Comparisons and Analyses of Theoretical Treatments of Micellar

Langmuir 2000, 16, 5921-5931

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Comparisons and Analyses of Theoretical Treatments of Micellar Effects upon Ion-Molecule Reactions. Relevance to Amide Exchange Clifford A. Bunton* Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106

Anatoly K. Yatsimirsky* Facultad de Quı´mica, Universidad Nacional Auto´ noma de Me´ xico, Me´ xico D.F., 04510, Me´ xico Received January 20, 2000. In Final Form: April 10, 2000 Reported second-order rate constants of H+ and OH- catalyzed amide exchanges in micellar solutions, relative to those in water, have been claimed to be inexplicable in terms of pseudophase treatments of micellar rate effects, and the Bro¨nsted-Bjerrum treatment was invoked to fit the data (Perrin, C. L.; et al. J. Am. Chem. Soc. 1999, 121, 2448). Rate constants of amide exchange, based on pH measurements in surfactant solutions, are only approximate, but examination of the data and comparisons with evidence on other reactions show that they are qualitatively consistent with pseudophase treatments. Micellar effects upon rate constants of deacylations by OH- and acid hydrolyses of dioxolanes, analyzed with pseudophase treatments, were considered for the purpose of comparison. The pseudophase and Bro¨nstedBjerrum formalisms are equivalent in rationalizing micellar rate data, although the former appears to be descriptively more useful as applied to reactions of apolar organic compounds. Interrelations between the two approaches are analyzed in terms of transfer free energies of reactants and transition states. Potentiometric titrations of HCl with NaOH were made in solutions of sodium dodecyl sulfate and cetyl trimethylammonium chloride in order to estimate the autoprotolysis constant of water and to establish the relation of pH to concentrations of H+ and OH- in unbuffered micellar solutions.

Introduction The ability of micellized surfactants to control rates of moderately slow reactions is well established and is extensively reviewed.1-5 Most of the reactions studied to date involve ionic reagents and/or generate ionic products or intermediates. Micellar charge is clearly important, and cationic micelles typically accelerate reactions of anionic nucleophiles or bases with nonionic substrates and inhibit those of cationic reagents. Conversely anionic micelles accelerate reactions of cationic and inhibit those of anionic reagents. However, nonelectrostatic interactions with ions are also important, for example, affinities of anions for cationic micelles increase with decreasing charge densities and follow the Hofmeister series.2,6 Effects of normal micelles on reaction rates and equilibria in water, or in solvents such as diols, are often * To whom correspondence may be addressed: Clifford A. Bunton, phone (805) 893-2605, e-mail [email protected]; Anatoly K. Yatsimirsky, e-mail [email protected]. (1) (a) Bunton, C. A.; Savelli, G. Adv. Phys. Org. Chem. 1986, 22, 213. (b) Bunton, C. A. In Kinetics and Catalysis in Microheterogeneous Systems; Gratzel, M., Kalyanasundaram, K., Eds.; Marcel Dekker: New York, 1991; Chapter 2. (c) Fendler, J. H. Membrane-Mimetic Chemistry; Wiley-Interscience: New York, 1982. (2) Bunton, C. A.; Nome, F.; Quina, F. H.; Romsted, L. S. Acc. Chem. Res. 1991, 24, 357. (3) Tascioglu, S. Tetrahedron 1996, 52, 11113. (4) Romsted, L. S.; Bunton, C. A.; Yao, J. Curr. Opin. Colloid Interface Sci. 1997, 2, 622. (5) (a) Berezin, I. V.; Martinek, K.; Yatsimirsky, A. K. Russ.Chem. Rev. (Engl. Transl.) 1973, 42, 787. (b) Martinek, K.; Yatsimirsky, A. K.; Levashov, A. V.; Berezin, I. V. In Micellization, Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2, p 489. (6) Morgan, J. D.; Napper, D. H.; Warr, S. S. J. Phys. Chem. 1995, 99, 9458.

treated in terms of pseudophase models with water and micelles being treated as distinct reaction regions.1-5 The overall rate is the sum of rates in each region, which, for bimolecular reactions, depend on local concentrations and second-order rate constants. This treatment allows development of equations that predict variations of observed rate constants in terms of concentrations and structures of reactants and surfactants and can be applied to other association colloids, e.g., microemulsions and vesicles.7 It also fits effects of inert solutes, e.g., electrolytes, on overall reaction rates. In favorable cases the transfer equilibria of reactants between water and micelles can be examined independently and used in analyzing the rate effects. However, all the quantitative treatments involve approximations and assumptions, and in some cases observed first-order rate constants can be fitted by various combinations of rate and equilibrium constants. Much of the work has involved apolar organic substrates (S) which interact strongly with micelles, and except in very dilute surfactant, reaction is then assumed to be largely in the micellar pseudophase. In these conditions the observed free energy of activation relative to that in water (the micellar effect) depends on the transfer free energy of the second reactant between water and micelles and the difference between free energies of activation in the two pseudophases. In an alternative description one need not regard water and micelles as distinct reaction regions, but simply consider changes in free energies of initial and transition states induced by addition of micelles to water or other (7) (a) Schwuger, M.-J.; Stickdorn, K.; Schomaker, R. Chem. Rev. 1995, 95, 849. (b) Chaimovich, H.; Cuccovia, I. M. Prog. Colloid Polym. Sci. 1997, 103, 67. (c) Mackay, R. A. J. Phys. Chem. 1982, 86, 4756.

10.1021/la000068s CCC: $19.00 © 2000 American Chemical Society Published on Web 05/27/2000

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Bunton and Yatsimirsky

solvent.8,9 This approach is described by applying the Bro¨nsted-Bjerrum equation (1) to the second-order reac-

k2,app ) k0γSγB/γ*

(1)

tion of S and reactant B to form the transition state T*; k2,app is the apparent second-order rate constant of the overall reaction and k0 is the second-order rate constant in the reference conditions, typically water. In this formalism interactions of micelles with S and B decrease the activity coefficients, γS and γB, which inhibits reaction, but can be more than offset by a decrease in γ*, and application of eq 1 requires estimation of activity coefficients. Another approach involves estimation of the binding constant (M-1) of the transition state to micelles (KT*) (eq 2)

KT* ) (km′/k0)KSKB

(2)

where km′ is the second-order rate constant in the micellar pseudophase with concentrations as mole fractions and KS and KB are binding constants (M-1) of reactants.8,10 This approach is popular in analyses of enzymic11 and other catalytic (e.g., as in cyclodextrins) reactions,12 which often are single-substrate reactions following classical Michaelis-Menten kinetics, and KT* is calculated from eq 3

KT* ) (kc/ku)KS

Scheme 1

(3)

where kc and ku are first-order rate constants of the catalytic and uncatalyzed reactions, respectively. Equation 3 was also applied formally to second-order micellar reactions, e.g., alkaline ester hydrolysis in cationic micelles,12 treated in terms of single-substrate MichaelisMenten kinetics. The choice of the formalism is a matter for predilection and convenience. For example, reactions of apolar organic compounds are typically treated by applying the pseudophase model, and estimated rate constants in the micellar pseudophase are consistent with reaction in a medium that is somewhat less polar than water. The very striking accelerations of some moderately slow reactions of hydrophilic reagents by reverse micelles1c,13 are readily understandable in terms of concentration of ions or polar molecules in the small volume of the “water pool” in the interior of a reverse micelle. However, for reactions of polyvalent inorganic ions in aqueous ionic micelles, which occur largely in the aqueous region, electrostatic interactions become very important, and eq 1, with allowance for ionic interactions, provides a convenient treatment.9 Perrin et al.14 recently examined hydrogen and hydroxide ion catalyzed hydrogen exchanges of amides and (8) Hall, D. G. J. Phys. Chem. 1987, 91, 4287. (9) (a) Lo´pez-Cornejo, P. L.; Jimeńez, R.; Moya´, M. L.; Sańchez, F.; Burgess, J. Langmuir 1996, 12, 4981. (b) Muriel-Delgado, F.; Jimeńez, R.; Go´mez-Herrera, C.; Sańchez, F. Langmuir 1999, 15, 4344. (10) Davies, D. M.; Gillitt, N. D.; Paradis, P. M. J. Chem. Soc., Perkin Trans. 2 1996, 659. (11) (a) Wolfenden, R. Acc. Chem. Res. 1972, 5, 10. (b) Lienhard, G. E. Science 1973, 180, 149. (c) Mader, M. M.; Bartlett, P. A. Chem. Rev. 1997, 97, 1281. (12) (a) Tee, O. S. Adv. Phys. Org. Chem. 1994, 29, 1. (b) Tee, O. S.; Fedortchenko, A. A. Can. J. Chem. 1997, 75, 1434. (13) (a) Luisi, P. P. In Kinetics and Catalysis in Microheterogeneous Systems; Gratzel, M., Kalyanasundaram, K., Eds.; Marcel Dekker: New York, 1991; Chapter 5. (b) El Seoud, O. A. Adv. Colloid Interface Sci. 1989, 30, 1. (14) Perrin, C. L.; Chen, J.-H.; Ohta, B. K. J. Am. Chem. Soc. 1999, 121, 2448.

ureas in water and ionic micelles. These reactions are attractive because of their mechanistic simplicity and involve comparisons of apparent second-order rate constants of exchange of a short-chain amide, N-methylbutyramide, MBA, in water, and of a long-chain, amphiphilic, amide, N-methyllauramide, MLA, in cationic and anionic micelles. Exchanges of the ureas were not examined in all conditions. The second-order rate constants were not calculated from total concentrations of H+ and OH-, but were based on pH of the reaction mixtures and the autoprotolysis constant, Kw, in water. Second-order rate constants of exchange in water, calculated in this way, should be similar to those calculated with stoichiometric concentrations, because in dilute aqueous electrolyte pH measured with an instrument calibrated with standard buffers is close to -log[H+] (Results), but this situation may not apply to reactions in aqueous surfactants. As a result, reported second-order rate constants in water and aqueous surfactant are based on different estimates of concentrations which obscures comparison of their values. The situation is similar to that in comparison of secondorder rate constants in different solvents calculated in terms of observed pH. We also have to consider estimation of [OH-] from observed pH and Kw in aqueous surfactants, and we attempt to answer this question experimentally. The micelles were derived from sodium dodecyl sulfate, SDS, cetylpyridinium chloride, CPCl, dodecylpyridinium chloride, DPCl, and cetyltrimethylammonium chloride, CTACl. Reactions were, of necessity, followed with higher [substrate], typically 0.05 M, than is customarily used in micellar work,1-5 and [surfactant] was generally 0.25 or 0.5 M. First-order rate constants, kobs, were estimated over ranges of pH, second-order rate constants, kH and kOH, were calculated from plots of kobs against [H+] or [OH-], with pH ) -log[H+], and [OH-] was given by pH and pKw ) 13.71, at 34 °C for most experiments. The gist of the conclusions was the observation of “puzzling” apparent asymmetry in micellar charge effects, namely, that anionic micelles significantly increase kH and decrease kOH, as expected, but the cationic micelles, which behave similarly, only modestly decrease kH and have little effect upon kOH. Some experiments were made with added ionic or nonionic solutes which did not markedly affect rate constants. Hydroxide-ion catalyzed exchange involves deprotonation of NH with negative charge largely on oxygen and acid-catalyzed exchange of primary amides is believed to involve N-protonation (Scheme 1), but an imidic acid mechanism has also been observed.15 These mechanistically different acid mechanisms may be affected differently by ionic micelles, but there seems to be no evidence on this possibility. Exchanges are apparently not buffercatalyzed, at least in the conditions used by Perrin et al.14 These authors conclude that their results are inconsistent with the pseudophase treatment and that several features defy simple interpretation. Our aim is to examine these (15) Perrin, C. L.; Lollo, C. P. J. Am. Chem. Soc. 1984, 106, 2754.

Micellar Effects on Ion-Molecule Reactions

questions, and we also consider evidence on other ionic reactions carried out, as far as is possible, in similar conditions of high [surfactant]. We consider several aspects of the problem: (i) the significance of pH in surfactant solutions; (ii) analysis of micellar rate effects in terms of various formalisms; (iii) the extent to which micelles may affect reactivity by changing mechanism or structures of reactants. We note that experiments described by Perrin et al.14 provide an excellent opportunity for discussion of micellar charge effects because this is a system where both positively and negatively charged reactants are studied with both anionic and cationic micelles. This, and the relative simplicity of the reaction mechanism, makes the system attractive for discussion of different approaches to micellar catalysis, which is the key purpose of this paper. Application of the pseudophase treatment to bimolecular reactions of hydrophilic ions requires estimation of their distribution between water and micelles. Experimental methods are available for some ions,16,17 but theoretical approaches are generally used.1,2,18 Competition between counterions can be described in terms of ion-exchange, PIE, which, with the assumption of constant fractional micellar ionization, R, treats ionic distributions in terms of an ion-exchange constant.18 An alternative treatment describes competition without requiring a constant value of R or β ) 1 - R.19 A third treatment estimates local ionic concentrations by solving the Poisson-Boltzmann equation, PBE, with allowance for nonspecific, Coulombic, and specific, ion-micelle interactions.20 These treatments, when used appropriately, are self-consistent and fit extensive kinetic and equilibrium data, including variations of overall first-order rate constants with changes in concentrations of surfactant, reactants, and inert solutes.1,2,18-21 We use both the PIE and PBE formalisms, as convenient, in showing how the pseudophase model can be applied to micellar-mediated amide exchange.22 However, quantitative applications of these treatments require information on total concentrations of inert and reactive ions. As a result it is not feasible to analyze unambiguously apparent second-order rate constants calculated from pH values in unspecified buffers where total concentrations of H+ or OH- are unknown. In these situations one can only attempt to interpret qualitative trends in experimental results. Therefore, we examined effects of SDS and CTACl upon the pH of dilute HCl under conditions of defined [H+]T in order to decide whether reliance on the pH scale led to the purported failure of the pseudophase treatment.14 For example, if micelles strongly affect the response of the glass electrode, estimates of aH or [H+] will be in error, and if they also affect Kw there will be an additional error in aOH or [OH-]. Experimental Section Materials. SDS was a BDH “specially pure” sample; CTACl had been prepared from hexadecyl chloride and dry Me3N in (16) (a) Lianos, P.; Zana, R. J. Colloid Interface Sci. 1982, 88, 594. (b) Bunton, C. A.; Ohmenzetter, K.; Sepulveda, L. J. Phys. Chem. 1977, 81, 2000. (17) Blasko, A.; Bunton, C. A.; Cerichelli, G.; McKenzie, D. C. J. Phys. Chem. 1993, 97, 11324 and ref cited. (18) (a) Romsted, L. S. In Micellization, Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2, p 509. (b) Romsted, L. S. In Surfactants in Solution; Lindman, B., Mittal, K. L., Eds.; Plenum Press: New York, 1984; Vol. 2, p 1015. (19) (a) Bunton, C. A.; Gan, L.-H.; Moffatt, J. R.; Romsted, L. S.; Savelli, S. J. Phys. Chem. 1981, 85, 4118. (b) Rodenas, E.; Vera, S. J. Phys. Chem. 1985, 89, 513. (20) (a) Bunton, C. A.; Moffatt, J. R. J. Phys. Chem. 1986, 90, 538. (b) Ortega, F.; Rodenas, E. J. Phys. Chem. 1987, 91, 837. (21) Romsted, L. S. J. Phys. Chem. 1985, 89, 5107 and references cited. (22) The limits of validity of these treaments, and related approximations and assumptions, have been discussed extensively.1-4,18

Langmuir, Vol. 16, No. 14, 2000 5923 i-PrOH and had no minimum in the surface tension,17 but the pH titration indicates that it contains a small amount of basic impurity which we assume is Me3N. pH Titration. Solutions were made up in freshly boiled distilled deionized water under N2, and 1 M NaOH was added with a syringe with little change of overall volume. The variation of potential of the glass electrode was monitored as a function of added NaOH on a Fisher Accumet 925 pH meter with an Accumet combination electrode. Data were fitted to a nonlinear least-squares regression by using the Origin 5 program. A titration carried out with commercial CTACl indicated the presence of a significant amount (ca. 1 mol %) of an acidic impurity (data not shown).

Results Potentiometric Acid-Base Titration and Significance of pH in Micellar Solutions. Interpretation of reported second-order rate constants of amide exchange14 requires an understanding of what is actually measured as [H+] and [OH-], because there are questions regarding surfactant effects upon the response of the glass electrode and whether hydrogen ion activity or concentration is being measured. The widespread belief that the glass electrode calibrated with standard buffer solutions unambiguously measures hydrogen ion activity (Perrin et al.14 do not specify how the electrode was calibrated, but supposedly they used standard buffers) is an oversimplification. The measured electrode potential is related to hydrogen ion concentration by eq 4

E ) A + B log[H+]

(4)

where A ) E° + Eref + Ej + B log γH and B ) 2.3RT/F (here E°, Eref, and Ej are the standard, reference, and junction potentials, respectively, T is in kelvins, and F is Faraday’s constant). Calibration with standard buffers is based on the assumption that γH (more precisely the mean activity coefficient) in these buffers is known and one can therefore replace [H+] by aH in eq 5

E ) A′ + B log aH

(5)

where A′ ) E° + Eref + Ej and -log aH ) pH. However, Ej is different in any solution other than that used for calibration. Moreover, in practice B for a given instrument may not exactly equal its theoretical value, and its value, and those of A or A′, must be found by calibration. Such a calibration must be done with at least two buffers of different compositions, which inevitably makes the instrumental pH scale to some extent approximate. It was shown23 that a pH-meter calibrated with standard buffers measures neither aH, nor [H+], although in aqueous solutions of moderate ionic strength the difference is not large (about 0.2-0.3 log units) and, surprisingly, measured pH is closer to -log[H+] than to -log aH. In organic or mixed aqueous-organic solvents, differences will be much larger and one must calibrate the electrode with standard solutions (when available) in the given solvents.24 The situation with micellar solutions is ambiguous: on one hand, these are predominantly aqueous, but they have much in common with mixed organic solvents, e.g., in respect to solubilities of apolar compounds25 and apparent (23) (a) Sigel, H.; Zuberbu¨hler, A. D.; Yamauchi, O. Anal. Chim. Acta 1991, 255, 63. (b) Irving, H. M.; Miles, M. G.; Pettit, L. D. Anal. Chim. Acta 1967, 38, 475. (24) Bates, R. G. Determination of pH, Theory and Practice; Wiley: New York, 1964. (25) Sepulveda, L.; Lissi, E.; Quina, F. Adv. Colloid Interface Sci. 1986, 25, 7.

5924



trode, which senses only free Hw+. Fitting to eq 6b gives

[H+]T ) [H+]w + [OH-]T - [OH-] + [H+]m ) [H+] w (1 + KH[SDS]) + [OH-]T - Kw/[H+]w (6b)

Figure 1. Potentiometric titration curves of 0.005 M HCl with 1 M NaOH in 0.1 M NaCl (triangles), 0.1 M SDS (solid circles), and 0.1 M CTACl (open circles). Lines are best fit curves. Note the overlap of data in NaCl and CTACl.

polarities based on probes.26 The problem of pH in micellar catalyzed reactions was addressed previously, and it was concluded that the observed increase in pH reading in HCl solutions on addition of SDS can be attributed to binding of H+ to micelles which reduces the amount of free H+ sensed by the glass electrode.16b,27 We attempted to check the behavior of a glass electrode in typical micellar media by titrating a strong acid with a strong base in aqueous SDS and CTACl, Figure 1. Calibration of the electrode involved titrating 0.005 M HCl with 1 M NaOH in aqueous 0.1 M NaCl. The fitting of the titration curve to eq 6a28 (subscript T denotes total concentrations) gives

[H+]T ) [H+] + [OH-]T - [OH-] ) [H+] + [OH-]T - Kw/[H+] (6a) pKw ) 13.80 together with values of parameters A and B in eq 4, which coincide in limits of errors with parameters A′ and B in eq 5 determined for comparison by a threepoint calibration with standard Fisher buffers. This coincidence means that the “activity” of H+ estimated from the buffer calibration is close to its concentration, although in 0.1 M NaCl the Debye-Huckel equation predicts γH ) 0.75 and the predicted activity of H+ should be considerably lower than its concentration. Titration of 0.005 M HCl in 0.1 M SDS was fitted initially to the same equation by using an adjustable parameter f in the expression [H+] ) fB × 10E/A, which, in accordance with eq 4 gives f ) (γHNaCl/γHSDS)10(EjSDS-EjNaCl)/B. The use of such a parameter was suggested by the Johanssons28 for correction of variations in junction potential and activity coefficients in analyses of potentiometric titration data. The fitting is reasonably good, yielding f ) 1.88 and pKwSDS ) 13.31. Note that Kw is here a stoichiometric “concentration” constant of self-ionization of water. It is three times larger than that in aqueous 0.1 M NaCl, most probably due to reduction in γH, because micelles of an anionic surfactant may not affect the activity coefficient of OHbut should reduce that of H+. Results in SDS can be analyzed differently, e.g., by assuming that the fraction of H+ bound to the surface of anionic micelles becomes unavailable to the glass elec(26) Novaki, L. P.; El Seoud, O. A. Phys. Chem. Chem. Phys. 1999, 1, 1957 and references cited. (27) Bunton, C. A.; Wolfe, B. J. Am. Chem. Soc. 1973, 95, 3742. (28) Johansson, A.; Johansson, S. Analyst 1978, 103, 1225.

where [H+]m is the concentration of micellar-bound protons and the binding constant KH is defined as KH ) [H+]m/ ([H+]w[SDS]), with [SDS] . [H+]. The fit is good and allows one to estimate the binding constant for H+, KH ) 14.3 M-1, and pKw ) 13.80 with f ) 0.82. Note that the required fitting value of f in this model is close, but not equal, to unity, which may be due to differences in activity coefficients of “free” H+ or junction potentials in NaCl and SDS (these contributions cannot be separated within a given model). The value of KH agrees with that expected from the ion-exchange, PIE, model:18 KH ) KH/Naβ/[Na+]w, where β is the fractional micellar neutralization by Na+. The exchange constant KH/Na between H+ and Na+ for SDS micelles is ca. unity,16b,29 β ≈ 0.65 and [Na+]w ) (1 - β)([SDS]T - cmc) + cmc. Therefore, with [SDS]T ) 0.1 M one predicts KH ≈ 17 M-1 (with cmc ) 6 mM). The value of pKw in this model should be, and is, very close to that in 0.1 M NaCl. We note that the concentration of OH- calculated from that of H+ with f ) 1.88 and pKwSDS ) 13.31 in 0.1 M SDS will be 1.6-fold higher than that calculated in the same solution from Kw in aqueous NaCl and pH read directly from the meter. At the same time, the instrumental pH does not correspond exactly to the negative logarithm of either free or total [H+] but is, however, considerably closer to the former: it is ca. 0.1 lower than -log[H+]w, where [H+]w is the concentration of free protons calculated from KH ) 14.3 M-1 at a given concentration of SDS, but is ca. 0.3 higher than -log[H+]T. The titration curve of 0.005 M HCl in 0.1 M CTACl practically coincides with that in 0.1 M NaCl (Figure 1). The only difference is due to the presence of a small (ca. 0.2 mol %) unidentified impurity in the surfactant sample which is titrated as a weak acid, pKa ) 7.7. Titration of commercially available CTACl revealed the presence of ca. 1 mol % of the same impurity. There is no change in pKw in this system. In another set of experiments the instrumental pH of 0.005 M HCl was measured at increasing concentrations (0-0.2 M) of SDS and CTACl. In CTACl the pH reading was unchanged, but in SDS it increased by ca. 0.3 in 0.05 M SDS and then remained practically constant. Such behavior is consistent with the assumption that the glass electrode reacts only to free H+. Indeed, the PIE treatment predicts that with [SDS] . [HCl] and [SDS] . cmc

KNa/H ) ([H+]w[Na+]m)/([H+]m[Na+]w) ≈ ([H+]wβ[SDS]T)/{([H+]T - [H+]m)(1 - β)[SDS]T} ) ([H+]wβ)/{([H+]T - [H+]m)(1 - β)} (7a) and therefore

∆pH ) log([H+]T/[H+]w) ) log(1 + β/(1 - β)KNa/H) (7b) These results indicate that the glass electrode behaves normally in unbuffered surfactant solutions and the pH meter reading is similar to the negative logarithm of concentration of free H+, as in electrolyte solutions. A (29) (a) Quina, F. H.; Politi, M. J.; Cuccovia, I. M.; Martins-Franchetti, S. M.; Chaimovich, H. In Solution Behavior of Surfactants; Mittal, K. L., Fendler, E. J., Eds.; Plenum Press: New York, 1982; Vol. 2, p 1125. (b) Perez-Benito, E.; Rodenas, E. J. Colloid Interface Sci. 1990, 139, 87.


Langmuir, Vol. 16, No. 14, 2000 5925

Table 1. Selected Second-Order Rate Constants of Amide Exchange and “Average Micellar Charge Effects” in Aqueous Surfactantsa Selected Second-Order Rate Constants conditions

kH, M-1 s-1

kOH, M-1 s-1

kH/kH0

kOH0/kOH

water 0.25 M SDS 0.25 M SDS + 0.25 M NaCl 0.5 M SDS 0.25 M CPCl 0.25 M CPCl + 0.25 M NaCl 0.5 M CPCl 0.5 M CTACl

1.03 × 1.37 × 105 6.1 × 104 1.44 × 105 1.98 × 102 2.16 × 102 1.82 × 102 2.11 × 102

1.07 × 5.2 × 103 3.3 × 103 6.6 × 103 7.5 × 106 2.5 × 106 8.3 × 106 3.9 × 106

133 59 140 0.19 0.21 0.17 0.2

2060 3200 1620 1.4 4.3 1.2 2.8

substrate MBA MLA

anionic micelles cationic micelles a

103

107

Average Micellar Charge Effects log(kH/kH0) ) 2.0 ( 0.2 and log(kOH/kOH0) ) -3.4 ( 0.2 log(kH/kH0) ) -0.75 ( 0.06 and log(kOH/kOH0) ) -0.18 ( 0.25

Reference 14.

decrease in the activity of H+ in SDS is ascribed to binding of H+ to anionic micelles, as in the PIE.18 There are problems in discriminating between “free” and “bound” counterions in micellar and polyelectrolyte solutions,8 because long-range Coulombic interactions do not require ions to be in contact, i.e., to be “bound”. However, present pH measurements as well as measurements with other ion-selective elctrodes16,30 indicate that a fraction of counterions is “bound”. In terms of this approach the estimated activity of bulk H+ in a surfactant solution is similar to that in equimolar NaCl, reflecting similar ionic strengths of a surfactant and a simple 1:1 electrolyte (see ref 31 for estimation of ionic strength in surfactant solutions). In CTACl one expects a decrease in the “activity” of OH-; however, the binding constant of OHto CTACl micelles is significantly smaller than that of H+ to SDS micelles, based on the PIE model.18 As a result the extent of binding of OH- to micellized 0.1 M CTACl should be small and not significantly change the observed Kw. In conclusion, pH measured in aqueous surfactants, in the absence of buffer, allows one to estimate, with an uncertainty within a factor of ca. 2, concentrations of free H+ and OH-, which in CTACl are close to their total concentrations, but in SDS free H+ accounts for approximately half the total H+ concentration and there is a greater uncertainty in estimation of free OH-. In a practical sense the meaning of second-order rate constants of acid- and base-catalyzed exchange reactions in ref 14, calculated on the basis of H+ and OH- “concentrations” taken from pH meter readings, is obscure, especially in SDS, where pKw is shifted. Nevertheless, ranges of observed micellar effects14 are much larger than probable uncertainties in ionic reactant concentrations. In the following discussion we have no choice but to assume that second-order rate constants calculated in micellar solutions refer approximately to concentrations of free H+ and OH- in the aqueous region, rather than to total concentrations. We cannot set limits to the consequent uncertainties in apparent second-order rate constants, but they should be within 1 order of magnitude of those which would be estimated from total concentrations. There are significant variations in reported second-order rate constants of exchange in both anionic and cationic micelles (Tables 3 and 4 of ref 14). Some of them can be ascribed to differences in the reaction media or to differences in the behavior of the cationic surfactants,14 but others are probably related to uncertainties in concentrations of H+ and OH- based on measured pH. (30) (a) Mathews, W. K.; Larsen, J. W.; Pikal, M. J. Tetrahedron Lett. 1972, 513. (b) Morini, M. A.; Schulz, P. C.; Puig, J. E. Colloid. Polym. Sci. 1996, 274, 662. (31) Burchfield, T.; Woolley, E. J. Phys. Chem. 1984, 88, 2149.

Discussion of Amide Exchange Kinetics in Terms of Pseudophase Theory. Table 1 contains selected results from ref 14, which illustrate the main experimental findings, and cover data for similar conditions. In their discussion of the Bro¨nsted-Bjerrum equation Perrin et al. applied eq 12 of ref 14 to their data, and we use it for the H+-catalyzed exchange (k0 denotes second-order rate constants for exchanges of MBA in water):

v ) kH0[amide][H+]γamideγH/γ* ) kH0aamideaH/γ* (8) However, rates or first-order rate constants of exchange are not discussed, but data are given as second-order rate constants, kH, calculated according to:

kobs ) kH(antilog(-pH))

(9)

As shown earlier, antilog(-pH) does not, in general, equal either aH or [H+]. The deviations may not be large, but we cannot compare reported second-order rate constants in water and micellar solutions with certainty. These complications also apply to analysis of second-order rate constants of the OH--catalyzed exchange. We note that kobs calculated by line shape analysis14 refers to total concentration, rather than activity, of the amide. The reported second-order rate constants of these exchanges depend primarily on surfactant charge and are not very sensitive to the chemical nature of surfactants and to the presence of various additives such as inorganic salts and nonionic surfactants. Therefore the authors give “average micellar charge effects”,14 Table 1. These comparisons involve the assumption that had it been possible to follow exchanges of MLA in water, rate constants would be the same as those of MBA. This assumption is reasonable, although Guthrie found a dependence of second-order rate constants of nucleophilic attack on p-nitrophenyl alkanoates on the length of the alkyl group.32 However, the amide group is very hydrophilic and the effects noted by Guthrie may not be important in amide exchange. It was also assumed that micelles do not change reaction mechanism or substrate structure, but the 0.05 M nonionic amphiphile, MLA, changes the micellar charge density, which may have different effects on the acid- and base-catalyzed exchanges in the differently charged micelles, although nonionic polyoxyethylenes do not significantly affect second-order rate constants.14 Perrin et al. concluded that their data for micellar effects on exchange of MLA, relative to MBA, are incompatible with an ionexchange, pseudophase, treatment but can be interpreted by applying the Bronsted-Bjerrum formalism.14 It will (32) Guthrie, J. P. Can. J. Chem. 1973, 51, 3494.

5926



therefore be useful to consider what has to be explained, and we first discuss the second-order rate constants given in Table 1 in terms of a pseudophase formalism, on the basis of average rate constants in the hope that there will be cancellation of some uncertainties, e.g., in the meaning of pH. Equations 10 and 11 describe the rate data as presented

H+ reaction: rate ) kH[H+]w[S]T

(10)

rate ) kOH[OH-]w[S]T

(11)

OH- reaction:

of total H+ will be in water. However, the local molar concentration of H+ in the micellar interfacial region, which appears in eq 14, will be higher than [H+]w in anionic, and lower in cationic, micelles. Available experimental estimates of [H+m] are in dilute SDS, see, e.g., refs 16b and 33, and cannot be easily extrapolated to the high surfactant concentrations employed in ref 14. Very approximately [H+m] may be estimated in terms of the PIE,33 although so far as we are aware this treatment has not been applied to relatively concentrated SDS. The values of [H+]m and [H+m] are related in accordance with eq 16 as

[H+m]/[H+]m ) 1/([SDS]mVm)

(16)

where kHm and kOHm are second-order rate constants (M-1 s-1) in the micellar interfacial region. These concentrations have to be estimated for defined conditions, in particular, concentrations of surfactant, H+, OH-, and added salts. Only surfactant and salt concentrations are specified for amide exchange. Data in Figure 1 of ref 14 indicate that some experiments in SDS were made with [H+]w in the range of 10-4-10-3 M, but much higher concentrations appear to have been used in other experiments. Reactions analyzed by using pseudophase treatments are typically made with defined ionic concentrations,1,2,18 which may be as low as 10-3 M, and concentrations of OH- and H+ in water and ionic micelles are then estimated. We consider first the H+-catalyzed exchange. In the experimental conditions H+ will not be transferred extensively into either anionic16b,33 or cationic34 micelles, based on a simple consideration of ionic competition; e.g., with the ion-exchange constant KNa/H ) 1 in SDS as described by eq 7a without added salt, if β ≈ 0.65, ca. 50%

where Vm is the effective surfactant molar volume and [SDS]mVm gives the volume fraction of the micellar pseudophase. By assuming an approximate value of Vm ≈ 0.3 M-1 (this value of Vm is within the range of values used in fitting kinetic data with the PIE1-5,18), one obtains from eqs 7a and 16 the ratio [H+m]/[H+]w ) 20 and 10 in 0.25 and 0.5 M SDS, respectively, and 6 in 0.25 M SDS plus 0.25 M NaCl. Addition of 0.25 M NaCl to 0.25 M SDS should decrease [H+m]/[H+]w and kH (eq 14) approximately 3-fold. This prediction agrees with results in Table 1. However, rate constants in 0.25 and 0.5 M SDS disagree with the estimated 2-fold difference in [H+m]/[H+]w, but this disagreement is not unexpected, taking into account possible structural changes in concentrated micellar solutions and uncertainties stemming from reliance on pH data. In 0.5 M CTACl [H+m]/[H+]w ) 0.1 was estimated by solving the PBE.34 Thus, a pseudophase treatment predicts that if micellar effects are due solely to changes in H+ concentration in anionic and cationic micelles while kHm ) kH0, an anionic surfactant should accelerate the reaction ca. 10-fold and a cationic surfactant should also inhibit it ca. 10 times. Approximate “average micellar charge effects” for the H+ reaction are 100-fold acceleration by anionic and 6-fold inhibition by cationic surfactants, respectively (Table 1). Bearing in mind the above-mentioned uncertainty in using pH measurements for determination of [H+] in micellar solutions, the observed effects are in reasonable agreement with a pseudophase treatment, even assuming kHm ≈ kH0, which, for many reactions, is not correct.1-5 The next question concerns the applicability of pseudophase models to the OH--catalyzed exchange. As noted, uncertainties in the estimation of [OH-] from pH are larger than those for [H+] due to micellar effects on Kw, which cloud comparisons of kOH with kOH0. Anionic micelles inhibit, but do not completely suppress, bimolecular reactions of OH-.35 This behavior is explained qualitatively in terms of a pseudophase, ion-exchange, treatment and quantitatively by solving the PBE.20,36 Reactions of various p-nitrophenyl alkanoates with stoichiometric OH- have been examined over a range of SDS concentrations,35 and for p-nitrophenyl dodecanoate, which should be extensively micellar-bound, observed rate constants become approximately constant in 0.13 M SDS with inhibition, relative to reaction in aqueous 0.0193 M NaOH, by a factor of ca. 400, i.e., the inhibition is lower than those reported for amide exchange14 by a factor of 4-5. The estimated second-order rate constant of deacy-

(33) (a) Rubio, D. A. R.; Zanette, D.; Nome, F.; Bunton, C. A. Langmuir 1994, 10, 1155. (b) Ferreira, L. C. M.; Zucco, C.; Zanette, D.; Nome, F. J. Phys. Chem. 1992, 96, 9058. (34) Blasko, A.; Bunton, C. A.; Armstrong, C.; Gotham, W.; He, Z.M.; Nikles, J.; Romsted, L. S. J. Phys. Chem. 1991, 95, 6747.

(35) Chaimovich, H.; Aleixo, R. M. V.; Cuccovia, I. M.; Zanette, D.; Quina, F. H. In Solution Behavior of Surfactants; Mittal, K. L., Fendler, E. J., Eds.; Plenum: New York, 1982; Vol. 2, p 949. (36) Bunton, C. A.; Mhala, M. M.; Moffatt, J. R. J. Phys. Chem. 1989, 93, 7851 and references therein.

where kH and kOH are second-order rate constants as given in ref 14. We use the pseudophase formalism (subscript m inside the square brackets denotes local concentration in the micellar pseudophase, i.e., in moles per liter of the reaction region at the micellar surface, but a subscript outside the square brackets denotes concentration (molarity) in terms of total solution volume):

H+ reaction: rate ) kHm[H+m][S]m (12)

(12)

OH- reaction: rate ) kOHm[OH-m][S]m

(13)

where [H+m] and [OH-m] are concentrations in the micellar pseudophase and [S]m ) [S]T. Therefore eqs 14 and 15 indicate relationships between these rate constants

H+ reaction: kH ) kHm[H+m]/[H+]w

(14)

kOH ) kOHm[OH-m]/[OH-]w

(15)

OH- reaction:


lation in the micellar pseudophase is ca. 10-fold lower than that in water and the rest of the inhibitory effect is due to a 40-fold decrease in the concentration of OH- in the micellar pseudophase, estimated by solving the PBE.36 Reactions of OH- with organic substrates in cationic micelles have been studied extensively over a range of conditions. Rate enhancements vary widely, depending upon, inter alia, substrate hydrophobicity and reaction mechanism.1-5,18 Typically, overall saponifications of carboxylic esters are not strongly accelerated, often by no more than 1 order of magnitude,1a,18b and these effects are readily accommodated by pseudophase treatments which indicate that second-order rate constants in both cationic and anionic micelles are somewhat lower than those in water. We do not attach much significance to overall rate constants, unless they are determined in well-defined conditions, but we note that acceleration of ester saponification of ca. 10 by cationic micelles18 and inhibition of saponification of p-nitrophenyl dodecanoate by SDS of ca. 40035 correspond to an overall difference of ca. 4000, which is similar to those reported by Perrin et al. (Table 1) for the OH--catalyzed exchange of MLA.14 These comparisons involve the assumption that the relevant second-order rate constants in the micellar pseudophase will be not be very sensitive to charge. The limited evidence on reactions involving OH- and H+ is consistent with this assumption, although it does not apply universally to reactions of other ions.37 Following the treatment applied above for kinetic analysis of the acid-catalyzed reaction, we can also estimate “would be” cationic micellar effects in OH-catalyzed amide exchange. For CTACl one can use a PIE model with KCl/OH ) 418b,38 and β ) 0.7, which gives (cf. eq 7a) [OHm]/[OH]w ) 10 in 0.5 M CTACl. Second-order rate constants of deacylation in cationic micelles, calculated by using the PIE and other pseudophase treatments, are lower than those in water by approximately 1 order of magnitude.1a,18b If this difference applies to the OH-catalyzed exchange of amides, the lack of acceleration by cationic micelles is understandable and is similar to observations on deacylations of hydrophobic esters in relatively concentrated (ca. 0.2 M) cationic surfactant, where observed rate constants tend toward values in water.1-5,18,39 Later in the discussion we consider factors that may inhibit the OH--catalyzed amide exchange in cationic micelles. So far as we know the PBE has only been applied to dilute cationic sufactants.20 We see again that the observed ca. 1.5-fold inhibition of exchange by cationic surfactants (from average values) indicates that there is a decrease in kOHm relative to kOH0 in cationic surfactants. In the H+-catalyzed reaction, observed effects in anionic and cationic micelles (Table 1) are explicable, at least qualitatively, by assuming the absence of major effects of the micellar medium on the intrinsic rate constant. The above discussion shows that the “puzzles” discussed in ref 14 are imaginary and simply reflect different sensitivities of acid- and base-catalyzed reactions to the intramicellar medium and the significance of ionic concentrations in that medium. Unlike the acid-catalyzed reaction, the base-catalyzed exchange appears to be retarded in micelles; this effect partially cancels expected electrostatic effects of cationic micelles and enhances the (37) (a) Bacaloglu, R.; Blasko, A.; Bunton, C. A.; Foroudian, H. J. J. Phys. Org. Chem. 1992, 5, 171. (b) Cerichelli, S.; Grande, C.; Luchetti, L.; Mancini, G. J. Org. Chem. 1991, 56, 3025. (38) Quina, F. H.; Chaimovich, H. J. Phys. Chem. 1979, 83, 1844. (39) (a) Romsted, L. S.; Cordes, E. H. J. Am. Chem. Soc. 1968, 90, 4404. (b) Cordes, E. H.; Gitler, C. Prog. Bioorg. Chem. 1973, 2, 1.

Langmuir, Vol. 16, No. 14, 2000 5927

electrostatic inhibition by anionic micelles, thus creating the apparent asymmetry. Two points should be emphasized: (i) if micellar environmental effects on exchange are similar in cationic and anionic micelles, differences between average exchange rate constants in anionic and cationic micelles (Table 1) are approximately the same in absolute terms, log(kH/kH0)anionic - log(kH/kH0)cationic ) log{(kH)anionic/(kH)cationic} ) 2.75 ( 0.26 and log(kOH/kOH0)anionic - log(kOH/kOH0)cationic ) log{(kOH)anionic/(kOH)cationic} ) -3.22 ( 0.45, and we will show that they are similar to those expected by analogy with other systems; (ii) application of the pseudophase model shows that it is necessary to consider effects of micellar environments on reactivity while the discussion in ref 14 in terms of the BronstedBjerrum eq 1 leaves major questions unanswered. Note that discussion of ratios of rate constants in micelles of opposite charges, instead of ratios of rate constants in the presence and absence of micelles, has some obvious advantages: first, effects of the micellar environment tend to cancel, thus allowing one to extract Coulombic contributions in a simple form, second, ambiguities related to interpretation of pH measurements in water and micellar solutions should be less significant when the reaction in water is excluded from consideration. In addition it eliminates questions regarding the use of MBA to estimate rate constants in water (cf. ref 32). Analysis in Terms of a Bro1 nsted-Bjerrum Formalism. Application of eq 1 to second-order rate constants defined in accordance with eqs 10 and 11 gives

kH ) kH0γSγH/γ*

(17)

kOH ) kOH0γSγOH/γ*

(18)

and

Rate constants kH0 and kOH0 refer to MBA, rather than to MLA, on the assumption that the long- and short-chain substrates would have the same reactivities in water. Choosing water as the reference medium for estimation of micellar effects dictates also choosing it as the reference medium for definition of activity coefficients which are related40 to the standard free energy of transfer of the ith component (∆Gtri) from a reference medium, where all activity coefficients are set equal to unity, to a given medium (a micellar solution in our discussion):

RT ln γi ) ∆Gtri

(19)

Activity coefficients for MLA (γS) could in principle be determined experimentally from, e.g., solubility measurements.25 No relevant data are available, but we expect γS to be much less than unity because micelles strongly increase solubilities of such highly hydrophobic substances as MLA (∆GtrS is large and negative). Transfer free energies of transition states also involve large negative contributions from hydrophobic interactions of the MLA alkyl group with micelles, and activity coefficients of transition states should also be low, but different from γS because of structural differences generated in the amide group, including charge development, on transition state formation. Activity coefficients for H+ and OH- should not be unity, although deviations may not be large because the second-order rate constants are calculated on the basis of concentrations of free ions rather than their total concentrations and corresponding ∆Gtri values approxi(40) Ritchie, C. D. In Solute-Solvent Interactions; Coetzee, J. F., Ritchie, C. D., Eds.; Marcel Dekker: New York, 1969; p 219.

5928



Table 2. Ratios of Ground and Transition State Activity Coefficients of Amide Exchanges and Respective Transfer Free Energies anionic micelles cationic micelles a

H+ reaction

OH- reaction

log(γS/γTH*) ) 2.0 ( 0.2 ∆∆GtrS/T* ) 11.5 ( 1.1 kJ/mol log(γS/γTH*) ) -0.75 ( 0.06 ∆∆GtrS/T* ) -4.3 ( 0.3 kJ/mol

log(γS/γTOH*) ) -3.4 ( 0.2 ∆∆GtrS/T* ) -19.5 ( 1.1 kJ/mol log(γS/γTOH*) ) -0.18 ( 0.25 ∆∆GtrS/T* ) -1.0 ( 1.4 kJ/mol

From data in Table 1.

mately reflect free energy changes upon transfer of these ions from water to the aqueous intermicellar medium (cf. Results, discussion of pH). Therefore, we obtain from eqs 17 and 18 the following expressions for micellar effects

kH/kH0 ) γS/γTH*

(20)

kOH/kOH0 ) γS/γTOH*

(21)

and

where γTH* and γTOH* are the activity coefficients of transition states of acid- and base-catalyzed reactions, respectively. Equations 20 and 21 also follow from consideration of second-order rate constants as being calculated on the basis of H+ (or OH-) activity, as derived from the pHmeter reading; cf. ref 14. This coincidence results from the particular model on which we base the above discussion of what is really measured by the glass electrode. If a fraction of H+ is bound to anionic micelles, this binding gives the observed decrease in activity which becomes approximately equal to the free concentration. Cationic micelles do not significantly perturb the state of H+ and do not extensively bind OH-. To interpret micellar charge effects in terms of eqs 20 and 21, one needs to find explanations for the activity coefficient ratios given in Table 2. In terms of eq 19 these relations reflect differences in transfer free energies of substrate and transition state from water to micelles (∆∆GtrS/T* ) 2.3RT log(γS/γ*)) given also in Table 2. In the simplest case we assume that hydrophobic contributions to transfer free energies of S and T* are similar and ∆∆GtrS/T* involves only differences in electrostatic interactions of ionic transition states with ionic micelles. If positive and negative charges on transition states of H+ and OH- reactions are similar in absolute values and also interact with similar, but oppositely charged cationic and anionic micelles, one would observe symmetrical ∆∆GtrS/T* values, with opposite signs for oppositely charged micelles and transition states. Evidently this is not the case, and more than simple electrostatics must be involved. However, first, one needs to estimate the electrostatic contributions (∆∆Gtrelectr). In the pseudophase models these contributions are included in the ratios [H+m]/[H+]w and [OH-m]/[OH-]w estimated independently, but for similar conditions. In the present case we need to estimate electrostatic contributions to the binding of ionic transition states, and this can be done only theoretically. One approximate approach is to use apparent micellar surface potentials (ψ) based on apparent acid dissociation constants of solubilized indicators calculated in terms of conventional pH measurements with a glass electrode41 and calculate ∆∆Gtrelectr as (41) (a) Fernańdez, M. S.; Fromherz, P. J. Phys. Chem. 1977, 81, 1755. (b) Grieser, F.; Drummond, C. F. J. Phys. Chem. 1988, 92, 5580. (c) Drummond, C. J.; Grieser, F.; Healy, T. W. J. Chem. Soc., Faraday Trans. 1 1989, 85, 537.

∆∆Gtrelectr ) (Fψ

(22)

In the concentrated surfactant solutions employed in ref 14, absolute values of ψ should be smaller than those reported in more dilute (0.024 M) SDS and CTABr (-134 and 148 mV, respectively).41a By assuming |ψ| ≈ 100 mV for both SDS and CTACl, one obtains ∆∆Gtrelectr ≈ (10 kJ/mol, which is close to ∆∆GtrS/T* for the H+ reaction in anionic micelles (Table 2) but larger by ca. 6 kJ/mol than ∆∆GtrS/T* in cationic micelles. However, for the OHreaction in both types of surfactants ∆∆GtrS/T* values are ca. 10 kJ/mol more negative than expected on purely electrostatic considerations. In making these comparisons between the indicator and kinetic data, we are simply comparing two processes which involve transfer of unit charge in the overall reactions, and nothing more. This comparison does not depend on the validity of indicator data in estimation of micellar potentials.We come therefore to the same conclusion as that in terms of a pseudophase model. The OH- reaction is inhibited in micellar media, regardless of charge, as for many bimolecular anionic reactions which are slower at micellar surfaces than in water.1a,b,18b Excluding consideration of reaction in water relative to micelles simplifies interpretation of micellar charge effects on amide exchange. Micellar environments affect H+ and OH- reactions differently, but this does not necessarily require asymmetry in micellar charge effects, because environmental contributions to reactivity may oppose or enhance electrostatic contributions, or even apparently preclude their appearance. From eq 22 the electrostatic contribution to transition state stabilization on going from cationic to anionic micelles is 2Fψ ≈ 20 kJ/mol, with absolute values of |ψ| ≈ 100 mV for cationic and anionic micelles. Differences in activation free energies from the ratios (kH)anionic/(kH)cationic and (kOH)anionic/(kOH)cationic are -15.8 and 18.5 kJ/mol, respectively (Tables 1 and 2). Exclusion of consideration of reaction in water demonstrates that micellar charge effects are close to those expected on the basis of plausible surface potentials and are approximately symmetrical. Even if micelles change substrate conformation or reaction mechanism, this qualitative estimate of the charge effect remains correct, provided that such changes are unaffected by micellar charge. Comparison of Treatments of Micellar Rate Effects. The distinction between the pseudophase and Bro¨nsted-Bjerrum approaches is in the treatment of local concentrations of reactants in water and micelles: the former considers the change in local concentrations as a significant source of micellar effects and the latter ignores these changes. The expression for the reaction rate, which follows from eq 1, has the form

rate ) k0aSaB/γ*

(23)

where aS and aB are activities of reactants, in equilibrium between the aqueous and micellar phases, and a textbook definition of equilibrium requires that activities are


Langmuir, Vol. 16, No. 14, 2000 5929

identical across phase boundaries. This logic led Perrin et al.14 to conclude that a change in local concentrations of reacting species “does not itself account for the rate effects” and that “since activities are constant, the rate effect can be ascribed entirely to the activity coefficient of the transition state”. However, what is identical in every phase under equilibrium is the chemical potential of each species, and identity of activities implies choosing the same standard state for all phases (we are not considering socalled absolute activities, which indeed are identical in every phase, but have nothing to do with the Bro¨nstedBjerrum approach, eq 1). In the pseudophase treatment the standard state of each solute in every phase is a hypothetical 1 M solution of this solute in the given phase, as in treatments of liquid-liquid partition equilibria.42 Also the activation free energy of the micellar reaction is the difference between free energies of reactants and the transition state in the micellar phase, which is not an apparent parameter, but a “normal” activation free energy for reaction in the micelle treated as a separate phase. It can be directly compared with that for reaction in water as a different phase and any difference between them is due to medium effects. In contrast, the Bronsted-Bjerrum approach always sets the standard states of reactants and the transition state in water and then corrects them by using activity coefficients, which, in accordance with eq 19, account for differences between water and the micellar solution. If the rate constant is calculated on the basis of aqueous concentration or activity of one of the reactants, e.g., H+ or OH- in amide exchange, the respective activation free energy will be an apparent parameter equal to the difference between the free energy of the transition state in the micellar solution and free energies of the substrate, also in the micellar solution, but with H+ or OH- in water. Evidently, no correction for H+ or OH- will be necessary and respective activity coefficients disappear from equations for the micellar effect, provided that activities are measured correctly. Free energy changes involved for the general case of a bimolecular reaction between S and B in micellar solutions are shown in Scheme 2, which is similar to free energy diagrams widely used to interpret solvent effects.43 It follows from Scheme 2 that

∆Gw* + ∆GtrT* ) ∆Gm* + ∆GtrS + ∆GtrB

(24)

Note that eq 2 expresses the same relationship in terms of binding constants, provided that transfer free energies are considered as binding free energies.44 Therefore, despite different conceptual bases (micelles are treated as distinct species rather than as a phase) the third approach mentioned in the Introduction does not introduce any new terms for discussion of micellar effects. An often encountered situation when k2,m ≈ k0 means, in terms of eq 24, that ∆GtrT* ≈ ∆GtrS + ∆GtrB, that is noncovalent intermolecular interactions which transfer (42) The concept of a partition (or distribution) constant implies choosing different standard states for two immiscible phases, otherwise observed differences in concentrations of a given solute in two phases will be treated as differences in activity coefficients. The use of partition constants is preferred purely for practical reasons: it is convenient to use activity coefficients as factors which account for deviations in solute behavior from that expected at infinite dilution; these deviations are different in each phase, and it is then convenient to introduce different activity coefficients in each phase. (43) (a) Buncel, E.; Wilson, H. Acc. Chem. Res. 1979, 12, 42. (b) Blandamer, M. J.; Burgess, J.; Engberts, J. B. F. N. Chem. Soc. Rev. 1985, 14, 237. (44) Transfer free energies are related to partition constants P rather than to binding constants K; however, one can prove the equivalence of eqs 2 and 24 by using the relationship K ) PVm, derived in ref 5.

Scheme 2

reactants into micelles persist and contribute additively to the binding of the transition state to the micelle. Such additivity is understandable for noncovalent, e.g., electrostatic or hydrophobic interactions, the free energies of which depend simply on the number of charges and the total surface area of apolar moieties, respectively. A special case is when substrate S has a very high affinity for the micelle and B remains largely in water, as with amide exchange, where S is MLA and B is H+ or OH-. Such a case is illustrated in Scheme 2 by introducing an intermediate free energy level for Sm + Bw and the activation free energy ∆Gmw*. This free energy is the observed activation free energy and the scheme then illustrates directly the micellar effect as a difference between ∆Gmw* and ∆Gw*, as for the case represented by eqs 20 and 21.45 One can write the expression for observed micellar effects in this case either as

kobs/k0 ) exp{(∆GtrS - ∆GtrT*)/RT}

(25)

or by taking into account eq 24 as

kobs/k0 ) exp{(∆Gw* - ∆Gm* - ∆GtrB)/RT} (26) Equation 25 corresponds to interpretation of micellar effects in terms of the Bronsted-Bjerrum approach with different stabilizations of initial and transition states, and eq 26 corresponds to the pseudophase interpretation of micellar effects as being due to micellar microenvironmental and “concentration” effects. These approaches explain micellar effects in terms of different, but interrelated, free energy contributions to binding and activation of reactants. The choice in discussion of the nature of micellar effects at the molecular level is given by consideration of different paths connecting initial and transition states in Scheme 2: one can consider the difference (45) Transfer free energies shown in Scheme 4 and those in eq 18 have different meanings: Scheme 4 gives the values for transfers of solutes from water to micelles as a separate phase, while in eq 18 the value for transfer from water to the micellar solution (micelles + water are considered as a single phase) must be used. It can be shown easily, however, that in conditions when substrate and transition state are both predominantly micellar bound, the ratio γS/γ* is indeed given by eq 24.

5930

Langmuir, Vol. 16, No. 14, 2000 Scheme 3

between ∆Gm* and ∆Gw* (the ratio of the rate constants in two pseudophases) corrected for the transfer free energies of reactants (concentration effect), or consider the difference between ∆GtrS and ∆GtrT* (ratio γS/γ*) as a correction factor to the rate constant in water. Generally when both reactants are significantly distributed between aqueous and micellar phases in similar amounts, Scheme 2 does not show the observed activation free energy, which is a weighted average of activation free energies of reactions in water and micelles. However, at the molecular level one always needs to discuss only contributions shown in this scheme. Scheme 3 shows the results for amide exchange in terms of the free energy diagram calculated from average secondorder rate constants (Table 1). The transfer free energy of MLA is unknown, but in order to discuss only micellar effects, we shift the levels of ground and transition states by ∆GtrMLA as shown in Scheme 4, based on average secondorder rate constants. Now all activation free energies are calculated from a common zero level, and differences between levels of the transition states show the differences in observed activation free energies, with results for the OH- and H+ reactions on the left and right sides, respectively. Micellar charge effects are symmetrical: differences between levels for cationic and anionic micelles are similar, but the level for reaction in water is highly asymmetrical for the OH- reaction, out of the range between micelles of opposite charges, and inside the range, although not at the midpoint, for the H+ reaction.

Bunton and Yatsimirsky Scheme 4

Reaction Mechanism and Possible Micellar-Induced Changes. Perrin et al.14 do not comment on the possibility that micelles may affect reactivities by changing either mechanism or reactant structure or conformation, although they note alternative mechanisms of acid exchange, and we consider this possibility in the context of micellar effects on amide exchange. Amides exist as equilibriating E and Z isomers, and micelles may affect both inherent rates and the position of the equilibrium, which may affect rates of exchange (Scheme 1). We do not know of any evidence on this question, although micelles and solvents affect E-Z equilibria of hydroxamic acids and their anions.46 Perrin et al.14 conclude that N-methyl amides MBA and MLA exist predominantly as the Z-isomers, in agreement with extensive evidence. But incorporation in a micelle could favor the E-isomer due to favorable hydrophobic interactions of the syn-alkyl groups with alkyl groups of the micelle. A similar micellar-induced change of structure is very evident with phenyl alkyl hydroxamic acids and their anions where E- and Z-isomers have different NMR spectra.46a In water, with the short-chain derivative, Eand Z-isomers coexist with equilibrium favoring the former, but in cationic and anionic micelles the Z-isomer of the long-chain derivative is dominant, with syn-phenyl and alkyl groups although locations depend on micellar charge.46b Deprotonation of the (hypothetical) E-amide gives an anion-like transition state with unfavorable interactions between syn-carbonyl oxygen and the nitrogen lone pair, which should inhibit this reaction, relative to that of the Z-amide. However, evidence on base-catalyzed exchange in solution shows that this effect is not large and, in some systems, is less important than steric interactions.47

The situation will be different for the hydrogen ion catalyzed exchange, with protonation on nitrogen, which (46) (a) Brown, Z. A.; Glass; Mageswaran, R.; Mohammed, S. A. Magn. Reson. Chem. 1991, 29, 40. (b) Blasko, A.; Bunton, C. A.; Gillitt, N. D. Langmuir 1997, 13, 6439. (47) Perrin, C. L.; Johnston, E. R.; Lollo, C. P.; Kobrin, P. A. J. Am. Chem. Soc. 1981, 103, 4691.


should be relatively insensitive to the geometry of the initial state, or incorporation in micelles.

Langmuir, Vol. 16, No. 14, 2000 5931

tion will increase modestly. The exchanges will have to be followed at defined reactant concentrations, and buffer and electrolyte composition and MLA concentration will have to be low enough to limit effects on micellar structure and charge density. We cannot judge whether the limitations of the experimental conditions prevent these requirements from being met. Conclusions

On this hypothesis we expect acceleration of the H+catalyzed exchange in SDS micelles to be the approximate inverse of inhibition by cationic micelles. We emphasize the term “approximate” because of the earlier noted uncertainties in values of kH and differences of interactions of solutes with micelles of different charges. The situation will be different for reaction catalyzed by OH-, in part because values of kOH may not be calculated correctly but also because if micelles affect initial or transition state structures comparisons of kOH in water and micelles will have little meaning, unless we have independent evidence on this question. Perrin et al.14 comment on a “hitherto unrecognized difference” in behaviors of anionic and cationic micelles, although they believe that it will affect electrostatic interactions. Qualitatively, a micellarinduced shift of structure may account for at least part of the above-mentioned inhibition of the OH--catalyzed exchange by micelles. There are many examples of relations between mechanism and reactivities in micellar interfacial regions. They are very obvious in spontaneous reactions, but pseudophase treatments of bimolecular reactions with anions indicate how reactivities in micellar pseudophases depend on headgroup charge and mechanism.1-5,37,48 These considerations of kinetic models indicate that, despite uncertainties in the significance of concentrations (or activities) based on the use of the glass electrode, the H+-catalyzed amide exchange probably has similar mechanisms in water and micelles. This generalization may not apply to the OH--catalyzed exchange if simple assumptions regarding mechanisms are inadequate, and naive interpretations based on either the pseudophase or the Bro¨nsted-Bjerrum formalisms will then not fit relative reactivities in micelles and water at the quantitative level. We predict, on the basis of pseudophase treatments of micellar effects in bimolecular ionic reactions, that if amide exchanges can be followed over a range of conditions, a decrease in [surfactant] will significantly increase rate constants of the OH-- and H+-catalyzed exchanges in cationic and anionic micelles, respectively.49 A decrease in surfactant concentration will have less effect on the micellar-inhibited reactions with co-ions,34-36 but inhibi(48) Possidonio, S.; Silviero, F.; El Seoud, O. A. J. Phys. Org. Chem. 1999, 12, 325.

Micellar effects upon amide exchange cannot be analyzed rigorously because of assumptions involved in the use of pH measurements for estimation of concentrations (or activities) of H+ and OH-, effects of MLA on micellar structure and charge density, and the possibility that rate constants in water cannot be reliably estimated from exchange of MBA. The reported micellar rate effects are qualitatively understandable in terms of pseudophase treatments and could have been predicted from analogies with data on other reactions involving H+ and OH- and evidence on the extent to which reactivities in micellar interfacial regions depend on mechanism. An alternative formalism, based on the Bro¨nsted-Bjerrum equation, can also be applied to the data but is descriptively less informative, although it allows simple comparisons of effects of micellar charge on these exchanges and acidbase equilibria. Insofar as these formalisms provide alternative treatments, there is no reason to believe that one could fail and the other succeed in fitting experimental results. In principle, it should be possible to use the linear solvation free energy relationships that have been used successfully to predict transfer equilibria of neutral solutes between water and micelles50 to predict the corresponding transfer equilibria for transition states. These treatments have been developed for neutral solutes, and this approach will probably not be applicable to ionic reactions, at least at present. Acknowledgment. We are grateful to Professors L. S. Romsted, O. A. El Seoud, and F. Nome for valuable discussions made possible by the NSF-Brazil CNPQ Cooperative Program, and to Professor C. L. Perrin for valuable comments on the mechanisms of amide exchange. A. K. Yatsimirsky thanks CONACYT for support of Sabbatical leave at UCSB. LA000068S (49) This prediction appears to be consistent with the limited available evidence14 because second-order rate constants for the OH--catalyzed exchange appear to increase with a 20-fold decrease in cetylpyridinium chloride concentration, despite a decrease of temperature from 34 to 22 °C. (50) (a) Quina, F. H.; Alonso, E. O.; Farah, J. P. S. J. Phys. Chem. 1995, 99, 11708. (b) Abraham. M. H.; Chadha, H. S.; Dixon, J. P.; Rafols, C.; Treiner, C. J. Chem. Soc., Perkin Trans. 2 1995, 887. (c) Abraham, M. H.; Chadha, H.; Dixon, J. P.; Rafols, C.; Treiner, C. J. Chem. Soc., Perkin Trans. 2 1997, 19.

Comparisons and Analyses of Theoretical Treatments of Micellar

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