catalyzed hydrolysis of p-nitrophenyl diphenyl phosphate in (CTA)F (Figure 4). The present results show that the apparent breakdown of the PPIE approach in the case of reactive counterion surfactants such as (CTA)OH and (CTA)F is due not to defects of the model itself, but to the inadequacy of one of the usual simplifying assumptions, viz., that the net degree of micellar dissociation (a)could be treated as a constant under all conditions. The PPIE formalism works quite well when the fundamental pseudophase condition (equilibrium redistribution of the reagents prior to reaction) is met, when amphiphile and counterion concentrations are moderate and do not provoke marked micelle growth, and when nonreactive counterions (usually those of the surfactant itself) are present in large excess over the reactive counterion. It would thus appear to be premature to abandon the PPIE approach. Indeed, unlike Poisson-Boltzmann cell models, PPIE allows one to treat the effects of charged aqueous interfaces on reaction rates and equilibria without explicit consideration of factors such as the size, shape, curvature, or dynamics of the interface, the presence of an electrical double layer, or the magnitude of the surface potential and the interaggregate interactions. The ability to ignore such factors automatically endows the PPIE approach with a generality beyond that of just aqueous micellar solutions. The PPIE approach and/or the assumption of constant a tend to break down at high detergent or salt concentration and in the presence of an excess of very hydrophilic counterions that bind inefficiently to the micellar surface (such as OH- and F). Nonetheless, as shown in the present work, PPIE can be quite successfully applied to kinetic data in such systems, if the variation of a under the reaction conditions (whose determination requires little additional experimental effort) is taken into account. Acknowledgment. We are grateful to CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnolbgico, Brazil) for financial support of this work. Registry No. (CTA)Br, 57-09-0; (CTA)CI, 112-02-7; (CTA)F, 14002-56-3; (CTA)OH, 505-86-2.
