comparisons and analyses of theoretical treatments of micellar effects upon ion−molecule...

Comparisons and Analyses of Theoretical Treatments ofMicellar 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 Quımica, Universidad Nacional Autonoma de Mexico, Mexico D.F., 04510, Mexico

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 ofmicellar rate effects, and the Bronsted-Bjerrum treatment was invoked to fit the data (Perrin, C. L.; etal. J. Am. Chem. Soc. 1999, 121, 2448). Rate constants of amide exchange, based on pH measurementsin surfactant solutions, are only approximate, but examination of the data and comparisons with evidenceon other reactions show that they are qualitatively consistent with pseudophase treatments. Micellareffects upon rate constants of deacylations by OH- and acid hydrolyses of dioxolanes, analyzed withpseudophase treatments, were considered for the purpose of comparison. The pseudophase and Bronsted-Bjerrum formalisms are equivalent in rationalizing micellar rate data, although the former appears to bedescriptively more useful as applied to reactions of apolar organic compounds. Interrelations between thetwo 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 cetyltrimethylammonium chloride in order to estimate the autoprotolysis constant of water and to establishthe relation of pH to concentrations of H+ and OH- in unbuffered micellar solutions.

Introduction

The ability of micellized surfactants to control rates ofmoderately slow reactions is well established and isextensively reviewed.1-5 Most of the reactions studied todate involve ionic reagents and/or generate ionic productsor intermediates. Micellar charge is clearly important,and cationic micelles typically accelerate reactions ofanionic nucleophiles or bases with nonionic substratesand inhibit those of cationic reagents. Conversely anionicmicelles accelerate reactions of cationic and inhibit thoseof anionic reagents. However, nonelectrostatic interactionswith ions are also important, for example, affinities ofanions for cationic micelles increase with decreasingcharge densities and follow the Hofmeister series.2,6

Effects of normal micelles on reaction rates andequilibria in water, or in solvents such as diols, are often

treated in terms of pseudophase models with water andmicelles being treated as distinct reaction regions.1-5 Theoverall rate is the sum of rates in each region, which, forbimolecular reactions, depend on local concentrations andsecond-order rate constants. This treatment allows de-velopment of equations that predict variations of observedrate constants in terms of concentrations and structuresof reactants and surfactants and can be applied to otherassociation colloids, e.g., microemulsions and vesicles.7 Italso fits effects of inert solutes, e.g., electrolytes, on overallreaction rates. In favorable cases the transfer equilibriaof reactants between water and micelles can be examinedindependently and used in analyzing the rate effects.However, all the quantitative treatments involve ap-proximations and assumptions, and in some cases ob-served first-order rate constants can be fitted by variouscombinations of rate and equilibrium constants.

Much of the work has involved apolar organic substrates(S) which interact strongly with micelles, and except invery dilute surfactant, reaction is then assumed to belargely in the micellar pseudophase. In these conditionsthe observed free energy of activation relative to that inwater (the micellar effect) depends on the transfer freeenergy of the second reactant between water and micellesand the difference between free energies of activation inthe two pseudophases.

In an alternative description one need not regard waterand micelles as distinct reaction regions, but simplyconsider changes in free energies of initial and transitionstates induced by addition of micelles to water or other

* Towhomcorrespondencemaybeaddressed: CliffordA.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 MicroheterogeneousSystems; Gratzel, M., Kalyanasundaram, K., Eds.; Marcel Dekker: NewYork, 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 andMicroemulsions; 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.

(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.

5921Langmuir 2000, 16, 5921-5931

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

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

tion of S and reactant B to form the transition state T*;k2,app is the apparent second-order rate constant of theoverall reaction and k0 is the second-order rate constantin the reference conditions, typically water. In thisformalism interactions of micelles with S and B decreasethe activity coefficients, γS and γB, which inhibits reaction,but can be more than offset by a decrease in γ*, andapplication of eq 1 requires estimation of activity coef-ficients.

Another approach involves estimation of the bindingconstant (M-1) of the transition state to micelles (KT*)(eq 2)

where km′ is the second-order rate constant in the micellarpseudophase with concentrations as mole fractions andKS and KB are binding constants (M-1) of reactants.8,10

This approach is popular in analyses of enzymic11 andother catalytic (e.g., as in cyclodextrins) reactions,12 whichoften are single-substrate reactions following classicalMichaelis-Menten kinetics, and KT* is calculated fromeq 3

where kc and ku are first-order rate constants of thecatalyticanduncatalyzedreactions, respectively.Equation3 was also applied formally to second-order micellarreactions, e.g., alkaline ester hydrolysis in cationic mi-celles,12 treated in terms of single-substrate Michaelis-Menten kinetics.

The choice of the formalism is a matter for predilectionand convenience. For example, reactions of apolar organiccompounds are typically treated by applying the pseudo-phase model, and estimated rate constants in the micellarpseudophase are consistent with reaction in a mediumthat is somewhat less polar than water. The very strikingaccelerations of some moderately slow reactions of hy-drophilic reagents by reverse micelles1c,13 are readilyunderstandable in terms of concentration of ions or polarmolecules in the small volume of the “water pool” in theinterior of a reverse micelle. However, for reactions ofpolyvalent inorganic ions in aqueous ionic micelles, whichoccur largely in the aqueous region, electrostatic interac-tions become very important, and eq 1, with allowance forionic interactions, provides a convenient treatment.9

Perrin et al.14 recently examined hydrogen and hy-droxide ion catalyzed hydrogen exchanges of amides and

ureas in water and ionic micelles. These reactions areattractive because of their mechanistic simplicity andinvolve comparisons of apparent second-order rate con-stants of exchange of a short-chain amide, N-methylbu-tyramide, MBA, in water, and of a long-chain, amphiphilic,amide, N-methyllauramide, MLA, in cationic and anionicmicelles. Exchanges of the ureas were not examined in allconditions. The second-order rate constants were notcalculated from total concentrations of H+ and OH-, butwere based on pH of the reaction mixtures and theautoprotolysis constant, Kw, in water. Second-order rateconstants of exchange in water, calculated in this way,should be similar to those calculated with stoichiometricconcentrations, because in dilute aqueous electrolyte pHmeasured with an instrument calibrated with standardbuffers is close to -log[H+] (Results), but this situationmay not apply to reactions in aqueous surfactants. As aresult, reported second-order rate constants in water andaqueous surfactant are based on different estimates ofconcentrations which obscures comparison of their values.The situation is similar to that in comparison of second-order rate constants in different solvents calculated interms of observed pH. We also have to consider estimationof [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, dodecylpyridiniumchloride, DPCl, and cetyltrimethylammonium chloride,CTACl. Reactions were, of necessity, followed with higher[substrate], typically 0.05 M, than is customarily used inmicellar work,1-5 and [surfactant] was generally 0.25 or0.5 M. First-order rate constants, kobs, were estimated overranges 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 kHand decrease kOH, as expected, but the cationic micelles,which behave similarly, only modestly decrease kH andhave little effect upon kOH. Some experiments were madewith added ionic or nonionic solutes which did notmarkedly affect rate constants.

Hydroxide-ion catalyzed exchange involves deprotona-tion of NH with negative charge largely on oxygen andacid-catalyzed exchange of primary amides is believed toinvolve N-protonation (Scheme 1), but an imidic acidmechanism has also been observed.15 These mechanisti-cally different acid mechanisms may be affected differentlyby ionic micelles, but there seems to be no evidence onthis possibility. Exchanges are apparently not buffer-catalyzed, at least in the conditions used by Perrin et al.14

These authors conclude that their results are inconsistentwith the pseudophase treatment and that several featuresdefy simple interpretation. Our aim is to examine these

(8) Hall, D. G. J. Phys. Chem. 1987, 91, 4287.(9) (a) Lopez-Cornejo, P. L.; Jimenez, R.; Moya, M. L.; Sanchez, F.;

Burgess, J. Langmuir 1996, 12, 4981. (b) Muriel-Delgado, F.; Jimenez,R.; Gomez-Herrera, C.; Sanchez, F. Langmuir 1999, 15, 4344.

(10) Davies, D. M.; Gillitt, N. D.; Paradis, P. M. J. Chem. Soc., PerkinTrans. 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 MicroheterogeneousSystems; Gratzel, M., Kalyanasundaram, K., Eds.; Marcel Dekker: NewYork, 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. (15) Perrin, C. L.; Lollo, C. P. J. Am. Chem. Soc. 1984, 106, 2754.

k2,app ) k0γSγB/γ* (1)

KT* ) (km′/k0)KSKB (2)

KT* ) (kc/ku)KS (3)

Scheme 1

5922 Langmuir, Vol. 16, No. 14, 2000 Bunton and Yatsimirsky

questions, and we also consider evidence on other ionicreactions carried out, as far as is possible, in similarconditions of high [surfactant]. We consider several aspectsof the problem: (i) the significance of pH in surfactantsolutions; (ii) analysis of micellar rate effects in terms ofvarious formalisms; (iii) the extent to which micelles mayaffect reactivity by changing mechanism or structures ofreactants. We note that experiments described by Perrinet al.14 provide an excellent opportunity for discussion ofmicellar charge effects because this is a system whereboth positively and negatively charged reactants arestudied with both anionic and cationic micelles. This, andthe relative simplicity of the reaction mechanism, makesthe system attractive for discussion of different approachesto micellar catalysis, which is the key purpose of this paper.

Applicationof thepseudophase treatment tobimolecularreactions of hydrophilic ions requires estimation of theirdistribution between water and micelles. Experimentalmethods are available for some ions,16,17 but theoreticalapproaches are generally used.1,2,18 Competition betweencounterions can be described in terms of ion-exchange,PIE, which, with the assumption of constant fractionalmicellar ionization, R, treats ionic distributions in termsof an ion-exchange constant.18 An alternative treatmentdescribes competition without requiring a constant valueof R or â ) 1 - R.19 A third treatment estimates local ionicconcentrations by solving the Poisson-Boltzmann equa-tion, PBE, with allowance for nonspecific, Coulombic, andspecific, ion-micelle interactions.20 These treatments,when used appropriately, are self-consistent and fitextensive kinetic and equilibrium data, including varia-tions of overall first-order rate constants with changesin concentrations of surfactant, reactants, and inertsolutes.1,2,18-21 We use both the PIE and PBE formalisms,as convenient, in showing how the pseudophase modelcan be applied to micellar-mediated amide exchange.22

However, quantitative applications of these treatmentsrequire information on total concentrations of inert andreactive ions. As a result it is not feasible to analyzeunambiguously apparent second-order rate constantscalculated from pH values in unspecified buffers wheretotal concentrations of H+ or OH- are unknown. In thesesituations one can only attempt to interpret qualitativetrends in experimental results. Therefore, we examinedeffects of SDS and CTACl upon the pH of dilute HCl underconditions of defined [H+]T in order to decide whetherreliance on the pH scale led to the purported failure of thepseudophase treatment.14 For example, if micelles stronglyaffect the response of the glass electrode, estimates of aHor [H+] will be in error, and if they also affect Kw there willbe an additional error in aOH or [OH-].

Experimental SectionMaterials. SDS was a BDH “specially pure” sample; CTACl

had been prepared from hexadecyl chloride and dry Me3N in

i-PrOH and had no minimum in the surface tension,17 but thepH titration indicates that it contains a small amount of basicimpurity which we assume is Me3N.

pH Titration. Solutions were made up in freshly boileddistilled deionized water under N2, and 1 M NaOH was addedwith a syringe with little change of overall volume. The variationof potential of the glass electrode was monitored as a functionof added NaOH on a Fisher Accumet 925 pH meter with anAccumet combination electrode. Data were fitted to a nonlinearleast-squares regression by using the Origin 5 program. Atitration carried out with commercial CTACl indicated thepresence of a significant amount (ca. 1 mol %) of an acidic impurity(data not shown).

Results

Potentiometric Acid-Base Titration and Signifi-cance of pH in Micellar Solutions. Interpretation ofreported second-order rate constants of amide exchange14

requires an understanding of what is actually measuredas [H+] and [OH-], because there are questions regardingsurfactant effects upon the response of the glass electrodeand whether hydrogen ion activity or concentration isbeing measured. The widespread belief that the glasselectrode calibrated with standard buffer solutions un-ambiguously measures hydrogen ion activity (Perrin etal.14 do not specify how the electrode was calibrated, butsupposedly they used standard buffers) is an oversim-plification. The measured electrode potential is related tohydrogen ion concentration by eq 4

where A ) E° + Eref + Ej + B log γH and B ) 2.3RT/F (hereE°, Eref, and Ej are the standard, reference, and junctionpotentials, respectively, T is in kelvins, and F is Faraday’sconstant). Calibration with standard buffers is based onthe assumption that γH (more precisely the mean activitycoefficient) in these buffers is known and one can thereforereplace [H+] by aH in eq 5

where A′ ) E° + Eref + Ej and -log aH ) pH. However,Ej is different in any solution other than that used forcalibration. Moreover, in practice B for a given instrumentmay not exactly equal its theoretical value, and its value,and those of A or A′, must be found by calibration. Sucha calibration must be done with at least two buffers ofdifferent compositions, which inevitably makes the in-strumental pH scale to some extent approximate. It wasshown23 that a pH-meter calibrated with standard buffersmeasures neither aH, nor [H+], although in aqueoussolutions of moderate ionic strength the difference is notlarge (about 0.2-0.3 log units) and, surprisingly, measuredpH is closer to -log[H+] than to -log aH. In organic ormixed aqueous-organic solvents, differences will be muchlarger and one must calibrate the electrode with standardsolutions (when available) in the given solvents.24

The situation with micellar solutions is ambiguous: onone hand, these are predominantly aqueous, but they havemuch in common with mixed organic solvents, e.g., inrespect to solubilities of apolar compounds25 and apparent

(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 Micro-emulsions; 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 referencescited.

(22) The limits of validity of these treaments, and related ap-proximations and assumptions, have been discussed extensively.1-4,18

(23) (a) Sigel, H.; Zuberbuhler, A. D.; Yamauchi, O. Anal. Chim. Acta1991, 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.

E ) A + B log[H+] (4)

E ) A′ + B log aH (5)

Micellar Effects on Ion-Molecule Reactions Langmuir, Vol. 16, No. 14, 2000 5923

polarities based on probes.26 The problem of pH in micellarcatalyzed reactions was addressed previously, and it wasconcluded that the observed increase in pH reading inHCl solutions on addition of SDS can be attributed tobinding of H+ to micelles which reduces the amount offree H+ sensed by the glass electrode.16b,27 We attemptedto check the behavior of a glass electrode in typical micellarmedia by titrating a strong acid with a strong base inaqueous SDS and CTACl, Figure 1. Calibration of theelectrode involved titrating 0.005 M HCl with 1 M NaOHin aqueous 0.1 M NaCl. The fitting of the titration curveto eq 6a28 (subscript T denotes total concentrations) gives

pKw ) 13.80 together with values of parameters A and Bin eq 4, which coincide in limits of errors with parametersA′ and B in eq 5 determined for comparison by a three-point calibration with standard Fisher buffers. Thiscoincidence means that the “activity” of H+ estimated fromthe buffer calibration is close to its concentration, althoughin 0.1 M NaCl the Debye-Huckel equation predicts γH )0.75 and the predicted activity of H+ should be considerablylower than its concentration.

Titration of 0.005 M HCl in 0.1 M SDS was fitted initiallyto the same equation by using an adjustable parameterf in the expression [H+] ) fB × 10E/A, which, in accordancewith eq 4 gives f ) (γH

NaCl/γHSDS)10(Ej

SDS-EjNaCl)/B. The use of

such a parameter was suggested by the Johanssons28 forcorrection of variations in junction potential and activitycoefficients in analyses of potentiometric titration data.The fitting is reasonably good, yielding f ) 1.88 and pKw

SDS

) 13.31. Note that Kw is here a stoichiometric “concentra-tion” constant of self-ionization of water. It is three timeslarger than that in aqueous 0.1 M NaCl, most probablydue to reduction in γH, because micelles of an anionicsurfactant may not affect the activity coefficient of OH-

but 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 ofanionic micelles becomes unavailable to the glass elec-

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

where [H+]m is the concentration of micellar-bound protonsand the binding constant KH is defined as KH ) [H+]m/([H+]w[SDS]), with [SDS] . [H+]. The fit is good and allowsone to estimate the binding constant for H+, KH ) 14.3M-1, and pKw ) 13.80 with f ) 0.82. Note that the requiredfitting value of f in this model is close, but not equal, tounity, which may be due to differences in activitycoefficients of “free” H+ or junction potentials in NaCl andSDS (these contributions cannot be separated within agiven model). The value of KH agrees with that expectedfrom the ion-exchange, PIE, model:18 KH ) KH/Naâ/[Na+]w,where â is the fractional micellar neutralization by Na+.The exchange constant KH/Na between H+ and Na+ for SDSmicelles is ca. unity,16b,29 â ≈ 0.65 and [Na+]w ) (1 - â)-([SDS]T - cmc) + cmc. Therefore, with [SDS]T ) 0.1 M onepredicts KH ≈ 17 M-1 (with cmc ) 6 mM). The value of pKwin this model should be, and is, very close to that in 0.1M NaCl. We note that the concentration of OH- calculatedfrom that of H+ with f ) 1.88 and pKw

SDS ) 13.31 in 0.1M SDS will be 1.6-fold higher than that calculated in thesame solution from Kw in aqueous NaCl and pH readdirectly from the meter. At the same time, the instru-mental pH does not correspond exactly to the negativelogarithm 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 protonscalculated from KH ) 14.3 M-1 at a given concentrationof SDS, but is ca. 0.3 higher than -log[H+]T.

The titration curve of 0.005 M HCl in 0.1 M CTAClpractically 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 samplewhich is titrated as a weak acid, pKa ) 7.7. Titration ofcommercially available CTACl revealed the presence ofca. 1 mol % of the same impurity. There is no change inpKw in this system.

In another set of experiments the instrumental pH of0.005 M HCl was measured at increasing concentrations(0-0.2 M) of SDS and CTACl. In CTACl the pH readingwas unchanged, but in SDS it increased by ca. 0.3 in 0.05M SDS and then remained practically constant. Suchbehavior is consistent with the assumption that the glasselectrode reacts only to free H+. Indeed, the PIE treatmentpredicts that with [SDS] . [HCl] and [SDS] . cmc

and therefore

These results indicate that the glass electrode behavesnormally in unbuffered surfactant solutions and the pHmeter reading is similar to the negative logarithm ofconcentration of free H+, as in electrolyte solutions. A

(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.

(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.

Figure 1. Potentiometric titration curves of 0.005 M HCl with1 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. Notethe overlap of data in NaCl and CTACl.

[H+]T ) [H+] + [OH-]T - [OH-] )

[H+] + [OH-]T - Kw/[H+] (6a)

[H+]T ) [H+]w + [OH-]T - [OH-] + [H+]m )

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

KNa/H ) ([H+]w[Na+]m)/([H+]m[Na+]w) ≈([H+]wâ[SDS]T)/{([H+]T - [H+]m)(1 - â)[SDS]T} )

([H+]wâ)/{([H+]T - [H+]m)(1 - â)} (7a)

∆pH ) log([H+]T/[H+]w) ) log(1 + â/(1 - â)KNa/H)(7b)


decrease in the activity of H+ in SDS is ascribed to bindingof H+ to anionic micelles, as in the PIE.18 There areproblems in discriminating between “free” and “bound”counterions in micellar and polyelectrolyte solutions,8because long-range Coulombic interactions do not requireions to be in contact, i.e., to be “bound”. However, presentpH measurements as well as measurements with otherion-selective elctrodes16,30 indicate that a fraction ofcounterions is “bound”. In terms of this approach theestimated activity of bulk H+ in a surfactant solution issimilar to that in equimolar NaCl, reflecting similar ionicstrengths of a surfactant and a simple 1:1 electrolyte (seeref 31 for estimation of ionic strength in surfactantsolutions). In CTACl one expects a decrease in the“activity” of OH-; however, the binding constant of OH-

to CTACl micelles is significantly smaller than that of H+

to SDS micelles, based on the PIE model.18 As a result theextent of binding of OH- to micellized 0.1 M CTACl shouldbe small and not significantly change the observed Kw.

In conclusion, pH measured in aqueous surfactants, inthe absence of buffer, allows one to estimate, with anuncertainty within a factor of ca. 2, concentrations of freeH+ and OH-, which in CTACl are close to their totalconcentrations, but in SDS free H+ accounts for ap-proximately half the total H+ concentration and there isa greater uncertainty in estimation of free OH-. In apractical sense the meaning of second-order rate constantsof 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 inSDS, where pKw is shifted. Nevertheless, ranges ofobserved micellar effects14 are much larger than probableuncertainties in ionic reactant concentrations. In thefollowing discussion we have no choice but to assume thatsecond-order rate constants calculated in micellar solu-tions refer approximately to concentrations of free H+ andOH- in the aqueous region, rather than to total concen-trations. We cannot set limits to the consequent uncer-tainties in apparent second-order rate constants, but theyshould be within 1 order of magnitude of those which wouldbe estimated from total concentrations. There are sig-nificant variations in reported second-order rate constantsof exchange in both anionic and cationic micelles (Tables3 and 4 of ref 14). Some of them can be ascribed todifferences in the reaction media or to differences in thebehavior of the cationic surfactants,14 but others areprobably related to uncertainties in concentrations of H+

and OH- based on measured pH.

Discussion of Amide Exchange Kinetics in Termsof Pseudophase Theory. Table 1 contains selectedresults from ref 14, which illustrate the main experimentalfindings, and cover data for similar conditions. In theirdiscussion of the Bronsted-Bjerrum equation Perrin etal. applied eq 12 of ref 14 to their data, and we use it forthe H+-catalyzed exchange (k0 denotes second-order rateconstants for exchanges of MBA in water):

However, rates or first-order rate constants of exchangeare not discussed, but data are given as second-order rateconstants, kH, calculated according to:

As shown earlier, antilog(-pH) does not, in general, equaleither aH or [H+]. The deviations may not be large, but wecannot compare reported second-order rate constants inwater and micellar solutions with certainty. These com-plications also apply to analysis of second-order rateconstants of the OH--catalyzed exchange. We note thatkobs calculated by line shape analysis14 refers to totalconcentration, rather than activity, of the amide.

The reported second-order rate constants of theseexchanges depend primarily on surfactant charge and arenot very sensitive to the chemical nature of surfactantsand to the presence of various additives such as inorganicsalts and nonionic surfactants. Therefore the authors give“average micellar charge effects”,14 Table 1. These com-parisons involve the assumption that had it been possibleto follow exchanges of MLA in water, rate constants wouldbe the same as those of MBA. This assumption isreasonable, although Guthrie found a dependence ofsecond-order rate constants of nucleophilic attack onp-nitrophenyl alkanoates on the length of the alkyl group.32

However, the amide group is very hydrophilic and theeffects noted by Guthrie may not be important in amideexchange. It was also assumed that micelles do not changereaction mechanism or substrate structure, but the 0.05M nonionic amphiphile, MLA, changes the micellar chargedensity, which may have different effects on the acid- andbase-catalyzed exchanges in the differently charged mi-celles, although nonionic polyoxyethylenes do not signifi-cantly affect second-order rate constants.14 Perrin et al.concluded that their data for micellar effects on exchangeof MLA, relative to MBA, are incompatible with an ion-exchange, pseudophase, treatment but can be interpretedby applying the Bronsted-Bjerrum formalism.14 It will(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. (32) Guthrie, J. P. Can. J. Chem. 1973, 51, 3494.

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

Selected Second-Order Rate Constants

substrate conditions kH, M-1 s-1 kOH, M-1 s-1 kH/kH0 kOH

0/kOH

MBA water 1.03 × 103 1.07 × 107

MLA 0.25 M SDS 1.37 × 105 5.2 × 103 133 20600.25 M SDS + 0.25 M NaCl 6.1 × 104 3.3 × 103 59 32000.5 M SDS 1.44 × 105 6.6 × 103 140 16200.25 M CPCl 1.98 × 102 7.5 × 106 0.19 1.40.25 M CPCl + 0.25 M NaCl 2.16 × 102 2.5 × 106 0.21 4.30.5 M CPCl 1.82 × 102 8.3 × 106 0.17 1.20.5 M CTACl 2.11 × 102 3.9 × 106 0.2 2.8

Average Micellar Charge Effectsanionic micelles log(kH/kH

0) ) 2.0 ( 0.2 and log(kOH/kOH0) ) -3.4 ( 0.2

cationic micelles log(kH/kH0) ) -0.75 ( 0.06 and log(kOH/kOH

0) ) -0.18 ( 0.25a Reference 14.

v ) kH0[amide][H+]γamideγH/γ* ) kH

0aamideaH/γ* (8)

kobs ) kH(antilog(-pH)) (9)


therefore be useful to consider what has to be explained,and we first discuss the second-order rate constants givenin Table 1 in terms of a pseudophase formalism, on thebasis of average rate constants in the hope that there willbe cancellation of some uncertainties, e.g., in the meaningof pH.

Equations 10 and 11 describe the rate data as presented

where kH and kOH are second-order rate constants as givenin ref 14.

We use the pseudophase formalism (subscript m insidethe square brackets denotes local concentration in themicellar pseudophase, i.e., in moles per liter of the reactionregion at the micellar surface, but a subscript outside thesquare brackets denotes concentration (molarity) in termsof total solution volume):

where [H+m] and [OH-

m] are concentrations in the micellarpseudophase and [S]m ) [S]T. Therefore eqs 14 and 15indicate relationships between these rate constants

where kHm and kOH

m are second-order rate constants (M-1

s-1) in the micellar interfacial region. These concentrationshave to be estimated for defined conditions, in particular,concentrations of surfactant, H+, OH-, and added salts.Only surfactant and salt concentrations are specified foramide exchange. Data in Figure 1 of ref 14 indicate thatsome experiments in SDS were made with [H+]w in therange of 10-4-10-3 M, but much higher concentrationsappear to have been used in other experiments. Reactionsanalyzed by using pseudophase treatments are typicallymade with defined ionic concentrations,1,2,18 which maybe 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 transferredextensively 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 asdescribed by eq 7a without added salt, if â ≈ 0.65, ca. 50%

of total H+ will be in water. However, the local molarconcentration of H+ in the micellar interfacial region,which appears in eq 14, will be higher than [H+]w inanionic, and lower in cationic, micelles. Available experi-mental estimates of [H+

m] are in dilute SDS, see, e.g., refs16b and 33, and cannot be easily extrapolated to the highsurfactant concentrations employed in ref 14. Very ap-proximately [H+

m] may be estimated in terms of the PIE,33

although so far as we are aware this treatment has notbeen applied to relatively concentrated SDS. The valuesof [H+]m and [H+

m] are related in accordance with eq 16as

where Vm is the effective surfactant molar volume and[SDS]mVm gives the volume fraction of the micellarpseudophase. By assuming an approximate value of Vm≈ 0.3 M-1 (this value of Vm is within the range of valuesused in fitting kinetic data with the PIE1-5,18), one obtainsfrom eqs 7a and 16 the ratio [H+

m]/[H+]w ) 20 and 10 in0.25 and 0.5 M SDS, respectively, and 6 in 0.25 M SDSplus 0.25 M NaCl. Addition of 0.25 M NaCl to 0.25 M SDSshould decrease [H+

m]/[H+]w and kH (eq 14) approximately3-fold. This prediction agrees with results in Table 1.However, rate constants in 0.25 and 0.5 M SDS disagreewith the estimated 2-fold difference in [H+

m]/[H+]w, butthis disagreement is not unexpected, taking into accountpossible structural changes in concentrated micellarsolutions and uncertainties stemming from reliance onpH data.

In 0.5 M CTACl [H+m]/[H+]w ) 0.1 was estimated by

solving the PBE.34 Thus, a pseudophase treatment predictsthat 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 itca.10 times.Approximate “averagemicellar chargeeffects”for the H+ reaction are 100-fold acceleration by anionicand 6-fold inhibition by cationic surfactants, respectively(Table 1). Bearing in mind the above-mentioned uncer-tainty in using pH measurements for determination of[H+] in micellar solutions, the observed effects are inreasonableagreementwithapseudophase treatment, evenassuming kH

m ≈ kH0, which, for many reactions, is not

correct.1-5

The next question concerns the applicability of pseudo-phase models to the OH--catalyzed exchange. As noted,uncertainties in the estimation of [OH-] from pH are largerthan those for [H+] due to micellar effects on Kw, whichcloud comparisons of kOH with kOH

0.Anionic micelles inhibit, but do not completely suppress,

bimolecular reactions of OH-.35 This behavior is explainedqualitatively in terms of a pseudophase, ion-exchange,treatment and quantitatively by solving the PBE.20,36

Reactions of various p-nitrophenyl alkanoates with sto-ichiometric OH- have been examined over a range of SDSconcentrations,35 and forp-nitrophenyldodecanoate,whichshould be extensively micellar-bound, observed rateconstants become approximately constant in 0.13 M SDSwith inhibition, relative to reaction in aqueous 0.0193 MNaOH, by a factor of ca. 400, i.e., the inhibition is lowerthan those reported for amide exchange14 by a factor of4-5. The estimated second-order rate constant of deacy-

(33) (a) Rubio, D. A. R.; Zanette, D.; Nome, F.; Bunton, C. A. Langmuir1994, 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.

H+ reaction:

rate ) kH[H+]w[S]T (10)

OH- reaction:

rate ) kOH[OH-]w[S]T (11)

H+ reaction:

rate ) kHm[H+

m][S]m (12) (12)

OH- reaction:

rate ) kOHm[OH-

m][S]m (13)

H+ reaction:

kH ) kHm[H+

m]/[H+]w (14)

OH- reaction:

kOH ) kOHm[OH-

m]/[OH-]w (15)

[H+m]/[H+]m ) 1/([SDS]mVm) (16)


lation in the micellar pseudophase is ca. 10-fold lowerthan that in water and the rest of the inhibitory effect isdue to a 40-fold decrease in the concentration of OH- inthe micellar pseudophase, estimated by solving the PBE.36

Reactions of OH- with organic substrates in cationicmicelles have been studied extensively over a range ofconditions. Rate enhancements vary widely, dependingupon, inter alia, substrate hydrophobicity and reactionmechanism.1-5,18 Typically, overall saponifications ofcarboxylic esters are not strongly accelerated, often by nomore than 1 order of magnitude,1a,18b and these effects arereadily accommodated by pseudophase treatments whichindicate that second-order rate constants in both cationicand anionic micelles are somewhat lower than those inwater. We do not attach much significance to overall rateconstants, unless they are determined in well-definedconditions, but we note that acceleration of ester saponi-fication of ca. 10 by cationic micelles18 and inhibition ofsaponification of p-nitrophenyl dodecanoate by SDS of ca.40035 correspond to an overall difference of ca. 4000, whichis similar to those reported by Perrin et al. (Table 1) forthe OH--catalyzed exchange of MLA.14 These comparisonsinvolve the assumption that the relevant second-orderrate constants in the micellar pseudophase will be not bevery sensitive to charge. The limited evidence on reac-tions involving OH- and H+ is consistent with thisassumption, although it does not apply universally toreactions of other ions.37

Following the treatment applied above for kineticanalysis of the acid-catalyzed reaction, we can alsoestimate “would be” cationic micellar effects in OH--catalyzed amide exchange. For CTACl one can use a PIEmodel with KCl/OH ) 418b,38 and â ) 0.7, which gives (cf. eq7a) [OHm]/[OH]w ) 10 in 0.5 M CTACl. Second-order rateconstants of deacylation in cationic micelles, calculatedby using the PIE and other pseudophase treatments, arelower than those in water by approximately 1 order ofmagnitude.1a,18b If this difference applies to the OH--catalyzed exchange of amides, the lack of acceleration bycationic micelles is understandable and is similar toobservations on deacylations of hydrophobic esters inrelatively concentrated (ca. 0.2 M) cationic surfactant,where observed rate constants tend toward values inwater.1-5,18,39 Later in the discussion we consider factorsthat may inhibit the OH--catalyzed amide exchange incationic micelles. So far as we know the PBE has onlybeen applied to dilute cationic sufactants.20 We see againthat the observed ca. 1.5-fold inhibition of exchange bycationic surfactants (from average values) indicates thatthere is a decrease in kOH

m relative to kOH0 in cationic

surfactants. In the H+-catalyzed reaction, observed effectsin anionic and cationic micelles (Table 1) are explicable,at least qualitatively, by assuming the absence of majoreffects of the micellar medium on the intrinsic rateconstant.

The above discussion shows that the “puzzles” discussedin ref 14 are imaginary and simply reflect differentsensitivities of acid- and base-catalyzed reactions to theintramicellar medium and the significance of ionic con-centrations in that medium. Unlike the acid-catalyzedreaction, the base-catalyzed exchange appears to beretarded in micelles; this effect partially cancels expectedelectrostatic effects of cationic micelles and enhances the

electrostatic inhibition by anionic micelles, thus creatingthe apparent asymmetry. Two points should be empha-sized: (i) if micellar environmental effects on exchangeare similar in cationic and anionic micelles, differencesbetween average exchange rate constants in anionic andcationic micelles (Table 1) are approximately the same inabsolute terms, log(kH/kH

0)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 thoseexpected by analogy with other systems; (ii) applicationof the pseudophase model shows that it is necessary toconsider effects of micellar environments on reactivitywhile the discussion in ref 14 in terms of the Bronsted-Bjerrum eq 1 leaves major questions unanswered. Notethat discussion of ratios of rate constants in micelles ofopposite charges, instead of ratios of rate constants in thepresence and absence of micelles, has some obviousadvantages: first, effects of the micellar environment tendto cancel, thus allowing one to extract Coulombic contri-butions in a simple form, second, ambiguities related tointerpretation of pH measurements in water and micellarsolutions should be less significant when the reaction inwater is excluded from consideration. In addition iteliminates questions regarding the use of MBA to estimaterate constants in water (cf. ref 32).

Analysis in Terms of a Bro1nsted-Bjerrum For-malism. Application of eq 1 to second-order rate constantsdefined in accordance with eqs 10 and 11 gives

and

Rate constants kH0 and kOH

0 refer to MBA, rather than toMLA, on the assumption that the long- and short-chainsubstrates would have the same reactivities in water.Choosing water as the reference medium for estimationof micellar effects dictates also choosing it as the referencemedium for definition of activity coefficients which arerelated40 to the standard free energy of transfer of the ithcomponent (∆Gtr

i) from a reference medium, where allactivity coefficients are set equal to unity, to a givenmedium (a micellar solution in our discussion):

Activity coefficients for MLA (γS) could in principle bedetermined experimentally from, e.g., solubility measure-ments.25 No relevant data are available, but we expect γSto be much less than unity because micelles stronglyincrease solubilities of such highly hydrophobic substancesas MLA (∆Gtr

S is large and negative). Transfer freeenergies of transition states also involve large negativecontributions from hydrophobic interactions of the MLAalkyl group with micelles, and activity coefficients oftransition states should also be low, but different from γSbecause of structural differences generated in the amidegroup, including charge development, on transition stateformation. Activity coefficients for H+ and OH- shouldnot be unity, although deviations may not be large becausethe second-order rate constants are calculated on the basisof concentrations of free ions rather than their totalconcentrations and corresponding ∆Gtr

i values approxi-(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.(40) Ritchie, C. D. In Solute-Solvent Interactions; Coetzee, J. F.,

Ritchie, C. D., Eds.; Marcel Dekker: New York, 1969; p 219.

kH ) kH0γSγH/γ* (17)

kOH ) kOH0γSγOH/γ* (18)

RT ln γi ) ∆Gtri (19)


mately reflect free energy changes upon transfer of theseions from water to the aqueous intermicellar medium (cf.Results, discussion of pH). Therefore, we obtain from eqs17 and 18 the following expressions for micellar effects

and

where γTH* and γTOH* are the activity coefficients oftransition states of acid- and base-catalyzed reactions,respectively.

Equations 20 and 21 also follow from consideration ofsecond-order rate constants as being calculated on thebasis of H+ (or OH-) activity, as derived from the pH-meter reading; cf. ref 14. This coincidence results fromthe particular model on which we base the above discussionof what is really measured by the glass electrode. If afraction of H+ is bound to anionic micelles, this bindinggives the observed decrease in activity which becomesapproximately equal to the free concentration. Cationicmicelles do not significantly perturb the state of H+ anddo not extensively bind OH-.

To interpret micellar charge effects in terms of eqs 20and 21, one needs to find explanations for the activitycoefficient ratios given in Table 2. In terms of eq 19 theserelations reflect differences in transfer free energies ofsubstrate and transition state from water to micelles(∆∆Gtr

S/T* ) 2.3RT log(γS/γ*)) given also in Table 2. In thesimplest case we assume that hydrophobic contributionsto transfer free energies of S and T* are similar and∆∆Gtr

S/T* involves only differences in electrostatic interac-tions of ionic transition states with ionic micelles. Ifpositive and negative charges on transition states of H+

and OH- reactions are similar in absolute values and alsointeract with similar, but oppositely charged cationic andanionic micelles, one would observe symmetrical ∆∆Gtr

S/T*

values, with opposite signs for oppositely charged micellesand transition states. Evidently this is not the case, andmore than simple electrostatics must be involved. How-ever, first, one needs to estimate the electrostatic con-tributions (∆∆Gtr

electr). In the pseudophase models thesecontributions are included in the ratios [H+

m]/[H+]w and[OH-

m]/[OH-]w estimated independently, but for similarconditions. In the present case we need to estimateelectrostatic contributions to the binding of ionic transitionstates, and this can be done only theoretically. Oneapproximate approach is to use apparent micellar surfacepotentials (ψ) based on apparent acid dissociation con-stants of solubilized indicators calculated in terms ofconventional pH measurements with a glass electrode41

and calculate ∆∆Gtrelectr as

In the concentrated surfactant solutions employed in ref14, absolute values of ψ should be smaller than thosereported in more dilute (0.024 M) SDS and CTABr (-134and 148 mV, respectively).41a By assuming |ψ| ≈ 100 mVfor both SDS and CTACl, one obtains ∆∆Gtr

electr ≈ (10kJ/mol, which is close to ∆∆Gtr

S/T* for the H+ reaction inanionic micelles (Table 2) but larger by ca. 6 kJ/mol than∆∆Gtr

S/T* in cationic micelles. However, for the OH-

reaction in both types of surfactants ∆∆GtrS/T* values are

ca. 10 kJ/mol more negative than expected on purelyelectrostatic considerations. In making these comparisonsbetween the indicator and kinetic data, we are simplycomparing two processes which involve transfer of unitcharge in the overall reactions, and nothing more. Thiscomparison does not depend on the validity of indicatordata inestimationofmicellarpotentials.Wecomethereforeto the same conclusion as that in terms of a pseudophasemodel. The OH- reaction is inhibited in micellar media,regardless of charge, as for many bimolecular anionicreactions which are slower at micellar surfaces than inwater.1a,b,18b

Excluding consideration of reaction in water relative tomicelles simplifies interpretation of micellar charge effectson amide exchange. Micellar environments affect H+ andOH- reactions differently, but this does not necessarilyrequire asymmetry in micellar charge effects, becauseenvironmental contributions to reactivity may oppose orenhance electrostatic contributions, or even apparentlypreclude their appearance. From eq 22 the electrostaticcontribution to transition state stabilization on going fromcationic to anionic micelles is 2Fψ ≈ 20 kJ/mol, withabsolute values of |ψ| ≈ 100 mV for cationic and anionicmicelles. Differences in activation free energies from theratios (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 demon-strates that micellar charge effects are close to thoseexpected on the basis of plausible surface potentials andare approximately symmetrical. Even if micelles changesubstrate conformation or reaction mechanism, thisqualitative estimate of the charge effect remains correct,provided that such changes are unaffected by micellarcharge.

Comparison of Treatments of Micellar Rate Ef-fects. The distinction between the pseudophase andBronsted-Bjerrum approaches is in the treatment of localconcentrations of reactants in water and micelles: theformer considers the change in local concentrations as asignificant source of micellar effects and the latter ignoresthese changes. The expression for the reaction rate, whichfollows from eq 1, has the form

where aS and aB are activities of reactants, in equilibriumbetween the aqueous and micellar phases, and a textbookdefinition of equilibrium requires that activities are

(41) (a) Fernandez, 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., FaradayTrans. 1 1989, 85, 537.

Table 2. Ratios of Ground and Transition State Activity Coefficients of Amide Exchanges and Respective Transfer FreeEnergies

H+ reaction OH- reaction

anionic micelles log(γS/γTH*) ) 2.0 ( 0.2 log(γS/γTOH*) ) -3.4 ( 0.2∆∆GtrS/T* ) 11.5 ( 1.1 kJ/mol ∆∆GtrS/T* ) -19.5 ( 1.1 kJ/mol

cationic micelles log(γS/γTH*) ) -0.75 ( 0.06 log(γS/γTOH*) ) -0.18 ( 0.25∆∆GtrS/T* ) -4.3 ( 0.3 kJ/mol ∆∆GtrS/T* ) -1.0 ( 1.4 kJ/mol

a From data in Table 1.

kH/kH0 ) γS/γTH* (20)

kOH/kOH0 ) γS/γTOH* (21)

∆∆Gtrelectr ) (Fψ (22)

rate ) k0aSaB/γ* (23)


identical across phase boundaries. This logic led Perrinet al.14 to conclude that a change in local concentrationsof reacting species “does not itself account for the rateeffects” and that “since activities are constant, the rateeffect can be ascribed entirely to the activity coefficientof the transition state”. However, what is identical in everyphase under equilibrium is the chemical potential of eachspecies, and identity of activities implies choosing the samestandard state for all phases (we are not considering so-called absolute activities, which indeed are identical inevery phase, but have nothing to do with the Bronsted-Bjerrum approach, eq 1). In the pseudophase treatmentthe standard state of each solute in every phase is ahypothetical 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 isthe difference between free energies of reactants and thetransition state in the micellar phase, which is not anapparent parameter, but a “normal” activation free energyfor reaction in the micelle treated as a separate phase. Itcan be directly compared with that for reaction in wateras a different phase and any difference between them isdue to medium effects. In contrast, the Bronsted-Bjerrumapproach always sets the standard states of reactants andthe transition state in water and then corrects them byusing activity coefficients, which, in accordance with eq19, account for differences between water and the micellarsolution. If the rate constant is calculated on the basis ofaqueous concentration or activity of one of the reactants,e.g., H+ or OH- in amide exchange, the respectiveactivation free energy will be an apparent parameter equalto the difference between the free energy of the transitionstate in the micellar solution and free energies of thesubstrate, also in the micellar solution, but with H+ orOH- in water. Evidently, no correction for H+ or OH- willbe necessary and respective activity coefficients disappearfrom equations for the micellar effect, provided thatactivities are measured correctly.

Free energy changes involved for the general case of abimolecular reaction between S and B in micellar solutionsare shown in Scheme 2, which is similar to free energydiagrams widely used to interpret solvent effects.43

It follows from Scheme 2 that

Note that eq 2 expresses the same relationship in termsof binding constants, provided that transfer free energiesare considered as binding free energies.44 Therefore,despite different conceptual bases (micelles are treatedas distinct species rather than as a phase) the thirdapproach mentioned in the Introduction does not introduceany new terms for discussion of micellar effects.

An often encountered situation when k2,m ≈ k0 means,in terms of eq 24, that ∆Gtr

T* ≈ ∆GtrS + ∆Gtr

B, that isnoncovalent intermolecular interactions which transfer

reactants into micelles persist and contribute additivelyto the binding of the transition state to the micelle. Suchadditivity is understandable for noncovalent, e.g., elec-trostatic or hydrophobic interactions, the free energies ofwhich depend simply on the number of charges and thetotal surface area of apolar moieties, respectively.

A special case is when substrate S has a very highaffinity for the micelle and B remains largely in water, aswith amide exchange, where S is MLA and B is H+ orOH-. Such a case is illustrated in Scheme 2 by introducingan intermediate free energy level for Sm + Bw and theactivation free energy ∆Gmw*. This free energy is theobserved activation free energy and the scheme thenillustrates directly the micellar effect as a differencebetween ∆Gmw* and ∆Gw*, as for the case represented byeqs 20 and 21.45 One can write the expression for observedmicellar effects in this case either as

or by taking into account eq 24 as

Equation 25 corresponds to interpretation of micellareffects in terms of the Bronsted-Bjerrum approach withdifferent stabilizations of initial and transition states, andeq 26 corresponds to the pseudophase interpretation ofmicellar effects as being due to micellar microenviron-mental and “concentration” effects. These approachesexplain micellar effects in terms of different, but inter-related, free energy contributions to binding and activationof reactants. The choice in discussion of the nature ofmicellar effects at the molecular level is given by con-sideration of different paths connecting initial and transi-tion states in Scheme 2: one can consider the difference

(42) The concept of a partition (or distribution) constant implieschoosing different standard states for two immiscible phases, otherwiseobserved differences in concentrations of a given solute in two phaseswill be treated as differences in activity coefficients. The use of partitionconstants is preferred purely for practical reasons: it is convenient touse activity coefficients as factors which account for deviations in solutebehavior from that expected at infinite dilution; these deviations aredifferent in each phase, and it is then convenient to introduce differentactivity 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 ratherthan to binding constants K; however, one can prove the equivalenceof eqs 2 and 24 by using the relationship K ) PVm, derived in ref 5.

(45) Transfer free energies shown in Scheme 4 and those in eq 18have different meanings: Scheme 4 gives the values for transfers ofsolutes from water to micelles as a separate phase, while in eq 18 thevalue for transfer from water to the micellar solution (micelles + waterare considered as a single phase) must be used. It can be shown easily,however, that in conditions when substrate and transition state areboth predominantly micellar bound, the ratio γS/γ* is indeed given byeq 24.

∆Gw* + ∆GtrT* ) ∆Gm* + ∆Gtr

S + ∆GtrB (24)

Scheme 2

kobs/k0 ) exp{(∆Gtr

S - ∆GtrT*)/RT} (25)

kobs/k0 ) exp{(∆Gw* - ∆Gm* - ∆Gtr

B)/RT} (26)


between ∆Gm* and ∆Gw* (the ratio of the rate constantsin two pseudophases) corrected for the transfer freeenergies of reactants (concentration effect), or considerthe difference between ∆Gtr

S and ∆GtrT* (ratio γS/γ*) as

a correction factor to the rate constant in water.Generally when both reactants are significantly dis-

tributed between aqueous and micellar phases in similaramounts, Scheme 2 does not show the observed activationfree energy, which is a weighted average of activationfree energies of reactions in water and micelles. However,at the molecular level one always needs to discuss onlycontributions shown in this scheme.

Scheme 3 shows the results for amide exchange in termsof the free energy diagram calculated from average second-order rate constants (Table 1). The transfer free energyof MLA is unknown, but in order to discuss only micellareffects, we shift the levels of ground and transition statesby ∆Gtr

MLA as shown in Scheme 4, based on average second-order rate constants. Now all activation free energies arecalculated from a common zero level, and differencesbetween levels of the transition states show the differencesin observed activation free energies, with results for theOH- and H+ reactions on the left and right sides,respectively. Micellar charge effects are symmetrical:differences between levels for cationic and anionic micellesare similar, but the level for reaction in water is highlyasymmetrical for the OH- reaction, out of the rangebetween micelles of opposite charges, and inside the range,although not at the midpoint, for the H+ reaction.

Reaction Mechanism and Possible Micellar-In-duced Changes. Perrin et al.14 do not comment on thepossibility that micelles may affect reactivities by changingeither mechanism or reactant structure or conformation,although they note alternative mechanisms of acidexchange, and we consider this possibility in the contextof micellar effects on amide exchange.

Amides exist as equilibriating E and Z isomers, andmicelles may affect both inherent rates and the positionof the equilibrium, which may affect rates of exchange(Scheme 1). We do not know of any evidence on thisquestion, although micelles and solvents affect E-Zequilibria of hydroxamic acids and their anions.46 Perrinet al.14 conclude that N-methyl amides MBA and MLAexist predominantly as the Z-isomers, in agreement withextensive evidence. But incorporation in a micelle couldfavor the E-isomer due to favorable hydrophobic interac-tions of the syn-alkyl groups with alkyl groups of themicelle. A similar micellar-induced change of structure isvery evident with phenyl alkyl hydroxamic acids and theiranions where E- and Z-isomers have different NMRspectra.46a In water, with the short-chain derivative, E-and Z-isomers coexist with equilibrium favoring theformer, but in cationic and anionic micelles the Z-isomerof the long-chain derivative is dominant, with syn-phenyland alkyl groups although locations depend on micellarcharge.46b Deprotonation of the (hypothetical) E-amidegives an anion-like transition state with unfavorableinteractionsbetween syn-carbonyloxygenandthenitrogenlone pair, which should inhibit this reaction, relative tothat of the Z-amide. However, evidence on base-catalyzedexchange in solution shows that this effect is not largeand, in some systems, is less important than stericinteractions.47

The situation will be different for the hydrogen ioncatalyzed 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.

Scheme 3 Scheme 4


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

On this hypothesis we expect acceleration of the H+-catalyzed exchange in SDS micelles to be the approximateinverse of inhibition by cationic micelles. We emphasizethe term “approximate” because of the earlier noteduncertainties in values ofkH and differences of interactionsof solutes with micelles of different charges. The situationwill be different for reaction catalyzed by OH-, in partbecause values of kOH may not be calculated correctly butalso because if micelles affect initial or transition statestructures comparisons of kOH in water and micelles willhave little meaning, unless we have independent evidenceon this question. Perrin et al.14 comment on a “hithertounrecognized difference” in behaviors of anionic andcationic micelles, although they believe that it will affectelectrostatic interactions. Qualitatively, a micellar-induced shift of structure may account for at least partof the above-mentioned inhibition of the OH--catalyzedexchange by micelles.

There are many examples of relations between mech-anism and reactivities in micellar interfacial regions. Theyareveryobviousinspontaneousreactions,butpseudophasetreatments of bimolecular reactions with anions indicatehow reactivities in micellar pseudophases depend onheadgroup 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, theH+-catalyzed amide exchange probably has similar mech-anisms in water and micelles. This generalization maynot apply to the OH--catalyzed exchange if simpleassumptions regarding mechanisms are inadequate, andnaive interpretations based on either the pseudophase ortheBronsted-Bjerrumformalismswill thennot fit relativereactivities in micelles and water at the quantitative level.

We predict, on the basis of pseudophase treatments ofmicellar effects in bimolecular ionic reactions, that if amideexchanges can be followed over a range of conditions, adecrease in [surfactant] will significantly increase rateconstants of the OH-- and H+-catalyzed exchanges incationic and anionic micelles, respectively.49 A decreasein surfactant concentration will have less effect on themicellar-inhibited reactions with co-ions,34-36 but inhibi-

tion will increase modestly. The exchanges will have tobe followed at defined reactant concentrations, and bufferand electrolyte composition and MLA concentration willhave to be low enough to limit effects on micellar structureand charge density. We cannot judge whether the limita-tions of the experimental conditions prevent these re-quirements from being met.

Conclusions

Micellar effects upon amide exchange cannot be ana-lyzed rigorously because of assumptions involved in theuse of pH measurements for estimation of concentrations(or activities) of H+ and OH-, effects of MLA on micellarstructure and charge density, and the possibility that rateconstants in water cannot be reliably estimated fromexchange of MBA. The reported micellar rate effects arequalitatively understandable in terms of pseudophasetreatments and could have been predicted from analogieswith data on other reactions involving H+ and OH- andevidence on the extent to which reactivities in micellarinterfacial regions depend on mechanism. An alternativeformalism, based on the Bronsted-Bjerrum equation, canalso be applied to the data but is descriptively lessinformative, although it allows simple comparisons ofeffects of micellar charge on these exchanges and acid-base equilibria. Insofar as these formalisms providealternative treatments, there is no reason to believe thatone could fail and the other succeed in fitting experimentalresults. In principle, it should be possible to use the linearsolvation free energy relationships that have been usedsuccessfully to predict transfer equilibria of neutral solutesbetween water and micelles50 to predict the correspondingtransfer equilibria for transition states. These treatmentshave been developed for neutral solutes, and this approachwill probably not be applicable to ionic reactions, at leastat present.

Acknowledgment. We are grateful to Professors L.S. Romsted, O. A. El Seoud, and F. Nome for valuablediscussions made possible by the NSF-Brazil CNPQCooperative Program, and to Professor C. L. Perrin forvaluable comments on the mechanisms of amide exchange.A. K. Yatsimirsky thanks CONACYT for support ofSabbatical leave at UCSB.

LA000068S

(48) Possidonio, S.; Silviero, F.; El Seoud, O. A. J. Phys. Org. Chem.1999, 12, 325.

(49) This prediction appears to be consistent with the limited availableevidence14 because second-order rate constants for the OH--cata-lyzed exchange appear to increase with a 20-fold decrease in cetylpy-ridinium chloride concentration, despite a decrease of temperature from34 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 effects upon ion−molecule...

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